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All people who regularly drink coffee are dependent on caffeine. People regularly drink coffee, or they don't want to be addicted to caffeine, or both. No one who doesn't want to be addicted to caffeine is unaware that caffeine is a drug. Rina is either a student who is dependent on caffeine, or she is not a student and not dependent on caffeine.
Rina doesn't want to be addicted to caffeine or is unaware that caffeine is a drug.
¬WantToBeAddictedTo(rina, caffeine) ∨ (¬AwareThatDrug(rina, caffeine))
Rina is either a student who is unaware that caffeine is a drug, or she is not a student and is she aware that caffeine is a drug.
0
False
∀x (DrinkRegularly(x, coffee) → IsDependentOn(x, caffeine)) ∀x (DrinkRegularly(x, coffee) ∨ (¬WantToBeAddictedTo(x, caffeine))) ∀x (¬WantToBeAddictedTo(x, caffeine) → ¬AwareThatDrug(x, caffeine)) ¬(IsDependentOn(rina, caffeine) ⊕ Student(rina))
¬(Student(rina) ⊕ ¬AwareThatDrug(rina, caffeine))
All people who regularly drink coffee are dependent on caffeine. People regularly drink coffee, or they don't want to be addicted to caffeine, or both. No one who doesn't want to be addicted to caffeine is unaware that caffeine is a drug. Rina is either a student who is unaware that caffeine is a drug, or she is not a student and is she aware that caffeine is a drug. Rina is either a student who is dependent on caffeine, or she is not a student and not dependent on caffeine.
Rina eith doesn't want to be addicted to caffeine or is unaware that caffeine is a drug.
¬WantToBeAddictedTo(rina, caffeine) ⊕ ¬AwareThatDrug(rina, caffeine)
None
1
True
∀x (DrinkRegularly(x, coffee) → IsDependentOn(x, caffeine)) ∀x (DrinkRegularly(x, coffee) ∨ (¬WantToBeAddictedTo(x, caffeine))) ∀x (¬WantToBeAddictedTo(x, caffeine) → ¬AwareThatDrug(x, caffeine)) ¬(Student(rina) ⊕ ¬AwareThatDrug(rina, caffeine)) ¬(IsDependentOn(rina, caffeine) ⊕ Student(rina))
None
All people who regularly drink coffee are dependent on caffeine. People regularly drink coffee, or they don't want to be addicted to caffeine, or both. Rina is either a student who is unaware that caffeine is a drug, or she is not a student and is she aware that caffeine is a drug. Rina is either a student who is dependent on caffeine, or she is not a student and not dependent on caffeine.
If Rina either doesn't want to be addicted to caffeine and is unaware that caffeine is a drug, or neither doesn't want to be addicted to caffeine nor is unaware that caffeine is a drug, then Rina doesn't want to be addicted to caffeine and regularly drinks coffee.
(DoNotWantToBeAddictedToCaffeine(rina) ⊕ ¬AwareThatDrug(rina, caffeine)) → ¬(¬WantToBeAddictedTo(rina, caffeine) ∧ DrinkRegularly(rina, coffee))
No one who doesn't want to be addicted to caffeine is unaware that caffeine is a drug.
2
False
∀x (DrinkRegularly(x, coffee) → IsDependentOn(x, caffeine)) ∀x (DrinkRegularly(x, coffee) ∨ (¬WantToBeAddictedTo(x, caffeine))) ¬(Student(rina) ⊕ ¬AwareThatDrug(rina, caffeine)) ¬(IsDependentOn(rina, caffeine) ⊕ Student(rina))
∀x (¬WantToBeAddictedTo(x, caffeine) → ¬AwareThatDrug(x, caffeine))
Miroslav Venhoda was a Czech choral conductor who specialized in the performance of Renaissance and Baroque music. Any choral conductor is a musician. Miroslav Venhoda published a book in 1946 called Method of Studying Gregorian Chant.
A Czech published a book in 1946.
∃x ∃y (Czech(x) ∧ PublishedBook(x, y, year1946))
Some musicians love music.
3
False
Czech(miroslav) ∧ ChoralConductor(miroslav) ∧ SpecializeInPerformanceOf(miroslav, renaissanceMusic) ∧ SpecializeInPerformanceOf(miroslav, baroqueMusic) ∀x (ChoralConductor(x) → Musician(x)) PublishedBook(miroslav, methodOfStudyingGregorianChant, yr1946)
∃x ∃y ((Musician(x) → Love(x, music)) ∧ (¬(x=y) ∧ Musician(y) → Love(y, music)))
All eels are fish. No fish are plants. Everything displayed in the collection is either a plant or an animal. All multicellular animals are not bacteria. All animals displayed in the collection are multicellular. A sea eel is displayed in the collection. The sea eel is an eel or an animal or not a plant.
The sea eel is multicellular or is bacteria.
Multicellular(seaEel) ∨ Bacteria(seaEel)
None
4
True
∀x (Eel(x) → Fish(x)) ∀x (Fish(x) → ¬Plant(x)) ∀x (DisplayedIn(x, collection) → Plant(x) ⊕ Animal(x)) ∀x (Multicellular(x) → ¬Bacteria(x)) ∀x (DisplayedIn(x, collection) ∧ Animal(x) → Multicellular(x)) DisplayedIn(seaEel, collection) Eel(seaEel) ∨ Animal(seaEel) ∨ ¬Plant(seaEel)
None
The Emmet Building is a five-story building in Portland, Oregon. The Emmet Building was built in 1915. The Emmet Building is another name for the Blake McFall Company Building. John works at the Emmet Building.
A five-story building is built in 1915.
∃x (Building(x) ∧ Five-Story(x) ∧ ConstructedIn(x, year1915))
The Blake McFall Company Building is a building added to the National Register of Historic Places in 1990.
5
False
Building(emmetBuilding) ∧ Five-Story(emmetBuilding) ∧ LocatedIn(emmetBuilding, portland) ∧ LocatedIn(portland, oregon)) BuiltIn(emmetBuilding, year1915) emmetBuiling=blakeMcFallCompanyBuilding WorkAt(john, emmetBuilding)
Building(blakeMcFallCompanyBuilding) ∧ AddedToIn(blakeMcFallCompanyBuilding, theNationalRegisterOfHistoricPlaces, year1990)
The Blake McFall Company Building is a building added to the National Register of Historic Places in 1990. The Emmet Building is a five-story building in Portland, Oregon. The Emmet Building was built in 1915. The Emmet Building is another name for the Blake McFall Company Building. John works at the Emmet Building.
The Blake McFall Company Building is located in Portland, Oregon.
LocatedIn(blakeMcFallCompanyBuilding, portland)
None
6
True
Building(blakeMcFallCompanyBuilding) ∧ AddedToIn(blakeMcFallCompanyBuilding, theNationalRegisterOfHistoricPlaces, year1990) Building(emmetBuilding) ∧ Five-Story(emmetBuilding) ∧ LocatedIn(emmetBuilding, portland) ∧ LocatedIn(portland, oregon)) BuiltIn(emmetBuilding, year1915) emmetBuiling=blakeMcFallCompanyBuilding WorkAt(john, emmetBuilding)
None
William Dickinson was a British politician who sat in the House of Commons The University of Edinburgh is a university located in the United Kingdom. William Dickinson supported the Portland Whigs. People who supported the Portland Whigs did not get a seat in the Parliament.
William Dickinson did not get a seat in Parliament.
SatIn(williamDickinson, parliament)
William Dickinson attended Westminster school for high school and then the University of Edinburgh.
7
False
British(williamDickinson) ∧ Politician(williamDickinson) ∧ SatIn(williamDickinson, houseOfCommons) University(universityOfEdinburgh) ∧ LocatedIn(universityOfEdinburgh, unitedKingdom) Supported(williamDickinson, portlandWhigs) ∀x (Supported(x, portlandWhigs) → ¬SatIn(x, parliament))
Attended(williamDickinson, westminsterSchool) ∧ Highschool(westminsterSchool) ∧ Attended(williamDickinson, universityOfEdinburgh)
William Dickinson was a British politician who sat in the House of Commons The University of Edinburgh is a university located in the United Kingdom. William Dickinson supported the Portland Whigs. People who supported the Portland Whigs did not get a seat in the Parliament.
William Dickinson attended university in the United Kingdom.
∃x (Attended(williamDickinson, x) ∧ University(x) ∧ LocatedIn(x, unitedKingdom))
William Dickinson attended Westminster school for high school and then the University of Edinburgh.
8
False
British(williamDickinson) ∧ Politician(williamDickinson) ∧ SatIn(williamDickinson, houseOfCommons) University(universityOfEdinburgh) ∧ LocatedIn(universityOfEdinburgh, unitedKingdom) Supported(williamDickinson, portlandWhigs) ∀x (Supported(x, portlandWhigs) → ¬SatIn(x, parliament))
Attended(williamDickinson, westminsterSchool) ∧ Highschool(westminsterSchool) ∧ Attended(williamDickinson, universityOfEdinburgh)
William Dickinson was a British politician who sat in the House of Commons William Dickinson attended Westminster school for high school and then the University of Edinburgh. The University of Edinburgh is a university located in the United Kingdom. William Dickinson supported the Portland Whigs. People who supported the Portland Whigs did not get a seat in the Parliament.
William Dickinson sat in the House of Commons.
SatIn(williamDickinson, houseOfCommons)
None
9
True
British(williamDickinson) ∧ Politician(williamDickinson) ∧ SatIn(williamDickinson, houseOfCommons) Attended(williamDickinson, westminsterSchool) ∧ Highschool(westminsterSchool) ∧ Attended(williamDickinson, universityOfEdinburgh) University(universityOfEdinburgh) ∧ LocatedIn(universityOfEdinburgh, unitedKingdom) Supported(williamDickinson, portlandWhigs) ∀x (Supported(x, portlandWhigs) → ¬SatIn(x, parliament))
None
All customers in James' family who subscribe to AMC A-List are eligible to watch three movies every week without any additional fees. Some of the customers in James' family go to the cinema every week. Customers in James' family subscribe to AMC A-List or HBO service. Customers in James' family who prefer TV series will not watch TV series in cinemas. All customers in James' family who subscribe to HBO services prefer TV series to movies. Lily is in James' family; she watches TV series in cinemas.
Lily goes to cinemas every week or watches 3 movies every week without any additional fees.
GoToEveryWeek(lily, cinema) ∨ EligibleForThreeFreeMoviesWithoutAdditionalFees(lily)
None
10
True
∀x ((Customer(x) ∧ In(x, jameSFamily) ∧ SubscribedTo(x, aMCAList)) → EligibleForThreeFreeMoviesEveryWeekWithoutAdditionalFees(x)) ∃x ∃y (Customer(x) ∧ In(x, jameSFamily) ∧ GoToEveryWeek(x, cinema) ∧ (¬(x=y)) ∧ Customer(y) ∧ In(y, jameSFamily) ∧ GoToEveryWeek(y, cinema)) ∀x (Customer(x) ∧ In(x, jameSFamily) ∧ (SubscribedTo(x, aMCAList) ∨ SubscribedTo(x, hBO))) ∀x ((Customer(x) ∧ In(x, jameSFamily) ∧ Prefer(x, tVSeries)) → (¬WatchIn(x, tV, cinema))) ∀x ((Customer(x) ∧ In(x, jameSFamily) ∧ SubscribedTo(x, hBO)) → Prefer(x, tVSeries)) Customer(lily) ∧ In(lily, jameSFamily ∧ WatchIn(lily, tV, cinema)
None
All customers in James' family who subscribe to AMC A-List are eligible to watch three movies every week without any additional fees. Some of the customers in James' family go to the cinema every week. Customers in James' family subscribe to AMC A-List or HBO service. Customers in James' family who prefer TV series will not watch TV series in cinemas. All customers in James' family who subscribe to HBO services prefer TV series to movies. Lily is in James' family; she watches TV series in cinemas.
If Lily does not both go to cinemas every week and subscribe to HBO service, then Lily is either available to watch 3 movies every week without any additional fees or she prefers TV more.
