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Barbara Ann Marshall is a former swimmer and former world record-holder. Barbara Ann Marshall participated in the 1972 Summer Olympics. Barbara Ann Marshall's home country is the United States. All people who competed in the 1972 Summer Olympics represented their home country. Barbara Ann Marshall participated in the preliminary heat in the freestyle relay. Barbara Ann Marshall did not participate in the event final of the 1972 Summer Olympics freestyle relay. Only relay swimmers who participated in the final event at the 1972 Summer Olympics received medals.

FormerSwimmer(barbaraAnnMarshall) ∧ FormerWorldRecordHolder(barbaraAnnMarshall) ParticipatedIn(barbaraAnnMarshall, 1972SummerOlympics) HomeCountry(barbaraAnnMarshall, unitedStates) ∀x ∃y (ParticipatedIn(x, 1972SummerOlympics) ∧ HomeCountry(x, y) → Represented(x, y)) ParticipatedIn(barbaraAnnMarshall, preliminaryHeatFreestyleRelay) ¬ParticipatedIn(barbaraAnnMarshall, finalHeatFreestyleRelay) ∀x ((ParticipatedIn(x, 1972SummerOlympics) ∧ RelaySwimmer(x) ∧ ¬ParticipatedIn(x, finalHeatFreestyleRelay)) ↔ ¬Recieved(x, medal)))

Barbara Ann Marshall did not receive medals.

¬Recieved(barbaraAnnMarshall, medal)

Uncertain

Barbara Ann Marshall is a former swimmer and former world record-holder. Barbara Ann Marshall participated in the 1972 Summer Olympics. Barbara Ann Marshall's home country is the United States. All people who competed in the 1972 Summer Olympics represented their home country. Barbara Ann Marshall participated in the preliminary heat in the freestyle relay. Barbara Ann Marshall did not participate in the event final of the 1972 Summer Olympics freestyle relay. Only relay swimmers who participated in the final event at the 1972 Summer Olympics received medals.

FormerSwimmer(barbaraAnnMarshall) ∧ FormerWorldRecordHolder(barbaraAnnMarshall) ParticipatedIn(barbaraAnnMarshall, 1972SummerOlympics) HomeCountry(barbaraAnnMarshall, unitedStates) ∀x ∃y (ParticipatedIn(x, 1972SummerOlympics) ∧ HomeCountry(x, y) → Represented(x, y)) ParticipatedIn(barbaraAnnMarshall, preliminaryHeatFreestyleRelay) ¬ParticipatedIn(barbaraAnnMarshall, finalHeatFreestyleRelay) ∀x ((ParticipatedIn(x, 1972SummerOlympics) ∧ RelaySwimmer(x) ∧ ¬ParticipatedIn(x, finalHeatFreestyleRelay)) ↔ ¬Recieved(x, medal)))

Barbara Ann Marshall represented the United States in the 1972 Summer Olympics.

Represented(barbaraAnnMarshall, unitedStates)

True

A game is played with three stages: red stage, yellow stage, and green stage. Each player begins at the red stage. All players must reach the yellow stage before they can reach the green stage. The yellow stage comes after the red stage. All players must proceed one stage at a time.

∃x ∃y ∃y ∃w (Game(x) ∧ StageNumber(x,3) ∧ Stage(y) ∧ Stage(z) ∧ Stage(w) ∧ ¬(y=z) ∧ ¬(z=w) ∧ ¬(y=w) ∧ Red(y) ∧ Yellow(z) ∧ Green(w)) ∀x (Player(x) → StartRed(x)) ∀x (Player(x) ∧ ¬ReachYellow(x) → ¬ReachGreen(x)) ∀x (Player(x) ∧ StartRed(x) → ReachYellow(x)) ∀x (Player(x) ∧ StartRed(x) ∧ ¬ReachYellow(x) → ¬ReachGreen(x))

It is possible to move to the green stage without ever reaching the yellow stage.

∃x (Player(x) ∧ RedToGreen(x))

False

A game is played with three stages: red stage, yellow stage, and green stage. Each player begins at the red stage. All players must reach the yellow stage before they can reach the green stage. The yellow stage comes after the red stage. All players must proceed one stage at a time.

∃x ∃y ∃y ∃w (Game(x) ∧ StageNumber(x,3) ∧ Stage(y) ∧ Stage(z) ∧ Stage(w) ∧ ¬(y=z) ∧ ¬(z=w) ∧ ¬(y=w) ∧ Red(y) ∧ Yellow(z) ∧ Green(w)) ∀x (Player(x) → StartRed(x)) ∀x (Player(x) ∧ ¬ReachYellow(x) → ¬ReachGreen(x)) ∀x (Player(x) ∧ StartRed(x) → ReachYellow(x)) ∀x (Player(x) ∧ StartRed(x) ∧ ¬ReachYellow(x) → ¬ReachGreen(x))

It is possible to reach the yellow stage without ever reaching the green stage.

∃x (Player(x) ∧ RedToYellow(x))

True

A game is played with three stages: red stage, yellow stage, and green stage. Each player begins at the red stage. All players must reach the yellow stage before they can reach the green stage. The yellow stage comes after the red stage. All players must proceed one stage at a time.

∃x ∃y ∃y ∃w (Game(x) ∧ StageNumber(x,3) ∧ Stage(y) ∧ Stage(z) ∧ Stage(w) ∧ ¬(y=z) ∧ ¬(z=w) ∧ ¬(y=w) ∧ Red(y) ∧ Yellow(z) ∧ Green(w)) ∀x (Player(x) → StartRed(x)) ∀x (Player(x) ∧ ¬ReachYellow(x) → ¬ReachGreen(x)) ∀x (Player(x) ∧ StartRed(x) → ReachYellow(x)) ∀x (Player(x) ∧ StartRed(x) ∧ ¬ReachYellow(x) → ¬ReachGreen(x))

It is possible to complete the game without ever reaching the green stage.

∃x (Player(x) ∧ CompleteGame(x))

Uncertain

In Love City, everyone considers physical touch or words of affirmation to be their most important love language. If someone in Love City considers physical touch as their most important love language, then they are good with pets. If someone in Love City is good with pets, then they are not scared of animals. In Love City, everyone is scared of animals, or loves animals, or both. Adam, who is in Love City, either values physical touch as his most important love language or loves animals.

∀x (In(x, loveCity) → (ConsidersMostImportantLoveLanguage(x, physicalTouch) ∨ ConsidersMostImportantLoveLanguage(x, wordOfAffirmation)) ∀x ((ConsidersMostImportantLoveLanguage(x, physicalTouch) ∧ In(x, loveCity) → GoodWith(x, pet)) ∀x ((GoodWith(x, pet) ∧ In(x, loveCity)) → ¬ScaredOf(x, animal)) ∀x (In(x, loveCity) → (ScaredOf(x, animal) ∨ Loves(x, animal))) (ConsidersMostImportantLoveLanguage(adam, physicalTouch) ⊕ Loves(adam, animal)) ∧ In(adam, loveCity)

Adam is scared of animals.

ScaredOf(adam, animal)

Uncertain

In Love City, everyone considers physical touch or words of affirmation to be their most important love language. If someone in Love City considers physical touch as their most important love language, then they are good with pets. If someone in Love City is good with pets, then they are not scared of animals. In Love City, everyone is scared of animals, or loves animals, or both. Adam, who is in Love City, either values physical touch as his most important love language or loves animals.

∀x (In(x, loveCity) → (ConsidersMostImportantLoveLanguage(x, physicalTouch) ∨ ConsidersMostImportantLoveLanguage(x, wordOfAffirmation)) ∀x ((ConsidersMostImportantLoveLanguage(x, physicalTouch) ∧ In(x, loveCity) → GoodWith(x, pet)) ∀x ((GoodWith(x, pet) ∧ In(x, loveCity)) → ¬ScaredOf(x, animal)) ∀x (In(x, loveCity) → (ScaredOf(x, animal) ∨ Loves(x, animal))) (ConsidersMostImportantLoveLanguage(adam, physicalTouch) ⊕ Loves(adam, animal)) ∧ In(adam, loveCity)

Adam considers words of affirmation to be the most important love language.

ConsidersMostImportantLoveLanguage(adam, wordOfAffirmation)

True

In Love City, everyone considers physical touch or words of affirmation to be their most important love language. If someone in Love City considers physical touch as their most important love language, then they are good with pets. If someone in Love City is good with pets, then they are not scared of animals. In Love City, everyone is scared of animals, or loves animals, or both. Adam, who is in Love City, either values physical touch as his most important love language or loves animals.

∀x (In(x, loveCity) → (ConsidersMostImportantLoveLanguage(x, physicalTouch) ∨ ConsidersMostImportantLoveLanguage(x, wordOfAffirmation)) ∀x ((ConsidersMostImportantLoveLanguage(x, physicalTouch) ∧ In(x, loveCity) → GoodWith(x, pet)) ∀x ((GoodWith(x, pet) ∧ In(x, loveCity)) → ¬ScaredOf(x, animal)) ∀x (In(x, loveCity) → (ScaredOf(x, animal) ∨ Loves(x, animal))) (ConsidersMostImportantLoveLanguage(adam, physicalTouch) ⊕ Loves(adam, animal)) ∧ In(adam, loveCity)

Adam considers physical touch as the most important love language and considers words of affirmation as the most important love language.

ConsidersMostImportantLoveLanguage(adam, physicalTouch) ∧ ConsidersMostImportantLoveLanguage(adam, wordOfAffirmation)

False

In Love City, everyone considers physical touch or words of affirmation to be their most important love language. If someone in Love City considers physical touch as their most important love language, then they are good with pets. If someone in Love City is good with pets, then they are not scared of animals. In Love City, everyone is scared of animals, or loves animals, or both. Adam, who is in Love City, either values physical touch as his most important love language or loves animals.

∀x (In(x, loveCity) → (ConsidersMostImportantLoveLanguage(x, physicalTouch) ∨ ConsidersMostImportantLoveLanguage(x, wordOfAffirmation)) ∀x ((ConsidersMostImportantLoveLanguage(x, physicalTouch) ∧ In(x, loveCity) → GoodWith(x, pet)) ∀x ((GoodWith(x, pet) ∧ In(x, loveCity)) → ¬ScaredOf(x, animal)) ∀x (In(x, loveCity) → (ScaredOf(x, animal) ∨ Loves(x, animal))) (ConsidersMostImportantLoveLanguage(adam, physicalTouch) ⊕ Loves(adam, animal)) ∧ In(adam, loveCity)

Adam either values physical touch as an especially important love language or values words of affirmation as an especially important love language.

ConsidersMostImportantLoveLanguage(adam, physicalTouch) ⊕ ConsidersMostImportantLoveLanguage(adam, wordOfAffirmation)

True

In Love City, everyone considers physical touch or words of affirmation to be their most important love language. If someone in Love City considers physical touch as their most important love language, then they are good with pets. If someone in Love City is good with pets, then they are not scared of animals. In Love City, everyone is scared of animals, or loves animals, or both. Adam, who is in Love City, either values physical touch as his most important love language or loves animals.

∀x (In(x, loveCity) → (ConsidersMostImportantLoveLanguage(x, physicalTouch) ∨ ConsidersMostImportantLoveLanguage(x, wordOfAffirmation)) ∀x ((ConsidersMostImportantLoveLanguage(x, physicalTouch) ∧ In(x, loveCity) → GoodWith(x, pet)) ∀x ((GoodWith(x, pet) ∧ In(x, loveCity)) → ¬ScaredOf(x, animal)) ∀x (In(x, loveCity) → (ScaredOf(x, animal) ∨ Loves(x, animal))) (ConsidersMostImportantLoveLanguage(adam, physicalTouch) ⊕ Loves(adam, animal)) ∧ In(adam, loveCity)

If Adam values physical touch as an especially important love language or is good with pets, then Adam values words of affirmation as an especially important love language.

