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

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

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

Hypothesis: Rita can now know that Merle 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 Betty. Donald's card is shown to Mildred. Betty's card is shown to James. Betty's card is shown to Donald. It is publicly announced that someone picked a red card.

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

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

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


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

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

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

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


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

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

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


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

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

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

Hypothesis: Traci can now know whether Clayton 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). Patricia's card is shown to Eva. Ronald's card is shown to Ronald. Eva's card is shown to Ilene. Ronald's card is shown to Ilene. 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:4 Agentb:2 Agentc:1,2 Agentd:4 VALID? [ ! (1|2|3|4) ] (Agentb knows whether (1&2&3&4))

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

Hypothesis: Ronald 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). Marian's card is shown to James. Marian's card is shown to Marian. James's card is shown to Olivia. Olivia's card is shown to Olivia. It is publicly announced that someone picked a red card.

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

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

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


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

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

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

Hypothesis: Allison 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). Tracey's card is shown to Jeffery. Jeffery's card is shown to Tracey. Concetta's card is shown to Tracey. Jeffery's card is shown to Concetta. Tracey's card is shown to Concetta. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Concetta 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). Lahoma's card is shown to Justin. Nathaniel's card is shown to Matthew. Lahoma's card is shown to Nathaniel. Nathaniel's card is shown to Lahoma. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Justin can now know that Nathaniel 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). Arturo's card is shown to Arturo. Randy's card is shown to Sally. Phillip's card is shown to Randy. Randy's card is shown to Phillip. It is publicly announced that someone picked a red card.

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

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

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


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

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

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

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


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

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

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

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


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

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

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

Hypothesis: Joseph can now know whether Melanie can know whether Melanie 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 Joseph. Steven's card is shown to Joseph. Steven's card is shown to Jennifer. Jennifer's card is shown to Steven. Steven's card is shown to Steven. It is publicly announced that someone picked a red card. It is publicly announced that Joseph knows whether Jennifer picked a red card.

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

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

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

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

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

Hypothesis: Anthony 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). Joseph's card is shown to Jeffrey. Jeffrey's card is shown to Joseph. Joseph's card is shown to Joseph. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Jeffrey picked a red card. It is publicly announced that Joseph picked a red card.

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

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


Premise: There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Michelle's card is shown to Karen. Charles's card is shown to Theodore. Theodore's card is shown to Michelle. Michelle's card is shown to Michelle. Karen's card is shown to Charles. It is publicly announced that someone picked a red card. It is publicly announced that Karen does not know whether Charles picked a red card. It is publicly announced that Theodore 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 (1&2&3&4))

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: Charles 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). Florence's card is shown to Florence. Andrew's card is shown to Florence. Andrew's card is shown to Andrew. Daniel's card is shown to Daniel. It is publicly announced that someone picked a red card.

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

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

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


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

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

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


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

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

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

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


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

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

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

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


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

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

Hypothesis: Wendy 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). Francisco's card is shown to Patricia. Mary's card is shown to Francisco. Mary's card is shown to Mary. It is publicly announced that someone picked a red card. It is publicly announced that Francisco knows whether Mary picked a red card. It is publicly announced that Mary does not know whether or not everyone picked a red card. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Francisco can now know whether Mary can know that nobody picked a red card.


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

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

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

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


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

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

Hypothesis: Chester 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). Melissa's card is shown to Teresa. Teresa's card is shown to Melissa. Teresa's card is shown to Mark. Melissa's card is shown to Mark. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Teresa can now know that Melissa 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). Roland's card is shown to Charles. Roland's card is shown to Eric. Charles's card is shown to Roland. Michael's card is shown to Michael. It is publicly announced that someone picked a red card.

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

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

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


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

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

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

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


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

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

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

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


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

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

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

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


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

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

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

Hypothesis: Maurice 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). Raymond's card is shown to Raymond. Earl's card is shown to Raymond. Donald's card is shown to Raymond. Raymond's card is shown to Earl. Donald's card is shown to Earl. Raymond's card is shown to Donald. It is publicly announced that someone picked a red card.

