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People in this club who perform in school talent shows often attend and are very engaged with school events. | ∀x (InThisClub(x) ∧ PerformOftenIn(x, schoolTalentShow) → Attend(x, schoolEvent) ∧ VeryEngagedWith(x, schoolEvent)) |
People in this club either perform in school talent shows often or are inactive and disinterested community members. | ∀x (InThisClub(x) → PerformOftenIn(x, schoolTalentShow) ⊕ (InActive(x) ∧ Disinterested(x) ∧ MemberOf(x, community))) |
People in this club who chaperone high school dances are not students who attend the school. | ∀x (InThisClub(x) ∧ Chaperone(x, highSchoolDance) → ¬(Studen(x) ∧ AttendSchool(x))) |
All people in this club who are inactive and disinterested members of their community chaperone high school dances. | ∀x (InThisClub(x) ∧ (InActive(x) ∧ Disinterested(x) ∧ MemberOf(x, community)) → Chaperone(x, highSchoolDances)) |
All young children and teenagers in this club who wish to further their academic careers and educational opportunities are students who attend the school. | ∀x (InThisClub(x) ∧ (YoungChildren(x) ⊕ Teenager(x)) ∧ WishToFurther(x, academicCareer)) → Studen(x) ∧ AttendSchool(x)) |
Bonnie is in this club and she either both attends and is very engaged with school events and is a student who attends the school or is not someone who both attends and is very engaged with school events and is not a student who attends the school. | InThisClub(bonnie) ∧ ¬((Attend(x, schoolEvent) ∧ VeryEngagedWith(bonnie, schoolEvent)) ⊕ (Studen(bonne) ∧ AttendSchool(bonnie))) |
All employees who schedule a meeting with their customers will go to the company building today. | ∀x ((Employee(x) ∧ Schedule(x, meeting, customers)) → AppearIn(x, company)) |
Everyone who has lunch in the company building schedules meetings with their customers. | ∀x ((Employee(x) ∧ HasLunch(x, company)) → Schedule(x, meeting, customers)) |
Employees have lunch either in the company building or at home. | ∀x (Employee(x) → (HasLunch(x, company) ⊕ HasLunch(x, home))) |
If an employee has lunch at home, they are working remotely from home. | ∀x ((Employee(x) ∧ HasLunch(x, home)) → Work(x, home)) |
All employees who are in other countries work remotely from home. | ∀x ((Employee(x) ∧ (¬In(x, homecountry))) → Work(x, home)) |
No managers work remotely from home. | ∀x (Manager(x) → ¬Work(x, home)) |
James will appear in the company today if and only if he is a manager. | ¬(Manager(james) ⊕ AppearIn(james, company)) |
When the Monkeypox virus occurs in a being, it may get Monkeypox. | ∃x (OccurIn(monkeypoxVirus, x) ∧ Get(x, monkeypoxVirus)) |
Monkeypox virus can occur in certain animals. | ∃x (Animal(x) ∧ OccurIn(monkeypoxVirus, x)) |
Humans are mammals. | ∀x (Human(x) → Mammal(x)) |
Mammals are animals. | ∀x (Mammal(x) → Animal(x)) |
Symptoms of Monkeypox include fever, headache, muscle pains, and tiredness. | ∃x (SymptonOf(x, monkeypoxVirus) ∧ (Fever(x) ∨ Headache(x) ∨ MusclePain(x) ∨ Tired(x))) |
People feel tired when they get the flu. | ∀x (Human(x) ∧ Get(x, flu) → Feel(x, tired)) |
There are six types of wild turkeys: Eastern wild turkey, Osceola wild turkey, Gould’s wild turkey, Merriam’s wild turkey, Rio Grande wild turkey, and Ocellated wild turkey. | ∀x (WildTurkey(x) → (EasternWildTurkey(x) ∨ OsceolaWildTurkey(x) ∨ GouldsWildTurkey(x) ∨ MerriamsWildTurkey(x) ∨ RiograndeWildTurkey(x) ∨ OcellatedWildTurkey(x))) |
