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))


Rina eith doesn't want to be addicted to caffeine or is unaware that caffeine is a drug.

¬WantToBeAddictedTo(rina, caffeine) ⊕ ¬AwareThatDrug(rina, caffeine)


Rina either regularly drinks coffee or is unaware that caffeine is a drug.

DrinkRegularly(rina, coffee)  ⊕ IsUnawareThatCaffeineIsADrug(rina)


If Rina either doesn't want to be addicted to caffeine and is unaware that caffeine is a drug, or neither doesn't want to be addicted to caffeine nor is unaware that caffeine is a drug, then Rina doesn't want to be addicted to caffeine and regularly drinks coffee.

(DoNotWantToBeAddictedToCaffeine(rina) ⊕ ¬AwareThatDrug(rina, caffeine)) → ¬(¬WantToBeAddictedTo(rina, caffeine) ∧ DrinkRegularly(rina, coffee))


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)


∃x ∃y (Czech(x) ∧ PublishedBook(x, y, year1946))


No choral conductor specialized in the performance of Renaissance.

∀x (ChoralConductor(x) → ¬SpecializeInPerformanceOf(x, renaissanceMusic))


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.


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)

∃x (Building(x) ∧ Five-Story(x) ∧ ConstructedIn(x, year1915))


The Blake McFall Company Building is located in Portland, Oregon.


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 did not get a seat in 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))


William Dickinson attended university in the United Kingdom.

∃x (Attended(williamDickinson, x) ∧ University(x) ∧ LocatedIn(x, unitedKingdom))


William Dickinson sat in the House of Commons.


LanguageA is a universal language
If a universal language exists, then for every two people if they both know the same universal language they can communicate.
Katya cannot communicate with Danil.
Katya knows LanguageA.

UniversalLanguage(languageA)
∀x ∀y (∃z (¬(x=y) ∧ Know(x, z) ∧ Know(y, z) ∧ UniversalLanguage(z)) → CanCommunicateWith(x, y) ∧ CanCommunicateWith(y, x))
¬CanCommunicateWith(katya, danil)
Know(katya, languageA)


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 or watches 3 movies every week without any additional fees.

GoToEveryWeek(lily, cinema) ∨ EligibleForThreeFreeMoviesWithoutAdditionalFees(lily)


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))


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))


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.


Barcelona ranks higher than Real Madrid.


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)


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.


Tiffany T. Alston was not suspended from the Maryland House of Delegates.


Tiffany T. Alston went to prison for stealing government funds.


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))


Stings of some fish can cause death if not treated.

∃x ∃y (Fish(x) ∧ Sting(x, y) ∧ ¬Treated(y) → CauseDeathTo(x, y))


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))


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)


The L-2021 monitor either has a type-c port or is produced by LG.

Have(l-2021, typeCPort) ⊕ ProducedBy(l-2021, lG)


If the L-2021 monitor is either in the library and produced by LG, or neither in the library nor produced by LG,  then L-2021 neither has a type-c port nor is produced by LG.

¬(In(l-2021, library) ⊕ ProducedBy(l-2021, lG)) → (¬Have(x, typeCPort) ∧ ¬ProducedBy(x, 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))


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 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)


If PSO J318.5−22 is an orphan planet or it does not have the Sun as the star, or both, then PSO J318.5−22 neither is an orphan planet nor does it have the Sun as the star.

(Planet(pSOJ318.5-22) ∧ Orphan(pSOJ318.5-22)) ∨ ¬SunAs(pSOJ318.5-22, star) → (¬(Planet(pSOJ318.5-22) ∧ Orphan(pSOJ318.5-22)) ∧ ¬SunAs(pSOJ318.5-22, star))


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 project Sam is doing is written in C++.

∀x (Project(x) ∧ Do(sam, x) ∧ WrittenIn(x, cplusplus))


The song Sam is playing is titled "Perfect".

∀x (Song(x) ∧ Play(sam, x) ∧ Titled(x, perfect))


If a song is titled "Perfect", Sam will play it.


All rabbits have fur
Some pets are rabbits.

∀x (Rabbit(x) → Have(x, fur))
∃x (Pet(x) ∧ Rabbit(x))

∃x ∃y (Pet(x) ∧ Pet(y) ∧ ¬Have(x, fur) ∧ ¬Have(y, fur))


All social media applications containing chat features are software.
All social media applications that allow users to send messages to each other have chat features.
All social media applications have chat features or video features.
All social media applications that have video features allow users to upload videos.
All software that is social media applications are computer programs.
All social media applications that have high engagement metrics are addictive.
If a social media application is addictive, then it is not ideal for preteens.
TikTok is a social media application, and it is not ideal for preteens.

∀x (SocialMedia(x) ∧ Application(x) ∧ Contain(x, chatFeature) → Software(x))
∀x (SocialMedia(x) ∧ Application(x) ∧ AllowToSendTo(x, user, message) → Contain(x, chatFeature))
∀x (SocialMedia(x) ∧ Application(x) → Contain(x, chatFeature) ∨ Contain(x, videoFeature))
∀x (SocialMedia(x) ∧ Application(x) ∧ Contain(x, videoFeature) → Allow(x, user, uploadVideo))
∀x (SocialMedia(x) ∧ Application(x) ∧ Software(x) → ComputerProgram(x))
∀x (SocialMedia(x) ∧ Application(x) ∧Have(x, highEngagementMetric) → Addictive(x))
∀x (SocialMedia(x) ∧ Application(x) ∧ Addictive(x) → ¬IdealFor(x, preteen))
SocialMedia(tikTok) ∧ Application(tikTok) ∧ ¬IdealFor(tikTok, preteen)


TikTok is either ideal for preteens or a computer program.

IdealFor(tikTok, preteen) ⊕ ComputerProgram(tikTok)


TikTok is does not have chat features or it is not a computer program.

¬Contain(tikTok, chatFeature) ∨ ¬ComputerProgram(tikTok))


TikTok either has chat features or is a computer program.

Contain(tikTok, chatFeature) ⊕ ComputerProgram(tikTok))


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))


There is an unincorporated community located in Elliot County.

∃x (UnincorporatedCommunity(x) ∧ LocatedIn(x, elliotCounty))


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)


Susan is not both diligent and likes independence.

¬(Like(susan, independence) ∧ Diligent(susan))


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)


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.


If Amy is not an Olympic gold medal winner, then Amy is a Nobel physics laureate.


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)


The cherries are either on a warning list or are red.

On(cherry, warningList) ⊕ RedFruit(cherry)


If the cherries are either healthy or are on a warning list, then they are not red.

BeneficialTo(cherry, people) ⊕ On(cherry, warningList))) → ¬RedFruit(cherry)


If the cherries are either on a warning list or are red, then they are not healthy and do not contain any amount of vitamin C.

On(cherry, warningList) ⊕ RedFruit(cherry)) → ¬(BeneficialTo(cherry, people) ∧ Contain(cherry, vitaminC)


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(x, drive) ∨ Student(james)


James either drives to their destination or is a student.

MeansToDestination(x, drive) ⊕ Student(james)


If James either drives to his destination or is a student, then he has a high income and is a student.

(MeansToDestination(x, drive) ⊕ Student(james)) → (HighIncome(james) ∧ Student(james))


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 an investor or is not an ardent communist.


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))


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)))


GoodAt(james, chemistry) ∧ GoodAt(james, math)


James failed the class and is good at math.

Failed(james, james) ∧ GoodAt(james, math)


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))


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 (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.


4Sum is a Leetcode problem recommended to the novice.


2Sum has an AC rate higher than 20 percent.

∃y(GreaterThan(y, percent20) ∧ ACRate(2Sum,y))


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))


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 (Attend(x, wedding) → GettingMarried(x) ∨ (∃y (Know(x, y) ∧ GettingMarried(y)))
∀x (PreTeen(x) ∨ YoungChild(x) → ¬(GettingMarried(x) ⊕ (∃y (Know(x, y) ∧ GettingMarried(y)))))
∀x (∃y ∃z (¬(x=y) ∧ ¬(x=z) ∧ ¬(y=z) ∧ Enjoy(x, celebratingLifeMileStoneEvent, y) ∧ Enjoy(x, celebratingLifeStoneEvent, z)) → Attend(x, wedding))
∀x (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 neither enjoys celebrating life milestone events with other people nor is outgoing and very spirited.

¬((∃y ∃z (¬(x=y) ∧ ¬(x=z) ∧ ¬(y=z) ∧ Enjoy(x, celebratingLifeMileStoneEvent, y) ∧ Enjoy(x, celebratingLifeStoneEvent, z)) ∨ (Outgoing(carol) ∧ Sprited(carol)))


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))

ROUGE Dior Colored Lip Balm 999 has a satin finish.


ROUGE Dior Colored Lip Balm 999 has a satin finish and has "rosewood" in its official description.


ROUGE Dior Colored Lip Balm 999 either is refillable or has "rosewood" in its official description.


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)))


If ROUGE Dior Colored Lip Balm 999 is refillable and has "rosewood" in its official description, then it either has a velvet-finish or has "rosewood" in its official description.

