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

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

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

Hypothesis: Emily can now know that Deanna can know that Deanna picked a red card.


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

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

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

Hypothesis: Anna can now know that Kara can know whether Leslie 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 Linda. Dollie's card is shown to Linda. Miriam's card is shown to Richard. Dollie's card is shown to Richard. It is publicly announced that someone picked a red card.

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

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


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

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

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

Hypothesis: Leon 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). Donald's card is shown to Donald. Margret's card is shown to Margret. Roberto's card is shown to Margret. Margret's card is shown to Roberto. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Donald can now know that Margret 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). Helen's card is shown to Mercedes. Mary's card is shown to Mercedes. Mercedes's card is shown to Richard. Mercedes's card is shown to Mary. Mary's card is shown to Mary. It is publicly announced that someone picked a red card.

VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:2 Agentc:2,4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentc 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: Helen can now know that Richard can know whether Helen picked a red card.


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

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

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

Hypothesis: Christy can now know whether Leslie 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). Sue's card is shown to Jacob. Lois's card is shown to Lois. Jacob's card is shown to Sue. It is publicly announced that someone picked a red card. It is publicly announced that Sue picked a red card.

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

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

Hypothesis: Lois 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). James's card is shown to James. Donald's card is shown to Donald. Larry's card is shown to Donald. Larry's card is shown to Larry. 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 that (1&2&3))

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

Hypothesis: Larry 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). Melissa's card is shown to Tawana. Shelley's card is shown to Thelma. Shelley's card is shown to Shelley. Tawana's card is shown to Melissa. Thelma's card is shown to Melissa. It is publicly announced that someone picked a red card. It is publicly announced that Shelley does not know whether or not everyone picked a red card.

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

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

Hypothesis: Tawana can now know whether Melissa can know whether Shelley picked a red card.


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

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

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

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


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

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

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

Hypothesis: Tonda can now know that Jerry picked a red card.


Premise: There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Doug's card is shown to Travis. Travis's card is shown to Ada. William's card is shown to Ada. Travis's card is shown to Doug. Travis'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:3 Agentb:1,4 Agentc:1 Agentd: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:3 Agentb:1,4 Agentc:1 Agentd:1 VALID? [ ! (1|2|3|4) ] 0

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


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

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

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

Hypothesis: Mildred can now know that Joesph 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). Rhonda's card is shown to James. James's card is shown to Randy. Rhonda's card is shown to Randy. James's card is shown to Rhonda. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Rhonda 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). Pamela's card is shown to Pamela. Bettye's card is shown to Pamela. Lee's card is shown to Valarie. Pamela's card is shown to Lee. Valarie's card is shown to Lee. Bettye's card is shown to Bettye. It is publicly announced that someone picked a red card. It is publicly announced that Bettye does not know whether Pamela picked a red card. It is publicly announced that Lee knows whether someone picked a red card. It is publicly announced that not everyone picked a red card.

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

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

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


Premise: There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Guadalupe's card is shown to Guadalupe. Melinda's card is shown to Guadalupe. Nellie's card is shown to Melinda. Melinda's card is shown to Nellie. 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) ] (Agentb 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: Melinda 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). Jenny's card is shown to Edgar. Edgar's card is shown to Jenny. Thomas's card is shown to Jenny. Jenny's card is shown to Thomas. Willie's card is shown to Thomas. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Jenny 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). Elisa's card is shown to Lorna. Lorna's card is shown to Elisa. Elisa's card is shown to Elisa. Tom's card is shown to Elisa. Elisa's card is shown to Tom. Jeri's card is shown to Jeri. It is publicly announced that someone picked a red card. It is publicly announced that Jeri picked a red card. It is publicly announced that Lorna picked a black card.

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

Hypothesis: Elisa 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). Lowell's card is shown to Pamela. Lowell's card is shown to Sarah. Kevin's card is shown to Lowell. It is publicly announced that someone picked a red card.

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

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

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


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

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

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

Hypothesis: Bennett can now know whether Jenna can know that Matthew picked a red card.


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

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

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

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


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

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

Hypothesis: Mildred can now know whether Gregory picked a red card.


