nl premises stringlengths 41 1.12k | fol premises stringlengths 41 1.43k | nl conclusion stringlengths 12 378 | fol conclusion stringlengths 8 426 | label stringclasses 3
values |
|---|---|---|---|---|
All people who regularly drink coffee are dependent on caffeine.
People regularly drink coffee, or they don't want to be addicted to caffeine, or both.
No one who doesn't want to be addicted to caffeine is unaware that caffeine is a drug.
Rina is either a student who is unaware that caffeine is a drug, or she is not a student and is she aware that caffeine is a drug.
Rina is either a student who is dependent on caffeine, or she is not a student and not dependent on caffeine. | ∀x (DrinkRegularly(x, coffee) → IsDependentOn(x, caffeine))
∀x (DrinkRegularly(x, coffee) ∨ (¬WantToBeAddictedTo(x, caffeine)))
∀x (¬WantToBeAddictedTo(x, caffeine) → ¬AwareThatDrug(x, caffeine))
¬(Student(rina) ⊕ ¬AwareThatDrug(rina, caffeine))
¬(IsDependentOn(rina, caffeine) ⊕ Student(rina)) | Rina doesn't want to be addicted to caffeine or is unaware that caffeine is a drug. | ¬WantToBeAddictedTo(rina, caffeine) ∨ (¬AwareThatDrug(rina, caffeine)) | True |
All people who regularly drink coffee are dependent on caffeine.
People regularly drink coffee, or they don't want to be addicted to caffeine, or both.
No one who doesn't want to be addicted to caffeine is unaware that caffeine is a drug.
Rina is either a student who is unaware that caffeine is a drug, or she is not a student and is she aware that caffeine is a drug.
Rina is either a student who is dependent on caffeine, or she is not a student and not dependent on caffeine. | ∀x (DrinkRegularly(x, coffee) → IsDependentOn(x, caffeine))
∀x (DrinkRegularly(x, coffee) ∨ (¬WantToBeAddictedTo(x, caffeine)))
∀x (¬WantToBeAddictedTo(x, caffeine) → ¬AwareThatDrug(x, caffeine))
¬(Student(rina) ⊕ ¬AwareThatDrug(rina, caffeine))
¬(IsDependentOn(rina, caffeine) ⊕ Student(rina)) | Rina eith doesn't want to be addicted to caffeine or is unaware that caffeine is a drug. | ¬WantToBeAddictedTo(rina, caffeine) ⊕ ¬AwareThatDrug(rina, caffeine) | True |
Miroslav Venhoda was a Czech choral conductor who specialized in the performance of Renaissance and Baroque music.
Any choral conductor is a musician.
Some musicians love music.
Miroslav Venhoda published a book in 1946 called Method of Studying Gregorian Chant. | Czech(miroslav) ∧ ChoralConductor(miroslav) ∧ SpecializeInPerformanceOf(miroslav, renaissanceMusic) ∧ SpecializeInPerformanceOf(miroslav, baroqueMusic)
∀x (ChoralConductor(x) → Musician(x))
∃x ∃y ((Musician(x) → Love(x, music)) ∧ (¬(x=y) ∧ Musician(y) → Love(y, music)))
PublishedBook(miroslav, methodOfStudyingGregorianChant, yr1946) | Miroslav Venhoda loved music. | Love(miroslav, music) | Uncertain |
Miroslav Venhoda was a Czech choral conductor who specialized in the performance of Renaissance and Baroque music.
Any choral conductor is a musician.
Some musicians love music.
Miroslav Venhoda published a book in 1946 called Method of Studying Gregorian Chant. | Czech(miroslav) ∧ ChoralConductor(miroslav) ∧ SpecializeInPerformanceOf(miroslav, renaissanceMusic) ∧ SpecializeInPerformanceOf(miroslav, baroqueMusic)
∀x (ChoralConductor(x) → Musician(x))
∃x ∃y ((Musician(x) → Love(x, music)) ∧ (¬(x=y) ∧ Musician(y) → Love(y, music)))
PublishedBook(miroslav, methodOfStudyingGregorianChant, yr1946) | A Czech published a book in 1946. | ∃x ∃y (Czech(x) ∧ PublishedBook(x, y, year1946)) | True |
All eels are fish.
No fish are plants.
Everything displayed in the collection is either a plant or an animal.
All multicellular animals are not bacteria.
All animals displayed in the collection are multicellular.
A sea eel is displayed in the collection.
The sea eel is an eel or an animal or not a plant. | ∀x (Eel(x) → Fish(x))
∀x (Fish(x) → ¬Plant(x))
∀x (DisplayedIn(x, collection) → Plant(x) ⊕ Animal(x))
∀x (Multicellular(x) → ¬Bacteria(x))
∀x (DisplayedIn(x, collection) ∧ Animal(x) → Multicellular(x))
DisplayedIn(seaEel, collection)
Eel(seaEel) ∨ Animal(seaEel) ∨ ¬Plant(seaEel) | The sea eel is an eel. | Eel(seaEel) | Uncertain |
All eels are fish.
No fish are plants.
Everything displayed in the collection is either a plant or an animal.
All multicellular animals are not bacteria.
All animals displayed in the collection are multicellular.
A sea eel is displayed in the collection.
The sea eel is an eel or an animal or not a plant. | ∀x (Eel(x) → Fish(x))
∀x (Fish(x) → ¬Plant(x))
∀x (DisplayedIn(x, collection) → Plant(x) ⊕ Animal(x))
∀x (Multicellular(x) → ¬Bacteria(x))
∀x (DisplayedIn(x, collection) ∧ Animal(x) → Multicellular(x))
DisplayedIn(seaEel, collection)
Eel(seaEel) ∨ Animal(seaEel) ∨ ¬Plant(seaEel) | The sea eel is bacteria. | Bacteria(seaEel) | False |
All eels are fish.
No fish are plants.
Everything displayed in the collection is either a plant or an animal.
All multicellular animals are not bacteria.
All animals displayed in the collection are multicellular.
A sea eel is displayed in the collection.
The sea eel is an eel or an animal or not a plant. | ∀x (Eel(x) → Fish(x))
∀x (Fish(x) → ¬Plant(x))
∀x (DisplayedIn(x, collection) → Plant(x) ⊕ Animal(x))
∀x (Multicellular(x) → ¬Bacteria(x))
∀x (DisplayedIn(x, collection) ∧ Animal(x) → Multicellular(x))
DisplayedIn(seaEel, collection)
Eel(seaEel) ∨ Animal(seaEel) ∨ ¬Plant(seaEel) | The sea eel is multicellular or is bacteria. | Multicellular(seaEel) ∨ Bacteria(seaEel) | True |
The Blake McFall Company Building is a building added to the National Register of Historic Places in 1990.
The Emmet Building is a five-story building in Portland, Oregon.
The Emmet Building was built in 1915.
The Emmet Building is another name for the Blake McFall Company Building.
John works at the Emmet Building. | Building(blakeMcFallCompanyBuilding) ∧ AddedToIn(blakeMcFallCompanyBuilding, theNationalRegisterOfHistoricPlaces, year1990)
Building(emmetBuilding) ∧ Five-Story(emmetBuilding) ∧ LocatedIn(emmetBuilding, portland) ∧ LocatedIn(portland, oregon)
BuiltIn(emmetBuilding, year1915)
emmetBuiling=blakeMcFallCompanyBuilding
WorkAt(john, emmetBuilding) | John started his current job in 1990. | StartCurrentJobIn(john, year1990) | Uncertain |
William Dickinson was a British politician who sat in the House of Commons
William Dickinson attended Westminster school for high school and then the University of Edinburgh.
The University of Edinburgh is a university located in the United Kingdom.
William Dickinson supported the Portland Whigs.
People who supported the Portland Whigs did not get a seat in the Parliament. | British(williamDickinson) ∧ Politician(williamDickinson) ∧ SatIn(williamDickinson, houseOfCommons)
Attended(williamDickinson, westminsterSchool) ∧ Highschool(westminsterSchool) ∧ Attended(williamDickinson, universityOfEdinburgh)
University(universityOfEdinburgh) ∧ LocatedIn(universityOfEdinburgh, unitedKingdom)
Supported(williamDickinson, portlandWhigs)
∀x (Supported(x, portlandWhigs) → ¬SatIn(x, parliament)) | William Dickinson went to schools located in the United Kingdom for both high school and university. | ∃x ∃y (Attended(williamDickinson, x) ∧ Highschool(x) ∧ LocatedIn(x, unitedKingdom) ∧ Attended(williamDickinson, y) ∧ University(y) ∧ LocatedIn(y, unitedKingdom)) | Uncertain |
William Dickinson was a British politician who sat in the House of Commons
William Dickinson attended Westminster school for high school and then the University of Edinburgh.
The University of Edinburgh is a university located in the United Kingdom.
William Dickinson supported the Portland Whigs.
People who supported the Portland Whigs did not get a seat in the Parliament. | British(williamDickinson) ∧ Politician(williamDickinson) ∧ SatIn(williamDickinson, houseOfCommons)
Attended(williamDickinson, westminsterSchool) ∧ Highschool(westminsterSchool) ∧ Attended(williamDickinson, universityOfEdinburgh)
University(universityOfEdinburgh) ∧ LocatedIn(universityOfEdinburgh, unitedKingdom)
Supported(williamDickinson, portlandWhigs)
∀x (Supported(x, portlandWhigs) → ¬SatIn(x, parliament)) | William Dickinson attended university in the United Kingdom. | ∃x (Attended(williamDickinson, x) ∧ University(x) ∧ LocatedIn(x, unitedKingdom)) | True |
William Dickinson was a British politician who sat in the House of Commons
William Dickinson attended Westminster school for high school and then the University of Edinburgh.
The University of Edinburgh is a university located in the United Kingdom.
William Dickinson supported the Portland Whigs.
People who supported the Portland Whigs did not get a seat in the Parliament. | British(williamDickinson) ∧ Politician(williamDickinson) ∧ SatIn(williamDickinson, houseOfCommons)
Attended(williamDickinson, westminsterSchool) ∧ Highschool(westminsterSchool) ∧ Attended(williamDickinson, universityOfEdinburgh)
University(universityOfEdinburgh) ∧ LocatedIn(universityOfEdinburgh, unitedKingdom)
Supported(williamDickinson, portlandWhigs)
∀x (Supported(x, portlandWhigs) → ¬SatIn(x, parliament)) | William Dickinson sat in the House of Commons. | SatIn(williamDickinson, houseOfCommons) | True |
All customers in James' family who subscribe to AMC A-List are eligible to watch three movies every week without any additional fees.
Some of the customers in James' family go to the cinema every week.
Customers in James' family subscribe to AMC A-List or HBO service.
Customers in James' family who prefer TV series will not watch TV series in cinemas.
All customers in James' family who subscribe to HBO services prefer TV series to movies.
