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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 unpredictable and changing.

Unpredictable(bird) ∧ Changing(bird)

True

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 unpredictable or changing.

Unpredictable(bird) ∨ Changing(bird)

True

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 either unpredictable or changing.

Unpredictable(bird) ⊕ Changing(bird)

False

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))

If the bird is small or still, then it is either unpredictable or changing.

Small(bird) ∨ Still(bird) → Unpredictable(bird) ⊕ Changing(bird)

False

DI Ray is a police procedural television series. DI Ray was created and written by Maya Sondhi. DI Ray was produced by Jed Mercurio. Maya Sondhi and Jed Mercurio are both British.

TelevisionSeries(dIRay) ∧ PoliceProcedural(dIRay) Creates(maya, dIRay) ∧ Writes(maya, dIRay) Produces(jed, dIRay) British(maya) ∧ British(jed)

DI Ray was created by a Brit.

∃x (British(x) ∧ Creates(x, dIRay))

True

DI Ray is a police procedural television series. DI Ray was created and written by Maya Sondhi. DI Ray was produced by Jed Mercurio. Maya Sondhi and Jed Mercurio are both British.

TelevisionSeries(dIRay) ∧ PoliceProcedural(dIRay) Creates(maya, dIRay) ∧ Writes(maya, dIRay) Produces(jed, dIRay) British(maya) ∧ British(jed)

Some Brit produced a television series.

∃x ∃y(British(x) ∧ TelevisionSeries(y) ∧ Produces(x, y))

True

Everyone who took the bar exam can read. All lawyers took the bar exam. Everyone who took the bar exam is knowledgeable about criminal procedures. All people who got a score of 180 on the LSAT can read. No elephants can read. If Mike can not read or is not an elephant, then Mike either took the bar exam or can read.

∀x (Take(x, barExam) → CanRead(x)) ∀x (Lawyer(x) → Take(x, barExam)) ∀x (Take(x, barExam) → KnowledgeableAbout(x, criminalProceeder)) ∀x (GetOn(x, scoreOf180, lSAT) → CanRead(x)) ∀x (Elephant(x) → ¬CanRead(x)) ¬(CanRead(mike) ∧ Elephant(mike)) → Take(mike, barExam) ⊕ CanRead(mike)

Mike got 180 on the LSAT.

GetOn(mike, 180, lSAT)

Uncertain

Everyone who took the bar exam can read. All lawyers took the bar exam. Everyone who took the bar exam is knowledgeable about criminal procedures. All people who got a score of 180 on the LSAT can read. No elephants can read. If Mike can not read or is not an elephant, then Mike either took the bar exam or can read.

∀x (Take(x, barExam) → CanRead(x)) ∀x (Lawyer(x) → Take(x, barExam)) ∀x (Take(x, barExam) → KnowledgeableAbout(x, criminalProceeder)) ∀x (GetOn(x, scoreOf180, lSAT) → CanRead(x)) ∀x (Elephant(x) → ¬CanRead(x)) ¬(CanRead(mike) ∧ Elephant(mike)) → Take(mike, barExam) ⊕ CanRead(mike)

Mike did not take the bar exam and is not both knowledgeable about criminal procedures and someone who got 180 on the LSAT.

¬Take(mike, barExam) ∧ ¬(KnowledgeableAbout(mike, criminalProcedures)∧ GetOn(mike, 180, lSAT))

True

Everyone who took the bar exam can read. All lawyers took the bar exam. Everyone who took the bar exam is knowledgeable about criminal procedures. All people who got a score of 180 on the LSAT can read. No elephants can read. If Mike can not read or is not an elephant, then Mike either took the bar exam or can read.

∀x (Take(x, barExam) → CanRead(x)) ∀x (Lawyer(x) → Take(x, barExam)) ∀x (Take(x, barExam) → KnowledgeableAbout(x, criminalProceeder)) ∀x (GetOn(x, scoreOf180, lSAT) → CanRead(x)) ∀x (Elephant(x) → ¬CanRead(x)) ¬(CanRead(mike) ∧ Elephant(mike)) → Take(mike, barExam) ⊕ CanRead(mike)

Mike took the bar exam.

Take(mike, barExam)

False

Some soccer defenders are center-backs. All soccer defenders are soccer players. No soccer players are professional basketball players. All NBA players are professional basketball players. Stephen Curry is an NBA player.

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

Stephen Curry is a center-back.

ProfessionalCenterback(stephenCurry)

Uncertain

Some soccer defenders are center-backs. All soccer defenders are soccer players. No soccer players are professional basketball players. All NBA players are professional basketball players. Stephen Curry is an NBA player.

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

Stephen Curry is not both a centerback and a soccer defender.

¬(ProfessionalCenterback(stephenCurry) ∧ ProfessionalSoccerDefender(stephenCurry))

False

Some soccer defenders are center-backs. All soccer defenders are soccer players. No soccer players are professional basketball players. All NBA players are professional basketball players. Stephen Curry is an NBA player.

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

If Stephen Curry is not both a centerback and a soccer defender, then Stephen Curry is neither a soccer player nor a professional basketball player.

¬(Centerback(stephenCurry) ∧ SoccerDefender(stephenCurry)) → ¬(SoccerPlayer(stephenCurry) ∨ ProfessionalBasketballPlayer(stephenCurry))

True

If a person doesn't have enough money to buy a product, then that person can't buy it. Monitors are products. 4k monitors are more expensive than 1080 monitors and 2k monitors. John is a person. John doesn't have enough money to buy a 2k monitor.

∀x ∀y (Person(x) ∧ Product(y) ∧ ¬HaveEnoughMoneyFor(x, y) → ¬Buy(x, y)) ∀x (Monitor(x) → Product(x)) ∀x ∀y ∀z (Monitor(x) ∧ Monitor(y) ∧ Monitor(z) ∧ FourK(x) ∧ OneOEightO(y) ∧ TwoK(z) → MoreExpensive(x, y) ∧ MoreExpensive(x, z)) Person(john) ∀x (Monitor(x) ∧ TwoK(x) → ¬HaveEnoughMoneyFor(john, x))

John can't buy a 1080 monitor.

∀x (Monitor(x) ∧ OneOEightO(x) → ¬Buy(john, x))

Uncertain

If a person doesn't have enough money to buy a product, then that person can't buy it. Monitors are products. 4k monitors are more expensive than 1080 monitors and 2k monitors. John is a person. John doesn't have enough money to buy a 2k monitor.

∀x ∀y (Person(x) ∧ Product(y) ∧ ¬HaveEnoughMoneyFor(x, y) → ¬Buy(x, y)) ∀x (Monitor(x) → Product(x)) ∀x ∀y ∀z (Monitor(x) ∧ Monitor(y) ∧ Monitor(z) ∧ FourK(x) ∧ OneOEightO(y) ∧ TwoK(z) → MoreExpensive(x, y) ∧ MoreExpensive(x, z)) Person(john) ∀x (Monitor(x) ∧ TwoK(x) → ¬HaveEnoughMoneyFor(john, x))

John can't buy a 2k monitor.

∀x (Monitor(x) ∧ TwoK(x) → ¬Buy(john, x))

True

All artificial satellites are important scientific achievements. Some artificial satellites are not U.S. inventions.

∀x (ArtificialSatellite(x) → ImportantScientificAchievement(x)) ∃x (ArtificialSatellite(x) ∧ ¬USInvention(x))

All important scientific achievements are U.S. inventions.

∀x (ImportantScientificAchievement(x) ∧ USInvention(x))

False

Some cats are not pets. All cats are mammals.

∃x (Cat(x) ∧ ¬Pet(x)) ∀x (Cat(x) → Mammal(x))

Some mammals are not pets.

∃x ∃y (Mammal(x) ∧ Mammal(y) ∧ ¬Pet(x) ∧ ¬Pet(y))

True

If people in this neighborhood visit a coffee shop regularly, then they are addicted to coffee. People in this neighborhood visit a coffee shop regularly or order takeout at least once a day. If people in this neighborhood make a lot of their own food at home using recipes and online guides, then they order takeout at least once a day. If people in this neighborhood own at least one coffeemaker and one blender in their home, then they do not order takeout at least once a day. All people in this neighborhood who lead very busy lives that include 12-hour work hours make a lot of their own food at home using recipes and online guides. Sam is living in this neighborhood, and he is either addicted to coffee or other caffeinated drinks and leads a very busy life that include 12-hour work hours, or is not addicted to coffee and does not lead a very busy life that include 12-hour work hours

∀x (In(x, thisNeighborhood) ∧ VisitRegularly(x, coffeeShop) → AddictedTo(x, coffee)) ∀x (In(x, thisNeighborhood) → (VisitRegularly(x, coffeeShop) ∨ (∃y (TakeOut(y) ∧ Order(x, y, aDay)))) ∀x (In(x, thisNeighborhood) ∧ MakeAtUsing(x, home, ownFood, recipe) → ∃y (TakeOut(y) ∧ Order(x, y))) ∀x (In(x, thisNeighborhood) ∧ ∃y (CoffeemakerAndBlender(y) ∧ Own(x, y)) → ¬OrderAtLeastOnceADay(x, takeout)) ∀x (In(x, thisNeighborhood) ∧ BusyWith(x, 12HourWorkHour) → MakeAtUsing(x, home, ownFood, recipe)) In(sam, thisNeighborhood) ∧ ¬(AddictedTo(sam, coffee) ⊕ BusyWith(sam, 12HourWorkHour))

Sam is living in this neighborhood and he is addicted to coffee.

InThisNeighborhood(sam) ∧ AddictedTo(sam, coffee)

Uncertain

If people in this neighborhood visit a coffee shop regularly, then they are addicted to coffee. People in this neighborhood visit a coffee shop regularly or order takeout at least once a day. If people in this neighborhood make a lot of their own food at home using recipes and online guides, then they order takeout at least once a day. If people in this neighborhood own at least one coffeemaker and one blender in their home, then they do not order takeout at least once a day. All people in this neighborhood who lead very busy lives that include 12-hour work hours make a lot of their own food at home using recipes and online guides. Sam is living in this neighborhood, and he is either addicted to coffee or other caffeinated drinks and leads a very busy life that include 12-hour work hours, or is not addicted to coffee and does not lead a very busy life that include 12-hour work hours

∀x (In(x, thisNeighborhood) ∧ VisitRegularly(x, coffeeShop) → AddictedTo(x, coffee)) ∀x (In(x, thisNeighborhood) → (VisitRegularly(x, coffeeShop) ∨ (∃y (TakeOut(y) ∧ Order(x, y, aDay)))) ∀x (In(x, thisNeighborhood) ∧ MakeAtUsing(x, home, ownFood, recipe) → ∃y (TakeOut(y) ∧ Order(x, y))) ∀x (In(x, thisNeighborhood) ∧ ∃y (CoffeemakerAndBlender(y) ∧ Own(x, y)) → ¬OrderAtLeastOnceADay(x, takeout)) ∀x (In(x, thisNeighborhood) ∧ BusyWith(x, 12HourWorkHour) → MakeAtUsing(x, home, ownFood, recipe)) In(sam, thisNeighborhood) ∧ ¬(AddictedTo(sam, coffee) ⊕ BusyWith(sam, 12HourWorkHour))

Sam is living in this neighborhood and he owns at least one coffeemaker and one blender in his home.

