A cutman is responsible for preventing and treating physical damage to a fighter.
Cutmen appear in boxing matches, kickboxing matches, or mixed martial arts matches bout.
Cutmen handle swelling, nosebleeds and lacerations.
Jack is a cutman.

∀x (Cutman(x) → Prevent(x, physicalDamageToAFighter) ∧ Treat(x, physicalDamageToAFighter))
∀x (Cutman(x) → AppearIn(x, boxingMatch) ∨ AppearIn(x, kickboxingMatch) ∨ AppearIn(x, mixedMartialArtsMatchBout))
∀x (Cutman(x) → Handle(x, swelling) ∧ Handle(x, nosebleed) ∧ Handle(x, laceration))
Cutman(jack)

¬(∃x (Cutman(x) ∧ AppearIn(x, boxingMatch)))


If someone is not a cutman, then they cannot handle nosebleeds.


Jack is responsible for treating physical damage to a fighter.


The Mona Lisa is a world's best-known painting.
The Mona Lisa is a portrait painted by Leonardo da Vinci.
Leonardo da Vinci was a scientist and painter.
Painting genres can be history, portrait, animal, landscape, and still life.

Painting(monaLisa) ∧ TheWorldsBestKnown(monaLisa)
PaintedBy(monaLisa, leonardodaVinci) ∧ Portrait(monaLisa)
Scientist(leonardodaVinci) ∧ Painter(leonardodaVinci)
∀x (Painting(x) → (History(x) ∨ Portrait(x) ∨ Animal(x) ∨ Landscape(x) ∨ StillLife(x)))

A world's best-known artwork is painted by a scientist.

∃x ∃y (Painting(x) ∧ TheWorldsBestKnown(x) ∧ PaintedBy(x, y) ∧ Scientist(y))


Leonardo da Vinci has artworks in the landscape genre.

∃x (PaintedBy(x, leonardodaVinci) ∧ Landscape(x))


No world's best-known artworks are portraits.


No professional tennis umpires are professional tennis players.
If you are a World Tour player, then you are a professional tennis player.
All Grand Slam champions are World Tour players.
All Grand Slam umpires are professional tennis umpires.
Nadal is a World Tour player or a Grand Slam champion

∀x (ProfessionalTennisUmpire(x) → ¬ProfessionalTennisPlayer(x))
∀x (WorldTourPlayer(x) → ProfessionalTennisPlayer(x))
∀x (GrandSlamChampion(x) → WorldTourPlayer(x))
∀x (GrandSlamUmpire(x) → ProfessionalTennisUmpire(x))
WorldTourPlayer(nadal) ∨ GrandSlamChampion(nadal)


Nadal is neither a Grand Slam umpire nor a professional tennis umpire.


If Nadal is a professional tennis umpire, then Nadal is a Grand Slam Umpire.


If Nadal is a Grand Slam umpire or a professional tennis player, then Nadal is a Grand Slam umpire.

GrandSlamUmpire(nadal) ∨ ProfessionalTennisPlayer(nadal) → GrandSlamUmpire(nadal)


Businesses are either sanctioned or unsanctioned.
Sanctioned businesses are limited.
Unsanctioned businesses are free.
The Crude Oil Data Exchange is a business that isn't free.

∀x (Buisness(x) → Sanctioned(x) ⊕ ¬Sanctioned(x))
∀x (Buisness(x) ∧ Sanctioned(x) → Limited(x))
∀x (Buisness(x) ∧ ¬Sanctioned(x) → Free(x))
Buisness(crudeOilDataExchange) ∧ ¬Free(crudeOilDataExchange)


Crude Oil Data Exchange is unsanctioned.


When something is depressing, it is sad.
The end of a relationship is depressing.

∀x (Depressing(x) → Sad(x))
Depressing(v)

The end of a relationship is invigorating


Palstaves are a type of early bronze axe.
Palstaves are found in northern, western, and southwestern Europe and are cast in molds.
John Evans is an archeologist who popularized the term "palstave."
Paalstabs are not a type of axe but rather a digging shovel.

EarlyBronzeAge(palstave) ∧ Axe(palstave)
FoundIn(palstave, northernEurope) ∨ FoundIn(palstave, westernEurope) ∨ FoundIn(palstave, southWesternEurope)) ∧ CastIn(palstave, molds)
Archeologist(johnEvans) ∧ Popularize(johnEvans, termPalstave)
¬Axe(paalstab) ∧ DiggingShovel(paalstab)

John Evans Popularized the term paalstab.


There is an axe that is found in Western Europe.


Archeologists haven't popularized anything.

∀x ∀y (Archeologist(x) → ¬Popularize(x, y))


Koei Tecmo is a Japanese video game and anime holding company.
Holding companies hold several companies.
Tecmo was disbanded in Japan, while Koei survived but was renamed.
Video game holding companies are holding companies.

Japanese(koeitecmo) ∧ VideoGameHoldingCompany(koeitecmo) ∧ AnimeHoldingCompany(koeitecmo) ∧ HoldingCompany(x)
∀x (HoldingCompany(x) → ∃y(Company(y) ∧ Holds(x, y)))
DisbandsIn(tecmo, japan) ∧ Survives(koei) ∧ Renames(koei)
∀x (VideoGameHoldingCompany(x) → HoldingCompany(x))


The PlayStation EyeToy is a camera accessory for the PlayStation 2 system.
The PlayStation Eye is a camera accessory for the PlayStation 3 system.
The PlayStation Camera is a camera accessory for the PlayStation 4 and the PlayStation 5 systems.
Camera accessories for a system are compatible with that system.
Playstation 2, 3,4, and 5 are all different.
Only the PlayStation Camera camera system is compatible with different systems.

System(playStation2) ∧ CameraAccessoryFor(playStationEyeToy, playStation2)
System(playStation3) ∧ CameraAccessoryFor(playStationEye, playStation3)
System(playStation4) ∧ System(playStation5) ∧ CameraAccessoryFor(playStationCamera, playStation4) ∧ CameraAccessoryFor(playStationCamera, playStation5)
∀x ∀y (CameraAccessoryFor(x, y) ∧ System(y) → CompatibleWith(x, y))
¬(playStation2=playStation3) ∧ ¬(playStation2=playStation4) ∧ ¬(playStation2=playStation5) ∧ ¬(playStation3=playStation4) ∧ ¬(playStation3=playStation5) ∧ ¬(playStation4=playStation5)
∀x ∃y ∃z (System(y) ∧ System(z) ∧ ¬(y=z) ∧ CompatibleWith(x, y) ∧ CompatibleWith(x, z) → x=playstationCamera)

The Playstation Eye is compatible with the PlayStation 2 and the PlayStation 3.

Compatible(playStationEye, playStation2) ∧ Compatible(playStationEye, playStation3)


The Playstation EyeToy is compatible with the PlayStation 2.


The Playstation Camera can be used for all Playstation consoles.

Compatible(playStationCamera, playStation2) ∧ Compatible(playStationCamera, playStation3) ∧ Compatible(playStationCamera, playStation4) ∧ Compatible(playStationCamera, playStation5)


Adam Buska is a European football player.
If a European plays football, they play what Americans call soccer.

FootballPlayer(adamBuska) ∧ European(adamBuska)
∀x (FootballPlayer(x) ∧ European(x) → ∃y (Call(american, y, soccer) ∧ Play(x, y)))

Adam Buska plays what Americans call soccer.

∃y (Call(american, y, soccer) ∧ Play(adamBuska, y))


If a game is one of the top-3 best selling video-games, then it is multiplatform.
If a game has sold more than 100 million copies, then it is one of the top-3 best-selling video games.
Some games that support Windows are developed by Nintendo.
All multiplatform games can be played on a wide range of devices.
Pokemon Diamond version is neither developed by Nintendo nor can be played on a wide range of devices.

∀x (ATop3BestSellingVideoGame(x) → Multiplatform(x))
∀x (SoldMoreThan100MillionCopies(x) → ATop3BestSellingVideoGame(x))
∃x ((SupportsWindows(x) ∧ AGameDevelopedByNintendo(x)))
∀x (Multiplatform(x) → CanBePlayedOnAWideRangeOfDevices(x))
¬(DevelopedByNintendo(PokemonDiamond) ∨ CanBePlayedOnAWideRangeOfDevices(PokemonDiamond))

Pokemon Diamond version supports Windows.


Pokemon Diamond version supports Windows and has sold more than 100 million copies.

(Game(PokemonDiamond) ∧ SupportsWindows(PokemonDiamond)) ∧ (Game(PokemonDiamond) ∧ SoldMoreThan100MillionCopies(PokemonDiamond))


If Pokemon Diamond version either supports Windows or has sold more than 100 million copies, then Pokemon Diamond version either is both multiplatform and one of the top-3 best selling video games, or is neither multiplatform nor one of the top-3 best selling video games.

((Game(PokemonDiamond) ∧ SupportsWindows(PokemonDiamond)) ⊕ ((Game(PokemonDiamond) v (SoldMoreThan100MillionCopies(PokemonDiamond))) → (Multiplatform(PokemonDiamond) ∧ (Game(PokemonDiamond) ∧ ATop3BestSellingVideoGame(PokemonDiamond))) ⊕ (¬Multiplatform(PokemonDiamond) ∧ ¬(Game(PokemonDiamond) ∧ ATop3BestSellingVideoGame(PokemonDiamond)))


China is one of the BRICS, and its economy is emerging.
If someone is from China, then they are from a country of BRICS.
India is one of the BRICS, and its economy is emerging.
If someone is from India, then they are in a country of BRICS.
All people from China are Chinese people.
All people from India are Indian people.
There is a person from India.

∃x (BRIC(x) ∧ ¬(x=china) ∧ BRIC(china) ∧ Emerging(chinaEconomy))
∀x (From(x, china) → From(x, bric))
BRIC(india) ∧ Emerging(indiaEconomy)
∀x (From(x, india) → From(x, bric))
∀x (From(x, china) → Chinese(x))
∀x (From(x, india) → Indian(x))
∃x (From(x, india))

∀x (From(x, countryOfBRICS) → ¬IndianPeople(x))


∃x (IndianPeople(x) ∧ From(x, countryOfBRICS))


Daveed Diggs is an actor and film producer.
Daveed Diggs played two roles in the musical Hamilton on Broadway.
One of the actors from Hamilton won the best actor award.
The actor playing Thomas Jefferson won the best actor award.
Daveed Diggs played Thomas Jefferson.
Musicals on Broadway are not films.

Actor(daveedDiggs) ∧ FilmProducer(daveedDiggs)
∃x ∃y(PlaysIn(daveedDiggs, x, hamilton) ∧ (¬(x=y)) ∧ PlaysIn(daveedDiggs, y, hamilton)) ∧ OnBroadway(hamilton) ∧ Musical(hamilton)
∃x ∃y(Actor(x) ∧ PlaysIn(x, y, hamilton) ∧ Wins(x, bestActorAward))
∃x (Actor(x) ∧ PlaysIn(x, thomasJefferson, hamilton) ∧ Wins(x, bestActorAward))
Plays(daveedDiggs, thomasJefferson)
∀x ((Musical(x) ∧ OnBroadway(x)) → ¬Film(x))


∃x ∃y(Wins(hamilton, x) ∧ (¬(x=y)) ∧ Wins(hamilton, y))


Ernest Pohl was a Polish football player.
A football player in the Polish First Division has scored over 180 goals.
Ernest Pohl scored more than 180 goals in the Polish First Division.
Górnik Zabrze's stadium was named after a soccer player from Ruda Śląska.
Ernest Pohl is from Ruda Śląska.

Polish(ernestPohl) ∧ FootballPlayer(ernestPohl)
∃x (FootballPlayer(x) ∧ In(x, polishFirstDivision) ∧ ScoredOver(x, 180Goals))
In(ernestPohl, polishFirstDivision) ∧ ScoredOver(ernestPohl, 180Goals)
∃x ∃y (GornikZabrzes(x) ∧ Stadium(x) ∧ NamedAfter(x, y) ∧ SoccerPlayer(y) ∧ From(y, rudaŚląska))
From(ernestPohl, rudaŚląska))

Ernest Pohl has not scored more than 180 goals.


Górnik Zabrze's stadium was named after Ernest Pohl.

∀x (GornikZabrzes(x) ∧ Stadium(x) → NamedAfter(x, ernestPohl))


Ann J. Land was a member of the Philadelphia City Council and the Democratic Party.
Ann J. Land ran unopposed for the Philadelphia City Council in 1980.
People who run unopposed for the Philadelphia City Council are elected to the positions they run for in the same year.
Michael Nutter was a political challenger.
Ann J. Land defeated Michael Nutter and ran for the Philadelphia City Council in 1987.

MemberOf(annJLand, philadelphiaCityCouncil) ∧ MemberOf(annJLand, democraticParty)
RunUnopposedFor(ann, philadelphiaCityCouncil, year1980)
∀x ∀y (RunUnopposedFor(x, philadelphiaCityCouncil, y) → ElectedTo(x, philadelphiaCityCouncil, y))
PoliticalChallenger(michaelNutter)
Defeat(annJLand, michaelNutter) ∧ RunFor(annJLand, philadelphiaCityCouncil, year1987)

Ann J. Land was elected to the Philadelphia City Council in 1980.


Ann J. Land was elected to the Philadelphia City Council in 1987.


There was some member of the Democratic Party elected to the Philadelphia City Council in 1980.

∃x (MemberOf(x, democraticParty) ∧ ElectedTo(x, philadelphiaCouncil, year1980))


Aberdeen won the cup in the 2013 final.
Rangers won the cup in the 2014 final.
Aberdeen and Rangers are different teams.
Different teams cannot win the cup in the same year's final.

WonCup(aberdeen, year2013Final)
WonCup(rangers, year2014Final)
¬(aberdeen=rangers)
∀x ∀y ∀z ∀w (¬(x=y) ∧ WonCup(x, z) ∧ WonCup(y, w) → ¬(z=w))


All young working professionals who have regular 9-5 jobs have stable jobs.
Some people living in Manhattan are young professionals with regular 9-5 jobs.
All people who have stable jobs are people who work regularly.
People who work regularly do not frequently disobey their bosses.
Mary either frequently disobeys her bosses and works regularly, or that she neither frequently disobeys her bosses nor works regularly.

∀x (YoungWorkingProfessional(x) ∧ Have(x, regular9To5Job) → Have(x, stableJob))
∃x (LiveIn(x, manhattan) ∧ YoungWorkingProfessional(x) ∧ Have(x, regular9To5Job))
∀x (Have(x, stableJob) → WorkRegularly(x))
∀x (WorkRegularly(x) → ¬DisobeyFrequently(x, boss))
¬(DisobeyFrequently(mary, boss) ⊕ WorkRegularly(mary))


Mary lives in Manhattan and is a young working professional who has a regular 9-5 job.