Lily is in James' family; she watches TV series in cinemas. | ∀x ((Customer(x) ∧ In(x, jameSFamily) ∧ SubscribedTo(x, aMCAList)) → EligibleForThreeFreeMoviesEveryWeekWithoutAdditionalFees(x))
∃x ∃y (Customer(x) ∧ In(x, jameSFamily) ∧ GoToEveryWeek(x, cinema) ∧ (¬(x=y)) ∧ Customer(y) ∧ In(y, jameSFamily) ∧ GoToEveryWeek(y, cinema))
∀x (Customer(x) ∧ In(x, jameSFamily) ∧ (SubscribedTo(x, aMCAList) ∨ SubscribedTo(x, hBO)))
∀x ((Customer(x) ∧ In(x, jameSFamily) ∧ Prefer(x, tVSeries)) → (¬WatchIn(x, tV, cinema)))
∀x ((Customer(x) ∧ In(x, jameSFamily) ∧ SubscribedTo(x, hBO)) → Prefer(x, tVSeries))
Customer(lily) ∧ In(lily, jameSFamily ∧ WatchIn(lily, tV, cinema)) | Lily goes to cinemas every week. | GoToEveryWeek(lily, cinema) | Uncertain |
All customers in James' family who subscribe to AMC A-List are eligible to watch three movies every week without any additional fees.
Some of the customers in James' family go to the cinema every week.
Customers in James' family subscribe to AMC A-List or HBO service.
Customers in James' family who prefer TV series will not watch TV series in cinemas.
All customers in James' family who subscribe to HBO services prefer TV series to movies.
Lily is in James' family; she watches TV series in cinemas. | ∀x ((Customer(x) ∧ In(x, jameSFamily) ∧ SubscribedTo(x, aMCAList)) → EligibleForThreeFreeMoviesEveryWeekWithoutAdditionalFees(x))
∃x ∃y (Customer(x) ∧ In(x, jameSFamily) ∧ GoToEveryWeek(x, cinema) ∧ (¬(x=y)) ∧ Customer(y) ∧ In(y, jameSFamily) ∧ GoToEveryWeek(y, cinema))
∀x (Customer(x) ∧ In(x, jameSFamily) ∧ (SubscribedTo(x, aMCAList) ∨ SubscribedTo(x, hBO)))
∀x ((Customer(x) ∧ In(x, jameSFamily) ∧ Prefer(x, tVSeries)) → (¬WatchIn(x, tV, cinema)))
∀x ((Customer(x) ∧ In(x, jameSFamily) ∧ SubscribedTo(x, hBO)) → Prefer(x, tVSeries))
Customer(lily) ∧ In(lily, jameSFamily ∧ WatchIn(lily, tV, cinema)) | Lily does not go to cinemas every week. | ¬GoToEveryWeek(lily, cinema) | Uncertain |
All customers in James' family who subscribe to AMC A-List are eligible to watch three movies every week without any additional fees.
Some of the customers in James' family go to the cinema every week.
Customers in James' family subscribe to AMC A-List or HBO service.
Customers in James' family who prefer TV series will not watch TV series in cinemas.
All customers in James' family who subscribe to HBO services prefer TV series to movies.
Lily is in James' family; she watches TV series in cinemas. | ∀x ((Customer(x) ∧ In(x, jameSFamily) ∧ SubscribedTo(x, aMCAList)) → EligibleForThreeFreeMoviesEveryWeekWithoutAdditionalFees(x))
∃x ∃y (Customer(x) ∧ In(x, jameSFamily) ∧ GoToEveryWeek(x, cinema) ∧ (¬(x=y)) ∧ Customer(y) ∧ In(y, jameSFamily) ∧ GoToEveryWeek(y, cinema))
∀x (Customer(x) ∧ In(x, jameSFamily) ∧ (SubscribedTo(x, aMCAList) ∨ SubscribedTo(x, hBO)))
∀x ((Customer(x) ∧ In(x, jameSFamily) ∧ Prefer(x, tVSeries)) → (¬WatchIn(x, tV, cinema)))
∀x ((Customer(x) ∧ In(x, jameSFamily) ∧ SubscribedTo(x, hBO)) → Prefer(x, tVSeries))
Customer(lily) ∧ In(lily, jameSFamily ∧ WatchIn(lily, tV, cinema)) | If Lily does not both go to cinemas every week and subscribe to HBO service, then Lily is either available to watch 3 movies every week without any additional fees or she prefers TV more. | (GoToEveryWeek(lily, cinema) ∧ SubscribedTo(lily, hBO) → (EligibleForThreeFreeMoviesEveryWeek(lily) ⊕ Prefer(lily, tVSeries))) | True |
All customers in James' family who subscribe to AMC A-List are eligible to watch three movies every week without any additional fees.
Some of the customers in James' family go to the cinema every week.
Customers in James' family subscribe to AMC A-List or HBO service.
Customers in James' family who prefer TV series will not watch TV series in cinemas.
All customers in James' family who subscribe to HBO services prefer TV series to movies.
Lily is in James' family; she watches TV series in cinemas. | ∀x ((Customer(x) ∧ In(x, jameSFamily) ∧ SubscribedTo(x, aMCAList)) → EligibleForThreeFreeMoviesEveryWeekWithoutAdditionalFees(x))
∃x ∃y (Customer(x) ∧ In(x, jameSFamily) ∧ GoToEveryWeek(x, cinema) ∧ (¬(x=y)) ∧ Customer(y) ∧ In(y, jameSFamily) ∧ GoToEveryWeek(y, cinema))
∀x (Customer(x) ∧ In(x, jameSFamily) ∧ (SubscribedTo(x, aMCAList) ∨ SubscribedTo(x, hBO)))
∀x ((Customer(x) ∧ In(x, jameSFamily) ∧ Prefer(x, tVSeries)) → (¬WatchIn(x, tV, cinema)))
∀x ((Customer(x) ∧ In(x, jameSFamily) ∧ SubscribedTo(x, hBO)) → Prefer(x, tVSeries))
Customer(lily) ∧ In(lily, jameSFamily ∧ WatchIn(lily, tV, cinema)) | If Lily is available to watch 3 movies every week without any additional fees and she watches TV series in cinemas, then she goes to cinemas every week and prefers TV series more. | (EligibleForThreeFreeMoviesEveryWeekWithoutAdditionalFees(lily) ∧ WatchIn(lily, tV, cinema) → (GoToEveryWeek(lily, cinema) ∧ Prefer(lily, tVSeries))) | False |
A La Liga soccer team ranks higher than another La Liga soccer team if it receives more points.
If there are two La Liga soccer teams and neither has more points than the other, then the team which receives more points from the games between the two teams ranks higher.
Real Madrid and Barcelona are both La Liga soccer teams.
Real Madrid received more points than Barcelona.
Neither Real Madrid nor Barcelona received more points from the games between them. | ∀x ∀y (LaLigaSoccerTeam(x) ∧ LaLigaSoccerTeam(y) ∧ MorePoints(x, y) → RankHigherThan(x, y))
∀x ∀y (LaLigaSoccerTeam(x) ∧ LaLigaSoccerTeam(y) ∧ ¬MorePoints(x, y) ∧ ¬MorePoints(y, x) ∧ MorePointsInGameBetween(x, y) → RankHigherThan(x, y))
LaLigaSoccerTeam(realMadrid) ∧ LaLigaSoccerTeam(barcelona)
MorePoints(realMadrid, barcelona)
¬MorePointsInGameBetween(realMadrid, barcelona) ∧ ¬MorePointsInGameBetween(barcelona, realMadrid) | Real Madrid ranks higher than Barcelona. | RankHigherThan(realMadrid, barcelona) | True |
Lawton Park is a neighborhood in Seattle.
All citizens of Lawton Park use the zip code 98199.
Tom is a citizen of Lawton Park.
Daniel uses the zip code 98199. | NeighbourhoodIn(lawtonPark, seattle)
∀x (ResidentOf(x, lawtonPark) → UseZipCode(x, num98199))
ResidentOf(tom, lawtonPark)
UseZipCode(daniel, num98199) | Tom uses the zip code 98199. | UseZipCode(tom, num98199) | True |
Lawton Park is a neighborhood in Seattle.
All citizens of Lawton Park use the zip code 98199.
Tom is a citizen of Lawton Park.
Daniel uses the zip code 98199. | NeighbourhoodIn(lawtonPark, seattle)
∀x (ResidentOf(x, lawtonPark) → UseZipCode(x, num98199))
ResidentOf(tom, lawtonPark)
UseZipCode(daniel, num98199) | Tom doesn't use the zip code 98199. | ¬UseZipCode(tom, num98199) | False |
Lawton Park is a neighborhood in Seattle.
All citizens of Lawton Park use the zip code 98199.
Tom is a citizen of Lawton Park.
Daniel uses the zip code 98199. | NeighbourhoodIn(lawtonPark, seattle)
∀x (ResidentOf(x, lawtonPark) → UseZipCode(x, num98199))
ResidentOf(tom, lawtonPark)
UseZipCode(daniel, num98199) | Tom is a citizen of Washington. | ResidentOf(tom, washington) | Uncertain |
Lawton Park is a neighborhood in Seattle.
All citizens of Lawton Park use the zip code 98199.
Tom is a citizen of Lawton Park.
Daniel uses the zip code 98199. | NeighbourhoodIn(lawtonPark, seattle)
∀x (ResidentOf(x, lawtonPark) → UseZipCode(x, num98199))
ResidentOf(tom, lawtonPark)
UseZipCode(daniel, num98199) | Daniel is a citizen of Lawton Park. | ResidentOf(daniel, lawtonPark) | Uncertain |
If a legislator is found guilty of stealing government funds, they will be suspended from office.
Tiffany T. Alston was a legislator in Maryland's House of Delegates from 2011 to 2013.
Tiffany T. Alston was found guilty of stealing government funds in 2012. | ∀x ((Legislator(x) ∧ StealsFunds(x)) → Suspended(x))
Legislator(tiffanyTAlston)
StealsFunds(tiffanyTAlston) ∧ StealsFundsInYr(tiffanyTAlston, yr2012) | Tiffany T. Alston was suspended from the Maryland House of Delegates. | Suspended(tiffanyTAlston) | True |
If a legislator is found guilty of stealing government funds, they will be suspended from office.
Tiffany T. Alston was a legislator in Maryland's House of Delegates from 2011 to 2013.
Tiffany T. Alston was found guilty of stealing government funds in 2012. | ∀x ((Legislator(x) ∧ StealsFunds(x)) → Suspended(x))
Legislator(tiffanyTAlston)
StealsFunds(tiffanyTAlston) ∧ StealsFundsInYr(tiffanyTAlston, yr2012) | Tiffany T. Alston was not suspended from the Maryland House of Delegates. | ¬Suspended(tiffanyTAlston) | False |
If a legislator is found guilty of stealing government funds, they will be suspended from office.
Tiffany T. Alston was a legislator in Maryland's House of Delegates from 2011 to 2013.
Tiffany T. Alston was found guilty of stealing government funds in 2012. | ∀x ((Legislator(x) ∧ StealsFunds(x)) → Suspended(x))
Legislator(tiffanyTAlston)
StealsFunds(tiffanyTAlston) ∧ StealsFundsInYr(tiffanyTAlston, yr2012) | Tiffany T. Alston went to prison for stealing government funds. | Prison(tiffanyTAlston) | Uncertain |
Some fish stings people.
Stonefish is a fish.