(Refillable(rougeDiorColoredLipBalm999) ∧ RosewoodInDescription(rougeDiorColoredLipBalm999)) —> (VelvetFinish(rougeDiorColoredLipBalm999) ∨ RosewoodInDescription(rougeDiorColoredLipBalm999))


If ROUGE Dior Colored Lip Balm 999 either does not have "rosewood" in its official description or is refillable, then it has "rosewood" in its official description.

(¬RosewoodInDescription(rougeEDiorColoredLipBalm999) ⊕ Refillable(rougeDiorColoredLipBalm999)) → RosewoodInDescription(rougeDiorColoredLipBalm999)


If ROUGE Dior Colored Lip Balm 999 either does not have "rosewood" in its official description or is refillable, then it neither has a satin-finish nor has "rosewood" in its official description.

(RosewoodInDescription(rougeDiorColoredLipBalm999) ⊕ Refillable(rougeDiorColoredLipBalm999)) → ¬(SatinFinish(rougeDiorColoredLipBalm999) ∨ RosewoodInDescription(rougeDiorColoredLipBalm999))


If ROUGE Dior Colored Lip Balm 999 is refillable or has "rosewood" in its official description, then it either is refillable or has "rosewood" in its official description..

(Refillable(rougeDiorColoredLipBalm999) ∨ RosewoodInDescription(rougeDiorColoredLipBalm999)) → (Refillable(rougeEDiorColoredLipBalm999) ⊕ RosewoodInDescription(rougeDiorColoredLipBalm999))


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))


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))


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 either both a pirate and a toddler, or neither a pirate nor a toddler.


If Nancy is not either a pirate or a toddler, then she is young and is a kid.

¬(Pirate(nancy) ⊕ Toddler(nancy)) → Young(nancy) ∧ Kid(nancy)


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)

From(lanaWilson, unitedStates) ∧ Filmmaker(lanaWilson)


Miss Americana is not directed by a filmmaker from Kirkland.

¬∃x(Filmmaker(x) ∧ From(x, kirkland) ∧ DirectedBy(missAmericana, x))


Lana Wilson has won the Independent Spirit Award.


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))


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.


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 (GoTo(x, claysSchool) ∧ ¬(Have(x, y) ∧ Regular(y) ∧ NineToFiveJob(y)) → WorkInAs(x, entertainmentIndustry, highProfileCelebrity))
∀x (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))

Have(bunny, y) ∧ Regular(y) ∧ NineToFiveJob(y)


Bunny went to Clay's school and she lives in California and attends yoga classes regularly.

LiveIn(bunny, california) ∧ AttendRegularly(bunny, yogaClass)


Bunny went to Clay's school and she neither prefers working at home over going to the office nor lives in California and attends yoga classes regularly.

¬(Prefer(bunny, workingAtHome, goingToTheOffice) ∨ (LiveIn(bunny, california) ∧ AttendRegularly(bunny, yogaClass)))


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)


An English professional footballer scored the winning goal in the 1913 FA Cup Final.

∃x (English(x) ∧ ProfessionalFootballer(x) ∧ ScoredTheWinningGoalIn(x, facupfinal1913))


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))


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(x))


Archie has functional leg muscles and can control his balance.

FunctionalLegMuscle(archie) ∧ CanControl(archie, balance)


Archie cannot control his balance and doesn't have functional leg muscles.

¬CanControl(archie, balance) ∧ ¬FunctionalLegMuscle(x)


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) ∧ ¬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))


P value represents the selection intensity for somatic variants in cancer cell lineages.


Cancer effect size is preferred by cancer researchers.


P values don't represent metrics of effect.


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)


No reptile has fur.
All snakes are reptiles.

∀x (Reptile(x) → ¬Have(x, fur))
∀x (Snake(x) → Reptile(x))


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)


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.


Ron is either both a penguin and endothermic, or he is nether.


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))


There is a species of Ambiortus that doesn't live in Mongolia.

∃x (KnownSpeciesOf(x, ambiortus) ∧ ¬LiveIn(x, mongolia))


All species of Ambiortus live in Mongolia.

∀x (SpeciesOf(x, ambiortus) → LiveIn(x, mongolia))


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)


Jack cannot be deprived of their rights without due process of law.


Jack can be deprived of their rights without due process of law.


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))


Pierre de Rigaud de Vaudreuil built a fort in New England.

∃x (Built(pierredeRigauddeVaudreuil, x) ∧ LocatedIn(x, newEngland))


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) ⊕ ProfessionalSoccerPlayer(stephencurry)) → ProfessionalBasketballPlayer(stephencurry)


Stephen Curry is not a centerback player.


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.


All inductive reasoning processes derive general principles from a body of observations.
Two major types of reasoning rules are inductive reasoning and deductive reasoning.
All deductive reasoning processes are only based on facts and rules.
Nothing only based on facts and rules is used for statistical generalization.
Modus Ponens is not both used in inductive reasoning and used for statistical generalization.
Modus Ponens is a component of a major part of reasoning rule.

∀x (InductiveReasoning(x) → DeriveFrom(generalPrinciple, observations))
∀x (MajorArgumentForm(x) → (InductiveReasoning(x) ⊕ DeductiveReasoning(x))
∀x (DeductiveReasoning(x) → (BasedOn(x, fact) ∨ BasedOn(x, rule)))
∀x ((BasedOn(x, fact) ∨ BasedOn(x, rule)) → (¬UsedFor(x, statisticalGeneralization)))
¬(InductiveReasoning(modusPonens) ∧ UsedFor(modusPonens, statisticalGeneralization))
ArgumentForm(modusPonens)

Reasoning with Modus Ponens is based on facts and rules.


Modus Ponens derives general principles from a body of observations and is used for statistical generalization.

DeriveFrom(generalPrinciple, observations) ∧ UsedFor(x, statisticalGeneralization)


If Modus Ponens either derives general principles from a body of observations and is used for statistical generalization, or neither, then Modus Ponens is is neither used in inductive reasoning  nor used for statistical generalization.

¬(Derive(generalPrinciple, observations) ⊕ UsedFor(x, statisticalGeneralization)) → (¬InductiveReasoning(modusPonens) ∧ (¬UsedFor(modusPonens, statisticalGeneralization)))


No trick-shot artist in Yale's varsity team struggles with half court shots.
Everyone on Yale's varsity team is someone who struggles with half court shots or who successfully shoots a high percentage of 3-pointers.
Everyone on Yale's varsity team who successfully shoots a high percentage of 3-pointers is solid at shooting 2-pointers.
No one on Yale's varsity team who is solid at shooting 2-pointers is bad at mid-range shots.
Jack is on Yale's varsity team, and he is either a trick-shot artist or he successfully shoots a high percentage of 3-pointers.

∀x ((In(x, yaleSVarsityTeam) ∧ TrickShotArtist(x)) → ¬StruggleAt(x, halfCourtShot))
∀x (In(x, yaleSVarsityTeam) → (StruggleAt(x, halfCourtShot) ∨ GoodAt(x, threes)))
∀x ((In(x, yaleSVarsityTeam) ∧ GoodAt(x, threes)) → GoodAt(x, twos))
∀x ((In(x, yaleSVarsityTeam) ∧ GoodAt(x, twos)) → BadAt(x, midRangeShot))
In(jack, yaleSVarsityTeam) ∧ (TrickShotArtist(jack) ⊕  GoodAt(jack, threes))


Jack is solid at shooting 2-pointers or bad at mid-range shots.

GoodAt(jack, twos) ∨ BadAt(jack, midRangeShot)


Jack is either solid at shooting 2-pointers or bad at mid-range shots.

GoodAt(jack, twos) ⊕ BadAt(jack, midRangeShot)


Jack is a trick-shot artist or bad at mid-range shots.

TrickShotArtist(jack) ∨ BadAt(jack, midRangeShot))


Jack is either a trick-shot artist or bad at mid-range shots.

TrickShotArtist(jack) ⊕ BadAt(jack, midRangeShots)


Jack is either a player who successfully shoots a high percentage of 3-pointers or is bad at mid-range shots.

GoodAt(jack, threes) ⊕ BadAt(jack, midRangeShot)


If Jack is not solid at shooting 2-pointers and bad at mid-range shots, then Jack is not solid at shooting 2-pointers and is a player who successfully shoots a high percentage of 3-pointers.

BadAt(jack, midRangeShot) ∧ GoodAt(jack, twos) → ¬GoodAt(jack, twos) ∧ GoodAt(jack, threes)


If Jack is solid at shooting 2-pointers or successfully shoots a high percentage of 3-pointers, then Jack struggles at half court shots and is bad at mid-range shots.

GoodAt(jack, twos) ∨ GoodAt(jack, threes) → BadAt(jack, halfCourtShot) ∧ BadAt(jack, midRangeShot)


No plants are fungi.
Mushrooms are fungi.

∀x (Plant(x) → ¬Fungi(x))
∀x (Mushroom(x) → Fungi(x))


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))

∃x ∃y (Street(x) ∧ Street(y) ∧ Dustless(x) ∧ Dustless(y) ∧ ¬(x=y))


New York City is located on the East Coast.
Seattle is located on the West Coast.
If a person is somewhere located on the East coast and is traveling to somewhere located on the west coast, they will be on a long flight.
People in business class from New York City to Seattle are not in first class.
People on long flights are uncomfortable unless they're in first class.

