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Clyde is a professor who takes a historical approach, or is a contemporary academic.
(Professor(clyde) ∧ Take(clyde, historicalApproach)) ∨ (ContemporaryAcademic(clyde) ∧ Enjoy(clyde, learning))
No sports cars are vehicles intended to be driven at moderate speeds.
∀x (SportsCar(x) → ¬IntendedToBeDrivenAt(x, moderateSpeed))
All automobiles designed for family use are vehicles intended to be driven at moderate speeds.
∀x (DesignedFor(x, familyUse) → IntendedToBeDrivenAt(x, moderateSpeed))
No sports cars are automobiles designed for family use.
∀x (SportsCar(x) → ¬For(x, familyUse))
If people work well in teams in the workplace, then they get along with all their colleagues at their work.
∀x (WorkWellInTeamsIn(x, workPlace) → ∀y (Colleague(y) ∧ GetAlongWithAtWork(x, y)))
If people come to work every day with a positive attitude, then they work well in teams in the workplace.
∀x (ComeToWorkWithEveryDay(x, positiveAttitude) → WorkWellInTeamsIn(x, workPlace))
People either come to work every day with a positive attitude or are always tired every morning.
∀x (ComeToWorkWithEveryDay(x, positiveAttitude) ⊕ AlwaysTiredInMorning(x))
If people are always tired in the morning, then they are criticized by their boss.
∀x (AlwaysTiredInMorning(x) → CriticizedBy(x, boss))
If people are criticized by their boss, then they do not receive positive feedback from teams at work.
∀x (CriticizedBy(x, boss) → ¬ReceiveFromAtWork(x, positiveFeedback, team))
Kat either is a person who works well in teams in the workplac and is always tired every morning, or she is neither.
¬(WorkWellInTeamsIn(kat, workPlace) ⊕ Tired(kat))
Kat is a person who comes to work every day with a positive attitude.
ComeToWorkWithEveryDay(kat, positiveAttitude)
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)
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)
Drishti is an open-source software.
OpenSourceSoftware(drishti)
Open-source software is free to modify.
∀x (OpenSourceSoftware(x) → FreeToModify(x))
Drishti is free to modify.
FreeToModify(drishti)
There are five grades in English class: A+, A, B+, B, and C.
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))
If a student gets an A+ in English class, then his score is greater than 95.
∀x ∀y (Student(x) ∧ GetGradeIn(x, aPlus, englishClass) → EnglishClassScore(x, y) ∧ GreaterThan95(y))
If a student gets an A in English class, then his score is greater than 90 but lower than 95.
∀x ∀y (Student(x) ∧ GetGradeIn(x, a, englishClass) → EnglishClassScore(x, y) ∧ GreaterThan90(y) ∧ LowerThan95(y))
Zhang got an A in English class.
Student(zhang) ∧ GetGradeIn(zhang, a, englishClass)
Wang's English class score is better than Zhang's.
∀x ∀y (Student(zhang) ∧ Student(wang) ∧ EnglishScore(zhang, x) ∧ EnglishScore(wang, y) ∧ Better(y, x))
Wu's English class score is lower than 90.
∀x (Student(wu) ∧ EnglishScore(wu, x) ∧ LowerThan90(x))
If a student's English class score is lower than 90, then it is not greater than 95 or 90, and lower than 95.
∀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))
Wang got an A+ in English class.
GetGradeIn(wang, aPlus, englishClass)
Wu does not get an A or A+ in English class.
¬GetGradeIn(wu, aPlus, englishClass) ∧¬GetGradeIn(wu, a, englishClass)
Olivia doesn't prefer warm temperatures during the day.
∀x (Day(x) → ¬Prefer(olivia, warmTemperature, x))
When Olivia sleeps, she prefers a cool temperature.
∀x (Sleep(olivia, x) → Prefer(olivia, coolTemperature, x))
Olivia sleeps during the night.
∀x (Night(x) → Sleep(olivia, x))
Olivia works during the day.
∀x (Day(x) → Work(olivia, x))
Olivia either works or sleeps.
Work(olivia) ⊕ Sleep(olivia)
It is either the day or the night.
