minimario/FOLIO huggingface dataset:
Premises:
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.

Premises in first-order logic:
∀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)

Conclusion: Dried Thai chilies are a product of Baked by Melissa.
Label: False

Conclusion: Dried Thai chilies are not a product of Baked by Melissa.
Label: True

Conclusion: Dried Thai chilies are a hotpot.
Label: Unknown

Conclusion: Dried Thai chilies are neither a product of Baked by Melissa nor a bakery.
Label: True

Conclusion: Dried Thai chilies are cupcakes and a product of Baked by Melissa.
Label: False
Premises:
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.

Premises in first-order logic:
∀x (YelpRecommendation(x) → ¬NegativeReview(x))
∀x (RatingGreaterThan9(x) → YelpRecommendation(x))
∃x (NoTakeOutService(x) ∧ NegativeReview(x))
∀x (PopularAmongLocalResidents(x) → RatingGreaterThan9(x))
RatingGreaterThan9(subway) ⊕ PopularAmongLocalResidents(subway)

Conclusion: 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.
Label: Unknown

Conclusion: Subway provides take-out service and does not receive many negative reviews.
Label: True

Conclusion: Subway does not provide take-out service.
Label: False
Premises:
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.

Premises in first-order logic:
∀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))

Conclusion: Sir Digby’s nemesis loses.
Label: True
Premises:
[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.

Premises in first-order logic:
∀x (Book(x) → Knowledge(x))
∀x ∀y (ReadBook(x, y) → GainKnowledge(x))
∀x (GainKnowledge(x) → Smarter(x))
ReadBook(harry, walden) ∧ Book(walden)

Conclusion: Walden contains knowledge.
Label: True

Conclusion: Harry is smarter than before.
Label: True

Conclusion: A person who is smarter has gained knowledge.
Label: Unknown
Premises:
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.

Premises in first-order logic:
∀x (NLP(x) → NLG(x) ⊕ NLU(x))
∀x (NLP(x) ∧ OutputSequence(x) → NLG(x))
NLP(machineTranslation)
OutputSequence(machineTranslation)

Conclusion: Machine translation is a language generation task.
Label: True

Conclusion: Machine translation is a language understanding task.
Label: False
Premises:
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.

Premises in first-order logic:
∃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)))

Conclusion: Tom will rent an apartment in The Olive Garden.
Label: False

Conclusion: Tom is allowed to move in an apartment in The Olive Garden with Fluffy.
Label: Unknown

Conclusion: The security deposit at the Olive Garden is either $2000 or more.
Label: True
Premises:
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.

Premises in first-order logic:
∀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)

Conclusion: Koalas love to sleep.
Label: Unknown

Conclusion: Koalas love to sleep and are quokka.
Label: False

Conclusion: If a koala is a quokka, then the koala either loves to sleep or is very fluffy.
Label: True
Premises:
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.

Premises in first-order logic:
∀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)

Conclusion: Harry is a CEO.
Label: Unknown

Conclusion: Harry is kind or a CEO.
Label: True

Conclusion: If Harry is either both evil and ugly, or neither evil nor ugly, then Harry is neither kind nor a CEO.
Label: False
Premises:
If people are twins or triplets, then they spend a lot of time hanging out with and playing with their siblings.
If people have siblings who are the same age, then they are twins or triplets.
If people complain often about annoying siblings, then they have siblings who are the same age.
If people do not live at home regularly, then they do not develop strong bonds with their family members.
If people spend a lot of time hanging out with and playing with their siblings, then they often did not live at home regularly.
Luke is either both a twin or triplet and develops strong bonds with his family members, or he neither is a twin or triplet nor develops strong bonds with his family members.   

Premises in first-order logic:
∀x (TwinTriplet(x) → Playing(x))
∀x (SameAge(x) → TwinTriplet(x))
∀x (Complain(x) → SameAge(x))
∀x (NotHome(x) → ¬StrongBonds(x))
∀x (Playing(x) → NotHome(x))
(TwinTriplet(luke) ∧ StrongBonds(luke)) ⊕ (¬TwinTriplet(luke) ∧ ¬StrongBonds(luke))

Conclusion: Luke spends a lot of time hanging out and playing with his siblings.
Label: Unknown

Conclusion: Luke complains often about annoying siblings.
Label: False

Conclusion: Luke is neither a twin nor triplet nor complains often about annoying siblings.
Label: True
Premises:
It costs US $205 to take the GRE test.
ETS provides financial aid to those GRE applicants who prove economic hardship.
Economic hardship refers to difficulty caused by having too little money or too few resources.
Tom lives in a single-parent family.
His dad has been out of work for more than a year.

