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[ "\"Your Woman\" is a song by British one-man band White Town.", "\"Your Woman\" song peaked at No. 1 on the UK Singles Chart.", "If a song peaked at No.1 at a cetain place, then it was extremely popular.", "\"Your Woman\" also peaked No. 1 in Iceland, Israel and Spain." ]

[ "Produce(whiteTown, yourWoman)", "Peak(yourWoman, uKSinglesChart)", "∀x ∀y (Peak(x, y) → Popular(x))", "Peak(yourWoman, iceland) ∧ Peak(yourWoman, isarel) ∧ Peak(yourWoman, spain)" ]

[ "All people who limp often and regularly have long-term medical issues with underlying causes.", "If people have long-term medical issues with underlying causes, then they are not often spry and energetic.", "People either stay indoors and rest a lot at home or people are often tired and disinterested in their activities.", "If people stay indoors and rest a lot at home, then they do not visit the gym at least once a day.", "If Mark either limps often and regularly or is often spry and energetic, then Mark limps often and regularly or is often tired and disinterested in his activities." ]

[ "∀x (Limp(x) → Medical(x))", "∀x (Medical(x) → ¬Spry(x))", "∀x (Spry(x) ⊕ Tired(x)) ∧ (∀x (Tired(x) → Indoors(x)))", "∀x (Indoors(x) → ¬Gym(x))", "(Limp(Mark) ⊕ Spry(Mark)) → Limp(Mark) ∨ Tired(Mark)" ]

[ "All people who limp often and regularly have long-term medical issues with underlying causes.", "If people have long-term medical issues with underlying causes, then they are not often spry and energetic.", "People either stay indoors and rest a lot at home or people are often tired and disinterested in their activities.", "If people stay indoors and rest a lot at home, then they do not visit the gym at least once a day.", "If Mark either limps often and regularly or is often spry and energetic, then Mark limps often and regularly or is often tired and disinterested in his activities." ]

[ "∀x (Limp(x) → Medical(x))", "∀x (Medical(x) → ¬Spry(x))", "∀x (Spry(x) ⊕ Tired(x)) ∧ (∀x (Tired(x) → Indoors(x)))", "∀x (Indoors(x) → ¬Gym(x))", "(Limp(Mark) ⊕ Spry(Mark)) → Limp(Mark) ∨ Tired(Mark)" ]

[ "All people who limp often and regularly have long-term medical issues with underlying causes.", "If people have long-term medical issues with underlying causes, then they are not often spry and energetic.", "People either stay indoors and rest a lot at home or people are often tired and disinterested in their activities.", "If people stay indoors and rest a lot at home, then they do not visit the gym at least once a day.", "If Mark either limps often and regularly or is often spry and energetic, then Mark limps often and regularly or is often tired and disinterested in his activities." ]

[ "∀x (Limp(x) → Medical(x))", "∀x (Medical(x) → ¬Spry(x))", "∀x (Spry(x) ⊕ Tired(x)) ∧ (∀x (Tired(x) → Indoors(x)))", "∀x (Indoors(x) → ¬Gym(x))", "(Limp(Mark) ⊕ Spry(Mark)) → Limp(Mark) ∨ Tired(Mark)" ]

[ "If two soccer teams score the same number of goals in one UCL final during the regular time, they need to play for the extra time.", "If two soccer teams score the same number of goals in one UCL final during both the regular time and extra time, they need to play the penalty shoot-out.", "Real Madrid and Atlético Madrid both scored one goal in 2016 UCL final during the regular time.", "Real Madrid and Atlético Madrid both scored zero goals in 2016 UCL final during the extra time." ]

[ "∀x ∀y (SoccerTeam(x) ∧ SoccerTeam(y) ∧ SameScore(x, y) ∧ During(regularTime) → PlayExtra(x, y))", "∀x ∀y (SoccerTeam(x) ∧ SoccerTeam(y) ∧ SameScore(x, y) ∧ During(regularTime) ∧ During(extraTime) → PlayPenalty(x, y))", "SoccerTeam(realMadrid) ∧ SoccerTeam(atleticoMadrid) ∧ SameScore(realMadrid, atleticoMadrid) ∧ During(regularTime)", "SoccerTeam(realMadrid) ∧ SoccerTeam(atleticoMadrid) ∧ SameScore(realMadrid, atleticoMadrid) ∧ During(extraTime)" ]

[ "If two soccer teams score the same number of goals in one UCL final during the regular time, they need to play for the extra time.", "If two soccer teams score the same number of goals in one UCL final during both the regular time and extra time, they need to play the penalty shoot-out.", "Real Madrid and Atlético Madrid both scored one goal in 2016 UCL final during the regular time.", "Real Madrid and Atlético Madrid both scored zero goals in 2016 UCL final during the extra time." ]

[ "∀x ∀y (SoccerTeam(x) ∧ SoccerTeam(y) ∧ SameScore(x, y) ∧ During(regularTime) → PlayExtra(x, y))", "∀x ∀y (SoccerTeam(x) ∧ SoccerTeam(y) ∧ SameScore(x, y) ∧ During(regularTime) ∧ During(extraTime) → PlayPenalty(x, y))", "SoccerTeam(realMadrid) ∧ SoccerTeam(atleticoMadrid) ∧ SameScore(realMadrid, atleticoMadrid) ∧ During(regularTime)", "SoccerTeam(realMadrid) ∧ SoccerTeam(atleticoMadrid) ∧ SameScore(realMadrid, atleticoMadrid) ∧ During(extraTime)" ]

[ "System 7 is a UK-based electronic dance music band.", "Steve Hillage and Miquette Giraudy formed System 7.", "Steve Hillage and Miquette Giraudy are former members of the band Gong.", "Electric dance music bands are bands.", "System 7 has released several club singles.", "Club singles are not singles." ]

[ "BasedOn(system7, uk) ∧ ElectronicDanceMusicBand(system7)", "Formed(stevehillage, system7) ∧ Formed(miquettegiraudy, system7)", "FormerMemberOf(stevehillage, gong) ∧ FormerMemberOf(miquettegiraudy, gong)", "∀x (ElectronicDanceMusicBand(x) → Band(x))", "∃x (ClubSingle(x) ∧ Released(system7, x))", "∀x (ClubSingle(x) → ¬Single(x))" ]

[ "System 7 is a UK-based electronic dance music band.", "Steve Hillage and Miquette Giraudy formed System 7.", "Steve Hillage and Miquette Giraudy are former members of the band Gong.", "Electric dance music bands are bands.", "System 7 has released several club singles.", "Club singles are not singles." ]

[ "BasedOn(system7, uk) ∧ ElectronicDanceMusicBand(system7)", "Formed(stevehillage, system7) ∧ Formed(miquettegiraudy, system7)", "FormerMemberOf(stevehillage, gong) ∧ FormerMemberOf(miquettegiraudy, gong)", "∀x (ElectronicDanceMusicBand(x) → Band(x))", "∃x (ClubSingle(x) ∧ Released(system7, x))", "∀x (ClubSingle(x) → ¬Single(x))" ]

[ "System 7 is a UK-based electronic dance music band.", "Steve Hillage and Miquette Giraudy formed System 7.", "Steve Hillage and Miquette Giraudy are former members of the band Gong.", "Electric dance music bands are bands.", "System 7 has released several club singles.", "Club singles are not singles." ]

[ "BasedOn(system7, uk) ∧ ElectronicDanceMusicBand(system7)", "Formed(stevehillage, system7) ∧ Formed(miquettegiraudy, system7)", "FormerMemberOf(stevehillage, gong) ∧ FormerMemberOf(miquettegiraudy, gong)", "∀x (ElectronicDanceMusicBand(x) → Band(x))", "∃x (ClubSingle(x) ∧ Released(system7, x))", "∀x (ClubSingle(x) → ¬Single(x))" ]

[ "A summarization model is always faithful if it uses content from the input documents.", "Extractive models are a kind of summarization models.", "Extractive model can only use content from the input documents." ]

[ "∀x (Model(x) ∧ Summarization(x) ∧ OnlyUseInputDocument(x) → Faithful(x))", "∀x (Model(x) ∧ Extractive(x) → Summarization(x))", "∀x (Model(x) ∧ Extractive(x) → OnlyUseInputDocument(x))" ]

[ "A summarization model is always faithful if it uses content from the input documents.", "Extractive models are a kind of summarization models.", "Extractive model can only use content from the input documents." ]

[ "∀x (Model(x) ∧ Summarization(x) ∧ OnlyUseInputDocument(x) → Faithful(x))", "∀x (Model(x) ∧ Extractive(x) → Summarization(x))", "∀x (Model(x) ∧ Extractive(x) → OnlyUseInputDocument(x))" ]

