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

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


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

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

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

Hypothesis: Amy can now know that Paul 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). Lawrence's card is shown to Linda. Linda's card is shown to Linda. Patricia's card is shown to Linda. Arnold's card is shown to Patricia. It is publicly announced that someone picked a red card. It is publicly announced that Arnold does not know whether Linda picked a red card. It is publicly announced that Patricia picked a red card.

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

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

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


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

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

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

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


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

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

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

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


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

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

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

Hypothesis: Timothy can now know whether Juanita 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). Juana's card is shown to Linda. Linda's card is shown to Juana. Juana's card is shown to Juana. Juana's card is shown to Beatrice. It is publicly announced that someone picked a red card. It is publicly announced that Linda does not know whether Beatrice picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that Beatrice knows whether someone picked a red card.

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

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

Hypothesis: Beatrice can now know whether Juana 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). Carrol's card is shown to Carly. Carly's card is shown to Carrol. Carrol's card is shown to Carrol. Glenn's card is shown to Carrol. Glenn's card is shown to Glenn. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Glenn can now know whether Carly 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). Enrique's card is shown to Enrique. Alexandra's card is shown to Enrique. Enrique's card is shown to Alexandra. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Stewart 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). Marlene's card is shown to Bernie. Stacie's card is shown to Stacie. Bernie's card is shown to Craig. Marlene's card is shown to Marlene. It is publicly announced that someone picked a red card.

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

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

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


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

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

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

Hypothesis: Gary can now know whether Thomas can know that Gary 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 Rodney. Rodney's card is shown to Kevin. It is publicly announced that someone picked a red card. It is publicly announced that Richard does not know whether or not everyone picked a red card.

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

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

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


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

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

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

Hypothesis: Kevin can now know whether Meredith 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). Sonya's card is shown to Frank. Frank's card is shown to Sonya. Timothy's card is shown to Sonya. Patricia's card is shown to Timothy. It is publicly announced that someone picked a red card. It is publicly announced that Patricia does not know whether Frank picked a red card.

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

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

Hypothesis: Frank 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). Shante's card is shown to Oscar. Oscar's card is shown to Janice. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Oscar can now know that Earlene picked a red card.


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

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

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

Hypothesis: Roy can now know that Rose can know whether Roy picked a red card.


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

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

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

Hypothesis: Lacey can now know whether Roseanne can know that Lacey picked a red card.


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

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

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

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


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

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

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


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

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

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

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


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

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

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

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


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

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

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


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

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

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

Hypothesis: Betty can now know whether Frances can know whether Debi picked a red card.


Premise: There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mary's card is shown to Mary. Mary's card is shown to Roger. Roger's card is shown to Roger. Melanie's card is shown to Roger. Mary's card is shown to Melanie. Roger's card is shown to Melanie. 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: Roger 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). Eugene's card is shown to Eugene. Michael's card is shown to Eugene. Louis's card is shown to Eugene. Michael's card is shown to Michael. Louis's card is shown to Louis. It is publicly announced that someone picked a red card. It is publicly announced that Michael does not know whether Louis 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) ] Agentc knows whether (Agentb knows that 2)

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


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

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

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

Hypothesis: Darlene can now know that Jerry 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). Diana's card is shown to Deborah. Scott's card is shown to Scott. Deborah's card is shown to Diana. Scott's card is shown to Diana. It is publicly announced that someone picked a red card. It is publicly announced that Deborah does not know whether or not everyone picked a red card.

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

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

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


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

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

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

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


Premise: There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Stephen's card is shown to Stephen. Stephen's card is shown to Will. Bertha's card is shown to Will. Will's card is shown to Bertha. Adam's card is shown to Bertha. Will's card is shown to Adam. 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 Stephen knows whether Stephen picked a red card.

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

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

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


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

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

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

Hypothesis: Kimberly 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). Ashlee's card is shown to Edward. Julie's card is shown to Edward. Ashlee's card is shown to Reuben. Reuben's card is shown to Reuben. Reuben's card is shown to Julie. Julie's card is shown to Julie. It is publicly announced that someone picked a red card. It is publicly announced that Ashlee does not know whether or not everyone picked a red card. It is publicly announced that everyone picked a red card.

