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

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

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

Hypothesis: Velma can now know whether Velma 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 Hailey. Hailey's card is shown to Connie. 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 that (Agentb knows that (~(1|2|3)))

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

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


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

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

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

Hypothesis: Mike can now know that Jerri picked a red card.


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

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

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

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


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

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

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

Hypothesis: Thomas 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). James's card is shown to Anna. Donald's card is shown to Donald. James's card is shown to James. It is publicly announced that someone picked a red card.

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

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

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


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

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

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

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


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

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


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

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

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

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


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

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

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

Hypothesis: Eric can now know whether Harold 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). Johnson's card is shown to Leonard. Leonard's card is shown to Phyllis. Leonard's card is shown to Johnson. Phyllis's card is shown to Johnson. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Johnson can now know that Phyllis picked a red card.


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

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

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

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


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

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

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

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


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

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

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

Hypothesis: Irene can now know that Carmen picked a red card.


Premise: There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Irving's card is shown to Irving. Irving's card is shown to Gregory. It is publicly announced that someone picked a red card. It is publicly announced that Gregory 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 that 1)

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

Hypothesis: Irving can now know that Irving 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. John's card is shown to Mack. Robert's card is shown to Mack. It is publicly announced that someone picked a red card. It is publicly announced that Mack picked a red card.

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

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

Hypothesis: John 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). Thomas's card is shown to Roland. Shirley's card is shown to Roland. Thomas's card is shown to Thomas. Roland's card is shown to Shirley. It is publicly announced that someone picked a red card. It is publicly announced that Roland knows whether Thomas picked a red card.

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

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

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


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

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

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

Hypothesis: Phyllis can now know whether Ann 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). Helen's card is shown to Helen. Robert's card is shown to Helen. Debbie's card is shown to Robert. Robert's card is shown to Debbie. It is publicly announced that someone picked a red card. It is publicly announced that Helen does not know whether or not everyone picked a red card.

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

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

Hypothesis: Helen can now know whether Debbie 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). Robert's card is shown to Robert. Beverly's card is shown to Sheila. Beverly's card is shown to Beverly. It is publicly announced that someone picked a red card. It is publicly announced that Beverly does not know whether or not everyone picked a red card.

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

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

Hypothesis: Robert 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). Ernestine's card is shown to Ernestine. Ernestine's card is shown to Janet. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Janet can now know whether Ernestine 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). Yolanda's card is shown to Yolanda. Lissette's card is shown to Yolanda. Derek's card is shown to Yolanda. Yolanda's card is shown to Lissette. Lissette's card is shown to Lissette. Yolanda's card is shown to Derek. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Alexis can now know whether Yolanda can know whether Yolanda picked a red card.


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

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

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

Hypothesis: Shane can now know whether Debra picked a red card.


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

Hypothesis: Rita can now know that Jill 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). Doreen's card is shown to Doreen. Doreen's card is shown to Carolyn. It is publicly announced that someone picked a red card. It is publicly announced that Carolyn knows whether someone picked a red card. It is publicly announced that Carolyn does not know whether Carolyn picked a red card. It is publicly announced that Carolyn does not know whether Carolyn picked a red card. It is publicly announced that Carolyn does not know whether Carolyn picked a red card.

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

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

Hypothesis: Carolyn can now know that Doreen can know that Carolyn picked a red card.


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

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

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

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


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

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

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


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

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

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

Hypothesis: Latesha 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). Marvin's card is shown to Marvin. Jennie's card is shown to Marvin. Jason's card is shown to Marvin. Jennie's card is shown to Luis. Marvin's card is shown to Jason. Jennie's card is shown to Jason. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Marvin can now know that Jennie 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). Gloria's card is shown to Gloria. Judith's card is shown to Gloria. Judith's card is shown to Judith. Brian's card is shown to Judith. Gloria's card is shown to Eric. Judith's card is shown to Eric. Gloria's card is shown to Brian. Brian's card is shown to Brian. It is publicly announced that someone picked a red card. It is publicly announced that Gloria knows whether Gloria picked a red card.