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

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

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

Hypothesis: Juan 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). Beverly's card is shown to Terry. Christopher's card is shown to Christopher. Beverly's card is shown to Christopher. Beverly's card is shown to Beverly. It is publicly announced that someone picked a red card. It is publicly announced that Beverly does not know whether Philomena picked a red card. It is publicly announced that Terry does not know whether Christopher picked a red card. It is publicly announced that Beverly does not know whether or not everyone picked a red card. It is publicly announced that Christopher does not know whether Philomena picked a red card.

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

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

Hypothesis: Christopher 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). Joyce's card is shown to Stephanie. Stephanie's card is shown to Maureen. Maureen's card is shown to Maureen. Joyce's card is shown to Maureen. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Stephanie 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). Jocelyn's card is shown to John. John's card is shown to Brain. Jocelyn's card is shown to Brain. It is publicly announced that someone picked a red card. It is publicly announced that John knows whether Jocelyn picked a red card.

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

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

Hypothesis: John 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). Anthony's card is shown to Anthony. Forest's card is shown to Forest. Rose's card is shown to Forest. Anthony's card is shown to Rose. Forest's card is shown to Rose. It is publicly announced that someone picked a red card. It is publicly announced that Forest picked a black card. It is publicly announced that Anthony knows whether Anthony 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 2)

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


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

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

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

Hypothesis: Fernando can now know whether Rose 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). Erika's card is shown to Evelyn. Rowena's card is shown to Rowena. Evelyn's card is shown to Erika. Roman's card is shown to Erika. Rowena's card is shown to Erika. It is publicly announced that someone picked a red card. It is publicly announced that Evelyn does not know whether Rowena picked a red card.

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

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

Hypothesis: Rowena 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). Richard's card is shown to Deloris. Camille's card is shown to Elizabeth. Elizabeth's card is shown to Richard. Camille's card is shown to Richard. Deloris's card is shown to Camille. Elizabeth's card is shown to Camille. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Richard can now know that Elizabeth 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). Brian's card is shown to Brian. John's card is shown to Brian. John's card is shown to John. Brian's card is shown to Kelli. It is publicly announced that someone picked a red card. It is publicly announced that John does not know whether or not everyone picked a red card. It is publicly announced that not everyone picked a red card.

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

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

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


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

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

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

Hypothesis: Prince can now know that Michael 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). Francis's card is shown to Francis. Brian's card is shown to Francis. Francis's card is shown to Brian. Linda's card is shown to Brian. Paul's card is shown to Linda. It is publicly announced that someone picked a red card.

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

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

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


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

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

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

Hypothesis: Phillis can now know that Paula 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). Marvin's card is shown to Florida. Marvin's card is shown to Marvin. It is publicly announced that someone picked a red card. It is publicly announced that Florida knows whether someone picked a red card. It is publicly announced that Dan does not know whether or not everyone picked a red card.

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

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

Hypothesis: Florida can now know whether Dan 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). Marian's card is shown to Kelly. Kelly's card is shown to Billy. Billy's card is shown to Billy. Marian's card is shown to Billy. Kelly's card is shown to Marian. It is publicly announced that someone picked a red card. It is publicly announced that Marian does not know whether or not everyone picked a red card.

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

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

Hypothesis: Marian can now know that Kelly 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). Judith's card is shown to George. Michelle's card is shown to Michelle. Michelle's card is shown to Judith. Judith's card is shown to Judith. Judith's card is shown to Claudia. It is publicly announced that someone picked a red card. It is publicly announced that George knows whether or not nobody picked a red card.

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

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

Hypothesis: Claudia 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). Jennifer's card is shown to Jennifer. Robert's card is shown to Jennifer. Joel's card is shown to Gloria. Jennifer's card is shown to Robert. Joel's card is shown to Robert. Gloria's card is shown to Joel. It is publicly announced that someone picked a red card. It is publicly announced that Joel does not know whether Jennifer picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Joel does not know whether Robert picked a red card.

