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

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

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

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


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

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

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

Hypothesis: Vivian can now know that Ellan can know whether Vivian picked a red card.


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

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

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

Hypothesis: Joseph can now know that Robert 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). Shannon's card is shown to Shannon. Elsie's card is shown to Gilbert. Jessie's card is shown to Jessie. Shannon's card is shown to Elsie. It is publicly announced that someone picked a red card. It is publicly announced that Gilbert does not know whether Shannon picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that Shannon picked a black card.

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

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

Hypothesis: Gilbert can now know whether Elsie can know that Shannon picked a red card.


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

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

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

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


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

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

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

Hypothesis: Galen 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). Gladys's card is shown to Gladys. Evelyn's card is shown to Gladys. Karon's card is shown to Jeffrey. Evelyn's card is shown to Evelyn. It is publicly announced that someone picked a red card. It is publicly announced that Karon does not know whether Evelyn picked a red card. 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 Jeffrey does not know whether or not everyone picked a red card.

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

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


Premise: There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nydia's card is shown to Lynn. Lynn's card is shown to Nydia. It is publicly announced that someone picked a red card. It is publicly announced that Sonia 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) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agentb knows whether (1&2&3))

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

Hypothesis: Sonia 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). Matthew's card is shown to Matthew. John's card is shown to Cynthia. It is publicly announced that someone picked a red card. It is publicly announced that Matthew does not know whether Cynthia picked a red card.

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

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

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


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

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

Hypothesis: James can now know that Randall 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). Eddie's card is shown to Eddie. Eric's card is shown to Eddie. Jody's card is shown to John. It is publicly announced that someone picked a red card. It is publicly announced that Jody picked a black card. It is publicly announced that John picked a red card.

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

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


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

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

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

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


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

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

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

Hypothesis: James can now know that Kimberley 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). Tommy's card is shown to Tommy. 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 whether 4)

Hypothesis: Victoria can now 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). Dennis's card is shown to Dennis. Dennis'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 Dennis does not know whether Richard picked a red card.

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

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

Hypothesis: Richard can now know that Dennis 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). Nathaniel's card is shown to Dana. Dana's card is shown to Nathaniel. Richard's card is shown to Nathaniel. Dana's card is shown to Richard. Richard's card is shown to Richard. It is publicly announced that someone picked a red card.

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

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

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


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

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

Hypothesis: Andrew can now know that Cynthia 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). Jessica's card is shown to Jessica. Nicolas's card is shown to Jessica. Jessica's card is shown to Carl. Nicolas's card is shown to Nicolas. Nicolas's card is shown to Ruth. It is publicly announced that someone picked a red card.

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

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

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


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

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

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

Hypothesis: Jennifer 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). Dean's card is shown to Gloria. Elizabeth's card is shown to Gloria. Jessica's card is shown to Dean. Jessica's card is shown to Elizabeth. Gloria's card is shown to Jessica. Dean's card is shown to Jessica. It is publicly announced that someone picked a red card. It is publicly announced that Jessica picked a red card.

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

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

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


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

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

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

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


Premise: There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joyce's card is shown to Joyce. Lorena's card is shown to Lorena. 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) ] Agenta knows whether (Agentb knows that (~(1|2)))

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

Hypothesis: Joyce can now know whether Lorena 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). Lori's card is shown to Edward. Edward's card is shown to Lori. Lori's card is shown to Clifford. Lori's card is shown to Kathy. It is publicly announced that someone picked a red card. It is publicly announced that Clifford knows whether or not everyone picked a red card. It is publicly announced that Kathy does not know whether Clifford picked a red card.

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

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

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


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

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

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

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


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

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

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

Hypothesis: Enrique can now know that Eric 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). Steven's card is shown to Steven. Steven's card is shown to Brendan. Steven's card is shown to Bobby. Brendan's card is shown to Cedric. 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.

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

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

Hypothesis: Bobby can now know whether Cedric 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). Gail's card is shown to Susan. Bryan's card is shown to Bryan. Bryan's card is shown to Robert. It is publicly announced that someone picked a red card. It is publicly announced that Bryan does not know whether Gail picked a red card. It is publicly announced that Bryan does not know whether Gail picked a red card. It is publicly announced that not everyone picked a red card.

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

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

Hypothesis: Susan 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). Erich's card is shown to Mary. Debra's card is shown to Gregoria. Mary's card is shown to Erich. 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 someone picked a red card.

Hypothesis: Debra 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). Joseph's card is shown to Patricia. Joseph's card is shown to Joseph. Joan's card is shown to Joseph. Patricia's card is shown to Joan. Joan's card is shown to Joan. It is publicly announced that someone picked a red card. It is publicly announced that Joan knows whether Patricia picked a red card.