Hypothesis: Ashlee 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). Patricia's card is shown to Patricia. Harry's card is shown to Patricia. Edna's card is shown to Harry. Edna's card is shown to Edna. Jack's card is shown to Jack. 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) ] (Agentd knows whether (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: Jack 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). Marion's card is shown to Stacy. Susan's card is shown to Susan. Susan's card is shown to Marion. It is publicly announced that someone picked a red card. It is publicly announced that Stacy picked a red card. It is publicly announced that Stacy knows whether someone picked a red card.

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

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

Hypothesis: Marion can now know whether Susan 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). Mary's card is shown to Leon. Mary's card is shown to Mary. Leon's card is shown to Justin. Mary's card is shown to Justin. It is publicly announced that someone picked a red card. It is publicly announced that Justin does not know whether Justin picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Justin does not know whether or not everyone picked a red card.

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

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

Hypothesis: Leon 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). Helen's card is shown to Helen. Margie's card is shown to Helen. Helen's card is shown to Jeffery. Bryan's card is shown to Margie. Helen's card is shown to Bryan. Jeffery's card is shown to Bryan. It is publicly announced that someone picked a red card. It is publicly announced that Jeffery does not know whether Jeffery picked a red card. It is publicly announced that Jeffery does not know whether Margie picked a red card.

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

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

Hypothesis: Jeffery can now know whether Bryan 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). Victor's card is shown to Genevieve. Victor's card is shown to Victor. Mike's card is shown to Victor. Victor's card is shown to Mike. It is publicly announced that someone picked a red card.

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

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

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


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

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

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

Hypothesis: Ida 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). Carl's card is shown to Carl. Velva's card is shown to Carl. Deborah's card is shown to Carl. Carl's card is shown to Donald. Donald's card is shown to Deborah. Deborah's card is shown to Deborah. It is publicly announced that someone picked a red card.

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

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

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


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

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

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

Hypothesis: Jonathan can now know that Michael 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). Joan's card is shown to Alice. Alice's card is shown to Joan. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.

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

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


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

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

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

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


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

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

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

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


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

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

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

Hypothesis: Dennis can now know that Helen can know that 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). Anthony's card is shown to Mike. Christopher's card is shown to Anthony. It is publicly announced that someone picked a red card.

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

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

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


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

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

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

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


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

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

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

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


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

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

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

Hypothesis: Ashley can now know whether Jennifer can know whether 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). Robert's card is shown to Richard. Craig's card is shown to Richard. Robert's card is shown to Craig. It is publicly announced that someone picked a red card.

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

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

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


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

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

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

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

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

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

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


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

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

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

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


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

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

Hypothesis: Jacob can now know whether Sadie 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). Brittney's card is shown to Brittney. Nicolas's card is shown to Kimberly. Kimberly's card is shown to Naomi. Brittney's card is shown to Nicolas. Kimberly's card is shown to Nicolas. It is publicly announced that someone picked a red card. It is publicly announced that Naomi knows whether or not everyone picked a red card.

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

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

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

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

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

Hypothesis: Wade 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). Desiree's card is shown to Desiree. Desiree's card is shown to Angie. Julio's card is shown to Angie. Julio's card is shown to Julio. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Julio can now know that Angie can know whether Angie picked a red card.


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

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

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

Hypothesis: Heidi can now know whether Valerie 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). Brian's card is shown to Tony. Tony's card is shown to Brian. Jeremy's card is shown to Brian. Tony's card is shown to Jeremy. Brian's card is shown to Jeremy. Jeremy's card is shown to Boyd. It is publicly announced that someone picked a red card. It is publicly announced that Boyd knows whether or not nobody picked a red card.

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

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

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


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

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


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

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

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

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


Premise: There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mark's card is shown to Shella. Mark's card is shown to Mark. Maria's card is shown to Maria. It is publicly announced that someone picked a red card. It is publicly announced that Mark does not know whether Lori 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 whether 1) ] Agenta knows whether (Agentb knows that 4)

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

Hypothesis: Lori can now know whether Shella can know that Maria 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. Hazel's card is shown to Eileen. Tyree's card is shown to Hazel. Eileen's card is shown to Tyree. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Hazel can now know that Tyree 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). Kelly's card is shown to Kelly. Joseph's card is shown to Kelly. Isidro's card is shown to Kelly. Isidro's card is shown to Joseph. Kelly's card is shown to Isidro. Isidro's card is shown to Isidro. It is publicly announced that someone picked a red card.

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

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

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


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

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

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

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


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

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

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

Hypothesis: Louise can now know whether Imogene can know whether Louise picked a red card.