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

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

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


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

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

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

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


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

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

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

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


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

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

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

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


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

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

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

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


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

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

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

Hypothesis: Bill can now know that Clarence 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). Clyde's card is shown to Clyde. Clyde's card is shown to Heather. Heather's card is shown to Janet. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Clyde 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). Burl's card is shown to Daniel. Burl's card is shown to Leticia. Leticia's card is shown to Leticia. It is publicly announced that someone picked a red card. It is publicly announced that Burl knows whether someone picked a red card. It is publicly announced that Burl does not know whether or not everyone picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that Burl picked a red card.

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

Hypothesis: Burl can now know whether Leticia picked a red card.


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

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

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

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


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

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

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

Hypothesis: Richard can now know whether Richard 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 Leroy. Leroy's card is shown to Martin. Joseph's card is shown to Martin. It is publicly announced that someone picked a red card.

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

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

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


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

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

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

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


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

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

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

Hypothesis: Herbert can now know whether Sharon 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). Amelia's card is shown to Amelia. John's card is shown to Amelia. Amelia's card is shown to John. It is publicly announced that someone picked a red card. It is publicly announced that Isabel does not know whether or not everyone picked a red card.

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

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

Hypothesis: Amelia can now know whether Isabel can know whether Isabel picked a red card.


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

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

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

Hypothesis: Ginger 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). Raymond's card is shown to James. James's card is shown to Gerald. Gerald's card is shown to Gerald. Raymond's card is shown to Raymond. It is publicly announced that someone picked a red card. It is publicly announced that Raymond picked a red card. It is publicly announced that James does not know whether James picked a red card.

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

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

Hypothesis: James 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). Jackie's card is shown to Luke. Jackie's card is shown to Linda. Linda's card is shown to Fabian. Linda's card is shown to Jackie. Jackie's card is shown to Jackie. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Luke 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). Russel's card is shown to Michael. Russel's card is shown to Ruby. It is publicly announced that someone picked a red card. It is publicly announced that Timothy does not know whether Ruby picked a red card.

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

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

Hypothesis: Michael 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). Lillian's card is shown to Helen. Rhonda's card is shown to Helen. Helen's card is shown to Helen. Maria's card is shown to Helen. Helen's card is shown to Maria. It is publicly announced that someone picked a red card.

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

Hypothesis: Lillian can now know that Rhonda picked a red card.


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

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

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

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


Premise: There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Allen's card is shown to Lisa. Emily's card is shown to Emily. Allen's card is shown to Emily. Emily's card is shown to Allen. Allen's card is shown to Allen. It is publicly announced that someone picked a red card. It is publicly announced that Allen picked a red card. It is publicly announced that Allen does not know whether Lisa picked a red card. It is publicly announced that Allen knows whether 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:2,3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! ~(Agentc knows whether 1) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (1|2|3) ] (Agenta knows that (1|2|3))

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

Hypothesis: Lisa 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). Rosemary's card is shown to Judith. Judith's card is shown to Rosemary. Rosemary's card is shown to Rosemary. It is publicly announced that someone picked a red card. It is publicly announced that Judith picked a red card.

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

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

Hypothesis: Rosemary 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). Tina's card is shown to Meta. Henrietta's card is shown to Tina. Henrietta's card is shown to Henrietta. It is publicly announced that someone picked a red card. It is publicly announced that Henrietta knows whether someone picked a red card. It is publicly announced that Tina does not know whether Meta picked a red card.

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

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

Hypothesis: Tina can now know that Meta 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). Edward's card is shown to Edward. Rosa's card is shown to Rosa. Edward's card is shown to Alfonso. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Alfonso can now know whether Edward 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). Marlene's card is shown to Marlene. Don's card is shown to Marlene. Marlene's card is shown to Don. It is publicly announced that someone picked a red card. It is publicly announced that Thomas knows whether or not everyone picked a red card. It is publicly announced that Marlene knows whether someone picked a red card.

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

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

Hypothesis: Thomas 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). Michael's card is shown to Michael. Basil's card is shown to Michael. Basil's card is shown to Basil. 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 Basil does not know whether or not everyone picked a red card.

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

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

Hypothesis: Michael can now know that Basil can know that 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). Francisco's card is shown to Harry. Harry's card is shown to Ginger. Francisco's card is shown to Ginger. Harry's card is shown to Francisco. It is publicly announced that someone picked a red card. It is publicly announced that Harry does not know whether Colleen picked a red card. It is publicly announced that Colleen does not know whether Ginger picked a red card.

