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All kids are young. All toddlers are kids. If someone is young, then they are not elderly. All pirates are seafarers. If Nancy is not a pirate, then Nancy is young. If Nancy is not a toddler, then Nancy is a seafarer.

∀x (Kid(x) → Young(x)) ∀x (Toddler(x) → Kid(x)) ∀x (Young(x) → ¬Elderly(x)) ∀x (Pirate(x) → Seafarer(x)) ¬Pirate(nancy) → Young(nancy) ¬Toddler(nancy) → Seafarer(nancy)

If Nancy is not either a pirate or a toddler, then she is young and is a kid.

¬(Pirate(nancy) ⊕ Toddler(nancy)) → Young(nancy) ∧ Kid(nancy)

True

Lana Wilson directed After Tiller, The Departure, and Miss Americana. If a film is directed by a person, the person is a filmmaker. After Tiller is a documentary. The documentary is a type of film. Lana Wilson is from Kirkland. Kirkland is a US city. If a person is from a city in a country, the person is from the country. After Tiller is nominated for the Independent Spirit Award for Best Documentary.

DirectedBy(afterTiller, lanaWilson) ∧ DirectedBy(theDeparture, lanaWilson) ∧ DirectedBy(missAmericana, lanaWilson) ∀x ∀y (DirectedBy(x, y) → Filmmaker(y)) Documentary(afterTiller) ∀x (Documentary(x) → Film(x)) From(lanaWilson, kirkland) In(kirkland, unitedStates) ∀x ∀y ∀z ((From(x, y) ∧ In(y, z)) → From(x, z)) Nomination(afterTiller, theIndependentSpiritAwardForBestDocumentary)

Lana Wilson is a US filmmaker.

From(lanaWilson, unitedStates) ∧ Filmmaker(lanaWilson)

True

Lana Wilson directed After Tiller, The Departure, and Miss Americana. If a film is directed by a person, the person is a filmmaker. After Tiller is a documentary. The documentary is a type of film. Lana Wilson is from Kirkland. Kirkland is a US city. If a person is from a city in a country, the person is from the country. After Tiller is nominated for the Independent Spirit Award for Best Documentary.

DirectedBy(afterTiller, lanaWilson) ∧ DirectedBy(theDeparture, lanaWilson) ∧ DirectedBy(missAmericana, lanaWilson) ∀x ∀y (DirectedBy(x, y) → Filmmaker(y)) Documentary(afterTiller) ∀x (Documentary(x) → Film(x)) From(lanaWilson, kirkland) In(kirkland, unitedStates) ∀x ∀y ∀z ((From(x, y) ∧ In(y, z)) → From(x, z)) Nomination(afterTiller, theIndependentSpiritAwardForBestDocumentary)

Miss Americana is not directed by a filmmaker from Kirkland.

¬∃x(Filmmaker(x) ∧ From(x, kirkland) ∧ DirectedBy(missAmericana, x))

False

Lana Wilson directed After Tiller, The Departure, and Miss Americana. If a film is directed by a person, the person is a filmmaker. After Tiller is a documentary. The documentary is a type of film. Lana Wilson is from Kirkland. Kirkland is a US city. If a person is from a city in a country, the person is from the country. After Tiller is nominated for the Independent Spirit Award for Best Documentary.

DirectedBy(afterTiller, lanaWilson) ∧ DirectedBy(theDeparture, lanaWilson) ∧ DirectedBy(missAmericana, lanaWilson) ∀x ∀y (DirectedBy(x, y) → Filmmaker(y)) Documentary(afterTiller) ∀x (Documentary(x) → Film(x)) From(lanaWilson, kirkland) In(kirkland, unitedStates) ∀x ∀y ∀z ((From(x, y) ∧ In(y, z)) → From(x, z)) Nomination(afterTiller, theIndependentSpiritAwardForBestDocumentary)

Lana Wilson has won the Independent Spirit Award.

FilmmakerAward(lanaWilson, theIndependentSpiritAwardForBestDocumentary)

Uncertain

All bears in zoos are not wild. Some bears are in zoos.

∀x ((Bear(x) ∧ In(x, zoo)) → ¬Wild(x)) ∃x ∃y (Bear(x) ∧ Bear(y) ∧ In(x, zoo) ∧ In(y, zoo) ∧ ¬(x=y))

Not all bears are wild.

∃x (Bear(x) ∧ ¬Wild(x))

True

If a person is the leader of a country for life, that person has power. Leaders of a country for life are either a king or a queen. Queens are female. Kings are male. Elizabeth is a queen. Elizabeth is a leader of a country for life.

∀x (Leader(x) → HavePower(x)) ∀x (Leader(x) → (King(x) ⊕ Queen(x))) ∀x (Queen(x) → Female(x)) ∀x (King(x) → Male(x)) Queen(elizabeth) Leader(elizabeth)

Elizabeth is a king.

King(elizabeth)

False

If a person is the leader of a country for life, that person has power. Leaders of a country for life are either a king or a queen. Queens are female. Kings are male. Elizabeth is a queen. Elizabeth is a leader of a country for life.

∀x (Leader(x) → HavePower(x)) ∀x (Leader(x) → (King(x) ⊕ Queen(x))) ∀x (Queen(x) → Female(x)) ∀x (King(x) → Male(x)) Queen(elizabeth) Leader(elizabeth)

Elizabeth has power.

HavePower(elizabeth)

True

If a person is the leader of a country for life, that person has power. Leaders of a country for life are either a king or a queen. Queens are female. Kings are male. Elizabeth is a queen. Elizabeth is a leader of a country for life.

∀x (Leader(x) → HavePower(x)) ∀x (Leader(x) → (King(x) ⊕ Queen(x))) ∀x (Queen(x) → Female(x)) ∀x (King(x) → Male(x)) Queen(elizabeth) Leader(elizabeth)

Elizabeth is a leader of a country for life.

Leader(elizabeth)

True

All people who went to Clay's school and who make their own matcha teas every morning with ceremonial-grade matcha powder do not wake up late and start their schedules past noon regularly. All people who went to Clay's school, who live in California, and attend yoga classes regularly, make their own matcha teas every morning with ceremonial-grade matcha powder. All people who went to Clay's school, and work in the entertainment industry as high-profile celebrities, wake up late and start their schedules past noon regularly. All people who went to Clay's school that do not have regular 9-5 jobs, work in the entertainment industry as high-profile celebrities. All people who went to Clay's school and prefer working at home over going to the office daily do not have regular 9-5 jobs. Bunny went to Clay's school, and she either prefers to work at home over going to the office and makes her own matcha teas every morning with ceremonial-grade matcha powder, or does not prefer to work at home over going to the office every day and does not make her own matcha teas every morning with ceremonial-grade matcha powder.

∀x (GoTo(x, claysSchool) ∧ MakeWith(x, theirOwnMatchTea, ceremonialGradePowder) → ¬(WakeUpLate(x) ∧ StartPastNoonRegularly(x, schedule))) ∀x (GoTo(x, claysSchool) ∧ LiveIn(x, california) ∧ AttendRegularly(x, yogaClass) → MakeWith(x, ownMatch, ceremonialGradePowder)) ∀x (GoTo(x, claysSchool) ∧ WorkInAs(x, entertainmentIndustry, highProfileCelebrity) → (WakeUpLate(x) ∧ StartPastNoonRegularly(x, schedule))) ∀x (GoTo(x, claysSchool) ∧ ¬(Have(x, y) ∧ Regular(y) ∧ NineToFiveJob(y)) → WorkInAs(x, entertainmentIndustry, highProfileCelebrity)) ∀x (GoTo(x, claysSchool) ∧ Prefer(x, workingAtHome, goingToTheOffice) → ¬(Have(x, y) ∧ Regular(y) ∧ NineToFiveJob(y))) GoTo(bunny, claysSchool) ∧ ¬(Prefer(bunny, workingAtHome, goingToTheOffice) ⊕ MakeWith(bunny, theirOwnMatchTea, ceremonialGradePowder))

Bunny does not have a regular 9-5 job.

Have(bunny, y) ∧ Regular(y) ∧ NineToFiveJob(y)

Uncertain

All people who went to Clay's school and who make their own matcha teas every morning with ceremonial-grade matcha powder do not wake up late and start their schedules past noon regularly. All people who went to Clay's school, who live in California, and attend yoga classes regularly, make their own matcha teas every morning with ceremonial-grade matcha powder. All people who went to Clay's school, and work in the entertainment industry as high-profile celebrities, wake up late and start their schedules past noon regularly. All people who went to Clay's school that do not have regular 9-5 jobs, work in the entertainment industry as high-profile celebrities. All people who went to Clay's school and prefer working at home over going to the office daily do not have regular 9-5 jobs. Bunny went to Clay's school, and she either prefers to work at home over going to the office and makes her own matcha teas every morning with ceremonial-grade matcha powder, or does not prefer to work at home over going to the office every day and does not make her own matcha teas every morning with ceremonial-grade matcha powder.

∀x (GoTo(x, claysSchool) ∧ MakeWith(x, theirOwnMatchTea, ceremonialGradePowder) → ¬(WakeUpLate(x) ∧ StartPastNoonRegularly(x, schedule))) ∀x (GoTo(x, claysSchool) ∧ LiveIn(x, california) ∧ AttendRegularly(x, yogaClass) → MakeWith(x, ownMatch, ceremonialGradePowder)) ∀x (GoTo(x, claysSchool) ∧ WorkInAs(x, entertainmentIndustry, highProfileCelebrity) → (WakeUpLate(x) ∧ StartPastNoonRegularly(x, schedule))) ∀x (GoTo(x, claysSchool) ∧ ¬(Have(x, y) ∧ Regular(y) ∧ NineToFiveJob(y)) → WorkInAs(x, entertainmentIndustry, highProfileCelebrity)) ∀x (GoTo(x, claysSchool) ∧ Prefer(x, workingAtHome, goingToTheOffice) → ¬(Have(x, y) ∧ Regular(y) ∧ NineToFiveJob(y))) GoTo(bunny, claysSchool) ∧ ¬(Prefer(bunny, workingAtHome, goingToTheOffice) ⊕ MakeWith(bunny, theirOwnMatchTea, ceremonialGradePowder))

Bunny went to Clay's school and she lives in California and attends yoga classes regularly.

LiveIn(bunny, california) ∧ AttendRegularly(bunny, yogaClass)

False

All people who went to Clay's school and who make their own matcha teas every morning with ceremonial-grade matcha powder do not wake up late and start their schedules past noon regularly. All people who went to Clay's school, who live in California, and attend yoga classes regularly, make their own matcha teas every morning with ceremonial-grade matcha powder. All people who went to Clay's school, and work in the entertainment industry as high-profile celebrities, wake up late and start their schedules past noon regularly. All people who went to Clay's school that do not have regular 9-5 jobs, work in the entertainment industry as high-profile celebrities. All people who went to Clay's school and prefer working at home over going to the office daily do not have regular 9-5 jobs. Bunny went to Clay's school, and she either prefers to work at home over going to the office and makes her own matcha teas every morning with ceremonial-grade matcha powder, or does not prefer to work at home over going to the office every day and does not make her own matcha teas every morning with ceremonial-grade matcha powder.