(GoToEveryWeek(lily, cinema) ∧ SubscribedTo(lily, hBO)) → (EligibleForThreeFreeMoviesEveryWeek(lily) ⊕ Prefer(lily, tVSeries))
None
11
True
∀x ((Customer(x) ∧ In(x, jameSFamily) ∧ SubscribedTo(x, aMCAList)) → EligibleForThreeFreeMoviesEveryWeekWithoutAdditionalFees(x)) ∃x ∃y (Customer(x) ∧ In(x, jameSFamily) ∧ GoToEveryWeek(x, cinema) ∧ (¬(x=y)) ∧ Customer(y) ∧ In(y, jameSFamily) ∧ GoToEveryWeek(y, cinema)) ∀x (Customer(x) ∧ In(x, jameSFamily) ∧ (SubscribedTo(x, aMCAList) ∨ SubscribedTo(x, hBO))) ∀x ((Customer(x) ∧ In(x, jameSFamily) ∧ Prefer(x, tVSeries)) → (¬WatchIn(x, tV, cinema))) ∀x ((Customer(x) ∧ In(x, jameSFamily) ∧ SubscribedTo(x, hBO)) → Prefer(x, tVSeries)) Customer(lily) ∧ In(lily, jameSFamily ∧ WatchIn(lily, tV, cinema)
None
A La Liga soccer team ranks higher than another La Liga soccer team if it receives more points. Real Madrid and Barcelona are both La Liga soccer teams. Real Madrid received more points than Barcelona. Neither Real Madrid nor Barcelona received more points from the games between them.
Real Madrid ranks higher than Barcelona.
RankHigherThan(realMadrid, barcelona)
If there are two La Liga soccer teams and neither has more points than the other, then the team which receives more points from the games between the two teams ranks higher.
12
True
∀x ∀y (LaLigaSoccerTeam(x) ∧ LaLigaSoccerTeam(y) ∧ MorePoints(x, y) → RankHigherThan(x, y)) LaLigaSoccerTeam(realMadrid) ∧ LaLigaSoccerTeam(barcelona) MorePoints(realMadrid, barcelona) ¬MorePointsInGameBetween(realMadrid, barcelona) ∧ ¬MorePointsInGameBetween(barcelona, realMadrid)
∀x ∀y (LaLigaSoccerTeam(x) ∧ LaLigaSoccerTeam(y) ∧ ¬MorePoints(x, y) ∧ ¬MorePoints(y, x) ∧ MorePointsInGameBetween(x, y) → RankHigherThan(x, y))
Lawton Park is a neighborhood in Seattle. Tom is a citizen of Lawton Park. Daniel uses the zip code 98199.
Tom uses the zip code 98199.
UseZipCode(tom, num98199)
All citizens of Lawton Park use the zip code 98199.
13
False
NeighbourhoodIn(lawtonPark, seattle) ResidentOf(tom, lawtonPark) UseZipCode(daniel, num98199)
∀x (Residentof(x, lawtonPark) → UseZipCode(x, num98199))
Tiffany T. Alston was a legislator in Maryland's House of Delegates from 2011 to 2013. Tiffany T. Alston was found guilty of stealing government funds in 2012.
Tiffany T. Alston was suspended from the Maryland House of Delegates.
Suspended(tiffanyTAlston)
If a legislator is found guilty of stealing government funds, they will be suspended from office.
14
False
Legislator(tiffanyTAlston) StealsFunds(tiffanyTAlston) ∧ StealsFundsInYr(tiffanyTAlston, yr2012)
∀x ((Legislator(x) ∧ StealsFunds(x)) → Suspended(x))
Some fish stings people. Stonefish is a fish. Stonefish stings when stepped on. If a stonefish stings someone and they are not treated, it can cause death to them. To treat stonefish stings, apply heat to the affected area or use an antivenom.
Stings of some fish can cause death if not treated.
∃x ∃y (Fish(x) ∧ Sting(x, y) ∧ ¬Treated(y) → CauseDeathTo(x, y))
None
15
True
∃x ∃y (Fish(x) → Sting(x,y)) Fish(stonefish) ∀x (SteppedOnBy(stonefish, x) → Sting(stonefish, x)) ∀x (Sting(stonefish, x) ∧ ¬Treated(x) → CauseDeathTo(stonefish, x)) ∀x (Sting(stonefish, x) ∧ (ApplyHeatTo(x) ∨ UseAntivenomOn(x)) → Treated(x))
None
Some monitors made by LG have a type-c port. Monitors that have a type-c port were not made before 2010. The L-2021 monitor is either used in the library or has a type-c port. The L-2021 monitor is either both produced before 2010 and made by LG, or neither is true.
The L-2021 monitor either has a type-c port or is produced by LG.
Have(l-2021, typeCPort) ⊕ ProducedBy(l-2021, lG)
All monitors in the library are made before 2010.
16
False
∃x (Monitor(x) ∧ ProducedBy(x, lG) ∧ Have(x, typeCPort) ∧ (¬(x=y)) ∧ Monitor(y) ∧ ProducedBy(y, lG) ∧ Have(y, typeCPort)) ∀x (Have(x, typeCPort) → ¬ProducedBefore(x, yr2010)) Monitor(l-2021) ∧ (In(l-2021, library) ⊕ Have(l-2021, typeCPort)) ¬(ProducedBefore(l-2021, yr2010) ⊕ ProducedBy(l-2021, lG))
∀x ((Monitor(x) ∧ In(x, library)) → ProducedBefore(x, yr2010))
Everything is either outside the solar system or in the solar system. Nothing outside the solar system has the Sun as its star. No planets gravitationally bound by the Sun are rogue planets. All orphan planets are rogue planets. If PSO J318.5−22 is not both a rogue planet and a planet gravitationally bound by the Sun, then it is a rogue planet.
PSO J318.5−22 is an orphan planet or it does not have the Sun as its star, or both.
(Planet(pSOJ318.5-22) ∧ Orphan(pSOJ318.5-22)) ∨ ¬SunAs(pSOJ318.5-22, star)
Everything in the solar system is gravitationally bound by the Sun.
17
False
∀x (Outside(x, solarSystem) ⊕ In(x, solarSystem)) ∀x (Outside(x, solarSystem) → ¬SunAs(x, star)) ∀x (Planet(x) ∧ BoundBy(x, sun, gravitationally) → ¬(Planet(x) ∧ Rogue(x))) ∀x (Planet(x) ∧ Orphan(x) → Planet(x) ∧ Rogue(x)) ¬(Planet(pSOJ318.5-22) ∧ Rogue(pSOJ318.5-22) ∧ BoundBy(pSOJ318.5-22, sun, gravitationally)) → (Planet(pSOJ318.5-22) ∧ Rogue(pSOJ318.5-22))
∀x (In(x, solarSystem) → BoundBy(x, sun, gravitationally))
Sam is doing a project. A project is written either in C++ or Python. If Sam does a project written in Python, he will not use a Mac. If Sam uses a Mac, he will play a song. If a song is not titled "Perfect," Sam will never play it.
The project Sam is doing is written in C++.
∀x (Project(x) ∧ Do(sam, x) ∧ WrittenIn(x, cplusplus))
Sam is using a Mac.
18
False
∃x (Project(x) ∧ Do(sam, x)) ∀x (Project(x) → (WrittenIn(x, cplusplus) ⊕ WrittenIn(x, python))) ∀x (Project(x) ∧ WrittenIn(x, python) ∧ Do(sam, x) → ¬Use(sam, mac)) ∃x (Use(sam, mac) ∧ Song(x) → Play(sam, x)) ∀x (Song(x) ∧ Play(sam, x) → Titled(x, perfect))
Use(sam, mac)
All social media applications containing chat features are software. All social media applications that allow users to send messages to each other have chat features. All social media applications have chat features or video features. All social media applications that have video features allow users to upload videos. All social media applications that have high engagement metrics are addictive. If a social media application is addictive, then it is not ideal for preteens. TikTok is a social media application, and it is not ideal for preteens.
TikTok is a computer program.
ComputerProgram(tikTok)
All software that is social media applications are computer programs.
19
False
∀x (SocialMedia(x) ∧ Application(x) ∧ Contain(x, chatFeature) → Software(x)) ∀x (SocialMedia(x) ∧ Application(x) ∧ AllowToSendTo(x, user, message) → Contain(x, chatFeature)) ∀x (SocialMedia(x) ∧ Application(x) → Contain(x, chatFeature) ∨ Contain(x, videoFeature)) ∀x (SocialMedia(x) ∧ Application(x) ∧ Contain(x, videoFeature) → Allow(x, user, uploadVideo)) ∀x (SocialMedia(x) ∧ Application(x) ∧Have(x, highEngagementMetric) → Addictive(x)) ∀x (SocialMedia(x) ∧ Application(x) ∧ Addictive(x) → ¬IdealFor(x, preteen)) SocialMedia(tikTok) ∧ Application(tikTok) ∧ ¬IdealFor(tikTok, preteen)
∀x (SocialMedia(x) ∧ Application(x) ∧ Software(x) → ComputerProgram(x))
All social media applications containing chat features are software. All social media applications that allow users to send messages to each other have chat features. All social media applications have chat features or video features. All social media applications that have video features allow users to upload videos. All software that is social media applications are computer programs. All social media applications that have high engagement metrics are addictive. If a social media application is addictive, then it is not ideal for preteens. TikTok is a social media application, and it is not ideal for preteens.
TikTok is either ideal for preteens or a computer program.
IdealFor(tikTok, preteen) ⊕ ComputerProgram(tikTok)
None
20
True
∀x (SocialMedia(x) ∧ Application(x) ∧ Contain(x, chatFeature) → Software(x)) ∀x (SocialMedia(x) ∧ Application(x) ∧ AllowToSendTo(x, user, message) → Contain(x, chatFeature)) ∀x (SocialMedia(x) ∧ Application(x) → Contain(x, chatFeature) ∨ Contain(x, videoFeature)) ∀x (SocialMedia(x) ∧ Application(x) ∧ Contain(x, videoFeature) → Allow(x, user, uploadVideo)) ∀x (SocialMedia(x) ∧ Application(x) ∧ Software(x) → ComputerProgram(x)) ∀x (SocialMedia(x) ∧ Application(x) ∧Have(x, highEngagementMetric) → Addictive(x)) ∀x (SocialMedia(x) ∧ Application(x) ∧ Addictive(x) → ¬IdealFor(x, preteen)) SocialMedia(tikTok) ∧ Application(tikTok) ∧ ¬IdealFor(tikTok, preteen)
None
Ordinary is an unincorporated community. Located within Elliot County, Ordinary is on Kentucky Route 32.
There is an unincorporated community located in Elliot County.
∃x (UnincorporatedCommunity(x) ∧ LocatedIn(x, elliotCounty))
Ordinary is located northwest of Sandy Hook.
21
True
UnincorporatedCommunity(ordinary) LocatedIn(ordinary, elliotCounty) ∧ On(ordinary, kentuckyRoute32)
LocatedNorthwestOf(ordinary, sandyHook)
All young adults at the event like independence. All college students at the event are young adults. All Yale students at the event are college students. Everyone at the event is a Yale student or a Harvard student. All Harvard students at the event are diligent. Susan is at the event, and if Susan is a Harvard student, then she is a young adult. If Susan is a Yale student, then she does not like independence.
Susan likes independence and is diligent.
Like(susan, independence) ∧ Diligent(susan)
None
22
True
∀x (At(x, event) ∧ YoungAdult(x) → Like(x, independence)) ∀x (At(x, event) ∧ CollegeStudent(x) → YoungAdult(x)) ∀x (At(x, event) ∧ YaleStudent(x) → CollegeStudent(x)) ∀x (At(x, event) → (YaleStudent(x) ⊕ HarvardStudent(x))) ∀x (At(x, event) ∧ HarvardStudent(x) → Diligent(x)) At(susan, event) ∧ (HarvardStudent(susan) → YoungAdult(susan)) YaleStudent(susan) → ¬Like(susan, independence)
None
The only style of music Vic DiCara plays is punk music. Vic DiCara played in the band Inside Out.
A musician from Inside Out plays bass.
∃x (Band(x, insideOut) ∧ Play(x, bass))
Vic DiCara plays guitar and bass.
23
False
∀x (Music(vicDicara, x) → ¬(x=punk))) Band(vicDicara, insideOut)
Play(vicDicara, guitar) ∧ Play(vicDicara, bass)
All Olympic gold medal winners are professional athletes. No full-time scientists spend the majority of their time on sports. All Nobel physics laureates are full-time scientists. Amy spends the most time on sports, or Amy is an Olympic gold medal winner. If Amy is not a Nobel physics laureate, then Amy is not an Olympic gold medal winner.
Amy is neither a full-time scientist nor an Olympic gold medal winner.
¬(FullTimeScientist(amy) ∨ OlympicGoldMedalWinner(amy))
All professional athletes spend most of their time on sports.