∃y (CoffeemakerAndBlender(y) ∧ Own(sam, y))

False

If people in this neighborhood visit a coffee shop regularly, then they are addicted to coffee. People in this neighborhood visit a coffee shop regularly or order takeout at least once a day. If people in this neighborhood make a lot of their own food at home using recipes and online guides, then they order takeout at least once a day. If people in this neighborhood own at least one coffeemaker and one blender in their home, then they do not order takeout at least once a day. All people in this neighborhood who lead very busy lives that include 12-hour work hours make a lot of their own food at home using recipes and online guides. Sam is living in this neighborhood, and he is either addicted to coffee or other caffeinated drinks and leads a very busy life that include 12-hour work hours, or is not addicted to coffee and does not lead a very busy life that include 12-hour work hours

∀x (In(x, thisNeighborhood) ∧ VisitRegularly(x, coffeeShop) → AddictedTo(x, coffee)) ∀x (In(x, thisNeighborhood) → (VisitRegularly(x, coffeeShop) ∨ (∃y (TakeOut(y) ∧ Order(x, y, aDay)))) ∀x (In(x, thisNeighborhood) ∧ MakeAtUsing(x, home, ownFood, recipe) → ∃y (TakeOut(y) ∧ Order(x, y))) ∀x (In(x, thisNeighborhood) ∧ ∃y (CoffeemakerAndBlender(y) ∧ Own(x, y)) → ¬OrderAtLeastOnceADay(x, takeout)) ∀x (In(x, thisNeighborhood) ∧ BusyWith(x, 12HourWorkHour) → MakeAtUsing(x, home, ownFood, recipe)) In(sam, thisNeighborhood) ∧ ¬(AddictedTo(sam, coffee) ⊕ BusyWith(sam, 12HourWorkHour))

Sam is living in this neighborhood and he owns at least one coffeemaker and one blender in his home or orders takeout at least once a day.

(∃y (CoffeemakerAndBlender(y) ∧ Own(sam, y)) ∨ (∃y (TakeOut(y) ∧ Order(sam, y, aDay)))

True

No professional basketball players are soccer players. All NBA players are professional basketball players. All soccer defenders are soccer players. All centerbacks are soccer defenders. Roger Federer is either both an NBA player and a soccer defender, or neither.

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

Roger Federer is a centerback.

ProfessionalCenterback(rogerFederer)

False

No professional basketball players are soccer players. All NBA players are professional basketball players. All soccer defenders are soccer players. All centerbacks are soccer defenders. Roger Federer is either both an NBA player and a soccer defender, or neither.

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

Roger Federer is not a centerback.

¬ProfessionalCenterback(rogerFederer)

True

No professional basketball players are soccer players. All NBA players are professional basketball players. All soccer defenders are soccer players. All centerbacks are soccer defenders. Roger Federer is either both an NBA player and a soccer defender, or neither.

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

Roger Federer is a soccer player.

ProfessionalSoccerPlayer(rogerFederer)

Uncertain

Some teachers who work at pools are not nice. All teachers working at pools are pool managers. All pool managers are lifeguards. If someone is a lifeguard, then they work at a pool. Mary does not work at a pool.

∃x (Teacher(x) ∧ WorkAt(x, pool) ∧ ¬Nice(x)) ∀x (Teacher(x) ∧ WorkAt(x, pool) → PoolManager(x)) ∀x (PoolManager(x) → Lifeguard(x)) ∀x (Lifeguard(x) → WorkAt(x, pool)) ¬WorkAt(mary, pool)

Mary is nice.

Nice(mary)

Uncertain

Some teachers who work at pools are not nice. All teachers working at pools are pool managers. All pool managers are lifeguards. If someone is a lifeguard, then they work at a pool. Mary does not work at a pool.

∃x (Teacher(x) ∧ WorkAt(x, pool) ∧ ¬Nice(x)) ∀x (Teacher(x) ∧ WorkAt(x, pool) → PoolManager(x)) ∀x (PoolManager(x) → Lifeguard(x)) ∀x (Lifeguard(x) → WorkAt(x, pool)) ¬WorkAt(mary, pool)

Mary is not a nice teacher working at a pool.

¬(Nice(mary) ∧ Teacher(mary) ∧ WorkAt(mary, pool))

True

Some teachers who work at pools are not nice. All teachers working at pools are pool managers. All pool managers are lifeguards. If someone is a lifeguard, then they work at a pool. Mary does not work at a pool.

∃x (Teacher(x) ∧ WorkAt(x, pool) ∧ ¬Nice(x)) ∀x (Teacher(x) ∧ WorkAt(x, pool) → PoolManager(x)) ∀x (PoolManager(x) → Lifeguard(x)) ∀x (Lifeguard(x) → WorkAt(x, pool)) ¬WorkAt(mary, pool)

Mary is is a nice teacher working at a pool.

Nice(mary) ∧ Teacher(mary) ∧ WorkAt(mary, pool)

False

Not all art pieces require talent. Everything that requires talent requires practice.

∃x (ArtPiece(x) ∧ ¬Require(x, talent)) ∀x (Require(x, talent) → Require(x, practice))

There exist art pieces that do not require practice.

∃x ∃y (ArtPiece(x) ∧ ¬Require(x, practice) ∧ ArtPiece(y) ∧ ¬Require(y, practice) ∧ ¬(x=y))

True

Bernarda Bryson Shahn was a painter and lithographer. Bernarda Bryson Shahn was born in Athens, Ohio. Bernarda Bryson Shahn was married to Ben Shahn. People born in Athens, Ohio, are Americans.

Painter(bernardaBrysonShahn) ∧ Lithographer(bernardaBrysonShahn) BornIn(bernardaBrysonShahn, athensOhio) MarriedTo(bernardaBrysonShahn, benShahn) ∀x (BornIn(x, athensOhio) → American(x))

Bernarda Bryson Shahn was born in Greece.

BornIn(bernardaBrysonShahn, greece)

Uncertain

Bernarda Bryson Shahn was a painter and lithographer. Bernarda Bryson Shahn was born in Athens, Ohio. Bernarda Bryson Shahn was married to Ben Shahn. People born in Athens, Ohio, are Americans.

Painter(bernardaBrysonShahn) ∧ Lithographer(bernardaBrysonShahn) BornIn(bernardaBrysonShahn, athensOhio) MarriedTo(bernardaBrysonShahn, benShahn) ∀x (BornIn(x, athensOhio) → American(x))

Bernarda Bryson Shahn was American.

American(bernardaBrysonShahn)

True

Bernarda Bryson Shahn was a painter and lithographer. Bernarda Bryson Shahn was born in Athens, Ohio. Bernarda Bryson Shahn was married to Ben Shahn. People born in Athens, Ohio, are Americans.

Painter(bernardaBrysonShahn) ∧ Lithographer(bernardaBrysonShahn) BornIn(bernardaBrysonShahn, athensOhio) MarriedTo(bernardaBrysonShahn, benShahn) ∀x (BornIn(x, athensOhio) → American(x))

Bernarda Bryson Shahn had been divorced once.

Divorced(bernardaBrysonShahn)

Uncertain

Everybody in Emma's family who upgrade to the newest iPhone model every year, are not saving money for a down payment on a new house. Everybody in Emma's family who enjoy reading about tech specs and keeping up to date on the latest technology upgrade to the newest iPhone model every year. Everybody in Emma's family is saving money for a down payment on a new house, or lives in an apartment in a big metropolitan cities. Everybody in Emma's family live with at least one roommate, does not own any pets. Everybody in Emma's family who owns at least one pet lives with at least one roommate. Emily is in Emma's family. If Emily does not both own at least one pet and lives in apartments in big metropolitan cities, then Emily either owns at least one pet and lives in an apartment in big metropolitan cities, or she neither owns a pet nor lives in an apartment in big metropolitan cities.

∀x (InEmmasFamily(x) ∧ UpgradeToEveryYear(x, newestIphoneModel) → ¬SavingMoneyForOn(x, downPayment, newHouse)) ∀x (InEmmasFamily(x) ∧ EnjoyReading(x, techSpec) ∧ KeepUpdatedOn(x, latestTechnology) → UpgradeToEveryYear(x, newestIphoneModel)) ∀x (InEmmasFamily(x) ∧ (SavingMoneyForOn(x, downPayment, newHouse) ∨ LiveIn(x, apartment, bigMetropolitanCity))) ∀x (InEmmasFamily(x) ∧ (∃y (LiveWith(x, y) ∧ Roommate(y))) → ¬(∃y (Own(x, y) ∧ Pet(y)))) ∀x (InEmmasFamily(x) ∧ (∃y (Own(x, y) ∧ Pet(y))) → (∃y (LiveWith(x, y) ∧ Roommate(y)))) InEmmasFamily(emily) ((∃y (Own(emily, y) ∧ Roommate(y))) ∧ LiveIn(emily, apartment, bigMetropolitanCity)) → ((∃y (Own(emily, y) ∧ Pet(y))) ∧ LiveIn(emily, apartment, bigMetropolitanCity)) ⊕ ¬((∃y (Own(emily, y) ∧ Roommate(y))) ∨ LiveIn(emily, apartment, bigMetropolitanCity))

Emily is in Emma's family and she lives with at least one roommate.

∃y (LiveWith(emily, y) ∧ Roommate(y))

Uncertain

Everybody in Emma's family who upgrade to the newest iPhone model every year, are not saving money for a down payment on a new house. Everybody in Emma's family who enjoy reading about tech specs and keeping up to date on the latest technology upgrade to the newest iPhone model every year. Everybody in Emma's family is saving money for a down payment on a new house, or lives in an apartment in a big metropolitan cities. Everybody in Emma's family live with at least one roommate, does not own any pets. Everybody in Emma's family who owns at least one pet lives with at least one roommate. Emily is in Emma's family. If Emily does not both own at least one pet and lives in apartments in big metropolitan cities, then Emily either owns at least one pet and lives in an apartment in big metropolitan cities, or she neither owns a pet nor lives in an apartment in big metropolitan cities.

