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

Hypothesis: Jon 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). Stephen's card is shown to Cecilia. Benjamin's card is shown to Cecilia. Benjamin's card is shown to Stephen. Cecilia's card is shown to Benjamin. It is publicly announced that someone picked a red card. It is publicly announced that Cecilia picked a red card. It is publicly announced that Benjamin does not know whether or not everyone picked a red card. It is publicly announced that Benjamin does not know whether Stephen picked a red card.

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

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

Hypothesis: Stephen can now know that Cecilia 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). Eva's card is shown to Mildred. Savannah's card is shown to Mildred. Eva's card is shown to Savannah. Eva's card is shown to Lester. It is publicly announced that someone picked a red card. It is publicly announced that Eva does not know whether Mildred picked a red card. It is publicly announced that Savannah picked a black card.

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

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

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


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

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

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

Hypothesis: Kenneth 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). Russel's card is shown to Florence. Michael's card is shown to Michael. Michael's card is shown to Kathryn. Russel's card is shown to Kathryn. Florence's card is shown to Russel. Michael's card is shown to Russel. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Kathryn can now know whether Russel picked a red card.


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

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

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

Hypothesis: Louise can now know that Lois 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. Hazel's card is shown to James. John's card is shown to Hazel. Hazel's card is shown to Hazel. It is publicly announced that someone picked a red card. It is publicly announced that James picked a red card.

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

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

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


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

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

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

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


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

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

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

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


Premise: There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Michael's card is shown to Richard. Timothy's card is shown to Timothy. Michael's card is shown to Michael. Michael's card is shown to Dana. Dana's card is shown to Dana. It is publicly announced that someone picked a red card. It is publicly announced that Dana does not know whether Richard picked a red card. It is publicly announced that Richard does not know whether Richard 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) ] Agentc knows whether (Agentd knows whether 1)

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: Michael can now know whether Dana can know whether Richard picked a red card.


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

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

Hypothesis: Susan can now know that Joseph can know whether or not nobody picked a red card.


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

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

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

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


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

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

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

Hypothesis: Thomas 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). Thelma's card is shown to Emma. Clifton's card is shown to Clifton. Thelma's card is shown to Clifton. Thelma's card is shown to Pamela. Pamela's card is shown to Thelma. 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) ] Agentb knows that (Agentd knows whether 1)

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: Clifton can now know that Thelma can know whether Emma picked a red card.


Premise: There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Linda's card is shown to Evelyn. Kenneth's card is shown to Evelyn. Linda's card is shown to Linda. Kenneth's card is shown to Linda. Kenneth's card is shown to Kenneth. Lisa's card is shown to Kenneth. Lisa's card is shown to Lisa. 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 everyone picked a red card.

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


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

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

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

Hypothesis: Sharon 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). Ladonna's card is shown to Pedro. Pedro's card is shown to Ladonna. Harry's card is shown to Ladonna. Pedro's card is shown to Harry. It is publicly announced that someone picked a red card.

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

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

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


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

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

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

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


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

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

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

Hypothesis: Enid can now know whether John can know whether Enid picked a red card.


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

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

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

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


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

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

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

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


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

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

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

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


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

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

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

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


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

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

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

Hypothesis: Norene can now know whether Rose can know whether Rose picked a red card.


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

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

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

Hypothesis: Vivian can now know whether Thomas 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). Gregory's card is shown to George. Judy's card is shown to George. Magnolia's card is shown to George. Magnolia's card is shown to Magnolia. 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:2,3,4 Agentb:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (Agentb knows whether 4)

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

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


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

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

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

Hypothesis: Kathleen can now know that 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). Casey's card is shown to Edith. Michael's card is shown to Edith. Edith's card is shown to Michael. Edith's card is shown to John. Casey's card is shown to John. Michael's card is shown to John. John's card is shown to John. It is publicly announced that someone picked a red card. It is publicly announced that Edith does not know whether or not everyone picked a red card.

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

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

Hypothesis: Edith 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). Denise's card is shown to Sierra. Denise's card is shown to Tracey. Tracey's card is shown to Tracey. Dianna's card is shown to Tracey. Dianna's card is shown to Dianna. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Denise can now know that Sierra can know that Denise 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 Jeffrey. Sheryl's card is shown to Kerry. Kerry's card is shown to Sheryl. Sheryl's card is shown to Sheryl. It is publicly announced that someone picked a red card. It is publicly announced that Jeffrey knows whether someone picked a red card.