∀x (GoTo(x, claysSchool) ∧ MakeWith(x, theirOwnMatchTea, ceremonialGradePowder) → ¬(WakeUpLate(x) ∧ StartPastNoonRegularly(x, schedule))) ∀x (GoTo(x, claysSchool) ∧ LiveIn(x, california) ∧ AttendRegularly(x, yogaClass) → MakeWith(x, ownMatch, ceremonialGradePowder)) ∀x (GoTo(x, claysSchool) ∧ WorkInAs(x, entertainmentIndustry, highProfileCelebrity) → (WakeUpLate(x) ∧ StartPastNoonRegularly(x, schedule))) ∀x (GoTo(x, claysSchool) ∧ ¬(Have(x, y) ∧ Regular(y) ∧ NineToFiveJob(y)) → WorkInAs(x, entertainmentIndustry, highProfileCelebrity)) ∀x (GoTo(x, claysSchool) ∧ Prefer(x, workingAtHome, goingToTheOffice) → ¬(Have(x, y) ∧ Regular(y) ∧ NineToFiveJob(y))) GoTo(bunny, claysSchool) ∧ ¬(Prefer(bunny, workingAtHome, goingToTheOffice) ⊕ MakeWith(bunny, theirOwnMatchTea, ceremonialGradePowder))

Bunny went to Clay's school and she neither prefers working at home over going to the office nor lives in California and attends yoga classes regularly.

¬(Prefer(bunny, workingAtHome, goingToTheOffice) ∨ (LiveIn(bunny, california) ∧ AttendRegularly(bunny, yogaClass)))

True

Thomas Barber was an English professional footballer. Thomas Barber played in the Football League for Aston Villa. Thomas Barber played as a halfback and inside left. Thomas Barber scored the winning goal in the 1913 FA Cup Final.

English(thomasBarber) ∧ ProfessionalFootballer(thomasBarber) PlayedFor(thomasBarber, astonVilla) ∧ PlayedIn(astonVilla,theFootballLeague) PlayedAs(thomasBarber, halfBack) ∧ PlayedAs(thomasBarber, insideLeft) ScoredTheWinningGoalIn(thomasBarber, facupfinal1913)

Thomas Barber played in the Football League for Bolton Wanderers

PlayedFor(thomasBarber, boltonWanderers) ∧ PlayedIn(boltonWanderers,theFootballLeague)

Uncertain

Thomas Barber was an English professional footballer. Thomas Barber played in the Football League for Aston Villa. Thomas Barber played as a halfback and inside left. Thomas Barber scored the winning goal in the 1913 FA Cup Final.

English(thomasBarber) ∧ ProfessionalFootballer(thomasBarber) PlayedFor(thomasBarber, astonVilla) ∧ PlayedIn(astonVilla,theFootballLeague) PlayedAs(thomasBarber, halfBack) ∧ PlayedAs(thomasBarber, insideLeft) ScoredTheWinningGoalIn(thomasBarber, facupfinal1913)

Thomas Barber played as an inside left.

PlayedAs(thomasBarber, insideLeft)

True

Thomas Barber was an English professional footballer. Thomas Barber played in the Football League for Aston Villa. Thomas Barber played as a halfback and inside left. Thomas Barber scored the winning goal in the 1913 FA Cup Final.

English(thomasBarber) ∧ ProfessionalFootballer(thomasBarber) PlayedFor(thomasBarber, astonVilla) ∧ PlayedIn(astonVilla,theFootballLeague) PlayedAs(thomasBarber, halfBack) ∧ PlayedAs(thomasBarber, insideLeft) ScoredTheWinningGoalIn(thomasBarber, facupfinal1913)

An English professional footballer scored the winning goal in the 1913 FA Cup Final.

∃x (English(x) ∧ ProfessionalFootballer(x) ∧ ScoredTheWinningGoalIn(x, facupfinal1913))

True

If a person plays an instrument in a concert, they are good at playing this kind of instrument. Peter plays piano, violin, and saxophone. Peter plays piano in a concert. Oliver and Peter both play instruments in a concert. Oliver plays a different musical instrument from Peter in the concert.

∀x ∀y (PlayIn(y, x, concert) → GoodAtPlaying(y, x)) Play(peter, piano) ∧ Play(peter, violin) ∧ Play(peter, saxophone) PlayIn(peter, piano, concert) ∃x ∃y (PlayIn(peter, x, concert) ∧ PlayIn(oliver, y, concert)) ∀x (PlayIn(oliver, x, concert) → ¬PlayIn(peter, y, concert))

Oliver plays piano in the concert.

PlayIn(oliver, piano, concert)

False

If a person plays an instrument in a concert, they are good at playing this kind of instrument. Peter plays piano, violin, and saxophone. Peter plays piano in a concert. Oliver and Peter both play instruments in a concert. Oliver plays a different musical instrument from Peter in the concert.

∀x ∀y (PlayIn(y, x, concert) → GoodAtPlaying(y, x)) Play(peter, piano) ∧ Play(peter, violin) ∧ Play(peter, saxophone) PlayIn(peter, piano, concert) ∃x ∃y (PlayIn(peter, x, concert) ∧ PlayIn(oliver, y, concert)) ∀x (PlayIn(oliver, x, concert) → ¬PlayIn(peter, y, concert))

Oliver plays violin in the concert.

PlayIn(oliver, violin, concert)

Uncertain

If a person plays an instrument in a concert, they are good at playing this kind of instrument. Peter plays piano, violin, and saxophone. Peter plays piano in a concert. Oliver and Peter both play instruments in a concert. Oliver plays a different musical instrument from Peter in the concert.

∀x ∀y (PlayIn(y, x, concert) → GoodAtPlaying(y, x)) Play(peter, piano) ∧ Play(peter, violin) ∧ Play(peter, saxophone) PlayIn(peter, piano, concert) ∃x ∃y (PlayIn(peter, x, concert) ∧ PlayIn(oliver, y, concert)) ∀x (PlayIn(oliver, x, concert) → ¬PlayIn(peter, y, concert))

Peter is good at playing piano.

GoodAtPlaying(peter, piano)

True

Functional brainstems are necessary for breath control. All humans that can swim can control their breath. Humans can swim or walk. Humans who can walk can stand on the ground by themselves. Humans whose brainstems are functional can control their balance. Every human who can stand on the ground by themselves has functional leg muscles. George and Archie are humans. George can control his balance and can swim. Archie can walk if and only if he has functional brainstems.

∀x (CanControl(x, breath) → FunctionalBrainStem(x)) ∀x (Human(x) ∧ CanSwim(x) → CanControl(x, breath)) ∀x (Human(x) → (CanSwim(x) ∨ CanWalk(x))) ∀x (Human(x) ∧ CanWalk(x) → CanStandOnTheGround(x, themselves)) ∀x (Human(x) ∧ FunctionalBrainStem(x) → CanControl(x, balance)) ∀x (Human(x) ∧ CanStandOnTheGround(x, themselves) → FunctionalLegMuscle(x))) Human(george) ∧ Human(archie) CanControl(george, balance) ∧ CanSwim(george) ¬(CanWalk(archie) ⊕ FunctionalBrainStem(x))

George has functional leg muscles.

FunctionalLegMuscle(archie)

Uncertain

Functional brainstems are necessary for breath control. All humans that can swim can control their breath. Humans can swim or walk. Humans who can walk can stand on the ground by themselves. Humans whose brainstems are functional can control their balance. Every human who can stand on the ground by themselves has functional leg muscles. George and Archie are humans. George can control his balance and can swim. Archie can walk if and only if he has functional brainstems.

∀x (CanControl(x, breath) → FunctionalBrainStem(x)) ∀x (Human(x) ∧ CanSwim(x) → CanControl(x, breath)) ∀x (Human(x) → (CanSwim(x) ∨ CanWalk(x))) ∀x (Human(x) ∧ CanWalk(x) → CanStandOnTheGround(x, themselves)) ∀x (Human(x) ∧ FunctionalBrainStem(x) → CanControl(x, balance)) ∀x (Human(x) ∧ CanStandOnTheGround(x, themselves) → FunctionalLegMuscle(x))) Human(george) ∧ Human(archie) CanControl(george, balance) ∧ CanSwim(george) ¬(CanWalk(archie) ⊕ FunctionalBrainStem(x))

Archie has functional leg muscles and can control his balance.

FunctionalLegMuscle(archie) ∧ CanControl(archie, balance)

True

Functional brainstems are necessary for breath control. All humans that can swim can control their breath. Humans can swim or walk. Humans who can walk can stand on the ground by themselves. Humans whose brainstems are functional can control their balance. Every human who can stand on the ground by themselves has functional leg muscles. George and Archie are humans. George can control his balance and can swim. Archie can walk if and only if he has functional brainstems.

∀x (CanControl(x, breath) → FunctionalBrainStem(x)) ∀x (Human(x) ∧ CanSwim(x) → CanControl(x, breath)) ∀x (Human(x) → (CanSwim(x) ∨ CanWalk(x))) ∀x (Human(x) ∧ CanWalk(x) → CanStandOnTheGround(x, themselves)) ∀x (Human(x) ∧ FunctionalBrainStem(x) → CanControl(x, balance)) ∀x (Human(x) ∧ CanStandOnTheGround(x, themselves) → FunctionalLegMuscle(x))) Human(george) ∧ Human(archie) CanControl(george, balance) ∧ CanSwim(george) ¬(CanWalk(archie) ⊕ FunctionalBrainStem(x))

Archie cannot control his balance and doesn't have functional leg muscles.

¬CanControl(archie, balance) ∧ ¬FunctionalLegMuscle(x)

False

Cancer biology is finding genetic alterations that confer a selective advantage to cancer cells. Cancer researchers have frequently ranked the importance of substitutions to cancer growth by the P value. P values are thresholds for belief, not metrics of effect.

Finding(cancerBiology, geneticAlteration) ∧ Confer(geneticAlteration, selectiveAdvantage, toCancerCell) ∃x ∃y (CancerResearcher(x) ∧ Ranked(x, importanceOfSubstitutionsToCancerGrowth) ∧ PValue(y) ∧ RankedBy(importanceOfSubstitutionsToCancerGrowth, y)) ∀x (PValue(x) → ThresholdForBelief(x) ∧ ¬MetricOfEffect(x))

Cancer researchers tend to use the cancer effect size to determine the relative importance of the genetic alterations that confer selective advantage to cancer cells.

∃x ∃y (CancerResearcher(x) ∧ Use(x, cancerEffectSize) ∧ UsedToDetermine(cancerEffectSize, relativeImportanceOfGeneteticAlterations))

Uncertain

Cancer biology is finding genetic alterations that confer a selective advantage to cancer cells. Cancer researchers have frequently ranked the importance of substitutions to cancer growth by the P value. P values are thresholds for belief, not metrics of effect.

Finding(cancerBiology, geneticAlteration) ∧ Confer(geneticAlteration, selectiveAdvantage, toCancerCell) ∃x ∃y (CancerResearcher(x) ∧ Ranked(x, importanceOfSubstitutionsToCancerGrowth) ∧ PValue(y) ∧ RankedBy(importanceOfSubstitutionsToCancerGrowth, y)) ∀x (PValue(x) → ThresholdForBelief(x) ∧ ¬MetricOfEffect(x))

P value represents the selection intensity for somatic variants in cancer cell lineages.

SelectionIntensitySomaticVariants(pValue)

Uncertain

Cancer biology is finding genetic alterations that confer a selective advantage to cancer cells. Cancer researchers have frequently ranked the importance of substitutions to cancer growth by the P value. P values are thresholds for belief, not metrics of effect.