LiveIn(mary, manhattan) ∧ YoungWorkingProfessional(mary) ∧ Have(mary, regular9-5Job)


If Mary is a young working professional who has a regular 9-5 job, then Mary does not live in Manhattan.

YoungWorkingProfessional(mary) ∧ Have(mary, regular9-5Job) → ¬LiveIn(mary, manhattan)


All brain study designs are either block designs or event-related designs.
All event-related brain study designs are brain image acquisition.
All brain image acquisition in brain study designs is preceded by data processing.
Nothing in brain study designs preceded by data processing analyzes data.
Picture memory is a type of brain study design that is not either event-related or analyzing data.

∀x (BrainStudy(x) → (BlockDesign(x) ⊕ Event-relatedDesign(x)))
∀x ((BrainStudy(x) ∧ EventRelatedDesign(x)) → BrainImageAcquisition(x))
∀x ((BrainStudy(x) ∧ BrainImageAcquisition(x)) → PrecededBy(x, dataProcessing))
∀x ((BrainStudy(x) ∧ PrecededBy(x, dataProcessing)) → ¬Analyze(x, data))
BrainStudy(pictureMemory) ∧ (¬(EventRelatedDesign(pictureMemory) ⊕ AnalyzingData(pictureMemory)))

Picture memory is preceded by data processing.


Picture memory is either a block design or analyzing data.

BlockDesign(pictureMemory) ⊕ Analyze(pictureMemory, data)


If picture memory is not analyzing data, then picture memory is a block design and analyzing data.

¬Analyze(pictureMemory, data) → (BlockDesign(pictureMemory) ∧ Analyze(pictureMemory, data))


The USS Lyon was a US Navy ship involved in WWII.
All ships involved in WWII are currently decommissioned or in a museum.

USNavyShip(theUSSLyon) ∧ InvolvedIn(theUSSLyon, wWII)
∀x (InvolvedIn(x, wWII) → (CurrentlyDecommissioned(x) ∨ In(x, museum)))

The USS Lyon is currently decommissioned.


All disposables are designed to be used only once.
Some items used in Tom's house are eco-friendly.
Every item used in Tom's house is either disposable or reusable.
If something is made from metal, then it is not made from plastic.
All reusable items used in Tom's house are made from metal.
The chopsticks used in Tom's house are either made from metals and plastics, or that they are neither made from metals nor plastics.

∀x (Disposable(x) → DesignedToBeOnlyUsedOnce(x))
∃x (EcoFriendly(x))
∀x (UsedIn(x, tomsHouse) → Disposable(x) ⊕ Reusable(x))
∀x (MadeFrom(x, metal) → ¬MadeFrom(x, plastic))
∀x (Reusable(x) → MadeFrom(x, metal))
¬(MadeFrom(chopsticksUsedInTomsHouse, metal) ⊕ MadeFrom(chopsticksUsedInTomsHouse, plastic))

The chopsticks used in Tom's house are eco-friendly.


The chopsticks used in Tom's house are eco-friendly or designed to be used only once.


If chopsticks used in Tom's house are made from plastic or designed to be used only once, then they are made from plastic and are eco-friendly.

MadeFrom(chopsticks, plastic) ∨ DesignedBeOnlyUsedOnce(chopsticks) → MadeFrom(chopsticks, plastic) ∧ EcoFriendly(chopsticks)


Anything lazy is unproductive.
No one unproductive is energetic.
If something is a sloth, then it is lazy.
Some animals are sloths.
Sid is neither an energetic person nor a sloth.

∀x (Lazy(x) → Unproductive(x))
∀x (Unproductive(x) → ¬Energetic(x))
∀x (Sloth(x) → Lazy(x))
∃x (Animal(x) ∧ Sloth(x))
¬Energetic(sid) ∧ ¬Sloth(sid))


Sid is an energetic person and an animal.


If Sid is either an animal or unproductive, then Sid is not an energetic person.

Animal(sid) ⊕ Unproductive(sid)) → ¬Energetic(sid)


European soccer clubs can attend UCL, UEL, and UECL.
A soccer club eligible to attend UCL has a higher ranking than a soccer club eligible to attend UEL.
A soccer club eligible to attend UEL has a higher ranking than a soccer club eligible to attend UECL.
Manchester United and Machester City are both European soccer clubs.
Manchester United is eligible to attend UEL next season.
Manchester City is eligible to attend UCL next season.

∀x (EuropeanSoccerClub(x) → Attend(x, ucl) ∨ Attend(x, uel) ∨ Attend(x, uecl))
∀x ∀y (EuropeanSoccerClub(x) ∧ EuropeanSoccerClub(y) ∧ Attend(x, ucl) ∧ Attend(y, uel) → HigherRank(x, y))
∀x ∀y (EuropeanSoccerClub(x) ∧ EuropeanSoccerClub(y) ∧ Attend(x, uel) ∧ Attend(y, uecl) → HigherRank(x, y))
EuropeanSoccerClub(manchesterUnited) ∧ EuropeanSoccerClub(manchesterCity)
Attend(manchesterunited, uel)
Attend(manchestercity, ucl)

Manchester City has a higher ranking than Manchester United.


If a person coaches a football club, the person is a football coach.
If a person has a position in a club in a year, and the club is in NFL in the same year, the person plays in NFL.
Minnesota Vikings is a football club.
Dennis Green coached Minnesota Vikings.
Cris Carter had 13 touchdown receptions.
Minnesota Vikings were in the National Football League in 1997.
John Randle was Minnesota Vikings defensive tackle in 1997.

∀x ∀y ((Coach(x, y) ∧ FootballClub(y)) → FootballCoach(x))
∀w ∀x ∀y ∀z ((PlayPositionFor(x, w, y, z) ∧ InNFL(y, z)) → PlayInNFL(x))
FootballClub(minnesotaVikings)
Coach(dennisGreen, minnesotaVikings)
ReceiveTD(crisCarter, num13)
InNFL(minnesotaVikings, yr1997)
PlayPositionFor(johnRandle, defensiveTackle, minnesotaVikings, yr1997)


John Randle didn't play in the National Football League.


Cris Carter played for Minnesota Vikings.

PlayPositionFor(crisCarter, wr, minnesotaVikings, year1997)


All classrooms in William L. Harkness Hall that are used for lectures are booked during the day.
None of the classrooms in William L. Harkness Hall are private study spots.
All classrooms in William L. Harkness Hall are used for lectures or used for office hours.
If a classroom in William L. Harkness Hall is booked in the evening, then it is not freely usable at night.
If a classroom in William L. Harkness Hall is used for office hours, then it is booked in the evening.
Room 116 is a classroom in William L. Harkness Hall that is either both used for lecture and used for office hours or not used for either.

∀x (ClassroomIn(x, williamLHarknessHall) ∧ UsedFor(x, lecture) → BookedDuring(x, day))
∀x (ClassroomIn(x, williamLHarknessHall) ∧ ¬PrivateStudySpot(x))
∀x (ClassroomIn(x, williamLHarknessHall) ∧ (UsedFor(x, lecture) ∨ UsedFor(x, officeHours)))
∀x (ClassroomIn(x, williamLHarknessHall) ∧ BookedIn(x, evening) → ¬FreelyUsableAtNight(x))
∀x (ClassroomIn(x, williamLHarknessHall) ∧ UsedFor(x, officeHours) → BookedIn(x, evening))
ClassroomIn(116, williamLHarknessHall) ∧ ¬(UsedFor(116, lecture) ⊕ UsedFor(116, officeHours))


If Room 116 is either both booked during the day and freely usable at night, or neither, then it is either used for office hours or for private study spots.

¬(BookedDuring(room116, day) ⊕ FreelyUsableAtNight(room116) → (UsedFor(room116, officeHour) ⊕ PrivateStudySpot(room116))


If Room 116 is not both a private study spot and freely useable at night, then it is either used for lectures or booked during the day.

¬(PrivateStudySpot(room116) ∧ FreelyUsableAtNight(room116)) → (UsedFor(room116, lecture) ∨ BookedIn(room116, evening))


Shafaq-Asiman is a large complex of offshore geological structures in the Caspian Sea.
Baku is northwest of Shafaq-Asiman.
If place A is northwest of place B, then place B is southeast of place A.

LargeComplex(shafaq-asiman) ∧ LargeComplex(shafaq-asiman) ∧ Offshore(shafaq-asiman) ∧ GeologicalStructures(shafaq-asiman) ∧ In(shafaq-asiman, caspiansea)
NorthwestOf(baku, shafaq-asiman)
∀x ∀y (NorthwestOf(x, y) → SoutheastOf(y, x))


∃x (LargeComplex(x) ∧ SoutheastOf(x, baku))


Baku is not northwest of offshore geological structures.

∀x (GeologicalStructures(x) ∧ Offshore(x) → ¬NorthwestOf(baku, x))


Herodicus was a Greek physician, dietician, sophist, and gymnast.
Herodicus was born in the city of Selymbria.
Selymbria is a colony of the city-state Megara.
One of the tutors of Hippocrates was Herodicus.
Massages were recommended by Herodicus.
Some of the theories of Herodicus are considered to be the foundation of sports medicine.

Greek(herodicus) ∧ Physician(herodicus) ∧ Dietician(herodicus) ∧ Sophist(herodicus) ∧ Gymnast(herodicus)
Born(herodicus, selymbia) ∧ City(selymbia)
Colony(selymbia, megara) ∧ CityState(megara)
Tutor(herodicus, hippocrates)
Recommend(herodicus, massages)
∃x ∃y (Theory(x) ∧ From(x, herodicus) ∧ FoundationOf(x, sportsMedicine) ∧ (¬(x=y)) ∧ Theory(y) ∧ From(y, herodicus) ∧ FoundationOf(y, sportsMedicine))


Herodicus was born in a colony of a city-state.

∃x ∃y (Born(herodicus, x) ∧ Colony(x, y) ∧ CityState(y))


None of the kids in our family love the opera.
All of the adults in our family love the opera.
If someone in our family is a scientist, then they are an adult.
Some students in our family are kids.
Billy is a kid in our family.

∀x ((Kid(x) ∧ In(x, ourFamily)) → ¬Love(x, opera))
∀x ((Adult(x) ∧ In(x, ourFamily)) → Love(x, opera))
∀x ((Scientist(x) ∧ In(x, ourFamily)) → Adult(x))
∃x (Student(x) ∧ In(x, ourFamily) ∧ Kid(x))
Kid(billy) ∧ In(billy, ourFamily)


If Billy is a student or a scientist, then Billy is a student and a kid.

(Student(billy) ∨ Scientist(billy)) → (Student(billy) ∧ Kid(billy))


Brian Winter is a Scottish football referee.
After being injured, Brian Winter retired in 2012.
Brian Winter was appointed as a referee observer after his retirement.
Some football referees become referee observers.
The son of Brian Winter, Andy Winter, is a football player who plays for Hamilton Academical.

Scottish(brianWinter) ∧ FootballReferee(brianWinter)
Retired(brianWinter) ∧ RetiredIn(brianWinter, yr2012)
RefereeObserver(brianWinter)
∃x (FootballReferee(x) ∧ RefereeObserver(x))
SonOf(andyWinter, brianWinter) ∧ FootballPlayer(andyWinter) ∧ PlaysFor(andyWinter, hamiltonAcademical)

There is a son of a referee observer that plays football.

∃x ∃y(SonOf(x, y) ∧ RefereeObserver(y) ∧ FootballPlayer(x))


Brian Winter was not a referee observer.


Everyone at 'Board Game night' is interested in puzzles, or they are bad at chess, or both.
If a person at 'Board Game night' is bad at chess, then they don't play a lot of chess.
There is a person at 'Board Game night' who is either a planner or a creative person.
Erica is at 'Board Game night,' and she is someone who plays a lot of chess.
If Erica is neither bad at chess nor creative, then Erica is either someone who plans and is creative, or she is neither of these things.

∀x (At(x, boardGameNight) → (InterestedIn(x, puzzle) ∨ BadAt(x, chess)))
∀x ((At(x, boardGameNight) ∧ BadAt(x, chess)) → ¬PlaysOften(x, chess))
∃x (At(x, boardGameNight) ∧ (Planner(x) ∨ Creative(x)))
At(erica, boardGameNight) ∧ PlaysOften(erica, chess)
(At(erica, boardGameNight) ∧ (¬(BadAt(erica, chess) ∨ Creative(erica)))) → ¬(Planner(erica) ⊕  Creative(erica))


Erica is interested in puzzles and is creative.

InterestedIn(erica, puzzle) ∧ Creative(erica)


Erica is either interested in puzzles or is creative.

InterestedIn(erica, puzzle) ⊕ Creative(erica)


If Erica plans ahead or plays a lot of chess matches, then Erica is not interested in puzzles and creative.

Planner(erica) ∨ PlaysOften(erica, chess))) → (¬(InterestedIn(erica, puzzle) ∧ Creative(erica))


If Erica is creative, then Erica is not interested in puzzles and creative.

Creative(erica)) → (¬(InterestedIn(erica, puzzle) ∧ Creative(erica))


If Erica is interested in puzzles and is creative, then Erica is not creative.

InterestedIn(erica, puzzle) ∧ Creative(erica)) → ¬Creative(erica)


If Erica either plays a lot of chess matches or is creative, then Erica is neither interested in puzzles nor a person who plays a lot of chess matches.

PlaysOften(erica, chess) ⊕ InterestedIn(erica, puzzle) → ¬(InterestedIn(erica, puzzle) ∨ PlaysOften(erica, chess))


If Erica is interested in puzzles and plays a lot of chess matches, then Erica is either a person who plays a lot of chess matches or a person that is creative.

PlaysOften(erica, chess) ⊕ InterestedIn(erica, puzzle)) → ¬(InterestedIn(erica, puzzle) ∨ PlaysOften(erica, chess)


If Erica plans ahead or is interested in puzzles, then Erica is creative.

Planner(erica) ∨ InterestedIn(erica, puzzle) → Creative(erica)


If Erica is either bad at chess or interested in puzzles, then Erica is not a person who plays a lot of chess matches and creative.

BadAt(erica, chess) ⊕ InterestedIn(erica, puzzle) → ¬(PlaysOften(erica, chess) ∧ Creative(erica))


Soccer players have a right foot and a left foot.
Top soccer players are soccer players who can use both the left foot and right foot very efficiently.
If a soccer player can score many goals using the left foot, they can use that foot very efficiently.
If a soccer player can score many goals using the right foot, they can use that foot very efficiently.
Cristiano Ronaldo is a soccer player.
Cristiano Ronaldo can use his right foot very efficiently.
Cristiano Ronaldo has scored many goals using his left foot.