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

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

Hypothesis: Colleen can now know whether Ginger 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). Freda's card is shown to Freda. Freda's card is shown to Thomas. Clarence's card is shown to Thomas. Clarence's card is shown to Clarence. It is publicly announced that someone picked a red card.

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

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

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


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

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

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

Hypothesis: Kenneth can now know that Ricky can know whether or not nobody picked a red card.


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

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

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

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


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

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

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


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

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

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

Hypothesis: Mario can now know whether Theresa picked a red card.


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

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

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

Hypothesis: Gloria 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). Stacy's card is shown to Stacy. Stacy's card is shown to Matthew. Matthew's card is shown to Matthew. It is publicly announced that someone picked a red card. It is publicly announced that Stacy picked a black card.

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

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

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


Premise: There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kyle's card is shown to Kyle. Gustavo's card is shown to Kyle. Kyle's card is shown to Gustavo. It is publicly announced that someone picked a red card. It is publicly announced that Kyle knows whether or not everyone picked a red card. It is publicly announced that Gustavo knows whether or not nobody 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))) ] (Agentb knows that 2)

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

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


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

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

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

Hypothesis: John 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). Lonnie's card is shown to Anthony. Betty's card is shown to Lonnie. Anthony's card is shown to Betty. Betty's card is shown to Betty. It is publicly announced that someone picked a red card.

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

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

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


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

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

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

Hypothesis: Andrew 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). Cristina's card is shown to David. Alana's card is shown to David. David's card is shown to Cristina. David's card is shown to Alana. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Cristina 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 Shawn. Shawn's card is shown to Jimmie. Lawrence's card is shown to Jimmie. Jimmie's card is shown to Lawrence. Lawrence's card is shown to Lawrence. It is publicly announced that someone picked a red card. It is publicly announced that Shawn does not know whether or not everyone picked a red card. It is publicly announced that Lawrence picked a red card.

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

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

Hypothesis: Jimmie can now know whether Shawn 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). Joshua's card is shown to Ilda. Ilda's card is shown to Joshua. Joshua's card is shown to Joshua. Ilda's card is shown to Michael. Joshua's card is shown to Michael. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Joshua can now 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). William's card is shown to William. Teresa's card is shown to William. Delphine's card is shown to Teresa. Kevin's card is shown to Delphine. Teresa's card is shown to Delphine. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Teresa 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). Juanita's card is shown to Timmy. Delores's card is shown to Timmy. Delores's card is shown to Delores. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Juanita 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). Amy's card is shown to Melissa. Christina's card is shown to Amy. Melissa's card is shown to Christina. Christina's card is shown to Christina. It is publicly announced that someone picked a red card. It is publicly announced that Christina does not know whether Amy picked a red card. It is publicly announced that Melissa does not know whether Christina picked a red card. It is publicly announced that not everyone picked a red card.

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

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

Hypothesis: Christina 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). Ernestina's card is shown to Ernestina. Anthony's card is shown to Daniel. It is publicly announced that someone picked a red card. It is publicly announced that Daniel does not know whether Daniel picked a red card.

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

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

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


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


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

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

Hypothesis: Linda can now know that Jerry 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). Sharon's card is shown to Sharon. Donald's card is shown to Sharon. Sharon's card is shown to Donald. Dorothy's card is shown to Donald. Donald's card is shown to Donald. It is publicly announced that someone picked a red card.

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

VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,2,3 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). Dorothy's card is shown to Dorothy. Warren's card is shown to Dorothy. Dorothy's card is shown to Yolanda. Warren's card is shown to Yolanda. Yolanda's card is shown to Brian. It is publicly announced that someone picked a red card. It is publicly announced that Dorothy knows whether or not everyone picked a red card.

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

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

Hypothesis: Brian can now know that Warren picked a red card.


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

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

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

Hypothesis: Jessica can now know whether Harriet can know that Harriet picked a red card.