Tom is not an Eastern wild turkey. | ¬(EasternWildTurkey(tom)) |
Tom is not an Osceola wild turkey. | ¬(OsceolaWildTurkey(tom)) |
Tom is not a Gould's wild turkey. | ¬(GouldsWildTurkey(tom)) |
Tom is neither a Merriam's wild turkey nor a Rio Grande wild turkey. | ¬(MerriamsWildTurkey(tom) ∨ RiograndeWildTurkey(tom)) |
Tom is a wild turkey. | WildTurkey(tom) |
A Japanese game company created the game the Legend of Zelda. | Game(theLegendofZelda) ∧ ∃x (Japanese(x) ∧ VideoGameCompany(x) ∧ Created(x, theLegendofZelda)) |
All games on the Top 10 list are made by Japanese game companies. | ∀x ∀y ((Game(x) ∧ InTop10(x) ∧ Created(y,x)) → Japanese(y)) |
If a game sells more than one million copies, then it will be included in the Top 10 list. | ∀x ((Game(x) ∧ ∃y(GreaterThan(y, oneMillion) ∧ CopiesSold(x, y))) → Top10(x))) |
The Legend of Zelda sold more than one million copies. | ∃y(GreaterThan(y, oneMillion) ∧ CopiesSold(theLegendofZelda,y)) |
All squares are four-sided. | ∀x (Square(x) → FourSided(x)) |
All four-sided things are shapes. | ∀x (FourSided(x) → Shape(x)) |
All rabbits that can be spotted near the campus are cute. | ∀x (Rabbit(x) ∧ CanBeSpottedNear(x, campus) → Cute(x)) |
Some turtles can be spotted near the campus. | ∃x (Turtle(x) ∧ CanBeSpottedNear(x, campus)) |
The only animals that can be spotted near the campus are rabbits and squirrels. | ∀x (CanBeSpottedNear(x, campus) → (Rabbit(x) ⊕ Squirrel(x))) |
If something is skittish, then it is not calm. | ∀x (Skittish(x) → ¬Calm(x)) |
All the squirrels that can be spotted near the campus are skittish. | ∀x (Squirrel(x) ∧ CanBeSpottedNear(x, campus) → Skittish(x)) |
Rockie can be spotted near the campus, and it is calm. | CanBeSpottedNear(rockie, campus) ∧ Calm(rockie) |
"Stranger Things" is a popular Netflix show. | NetflixShow(strangerThings) ∧ Popular(strangerThings) |
If a Netflix show is popular, Karen will binge-watch it. | ∀x ((NetflixShow(x) ∧ Popular(x)) → BingeWatch(karen, x)) |
If and only if Karen binge-watches a Netflix show, she will download it. | ∀x ((NetflixShow(x) ∧ BingeWatch(karen, x)) ↔ Download(karen, x)) |
Karen does not download "Black Mirror." | ¬Download(karen, blackMirror) |
"Black Mirror" is a Netflix show. | NetflixShow(blackMirror) |
If Karen binge-watches a Netflix show, she will share it with Lisa. | ∀x ((NetflixShow(x) ∧ BingeWatch(karen, x)) → ShareWith(karen, x, lisa)) |
Beijing is the capital of the People's Republic of China. | CapitalOf(beijing, peoplesRepublicOfChina) |
Beijing is the capital city of the world's most populous nation. | ∃x (CapitalOf(beijing, x) → WorldsMostPopulousNation(x)) |
Beijing is located in Northern China. | LocatedIn(beijing, northernChina) |
Beijing hosted the 2008 Summer Olympics and 2008 Summer Paralympics Games. | Hosted(beijing, 2008SummerOlympics) ∧ Hosted(beijing, 2008SummerParalympicGames) |
Beijing has hosted the Summer and Winter Olympics and the Summer and Winter Paralympics. | Hosted(beijing, summerOlympics) ∧ Hosted(beijing, winterOlympics) ∧ Hosted(beijing, summerParalympicGames) ∧ Hosted(beijing, winterParalympicGames) |