Premises in first-order logic:
Cost205(gre)
∀x (Cost205(x) → CostBelow300(x))
∀x (Hardship(x) → FinancialAid(x))
∀x (SingleParent(x) ∨ FewResources(x) → Hardship(x))
SingleParent(tom)
FewResources(tom)

Conclusion: Tom can apply for financial aid from ETS to take the GRE test.
Label: True

Conclusion: It cost below US $300 to take the GRE test.
Label: True

Conclusion: There is no financial aid available for the GRE test.
Label: False
Premises:
If people spill a lot of food on their clothing, then they do not tidy their spaces consistently and enjoy the process of cleaning.
All foodies who go out frequently to find new food restaurants to try are people who spill a lot of food on their clothing.
If people grew up as only children with no siblings, then they tidy their spaces consistently and enjoy the process of cleaning.
If people have parents who are very busy with their regular jobs, then they grew up as only children with no siblings.
All households with a high net income have people who have parents who are very busy with their regular jobs.
Peter is either both a person who spills a lot of food on his clothing and grew up as an only child with no siblings, or he is neither a person who spills a lot of food on his clothing nor grew up as an only child with no siblings. 

Premises in first-order logic:
∀x (Spill(x) → ¬Tidy(x))
∀x (Foodie(x) → Spill(x))
∀x (OnlyChild(x) → Tidy(x))
∀x (BusyParents(x) → OnlyChild(x))
∀x (HighIncome(x) → BusyParents(x))
(Spill(peter) ∧ OnlyChild(peter)) ∨ ¬Spill(peter) ∧ ¬OnlyChild(peter))

Conclusion: Peter tidies his space consistently and enjoys the process of cleaning.
Label: Unknown

Conclusion: Peter is either a foodie who goes out frequently to find new food restaurants to try or belongs to a household with a high net income.
Label: False

Conclusion: Peter is either a foodie who goes out frequently to find new food restaurants to try and belong to a household with a high net income or he is a foodie who goes out frequently to find new food restaurants to try nor belongs to a household with a high net income.
Label: True
Premises:
All fir trees are evergreens.
Some objects of worship are fir trees.

Premises in first-order logic:
∀x (FirTree(x) → Evergreen(x))
∃x (ObjectOfWorship(x) ∧ FirTree(x))

Conclusion: Some evergreens are not objects of worship.
Label: Unknown
Premises:
The Picuris Mountains are a mountain range in New Mexico or Texas.
Juan de Onate visited the Picuris Mountains.
The Harding Pegmatite Mine, located in the Picuris Mountains, was donated.
There are no mountain ranges in texas that have mines which have been donated.

Premises in first-order logic:
MountainRange(picurismountains) ∧ In(picurismountains, newmexico) ∨ In(picurismountains, texas)
Visited(juandeonate, picurismountains)
In(hardingpegmatitemine, picurismountains) ∧ Mine(hardingpegmatitemine) ∧ Donated(hardingpegmatitemine)
∀x ∀y (Mine(x) ∧ Donated(x) ∧ In(x, y) ∧ MountainRange(y) → ¬In(y, texas))

Conclusion: Juan de Onate visited a mountain range in New Mexico.
Label: True

Conclusion: Juan de Onate visited a mountain range in Texas.
Label: Unknown

Conclusion: The Harding Pegmatite Mine is not located in a mountain range in New Mexico.
Label: False
Premises:
If a man is taller than another man, the taller one can block the other's shooting.
Michael is a man who is taller than everyone else in his class.
If person x is taller than person y, and person y is taller than person z, than x is taller than z
Peter is a man who is taller than Michael.
Michael can block any shooting from a person as long as the person does not jump when shooting.
Michael cannot block Windy's shooting.
Every shooter who can jump when shooting is a great shooter.