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

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

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


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

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

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

Hypothesis: Philip can now know whether Brenda 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). Linda's card is shown to Mary. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card.

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

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


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

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

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

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


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

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

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

Hypothesis: William can now know whether Harold 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). Bruce's card is shown to Bruce. Christina's card is shown to Bruce. Jake's card is shown to Christina. Bruce's card is shown to Jake. Jake's card is shown to Jake. It is publicly announced that someone picked a red card. It is publicly announced that Jake does not know whether or not everyone picked a red card.

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

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

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


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

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

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

Hypothesis: Paul 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). William's card is shown to Gustavo. Natasha's card is shown to Gustavo. Gustavo's card is shown to Natasha. Natasha's card is shown to Shannon. It is publicly announced that someone picked a red card. It is publicly announced that Natasha 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 ] Agentc knows whether (Agenta knows that (~(1|2|3|4)))

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

Hypothesis: Natasha can now know whether William can know that nobody picked a red card.


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

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

Hypothesis: Geoffrey can now know that Alan 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). Barbara's card is shown to John. James's card is shown to James. James's card is shown to Molly. 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:1 Agentb:3 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] (Agentc knows that 4)

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


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

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

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

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


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

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

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

Hypothesis: Paul 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). Kathy's card is shown to Kathy. Kathryn's card is shown to Kathy. Kathy's card is shown to Terry. Terry's card is shown to Terry. Kathryn's card is shown to Terry. Kathy's card is shown to Kathryn. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Kathryn can now know that Kathy 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). Myrna's card is shown to Jimmie. Jimmie's card is shown to Myrna. It is publicly announced that someone picked a red card.

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

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

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


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

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

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

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


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

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

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

Hypothesis: Gloria can now know that Steven 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). Leo's card is shown to Leo. Alva's card is shown to Leo. Susann's card is shown to Alva. Susann's card is shown to Susann. Melissa's card is shown to Melissa. It is publicly announced that someone picked a red card.

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

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

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


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

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

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

Hypothesis: Elizabeth can now know that Pauline 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). Aaron's card is shown to Francis. Susan's card is shown to Susan. Susan's card is shown to James. Aaron's card is shown to James. Francis's card is shown to Aaron. Susan's card is shown to Aaron. It is publicly announced that someone picked a red card.

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

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

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


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

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

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

Hypothesis: James 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). Brian's card is shown to Donald. Brian's card is shown to Brian. Paula's card is shown to Brian. It is publicly announced that someone picked a red card. It is publicly announced that Donald 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)) ] (Agentb knows whether 1)

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: Brian can now know whether Donald picked a red card.


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

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

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

Hypothesis: Erin can now 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). Rolando's card is shown to Rolando. James's card is shown to Rolando. Rolando's card is shown to Peter. Kyle's card is shown to Peter. Rolando's card is shown to Kyle. James's card is shown to Kyle. It is publicly announced that someone picked a red card. It is publicly announced that Kyle picked a black card.

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

Hypothesis: Kyle can now know that Rolando can know that Rolando picked a red card.


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

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

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

Hypothesis: Lucy can now know that Jim picked a red card.


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

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

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

Hypothesis: Sergio can now know that Lorenza picked a red card.


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

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

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

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


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

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

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

Hypothesis: Leon 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). Jessica's card is shown to Jeremy. Susan's card is shown to Jessica. Susan's card is shown to Susan. Hilda's card is shown to Susan. Susan's card is shown to Hilda. Hilda's card is shown to Hilda. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Jeremy can now know whether Hilda 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). Phuong's card is shown to Keith. Keith's card is shown to Phuong. Phuong's card is shown to Phuong. It is publicly announced that someone picked a red card. It is publicly announced that Phuong knows whether someone picked a red card. It is publicly announced that Keith knows whether someone picked a red card. It is publicly announced that Phuong knows whether Keith picked a red card. It is publicly announced that Phuong knows whether someone picked a red card.

