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

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

Hypothesis: Roger 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). Edwina's card is shown to John. John's card is shown to Janice. 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 Janice does not know whether or not everyone picked a red card.

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

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

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


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

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

Hypothesis: Dennis 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). Jesse's card is shown to Jesse. Wilfred's card is shown to Jesse. Nancy's card is shown to Wilfred. Jesse's card is shown to Richard. Richard's card is shown to Richard. It is publicly announced that someone picked a red card. It is publicly announced that Wilfred picked a black card.

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

Hypothesis: Nancy can now know whether Wilfred 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). Richard's card is shown to Richard. Tisha's card is shown to Richard. Richard's card is shown to Erica. Erica's card is shown to Tisha. Tisha's card is shown to Tisha. Tisha's card is shown to Thomas. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Richard can now know whether Thomas 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). Theresa's card is shown to Theresa. Theresa's card is shown to Jose. David's card is shown to David. Jose's card is shown to Morris. It is publicly announced that someone picked a red card. It is publicly announced that Theresa does not know whether Morris picked a red card.

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

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

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


Premise: There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Michael's card is shown to Michael. Sarah's card is shown to Sarah. 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 Agentb:2 VALID? [ ! (1|2) ] [ ! (1&2) ] Agentb knows that (Agenta knows whether (1&2))

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

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


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

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

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

Hypothesis: Angie can now know that Richard can know whether Angie 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 Sheena. Leroy's card is shown to Sheena. Elizabeth's card is shown to Joe. Joe's card is shown to Joe. Elizabeth's card is shown to Leroy. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Sheena can now know whether Joe can know whether Sheena picked a red card.


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

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

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

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


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

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

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

Hypothesis: Jill 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). Phillip's card is shown to Tim. Tim's card is shown to Carla. Tim's card is shown to Phillip. It is publicly announced that someone picked a red card. It is publicly announced that Phillip does not know whether Phillip picked a red card. It is publicly announced that Carla knows whether or not everyone picked a red card. It is publicly announced that Carla picked a red card.

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

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

Hypothesis: Phillip can now 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). Nicholas's card is shown to Nicholas. Nicholas's card is shown to Richard. It is publicly announced that someone picked a red card. It is publicly announced that Richard does not know whether Richard picked a red card.

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

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

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


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

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

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

Hypothesis: Brandon can now know whether Jesse can know that Jesse picked a red card.


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

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

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

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


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

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

Hypothesis: Michelle can now know that 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). John's card is shown to John. John's card is shown to Marvin. Marvin's card is shown to Marvin. John's card is shown to Dorothy. Marvin's card is shown to Dorothy. Dorothy's card is shown to Dorothy. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card.

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

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


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

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

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

Hypothesis: Marion can now know whether Stephen 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). Peter's card is shown to Peter. Carroll's card is shown to Heather. Heather's card is shown to Heather. It is publicly announced that someone picked a red card.

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

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

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


Premise: There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Maynard's card is shown to Yolanda. Maynard's card is shown to Maynard. It is publicly announced that someone picked a red card. It is publicly announced that Yolanda does not know whether or not everyone picked a red card. It is publicly announced that Yolanda does not know whether Yolanda picked a red card. It is publicly announced that Yolanda does not know whether or not everyone 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) ] [ ! ~(Agenta knows whether (1&2)) ] (Agenta knows whether 1)

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

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


Premise: There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Denise's card is shown to Denise. Denise's card is shown to Ronald. Denise's card is shown to Tracy. 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:1 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] (Agentb knows whether 1)

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

Hypothesis: Ronald can now know whether Denise picked a red card.


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

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

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

Hypothesis: Curt 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). Mabel's card is shown to Alexandra. Carmelo's card is shown to Carmelo. Carmelo's card is shown to Mabel. Alexandra's card is shown to Justin. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Carmelo can now know that Alexandra 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). Charles's card is shown to Charles. Kenneth's card is shown to Charles. Brian's card is shown to Charles. Patrice's card is shown to Kenneth. Charles's card is shown to Brian. Charles's card is shown to Patrice. Kenneth's card is shown to Patrice. Brian's card is shown to Patrice. Patrice's card is shown to Patrice. It is publicly announced that someone picked a red card. It is publicly announced that Kenneth does not know whether Brian picked a red card.

