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. Raymond's card is shown to Matthew. Robert's card is shown to Matthew. Raymond's card is shown to Brooke. Raymond's card is shown to Robert. Matthew's card is shown to Robert. It is publicly announced that someone picked a red card. It is publicly announced that Raymond does not know whether Robert picked a red card.

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

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

Hypothesis: Robert 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). Douglas's card is shown to Beatrice. Grace's card is shown to Grace. Grace's card is shown to Douglas. Douglas's card is shown to Douglas. Douglas's card is shown to Alan. It is publicly announced that someone picked a red card. It is publicly announced that Beatrice knows whether or not nobody picked a red card.

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

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

Hypothesis: Beatrice can now know that Grace picked a red card.


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

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

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

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


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

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

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

Hypothesis: Rosa 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). Richard's card is shown to Kathy. Kathy's card is shown to Richard. Richard's card is shown to Richard. Frankie's card is shown to Richard. Richard's card is shown to Frankie. It is publicly announced that someone picked a red card. It is publicly announced that Frankie knows whether someone picked a red card. It is publicly announced that Richard picked a black card. It is publicly announced that Richard picked a black card.

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

Hypothesis: Kathy can now know whether Frankie picked a red card.


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

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

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

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


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

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

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


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

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

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


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

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

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

Hypothesis: James 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 Betty. Mack's card is shown to Betty. Betty's card is shown to Betty. Jason's card is shown to Mark. It is publicly announced that someone picked a red card.

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

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


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

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

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

Hypothesis: Levi 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). Albert's card is shown to Richard. Cathy's card is shown to Richard. Albert's card is shown to Albert. Albert's card is shown to Cathy. It is publicly announced that someone picked a red card. It is publicly announced that Richard picked a black card. It is publicly announced that Albert knows whether or not nobody picked a red card.

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

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

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


Premise: There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). James's card is shown to James. Dwight's card is shown to James. Lela's card is shown to Dwight. 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 whether (Agentb knows that 1)

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

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


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

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

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

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


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

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

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

Hypothesis: Mary can now know whether Brandie 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). Sarah's card is shown to Pamela. Pamela's card is shown to Sarah. Sarah's card is shown to William. William's card is shown to William. It is publicly announced that someone picked a red card.

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

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

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


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

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

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


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

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

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

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


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

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

Hypothesis: William can now know that Leah can know that Dorothy picked a red card.


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

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

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

Hypothesis: Robert can now know that James 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). Stephanie's card is shown to Mary. Mary's card is shown to Stephanie. Stephanie's card is shown to Stephanie. Elisha's card is shown to Stephanie. Edna's card is shown to Stephanie. Mary's card is shown to Edna. Edna's card is shown to Edna. It is publicly announced that someone picked a red card. It is publicly announced that Elisha does not know whether or not everyone picked a red card. It is publicly announced that Elisha does not know whether Elisha picked a red card. It is publicly announced that Stephanie knows whether Stephanie picked a red card.

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

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

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

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

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

Hypothesis: Donna can now know whether Ralph can 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). Tiffany's card is shown to Berta. Tiffany's card is shown to Tiffany. Derick's card is shown to Tiffany. Tiffany's card is shown to Derick. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Tiffany can now know that Berta picked a red card.


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

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

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

Hypothesis: Gabriel 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). Kenneth's card is shown to Dwayne. William's card is shown to William. Dwayne's card is shown to Kenneth. Kenneth's card is shown to Kenneth. It is publicly announced that someone picked a red card. It is publicly announced that Kenneth knows whether Dwayne picked a red card. It is publicly announced that William does not know whether Dwayne picked a red card.

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

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

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


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

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

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

Hypothesis: Albert can now know that Gary 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). Lisa's card is shown to Lisa. Gregory's card is shown to Gregory. 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)) ] (Agenta knows whether (1|2))

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

Hypothesis: Lisa 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). Ralph's card is shown to Robert. Ralph's card is shown to Mable. Joseph's card is shown to Ralph. Mable's card is shown to Ralph. It is publicly announced that someone picked a red card.

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

Hypothesis: Mable can now know whether Robert 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). Lorenzo's card is shown to Arnold. Arnold's card is shown to Arnold. It is publicly announced that someone picked a red card. It is publicly announced that Arnold picked a black card.

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

Hypothesis: Lorenzo can now know whether Arnold picked a red card.