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

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

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


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

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

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

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


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

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

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

Hypothesis: Kate 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). John's card is shown to Danny. Danny's card is shown to Thomas. Thomas's card is shown to John. 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 whether (~(1|2|3)))

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

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


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

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

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

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


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

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

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

Hypothesis: Kathryn 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). Edward's card is shown to James. James's card is shown to Edward. Ericka's card is shown to Ericka. Ericka's card is shown to Keith. It is publicly announced that someone picked a red card. It is publicly announced that Keith does not know whether Edward picked a red card.

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

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

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


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

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

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

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


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

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

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

Hypothesis: Ashley can now know whether Ashley 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 Donna. Donna's card is shown to Brent. Brenda'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 Donna picked a red card. It is publicly announced that Brenda does not know whether Donna picked a red card. It is publicly announced that Brenda does not know whether Donna picked a red card. It is publicly announced that not everyone picked a red card.

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

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

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


Premise: There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Charlotte's card is shown to Charlotte. Susan's card is shown to Charlotte. Brenda's card is shown to Brenda. Charlotte's card is shown to Susan. 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) ] Agenta knows whether (Agentc knows whether (~(1|2|3)))

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

Hypothesis: Charlotte can now know whether Susan 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). Karen's card is shown to Louise. Michael's card is shown to Louise. Joyce's card is shown to Karen. Louise's card is shown to Michael. Michael's card is shown to Michael. Michael's card is shown to Joyce. Joyce's card is shown to Joyce. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Louise can now know that Karen can know whether someone picked a red card.


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

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

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

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


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

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

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

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


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

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

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

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


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

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

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


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

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

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

Hypothesis: Robert can now know whether Alysia 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). Justin's card is shown to Justin. Justin's card is shown to Robert. Carter's card is shown to Robert. Robert's card is shown to Carter. Shane's card is shown to Carter. It is publicly announced that someone picked a red card. It is publicly announced that Justin does not know whether Shane picked a red card. It is publicly announced that not everyone picked a red card.

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

Hypothesis: Carter can now know that Shane picked a red card.


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

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

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

Hypothesis: Lee 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). Marla's card is shown to Karl. Karl's card is shown to Willie. Marla's card is shown to Willie. Willie's card is shown to Marla. Marla's card is shown to Marla. It is publicly announced that someone picked a red card. It is publicly announced that Willie does not know whether Willie picked a red card.

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

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

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


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

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

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

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


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

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

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

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


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

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

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

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


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

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

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

Hypothesis: Peter 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). Ella's card is shown to Brenda. Karen's card is shown to Brenda. Brenda's card is shown to Jose. Ella's card is shown to Jose. Karen's card is shown to Jose. Brenda's card is shown to Ella. Brenda's card is shown to Karen. 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:1 VALID? [ ! (1|2|3|4) ] (Agentc knows whether 4)

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

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


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

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

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

Hypothesis: Kerrie 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). Edward's card is shown to Newton. Eli's card is shown to Eli. Edward's card is shown to Eli. Newton's card is shown to Edward. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card.

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

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


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

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

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

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


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

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

Hypothesis: Victoria can now know whether Benjamin 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). Violet's card is shown to Sharon. Sharon's card is shown to Judy. Violet's card is shown to Judy. Judy's card is shown to Violet. Violet's card is shown to Violet. It is publicly announced that someone picked a red card. It is publicly announced that Judy knows whether or not everyone picked a red card. It is publicly announced that Judy knows whether Violet picked a red card. It is publicly announced that Judy knows whether or not everyone picked a red card. It is publicly announced that not everyone picked a red card.

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

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

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


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

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

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

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


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

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

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

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


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

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

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

Hypothesis: Andrew can now know whether Jessie can know that 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). Pennie's card is shown to Pennie. Matt's card is shown to Matt. Jennifer's card is shown to Jennifer. Pennie's card is shown to Ebony. Jennifer's card is shown to Ebony. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Ebony can now know that Jennifer 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). Melissa's card is shown to Ryan. Michael's card is shown to Michael. Ryan's card is shown to Melissa. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card.