Finding(cancerBiology, geneticAlteration) ∧ Confer(geneticAlteration, selectiveAdvantage, toCancerCell) ∃x ∃y (CancerResearcher(x) ∧ Ranked(x, importanceOfSubstitutionsToCancerGrowth) ∧ PValue(y) ∧ RankedBy(importanceOfSubstitutionsToCancerGrowth, y)) ∀x (PValue(x) → ThresholdForBelief(x) ∧ ¬MetricOfEffect(x))

Cancer effect size is preferred by cancer researchers.

Preferred(cancerResearchers, cancerEffectSize)

Uncertain

Cancer biology is finding genetic alterations that confer a selective advantage to cancer cells. Cancer researchers have frequently ranked the importance of substitutions to cancer growth by the P value. P values are thresholds for belief, not metrics of effect.

Finding(cancerBiology, geneticAlteration) ∧ Confer(geneticAlteration, selectiveAdvantage, toCancerCell) ∃x ∃y (CancerResearcher(x) ∧ Ranked(x, importanceOfSubstitutionsToCancerGrowth) ∧ PValue(y) ∧ RankedBy(importanceOfSubstitutionsToCancerGrowth, y)) ∀x (PValue(x) → ThresholdForBelief(x) ∧ ¬MetricOfEffect(x))

P values don't represent metrics of effect.

∀x (PValue(x) → ¬MetricsOfEffect(x))

True

All biodegradable things are environment-friendly. All woodware is biodegradable. All paper is woodware. Nothing is a good thing and also a bad thing. All environment-friendly things are good. A worksheet is either paper or environment-friendly.

∀x (Biodegradable(x) → EnvironmentFriendly(x)) ∀x (Woodware(x) → Biodegradable(x)) ∀x (Paper(x) → Woodware(x)) ¬(∃x (Good(x) ∧ Bad(x))) ∀x (EnvironmentFriendly(x) → Good(x)) Paper(worksheet) ⊕ EnvironmentFriendly(worksheet)

A worksheet is biodegradable.

Bioegradable(worksheet)

Uncertain

All biodegradable things are environment-friendly. All woodware is biodegradable. All paper is woodware. Nothing is a good thing and also a bad thing. All environment-friendly things are good. A worksheet is either paper or environment-friendly.

∀x (Biodegradable(x) → EnvironmentFriendly(x)) ∀x (Woodware(x) → Biodegradable(x)) ∀x (Paper(x) → Woodware(x)) ¬(∃x (Good(x) ∧ Bad(x))) ∀x (EnvironmentFriendly(x) → Good(x)) Paper(worksheet) ⊕ EnvironmentFriendly(worksheet)

A worksheet is not biodegradable.

¬Bioegradable(worksheet)

Uncertain

All biodegradable things are environment-friendly. All woodware is biodegradable. All paper is woodware. Nothing is a good thing and also a bad thing. All environment-friendly things are good. A worksheet is either paper or environment-friendly.

∀x (Biodegradable(x) → EnvironmentFriendly(x)) ∀x (Woodware(x) → Biodegradable(x)) ∀x (Paper(x) → Woodware(x)) ¬(∃x (Good(x) ∧ Bad(x))) ∀x (EnvironmentFriendly(x) → Good(x)) Paper(worksheet) ⊕ EnvironmentFriendly(worksheet)

A worksheet is bad.

Bad(worksheet)

False

All biodegradable things are environment-friendly. All woodware is biodegradable. All paper is woodware. Nothing is a good thing and also a bad thing. All environment-friendly things are good. A worksheet is either paper or environment-friendly.

∀x (Biodegradable(x) → EnvironmentFriendly(x)) ∀x (Woodware(x) → Biodegradable(x)) ∀x (Paper(x) → Woodware(x)) ¬(∃x (Good(x) ∧ Bad(x))) ∀x (EnvironmentFriendly(x) → Good(x)) Paper(worksheet) ⊕ EnvironmentFriendly(worksheet)

A worksheet is not bad.

¬Bad(worksheet)

True

No reptile has fur. All snakes are reptiles.

∀x (Reptile(x) → ¬Have(x, fur)) ∀x (Snake(x) → Reptile(x))

Some snake has fur.

∃x (Snake(x) ∧ Have(x, fur))

False

All buildings in New Haven are not high. All buildings managed by Yale Housing are located in New Haven. All buildings in Manhattans are high. All buildings owned by Bloomberg are located in Manhattans. All buildings with the Bloomberg logo are owned by Bloomberg. Tower A is managed by Yale Housing. Tower B is with the Bloomberg logo.

∀x (In(x, newHaven) → ¬High(x)) ∀x (YaleHousing(x) → In(x, newHaven)) ∀x (In(x, manhattan) → High(x)) ∀x (Bloomberg(x) → In(x, manhattan)) ∀x (BloombergLogo(x) → Bloomberg(x)) YaleHousing(tower-a) BloombergLogo(tower-b)

Tower A is low.

¬High(tower-a)

True

All buildings in New Haven are not high. All buildings managed by Yale Housing are located in New Haven. All buildings in Manhattans are high. All buildings owned by Bloomberg are located in Manhattans. All buildings with the Bloomberg logo are owned by Bloomberg. Tower A is managed by Yale Housing. Tower B is with the Bloomberg logo.

∀x (In(x, newHaven) → ¬High(x)) ∀x (YaleHousing(x) → In(x, newHaven)) ∀x (In(x, manhattan) → High(x)) ∀x (Bloomberg(x) → In(x, manhattan)) ∀x (BloombergLogo(x) → Bloomberg(x)) YaleHousing(tower-a) BloombergLogo(tower-b)

Tower B is not located in Manhattans.

¬In(tower-b, manhattan)

False

All buildings in New Haven are not high. All buildings managed by Yale Housing are located in New Haven. All buildings in Manhattans are high. All buildings owned by Bloomberg are located in Manhattans. All buildings with the Bloomberg logo are owned by Bloomberg. Tower A is managed by Yale Housing. Tower B is with the Bloomberg logo.

∀x (In(x, newHaven) → ¬High(x)) ∀x (YaleHousing(x) → In(x, newHaven)) ∀x (In(x, manhattan) → High(x)) ∀x (Bloomberg(x) → In(x, manhattan)) ∀x (BloombergLogo(x) → Bloomberg(x)) YaleHousing(tower-a) BloombergLogo(tower-b)

Tower B is located in New Haven.

¬In(tower-b, newHaven)

False

No birds are ectothermic. All penguins are birds. An animal is ectothermic or endothermic. All endothermic animals produce heat within the body. Ron and Henry are both animals. Ron is not a bird and does not produce heat with the body. Henry is not a cat and does not produce heat with the body.

∀x (Bird(x) → ¬Ectothermic(x)) ∀x (Penguin(x) → Bird(x)) ∀x (Animal(x) → Ectothermic(x) ∨ Endothermic(x)) ∀x (Endothermic(x) → ProduceWithIn(x, heat, body)) Animal(ron) ∧ Animal(henry) ¬Bird(ron) ∧ ¬ProduceWithIn(ron, heat, body) ¬Cat(henry) ∧ ¬ProduceWithIn(henry, heat, body)

Ron is a cat.

Cat(ron)

Uncertain

No birds are ectothermic. All penguins are birds. An animal is ectothermic or endothermic. All endothermic animals produce heat within the body. Ron and Henry are both animals. Ron is not a bird and does not produce heat with the body. Henry is not a cat and does not produce heat with the body.

∀x (Bird(x) → ¬Ectothermic(x)) ∀x (Penguin(x) → Bird(x)) ∀x (Animal(x) → Ectothermic(x) ∨ Endothermic(x)) ∀x (Endothermic(x) → ProduceWithIn(x, heat, body)) Animal(ron) ∧ Animal(henry) ¬Bird(ron) ∧ ¬ProduceWithIn(ron, heat, body) ¬Cat(henry) ∧ ¬ProduceWithIn(henry, heat, body)

Either Henry is a penguin or Henry is endothermic.

Penguin(henry) ⊕ Endothermic(henry)

False

No birds are ectothermic. All penguins are birds. An animal is ectothermic or endothermic. All endothermic animals produce heat within the body. Ron and Henry are both animals. Ron is not a bird and does not produce heat with the body. Henry is not a cat and does not produce heat with the body.

∀x (Bird(x) → ¬Ectothermic(x)) ∀x (Penguin(x) → Bird(x)) ∀x (Animal(x) → Ectothermic(x) ∨ Endothermic(x)) ∀x (Endothermic(x) → ProduceWithIn(x, heat, body)) Animal(ron) ∧ Animal(henry) ¬Bird(ron) ∧ ¬ProduceWithIn(ron, heat, body) ¬Cat(henry) ∧ ¬ProduceWithIn(henry, heat, body)

Ron is either both a penguin and endothermic, or he is nether.

¬(Penguin(ron) ⊕ Endothermic(henry))

True

Ambiortus is a prehistoric bird genus. Ambiortus Dementjevi is the only known species of Ambiortus. Mongolia was where Ambiortus Dementjevi lived. Yevgeny Kurochkin was the discoverer of Ambiortus.

Prehistoric(ambiortus) ∧ BirdGenus(ambiortus) ∀x(KnownSpeciesOf(x, ambiortus) → IsSpecies(x, ambiortusDementjevi)) LiveIn(ambiortusDementjevi, mongolia) Discover(yevgenykurochkin, ambiortus)

Yevgeny Kurochkin discovered a new bird genus.

∃x (Discover(yevgenykurochkin, x) ∧ BirdGenus(x))

True

Ambiortus is a prehistoric bird genus. Ambiortus Dementjevi is the only known species of Ambiortus. Mongolia was where Ambiortus Dementjevi lived. Yevgeny Kurochkin was the discoverer of Ambiortus.

Prehistoric(ambiortus) ∧ BirdGenus(ambiortus) ∀x(KnownSpeciesOf(x, ambiortus) → IsSpecies(x, ambiortusDementjevi)) LiveIn(ambiortusDementjevi, mongolia) Discover(yevgenykurochkin, ambiortus)

There is a species of Ambiortus that doesn't live in Mongolia.

∃x (KnownSpeciesOf(x, ambiortus) ∧ ¬LiveIn(x, mongolia))

False

Ambiortus is a prehistoric bird genus. Ambiortus Dementjevi is the only known species of Ambiortus. Mongolia was where Ambiortus Dementjevi lived. Yevgeny Kurochkin was the discoverer of Ambiortus.

Prehistoric(ambiortus) ∧ BirdGenus(ambiortus) ∀x(KnownSpeciesOf(x, ambiortus) → IsSpecies(x, ambiortusDementjevi)) LiveIn(ambiortusDementjevi, mongolia) Discover(yevgenykurochkin, ambiortus)

Yevgeny Kurochkin lived in Mongolia.

LiveIn(yevgenykurochkin, mongolia)

Uncertain

Ambiortus is a prehistoric bird genus. Ambiortus Dementjevi is the only known species of Ambiortus. Mongolia was where Ambiortus Dementjevi lived. Yevgeny Kurochkin was the discoverer of Ambiortus.