[ "If people practice coding questions, then they are not studying to go to medical school to become a doctor.", "If people want to work in the software engineering industry, then they practice coding questions.", "If people enjoy healthcare fields and want to help people with medical issues, then they are studying to go to medical school to become a doctor.", "If people grew up with parents who worked as doctors, then they enjoy healthcare fields and want to help people with medical issues.", "If people study hard, then they grew up with parents who worked as doctors.", "If Robin neither enjoys healthcare fields and wants to help people with medical issues nor grew up with parents who worked as doctors, then Robin is either a person who studies hard or grew up with parents who worked as doctors." ]

[ "∀x Coding(x) → ¬StudyingToBeDoctor(x)", "∀x Industry(x) → Coding(x)", "∀x Healthcare(x) → StudyingToBeDoctor(x)", "∀x ParentDoctors(x) → Healthcare(x)", "∀x Study(x) → ParentDoctors(x)", "¬(Healthcare(Robin) ∨ ParentDoctors(Robin)) → (Study(Robin) ∨ ParentDoctors(Robin)) " ]

[ "If people practice coding questions, then they are not studying to go to medical school to become a doctor.", "If people want to work in the software engineering industry, then they practice coding questions.", "If people enjoy healthcare fields and want to help people with medical issues, then they are studying to go to medical school to become a doctor.", "If people grew up with parents who worked as doctors, then they enjoy healthcare fields and want to help people with medical issues.", "If people study hard, then they grew up with parents who worked as doctors.", "If Robin neither enjoys healthcare fields and wants to help people with medical issues nor grew up with parents who worked as doctors, then Robin is either a person who studies hard or grew up with parents who worked as doctors." ]

[ "∀x Coding(x) → ¬StudyingToBeDoctor(x)", "∀x Industry(x) → Coding(x)", "∀x Healthcare(x) → StudyingToBeDoctor(x)", "∀x ParentDoctors(x) → Healthcare(x)", "∀x Study(x) → ParentDoctors(x)", "¬(Healthcare(Robin) ∨ ParentDoctors(Robin)) → (Study(Robin) ∨ ParentDoctors(Robin)) " ]

[ "If people practice coding questions, then they are not studying to go to medical school to become a doctor.", "If people want to work in the software engineering industry, then they practice coding questions.", "If people enjoy healthcare fields and want to help people with medical issues, then they are studying to go to medical school to become a doctor.", "If people grew up with parents who worked as doctors, then they enjoy healthcare fields and want to help people with medical issues.", "If people study hard, then they grew up with parents who worked as doctors.", "If Robin neither enjoys healthcare fields and wants to help people with medical issues nor grew up with parents who worked as doctors, then Robin is either a person who studies hard or grew up with parents who worked as doctors." ]

[ "∀x Coding(x) → ¬StudyingToBeDoctor(x)", "∀x Industry(x) → Coding(x)", "∀x Healthcare(x) → StudyingToBeDoctor(x)", "∀x ParentDoctors(x) → Healthcare(x)", "∀x Study(x) → ParentDoctors(x)", "¬(Healthcare(Robin) ∨ ParentDoctors(Robin)) → (Study(Robin) ∨ ParentDoctors(Robin)) " ]

[ "If people go to the spa at least once a week, then they are not people who are miserly and need to save a large portion of their income.", "People are either miserly and need to save a large portion of their income, or people that frivolously spend a lot of money every time they go out.", "If people frivolously spend a lot of money every time they go out, then they value quality manufacturing and luxury items.", "If people value quality manufacturing and luxury items, then they enjoy shopping for materialistic items in their free time.", "If Jess is not miserly and needs to save a large portion of their income, then Jess does not value quality manufacturing and luxury items.", "If Jess either values quality manufacturing and luxury items or, if he does not, then he is miserly and needs to save a large portion of his income, then Jess frivolously spends a lot of money every time he goes out." ]

[ "∀x Spa(x) → ¬Miserly(x)", "∀x Miserly(x) ∨ Frivolous(x)", "∀x Frivolous(x) → Luxury(x)", "∀x Luxury(x) → Shopping(x)", "¬Miserly(Jess) → ¬Luxury(Jess)", "Luxury(Jess) ⊕ Miserly(Jess)) → Luxury(Jess)" ]

[ "If people go to the spa at least once a week, then they are not people who are miserly and need to save a large portion of their income.", "People are either miserly and need to save a large portion of their income, or people that frivolously spend a lot of money every time they go out.", "If people frivolously spend a lot of money every time they go out, then they value quality manufacturing and luxury items.", "If people value quality manufacturing and luxury items, then they enjoy shopping for materialistic items in their free time.", "If Jess is not miserly and needs to save a large portion of their income, then Jess does not value quality manufacturing and luxury items.", "If Jess either values quality manufacturing and luxury items or, if he does not, then he is miserly and needs to save a large portion of his income, then Jess frivolously spends a lot of money every time he goes out." ]

[ "∀x Spa(x) → ¬Miserly(x)", "∀x Miserly(x) ∨ Frivolous(x)", "∀x Frivolous(x) → Luxury(x)", "∀x Luxury(x) → Shopping(x)", "¬Miserly(Jess) → ¬Luxury(Jess)", "Luxury(Jess) ⊕ Miserly(Jess)) → Luxury(Jess)" ]

[ "If people go to the spa at least once a week, then they are not people who are miserly and need to save a large portion of their income.", "People are either miserly and need to save a large portion of their income, or people that frivolously spend a lot of money every time they go out.", "If people frivolously spend a lot of money every time they go out, then they value quality manufacturing and luxury items.", "If people value quality manufacturing and luxury items, then they enjoy shopping for materialistic items in their free time.", "If Jess is not miserly and needs to save a large portion of their income, then Jess does not value quality manufacturing and luxury items.", "If Jess either values quality manufacturing and luxury items or, if he does not, then he is miserly and needs to save a large portion of his income, then Jess frivolously spends a lot of money every time he goes out." ]

[ "∀x Spa(x) → ¬Miserly(x)", "∀x Miserly(x) ∨ Frivolous(x)", "∀x Frivolous(x) → Luxury(x)", "∀x Luxury(x) → Shopping(x)", "¬Miserly(Jess) → ¬Luxury(Jess)", "Luxury(Jess) ⊕ Miserly(Jess)) → Luxury(Jess)" ]

[ "The indie pop band Phoenix has released 6 albums. ", "Phoenix's album \"Wolfgang Amadeus Phoenix\" sold over 500,000 copies. ", "A certified gold album or single is one which sold over half a million copies. ", "\"1901\" is a single from Phoenix's album \"Wolfgang Amadeus Phoenix.\"", "Over 400,000 copies of \"1901\" have been sold. " ]

[ "AlbumsReleased(phoenix, l6)", "Album(wolfgangamadeusphoenix) ∧ IsAlbumOf(wolfgangamadeusphoenix, phoenix) ∧ SoldOver(wolfgangamadeusphoenix, l500000)", "∀x ((Album(x) ∨ Single(x)) ∧ SoldOver(x, l500000) → CertifiedGold(x))", "Single(l1901) ∧ From(l1901, wolfgangamadeusphoenix) ∧ By(l1901, phoenix)", "SoldOver(l1901, l400000)" ]

[ "The indie pop band Phoenix has released 6 albums. ", "Phoenix's album \"Wolfgang Amadeus Phoenix\" sold over 500,000 copies. ", "A certified gold album or single is one which sold over half a million copies. ", "\"1901\" is a single from Phoenix's album \"Wolfgang Amadeus Phoenix.\"", "Over 400,000 copies of \"1901\" have been sold. " ]

[ "AlbumsReleased(phoenix, l6)", "Album(wolfgangamadeusphoenix) ∧ IsAlbumOf(wolfgangamadeusphoenix, phoenix) ∧ SoldOver(wolfgangamadeusphoenix, l500000)", "∀x ((Album(x) ∨ Single(x)) ∧ SoldOver(x, l500000) → CertifiedGold(x))", "Single(l1901) ∧ From(l1901, wolfgangamadeusphoenix) ∧ By(l1901, phoenix)", "SoldOver(l1901, l400000)" ]

[ "Peter Parker is a either a superhero or a civilian.", "The Hulk is a destroyer.", "The Hulk wakes up when he is angry.", "If the Hulk wakes up, then he will break a bridge.", "Thor is a god.", "Thor will break a bridge when he is happy.", "A god is not a destroyer and a destroyer is not a god.", "Peter Parker wears a uniform when he is a superhero.", "Peter Parker is not a civilian if and only if a destroyer is breaking a bridge.", "If Thor is happy, the Hulk is angry." ]