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

Hypothesis: Melissa 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). Jimmy's card is shown to Sara. Rhonda's card is shown to Sara. Rhonda's card is shown to Jimmy. Rhonda's card is shown to Star. It is publicly announced that someone picked a red card. It is publicly announced that Star does not know whether Sara picked a red card.

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

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

Hypothesis: Sara can now know that Star can know whether Sara picked a red card.


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

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

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

Hypothesis: Kevin can now know that Byron 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). Alice's card is shown to Alice. Alice's card is shown to Eugene. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card. It is publicly announced that Eugene knows whether or not nobody picked a red card.

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

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

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


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

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

Hypothesis: Christine 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). Norma's card is shown to Norma. David's card is shown to David. It is publicly announced that someone picked a red card. It is publicly announced that Norma picked a black card.

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

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

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


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

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

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

Hypothesis: Chelsea 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). Mary's card is shown to Lloyd. Mary's card is shown to Christopher. Christopher's card is shown to Christopher. Eric's card is shown to Christopher. Lloyd's card is shown to Eric. Eric's card is shown to Eric. It is publicly announced that someone picked a red card. It is publicly announced that Christopher picked a black card.

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

Hypothesis: Christopher can now know that Lloyd can know whether or not everyone picked a red card.


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

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

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

Hypothesis: Richard 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). Julia's card is shown to Julia. Lyndsey's card is shown to Julia. Julia's card is shown to Denise. Michael's card is shown to Michael. Denise's card is shown to Lyndsey. Michael's card is shown to Lyndsey. Lyndsey's card is shown to Lyndsey. 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) ] (Agentd knows whether (1|2|3|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: Lyndsey 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). Carol's card is shown to Jennifer. Ronald's card is shown to Jennifer. Jennifer's card is shown to Linda. Jennifer'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:1,4 Agentb:2 Agentc:2 VALID? [ ! (1|2|3|4) ] (Agentb knows that (1&2&3&4))

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

Hypothesis: Jennifer 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). Kimberly's card is shown to Mi. Mi's card is shown to Virginia. Virginia's card is shown to Kimberly. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Mi can now know whether Virginia 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). Walter's card is shown to Kevin. Kevin's card is shown to Ana. Ana's card is shown to Ana. Ana's card is shown to Walter. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Walter can now know that Kevin 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). James's card is shown to Demetrius. Demetrius's card is shown to Demetrius. Leroy's card is shown to Demetrius. Leroy's card is shown to Leroy. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Demetrius can now know whether James can know whether Demetrius 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. Katie's card is shown to Frank. Jesse's card is shown to Katie. Katie's card is shown to Katie. It is publicly announced that someone picked a red card.

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

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

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


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

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

Hypothesis: Andrew 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). Avril's card is shown to Sandra. David's card is shown to Sandra. Marie's card is shown to Sandra. Sandra's card is shown to David. David's card is shown to David. David's card is shown to Marie. 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 whether 3)

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


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

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

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

Hypothesis: Judy 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). Joe's card is shown to Joe. Joe's card is shown to Joseph. Joseph's card is shown to Joseph. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Grant can now know whether Joe 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). Mitchell's card is shown to Mitchell. Bruce's card is shown to Mitchell. Edward's card is shown to George. Bruce's card is shown to Edward. It is publicly announced that someone picked a red card.

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

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

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


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

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

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

Hypothesis: Sharon 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). Todd's card is shown to Todd. Wendy's card is shown to Todd. Todd's card is shown to Wendy. Wendy's card is shown to Wendy. Michael's card is shown to Wendy. Wendy's card is shown to Michael. It is publicly announced that someone picked a red card.

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

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

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


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

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

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

Hypothesis: Rosa can now know that Debra 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). David's card is shown to David. David's card is shown to Robert. Robert's card is shown to Robert. Robert's card is shown to Mary. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card.