Premises in first-order logic:
∀x ∀y (IsMan(x) ∧ IsMan(y) ∧ Taller(x, y) → CanBlock(x, y))
∀x (IsMan(x) ∧ SameClass(x, michael) ∧ ¬Be(x, michael) → Taller(michael, x))
∀x ∀y ∀z ((Taller(x, y) ∧ Taller(y, z)) → Taller(x, z))
IsMan(peter) ∧ Taller(peter, michael)
∀x (¬JumpWhenShooting(x) → CanBlock(michael, x))
¬CanBlock(michael, windy)
∀x (JumpWhenShooting(x) → GreatShooter(x))

Conclusion: Peter is shorter than a man in Michael's class.
Label: False

Conclusion: Windy is a great shooter.
Label: True

Conclusion: Peter can block Windy's shooting.
Label: Unknown
Premises:
Barutin Cove is named after the Bulgarian settlement of Barutin.
Barutin Cove is on the southwest coast of Snow Island.
The South Shetland Islands include Snow Island, Greenwich Island, and Deception Island.
The South Shetland Islands are considered part of Antarctica.
If A is located in B and B is located in C, then A is located in C.

Premises in first-order logic:
Cove(barutin) ∧ NameAfter(barutin, settlement) ∧ Locate(settlement, bulgaria)
Locate(barutin, snow)
Locate(snow, shetland) ∧ Locate(greenwich, shetland) ∧ Locate(deception, shetland)
Locate(shetland, antarctica)
∀x ∀y ∀z ((Locate(x, y) ∧ Locate(y, z)) → Locate(x, z))

Conclusion: Barutin is named after all islands in Antarctica.
Label: Unknown

Conclusion: There is at least one cove in Antarctica named after a place in Bulgaria.
Label: True

Conclusion: Barutin is not located in Antarctica.
Label: False
Premises:
Some affection is love.
Some love is positive.

Premises in first-order logic:
∃x (Affection(x) ∧ Love(x))
∃x (Love(x) ∧ Positive(x))

Conclusion: Some affection is positive.
Label: Unknown
Premises:
If something can transport multiple passengers, then they are not empty.
All airlines can transport multiple passengers.
All planes are empty.
All Boeing 707s are planes.
If Greyhound is not an airline, then there are no Greyhound planes.

Premises in first-order logic:
∀x (TransportMultiplePassengers(x) → ¬Empty(x))
∀x (Airline(x) → TransportMultiplePassengers(x))
∀x (Plane(x) → Empty(x))
∀x (Boeing707(x) → Plane(x))
¬Airline(greyhound) → ¬(Airline(greyhound) ∨ Plane(greyhound))

Conclusion: Greyhound is an airline.
Label: Unknown

Conclusion: A Greyhound is a Boeing 707.
Label: False

Conclusion: A Greyhound is not a Boeing 707.
Label: True
Premises:
All mammals are animals.
All monkeys are mammals. 
An animal is either a monkey or a bird.
All birds fly.
All animals breathe.
If something can fly, then it has wings.
If Rock is neither a fly nor a bird, then Rock neither flies nor breathes.

Premises in first-order logic:
∀x  (Mammal (x)→  Animal (x))
∀x  (Monkey (x)→  Mammal (x))
∀x ( Monkey (x) ∨  Bird (x))
∀x  (Bird (x)→  Fly (x))
∀x  (Animal (x)→  Breathe (x))
∀x  (Fly (x)→  HaveWings (x))
¬ Fly (rock) ∧ ¬ Bird (rock) → ¬ Fly (rock) ∧ ¬ Breathe (rock)

Conclusion: Rock is a monkey.
Label: Unknown

Conclusion: Rock has wings.
Label: True

Conclusion: Rock does not have wings.
Label: False
Premises:
All people who have a wedding are people who have at least one child.
All people who travel to Paris for their honeymoon are people who have a wedding.
All weddings that occur in July belong to people who travel to Paris for their honeymoon.
Some weddings in July are well-attended.
If John has at least one child, then John does not travel to Paris for his honeymoon and does not have a wedding.
If John has a wedding that is well-attended, then John has a wedding in July or, if not, then John travels to Paris for their honeymoon. 

Premises in first-order logic:
∀x (Wedding(x) → Child(x))
∀x (Paris(x) → Wedding(x))
∀x (July(x) → Paris(x))
∃x (July(x) ∧ WellAttended(x))
Child(john) → ¬(Paris(john) ∧ Wedding(john))
WellAttended(john) → July(john) ⊕ Paris(john)

Conclusion: John has a wedding that is well-attended.
Label: False

Conclusion: John does not have a wedding that is well-attended.
Label: True

Conclusion: John has at least one child.
Label: Unknown

Conclusion: John has neither a wedding that is well-attended nor does he travel to Paris for his honeymoon.
Label: True
Premises:
[BG] Some mammals have teeth.
Platypus have no teeth.
Platypus are mammals. 
Humans have teeth.