Stonefish stings when stepped on.
If a stonefish stings someone and they are not treated, it can cause death to them.
To treat stonefish stings, apply heat to the affected area or use an antivenom. | ∃x ∃y (Fish(x) → Sting(x,y))
Fish(stonefish)
∀x (SteppedOnBy(stonefish, x) → Sting(stonefish, x))
∀x (Sting(stonefish, x) ∧ ¬Treated(x) → CauseDeathTo(stonefish, x))
∀x (Sting(stonefish, x) ∧ (ApplyHeatTo(x) ∨ UseAntivenomOn(x)) → Treated(x)) | If a stonefish stings you and you don’t use an antivenom, it can cause death to you. | ∀x (Sting(stonefish, x) ∧ ¬UseAntivenomOn(x) → CauseDeathTo(stonefish, x)) | Uncertain |
Some fish stings people.
Stonefish is a fish.
Stonefish stings when stepped on.
If a stonefish stings someone and they are not treated, it can cause death to them.
To treat stonefish stings, apply heat to the affected area or use an antivenom. | ∃x ∃y (Fish(x) → Sting(x,y))
Fish(stonefish)
∀x (SteppedOnBy(stonefish, x) → Sting(stonefish, x))
∀x (Sting(stonefish, x) ∧ ¬Treated(x) → CauseDeathTo(stonefish, x))
∀x (Sting(stonefish, x) ∧ (ApplyHeatTo(x) ∨ UseAntivenomOn(x)) → Treated(x)) | Stings of some fish can cause death if not treated. | ∃x ∃y (Fish(x) ∧ Sting(x, y) ∧ ¬Treated(y) → CauseDeathTo(x, y)) | True |
Some fish stings people.
Stonefish is a fish.
Stonefish stings when stepped on.
If a stonefish stings someone and they are not treated, it can cause death to them.
To treat stonefish stings, apply heat to the affected area or use an antivenom. | ∃x ∃y (Fish(x) → Sting(x,y))
Fish(stonefish)
∀x (SteppedOnBy(stonefish, x) → Sting(stonefish, x))
∀x (Sting(stonefish, x) ∧ ¬Treated(x) → CauseDeathTo(stonefish, x))
∀x (Sting(stonefish, x) ∧ (ApplyHeatTo(x) ∨ UseAntivenomOn(x)) → Treated(x)) | If you step on a stonefish and apply heat to the affected area, it can cause death to you. | ∀x (SteppedOnBy(stonefish, x) ∧ ApplyHeatTo(x) → CauseDeathTo(stonefish, x)) | Uncertain |
Some monitors made by LG have a type-c port.
Monitors that have a type-c port were not made before 2010.
All monitors in the library are made before 2010.
The L-2021 monitor is either used in the library or has a type-c port.
The L-2021 monitor is either both produced before 2010 and made by LG, or neither is true. | ∃x (Monitor(x) ∧ ProducedBy(x, lG) ∧ Have(x, typeCPort) ∧ (¬(x=y)) ∧ Monitor(y) ∧ ProducedBy(y, lG) ∧ Have(y, typeCPort))
∀x (Have(x, typeCPort) → ¬ProducedBefore(x, yr2010))
∀x ((Monitor(x) ∧ In(x, library)) → ProducedBefore(x, yr2010))
Monitor(l-2021) ∧ (In(l-2021, library) ⊕ Have(l-2021, typeCPort))
¬(ProducedBefore(l-2021, yr2010) ⊕ ProducedBy(l-2021, lG)) | The monitor L-2021 is in the library. | In(l-2021, library) | Uncertain |
Some monitors made by LG have a type-c port.
Monitors that have a type-c port were not made before 2010.
All monitors in the library are made before 2010.
The L-2021 monitor is either used in the library or has a type-c port.
The L-2021 monitor is either both produced before 2010 and made by LG, or neither is true. | ∃x (Monitor(x) ∧ ProducedBy(x, lG) ∧ Have(x, typeCPort) ∧ (¬(x=y)) ∧ Monitor(y) ∧ ProducedBy(y, lG) ∧ Have(y, typeCPort))
∀x (Have(x, typeCPort) → ¬ProducedBefore(x, yr2010))
∀x ((Monitor(x) ∧ In(x, library)) → ProducedBefore(x, yr2010))
Monitor(l-2021) ∧ (In(l-2021, library) ⊕ Have(l-2021, typeCPort))
¬(ProducedBefore(l-2021, yr2010) ⊕ ProducedBy(l-2021, lG)) | The monitor L-2021 is either in the library or produced by LG. | In(l-2021, library) ⊕ ProducedBy(l-2021, lG) | False |
Some monitors made by LG have a type-c port.
Monitors that have a type-c port were not made before 2010.
All monitors in the library are made before 2010.
The L-2021 monitor is either used in the library or has a type-c port.
The L-2021 monitor is either both produced before 2010 and made by LG, or neither is true. | ∃x (Monitor(x) ∧ ProducedBy(x, lG) ∧ Have(x, typeCPort) ∧ (¬(x=y)) ∧ Monitor(y) ∧ ProducedBy(y, lG) ∧ Have(y, typeCPort))
∀x (Have(x, typeCPort) → ¬ProducedBefore(x, yr2010))
∀x ((Monitor(x) ∧ In(x, library)) → ProducedBefore(x, yr2010))
Monitor(l-2021) ∧ (In(l-2021, library) ⊕ Have(l-2021, typeCPort))
¬(ProducedBefore(l-2021, yr2010) ⊕ ProducedBy(l-2021, lG)) | The L-2021 monitor either has a type-c port or is produced by LG. | Have(l-2021, typeCPort) ⊕ ProducedBy(l-2021, lG) | True |
Some monitors made by LG have a type-c port.
Monitors that have a type-c port were not made before 2010.
All monitors in the library are made before 2010.
The L-2021 monitor is either used in the library or has a type-c port.
The L-2021 monitor is either both produced before 2010 and made by LG, or neither is true. | ∃x (Monitor(x) ∧ ProducedBy(x, lG) ∧ Have(x, typeCPort) ∧ (¬(x=y)) ∧ Monitor(y) ∧ ProducedBy(y, lG) ∧ Have(y, typeCPort))
∀x (Have(x, typeCPort) → ¬ProducedBefore(x, yr2010))
∀x ((Monitor(x) ∧ In(x, library)) → ProducedBefore(x, yr2010))
Monitor(l-2021) ∧ (In(l-2021, library) ⊕ Have(l-2021, typeCPort))
¬(ProducedBefore(l-2021, yr2010) ⊕ ProducedBy(l-2021, lG)) | If the monitor L-2021 is either produced by LG and produced before 2010 or neither produced by LG nor produced before 2010, then L-2021 is either in the library or produced by LG. | ¬(ProducedBefore(l-2021, year2010) ⊕ ProducedBy(l-2021, lG) → (In(l-2021, library) ⊕ ProducedBy(l-2021, lG))) | False |
Everything is either outside the solar system or in the solar system.
Nothing outside the solar system has the Sun as its star.
Everything in the solar system is gravitationally bound by the Sun.
No planets gravitationally bound by the Sun are rogue planets.
All orphan planets are rogue planets.
If PSO J318.5−22 is not both a rogue planet and a planet gravitationally bound by the Sun, then it is a rogue planet. | ∀x (Outside(x, solarSystem) ⊕ In(x, solarSystem))
∀x (Outside(x, solarSystem) → ¬SunAs(x, star))
∀x (In(x, solarSystem) → BoundBy(x, sun, gravitationally))
∀x (Planet(x) ∧ BoundBy(x, sun, gravitationally) → ¬(Planet(x) ∧ Rogue(x)))
∀x (Planet(x) ∧ Orphan(x) → Planet(x) ∧ Rogue(x))
¬(Planet(pSOJ318.5-22) ∧ Rogue(pSOJ318.5-22) ∧ BoundBy(pSOJ318.5-22, sun, gravitationally)) → (Planet(pSOJ318.5-22) ∧ Rogue(pSOJ318.5-22)) | PSO J318.5−22 is an orphan planet. | Planet(pSOJ318.5-22) ∧ Orphan(pSOJ318.5-22) | Uncertain |
Sam is doing a project.
A project is written either in C++ or Python.
If Sam does a project written in Python, he will not use a Mac.
Sam is using a Mac.
If Sam uses a Mac, he will play a song.
If a song is not titled "Perfect," Sam will never play it. | ∃x (Project(x) ∧ Do(sam, x))
∀x (Project(x) → (WrittenIn(x, cplusplus) ⊕ WrittenIn(x, python)))
∀x (Project(x) ∧ WrittenIn(x, python) ∧ Do(sam, x) → ¬Use(sam, mac))
Use(sam, mac)
∃x (Use(sam, mac) ∧ Song(x) → Play(sam, sam))
∀x (Song(x) ∧ Play(sam, x) → Titled(x, perfect)) | The song Sam is playing is titled "Perfect". | ∀x (Song(x) ∧ Play(sam, x) ∧ Titled(x, perfect)) | Uncertain |
Sam is doing a project.
A project is written either in C++ or Python.
If Sam does a project written in Python, he will not use a Mac.
Sam is using a Mac.
If Sam uses a Mac, he will play a song.
If a song is not titled "Perfect," Sam will never play it. | ∃x (Project(x) ∧ Do(sam, x))
∀x (Project(x) → (WrittenIn(x, cplusplus) ⊕ WrittenIn(x, python)))
∀x (Project(x) ∧ WrittenIn(x, python) ∧ Do(sam, x) → ¬Use(sam, mac))
Use(sam, mac)
∃x (Use(sam, mac) ∧ Song(x) → Play(sam, sam))
∀x (Song(x) ∧ Play(sam, x) → Titled(x, perfect)) | If a song is titled "Perfect", Sam will play it. | ∀x (Titled(x, perfect) → Play(sam, x)) | Uncertain |
All rabbits have fur
Some pets are rabbits. | ∀x (Rabbit(x) → Have(x, fur))
∃x (Pet(x) ∧ Rabbit(x)) | Some pets do not have fur. | ∃x ∃y (Pet(x) ∧ Pet(y) ∧ ¬Have(x, fur) ∧ ¬Have(y, fur)) | Uncertain |
Ordinary is an unincorporated community.
Located within Elliot County, Ordinary is on Kentucky Route 32.
Ordinary is located northwest of Sandy Hook. | UnincorporatedCommunity(ordinary)
LocatedIn(ordinary, elliotCounty) ∧ On(ordinary, kentuckyRoute32)
LocatedNorthwestOf(ordinary, sandyHook) | There is an unincorporated community located in Elliot County. | ∃x (UnincorporatedCommunity(x) ∧ LocatedIn(x, elliotCounty)) | True |
All young adults at the event like independence.
All college students at the event are young adults.
All Yale students at the event are college students.
Everyone at the event is a Yale student or a Harvard student.
All Harvard students at the event are diligent.
Susan is at the event, and if Susan is a Harvard student, then she is a young adult.