24
False
∀x (OlympicGoldMedalWinner(x) → ProfessionalAthlete(x)) ∀x (FullTimeScientist(x) → ¬SpendOn(x, mostOfTheirTime, sports)) ∀x (NobelPhysicsLaureate(x) → FullTimeScientist(x)) SpendOn(amy, mostOfTheirTime, sports) ∨ OlympicGoldMedalWinner(amy) ¬NobelPhysicsLaureate(amy) → ¬OlympicGoldMedalWinner(amy)
∀x (ProfessionalAthlete(x) → SpendOn(x, mostOfTheirTime, sports))
All red fruits that grow in Ben's yard contain some Vitamin C. All apples that grow in Ben's yard are red fruits. All fruits that grow in Ben's yard and contain some Vitamin C are healthy. No fruits that grow in Ben's yard and are healthy are on a warning list. The cherries grow in Ben's yard. If cherries are not apples and are not healthy, then they are red fruits.
The cherries either contain some amount of vitamin C or are on a warning list.
Contain(cherry, vitaminC) ⊕ On(cherry, warningList)
None
25
True
∀x ((GrownIn(x, benSYard) ∧ RedFruit(x)) → Contain(x, vitaminC)) ∀x (GrownIn(x, benSYard) ∧ Is(x, apple) → RedFruit(x)) ∀x ((GrownIn(x, benSYard) ∧ Contain(x, vitaminC)) → healthy(x)) ∀x ((GrownIn(x, benSYard) ∧ Healthy(x)) → ¬On(x, warningList)) GrownIn(cherry, benSYard) ¬(Healthy(cherry) ∧ Is(cherry, apple)) → RedFruit(cherry)
None
All red fruits that grow in Ben's yard contain some Vitamin C. All apples that grow in Ben's yard are red fruits. All fruits that grow in Ben's yard and contain some Vitamin C are healthy. No fruits that grow in Ben's yard and are healthy are on a warning list. The cherries grow in Ben's yard. If cherries are not apples and are not healthy, then they are red fruits.
The cherries are either on a warning list or are red.
On(cherry, warningList) ⊕ RedFruit(cherry)
None
26
True
∀x ((GrownIn(x, benSYard) ∧ RedFruit(x)) → Contain(x, vitaminC)) ∀x (GrownIn(x, benSYard) ∧ Is(x, apple) → RedFruit(x)) ∀x ((GrownIn(x, benSYard) ∧ Contain(x, vitaminC)) → healthy(x)) ∀x ((GrownIn(x, benSYard) ∧ Healthy(x)) → ¬On(x, warningList)) GrownIn(cherry, benSYard) ¬(Healthy(cherry) ∧ Is(cherry, apple)) → RedFruit(cherry)
None
Everyone working at Meta has a high income. A person with a high income will not take a bus to their destination. People will either take a bus or drive to their destination. Everyone who has a car will choose to drive to their destination. No students drive to their destination.
James drives to his destination or he is a student.
MeansToDestination(x, drive) ∨ Student(james)
James has a car or works at Meta.
27
False
∀x (WorkAt(x, meta) → HighIncome(x)) ∀x (HighIncome(x) → ¬MeansToDestination(x, bus)) ∀x (MeansToDestination(x, bus) ⊕ MeansToDestination(x, drive)) ∀x (HaveCar(x) → MeansToDestination(x, drive)) ∀x (Student(x) → ¬ MeansToDestination(x, drive))
HaveCar(james) ∨ WorkAt(james, meta)
Everyone working at Meta has a high income. People will either take a bus or drive to their destination. Everyone who has a car will choose to drive to their destination. No students drive to their destination. James has a car or works at Meta.
James either drives to their destination or is a student.
MeansToDestination(x, drive) ⊕ Student(james)
A person with a high income will not take a bus to their destination.
28
False
∀x (WorkAt(x, meta) → HighIncome(x)) ∀x (MeansToDestination(x, bus) ⊕ MeansToDestination(x, drive)) ∀x (HaveCar(x) → MeansToDestination(x, drive)) ∀x (Student(x) → ¬ MeansToDestination(x, drive)) HaveCar(james) ∨ WorkAt(james, meta)
∀x (HighIncome(x) → ¬MeansToDestination(x, bus))
Everyone at the business conference is either an investor or an entrepreneur. None of those at the business conference who enjoy the opportunity of starting a business prefer a planned economy. All entrepreneurs at the business conference enjoy the opportunity of starting a business. Everyone at the business conference who enjoys state ownership of means of production prefers a planned economy. Everyone at the business conference who is an ardent communist prefers state ownership of the means of production.
Ho is an investor or is not an ardent communist.
Investor(ho) ∨ (¬ArdentCommunist(ho))
Ho is at the business conference and prefers state ownership of the means of production.
29
False
∀x (At(x, businessConference) → (Investor(x) ⊕ Entrepreneur(x))) ∀x ((At(x, businessConference) ∧ Enjoy(x, opportunityOfStartingOwnBusiness)) → ¬Prefer(x, plannedEconomy)) ∀x ((At(x, businessConference) ∧ Entrepreneur(x)) → Enjoy(x, opportunityOfStartingOwnBusiness)) ∀x ((At(x, businessConference) ∧ Enjoy(x, stateOwnershipOfMeansOfProduction)) → Prefer(x, plannedEconomy)) ∀x ((At(x, businessConference) ∧ ArdentCommunist(x)) → Prefer(x, stateOwnershipOfMeansOfProduction))
At(ho, businessConference) ∧ Prefer(ho, stateOwnershipOfMeansOfProduction)
Some students in the class who are good at math are also good at chemistry. All students in the class who are good at chemistry enjoy conducting experiments. All students in the class that enjoy conducting experiments are good at planning. None of the students who are good at planning failed the class. James is a student in the class; he is either good at chemistry and failed the class, or bad at chemistry and passed the class.
If James is good at Chemistry or failed the class, then James is either good at planning or good at math.
(GoodAt(james, chemistry) ∨ Failed(james, theClass)) → (GoodAt(james, planning) ⊕ GoodAt(james, math))
None
30
True
∃x ∃y (StudentInTheClass(x) ∧ GoodAt(x, math) ∧ GoodAt(x, chemistry) ∧ (¬(x=y)) ∧ StudentInTheClass(y) ∧ GoodAt(y, math) ∧ GoodAt(y, chemistry)) ∀x ((StudentInTheClass(x) ∧ GoodAt(x, chemistry)) → Enjoy(x, conductingExperiment)) ∀x ((StudentInTheClass(x) ∧ Enjoy(x, conductingExperiment)) → GoodAt(x, planning)) ∀x ((StudentInTheClass(x) ∧ GoodAt(x, planning)) → ¬Failed(x, theClass)) StudentInTheClass(james) ∧ (¬(GoodAt(james, chemistry) ⊕ Failed(james, theClass)))
None
If a Leetcode problem is at the easy level, then its AC rate is lower than 20 percent. All Leetcode problems that are recommended to novices are easy. A Leetode problem is either easy or hard. Leetcode problems that are starred by more than one thousand users are hard. 4Sum is starred by more than 1,000 users.
2Sum is a Leetcode problem at the easy level.
Easy(twosum)
2Sum is recommended to novices.
31
False
∀x (Easy(x) → ∃y (LessThan(y, percent20) ∧ ACRate(x,y))) ∀x (Recommended(x) → Easy(x)) ∀x (Easy(x) ⊕ Hard(x)) ∀x (Starred(x)) → Hard(x)) Starred(foursum)
Recommended(twosum)
Everyone who rents a car spends money. Someone who does not own a car to drive somewhere must either borrow a car or rent a car. Sarah doesn’t own a car. Sarah never borrows a car to go camping. Sarah is going to go camping in Vermont. To go camping somewhere, you must go to that place.
Sarah will spend money this weekend.
Spend(sarah, money)
Whenever Sarah goes to Vermont, Sarah drives there.
32
False
∀x (Rent(x, car) → Spend(x, money)) ∀x ∀y (¬Own(x, car) ∧ DriveTo(x, y) → Borrow(x, car) ⊕ Rent(x, car)) ¬Own(sarah, car) ∀x (Camping(sarah, x) → ¬(Borrow(sarah, car))) Camping(sarah, vermont) ∀x ∀y (Camping(x, y) → GoTo(x, y))
GoTo(sarah, vermont) → DriveTo(sarah, vermont)
All people who attend weddings are getting married or know the people who are getting married. No preteens or young children are getting married or know the people who are getting married. People who enjoy celebrating life milestone events with other people attend weddings. People who are fond of large group functions enjoy celebrating life milestone events with other people. All people who are outgoing and spirited are fond of large group functions.
Carol neither enjoys celebrating life milestone events with other people nor is outgoing and very spirited.
¬((∃y ∃z (¬(x=y) ∧ ¬(x=z) ∧ ¬(y=z) ∧ Enjoy(x, celebratingLifeMileStoneEvent, y) ∧ Enjoy(x, celebratingLifeStoneEvent, z)) ∨ (Outgoing(carol) ∧ Sprited(carol)))
If Carol is not both a pre-teen or young child and attends a wedding, then Carol is not getting married or knows the people who are getting married.
33
False
∀x (Attend(x, wedding) → GettingMarried(x) ∨ (∃y (Know(x, y) ∧ GettingMarried(y))) ∀x (PreTeen(x) ∨ YoungChild(x) → ¬(GettingMarried(x) ⊕ (∃y (Know(x, y) ∧ GettingMarried(y))))) ∀x (∃y ∃z (¬(x=y) ∧ ¬(x=z) ∧ ¬(y=z) ∧ Enjoy(x, celebratingLifeMileStoneEvent, y) ∧ Enjoy(x, celebratingLifeStoneEvent, z)) → Attend(x, wedding)) ∀x (FondOf(x, largeGroupFunction) → ∃y ∃z (¬(x=y) ∧ ¬(x=z) ∧ ¬(y=z) ∧ Enjoy(x, celebratingLifeMileStoneEventWith, y) ∧ Enjoy(x, celebratingLifeStoneEvent, z))) ∀x (Outgoing(x) ∧ Sprited(x) → FondOf(x, largeGroupFunction))
¬((PreTeen(carol) ∨ YoungChildren(carol)) ∧ Attend(carol, wedding)) → ¬(GettingMarried(carol) ∨ (∃y (Know(carol, y) ∧ GettingMarried(y))))
All velvet-finish lipsticks in the Rouge Dior set, Lunar New Year Limited Edition are refillable. Lipsticks in the Rouge Dior set, Lunar New Year Limited Edition have either a velvet-finish or a satin-finish. No satin-finish lipsticks in the set do not have "rosewood" in its offical description. ROUGE Dior Colored Lip Balm 999 is a lipstick in the set, and it either has "rosewood" in its official description or has a velvet finish.
ROUGE Dior Colored Lip Balm 999 has a satin finish and has "rosewood" in its official description.
Refillable(rougeDiorColoredLipBalm999) ∧ RosewoodInDescription(rougeDiorColoredLipBalm999)
Lipstcks in the Rouge Dior set, Lunar New Year Limited Edition either does not have "rosewood" in its offical description or it has "rosewood" in its official description.
34
False
∀x ((Lipstick(x) ∧ In(x, rougeDiorSet) ∧ In(x, lunarNewYearLimitedEdition) ∧ VelvetFinish(x)) → Refillable(x)) ∀x ((Lipstick(x) ∧ In(x, rougeDiorSet) ∧ In(x, lunarNewYearLimitedEdition)) → (VelvetFinish(x) ⊕ SatinFinish(x)) ∀x ((Lipstick(x) ∧ In(x, rougeDiorSet) ∧ In(x, lunarNewYearLimitedEdition) ∧ SatinFinish(x)) → ¬RosewoodInDescription(x)) Lipstick(rougeDiorColoredLipBalm999) ∧ In(rougeDiorColoredLipBalm999, rougeDiorSet) ∧ In(rougeDiorColoredLipBalm999, lunarNewYearLimitedEdition) ∧ (RosewoodInDescription(rougeDiorColoredLipBalm999) ⊕ VelvetFinish(rougeDiorColoredLipBalm999))
∀x ((Lipstick(x) ∧ In(x, rougeDiorSet) ∧ In(x, lunarNewYearLimitedEdition)) → (RosewoodInDescription(x) ⊕ ¬RosewoodInDescription(x)))
All velvet-finish lipsticks in the Rouge Dior set, Lunar New Year Limited Edition are refillable. Lipsticks in the Rouge Dior set, Lunar New Year Limited Edition have either a velvet-finish or a satin-finish. No satin-finish lipsticks in the set do not have "rosewood" in its offical description. ROUGE Dior Colored Lip Balm 999 is a lipstick in the set, and it either has "rosewood" in its official description or has a velvet finish.
If ROUGE Dior Colored Lip Balm 999 is not both a velvet finish ipstick in the set and refillable, then it neither is refillable nor has "rosewood" in its official description.