(ConsidersMostImportantLoveLanguage(adam, physicalTouch, mostImportantLoveLanguage) ∨ GoodWith(x, pet)) → ConsidersMostImportantLoveLanguage(adam, wordOfAffirmation)

True

All birds have wings. Animals with wings aren't reptiles. Some animals that fly are birds. If something is an iguana, then it is a reptile. Simeng: All iguanas are reptiles. John is either both an iguana and a bird, or he is neither. John is an animal.

∀x (Bird(x) → ∃y ∃z (¬(y=z) ∧ Wing(y) ∧ Wing(z) ∧ Have(x, y) ∧ Have(x, z))) ∀x (Animal(x) ∧ (∃y ∃z (¬(y=z) ∧ Wing(y) ∧ Wing(z) ∧ Have(x, y) ∧ Have(x, z))) → ¬Reptile(x)) ∃x (Animal(x) ∧ Fly(x) ∧ Bird(x)) ∀x (Iguana(x) → Reptile(x)) ¬(Iguana(john) ⊕ Bird(john)) Animal(john)

John is a reptile.

Reptile(john)

Uncertain

All birds have wings. Animals with wings aren't reptiles. Some animals that fly are birds. If something is an iguana, then it is a reptile. Simeng: All iguanas are reptiles. John is either both an iguana and a bird, or he is neither. John is an animal.

∀x (Bird(x) → ∃y ∃z (¬(y=z) ∧ Wing(y) ∧ Wing(z) ∧ Have(x, y) ∧ Have(x, z))) ∀x (Animal(x) ∧ (∃y ∃z (¬(y=z) ∧ Wing(y) ∧ Wing(z) ∧ Have(x, y) ∧ Have(x, z))) → ¬Reptile(x)) ∃x (Animal(x) ∧ Fly(x) ∧ Bird(x)) ∀x (Iguana(x) → Reptile(x)) ¬(Iguana(john) ⊕ Bird(john)) Animal(john)

John is not both an iguana and an animal that can fly.

¬(Iguana(john) ∧ Fly(john))

True

All birds have wings. Animals with wings aren't reptiles. Some animals that fly are birds. If something is an iguana, then it is a reptile. Simeng: All iguanas are reptiles. John is either both an iguana and a bird, or he is neither. John is an animal.

∀x (Bird(x) → ∃y ∃z (¬(y=z) ∧ Wing(y) ∧ Wing(z) ∧ Have(x, y) ∧ Have(x, z))) ∀x (Animal(x) ∧ (∃y ∃z (¬(y=z) ∧ Wing(y) ∧ Wing(z) ∧ Have(x, y) ∧ Have(x, z))) → ¬Reptile(x)) ∃x (Animal(x) ∧ Fly(x) ∧ Bird(x)) ∀x (Iguana(x) → Reptile(x)) ¬(Iguana(john) ⊕ Bird(john)) Animal(john)

John is an animal that can fly and John is a bird.

Animal(john) ∧ Fly(john) ∧ Bird(john)

False

EndGame is a movie released in 2006. EndGame was set in Washington. EndGame was filmed outside of Washington. Some movies are filmed in New York. Andy Chang directed EndGame. Andy Chang is from Hong Kong.

Movie(endGame) ∧ Released(endGame, yr2006) SetIn(endGame, washington) ¬(FilmedIn(endGame, washington)) ∃x∃y(FilmedIn(x, newYork) ∧ (¬(x=y)) ∧ FilmedIn(y, newYork)) Directed(andyChang, endGame) From(andyChang, hongKong)

EndGame was filmed in New York.

FilmedIn(endGame, newYork)

Uncertain

EndGame is a movie released in 2006. EndGame was set in Washington. EndGame was filmed outside of Washington. Some movies are filmed in New York. Andy Chang directed EndGame. Andy Chang is from Hong Kong.

Movie(endGame) ∧ Released(endGame, yr2006) SetIn(endGame, washington) ¬(FilmedIn(endGame, washington)) ∃x∃y(FilmedIn(x, newYork) ∧ (¬(x=y)) ∧ FilmedIn(y, newYork)) Directed(andyChang, endGame) From(andyChang, hongKong)

EndGame was not directed by someone from Hong Kong.

∀x (¬(Directed(x, endGame) ∧ From(x, hongKong)))

False

EndGame is a movie released in 2006. EndGame was set in Washington. EndGame was filmed outside of Washington. Some movies are filmed in New York. Andy Chang directed EndGame. Andy Chang is from Hong Kong.

Movie(endGame) ∧ Released(endGame, yr2006) SetIn(endGame, washington) ¬(FilmedIn(endGame, washington)) ∃x∃y(FilmedIn(x, newYork) ∧ (¬(x=y)) ∧ FilmedIn(y, newYork)) Directed(andyChang, endGame) From(andyChang, hongKong)

All of Andy Chang's movies are filmed outside of Washington.

∀x (Directed(andyChang, x) → ¬(FilmedIn(x, washington)))

Uncertain

Six, seven and eight are real numbers. If a real number equals another real number added by one, the first number is larger. If the number x is larger than the number y, then y is not larger than x. Seven equals six plus one. Eight equals seven plus one. Two is positive. If a number is positive, then the double of it is also positive. Eight is the double of four. Four is the double of two.

RealNum(num6) ∧ RealNum(num7) ∧ RealNum(num8) ∀x ∀y ((RealNum(x) ∧ RealNum(y) ∧ IsSuccessorOf(x, y)) → Larger(x, y)) ∀x ∀y (Larger(x, y) → ¬Larger(y, x)) ∃y(IsSuccessorOf(y, num6) ∧ Equals(num7, y)) ∃y(IsSuccessorOf(y, num7) ∧ Equals(num8, y)) Positive(num2) ∀x ∀y ((Positive(x) ∧ IsDouble(y, x)) → Positive(y)) IsDouble(num8, num4) IsDouble(num4, num2)

Eight is larger than seven.

Larger(eight, seven)

True

Six, seven and eight are real numbers. If a real number equals another real number added by one, the first number is larger. If the number x is larger than the number y, then y is not larger than x. Seven equals six plus one. Eight equals seven plus one. Two is positive. If a number is positive, then the double of it is also positive. Eight is the double of four. Four is the double of two.

RealNum(num6) ∧ RealNum(num7) ∧ RealNum(num8) ∀x ∀y ((RealNum(x) ∧ RealNum(y) ∧ IsSuccessorOf(x, y)) → Larger(x, y)) ∀x ∀y (Larger(x, y) → ¬Larger(y, x)) ∃y(IsSuccessorOf(y, num6) ∧ Equals(num7, y)) ∃y(IsSuccessorOf(y, num7) ∧ Equals(num8, y)) Positive(num2) ∀x ∀y ((Positive(x) ∧ IsDouble(y, x)) → Positive(y)) IsDouble(num8, num4) IsDouble(num4, num2)

Eight is positive.

Positive(eight)

True

Six, seven and eight are real numbers. If a real number equals another real number added by one, the first number is larger. If the number x is larger than the number y, then y is not larger than x. Seven equals six plus one. Eight equals seven plus one. Two is positive. If a number is positive, then the double of it is also positive. Eight is the double of four. Four is the double of two.

RealNum(num6) ∧ RealNum(num7) ∧ RealNum(num8) ∀x ∀y ((RealNum(x) ∧ RealNum(y) ∧ IsSuccessorOf(x, y)) → Larger(x, y)) ∀x ∀y (Larger(x, y) → ¬Larger(y, x)) ∃y(IsSuccessorOf(y, num6) ∧ Equals(num7, y)) ∃y(IsSuccessorOf(y, num7) ∧ Equals(num8, y)) Positive(num2) ∀x ∀y ((Positive(x) ∧ IsDouble(y, x)) → Positive(y)) IsDouble(num8, num4) IsDouble(num4, num2)

Six is larger than seven.

Larger(six, seven)

False

All dogs sleep. Some four-legged animals are dogs.

∀x (Dog(x) → Sleep(x)) ∃x ∃y (FourLegged(x) ∧ Animal(x) ∧ Dog(x) ∧ FourLegged(y) ∧ Animal(y) ∧ Dog(y) ∧ ¬(x=y))

Some four-legged animals sleep.

∃x ∃y (FourLegged(x) ∧ Animal(x) ∧ Sleeps(x) ∧ FourLegged(y) ∧ Animal(y) ∧ Sleeps(y) ∧ ¬(x=y))

True

Everyone who is entitled to national social insurance coverage can have their medical bills partially covered. All PRC nationals are entitled to national social insurance coverage. Everyone in the Franco-China diplomatic conference is either a PRC national or a French national, but not both. All French nationals are citizens of the European Union. All Spanish nationals are citizens of the European Union. No North Korean nationals are citizens of the European Union. Mei is at the Franco-China diplomatic conference. Either Mei is a North Korean and can have medical bills partially covered, or neither is true.

∀x (EntitledTo(x, nationalSocialInsuranceCoverage) → CanHavePartiallyCovered(x, medicalBills)) ∀x (PRCNational(x) → EntitledTo(x, nationalSocialInsuranceCoverage)) ∀x (In(x, franco-ChinaDiplomaticConference) → PRCNational(x) ⊕ FrenchNational(x)) ∀x (FrenchNational(x) → CitizenOf(x, europeanUnion)) ∀x (SpanishNational(x) → CitizenOf(x, europeanUnion)) ∀x (NorthKoreanNational(x) → ¬CitizenOf(x, europeanUnion)) In(mei, franco-ChinaDiplomaticConference) ¬(NorthKoreanNational(mei) ⊕ CanHavePartiallyCovered(mei, medicalBills))

Mei is a PRC national.

PRCNational(mei)

Uncertain

Everyone who is entitled to national social insurance coverage can have their medical bills partially covered. All PRC nationals are entitled to national social insurance coverage. Everyone in the Franco-China diplomatic conference is either a PRC national or a French national, but not both. All French nationals are citizens of the European Union. All Spanish nationals are citizens of the European Union. No North Korean nationals are citizens of the European Union. Mei is at the Franco-China diplomatic conference. Either Mei is a North Korean and can have medical bills partially covered, or neither is true.

∀x (EntitledTo(x, nationalSocialInsuranceCoverage) → CanHavePartiallyCovered(x, medicalBills)) ∀x (PRCNational(x) → EntitledTo(x, nationalSocialInsuranceCoverage)) ∀x (In(x, franco-ChinaDiplomaticConference) → PRCNational(x) ⊕ FrenchNational(x)) ∀x (FrenchNational(x) → CitizenOf(x, europeanUnion)) ∀x (SpanishNational(x) → CitizenOf(x, europeanUnion)) ∀x (NorthKoreanNational(x) → ¬CitizenOf(x, europeanUnion)) In(mei, franco-ChinaDiplomaticConference) ¬(NorthKoreanNational(mei) ⊕ CanHavePartiallyCovered(mei, medicalBills))

Mei is not a PRC national.

¬PRCNational(mei)

Uncertain

Everyone who is entitled to national social insurance coverage can have their medical bills partially covered. All PRC nationals are entitled to national social insurance coverage. Everyone in the Franco-China diplomatic conference is either a PRC national or a French national, but not both. All French nationals are citizens of the European Union. All Spanish nationals are citizens of the European Union. No North Korean nationals are citizens of the European Union. Mei is at the Franco-China diplomatic conference. Either Mei is a North Korean and can have medical bills partially covered, or neither is true.

∀x (EntitledTo(x, nationalSocialInsuranceCoverage) → CanHavePartiallyCovered(x, medicalBills)) ∀x (PRCNational(x) → EntitledTo(x, nationalSocialInsuranceCoverage)) ∀x (In(x, franco-ChinaDiplomaticConference) → PRCNational(x) ⊕ FrenchNational(x)) ∀x (FrenchNational(x) → CitizenOf(x, europeanUnion)) ∀x (SpanishNational(x) → CitizenOf(x, europeanUnion)) ∀x (NorthKoreanNational(x) → ¬CitizenOf(x, europeanUnion)) In(mei, franco-ChinaDiplomaticConference) ¬(NorthKoreanNational(mei) ⊕ CanHavePartiallyCovered(mei, medicalBills))

If Mei is either a North Korean or a Spanish national, then Mei is either both a French national and a citizen of the European Union, or neither a French national nor a citizen of the European Union.