∀x (InEmmasFamily(x) ∧ UpgradeToEveryYear(x, newestIphoneModel) → ¬SavingMoneyForOn(x, downPayment, newHouse)) ∀x (InEmmasFamily(x) ∧ EnjoyReading(x, techSpec) ∧ KeepUpdatedOn(x, latestTechnology) → UpgradeToEveryYear(x, newestIphoneModel)) ∀x (InEmmasFamily(x) ∧ (SavingMoneyForOn(x, downPayment, newHouse) ∨ LiveIn(x, apartment, bigMetropolitanCity))) ∀x (InEmmasFamily(x) ∧ (∃y (LiveWith(x, y) ∧ Roommate(y))) → ¬(∃y (Own(x, y) ∧ Pet(y)))) ∀x (InEmmasFamily(x) ∧ (∃y (Own(x, y) ∧ Pet(y))) → (∃y (LiveWith(x, y) ∧ Roommate(y)))) InEmmasFamily(emily) ((∃y (Own(emily, y) ∧ Roommate(y))) ∧ LiveIn(emily, apartment, bigMetropolitanCity)) → ((∃y (Own(emily, y) ∧ Pet(y))) ∧ LiveIn(emily, apartment, bigMetropolitanCity)) ⊕ ¬((∃y (Own(emily, y) ∧ Roommate(y))) ∨ LiveIn(emily, apartment, bigMetropolitanCity))

Emily enjoys reading about tech specs and keeping up to date on the latest technology.

EnjoyReading(emily, techSpec) ∧ KeepUpdatedOn(emily, latestTechnology)

False

People on the payroll are being paid by the school. If someone has a job at a school, then they are on the payroll. All faculty members have a job at a school. If someone teaches students, they are a faculty member or a teacher. Every teacher has students. If Nancy is a teacher, then they are on the payroll. If Nancy is not a teacher, then they are not paid by the school. Nancy teaches students.

∀x (OnPayroll(x) → PaidBy(x, school)) ∀x (HaveJobAt(x, school) → OnPayroll(x)) ∀x (FacultyMember(x) → HaveJobAt(x, school)) ∀x (Teach(x, student) → FacultyMember(x) ∨ Teacher(x)) ∀x (Teacher(x) → Have(x, student)) Teacher(nancy) → OnPayroll(nancy) ¬Teacher(nancy) → ¬OnPayroll(nancy) Teach(nancy, student)

Nancy is a faculty member.

FacultyMember(nancy)

Uncertain

People on the payroll are being paid by the school. If someone has a job at a school, then they are on the payroll. All faculty members have a job at a school. If someone teaches students, they are a faculty member or a teacher. Every teacher has students. If Nancy is a teacher, then they are on the payroll. If Nancy is not a teacher, then they are not paid by the school. Nancy teaches students.

∀x (OnPayroll(x) → PaidBy(x, school)) ∀x (HaveJobAt(x, school) → OnPayroll(x)) ∀x (FacultyMember(x) → HaveJobAt(x, school)) ∀x (Teach(x, student) → FacultyMember(x) ∨ Teacher(x)) ∀x (Teacher(x) → Have(x, student)) Teacher(nancy) → OnPayroll(nancy) ¬Teacher(nancy) → ¬OnPayroll(nancy) Teach(nancy, student)

Nancy is paid by the school and has students.

PaidBy(nancy, school) ∧ Have(nancy, student)

True

People on the payroll are being paid by the school. If someone has a job at a school, then they are on the payroll. All faculty members have a job at a school. If someone teaches students, they are a faculty member or a teacher. Every teacher has students. If Nancy is a teacher, then they are on the payroll. If Nancy is not a teacher, then they are not paid by the school. Nancy teaches students.

∀x (OnPayroll(x) → PaidBy(x, school)) ∀x (HaveJobAt(x, school) → OnPayroll(x)) ∀x (FacultyMember(x) → HaveJobAt(x, school)) ∀x (Teach(x, student) → FacultyMember(x) ∨ Teacher(x)) ∀x (Teacher(x) → Have(x, student)) Teacher(nancy) → OnPayroll(nancy) ¬Teacher(nancy) → ¬OnPayroll(nancy) Teach(nancy, student)

Nancy is not paid by the school or does not have students.

¬PaidBy(nancy, school) ∨ ¬Have(nancy, student))

False

Kangaroos are an animal. No Kangaroos live in Germany. Jane will fly to Germany if she saves enough money for the summer. If Jane flies to Germany, she will go to the Berlin Zoo. If someone goes to the Berlin Zoo, they will see some of the animals in Germany.

∀x (Kangaroo(x) → Animal(x)) ∀x (Kangaroo(x) → ¬LiveIn(x, germany)) SavesFor(jane, enoughMoney, theSummer) → FlyTo(jane, germany) FlyTo(jane, germany) → GoTo(jane, berlinzoo) ∀x ∃y (GoTo(x, berlinzoo) ∧ LiveIn(x, germany) ∧ Animal(y) → WillSee(y, x, berlinzoo))

Jane will see a kangaroo if she saves enough money for the summer.

∃x (SavesFor(jane, enoughMoney, theSummer) ∧ Kangaroo(x) → WillSee(x, jane, berlinzoo))

False

If a class has prerequisites, the student must take the prerequisites to take the class. If a class has no prerequisites, then the student can take the class CPSC 201 and CPSC 223 are prerequisites for CPSC 323. Intro Microeconomics is the only prerequisite for Intermediate Microeconomics. Intro Geology has no prerequisites.

∀x ∀y ∀z (Class(x) ∧ Student(y) ∧ Prereq(z,x) ∧ ¬Take(y, z) → ¬CanTake(y, x)) ∀x ∀y ((Class(x) ∧ Student(y) ∧ ¬∃z Prereq(z,x)) → CanTake(y, x)) Prereq(cpsc201, cpsc323) ∧ Prereq(cpsc223, cpsc323) ∀x (Prereq(x,intermediateMicro) → x=introMicroeconomics) ¬(∃x (Prereq(x, introGeology)))

CPSC 201 has no prerequisites.

∀x (¬Prereq(x, cpsc201))

Uncertain

If a class has prerequisites, the student must take the prerequisites to take the class. If a class has no prerequisites, then the student can take the class CPSC 201 and CPSC 223 are prerequisites for CPSC 323. Intro Microeconomics is the only prerequisite for Intermediate Microeconomics. Intro Geology has no prerequisites.

∀x ∀y ∀z (Class(x) ∧ Student(y) ∧ Prereq(z,x) ∧ ¬Take(y, z) → ¬CanTake(y, x)) ∀x ∀y ((Class(x) ∧ Student(y) ∧ ¬∃z Prereq(z,x)) → CanTake(y, x)) Prereq(cpsc201, cpsc323) ∧ Prereq(cpsc223, cpsc323) ∀x (Prereq(x,intermediateMicro) → x=introMicroeconomics) ¬(∃x (Prereq(x, introGeology)))

If a student took CPSC 201 but did not take CPSC 223, they can take CPSC 323.

Taken(cpsc201) ∧ ¬Taken(cpsc223) ∧ CanTake(cpsc323)

False

If a class has prerequisites, the student must take the prerequisites to take the class. If a class has no prerequisites, then the student can take the class CPSC 201 and CPSC 223 are prerequisites for CPSC 323. Intro Microeconomics is the only prerequisite for Intermediate Microeconomics. Intro Geology has no prerequisites.

∀x ∀y ∀z (Class(x) ∧ Student(y) ∧ Prereq(z,x) ∧ ¬Take(y, z) → ¬CanTake(y, x)) ∀x ∀y ((Class(x) ∧ Student(y) ∧ ¬∃z Prereq(z,x)) → CanTake(y, x)) Prereq(cpsc201, cpsc323) ∧ Prereq(cpsc223, cpsc323) ∀x (Prereq(x,intermediateMicro) → x=introMicroeconomics) ¬(∃x (Prereq(x, introGeology)))

A student cannot take Intro Geology.

¬CanTake(introgeology)

False

If a class has prerequisites, the student must take the prerequisites to take the class. If a class has no prerequisites, then the student can take the class CPSC 201 and CPSC 223 are prerequisites for CPSC 323. Intro Microeconomics is the only prerequisite for Intermediate Microeconomics. Intro Geology has no prerequisites.

∀x ∀y ∀z (Class(x) ∧ Student(y) ∧ Prereq(z,x) ∧ ¬Take(y, z) → ¬CanTake(y, x)) ∀x ∀y ((Class(x) ∧ Student(y) ∧ ¬∃z Prereq(z,x)) → CanTake(y, x)) Prereq(cpsc201, cpsc323) ∧ Prereq(cpsc223, cpsc323) ∀x (Prereq(x,intermediateMicro) → x=introMicroeconomics) ¬(∃x (Prereq(x, introGeology)))

Intermediate Microeconomics has one prerequisite.

∃x (Taken(x) → CanTake(intermediatemicro))

True

Heptalogyy is a compound literary or narrative work that is made up of seven distinct works. The Harry Potter series consists of 7 distinct works. The Chronicles of Narnia consists of 7 distinct works.

∀x (SevenDistinctWorks(x) → Heptalogy(x)) SevenDistinctWorks(harryPotter) SevenDistinctWorks(chroniclesOfNarnia)

The Harry Potter series of books is Heptalogy.

Heptalogy(harryPotter)

True

Heptalogyy is a compound literary or narrative work that is made up of seven distinct works. The Harry Potter series consists of 7 distinct works. The Chronicles of Narnia consists of 7 distinct works.

∀x (SevenDistinctWorks(x) → Heptalogy(x)) SevenDistinctWorks(harryPotter) SevenDistinctWorks(chroniclesOfNarnia)

The Chronicles of Narnia series of books is not Heptalogy.

¬Heptalogy(chroniclesOfNarnia)

False

Heptalogyy is a compound literary or narrative work that is made up of seven distinct works. The Harry Potter series consists of 7 distinct works. The Chronicles of Narnia consists of 7 distinct works.

∀x (SevenDistinctWorks(x) → Heptalogy(x)) SevenDistinctWorks(harryPotter) SevenDistinctWorks(chroniclesOfNarnia)

The Lord of the Rings is Heptalogy.

Heptalogy(lordOfRings)

Uncertain

All people who attend Renaissance fairs regularly enjoy dressing up in old-fashioned and historical period clothing. If people are fascinated by the history of the Renaissance and other past eras, then they attend Renaissance fairs regularly. People are fascinated by the history of the Renaissance and other past eras, or they are contemporary academics who enjoy learning. People who are focused on futuristic and vocational subjects are contemporary academics who enjoy learning. If people are professors who take a historical approach, then they are not contemporary academics who enjoy learning. If Clyde is not focused on futuristic and voctional subjects, then he is neither focused on futuristic and vocational subjects nor enjoys dressing up in old-fashioned and historical period clothing.

∀x (AttendRegularly(x, renaissanceFair) → Enjoy(x, dressingUp, oldFashionedClothing) ∧ Enjoy(x, dressingUp, historicalPeriodClothing)) ∀x (FascinatedBy(x, historyOfRenaissance) → AttendRegularly(x, renaissanceFair)) ∀x (FascinatedBy(x, historyOfRenaissance) ⊕ (ContemporaryAcademic(x) ∧ Enjoy(x, learning))) ∀x (FocusedOn(x, futuristicSubject) ∧ FocusedOn(x, vocationalSubject) → ContemporaryAcademic(x) ∧ Enjoy(x, learning)) ∀x (Professor(x) ∧ Take(x, historicalApproach) → ¬(ContemporaryAcademic(x) ∧ Enjoy(x, learning))) ¬(FocusedOn(clyde, futuristicSubject) ∧ FocusedOn(clyde, vocationalSubject))→ ¬(FocusedOn(clyde, futuristicSubject) ∧ FocusedOn(clyde, vocationalSubject) ∨ (Enjoy(clyde, dressingUp, oldFashionedClothing) ∧ Enjoy(clyde, dressingUp, historicalPeriodClothing)))

Clyde attends Renaissance fairs regularly.

