premises
sequence | premises-FOL
sequence | conclusion
stringlengths 12
386
| conclusion-FOL
stringlengths 8
140
| label
stringclasses 3
values |
|---|---|---|---|---|
[
"If people perform in school talent shows often, then they attend and are very engaged with school events.",
"People either perform in school talent shows often or are inactive and disinterested members of their community.",
"If people chaperone high school dances, then they are not students who attend the school.",
"All people who are inactive and disinterested members of their community chaperone high school dances.",
"All young children and teenagers who wish to further their academic careers and educational opportunities are students who attend the school.",
"Bonnie either both attends and is very engaged with school events and is a student who attends the school, or she neither attends and is very engaged with school events nor is a student who attends the school. "
] | [
"∀x (TalentShows(x) → Engaged(x))",
"∀x (TalentShows(x) ∨ Inactive(x))",
"∀x (Chaperone(x) → ¬Students(x))",
"∀x (Inactive(x) → Chaperone(x))",
"∀x (AcademicCareer(x) → Students(x))",
"(Engaged(bonnie) ∧ Students(bonnie)) ⊕ (¬Engaged(bonnie) ∧ ¬Students(bonnie))"
] | Bonnie performs in school talent shows often. | Engaged(bonnie) | Uncertain |
[
"If people perform in school talent shows often, then they attend and are very engaged with school events.",
"People either perform in school talent shows often or are inactive and disinterested members of their community.",
"If people chaperone high school dances, then they are not students who attend the school.",
"All people who are inactive and disinterested members of their community chaperone high school dances.",
"All young children and teenagers who wish to further their academic careers and educational opportunities are students who attend the school.",
"Bonnie either both attends and is very engaged with school events and is a student who attends the school, or she neither attends and is very engaged with school events nor is a student who attends the school. "
] | [
"∀x (TalentShows(x) → Engaged(x))",
"∀x (TalentShows(x) ∨ Inactive(x))",
"∀x (Chaperone(x) → ¬Students(x))",
"∀x (Inactive(x) → Chaperone(x))",
"∀x (AcademicCareer(x) → Students(x))",
"(Engaged(bonnie) ∧ Students(bonnie)) ⊕ (¬Engaged(bonnie) ∧ ¬Students(bonnie))"
] | If Bonnie is either both a young child or teenager who wishes to further her academic career and educational opportunities and chaperones high school dances or neither is a young child nor teenager who wishes to further her academic career and educational opportunities, then Bonnie is either a student who attends the school or is an inactive and disinterested member of the community. | AcademicCareer(bonnie) ⊕ Chaperone(bonnie) → AcademicCareer(bonnie) ⊕ Inactive(bonnie) | True |
[
"If people perform in school talent shows often, then they attend and are very engaged with school events.",
"People either perform in school talent shows often or are inactive and disinterested members of their community.",
"If people chaperone high school dances, then they are not students who attend the school.",
"All people who are inactive and disinterested members of their community chaperone high school dances.",
"All young children and teenagers who wish to further their academic careers and educational opportunities are students who attend the school.",
"Bonnie either both attends and is very engaged with school events and is a student who attends the school, or she neither attends and is very engaged with school events nor is a student who attends the school. "
] | [
"∀x (TalentShows(x) → Engaged(x))",
"∀x (TalentShows(x) ∨ Inactive(x))",
"∀x (Chaperone(x) → ¬Students(x))",
"∀x (Inactive(x) → Chaperone(x))",
"∀x (AcademicCareer(x) → Students(x))",
"(Engaged(bonnie) ∧ Students(bonnie)) ⊕ (¬Engaged(bonnie) ∧ ¬Students(bonnie))"
] | If Bonnie either chaperones high school dances or, if she does not, she performs in school talent shows often, then Bonnie is both a young child or teenager who wishes to further her academic career and educational opportunities and an inactive and disinterested member of the community. | Chaperone(bonnie) ⊕ TalentShows(bonnie) → AcademicCareer(bonnie) ∧ Inactive(bonnie)) | False |
[
"All employees who schedule a meeting with their customers will appear in the company today. ",
"Everyone who has lunch in the company schedules meetings with their customers. ",
"Employees will either have lunch in the company or have lunch at home.",
"If an employee has lunch at home, then he/she is working remotely from home.",
"All employees who are in other countries work remotely from home. ",
"No managers work remotely from home. ",
"James is either a manager and appears in the company today or neither a manager nor appears in the company today."
] | [
"∀x (Meeting(x) → AppearInCompany(x))",
"∀x (LunchInCompany(x) → Meetings(x))",
"∀x (LunchInCompany(x) ∨ LunchAtHome(x))",
"∀x (LunchAtHome(x) → WorkRemotelyFromHome(x))",
"∀x (InOtherCountries(x) → WorkRemotelyFromHome(x))",
"∀x (Manager(x) → ¬WorkRemotelyFromHome(x))",
"Manager(james) ⊕ AppearInCompany(james)"
] | James has lunch in the company. | LunchInCompany(james) | Uncertain |
[
"All employees who schedule a meeting with their customers will appear in the company today. ",
"Everyone who has lunch in the company schedules meetings with their customers. ",
"Employees will either have lunch in the company or have lunch at home.",
"If an employee has lunch at home, then he/she is working remotely from home.",
"All employees who are in other countries work remotely from home. ",
"No managers work remotely from home. ",
"James is either a manager and appears in the company today or neither a manager nor appears in the company today."
] | [
"∀x (Meeting(x) → AppearInCompany(x))",
"∀x (LunchInCompany(x) → Meetings(x))",
"∀x (LunchInCompany(x) ∨ LunchAtHome(x))",
"∀x (LunchAtHome(x) → WorkRemotelyFromHome(x))",
"∀x (InOtherCountries(x) → WorkRemotelyFromHome(x))",
"∀x (Manager(x) → ¬WorkRemotelyFromHome(x))",
"Manager(james) ⊕ AppearInCompany(james)"
] | James does not have lunch in the company. | ¬LunchInCompany(james) | Uncertain |
[
"All employees who schedule a meeting with their customers will appear in the company today. ",
"Everyone who has lunch in the company schedules meetings with their customers. ",
"Employees will either have lunch in the company or have lunch at home.",
"If an employee has lunch at home, then he/she is working remotely from home.",
"All employees who are in other countries work remotely from home. ",
"No managers work remotely from home. ",
"James is either a manager and appears in the company today or neither a manager nor appears in the company today."
] | [
"∀x (Meeting(x) → AppearInCompany(x))",
"∀x (LunchInCompany(x) → Meetings(x))",
"∀x (LunchInCompany(x) ∨ LunchAtHome(x))",
"∀x (LunchAtHome(x) → WorkRemotelyFromHome(x))",
"∀x (InOtherCountries(x) → WorkRemotelyFromHome(x))",
"∀x (Manager(x) → ¬WorkRemotelyFromHome(x))",
"Manager(james) ⊕ AppearInCompany(james)"
] | If James is either a manager or in other countries, then James either has lunch at home and works remotely from home, or neither has lunch at home nor works remotely from home. | (Manager(james) ⊕ InOtherCountries(james)) → (LunchAtHome(james) ⊕ WorkRemotelyFromHome(james)) | True |
[
"Monkeypox is an infectious disease caused by the monkeypox virus.",
"Monkeypox virus can occur in certain animals, including humans.",
"Humans are mammals.",
"Mammals are animals.",
"Symptons of Monkeypox include fever, headache, muscle pains, feeling tired, and so on.",
"People feel tired when they get a glu."
] | [
"∃x (OccurMonkeypoxVirus(x) ∧ GetMonkeypox(x))",
"∃x (Animal(x) ∧ OccurMonkeypoxVirus(x))",
"∀x (Human(x) → Mammal(x))",
"∀x (Mammal(x) → Animal(x))",
"∃x (GetMonkeypox(x) ∧ (Fever(x) ∨ Headache(x) ∨ MusclePain(x) ∨ Tired(x)))",
"∀x (Human(x) ∧ Flu(x) → Tired(x))"
] | There is an animal. | ∃x (Animal(x)) | True |
[
"Monkeypox is an infectious disease caused by the monkeypox virus.",
"Monkeypox virus can occur in certain animals, including humans.",
"Humans are mammals.",
"Mammals are animals.",
"Symptons of Monkeypox include fever, headache, muscle pains, feeling tired, and so on.",
"People feel tired when they get a glu."
] | [
"∃x (OccurMonkeypoxVirus(x) ∧ GetMonkeypox(x))",
"∃x (Animal(x) ∧ OccurMonkeypoxVirus(x))",
"∀x (Human(x) → Mammal(x))",
"∀x (Mammal(x) → Animal(x))",
"∃x (GetMonkeypox(x) ∧ (Fever(x) ∨ Headache(x) ∨ MusclePain(x) ∨ Tired(x)))",
"∀x (Human(x) ∧ Flu(x) → Tired(x))"
] | No one gets flu. | ∀x (Human(x) → ¬Flu(x)) | Uncertain |
[
"Monkeypox is an infectious disease caused by the monkeypox virus.",
"Monkeypox virus can occur in certain animals, including humans.",
"Humans are mammals.",
"Mammals are animals.",
"Symptons of Monkeypox include fever, headache, muscle pains, feeling tired, and so on.",
"People feel tired when they get a glu."
] | [
"∃x (OccurMonkeypoxVirus(x) ∧ GetMonkeypox(x))",
"∃x (Animal(x) ∧ OccurMonkeypoxVirus(x))",
"∀x (Human(x) → Mammal(x))",
"∀x (Mammal(x) → Animal(x))",
"∃x (GetMonkeypox(x) ∧ (Fever(x) ∨ Headache(x) ∨ MusclePain(x) ∨ Tired(x)))",
"∀x (Human(x) ∧ Flu(x) → Tired(x))"
] | Symptons of Monkeypox include coughing. | ∃x (GetMonkeypox(x) ∧ Coughing(x)) | Uncertain |
[
"There are six types of wild turkeys: Eastern wild turkey, Osceola wild turkey, Gould’s wild turkey, Merriam’s wild",
"turkey, Rio Grande wild turkey, and Ocellated wild turkey.",
"Tom is not an Eastern wild turkey.",
"Tom is not an Osceola wild turkey.",
"Tom is also not a Gould's wild turkey, or a Merriam's wild turkey, or a Rio Grande wild turkey.",
"Tom is a wild turkey."
] | [
"∀x (WildTurkey(x) → (Eastern(x) ∨ Osceola(x) ∨ Goulds(x) ∨ Merriams(x) ∨ Riogrande(x) ∨ Ocellated(x)))",
"¬(WildTurkey(tom) ∧ Eastern(tom))",
"¬(WildTurkey(tom) ∧ Osceola(tom))",
"WildTurkey(tom) → ¬(Goulds(tom) ∨ Merriams(tom) ∨ Riogrande(tom))",
"WildTurkey(tom)"
] | Tom is an Ocellated wild turkey. | Ocellated(tom) | True |
[
"There are six types of wild turkeys: Eastern wild turkey, Osceola wild turkey, Gould’s wild turkey, Merriam’s wild",
"turkey, Rio Grande wild turkey, and Ocellated wild turkey.",
"Tom is not an Eastern wild turkey.",
"Tom is not an Osceola wild turkey.",
"Tom is also not a Gould's wild turkey, or a Merriam's wild turkey, or a Rio Grande wild turkey.",
"Tom is a wild turkey."
