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All fruits sold at Nica's market are shipped from Colombia. Some fruits sold in New Haven are shipped from Mexico. No fruits shipped from Colombia are sold at the local farmers market in New Haven. Avocados are a kind of fruit sold at the local farmers market in New Haven or at Nica's market. Avocados are either shipped from Colombia and sold in New Haven, or neither.

∀x ((Fruit(x) ∧ SoldAt(x, nicasMarket)) → ShippedFrom(x, colombia)) ∃x ∃y (Fruit(x) ∧ SoldIn(x, newHaven) ∧ ShippedFrom(x, mexico) ∧ (¬(x=y)) ∧ Fruit(y) ∧ SoldIn(y, newHaven) ∧ ShippedFrom(y, mexico)) ∀x ((Fruit(x) ∧ ShippedFrom(x, colombia)) → ¬(SoldAt(x, localFarmersMarket))) Fruit(avocado) ∧ (SoldAt(avocado, localFarmersMarket) ∨ SoldAt(avocado, nica'sMarket)) ¬(ShippedFrom(avocado, colombia) ⊕ SoldIn(avocado, newHaven))

Avocados are either sold at the local farmers market in New Haven or are sold in New Haven.

SoldAt(avocado, localFarmersMarket) ⊕ SoldIn(avocado, newHaven)

True

All fruits sold at Nica's market are shipped from Colombia. Some fruits sold in New Haven are shipped from Mexico. No fruits shipped from Colombia are sold at the local farmers market in New Haven. Avocados are a kind of fruit sold at the local farmers market in New Haven or at Nica's market. Avocados are either shipped from Colombia and sold in New Haven, or neither.

∀x ((Fruit(x) ∧ SoldAt(x, nicasMarket)) → ShippedFrom(x, colombia)) ∃x ∃y (Fruit(x) ∧ SoldIn(x, newHaven) ∧ ShippedFrom(x, mexico) ∧ (¬(x=y)) ∧ Fruit(y) ∧ SoldIn(y, newHaven) ∧ ShippedFrom(y, mexico)) ∀x ((Fruit(x) ∧ ShippedFrom(x, colombia)) → ¬(SoldAt(x, localFarmersMarket))) Fruit(avocado) ∧ (SoldAt(avocado, localFarmersMarket) ∨ SoldAt(avocado, nica'sMarket)) ¬(ShippedFrom(avocado, colombia) ⊕ SoldIn(avocado, newHaven))

Avocados are either sold in New Haven or sold at Nica's market.

SoldIn(avocado, newHaven) ⊕ SoldAt(x, nica'sMarket)

False

All fruits sold at Nica's market are shipped from Colombia. Some fruits sold in New Haven are shipped from Mexico. No fruits shipped from Colombia are sold at the local farmers market in New Haven. Avocados are a kind of fruit sold at the local farmers market in New Haven or at Nica's market. Avocados are either shipped from Colombia and sold in New Haven, or neither.

∀x ((Fruit(x) ∧ SoldAt(x, nicasMarket)) → ShippedFrom(x, colombia)) ∃x ∃y (Fruit(x) ∧ SoldIn(x, newHaven) ∧ ShippedFrom(x, mexico) ∧ (¬(x=y)) ∧ Fruit(y) ∧ SoldIn(y, newHaven) ∧ ShippedFrom(y, mexico)) ∀x ((Fruit(x) ∧ ShippedFrom(x, colombia)) → ¬(SoldAt(x, localFarmersMarket))) Fruit(avocado) ∧ (SoldAt(avocado, localFarmersMarket) ∨ SoldAt(avocado, nica'sMarket)) ¬(ShippedFrom(avocado, colombia) ⊕ SoldIn(avocado, newHaven))

If avocados are not both sold at the local farmers market in New Haven and shipped from Columbia, then they are neither sold at the local farmers market in New Haven nor in New Haven generally.

¬(SoldAt(avocado, localFarmersMarket) ∧ ShippedFrom(avocado, colombia)) → ¬SoldAt(avocado, localFarmersMarket) ∧ ¬SoldIn(avocado, newHaven)

False

Some monitors equipped in the library are produced by AOC. All monitors equipped in the library are cheaper than 800 dollars. All monitors cheaper than 800 dollars are with a resolution lower than 1080p. If a monitor has a resolution lower than 1080p, then it does not support the type-c port. A-2017 supports the type-c port.

∃x ∃y(Monitor(x) ∧ ProducedBy(x, aOC) ∧ In(x, library) ∧ (¬(x=y)) ∧ Monitor(y) ∧ ProducedBy(y, aOC) ∧ In(y, library)) ∀x ((Monitor(x) ∧ In(x, library)) → CheaperThan(x, dollars800)) ∀x ((Monitor(x) ∧ CheaperThan(x, dollars800)) → ResolutionLessThan(x, p1080)) ∀x ((Monitor(x) ∧ ResolutionLessThan(x, p1080)) → ¬Supports(x, type-CPort)) Supports(a-2017, type-CPort)

A-2017 is produced by AOC.

ProducedBy(x, aOC)

Uncertain

Some monitors equipped in the library are produced by AOC. All monitors equipped in the library are cheaper than 800 dollars. All monitors cheaper than 800 dollars are with a resolution lower than 1080p. If a monitor has a resolution lower than 1080p, then it does not support the type-c port. A-2017 supports the type-c port.

∃x ∃y(Monitor(x) ∧ ProducedBy(x, aOC) ∧ In(x, library) ∧ (¬(x=y)) ∧ Monitor(y) ∧ ProducedBy(y, aOC) ∧ In(y, library)) ∀x ((Monitor(x) ∧ In(x, library)) → CheaperThan(x, dollars800)) ∀x ((Monitor(x) ∧ CheaperThan(x, dollars800)) → ResolutionLessThan(x, p1080)) ∀x ((Monitor(x) ∧ ResolutionLessThan(x, p1080)) → ¬Supports(x, type-CPort)) Supports(a-2017, type-CPort)

A-2017 is produced by AOC and equipped in the library.

ProducedBy(a-2017, aOC) ∧ In(a-2017, library)

False

Some monitors equipped in the library are produced by AOC. All monitors equipped in the library are cheaper than 800 dollars. All monitors cheaper than 800 dollars are with a resolution lower than 1080p. If a monitor has a resolution lower than 1080p, then it does not support the type-c port. A-2017 supports the type-c port.

∃x ∃y(Monitor(x) ∧ ProducedBy(x, aOC) ∧ In(x, library) ∧ (¬(x=y)) ∧ Monitor(y) ∧ ProducedBy(y, aOC) ∧ In(y, library)) ∀x ((Monitor(x) ∧ In(x, library)) → CheaperThan(x, dollars800)) ∀x ((Monitor(x) ∧ CheaperThan(x, dollars800)) → ResolutionLessThan(x, p1080)) ∀x ((Monitor(x) ∧ ResolutionLessThan(x, p1080)) → ¬Supports(x, type-CPort)) Supports(a-2017, type-CPort)

If either A-2017 is both with a resolution of 1080p and produced by AOC or it is neither, then it is not equipped in the library.

¬(ResolutionLessThan(a-2017, p1080) ⊕ ProducedBy(x, aOC)) → ¬(In(a-2017, library))

True

Sūduva Marijampolė holds the Lithuanian Super Cup. Sūduva Marijampolė is a soccer team.

Holds(suduva, theLithuanianSuperCup) SoccerTeam(suduva)

Some soccer team holds the Lithuanian Super Cup.

∃x (SoccerTeam(x) ∧ Holds(x, theLithuanianSuperCup))

True

Ainderby Quernhow is a village and civil parish in the Hambleton District. Hambleton District is in North Yorkshire. North Yorkshire is in England. If place A is located in place B and place B is located in place C, then place A is located in place C.

Village(ainderbyQuernhow) ∧ CivilParish(ainderbyQuernhow) ∧ In(ainderbyQuernhow, hambletonDistrict) In(hambletonDistrict, northYorkshire) In(northYorkshire, england) ∀x ∀y ∀z ((In(x, y) ∧ In(y, z)) → In(x, z))

There is a village in England.

∃x (Village(x) ∧ In(x, england))

True

Ainderby Quernhow is a village and civil parish in the Hambleton District. Hambleton District is in North Yorkshire. North Yorkshire is in England. If place A is located in place B and place B is located in place C, then place A is located in place C.

Village(ainderbyQuernhow) ∧ CivilParish(ainderbyQuernhow) ∧ In(ainderbyQuernhow, hambletonDistrict) In(hambletonDistrict, northYorkshire) In(northYorkshire, england) ∀x ∀y ∀z ((In(x, y) ∧ In(y, z)) → In(x, z))

There is no civil parish in England.

¬(∃x (CivilParish(x) ∧ In(x, england)))

False

Douglas Adams is an author who created the book collection called The Salmon of Doubt. The Salmon of Doubt is about life experiences and technology. All authors are writers. Writers create innovative ideas. Some books that contain innovative ideas are about technology.

Author(douglasAdams) ∧ Authored(douglasAdams, theSalmonOfDoubt) ∧ Book(theSalmonOfDoubt) About(theSalmonOfDoubt, lifeExperience) ∧ About(theSalmonOfDoubt, technology) ∀x (Author(x) → Writer(x)) ∀x (Writer(x) → Create(x, innovativeIdea)) ∃x ∃y (Contain(x, innovativeIdea) ∧ About(x, technology) ∧ (¬(x=y)) ∧ (Contain(y, innovativeIdea) ∧ About(y, technology)))

Douglas Adams is a writer.

Writer(douglasAdams)

True

Douglas Adams is an author who created the book collection called The Salmon of Doubt. The Salmon of Doubt is about life experiences and technology. All authors are writers. Writers create innovative ideas. Some books that contain innovative ideas are about technology.

Author(douglasAdams) ∧ Authored(douglasAdams, theSalmonOfDoubt) ∧ Book(theSalmonOfDoubt) About(theSalmonOfDoubt, lifeExperience) ∧ About(theSalmonOfDoubt, technology) ∀x (Author(x) → Writer(x)) ∀x (Writer(x) → Create(x, innovativeIdea)) ∃x ∃y (Contain(x, innovativeIdea) ∧ About(x, technology) ∧ (¬(x=y)) ∧ (Contain(y, innovativeIdea) ∧ About(y, technology)))

Douglas Adams created innovative ideas.

Create(douglasAdams, innovativeIdea)

True

Douglas Adams is an author who created the book collection called The Salmon of Doubt. The Salmon of Doubt is about life experiences and technology. All authors are writers. Writers create innovative ideas. Some books that contain innovative ideas are about technology.

Author(douglasAdams) ∧ Authored(douglasAdams, theSalmonOfDoubt) ∧ Book(theSalmonOfDoubt) About(theSalmonOfDoubt, lifeExperience) ∧ About(theSalmonOfDoubt, technology) ∀x (Author(x) → Writer(x)) ∀x (Writer(x) → Create(x, innovativeIdea)) ∃x ∃y (Contain(x, innovativeIdea) ∧ About(x, technology) ∧ (¬(x=y)) ∧ (Contain(y, innovativeIdea) ∧ About(y, technology)))

The Salmon of Doubt has no innovative Ideas.

¬Contain(theSalmonOfDoubt, innovativeIdea)

Uncertain

No disposable products can help slow down global warming. All eco-friendly brands can help slow down global warming. All sustainable fashion brands are eco-friendly brands. All fast fashion products are disposable products. If Reformation is not helping slow down global warming, then Reformation is an eco-friendly brand or a sustainable fashion brand.

∀x (Disposable(x) ∧ Product(x) → ¬HelpSlowDown(x, globalWarming)) ∀x (EcoFriendly(x) ∧ Brand(x) → Help(x, slowDownGlobalWarming)) ∀x (Sustainable(x) ∧ FashionBrand(x) → EcoFriendly(x) ∧ Brand(x)) ∀x (FastFashion(x) ∧ Product(x) → Disposable(x) ∧ Product(x)) ¬HelpSlowDown(reformation, globalWarming) → (EcoFriendly(reformation) ∧ Brand(reformation)) ∨ (Sustainable(reformation) ∧ FashionBrand(reformation))

Reformation is an eco-friendly brand.

