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

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

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

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


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

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

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

Hypothesis: Sam can now know that Jay 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). Wayne's card is shown to Wayne. Marvin's card is shown to Wayne. Wayne's card is shown to Robert. Marvin's card is shown to Robert. Robert's card is shown to Christine. It is publicly announced that someone picked a red card. It is publicly announced that Marvin does not know whether or not everyone picked a red card.

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

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

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


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

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

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

Hypothesis: Allison can now know whether Julia can know that Allison picked a red card.


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

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

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


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

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

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

Hypothesis: John can now know whether Helene can 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). Bonnie's card is shown to Candice. Jayme's card is shown to Cecila. Cecila's card is shown to Bonnie. Candice's card is shown to Jayme. It is publicly announced that someone picked a red card. It is publicly announced that Jayme does not know whether or not everyone picked a red card. It is publicly announced that Cecila picked a red card.

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

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

Hypothesis: Cecila can now know whether Candice can know whether Bonnie picked a red card.


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

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

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

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


Premise: There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marie's card is shown to Eric. Natalie's card is shown to Eric. Natalie's card is shown to Marie. Eric's card is shown to Natalie. Natalie's card is shown to Natalie. It is publicly announced that someone picked a red card. It is publicly announced that Eric does not know whether Eric picked a red card. It is publicly announced that Marie does not know whether or not everyone picked a red card. It is publicly announced that Natalie picked a red card. It is publicly announced that Marie 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 that (Agentb knows whether (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: Natalie can now know that Marie 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). Kenneth's card is shown to Kenneth. Harriet's card is shown to Leland. It is publicly announced that someone picked a red card. It is publicly announced that Harriet knows whether or not everyone picked a red card.

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

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

Hypothesis: Kenneth can now 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). Christine's card is shown to Kay. Christine's card is shown to Christine. Bertha's card is shown to Christine. Christine's card is shown to Bertha. It is publicly announced that someone picked a red card. It is publicly announced that Kay picked a red card.

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

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

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


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

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

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

Hypothesis: Daniel can now know that Patricia 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). Dale's card is shown to Dale. Leah's card is shown to Dale. Dale's card is shown to Leah. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that Leah picked a black card.

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

Hypothesis: Leah can now know whether Dale 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). Sylvia's card is shown to Jason. Kevin's card is shown to Jason. Sylvia's card is shown to Sylvia. Jason's card is shown to Kevin. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Sylvia can now know whether Kevin picked a red card.


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

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

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

Hypothesis: Rodney can now know whether Matthew 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). Wayne's card is shown to Marion. Albert's card is shown to Wayne. Marion'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:3 Agentc:1 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentc knows that (1&2&3))

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

Hypothesis: Marion can now know whether Albert 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). Brittney's card is shown to Brittney. John's card is shown to Brittney. Brittney's card is shown to John. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.

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

Hypothesis: John can now know whether Brittney 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. Crystal's card is shown to Barbara. Crystal's card is shown to Crystal. Mark's card is shown to Crystal. Barbara's card is shown to Mark. It is publicly announced that someone picked a red card. It is publicly announced that Barbara knows whether someone picked a red card.

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

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

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


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

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

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

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


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

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

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


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

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

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


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

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

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

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


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

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

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

Hypothesis: Octavio can now know that Ron picked a red card.


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

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

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

Hypothesis: Nathan 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). Jessie's card is shown to Nicole. Chantal's card is shown to Nicole. Nicole's card is shown to Joseph. Joseph's card is shown to Chantal. It is publicly announced that someone picked a red card. It is publicly announced that Nicole does not know whether Jessie picked a red card.

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

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

Hypothesis: Jessie can now know that Nicole 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 Rachael. Joyce's card is shown to Sarah. Lavern's card is shown to Sarah. Rachael's card is shown to Lavern. Sarah's card is shown to Lavern. 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) ] Agentc knows whether (Agenta knows that 2)

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

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


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

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

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

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


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

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

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


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

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

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

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


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

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

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

Hypothesis: Forrest can now know whether Frankie can know that Danielle 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 Sean. Timothy's card is shown to Timothy. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Sean can now know whether Aaron 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 Elizabeth. Elizabeth's card is shown to Elizabeth. Gail's card is shown to Elizabeth. Gail's card is shown to Gail. It is publicly announced that someone picked a red card.