] | [
"∀x (WildTurkey(x) → (Eastern(x) ∨ Osceola(x) ∨ Goulds(x) ∨ Merriams(x) ∨ Riogrande(x) ∨ Ocellated(x)))",
"¬(WildTurkey(tom) ∧ Eastern(tom))",
"¬(WildTurkey(tom) ∧ Osceola(tom))",
"WildTurkey(tom) → ¬(Goulds(tom) ∨ Merriams(tom) ∨ Riogrande(tom))",
"WildTurkey(tom)"
] | Tom is an Eastern wild turkey. | Eastern(tom) | False |
[
"There are six types of wild turkeys: Eastern wild turkey, Osceola wild turkey, Gould’s wild turkey, Merriam’s wild",
"turkey, Rio Grande wild turkey, and Ocellated wild turkey.",
"Tom is not an Eastern wild turkey.",
"Tom is not an Osceola wild turkey.",
"Tom is also not a Gould's wild turkey, or a Merriam's wild turkey, or a Rio Grande wild turkey.",
"Tom is a wild turkey."
] | [
"∀x (WildTurkey(x) → (Eastern(x) ∨ Osceola(x) ∨ Goulds(x) ∨ Merriams(x) ∨ Riogrande(x) ∨ Ocellated(x)))",
"¬(WildTurkey(tom) ∧ Eastern(tom))",
"¬(WildTurkey(tom) ∧ Osceola(tom))",
"WildTurkey(tom) → ¬(Goulds(tom) ∨ Merriams(tom) ∨ Riogrande(tom))",
"WildTurkey(tom)"
] | Joey is a wild turkey. | WildTurkey(joey) | Uncertain |
[
"A Japanese game company created the game the Legend of Zelda.",
"All games in the Top 10 list are made by Japanese game companies.",
"[BG] If a game sells more than one million copies, then it will be selected into the Top 10 list.",
"The Legend of Zelda sold more than one million copies."
] | [
"∃x (Japanese(x) ∧ VideoGameCompany(x) ∧ Game(thelegendofzelda) ∧ Created(x, thelegendofzelda))",
"∀x ∀y (Game(x) ∧ InTop10(x) ∧ Created(x, y) → Japanese(y))",
"∀x (Game(x) ∧ SellsMoreThan(x, onemillioncopies) → Top10(x))",
"SellsMoreThan(thelegendofzelda, onemillioncopies)"
] | The Legend of Zelda is in the Top 10 list. | Top10(thelegendofzelda) | True |
[
"A Japanese game company created the game the Legend of Zelda.",
"All games in the Top 10 list are made by Japanese game companies.",
"[BG] If a game sells more than one million copies, then it will be selected into the Top 10 list.",
"The Legend of Zelda sold more than one million copies."
] | [
"∃x (Japanese(x) ∧ VideoGameCompany(x) ∧ Game(thelegendofzelda) ∧ Created(x, thelegendofzelda))",
"∀x ∀y (Game(x) ∧ InTop10(x) ∧ Created(x, y) → Japanese(y))",
"∀x (Game(x) ∧ SellsMoreThan(x, onemillioncopies) → Top10(x))",
"SellsMoreThan(thelegendofzelda, onemillioncopies)"
] | FIFA 22 is made by a Japanese video game company. | ∀x (Created(fifa22, x) → Japanese(x) ∧ VideoGameCompany(x)) | Uncertain |
[
"A Japanese game company created the game the Legend of Zelda.",
"All games in the Top 10 list are made by Japanese game companies.",
"[BG] If a game sells more than one million copies, then it will be selected into the Top 10 list.",
"The Legend of Zelda sold more than one million copies."
] | [
"∃x (Japanese(x) ∧ VideoGameCompany(x) ∧ Game(thelegendofzelda) ∧ Created(x, thelegendofzelda))",
"∀x ∀y (Game(x) ∧ InTop10(x) ∧ Created(x, y) → Japanese(y))",
"∀x (Game(x) ∧ SellsMoreThan(x, onemillioncopies) → Top10(x))",
"SellsMoreThan(thelegendofzelda, onemillioncopies)"
] | The Legend of Zelda is not in the Top 10 list. | ¬Top10(thelegendofzelda) | False |
[
"All squares have four sides.",
"All four-sided things are shapes. "
] | [
"∀x (Square(x) → FourSides(x))",
"∀x (FourSides(x) → IsShape(x))"
] | All squares are shapes. | ∀x (Square(x) → IsShape(x)) | True |
[
"All rabbits are cute. ",
"Some turtles exist. ",
"An animal is either a rabbit or a squirrel.",
"If something is skittish, then it is not still.",
"All squirrels are skittish.",
"Rock is still."
] | [
"∀x (Rabbit(x) → Cute(x))",
"∃x (Turtle(x))",
"∀x (Rabbit(x) ∨ Squirrel(x))",
"∀x (Skittish(x) → ¬Still(x))",
"∀x (Squirrel(x) → Skittish(x))",
"Still(rock)"
] | Rock is a turtle. | Turtle(rock) | Uncertain |
[
"All rabbits are cute. ",
"Some turtles exist. ",
"An animal is either a rabbit or a squirrel.",
"If something is skittish, then it is not still.",
"All squirrels are skittish.",
"Rock is still."
] | [
"∀x (Rabbit(x) → Cute(x))",
"∃x (Turtle(x))",
"∀x (Rabbit(x) ∨ Squirrel(x))",
"∀x (Skittish(x) → ¬Still(x))",
"∀x (Squirrel(x) → Skittish(x))",
"Still(rock)"
] | Rock is not a turtle. | ¬Turtle(rock) | Uncertain |
[
"All rabbits are cute. ",
"Some turtles exist. ",
"An animal is either a rabbit or a squirrel.",
"If something is skittish, then it is not still.",
"All squirrels are skittish.",
"Rock is still."
] | [
"∀x (Rabbit(x) → Cute(x))",
"∃x (Turtle(x))",
"∀x (Rabbit(x) ∨ Squirrel(x))",
"∀x (Skittish(x) → ¬Still(x))",
"∀x (Squirrel(x) → Skittish(x))",
"Still(rock)"
] | Rock is a turtle or cute. | Turtle(rock) ∨ Cute(rock) | True |
[
"All rabbits are cute. ",
"Some turtles exist. ",
"An animal is either a rabbit or a squirrel.",
"If something is skittish, then it is not still.",
"All squirrels are skittish.",
"Rock is still."
] | [
"∀x (Rabbit(x) → Cute(x))",
"∃x (Turtle(x))",
"∀x (Rabbit(x) ∨ Squirrel(x))",
"∀x (Skittish(x) → ¬Still(x))",
"∀x (Squirrel(x) → Skittish(x))",
"Still(rock)"
] | If Rock is not both a turtle and a squirrel, then Rock is either cute or skittish. | ¬(Turtle(rock) ∧ Squirrel(rock)) → Cute(rock) ⊕ Skittish(rock) | True |
[
"All rabbits are cute. ",
"Some turtles exist. ",
"An animal is either a rabbit or a squirrel.",
"If something is skittish, then it is not still.",
"All squirrels are skittish.",
"Rock is still."
] | [
"∀x (Rabbit(x) → Cute(x))",
"∃x (Turtle(x))",
"∀x (Rabbit(x) ∨ Squirrel(x))",
"∀x (Skittish(x) → ¬Still(x))",
"∀x (Squirrel(x) → Skittish(x))",
"Still(rock)"
] | If Rock is cute and still, then Rock is a turtle and skittish. | Cute(rock) ∧ Still(rock) → Turtle(rock) ∧ Skittish(rock) | False |
[
"\"Stranger Things\" is a popular Netflix show.",
"If a Netflix show is popular, Karen will binge-watch it.",
"If and only if Karen binge-watches a Netflix show, she will download it.",
"Karen does not download \"Black Mirror\".",
"\"Black Mirror\" is a Netflix show.",
"If Karen binge-watches a Netflix show, she will share it to Lisa."
] | [
"NetflixShow(strangerThings) ∧ Popular(strangerThings)",
"∀x ((NetflixShow(x) ∧ Popular(x)) → BingeWatch(karen, x))",
"∀x ((NetflixShow(x) ∧ BingeWatch(karen, x)) ↔ Download(karen, x))",
"¬Download(karen, blackMirror)",
"NetflixShow(blackMirror)",
"∀x ((NetflixShow(x) ∧ BingeWatch(karen, x)) → Share(x, lisa))"
] | Karen will share "Stranger Things" to Lisa. | Share(strangerThings, lisa) | True |
[
"\"Stranger Things\" is a popular Netflix show.",
"If a Netflix show is popular, Karen will binge-watch it.",
"If and only if Karen binge-watches a Netflix show, she will download it.",
"Karen does not download \"Black Mirror\".",
"\"Black Mirror\" is a Netflix show.",
"If Karen binge-watches a Netflix show, she will share it to Lisa."
] | [
"NetflixShow(strangerThings) ∧ Popular(strangerThings)",
"∀x ((NetflixShow(x) ∧ Popular(x)) → BingeWatch(karen, x))",
"∀x ((NetflixShow(x) ∧ BingeWatch(karen, x)) ↔ Download(karen, x))",
"¬Download(karen, blackMirror)",
"NetflixShow(blackMirror)",
"∀x ((NetflixShow(x) ∧ BingeWatch(karen, x)) → Share(x, lisa))"
] | "Black Mirror" is popular. | Popular(blackMirror) | False |
[
"\"Stranger Things\" is a popular Netflix show.",
"If a Netflix show is popular, Karen will binge-watch it.",
"If and only if Karen binge-watches a Netflix show, she will download it.",
"Karen does not download \"Black Mirror\".",
"\"Black Mirror\" is a Netflix show.",
"If Karen binge-watches a Netflix show, she will share it to Lisa."
] | [
"NetflixShow(strangerThings) ∧ Popular(strangerThings)",
"∀x ((NetflixShow(x) ∧ Popular(x)) → BingeWatch(karen, x))",
"∀x ((NetflixShow(x) ∧ BingeWatch(karen, x)) ↔ Download(karen, x))",
"¬Download(karen, blackMirror)",
"NetflixShow(blackMirror)",
"∀x ((NetflixShow(x) ∧ BingeWatch(karen, x)) → Share(x, lisa))"
] | Karen will share "Black Mirror" to Lisa. | Share(blackMirror, lisa) | Uncertain |
[
"Beijing is the capital of the People's Republic of China. ",
"Beijing is the world's most populous national capital city.",
"Beijing is located in Northern China.",
"Beijing hosted the 2008 Summer Olympics and 2008 Summer Paralympics Games.",
"Beijing has hosted both the Summer and Winter Olympics, along with the Summer and Winter Paralympics",
"Many of Beijing's 91 universities consistently rank among the best in the Asia-Pacific and the world."
] | [
"CapitalOf(beijing, prx)",
"MostPopulousNationalCapitalCity(beijing)",
"InNorthernChina(beijing)",
"Hosted(beijing, summer2008olympic) ∧ Hosted(beijing, summer2008paralympicgames)",
"Hosted(beijing, summerolympic) ∧ Hosted(beijing, winterolympic) ∧ Hosted(beijing, summerparalympicgames) ∧ Hosted(beijing, winterparalympicgames)",
"∃x (BeijingUniversity(x) ∧ ConsistentlyRankAmongTheBest(x))"
] | Beijing has hosted both the 2008 Summer Olympics and a winter olympics. | Hosted(beijing, summer2008olympic) ∧ Hosted(beijing, winterolympic) | True |
[
"Beijing is the capital of the People's Republic of China. ",
"Beijing is the world's most populous national capital city.",
"Beijing is located in Northern China.",
"Beijing hosted the 2008 Summer Olympics and 2008 Summer Paralympics Games.",
"Beijing has hosted both the Summer and Winter Olympics, along with the Summer and Winter Paralympics",
"Many of Beijing's 91 universities consistently rank among the best in the Asia-Pacific and the world."
