Datasets:

minimario

/

FOLIO

like 1

[ "All people who regularly drink coffee are dependent on caffeine.", "People either regularly drink coffee or joke about being addicted to caffeine.", "No one who jokes about being addicted to caffeine is unaware that caffeine is a drug.", "Rina is either a student and unaware that caffeine is a drug, or neither a student nor unaware that caffeine is a drug.", "If Rina is not a person dependent on caffeine and a student, then Rina is either a person dependent on caffeine and a student, or neither a person dependent on caffeine nor a student. " ]

[ "∀x (Drinks(x) → Dependent(x))", "∀x (Drinks(x) ⊕ Jokes(x))", "∀x (Jokes(x) → ¬Unaware(x))", "(Student(rina) ∧ Unaware(rina)) ⊕ ¬(Student(rina) ∨ Unaware(rina))", "¬(Dependent(rina) ∧ Student(rina)) → (Dependent(rina) ∧ Student(rina)) ⊕ ¬(Dependent(rina) ∨ Student(rina))" ]

[ "All people who regularly drink coffee are dependent on caffeine.", "People either regularly drink coffee or joke about being addicted to caffeine.", "No one who jokes about being addicted to caffeine is unaware that caffeine is a drug.", "Rina is either a student and unaware that caffeine is a drug, or neither a student nor unaware that caffeine is a drug.", "If Rina is not a person dependent on caffeine and a student, then Rina is either a person dependent on caffeine and a student, or neither a person dependent on caffeine nor a student. " ]

[ "∀x (Drinks(x) → Dependent(x))", "∀x (Drinks(x) ⊕ Jokes(x))", "∀x (Jokes(x) → ¬Unaware(x))", "(Student(rina) ∧ Unaware(rina)) ⊕ ¬(Student(rina) ∨ Unaware(rina))", "¬(Dependent(rina) ∧ Student(rina)) → (Dependent(rina) ∧ Student(rina)) ⊕ ¬(Dependent(rina) ∨ Student(rina))" ]

[ "All people who regularly drink coffee are dependent on caffeine.", "People either regularly drink coffee or joke about being addicted to caffeine.", "No one who jokes about being addicted to caffeine is unaware that caffeine is a drug.", "Rina is either a student and unaware that caffeine is a drug, or neither a student nor unaware that caffeine is a drug.", "If Rina is not a person dependent on caffeine and a student, then Rina is either a person dependent on caffeine and a student, or neither a person dependent on caffeine nor a student. " ]

[ "∀x (Drinks(x) → Dependent(x))", "∀x (Drinks(x) ⊕ Jokes(x))", "∀x (Jokes(x) → ¬Unaware(x))", "(Student(rina) ∧ Unaware(rina)) ⊕ ¬(Student(rina) ∨ Unaware(rina))", "¬(Dependent(rina) ∧ Student(rina)) → (Dependent(rina) ∧ Student(rina)) ⊕ ¬(Dependent(rina) ∨ Student(rina))" ]

[ "All people who regularly drink coffee are dependent on caffeine.", "People either regularly drink coffee or joke about being addicted to caffeine.", "No one who jokes about being addicted to caffeine is unaware that caffeine is a drug.", "Rina is either a student and unaware that caffeine is a drug, or neither a student nor unaware that caffeine is a drug.", "If Rina is not a person dependent on caffeine and a student, then Rina is either a person dependent on caffeine and a student, or neither a person dependent on caffeine nor a student. " ]

[ "∀x (Drinks(x) → Dependent(x))", "∀x (Drinks(x) ⊕ Jokes(x))", "∀x (Jokes(x) → ¬Unaware(x))", "(Student(rina) ∧ Unaware(rina)) ⊕ ¬(Student(rina) ∨ Unaware(rina))", "¬(Dependent(rina) ∧ Student(rina)) → (Dependent(rina) ∧ Student(rina)) ⊕ ¬(Dependent(rina) ∨ Student(rina))" ]

[ "Miroslav Venhoda was a Czech choral conductor who specialized in the performance of Renaissance and Baroque music.", "Any choral conductor is a musician.", "Some musicians love music.", "Miroslav Venhoda published a book in 1946 called Method of Studying Gregorian Chant." ]

[ "Czech(miroslav) ∧ ChoralConductor(miroslav) ∧ Specialize(miroslav, renaissance) ∧ Specialize(miroslav, baroque)", "∀x (ChoralConductor(x) → Musician(x))", "∃x (Musician(x) → Love(x, music))", "Book(methodOfStudyingGregorianChant) ∧ Author(miroslav, methodOfStudyingGregorianChant) ∧ Publish(methodOfStudyingGregorianChant, year1946)" ]

[ "Miroslav Venhoda was a Czech choral conductor who specialized in the performance of Renaissance and Baroque music.", "Any choral conductor is a musician.", "Some musicians love music.", "Miroslav Venhoda published a book in 1946 called Method of Studying Gregorian Chant." ]

[ "Czech(miroslav) ∧ ChoralConductor(miroslav) ∧ Specialize(miroslav, renaissance) ∧ Specialize(miroslav, baroque)", "∀x (ChoralConductor(x) → Musician(x))", "∃x (Musician(x) → Love(x, music))", "Book(methodOfStudyingGregorianChant) ∧ Author(miroslav, methodOfStudyingGregorianChant) ∧ Publish(methodOfStudyingGregorianChant, year1946)" ]

[ "Miroslav Venhoda was a Czech choral conductor who specialized in the performance of Renaissance and Baroque music.", "Any choral conductor is a musician.", "Some musicians love music.", "Miroslav Venhoda published a book in 1946 called Method of Studying Gregorian Chant." ]

[ "Czech(miroslav) ∧ ChoralConductor(miroslav) ∧ Specialize(miroslav, renaissance) ∧ Specialize(miroslav, baroque)", "∀x (ChoralConductor(x) → Musician(x))", "∃x (Musician(x) → Love(x, music))", "Book(methodOfStudyingGregorianChant) ∧ Author(miroslav, methodOfStudyingGregorianChant) ∧ Publish(methodOfStudyingGregorianChant, year1946)" ]

[ "All eels are fish. ", "No fish are plants. ", "A thing is either a plant or animal.", "Nothing that breathes is paper. ", "All animals breathe.", "If a sea eel is either an eel or a plant, then a sea eel is an eel or an animal." ]

[ "∀x (Eel (x)→ Fish (x))", "∀x (Fish (x)→ ¬ Plant (x))", "∀x ( Plant (x) ∨ Animal (x))", "∀x (Breathe (x)→ ¬ Paper (x))", "∀x (Animal (x)→ Breathe (x))", " Eel (seaEel) ⊕ Plant (seaEel) → Eel (seaEel) ∨ Animal (seaEel) " ]

[ "All eels are fish. ", "No fish are plants. ", "A thing is either a plant or animal.", "Nothing that breathes is paper. ", "All animals breathe.", "If a sea eel is either an eel or a plant, then a sea eel is an eel or an animal." ]

[ "∀x (Eel (x)→ Fish (x))", "∀x (Fish (x)→ ¬ Plant (x))", "∀x ( Plant (x) ∨ Animal (x))", "∀x (Breathe (x)→ ¬ Paper (x))", "∀x (Animal (x)→ Breathe (x))", " Eel (seaEel) ⊕ Plant (seaEel) → Eel (seaEel) ∨ Animal (seaEel) " ]

[ "All eels are fish. ", "No fish are plants. ", "A thing is either a plant or animal.", "Nothing that breathes is paper. ", "All animals breathe.", "If a sea eel is either an eel or a plant, then a sea eel is an eel or an animal." ]