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

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

Hypothesis: Patrice can now know whether Brian 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). Larry's card is shown to Larry. Larry's card is shown to Jeff. Jeff's card is shown to Jeff. Steven's card is shown to Jeff. Larry's card is shown to Steven. It is publicly announced that someone picked a red card.

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

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

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


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

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

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

Hypothesis: Yvonne can now know that Sarah picked a red card.


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

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

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

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

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

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

Hypothesis: James 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). Bobby's card is shown to Bobby. Ariana's card is shown to Ariana. It is publicly announced that someone picked a red card. It is publicly announced that Bobby does not know whether Bobby picked a red card. It is publicly announced that Marty picked a black card.

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

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

Hypothesis: Marty can now know whether Bobby can know that Marty 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. Dorothy's card is shown to Gary. Kenneth's card is shown to Gary. Jennifer's card is shown to Jennifer. Kenneth's card is shown to Jennifer. It is publicly announced that someone picked a red card.

VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,4 Agentc:3,4 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentb knows whether 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: Jennifer can now know that Gary can know whether Kenneth picked a red card.


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

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

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

Hypothesis: Frank can now know that Angela 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). Thomas's card is shown to Thomas. Thomas's card is shown to Barbara. James's card is shown to Barbara. It is publicly announced that someone picked a red card. It is publicly announced that Barbara picked a red card.

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

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

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


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

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

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

Hypothesis: Maria can now know that Sigrid 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). Minnie's card is shown to Anthony. Minnie's card is shown to Minnie. Minnie's card is shown to Gerardo. 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 not everyone picked a red card.

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

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


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

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

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

Hypothesis: Ofelia can now know that Melissa can know that Ofelia picked a red card.


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

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

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

Hypothesis: Jose 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). David's card is shown to Larry. Gary's card is shown to Gary. David's card is shown to Gary. Gary's card is shown to David. David's card is shown to David. It is publicly announced that someone picked a red card. It is publicly announced that David picked a red card. It is publicly announced that David does not know whether Larry picked a red card. It is publicly announced that David knows whether someone picked a red card. It is publicly announced that someone picked a red card.

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

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

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


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

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

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

Hypothesis: Carrie can now know that Eugene picked a red card.


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

Hypothesis: Jessie 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). Sharon's card is shown to Richard. Mark's card is shown to Lacresha. Richard's card is shown to Mark. Mark's card is shown to Mark. It is publicly announced that someone picked a red card. It is publicly announced that Mark does not know whether or not everyone picked a red card.

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

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

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


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

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

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

Hypothesis: Regina 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). Adriana's card is shown to Charles. Truman's card is shown to Truman. Adriana's card is shown to Truman. Grace's card is shown to Adriana. Grace's card is shown to Grace. It is publicly announced that someone picked a red card. It is publicly announced that Charles does not know whether Grace picked a red card.

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

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

Hypothesis: Grace can now know whether Adriana can know that Charles 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 James. Donald's card is shown to Donald. Richard's card is shown to Richard. 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 Richard picked a red card. It is publicly announced that James does not know whether James picked a red card.

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

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

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


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

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

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

Hypothesis: Sandy can now know whether Marie can know that Marie 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 Jeannette. Scott's card is shown to Jeannette. Jose's card is shown to Scott. Anthony's card is shown to Scott. 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:1,3 Agentb:1,4 Agentc:4 VALID? [ ! (1|2|3|4) ] (Agentb knows that (1&2&3&4))

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

Hypothesis: Jeannette 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). Glenda's card is shown to Glenda. Glenda's card is shown to Sandy. Sandy's card is shown to Sandy. It is publicly announced that someone picked a red card. It is publicly announced that Sandy knows whether or not nobody picked a red card. It is publicly announced that Sandy knows whether Glenda picked a red card.

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

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

Hypothesis: Sandy 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). Gregory's card is shown to Gregory. Cynthia's card is shown to Cynthia. Susan's card is shown to Susan. It is publicly announced that someone picked a red card. It is publicly announced that Susan does not know whether Gregory picked a red card. It is publicly announced that Gregory does not know whether Cynthia picked a red card.