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

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

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


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

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

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

Hypothesis: Darren 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). Ryan's card is shown to Ryan. Ryan's card is shown to Crystal. Evan's card is shown to Crystal. Crystal's card is shown to Evan. Dustin's card is shown to Evan. It is publicly announced that someone picked a red card. It is publicly announced that Ryan does not know whether Dustin picked a red card. It is publicly announced that not everyone picked a red card.

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

Hypothesis: Ryan 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). Sally's card is shown to Angela. Sally's card is shown to Sally. It is publicly announced that someone picked a red card. It is publicly announced that Angela does not know whether Angela picked a red card.

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

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

Hypothesis: Angela can now know that Sally 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). Debbie's card is shown to Scott. Delpha's card is shown to Delpha. Debbie's card is shown to Delpha. Debbie's card is shown to Debbie. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Scott can now know whether Delpha can know that Debbie picked a red card.


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

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

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

Hypothesis: Carlos can now know whether George picked a red card.


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

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

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

Hypothesis: Matthew 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). Dana's card is shown to Dana. Dana's card is shown to Amy. Don's card is shown to Amy. It is publicly announced that someone picked a red card. It is publicly announced that Amy picked a red card.

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

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

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


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

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

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

Hypothesis: Eric can now know that Patricia can know that Eric 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 Joan. Gary's card is shown to Joan. Gary's card is shown to Gary. Barbara's card is shown to Gary. Clifton's card is shown to Barbara. Barbara's card is shown to Barbara. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Gary 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). Manuel's card is shown to Manuel. Vernon's card is shown to Dwayne. Dwayne's card is shown to Vernon. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Dwayne can now know that Manuel 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). Collin's card is shown to Collin. Bill's card is shown to Collin. Don's card is shown to Wilma. Collin's card is shown to Bill. Wilma's card is shown to Don. Bill's card is shown to Don. 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 whether (Agenta knows that (1&2&3&4))

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: Don can now know whether Collin 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). Kayla's card is shown to William. Michael's card is shown to Michael. Kayla's card is shown to Michael. Kayla's card is shown to Mary. Mary's card is shown to Kayla. It is publicly announced that someone picked a red card.

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

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

Hypothesis: William can now know whether Kayla 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). Raquel's card is shown to Hope. David's card is shown to Hope. Hope's card is shown to Raquel. Hope's card is shown to David. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Hope can now know whether Raquel picked a red card.


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

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

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

Hypothesis: Josephine can now know whether Maurice can know whether Chris picked a red card.


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

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

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

Hypothesis: Rachel 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). Helen's card is shown to Karla. Helen's card is shown to Helen. Helen's card is shown to Charles. Charles's card is shown to Charles. It is publicly announced that someone picked a red card. It is publicly announced that Karla does not know whether Charles picked a red card.

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

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

Hypothesis: Karla can now know that Charles 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). John's card is shown to John. Rosa's card is shown to John. Robert's card is shown to John. John's card is shown to Robert. It is publicly announced that someone picked a red card.

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

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

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


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

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

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

Hypothesis: Michael can now know whether Kerry 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). Thomas's card is shown to Berta. Troy's card is shown to Berta. Davis's card is shown to Davis. Berta's card is shown to Troy. Thomas's card is shown to Troy. It is publicly announced that someone picked a red card. It is publicly announced that Davis picked a black card.

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

Hypothesis: Davis 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). Donna's card is shown to Donna. Donna's card is shown to Becky. It is publicly announced that someone picked a red card.

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

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

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


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

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

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

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

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

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

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


Premise: There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Troy's card is shown to Jonathan. Diana's card is shown to Diana. Jonathan's card is shown to Troy. Dorothy's card is shown to Troy. Diana's card is shown to Troy. It is publicly announced that someone picked a red card. It is publicly announced that Jonathan does not know whether Diana 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) ] (Agenta knows whether 2)

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: Jonathan can now know whether Dorothy picked a red card.