¬((Lipstick(rougeDiorColoredLipBalm999) ∧ In(rougeDiorColoredLipBalm999, rougeDiorSet) ∧ In(rougeDiorColoredLipBalm999, lunarNewYearLimitedEdition) ∧ VelvetFinish(rougeDiorColoredLipBalm999) ∧ Refillable(rougeDiorColoredLipBalm999)) → (¬Refillable(rougeDiorColoredLipBalm999) ∧ ¬RosewoodInDescription(rougeDiorColoredLipBalm999)))
Lipstcks in the Rouge Dior set, Lunar New Year Limited Edition either does not have "rosewood" in its offical description or it has "rosewood" in its official description.
35
False
∀x ((Lipstick(x) ∧ In(x, rougeDiorSet) ∧ In(x, lunarNewYearLimitedEdition) ∧ VelvetFinish(x)) → Refillable(x)) ∀x ((Lipstick(x) ∧ In(x, rougeDiorSet) ∧ In(x, lunarNewYearLimitedEdition)) → (VelvetFinish(x) ⊕ SatinFinish(x)) ∀x ((Lipstick(x) ∧ In(x, rougeDiorSet) ∧ In(x, lunarNewYearLimitedEdition) ∧ SatinFinish(x)) → ¬RosewoodInDescription(x)) Lipstick(rougeDiorColoredLipBalm999) ∧ In(rougeDiorColoredLipBalm999, rougeDiorSet) ∧ In(rougeDiorColoredLipBalm999, lunarNewYearLimitedEdition) ∧ (RosewoodInDescription(rougeDiorColoredLipBalm999) ⊕ VelvetFinish(rougeDiorColoredLipBalm999))
∀x ((Lipstick(x) ∧ In(x, rougeDiorSet) ∧ In(x, lunarNewYearLimitedEdition)) → (RosewoodInDescription(x) ⊕ ¬RosewoodInDescription(x)))
No athletes never exercise. All NBA players are professional basketball players. All Knicks players are NBA players. Either John is a professional basketball player and he never exercises, or he is not a professional basketball player and he sometimes exercises.
Jim is not a Knicks player.
¬KnicksPlayer(jim)
All professional basketball players are athletes.
36
False
∀x (Athlete(x) → ¬NeverExercises(x)) Never: does not exist a time ∀x (NBAPlayer(x) → ProfessionalBasketballPlayer(x)) ∀x (KnicksPlayer(x) → NBAPlayer(x)) ¬(ProfessionalBasketballPlayer(jim) ⊕ NeverExercises(jim))
∀x (ProfessionalBasketballPlayer(x) → Athlete(x))
All toddlers are kids. If someone is young, then they are not elderly. All pirates are seafarers. If Nancy is not a pirate, then Nancy is young. If Nancy is not a toddler, then Nancy is a seafarer.
If Nancy is not either a pirate or a toddler, then she is young and is a kid.
¬(Pirate(nancy) ⊕ Toddler(nancy)) → Young(nancy) ∧ Kid(nancy)
All kids are young.
37
False
∀x (Toddler(x) → Kid(x)) ∀x (Young(x) → ¬Elderly(x)) ∀x (Pirate(x) → Seafarer(x)) ¬Pirate(nancy) → Young(nancy) ¬Toddler(nancy) → Seafarer(nancy)
∀x (Kid(x) → Young(x))
Lana Wilson directed After Tiller, The Departure, and Miss Americana. If a film is directed by a person, the person is a filmmaker. After Tiller is a documentary. Lana Wilson is from Kirkland. Kirkland is a US city. If a person is from a city in a country, the person is from the country. After Tiller is nominated for the Independent Spirit Award for Best Documentary.
Lana Wilson is a US filmmaker.
From(lanaWilson, unitedStates) ∧ Filmmaker(lanaWilson)
The documentary is a type of film.
38
True
DirectedBy(afterTiller, lanaWilson) ∧ DirectedBy(theDeparture, lanaWilson) ∧ DirectedBy(missAmericana, lanaWilson) ∀x ∀y (DirectedBy(x, y) → Filmmaker(y)) Documentary(afterTiller) From(lanaWilson, kirkland) In(kirkland, unitedStates) ∀x ∀y ∀z ((From(x, y) ∧ In(y, z)) → From(x, z)) Nomination(afterTiller, theIndependentSpiritAwardForBestDocumentary)
∀x (Documentary(x) → Film(x))
Some bears are in zoos.
Not all bears are wild.
∃x (Bear(x) ∧ ¬Wild(x))
All bears in zoos are not wild.
39
False
∃x ∃y (Bear(x) ∧ Bear(y) ∧ In(x, zoo) ∧ In(y, zoo) ∧ ¬(x=y))
∀x ((Bear(x) ∧ In(x, zoo)) → ¬Wild(x))
If a person is the leader of a country for life, that person has power. Leaders of a country for life are either a king or a queen. Queens are female. Kings are male. Elizabeth is a queen.
Elizabeth has power.
HavePower(elizabeth)
Elizabeth is a leader of a country for life.
40
False
∀x (Leader(x) → HavePower(x)) ∀x (Leader(x) → (King(x) ⊕ Queen(x))) ∀x (Queen(x) → Female(x)) ∀x (King(x) → Male(x)) Queen(elizabeth)
Leader(elizabeth)
If a person is the leader of a country for life, that person has power. Queens are female. Kings are male. Elizabeth is a queen. Elizabeth is a leader of a country for life.
Elizabeth is a leader of a country for life.
Leader(elizabeth)
Leaders of a country for life are either a king or a queen.
41
True
∀x (Leader(x) → HavePower(x)) ∀x (Queen(x) → Female(x)) ∀x (King(x) → Male(x)) Queen(elizabeth) Leader(elizabeth)
∀x (Leader(x) → (King(x) ⊕ Queen(x)))
All people who went to Clay's school and who make their own matcha teas every morning with ceremonial-grade matcha powder do not wake up late and start their schedules past noon regularly. All people who went to Clay's school, who live in California, and attend yoga classes regularly, make their own matcha teas every morning with ceremonial-grade matcha powder. All people who went to Clay's school, and work in the entertainment industry as high-profile celebrities, wake up late and start their schedules past noon regularly. All people who went to Clay's school that do not have regular 9-5 jobs, work in the entertainment industry as high-profile celebrities. All people who went to Clay's school and prefer working at home over going to the office daily do not have regular 9-5 jobs. Bunny went to Clay's school, and she either prefers to work at home over going to the office and makes her own matcha teas every morning with ceremonial-grade matcha powder, or does not prefer to work at home over going to the office every day and does not make her own matcha teas every morning with ceremonial-grade matcha powder.
Bunny went to Clay's school and she neither prefers working at home over going to the office nor lives in California and attends yoga classes regularly.
¬(Prefer(bunny, workingAtHome, goingToTheOffice) ∨ (LiveIn(bunny, california) ∧ AttendRegularly(bunny, yogaClass)))
None
42
True
∀x (GoTo(x, claysSchool) ∧ MakeWith(x, theirOwnMatchTea, ceremonialGradePowder) → ¬(WakeUpLate(x) ∧ StartPastNoonRegularly(x, schedule))) ∀x (GoTo(x, claysSchool) ∧ LiveIn(x, california) ∧ AttendRegularly(x, yogaClass) → MakeWith(x, ownMatch, ceremonialGradePowder)) ∀x (GoTo(x, claysSchool) ∧ WorkInAs(x, entertainmentIndustry, highProfileCelebrity) → (WakeUpLate(x) ∧ StartPastNoonRegularly(x, schedule))) ∀x (GoTo(x, claysSchool) ∧ ¬(Have(x, y) ∧ Regular(y) ∧ NineToFiveJob(y)) → WorkInAs(x, entertainmentIndustry, highProfileCelebrity)) ∀x (GoTo(x, claysSchool) ∧ Prefer(x, workingAtHome, goingToTheOffice) → ¬(Have(x, y) ∧ Regular(y) ∧ NineToFiveJob(y))) GoTo(bunny, claysSchool) ∧ ¬(Prefer(bunny, workingAtHome, goingToTheOffice) ⊕ MakeWith(bunny, theirOwnMatchTea, ceremonialGradePowder))
None
Thomas Barber was an English professional footballer. Thomas Barber played in the Football League for Aston Villa. Thomas Barber played as a halfback and inside left. Thomas Barber scored the winning goal in the 1913 FA Cup Final.
Thomas Barber played as an inside left.
PlayedAs(thomasBarber, insideLeft)
None
43
True
English(thomasBarber) ∧ ProfessionalFootballer(thomasBarber) PlayedFor(thomasBarber, astonVilla) ∧ PlayedIn(astonVilla,theFootballLeague) PlayedAs(thomasBarber, halfBack) ∧ PlayedAs(thomasBarber, insideLeft) ScoredTheWinningGoalIn(thomasBarber, facupfinal1913)
None
Thomas Barber played in the Football League for Aston Villa. Thomas Barber played as a halfback and inside left. Thomas Barber scored the winning goal in the 1913 FA Cup Final.
An English professional footballer scored the winning goal in the 1913 FA Cup Final.
∃x (English(x) ∧ ProfessionalFootballer(x) ∧ ScoredTheWinningGoalIn(x, facupfinal1913))
Thomas Barber was an English professional footballer.
44
False
PlayedFor(thomasBarber, astonVilla) ∧ PlayedIn(astonVilla,theFootballLeague) PlayedAs(thomasBarber, halfBack) ∧ PlayedAs(thomasBarber, insideLeft) ScoredTheWinningGoalIn(thomasBarber, facupfinal1913)
English(thomasBarber) ∧ ProfessionalFootballer(thomasBarber)
If a person plays an instrument in a concert, they are good at playing this kind of instrument. Peter plays piano, violin, and saxophone. Peter plays piano in a concert. Oliver plays a different musical instrument from Peter in the concert.
Peter is good at playing piano.
GoodAtPlaying(peter, piano)
Oliver and Peter both play instruments in a concert.
45
True
∀x ∀y (PlayIn(y, x, concert) → GoodAtPlaying(y, x)) Play(peter, piano) ∧ Play(peter, violin) ∧ Play(peter, saxophone) PlayIn(peter, piano, concert) ∀x (PlayIn(oliver, x, concert) → ¬PlayIn(peter, y, concert))
∃x ∃y (PlayIn(peter, x, concert) ∧ PlayIn(oliver, y, concert))
Functional brainstems are necessary for breath control. All humans that can swim can control their breath. Humans can swim or walk. Humans who can walk can stand on the ground by themselves. Humans whose brainstems are functional can control their balance. George and Archie are humans. George can control his balance and can swim. Archie can walk if and only if he has functional brainstems.
Archie has functional leg muscles and can control his balance.
FunctionalLegMuscle(archie) ∧ CanControl(archie, balance)
Every human who can stand on the ground by themselves has functional leg muscles.
46
False
∀x (CanControl(x, breath) → FunctionalBrainStem(x)) ∀x (Human(x) ∧ CanSwim(x) → CanControl(x, breath)) ∀x (Human(x) → (CanSwim(x) ∨ CanWalk(x))) ∀x (Human(x) ∧ CanWalk(x) → CanStandOnTheGround(x, themselves)) ∀x (Human(x) ∧ FunctionalBrainStem(x) → CanControl(x, balance)) Human(george) ∧ Human(archie) CanControl(george, balance) ∧ CanSwim(george) ¬(CanWalk(archie) ⊕ FunctionalBrainStem(x))
∀x (Human(x) ∧ CanStandOnTheGround(x, themselves) → FunctionalLegMuscle(x)))
Cancer biology is finding genetic alterations that confer a selective advantage to cancer cells. Cancer researchers have frequently ranked the importance of substitutions to cancer growth by the P value. P values are thresholds for belief, not metrics of effect.
P values don't represent metrics of effect.
∀x (PValue(x) → ¬MetricsOfEffect(x))
None
47
True
Finding(cancerBiology, geneticAlteration) ∧ Confer(geneticAlteration, selectiveAdvantage, toCancerCell) ∃x ∃y (CancerResearcher(x) ∧ Ranked(x, importanceOfSubstitutionsToCancerGrowth) ∧ PValue(y) ∧ RankedBy(importanceOfSubstitutionsToCancerGrowth, y)) ∀x (PValue(x) → ThresholdForBelief(x) ∧ ¬MetricOfEffect(x))
None
All biodegradable things are environment-friendly. All woodware is biodegradable. All paper is woodware. Nothing is a good thing and also a bad thing. All environment-friendly things are good. A worksheet is either paper or environment-friendly.
A worksheet is not bad.