] | [
"CapitalOf(beijing, prx)",
"MostPopulousNationalCapitalCity(beijing)",
"InNorthernChina(beijing)",
"Hosted(beijing, summer2008olympic) ∧ Hosted(beijing, summer2008paralympicgames)",
"Hosted(beijing, summerolympic) ∧ Hosted(beijing, winterolympic) ∧ Hosted(beijing, summerparalympicgames) ∧ Hosted(beijing, winterparalympicgames)",
"∃x (BeijingUniversity(x) ∧ ConsistentlyRankAmongTheBest(x))"
] | Beijing is located in southern China. | InSouthernChina(beijing) | Uncertain |
[
"Beijing is the capital of the People's Republic of China. ",
"Beijing is the world's most populous national capital city.",
"Beijing is located in Northern China.",
"Beijing hosted the 2008 Summer Olympics and 2008 Summer Paralympics Games.",
"Beijing has hosted both the Summer and Winter Olympics, along with the Summer and Winter Paralympics",
"Many of Beijing's 91 universities consistently rank among the best in the Asia-Pacific and the world."
] | [
"CapitalOf(beijing, prx)",
"MostPopulousNationalCapitalCity(beijing)",
"InNorthernChina(beijing)",
"Hosted(beijing, summer2008olympic) ∧ Hosted(beijing, summer2008paralympicgames)",
"Hosted(beijing, summerolympic) ∧ Hosted(beijing, winterolympic) ∧ Hosted(beijing, summerparalympicgames) ∧ Hosted(beijing, winterparalympicgames)",
"∃x (BeijingUniversity(x) ∧ ConsistentlyRankAmongTheBest(x))"
] | Beijing is the second largest Chinese city by urban population. | SecondLargestChineseCity(beijing) | Uncertain |
[
"All aliens are extraterrestrial.",
"If someone is from Mars, then they are aliens.",
"No extraterrestrial is human.",
"Everyone from Earth is a human.",
"Marvin cannot be from Earth and from Mars.",
"If Marvin is not from Earth, then Marvin is an extraterrestrial."
] | [
"∀x (Alien(x) → Extraterrestrial(x))",
"∀x (FromMars(x) → Alien(x))",
"∀x (Extraterrestrial(x) → ¬Human(x))",
"∀x (FromEarth(x) → Human(x))",
"¬FromEarth(marvin) ∧ ¬FromMars(marvin)",
"¬FromEarth(marvin) → Extraterrestrial(marvin)"
] | Marvin is an alien. | Alien(marvin) | False |
[
"All aliens are extraterrestrial.",
"If someone is from Mars, then they are aliens.",
"No extraterrestrial is human.",
"Everyone from Earth is a human.",
"Marvin cannot be from Earth and from Mars.",
"If Marvin is not from Earth, then Marvin is an extraterrestrial."
] | [
"∀x (Alien(x) → Extraterrestrial(x))",
"∀x (FromMars(x) → Alien(x))",
"∀x (Extraterrestrial(x) → ¬Human(x))",
"∀x (FromEarth(x) → Human(x))",
"¬FromEarth(marvin) ∧ ¬FromMars(marvin)",
"¬FromEarth(marvin) → Extraterrestrial(marvin)"
] | Marvin is neither a human nor from Mars. | ¬Human(marvin) ∧ ¬FromMars(marvin) | True |
[
"All aliens are extraterrestrial.",
"If someone is from Mars, then they are aliens.",
"No extraterrestrial is human.",
"Everyone from Earth is a human.",
"Marvin cannot be from Earth and from Mars.",
"If Marvin is not from Earth, then Marvin is an extraterrestrial."
] | [
"∀x (Alien(x) → Extraterrestrial(x))",
"∀x (FromMars(x) → Alien(x))",
"∀x (Extraterrestrial(x) → ¬Human(x))",
"∀x (FromEarth(x) → Human(x))",
"¬FromEarth(marvin) ∧ ¬FromMars(marvin)",
"¬FromEarth(marvin) → Extraterrestrial(marvin)"
] | If Marvin is not from Mars, then Marvin is a human. | ¬FromMars(marvin) → Human(marvin) | Uncertain |
[
"A person is either a Grand Slam champion or an Oscar-nominated actor.",
"All people who are Grand Slam champions are professional tennis players.",
"All Oscar-nominated actors are celebrities.",
"All professional tennis players are athletes.",
"If a person is a celebrity then they are well paid.",
"If a person is an athlete then they are famous.",
"All well-paid people live in tax havens.",
"If Djokovic is famous and is an athlete, then Djokovic lives in well paid."
] | [
"∀x (GrandSlamChampion(x) ⊕ OscarNominatedActor(x))",
"∀x (GrandSlamChampion(x) → ProfessionalTennisPlayer(x))",
"∀x (OscarNominatedActor(x) → Celebrity(x))",
"∀x (ProfessionalTennisPlayer(x) → Athlete(x))",
"∀x (Celebrity(x) → WellPaid(x))",
"∀x (Athlete(x) → Famous(x))",
"∀x (WellPaid(x) → LivesInTaxHaven(x))",
"Famous(djokovic) ∧ Athlete(djokovic) → LivesInTaxHaven(djokovic)"
] | Djokovic is a Grand Slam champion. | GrandSlamChampion(djokovic) | Uncertain |
[
"A person is either a Grand Slam champion or an Oscar-nominated actor.",
"All people who are Grand Slam champions are professional tennis players.",
"All Oscar-nominated actors are celebrities.",
"All professional tennis players are athletes.",
"If a person is a celebrity then they are well paid.",
"If a person is an athlete then they are famous.",
"All well-paid people live in tax havens.",
"If Djokovic is famous and is an athlete, then Djokovic lives in well paid."
] | [
"∀x (GrandSlamChampion(x) ⊕ OscarNominatedActor(x))",
"∀x (GrandSlamChampion(x) → ProfessionalTennisPlayer(x))",
"∀x (OscarNominatedActor(x) → Celebrity(x))",
"∀x (ProfessionalTennisPlayer(x) → Athlete(x))",
"∀x (Celebrity(x) → WellPaid(x))",
"∀x (Athlete(x) → Famous(x))",
"∀x (WellPaid(x) → LivesInTaxHaven(x))",
"Famous(djokovic) ∧ Athlete(djokovic) → LivesInTaxHaven(djokovic)"
] | Djokovic lives in a tax haven. | LivesInTaxHaven(djokovic) | True |
[
"A person is either a Grand Slam champion or an Oscar-nominated actor.",
"All people who are Grand Slam champions are professional tennis players.",
"All Oscar-nominated actors are celebrities.",
"All professional tennis players are athletes.",
"If a person is a celebrity then they are well paid.",
"If a person is an athlete then they are famous.",
"All well-paid people live in tax havens.",
"If Djokovic is famous and is an athlete, then Djokovic lives in well paid."
] | [
"∀x (GrandSlamChampion(x) ⊕ OscarNominatedActor(x))",
"∀x (GrandSlamChampion(x) → ProfessionalTennisPlayer(x))",
"∀x (OscarNominatedActor(x) → Celebrity(x))",
"∀x (ProfessionalTennisPlayer(x) → Athlete(x))",
"∀x (Celebrity(x) → WellPaid(x))",
"∀x (Athlete(x) → Famous(x))",
"∀x (WellPaid(x) → LivesInTaxHaven(x))",
"Famous(djokovic) ∧ Athlete(djokovic) → LivesInTaxHaven(djokovic)"
] | Djokovic does not live in a tax haven. | ¬LivesInTaxHaven(djokovic) | False |
[
"Diamond Mine is a professional wrestling stable, formed in WWE.",
"Roderick Strong leads Diamond Mine.",
"Diamond Mine includes the Creed Brothers, and Ivy Nile.",
"Imperium has a feud with Diamond Mine."
] | [
"ProfessionalWrestlingStable(diamondmine) ∧ FormedIn(diamondmine, wwe)",
"Leads(roderickstrong, diamondmine)",
"Includes(diamondmine, creedbrothers) ∧ Includes(diamondmine, ivynile)",
"HasFeud(imperium, diamondmine)"
] | Roderick strong leads a professional wrestling stable. | ∃x (Leads(roderickstrong, x) ∧ ProfessionalWrestlingStable(x)) | True |
[
"Diamond Mine is a professional wrestling stable, formed in WWE.",
"Roderick Strong leads Diamond Mine.",
"Diamond Mine includes the Creed Brothers, and Ivy Nile.",
"Imperium has a feud with Diamond Mine."
] | [
"ProfessionalWrestlingStable(diamondmine) ∧ FormedIn(diamondmine, wwe)",
"Leads(roderickstrong, diamondmine)",
"Includes(diamondmine, creedbrothers) ∧ Includes(diamondmine, ivynile)",
"HasFeud(imperium, diamondmine)"
] | Roderick strong leads the Creed Brothers. | Leads(roderickstrong, creedbrothers) | Uncertain |
[
"Diamond Mine is a professional wrestling stable, formed in WWE.",
"Roderick Strong leads Diamond Mine.",
"Diamond Mine includes the Creed Brothers, and Ivy Nile.",
"Imperium has a feud with Diamond Mine."
] | [
"ProfessionalWrestlingStable(diamondmine) ∧ FormedIn(diamondmine, wwe)",
"Leads(roderickstrong, diamondmine)",
"Includes(diamondmine, creedbrothers) ∧ Includes(diamondmine, ivynile)",
"HasFeud(imperium, diamondmine)"
] | Imperium doesn't have a feud with a professional wrestling stable that includes Ivy Nile. | ∀x (ProfessionalWrestlingStable(x) ∧ Includes(x, ivynile) → ¬HasFeud(imperium, x)) | False |
[
"Symphony No. 9 is a music piece.",
"Composers write music pieces.",
"Beethoven wrote Symphony No. 9.",
"Vienna Music Society premiered Symphony No. 9.",
"Vienna Music Society is an orchestra.",
"Beethoven leads the Vienna Music Society.",
"Orchestras are led by conductors."
] | [
"MusicPiece(symphony9)",
"∀x ∀y ((MusicPiece(x) ∧ Writtenby(x, y)) → Composer(y))",
"Writtenby(symphony9, beethoven)",
"Premiered(viennamusicsociety, symphony9)",
"Orchestra(viennamusicsociety)",
"Lead(beethoven, viennamusicsociety)",
"∀x ∀y ((Orchestra(x) ∧ Lead(y, x)) → Conductor(y))"
] | Beethoven is a composer. | Composer(beethoven) | True |
[
"Symphony No. 9 is a music piece.",
"Composers write music pieces.",
"Beethoven wrote Symphony No. 9.",
"Vienna Music Society premiered Symphony No. 9.",
"Vienna Music Society is an orchestra.",
"Beethoven leads the Vienna Music Society.",
"Orchestras are led by conductors."
] | [
"MusicPiece(symphony9)",
"∀x ∀y ((MusicPiece(x) ∧ Writtenby(x, y)) → Composer(y))",
"Writtenby(symphony9, beethoven)",
"Premiered(viennamusicsociety, symphony9)",
"Orchestra(viennamusicsociety)",
"Lead(beethoven, viennamusicsociety)",
"∀x ∀y ((Orchestra(x) ∧ Lead(y, x)) → Conductor(y))"
] | Some orchestras premiered music pieces. | ∃x ∃y (Orchestra(x) ∧ MusicPiece(y) ∧ Premiered(x, y)) | True |
[
"Symphony No. 9 is a music piece.",
"Composers write music pieces.",
"Beethoven wrote Symphony No. 9.",
"Vienna Music Society premiered Symphony No. 9.",
"Vienna Music Society is an orchestra.",
"Beethoven leads the Vienna Music Society.",
"Orchestras are led by conductors."