If Susan is a Yale student, then she does not like independence. | ∀x (At(x, event) ∧ YoungAdult(x) → Like(x, independence))
∀x (At(x, event) ∧ CollegeStudent(x) → YoungAdult(x))
∀x (At(x, event) ∧ YaleStudent(x) → CollegeStudent(x))
∀x (At(x, event) → (YaleStudent(x) ⊕ HarvardStudent(x)))
∀x (At(x, event) ∧ HarvardStudent(x) → Diligent(x))
At(susan, event) ∧ (HarvardStudent(susan) → YoungAdult(susan))
YaleStudent(susan) → ¬Like(susan, independence) | Susan is a college student. | CollegeStudent(susan) | Uncertain |
All young adults at the event like independence.
All college students at the event are young adults.
All Yale students at the event are college students.
Everyone at the event is a Yale student or a Harvard student.
All Harvard students at the event are diligent.
Susan is at the event, and if Susan is a Harvard student, then she is a young adult.
If Susan is a Yale student, then she does not like independence. | ∀x (At(x, event) ∧ YoungAdult(x) → Like(x, independence))
∀x (At(x, event) ∧ CollegeStudent(x) → YoungAdult(x))
∀x (At(x, event) ∧ YaleStudent(x) → CollegeStudent(x))
∀x (At(x, event) → (YaleStudent(x) ⊕ HarvardStudent(x)))
∀x (At(x, event) ∧ HarvardStudent(x) → Diligent(x))
At(susan, event) ∧ (HarvardStudent(susan) → YoungAdult(susan))
YaleStudent(susan) → ¬Like(susan, independence) | Susan likes independence and is diligent. | Like(susan, independence) ∧ Diligent(susan) | True |
All young adults at the event like independence.
All college students at the event are young adults.
All Yale students at the event are college students.
Everyone at the event is a Yale student or a Harvard student.
All Harvard students at the event are diligent.
Susan is at the event, and if Susan is a Harvard student, then she is a young adult.
If Susan is a Yale student, then she does not like independence. | ∀x (At(x, event) ∧ YoungAdult(x) → Like(x, independence))
∀x (At(x, event) ∧ CollegeStudent(x) → YoungAdult(x))
∀x (At(x, event) ∧ YaleStudent(x) → CollegeStudent(x))
∀x (At(x, event) → (YaleStudent(x) ⊕ HarvardStudent(x)))
∀x (At(x, event) ∧ HarvardStudent(x) → Diligent(x))
At(susan, event) ∧ (HarvardStudent(susan) → YoungAdult(susan))
YaleStudent(susan) → ¬Like(susan, independence) | Susan is not both diligent and likes independence. | ¬(Like(susan, independence) ∧ Diligent(susan)) | False |
Vic DiCara plays guitar and bass.
The only style of music Vic DiCara plays is punk music.
Vic DiCara played in the band Inside Out. | Play(vicDicara, guitar) ∧ Play(vicDicara, bass)
∀x (Music(vicDicara, x) → ¬(x=punk))
Band(vicDicara, insideOut) | Inside Out was a punk band. | Music(insideOut, punk) | Uncertain |
Vic DiCara plays guitar and bass.
The only style of music Vic DiCara plays is punk music.
Vic DiCara played in the band Inside Out. | Play(vicDicara, guitar) ∧ Play(vicDicara, bass)
∀x (Music(vicDicara, x) → ¬(x=punk))
Band(vicDicara, insideOut) | A musician from Inside Out plays bass. | ∃x (Band(x, insideOut) ∧ Play(x, bass)) | True |
All professional athletes spend most of their time on sports.
All Olympic gold medal winners are professional athletes.
No full-time scientists spend the majority of their time on sports.
All Nobel physics laureates are full-time scientists.
Amy spends the most time on sports, or Amy is an Olympic gold medal winner.
If Amy is not a Nobel physics laureate, then Amy is not an Olympic gold medal winner. | ∀x (ProfessionalAthlete(x) → SpendOn(x, mostOfTheirTime, sports))
∀x (OlympicGoldMedalWinner(x) → ProfessionalAthlete(x))
∀x (FullTimeScientist(x) → ¬SpendOn(x, mostOfTheirTime, sports))
∀x (NobelPhysicsLaureate(x) → FullTimeScientist(x))
SpendOn(amy, mostOfTheirTime, sports) ∨ OlympicGoldMedalWinner(amy)
¬NobelPhysicsLaureate(amy) → ¬OlympicGoldMedalWinner(amy) | Amy is a professional athlete. | ProfessionalAthlete(amy) | Uncertain |
All professional athletes spend most of their time on sports.
All Olympic gold medal winners are professional athletes.
No full-time scientists spend the majority of their time on sports.
All Nobel physics laureates are full-time scientists.
Amy spends the most time on sports, or Amy is an Olympic gold medal winner.
If Amy is not a Nobel physics laureate, then Amy is not an Olympic gold medal winner. | ∀x (ProfessionalAthlete(x) → SpendOn(x, mostOfTheirTime, sports))
∀x (OlympicGoldMedalWinner(x) → ProfessionalAthlete(x))
∀x (FullTimeScientist(x) → ¬SpendOn(x, mostOfTheirTime, sports))
∀x (NobelPhysicsLaureate(x) → FullTimeScientist(x))
SpendOn(amy, mostOfTheirTime, sports) ∨ OlympicGoldMedalWinner(amy)
¬NobelPhysicsLaureate(amy) → ¬OlympicGoldMedalWinner(amy) | Amy is neither a full-time scientist nor an Olympic gold medal winner. | ¬(FullTimeScientist(amy) ∨ OlympicGoldMedalWinner(amy)) | True |
All professional athletes spend most of their time on sports.
All Olympic gold medal winners are professional athletes.
No full-time scientists spend the majority of their time on sports.
All Nobel physics laureates are full-time scientists.
Amy spends the most time on sports, or Amy is an Olympic gold medal winner.
If Amy is not a Nobel physics laureate, then Amy is not an Olympic gold medal winner. | ∀x (ProfessionalAthlete(x) → SpendOn(x, mostOfTheirTime, sports))
∀x (OlympicGoldMedalWinner(x) → ProfessionalAthlete(x))
∀x (FullTimeScientist(x) → ¬SpendOn(x, mostOfTheirTime, sports))
∀x (NobelPhysicsLaureate(x) → FullTimeScientist(x))
SpendOn(amy, mostOfTheirTime, sports) ∨ OlympicGoldMedalWinner(amy)
¬NobelPhysicsLaureate(amy) → ¬OlympicGoldMedalWinner(amy) | If Amy is not an Olympic gold medal winner, then Amy is a Nobel physics laureate. | ¬OlympicGoldMedalWinner(amy) → NobelPhysicsLaureate(amy) | False |
All red fruits that grow in Ben's yard contain some Vitamin C.
All apples that grow in Ben's yard are red fruits.
All fruits that grow in Ben's yard and contain some Vitamin C are healthy.
No fruits that grow in Ben's yard and are healthy are on a warning list.
The cherries grow in Ben's yard.
If cherries are not apples and are not healthy, then they are red fruits. | ∀x ((GrownIn(x, benSYard) ∧ RedFruit(x)) → Contain(x, vitaminC))
∀x (GrownIn(x, benSYard) ∧ Is(x, apple) → RedFruit(x))
∀x ((GrownIn(x, benSYard) ∧ Contain(x, vitaminC)) → healthy(x))
∀x ((GrownIn(x, benSYard) ∧ Healthy(x)) → ¬On(x, warningList))
GrownIn(cherry, benSYard)
¬(Healthy(cherry) ∧ Is(cherry, apple)) → RedFruit(cherry) | The cherries either contain some amount of vitamin C or are on a warning list. | Contain(cherry, vitaminC) ⊕ On(cherry, warningList) | True |
All red fruits that grow in Ben's yard contain some Vitamin C.
All apples that grow in Ben's yard are red fruits.
All fruits that grow in Ben's yard and contain some Vitamin C are healthy.
No fruits that grow in Ben's yard and are healthy are on a warning list.
The cherries grow in Ben's yard.
If cherries are not apples and are not healthy, then they are red fruits. | ∀x ((GrownIn(x, benSYard) ∧ RedFruit(x)) → Contain(x, vitaminC))
∀x (GrownIn(x, benSYard) ∧ Is(x, apple) → RedFruit(x))
∀x ((GrownIn(x, benSYard) ∧ Contain(x, vitaminC)) → healthy(x))
∀x ((GrownIn(x, benSYard) ∧ Healthy(x)) → ¬On(x, warningList))
GrownIn(cherry, benSYard)
¬(Healthy(cherry) ∧ Is(cherry, apple)) → RedFruit(cherry) | The cherries are either on a warning list or are red. | On(cherry, warningList) ⊕ RedFruit(cherry) | True |
Everyone working at Meta has a high income.
A person with a high income will not take a bus to their destination.
People will either take a bus or drive to their destination.
Everyone who has a car will choose to drive to their destination.
No students drive to their destination.
James has a car or works at Meta. | ∀x (WorkAt(x, meta) → HighIncome(x))
∀x (HighIncome(x) → ¬MeansToDestination(x, bus))
∀x (MeansToDestination(x, bus) ⊕ MeansToDestination(x, drive))
∀x (HaveCar(x) → MeansToDestination(x, drive))
∀x (Student(x) → ¬ MeansToDestination(x, drive))
HaveCar(james) ∨ WorkAt(james, meta) | James has a high income. | HighIncome(james) | Uncertain |
Everyone working at Meta has a high income.
A person with a high income will not take a bus to their destination.
People will either take a bus or drive to their destination.
Everyone who has a car will choose to drive to their destination.
No students drive to their destination.
James has a car or works at Meta. | ∀x (WorkAt(x, meta) → HighIncome(x))
∀x (HighIncome(x) → ¬MeansToDestination(x, bus))
∀x (MeansToDestination(x, bus) ⊕ MeansToDestination(x, drive))
∀x (HaveCar(x) → MeansToDestination(x, drive))
∀x (Student(x) → ¬ MeansToDestination(x, drive))
HaveCar(james) ∨ WorkAt(james, meta) | James does not have a high income. | ¬HighIncome(james) | Uncertain |
Everyone working at Meta has a high income.
A person with a high income will not take a bus to their destination.
People will either take a bus or drive to their destination.
Everyone who has a car will choose to drive to their destination.
No students drive to their destination.
James has a car or works at Meta. | ∀x (WorkAt(x, meta) → HighIncome(x))
∀x (HighIncome(x) → ¬MeansToDestination(x, bus))
∀x (MeansToDestination(x, bus) ⊕ MeansToDestination(x, drive))
∀x (HaveCar(x) → MeansToDestination(x, drive))
∀x (Student(x) → ¬ MeansToDestination(x, drive))
HaveCar(james) ∨ WorkAt(james, meta) | James is a student. | Student(james) | False |
Everyone working at Meta has a high income.
A person with a high income will not take a bus to their destination.
People will either take a bus or drive to their destination.
Everyone who has a car will choose to drive to their destination.
No students drive to their destination.