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

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

Hypothesis: Joseph 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). Christy's card is shown to Christy. Kristine's card is shown to Christy. Christy's card is shown to Bryan. Bryan's card is shown to Bryan. Bryan's card is shown to Jessica. It is publicly announced that someone picked a red card.

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

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

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


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

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

Hypothesis: Dudley 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). Amber's card is shown to Amber. Debra's card is shown to Amber. Amber's card is shown to Isaac. Isaac's card is shown to Isaac. Mike's card is shown to Isaac. Amber's card is shown to Debra. Amber's card is shown to Mike. Debra's card is shown to Mike. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Mike can now know that Debra 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 Christopher. It is publicly announced that someone picked a red card. It is publicly announced that Christopher knows whether someone picked a red card.

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

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

Hypothesis: Christopher 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). Marissa's card is shown to Marissa. Patricia's card is shown to Patricia. Cindy's card is shown to Patricia. Cindy's card is shown to Terri. It is publicly announced that someone picked a red card.

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

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

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


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

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

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

Hypothesis: Milton can now know whether Carmen can know that Marcia picked a red card.


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

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

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

Hypothesis: Gladys can now know that Norma 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). Jason's card is shown to Jason. Jason's card is shown to Vernon. 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 whether (Agenta knows that (1&2))

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

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


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

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

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

Hypothesis: Mae can now know whether Tami can know that Blaine picked a red card.


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

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

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

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


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

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

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

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


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

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

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

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


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

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

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

Hypothesis: Richard can now know that Mona 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). Andree's card is shown to Andree. Clyde's card is shown to Andree. Andree's card is shown to Fred. Clyde's card is shown to Fred. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Andree can now know whether Clyde can know that Andree picked a red card.


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

Hypothesis: Rhonda can now know that Jordan can know whether Rhonda picked a red card.


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

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

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

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


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

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

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

Hypothesis: Andrew can now know that Joann 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). Matthew's card is shown to Matthew. Suzan's card is shown to Roger. It is publicly announced that someone picked a red card.

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

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

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


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

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

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

Hypothesis: Grover can now know that Lisa 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 Rochel. Rochel's card is shown to David. Rochel's card is shown to Christopher. It is publicly announced that someone picked a red card. It is publicly announced that Christopher knows whether or not everyone picked a red card. It is publicly announced that David knows whether or not everyone picked a red card.

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

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

Hypothesis: David 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). Marsha's card is shown to James. James's card is shown to James. William's card is shown to James. Marsha's card is shown to William. It is publicly announced that someone picked a red card.

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

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

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

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

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

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


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

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

Hypothesis: Katie 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). Donald's card is shown to Donald. Donald's card is shown to Meridith. Meridith's card is shown to Meridith. 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 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (~(1&2)) ] Agenta knows whether (Agentb knows whether (1|2))

Hypothesis: Donald can now know whether Meridith 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). Richard's card is shown to Richard. Princess's card is shown to Princess. Clarissa's card is shown to Princess. Princess's card is shown to Clarissa. Clarissa's card is shown to Clarissa. It is publicly announced that someone picked a red card. It is publicly announced that Richard does not know whether Princess picked a red card. It is publicly announced that Clarissa knows whether Princess picked a red card.

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

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

Hypothesis: Princess can now know whether Richard 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). Brian's card is shown to Brian. Latoya's card is shown to Latoya. Latoya's card is shown to Ida. Ida's card is shown to Ida. It is publicly announced that someone picked a red card. It is publicly announced that Brian does not know whether or not everyone picked a red card.

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

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

Hypothesis: Latoya can now know whether Ida picked a red card.


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

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

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

Hypothesis: Stacy 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). Jared's card is shown to Jared. Aaron's card is shown to Aaron. Lisa's card is shown to Robert. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Jared can now know that Robert can 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). Philip's card is shown to Philip. Andrea's card is shown to Philip. Barbara's card is shown to Andrea. Philip's card is shown to Barbara. Barbara's card is shown to Barbara. Laverne's card is shown to Barbara. Barbara's card is shown to Laverne. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Barbara can now know that Andrea 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). Cheryl's card is shown to Betty. Cheryl's card is shown to David. David's card is shown to Cheryl. It is publicly announced that someone picked a red card.

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

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

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


Premise: There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Emmy's card is shown to Clyde. Emmy's card is shown to Emmy. 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 Emmy knows whether Clyde picked a red card.

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

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

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


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

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

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

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


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

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

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

Hypothesis: Arnold can now know that Joyce can know that Joyce picked a red card.