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

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

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

Hypothesis: Michael can now know that William 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). Deborah's card is shown to Deborah. James's card is shown to Deborah. Deborah's card is shown to Margaret. James's card is shown to Margaret. Margaret's card is shown to James. It is publicly announced that someone picked a red card. It is publicly announced that James does not know whether Deborah picked a red card.

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

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

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


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

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

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

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


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

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

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

Hypothesis: Ross can now know that Arletta 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). Etta's card is shown to Etta. Jack's card is shown to Jack. Jack's card is shown to Christopher. Etta's card is shown to Joseph. It is publicly announced that someone picked a red card.

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

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

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


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

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

Hypothesis: Arthur can now know whether Michael 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). Tony's card is shown to Chris. Susana's card is shown to Susana. Tony's card is shown to Susana. Tony's card is shown to Tony. It is publicly announced that someone picked a red card. It is publicly announced that Tony does not know whether Susana picked a red card.

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

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

Hypothesis: Chris can now know that Tony 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). Betty's card is shown to Betty. Herbert's card is shown to Betty. Alex's card is shown to William. Betty's card is shown to Herbert. William's card is shown to Alex. Herbert's card is shown to Alex. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Alex can now know that Herbert can know that Betty picked a red card.


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

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

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

Hypothesis: John 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). Frances's card is shown to Carl. Carl's card is shown to Carl. Edith's card is shown to Carl. Frances's card is shown to Edith. It is publicly announced that someone picked a red card.

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

Hypothesis: Bill 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). Sandra's card is shown to Sandra. Josephine's card is shown to Edith. It is publicly announced that someone picked a red card. It is publicly announced that Josephine does not know whether Edith picked a red card. 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) ] [ ! ~(Agentb knows whether 3) ] [ ! (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) ] [ ! ~(Agentb knows whether 3) ] [ ! (1|2|3) ] 0

Hypothesis: Sandra 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 Maria. Cherly's card is shown to Patrick. Patrick's card is shown to Cherly. It is publicly announced that someone picked a red card. It is publicly announced that Patrick does not know whether Timothy picked a red card.

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

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

Hypothesis: Patrick can now know whether Maria 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). Thomas's card is shown to Jennifer. Lance's card is shown to Thomas. Jennifer's card is shown to Victoria. Lance's card is shown to Victoria. 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) ] Agenta knows whether (Agentb knows whether (1|2|3|4))

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

Hypothesis: Jennifer can now know whether Thomas 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). John's card is shown to Ebony. Ebony's card is shown to John. John's card is shown to Joseph. It is publicly announced that someone picked a red card. It is publicly announced that Ebony picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that Joseph picked a black card.

Hypothesis: Ebony 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). Anna's card is shown to Anna. Anna's card is shown to Roberta. Vennie's card is shown to Roberta. It is publicly announced that someone picked a red card.

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

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

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


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

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

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

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


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

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

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

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


Premise: There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Vivian's card is shown to Brad. Vivian's card is shown to Vivian. It is publicly announced that someone picked a red card. It is publicly announced that Brad knows whether Vivian picked a red card. It is publicly announced that Brad 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 2) ] [ ! ~(Agenta knows whether (1&2)) ] (Agentb knows that (1&2))

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

Hypothesis: Vivian 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). Rachel's card is shown to David. David's card is shown to Rachel. Frank's card is shown to Rachel. Rachel's card is shown to Frank. John's card is shown to Frank. It is publicly announced that someone picked a red card.

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

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

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


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

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

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

Hypothesis: Mildred 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). Charlie's card is shown to Charlie. Charlie's card is shown to Virginia. Virginia's card is shown to Virginia. Darin's card is shown to Virginia. Charlie's card is shown to Darin. Darin's card is shown to Darin. Charlie's card is shown to Norman. 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:1,3 Agentd:1 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentb knows that 2)

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

Hypothesis: Darin can now know that Virginia can know that 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). Delores's card is shown to Charles. Priscilla's card is shown to Alta. Charles's card is shown to Priscilla. Priscilla's card is shown to Priscilla. It is publicly announced that someone picked a red card. It is publicly announced that Priscilla does not know whether or not everyone picked a red card.

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

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

Hypothesis: Alta can now know whether Priscilla 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). Kyle's card is shown to Howard. Kyle's card is shown to Kyle. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Kyle can now know that Howard can know whether someone picked a red card.