NorthKoreanNational(mei) ⊕ SpanishNational(mei) → ¬(FrenchNational(mei) ⊕ European(mei))

True

No people who do not admit a mistake are good teachers. Some well-informed people are people who do not admit a mistake.

∀x (¬Admit(x, mistake) → ¬GoodTeacher(x)) ∃x ∃y (WellInformed(x) ∧ WellInformed(y) ∧ ¬Admit(x, mistake) ∧ ¬Admit(y, mistake) ∧ ¬(x=y))

Some good teachers are not well-informed people.

∃x ∃y (GoodTeacher(x) ∧ GoodTeacher(y) ∧ ¬WellInformed(x) ∧ ¬WellInformed(y) ∧ ¬(x=y))

Uncertain

Philatelic literature is divided into the following categories: Stamp catalogs, Periodicals, Auction catalogs, Books, Bibliographies, and Background Material. Mort is not a Stamp catalog. Mort is not a periodical, auction catalog, bibliography, or background material. Mort is a piece of Philatelic literature.

∀x (PhilatelicLit(x) → (Stamp(x) ∨ Periodical(x) ∨ Auction(x) ∨ Book(x) ∨ Bibliography(x) ∨ Background(x))) ¬Stamp(mort) ¬(Periodical(mort) ∨ Auction(mort) ∨ Bibliography(mort) ∨ Background(mort)) PhilatelicLit(mort)

Mort is background material.

Background(mort)

False

Philatelic literature is divided into the following categories: Stamp catalogs, Periodicals, Auction catalogs, Books, Bibliographies, and Background Material. Mort is not a Stamp catalog. Mort is not a periodical, auction catalog, bibliography, or background material. Mort is a piece of Philatelic literature.

∀x (PhilatelicLit(x) → (Stamp(x) ∨ Periodical(x) ∨ Auction(x) ∨ Book(x) ∨ Bibliography(x) ∨ Background(x))) ¬Stamp(mort) ¬(Periodical(mort) ∨ Auction(mort) ∨ Bibliography(mort) ∨ Background(mort)) PhilatelicLit(mort)

Eragon is a piece of Philatelic literature.

PhilatelicLit(eragon)

Uncertain

Adventures of Rusty is a drama film and children's film. Columbia Pictures produced Adventures of Rusty. Tintin was produced by Paramount. Tintin is an adventure film.

DramaFilm(adventuresOfRusty) ∧ ChildrensFilm(adventuresOfRusty) Produces(columbiaPictures, adventuresOfRusty) Produces(paramount, tintin) AdventureFilm(tintin)

Columbia pictures produced some drama film.

∃x (DramaFilm(x) ∧ Produces(columbiaPictures, x))

True

Adventures of Rusty is a drama film and children's film. Columbia Pictures produced Adventures of Rusty. Tintin was produced by Paramount. Tintin is an adventure film.

DramaFilm(adventuresOfRusty) ∧ ChildrensFilm(adventuresOfRusty) Produces(columbiaPictures, adventuresOfRusty) Produces(paramount, tintin) AdventureFilm(tintin)

Columbia pictures produced some adventure film.

∃x (AdventureFilm(x) ∧ Produces(columbiaPictures, x))

Uncertain

Adventures of Rusty is a drama film and children's film. Columbia Pictures produced Adventures of Rusty. Tintin was produced by Paramount. Tintin is an adventure film.

DramaFilm(adventuresOfRusty) ∧ ChildrensFilm(adventuresOfRusty) Produces(columbiaPictures, adventuresOfRusty) Produces(paramount, tintin) AdventureFilm(tintin)

Paramount produces children's films.

∃x (ChildrensFilm(x) ∧ Produces(paramount, x))

Uncertain

Adventures of Rusty is a drama film and children's film. Columbia Pictures produced Adventures of Rusty. Tintin was produced by Paramount. Tintin is an adventure film.

DramaFilm(adventuresOfRusty) ∧ ChildrensFilm(adventuresOfRusty) Produces(columbiaPictures, adventuresOfRusty) Produces(paramount, tintin) AdventureFilm(tintin)

Paramount produces adventure films.

∃x (AdventureFilm(x) ∧ Produces(paramount, x))

True

Deng Xiaoping served as the paramount leader of the People's Republic of China. Deng Xiaoping was praised for his reaffirmation of the reform program, as well as the reversion of Hong Kong to Chinese control and the return of Macau. As the party's Secretary-General under Mao and Vice Premier in the 1950s, Deng Xiaoping presided over the Anti-Rightist Campaign launched by Mao. Deng Xiaoping became instrumental in China's economic reconstruction following the disastrous Great Leap Forward. Mao Zedong died in 1976. After Mao Zedong's death, Deng Xiaoping gradually rose to supreme power.

ParamountLeaderOf(dengXiaoping, peoplesRepublicOfChina) PraisedFor(dengXiaoping, reaffirmationOfReformProgram) ∧ PraisedFor(dengXiaoping, reversionOfHongKong) ∧ PraisedFor(dengXiaoping, returnOfMacau) PartysSecretaryGeneral(dengXiaoping) ∧ Under(dengXiaoping, mao) ∧ VicePremierInThe1950s(dengXiaoping) ∧ PresidedOver(dengXiaoping, antiRightistCampaign) ∧ LaunchedBy(antiRightistCampaign, mao) InstrumentalIn(dengXiaoping, chinasEconomicReconstruction) ∧ Following(chinasEconomicReconstruction, greatLeapForward) ∧ Disastrous(greatLeapForward) DiedIn(mao, year1976) GraduallyRoseTo(dengXiaoping, supremePower)

The paramount leader of the PRC was also the vice premier.

∃x (ParamountLeaderOf(x, prc) ∧ VicePremier(x))

True

Deng Xiaoping served as the paramount leader of the People's Republic of China. Deng Xiaoping was praised for his reaffirmation of the reform program, as well as the reversion of Hong Kong to Chinese control and the return of Macau. As the party's Secretary-General under Mao and Vice Premier in the 1950s, Deng Xiaoping presided over the Anti-Rightist Campaign launched by Mao. Deng Xiaoping became instrumental in China's economic reconstruction following the disastrous Great Leap Forward. Mao Zedong died in 1976. After Mao Zedong's death, Deng Xiaoping gradually rose to supreme power.

ParamountLeaderOf(dengXiaoping, peoplesRepublicOfChina) PraisedFor(dengXiaoping, reaffirmationOfReformProgram) ∧ PraisedFor(dengXiaoping, reversionOfHongKong) ∧ PraisedFor(dengXiaoping, returnOfMacau) PartysSecretaryGeneral(dengXiaoping) ∧ Under(dengXiaoping, mao) ∧ VicePremierInThe1950s(dengXiaoping) ∧ PresidedOver(dengXiaoping, antiRightistCampaign) ∧ LaunchedBy(antiRightistCampaign, mao) InstrumentalIn(dengXiaoping, chinasEconomicReconstruction) ∧ Following(chinasEconomicReconstruction, greatLeapForward) ∧ Disastrous(greatLeapForward) DiedIn(mao, year1976) GraduallyRoseTo(dengXiaoping, supremePower)

Deng Xiaoping presided over something launched by someone he was under.

∃x ∃y (PresidedOver(dengxiaoping, x) ∧ Under(dengxiaoping, y) ∧ LaunchedBy(x, y))

True

Deng Xiaoping served as the paramount leader of the People's Republic of China. Deng Xiaoping was praised for his reaffirmation of the reform program, as well as the reversion of Hong Kong to Chinese control and the return of Macau. As the party's Secretary-General under Mao and Vice Premier in the 1950s, Deng Xiaoping presided over the Anti-Rightist Campaign launched by Mao. Deng Xiaoping became instrumental in China's economic reconstruction following the disastrous Great Leap Forward. Mao Zedong died in 1976. After Mao Zedong's death, Deng Xiaoping gradually rose to supreme power.

ParamountLeaderOf(dengXiaoping, peoplesRepublicOfChina) PraisedFor(dengXiaoping, reaffirmationOfReformProgram) ∧ PraisedFor(dengXiaoping, reversionOfHongKong) ∧ PraisedFor(dengXiaoping, returnOfMacau) PartysSecretaryGeneral(dengXiaoping) ∧ Under(dengXiaoping, mao) ∧ VicePremierInThe1950s(dengXiaoping) ∧ PresidedOver(dengXiaoping, antiRightistCampaign) ∧ LaunchedBy(antiRightistCampaign, mao) InstrumentalIn(dengXiaoping, chinasEconomicReconstruction) ∧ Following(chinasEconomicReconstruction, greatLeapForward) ∧ Disastrous(greatLeapForward) DiedIn(mao, year1976) GraduallyRoseTo(dengXiaoping, supremePower)

The person instrumental in china's economic reconstruction gradually rose to supreme power.

∃x (InstrumentalIn(x, chinaseconomicreconstruction) ∧ GraduallyRoseTo(x, supremepower))

True

All imaginative processes that Dan knows are results of creative processes. All science fiction that Dan knows comes from an imaginative process. Everthing that Dan knows comes from either science-fiction or realistic fiction. No facts that Dan knows have proven to be false. Dan knows that Dune is science fiction or has proven to be false.

∀x ((Knows(dan, x) ∧ ImaginativeProcess(x)) → ResultOf(x, creativeProcess)) ∀x ((Knows(dan, x) ∧ ScienceFiction(x)) → ImaginativeProcess(x)) ∀x (Knows(dan, x) → (ScienceFiction(x) ⊕ RealisticFiction(x))) ∀x ((Knows(dan, x) ∧ Fact(x)) → ¬ProvedToBe(x, false)) (Knows(dan, dune) ∧ ScienceFiction(dune)) ∨ ProvedToBe(dune, false))

Dune is realistic fiction.

RealisticFiction(dune)

Uncertain

All imaginative processes that Dan knows are results of creative processes. All science fiction that Dan knows comes from an imaginative process. Everthing that Dan knows comes from either science-fiction or realistic fiction. No facts that Dan knows have proven to be false. Dan knows that Dune is science fiction or has proven to be false.

∀x ((Knows(dan, x) ∧ ImaginativeProcess(x)) → ResultOf(x, creativeProcess)) ∀x ((Knows(dan, x) ∧ ScienceFiction(x)) → ImaginativeProcess(x)) ∀x (Knows(dan, x) → (ScienceFiction(x) ⊕ RealisticFiction(x))) ∀x ((Knows(dan, x) ∧ Fact(x)) → ¬ProvedToBe(x, false)) (Knows(dan, dune) ∧ ScienceFiction(dune)) ∨ ProvedToBe(dune, false))

Dune is a result of creative and imaginative process.

ResultOf(dune, creativeProcess) ∧ ImaginativeProcess(dune)

True

All imaginative processes that Dan knows are results of creative processes. All science fiction that Dan knows comes from an imaginative process. Everthing that Dan knows comes from either science-fiction or realistic fiction. No facts that Dan knows have proven to be false. Dan knows that Dune is science fiction or has proven to be false.

∀x ((Knows(dan, x) ∧ ImaginativeProcess(x)) → ResultOf(x, creativeProcess)) ∀x ((Knows(dan, x) ∧ ScienceFiction(x)) → ImaginativeProcess(x)) ∀x (Knows(dan, x) → (ScienceFiction(x) ⊕ RealisticFiction(x))) ∀x ((Knows(dan, x) ∧ Fact(x)) → ¬ProvedToBe(x, false)) (Knows(dan, dune) ∧ ScienceFiction(dune)) ∨ ProvedToBe(dune, false))

Dune is either a result of creative processes or came from an imaginative process.