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

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

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

Hypothesis: Roger 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). Nellie's card is shown to Nellie. Armand's card is shown to Nellie. Antonio's card is shown to Nellie. Antonio's card is shown to Armand. Nellie's card is shown to Antonio. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Antonio can now know that Armand 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). Joseph's card is shown to Joan. Betty's card is shown to Robert. Joseph's card is shown to Betty. It is publicly announced that someone picked a red card. It is publicly announced that Robert knows whether or not nobody picked a red card. It is publicly announced that Joseph knows whether or not everyone picked a red card.

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

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

Hypothesis: Joan 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). Kristi's card is shown to Kristi. Donna's card is shown to Kristi. Kristi's card is shown to Donna. Donna's card is shown to Donna. Zachary's card is shown to Donna. Kristi's card is shown to Zachary. Zachary's card is shown to Zachary. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Donna can now know whether Kristi 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). Margaret's card is shown to Stacey. Margaret's card is shown to Margaret. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card.

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

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

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


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

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

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

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


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

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

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

Hypothesis: Victoria 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). Teddy's card is shown to Ronald. John's card is shown to Evelyn. Ronald's card is shown to John. Evelyn's card is shown to John. John's card is shown to John. It is publicly announced that someone picked a red card.

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

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

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


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

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

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

Hypothesis: Donna 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). Barbara's card is shown to Barbara. Paula's card is shown to Barbara. Barbara's card is shown to Tameka. Paula's card is shown to Tameka. Barbara's card is shown to Paula. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Barbara 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). Alice's card is shown to Alice. Kim's card is shown to Alice. Ashley's card is shown to Alice. Alice's card is shown to Kim. Ashley's card is shown to Ashley. It is publicly announced that someone picked a red card.

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

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

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


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

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

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

Hypothesis: Charles 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). Ian's card is shown to Ian. Gloria's card is shown to Ian. Gloria's card is shown to Gloria. 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 Gloria does not know whether or not everyone picked a red card.

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

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

Hypothesis: Gloria can now know that Ian 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). Paul's card is shown to Robert. Robert's card is shown to Elijah. Paul's card is shown to Marian. It is publicly announced that someone picked a red card. It is publicly announced that Robert picked a red card. It is publicly announced that Robert does not know whether Elijah picked a red card. It is publicly announced that Elijah does not know whether Marian picked a red card.

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

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

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


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

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

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

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


Premise: There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ron's card is shown to Ron. Edgar's card is shown to Ron. Edgar's card is shown to Edgar. Ron's card is shown to Brenda. 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) ] Agentb knows that (Agenta knows that 2)

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

Hypothesis: Edgar can now know that Ron can know that Edgar picked a red card.


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

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

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

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


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

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

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

Hypothesis: Lou 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). Roy's card is shown to Sarah. Sarah's card is shown to Karen. Roy's card is shown to Karen. Karen's card is shown to Roy. Roy's card is shown to Roy. It is publicly announced that someone picked a red card. It is publicly announced that Sarah does not know whether or not everyone picked a red card. It is publicly announced that Roy picked a red card.

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

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

Hypothesis: Karen can now know that Sarah 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). Thomas's card is shown to Lou. Thomas's card is shown to Thomas. Jennifer's card is shown to William. Lou'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:2 Agentb:2 Agentc:4 Agentd:1 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentb knows that (1|2|3|4))

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

Hypothesis: William can now know that Thomas 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). Luke's card is shown to Luke. Carolyn's card is shown to Luke. Gary's card is shown to Luke. Karen's card is shown to Karen. Carolyn's card is shown to Carolyn. Karen's card is shown to Gary. It is publicly announced that someone picked a red card. It is publicly announced that Karen does not know whether Gary picked a red card. It is publicly announced that Luke knows whether Carolyn picked a red card.

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

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

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


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

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

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

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


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

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

Hypothesis: Suzanne can now know whether Isaac can know that Kristin picked a red card.


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

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

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

Hypothesis: Franklin can now know whether Sybil picked a red card.


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

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

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

Hypothesis: Anna 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). George's card is shown to George. Glen's card is shown to Glen. George's card is shown to Hilton. Glen's card is shown to Hilton. It is publicly announced that someone picked a red card.