[ "∀x (Eel (x)→ Fish (x))", "∀x (Fish (x)→ ¬ Plant (x))", "∀x ( Plant (x) ∨ Animal (x))", "∀x (Breathe (x)→ ¬ Paper (x))", "∀x (Animal (x)→ Breathe (x))", " Eel (seaEel) ⊕ Plant (seaEel) → Eel (seaEel) ∨ Animal (seaEel) " ]

[ "The Blake McFall Company Building is a commercial warehouse listed on the National Register of Historic Places.", "The Blake McFall Company Building was 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." ]

[ "∀x (Blake(x) → Building(x))", "∀x (Blake(x) → Historic(x, year1990))", "∀x (Emmet(x) → Building(x) ∧ FiveStory(x) ∧ Locate(x, portland))", "∀x (Emmet(x) → Construct(x, year1915))", "∀x (Emmet(x) ↔ Blake(x))", "∃x (Emmet(x) ∧ Work(john, x))" ]

[ "The Blake McFall Company Building is a commercial warehouse listed on the National Register of Historic Places.", "The Blake McFall Company Building was 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." ]

[ "∀x (Blake(x) → Building(x))", "∀x (Blake(x) → Historic(x, year1990))", "∀x (Emmet(x) → Building(x) ∧ FiveStory(x) ∧ Locate(x, portland))", "∀x (Emmet(x) → Construct(x, year1915))", "∀x (Emmet(x) ↔ Blake(x))", "∃x (Emmet(x) ∧ Work(john, x))" ]

[ "The Blake McFall Company Building is a commercial warehouse listed on the National Register of Historic Places.", "The Blake McFall Company Building was 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." ]

[ "∀x (Blake(x) → Building(x))", "∀x (Blake(x) → Historic(x, year1990))", "∀x (Emmet(x) → Building(x) ∧ FiveStory(x) ∧ Locate(x, portland))", "∀x (Emmet(x) → Construct(x, year1915))", "∀x (Emmet(x) ↔ Blake(x))", "∃x (Emmet(x) ∧ Work(john, x))" ]

[ "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." ]

[ "BritishPolitician(williamdickinson) ∧ SatInHouseOfCommons(williamdickinson)", "Attended(williamdickinson, westminster) ∧ Highschool(westminster) ∧ Attended(williamdickinson, universityofedinburgh)", "LocatedIn(universityofedinburgh, unitedkingdom) ∧ University(universityofedinburgh)", "Supported(williamdickinson, portlandwhigs)", "∀x (Supported(x, portlandwhigs) → ¬SeatInParliament(x))" ]

[ "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." ]

[ "BritishPolitician(williamdickinson) ∧ SatInHouseOfCommons(williamdickinson)", "Attended(williamdickinson, westminster) ∧ Highschool(westminster) ∧ Attended(williamdickinson, universityofedinburgh)", "LocatedIn(universityofedinburgh, unitedkingdom) ∧ University(universityofedinburgh)", "Supported(williamdickinson, portlandwhigs)", "∀x (Supported(x, portlandwhigs) → ¬SeatInParliament(x))" ]

[ "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." ]

[ "BritishPolitician(williamdickinson) ∧ SatInHouseOfCommons(williamdickinson)", "Attended(williamdickinson, westminster) ∧ Highschool(westminster) ∧ Attended(williamdickinson, universityofedinburgh)", "LocatedIn(universityofedinburgh, unitedkingdom) ∧ University(universityofedinburgh)", "Supported(williamdickinson, portlandwhigs)", "∀x (Supported(x, portlandwhigs) → ¬SeatInParliament(x))" ]

[ "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." ]

[ "BritishPolitician(williamdickinson) ∧ SatInHouseOfCommons(williamdickinson)", "Attended(williamdickinson, westminster) ∧ Highschool(westminster) ∧ Attended(williamdickinson, universityofedinburgh)", "LocatedIn(universityofedinburgh, unitedkingdom) ∧ University(universityofedinburgh)", "Supported(williamdickinson, portlandwhigs)", "∀x (Supported(x, portlandwhigs) → ¬SeatInParliament(x))" ]

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

[ "UniversalLanguage(languageA)", "∀x ∀y (∃z (Know(x, z) ∧ Know(y, z) ∧ UniversalLanguage(z)) → Communicate(x, y))", "Know(katya, languageA)", "¬Communicate(katya, danil)" ]

[ "All customers who are subscribed to AMC List are available to watch 3 movies every week without any additional fees. ", "Some customers go to cinemas every week", "Customers either subscribe to AMC service or HBO service. ", "Customers who prefer TV series more and will not watch TV series in cinemas.", "All customers who subscribe to HBO services prefer TV series to movies. ", "James watches TV series in cinemas. " ]

[ "∀x (AMC(x) → ThreeMovies(x))", "∃x (CinemaEveryWeek(x))", "∀x (AMC(x) ∨ HBO(x))", "∀x (PreferTVSeries(x) → ¬WatchTVInCinema(x))", "∀x (HBO(x) → PreferTVSeries(x))", "WatchTVInCinema(james)" ]

[ "All customers who are subscribed to AMC List are available to watch 3 movies every week without any additional fees. ", "Some customers go to cinemas every week", "Customers either subscribe to AMC service or HBO service. ", "Customers who prefer TV series more and will not watch TV series in cinemas.", "All customers who subscribe to HBO services prefer TV series to movies. ", "James watches TV series in cinemas. " ]

[ "∀x (AMC(x) → ThreeMovies(x))", "∃x (CinemaEveryWeek(x))", "∀x (AMC(x) ∨ HBO(x))", "∀x (PreferTVSeries(x) → ¬WatchTVInCinema(x))", "∀x (HBO(x) → PreferTVSeries(x))", "WatchTVInCinema(james)" ]

[ "All customers who are subscribed to AMC List are available to watch 3 movies every week without any additional fees. ", "Some customers go to cinemas every week", "Customers either subscribe to AMC service or HBO service. ", "Customers who prefer TV series more and will not watch TV series in cinemas.", "All customers who subscribe to HBO services prefer TV series to movies. ", "James watches TV series in cinemas. " ]

[ "∀x (AMC(x) → ThreeMovies(x))", "∃x (CinemaEveryWeek(x))", "∀x (AMC(x) ∨ HBO(x))", "∀x (PreferTVSeries(x) → ¬WatchTVInCinema(x))", "∀x (HBO(x) → PreferTVSeries(x))", "WatchTVInCinema(james)" ]

[ "All customers who are subscribed to AMC List are available to watch 3 movies every week without any additional fees. ", "Some customers go to cinemas every week", "Customers either subscribe to AMC service or HBO service. ", "Customers who prefer TV series more and will not watch TV series in cinemas.", "All customers who subscribe to HBO services prefer TV series to movies. ", "James watches TV series in cinemas. " ]

[ "∀x (AMC(x) → ThreeMovies(x))", "∃x (CinemaEveryWeek(x))", "∀x (AMC(x) ∨ HBO(x))", "∀x (PreferTVSeries(x) → ¬WatchTVInCinema(x))", "∀x (HBO(x) → PreferTVSeries(x))", "WatchTVInCinema(james)" ]

[ "All customers who are subscribed to AMC List are available to watch 3 movies every week without any additional fees. ", "Some customers go to cinemas every week", "Customers either subscribe to AMC service or HBO service. ", "Customers who prefer TV series more and will not watch TV series in cinemas.", "All customers who subscribe to HBO services prefer TV series to movies. ", "James watches TV series in cinemas. " ]

[ "∀x (AMC(x) → ThreeMovies(x))", "∃x (CinemaEveryWeek(x))", "∀x (AMC(x) ∨ HBO(x))", "∀x (PreferTVSeries(x) → ¬WatchTVInCinema(x))", "∀x (HBO(x) → PreferTVSeries(x))", "WatchTVInCinema(james)" ]

