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All songs that are full of lyrics need to be written with words | ∀x (Song(x) ∧ FullOfLyrics(x) → NeedToBeWrittenWith(x, words)) |
It is not true that “As it was” by Harry Styles is classical music that Max listens to and is from the 12th century. | ¬(ClassicalMusic(asItWasByHarryStyles) ∧ Song(asItWasByHarryStyles) ∧ From(asItWasByHarryStyles, 12thCentury)) |
Max listens to "As it was" by Harry Styles. | MaxListenTo(asItWasByHarryStyles) |
“As it was” by Harry Styles needs to be written with words. | NeedToBeWrittenWith(asItWasByHarryStyles, words) |
"As it was” by Harry Styles is a song from the 12th century. | Song(asItWasByHarryStyles) ∧ From(asItWasByHarryStyles, 12thCentury) |
"As it was” by Harry Styles is not both a song from Kanye West and needed to be written with words. | ¬(Song(asItWasByHarryStyles) ∧ By(asItWasByHarryStyles, kanyeWest) ∧ NeedToBeWrittenWith(asItWasByHarryStyles, words)) |
"Your Woman" is a song by the British one-person band White Town. | Produce(whiteTown, yourWoman) ∧ OnePersonBand(whiteTown) |
"Your Woman" song peaked at No. 1 on the UK Singles Chart. | Peak(yourWoman, uKSinglesChart) |
If a song peaked at No.1 at a particular place, it was extremely popular. | ∀x ((∃y(Peak(x, y))) → Popular(x)) |
"Your Woman" peaked at No. 1 in Iceland, Israel, and Spain. | Peak(yourWoman, iceland) ∧ Peak(yourWoman, israel) ∧ Peak(yourWoman, spain) |
"Your Woman" was extremely popular. | Popular(yourWoman) |
White Town did not produce any popular songs. | ∀x (Produce(whiteTown, x) → ¬Popular(x)) |
White Town was a successful band. | Successful(whiteTown) |
All functions that represent straight lines on the coordinate plane are linear functions. | ∀x (Function(x) ∧ RepresentOn(x, straightLine, coordinatePlane) → LinearFunction(x)) |
No linear functions are non-convex functions. | ∀x (LinearFunction(x) → ¬NonConvexFunction(x)) |
A function is either a non-convex fuction or a convex function. | ∀x (Function(x) → NonConvexFunction(x) ⊕ ConvexFunction(x)) |
All quasi-convex functions are real-valued functions. | ∀x (QuasiConvexFunction(x) → RealValuedFunction(x)) |
All convex functions are quasi-convex functions. | ∀x (ConvexFunction(x) → QuasiConvexFunction(x)) |
The maximum of quasiconvex functions is a function. | Function(maximumOfQuasiConvexFunction) |
The maximum of quasiconvex functions is a function that represents straight lines on the coordinate plane or it is a convex function or it is not a non-convex function. | (Function(maximumOfQuasiConvexFunction) ∧ RepresentOn(maximumOfQuasiConvexFunction, straightLine, coordinatePlane)) ∨ ConvexFunction(maximumOfQuasiConvexFunction) ∨ ¬NonConvexFunction(maximumOfQuasiConvexFunction) |
The maximum of quasiconvex functions is a function that represent straight lines on the coordinate plane. | Function(maximumOfQuasiConvexFunction) ∧ RepresentOn(maximumOfQuasiConvexFunction, straightLine, coordinatePlane) |
The maximum of quasiconvex functions is not a real-valued function. | ¬RealValuedFunction(maximumOfQuasiConvexFunction) |
The maximum of quasiconvex functions is a quasi-convex function or it is not a real-valued function. | QuasiConvexFunction(maximumOfQuasiConvexFunction) ∨ ¬RealValuedFunction(maximumOfQuasiConvexFunction) |
If two soccer teams score the same number of goals in one UCL final during the regular time, they need to play for the extra time. | ∀w ∀x ∀y ∀z (SoccerTeam(x) ∧ SoccerTeam(y) ∧ NumberOfGoalScored(x, z) ∧ NumberOfGoalScored(y, w) ∧ y=w ∧ During(regularTime) → PlayExtra(x, y)) |