EcoFriendly(reformation) ∧ Brand(reformation)

Uncertain

No disposable products can help slow down global warming. All eco-friendly brands can help slow down global warming. All sustainable fashion brands are eco-friendly brands. All fast fashion products are disposable products. If Reformation is not helping slow down global warming, then Reformation is an eco-friendly brand or a sustainable fashion brand.

∀x (Disposable(x) ∧ Product(x) → ¬HelpSlowDown(x, globalWarming)) ∀x (EcoFriendly(x) ∧ Brand(x) → Help(x, slowDownGlobalWarming)) ∀x (Sustainable(x) ∧ FashionBrand(x) → EcoFriendly(x) ∧ Brand(x)) ∀x (FastFashion(x) ∧ Product(x) → Disposable(x) ∧ Product(x)) ¬HelpSlowDown(reformation, globalWarming) → (EcoFriendly(reformation) ∧ Brand(reformation)) ∨ (Sustainable(reformation) ∧ FashionBrand(reformation))

Reformation produces fast fashion products.

FastFashion(reformation) ∧ Product(reformation)

False

No disposable products can help slow down global warming. All eco-friendly brands can help slow down global warming. All sustainable fashion brands are eco-friendly brands. All fast fashion products are disposable products. If Reformation is not helping slow down global warming, then Reformation is an eco-friendly brand or a sustainable fashion brand.

∀x (Disposable(x) ∧ Product(x) → ¬HelpSlowDown(x, globalWarming)) ∀x (EcoFriendly(x) ∧ Brand(x) → Help(x, slowDownGlobalWarming)) ∀x (Sustainable(x) ∧ FashionBrand(x) → EcoFriendly(x) ∧ Brand(x)) ∀x (FastFashion(x) ∧ Product(x) → Disposable(x) ∧ Product(x)) ¬HelpSlowDown(reformation, globalWarming) → (EcoFriendly(reformation) ∧ Brand(reformation)) ∨ (Sustainable(reformation) ∧ FashionBrand(reformation))

Reformation does not produce fast fashion products.

¬(FastFashion(reformation) ∧ Product(reformation))

True

No disposable products can help slow down global warming. All eco-friendly brands can help slow down global warming. All sustainable fashion brands are eco-friendly brands. All fast fashion products are disposable products. If Reformation is not helping slow down global warming, then Reformation is an eco-friendly brand or a sustainable fashion brand.

∀x (Disposable(x) ∧ Product(x) → ¬HelpSlowDown(x, globalWarming)) ∀x (EcoFriendly(x) ∧ Brand(x) → Help(x, slowDownGlobalWarming)) ∀x (Sustainable(x) ∧ FashionBrand(x) → EcoFriendly(x) ∧ Brand(x)) ∀x (FastFashion(x) ∧ Product(x) → Disposable(x) ∧ Product(x)) ¬HelpSlowDown(reformation, globalWarming) → (EcoFriendly(reformation) ∧ Brand(reformation)) ∨ (Sustainable(reformation) ∧ FashionBrand(reformation))

Reformation does not produce fast fashion products or does not produce disposable products.

¬(FastFashion(reformation) ∧ Product(reformation)) ∨ ¬(Disposable(x) ∧ Product(x))

True

No disposable products can help slow down global warming. All eco-friendly brands can help slow down global warming. All sustainable fashion brands are eco-friendly brands. All fast fashion products are disposable products. If Reformation is not helping slow down global warming, then Reformation is an eco-friendly brand or a sustainable fashion brand.

∀x (Disposable(x) ∧ Product(x) → ¬HelpSlowDown(x, globalWarming)) ∀x (EcoFriendly(x) ∧ Brand(x) → Help(x, slowDownGlobalWarming)) ∀x (Sustainable(x) ∧ FashionBrand(x) → EcoFriendly(x) ∧ Brand(x)) ∀x (FastFashion(x) ∧ Product(x) → Disposable(x) ∧ Product(x)) ¬HelpSlowDown(reformation, globalWarming) → (EcoFriendly(reformation) ∧ Brand(reformation)) ∨ (Sustainable(reformation) ∧ FashionBrand(reformation))

If Reformation produces disposable products, then Reformation produces fast fashion products.

(Disposable(reformation) ∧ Product(reformation)) → (FastFashion(reformation) ∧ Product(reformation))

True

No disposable products can help slow down global warming. All eco-friendly brands can help slow down global warming. All sustainable fashion brands are eco-friendly brands. All fast fashion products are disposable products. If Reformation is not helping slow down global warming, then Reformation is an eco-friendly brand or a sustainable fashion brand.

∀x (Disposable(x) ∧ Product(x) → ¬HelpSlowDown(x, globalWarming)) ∀x (EcoFriendly(x) ∧ Brand(x) → Help(x, slowDownGlobalWarming)) ∀x (Sustainable(x) ∧ FashionBrand(x) → EcoFriendly(x) ∧ Brand(x)) ∀x (FastFashion(x) ∧ Product(x) → Disposable(x) ∧ Product(x)) ¬HelpSlowDown(reformation, globalWarming) → (EcoFriendly(reformation) ∧ Brand(reformation)) ∨ (Sustainable(reformation) ∧ FashionBrand(reformation))

If Reformation produces fast fashion products or helps slow down global warming, then Reformation produces fast fashion products.

(FastFashion(reformation) ∧ Product(reformation)) ∨ ¬HelpSlowDown(reformation, globalWarming)

False

Roy Richardson was a cricketer who played for Sint Maarten, a constituent country. Roy Richardson was a right-handed batsman and medium-pace bowler. Roy Richardson was old when he debuted in cricket. Sherville Huggins dismissed Roy Richardson.

Cricketeer(royRichardson) ∧ PlaysFor(royRichardson, sintMaarten) ∧ ConstituentCountry(sintMaarten) RightHanded(royRichardson) ∧ Batsman(royRichardson) ∧ MediumPaceBowler(royRichardson) OldAtDebut(royRichardson) Dismisses(shervilleHuggins, royRichardson)

Sherville Huggins has never dismissed anyone playing cricket for a constituent country.

∀x ∀y ((ConsituentCountry(y) ∧ PlayedFor(x, y)) → ¬Dismissed(shervillehuggins, x))

False

Roy Richardson was a cricketer who played for Sint Maarten, a constituent country. Roy Richardson was a right-handed batsman and medium-pace bowler. Roy Richardson was old when he debuted in cricket. Sherville Huggins dismissed Roy Richardson.

Cricketeer(royRichardson) ∧ PlaysFor(royRichardson, sintMaarten) ∧ ConstituentCountry(sintMaarten) RightHanded(royRichardson) ∧ Batsman(royRichardson) ∧ MediumPaceBowler(royRichardson) OldAtDebut(royRichardson) Dismisses(shervilleHuggins, royRichardson)

No right-handed medium-pace bowlers were playing for Sint Maarten.

∀x ((RightHanded(x) ∧ MediumPaceBowler(x)) → ¬PlayedFor(x, sintMaarten))

False

To get a job at Google, you need to have a lot of work experience or a good education. One needs to submit their resume to Google to get a job there. John has a lot of work experience. John submitted his resume to Google and got a job there.

∀x (GetAJobAt(x, google) → Have(x, aLotOfWorkExperience) ∨ Have(x, goodEducation)) ∀x (GetAJobAt(x, google) → Submitted(x, resume, google)) Have(john, aLotOfWorkExperience) Submitted(john, resume, google) ∧ GetAJobAt(john, google)

John is a Yale graduate.

YaleGraduate(john)

Uncertain

No iPhones are standalone desktops. All Apple-made cellphones are iPhones. All phones with A15 Bionic chips are Apple-made cell phones. All phones equipped with four core-GPU made by Apple are phones with A15 Bionic chips. If an unannounced Huawei phone is either a phone with A15 Bionic chips or equipped with four core-GPU made by Apple, then unannounced Huawei phone is neither a phone with A15 Bionic chips nor a standalone desktop.

∀x (IPhone(x) → ¬StandaloneDesktop(x)) ∀x (AppleMade(x) ∧ Cellphone(x) → IPhone(x)) ∀x (Phone(x) ∧ With(x, a15BionicChip) → AppleMade(x) ∧ Cellphone(x)) ∀x (Phone(x) ∧ EquippedWith(x, fourCoreGPU) ∧ MadeBy(x, apple) → Phone(x) ∧ With(x, a15BionicChip)) (Phone(unannouncedHuaweiPhone) ∧ With(unannouncedHuaweiPhone, a15BionicChip)) ⊕ (Phone(unannouncedHuaweiPhone) ∧ EquippedWith(unannouncedHuaweiPhone, fourCoreGPU) ∧ MadeBy(unannouncedHuaweiPhone, apple)) → ¬(Phone(unannouncedHuaweiPhone) ∧ With(unannouncedHuaweiPhone, a15BionicChip) ∧ StandaloneDesktop(unannouncedHuaweiPhone))

Joe is a person taking classes.

AppleMade(unannouncedHuaweiPhone) ∧ Cellphone(unannouncedHuaweiPhone)

Uncertain

No iPhones are standalone desktops. All Apple-made cellphones are iPhones. All phones with A15 Bionic chips are Apple-made cell phones. All phones equipped with four core-GPU made by Apple are phones with A15 Bionic chips. If an unannounced Huawei phone is either a phone with A15 Bionic chips or equipped with four core-GPU made by Apple, then unannounced Huawei phone is neither a phone with A15 Bionic chips nor a standalone desktop.

∀x (IPhone(x) → ¬StandaloneDesktop(x)) ∀x (AppleMade(x) ∧ Cellphone(x) → IPhone(x)) ∀x (Phone(x) ∧ With(x, a15BionicChip) → AppleMade(x) ∧ Cellphone(x)) ∀x (Phone(x) ∧ EquippedWith(x, fourCoreGPU) ∧ MadeBy(x, apple) → Phone(x) ∧ With(x, a15BionicChip)) (Phone(unannouncedHuaweiPhone) ∧ With(unannouncedHuaweiPhone, a15BionicChip)) ⊕ (Phone(unannouncedHuaweiPhone) ∧ EquippedWith(unannouncedHuaweiPhone, fourCoreGPU) ∧ MadeBy(unannouncedHuaweiPhone, apple)) → ¬(Phone(unannouncedHuaweiPhone) ∧ With(unannouncedHuaweiPhone, a15BionicChip) ∧ StandaloneDesktop(unannouncedHuaweiPhone))

Joe is a PhD student.

Phone(unannouncedHuaweiPhone) ∧ EquippedWith(unannouncedHuaweiPhone, fourCoreGPU) ∧ MadeByApple(unannouncedHuaweiPhone)

False

No iPhones are standalone desktops. All Apple-made cellphones are iPhones. All phones with A15 Bionic chips are Apple-made cell phones. All phones equipped with four core-GPU made by Apple are phones with A15 Bionic chips. If an unannounced Huawei phone is either a phone with A15 Bionic chips or equipped with four core-GPU made by Apple, then unannounced Huawei phone is neither a phone with A15 Bionic chips nor a standalone desktop.

∀x (IPhone(x) → ¬StandaloneDesktop(x)) ∀x (AppleMade(x) ∧ Cellphone(x) → IPhone(x)) ∀x (Phone(x) ∧ With(x, a15BionicChip) → AppleMade(x) ∧ Cellphone(x)) ∀x (Phone(x) ∧ EquippedWith(x, fourCoreGPU) ∧ MadeBy(x, apple) → Phone(x) ∧ With(x, a15BionicChip)) (Phone(unannouncedHuaweiPhone) ∧ With(unannouncedHuaweiPhone, a15BionicChip)) ⊕ (Phone(unannouncedHuaweiPhone) ∧ EquippedWith(unannouncedHuaweiPhone, fourCoreGPU) ∧ MadeBy(unannouncedHuaweiPhone, apple)) → ¬(Phone(unannouncedHuaweiPhone) ∧ With(unannouncedHuaweiPhone, a15BionicChip) ∧ StandaloneDesktop(unannouncedHuaweiPhone))

Joe is not a PhD student.