∀x (Day(x) ⊕ Night(x))
Olivia either prefers warm temperatures or prefers cool temperatures.
∀x (Prefer(olivia, warmTemperature, x) ⊕ Prefer(olivia, coolTemperature, x))
At all times, Olivia prefers a cool temperature.
∀x (Prefer(olivia, coolTemperature, x))
TOra is a GUI.
GUI(tora)
GUIs are software.
∀x (GUI(x) → Software(x))
Software can be free or paid.
∀x (Software(x) → Free(x) ⊕ Paid(x))
Paid Software is not under the GNU General Public License.
∀x (Paid(x) ∧ Software(x) → ¬UnderGNULicense(x))
TOra is under the GNU General Public License.
UnderGNULicense(tora)
TOra is a paid software.
Paid(tora) ∧ Software(tora)
TOra is a free software.
Free(tora) ∧ Software(tora)
Customers choose a Prime Video plan or an HBO Max Plan, or both.
∀x (Customer(x) → (Choose(x, primeVideoPlan) ∨ Choose(x, hBOMaxPlan)))
All customers who choose a Prime Video Plan are rewarded with a $30 gift card.
∀x ((Customer(x) ∧ Choose(x, hBOMaxPlan)) → RewardWith(x, giftCard))
There are no customers who do not choose any plan.
∀x (Customer(x) → (∃y(Plan(y) ∧ Choose(x, y))))
None of the customers who are rewarded with a $30 gift card are older than 80.
∀x ((Customer(x) ∧ RewardWith(x, giftCard)) → (¬OlderThan(x, num80)))
All the customers are either older than 80 or between the ages of 60 and 80.
∀x (Customer(x) → (∃y(GreaterThan(y, num80) ∧ Age(james,y)) ⊕ (∃y(Between(y, num60, num80) ∧ Age(james, y)))))
James is a customer who is not between the ages of 60 and 80.
Customer(james) ∧ (¬∃y(Between(y, num60, num80) ∧ Age(james, y)))
James is a customer who does not choose any plans.
Choose(james, noPlan)
James is a customer who chooses a Prime Video plan or does not choose any plans.
Choose(james, planA) ∨ Choose(james, noPlan)
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)
Detroit City is a horse.
Horse(detroitcity)
Some horses are racehorses.
∃x (Horse(x) ∧ Racehorse(x))
If a horse falls in a race, it poses risks to its rider.
∀x (Horse(x) ∧ InRace(x) ∧ Falls(x) → PoseRiskTo(x, rider))
Detroit City fell in a race.
InRace(detroitcity) ∧ Fall(detroitcity)
A horse is a racehorse if it is in a race.
∀x (Horse(x) ∧ InRace(x) → Racehorse(x))
Detroit City has been in multiple races.
MultipleRace(detroitcity)
Detroit City poses risks to its rider.
PoseRiskTo(detroitcity, rider)
Detroit City is a racehorse.
Racehorse(detroitcity)
Frederick Monhoff was an architect, artist, and illustrator.
Architect(monhoff) ∧ Artist(monhoff) ∧ Illustrator(monhoff)
Frederick Monhoff was an American.
American(monhoff)
An artist is good at physical or conceptual art.
∀x (Artist(x) → GoodAt(x, physicalArt) ∨ GoodAt(x, conceptualArt))
All Americans are American citizens.
∀x (American(x) → AmericanCitizen(x))
Frederick Monhoff was good at physical art.
GoodAt(monhoff, physicalArt)
No illustrator was an American citizen.
¬(∃x (Illustrator(x) ∧ AmericanCitizen(x)))
Miroslav Fiedler was a Czech mathematician.
Czech(miroslavFiedler) ∧ Mathematician(miroslavFiedler)
Miroslav Fiedler is known for his contributions to linear algebra and graph theory.
KnownFor(miroslavFiedler, contributionsToLinearAlgebraAndGraphTheory)
Miroslav Fiedler is honored by the Fiedler eigenvalue.
HonoredBy(miroslavFiedler, fiedlerEigenvalue)
Fiedler eigenvalue is the second smallest eigenvalue of the graph Laplacian.
TheSecondSmallestEigenvalueOf(fiedlerEigenvalue, theGraphLaplacian)
Miroslav Fiedler is honored by the second smallest eigenvalue of the graph Laplacian.