AttendRegularly(clyde, renaissanceFair)

Uncertain

All people who attend Renaissance fairs regularly enjoy dressing up in old-fashioned and historical period clothing. If people are fascinated by the history of the Renaissance and other past eras, then they attend Renaissance fairs regularly. People are fascinated by the history of the Renaissance and other past eras, or they are contemporary academics who enjoy learning. People who are focused on futuristic and vocational subjects are contemporary academics who enjoy learning. If people are professors who take a historical approach, then they are not contemporary academics who enjoy learning. If Clyde is not focused on futuristic and voctional subjects, then he is neither focused on futuristic and vocational subjects nor enjoys dressing up in old-fashioned and historical period clothing.

∀x (AttendRegularly(x, renaissanceFair) → Enjoy(x, dressingUp, oldFashionedClothing) ∧ Enjoy(x, dressingUp, historicalPeriodClothing)) ∀x (FascinatedBy(x, historyOfRenaissance) → AttendRegularly(x, renaissanceFair)) ∀x (FascinatedBy(x, historyOfRenaissance) ⊕ (ContemporaryAcademic(x) ∧ Enjoy(x, learning))) ∀x (FocusedOn(x, futuristicSubject) ∧ FocusedOn(x, vocationalSubject) → ContemporaryAcademic(x) ∧ Enjoy(x, learning)) ∀x (Professor(x) ∧ Take(x, historicalApproach) → ¬(ContemporaryAcademic(x) ∧ Enjoy(x, learning))) ¬(FocusedOn(clyde, futuristicSubject) ∧ FocusedOn(clyde, vocationalSubject))→ ¬(FocusedOn(clyde, futuristicSubject) ∧ FocusedOn(clyde, vocationalSubject) ∨ (Enjoy(clyde, dressingUp, oldFashionedClothing) ∧ Enjoy(clyde, dressingUp, historicalPeriodClothing)))

Clyde is a professor who takes a historical approach.

Professor(clyde) ∧ Take(clyde, historicalApproach)

False

All people who attend Renaissance fairs regularly enjoy dressing up in old-fashioned and historical period clothing. If people are fascinated by the history of the Renaissance and other past eras, then they attend Renaissance fairs regularly. People are fascinated by the history of the Renaissance and other past eras, or they are contemporary academics who enjoy learning. People who are focused on futuristic and vocational subjects are contemporary academics who enjoy learning. If people are professors who take a historical approach, then they are not contemporary academics who enjoy learning. If Clyde is not focused on futuristic and voctional subjects, then he is neither focused on futuristic and vocational subjects nor enjoys dressing up in old-fashioned and historical period clothing.

∀x (AttendRegularly(x, renaissanceFair) → Enjoy(x, dressingUp, oldFashionedClothing) ∧ Enjoy(x, dressingUp, historicalPeriodClothing)) ∀x (FascinatedBy(x, historyOfRenaissance) → AttendRegularly(x, renaissanceFair)) ∀x (FascinatedBy(x, historyOfRenaissance) ⊕ (ContemporaryAcademic(x) ∧ Enjoy(x, learning))) ∀x (FocusedOn(x, futuristicSubject) ∧ FocusedOn(x, vocationalSubject) → ContemporaryAcademic(x) ∧ Enjoy(x, learning)) ∀x (Professor(x) ∧ Take(x, historicalApproach) → ¬(ContemporaryAcademic(x) ∧ Enjoy(x, learning))) ¬(FocusedOn(clyde, futuristicSubject) ∧ FocusedOn(clyde, vocationalSubject))→ ¬(FocusedOn(clyde, futuristicSubject) ∧ FocusedOn(clyde, vocationalSubject) ∨ (Enjoy(clyde, dressingUp, oldFashionedClothing) ∧ Enjoy(clyde, dressingUp, historicalPeriodClothing)))

Clyde is a professor who takes a historical approach, or is a contemporary academic.

(Professor(clyde) ∧ Take(clyde, historicalApproach)) ∨ (ContemporaryAcademic(clyde) ∧ Enjoy(clyde, learning))

True

No sports cars are vehicles intended to be driven at moderate speeds. All automobiles designed for family use are vehicles intended to be driven at moderate speeds.

∀x (SportsCar(x) → ¬IntendedToBeDrivenAt(x, moderateSpeed)) ∀x (DesignedFor(x, familyUse) → IntendedToBeDrivenAt(x, moderateSpeed))

No sports cars are automobiles designed for family use.

∀x (SportsCar(x) → ¬For(x, familyUse))

True

If people work well in teams in the workplace, then they get along with all their colleagues at their work. If people come to work every day with a positive attitude, then they work well in teams in the workplace. People either come to work every day with a positive attitude or are always tired every morning. If people are always tired in the morning, then they are criticized by their boss. If people are criticized by their boss, then they do not receive positive feedback from teams at work. Kat either is a person who works well in teams in the workplac and is always tired every morning, or she is neither.

∀x (WorkWellInTeamsIn(x, workPlace) → ∀y (Colleague(y) ∧ GetAlongWithAtWork(x, y))) ∀x (ComeToWorkWithEveryDay(x, positiveAttitude) → WorkWellInTeamsIn(x, workPlace)) ∀x (ComeToWorkWithEveryDay(x, positiveAttitude) ⊕ AlwaysTiredInMorning(x)) ∀x (AlwaysTiredInMorning(x) → CriticizedBy(x, boss)) ∀x (CriticizedBy(x, boss) → ¬ReceiveFromAtWork(x, positiveFeedback, team)) ¬(WorkWellInTeamsIn(kat, workPlace) ⊕ Tired(kat))

Kat is a person who comes to work every day with a positive attitude.

ComeToWorkWithEveryDay(kat, positiveAttitude)

Uncertain

If people work well in teams in the workplace, then they get along with all their colleagues at their work. If people come to work every day with a positive attitude, then they work well in teams in the workplace. People either come to work every day with a positive attitude or are always tired every morning. If people are always tired in the morning, then they are criticized by their boss. If people are criticized by their boss, then they do not receive positive feedback from teams at work. Kat either is a person who works well in teams in the workplac and is always tired every morning, or she is neither.

∀x (WorkWellInTeamsIn(x, workPlace) → ∀y (Colleague(y) ∧ GetAlongWithAtWork(x, y))) ∀x (ComeToWorkWithEveryDay(x, positiveAttitude) → WorkWellInTeamsIn(x, workPlace)) ∀x (ComeToWorkWithEveryDay(x, positiveAttitude) ⊕ AlwaysTiredInMorning(x)) ∀x (AlwaysTiredInMorning(x) → CriticizedBy(x, boss)) ∀x (CriticizedBy(x, boss) → ¬ReceiveFromAtWork(x, positiveFeedback, team)) ¬(WorkWellInTeamsIn(kat, workPlace) ⊕ Tired(kat))

Kat gets along with her colleagues at her work and receives positive feedback from teams at her work.

(∀y (Colleague(y) ∧ GetAlongWithAtWork(kat, y))) ∧ ReceiveFromAtWork(kat, positiveFeedback, team)

False

If people work well in teams in the workplace, then they get along with all their colleagues at their work. If people come to work every day with a positive attitude, then they work well in teams in the workplace. People either come to work every day with a positive attitude or are always tired every morning. If people are always tired in the morning, then they are criticized by their boss. If people are criticized by their boss, then they do not receive positive feedback from teams at work. Kat either is a person who works well in teams in the workplac and is always tired every morning, or she is neither.

∀x (WorkWellInTeamsIn(x, workPlace) → ∀y (Colleague(y) ∧ GetAlongWithAtWork(x, y))) ∀x (ComeToWorkWithEveryDay(x, positiveAttitude) → WorkWellInTeamsIn(x, workPlace)) ∀x (ComeToWorkWithEveryDay(x, positiveAttitude) ⊕ AlwaysTiredInMorning(x)) ∀x (AlwaysTiredInMorning(x) → CriticizedBy(x, boss)) ∀x (CriticizedBy(x, boss) → ¬ReceiveFromAtWork(x, positiveFeedback, team)) ¬(WorkWellInTeamsIn(kat, workPlace) ⊕ Tired(kat))

Kat either gets along with her colleagues at her work or receives positive feedback from teams at her work.

(∀y (Colleague(y) ∧ GetAlongWithAtWork(kat, y))) ⊕ ReceiveFromAtWork(kat, positiveFeedback, team)

True

Drishti is an open-source software. Open-source software is free to modify.

OpenSourceSoftware(drishti) ∀x (OpenSourceSoftware(x) → FreeToModify(x))

Drishti is free to modify.

FreeToModify(drishti)

True

There are five grades in English class: A+, A, B+, B, and C. If a student gets an A+ in English class, then his score is greater than 95. If a student gets an A in English class, then his score is greater than 90 but lower than 95. Zhang got an A in English class. Wang's English class score is better than Zhang's. Wu's English class score is lower than 90. If a student's English class score is lower than 90, then it is not greater than 95 or 90, and lower than 95.

GradeIn(aPlus, englishClass) ∨ GradeIn(a, englishClass) ∨ GradeIn(bPlus, englishClass) ∨ GradeIn(b, englishClass) ∨ GradeIn(c, englishClass) ∧ (GradeIn(aPlus, englishClass) → ¬GradeIn(a, englishClass) ∧ ¬GradeIn(bPlus, englishClass) ∧ ¬GradeIn(b, englishClass) ∧ ¬GradeIn(c, englishClass)) ∧ (GradeIn(a, englishClass) → ¬GradeIn(aPlus, englishClass) ∧ ¬GradeIn(bPlus, englishClass) ∧ ¬GradeIn(b, englishClass) ∧ ¬GradeIn(c, englishClass)) ∧ (GradeIn(bPlus, englishClass) → ¬GradeIn(aPlus, englishClass) ∧ ¬GradeIn(a, englishClass) ∧ ¬GradeIn(b, englishClass) ∧ ¬GradeIn(c, englishClass)) ∧ (GradeIn(b, englishClass) → ¬GradeIn(aPlus, englishClass) ∧ ¬GradeIn(a, englishClass) ∧ ¬GradeIn(bPlus, englishClass) ∧ ¬GradeIn(c, englishClass)) ∧ (GradeIn(c, englishClass) → ¬GradeIn(aPlus, englishClass) ∧ ¬GradeIn(a, englishClass) ∧ ¬GradeIn(bPlus, englishClass) ∧ ¬GradeIn(b, englishClass)) ∀x ∀y (Student(x) ∧ GetGradeIn(x, aPlus, englishClass) → EnglishClassScore(x, y) ∧ GreaterThan95(y)) ∀x ∀y (Student(x) ∧ GetGradeIn(x, a, englishClass) → EnglishClassScore(x, y) ∧ GreaterThan90(y) ∧ LowerThan95(y)) Student(zhang) ∧ GetGradeIn(zhang, a, englishClass) ∀x ∀y (Student(zhang) ∧ Student(wang) ∧ EnglishScore(zhang, x) ∧ EnglishScore(wang, y) ∧ Better(y, x)) ∀x (Student(wu) ∧ EnglishScore(wu, x) ∧ LowerThan90(x)) ∀x ∀y (Student(x) ∧ EnglishScore(x, y) ∧ LowerThan90(y) → ¬GreaterThan95(y) ∧ ¬GreaterThan90(y) ∧ LowerThan95(y))

Zhang's English class score is lower than 95.