¬(Phone(unannouncedHuaweiPhone) ∧ EquippedWith(unannouncedHuaweiPhone, fourCoreGPU) ∧ MadeByApple(unannouncedHuaweiPhone))

True

Hugh Vanstone is one of the world's leading lighting designers. Hugh Vanstone is from the UK. Hugh Vanstone has lit more than 160 productions. Hugh Vanstone attended a school where he is from.

WorldLeadingLightingDesigner(hughVanstone) From(hughVanstone, unitedKingdom) ∃x(GreaterThan(x, num160) ∧ LitProductions(hughVanstone,x)) ∃x(Hometown(hughVanstone,x) ∧ AttendedSchoolIn(hughVanstone,x))

Hugh Vanstone is one of the world's leading lighting designers and is from the UK.

WorldLeadingLightingDesigner(hughVanstone) ∧ From(hughVanstone, unitedKingdom)

True

Hugh Vanstone is one of the world's leading lighting designers. Hugh Vanstone is from the UK. Hugh Vanstone has lit more than 160 productions. Hugh Vanstone attended a school where he is from.

WorldLeadingLightingDesigner(hughVanstone) From(hughVanstone, unitedKingdom) ∃x(GreaterThan(x, num160) ∧ LitProductions(hughVanstone,x)) ∃x(Hometown(hughVanstone,x) ∧ AttendedSchoolIn(hughVanstone,x))

Hugh Vanstone has lit 170 productions.

∃x(GreaterThan(x, num170) ∧ LitProductions(hughVanstone,x))

Uncertain

Hugh Vanstone is one of the world's leading lighting designers. Hugh Vanstone is from the UK. Hugh Vanstone has lit more than 160 productions. Hugh Vanstone attended a school where he is from.

WorldLeadingLightingDesigner(hughVanstone) From(hughVanstone, unitedKingdom) ∃x(GreaterThan(x, num160) ∧ LitProductions(hughVanstone,x)) ∃x(Hometown(hughVanstone,x) ∧ AttendedSchoolIn(hughVanstone,x))

Hugh Vanstone attended a school in the United States.

AttendedSchoolIn(hughVanstone, unitedStates)

Uncertain

No man can run faster than Bolt. Superman is not a man.

∀x (Man(x) → ¬RunFasterThan(xm bolt)) ¬Man(superman)

Superman can run faster than Bolt.

RunFasterThan(superman, bolt)

Uncertain

Donald Ervin Knuth is an American computer scientist, mathematician, and Professor Emeritus at Stanford University. Knuth has been called the "father of the analysis of algorithms."

American(donaldErvinKnuth) ∧ ComputerScientist(donaldErvinKnuth) ∧ Mathematician(donaldErvinKnuth) ∧ ProfessorEmeritusAt(donaldErvinKnuth, stanford) Called(donaldErvinKnuth, fatherOfTheAnalysisOfAlgorithms)

An American scientist has been called the "father of the analysis of algorithms".

∃x (American(x) ∧ ComputerScientist(x) ∧ Called(x, fatherOfTheAnalysisOfAlgorithms))

True

Donald Ervin Knuth is an American computer scientist, mathematician, and Professor Emeritus at Stanford University. Knuth has been called the "father of the analysis of algorithms."

American(donaldErvinKnuth) ∧ ComputerScientist(donaldErvinKnuth) ∧ Mathematician(donaldErvinKnuth) ∧ ProfessorEmeritusAt(donaldErvinKnuth, stanford) Called(donaldErvinKnuth, fatherOfTheAnalysisOfAlgorithms)

A mathematician has been called the "father of the analysis of algorithms".

∃x (Mathematician(x) ∧ Called(x, fatherOfTheAnalysisOfAlgorithms))

True

Donald Ervin Knuth is an American computer scientist, mathematician, and Professor Emeritus at Stanford University. Knuth has been called the "father of the analysis of algorithms."

American(donaldErvinKnuth) ∧ ComputerScientist(donaldErvinKnuth) ∧ Mathematician(donaldErvinKnuth) ∧ ProfessorEmeritusAt(donaldErvinKnuth, stanford) Called(donaldErvinKnuth, fatherOfTheAnalysisOfAlgorithms)

Donald Knuth is a well-known figure in the field of artificial intelligence.

WellKnownFigureIn(donaldErvinKnuth, artificialIntelligence)

Uncertain

Neocrepidodera Corpulentas are flea beetles or moths, or both. Neocrepidodera Corpulentas are in the Chrysomelidae family. There are no moths within the Chrysomelidae family. There is a Neocrepidodera Corpulenta.

∀x (NeocrepidoderaCorpulenta(x) → (FleaBeetle(x) ∨ Moth(x))) ∀x (NeocrepidoderaCorpulenta(x) → In(x, chrysomelidaeFamily)) ∀x (In(x, chrysomelidaeFamily) → ¬Moth(x)) ∃x (NeocrepidoderaCorpulenta(x))

There is a flea beetle within the Chrysomelidae family.

∃x (FleaBeetle(x) ∧ In(x, chrysomelidaeFamily))

True

Neocrepidodera Corpulentas are flea beetles or moths, or both. Neocrepidodera Corpulentas are in the Chrysomelidae family. There are no moths within the Chrysomelidae family. There is a Neocrepidodera Corpulenta.

∀x (NeocrepidoderaCorpulenta(x) → (FleaBeetle(x) ∨ Moth(x))) ∀x (NeocrepidoderaCorpulenta(x) → In(x, chrysomelidaeFamily)) ∀x (In(x, chrysomelidaeFamily) → ¬Moth(x)) ∃x (NeocrepidoderaCorpulenta(x))

There are no flea beetles within the Chrysomelidae family.

∀x (FleaBeetle(x) → ¬In(x, chrysomelidaeFamily))

False

Carrozzeria Colli is a Milanese coachbuilder company established by Giuseppe Colli in 1931. Carrozzeria Colli is a company that specializes in using aluminum. The first automobiles built by Carrozzeria Colli were racing cars. Some racing cars built by Carrozzeria Colli used Fiat 1100 mechanicals and chassis. Carrozzeria Colli worked for airforces. Carrozzeria Colli made car bodies.

Milanese(carrozzeriaColli) ∧ CoachBuilder(carrozzeriaColli) ∧ Company(carrozzeriaColli) ∧ EstablishedBy(carrozzeriaColli, giuseppeColli) ∧ EstablishedIn(carrozzeriaColli, 1931) Company(carrozzeriaColli) ∧ SpecializesIn(carrozzeriaColli, usingAluminum) ∀x (BuiltBy(x, carrozzeriaColli) ∧ FirstAutomobile(x) → RacingCar(x)) ∃x (BuiltBy(x, carrozzeriaColli) ∧ RacingCar(x) ∧ Used(x, fiat1100mechanicals) ∧ Used(x, chassis)) ∃x (Airforce(x) ∧ WorkedFor(carrozzeriaColli, x)) ∃(CarBody(x) ∧ Made(x, carrozzeriaColli))

Carrozzeria Colli made car bodies in 1931.

∃x (CarBody(x) ∧ Made(x, carrozzeriaColli) ∧ MadeIn(x, 1931))

Uncertain

Carrozzeria Colli is a Milanese coachbuilder company established by Giuseppe Colli in 1931. Carrozzeria Colli is a company that specializes in using aluminum. The first automobiles built by Carrozzeria Colli were racing cars. Some racing cars built by Carrozzeria Colli used Fiat 1100 mechanicals and chassis. Carrozzeria Colli worked for airforces. Carrozzeria Colli made car bodies.

Milanese(carrozzeriaColli) ∧ CoachBuilder(carrozzeriaColli) ∧ Company(carrozzeriaColli) ∧ EstablishedBy(carrozzeriaColli, giuseppeColli) ∧ EstablishedIn(carrozzeriaColli, 1931) Company(carrozzeriaColli) ∧ SpecializesIn(carrozzeriaColli, usingAluminum) ∀x (BuiltBy(x, carrozzeriaColli) ∧ FirstAutomobile(x) → RacingCar(x)) ∃x (BuiltBy(x, carrozzeriaColli) ∧ RacingCar(x) ∧ Used(x, fiat1100mechanicals) ∧ Used(x, chassis)) ∃x (Airforce(x) ∧ WorkedFor(carrozzeriaColli, x)) ∃(CarBody(x) ∧ Made(x, carrozzeriaColli))

Carrozzeria Colli built airplanes during World War II.

∃x (Airplane(x) ∧ Made(x, carrozzeriaColli) ∧ MadeDuring(x, worldWarII))

Uncertain

Carrozzeria Colli is a Milanese coachbuilder company established by Giuseppe Colli in 1931. Carrozzeria Colli is a company that specializes in using aluminum. The first automobiles built by Carrozzeria Colli were racing cars. Some racing cars built by Carrozzeria Colli used Fiat 1100 mechanicals and chassis. Carrozzeria Colli worked for airforces. Carrozzeria Colli made car bodies.

Milanese(carrozzeriaColli) ∧ CoachBuilder(carrozzeriaColli) ∧ Company(carrozzeriaColli) ∧ EstablishedBy(carrozzeriaColli, giuseppeColli) ∧ EstablishedIn(carrozzeriaColli, 1931) Company(carrozzeriaColli) ∧ SpecializesIn(carrozzeriaColli, usingAluminum) ∀x (BuiltBy(x, carrozzeriaColli) ∧ FirstAutomobile(x) → RacingCar(x)) ∃x (BuiltBy(x, carrozzeriaColli) ∧ RacingCar(x) ∧ Used(x, fiat1100mechanicals) ∧ Used(x, chassis)) ∃x (Airforce(x) ∧ WorkedFor(carrozzeriaColli, x)) ∃(CarBody(x) ∧ Made(x, carrozzeriaColli))

Giuseppe Colli established a company that made car bodies.

∃x ∃y (Company(x) ∧ EstablishedBy(x, giuseppeColli) ∧ CarBody(y) ∧ Made(y, x))

True

Carrozzeria Colli is a Milanese coachbuilder company established by Giuseppe Colli in 1931. Carrozzeria Colli is a company that specializes in using aluminum. The first automobiles built by Carrozzeria Colli were racing cars. Some racing cars built by Carrozzeria Colli used Fiat 1100 mechanicals and chassis. Carrozzeria Colli worked for airforces. Carrozzeria Colli made car bodies.

Milanese(carrozzeriaColli) ∧ CoachBuilder(carrozzeriaColli) ∧ Company(carrozzeriaColli) ∧ EstablishedBy(carrozzeriaColli, giuseppeColli) ∧ EstablishedIn(carrozzeriaColli, 1931) Company(carrozzeriaColli) ∧ SpecializesIn(carrozzeriaColli, usingAluminum) ∀x (BuiltBy(x, carrozzeriaColli) ∧ FirstAutomobile(x) → RacingCar(x)) ∃x (BuiltBy(x, carrozzeriaColli) ∧ RacingCar(x) ∧ Used(x, fiat1100mechanicals) ∧ Used(x, chassis)) ∃x (Airforce(x) ∧ WorkedFor(carrozzeriaColli, x)) ∃(CarBody(x) ∧ Made(x, carrozzeriaColli))

Giuseppe Colli established a Milanese coachbuilder company that specialized in using aluminum.

∃x (Milanese(x) ∧ CoachBuilder(x) ∧ Company(x) ∧ EstablishedBy(x, giuseppeColli) ∧ SpecializesIn(x, usingAluminum))

True

Carrozzeria Colli is a Milanese coachbuilder company established by Giuseppe Colli in 1931. Carrozzeria Colli is a company that specializes in using aluminum. The first automobiles built by Carrozzeria Colli were racing cars. Some racing cars built by Carrozzeria Colli used Fiat 1100 mechanicals and chassis. Carrozzeria Colli worked for airforces. Carrozzeria Colli made car bodies.