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

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

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


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

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

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

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


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

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

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

Hypothesis: Brian can now know whether Vanessa 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). Clarence's card is shown to Margo. Cecil's card is shown to Donald. Margo's card is shown to Cecil. Cecil's card is shown to Clarence. Clarence's card is shown to Clarence. It is publicly announced that someone picked a red card. It is publicly announced that Cecil does not know whether or not everyone picked a red card. It is publicly announced that Cecil picked a red card.

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

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

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


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

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

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


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

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

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

Hypothesis: David can now know whether Charles 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). Evelyn's card is shown to Evelyn. Evelyn's card is shown to Brett. Evelyn's card is shown to Nolan. It is publicly announced that someone picked a red card. It is publicly announced that Nolan does not know whether or not everyone picked a red card. It is publicly announced that Evelyn picked a red card. It is publicly announced that Brett does not know whether Brett picked a red card.

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

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

Hypothesis: Nolan can now know that Brett can know that Brett picked a red card.


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

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

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

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


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

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

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

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


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

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

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

Hypothesis: Vanessa can now know whether Ryan can know whether 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). Agnes's card is shown to Agnes. Agnes's card is shown to Arthur. Jessica's card is shown to Arthur. Agnes's card is shown to Jessica. Edward's card is shown to Jessica. Arthur's card is shown to Jessica. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Agnes can now know whether Edward picked a red card.


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

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

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

Hypothesis: Raymond can now know whether Mary 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). Homer's card is shown to Homer. Marquetta's card is shown to Marquetta. Nancy's card is shown to Elizabeth. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Marquetta can now know that Homer can know whether Marquetta picked a red card.


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

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

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

Hypothesis: Grace 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). Kai's card is shown to Carrie. Paula's card is shown to Carrie. Kai's card is shown to Kai. Pat's card is shown to Kai. Kai's card is shown to Pat. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Kai can now know that Carrie can know that Kai picked a red card.


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

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

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

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


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

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

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

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


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

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

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

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


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

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

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

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

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

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

Hypothesis: Christina 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). Dewey's card is shown to Beatrice. Dewey's card is shown to Dewey. Frances's card is shown to Dewey. Beatrice's card is shown to Frances. It is publicly announced that someone picked a red card.

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

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

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


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

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

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

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


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

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

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

Hypothesis: Ralph can now know that Nancy 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). Frances's card is shown to Frances. Frances's card is shown to Cori. Cori's card is shown to Cori. It is publicly announced that someone picked a red card. It is publicly announced that Cori knows whether Cori picked a red card.

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

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

Hypothesis: Frances can now know whether Cori can know that Frances picked a red card.


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

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

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


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

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

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

Hypothesis: Opal can now know whether Katherine can know that Opal picked a red card.


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

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

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

Hypothesis: Shari can now know whether Frank can know whether Bobbie 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 Mary. Judith's card is shown to Judith. Mary's card is shown to Gerald. It is publicly announced that someone picked a red card. It is publicly announced that Gerald knows whether Mary picked a red card.

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

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

Hypothesis: Mary can now know whether Gerald 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). Ricardo's card is shown to Maryann. Anita's card is shown to Ricardo. Maryann's card is shown to Anita. Ricardo's card is shown to Anita. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Ricardo can now know that Maryann can know that Maryann picked a red card.


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

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

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

Hypothesis: Helen can now know that Tina can know whether or not nobody picked a red card.


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

Hypothesis: Helen can now know whether Cheryl 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). Anita's card is shown to Mike. Anita's card is shown to Anita. It is publicly announced that someone picked a red card. It is publicly announced that Mike picked a red card.

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

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

Hypothesis: Anita can now know that Mike can know that Mike picked a red card.