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

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

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

Hypothesis: Chester can now know whether John 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). Christine's card is shown to Maria. Dennis's card is shown to Maria. Christine's card is shown to Christine. Christine's card is shown to Dennis. It is publicly announced that someone picked a red card. It is publicly announced that Christine knows whether Christine picked a red card. It is publicly announced that Christine does not know whether or not everyone picked a red card. It is publicly announced that Maria does not know whether or not everyone picked a red card.

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

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

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


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

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

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

Hypothesis: Michael can now know whether Ardith 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). Jose's card is shown to Georgina. Jose's card is shown to Tom. Tom's card is shown to Tom. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Jose can now know that Georgina 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. Velma's card is shown to Richard. Richard's card is shown to Robin. Richard's card is shown to Velma. Velma's card is shown to Velma. 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) ] (Agenta knows that (~(1|2|3)))

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

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). Carol's card is shown to Carol. Joyce's card is shown to Carol. Carol's card is shown to Donnette. Donnette's card is shown to Donnette. Carol's card is shown to Joyce. It is publicly announced that someone picked a red card.

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

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

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


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

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

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

Hypothesis: James 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). Jean's card is shown to Rose. Brandon's card is shown to Jean. Erick's card is shown to Jean. Rose's card is shown to Brandon. Jean's card is shown to Brandon. Jean's card is shown to Erick. Brandon's card is shown to Erick. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Brandon can now know that Rose can know whether or not nobody picked a red card.


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

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

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

Hypothesis: James can now know whether Carole 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). Kevin's card is shown to Kevin. Todd's card is shown to Kevin. Kevin's card is shown to Todd. Todd's card is shown to Todd. Douglas's card is shown to Todd. Todd's card is shown to Douglas. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Jennifer 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). John's card is shown to John. Liz's card is shown to Karen. Karen's card is shown to Liz. It is publicly announced that someone picked a red card.

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

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

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


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

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

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

Hypothesis: Gary can now know whether Irene 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). Andrew's card is shown to Andrew. Jeffrey's card is shown to Andrew. Sharda's card is shown to Sharda. Sharda's card is shown to Jeffrey. Jeffrey's card is shown to Stephen. It is publicly announced that someone picked a red card. It is publicly announced that Jeffrey does not know whether or not everyone picked a red card. It is publicly announced that Jeffrey does not know whether Jeffrey picked a red card. It is publicly announced that Andrew knows whether Jeffrey picked a red card.

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

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

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


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

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

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

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


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

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

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

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


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

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

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

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


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

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

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


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

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

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

Hypothesis: Tammi can now know that Theresa 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). Timothy's card is shown to Timothy. Timothy's card is shown to Christopher. Christopher's card is shown to Christopher. 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 that (Agentb knows whether 3)

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

Hypothesis: Timothy can now know that Christopher can know whether Joanne picked a red card.


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

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

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

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


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

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

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

Hypothesis: Jean can now know whether Jerry 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). Sally's card is shown to Sally. Viola's card is shown to Sally. Gertrude's card is shown to Stella. Stella's card is shown to Stella. It is publicly announced that someone picked a red card.

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

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


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

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

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

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

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

Hypothesis: Emilio can now know that James 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). Sophie's card is shown to Sophie. Wilmer's card is shown to Sophie. Sophie's card is shown to Charles. Sophie's card is shown to Wilmer. Wilmer's card is shown to Wilmer. 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 whether (1&2&3))

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

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


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

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

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

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


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

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

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

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


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

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

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

Hypothesis: Anna can now 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). Kelly's card is shown to Grace. Kelly's card is shown to Julie. Randy's card is shown to Julie. Grace's card is shown to Randy. Julie's card is shown to Randy. 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 whether (Agentc knows whether (1&2&3&4))

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

Hypothesis: Kelly can now know whether Julie 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). David's card is shown to Marisa. David's card is shown to Bessie. Lionel's card is shown to David. Marisa's card is shown to Lionel. David's card is shown to Lionel. It is publicly announced that someone picked a red card. It is publicly announced that Bessie does not know whether or not everyone picked a red card.

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

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

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