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

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

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

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


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

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

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


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

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

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

Hypothesis: Tracie can now know whether Betty 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). Nancy's card is shown to Nancy. Robert's card is shown to Nancy. Nancy's card is shown to Jason. Nancy's card is shown to Robert. Robert's card is shown to Robert. It is publicly announced that someone picked a red card.

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

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

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


Premise: There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Julia's card is shown to Julia. Walter's card is shown to Julia. Walter's card is shown to Walter. It is publicly announced that someone picked a red card. It is publicly announced that Walter does not know whether Julia picked a red card. It is publicly announced that Walter does not know whether or not everyone picked a red card. It is publicly announced that Walter 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) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] (Agentb knows that (1&2))

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

Hypothesis: Walter 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). Terri's card is shown to Terri. Terri's card is shown to Maria. Terri's card is shown to Steven. Maria's card is shown to Teresa. It is publicly announced that someone picked a red card. It is publicly announced that Steven does not know whether Steven picked a red card.

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

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

Hypothesis: Steven can now know that Teresa can know whether Terri picked a red card.


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

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

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

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


Premise: There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sharon's card is shown to John. John's card is shown to Linda. 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 Sharon knows whether someone picked a red card.

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

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

Hypothesis: Sharon 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). Timothy's card is shown to Timothy. Richard's card is shown to Timothy. Timothy's card is shown to Richard. Richard's card is shown to Richard. Melvin's card is shown to Richard. Timothy's card is shown to Melvin. Melvin's card is shown to Melvin. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Timothy can now know that Richard 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). Kenny's card is shown to Kenny. Kenny's card is shown to Jose. Jose's card is shown to Jose. It is publicly announced that someone picked a red card. It is publicly announced that Kenny knows whether or not nobody picked a red card. It is publicly announced that Kenny knows whether Jose picked a red card. It is publicly announced that Jose knows whether or not nobody picked a red card. It is publicly announced that Jose knows whether Jose picked a red card.

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

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

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


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

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

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

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


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

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

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

Hypothesis: Mavis can now know that Lonnie can know that Debra picked a red card.


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

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

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

Hypothesis: Nidia 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). Alice's card is shown to Steven. Harry's card is shown to Harry. Harry's card is shown to Alice. It is publicly announced that someone picked a red card. It is publicly announced that Harry picked a red card.

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

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

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


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

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

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

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


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

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

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

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


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

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

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

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


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

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

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

Hypothesis: Louis can now know that Eda 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). Carol's card is shown to Carol. William's card is shown to Carol. William's card is shown to Miguel. William's card is shown to Ralph. Ralph's card is shown to William. 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:1,4 Agentb:4 Agentc:4 Agentd:3,4 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentc knows whether 1)

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

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


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

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

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

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


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

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

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

Hypothesis: Margareta can now know that Ann 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). Wallace's card is shown to Diane. Emma's card is shown to Diane. Emma's card is shown to Wallace. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Wallace can now know that Diane can know whether Emma 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. Otis's card is shown to Otis. It is publicly announced that someone picked a red card. It is publicly announced that Robert knows whether or not nobody picked a red card. It is publicly announced that Otis does not know whether Robert picked a red card.

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

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

Hypothesis: Robert can now know that Otis 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). Frank's card is shown to Frank. Jennifer's card is shown to Frank. It is publicly announced that someone picked a red card. It is publicly announced that Frank knows whether or not nobody picked a red card. It is publicly announced that everyone picked a red card.

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

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

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


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

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

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

Hypothesis: Peggy can now know that 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). Gerald's card is shown to Maryalice. Jesus's card is shown to Jesus. Maryalice's card is shown to Gerald. Gerald's card is shown to Gerald. It is publicly announced that someone picked a red card. It is publicly announced that Gerald knows whether Maryalice picked a red card. It is publicly announced that Jesus does not know whether Maryalice 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) ] (Agenta knows that (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: Maryalice 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). Venice's card is shown to Venice. Ina's card is shown to Ina. Ina's card is shown to Elizabeth. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Venice can now know whether Venice 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 Nellie. Elizabeth's card is shown to Kay. It is publicly announced that someone picked a red card. It is publicly announced that Nellie knows whether Elizabeth picked a red card. It is publicly announced that Nellie does not know whether Donna picked a red card. It is publicly announced that Kay picked a black card.

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

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

Hypothesis: Nellie 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). Ruth's card is shown to Franklin. Jonathan's card is shown to Franklin. Jeremy's card is shown to Franklin. Jonathan's card is shown to Ruth. Jonathan's card is shown to Jeremy. Jeremy's card is shown to Jeremy. It is publicly announced that someone picked a red card.