James has a car or works at Meta. | ∀x (WorkAt(x, meta) → HighIncome(x))
∀x (HighIncome(x) → ¬MeansToDestination(x, bus))
∀x (MeansToDestination(x, bus) ⊕ MeansToDestination(x, drive))
∀x (HaveCar(x) → MeansToDestination(x, drive))
∀x (Student(x) → ¬ MeansToDestination(x, drive))
HaveCar(james) ∨ WorkAt(james, meta) | James drives to his destination or he is a student. | MeansToDestination(james, drive) ∨ Student(james) | True |
Everyone working at Meta has a high income.
A person with a high income will not take a bus to their destination.
People will either take a bus or drive to their destination.
Everyone who has a car will choose to drive to their destination.
No students drive to their destination.
James has a car or works at Meta. | ∀x (WorkAt(x, meta) → HighIncome(x))
∀x (HighIncome(x) → ¬MeansToDestination(x, bus))
∀x (MeansToDestination(x, bus) ⊕ MeansToDestination(x, drive))
∀x (HaveCar(x) → MeansToDestination(x, drive))
∀x (Student(x) → ¬ MeansToDestination(x, drive))
HaveCar(james) ∨ WorkAt(james, meta) | James either drives to their destination or is a student. | MeansToDestination(james, drive) ⊕ Student(james) | True |
Everyone working at Meta has a high income.
A person with a high income will not take a bus to their destination.
People will either take a bus or drive to their destination.
Everyone who has a car will choose to drive to their destination.
No students drive to their destination.
James has a car or works at Meta. | ∀x (WorkAt(x, meta) → HighIncome(x))
∀x (HighIncome(x) → ¬MeansToDestination(x, bus))
∀x (MeansToDestination(x, bus) ⊕ MeansToDestination(x, drive))
∀x (HaveCar(x) → MeansToDestination(x, drive))
∀x (Student(x) → ¬ MeansToDestination(x, drive))
HaveCar(james) ∨ WorkAt(james, meta) | If James either drives to his destination or is a student, then he has a high income and is a student. | (MeansToDestination(james, drive) ⊕ Student(james) → (HighIncome(james) ∧ Student(james))) | False |
Everyone at the business conference is either an investor or an entrepreneur.
None of those at the business conference who enjoy the opportunity of starting a business prefer a planned economy.
All entrepreneurs at the business conference enjoy the opportunity of starting a business.
Everyone at the business conference who enjoys state ownership of means of production prefers a planned economy.
Everyone at the business conference who is an ardent communist prefers state ownership of the means of production.
Ho is at the business conference and prefers state ownership of the means of production. | ∀x (At(x, businessConference) → (Investor(x) ⊕ Entrepreneur(x)))
∀x ((At(x, businessConference) ∧ Enjoy(x, opportunityOfStartingOwnBusiness)) → ¬Prefer(x, plannedEconomy))
∀x ((At(x, businessConference) ∧ Entrepreneur(x)) → Enjoy(x, opportunityOfStartingOwnBusiness))
∀x ((At(x, businessConference) ∧ Enjoy(x, stateOwnershipOfMeansOfProduction)) → Prefer(x, plannedEconomy))
∀x ((At(x, businessConference) ∧ ArdentCommunist(x)) → Prefer(x, stateOwnershipOfMeansOfProduction))
At(ho, businessConference) ∧ Prefer(ho, stateOwnershipOfMeansOfProduction) | Ho is not an ardent communist. | ¬ArdentCommunist(ho) | Uncertain |
No television stars are certified public accountants.
All certified public accountants have good business sense. | ∀x (TelevisionStar(x) → ¬CertifiedPublicAccoutant(x))
∀x (CertifiedPublicAccoutant(x) → Have(x, goodBusinessSense)) | All television stars have good business sense. | ∀x (TelevisionStar(x) → Have(x, goodBusinessSense)) | Uncertain |
Some students in the class who are good at math are also good at chemistry.
All students in the class who are good at chemistry enjoy conducting experiments.
All students in the class that enjoy conducting experiments are good at planning.
None of the students who are good at planning failed the class.
James is a student in the class; he is either good at chemistry and failed the class, or bad at chemistry and passed the class. | ∃x ∃y (StudentInTheClass(x) ∧ GoodAt(x, math) ∧ GoodAt(x, chemistry) ∧ (¬(x=y)) ∧ StudentInTheClass(y) ∧ GoodAt(y, math) ∧ GoodAt(y, chemistry))
∀x ((StudentInTheClass(x) ∧ GoodAt(x, chemistry)) → Enjoy(x, conductingExperiment))
∀x ((StudentInTheClass(x) ∧ Enjoy(x, conductingExperiment)) → GoodAt(x, planning))
∀x ((StudentInTheClass(x) ∧ GoodAt(x, planning)) → ¬Failed(x, theClass))
StudentInTheClass(james) ∧ (¬(GoodAt(james, chemistry) ⊕ Failed(james, theClass))) | James is good at planning. | GoodAt(james, planning) | Uncertain |
Some students in the class who are good at math are also good at chemistry.
All students in the class who are good at chemistry enjoy conducting experiments.
All students in the class that enjoy conducting experiments are good at planning.
None of the students who are good at planning failed the class.
James is a student in the class; he is either good at chemistry and failed the class, or bad at chemistry and passed the class. | ∃x ∃y (StudentInTheClass(x) ∧ GoodAt(x, math) ∧ GoodAt(x, chemistry) ∧ (¬(x=y)) ∧ StudentInTheClass(y) ∧ GoodAt(y, math) ∧ GoodAt(y, chemistry))
∀x ((StudentInTheClass(x) ∧ GoodAt(x, chemistry)) → Enjoy(x, conductingExperiment))
∀x ((StudentInTheClass(x) ∧ Enjoy(x, conductingExperiment)) → GoodAt(x, planning))
∀x ((StudentInTheClass(x) ∧ GoodAt(x, planning)) → ¬Failed(x, theClass))
StudentInTheClass(james) ∧ (¬(GoodAt(james, chemistry) ⊕ Failed(james, theClass))) | James is good at math and chemistry. | GoodAt(james, chemistry) ∧ GoodAt(james, math) | False |
Some students in the class who are good at math are also good at chemistry.
All students in the class who are good at chemistry enjoy conducting experiments.
All students in the class that enjoy conducting experiments are good at planning.
None of the students who are good at planning failed the class.
James is a student in the class; he is either good at chemistry and failed the class, or bad at chemistry and passed the class. | ∃x ∃y (StudentInTheClass(x) ∧ GoodAt(x, math) ∧ GoodAt(x, chemistry) ∧ (¬(x=y)) ∧ StudentInTheClass(y) ∧ GoodAt(y, math) ∧ GoodAt(y, chemistry))
∀x ((StudentInTheClass(x) ∧ GoodAt(x, chemistry)) → Enjoy(x, conductingExperiment))
∀x ((StudentInTheClass(x) ∧ Enjoy(x, conductingExperiment)) → GoodAt(x, planning))
∀x ((StudentInTheClass(x) ∧ GoodAt(x, planning)) → ¬Failed(x, theClass))
StudentInTheClass(james) ∧ (¬(GoodAt(james, chemistry) ⊕ Failed(james, theClass))) | If James is good at Chemistry or failed the class, then James is either good at planning or good at math. | (GoodAt(james, chemistry) ∨ Failed(james, theClass) → (GoodAt(james, planning) ⊕ GoodAt(james, math))) | True |
If a Leetcode problem is at the easy level, then its AC rate is lower than 20 percent.
All Leetcode problems that are recommended to novices are easy.
A Leetode problem is either easy or hard.
Leetcode problems that are starred by more than one thousand users are hard.
2Sum is recommended to novices.
4Sum is starred by more than 1,000 users. | ∀x ∀y (Easy(x) → ∃y (LessThan(y, percent20) ∧ ACRate(x,y)))
∀x (Recommended(x) → Easy(x))
∀x (Easy(x) ⊕ Hard(x))
∀x ((Starred(x)) → Hard(x))
Recommended(twosum)
Starred(foursum) | 2Sum is a Leetcode problem at the easy level. | Easy(twosum) | True |
If a Leetcode problem is at the easy level, then its AC rate is lower than 20 percent.
All Leetcode problems that are recommended to novices are easy.
A Leetode problem is either easy or hard.
Leetcode problems that are starred by more than one thousand users are hard.
2Sum is recommended to novices.
4Sum is starred by more than 1,000 users. | ∀x ∀y (Easy(x) → ∃y (LessThan(y, percent20) ∧ ACRate(x,y)))
∀x (Recommended(x) → Easy(x))
∀x (Easy(x) ⊕ Hard(x))
∀x ((Starred(x)) → Hard(x))
Recommended(twosum)
Starred(foursum) | 4Sum is a Leetcode problem recommended to the novice. | Recommended(foursum) | False |
Everyone who rents a car spends money.
Whenever Sarah goes to Vermont, Sarah drives there.
Someone who does not own a car to drive somewhere must either borrow a car or rent a car.
Sarah doesn’t own a car.
Sarah never borrows a car to go camping.
Sarah is going to go camping in Vermont.
To go camping somewhere, you must go to that place. | ∀x (Rent(x, car) → Spend(x, money))
GoTo(sarah, vermont) → DriveTo(sarah, vermont)
∀x ∀y (¬Own(x, car) ∧ DriveTo(x, y) → Borrow(x, car) ⊕ Rent(x, car))
¬Own(sarah, car)
∀x (Camping(sarah, x) → ¬(Borrow(sarah, car)))
Camping(sarah, vermont)
∀x ∀y (Camping(x, y) → GoTo(x, y)) | Sarah will spend money this weekend. | Spend(sarah, money) | True |
All people who attend weddings are getting married or know the people who are getting married.
No preteens or young children are getting married or know the people who are getting married.
People who enjoy celebrating life milestone events with other people attend weddings.
People who are fond of large group functions enjoy celebrating life milestone events with other people.
All people who are outgoing and spirited are fond of large group functions.
If Carol is not both a pre-teen or young child and attends a wedding, then Carol is not getting married or knows the people who are getting married. | ∀x ∀y (Attend(x, wedding) → GettingMarried(x) ∨ (∃y (Know(x, y) ∧ GettingMarried(y))))
∀x ∀y (PreTeen(x) ∨ YoungChild(x) → ¬(GettingMarried(x) ⊕ (∃y (Know(x, y) ∧ GettingMarried(y)))))
∀x ∀y (∃y ∃z (¬(x=y) ∧ ¬(x=z) ∧ ¬(y=z) ∧ Enjoy(x, celebratingLifeMileStoneEvent, y) ∧ Enjoy(x, celebratingLifeStoneEvent, z)) → Attend(x, wedding))
∀x ∀y (FondOf(x, largeGroupFunction) → ∃y ∃z (¬(x=y) ∧ ¬(x=z) ∧ ¬(y=z) ∧ Enjoy(x, celebratingLifeMileStoneEventWith, y) ∧ Enjoy(x, celebratingLifeStoneEvent, z)))
∀x (Outgoing(x) ∧ Sprited(x) → FondOf(x, largeGroupFunction))
¬((PreTeen(carol) ∨ YoungChildren(carol)) ∧ Attend(carol, wedding)) → ¬(GettingMarried(carol) ∨ (∃y (Know(carol, y) ∧ GettingMarried(y)))) | Carol is a preteen or a young child. | PreTeen(carol) ∨ YoungChild(carol) | Uncertain |
All velvet-finish lipsticks in the Rouge Dior set, Lunar New Year Limited Edition are refillable.