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

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

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

Hypothesis: Larraine can now know that Kevin can know whether Larraine picked a red card.


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

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

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: Mark can now know that Michael 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). Clarence's card is shown to Joseph. Alexander's card is shown to Kelly. Clarence's card is shown to Clarence. It is publicly announced that someone picked a red card. It is publicly announced that Kelly knows whether Clarence picked a red card. It is publicly announced that Alexander does not know whether Joseph picked a red card.

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

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

Hypothesis: Alexander can now know that Joseph 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 Christopher. Timothy's card is shown to Christopher. Christopher's card is shown to Timothy. Timothy's card is shown to Timothy. It is publicly announced that someone picked a red card. It is publicly announced that Christopher picked a red card.

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

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

Hypothesis: Christopher 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). Margaret's card is shown to Julia. Julia's card is shown to Eddie. It is publicly announced that someone picked a red card. It is publicly announced that Margaret picked a black card. It is publicly announced that Julia knows whether or not everyone picked a red card.

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

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

Hypothesis: Margaret can now know that Julia 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). Margaret's card is shown to Calvin. Margaret's card is shown to Margaret. Tina's card is shown to Margaret. Calvin's card is shown to Tina. Tina's card is shown to Tina. It is publicly announced that someone picked a red card. It is publicly announced that Tina knows whether Calvin picked a red card.

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

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

Hypothesis: Margaret 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). Ellie's card is shown to Ellie. Kenny's card is shown to Ellie. Sylvia's card is shown to Sylvia. Sylvia's card is shown to Kenny. It is publicly announced that someone picked a red card.

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

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

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


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

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

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

Hypothesis: Cameron can now know that Mack 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). Janie's card is shown to Larry. Sarah's card is shown to Larry. Sarah's card is shown to Wesley. Larry's card is shown to Janie. Wesley's card is shown to Sarah. Janie's card is shown to Sarah. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Larry can now know whether Wesley 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). Corey's card is shown to Cynthia. Cynthia's card is shown to Daniel. Daniel's card is shown to Daniel. Corey's card is shown to Daniel. Daniel's card is shown to Corey. Corey's card is shown to Corey. It is publicly announced that someone picked a red card. It is publicly announced that Cynthia 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:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentb knows that (Agenta knows that (~(1|2|3)))

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

Hypothesis: Daniel can now know that Cynthia 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). Wilma's card is shown to Marie. Janice's card is shown to Marie. Wilma's card is shown to Wilma. Marie's card is shown to Janice. Wilma's card is shown to Janice. Janice's card is shown to Janice. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Janice 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). Katherine's card is shown to Nicole. Michael's card is shown to Michael. Katherine's card is shown to Michael. Michael's card is shown to Katherine. Katherine's card is shown to Katherine. 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) ] Agentb knows whether (Agenta knows that 2)

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

Hypothesis: Michael can now know whether Nicole 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). Emerson's card is shown to Emerson. Glenn's card is shown to Emerson. Emerson's card is shown to Shirley. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Emerson 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). Jeremy's card is shown to Michael. Mary's card is shown to Michael. Mary's card is shown to Jeremy. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Michael 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). Jeffrey's card is shown to Letha. Letha's card is shown to Jeffrey. Jeffrey's card is shown to Jeffrey. It is publicly announced that someone picked a red card. It is publicly announced that Jeffrey picked a black card.

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

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

Hypothesis: Jeffrey can now know that Letha picked a red card.


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

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

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

Hypothesis: Joanne 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). Diane's card is shown to Diane. Diane's card is shown to Linda. Diane's card is shown to Angela. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card.

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

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

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


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

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

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

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


Premise: There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Maria's card is shown to Lauren. Antonio's card is shown to Timothy. Antonio's card is shown to Antonio. Lauren's card is shown to Maria. Timothy's card is shown to Maria. It is publicly announced that someone picked a red card. It is publicly announced that Antonio 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)) ] Agentc knows whether (Agentd knows that 2)

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: Antonio can now know whether Maria can know that Timothy picked a red card.


