The video game "Be Lionel" is in the pokemon series.

No video games released by Nintendo support the PS4 platform.

All video games in the Pokemon series are released by Nintendo.

All video games in the FIFA series support the PS4 platform.

All video games supporting users to simulate playing soccer games online are in the FIFA series.

The video game named “Be Lionel” is in the Pokemon series or supports users to simulate playing football games online.


The video game named “Be Lionel” is not in the FIFA series or supports the PS4 platform.


The video game named “Be Lionel” is in the FIFA series or supports the PS4 platform.


The video game named “Be Lionel”  is not in the FIFA or Pokemon series.


Bank of America payment cards are international.

No payment cards issued by Russian banks can be used with ApplePay.

All MIR payment cards are issued by Russian banks.

Some international payment cards can be used with ApplePay.

Social payments in Russia can only be transferred to MIR payment cards.

Bank of America payment cards can be used with ApplePay.

∀x (RussianBank(x) → ¬ApplePay(x))
∀x (Mir(x) → RussianBank(x))
∃x (International(x) → ApplePay(x))
∀x (SocialRussia(x) → Mir(x))
ApplePay(boapaymentcards)


Bank of America payment cards are international and can be used to transfer social payments in Russia.


If Bank of America payment cards are international or issued by Russian banks, then they can not be used to transfer social payments in Russia.


The Lumina APV is produced by Chevrolet.

The Astro is a van produced by Chevrolet.

Cars produced by Chevrolet are either cars or vans.

Chevrolet(luminaAPV)
Chevrolet(astro) ∧ Van(astro)
∀x (Chevrolet(x) → Car(x) ⊕ Van(x))


The Lumina APV is either a car or a van.


Everyone who works in person is a commuter.

People either work in person or work from home.

Everyone who works from home has a relaxed schedule.

George is either a commuter or has a home office setup.

If George is either a person who works from home or has a home office setup, then George is not a person who works from home and a commuter.

FromHome(george) ⊕ HomeOffice(george) → ¬(FromHome(george) ∧ Commuter(george))


If George is not a person who works from home and a person who works in person, then George is neither a commuter nor a person who has a relaxed schedule.


If George is either a person who has a home office setup and a person who works in person, or neither a person who has a home office setup nor a person who works in person, then George is either a person who works from home or a person who has a relaxed schedule.


Jason Kramer is an American music supervisor.

Some American radio personalities are also music supervisors.

Anyone who hosts a show on a public radio station is a radio personality.

Jason Kramer hosted a show on a public radio station.

∃x (American(x) ∧ MusicSupervisor(x) ∧ RadioPersonality(x))

∀x (HostShowOnPublicRadioStation(x) → RadioPersonality(x))


No coffee sold in Walmart is produced in France.

All coffee supplied by the company is sold in Walmart.

All coffee produced in Columbia is produced in France.

All coffee favored by local residents is coffee produced in Columbia.

All coffee with high prices is favored by local residents.

Civet Coffee is not produced in Columbia and is cheap.

Jamaica Blue is sold in Walmart or favored by local residents.


Jamaica Blue is expensive and supplied by the company.


Jamaica Blue is not expensive and is not supplied by the company.


There are two places named Galicia: either in Spain or in Poland.

∀x (Galicia(x) → Spain(x) ⊕ Poland(x))
∀x (Spain(x) → Europe(x))
∀x (Poland(x) → Europe(x))
∀x (RochelleLive(x) → Europe(x))
∀x (DominiqueLive(x) → ¬Europe(x))
∀x (AlfonsoLive(x) → Galicia(x))


Ralph Hammerthaler is a writer born in Asia.

Ralph Hammerthaler was born in Wasserburg am Inn.


2001 is a book that has won a Hugo Award.

All books written by Tomas have sold more than 1 million copies.

Some books that have won Hugo Awards are written by Tomas.

All books about the future are inspired by Shakespeare.

2001 is a book either inspired from Shakespeare or it has sold more than 1 million copies.

2001 is a book that has either sold more than 1 million copies or it was written by Tomas.

∀x (WrittenByTomas(x) → SoldOneMillion(x))

∃x (WinningHugoAward(x) ∧ WrittenByTomas(x))

∀x (AboutFuture(x) → InspiredFromShakespeare(x))


2001 is a book that has won a Hugo Award and is about the future.


If 2001 either has won a Hugo Award and is about the future, or neither has won a Hugo Award nor is about the future, then 2001 has neither won a Hugo Award nor is written by Tomas.


No grass is food.
All meadows are grass.
All edible things are food.
All fruits are edible.
All lemons are fruit.
Grapes are not edible and lemons.
Bananas are grass or fruit.

∀x (Grass(x) → ¬Food(x))
∀x (Meadow(x) → Grass(x))
∀x (Edible(x) → Food(x))
∀x (Fruit(x) → Edible(x))
∀x (Lemon(x) → Fruit(x))
¬(Edible(grape) ∧ Lemon(grape))
Grass(banana) ∨ Fruit(banana)


Bananas are not both a lemon and a meadow.


The Boston Celtics is from San Francisco.

The Golden State Warriors are a team from San Francisco.

The Golden State Warriors won the NBA finals.

All teams attending the NBA finals have more than thirty years of history.

Boston Celtics are a team that lost the NBA finals.

If a team wins the NBA finals, then they will have more income.

If a team wins or loses at the NBA finals, then they are attending the finals.

Team(goldenstatewarriors) ∧ From(goldenstatewarriors, sanfrancisco)

∀x (team(x) ∧ Attending(x, nbafinals) → HasMoreThan(x, thirtyyearsofhistory))

Team(bostonceltics) ∧ Lost(bostonceltics, nbafinals)

∀x (Team(x) ∧ Won(x, nbafinals) → MoreIncome(x))

∀x (Won(x, nbafinals) ∨ Lost(x, nbafinals) → Attending(x, nbafinals))


The Boston Celtics has more than 30 years of experience.


The Golden State Warriors will have more income for gate receipts.


Maya will play violin if and only if she never injures her fingers.

Volleyball players can injure their ankle, fingers, or shoulder.

∀x (VolleyballPlayer(x) → CanInjureFingures(x))


All devices belonging to the company are connected to Google Home.

All devices with the company logo belong to the company.

A device is either with the company logo or belongs to employees.

All devices belonging to employees are available to connect to the company's wifi.

All devices connected to Google Home are controlled by managers.

All devices that connect to the company's wifi are easy to operate.

All devices that are easy to operate are produced after 2020.

∀x (GoogleHome(x) → ControlledByManager(x))

∀x (EasyToOperate(x) → ProducedAfter2020(x))


IPod1 is either produced after 2020 or controlled by managers.


IPod1 is not with the company logo, and managers do not control it.


IPod1 is either with the company logo or controlled by managers.


Some CD players are suitable toys for children.

No delicate mechanisms are suitable toys for children.

∀x (DelicateMechanism(x) → ¬SuitableToyForChildren(x))


If Jumbo is a living being, then Jumbo is not an elephant or a mammal.

If Jumbo is sleepy, then Jumbo is a baby elephant or an elephant.

LivingBeing(jumbo) → ¬(Elephant(jumbo) ∨ Mammal(jumbo))

Sleepy(jumbo) → BabyElephant(jumbo) ∨ Mammal(jumbo)


Jumbo is neither sleepy nor a baby elephant.


If someone works at a school, then they are faculty.

If Jill works at a school or is a teacher, then Jill works at a school.

WorkAtSchool(jill) ∨ DoesHomework(jill) → WorkAtSchool(jill)


“As it was” by Harry Styles needs to be written with words.

Either Max listens to classical music or Max listens to rap.

All the songs that Max listens to that are classical music are from the 12th century.

If the song Max listens to is rap, then the song is from Kanye West.

If a songs is from Kanye West, then the song is full of lyrics.

All songs that are full of lyrics need to be written with words

If “As it was” by Harry Styles is classical music that Max listens to or  from the 12th century, then “As it was” by Harry Styles is either classical music that Max listens to, or the songs are from 12th century.

∀x (MaxListensToClassicalMusic(x) ∨ MaxListensToRap(x))

∀x (MaxListensToClassicalMusic(x) → SongsFrom12thCentury(x))

∀x (MaxListensToRap(x) → SongsFromKanyeWest(x))

∀x (SongsFromKanyeWest(x) → SongsFullOfLyrics(x))

∀x (SongsFullOfLyrics(x) → NeedToBeWrittenWithWords(x))

MaxListensToClassicalMusic(asItWasByHarryStyles) ∨ SongsFrom12thCentury(asItWasByHarryStyles) → MaxListensToClassicalMusic(asItWasByHarryStyles) ⊕ SongsFrom12thCentury(asItWasByHarryStyles)


"As it was” by Harry Styles is a song from the 12th century.


"As it was” by Harry Styles is not a song from Kanye West and needs to be written with words.


"Your Woman" is a song by British one-man band White Town.

"Your Woman" song peaked at No. 1 on the UK Singles Chart.