¬Bad(worksheet)
None
48
True
∀x (Biodegradable(x) → EnvironmentFriendly(x)) ∀x (Woodware(x) → Biodegradable(x)) ∀x (Paper(x) → Woodware(x)) ¬(∃x (Good(x) ∧ Bad(x))) ∀x (EnvironmentFriendly(x) → Good(x)) Paper(worksheet) ⊕ EnvironmentFriendly(worksheet)
None
All buildings in New Haven are not high. All buildings managed by Yale Housing are located in New Haven. All buildings in Manhattans are high. All buildings owned by Bloomberg are located in Manhattans. All buildings with the Bloomberg logo are owned by Bloomberg. Tower B is with the Bloomberg logo.
Tower A is low.
¬High(tower-a)
Tower A is managed by Yale Housing.
49
False
∀x (In(x, newHaven) → ¬High(x)) ∀x (YaleHousing(x) → In(x, newHaven)) ∀x (In(x, manhattan) → High(x)) ∀x (Bloomberg(x) → In(x, manhattan)) ∀x (BloombergLogo(x) → Bloomberg(x)) BloombergLogo(tower-b)
YaleHousing(tower-a)
No birds are ectothermic. All penguins are birds. All endothermic animals produce heat within the body. Ron and Henry are both animals. Ron is not a bird and does not produce heat with the body. Henry is not a cat and does not produce heat with the body.
Ron is either both a penguin and endothermic, or he is nether.
¬(Penguin(ron) ⊕ Endothermic(henry))
An animal is ectothermic or endothermic.
50
True
∀x (Bird(x) → ¬Ectothermic(x)) ∀x (Penguin(x) → Bird(x)) ∀x (Endothermic(x) → ProduceWithIn(x, heat, body)) Animal(ron) ∧ Animal(henry) ¬Bird(ron) ∧ ¬ProduceWithIn(ron, heat, body) ¬Cat(henry) ∧ ¬ProduceWithIn(henry, heat, body)
∀x (Animal(x) → Ectothermic(x) ∨ Endothermic(x))
Ambiortus is a prehistoric bird genus. Mongolia was where Ambiortus Dementjevi lived. Yevgeny Kurochkin was the discoverer of Ambiortus.
Yevgeny Kurochkin discovered a new bird genus.
∃x (Discover(yevgenykurochkin, x) ∧ BirdGenus(x))
Ambiortus Dementjevi is the only known species of Ambiortus.
51
True
Prehistoric(ambiortus) ∧ BirdGenus(ambiortus) LiveIn(ambiortusDementjevi, mongolia) Discover(yevgenykurochkin, ambiortus)
∀x(KnownSpeciesOf(x, ambiortus) → IsSpecies(x, ambiortusDementjevi))
Ambiortus Dementjevi is the only known species of Ambiortus. Mongolia was where Ambiortus Dementjevi lived. Yevgeny Kurochkin was the discoverer of Ambiortus.
All species of Ambiortus live in Mongolia.
∀x (SpeciesOf(x, ambiortus) → LiveIn(x, mongolia))
Ambiortus is a prehistoric bird genus.
52
False
∀x(KnownSpeciesOf(x, ambiortus) → IsSpecies(x, ambiortusDementjevi)) LiveIn(ambiortusDementjevi, mongolia) Discover(yevgenykurochkin, ambiortus)
Prehistoric(ambiortus) ∧ BirdGenus(ambiortus)
Everyone that knows about breath-first-search knows how to use a queue. If someone is a seasoned software engineer interviewer at Google, then they know what breath-first-search is. Someone is either a seasoned software engineer interviewer at Google, has human rights, or both. Every person who has human rights is entitled to the right to life and liberty. Everyone that knows how to use a queue knows about the first-in-first-out data structure. Jack is entitled to the right to life and liberty, has human rights, or knows about the first-in-first-out data structure.
Jack cannot be deprived of their rights without due process of law.
¬DeprivedOfWithout(jack, rights, dueProcessOfLaw)
Everyone that is entitled to the right to life and liberty cannot be deprived of their rights without due process of law.
53
False
∀x (Know(x, breathFirstSearch) → Know(x, howToUseQueue)) ∀x (Seasoned(x) ∧ SoftwareEngineerInterviewer(x) ∧ At(x, google) → Know(x, breathFirstSearch)) ∀x ((Seasoned(x) ∧ SoftwareEngineerInterviewer(x) ∧ At(x, google)) ∨ Have(x, humanRights)) ∀x (Have(x, humanRights) → EntitledTo(x, rightToLifeAndLiberty)) ∀x (Know(x, howToUseQueue) → Know(x, firstInFirstOutDataStructure)) (EntitledTo(jack, rightToLifeAndLiberty) ∨ Have(jack, humanRights) ∨ Know(jack, firstInFirstOutDataStructure))
∀x (EntitledTo(x, rightToLifeAndLiberty) → ¬DeprivedOfWithout(x, rights, dueProcessOfLaw))
Fort Ticonderoga is the current name for Fort Carillon. Pierre de Rigaud de Vaudreuil built Fort Carillon. Fort Carillon was located in New France. New France is not in Europe.
Pierre de Rigaud de Vaudreuil built a fort in New France.
∃x (Built(pierredeRigauddeVaudreuil, x) ∧ LocatedIn(x, newFrance))
None
54
True
RenamedAs(fortCarillon, fortTiconderoga) Built(pierredeRigauddeVaudreuil, fortCarillon) LocatedIn(fortCarillon, newFrance) ¬LocatedIn(newFrance, europe)
None
No soccer players are professional basketball players. All NBA players are professional basketball players. All soccer defenders are soccer players. All centerback players are soccer defenders. If Stephen Curry is an NBA player or a soccer player, then he is a professional basketball player.
Stephen Curry is not a centerback player.
¬ProfessionalCenterback(stephenCurry)
None
55
True
∀x (ProfessionalSoccerPlayer(x) → ¬ProfessionalBasketballPlayer(x)) ∀x (NBAPlayer(x) → ProfessionalBasketballPlayer(x)) ∀x (ProfessionalSoccerDefender(x) → ProfessionalSoccerPlayer(x)) ∀x (ProfessionalCenterback(x) → ProfessionalSoccerDefender(x)) (NBAPlayer(stephencurry) ⊕ ProfessionalSoccerPlayer(stephencurry)) → ProfessionalBasketballPlayer(stephencurry)
None
No songs are visuals. All folk songs are songs. All videos are visuals. All movies are videos. Inception is a sci-fi movie. Mac is neither a folk song nor a sci-fi movie.
Inception is not a folk song.
¬FolkSong(inception)
All sci-fi movies are movies.
56
False
∀x (Song(x) → ¬Visual(x)) ∀x (FolkSong(x) → Song(x)) ∀x (Video(x) → Visual(x)) ∀x (Movie(x) → Video(x)) ScifiMovie(inception) ¬FolkSong(mac) ∧ ¬ScifiMovie(mac)
∀x (ScifiMovie(x) → Movie(x))
No songs are visuals. All folk songs are songs. All videos are visuals. All movies are videos. All sci-fi movies are movies. Inception is a sci-fi movie.
Inception is either a video or a folk song.
Video(inception) ⊕ FolkSong(inception)
Mac is neither a folk song nor a sci-fi movie.
57
True
∀x (Song(x) → ¬Visual(x)) ∀x (FolkSong(x) → Song(x)) ∀x (Video(x) → Visual(x)) ∀x (Movie(x) → Video(x)) ∀x (ScifiMovie(x) → Movie(x)) ScifiMovie(inception)
¬FolkSong(mac) ∧ ¬ScifiMovie(mac)
All inductive reasoning processes derive general principles from a body of observations. Two major types of reasoning rules are inductive reasoning and deductive reasoning. All deductive reasoning processes are only based on facts and rules. Nothing only based on facts and rules is used for statistical generalization. Modus Ponens is not both used in inductive reasoning and used for statistical generalization.
If Modus Ponens either derives general principles from a body of observations and is used for statistical generalization, or neither, then Modus Ponens is is neither used in inductive reasoning nor used for statistical generalization.
¬(Derive(generalPrinciple, observations) ⊕ UsedFor(x, statisticalGeneralization)) → (¬InductiveReasoning(modusPonens) ∧ (¬UsedFor(modusPonens, statisticalGeneralization)))
Modus Ponens is a component of a major part of reasoning rule.
58
False
∀x (InductiveReasoning(x) → DeriveFrom(generalPrinciple, observations)) ∀x (MajorArgumentForm(x) → (InductiveReasoning(x) ⊕ DeductiveReasoning(x)) ∀x (DeductiveReasoning(x) → (BasedOn(x, fact) ∨ BasedOn(x, rule))) ∀x ((BasedOn(x, fact) ∨ BasedOn(x, rule)) → (¬UsedFor(x, statisticalGeneralization))) ¬(InductiveReasoning(modusPonens) ∧ UsedFor(modusPonens, statisticalGeneralization))
ArgumentForm(modusPonens)
No trick-shot artist in Yale's varsity team struggles with half court shots. Everyone on Yale's varsity team who successfully shoots a high percentage of 3-pointers is solid at shooting 2-pointers. No one on Yale's varsity team who is solid at shooting 2-pointers is bad at mid-range shots. Jack is on Yale's varsity team, and he is either a trick-shot artist or he successfully shoots a high percentage of 3-pointers.
Jack is solid at shooting 2-pointers or bad at mid-range shots.
GoodAt(jack, twos) ∨ BadAt(jack, midRangeShot)
Everyone on Yale's varsity team is someone who struggles with half court shots or who successfully shoots a high percentage of 3-pointers.
59
False
∀x ((In(x, yaleSVarsityTeam) ∧ TrickShotArtist(x)) → ¬StruggleAt(x, halfCourtShot)) ∀x ((In(x, yaleSVarsityTeam) ∧ GoodAt(x, threes)) → GoodAt(x, twos)) ∀x ((In(x, yaleSVarsityTeam) ∧ GoodAt(x, twos)) → BadAt(x, midRangeShot)) In(jack, yaleSVarsityTeam) ∧ (TrickShotArtist(jack) ⊕ GoodAt(jack, threes))
∀x (In(x, yaleSVarsityTeam) → (StruggleAt(x, halfCourtShot) ∨ GoodAt(x, threes)))
No trick-shot artist in Yale's varsity team struggles with half court shots. Everyone on Yale's varsity team who successfully shoots a high percentage of 3-pointers is solid at shooting 2-pointers. No one on Yale's varsity team who is solid at shooting 2-pointers is bad at mid-range shots. Jack is on Yale's varsity team, and he is either a trick-shot artist or he successfully shoots a high percentage of 3-pointers.
Jack is either solid at shooting 2-pointers or bad at mid-range shots.
GoodAt(jack, twos) ⊕ BadAt(jack, midRangeShot)
Everyone on Yale's varsity team is someone who struggles with half court shots or who successfully shoots a high percentage of 3-pointers.
60
False
∀x ((In(x, yaleSVarsityTeam) ∧ TrickShotArtist(x)) → ¬StruggleAt(x, halfCourtShot)) ∀x ((In(x, yaleSVarsityTeam) ∧ GoodAt(x, threes)) → GoodAt(x, twos)) ∀x ((In(x, yaleSVarsityTeam) ∧ GoodAt(x, twos)) → BadAt(x, midRangeShot)) In(jack, yaleSVarsityTeam) ∧ (TrickShotArtist(jack) ⊕ GoodAt(jack, threes))
∀x (In(x, yaleSVarsityTeam) → (StruggleAt(x, halfCourtShot) ∨ GoodAt(x, threes)))
No trick-shot artist in Yale's varsity team struggles with half court shots. Everyone on Yale's varsity team is someone who struggles with half court shots or who successfully shoots a high percentage of 3-pointers. Everyone on Yale's varsity team who successfully shoots a high percentage of 3-pointers is solid at shooting 2-pointers. Jack is on Yale's varsity team, and he is either a trick-shot artist or he successfully shoots a high percentage of 3-pointers.
Jack is either a player who successfully shoots a high percentage of 3-pointers or is bad at mid-range shots.
GoodAt(jack, threes) ⊕ BadAt(jack, midRangeShot)
No one on Yale's varsity team who is solid at shooting 2-pointers is bad at mid-range shots.
61
False
∀x ((In(x, yaleSVarsityTeam) ∧ TrickShotArtist(x)) → ¬StruggleAt(x, halfCourtShot)) ∀x (In(x, yaleSVarsityTeam) → (StruggleAt(x, halfCourtShot) ∨ GoodAt(x, threes))) ∀x ((In(x, yaleSVarsityTeam) ∧ GoodAt(x, threes)) → GoodAt(x, twos)) In(jack, yaleSVarsityTeam) ∧ (TrickShotArtist(jack) ⊕ GoodAt(jack, threes))
∀x ((In(x, yaleSVarsityTeam) ∧ GoodAt(x, twos)) → BadAt(x, midRangeShot))
Mushrooms are fungi.