Prehistoric(ambiortus) ∧ BirdGenus(ambiortus) ∀x(KnownSpeciesOf(x, ambiortus) → IsSpecies(x, ambiortusDementjevi)) LiveIn(ambiortusDementjevi, mongolia) Discover(yevgenykurochkin, ambiortus)

All species of Ambiortus live in Mongolia.

∀x (SpeciesOf(x, ambiortus) → LiveIn(x, mongolia))

True

Everyone that knows about breath-first-search knows how to use a queue. If someone is a seasoned software engineer interviewer at Google, then they know what breath-first-search is. Someone is either a seasoned software engineer interviewer at Google, has human rights, or both. Every person who has human rights is entitled to the right to life and liberty. Everyone that knows how to use a queue knows about the first-in-first-out data structure. Everyone that is entitled to the right to life and liberty cannot be deprived of their rights without due process of law. Jack is entitled to the right to life and liberty, has human rights, or knows about the first-in-first-out data structure.

∀x (Know(x, breathFirstSearch) → Know(x, howToUseQueue)) ∀x (Seasoned(x) ∧ SoftwareEngineerInterviewer(x) ∧ At(x, google) → Know(x, breathFirstSearch)) ∀x ((Seasoned(x) ∧ SoftwareEngineerInterviewer(x) ∧ At(x, google)) ∨ Have(x, humanRights)) ∀x (Have(x, humanRights) → EntitledTo(x, rightToLifeAndLiberty)) ∀x (Know(x, howToUseQueue) → Know(x, firstInFirstOutDataStructure)) ∀x (EntitledTo(x, rightToLifeAndLiberty) → ¬DeprivedOfWithout(x, rights, dueProcessOfLaw)) (EntitledTo(jack, rightToLifeAndLiberty) ∨ Have(jack, humanRights) ∨ Know(jack, firstInFirstOutDataStructure))

Jack is a seasoned software engineer interviewer.

Seasoned(jack) ∧ SoftwareEngineerInterviewer(jack) ∧ At(jack, google)

Uncertain

Everyone that knows about breath-first-search knows how to use a queue. If someone is a seasoned software engineer interviewer at Google, then they know what breath-first-search is. Someone is either a seasoned software engineer interviewer at Google, has human rights, or both. Every person who has human rights is entitled to the right to life and liberty. Everyone that knows how to use a queue knows about the first-in-first-out data structure. Everyone that is entitled to the right to life and liberty cannot be deprived of their rights without due process of law. Jack is entitled to the right to life and liberty, has human rights, or knows about the first-in-first-out data structure.

∀x (Know(x, breathFirstSearch) → Know(x, howToUseQueue)) ∀x (Seasoned(x) ∧ SoftwareEngineerInterviewer(x) ∧ At(x, google) → Know(x, breathFirstSearch)) ∀x ((Seasoned(x) ∧ SoftwareEngineerInterviewer(x) ∧ At(x, google)) ∨ Have(x, humanRights)) ∀x (Have(x, humanRights) → EntitledTo(x, rightToLifeAndLiberty)) ∀x (Know(x, howToUseQueue) → Know(x, firstInFirstOutDataStructure)) ∀x (EntitledTo(x, rightToLifeAndLiberty) → ¬DeprivedOfWithout(x, rights, dueProcessOfLaw)) (EntitledTo(jack, rightToLifeAndLiberty) ∨ Have(jack, humanRights) ∨ Know(jack, firstInFirstOutDataStructure))

Jack cannot be deprived of their rights without due process of law.

¬DeprivedOfWithout(jack, rights, dueProcessOfLaw)

True

Everyone that knows about breath-first-search knows how to use a queue. If someone is a seasoned software engineer interviewer at Google, then they know what breath-first-search is. Someone is either a seasoned software engineer interviewer at Google, has human rights, or both. Every person who has human rights is entitled to the right to life and liberty. Everyone that knows how to use a queue knows about the first-in-first-out data structure. Everyone that is entitled to the right to life and liberty cannot be deprived of their rights without due process of law. Jack is entitled to the right to life and liberty, has human rights, or knows about the first-in-first-out data structure.

∀x (Know(x, breathFirstSearch) → Know(x, howToUseQueue)) ∀x (Seasoned(x) ∧ SoftwareEngineerInterviewer(x) ∧ At(x, google) → Know(x, breathFirstSearch)) ∀x ((Seasoned(x) ∧ SoftwareEngineerInterviewer(x) ∧ At(x, google)) ∨ Have(x, humanRights)) ∀x (Have(x, humanRights) → EntitledTo(x, rightToLifeAndLiberty)) ∀x (Know(x, howToUseQueue) → Know(x, firstInFirstOutDataStructure)) ∀x (EntitledTo(x, rightToLifeAndLiberty) → ¬DeprivedOfWithout(x, rights, dueProcessOfLaw)) (EntitledTo(jack, rightToLifeAndLiberty) ∨ Have(jack, humanRights) ∨ Know(jack, firstInFirstOutDataStructure))

Jack can be deprived of their rights without due process of law.

DeprivedOfWithout(jack, rights, dueProcessOfLaw)

False

Fort Ticonderoga is the current name for Fort Carillon. Pierre de Rigaud de Vaudreuil built Fort Carillon. Fort Carillon was located in New France. New France is not in Europe.

RenamedAs(fortCarillon, fortTiconderoga) Built(pierredeRigauddeVaudreuil, fortCarillon) LocatedIn(fortCarillon, newFrance) ¬LocatedIn(newFrance, europe)

Pierre de Rigaud de Vaudreuil built a fort in New France.

∃x (Built(pierredeRigauddeVaudreuil, x) ∧ LocatedIn(x, newFrance))

True

Fort Ticonderoga is the current name for Fort Carillon. Pierre de Rigaud de Vaudreuil built Fort Carillon. Fort Carillon was located in New France. New France is not in Europe.

RenamedAs(fortCarillon, fortTiconderoga) Built(pierredeRigauddeVaudreuil, fortCarillon) LocatedIn(fortCarillon, newFrance) ¬LocatedIn(newFrance, europe)

Pierre de Rigaud de Vaudreuil built a fort in New England.

∃x (Built(pierredeRigauddeVaudreuil, x) ∧ LocatedIn(x, newEngland))

Uncertain

Fort Ticonderoga is the current name for Fort Carillon. Pierre de Rigaud de Vaudreuil built Fort Carillon. Fort Carillon was located in New France. New France is not in Europe.

RenamedAs(fortCarillon, fortTiconderoga) Built(pierredeRigauddeVaudreuil, fortCarillon) LocatedIn(fortCarillon, newFrance) ¬LocatedIn(newFrance, europe)

Fort Carillon was located in Europe.

LocatedIn(fortCarillon, europe)

Uncertain

No soccer players are professional basketball players. All NBA players are professional basketball players. All soccer defenders are soccer players. All centerback players are soccer defenders. If Stephen Curry is an NBA player or a soccer player, then he is a professional basketball player.

∀x (ProfessionalSoccerPlayer(x) → ¬ProfessionalBasketballPlayer(x)) ∀x (NBAPlayer(x) → ProfessionalBasketballPlayer(x)) ∀x (ProfessionalSoccerDefender(x) → ProfessionalSoccerPlayer(x)) ∀x (ProfessionalCenterback(x) → ProfessionalSoccerDefender(x)) (NBAPlayer(stephencurry) ⊕ ProfessionalSoccerPlayer(stephencurry)) → ProfessionalBasketballPlayer(stephencurry)

Stephen Curry is an NBA player.

NBAPlayer(stephenCurry)

Uncertain

No soccer players are professional basketball players. All NBA players are professional basketball players. All soccer defenders are soccer players. All centerback players are soccer defenders. If Stephen Curry is an NBA player or a soccer player, then he is a professional basketball player.

∀x (ProfessionalSoccerPlayer(x) → ¬ProfessionalBasketballPlayer(x)) ∀x (NBAPlayer(x) → ProfessionalBasketballPlayer(x)) ∀x (ProfessionalSoccerDefender(x) → ProfessionalSoccerPlayer(x)) ∀x (ProfessionalCenterback(x) → ProfessionalSoccerDefender(x)) (NBAPlayer(stephencurry) ⊕ ProfessionalSoccerPlayer(stephencurry)) → ProfessionalBasketballPlayer(stephencurry)

Stephen Curry is a centerback player.

ProfessionalCenterback(stephenCurry)

False

No soccer players are professional basketball players. All NBA players are professional basketball players. All soccer defenders are soccer players. All centerback players are soccer defenders. If Stephen Curry is an NBA player or a soccer player, then he is a professional basketball player.

∀x (ProfessionalSoccerPlayer(x) → ¬ProfessionalBasketballPlayer(x)) ∀x (NBAPlayer(x) → ProfessionalBasketballPlayer(x)) ∀x (ProfessionalSoccerDefender(x) → ProfessionalSoccerPlayer(x)) ∀x (ProfessionalCenterback(x) → ProfessionalSoccerDefender(x)) (NBAPlayer(stephencurry) ⊕ ProfessionalSoccerPlayer(stephencurry)) → ProfessionalBasketballPlayer(stephencurry)

Stephen Curry is not a centerback player.

¬ProfessionalCenterback(stephenCurry)

True

No songs are visuals. All folk songs are songs. All videos are visuals. All movies are videos. All sci-fi movies are movies. Inception is a sci-fi movie. Mac is neither a folk song nor a sci-fi movie.

∀x (Song(x) → ¬Visual(x)) ∀x (FolkSong(x) → Song(x)) ∀x (Video(x) → Visual(x)) ∀x (Movie(x) → Video(x)) ∀x (ScifiMovie(x) → Movie(x)) ScifiMovie(inception) ¬FolkSong(mac) ∧ ¬ScifiMovie(mac)

Inception is a folk song.

FolkSong(inception)

False

No songs are visuals. All folk songs are songs. All videos are visuals. All movies are videos. All sci-fi movies are movies. Inception is a sci-fi movie. Mac is neither a folk song nor a sci-fi movie.

∀x (Song(x) → ¬Visual(x)) ∀x (FolkSong(x) → Song(x)) ∀x (Video(x) → Visual(x)) ∀x (Movie(x) → Video(x)) ∀x (ScifiMovie(x) → Movie(x)) ScifiMovie(inception) ¬FolkSong(mac) ∧ ¬ScifiMovie(mac)

Inception is not a folk song.

¬FolkSong(inception)

True

No songs are visuals. All folk songs are songs. All videos are visuals. All movies are videos. All sci-fi movies are movies. Inception is a sci-fi movie. Mac is neither a folk song nor a sci-fi movie.

∀x (Song(x) → ¬Visual(x)) ∀x (FolkSong(x) → Song(x)) ∀x (Video(x) → Visual(x)) ∀x (Movie(x) → Video(x)) ∀x (ScifiMovie(x) → Movie(x)) ScifiMovie(inception) ¬FolkSong(mac) ∧ ¬ScifiMovie(mac)

Inception is either a video or a folk song.

Video(inception) ⊕ FolkSong(inception)

True

No songs are visuals. All folk songs are songs. All videos are visuals. All movies are videos. All sci-fi movies are movies. Inception is a sci-fi movie. Mac is neither a folk song nor a sci-fi movie.

∀x (Song(x) → ¬Visual(x)) ∀x (FolkSong(x) → Song(x)) ∀x (Video(x) → Visual(x)) ∀x (Movie(x) → Video(x)) ∀x (ScifiMovie(x) → Movie(x)) ScifiMovie(inception) ¬FolkSong(mac) ∧ ¬ScifiMovie(mac)

Mac is a video.