∀x (SoccerPlayer(x) → Have(x, leftFoot) ∧ Have(x, rightFoot))
∀x (SoccerPlayer(x) ∧ UseEfficiently(x, leftFoot) ∧ UseEfficiently(x, rightFoot) → TopSoccerPlayer(x))
∀x (SoccerPlayer(x) ∧ ScoreUsing(x, manyGoals, leftFoot) → UseEfficiently(x, leftFoot))
∀x (SoccerPlayer(x) ∧ ScoreUsing(x, manyGoals, rightFoot) → UseEfficiently(x, rightFoot))
SoccerPlayer(ronaldo)
UseEfficiently(ronaldo, rightFoot)
ScoreUsing(ronaldo, manyGoals, leftFoot)

Cristiano Ronaldo is a top soccer player.


Cristiano Ronaldo is not a top soccer player.


The National Lobster Hatchery is a hatchery located in Padstow, England.
The National Lobster Hatchery is open to visitors.
A hatchery is either for profit or for conservation.
If a hatchery is for conservation, it might release animals into the wild.
The National Lobster Hatchery is not for profit.

Hatchery(nationalLobsterHatchery) ∧ LocatedIn(nationalLobsterHatchery, padstowEngland)
OpenToVisitor(nationalLobsterHatchery)
∀x (Hatchery(x) → ForConservation(x) ⊕ ForProfit(x))
∃x (Hatchery(x) ∧ ForConservation(x) ∧ ReleaseAnimalToWild(x))
¬ForProfit(nationalLobsterHatchery)

The National Lobster Hatchery is for conservation.


The National Lobster Hatchery releases animals into the wild.


Rhos Aelwyd F.C. is a Welsh football club.
Rhos Aelwyd F.C. is the only football club located in Ponciau.
The Premier Division was won in June 2005 by a team from Ponciau.
The winner of the Premier Division in October 2009 was promoted to the Cymru Alliance.
The Premier Division in October 2009 was won by the same team that won in June 2005.

∀x (Rhosaelwydfc(x) → FootballClub(x) ∧ Welsh(x))
∀x (FootballClub(x) ∧ LocatedIn(x, ponciau) ↔ Rhosaelwydfc(x))
∃x (LocatedIn(x, ponciau) ∧ WonPremierDivisionDuring(x, year2005MonthJune))
∀x (WonPremierDivisionDuring(x, year2009MonthOctober) → PromotedTo(x, cymruAlliance))
∀x (WonPremierDivisionDuring(x, year2009MonthOctober) ↔ WonPremierDivisionDuring(x, y2005MonthJune))

Rhos Aelwyd F.C. won Premier Division in June 2005.

∃x (Rhosaelwydfc(x) ∧ WonPremierDivisionDuring(x, year2005MonthJune))


Rhos Aelwyd F.C. was promoted to the Cymru Alliance.

∃x (Rhosaelwydfc(x) ∧ PromotedTo(x, cymruAlliance))


A Unix operating system used in the lab computers is a piece of software.
All versions of MacOS used in the lab computer are based on Unix operating systems.
A lab computer uses either MacOS or Linux.
All Linux computers in the lab are convenient.
All software used in the lab computers is written with code.
If something is convenient in the lab computer, then it is popular.
Burger is used in the lab computer, and it is written with code and a new version of MacOS.
PyTorch is used in the lab computer, and PyTorch is neither a Linux system nor a piece of software.

∀x (UsedIn(x, labComputer) ∧ UnixOperatingSystem(x) → Software(x))
∀x (UsedIn(x, labComputer) ∧ MacOS(x) → UnixOperatingSystem(x))
∀x (UsedIn(x, labComputer) → MacOS(x) ⊕ Linux(x))
∀x (UsedIn(x, labComputer) ∧ Linux(x) → Convenient(x))
∀x (UsedIn(x, labComputer) ∧ Software(x) → WrittenWithCode(x))
∀x (UsedIn(x, labComputer) ∧ Convenient(x) → Popular(x))
UsedIn(burger, labComputer) ∧ WrittenWithCode(burger) ∧ MacOS(burger))
UsedIn(pytorch, labComputer) ∧ ¬(Linux(pytorch) ⊕ Software(pytorch))


PyTorch is popular and written with code.


PyTorch is not popular and it is not written with code.


Roads are made of either concrete or asphalt.
Roads made of concrete last longer than roads made with asphalt.
Roads made of asphalt are smoother than roads made of concrete.
Everyone prefers the smoother of two roads.
The first road is made of concrete, and the second road is made of asphalt.

∀x (Road(x) → (MadeOf(x, concrete) ⊕ MadeOf(x, asphalt))
∀x ∀y (Road(x) ∧ MadeOf(x, concrete) ∧ Road(y) ∧ MadeOf(y, asphalt) → LastLonger(x, y))
∀x ∀y (Road(x) ∧ MadeOf(x, asphalt) ∧ Road(y) ∧ MadeOf(y, concrete) → Smoother(x, y))
∀x ∀y ∀z (Road(x) ∧ Road(y) ∧ Smoother(x, y) → Prefer(z, x))
Road(firstRoad) ∧ MadeOf(secondRoad, concrete) ∧ Road(firstRoad) ∧ MadeOf(secondRoad, asphalt)

The first road will last longer than the second road.


The second road is not smoother than the first one.


Camp Davern is a traditional summer camp for boys and girls.
Camp Davern was established in the year 1946.
Camp Davern was operated by the YMCA until the year 2015.
Camp Davern is an old summer camp.

TraditionalSummerCamp(campDavern) ∧ ForBoysAndGirls(campDavern)
EstablishedIn(campDavern, year1946)
OperatedUntil(yMCA, campDavern, year2015)
Old(campDavern)

One of Ontario's oldest summer camps is a traditional summer camp for boys and girls.

∃x (Old(x) ∧ TraditionalSummerCamp(x) ∧ ForBoysAndGirls(x))


A traditional summer camp for boys and girls was operated by the YMCA until the year 2015.

∃x (TraditionalSummerCamp(x) ∧ ForBoysAndGirls(x) ∧ OperatedUntil(YMCA, x, year2015))


If Emily's friends publish journals, then they do not work in the entertainment industry.
All of Emily's friends who are award-winning novelists publish journals.
Emily's friends work in the entertainment industry or are highly acclaimed in their profession.
If Emily's friends are highly acclaimed in their profession, then they often hold tenured and high-ranking positions at their workplace.
If Emily's friends are highly acclaimed in their profession, then they often receive glowing feedback and recommendations from their colleagues.
Taylor is Emily's friend.
It is not true that Taylor both holds highly acclaimed in her profession and often holds tenured and high-ranking positions at her workplace.

∀x (EmilysFriend(x) ∧ Publish(x, journal) → ¬WorkIn(x, entertainmentIndustry))
∀x (EmilysFriend(x) ∧ AwardWinningNovelist(x) → Publish(x, journal))
∀x (EmilysFriend(x) → WorkIn(x, entertainmentIndustry) ∨ HighlyAcclaimedIn(x, theirProfession))
∀x (EmilysFriend(x) ∧ HighlyAcclaimedIn(x, theirProfession) → ∃y (HoldAt(x, y, workPlace) ∧ Tenured(y) ∧ HighRanking(y) ∧ Position(y)))
∀x (EmilysFriend(x) ∧ HighlyAcclaimedIn(x, theirProfession) → ReceiveFrom(x, glowingFeedback, colleague) ∧ ReceiveFrom(x, glowingRecommendation, colleague))
EmilysFriends(taylor)
¬(HighlyAcclaimedIn(taylor, theirProfession) ∧ (∃y (HoldAt(taylor, y, workPlace) ∧ Tenured(y) ∧ HighRanking(y) ∧ Position(y)))

Taylor is Emily's friend and she often holds tenured and high-ranking positions at her workplace.

EmilysFriends(taylor) ∧ (∃y (HoldAt(taylor, y, workPlace) ∧ Tenured(y) ∧ HighRanking(y) ∧ Position(y)))


Taylor is Emily's friend and she often receives glowing feedback and recommendations from their colleagues and is an award-winning novelist.

EmilysFriends(taylor) ∧ (Receive(taylor, glowingFeedback, colleague) ∧ Receive(taylor, glowingRecommendation, colleague) ∧ AwardWinningNovelist(taylor))


Taylor is Emily's friend and she does not both publish journals and is an award-winning novelist.

EmilysFriends(taylor) ∧ ¬(Publish(taylor, journal) ∧ AwardWinningNovelist(taylor))


Thick as Thieves is a young adult fantasy novel written by Megan Whalen Turner.
Thick as Thieves was published by Greenwillow Books.
If a book was published by a company, then the author of that book worked with the company that published the book.
The fictional Mede Empire is where Thick as Thieves is set.
The Mede Empire plots to swallow up some nearby countries.
Attolia and Sounis are countries near the Mede Empire.
Thick as Thieves was sold both as a hardcover and an e-book.

YoungAdultFantasy(thickAsTheives) ∧ Novel(thickAsTheives) ∧ WrittenBy(thickAsTheives, meganWhalenTurner)
PublishedBy(thickAsTheives, greenWillowBooks)
∀x ∀y ∀z ((WrittenBy(x, y) ∧ PublishedBy(x, z)) → WorkedWith(y, z))
Fictional(medeEmpire) ∧ SetIn(thickAsTheives, medeEmpire)
∃x ∃y ((Country(x) ∧ Near(x, medeEmpire) ∧ PlotsToSwallowUp(medeEmpire, x)) ∧ (¬(x=y) ∧ Near(y, medeEmpire) ∧ PlotsToSwallowUp(medeEmpire, y)))
Country(attolia) ∧ Near(attolia, medeEmpire) ∧ Country(sounis) ∧ Near(sounis, medeEmpire)
SoldAs(thickAsTheives, hardCover) ∧ SoldAs(thickAsTheives, softCover)

Megan Whalen Turner worked with Greenwillow Books.


The Mede Empire plans to swallow up Attolia.


Thick as Thieves is not set in the Mede Empire.


Megan Whalen Turner did not work with Greenwillow Books.


WeTab is a MeeGo-based tablet computer.
WeTab was announced by Neofonie.
Neofonie is a German producer.
Germans live in Germany or abroad.

MeeGoBased(weTab) ∧ TabletComputer(weTab)
∀x (AnnouncedBy(weTab, neofonie))
German(neofonie) ∧ Producer(neofonie)
∀x (German(x) → LiveIn(x, german) ⊕ LiveAbroad(x))

There is a tablet computer announced by a German producer.

∃x ∃y (TabletComputer(x) ∧ German(y) ∧ Producer(y) ∧ AnnouncedBy(x, y))


Neofonie doesn't speak English or German.

¬Speak(neofonie, english) ∧ ¬Speak(neofonie, german)


Some employees in James's town who work in business analysis are good at math.
All of the employees in James's town who work in business analysis are working for this company.
None of the employees in James's town who work for this company are from China.
All of the employees in James's town working in software engineering are from China.
Leif is an employee in James's town, and he is working in software engineering.

∃x ∃y (EmployeeIn(x, jamesSTown) ∧ WorkIn(x, businessAnalysis) ∧ GoodAt(x, math) ∧ (¬(x=y)) ∧ EmployeeIn(y, jamesSTown) ∧ WorkIn(y, businessAnalysis) ∧ GoodAt(y, math))
∀x ((EmployeeIn(x, jamesSTown) ∧ WorkIn(x, businessAnalysis)) → WorkFor(x, thisCompany))
∀x ((EmployeeIn(x, jamesSTown) ∧ WorkFor(x, thisCompany)) → ¬From(x, china))
∀x (EmployeeIn(x, jamesSTown) ∧ WorkIn(x, softwareEngineering) → From(x, china))
EmployeeIn(leif, jamesSTown) ∧ WorkIn(leif, softwareEngineering)

EmployeesInJamesSTown(leif) ∧ GoodAt(leif, math)


Leif is not both good at math and working in business analysis.

¬(GoodAt(leif, math) ∧ WorkIn(leif, businessAnalysis))


If Leif is not both good at math and in business analysis, then he is neither working in this company nor working in software engineering.

¬(GoodAt(leif, math) ∧ WorkIn(leif, businessAnalysis)) → (¬WorkFor(x, thisCompany) ∧ ¬WorkIn(x, softwareEngineering))


The party provides five kinds of fruits: strawberry, orange, blueberry, grape, and cherry.
If the fruit had the lowest remaining weight at the end of the party, then it means it was the most popular fruit.
At the end of the party, strawberries had the lowest remaining weight.
At the end of the party, the number of leftover blueberries was lower than that of cherries.
Benjamin only ate oranges and grapes at the party.

Provide(party, strawberry) ∧ Provide(party, orange) ∧ Provide(party, blueberry) ∧ Provide(party, grape) ∧ Provide(party, cherry)
∀x (LowestWeightRemainingAt(x, endOfParty) → MostPopular(x))
LowestWeightRemainingAt(strawberries, endOfParty)
LowerWeightAt(blueberry, cherry, endOfParty)
Eat(benjamin, orange) ∧ Eat(benjamin, grape) ∧ ¬Eat(benjamin, blueberry) ∧ ¬Eat(benjamin, cherry) ∧ ¬Eat(benjamin, strawberry)

Blueberries were the most popular fruit at the party.


Cherries were the most popular fruit at the party.


All students who attend in person have registered for the conference.
Students either attend the conference in person or remotely.
No students from China attend the conference remotely.
James attends the conference, but he does not attend the conference remotely.
Jack attends the conference, and he is a student from China.

∀x (AttendInPerson(x) → Registered(x))
∀x (Attend(x) → (AttendInPerson(x) ⊕ AttendRemotely(x)))
∀x ((Attend(x) ∧ FromChina(x)) → ¬AttendRemotely(x))
Attend(james) ∧ (¬AttendRemotely(james))
FromChina(jack) ∧ Attend(jack)

James attends the conference but not in person.


David Ha'ivri is a political strategist.
If you are born in Israel to at least one Israeli parent, you receive Israeli citizenship at birth.
David Ha'ivri emigrated to the United States from Israel, where he was born to Israeli parents.
Several Zionist leaders have been elected to the Shomron Regional Municipal council.
David Ha'ivri is a Zionist leader.