No plants are mushrooms.
∀x (Plant(x) → ¬Mushroom(x))
No plants are fungi.
62
False
∀x (Mushroom(x) → Fungi(x))
∀x (Plant(x) → ¬Fungi(x))
New York City is located on the East Coast. Seattle is located on the West Coast. If a person is somewhere located on the East coast and is traveling to somewhere located on the west coast, they will be on a long flight. People on long flights are uncomfortable unless they're in first class.
People traveling in business class from New York City to Seattle will be uncomfortable.
∃x (TravelingTo(x, seattle) ∧ TravelingFrom(x, newYorkCity) ∧ uncomfortable(x))
People in business class from New York City to Seattle are not in first class.
63
False
LocatedOn(newYorkCity, eastCoast) LocatedOn(seattle, westCoast) ∀x ∀y ∀z ((TravelingFrom(x, y) ∧ LocatedOn(y, eastcoast) ∧ TravelingTo(x, z) ∧ LocatedOn(z, westcoast)) → OnLongFlight(x)) ∀x (OnLongFlight(x) ∧ ¬InFirstClass(x) → Uncomfortable(x))
∀x (InBuisnessClass(x) ∧ TravelingTo(x, seattle) ∧ TravelingFrom(x, newYorkCity) → ¬InFirstClass(x))
Musicians have very busy lives. Singh Kaur is a musician and famous. If a musician is not famous, that musician will not make a lot of money. A musician can be a singer or a writer.
Singh Kaur has a very busy life.
Have(singhKaur, busyLife)
None
64
True
∀x (Musician(x) → Have(x, busyLife)) Musician(singhKaur) ∧ Famous(singhKaur) ∀x (Musician(x) ∧ ¬Famous(x) → ¬MakeALotOfMoney(x)) ∃x (Musician(x) ∧ (Singer(x) ∨ Writer(x)))
None
A cat named Garfield, the main character of the film Garfield, is orange and fat and likes having lasagna. Garfield shares a home with Odie, another pet of Jon's. Garfield hates Odie.
The main character of the film Garfield is childish and possessive.
∃x (MainCharacterOf(x, garfield) ∧ Childish(x) ∧ Possessive(x))
A pet who hates the pet with whom he shares the same owner is childish and possessive.
65
False
Cat(garfield) ∧ MainCharacterOf(garfield, filmGarfield) ∧ Orange(garfield) ∧ Fat(garfield) ∧ Like(garfield, lasagna) PetOf(garfield, jon) ∧ PetOf(odie, jon) ∧ ShareHomeWith(garfield, odie) Hate(garfield, odie)
∀x ∀y ∃z (PetOf(x, z) ∧ PetOf(y, z) ∧ Hate(x, y) → Childish(x) ∧ Possessive(x))
All humans are capable of abstract thoughts. All multicellular creatures that are autotrophic or digest food internally are plants and animals. All goats are animals. Dirt is not an animal. Hulu is a goat or a human. Hulu is a multicellular creature that is autotrophic or digests food internally.
Hulu is an animal or dirt.
Animal(hulu) ∨ Dirt(hulu)
Plants are not capable of abstract thoughts.
66
False
∀x (Human(x) → CapableOf(x, abstractThought)) ∀x (MulticellularCreature(x) ∧ (Autotrophic(x) ∨ DigestFoodInternally (x)) → Plant(x) ⊕ Animal(x)) ∀x (Goat(x) → Animal(x)) ∀x (Dirt(x) → ¬Animal(x)) Goat(hulu) ∨ HumanBeing(hulu) (MulticellularCreature(hulu) ∧ (Autotrophic(hulu) ∨ DigestFoodInternally (hulu))
∀x (Plant(x) → ¬CapableOf(x, abstractThought))
All humans are capable of abstract thoughts. Plants are not capable of abstract thoughts. All multicellular creatures that are autotrophic or digest food internally are plants and animals. All goats are animals. Dirt is not an animal. Hulu is a multicellular creature that is autotrophic or digests food internally.
Hulu is either an animal or dirt, but not both.
Animal(hulu) ⊕ Dirt(hulu)
Hulu is a goat or a human.
67
False
∀x (Human(x) → CapableOf(x, abstractThought)) ∀x (Plant(x) → ¬CapableOf(x, abstractThought)) ∀x (MulticellularCreature(x) ∧ (Autotrophic(x) ∨ DigestFoodInternally (x)) → Plant(x) ⊕ Animal(x)) ∀x (Goat(x) → Animal(x)) ∀x (Dirt(x) → ¬Animal(x)) (MulticellularCreature(hulu) ∧ (Autotrophic(hulu) ∨ DigestFoodInternally (hulu))
Goat(hulu) ∨ HumanBeing(hulu)
A controlled substance is a drug. There exist both harmful and beneficial controlled substances. If a child is exposed to a controlled substance, they are in chemical endangerment. Chemical Endangerment is harmful. The Controlled Substances Act was an act passed in 1971. Some Acts prevent harmful things.
Some drugs are beneficial.
∃x ∃y(Drugs(x) ∧ Beneficial(x) ∧ (¬(x=y)) ∧ Drugs(y) ∧ Beneficial(y))
None
68
True
∀x (ControlledSubstances(x) → Drugs(x)) ∃x ∃y (ControlledSubstances(x) ∧ ControlledSubstances(y) ∧ (¬(x=y)) ∧ Beneficial(x) ∧ Harmful(y)) ∀x ∀y ((Child(x) ∧ ControlledSubstances(y) ∧ ExposedTo(x, y)) → InChemicalEndangerment(x)) ∀x (InChemicalEndangerment(x) → Harmful(x)) PassedIn(controlledSubstancesAct, yr1971) ∧ Act(controlledSubstancesAct) ∃x ∃y(Act(x) ∧ PreventsHarm(x) ∧ (¬(x=y)) ∧ Act(y) ∧ PreventsHarm(y))
None
A controlled substance is a drug. There exist both harmful and beneficial controlled substances. If a child is exposed to a controlled substance, they are in chemical endangerment. The Controlled Substances Act was an act passed in 1971. Some Acts prevent harmful things.
A child in chemical endangerment is in harm.
∀x ((Child(x) ∧ InChemicalEndangerment(x)) → Harmful(x))
Chemical Endangerment is harmful.
69
False
∀x (ControlledSubstances(x) → Drugs(x)) ∃x ∃y (ControlledSubstances(x) ∧ ControlledSubstances(y) ∧ (¬(x=y)) ∧ Beneficial(x) ∧ Harmful(y)) ∀x ∀y ((Child(x) ∧ ControlledSubstances(y) ∧ ExposedTo(x, y)) → InChemicalEndangerment(x)) PassedIn(controlledSubstancesAct, yr1971) ∧ Act(controlledSubstancesAct) ∃x ∃y(Act(x) ∧ PreventsHarm(x) ∧ (¬(x=y)) ∧ Act(y) ∧ PreventsHarm(y))
∀x (InChemicalEndangerment(x) → Harmful(x))
No people who have corporate jobs are taking more than normal financial risks. All entrepreneurs are taking more than normal financial risks. All risk-averse working people are people who have corporate jobs. All working people who hate working for others want to be entrepreneurs. If Mark Zuckerberg is neither an entrepreneur nor a person who hates working for others, then Mark Zuckerberg is not a risk-averse working person.
Mark Zuckerberg is not a risk-averse person.
¬RiskAverse(markZuckerberg)
None
70
True
∀x (Have(x, corporateJob) → ¬Take(x, financialRisk)) ∀x (Entrepreneur(x) → Take(x, financialRisk)) ∀x (RiskAverse(x) → Have(x, corporateJob)) ∀x (∃y ∃z (¬(y=x) ∧ ¬(z=x) ∧ ¬(y=z) ∧ HateWorkingFor(x, y) ∧ HateWorkingFor(x, z)) → Entrepreneur(x)) ¬Entrepreneur(markZuckerberg) ∧ ¬(∃y ∃z (¬(y=markZuckerberg) ∧ ¬(z=markZuckerberg) ∧ ¬(y=z) ∧ HateWorkingFor(markZuckerberg, y) ∧ HateWorkingFor(markZuckerberg, z))) → ¬RiskAverse(markZuckerberg)
None
Wildfeed exists as an unannounced program. Wildfeed can be sporting events, news, or syndicated shows. Pre-recorded content is a copyright violation.
Some wildfeed is violating copyright laws.
∃x (Wildfeed(x) ∧ CopyrightViolation(x))
Programs are pre-recorded.
71
False
∃x (Wildfeed(x) ∧ Unannounced(x) ∧ Program(x)) ∀x (Wildfeed(x) → SportingEvent(x) ∨ News(x) ∨ SyndicatedShow(x)) ∀x (Prerecorded(x) → CopyrightViolation(x))
∀x (Program(x) → Prerecorded(x))
Wildfeed exists as an unannounced program. Wildfeed can be sporting events, news, or syndicated shows. Pre-recorded content is a copyright violation.
Wildfeed can be prerecorded.
∃x (Wildfeed(x) ∧ Prerecorded(x))
Programs are pre-recorded.
72
False
∃x (Wildfeed(x) ∧ Unannounced(x) ∧ Program(x)) ∀x (Wildfeed(x) → SportingEvent(x) ∨ News(x) ∨ SyndicatedShow(x)) ∀x (Prerecorded(x) → CopyrightViolation(x))
∀x (Program(x) → Prerecorded(x))
New York City is Located in the United States of America. The United States of America is part of North America. North America is in the western hemisphere of the earth. If place A is located in place B and place B is located in place C, then place A is located in place C.
A highly developed city is located in the western hemisphere of the earth.
∃x (HighlyDeveloped(x) ∧ LocatedIn(x, westernHemisphere))
New York City is a highly developed city.
73
False
LocatedIn(newYorkCity, unitedStatesOfAmerica) LocatedIn(usa, northAmerica) LocatedIn(northAmerica, westernHemisphere) ∀x ∀y ∀z ((LocatedIn(x, y) ∧ LocatedIn(y, z)) → LocatedIn(x, z))
HighlyDeveloped(newYorkCity)
Catullus 4 is a poem written by the ancient Roman writer Catullus. Catullus 4 is a story about the retirement of a well-traveled ship. There is a strong analogy of human aging in the poem Catullus 4. Catullus 4 is written in an unusual iambic trimeter to convey a sense of speed over the waves.
There is a poem written by an ancient Roman writer with a strong analogy of human aging.
∃x ∃y (Poem(x) ∧ WrittenBy(x, y) ∧ AncietRomanWriter(y) ∧ StrongAgingAnalogy(x))
None
74
True
Poem(catullus4) ∧ WrittenBy(catullus4, catullus) ∧ AncientRomanWriter(catullus) Story(catullus4) ∧ About(catullus4, retirementOfAWellTraveledShip) Poem(catullus4) ∧ StrongAgingAnalogy(catullus4) Poem(catullus4) ∧ WrittenIn(catullus4, iambicTrimeter) ∧ Convey(catullus4, aSenseOfSpeedOverTheWaves)
None
Catullus 4 is a poem written by the ancient Roman writer Catullus. Catullus 4 is a story about the retirement of a well-traveled ship. There is a strong analogy of human aging in the poem Catullus 4.
Callus 4 is written in an unusual iambic trimeter to convey a strong analogy of human aging.
Poem(catullus4) ∧ WrittenIn(catullus4, iambicTrimeter) ∧ StrongAgingAnalogy(catullus4)
Catullus 4 is written in an unusual iambic trimeter to convey a sense of speed over the waves.
75
False
Poem(catullus4) ∧ WrittenBy(catullus4, catullus) ∧ AncientRomanWriter(catullus) Story(catullus4) ∧ About(catullus4, retirementOfAWellTraveledShip) Poem(catullus4) ∧ StrongAgingAnalogy(catullus4)
Poem(catullus4) ∧ WrittenIn(catullus4, iambicTrimeter) ∧ Convey(catullus4, aSenseOfSpeedOverTheWaves)
Westworld is an American science fiction-thriller TV series. In 2016, a television series named Westworld debuted on HBO. The 1973 film Westworld is about robots that malfunction and begin killing human visitors.
Michael Crichton has directed a film about malfunctioning robots.
∃x (Film(x) ∧ Directed(michael, x) ∧ About(x, malfunctioningRobots))
The TV series Westworld is adapted from the original film in 1973, which was written and directed by Michael Crichton.