Milanese(carrozzeriaColli) ∧ CoachBuilder(carrozzeriaColli) ∧ Company(carrozzeriaColli) ∧ EstablishedBy(carrozzeriaColli, giuseppeColli) ∧ EstablishedIn(carrozzeriaColli, 1931) Company(carrozzeriaColli) ∧ SpecializesIn(carrozzeriaColli, usingAluminum) ∀x (BuiltBy(x, carrozzeriaColli) ∧ FirstAutomobile(x) → RacingCar(x)) ∃x (BuiltBy(x, carrozzeriaColli) ∧ RacingCar(x) ∧ Used(x, fiat1100mechanicals) ∧ Used(x, chassis)) ∃x (Airforce(x) ∧ WorkedFor(carrozzeriaColli, x)) ∃(CarBody(x) ∧ Made(x, carrozzeriaColli))

The first automobiles built by Carrozzeria Colli were built using Fiat 1100 mechanicals and chassis.

∃x (BuiltBy(x, carrozzeriaColli) ∧ FirstAutomobil(x) ∧ Used(x, fiat1100mechanicals) ∧ Used(x, chassis))

Uncertain

John will go to the cinema if and only if Jack goes to the cinema today. Jack will go to the cinema if and only if Iron Man is on and the weather is not bad today. Some days in March have bad weather. Iron Man is on. It's March now.

(GoTo(john, theCinema) ∧ GoTo(john, today)) ↔ GoTo(jack, theCinema) ∧ GoTo(jack, today) (GoTo(john, theCinema) ∧ GoTo(john, today)) ↔ (On(ironman) ∧ ¬Bad(weather, today)) ∃x (Day(x) ∧ March(x) → ¬Bad(weather, x)) On(ironman) Day(presentMoment) ∧ March(presentMoment)

John will go to the cinema.

GoTo(john, theCinema) ∧ GoTo(john, today)

Uncertain

John will go to the cinema if and only if Jack goes to the cinema today. Jack will go to the cinema if and only if Iron Man is on and the weather is not bad today. Some days in March have bad weather. Iron Man is on. It's March now.

(GoTo(john, theCinema) ∧ GoTo(john, today)) ↔ GoTo(jack, theCinema) ∧ GoTo(jack, today) (GoTo(john, theCinema) ∧ GoTo(john, today)) ↔ (On(ironman) ∧ ¬Bad(weather, today)) ∃x (Day(x) ∧ March(x) → ¬Bad(weather, x)) On(ironman) Day(presentMoment) ∧ March(presentMoment)

The weather is good today.

¬Bad(weather, today)

Uncertain

Quiksilver sells sportswear, clothing, footwear, and accessories. Flannels are a type of clothing. Joe owns an item from Quiksilver.

∀x (Sells(quiksilver, x) → (Sportswear(x) ∨ Clothing(x) ∨ Footwear(x) ∨ Accessory(x))) Clothing(flannel) ∃x (Sells(quiksilver, x) ∧ Owns(joe, x))

Quiksilver sells beer.

Sells(quiksilver, beer)

Uncertain

Quiksilver sells sportswear, clothing, footwear, and accessories. Flannels are a type of clothing. Joe owns an item from Quiksilver.

∀x (Sells(quiksilver, x) → (Sportswear(x) ∨ Clothing(x) ∨ Footwear(x) ∨ Accessory(x))) Clothing(flannel) ∃x (Sells(quiksilver, x) ∧ Owns(joe, x))

Joe owns a flannel.

Owns(joe, flannel)

Uncertain

Quiksilver sells sportswear, clothing, footwear, and accessories. Flannels are a type of clothing. Joe owns an item from Quiksilver.

∀x (Sells(quiksilver, x) → (Sportswear(x) ∨ Clothing(x) ∨ Footwear(x) ∨ Accessory(x))) Clothing(flannel) ∃x (Sells(quiksilver, x) ∧ Owns(joe, x))

Joe owns at least one piece of sportswear, clothing, footwear, or accessory

∃x (Owns(joe, x) ∧ Sportswear(x) ∨ Clothing(x) ∨ Footwear(x) ∨ Accessory(x))

True

No video games released by Nintendo support the PS4 platform. All video games in the Pokemon series are released by Nintendo. All video games in the FIFA series support the PS4 platform. All video games that allow users to simulate playing online soccer using licensed players are in the FIFA series. The video game named “Be Lionel” is in the Pokemon series, or it allows users to simulate playing online soccer games using licensed players.

∀x (VideoGame(x) ∧ ReleasedBy(x, nintendo) → ¬Support(x, pS4)) ∀x (VideoGame(x) ∧ In(x, pokemonSeries) → ReleasedBy(x, nintendo)) ∀x (VideoGame(x) ∧ In(x, fIFASeries) → Support(x, pS4)) ∀x (VideoGame(x) ∧ Simulate(x, onlineSoccer) ∧ Use(x, licensedPlayer) → In(x, fIFASeries)) VideoGame(beLionel) ∧ In(beLionel, pokemonSeries) ∨ (Simulate(beLionel, onlineSoccer) ∧ Use(beLionel, licensedPlayer))

The video game "Be Lionel" is in the pokemon series.

VideoGame(beLionel) ∧ PokemonSeries(beLionel)

Uncertain

No video games released by Nintendo support the PS4 platform. All video games in the Pokemon series are released by Nintendo. All video games in the FIFA series support the PS4 platform. All video games that allow users to simulate playing online soccer using licensed players are in the FIFA series. The video game named “Be Lionel” is in the Pokemon series, or it allows users to simulate playing online soccer games using licensed players.

∀x (VideoGame(x) ∧ ReleasedBy(x, nintendo) → ¬Support(x, pS4)) ∀x (VideoGame(x) ∧ In(x, pokemonSeries) → ReleasedBy(x, nintendo)) ∀x (VideoGame(x) ∧ In(x, fIFASeries) → Support(x, pS4)) ∀x (VideoGame(x) ∧ Simulate(x, onlineSoccer) ∧ Use(x, licensedPlayer) → In(x, fIFASeries)) VideoGame(beLionel) ∧ In(beLionel, pokemonSeries) ∨ (Simulate(beLionel, onlineSoccer) ∧ Use(beLionel, licensedPlayer))

The video game named “Be Lionel” either is in the FIFA series and supports the PS4 platform, or it neither is in the FIFA series nor supports the PS4 platform.

VideoGame(beLionel) ∧ ¬(FIFASeries(beLionel) ⊕ Support(beLionel, pS4))

True

No video games released by Nintendo support the PS4 platform. All video games in the Pokemon series are released by Nintendo. All video games in the FIFA series support the PS4 platform. All video games that allow users to simulate playing online soccer using licensed players are in the FIFA series. The video game named “Be Lionel” is in the Pokemon series, or it allows users to simulate playing online soccer games using licensed players.

∀x (VideoGame(x) ∧ ReleasedBy(x, nintendo) → ¬Support(x, pS4)) ∀x (VideoGame(x) ∧ In(x, pokemonSeries) → ReleasedBy(x, nintendo)) ∀x (VideoGame(x) ∧ In(x, fIFASeries) → Support(x, pS4)) ∀x (VideoGame(x) ∧ Simulate(x, onlineSoccer) ∧ Use(x, licensedPlayer) → In(x, fIFASeries)) VideoGame(beLionel) ∧ In(beLionel, pokemonSeries) ∨ (Simulate(beLionel, onlineSoccer) ∧ Use(beLionel, licensedPlayer))

The video game named “Be Lionel” is either in the FIFA series or supports the PS4 platform.

VideoGame(beLionel) ∧ FIFASeries(beLionel) ⊕ Support(beLionel, pS4)

False

No video games released by Nintendo support the PS4 platform. All video games in the Pokemon series are released by Nintendo. All video games in the FIFA series support the PS4 platform. All video games that allow users to simulate playing online soccer using licensed players are in the FIFA series. The video game named “Be Lionel” is in the Pokemon series, or it allows users to simulate playing online soccer games using licensed players.

∀x (VideoGame(x) ∧ ReleasedBy(x, nintendo) → ¬Support(x, pS4)) ∀x (VideoGame(x) ∧ In(x, pokemonSeries) → ReleasedBy(x, nintendo)) ∀x (VideoGame(x) ∧ In(x, fIFASeries) → Support(x, pS4)) ∀x (VideoGame(x) ∧ Simulate(x, onlineSoccer) ∧ Use(x, licensedPlayer) → In(x, fIFASeries)) VideoGame(beLionel) ∧ In(beLionel, pokemonSeries) ∨ (Simulate(beLionel, onlineSoccer) ∧ Use(beLionel, licensedPlayer))

The video game named “Be Lionel” is not in the FIFA or Pokemon series.

VideoGame(beLionel) ∧ ¬(FIFASeries(beLionel) ∨ Support(beLionel, pS4))

False

No payment cards issued by Russian banks can be used with ApplePay. All MIR payment cards are issued by Russian banks. Some international payment cards can be used with ApplePay. Social payments in Russia can only be transferred to MIR payment cards. Bank of America payment cards can be used with ApplePay.

∀x ∀y (PaymentCard(x) ∧ RussianBank(y) ∧ IssuedBy(x, y) → ¬UsedWith(x, applePay)) ∀x ∀y (PaymentCard(x) ∧ MIR(x) → RussianBank(y) ∧ IssuedBy(x, y)) ∃x (PaymentCard(x) ∧ International(x) → UsedWith(x, applePay)) ∀x ∀y (SocialPayment(x) ∧TransferredTo(x, y) → PaymentCard(y) ∧ MIR(y)) PaymentCard(bankOfAmerica) ∧ UsedWith(bankOfAmerica, applePay)

Bank of America payment cards are international.

PaymentCard(bankOfAmerica) ∧ International(bankOfAmerica)

Uncertain

No payment cards issued by Russian banks can be used with ApplePay. All MIR payment cards are issued by Russian banks. Some international payment cards can be used with ApplePay. Social payments in Russia can only be transferred to MIR payment cards. Bank of America payment cards can be used with ApplePay.

∀x ∀y (PaymentCard(x) ∧ RussianBank(y) ∧ IssuedBy(x, y) → ¬UsedWith(x, applePay)) ∀x ∀y (PaymentCard(x) ∧ MIR(x) → RussianBank(y) ∧ IssuedBy(x, y)) ∃x (PaymentCard(x) ∧ International(x) → UsedWith(x, applePay)) ∀x ∀y (SocialPayment(x) ∧TransferredTo(x, y) → PaymentCard(y) ∧ MIR(y)) PaymentCard(bankOfAmerica) ∧ UsedWith(bankOfAmerica, applePay)

Bank of America payment cards are international and can be used to transfer social payments in Russia.

∀x (PaymentCard(bankOfAmerica) ∧ International(bankOfAmerica) ∧ SocialPayment(x) ∧TransferredTo(x, bankOfAmerica))

False

No payment cards issued by Russian banks can be used with ApplePay. All MIR payment cards are issued by Russian banks. Some international payment cards can be used with ApplePay. Social payments in Russia can only be transferred to MIR payment cards. Bank of America payment cards can be used with ApplePay.

∀x ∀y (PaymentCard(x) ∧ RussianBank(y) ∧ IssuedBy(x, y) → ¬UsedWith(x, applePay)) ∀x ∀y (PaymentCard(x) ∧ MIR(x) → RussianBank(y) ∧ IssuedBy(x, y)) ∃x (PaymentCard(x) ∧ International(x) → UsedWith(x, applePay)) ∀x ∀y (SocialPayment(x) ∧TransferredTo(x, y) → PaymentCard(y) ∧ MIR(y)) PaymentCard(bankOfAmerica) ∧ UsedWith(bankOfAmerica, applePay)

If Bank of America payment cards are international and can be used to transfer social payments in Russia, then they are international.

∀x ((PaymentCard(bandOfAmerica) ∧ International(bandOfAmerica) ∧ SocialPayment(x) ∧ TransferredTo(x, bandOfAmerica)) → International(bandOfAmerica))

True

The Lumina APV is produced by Chevrolet. The Astro is a van produced by Chevrolet. Vehicles produced by Chevrolet in this batch are either cars or vans.