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

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

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


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

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

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

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


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

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

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

Hypothesis: Michelle can now know whether Frank can know that 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). Mariano's card is shown to Geneva. Nancy's card is shown to Nancy. Geneva's card is shown to Mariano. Nancy's card is shown to Mariano. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Nancy can now know whether Mariano can know that nobody picked a red card.


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

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

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

Hypothesis: Louie can now know that Elbert can know that Louie picked a red card.


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

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

Hypothesis: Joshua can now know whether Kenneth can know whether Byron 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 Linda. David's card is shown to Michael. Linda's card is shown to Michael. It is publicly announced that someone picked a red card. It is publicly announced that David knows whether David picked a red card.

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

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

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


Premise: There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kathleen's card is shown to Kathleen. Kathleen's card is shown to Jason. It is publicly announced that someone picked a red card. It is publicly announced that Jason does not know whether Jason picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that Kathleen knows 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) ] [ ! (~(1&2)) ] [ ! (Agenta knows whether (1&2)) ] Agentb knows whether (Agenta knows that 1)

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

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


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

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

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

Hypothesis: Debra can now know that Beulah picked a red card.


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

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

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

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


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

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

Hypothesis: Jacqulyn can now know that Frank can know whether Jacqulyn picked a red card.


Premise: There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Benjamin's card is shown to Benjamin. Michael's card is shown to Michael. 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 whether 3)

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

Hypothesis: Benjamin can now know whether Ivory picked a red card.


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

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

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

Hypothesis: Lorraine can now know whether Anthony 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). Annie's card is shown to Annie. Edna's card is shown to Annie. Charles's card is shown to Charles. Danielle's card is shown to Edna. Charles's card is shown to Danielle. It is publicly announced that someone picked a red card. It is publicly announced that Edna does not know whether or not everyone picked a red card. It is publicly announced that Charles knows whether or not everyone picked a red card.

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

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

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


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

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

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


Premise: There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Derrick's card is shown to Derrick. Vera's card is shown to Maria. Derrick's card is shown to Vera. Vera's card is shown to Vera. 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) ] (Agentb knows that 3)

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

Hypothesis: Maria can now know that Vera 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 Pamela. Pamela's card is shown to Pamela. 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:2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] (Agenta knows that (1|2|3))

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

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

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

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


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

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

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

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


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

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

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

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


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

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

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

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


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

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

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

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

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

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

Hypothesis: Leo 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). Jessie's card is shown to Patricia. Jessie's card is shown to Jessie. Jessie's card is shown to Alicia. It is publicly announced that someone picked a red card.

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

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

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


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

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

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

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


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

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

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

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


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

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

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

Hypothesis: Annie 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). Gregory's card is shown to David. Salvador's card is shown to Gregory. Jeannette's card is shown to Gregory. Jeannette's card is shown to Salvador. Gregory's card is shown to Jeannette. It is publicly announced that someone picked a red card.

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

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

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


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

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

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

Hypothesis: Gregory can now know whether Robert 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). Monica's card is shown to Doris. Doris's card is shown to Monica. Monica's card is shown to Thanh. It is publicly announced that someone picked a red card. It is publicly announced that Thanh knows whether Monica picked a red card. It is publicly announced that Monica does not know whether Thanh picked a red card.

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

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

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


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

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


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

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

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

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


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

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

Hypothesis: Rose 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). Derek's card is shown to Pam. Eileen's card is shown to Eileen. Derek's card is shown to Derek. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Eileen 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). Barry's card is shown to Barry. Darren's card is shown to Darren. Darren's card is shown to Sherri. Sherri's card is shown to Sherri. It is publicly announced that someone picked a red card. It is publicly announced that Barry does not know whether or not everyone picked a red card.

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

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

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


Premise: There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Maria's card is shown to Sandy. Travis's card is shown to Travis. Travis's card is shown to Jake. It is publicly announced that someone picked a red card. It is publicly announced that Travis does not know whether Maria picked a red card. It is publicly announced that Travis does not know whether Maria 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:3 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentc knows whether 1) ] [ ! (~(1&2&3&4)) ] (Agentb knows whether 2)

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

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


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

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

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

Hypothesis: Cora can now know whether Mae 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). Ana's card is shown to Mildred. Luke's card is shown to Paula. Paula's card is shown to Paula. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Mildred can now know that Luke 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). Robert's card is shown to Robert. Brenda's card is shown to Brenda. Robert's card is shown to Catherine. Robert's card is shown to Margaret. It is publicly announced that someone picked a red card.