Lipsticks in the Rouge Dior set, Lunar New Year Limited Edition have either a velvet-finish or a satin-finish.
No satin-finish lipsticks in the set do not have "rosewood" in its offical description.
Lipstcks in the Rouge Dior set, Lunar New Year Limited Edition either does not have "rosewood" in its offical description or it has "rosewood" in its official description.
ROUGE Dior Colored Lip Balm 999 is a lipstick in the set, and it either has "rosewood" in its official description or has a velvet finish. | ∀x ((Lipstick(x) ∧ In(x, rougeDiorSet) ∧ In(x, lunarNewYearLimitedEdition) ∧ VelvetFinish(x)) → Refillable(x))
∀x ((Lipstick(x) ∧ In(x, rougeDiorSet) ∧ In(x, lunarNewYearLimitedEdition)) → (VelvetFinish(x) ⊕ SatinFinish(x)))
∀x ((Lipstick(x) ∧ In(x, rougeDiorSet) ∧ In(x, lunarNewYearLimitedEdition) ∧ SatinFinish(x)) → ¬RosewoodInDescription(x))
∀x ((Lipstick(x) ∧ In(x, rougeDiorSet) ∧ In(x, lunarNewYearLimitedEdition)) → (RosewoodInDescription(x) ⊕ ¬RosewoodInDescription(x)))
Lipstick(rougeDiorColoredLipBalm999) ∧ In(rougeDiorColoredLipBalm999, rougeDiorSet) ∧ In(rougeDiorColoredLipBalm999, lunarNewYearLimitedEdition) ∧ (RosewoodInDescription(rougeDiorColoredLipBalm999) ⊕ VelvetFinish(rougeDiorColoredLipBalm999)) | If ROUGE Dior Colored Lip Balm 999 is not both a velvet finish ipstick in the set and refillable, then it neither is refillable nor has "rosewood" in its official description. | ¬((Lipstick(rougeDiorColoredLipBalm999) ∧ In(rougeDiorColoredLipBalm999, rougeDiorSet) ∧ In(rougeDiorColoredLipBalm999, lunarNewYearLimitedEdition) ∧ VelvetFinish(rougeDiorColoredLipBalm999) ∧ Refillable(rougeDiorColoredLipBalm999) → (¬Refillable(rougeDiorColoredLipBalm999) ∧ ¬RosewoodInDescription(rougeDiorColoredLipBalm999)))) | True |
All Senate Republicans are elected officials.
Some elected officials are not conservatives. | ∀x (SenateRepublican(x) → ElectedOfficial(x))
∃x ∃y (ElectedOfficial(x) ∧ ElectedOfficial(y) ∧ ¬Conservative(x) ∧ ¬Conservative(y) ∧ ¬(x=y)) | Some conservatives are not Senate Republicans. | ∃x ∃y (Conservative(x) ∧ Conservative(y) ∧ ¬SenateRepublican(x) ∧ ¬SenateRepublican(y) ∧ ¬(x=y)) | Uncertain |
No athletes never exercise.
All professional basketball players are athletes.
All NBA players are professional basketball players.
All Knicks players are NBA players.
Either John is a professional basketball player and he never exercises, or he is not a professional basketball player and he sometimes exercises. | ∀x (Athlete(x) → ¬NeverExercises(x)) Never: does not exist a time
∀x (ProfessionalBasketballPlayer(x) → Athlete(x))
∀x (NBAPlayer(x) → ProfessionalBasketballPlayer(x))
∀x (KnicksPlayer(x) → NBAPlayer(x))
¬(ProfessionalBasketballPlayer(jim) ⊕ NeverExercises(jim)) | Jim is a Knicks player. | KnicksPlayer(jim) | False |
No athletes never exercise.
All professional basketball players are athletes.
All NBA players are professional basketball players.
All Knicks players are NBA players.
Either John is a professional basketball player and he never exercises, or he is not a professional basketball player and he sometimes exercises. | ∀x (Athlete(x) → ¬NeverExercises(x)) Never: does not exist a time
∀x (ProfessionalBasketballPlayer(x) → Athlete(x))
∀x (NBAPlayer(x) → ProfessionalBasketballPlayer(x))
∀x (KnicksPlayer(x) → NBAPlayer(x))
¬(ProfessionalBasketballPlayer(jim) ⊕ NeverExercises(jim)) | Jim is not a Knicks player. | ¬KnicksPlayer(jim) | True |
No athletes never exercise.
All professional basketball players are athletes.
All NBA players are professional basketball players.
All Knicks players are NBA players.
Either John is a professional basketball player and he never exercises, or he is not a professional basketball player and he sometimes exercises. | ∀x (Athlete(x) → ¬NeverExercises(x)) Never: does not exist a time
∀x (ProfessionalBasketballPlayer(x) → Athlete(x))
∀x (NBAPlayer(x) → ProfessionalBasketballPlayer(x))
∀x (KnicksPlayer(x) → NBAPlayer(x))
¬(ProfessionalBasketballPlayer(jim) ⊕ NeverExercises(jim)) | Jim is an athlete. | Athlete(jim) | Uncertain |
All kids are young.
All toddlers are kids.
If someone is young, then they are not elderly.
All pirates are seafarers.
If Nancy is not a pirate, then Nancy is young.
If Nancy is not a toddler, then Nancy is a seafarer. | ∀x (Kid(x) → Young(x))
∀x (Toddler(x) → Kid(x))
∀x (Young(x) → ¬Elderly(x))
∀x (Pirate(x) → Seafarer(x))
¬Pirate(nancy) → Young(nancy)
¬Toddler(nancy) → Seafarer(nancy) | Nancy is a pirate. | Pirate(nancy) | Uncertain |
Lana Wilson directed After Tiller, The Departure, and Miss Americana.
If a film is directed by a person, the person is a filmmaker.
After Tiller is a documentary.
The documentary is a type of film.
Lana Wilson is from Kirkland.
Kirkland is a US city.
If a person is from a city in a country, the person is from the country.
After Tiller is nominated for the Independent Spirit Award for Best Documentary. | DirectedBy(afterTiller, lanaWilson) ∧ DirectedBy(theDeparture, lanaWilson) ∧ DirectedBy(missAmericana, lanaWilson)
∀x ∀y (DirectedBy(x, y) → Filmmaker(y))
Documentary(afterTiller)
∀x (Documentary(x) → Film(x))
From(lanaWilson, kirkland)
In(kirkland, unitedStates)
∀x ∀y ∀z ((From(x, y) ∧ In(y, z)) → From(x, z))
Nomination(afterTiller, theIndependentSpiritAwardForBestDocumentary) | Lana Wilson is a US filmmaker. | From(lanaWilson, unitedStates) ∧ Filmmaker(lanaWilson) | True |
Lana Wilson directed After Tiller, The Departure, and Miss Americana.
If a film is directed by a person, the person is a filmmaker.
After Tiller is a documentary.
The documentary is a type of film.
Lana Wilson is from Kirkland.
Kirkland is a US city.
If a person is from a city in a country, the person is from the country.
After Tiller is nominated for the Independent Spirit Award for Best Documentary. | DirectedBy(afterTiller, lanaWilson) ∧ DirectedBy(theDeparture, lanaWilson) ∧ DirectedBy(missAmericana, lanaWilson)
∀x ∀y (DirectedBy(x, y) → Filmmaker(y))
Documentary(afterTiller)
∀x (Documentary(x) → Film(x))
From(lanaWilson, kirkland)
In(kirkland, unitedStates)
∀x ∀y ∀z ((From(x, y) ∧ In(y, z)) → From(x, z))
Nomination(afterTiller, theIndependentSpiritAwardForBestDocumentary) | Lana Wilson has won the Independent Spirit Award. | FilmmakerAward(lanaWilson, theIndependentSpiritAwardForBestDocumentary) | Uncertain |
All bears in zoos are not wild.
Some bears are in zoos. | ∀x ((Bear(x) ∧ In(x, zoo)) → ¬Wild(x))
∃x ∃y (Bear(x) ∧ Bear(y) ∧ In(x, zoo) ∧ In(y, zoo) ∧ ¬(x=y)) | Not all bears are wild. | ∃x (Bear(x) ∧ ¬Wild(x)) | True |
If a person is the leader of a country for life, that person has power.
Leaders of a country for life are either a king or a queen.
Queens are female.
Kings are male.
Elizabeth is a queen.
Elizabeth is a leader of a country for life. | ∀x (Leader(x) → HavePower(x))
∀x (Leader(x) → (King(x) ⊕ Queen(x)))
∀x (Queen(x) → Female(x))
∀x (King(x) → Male(x))
Queen(elizabeth)
Leader(elizabeth) | Elizabeth is a king. | King(elizabeth) | False |
If a person is the leader of a country for life, that person has power.
Leaders of a country for life are either a king or a queen.
Queens are female.
Kings are male.
Elizabeth is a queen.
Elizabeth is a leader of a country for life. | ∀x (Leader(x) → HavePower(x))
∀x (Leader(x) → (King(x) ⊕ Queen(x)))
∀x (Queen(x) → Female(x))
∀x (King(x) → Male(x))
Queen(elizabeth)
Leader(elizabeth) | Elizabeth has power. | HavePower(elizabeth) | True |
If a person is the leader of a country for life, that person has power.
Leaders of a country for life are either a king or a queen.
Queens are female.
Kings are male.
Elizabeth is a queen.
Elizabeth is a leader of a country for life. | ∀x (Leader(x) → HavePower(x))
∀x (Leader(x) → (King(x) ⊕ Queen(x)))
∀x (Queen(x) → Female(x))
∀x (King(x) → Male(x))
Queen(elizabeth)
Leader(elizabeth) | Elizabeth is a leader of a country for life. | Leader(elizabeth) | True |
All people who went to Clay's school and who make their own matcha teas every morning with ceremonial-grade matcha powder do not wake up late and start their schedules past noon regularly.
All people who went to Clay's school, who live in California, and attend yoga classes regularly, make their own matcha teas every morning with ceremonial-grade matcha powder.
All people who went to Clay's school, and work in the entertainment industry as high-profile celebrities, wake up late and start their schedules past noon regularly.
All people who went to Clay's school that do not have regular 9-5 jobs, work in the entertainment industry as high-profile celebrities.
All people who went to Clay's school and prefer working at home over going to the office daily do not have regular 9-5 jobs.