PoliticalStrategist(davidHaivri)
∀x ∃y (BornInIsrael(x) ∧ ParentOf(y, x) ∧ Israeli(y) → Israeli(x))
∃x (EmigratedTo(davidHaivri, america) ∧ BornInIsrael(davidHaivri) ∧ ParentOf(davidHaivri, x) ∧ Israeli(x))
∃x (ZionistLeader(x) ∧ ElectedTo(x, shomronMunicipalCouncil))
ZionstLeader(davidHaivri)


David Ha'ivri is a United States citizen.


David Ha'ivri has been elected to the Shomron Regional Municipal council.


Mary has the flu.
If someone has the flu, then they have influenza.
Susan doesn't have influenza.

Has(mary, flu)
∀x (Has(x, flu) → Has(x, influenza))
¬Has(susan, influenza)

Has(mary, influenza) ⊕ Has(susan, influenza)


James Cocks was a British lawyer.
James Cocks was a Whig politician who sat in the House of Commons.
A British is a European.
Any lawyer is familiar with laws.
Some Whigs speak French.

British(james) ∧ Lawyer(james)
Whig(james) ∧ Politician(james) ∧ SatInHouseOfCommons(james)
∀x (British(x) → European(x))
∀x (Lawyer(x) → FamiliarWithLaws(x))
∃x ∃y (Whig(x) ∧ SpeakFrench(x)) ∧ (¬(x=y)) ∧ (Whig(y) ∧ SpeakFrench(y))

No lawyer ever sat in the House of Commons.

∀x (Lawyer(x) → ¬SatInHouseOfCommons(x))


Beasts of Prey is a fantasy novel or a science fiction novel, or both.
Science fiction novels are not about mythological creatures
Beasts of Prey Is about a creature known as the Shetani.
Shetanis are mythological.

Novel(beastsOfPrey) → (Fantasy(beastsOfPrey) ∨ ScienceFiction(beastsOfPrey))
∀x ∀y (ScienceFiction(x) ∧ Mythological(y) ∧ Creature(y) → ¬About(x, y))
About(beastsOfPrey, shetani) ∧ Creature(shetani)
Mythological(shetani)


Beasts of prey isn't a science fiction novel.


A shetani is either mythological or a creature.


Odell is an English surname originating in Odell, Bedfordshire.
In some families, Odell is spelled O'Dell in a mistaken Irish adaptation.
Notable people with surnames include Amy Odell, Jack Odell, and Mats Odell.
Amy Odell is a British singer-songwriter.
Jack Odell is an English toy inventor.

Surname(nameODell) ∧ From(nameODell, oDellBedfordshire)
MistakenSpellingOf(nameO'Dell, nameODell) ∧ (∃x∃y(Family(x) ∧ Named(x, nameO'Dell) ∧ (¬(x=y)) ∧ Family(y) ∧ Named(y, nameO'Dell))
Named(amyODell, nameODell) ∧ NotablePerson(amyODell) ∧ Named(jackODell, nameODell) ∧ NotablePerson(jackODell) ∧ Named(matsODell, nameODell) ∧ NotablePerson(matsODell)
British(amyODell) ∧ Singer(amyODell) ∧ SongWriter(amyODell)
English(jackODell) ∧ ToyInventor(jackODell)


Named(amyODell, nameODell) ∧ Named(amyODell, nameO'Dell)


If you go somewhere by train, you will not lose time.
If you go somewhere by car and meet a traffic jam, you will lose time.
If you lose time, you will be late for work.
Mary can get from New Haven to New York City either by train or car.
Mary is late for work.

∀x (GoByTrain(x) → ¬LoseTime(x))
∀x((GoByCar(x) ∧ Meet(x, trafficJam)) → LoseTime(x))
∀x (LoseTime(x) → LateForWork(x))
FromAndTo(newHaven, newYork) ∧ (GoByTrain(mary) ⊕ GoByCar(mary))
LateForWork(mary)

Mary gets from New Haven to New York City by train.

FromAndTo(newHaven, newYork) ∧ GoByTrain(mary)


Mary gets from New Haven to New York City by car.

FromAndTo(newHaven, newYork) ∧ GoByCar(mary)


If a person is hungry, the person is uncomfortable.
If a person is uncomfortable, the person is unhappy.

∀x (Hungry(x) → Uncomfortable(x))
∀x (Uncomfortable(x) → ¬Happy(x))

If a person is not hungry, the person is unhappy.


Tipped employees are not entitled to be paid the federal minimum wage by their employees.
If a person is a white-collar worker, they are entitled to be paid the federal minimum wage by their employees.
All lawyers are white-collar workers.
Every advocate is a lawyer.
Mary is not a lawyer or a tipped employee.

∀x (TippedEmployee(x) → ¬EntitledTo(x, federalMinimumWage))
∀x (WhiteCollarWorker(x) → EntitledTo(x, federalMinimumWage))
∀x (Lawyer(x) → WhiteCollarWorker(x))
∀x (Advocate(x) → Lawyer(x))
¬(Lawyer(mary) ⊕ TippedEmployee(mary))


Mary is either an advocate or a tipped employee.


If Mary is not both an advocate and is entitled to be paid the federal minimum wage by their employees, she is not a tipped employee.

(¬(Advocate(mary) ∧ EntitledTo(mary, federalMinimumWage))) → ¬TippedEmployee(mary)


If Mary is either an advocate or a tipped employee, she is an advocate.

(Advocate(mary) ⊕ TippedEmployee(mary)) → Advocate(mary)


Asa Hoffmann was born in New York City.
Asa Hoffman lives in Manhattan.
Asa Hoffman is a chess player.
Some chess players are grandmasters.
People born and living in New York City are New Yorkers.
People living in Manhattan live in New York City.

BornIn(asaHoffmann, newYorkCity)
LiveIn(asaHoffmann, manhattan)
ChessPlayer(asaHoffmann)
∃x ∃y (ChessPlayer(x) ∧ GrandMaster(x) ∧ (¬(x=y)) ∧ ChessPlayer(y) ∧ GrandMaster(y))
∀x ((BornIn(x, newYorkCity) ∧ LiveIn(x, newYorkCity)) → NewYorker(x))
∀x (LiveIn(x, manhattan) → LiveIn(x, newYorkCity))


Some of those who apply for a Schengen visa get it.
To apply for a Schengen Visa, you need to provide financial guarantees.
If you need to provide financial guarantees, you must request documents from the bank.
Do not close your bank account if you request documents from the bank.
Philip closed his bank account.

∃x (Apply(x, schengenVisa) → Get(x, schengenVisa))
∀x (Apply(x, schengenVisa) → Provide(x, financialGuarantees))
∀x (Provide(x, financialGuarantees) → Request(x, documentsFromBank))
∀x (Request(x, documentsFromBank) → ¬Close(x, bankAccount))
Close(philip, bankAccount)


Philip applied for a Schengen visa and got it.

Apply(philip, schengenVisa) ∧ Get(philip, schengenVisa)


If Philip did not request documents from the bank or get a Schengen visa, he didn’t apply for a Schengen visa.

(¬Request(philip, documentsFromBank) ∧ ¬Get(x, schengenVisa)) → Apply(x, schengenVisa)


Some fears lead to anxiety.
Some anxiety leads to terror.

∃x ∃y (Fear(x) ∧ Anxiety(y) ∧ LeadTo(x, y) ∧ ¬(x=y))
∃x ∃y (Anxiety(x) ∧ Terror(y) ∧ LeadTo(x, y))

∀x ∀y (Fear(x) → ¬(Terror(y) ∧ LeadTo(x, y)))


The Great Lakes are Lake Superior, Lake Michigan, Lake Huron, Lake Erie, and Lake Ontario.
Some major settlements of Lake Erie are in NY, PA, OH, and MI.
NY, PA, OH, and MI are states in the US.
ON is a state of Canada.
There is a major settlement of Lake Huron in ON.
All states are in their country.
The US is in North America.
The Great Lakes began to form at the end of the Last Glacial Period.

∀x (GreatLake(x) → Superior(x) ⊕ Michigan(x) ⊕ Huron(x) ⊕ Erie(x) ⊕ Ontario(x))
∀x (Erie (x) ∧ MajorSettlement(x) → In(x, nY) ∨ In(x, pA) ∨ In(x, oH) ∨ In(x, mI))
StateOf(nY, uS) ∧ StateOf(pA, uS) ∧ StateOf(oH, uS) ∧ StateOf(mI, uS)
StateOf(oN, canada)
∃x (Huron(x) ∧ MajorSettlement(x) ∧ In(x, oN))
∀x ∀y (StateOf(x, y) → In(x, y))
In(us, northAmerica)
∀x (GreatLake(x) → FormAtEndOf(x, lastGlacialPeriod))

∃x ∃y (Erie(y) ∧ MajorSettlementOf(x, y))


There is a great lake that did not form at the end of the Last Glacial Period.

∃x (GreatLake(x) ∧ ¬FormAtEndOf(x, lastGlacialPeriod))


All professional soccer defenders are professional soccer players.
No professional soccer players are professional basketball players.
All professional centerbacks are professional soccer defenders.
All NBA players are professional basketball players.
Stephen Curry is an NBA player.

∀x ((Professional(x) ∧ Defender(x)) → (Professional(x) ∧ SoccerPlayer(x)))
∀x ((Professional(x) ∧ SoccerPlayer(x)) → ¬(Professional(x) ∧ BasketballPlayer(x)))
∀x ((Professional(x) ∧ CenterBack(x)) → (Professional(x) ∧ Defender(x))
∀x (NBAPlayer(x) → (Professional(x) ∧ BasketballPlayer(x)))
NBAPlayer(stephenCurry)

Stephen Curry is a professional basketball player.


Stephen Curry is a professional centerback.


Naive cynicism was proposed by Justin Kruger and a colleague.
Thomas Gilovich is a colleague of Justin Kruger.
Naive cynicism is a philosophy of mind.

Proposed(justinKruger, naiveCynicism) ∧ ∃y (colleagueOfJustinKruger(y) ∧ Proposed(y, naiveCynicism))
Colleagues(thomasGilovich, justinKruger)
PhilosophyOfMind(naiveCynicism)

Thomas Gilovich proposed naive cynicism.


Justin Kruger proposed a philosophy of mind.

∃x (Proposed(justinKruger, x) ∧ PhilosophyOfMind(x))


Thomas Gilovich worked on philosophies of mind.

∃x (WorkedOn(thomasGilovich, x) ∧ PhilosophyOfMind(x))


The Turing Award has been awarded to Donald Knuth, Marvin Minsky, Richard Hamming, and John McCarthy.
Donald Knuth made contributions to the analysis of algorithms.
Marvin Minsky is recognized for his contributions to the field of artificial intelligence.
Richard Hamming researched numerical methods.
John McCarthy made contributions to the field of artificial intelligence.

AwardedTo(turingAward, donaldKnuth) ∧ AwardedTo(turingAward, marvinMinsky) ∧ AwardedTo(turingAward, richardHamming) ∧ AwardedTo(turingAward, johnMccarthy)
ContributedTo(donaldKnuth, analysisOfAlgorithms)
ContributedTo(marvinMinsky, artificialIntelligence)
ContributedTo(richardHamming, numericalMethods)
ContributedTo(johnMccarthy, artificialIntelligence)

At least two people who have won the Turing Award worked in artificial intelligence.

∃x ∃y (¬(x=y) ∧ AwardedTo(turingAward, x) ∧ AwardedTo(turingAward, y) ∧ ContributedTo(x, artificialIntelligence)  ∧ ContributedTo(y, artificialIntelligence))


At least two people who worked in artificial intelligence have won the Turing Award.

∃x ∃y (¬(x=y) ∧ ContributedTo(x, artificialIntelligence) ∧ ContributedTo(x, artificialIntelligence) ∧ AwardedTo(turingAward, x) ∧ AwardedTo(turingAward, y))


Only one person who won the Turing Award made significant contributions to the analysis of algorithms.

∃x ∀y ((AwardedTo(turingAward, x) ∧ AwardedTo(turingAward, y) ∧ ContributedTo(y, algorithms) ∧ ¬(x=y)) → ¬ContributedTo(y, algorithms))


No Turing Award winners worked in the field of numerical methods.

∀x (AwardedTo(turingAward, x) → ¬ContributedTo(x, numericalMethods))


None of the easy Leetcode problems have an AC rate lower than 20 percent.
All Leetcode problems recommended to novices are easy.
Leetcode problems either have an AC rate lower than 20 percent or are starred by more than 1 thousand users.
All hard Leetcode problems are starred by more than 1,000 users.
No Leetcode problems published after 2022 are starred by more than 1,000 users.
'2Sum' is not both hard and also recommended to novices.
'4Sum' is either starred by more than 1,000 users and published after 2022, or it is neither.

∀x ((LeetcodeProblems(x) ∧ Easy(x)) → ¬HaveAnACRateLowerThan(x, percent20))
∀x ((LeetcodeProblems(x) ∧ RecommendedTo(x, novices)) → Easy(x))
∀x (LeetcodeProblems(x) → HaveAnACRateLowerThan(x, percent20) ⊕ StarredByMoreThan(x, num1000))
∀x ((LeetcodeProblems(x) ∧ Hard(x)) → StarredByMoreThan(x, num1000))
∀x ((LeetcodeProblems(x) ∧ PublishedAfter(x, yr2022)) → (¬StarredByMoreThan(x, num1000)))
¬(RecommendedTo(twosum, novices) ∧ Hard(twosum)) ∧ LeetcodeProblems(twosum)
¬(StarredByMoreThan(foursum, num1000) ⊕ PublishedAfter(foursum, yr2022)) ∧ LeetcodeProblems(twosum)


4Sum is recommended to novices or is hard.

RecommendedTo(foursum, novices) ∨ Hard(foursum)


4Sum is neither recommended to the novice nor a Leetcode problem that's hard.

¬RecommendedTo(foursum, novices) ∧ ¬Hard(foursum)


Show Your Love is a song recorded by the South Korean boy band BtoB 4u.
The lead single of the extended play Inside is Show Your Love.
Show Your Love contains a hopeful message.
BtoB 4u member Hyunsik wrote Show Your Love.
There is a music video for Show Your Love.

Song(showYourLove) ∧ RecordedBy(showYourLove, bToB4u) ∧ SouthKorean(bToB4u) ∧ BoyBand(bToB4u)
ExtendedPlay(inside) ∧ LeadSingleOf(showYourLove, inside)
Contains(showYourLove, hopefulMessage)
Member(hyunsik, btob4u) ∧ Wrote(hyunsik, showYourLove)
Have(showYourLove, musicVideo)

Show Your Love wasn't written by a member of a boy band.