If a song peaked at No.1 at a cetain place, then it was extremely popular.

"Your Woman" also peaked No. 1 in Iceland, Israel and Spain.

Peak(yourWoman, iceland) ∧ Peak(yourWoman, isarel) ∧ Peak(yourWoman, spain)


White Town did not produce any popular song.


All people who limp often and regularly have long-term medical issues with underlying causes.

If people have long-term medical issues with underlying causes, then they are not often spry and energetic.

People either stay indoors and rest a lot at home or people are often tired and disinterested in their activities.

If people stay indoors and rest a lot at home, then they do not visit the gym at least once a day.

If Mark either limps often and regularly or is often spry and energetic, then Mark limps often and regularly or is often tired and disinterested in his activities.

∀x (Spry(x) ⊕ Tired(x)) ∧ (∀x (Tired(x) → Indoors(x)))

(Limp(Mark) ⊕ Spry(Mark)) → Limp(Mark) ∨ Tired(Mark)


Mark visits the gym at least once a day.


Mark stays indoors and rests regularly at his home or visits the gym at least once a day.


Real Madrid and Atlético Madrid needed to play a penalty shoot-out in 2016 UCL final.

If two soccer teams score the same number of goals in one UCL final during the regular time, they need to play for the extra time.

If two soccer teams score the same number of goals in one UCL final during both the regular time and extra time, they need to play the penalty shoot-out.

Real Madrid and Atlético Madrid both scored one goal in 2016 UCL final during the regular time.

Real Madrid and Atlético Madrid both scored zero goals in 2016 UCL final during the extra time.

∀x ∀y (SoccerTeam(x) ∧ SoccerTeam(y) ∧ SameScore(x, y) ∧ During(regularTime) → PlayExtra(x, y))

∀x ∀y (SoccerTeam(x) ∧ SoccerTeam(y) ∧ SameScore(x, y) ∧ During(regularTime) ∧ During(extraTime) → PlayPenalty(x, y))

SoccerTeam(realMadrid) ∧ SoccerTeam(atleticoMadrid) ∧ SameScore(realMadrid, atleticoMadrid) ∧ During(regularTime)

SoccerTeam(realMadrid) ∧ SoccerTeam(atleticoMadrid) ∧ SameScore(realMadrid, atleticoMadrid) ∧ During(extraTime)


Real Madrid and Atlético Madrid did not need to play a penalty shoot-out in 2016 UCL final.


System 7 was formed by former members of Gong.

System 7 is a UK-based electronic dance music band.

Steve Hillage and Miquette Giraudy formed System 7.

Steve Hillage and Miquette Giraudy are former members of the band Gong.

System 7 has released several club singles.

BasedOn(system7, uk) ∧ ElectronicDanceMusicBand(system7)

Formed(stevehillage, system7) ∧ Formed(miquettegiraudy, system7)

FormerMemberOf(stevehillage, gong) ∧ FormerMemberOf(miquettegiraudy, gong)

∀x (ElectronicDanceMusicBand(x) → Band(x))

∃x (ClubSingle(x) ∧ Released(system7, x))


A summarization model is always faithful if it uses content from the input documents.

Extractive models are a kind of summarization models.

Extractive model can only use content from the input documents.

∀x (Model(x) ∧ Summarization(x) ∧ OnlyUseInputDocument(x) → Faithful(x))

∀x (Model(x) ∧ Extractive(x) → Summarization(x))

∀x (Model(x) ∧ Extractive(x) → OnlyUseInputDocument(x))


Extractive models are not always faithful.


If people practice coding questions, then they are not studying to go to medical school to become a doctor.

If people want to work in the software engineering industry, then they practice coding questions.

If people enjoy healthcare fields and want to help people with medical issues, then they are studying to go to medical school to become a doctor.

If people grew up with parents who worked as doctors, then they enjoy healthcare fields and want to help people with medical issues.

If people study hard, then they grew up with parents who worked as doctors.

If Robin neither enjoys healthcare fields and wants to help people with medical issues nor grew up with parents who worked as doctors, then Robin is either a person who studies hard or grew up with parents who worked as doctors.

∀x Healthcare(x) → StudyingToBeDoctor(x)

¬(Healthcare(Robin) ∨ ParentDoctors(Robin)) → (Study(Robin) ∨ ParentDoctors(Robin))


Robin practices coding questions and wants to work in the software engineering industry.


Robin neither practices coding questions nor works to work in the software engineering industry.


Jess frivolously spends a lot of money every time they go out.

If people go to the spa at least once a week, then they are not people who are miserly and need to save a large portion of their income.

People are either miserly and need to save a large portion of their income, or people that frivolously spend a lot of money every time they go out.

If people frivolously spend a lot of money every time they go out, then they value quality manufacturing and luxury items.

If people value quality manufacturing and luxury items, then they enjoy shopping for materialistic items in their free time.

If Jess is not miserly and needs to save a large portion of their income, then Jess does not value quality manufacturing and luxury items.

If Jess either values quality manufacturing and luxury items or, if he does not, then he is miserly and needs to save a large portion of his income, then Jess frivolously spends a lot of money every time he goes out.

Luxury(Jess) ⊕ Miserly(Jess)) →  Luxury(Jess)


Jess either enjoys shopping for materialistic items in his free time or, if he does not, then he goes to the spa at least once a week.


If Jess either enjoys shopping for materialistic items in his free time or, if he does not, then he goes to the spa at least once a week, then Jess neither values quality manufacturing and luxury items nor goes to the spa at least once a week.


The album "Wolfgang Amadeus Phoenix" is a certified gold album.

The indie pop band Phoenix has released 6 albums.

Phoenix's album "Wolfgang Amadeus Phoenix" sold over 500,000 copies.

A certified gold album or single is one which sold over half a million copies.

"1901" is a single from Phoenix's album "Wolfgang Amadeus Phoenix."

Over 400,000 copies of "1901" have been sold.

Album(wolfgangamadeusphoenix) ∧ IsAlbumOf(wolfgangamadeusphoenix, phoenix) ∧ SoldOver(wolfgangamadeusphoenix, l500000)

∀x ((Album(x) ∨ Single(x)) ∧ SoldOver(x, l500000) → CertifiedGold(x))

Single(l1901) ∧ From(l1901, wolfgangamadeusphoenix) ∧ By(l1901, phoenix)


The single "1901" is a certified gold single.


If the Hulk does not wake up, then Thor is not happy.

Peter Parker is a either a superhero or a civilian.

If the Hulk wakes up, then he will break a bridge.

Thor will break a bridge when he is happy.

A god is not a destroyer and a destroyer is not a god.

Peter Parker wears a uniform when he is a superhero.

Peter Parker is not a civilian if and only if a destroyer is breaking a bridge.

∀x (¬Civilian(peter) ↔ (Destroyer(x) ∧ BreakBridge(x)))


If Thor is happy, then Peter Parker wears a uniform.


If Thor is not happy, then no bridge will be broken.


Diethylcarbamazine is not preferred for the treatment of river blindness.

Diethylcarbamazine is a medication discovered in the year 1947.

Diethylcarbamazine can be used to treat river blindness.

The only preferred treatment for river blindness is ivermectin.

∀x (Diethylcarbamazine(x) ∧ Medication(x) ∧ DiscoveredIn(x, year1947))

∀x ∀y (Diethylcarbamazine(x) ∧ RiverBlindness(y) → Treats(x, y))

∀x ∀y (RiverBlindness(y) ∧ PreferredTreatment(x, y) → Ivermectin(x))

∀x (Diethylcarbamazine(x) → ¬Ivermectin(x))


Diethylcarbamazine was often used to treat river blindness.


Diethylcarbamazine is used in the treatment of filariasis.


Latent Dirichlet allocation model is implementing machine learning algorithms.

All univariate analyses use a generalized linear model.

All multivoxel (pattern) analyses are implementing machine learning algorithms.

All implementing machine learning algorithms are to learn and classify multivariate data.

The Latent Dirichlet allocation model uses a generalized linear model or a univariate analysis.

If the Latent Dirichlet allocation model does not learn and classify multivariate data, then the Latent Dirichlet allocation model uses a generalized linear model and a multivoxel (pattern) analysis.

∀x (UnivariateAnalysis(x) → UsesGeneralizedLinearModel(x))

∀x (MultivoxelPatternAnalysis(x) → ImplementingMachineLearningAlgorithms(x))

∀x (ImplementingMachineLearningAlgorithms(x) → LearnAndClassifyMultivariateData(x))


Latent Dirichlet allocation model uses a generalized linear model and learns and classifies multivariate data.


Latent Dirichlet allocation model either uses a generalized linear model or learns and classifies multivariate data.


If something requires a medical diagnosis, then lab tests or imaging is required.

All rare diseases require a medical diagnosis.

If something is mild, then no lab tests or imaging is required.

If bladder cancer is either both blood cancer and Leukemia or neither blood cancer nor Leukemia, then bladder cancer is Leukemia.