LocatedOn(newYorkCity, eastCoast)
LocatedOn(seattle, westCoast)
∀x ∀y ∀z ((TravelingFrom(x, y) ∧ LocatedOn(y, eastcoast) ∧ TravelingTo(x, z) ∧ LocatedOn(z, westcoast)) → OnLongFlight(x))
∀x (InBuisnessClass(x) ∧ TravelingTo(x, seattle) ∧ TravelingFrom(x, newYorkCity) → ¬InFirstClass(x))
∀x (OnLongFlight(x) ∧ ¬InFirstClass(x) → Uncomfortable(x))

People traveling in business class from New York City to Seattle will be uncomfortable.

∃x (TravelingTo(x, seattle) ∧ TravelingFrom(x, newYorkCity) ∧ uncomfortable(x))


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)))


Each building is tall.
Everything tall has height.

∀x (Building(x) → Tall(x))
∀x (Tall(x) → Height(x))


A cat named Garfield, the main character of the film Garfield, is orange and fat and likes having lasagna.
Garfield shares a home with Odie, another pet of Jon's.
Garfield hates Odie.
A pet who hates the pet with whom he shares the same owner is childish and possessive.

Cat(garfield) ∧ MainCharacterOf(garfield, filmGarfield) ∧ Orange(garfield) ∧ Fat(garfield) ∧ Like(garfield, lasagna)
PetOf(garfield, jon) ∧ PetOf(odie, jon) ∧ ShareHomeWith(garfield, odie)
Hate(garfield, odie)
∀x ∀y ∃z (PetOf(x, z) ∧ PetOf(y, z) ∧ Hate(x, y) → Childish(x) ∧ Possessive(x))

The main character of the film Garfield is childish and possessive.

∃x (MainCharacterOf(x, garfield) ∧ Childish(x) ∧ Possessive(x))


All humans are capable of abstract thoughts.
Plants are not capable of abstract thoughts.
All multicellular creatures that are autotrophic or digest food internally are plants and animals.
All goats are animals.
Dirt is not an animal.
Hulu is a goat or a human.
Hulu is a multicellular creature that is autotrophic or digests food internally.

∀x (Human(x) → CapableOf(x, abstractThought))
∀x (Plant(x) → ¬CapableOf(x, abstractThought))
∀x (MulticellularCreature(x) ∧ (Autotrophic(x) ∨ DigestFoodInternally (x)) → Plant(x) ⊕ Animal(x))
∀x (Goat(x) → Animal(x))
∀x (Dirt(x) → ¬Animal(x))
Goat(hulu) ∨ HumanBeing(hulu)
(MulticellularCreature(hulu) ∧ (Autotrophic(hulu) ∨ DigestFoodInternally (hulu))


Hulu is not capable of abstract thoughts.


Hulu is either an animal or dirt, but not both.


If Hulu is either an animal or dirt, then Hulu is capable of abstract thoughts and is dirt.

Animal(hulu) ⊕ Dirt(hulu) → CapableOf(hulu, abstractThought) ∧ Dirt(hulu)


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 harmful things.

∀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(controlledSubstancesAct, yr1971) ∧ Act(controlledSubstancesAct)
∃x ∃y(Act(x) ∧ PreventsHarm(x) ∧ (¬(x=y)) ∧ Act(y) ∧ PreventsHarm(y))

The Controlled Substances Act prevents harmful things.


∃x ∃y(Drugs(x) ∧ Beneficial(x) ∧ (¬(x=y)) ∧ Drugs(y) ∧ Beneficial(y))


A child in chemical endangerment is in harm.

∀x ((Child(x) ∧ InChemicalEndangerment(x)) → Harmful(x))


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 Zuckerberg is neither an entrepreneur nor a person who hates working for others, then Mark Zuckerberg is not a risk-averse working person.

∀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=markZuckerberg) ∧ ¬(z=markZuckerberg) ∧ ¬(y=z) ∧ HateWorkingFor(markZuckerberg, y) ∧ HateWorkingFor(markZuckerberg, z))) → ¬RiskAverse(markZuckerberg)


Mark Zuckerberg is a risk-averse person.


Mark Zuckerberg is not a risk-averse person.


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))


Syndicated shows are copyright violations.

∃x (SyndicatedShows(x) ∧ CopyrightViolation(x))


New York City is Located in the United States of America.
The United States of America is part of North America.
North America is in the western hemisphere of the earth.
New York City is a highly developed city.
If place A is located in place B and place B is located in place C, then place A is located in place C.

LocatedIn(newYorkCity, unitedStatesOfAmerica)
LocatedIn(usa, northAmerica)
LocatedIn(northAmerica, westernHemisphere)
HighlyDeveloped(newYorkCity)
∀x ∀y ∀z ((LocatedIn(x, y) ∧ LocatedIn(y, z)) → LocatedIn(x, z))

A highly developed city is located in the western hemisphere of the earth.

∃x (HighlyDeveloped(x) ∧ LocatedIn(x, westernHemisphere))


The United States of America is not located in the western hemisphere of the earth.


New York City is located in New York State.


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)

There is a poem written by an ancient Roman writer with a strong analogy of human aging.

∃x ∃y (Poem(x) ∧ WrittenBy(x, y) ∧ AncietRomanWriter(y) ∧ StrongAgingAnalogy(x))


There is a poem written by an ancient Roman writer in iambic trimeter.

∃x ∃y (Poem(x) ∧ WrittenBy(x, y) ∧ AncientRomanWriter(y) ∧ WrittenIn(x, iambicTrimeter))


Callus 4 is written in an unusual iambic trimeter to convey a strong analogy of human aging.

Poem(catullus4) ∧ WrittenIn(catullus4, iambicTrimeter) ∧ StrongAgingAnalogy(catullus4)


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 and begin killing human visitors.

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, malfunctioningRobots)

Michael Crichton has directed a film about malfunctioning robots.

∃x (Film(x) ∧ Directed(michael, x) ∧ About(x, malfunctioningRobots))


∃x (TVSeries(x) ∧ American(x) ∧ Debut(x, year2016))


The 2008 Summer Olympics were held in Beijing, China.
The 2008 Summer Olympics was the second Summer Olympic Games held in a communist state.
China won the most gold medals (48) in the 2008 Summer Olympics.
The United States placed second in the gold medal tally but won the highest number of medals overall (112) in the 2008 Summer Olympics.
The third place in the gold medal tally was achieved by Russia in the 2008 Summer Olympics.
If a country placed third in gold medals, then it had fewer gold medals than the team that won the most gold medals.

HeldIn(2008SummerOlympics, beijingChina)
SecondSummerOlympicsGames(2008SummerOlympics) ∧ BeHeldIn(2008SummerOlympics, communistState)
Won(china, theMostGoldMedals)
PlacedSecondInGoldMedalsIn(unitedStates, 2008SummerOlympics) ∧ Won(unitedStates, highestNumberOfMedals)
PlacedThirdInGoldMedalsIn(russia, 2008SummerOlympics)
∀x ∀y (Placed(x, thirdInGoldMedals) ∧ Won(y, mostGoldMedals) → FewerGoldMedalsThan(x, y))

Russia did not win fewer gold medals than China.


Russia won fewer gold medals than China.


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))


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 their own fresh vegetables in their home garden.
All of Michael's neighbors who enjoy going out often to restaurants with friends order takeout from delivery services often.
All of Michael's neighbors who regularly tout the benefits of homegrown and homecooked meals over fast food enjoy going out often to restaurants with friends.
Peter, Michael's neighbor, grows his own fresh vegetables in his home garden, or regularly touts the benefits of homegrown and homecooked meals over fast food, or both.

∀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) ∧ EnjoyGoingOutOftenToWith(x, restaurant, friend) → OrderOften(x, takeout))
∀x (MichaelsNeightbor(x) ∧ ToutOver(x, homecookedMeals, fastFood) → EnjoyGoingOutOftenToWith(x, restaurant, friend))
MichaelsNeightbor(peter) ∧ (GrowIn(peter, vegetable, garden) ∨ ToutOver(peter, homecookedMeals, fastFood))

Peter enjoys going out often to restaurants with friends.


Peter is a young working professional who lives in large cities.

YoungWorkingProfession(peter) ∧ LiveIn(peter, largeCity)


Peter grows his own fresh vegetables in their home garden or is a young working professional who lives in large cities.

GrowIn(peter, vegetable, garden) ∨ (YoungWorkingProfession(peter) ∧ LiveIn(peter, largeCity))


All devices belonging to the company are connected to Google Home.
All devices belonging to employees are connected to the company's wifi.
All devices connected to Google Home are controlled by the managers.
All devices that connect to the company's wifi are easy to operate.
ModelXX belongs to employees.

∀x (OwnedBy(x, company) → ConnectedTo(x, googleHome))
∀x (OwnedBy(x, employee) → ConnectedTo(x, companyWiFi))
∀x (ConnectedTo(x, googleHome) → ControlledBy(x, managers))
∀x (ConnectedTo(x, companyWiFi) → EasyToOperate(x))
OwnedBy(modelXX, employee)


No touring musicians who perform at the New Haven Symphony Orchestra are permanent members of the orchestra.
Musicians who perform at the New Haven Symphony Orchestra are permanent members of an orchestra, or they have temporary roles at the orchestra.
All touring musicians who perform at the New Haven Symphony Orchestra have temporary roles at the orchestra.
All musicians performing at the New Haven Symphony Orchestra who have temporary roles at the orchestra are interesting soloists.
All musicians performing at New Haven Symphony Orchestra who are interesting soloists are capable of attracting audiences.
Ryan is performing at New Haven Symphony Orchestra.
If Ryan is an interesting soloist and has a temporary role at the orchestra, then he is capable of attracting large audiences if and only if he is a touring soloist musician.

