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[ "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, metho...
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, metho...
No choral conductor specialized in the performance of Renaissance.
∀x (ChoralConductor(x) → ¬SpecializeInPerformanceOf(x, renaissanceMusic))
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 an...
[ "∀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 an...
[ "∀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 an...
[ "∀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
[ "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.", ...
[ "British(williamDickinson) ∧ Politician(williamDickinson) ∧ SatIn(williamDickinson, houseOfCommons)", "Attended(williamDickinson, westminsterSchool) ∧ Highschool(westminsterSchool) ∧ Attended(williamDickinson, universityOfEdinburgh)", "University(universityOfEdinburgh) ∧ LocatedIn(universityOfEdinburgh, unitedK...
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.", ...
[ "British(williamDickinson) ∧ Politician(williamDickinson) ∧ SatIn(williamDickinson, houseOfCommons)", "Attended(williamDickinson, westminsterSchool) ∧ Highschool(westminsterSchool) ∧ Attended(williamDickinson, universityOfEdinburgh)", "University(universityOfEdinburgh) ∧ LocatedIn(universityOfEdinburgh, unitedK...
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.", ...
[ "British(williamDickinson) ∧ Politician(williamDickinson) ∧ SatIn(williamDickinson, houseOfCommons)", "Attended(williamDickinson, westminsterSchool) ∧ Highschool(westminsterSchool) ∧ Attended(williamDickinson, universityOfEdinburgh)", "University(universityOfEdinburgh) ∧ LocatedIn(universityOfEdinburgh, unitedK...
William Dickinson sat in the House of Commons.
SatIn(williamDickinson, houseOfCommons)
True
[ "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 ...
[ "∀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)", "Mor...
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 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...
[ "∃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, typeCPor...
The L-2021 monitor either has a type-c port or is produced by LG.
Have(l-2021, typeCPort) ⊕ ProducedBy(l-2021, lG)
True
[ "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...
[ "∀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...
PSO J318.5−22 is an orphan planet.
Planet(pSOJ318.5-22) ∧ Orphan(pSOJ318.5-22)
Uncertain
[ "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...
[ "∀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...
PSO J318.5−22 is an orphan planet or it does not have the Sun as its star, or both.
(Planet(pSOJ318.5-22) ∧ Orphan(pSOJ318.5-22)) ∨ ¬SunAs(pSOJ318.5-22, star)
True
[ "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, x))", "∀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, x))", "∀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 are no unincorporated communities along Kentucky Route 32.
∀x (On(x, kentuckyRoute32) → ¬UnincorporatedCommunity(x))
False
[ "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...
[ "∀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, even...
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...
[ "∀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, even...
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...
[ "∀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, even...
Susan is not both diligent and likes independence.
¬(Like(susan, independence) ∧ Diligent(susan))
False
[ "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 Olym...
[ "∀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) ∨ OlympicGoldMedal...
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 Olym...
[ "∀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) ∨ OlympicGoldMedal...
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 Olym...
[ "∀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) ∨ OlympicGoldMedal...
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."...
[ "∀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)...
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."...