∀x ∀y (Wrote(x, showYourLove) → ¬(BoyBand(y) ∧ MemberOf(x, y)))


A lead single of Inside contains a hopeful message.

∃x (LeadSingleOf(x, inside) ∧ Contains(x, hopefulMessage))


All tables are round.
Some pieces of furniture are tables.

∀x (Table(x) → Round(x))
∃x ∃y (Furniture(x) ∧ Furniture(y) ∧ Table(x) ∧ Table(y) ∧ ¬(x=y))

∃x ∃y (Furniture(x) ∧ Furniture(y) ∧ Round(x) ∧ Round(y) ∧ ¬(x=y))


All juvenile delinquents have committed a crime.
Some juvenile delinquents are products of broken homes.

∀x (JuvenileDelinquent(x) → Commited(x, crime))
∃x ∃y (JuvenileDelinquent(x) ∧ JuvenileDelinquent(y) ∧ ProductOf(x, brokenHome) ∧ ProductOf(y, brokenHome) ∧ ¬(x=y))

Some people who have committed a crime are products of broken homes.

∃x ∃y (Commited(x, crime) ∧ Commited(y, crime) ∧ ProductOf(x, brokenHome) ∧ ProductOf(y, brokenHome) ∧ ¬(x=y))


All mind-reading is either brain reading or brain decoding.
All brain decoding that is mind-reading is extracting information from BOLD signals.
No studies that are mind-reading and extract information from BOLD signals are without statistical pattern analysis.
Writing a novel is without statistical pattern analysis.
If multivoxel (pattern) analysis is without statistical pattern analysis and a brain reading, then multivoxel (pattern) analysis is without statistical pattern analysis and brain decoding.
Multivoxel (pattern) analysis is a type of mind-reading.

∀x (MindReading(x) ∧ (BrainReading(x) ⊕ BrainDecoding(x)))
∀x ((MindReading(x) ∧ BrainDecoding(x)) → ExtractingFrom(x, information, bOLDSignals))
∀x ((MindReading(x) ∧ ExtractingFrom(x, information, bOLDSignals)) → Uses(x, statisticalPatternAnalysis))
∀x (NovelWriting(x) → ¬Uses(x, statisticalPatternAnalysis))
MindReading(multivoxelPatternAnalysis) ∧ (¬Uses(multivoxelPatternAnalysis, statisticalPatternAnalysis) ∧ BrainReading(multivoxelPatternAnalysis)) →  (¬Uses(multivoxelPatternAnalysis, statisticalPatternAnalysis) ∧ (¬BrainDecoding(multivoxelPatternAnalysis)))
MindReading(multivoxelPatternAnalysis)

Multivoxel (pattern) analysis is a brain decoding.


Multivoxel (pattern) analysis is the writing of a novel.


Multivoxel (pattern) analysis is without statistical pattern analysis and writing a novel.

¬(Uses(multivoxelPatternAnalysis, statisticalPatternAnalysis) ∧ NovelWriting(multivoxelPatternAnalysis))


Multivoxel (pattern) analysis is without statistical pattern analysis or writing a novel.

¬(Uses(multivoxelPatternAnalysis, statisticalPatternAnalysis) ∨ NovelWriting(multivoxelPatternAnalysis))


Multivoxel (pattern) analysis is either without statistical pattern analysis or writing a novel.

¬Uses(multivoxelPatternAnalysis, statisticalPatternAnalysis) ⊕ Writing(multivoxelPatternAnalysis, aNovel)


If multivoxel (pattern) analysis is writing a novel, then multivoxel (pattern) analysis is neither without statistical pattern analysis nor writing a novel.

(MindReading(multivoxelPatternAnalysis) ∧ NovelWriting(multivoxelPatternAnalysis)) → (Uses(multivoxelPatternAnalysis, statisticalPatternAnalysis) ∨ ¬NovelWriting(multivoxelPatternAnalysis))


If you have room for dessert, you have room for broccoli.
Everyone at Luis's dinner party has room for dessert, including Luis.
Mauricia does not have room for broccoli.
Luis's dinner party is the first ever dinner party that Allison has attended.
Gustave has room for both broccoli and asparagus.
Broccoli and asparagus are both vegetables.

∀x (RoomFor(x, dessert) → RoomFor(x, broccoli))
∀x (AtLuisParty(x) → RoomFor(x, dessert))
¬RoomFor(mauricia, broccoli)
AtLuisParty(allison) ∧ FirstDinnerPartyFor(luisparty, allison)
RoomFor(gustave, broccoli) ∧ RoomFor(gustave, asparagus)
Vegetable(broccoli) ∧ Vegetable(asparagus)


Imagine Dragons are an American pop-rock band.
The lead singer of Imagine Dragons is Dan.
Dan is also a songwriter.
All lead singers are singers.
All singers are musicians.
Demons is one of the most popular singles of Imagine Dragons.
Some singles of Imagine Dragons have been on Billboard Hot 100.

American(imagineDragon) ∧ RockBand(imagineDragon)
LeadSinger(imagineDragon, dan)
SongWriter(dan)
∀x ∀y (LeadSinger(x, y) → Singer(y))
∀x (Singer(x) → Musician(x))
PopularSingle(imagineDragon, demons)
∃x ∃y (PopularSingle(imagineDragon, x) ∧ BillboardHot100(x)) ∧ (¬(x=y)) ∧ (PopularSingle(imagineDragon, y) ∧ BillboardHot100(y))

Some rock band has a lead singer who is also a songwriter.

∃x ∃y (RockBand(x) ∧ LeadSinger(x, y) ∧ SongWriter(y))


All philosophers reason.
Some sophists reason.
All who can reason can distinguish truth from falsehood.
Nobody who can distinguish truth from falsehood is morally perfect.
The theistic God is morally perfect.

∀x (Philosopher(x) → Reason(x))
∃x (Sophist(x) ∧ Reason(x))
∀x (Reason(x) → CanDistinguishFrom(x, truth, falsehood))
∀x (CanDistinguishFrom(x, truth, falsehood) → ¬MorallyPerfect(x))
MorallyPerfect(theisticGod)


The theistic God is a sophist and a philosopher.


if the theistic God is a philosopher, then he is not a sophist.


Common utilities include water, electricity, gas, heating, sewer, trash, and recycling.
Many apartment rents cover the cost of water and electricity.
Susan lives in an apartment where the rent covers all utilities.
The rent of the apartment where Ava lives does not cover any utility expenses.
Noah lives in an apartment where the rent does not cover heating.

CommonUtilities(water) ∧ CommonUtilities(electricity) ∧ CommonUtilities(gas) ∧ CommonUtilities(heating)
∃x (Apartment(x) ∧ Cover(x, water) ∧ Cover(x, electricity))
∀x (Apartment(x) ∧ LiveIn(susan, x) ∧ Cover(x, water) ∧ Cover(x, electricity) ∧ Cover(x, gas) ∧ Cover(x, heating))
∀x (Apartment(x) ∧ LiveIn(ava, x) ∧ ¬Cover(x, water) ∧ ¬Cover(x, electricity) ∧ ¬Cover(x, gas) ∧ ¬Cover(x, heating))
∀x (Apartment(x) ∧ LiveIn(noah, x) ∧ ¬Cover(x, heating))

∀x (Apartment(x) ∧ LiveIn(noah, x) ∧ ¬Cover(x, water))


Noah and Ava both need to pay the heating bill.

¬Cover(noah, heating) ∧ ¬Cover(ava, heating)


Susan does not need to pay the water bill.

∀x (Apartment(x) ∧ LiveIn(susan, x) ∧ Cover(x, water))


All clothes are products.
No products are perfect.
All dresses are clothes.
All skirts are dresses.
If the fabric bundle is a piece of clothing, then the fabric bundle is a perfect dress.

∀x (Clothes(x) → Product(x))
∀x (Product(x) → ¬Perfect(x))
∀x (Dress(x) → Clothes(x))
∀x (Skirt(x) → Dress(x))
Clothes(fabricBundle) → Perfect(fabricBundle) ∧ Dress(fabricBundle)


All pets are animals.
Pets can be either a dog or a cat.
If a person has a pet, they care for that pet.
Dogs and cats can be naughty.
Pets who are naughty are not liked as much.
Charlie has a naughty pet dog named Leo.

∀x (Pet(x) → Animal(x))
∀x (Pet(x) → (Dog(x) ⊕ Cat(x)))
∀x ∀y ((Pet(y) ∧ OwnedBy(x,y)) → Cares(x, y))
∃x ∃y (Cat(x) ∧ Naughty(x) ∧ (¬(x=y)) ∧ Dog(y) ∧ Naughty(y))
∀x ∀y ((Pet(x) ∧ Naughty(x) ∧ OwnedBy(x,y)) → ¬Liked(x, y))
OwnedBy(leo, charlie) ∧ Pet(leo) ∧ Dog(leo) ∧ Naughty(leo)


Charlie does not like Leo and does not care for Leo.

¬Liked(leo, charlie) ∧ ¬Cares(charlie, leo)


Surprises are either fun or dreadful.
All scares are surprises.

∀x (Surprise(x) → (Fun(x) ⊕ Dreadful(x)))
∀x (Scare(x) → Surprise(x))


All books written by Cixin Liu have sold more than 1 million copies.
Some books that have won the Hugo Award were written by Cixin Liu.
All books about the future are forward-looking.
The book Three-Body Problem has sold more than 1 million copies.
The Three-Body Problem is about the future.

∀x ((Book(x) ∧ WrittenBy(x, cixinLiu)) → ∃y(MoreThan(y, oneMillion) ∧ Sold(x,y)))
∃x (Won(x, hugoAward) ∧ Book(x) ∧ WrittenBy(x, cixinLiu))
∀x ((Book(x) ∧ AboutFuture(x)) → FowardLooking(x))
Book(threeBodyProblem) ∧ ∃y(MoreThan(y, oneMillion) ∧ Sold(threeBodyProblem,y))
AboutFuture(threeBodyProblem)

The Three-Body Problem won the Hugo Award.


The Three-Body Problem is forward-looking.


The Three-Body Problem was written by Cixin Liu.


Some people are both late-night and early-morning people.
If a person is an earl- morning person, they have early-morning habits.
Everyone who has early-morning habits gets up early.
Everyone who gets up early catches the sunrise.
James doesn't catch the sunrise.

∃x (LateNightPerson(x) ∧ EarlyMorningPerson(x))
∀x (EarlyMorningPerson(x) → Have(x, earlyMorningHabit))
∀x (Have(x, earlyMorningHabit) → GetUpEarly(x))
∀x (GetUpEarly(x) → CatchTheSunrise(x))
¬CatchTheSunrise(james)


James is a late night person and an early-morning person.


If James is an early-morning person, then he is a late night person.


There is no dog on the roof.
If there is a dog on the roof, something went wrong.

∀x (Dog(x) → ¬OnRoof(x)))
∀x ∃y ((Dog(x) ∧ OnRoof(x)) → GoWrong(y))


Elephantopus is a genus of perennial plants in the daisy family.
Elephantopus is widespread over much of Africa, southern Asia, Australia, and the Americas.
Several species of Elephantopus are native to the southeastern United States.
Elephantopus scaber is a traditional medicine.

∀x (Elephantopus(x) → (Genus(x, perennialplants) ∧ BelongTo(x, daisyfamily)))
∃x ∃y ∃z(Elephantopus(x) ∧ In(x,africa) ∧ (¬(x=y)) ∧ Elephantopus(y) ∧ In(y, southernasia) ∧ (¬(x=z)) ∧ (¬(y=z)) ∧ Elephantopus(z) ∧ In(z, australia))
∃x ∃y (Elephantopus(x) ∧ NativeTo(x, southeasternunitedstates) ∧ (¬(x=y)) ∧ Elephantopus(y) ∧ NativeTo(y, southeasternunitedstates))
∀x (ElephantopusScaber(x) → TraditionalMedicine(x))

Elephantopus is found in Australia and Southern Asia.

∃x∃y(Elephantopus(x) ∧ In(x,africa) ∧ Elephantopus(y) ∧ In(y,africa))


No Elephantopus is native to the southeastern United States.

∀x (Elephantopus(x) → ¬NativeTo(x, southeasternunitedstates))


∀x (Elephantopus(x) → TraditionalMedicine(x))


All Yale dormitories are located on the Yale campus.
All Yale buildings managed by Yale Housing are dormitories.
All Yale buildings operated by Yale Housing staff are managed by Yale Housing.
None of the Yale buildings open to students were built before 1701.
All Yale buildings located on the Yale campus are open to students.
Harkness is either a Yale building operated by Yale Housing staff, or it is located on York Street.

∀x (YaleDormitory(x) → LocatedOn(x, yaleCampus))
∀x ((YaleBuildings(x) ∧ ManagedBy(x, yaleHousing)) → YaleDormitory(x))
∀x ((YaleBuildings(x) ∧ OperatedBy(x, yaleHousingStaff)) → ManagedBy(x, yaleHousing))
∀x ((YaleBuildings(x) ∧ OpenToStudents(x)) → (¬∃y(Before(y, yr1701) ∧ Established(x, y))))
∀x ((YaleBuildings(x) ∧ LocatedOn(x, yaleCampus)) → OpenToStudents(x))
YaleBuildings(harkness) ∧ (OperatedBy(x, harkness) ⊕ LocatedOn(harkness, yaleCampus))


∃y(Before(y, year1701) ∧ Established(x, y))


Harkness is not established before 1701.

¬∃y(Before(y, year1701) ∧ Established(x, y))


There are no mansion houses in an urban area.
All skyscrapers are in urban areas.
Every creepy haunted house is a mansion house.
Every terrifying building on Halloween is a creepy haunted house.
The LaLaurie House is a creepy haunted house or a terrifying building on Halloween.

∀x (InUrbanArea(x) → ¬MansionHouse(x))
∀x (Skyscraper(x) → InUrbanArea(x))
∀x (CreepyHauntedHouse(x) → MansionHouse(x))
∀x (TerrifyingBuilding(x) ∧ OnHalloween(x) → CreepyHauntedHouse(x))
CreepyHauntedHouse(laLaurieHouse) ∨ TerrifyingBuilding(laLaurieHouse) ∧ OnHalloween(laLaurieHouse)


The LaLaurie House is a terrifying building on Halloween.


The LaLaurie House is either a skyscraper or a mansion house.


The LaLaurie House is either a skyscraper or in an urban area.


The LaLaurie House is either a skyscraper or a creepy haunted house.


If the LaLaurie House is not a mansion or not in an urban area, then it is either a skyscraper or in an urban area.

