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

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

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


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

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

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

Hypothesis: Karen 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). Adele's card is shown to Sharon. Jose's card is shown to Sharon. Adele's card is shown to Jose. Sharon's card is shown to Jose. Adele's card is shown to Ronald. Sharon's card is shown to Ronald. It is publicly announced that someone picked a red card. It is publicly announced that Jose does not know whether Jose picked a red card.

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

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

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


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

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

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

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


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

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

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

Hypothesis: Elisabeth can now know that Edmond can know whether Angela picked a red card.


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

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

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

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


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

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

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

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


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

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

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

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


Premise: There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Shirley's card is shown to Marian. Tara's card is shown to Shirley. Tara's card is shown to Tara. It is publicly announced that someone picked a red card. It is publicly announced that Tara knows whether someone picked a red card. It is publicly announced that Shirley does not know whether Marian 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) ] Agentb knows whether (Agentc knows whether 1)

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: Shirley can now know whether Tara can know whether Marian picked a red card.


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

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

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

Hypothesis: Shane 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). Michael's card is shown to Christa. Jeffrey's card is shown to Julia. Christa'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:4 Agentb:1 Agentc:2 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentc knows that 1)

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

Hypothesis: Jeffrey can now know that Julia can know that 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). Norman's card is shown to Dale. Dale's card is shown to Warren. Norman's card is shown to Warren. Dale's card is shown to Norman. Norman's card is shown to Norman. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Warren can now know whether Norman 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). Dennis's card is shown to Dennis. Janet's card is shown to Janet. It is publicly announced that someone picked a red card. It is publicly announced that Charlotte does not know whether Carmen picked a red card.

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

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

Hypothesis: Charlotte 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). Mattie's card is shown to Mattie. Micah's card is shown to Tracy. Mattie's card is shown to Tracy. Tracy's card is shown to Tracy. It is publicly announced that someone picked a red card. It is publicly announced that Micah does not know whether or not everyone picked a red card. It is publicly announced that Tracy picked a red card.

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

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

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


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

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

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

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


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

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

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


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

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

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

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


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

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


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

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

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

Hypothesis: David can now know whether Brett can know whether Brett 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. Joy's card is shown to Richard. Jeff's card is shown to Jeff. Jeff's card is shown to Joy. It is publicly announced that someone picked a red card. It is publicly announced that Jeff does not know whether Richard 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 1) ] Agentb knows that (Agenta knows that (~(1|2|3)))

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

Hypothesis: Jeff can now know that 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). Thelma's card is shown to Thelma. Samuel's card is shown to Thelma. Thelma's card is shown to Edward. Edward's card is shown to Edward. Samuel's card is shown to Edward. Thelma's card is shown to Samuel. Samuel's card is shown to Samuel. It is publicly announced that someone picked a red card.

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

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

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


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

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

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


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

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

Hypothesis: Genevieve can now know that Danna can know whether Genevieve picked a red card.


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

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

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

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


Premise: There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Harlan's card is shown to Harlan. Joseph's card is shown to Harlan. Harlan's card is shown to Joseph. 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) ] (Agentb knows that 1)

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

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


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

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

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

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


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

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

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

Hypothesis: David can now know whether Clara 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). David's card is shown to David. James's card is shown to James. David's card is shown to John. John's card is shown to John. It is publicly announced that someone picked a red card. It is publicly announced that James picked a red card. It is publicly announced that John knows whether John picked a red card.

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

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

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


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

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

Hypothesis: Paul 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). Elisa's card is shown to Mary. Dorla's card is shown to Mary. Mary's card is shown to Elisa. Mary's card is shown to Dorla. It is publicly announced that someone picked a red card. It is publicly announced that Elisa does not know whether Elisa picked a red card.

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

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

Hypothesis: Dorla 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). Jason's card is shown to Jason. Elijah's card is shown to Jason. Jason's card is shown to Elijah. It is publicly announced that someone picked a red card. It is publicly announced that Elijah does not know whether Elijah picked a red card.

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

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

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


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

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

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

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


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

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

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

Hypothesis: Francisco can now know that Jose 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). Jason's card is shown to Mariano. Mariano's card is shown to Stacey. Mariano's card is shown to Nicole. Mariano's card is shown to Jason. Jason's card is shown to Jason. It is publicly announced that someone picked a red card. It is publicly announced that Mariano does not know whether Nicole picked a red card.

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

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

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


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

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

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

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


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

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

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

Hypothesis: Toni can now know that Dean 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). Amy's card is shown to Amy. Mary's card is shown to Amy. Amy's card is shown to Patricia. Patricia's card is shown to Patricia. Sandra's card is shown to Sandra. Mary's card is shown to Sandra. Amy's card is shown to Mary. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Sandra can now know whether Amy 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). Regina's card is shown to Regina. Regina's card is shown to Michael. Michael's card is shown to Yolanda. Yolanda's card is shown to Yolanda. Yolanda's card is shown to Calvin. It is publicly announced that someone picked a red card.