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

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

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


Premise: There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dawn's card is shown to Margaret. Sally's card is shown to Teddy. Teddy's card is shown to Dawn. Dawn's card is shown to Dawn. Sally's card is shown to Dawn. Teddy's card is shown to Sally. 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) ] (Agentd 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: Sally can now know whether or not nobody picked a red card.


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

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


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

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

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

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


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

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

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

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


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

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

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

Hypothesis: Linda can now know whether Ruth 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). Carolyn's card is shown to Alex. Aurelia's card is shown to Alex. Carolyn's card is shown to Lois. Lois's card is shown to Lois. Carolyn's card is shown to Aurelia. It is publicly announced that someone picked a red card.

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

Hypothesis: Lois can now know that Carolyn 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). Rafael's card is shown to Rafael. Gertrude's card is shown to Gertrude. Rafael's card is shown to Clarence. It is publicly announced that someone picked a red card. It is publicly announced that Clarence does not know whether Clarence picked a red card.

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

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

Hypothesis: Gertrude 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). Jennifer's card is shown to Hazel. Hazel's card is shown to Leon. Hazel's card is shown to Sheila. It is publicly announced that someone picked a red card.

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

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

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


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

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

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

Hypothesis: Raymond can now know that Robert 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). Madge's card is shown to Madge. Erik's card is shown to Madge. Madge's card is shown to Barbara. Barbara's card is shown to Barbara. David's card is shown to Barbara. Erik's card is shown to Barbara. Madge's card is shown to David. Barbara's card is shown to Erik. It is publicly announced that someone picked a red card.

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

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

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


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

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

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

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


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

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

Hypothesis: Marla 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). Jerri's card is shown to Linda. Linda's card is shown to Jerri. It is publicly announced that someone picked a red card. It is publicly announced that Linda knows 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)) ] 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)) ] 0

Hypothesis: Linda can now know that Jerri can know that Jerri 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 David. Dianne's card is shown to David. Dianne's card is shown to Dianne. It is publicly announced that 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:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] (Agenta knows whether (~(1|2)))

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

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

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

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

Hypothesis: Fred can now know whether Barbara 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). Tony's card is shown to Sheila. Alexander's card is shown to Scott. Tony's card is shown to Scott. Tony's card is shown to Tony. It is publicly announced that someone picked a red card. It is publicly announced that Scott does not know whether Sheila picked a red card. It is publicly announced that Alexander does not know whether Sheila picked a red card.

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

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

Hypothesis: Sheila can now know that Tony 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 Mary. Mary's card is shown to Ruby. Ruby's card is shown to Ruby. Ruby's card is shown to Esther. Esther's card is shown to Esther. It is publicly announced that someone picked a red card.

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

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

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


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

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

Hypothesis: Kimberly can now know that Cora can know whether Kimberly picked a red card.


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

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

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

Hypothesis: Joseph 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). Carol's card is shown to Ramona. Ramona's card is shown to Willie. Ramona's card is shown to Carol. Willie's card is shown to Carol. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Ramona 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). Anna's card is shown to Anna. Armando's card is shown to Edwin. Edwin's card is shown to Armando. Armando's card is shown to Armando. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Armando can now know whether Anna can know whether Anna picked a red card.


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

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

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

Hypothesis: Joann can now know whether Heather 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). Elaine's card is shown to Paul. Elaine's card is shown to Daniel. Paul's card is shown to Daniel. It is publicly announced that someone picked a red card. It is publicly announced that Elaine does not know whether or not everyone picked a red card. It is publicly announced that Elaine 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:1 Agentb:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (1|2|3) ] (Agentb knows that (1&2&3))

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

Hypothesis: Paul 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). Valerie's card is shown to Valerie. Adelia's card is shown to Valerie. Valerie's card is shown to Tracy. Tracy's card is shown to Tracy. Adelia's card is shown to Tracy. Charles's card is shown to Tracy. Tracy's card is shown to Adelia. Charles's card is shown to Adelia. Valerie's card is shown to Charles. Adelia's card is shown to Charles. It is publicly announced that someone picked a red card. It is publicly announced that Charles does not know whether or not everyone picked a red card.

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

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

Hypothesis: Valerie can now know that Tracy 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). Julio's card is shown to Joseph. Bob's card is shown to Bob. Bob's card is shown to Julio. It is publicly announced that someone picked a red card. It is publicly announced that Bob does not know whether or not everyone picked a red card.