If two soccer teams score the same number of goals in one UCL final during both regular and extra time, they need to play the penalty shoot-out. | ∀x ∀y (SoccerTeam(x) ∧ SoccerTeam(y) ∧ SameScore(x, y) ∧ During(regularTime) ∧ During(extraTime) → PlayPenalty(x, y)) |
Real Madrid and Atlético Madrid both scored one goal in the 2016 UCL final during the regular time. | SoccerTeam(realMadrid) ∧ SoccerTeam(atleticoMadrid) ∧ SameScore(realMadrid, atleticoMadrid) ∧ During(regularTime) |
Real Madrid and Atlético Madrid both scored zero goals in the 2016 UCL final during the extra time. | SoccerTeam(realMadrid) ∧ SoccerTeam(atleticoMadrid) ∧ SameScore(realMadrid, atleticoMadrid) ∧ During(extraTime) |
Real Madrid and Atlético Madrid needed to play a penalty shoot-out in the 2016 UCL final. | PlayPenalty(realMadrid, atleticoMadrid) |
Real Madrid and Atlético Madrid did not need to play a penalty shoot-out in the 2016 UCL final. | ¬PlayPenalty(realMadrid, atleticoMadrid) |
System 7 is a UK-based electronic dance music band. | BasedIn(system7, uk) ∧ ElectronicDanceMusicBand(system7) |
Steve Hillage and Miquette Giraudy formed System 7. | Form(stevehillage, system7) ∧ Form(miquettegiraudy, system7) |
Steve Hillage and Miquette Giraudy are former members of the band Gong. | FormerMemberOf(stevehillage, gong) ∧ FormerMemberOf(miquettegiraudy, gong) |
Electric dance music bands are bands. | ∀x (ElectronicDanceMusicBand(x) → Band(x)) |
System 7 has released several club singles. | ∃x (ClubSingle(x) ∧ Release(system7, x)) |
Club singles are not singles. | ∀x (ClubSingle(x) → ¬Single(x)) |
System 7 was formed by former members of Gong. | ∃x (Form(x, system7) ∧ FormerMemberOf(x, gong)) |
System 7 has released several singles. | ∃x (Single(x) ∧ Release(system7, x)) |
System 7 is not a band. | ¬Band(system7) |
A summarization model is always faithful if it uses content from the input documents. | ∀x (Model(x) ∧ Summarization(x) ∧ OnlyUseInputDocument(x) → Faithful(x)) |
Extractive models are summarization models. | ∀x (Model(x) ∧ Extractive(x) → Model(x) ∧ Summarization(x)) |
An extractive model can only use content from the input documents. | ∀x (Model(x) ∧ Extractive(x) → OnlyUseInputDocument(x)) |
Extractive models are always faithful. | ∀x (Model(x) ∧ Extractive(x) → Faithful(x)) |
Extractive models are not always faithful. | ∃x (Model(x) ∧ Extractive(x) ∧ ¬Faithful(x)) |
If Robin's friends practice coding questions, then they are not studying to go to medical school to become a doctor. | ∀x (RobinsFriends(x) ∧ Practice(x, codingQuestion) → ¬StudyingToGoToToBecome(x, medicalSchool, doctor)) |
If Robin's friends want to work in the software engineering industry, then they practice coding questions. | ∀x (RobinsFriends(x) ∧ WantToWorkIn(x, softwareEngineeringIndustry) → PracticeCodingQuestions(x)) |
If Robin's friends enjoy healthcare fields and want to help people with medical issues, then they are studying to go to medical school to become a doctor. | ∀x (RobinsFriends(x) ∧ Enjoy(x, healthcareField) ∧ WantToHelp(x, peopleWithMedicalIssue) → StudyingToGoToToBecome(x, medicalSchool, doctor)) |
If Robin's friends grew up with parents who worked as doctors, then they enjoy healthcare fields and want to help people with medical issues. | ∀x (RobinsFriends(x) ∧ (∃y ∃z (¬(y=z) ∧ GrowUpWith(x, y) ∧ GrowUpWith(x, z) ∧ ParentOf(y, x) ∧ ParentOf(z, x) ∧ Doctor(y) ∧ Doctor(z))) → EnjoyHealthcareFields(x) ∧ WantToHelp(x, peopleWithMedicalIssue)) |
If Robin's friends study hard, then they grew up with parents who worked as doctors. | ∀x (RobinsFriends(x) ∧ StudyHard(x) → ∃y ∃z (¬(y=z) ∧ GrowUpWith(x, y) ∧ GrowUpWith(x, z) ∧ ParentOf(y, x) ∧ ParentOf(z, x) ∧ Doctor(y) ∧ Doctor(z))) |