ResultOf(dune, creativeProcess) ⊕ ImaginativeProcess(dune)

False

All imaginative processes that Dan knows are results of creative processes. All science fiction that Dan knows comes from an imaginative process. Everthing that Dan knows comes from either science-fiction or realistic fiction. No facts that Dan knows have proven to be false. Dan knows that Dune is science fiction or has proven to be false.

∀x ((Knows(dan, x) ∧ ImaginativeProcess(x)) → ResultOf(x, creativeProcess)) ∀x ((Knows(dan, x) ∧ ScienceFiction(x)) → ImaginativeProcess(x)) ∀x (Knows(dan, x) → (ScienceFiction(x) ⊕ RealisticFiction(x))) ∀x ((Knows(dan, x) ∧ Fact(x)) → ¬ProvedToBe(x, false)) (Knows(dan, dune) ∧ ScienceFiction(dune)) ∨ ProvedToBe(dune, false))

Dune is a result of creative processes and is science fiction.

ResultOf(dune, creativeProcess) ∧ ScienceFiction(dune))

True

All imaginative processes that Dan knows are results of creative processes. All science fiction that Dan knows comes from an imaginative process. Everthing that Dan knows comes from either science-fiction or realistic fiction. No facts that Dan knows have proven to be false. Dan knows that Dune is science fiction or has proven to be false.

∀x ((Knows(dan, x) ∧ ImaginativeProcess(x)) → ResultOf(x, creativeProcess)) ∀x ((Knows(dan, x) ∧ ScienceFiction(x)) → ImaginativeProcess(x)) ∀x (Knows(dan, x) → (ScienceFiction(x) ⊕ RealisticFiction(x))) ∀x ((Knows(dan, x) ∧ Fact(x)) → ¬ProvedToBe(x, false)) (Knows(dan, dune) ∧ ScienceFiction(dune)) ∨ ProvedToBe(dune, false))

Dune is either a result of creative processes or is science fiction.

Knows(dan, dune) ∧ (ResultOf(dune, creativeProcess) ⊕ ScienceFiction(dune))

False

All imaginative processes that Dan knows are results of creative processes. All science fiction that Dan knows comes from an imaginative process. Everthing that Dan knows comes from either science-fiction or realistic fiction. No facts that Dan knows have proven to be false. Dan knows that Dune is science fiction or has proven to be false.

∀x ((Knows(dan, x) ∧ ImaginativeProcess(x)) → ResultOf(x, creativeProcess)) ∀x ((Knows(dan, x) ∧ ScienceFiction(x)) → ImaginativeProcess(x)) ∀x (Knows(dan, x) → (ScienceFiction(x) ⊕ RealisticFiction(x))) ∀x ((Knows(dan, x) ∧ Fact(x)) → ¬ProvedToBe(x, false)) (Knows(dan, dune) ∧ ScienceFiction(dune)) ∨ ProvedToBe(dune, false))

If Dune is a result of creative and imaginative processes, then Dune is not a result of creative processes and science-fiction.

(ResultOf(dune, creativeProcess) ∧ ImaginativeProcess(dune)) → (¬ResultOf(dune, creativeProcess) ∧ ¬ScienceFiction(dune))

False

All imaginative processes that Dan knows are results of creative processes. All science fiction that Dan knows comes from an imaginative process. Everthing that Dan knows comes from either science-fiction or realistic fiction. No facts that Dan knows have proven to be false. Dan knows that Dune is science fiction or has proven to be false.

∀x ((Knows(dan, x) ∧ ImaginativeProcess(x)) → ResultOf(x, creativeProcess)) ∀x ((Knows(dan, x) ∧ ScienceFiction(x)) → ImaginativeProcess(x)) ∀x (Knows(dan, x) → (ScienceFiction(x) ⊕ RealisticFiction(x))) ∀x ((Knows(dan, x) ∧ Fact(x)) → ¬ProvedToBe(x, false)) (Knows(dan, dune) ∧ ScienceFiction(dune)) ∨ ProvedToBe(dune, false))

If Dune is either a fact and a result of creative processes, or neither a fact nor a result of creative processes, then Dune is a result of creative processes and science-fiction.

Knows(dan, dune) ∧ (¬(Fact(dune) ⊕ ResultOf(dune, creativeProcess))) → (ResultOf(dune, creativeProcess) ∧ ScienceFiction(dune))

True

All imaginative processes that Dan knows are results of creative processes. All science fiction that Dan knows comes from an imaginative process. Everthing that Dan knows comes from either science-fiction or realistic fiction. No facts that Dan knows have proven to be false. Dan knows that Dune is science fiction or has proven to be false.

∀x ((Knows(dan, x) ∧ ImaginativeProcess(x)) → ResultOf(x, creativeProcess)) ∀x ((Knows(dan, x) ∧ ScienceFiction(x)) → ImaginativeProcess(x)) ∀x (Knows(dan, x) → (ScienceFiction(x) ⊕ RealisticFiction(x))) ∀x ((Knows(dan, x) ∧ Fact(x)) → ¬ProvedToBe(x, false)) (Knows(dan, dune) ∧ ScienceFiction(dune)) ∨ ProvedToBe(dune, false))

If Dune is science-fiction, then Dune is not a result of creative processes and science-fiction.

Knows(dan, dune) ∧ (ScienceFiction(dune)) → (¬(ResultOf(dune, creativeProcess) ∧ ScienceFiction(dune)))

False

All imaginative processes that Dan knows are results of creative processes. All science fiction that Dan knows comes from an imaginative process. Everthing that Dan knows comes from either science-fiction or realistic fiction. No facts that Dan knows have proven to be false. Dan knows that Dune is science fiction or has proven to be false.

∀x ((Knows(dan, x) ∧ ImaginativeProcess(x)) → ResultOf(x, creativeProcess)) ∀x ((Knows(dan, x) ∧ ScienceFiction(x)) → ImaginativeProcess(x)) ∀x (Knows(dan, x) → (ScienceFiction(x) ⊕ RealisticFiction(x))) ∀x ((Knows(dan, x) ∧ Fact(x)) → ¬ProvedToBe(x, false)) (Knows(dan, dune) ∧ ScienceFiction(dune)) ∨ ProvedToBe(dune, false))

If Dune is not a result of creative processes and science-fiction, then Dune neither came from an imaginative process nor proved to be false.

Knows(dan, dune) ∧ (¬(ResultOf(dune, creativeProcess) ∧ ScienceFiction(dune))) → (¬(ImaginativeProcess(dune) ∨ ProvedToBe(dune, false)))

True

All imaginative processes that Dan knows are results of creative processes. All science fiction that Dan knows comes from an imaginative process. Everthing that Dan knows comes from either science-fiction or realistic fiction. No facts that Dan knows have proven to be false. Dan knows that Dune is science fiction or has proven to be false.

∀x ((Knows(dan, x) ∧ ImaginativeProcess(x)) → ResultOf(x, creativeProcess)) ∀x ((Knows(dan, x) ∧ ScienceFiction(x)) → ImaginativeProcess(x)) ∀x (Knows(dan, x) → (ScienceFiction(x) ⊕ RealisticFiction(x))) ∀x ((Knows(dan, x) ∧ Fact(x)) → ¬ProvedToBe(x, false)) (Knows(dan, dune) ∧ ScienceFiction(dune)) ∨ ProvedToBe(dune, false))

If Dune is did not come from imaginative process and is not science-fiction, then Dune is neither a result of creative processes nor came from an imaginative process.

Knows(dan, dune) ∧ (¬(ImaginativeProcess(dune) ∧ ScienceFiction(dune))) → (¬(ResultOf(dune, creativeProcess) ∨ ImaginativeProcess(dune)))

True

American superheroes come from either the DC Universe or Marvel Universe. Captain America is one of America's top-ten favorite superheroes Captain America does not come from the DC Universe. America's top-ten favorite superheroes speak English. Some superheroes speak both English and Spanish.

∀x (Superhero(x) ∧ American(x) → ComeFrom(x, dCUniverse) ⊕ ComeFrom(x, marvelUniverse)) American(captainAmerica) ∧ TopTenFavorite(captainAmerica) ∧ Superhero(captainAmerica) ¬ComeFrom(captainAmerica, dCUniverse) ∀x (American(x) ∧ TopTenFavorite(x) ∧ Superhero(x) → Speak(x, english)) ∃x (Superhero(x) → (Speak(x, english) ∧ Speak(x, spanish)))

Captain America does not speak English.

¬Speak(captainAmerica, english)

False

American superheroes come from either the DC Universe or Marvel Universe. Captain America is one of America's top-ten favorite superheroes Captain America does not come from the DC Universe. America's top-ten favorite superheroes speak English. Some superheroes speak both English and Spanish.

∀x (Superhero(x) ∧ American(x) → ComeFrom(x, dCUniverse) ⊕ ComeFrom(x, marvelUniverse)) American(captainAmerica) ∧ TopTenFavorite(captainAmerica) ∧ Superhero(captainAmerica) ¬ComeFrom(captainAmerica, dCUniverse) ∀x (American(x) ∧ TopTenFavorite(x) ∧ Superhero(x) → Speak(x, english)) ∃x (Superhero(x) → (Speak(x, english) ∧ Speak(x, spanish)))

Captain America comes from the Marvel universe.

ComeFrom(captainAmerica, marvelUniverse)

True

American superheroes come from either the DC Universe or Marvel Universe. Captain America is one of America's top-ten favorite superheroes Captain America does not come from the DC Universe. America's top-ten favorite superheroes speak English. Some superheroes speak both English and Spanish.

∀x (Superhero(x) ∧ American(x) → ComeFrom(x, dCUniverse) ⊕ ComeFrom(x, marvelUniverse)) American(captainAmerica) ∧ TopTenFavorite(captainAmerica) ∧ Superhero(captainAmerica) ¬ComeFrom(captainAmerica, dCUniverse) ∀x (American(x) ∧ TopTenFavorite(x) ∧ Superhero(x) → Speak(x, english)) ∃x (Superhero(x) → (Speak(x, english) ∧ Speak(x, spanish)))

Captain America speaks Spanish.

Speak(captainAmerica, spanish)

Uncertain

Robert Zimmer was a philosopher born in Germany. Robert Zimmer is an essayist. Robert Zimmer was born in 1953. Every essayist is a writer.

BornIn(robertZimmer, germany) ∧ Philosopher(robertZimmer) Essayist(robertZimmer) BornIn(robertZimmer, yr1953) ∀x (Essayist(x) → Writer(x))

Robert Zimmer is German.

BornIn(robertZimmer, germany)

Uncertain

Robert Zimmer was a philosopher born in Germany. Robert Zimmer is an essayist. Robert Zimmer was born in 1953. Every essayist is a writer.

BornIn(robertZimmer, germany) ∧ Philosopher(robertZimmer) Essayist(robertZimmer) BornIn(robertZimmer, yr1953) ∀x (Essayist(x) → Writer(x))

Robert Zimmer is not a writer.

¬Writer(robertZimmer)

False

Robert Zimmer was a philosopher born in Germany. Robert Zimmer is an essayist. Robert Zimmer was born in 1953. Every essayist is a writer.

BornIn(robertZimmer, germany) ∧ Philosopher(robertZimmer) Essayist(robertZimmer) BornIn(robertZimmer, yr1953) ∀x (Essayist(x) → Writer(x))

Robert Zimmer is a biographer.

Biographer(robertZimmer)

Uncertain

All people who repay their loans on time have a high credit score. Some people with high credit scores and high salaries are approved for mortgages. John has a high salary.

∀x (RepayOnTime(x) → Has(x, highCreditScore)) ∃x ((Has(x, highCreditScore) ∧ Has(x, highSalary)) → ApprovedFor(x, mortgage)) Has(john, highSalary)

If John repays his loans on time, he will be approved for a mortgage.

RepayOnTime(john) → ApprovedFor(john, mortgage)

Uncertain

All students are members of the university. All graduate students are students. All PhD students are graduate students. Some PhD students are Teaching Fellows. If John is not a PhD student, then he is not a member of the university. If John is a Teaching Fellow, then he is a PhD student or a graduate student.