∀x (EnglishScore(zhang, x) ∧ LowerThan95(x))

True

There are five grades in English class: A+, A, B+, B, and C. If a student gets an A+ in English class, then his score is greater than 95. If a student gets an A in English class, then his score is greater than 90 but lower than 95. Zhang got an A in English class. Wang's English class score is better than Zhang's. Wu's English class score is lower than 90. If a student's English class score is lower than 90, then it is not greater than 95 or 90, and lower than 95.

GradeIn(aPlus, englishClass) ∨ GradeIn(a, englishClass) ∨ GradeIn(bPlus, englishClass) ∨ GradeIn(b, englishClass) ∨ GradeIn(c, englishClass) ∧ (GradeIn(aPlus, englishClass) → ¬GradeIn(a, englishClass) ∧ ¬GradeIn(bPlus, englishClass) ∧ ¬GradeIn(b, englishClass) ∧ ¬GradeIn(c, englishClass)) ∧ (GradeIn(a, englishClass) → ¬GradeIn(aPlus, englishClass) ∧ ¬GradeIn(bPlus, englishClass) ∧ ¬GradeIn(b, englishClass) ∧ ¬GradeIn(c, englishClass)) ∧ (GradeIn(bPlus, englishClass) → ¬GradeIn(aPlus, englishClass) ∧ ¬GradeIn(a, englishClass) ∧ ¬GradeIn(b, englishClass) ∧ ¬GradeIn(c, englishClass)) ∧ (GradeIn(b, englishClass) → ¬GradeIn(aPlus, englishClass) ∧ ¬GradeIn(a, englishClass) ∧ ¬GradeIn(bPlus, englishClass) ∧ ¬GradeIn(c, englishClass)) ∧ (GradeIn(c, englishClass) → ¬GradeIn(aPlus, englishClass) ∧ ¬GradeIn(a, englishClass) ∧ ¬GradeIn(bPlus, englishClass) ∧ ¬GradeIn(b, englishClass)) ∀x ∀y (Student(x) ∧ GetGradeIn(x, aPlus, englishClass) → EnglishClassScore(x, y) ∧ GreaterThan95(y)) ∀x ∀y (Student(x) ∧ GetGradeIn(x, a, englishClass) → EnglishClassScore(x, y) ∧ GreaterThan90(y) ∧ LowerThan95(y)) Student(zhang) ∧ GetGradeIn(zhang, a, englishClass) ∀x ∀y (Student(zhang) ∧ Student(wang) ∧ EnglishScore(zhang, x) ∧ EnglishScore(wang, y) ∧ Better(y, x)) ∀x (Student(wu) ∧ EnglishScore(wu, x) ∧ LowerThan90(x)) ∀x ∀y (Student(x) ∧ EnglishScore(x, y) ∧ LowerThan90(y) → ¬GreaterThan95(y) ∧ ¬GreaterThan90(y) ∧ LowerThan95(y))

Wang got an A+ in English class.

GetGradeIn(wang, aPlus, englishClass)

Uncertain

There are five grades in English class: A+, A, B+, B, and C. If a student gets an A+ in English class, then his score is greater than 95. If a student gets an A in English class, then his score is greater than 90 but lower than 95. Zhang got an A in English class. Wang's English class score is better than Zhang's. Wu's English class score is lower than 90. If a student's English class score is lower than 90, then it is not greater than 95 or 90, and lower than 95.

GradeIn(aPlus, englishClass) ∨ GradeIn(a, englishClass) ∨ GradeIn(bPlus, englishClass) ∨ GradeIn(b, englishClass) ∨ GradeIn(c, englishClass) ∧ (GradeIn(aPlus, englishClass) → ¬GradeIn(a, englishClass) ∧ ¬GradeIn(bPlus, englishClass) ∧ ¬GradeIn(b, englishClass) ∧ ¬GradeIn(c, englishClass)) ∧ (GradeIn(a, englishClass) → ¬GradeIn(aPlus, englishClass) ∧ ¬GradeIn(bPlus, englishClass) ∧ ¬GradeIn(b, englishClass) ∧ ¬GradeIn(c, englishClass)) ∧ (GradeIn(bPlus, englishClass) → ¬GradeIn(aPlus, englishClass) ∧ ¬GradeIn(a, englishClass) ∧ ¬GradeIn(b, englishClass) ∧ ¬GradeIn(c, englishClass)) ∧ (GradeIn(b, englishClass) → ¬GradeIn(aPlus, englishClass) ∧ ¬GradeIn(a, englishClass) ∧ ¬GradeIn(bPlus, englishClass) ∧ ¬GradeIn(c, englishClass)) ∧ (GradeIn(c, englishClass) → ¬GradeIn(aPlus, englishClass) ∧ ¬GradeIn(a, englishClass) ∧ ¬GradeIn(bPlus, englishClass) ∧ ¬GradeIn(b, englishClass)) ∀x ∀y (Student(x) ∧ GetGradeIn(x, aPlus, englishClass) → EnglishClassScore(x, y) ∧ GreaterThan95(y)) ∀x ∀y (Student(x) ∧ GetGradeIn(x, a, englishClass) → EnglishClassScore(x, y) ∧ GreaterThan90(y) ∧ LowerThan95(y)) Student(zhang) ∧ GetGradeIn(zhang, a, englishClass) ∀x ∀y (Student(zhang) ∧ Student(wang) ∧ EnglishScore(zhang, x) ∧ EnglishScore(wang, y) ∧ Better(y, x)) ∀x (Student(wu) ∧ EnglishScore(wu, x) ∧ LowerThan90(x)) ∀x ∀y (Student(x) ∧ EnglishScore(x, y) ∧ LowerThan90(y) → ¬GreaterThan95(y) ∧ ¬GreaterThan90(y) ∧ LowerThan95(y))

Wu does not get an A or A+ in English class.

¬GetGradeIn(wu, aPlus, englishClass) ∧¬GetGradeIn(wu, a, englishClass)

True

Olivia doesn't prefer warm temperatures during the day. When Olivia sleeps, she prefers a cool temperature. Olivia sleeps during the night. Olivia works during the day. Olivia either works or sleeps. It is either the day or the night. Olivia either prefers warm temperatures or prefers cool temperatures.

∀x (Day(x) → ¬Prefer(olivia, warmTemperature, x)) ∀x (Sleep(olivia, x) → Prefer(olivia, coolTemperature, x)) ∀x (Night(x) → Sleep(olivia, x)) ∀x (Day(x) → Work(olivia, x)) Work(olivia) ⊕ Sleep(olivia) ∀x (Day(x) ⊕ Night(x)) ∀x (Prefer(olivia, warmTemperature, x) ⊕ Prefer(olivia, coolTemperature, x))

At all times, Olivia prefers a cool temperature.

∀x (Prefer(olivia, coolTemperature, x))

True

TOra is a GUI. GUIs are software. Software can be free or paid. Paid Software is not under the GNU General Public License. TOra is under the GNU General Public License.

GUI(tora) ∀x (GUI(x) → Software(x)) ∀x (Software(x) → Free(x) ⊕ Paid(x)) ∀x (Paid(x) ∧ Software(x) → ¬UnderGNULicense(x)) UnderGNULicense(tora)

TOra is a paid software.

Paid(tora) ∧ Software(tora)

False

TOra is a GUI. GUIs are software. Software can be free or paid. Paid Software is not under the GNU General Public License. TOra is under the GNU General Public License.

GUI(tora) ∀x (GUI(x) → Software(x)) ∀x (Software(x) → Free(x) ⊕ Paid(x)) ∀x (Paid(x) ∧ Software(x) → ¬UnderGNULicense(x)) UnderGNULicense(tora)

TOra is a free software.

Free(tora) ∧ Software(tora)

True

Customers choose a Prime Video plan or an HBO Max Plan, or both. All customers who choose a Prime Video Plan are rewarded with a $30 gift card. There are no customers who do not choose any plan. None of the customers who are rewarded with a $30 gift card are older than 80. All the customers are either older than 80 or between the ages of 60 and 80. James is a customer who is not between the ages of 60 and 80.

∀x (Customer(x) → (Choose(x, primeVideoPlan) ∨ Choose(x, hBOMaxPlan))) ∀x ((Customer(x) ∧ Choose(x, hBOMaxPlan)) → RewardWith(x, giftCard)) ∀x (Customer(x) → (∃y(Plan(y) ∧ Choose(x, y)))) ∀x ((Customer(x) ∧ RewardWith(x, giftCard)) → (¬OlderThan(x, num80))) ∀x (Customer(x) → (∃y(GreaterThan(y, num80) ∧ Age(james,y)) ⊕ (∃y(Between(y, num60, num80) ∧ Age(james, y))))) Customer(james) ∧ (¬∃y(Between(y, num60, num80) ∧ Age(james, y)))

James is a customer who does not choose any plans.

Choose(james, noPlan)

False

Customers choose a Prime Video plan or an HBO Max Plan, or both. All customers who choose a Prime Video Plan are rewarded with a $30 gift card. There are no customers who do not choose any plan. None of the customers who are rewarded with a $30 gift card are older than 80. All the customers are either older than 80 or between the ages of 60 and 80. James is a customer who is not between the ages of 60 and 80.

∀x (Customer(x) → (Choose(x, primeVideoPlan) ∨ Choose(x, hBOMaxPlan))) ∀x ((Customer(x) ∧ Choose(x, hBOMaxPlan)) → RewardWith(x, giftCard)) ∀x (Customer(x) → (∃y(Plan(y) ∧ Choose(x, y)))) ∀x ((Customer(x) ∧ RewardWith(x, giftCard)) → (¬OlderThan(x, num80))) ∀x (Customer(x) → (∃y(GreaterThan(y, num80) ∧ Age(james,y)) ⊕ (∃y(Between(y, num60, num80) ∧ Age(james, y))))) Customer(james) ∧ (¬∃y(Between(y, num60, num80) ∧ Age(james, y)))

James is a customer who chooses a Prime Video plan or does not choose any plans.

Choose(james, planA) ∨ Choose(james, noPlan)

True

Customers choose a Prime Video plan or an HBO Max Plan, or both. All customers who choose a Prime Video Plan are rewarded with a $30 gift card. There are no customers who do not choose any plan. None of the customers who are rewarded with a $30 gift card are older than 80. All the customers are either older than 80 or between the ages of 60 and 80. James is a customer who is not between the ages of 60 and 80.

