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

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

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

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


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

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

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

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

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

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

Hypothesis: Michael can now know that Francis 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). Doris's card is shown to Doris. David's card is shown to Doris. Nathaniel's card is shown to Nancy. David's card is shown to David. David's card is shown to Nathaniel. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Nathaniel can now know whether Doris 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). Bonnie's card is shown to Bonnie. Jack's card is shown to Bonnie. Mark's card is shown to Jack. Mark's card is shown to Roger. Jack's card is shown to Mark. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Jack can now know that Bonnie picked a red card.


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

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

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

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


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

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

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

Hypothesis: Darrin 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). Donald's card is shown to Donald. Joshua's card is shown to Donald. Barbara's card is shown to Joshua. Donald's card is shown to Sal. Sal's card is shown to Sal. It is publicly announced that someone picked a red card. It is publicly announced that Joshua picked a black card.

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

Hypothesis: Donald can now know that Joshua 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). Craig's card is shown to Craig. James's card is shown to Craig. James's card is shown to James. It is publicly announced that someone picked a red card. It is publicly announced that James does not know whether Craig picked a red card.

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

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

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


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

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

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

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


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

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

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

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


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

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

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

Hypothesis: Arnold can now know whether Joaquin 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). Lida's card is shown to Lida. Lida's card is shown to Louis. Kurt's card is shown to Louis. Kurt's card is shown to Kurt. Kurt's card is shown to Patricia. Patricia's card is shown to Patricia. 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 Agentd:3,4 VALID? [ ! (1|2|3|4) ] (Agentc knows that (1|2|3|4))

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

Hypothesis: Kurt 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). Andy's card is shown to Randy. Kenneth's card is shown to Randy. Andy's card is shown to Andy. Jamie's card is shown to Andy. Randy's card is shown to Kenneth. Kenneth's card is shown to Kenneth. Randy's card is shown to Jamie. Kenneth's card is shown to Jamie. It is publicly announced that someone picked a red card. It is publicly announced that Andy does not know whether Kenneth picked a red card.

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

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

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


Premise: There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Warren's card is shown to Warren. Donald's card is shown to Warren. Warren's card is shown to Heriberto. Warren's card is shown to Donald. 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) ] (Agentb knows that (1|2|3))

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

Hypothesis: Heriberto 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). Emma's card is shown to Anna. Anna's card is shown to Stephan. Stephan's card is shown to Stephan. Bertha's card is shown to Stephan. Emma's card is shown to Stephan. Stephan's card is shown to Bertha. Emma's card is shown to Emma. 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 Agentd:4 VALID? [ ! (1|2|3|4) ] (Agentc knows whether (1|2|3|4))

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

Hypothesis: Bertha 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). Rafael's card is shown to Rafael. Ellen's card is shown to Maria. Maria's card is shown to Chris. Ellen's card is shown to Chris. Chris's card is shown to Chris. It is publicly announced that someone picked a red card. It is publicly announced that Maria does not know whether Rafael picked a red card. It is publicly announced that Maria picked a red card.

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

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

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


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

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

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

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


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

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

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

Hypothesis: Ruth can now know whether Lessie can know that Ruth 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 Kathleen. Lisa's card is shown to Henry. Henry's card is shown to Lisa. It is publicly announced that someone picked a red card. It is publicly announced that Kathleen 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)) ] (Agentb knows whether 2)

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


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

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

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

Hypothesis: Anthony can now know that Alisha can know whether Lewis 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 Matthew. Jonathan's card is shown to Matthew. Matthew's card is shown to Robert. It is publicly announced that someone picked a red card. It is publicly announced that Robert does not know whether Robert picked a red card. It is publicly announced that Matthew 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) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether (~(1|2|3))) ] (Agentb knows that 1)

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

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


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

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

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

Hypothesis: Anne can now know that Mickie can know that Anne picked a red card.


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

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

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

Hypothesis: Betty 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). Craig's card is shown to Craig. Cruz's card is shown to Craig. Edwin's card is shown to Craig. Cruz's card is shown to Cruz. Edwin's card is shown to Cruz. Cruz's card is shown to Wesley. Craig's card is shown to Edwin. Cruz's card is shown to Edwin. It is publicly announced that someone picked a red card.