Video(mac)

Uncertain

All inductive reasoning processes derive general principles from a body of observations. Two major types of reasoning rules are inductive reasoning and deductive reasoning. All deductive reasoning processes are only based on facts and rules. Nothing only based on facts and rules is used for statistical generalization. Modus Ponens is not both used in inductive reasoning and used for statistical generalization. Modus Ponens is a component of a major part of reasoning rule.

∀x (InductiveReasoning(x) → DeriveFrom(generalPrinciple, observations)) ∀x (MajorArgumentForm(x) → (InductiveReasoning(x) ⊕ DeductiveReasoning(x)) ∀x (DeductiveReasoning(x) → (BasedOn(x, fact) ∨ BasedOn(x, rule))) ∀x ((BasedOn(x, fact) ∨ BasedOn(x, rule)) → (¬UsedFor(x, statisticalGeneralization))) ¬(InductiveReasoning(modusPonens) ∧ UsedFor(modusPonens, statisticalGeneralization)) ArgumentForm(modusPonens)

Reasoning with Modus Ponens is based on facts and rules.

BasedOn(x, fact) ∨ BasedOn(x, rule)

Uncertain

All inductive reasoning processes derive general principles from a body of observations. Two major types of reasoning rules are inductive reasoning and deductive reasoning. All deductive reasoning processes are only based on facts and rules. Nothing only based on facts and rules is used for statistical generalization. Modus Ponens is not both used in inductive reasoning and used for statistical generalization. Modus Ponens is a component of a major part of reasoning rule.

∀x (InductiveReasoning(x) → DeriveFrom(generalPrinciple, observations)) ∀x (MajorArgumentForm(x) → (InductiveReasoning(x) ⊕ DeductiveReasoning(x)) ∀x (DeductiveReasoning(x) → (BasedOn(x, fact) ∨ BasedOn(x, rule))) ∀x ((BasedOn(x, fact) ∨ BasedOn(x, rule)) → (¬UsedFor(x, statisticalGeneralization))) ¬(InductiveReasoning(modusPonens) ∧ UsedFor(modusPonens, statisticalGeneralization)) ArgumentForm(modusPonens)

Modus Ponens derives general principles from a body of observations and is used for statistical generalization.

DeriveFrom(generalPrinciple, observations) ∧ UsedFor(x, statisticalGeneralization)

False

All inductive reasoning processes derive general principles from a body of observations. Two major types of reasoning rules are inductive reasoning and deductive reasoning. All deductive reasoning processes are only based on facts and rules. Nothing only based on facts and rules is used for statistical generalization. Modus Ponens is not both used in inductive reasoning and used for statistical generalization. Modus Ponens is a component of a major part of reasoning rule.

∀x (InductiveReasoning(x) → DeriveFrom(generalPrinciple, observations)) ∀x (MajorArgumentForm(x) → (InductiveReasoning(x) ⊕ DeductiveReasoning(x)) ∀x (DeductiveReasoning(x) → (BasedOn(x, fact) ∨ BasedOn(x, rule))) ∀x ((BasedOn(x, fact) ∨ BasedOn(x, rule)) → (¬UsedFor(x, statisticalGeneralization))) ¬(InductiveReasoning(modusPonens) ∧ UsedFor(modusPonens, statisticalGeneralization)) ArgumentForm(modusPonens)

If Modus Ponens either derives general principles from a body of observations and is used for statistical generalization, or neither, then Modus Ponens is is neither used in inductive reasoning nor used for statistical generalization.

¬(Derive(generalPrinciple, observations) ⊕ UsedFor(x, statisticalGeneralization)) → (¬InductiveReasoning(modusPonens) ∧ (¬UsedFor(modusPonens, statisticalGeneralization)))

True

No trick-shot artist in Yale's varsity team struggles with half court shots. Everyone on Yale's varsity team is someone who struggles with half court shots or who successfully shoots a high percentage of 3-pointers. Everyone on Yale's varsity team who successfully shoots a high percentage of 3-pointers is solid at shooting 2-pointers. No one on Yale's varsity team who is solid at shooting 2-pointers is bad at mid-range shots. Jack is on Yale's varsity team, and he is either a trick-shot artist or he successfully shoots a high percentage of 3-pointers.

∀x ((In(x, yaleSVarsityTeam) ∧ TrickShotArtist(x)) → ¬StruggleAt(x, halfCourtShot)) ∀x (In(x, yaleSVarsityTeam) → (StruggleAt(x, halfCourtShot) ∨ GoodAt(x, threes))) ∀x ((In(x, yaleSVarsityTeam) ∧ GoodAt(x, threes)) → GoodAt(x, twos)) ∀x ((In(x, yaleSVarsityTeam) ∧ GoodAt(x, twos)) → BadAt(x, midRangeShot)) In(jack, yaleSVarsityTeam) ∧ (TrickShotArtist(jack) ⊕ GoodAt(jack, threes))

Jack struggles at half court shots.

StruggleAt(jack, halfCourtShot)

Uncertain

No trick-shot artist in Yale's varsity team struggles with half court shots. Everyone on Yale's varsity team is someone who struggles with half court shots or who successfully shoots a high percentage of 3-pointers. Everyone on Yale's varsity team who successfully shoots a high percentage of 3-pointers is solid at shooting 2-pointers. No one on Yale's varsity team who is solid at shooting 2-pointers is bad at mid-range shots. Jack is on Yale's varsity team, and he is either a trick-shot artist or he successfully shoots a high percentage of 3-pointers.

∀x ((In(x, yaleSVarsityTeam) ∧ TrickShotArtist(x)) → ¬StruggleAt(x, halfCourtShot)) ∀x (In(x, yaleSVarsityTeam) → (StruggleAt(x, halfCourtShot) ∨ GoodAt(x, threes))) ∀x ((In(x, yaleSVarsityTeam) ∧ GoodAt(x, threes)) → GoodAt(x, twos)) ∀x ((In(x, yaleSVarsityTeam) ∧ GoodAt(x, twos)) → BadAt(x, midRangeShot)) In(jack, yaleSVarsityTeam) ∧ (TrickShotArtist(jack) ⊕ GoodAt(jack, threes))

Jack is bad at mid-range shots.

BadAt(jack, midRangeShot)

False

No trick-shot artist in Yale's varsity team struggles with half court shots. Everyone on Yale's varsity team is someone who struggles with half court shots or who successfully shoots a high percentage of 3-pointers. Everyone on Yale's varsity team who successfully shoots a high percentage of 3-pointers is solid at shooting 2-pointers. No one on Yale's varsity team who is solid at shooting 2-pointers is bad at mid-range shots. Jack is on Yale's varsity team, and he is either a trick-shot artist or he successfully shoots a high percentage of 3-pointers.

∀x ((In(x, yaleSVarsityTeam) ∧ TrickShotArtist(x)) → ¬StruggleAt(x, halfCourtShot)) ∀x (In(x, yaleSVarsityTeam) → (StruggleAt(x, halfCourtShot) ∨ GoodAt(x, threes))) ∀x ((In(x, yaleSVarsityTeam) ∧ GoodAt(x, threes)) → GoodAt(x, twos)) ∀x ((In(x, yaleSVarsityTeam) ∧ GoodAt(x, twos)) → BadAt(x, midRangeShot)) In(jack, yaleSVarsityTeam) ∧ (TrickShotArtist(jack) ⊕ GoodAt(jack, threes))

Jack is solid at shooting 2-pointers or bad at mid-range shots.

GoodAt(jack, twos) ∨ BadAt(jack, midRangeShot)

True

No trick-shot artist in Yale's varsity team struggles with half court shots. Everyone on Yale's varsity team is someone who struggles with half court shots or who successfully shoots a high percentage of 3-pointers. Everyone on Yale's varsity team who successfully shoots a high percentage of 3-pointers is solid at shooting 2-pointers. No one on Yale's varsity team who is solid at shooting 2-pointers is bad at mid-range shots. Jack is on Yale's varsity team, and he is either a trick-shot artist or he successfully shoots a high percentage of 3-pointers.

∀x ((In(x, yaleSVarsityTeam) ∧ TrickShotArtist(x)) → ¬StruggleAt(x, halfCourtShot)) ∀x (In(x, yaleSVarsityTeam) → (StruggleAt(x, halfCourtShot) ∨ GoodAt(x, threes))) ∀x ((In(x, yaleSVarsityTeam) ∧ GoodAt(x, threes)) → GoodAt(x, twos)) ∀x ((In(x, yaleSVarsityTeam) ∧ GoodAt(x, twos)) → BadAt(x, midRangeShot)) In(jack, yaleSVarsityTeam) ∧ (TrickShotArtist(jack) ⊕ GoodAt(jack, threes))

Jack is either solid at shooting 2-pointers or bad at mid-range shots.

GoodAt(jack, twos) ⊕ BadAt(jack, midRangeShot)

True

No trick-shot artist in Yale's varsity team struggles with half court shots. Everyone on Yale's varsity team is someone who struggles with half court shots or who successfully shoots a high percentage of 3-pointers. Everyone on Yale's varsity team who successfully shoots a high percentage of 3-pointers is solid at shooting 2-pointers. No one on Yale's varsity team who is solid at shooting 2-pointers is bad at mid-range shots. Jack is on Yale's varsity team, and he is either a trick-shot artist or he successfully shoots a high percentage of 3-pointers.

∀x ((In(x, yaleSVarsityTeam) ∧ TrickShotArtist(x)) → ¬StruggleAt(x, halfCourtShot)) ∀x (In(x, yaleSVarsityTeam) → (StruggleAt(x, halfCourtShot) ∨ GoodAt(x, threes))) ∀x ((In(x, yaleSVarsityTeam) ∧ GoodAt(x, threes)) → GoodAt(x, twos)) ∀x ((In(x, yaleSVarsityTeam) ∧ GoodAt(x, twos)) → BadAt(x, midRangeShot)) In(jack, yaleSVarsityTeam) ∧ (TrickShotArtist(jack) ⊕ GoodAt(jack, threes))

Jack is a trick-shot artist or bad at mid-range shots.

TrickShotArtist(jack) ∨ BadAt(jack, midRangeShot))

False

No trick-shot artist in Yale's varsity team struggles with half court shots. Everyone on Yale's varsity team is someone who struggles with half court shots or who successfully shoots a high percentage of 3-pointers. Everyone on Yale's varsity team who successfully shoots a high percentage of 3-pointers is solid at shooting 2-pointers. No one on Yale's varsity team who is solid at shooting 2-pointers is bad at mid-range shots. Jack is on Yale's varsity team, and he is either a trick-shot artist or he successfully shoots a high percentage of 3-pointers.

∀x ((In(x, yaleSVarsityTeam) ∧ TrickShotArtist(x)) → ¬StruggleAt(x, halfCourtShot)) ∀x (In(x, yaleSVarsityTeam) → (StruggleAt(x, halfCourtShot) ∨ GoodAt(x, threes))) ∀x ((In(x, yaleSVarsityTeam) ∧ GoodAt(x, threes)) → GoodAt(x, twos)) ∀x ((In(x, yaleSVarsityTeam) ∧ GoodAt(x, twos)) → BadAt(x, midRangeShot)) In(jack, yaleSVarsityTeam) ∧ (TrickShotArtist(jack) ⊕ GoodAt(jack, threes))

Jack is either a trick-shot artist or bad at mid-range shots.

