yuansui/folio huggingface dataset:
Premises:
Tissues are soft.
Some papers are tissues.

Premises in first-order logic:
∀x (Tissue(x) → Soft(x))
∃x ∃y (Paper(x) ∧ Paper(x) ∧ Tissue(x) ∧ Tissue(y) ∧ ¬(x=y))

Conclusions:
Some papers are hard.

Conclusions in first-order logic:
∃x ∃y (Paper(x) ∧ Paper(y) ∧ Hard(x) ∧ Hard(y) ∧ ¬(x=y))

Truth value of each conclusion (T = true, F = false, U = unknown):
U
Premises:
Heinrich Schmidt was a German politician. 
Heinrich Schmidt was also a member of the Prussian State Parliament and the Nazi Reichstag.

Premises in first-order logic:
German(heinrichSchmidt) ∧ Politician(heinrichSchmidt)
Member(heinrichSchmidt, prussianStateParliament) ∧ Member(heinrichSchmidt, naziReichstag)

Conclusions:
Heinrich Schmidt was German or Russian or both. 
Some German politician was part of both the Prussian State Parliament and the Nazi Reichstag. 
No politicians are part of the Nazi Reichstag. 

Conclusions in first-order logic:
German(heinrichSchmidt) ∨ Russian(heinrichSchmidt)
∃x (German(x) ∧ Politician(x) ∧ Member(x, prussianStateParliament) ∧ Member(x, naziReichstag))
∀x (Politician(x) → ¬Member(x, naziReichstag))

Truth value of each conclusion (T = true, F = false, U = unknown):
T
T
F
Premises:
The taiga vole is a large vole found in northwestern North America. 
Cats like playing with all voles.
The taiga vole lives in the boreal taiga zone.
The boreal taiga zone in North America is a cold place to live in.

Premises in first-order logic:
Vole(taigaVole) ∧ LiveIn(taigaVole, northAmerica)
LikePlayingWith(cat, taigaVole)
LiveIn(taigaVole, borealTaigaZone)
∀x ((LiveIn(x, northAmerica) ∧ LiveIn(x, borealTaigaZone)) → LiveIn(x, coldPlace))

Conclusions:
Cats like playing with taiga vole.
Taiga vole's living place is not cold.

Conclusions in first-order logic:
LikePlayingWith(cat, taigaVole)
¬LiveIn(taigaVole, coldPlace)

Truth value of each conclusion (T = true, F = false, U = unknown):
T
F
Premises:
Miroslav Fiedler was a Czech mathematician.
Miroslav Fiedler is known for his contributions to linear algebra and graph theory.
Miroslav Fiedler is honored by the Fiedler eigenvalue.
Fiedler eigenvalue is the second smallest eigenvalue of the graph Laplacian.

Premises in first-order logic:
Czech(miroslavFiedler) ∧ Mathematician(miroslavFiedler)
KnownFor(miroslavFiedler, contributionsToLinearAlgebraAndGraphTheory)
HonoredBy(miroslavFiedler, fiedlerEigenvalue)
TheSecondSmallestEigenvalueOf(fiedlerEigenvalue, theGraphLaplacian)

Conclusions:
Miroslav Fiedler is honored by the second smallest eigenvalue of the graph Laplacian.
Miroslav Fiedler was a French mathematician.
A Czech mathematician is known for his contributions to linear algebra and graph theory.

Conclusions in first-order logic:
∃x (TheSecondSmallestEigenvalueOf(x, theGraphLaplacian) ∧ HonoredBy(miroslavFiedler, x))
French(miroslavFiedler) ∧ Mathematician(miroslavFiedler)
∃x (Czech(x) ∧ Mathematician(x) ∧ KnownFor(x, contributionsToLinearAlgebraAndGraphTheory))

Truth value of each conclusion (T = true, F = false, U = unknown):
T
U
T
Premises:
Asa Hoffmann was born in New York City.
Asa Hoffman lives in Manhattan.
Asa Hoffman is a chess player.
Some chess players are grandmasters.
People born and living in New York City are New Yorkers.
People living in Manhattan live in New York City.