∀x (Student(x) → MemberOf(x, university)) ∀x (GraduateStudent(x) → Student(x)) ∀x (PhDStudent(x) → GraduateStudent(x)) ∃x (PhDStudent(x) ∧ TeachingFellow(x)) ¬PhDStudent(john) → ¬MemberOf(john, university) TeachingFellow(john) → PhDStudent(john) ⊕ GraduateStudent(john)

John is a Teaching Fellow

TF(john)

False

All students are members of the university. All graduate students are students. All PhD students are graduate students. Some PhD students are Teaching Fellows. If John is not a PhD student, then he is not a member of the university. If John is a Teaching Fellow, then he is a PhD student or a graduate student.

∀x (Student(x) → MemberOf(x, university)) ∀x (GraduateStudent(x) → Student(x)) ∀x (PhDStudent(x) → GraduateStudent(x)) ∃x (PhDStudent(x) ∧ TeachingFellow(x)) ¬PhDStudent(john) → ¬MemberOf(john, university) TeachingFellow(john) → PhDStudent(john) ⊕ GraduateStudent(john)

John is not a Teaching Fellow.

¬TF(john)

True

All students are members of the university. All graduate students are students. All PhD students are graduate students. Some PhD students are Teaching Fellows. If John is not a PhD student, then he is not a member of the university. If John is a Teaching Fellow, then he is a PhD student or a graduate student.

∀x (Student(x) → MemberOf(x, university)) ∀x (GraduateStudent(x) → Student(x)) ∀x (PhDStudent(x) → GraduateStudent(x)) ∃x (PhDStudent(x) ∧ TeachingFellow(x)) ¬PhDStudent(john) → ¬MemberOf(john, university) TeachingFellow(john) → PhDStudent(john) ⊕ GraduateStudent(john)

John is a PhD student.

PhDStudent(john)

Uncertain

Belgium, France, and Germany are European countries. Paris is the capital of France. The Eiffel Tower is one of the main tourist attractions located in Paris. Some people who live in Belgium speak French. If John goes to Europe, he will see some tourist attractions. John speaks French.

EuropeanCountry(belgium) ∧ EuropeanCountry(france) ∧ EuropeanCountry(germany) CapitalOf(paris, france) TouristAttraction(eiffelTower) ∧ LocatedIn(eiffelTower, paris) ∃x (LiveIn(x, belgium) → Speak(x, french)) ∃x (GoTo(john, europe) → (See(john, x) ∧ TouristAttraction(x))) Speak(john, french)

If John goes to Europe, he will see the Eiffel Tower.

GoTo(john, europe) → See(john, eiffelTower)

Uncertain

Belgium, France, and Germany are European countries. Paris is the capital of France. The Eiffel Tower is one of the main tourist attractions located in Paris. Some people who live in Belgium speak French. If John goes to Europe, he will see some tourist attractions. John speaks French.

EuropeanCountry(belgium) ∧ EuropeanCountry(france) ∧ EuropeanCountry(germany) CapitalOf(paris, france) TouristAttraction(eiffelTower) ∧ LocatedIn(eiffelTower, paris) ∃x (LiveIn(x, belgium) → Speak(x, french)) ∃x (GoTo(john, europe) → (See(john, x) ∧ TouristAttraction(x))) Speak(john, french)

The Eiffel Tower is located in the capital of France.

∃x (CapitalOf(x, france) ∧ LocatedIn(eiffelTower, x))

True

Belgium, France, and Germany are European countries. Paris is the capital of France. The Eiffel Tower is one of the main tourist attractions located in Paris. Some people who live in Belgium speak French. If John goes to Europe, he will see some tourist attractions. John speaks French.

EuropeanCountry(belgium) ∧ EuropeanCountry(france) ∧ EuropeanCountry(germany) CapitalOf(paris, france) TouristAttraction(eiffelTower) ∧ LocatedIn(eiffelTower, paris) ∃x (LiveIn(x, belgium) → Speak(x, french)) ∃x (GoTo(john, europe) → (See(john, x) ∧ TouristAttraction(x))) Speak(john, french)

John lives in Belgium.

LiveIn(john, belgium)

Uncertain

All sports cars are loud. No loud cars are electric. If a car is a Ferrari, then it is a sports car. All cars made in Maranello are Ferraris. The Toyota Prius is made in Maranello or is a loud car, or both.

∀x (SportsCar(x) → LoudCar(x)) ∀x (LoudCar(x) → ¬ElectricCar(x)) ∀x (Ferrari(x) → SportsCar(x)) ∀x ((Car(x) ∧ MadeIn(x, maranello)) → Ferrari(x)) (Car(toyotaPrius) ∧ MadeIn(toyotaPrius, maranello)) ∨ LoudCar(toyotaPrius)

Prius is an electric car.

ElectricCar(toyotaPrius)

False

All sports cars are loud. No loud cars are electric. If a car is a Ferrari, then it is a sports car. All cars made in Maranello are Ferraris. The Toyota Prius is made in Maranello or is a loud car, or both.

∀x (SportsCar(x) → LoudCar(x)) ∀x (LoudCar(x) → ¬ElectricCar(x)) ∀x (Ferrari(x) → SportsCar(x)) ∀x ((Car(x) ∧ MadeIn(x, maranello)) → Ferrari(x)) (Car(toyotaPrius) ∧ MadeIn(toyotaPrius, maranello)) ∨ LoudCar(toyotaPrius)

The Toyota Prius is not an electric car.

¬ElectricCar(toyotaPrius)

True

All sports cars are loud. No loud cars are electric. If a car is a Ferrari, then it is a sports car. All cars made in Maranello are Ferraris. The Toyota Prius is made in Maranello or is a loud car, or both.

∀x (SportsCar(x) → LoudCar(x)) ∀x (LoudCar(x) → ¬ElectricCar(x)) ∀x (Ferrari(x) → SportsCar(x)) ∀x ((Car(x) ∧ MadeIn(x, maranello)) → Ferrari(x)) (Car(toyotaPrius) ∧ MadeIn(toyotaPrius, maranello)) ∨ LoudCar(toyotaPrius)

The Toyota Prius is a equipped with a Ferrari V12 engine.

MadeIn(toyotaPrius, maranello)

Uncertain

All sports cars are loud. No loud cars are electric. If a car is a Ferrari, then it is a sports car. All cars made in Maranello are Ferraris. The Toyota Prius is made in Maranello or is a loud car, or both.

∀x (SportsCar(x) → LoudCar(x)) ∀x (LoudCar(x) → ¬ElectricCar(x)) ∀x (Ferrari(x) → SportsCar(x)) ∀x ((Car(x) ∧ MadeIn(x, maranello)) → Ferrari(x)) (Car(toyotaPrius) ∧ MadeIn(toyotaPrius, maranello)) ∨ LoudCar(toyotaPrius)

If The Toyota Prius is a Ferrari or a loud car, then The Toyota Prius is an electric car.

Ferrari(toyotaPrius) ∨ LoudCar(toyotaPrius) → ElectricCar(toyotaPrius)

False

If something is a plant, then it is not a cute animal. Simeng: All plants are not cute animals. All flowers are plants. Every kitten is a cute animal. If something is grown in a garden, then it is a flower. Piper is a kitten or a cute animal.

∀x (Plant(x) → ¬CuteAnimal(x)) ∀x (Flower(x) → Plant(x)) ∀x (Kitten(x) → CuteAnimal(x)) ∀x (GrownIn(x, garden) → Flower(x)) Kitten(piper) ∨ CuteAnimal(piper)

Piper was grown in a garden.

GrownIn(piper, garden)

False

If something is a plant, then it is not a cute animal. Simeng: All plants are not cute animals. All flowers are plants. Every kitten is a cute animal. If something is grown in a garden, then it is a flower. Piper is a kitten or a cute animal.

∀x (Plant(x) → ¬CuteAnimal(x)) ∀x (Flower(x) → Plant(x)) ∀x (Kitten(x) → CuteAnimal(x)) ∀x (GrownIn(x, garden) → Flower(x)) Kitten(piper) ∨ CuteAnimal(piper)

Piper was not grown in a garden.

¬GrownIn(piper, garden)

True

If something is a plant, then it is not a cute animal. Simeng: All plants are not cute animals. All flowers are plants. Every kitten is a cute animal. If something is grown in a garden, then it is a flower. Piper is a kitten or a cute animal.

∀x (Plant(x) → ¬CuteAnimal(x)) ∀x (Flower(x) → Plant(x)) ∀x (Kitten(x) → CuteAnimal(x)) ∀x (GrownIn(x, garden) → Flower(x)) Kitten(piper) ∨ CuteAnimal(piper)

Piper is a kitten.

Kitten(piper)

Uncertain

Guam sent an athlete to the Calgary Winter Olympics. If Guan sent an athlete to the Calgary Winter Olympics, then the athelete participated in the Olympics in 1988. Judd Bankert is the only athlete from Guam who has ever competed in the Winter Olympics.

∃x (Send(guam, athlete, calgaryWinterOlympics)) ∀x (Athlete(x) ∧ SendTo(guam, x, calgaryWinterOlympics) → ParticipatedIn(x, winterOlympics, year1988)) ∀x ∀y (Athlete(x) ∧ From(x, guam) ∧ ParticipatedIn(x, winterOlympics, y) → x=juddBankert)

Judd Bankert competed in the 1988 Winter Olympics.

ParticipatedIn(juddBankert, winterOlympics, year1988)

True

Guam sent an athlete to the Calgary Winter Olympics. If Guan sent an athlete to the Calgary Winter Olympics, then the athelete participated in the Olympics in 1988. Judd Bankert is the only athlete from Guam who has ever competed in the Winter Olympics.

∃x (Send(guam, athlete, calgaryWinterOlympics)) ∀x (Athlete(x) ∧ SendTo(guam, x, calgaryWinterOlympics) → ParticipatedIn(x, winterOlympics, year1988)) ∀x ∀y (Athlete(x) ∧ From(x, guam) ∧ ParticipatedIn(x, winterOlympics, y) → x=juddBankert)

Guam has participated in the Summer Olympics at least once.

∃x (ParticipatedIn(guam, summerOlympics, x))

Uncertain

Michael O'Donnell is a British physician, journalist, author, and broadcaster. One of the word-setters of My Word! was Michael O'Donnell. The magazine World Medicine was edited by Michael O'Donnell. Michael O'Donnell was born in Yorkshire as the son of a general practitioner.

British(michael) ∧ Physician(michael) ∧ Journalist(michael) ∧ Author(michael) ∧ Broadcaster(michael) WordSetter(michael) Magazine(worldMedicine) ∧ EditedBy(worldMedicine, michael) BornIn(michael, yorkshire) ∧ ∃x(SonOf(michael, x) ∧ GeneralPractitioner(x))

The son of a general practitioner was a word-setter of My Word!.

∃x ∃y (SonOf(x, y) ∧ GeneralPractitioner(y) ∧ WordSetter(x))

True

Michael O'Donnell is a British physician, journalist, author, and broadcaster. One of the word-setters of My Word! was Michael O'Donnell. The magazine World Medicine was edited by Michael O'Donnell. Michael O'Donnell was born in Yorkshire as the son of a general practitioner.

British(michael) ∧ Physician(michael) ∧ Journalist(michael) ∧ Author(michael) ∧ Broadcaster(michael) WordSetter(michael) Magazine(worldMedicine) ∧ EditedBy(worldMedicine, michael) BornIn(michael, yorkshire) ∧ ∃x(SonOf(michael, x) ∧ GeneralPractitioner(x))

World Medicine is not a magazine.

¬Magazine(worldmedicine)

False

Michael O'Donnell is a British physician, journalist, author, and broadcaster. One of the word-setters of My Word! was Michael O'Donnell. The magazine World Medicine was edited by Michael O'Donnell. Michael O'Donnell was born in Yorkshire as the son of a general practitioner.