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

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


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

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

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

Hypothesis: Deborah can now know whether Ted 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). Lorene's card is shown to Lorene. Kathleen's card is shown to Kathleen. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card.

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

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

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


Premise: There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Arlene's card is shown to Thomas. Thomas's card is shown to Linda. Arlene's card is shown to Linda. Linda's card is shown to Arlene. Arlene's card is shown to Arlene. It is publicly announced that someone picked a red card. It is publicly announced that Linda 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))) ] (Agentc knows whether (1|2|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: Arlene 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). Desiree's card is shown to Desiree. Carol's card is shown to Desiree. Wayne's card is shown to David. David's card is shown to Wayne. Carol's card is shown to Carol. It is publicly announced that someone picked a red card. It is publicly announced that Desiree does not know whether Wayne picked a red card.

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

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

Hypothesis: David can now know whether Carol 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). Joseph's card is shown to Joseph. Lewis's card is shown to Joseph. Joseph's card is shown to Lewis. Lewis's card is shown to Lewis. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Lewis can now know whether Joseph 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). Howard's card is shown to Howard. Howard's card is shown to Deangelo. It is publicly announced that someone picked a red card. It is publicly announced that Ivy does not know whether or not everyone picked a red card. It is publicly announced that Ivy does not know whether or not everyone picked a red card. It is publicly announced that Ivy knows whether Howard picked a red card.

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

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

Hypothesis: Ivy can now know that Deangelo picked a red card.


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

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

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

Hypothesis: Richard 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). David's card is shown to David. Shawn's card is shown to David. David's card is shown to Shawn. David's card is shown to Guy. It is publicly announced that someone picked a red card. It is publicly announced that Guy knows whether David picked a red card.

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

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

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


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

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

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

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


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

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

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


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

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

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

Hypothesis: Lloyd 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). Jan's card is shown to Jan. Jan's card is shown to Jill. Jill's card is shown to Jill. Jan's card is shown to Nicholas. Jill's card is shown to Nicholas. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Jan can now know that Nicholas picked a red card.


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

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

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

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


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

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

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


Premise: There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kimberly's card is shown to Kimberly. Claudia's card is shown to Kimberly. Claudia's card is shown to Claudia. Thomas's card is shown to Claudia. Kimberly's card is shown to Angelique. Claudia's card is shown to Angelique. Kimberly'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 Kimberly knows whether Kimberly picked a red card.

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

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

Hypothesis: Thomas can now know whether Claudia can know whether Angelique picked a red card.


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

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

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

Hypothesis: Beth can now know that Yee can know that Todd picked a red card.


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

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

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

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


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

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

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

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


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

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

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

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


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

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

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

Hypothesis: William can now know that Ferdinand 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). Brian's card is shown to Vivian. Brian's card is shown to Brian. Julie's card is shown to Julie. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Vivian 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). Virginia's card is shown to Virginia. Kenya's card is shown to Lisa. Lisa's card is shown to Kenya. It is publicly announced that someone picked a red card.

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

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

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


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

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

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

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

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


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

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

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

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


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

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

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


Premise: There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Vickie's card is shown to Vickie. Vickie's card is shown to Thomas. Thomas'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 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] (Agentc 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: William 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). Shirley's card is shown to Shirley. Candice's card is shown to Shirley. Julie's card is shown to Julie. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Shirley can now know whether Julie can know whether Candice picked a red card.


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

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

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

Hypothesis: Juan can now know that Stella can know whether Marvin picked a red card.


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

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

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

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


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

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

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

Hypothesis: Tammy can now know that Erica picked a red card.


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

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

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


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

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

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


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

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

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

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


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

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

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

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


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

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

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

Hypothesis: Kelsey can now know whether Dorothy 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). Gwendolyn's card is shown to Gwendolyn. Shawn's card is shown to Tammy. Gwendolyn's card is shown to Tammy. It is publicly announced that someone picked a red card. It is publicly announced that Shawn knows whether or not everyone picked a red card.

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

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

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


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

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


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

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

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

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


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

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

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

Hypothesis: Dean can now know that Jane can know whether Angel picked a red card.


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

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

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

Hypothesis: Robert can now know whether Raymond 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). Vernell's card is shown to Vernell. Ryan's card is shown to Vernell. Alice's card is shown to Vernell. Vernell's card is shown to Don. Ryan's card is shown to Don. Alice's card is shown to Ryan. Vernell's card is shown to Alice. Ryan's card is shown to Alice. It is publicly announced that someone picked a red card.