[ "Superhero(peter) ⊕ Civilian(peter)", "Destroyer(hulk)", "Angry(hulk) → Wake(hulk)", "Wake(hulk) → BreakBridge(hulk)", "God(thor)", "Happy(thor) → BreakBridge(thor)", "∀x (God(x) ↔ ¬Destroyer(x))", "Superhero(peter) → WearUniform(peter)", "∀x (¬Civilian(peter) ↔ (Destroyer(x) ∧ BreakBridge(x)))", "Happy(thor) → Angry(hulk)" ]

[ "Peter Parker is a either a superhero or a civilian.", "The Hulk is a destroyer.", "The Hulk wakes up when he is angry.", "If the Hulk wakes up, then he will break a bridge.", "Thor is a god.", "Thor will break a bridge when he is happy.", "A god is not a destroyer and a destroyer is not a god.", "Peter Parker wears a uniform when he is a superhero.", "Peter Parker is not a civilian if and only if a destroyer is breaking a bridge.", "If Thor is happy, the Hulk is angry." ]

[ "Superhero(peter) ⊕ Civilian(peter)", "Destroyer(hulk)", "Angry(hulk) → Wake(hulk)", "Wake(hulk) → BreakBridge(hulk)", "God(thor)", "Happy(thor) → BreakBridge(thor)", "∀x (God(x) ↔ ¬Destroyer(x))", "Superhero(peter) → WearUniform(peter)", "∀x (¬Civilian(peter) ↔ (Destroyer(x) ∧ BreakBridge(x)))", "Happy(thor) → Angry(hulk)" ]

[ "Peter Parker is a either a superhero or a civilian.", "The Hulk is a destroyer.", "The Hulk wakes up when he is angry.", "If the Hulk wakes up, then he will break a bridge.", "Thor is a god.", "Thor will break a bridge when he is happy.", "A god is not a destroyer and a destroyer is not a god.", "Peter Parker wears a uniform when he is a superhero.", "Peter Parker is not a civilian if and only if a destroyer is breaking a bridge.", "If Thor is happy, the Hulk is angry." ]

[ "Superhero(peter) ⊕ Civilian(peter)", "Destroyer(hulk)", "Angry(hulk) → Wake(hulk)", "Wake(hulk) → BreakBridge(hulk)", "God(thor)", "Happy(thor) → BreakBridge(thor)", "∀x (God(x) ↔ ¬Destroyer(x))", "Superhero(peter) → WearUniform(peter)", "∀x (¬Civilian(peter) ↔ (Destroyer(x) ∧ BreakBridge(x)))", "Happy(thor) → Angry(hulk)" ]

[ "Diethylcarbamazine is a medication discovered in the year 1947.", "Diethylcarbamazine can be used to treat river blindness.", "The only preferred treatment for river blindness is ivermectin.", "Diethylcarbamazine is not ivermectin." ]

[ "∀x (Diethylcarbamazine(x) ∧ Medication(x) ∧ DiscoveredIn(x, year1947))", "∀x ∀y (Diethylcarbamazine(x) ∧ RiverBlindness(y) → Treats(x, y))", "∀x ∀y (RiverBlindness(y) ∧ PreferredTreatment(x, y) → Ivermectin(x))", "∀x (Diethylcarbamazine(x) → ¬Ivermectin(x))" ]

[ "Diethylcarbamazine is a medication discovered in the year 1947.", "Diethylcarbamazine can be used to treat river blindness.", "The only preferred treatment for river blindness is ivermectin.", "Diethylcarbamazine is not ivermectin." ]

[ "∀x (Diethylcarbamazine(x) ∧ Medication(x) ∧ DiscoveredIn(x, year1947))", "∀x ∀y (Diethylcarbamazine(x) ∧ RiverBlindness(y) → Treats(x, y))", "∀x ∀y (RiverBlindness(y) ∧ PreferredTreatment(x, y) → Ivermectin(x))", "∀x (Diethylcarbamazine(x) → ¬Ivermectin(x))" ]

[ "Diethylcarbamazine is a medication discovered in the year 1947.", "Diethylcarbamazine can be used to treat river blindness.", "The only preferred treatment for river blindness is ivermectin.", "Diethylcarbamazine is not ivermectin." ]

[ "∀x (Diethylcarbamazine(x) ∧ Medication(x) ∧ DiscoveredIn(x, year1947))", "∀x ∀y (Diethylcarbamazine(x) ∧ RiverBlindness(y) → Treats(x, y))", "∀x ∀y (RiverBlindness(y) ∧ PreferredTreatment(x, y) → Ivermectin(x))", "∀x (Diethylcarbamazine(x) → ¬Ivermectin(x))" ]

[ "All univariate analyses use a generalized linear model. ", "All multivoxel (pattern) analyses are implementing machine learning algorithms.", "All implementing machine learning algorithms are to learn and classify multivariate data.", "The Latent Dirichlet allocation model uses a generalized linear model or a univariate analysis. ", "If the Latent Dirichlet allocation model does not learn and classify multivariate data, then the Latent Dirichlet allocation model uses a generalized linear model and a multivoxel (pattern) analysis." ]

[ "∀x (UnivariateAnalysis(x) → UsesGeneralizedLinearModel(x)) ", " ∀x (MultivoxelPatternAnalysis(x) → ImplementingMachineLearningAlgorithms(x))", " ∀x (ImplementingMachineLearningAlgorithms(x) → LearnAndClassifyMultivariateData(x)) ", " UsesGeneralizedLinearModel(latentDirichletAllocationModel) ∨ UnivariateAnalysis(latentDirichletAllocationModel)", " ¬LearnAndClassifyMultivariateData(latentDirichletAllocationModel) → UsesGeneralizedLinearModel(latentDirichletAllocationModel) ∧ MultivoxelPatternAnalysis(latentDirichletAllocationModel)" ]

[ "All univariate analyses use a generalized linear model. ", "All multivoxel (pattern) analyses are implementing machine learning algorithms.", "All implementing machine learning algorithms are to learn and classify multivariate data.", "The Latent Dirichlet allocation model uses a generalized linear model or a univariate analysis. ", "If the Latent Dirichlet allocation model does not learn and classify multivariate data, then the Latent Dirichlet allocation model uses a generalized linear model and a multivoxel (pattern) analysis." ]

[ "∀x (UnivariateAnalysis(x) → UsesGeneralizedLinearModel(x)) ", " ∀x (MultivoxelPatternAnalysis(x) → ImplementingMachineLearningAlgorithms(x))", " ∀x (ImplementingMachineLearningAlgorithms(x) → LearnAndClassifyMultivariateData(x)) ", " UsesGeneralizedLinearModel(latentDirichletAllocationModel) ∨ UnivariateAnalysis(latentDirichletAllocationModel)", " ¬LearnAndClassifyMultivariateData(latentDirichletAllocationModel) → UsesGeneralizedLinearModel(latentDirichletAllocationModel) ∧ MultivoxelPatternAnalysis(latentDirichletAllocationModel)" ]

[ "All univariate analyses use a generalized linear model. ", "All multivoxel (pattern) analyses are implementing machine learning algorithms.", "All implementing machine learning algorithms are to learn and classify multivariate data.", "The Latent Dirichlet allocation model uses a generalized linear model or a univariate analysis. ", "If the Latent Dirichlet allocation model does not learn and classify multivariate data, then the Latent Dirichlet allocation model uses a generalized linear model and a multivoxel (pattern) analysis." ]

[ "∀x (UnivariateAnalysis(x) → UsesGeneralizedLinearModel(x)) ", " ∀x (MultivoxelPatternAnalysis(x) → ImplementingMachineLearningAlgorithms(x))", " ∀x (ImplementingMachineLearningAlgorithms(x) → LearnAndClassifyMultivariateData(x)) ", " UsesGeneralizedLinearModel(latentDirichletAllocationModel) ∨ UnivariateAnalysis(latentDirichletAllocationModel)", " ¬LearnAndClassifyMultivariateData(latentDirichletAllocationModel) → UsesGeneralizedLinearModel(latentDirichletAllocationModel) ∧ MultivoxelPatternAnalysis(latentDirichletAllocationModel)" ]

[ "If something requires a medical diagnosis, then lab tests or imaging is required. ", "All rare diseases require a medical diagnosis.", "If something is mild, then no lab tests or imaging is required. ", "All blood cancers are rare diseases.", "All Leukemia is blood cancer. ", "If bladder cancer is either both blood cancer and Leukemia or neither blood cancer nor Leukemia, then bladder cancer is Leukemia." ]

[ "∀x (RequiresAMedicalDiagnosis(x) → LabTestsOrImagingRequired(x)) ", "∀x (RareDiseases(x) → RequiresAMedicalDiagnosis(x))", "∀x (Mild(x) → ¬LabTestsOrImagingRequired(x)) ", "∀x (BloodCancer(x) → RareDiseases(x))", "∀x (Leukemia(x) → BloodCancer(x))", "¬(BloodCancer(bladderCancer) ⊕ Leukemia(bladderCancer)) → Leukemia(bladderCancer)" ]