∀x (RequiresAMedicalDiagnosis(x) → LabTestsOrImagingRequired(x))

∀x (RareDiseases(x) → RequiresAMedicalDiagnosis(x))

∀x (Mild(x) → ¬LabTestsOrImagingRequired(x))

¬(BloodCancer(bladderCancer) ⊕ Leukemia(bladderCancer)) → Leukemia(bladderCancer)


Bladder cancer is either a rare disease or mild.


All non-rare earth metals are not scarce.

Either non-rare earth metals or rare earth metals.

All rare earth metals can be used for batteries.

All rare earth metals are essential for electric vehicles.

Lithium is neither a non-rare earth metal nor essential for electric vehicles.

∀x (Non-rareEarthMetals(x) → NotScarce(x))

∀x (Non-rareEarthMetals(x) ∨ RareEarthMetals(x))

∀x (RareEarthMetals(x) → BeUsedForBatteries(x))

∀x (RareEarthMetals(x) → EssentialForElectricVehicles(x))


Lithium is a precious metal and is used for batteries.


If Lithium is not essential for electric vehicles or a precious metal, then Lithium is not a non-rare earth metal or usable for batteries.


If people own at least one pet, then they do not have tidy houses.

If people grew up with childhood pets, then they own at least one pet.

If people hire a maid or cleaning service, then they have tidy houses.

If people live in the suburbs, then they have tidy houses.

Jack either does not hire a maid or cleaning service or, if he does, then he does not own at least one pet.

∀x (OwnPet(x) → ¬TidyHouse(x))
∀x (ChildhoodPet(x) → OwnPet(x))
∀x (HireCleaning(x) → TidyHouse(x))
∀x (Suburbs(x) → ChildhoodPet(x))
¬(HireCleaning(jack) ⊕ OwnPet(jack))


Jack neither lives in the suburbs nor owns at least one pet.


Jack grew up with childhood pets and lives in the suburbs.


A bottle is either standing upright or toppled over.

Upright(bottle) ⊕ ToppledOver(bottle)
¬Upright(bottle)


John is good at staying organized and motivated.

If people eat cereal and milk every day for breakfast, then they have very busy morning schedules every day.

All young children below the age of ten eat cereal and milk every day for breakfast.

People are either young children below the age of ten or have a lot of commitments they voluntarily signed up for.

If people have a lot of commitments they voluntarily signed up for, then they are hardworking individuals with high ambitions and goals for the future.

If people are hardworking individuals with high ambitions and goals for the future, then they are not good at staying organized and motivated.

John either is both a hardworking individual with high ambitions and goals for the future and has busy morning schedules every day, or he is neither a hardworking individual with high ambitions and goals for the future nor does he have a busy morning schedule every day.

(Hardworking(john) ∧ BusyMorning(john)) ⊕ (¬Hardworking(john) ∧ ¬BusyMorning(john))


John eats cereal and milk every day for breakfast.


John is either a hardworking individual with high ambitions and goals for the future or is good at staying organized and motivated.


USA and Germany are different countries.

Any company that has offices in different countries is a multinational company.

∀x ∀y ∀z (OfficeIn(x, y) ∧ OfficeIn(x, z) ∧ ¬SameCountry(y, z) → IsMultinationalCompany(x))


Ableton does not have an office in Germany.


Everyone that eats fish they catch themselves is a swimmer.

Every penguin eats fish they catch themselves.

All nonflying birds in Antarctica are penguins.

∀x (EatsFishCaughtThemselves(x) → Swimmer(x))

∀x (Penguin(x) → EatsFishCaughtThemselves(x))

∀x (NonFlyingBirdAntartica(x) → Penguin(x))


Fido is neither a non-flying bird nor can Fido go underwater.


If Fido can either go underwater or is a swimmer, then Fido is a nonflying bird in Antartica.


If Leon is not studying, then Leon is a teacher.

∀x (Professor(x) → Teacher(x))
∀x (Researcher(x) → Professor(x))
∀x (Teacher(x) → ¬Student(x))
∀x (Study(x) → Student(x))
¬Study(leon) ⊕ Researcher(leon)
¬Study(leon) → Teacher(leon)


Leon is neither a student nor a researcher.


If Leon is not a researcher, then Leon is a student.


A cutman is responsible for preventing and treating physical damage to a fighter.

Cutmen appear in matches such as a boxing, kickboxing or a mixed martial arts bout.

Cutmen typically handle swelling, nosebleeds and lacerations.

∀x (Cutman(x) → Prevent(x, physicalDamage) ∧ Treat(x, physicalDamage))

∀x (Cutman(x) → Appear(x, boxing) ∨ Appear(x, kickboxing) ∨ Appear(x, mixedMartialBout))

∀x (Cutman(x) → Handle(x, swelling) ∧ Handle(x, nosebleeds) ∧ Handle(x, lacerations))


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


One of the world's best-known artworks is painted by a scientist.

The Mona Lisa is one of the world's best-known artworks.

The Mona Lisa is a portrait painted by Leonardo da Vinci.

Leonardo da Vinci was a scientist and painter.

Painting genres are history, portrait, animal, landscape, and still life.

PaintedBy(monaLisa, leonardodaVinci) ∧ Portrait(monaLisa)

∀x (Painting(x) → (History(x) ∨ Portrait(x) ∨ Animal(x) ∨ Landscape(x) ∨ StillLife(x)))


Leonardo da Vinci has artworks in the landscape genre.


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))


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.


Buisnesses are either sanctioned or unsanctioned.

The Crude Oil Data Exchange is a buisness 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))


Crude Oil Data Exchange is unsanctioned.


When something is depressing, it is sad.

∀x (Depressing(x) → Sad(x))
∀x (V(x) → Depressing(x))


John Evans Popularized the term paalstab.

Palstaves are a type of early bronze axe.

Commonly found in northern, western and south-western Europe, palstaves are cast in moulds.

John Evans is an archeologist who popularized the term "palstave".

A paalstab is not an axe, but rather a digging shovel.

∀x (Palstave(x) → From(x, earlybronzeage) ∧ Axe(x))

∀x ∀y (Palstave(x) ∧ Mould(y) → FoundIn(x, northerneurope) ∧ FoundIn(x, westerneurope) ∧ FoundIn(x, south-westerneurope) ∧ CastIn(x, y))

Archeologist(johnevans) ∧ Popularized(johnevans, termpalstave)

∀x (Paalstab(x) → ¬Axe(x) ∧ DiggingShovel(x))


There is an axe that is commonly found in Western Europe.


Archeologists haven't popularized anything.


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)

∀x ∃y (HoldingCompany(x) → Company(y) ∧ Holds(x, y))

Disbanded(tecmo) ∧ DisbandedIn(tecmo, japan) ∧ Survived(koei) ∧ Renamed(koei)

∀x (VideoGameHoldingCompany(x) → HoldingCompany(x))


The Playstation Eye can be used with the Playstation 2 and the Playstation 3.

The PlayStation EyeToy is a camera accessory for the Playstation 2.

The PlayStation Eye is a camera accessory for the Playstation 3.

The Playstation Camera is a camera accessory for the Playstation 4 and the Playstation 5.

Camera accessory for the system is compatible with that system

Only the Playstation Camera is compatible with more than one system.

Accessory(pscamera, ps4) ∧ Accessory(pscamera, ps5)

∀x ∀y (Accessory(x, y) → Compatible(x, y))

¬Compatible(pseye, ps2) ∧ ¬Compatible(pseye, ps4)∧¬Compatible(pseye, ps5)∧¬Compatible(pseyetoy, ps3)∧¬Compatible(pseyetoy, ps4)∧¬Compatible(pseyetoy, ps5)


The Playstation EyeToy is compatible with the Playstation 2.


The Playstation Camera can be used for all Playstation consoles.


Adam Buska plays what Americans call soccer.

Adam Buska is a European football player.

If a European plays football, they play what Americans call soccer.

∀x ((FootballPlayer(x) ∧ European(x)) → PlaysAmericanSoccer(x))


If the game has sold more than 1 million copies, then it is on the Best Seller list.

All Games developed by Paradox Development Studio sold more than 1 million copies.

Some games published before 2010 support the Linux OS system.

All games on the Best Seller list are popular among young people.

FIFA22 neither supports the Linux OS system nor is it popular among young people.

∀x (DevelopedByParadox(x) → SoldMillion(x))

∃x ((PublishedBefore2010(x) ∧ SupportLinuxSystem(x)))


FIFA21 is published before 2010 and developed by Paradox Development Studio


if FIFA21 is either a game published before 2010 or developed by Paradox Development Studio, then it is either in the Best Seller list and sold more than 1 million copies; or not in the Best Seller list and hasn't sold more than 1 million copies.


All people from BRICS neither speak Hindi nor speak English.

China is one of BRICS and its economy is emerging.

India is one of BRICS and its economy is emerging.

All people from India speak Hindi or English.