ProducedBy(luminaAPV, chevrolet) ProducedBy(astro, chevrolet) ∧ Van(astro) ∀x (Vehicle(x) ∧ ProducedBy(x, chevrolet) ∧ InThisBatch(x) → (Car(x) ⊕ Van(x)))

The Lumina APV is a van.

Van(luminaAPV)

Uncertain

The Lumina APV is produced by Chevrolet. The Astro is a van produced by Chevrolet. Vehicles produced by Chevrolet in this batch are either cars or vans.

ProducedBy(luminaAPV, chevrolet) ProducedBy(astro, chevrolet) ∧ Van(astro) ∀x (Vehicle(x) ∧ ProducedBy(x, chevrolet) ∧ InThisBatch(x) → (Car(x) ⊕ Van(x)))

The Lumina APV is either a car or a van.

Car(luminaAPV) ⊕ Van(luminaAPV)

True

The Lumina APV is produced by Chevrolet. The Astro is a van produced by Chevrolet. Vehicles produced by Chevrolet in this batch are either cars or vans.

ProducedBy(luminaAPV, chevrolet) ProducedBy(astro, chevrolet) ∧ Van(astro) ∀x (Vehicle(x) ∧ ProducedBy(x, chevrolet) ∧ InThisBatch(x) → (Car(x) ⊕ Van(x)))

The Astro is a van.

Van(astro)

True

The Lumina APV is produced by Chevrolet. The Astro is a van produced by Chevrolet. Vehicles produced by Chevrolet in this batch are either cars or vans.

ProducedBy(luminaAPV, chevrolet) ProducedBy(astro, chevrolet) ∧ Van(astro) ∀x (Vehicle(x) ∧ ProducedBy(x, chevrolet) ∧ InThisBatch(x) → (Car(x) ⊕ Van(x)))

The Astro is a car.

Car(astro)

False

Everyone who works in the office is a commuter. People either work in the office or work from home. Everyone who works from home has a relaxed schedule. George is either a commuter or has a home office setup. If George is either a person who works from home or has a home office setup, then George is a commuter and is not a person who works from home.

∀x (WorkIn(x, office) → Commuter(x)) ∀x (WorkIn(x, office) ⊕ WorkFrom(x, home)) ∀x (WorkFrom(x, home) → Have(x, relaxedSchedule)) Commuter(george) ⊕ Have(george, homeOffice) (WorkFrom(george, home) ⊕ Have(george, homeOffice)) → ¬WorkFrom(george, home) ∧ Commuter(george)

George is a person who works from home.

WorkFrom(george, home)

Uncertain

Everyone who works in the office is a commuter. People either work in the office or work from home. Everyone who works from home has a relaxed schedule. George is either a commuter or has a home office setup. If George is either a person who works from home or has a home office setup, then George is a commuter and is not a person who works from home.

∀x (WorkIn(x, office) → Commuter(x)) ∀x (WorkIn(x, office) ⊕ WorkFrom(x, home)) ∀x (WorkFrom(x, home) → Have(x, relaxedSchedule)) Commuter(george) ⊕ Have(george, homeOffice) (WorkFrom(george, home) ⊕ Have(george, homeOffice)) → ¬WorkFrom(george, home) ∧ Commuter(george)

If George is not a person who works from home and a person who works in the office, then George is neither a commuter nor a person who has a relaxed schedule.

¬(WorkFrom(george, home) ∧ WorkIn(george, office)) → ¬(Commuter(george) ∨ Have(george, relaxedSchedule))

False

Everyone who works in the office is a commuter. People either work in the office or work from home. Everyone who works from home has a relaxed schedule. George is either a commuter or has a home office setup. If George is either a person who works from home or has a home office setup, then George is a commuter and is not a person who works from home.

∀x (WorkIn(x, office) → Commuter(x)) ∀x (WorkIn(x, office) ⊕ WorkFrom(x, home)) ∀x (WorkFrom(x, home) → Have(x, relaxedSchedule)) Commuter(george) ⊕ Have(george, homeOffice) (WorkFrom(george, home) ⊕ Have(george, homeOffice)) → ¬WorkFrom(george, home) ∧ Commuter(george)

If George is either a person who has a home office setup and a person who works in the office, or neither a person who has a home office setup nor a person who works in the office, then George is either a person who works from home or a person who has a relaxed schedule.

¬(Have(george, homeOffice) ⊕ WorkIn(george, office)) → (WorkFrom(george, home) ⊕ Have(george, relaxedSchedule))

True

Jason Kramer is an American music supervisor. Some American radio personalities are also music supervisors. Anyone who hosts a show on a public radio station is a radio personality. Joe Rogan is a radio personality. Jason Kramer hosted a show on a public radio station.

MusicSupervisor(jasonKramer) ∧ American(jasonKramer) ∃x ∃y (American(x) ∧ MusicSupervisor(x) ∧ RadioPersonality(x) ∧ (¬(x=y)) ∧ American(y) ∧ MusicSupervisor(y) ∧ RadioPersonality(y)) ∀x ∀y((HostShowOn(x, y) ∧ PublicRadioStation(x)) → RadioPersonality(x)) RadioPersonality(joeRogan) ∃x(HostShowOn(jasonKramer, x) ∧ PublicRadioStation(x))

Joe Rogan is American.

American(joeRogan)

Uncertain

Jason Kramer is an American music supervisor. Some American radio personalities are also music supervisors. Anyone who hosts a show on a public radio station is a radio personality. Joe Rogan is a radio personality. Jason Kramer hosted a show on a public radio station.

MusicSupervisor(jasonKramer) ∧ American(jasonKramer) ∃x ∃y (American(x) ∧ MusicSupervisor(x) ∧ RadioPersonality(x) ∧ (¬(x=y)) ∧ American(y) ∧ MusicSupervisor(y) ∧ RadioPersonality(y)) ∀x ∀y((HostShowOn(x, y) ∧ PublicRadioStation(x)) → RadioPersonality(x)) RadioPersonality(joeRogan) ∃x(HostShowOn(jasonKramer, x) ∧ PublicRadioStation(x))

Jason Kramer is a music supervisor.

MusicSupervisor(jasonKramer)

True

Jason Kramer is an American music supervisor. Some American radio personalities are also music supervisors. Anyone who hosts a show on a public radio station is a radio personality. Joe Rogan is a radio personality. Jason Kramer hosted a show on a public radio station.

MusicSupervisor(jasonKramer) ∧ American(jasonKramer) ∃x ∃y (American(x) ∧ MusicSupervisor(x) ∧ RadioPersonality(x) ∧ (¬(x=y)) ∧ American(y) ∧ MusicSupervisor(y) ∧ RadioPersonality(y)) ∀x ∀y((HostShowOn(x, y) ∧ PublicRadioStation(x)) → RadioPersonality(x)) RadioPersonality(joeRogan) ∃x(HostShowOn(jasonKramer, x) ∧ PublicRadioStation(x))

Jason Kramer is a radio personality.

RadioPersonality(jasonKramer)

True

Hermès bags are not made in Italy. All Birkin bags are Hermès bags. All Ferraris are made in Italy. All cars that carry a Ferrari V12 engine are Ferraris. All cars that are made in Maranello carry a Ferrari V12 engine. A Lamborghini SUV is not both a Ferrari and made in Maranello. A Kelly bag is a Hermès bag, or it is a car that carries a Ferrari V12 engine.

∀x ((Bag(x) ∧ Hermès(x)) → ¬MadeIn(x, italy)) ∀x ((Bag(x) ∧ Birkin(x)) → Hermès(x)) ∀x (Ferrari(x) → MadeIn(x, italy)) ∀x ((Car(x) ∧ Carry(x, ferrariV12Engine)) → Ferrrari(x)) ∀x ((Car(x) ∧ MadeIn(x, maranello)) → Carry(x, ferrariV12Engine)) ¬(Ferrari(lamborghiniSUV) ∧ MadeIn(lamborghiniSUV, maranello)) (Bag(kelly) ∧ Hermès(kelly)) ∨ (Bag(kelly) ∧ Car(kelly) ∧ Carry(kelly, ferrariV12Engine))

A Lamborghini SUV is made in Italy.

MadeIn(lamborghiniSUV, italy)

Uncertain

Hermès bags are not made in Italy. All Birkin bags are Hermès bags. All Ferraris are made in Italy. All cars that carry a Ferrari V12 engine are Ferraris. All cars that are made in Maranello carry a Ferrari V12 engine. A Lamborghini SUV is not both a Ferrari and made in Maranello. A Kelly bag is a Hermès bag, or it is a car that carries a Ferrari V12 engine.

∀x ((Bag(x) ∧ Hermès(x)) → ¬MadeIn(x, italy)) ∀x ((Bag(x) ∧ Birkin(x)) → Hermès(x)) ∀x (Ferrari(x) → MadeIn(x, italy)) ∀x ((Car(x) ∧ Carry(x, ferrariV12Engine)) → Ferrrari(x)) ∀x ((Car(x) ∧ MadeIn(x, maranello)) → Carry(x, ferrariV12Engine)) ¬(Ferrari(lamborghiniSUV) ∧ MadeIn(lamborghiniSUV, maranello)) (Bag(kelly) ∧ Hermès(kelly)) ∨ (Bag(kelly) ∧ Car(kelly) ∧ Carry(kelly, ferrariV12Engine))

A Lamborghini SUV is not made in Italy.

¬MadeIn(lamborghiniSUV, italy)

Uncertain

Hermès bags are not made in Italy. All Birkin bags are Hermès bags. All Ferraris are made in Italy. All cars that carry a Ferrari V12 engine are Ferraris. All cars that are made in Maranello carry a Ferrari V12 engine. A Lamborghini SUV is not both a Ferrari and made in Maranello. A Kelly bag is a Hermès bag, or it is a car that carries a Ferrari V12 engine.

∀x ((Bag(x) ∧ Hermès(x)) → ¬MadeIn(x, italy)) ∀x ((Bag(x) ∧ Birkin(x)) → Hermès(x)) ∀x (Ferrari(x) → MadeIn(x, italy)) ∀x ((Car(x) ∧ Carry(x, ferrariV12Engine)) → Ferrrari(x)) ∀x ((Car(x) ∧ MadeIn(x, maranello)) → Carry(x, ferrariV12Engine)) ¬(Ferrari(lamborghiniSUV) ∧ MadeIn(lamborghiniSUV, maranello)) (Bag(kelly) ∧ Hermès(kelly)) ∨ (Bag(kelly) ∧ Car(kelly) ∧ Carry(kelly, ferrariV12Engine))

A Kelly bag is a Birkin bag made in Maranello.

Bag(kelly) ∧ MadeIn(kelly, maranello) ∧ Birkin(kelly)

False

Hermès bags are not made in Italy. All Birkin bags are Hermès bags. All Ferraris are made in Italy. All cars that carry a Ferrari V12 engine are Ferraris. All cars that are made in Maranello carry a Ferrari V12 engine. A Lamborghini SUV is not both a Ferrari and made in Maranello. A Kelly bag is a Hermès bag, or it is a car that carries a Ferrari V12 engine.

∀x ((Bag(x) ∧ Hermès(x)) → ¬MadeIn(x, italy)) ∀x ((Bag(x) ∧ Birkin(x)) → Hermès(x)) ∀x (Ferrari(x) → MadeIn(x, italy)) ∀x ((Car(x) ∧ Carry(x, ferrariV12Engine)) → Ferrrari(x)) ∀x ((Car(x) ∧ MadeIn(x, maranello)) → Carry(x, ferrariV12Engine)) ¬(Ferrari(lamborghiniSUV) ∧ MadeIn(lamborghiniSUV, maranello)) (Bag(kelly) ∧ Hermès(kelly)) ∨ (Bag(kelly) ∧ Car(kelly) ∧ Carry(kelly, ferrariV12Engine))

A Kelly bag is not both made in Maranello and a Birkin bag.