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

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

Hypothesis: Kristine 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). Victor's card is shown to Victor. Rebecca's card is shown to Victor. Rebecca's card is shown to Rebecca. 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:1,2 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] Agentc knows whether (Agenta knows that (1&2&3))

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

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


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

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

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

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


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

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

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

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


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

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

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

Hypothesis: Helen 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). Kathryn's card is shown to Kathryn. Felton's card is shown to Kathryn. Robert's card is shown to Robert. It is publicly announced that someone picked a red card.

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

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

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


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

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

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

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

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

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

Hypothesis: Debbie 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). Paul's card is shown to Paul. Paula's card is shown to Frances. Paul's card is shown to Sharon. Frances's card is shown to Paula. It is publicly announced that someone picked a red card. It is publicly announced that Paul does not know whether or not everyone picked a red card.

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

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

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


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

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

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

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


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

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

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

Hypothesis: Andrea 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). Crystal's card is shown to Crystal. Michael's card is shown to Nicole. Eddie's card is shown to Eddie. Nicole's card is shown to Michael. It is publicly announced that someone picked a red card.

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

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

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


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

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

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

Hypothesis: Cory 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). Jill's card is shown to Yesenia. Barbara's card is shown to Jill. Yesenia's card is shown to Barbara. It is publicly announced that someone picked a red card. It is publicly announced that Jill does not know whether Jill picked a red card.

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

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

Hypothesis: Jill can now know that Barbara 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). Delores's card is shown to Delores. Donald's card is shown to Delores. John's card is shown to Donald. Donald's card is shown to John. It is publicly announced that someone picked a red card. It is publicly announced that Delores 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)) ] Agentc knows whether (Agentb knows that (~(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: John can now know whether Donald 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). Randall's card is shown to Brian. Frances's card is shown to Brian. Brian's card is shown to Frances. It is publicly announced that someone picked a red card.

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

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

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


Premise: There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jeffrey's card is shown to Patricia. Manuel's card is shown to Manuel. Patricia's card is shown to Jeffrey. It is publicly announced that someone picked a red card. It is publicly announced that Jeffrey knows whether Patricia 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) ] Agentc knows whether (Agentb 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: Jeffrey can now know whether Manuel 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). Brad's card is shown to Brad. John's card is shown to Brad. John's card is shown to John. Mildred's card is shown to John. Duane's card is shown to Mildred. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Duane 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). Marcus's card is shown to Marcus. Nelson's card is shown to Johnny. Laura's card is shown to Johnny. Marcus's card is shown to Nelson. Nelson's card is shown to Nelson. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Nelson can now know that Marcus can know that Marcus picked a red card.


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

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

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

Hypothesis: Sara can now know that Jody can know whether or not nobody picked a red card.


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

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

Hypothesis: Judith can now know whether Robert 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). George's card is shown to Robert. Joseph's card is shown to Joseph. George's card is shown to Joseph. George's card is shown to George. It is publicly announced that someone picked a red card.

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

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

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


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

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

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

Hypothesis: Jack can now know whether Karen can know that nobody picked a red card.


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

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

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

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


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

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

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

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


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

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

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

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


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

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

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

Hypothesis: Ryan 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). Shakira's card is shown to Anna. Anna's card is shown to Dave. Dave's card is shown to Dave. Anna's card is shown to Shakira. Dave's card is shown to Rebecca. Rebecca's card is shown to Rebecca. It is publicly announced that someone picked a red card. It is publicly announced that Rebecca does not know whether Shakira picked a red card. It is publicly announced that Anna knows whether Shakira picked a red card.

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

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

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


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

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

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

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


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

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

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

Hypothesis: Randolph can now know that June picked a red card.


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

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

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

Hypothesis: Patricia can now know whether John 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). Oswaldo's card is shown to Oswaldo. Oswaldo's card is shown to Meghan. Meghan's card is shown to Meghan. Tosha's card is shown to Meghan. Oswaldo's card is shown to Tosha. 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 that 2)

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

Hypothesis: Oswaldo can now know that Meghan picked a red card.


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

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

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


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

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

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

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


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

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

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

Hypothesis: Rhoda can now know that Jerold 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). Charlotte's card is shown to Charlotte. Harry's card is shown to Susan. Bernard's card is shown to Susan. Bernard's card is shown to Bernard. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Harry can now know whether Charlotte picked a red card.