∀x (China(x) → BRICS(x) ∧ EmergingEconomy(x))

∀x (India(x) → BRICS(x) ∧ EmergingEconomy(x))

∀x ∀y (From(x, y) ∧ China(y) → Speak(x, chinese))

∀x ∀y (From(x, y) ∧ India(y) → Speak(x, hindi) ∨ Speak(x, english))


There is a person from BRICS speaking Hindi.


Daveed Diggs is an actor and film producer.

Daveed Diggs played two roles in the musical Hamilton.

One of the actors from Hamilton won the best actor award.

The actor playing Thomas Jefferson won the best actor award.

PlayedTwoRoles(daveedDiggs) ∧ PlayedIn(daveedDiggs, hamilton) ∧ Musical(hamilton)

∃x (Actor(x) ∧ PlayedIn(x, hamilton) ∧ WonBestActorAward(x))

∀x (Actor(x) ∧ Played(x, thomasJefferson) → WonBestActorAward(x))


Ernest Pohl has not scored more than 180 goals.

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.

∃x (In(x, polishfirstdivision) ∧ ScoredMoreThan180Goals(x))

ScoredMoreThan180Goals(ernestpohl) ∧ In(ernestpohl, polishfirstdivision)

∃x (NamedAfter(gornikzabrze, x) ∧ FootballPlayer(x) ∧ From(x, rudaslaska))


Górnik Zabrze's stadium was named after Ernest Pohl.


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

Ann J. Land was a member of the Philadelphia City Council and was also a member of the Democratic Party.

Ann J. Land ran unopposed for the Philadephia 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.

Year(y1980) → PhiladephiaCouncil(annJLand) ∧ RunFor(annJLand)

∀x (RunFor(x) ∧ PhiladephiaCouncil(x) → Elected(x))

Year(y1987) → PhiladephiaCouncil(annJLand) ∧ RunFor(annJLand) ∧ Defeated(annJLand, nutter)


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.


Aberdeen and Rangers are different teams.

Different teams cannot win the same cup in a given year's final.

Different(aberdeen, rangers) ∧ Different(rangers, aberdeen)

∀x ∀y ∀z (Different(x, y)  ∧ WonCup(x, z)  → ¬WonCup(y, z))


Mary is a person who lives in Manhattan.

All young working professionals who have regular 9-5 jobs also have pets.

Some people who live in Manhattan are young working professionals who have regular 9-5 jobs.

All people who have pets are people who have at least one child.

People who do not have at least one child are people who own a sports car.

Mary either does not own a sports car or, if they do, then they do not have at least one child.

∀x (Working(x) → Pets(x))
∃x (Manhattan(x) ∧ Working(x))
∀x (Pets(x) → Child(x))
∀x (Child(x) → ¬Car(x))
¬(Car(mary) ⊕ Child(mary))


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


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


Picture memory is preceded by data processing.

Either block design or event-related design.

All event-related designs are brain image acquisition.

All brain image acquisition is preceded by data processing.

Nothing preceded by data processing acquires data.

Picture memory is either an event-related design and acquiring data or neither an event-related design nor acquiring data.

∀x (BlockDesign(x) ∨ Event-relatedDesign(x))

∀x (Event-relatedDesign(x) → BrainImageAcquisition(x))

∀x (BrainImageAcquisition(x) → PrecededByDataProcessing(x))

∀x (PrecededByDataProcessing(x) → ¬AcquiringData(x))

(Event-relatedDesign(pictureMemory) ∧ AcquiringData(pictureMemory)) ∨ (¬Event-relatedDesign(pictureMemory) ∧ ¬AcquiringData(pictureMemory))


Picture memory is either a block design or acquiring data.


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


The USS Lyon was a US Navy ship involved in WWII.

All ships involved in WWII are currently decommissioned or in a museum.

∀x (InWWII(x) → (Decommissioned(x) ∨ InMuseum(x)))


Chopsticks at restaurants are eco-friendly.

All disposable chopsticks are made from trees.

Either disposable chopsticks or reusable chopsticks.

If chopsticks are made from metals, then they are not made from plastics.

All reusable chopsticks are made from metal.

Chopsticks at restaurants are either made from metals and made from plastics, or neither made from metals nor made from plastics.

∀x (DisposableChopsticks(x) → MadeFromTrees(x))

∀x (DisposableChopsticks(x) ⊕ Reusable(x))

∀x (MadeFromMetals(x) → ¬MadeFromPlastics(x))


Chopsticks at restaurants are eco-friendly or made from trees.


If Chopsticks at restaurants are made from plastics or made from trees, then Chopsticks at restaurants are made from plastics and are eco-friendly.


No one unproductive is an energetic person.

If something is a sloth, then it is lazy.

Sid is not either an energetic person or 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.


Manchester City has a higher ranking than Manchester United.

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 (European(x) ∧ SoccerClub(x) → Attend(x, ucl) ∨ Attend(x, uel) ∨ Attend(x, uecl))

∀x ∀y (SoccerClub(x) ∧ SoccerClub(y) ∧ Attend(x, ucl) ∧ Attend(y, uel) → HigherRank(x, y))

∀x ∀y (SoccerClub(x) ∧ SoccerClub(y) ∧ Attend(x, uel) ∧ Attend(y, uecl) → HigherRank(x, y))

European(manchesterunited) ∧ SoccerClub(manchesterunited) ∧ European(manchestercity) ∧ SoccerClub(manchestercity)


If a person coach a football club, the person is a football coach.

If a person has a position in a club for a position in a year, and the club is in NFL in the same year, the person plays in NFL.

Cris Carter had 13 touchdown receptions.

Minnesota Vikings was in the National Football League in 1997.

John Randle was Minnesota Vikings defensive tackle in 1997.

∀x ∀y (Coach(x, y) ∧ IsFootballClub(y) → IsFootballCoach(x))

∀x ∀y ∀z (PlayFor(x, y) ∧ NFLTeamYear(y, z) ∧ InTeam(x, z) → PlayInNFL(x))

Position(john_Randle, defensive_tackle) ∧ InTeam(john_Randle, y1997) ∧ PlayFor(john_Randle, minnesota_Vikings)


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


Cris Carter played for Minnesota Vikings.


Grace is either a cat and a dog, or neither a cat nor a dog.

(Cat(grace) ∧ Dog(grace)) ⊕ (¬Cat(grace) ∧ ¬Dog(grace))


If Grace is either both cute and lovely, or neither cute nor lovely, then Grace is either a dog or a ghost.


If Grace is not both a ghost and lovely, then Grace is either a cat or cute.


Shafaq-Asiman is a large complex of offshore geological structures in the Caspian Sea.

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)

∀x ∀y (NorthwestOf(x, y) → SoutheastOf(y, x))


Baku is not northwest of an offshore geological structures.


Herodicus was a Greek physician, dietician, sophist, and gymnastic-master.

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.

Some of theories of Herodicus are considered to be the foundation of sports medicine.

Greek(herodicus) ∧ Physician(herodicus) ∧ Dietician(herodicus) ∧ Sophist(herodicus) ∧ GymnasticMaster(herodicus)

Born(herodicus, selymbia) ∧ City(selymbia)

Colony(selymbia, megara) ∧ CityState(megara)

∃x (Theory(x) ∧ From(x, herodicus) ∧ FoundationOf(x, sportsMedicine))


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


If someone is a scientist, then they are an adult.

∀x (Kid(x) → ¬OperaLover(x))
∀x (Adult(x) → OperaLover(x))
∀x (Scientist(x) → Adult(x))
∃x (Student(x) ∧ Kid(x))
Kid(billy)


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


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

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.

∃x (FootballReferee(x) ∧ RefereeObserver(x))

Son(andywinter, brianwinter) ∧ FootballPlayer(andywinter) ∧ PlaysFor(andywinter, hamiltonacademical)


People are either interested in puzzles or bad at chess.

If a person is bad at chess, then they don't play a lot of chess.

A person is either a planner or a creative person.

Erica 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 someone who neither plans nor is creative.

¬(BadChess(erica) ∨ Creative(erica)) → (Plans(erica) ⊕ Creative(erica))


Erica is interested in puzzles and is creative.


Erica is either interested in puzzles or is creative.


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


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


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


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.


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.


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


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.


Cristiano Ronaldo is a top soccer player.

Soccer players have a right foot and a left foot.

Top soccer players are soccer players who can use their both feet very efficiently.

If a soccer player can score many goals using left foot, then they can use that foot very efficiently.

If a soccer player can score many goals using right foot, then they can use that foot very efficiently.

Cristiano Ronaldo can use his right foot very efficiently.

Cristiano Ronaldo have scored more than one hundred goals using his left foot.

∀x (SoccerPlayer(x) → HasLeftFoot(x) ∧ HasRightFoot(x))

∀x (SoccerPlayer(x) ∧ Efficient(x, left) ∧ Efficient(x, right) → Top(x))

∀x (SoccerPlayer(x) ∧ ScoreManyGoals(x, left) → Efficient(x, left))

∀x (SoccerPlayer(x) ∧ ScoreManyGoals(x, right) → Efficient(x, right))


Cristiano Ronaldo is not a top soccer player.