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

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

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


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

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

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

Hypothesis: Laura can now know whether Jason can know whether Laura 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 Christopher. Christopher's card is shown to Cheryl. Cheryl's card is shown to James. It is publicly announced that someone picked a red card. It is publicly announced that James does not know whether or not everyone picked a red card.

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

VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 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). Lisa's card is shown to Grace. Thomas's card is shown to Grace. Grace's card is shown to Lisa. Thomas's card is shown to Thomas. It is publicly announced that someone picked a red card.

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

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

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


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

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

Hypothesis: Robert can now know whether Lynn 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). Sara's card is shown to Sara. Joanne's card is shown to Tim. Latanya's card is shown to Tim. Tim's card is shown to Joanne. Tim's card is shown to Latanya. Joanne's card is shown to Latanya. It is publicly announced that someone picked a red card.

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

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

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


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

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

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

Hypothesis: Betty 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). Joann's card is shown to Rick. Howard's card is shown to Rick. Howard's card is shown to Joann. Rick's card is shown to Howard. Howard's card is shown to Howard. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Howard 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). Magda's card is shown to Magda. James's card is shown to Magda. Patrick's card is shown to Magda. Patrick's card is shown to Sharon. Magda's card is shown to Patrick. James's card is shown to Patrick. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Magda can now know whether 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). Melissa's card is shown to Melissa. Melissa's card is shown to Alberto. It is publicly announced that someone picked a red card. It is publicly announced that Alberto 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 (Agenta knows that (1&2))

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

Hypothesis: Alberto can now know whether Melissa 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). Chrissy's card is shown to Chrissy. Sophie's card is shown to Chrissy. Sophie's card is shown to Sophie. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Sophie can now know that Chrissy 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). William's card is shown to William. Harlan's card is shown to William. Joyce's card is shown to Harlan. It is publicly announced that someone picked a red card.

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

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

Hypothesis: William 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). Richard's card is shown to Wayne. Richard's card is shown to Richard. Tom's card is shown to Richard. David's card is shown to Richard. Richard's card is shown to David. David's card is shown to David. It is publicly announced that someone picked a red card. It is publicly announced that Wayne does not know whether or not everyone picked a red card.

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

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

Hypothesis: Tom can now know that Wayne picked a red card.


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

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

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

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


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

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

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

Hypothesis: Kelvin 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). Brent's card is shown to Janie. Janie's card is shown to Barbara. Barbara's card is shown to Barbara. Barbara's card is shown to Brent. It is publicly announced that someone picked a red card.

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

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

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


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

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

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

Hypothesis: Mary can now know whether Darryl 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). Hilda's card is shown to Hilda. Ernestine's card is shown to Hilda. Margaret's card is shown to Ernestine. Marilyn's card is shown to Ernestine. It is publicly announced that someone picked a red card.

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

Hypothesis: Hilda 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). Jayne's card is shown to Jayne. Ruby's card is shown to Jayne. Jayne's card is shown to Christopher. Christopher's card is shown to Christopher. Ruby's card is shown to Christopher. Christopher's card is shown to Ruby. It is publicly announced that someone picked a red card. It is publicly announced that Ruby knows whether someone picked a red card. It is publicly announced that Christopher picked a black card.

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

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

Hypothesis: Christopher can now know whether Ruby 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). Caroline's card is shown to Caroline. Charles's card is shown to Caroline. Jay's card is shown to Caroline. Caroline's card is shown to Charles. Charles's card is shown to Charles. Caroline's card is shown to Jay. Charles's card is shown to Jay. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Jay can now know whether Caroline can know whether Caroline picked a red card.


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

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

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

Hypothesis: Richard can now know that Hildegard 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). Erin's card is shown to George. George's card is shown to Rita. Erin's card is shown to Erin. It is publicly announced that someone picked a red card. It is publicly announced that George picked a black card.

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

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

Hypothesis: Erin can now know that Rita can know that Rita 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. Randy's card is shown to Donald. Adam's card is shown to Donald. Donald's card is shown to Adam. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Donald 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). Jean's card is shown to Jean. Harvey's card is shown to Harvey. Martha's card is shown to Harvey. Jean's card is shown to Perry. Perry's card is shown to Perry. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Martha can now know that Harvey 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. Karen's card is shown to Susan. Ronald's card is shown to Brenda. Ronald's card is shown to Karen. Ronald's card is shown to Ronald. It is publicly announced that someone picked a red card. It is publicly announced that Karen does not know whether or not everyone picked a red card.