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

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

Hypothesis: Gregory can now know whether Cynthia picked a red card.


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

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

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

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


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

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

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

Hypothesis: Kim 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). Betty's card is shown to Traci. Betty's card is shown to Betty. Betty's card is shown to Carl. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Traci can now know that Betty 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). Deborah's card is shown to Jamaal. Eva's card is shown to Jamaal. Deborah's card is shown to Deborah. Eva's card is shown to Deborah. Jamaal's card is shown to Eva. Deborah's card is shown to Eva. Eva's card is shown to Eva. It is publicly announced that someone picked a red card. It is publicly announced that Eva picked a red card.

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

Hypothesis: Jamaal can now know whether 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). Sidney's card is shown to Sidney. Anthony's card is shown to Anthony. Kelly's card is shown to Anthony. Sidney's card is shown to Kelly. 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|2|3)))

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

Hypothesis: Kelly can now know whether Anthony 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). Rose's card is shown to Rose. Helen's card is shown to Helen. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Helen can now know whether Adam picked a red card.


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

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

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

Hypothesis: Jennifer can now know whether Carmen 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 Vicky. Vicky's card is shown to James. It is publicly announced that someone picked a red card. It is publicly announced that Vicky knows whether Vicky picked a red card.

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

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

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


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

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

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

Hypothesis: Monica can now know whether Teri can know that Kenneth picked a red card.


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

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

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

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


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

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

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

Hypothesis: Dustin 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). Gary's card is shown to Gary. Moises's card is shown to Gary. Moises's card is shown to Moises. Gary's card is shown to Deborah. Deborah's card is shown to Deborah. Moises's card is shown to Clyde. Clyde's card is shown to Clyde. 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 Moises picked a red card. It is publicly announced that Moises knows whether or not nobody picked a red card.

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

Hypothesis: Deborah can now know that Gary 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). Rosemarie's card is shown to Eva. Eva's card is shown to Rosemarie. Rosemarie's card is shown to Donna. It is publicly announced that someone picked a red card. It is publicly announced that Eva picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that Donna picked a black card.

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


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

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

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

Hypothesis: Robert can now know that Timothy 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). Mary's card is shown to Mary. Mary's card is shown to Lucas. Lucas's card is shown to Lucas. Rachel's card is shown to Rachel. It is publicly announced that someone picked a red card.

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

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

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


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

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

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

Hypothesis: James can now know that Angelic 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). Estelle's card is shown to Patricia. Susan's card is shown to Estelle. Estelle's card is shown to Estelle. It is publicly announced that someone picked a red card. It is publicly announced that Susan knows whether or not everyone picked a red card.

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

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

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


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

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

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

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


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

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

Hypothesis: Dianne can now know that Ernie picked a red card.


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

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

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

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


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

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

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

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


Premise: There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mary's card is shown to Mary. Mary's card is shown to Joshua. Mary's card is shown to Hugh. 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:1 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] (Agenta knows whether (1&2&3))

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

Hypothesis: Mary 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). Josh's card is shown to Josh. Joshua's card is shown to Josh. Joshua's card is shown to Joshua. Vonda's card is shown to Joshua. Josh's card is shown to James. Joshua's card is shown to James. Josh's card is shown to Vonda. Vonda's card is shown to Vonda. It is publicly announced that someone picked a red card. It is publicly announced that Josh knows whether Josh 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) ] Agentc knows whether (Agentd knows that (1|2|3|4))

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: James can now know whether Vonda 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). Brittany's card is shown to Dennis. Marshall's card is shown to Brittany. Dennis's card is shown to Marshall. Marshall's card is shown to Marshall. It is publicly announced that someone picked a red card. It is publicly announced that Brittany does not know whether Dennis picked a red card.

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

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

Hypothesis: Marshall 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). Dwight's card is shown to Sandra. Sandra's card is shown to Dwight. Sandra's card is shown to Cathy. Dwight's card is shown to Cathy. It is publicly announced that someone picked a red card.