∀x (Customer(x) → (Choose(x, primeVideoPlan) ∨ Choose(x, hBOMaxPlan))) ∀x ((Customer(x) ∧ Choose(x, hBOMaxPlan)) → RewardWith(x, giftCard)) ∀x (Customer(x) → (∃y(Plan(y) ∧ Choose(x, y)))) ∀x ((Customer(x) ∧ RewardWith(x, giftCard)) → (¬OlderThan(x, num80))) ∀x (Customer(x) → (∃y(GreaterThan(y, num80) ∧ Age(james,y)) ⊕ (∃y(Between(y, num60, num80) ∧ Age(james, y))))) Customer(james) ∧ (¬∃y(Between(y, num60, num80) ∧ Age(james, y)))

Suppose James is a customer who chooses the Prime Video plan or does not choose any plans, then he is either rewarded a $30 gift card or chooses the HBO Max plan.

Choose(james, planA) ∨ Choose(james, noPlan) → RewardWith(james, giftCard) ⊕ Choose(james, planB)

False

Detroit City is a horse. Some horses are racehorses. If a horse falls in a race, it poses risks to its rider. Detroit City fell in a race. A horse is a racehorse if it is in a race.

Horse(detroitcity) ∃x (Horse(x) ∧ Racehorse(x)) ∀x (Horse(x) ∧ InRace(x) ∧ Falls(x) → PoseRiskTo(x, rider)) InRace(detroitcity) ∧ Fall(detroitcity) ∀x (Horse(x) ∧ InRace(x) → Racehorse(x))

Detroit City has been in multiple races.

MultipleRace(detroitcity)

Uncertain

Detroit City is a horse. Some horses are racehorses. If a horse falls in a race, it poses risks to its rider. Detroit City fell in a race. A horse is a racehorse if it is in a race.

Horse(detroitcity) ∃x (Horse(x) ∧ Racehorse(x)) ∀x (Horse(x) ∧ InRace(x) ∧ Falls(x) → PoseRiskTo(x, rider)) InRace(detroitcity) ∧ Fall(detroitcity) ∀x (Horse(x) ∧ InRace(x) → Racehorse(x))

Detroit City poses risks to its rider.

PoseRiskTo(detroitcity, rider)

True

Detroit City is a horse. Some horses are racehorses. If a horse falls in a race, it poses risks to its rider. Detroit City fell in a race. A horse is a racehorse if it is in a race.

Horse(detroitcity) ∃x (Horse(x) ∧ Racehorse(x)) ∀x (Horse(x) ∧ InRace(x) ∧ Falls(x) → PoseRiskTo(x, rider)) InRace(detroitcity) ∧ Fall(detroitcity) ∀x (Horse(x) ∧ InRace(x) → Racehorse(x))

Detroit City is a racehorse.

Racehorse(detroitcity)

True

Frederick Monhoff was an architect, artist, and illustrator. Frederick Monhoff was an American. An artist is good at physical or conceptual art. All Americans are American citizens.

Architect(monhoff) ∧ Artist(monhoff) ∧ Illustrator(monhoff) American(monhoff) ∀x (Artist(x) → GoodAt(x, physicalArt) ∨ GoodAt(x, conceptualArt)) ∀x (American(x) → AmericanCitizen(x))

Frederick Monhoff was good at physical art.

GoodAt(monhoff, physicalArt)

Uncertain

Frederick Monhoff was an architect, artist, and illustrator. Frederick Monhoff was an American. An artist is good at physical or conceptual art. All Americans are American citizens.

Architect(monhoff) ∧ Artist(monhoff) ∧ Illustrator(monhoff) American(monhoff) ∀x (Artist(x) → GoodAt(x, physicalArt) ∨ GoodAt(x, conceptualArt)) ∀x (American(x) → AmericanCitizen(x))

No illustrator was an American citizen.

¬(∃x (Illustrator(x) ∧ AmericanCitizen(x)))

False

Miroslav Fiedler was a Czech mathematician. Miroslav Fiedler is known for his contributions to linear algebra and graph theory. Miroslav Fiedler is honored by the Fiedler eigenvalue. Fiedler eigenvalue is the second smallest eigenvalue of the graph Laplacian.

Czech(miroslavFiedler) ∧ Mathematician(miroslavFiedler) KnownFor(miroslavFiedler, contributionsToLinearAlgebraAndGraphTheory) HonoredBy(miroslavFiedler, fiedlerEigenvalue) TheSecondSmallestEigenvalueOf(fiedlerEigenvalue, theGraphLaplacian)

Miroslav Fiedler is honored by the second smallest eigenvalue of the graph Laplacian.

∃x (TheSecondSmallestEigenvalueOf(x, theGraphLaplacian) ∧ HonoredBy(miroslavFiedler, x))

True

Miroslav Fiedler was a Czech mathematician. Miroslav Fiedler is known for his contributions to linear algebra and graph theory. Miroslav Fiedler is honored by the Fiedler eigenvalue. Fiedler eigenvalue is the second smallest eigenvalue of the graph Laplacian.

Czech(miroslavFiedler) ∧ Mathematician(miroslavFiedler) KnownFor(miroslavFiedler, contributionsToLinearAlgebraAndGraphTheory) HonoredBy(miroslavFiedler, fiedlerEigenvalue) TheSecondSmallestEigenvalueOf(fiedlerEigenvalue, theGraphLaplacian)

Miroslav Fiedler was a French mathematician.

French(miroslavFiedler) ∧ Mathematician(miroslavFiedler)

Uncertain

Miroslav Fiedler was a Czech mathematician. Miroslav Fiedler is known for his contributions to linear algebra and graph theory. Miroslav Fiedler is honored by the Fiedler eigenvalue. Fiedler eigenvalue is the second smallest eigenvalue of the graph Laplacian.

Czech(miroslavFiedler) ∧ Mathematician(miroslavFiedler) KnownFor(miroslavFiedler, contributionsToLinearAlgebraAndGraphTheory) HonoredBy(miroslavFiedler, fiedlerEigenvalue) TheSecondSmallestEigenvalueOf(fiedlerEigenvalue, theGraphLaplacian)

A Czech mathematician is known for his contributions to linear algebra and graph theory.

∃x (Czech(x) ∧ Mathematician(x) ∧ KnownFor(x, contributionsToLinearAlgebraAndGraphTheory))

True

A laptop is a computer. You can play games on a computer. A phone is not a computer.

∀x (Laptop(x) → Computer(x)) ∀x (Computer(x) → CanPlayGameOn(x)) ∀x (Phone(x) → ¬Computer(x))

You can play games on a laptop.

∀x (Laptop(x) → CanPlayGameOn(x))

True

A laptop is a computer. You can play games on a computer. A phone is not a computer.

∀x (Laptop(x) → Computer(x)) ∀x (Computer(x) → CanPlayGameOn(x)) ∀x (Phone(x) → ¬Computer(x))

You can not play games on a phone.

∀x (Phone(x) → ¬CanPlayGameOn(x))

Uncertain

Walter Folger Brown was an American politician and lawyer who served as the postmaster general. Walter Folger Brown graduated from Harvard University with a Bachelor of Arts. While they were both in Toledo, Walter Folger Brown's father practiced law with Walter Folger Brown. Katherin Hafer married Walter Folger Brown.

AmericanPolitician(walterBrown) ∧ Lawyer(walterBrown) ∧ ServedAs(walterBrown, postMasterGeneral) Graduated(walterBrown, harvard) ∧ GraduatedWith(walterBrown, bachelorsOfArt) ∃t(In(walterBrown, toledo, t) ∧ In(walterBrownFather, toledo, t) ∧ PracticedLawTogether(walterBrown, walterBrownFather, t)) Married(katherinHafer, walterBrown)

Walter Folger Brown graduated with a Bachelor of Arts.

GraduatedWith(walterBrown, bachelorsOfArt)

True

Walter Folger Brown was an American politician and lawyer who served as the postmaster general. Walter Folger Brown graduated from Harvard University with a Bachelor of Arts. While they were both in Toledo, Walter Folger Brown's father practiced law with Walter Folger Brown. Katherin Hafer married Walter Folger Brown.

AmericanPolitician(walterBrown) ∧ Lawyer(walterBrown) ∧ ServedAs(walterBrown, postMasterGeneral) Graduated(walterBrown, harvard) ∧ GraduatedWith(walterBrown, bachelorsOfArt) ∃t(In(walterBrown, toledo, t) ∧ In(walterBrownFather, toledo, t) ∧ PracticedLawTogether(walterBrown, walterBrownFather, t)) Married(katherinHafer, walterBrown)

Walter Folger Brown's father was in Toledo.

∃t(In(walterBrownFather, toledo, t))

True

Walter Folger Brown was an American politician and lawyer who served as the postmaster general. Walter Folger Brown graduated from Harvard University with a Bachelor of Arts. While they were both in Toledo, Walter Folger Brown's father practiced law with Walter Folger Brown. Katherin Hafer married Walter Folger Brown.

AmericanPolitician(walterBrown) ∧ Lawyer(walterBrown) ∧ ServedAs(walterBrown, postMasterGeneral) Graduated(walterBrown, harvard) ∧ GraduatedWith(walterBrown, bachelorsOfArt) ∃t(In(walterBrown, toledo, t) ∧ In(walterBrownFather, toledo, t) ∧ PracticedLawTogether(walterBrown, walterBrownFather, t)) Married(katherinHafer, walterBrown)

Walter Folger Brown was not in Toledo.

∃t(¬In(walterBrownFather, toledo, t))

False

All products designed by Apple are sold at Apple Stores. All products with Apple logos are designed by Apple. All Macbooks have Apple logos. All products with Apple M2 chips are Mackbooks. A Thinkpad X1 is not both sold in Apple Stores and is a Macbook.

∀x ((Product(x) ∧ DesignedBy(x, apple)) → SoldIn(x, appleStore)) ∀x ((Product(x) ∧ With(x, appleLogo)) → DesignedBy(x, apple)) ∀x (Macbook(x) → With(x, appleLogo)) ∀x ((Product(x) ∧ With(x, appleM2Chip)) → Macbook(x)) ¬(SoldIn(thinkpadX1, appleStore) ∧ Macbook(thinkpadX1))

The Thinkpad X1 has an Apple M2 chip.

With(thinkpadX1, appleM2Chip)

False

All products designed by Apple are sold at Apple Stores. All products with Apple logos are designed by Apple. All Macbooks have Apple logos. All products with Apple M2 chips are Mackbooks. A Thinkpad X1 is not both sold in Apple Stores and is a Macbook.