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

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

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

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


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

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

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

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


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

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

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

Hypothesis: Dorothy 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). Joy's card is shown to Lillian. Sergio's card is shown to Lillian. Lillian's card is shown to Joy. Lillian's card is shown to Sergio. It is publicly announced that someone picked a red card. It is publicly announced that Lillian picked a red card. It is publicly announced that Joy knows whether or not nobody picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Lillian knows whether Sergio picked a red card.

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

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

Hypothesis: Lillian can now know that Sergio 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). Charles's card is shown to Morgan. Vicki's card is shown to Morgan. Morgan's card is shown to Vicki. Vicki's card is shown to Vicki. It is publicly announced that someone picked a red card.

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

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

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


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

VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,3,4 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] Agenta knows that (Agentc knows that (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: Dawn can now know that Cheryl 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). Alonzo's card is shown to Alonzo. Hattie's card is shown to Alonzo. Alonzo's card is shown to Hazel. Hazel's card is shown to Hazel. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Alonzo 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). James's card is shown to Kelly. Kelly's card is shown to James. Meta's card is shown to James. James's card is shown to Meta. It is publicly announced that someone picked a red card. It is publicly announced that James does not know whether James picked a red card. It is publicly announced that Meta does not know whether Kelly picked a red card. It is publicly announced that Kelly does not know whether or not everyone picked a red card.

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

Hypothesis: Kelly 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). Roland's card is shown to Tiffany. Tiffany's card is shown to Jackie. Jackie's card is shown to Jackie. Roland's card is shown to Roland. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Tiffany can now know whether Tiffany 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 Patricia. Marc's card is shown to Patricia. Debra's card is shown to Debra. Debra's card is shown to Marc. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Patricia can now know that Debra 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). Rebecca's card is shown to Miriam. David's card is shown to Rebecca. Miriam's card is shown to David. Rebecca's card is shown to David. It is publicly announced that someone picked a red card.

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

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

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


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

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

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

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


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

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

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

Hypothesis: Bobby can now know that David 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). Judith's card is shown to Judith. Laura's card is shown to Laura. Laura's card is shown to Geri. It is publicly announced that someone picked a red card. It is publicly announced that Laura does not know whether or not everyone picked a red card.

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

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

Hypothesis: Laura can now know whether Judith picked a red card.


Premise: There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kim's card is shown to Victor. Victor's card is shown to Kim. Kim's card is shown to Kim. Victor's card is shown to Evelyn. It is publicly announced that someone picked a red card. It is publicly announced that Kim knows whether Kim 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 2) ] Agentc knows whether (Agenta knows that (1&2&3))

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

Hypothesis: Evelyn can now know whether Victor 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). Cherlyn's card is shown to Nick. Nick's card is shown to Cherlyn. Shirley's card is shown to Cherlyn. Nick's card is shown to Shirley. Cherlyn's card is shown to Shirley. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Cherlyn 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). William's card is shown to Edwin. William's card is shown to William. Annette's card is shown to Annette. It is publicly announced that someone picked a red card.

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

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

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


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

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

Hypothesis: Graham 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). Kelvin's card is shown to Thomas. Kelvin's card is shown to Kelvin. It is publicly announced that someone picked a red card. It is publicly announced that Kelvin knows whether or not nobody picked a red card. It is publicly announced that Kelvin does not know whether or not everyone picked a red card.

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

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

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


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

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

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

Hypothesis: Elizabeth 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). Juan's card is shown to Glenn. Ruby's card is shown to Glenn. Glenn's card is shown to Juan. Juan's card is shown to Juan. Gordon's card is shown to Ruby. It is publicly announced that someone picked a red card.

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

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

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


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

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

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

Hypothesis: Douglas can now know that Brenda 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). Kevin's card is shown to Kevin. Kevin's card is shown to Joyce. Joyce's card is shown to Joyce. 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 Joyce knows whether Joyce picked a red card. It is publicly announced that Kevin knows whether Kevin picked a red card.