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

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

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


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

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

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

Hypothesis: Kimberly 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). Olivia's card is shown to Olivia. Michael's card is shown to Olivia. Olivia's card is shown to Wanda. Michael's card is shown to Wanda. Wanda's card is shown to Leona. Leona's card is shown to Leona. Wanda's card is shown to Michael. It is publicly announced that someone picked a red card. It is publicly announced that Wanda knows whether or not nobody picked a red card.

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

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

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


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

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

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


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

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

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

Hypothesis: Kim 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). Annie's card is shown to Annie. Barbara's card is shown to Annie. Douglas's card is shown to Apryl. Apryl's card is shown to Douglas. Barbara's card is shown to Barbara. It is publicly announced that someone picked a red card. It is publicly announced that Annie does not know whether Douglas picked a red card.

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

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

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


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

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

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

Hypothesis: Priscilla can now know whether Carey can know that Carey 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 Willis. Mary's card is shown to Willis. Mary's card is shown to Elaine. Willis's card is shown to Patrick. Mary's card is shown to Mary. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Patrick 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). Eric's card is shown to Alexander. Alexander's card is shown to Alexander. Jose's card is shown to Melody. Eric's card is shown to Jose. Alexander's card is shown to Jose. Melody's card is shown to Jose. It is publicly announced that someone picked a red card.

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

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

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


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

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

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

Hypothesis: James can now know whether Ashley can know that Ashley 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 Timothy. Timothy's card is shown to Jeffrey. Daniel's card is shown to Jeffrey. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.

Hypothesis: Timothy 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). Mae's card is shown to Ruben. Mae's card is shown to Mae. Amelia's card is shown to Amelia. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Mae can now know that Alan picked a red card.


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

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

Hypothesis: Katherine can now know that Robert can know that Katherine 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 Joslyn. Joslyn's card is shown to Catherine. Catherine's card is shown to Catherine. David's card is shown to Catherine. Catherine's card is shown to David. David's card is shown to David. It is publicly announced that someone picked a red card. It is publicly announced that Joslyn 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)) ] Agenta knows that (Agentc 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: Joslyn can now know that David 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). Florence's card is shown to Florence. Joycelyn's card is shown to Florence. Florence's card is shown to Brittany. James's card is shown to Joycelyn. James's card is shown to James. It is publicly announced that someone picked a red card.

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

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

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


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

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

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

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


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

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

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

Hypothesis: Philip 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). John's card is shown to John. Bertha's card is shown to James. It is publicly announced that someone picked a red card.

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

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

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


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

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

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

Hypothesis: Bradley 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). Lucy's card is shown to Kimberly. Todd's card is shown to Lucy. Kimberly's card is shown to Todd. Louise's card is shown to Todd. Kimberly's card is shown to Louise. 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) ] Agenta knows whether (Agentb knows whether (1|2|3|4))

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

Hypothesis: Kimberly can now know whether Lucy can know whether someone picked a red card.


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

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

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

Hypothesis: Austin can now know whether Miles can know that Miles picked a red card.


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

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

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

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


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

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

Hypothesis: Angela can now know whether Susie 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). Janet's card is shown to Janet. Scott's card is shown to Scott. Mary's card is shown to Mary. It is publicly announced that someone picked a red card. It is publicly announced that Mary does not know whether Janet picked a red card. It is publicly announced that Scott picked a black card.

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

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

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


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

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

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

Hypothesis: George can now know that Robert can know whether or not everyone picked a red card.


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

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

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

Hypothesis: Eugenia can now know whether Erik picked a red card.


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

Hypothesis: Marie can now know that Tonya picked a red card.


Premise: There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Caroline's card is shown to Caroline. Caroline's card is shown to Tatiana. Caroline's card is shown to Elinor. 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 whether (~(1|2|3)))

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

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


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

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

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

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


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

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

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

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


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

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

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

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


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

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

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

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


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

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

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

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


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

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

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

Hypothesis: Carmen can now know whether Judy 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). Jennifer's card is shown to Jennifer. Angelita's card is shown to Angelita. Isela's card is shown to Angelita. Jennifer's card is shown to Isela. Angelita's card is shown to Isela. It is publicly announced that someone picked a red card. It is publicly announced that Angelita picked a black card. It is publicly announced that Jennifer knows whether Jennifer 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)) ] (Agentc knows that (1&2&3))

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


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

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

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

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


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

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

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

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


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

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

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

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


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

Hypothesis: Teodoro 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). Gregory's card is shown to Robert. Linda's card is shown to Linda. Gregory's card is shown to Linda. Linda's card is shown to Mark. Mark's card is shown to Mark. Gregory's card is shown to Gregory. It is publicly announced that someone picked a red card.