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

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

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

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


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

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

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

Hypothesis: Sandy can now know that Kerry can know that Lauren picked a red card.


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

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

Hypothesis: Ashley can now know that Joseph 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). Noel's card is shown to Bettye. Ursula's card is shown to Noel. Ursula's card is shown to Ursula. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Ursula can now know that Noel picked a red card.


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

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

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

Hypothesis: Tamara can now know whether Melinda 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). Zelma's card is shown to Paul. Paul's card is shown to Dennis. Paul's card is shown to William. It is publicly announced that someone picked a red card.

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

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


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

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

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

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


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

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

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

Hypothesis: Steven can now know that Lorraine can know whether or not nobody picked a red card.


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

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

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

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


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

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

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

Hypothesis: Clara 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). James's card is shown to Aida. Aida's card is shown to James. James's card is shown to James. It is publicly announced that someone picked a red card.

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

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

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


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

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

Hypothesis: Angie can now know that Charles can know whether Bobby picked a red card.


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

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

Hypothesis: James can now know whether Lisa 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). Cathryn's card is shown to Anne. Walter's card is shown to Walter. Cathryn's card is shown to Walter. Walter's card is shown to Tommy. Anne's card is shown to Cathryn. It is publicly announced that someone picked a red card. It is publicly announced that Walter picked a black card. It is publicly announced that Walter does not know whether Anne picked a red card. It is publicly announced that Walter knows whether someone picked a red card. It is publicly announced that Walter does not know whether Anne picked a red card.

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

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

Hypothesis: Walter can now know that Anne 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). Windy's card is shown to Windy. Aleida's card is shown to Windy. Aleida's card is shown to Aleida. Windy's card is shown to Calvin. It is publicly announced that someone picked a red card. It is publicly announced that Aleida does not know whether or not everyone picked a red card. It is publicly announced that not everyone picked a red card.

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

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

Hypothesis: Calvin 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). Marilyn's card is shown to Marilyn. Marilyn's card is shown to Michael. Michael's card is shown to Michael. Michael's card is shown to Katherine. It is publicly announced that someone picked a red card. It is publicly announced that Katherine knows whether or not nobody picked a red card.

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

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

Hypothesis: Katherine 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). Matthew's card is shown to Matthew. Terry's card is shown to Matthew. Matthew's card is shown to Jason. Terry's card is shown to Jason. Jason's card is shown to Terry. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Jason can now know that Matthew can know that Jason 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. Jesse's card is shown to Robert. Robert's card is shown to Jesse. Robert's card is shown to Hector. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Jesse can now know that Robert 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). Liza's card is shown to Robert. Gabriel's card is shown to James. Liza's card is shown to James. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Robert 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). Emma's card is shown to Emma. Chandra's card is shown to Chandra. Emma's card is shown to Zachary. Kevin's card is shown to Zachary. Kevin's card is shown to Kevin. It is publicly announced that someone picked a red card. It is publicly announced that Chandra picked a red card. It is publicly announced that Emma picked a red card. It is publicly announced that someone picked a red card.

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

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


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

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

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

Hypothesis: Amanda can now know whether Zachary 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). Amanda's card is shown to Amanda. Dolores's card is shown to Amanda. Dolores's card is shown to Dolores. Mary's card is shown to Dolores. Amanda's card is shown to Mary. Dolores'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 Agentb:2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] (Agenta knows that (1|2|3))

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

Hypothesis: Amanda 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). Dennis's card is shown to Timothy. Joy's card is shown to Timothy. Dennis's card is shown to Joy. It is publicly announced that someone picked a red card. It is publicly announced that Dennis does not know whether Timothy picked a red card.

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

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

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


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

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


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

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

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

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


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

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

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

Hypothesis: Rita can now know whether Velma 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). Jennifer's card is shown to Martha. Doug's card is shown to Martha. Jennifer's card is shown to Jennifer. Martha's card is shown to Doug. It is publicly announced that someone picked a red card. It is publicly announced that Jennifer does not know whether or not everyone picked a red card.

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

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

Hypothesis: Doug 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). Mary's card is shown to Sheila. Christa's card is shown to Christa. Clifford's card is shown to Christa. Mary's card is shown to Christa. Christa's card is shown to Clifford. Clifford's card is shown to Mary. It is publicly announced that someone picked a red card. It is publicly announced that Mary does not know whether or not everyone picked a red card.