∀x ((Product(x) ∧ DesignedBy(x, apple)) → SoldIn(x, appleStore)) ∀x ((Product(x) ∧ With(x, appleLogo)) → DesignedBy(x, apple)) ∀x (Macbook(x) → With(x, appleLogo)) ∀x ((Product(x) ∧ With(x, appleM2Chip)) → Macbook(x)) ¬(SoldIn(thinkpadX1, appleStore) ∧ Macbook(thinkpadX1))

The Thinkpad X1 is sold in Apple Stores.

SoldIn(thinkpadX1, appleStore)

Uncertain

All products designed by Apple are sold at Apple Stores. All products with Apple logos are designed by Apple. All Macbooks have Apple logos. All products with Apple M2 chips are Mackbooks. A Thinkpad X1 is not both sold in Apple Stores and is a Macbook.

∀x ((Product(x) ∧ DesignedBy(x, apple)) → SoldIn(x, appleStore)) ∀x ((Product(x) ∧ With(x, appleLogo)) → DesignedBy(x, apple)) ∀x (Macbook(x) → With(x, appleLogo)) ∀x ((Product(x) ∧ With(x, appleM2Chip)) → Macbook(x)) ¬(SoldIn(thinkpadX1, appleStore) ∧ Macbook(thinkpadX1))

The Thinkpad X1 has an Apple M2 chip and is a Macbook.

With(thinkpadX1, appleM2Chip) ∧ Macbook(thinkpadX1)

False

All products designed by Apple are sold at Apple Stores. All products with Apple logos are designed by Apple. All Macbooks have Apple logos. All products with Apple M2 chips are Mackbooks. A Thinkpad X1 is not both sold in Apple Stores and is a Macbook.

∀x ((Product(x) ∧ DesignedBy(x, apple)) → SoldIn(x, appleStore)) ∀x ((Product(x) ∧ With(x, appleLogo)) → DesignedBy(x, apple)) ∀x (Macbook(x) → With(x, appleLogo)) ∀x ((Product(x) ∧ With(x, appleM2Chip)) → Macbook(x)) ¬(SoldIn(thinkpadX1, appleStore) ∧ Macbook(thinkpadX1))

The Thinkpad X1 either has an Apple M2 chip or is a Macbook.

With(thinkpadX1, appleM2Chip)) ⊕ Macbook(thinkpadX1)

False

All products designed by Apple are sold at Apple Stores. All products with Apple logos are designed by Apple. All Macbooks have Apple logos. All products with Apple M2 chips are Mackbooks. A Thinkpad X1 is not both sold in Apple Stores and is a Macbook.

∀x ((Product(x) ∧ DesignedBy(x, apple)) → SoldIn(x, appleStore)) ∀x ((Product(x) ∧ With(x, appleLogo)) → DesignedBy(x, apple)) ∀x (Macbook(x) → With(x, appleLogo)) ∀x ((Product(x) ∧ With(x, appleM2Chip)) → Macbook(x)) ¬(SoldIn(thinkpadX1, appleStore) ∧ Macbook(thinkpadX1))

If the Thinkpad X1 has an Apple M2 chip and is a Macbook, then it neither has an Apple M2 chip nor is sold in Apple Stores.

(With(thinkpadX1, appleM2Chip) ∧ Macbook(thinkpadX1)) → ¬(With(thinkpadX1, appleM2Chip) ∨ SoldIn(thinkpadX1, appleStore))

True

Oxford Circus is a road junction connecting Oxford Street and Regent Street. Oxford Street and Regent Street are in London. John Nash designed a construction on Regent Street. John Nash designed Oxford Circus. John Nash is a British architect. Oxford Circus is the entrance to Oxford Circus tube station, a part of the Central line in 1900.

RoadJunction(oxfordCircus) ∧ Connect(oxfordCircus, oxfordSt, regentSt) In(oxfordSt, london) ∧ In(regentSt, london) Designed(nash, construction) ∧ On(construction, regentSt) Designed(nash, oxfordCircus) Architect(nash) ∧ British(nash) EntraceTo(oxfordCircus, tubeStation) ∧ PartOf(tubeStation, centralline) ∧ In(tubeStation, 1900)

Oxford Circus is in London.

In(oxfordCircus, london)

True

Oxford Circus is a road junction connecting Oxford Street and Regent Street. Oxford Street and Regent Street are in London. John Nash designed a construction on Regent Street. John Nash designed Oxford Circus. John Nash is a British architect. Oxford Circus is the entrance to Oxford Circus tube station, a part of the Central line in 1900.

RoadJunction(oxfordCircus) ∧ Connect(oxfordCircus, oxfordSt, regentSt) In(oxfordSt, london) ∧ In(regentSt, london) Designed(nash, construction) ∧ On(construction, regentSt) Designed(nash, oxfordCircus) Architect(nash) ∧ British(nash) EntraceTo(oxfordCircus, tubeStation) ∧ PartOf(tubeStation, centralline) ∧ In(tubeStation, 1900)

Oxford Circus is designed by a British architect.

∃x (British(x) ∧ Architect(x) ∧ Design(x, oxfordCircus))

True

Oxford Circus is a road junction connecting Oxford Street and Regent Street. Oxford Street and Regent Street are in London. John Nash designed a construction on Regent Street. John Nash designed Oxford Circus. John Nash is a British architect. Oxford Circus is the entrance to Oxford Circus tube station, a part of the Central line in 1900.

RoadJunction(oxfordCircus) ∧ Connect(oxfordCircus, oxfordSt, regentSt) In(oxfordSt, london) ∧ In(regentSt, london) Designed(nash, construction) ∧ On(construction, regentSt) Designed(nash, oxfordCircus) Architect(nash) ∧ British(nash) EntraceTo(oxfordCircus, tubeStation) ∧ PartOf(tubeStation, centralline) ∧ In(tubeStation, 1900)

John Nash designed the Central line in 1900.

∀x (PartOf(x, centralLine) → Design(johnNash, x))

Uncertain

Oxford Circus is a road junction connecting Oxford Street and Regent Street. Oxford Street and Regent Street are in London. John Nash designed a construction on Regent Street. John Nash designed Oxford Circus. John Nash is a British architect. Oxford Circus is the entrance to Oxford Circus tube station, a part of the Central line in 1900.

RoadJunction(oxfordCircus) ∧ Connect(oxfordCircus, oxfordSt, regentSt) In(oxfordSt, london) ∧ In(regentSt, london) Designed(nash, construction) ∧ On(construction, regentSt) Designed(nash, oxfordCircus) Architect(nash) ∧ British(nash) EntraceTo(oxfordCircus, tubeStation) ∧ PartOf(tubeStation, centralline) ∧ In(tubeStation, 1900)

Regent Street is not in London.

¬In(regentStreet, london)

False

All pets in my house are either cats or dogs. All the dogs in my house bark. Ghosts do not exist. If some pet in my house barks, then it is not dead. All of the pets in my house are either dead or alive. Jojo is a pet in my house, and it is not alive.

∀x (Pet(x) ∧ In(x, myHouse) → Cat(x) ⊕ Dog(x)) ∀x (Dog(x) ∧ In(x, myHouse) → Bark(x)) ∀x (¬Ghost(x)) ∀x (Bark(x) ∧ Pet(x) ∧ In(x, myHouse) → ¬Dead(x)) ∀x (Pet(x) ∧ In(x, myHouse) → Dead(x) ⊕ Alive(x)) Pet(jojo) ∧ InMyHouse(jojo)∧ ¬Alive(jojo)

Jojo is a ghost.

Ghost(jojo)

False

All pets in my house are either cats or dogs. All the dogs in my house bark. Ghosts do not exist. If some pet in my house barks, then it is not dead. All of the pets in my house are either dead or alive. Jojo is a pet in my house, and it is not alive.

∀x (Pet(x) ∧ In(x, myHouse) → Cat(x) ⊕ Dog(x)) ∀x (Dog(x) ∧ In(x, myHouse) → Bark(x)) ∀x (¬Ghost(x)) ∀x (Bark(x) ∧ Pet(x) ∧ In(x, myHouse) → ¬Dead(x)) ∀x (Pet(x) ∧ In(x, myHouse) → Dead(x) ⊕ Alive(x)) Pet(jojo) ∧ InMyHouse(jojo)∧ ¬Alive(jojo)

Jojo is a cat or a ghost.

Cat(jojo) ∨ Ghost(jojo)

True

All pets in my house are either cats or dogs. All the dogs in my house bark. Ghosts do not exist. If some pet in my house barks, then it is not dead. All of the pets in my house are either dead or alive. Jojo is a pet in my house, and it is not alive.

∀x (Pet(x) ∧ In(x, myHouse) → Cat(x) ⊕ Dog(x)) ∀x (Dog(x) ∧ In(x, myHouse) → Bark(x)) ∀x (¬Ghost(x)) ∀x (Bark(x) ∧ Pet(x) ∧ In(x, myHouse) → ¬Dead(x)) ∀x (Pet(x) ∧ In(x, myHouse) → Dead(x) ⊕ Alive(x)) Pet(jojo) ∧ InMyHouse(jojo)∧ ¬Alive(jojo)

If Jojo is a cat or a ghost, then Jojo either barks or is a dog.

Cat(jojo) ∨ Ghost(jojo) → Bark(jojo) ⊕ Dog(jojo)

False

All tigers are cats. No cats are dogs. All Bengal tigers are tigers. All huskies are dogs. Fido is either a Bengal tiger or a cat.

∀x (Tiger(x) → Cat(x)) ∀x (Cat(x) → ¬Dog(x)) ∀x (BengalTiger(x) → Tiger(x)) ∀x (Husky(x) → Dog(x)) BengalTiger(fido) ⊕ Cat(fido)

Fido is a husky animal.

Husky(fido)

False

All tigers are cats. No cats are dogs. All Bengal tigers are tigers. All huskies are dogs. Fido is either a Bengal tiger or a cat.

∀x (Tiger(x) → Cat(x)) ∀x (Cat(x) → ¬Dog(x)) ∀x (BengalTiger(x) → Tiger(x)) ∀x (Husky(x) → Dog(x)) BengalTiger(fido) ⊕ Cat(fido)

Fido is not a husky.

¬Husky(fido)

True

All tigers are cats. No cats are dogs. All Bengal tigers are tigers. All huskies are dogs. Fido is either a Bengal tiger or a cat.

∀x (Tiger(x) → Cat(x)) ∀x (Cat(x) → ¬Dog(x)) ∀x (BengalTiger(x) → Tiger(x)) ∀x (Husky(x) → Dog(x)) BengalTiger(fido) ⊕ Cat(fido)

Fido is a Bengal tiger.

BengalTiger(fido)

Uncertain

All tigers are cats. No cats are dogs. All Bengal tigers are tigers. All huskies are dogs. Fido is either a Bengal tiger or a cat.

∀x (Tiger(x) → Cat(x)) ∀x (Cat(x) → ¬Dog(x)) ∀x (BengalTiger(x) → Tiger(x)) ∀x (Husky(x) → Dog(x)) BengalTiger(fido) ⊕ Cat(fido)

Fido is neither a dog nor a husky.