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

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

Hypothesis: Kevin 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). Brian's card is shown to Brian. Ralph's card is shown to Brian. Miguel's card is shown to Miguel. Miguel's card is shown to Lori. Ralph's card is shown to Lori. Ralph's card is shown to Ralph. It is publicly announced that someone picked a red card. It is publicly announced that Brian does not know whether or not everyone picked a red card. It is publicly announced that someone picked a red card.

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

Hypothesis: Lori can now know that Ralph can know that Lori 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. Serena's card is shown to David. David's card is shown to Serena. Serena's card is shown to Serena. Adam's card is shown to Serena. David's card is shown to Adam. Serena's card is shown to Adam. Adam's card is shown to Adam. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Adam can now know whether Adam 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 Chester. 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 VALID? [ ! (1|2) ] [ ! (1|2) ] (Agenta knows that (1&2))

Hypothesis: Tommy 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 Robert. David's card is shown to Robert. Anna's card is shown to Octavia. David's card is shown to Octavia. David's card is shown to Anna. Robert's card is shown to David. It is publicly announced that someone picked a red card. It is publicly announced that Octavia knows whether Anna picked a red card. It is publicly announced that Octavia knows whether someone picked a red card. It is publicly announced that Octavia picked a red card.

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

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

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


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

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

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

Hypothesis: Nellie can now know whether Virgil can know that Louis picked a red card.


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

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

Hypothesis: Thomas can now know whether Jessica 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). Clara's card is shown to Lashanda. Linda's card is shown to Lashanda. Clara's card is shown to Linda. Michael's card is shown to Linda. Michael's card is shown to Michael. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Clara 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). Julio's card is shown to Michael. Michael's card is shown to Michael. Michael's card is shown to Beverly. Beverly's card is shown to Denis. Denis's card is shown to Denis. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.

Hypothesis: Julio 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). John's card is shown to Deanna. Brandon's card is shown to Brandon. Tanya's card is shown to John. Deanna's card is shown to John. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Brandon can now know whether Deanna 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). Anna's card is shown to Lawrence. Anna's card is shown to Phillip. Phillip's card is shown to Anna. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.

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

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


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

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

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

Hypothesis: Dale can now know that Amanda 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). Andrea's card is shown to Jennifer. Sandra's card is shown to Sandra. Andrea's card is shown to Andrea. Andrea's card is shown to Therese. Therese's card is shown to Therese. It is publicly announced that someone picked a red card. It is publicly announced that Therese does not know whether Jennifer picked a red card. It is publicly announced that Jennifer does not know whether Jennifer picked a red card.

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

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

Hypothesis: Therese can now know whether Jennifer can know whether Sandra picked a red card.


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

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

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

Hypothesis: Charles can now know whether James 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). Eve's card is shown to Joseph. Cami's card is shown to Joseph. Eve's card is shown to Cami. Kenneth's card is shown to Cami. Cami's card is shown to Kenneth. 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:3 VALID? [ ! (1|2|3|4) ] (Agentb knows whether 4)

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

Hypothesis: Eve can now know whether Kenneth picked a red card.


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

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

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

Hypothesis: Karen can now know whether Charles 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). Janet's card is shown to Doris. Janet's card is shown to Janet. Kathleen's card is shown to Janet. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Doris can now know that Janet can know whether Kathleen 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 Leland. Leland's card is shown to Julius. Carlos's card is shown to Julius. Leland's card is shown to Carlos. It is publicly announced that someone picked a red card. It is publicly announced that Carlos does not know whether Kevin picked a red card.

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

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

Hypothesis: Carlos can now know whether Julius can know that nobody picked a red card.