] | [
"MusicPiece(symphony9)",
"∀x ∀y ((MusicPiece(x) ∧ Writtenby(x, y)) → Composer(y))",
"Writtenby(symphony9, beethoven)",
"Premiered(viennamusicsociety, symphony9)",
"Orchestra(viennamusicsociety)",
"Lead(beethoven, viennamusicsociety)",
"∀x ∀y ((Orchestra(x) ∧ Lead(y, x)) → Conductor(y))"
] | Beethoven is not a conductor. | ¬Conductor(beethoven) | False |
[
"All of Zaha Hadid's design styles are timeless.",
"No mass product design is timeless.",
"Either Zaha Hadid's design style or Kelly Wearstler's design style. ",
"All of Kelly Wearstler's design styles are evocative.",
"All of Kelly Wearstler's design styles are dreamy.",
"If a design by Max is timeless, then a design by Max is a mass product design and evocative."
] | [
"∀x (ZahaHadidDesignStyle(x) → Timeless(x))",
"∀x (MassProductDesign(x) → ¬Timeless(x))",
"∀x (ZahaHadidDesignStyle(x) ∨ KellyWearstlerDesignStyle(x)) ",
"∀x (KellyWearstlerDesignStyle(x) → Evocative(x))",
"∀x (KellyWearstlerDesignStyle(x) → Dreamy(x))",
"Timeless(aDesignByMax) → MassProductDesign(aDesignByMax) ∧ Evocative(aDesignByMax)"
] | A design by Max is a mass product design. | MassProductDesign(aDesignByMax) | Uncertain |
[
"All of Zaha Hadid's design styles are timeless.",
"No mass product design is timeless.",
"Either Zaha Hadid's design style or Kelly Wearstler's design style. ",
"All of Kelly Wearstler's design styles are evocative.",
"All of Kelly Wearstler's design styles are dreamy.",
"If a design by Max is timeless, then a design by Max is a mass product design and evocative."
] | [
"∀x (ZahaHadidDesignStyle(x) → Timeless(x))",
"∀x (MassProductDesign(x) → ¬Timeless(x))",
"∀x (ZahaHadidDesignStyle(x) ∨ KellyWearstlerDesignStyle(x)) ",
"∀x (KellyWearstlerDesignStyle(x) → Evocative(x))",
"∀x (KellyWearstlerDesignStyle(x) → Dreamy(x))",
"Timeless(aDesignByMax) → MassProductDesign(aDesignByMax) ∧ Evocative(aDesignByMax)"
] | A design by Max is evocative and dreamy. | Evocative(aDesignByMax) ∧ Dreamy(aDesignByMax) | True |
[
"All of Zaha Hadid's design styles are timeless.",
"No mass product design is timeless.",
"Either Zaha Hadid's design style or Kelly Wearstler's design style. ",
"All of Kelly Wearstler's design styles are evocative.",
"All of Kelly Wearstler's design styles are dreamy.",
"If a design by Max is timeless, then a design by Max is a mass product design and evocative."
] | [
"∀x (ZahaHadidDesignStyle(x) → Timeless(x))",
"∀x (MassProductDesign(x) → ¬Timeless(x))",
"∀x (ZahaHadidDesignStyle(x) ∨ KellyWearstlerDesignStyle(x)) ",
"∀x (KellyWearstlerDesignStyle(x) → Evocative(x))",
"∀x (KellyWearstlerDesignStyle(x) → Dreamy(x))",
"Timeless(aDesignByMax) → MassProductDesign(aDesignByMax) ∧ Evocative(aDesignByMax)"
] | A design by Max is either evocative or dreamy. | Evocative(aDesignByMax) ⊕ Dreamy(aDesignByMax) | False |
[
"If a player is ranked highly by the Women's Tennis Association, then they are among the most active players in major tennis. ",
"Everyone who lost to Iga Świątek is ranked highly by the Women's Tennis Association.",
"All female tennis players at Roland Garros 2022 lost to Iga Świątek.",
"Either female tennis players at Roland Garros 2022 or male tennis players at Roland Garros 2022. ",
"All male tennis players at Roland Garros 2022 lost to Rafael Nadal.",
"If Coco Gauff is a player who is ranked highly by the Women's Tennis Association or a player who lost to Rafael Nadal, then Coco Gauff is not a male tennis player at Roland Garros 2022."
] | [
"∀x (RankedHighlyByWomenTennisAssociation(x) → AmongMostActivePlayersInMajorTennis(x))",
"∀x (LostToIgaŚwiątek(x) → RankedHighlyByWomenTennisAssociation(x))",
"∀x (FemaleTennisPlayersAtRolandGarros2022(x) → LostToIgaŚwiątek(x)) ",
"∀x (FemaleTennisPlayersAtRolandGarros2022(x) ∨ MaleTennisPlayersAtRolandGarros2022(x)) ",
"∀x (MaleTennisPlayersAtRolandGarros2022(x) → LostToRafaelNadal(x))",
"RankedHighlyByWomenTennisAssociation(cocoGauff) ∨ LostToRafaelNadal(cocoGauff) → ¬MaleTennisPlayersAtRolandGarros2022(cocoGauff)"
] | Coco Gauff is among the most active players in major tennis. | AmongMostActivePlayersInMajorTennis(cocoGauff) | True |
[
"If a player is ranked highly by the Women's Tennis Association, then they are among the most active players in major tennis. ",
"Everyone who lost to Iga Świątek is ranked highly by the Women's Tennis Association.",
"All female tennis players at Roland Garros 2022 lost to Iga Świątek.",
"Either female tennis players at Roland Garros 2022 or male tennis players at Roland Garros 2022. ",
"All male tennis players at Roland Garros 2022 lost to Rafael Nadal.",
"If Coco Gauff is a player who is ranked highly by the Women's Tennis Association or a player who lost to Rafael Nadal, then Coco Gauff is not a male tennis player at Roland Garros 2022."
] | [
"∀x (RankedHighlyByWomenTennisAssociation(x) → AmongMostActivePlayersInMajorTennis(x))",
"∀x (LostToIgaŚwiątek(x) → RankedHighlyByWomenTennisAssociation(x))",
"∀x (FemaleTennisPlayersAtRolandGarros2022(x) → LostToIgaŚwiątek(x)) ",
"∀x (FemaleTennisPlayersAtRolandGarros2022(x) ∨ MaleTennisPlayersAtRolandGarros2022(x)) ",
"∀x (MaleTennisPlayersAtRolandGarros2022(x) → LostToRafaelNadal(x))",
"RankedHighlyByWomenTennisAssociation(cocoGauff) ∨ LostToRafaelNadal(cocoGauff) → ¬MaleTennisPlayersAtRolandGarros2022(cocoGauff)"
] | Coco Gauff has lost to Rafael Nadal. | LostToRafaelNadal(cocoGauff) | Uncertain |
[
"If a player is ranked highly by the Women's Tennis Association, then they are among the most active players in major tennis. ",
"Everyone who lost to Iga Świątek is ranked highly by the Women's Tennis Association.",
"All female tennis players at Roland Garros 2022 lost to Iga Świątek.",
"Either female tennis players at Roland Garros 2022 or male tennis players at Roland Garros 2022. ",
"All male tennis players at Roland Garros 2022 lost to Rafael Nadal.",
"If Coco Gauff is a player who is ranked highly by the Women's Tennis Association or a player who lost to Rafael Nadal, then Coco Gauff is not a male tennis player at Roland Garros 2022."
] | [
"∀x (RankedHighlyByWomenTennisAssociation(x) → AmongMostActivePlayersInMajorTennis(x))",
"∀x (LostToIgaŚwiątek(x) → RankedHighlyByWomenTennisAssociation(x))",
"∀x (FemaleTennisPlayersAtRolandGarros2022(x) → LostToIgaŚwiątek(x)) ",
"∀x (FemaleTennisPlayersAtRolandGarros2022(x) ∨ MaleTennisPlayersAtRolandGarros2022(x)) ",
"∀x (MaleTennisPlayersAtRolandGarros2022(x) → LostToRafaelNadal(x))",
"RankedHighlyByWomenTennisAssociation(cocoGauff) ∨ LostToRafaelNadal(cocoGauff) → ¬MaleTennisPlayersAtRolandGarros2022(cocoGauff)"
] | Coco Gauff is not a player who lost to Iga Świątek or one of the most active players in major tennis. | ¬LostToIgaŚwiątek(cocoGauff) ∨ ¬AmongMostActivePlayersInMajorTennis(cocoGauff) | False |
[
"All cats are mammals.",
"Some pets are not mammals."
] | [
"∀x (Cat(x) → Mammal(x))",
"∃x (Pet(x) ∧ ¬Mammal(x))"
] | No pets are cats. | ∀x (Pet(x) → ¬Cat(x)) | Uncertain |
[
"[BG] There are four seasons in a year: Spring, Summer, Fall, and Winter.",
"All students who want to have a long vacation love summer the most.",
"Emma's favorite season is summer.",
"Mia's favorite season is not the same as Emma's. ",
"James wants to have a long vacation."
] | [
"Season(spring) ∨ Season(summer) ∨ Season(fall) ∨ Season(winter)",
"∀x (WantlongVacation(x) → Love(x, summer))",
"Love(emma, summer)",
"¬Love(mia, emma)",
"WantlongVacation(james)"
] | James's favorite season is summer. | Love(james, summer) | True |
[
"[BG] There are four seasons in a year: Spring, Summer, Fall, and Winter.",
"All students who want to have a long vacation love summer the most.",
"Emma's favorite season is summer.",
"Mia's favorite season is not the same as Emma's. ",
"James wants to have a long vacation."
] | [
"Season(spring) ∨ Season(summer) ∨ Season(fall) ∨ Season(winter)",
"∀x (WantlongVacation(x) → Love(x, summer))",
"Love(emma, summer)",
"¬Love(mia, emma)",
"WantlongVacation(james)"
] | James's favorite season is fall. | Love(james, fall) | False |
[
"[BG] There are four seasons in a year: Spring, Summer, Fall, and Winter.",
"All students who want to have a long vacation love summer the most.",
"Emma's favorite season is summer.",
"Mia's favorite season is not the same as Emma's. ",
"James wants to have a long vacation."
] | [
"Season(spring) ∨ Season(summer) ∨ Season(fall) ∨ Season(winter)",
"∀x (WantlongVacation(x) → Love(x, summer))",
"Love(emma, summer)",
"¬Love(mia, emma)",
"WantlongVacation(james)"
] | Mia's favorite season is spring. | Love(mia, spring) | Uncertain |
[
"No digital media are analog.",
"Every printed text is analog.",
"All streaming services are digital.",
"If an object is a hardcover book then it is printed text.",
"If 1984 is a streaming service, then 1984 is a hardcover book."
] | [
"∀x (Digital(x) → ¬Analog(x))",
"∀x (PrintedText(x) → Analog(x))",
"∀x (StreamingService(x) → Digital(x))",
"∀x (HardcoverBook(x) → PrintedText(x))",
"StreamingService(y1984) → HardcoverBook(y1984)"
] | 1984 is printed text. | PrintedText(y1984) | Uncertain |
[
"No digital media are analog.",
"Every printed text is analog.",
"All streaming services are digital.",
"If an object is a hardcover book then it is printed text.",
"If 1984 is a streaming service, then 1984 is a hardcover book."