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

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

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


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

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

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


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

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

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


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

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

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

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


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

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

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

Hypothesis: Christine can now know that Lois 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). Claude's card is shown to Claude. Jeff's card is shown to Mae. Mae's card is shown to Jeff. Jeff's card is shown to Jeff. It is publicly announced that someone picked a red card.

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

Hypothesis: Claude 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). Ethel's card is shown to Nancy. Martha's card is shown to Martha. Nancy's card is shown to Ethel. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card.

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

Hypothesis: Martha 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). Donald's card is shown to Corey. Michael's card is shown to Donald. Michael's card is shown to Christine. It is publicly announced that someone picked a red card. It is publicly announced that Michael knows whether or not nobody picked a red card. It is publicly announced that Donald picked a red card.

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

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

Hypothesis: Corey 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). Susanna's card is shown to David. Donald's card is shown to David. Patrick's card is shown to Susanna. David's card is shown to Susanna. Donald's card is shown to Donald. It is publicly announced that someone picked a red card.

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

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

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


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

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

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

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


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

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

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

Hypothesis: Connie 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). Harrison's card is shown to Harrison. Anne's card is shown to Anne. Harrison's card is shown to Miguel. Anne's card is shown to Miguel. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Anne can now know whether Harrison 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). Willie's card is shown to Willie. Ruby's card is shown to Willie. Willie's card is shown to Rick. Arlene's card is shown to Ruby. Arlene's card is shown to Arlene. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Rick can now know whether Willie 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). Bernard's card is shown to Paul. Paul's card is shown to Bernard. It is publicly announced that someone picked a red card. It is publicly announced that Bernard does not know whether Bernard picked a red card.

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

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

Hypothesis: Bernard can now know whether Paul can know whether someone picked a red card.


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

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

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

Hypothesis: Amy 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). Viola's card is shown to Barbara. Kristel's card is shown to Kristel. It is publicly announced that someone picked a red card.

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

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

Hypothesis: John 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). Maude's card is shown to Maude. Maude's card is shown to Pamela. Bertram's card is shown to Pamela. Maude's card is shown to Gregory. It is publicly announced that someone picked a red card. It is publicly announced that Maude does not know whether Bertram picked a red card. It is publicly announced that Gregory knows whether or not everyone picked a red card. It is publicly announced that Maude does not know whether Pamela 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) ] Agentb knows that (Agentc knows that 3)

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: Pamela can now know that Gregory can know that Gregory picked a red card.


Premise: There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Phyllis's card is shown to William. Krystal's card is shown to Krystal. Phyllis's card is shown to Krystal. Krystal's card is shown to Phyllis. Phyllis's card is shown to Phyllis. 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) ] Agenta knows that (Agentb knows whether (1|2|3))

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

Hypothesis: William can now know that Krystal 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). Gerri's card is shown to Gerri. Gary's card is shown to Gerri. Gerri's card is shown to Wanita. Gerri's card is shown to Gary. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Gerri 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). Violet's card is shown to David. David's card is shown to Joseph. Violet's card is shown to Joseph. Joseph's card is shown to Velma. David's card is shown to Violet. Velma's card is shown to Violet. It is publicly announced that someone picked a red card. It is publicly announced that Violet does not know whether Violet picked a red card. It is publicly announced that David knows whether or not nobody picked a red card. It is publicly announced that Velma picked a black card.

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

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

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


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

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

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

Hypothesis: Charles can now know that Charles 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 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 or not everyone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Patricia does not know whether Douglas picked a red card.

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

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

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


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

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

Hypothesis: Peggy can now know that Peggy 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 Clarence. Gertrude's card is shown to Barbara. Barbara's card is shown to Gertrude. It is publicly announced that someone picked a red card. It is publicly announced that Barbara does not know whether Alice picked a red card.