[ "∀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)...
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...
[ "∀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...
[ "∀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...
[ "∀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 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...
[ "∀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) ∧...
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 cla...
[ "∃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, plan...
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 cla...
[ "∃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, plan...
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 cla...
[ "∃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, plan...
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
[ "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.", ...
[ "∀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 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
[ "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 co...
[ "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)...
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 co...
[ "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)...
Miss Americana is not directed by a filmmaker from Kirkland.
¬∃x(Filmmaker(x) ∧ From(x, kirkland) ∧ DirectedBy(missAmericana, x))
False
[ "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 co...
[ "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)...
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 te...
[ "∀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,...
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))", "Play(peter, piano) ∧ Play(peter, violin) ∧ Play(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
[ "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) ∧ Ranked(x, importanceOfSubstitutionsToCancerGrowth) ∧ PValue(y) ∧ RankedBy(importanceOfSubstitutionsToCancerGrowth, y))", "∀x (PValue(x) → ThresholdForBelief(x) ∧ ¬MetricOfEffe...
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) ∧ Ranked(x, importanceOfSubstitutionsToCancerGrowth) ∧ PValue(y) ∧ RankedBy(importanceOfSubstitutionsToCancerGrowth, y))", "∀x (PValue(x) → ThresholdForBelief(x) ∧ ¬MetricOfEffe...
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) ∧ Ranked(x, importanceOfSubstitutionsToCancerGrowth) ∧ PValue(y) ∧ RankedBy(importanceOfSubstitutionsToCancerGrowth, y))", "∀x (PValue(x) → ThresholdForBelief(x) ∧ ¬MetricOfEffe...
Cancer effect size is preferred by cancer researchers.
Preferred(cancerResearchers, cancerEffectSize)
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 biodegradable.
Bioegradable(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.
¬Bioegradable(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 Yal...
[ "∀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 Yal...
[ "∀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...
[ "∀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...
[ "∀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...
[ "∀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 ...
[ "∀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, rightToLifeAndLi...
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
[ "No soccer players are professional basketball players.", "All NBA players are professional basketball players.", "All soccer defenders are soccer players.", "All centerback players are soccer defenders.", "If Stephen Curry is an NBA player or a soccer player, then he is a professional basketball player." ]
[ "∀x (ProfessionalSoccerPlayer(x) → ¬ProfessionalBasketballPlayer(x))", "∀x (NBAPlayer(x) → ProfessionalBasketballPlayer(x))", "∀x (ProfessionalSoccerDefender(x) → ProfessionalSoccerPlayer(x))", "∀x (ProfessionalCenterback(x) → ProfessionalSoccerDefender(x))", "(NBAPlayer(stephencurry) ⊕ ProfessionalSoccerPl...
Stephen Curry is an NBA player.
NBAPlayer(stephenCurry)
Uncertain
[ "No songs are visuals.", "All folk songs are songs.", "All videos are visuals.", "All movies are videos.", "All sci-fi movies are movies.", "Inception is a sci-fi movie.", "Mac is neither a folk song nor a sci-fi movie." ]