[ "A La Liga soccer team ranks higher than another if it receives more points.", "If two La Liga soccer teams recieve the same points, the team which recieves more points from the games between the two teams ranks higher.", "Real Madrid and Barcelona are both La Liga soccer teams.", "In La Liga 2021-2022, Real Madrid recieves 86 points and Barcelon recieves 73 points.", "In La Liga 2021-2022, Real Madrid and Barcelona both recieve 3 points from the games between them." ]

[ "∀x ∀y (LaLiga(x) ∧ LaLiga(y) ∧ MorePoints(x, y) → HigherRank(x, y))", "∀x ∀y (LaLiga(x) ∧ LaLiga(y) ∧ ¬MorePoints(x, y) ∧ ¬MorePoints(y, x) ∧ MorePointsInGameBetween(x, y) → HigherRank(x, y))", "LaLiga(realMadrid) ∧ LaLiga(barcelona)", "MorePoints(realMadrid, barcelona)", "¬MorePointsInGameBetween(realMadrid, barcelona) ∧ ¬MorePointsInGameBetween(barcelona, realMadrid)" ]

[ "A La Liga soccer team ranks higher than another if it receives more points.", "If two La Liga soccer teams recieve the same points, the team which recieves more points from the games between the two teams ranks higher.", "Real Madrid and Barcelona are both La Liga soccer teams.", "In La Liga 2021-2022, Real Madrid recieves 86 points and Barcelon recieves 73 points.", "In La Liga 2021-2022, Real Madrid and Barcelona both recieve 3 points from the games between them." ]

[ "∀x ∀y (LaLiga(x) ∧ LaLiga(y) ∧ MorePoints(x, y) → HigherRank(x, y))", "∀x ∀y (LaLiga(x) ∧ LaLiga(y) ∧ ¬MorePoints(x, y) ∧ ¬MorePoints(y, x) ∧ MorePointsInGameBetween(x, y) → HigherRank(x, y))", "LaLiga(realMadrid) ∧ LaLiga(barcelona)", "MorePoints(realMadrid, barcelona)", "¬MorePointsInGameBetween(realMadrid, barcelona) ∧ ¬MorePointsInGameBetween(barcelona, realMadrid)" ]

[ "Lawton Park is a neighbourhood in Seattle. ", "All citizens of Lawton Park use the zip code 98199. ", "Tom is a citizen of Lawton Park.", "Daniel uses the zip code 98199. " ]

[ "Neighbourhoodin(lawtonPark, seattle)", "∀x (Citizenof(x, lawtonPark) → Usezipcode(x, number98199))", "Citizenof(tom, lawtonPark)", "Usezipcode(daniel, number98199)" ]

[ "Lawton Park is a neighbourhood in Seattle. ", "All citizens of Lawton Park use the zip code 98199. ", "Tom is a citizen of Lawton Park.", "Daniel uses the zip code 98199. " ]

[ "Neighbourhoodin(lawtonPark, seattle)", "∀x (Citizenof(x, lawtonPark) → Usezipcode(x, number98199))", "Citizenof(tom, lawtonPark)", "Usezipcode(daniel, number98199)" ]

[ "Lawton Park is a neighbourhood in Seattle. ", "All citizens of Lawton Park use the zip code 98199. ", "Tom is a citizen of Lawton Park.", "Daniel uses the zip code 98199. " ]

[ "Neighbourhoodin(lawtonPark, seattle)", "∀x (Citizenof(x, lawtonPark) → Usezipcode(x, number98199))", "Citizenof(tom, lawtonPark)", "Usezipcode(daniel, number98199)" ]

[ "Lawton Park is a neighbourhood in Seattle. ", "All citizens of Lawton Park use the zip code 98199. ", "Tom is a citizen of Lawton Park.", "Daniel uses the zip code 98199. " ]

[ "Neighbourhoodin(lawtonPark, seattle)", "∀x (Citizenof(x, lawtonPark) → Usezipcode(x, number98199))", "Citizenof(tom, lawtonPark)", "Usezipcode(daniel, number98199)" ]

[ "If a legislator is found guilty of stealing government funds, they will be suspended from office.", "Tiffany T. Alston was a legislator in Maryland's House of Delegates from 2011 to 2013.", "Tiffany T. Alston was found guilty of stealing government funds in 2012." ]

[ "∀x (IsLegislator(x) ∧ StealsFunds(x) → Suspended(x))", "IsLegislator(tiffanyTAlston)", "StealsFunds(tiffanyTAlston)" ]

[ "If a legislator is found guilty of stealing government funds, they will be suspended from office.", "Tiffany T. Alston was a legislator in Maryland's House of Delegates from 2011 to 2013.", "Tiffany T. Alston was found guilty of stealing government funds in 2012." ]

[ "∀x (IsLegislator(x) ∧ StealsFunds(x) → Suspended(x))", "IsLegislator(tiffanyTAlston)", "StealsFunds(tiffanyTAlston)" ]

[ "If a legislator is found guilty of stealing government funds, they will be suspended from office.", "Tiffany T. Alston was a legislator in Maryland's House of Delegates from 2011 to 2013.", "Tiffany T. Alston was found guilty of stealing government funds in 2012." ]

[ "∀x (IsLegislator(x) ∧ StealsFunds(x) → Suspended(x))", "IsLegislator(tiffanyTAlston)", "StealsFunds(tiffanyTAlston)" ]

[ "Some fish may sting.", "Stonefish is a fish.", "It stings to step on a stonefish.", "Stonefish stings cause death if not treated.", "To treat stonefish stings, apply heat to the affected area or use an antivenom." ]

[ "∃x ∃y (Fish(x) → Sting(x,y))", "Fish(stonefish)", "∀x (StepOn(stonefish, x) → Sting(stonefish, x))", "∀x (Sting(stonefish, x) ∧ ¬Treated(x) → CauseDeath(x))", "∀x (Sting(stonefish, x) ∧ (ApplyHeat(x) ∨ UseAntivenom(x)) → Treated(x))" ]

[ "Some fish may sting.", "Stonefish is a fish.", "It stings to step on a stonefish.", "Stonefish stings cause death if not treated.", "To treat stonefish stings, apply heat to the affected area or use an antivenom." ]

[ "∃x ∃y (Fish(x) → Sting(x,y))", "Fish(stonefish)", "∀x (StepOn(stonefish, x) → Sting(stonefish, x))", "∀x (Sting(stonefish, x) ∧ ¬Treated(x) → CauseDeath(x))", "∀x (Sting(stonefish, x) ∧ (ApplyHeat(x) ∨ UseAntivenom(x)) → Treated(x))" ]

[ "Some fish may sting.", "Stonefish is a fish.", "It stings to step on a stonefish.", "Stonefish stings cause death if not treated.", "To treat stonefish stings, apply heat to the affected area or use an antivenom." ]

[ "∃x ∃y (Fish(x) → Sting(x,y))", "Fish(stonefish)", "∀x (StepOn(stonefish, x) → Sting(stonefish, x))", "∀x (Sting(stonefish, x) ∧ ¬Treated(x) → CauseDeath(x))", "∀x (Sting(stonefish, x) ∧ (ApplyHeat(x) ∨ UseAntivenom(x)) → Treated(x))" ]

[ "Some monitors produced by LG have a type-c port.", "If the monitor has a type-c port, then it is not produced by AOC.", "All monitors in the library are produced by AOC. ", "L-2021 is either in the library or has a type-c port.", "L-2021 is either produced by AOC and produced by LG, or neither produced by AOC nor produced by LG." ]

[ "∃x (LG(x) ∧ TypeC(x))", "∀x (TypeC(x) → ¬AOC(x))", "∀x (Library(x) → AOC(x))", "Library(l-2021) ⊕ TypeC(l-2021) ", "¬(AOC(l-2021) ⊕ LG(l-2021))" ]

