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

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

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

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


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

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

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

Hypothesis: Ronald can now know whether Conrad can know whether Conrad picked a red card.


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

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

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

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


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

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

Hypothesis: Lewis 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). Brad's card is shown to Linda. Linda's card is shown to Amanda. Linda's card is shown to Kevin. Linda's card is shown to Brad. Brad's card is shown to Brad. It is publicly announced that someone picked a red card. It is publicly announced that Linda does not know whether Kevin picked a red card.

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

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

Hypothesis: Brad can now know whether Kevin 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). Vincent's card is shown to Vincent. Gail's card is shown to Carl. John's card is shown to Gail. Vincent's card is shown to John. Carl's card is shown to John. Gail's card is shown to John. John's card is shown to John. It is publicly announced that someone picked a red card. It is publicly announced that Vincent does not know whether John picked a red card.

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

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

Hypothesis: Gail can now know that Vincent 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). Gerard's card is shown to Gerard. Gerard's card is shown to Shaneka. Shaneka's card is shown to Shaneka. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Gerard can now know that Shaneka 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). Carol's card is shown to Marjorie. Marjorie's card is shown to Carol. Christina's card is shown to Carol. James's card is shown to James. Christina's card is shown to James. Marjorie's card is shown to Christina. James's card is shown to Christina. Christina's card is shown to Christina. It is publicly announced that someone picked a red card.

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

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

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


Premise: There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Leslie's card is shown to Jessica. Jessica's card is shown to Leslie. Eliza's card is shown to Leslie. Eliza's card is shown to Eliza. It is publicly announced that someone picked a red card. It is publicly announced that Eliza does not know whether Jessica 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 (Agentb knows whether (1&2&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: Eliza can now know whether Leslie 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). Irene's card is shown to Wanda. Wanda's card is shown to Dorothy. It is publicly announced that someone picked a red card. It is publicly announced that Irene picked a black card.

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

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

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


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

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: Lloyd can now know whether Kirk can know whether Lloyd picked a red card.


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

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

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

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


Premise: There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Theresa's card is shown to Theresa. Rita's card is shown to Theresa. Vincent's card is shown to Theresa. Vincent's card is shown to Rita. 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 that (Agenta knows that 1)

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

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


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

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

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

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


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

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

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

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

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

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

Hypothesis: Leah 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). Nichole's card is shown to Nichole. Paula's card is shown to Nichole. Nichole's card is shown to Paula. Paula's card is shown to Paula. Jovita's card is shown to Paula. Paula's card is shown to Jovita. 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) ] (Agentc knows whether 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: Paula can now know whether Jovita picked a red card.


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

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

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

Hypothesis: Mckinley can now know that Lynn picked a red card.


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

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

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

Hypothesis: Christopher 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). Heather's card is shown to Nicholas. James's card is shown to James. It is publicly announced that someone picked a red card. It is publicly announced that Heather does not know whether Nicholas picked a red card.

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

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

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


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

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

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

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


Premise: There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Steven's card is shown to Steven. Linda's card is shown to Linda. It is publicly announced that someone picked a red card. It is publicly announced that Steven knows whether someone 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: Steven can now know whether Linda 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). Elizabeth's card is shown to Michael. Frank's card is shown to Michael. Elizabeth's card is shown to Bridget. Bridget's card is shown to Frank. Frank's card is shown to Frank. It is publicly announced that someone picked a red card. It is publicly announced that Frank picked a black card.

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

Hypothesis: Elizabeth can now know that Bridget can know that Frank 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. Michael's card is shown to Maria. 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:2 Agentb:2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agenta knows whether (Agentb knows whether 2)

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


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

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

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

Hypothesis: Wade 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). David's card is shown to Daisy. David's card is shown to David. Robert's card is shown to David. David's card is shown to Robert. It is publicly announced that someone picked a red card.

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

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

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


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

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

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

Hypothesis: Ann can now know whether Jonathan 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). Clarence's card is shown to Larry. Larry's card is shown to Larry. Jamie's card is shown to Larry. Clarence's card is shown to Jamie. Helen's card is shown to Jamie. Helen's card is shown to Helen. It is publicly announced that someone picked a red card. It is publicly announced that Helen picked a red card.

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

Hypothesis: Clarence can now know that Jamie can know that Clarence picked a red card.


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

Hypothesis: Frank 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). Janice's card is shown to Janice. Linda's card is shown to Janice. Patricia's card is shown to Janice. Patricia's card is shown to Jennifer. Janice's card is shown to Linda. Janice's card is shown to Patricia. It is publicly announced that someone picked a red card. It is publicly announced that Jennifer does not know whether or not everyone picked a red card.

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

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

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


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

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

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

Hypothesis: Michele can now know whether Arthur picked a red card.


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

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

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

Hypothesis: Judith can now know whether 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). Sharon's card is shown to Greg. Cynthia's card is shown to Sharon. Cynthia's card is shown to Gregory. Sharon's card is shown to Gregory. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Cynthia can now know that Sharon 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). Jose's card is shown to Jose. Billy's card is shown to Jose. Tommie's card is shown to Tommie. Billy's card is shown to Tommie. Jose's card is shown to Billy. Tommie's card is shown to Billy. It is publicly announced that someone picked a red card. It is publicly announced that Jose knows whether someone picked a red card. It is publicly announced that Billy picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Jose does not know whether or not everyone picked a red card.

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

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

Hypothesis: Tommie can now know whether Billy picked a red card.


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

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

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

Hypothesis: Kathleen 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). Deborah's card is shown to Deborah. Jessica's card is shown to Aurea. It is publicly announced that someone picked a red card. It is publicly announced that Jessica does not know whether or not everyone picked a red card. It is publicly announced that Jessica does not know whether Deborah picked a red card.

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

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

Hypothesis: Deborah 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). Karen's card is shown to Karen. Wallace's card is shown to Karen. Harold's card is shown to Karen. Harold's card is shown to Billie. Karen's card is shown to Wallace. Karen's card is shown to Harold. It is publicly announced that someone picked a red card. It is publicly announced that Billie does not know whether or not everyone picked a red card.

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

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


Premise: There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ryan's card is shown to Randy. Ryan's card is shown to Ryan. David's card is shown to Ryan. It is publicly announced that someone picked a red card. It is publicly announced that Randy 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 that (1&2&3&4))

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

Hypothesis: Ryan 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). Rosemarie's card is shown to Rosemarie. Brandon's card is shown to Rosemarie. Rosemarie's card is shown to Brandon. It is publicly announced that someone picked a red card. It is publicly announced that Brandon does not know whether 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&2))

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

Hypothesis: Brandon can now know whether Rosemarie 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). Carol's card is shown to Carol. Joann's card is shown to Carol. Jerry's card is shown to Joann. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Carol can now know whether Joann can know that Jerry picked a red card.


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

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

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

Hypothesis: Malika can now know whether Gary 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). Barbara's card is shown to Keri. Keri's card is shown to Barbara. It is publicly announced that someone picked a red card. It is publicly announced that Keri does not know whether or not everyone picked a red card.

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

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

Hypothesis: Barbara 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). Eura's card is shown to Deborah. Deborah's card is shown to David. Eura's card is shown to David. David's card is shown to Nellie. Deborah's card is shown to Eura. Nellie's card is shown to Eura. It is publicly announced that someone picked a red card. It is publicly announced that Eura does not know whether Eura picked a red card. It is publicly announced that Deborah knows whether or not nobody picked a red card. It is publicly announced that Nellie picked a black card.

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

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

Hypothesis: Deborah can now know whether Nellie can know whether Eura picked a red card.