[ "∀x (Song(x) → ¬Visual(x))", "∀x (FolkSong(x) → Song(x))", "∀x (Video(x) → Visual(x))", "∀x (Movie(x) → Video(x))", "∀x (ScifiMovie(x) → Movie(x))", "ScifiMovie(inception)", "¬FolkSong(mac) ∧ ¬ScifiMovie(mac)" ]
Inception is a folk song.
FolkSong(inception)
False
[ "No songs are visuals.", "All folk songs are songs.", "All videos are visuals.", "All movies are videos.", "All sci-fi movies are movies.", "Inception is a sci-fi movie.", "Mac is neither a folk song nor a sci-fi movie." ]
[ "∀x (Song(x) → ¬Visual(x))", "∀x (FolkSong(x) → Song(x))", "∀x (Video(x) → Visual(x))", "∀x (Movie(x) → Video(x))", "∀x (ScifiMovie(x) → Movie(x))", "ScifiMovie(inception)", "¬FolkSong(mac) ∧ ¬ScifiMovie(mac)" ]
Inception is not a folk song.
¬FolkSong(inception)
True
[ "No songs are visuals.", "All folk songs are songs.", "All videos are visuals.", "All movies are videos.", "All sci-fi movies are movies.", "Inception is a sci-fi movie.", "Mac is neither a folk song nor a sci-fi movie." ]
[ "∀x (Song(x) → ¬Visual(x))", "∀x (FolkSong(x) → Song(x))", "∀x (Video(x) → Visual(x))", "∀x (Movie(x) → Video(x))", "∀x (ScifiMovie(x) → Movie(x))", "ScifiMovie(inception)", "¬FolkSong(mac) ∧ ¬ScifiMovie(mac)" ]
Inception is either a video or a folk song.
Video(inception) ⊕ FolkSong(inception)
True
[ "No songs are visuals.", "All folk songs are songs.", "All videos are visuals.", "All movies are videos.", "All sci-fi movies are movies.", "Inception is a sci-fi movie.", "Mac is neither a folk song nor a sci-fi movie." ]
[ "∀x (Song(x) → ¬Visual(x))", "∀x (FolkSong(x) → Song(x))", "∀x (Video(x) → Visual(x))", "∀x (Movie(x) → Video(x))", "∀x (ScifiMovie(x) → Movie(x))", "ScifiMovie(inception)", "¬FolkSong(mac) ∧ ¬ScifiMovie(mac)" ]
Mac is a video.
Video(mac)
Uncertain
[ "No plants are fungi.", "Mushrooms are fungi." ]
[ "∀x (Plant(x) → ¬Fungi(x))", "∀x (Mushroom(x) → Fungi(x))" ]
No plants are mushrooms.
∀x (Plant(x) → ¬Mushroom(x))
True
[ "No road is dustless.", "Some streets are roads." ]
[ "∀x (Road(x) → ¬Dustless(x))", "∃x ∃y (Street(x) ∧ Street(y) ∧ Road(x) ∧ Road(y) ∧ ¬(x=y))" ]
Some streets are dustless.
∃x ∃y (Street(x) ∧ Street(y) ∧ Dustless(x) ∧ Dustless(y) ∧ ¬(x=y))
Uncertain
[ "Musicians have very busy lives.", "Singh Kaur is a musician and famous.", "If a musician is not famous, that musician will not make a lot of money.", "A musician can be a singer or a writer." ]
[ "∀x (Musician(x) → Have(x, busyLife))", "Musician(singhKaur) ∧ Famous(singhKaur)", "∀x (Musician(x) ∧ ¬Famous(x) → ¬MakeALotOfMoney(x))", "∃x (Musician(x) ∧ (Singer(x) ∨ Writer(x)))" ]
Singh Kaur makes a lot of money.
MakeALotOfMoney(singhKaur)
Uncertain
[ "Musicians have very busy lives.", "Singh Kaur is a musician and famous.", "If a musician is not famous, that musician will not make a lot of money.", "A musician can be a singer or a writer." ]
[ "∀x (Musician(x) → Have(x, busyLife))", "Musician(singhKaur) ∧ Famous(singhKaur)", "∀x (Musician(x) ∧ ¬Famous(x) → ¬MakeALotOfMoney(x))", "∃x (Musician(x) ∧ (Singer(x) ∨ Writer(x)))" ]
Singh Kaur is a writer.
Writer(singhKaur)
Uncertain
[ "Musicians have very busy lives.", "Singh Kaur is a musician and famous.", "If a musician is not famous, that musician will not make a lot of money.", "A musician can be a singer or a writer." ]
[ "∀x (Musician(x) → Have(x, busyLife))", "Musician(singhKaur) ∧ Famous(singhKaur)", "∀x (Musician(x) ∧ ¬Famous(x) → ¬MakeALotOfMoney(x))", "∃x (Musician(x) ∧ (Singer(x) ∨ Writer(x)))" ]
Singh Kaur has a very busy life.
Have(singhKaur, busyLife)
True
[ "Each building is tall.", "Everything tall has height." ]
[ "∀x (Building(x) → Tall(x))", "∀x (Tall(x) → Height(x))" ]
All buildings are magnificent.
∀x (Building(x) → Magnificent(x))
Uncertain
[ "A controlled substance is a drug.", "There exist both harmful and beneficial controlled substances.", "If a child is exposed to a controlled substance, they are in chemical endangerment.", "Chemical Endangerment is harmful.", "The Controlled Substances Act was an act passed in 1971.", "Some Acts prevent ...