The National Lobster Hatchery is for conservation.

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)

∀x (Hatchery(x) → ForConservation(x) ∨ ForProfit(x))

∃x (Hatchery(x) ∧ ForConservation(x) ∧ ReleasesAnimalsToWild(x))


The National Lobster Hatchery releases animals into the wild.


Rhos Aelwyd F.C. won the 2005-06 Premier Division.

Rhos Aelwyd F.C. is a Welsh football club.

Rhos Aelwyd F.C. is the only club based in Ponciau.

The Premier Division was won in 2005–06 by a team from Ponciau.

The winner of the Premier Division in 2009–10 was promoted back to the Cymru Alliance.

The Premier Division in 2009–10 was won by the same team that won in 2005-06.

∀x (Rhosaelwydfc(x) → FootballClub(x) ∧ BasedInPonciau(x) ∧ Welsh(x))

∀x (BasedInPonciau(x) ↔ Rhosaelwydfc(x))

∃x (BasedInPonciau(x) ∧ WonPremierDivisionDuring(x, y2005))

∀x (WonPremierDivisionDuring(x, y2009) → Promoted(x))

∀x (WonPremierDivisionDuring(x, y2009) ↔ WonPremierDivisionDuring(x, y2005))


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


If something is convenient, then it is popular.

PyTorch is either Windows and software, or neither Windows nor software.

(Windows(pytorch) ∧ Software(pytorch)) ⊕ (¬Windows(pytorch) ∧ ¬Software(pytorch))


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.

Road one is made of concrete and Road two is made of asphalt.

∀x (Road(x) → (MadeOfConcrete(x) ∨ MadeOfAsphalt(x))

∀x ∀y (Road(x) ∧ MadeOfConcrete(x) ∧ Road(y) ∧ MadeOfAsphalt(y) → LastLonger(x, y))

∀x ∀y (Road(x) ∧ MadeOfAsphalt(x) ∧ Road(y) ∧ MadeOfConcrete(y) → Smoother(x, y))

∀x ∀y ∀z (Road(x) ∧ Road(y) ∧ Smoother(x, y) → Prefers(z, x))

Road(one) ∧ MadeOfConcrete(one) ∧ Road(two) ∧ MadeOfAsphalt(two)


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

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 one of Ontario's oldest summer camps.


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


Emily often holds tenured and high-ranking positions at her workplace.

If people publish journals, then they do not work in the entertainment industry.

All people who are award-winning novelists publish journals.

People either work in the entertainment industry or are highly acclaimed in their profession.

If people are highly acclaimed in their profession, then they often hold tenured and high-ranking positions at their workplace.

If people are highly acclaimed in their profession, then they often receive glowing feedback and recommendations from their colleagues.

If Emily is either both highly acclaimed in her profession and often holds tenured and high-ranking positions at her workplace, or she is neither highly acclaimed in her profession nor often holds tenured and high-ranking positions at her workplace, then Emily is not highly acclaimed in her profession.

∀x (PublishJournals(x) → ¬Entertainment(x))

(Acclaimed(emily) ∧ Tenured(emily)) ∨ (¬Acclaimed(emily) ∧ ¬Tenured(emily)) → ¬Acclaimed(emily)


Emily often receives glowing feedback and recommendations from their colleagues and is an award-winning novelist.


If Emily either often receives glowing feedback and recommendations from her colleagues or is an award-winning novelist, then Emily does not both publish journals and is an award-winning novelist.


Megan Whalen Turner worked with Greenwillow Books.

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, than 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.

YoungAdultFantasyNovel(thickastheives) ∧ WrittenBy(thickastheives, megan)

∀x ∀y ∀z (WrittenBy(x, y) ∧ PublishedBy(x, z) → WorkedWith(y, z))

Fictional(medeempire) ∧ SetIn(thickastheives, medeempire)

∃x (Country(x) Nearby(medeempire, x) ∧ PlotsToSwallowUp(medeempire, x))

Country(attolia) ∧ Nearby(medeempire, attolia) ∧ Country(sounis) ∧ Nearby(medeempire, sounis)

SoldAs(thickastheives, hardcover) ∧ SoldAs(thickastheives, softcover)


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.


There is a tablet computer that was announced by a German.

WeTab is a MeeGo-based tablet computer.
There is a WeTab product.
WeTab was announced by Neofonie.
Neofonie is a German producer.
Germans speak English or German.

∀x (WeTab(x) → MeeGoBased(x) ∧ TabletComputer(x))

∀x (German(x) → Speak(x, english) ∨ Speak(x, german))


Neofonie doesn't speak English or German.


Some employees working in business analysis are good at math.

All employees working in business analysis are working in this company.

No employees working in this company are from China.

All employees working in software engineering are from China.

James is working in software engineering.

∃x ( BusinessAnalysis(x) ∧ GoodAtMath(x))

∀x (BusinessAnalysis(x) → WorkInCompany(x))

∀x (SoftwareEngineering(x) → FromChina(x))


James is not good at math and he is working in business analysis.


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


Blueberries were the most popular fruit at the party.

The party provides five kinds of fruits: strawberry, orange, blueberry, grape, and cherry.

All fruits are provided in the same weight at the beginning of the party.

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 amount of leftover blueberries was lower than that of cherries.

Benjamin only ate oranges and grapes at the party.

Party(strawberry) ∨ Party(orange) ∨ Party(blueberry) ∨ Party(grape) ∨ Party(cherry)

Eat(orange, benjamin) ∧ Eat(grape, benjamin) ∧ ¬Eat(blueberry, benjamin) ∧ ¬Eat(cherry, benjamin) ∧ ¬Eat(strawberry, benjamin)


Cherries were the most popular fruit at the party.


James attends the conference but not in person.

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 (Attend(x) → InPerson(x) ⊕ Remotely(x))

∀x ((Attend(x) ∧ China(x)) → ¬Remotely(x))


David Ha'ivri is a political strategist.

If you are born in Israel to at least one Israeli parent, then you receive 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.

∀x ∃y (BornInIsrael(x) ∧ ParentOf(x, y) ∧ Israeli(y) → IsraeliCitizen(x))

∃x (EmigratedTo(davidhaivri, america) ∧ BornInIsrael(davidhaivri) ∧ ParentOf(davidhaivri, x) ∧ Israeli(x))

∃x (ZionistLeader(x) ∧ ElectedTo(x, shomronmunicipalcouncil))


David Ha'ivri is a United States citizen.


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


Mary has the flu.
Flu and influenza are the same disease.
Susan doesn't have influenza.

Have(mary, flu)
∀x (Have(x, flu) ↔ Have(x, influenza))
¬Have(susan, influenza)


No lawyer ever sat in the House of Commons.

James Cocks was a Whig politician who sat in the House of Commons.

Whig(james) ∧ Politician(james) ∧ SatInHouseOfCommons(james)


Beasts of Prey is either a fantasy novel or a science fiction novel.

Science fiction novels are not about mythological creatures

Beasts of Prey Is about a creature known as the Shetani.

Novel(beastsofprey) ∧ Fantasy(beastsofprey) ∨ ScienceFiction(beastsofprey)

∀x ∀y (ScienceFiction(x) ∧ Mythological(y) ∧ Creature(y) → ¬About(x, y))

About(beastsofprey, shetani) ∧ Creature(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 the surname include Amy Odell, Jack Odell, and Mats Odell.

Amy Odell is a British singer-songwriter.

Odell(amyOdell) ∧ NotablePeople(amyOdell) ∧ Odell(jackOdell) ∧ NotablePeople(jackOdell) ∧ Odell(matsOdell) ∧ NotablePeople(matsOdell)

British(amyOdell) ∧ Singer(amyOdell) ∧ SongWriter(amyOdell)


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

If you go somewhere by train, you will not lose time.

If you go somewhere by car and meet 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.

∀x ((Car(x) ∧ MeetJam(x)) → LoseTime(x))


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


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

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))


Tipped employees do not get a guaranteed minimum wage.

If a person is a white-collar worker, they will get a guaranteed minimum wage (All white-collar workers get a guaranteed minimum wage).

Mary is not a lawyer or a tipped employee.

∀x (Tipped(x) → ¬GetMinWage(x))
∀x (WhiteCollar(x) → GetMinWage(x))
∀x (Lawyer(x) → WhiteCollar(x))
∀x (Advocate(x) → Lawyer(x))
¬Lawyer(mary) ⊕ Tipped(mary)


Mary is either an advocate or a tipped employee.


If Mary is not an advocate and gets a guaranteed minimum wage, she is not a tipped employee.


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


People born and living in New York City are New Yorkers.

People liviing in Manhattan live in New York City.

∃x (IsChestPlayer(x) ∧ IsGrandMaster(x))

∀x (BornIn(x, newyorkcity) ∧ LivesIn(x, newyorkcity) → IsNewYorker(x))

∀x (LivesIn(x, manhattan) → LivesIn(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.