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

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

Hypothesis: Julio can now know that Julio 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 Laura. Justin's card is shown to Justin. Justin's card is shown to Victor. Victor's card is shown to Victor. Victor'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:2 Agentb:2 Agentc:2,3 Agentd:3 VALID? [ ! (1|2|3|4) ] (Agentc knows that 3)

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

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


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

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

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


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

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

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

Hypothesis: Joel can now know whether John 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). Dominick's card is shown to Dominick. Mary's card is shown to Mary. It is publicly announced that someone picked a red card. It is publicly announced that Mary does not know whether or not everyone picked a red card.

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

Hypothesis: Mary can now know whether Dominick 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). Marguerite's card is shown to Marguerite. Glenna's card is shown to Marguerite. Marguerite's card is shown to Thomas. Thomas's card is shown to Thomas. Anita's card is shown to Anita. Marguerite's card is shown to Glenna. Thomas's card is shown to Glenna. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Marguerite can now know that Glenna 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). Francis's card is shown to Dorothy. Michelle's card is shown to Francis. Francis's card is shown to Michelle. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Dorothy 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). Roberta's card is shown to Dorothy. John's card is shown to Dorothy. Dorothy's card is shown to James. Dorothy'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:1,4 Agentb:2 Agentc:2,4 VALID? [ ! (1|2|3|4) ] (Agentb knows whether 1)

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

Hypothesis: Dorothy can now know whether Roberta picked a red card.


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

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

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

Hypothesis: Theodore can now know whether Kenneth can know whether Kenneth 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 Jerry. David's card is shown to David. James's card is shown to David. Jerry's card is shown to James. David's card is shown to James. James's card is shown to James. David's card is shown to George. It is publicly announced that someone picked a red card.

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

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

Hypothesis: James can now know that George 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). Shirley's card is shown to Shirley. David's card is shown to Shirley. David's card is shown to Margaret. Margaret's card is shown to Margaret. It is publicly announced that someone picked a red card. It is publicly announced that David does not know whether or not everyone picked a red card.

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

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


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

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

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

Hypothesis: Roberta can now know whether Logan picked a red card.


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

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

Hypothesis: Everett 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). Francisco's card is shown to Francisco. Francisco's card is shown to William. It is publicly announced that someone picked a red card. It is publicly announced that William knows whether William picked a red card.

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

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

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


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

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

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

Hypothesis: Joey can now know whether Dorian 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). Carmel's card is shown to Carmel. Jonathon's card is shown to Carmel. Carmel's card is shown to Jonathon. Jonathon's card is shown to Jonathon. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Jonathon can now know whether Carmel 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). Carol's card is shown to Carol. Mark's card is shown to Mark. Michael's card is shown to Mark. Virginia's card is shown to Virginia. It is publicly announced that someone picked a red card. It is publicly announced that Mark does not know whether Carol picked a red card.

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

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

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


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

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

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

Hypothesis: Carolee can now know whether Anastasia picked a red card.


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

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

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

Hypothesis: Charles 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). Steven's card is shown to Steven. Fred's card is shown to Steven. Daisy's card is shown to Steven. Daisy's card is shown to Frank. Steven's card is shown to Daisy. Fred's card is shown to Daisy. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Steven can now know that Frank can know that Fred picked a red card.


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

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

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

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


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

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

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

Hypothesis: Annett can now know whether Belinda 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). Terina's card is shown to Marylou. Bethann's card is shown to Bethann. Marylou's card is shown to Terina. Terina's card is shown to Terina. It is publicly announced that someone picked a red card.

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

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

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


Premise: There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). James's card is shown to James. Stanley's card is shown to James. James's card is shown to Stanley. Stanley's card is shown to Stanley. It is publicly announced that someone picked a red card. It is publicly announced that James knows whether or not nobody 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) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (~(1&2)) ] Agenta knows whether (Agentb knows whether (~(1|2)))

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

Hypothesis: James can now know whether Stanley 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). George's card is shown to Jerome. Doreen's card is shown to Louis. Louis's card is shown to George. Louis's card is shown to Doreen. Doreen's card is shown to Doreen. It is publicly announced that someone picked a red card.

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

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

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


Premise: There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Brett's card is shown to Brett. Nicole's card is shown to Nicole. Ruby's card is shown to Nicole. Ruby's card is shown to Ruby. 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) ] (Agentc knows whether 1)

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

Hypothesis: Ruby can now know whether Brett picked a red card.