[ "∀x (ControlledSubstances(x) → Drugs(x))", "∃x ∃y (ControlledSubstances(x) ∧ ControlledSubstances(y) ∧ (¬(x=y)) ∧ Beneficial(x) ∧ Harmful(y))", "∀x ∀y ((Child(x) ∧ ControlledSubstances(y) ∧ ExposedTo(x, y)) → InChemicalEndangerment(x))", "∀x (InChemicalEndangerment(x) → Harmful(x))", "PassedIn(controlledSub...
The Controlled Substances Act prevents harmful things.
PreventsHarm(controlledSubstancesAct)
Uncertain
[ "A controlled substance is a drug.", "There exist both harmful and beneficial controlled substances.", "If a child is exposed to a controlled substance, they are in chemical endangerment.", "Chemical Endangerment is harmful.", "The Controlled Substances Act was an act passed in 1971.", "Some Acts prevent ...
[ "∀x (ControlledSubstances(x) → Drugs(x))", "∃x ∃y (ControlledSubstances(x) ∧ ControlledSubstances(y) ∧ (¬(x=y)) ∧ Beneficial(x) ∧ Harmful(y))", "∀x ∀y ((Child(x) ∧ ControlledSubstances(y) ∧ ExposedTo(x, y)) → InChemicalEndangerment(x))", "∀x (InChemicalEndangerment(x) → Harmful(x))", "PassedIn(controlledSub...
A child in chemical endangerment is in harm.
∀x ((Child(x) ∧ InChemicalEndangerment(x)) → Harmful(x))
True
[ "No people who have corporate jobs are taking more than normal financial risks.", "All entrepreneurs are taking more than normal financial risks.", "All risk-averse working people are people who have corporate jobs.", "All working people who hate working for others want to be entrepreneurs.", "If Mark Zucke...
[ "∀x (Have(x, corporateJob) → ¬Take(x, financialRisk))", "∀x (Entrepreneur(x) → Take(x, financialRisk))", "∀x (RiskAverse(x) → Have(x, corporateJob))", "∀x (∃y ∃z (¬(y=x) ∧ ¬(z=x) ∧ ¬(y=z) ∧ HateWorkingFor(x, y) ∧ HateWorkingFor(x, z)) → Entrepreneur(x))", "¬Entrepreneur(markZuckerberg) ∧ ¬(∃y ∃z (¬(y=markZu...
Mark Zuckerberg is an entrepreneur.
Entrepreneur(markZuckerberg)
Uncertain
[ "No people who have corporate jobs are taking more than normal financial risks.", "All entrepreneurs are taking more than normal financial risks.", "All risk-averse working people are people who have corporate jobs.", "All working people who hate working for others want to be entrepreneurs.", "If Mark Zucke...
[ "∀x (Have(x, corporateJob) → ¬Take(x, financialRisk))", "∀x (Entrepreneur(x) → Take(x, financialRisk))", "∀x (RiskAverse(x) → Have(x, corporateJob))", "∀x (∃y ∃z (¬(y=x) ∧ ¬(z=x) ∧ ¬(y=z) ∧ HateWorkingFor(x, y) ∧ HateWorkingFor(x, z)) → Entrepreneur(x))", "¬Entrepreneur(markZuckerberg) ∧ ¬(∃y ∃z (¬(y=markZu...
Mark Zuckerberg is a risk-averse person.
RiskAverse(markZuckerberg)
False
[ "No people who have corporate jobs are taking more than normal financial risks.", "All entrepreneurs are taking more than normal financial risks.", "All risk-averse working people are people who have corporate jobs.", "All working people who hate working for others want to be entrepreneurs.", "If Mark Zucke...
[ "∀x (Have(x, corporateJob) → ¬Take(x, financialRisk))", "∀x (Entrepreneur(x) → Take(x, financialRisk))", "∀x (RiskAverse(x) → Have(x, corporateJob))", "∀x (∃y ∃z (¬(y=x) ∧ ¬(z=x) ∧ ¬(y=z) ∧ HateWorkingFor(x, y) ∧ HateWorkingFor(x, z)) → Entrepreneur(x))", "¬Entrepreneur(markZuckerberg) ∧ ¬(∃y ∃z (¬(y=markZu...
Mark Zuckerberg is not a risk-averse person.
¬RiskAverse(markZuckerberg)
True
[ "Wildfeed exists as an unannounced program.", "Wildfeed can be sporting events, news, or syndicated shows.", "Pre-recorded content is a copyright violation.", "Programs are pre-recorded." ]
[ "∃x (Wildfeed(x) ∧ Unannounced(x) ∧ Program(x))", "∀x (Wildfeed(x) → SportingEvent(x) ∨ News(x) ∨ SyndicatedShow(x))", "∀x (Prerecorded(x) → CopyrightViolation(x))", "∀x (Program(x) → Prerecorded(x))" ]
Some wildfeed is violating copyright laws.
∃x (Wildfeed(x) ∧ CopyrightViolation(x))
True
[ "Wildfeed exists as an unannounced program.", "Wildfeed can be sporting events, news, or syndicated shows.", "Pre-recorded content is a copyright violation.", "Programs are pre-recorded." ]
[ "∃x (Wildfeed(x) ∧ Unannounced(x) ∧ Program(x))", "∀x (Wildfeed(x) → SportingEvent(x) ∨ News(x) ∨ SyndicatedShow(x))", "∀x (Prerecorded(x) → CopyrightViolation(x))", "∀x (Program(x) → Prerecorded(x))" ]