Bunny went to Clay's school, and she either prefers to work at home over going to the office and makes her own matcha teas every morning with ceremonial-grade matcha powder, or does not prefer to work at home over going to the office every day and does not make her own matcha teas every morning with ceremonial-grade matcha powder. | ∀x (GoTo(x, claysSchool) ∧ MakeWith(x, theirOwnMatchTea, ceremonialGradePowder) → ¬(WakeUpLate(x) ∧ StartPastNoonRegularly(x, schedule)))
∀x (GoTo(x, claysSchool) ∧ LiveIn(x, california) ∧ AttendRegularly(x, yogaClass) → MakeWith(x, ownMatch, ceremonialGradePowder))
∀x (GoTo(x, claysSchool) ∧ WorkInAs(x, entertainmentIndustry, highProfileCelebrity) → (WakeUpLate(x) ∧ StartPastNoonRegularly(x, schedule)))
∀x ∀y (GoTo(x, claysSchool) ∧ ¬(Have(x, y) ∧ Regular(y) ∧ NineToFiveJob(y)) → WorkInAs(x, entertainmentIndustry, highProfileCelebrity))
∀x ∀y (GoTo(x, claysSchool) ∧ Prefer(x, workingAtHome, goingToTheOffice) → ¬(Have(x, y) ∧ Regular(y) ∧ NineToFiveJob(y)))
GoTo(bunny, claysSchool) ∧ ¬(Prefer(bunny, workingAtHome, goingToTheOffice) ⊕ MakeWith(bunny, theirOwnMatchTea, ceremonialGradePowder)) | Bunny does not have a regular 9-5 job. | Have(bunny, y) ∧ Regular(y) ∧ NineToFiveJob(y) | Uncertain |
Thomas Barber was an English professional footballer.
Thomas Barber played in the Football League for Aston Villa.
Thomas Barber played as a halfback and inside left.
Thomas Barber scored the winning goal in the 1913 FA Cup Final. | English(thomasBarber) ∧ ProfessionalFootballer(thomasBarber)
PlayedFor(thomasBarber, astonVilla) ∧ PlayedIn(astonVilla,theFootballLeague)
PlayedAs(thomasBarber, halfBack) ∧ PlayedAs(thomasBarber, insideLeft)
ScoredTheWinningGoalIn(thomasBarber, facupfinal1913) | Thomas Barber played in the Football League for Bolton Wanderers | PlayedFor(thomasBarber, boltonWanderers) ∧ PlayedIn(boltonWanderers,theFootballLeague) | Uncertain |
Thomas Barber was an English professional footballer.
Thomas Barber played in the Football League for Aston Villa.
Thomas Barber played as a halfback and inside left.
Thomas Barber scored the winning goal in the 1913 FA Cup Final. | English(thomasBarber) ∧ ProfessionalFootballer(thomasBarber)
PlayedFor(thomasBarber, astonVilla) ∧ PlayedIn(astonVilla,theFootballLeague)
PlayedAs(thomasBarber, halfBack) ∧ PlayedAs(thomasBarber, insideLeft)
ScoredTheWinningGoalIn(thomasBarber, facupfinal1913) | Thomas Barber played as an inside left. | PlayedAs(thomasBarber, insideLeft) | True |
Thomas Barber was an English professional footballer.
Thomas Barber played in the Football League for Aston Villa.
Thomas Barber played as a halfback and inside left.
Thomas Barber scored the winning goal in the 1913 FA Cup Final. | English(thomasBarber) ∧ ProfessionalFootballer(thomasBarber)
PlayedFor(thomasBarber, astonVilla) ∧ PlayedIn(astonVilla,theFootballLeague)
PlayedAs(thomasBarber, halfBack) ∧ PlayedAs(thomasBarber, insideLeft)
ScoredTheWinningGoalIn(thomasBarber, facupfinal1913) | An English professional footballer scored the winning goal in the 1913 FA Cup Final. | ∃x (English(x) ∧ ProfessionalFootballer(x) ∧ ScoredTheWinningGoalIn(x, facupfinal1913)) | True |
If a person plays an instrument in a concert, they are good at playing this kind of instrument.
Peter plays piano, violin, and saxophone.
Peter plays piano in a concert.
Oliver and Peter both play instruments in a concert.
Oliver plays a different musical instrument from Peter in the concert. | ∀x ∀y (PlayIn(y, x, concert) → GoodAtPlaying(y, x))
PlayIn(peter, piano) ∧ PlayIn(peter, violin) ∧ PlayIn(peter, saxophone)
PlayIn(peter, piano, concert)
∃x ∃y (PlayIn(peter, x, concert) ∧ PlayIn(oliver, y, concert))
∀x (PlayIn(oliver, x, concert) → ¬PlayIn(peter, y, concert)) | Oliver plays violin in the concert. | PlayIn(oliver, violin, concert) | Uncertain |
If a person plays an instrument in a concert, they are good at playing this kind of instrument.
Peter plays piano, violin, and saxophone.
Peter plays piano in a concert.
Oliver and Peter both play instruments in a concert.
Oliver plays a different musical instrument from Peter in the concert. | ∀x ∀y (PlayIn(y, x, concert) → GoodAtPlaying(y, x))
PlayIn(peter, piano) ∧ PlayIn(peter, violin) ∧ PlayIn(peter, saxophone)
PlayIn(peter, piano, concert)
∃x ∃y (PlayIn(peter, x, concert) ∧ PlayIn(oliver, y, concert))
∀x (PlayIn(oliver, x, concert) → ¬PlayIn(peter, y, concert)) | Peter is good at playing piano. | GoodAtPlaying(peter, piano) | True |
Functional brainstems are necessary for breath control.
All humans that can swim can control their breath.
Humans can swim or walk.
Humans who can walk can stand on the ground by themselves.
Humans whose brainstems are functional can control their balance.
Every human who can stand on the ground by themselves has functional leg muscles.
George and Archie are humans.
George can control his balance and can swim.
Archie can walk if and only if he has functional brainstems. | ∀x (CanControl(x, breath) → FunctionalBrainStem(x))
∀x (Human(x) ∧ CanSwim(x) → CanControl(x, breath))
∀x (Human(x) → (CanSwim(x) ∨ CanWalk(x)))
∀x (Human(x) ∧ CanWalk(x) → CanStandOnTheGround(x, themselves))
∀x (Human(x) ∧ FunctionalBrainStem(x) → CanControl(x, balance))
∀x (Human(x) ∧ CanStandOnTheGround(x, themselves) → FunctionalLegMuscle(x))
Human(george) ∧ Human(archie)
CanControl(george, balance) ∧ CanSwim(george)
¬(CanWalk(archie) ⊕ FunctionalBrainStem(archie)) | Archie has functional leg muscles and can control his balance. | FunctionalLegMuscle(archie) ∧ CanControl(archie, balance) | True |
Functional brainstems are necessary for breath control.
All humans that can swim can control their breath.
Humans can swim or walk.
Humans who can walk can stand on the ground by themselves.
Humans whose brainstems are functional can control their balance.
Every human who can stand on the ground by themselves has functional leg muscles.
George and Archie are humans.
George can control his balance and can swim.
Archie can walk if and only if he has functional brainstems. | ∀x (CanControl(x, breath) → FunctionalBrainStem(x))
∀x (Human(x) ∧ CanSwim(x) → CanControl(x, breath))
∀x (Human(x) → (CanSwim(x) ∨ CanWalk(x)))
∀x (Human(x) ∧ CanWalk(x) → CanStandOnTheGround(x, themselves))
∀x (Human(x) ∧ FunctionalBrainStem(x) → CanControl(x, balance))
∀x (Human(x) ∧ CanStandOnTheGround(x, themselves) → FunctionalLegMuscle(x))
Human(george) ∧ Human(archie)
CanControl(george, balance) ∧ CanSwim(george)
¬(CanWalk(archie) ⊕ FunctionalBrainStem(archie)) | Archie cannot control his balance and doesn't have functional leg muscles. | ¬CanControl(archie, balance) ∧ ¬FunctionalLegMuscle(archie) | False |
Cancer biology is finding genetic alterations that confer a selective advantage to cancer cells.
Cancer researchers have frequently ranked the importance of substitutions to cancer growth by the P value.
P values are thresholds for belief, not metrics of effect. | Finding(cancerBiology, geneticAlteration) ∧ Confer(geneticAlteration, selectiveAdvantage, toCancerCell)
∃x ∃y (CancerResearcher(x) ∧ RankedBy(x, importanceOfSubstitutionsToCancerGrowth) ∧ PValue(y) ∧ RankedBy(importanceOfSubstitutionsToCancerGrowth, y))
∀x (PValue(x) → ThresholdForBelief(x) ∧ ¬MetricOfEffect(x)) | Cancer researchers tend to use the cancer effect size to determine the relative importance of the genetic alterations that confer selective advantage to cancer cells. | ∃x ∃y (CancerResearcher(x) ∧ Use(x, cancerEffectSize) ∧ UsedToDetermine(cancerEffectSize, relativeImportanceOfGeneteticAlterations)) | Uncertain |
Cancer biology is finding genetic alterations that confer a selective advantage to cancer cells.
Cancer researchers have frequently ranked the importance of substitutions to cancer growth by the P value.
P values are thresholds for belief, not metrics of effect. | Finding(cancerBiology, geneticAlteration) ∧ Confer(geneticAlteration, selectiveAdvantage, toCancerCell)
∃x ∃y (CancerResearcher(x) ∧ RankedBy(x, importanceOfSubstitutionsToCancerGrowth) ∧ PValue(y) ∧ RankedBy(importanceOfSubstitutionsToCancerGrowth, y))
∀x (PValue(x) → ThresholdForBelief(x) ∧ ¬MetricOfEffect(x)) | P value represents the selection intensity for somatic variants in cancer cell lineages. | SelectionIntensitySomaticVariants(pValue) | Uncertain |
Cancer biology is finding genetic alterations that confer a selective advantage to cancer cells.
Cancer researchers have frequently ranked the importance of substitutions to cancer growth by the P value.
P values are thresholds for belief, not metrics of effect. | Finding(cancerBiology, geneticAlteration) ∧ Confer(geneticAlteration, selectiveAdvantage, toCancerCell)
∃x ∃y (CancerResearcher(x) ∧ RankedBy(x, importanceOfSubstitutionsToCancerGrowth) ∧ PValue(y) ∧ RankedBy(importanceOfSubstitutionsToCancerGrowth, y))
∀x (PValue(x) → ThresholdForBelief(x) ∧ ¬MetricOfEffect(x)) | Cancer effect size is preferred by cancer researchers. | Preferred(cancerResearchers, cancerEffectSize) | Uncertain |
Cancer biology is finding genetic alterations that confer a selective advantage to cancer cells.
Cancer researchers have frequently ranked the importance of substitutions to cancer growth by the P value.
P values are thresholds for belief, not metrics of effect. | Finding(cancerBiology, geneticAlteration) ∧ Confer(geneticAlteration, selectiveAdvantage, toCancerCell)
∃x ∃y (CancerResearcher(x) ∧ RankedBy(x, importanceOfSubstitutionsToCancerGrowth) ∧ PValue(y) ∧ RankedBy(importanceOfSubstitutionsToCancerGrowth, y))
∀x (PValue(x) → ThresholdForBelief(x) ∧ ¬MetricOfEffect(x)) | P values don't represent metrics of effect. | ∀x (PValue(x) → ¬MetricOfEffect(x)) | True |
All biodegradable things are environment-friendly.
All woodware is biodegradable.
All paper is woodware.
Nothing is a good thing and also a bad thing.
All environment-friendly things are good.