] | [
"∀x (Digital(x) → ¬Analog(x))",
"∀x (PrintedText(x) → Analog(x))",
"∀x (StreamingService(x) → Digital(x))",
"∀x (HardcoverBook(x) → PrintedText(x))",
"StreamingService(y1984) → HardcoverBook(y1984)"
] | 1984 is a streaming service. | StreamingService(y1984) | False |
[
"No digital media are analog.",
"Every printed text is analog.",
"All streaming services are digital.",
"If an object is a hardcover book then it is printed text.",
"If 1984 is a streaming service, then 1984 is a hardcover book."
] | [
"∀x (Digital(x) → ¬Analog(x))",
"∀x (PrintedText(x) → Analog(x))",
"∀x (StreamingService(x) → Digital(x))",
"∀x (HardcoverBook(x) → PrintedText(x))",
"StreamingService(y1984) → HardcoverBook(y1984)"
] | 1984 is not a streaming service. | ¬StreamingService(y1984) | True |
[
"All Romance languages are Indo-European languages.",
"The Romance languages are a language family.",
"All languages within a language family are related to each other.",
"French and Spanish are both Romance languages.",
"German is related to Spanish.",
"Basque is not related to any other language."
] | [
"∀x (RomanceLanguage(x) → IndoEuropeanLanguage(x))",
"∀x (RomanceLanguage(x) → MemberOf(x, romancefamily))",
"∀x ∀y ∀z ((MemberOf(x, z) ∧ MemberOf(y, z)) → (Related(x, y) ∧ Related(y, x)))",
"RomanceLanguage(french) ∧ RomanceLanguage(spanish)",
"Related(german, spanish)",
"∀x (¬Related(basque, x))"
] | Basque is a Romance language. | RomanceLanguage(basque) | False |
[
"All Romance languages are Indo-European languages.",
"The Romance languages are a language family.",
"All languages within a language family are related to each other.",
"French and Spanish are both Romance languages.",
"German is related to Spanish.",
"Basque is not related to any other language."
] | [
"∀x (RomanceLanguage(x) → IndoEuropeanLanguage(x))",
"∀x (RomanceLanguage(x) → MemberOf(x, romancefamily))",
"∀x ∀y ∀z ((MemberOf(x, z) ∧ MemberOf(y, z)) → (Related(x, y) ∧ Related(y, x)))",
"RomanceLanguage(french) ∧ RomanceLanguage(spanish)",
"Related(german, spanish)",
"∀x (¬Related(basque, x))"
] | German is a Romance language. | RomanceLanguage(german) | Uncertain |
[
"All Romance languages are Indo-European languages.",
"The Romance languages are a language family.",
"All languages within a language family are related to each other.",
"French and Spanish are both Romance languages.",
"German is related to Spanish.",
"Basque is not related to any other language."
] | [
"∀x (RomanceLanguage(x) → IndoEuropeanLanguage(x))",
"∀x (RomanceLanguage(x) → MemberOf(x, romancefamily))",
"∀x ∀y ∀z ((MemberOf(x, z) ∧ MemberOf(y, z)) → (Related(x, y) ∧ Related(y, x)))",
"RomanceLanguage(french) ∧ RomanceLanguage(spanish)",
"Related(german, spanish)",
"∀x (¬Related(basque, x))"
] | French is an Indo-European language. | IndoEuropeanLanguage(french) | True |
[
"Robert Lewandowski is a striker.",
"[BG] Strikers are soccer players.",
"Robert Lewandowski left Bayern Munchen.",
"[BG] If a player left a team they no longer play for that team."
] | [
"IsStriker(robertLewandowski)",
"∀x (IsStriker(x) → IsSoccerPlayer(x))",
"LeftTeam(robertLewandowski, bayernMunchen)",
"∀x ∀y (LeftTeam(x, y) → ¬PlaysForTeam(x, y))"
] | Robert Lewandowski is a soccer player. | IsSoccerPlayer(robertLewandowski) | True |
[
"Robert Lewandowski is a striker.",
"[BG] Strikers are soccer players.",
"Robert Lewandowski left Bayern Munchen.",
"[BG] If a player left a team they no longer play for that team."
] | [
"IsStriker(robertLewandowski)",
"∀x (IsStriker(x) → IsSoccerPlayer(x))",
"LeftTeam(robertLewandowski, bayernMunchen)",
"∀x ∀y (LeftTeam(x, y) → ¬PlaysForTeam(x, y))"
] | Robert Lewandowski plays for Bayern Munchen. | PlaysForTeam(robertLewandowski, bayernMunchen) | False |
[
"Robert Lewandowski is a striker.",
"[BG] Strikers are soccer players.",
"Robert Lewandowski left Bayern Munchen.",
"[BG] If a player left a team they no longer play for that team."
] | [
"IsStriker(robertLewandowski)",
"∀x (IsStriker(x) → IsSoccerPlayer(x))",
"LeftTeam(robertLewandowski, bayernMunchen)",
"∀x ∀y (LeftTeam(x, y) → ¬PlaysForTeam(x, y))"
] | Robert Lewandowski is a star. | IsSoccerStar(robertLewandowski) | Uncertain |
[
"Billings is a city in Montana.",
"Montana includes the cities of Butte, Helena, and Missoula.",
"White Sulphur Springs and Butte are cities in the same state.",
"The city of Pierre is not in Montana.",
"Any city in Butte is not in Pierre."
] | [
"CityIn(billings, montana)",
"CityIn(butte, montana) ∧ CityIn(helena, montana) ∧ CityIn(missoula, montana)",
"∃x (CityIn(whitesulphursprings, x) ∧ CityIn(butte, x))",
"¬CityIn(pierre, montana)",
"∀x (CityIn(butte, x) → ¬CityIn(pierre, x))"
] | Butte and Pierre are in the same state. | ∃x (CityIn(butte, x) ∧ CityIn(pierre, x)) | False |
[
"Billings is a city in Montana.",
"Montana includes the cities of Butte, Helena, and Missoula.",
"White Sulphur Springs and Butte are cities in the same state.",
"The city of Pierre is not in Montana.",
"Any city in Butte is not in Pierre."
] | [
"CityIn(billings, montana)",
"CityIn(butte, montana) ∧ CityIn(helena, montana) ∧ CityIn(missoula, montana)",
"∃x (CityIn(whitesulphursprings, x) ∧ CityIn(butte, x))",
"¬CityIn(pierre, montana)",
"∀x (CityIn(butte, x) → ¬CityIn(pierre, x))"
] | Pierre and Bismarck are in the same state. | ∃x (CityIn(pierre, x) ∧ CityIn(bismarck, x)) | Uncertain |
[
"Billings is a city in Montana.",
"Montana includes the cities of Butte, Helena, and Missoula.",
"White Sulphur Springs and Butte are cities in the same state.",
"The city of Pierre is not in Montana.",
"Any city in Butte is not in Pierre."
] | [
"CityIn(billings, montana)",
"CityIn(butte, montana) ∧ CityIn(helena, montana) ∧ CityIn(missoula, montana)",
"∃x (CityIn(whitesulphursprings, x) ∧ CityIn(butte, x))",
"¬CityIn(pierre, montana)",
"∀x (CityIn(butte, x) → ¬CityIn(pierre, x))"
] | Montana is home to the city of Missoula. | CityIn(missoula, montana) | True |
[
"International students in US have either an F1 visa or a J1 visa.",
"An international student in US with an F1 visa needs to apply for CPT or OPT if the student wants to work in the US.",
"Mike is an international student.",
"Mike needs to apply for CPT if he wants to work in the US."
] | [
"∀x (InternationalStudent(x) → F1(x) ⊕ J1(x))",
"∀x (InternationalStudent(x) ∧ F1(x) ∧ WantWorkInUS(x) → Apply(x, cpt) ∨ Apply(x, opt))",
"InternationalStudent(mike)",
"WantWorkInUS(mike) → Apply(mike, cpt)"
] | Mike has an F1 visa. | F1(mike) | Uncertain |
[
"International students in US have either an F1 visa or a J1 visa.",
"An international student in US with an F1 visa needs to apply for CPT or OPT if the student wants to work in the US.",
"Mike is an international student.",
"Mike needs to apply for CPT if he wants to work in the US."
] | [
"∀x (InternationalStudent(x) → F1(x) ⊕ J1(x))",
"∀x (InternationalStudent(x) ∧ F1(x) ∧ WantWorkInUS(x) → Apply(x, cpt) ∨ Apply(x, opt))",
"InternationalStudent(mike)",
"WantWorkInUS(mike) → Apply(mike, cpt)"
] | Mike has a J1 visa. | J1(mike) | Uncertain |
[
"All cows are bovines.",
"Some pets are cows.",
"If something is a bovine, then it is domesticated.",
"No domesticated animals are alligators.",
"Ted is an aligator."
] | [
"∀x (Cow(x) → Bovine(x))",
"∃x (Pet(x) ∧ Cow(x))",
"∀x (Bovine(x) → Domesticated(x))",
"∀x (Domesticated(x) → ¬Aligator(x))",
"Aligator(ted)"
] | Ted is a pet. | Pet(ted) | Uncertain |
[
"All cows are bovines.",
"Some pets are cows.",
"If something is a bovine, then it is domesticated.",
"No domesticated animals are alligators.",
"Ted is an aligator."
] | [
"∀x (Cow(x) → Bovine(x))",
"∃x (Pet(x) ∧ Cow(x))",
"∀x (Bovine(x) → Domesticated(x))",
"∀x (Domesticated(x) → ¬Aligator(x))",
"Aligator(ted)"
] | Ted is a pet and a cow. | Pet(ted) ∧ Cow(ted) | False |
[
"All cows are bovines.",
"Some pets are cows.",
"If something is a bovine, then it is domesticated.",
"No domesticated animals are alligators.",
"Ted is an aligator."
] | [
"∀x (Cow(x) → Bovine(x))",
"∃x (Pet(x) ∧ Cow(x))",
"∀x (Bovine(x) → Domesticated(x))",
"∀x (Domesticated(x) → ¬Aligator(x))",
"Aligator(ted)"
] | If Ted is a cow, then Ted is not a pet. | Cow(ted) → ¬Pet(ted) | True |
[
"Yale University is a private Ivy League research university.",
"Yale University moved to New Haven in 1716.",
"Yale university's endowment was valued at $42.3 billion.",
"Yale University has been organized into 27 constituent colleges and schools: the residential colleges, the Yale Graduate School of Arts and Sciences, and twelve professional schools.",
"A list of residential colleges at Yale: Benjamin Franklin College, Berkeley College, Branford College, Davenport College, Ezra Stiles College, Grace Hopper College, Jonathan Edwards College, Morse College, Pauli Murray College, Pierson College, Saybrook College, Silliman College, Timothy Dwight College, and Trumbull College."