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

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

Hypothesis: Barbara can now know whether Clarence can know that 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). Andrea's card is shown to Andrea. Yesenia's card is shown to Andrea. Yesenia's card is shown to Yesenia. Robert's card is shown to Yesenia. Evelyn's card is shown to Robert. Yesenia's card is shown to Evelyn. It is publicly announced that someone picked a red card.

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

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

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


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

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

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

Hypothesis: Latasha can now know whether Alice 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). Mary's card is shown to Angelica. Troy's card is shown to Angelica. Angelica's card is shown to Mary. Troy's card is shown to Mary. Mary's card is shown to Troy. It is publicly announced that someone picked a red card. It is publicly announced that Angelica does not know whether or not everyone picked a red card.

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

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

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


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

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

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

Hypothesis: Clifton can now know whether Matilda picked a red card.


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

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

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

Hypothesis: Cecil can now know that Jason 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). Daniel's card is shown to Dalton. Dalton's card is shown to Daniel. Daniel's card is shown to Daniel. It is publicly announced that someone picked a red card. It is publicly announced that Daniel knows whether or not everyone picked a red card.

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

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

Hypothesis: Dalton 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). Estela's card is shown to Fran. Crystal's card is shown to Fran. Fran's card is shown to Donald. Donald's card is shown to Estela. Estela's card is shown to Estela. Donald's card is shown to Crystal. Estela's card is shown to Crystal. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Crystal 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). Dorothy's card is shown to Theresa. William's card is shown to Theresa. Dorothy's card is shown to Dorothy. Dorothy's card is shown to William. It is publicly announced that someone picked a red card. It is publicly announced that Dorothy does not know whether Theresa picked a red card.

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

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

Hypothesis: William can now know whether Theresa can 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). Jesus's card is shown to Darryl. Paula's card is shown to Brenda. Jesus's card is shown to Paula. Paula's card is shown to Paula. It is publicly announced that someone picked a red card.

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

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

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


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

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

Hypothesis: Robert can now know whether Lane 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). Marlene's card is shown to Marlene. James's card is shown to Marlene. Betsy's card is shown to Woodrow. Woodrow's card is shown to James. It is publicly announced that someone 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 (Agenta knows whether 4)

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

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


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

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

Hypothesis: Stuart can now know whether Micheal 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). Lula's card is shown to Lula. Anthony's card is shown to Lula. Anthony's card is shown to Anthony. It is publicly announced that someone picked a red card. It is publicly announced that Anthony does not know whether Lula 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.

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

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

Hypothesis: Lula 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). Alan's card is shown to Alan. Margaret's card is shown to Alan. Alan's card is shown to Hazel. Hazel's card is shown to Hazel. Margaret's card is shown to Hazel. Alan's card is shown to Margaret. It is publicly announced that someone picked a red card. It is publicly announced that Hazel knows whether or not nobody picked a red card. It is publicly announced that Alan does not know whether Hazel 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) ] (Agentc knows that 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: Margaret can now know that Margaret picked a red card.


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

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

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

Hypothesis: Judy can now know whether Frank can know that Judy 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 Catherine. James's card is shown to James. Catherine's card is shown to Susan. James's card is shown to Howard. It is publicly announced that someone picked a red card.

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

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

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


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

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

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

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


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

Hypothesis: Antone can now know whether Tiffany 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). Andres's card is shown to Andres. Andres's card is shown to James. Andres's card is shown to Timothy. James's card is shown to Timothy. Timothy's card is shown to Timothy. It is publicly announced that someone picked a red card.

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

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

Hypothesis: James can now know whether Andres 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 Ramon. Kevin's card is shown to Paul. Ramon's card is shown to Kevin. Kevin's card is shown to Kevin. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card.

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

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


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

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

Hypothesis: Ryan can now know that Amber 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). Maria's card is shown to Maria. Percy's card is shown to Maria. Maria's card is shown to Dexter. Percy's card is shown to Dexter. Maria's card is shown to Percy. Dexter's card is shown to Percy. 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 Maria picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Dexter knows whether Percy picked a red card.

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

Hypothesis: Maria can now know whether Percy picked a red card.


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

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

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

Hypothesis: Conrad can now know whether Amy 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 Emmett. Christopher's card is shown to Michele. Christopher's card is shown to Christopher. Catherine's card is shown to Catherine. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Michele can now know that Emmett can know whether or not nobody picked a red card.