Premises in first-order logic:
BornIn(asaHoffmann, newYorkCity)
LiveIn(asaHoffmann, manhattan)
ChessPlayer(asaHoffmann)
∃x ∃y (ChessPlayer(x) ∧ GrandMaster(x) ∧ (¬(x=y)) ∧ ChessPlayer(y) ∧ GrandMaster(y))
∀x ((BornIn(x, newYorkCity) ∧ LiveIn(x, newYorkCity)) → NewYorker(x))
∀x (LiveIn(x, manhattan) → LiveIn(x, newYorkCity))

Conclusions:
Asa Hoffmann is a New Yorker.
Asa Hoffmann is a grandmaster.
Asa Hoffmann does not live in New York.

Conclusions in first-order logic:
NewYorker(asaHoffmann)
GrandMaster(asaHoffmann)
¬LiveIn(asaHoffmann, newYorkCity)

Truth value of each conclusion (T = true, F = false, U = unknown):
T
U
F
Premises:
There is no dog on the roof.
If there is a dog on the roof, something went wrong.

Premises in first-order logic:
∀x (Dog(x) → ¬OnRoof(x)))
∀x ∃y ((Dog(x) ∧ OnRoof(x)) → GoWrong(y))

Conclusions:
Something went wrong.

Conclusions in first-order logic:
∃x (GoWrong(x))

Truth value of each conclusion (T = true, F = false, U = unknown):
U
Premises:
A laptop is a computer.
You can play games on a computer.
A phone is not a computer.

Premises in first-order logic:
∀x (Laptop(x) → Computer(x))
∀x (Computer(x) → CanPlayGameOn(x))
∀x (Phone(x) → ¬Computer(x))

Conclusions:
You can play games on a laptop.
You can not play games on a phone.

Conclusions in first-order logic:
∀x (Laptop(x) → CanPlayGameOn(x))
∀x (Phone(x) → ¬CanPlayGameOn(x))

Truth value of each conclusion (T = true, F = false, U = unknown):
T
U
Premises:
All books written by Cixin Liu have sold more than 1 million copies. 
Some books that have won the Hugo Award were written by Cixin Liu.
All books about the future are forward-looking.
The book Three-Body Problem has sold more than 1 million copies.
The Three-Body Problem is about the future.

Premises in first-order logic:
∀x ((Book(x) ∧ WrittenBy(x, cixinLiu)) → ∃y(MoreThan(y, oneMillion) ∧ Sold(x,y)))
∃x (Won(x, hugoAward) ∧ Book(x) ∧ WrittenBy(x, cixinLiu))
∀x ((Book(x) ∧ AboutFuture(x)) → FowardLooking(x))
Book(threeBodyProblem) ∧ ∃x (MoreThan(x, oneMillion) ∧ Sold(threeBodyProblem,x))
AboutFuture(threeBodyProblem)

Conclusions:
The Three-Body Problem won the Hugo Award.
The Three-Body Problem is forward-looking.
The Three-Body Problem was written by Cixin Liu.

Conclusions in first-order logic:
Won(threeBodyProblem, hugoAward)
AboutFuture(threeBodyProblem)
WrittenBy(threeBodyProblem, cixinLiu)

Truth value of each conclusion (T = true, F = false, U = unknown):
U
T
U
Premises:
Rosa was born in Santiago. 
Santiago is the capital and largest city of Chile.
Rosa is the daughter of a Catalan building contractor, Jose.
Jose has a Chilean wife, Carmen.
Carmen and Jose are Rosa's parents.
People from Catalan are not from Chile.
A building contractor is responsible for the day-to-day oversight of a construction site. 