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

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

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


Premise: There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ezekiel's card is shown to Lisa. Lisa's card is shown to Jonelle. Jonelle's card is shown to Jonelle. Ezekiel's card is shown to Jonelle. Jonelle's card is shown to Ezekiel. 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 someone picked a red card.

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

Hypothesis: Jonelle can now know whether Ezekiel picked a red card.


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

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

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

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


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

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

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

Hypothesis: Richard can now know that Gabriel 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). Miriam's card is shown to Miriam. Marla's card is shown to Miriam. Jose's card is shown to Jose. Jose's card is shown to Marla. Marla's card is shown to Marla. Jose's card is shown to Harry. It is publicly announced that someone picked a red card. It is publicly announced that Miriam does not know whether Harry picked a red card. It is publicly announced that Marla picked a black card.

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

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

Hypothesis: Miriam can now know that Harry picked a red card.


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

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

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

Hypothesis: Theresa 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). Charlene's card is shown to Charlene. Ethel's card is shown to Charlene. Carol'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:1,2 Agentb:4 VALID? [ ! (1|2|3|4) ] (Agenta knows whether 2)

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

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


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

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

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

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


Premise: There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Debra's card is shown to Paul. Wanda's card is shown to Paul. Jonathan's card is shown to Paul. Paul's card is shown to Wanda. Wanda's card is shown to Wanda. Wanda's card is shown to Jonathan. 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) ] (Agentc 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: Wanda 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). Brenda's card is shown to Roosevelt. Brenda's card is shown to Mark. Roosevelt's card is shown to Brenda. Mark's card is shown to Brenda. It is publicly announced that someone picked a red card. It is publicly announced that Brenda does not know whether Brenda picked a red card. It is publicly announced that Roosevelt knows whether someone picked a red card.

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

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

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


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

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

Hypothesis: Brandy 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). Joy's card is shown to Anita. Donna's card is shown to Joy. Anita's card is shown to Donna. Joy's card is shown to Donna. 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) ] Agenta knows whether (Agentc knows whether 2)

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

Hypothesis: Anita can now know whether Donna can know whether Joy picked a red card.


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

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

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

Hypothesis: Marjorie 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). John's card is shown to Corey. Corey's card is shown to Mercedes. John's card is shown to Mercedes. Emil's card is shown to Mercedes. Corey's card is shown to Emil. It is publicly announced that someone picked a red card. It is publicly announced that John does not know whether John picked a red card. It is publicly announced that John does not know whether Mercedes picked a red card. It is publicly announced that Corey knows whether someone picked a red card.

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

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

Hypothesis: John can now know that Mercedes 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). William's card is shown to Mary. William's card is shown to William. Wanda's card is shown to William. It is publicly announced that someone picked a red card.

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

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

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


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

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

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

Hypothesis: Jimmy can now know that Bess picked a red card.


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

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

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

Hypothesis: Wayne 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). Steven's card is shown to Jarvis. Jarvis's card is shown to Paul. Paul's card is shown to Steven. Mark's card is shown to Steven. Steven's card is shown to Mark. It is publicly announced that someone picked a red card. It is publicly announced that Paul knows whether Jarvis picked a red card.

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

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

Hypothesis: Mark can now 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). Cody's card is shown to Lindsay. Mary's card is shown to Marie. Marie's card is shown to Cody. Cody's card is shown to Cody. Lindsay's card is shown to Mary. It is publicly announced that someone picked a red card. It is publicly announced that Lindsay does not know whether Mary picked a red card. It is publicly announced that Marie picked a black card.

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

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

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


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

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

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

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


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

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

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

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


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

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

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

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


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

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

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


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

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

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

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


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

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

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

Hypothesis: Jessie can now know whether Candace can know that Carol picked a red card.


Premise: There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Howard's card is shown to Maria. Wilhelmina's card is shown to Wilhelmina. Maria's card is shown to Christina. Howard's card is shown to Howard. 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) ] (Agentc knows whether 4)

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

Hypothesis: Christina can now know whether Howard picked a red card.


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

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

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

Hypothesis: John 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). Michael's card is shown to Gertrude. Jesus's card is shown to Michael. Michael's card is shown to Michael. Jesus's card is shown to Cindy. Gertrude's card is shown to Cindy. It is publicly announced that someone picked a red card. It is publicly announced that Gertrude knows whether or not everyone picked a red card. It is publicly announced that Jesus picked a black card.