[ "Some monitors produced by LG have a type-c port.", "If the monitor has a type-c port, then it is not produced by AOC.", "All monitors in the library are produced by AOC. ", "L-2021 is either in the library or has a type-c port.", "L-2021 is either produced by AOC and produced by LG, or neither produced by AOC nor produced by LG." ]

[ "∃x (LG(x) ∧ TypeC(x))", "∀x (TypeC(x) → ¬AOC(x))", "∀x (Library(x) → AOC(x))", "Library(l-2021) ⊕ TypeC(l-2021) ", "¬(AOC(l-2021) ⊕ LG(l-2021))" ]

[ "Some monitors produced by LG have a type-c port.", "If the monitor has a type-c port, then it is not produced by AOC.", "All monitors in the library are produced by AOC. ", "L-2021 is either in the library or has a type-c port.", "L-2021 is either produced by AOC and produced by LG, or neither produced by AOC nor produced by LG." ]

[ "∃x (LG(x) ∧ TypeC(x))", "∀x (TypeC(x) → ¬AOC(x))", "∀x (Library(x) → AOC(x))", "Library(l-2021) ⊕ TypeC(l-2021) ", "¬(AOC(l-2021) ⊕ LG(l-2021))" ]

[ "Some monitors produced by LG have a type-c port.", "If the monitor has a type-c port, then it is not produced by AOC.", "All monitors in the library are produced by AOC. ", "L-2021 is either in the library or has a type-c port.", "L-2021 is either produced by AOC and produced by LG, or neither produced by AOC nor produced by LG." ]

[ "∃x (LG(x) ∧ TypeC(x))", "∀x (TypeC(x) → ¬AOC(x))", "∀x (Library(x) → AOC(x))", "Library(l-2021) ⊕ TypeC(l-2021) ", "¬(AOC(l-2021) ⊕ LG(l-2021))" ]

[ "Some monitors produced by LG have a type-c port.", "If the monitor has a type-c port, then it is not produced by AOC.", "All monitors in the library are produced by AOC. ", "L-2021 is either in the library or has a type-c port.", "L-2021 is either produced by AOC and produced by LG, or neither produced by AOC nor produced by LG." ]

[ "∃x (LG(x) ∧ TypeC(x))", "∀x (TypeC(x) → ¬AOC(x))", "∀x (Library(x) → AOC(x))", "Library(l-2021) ⊕ TypeC(l-2021) ", "¬(AOC(l-2021) ⊕ LG(l-2021))" ]

[ "People eat meat regularly or are vegetation.", "If people eat meat regularly, then they enjoy eating hamburgers and steaks.", "All people who are vegetarian are conscious of the environment or their health.", "If people are conscious about the environment or their health, then they do not go to fast food places often.", "If people have busy schedules without time to cook, then they go to fast food places often.", "If Jeremy does not both go to fast food places often and is conscious about the environment or their health, then he goes to fast food places often." ]

[ "∀x (Meat(x) ∨ Vegetarian(x))", "∀x (Meat(x) → Hamburgers(x))", "∀x (Vegetarian(x) → Conscious(x))", "∀x (Conscious(x) → ¬FastFood(x))", "∀x (Busy(x) → FastFood(x))", "¬(FastFood(jeremy) ∧ Conscious(jeremy)) → FastFood(jeremy)" ]

[ "People eat meat regularly or are vegetation.", "If people eat meat regularly, then they enjoy eating hamburgers and steaks.", "All people who are vegetarian are conscious of the environment or their health.", "If people are conscious about the environment or their health, then they do not go to fast food places often.", "If people have busy schedules without time to cook, then they go to fast food places often.", "If Jeremy does not both go to fast food places often and is conscious about the environment or their health, then he goes to fast food places often." ]

[ "∀x (Meat(x) ∨ Vegetarian(x))", "∀x (Meat(x) → Hamburgers(x))", "∀x (Vegetarian(x) → Conscious(x))", "∀x (Conscious(x) → ¬FastFood(x))", "∀x (Busy(x) → FastFood(x))", "¬(FastFood(jeremy) ∧ Conscious(jeremy)) → FastFood(jeremy)" ]

[ "People eat meat regularly or are vegetation.", "If people eat meat regularly, then they enjoy eating hamburgers and steaks.", "All people who are vegetarian are conscious of the environment or their health.", "If people are conscious about the environment or their health, then they do not go to fast food places often.", "If people have busy schedules without time to cook, then they go to fast food places often.", "If Jeremy does not both go to fast food places often and is conscious about the environment or their health, then he goes to fast food places often." ]

[ "∀x (Meat(x) ∨ Vegetarian(x))", "∀x (Meat(x) → Hamburgers(x))", "∀x (Vegetarian(x) → Conscious(x))", "∀x (Conscious(x) → ¬FastFood(x))", "∀x (Busy(x) → FastFood(x))", "¬(FastFood(jeremy) ∧ Conscious(jeremy)) → FastFood(jeremy)" ]

[ "Sam is doing a project.", "A project is written either in C++ or in Python.", "If Sam does a project written in Python, he will not use a Mac.", "Sam is using a Mac.", "If Sam uses a Mac, he will play a song.", "If a song is not \"Perfect\", Sam will never play it." ]

[ "∃x (Project(x) ∧ Do(sam, x))", " ∀x (Project(x) → (WrittenIn(x, python) ⊕ WrittenIn(x, c++)))", " ∀x (Project(x) ∧ WrittenIn(x, python) ∧ Do(sam, x) → ¬Use(sam, mac))", " Use(sam, mac)", " Use(sam, mac) → ∃x (Song(x) ∧ Play(sam, x))", " ∀x (¬Be(x, perfect) → ¬Play(sam, x))" ]

[ "Sam is doing a project.", "A project is written either in C++ or in Python.", "If Sam does a project written in Python, he will not use a Mac.", "Sam is using a Mac.", "If Sam uses a Mac, he will play a song.", "If a song is not \"Perfect\", Sam will never play it." ]

[ "∃x (Project(x) ∧ Do(sam, x))", " ∀x (Project(x) → (WrittenIn(x, python) ⊕ WrittenIn(x, c++)))", " ∀x (Project(x) ∧ WrittenIn(x, python) ∧ Do(sam, x) → ¬Use(sam, mac))", " Use(sam, mac)", " Use(sam, mac) → ∃x (Song(x) ∧ Play(sam, x))", " ∀x (¬Be(x, perfect) → ¬Play(sam, x))" ]

[ "Sam is doing a project.", "A project is written either in C++ or in Python.", "If Sam does a project written in Python, he will not use a Mac.", "Sam is using a Mac.", "If Sam uses a Mac, he will play a song.", "If a song is not \"Perfect\", Sam will never play it." ]

[ "∃x (Project(x) ∧ Do(sam, x))", " ∀x (Project(x) → (WrittenIn(x, python) ⊕ WrittenIn(x, c++)))", " ∀x (Project(x) ∧ WrittenIn(x, python) ∧ Do(sam, x) → ¬Use(sam, mac))", " Use(sam, mac)", " Use(sam, mac) → ∃x (Song(x) ∧ Play(sam, x))", " ∀x (¬Be(x, perfect) → ¬Play(sam, x))" ]

[ "All rabbits have fur", "Some pets are rabbits." ]

[ "∀x (Rabbit(x) → HasFur(x))", "∃x (Pet(x) ∧ Reptile(x))" ]

[ "All video applications are software.", "All YouTube-related applications are video applications. ", "An APP is either related to YouTube or Instagram.", "All Instagram is entertainment. ", "All software is programmed. ", "All entertainments are interesting.", "If something is interesting, then it is good.", "TikTok is not good." ]