Premises in first-order logic:
BornIn(rosa, santiago)
CapitalOf(santiago, chile) ∧ LargestCityOf(santiago, chile)
DaughterOf(rosa, jose) ∧ BuildingContractor(jose) ∧ Catalan(jose)
WifeOf(jose, carmen) ∧ Chilean(carmen)
ParentOf(jose, rosa) ∧ ParentOf(carmen, rosa)
∀x (Catalan(x) → ¬Chilean(x))
∀x ∃y (BuildingContractor(x) → ConstructionSite(y) ∧ Oversee(x, y))

Conclusions:
Rosa was born in the largest city of Chile.
Neither of Rosa's parents is Chilean.
Rosa is the daughter of someone who is responsible for the oversight of traffic.

Conclusions in first-order logic:
∃x (BornIn(rosa, x) ∧ LargestCityOf(x, chile))
¬Chilean(jose) ∧ ¬Chilean(carmen)
∃x (DaughterOf(rosa, x) ∧ Oversee(x, traffic))

Truth value of each conclusion (T = true, F = false, U = unknown):
T
F
T
Premises:
Bobby Flynn is a singer-songwriter. 
Bobby Flynn finished 7th while competing on Australian Idol.
Australian Idol competitors are Australian citizens.
The Omega Three band made a nationwide tour in 2007.
Bobby Flynn is a member of The Omega Three band.
Bobby Flynn was born in Queensland.

Premises in first-order logic:
Singer(bobbyFlynn) ∧ SongWriter(bobbyFlynn)
FinishesIn(bobbyFlynn, number7) ∧ CompetesOnAustralianIdol(bobbyFlynn)
∀x (CompetesOnAustralianIdol(x) → AustralianCitizen(x))
NationWideTourIn(theOmegaThreeBand, year2007) 
Member(bobbyFlynn, theOmegaThreeBand)
BornIn(bobbyFlynn, queensland)

Conclusions:
Bobby Flynn is an Australian citizen.
Bobby Flynn flew to America in 2007.
Bobby Flynn was born in Queens.

Conclusions in first-order logic:
AustralianCitizen(bobbyFlynn)
FlewToIn(bobbyFlynn, america, year2007)
BornIn(bobbyFlynn, queens)

Truth value of each conclusion (T = true, F = false, U = unknown):
T
U
U
Premises:
Surprises are either fun or dreadful.
All scares are surprises.

Premises in first-order logic:
∀x (Surprise(x) → (Fun(x) ⊕ Dreadful(x)))
∀x (Scare(x) → Surprise(x))

Conclusions:
All scares are fun.

Conclusions in first-order logic:
∀x (Scare(x) → Fun(x))

Truth value of each conclusion (T = true, F = false, U = unknown):
U
Premises:
A boat floats on water.
There are bricks on the boat.

Premises in first-order logic:
FloatOn(boat, water)
∃x (Brick(x) ∧ On(x, boat))

Conclusions:
Bricks float on water.

Conclusions in first-order logic:
∀x (Brick(x) ∧ FloatOn(x, water))

Truth value of each conclusion (T = true, F = false, U = unknown):
U
Premises:
All humans are mortal.
All Greeks are humans.

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

Conclusions:
Some Greeks are mortal.

Conclusions in first-order logic:
∃x ∃y (Greek(x) ∧ Greek(y) ∧ Mortal(x) ∧ Mortal(y) ∧ ¬(x=y))

Truth value of each conclusion (T = true, F = false, U = unknown):
T
Premises:
All tables are round.
Some pieces of furniture are tables.

Premises in first-order logic:
∀x (Table(x) → Round(x))
∃x ∃y (Furniture(x) ∧ Furniture(y) ∧ Table(x) ∧ Table(y) ∧ ¬(x=y))

Conclusions:
Some pieces of furniture are round.