[ "If something requires a medical diagnosis, then lab tests or imaging is required. ", "All rare diseases require a medical diagnosis.", "If something is mild, then no lab tests or imaging is required. ", "All blood cancers are rare diseases.", "All Leukemia is blood cancer. ", "If bladder cancer is either both blood cancer and Leukemia or neither blood cancer nor Leukemia, then bladder cancer is Leukemia." ]

[ "∀x (RequiresAMedicalDiagnosis(x) → LabTestsOrImagingRequired(x)) ", "∀x (RareDiseases(x) → RequiresAMedicalDiagnosis(x))", "∀x (Mild(x) → ¬LabTestsOrImagingRequired(x)) ", "∀x (BloodCancer(x) → RareDiseases(x))", "∀x (Leukemia(x) → BloodCancer(x))", "¬(BloodCancer(bladderCancer) ⊕ Leukemia(bladderCancer)) → Leukemia(bladderCancer)" ]

[ "If something requires a medical diagnosis, then lab tests or imaging is required. ", "All rare diseases require a medical diagnosis.", "If something is mild, then no lab tests or imaging is required. ", "All blood cancers are rare diseases.", "All Leukemia is blood cancer. ", "If bladder cancer is either both blood cancer and Leukemia or neither blood cancer nor Leukemia, then bladder cancer is Leukemia." ]

[ "∀x (RequiresAMedicalDiagnosis(x) → LabTestsOrImagingRequired(x)) ", "∀x (RareDiseases(x) → RequiresAMedicalDiagnosis(x))", "∀x (Mild(x) → ¬LabTestsOrImagingRequired(x)) ", "∀x (BloodCancer(x) → RareDiseases(x))", "∀x (Leukemia(x) → BloodCancer(x))", "¬(BloodCancer(bladderCancer) ⊕ Leukemia(bladderCancer)) → Leukemia(bladderCancer)" ]

[ "No precious metals aren't scarce.", "All non-rare earth metals are not scarce.", "Either non-rare earth metals or rare earth metals. ", "All rare earth metals can be used for batteries.", "All rare earth metals are essential for electric vehicles.", "Lithium is neither a non-rare earth metal nor essential for electric vehicles." ]

[ "∀x (PreciousMetals(x) → ¬NotScarce(x))", " ∀x (Non-rareEarthMetals(x) → NotScarce(x)) ", " ∀x (Non-rareEarthMetals(x) ∨ RareEarthMetals(x)) ", " ∀x (RareEarthMetals(x) → BeUsedForBatteries(x)) ", " ∀x (RareEarthMetals(x) → EssentialForElectricVehicles(x))", " ¬Non-rareEarthMetals(lithium) ⊕ ¬EssentialForElectricVehicles(lithium)" ]

[ "No precious metals aren't scarce.", "All non-rare earth metals are not scarce.", "Either non-rare earth metals or rare earth metals. ", "All rare earth metals can be used for batteries.", "All rare earth metals are essential for electric vehicles.", "Lithium is neither a non-rare earth metal nor essential for electric vehicles." ]

[ "∀x (PreciousMetals(x) → ¬NotScarce(x))", " ∀x (Non-rareEarthMetals(x) → NotScarce(x)) ", " ∀x (Non-rareEarthMetals(x) ∨ RareEarthMetals(x)) ", " ∀x (RareEarthMetals(x) → BeUsedForBatteries(x)) ", " ∀x (RareEarthMetals(x) → EssentialForElectricVehicles(x))", " ¬Non-rareEarthMetals(lithium) ⊕ ¬EssentialForElectricVehicles(lithium)" ]

[ "No precious metals aren't scarce.", "All non-rare earth metals are not scarce.", "Either non-rare earth metals or rare earth metals. ", "All rare earth metals can be used for batteries.", "All rare earth metals are essential for electric vehicles.", "Lithium is neither a non-rare earth metal nor essential for electric vehicles." ]

[ "∀x (PreciousMetals(x) → ¬NotScarce(x))", " ∀x (Non-rareEarthMetals(x) → NotScarce(x)) ", " ∀x (Non-rareEarthMetals(x) ∨ RareEarthMetals(x)) ", " ∀x (RareEarthMetals(x) → BeUsedForBatteries(x)) ", " ∀x (RareEarthMetals(x) → EssentialForElectricVehicles(x))", " ¬Non-rareEarthMetals(lithium) ⊕ ¬EssentialForElectricVehicles(lithium)" ]

[ "If people own at least one pet, then they do not have tidy houses.", "If people grew up with childhood pets, then they own at least one pet.", "If people hire a maid or cleaning service, then they have tidy houses.", "If people live in the suburbs, then they have tidy houses.", "Jack either does not hire a maid or cleaning service or, if he does, then he does not own at least one pet." ]

[ "∀x (OwnPet(x) → ¬TidyHouse(x))", "∀x (ChildhoodPet(x) → OwnPet(x))", "∀x (HireCleaning(x) → TidyHouse(x))", "∀x (Suburbs(x) → ChildhoodPet(x))", "¬(HireCleaning(jack) ⊕ OwnPet(jack))" ]

[ "If people own at least one pet, then they do not have tidy houses.", "If people grew up with childhood pets, then they own at least one pet.", "If people hire a maid or cleaning service, then they have tidy houses.", "If people live in the suburbs, then they have tidy houses.", "Jack either does not hire a maid or cleaning service or, if he does, then he does not own at least one pet." ]

[ "∀x (OwnPet(x) → ¬TidyHouse(x))", "∀x (ChildhoodPet(x) → OwnPet(x))", "∀x (HireCleaning(x) → TidyHouse(x))", "∀x (Suburbs(x) → ChildhoodPet(x))", "¬(HireCleaning(jack) ⊕ OwnPet(jack))" ]

[ "If people own at least one pet, then they do not have tidy houses.", "If people grew up with childhood pets, then they own at least one pet.", "If people hire a maid or cleaning service, then they have tidy houses.", "If people live in the suburbs, then they have tidy houses.", "Jack either does not hire a maid or cleaning service or, if he does, then he does not own at least one pet." ]

[ "∀x (OwnPet(x) → ¬TidyHouse(x))", "∀x (ChildhoodPet(x) → OwnPet(x))", "∀x (HireCleaning(x) → TidyHouse(x))", "∀x (Suburbs(x) → ChildhoodPet(x))", "¬(HireCleaning(jack) ⊕ OwnPet(jack))" ]

[ "If people own at least one pet, then they do not have tidy houses.", "If people grew up with childhood pets, then they own at least one pet.", "If people hire a maid or cleaning service, then they have tidy houses.", "If people live in the suburbs, then they have tidy houses.", "Jack either does not hire a maid or cleaning service or, if he does, then he does not own at least one pet." ]

[ "∀x (OwnPet(x) → ¬TidyHouse(x))", "∀x (ChildhoodPet(x) → OwnPet(x))", "∀x (HireCleaning(x) → TidyHouse(x))", "∀x (Suburbs(x) → ChildhoodPet(x))", "¬(HireCleaning(jack) ⊕ OwnPet(jack))" ]

[ "If people own at least one pet, then they do not have tidy houses.", "If people grew up with childhood pets, then they own at least one pet.", "If people hire a maid or cleaning service, then they have tidy houses.", "If people live in the suburbs, then they have tidy houses.", "Jack either does not hire a maid or cleaning service or, if he does, then he does not own at least one pet." ]

[ "∀x (OwnPet(x) → ¬TidyHouse(x))", "∀x (ChildhoodPet(x) → OwnPet(x))", "∀x (HireCleaning(x) → TidyHouse(x))", "∀x (Suburbs(x) → ChildhoodPet(x))", "¬(HireCleaning(jack) ⊕ OwnPet(jack))" ]

[ "A bottle is either standing upright or toppled over. ", "The bottle is not upright." ]

[ "Upright(bottle) ⊕ ToppledOver(bottle)", "¬Upright(bottle)" ]

[ "If people eat cereal and milk every day for breakfast, then they have very busy morning schedules every day.", "All young children below the age of ten eat cereal and milk every day for breakfast.", "People are either young children below the age of ten or have a lot of commitments they voluntarily signed up for.", "If people have a lot of commitments they voluntarily signed up for, then they are hardworking individuals with high ambitions and goals for the future.", "If people are hardworking individuals with high ambitions and goals for the future, then they are not good at staying organized and motivated.", "John either is both a hardworking individual with high ambitions and goals for the future and has busy morning schedules every day, or he is neither a hardworking individual with high ambitions and goals for the future nor does he have a busy morning schedule every day." ]