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

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

Hypothesis: Ronald can now know that Brenda 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). David's card is shown to Joseph. James's card is shown to James. David's card is shown to James. Robert's card is shown to David. Robert's card is shown to Robert. It is publicly announced that someone picked a red card. It is publicly announced that Joseph does not know whether Robert picked a red card.

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

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

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


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

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

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

Hypothesis: Cindy 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). Charles's card is shown to Charles. Chad's card is shown to Charles. Robin's card is shown to Adrianne. It is publicly announced that someone picked a red card. It is publicly announced that Adrianne does not know whether Adrianne picked a red card.

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

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

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


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

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

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

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


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

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

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

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


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

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

Hypothesis: Hung can now know whether Roxie picked a red card.


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

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

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

Hypothesis: Clyde can now know that Jason can know that Jonathan picked a red card.


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

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

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

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


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

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

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

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


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

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

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

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


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

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

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

Hypothesis: Christopher 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). Kathryn's card is shown to Kathryn. Charles's card is shown to Kathryn. Kathryn's card is shown to Walter. Walter's card is shown to Walter. Charles's card is shown to Walter. Kathryn's card is shown to Charles. Walter's card is shown to Charles. 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:1,2 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentc knows that 2)

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

Hypothesis: Kathryn can now know whether Charles can know that Walter picked a red card.


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

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

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

Hypothesis: Barbara 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). Janice's card is shown to David. David's card is shown to Carmen. Carmen's card is shown to Carmen. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Janice 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). Amy's card is shown to Dorothy. Amy's card is shown to Troy. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.

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

Hypothesis: Troy 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). Leslie's card is shown to Jason. Ruth's card is shown to Ruth. It is publicly announced that someone picked a red card. It is publicly announced that Ruth picked a red card. It is publicly announced that Jason picked a red card.

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

Hypothesis: Jason 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). George's card is shown to Cecil. Richard's card is shown to Richard. Nelson's card is shown to George. Cecil's card is shown to George. Richard's card is shown to George. George's card is shown to George. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card. It is publicly announced that everyone picked a red card.

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


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

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

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

Hypothesis: Richard can now know that Jonathan 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). Ramon's card is shown to William. Juan's card is shown to William. Juan's card is shown to Ramon. William's card is shown to Carmella. Juan's card is shown to Juan. It is publicly announced that someone picked a red card.

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

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

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


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

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

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

Hypothesis: Mattie 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). Betty's card is shown to Myrtle. Victor's card is shown to Nathaniel. Myrtle's card is shown to Betty. 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 whether (Agentc knows that 2)

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

Hypothesis: Victor can now know whether Nathaniel can know that Myrtle picked a red card.


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

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

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

Hypothesis: Eusebio can now know that Robert 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). Bobby's card is shown to Debbie. Bobby's card is shown to Marie. Marie's card is shown to Bobby. Bobby's card is shown to Bobby. It is publicly announced that someone picked a red card. It is publicly announced that Marie does not know whether or not everyone picked a red card.

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

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

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


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

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

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

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


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

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

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

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


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

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

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

Hypothesis: Jennifer can now know that Miguel can know whether Victor picked a red card.


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

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

Hypothesis: Norma can now know that Francis can know that Wayne picked a red card.


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

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

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

Hypothesis: June can now know whether Mary 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). Thelma's card is shown to Thelma. Kristina's card is shown to Thelma. Kristina's card is shown to Kristina. Thelma's card is shown to Antonio. Antonio's card is shown to Antonio. Kristina's card is shown to Carlos. Carlos's card is shown to Carlos. 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 Kristina picked a red card. It is publicly announced that Kristina 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))) ] Agenta knows that (Agentd knows whether (1|2|3|4))

Hypothesis: Thelma can now know that Carlos 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). Angela's card is shown to Mark. Mark's card is shown to Jose. Jose's card is shown to Jose. Mark's card is shown to Angela. Jose's card is shown to Ruth. Ruth's card is shown to Ruth. It is publicly announced that someone picked a red card. It is publicly announced that Ruth does not know whether Angela picked a red card. It is publicly announced that Mark knows whether Angela picked a red card.

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

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

Hypothesis: Ruth can now know that Mark 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). Charles's card is shown to Charles. Stanley's card is shown to Eugenio. It is publicly announced that someone picked a red card. It is publicly announced that Charles does not know whether Eugenio picked a red card.

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

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

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