TrickShotArtist(jack) ⊕ BadAt(jack, midRangeShots)

False

No trick-shot artist in Yale's varsity team struggles with half court shots. Everyone on Yale's varsity team is someone who struggles with half court shots or who successfully shoots a high percentage of 3-pointers. Everyone on Yale's varsity team who successfully shoots a high percentage of 3-pointers is solid at shooting 2-pointers. No one on Yale's varsity team who is solid at shooting 2-pointers is bad at mid-range shots. Jack is on Yale's varsity team, and he is either a trick-shot artist or he successfully shoots a high percentage of 3-pointers.

∀x ((In(x, yaleSVarsityTeam) ∧ TrickShotArtist(x)) → ¬StruggleAt(x, halfCourtShot)) ∀x (In(x, yaleSVarsityTeam) → (StruggleAt(x, halfCourtShot) ∨ GoodAt(x, threes))) ∀x ((In(x, yaleSVarsityTeam) ∧ GoodAt(x, threes)) → GoodAt(x, twos)) ∀x ((In(x, yaleSVarsityTeam) ∧ GoodAt(x, twos)) → BadAt(x, midRangeShot)) In(jack, yaleSVarsityTeam) ∧ (TrickShotArtist(jack) ⊕ GoodAt(jack, threes))

Jack is either a player who successfully shoots a high percentage of 3-pointers or is bad at mid-range shots.

GoodAt(jack, threes) ⊕ BadAt(jack, midRangeShot)

True

No trick-shot artist in Yale's varsity team struggles with half court shots. Everyone on Yale's varsity team is someone who struggles with half court shots or who successfully shoots a high percentage of 3-pointers. Everyone on Yale's varsity team who successfully shoots a high percentage of 3-pointers is solid at shooting 2-pointers. No one on Yale's varsity team who is solid at shooting 2-pointers is bad at mid-range shots. Jack is on Yale's varsity team, and he is either a trick-shot artist or he successfully shoots a high percentage of 3-pointers.

∀x ((In(x, yaleSVarsityTeam) ∧ TrickShotArtist(x)) → ¬StruggleAt(x, halfCourtShot)) ∀x (In(x, yaleSVarsityTeam) → (StruggleAt(x, halfCourtShot) ∨ GoodAt(x, threes))) ∀x ((In(x, yaleSVarsityTeam) ∧ GoodAt(x, threes)) → GoodAt(x, twos)) ∀x ((In(x, yaleSVarsityTeam) ∧ GoodAt(x, twos)) → BadAt(x, midRangeShot)) In(jack, yaleSVarsityTeam) ∧ (TrickShotArtist(jack) ⊕ GoodAt(jack, threes))

If Jack is not solid at shooting 2-pointers and bad at mid-range shots, then Jack is not solid at shooting 2-pointers and is a player who successfully shoots a high percentage of 3-pointers.

BadAt(jack, midRangeShot) ∧ GoodAt(jack, twos) → ¬GoodAt(jack, twos) ∧ GoodAt(jack, threes)

False

No trick-shot artist in Yale's varsity team struggles with half court shots. Everyone on Yale's varsity team is someone who struggles with half court shots or who successfully shoots a high percentage of 3-pointers. Everyone on Yale's varsity team who successfully shoots a high percentage of 3-pointers is solid at shooting 2-pointers. No one on Yale's varsity team who is solid at shooting 2-pointers is bad at mid-range shots. Jack is on Yale's varsity team, and he is either a trick-shot artist or he successfully shoots a high percentage of 3-pointers.

∀x ((In(x, yaleSVarsityTeam) ∧ TrickShotArtist(x)) → ¬StruggleAt(x, halfCourtShot)) ∀x (In(x, yaleSVarsityTeam) → (StruggleAt(x, halfCourtShot) ∨ GoodAt(x, threes))) ∀x ((In(x, yaleSVarsityTeam) ∧ GoodAt(x, threes)) → GoodAt(x, twos)) ∀x ((In(x, yaleSVarsityTeam) ∧ GoodAt(x, twos)) → BadAt(x, midRangeShot)) In(jack, yaleSVarsityTeam) ∧ (TrickShotArtist(jack) ⊕ GoodAt(jack, threes))

If Jack is solid at shooting 2-pointers or successfully shoots a high percentage of 3-pointers, then Jack struggles at half court shots and is bad at mid-range shots.

GoodAt(jack, twos) ∨ GoodAt(jack, threes) → BadAt(jack, halfCourtShot) ∧ BadAt(jack, midRangeShot)

Uncertain

No plants are fungi. Mushrooms are fungi.

∀x (Plant(x) → ¬Fungi(x)) ∀x (Mushroom(x) → Fungi(x))

No plants are mushrooms.

∀x (Plant(x) → ¬Mushroom(x))

True

No road is dustless. Some streets are roads.

∀x (Road(x) → ¬Dustless(x)) ∃x ∃y (Street(x) ∧ Street(y) ∧ Road(x) ∧ Road(y) ∧ ¬(x=y))

Some streets are dustless.

∃x ∃y (Street(x) ∧ Street(y) ∧ Dustless(x) ∧ Dustless(y) ∧ ¬(x=y))

Uncertain

New York City is located on the East Coast. Seattle is located on the West Coast. If a person is somewhere located on the East coast and is traveling to somewhere located on the west coast, they will be on a long flight. People in business class from New York City to Seattle are not in first class. People on long flights are uncomfortable unless they're in first class.

LocatedOn(newYorkCity, eastCoast) LocatedOn(seattle, westCoast) ∀x ∀y ∀z ((TravelingFrom(x, y) ∧ LocatedOn(y, eastcoast) ∧ TravelingTo(x, z) ∧ LocatedOn(z, westcoast)) → OnLongFlight(x)) ∀x (InBuisnessClass(x) ∧ TravelingTo(x, seattle) ∧ TravelingFrom(x, newYorkCity) → ¬InFirstClass(x)) ∀x (OnLongFlight(x) ∧ ¬InFirstClass(x) → Uncomfortable(x))

People traveling in business class from New York City to Seattle will be uncomfortable.

∃x (TravelingTo(x, seattle) ∧ TravelingFrom(x, newYorkCity) ∧ uncomfortable(x))

True

Musicians have very busy lives. Singh Kaur is a musician and famous. If a musician is not famous, that musician will not make a lot of money. A musician can be a singer or a writer.

∀x (Musician(x) → Have(x, busyLife)) Musician(singhKaur) ∧ Famous(singhKaur) ∀x (Musician(x) ∧ ¬Famous(x) → ¬MakeALotOfMoney(x)) ∃x (Musician(x) ∧ (Singer(x) ∨ Writer(x)))

Singh Kaur makes a lot of money.

MakeALotOfMoney(singhKaur)

Uncertain

Musicians have very busy lives. Singh Kaur is a musician and famous. If a musician is not famous, that musician will not make a lot of money. A musician can be a singer or a writer.

∀x (Musician(x) → Have(x, busyLife)) Musician(singhKaur) ∧ Famous(singhKaur) ∀x (Musician(x) ∧ ¬Famous(x) → ¬MakeALotOfMoney(x)) ∃x (Musician(x) ∧ (Singer(x) ∨ Writer(x)))

Singh Kaur is a writer.

Writer(singhKaur)

Uncertain

Musicians have very busy lives. Singh Kaur is a musician and famous. If a musician is not famous, that musician will not make a lot of money. A musician can be a singer or a writer.

∀x (Musician(x) → Have(x, busyLife)) Musician(singhKaur) ∧ Famous(singhKaur) ∀x (Musician(x) ∧ ¬Famous(x) → ¬MakeALotOfMoney(x)) ∃x (Musician(x) ∧ (Singer(x) ∨ Writer(x)))

Singh Kaur has a very busy life.

Have(singhKaur, busyLife)

True

Each building is tall. Everything tall has height.

∀x (Building(x) → Tall(x)) ∀x (Tall(x) → Height(x))

All buildings are magnificent.

∀x (Building(x) → Magnificent(x))

Uncertain

A cat named Garfield, the main character of the film Garfield, is orange and fat and likes having lasagna. Garfield shares a home with Odie, another pet of Jon's. Garfield hates Odie. A pet who hates the pet with whom he shares the same owner is childish and possessive.

Cat(garfield) ∧ MainCharacterOf(garfield, filmGarfield) ∧ Orange(garfield) ∧ Fat(garfield) ∧ Like(garfield, lasagna) PetOf(garfield, jon) ∧ PetOf(odie, jon) ∧ ShareHomeWith(garfield, odie) Hate(garfield, odie) ∀x ∀y ∃z (PetOf(x, z) ∧ PetOf(y, z) ∧ Hate(x, y) → Childish(x) ∧ Possessive(x))

The main character of the film Garfield is childish and possessive.

∃x (MainCharacterOf(x, garfield) ∧ Childish(x) ∧ Possessive(x))

True

All humans are capable of abstract thoughts. Plants are not capable of abstract thoughts. All multicellular creatures that are autotrophic or digest food internally are plants and animals. All goats are animals. Dirt is not an animal. Hulu is a goat or a human. Hulu is a multicellular creature that is autotrophic or digests food internally.

∀x (Human(x) → CapableOf(x, abstractThought)) ∀x (Plant(x) → ¬CapableOf(x, abstractThought)) ∀x (MulticellularCreature(x) ∧ (Autotrophic(x) ∨ DigestFoodInternally (x)) → Plant(x) ⊕ Animal(x)) ∀x (Goat(x) → Animal(x)) ∀x (Dirt(x) → ¬Animal(x)) Goat(hulu) ∨ HumanBeing(hulu) (MulticellularCreature(hulu) ∧ (Autotrophic(hulu) ∨ DigestFoodInternally (hulu))

Hulu is capable of abstract thoughts.

CapableOf(hulu, abstractThought)

Uncertain

All humans are capable of abstract thoughts. Plants are not capable of abstract thoughts. All multicellular creatures that are autotrophic or digest food internally are plants and animals. All goats are animals. Dirt is not an animal. Hulu is a goat or a human. Hulu is a multicellular creature that is autotrophic or digests food internally.

∀x (Human(x) → CapableOf(x, abstractThought)) ∀x (Plant(x) → ¬CapableOf(x, abstractThought)) ∀x (MulticellularCreature(x) ∧ (Autotrophic(x) ∨ DigestFoodInternally (x)) → Plant(x) ⊕ Animal(x)) ∀x (Goat(x) → Animal(x)) ∀x (Dirt(x) → ¬Animal(x)) Goat(hulu) ∨ HumanBeing(hulu) (MulticellularCreature(hulu) ∧ (Autotrophic(hulu) ∨ DigestFoodInternally (hulu))

Hulu is not capable of abstract thoughts.

¬CapableOf(hulu, abstractThought)

Uncertain

All humans are capable of abstract thoughts. Plants are not capable of abstract thoughts. All multicellular creatures that are autotrophic or digest food internally are plants and animals. All goats are animals. Dirt is not an animal. Hulu is a goat or a human. Hulu is a multicellular creature that is autotrophic or digests food internally.