76
False
American(westworld) ∧ ScienceFictionThriller(westworld) Debut(westworld, year2016) ∧ TvSeries(westworld) Film(westworldTheFilm) ∧ About(westworldTheFilm, malfunctioningRobots)
Adapted(westworld, westworldTheFilm) ∧ Produce(westworldTheFilm, year1973) ∧ Wrote(michael, westworldTheFilm) ∧ Directed(michael, westworldTheFilm)
In 2016, a television series named Westworld debuted on HBO. The TV series Westworld is adapted from the original film in 1973, which was written and directed by Michael Crichton. The 1973 film Westworld is about robots that malfunction and begin killing human visitors.
An American TV series debuted in 2016.
∃x (TVSeries(x) ∧ American(x) ∧ Debut(x, year2016))
Westworld is an American science fiction-thriller TV series.
77
False
Debut(westworld, year2016) ∧ TvSeries(westworld) Adapted(westworld, westworldTheFilm) ∧ Produce(westworldTheFilm, year1973) ∧ Wrote(michael, westworldTheFilm) ∧ Directed(michael, westworldTheFilm) Film(westworldTheFilm) ∧ About(westworldTheFilm, malfunctioningRobots)
American(westworld) ∧ ScienceFictionThriller(westworld)
The 2008 Summer Olympics were held in Beijing, China. The 2008 Summer Olympics was the second Summer Olympic Games held in a communist state. The United States placed second in the gold medal tally but won the highest number of medals overall (112) in the 2008 Summer Olympics. The third place in the gold medal tally was achieved by Russia in the 2008 Summer Olympics. If a country placed third in gold medals, then it had fewer gold medals than the team that won the most gold medals.
Russia won fewer gold medals than China.
FewerGoldMedalsThan(russia, china)
China won the most gold medals (48) in the 2008 Summer Olympics.
78
False
HeldIn(2008SummerOlympics, beijingChina) SecondSummerOlympicsGames(2008SummerOlympics) ∧ BeHeldIn(2008SummerOlympics, communistState) PlacedSecondInGoldMedalsIn(unitedStates, 2008SummerOlympics) ∧ Won(unitedStates, highestNumberOfMedals) PlacedThirdInGoldMedalsIn(russia, 2008SummerOlympics) ∀x ∀y (Placed(x, thirdInGoldMedals) ∧ Won(y, mostGoldMedals) → FewerGoldMedalsThan(x, y))
Won(china, theMostGoldMedals)
Yangshuo is not a district in Guilin.
Xiangshan and Diecai are districts in the same city.
∃x (DistrictIn(xiangshan, x) ∧ DistrictIn(diecai, x) ∧ City(x))
Xiufeng, Xiangshan, Diecai, Qixing are districts in the city of Guilin.
79
False
¬DistrictIn(yangshuo, guilin)
DistrictIn(xiufeng, guilin) ∧ DistrictIn(xiangshan, guilin) ∧ DistrictIn(diecai, guilin) ∧ DistrictIn(qixing, guilin) ∧ City(guilin)
Yangshuo is not a district in Guilin.
Xiufeng is a district in Guilin.
DistrictIn(xiufeng, guilin)
Xiufeng, Xiangshan, Diecai, Qixing are districts in the city of Guilin.
80
False
¬DistrictIn(yangshuo, guilin)
DistrictIn(xiufeng, guilin) ∧ DistrictIn(xiangshan, guilin) ∧ DistrictIn(diecai, guilin) ∧ DistrictIn(qixing, guilin) ∧ City(guilin)
All of Michael's neighbors who grow their own fresh vegetables in their home gardens also have ample space. All of Michael's neighbors who are young working professionals and live in large cities, do not have ample space. All of Michael's neighbors who order takeout from delivery services often grow their own fresh vegetables in their home garden. All of Michael's neighbors who regularly tout the benefits of homegrown and homecooked meals over fast food enjoy going out often to restaurants with friends. Peter, Michael's neighbor, grows his own fresh vegetables in his home garden, or regularly touts the benefits of homegrown and homecooked meals over fast food, or both.
Peter grows his own fresh vegetables in their home garden or is a young working professional who lives in large cities.
GrowIn(peter, vegetable, garden) ∨ (YoungWorkingProfession(peter) ∧ LiveIn(peter, largeCity))
All of Michael's neighbors who enjoy going out often to restaurants with friends order takeout from delivery services often.
81
False
∀x (MichaelsNeightbor(x) ∧ GrowIn(x, vegetable, garden) → Have(x, ampleSpace)) ∀x (MichaelsNeightbor(x) ∧ YoungWorkingProfession(x) ∧ LiveIn(x, largeCity) → ¬Have(x, ampleSpace)) ∀x (MichaelsNeightbor(x) ∧ OrderOften(x, takeout) → Grow(x, vegetable, garden)) ∀x (MichaelsNeightbor(x) ∧ ToutOver(x, homecookedMeals, fastFood) → EnjoyGoingOutOftenToWith(x, restaurant, friend)) MichaelsNeightbor(peter) ∧ (GrowIn(peter, vegetable, garden) ∨ ToutOver(peter, homecookedMeals, fastFood))
∀x (MichaelsNeightbor(x) ∧ EnjoyGoingOutOftenToWith(x, restaurant, friend) → OrderOften(x, takeout))
All devices belonging to the company are connected to Google Home. All devices belonging to employees are connected to the company's wifi. All devices that connect to the company's wifi are easy to operate. ModelXX belongs to employees.
ModelXX is easy to operate.
EasyToOperate(modelXX)
All devices connected to Google Home are controlled by the managers.
82
True
∀x (OwnedBy(x, company) → ConnectedTo(x, googleHome)) ∀x (OwnedBy(x, employee) → ConnectedTo(x, companyWiFi)) ∀x (ConnectedTo(x, companyWiFi) → EasyToOperate(x)) OwnedBy(modelXX, employee)
∀x (ConnectedTo(x, googleHome) → ControlledBy(x, managers))
No touring musicians who perform at the New Haven Symphony Orchestra are permanent members of the orchestra. Musicians who perform at the New Haven Symphony Orchestra are permanent members of an orchestra, or they have temporary roles at the orchestra. All touring musicians who perform at the New Haven Symphony Orchestra have temporary roles at the orchestra. All musicians performing at the New Haven Symphony Orchestra who have temporary roles at the orchestra are interesting soloists. All musicians performing at New Haven Symphony Orchestra who are interesting soloists are capable of attracting audiences. If Ryan is an interesting soloist and has a temporary role at the orchestra, then he is capable of attracting large audiences if and only if he is a touring soloist musician.
Ryan is either a permanent member of an orchestra or a touring soloist musician.
(PermanentMemberOf(ryan, orchestra) ⊕ TouringMusician(ryan))
Ryan is performing at New Haven Symphony Orchestra.
83
False
∀x ((PerformAt(x, newHavenSymphonyOrchestra) ∧ TouringMusician(x)) → ¬PermanentMemberOf(x, theOrchestra)) ∀x (PerformAt(x, newHavenSymphonyOrchestra) → (PermanentMemberOf(x, theOrchestra) ∨ HaveTemporaryRoleAt(x, theOrchestra))) ∀x ((PerformAt(x, newHavenSymphonyOrchestra) ∧ TouringMusicians(x)) → HaveTemporaryRoleAt(x, theOrchestra)) ∀x ((PerformAt(x, newHavenSymphonyOrchestra) ∧ HaveTemporaryRoleAt(x, theOrchestra)) → InterestingSoloist(x)) ∀x ((PerformAt(x, newHavenSymphonyOrchestra) ∧ InterestingSoloist(x)) → CapableOfAttractingAudiences(x)) (InterestingSoloist(ryan) ∧ HaveTemporaryRoleAt(ryan, theOrchestra)) → ¬(TouringMusician(ryan) ⊕ CapableOfAttractingAudiences(ryan))
PerformAt(ryan, newHavenSymphonyOrchestra)
No touring musicians who perform at the New Haven Symphony Orchestra are permanent members of the orchestra. Musicians who perform at the New Haven Symphony Orchestra are permanent members of an orchestra, or they have temporary roles at the orchestra. All touring musicians who perform at the New Haven Symphony Orchestra have temporary roles at the orchestra. All musicians performing at the New Haven Symphony Orchestra who have temporary roles at the orchestra are interesting soloists. All musicians performing at New Haven Symphony Orchestra who are interesting soloists are capable of attracting audiences. If Ryan is an interesting soloist and has a temporary role at the orchestra, then he is capable of attracting large audiences if and only if he is a touring soloist musician.
Ryan is either a permanent member of an orchestra or has a temporary role at the orchestra.
(PermanentMemberOf(ryan, orchestra) ⊕ HaveTemporaryRoleAt(ryan, orchestra))
Ryan is performing at New Haven Symphony Orchestra.
84
False
∀x ((PerformAt(x, newHavenSymphonyOrchestra) ∧ TouringMusician(x)) → ¬PermanentMemberOf(x, theOrchestra)) ∀x (PerformAt(x, newHavenSymphonyOrchestra) → (PermanentMemberOf(x, theOrchestra) ∨ HaveTemporaryRoleAt(x, theOrchestra))) ∀x ((PerformAt(x, newHavenSymphonyOrchestra) ∧ TouringMusicians(x)) → HaveTemporaryRoleAt(x, theOrchestra)) ∀x ((PerformAt(x, newHavenSymphonyOrchestra) ∧ HaveTemporaryRoleAt(x, theOrchestra)) → InterestingSoloist(x)) ∀x ((PerformAt(x, newHavenSymphonyOrchestra) ∧ InterestingSoloist(x)) → CapableOfAttractingAudiences(x)) (InterestingSoloist(ryan) ∧ HaveTemporaryRoleAt(ryan, theOrchestra)) → ¬(TouringMusician(ryan) ⊕ CapableOfAttractingAudiences(ryan))
PerformAt(ryan, newHavenSymphonyOrchestra)
If someone in Potterville yells, then they are not cool. If someone in Potterville is angry, then they yell. If someone in Potterville flies, then they are cool. Every person in Potterville that knows magic flies. All wizards in Potterville know magic. Harry, who lives in Potterville either yells or flies. Potter, who lives in Potterville, is a wizard and flies.
Harry is neither a wizard nor angry.
¬Wizard(harry) ∧ ¬Angry(harry)
None
85
True
∀x (In(x, potterville) ∧ Yell(x) → ¬Cool(x)) ∀x (In(x, potterville) ∧ Angry(x) → Yell(x)) ∀x (In(x, potterville) ∧ Fly(x) → Cool(x)) ∀x (In(x, potterville) ∧ Know(x, magic) → Fly(x)) ∀x (In(x, potterville) ∧ Wizard(x) → Know(x, magic)) In(harry, potterville) ∧ (Yell(harry) ⊕ Fly(harry)) Wizard(potter) ∧ Fly(potter)
None
All of this brand's products are either produced in China or in the US. All of this brand's products produced in China are labeled. All of this brand's products produced in the US are sold in the US. The products of this brand that are labeled are cheaper. All of this brand's products sold in the US are sold at Walmart. All products of this brand displayed on the homepage are sold at Walmart. None of this brand's products that are returned by customers are sold at Walmart. G-910 is a product of this brand, and it is either displayed on the homepage and is cheaper, or it is neither displayed on the homepage nor is it cheaper.
G-910 is a product returned by customers or sold in Walmart.
ThisBrand(g910) ∧ (ReturnedBy(g910, customer) ∨ SoldIn(g910, walmart))
None
86
True
∀x (ThisBrand(x) ∧ Product(x) → (ProducedIn(x, china) ⊕ ProducedIn(x, uS))) ∀x ((ThisBrand(x) ∧ Product(x) ∧ ProducedIn(x, china)) → Labeled(x)) ∀x ((ThisBrand(x) ∧ Product(x) ∧ ProducedIn(x, us)) → SoldIn(x, us)) ∀x ((ThisBrand(x) ∧ Product(x) ∧ Labeled(x)) → Cheaper(x)) ∀x ((ThisBrand(x) ∧ Product(x) ∧ SoldIn(x, us)) → SoldIn(x, walmart)) ∀x (ThisBrand(x) ∧ Product(x) ∧ DisplayedIn(x, homepage) → SoldIn(x, walmart)) ∀x (ThisBrand(x) ∧ Product(x) ∧ ReturnedBy(x, customer) → ¬SoldIn(x, walmart)) Product(g910) ∧ ThisBrand(g910) ∧ (¬(DisplayedIn(g910, homepage) ⊕ Cheaper(g910)))
None
All of this brand's products are either produced in China or in the US. All of this brand's products produced in China are labeled. All of this brand's products produced in the US are sold in the US. All of this brand's products sold in the US are sold at Walmart. All products of this brand displayed on the homepage are sold at Walmart. None of this brand's products that are returned by customers are sold at Walmart. G-910 is a product of this brand, and it is either displayed on the homepage and is cheaper, or it is neither displayed on the homepage nor is it cheaper.