[ "∀x (App(x) → Software(x))", "∀x (Youtube(x) → App(x))", "∀x (Youtube(x) ∨ Instagram(x))", "∀x (Instagram(x) → Entertainment(x))", "∀x (Software(x) → Program(x))", "∀x (Entertainment(x) → Interesting(x))", "∀x (Interesting(x) → Good(x))", "¬Good(tiktok)" ]

[ "All video applications are software.", "All YouTube-related applications are video applications. ", "An APP is either related to YouTube or Instagram.", "All Instagram is entertainment. ", "All software is programmed. ", "All entertainments are interesting.", "If something is interesting, then it is good.", "TikTok is not good." ]

[ "∀x (App(x) → Software(x))", "∀x (Youtube(x) → App(x))", "∀x (Youtube(x) ∨ Instagram(x))", "∀x (Instagram(x) → Entertainment(x))", "∀x (Software(x) → Program(x))", "∀x (Entertainment(x) → Interesting(x))", "∀x (Interesting(x) → Good(x))", "¬Good(tiktok)" ]

[ "All video applications are software.", "All YouTube-related applications are video applications. ", "An APP is either related to YouTube or Instagram.", "All Instagram is entertainment. ", "All software is programmed. ", "All entertainments are interesting.", "If something is interesting, then it is good.", "TikTok is not good." ]

[ "∀x (App(x) → Software(x))", "∀x (Youtube(x) → App(x))", "∀x (Youtube(x) ∨ Instagram(x))", "∀x (Instagram(x) → Entertainment(x))", "∀x (Software(x) → Program(x))", "∀x (Entertainment(x) → Interesting(x))", "∀x (Interesting(x) → Good(x))", "¬Good(tiktok)" ]

[ "All video applications are software.", "All YouTube-related applications are video applications. ", "An APP is either related to YouTube or Instagram.", "All Instagram is entertainment. ", "All software is programmed. ", "All entertainments are interesting.", "If something is interesting, then it is good.", "TikTok is not good." ]

[ "∀x (App(x) → Software(x))", "∀x (Youtube(x) → App(x))", "∀x (Youtube(x) ∨ Instagram(x))", "∀x (Instagram(x) → Entertainment(x))", "∀x (Software(x) → Program(x))", "∀x (Entertainment(x) → Interesting(x))", "∀x (Interesting(x) → Good(x))", "¬Good(tiktok)" ]

[ "Ordinary is an unincorporated community.", "Located within Elliot County, Ordinary is on Kentucky Route 32.", "Ordinary is located northwest of Sandy Hook." ]

[ "UnincorporatedCommunity(ordinary)", "In(ordinary, elliotcounty) ∧ On(ordinary, kentuckyroute32)", "NorthwestOf(ordinary, sandyhook)" ]

[ "Ordinary is an unincorporated community.", "Located within Elliot County, Ordinary is on Kentucky Route 32.", "Ordinary is located northwest of Sandy Hook." ]

[ "UnincorporatedCommunity(ordinary)", "In(ordinary, elliotcounty) ∧ On(ordinary, kentuckyroute32)", "NorthwestOf(ordinary, sandyhook)" ]

[ "All young adults go on a diet.", "All college students are young adults.", "All Yale students are college students.", "Someone is either a Yale student or a Harvard student.", "All Harvard students are diligent.", "If Susan is a Harvard student, then she is a young adult.", "If Susan is a Yale student, then she does not go on a diet." ]

[ "∀x (YoungAdult(x) → GoOnDiet(x))", "∀x (CollegeStudent(x) → YoungAdult(x))", "∀x (YaleStudent(x) → CollegeStudent(x))", "∀x (YaleStudent(x) ∨ HarvardStudent(x))", "∀x (HarvardStudent(x) → Diligent(x))", "HarvardStudent(susan) → YoungAdult(susan)", "YaleStudent(susan) → ¬GoOnDiet(susan)" ]

[ "All young adults go on a diet.", "All college students are young adults.", "All Yale students are college students.", "Someone is either a Yale student or a Harvard student.", "All Harvard students are diligent.", "If Susan is a Harvard student, then she is a young adult.", "If Susan is a Yale student, then she does not go on a diet." ]

[ "∀x (YoungAdult(x) → GoOnDiet(x))", "∀x (CollegeStudent(x) → YoungAdult(x))", "∀x (YaleStudent(x) → CollegeStudent(x))", "∀x (YaleStudent(x) ∨ HarvardStudent(x))", "∀x (HarvardStudent(x) → Diligent(x))", "HarvardStudent(susan) → YoungAdult(susan)", "YaleStudent(susan) → ¬GoOnDiet(susan)" ]

[ "All young adults go on a diet.", "All college students are young adults.", "All Yale students are college students.", "Someone is either a Yale student or a Harvard student.", "All Harvard students are diligent.", "If Susan is a Harvard student, then she is a young adult.", "If Susan is a Yale student, then she does not go on a diet." ]

[ "∀x (YoungAdult(x) → GoOnDiet(x))", "∀x (CollegeStudent(x) → YoungAdult(x))", "∀x (YaleStudent(x) → CollegeStudent(x))", "∀x (YaleStudent(x) ∨ HarvardStudent(x))", "∀x (HarvardStudent(x) → Diligent(x))", "HarvardStudent(susan) → YoungAdult(susan)", "YaleStudent(susan) → ¬GoOnDiet(susan)" ]

[ "Vic DiCara plays guitar and bass.", "The only style of music Vic DiCara plays is punk music.", "Vic DiCara played in the band Inside Out." ]

[ "Play(vicdicara, guitar) ∧ Play(vicdicara, bass)", "¬(∃x (Music (vicdicara, punk) ∧ Music (vicdicara, x)))", "Band(vicdicara, insideOut)" ]

[ "Vic DiCara plays guitar and bass.", "The only style of music Vic DiCara plays is punk music.", "Vic DiCara played in the band Inside Out." ]

[ "Play(vicdicara, guitar) ∧ Play(vicdicara, bass)", "¬(∃x (Music (vicdicara, punk) ∧ Music (vicdicara, x)))", "Band(vicdicara, insideOut)" ]

[ "All athletes are good at sports.", "All Olympic gold medal winners are good athletes.", "No scientists are good at sports.", "All Nobel laureates are scientists.", "Amy is good at sports or Amy is an Olympic gold medal winner.", "If Amy is not a Nobel laureate, then Amy is not an Olympic gold medal winner." ]

[ "∀x (Athlete(x) → GoodAtSports(x))", "∀x (OlympicGoldMedalWinner(x) → Athlete(x))", "∀x (Scientist(x) → ¬GoodAtSports(x))", "∀x (NobelLaureate(x) → Scientist(x))", "GoodAtSports(amy) ∨ OlympicGoldMedalWinner(amy)", "¬NobelLaureate(amy) → ¬OlympicGoldMedalWinner(amy)" ]

[ "All athletes are good at sports.", "All Olympic gold medal winners are good athletes.", "No scientists are good at sports.", "All Nobel laureates are scientists.", "Amy is good at sports or Amy is an Olympic gold medal winner.", "If Amy is not a Nobel laureate, then Amy is not an Olympic gold medal winner." ]

[ "∀x (Athlete(x) → GoodAtSports(x))", "∀x (OlympicGoldMedalWinner(x) → Athlete(x))", "∀x (Scientist(x) → ¬GoodAtSports(x))", "∀x (NobelLaureate(x) → Scientist(x))", "GoodAtSports(amy) ∨ OlympicGoldMedalWinner(amy)", "¬NobelLaureate(amy) → ¬OlympicGoldMedalWinner(amy)" ]

[ "All athletes are good at sports.", "All Olympic gold medal winners are good athletes.", "No scientists are good at sports.", "All Nobel laureates are scientists.", "Amy is good at sports or Amy is an Olympic gold medal winner.", "If Amy is not a Nobel laureate, then Amy is not an Olympic gold medal winner." ]