∀x ((PerformAt(x, newHavenSymphonyOrchestra) ∧ TouringMusician(x)) → ¬PermanentMemberOf(x, theOrchestra))
∀x (PerformAt(x, newHavenSymphonyOrchestra) → (PermanentMemberOf(x, theOrchestra) ∨ HaveTemporaryRoleAt(x, theOrchestra)))
∀x ((PerformAt(x, newHavenSymphonyOrchestra) ∧ TouringMusicians(x)) → HaveTemporaryRoleAt(x, theOrchestra))
∀x ((PerformAt(x, newHavenSymphonyOrchestra) ∧ HaveTemporaryRoleAt(x, theOrchestra)) → InterestingSoloist(x))
∀x ((PerformAt(x, newHavenSymphonyOrchestra) ∧ InterestingSoloist(x)) → CapableOfAttractingAudiences(x))
PerformAt(ryan, newHavenSymphonyOrchestra)
(InterestingSoloist(ryan) ∧ HaveTemporaryRoleAt(ryan, theOrchestra)) → ¬(TouringMusician(ryan) ⊕ CapableOfAttractingAudiences(ryan))


Ryan is either a permanent member of an orchestra or a touring soloist musician.

(PermanentMemberOf(ryan, orchestra) ⊕ TouringMusician(ryan))


Ryan is either a permanent member of an orchestra or has a temporary role at the orchestra.

(PermanentMemberOf(ryan, orchestra) ⊕ HaveTemporaryRoleAt(ryan, orchestra))


If someone in Potterville yells, then they are not cool.
If someone in Potterville is angry, then they yell.
If someone in Potterville flies, then they are cool.
Every person in Potterville that knows magic flies.
All wizards in Potterville know magic.
Harry, who lives in Potterville either yells or flies.
Potter, who lives in Potterville, is a wizard and flies.

∀x (In(x, potterville) ∧ Yell(x) → ¬Cool(x))
∀x (In(x, potterville) ∧ Angry(x) → Yell(x))
∀x (In(x, potterville) ∧ Fly(x) → Cool(x))
∀x (In(x, potterville) ∧ Know(x, magic) → Fly(x))
∀x (In(x, potterville) ∧ Wizard(x) → Know(x, magic))
In(harry, potterville) ∧ (Yell(harry) ⊕ Fly(harry))
Wizard(potter) ∧ Fly(potter)


All of this brand's products are either produced in China or in the US.
All of this brand's products produced in China are labeled.
All of this brand's products produced in the US are sold in the US.
The products of this brand that are labeled are cheaper.
All of this brand's products sold in the US are sold at Walmart.
All products of this brand displayed on the homepage are sold at Walmart.
None of this brand's products that are returned by customers are sold at Walmart.
G-910 is a product of this brand, and it is either displayed on the homepage and is cheaper, or it is neither displayed on the homepage nor is it cheaper.

∀x (ThisBrand(x) ∧ Product(x) → (ProducedIn(x, china) ⊕ ProducedIn(x, uS)))
∀x ((ThisBrand(x) ∧ Product(x) ∧ ProducedIn(x, china)) → Labeled(x))
∀x ((ThisBrand(x) ∧ Product(x) ∧ ProducedIn(x, us)) → SoldIn(x, us))
∀x ((ThisBrand(x) ∧ Product(x) ∧ Labeled(x)) → Cheaper(x))
∀x ((ThisBrand(x) ∧ Product(x) ∧ SoldIn(x, us)) → SoldIn(x, walmart))
∀x (ThisBrand(x) ∧ Product(x) ∧ DisplayedIn(x, homepage) → SoldIn(x, walmart))
∀x (ThisBrand(x) ∧ Product(x) ∧ ReturnedBy(x, customer) → ¬SoldIn(x, walmart))
Product(g910) ∧ ThisBrand(g910) ∧ (¬(DisplayedIn(g910, homepage) ⊕ Cheaper(g910)))


G-910 is a product returned by customers.

ThisBrand(g910) ∧ ReturnedBy(g910, customer)


G-910 is a product returned by customers or sold in Walmart.

ThisBrand(g910) ∧ (ReturnedBy(g910, customer) ∨ SoldIn(g910, walmart))


G-910 is either returned by customers or sold in Walmart.

ReturnedBy(g910, customer) ⊕ SoldIn(g910, walmart)


People either believe in Santa Claus, or think he is made up.
People who believe in Santa Claus expect to get presents on Christmas morning.
People who think Santa Claus is made up, then they would be surprised to see him in their house.
People who expect presents on Christmas morning are excited for it to be Christmas.
If people would be surprised to see Santa Claus in their house, then they don't leave out cookies on Chrismtas Eve.
Mercy is not someone who expects presents Christmas morning, is excited for Chrismtas, and believes in Santa Claus.

∀x (BelieveIn(x, santaClaus) ⊕ ThinkMadeUp(x, santaClaus))
∀x (BelieveIn(x, santaClaus) → Expect(x, present, christmasMorning))
∀x (ThinkMadeUp(x, santaClaus) → WouldBeSurprisedToSeeIn(x, santaClaus, house))
∀x (Expect(x, present, christmasMorning) → ExcitedFor(x, christmas))
∀x (WouldBeSurprisedToSeeIn(x, santaClaus, house) → ¬LeaveOut(x, cookies))
¬(Expect(marcy, present, christmasMorning) ∧ ExcitedFor(marcy, christmas) ∧ BelieveIn(marcy, santaClaus))

Marcy either believes in Santa Claus or doesn't leave cookies out on Christmas Eve.

BelieveIn(marcy, santaClaus) ⊕ LeaveOut(marcy, cookies)


Marcy is not someone who both leaves out cookies on Chrismtas eve and thinks Santa Claus is made up, or Marcy believes in Santa Claus.

¬(LeaveOut(marcy, cookies) ∧ ThinkMadeUp(marcy, santaClaus)) ∨ BelieveIn(marcy, santaClaus)


Indonesia is a country.
In Indonesia, the prosecutor only personally investigates cases of some special crimes.
Corruption is a type of crime.
Once the police complete crime investigations, the evidence is handed to the prosecutor.
Evidence can be either satisfactory or unsatisfactory.
If the evidence is handed to the prosecutor and the evidence is satisfactory, the prosecutor will prosecute the offender in an appropriate court.

Country(indonesia)
∀x ∃y (In(indonesia) ∧ Prosecutor(x) ∧ SpecialCrime(y) → InvestigatePersonally(x, y))
Crime(corruption)
∀x ∀y ∀z (Crime(y) ∧ PoliceCompleteInvestigation(y) ∧ Prosecutor(x) → Evidence(z) ∧ HandedTo(z, x))
∀x (Evidence(x) ∧ (Satisfactory(x) ⊕ Unsatisfactory(x)))
∀x ∀y (Evidence(y) ∧ Prosecutor(x) ∧ HandedTo(x) ∧ Satisfactory(y) → ProsecuteInAppropriateCourt(x, theOffender))

When the police complete investigations, the prosecutor will prosecute the offender at an appropriate court.

∀x ∀y (Crime(y) ∧ PoliceCompleteInvestigation(y) ∧ Prosecutor(x) → ProsecuteInAppropriateCourt(x, theOffender))


In Indonesia, the prosecutor personally investigates cases of corruption.

∀x (Country(indonesia) ∧ Prosecutor(x) ∧ Crime(corruption) → InvestigatePersonally(x, corruption))


When the police complete investigations, the prosecutor investigates personally.

∀x ∀y (Crime(y) ∧ PoliceCompleteInvestigation(y) ∧ Prosecutor(x) → InvestigatePersonally(x, y))


No battery-powered watch is automatic.
All digital watches are battery-powered.
Some mechanical watches are automatic.
All smart watches are digital.
Moonwatch is either a digital watch and an automatic, or it is neither.

∀x (BatteryPoweredWatch(x) → ¬AutomaticWatch(x))
∀x (DigitalWatch(x) → BatteryPoweredWatch(x))
∃x (MechanicalWatch(x) ∧ AutomaticWatch(x))
∀x (SmartWatch(x) → DigitalWatch(x))
¬(DigitalWatch(moonwatch) ⊕ AutomaticWatch(moonwatch))


Moonwatch is a smartwatch and a mechanical watch.


If Moonwatch is a smartwatch and a mechanical watch, then Moonwatch is not a mechanical watch.

SmartWatch(moonwatch) ∧ MechanicalWatch(moonwatch) → ¬MechanicalWatch(moonwatch)


If Moonwatch is a mechanical or battery-powered watch, then Moonwatch is not a smartwatch.

MechanicalWatch(moonwatch)) ∨ BatteryPoweredWatch(moonwatch) → ¬SmartWatch(moonwatch)


If a person can distinguish the taste of different condiments, then they can also use different condiments for cooking.
People who have a talent of cooking can distinguish the taste of different condiments.
Only people with the talent of cooking can make delicious meals.
If the meal is popular at the party, then it is delicious.
John can make meals which are popular at the party.