Conclusions in first-order logic:
∃x ∃y (Furniture(x) ∧ Furniture(y) ∧ Round(x) ∧ Round(y) ∧ ¬(x=y))

Truth value of each conclusion (T = true, F = false, U = unknown):
T
Premises:
New Vessel Press is a publishing house specializing 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) ∧ SpecializesInTranslatingIntoEnglish(newVesselPress, foreignLiterature)
∀x ((Book(x) ∧ PublishedBy(x, newVesselPress)) → In(x, english))
Book(neapolitanChronicles) ∧ PublishedBy(neapolitanChronicles, newVesselPress)
TranslatedFrom(neapolitanChronicles, italian)
Book(palaceOfFlies) ∧ PublishedBy(palaceOfFlies, newVesselPress)

Conclusions:
Neapolitan Chronicles is an English book. 
Harry Potter was published by New Vessel Press. 
Palace of Flies was translated from Italian. 

Conclusions in first-order logic:
Book(neapolitanChronicles) ∧ In(neapolitanChronicles, english)
PublishedBy(harryPotter, newVesselPress)
TranslatedFrom(palaceOfFlies, italian)

Truth value of each conclusion (T = true, F = false, U = unknown):
T
U
U
Premises:
Brian Winter is a Scottish football referee.
After being injured, Brian Winter retired in 2012.
Brian Winter was appointed as a referee observer after his retirement.
Some football referees become referee observers.
The son of Brian Winter, Andy Winter, is a football player who plays for Hamilton Academical.

Premises in first-order logic:
Scottish(brianWinter) ∧ FootballReferee(brianWinter)
Retired(brianWinter) ∧ RetiredIn(brianWinter, yr2012)
RefereeObserver(brianWinter)
∃x (FootballReferee(x) ∧ RefereeObserver(x))
SonOf(andyWinter, brianWinter) ∧ FootballPlayer(andyWinter) ∧ PlaysFor(andyWinter, hamiltonAcademical)

Conclusions:
There is a son of a referee observer that plays football.
Brian Winter was not a referee observer.
Brian Winter is retired.
Andy Winter is a referee.

Conclusions in first-order logic:
∃x ∃y (SonOf(x, y) ∧ RefereeObserver(y) ∧ FootballPlayer(x))
¬RefereeObserver(brianWinter)
Retired(brianWinter)
Referee(andyWinter)

Truth value of each conclusion (T = true, F = false, U = unknown):
T
F
T
U
Premises:
New York City is Located in the United States of America.
The United States of America is part of North America.
North America is in the western hemisphere of the earth.
New York City is a highly developed city.
If place A is located in place B and place B is located in place C, then place A is located in place C.

Premises in first-order logic:
LocatedIn(newYorkCity, unitedStatesOfAmerica)
LocatedIn(usa, northAmerica)
LocatedIn(northAmerica, westernHemisphere)
HighlyDeveloped(newYorkCity)
∀x ∀y ∀z ((LocatedIn(x, y) ∧ LocatedIn(y, z)) → LocatedIn(x, z))

Conclusions:
A highly developed city is located in the western hemisphere of the earth.
The United States of America is not located in the western hemisphere of the earth. 
New York City is located in New York State.

Conclusions in first-order logic:
∃x (HighlyDeveloped(x) ∧ LocatedIn(x, westernHemisphere))
¬LocatedIn(unitedStatesOfAmerica, westHemisphere)
LocatedIn(newYorkCity, newYork)

Truth value of each conclusion (T = true, F = false, U = unknown):
T
F
U
Premises:
If a person coaches a football club, the person is a football coach.
If a person has a position in a club in a year, and the club is in NFL in the same year, the person plays in NFL.
Minnesota Vikings is a football club.
Dennis Green coached Minnesota Vikings.
Cris Carter had 13 touchdown receptions.
Minnesota Vikings were in the National Football League in 1997.
John Randle was Minnesota Vikings defensive tackle in 1997.