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

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

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

Hypothesis: William can now know that Damien 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). Louis's card is shown to Louis. Scott's card is shown to Louis. Louis's card is shown to Scott. Scott's card is shown to Scott. Scott's card is shown to Nancy. Nancy's card is shown to Nancy. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Nancy can now know that Scott 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). Joe's card is shown to Ross. Ross's card is shown to Ross. Paul's card is shown to Paul. 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) ] Agenta knows that (Agentb knows that 3)

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

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


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

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

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

Hypothesis: Erin can now know that Beverly can know whether or not nobody picked a red card.


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

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

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

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


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

Hypothesis: Suzanne 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). Deborah's card is shown to Estelle. Estelle's card is shown to Deborah. Mark's card is shown to Deborah. Estelle's card is shown to Mark. Deborah's card is shown to Mark. It is publicly announced that someone picked a red card.

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

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

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


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

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

Hypothesis: Bridgette can now know whether Lauren can know whether Jim picked a red card.


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

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

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

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


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

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

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

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


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

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

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

Hypothesis: Dawn can now know whether Faith 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). Virginia's card is shown to Virginia. Megan's card is shown to Megan. 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 that 1)

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

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


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

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

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


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

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

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

Hypothesis: Christine can now know whether Christine 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 Lucie. Lucie's card is shown to Lucie. Carol's card is shown to Carol. It is publicly announced that someone picked a red card.

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

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

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


Premise: There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Martha's card is shown to June. Martha's card is shown to Martha. Eugene's card is shown to Martha. Martha'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:3 Agentb:3,4 Agentc:3 VALID? [ ! (1|2|3|4) ] (Agenta knows whether 4)

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

Hypothesis: June can now know whether Eugene picked a red card.


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

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

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

Hypothesis: Alan 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). Angelica's card is shown to Fern. Richard's card is shown to Richard. Fern's card is shown to Teena. Fern's card is shown to Angelica. Richard's card is shown to Angelica. It is publicly announced that someone picked a red card.

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

Hypothesis: Fern can now know whether Richard 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). Abbey's card is shown to Francis. Francis's card is shown to Abbey. Abbey's card is shown to Abbey. Francis's card is shown to Robert. It is publicly announced that someone picked a red card. It is publicly announced that Abbey knows whether Abbey picked a red card.

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

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

Hypothesis: Francis can now know whether Abbey 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). Marcy's card is shown to John. Michael's card is shown to John. Marcy's card is shown to Marcy. Marcy's card is shown to Michael. It is publicly announced that someone picked a red card. It is publicly announced that Marcy does not know whether John picked a red card.

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

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

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


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

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

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

Hypothesis: James 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). Charles's card is shown to Charles. Charles's card is shown to Illa. Charles's card is shown to Lewis. Tina's card is shown to Lewis. It is publicly announced that someone picked a red card. It is publicly announced that Charles knows whether or not everyone picked a red card. It is publicly announced that Illa knows whether or not everyone picked a red card.

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

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

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


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

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

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

Hypothesis: Michael 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). Tanya's card is shown to Tanya. Lester's card is shown to Tanya. Tanya's card is shown to Lester. Lester's card is shown to Lester. It is publicly announced that someone picked a red card. It is publicly announced that Lester picked a black card. It is publicly announced that Tanya knows whether or not nobody picked a red card.

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

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

Hypothesis: Lester can now know that Tanya can know that Lester picked a red card.


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

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

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

Hypothesis: Tammie can now 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). Mildred's card is shown to Mildred. Mildred's card is shown to Tommie. Tommie's card is shown to Tommie. It is publicly announced that someone picked a red card. It is publicly announced that Tommie knows whether someone picked a red card. It is publicly announced that someone picked a red card.

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

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

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


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

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

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

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


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

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

Hypothesis: Annie can now know whether Donna 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). Laurena's card is shown to John. Laurena's card is shown to Kenneth. Kenneth's card is shown to Laurena. 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 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] Agentc knows whether (Agentb knows that (1|2|3))

Hypothesis: Laurena can now know whether Kenneth can know that someone picked a red card.


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

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

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

Hypothesis: Melvin can now know that 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). Anne's card is shown to Gary. Thomas's card is shown to Gary. Anne's card is shown to Anne. Thomas's card is shown to Anne. Gary's card is shown to Thomas. Anne'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 Thomas 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 that (1&2&3))

Hypothesis: Gary 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). Steve's card is shown to Steve. Steve's card is shown to Anna. Anna's card is shown to Anna. Steve's card is shown to Rita. Rita's card is shown to Rita. It is publicly announced that someone picked a red card. It is publicly announced that Anna knows whether Steve picked a red card.