] | [
"PrivateIvyLeagueResearchUniversity(yale)",
"MovedTo(yale, newhaven) ∧ MovedIn(yale, y1716)",
"ValuedAt(yalesendowment, y42.3billion)",
"∃x (OrganizedInto(yale, x) ∧ ConstituentCollegesandSchools(x) ∧ ((ResidentialCollege(x) ⊕ GraduateSchool(x)) ⊕ ProfessionalSchool(x)))",
"ResidentialCollege(benjaminfranklincollege) ∧ AtYale(benjaminfranklincollege) ∧ ResidentialCollege(berkeleycollege) ∧ AtYale(berkeleycollege) ∧ ResidentialCollege(branfordcollege) ∧ AtYale(branfordcollege) ∧ ResidentialCollege(davenportcollege) ∧ AtYale(davenportcollege) ∧ ResidentialCollege(ezrastilescollege) ∧ AtYale(ezrastilescollege) ∧ ResidentialCollege(gracehoppercollege) ∧ AtYale(gracehoppercollege) ∧ ResidentialCollege(jonathanedwardscollege) ∧ AtYale(jonathanedwardscollege) ∧ ResidentialCollege(morsecollege) ∧ AtYale(morsecollege) ∧ ResidentialCollege(paulimurraycollege) ∧ AtYale(paulimurraycollege) ∧ ResidentialCollege(piersoncollege) ∧ AtYale(piersoncollege) ∧ ResidentialCollege(saybrookcollege) ∧ AtYale(saybrookcollege) ∧ ResidentialCollege(sillimancollege) ∧ AtYale(sillimancollege) ∧ ResidentialCollege(timothydwightcollege) ∧ AtYale(timothydwightcollege) ∧ ResidentialCollege(trumbullcollege) ∧ AtYale(trumbullcollege)"
] | A private Ivy League research university moved to New Haven. | ∃x (PrivateIvyLeagueResearchUniversity(x) ∧ MovedTo(x, newhaven)) | True |
[
"Yale University is a private Ivy League research university.",
"Yale University moved to New Haven in 1716.",
"Yale university's endowment was valued at $42.3 billion.",
"Yale University has been organized into 27 constituent colleges and schools: the residential colleges, the Yale Graduate School of Arts and Sciences, and twelve professional schools.",
"A list of residential colleges at Yale: Benjamin Franklin College, Berkeley College, Branford College, Davenport College, Ezra Stiles College, Grace Hopper College, Jonathan Edwards College, Morse College, Pauli Murray College, Pierson College, Saybrook College, Silliman College, Timothy Dwight College, and Trumbull College."
] | [
"PrivateIvyLeagueResearchUniversity(yale)",
"MovedTo(yale, newhaven) ∧ MovedIn(yale, y1716)",
"ValuedAt(yalesendowment, y42.3billion)",
"∃x (OrganizedInto(yale, x) ∧ ConstituentCollegesandSchools(x) ∧ ((ResidentialCollege(x) ⊕ GraduateSchool(x)) ⊕ ProfessionalSchool(x)))",
"ResidentialCollege(benjaminfranklincollege) ∧ AtYale(benjaminfranklincollege) ∧ ResidentialCollege(berkeleycollege) ∧ AtYale(berkeleycollege) ∧ ResidentialCollege(branfordcollege) ∧ AtYale(branfordcollege) ∧ ResidentialCollege(davenportcollege) ∧ AtYale(davenportcollege) ∧ ResidentialCollege(ezrastilescollege) ∧ AtYale(ezrastilescollege) ∧ ResidentialCollege(gracehoppercollege) ∧ AtYale(gracehoppercollege) ∧ ResidentialCollege(jonathanedwardscollege) ∧ AtYale(jonathanedwardscollege) ∧ ResidentialCollege(morsecollege) ∧ AtYale(morsecollege) ∧ ResidentialCollege(paulimurraycollege) ∧ AtYale(paulimurraycollege) ∧ ResidentialCollege(piersoncollege) ∧ AtYale(piersoncollege) ∧ ResidentialCollege(saybrookcollege) ∧ AtYale(saybrookcollege) ∧ ResidentialCollege(sillimancollege) ∧ AtYale(sillimancollege) ∧ ResidentialCollege(timothydwightcollege) ∧ AtYale(timothydwightcollege) ∧ ResidentialCollege(trumbullcollege) ∧ AtYale(trumbullcollege)"
] | Yale University has the largest university endowment of any educational institution. | LargestUniversityEndowmentOf(yale, anyeducationalinstitution) | Uncertain |
[
"Yale University is a private Ivy League research university.",
"Yale University moved to New Haven in 1716.",
"Yale university's endowment was valued at $42.3 billion.",
"Yale University has been organized into 27 constituent colleges and schools: the residential colleges, the Yale Graduate School of Arts and Sciences, and twelve professional schools.",
"A list of residential colleges at Yale: Benjamin Franklin College, Berkeley College, Branford College, Davenport College, Ezra Stiles College, Grace Hopper College, Jonathan Edwards College, Morse College, Pauli Murray College, Pierson College, Saybrook College, Silliman College, Timothy Dwight College, and Trumbull College."
] | [
"PrivateIvyLeagueResearchUniversity(yale)",
"MovedTo(yale, newhaven) ∧ MovedIn(yale, y1716)",
"ValuedAt(yalesendowment, y42.3billion)",
"∃x (OrganizedInto(yale, x) ∧ ConstituentCollegesandSchools(x) ∧ ((ResidentialCollege(x) ⊕ GraduateSchool(x)) ⊕ ProfessionalSchool(x)))",
"ResidentialCollege(benjaminfranklincollege) ∧ AtYale(benjaminfranklincollege) ∧ ResidentialCollege(berkeleycollege) ∧ AtYale(berkeleycollege) ∧ ResidentialCollege(branfordcollege) ∧ AtYale(branfordcollege) ∧ ResidentialCollege(davenportcollege) ∧ AtYale(davenportcollege) ∧ ResidentialCollege(ezrastilescollege) ∧ AtYale(ezrastilescollege) ∧ ResidentialCollege(gracehoppercollege) ∧ AtYale(gracehoppercollege) ∧ ResidentialCollege(jonathanedwardscollege) ∧ AtYale(jonathanedwardscollege) ∧ ResidentialCollege(morsecollege) ∧ AtYale(morsecollege) ∧ ResidentialCollege(paulimurraycollege) ∧ AtYale(paulimurraycollege) ∧ ResidentialCollege(piersoncollege) ∧ AtYale(piersoncollege) ∧ ResidentialCollege(saybrookcollege) ∧ AtYale(saybrookcollege) ∧ ResidentialCollege(sillimancollege) ∧ AtYale(sillimancollege) ∧ ResidentialCollege(timothydwightcollege) ∧ AtYale(timothydwightcollege) ∧ ResidentialCollege(trumbullcollege) ∧ AtYale(trumbullcollege)"
] | Pierson College is a residential college at Yale. | ResidentialCollege(piersoncollege) ∧ AtYale(piersoncollege) | True |
[
"Badults is a British Sitcom series, starring members of Pappy's.",
"Badults piloted in July 2013 on BBC Three.",
"The Working title \"The Secret Dude Society\" was used for Badults.",
"Andrew Collins was the script editor for Badults"
] | [
"∃x (MemberOf(x, pappys) ∧ BritishSitcom(badults) ∧ Series(badults) ∧ Starring(badults, x))",
"PilotedIn(badults, july2013) ∧ PilotedOn(badults, bbcthree)",
"WorkingTitle(thesecretdudesociety, badults)",
"ScriptEditor(andrewcollins) ∧ ScriptEditorFor(andrewcollins, badults)"
] | Andrew Collins was the script editor for a series with the working title "The Secret Dude Society". | ∃x (ScriptEditorFor(andrewcollins, x) ∧ Series(x) ∧ WorkingTitle(thesecretdudesociety, x)) | True |
[
"Badults is a British Sitcom series, starring members of Pappy's.",
"Badults piloted in July 2013 on BBC Three.",
"The Working title \"The Secret Dude Society\" was used for Badults.",
"Andrew Collins was the script editor for Badults"
] | [
"∃x (MemberOf(x, pappys) ∧ BritishSitcom(badults) ∧ Series(badults) ∧ Starring(badults, x))",
"PilotedIn(badults, july2013) ∧ PilotedOn(badults, bbcthree)",
"WorkingTitle(thesecretdudesociety, badults)",
"ScriptEditor(andrewcollins) ∧ ScriptEditorFor(andrewcollins, badults)"
] | No members of Pappy's have starred for a show piloting on BBC Two or BBC Three. | ∀x ∀y (MemberOf(x, pappys) ∧ Starring(y, x) → ¬(PilotedOn(y, bbctwo) ∨ PilotedOn(y, bbcthree))) | False |
[
"All growth companies’ stocks are volatile.",
"If the stock price is volatile, then it is not suitable for a retirement fund.",
"Some companies’ stocks are growth companies’ stocks.",
"All mature companies’ stocks are suitable for a retirement fund.",
"KO is a mature company’s stock."
] | [
"∀x (GrowthCompanies’Stocks(x) → PriceVolatile(x))",
" ∀x (PriceVolatile(x) → ¬SuitableForRetirementRund(x)) ",
" ∃x (Companies’Stocks(x) ∧ GrowthCompanies’Stocks(x))",
" ∀x (MatureCompanies’Stocks(x) → SuitableForRetirementRund(x))",
" MatureCompanies’Stocks(kO)"
] | KO is a company stock. | Companies’Stocks(kO) | Uncertain |
[
"All growth companies’ stocks are volatile.",
"If the stock price is volatile, then it is not suitable for a retirement fund.",
"Some companies’ stocks are growth companies’ stocks.",
"All mature companies’ stocks are suitable for a retirement fund.",
"KO is a mature company’s stock."
] | [
"∀x (GrowthCompanies’Stocks(x) → PriceVolatile(x))",
" ∀x (PriceVolatile(x) → ¬SuitableForRetirementRund(x)) ",
" ∃x (Companies’Stocks(x) ∧ GrowthCompanies’Stocks(x))",
" ∀x (MatureCompanies’Stocks(x) → SuitableForRetirementRund(x))",
" MatureCompanies’Stocks(kO)"
] | KO is a company stock and a growth company’s stock. | Companies’Stocks(kO) ∧ GrowthCompanies’Stocks(kO) | False |
[
"All growth companies’ stocks are volatile.",
"If the stock price is volatile, then it is not suitable for a retirement fund.",
"Some companies’ stocks are growth companies’ stocks.",
"All mature companies’ stocks are suitable for a retirement fund.",
"KO is a mature company’s stock."
] | [
"∀x (GrowthCompanies’Stocks(x) → PriceVolatile(x))",
" ∀x (PriceVolatile(x) → ¬SuitableForRetirementRund(x)) ",
" ∃x (Companies’Stocks(x) ∧ GrowthCompanies’Stocks(x))",
" ∀x (MatureCompanies’Stocks(x) → SuitableForRetirementRund(x))",
" MatureCompanies’Stocks(kO)"
] | If KO is a growth company’s stock or if its price is volatile, then KO is neither a company’s stock nor is its price volatile. | GrowthCompanies’Stocks(kO) ∨ PriceVolatile(kO) → ¬Companies’Stocks(kO) ∨ ¬PriceVolatile(kO) | True |
[
"All vehicle registration plates in Istanbul begin with the number 34.",
"Plates that do not begin with the number 34 are not from Istanbul. ",
"Joe's vehicle registration plate is from Istanbul. ",
"Tom's license plate begins with the number 35. ",
"[BG] If a license plate begins with the number 35, then it does not begin with the number 34."
] | [
"∀x (Vehicleregistrationplate(x, istanbul) → Beginwith(x, number34))",
"∀x (¬Beginwith(x, number34) → ¬FromIstanbul(x))",
"Vehicleregistrationplate(joe, istanbul)",
"Beginwith(tom, number35)",
"∀x (Beginwith(x, number35) → ¬Beginwith(x, number34))"
] | Joe's license plate begins with the number 34. | Beginwith(joe, number34) | True |
[
"All vehicle registration plates in Istanbul begin with the number 34.",
"Plates that do not begin with the number 34 are not from Istanbul. ",
"Joe's vehicle registration plate is from Istanbul. ",
"Tom's license plate begins with the number 35. ",
"[BG] If a license plate begins with the number 35, then it does not begin with the number 34."