[ "∀x (Athlete(x) → GoodAtSports(x))", "∀x (OlympicGoldMedalWinner(x) → Athlete(x))", "∀x (Scientist(x) → ¬GoodAtSports(x))", "∀x (NobelLaureate(x) → Scientist(x))", "GoodAtSports(amy) ∨ OlympicGoldMedalWinner(amy)", "¬NobelLaureate(amy) → ¬OlympicGoldMedalWinner(amy)" ]

[ "All fruits with the color red contain a large amount of vitamin C.", "All apples are fruits with the color red.", "All fruits containing a large amount of vitamin C are beneficial to people. ", "No fruits that are beneficial to people are on a warning list.", "If K is not beneficial to people and also not an apple, then it is a fruit with the color red." ]

[ "∀x (RedFruit(x) → VC(x))", "∀x (Apple(x) → RedFruit(x))", "∀x (VC(x) → Benefit(x))", "∀x (Benefit(x) → ¬WarningList(x))", "¬(Benefit(k) ∧ Apple(k)) → RedFruit(k)" ]

[ "All fruits with the color red contain a large amount of vitamin C.", "All apples are fruits with the color red.", "All fruits containing a large amount of vitamin C are beneficial to people. ", "No fruits that are beneficial to people are on a warning list.", "If K is not beneficial to people and also not an apple, then it is a fruit with the color red." ]

[ "∀x (RedFruit(x) → VC(x))", "∀x (Apple(x) → RedFruit(x))", "∀x (VC(x) → Benefit(x))", "∀x (Benefit(x) → ¬WarningList(x))", "¬(Benefit(k) ∧ Apple(k)) → RedFruit(k)" ]

[ "All fruits with the color red contain a large amount of vitamin C.", "All apples are fruits with the color red.", "All fruits containing a large amount of vitamin C are beneficial to people. ", "No fruits that are beneficial to people are on a warning list.", "If K is not beneficial to people and also not an apple, then it is a fruit with the color red." ]

[ "∀x (RedFruit(x) → VC(x))", "∀x (Apple(x) → RedFruit(x))", "∀x (VC(x) → Benefit(x))", "∀x (Benefit(x) → ¬WarningList(x))", "¬(Benefit(k) ∧ Apple(k)) → RedFruit(k)" ]

[ "All fruits with the color red contain a large amount of vitamin C.", "All apples are fruits with the color red.", "All fruits containing a large amount of vitamin C are beneficial to people. ", "No fruits that are beneficial to people are on a warning list.", "If K is not beneficial to people and also not an apple, then it is a fruit with the color red." ]

[ "∀x (RedFruit(x) → VC(x))", "∀x (Apple(x) → RedFruit(x))", "∀x (VC(x) → Benefit(x))", "∀x (Benefit(x) → ¬WarningList(x))", "¬(Benefit(k) ∧ Apple(k)) → RedFruit(k)" ]

[ "All fruits with the color red contain a large amount of vitamin C.", "All apples are fruits with the color red.", "All fruits containing a large amount of vitamin C are beneficial to people. ", "No fruits that are beneficial to people are on a warning list.", "If K is not beneficial to people and also not an apple, then it is a fruit with the color red." ]

[ "∀x (RedFruit(x) → VC(x))", "∀x (Apple(x) → RedFruit(x))", "∀x (VC(x) → Benefit(x))", "∀x (Benefit(x) → ¬WarningList(x))", "¬(Benefit(k) ∧ Apple(k)) → RedFruit(k)" ]

[ "Everyone working at Meta has a high income. ", "If a person has a high income, then he/she will not take a bus to their destination.", "People will either take a bus or drive to their destination. ", "Everyone who has a car will choose to drive to their destination. ", "No students drive to their destination. ", "James has a car or works at Meta." ]

[ "∀x (Meta(x) → HighIncome(x))", "∀x (HighIncome(x) → ¬Bus(x))", "∀x (Bus(x) ∨ Drive(x))", "∀x (HaveCars(x) → Drive(x))", "∀x (Student(x) → ¬Drive(x))", "HaveCars(james) ∨ Meta(james)" ]

[ "Everyone working at Meta has a high income. ", "If a person has a high income, then he/she will not take a bus to their destination.", "People will either take a bus or drive to their destination. ", "Everyone who has a car will choose to drive to their destination. ", "No students drive to their destination. ", "James has a car or works at Meta." ]

[ "∀x (Meta(x) → HighIncome(x))", "∀x (HighIncome(x) → ¬Bus(x))", "∀x (Bus(x) ∨ Drive(x))", "∀x (HaveCars(x) → Drive(x))", "∀x (Student(x) → ¬Drive(x))", "HaveCars(james) ∨ Meta(james)" ]

[ "Everyone working at Meta has a high income. ", "If a person has a high income, then he/she will not take a bus to their destination.", "People will either take a bus or drive to their destination. ", "Everyone who has a car will choose to drive to their destination. ", "No students drive to their destination. ", "James has a car or works at Meta." ]

[ "∀x (Meta(x) → HighIncome(x))", "∀x (HighIncome(x) → ¬Bus(x))", "∀x (Bus(x) ∨ Drive(x))", "∀x (HaveCars(x) → Drive(x))", "∀x (Student(x) → ¬Drive(x))", "HaveCars(james) ∨ Meta(james)" ]

[ "Everyone working at Meta has a high income. ", "If a person has a high income, then he/she will not take a bus to their destination.", "People will either take a bus or drive to their destination. ", "Everyone who has a car will choose to drive to their destination. ", "No students drive to their destination. ", "James has a car or works at Meta." ]

[ "∀x (Meta(x) → HighIncome(x))", "∀x (HighIncome(x) → ¬Bus(x))", "∀x (Bus(x) ∨ Drive(x))", "∀x (HaveCars(x) → Drive(x))", "∀x (Student(x) → ¬Drive(x))", "HaveCars(james) ∨ Meta(james)" ]

[ "Everyone working at Meta has a high income. ", "If a person has a high income, then he/she will not take a bus to their destination.", "People will either take a bus or drive to their destination. ", "Everyone who has a car will choose to drive to their destination. ", "No students drive to their destination. ", "James has a car or works at Meta." ]

[ "∀x (Meta(x) → HighIncome(x))", "∀x (HighIncome(x) → ¬Bus(x))", "∀x (Bus(x) ∨ Drive(x))", "∀x (HaveCars(x) → Drive(x))", "∀x (Student(x) → ¬Drive(x))", "HaveCars(james) ∨ Meta(james)" ]

[ "Everyone working at Meta has a high income. ", "If a person has a high income, then he/she will not take a bus to their destination.", "People will either take a bus or drive to their destination. ", "Everyone who has a car will choose to drive to their destination. ", "No students drive to their destination. ", "James has a car or works at Meta." ]

[ "∀x (Meta(x) → HighIncome(x))", "∀x (HighIncome(x) → ¬Bus(x))", "∀x (Bus(x) ∨ Drive(x))", "∀x (HaveCars(x) → Drive(x))", "∀x (Student(x) → ¬Drive(x))", "HaveCars(james) ∨ Meta(james)" ]

[ "Students either go to the park or go to the movies. ", "No student who enjoys nature has free time during the weekend. ", "All students who go to the movies enjoy nature. ", "All students who do not have class during the weekend have free time during the weekend. ", "All students not in summer camp do not have class during the weekend. ", "James does not have class during the weekend." ]

[ "∀x (Park(x) ⊕ Movies(x))", "∀x (Nature(x) → ¬FreeTime(x))", "∀x (Movies(x) → Nature(x))", "∀x (NoClass(x) → FreeTime(x))", "∀x (SummerCamp(x) → NoClass(x))", "NoClass(james)" ]