British(michael) ∧ Physician(michael) ∧ Journalist(michael) ∧ Author(michael) ∧ Broadcaster(michael) WordSetter(michael) Magazine(worldMedicine) ∧ EditedBy(worldMedicine, michael) BornIn(michael, yorkshire) ∧ ∃x(SonOf(michael, x) ∧ GeneralPractitioner(x))

There are no British authors.

∀x (British(x) → ¬Author(x))

False

Michael O'Donnell is a British physician, journalist, author, and broadcaster. One of the word-setters of My Word! was Michael O'Donnell. The magazine World Medicine was edited by Michael O'Donnell. Michael O'Donnell was born in Yorkshire as the son of a general practitioner.

British(michael) ∧ Physician(michael) ∧ Journalist(michael) ∧ Author(michael) ∧ Broadcaster(michael) WordSetter(michael) Magazine(worldMedicine) ∧ EditedBy(worldMedicine, michael) BornIn(michael, yorkshire) ∧ ∃x(SonOf(michael, x) ∧ GeneralPractitioner(x))

There are no journalists that were born in Yorkshire.

∀x (Journalist(x) → ¬BornIn(x, yorkshire))

False

Michael O'Donnell is a British physician, journalist, author, and broadcaster. One of the word-setters of My Word! was Michael O'Donnell. The magazine World Medicine was edited by Michael O'Donnell. Michael O'Donnell was born in Yorkshire as the son of a general practitioner.

British(michael) ∧ Physician(michael) ∧ Journalist(michael) ∧ Author(michael) ∧ Broadcaster(michael) WordSetter(michael) Magazine(worldMedicine) ∧ EditedBy(worldMedicine, michael) BornIn(michael, yorkshire) ∧ ∃x(SonOf(michael, x) ∧ GeneralPractitioner(x))

There is a son of a general practitioner that is not an author.

∃x ∃y (Son(x, y) ∧ GeneralPractitioner(y) ∧ ¬Author(x))

Uncertain

No homework is fun. Some reading is homework.

∀x (Homework(x) → ¬Fun(x)) ∃x (Reading(x) ∧ Homework(x))

Some reading is fun.

∃x (Reading(x) ∧ Fun(x))

Uncertain

The handbrake of a car is either up or down. The handbrake is down when a car is parked.

∀x ∀y (HandbrakeOf(x, y) ∧ Car(y) → Up(x) ⊕ Down(x)) ∀x ∀y (HandbrakeOf(x, y) ∧ Parked(y) ∧ Car(y) → Down(x))

The handbrake is up when some cars are parked.

∃x ∃y (HandbrakeOf(x, y) ∧ Parked(y) ∧ Car(y) ∧ Up(x))

False

All people in this midwest town who own horse ranches regularly ride horses for pleasure and sport. All people in this midwest town with a lot of disposable income have a horse ranch. If people in this midwest town compete in horse dressage shows, then they have a lot of disposable income. If people in this midwest town compete in horse dressage shows, then they have invested in high-quality equestrian gear and equipment. If people in this midwest town regularly ride horses for pleasure and sport, then they do not live in cramped residential buildings. Manny is in this midwest town, and she either has a horse ranch and lives in a cramped residential building, or she does neither.

∀x (InThisMidwestTown(x) ∧ Have(x, horseRanch) → RegularlyRideHorseForPleasure(x)) ∀x (InThisMidwestTown(x) ∧ Have(x, disposableIncome) → Have(x, horseRank)) ∀x (InThisMidwestTown(x) ∧ CompeteIn(x, horseDressageShow) → Have(x, disposableIncome)) ∀x (InThisMidwestTown(x) ∧ CompeteIn(x, horseDressageShow) → InvestedIn(x, equestrianGearAndEquipment)) ∀x (InThisMidwestTown(x) ∧ RegularlyRideHorseForPleasure(x) → ¬LiveIn(x, crampedBuilding)) InThisMidwestTown(manny) ∧ ¬(Have(manny, horseRanch) ⊕ LiveIn(manny, crampedBuilding))

Manny regularly rides horses for pleasure and sport.

RegularlyRideHorsesForPleasure(manny)

Uncertain

All people in this midwest town who own horse ranches regularly ride horses for pleasure and sport. All people in this midwest town with a lot of disposable income have a horse ranch. If people in this midwest town compete in horse dressage shows, then they have a lot of disposable income. If people in this midwest town compete in horse dressage shows, then they have invested in high-quality equestrian gear and equipment. If people in this midwest town regularly ride horses for pleasure and sport, then they do not live in cramped residential buildings. Manny is in this midwest town, and she either has a horse ranch and lives in a cramped residential building, or she does neither.

∀x (InThisMidwestTown(x) ∧ Have(x, horseRanch) → RegularlyRideHorseForPleasure(x)) ∀x (InThisMidwestTown(x) ∧ Have(x, disposableIncome) → Have(x, horseRank)) ∀x (InThisMidwestTown(x) ∧ CompeteIn(x, horseDressageShow) → Have(x, disposableIncome)) ∀x (InThisMidwestTown(x) ∧ CompeteIn(x, horseDressageShow) → InvestedIn(x, equestrianGearAndEquipment)) ∀x (InThisMidwestTown(x) ∧ RegularlyRideHorseForPleasure(x) → ¬LiveIn(x, crampedBuilding)) InThisMidwestTown(manny) ∧ ¬(Have(manny, horseRanch) ⊕ LiveIn(manny, crampedBuilding))

Manny competes in horse dressage shows and has invested in high-quality equestrian equipment and gear.

CompeteIn(manny, horseDressageShow) ∧ InvestedIn(manny, equestrianGearAndEquipment)

False

All people in this midwest town who own horse ranches regularly ride horses for pleasure and sport. All people in this midwest town with a lot of disposable income have a horse ranch. If people in this midwest town compete in horse dressage shows, then they have a lot of disposable income. If people in this midwest town compete in horse dressage shows, then they have invested in high-quality equestrian gear and equipment. If people in this midwest town regularly ride horses for pleasure and sport, then they do not live in cramped residential buildings. Manny is in this midwest town, and she either has a horse ranch and lives in a cramped residential building, or she does neither.

∀x (InThisMidwestTown(x) ∧ Have(x, horseRanch) → RegularlyRideHorseForPleasure(x)) ∀x (InThisMidwestTown(x) ∧ Have(x, disposableIncome) → Have(x, horseRank)) ∀x (InThisMidwestTown(x) ∧ CompeteIn(x, horseDressageShow) → Have(x, disposableIncome)) ∀x (InThisMidwestTown(x) ∧ CompeteIn(x, horseDressageShow) → InvestedIn(x, equestrianGearAndEquipment)) ∀x (InThisMidwestTown(x) ∧ RegularlyRideHorseForPleasure(x) → ¬LiveIn(x, crampedBuilding)) InThisMidwestTown(manny) ∧ ¬(Have(manny, horseRanch) ⊕ LiveIn(manny, crampedBuilding))

If Manny either has a horse ranch or competes in horse dressage shows, then Manny has not invested in high-quality equestrian equipment and gear.

¬(HaveAHorseRanch(manny) ⊕ CompeteIn(manny, horseDressageShow)) → ¬InvestedIn(manny, equestrianGearAndEquipment)

True

A roundel is a rounded artillery fortification. A roundel is not higher than adjacent walls. Cannons can be deployed on artillery fortifications. Roundels are the oldest artillery fortifications. Battery towers are artillery fortifications.

∀x (Roundel(x) → (Rounded(x) ∧ ArtilleryFortification(x))) ∀x ∀y ((Roundel(x) ∧ AdjacentWalls(x,y)) → ¬Higher(x, y)) ∀x (ArtilleryFortification(x) → DeployCannons(x)) ∀x ∀y ((Roundel(x) ∧ ArtilleryFortification(y)) → Older(x, y)) ∀x (BatteryTower(x) → ArtilleryFortification(x))

Cannons can be deployed on battery towers.

∀x (BatteryTower(x) → DeployCannons(x))

True

A roundel is a rounded artillery fortification. A roundel is not higher than adjacent walls. Cannons can be deployed on artillery fortifications. Roundels are the oldest artillery fortifications. Battery towers are artillery fortifications.

∀x (Roundel(x) → (Rounded(x) ∧ ArtilleryFortification(x))) ∀x ∀y ((Roundel(x) ∧ AdjacentWalls(x,y)) → ¬Higher(x, y)) ∀x (ArtilleryFortification(x) → DeployCannons(x)) ∀x ∀y ((Roundel(x) ∧ ArtilleryFortification(y)) → Older(x, y)) ∀x (BatteryTower(x) → ArtilleryFortification(x))

Roundels are older than battery towers.

∀x ∀y ((Roundel(x) ∧ BatteryTower(y)) → Older(x, y))

True

A roundel is a rounded artillery fortification. A roundel is not higher than adjacent walls. Cannons can be deployed on artillery fortifications. Roundels are the oldest artillery fortifications. Battery towers are artillery fortifications.

∀x (Roundel(x) → (Rounded(x) ∧ ArtilleryFortification(x))) ∀x ∀y ((Roundel(x) ∧ AdjacentWalls(x,y)) → ¬Higher(x, y)) ∀x (ArtilleryFortification(x) → DeployCannons(x)) ∀x ∀y ((Roundel(x) ∧ ArtilleryFortification(y)) → Older(x, y)) ∀x (BatteryTower(x) → ArtilleryFortification(x))

Battery towers are higher than adjacent walls.

∀x ∀y ((BatteryTower(x) ∧ AdjacentWall(x,y)) → Higher(x, y))

Uncertain

A roundel is a rounded artillery fortification. A roundel is not higher than adjacent walls. Cannons can be deployed on artillery fortifications. Roundels are the oldest artillery fortifications. Battery towers are artillery fortifications.

∀x (Roundel(x) → (Rounded(x) ∧ ArtilleryFortification(x))) ∀x ∀y ((Roundel(x) ∧ AdjacentWalls(x,y)) → ¬Higher(x, y)) ∀x (ArtilleryFortification(x) → DeployCannons(x)) ∀x ∀y ((Roundel(x) ∧ ArtilleryFortification(y)) → Older(x, y)) ∀x (BatteryTower(x) → ArtilleryFortification(x))

Cannons can be deployed on roundels.

∀x (Roundel(x) → DeployCannons(x))

True

Tissues are soft. Some papers are tissues.

∀x (Tissue(x) → Soft(x)) ∃x ∃y (Paper(x) ∧ Paper(x) ∧ Tissue(x) ∧ Tissue(y) ∧ ¬(x=y))

Some papers are hard.

∃x ∃y (Paper(x) ∧ Paper(y) ∧ Hard(x) ∧ Hard(y) ∧ ¬(x=y))

Uncertain

All volunteers receive intangible benefits for their work. Volunteers work regularly or on an as-needed basis. Some volunteers are trained. Volunteers work in groups or individually. Environmental volunteers contribute toward environmental management or conservation. Participating in natural disaster response is an example of volunteers working in groups on an as-needed basis.

∀x (Volunteer(x) → Receive(x, intangibleBenefit)) ∀x (Volunteer(x) → WorkRegularly(x) ⊕ WorkAsNeeded(x)) ∃x (Volunteer(x) → Trained(x)) ∀x (Volunteer(x) → (WorkInGroup(x) ∨ WorkIndividually(x))) ∀x (Volunteer(x) ∧ Environmental(x) → (ContributeTo(x, environmentalManagement) ∨ ContributeTo(x, environmentalConservation))) ∃x (Volunteer(x) ∧ ContributeTo(x, naturalDisasterResponse) → WorkInGroup(x) ∧ WorkAsNeeded(x))

Volunteers who participate in natural disaster response receive intangible benefits for their work.

∀x (Volunteer(x) ∧ ContributeTo(x, naturalDisasterResponse) → Receive(x, intangibleBenefit))

True

All volunteers receive intangible benefits for their work. Volunteers work regularly or on an as-needed basis. Some volunteers are trained. Volunteers work in groups or individually. Environmental volunteers contribute toward environmental management or conservation. Participating in natural disaster response is an example of volunteers working in groups on an as-needed basis.