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

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

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

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


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

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

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

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


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

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

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

Hypothesis: Michael 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). Lee's card is shown to John. John's card is shown to Lee. John's card is shown to Russell. Lee's card is shown to Russell. It is publicly announced that someone picked a red card. It is publicly announced that Russell does not know whether Russell picked a red card.

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

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

Hypothesis: John 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). Fred's card is shown to Fred. Christie's card is shown to Fred. Christie's card is shown to Christie. John's card is shown to Christie. John's card is shown to John. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Fred 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). Carroll's card is shown to Calvin. Bradley's card is shown to Carroll. Carroll's card is shown to Dustin. It is publicly announced that someone picked a red card. It is publicly announced that Carroll does not know whether or not everyone picked a red card. It is publicly announced that Carroll does not know whether or not everyone picked a red card. It is publicly announced that Calvin does not know whether or not everyone picked a red card.

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

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

Hypothesis: Dustin can now know that Carroll picked a red card.


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

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

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

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


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

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

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

Hypothesis: Ian 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). Robert's card is shown to Tammy. Tammy's card is shown to Robert. John's card is shown to Robert. Tammy's card is shown to John. John's card is shown to John. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Tammy can now know whether Robert can know whether Tammy picked a red card.


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

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

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

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


Premise: There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Diann's card is shown to Joe. Joe's card is shown to Ismael. Diann's card is shown to Ismael. Joe's card is shown to Melissa. 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) ] (Agentb 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: Ismael can now know whether Joe picked a red card.


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

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

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

Hypothesis: William can now know that Eric 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). Mildred's card is shown to Mildred. Carol's card is shown to Mildred. Mildred's card is shown to Carol. It is publicly announced that someone picked a red card. It is publicly announced that Mildred knows whether Mildred picked a red card. It is publicly announced that Carol does not know whether or not everyone picked a red card. It is publicly announced that Carol does not know whether Carol picked a red card.

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

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

Hypothesis: Carol can now know whether Mildred 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). Maurice's card is shown to John. Darryl's card is shown to Darryl. Darryl's card is shown to Lucille. It is publicly announced that someone picked a red card.

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

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

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


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

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

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

Hypothesis: Chana can now know whether James 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). Ruby's card is shown to Thomas. Thomas's card is shown to Ruby. Ruby's card is shown to Ruby. It is publicly announced that someone picked a red card. It is publicly announced that Ruby knows whether Ruby picked a red card.

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

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

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


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

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

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

Hypothesis: Will 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). Jason's card is shown to Carol. Jason's card is shown to Carmen. Carol's card is shown to Jason. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Carol 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). Terry's card is shown to Terry. Burton's card is shown to Terry. Mary's card is shown to Terry. Terry's card is shown to Burton. Burton's card is shown to Burton. Mary's card is shown to Burton. Burton's card is shown to Mary. Mary's card is shown to Mary. It is publicly announced that someone picked a red card.

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

Hypothesis: Terry 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). Jared's card is shown to Jared. Marianne's card is shown to Jared. Jared's card is shown to Marianne. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.

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

Hypothesis: Jared 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). Timothy's card is shown to Timothy. Bonita's card is shown to Timothy. Candace's card is shown to Candace. Bonita's card is shown to Bonita. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Candace can now know whether Timothy can know whether Bonita 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 Kimberly. Kimberly's card is shown to John. It is publicly announced that someone picked a red card. It is publicly announced that Kimberly does not know whether or not everyone picked a red card. It is publicly announced that John picked a black card.

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

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


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

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


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

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

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

Hypothesis: William can now know whether Doris 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). David's card is shown to Stephen. David's card is shown to David. It is publicly announced that someone picked a red card. It is publicly announced that Stephen does not know whether or not everyone picked a red card. It is publicly announced that Stephen does not know whether or not everyone picked a red card. It is publicly announced that Stephen knows whether someone picked a red card. It is publicly announced that David knows whether or not nobody picked a red card.