Wildfeed can be prerecorded.
∃x (Wildfeed(x) ∧ Prerecorded(x))
True
[ "Wildfeed exists as an unannounced program.", "Wildfeed can be sporting events, news, or syndicated shows.", "Pre-recorded content is a copyright violation.", "Programs are pre-recorded." ]
[ "∃x (Wildfeed(x) ∧ Unannounced(x) ∧ Program(x))", "∀x (Wildfeed(x) → SportingEvent(x) ∨ News(x) ∨ SyndicatedShow(x))", "∀x (Prerecorded(x) → CopyrightViolation(x))", "∀x (Program(x) → Prerecorded(x))" ]
Syndicated shows are copyright violations.
∃x (SyndicatedShows(x) ∧ CopyrightViolation(x))
Uncertain
[ "Catullus 4 is a poem written by the ancient Roman writer Catullus.", "Catullus 4 is a story about the retirement of a well-traveled ship.", "There is a strong analogy of human aging in the poem Catullus 4.", "Catullus 4 is written in an unusual iambic trimeter to convey a sense of speed over the waves." ]
[ "Poem(catullus4) ∧ WrittenBy(catullus4, catullus) ∧ AncientRomanWriter(catullus)", "Story(catullus4) ∧ About(catullus4, retirementOfAWellTraveledShip)", "Poem(catullus4) ∧ StrongAgingAnalogy(catullus4)", "Poem(catullus4) ∧ WrittenIn(catullus4, iambicTrimeter) ∧ Convey(catullus4, aSenseOfSpeedOverTheWaves)" ]
Callus 4 is written in an unusual iambic trimeter to convey a strong analogy of human aging.
Poem(catullus4) ∧ WrittenIn(catullus4, iambicTrimeter) ∧ StrongAgingAnalogy(catullus4)
True
[ "Westworld is an American science fiction-thriller TV series.", "In 2016, a television series named Westworld debuted on HBO.", "The TV series Westworld is adapted from the original film in 1973, which was written and directed by Michael Crichton.", "The 1973 film Westworld is about robots that malfunction an...
[ "American(westworld) ∧ ScienceFictionThriller(westworld)", "Debut(westworld, year2016) ∧ TvSeries(westworld)", "Adapted(westworld, westworldTheFilm) ∧ Produce(westworldTheFilm, year1973) ∧ Wrote(michael, westworldTheFilm) ∧ Directed(michael, westworldTheFilm)", "Film(westworldTheFilm) ∧ About(westworldTheFilm...
Michael Crichton has directed a film about malfunctioning robots.
∃x (Film(x) ∧ Directed(michael, x) ∧ About(x, malfunctioningRobots))
True
[ "Xiufeng, Xiangshan, Diecai, Qixing are districts in the city of Guilin.", "Yangshuo is not a district in Guilin." ]
[ "DistrictIn(xiufeng, guilin) ∧ DistrictIn(xiangshan, guilin) ∧ DistrictIn(diecai, guilin) ∧ DistrictIn(qixing, guilin) ∧ City(guilin)", "¬DistrictIn(yangshuo, guilin)" ]
Xiangshan and Diecai are districts in the same city.
∃x (DistrictIn(xiangshan, x) ∧ DistrictIn(diecai, x) ∧ City(x))
True
[ "Xiufeng, Xiangshan, Diecai, Qixing are districts in the city of Guilin.", "Yangshuo is not a district in Guilin." ]
[ "DistrictIn(xiufeng, guilin) ∧ DistrictIn(xiangshan, guilin) ∧ DistrictIn(diecai, guilin) ∧ DistrictIn(qixing, guilin) ∧ City(guilin)", "¬DistrictIn(yangshuo, guilin)" ]
Xiufeng is a district in Guilin.
DistrictIn(xiufeng, guilin)
True
[ "Xiufeng, Xiangshan, Diecai, Qixing are districts in the city of Guilin.", "Yangshuo is not a district in Guilin." ]
[ "DistrictIn(xiufeng, guilin) ∧ DistrictIn(xiangshan, guilin) ∧ DistrictIn(diecai, guilin) ∧ DistrictIn(qixing, guilin) ∧ City(guilin)", "¬DistrictIn(yangshuo, guilin)" ]
Kowloon District is in Hong Kong.
DistrictIn(kowloon, hongKong)
Uncertain
[ "All of Michael's neighbors who grow their own fresh vegetables in their home gardens also have ample space.", "All of Michael's neighbors who are young working professionals and live in large cities, do not have ample space.", "All of Michael's neighbors who order takeout from delivery services often grow thei...
[ "∀x (MichaelsNeightbor(x) ∧ GrowIn(x, vegetable, garden) → Have(x, ampleSpace))", "∀x (MichaelsNeightbor(x) ∧ YoungWorkingProfession(x) ∧ LiveIn(x, largeCity) → ¬Have(x, ampleSpace))", "∀x (MichaelsNeightbor(x) ∧ OrderOften(x, takeout) → Grow(x, vegetable, garden))", "∀x (MichaelsNeightbor(x) ∧ EnjoyGoingOutO...
Peter enjoys going out often to restaurants with friends.
EnjoyGoingOutOftenTo(peter, restaurant, friend)
Uncertain
End of preview. Expand in Data Studio