Many of Beijing's 91 universities consistently rank among the best universities in the world. | ∃x (University(x) ∧ InBeijing(x) ∧ ConsistentlyRankAmongTheBestIn(x, theWorld)) |
All aliens are extraterrestrials. | ∀x (Alien(x) → Extraterrestrial(x)) |
If someone is from Mars, then they are an alien. | ∀x (From(x, mars) → Alien(x)) |
No extraterrestrials are human. | ∀x (Extraterrestrial(x) → ¬Human(x)) |
All highly intelligent beings from Earth are humans. | ∀x (HighlyIntelligentBeing(x) ∧ From(x, earth) → Human(x)) |
Marvin is a highly intelligent being. | HighlyIntelligentBeing(marvin) |
Marvin is either from Earth and from Mars, or he is from neither. | ¬(From(marvin, earth) ⊕ From(marvin, mars)) |
If Marvin is not from Earth, then Marvin is an extraterrestrial. | ¬From(marvin, earth) → Extraterrestrial(marvin) |
Everyone at the mixer is a Grand Slam champion or an Oscar-nominated actor. | ∀x (At(x, mixer) → (GrandSlam(x) ∧ Champion(x)) ∨ (OscarNominated(x) ∧ Actor(x))) |
Every Grand Slam champion at the mixer is a professional tennis player. | ∀x (At(x, mixer) ∧ (GrandSlam(x) ∧ Champion(x) → Professional(x) ∧ TennisPlayer(x)) |
All Oscar-nominated actors at the mixer are celebrities. | ∀x (At(x, mixer) ∧ (OscarNominated(x) ∧ Actor(x) → Celebrity(x)) |
All professional tennis players at the mixer are athletes. | ∀x (At(x, mixer) ∧ Professional(x) ∧ TennisPlayer(x) → Athlete(x)) |
If a person at the mixer is a celebrity, then they are well paid. | ∀x (At(x, mixer) ∧ Celebrity(x) → WellPaid(x)) |
If a person at the mixer is an athlete, then they are famous. | ∀x (At(x, mixer) ∧ Athlete(x) → Famous(x)) |
All well-paid people at the mixer live in tax havens. | ∀x (At(x, mixer) ∧ WellPaid(x) → LiveIn(x, taxHaven)) |
Djokovic is at the mixer: if Djokovic is a famous athlete, then Djokovic is well-paid. | At(djokovic, mixer) ∧ (Famous(djokovic) ∧ Athlete(djokovic) → WellPaid(djokovic)) |
Diamond Mine is a professional wrestling stable formed in WWE. | ProfessionalWrestlingStable(diamondMine) ∧ In(diamondMine, wWE) |
Roderick Strong leads Diamond Mine. | Leads(roderickStrong, diamondMine) |
Diamond Mine includes the Creed Brothers and Ivy Nile. | Includes(diamondMine, creedBrothers) ∧ Includes(diamondMine, ivyNile) |
Imperium has a feud with Diamond Mine. | Feuds(imperium, diamondMine) |
Symphony No. 9 is a music piece. | MusicPiece(symphony9) |
Composers write music pieces. | ∀x (MusicPiece(x) → ∃y (Composer(y) ∧ Write(y, x))) |
Beethoven wrote Symphony No. 9. | Writtenby(symphony9, beethoven) |
Vienna Music Society premiered Symphony No. 9. | Premiered(viennaMusicSociety, symphony9) |
Vienna Music Society is an orchestra. | Orchestra(viennaMusicSociety) |
Beethoven leads the Vienna Music Society. | Lead(beethoven, viennaMusicSociety) |
Orchestras are led by conductors. | ∀x (Orchestra(x) → (∃y Conductor(y) ∧ Lead(y, x))) |
All of Zaha Hadid's design styles that Max adores have interesting geometries. | ∀x (Adore(max, x) ∧ ZahaHadid(x) ∧ DesignStyle(x) → InterestingGeometry(x)) |
No brutalist buildings that Max adores have interesting geometries. | ∀x (Adore(max, x) ∧ BrutalistBuilding(x) → ¬InterestingGeometry(x)) |
Every style that Max adores is either Zaha Hadid's design style or Kelly Wearstler's design style. | ∀x (Adore(max, x) → ((ZahaHadid(x) ∧ DesignStyle(x)) ⊕ (KellyWearstler(x) ∧ DesignStyle(x))) |