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

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

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


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

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

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

Hypothesis: Floyd can now know that Sandra picked a red card.


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

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

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

Hypothesis: Robert can now know whether Harold 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). John's card is shown to Ralph. Ralph's card is shown to Catharine. Catharine's card is shown to Catharine. John's card is shown to Catharine. 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:3 Agentb:1,2,3 Agentc:3 VALID? [ ! (1|2|3) ] (Agenta knows that (1&2&3))

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

Hypothesis: Ralph 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). Laverne's card is shown to Penny. Laverne's card is shown to Laverne. Laverne's card is shown to Jose. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that not everyone picked a red card.

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

Hypothesis: Penny can now know whether Jose can know that Laverne 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 Scott. John's card is shown to Scott. Scott's card is shown to Mark. Scott'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:1,3 Agentb:1 Agentc:1,3 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows that (~(1|2|3)))

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

Hypothesis: Mark can now know that Scott 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). Edwin's card is shown to Jose. Gregory's card is shown to Eugene. Eugene's card is shown to Gregory. Gregory's card is shown to Edwin. It is publicly announced that someone picked a red card. It is publicly announced that Edwin does not know whether Jose picked a red card.

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

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

Hypothesis: Gregory 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). Sylvia's card is shown to Matthew. Sylvia's card is shown to Kim. Kim's card is shown to Kim. It is publicly announced that someone picked a red card. It is publicly announced that Sylvia knows whether someone picked a red card. It is publicly announced that Sylvia does not know whether or not everyone picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that Sylvia picked a red card.

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

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

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

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

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


Premise: There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Katherine's card is shown to Katherine. Howard's card is shown to Howard. 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 that (Agenta knows that (1|2))

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

Hypothesis: Howard can now know that Katherine 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). Scott's card is shown to Ingrid. Ingrid's card is shown to Donald. Donald's card is shown to Donald. Scott's card is shown to Donald. Ingrid's card is shown to Scott. It is publicly announced that someone picked a red card. It is publicly announced that Scott does not know whether or not everyone picked a red card.

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

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

Hypothesis: Donald can now know that Ingrid can know whether Scott 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 Isabel. Isabel's card is shown to Alex. Alex's card is shown to Alex. James's card is shown to Alex. Alex's card is shown to James. 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 someone picked a red card.

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

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


Premise: There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marcia's card is shown to Dorothy. Marcia's card is shown to Kenneth. Brenda's card is shown to Marcia. Dorothy's card is shown to Brenda. Marcia's card is shown to Brenda. 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 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agentc knows whether (Agentd knows whether 1)

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

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


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

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

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

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


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

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

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

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


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

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

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

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


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

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

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

Hypothesis: Nancy 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). Mike's card is shown to Joyce. Joyce's card is shown to Kathryn. Mike's card is shown to Kathryn. Joyce's card is shown to Mike. It is publicly announced that someone picked a red card. It is publicly announced that Joyce does not know whether Joyce picked a red card.

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

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

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


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

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

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

Hypothesis: David can now know that Larry 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). John's card is shown to John. John's card is shown to Heather. Heather's card is shown to Heather. It is publicly announced that someone picked a red card. It is publicly announced that John does not know whether Heather picked a red card.

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

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

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


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

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

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

Hypothesis: Malcolm can now know that Karen 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). Vanessa's card is shown to John. Carlton's card is shown to John. Carlton's card is shown to Brian. Brian's card is shown to Carlton. It is publicly announced that someone picked a red card.

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

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

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


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

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

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

Hypothesis: Jenny 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). Ronald's card is shown to Pat. Ronald's card is shown to Ronald. Ronald's card is shown to Sarah. 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) ] Agenta knows that (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: Pat can now know that Sarah 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). Melba's card is shown to Melba. Melba's card is shown to Douglas. It is publicly announced that someone picked a red card. It is publicly announced that Melba does not know whether Douglas picked a red card. It is publicly announced that Melba knows whether or not nobody picked a red card.

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

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

Hypothesis: Douglas 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). Thomas's card is shown to Randy. Sandra's card is shown to Thomas. Billy's card is shown to Billy. Randy's card is shown to Sandra. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card.