Mark is Robin's friend. | RobinsFriends(mark) |
If Mark neither enjoys healthcare fields and wants to help people with medical issues nor grew up with parents who worked as doctors, then Mark is either a person who studies hard or grew up with parents who worked as doctors. | ¬((Enjoy(x, healthcareField) ∧ WantToHelp(mark, peopleWithMedicalIssues)) ∧ ¬(∃y ∃z (¬(y=z) ∧ GrowUpWith(x, y) ∧ GrowUpWith(x, z) ∧ ParentOf(y, x) ∧ ParentOf(z, x) ∧ Doctor(y) ∧ Doctor(z))) → StudyHard(mark) ∨ (∃y ∃z (¬(y=z) ∧ GrowUpWith(x, y) ∧ GrowUpWith(x, z) ∧ ParentOf(y, x) ∧ ParentOf(z, x) ∧ Doctor(y) ∧ Doctor(z))) |
Mark is Robin's friend and he is a person who studies hard. | RobinsFriends(mark) ∧ StudyHard(mark) |
Mark is Robin's friend and he practices coding questions and wants to work in the software engineering industry. | RobinsFriends(mark) ∧ Practice(mark, codingQuestion) ∧ WantToWorkIn(mark, softwareEngineeringIndustry) |
Mark is Robin's friend and he neither practices coding questions nor works to work in the software engineering industry. | RobinsFriends(mark) ∧ ¬(Practice(mark, codingQuestion) ∨ WantToWorkIn(mark, softwareEngineeringIndustry)) |
People who work at Jess's company and go to the spa frequently are not people who are miserly and need to save a large portion of their income. | ∀x (WorkAt(x, jesssCompany) ∧ GoToSpafrequently(x) → ¬(Miserly(x) ∧ NeedToSave(x, aLargePortionOfIncome))) |
People who work at Jess's company are either miserly and need to save a large portion of their income, or frivolously spend a lot of money. | ∀x (WorkAt(x, jesssCompany) → Miserly(x) ∧ NeedToSave(x, aLargePortionOfIncome)⊕ SpendFrivolously(x, aLotOfMoney)) |
If people who work at Jess's company frivolously spend a lot of money when they go out, then they value quality manufacturing and luxury items. | ∀x (WorkAt(x, jesssCompany) ∧ SpendFrivolously(x, aLotOfMoney) → Value(x, qualityManufacturing) ∧ Value(x, luxuryItem)) |
If people who work at Jess's company value quality manufacturing and luxury items, then they enjoy shopping for materialistic items in their free time. | ∀x (WorkAt(x, jesssCompany) ∧ Value(x, qualityManufacturing) ∧ Value(x, luxuryItem) → Enjoy(x, shopping, materialisticItem)) |
Thomas works at Jess's company. | WorkAt(thomas, jesssCompany) |
If Thomas is not miserly and needs to save a large portion of his income, then Thomas does not value quality manufacturing and luxury items. | ¬(Miserly(thomas) ∧ NeedToSave(thomas, aLargePortionOfIncome)) → ¬((Value(thomas, qualityManufacturing) ∧ Value(thomas, luxuryItem))) |
Thomas values quality manufacturing and luxury items or he is not miserly. | (Value(thomas, qualityManufacturing) ∧ Value(thomas, luxuryItem)) ∨ ¬(Miserly(x) ∧ NeedToSave(x, aLargePortionOfIncome)) |
Thomas frivolously spends a lot of money. | SpendFrivolously(thomas, aLotOfMoney) |
Thomas either enjoys shopping for materialistic items in his free time or, if he does not, then he goes to the spa frequently. | Enjoy(thomas, shopping, materialisticItem) ⊕ GoToSpaFrequently(thomas) |
If Thomas either enjoys shopping for materialistic items in his free time or, if he does not, then he goes to the spa frequently, then Thomas neither values quality manufacturing and luxury items nor goes to the spa frequently. | Enjoy(thomas, shopping, materialisticItem) ⊕ GoToSpaFrequently(thomas) → ¬((Value(x, qualityManufacturing) ∧ Value(x, luxuryItem)) ∨ GoToSpaFrequently(thomas)) |
The indie pop band Phoenix has released six albums. | AlbumsReleased(phoenix, 6) |