∀x (ApplyVisa(x) → FinancialGuarantees(x))

∀x (FinancialGuarantees(x) → RequestDocuments(x))

∀x (RequestDocuments(x) → ¬CloseBankAccount(x))


Philip applied for a Schengen Visa and got it.


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


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

∃x (Fear(x) ∧ Anxiety(x))
∃x (Anxiety(x) ∧ Terror(x))


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.

There is a major settlement of Lake Huron in ON.

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 ∀y (Erie(y) ∧ MajorSettlementOf(x, y) ∧ In(x, ny) ∨ In(x, pa) ∨ In(x, oh) ∨ In(x, mi))

State(ny, us) ∧ State(pa, us) ∧ State(oh, us) ∧ State(mi, us)

∃x ∀y (Huron(y) ∧ MajorSettlementOf(x, y) ∧ In(x, on))

∀x (GreatLake(x) → FormAtEndOf(x, lastglacialperiod))


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


Stephen Curry is a professional basketball player.

No soccer players are professional basketball players.

All NBA players are professional basketball players.

If Stephen Curry is not an NBA player, then Stephen Curry is not an NBA player or a soccer player.

∀x (SoccerPlayer(x) → ¬ProfessionalBasketballPlayer(x))

∀x (NBAPlayer(x) → ProfessionalBasketballPlayer(x))

¬NBAPlayer(stephencurry) → ¬(NBAPlayer(stephencurry) ⊕ SoccerPlayer(stephencurry))


Thomas Gilovich proposed naive cynicism.

Naive cynicism was proposed by Justin Kruger and a colleague.

Thomas Gilovich is a colleague of Justin Kruger.

Proposed(justinKruger, naiveCynicism) ∧ Proposed(colleagueOfJustinKruger, naiveCynicism)


Justin Kruger propose a philosophy of mind.


Thomas Gilovich worked on philiophies of mind.


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

The Turing Award has been awarded to Donald Knuth, Marvin Minsky, Richard Hamming and John McCarthy.

Donald Knuth made major contributions to the analysis of algorithms.

Marvin Minsky is recognized by his contributions to the field of artificial intelligence.

Richard Hamming did research on numerical methods.

John McCarthy had a central role in creating and shaping the field of artificial inteligence.

TuringAwarded(donaldKnuth) ∧ TuringAwarded(marvinMinsky) ∧ TuringAwarded(richardHamming) ∧ TuringAwarded(johnMccarthy)


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


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


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


No 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 thousand users.

No Leetcode problems published after 2022 are starred by more than 1 thousand users.

2Sum is not recommended to novices and hard.

4Sum is either starred by more than 1 thousand users and published after 2022, or neither starred by more than 1 thousand users nor published after 2022.

∀x (PublishedAfter2022(x) → ¬Starred(x))


4Sum is a Leetcode problem recommended to the novice or is hard.


4Sum is neither a 2Sum Leetcode problem recommended to the novice nor a Leetcode problem that's hard.


Show your love wasn't written by a member of a boy band.

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) ∧ LeadSingle(showyourlove) ∧ LeadSingleOf(showyourlove, inside)

Member(hyunsik, btob4u) ∧ Wrote(hyunsik, showyourlove)


A lead single of inside contains a a hopeful message.


All tables are round.
Some furniture are tables.

∀x (Table(x) → Round(x))
∃x (Furniture(x) ∧ Table(x))


Some maladjusted individuals are products of broken homes.

All juvenile delinquents are maladjusted individuals.

Some juvenile delinquents are products of broken homes.

∀x (JuvenileDelinquent(x) → MaladjustedIndividual(x))

∃x (JuvenileDelinquent(x)  ∧ ProductOfBrokenHome(x))


Multivoxel (pattern) analysis is a brain decoding.

All brain decoding is extracting information from BOLD signals.

No extracting information from BOLD signals is 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.

∀x (BrainDecoding(x) → ExtractingInformationFromBOLDSignals(x))

∀x (ExtractingInformationFromBOLDSignals(x) → ¬WithoutStatisticalPatternAnalysis(x))

∀x (WritingANovel(x) → WithoutStatisticalPatternAnalysis(x))

WithoutStatisticalPatternAnalysis(multivoxelPatternAnalysis) ∧ BrainReading(multivoxelPatternAnalysis) → WithoutStatisticalPatternAnalysis(multivoxelPatternAnalysis) ∧ BrainDecoding(multivoxelPatternAnalysis)


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


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


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


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


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


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))

FirstDinnerParty(allison, luisparty) ∧ AtLuisParty(allison)

RoomFor(gustave, broccoli) ∧ RoomFor(gustave, asparagus)


Imagine Dragons is an American pop rock band.

The lead singer of Imagine Dragons is Dan.

Demons is one of the most popular singles of Imagine Dragons.

Some singles of Imagine Dragons have been on Billboard Hot 100.

∃x (PopularSingle(imagineDragon, x) ∧ BillboardHot100(x))


All bread is food.
Some sandwiches are bread.
All food is edible.
No edible things are poisonous.
Deodorant is poisonous.

∀x (Bread(x) → Food(x))
∃x (Sandwich(x) ∧ Bread(x))
∀x (Food(x) → Edible(x))
∀x (Edible(x) → ¬Poisonous(x))
Poisonous(deodorant)


If deodorant is a loaf of bread, then deodorant is not a sandwich.


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 (Cover(x, water) ∧ Cover(x, electricity))


Noah and Ava both need to pay the heating bill.


Susan does not need to pay the water bill.


If Nike is clothes, then Nike is perfect and a dress.

Clothes(nike) → Perfect(nike) ∧ Dress(nike)


If a person has a pet, they care for that pet.

Pets who are naughty are not liked as much.

Charlie has a naughty pet dog named Leo.

∃x ((Cat(x) ∧ Naughty(x)) ∨ (Dog(x) ∧ Naughty(x)))

∀x ∀y (Pet(x) ∧ Naughty(x) → ¬Liked(x, y))

HasPet(charlie) ∧ Pet(leo) ∧ Dog(leo) ∧ Naughty(leo)


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


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

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


The Three Body Problem won the Hugo Award.

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 influenced by Isaac Asimov.

The book the Three Body Problem has sold more than 1 million copies.

The Three Body Problem is about the future.

∀x (Book(x) ∧ WrittenBy(x, cixinliu) → SoldMoreThan(x, onemillion))

∃x (Won(x, hugoaward) ∧ Book(x) ∧ WrittenBy(x, cixinliu))

∀x (Book(x) ∧ AboutFuture(x) → InfluencedBy(x, isaacasimov))

Book(threebodyproblem) ∧ SoldMoreThan(threebodyproblem, onemillion)


The Three Body Problem was influenced by Isaac Asimov.


The Three Body Problem was written by Cixin Liu.


Some students who major in computer science get up early.

If a student gets up early, then he/she will study in the morning.

All students studying in the morning are good at time management.

All students good at time management are popular among students.

∀x (StudyMorning(x) → GoodAtTimeManagement(x))

∀x (GoodAtTimeManagement(x) → Popular(x))


James majors in computer science and gets up early.


If James gets up early, then he majors in computer science.


If there is a dog on the roof something went wrong.

∀x ∃y ((Dog(x) ∧ OnRoof(x)) → WentWrong(y))


Elephantopus is widespread over much of Australia and Southern Asia.

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 (Elephantopus(x) → WidespreadOver(x, africa) ∧ WidespreadOver(x, southernasia) ∧ WidespreadOver(x, australia) ∧ WidespreadOver(x, americas))

∃x (Elephantopus(x) ∧ NativeTo(x, southeasternunitedstates))

∀x (ElephantopusScaber(x) → TraditionalMedicine(x))


No Elephantopus is native to the southeastern United States.


All Yale dormitories are located on York Street.

All buildings managed by Yale Housing are dormitories.

All buildings operated by Yale Housing staff are managed by Yale Housing.

No buildings open to students are established after 1800.

All buildings located on York Street are open to students.

Harkness is either a building operated by Yale Housing staff or located on York Street.

∀x (ManagedByYaleHousing(x) → YaleDormitory(x))

∀x (OperatedByYaleHousingStaffs(x) → ManagedByYaleHousing(x))

∀x (OpenToStudents(x) → ¬EstablishedAfter1800(x))

∀x (InYorkStreet(x) → OpenToStudents(x))


There are no mansion houses in an urban area.

Every creepy haunted house is in a mansion house.

Every terrifying Halloween scare comes from a creepy haunted house.

The Scream is a creepy haunted house or a terrifying Halloween scare.

∀x (CreepyHauntedHouse(x) → MansionHouse(x))

∀x (TerrifyingHalloweenScare(x) → CreepyHauntedHouse(x))


The Scream is a terrifying Halloween scare.


The Scream is either a skyscraper or a mansion house.


The Scream is either a skyscraper or an urban area.


The Scream is either a skyscraper or a creepy haunted house.


If The Scream is not a mansion in an urban area, then it is either a skyscraper or an urban area.