∃x (TheSecondSmallestEigenvalueOf(x, theGraphLaplacian) ∧ HonoredBy(miroslavFiedler, x))
Miroslav Fiedler was a French mathematician.
French(miroslavFiedler) ∧ Mathematician(miroslavFiedler)
A Czech mathematician is known for his contributions to linear algebra and graph theory.
∃x (Czech(x) ∧ Mathematician(x) ∧ KnownFor(x, contributionsToLinearAlgebraAndGraphTheory))
A laptop is a computer.
∀x (Laptop(x) → Computer(x))
You can play games on a computer.
∀x (Computer(x) → CanPlayGameOn(x))
A phone is not a computer.
∀x (Phone(x) → ¬Computer(x))
You can play games on a laptop.
∀x (Laptop(x) → CanPlayGameOn(x))
You can not play games on a phone.
∀x (Phone(x) → ¬CanPlayGameOn(x))
Walter Folger Brown was an American politician and lawyer who served as the postmaster general.
AmericanPolitician(walterBrown) ∧ Lawyer(walterBrown) ∧ ServedAs(walterBrown, postMasterGeneral)
Walter Folger Brown graduated from Harvard University with a Bachelor of Arts.
Graduated(walterBrown, harvard) ∧ GraduatedWith(walterBrown, bachelorsOfArt)
While they were both in Toledo, Walter Folger Brown's father practiced law with Walter Folger Brown.
∃t(In(walterBrown, toledo, t) ∧ In(walterBrownFather, toledo, t) ∧ PracticedLawTogether(walterBrown, walterBrownFather, t))
Katherin Hafer married Walter Folger Brown.
Married(katherinHafer, walterBrown)
Walter Folger Brown graduated with a Bachelor of Arts.
GraduatedWith(walterBrown, bachelorsOfArt)
Walter Folger Brown's father was in Toledo.
∃t(In(walterBrownFather, toledo, t))
Walter Folger Brown was not in Toledo.
∃t(¬In(walterBrownFather, toledo, t))
All products designed by Apple are sold at Apple Stores.
∀x ((Product(x) ∧ DesignedBy(x, apple)) → SoldIn(x, appleStore))
All products with Apple logos are designed by Apple.
∀x ((Product(x) ∧ With(x, appleLogo)) → DesignedBy(x, apple))
All Macbooks have Apple logos.
∀x (Macbook(x) → With(x, appleLogo))
All products with Apple M2 chips are Mackbooks.
∀x ((Product(x) ∧ With(x, appleM2Chip)) → Macbook(x))
A Thinkpad X1 is not both sold in Apple Stores and is a Macbook.
¬(SoldIn(thinkpadX1, appleStore) ∧ Macbook(thinkpadX1))
The Thinkpad X1 has an Apple M2 chip.
With(thinkpadX1, appleM2Chip)
The Thinkpad X1 is sold in Apple Stores.
SoldIn(thinkpadX1, appleStore)
The Thinkpad X1 has an Apple M2 chip and is a Macbook.
With(thinkpadX1, appleM2Chip) ∧ Macbook(thinkpadX1)
The Thinkpad X1 either has an Apple M2 chip or is a Macbook.
With(thinkpadX1, appleM2Chip)) ⊕ 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))
Oxford Circus is a road junction connecting Oxford Street and Regent Street.
RoadJunction(oxfordCircus) ∧ Connect(oxfordCircus, oxfordSt, regentSt)
Oxford Street and Regent Street are in London.
In(oxfordSt, london) ∧ In(regentSt, london)
John Nash designed a construction on Regent Street.
Designed(nash, construction) ∧ On(construction, regentSt)
John Nash designed Oxford Circus.
Designed(nash, oxfordCircus)
John Nash is a British architect.
Architect(nash) ∧ British(nash)
Oxford Circus is the entrance to Oxford Circus tube station, a part of the Central line in 1900.
EntraceTo(oxfordCircus, tubeStation) ∧ PartOf(tubeStation, centralline) ∧ In(tubeStation, 1900)
Oxford Circus is in London.
In(oxfordCircus, london)