∀x (Person(x) ∧ Can(x, distinguishTheTasteOfDifferentCondiments) → Can(x, useDifferentCondimentsToCook))
∀x (Person(x) ∧ Has(x, talentOfCooking) → Can(x, distinguishTheTasteOfDifferentCondiments))
∀x ∀y (CanMake(x, y) ∧ Meal(y) ∧ Delicious(y) ∧ Person(x) → Has(x, talentOfCooking))
∀x ∀y (Meal(y) ∧ PopularAt(y, party) → Delicious(y))
∃x (Person(john) ∧ MakeMeal(john, x) ∧ Meal(x) ∧ PopularAt(x, party))

John cannot use different condiments for cooking.


For a country, if effective monetary policy is possible, it must have successful inflation control and a strong national currency.
A country cannot simultaneously regulate the exchange rate and successfully control inflation.
The introduction of an embargo on foreign trade goods in a country leads to a sharp decrease in exports.
If exports fall sharply, this country's national currency cannot be strong.
Inflation control is required to have a strong national currency.
There is an embargo on Russian foreign trade goods.

∀x (Country(x) ∧ PossibleEffectiveMonetaryPolicy(x) → SuccessfulInflationControl(x) ∧ StongNationalCurrency(x))
¬(∃x (Country(x) ∧ SuccessfulInflationControl(x) ∧ RegulateExchangeRate(x)))
∀x (IntroductionOfOn(x, embargo, foreightTradeGoods) → SharpDecreasesInExport(x))
∀x (SharpDecreasesInExport(x) → ¬StongNationalCurrency(x))
∀x (InflationControl(x) → StongNationalCurrency(x))
IntroductionOfOn(russia, embargo, foreightTradeGoods)

In Russia, an effective monetary policy is possible.


Video Gag is a French television series that airs weekly.
Video Gag airs on the French broadcast channel TF1.
If viewers send funny videos to the French broadcast channel TF1, then Video Gag airs them weekly.
All videos aired on Video Gag are in French.

FrenchTelevision(videoGag) ∧ AirWeekly(videoGag)
AirOn(videoGag, frenchBroadcastChannelTF1)
∀x (Funny(x) ∧ Video(x) ∧ SendIn(viewers, x, frenchBroadcastChannelTF1)  → AirWeekly(x) ) ∧ AirOn(videoGag, x))
∀x (Video(x) ∧ AirOn(videoGag, x) → In(x, french))

Viewers send funny videos to the French broadcast channel TF1 that are in French.

∃x (SendIn(viewers, x, frenchBroadcastChannelTF1) ∧ French(x))


Viewers send funny videos to the French broadcast channel that are in English.

∃x (SendIn(viewers, x, frenchBroadcastChannelTF1) ∧ English(x))


All phones are things.
All cell phones are phones.
All iPhones are cell phones.
All employees are wage earners.
All wage earners are human.
Jack is either an employee or a wage earner.
Jack is either a human or a phone.

∀x (Phone(x) → Thing(x))
∀x (Cellphone(x) → Phone(x))
∀x (Iphone(x) → Cellphone(x))
∀x (Employee(x) → WageEarner(x))
∀x (WageEarner(x) → Human(x))
Employee(jack) ⊕ WageEarner(jack)
Human(jack) ⊕ Phone(jack)


All iPhones are electronic.
Some phones are iPhones.

∀x (IPhone(x) → Electronic(x))
∃x ∃y (Phone(x) ∧ Phone(y) ∧ IPhone(x) ∧ IPhone(y) ∧ ¬(x=y))


The Metropolitan Museum of Art is a museum in NYC.
Whitney Museum of American Art is a museum in NYC.
The Museum of Modern Art (MoMA) is a museum in NYC.
The Metropolitan Museum of Art includes Byzantine and Islamic Art.
Whitney Museum of American Art includes American art.

Museum(metropolitanMuseumOfArt) ∧ In(metropolitanMuseumOfArt, nYC)
Museum(whitneyMuseumOfAmericanArt) ∧ In(metropolitanMuseumOfArt, nYC)
Museum(museumOfModernArt) ∧ In(museumOfModernArt, nYC)
Include(metropolitanMuseumOfArt, byzantineArt) ∧ Include(metropolitanMuseumOfArt, islamicArt)
Include(whitneyMuseumOfAmericanArt, americanArt)

A museum in NYC includes Byzantine and Islamic Art.

∃x (Museum(x) ∧ In(x, nYC) ∧ Include(x, byzantineArt) ∧ Include(x, islamicArt))


∃x (Museum(x) ∧ In(x, nYC) ∧ Include(x, americanArt))


∃x (Museum(x) ∧ In(x, nYC) ∧ Include(x, greekArt))


There's a person in Benji's family who likes eating cheese or is a francophile.
There is no francophile in Benji's family whose favorite country is Spain.
There is a person in Benji's family who likes eating cheese or whose favorite country is Spain.
Fabien is in Benji's family and  does not both study Spanish and also like eating cheese.
Fabien studies Spanish.

∃x (InBenjiSFamily(x) → (LikeEating(x, cheese) ∨ Francophile(x)))
∀x ((InBenjiSFamily(x) ∧ Francophile(x)) → ¬Favor(x, spain))
∃x (InBenjiSFamily(x) ∧ (Favor(x, spain) ∨ LikeEating(x, cheese)))
InBenjiSFamily(fabien) ∧ (¬(LikeEating(fabien, cheese) ∧ Study(fabien, spanish)))
Study(fabien, spanish)

Fabien is a person who likes eating cheese.


If Fabien is either a person who likes eating cheese or a francophile, then Fabien is neither a person who studies Spanish nor a person who is a francophile.

(LikeEating(fabien, cheese) ⊕ Francophile(fabien)) → (¬(Study(fabien, spanish) ∨ Francophile(fabien)))


If Fabien is a person who likes Spain as their favorite country or is a francophile, then Fabien is either a person who studies Spanish or a person who likes Spain as their favorite country.

(Favor(fabien, spain) ∨ Francophile(fabien)) → (Study(fabien, spanish) ⊕ Favor(fabien, spain))


Gasteren is a village located in the province of Drenthe.
Drenthe is a Dutch province.
No cities are villages.
The population of a village in Drenthe was 155 people.

Village(gasteren) ∧ Province(drenthe) ∧ In(gasteren, drenthe)
Province(drenthe) ∧ In(drenthe, netherlands)
∀x (City(x) → ¬Village(x))
∃x (Population(x, num155) ∧ Village(x) ∧ In(x, drenthe))

Village(gasteren) ∧ In(gasteren, netherlands)


The only types of mammals that lay eggs are either platypuses or echidnas.
Platypuses are not hyrax.
Echidnas are not hyrax.
No mammals are invertebrates.
All animals are either vertebrates or invertebrates.
Mammals are animals.
Hyraxes are mammals.
Grebes lay eggs.
Grebes are not platypuses and also not echidnas.

∀x ((Mammal(x) ∧ LayEgg(x)) → (Platypus(x) ⊕ Echidna(x)))
∀x (Platypuses(x) → ¬Hyrax(x))
∀x (Echidnas(x) → ¬Hyrax(x))
∀x (Mammal(x) → ¬Invertebrate(x))
∀x (Animal(x) → (Vertebrate(x) ∨ Invertebrate(x)))
∀x (Mammal(x) → Animal(x))
∀x (Hyrax(x) → Mammal(x))
∀x (Grebes(x) → LayEgg(x))
∀x (Grebes(x) → (¬Platypuses(x) ∧ ¬Echidnas(x)))


Bobby Flynn is a singer-songwriter.
Bobby Flynn finished 7th while competing on Australian Idol.
Australian Idol competitors are Australian citizens.
The Omega Three band made a nationwide tour in 2007.
Bobby Flynn is a member of The Omega Three band.
Bobby Flynn was born in Queensland.

Singer(bobbyFlynn) ∧ SongWriter(bobbyFlynn)
FinishesIn(bobbyFlynn, number7) ∧ CompetesOnAustralianIdol(bobbyFlynn)
∀x (CompetesOnAustralianIdol(x) → AustralianCitizen(x))
NationWideTourIn(theOmegaThreeBand, year2007)
Member(bobbyFlynn, theOmegaThreeBand)
BornIn(bobbyFlynn, queensland)


All proteins are organic compounds.
All enzymes are organic compounds.

∀x (Protein(x) → OrganicCompound(x))
∀x (Enzyme(x) → OrganicCompound(x))


Maggie Friedman is an American screenwriter and producer.
Maggie Friedman was the showrunner and executive producer of the lifetime television series Witches of East End.
Witches of East End is a fantasy-drama series.
Maggie Friedman produced and developed Eastwick.
Eastwick is a series by ABC.

American(maggieFriedman) ∧ Screenwriter(maggieFriedman) ∧ Producer(maggieFriedman)
ShowRunnerOf(maggieFriedman, witchesOfEastEnd) ∧ ExecutiveProducerOf(maggieFriedman, witchesOfEastEnd) ∧ LifetimeTelevisionSeries(maggieFriedman)
FantasyDrama(witchesOfEastEnd) ∧ Series(witchesOfEastEnd)
Produces(maggieFriedman, eastwick) ∧ Develops(maggieFriedman, eastwick)
Series(eastwick) ∧ AiredOn(eastwick, aBC)

There is a series by ABC that was developed by the showrunner of Witches of East End.