If The Scream is either a skyscraper or a mansion house, then it is in an urban area.


If The Scream is either a skyscraper or a mansion house, then it is neither a creepy haunted house nor a terrifying Halloween scare.


If The Scream is either a skyscraper or a creepy haunted house, then it is not a mansion house.


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 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) ∨ Mangedby(x, peoplesCommittee))


Phuoc Binh is managed by the People's Committee.


Greyhound racing is a competitive sport where spectators bet on greyhounds.

Some competitive sports where spectators bet on things are banned.

Coursing involves spectators betting on a hare being pursued by greyhounds.

If a competitive sport involves spectators betting on small game, then it is banned.

∀x ∃y (GreyhoundRacing(x) → CompetitiveSport(x) ∧ Greyhound(y) ∧ SpectatorsBetOn(x, y))

∃x ∃y (CompetitiveSport(x) ∧ SpectaorsBetOn(x, y) ∧ Banned(x))

∀x ∃y ∃z (Coursing(x) → Hare(y) ∧ SpectatorsBetOn(x, y) ∧ GreyHound(z) ∧ Pursue(z, y))

∀x ∃y (CompetitiveSport(x) ∧ SmallGame(y) ∧ SpectatorsBetOn(x, y) → Banned(x))


Greyhound racing is a competitive sport.


Henry will be ejected from the rest of the game.

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.

In one game, Henry first receives one yellow card, then he receives one red card.

∀x (SoccerPlayer(x) ∧ TwoYellow(x) → Eject(x))

∀x (SoccerPlayer(x) ∧ OneRed(x) → Eject(x))


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


All trees are plants.
Some living things are trees.

∀x (Tree(x) → Plant(x))
∃x (Living(x) ∧ Tree(x))


Notable people with the given name include Dagfinn Aarskog, Dagfinn Bakke and Dagfinn Dahl.

Dagfinn Aarskog is a Norwegian physician.

Dagfinn(dagfinnAarskog) ∧ NotablePeople(dagfinnAarskog) ∧ Dagfinn(dagfinnBakke) ∧ NotablePeople(dagfinnBakke) ∧ Dagfinn(dagfinnDahl) ∧ NotablePeople(dagfinnDahl)


Dagfinn is Dagfinn Aarskog's given name.


If entertainment is interesting, it will be well-known.

If entertainment is interesting, it will be popular.

∀x ((Entertainment(x) ∧ Interesting(x)) → Popular(x))


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.

¬(∃x (LanguageModel(x) ∧ Giant(x) ∧ ¬GoodPerformance(x)))

∀x ((LanguageModel(x) ∧ GoodPerformance(x)) → UsedBySomeResearchers(x))

∀x (UsedBySomeResearchers(x) → Popular(x))

(LanguageModel(bert) ∧ Giant(bert)) → (LanguageModel(gpt-3) ∧ Giant(gpt-3)).


At least one Scottish team has joined the Scottish Premiership.

St Johnstone is part of the Scottish Premiership.

If a team is part of the league, it has joined the league.

St Johnstone and Minsk are different teams.

For two different teams, either one team wins or the other team wins.

Different(misnk, johnstone) ∧ Different(johnstone, minsk)

∀x ∀y (Different(x, y) → WonGame(x, y) ⊕ WonGame(y, x))


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

No Boeing-737 plane is equipped with more than 300 seats.

All planes in Delta are of type Boeing-737.

Planes are either equipped with 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 in Delta.

T10 is either a Boeing-737 plane and in Delta, or neither a Boeing-737 plane nor in Delta.

∀x (Passengers100(x) → ShortDistance(x))

∀x (Passengers100(x) → ProducedBefore2010(x))


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


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


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


Since 2016 the SAT has been better aligned with high school curricula.

The SAT test is wholly owned and developed by the College Board.

The SAT test is intended to assess student's readiness for college.

The SAT was originally designed not to be aligned with high school curricula.

Several adjustments were made for the version of the SAT introduced in 2016 to reflect more closely on what students learn in high school.

Own(sat, collegeBoard) ∧ ¬Own(sat, others)

∀x (Year(x) ∧ Before2016(x) → ¬AlignHighSchool(x))

∃x (Year(x) ∧ Since2016(x) ∧ AlignHighSchool(x))


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


The SAT test assesses student's math skills.


Rafa Nadal is a professional tennis player.

All players in the Big 3 are professionals who have a high win ratio.

∀x (ProfessionalTennisPlayer(x) ∧ HighWinRatio(x) → InBig3(x))


Nadal is the greatest player of all time.


No cookie is healthy.
All oreos are cookies.

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


If Jack is a human or a flower, then Jack is a human and a flower.

Human(jack) ∨ Flower(jack) → Human(jack) ∧ Flower(jack)


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


If a watch is not airtight and clothes, then a watch is either both airtight and clothes, or neither airtight nor clothes.

¬(AirTight(watch) ∧ Clothes(watch)) → (AirTight(watch) ∧ Clothes(watch)) ⊕ (¬AirTight(watch) ∧ ¬Clothes(watch))


Watch is neither airtight 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.

∀x (DoesOlympicSport(x) ∧ GoesToOlympicGames(x) → IsOlympian(x))

∀x (IsWelterWeight(x) → ¬IsHeavyWeight(x))


Sam is a young teenage girl who attends college.

If people have a lot of decorations in their room, 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 decorations in their room.

All young teenage girls who attend college 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 (Decor(x) → ¬MoveOut(x))
∀x (Ambitious(x) → MoveOut(x))
∀x (Fans(x) → Decor(x))
∀x (CollegeTeen(x) → Ambitious(x))
Ambitious(sam) → Fans(sam)


Sam is not a young teenage girl who attends college.


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 who attends college.


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


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


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


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


A student who loves shrieking will be punished.

If a person swears, then he is a student.

If someone is a teacher, then Bob will talk to him.

If someone is not a gentlemen, then he is not nice.

∀x (Student(x) ∧ Shriek(x) → Punished(x))


Quincy McDuffie is a good wide receiver.

Quincy McDuffie is an American professional wide receiver in Canadian Football.

People who can catch balls are good wide receivers.

Quincy McDuffie can catch many footballs easily.

Good wide receivers play professionally.

Good wide receivers can catch with both their left and right hand.

American(quincymcduffie) ∧ Professional(quincymcduffie) ∧ WideReciever(quincymcduffie) ∧ In(quincymcduffie, canadianfootball)

∀x ∃y (CanCatch(x, y) ∧ Ball(y) → Good(x, widereciever))

∃x (Football(x) ∧ CanCatch(quincymcduffie, x))

∀x (Good(x, widereciever) → Professional(x))

∀x (Good(x, widereciever) → CanCatchWith(x, lefthand) ∧ CanCatchWith(x, righthand))


Professional wide receivers are good at catching balls.


Longueau is situated on the Paris–Lille railway.

Boves is a railway station located in France.

The preceding station of Boves is Longueau.

The preceding station of Dommartin is Boves.

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 A is located in B and B is located in C, then A is located in C.

If A precedes B and B preceds C, than A preceds C.

RailwayStation(boves) ∧ Locate(boves, france)

∀x ∀y ∀z ((Situate(x, z) ∧ (Precede(x, y) ∨ Precede(y, x))) → Situate(y, z))

∀x ∀y ∀z ((Locate(x, y) ∧ Locate(y, z)) → Locate(x, z))

∀x ∀y ∀z ((Precede(x, y) ∧ Precede(y, z)) → Precede(x, z))


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 buisness that was ran and owned by Edwin Smith, who was a sheetmetal worker.

From(edwinsmith, newzealand) ∧ Rower(edwinsmith) ∧ From(edwinsmith, auckland)

WentTo(edwinsmith, roseroadprimaryschool) ∧ LocatedIn(roseroadprimaryschool, greylynn)

Sergeant(edwinsmith) ∧ ServedWith(edwinsmith, newzealand24thbattalion) ∧ ServedIn(edwinsmith, italy) ∧ ServedIn(edwinsmith, egypt)

Buisness(broadwaysheetmetals) ∧ Ran(edwinsmith, broadwaysheetmetals) ∧ Owned(edwinsmith, broadwaysheetmetals) ∧ SheetmetalWorker(edwinsmith)


There are no rowers that own a buisness.


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, they have been attacked.

∀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 and was 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.

Injured people did not fight at UFC Fight Night.

Event(uFCFightNight) ∧ MixedMartial(uFCFightNight) ∧ Sweden(uFCFightNight)

Event(uFCFightNight) → ScheduledToFight(sadollah, musoke)

Event(uFCFightNight) → Fight(sadollah, akiyama)

Event(uFCFightNight) → Fight(musoke, yakovlev)


A juice is either an orange juice or an apple juice.

If coke is apple juice, then coke is a drink.

If coke is not apple juice, then coke is not edible.