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

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

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


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

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

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

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


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

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

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

Hypothesis: Francine 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). Justin's card is shown to Cheryl. Robert's card is shown to Cheryl. Cheryl's card is shown to Shawn. Cheryl's card is shown to Robert. Robert's card is shown to Robert. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Justin can now know whether Cheryl can know that Shawn picked a red card.


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

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

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

Hypothesis: Grace can now know that Leroy can know whether or not nobody picked a red card.


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

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

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

Hypothesis: Marvin can now know whether 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). Marquita's card is shown to Hattie. Marquita's card is shown to Eric. Jack's card is shown to Jack. It is publicly announced that someone picked a red card.

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

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

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


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

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

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

Hypothesis: Kathleen can now know that Mary 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). Elizabeth's card is shown to Gloria. Jason's card is shown to Elizabeth. Jason's card is shown to Leah. It is publicly announced that someone picked a red card.

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

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

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


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

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

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


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

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

Hypothesis: Ruby 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). Lynn's card is shown to Christopher. Christopher's card is shown to Shelley. Shelley's card is shown to Debra. Lynn's card is shown to Debra. It is publicly announced that someone picked a red card.

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

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

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


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

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

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

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


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

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

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

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


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

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

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

Hypothesis: Yvonne 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). William's card is shown to William. William's card is shown to Anna. William's card is shown to Stephen. Stephen's card is shown to Stephen. Barbara's card is shown to Stephen. Stephen's card is shown to Barbara. It is publicly announced that someone picked a red card.

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

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

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


Premise: There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Harold's card is shown to Gary. Harold's card is shown to Frank. Harold's card is shown to Jean. Frank's card is shown to Jean. 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 whether (1|2|3|4))

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

Hypothesis: Gary 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). William's card is shown to Jan. Justina's card is shown to Justina. Justina's card is shown to Rickey. Rickey's card is shown to Rickey. 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:2,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] (Agentc knows whether 1)

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


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

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

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

Hypothesis: Drew can now know whether James can know that everyone picked a red card.


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

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

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

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


Premise: There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Courtney's card is shown to Charles. Charles's card is shown to Courtney. Courtney's card is shown to Courtney. Courtney'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 does not know whether or not everyone picked a red card.

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

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

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


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

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

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

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


Premise: There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Norman's card is shown to Derrick. Derrick's card is shown to Steven. Norman's card is shown to Steven. Steven's card is shown to Clara. Derrick's card is shown to Norman. Clara's card is shown to Norman. It is publicly announced that someone picked a red card. It is publicly announced that Norman does not know whether Norman picked a red card. It is publicly announced that Derrick knows whether or not nobody picked a red card. It is publicly announced that Clara 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 that (Agenta 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: Clara can now know that Derrick can know whether Steven picked a red card.


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

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

Hypothesis: Mellisa can now know whether Hae picked a red card.


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

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

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

Hypothesis: Shelby can now know that Walter can know that Shelby picked a red card.


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

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

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

Hypothesis: Duane can now know that Joseph 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). Michael's card is shown to Robert. Robert's card is shown to Michael. 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 Michael picked a red card.

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

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


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

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

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

Hypothesis: Keith 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). Scott's card is shown to Nina. Nina's card is shown to Nina. Nellie's card is shown to Nellie. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Scott can now know that Nina 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). Calvin's card is shown to Florine. Calvin's card is shown to Anna. It is publicly announced that someone picked a red card. It is publicly announced that Calvin does not know whether or not everyone picked a red card. It is publicly announced that Calvin does not know whether Florine picked a red card.

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

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

Hypothesis: Calvin can now know whether Florine 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). Kenneth's card is shown to Kenneth. Kenneth's card is shown to Christy. Tyrell's card is shown to Helen. Kenneth's card is shown to Tyrell. Helen's card is shown to Tyrell. It is publicly announced that someone picked a red card. It is publicly announced that Helen does not know whether or not everyone picked a red card. It is publicly announced that Kenneth picked a black card.