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

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

Hypothesis: Michael 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). Benjamin's card is shown to John. Jennifer's card is shown to John. Jennifer's card is shown to Benjamin. John's card is shown to Jennifer. It is publicly announced that someone picked a red card. It is publicly announced that John picked a red card. It is publicly announced that Jennifer does not know whether or not everyone picked a red card. It is publicly announced that Jennifer does not know whether Benjamin picked a red card.

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

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

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


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

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

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

Hypothesis: Anthony can now know that Fernando can know that Wanda picked a red card.


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

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

Hypothesis: Allen can now know that Trudy can know that Trudy picked a red card.


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

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

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

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


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

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

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

Hypothesis: Bryce can now know whether Rebecca picked a red card.


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

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

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

Hypothesis: Stephan 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). Karla's card is shown to Mathew. Patricia's card is shown to Patricia. Mathew's card is shown to Karla. Patricia's card is shown to Karla. It is publicly announced that someone picked a red card.

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

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

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


Premise: There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Emma's card is shown to William. Carla's card is shown to Emma. William's card is shown to Carla. Emma's card is shown to Carla. 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) ] Agenta knows that (Agentc knows that 3)

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

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


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

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

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

Hypothesis: Brenda can now know whether Christine can know whether Christine 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. Betty's card is shown to Stephen. Stephen's card is shown to Betty. Jena's card is shown to Betty. Betty's card is shown to Jena. Stephen's card is shown to Harriet. It is publicly announced that someone picked a red card. It is publicly announced that Betty knows whether someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Betty picked a black card. It is publicly announced that Stephen does not know whether Harriet picked a red card.

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

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

Hypothesis: Jena can now know that Harriet 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). Elizabeth's card is shown to Pat. Elizabeth's card is shown to Jeff. Jeff's card is shown to Jeff. Jeff's card is shown to Ralph. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Pat can now know whether Jeff can know whether Ralph picked a red card.


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

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

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

Hypothesis: Vergie can now know whether Vickie can know whether Vickie picked a red card.


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

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

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


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

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

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

Hypothesis: Grace can now know that Grace 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 Leo. Keith's card is shown to Keith. John's card is shown to Keith. John's card is shown to John. Leo's card is shown to Daisy. It is publicly announced that someone picked a red card. It is publicly announced that Leo does not know whether or not everyone picked a red card.

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

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

Hypothesis: Leo can now know that Keith can know that Leo picked a red card.


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

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

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

Hypothesis: Kiera 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). Marcos's card is shown to Marcos. John's card is shown to Marcos. Ashley's card is shown to Ashley. Marcos's card is shown to John. Ashley's card is shown to John. John's card is shown to John. It is publicly announced that someone picked a red card. It is publicly announced that Marcos knows whether Marcos picked a red card.

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

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

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


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

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

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

Hypothesis: Francisco can now 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). John's card is shown to John. Jesse's card is shown to Linda. Jerrod's card is shown to Jerrod. It is publicly announced that someone picked a red card. It is publicly announced that Jesse does not know whether or not everyone picked a red card. It is publicly announced that Jerrod picked a red card.

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

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

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


Premise: There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rachal's card is shown to Matt. Margaret's card is shown to Matt. Debra's card is shown to Matt. Matt's card is shown to Margaret. Margaret's card is shown to Margaret. Margaret's card is shown to Debra. 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) ] (Agenta 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: Matt 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). Nancy's card is shown to Bianca. Bianca's card is shown to Nancy. Nancy's card is shown to Nancy. It is publicly announced that someone picked a red card. It is publicly announced that Bianca does not know whether Bianca picked a red card. It is publicly announced that Bianca does not know whether Bianca picked a red card.

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

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

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


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

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

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

Hypothesis: Ashley can now know whether Leah 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). Francisco's card is shown to Francisco. Mary's card is shown to Francisco. Francisco's card is shown to Mary. It is publicly announced that someone picked a red card. It is publicly announced that Earnest knows whether someone picked a red card.

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

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

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


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

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

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

Hypothesis: Darryl can now know whether Nicholas 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 Cynthia. Charles's card is shown to Mary. Mary's card is shown to Mary. Mary's card is shown to Sharon. It is publicly announced that someone picked a red card.