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

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

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


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

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

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

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


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

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

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

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


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

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

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

Hypothesis: Sherman can now know that Lynn 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). Sharon's card is shown to Sharon. Steven's card is shown to Sharon. Lillie's card is shown to Lillie. Steven's card is shown to Steven. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Steven can now know whether Sharon 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). Bryan's card is shown to Bryan. Harold's card is shown to Bryan. Clifford's card is shown to Bryan. Clifford's card is shown to Paul. Bryan's card is shown to Harold. Paul's card is shown to Clifford. Harold's card is shown to Clifford. It is publicly announced that someone picked a red card. It is publicly announced that Harold 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) ] Agentc knows whether (Agentd knows that (1&2&3&4))

Hypothesis: Harold can now know whether Clifford 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). Lisa's card is shown to Lisa. Grace's card is shown to Grace. Mary's card is shown to Grace. Lisa's card is shown to Mary. Lisa's card is shown to Bret. Grace's card is shown to Bret. It is publicly announced that someone picked a red card.

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

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

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


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

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

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

Hypothesis: Kelly can now know that Alice can know whether Alice picked a red card.


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

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

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

Hypothesis: Agustin can now know whether Larry can know that Jamel picked a red card.


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

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

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

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


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

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

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

Hypothesis: Laura can now know whether Robin picked a red card.


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

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

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

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


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

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

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


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

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

Hypothesis: Maureen can now know whether Amanda can know whether Harold picked a red card.


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

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

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

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


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

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

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

Hypothesis: Alton 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). Jeffery's card is shown to Jeffery. Joanne's card is shown to Joanne. Joan's card is shown to Joanne. Joanne's card is shown to Joan. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that Joan does not know whether Joan picked a red card.

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

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

Hypothesis: Joan 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). Tom's card is shown to Donald. Debra's card is shown to Shelley. Donald's card is shown to Tom. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Donald can now know whether Shelley 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). Jim's card is shown to Jim. Jim's card is shown to Carrie. Emanuel's card is shown to Carrie. Jim's card is shown to Kelly. It is publicly announced that someone picked a red card. It is publicly announced that Jim does not know whether Emanuel picked a red card. It is publicly announced that Kelly knows whether or not everyone picked a red card. It is publicly announced that Jim does not know whether Carrie picked a red card.

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

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

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


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

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

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

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


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

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

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

Hypothesis: Margaret can now know that Patrick can know that Enrique picked a red card.


Premise: There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mary's card is shown to Mary. Debra's card is shown to Debra. Dan's card is shown to Debra. Mary's card is shown to Dan. Debra's card is shown to Dan. It is publicly announced that someone picked a red card. It is publicly announced that Debra picked a black card. It is publicly announced that Mary knows whether Mary 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)) ] (Agenta knows whether (~(1|2|3)))

Hypothesis: Mary 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). Eldon's card is shown to Thelma. Matthew's card is shown to Matthew. Eldon's card is shown to Matthew. Matthew's card is shown to Eldon. Eldon's card is shown to Eldon. It is publicly announced that someone picked a red card. It is publicly announced that Eldon picked a red card. It is publicly announced that Eldon does not know whether Thelma picked a red card. It is publicly announced that Eldon 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) ] (Agentb knows whether 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: Matthew can now know whether Eldon picked a red card.


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

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

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

Hypothesis: Howard 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). Cheryl's card is shown to Cheryl. Mike's card is shown to Cheryl. Mike's card is shown to Mike. Stanley's card is shown to Mike. Anna's card is shown to Stanley. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Anna can now know that Cheryl picked a red card.


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

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

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

Hypothesis: Gary can now know whether Darlene 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). Johnny's card is shown to Buddy. Buddy's card is shown to Jaime. Jaime's card is shown to Donald. It is publicly announced that someone picked a red card. It is publicly announced that Johnny knows whether Johnny picked a red card.

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

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

Hypothesis: Johnny can now know whether Buddy can know whether Johnny picked a red card.


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

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

Hypothesis: Leonel 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). Anthony's card is shown to Kelly. Mark's card is shown to Anthony. Anthony's card is shown to Roy. It is publicly announced that someone picked a red card. It is publicly announced that Anthony does not know whether or not everyone picked a red card. It is publicly announced that Anthony does not know whether or not everyone picked a red card. It is publicly announced that Kelly does not know whether or not everyone picked a red card.

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

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

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