A worksheet is either paper or environment-friendly. | ∀x (Biodegradable(x) → EnvironmentFriendly(x))
∀x (Woodware(x) → Biodegradable(x))
∀x (Paper(x) → Woodware(x))
¬(∃x (Good(x) ∧ Bad(x)))
∀x (EnvironmentFriendly(x) → Good(x))
Paper(worksheet) ⊕ EnvironmentFriendly(worksheet) | A worksheet is biodegradable. | Biodegradable(worksheet) | Uncertain |
All biodegradable things are environment-friendly.
All woodware is biodegradable.
All paper is woodware.
Nothing is a good thing and also a bad thing.
All environment-friendly things are good.
A worksheet is either paper or environment-friendly. | ∀x (Biodegradable(x) → EnvironmentFriendly(x))
∀x (Woodware(x) → Biodegradable(x))
∀x (Paper(x) → Woodware(x))
¬(∃x (Good(x) ∧ Bad(x)))
∀x (EnvironmentFriendly(x) → Good(x))
Paper(worksheet) ⊕ EnvironmentFriendly(worksheet) | A worksheet is not biodegradable. | ¬Biodegradable(worksheet) | Uncertain |
All biodegradable things are environment-friendly.
All woodware is biodegradable.
All paper is woodware.
Nothing is a good thing and also a bad thing.
All environment-friendly things are good.
A worksheet is either paper or environment-friendly. | ∀x (Biodegradable(x) → EnvironmentFriendly(x))
∀x (Woodware(x) → Biodegradable(x))
∀x (Paper(x) → Woodware(x))
¬(∃x (Good(x) ∧ Bad(x)))
∀x (EnvironmentFriendly(x) → Good(x))
Paper(worksheet) ⊕ EnvironmentFriendly(worksheet) | A worksheet is bad. | Bad(worksheet) | False |
All biodegradable things are environment-friendly.
All woodware is biodegradable.
All paper is woodware.
Nothing is a good thing and also a bad thing.
All environment-friendly things are good.
A worksheet is either paper or environment-friendly. | ∀x (Biodegradable(x) → EnvironmentFriendly(x))
∀x (Woodware(x) → Biodegradable(x))
∀x (Paper(x) → Woodware(x))
¬(∃x (Good(x) ∧ Bad(x)))
∀x (EnvironmentFriendly(x) → Good(x))
Paper(worksheet) ⊕ EnvironmentFriendly(worksheet) | A worksheet is not bad. | ¬Bad(worksheet) | True |
No reptile has fur.
All snakes are reptiles. | ∀x (Reptile(x) → ¬Have(x, fur))
∀x (Snake(x) → Reptile(x)) | Some snake has fur. | ∃x (Snake(x) ∧ Have(x, fur)) | False |
All buildings in New Haven are not high.
All buildings managed by Yale Housing are located in New Haven.
All buildings in Manhattans are high.
All buildings owned by Bloomberg are located in Manhattans.
All buildings with the Bloomberg logo are owned by Bloomberg.
Tower A is managed by Yale Housing.
Tower B is with the Bloomberg logo. | ∀x (In(x, newHaven) → ¬High(x))
∀x (YaleHousing(x) → In(x, newHaven))
∀x (In(x, manhattan) → High(x))
∀x (Bloomberg(x) → In(x, manhattan))
∀x (BloombergLogo(x) → Bloomberg(x))
YaleHousing(tower-a)
BloombergLogo(tower-b) | Tower A is low. | ¬High(tower-a) | True |
All buildings in New Haven are not high.
All buildings managed by Yale Housing are located in New Haven.
All buildings in Manhattans are high.
All buildings owned by Bloomberg are located in Manhattans.
All buildings with the Bloomberg logo are owned by Bloomberg.
Tower A is managed by Yale Housing.
Tower B is with the Bloomberg logo. | ∀x (In(x, newHaven) → ¬High(x))
∀x (YaleHousing(x) → In(x, newHaven))
∀x (In(x, manhattan) → High(x))
∀x (Bloomberg(x) → In(x, manhattan))
∀x (BloombergLogo(x) → Bloomberg(x))
YaleHousing(tower-a)
BloombergLogo(tower-b) | Tower B is not located in Manhattans. | ¬In(tower-b, manhattan) | False |
No birds are ectothermic.
All penguins are birds.
An animal is ectothermic or endothermic.
All endothermic animals produce heat within the body.
Ron and Henry are both animals.
Ron is not a bird and does not produce heat with the body.
Henry is not a cat and does not produce heat with the body. | ∀x (Bird(x) → ¬Ectothermic(x))
∀x (Penguin(x) → Bird(x))
∀x (Animal(x) → Ectothermic(x) ∨ Endothermic(x))
∀x (Endothermic(x) → ProduceWithIn(x, heat, body))
Animal(ron) ∧ Animal(henry)
¬Bird(ron) ∧ ¬ProduceWithIn(ron, heat, body)
¬Cat(henry) ∧ ¬ProduceWithIn(henry, heat, body) | Ron is a cat. | Cat(ron) | Uncertain |
No birds are ectothermic.
All penguins are birds.
An animal is ectothermic or endothermic.
All endothermic animals produce heat within the body.
Ron and Henry are both animals.
Ron is not a bird and does not produce heat with the body.
Henry is not a cat and does not produce heat with the body. | ∀x (Bird(x) → ¬Ectothermic(x))
∀x (Penguin(x) → Bird(x))
∀x (Animal(x) → Ectothermic(x) ∨ Endothermic(x))
∀x (Endothermic(x) → ProduceWithIn(x, heat, body))
Animal(ron) ∧ Animal(henry)
¬Bird(ron) ∧ ¬ProduceWithIn(ron, heat, body)
¬Cat(henry) ∧ ¬ProduceWithIn(henry, heat, body) | Either Henry is a penguin or Henry is endothermic. | Penguin(henry) ⊕ Endothermic(henry) | False |
No birds are ectothermic.
All penguins are birds.
An animal is ectothermic or endothermic.
All endothermic animals produce heat within the body.
Ron and Henry are both animals.
Ron is not a bird and does not produce heat with the body.
Henry is not a cat and does not produce heat with the body. | ∀x (Bird(x) → ¬Ectothermic(x))
∀x (Penguin(x) → Bird(x))
∀x (Animal(x) → Ectothermic(x) ∨ Endothermic(x))
∀x (Endothermic(x) → ProduceWithIn(x, heat, body))
Animal(ron) ∧ Animal(henry)
¬Bird(ron) ∧ ¬ProduceWithIn(ron, heat, body)
¬Cat(henry) ∧ ¬ProduceWithIn(henry, heat, body) | Ron is either both a penguin and endothermic, or he is nether. | ¬(Penguin(ron) ⊕ Endothermic(henry)) | True |
Ambiortus is a prehistoric bird genus.
Ambiortus Dementjevi is the only known species of Ambiortus.
Mongolia was where Ambiortus Dementjevi lived.
Yevgeny Kurochkin was the discoverer of Ambiortus. | Prehistoric(ambiortus) ∧ BirdGenus(ambiortus)
∀x(KnownSpeciesOf(x, ambiortus) → IsSpecies(x, ambiortusDementjevi))
LiveIn(ambiortusDementjevi, mongolia)
Discover(yevgenykurochkin, ambiortus) | Yevgeny Kurochkin discovered a new bird genus. | ∃x (Discover(yevgenykurochkin, x) ∧ BirdGenus(x)) | True |
Ambiortus is a prehistoric bird genus.
Ambiortus Dementjevi is the only known species of Ambiortus.
Mongolia was where Ambiortus Dementjevi lived.
Yevgeny Kurochkin was the discoverer of Ambiortus. | Prehistoric(ambiortus) ∧ BirdGenus(ambiortus)
∀x(KnownSpeciesOf(x, ambiortus) → IsSpecies(x, ambiortusDementjevi))
LiveIn(ambiortusDementjevi, mongolia)
Discover(yevgenykurochkin, ambiortus) | Yevgeny Kurochkin lived in Mongolia. | LiveIn(yevgenykurochkin, mongolia) | Uncertain |
Everyone that knows about breath-first-search knows how to use a queue.
If someone is a seasoned software engineer interviewer at Google, then they know what breath-first-search is.
Someone is either a seasoned software engineer interviewer at Google, has human rights, or both.
Every person who has human rights is entitled to the right to life and liberty.
Everyone that knows how to use a queue knows about the first-in-first-out data structure.
Everyone that is entitled to the right to life and liberty cannot be deprived of their rights without due process of law.
Jack is entitled to the right to life and liberty, has human rights, or knows about the first-in-first-out data structure. | ∀x (Know(x, breathFirstSearch) → Know(x, howToUseQueue))
∀x (Seasoned(x) ∧ SoftwareEngineerInterviewer(x) ∧ At(x, google) → Know(x, breathFirstSearch))
∀x ((Seasoned(x) ∧ SoftwareEngineerInterviewer(x) ∧ At(x, google)) ∨ Have(x, humanRights))
∀x (Have(x, humanRights) → EntitledTo(x, rightToLifeAndLiberty))
∀x (Know(x, howToUseQueue) → Know(x, firstInFirstOutDataStructure))
∀x (EntitledTo(x, rightToLifeAndLiberty) → ¬DeprivedOfWithout(x, rights, dueProcessOfLaw))
(EntitledTo(jack, rightToLifeAndLiberty) ∨ Have(jack, humanRights) ∨ Know(jack, firstInFirstOutDataStructure)) | Jack is a seasoned software engineer interviewer. | Seasoned(jack) ∧ SoftwareEngineerInterviewer(jack) ∧ At(jack, google) | Uncertain |
Fort Ticonderoga is the current name for Fort Carillon.
Pierre de Rigaud de Vaudreuil built Fort Carillon.
Fort Carillon was located in New France.
New France is not in Europe. | RenamedAs(fortCarillon, fortTiconderoga)
Built(pierredeRigauddeVaudreuil, fortCarillon)
LocatedIn(fortCarillon, newFrance)
¬LocatedIn(newFrance, europe) | Pierre de Rigaud de Vaudreuil built a fort in New France. | ∃x (Built(pierredeRigauddeVaudreuil, x) ∧ LocatedIn(x, newFrance)) | True |
Fort Ticonderoga is the current name for Fort Carillon.
Pierre de Rigaud de Vaudreuil built Fort Carillon.
Fort Carillon was located in New France.
New France is not in Europe. | RenamedAs(fortCarillon, fortTiconderoga)
Built(pierredeRigauddeVaudreuil, fortCarillon)
LocatedIn(fortCarillon, newFrance)
¬LocatedIn(newFrance, europe) | Pierre de Rigaud de Vaudreuil built a fort in New England. | ∃x (Built(pierredeRigauddeVaudreuil, x) ∧ LocatedIn(x, newEngland)) | Uncertain |
Fort Ticonderoga is the current name for Fort Carillon.
Pierre de Rigaud de Vaudreuil built Fort Carillon.
Fort Carillon was located in New France.
New France is not in Europe. | RenamedAs(fortCarillon, fortTiconderoga)
Built(pierredeRigauddeVaudreuil, fortCarillon)
LocatedIn(fortCarillon, newFrance)
¬LocatedIn(newFrance, europe) | Fort Carillon was located in Europe. | LocatedIn(fortCarillon, europe) | Uncertain |
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