∃x ∃y (Series(x) ∧ AiredOn(x, aBC) ∧ Develops(y, x) ∧ ShowRunnerOf(y, witchesOfEastEnd))


No series by ABC was developed by the showrunner of Witches of East End.

∀x (Series(x) ∧ AiredOn(x, aBC) ∧ ∃y(ShowRunnerOf(y, witchesOfEastEnd)) → ¬Develops(y, x))


Maggie Friedman developed Witches of East End.


Evangelos Eleftheriou is a Greek electrical engineer.
Evangelos Eleftheriou worked for IBM in Zurich.
If a company has employees working for them somewhere, then they have an office there.
IBM is a company.

Greek(evangelosEleftheriou) ∧ ElectricalEngineer(evangelosEleftheriou)
WorkForIn(evangelosEleftheriou, iBM, zurich)
∀x ∀x ∀z (Company(x) ∧ WorkForIn(y, x, z) → HaveOfficeIn(x, z))
Company(ibm)

IBM has an office in London or Zurich or both.

HaveOfficeIn(ibm, london) ∨ HaveOfficeIn(ibm, zurich)


Boney M. had several German #1 singles.
"Hooray! Hooray! It's a Holi-Holiday!" was a big hit all over Europe.
"Hooray! Hooray! It's a Holi-Holiday!" was not in German #1 singles.
A song that peaks below #1 on the german charts is also a song that is not the #1 single in Germany.

∃x (Song(x) ∧ By(x, boneym,) ∧ Number1GermanSingle(x))
Song(hoorayHoorayItsAHoliHoliday) ∧ HitAllOverEurope(hoorayHoorayItsAHoliHoliday)
Song(hoorayHoorayItsAHoliHoliday) ∧ ¬Number1GermanSingle(hoorayHoorayItsAHoliHoliday)
∀x (PeakBelowOn(x, number1, germanChart) → ¬Number1GermanSingle(x))

"Hooray! Hooray! It's a Holi-Holiday!" was the #1 hit in Germany.


"Hooray! Hooray! It's a Holi-Holiday!" peaked below #1 on the German charts.


"Hooray! Hooray! It's a Holi-Holiday!" peaked at #3 on the UK charts.


Every chef can cook.
Some people who aren’t chefs can cook.
People who cook can make scrambled eggs and pasta.
If someone can make cookies and muffins, they are a baker.
Bakers who can also make scrambled eggs can make a good breakfast.
Luke can make cookies, scrambled eggs, and muffins, but not pasta.

∀x (Chef(x) → Can(x, cook))
∃x (¬Chef(x) ∧ Can(x, cook))
∀x (Can(x, cook) → (CanMake(x, scrambledEggs) ∧ CanMake(x, pasta)))
∀x (CanMake(x, cookies) ∧ CanMake(x, muffins) → Baker(x))
∀x ((Baker(x) ∧ CanMake(x, scrambledEggs)) → CanMake(x, goodBreakfast))
CanMake(luke, cookies) ∧ (CanMake(luke, scrambledEggs) ∧ CanMake(luke, muffins) ∧ ¬CanMake(luke, pasta)


ETS develops various standardized tests primarily in the United States for K-12 and higher education.
ETS administers international tests, including the TOEFL, TOEIC, GRE, and subject tests.
Many of the assessments ETS develops are associated with entry to the US tertiary and quaternary education institutions.
ETS also develops K-12 statewide assessments used for accountability testing in many states.

∃x ∃y (Develop(eTS, x) ∧ Develop(eTS, y) ∧ StandardizedTest(x) ∧ StandardizedTest(y) ∧ In(x, unitedState) ∧ In(y, unitedState) ∧ For(x, k12AndHigherEducation) ∧ For(y, k12AndHigherEducation))
∃x (Administer(eTS, x) ∧ InternationalTest(x) ∧ (TOEFL(x) ∨ TOEIC(x) ∨ GRE(x) ∨ SubjectTest(x)))
∃x (Develop(eTS, x) ∧ AssociatedWith(x, entryToUSEducationInstitution))
∃x (Develop(eTS, x) ∧ StateWideAssesment(x) ∧ UsedFor(x, accountabilityTesting))

ETS develops assessments for K-12 statewide as well as entry to US tertiary and quaternary education institutions.

∃x ∃y (Develop(eTS, x) ∧ StateWideAssesment(x) ∧ Develop(eTS, y) ∧ AssociatedWith(y, entryToUSEducationInstitution))


ETS doesn't administer tests internationally.

∀x (Administer(eTS, x) → ¬InternationalTest(x))


ETS administers international tests including the TOEFL, GRE and subject tests in China.

∃x (Administer(eTS, x) ∧ InChina(x) ∧ (TOEFL(x) ∨ TOEIC(x) ∨ GRE(x) ∨ SubjectTest(x)))


All hodophiles who enjoy eating gelato ice cream would enjoy a vacation to Italy.
No hodophiles can resist the hallmark delectable desserts famous in Italy.
Hodophiles enjoy eating gelato ice cream or love to travel and vacation often, or both.
No hodophiles who study abroad in Europe regret their college experiences.
If hodophiles love to travel and vacation often, then they study abroad in Europe.
Robert is a hodophile, and he either enjoys eating gelato ice cream and loves to travel and vacation often, or does not enjoy eating gelato ice cream and does not love to travel and vacation often.

∀x (Hodophiles(x) ∧ EnjoyEating(x, gelato) → Enjoy(x, vacationToItaly))
∀x (Hodophiles(x) ∧ ¬(∃y (Resist(x, y) ∧ Hallmark(y) ∧ Delectabl(y) ∧ Dessert(y) ∧ FamousIn(y, italy))))
∀x (Hodophiles(x) → (EnjoyEating(x, gelato) ∨ LoveToTravelOften(x))
∀x (Hodophiles(x) ∧ TakeIn(x, studyAbroadSemester, europe) → ¬Regret(x, collegeExperience))
∀x (Hodophiles(x) ∧ LoveToTravelOften(x) → TakeIn(x, studyAbroadSemester, europe))
Hodophiles(robert) ∧ ¬(EnjoyEating(robert, gelato) ⊕ LoveToTravelOften(robert))

Robert can resist the hallmark delectable desserts that are famous in Italy.

∃y (Resist(robert, y) ∧ Hallmark(y) ∧ Delectabl(y) ∧ Dessert(y) ∧ FamousIn(y, italy))


If Robert either would both enjoy a vacation to Italy and regrets his college experiences or neither would enjoy a vacation to Italy nor regrets his college experiences, then Robert would either enjoy a vacation to Italy or he can resist the hallmark delectable desserts that are famous in Italy.

¬((Enjoy(robert, vacation) ∧ In(vacation, italy)) ⊕ Regret(x, collegeExperiences)) → Enjoy(robert, vacation) ∧ In(vacation, italy) ⊕ (∃y (Resist(robert, y) ∧ Hallmark(y) ∧ Delectabl(y) ∧ Dessert(y) ∧ FamousIn(y, italy))


If Robert is not both a person who can resist the hallmark delectable desserts that are famous in Italy and regrets his college experiences, then Robert either enjoys eating gelato ice cream or would enjoy a vacation to Italy.

(∃y (Resist(robert, y) ∧ Hallmark(y) ∧ Delectabl(y) ∧ Dessert(y) ∧ FamousIn(y, italy))) ∧ Regret(robert, collegeExperience)) → (EnjoyEating(robert, gelato) ⊕ (Enjoy(robert, vacation) ∧ In(vacation, italy))


To have the authorization to study in the United States as a foreigner, you must be enrolled in an academic program.
Those who are enrolled in an academic program can not work full-time.
Every who studies in the United States as a foreigner has the authorization to study in the U.S.
All PhD graduate can work full-time.
If Tom does not study in the United States as a foreigner, he is enrolled in an academic program.

∀x (Have(x, authorization, studyIn, unitedStates) → EnrolledIn(x, academicProgram))
∀x (EnrolledIn(x, academicProgram) → ¬Work(x, fullTime))
∀x (StudyIn(x, unitedStates) → Have(x, authorization, studyIn, unitedStates))
∀x (PhDGraduate(x) → Work(x, fullTime))
¬StudyIn(x, unitedStates) → EnrolledIn(x, academicProgram)


Islip Speedway is the smallest race track.
There was a demolition derby on the smallest race track.
Islip is either demolished or still being used.
Speedways that are still being used have races held at them.
Islip doesn't have races held at it.

Speedway(islip) ∧ SmallestRaceTrack(islip)
∃x ∃y (DemolitionDerby(x) ∧ SmallestRaceTrack(y) ∧ On(x, y))
Demolished(islip) ⊕ StillUsed(islip)
∀x (Speedway(x) ∧ StillUsed(x) → Have(races, heldAt, x))
¬Have(races, heldAt, islip)

There has been a demolition derby somewhere that has since been demolished.