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

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


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

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

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

Hypothesis: Toni can now know that Dennis 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). Eleanor's card is shown to Eleanor. Eleanor's card is shown to Elizabeth. Elizabeth's card is shown to Elizabeth. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.

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

Hypothesis: Elizabeth can now know that Eleanor can know whether 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). John's card is shown to John. Raymond's card is shown to John. John's card is shown to Albert. Lee's card is shown to Lee. Albert's card is shown to Raymond. Lee's card is shown to Raymond. Raymond's card is shown to Raymond. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Lee can now know whether Raymond picked a red card.


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

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

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

Hypothesis: Dirk can now know that Vicki can know whether someone picked a red card.


Premise: There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). David's card is shown to Earl. Rebecca's card is shown to David. 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 (1|2|3))

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

Hypothesis: David 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). Rebecca's card is shown to Sidney. Sidney's card is shown to Mark. Mark's card is shown to Mark. Henrietta's card is shown to Mark. Mark's card is shown to Henrietta. It is publicly announced that someone picked a red card. It is publicly announced that Mark does not know whether Sidney picked a red card.

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

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

Hypothesis: Sidney can now know that Mark 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). Stephen's card is shown to Stephen. Joni's card is shown to Stephen. Stephen's card is shown to Joni. It is publicly announced that someone picked a red card. It is publicly announced that Will does not know whether Will picked a red card.

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

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

Hypothesis: Stephen can now know whether Joni picked a red card.


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

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

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

Hypothesis: Lloyd 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). Catherine's card is shown to Clara. John's card is shown to John. Catherine's card is shown to John. Catherine's card is shown to Catherine. It is publicly announced that someone picked a red card. It is publicly announced that Wayne picked a red card.

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

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

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


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

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

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

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


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

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

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

Hypothesis: Ronald 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). Marcus's card is shown to Marcus. Gia's card is shown to Marcus. Elin's card is shown to Marcus. Marcus's card is shown to Gia. Gia's card is shown to Gia. Albert's card is shown to Gia. Elin's card is shown to Gia. Marcus's card is shown to Albert. Elin's card is shown to Albert. Marcus's card is shown to Elin. It is publicly announced that someone picked a red card. It is publicly announced that Elin does not know whether Gia picked a red card. It is publicly announced that Elin does not know whether Albert picked a red card. It is publicly announced that Marcus does not know whether Albert picked a red card.

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

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

Hypothesis: Albert can now know whether Gia can know whether Albert picked a red card.


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

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

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

Hypothesis: Darius can now know whether Paige 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). Debbie's card is shown to Debbie. Evelyn's card is shown to Evelyn. It is publicly announced that someone picked a red card. It is publicly announced that Debbie picked a black card.

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

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

Hypothesis: Francis can now know whether Debbie picked a red card.


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

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

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


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

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

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

Hypothesis: Sarah can now know whether Sarah 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 Edwin. Edwin's card is shown to Donald. Donald's card is shown to Donald. Mary's card is shown to Donald. Donald's card is shown to Mary. It is publicly announced that someone picked a red card. It is publicly announced that Mary knows whether Donald picked a red card.

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

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

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


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

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

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

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


Premise: There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Thomas's card is shown to James. James's card is shown to James. Wilbert's card is shown to James. Thomas's card is shown to Wilbert. 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 that (Agentb knows whether (1&2&3))

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

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


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

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

Hypothesis: Jennifer 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). Mary's card is shown to Frederick. Mary's card is shown to Mary. James's card is shown to James. It is publicly announced that someone picked a red card.

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

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

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


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

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

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

Hypothesis: Mark 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). Cortez's card is shown to Angla. Maurice's card is shown to Angla. Maurice's card is shown to Cortez. Angla's card is shown to Benjamin. Maurice's card is shown to Maurice. 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) ] (Agentc knows that 3)

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: Benjamin can now know that Benjamin picked a red card.