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

Hypothesis: Sandra can now know whether Cathy can know whether Dwight picked a red card.


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

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

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

Hypothesis: Megan can now know whether Burton 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). Jackie's card is shown to Sarah. Jackie's card is shown to Jackie. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.

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

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

Hypothesis: Sarah can now know that Jackie 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). Ronald's card is shown to Velma. Velma's card is shown to Dana. It is publicly announced that someone picked a red card. It is publicly announced that Dana knows whether Velma picked a red card.

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

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

Hypothesis: Velma can now know that Velma 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 James. Maire's card is shown to Maire. 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 James does not know whether Maire picked a red card.

VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] Agentb knows that (Agenta 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: Maire can now know that James 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). Edward's card is shown to Edward. Thomas's card is shown to Edward. Roosevelt's card is shown to Edward. Janet's card is shown to Thomas. Janet's card is shown to Roosevelt. Roosevelt's card is shown to Roosevelt. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Janet 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). Shanda's card is shown to Dale. Shanda's card is shown to Shanda. It is publicly announced that someone picked a red card. It is publicly announced that Dale knows whether Shanda picked a red card.

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

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

Hypothesis: Dale 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). Leonard's card is shown to Leonard. Leonard's card is shown to Katherine. Katherine's card is shown to Katherine. Kevin's card is shown to Kevin. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Leonard can now know that Katherine 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). Deborah's card is shown to Aaron. Aaron's card is shown to Tony. Gwendolyn's card is shown to Gwendolyn. It is publicly announced that someone picked a red card.

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

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

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


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

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

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

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


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

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

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

Hypothesis: Christa 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). Mary's card is shown to Ross. Mary's card is shown to Helen. George's card is shown to Mary. It is publicly announced that someone picked a red card.

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

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

Hypothesis: George can now know whether Ross 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). Christine's card is shown to Christine. Christine's card is shown to Timothy. 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 (~(1|2)))

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

Hypothesis: Timothy can now know that Christine 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). Jacqueline's card is shown to James. Eldon's card is shown to Eldon. Paul's card is shown to Eldon. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Eldon can now 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). Debra's card is shown to Debra. Charles's card is shown to Evelyn. Evelyn's card is shown to Lezlie. Lezlie's card is shown to Lezlie. It is publicly announced that someone picked a red card. It is publicly announced that Charles does not know whether Lezlie picked a red card.

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

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

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


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

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

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

Hypothesis: Carroll can now know whether Blanche can know whether Blanche picked a red card.


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

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

Hypothesis: Mandy 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). Paul's card is shown to Paul. David's card is shown to Paul. Paul's card is shown to David. Raymond's card is shown to David. David's card is shown to David. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Raymond can now know that Paul can 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). Sam's card is shown to Rodney. Joanne's card is shown to Sam. Sam's card is shown to Joanne. It is publicly announced that someone picked a red card. It is publicly announced that Rodney knows whether someone picked a red card. It is publicly announced that Sam does not know whether Rodney picked a red card.

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

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

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


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

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

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

Hypothesis: Ruth can now know whether Nikki 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). Dave's card is shown to Robert. Alvin's card is shown to Robert. Dave's card is shown to Alvin. It is publicly announced that someone picked a red card. It is publicly announced that Dave does not know whether Robert picked a red card.

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

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

Hypothesis: Dave 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). Gladys's card is shown to Anthony. Anthony's card is shown to Gladys. Gladys's card is shown to Gladys. It is publicly announced that someone picked a red card. It is publicly announced that Anthony does not know whether or not everyone picked a red card. It is publicly announced that Gladys does not know whether Robert picked a red card.

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

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

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


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

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

Hypothesis: Donald 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). Paula's card is shown to Paula. Cathy's card is shown to Paula. Paula's card is shown to Nancy. Stephanie's card is shown to Cathy. It is publicly announced that someone picked a red card. It is publicly announced that Paula does not know whether Nancy picked a red card. It is publicly announced that Nancy does not know whether Nancy picked a red card.