[ "Students either go to the park or go to the movies. ", "No student who enjoys nature has free time during the weekend. ", "All students who go to the movies enjoy nature. ", "All students who do not have class during the weekend have free time during the weekend. ", "All students not in summer camp do not have class during the weekend. ", "James does not have class during the weekend." ]

[ "∀x (Park(x) ⊕ Movies(x))", "∀x (Nature(x) → ¬FreeTime(x))", "∀x (Movies(x) → Nature(x))", "∀x (NoClass(x) → FreeTime(x))", "∀x (SummerCamp(x) → NoClass(x))", "NoClass(james)" ]

[ "No television stars are certified public accountants.", "All certified public accountants have good business sense." ]

[ "∀x (TelevisionStar(x) → ¬CertifiedPublicAccoutant(x))", "∀x (CertifiedPublicAccoutant(x) → GoodBusinessSense(x))" ]

[ "Some students good at math are good at chemistry.", "All students good at chemistry enjoy conducting experiments. ", "All students that enjoy conducting experiments are good at planning. ", "No student good at planning is awarded the Dean's List. ", "James is either good at chemistry and awarded the Dean's List, or neither good at chemistry nor awarded the Dean's List." ]

[ "∃x (Math(x) ∧ Chemistry(x))", "∀x (Chemistry(x) → Experiment(x))", "∀x (Experiment(x) → Planning(x))", "∀x (Planning(x) → ¬Award(x))", "¬(Chemistry(james) ⊕ Award(james))" ]

[ "Some students good at math are good at chemistry.", "All students good at chemistry enjoy conducting experiments. ", "All students that enjoy conducting experiments are good at planning. ", "No student good at planning is awarded the Dean's List. ", "James is either good at chemistry and awarded the Dean's List, or neither good at chemistry nor awarded the Dean's List." ]

[ "∃x (Math(x) ∧ Chemistry(x))", "∀x (Chemistry(x) → Experiment(x))", "∀x (Experiment(x) → Planning(x))", "∀x (Planning(x) → ¬Award(x))", "¬(Chemistry(james) ⊕ Award(james))" ]

[ "Some students good at math are good at chemistry.", "All students good at chemistry enjoy conducting experiments. ", "All students that enjoy conducting experiments are good at planning. ", "No student good at planning is awarded the Dean's List. ", "James is either good at chemistry and awarded the Dean's List, or neither good at chemistry nor awarded the Dean's List." ]

[ "∃x (Math(x) ∧ Chemistry(x))", "∀x (Chemistry(x) → Experiment(x))", "∀x (Experiment(x) → Planning(x))", "∀x (Planning(x) → ¬Award(x))", "¬(Chemistry(james) ⊕ Award(james))" ]

[ "Some students good at math are good at chemistry.", "All students good at chemistry enjoy conducting experiments. ", "All students that enjoy conducting experiments are good at planning. ", "No student good at planning is awarded the Dean's List. ", "James is either good at chemistry and awarded the Dean's List, or neither good at chemistry nor awarded the Dean's List." ]

[ "∃x (Math(x) ∧ Chemistry(x))", "∀x (Chemistry(x) → Experiment(x))", "∀x (Experiment(x) → Planning(x))", "∀x (Planning(x) → ¬Award(x))", "¬(Chemistry(james) ⊕ Award(james))" ]

[ "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 1 thousand users are hard.", "2Sum is recommended to novices. ", "4Sum is starred by more than 1 thousand users." ]

[ "∀x (Easy(x) → LowerAC(x))", "∀x (Recommended(x) → Easy(x))", "∀x (Easy(x) ⊕ Hard(x))", "∀x (Starred(x) → Hard(x))", "Recommended(twosum) ", "Starred(foursum)" ]

[ "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 1 thousand users are hard.", "2Sum is recommended to novices. ", "4Sum is starred by more than 1 thousand users." ]

[ "∀x (Easy(x) → LowerAC(x))", "∀x (Recommended(x) → Easy(x))", "∀x (Easy(x) ⊕ Hard(x))", "∀x (Starred(x) → Hard(x))", "Recommended(twosum) ", "Starred(foursum)" ]

[ "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 1 thousand users are hard.", "2Sum is recommended to novices. ", "4Sum is starred by more than 1 thousand users." ]

[ "∀x (Easy(x) → LowerAC(x))", "∀x (Recommended(x) → Easy(x))", "∀x (Easy(x) ⊕ Hard(x))", "∀x (Starred(x) → Hard(x))", "Recommended(twosum) ", "Starred(foursum)" ]

[ "All rental cars cost the renter money.", "Whenever Sarah goes to Vermont, Sarah drives there.", "For someone who does not own a car to drive somewhere, they 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 this weekend.", "To go camping somewhere, you must go to that place." ]

[ "∀x (Rent(x, car) → Spend(x, money))", "GoesTo(sarah, vermont) → DriveTo(sarah, vermont)", "∀x ∀y (¬Own(x, car) ∧ DriveTo(x, y) → Borrow(x, car) ⊕ Rent(x, car))", "¬Own(sarah, car)", "∀x (Camping(sarah, x) → ¬(Borrow(sarah, car)))", "Camping(sarah, vermont)", "∀x ∀y (Camping(x, y) → GoesTo(x, y))" ]

[ "All people who attend weddings are getting married or have friends who are getting married.", "No preteens and other young children are getting married or have friends who are getting married.", "If people enjoy celebrating life milestone events with other people, then they attend weddings.", "If people are fond of large organized group functions, then they enjoy celebrating life milestone events with other people.", "All people who are outgoing and very spirited are fond of large organized group functions.", "If Carol is not both a pre-teen or other young child and attends weddings, then Carol is not getting married or has friends who are getting married. " ]

[ "∀x Weddings(x) → GettingMarried(x)", "∀x PreTeen(x) → ¬GettingMarried(x)", "∀x Celebrating(x) → Weddings(x)", "∀x LargeGathering(x) → Celebrating(x)", "∀x Outgoing(x) → LargeGathering(x)", "¬(PreTeen(Carol) ∧ Weddings(Carol)) → ¬GettingMarried(Carol)" ]

[ "All people who attend weddings are getting married or have friends who are getting married.", "No preteens and other young children are getting married or have friends who are getting married.", "If people enjoy celebrating life milestone events with other people, then they attend weddings.", "If people are fond of large organized group functions, then they enjoy celebrating life milestone events with other people.", "All people who are outgoing and very spirited are fond of large organized group functions.", "If Carol is not both a pre-teen or other young child and attends weddings, then Carol is not getting married or has friends who are getting married. " ]

[ "∀x Weddings(x) → GettingMarried(x)", "∀x PreTeen(x) → ¬GettingMarried(x)", "∀x Celebrating(x) → Weddings(x)", "∀x LargeGathering(x) → Celebrating(x)", "∀x Outgoing(x) → LargeGathering(x)", "¬(PreTeen(Carol) ∧ Weddings(Carol)) → ¬GettingMarried(Carol)" ]

[ "All people who attend weddings are getting married or have friends who are getting married.", "No preteens and other young children are getting married or have friends who are getting married.", "If people enjoy celebrating life milestone events with other people, then they attend weddings.", "If people are fond of large organized group functions, then they enjoy celebrating life milestone events with other people.", "All people who are outgoing and very spirited are fond of large organized group functions.", "If Carol is not both a pre-teen or other young child and attends weddings, then Carol is not getting married or has friends who are getting married. " ]

[ "∀x Weddings(x) → GettingMarried(x)", "∀x PreTeen(x) → ¬GettingMarried(x)", "∀x Celebrating(x) → Weddings(x)", "∀x LargeGathering(x) → Celebrating(x)", "∀x Outgoing(x) → LargeGathering(x)", "¬(PreTeen(Carol) ∧ Weddings(Carol)) → ¬GettingMarried(Carol)" ]