Bag(kelly) ∧ ¬(MadeIn(kelly, maranello) ∧ Birkin(kelly))

True

If someone lives in a place named Galicia, then they live in either Spain or Poland. Spain is in Europe. Poland is in Europe. Rochelle lives in Europe. Dominique does not live in Europe. Alfonso lives in a place named Galicia.

∀x (∃y (LiveIn(x, y) ∧ Place(y) ∧ Named(y, galicia)) → LiveIn(x, spain) ⊕ LiveIn(x, poland)) ∀x (LiveIn(x, spain) → LiveIn(x, europe)) ∀x (LiveIn(x, poland) → LiveIn(x, europe)) LiveIn(rochelle, europe) ¬LiveIn(dominique, europe) ∃y (LiveIn(alfonso, y) ∧ Place(y) ∧ Named(y, galicia))

Rochelle lives in a place namedGalicia.

∃y (LiveIn(rochelle, y) ∧ Place(y) ∧ Named(y, galicia))

Uncertain

If someone lives in a place named Galicia, then they live in either Spain or Poland. Spain is in Europe. Poland is in Europe. Rochelle lives in Europe. Dominique does not live in Europe. Alfonso lives in a place named Galicia.

∀x (∃y (LiveIn(x, y) ∧ Place(y) ∧ Named(y, galicia)) → LiveIn(x, spain) ⊕ LiveIn(x, poland)) ∀x (LiveIn(x, spain) → LiveIn(x, europe)) ∀x (LiveIn(x, poland) → LiveIn(x, europe)) LiveIn(rochelle, europe) ¬LiveIn(dominique, europe) ∃y (LiveIn(alfonso, y) ∧ Place(y) ∧ Named(y, galicia))

Dominique does not live in Spain.

∀x (Live(dominique, x) → ¬In(x, spain))

True

If someone lives in a place named Galicia, then they live in either Spain or Poland. Spain is in Europe. Poland is in Europe. Rochelle lives in Europe. Dominique does not live in Europe. Alfonso lives in a place named Galicia.

∀x (∃y (LiveIn(x, y) ∧ Place(y) ∧ Named(y, galicia)) → LiveIn(x, spain) ⊕ LiveIn(x, poland)) ∀x (LiveIn(x, spain) → LiveIn(x, europe)) ∀x (LiveIn(x, poland) → LiveIn(x, europe)) LiveIn(rochelle, europe) ¬LiveIn(dominique, europe) ∃y (LiveIn(alfonso, y) ∧ Place(y) ∧ Named(y, galicia))

Alfonso lives in Europe.

∀x (Live(alfonso, x) → In(x, europe))

True

Ralph Hammerthaler was born in Wasserburg am Inn. Wasserburg am Inn is in Germany. Germany is in Europe. Ralph Hammerthaler is a German writer. Ralph Hammerthaler was born in 1965.

BornIn(ralphHammerthaler, wasserburgamInn) LocatedIn(wasserbAmInn, germany) LocatedIn(germany, europe) Writer(ralphHammerthaler) ∧ German(ralphHammerthaler) BornIn1965(ralphHammerthaler)

Ralph Hammerthaler is a writer born in Asia.

Writer(ralphHammerthaler) ∧ BornIn(ralphHammerthaler, asia)

Uncertain

Ralph Hammerthaler was born in Wasserburg am Inn. Wasserburg am Inn is in Germany. Germany is in Europe. Ralph Hammerthaler is a German writer. Ralph Hammerthaler was born in 1965.

BornIn(ralphHammerthaler, wasserburgamInn) LocatedIn(wasserbAmInn, germany) LocatedIn(germany, europe) Writer(ralphHammerthaler) ∧ German(ralphHammerthaler) BornIn1965(ralphHammerthaler)

Ralph Hammerthaler lives in Germany.

LivesIn(ralphHammerthaler, germany)

Uncertain

All books written by Neil Gaiman have sold more than one thousand copies. Some books that have won Hugo Awards are written by Neil Gaiman. Tomas has read all books written by Tolkien. Either Tomas has read Hamlet, or it has sold more than one thousand copies. Hamlet has either sold more than one thousand copies or it is written by Neil Gaiman.

∀x ((Book(x) ∧ WrittenBy(x, neilGaiman)) → ∃y (MoreThan(y, num1000) ∧ SoldCopies(x, y))) ∃x ∃y (Book(x) ∧ Win(x, hugoAward) ∧ WrittenBy(x, neilGaiman) ∧ (¬(x=y)) ∧ Book(y) ∧ Win(y, hugoAward) ∧ WrittenBy(y, neilGaiman)) ∀x ((Book(x) ∧ WrittenBy(x, tolkien)) → ReadBy(x, tomas)) ReadBy(hamlet, tomas) ⊕ (∃y (MoreThan(y, num1000) ∧ SoldCopies(hamlet, y))) ∃y (MoreThan(y, num1000) ∧ SoldCopies(hamlet, y)) ⊕ WrittenBy(hamlet, neilGaiman)

Hamlet has won a Hugo Award.

Win(hamlet, hugoAward)

Uncertain

All books written by Neil Gaiman have sold more than one thousand copies. Some books that have won Hugo Awards are written by Neil Gaiman. Tomas has read all books written by Tolkien. Either Tomas has read Hamlet, or it has sold more than one thousand copies. Hamlet has either sold more than one thousand copies or it is written by Neil Gaiman.

∀x ((Book(x) ∧ WrittenBy(x, neilGaiman)) → ∃y (MoreThan(y, num1000) ∧ SoldCopies(x, y))) ∃x ∃y (Book(x) ∧ Win(x, hugoAward) ∧ WrittenBy(x, neilGaiman) ∧ (¬(x=y)) ∧ Book(y) ∧ Win(y, hugoAward) ∧ WrittenBy(y, neilGaiman)) ∀x ((Book(x) ∧ WrittenBy(x, tolkien)) → ReadBy(x, tomas)) ReadBy(hamlet, tomas) ⊕ (∃y (MoreThan(y, num1000) ∧ SoldCopies(hamlet, y))) ∃y (MoreThan(y, num1000) ∧ SoldCopies(hamlet, y)) ⊕ WrittenBy(hamlet, neilGaiman)

Hamlet has won a Hugo Award and is written by Tolkien.

Win(hamlet, hugoAward) ∧ WrittenBy(hamlet, tolkien)

False

All books written by Neil Gaiman have sold more than one thousand copies. Some books that have won Hugo Awards are written by Neil Gaiman. Tomas has read all books written by Tolkien. Either Tomas has read Hamlet, or it has sold more than one thousand copies. Hamlet has either sold more than one thousand copies or it is written by Neil Gaiman.

∀x ((Book(x) ∧ WrittenBy(x, neilGaiman)) → ∃y (MoreThan(y, num1000) ∧ SoldCopies(x, y))) ∃x ∃y (Book(x) ∧ Win(x, hugoAward) ∧ WrittenBy(x, neilGaiman) ∧ (¬(x=y)) ∧ Book(y) ∧ Win(y, hugoAward) ∧ WrittenBy(y, neilGaiman)) ∀x ((Book(x) ∧ WrittenBy(x, tolkien)) → ReadBy(x, tomas)) ReadBy(hamlet, tomas) ⊕ (∃y (MoreThan(y, num1000) ∧ SoldCopies(hamlet, y))) ∃y (MoreThan(y, num1000) ∧ SoldCopies(hamlet, y)) ⊕ WrittenBy(hamlet, neilGaiman)

If Hamlet has either won a Hugo Award and is written by Tolkien, or neither has won a Hugo Award nor is written by Tolkien, then Hamlet has neither won a Hugo Award nor is written by Neil Gaiman.

¬(Win(hamlet, hugoAward) ⊕ WrittenBy(hamlet, tolkien)) → (¬Win(hamlet, hugoAward) ∧ (¬WrittenBy(hamlet, neilGaiman)))

True

Grass is not food All meadows are grass. All edible things are food. All fruits are edible. All lemons are fruit. Grapes are not both edible and lemons. Bananas are grasses or fruits.

∀x (Grass(x) → ¬Food(x)) ∀x (Meadow(x) → Grass(x)) ∀x (Edible(x) → Food(x)) ∀x (Fruit(x) → Edible(x)) ∀x (Lemon(x) → Fruit(x)) ¬(Edible(grape) ∧ Lemon(grape)) Grass(banana) ∨ Fruit(banana)

Grapes are food.

Food(grape)

Uncertain

Grass is not food All meadows are grass. All edible things are food. All fruits are edible. All lemons are fruit. Grapes are not both edible and lemons. Bananas are grasses or fruits.

∀x (Grass(x) → ¬Food(x)) ∀x (Meadow(x) → Grass(x)) ∀x (Edible(x) → Food(x)) ∀x (Fruit(x) → Edible(x)) ∀x (Lemon(x) → Fruit(x)) ¬(Edible(grape) ∧ Lemon(grape)) Grass(banana) ∨ Fruit(banana)

Grapes are not a food.

¬Food(grape)

Uncertain

Grass is not food All meadows are grass. All edible things are food. All fruits are edible. All lemons are fruit. Grapes are not both edible and lemons. Bananas are grasses or fruits.

∀x (Grass(x) → ¬Food(x)) ∀x (Meadow(x) → Grass(x)) ∀x (Edible(x) → Food(x)) ∀x (Fruit(x) → Edible(x)) ∀x (Lemon(x) → Fruit(x)) ¬(Edible(grape) ∧ Lemon(grape)) Grass(banana) ∨ Fruit(banana)

Bananas are both lemons and meadows.

Lemon(banana) ∧ Meadow(banana)

False

Grass is not food All meadows are grass. All edible things are food. All fruits are edible. All lemons are fruit. Grapes are not both edible and lemons. Bananas are grasses or fruits.

∀x (Grass(x) → ¬Food(x)) ∀x (Meadow(x) → Grass(x)) ∀x (Edible(x) → Food(x)) ∀x (Fruit(x) → Edible(x)) ∀x (Lemon(x) → Fruit(x)) ¬(Edible(grape) ∧ Lemon(grape)) Grass(banana) ∨ Fruit(banana)

Bananas are not both a lemon and a meadow.

¬(Lemon(banana) ∧ Meadow(banana))

True

The Golden State Warriors are a team from San Francisco. The Golden State Warriors won the NBA finals. All teams attending the NBA finals have won many games. Boston Celtics are a team that lost the NBA finals. If a team wins the NBA finals, then they will have more income. If a team wins or loses at the NBA finals, then they are attending the finals.

Team(goldenStateWarriors) ∧ From(goldenStateWarriors, sanFrancisco) Won(goldenStateWarriors, nbaFinals) ∀x ((Team(x) ∧ Attending(x, nbaFinals)) → WonManyGames(x)) Team(bostonCeltics) ∧ Lost(bostonCeltics, nbaFinals) ∀x ((Team(x) ∧ Won(x, nbaFinals)) → MoreIncome(x)) ∀x ((Won(x, nbaFinals) ∨ Lost(x, nbaFinals)) → Attending(x, nbaFinals))

The Boston Celtics are from San Francisco.

From(bostonCeltics, sanFrancisco)

Uncertain

The Golden State Warriors are a team from San Francisco. The Golden State Warriors won the NBA finals. All teams attending the NBA finals have won many games. Boston Celtics are a team that lost the NBA finals. If a team wins the NBA finals, then they will have more income. If a team wins or loses at the NBA finals, then they are attending the finals.

Team(goldenStateWarriors) ∧ From(goldenStateWarriors, sanFrancisco) Won(goldenStateWarriors, nbaFinals) ∀x ((Team(x) ∧ Attending(x, nbaFinals)) → WonManyGames(x)) Team(bostonCeltics) ∧ Lost(bostonCeltics, nbaFinals) ∀x ((Team(x) ∧ Won(x, nbaFinals)) → MoreIncome(x)) ∀x ((Won(x, nbaFinals) ∨ Lost(x, nbaFinals)) → Attending(x, nbaFinals))

The Boston Celtics have more than 30 years of experience.