[ "∀x (Cereal(x) → BusyMorning(x))", "∀x (YoungChildren(x) → BusyMorning(x))", "∀x (YoungChildren(x) ⊕ Committments(x))", "∀x (Committments(x) → Hardworking(x))", "∀x (Hardworking(x) → ¬Organized(x))", "(Hardworking(john) ∧ BusyMorning(john)) ⊕ (¬Hardworking(john) ∧ ¬BusyMorning(john))" ]

[ "If people eat cereal and milk every day for breakfast, then they have very busy morning schedules every day.", "All young children below the age of ten eat cereal and milk every day for breakfast.", "People are either young children below the age of ten or have a lot of commitments they voluntarily signed up for.", "If people have a lot of commitments they voluntarily signed up for, then they are hardworking individuals with high ambitions and goals for the future.", "If people are hardworking individuals with high ambitions and goals for the future, then they are not good at staying organized and motivated.", "John either is both a hardworking individual with high ambitions and goals for the future and has busy morning schedules every day, or he is neither a hardworking individual with high ambitions and goals for the future nor does he have a busy morning schedule every day." ]

[ "∀x (Cereal(x) → BusyMorning(x))", "∀x (YoungChildren(x) → BusyMorning(x))", "∀x (YoungChildren(x) ⊕ Committments(x))", "∀x (Committments(x) → Hardworking(x))", "∀x (Hardworking(x) → ¬Organized(x))", "(Hardworking(john) ∧ BusyMorning(john)) ⊕ (¬Hardworking(john) ∧ ¬BusyMorning(john))" ]

[ "If people eat cereal and milk every day for breakfast, then they have very busy morning schedules every day.", "All young children below the age of ten eat cereal and milk every day for breakfast.", "People are either young children below the age of ten or have a lot of commitments they voluntarily signed up for.", "If people have a lot of commitments they voluntarily signed up for, then they are hardworking individuals with high ambitions and goals for the future.", "If people are hardworking individuals with high ambitions and goals for the future, then they are not good at staying organized and motivated.", "John either is both a hardworking individual with high ambitions and goals for the future and has busy morning schedules every day, or he is neither a hardworking individual with high ambitions and goals for the future nor does he have a busy morning schedule every day." ]

[ "∀x (Cereal(x) → BusyMorning(x))", "∀x (YoungChildren(x) → BusyMorning(x))", "∀x (YoungChildren(x) ⊕ Committments(x))", "∀x (Committments(x) → Hardworking(x))", "∀x (Hardworking(x) → ¬Organized(x))", "(Hardworking(john) ∧ BusyMorning(john)) ⊕ (¬Hardworking(john) ∧ ¬BusyMorning(john))" ]

[ "Ableton has an office in Germany.", "Ableton has an office in the USA.", "USA and Germany are different countries.", "Any company that has offices in different countries is a multinational company.", "Ableton makes music software." ]

[ "OfficeIn(ableton, germany)", "OfficeIn(ableton, usa)", "¬SameCountry(germany, usa)", "∀x ∀y ∀z (OfficeIn(x, y) ∧ OfficeIn(x, z) ∧ ¬SameCountry(y, z) → IsMultinationalCompany(x))", "MakesMusicSoftware(ableton)" ]

[ "Ableton has an office in Germany.", "Ableton has an office in the USA.", "USA and Germany are different countries.", "Any company that has offices in different countries is a multinational company.", "Ableton makes music software." ]

[ "OfficeIn(ableton, germany)", "OfficeIn(ableton, usa)", "¬SameCountry(germany, usa)", "∀x ∀y ∀z (OfficeIn(x, y) ∧ OfficeIn(x, z) ∧ ¬SameCountry(y, z) → IsMultinationalCompany(x))", "MakesMusicSoftware(ableton)" ]

[ "Ableton has an office in Germany.", "Ableton has an office in the USA.", "USA and Germany are different countries.", "Any company that has offices in different countries is a multinational company.", "Ableton makes music software." ]

[ "OfficeIn(ableton, germany)", "OfficeIn(ableton, usa)", "¬SameCountry(germany, usa)", "∀x ∀y ∀z (OfficeIn(x, y) ∧ OfficeIn(x, z) ∧ ¬SameCountry(y, z) → IsMultinationalCompany(x))", "MakesMusicSoftware(ableton)" ]

[ "Every swimmer can go underwater.", "Everyone that eats fish they catch themselves is a swimmer.", "Every penguin eats fish they catch themselves.", "All nonflying birds in Antarctica are penguins.", "Fido is a penguin or a swimmer." ]

[ "∀x (Swimmer(x) → GoesUnderwater(x))", "∀x (EatsFishCaughtThemselves(x) → Swimmer(x))", "∀x (Penguin(x) → EatsFishCaughtThemselves(x))", "∀x (NonFlyingBirdAntartica(x) → Penguin(x))", "Penguin(fido) ∨ Swimmer(fido)" ]

[ "Every swimmer can go underwater.", "Everyone that eats fish they catch themselves is a swimmer.", "Every penguin eats fish they catch themselves.", "All nonflying birds in Antarctica are penguins.", "Fido is a penguin or a swimmer." ]

[ "∀x (Swimmer(x) → GoesUnderwater(x))", "∀x (EatsFishCaughtThemselves(x) → Swimmer(x))", "∀x (Penguin(x) → EatsFishCaughtThemselves(x))", "∀x (NonFlyingBirdAntartica(x) → Penguin(x))", "Penguin(fido) ∨ Swimmer(fido)" ]

[ "Every swimmer can go underwater.", "Everyone that eats fish they catch themselves is a swimmer.", "Every penguin eats fish they catch themselves.", "All nonflying birds in Antarctica are penguins.", "Fido is a penguin or a swimmer." ]

[ "∀x (Swimmer(x) → GoesUnderwater(x))", "∀x (EatsFishCaughtThemselves(x) → Swimmer(x))", "∀x (Penguin(x) → EatsFishCaughtThemselves(x))", "∀x (NonFlyingBirdAntartica(x) → Penguin(x))", "Penguin(fido) ∨ Swimmer(fido)" ]

[ "All professors are teachers.", "All researchers are professors.", "No teachers are students.", "All people who study are students.", "Leon is not studying or a researcher.", "If Leon is not studying, then Leon is a teacher." ]

[ "∀x (Professor(x) → Teacher(x))", "∀x (Researcher(x) → Professor(x))", "∀x (Teacher(x) → ¬Student(x))", "∀x (Study(x) → Student(x))", "¬Study(leon) ⊕ Researcher(leon)", "¬Study(leon) → Teacher(leon)" ]

[ "All professors are teachers.", "All researchers are professors.", "No teachers are students.", "All people who study are students.", "Leon is not studying or a researcher.", "If Leon is not studying, then Leon is a teacher." ]

[ "∀x (Professor(x) → Teacher(x))", "∀x (Researcher(x) → Professor(x))", "∀x (Teacher(x) → ¬Student(x))", "∀x (Study(x) → Student(x))", "¬Study(leon) ⊕ Researcher(leon)", "¬Study(leon) → Teacher(leon)" ]

[ "All professors are teachers.", "All researchers are professors.", "No teachers are students.", "All people who study are students.", "Leon is not studying or a researcher.", "If Leon is not studying, then Leon is a teacher." ]

[ "∀x (Professor(x) → Teacher(x))", "∀x (Researcher(x) → Professor(x))", "∀x (Teacher(x) → ¬Student(x))", "∀x (Study(x) → Student(x))", "¬Study(leon) ⊕ Researcher(leon)", "¬Study(leon) → Teacher(leon)" ]

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

[ "∀x (Cutman(x) → Prevent(x, physicalDamage) ∧ Treat(x, physicalDamage))", "∀x (Cutman(x) → Appear(x, boxing) ∨ Appear(x, kickboxing) ∨ Appear(x, mixedMartialBout))", "∀x (Cutman(x) → Handle(x, swelling) ∧ Handle(x, nosebleeds) ∧ Handle(x, lacerations))", "Cutman(jack)" ]

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

[ "∀x (Cutman(x) → Prevent(x, physicalDamage) ∧ Treat(x, physicalDamage))", "∀x (Cutman(x) → Appear(x, boxing) ∨ Appear(x, kickboxing) ∨ Appear(x, mixedMartialBout))", "∀x (Cutman(x) → Handle(x, swelling) ∧ Handle(x, nosebleeds) ∧ Handle(x, lacerations))", "Cutman(jack)" ]

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

[ "∀x (Cutman(x) → Prevent(x, physicalDamage) ∧ Treat(x, physicalDamage))", "∀x (Cutman(x) → Appear(x, boxing) ∨ Appear(x, kickboxing) ∨ Appear(x, mixedMartialBout))", "∀x (Cutman(x) → Handle(x, swelling) ∧ Handle(x, nosebleeds) ∧ Handle(x, lacerations))", "Cutman(jack)" ]