Premises in first-order logic:
∃x (Mammal(x) ∧ Have(x, teeth))
¬Have(platypus, teeth)
Mammal(platypus)
Have(humans, teeth)

Conclusion: Platypus are mammals with no teeth.
Label: True

Conclusion: Platypus are reptiles.
Label: Unknown

Conclusion: Humans are mammals.
Label: Unknown
Premises:
Plungers suck.
Vacuums suck.
Vampires suck.
Space is a vacuum.
A duster is a household appliance that doesn't suck.

Premises in first-order logic:
∀x (Plunger(x) → Suck(x))
∀x (Vacuum(x) → Suck(x))
∀x (Vampire(x) → Suck(x))
Vacuum(space)
HouseHoldApp(duster) ∧ ¬ Suck(duster)

Conclusion: Space sucks.
Label: True

Conclusion: Space is a vampire.
Label: Unknown

Conclusion: If something is a household appliance, it sucks.
Label: False
Premises:
Machine Learning algorithms can be categorized as supervised learning, unsupervised learning, and reinforcement learning.
Unsupervised learning doesn't require labelled data.
The state-of-the-art text summarization model is trained with machine learning algorithms.
Reinforcement learning is not used to train the state-of-the-art text summarization model.
The Machine Learning algorithm for training text summarization model requires labelled data.

Premises in first-order logic:
MLAlgorithm(supervisedLearning) ∨ MLAlgorithm(unsupervisedLearning) ∨ MLAlgorithm(reinforcementLearning)
¬RequireLabelledData(unsupervisedLearning)
TrainTextSumModel(supervisedLearning) ∨ TrainTextSumModel(unsupervisedLearning) ∨ TrainTextSumModel(reinforcementLearning)
¬TrainTextSumModel(reinforcementLearning)
∀x ((MLAlgorithm(x) ∧ TrainTextSumModel(x)) → RequireLabelledData(x))

Conclusion: Supervised learning is used to train the state-of-the-art text summarization model.
Label: True

Conclusion: Unsupervised learning is used to train the state-of-the-art text summarization model.
Label: False
Premises:
If a cartoon character is funny, then it is popular.
If a cartoon character is ugly, then it is not popular.
If a cartoon character is loved by children, then it is funny.
If a cartoon character is from The Simpsons, then it is loved by children.
If a cartoon character is yellow, then it is from The Simpsons.
Ben is either from The Simpsons or funny.

Premises in first-order logic:
∀x (Funny(x) → Popular(x))
∀x (Ugly(x) → ¬Popular(x))
∀x (Love(children, x) → Funny(x))
∀x (Simpsons(x) → Love(children, x))
∀x (Yellow(x) → Simpsons(x))
Simpsons(ben) ⊕ Funny(ben)

Conclusion: Ben is loved by children.
Label: Unknown

Conclusion: Ben is ugly or yellow.
Label: False

Conclusion: Ben is either yellow and ugly or neither yellow nor ugly.
Label: True
Premises:
Breeding back is a form of artificial selection by the deliberate selective breeding of domestic animals.
Heck cattle were bred-back in the 1920s to resemble the aurochs.
[BG] Heck cattle are animals.
[BG] Aurochs are animals.
Some animals to be bred-back resemble animals that are extinct.

Premises in first-order logic:
∀x ∀y (BreedingBack(x, y) → ArtificiallySelect(x))
∃x ∃y (HeckCattle(x) ∧ Aurochs(y) ∧ BreedingBack(x, y))
∀x (HeckCattle(x) → Animal(x))
∀x (Aurochs(x) → Animal(x))
∃x ∃y (Animal(x) ∧ Animal(y) ∧ BreedingBack(x, y) ∧ Extinct(y))

Conclusion: Some Heck cattle are artificially selected.
Label: True

Conclusion: Aurochs are extinct.
Label: Unknown
Premises:
All students are humans. 
If someone studies, then they are a student.
A person either studys or teaches.
No young person teaches.
Jerry neither teaches nor is a manager.
Rose is young or a student.