¬(MansionHouse(laLaurieHouse) ∧ InUrbanArea(laLaurieHouse)) → (Skyscraper(laLaurieHouse) ⊕ InUrbanArea(laLaurieHouse))


If the LaLaurie House is either a skyscraper or a mansion house, then it is in an urban area.

Skyscraper(laLaurieHouse) ⊕ MansionHouse(laLaurieHouse) → InUrbanArea(laLaurieHouse)


If the LaLaurie House is either a skyscraper or a mansion house, then it is neither a creepy haunted house nor a terrifying building on Halloween.

Skyscraper(laLaurieHouse) ⊕ MansionHouse(laLaurieHouse) → ¬(CreepyHauntedHouse(laLaurieHouse) ∨ TerrifyingBuilding(laLaurieHouse) ∧ OnHalloween(laLaurieHouse))


If the LaLaurie House is either a skyscraper or a creepy haunted house, then it is not a mansion house.

Skyscraper(laLaurieHouse) ⊕ CreepyHauntedHouse(laLaurieHouse) → ¬MansionHouse(laLaurieHouse)


Phuoc Binh national park is a national park in Vietnam.
Any national park in Vietnam is classified as a nature reserve.
There is a national park in Vietnam classified as a UNESCO World Heritage Site.
All national parks in Vietnam are either managed by the Ministry of Agriculture or managed by the People's Committee.
Phuoc Binh is not managed by the Ministry of Agriculture.

NationalPark(phuocBinh) ∧ Locatedin(phuocBinh, vietnam)
∀x ((NationalPark(x) ∧ Locatedin(x, vietnam)) → NatureReserve(x))
∃x (NationalPark(x) ∧ Locatedin(x, vietnam) ∧ UNESCOWorldHeritageSite(x))
∀x ((NationalPark(x) ∧ Locatedin(x, vietnam)) → (Mangedby(x, ministryofAgriculture) ⊕ Managedby(x, peoplesCommittee)))
¬Mangedby(phuocBinh, ministryofAgriculture)

∃x (NatureReserve(x) ∧ LocatedIn(x, vietnam))


Phuoc Binh is managed by the People's Committee.


Greyhound racing is a competitive sport where spectators bet on greyhounds.
Greyhound racing involves coursing.
Some competitive sports where spectators bet on things are banned.
Coursing involves spectators betting on a hare being pursued by greyhounds.
Spectators betting on a hare is a small game.
If a competitive sport involves spectators betting on small games, then it is banned.

∀x (GreyhoundRacing(x) → ∃y (CompetitiveSport(x) ∧ Greyhound(y) ∧ BetOn(spectators, y, x)))
∀x (GreyhoundRacing(x) → Coursing(x))
∃x ∃y (CompetitiveSport(x) ∧ BetOn(spectators, y, x) ∧ Banned(x))
∀x ∃y ∃z (Coursing(x) → Hare(y) ∧ BetOn(spectators, y, x) ∧ GreyHound(z) ∧ PursuedBy(y, z))
∃x ∀y (Hare(x) ∧ BetOn(spectators, x, y) → SmallGame(y))
∀x ∃y (CompetitiveSport(x) ∧ SmallGame(y) ∧ BetOn(spectators, y, x) → Banned(x))


Greyhound racing is a competitive sport.

∀x (GreyhoundRacing(x) → CompetitiveSport(x))


If a soccer player receives two yellow cards in one game, this player will be ejected from the rest of the game.
If a soccer player receives one red card in one game, this player will be ejected from the rest of the game.
Henry is a soccer player.
In one game, Henry receives one yellow card and one red card.

∀x (SoccerPlayer(x) ∧ Receive(x, twoYellowCard) → EjectFromRestOfGame(x))
∀x (SoccerPlayer(x) ∧ Receive(x, oneRedCard)) → EjectFromRestOfGame(x))
SoccerPlayer(henry)
Receive(henry, oneYellowCard) ∧ Receive(x, oneRedCard)

Henry will be ejected from the rest of the game.


Henry will not be ejected from the rest of the game.


Trees are plants.
Some living things are trees.

∀x (Tree(x) → Plant(x))
∃x ∃y (Living(x) ∧ Living(y) ∧ Tree(x) ∧ Tree(y) ∧ ¬(x=y))

∃x ∃y (Living(x) ∧ Living(y) ∧ Plant(x) ∧ Plant(y) ∧ ¬(x=y))


Notable people with the given name include Dagfinn Aarskog, Dagfinn Bakke and Dagfinn Dahl.
Dagfinn Aarskog is a Norwegian physician.
Dagfinn Dahl is a Norwegian barrister.

GivenName(nameDagfinn) ∧ Named(dagfinnAarskog, nameDagfinn) ∧ NotablePerson(dagfinnAarskog) ∧ Named(dagfinnBakke, nameDagfinn) ∧ NotablePerson(dagfinnBakke)  ∧ Named(dagfinnDahl, nameDagfinn) ∧ NotablePerson(dagfinnDahl)
Norwegian(dagfinnAarskog) ∧ Physician(dagfinnAarskog)
Norwegian(dagfinnDahl) ∧ Barrister(dagfinnDahl)


Dagfinn is Dagfinn Aarskog's given name.


If a movie is popular, some people enjoy watching it.
All things that some people enjoy attract attention.

∀x (Movie(x) ∧ Popular(x) → ∃y ∃z (Person(y) ∧ EnjoyWatching(y, x) ∧ Person(z) ∧ EnjoyWatching(z, x) ∧ ¬(y=z)))
∀x (∃y ∃z (Person(y) ∧ EnjoyWatching(y, x) ∧ Person(z) ∧ EnjoyWatching(z, x)) → Attract(x, attention))

If a movie is popular, then it attracts attention.

∀x (Movie(x) ∧ Popular(x) → Attract(x, attention))


It is not true that some giant language models do not have good performance.
All language models with good performance are used by some researchers.
If a language model is used by some researchers, it is popular.
If BERT is a giant language model, then GPT-3 is also a giant language model.
BERT is a giant language model.

¬(∃x (LanguageModel(x) ∧ Giant(x) ∧ ¬GoodPerformance(x)))
∀x ∃y ∃z (LanguageModel(x) ∧ GoodPerformance(x) → ¬(x=y) ∧ Researcher(y) ∧ UsedBy(x, y) ∧ Researcher(z) ∧ UsedBy(x, z))
∀x ∃y ∃z (LanguageModel(x) ∧ ¬(x=y) ∧ Researcher(y) ∧ UsedBy(x, y) ∧ Researcher(z) ∧ UsedBy(x, z) → Popular(x))
(LanguageModel(bert) ∧ Giant(bert)) → (LanguageModel(gpt-3) ∧ Giant(gpt-3)).
LanguageModel(bert) ∧ Giant(bert)


St Johnstone is a Scottish team.
St Johnstone is part of the Scottish Premiership league.
If a team is part of the league, it has joined the league.
St Johnstone and Minsk are different teams.
For two teams, either one team wins, or the other team wins.
Minsk won against St Johnstone.

Scottish(stJohnstone) ∧ Team(stJohnstone)
PartOf(stJohnstone, scottishPremiership) ∧ League(scottishPremiership)
∀x ∀y (Team(x) ∧ League(y) ∧ PartOf(x, y) → Joined(x, y))
¬(misnk=stJohnstone)
∀x ∀y (¬(x=y) → WonAgainst(x, y) ⊕ WonAgainst(y, x))
WonAgainst(minsk, stJohnstone)

At least one Scottish team has joined the Scottish Premiership.

∃x (Scottish(x) ∧ Joined(x, scottishPremiership))


No Boeing-737 plane has more than 300 seats.
All of the planes acquired by Delta in this batch are Boeing-737.
Planes either have more than 300 seats or have a capacity of 100 passengers.
All planes with a capacity of 100 passengers are scheduled for a short-distance flight.
All planes with a capacity of 100 passengers are produced before 2010.
Jake32 is either a Boeing-737 plane or a plane acquired by Delta in this batch.
T10 is either both a Boeing-737 plane and acquired by Delta in this batch, or it is neither.

∀x (Plane(x) ∧ Boeing737(x) → (¬∃y(GreaterThan(y, num300) ∧ EquippedWithSeats(x,y)))
∀x (Plane(x) ∧ AcquiredBy(x, delta) → Boeing737(x))
∀x (Plane(x) → ((∃y(GreaterThan(y, num300) ∧ EquippedWithSeats(x,y))) ⊕ (∃y(Equals(y, num100) ∧ EquippedWithSeats(x,y))))
∀x (Plane(x) ∧ ∃y(Equals(y, num100) ∧ EquippedWithSeats(x,y)) → ScheduledFor(x, shortdistanceflight))
∀x (Plane(x) ∧ ∃y(Equals(y, num100) ∧ EquippedWithSeats(x,y)) → ∃z(Before(z, yr2010) ∧ Produced(x, z))
(Boeing737(jake32) ∧ Plane(jake32)) ⊕ (AcquiredByDeltaInThisBatch(jake32) ∧ Plane(jake32))
¬((Boeing737(t10) ∧ Plane(t10)) ⊕ (AcquiredByDeltaInThisBatch(t10) ∧ Plane(t10)))

Jake32 was produced before 2010 and is scheduled for a short-distance flight.

∃z(Before(z, year2010) ∧ Produced(jake32, z)) ∧ ScheduledFor(jake32, shortdistanceflight))


Jake32 is not produced before 2010 and is not scheduled for a short-distance flight.

¬(∃z(Before(z, year2010) ∧ Produced(jake32, z)) ∧ ScheduledFor(jake32, shortdistanceflight)))


Jake32 is produced before 2010 or scheduled for a short-distance flight.

∃z(Before(z, year2010) ∧ Produced(jake32, z)) ∨ ScheduledFor(jake32, shortdistanceflight))


Jake32 is neither produced before 2010 nor scheduled for a short-distance flight.

¬∃z(Before(z, year2010) ∧ Produced(jake32, z)) ∧ ¬ScheduledFor(jake32, shortdistanceflight))


The SAT test is wholly owned and developed by the College Board.
The SAT test is intended to assess students' readiness for college.
The SAT was originally designed not to be aligned with high school curricula.
Several adjustments were made to the version of the SAT introduced in 2016 to align with the high school curriculum.

OwnedBy(sAT, collegeBoard) ∧ DevelopedBy(sAT, collegeBoard) ∧ ¬(∃y (¬(y=collegeBoard) ∧ (OwnedBy(sAT, y) ∨ DevelopedBy(sAT, y)))
IntendedToAssess(sAT, studentsReadinessForCollege)
OriginallyDesignedToBeAlignedWith(sAT, highSchoolCurricula)
AdjustmentMadeIn(sAT, 2016, toAlignWithHighSchoolCurriculum)

The SAT test is owned by the College Board and other third parties.

OwnedBy(sAT, collegeBoard) ∧ OwnedBy(sAT, otherThirdParties)


The SAT test assesses students' math skills.


Rafa Nadal was born in Mallorca.
Rafa Nadal is a professional tennis player.
Nadal's win ratio is high.
All players in the Big 3 are professionals who have a high win ratio.

BornIn(rafaNadal, mallorca)
ProfessionalTennisPlayer(rafaNadal)
HighWinRatio(rafaNadal)
∀x ((ProfessionalTennisPlayer(x) ∧ HighWinRatio(x)) → InBig3(x))


Nadal is the greatest player of all time.


No sandwich cookies are healthy.
Oreos are sandwich cookies.

∀x (SandwichCookie(x) → ¬Healthy(x))
∀x (Oreo(x) → SandwichCookie(x))


No animals are plants.
All humans are animals.
All pupils are humans.
All flowers are plants.
Bailey is either both a human and a flower or neither a human nor a flower.

∀x (Animal(x) → ¬Plant(x))
∀x (Human(x) → Animal(x))
∀x (Pupil(x) → Human(x))
∀x (Flower(x) → Plant(x))
¬(Human(bailey) ⊕ Flower(bailey))


If Bailey is a human, then Bailey is not a pupil.


Shoes are not food.
All slippers are shoes.
Any object donated to the homeless charity is either clothes or food.
Wearable things are not edible.
All clothes are wearable.
The watch is donated to the homeless charify.
If the watch is not both edible and a piece of clothing, then the watch is either both edible and a piece of clothing or the watch is neither of them.

∀x (Shoe(x) → ¬Food(x))
∀x (Slipper(x) → Shoe(x))
∀x (DonatedTo(x, homelessCharity) → Food(x) ⊕ Clothes(x))
∀x (Wearable(x) → ¬Edible(x))
∀x (Clothes(x) → Wearable(x))
DonatedTo(watch, homelessCharify)
¬(Edible(watch) ∧ Clothes(watch)) → ¬(Edible(watch) ⊕ Clothes(watch))


A watch is neither edible nor a slipper.


An Olympian is a person who trains for an Olympic sport and goes to the Olympics.
Carlos Reyes trains for an Olympic sport.
Carlos Reyes went to the Olympics.
Carlos Reyes is a welterweight.
Heavy weights are not welterweights.

∀x ((DoesOlympicSport(x) ∧ GoesToOlympicGames(x)) → Olympian(x))
DoesOlympicSport(carlosReyes)
GoesToOlympicGames(carlosReyes)
WelterWeight(carlosReyes)
∀x (WelterWeight(x) → ¬ HeavyWeight(x))


If people have a lot of music decorations in their rooms, they cannot pack and move out of their rooms very easily.
If people have high ambitions and future career goals, then they can pack and move out of their rooms very easily.
If people are big fans of pop bands and singers, then they have a lot of music decorations in their room.
All young teenage girls who attend music festival frequently are big fans of pop bands and singers.
If Sam has high ambitions and future career goals, then Sam is a big fan of pop bands and singers.

∀x (HaveIn(x, aLotOfMusicDecoration, room) → ¬MoveOutEasily(x))
∀x (Ambitious(x) → MoveOutEasily(x))
∀x (BigFanOfMusic(x) → MusicDecorations(x, room))
∀x (AttendFrequently(x, musicFestival) ∧ YoungTeenageGirl(x) → BigFanOfPopBand(x) ∧ BigFanOfPopSinger(x))
Ambitious(sam) → BBigFanOfPopBand(sam) ∧ BigFanOfPopSinger(sam)

Sam is a young teenage girl who attends music festival frequently

Attend(sam, festival) ∧ YoungTeenageGirl(sam)


Sam is not a young teenage girl who attends music festival frequently

¬(Attend(sam, festival) ∧ YoungTeenageGirl(sam))


Sam is a big fan of pop bands and singers.