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

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

Hypothesis: Paula can now know that Stephanie 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 Amber. Amber's card is shown to Dora. Dora's card is shown to Dora. Amber's card is shown to David. Dora's card is shown to David. It is publicly announced that someone picked a red card. It is publicly announced that Dora knows whether Dora picked a red card. It is publicly announced that Amber does not know whether Dora picked a red card.

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

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

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


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

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

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

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


Premise: There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Paul's card is shown to Shawn. Shawn's card is shown to Burton. 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 Burton does not know whether or not everyone picked a red card.

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

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

Hypothesis: Burton can now know whether Shawn picked a red card.


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

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

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

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


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

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

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

Hypothesis: Christopher can now know that Joseph can know that Joseph 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 Cassondra. Beverly's card is shown to Cassondra. Linda's card is shown to Carol. Cassondra's card is shown to Carol. Beverly's card is shown to Beverly. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Cassondra 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). Clayton's card is shown to Alvin. Charles's card is shown to Alvin. Alvin's card is shown to Stephanie. Alvin's card is shown to Clayton. Stephanie's card is shown to Charles. Clayton's card is shown to Charles. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Stephanie can now know that Charles can know whether Clayton picked a red card.


Premise: There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rosa's card is shown to Barbara. 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: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:3 VALID? [ ! (1|2|3) ] 0

Hypothesis: Barbara can now know whether Rosa 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). Roberta's card is shown to David. Roberta's card is shown to Jocelyn. Jocelyn's card is shown to Roberta. It is publicly announced that someone picked a red card. It is publicly announced that Roberta picked a red card.

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

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

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


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

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

Hypothesis: Lane can now know whether Ruth 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). Jean's card is shown to Jean. Victoria's card is shown to Jean. Thomas's card is shown to Jean. Jaime's card is shown to Thomas. It is publicly announced that someone picked a red card. It is publicly announced that Victoria picked a red card.

Hypothesis: Jean 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). Brandon's card is shown to Arthur. Arthur's card is shown to Arthur. Betty's card is shown to Arthur. Brandon's card is shown to Betty. Patrick's card is shown to Betty. Patrick's card is shown to Patrick. 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:1,2,3 Agentb:1,4 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] Agentb knows that (Agentc knows whether (~(1|2|3|4)))

Hypothesis: Arthur can now know that Betty 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). Jeffrey's card is shown to William. William'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 William knows whether Jeffrey picked a red card.

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

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

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


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

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

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

Hypothesis: Pamela 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). Ashley's card is shown to Ashley. Kenneth's card is shown to Ashley. Kenneth's card is shown to Maria. Thomas's card is shown to Maria. Kenneth's card is shown to Kenneth. Maria's card is shown to Thomas. Thomas's card is shown to Thomas. It is publicly announced that someone picked a red card. It is publicly announced that Kenneth does not know whether or not everyone picked a red card.

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

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

Hypothesis: Kenneth can now know that Maria picked a red card.


Premise: There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Barbara's card is shown to Christopher. Barbara's card is shown to Barbara. Jason's card is shown to Barbara. Christopher'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 LAW Top OBS Agenta:2 Agentb:2,3 Agentc:1,3 VALID? [ ! (1|2|3) ] Agentb knows that (Agentc knows whether 3)

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

Hypothesis: Barbara can now know that Jason can know whether Jason picked a red card.


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

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

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

Hypothesis: Elizabeth can now know whether Imogene 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 Jessica. Matthew's card is shown to Matthew. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Jessica 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). Seth's card is shown to James. James's card is shown to Timothy. Timothy's card is shown to Debra. James's card is shown to Seth. Seth's card is shown to Seth. It is publicly announced that someone picked a red card. It is publicly announced that Debra does not know whether Debra picked a red card. It is publicly announced that James does not know whether or not everyone picked a red card.

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

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

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


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

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

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

Hypothesis: Kyle 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). Essie's card is shown to Essie. Irene's card is shown to Essie. Daniel's card is shown to Essie. Essie's card is shown to Irene. Daniel's card is shown to Irene. Irene's card is shown to Daniel. Daniel's card is shown to Alejandro. Alejandro's card is shown to Alejandro. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Essie can now know whether Irene picked a red card.