∀x (Volunteer(x) → Receive(x, intangibleBenefit)) ∀x (Volunteer(x) → WorkRegularly(x) ⊕ WorkAsNeeded(x)) ∃x (Volunteer(x) → Trained(x)) ∀x (Volunteer(x) → (WorkInGroup(x) ∨ WorkIndividually(x))) ∀x (Volunteer(x) ∧ Environmental(x) → (ContributeTo(x, environmentalManagement) ∨ ContributeTo(x, environmentalConservation))) ∃x (Volunteer(x) ∧ ContributeTo(x, naturalDisasterResponse) → WorkInGroup(x) ∧ WorkAsNeeded(x))

Environmental volunteers work in groups.

∀x (Volunteer(x) ∧ Environmental(x) → WorkInGroup(x))

Uncertain

All volunteers receive intangible benefits for their work. Volunteers work regularly or on an as-needed basis. Some volunteers are trained. Volunteers work in groups or individually. Environmental volunteers contribute toward environmental management or conservation. Participating in natural disaster response is an example of volunteers working in groups on an as-needed basis.

∀x (Volunteer(x) → Receive(x, intangibleBenefit)) ∀x (Volunteer(x) → WorkRegularly(x) ⊕ WorkAsNeeded(x)) ∃x (Volunteer(x) → Trained(x)) ∀x (Volunteer(x) → (WorkInGroup(x) ∨ WorkIndividually(x))) ∀x (Volunteer(x) ∧ Environmental(x) → (ContributeTo(x, environmentalManagement) ∨ ContributeTo(x, environmentalConservation))) ∃x (Volunteer(x) ∧ ContributeTo(x, naturalDisasterResponse) → WorkInGroup(x) ∧ WorkAsNeeded(x))

To be a volunteer, you must be trained.

∀x (Volunteer(x) → Trained(x))

Uncertain

All people in this tech company who are consistent and enjoy sticking to their regular routines do not like surprises. People in this tech company who wear the same flannel shirts every day are consistent and enjoy sticking to their regular routines. People in this tech company who do not like shopping for clothes wear the same flannel shirts every day. Old people living in stable homes do not like surprises. People in this tech company who have very high energy and are impulsive like surprises. Mike works in this tech company. If Mike is not a person who wears the same flannel shirts every day, has very high energy, and is impulsive, then Mike either is very consistent and enjoys sticking to his regular routines or does not like surprises.

∀x (InThisTechCompany(x) ∧ Consistent(x) ∧ StickTo(x, theirRegularRoutine) → ¬Like(x, surprise)) ∀x (InThisTechCompany(x) ∧ ∃y (flannelShirt(y) ∧ WearEveryday(x, y)) → Consistent(x) ∧ StickTo(x, theirRegularRoutine)) ∀x (InThisTechCompany(x) ∧ ¬LikeShoppingFor(x, clothes) → ∃y (flannelShirt(y) ∧ WearEveryday(x, y))) ∀x (InThisTechCompany(x) ∧ Old(x) ∧ LiveIn(x, stableHome) → ¬Like(x, surprise)) ∀x (InThisTechCompany(x) ∧ Have(x, highEnergy) ∧ Impulsive(x) → ¬Like(x, surprise)) InThisTechCompany(mike) ¬(∃y (flannelShirt(y) ∧ WearEveryday(x, y)) ∧ Have(mike, highEnergy) ∧ Impulsive(mike)) → (Consistent(mike) ∧ StickTo(mike, theirRegularRoutine)) ⊕ ¬Like(mike, surprise)

Mike is an old person living in a stable home.

Old(mike) ∧ LiveIn(mike, stableHome)

Uncertain

All people in this tech company who are consistent and enjoy sticking to their regular routines do not like surprises. People in this tech company who wear the same flannel shirts every day are consistent and enjoy sticking to their regular routines. People in this tech company who do not like shopping for clothes wear the same flannel shirts every day. Old people living in stable homes do not like surprises. People in this tech company who have very high energy and are impulsive like surprises. Mike works in this tech company. If Mike is not a person who wears the same flannel shirts every day, has very high energy, and is impulsive, then Mike either is very consistent and enjoys sticking to his regular routines or does not like surprises.

∀x (InThisTechCompany(x) ∧ Consistent(x) ∧ StickTo(x, theirRegularRoutine) → ¬Like(x, surprise)) ∀x (InThisTechCompany(x) ∧ ∃y (flannelShirt(y) ∧ WearEveryday(x, y)) → Consistent(x) ∧ StickTo(x, theirRegularRoutine)) ∀x (InThisTechCompany(x) ∧ ¬LikeShoppingFor(x, clothes) → ∃y (flannelShirt(y) ∧ WearEveryday(x, y))) ∀x (InThisTechCompany(x) ∧ Old(x) ∧ LiveIn(x, stableHome) → ¬Like(x, surprise)) ∀x (InThisTechCompany(x) ∧ Have(x, highEnergy) ∧ Impulsive(x) → ¬Like(x, surprise)) InThisTechCompany(mike) ¬(∃y (flannelShirt(y) ∧ WearEveryday(x, y)) ∧ Have(mike, highEnergy) ∧ Impulsive(mike)) → (Consistent(mike) ∧ StickTo(mike, theirRegularRoutine)) ⊕ ¬Like(mike, surprise)

If Mike wears the same flannel shirts every day or does not like shopping for clothes, then Mike is neither an old person living in a stable home nor does he like shopping for clothes.

(∃y (flannelShirt(y) ∧ WearEveryday(mike, y)) ∨ ¬LikeShoppingFor(mike, clothes)) → ¬(Old(mike) ∧ LiveIn(mike, stableHome)) ∧ ¬LikeShoppingFor(mike, clothes)

True

All people in this tech company who are consistent and enjoy sticking to their regular routines do not like surprises. People in this tech company who wear the same flannel shirts every day are consistent and enjoy sticking to their regular routines. People in this tech company who do not like shopping for clothes wear the same flannel shirts every day. Old people living in stable homes do not like surprises. People in this tech company who have very high energy and are impulsive like surprises. Mike works in this tech company. If Mike is not a person who wears the same flannel shirts every day, has very high energy, and is impulsive, then Mike either is very consistent and enjoys sticking to his regular routines or does not like surprises.

∀x (InThisTechCompany(x) ∧ Consistent(x) ∧ StickTo(x, theirRegularRoutine) → ¬Like(x, surprise)) ∀x (InThisTechCompany(x) ∧ ∃y (flannelShirt(y) ∧ WearEveryday(x, y)) → Consistent(x) ∧ StickTo(x, theirRegularRoutine)) ∀x (InThisTechCompany(x) ∧ ¬LikeShoppingFor(x, clothes) → ∃y (flannelShirt(y) ∧ WearEveryday(x, y))) ∀x (InThisTechCompany(x) ∧ Old(x) ∧ LiveIn(x, stableHome) → ¬Like(x, surprise)) ∀x (InThisTechCompany(x) ∧ Have(x, highEnergy) ∧ Impulsive(x) → ¬Like(x, surprise)) InThisTechCompany(mike) ¬(∃y (flannelShirt(y) ∧ WearEveryday(x, y)) ∧ Have(mike, highEnergy) ∧ Impulsive(mike)) → (Consistent(mike) ∧ StickTo(mike, theirRegularRoutine)) ⊕ ¬Like(mike, surprise)

If Mike is not an old person living in a stable home and does not like shopping for clothes, then Mike does not like shopping for clothes.

¬(Old(mike) ∧ LiveIn(mike, stableHome)) ∧ ¬LikeShoppingFor(mike, clothes)) → ¬LikeShoppingFor(mike, clothes)

False

Adam owns cars. Adam has a favorite car. Among the cars he owns, Adam's favorite car is European. Adam broke his favorite car.

∃x∃y (Car(x) ∧ Car(y) ∧ (x≠y) ∧ Owns(adam, x)) ∃x (Car(x) ∧ Favorite(adam, x)) ∀x ((Car(x) ∧ Owns(adam, x) ∧ Favorite(adam, x)) → European(x)) ∀x ((Car(x) ∧ Owns(adam, x) ∧ Favorite(adam, x)) → Broke(adam, x))

Adam owns a Japanese car.

∃x (Japanese(x) ∧ Owns(adam, x))

Uncertain

Adam owns cars. Adam has a favorite car. Among the cars he owns, Adam's favorite car is European. Adam broke his favorite car.

∃x∃y (Car(x) ∧ Car(y) ∧ (x≠y) ∧ Owns(adam, x)) ∃x (Car(x) ∧ Favorite(adam, x)) ∀x ((Car(x) ∧ Owns(adam, x) ∧ Favorite(adam, x)) → European(x)) ∀x ((Car(x) ∧ Owns(adam, x) ∧ Favorite(adam, x)) → Broke(adam, x))

Adam broke a European car.

∃x (European(x) ∧ Broke(adam, x))

True

There are no buildings in New Haven higher than 400 meters. All buildings managed by Yale Housing are in New Haven. All Manhattan skyscrapers are higher than 400 meters. All buildings owned by Bloomberg are in Manhattan. All buildings with the Bloomberg logo are buildings owned by Bloomberg. Tower A is neither a building in New Haven nor a skyscraper in Manhattan. Tower B is a skyscraper building in Manhattan with a Bloomberg logo.

∀x ((Buildings(x) ∧ In(x, newHaven)) → ¬HigherThan(x, num400)) ∀x ((Buildings(x) ∧ ManagedBy(x, yaleHousing)) → In(x, newHaven)) ∀x ((Buildings(x) ∧ Skyscraper(x) ∧ In(x, manhattan)) → HigherThan(x, num400)) ∀x ((Buildings(x) ∧ OwnedBy(x, bloomberg)) → Skyscraper(x) ∧ In(x, manhattan)) ∀x ((Buildings(x) ∧ HasLogo(x, bloomberg)) → OwnedBy(x, bloomberg)) Buildings(towerA) ∧ (¬InNewHaven(towerA)) ∧ (¬ManhattanSkyscraper(towerA)) Buildings(towerB) ∧ HasLogo(towerB, bloomberg) ∧ Skyscraper(towerB) ∧ In(towerB, manhattan)

Tower A is higher than 400 meters.

HigherThan(towerA, num400)

Uncertain

There are no buildings in New Haven higher than 400 meters. All buildings managed by Yale Housing are in New Haven. All Manhattan skyscrapers are higher than 400 meters. All buildings owned by Bloomberg are in Manhattan. All buildings with the Bloomberg logo are buildings owned by Bloomberg. Tower A is neither a building in New Haven nor a skyscraper in Manhattan. Tower B is a skyscraper building in Manhattan with a Bloomberg logo.

∀x ((Buildings(x) ∧ In(x, newHaven)) → ¬HigherThan(x, num400)) ∀x ((Buildings(x) ∧ ManagedBy(x, yaleHousing)) → In(x, newHaven)) ∀x ((Buildings(x) ∧ Skyscraper(x) ∧ In(x, manhattan)) → HigherThan(x, num400)) ∀x ((Buildings(x) ∧ OwnedBy(x, bloomberg)) → Skyscraper(x) ∧ In(x, manhattan)) ∀x ((Buildings(x) ∧ HasLogo(x, bloomberg)) → OwnedBy(x, bloomberg)) Buildings(towerA) ∧ (¬InNewHaven(towerA)) ∧ (¬ManhattanSkyscraper(towerA)) Buildings(towerB) ∧ HasLogo(towerB, bloomberg) ∧ Skyscraper(towerB) ∧ In(towerB, manhattan)

Tower A is not higher than 400 meters.

¬HigherThan(towerA, num400)

Uncertain

There are no buildings in New Haven higher than 400 meters. All buildings managed by Yale Housing are in New Haven. All Manhattan skyscrapers are higher than 400 meters. All buildings owned by Bloomberg are in Manhattan. All buildings with the Bloomberg logo are buildings owned by Bloomberg. Tower A is neither a building in New Haven nor a skyscraper in Manhattan. Tower B is a skyscraper building in Manhattan with a Bloomberg logo.