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

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

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


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

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

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

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


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

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

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

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


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

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

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

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

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

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

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


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

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

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

Hypothesis: Gearldine 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). Edgar's card is shown to Edgar. Victoria's card is shown to Richard. Beth's card is shown to Victoria. Richard's card is shown to Beth. It is publicly announced that someone picked a red card. It is publicly announced that Edgar knows whether or not nobody picked a red card. It is publicly announced that Richard knows whether or not nobody 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) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] Agenta knows that (Agentb knows whether (1&2&3&4))

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

Hypothesis: Edgar can now know that Richard 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). Nicole's card is shown to Laurette. Steve's card is shown to Laurette. Nicole's card is shown to Shannon. Shannon's card is shown to Shannon. Steve's card is shown to Shannon. Laurette's card is shown to Steve. Nicole's card is shown to Steve. Steve's card is shown to Steve. It is publicly announced that someone picked a red card. It is publicly announced that Shannon picked a red card.

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

Hypothesis: Nicole can now know whether Shannon can know whether Nicole picked a red card.


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

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

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

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


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

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

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

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

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

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

Hypothesis: Johnny 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). Herbert's card is shown to Herbert. Herbert's card is shown to Mike. Mike's card is shown to Gladys. It is publicly announced that someone picked a red card. It is publicly announced that Gladys does not know whether Gladys picked a red card.

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

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

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


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

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

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

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


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

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

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

Hypothesis: Mark can now know that Carlos can know whether Carlos 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 Roy. David's card is shown to David. It is publicly announced that someone picked a red card. It is publicly announced that David does not know whether or not everyone picked a red card.

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

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

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


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

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

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

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


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

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

Hypothesis: Julie can now know that 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). Luis's card is shown to Anthony. Anthony's card is shown to Leroy. Luis's card is shown to Leroy. Leroy's card is shown to Loretta. Anthony's card is shown to Luis. Loretta's card is shown to Luis. It is publicly announced that someone picked a red card. It is publicly announced that Luis does not know whether Luis picked a red card. It is publicly announced that Anthony knows whether or not nobody picked a red card. It is publicly announced that Loretta picked a black card.

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

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

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


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

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

Hypothesis: Prudence can now know that Margret 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). Vernon's card is shown to Vernon. Vernon's card is shown to Seymour. Seymour's card is shown to Seymour. Stephen's card is shown to Seymour. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Vernon can now know whether Seymour picked a red card.


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

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

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

Hypothesis: Barry 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). Dana's card is shown to Jayne. Jayne's card is shown to Owen. It is publicly announced that someone picked a red card. It is publicly announced that Owen picked a black card.

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

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

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


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

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

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

Hypothesis: Marilyn can now know whether Susan picked a red card.


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

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

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

Hypothesis: Eugene can now know that Emily can know whether Christin picked a red card.


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

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

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


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

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

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

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


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

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

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

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


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

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

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

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


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

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

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

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


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

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

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

Hypothesis: Daniel can now know whether Heather 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). Edward's card is shown to Edward. Charles's card is shown to Edward. Oscar's card is shown to Diane. Oscar's card is shown to Charles. Diane's card is shown to Charles. Charles's card is shown to Charles. It is publicly announced that someone picked a red card.

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

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

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


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

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

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

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


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

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

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

Hypothesis: Pauline 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). Kaye's card is shown to Emilio. Ronald's card is shown to Emilio. Ronald's card is shown to Marianne. Kaye's card is shown to Ronald. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Marianne 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). Jesse's card is shown to Jesse. Pamela's card is shown to Jesse. Ann's card is shown to Ann. Pamela's card is shown to Pamela. It is publicly announced that someone picked a red card. It is publicly announced that Pamela does not know whether Jesse picked a red card.

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

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

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


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

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

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

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


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

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

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

Hypothesis: Otis can now know that Kerry can know that Julian picked a red card.


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

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

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

Hypothesis: Robert can now know whether 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). Roy's card is shown to Roy. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card.

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

Hypothesis: Roy can now know that 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). Lorraine's card is shown to Venus. Charise's card is shown to Venus. Charise's card is shown to Lorraine. Venus's card is shown to Jesus. Charise's card is shown to Charise. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Venus 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). Wm's card is shown to Charles. Michael's card is shown to Charles. Charles's card is shown to Wm. Wm's card is shown to Wm. Wm's card is shown to Michael. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.

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

Hypothesis: Michael can now know whether Wm 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 John. Craig's card is shown to John. Mary's card is shown to Mary. It is publicly announced that someone picked a red card. It is publicly announced that John does not know whether John picked a red card.

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

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

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