] | [
"∀x (Vehicleregistrationplate(x, istanbul) → Beginwith(x, number34))",
"∀x (¬Beginwith(x, number34) → ¬FromIstanbul(x))",
"Vehicleregistrationplate(joe, istanbul)",
"Beginwith(tom, number35)",
"∀x (Beginwith(x, number35) → ¬Beginwith(x, number34))"
] | Tom's license plate is from Istanbul. | Vehicleregistrationplate(tom, istanbul) | False |
[
"If people work in student jobs on campus, then they need to earn money to help pay for their college tuition.",
"If people order takeout frequently in college, then they work in student jobs on campus.",
"People either order takeout frequently in college or enjoy the dining hall meals and recipes.",
"If people enjoy the dining hall meals and recipes, then they are not picky eaters.",
"If people enjoy the dining hall meals and recipes, then they spend a lot of their time eating and catching up with friends in the campus dining halls.",
"If Mary works in student jobs on campus and needs to earn money to help pay for her college tuition, then Mary is neither picky nor needs to earn money to help pay for her college tuition."
] | [
"∀x (StudentJobs(x) → Tuition(x))",
"∀x (Takeout(x) → StudentJobs(x))",
"∀x (Takeout(x) ∨ DiningHall(x))",
"∀x (DiningHall(x) → NotPicky(x))",
"∀x (DiningHall(x) → Eating(x))",
"StudentJobs(mary) ∧ Tuition(mary) → ¬(NotPicky(mary) ∨ Tuition(mary))"
] | Mary needs to earn money to help pay for her college tuition. | Tuition(mary) | Uncertain |
[
"If people work in student jobs on campus, then they need to earn money to help pay for their college tuition.",
"If people order takeout frequently in college, then they work in student jobs on campus.",
"People either order takeout frequently in college or enjoy the dining hall meals and recipes.",
"If people enjoy the dining hall meals and recipes, then they are not picky eaters.",
"If people enjoy the dining hall meals and recipes, then they spend a lot of their time eating and catching up with friends in the campus dining halls.",
"If Mary works in student jobs on campus and needs to earn money to help pay for her college tuition, then Mary is neither picky nor needs to earn money to help pay for her college tuition."
] | [
"∀x (StudentJobs(x) → Tuition(x))",
"∀x (Takeout(x) → StudentJobs(x))",
"∀x (Takeout(x) ∨ DiningHall(x))",
"∀x (DiningHall(x) → NotPicky(x))",
"∀x (DiningHall(x) → Eating(x))",
"StudentJobs(mary) ∧ Tuition(mary) → ¬(NotPicky(mary) ∨ Tuition(mary))"
] | Mary is not a picky eater and spends a lot of her time eating and catching up with friends in the campus dining halls. | NotPicky(mary) ∧ Eating(mary) | True |
[
"If people work in student jobs on campus, then they need to earn money to help pay for their college tuition.",
"If people order takeout frequently in college, then they work in student jobs on campus.",
"People either order takeout frequently in college or enjoy the dining hall meals and recipes.",
"If people enjoy the dining hall meals and recipes, then they are not picky eaters.",
"If people enjoy the dining hall meals and recipes, then they spend a lot of their time eating and catching up with friends in the campus dining halls.",
"If Mary works in student jobs on campus and needs to earn money to help pay for her college tuition, then Mary is neither picky nor needs to earn money to help pay for her college tuition."
] | [
"∀x (StudentJobs(x) → Tuition(x))",
"∀x (Takeout(x) → StudentJobs(x))",
"∀x (Takeout(x) ∨ DiningHall(x))",
"∀x (DiningHall(x) → NotPicky(x))",
"∀x (DiningHall(x) → Eating(x))",
"StudentJobs(mary) ∧ Tuition(mary) → ¬(NotPicky(mary) ∨ Tuition(mary))"
] | Mary either is not a picky eater or, if she is, then she spends a lot of her time eating and catching up with friends in the campus dining halls. | NotPicky(mary) ⊕ Eating(mary) | False |
[
"No bakery is spicy.",
"All cupcakes are bakeries.",
"All hotpots are spicy.",
"All products of Baked by Melissa are cupcakes.",
"If dried Thai chilies are spicy or a bakery, then dried Thai chilies are a hotpot or are spicy."
] | [
"∀x (Bakery(x) → ¬Spicy(x))",
"∀x (Cupcakes(x) → Bakery(x))",
"∀x (Hotpot(x) → Spicy(x))",
"∀x (ProductsOfBakedByMelissa(x) → Cupcakes(x))",
"Spicy(driedThaiChilies) ∨ Bakery(driedThaiChilies) → Hotpot(driedThaiChilies) ∨ Spicy(driedThaiChilies)"
] | Dried Thai chilies are a product of Baked by Melissa. | ProductsOfBakedByMelissa(driedThaiChilies) | False |
[
"No bakery is spicy.",
"All cupcakes are bakeries.",
"All hotpots are spicy.",
"All products of Baked by Melissa are cupcakes.",
"If dried Thai chilies are spicy or a bakery, then dried Thai chilies are a hotpot or are spicy."
] | [
"∀x (Bakery(x) → ¬Spicy(x))",
"∀x (Cupcakes(x) → Bakery(x))",
"∀x (Hotpot(x) → Spicy(x))",
"∀x (ProductsOfBakedByMelissa(x) → Cupcakes(x))",
"Spicy(driedThaiChilies) ∨ Bakery(driedThaiChilies) → Hotpot(driedThaiChilies) ∨ Spicy(driedThaiChilies)"
] | Dried Thai chilies are not a product of Baked by Melissa. | ¬ProductsOfBakedByMelissa(driedThaiChilies) | True |
[
"No bakery is spicy.",
"All cupcakes are bakeries.",
"All hotpots are spicy.",
"All products of Baked by Melissa are cupcakes.",
"If dried Thai chilies are spicy or a bakery, then dried Thai chilies are a hotpot or are spicy."
] | [
"∀x (Bakery(x) → ¬Spicy(x))",
"∀x (Cupcakes(x) → Bakery(x))",
"∀x (Hotpot(x) → Spicy(x))",
"∀x (ProductsOfBakedByMelissa(x) → Cupcakes(x))",
"Spicy(driedThaiChilies) ∨ Bakery(driedThaiChilies) → Hotpot(driedThaiChilies) ∨ Spicy(driedThaiChilies)"
] | Dried Thai chilies are a hotpot. | Hotpot(driedThaiChilies) | Uncertain |
[
"No bakery is spicy.",
"All cupcakes are bakeries.",
"All hotpots are spicy.",
"All products of Baked by Melissa are cupcakes.",
"If dried Thai chilies are spicy or a bakery, then dried Thai chilies are a hotpot or are spicy."
] | [
"∀x (Bakery(x) → ¬Spicy(x))",
"∀x (Cupcakes(x) → Bakery(x))",
"∀x (Hotpot(x) → Spicy(x))",
"∀x (ProductsOfBakedByMelissa(x) → Cupcakes(x))",
"Spicy(driedThaiChilies) ∨ Bakery(driedThaiChilies) → Hotpot(driedThaiChilies) ∨ Spicy(driedThaiChilies)"
] | Dried Thai chilies are neither a product of Baked by Melissa nor a bakery. | ¬ProductsOfBakedByMelissa(driedThaiChilies) ∧ ¬Bakery(driedThaiChilies) | True |
[
"No bakery is spicy.",
"All cupcakes are bakeries.",
"All hotpots are spicy.",
"All products of Baked by Melissa are cupcakes.",
"If dried Thai chilies are spicy or a bakery, then dried Thai chilies are a hotpot or are spicy."
] | [
"∀x (Bakery(x) → ¬Spicy(x))",
"∀x (Cupcakes(x) → Bakery(x))",
"∀x (Hotpot(x) → Spicy(x))",
"∀x (ProductsOfBakedByMelissa(x) → Cupcakes(x))",
"Spicy(driedThaiChilies) ∨ Bakery(driedThaiChilies) → Hotpot(driedThaiChilies) ∨ Spicy(driedThaiChilies)"
] | Dried Thai chilies are cupcakes and a product of Baked by Melissa. | Cupcake(driedThaiChilies) ∧ ProductsOfBakedByMelissa(driedThaiChilies) | False |
[
"If the restaurant is listed in Yelp’s recommendations, then the restaurant does not receive many negative reviews.",
"All restaurants with a rating greater than 9 are listed in Yelp’s recommendations.",
"Some restaurants that do not provide take-out service receive many negative reviews.",
"All restaurants that are popular among local residents have ratings greater than 9.",
"Subway has a rating greater than 9 or is popular among local residents."
] | [
"∀x (YelpRecommendation(x) → ¬NegativeReview(x))",
"∀x (RatingGreaterThan9(x) → YelpRecommendation(x))",
"∃x (NoTakeOutService(x) ∧ NegativeReview(x))",
"∀x (PopularAmongLocalResidents(x) → RatingGreaterThan9(x))",
"RatingGreaterThan9(subway) ⊕ PopularAmongLocalResidents(subway)"
] | If Subway provides take-out service and receives many negative reviews, then its rating is greater than 9 and it does not provide take-out service. | NoTakeOutService(subway) | Uncertain |
[
"If the restaurant is listed in Yelp’s recommendations, then the restaurant does not receive many negative reviews.",
"All restaurants with a rating greater than 9 are listed in Yelp’s recommendations.",
"Some restaurants that do not provide take-out service receive many negative reviews.",
"All restaurants that are popular among local residents have ratings greater than 9.",
"Subway has a rating greater than 9 or is popular among local residents."
] | [
"∀x (YelpRecommendation(x) → ¬NegativeReview(x))",
"∀x (RatingGreaterThan9(x) → YelpRecommendation(x))",
"∃x (NoTakeOutService(x) ∧ NegativeReview(x))",
"∀x (PopularAmongLocalResidents(x) → RatingGreaterThan9(x))",
"RatingGreaterThan9(subway) ⊕ PopularAmongLocalResidents(subway)"
] | Subway provides take-out service and does not receive many negative reviews. | ¬(NoTakeOutService(subway) ∧ NegativeReview(subway)) | True |
[
"If the restaurant is listed in Yelp’s recommendations, then the restaurant does not receive many negative reviews.",
"All restaurants with a rating greater than 9 are listed in Yelp’s recommendations.",
"Some restaurants that do not provide take-out service receive many negative reviews.",
"All restaurants that are popular among local residents have ratings greater than 9.",
"Subway has a rating greater than 9 or is popular among local residents."
] | [
"∀x (YelpRecommendation(x) → ¬NegativeReview(x))",
"∀x (RatingGreaterThan9(x) → YelpRecommendation(x))",
"∃x (NoTakeOutService(x) ∧ NegativeReview(x))",
"∀x (PopularAmongLocalResidents(x) → RatingGreaterThan9(x))",
"RatingGreaterThan9(subway) ⊕ PopularAmongLocalResidents(subway)"
] | Subway does not provide take-out service. | ¬(NoTakeOutService(subway) ∧ NegativeReview(subway)) → PopularAmongLocalResidents(subway) ∧ NoTakeOutService(subway) | False |
[
"In superhero movies, the good guys always win.",
"The Surprising Adventures of Sir Digby Chicken Caesar is a superhero movie.",
"Good guys fight bad guys and vice versa.",
"Sir Digby fights his nemesis.",
"If a superhero movie is named after a character, that character is a good guy.",
"The Surprising Adventures of Sir Digby Chicken Caesar is named after Sir Digby.",
"If somebody wins a fight, the person they are fighting loses.",
"If a superhero movie is named after a character, that character appears in the movie."