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

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


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

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

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

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


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

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

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


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

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

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

Hypothesis: Bryan 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). Denise's card is shown to Denise. Scott's card is shown to Denise. Ray's card is shown to Denise. Rose's card is shown to Ray. Ray's card is shown to Rose. Rose's card is shown to Rose. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Denise 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). Susan's card is shown to Albert. Vicky's card is shown to Albert. Maxine's card is shown to Albert. Albert's card is shown to Vicky. Maxine's card is shown to Vicky. Albert's card is shown to Maxine. Maxine's card is shown to Maxine. It is publicly announced that someone picked a red card. It is publicly announced that Vicky knows whether or not nobody picked a red card. It is publicly announced that Albert knows whether Susan picked a red card. It is publicly announced that Vicky knows whether or not nobody picked a red card. It is publicly announced that Vicky picked a black card.

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

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

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


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

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

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

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


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

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

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


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

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

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

Hypothesis: Marjorie can now know whether Dora can know that nobody picked a red card.


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

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

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

Hypothesis: Blanca can now know whether Donna 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). Larue's card is shown to Larue. Larue's card is shown to Roberta. It is publicly announced that someone picked a red card. It is publicly announced that Larue does not know whether Roberta picked a red card. It is publicly announced that Larue knows whether or not nobody picked a red card.

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

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

Hypothesis: Larue 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). Robert's card is shown to Robert. Joseph's card is shown to Robert. Joseph's card is shown to Joseph. Janet's card is shown to Janet. 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 (Agenta 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: Joseph can now know that Robert can know that nobody picked a red card.


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

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

VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] [ ! ~(Agentb knows whether 1) ] 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). Kent's card is shown to Felisa. George's card is shown to Felisa. Felisa's card is shown to Kent. George's card is shown to George. Earnest's card is shown to George. Earnest's card is shown to Earnest. It is publicly announced that someone picked a red card. It is publicly announced that Earnest does not know whether Kent picked a red card. It is publicly announced that Felisa knows whether George picked a red card.

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

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

Hypothesis: Earnest can now know whether Felisa can know that George picked a red card.


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

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

Hypothesis: Frank can now know whether Bruce 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). Amber's card is shown to Sandra. Katherine's card is shown to Amber. Katherine's card is shown to Benjamin. It is publicly announced that someone picked a red card. It is publicly announced that Katherine knows whether or not nobody picked a red card. It is publicly announced that Amber picked a red card.

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

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

Hypothesis: Amber 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). Karen's card is shown to Karen. Lee's card is shown to Karen. Karen's card is shown to Rita. Rita's card is shown to Rita. Jaclyn's card is shown to Jaclyn. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Lee 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). Otha's card is shown to Otha. Jacqueline's card is shown to Lori. Ginger's card is shown to Lori. Otha's card is shown to Jacqueline. Otha's card is shown to Ginger. It is publicly announced that someone picked a red card. It is publicly announced that Ginger does not know whether Ginger picked a red card. It is publicly announced that Jacqueline knows whether someone picked a red card.

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

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

Hypothesis: Ginger can now know whether Jacqueline picked a red card.


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

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

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

Hypothesis: Wade can now know whether Margaret can know whether Shirley picked a red card.


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

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

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

Hypothesis: Rosa can now know whether Christine can know whether Rosa picked a red card.


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

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

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

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


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

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

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

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


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

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

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

Hypothesis: John can now know whether Carmen 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). Gloria's card is shown to Gloria. James's card is shown to Gloria. Teresa's card is shown to Teresa. 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 Gloria 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 whether 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: James can now know whether Gloria can know whether James picked a red card.


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

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

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

Hypothesis: Xiomara 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). William's card is shown to Charles. Charles's card is shown to Mildred. Mildred's card is shown to Mildred. Rita's card is shown to Mildred. William's card is shown to Mildred. Mildred's card is shown to Rita. William's card is shown to William. 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) ] (Agenta knows that (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: Charles can now know that everyone picked a red card.


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

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

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

Hypothesis: Edward can now know that Ronnie can 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). Theresia's card is shown to Carolyn. Carolyn's card is shown to Julie. It is publicly announced that someone picked a red card.

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

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

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