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

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

Hypothesis: Anna can now know that Rita can know that Anna picked a red card.


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

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

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

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


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

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

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

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


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

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

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

Hypothesis: Sarah 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). Gertrude's card is shown to Gertrude. Joseph's card is shown to Gertrude. Gertrude's card is shown to Joseph. Gertrude's card is shown to Ashley. Ashley's card is shown to Ashley. Gertrude's card is shown to Lenora. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Lenora 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). Yoshiko's card is shown to Arnold. Yoshiko'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 Yoshiko knows whether someone picked a red card. It is publicly announced that Yoshiko does not know whether or not everyone picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that Yoshiko picked a red card.

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

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


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

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

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

Hypothesis: Jorge 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). Maria's card is shown to Maria. Darlene's card is shown to Darlene. 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 Maria does not know whether Darlene picked a red card.

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

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

Hypothesis: Maria can now know that Darlene can know whether 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). Blanche's card is shown to Blanche. Blanche's card is shown to Lillian. Lillian's card is shown to Lillian. Lillian's card is shown to Glenda. 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:2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agenta knows whether (Agentc knows whether 1)

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


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

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

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

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


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

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

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

Hypothesis: Sara 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). Anna's card is shown to Anna. John's card is shown to Anna. Anna's card is shown to John. Anna's card is shown to Joshua. Joshua's card is shown to Joshua. Anna's card is shown to Sheena. It is publicly announced that someone picked a red card.

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

Hypothesis: Anna 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). Jocelyn's card is shown to Jocelyn. Kevin's card is shown to Jocelyn. Kevin's card is shown to Kevin. It is publicly announced that someone picked a red card. It is publicly announced that Kevin does not know whether or not everyone picked a red card. It is publicly announced that Kevin knows whether or not nobody picked a red card.

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

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

Hypothesis: Kevin 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). Felicia's card is shown to Felicia. William's card is shown to Felicia. Charles's card is shown to Charles. William's card is shown to Charles. Charles's card is shown to Melissa. Melissa's card is shown to Melissa. Felicia's card is shown to William. It is publicly announced that someone picked a red card. It is publicly announced that Melissa does not know whether William picked a red card. It is publicly announced that Felicia does not know whether Charles picked a red card.

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

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

Hypothesis: Melissa can now know whether William 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). Daniel's card is shown to Daniel. Myrna's card is shown to Daniel. Myrna's card is shown to Kristin. Myrna's card is shown to Joseph. Joseph's card is shown to Myrna. Myrna's card is shown to Myrna. It is publicly announced that someone picked a red card.

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

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

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


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

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

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

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


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

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

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

Hypothesis: Lewis 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). Patricia's card is shown to Robert. Nikki's card is shown to Robert. It is publicly announced that someone picked a red card. It is publicly announced that Patricia knows whether Nikki picked a red card. It is publicly announced that Patricia picked a red card.

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

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

Hypothesis: Patricia 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). Eva's card is shown to Eva. Phillip's card is shown to Eva. Phillip's card is shown to Phillip. Frank's card is shown to Phillip. Phillip's card is shown to Frank. It is publicly announced that someone picked a red card. It is publicly announced that Frank does not know whether Eva picked a red card. It is publicly announced that Eva does not know whether Frank picked a red card. It is publicly announced that Frank 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:1,2 Agentb:2,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! (1|2|3) ] Agenta knows that (Agentb knows whether (~(1|2|3)))

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

Hypothesis: Eva can now know that Phillip 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). Olga's card is shown to Betty. Olga's card is shown to Derek. 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 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] (Agenta knows whether 2)

Hypothesis: Olga can now know whether Betty 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 Robert. Robert's card is shown to Larry. Terry's card is shown to Larry. It is publicly announced that someone picked a red card. It is publicly announced that Terry knows whether Robert picked a red card.

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

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

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


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

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

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

Hypothesis: Sara 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). Christopher's card is shown to Althea. Althea's card is shown to Althea. Helen's card is shown to Althea. Althea's card is shown to Marlene. Helen's card is shown to Marlene. Althea's card is shown to Helen. It is publicly announced that someone picked a red card.

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

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

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


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

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

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

Hypothesis: Marie 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). Elna's card is shown to Elna. India's card is shown to Elna. Daniel's card is shown to Elna. India's card is shown to Miles. Daniel's card is shown to Miles. Miles's card is shown to India. Elna's card is shown to Daniel. Daniel's card is shown to Daniel. It is publicly announced that someone picked a red card. It is publicly announced that India does not know whether India picked a red card.