] | [
"∀x ∀y (SuperheroMovie(x) ∧ GoodGuy(y) ∧ AppearsIn(y, x) → Wins(y))",
"SuperheroMovie(surprisingAdventuresofSirDigbyChickenCaesar)",
"∀x ∀y (GoodGuy(x) ∧ Fights(x, y) ⟷ BadGuy(y) ∧ Fights(y, x))",
"Fights(sirDigby, sirDigbyNemesis)",
"∀x ∀y (SuperheroMovie(x), NamedAfter(x, y) → GoodGuy(y))",
"NamedAfter(surprisingAdventuresofSirDigbyChickenCaesar, sirDigby)",
"∀x ∀y (Fights(x, y) ∧ Wins(x) → ¬Wins(y))"
] | Sir Digby’s nemesis loses. | ∀x ∀y (SuperheroMovie(x) ∧ AppearsIn(y, x) → GoodGuy(y)) | True |
[
"[BG] Books contain tons of knowledge.",
"[BG] When a person reads a book, that person gains knowledge. ",
"[BG] If a person gains knowledge, they become smarter.",
"Harry read the book “Walden” by Henry Thoreau."
] | [
"∀x (Book(x) → Knowledge(x))",
"∀x ∀y (ReadBook(x, y) → GainKnowledge(x))",
"∀x (GainKnowledge(x) → Smarter(x))",
"ReadBook(harry, walden) ∧ Book(walden)"
] | Walden contains knowledge. | Knowledge(walden) | True |
[
"[BG] Books contain tons of knowledge.",
"[BG] When a person reads a book, that person gains knowledge. ",
"[BG] If a person gains knowledge, they become smarter.",
"Harry read the book “Walden” by Henry Thoreau."
] | [
"∀x (Book(x) → Knowledge(x))",
"∀x ∀y (ReadBook(x, y) → GainKnowledge(x))",
"∀x (GainKnowledge(x) → Smarter(x))",
"ReadBook(harry, walden) ∧ Book(walden)"
] | Harry is smarter than before. | Smarter(harry) | True |
[
"[BG] Books contain tons of knowledge.",
"[BG] When a person reads a book, that person gains knowledge. ",
"[BG] If a person gains knowledge, they become smarter.",
"Harry read the book “Walden” by Henry Thoreau."
] | [
"∀x (Book(x) → Knowledge(x))",
"∀x ∀y (ReadBook(x, y) → GainKnowledge(x))",
"∀x (GainKnowledge(x) → Smarter(x))",
"ReadBook(harry, walden) ∧ Book(walden)"
] | A person who is smarter has gained knowledge. | ∀x (Smarter(x) → GainKnowledge(x)) | Uncertain |
[
"Natural language processing tasks can be categorized as either language generation task or language understanding task.",
"If the output of a natural language processing task is a text sequence, then it is a language generation task.",
"Machine translation is a natural language processing task.",
"The output of machine translation is a text sequence."
] | [
"∀x (NLP(x) → NLG(x) ⊕ NLU(x))",
"∀x (NLP(x) ∧ OutputSequence(x) → NLG(x))",
"NLP(machineTranslation)",
"OutputSequence(machineTranslation)"
] | Machine translation is a language generation task. | NLG(machineTranslation) | True |
[
"Natural language processing tasks can be categorized as either language generation task or language understanding task.",
"If the output of a natural language processing task is a text sequence, then it is a language generation task.",
"Machine translation is a natural language processing task.",
"The output of machine translation is a text sequence."
] | [
"∀x (NLP(x) → NLG(x) ⊕ NLU(x))",
"∀x (NLP(x) ∧ OutputSequence(x) → NLG(x))",
"NLP(machineTranslation)",
"OutputSequence(machineTranslation)"
] | Machine translation is a language understanding task. | NLU(machineTranslation) | False |
[
"Pets are allowed in some managed buildings.",
"[BG] A deposit is required to rent an apartment in a managed building.",
"The security deposit can be either equal to one month's rent or more.",
"Fluffy is Tom's cat.",
"Cats are pets.",
"The Olive Garden is a managed building.",
"The monthly rent at the Olive Garden is $2000.",
"Tom will rent an apartment in a managed building if and only if he is allowed to move in with Fluffy, and the security deposit is no more than $1500.",
"2000$ is more than $1500."
] | [
"∃x (ManagedBuilding(x) ∧ AllowPet(x))",
"∀x (ManagedBuilding(x) → RequireDeposit(x))",
"∀x (Rent2000(x) ↔ ¬DepositNoMoreThan1500(x))",
"∀x (Rent2000(x) ↔ DepositNoLessThan2000(x))",
"Cat(fluffy)",
"∀x (Cat(x) → Pet(x))",
"ManagedBuilding(oliveGarden)",
"Rent2000(oliveGarden)",
"∀x (TomRent(x) ↔ (ManagedBuilding(x) ∧ AllowPet(x) ∧ DepositNoMoreThan1500(x)))"
] | Tom will rent an apartment in The Olive Garden. | TomRent(oliveGarden) | False |
[
"Pets are allowed in some managed buildings.",
"[BG] A deposit is required to rent an apartment in a managed building.",
"The security deposit can be either equal to one month's rent or more.",
"Fluffy is Tom's cat.",
"Cats are pets.",
"The Olive Garden is a managed building.",
"The monthly rent at the Olive Garden is $2000.",
"Tom will rent an apartment in a managed building if and only if he is allowed to move in with Fluffy, and the security deposit is no more than $1500.",
"2000$ is more than $1500."
] | [
"∃x (ManagedBuilding(x) ∧ AllowPet(x))",
"∀x (ManagedBuilding(x) → RequireDeposit(x))",
"∀x (Rent2000(x) ↔ ¬DepositNoMoreThan1500(x))",
"∀x (Rent2000(x) ↔ DepositNoLessThan2000(x))",
"Cat(fluffy)",
"∀x (Cat(x) → Pet(x))",
"ManagedBuilding(oliveGarden)",
"Rent2000(oliveGarden)",
"∀x (TomRent(x) ↔ (ManagedBuilding(x) ∧ AllowPet(x) ∧ DepositNoMoreThan1500(x)))"
] | Tom is allowed to move in an apartment in The Olive Garden with Fluffy. | AllowPet(oliveGarden) | Uncertain |
[
"Pets are allowed in some managed buildings.",
"[BG] A deposit is required to rent an apartment in a managed building.",
"The security deposit can be either equal to one month's rent or more.",
"Fluffy is Tom's cat.",
"Cats are pets.",
"The Olive Garden is a managed building.",
"The monthly rent at the Olive Garden is $2000.",
"Tom will rent an apartment in a managed building if and only if he is allowed to move in with Fluffy, and the security deposit is no more than $1500.",
"2000$ is more than $1500."
] | [
"∃x (ManagedBuilding(x) ∧ AllowPet(x))",
"∀x (ManagedBuilding(x) → RequireDeposit(x))",
"∀x (Rent2000(x) ↔ ¬DepositNoMoreThan1500(x))",
"∀x (Rent2000(x) ↔ DepositNoLessThan2000(x))",
"Cat(fluffy)",
"∀x (Cat(x) → Pet(x))",
"ManagedBuilding(oliveGarden)",
"Rent2000(oliveGarden)",
"∀x (TomRent(x) ↔ (ManagedBuilding(x) ∧ AllowPet(x) ∧ DepositNoMoreThan1500(x)))"
] | The security deposit at the Olive Garden is either $2000 or more. | DepositNoLessThan2000(oliveGarden) | True |
[
"If animals are loved by tourists, then they are Max's favorite animals. ",
"All animals from Australia are loved by tourists. ",
"All quokka are animals from Australia. ",
"All of Max's favorite animals are very fluffy.",
"All of Max's favorite animals love to sleep. ",
"If a koala is very fluffy, then the koala is not a quokka."
] | [
"∀x (AnimalsLovedByTourists(x) → MaxFavoriteAnimals(x))",
" ∀x (AnimalsFromAustralia(x) → AnimalsLovedByTourists(x))",
" ∀x (Quokka(x) → AnimalsFromAustralia(x))",
" ∀x (MaxFavoriteAnimals(x) → VeryFluffy(x)) ",
" ∀x (MaxFavoriteAnimals(x) → LoveToSleep(x))",
" VeryFluffy(koala) → ¬Quokka(koala)"
] | Koalas love to sleep. | LoveToSleep(koala) | Uncertain |
[
"If animals are loved by tourists, then they are Max's favorite animals. ",
"All animals from Australia are loved by tourists. ",
"All quokka are animals from Australia. ",
"All of Max's favorite animals are very fluffy.",
"All of Max's favorite animals love to sleep. ",
"If a koala is very fluffy, then the koala is not a quokka."
] | [
"∀x (AnimalsLovedByTourists(x) → MaxFavoriteAnimals(x))",
" ∀x (AnimalsFromAustralia(x) → AnimalsLovedByTourists(x))",
" ∀x (Quokka(x) → AnimalsFromAustralia(x))",
" ∀x (MaxFavoriteAnimals(x) → VeryFluffy(x)) ",
" ∀x (MaxFavoriteAnimals(x) → LoveToSleep(x))",
" VeryFluffy(koala) → ¬Quokka(koala)"
] | Koalas love to sleep and are quokka. | LoveToSleep(koala) ∧ Quokka(koala) | False |
[
"If animals are loved by tourists, then they are Max's favorite animals. ",
"All animals from Australia are loved by tourists. ",
"All quokka are animals from Australia. ",
"All of Max's favorite animals are very fluffy.",
"All of Max's favorite animals love to sleep. ",
"If a koala is very fluffy, then the koala is not a quokka."
] | [
"∀x (AnimalsLovedByTourists(x) → MaxFavoriteAnimals(x))",
" ∀x (AnimalsFromAustralia(x) → AnimalsLovedByTourists(x))",
" ∀x (Quokka(x) → AnimalsFromAustralia(x))",
" ∀x (MaxFavoriteAnimals(x) → VeryFluffy(x)) ",
" ∀x (MaxFavoriteAnimals(x) → LoveToSleep(x))",
" VeryFluffy(koala) → ¬Quokka(koala)"
] | If a koala is a quokka, then the koala either loves to sleep or is very fluffy. | Quokka(koala) → LoveToSleep(koala) ⊕ VeryFluffy(koala) | True |
[
"A man is either kind or evil.",
"No ugly person is handsome.",
"All evil people are ugly.",
"All gentlemen are handsome.",
"All CEOs are gentlemen.",
"Harry is a gentleman."
] | [
"∀x (Kind(x) ⊕ Evil(x))",
"∀x (Ugly(x) → ¬Handsome(x))",
"∀x (Evil(x) → Ugly(x))",
"∀x (Gentleman(x) → Handsome(x))",
"∀x (CEO(x) → Gentleman(x))",
"Gentleman(harry)"
] | Harry is a CEO. | CEO(harry) | Uncertain |
End of preview. Expand
in Dataset Viewer.
@article{han2022folio,
title={FOLIO: Natural Language Reasoning with First-Order Logic},
author = {Han, Simeng and Schoelkopf, Hailey and Zhao, Yilun and Qi, Zhenting and Riddell, Martin and Benson, Luke and Sun, Lucy and Zubova, Ekaterina and Qiao, Yujie and Burtell, Matthew and Peng, David and Fan, Jonathan and Liu, Yixin and Wong, Brian and Sailor, Malcolm and Ni, Ansong and Nan, Linyong and Kasai, Jungo and Yu, Tao and Zhang, Rui and Joty, Shafiq and Fabbri, Alexander R. and Kryscinski, Wojciech and Lin, Xi Victoria and Xiong, Caiming and Radev, Dragomir},
journal={arXiv preprint arXiv:2209.00840},
url = {https://arxiv.org/abs/2209.00840},
year={2022}
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