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

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

Hypothesis: Tyrell can now know whether Christy picked a red card.


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

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

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

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


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

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

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

Hypothesis: Lauren can now know whether Alicia can know whether Alicia picked a red card.


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

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

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

Hypothesis: Karen 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). Amanda's card is shown to Amanda. German's card is shown to Amanda. Austin's card is shown to Austin. German's card is shown to German. It is publicly announced that someone picked a red card.

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

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

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


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

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

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

Hypothesis: David can now know whether Levi 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). Patricia's card is shown to Patricia. Ashley's card is shown to Patricia. Patricia's card is shown to Ashley. Ashley's card is shown to Ashley. Patricia's card is shown to Ray. Robert's card is shown to Ray. Ray's card is shown to Robert. Robert's card is shown to Robert. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Patricia can now know whether Ashley 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). Alice's card is shown to Katherine. Angel's card is shown to Alice. Katherine's card is shown to Angel. It is publicly announced that someone picked a red card.

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

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

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


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

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

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

Hypothesis: James can now know that Jose 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). Alexander's card is shown to Alexander. Paul's card is shown to Alexander. Paul's card is shown to Paul. Raymond's card is shown to Paul. Paul's card is shown to Raymond. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Alexander can now know that Raymond can know that Alexander picked a red card.


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

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

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

Hypothesis: Mary can now know that Jay 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). Clyde's card is shown to Clyde. Carla's card is shown to Clyde. Clyde's card is shown to Kim. Kim's card is shown to Kim. Carla's card is shown to Carla. Carla's card is shown to Cora. It is publicly announced that someone picked a red card. It is publicly announced that Cora does not know whether Clyde picked a red card. It is publicly announced that Clyde knows whether or not nobody picked a red card. It is publicly announced that Carla does not know whether Cora picked a red card. It is publicly announced that Kim knows whether someone picked a red card.

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

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

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


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

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

Hypothesis: Gladys 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). Hope's card is shown to Jonathan. Jonathan's card is shown to Virginia. Ashley's card is shown to Ashley. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Jonathan can now know whether Virginia can know that Hope 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 Troy. Maria's card is shown to Daniel. It is publicly announced that someone picked a red card.

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

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

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


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

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

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

Hypothesis: Brenda can now know that 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). Catherine's card is shown to Lisa. Traci's card is shown to John. John's card is shown to Catherine. Lisa's card is shown to Traci. It is publicly announced that someone picked a red card. It is publicly announced that Traci does not know whether or not everyone picked a red card. It is publicly announced that John picked a red card.

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

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

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


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

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

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

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

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

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

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


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

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

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

Hypothesis: Susan can now know that Pauline 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). Leo's card is shown to Jill. Bruce's card is shown to Bruce. Bruce's card is shown to Leo. It is publicly announced that someone picked a red card. It is publicly announced that Leo picked a red card. It is publicly announced that Denise knows whether or not everyone picked a red card.

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

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

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

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

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

Hypothesis: Kimberly can now know whether Joseph 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). Alisa's card is shown to Alisa. Josephine's card is shown to Alisa. Alisa's card is shown to Josephine. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Alisa 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). Brandon's card is shown to Felicia. Ruth's card is shown to Felicia. Felicia's card is shown to Felicia. It is publicly announced that someone picked a red card. It is publicly announced that Brandon knows whether Ruth picked a red card. It is publicly announced that Felicia picked a black card. It is publicly announced that Brandon knows whether Brandon picked a red card.

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

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

Hypothesis: Brandon can now know whether Felicia picked a red card.


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


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

Hypothesis: Terrell can now know that Freddie picked a red card.


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

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

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

Hypothesis: Nathan can now know whether Hallie picked a red card.


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

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

Hypothesis: Gary can now know whether Russell picked a red card.


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

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

Hypothesis: Ken can now know that Mitchell can know whether or not everyone picked a red card.


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

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

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

Hypothesis: Louis can now know that Lois can know whether someone picked a red card.