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

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

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


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

Hypothesis: Curtis 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). Michael's card is shown to Donna. Donna's card is shown to Maryann. Michael's card is shown to Maryann. Donna's card is shown to Dorothy. It is publicly announced that someone picked a red card. It is publicly announced that Dorothy picked a red card.

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

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

Hypothesis: Maryann 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). Anthony's card is shown to William. William's card is shown to Anthony. William's card is shown to Mary. Anthony's card is shown to Mary. It is publicly announced that someone picked a red card.

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

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

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


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

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


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

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

Hypothesis: Felipe 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). Hazel's card is shown to Hazel. Kenneth's card is shown to Hazel. Kenneth's card is shown to Kenneth. Hazel's card is shown to Cindy. Kenneth's card is shown to Cindy. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Hazel 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). Renita's card is shown to Renita. Mary's card is shown to Renita. Mary's card is shown to Mary. Michael's card is shown to Mary. Jane's card is shown to Michael. Mary's card is shown to Jane. It is publicly announced that someone picked a red card.

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

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

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


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

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

Hypothesis: Lawrence can now know that Leslie 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). Caroline's card is shown to William. Heather's card is shown to Rick. Rick's card is shown to Caroline. Rick's card is shown to Heather. Heather's card is shown to Heather. It is publicly announced that someone picked a red card.

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

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


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

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

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

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


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

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

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

Hypothesis: Erin 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). Lisa's card is shown to Lisa. Ayana's card is shown to Lisa. Isaias's card is shown to Ayana. Ayana's card is shown to Isaias. Isaias's card is shown to Isaias. 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) ] Agentc knows whether (Agenta knows that 1)

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

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


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

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

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

Hypothesis: Lee can now know that Ella 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). William's card is shown to William. John's card is shown to William. William's card is shown to James. John's card is shown to James. James's card is shown to Gina. It is publicly announced that someone picked a red card. It is publicly announced that John does not know whether or not everyone picked a red card.

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

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

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


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

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

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

Hypothesis: Nadine can now know whether Joseph 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). James's card is shown to James. Rosie's card is shown to James. James's card is shown to Heather. It is publicly announced that someone picked a red card. It is publicly announced that James knows whether someone picked a red card. It is publicly announced that James does not know whether or not everyone picked a red card.

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

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

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


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

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

Hypothesis: Helen 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). Grace's card is shown to Grace. Audrey's card is shown to Audrey. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card.

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

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

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


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

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

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

Hypothesis: Laura 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). Stella's card is shown to Stella. Bradley's card is shown to Stella. Stella's card is shown to Bradley. It is publicly announced that someone picked a red card. It is publicly announced that Stella picked a black card.

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

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

Hypothesis: Bradley can now know whether Stella 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). Michael's card is shown to Zachery. Erin's card is shown to Zachery. Michael's card is shown to Erin. Naomi's card is shown to Erin. Naomi's card is shown to Naomi. It is publicly announced that someone picked a red card.

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

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

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


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

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

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


Premise: There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lawrence's card is shown to Lawrence. Lawrence's card is shown to Patsy. Patsy's card is shown to Patsy. It is publicly announced that someone picked a red card. It is publicly announced that Patsy knows whether Patsy 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 2) ] [ ! (1|2) ] Agenta knows that (Agentb knows whether (~(1|2)))

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

Hypothesis: Lawrence can now know that Patsy 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). Camille's card is shown to Camille. Camille's card is shown to Jimmy. Jimmy's card is shown to Jimmy. Ralph's card is shown to Jimmy. Camille's card is shown to Ralph. Jimmy's card is shown to Ralph. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Jimmy 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). Douglas's card is shown to Douglas. Kristy's card is shown to Douglas. Douglas's card is shown to Carl. Erma's card is shown to Kristy. It is publicly announced that someone picked a red card. It is publicly announced that Douglas does not know whether Carl picked a red card. It is publicly announced that Carl does not know whether Carl picked a red card.

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

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

Hypothesis: Carl can now know whether Erma picked a red card.


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

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

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

Hypothesis: Carl can now know that Holly 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). Roslyn's card is shown to Charlene. Charlene's card is shown to Roslyn. Lorelei's card is shown to Roslyn. Charlene's card is shown to Lorelei. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Charlene can now know whether Lorelei can know whether Lorelei picked a red card.


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

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

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

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


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

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

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

Hypothesis: Barbara can now know whether Stephanie 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). Amanda's card is shown to Norman. Norman's card is shown to Amanda. Amanda's card is shown to Joe. Norman's card is shown to George. Amanda's card is shown to George. Joe's card is shown to George. It is publicly announced that someone picked a red card.