[ "The Mona Lisa is one of the world's best-known artworks.", "The Mona Lisa is a portrait painted by Leonardo da Vinci.", "Leonardo da Vinci was a scientist and painter.", "Painting genres are history, portrait, animal, landscape, and still life." ]

[ "Painting(monaLisa) ∧ WorldsBestKnown(monaLisa)", "PaintedBy(monaLisa, leonardodaVinci) ∧ Portrait(monaLisa)", "Scientist(leonardodaVinci) ∧ Painter(leonardodaVinci)", "∀x (Painting(x) → (History(x) ∨ Portrait(x) ∨ Animal(x) ∨ Landscape(x) ∨ StillLife(x)))" ]

[ "The Mona Lisa is one of the world's best-known artworks.", "The Mona Lisa is a portrait painted by Leonardo da Vinci.", "Leonardo da Vinci was a scientist and painter.", "Painting genres are history, portrait, animal, landscape, and still life." ]

[ "Painting(monaLisa) ∧ WorldsBestKnown(monaLisa)", "PaintedBy(monaLisa, leonardodaVinci) ∧ Portrait(monaLisa)", "Scientist(leonardodaVinci) ∧ Painter(leonardodaVinci)", "∀x (Painting(x) → (History(x) ∨ Portrait(x) ∨ Animal(x) ∨ Landscape(x) ∨ StillLife(x)))" ]

[ "The Mona Lisa is one of the world's best-known artworks.", "The Mona Lisa is a portrait painted by Leonardo da Vinci.", "Leonardo da Vinci was a scientist and painter.", "Painting genres are history, portrait, animal, landscape, and still life." ]

[ "Painting(monaLisa) ∧ WorldsBestKnown(monaLisa)", "PaintedBy(monaLisa, leonardodaVinci) ∧ Portrait(monaLisa)", "Scientist(leonardodaVinci) ∧ Painter(leonardodaVinci)", "∀x (Painting(x) → (History(x) ∨ Portrait(x) ∨ Animal(x) ∨ Landscape(x) ∨ StillLife(x)))" ]

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

[ "∀x (ProfessionalTennisUmpire(x) → ¬ProfessionalTennisPlayer(x))", "∀x (WorldTourPlayer(x) → ProfessionalTennisPlayer(x))", "∀x (GrandSlamChampion(x) → WorldTourPlayer(x))", "∀x (GrandSlamUmpire(x) → ProfessionalTennisUmpire(x))", "WorldTourPlayer(nadal) ∨ GrandSlamChampion(nadal)" ]

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

[ "∀x (ProfessionalTennisUmpire(x) → ¬ProfessionalTennisPlayer(x))", "∀x (WorldTourPlayer(x) → ProfessionalTennisPlayer(x))", "∀x (GrandSlamChampion(x) → WorldTourPlayer(x))", "∀x (GrandSlamUmpire(x) → ProfessionalTennisUmpire(x))", "WorldTourPlayer(nadal) ∨ GrandSlamChampion(nadal)" ]

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

[ "∀x (ProfessionalTennisUmpire(x) → ¬ProfessionalTennisPlayer(x))", "∀x (WorldTourPlayer(x) → ProfessionalTennisPlayer(x))", "∀x (GrandSlamChampion(x) → WorldTourPlayer(x))", "∀x (GrandSlamUmpire(x) → ProfessionalTennisUmpire(x))", "WorldTourPlayer(nadal) ∨ GrandSlamChampion(nadal)" ]

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

[ "∀x (ProfessionalTennisUmpire(x) → ¬ProfessionalTennisPlayer(x))", "∀x (WorldTourPlayer(x) → ProfessionalTennisPlayer(x))", "∀x (GrandSlamChampion(x) → WorldTourPlayer(x))", "∀x (GrandSlamUmpire(x) → ProfessionalTennisUmpire(x))", "WorldTourPlayer(nadal) ∨ GrandSlamChampion(nadal)" ]

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

[ "∀x (ProfessionalTennisUmpire(x) → ¬ProfessionalTennisPlayer(x))", "∀x (WorldTourPlayer(x) → ProfessionalTennisPlayer(x))", "∀x (GrandSlamChampion(x) → WorldTourPlayer(x))", "∀x (GrandSlamUmpire(x) → ProfessionalTennisUmpire(x))", "WorldTourPlayer(nadal) ∨ GrandSlamChampion(nadal)" ]

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

[ "∀x (ProfessionalTennisUmpire(x) → ¬ProfessionalTennisPlayer(x))", "∀x (WorldTourPlayer(x) → ProfessionalTennisPlayer(x))", "∀x (GrandSlamChampion(x) → WorldTourPlayer(x))", "∀x (GrandSlamUmpire(x) → ProfessionalTennisUmpire(x))", "WorldTourPlayer(nadal) ∨ GrandSlamChampion(nadal)" ]

[ "Buisnesses are either sanctioned or unsanctioned.", "Sanctioned buisnesses are limited.", "Unsanctioned buisnesses are free.", "The Crude Oil Data Exchange is a buisness that isn't free." ]

[ "∀x (Buisness(x) → Sanctioned(x) ⊕ ¬Sanctioned(x))", "∀x (Buisness(x) ∧ Sanctioned(x) → Limited(x))", "∀x (Buisness(x) ∧ ¬Sanctioned(x) → Free(x))", "Buisness(crudeoildataexchange) ∧ ¬Free(crudeoildataexchange)" ]

[ "Buisnesses are either sanctioned or unsanctioned.", "Sanctioned buisnesses are limited.", "Unsanctioned buisnesses are free.", "The Crude Oil Data Exchange is a buisness that isn't free." ]

[ "∀x (Buisness(x) → Sanctioned(x) ⊕ ¬Sanctioned(x))", "∀x (Buisness(x) ∧ Sanctioned(x) → Limited(x))", "∀x (Buisness(x) ∧ ¬Sanctioned(x) → Free(x))", "Buisness(crudeoildataexchange) ∧ ¬Free(crudeoildataexchange)" ]

[ "Buisnesses are either sanctioned or unsanctioned.", "Sanctioned buisnesses are limited.", "Unsanctioned buisnesses are free.", "The Crude Oil Data Exchange is a buisness that isn't free." ]

[ "∀x (Buisness(x) → Sanctioned(x) ⊕ ¬Sanctioned(x))", "∀x (Buisness(x) ∧ Sanctioned(x) → Limited(x))", "∀x (Buisness(x) ∧ ¬Sanctioned(x) → Free(x))", "Buisness(crudeoildataexchange) ∧ ¬Free(crudeoildataexchange)" ]

[ "When something is depressing, it is sad.", "V is depressing. " ]

[ "∀x (Depressing(x) → Sad(x))", "∀x (V(x) → Depressing(x))" ]

[ "Palstaves are a type of early bronze axe.", "Commonly found in northern, western and south-western Europe, palstaves are cast in moulds.", "John Evans is an archeologist who popularized the term \"palstave\".", "A paalstab is not an axe, but rather a digging shovel." ]

[ "∀x (Palstave(x) → From(x, earlybronzeage) ∧ Axe(x))", "∀x ∀y (Palstave(x) ∧ Mould(y) → FoundIn(x, northerneurope) ∧ FoundIn(x, westerneurope) ∧ FoundIn(x, south-westerneurope) ∧ CastIn(x, y))", "Archeologist(johnevans) ∧ Popularized(johnevans, termpalstave)", "∀x (Paalstab(x) → ¬Axe(x) ∧ DiggingShovel(x))" ]

[ "Palstaves are a type of early bronze axe.", "Commonly found in northern, western and south-western Europe, palstaves are cast in moulds.", "John Evans is an archeologist who popularized the term \"palstave\".", "A paalstab is not an axe, but rather a digging shovel." ]

[ "∀x (Palstave(x) → From(x, earlybronzeage) ∧ Axe(x))", "∀x ∀y (Palstave(x) ∧ Mould(y) → FoundIn(x, northerneurope) ∧ FoundIn(x, westerneurope) ∧ FoundIn(x, south-westerneurope) ∧ CastIn(x, y))", "Archeologist(johnevans) ∧ Popularized(johnevans, termpalstave)", "∀x (Paalstab(x) → ¬Axe(x) ∧ DiggingShovel(x))" ]

[ "Palstaves are a type of early bronze axe.", "Commonly found in northern, western and south-western Europe, palstaves are cast in moulds.", "John Evans is an archeologist who popularized the term \"palstave\".", "A paalstab is not an axe, but rather a digging shovel." ]