Sam neither has high ambitions and future career goals nor is she a young teenage girl attending music festival frequently

¬(Ambitious(sam) ∨ (Attend(sam, festival) ∧ YoungTeenageGirl(sam)))


Sam has high ambitions and future career goals and is a young teenage girl attending music festival frequently.

Ambitious(sam) ∧ Attend(sam, festival) ∧ YoungTeenageGirl(sam)


Sam has high ambitions and future career goals and is a young teenage girl attending college.


If Sam is a young teenage girl attending college, then Sam either does not have high ambitions and future career goals or is a big fan of pop bands and singers.

Attend(sam, festival) ∧ YoungTeenageGirl(sam) → ¬(Ambitious(sam) ∨ (BigFanOfPopBand(sam) ∧ BigFanOfPopSinger(sam)))


If Sam has high ambitions and future career goals and is a young teenage girl attending college, then Sam either does not have high ambitions and future career goals or is not a young teenage girl attending college.

Ambitious(sam) ∧ Attend(sam, festival) ∧ YoungTeenageGirl(sam) → ¬(Ambitious(sam) ∨ (Attend(sam, festival) ∧ YoungTeenageGirl(sam)))


If Sam has high ambitions and future career goals, then Sam is a young teenage girl attending college.

Ambitious(sam) → Attend(sam, festival) ∧ YoungTeenageGirl(sam)


Brita was a cargo ship built for Norwegians.
Brita was impressed into service by Germany.
Ships that have been impressed into service were seized by whoever impressed them into service.
The Britta was sold to Hong Kong.

CargoShip(britta) ∧ Ship(britta) ∧ BuiltFor(britta, norwegians)
ImpressedIntoServiceBy(britta, germany)
∀x ∀y (Ship(x) ∧ ImpressedIntoServiceBy(x, y) → SeizedBy(x, y))
SoldTo(britta, hongkong)

There was a cargo ship seized by Germany that was sold to Hong Kong.

∃x (CargoShip(x) ∧ SeizedBy(x, germany) ∧ SoldTo(x, hongkong))


Hong Kong hasn't had any seized ships sold to them.

∀x ∀y (SoldTo(x, hongkong) → ¬SeizedBy(x, y))


Quincy McDuffie is an American professional wide receiver in Canadian Football.
People who can catch balls are good wide receivers.
Quincy McDuffie can catch some footballs easily.
Good wide receivers play professionally.
Good wide receivers can catch with both their left and right hand.
All footballs are balls.

American(quincyMcduffie) ∧ Professional(quincyMcduffie) ∧ WideReciever(quincyMcduffie) ∧ PlaysIn(quincyMcduffie, cFL)
∀x ((∃y(CanCatch(x, y) ∧ Ball(y))) → GoodWideReceiver(x))
∃x ∃y (Football(x) ∧ CanCatch(quincymcduffie, x)) ∧ (¬(x=y) ∧ (Football(y) ∧ CanCatch(quincymcduffie, y))
∀x (GoodWideReceiver(x) → Professional(x))
∀x (GoodWideReceiver(x) → (CanCatchWith(x, lefthand) ∧ CanCatchWith(x, righthand)))
∀x (Football(x) → Ball(x))

Quincy McDuffie is a good wide receiver.


∀x (Ball(x) → CanCatch(quincymcduffie, x))


Professional wide receivers are good at catching balls.

∀x ((Professional(x) ∧ WideReciever(x)) → Good(x, catchingballs))


Boves is a railway station located in France.
The preceding station of Boves is Longueau.
The preceding station of Dommartin is Boves.
France is a European country.
Dommartin is situated on the Paris–Lille railway.
Any two contiguous stations are on the same railway.
Boves is served by regional TER Hauts-de-France trains.
If place A is located in place B and place B is located in place C, then place A is located in place C.
If place A precedes place B and place B precedes place C, then place A precedes place C.

RailwayStation(boves) ∧ In(boves, france)
Precede(longueau, boves)
Precede(boves, dommartin)
In(france, europe)
SituatedOn(dommartin, pairsLille)
∀x ∀y ∀z ((SituatedOn(x, z) ∧ (Precede(x, y) ∨ Precede(y, x)) → SituatedOn(y, z))
Serve(boves, hautsDeFrance)
∀x ∀y ∀z ((In(x, y) ∧ In(y, z)) → In(x, z))
∀x ∀y ∀z ((Precede(x, y) ∧ Precede(y, z)) → Precede(x, z))

Longueau is situated on the Paris–Lille railway.


Longueau is served by regional TER Hauts-de-France trains.


Edwin Smith was a New Zealand rower from Auckland.
Edwin Smith was also known as Ted Smith.
Edwin Smith went to Rose Road Primary School, located in Grey Lynn.
Edwin Smith was a sergeant who served with the New Zealand 24th battalion in Italy and Egypt.
Broadway Sheetmetals was a business run and owned by Edwin Smith, a sheet metal worker.

From(edwinSmith, newZealand) ∧ Rower(edwinSmith) ∧ From(edwinSmith, auckland)
edwinSmith=tedSmith
GoTo(edwinSmith, roseRoadPrimarySchool) ∧ LocatedIn(roseRoadPrimarySchool, greyLynn)
Sergeant(edwinSmith) ∧ ServeWith(edwinSmith, newZealand24thBattalion) ∧ ServeIn(edwinSmith, italy) ∧ ServeIn(edwinSmith, egypt)
Buisness(broadwaySheetmetals) ∧ Run(edwinSmith, broadwaySheetmetals) ∧ Own(edwinSmith, broadwaySheetmetals) ∧ SheetmetalWorker(edwinsmith)


There were no rowers that own a buisness.

∀x ∀y (Rower(x) ∧ Buisness(y) → ¬Own(x, y))


∀x ∀y (Buisness(x) ∧ Own(y, x) → ¬ServeIn(y, egypt))


A werewolf is a human that can turn into a wolf.
A werewolf has been scratched or bitten by another werewolf.
If someone has been scratched or bitten by some entity, they have been attacked by that entity.

∀x (Human(x) ∧ CanTurnInto(x, wolf) → Werewolf(x))
∀x ∃y (Werewolf(x) → (BittenBy(x, y) ∨ ScratchedBy(x, y)) ∧ Werewolf(y))
∀x ∃y (BittenBy(x, y) ∨ ScratchedBy(x, y)) → AttackedBy(x,y)


A werewolf has scratched someone before.


UFC Fight Night was a mixed martial arts event held in Sweden.
At UFC Fight Night, Sadollah was scheduled to fight Musoke.
Sadollah fought Akiyama at UFC Fight Night.
Musoke fought Yakovlev at UFC Fight Night.
Jung was injured at UFC Fight Night.
People injured at UFC Fight Night did not fight.

Event(uFCFightNight) ∧ MixedMartial(uFCFightNight) ∧ HeldIn(uFCFightNight, sweden)
ScheduledToFight(sadollah, musoke,uFCFightNight)
Fight(sadollah, akiyama, uFCFightNight)
Fight(musoke, yakovlev, uFCFightNight)
InjuredAt(jung, uFCFightNight)
∀x (InjuredAt(x, uFCFightNight) → ¬FightIn(x, uFCFightNight))


Event(uFCFightNight) ∧ ¬FightIn(jung, uFCFightNight)


Sadollah fought Musoke at UFC Fight Night.


All drinks on the counter are edible.
All juices on the counter are drinks.
Orange juice is a type of juice.
Everything on the counter is either orange juice or apple juice.
All apple juices on the counter are sweet.
The coke is on the counter and if the coke is apple juice, then the coke is a drink.
If the coke is not apple juice, then the coke is not edible.

∀x (OnCounter(x) ∧ Drink(x) → Edible(x))
∀x (OnCounter(x) ∧ Juice(x) → Drink(x))
∀x (OrangeJuice(x) → Juice(x))
∀x (OnCounter(x) → OrangeJuice(x) ⊕ AppleJuice(x))
∀x (OnCounter(x) ∧ AppleJuice(x) → Sweet(x))
OnCounter(coke) ∧ (AppleJuice(coke) → Drink(coke))
¬AppleJuice(coke) → ¬Edible(coke)


Federico Garcia Lorca was a talented Spanish poet, and he supported the Popular Front.
The Spanish Nationalists opposed anyone who supported the Popular Front
Talented poets are popular.
Spanish Nationalists killed anyone who they opposed and who was popular.
Daniel supported the Popular Front but was not popular.

TalentedPoet(lorca) ∧ Support(lorca, populists)
∀x (Support(x, populists) → Opposed(nationalists, x))
∀x (TalentedPoet(x) → Popular(x))
∀x ((Opposed(nationalists, x) ∧ Popular(x)) → Killed(nationalists, x))
Support(daniel, populists) ∧ (¬Popular(daniel))


People in Franny's family drink kombucha every day or drink Coca-Cola or a Pepsi product.
If people in Franny's family drink Coca-Cola or a Pepsi product every day, then they grew up with extremely busy parents who did not have time to pack them lunch.
If people in Franny's family drink Coca-Cola or another Pepsi product every day, then they have to visit the dentist frequently.
If people in Franny's family grew up with extremely busy parents who did not have time to pack them lunch, then they have erratic and diverse eating habits.
If people in Franny's family have erratic and diverse eating habits, then they do not have consistent everyday routines and like sticking to a solid schedule.
Damon is in Franny's family.
Damon either both grow up with extremely busy parents who did not have time to pack her lunch and have consistent everyday routines and like sticking to a solid schedule, or Damon did neither.

∀x (In(x, frannysFamily) ∧ (Drink(x, kombucha) ∨ (∃y (Drink(x, cocaCola) ∨ (PepsiProduct(y) ∧ Drink(x, y))))))
∀x (In(x, frannysFamily) ∧ (∃y (Drink(x, cocaCola) ∨ (PepsiProduct(y) ∧ Drink(x, y)))) → (∃y ∃z (¬(y=z) ∧ BusyParent(y) ∧ BusyParent(z) ∧ ¬Pack(y, lunch) ∧ ¬Pack(z, lunch) ∧ GrowUpWith(x, y) ∧ GrowUpWith(x, z))))
∀x (In(x, frannysFamily)) ∧ (∃y (Drink(x, cocaCola) ∨ (PepsiProduct(y) ∧ Drink(x, y)))) → HaveToVisitFrequently(x, dentist))
∀x (In(x, frannysFamily) ∧ (∃y ∃z (¬(y=z) ∧ BusyParent(y) ∧ BusyParent(z) ∧ ¬Pack(y, lunch) ∧ ¬Pack(z, lunch) ∧ GrowUpWith(x, y) ∧ GrowUpWith(x, z))) → ∃y (Have(x, y) ∧ Erratic(y) ∧ Diverse(y) ∧ EatingHabit(y)))
∀x (In(x, frannysFamily) ∧ ∃y (Have(x, y) ∧ Erratic(y) ∧ Diverse(y) ∧ EatingHabit(y))) → ¬(ConsistentEverydayRoutine(x) ∧ StickTo(damon, solidSchedule)))
In(damon, frannysFamily)
¬((∃y ∃z(¬(y=z) ∧ BusyParent(y) ∧ BusyParent(z) ∧ ¬Pack(y, lunch) ∧ ¬Pack(z, lunch) ∧ GrowUpWith(damon, y) ∧ GrowUpWith(damon, z))) ⊕ (ConsistentEverydayRoutine(damon) ∧ StickTo(damon, solidSchedule)))

Damon is in Franny's family and he has to visit the dentist frequently.


If Damon is in Franny's family and he either both grew up with extremely busy parents who did not have time to pack his lunch and drink kombucha every day or neither grew up with extremely busy parents who did not have time to pack his lunch nor drink kombucha every day, then Damon neither visits the dentist frequently nor drinks Coca Cola or Pepsi products.

¬((¬(y=z) ∧ ∃y ∃z (BusyParent(y) ∧ BusyParent(z) ∧ ¬Pack(y, lunch) ∧ ¬Pack(z, lunch) ∧ GrowUpWith(damon, y) ∧ GrowUpWith(damon, z))) ⊕ Drink(damon, kombucha)) → ¬(HaveToVisitFrequently(damon, dentist) ∨ (∃y (Have(damon, y) ∧ Erratic(y) ∧ Diverse(y) ∧ EatingHabit(y))))


If Damon is in Franny's family and he either visits the dentist frequently or drinks kombucha, then Damon both visits the dentist frequently and drinks Coca-Cola or Pepsi products every day.

HaveToVisitFrequently(damon, dentist) ∨ Drink(damon, kombucha, everyDay) → HaveToVisitFrequently(damon, dentist) ∧ (∃y (Drink(x, cocaCola) ∨ (PepsiProduct(y) ∧ Drink(x, y))))


If a customer subscribes to AMC A-List, then he/she can watch 3 movies every week without any additional fees.
Some customers go to cinemas every week.
Customers who prefer TV series will not watch TV series in cinemas.
James watches TV series in cinemas.
James subscribes to AMC A-List.
Peter prefers TV series.

∀x (SubscribedTo(x, aMCAList) → EligibleForThreeFreeMovies(x))
∃x (CinemaEveryWeek(x))
∀x (Prefer(x, tVSeries) → ¬WatchTVIn(x, cinemas))
WatchTVIn(james, cinemas)
SubscribedTo(james, aMCAList)
Prefer(peter, tVSeries)

James cannot watch 3 movies every week without any additional fees.


Peter will not watch TV series in cinemas.


Bulbophyllum attenuatum is in the genus Bulbophyllum.
All Bulbophyllum are orchids.

GenusBulbophyllum(bulbophyllumAttenuatum)
∀x (GenusBulbophyllum(x) → Orchid(x))

Bulbophyllum attenuatum is not an orchid.


There are eight federal districts of Russia: Central, Northwestern, Southern, North Caucasian, Volga, Ural, Siberian, and Far Eastern.
The Central federal district has the largest population among all federal districts in Russia.
Moscow is the administrative center of the Central federal district.
Yekaterinburg is the administrative center of the Ural federal district.
Vladivostok is the administrative center of the Far Eastern federal district.
The Far Eastern federal district has the largest area among all federal districts in Russia.
Some federal districts in Russia were established in 2000.

FederalDistrictOf(central, russia) ∧ FederalDistrictOf(northwestern, russia) ∧ FederalDistrictOf(southern, russia) ∧ FederalDistrictOf(northcaucasian, russia) ∧ FederalDistrictOf(volga, russia) ∧ FederalDistrictOf(ural, russia) ∧ FederalDistrictOf(siberian, russia) ∧ FederalDistrictOf(fareastern, russia)
LargestPopulation(central)
AdministrativeCenterOf(moscow, central)
AdministrativeCenterOf(yekaterinburg, ural)
AdministrativeCenterOf(vladivostok, farEastern)
LargestArea(farEastern)
∃x (FederalDistrictOf(x, russia) ∧ EstablishedIn(x, 2000))

Vladivostok is the administrative center of the federal district with the largest area.