Premise: There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cindy's card is shown to Susan. Cindy's card is shown to Cindy. It is publicly announced that someone picked a red card. It is publicly announced that Susan knows whether someone 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 2)

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

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


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

VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:1 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] Agentb knows that (Agentd knows that (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: Patricia can now know that Suzanne 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). Lorraine's card is shown to Anna. Catherine's card is shown to Gregory. Gregory's card is shown to Lorraine. Anna's card is shown to Catherine. It is publicly announced that someone picked a red card. It is publicly announced that Catherine does not know whether or not everyone picked a red card. It is publicly announced that Gregory picked a red card.

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

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

Hypothesis: Anna can now know whether Catherine 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). James's card is shown to Lavern. Carla's card is shown to Lavern. James's card is shown to James. Lavern's card is shown to Carla. It is publicly announced that someone picked a red card. It is publicly announced that James does not know whether or not everyone picked a red card.

VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agenta 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: Lavern can now know whether Carla picked a red card.


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

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

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

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

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

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

Hypothesis: Michael 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). Robert's card is shown to Eileen. Jack's card is shown to Valerie. Jack's card is shown to Robert. It is publicly announced that someone picked a red card. It is publicly announced that Valerie does not know whether Valerie picked a red card. It is publicly announced that Eileen does not know whether Jack picked a red card.

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

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

Hypothesis: Jack can now know whether Valerie 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). Evelyn's card is shown to Evelyn. Evelyn's card is shown to Philip. It is publicly announced that someone picked a red card. It is publicly announced that Evelyn knows whether Evelyn picked a red card. It is publicly announced that Evelyn knows whether Philip picked a red card.

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

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

Hypothesis: Evelyn 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). Felicia's card is shown to Mary. Jean's card is shown to Jean. Ruben's card is shown to Jean. It is publicly announced that someone picked a red card. It is publicly announced that Felicia does not know whether or not everyone picked a red card.

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

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

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


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

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

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

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


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

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

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

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


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

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

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

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


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

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

Hypothesis: Robert 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). Lizette's card is shown to Lizette. Alvin's card is shown to Lizette. Lizette's card is shown to Max. Alvin's card is shown to Max. It is publicly announced that someone picked a red card.

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

Hypothesis: Alvin can now know that Lizette 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). Arturo's card is shown to Arturo. Wendy's card is shown to Eric. Arturo's card is shown to Beatrice. Eric's card is shown to Wendy. It is publicly announced that someone picked a red card. It is publicly announced that Arturo does not know whether or not everyone picked a red card.

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

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

Hypothesis: Wendy 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). Linda's card is shown to Linda. Mildred's card is shown to Mildred. It is publicly announced that someone picked a red card.

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

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

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

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

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

Hypothesis: Ruth can now know whether Herbert picked a red card.


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

Hypothesis: Richard 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). Leah's card is shown to Leah. Priscilla's card is shown to Priscilla. Leah's card is shown to Elizabeth. Priscilla'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 Leah does not know whether or not everyone picked a red card. It is publicly announced that Priscilla knows whether Priscilla picked a red card.

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

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

Hypothesis: Priscilla can now know whether Leah can know whether Priscilla picked a red card.


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

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

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

Hypothesis: Nora can now know that Lisa 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). Carole's card is shown to Wesley. Carole's card is shown to Carole. Joseph's card is shown to Carole. Wesley's card is shown to Joshua. Carole's card is shown to Joshua. Wesley's card is shown to Joseph. Joshua's card is shown to Joseph. It is publicly announced that someone picked a red card. It is publicly announced that Wesley does not know whether Joshua picked a red card. It is publicly announced that Wesley knows whether Carole picked a red card.

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

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

Hypothesis: Carole can now know that Joseph 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). Rhonda's card is shown to Rhonda. Lonnie's card is shown to Rhonda. Rhonda's card is shown to Michael. Michael's card is shown to Michael. Lonnie's card is shown to Michael. William's card is shown to Michael. Michael's card is shown to Lonnie. William's card is shown to Lonnie. Rhonda's card is shown to William. Lonnie's card is shown to William. It is publicly announced that someone picked a red card. It is publicly announced that William does not know whether or not everyone picked a red card.

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

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

Hypothesis: Michael can now know whether Lonnie 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). Pamala's card is shown to Jorge. Jorge's card is shown to Jorge. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that not everyone picked a red card.

Hypothesis: Pamala 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). Linda's card is shown to Linda. Shane's card is shown to Shane. It is publicly announced that someone picked a red card. It is publicly announced that Shane does not know whether Linda picked a red card. It is publicly announced that Linda knows whether or not everyone picked a red card.

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

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

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