Premises in first-order logic:
∀x (Student(x) → Human(x))
∀x (Study(x) → Student(x))
∀x (Study(x) ∨ Teach(x))
∀x (Young(x) → ¬Teach(x))
¬Teach(jerry) ∧ ¬Manager(jerry)
Young(rose) ∨ Student(rose)

Conclusion: Jerry is young.
Label: Unknown

Conclusion: Jerry is not young.
Label: Unknown

Conclusion: Rose is a human or a manager.
Label: True

Conclusion: Rose is a human or Jerry is a manager.
Label: True

Conclusion: It is not true that Rose is a student and Jerry is a human.
Label: False
Premises:
New Vessel Press is a publishing house which specializes in translating foreign literature into English.
All of New Vessel Press's published books are in English.
Neapolitan Chronicles is a book published by New Vessel Press.
Neapolitan Chronicles was translated from Italian.
Palace of Flies is a book published by New Vessel Press.

Premises in first-order logic:
PublishingHouse(newvesselpress) ∧ SpecializesIn(newvessel, translatingforeignliteratureintoenglish)
∀x (Book(x) ∧ PublishedBy(x, newvesselpress) → In(x, english))
Book(neapolitanchronicles) ∧ PublishedBy(neapolitanchronicles, newvesselpress)
TranslatedFrom(neapolitanchronicles, italian)
Book(palaceofflies) ∧ PublishedBy(palaceofflies, newvesselpress)

Conclusion: Neapolitan Chronicles is an English book.
Label: True

Conclusion: Harry Potter was published by New Vessel Press.
Label: Unknown

Conclusion: Palace of Flies was translated from Italian.
Label: Unknown
Premises:
If people own a large desktop monitor at their home, then they work regularly and often at home.
All people who have a fully stocked and impressive home office are people who own a large desktop monitor at their home.
All people who work regularly and often at home spend their free time tidying and organizing the spaces in their homes.
All people who work regularly and often at home visit the office supply store regularly.
If people spend their free time tidying and organizing the spaces in their home, then they do not go to bed late and wake up every day after noon. 
Remy either both goes to bed late and wakes up every day after noon and spends their free time tidying and organizing the spaces in their home, or they do not go to bed late and wake up every day after noon nor spend their free time tidying and organizing the spaces in their home. 

Premises in first-order logic:
∀x (Desktop(x) → WorkHome(x))
∀x (HomeOffice(x) → Desktop(x))
∀x (WorkHome(x) → Tidying(x))
∀x (WorkHome(x) → OfficeStore(x))
∀x (Tidying(x) → ¬Late(x))
(Late(remy) ∧ Tidying(remy)) ⊕ (¬Late(remy) ∧ ¬Tidying(remy))

Conclusion: Remy visits the office supply store regularly.
Label: Unknown

Conclusion: Remy has a fully stocked and impressive home office and also visits the office supply store regularly.
Label: False

Conclusion: If Remy either goes to bed late and wakes up every day after noon or visits the office supply store regularly, then Remy neither spends their free time tidying and organizing the spaces in their home nor has a fully stocked and impressive home office.
Label: True
Premises:
All humans are mortal.
All Greeks are humans.

Premises in first-order logic:
∀x (Human(x) → Mortal(x))
∀x (Greek(x) → Human(x))

Conclusion: Some Greeks are mortal.
Label: Unknown
Premises:
No students who work in the library are from the computer science department. 
All students who have part-time jobs offered by the university are students who work in the library. 
All students who take the database course are from the computer science department. 
All students instructed by professor David are taking the database course. 
All students working in the lab are instructed by professor David. 
James is a student working in the lab. 
Jack neither has a part-time job offered by the university nor works in the lab. 

Premises in first-order logic:
∀x (WorkLibrary(x) → ¬ComputerScience(x))
∀x (PartTime(x) → WorkLibrary(x))
∀x (Database(x) → ComputerScience(x))
∀x (ProfessorDavid(x) → Database(x))
∀x (WorkInLab(x) → ProfessorDavid(x))
WorkInLab(james)
¬PartTime(jack) ∧ ¬WorkInLab(jack)

Conclusion: James has a part-time job offered by the university.
Label: False

Conclusion: James does not have a part-time job offered by the university.
Label: True

Conclusion: James either takes the database course or has a part-time job offered by the university.
Label: True

Conclusion: Jack takes the database course.
Label: Unknown