∃x (AdministrativeCenterOf(vladivostok, x) ∧ LargestArea(x))


Moscow is the administrative center of the federal district with the largest population.

∃x (AdministrativeCenterOf(moscow, x) ∧ LargestPopulationIn(x))


The Northwestern federal district was established in 2000.


All cancers have mutations.
No mutations can be treated at home.
All colorectal cancers are cancers.
A cold can be treated at home.
Arthritis either is a cold and has mutations or neither is a cold nor has mutations.

∀x (Cancer(x) → Have(x, mutation))
∀x (Have(x, mutation) → ¬CanBeTreatedAtHome(x))
∀x (ColorectalCancer(x) → Cancer(x))
∀x (Cold(x) → CanBeTreatedAtHome(x))
¬(Cold(arthritis) ⊕ Have(arthritis, mutation))


Arthritis is colorectal cancer or has mutations.

ColorectalCancer(arthritis) ∨ Have(arthritis, mutation)


Arthritis is colorectal cancer and a cancer.


If arthritis is not colorectal cancer, then arthritis has mutations.

¬ColorectalCancer(arthritis) → Have(arthritis, mutation)


Jerry should not worry about things outside of his control.
All traffic is outside of my control.

∀x (OutsideOfControl(x) → ¬ShouldWorry(jerry, x))
∀x (Traffic(x) → OutsideControl(x))


Roversi is an Italian surname.
Alba Roversi uses Roversi as a surname.
Paolo Roversi uses Roversi as a surname.
Roberto Roversi uses Roversi as a surname.
Paolo Roversi is a photographer.
A photographer is a professional or an amateur.

ItalianName(roversi) ∧ Surname(roversi)
UseAsSurname(albaRoversi, roversi)
UseAsSurname(paoloRoversi, roversi)
UseAsSurname(robertoRoversi, roversi)
Photographer(paoloRoversi)
∀x (Photographer(x) → Professional(x) ⊕ Amateur(x))

∃x (ItalianName(x) ∧ Surname(x) ∧ UseAsSurname(albaRoversi, x))


There are no photographers using an Italian surname.

¬(∃x ∃y (Photographer(x) ∧ ItalianName(y) ∧ Surname(y) ∧ UseAsSurname(x, y)))


Zaha Hadid is a British-Iraqi architect, artist, and designer.
Zaha Hadid was born on 31 October 1950 in Baghdad, Iraq.
Zaha Hadid was a visiting professor of Architectural Design at the Yale School of Architecture.
Max is an aspiring architecture student and plans to apply to the Yale School of Architecture.

British-Iraqi(zahaHadid) ∧ Architect(zahaHadid) ∧ Artist(zahaHadid) ∧ Designer(zahaHadid)
BornOn(zahaHadid, 31October1950) ∧ BornIn(zahaHadid, baghdadIraq)
VisitingProfessorOf(zahaHadid, architecturalDesign) ∧ VisitingProfessorAt(zahaHadid, yaleSchoolOfArchitecture)
AspiringArchitectureStudent(max) ∧ PlansToApplyTo(max, yaleSchoolofArchitecture)

Zaha Hadid was a citizen of Britain and Iraq.


Zaha Hadid did some work in interior design.


Zaha Hadid was born on the 31st of October in 1982.


A neuroimaging technique is either an invasive neuroimaging technique or a noninvasive neuroimaging technique.
All noninvasive neuroimaging techniques provide a spatial resolution of brains.
If a technique provides a spatial resolution of brains, then it is a measurement of brain activity.
All measurements of brain activity are used by neuroscience researchers.
FMRI is either a measurement of brain activity or a noninvasive neuroimaging technique.
FMRI is a neuroimaging technique.

∀x (NeuroimagingTechnique(x) → (Invasive(x) ⊕ Noninvasive(x)))
∀x (Noninvasive(x) → Provides(x, spatialResolutionOfBrains))
∀x (Provides(x, spatialResolutionOfBrains) → Measure(x, brainActivity))
∀x (Measure(x, brainActivity) → UsedBy(x, neuroscienceResearchers))
Measure(fMRI, brainActivity) ⊕ Noninvasive(fMRI)
NeuroimagingTechnique(fMRI)

FMRI provides a spatial resolution of brains.


FMRI is an invasive neuroimaging technique and is used by neuroscience researchers.

Invasive(fMRI) ∧ UsedBy(fMRI, neuroscienceResearchers)


FMRI is either an invasive neuroimaging technique or is used by neuroscience researchers.

Invasive(fMRI) ⊕ UsedBy(fMRI, neuroscienceResearchers)


If fMRI is not an invasive neuroimaging technique used by neuroscience researchers, then fMRI is neither a noninvasive neuroimaging technique nor provides a spatial resolution of brains.

¬(Invasive(fMRI) ∧ UsedBy(fMRI, neuroscienceResearchers)) → ¬(Noninvasive(fMRI) ∨ Provides(fMRI, spatialResolutionOfBrains))


Researchers present their work at the conference or provide a tutorial session there.
Everyone who presents their work at the conference will attend in person.
Everyone providing a tutorial session at the conference will be invited to join the club.
Everyone who attends the conference in person is provided with souvenirs.
Everyone invited to join the club is provided with delicious meals.
Everyone provided with delicious meals is happy to communicate with each other during the dinner.
Everyone who is provided with delicious meals is invited to take a photo with the audience.
It is not true that James both attended the conference in person and was provided with souvenirs.

∀x (PresentWorkAt(x, conference) ⊕ ProvideAt(x, tutorialSession, conference))
∀x (PresentWorkAt(x, conference) → AttendInPerson(x, conference))
∀x (ProvideSessionAt(x, tutorial, conference) → InvitedToJoin(x, club))
∀x (AttendInPerson(x, conference) → ProvidedWith(x, souvenir))
∀x (InvitedToJoin(x, club) → ProvidedWith(x, deliciousMeal))
∀x (ProvidedWith(x, deliciousMeal) ∧ ProvidedWith(y, deliciousMeal)  → ∃y ∃z (¬(y=x) ∧ ¬(z=x) ∧ ¬(y=z) ∧ HappyToCommunicateWithDuringTheDinner(x, y) ∧ HappyToCommunicateWithDuringTheDinner(x, z)))
∀x (ProvidedWith(x, deliciousMeal) → InvitedToTakePhotoWith(x, audience))
¬(AttendInPerson(james, conference) ∧ ProvidedWith(x, souvenir))


James is invited to take a photo with the audience and is happy to communicate with other guests at the dinner.

InvitedToTakePhotoWith(james, audience) → ∃y ∃z (¬(y=james) ∧ ¬(z=james) ∧ ¬(y=z) ∧ HappyToCommunicateWithDuringTheDinner(james, y) ∧ HappyToCommunicateWithDuringDinner(james, z)))


James is invited to take a photo with the audience or is happy to communicate with other guests(?) during the dinner.


James is either invited to take a photo with the audience or happy to communicate with other guests(?) during the dinner.


The USS Salem is a heavy cruiser built for the United States Navy.
The last heavy cruiser to enter service was the USS Salem.
The USS Salem is a museum ship.
Museum ships are open to the public.
The USS Salem served in the Atlantic and Mediterranean.

HeavyCruiser(usssalem) ∧ BuiltFor(usssalem, unitedstatesnavy)
LastHeavyCruiserToEnterService(usssalem)
MuseumShip(usssalem)
∀x (MuseumShip(x) → OpenToPublic(x))
ServedIn(usssalem, atlantic) ∧ ServedIn(usssalem, mediterranean)


There is a museum ship open to the public that served in the Mediterranean.

∃x (MuseumShip(x) ∧ OpenToPublic(x) ∧ ServedIn(x, mediterranean))


The USS Salem was not the last heavy cruiser to enter service.


TS Leda was a good passenger and cargo vessel.
TS Leda was a Norwegian vessel that was built with stabilizers.
Stabilizers are mechanical devices found only on ships with powerful steam turbine engines.
To be a good passenger and cargo vessel, ships must be quiet and good at sea.
Some ships that are quiet and good at sea have powerful steam turbine engines.
Vessels are ships.

∀x (TSLeda(x) → ((Passenger(x) ∧ Vessel(x)) ∧ (Cargo(x) ∧ Vessel(x)))
∀x (TSLeda(x) → (Norweigian(x) ∧ Vessel(x) ∧ Stabilizers(x)))
∀x (Stabilizers(x) → MechanicalDevice(x) ∧ OnlyOnShips(x) ∧ PowerfulSteamTurbine(x))
∀x ((Passenger(x) ∧ Vessel(x)) ∧ (Cargo(x) ∧ Vessel(x)) → (Quiet(x) ∧ GoodAt(x, sea)))
∃x (Quiet(x) ∧ GoodAt(x, sea) ∧ PowerfulSteamTurbine(x))
∀x (Ship(x) → Vessel(x))

∀x (TSLeda(x) → Quiet(x) ∧ GoodAt(x, sea))


TS Leda had powerful steam turbine engines.

∀x (TSLeda(x) → PowerfulSteamTurbine(x))


∀x (TSLeda(x) → ¬(Norweigian(x) ∧ Vessel(x)))


Rosa was born in Santiago.
Santiago is the capital and largest city of Chile.
Rosa is the daughter of a Catalan building contractor, Jose.
Jose has a Chilean wife, Carmen.
Carmen and Jose are Rosa's parents.
People from Catalan are not from Chile.
A building contractor is responsible for the day-to-day oversight of a construction site.

BornIn(rosa, santiago)
CapitalOf(santiago, chile) ∧ LargestCityOf(santiago, chile)
DaughterOf(rosa, jose) ∧ BuildingContractor(jose) ∧ Catalan(jose)
WifeOf(jose, carmen) ∧ Chilean(carmen)
ParentOf(jose, rosa) ∧ ParentOf(carmen, rosa)
∀x (Catalan(x) → ¬Chilean(x))
∀x ∃y (BuildingContractor(x) → ConstructionSite(y) ∧ Oversee(x, y))

Rosa was born in the largest city of Chile.

∃x (BornIn(rosa, x) ∧ LargestCityOf(x, chile))


Rosa is the daughter of someone who is responsible for the oversight of traffic.

∃x (DaughterOf(rosa, x) ∧ Oversee(x, traffic))


Tyga is a rapper.
Rappers release rap albums.
Tyga released the Well Done 3 album.
Rappers are not opera singers.

IsRapper(tyga)
∀x ∀y ((IsRapper(x) ∧ ReleasedAlbum(x, y)) → IsRapAlbum(y))
ReleasedAlbum(tyga, wellDone3)
∀x (IsRapper(x) → ¬IsOperaSinger(x))


Deborah Wallace is a Scottish-born actress, playwright, and producer.
Psyche is a play based on the life of James Miranda Barry.
Homesick, Psyche and The Void are plays by Deborah Wallace.
Deborah Wallace co-produced Gasland.

BornIn(deborahWallace, scotland) ∧ Actress(deborahWallace) ∧ Playwright(deborahWallace) ∧ Producer(deborahWallace)
Play(psyche) ∧ BasedOn(psyche, lifeOfJamesMirandaBarry)
Play(homesick) ∧ WrittenBy(homesick, deborahWallace) ∧ Play(psyche) ∧ WrittenBy(psyche, deborahWallace) ∧ Play(theVoid) ∧ WrittenBy(theVoid, deborahWallace)
CoProduce(deborahWallace, gasland)

Gasland was coproduced by the same person Homesick was from.

∃x (CoProduces(x, gasland) ∧ WrittenBy(homesick, x))


No plays by Deborah Wallace are based on the life of James Miranda Barry.

∀x (Play(x) ∧ WrittenBy(x, deborahwallace) → ¬BasedOn(x, lifeofjamesmirandabarry))


Animals who need large territory travel far.
Every animal that eats a lot needs a large territory.
If something is a big animal, then it will eat a lot.
Bears are big animals.
Larry is a big animal.

∀x (Animal(x) ∧ Need(x, largeTerritory) → TravelFar(x))
∀x (EatALot(x) → Need(x, largeTerritory))
∀x (Big(x) ∧ Animal(x) → EatALot(x))
∀x (Bear(x) → Big(x) ∧ Animal(x))
Big(larry) ∧ Animal(larry)


Larry is not a bear and does not travel far.


If Larry either travels far or needs a large territory, then Larry is a bear.

TravelFar(larry) ⊕ Need(larry, largeTerritory) → Bear(larry)


Any convicted criminal that is innocent is not truly guilty.
All convicted criminals who did not commit a crime are truly innocent.
All convicted criminals are truly guilty or found guilty.
If a convicted criminal is found guilty, then they are sentenced to a punishment.
If a convicted criminal is found guilty, then they can argue against their punishment.
Garry is a convicted criminal who not found guilty or is sentenced to punishment.

∀x (ConvictedCriminal(x) ∧ Innocent(x) → ¬TrulyGuilty(x))
∀x (ConvictedCriminal(x) ∧ ¬CommitCrime(x) → Innocent(x))
∀x (ConvictedCriminal(x) ∧ (TrulyGuilty(x) ∨ FoundGuilty(x)))
∀x (ConvictedCriminal(x) ∧ FoundGuilty(x) → SentencedToPunishment(x))
∀x (ConvictedCriminal(x) ∧ FoundGuilty(x) → CanArgueAgainst(x, punishment))
ConvictedCriminal(garry) ∧ (¬(FoundGuilty(garry) ∨ SentencedToPunishment(garry)))


Garry did not commit a crime and can argue against his punishment.

¬CommitCrime(garry) ∧ CanArgueAgainst(garry, punishment)


Garry is not both innocent and someone who did not commit a crime.


Phoneix's music is classified under the indie pop genre.
Phoenix is a band from France.
French bands write songs in French or in English.
Aside from indie pop, pop rock and synth-pop are two other genres of music.
Phoenix has no songs in French.

IndiePop(phoenix)
Band(phoenix) ∧ From(phoenix, france)
∀x ∃y (Band(x) ∧ From(x, france) ∧ Write(x, y) ∧ Song(y) → InFrench(y) ⊕ InEnglish(y))
∀x (IndiePop(x) → ¬PopRock(x) ∧ ¬SynthPop(x))
∀x (Song(x) ∧ By(phoenix, x) → ¬InFrench(x))

Phoneix's music is classified under the pop rock genre.


∃x (Write(phoenix, y) ∧ Song(x) → InFrench(x))