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

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

Hypothesis: George 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). Kathleen's card is shown to Kathleen. Barbara's card is shown to Kathleen. Alan's card is shown to Kathleen. Barbara's card is shown to Barbara. Alan's card is shown to Alan. It is publicly announced that someone picked a red card. It is publicly announced that Barbara does not know whether Alan picked a red card.

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

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

Hypothesis: Barbara can now know that Alan 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). Michael's card is shown to Michael. Michael's card is shown to Bobby. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Stephen 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). Dorthy's card is shown to Margaret. Margaret's card is shown to Dorthy. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Margaret can now know whether Dorthy 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). Betty's card is shown to Kara. Dan's card is shown to Betty. Dan's card is shown to Dan. It is publicly announced that someone picked a red card. It is publicly announced that Dan does not know whether Betty picked a red card.

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

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

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


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

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

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


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

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

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

Hypothesis: Jonathon can now know whether Jesica can know whether Jonathon picked a red card.


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

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

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

Hypothesis: Thomas can now know that Randee can know whether Sean picked a red card.


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

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

Hypothesis: Robert can now know that Ruth 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). Dennis's card is shown to Lillie. Dennis's card is shown to Grace. Dennis's card is shown to Kristin. Kristin's card is shown to Kristin. It is publicly announced that someone picked a red card. It is publicly announced that Grace does not know whether Kristin picked a red card. It is publicly announced that Lillie does not know whether or not everyone picked a red card.

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

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

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


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

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

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

Hypothesis: James 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). Jose's card is shown to Ruth. Twila's card is shown to Ruth. Jose's card is shown to Jose. Ruth's card is shown to Twila. It is publicly announced that someone picked a red card.

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

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

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


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

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

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

Hypothesis: Andrea can now know whether Matthew 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). Nancy's card is shown to Nancy. Nancy's card is shown to Janice. Johnnie's card is shown to Janice. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Janice can now know whether Nancy can know that everyone picked a red card.


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

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

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

Hypothesis: Claud 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). Justin's card is shown to Justin. Jose's card is shown to Justin. Pamela's card is shown to Carla. Jose's card is shown to Pamela. 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) ] Agentb knows whether (Agenta 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: Carla can now know whether Justin 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). Kevin's card is shown to Helen. Helen's card is shown to Darrell. Darrell's card is shown to Darrell. Kevin's card is shown to Darrell. Helen's card is shown to Kevin. Darrell's card is shown to Kevin. Kevin'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:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentc knows whether 2)

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

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


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

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

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

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


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

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

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

Hypothesis: Lorraine can now know whether Allan can know whether Meredith 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 Joseph. Christopher's card is shown to Joseph. Mary's card is shown to Mary. Christopher's card is shown to Mary. Joseph's card is shown to Christopher. Mary's card is shown to Christopher. It is publicly announced that someone picked a red card. It is publicly announced that Joseph knows whether someone picked a red card. It is publicly announced that Christopher picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Joseph does not know whether or not everyone picked a red card.

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

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

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


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

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

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

Hypothesis: Deanne can now know whether Katherine can know that Katherine picked a red card.


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

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

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

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


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

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

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

Hypothesis: Susan can now know that Randy 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). Kenneth's card is shown to Kenneth. Gilbert's card is shown to Gilbert. Gilbert's card is shown to Emily. It is publicly announced that someone picked a red card. It is publicly announced that Gilbert does not know whether or not everyone picked a red card.

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

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

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


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

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

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

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


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

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

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

Hypothesis: Amira can now know whether Adan picked a red card.


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

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

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

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


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

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

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

Hypothesis: Douglas 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). Louis's card is shown to Louis. Roland's card is shown to Louis. Roland's card is shown to Roland. Peter's card is shown to Roland. Roland's card is shown to Peter. It is publicly announced that someone picked a red card. It is publicly announced that Peter does not know whether Louis picked a red card. It is publicly announced that Louis does not know whether Peter picked a red card. It is publicly announced that Peter 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) ] Agentb knows that (Agenta knows whether 2)

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: Roland can now know that Louis can know whether Roland 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 Laura. Laura's card is shown to Lillian. David's card is shown to Lillian. Lillian's card is shown to Lillian. It is publicly announced that someone picked a red card. It is publicly announced that David knows whether Lillian picked a red card. It is publicly announced that Laura does not know whether Lillian picked a red card.

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

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

Hypothesis: Laura 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). Stella's card is shown to Stella. Stella's card is shown to Kevin. It is publicly announced that someone picked a red card. It is publicly announced that Kevin knows whether someone picked a red card. It is publicly announced that Kevin does not know whether Kevin picked a red card. It is publicly announced that Kevin does not know whether Kevin picked a red card. It is publicly announced that Kevin does not know whether Kevin picked a red card.

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

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

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


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

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

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


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

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

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

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