Phoenix's album "Wolfgang Amadeus Phoenix" sold over 500,000 copies. | Album(wolfgangamadeusphoenix) ∧ IsAlbumOf(wolfgangamadeusphoenix, phoenix) ∧ SoldOver(wolfgangamadeusphoenix, 500,000) |
A certified gold album or single is one which sold over half a million copies. | ∀x ((Album(x) ∨ Single(x)) ∧ SoldOver(x, 500,000) → CertifiedGold(x)) |
"1901" is a single from Phoenix's album "Wolfgang Amadeus Phoenix." | Single(1901) ∧ From(1901, wolfgangamadeusphoenix) ∧ By(1901, phoenix) |
Over 400,000 copies of "1901" have been sold. | SoldOver(l1901, 400,000) |
The album "Wolfgang Amadeus Phoenix" is a certified gold album. | CertifiedGold(wolfgangamAdeusPhoenix) |
The single "1901" is a certified gold single. | CertifiedGold(1901) |
Peter Parker is either a superhero or a civilian. | Superhero(peterParker) ⊕ Civilian(peterParker) |
The Hulk is a destroyer. | Destroyer(theHulk) |
The Hulk wakes up when he is angry. | Angry(theHulk) → WakesUp(theHulk) |
If the Hulk wakes up, then he will break a bridge. | WakesUp(theHulk) → Breaks(theHulk, bridge) |
Thor is a god. | God(thor) |
Thor will break a bridge when he is happy. | Happy(thor) → Breaks(thor, bridge) |
A god is not a destroyer. | ∀x (God(x) → ¬Destroyer(x)) |
Peter Parker wears a uniform when he is a superhero. | Superhero(peter) → Wears(peter, uniform) |
Peter Parker is not a civilian if a destroyer is breaking a bridge. | ∀x ((Destroyer(x) ∧ Breaks(x,bridge)) → ¬Civilian(peter)) |
If Thor is happy, the Hulk is angry. | Happy(thor) → Angry(theHulk) |
If the Hulk does not wake up, then Thor is not happy. | ¬WakesUp(theHulk) → ¬Happy(thor) |
If Thor is happy, then Peter Parker wears a uniform. | Happy(thor) → Wears(peterParker, uniform) |
If Thor is not happy, then no bridge will be broken. | ¬Happy(thor) → ¬Breaks(thor, bridge) |
Diethylcarbamazine is a medication discovered in the year 1947. | Medication(diethylcarbamazine) ∧ DiscoversIn(diethylcarbamazine, yr1947) |
Diethylcarbamazine can be used to treat river blindness. | Treats(diethylcarbamazine, riverBlindness) |
The only preferred treatment for river blindness is ivermectin. | PreferredTreatmentFor(riverBlindness, ivermectin) |
Diethylcarbamazine is not ivermectin. | ¬(Is(diethylcarbamazine, ivermectin)) |
Diethylcarbamazine is not preferred for the treatment of river blindness. | ¬(PreferredTreatmentFor(riverBlindness, diethylcarbamazine)) |
Diethylcarbamazine was often used to treat river blindness. | Treats(diethylcarbamazine, riverBlindness) |
Diethylcarbamazine is used in the treatment of filariasis. | Treats(diethylcarbamazine, filariasis) |
All prime numbers are natural numbers. | ∀x (PrimeNumber(x) → NaturalNumber(x)) |
All integers are real numbers. | ∀x (Integer(x) → RealNumber(x)) |
All real numbers are complex numbers. | ∀x (RealNumber(x) → ComplexNumber(x)) |
One is a prime number or a natural number or both. | PrimeNumber(one) ∨ NaturalNumber(one) |
If one is not a complex number, then one is a prime number and an integer. | ¬ComplexNumber(one) → (PrimeNumber(one) ∧ Integer(one)) |
One is a real number. | RealNumber(one) |
One is a prime number and a natural number. | PrimeNumber(one) ∧ NaturalNumber(one) |
One is either a prime number or a natural number. | PrimeNumber(one) ⊕ NaturalNumber(one) |
If some diseases require a medical diagnosis, then lab tests or imaging is required. | ∀x (Disease(x) ∧ Require(x, medicalDiagnosis) → RequiredFor(labTest, x) ∨ RequiredFor(imaging, x)) |
All rare diseases require a medical diagnosis. | ∀x (RareDisease(x) → Require(x, medicalDiagnosis)) |
Subsets and Splits