∃x ∃y (DemolitionDerby(x) ∧ On(x, y) ∧ Demolished(y))


If a person pays their taxes, then they contribute to the country.
Everyone who works for a government department pays a tax on their salary.
Everyone in the army is an employee of a government department.
Everyone convicted of murder goes to prison.
Everyone who has been to prison has a criminal record.
James was either once convicted of murder, or spent time in prison.
James either has a criminal record, or pays his taxes.

∀x (Taxpayer(x) → ContributeTo(x, country))
∀x (WorkFor(x, governmentAgency) → Taxpayer(x))
∀x (ServesIn(x, theArmy) → WorkFor(x, governmentAgency))
∀x (SentencedForMurder(x) → Imprisoned(x))
∀x (Imprisoned((x) → Has(x, criminalRecord))
SentencedForMurder(james) ⊕ Imprisoned(james)
Has(james, criminalRecord) ⊕ Taxpayer(james)


James does not contribute to the country.


James contributes to the country and he serves in the army.

ContributeTo(james, country) ∧ ServesIn(james, army)


James does not contribute to the country and does not serve in the army.

¬(ContributeTo(james, country) ∧ ServesIn(james, army))


The Croton River watershed is the drainage basin of the Croton River.
The Croton River is in southwestern New York.
Water from the Croton River watershed flows to the Bronx.
The Bronx is in New York.

DrainageBasinOf(crotonRiverWatershed, crotonRiver)
In(crotonRiver, southwesternNewYork)
∀x ((Water(x) ∧ In(x, crotonRiverWatershed)) → FlowsTo(x, bronx))
In(bronx, newYork)

Water from the Croton River watershed flows to somewhere in New York.

∀x ((Water(x) ∧ From(x, crotonRiverWatershed)) → ∃y(FlowsTo(x, y) ∧ In(y, newYork)))


The Croton River watershed is in the Bronx.


Water from the Croton River flows to the Bronx.

∀x (Water(x) ∧ From(x, crotonRiver) → FlowsTo(x, bronx))


All nuclear-powered submarines are warships.
No nuclear-powered submarines are commercial vessels.

∀x (NuclearPoweredSubmarine(x) → Warship(x))
∀x (NuclearPoweredSubmarine(x) → ¬CommercialVessel(x))


If an album is written by a rock band, then the genre of the album is rock.
If a band writes an album winning an award, then this band wins this award.
Trouble at the Henhouse is an album by The Tragically Hip.
The Tragically Hip is a Canadian rock band.
The song "Butts Wigglin'" is in Trouble at the Henhouse.
Trouble at the Henhouse won the Album of the Year award.
A song in Trouble at the Henhouse appeared in a film.

∀x ∀y ∀z (AlbumByBand(x, y) ∧ RockBand(y, z) → Genre(x, rock))
∀x ∀y ∀z (AlbumByBand(x, y) ∧ AlbumAward(x, z) → RockBandAward(y, z))
AlbumByBand(trouble_at_the_Henhouse, the_Tragically_Hip)
RockBand(the_Tragically_Hip, canada)
SongInAlbum(butts_Wigglin, trouble_at_the_Henhouse)
AlbumAward(trouble_at_the_Henhouse, the_Album_of_the_Year)
∃x (SongInFilm(x) ∧ SongInAlbum(x, trouble_at_the_Henhouse))

The genre of Trouble at the Henhouse is rock.


No Canadian rock band has won the Album of the Year award.

¬∃x(RockBand(x, canada) ∧ Award(x, theAlbumOfTheYear))


Daniel is a software engineer, and he works at Palantir Technologies.
Daniel studied bioengineering during his undergraduate at Rice University.
Daniel’s older sister works at Meta as a technical sourcer.
Daniel’s dad and older sister both graduated from Stanford University.
Daniel’s dad is a doctor practicing internal medicine at a veteran’s hospital in Minneapolis.

SoftwareEngineer(daniel) ∧ WorksAt(daniel, palantirTechnologies)
Studied(daniel, bioengineering) ∧ UndergraduateAt(daniel, riceUniversity)
WorksAtMeta(danielsOlderSister) ∧ TechnicalSourcer(danielsOlderSister)
 GraduatedFromStanfordUniversity(danielsOlderSister) ∧ GraduatedFromStanfordUniversity(danielsDad)
Doctor(danielsDad) ∧ Practicing(danielsDad, internalMedicine) ∧ PracticingAt(danielsDad, veteransHospital) ∧ In(veteransHospital, minneapolis)

Daniel once applied to Stanford University, but he couldn’t get in even though he has family members who are Stanford alumni.

AppliedTo(daniel, stanfordUniversity) ∧ ¬GotInto(daniel, stanfordUniversity) ∧ Alumni(danielsFamilyMembers, stanfordUniversity)


Daniel studied bioengineering as an undergraduate at Rice University.

Studied(daniel, bioengineering) ∧ UndergraduateAt(daniel, riceUniversity)


Daniel and his sister grew up in Minneapolis, Minnesota.

GrewUpIn(daniel, minneapolis) ∧ GrewUpIn(danielsOlderSister, minneapolis)


The world's only major large passenger aircraft manufacturers are Boeing and Airbus.
All American Airlines planes are from the world's major large passenger aircraft manufacturers.
Airbus made more revenue than Boeing last year.

∀x (WorldMajorLargePassengerAircraftManufacturer(x) → x=boeing ⊕ x=airbus)
∀x (AmericanAirlinesAircraft(x) → WorldMajorLargePassengerAircraftManufacturer(x))
MoreInRevenue(airbus, boeing)

An American Airlines plane is either a Boeing or Airbus plane.

∀x (AmericanAirlinesPlane(x) → x=boeing ⊕ x=airbus)


There exists a SpaceX commercial aircraft.


There does not exist a United Airlines plane produced by Boeing.

∀x (UnitedAirlinesAircraft(x) → ¬(x=boeing))


There is a commercial plane made by both Airbus and Boeing.

∃x (WorldMajorLargePassengerAircraftManufacturer(x) ∧ ProducedBy(x, airbus) ∧ ProducedBy(x, boeing))


Luzon is an island in the Philippines.
In December 1999, an earthquake struck Luzon.
People died in the December 1999 earthquake in Luzon.

Island(luzon) ∧ In(luzon, philippines)
∃x (Earthquake(x) ∧ StrikeInYr(x, year1999) ∧ StrikeInMo(x, december) ∧ StrikeInCity(x, luzon))
∃x (Earthquake(x) ∧ StrikeInYr(x, year1999) ∧ StrikeInMo(x, december) ∧ StrikeInCity(x, luzon) ∧ Deadly(x))


No one has ever died in an earthquake that struck the Philippines.

∀x ∀y ((Earthquake(x) ∧ StrikeInCity(x, y) ∧ In(y, philippines)) → ¬Deadly(x))


In 1999, there was at least one earthquake in the Philippines.

∃x ∃y (Earthquake(x) ∧ StrikeInYr(x, year1999) ∧ StrikeInMo(x, december) ∧ StrikeInCity(x, y) ∧ In(y, philippines))


People who like financial risks invest in the public stock market regularly or enjoy gambling regularly.
If people invest in the public stock market regularly, then they read the Wall Street Journal and other newspapers regularly to keep updated on financial metrics.
All people who enjoy enjoy gambling regularly spend a lot of money at casinos or other betting games.
People who spend a lot of money at casinos and other betting games would enjoy visiting the Las Vegas Strip.
People who spend a lot of money at casinos and other betting games are at risk of gambling addiction.
Matt does not invest in the public stock market regularly.
Matt likes financial risks.

∀x (Like(x, financialRisk) → InvestInRegularly(x, publicStockMarket) ∨ EnjoyRegularly(x, gambling))
∀x (InvestInRegularly(x, publicStockMarket) → ReadToKeepUpdatedOn(x, theWallStreetJournal, financialMetric) ∨ (∃y (¬(y=theWallStreetJournal) ∧ NewsPaper(y) ∧ ReadToKeepUpdatedOn(x, y, financialMetric))))
∀x (EnjoyRegularly(x, gambling) → SpendAt(x, alotOfMoney, casino) ∨ (∃y (¬(y=casino) ∧ BettingGame(y) ∧ SpendAt(x, aLotOfMoney, y)))
∀x (SpendAt(x, alotOfMoney, casino) ∨ (∃y (¬(y=casino) ∧ BettingGame(y) ∧ SpendAt(x, aLotOfMoney, y))) → EnjoyVisiting(x, theLasVegasStrip))
∀x (SpendAt(x, alotOfMoney, casino) ∨ (∃y (¬(y=casino) ∧ BettingGame(y) ∧ SpendAt(x, aLotOfMoney, y)) → AtRiskOf(x, gamblingAddiction))
InvestInRegularly(matt, publicStockMarket)
Like(matt, financialRisk)

Matt reads the Wall Street Journal and other newspapers regularly to keep updated on financial metrics.


If Matt is either both a person who is at risk of a gambling addiction and invests in the public stock market regularly, or neither is at risk of a gambling addiction nor invests in the public stock market regularly, then Matt neither visits the Las Vegas Strip regularly nor reads the Wall Street Journal and other newspapers regularly to keep updated on the financial metrics.