∀x (Human(x) → CapableOf(x, abstractThought)) ∀x (Plant(x) → ¬CapableOf(x, abstractThought)) ∀x (MulticellularCreature(x) ∧ (Autotrophic(x) ∨ DigestFoodInternally (x)) → Plant(x) ⊕ Animal(x)) ∀x (Goat(x) → Animal(x)) ∀x (Dirt(x) → ¬Animal(x)) Goat(hulu) ∨ HumanBeing(hulu) (MulticellularCreature(hulu) ∧ (Autotrophic(hulu) ∨ DigestFoodInternally (hulu))

Hulu is dirt.

Dirt(hulu)

False

All humans are capable of abstract thoughts. Plants are not capable of abstract thoughts. All multicellular creatures that are autotrophic or digest food internally are plants and animals. All goats are animals. Dirt is not an animal. Hulu is a goat or a human. Hulu is a multicellular creature that is autotrophic or digests food internally.

∀x (Human(x) → CapableOf(x, abstractThought)) ∀x (Plant(x) → ¬CapableOf(x, abstractThought)) ∀x (MulticellularCreature(x) ∧ (Autotrophic(x) ∨ DigestFoodInternally (x)) → Plant(x) ⊕ Animal(x)) ∀x (Goat(x) → Animal(x)) ∀x (Dirt(x) → ¬Animal(x)) Goat(hulu) ∨ HumanBeing(hulu) (MulticellularCreature(hulu) ∧ (Autotrophic(hulu) ∨ DigestFoodInternally (hulu))

Hulu is an animal or dirt.

Animal(hulu) ∨ Dirt(hulu)

True

All humans are capable of abstract thoughts. Plants are not capable of abstract thoughts. All multicellular creatures that are autotrophic or digest food internally are plants and animals. All goats are animals. Dirt is not an animal. Hulu is a goat or a human. Hulu is a multicellular creature that is autotrophic or digests food internally.

∀x (Human(x) → CapableOf(x, abstractThought)) ∀x (Plant(x) → ¬CapableOf(x, abstractThought)) ∀x (MulticellularCreature(x) ∧ (Autotrophic(x) ∨ DigestFoodInternally (x)) → Plant(x) ⊕ Animal(x)) ∀x (Goat(x) → Animal(x)) ∀x (Dirt(x) → ¬Animal(x)) Goat(hulu) ∨ HumanBeing(hulu) (MulticellularCreature(hulu) ∧ (Autotrophic(hulu) ∨ DigestFoodInternally (hulu))

Hulu is either an animal or dirt, but not both.

Animal(hulu) ⊕ Dirt(hulu)

True

All humans are capable of abstract thoughts. Plants are not capable of abstract thoughts. All multicellular creatures that are autotrophic or digest food internally are plants and animals. All goats are animals. Dirt is not an animal. Hulu is a goat or a human. Hulu is a multicellular creature that is autotrophic or digests food internally.

∀x (Human(x) → CapableOf(x, abstractThought)) ∀x (Plant(x) → ¬CapableOf(x, abstractThought)) ∀x (MulticellularCreature(x) ∧ (Autotrophic(x) ∨ DigestFoodInternally (x)) → Plant(x) ⊕ Animal(x)) ∀x (Goat(x) → Animal(x)) ∀x (Dirt(x) → ¬Animal(x)) Goat(hulu) ∨ HumanBeing(hulu) (MulticellularCreature(hulu) ∧ (Autotrophic(hulu) ∨ DigestFoodInternally (hulu))

If Hulu is either an animal or dirt, then Hulu is capable of abstract thoughts and is dirt.

Animal(hulu) ⊕ Dirt(hulu) → CapableOf(hulu, abstractThought) ∧ Dirt(hulu)

False

A controlled substance is a drug. There exist both harmful and beneficial controlled substances. If a child is exposed to a controlled substance, they are in chemical endangerment. Chemical Endangerment is harmful. The Controlled Substances Act was an act passed in 1971. Some Acts prevent harmful things.

∀x (ControlledSubstances(x) → Drugs(x)) ∃x ∃y (ControlledSubstances(x) ∧ ControlledSubstances(y) ∧ (¬(x=y)) ∧ Beneficial(x) ∧ Harmful(y)) ∀x ∀y ((Child(x) ∧ ControlledSubstances(y) ∧ ExposedTo(x, y)) → InChemicalEndangerment(x)) ∀x (InChemicalEndangerment(x) → Harmful(x)) PassedIn(controlledSubstancesAct, yr1971) ∧ Act(controlledSubstancesAct) ∃x ∃y(Act(x) ∧ PreventsHarm(x) ∧ (¬(x=y)) ∧ Act(y) ∧ PreventsHarm(y))

The Controlled Substances Act prevents harmful things.

PreventsHarm(controlledSubstancesAct)

Uncertain

A controlled substance is a drug. There exist both harmful and beneficial controlled substances. If a child is exposed to a controlled substance, they are in chemical endangerment. Chemical Endangerment is harmful. The Controlled Substances Act was an act passed in 1971. Some Acts prevent harmful things.

∀x (ControlledSubstances(x) → Drugs(x)) ∃x ∃y (ControlledSubstances(x) ∧ ControlledSubstances(y) ∧ (¬(x=y)) ∧ Beneficial(x) ∧ Harmful(y)) ∀x ∀y ((Child(x) ∧ ControlledSubstances(y) ∧ ExposedTo(x, y)) → InChemicalEndangerment(x)) ∀x (InChemicalEndangerment(x) → Harmful(x)) PassedIn(controlledSubstancesAct, yr1971) ∧ Act(controlledSubstancesAct) ∃x ∃y(Act(x) ∧ PreventsHarm(x) ∧ (¬(x=y)) ∧ Act(y) ∧ PreventsHarm(y))

Some drugs are beneficial.

∃x ∃y(Drugs(x) ∧ Beneficial(x) ∧ (¬(x=y)) ∧ Drugs(y) ∧ Beneficial(y))

True

A controlled substance is a drug. There exist both harmful and beneficial controlled substances. If a child is exposed to a controlled substance, they are in chemical endangerment. Chemical Endangerment is harmful. The Controlled Substances Act was an act passed in 1971. Some Acts prevent harmful things.

∀x (ControlledSubstances(x) → Drugs(x)) ∃x ∃y (ControlledSubstances(x) ∧ ControlledSubstances(y) ∧ (¬(x=y)) ∧ Beneficial(x) ∧ Harmful(y)) ∀x ∀y ((Child(x) ∧ ControlledSubstances(y) ∧ ExposedTo(x, y)) → InChemicalEndangerment(x)) ∀x (InChemicalEndangerment(x) → Harmful(x)) PassedIn(controlledSubstancesAct, yr1971) ∧ Act(controlledSubstancesAct) ∃x ∃y(Act(x) ∧ PreventsHarm(x) ∧ (¬(x=y)) ∧ Act(y) ∧ PreventsHarm(y))

A child in chemical endangerment is in harm.

∀x ((Child(x) ∧ InChemicalEndangerment(x)) → Harmful(x))

True

No people who have corporate jobs are taking more than normal financial risks. All entrepreneurs are taking more than normal financial risks. All risk-averse working people are people who have corporate jobs. All working people who hate working for others want to be entrepreneurs. If Mark Zuckerberg is neither an entrepreneur nor a person who hates working for others, then Mark Zuckerberg is not a risk-averse working person.

∀x (Have(x, corporateJob) → ¬Take(x, financialRisk)) ∀x (Entrepreneur(x) → Take(x, financialRisk)) ∀x (RiskAverse(x) → Have(x, corporateJob)) ∀x (∃y ∃z (¬(y=x) ∧ ¬(z=x) ∧ ¬(y=z) ∧ HateWorkingFor(x, y) ∧ HateWorkingFor(x, z)) → Entrepreneur(x)) ¬Entrepreneur(markZuckerberg) ∧ ¬(∃y ∃z (¬(y=markZuckerberg) ∧ ¬(z=markZuckerberg) ∧ ¬(y=z) ∧ HateWorkingFor(markZuckerberg, y) ∧ HateWorkingFor(markZuckerberg, z))) → ¬RiskAverse(markZuckerberg)

Mark Zuckerberg is an entrepreneur.

Entrepreneur(markZuckerberg)

Uncertain

No people who have corporate jobs are taking more than normal financial risks. All entrepreneurs are taking more than normal financial risks. All risk-averse working people are people who have corporate jobs. All working people who hate working for others want to be entrepreneurs. If Mark Zuckerberg is neither an entrepreneur nor a person who hates working for others, then Mark Zuckerberg is not a risk-averse working person.

∀x (Have(x, corporateJob) → ¬Take(x, financialRisk)) ∀x (Entrepreneur(x) → Take(x, financialRisk)) ∀x (RiskAverse(x) → Have(x, corporateJob)) ∀x (∃y ∃z (¬(y=x) ∧ ¬(z=x) ∧ ¬(y=z) ∧ HateWorkingFor(x, y) ∧ HateWorkingFor(x, z)) → Entrepreneur(x)) ¬Entrepreneur(markZuckerberg) ∧ ¬(∃y ∃z (¬(y=markZuckerberg) ∧ ¬(z=markZuckerberg) ∧ ¬(y=z) ∧ HateWorkingFor(markZuckerberg, y) ∧ HateWorkingFor(markZuckerberg, z))) → ¬RiskAverse(markZuckerberg)

Mark Zuckerberg is a risk-averse person.

RiskAverse(markZuckerberg)

False

No people who have corporate jobs are taking more than normal financial risks. All entrepreneurs are taking more than normal financial risks. All risk-averse working people are people who have corporate jobs. All working people who hate working for others want to be entrepreneurs. If Mark Zuckerberg is neither an entrepreneur nor a person who hates working for others, then Mark Zuckerberg is not a risk-averse working person.

∀x (Have(x, corporateJob) → ¬Take(x, financialRisk)) ∀x (Entrepreneur(x) → Take(x, financialRisk)) ∀x (RiskAverse(x) → Have(x, corporateJob)) ∀x (∃y ∃z (¬(y=x) ∧ ¬(z=x) ∧ ¬(y=z) ∧ HateWorkingFor(x, y) ∧ HateWorkingFor(x, z)) → Entrepreneur(x)) ¬Entrepreneur(markZuckerberg) ∧ ¬(∃y ∃z (¬(y=markZuckerberg) ∧ ¬(z=markZuckerberg) ∧ ¬(y=z) ∧ HateWorkingFor(markZuckerberg, y) ∧ HateWorkingFor(markZuckerberg, z))) → ¬RiskAverse(markZuckerberg)

Mark Zuckerberg is not a risk-averse person.

¬RiskAverse(markZuckerberg)

True

Wildfeed exists as an unannounced program. Wildfeed can be sporting events, news, or syndicated shows. Pre-recorded content is a copyright violation. Programs are pre-recorded.

∃x (Wildfeed(x) ∧ Unannounced(x) ∧ Program(x)) ∀x (Wildfeed(x) → SportingEvent(x) ∨ News(x) ∨ SyndicatedShow(x)) ∀x (Prerecorded(x) → CopyrightViolation(x)) ∀x (Program(x) → Prerecorded(x))

Some wildfeed is violating copyright laws.

∃x (Wildfeed(x) ∧ CopyrightViolation(x))

True

Wildfeed exists as an unannounced program. Wildfeed can be sporting events, news, or syndicated shows. Pre-recorded content is a copyright violation. Programs are pre-recorded.