HasMoreThanThirtyYearsOfHistory(bostonCeltics)

True

The Golden State Warriors are a team from San Francisco. The Golden State Warriors won the NBA finals. All teams attending the NBA finals have won many games. Boston Celtics are a team that lost the NBA finals. If a team wins the NBA finals, then they will have more income. If a team wins or loses at the NBA finals, then they are attending the finals.

Team(goldenStateWarriors) ∧ From(goldenStateWarriors, sanFrancisco) Won(goldenStateWarriors, nbaFinals) ∀x ((Team(x) ∧ Attending(x, nbaFinals)) → WonManyGames(x)) Team(bostonCeltics) ∧ Lost(bostonCeltics, nbaFinals) ∀x ((Team(x) ∧ Won(x, nbaFinals)) → MoreIncome(x)) ∀x ((Won(x, nbaFinals) ∨ Lost(x, nbaFinals)) → Attending(x, nbaFinals))

The Golden State Warriors will have more income from gate receipts.

MoreIncome(goldenStateWarriors)

True

Maya would only play the violin if her fingers could never be injured. Volleyball players can injure their ankles, fingers, or shoulder. Maya is a volleyball player.

Play(maya, violin) → ¬CanInjure(maya, fingers) ∀x (VolleyballPlayer(x) → (CanInjure(ankles) ∧ CanInjure(fingers) ∧ CanInjure(shoulder))) VolleyballPlayer(maya)

Maya will not play the violin.

¬Play(maya, violin)

True

All devices belonging to the company are connected to Google Home. All devices with the company logo belong to the company. Each device either has the company logo or belongs to employees. All of the devices belonging to employees can be connected to the company's wifi. All of the devices connected to Google Home are controlled by managers. All of the devices that connect to the company's wifi are easy to operate. All of the devices that are easy to operate were produced after a new CTO is appointed. ModelXX was not produced after a new CTO was appointed.

∀x ((Devices(x) ∧ BelongTo(x, company)) → ConnectTo(x, googleHome)) ∀x ((Devices(x) ∧ With(x, companyLogo)) → BelongTo(x, company)) ∀x ((Devices(x) → (With(x, companyLogo) ⊕ BelongTo(x, employee))) ∀x ((Devices(x) ∧ BelongTo(x, employee)) → CanBeConnectedTo(x, wifi)) ∀x ((Devices(x) ∧ ConnectTo(x, googleHome)) → ControlledBy(x, manager)) ∀x ((Devices(x) ∧ CanBeConnectedTo(x, wifi)) → EasyToOperate(x)) ∀x ((Devices(x) ∧ EasyToOperate(x)) → ProducedAfterNewCTOAppointed(x, company)) Devices(modelXX) ∧ (¬ProducedAfterNewCTOAppointed(modelXX, company))

ModelXX is controlled by managers.

ControlledBy(x, manager)

True

All devices belonging to the company are connected to Google Home. All devices with the company logo belong to the company. Each device either has the company logo or belongs to employees. All of the devices belonging to employees can be connected to the company's wifi. All of the devices connected to Google Home are controlled by managers. All of the devices that connect to the company's wifi are easy to operate. All of the devices that are easy to operate were produced after a new CTO is appointed. ModelXX was not produced after a new CTO was appointed.

∀x ((Devices(x) ∧ BelongTo(x, company)) → ConnectTo(x, googleHome)) ∀x ((Devices(x) ∧ With(x, companyLogo)) → BelongTo(x, company)) ∀x ((Devices(x) → (With(x, companyLogo) ⊕ BelongTo(x, employee))) ∀x ((Devices(x) ∧ BelongTo(x, employee)) → CanBeConnectedTo(x, wifi)) ∀x ((Devices(x) ∧ ConnectTo(x, googleHome)) → ControlledBy(x, manager)) ∀x ((Devices(x) ∧ CanBeConnectedTo(x, wifi)) → EasyToOperate(x)) ∀x ((Devices(x) ∧ EasyToOperate(x)) → ProducedAfterNewCTOAppointed(x, company)) Devices(modelXX) ∧ (¬ProducedAfterNewCTOAppointed(modelXX, company))

ModelXX is either produced after a new CTO was appointed or it is controlled by managers.

ProducedAfterNewCTOAppointed(modelXX, theCompany) ⊕ ControlledBy(x, manager)

True

All devices belonging to the company are connected to Google Home. All devices with the company logo belong to the company. Each device either has the company logo or belongs to employees. All of the devices belonging to employees can be connected to the company's wifi. All of the devices connected to Google Home are controlled by managers. All of the devices that connect to the company's wifi are easy to operate. All of the devices that are easy to operate were produced after a new CTO is appointed. ModelXX was not produced after a new CTO was appointed.

∀x ((Devices(x) ∧ BelongTo(x, company)) → ConnectTo(x, googleHome)) ∀x ((Devices(x) ∧ With(x, companyLogo)) → BelongTo(x, company)) ∀x ((Devices(x) → (With(x, companyLogo) ⊕ BelongTo(x, employee))) ∀x ((Devices(x) ∧ BelongTo(x, employee)) → CanBeConnectedTo(x, wifi)) ∀x ((Devices(x) ∧ ConnectTo(x, googleHome)) → ControlledBy(x, manager)) ∀x ((Devices(x) ∧ CanBeConnectedTo(x, wifi)) → EasyToOperate(x)) ∀x ((Devices(x) ∧ EasyToOperate(x)) → ProducedAfterNewCTOAppointed(x, company)) Devices(modelXX) ∧ (¬ProducedAfterNewCTOAppointed(modelXX, company))

ModelXX is not with the company logo, and managers do not control it.

¬With(modelXX, companyLogo) ∧ (¬ControlledBy(x, manager))

False

All devices belonging to the company are connected to Google Home. All devices with the company logo belong to the company. Each device either has the company logo or belongs to employees. All of the devices belonging to employees can be connected to the company's wifi. All of the devices connected to Google Home are controlled by managers. All of the devices that connect to the company's wifi are easy to operate. All of the devices that are easy to operate were produced after a new CTO is appointed. ModelXX was not produced after a new CTO was appointed.

∀x ((Devices(x) ∧ BelongTo(x, company)) → ConnectTo(x, googleHome)) ∀x ((Devices(x) ∧ With(x, companyLogo)) → BelongTo(x, company)) ∀x ((Devices(x) → (With(x, companyLogo) ⊕ BelongTo(x, employee))) ∀x ((Devices(x) ∧ BelongTo(x, employee)) → CanBeConnectedTo(x, wifi)) ∀x ((Devices(x) ∧ ConnectTo(x, googleHome)) → ControlledBy(x, manager)) ∀x ((Devices(x) ∧ CanBeConnectedTo(x, wifi)) → EasyToOperate(x)) ∀x ((Devices(x) ∧ EasyToOperate(x)) → ProducedAfterNewCTOAppointed(x, company)) Devices(modelXX) ∧ (¬ProducedAfterNewCTOAppointed(modelXX, company))

ModelXX is either with the company logo or controlled by managers.

With(modelXX, companyLogo) ⊕ ControlledBy(x, manager)

False

All CD players are delicate mechanisms. No delicate mechanisms are suitable toys for children.

∀x (CDPlayer(x) → DelicateMechanism(x)) ∀x (DelicateMechanism(x) → ¬(Toy(x) ∧ SuitableFor(x, children)))

Some CD players are suitable toys for children.

∃x ∃y (CDPlayer(x) ∧ CDPlayer(y) ∧ Toy(x) ∧ Toy(y) ∧ SuitableFor(x, children) ∧ SuitableFor(y, children) ∧ ¬(x=y))

Uncertain

All mammals are living beings. All elephants are mammals. All baby elephants are elephants. Some baby elephants are sleepy. If Jumbo is a living being, then Jumbo is not both an elephant and a mammal. If Jumbo is sleepy, then Jumbo is either a baby elephant or a mammal.

∀x (Mammal(x) → LivingBeing(x)) ∀x (Elephant(x) → Mammal(x)) ∀x (BabyElephant(x) → Elephant(x)) ∃x (BabyElephant(x) ∧ Sleepy(x)) LivingBeing(jumbo) → ¬(Elephant(jumbo) ∧ Mammal(jumbo)) Sleepy(jumbo) → BabyElephant(jumbo) ⊕ Mammal(jumbo)

Jumbo is sleepy.

Sleepy(jumbo)

False

All mammals are living beings. All elephants are mammals. All baby elephants are elephants. Some baby elephants are sleepy. If Jumbo is a living being, then Jumbo is not both an elephant and a mammal. If Jumbo is sleepy, then Jumbo is either a baby elephant or a mammal.

∀x (Mammal(x) → LivingBeing(x)) ∀x (Elephant(x) → Mammal(x)) ∀x (BabyElephant(x) → Elephant(x)) ∃x (BabyElephant(x) ∧ Sleepy(x)) LivingBeing(jumbo) → ¬(Elephant(jumbo) ∧ Mammal(jumbo)) Sleepy(jumbo) → BabyElephant(jumbo) ⊕ Mammal(jumbo)

Jumbo is not sleepy.

¬Sleepy(jumbo)

True

All mammals are living beings. All elephants are mammals. All baby elephants are elephants. Some baby elephants are sleepy. If Jumbo is a living being, then Jumbo is not both an elephant and a mammal. If Jumbo is sleepy, then Jumbo is either a baby elephant or a mammal.

∀x (Mammal(x) → LivingBeing(x)) ∀x (Elephant(x) → Mammal(x)) ∀x (BabyElephant(x) → Elephant(x)) ∃x (BabyElephant(x) ∧ Sleepy(x)) LivingBeing(jumbo) → ¬(Elephant(jumbo) ∧ Mammal(jumbo)) Sleepy(jumbo) → BabyElephant(jumbo) ⊕ Mammal(jumbo)

Jumbo is a living being.

LivingBeing(jumbo)

Uncertain

All mammals are living beings. All elephants are mammals. All baby elephants are elephants. Some baby elephants are sleepy. If Jumbo is a living being, then Jumbo is not both an elephant and a mammal. If Jumbo is sleepy, then Jumbo is either a baby elephant or a mammal.

∀x (Mammal(x) → LivingBeing(x)) ∀x (Elephant(x) → Mammal(x)) ∀x (BabyElephant(x) → Elephant(x)) ∃x (BabyElephant(x) ∧ Sleepy(x)) LivingBeing(jumbo) → ¬(Elephant(jumbo) ∧ Mammal(jumbo)) Sleepy(jumbo) → BabyElephant(jumbo) ⊕ Mammal(jumbo)

Jumbo is neither sleepy nor a baby elephant.

¬Sleepy(jumbo) ∧ ¬BabyElephant(jumbo))

True

All mammals are living beings. All elephants are mammals. All baby elephants are elephants. Some baby elephants are sleepy. If Jumbo is a living being, then Jumbo is not both an elephant and a mammal. If Jumbo is sleepy, then Jumbo is either a baby elephant or a mammal.

∀x (Mammal(x) → LivingBeing(x)) ∀x (Elephant(x) → Mammal(x)) ∀x (BabyElephant(x) → Elephant(x)) ∃x (BabyElephant(x) ∧ Sleepy(x)) LivingBeing(jumbo) → ¬(Elephant(jumbo) ∧ Mammal(jumbo)) Sleepy(jumbo) → BabyElephant(jumbo) ⊕ Mammal(jumbo)

Jumbo is not sleepy or an elephant.

¬(Sleepy(jumbo) ⊕ Elephant(jumbo))

True

No planet in the solar system relies on nuclear fusion to generate light. All stars in the solar system rely on nuclear fusion to generate light. All celestial bodies in the solar systems that have greater than 0.08 solar masses are stars. If a celestial body in the solar system has cleared its orbit of other debris and has a nearly spherical shape due to its own gravity, then it is a planet. If Europa is a celestial body in the solar system that has cleared its orbit of other debris and has a nearly spherical shape due to its own gravity or relies on nuclear fusion to generate light, then Europa is a celestial body in the solar system.