∀x ((Buildings(x) ∧ In(x, newHaven)) → ¬HigherThan(x, num400)) ∀x ((Buildings(x) ∧ ManagedBy(x, yaleHousing)) → In(x, newHaven)) ∀x ((Buildings(x) ∧ Skyscraper(x) ∧ In(x, manhattan)) → HigherThan(x, num400)) ∀x ((Buildings(x) ∧ OwnedBy(x, bloomberg)) → Skyscraper(x) ∧ In(x, manhattan)) ∀x ((Buildings(x) ∧ HasLogo(x, bloomberg)) → OwnedBy(x, bloomberg)) Buildings(towerA) ∧ (¬InNewHaven(towerA)) ∧ (¬ManhattanSkyscraper(towerA)) Buildings(towerB) ∧ HasLogo(towerB, bloomberg) ∧ Skyscraper(towerB) ∧ In(towerB, manhattan)

Tower A is a building with the Bloomberg logo or it is managed by Yale Housing.

HasLogo(towerB, bloomberg) ∨ ManagedBy(x, yaleHousing)

False

There are no buildings in New Haven higher than 400 meters. All buildings managed by Yale Housing are in New Haven. All Manhattan skyscrapers are higher than 400 meters. All buildings owned by Bloomberg are in Manhattan. All buildings with the Bloomberg logo are buildings owned by Bloomberg. Tower A is neither a building in New Haven nor a skyscraper in Manhattan. Tower B is a skyscraper building in Manhattan with a Bloomberg logo.

∀x ((Buildings(x) ∧ In(x, newHaven)) → ¬HigherThan(x, num400)) ∀x ((Buildings(x) ∧ ManagedBy(x, yaleHousing)) → In(x, newHaven)) ∀x ((Buildings(x) ∧ Skyscraper(x) ∧ In(x, manhattan)) → HigherThan(x, num400)) ∀x ((Buildings(x) ∧ OwnedBy(x, bloomberg)) → Skyscraper(x) ∧ In(x, manhattan)) ∀x ((Buildings(x) ∧ HasLogo(x, bloomberg)) → OwnedBy(x, bloomberg)) Buildings(towerA) ∧ (¬InNewHaven(towerA)) ∧ (¬ManhattanSkyscraper(towerA)) Buildings(towerB) ∧ HasLogo(towerB, bloomberg) ∧ Skyscraper(towerB) ∧ In(towerB, manhattan)

Tower A is neither a building with the Bloomberg logo nor managed by Yale Housing.

¬HasLogo(towerB, bloomberg) ∧ (¬ManagedBy(x, yaleHousing))

True

No fish are birds. An osprey is a bird. A carp is a fish. All goldfish are carp. If Bubbles is either an osprey or a goldfish, then Bubbles is not also a fish.

∀x (Fish(x) → ¬Bird(x)) ∀x (Osprey(x) → Bird(x)) ∀x (Carp(x) → Fish(x)) ∀x (Goldfish(x) → Carp(x)) Osprey(bubbles) ⊕ Goldfish(bubbles) → ¬Fish(bubbles)

Bubbles is an Osprey.

Osprey(bubbles)

Uncertain

No fish are birds. An osprey is a bird. A carp is a fish. All goldfish are carp. If Bubbles is either an osprey or a goldfish, then Bubbles is not also a fish.

∀x (Fish(x) → ¬Bird(x)) ∀x (Osprey(x) → Bird(x)) ∀x (Carp(x) → Fish(x)) ∀x (Goldfish(x) → Carp(x)) Osprey(bubbles) ⊕ Goldfish(bubbles) → ¬Fish(bubbles)

Bubbles is a goldfish.

Goldfish(bubbles)

False

No fish are birds. An osprey is a bird. A carp is a fish. All goldfish are carp. If Bubbles is either an osprey or a goldfish, then Bubbles is not also a fish.

∀x (Fish(x) → ¬Bird(x)) ∀x (Osprey(x) → Bird(x)) ∀x (Carp(x) → Fish(x)) ∀x (Goldfish(x) → Carp(x)) Osprey(bubbles) ⊕ Goldfish(bubbles) → ¬Fish(bubbles)

Bubbles is not a goldfish.

¬Goldfish(bubbles)

True

Mr. and Mrs. Smith make a travel plan: they want to go to a city in California or Florida where neither of them has ever been. The cities in California that they are interested in are San Francisco, Los Angeles, and San Diego. Cities in Florida that they are interested in are Orlando and Miami. Mr. Smith has been to two cities in California. Mrs. Smith has been to one city in Florida.

∀x (WantToGoTo(mr.AndMrs.Smith, x) ∧ City(x) → (California(x) ∨ Florida(x)) ∧ NeverGo(x)) City(sanFrancisco) ∧ California(sanFrancisco) ∧ WantToGoTo(mr.AndMrs.Smith, sanFrancisco) ∧ City(losAngeles) ∧ California(losAngeles) ∧ WantToGoTo(mr.AndMrs.Smith, losAngeles) ∧ City(sanDiego) ∧ California(sanDiego) ∧ WantToGoTo(mr.AndMrs.Smith, sanDiego) City(orlando) ∧ Florida(orlando) ∧ WantToGo(mr.AndMrs.Smith, orlando) ∧ City(miami) ∧ Florida(miami) ∧ WantToGo(mr.AndMrs.Smith, miami) ∃x ∃y ∀z (¬(x=z) ∧ ¬(y=z) ∧ ¬(x=y) ∧ City(x) ∧ City(y) ∧ City(z) ∧ California(x) ∧ California(y) ∧ California(z) → Visit(mr.smith, x) ∧ Visit(mr.smith, y) ∧ ¬Visit(mr.smith, z)) ∃x ∀y (¬(x=y) ∧ City(x) ∧ City(y) ∧ Florida(x) ∧ Florida(y) → Visit(mrs.smith, x) ∧ ¬Visit(mrs.smith, y))

Mr. Smith has been to San Francisco.

∃x (City(x) ∧ Visit(mr.smith, sanFrancisco))

Uncertain

Mr. and Mrs. Smith make a travel plan: they want to go to a city in California or Florida where neither of them has ever been. The cities in California that they are interested in are San Francisco, Los Angeles, and San Diego. Cities in Florida that they are interested in are Orlando and Miami. Mr. Smith has been to two cities in California. Mrs. Smith has been to one city in Florida.

∀x (WantToGoTo(mr.AndMrs.Smith, x) ∧ City(x) → (California(x) ∨ Florida(x)) ∧ NeverGo(x)) City(sanFrancisco) ∧ California(sanFrancisco) ∧ WantToGoTo(mr.AndMrs.Smith, sanFrancisco) ∧ City(losAngeles) ∧ California(losAngeles) ∧ WantToGoTo(mr.AndMrs.Smith, losAngeles) ∧ City(sanDiego) ∧ California(sanDiego) ∧ WantToGoTo(mr.AndMrs.Smith, sanDiego) City(orlando) ∧ Florida(orlando) ∧ WantToGo(mr.AndMrs.Smith, orlando) ∧ City(miami) ∧ Florida(miami) ∧ WantToGo(mr.AndMrs.Smith, miami) ∃x ∃y ∀z (¬(x=z) ∧ ¬(y=z) ∧ ¬(x=y) ∧ City(x) ∧ City(y) ∧ City(z) ∧ California(x) ∧ California(y) ∧ California(z) → Visit(mr.smith, x) ∧ Visit(mr.smith, y) ∧ ¬Visit(mr.smith, z)) ∃x ∀y (¬(x=y) ∧ City(x) ∧ City(y) ∧ Florida(x) ∧ Florida(y) → Visit(mrs.smith, x) ∧ ¬Visit(mrs.smith, y))

They have at leat one candidate city in Florida to visit.

∃x (WantToGoTo(x) ∧ City(x) ∧ Florida(x))

Uncertain

Mr. and Mrs. Smith make a travel plan: they want to go to a city in California or Florida where neither of them has ever been. The cities in California that they are interested in are San Francisco, Los Angeles, and San Diego. Cities in Florida that they are interested in are Orlando and Miami. Mr. Smith has been to two cities in California. Mrs. Smith has been to one city in Florida.

∀x (WantToGoTo(mr.AndMrs.Smith, x) ∧ City(x) → (California(x) ∨ Florida(x)) ∧ NeverGo(x)) City(sanFrancisco) ∧ California(sanFrancisco) ∧ WantToGoTo(mr.AndMrs.Smith, sanFrancisco) ∧ City(losAngeles) ∧ California(losAngeles) ∧ WantToGoTo(mr.AndMrs.Smith, losAngeles) ∧ City(sanDiego) ∧ California(sanDiego) ∧ WantToGoTo(mr.AndMrs.Smith, sanDiego) City(orlando) ∧ Florida(orlando) ∧ WantToGo(mr.AndMrs.Smith, orlando) ∧ City(miami) ∧ Florida(miami) ∧ WantToGo(mr.AndMrs.Smith, miami) ∃x ∃y ∀z (¬(x=z) ∧ ¬(y=z) ∧ ¬(x=y) ∧ City(x) ∧ City(y) ∧ City(z) ∧ California(x) ∧ California(y) ∧ California(z) → Visit(mr.smith, x) ∧ Visit(mr.smith, y) ∧ ¬Visit(mr.smith, z)) ∃x ∀y (¬(x=y) ∧ City(x) ∧ City(y) ∧ Florida(x) ∧ Florida(y) → Visit(mrs.smith, x) ∧ ¬Visit(mrs.smith, y))

They have at least two candidate cities in California to visit.

∃x ∃y (¬(x=y) ∧ City(x) ∧ City(y) ∧ WantToGoTo(mr.AndMrs.Smith, x) ∧ California(x) ∧ WantToGoTo(mr.AndMrs.Smith, y) ∧ California(y))

Uncertain

Everything in Size Town is big or small. All big things in Size Town are heavy. All small things in Size Town are light. All heavy things in Size Town are still. All light things in Size Town are unstable. All unstable things in Size Town are changing. All unstable things in Size Town are unpredictable. The bird is in Size Town and it is not both heavy and still.

∀x (In(x, sizeTown) → (Big(x) ∨ Small(x))) ∀x (Big(x) ∧ In(x, sizeTown) → Heavy(x)) ∀x (Small(x) ∧ In(x, sizeTown) → Light(x)) ∀x (Heavy(x) ∧ In(x, sizeTown) → Still(x)) ∀x (Light(x) ∧ In(x, sizeTown) → Unstable(x)) ∀x (Unstable(x) ∧ In(x, sizeTown) → Changing(x)) ∀x (Unstable(x) ∧ In(x, sizeTown) → Unpredictable(x)) In(bird, sizeTown) ∧ ¬(Heavy(bird) ∧ Still(bird))

The bird is still.

Still(bird)

Uncertain

Everything in Size Town is big or small. All big things in Size Town are heavy. All small things in Size Town are light. All heavy things in Size Town are still. All light things in Size Town are unstable. All unstable things in Size Town are changing. All unstable things in Size Town are unpredictable. The bird is in Size Town and it is not both heavy and still.

∀x (In(x, sizeTown) → (Big(x) ∨ Small(x))) ∀x (Big(x) ∧ In(x, sizeTown) → Heavy(x)) ∀x (Small(x) ∧ In(x, sizeTown) → Light(x)) ∀x (Heavy(x) ∧ In(x, sizeTown) → Still(x)) ∀x (Light(x) ∧ In(x, sizeTown) → Unstable(x)) ∀x (Unstable(x) ∧ In(x, sizeTown) → Changing(x)) ∀x (Unstable(x) ∧ In(x, sizeTown) → Unpredictable(x)) In(bird, sizeTown) ∧ ¬(Heavy(bird) ∧ Still(bird))

The bird is not still.

¬Still(bird)

Uncertain