G-910 is either returned by customers or sold in Walmart.
ReturnedBy(g910, customer) ⊕ SoldIn(g910, walmart)
The products of this brand that are labeled are cheaper.
87
False
∀x (ThisBrand(x) ∧ Product(x) → (ProducedIn(x, china) ⊕ ProducedIn(x, uS))) ∀x ((ThisBrand(x) ∧ Product(x) ∧ ProducedIn(x, china)) → Labeled(x)) ∀x ((ThisBrand(x) ∧ Product(x) ∧ ProducedIn(x, us)) → SoldIn(x, us)) ∀x ((ThisBrand(x) ∧ Product(x) ∧ SoldIn(x, us)) → SoldIn(x, walmart)) ∀x (ThisBrand(x) ∧ Product(x) ∧ DisplayedIn(x, homepage) → SoldIn(x, walmart)) ∀x (ThisBrand(x) ∧ Product(x) ∧ ReturnedBy(x, customer) → ¬SoldIn(x, walmart)) Product(g910) ∧ ThisBrand(g910) ∧ (¬(DisplayedIn(g910, homepage) ⊕ Cheaper(g910)))
∀x ((ThisBrand(x) ∧ Product(x) ∧ Labeled(x)) → Cheaper(x))
People either believe in Santa Claus, or think he is made up. People who believe in Santa Claus expect to get presents on Christmas morning. People who think Santa Claus is made up, then they would be surprised to see him in their house. People who expect presents on Christmas morning are excited for it to be Christmas. If people would be surprised to see Santa Claus in their house, then they don't leave out cookies on Chrismtas Eve. Mercy is not someone who expects presents Christmas morning, is excited for Chrismtas, and believes in Santa Claus.
Marcy either believes in Santa Claus or doesn't leave cookies out on Christmas Eve.
BelieveIn(marcy, santaClaus) ⊕ LeaveOut(marcy, cookies)
None
88
True
∀x (BelieveIn(x, santaClaus) ⊕ ThinkMadeUp(x, santaClaus)) ∀x (BelieveIn(x, santaClaus) → Expect(x, present, christmasMorning)) ∀x (ThinkMadeUp(x, santaClaus) → WouldBeSurprisedToSeeIn(x, santaClaus, house)) ∀x (Expect(x, present, christmasMorning) → ExcitedFor(x, christmas)) ∀x (WouldBeSurprisedToSeeIn(x, santaClaus, house) → ¬LeaveOut(x, cookies)) ¬(Expect(marcy, present, christmasMorning) ∧ ExcitedFor(marcy, christmas) ∧ BelieveIn(marcy, santaClaus))
None
No battery-powered watch is automatic. All digital watches are battery-powered. All smart watches are digital. Moonwatch is either a digital watch and an automatic, or it is neither.
If Moonwatch is a smartwatch and a mechanical watch, then Moonwatch is not a mechanical watch.
SmartWatch(moonwatch) ∧ MechanicalWatch(moonwatch) → ¬MechanicalWatch(moonwatch)
Some mechanical watches are automatic.
89
True
∀x (BatteryPoweredWatch(x) → ¬AutomaticWatch(x)) ∀x (DigitalWatch(x) → BatteryPoweredWatch(x)) ∀x (SmartWatch(x) → DigitalWatch(x)) ¬(DigitalWatch(moonwatch) ⊕ AutomaticWatch(moonwatch))
∃x (MechanicalWatch(x) ∧ AutomaticWatch(x))
No battery-powered watch is automatic. All digital watches are battery-powered. Some mechanical watches are automatic. All smart watches are digital. Moonwatch is either a digital watch and an automatic, or it is neither.
If Moonwatch is a mechanical or battery-powered watch, then Moonwatch is not a smartwatch.
MechanicalWatch(moonwatch)) ∨ BatteryPoweredWatch(moonwatch) → ¬SmartWatch(moonwatch)
None
90
True
∀x (BatteryPoweredWatch(x) → ¬AutomaticWatch(x)) ∀x (DigitalWatch(x) → BatteryPoweredWatch(x)) ∃x (MechanicalWatch(x) ∧ AutomaticWatch(x)) ∀x (SmartWatch(x) → DigitalWatch(x)) ¬(DigitalWatch(moonwatch) ⊕ AutomaticWatch(moonwatch))
None
All phones are things. All cell phones are phones. All employees are wage earners. All wage earners are human. Jack is either an employee or a wage earner. Jack is either a human or a phone.
Jack is not both a thing and an iPhone.
¬(Thing(jack) ∧ Iphone(jack))
All iPhones are cell phones.
91
False
∀x (Phone(x) → Thing(x)) ∀x (Cellphone(x) → Phone(x)) ∀x (Employee(x) → WageEarner(x)) ∀x (WageEarner(x) → Human(x)) Employee(jack) ⊕ WageEarner(jack) Human(jack) ⊕ Phone(jack)
∀x (Iphone(x) → Cellphone(x))
The Metropolitan Museum of Art is a museum in NYC. Whitney Museum of American Art is a museum in NYC. The Museum of Modern Art (MoMA) is a museum in NYC. The Metropolitan Museum of Art includes Byzantine and Islamic Art.
A museum in NYC includes Byzantine and Islamic Art.
∃x (Museum(x) ∧ In(x, nYC) ∧ Include(x, byzantineArt) ∧ Include(x, islamicArt))
Whitney Museum of American Art includes American art.
92
True
Museum(metropolitanMuseumOfArt) ∧ In(metropolitanMuseumOfArt, nYC) Museum(whitneyMuseumOfAmericanArt) ∧ In(metropolitanMuseumOfArt, nYC) Museum(museumOfModernArt) ∧ In(museumOfModernArt, nYC) Include(metropolitanMuseumOfArt, byzantineArt) ∧ Include(metropolitanMuseumOfArt, islamicArt)
Include(whitneyMuseumOfAmericanArt, americanArt)
The Metropolitan Museum of Art is a museum in NYC. Whitney Museum of American Art is a museum in NYC. The Museum of Modern Art (MoMA) is a museum in NYC. The Metropolitan Museum of Art includes Byzantine and Islamic Art. Whitney Museum of American Art includes American art.
A museum in NYC includes American art.
∃x (Museum(x) ∧ In(x, nYC) ∧ Include(x, americanArt))
None
93
True
Museum(metropolitanMuseumOfArt) ∧ In(metropolitanMuseumOfArt, nYC) Museum(whitneyMuseumOfAmericanArt) ∧ In(metropolitanMuseumOfArt, nYC) Museum(museumOfModernArt) ∧ In(museumOfModernArt, nYC) Include(metropolitanMuseumOfArt, byzantineArt) ∧ Include(metropolitanMuseumOfArt, islamicArt) Include(whitneyMuseumOfAmericanArt, americanArt)
None
There's a person in Benji's family who likes eating cheese or is a francophile. There is no francophile in Benji's family whose favorite country is Spain. There is a person in Benji's family who likes eating cheese or whose favorite country is Spain. Fabien is in Benji's family and does not both study Spanish and also like eating cheese. Fabien studies Spanish.
If Fabien is either a person who likes eating cheese or a francophile, then Fabien is neither a person who studies Spanish nor a person who is a francophile.
(LikeEating(fabien, cheese) ⊕ Francophile(fabien)) → (¬(Study(fabien, spanish) ∨ Francophile(fabien)))
None
94
True
∃x (InBenjiSFamily(x) → (LikeEating(x, cheese) ∨ Francophile(x))) ∀x ((InBenjiSFamily(x) ∧ Francophile(x)) → ¬Favor(x, spain)) ∃x (InBenjiSFamily(x) ∧ (Favor(x, spain) ∨ LikeEating(x, cheese))) InBenjiSFamily(fabien) ∧ (¬(LikeEating(fabien, cheese) ∧ Study(fabien, spanish))) Study(fabien, spanish)
None
The only types of mammals that lay eggs are either platypuses or echidnas. Platypuses are not hyrax. Echidnas are not hyrax. No mammals are invertebrates. Mammals are animals. Hyraxes are mammals. Grebes lay eggs. Grebes are not platypuses and also not echidnas.
Grebes are not mammals.
∀x (Grebes(x) → ¬Mammal(x))
All animals are either vertebrates or invertebrates.
95
False
∀x ((Mammal(x) ∧ LayEgg(x)) → (Platypus(x) ⊕ Echidna(x))) ∀x (Platypuses(x) → ¬Hyrax(x)) ∀x (Echidnas(x) → ¬Hyrax(x)) ∀x (Mammal(x) → ¬Invertebrate(x)) ∀x (Mammal(x) → Animal(x)) ∀x (Hyrax(x) → Mammal(x)) ∀x (Grebes(x) → LayEgg(x)) ∀x (Grebes(x) → (¬Platypuses(x) ∧ ¬Echidnas(x)))
∀x (Animal(x) → (Vertebrate(x) ∨ Invertebrate(x)))
Bobby Flynn is a singer-songwriter. Australian Idol competitors are Australian citizens. The Omega Three band made a nationwide tour in 2007. Bobby Flynn is a member of The Omega Three band. Bobby Flynn was born in Queensland.
Bobby Flynn is an Australian citizen.
AustralianCitizen(bobbyFlynn)
Bobby Flynn finished 7th while competing on Australian Idol.
96
False
Singer(bobbyFlynn) ∧ SongWriter(bobbyFlynn) ∀x (CompetesOnAustralianIdol(x) → AustralianCitizen(x)) NationWideTourIn(theOmegaThreeBand, year2007) Member(bobbyFlynn, theOmegaThreeBand) BornIn(bobbyFlynn, queensland)
FinishesIn(bobbyFlynn, number7) ∧ CompetesOnAustralianIdol(bobbyFlynn)
Maggie Friedman is an American screenwriter and producer. Maggie Friedman was the showrunner and executive producer of the lifetime television series Witches of East End. Witches of East End is a fantasy-drama series. Maggie Friedman produced and developed Eastwick. Eastwick is a series by ABC.
There is a series by ABC that was developed by the showrunner of Witches of East End.
∃x ∃y (Series(x) ∧ AiredOn(x, aBC) ∧ Develops(y, x) ∧ ShowRunnerOf(y, witchesOfEastEnd))
None
97
True
American(maggieFriedman) ∧ Screenwriter(maggieFriedman) ∧ Producer(maggieFriedman) ShowRunnerOf(maggieFriedman, witchesOfEastEnd) ∧ ExecutiveProducerOf(maggieFriedman, witchesOfEastEnd) ∧ LifetimeTelevisionSeries(maggieFriedman) FantasyDrama(witchesOfEastEnd) ∧ Series(witchesOfEastEnd) Produces(maggieFriedman, eastwick) ∧ Develops(maggieFriedman, eastwick) Series(eastwick) ∧ AiredOn(eastwick, aBC)
None
Evangelos Eleftheriou is a Greek electrical engineer. If a company has employees working for them somewhere, then they have an office there. IBM is a company.
IBM has an office in London or Zurich or both.
HaveOfficeIn(ibm, london) ∨ HaveOfficeIn(ibm, zurich)
Evangelos Eleftheriou worked for IBM in Zurich.
98
False
Greek(evangelosEleftheriou) ∧ ElectricalEngineer(evangelosEleftheriou) ∀x ∀x ∀z (Company(x) ∧ WorkForIn(y, x, z) → HaveOfficeIn(x, z)) Company(ibm)
WorkForIn(evangelosEleftheriou, iBM, zurich)
"Hooray! Hooray! It's a Holi-Holiday!" was a big hit all over Europe. "Hooray! Hooray! It's a Holi-Holiday!" was not in German #1 singles. A song that peaks below #1 on the german charts is also a song that is not the #1 single in Germany.
"Hooray! Hooray! It's a Holi-Holiday!" peaked below #1 on the German charts.
PeaksBelowOn(hoorayHoorayItsAHoliHoliday, number1, germanChart)
Boney M. had several German #1 singles.
99
False
Song(hoorayHoorayItsAHoliHoliday) ∧ HitAllOverEurope(hoorayHoorayItsAHoliHoliday) Song(hoorayHoorayItsAHoliHoliday) ∧ ¬Number1GermanSingle(hoorayHoorayItsAHoliHoliday) ∀x (PeakBelowOn(x, number1, germanChart) → ¬Number1GermanSingle(x))
∃x (Song(x) ∧ By(x, boneym,) ∧ Number1GermanSingle(x))
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