∀x (Planet(x) ∧ In(x, solarSystem) → ¬RelyOnToGenerate(x, nuclearFusion, light)) ∀x (Star(x) ∧ In(x, solarSystem) → RelyOnToGenerate(x, nuclearFusion, light)) ∀x (CelestialBody(x) ∧ In(x, solarSystem) ∧ GreaterThan(x, solarMass, 0point08) → Star(x)) ∀x (CelestialBody(x) ∧ In(x, solarSystem) ∧ (∃y (OrbitOf(y, x) ∧ Clear(x, y) ∧ DebrisFree(y))) ∧ NearlySphericalShape(x, gravity) → Planet(x)) (CelestialBody(europa) ∧ In(europa, solarSystem) ∧ (∃y (OrbitOf(y, x) ∧ Clear(x, y) ∧ DebrisFree(y))) ∧ NearlySphericalShape(europa, gravity)) ∨ RelyOnToGenerate(europa, nuclearFusion, light) → CelestialBody(europa) ∧ In(europa, solarSystem)

Europa is a celestial body in the solar system has cleared its orbit of other debris and has a nearly spherical shape due to its own gravity.

CelestialBody(europa) ∧ In(europa, solarSystem) ∧ (∃y (OrbitOf(y, x) ∧ Clear(x, y) ∧ DebrisFree(y))) ∧ NearlySphericalShape(europa, gravity)

Uncertain

No planet in the solar system relies on nuclear fusion to generate light. All stars in the solar system rely on nuclear fusion to generate light. All celestial bodies in the solar systems that have greater than 0.08 solar masses are stars. If a celestial body in the solar system has cleared its orbit of other debris and has a nearly spherical shape due to its own gravity, then it is a planet. If Europa is a celestial body in the solar system that has cleared its orbit of other debris and has a nearly spherical shape due to its own gravity or relies on nuclear fusion to generate light, then Europa is a celestial body in the solar system.

∀x (Planet(x) ∧ In(x, solarSystem) → ¬RelyOnToGenerate(x, nuclearFusion, light)) ∀x (Star(x) ∧ In(x, solarSystem) → RelyOnToGenerate(x, nuclearFusion, light)) ∀x (CelestialBody(x) ∧ In(x, solarSystem) ∧ GreaterThan(x, solarMass, 0point08) → Star(x)) ∀x (CelestialBody(x) ∧ In(x, solarSystem) ∧ (∃y (OrbitOf(y, x) ∧ Clear(x, y) ∧ DebrisFree(y))) ∧ NearlySphericalShape(x, gravity) → Planet(x)) (CelestialBody(europa) ∧ In(europa, solarSystem) ∧ (∃y (OrbitOf(y, x) ∧ Clear(x, y) ∧ DebrisFree(y))) ∧ NearlySphericalShape(europa, gravity)) ∨ RelyOnToGenerate(europa, nuclearFusion, light) → CelestialBody(europa) ∧ In(europa, solarSystem)

Europa is a celestial body in one of the solar systems that have greater than 0.08 solar masses.

CelestialBody(europa) ∧ In(europa, solarSystem) ∧ GreaterThan(europa, solarMass, 0.08)

False

No planet in the solar system relies on nuclear fusion to generate light. All stars in the solar system rely on nuclear fusion to generate light. All celestial bodies in the solar systems that have greater than 0.08 solar masses are stars. If a celestial body in the solar system has cleared its orbit of other debris and has a nearly spherical shape due to its own gravity, then it is a planet. If Europa is a celestial body in the solar system that has cleared its orbit of other debris and has a nearly spherical shape due to its own gravity or relies on nuclear fusion to generate light, then Europa is a celestial body in the solar system.

∀x (Planet(x) ∧ In(x, solarSystem) → ¬RelyOnToGenerate(x, nuclearFusion, light)) ∀x (Star(x) ∧ In(x, solarSystem) → RelyOnToGenerate(x, nuclearFusion, light)) ∀x (CelestialBody(x) ∧ In(x, solarSystem) ∧ GreaterThan(x, solarMass, 0point08) → Star(x)) ∀x (CelestialBody(x) ∧ In(x, solarSystem) ∧ (∃y (OrbitOf(y, x) ∧ Clear(x, y) ∧ DebrisFree(y))) ∧ NearlySphericalShape(x, gravity) → Planet(x)) (CelestialBody(europa) ∧ In(europa, solarSystem) ∧ (∃y (OrbitOf(y, x) ∧ Clear(x, y) ∧ DebrisFree(y))) ∧ NearlySphericalShape(europa, gravity)) ∨ RelyOnToGenerate(europa, nuclearFusion, light) → CelestialBody(europa) ∧ In(europa, solarSystem)

Europa is not a celestial body in one of the solar systems that have greater than 0.08 solar masses.

¬(CelestialBody(europa) ∧ In(europa, solarSystem) ∧ GreaterThan(europa, solarMass, 0.08))

True

If Max listens to music, he either listens to classical music or rap. All the classical songs that Max listens to are from the 12th century. If Max is listening to a rap song, then the song is by Kanye West. All songs by Kanye West are full of lyrics. All songs that are full of lyrics need to be written with words It is not true that “As it was” by Harry Styles is classical music that Max listens to and is from the 12th century. Max listens to "As it was" by Harry Styles.

∀x (MaxListenTo(x) → (ClassicalMusic(x) ⊕ Rap(x))) ∀x (MaxListenTo(x) ∧ ClassicalMusic(x) → Song(x) ∧ From(x, 12thCentury)) ∀x (MaxListenTo(x) ∧ Rap(x) → Song(x) ∧ By(x, kanyeWest)) ∀x (Song(x) ∧ By(x, kanyeWest) → Song(x) ∧ FullOfLyrics(x)) ∀x (Song(x) ∧ FullOfLyrics(x) → NeedToBeWrittenWith(x, words)) ¬(ClassicalMusic(asItWasByHarryStyles) ∧ Song(asItWasByHarryStyles) ∧ From(asItWasByHarryStyles, 12thCentury)) MaxListenTo(asItWasByHarryStyles)

“As it was” by Harry Styles needs to be written with words.

NeedToBeWrittenWith(asItWasByHarryStyles, words)

True

If Max listens to music, he either listens to classical music or rap. All the classical songs that Max listens to are from the 12th century. If Max is listening to a rap song, then the song is by Kanye West. All songs by Kanye West are full of lyrics. All songs that are full of lyrics need to be written with words It is not true that “As it was” by Harry Styles is classical music that Max listens to and is from the 12th century. Max listens to "As it was" by Harry Styles.

∀x (MaxListenTo(x) → (ClassicalMusic(x) ⊕ Rap(x))) ∀x (MaxListenTo(x) ∧ ClassicalMusic(x) → Song(x) ∧ From(x, 12thCentury)) ∀x (MaxListenTo(x) ∧ Rap(x) → Song(x) ∧ By(x, kanyeWest)) ∀x (Song(x) ∧ By(x, kanyeWest) → Song(x) ∧ FullOfLyrics(x)) ∀x (Song(x) ∧ FullOfLyrics(x) → NeedToBeWrittenWith(x, words)) ¬(ClassicalMusic(asItWasByHarryStyles) ∧ Song(asItWasByHarryStyles) ∧ From(asItWasByHarryStyles, 12thCentury)) MaxListenTo(asItWasByHarryStyles)

"As it was” by Harry Styles is a song from the 12th century.

Song(asItWasByHarryStyles) ∧ From(asItWasByHarryStyles, 12thCentury)

Uncertain

If Max listens to music, he either listens to classical music or rap. All the classical songs that Max listens to are from the 12th century. If Max is listening to a rap song, then the song is by Kanye West. All songs by Kanye West are full of lyrics. All songs that are full of lyrics need to be written with words It is not true that “As it was” by Harry Styles is classical music that Max listens to and is from the 12th century. Max listens to "As it was" by Harry Styles.

∀x (MaxListenTo(x) → (ClassicalMusic(x) ⊕ Rap(x))) ∀x (MaxListenTo(x) ∧ ClassicalMusic(x) → Song(x) ∧ From(x, 12thCentury)) ∀x (MaxListenTo(x) ∧ Rap(x) → Song(x) ∧ By(x, kanyeWest)) ∀x (Song(x) ∧ By(x, kanyeWest) → Song(x) ∧ FullOfLyrics(x)) ∀x (Song(x) ∧ FullOfLyrics(x) → NeedToBeWrittenWith(x, words)) ¬(ClassicalMusic(asItWasByHarryStyles) ∧ Song(asItWasByHarryStyles) ∧ From(asItWasByHarryStyles, 12thCentury)) MaxListenTo(asItWasByHarryStyles)

"As it was” by Harry Styles is not both a song from Kanye West and needed to be written with words.

¬(Song(asItWasByHarryStyles) ∧ By(asItWasByHarryStyles, kanyeWest) ∧ NeedToBeWrittenWith(asItWasByHarryStyles, words))

False

"Your Woman" is a song by the British one-person band White Town. "Your Woman" song peaked at No. 1 on the UK Singles Chart. If a song peaked at No.1 at a particular place, it was extremely popular. "Your Woman" peaked at No. 1 in Iceland, Israel, and Spain.

Produce(whiteTown, yourWoman) ∧ OnePersonBand(whiteTown) Peak(yourWoman, uKSinglesChart) ∀x ((∃y(Peak(x, y))) → Popular(x)) Peak(yourWoman, iceland) ∧ Peak(yourWoman, israel) ∧ Peak(yourWoman, spain)

"Your Woman" was extremely popular.

Popular(yourWoman)

True

"Your Woman" is a song by the British one-person band White Town. "Your Woman" song peaked at No. 1 on the UK Singles Chart. If a song peaked at No.1 at a particular place, it was extremely popular. "Your Woman" peaked at No. 1 in Iceland, Israel, and Spain.

Produce(whiteTown, yourWoman) ∧ OnePersonBand(whiteTown) Peak(yourWoman, uKSinglesChart) ∀x ((∃y(Peak(x, y))) → Popular(x)) Peak(yourWoman, iceland) ∧ Peak(yourWoman, israel) ∧ Peak(yourWoman, spain)

White Town did not produce any popular songs.

∀x (Produce(whiteTown, x) → ¬Popular(x))

False

"Your Woman" is a song by the British one-person band White Town. "Your Woman" song peaked at No. 1 on the UK Singles Chart. If a song peaked at No.1 at a particular place, it was extremely popular. "Your Woman" peaked at No. 1 in Iceland, Israel, and Spain.

Produce(whiteTown, yourWoman) ∧ OnePersonBand(whiteTown) Peak(yourWoman, uKSinglesChart) ∀x ((∃y(Peak(x, y))) → Popular(x)) Peak(yourWoman, iceland) ∧ Peak(yourWoman, israel) ∧ Peak(yourWoman, spain)

White Town was a successful band.

Successful(whiteTown)

Uncertain

All functions that represent straight lines on the coordinate plane are linear functions. No linear functions are non-convex functions. A function is either a non-convex fuction or a convex function. All quasi-convex functions are real-valued functions. All convex functions are quasi-convex functions. The maximum of quasiconvex functions is a function. The maximum of quasiconvex functions is a function that represents straight lines on the coordinate plane or it is a convex function or it is not a non-convex function.

∀x (Function(x) ∧ RepresentOn(x, straightLine, coordinatePlane) → LinearFunction(x)) ∀x (LinearFunction(x) → ¬NonConvexFunction(x)) ∀x (Function(x) → NonConvexFunction(x) ⊕ ConvexFunction(x)) ∀x (QuasiConvexFunction(x) → RealValuedFunction(x)) ∀x (ConvexFunction(x) → QuasiConvexFunction(x)) Function(maximumOfQuasiConvexFunction) (Function(maximumOfQuasiConvexFunction) ∧ RepresentOn(maximumOfQuasiConvexFunction, straightLine, coordinatePlane)) ∨ ConvexFunction(maximumOfQuasiConvexFunction) ∨ ¬NonConvexFunction(maximumOfQuasiConvexFunction)

The maximum of quasiconvex functions is a function that represent straight lines on the coordinate plane.

Function(maximumOfQuasiConvexFunction) ∧ RepresentOn(maximumOfQuasiConvexFunction, straightLine, coordinatePlane)

Uncertain