∀x (Drink(x) → Edible(x))
∀x (Juice(x) → Drink(x))
∀x (OrangeJuice(x) → Juice(x))
∀x (OrangeJuice(x) ∨ AppleJuice(x))
∀x (AppleJuice(x) → Sweet(x))
AppleJuice(coke) → Drink(coke)
¬AppleJuice(coke) → ¬Edible(coke)


Daniel was not killed by the Spanish Nationalists.

Federico Garcia Lorca was a talented Spanish poet and he supported the Popular Front.

The Spanish Nationalists opposed anyone who supported the Popular Front

Spanish Nationalists killed anyone who they opposed and were popular.

Daniel supported the Popular Front but was not popular.

∀x (SupportPopulists(x) → Opposed(nationalists, x))

∀x (Opposed(nationalists, x) ∧ Popular(x) → Killed(nationalists, x))


Lorca was killed by the Spanish Nationalists.


Franny has to visit the dentist frequently.

People either drink kombucha every day or drink Coca-Cola or Pepsi products every day.

If people drink Coca-Cola or Pepsi products every day, then they grew up with extremely busy parents who did not have time to pack them lunch.

If people drink Coca-Cola or Pepsi products every day, then they have to visit the dentist frequently.

If people 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 have erratic and diverse eating habits, then they do not have consistent everyday routines and like sticking to a solid schedule.

Franny either both grew up with extremely busy parents who did not have time to pack her lunch and has consistent everyday routines and like sticking to a solid schedule, or she neither grew up with extremely busy parents who did not have time to pack her lunch nor has consistent everyday routines and likes sticking to a schedule.

(BusyParents(franny) ∧ Consistent(franny)) ⊕ (¬BusyParents(franny) ∧ ¬Consistent(franny))


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


If Franny either visits the dentist frequently or drinks kombucha every day, then Franny both visits the dentist frequently and drinks Coca-Cola or Pepsi products every day.


James is not able to watch 3 movies every week without any additional fees.

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.

∀x (SubscribedTo(x, amcalist) → ThreeMovies(x) ∧ NoFees(x))

∀x (Prefer(x, tvseries) → ¬WatchTVIn(x, cinemas))


Peter will not watch TV series in cinemas.


Bulbophyllum attenuatum is not an orchid.

Bulbophyllum attenuatum is in the genus bulbophyllum.

∀x (InGenus(x, bulbophyllum) → Orchid(x))


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

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 of Russia were established in 2000.

FederalDistrictOfRussia(central) ∨ FederalDistrictOfRussia(northwestern) ∨ FederalDistrictOfRussia(southern) ∨ FederalDistrictOfRussia(northcaucasian) ∨ FederalDistrictOfRussia(volga) ∨ FederalDistrictOfRussia(ural) ∨ FederalDistrictOfRussia(siberian) ∨ FederalDistrictOfRussia(fareastern)

∃x (FederalDistrictOfRussia(x) → EstablishedIn(x, 2000))


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


The Northwestern federal district was established in 2000.


No malignant tumor can be treated at home.

Breast cancer is neither having a cold nor a malignant tumor (exclusive).

∀x (MalignantTumor(x) → ¬CanBeTreatedAtHome(x))

∀x (HavingACold(x) → CanBeTreatedAtHome(x))


Breast cancer is colorectal cancer or a malignant tumor.


Breast cancer is colorectal cancer and a cancer.


If breast cancer is not colorectal cancer, then breast cancer is a malignant tumor.


I should not worry about things outside of my control.

∀x (OutsideControl(x) → ¬ShouldWorry(x))


Paolo Roversi uses Roversi as a surname.

Roberto Roversi uses Roversi as a surname.

A photographer is a professional or an amateur.

∀x (UseAsSurname(x, roversi) → UseItalianSurname(x))

∀x (Photographer(x) → Professional(x) ∨ Amateur(x))


There are no photographers using an Italian surname.


Hadid became a UK citizen later in her life.

Zaha Hadid is a British-Iraqi architect, artist and designer.

Zaha Hadid was born on 31 October 1950 in Baghdad, Iraq.

Hadid was a visiting professor of Architectural Design at the Yale School of Architecture.

Max is an aspiring architecture student, and he plans to apply to Yale School of Architecture.

AspiringArchitectureStudent(max) ∧ PlansToApplyTo(max, yaleSchoolofArchitecture)


FMRI provides a spatial resolution of brains.

Something 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.

∀x (InvasiveNeuroimagingTechnique(x) ∨ NoninvasiveNeuroimagingTechnique(x))

∀x (NoninvasiveNeuroimagingTechnique(x) → ProvidesSpatialResolutionOfBrains(x))

∀x (ProvidesSpatialResolutionOfBrains(x) → MeasurementOfBrainActivity(x))

∀x (MeasurementOfBrainActivity(x) → UsedByNeuroscienceResearchers(x))


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


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


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


Either present their work at the conference or provide a tutorial session at the conference.

All who present their work at the conference will attend in person.

All those providing a tutorial session at the conference are invited to join the club.

All who attend the conference in person are provided with souvenirs.

All invited to join the club are provided with delicious meals.

All provided with delicious meals are happy to communicate with each other during the dinner.

All provided with delicious meals are invited to take a photo with the audience.

James does not attend the conference in person and is not provided with souvenirs.

∀x ( Present(x) ∨ Tutorial(x))
∀x (Present(x) → InPerson(x))
∀x (Tutorial(x) → Invited(x))
∀x (InPerson(x) → Souvenirs(x))
∀x (Invited(x) → Meals(x))
∀x (Meals(x) → HappyCommunicate(x))
∀x (Meals(x) → InvitedTakePhoto(x))
¬(InPerson(james) ∧ Souvenirs(james))


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


James is invited to take a photo with the audience or is happy to communicate with each other during the dinner.


James is either invited to take a photo with the audience or happy to communicate with each other 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 served in the Atlantic and Mediterranean.

HeavyCruiser(usssalem) ∧ BuiltFor(usssalem, unitedstatesnavy)

ServedIn(usssalem, atlantic) ∧ ServedIn(usssalem, mediterranean)


There is a museum ship open to the public that served in the 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 the first Norweigian vessel that was built with stabilizers.

Stabilizers are mechanical devices that are only on ships that have 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.

∀x (TSLeda(x) → Passenger(x) ∧ CargoVessel(x))

∀x (TSLeda(x) → Norweigian(x) ∧ Stabilizers(x))

∀x (Stabilizers(x) → OnlyOnShips(x) ∧ SteamTurbine(x))

∀x (Passenger(x) ∧ CargoVessel(x) → Quiet(x) ∧ GoodSea(x))

∃x (Quiet(x) ∧ GoodSea(x) ∧ SteamTurbine(x))


TS Leda had powerful steam turbine engines.


Rosa was born in the largest city of Chile.

Santiago is the capital and largest city of Chile.

Rosa is the daughter of a Catalan building contractor, Jose.

A building contractor is responsible for the day-to-day oversight of a construction site.

Capital(santiago, chile) ∧ LargestCity(santiago, chile)

Daughter(rosa, jose) ∧ BuildingContractor(jose) ∧ ¬Chilean(jose)

∀x ∃y (BuildingContractor(x) ∧ ConstructionSite(y) → Oversee(x, y))


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


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

∀x ∀y (IsRapper(x) ∧ ReleasedAlbum(x, y) → IsRapAlbum(y))


Gasland was coproduced by the same person Homesick is from.

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 from Deborah Wallace.

BornIn(deborahwallace, scotland) ∧ Actress(deborahwallace) ∧ Playwright(deborahwallace) ∧ Producer(deborahwallace)

Play(psyche) ∧ BasedOn(psyche, lifeofjamesmirandabarry)

Play(homesick) ∧ From(homesick, deborahwallace) ∧ Play(psyche) ∧ From(psyche, deborahwallace) ∧ Play(thevoid) ∧ From(thevoid, deborahwallace)


There isn't a play from Deborah Wallace that is based on the life of James Miranda Barry.


If an animal needs a large territory, then it travels far.

Everything that eats a lot needs a large territory.

If something is a big animal, then it will eat a lot.

∀x (NeedsLargeTerritory(x) → TravelFar(x))

∀x (EatsALot(x) → NeedsLargeTerritory(x))


Larry is neither a bear nor travels far.


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


All person who breaks the law is a criminals.

If someone is evil, then they are cold-blood.

If Garry is either evil and ugly or neither evil nor ugly, then Garry is not evil.

((Evil(garry) ∧ Ugly(garry)) ⊕ (¬Evil(garry) ∧ ¬Ugly(garry))) → ¬Evil(garry)


Garry is cold-blooded and breaks the law.


If Garry is evil or breaks the law, then Garry is not both a criminal and breaking the law.


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

French bands write songs in French or in English.

Aside from indie pop, pop rock and synth-pop are two other genres of music.

∀x ∀y (Band(x) ∧ France(x) ∧ Make(x, y) → FrenchSong(y) ⊕ EnglishSong(y))

∀x (IndiePop(x) → ¬PopRock(x) ∧ ¬SynthPop(x))