AtRiskOf(matt, gamblingAddiction) ⊕ InvestInRegularly(matt, publicStockMarket) → ¬EnjoyVisiting(matt, theLasVegasStrip) ∧  ¬(ReadToKeepUpdatedOn(matt, theWallStreetJournal, financialMetric) ∨  (∃y (¬(y=theWallStreetJournal) ∧ NewsPaper(y) ∧ ReadToKeepUpdatedOn(matt, y, financialMetric))))


Matt is not at risk of a gambling addiction and Mike does not both read the Wall Street Journal and other newspapers regularly and visits the Las Vegas Strip regularly.

¬AtRiskOf(matt, gamblingAddiction) ∧ ¬(ReadToKeepUpdatedOn(x, theWallStreetJournal, financialMetric) ∨ (∃y (¬(y=theWallStreetJournal) ∧ NewsPaper(y) ∧ ReadToKeepUpdatedOn(x, y, financialMetric))) ∧ EnjoyVisiting(matt, theLasVegasStrip))


All students learning piano can strike the right notes.
All students who can strike the right note can get the rhythms right.
If a student can get the rhythms right, he will start working on coordination between the left and the right hands.
Some students who start working on coordination between the left and the right hands become good at it, while other students find it challenging.
If John can strike the right notes, get the rhythms right, and is good at coordination between right and left hands, then he puts emotions into his playing.
John is a student learning piano.
John does not find coordination between the left and the right hands challenging.

∀x (Student(x) ∧ LearningPiano(x) → Can(x, strike, rightNote))
∀x (Student(x) ∧  Can(x, strike, rightNote) → Can(x, getTheRhythmRight))
∀x (Student(x) ∧ Can(x, getTheRhythmRight) → Start(x, workingOnCoordinationBetweenTheLeftAndRightHands))
∀x (Student(x) ∧ Start(x, workingOnCoordinationBetweenTheLeftAndRightHands) → Become(x, goodAtCoordination) ⊕ Find(x, coordinationChallenging))
(Can(john, getTheRhythmRight) ∧ Can(john, getTheRhythmRight)) ∧  Become(john, goodAtCoordination)  → PutEmotionInto(john, hisPlaying)
Student(john) ∧ LearningPiano(john)
¬Find(john, coordinationChallenging)


John does not put emotions into his playing.


Barbara Ann Marshall is a former swimmer and former world record-holder.
Barbara Ann Marshall participated in the 1972 Summer Olympics.
Barbara Ann Marshall's home country is the United States.
All people who competed in the 1972 Summer Olympics represented their home country.
Barbara Ann Marshall participated in the preliminary heat in the freestyle relay.
Barbara Ann Marshall did not participate in the event final of the 1972 Summer Olympics freestyle relay.
Only relay swimmers who participated in the final event at the 1972 Summer Olympics received medals.

FormerSwimmer(barbaraAnnMarshall) ∧ FormerWorldRecordHolder(barbaraAnnMarshall)
ParticipatedIn(barbaraAnnMarshall, 1972SummerOlympics)
HomeCountry(barbaraAnnMarshall, unitedStates)
∀x ∃y (ParticipatedIn(x, 1972SummerOlympics) ∧ HomeCountry(x, y) → Represented(x, y))
ParticipatedIn(barbaraAnnMarshall, preliminaryHeatFreestyleRelay)
¬ParticipatedIn(barbaraAnnMarshall, finalHeatFreestyleRelay)
∀x ((ParticipatedIn(x, 1972SummerOlympics) ∧ RelaySwimmer(x) ∧ ¬ParticipatedIn(x, finalHeatFreestyleRelay)) ↔ ¬Recieved(x, medal)))

Barbara Ann Marshall did not receive medals.


Barbara Ann Marshall represented the United States in the 1972 Summer Olympics.


A game is played with three stages: red stage, yellow stage, and green stage.
Each player begins at the red stage.
All players must reach the yellow stage before they can reach the green stage.
The yellow stage comes after the red stage.
All players must proceed one stage at a time.

∃x ∃y ∃y ∃w (Game(x) ∧ StageNumber(x,3) ∧ Stage(y) ∧ Stage(z) ∧ Stage(w) ∧ ¬(y=z) ∧ ¬(z=w) ∧ ¬(y=w) ∧ Red(y) ∧ Yellow(z) ∧ Green(w))
∀x (Player(x) → StartRed(x))
∀x (Player(x) ∧ ¬ReachYellow(x) → ¬ReachGreen(x))
∀x (Player(x) ∧ StartRed(x) → ReachYellow(x))
∀x (Player(x) ∧ StartRed(x) ∧ ¬ReachYellow(x) → ¬ReachGreen(x))

It is possible to move to the green stage without ever reaching the yellow stage.


It is possible to reach the yellow stage without ever reaching the green stage.


It is possible to complete the game without ever reaching the green stage.


In Love City, everyone considers physical touch or words of affirmation to be their most important love language.
If someone in Love City considers physical touch as their most important love language, then they are good with pets.
If someone in Love City is good with pets, then they are not scared of animals.
In Love City, everyone is scared of animals, or loves animals, or both.
Adam, who is in Love City, either values physical touch as his most important love language or loves animals.

∀x (In(x, loveCity) → (ConsidersMostImportantLoveLanguage(x, physicalTouch)  ∨ ConsidersMostImportantLoveLanguage(x, wordOfAffirmation))
∀x ((ConsidersMostImportantLoveLanguage(x, physicalTouch)  ∧ In(x, loveCity) → GoodWith(x, pet))
∀x ((GoodWith(x, pet) ∧ In(x, loveCity)) → ¬ScaredOf(x, animal))
∀x (In(x, loveCity) → (ScaredOf(x, animal) ∨ Loves(x, animal)))
(ConsidersMostImportantLoveLanguage(adam, physicalTouch) ⊕ Loves(adam, animal)) ∧ In(adam, loveCity)


Adam considers words of affirmation to be the most important love language.


Adam considers physical touch as the most important love language and considers words of affirmation as the most important love language.

ConsidersMostImportantLoveLanguage(adam, physicalTouch) ∧ ConsidersMostImportantLoveLanguage(adam, wordOfAffirmation)


Adam either values physical touch as an especially important love language or values words of affirmation as an especially important love language.

ConsidersMostImportantLoveLanguage(adam, physicalTouch) ⊕ ConsidersMostImportantLoveLanguage(adam, wordOfAffirmation)


If Adam values physical touch as an especially important love language or is good with pets, then Adam values words of affirmation as an especially important love language.

(ConsidersMostImportantLoveLanguage(adam, physicalTouch, mostImportantLoveLanguage) ∨ GoodWith(x, pet)) → ConsidersMostImportantLoveLanguage(adam, wordOfAffirmation)


All birds have wings.
Animals with wings aren't reptiles.
Some animals that fly are birds.
If something is an iguana, then it is a reptile. Simeng: All iguanas are reptiles.
John is either both an iguana and a bird, or he is neither.
John is an animal.

∀x (Bird(x) → ∃y ∃z (¬(y=z) ∧ Wing(y) ∧ Wing(z) ∧ Have(x, y) ∧ Have(x, z)))
∀x (Animal(x) ∧ (∃y ∃z (¬(y=z) ∧ Wing(y) ∧ Wing(z) ∧ Have(x, y) ∧ Have(x, z))) → ¬Reptile(x))
∃x (Animal(x) ∧ Fly(x) ∧ Bird(x))
∀x (Iguana(x) → Reptile(x))
¬(Iguana(john) ⊕ Bird(john))
Animal(john)


John is not both an iguana and an animal that can fly.


John is an animal that can fly and John is a bird.


EndGame is a movie released in 2006.
EndGame was set in Washington.
EndGame was filmed outside of Washington.
Some movies are filmed in New York.
Andy Chang directed EndGame.
Andy Chang is from Hong Kong.

Movie(endGame) ∧ Released(endGame, yr2006)
SetIn(endGame, washington)
¬(FilmedIn(endGame, washington))
∃x∃y(FilmedIn(x, newYork) ∧ (¬(x=y)) ∧ FilmedIn(y, newYork))
Directed(andyChang, endGame)
From(andyChang, hongKong)


EndGame was not directed by someone from Hong Kong.

∀x (¬(Directed(x, endGame) ∧ From(x, hongKong)))


All of Andy Chang's movies are filmed outside of Washington.

∀x (Directed(andyChang, x) → ¬(FilmedIn(x, washington)))


Six, seven and eight are real numbers.
If a real number equals another real number added by one, the first number is larger.
If the number x is larger than the number y, then y is not larger than x.
Seven equals six plus one.
Eight equals seven plus one.
Two is positive.
If a number is positive, then the double of it is also positive.
Eight is the double of four.
Four is the double of two.

RealNum(num6) ∧ RealNum(num7) ∧ RealNum(num8)
∀x ∀y ((RealNum(x) ∧ RealNum(y) ∧ IsSuccessorOf(x, y)) → Larger(x, y))
∀x ∀y (Larger(x, y) → ¬Larger(y, x))
∃y(IsSuccessorOf(y, num6) ∧ Equals(num7, y))
∃y(IsSuccessorOf(y, num7) ∧ Equals(num8, y))
Positive(num2)
∀x ∀y ((Positive(x) ∧ IsDouble(y, x)) → Positive(y))
IsDouble(num8, num4)
IsDouble(num4, num2)