All of Kelly Wearstler's design styles that Max adores are evocative. | ∀x (Adore(max, x) ∧ KellyWearstler(x) ∧ DesignStyle(x) → Evocative(x)) |
All of Kelly Wearstler's design styles that Max adores are dreamy. | ∀x (Adore(max, x) ∧ KellyWearstler(x) ∧ DesignStyle(x) → Dreamy(x)) |
If a design by Max that he adores has interesting geometries, then the design is a brutalist building and evocative. | ∃x (Adore(max, x) ∧ Design(x) ∧ ByMax(x) ∧ InterestingGeometry(x) → BrutalistBuilding(x) ∧ Evocative(x)) |
If someone is ranked highly by the Women's Tennis Association, then they are one of the most active players in major tennis. | ∀x (RankedHighlyBy(x, womensTennisAssociation) → MostActivePlayerIn(x, majorTennis)) |
Everyone who lost to Iga Świątek at Roland Garros 2022 is ranked highly by the Women's Tennis Association. | ∀x (LostTo(x, świątek) ∧ At(x, rolandGarros2022) → RankedHighlyBy(x, womensTennisAssociation)) |
All female tennis players at Roland Garros 2022 lost to Iga Świątek. | ∀x (FemaleTennisPlayer(x) ∧ At(x, rolandGarros2022) → LostTo(x, świątek) ∧ At(x, rolandGarros2022)) |
All tennis players at Roland Garros 2022 are either female or male. | ∀x (TennisPlayer(x) ∧ At(x, rolandGarros2022) → (Female(x) ∧ TennisPlayer(x)) ⊕ (Male(x) ∧ TennisPlayer(x))) |
All male tennis players at Roland Garros in 2022 lost to Rafael Nadal. | ∀x (Male(x) ∧ TennisPlayer(x) ∧ At(x, rolandGarros2022) → LostTo(x, świątek) ∧ At(x, rolandGarros2022)) |
If Coco Gauff is ranked highly by the Women's Tennis Association or lost to Rafael Nadal, then Coco Gauff is not a male tennis player at Roland Garros 2022. | RankedHighlyBy(cocoGauff, womensTennisAssociation) ∨ (LostTo(cocoGauff, świątek) ∧ LostAt(cocoGauff, rolandGarros2022)) → ¬(Male(cocoGauff) ∧ TennisPlayer(cocoGauff) ∧ AtRolandGarros2022(cocoGauff)) |
Coco Gauff is at Roland Garros 2022. | TennisPlayer(cocoGauff) ∧ At(cocoGauff, rolandGarros2022) |
All cats are mammals. | ∀x (Cat(x) → Mammal(x)) |
Some pets are not mammals. | ∃x (Pet(x) ∧ ¬Mammal(x)) |
There are four seasons in a year: Spring, Summer, Fall, and Winter. | Season(spring) ∨ Season(summer) ∨ Season(fall) ∨ Season(winter) ∧ (Season(spring) → ¬Season(summer) ∧ ¬Season(fall) ∧ ¬Season(winter)) ∧ (Season(summer) → ¬Season(spring) ∧ ¬Season(fall) ∧ ¬Season(winter)) ∧ (Season(fall) → ¬Season(spring) ∧ ¬Season(summer) ∧ ¬Season(winter)) ∧ (Season(winter) → ¬Season(spring) ∧ ¬Season(summer) ∧ ¬Season(fall)) |
All students who want to have a long vacation have summer as their favorite season. | ∀x (Want(x, longvacation) → Favorite(x, summer)) |
Emma's favorite season is summer. | Favorite(emma, summer) |
Mia's favorite season is not the same as Emma's. | ∀x ∀y (Season(x) ∧ Season(y) ∧ Favorite(mia, x) ∧ Favorite(emma, y) → ¬(x=y)) |
James wants to have a long vacation. | Want(james, longVacation) |
No digital media are analog. | ∀x (DigitalMedia(x) → ¬AnalogMedia(x)) |
Every printed text is analog media. | ∀x (PrintedText(x) → AnalogMedia(x)) |
All streaming services are digital media. | ∀x (StreamingService(x) → DigitalMedia(x)) |
If an object is a hardcover book, then it is printed text. | ∀x (HardcoverBook(x) → PrintedText(x)) |
If 1984 is a streaming service, then 1984 is a hardcover book. | StreamingService(1984) → HardcoverBook(1984) |
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