Overview

This is a filtered version of the FOLIO (First-Order Logic Inference) dataset, containing only examples where the gold FOL premises and conclusion can be correctly evaluated by Prover9, a first-order logic theorem prover. This filtered dataset serves as a "SKYLINE" baseline, ensuring that all examples have valid, parseable FOL that Prover9 can process correctly.

Dataset Creation Process

The filtered dataset was created by running the fol-gold-to-prover9 experiment, which:

  1. Takes the gold FOL premises and conclusion from each example
  2. Evaluates them using Prover9
  3. Compares Prover9's output with the gold answer (True/False/Uncertain)
  4. Retains only examples where Prover9's evaluation matches the gold answer

Source Datasets

The filtered dataset combines examples from two sources:

  • Validation Split: Loaded from benlipkin/folio (validation split)

    • This dataset has approximately 93% accuracy when evaluated with Prover9
    • All correct examples from this validation split are included
  • Train Split: Loaded from yale-nlp/FOLIO (train split)

    • Up to 200 correct examples are included (or fewer if not enough correct examples are found)
    • Processing stops early once 200 correct examples are collected

Filtering Criteria

An example is included in the filtered dataset if:

  1. The gold FOL premises and conclusion can be successfully parsed and evaluated by Prover9
  2. Prover9's output (True/False/Uncertain) matches the gold answer exactly
  3. No errors occur during FOL parsing or Prover9 evaluation

Examples are excluded if:

  • Prover9 produces an error during evaluation
  • Prover9's output does not match the gold answer
  • The FOL cannot be parsed or reformatted correctly

Dataset Structure

The filtered dataset consists of two splits:

Validation Split (validation.json)

  • Source: benlipkin/folio validation split
  • Content: All examples from the source validation split where fol-gold-to-prover9 produces the correct answer
  • Purpose: Used for validation/testing in experiments

Train Split (train.json)

  • Source: yale-nlp/FOLIO train split
  • Content: Up to 200 correct examples (or fewer if not enough are found)
  • Purpose: Used for training/few-shot examples in experiments

Data Format

Each example in the dataset follows the standard FOLIO format:

{
  "id": "example_id",
  "premises": ["premise 1 in natural language", "premise 2 in natural language", ...],
  "conclusion": "conclusion statement in natural language",
  "premises-FOL": ["premise1_fol", "premise2_fol", ...],
  "conclusion-FOL": "conclusion_fol",
  "label": "True" | "False" | "Uncertain",
  ...
}

Statistics

The exact number of examples in each split depends on the filtering results:

  • Validation: All correct examples from benlipkin/folio validation split
  • Train: Up to 200 correct examples from yale-nlp/FOLIO train split
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