[ "∀x (Palstave(x) → From(x, earlybronzeage) ∧ Axe(x))", "∀x ∀y (Palstave(x) ∧ Mould(y) → FoundIn(x, northerneurope) ∧ FoundIn(x, westerneurope) ∧ FoundIn(x, south-westerneurope) ∧ CastIn(x, y))", "Archeologist(johnevans) ∧ Popularized(johnevans, termpalstave)", "∀x (Paalstab(x) → ¬Axe(x) ∧ DiggingShovel(x))" ]

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

[ "Japanese(koeitecmo) ∧ VideoGameHoldingCompany(koeitecmo) ∧ AnimeHoldingCompany(koeitecmo)", "∀x ∃y (HoldingCompany(x) → Company(y) ∧ Holds(x, y))", "Disbanded(tecmo) ∧ DisbandedIn(tecmo, japan) ∧ Survived(koei) ∧ Renamed(koei)", "∀x (VideoGameHoldingCompany(x) → HoldingCompany(x))" ]

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

[ "Japanese(koeitecmo) ∧ VideoGameHoldingCompany(koeitecmo) ∧ AnimeHoldingCompany(koeitecmo)", "∀x ∃y (HoldingCompany(x) → Company(y) ∧ Holds(x, y))", "Disbanded(tecmo) ∧ DisbandedIn(tecmo, japan) ∧ Survived(koei) ∧ Renamed(koei)", "∀x (VideoGameHoldingCompany(x) → HoldingCompany(x))" ]

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

[ "Japanese(koeitecmo) ∧ VideoGameHoldingCompany(koeitecmo) ∧ AnimeHoldingCompany(koeitecmo)", "∀x ∃y (HoldingCompany(x) → Company(y) ∧ Holds(x, y))", "Disbanded(tecmo) ∧ DisbandedIn(tecmo, japan) ∧ Survived(koei) ∧ Renamed(koei)", "∀x (VideoGameHoldingCompany(x) → HoldingCompany(x))" ]

[ "The PlayStation EyeToy is a camera accessory for the Playstation 2. ", "The PlayStation Eye is a camera accessory for the Playstation 3.", "The Playstation Camera is a camera accessory for the Playstation 4 and the Playstation 5.", "Camera accessory for the system is compatible with that system", "Only the Playstation Camera is compatible with more than one system." ]

[ "Accessory(pseyetoy, ps2)", "Accessory(pseye, ps3)", "Accessory(pscamera, ps4) ∧ Accessory(pscamera, ps5)", "∀x ∀y (Accessory(x, y) → Compatible(x, y))", "¬Compatible(pseye, ps2) ∧ ¬Compatible(pseye, ps4)∧¬Compatible(pseye, ps5)∧¬Compatible(pseyetoy, ps3)∧¬Compatible(pseyetoy, ps4)∧¬Compatible(pseyetoy, ps5)" ]

[ "The PlayStation EyeToy is a camera accessory for the Playstation 2. ", "The PlayStation Eye is a camera accessory for the Playstation 3.", "The Playstation Camera is a camera accessory for the Playstation 4 and the Playstation 5.", "Camera accessory for the system is compatible with that system", "Only the Playstation Camera is compatible with more than one system." ]

[ "Accessory(pseyetoy, ps2)", "Accessory(pseye, ps3)", "Accessory(pscamera, ps4) ∧ Accessory(pscamera, ps5)", "∀x ∀y (Accessory(x, y) → Compatible(x, y))", "¬Compatible(pseye, ps2) ∧ ¬Compatible(pseye, ps4)∧¬Compatible(pseye, ps5)∧¬Compatible(pseyetoy, ps3)∧¬Compatible(pseyetoy, ps4)∧¬Compatible(pseyetoy, ps5)" ]

[ "The PlayStation EyeToy is a camera accessory for the Playstation 2. ", "The PlayStation Eye is a camera accessory for the Playstation 3.", "The Playstation Camera is a camera accessory for the Playstation 4 and the Playstation 5.", "Camera accessory for the system is compatible with that system", "Only the Playstation Camera is compatible with more than one system." ]

[ "Accessory(pseyetoy, ps2)", "Accessory(pseye, ps3)", "Accessory(pscamera, ps4) ∧ Accessory(pscamera, ps5)", "∀x ∀y (Accessory(x, y) → Compatible(x, y))", "¬Compatible(pseye, ps2) ∧ ¬Compatible(pseye, ps4)∧¬Compatible(pseye, ps5)∧¬Compatible(pseyetoy, ps3)∧¬Compatible(pseyetoy, ps4)∧¬Compatible(pseyetoy, ps5)" ]

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

[ "FootballPlayer(adambuska) ∧ European(adambuska)", "∀x ((FootballPlayer(x) ∧ European(x)) → PlaysAmericanSoccer(x))" ]

[ "If the game has sold more than 1 million copies, then it is on the Best Seller list. ", "All Games developed by Paradox Development Studio sold more than 1 million copies. ", "Some games published before 2010 support the Linux OS system. ", "All games on the Best Seller list are popular among young people. ", "FIFA22 neither supports the Linux OS system nor is it popular among young people." ]

[ "∀x (SoldMillion(x) → BestSeller(x))", "∀x (DevelopedByParadox(x) → SoldMillion(x))", "∃x ((PublishedBefore2010(x) ∧ SupportLinuxSystem(x)))", "∀x (BestSeller(x) → Popular(x))", "¬(SupportLinuxSystem(fifa21) ∨ Popular(fifa21))" ]

[ "If the game has sold more than 1 million copies, then it is on the Best Seller list. ", "All Games developed by Paradox Development Studio sold more than 1 million copies. ", "Some games published before 2010 support the Linux OS system. ", "All games on the Best Seller list are popular among young people. ", "FIFA22 neither supports the Linux OS system nor is it popular among young people." ]

[ "∀x (SoldMillion(x) → BestSeller(x))", "∀x (DevelopedByParadox(x) → SoldMillion(x))", "∃x ((PublishedBefore2010(x) ∧ SupportLinuxSystem(x)))", "∀x (BestSeller(x) → Popular(x))", "¬(SupportLinuxSystem(fifa21) ∨ Popular(fifa21))" ]

[ "If the game has sold more than 1 million copies, then it is on the Best Seller list. ", "All Games developed by Paradox Development Studio sold more than 1 million copies. ", "Some games published before 2010 support the Linux OS system. ", "All games on the Best Seller list are popular among young people. ", "FIFA22 neither supports the Linux OS system nor is it popular among young people." ]

[ "∀x (SoldMillion(x) → BestSeller(x))", "∀x (DevelopedByParadox(x) → SoldMillion(x))", "∃x ((PublishedBefore2010(x) ∧ SupportLinuxSystem(x)))", "∀x (BestSeller(x) → Popular(x))", "¬(SupportLinuxSystem(fifa21) ∨ Popular(fifa21))" ]

[ "China is one of BRICS and its economy is emerging.", "India is one of BRICS and its economy is emerging.", "All people from China speak Chinese.", "All people from India speak Hindi or English.", "There is an Indian." ]

[ "∀x (China(x) → BRICS(x) ∧ EmergingEconomy(x))", "∀x (India(x) → BRICS(x) ∧ EmergingEconomy(x))", "∀x ∀y (From(x, y) ∧ China(y) → Speak(x, chinese))", "∀x ∀y (From(x, y) ∧ India(y) → Speak(x, hindi) ∨ Speak(x, english))", "∃x ∃y (From(x, y) ∧ India(y))" ]

[ "China is one of BRICS and its economy is emerging.", "India is one of BRICS and its economy is emerging.", "All people from China speak Chinese.", "All people from India speak Hindi or English.", "There is an Indian." ]

[ "∀x (China(x) → BRICS(x) ∧ EmergingEconomy(x))", "∀x (India(x) → BRICS(x) ∧ EmergingEconomy(x))", "∀x ∀y (From(x, y) ∧ China(y) → Speak(x, chinese))", "∀x ∀y (From(x, y) ∧ India(y) → Speak(x, hindi) ∨ Speak(x, english))", "∃x ∃y (From(x, y) ∧ India(y))" ]

[ "China is one of BRICS and its economy is emerging.", "India is one of BRICS and its economy is emerging.", "All people from China speak Chinese.", "All people from India speak Hindi or English.", "There is an Indian." ]

[ "∀x (China(x) → BRICS(x) ∧ EmergingEconomy(x))", "∀x (India(x) → BRICS(x) ∧ EmergingEconomy(x))", "∀x ∀y (From(x, y) ∧ China(y) → Speak(x, chinese))", "∀x ∀y (From(x, y) ∧ India(y) → Speak(x, hindi) ∨ Speak(x, english))", "∃x ∃y (From(x, y) ∧ India(y))" ]