¬Dog(fido) ∧ ¬Husky(fido)

True

If a city holds a Summer Olympics, and the city is a US city, then the Summer Olympics will be in the US. If a city is in a state in the US, the city is a US city. If a city is in a state, and a Summer Olympics is in this city, then the Summer Olympics is in this state. The 2028 Summer Olympics is scheduled to take place in Los Angeles. Los Angeles is a city in California. Atlanta is a US city. Atlanta is in Georgia. California is a state in the United States. Boxing, modern pentathlon, and weightlifting will be removed from The 2028 Summer Olympics. Atlanta in the United States held the 1996 Summer Olympics.

∀x ∀y ((SummerOlympicsIn(x,y) ∧ In(x, unitedStates)) → SummerOlympicsIn(x, unitedStates)) ∀x ∀y ((In(x, y) ∧ In(y, unitedStates)) → In(x, unitedStates)) ∀x ∀y ∀z ((In(x, z) ∧ State(z) ∧ SummerOlympicsIn(x,y)) → SummerOlympicsIn(z, y)) SummerOlympicsIn(losAngeles, yr2028) In(losAngeles, california) In(atlanta, unitedStates) In(california, unitedStates) In(atlanta, georgia) ¬InSummerOlympicsIn(boxing, yr2028) ∧ (¬InSummerOlympicsIn(modern_pentathlon, yr2028)) ∧ (¬InSummerOlympicsIn(weightlifting, yr2028)) SummerOlympicsIn(atlanta, yr1996)

The 2028 Summer Olympics will take place in the US.

SummerOlympicsIn(unitedStates, yr2028)

True

If a city holds a Summer Olympics, and the city is a US city, then the Summer Olympics will be in the US. If a city is in a state in the US, the city is a US city. If a city is in a state, and a Summer Olympics is in this city, then the Summer Olympics is in this state. The 2028 Summer Olympics is scheduled to take place in Los Angeles. Los Angeles is a city in California. Atlanta is a US city. Atlanta is in Georgia. California is a state in the United States. Boxing, modern pentathlon, and weightlifting will be removed from The 2028 Summer Olympics. Atlanta in the United States held the 1996 Summer Olympics.

∀x ∀y ((SummerOlympicsIn(x,y) ∧ In(x, unitedStates)) → SummerOlympicsIn(x, unitedStates)) ∀x ∀y ((In(x, y) ∧ In(y, unitedStates)) → In(x, unitedStates)) ∀x ∀y ∀z ((In(x, z) ∧ State(z) ∧ SummerOlympicsIn(x,y)) → SummerOlympicsIn(z, y)) SummerOlympicsIn(losAngeles, yr2028) In(losAngeles, california) In(atlanta, unitedStates) In(california, unitedStates) In(atlanta, georgia) ¬InSummerOlympicsIn(boxing, yr2028) ∧ (¬InSummerOlympicsIn(modern_pentathlon, yr2028)) ∧ (¬InSummerOlympicsIn(weightlifting, yr2028)) SummerOlympicsIn(atlanta, yr1996)

The 1996 Summer Olympics is not in Georgia.

¬SummerOlympicsIn(georgia, yr1996)

False

If a city holds a Summer Olympics, and the city is a US city, then the Summer Olympics will be in the US. If a city is in a state in the US, the city is a US city. If a city is in a state, and a Summer Olympics is in this city, then the Summer Olympics is in this state. The 2028 Summer Olympics is scheduled to take place in Los Angeles. Los Angeles is a city in California. Atlanta is a US city. Atlanta is in Georgia. California is a state in the United States. Boxing, modern pentathlon, and weightlifting will be removed from The 2028 Summer Olympics. Atlanta in the United States held the 1996 Summer Olympics.

∀x ∀y ((SummerOlympicsIn(x,y) ∧ In(x, unitedStates)) → SummerOlympicsIn(x, unitedStates)) ∀x ∀y ((In(x, y) ∧ In(y, unitedStates)) → In(x, unitedStates)) ∀x ∀y ∀z ((In(x, z) ∧ State(z) ∧ SummerOlympicsIn(x,y)) → SummerOlympicsIn(z, y)) SummerOlympicsIn(losAngeles, yr2028) In(losAngeles, california) In(atlanta, unitedStates) In(california, unitedStates) In(atlanta, georgia) ¬InSummerOlympicsIn(boxing, yr2028) ∧ (¬InSummerOlympicsIn(modern_pentathlon, yr2028)) ∧ (¬InSummerOlympicsIn(weightlifting, yr2028)) SummerOlympicsIn(atlanta, yr1996)

Skateboarding will appear at The 2028 Summer Olympics.

InSummerOlympicsIn(skateboarding, yr2028)

Uncertain

The taiga vole is a large vole found in northwestern North America. Cats like playing with all voles. The taiga vole lives in the boreal taiga zone. The boreal taiga zone in North America is a cold place to live in.

Vole(taigaVole) ∧ LiveIn(taigaVole, northAmerica) LikePlayingWith(cat, taigaVole) LiveIn(taigaVole, borealTaigaZone) ∀x ((LiveIn(x, northAmerica) ∧ LiveIn(x, borealTaigaZone)) → LiveIn(x, coldPlace))

Cats like playing with taiga vole.

LikePlayingWith(cat, taigaVole)

True

The taiga vole is a large vole found in northwestern North America. Cats like playing with all voles. The taiga vole lives in the boreal taiga zone. The boreal taiga zone in North America is a cold place to live in.

Vole(taigaVole) ∧ LiveIn(taigaVole, northAmerica) LikePlayingWith(cat, taigaVole) LiveIn(taigaVole, borealTaigaZone) ∀x ((LiveIn(x, northAmerica) ∧ LiveIn(x, borealTaigaZone)) → LiveIn(x, coldPlace))

Taiga vole's living place is not cold.

¬LiveIn(taigaVole, coldPlace)

False

A diseases affect females or males. No women have prostate cancer. A cancer is either prostate cancer or non-prostate cancer. No type of cancer is without mutations. All non-prostate cancers are a type of cancer. If adenocarcinoma is a type of cancer or without mutations or both, then adenocarcinoma is in women or without mutations or both.

∀x (Disease(x) → (Affects(x, female) ∨ Affects(x, male)) ) ∀x (Affect(x, female) → ¬ProstateCancer(x)) ∀x (ProstateCancer(x) ∨ NonProstateCancer(x)) ∀x (Cancer(x) → ¬Without(x, mutation)) ∀x (NonProstateCancer(x) → Cancer(x)) (Cancer(adenocarcinoma) ∨ Without(adenocarcinoma, mutation)) → (Affect(adenocarcinoma, female) ∨ Without(adenocarcinoma, mutation))

Adenocarcinoma is a prostate cancer.

ProstateCancer(adenocarcinoma)

Uncertain

A diseases affect females or males. No women have prostate cancer. A cancer is either prostate cancer or non-prostate cancer. No type of cancer is without mutations. All non-prostate cancers are a type of cancer. If adenocarcinoma is a type of cancer or without mutations or both, then adenocarcinoma is in women or without mutations or both.

∀x (Disease(x) → (Affects(x, female) ∨ Affects(x, male)) ) ∀x (Affect(x, female) → ¬ProstateCancer(x)) ∀x (ProstateCancer(x) ∨ NonProstateCancer(x)) ∀x (Cancer(x) → ¬Without(x, mutation)) ∀x (NonProstateCancer(x) → Cancer(x)) (Cancer(adenocarcinoma) ∨ Without(adenocarcinoma, mutation)) → (Affect(adenocarcinoma, female) ∨ Without(adenocarcinoma, mutation))

Adenocarcinoma is a disease in women.

Affect(adenocarcinoma, men)

True

A diseases affect females or males. No women have prostate cancer. A cancer is either prostate cancer or non-prostate cancer. No type of cancer is without mutations. All non-prostate cancers are a type of cancer. If adenocarcinoma is a type of cancer or without mutations or both, then adenocarcinoma is in women or without mutations or both.

∀x (Disease(x) → (Affects(x, female) ∨ Affects(x, male)) ) ∀x (Affect(x, female) → ¬ProstateCancer(x)) ∀x (ProstateCancer(x) ∨ NonProstateCancer(x)) ∀x (Cancer(x) → ¬Without(x, mutation)) ∀x (NonProstateCancer(x) → Cancer(x)) (Cancer(adenocarcinoma) ∨ Without(adenocarcinoma, mutation)) → (Affect(adenocarcinoma, female) ∨ Without(adenocarcinoma, mutation))

If adenocarcinoma is a disease in women or without mutations, then adenocarcinoma is without mutations and a non-prostate cancer.

(Affect(adenocarcinoma, men) ∨ Without(adenocarcinoma, mutation)) → (NonProstateCancer(adenocarcinoma) ∧ Without(adenocarcinoma, mutation))

False

Some monitors equipped in the lab are produced by the company named AOC. All monitors equipped in the lab are cheaper than their original prices. If a monitor is cheaper than its original price, then its resolution is 1080p. If a monitor has a resolution of 1080p, then it does not support the type-c port. LG34 is equipped in the lab.

∃x ∃y (LabMonitor(x) ∧ AOC(x) ∧ (¬(x=y)) ∧ LabMonitor(y) ∧ AOC(y)) ∀x (LabMonitor(x) → Discounted(x)) ∀x (Discounted(x) → A1080p(x)) ∀x (A1080p(x) → ¬TypeC(x)) LabMonitor(lg-34)

LG34 machine is produced by AOC.

AOC(lg-34)

Uncertain

Some monitors equipped in the lab are produced by the company named AOC. All monitors equipped in the lab are cheaper than their original prices. If a monitor is cheaper than its original price, then its resolution is 1080p. If a monitor has a resolution of 1080p, then it does not support the type-c port. LG34 is equipped in the lab.

∃x ∃y (LabMonitor(x) ∧ AOC(x) ∧ (¬(x=y)) ∧ LabMonitor(y) ∧ AOC(y)) ∀x (LabMonitor(x) → Discounted(x)) ∀x (Discounted(x) → A1080p(x)) ∀x (A1080p(x) → ¬TypeC(x)) LabMonitor(lg-34)

LG34 machine does not support the type-c port.

¬TypeC(lg-34)

True

Some monitors equipped in the lab are produced by the company named AOC. All monitors equipped in the lab are cheaper than their original prices. If a monitor is cheaper than its original price, then its resolution is 1080p. If a monitor has a resolution of 1080p, then it does not support the type-c port. LG34 is equipped in the lab.

∃x ∃y (LabMonitor(x) ∧ AOC(x) ∧ (¬(x=y)) ∧ LabMonitor(y) ∧ AOC(y)) ∀x (LabMonitor(x) → Discounted(x)) ∀x (Discounted(x) → A1080p(x)) ∀x (A1080p(x) → ¬TypeC(x)) LabMonitor(lg-34)

LG34 is not with a resolution of 1080p.

¬A1080p(lg-34)

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))

Avocados are a kind of fruit sold at the local farmers market in New Haven.

Fruit(avocado) ∧ SoldAt(avocado, localFarmersMarket)

Uncertain