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

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


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

Hypothesis: Lisa can now know whether Tom can know whether Marie picked a red card.


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

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

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

Hypothesis: Sheree 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). Mary's card is shown to Rhonda. Mary's card is shown to Mary. It is publicly announced that someone picked a red card. It is publicly announced that Rhonda does not know whether Rhonda picked a red card.

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

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

Hypothesis: Mary can now know whether Rhonda 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). Kelley's card is shown to Kelley. Bonnie's card is shown to Kelley. Kelley's card is shown to Christine. Kelley's card is shown to Bonnie. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Kelley can now know that Bonnie picked a red card.


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

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

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

Hypothesis: Alan 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). Lamar's card is shown to Lamar. Kayla's card is shown to Kayla. Lamar's card is shown to Miriam. It is publicly announced that someone picked a red card. It is publicly announced that Miriam picked a black card.

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

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

Hypothesis: Lamar can now know whether Miriam 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). Mary's card is shown to Mary. Mary's card is shown to Edward. It is publicly announced that someone picked a red card. It is publicly announced that Mary knows whether or not nobody picked a red card.

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

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

Hypothesis: Mary can now know whether Edward 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). Arthur's card is shown to Pedro. Shirley's card is shown to Danielle. Shirley's card is shown to Shirley. Pedro's card is shown to Arthur. Danielle's card is shown to Arthur. It is publicly announced that someone picked a red card. It is publicly announced that Shirley does not know whether or not everyone picked a red card.

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

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

Hypothesis: Pedro can now know that Arthur 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). Robert's card is shown to Paul. Paul's card is shown to Robyn. Robyn's card is shown to Robyn. Paul's card is shown to John. Robyn's card is shown to John. Paul's card is shown to Robert. Robert's card is shown to Robert. It is publicly announced that someone picked a red card. It is publicly announced that Robyn picked a black card. It is publicly announced that Robyn does not know whether Robert picked a red card. It is publicly announced that not everyone picked a red card.

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

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


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

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

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

Hypothesis: Rachel can now know that Ralph can know that Rachel picked a red card.


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

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

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

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


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

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

Hypothesis: Lakisha 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). Nicole's card is shown to Nicole. Richard's card is shown to Nicole. Nicole's card is shown to Richard. It is publicly announced that someone picked a red card. It is publicly announced that Richard knows whether or not everyone picked a red card.

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

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

Hypothesis: Richard can now know whether Nicole 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). Julie's card is shown to Julie. Lisa's card is shown to Julie. Ashley's card is shown to Julie. Brian's card is shown to Ashley. Ashley's card is shown to Brian. Brian's card is shown to Brian. It is publicly announced that someone picked a red card.

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

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

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


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

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

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

Hypothesis: Mohammad 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). Floyd's card is shown to Floyd. Herbert's card is shown to Herbert. Floyd's card is shown to Edward. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Floyd can now know that Herbert 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). Dan's card is shown to Dan. Denise's card is shown to Denise. Carolyn's card is shown to Denise. Denise's card is shown to Carolyn. It is publicly announced that someone picked a red card.

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

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

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


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

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

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

Hypothesis: Myrtle can now know that 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). Julie's card is shown to Tracy. Kevin's card is shown to Kurtis. Kevin's card is shown to Kevin. Kurtis's card is shown to Julie. Kevin's card is shown to Julie. It is publicly announced that someone picked a red card. It is publicly announced that Tracy does not know whether Tracy picked a red card. It is publicly announced that Julie does not know whether Julie picked a red card.

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

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

Hypothesis: Kevin can now know that Julie 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). Crystal's card is shown to Mario. Martin's card is shown to Piedad. Mario's card is shown to Martin. Piedad's card is shown to Martin. Martin's card is shown to Martin. Crystal's card is shown to Martin. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Mario 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). Edwin's card is shown to Edwin. Christopher's card is shown to Christopher. David's card is shown to Christopher. Christopher's card is shown to David. 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 David does not know whether David picked a red card.

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

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

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


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

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

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

Hypothesis: Jose can now know that Katherine 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). William's card is shown to Jacob. Johnathan's card is shown to William. William's card is shown to Martin. It is publicly announced that someone picked a red card. It is publicly announced that Jacob does not know whether Jacob picked a red card.

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

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

Hypothesis: Jacob can now know whether Johnathan can know that Johnathan picked a red card.


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

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

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

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