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

[ "Actor(daveedDiggs) ∧ FilmProducer(daveedDiggs)", "PlayedTwoRoles(daveedDiggs) ∧ PlayedIn(daveedDiggs, hamilton) ∧ Musical(hamilton)", "∃x (Actor(x) ∧ PlayedIn(x, hamilton) ∧ WonBestActorAward(x))", "∀x (Actor(x) ∧ Played(x, thomasJefferson) → WonBestActorAward(x))", "Played(daveedDiggs, thomasJefferson)", "∀x (Musical(x) → ¬Film(x))" ]

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

[ "Actor(daveedDiggs) ∧ FilmProducer(daveedDiggs)", "PlayedTwoRoles(daveedDiggs) ∧ PlayedIn(daveedDiggs, hamilton) ∧ Musical(hamilton)", "∃x (Actor(x) ∧ PlayedIn(x, hamilton) ∧ WonBestActorAward(x))", "∀x (Actor(x) ∧ Played(x, thomasJefferson) → WonBestActorAward(x))", "Played(daveedDiggs, thomasJefferson)", "∀x (Musical(x) → ¬Film(x))" ]

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

[ "Actor(daveedDiggs) ∧ FilmProducer(daveedDiggs)", "PlayedTwoRoles(daveedDiggs) ∧ PlayedIn(daveedDiggs, hamilton) ∧ Musical(hamilton)", "∃x (Actor(x) ∧ PlayedIn(x, hamilton) ∧ WonBestActorAward(x))", "∀x (Actor(x) ∧ Played(x, thomasJefferson) → WonBestActorAward(x))", "Played(daveedDiggs, thomasJefferson)", "∀x (Musical(x) → ¬Film(x))" ]

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

[ "PolishFootballPlayer(ernestpohl)", "∃x (In(x, polishfirstdivision) ∧ ScoredMoreThan180Goals(x))", "ScoredMoreThan180Goals(ernestpohl) ∧ In(ernestpohl, polishfirstdivision)", "∃x (NamedAfter(gornikzabrze, x) ∧ FootballPlayer(x) ∧ From(x, rudaslaska))", "From(ernestpohl, rudaslaska)" ]

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

[ "PolishFootballPlayer(ernestpohl)", "∃x (In(x, polishfirstdivision) ∧ ScoredMoreThan180Goals(x))", "ScoredMoreThan180Goals(ernestpohl) ∧ In(ernestpohl, polishfirstdivision)", "∃x (NamedAfter(gornikzabrze, x) ∧ FootballPlayer(x) ∧ From(x, rudaslaska))", "From(ernestpohl, rudaslaska)" ]

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

[ "PhiladephiaCouncil(annJLand) ∧ DemocraticParty(annJLand)", "Year(y1980) → PhiladephiaCouncil(annJLand) ∧ RunFor(annJLand)", "∀x (RunFor(x) ∧ PhiladephiaCouncil(x) → Elected(x))", "Challenger(nutter)", "Year(y1987) → PhiladephiaCouncil(annJLand) ∧ RunFor(annJLand) ∧ Defeated(annJLand, nutter)" ]

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

[ "PhiladephiaCouncil(annJLand) ∧ DemocraticParty(annJLand)", "Year(y1980) → PhiladephiaCouncil(annJLand) ∧ RunFor(annJLand)", "∀x (RunFor(x) ∧ PhiladephiaCouncil(x) → Elected(x))", "Challenger(nutter)", "Year(y1987) → PhiladephiaCouncil(annJLand) ∧ RunFor(annJLand) ∧ Defeated(annJLand, nutter)" ]

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

[ "PhiladephiaCouncil(annJLand) ∧ DemocraticParty(annJLand)", "Year(y1980) → PhiladephiaCouncil(annJLand) ∧ RunFor(annJLand)", "∀x (RunFor(x) ∧ PhiladephiaCouncil(x) → Elected(x))", "Challenger(nutter)", "Year(y1987) → PhiladephiaCouncil(annJLand) ∧ RunFor(annJLand) ∧ Defeated(annJLand, nutter)" ]

[ "Aberdeen won the cup in the 2013 final.", "Rangers won the cup in 2014 final.", "Aberdeen and Rangers are different teams.", "Different teams cannot win the same cup in a given year's final." ]

[ "WonCup(aberdeen, twentythirteen)", "WonCup(rangers, twentyfourteen)", "Different(aberdeen, rangers) ∧ Different(rangers, aberdeen)", "∀x ∀y ∀z (Different(x, y) ∧ WonCup(x, z) → ¬WonCup(y, z))" ]

[ "Aberdeen won the cup in the 2013 final.", "Rangers won the cup in 2014 final.", "Aberdeen and Rangers are different teams.", "Different teams cannot win the same cup in a given year's final." ]

[ "WonCup(aberdeen, twentythirteen)", "WonCup(rangers, twentyfourteen)", "Different(aberdeen, rangers) ∧ Different(rangers, aberdeen)", "∀x ∀y ∀z (Different(x, y) ∧ WonCup(x, z) → ¬WonCup(y, z))" ]

[ "Aberdeen won the cup in the 2013 final.", "Rangers won the cup in 2014 final.", "Aberdeen and Rangers are different teams.", "Different teams cannot win the same cup in a given year's final." ]

[ "WonCup(aberdeen, twentythirteen)", "WonCup(rangers, twentyfourteen)", "Different(aberdeen, rangers) ∧ Different(rangers, aberdeen)", "∀x ∀y ∀z (Different(x, y) ∧ WonCup(x, z) → ¬WonCup(y, z))" ]

[ "All young working professionals who have regular 9-5 jobs also have pets.", "Some people who live in Manhattan are young working professionals who have regular 9-5 jobs.", "All people who have pets are people who have at least one child.", "People who do not have at least one child are people who own a sports car.", "Mary either does not own a sports car or, if they do, then they do not have at least one child." ]

[ "∀x (Working(x) → Pets(x))", "∃x (Manhattan(x) ∧ Working(x))", "∀x (Pets(x) → Child(x))", "∀x (Child(x) → ¬Car(x))", "¬(Car(mary) ⊕ Child(mary))" ]

[ "All young working professionals who have regular 9-5 jobs also have pets.", "Some people who live in Manhattan are young working professionals who have regular 9-5 jobs.", "All people who have pets are people who have at least one child.", "People who do not have at least one child are people who own a sports car.", "Mary either does not own a sports car or, if they do, then they do not have at least one child." ]

[ "∀x (Working(x) → Pets(x))", "∃x (Manhattan(x) ∧ Working(x))", "∀x (Pets(x) → Child(x))", "∀x (Child(x) → ¬Car(x))", "¬(Car(mary) ⊕ Child(mary))" ]

[ "All young working professionals who have regular 9-5 jobs also have pets.", "Some people who live in Manhattan are young working professionals who have regular 9-5 jobs.", "All people who have pets are people who have at least one child.", "People who do not have at least one child are people who own a sports car.", "Mary either does not own a sports car or, if they do, then they do not have at least one child." ]

[ "∀x (Working(x) → Pets(x))", "∃x (Manhattan(x) ∧ Working(x))", "∀x (Pets(x) → Child(x))", "∀x (Child(x) → ¬Car(x))", "¬(Car(mary) ⊕ Child(mary))" ]

[ "Either block design or event-related design. ", "All event-related designs are brain image acquisition.", "All brain image acquisition is preceded by data processing.", "Nothing preceded by data processing acquires data.", "Picture memory is either an event-related design and acquiring data or neither an event-related design nor acquiring data." ]

[ "∀x (BlockDesign(x) ∨ Event-relatedDesign(x))", "∀x (Event-relatedDesign(x) → BrainImageAcquisition(x))", "∀x (BrainImageAcquisition(x) → PrecededByDataProcessing(x))", "∀x (PrecededByDataProcessing(x) → ¬AcquiringData(x))", "(Event-relatedDesign(pictureMemory) ∧ AcquiringData(pictureMemory)) ∨ (¬Event-relatedDesign(pictureMemory) ∧ ¬AcquiringData(pictureMemory))" ]

[ "Either block design or event-related design. ", "All event-related designs are brain image acquisition.", "All brain image acquisition is preceded by data processing.", "Nothing preceded by data processing acquires data.", "Picture memory is either an event-related design and acquiring data or neither an event-related design nor acquiring data." ]

[ "∀x (BlockDesign(x) ∨ Event-relatedDesign(x))", "∀x (Event-relatedDesign(x) → BrainImageAcquisition(x))", "∀x (BrainImageAcquisition(x) → PrecededByDataProcessing(x))", "∀x (PrecededByDataProcessing(x) → ¬AcquiringData(x))", "(Event-relatedDesign(pictureMemory) ∧ AcquiringData(pictureMemory)) ∨ (¬Event-relatedDesign(pictureMemory) ∧ ¬AcquiringData(pictureMemory))" ]