∃x (Wildfeed(x) ∧ Unannounced(x) ∧ Program(x)) ∀x (Wildfeed(x) → SportingEvent(x) ∨ News(x) ∨ SyndicatedShow(x)) ∀x (Prerecorded(x) → CopyrightViolation(x)) ∀x (Program(x) → Prerecorded(x))

Wildfeed can be prerecorded.

∃x (Wildfeed(x) ∧ Prerecorded(x))

True

Wildfeed exists as an unannounced program. Wildfeed can be sporting events, news, or syndicated shows. Pre-recorded content is a copyright violation. Programs are pre-recorded.

∃x (Wildfeed(x) ∧ Unannounced(x) ∧ Program(x)) ∀x (Wildfeed(x) → SportingEvent(x) ∨ News(x) ∨ SyndicatedShow(x)) ∀x (Prerecorded(x) → CopyrightViolation(x)) ∀x (Program(x) → Prerecorded(x))

Syndicated shows are copyright violations.

∃x (SyndicatedShows(x) ∧ CopyrightViolation(x))

Uncertain

New York City is Located in the United States of America. The United States of America is part of North America. North America is in the western hemisphere of the earth. New York City is a highly developed city. If place A is located in place B and place B is located in place C, then place A is located in place C.

LocatedIn(newYorkCity, unitedStatesOfAmerica) LocatedIn(usa, northAmerica) LocatedIn(northAmerica, westernHemisphere) HighlyDeveloped(newYorkCity) ∀x ∀y ∀z ((LocatedIn(x, y) ∧ LocatedIn(y, z)) → LocatedIn(x, z))

A highly developed city is located in the western hemisphere of the earth.

∃x (HighlyDeveloped(x) ∧ LocatedIn(x, westernHemisphere))

True

New York City is Located in the United States of America. The United States of America is part of North America. North America is in the western hemisphere of the earth. New York City is a highly developed city. If place A is located in place B and place B is located in place C, then place A is located in place C.

LocatedIn(newYorkCity, unitedStatesOfAmerica) LocatedIn(usa, northAmerica) LocatedIn(northAmerica, westernHemisphere) HighlyDeveloped(newYorkCity) ∀x ∀y ∀z ((LocatedIn(x, y) ∧ LocatedIn(y, z)) → LocatedIn(x, z))

The United States of America is not located in the western hemisphere of the earth.

¬LocatedIn(unitedStatesOfAmerica, westHemisphere)

False

New York City is Located in the United States of America. The United States of America is part of North America. North America is in the western hemisphere of the earth. New York City is a highly developed city. If place A is located in place B and place B is located in place C, then place A is located in place C.

LocatedIn(newYorkCity, unitedStatesOfAmerica) LocatedIn(usa, northAmerica) LocatedIn(northAmerica, westernHemisphere) HighlyDeveloped(newYorkCity) ∀x ∀y ∀z ((LocatedIn(x, y) ∧ LocatedIn(y, z)) → LocatedIn(x, z))

New York City is located in New York State.

LocatedIn(newYorkCity, newYork)

Uncertain

Catullus 4 is a poem written by the ancient Roman writer Catullus. Catullus 4 is a story about the retirement of a well-traveled ship. There is a strong analogy of human aging in the poem Catullus 4. Catullus 4 is written in an unusual iambic trimeter to convey a sense of speed over the waves.

Poem(catullus4) ∧ WrittenBy(catullus4, catullus) ∧ AncientRomanWriter(catullus) Story(catullus4) ∧ About(catullus4, retirementOfAWellTraveledShip) Poem(catullus4) ∧ StrongAgingAnalogy(catullus4) Poem(catullus4) ∧ WrittenIn(catullus4, iambicTrimeter) ∧ Convey(catullus4, aSenseOfSpeedOverTheWaves)

There is a poem written by an ancient Roman writer with a strong analogy of human aging.

∃x ∃y (Poem(x) ∧ WrittenBy(x, y) ∧ AncietRomanWriter(y) ∧ StrongAgingAnalogy(x))

True

Catullus 4 is a poem written by the ancient Roman writer Catullus. Catullus 4 is a story about the retirement of a well-traveled ship. There is a strong analogy of human aging in the poem Catullus 4. Catullus 4 is written in an unusual iambic trimeter to convey a sense of speed over the waves.

Poem(catullus4) ∧ WrittenBy(catullus4, catullus) ∧ AncientRomanWriter(catullus) Story(catullus4) ∧ About(catullus4, retirementOfAWellTraveledShip) Poem(catullus4) ∧ StrongAgingAnalogy(catullus4) Poem(catullus4) ∧ WrittenIn(catullus4, iambicTrimeter) ∧ Convey(catullus4, aSenseOfSpeedOverTheWaves)

There is a poem written by an ancient Roman writer in iambic trimeter.

∃x ∃y (Poem(x) ∧ WrittenBy(x, y) ∧ AncientRomanWriter(y) ∧ WrittenIn(x, iambicTrimeter))

Uncertain

Catullus 4 is a poem written by the ancient Roman writer Catullus. Catullus 4 is a story about the retirement of a well-traveled ship. There is a strong analogy of human aging in the poem Catullus 4. Catullus 4 is written in an unusual iambic trimeter to convey a sense of speed over the waves.

Poem(catullus4) ∧ WrittenBy(catullus4, catullus) ∧ AncientRomanWriter(catullus) Story(catullus4) ∧ About(catullus4, retirementOfAWellTraveledShip) Poem(catullus4) ∧ StrongAgingAnalogy(catullus4) Poem(catullus4) ∧ WrittenIn(catullus4, iambicTrimeter) ∧ Convey(catullus4, aSenseOfSpeedOverTheWaves)

Callus 4 is written in an unusual iambic trimeter to convey a strong analogy of human aging.

Poem(catullus4) ∧ WrittenIn(catullus4, iambicTrimeter) ∧ StrongAgingAnalogy(catullus4)

True

Westworld is an American science fiction-thriller TV series. In 2016, a television series named Westworld debuted on HBO. The TV series Westworld is adapted from the original film in 1973, which was written and directed by Michael Crichton. The 1973 film Westworld is about robots that malfunction and begin killing human visitors.

American(westworld) ∧ ScienceFictionThriller(westworld) Debut(westworld, year2016) ∧ TvSeries(westworld) Adapted(westworld, westworldTheFilm) ∧ Produce(westworldTheFilm, year1973) ∧ Wrote(michael, westworldTheFilm) ∧ Directed(michael, westworldTheFilm) Film(westworldTheFilm) ∧ About(westworldTheFilm, malfunctioningRobots)

Michael Crichton has directed a film about malfunctioning robots.

∃x (Film(x) ∧ Directed(michael, x) ∧ About(x, malfunctioningRobots))

True

Westworld is an American science fiction-thriller TV series. In 2016, a television series named Westworld debuted on HBO. The TV series Westworld is adapted from the original film in 1973, which was written and directed by Michael Crichton. The 1973 film Westworld is about robots that malfunction and begin killing human visitors.

American(westworld) ∧ ScienceFictionThriller(westworld) Debut(westworld, year2016) ∧ TvSeries(westworld) Adapted(westworld, westworldTheFilm) ∧ Produce(westworldTheFilm, year1973) ∧ Wrote(michael, westworldTheFilm) ∧ Directed(michael, westworldTheFilm) Film(westworldTheFilm) ∧ About(westworldTheFilm, malfunctioningRobots)

An American TV series debuted in 2016.

∃x (TVSeries(x) ∧ American(x) ∧ Debut(x, year2016))

True

The 2008 Summer Olympics were held in Beijing, China. The 2008 Summer Olympics was the second Summer Olympic Games held in a communist state. China won the most gold medals (48) in the 2008 Summer Olympics. The United States placed second in the gold medal tally but won the highest number of medals overall (112) in the 2008 Summer Olympics. The third place in the gold medal tally was achieved by Russia in the 2008 Summer Olympics. If a country placed third in gold medals, then it had fewer gold medals than the team that won the most gold medals.

HeldIn(2008SummerOlympics, beijingChina) SecondSummerOlympicsGames(2008SummerOlympics) ∧ BeHeldIn(2008SummerOlympics, communistState) Won(china, theMostGoldMedals) PlacedSecondInGoldMedalsIn(unitedStates, 2008SummerOlympics) ∧ Won(unitedStates, highestNumberOfMedals) PlacedThirdInGoldMedalsIn(russia, 2008SummerOlympics) ∀x ∀y (Placed(x, thirdInGoldMedals) ∧ Won(y, mostGoldMedals) → FewerGoldMedalsThan(x, y))

Russia did not win fewer gold medals than China.

¬FewerGoldMedalsThan(russia, china)

False

The 2008 Summer Olympics were held in Beijing, China. The 2008 Summer Olympics was the second Summer Olympic Games held in a communist state. China won the most gold medals (48) in the 2008 Summer Olympics. The United States placed second in the gold medal tally but won the highest number of medals overall (112) in the 2008 Summer Olympics. The third place in the gold medal tally was achieved by Russia in the 2008 Summer Olympics. If a country placed third in gold medals, then it had fewer gold medals than the team that won the most gold medals.

HeldIn(2008SummerOlympics, beijingChina) SecondSummerOlympicsGames(2008SummerOlympics) ∧ BeHeldIn(2008SummerOlympics, communistState) Won(china, theMostGoldMedals) PlacedSecondInGoldMedalsIn(unitedStates, 2008SummerOlympics) ∧ Won(unitedStates, highestNumberOfMedals) PlacedThirdInGoldMedalsIn(russia, 2008SummerOlympics) ∀x ∀y (Placed(x, thirdInGoldMedals) ∧ Won(y, mostGoldMedals) → FewerGoldMedalsThan(x, y))

Russia won fewer gold medals than China.

FewerGoldMedalsThan(russia, china)

True

Xiufeng, Xiangshan, Diecai, Qixing are districts in the city of Guilin. Yangshuo is not a district in Guilin.

DistrictIn(xiufeng, guilin) ∧ DistrictIn(xiangshan, guilin) ∧ DistrictIn(diecai, guilin) ∧ DistrictIn(qixing, guilin) ∧ City(guilin) ¬DistrictIn(yangshuo, guilin)

Xiangshan and Diecai are districts in the same city.

∃x (DistrictIn(xiangshan, x) ∧ DistrictIn(diecai, x) ∧ City(x))

True

Xiufeng, Xiangshan, Diecai, Qixing are districts in the city of Guilin. Yangshuo is not a district in Guilin.

DistrictIn(xiufeng, guilin) ∧ DistrictIn(xiangshan, guilin) ∧ DistrictIn(diecai, guilin) ∧ DistrictIn(qixing, guilin) ∧ City(guilin) ¬DistrictIn(yangshuo, guilin)

Xiufeng is a district in Guilin.

DistrictIn(xiufeng, guilin)

True

Xiufeng, Xiangshan, Diecai, Qixing are districts in the city of Guilin. Yangshuo is not a district in Guilin.

DistrictIn(xiufeng, guilin) ∧ DistrictIn(xiangshan, guilin) ∧ DistrictIn(diecai, guilin) ∧ DistrictIn(qixing, guilin) ∧ City(guilin) ¬DistrictIn(yangshuo, guilin)

Kowloon District is in Hong Kong.

DistrictIn(kowloon, hongKong)

Uncertain