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

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

Hypothesis: Miles can now know whether Elna picked a red card.


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

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

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

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


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

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

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

Hypothesis: Jorge 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). Vincent's card is shown to Kirk. Vincent's card is shown to Tracy. It is publicly announced that someone picked a red card. It is publicly announced that Kirk picked a red card.

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

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

Hypothesis: Kirk can now know that Vincent can know whether Tracy picked a red card.


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

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

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

Hypothesis: Linda 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). Kenneth's card is shown to Joanne. Tony's card is shown to Tony. Tony's card is shown to Kenneth. It is publicly announced that someone picked a red card. It is publicly announced that Kenneth picked a red card. It is publicly announced that Rachel knows whether or not everyone picked a red card.

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

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

Hypothesis: Tony can now know that Rachel can know that Joanne picked a red card.


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

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

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

Hypothesis: Florence can now know whether Derick can know that someone picked a red card.


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

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

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

Hypothesis: Michael can now know whether Simon 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). Jeffrey's card is shown to Jeffrey. Luciano's card is shown to Jeffrey. Nancy's card is shown to Luciano. Jeffrey's card is shown to Nancy. It is publicly announced that someone picked a red card. It is publicly announced that Nancy 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 whether (Agentc knows that 1)

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: Jeffrey can now know whether Nancy can know that Jeffrey picked a red card.


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

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

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

Hypothesis: Brandon can now know that Nancy 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). Brant's card is shown to Charlotte. Charlotte's card is shown to Charlotte. Jessica's card is shown to Charlotte. Karen's card is shown to Jessica. Jessica's card is shown to Jessica. It is publicly announced that someone picked a red card.

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

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


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

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

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

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


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

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

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

Hypothesis: Philip can now know that Bessie 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). Lauren's card is shown to Shawn. Shawn's card is shown to Shawn. Lauren's card is shown to Holly. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Lauren can now know that Shawn 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). Patricia's card is shown to Patricia. Patricia's card is shown to Gary. Gary's card is shown to Gary. It is publicly announced that someone picked a red card. It is publicly announced that Gary knows whether Gary picked a red card.

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

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

Hypothesis: Gary can now know whether Patricia 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). Ollie's card is shown to Mary. Mary's card is shown to Ollie. Ollie's card is shown to Ollie. Mary's card is shown to Luis. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Mary 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). Terry's card is shown to Terry. Mike's card is shown to Terry. Betty's card is shown to Terry. Juanita's card is shown to Mike. Betty's card is shown to Mike. Mike's card is shown to Betty. Betty's card is shown to Betty. It is publicly announced that someone picked a red card. It is publicly announced that Terry does not know whether Terry picked a red card. It is publicly announced that Terry does not know whether Terry picked a red card.

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

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

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


Premise: There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Stephen's card is shown to Stephen. Hien's card is shown to Stephen. Stephen's card is shown to Hien. It is publicly announced that someone picked a red card. It is publicly announced that Michelle 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) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agenta knows that (1&2&3))

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

Hypothesis: Michelle 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). Lorraine's card is shown to Lorraine. Teresa's card is shown to Teresa. Lorraine's card is shown to Megan. Teresa's card is shown to Megan. Megan's card is shown to Megan. It is publicly announced that someone picked a red card. It is publicly announced that Lorraine does not know whether or not everyone picked a red card. It is publicly announced that Teresa knows whether Teresa picked a red card.

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

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

Hypothesis: Teresa can now know whether Lorraine can know that everyone picked a red card.


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

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

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

Hypothesis: Johnny 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). Odessa's card is shown to Odessa. Odessa's card is shown to Maria. It is publicly announced that someone picked a red card. It is publicly announced that Odessa does not know whether Maria picked a red card. It is publicly announced that Odessa knows whether or not nobody picked a red card.

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

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

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


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

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

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

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


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

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

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

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


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

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

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


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

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

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

Hypothesis: Henry can now know that Vivian can know that Wanda picked a red card.


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

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

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

Hypothesis: Alberta can now know whether Kevin 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). Jesse's card is shown to Jesse. Alice's card is shown to Jesse. John's card is shown to John. John's card is shown to Alice. It is publicly announced that someone picked a red card.

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

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

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


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

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

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


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

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

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

Hypothesis: Lynne can now know that 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). Oliver's card is shown to Jessica. Kathy's card is shown to Oliver. Kenneth's card is shown to Kenneth. Jessica's card is shown to Kathy. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card.

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

Hypothesis: Oliver can now know whether Kathy can know whether Oliver picked a red card.