[ "All Republicans are anti-abortion.", "Either Republicans or Democrats. ", "No Democrats are conservative.", "Either conservative or liberal. ", "A U.S government official is either conservative or a Republican." ]

[ "∀x (Republicans(x) → Anti-abortion(x))", " ∀x (Republicans(x) ∨ Democrats(x))", " ∀x (Democrats(x) → ¬Conservative(x))", " ∀x (Conservative(x) ∨ Liberal(x))", " Conservative(anU.SGovernmentOfficial) ⊕ Republicans(anU.SGovernmentOfficial)" ]

[ "All Republicans are anti-abortion.", "Either Republicans or Democrats. ", "No Democrats are conservative.", "Either conservative or liberal. ", "A U.S government official is either conservative or a Republican." ]

[ "∀x (Republicans(x) → Anti-abortion(x))", " ∀x (Republicans(x) ∨ Democrats(x))", " ∀x (Democrats(x) → ¬Conservative(x))", " ∀x (Conservative(x) ∨ Liberal(x))", " Conservative(anU.SGovernmentOfficial) ⊕ Republicans(anU.SGovernmentOfficial)" ]

[ "All Republicans are anti-abortion.", "Either Republicans or Democrats. ", "No Democrats are conservative.", "Either conservative or liberal. ", "A U.S government official is either conservative or a Republican." ]

[ "∀x (Republicans(x) → Anti-abortion(x))", " ∀x (Republicans(x) ∨ Democrats(x))", " ∀x (Democrats(x) → ¬Conservative(x))", " ∀x (Conservative(x) ∨ Liberal(x))", " Conservative(anU.SGovernmentOfficial) ⊕ Republicans(anU.SGovernmentOfficial)" ]

[ "All Republicans are anti-abortion.", "Either Republicans or Democrats. ", "No Democrats are conservative.", "Either conservative or liberal. ", "A U.S government official is either conservative or a Republican." ]

[ "∀x (Republicans(x) → Anti-abortion(x))", " ∀x (Republicans(x) ∨ Democrats(x))", " ∀x (Democrats(x) → ¬Conservative(x))", " ∀x (Conservative(x) ∨ Liberal(x))", " Conservative(anU.SGovernmentOfficial) ⊕ Republicans(anU.SGovernmentOfficial)" ]

[ "All Republicans are anti-abortion.", "Either Republicans or Democrats. ", "No Democrats are conservative.", "Either conservative or liberal. ", "A U.S government official is either conservative or a Republican." ]

[ "∀x (Republicans(x) → Anti-abortion(x))", " ∀x (Republicans(x) ∨ Democrats(x))", " ∀x (Democrats(x) → ¬Conservative(x))", " ∀x (Conservative(x) ∨ Liberal(x))", " Conservative(anU.SGovernmentOfficial) ⊕ Republicans(anU.SGovernmentOfficial)" ]

[ "All Republicans are anti-abortion.", "Either Republicans or Democrats. ", "No Democrats are conservative.", "Either conservative or liberal. ", "A U.S government official is either conservative or a Republican." ]

[ "∀x (Republicans(x) → Anti-abortion(x))", " ∀x (Republicans(x) ∨ Democrats(x))", " ∀x (Democrats(x) → ¬Conservative(x))", " ∀x (Conservative(x) ∨ Liberal(x))", " Conservative(anU.SGovernmentOfficial) ⊕ Republicans(anU.SGovernmentOfficial)" ]

[ "All Republicans are anti-abortion.", "Either Republicans or Democrats. ", "No Democrats are conservative.", "Either conservative or liberal. ", "A U.S government official is either conservative or a Republican." ]

[ "∀x (Republicans(x) → Anti-abortion(x))", " ∀x (Republicans(x) ∨ Democrats(x))", " ∀x (Democrats(x) → ¬Conservative(x))", " ∀x (Conservative(x) ∨ Liberal(x))", " Conservative(anU.SGovernmentOfficial) ⊕ Republicans(anU.SGovernmentOfficial)" ]

[ "All Republicans are anti-abortion.", "Either Republicans or Democrats. ", "No Democrats are conservative.", "Either conservative or liberal. ", "A U.S government official is either conservative or a Republican." ]

[ "∀x (Republicans(x) → Anti-abortion(x))", " ∀x (Republicans(x) ∨ Democrats(x))", " ∀x (Democrats(x) → ¬Conservative(x))", " ∀x (Conservative(x) ∨ Liberal(x))", " Conservative(anU.SGovernmentOfficial) ⊕ Republicans(anU.SGovernmentOfficial)" ]

[ "All advocates of high tariff rates are Republicans.", "Some Republicans are not conservatives." ]

[ "∀x (AdvocateOfHighTariff(x) → Republican(x))", "∃x (Republican(x) ∧ ¬Conservative(x))" ]

[ "No athletes are slow runners. ", "All professional basketball players are athletes. ", "All NBA players are professional basketball players. ", "All Knicks players are NBA players. ", "Jim is either not a professional basketball player or not a slow runner. " ]

[ "∀x (Athlete(x) → ¬SlowRunner(x))", "∀x (ProfessionalBasketballPlayer(x) → Athlete(x))", "∀x (NBAPlayer(x) → ProfessionalBasketballPlayer(x))", "∀x (KnicksPlayer(x) → NBAPlayer(x))", "¬(ProfessionalBasketballPlayer(jim) ⊕ SlowRunner(jim))" ]

[ "No athletes are slow runners. ", "All professional basketball players are athletes. ", "All NBA players are professional basketball players. ", "All Knicks players are NBA players. ", "Jim is either not a professional basketball player or not a slow runner. " ]

[ "∀x (Athlete(x) → ¬SlowRunner(x))", "∀x (ProfessionalBasketballPlayer(x) → Athlete(x))", "∀x (NBAPlayer(x) → ProfessionalBasketballPlayer(x))", "∀x (KnicksPlayer(x) → NBAPlayer(x))", "¬(ProfessionalBasketballPlayer(jim) ⊕ SlowRunner(jim))" ]

[ "No athletes are slow runners. ", "All professional basketball players are athletes. ", "All NBA players are professional basketball players. ", "All Knicks players are NBA players. ", "Jim is either not a professional basketball player or not a slow runner. " ]

[ "∀x (Athlete(x) → ¬SlowRunner(x))", "∀x (ProfessionalBasketballPlayer(x) → Athlete(x))", "∀x (NBAPlayer(x) → ProfessionalBasketballPlayer(x))", "∀x (KnicksPlayer(x) → NBAPlayer(x))", "¬(ProfessionalBasketballPlayer(jim) ⊕ SlowRunner(jim))" ]

[ "All kids love animals.", "All toddlers are kids.", "If someone loves animals, then they are not bad.", "All pirates are bad.", "If Nancy is not a pirate, then Nancy loves animals.", "If Nancy is not a toddler, then Nancy is bad." ]

[ "∀x (Kid(x) → LoveAnimals(x))", "∀x (Toddler(x) → Kid(x))", "∀x (LoveAnimals(x) → ¬Bad(x))", "∀x (Pirate(x) → Bad(x))", "¬Pirate(nancy) → LoveAnimals(nancy)", "¬Toddler(nancy) → Bad(nancy)" ]

[ "All kids love animals.", "All toddlers are kids.", "If someone loves animals, then they are not bad.", "All pirates are bad.", "If Nancy is not a pirate, then Nancy loves animals.", "If Nancy is not a toddler, then Nancy is bad." ]

[ "∀x (Kid(x) → LoveAnimals(x))", "∀x (Toddler(x) → Kid(x))", "∀x (LoveAnimals(x) → ¬Bad(x))", "∀x (Pirate(x) → Bad(x))", "¬Pirate(nancy) → LoveAnimals(nancy)", "¬Toddler(nancy) → Bad(nancy)" ]