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

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

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

Hypothesis: Elvin 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). Pamela's card is shown to Pamela. Walter's card is shown to Walter. Leon's card is shown to Walter. Walter's card is shown to Leon. Leon's card is shown to Leon. It is publicly announced that someone picked a red card. It is publicly announced that Pamela does not know whether Walter picked a red card. It is publicly announced that Leon knows whether Walter picked a red card.

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

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

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


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

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

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

Hypothesis: Roberta can now know that Jonathan picked a red card.


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

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

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

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


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

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

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

Hypothesis: Jennie can now know that Tiffany 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). Janet's card is shown to Janet. Janet's card is shown to Tuyet. Tuyet's card is shown to Tuyet. Janet's card is shown to Julianne. Julianne's card is shown to Julianne. It is publicly announced that someone picked a red card. It is publicly announced that Janet does not know whether Tuyet picked a red card. It is publicly announced that Tuyet 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 Agentb:1,2 Agentc:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (1|2|3|4) ] Agentb knows that (Agentc knows that (~(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 2) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (1|2|3|4) ] 0

Hypothesis: Tuyet can now know that Jo 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). Joseph's card is shown to Joseph. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Joseph 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). Nina's card is shown to Nina. David's card is shown to Nina. David's card is shown to Colleen. Nina's card is shown to David. Connie's card is shown to David. Connie's card is shown to Connie. It is publicly announced that someone picked a red card.

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

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

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


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

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

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

Hypothesis: Doris 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). Eric's card is shown to Elias. Elias's card is shown to Elias. Eric's card is shown to Matthew. Elias's card is shown to Matthew. Matthew's card is shown to Matthew. It is publicly announced that someone picked a red card. It is publicly announced that Eric does not know whether Matthew picked a red card.

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

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

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


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

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

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

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


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

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

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

Hypothesis: George can now know whether Valerie 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). Yvonne's card is shown to Sharon. Leonard's card is shown to Carl. Sharon's card is shown to Yvonne. 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) ] Agentc knows whether (Agenta knows that (~(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: Carl can now know whether Leonard 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). Ida's card is shown to Ida. Donald's card is shown to Ida. Timothy's card is shown to Jeanette. Ida's card is shown to Jeanette. Donald's card is shown to Donald. It is publicly announced that someone picked a red card. It is publicly announced that Ida does not know whether Donald picked a red card.

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

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

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


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

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

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

Hypothesis: Dave 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). Vicky's card is shown to Vicky. Jacquelyn's card is shown to Vicky. Arthur's card is shown to Vicky. Jacquelyn's card is shown to Jacquelyn. Robert's card is shown to Jacquelyn. Arthur's card is shown to Arthur. Robert's card is shown to Arthur. Jacquelyn's card is shown to Robert. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Arthur can now know that Jacquelyn picked a red card.


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

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

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

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


Premise: There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rosemary's card is shown to Jose. Jose's card is shown to Rosemary. Rosemary's card is shown to Rosemary. Hershel's card is shown to Rosemary. Rosemary's card is shown to Hershel. Dewayne's card is shown to Dewayne. It is publicly announced that someone picked a red card. It is publicly announced that Dewayne 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:1,2,3 Agentc:2 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! ~(1) ] (Agenta knows whether (1&2&3&4))

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


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

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

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

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


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

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

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

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


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

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

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

Hypothesis: Guadalupe can now know that Mary 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). Victoria's card is shown to Kenneth. Gregory's card is shown to Kenneth. Frank's card is shown to Victoria. Frank's card is shown to Gregory. Kenneth's card is shown to Frank. Victoria's card is shown to Frank. It is publicly announced that someone picked a red card. It is publicly announced that Frank picked a red card.

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

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

Hypothesis: Kenneth can now know whether Gregory can know that Frank 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 Brandon. Christopher's card is shown to Brandon. Christopher's card is shown to John. Christopher's card is shown to Orlando. It is publicly announced that someone picked a red card. It is publicly announced that Orlando does not know whether Brandon picked a red card.

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

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

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


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

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

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

Hypothesis: Lynn can now know whether Kevin 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). Shawn's card is shown to Robert. Robert's card is shown to Shawn. Anthony's card is shown to Anthony. It is publicly announced that someone picked a red card.

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

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

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


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

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

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

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