Premise: There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Roy's card is shown to Richard. Richard's card is shown to Fred. Fred's card is shown to Fred. It is publicly announced that someone picked a red card. It is publicly announced that Roy does not know whether James 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) ] (Agenta knows whether (~(1|2|3|4)))

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: Richard 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). Alice's card is shown to Alice. It is publicly announced that someone picked a red card.

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

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


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

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

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

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


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

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

Hypothesis: Pauline can now know whether James 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). Sharon's card is shown to Sharon. Erin's card is shown to Sharon. Beatrice's card is shown to Beatrice. Sharon's card is shown to Erin. Erin's card is shown to Erin. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Erin 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). Robert's card is shown to Penny. Jason's card is shown to Martin. Robert's card is shown to Robert. It is publicly announced that someone picked a red card. It is publicly announced that Martin knows whether Robert picked a red card. It is publicly announced that Jason does not know whether Penny picked a red card.

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

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

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


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

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

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

Hypothesis: Barbara can now know whether Barbara 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 Joan. Leon's card is shown to Joan. Sherri's card is shown to Leon. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Leon can now know that Joan can know whether or not everyone picked a red card.


Premise: There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Todd's card is shown to Todd. Todd's card is shown to Timothy. Timothy's card is shown to Timothy. Todd's card is shown to Darrin. Darrin's card is shown to Darrin. It is publicly announced that someone picked a red card. It is publicly announced that Todd 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 whether 1)

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: Todd can now know whether Todd picked a red card.


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

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

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

Hypothesis: Cecelia can now know whether Joe can know that Jame picked a red card.


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

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

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

Hypothesis: Charles 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). Michael's card is shown to Lena. Michael's card is shown to Ian. Lena's card is shown to Beverly. Beverly's card is shown to Beverly. It is publicly announced that someone picked a red card.

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

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

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


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

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

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

Hypothesis: Raymundo can now know whether Charles 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). Cynthia's card is shown to Patricia. Margie's card is shown to Patricia. Samuel's card is shown to Patricia. Patricia's card is shown to Margie. Cynthia's card is shown to Margie. Samuel's card is shown to Margie. Cynthia's card is shown to Samuel. It is publicly announced that someone picked a red card.

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

Hypothesis: Cynthia can now know that Samuel picked a red card.


Premise: There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Christopher's card is shown to Dana. Mary's card is shown to Dana. Christopher's card is shown to Christopher. Mary's card is shown to Christopher. Mary's card is shown to Alice. Christopher's card is shown to Mary. It is publicly announced that someone picked a red card. It is publicly announced that Alice does not know whether Christopher 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) ] Agentc knows that (Agentd knows that 4)

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: Alice can now know that Mary can 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). Jose's card is shown to Carolyn. Carolyn's card is shown to Jose. Jose's card is shown to Jose. 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 Carolyn picked a red card. It is publicly announced that Jose picked a red card.

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

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


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

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

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

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


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

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

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

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


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

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

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

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


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

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

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

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


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

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

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

Hypothesis: Katherine can now know that Phillip 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. Artie's card is shown to Donald. Artie's card is shown to Artie. 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 Artie 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) ] [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] Agentb knows that (Agenta knows whether 1)

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

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


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

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

Hypothesis: Jeannetta 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). Wayne's card is shown to Wayne. William's card is shown to Wayne. Gregory's card is shown to Gregory. William's card is shown to Gregory. Wayne's card is shown to William. William's card is shown to William. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Gregory can now know that William 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). Charles's card is shown to Charles. Charles's card is shown to Darron. William's card is shown to Darron. 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) ] (Agentb knows that 3)

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

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


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

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

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

Hypothesis: Beverlee can now know that Antoinette 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). Norman's card is shown to Norman. Craig's card is shown to Craig. Norman's card is shown to William. It is publicly announced that someone picked a red card. It is publicly announced that Norman picked a black card.

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

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

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


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

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

Hypothesis: Lanette 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). Stephen's card is shown to Brett. Brett's card is shown to Ann. Stephen'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:4 Agentb:2,4 VALID? [ ! (1|2|3|4) ] (Agentb knows whether (~(1|2|3|4)))

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

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