Premises in first-order logic:
∀x ∀y ((Coach(x, y) ∧ FootballClub(y)) → FootballCoach(x))
∀w ∀x ∀y ∀z ((PlayPositionFor(x, w, y, z) ∧ InNFL(y, z)) → PlayInNFL(x))
FootballClub(minnesotaVikings)
Coach(dennisGreen, minnesotaVikings)
ReceiveTD(crisCarter, num13)
InNFL(minnesotaVikings, yr1997)
PlayPositionFor(johnRandle, defensiveTackle, minnesotaVikings, yr1997)

Conclusions:
Dennis Green is a football coach.
John Randle didn't play in the National Football League.
Cris Carter played for Minnesota Vikings.

Conclusions in first-order logic:
FootballCoach(dennisGreen)
¬PlayInNFL(johnRandle)
PlayPositionFor(crisCarter, wr, minnesotaVikings, year1997)

Truth value of each conclusion (T = true, F = false, U = unknown):
T
F
U
Premises:
All fir trees are evergreens.
Some objects of worship are fir trees.

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

Conclusions:
Some evergreens are not objects of worship.

Conclusions in first-order logic:
∃x ∃y (Evergreen(x) ∧ Evergreen(y) ∧ ¬ObjectOfWorship(x) ∧ ¬ObjectOfWorship(y) ∧ ¬(x=y))

Truth value of each conclusion (T = true, F = false, U = unknown):
U
Premises:
A fortification is a military construction designed to defend territories in warfare.
Borj Masouda is one of the four main fortifications of the medina of Sfax.
The Sfax medina is in Tunisia.
The defensive wall is a type of fortification.

Premises in first-order logic:
∀x (Fortification(x) → MilitaryConstruction(x) ∧ DesignedtoDefendTerritoriesinWarfare(x))
∃x (MainFortification(x,4) ∧ MainFortification(borjMasouda) ∧ In(borjMasouda, sfaxMedina))
In(sfaxMedina, tunisia)
∀x (DefensiveWall(x) → Fortification(x))

Conclusions:
Borj Masouda is a construction.
Borj Masouda is in the medina of Sfax.
Borj Masouda is not in Tunisian.
Borj Masouda is a defensive wall.

Conclusions in first-order logic:
MilitaryConstructionDesignedToDefendTerritoriesInWarfare(borjMasouda)
In(borjMasouda, medinaSfax)
¬In(borjMasouda, tunisia)
DefensiveWall(borjMasouda)

Truth value of each conclusion (T = true, F = false, U = unknown):
T
T
F
U
Premises:
All artificial satellites are important scientific achievements.
Some artificial satellites are not U.S. inventions.

Premises in first-order logic:
∀x (ArtificialSatellite(x) → ImportantScientificAchievement(x))
∃x (ArtificialSatellite(x) ∧ ¬USInvention(x))

Conclusions:
All important scientific achievements are U.S. inventions.

Conclusions in first-order logic:
∀x (ImportantScientificAchievement(x) ∧ USInvention(x))

Truth value of each conclusion (T = true, F = false, U = unknown):
F
Premises:
New York City is located on the East Coast. 
Seattle is located on the West Coast. 
If a person is somewhere located on the East coast and is traveling to somewhere located on the west coast, they will be on a long flight.
People in business class from New York City to Seattle are not in first class.
People on long flights are uncomfortable unless they're in first class.

Premises in first-order logic:
LocatedOn(newYorkCity, eastCoast)
LocatedOn(seattle, westCoast)
∀x ∀y ∀z ((TravelingFrom(x, y) ∧ LocatedOn(y, eastcoast) ∧ TravelingTo(x, z) ∧ LocatedOn(z, westcoast)) → OnLongFlight(x))
∀x (InBuisnessClass(x) ∧ TravelingTo(x, seattle) ∧ TravelingFrom(x, newYorkCity) → ¬InFirstClass(x))
∀x (OnLongFlight(x) ∧ ¬InFirstClass(x) → Uncomfortable(x))

Conclusions:
People traveling in business class from New York City to Seattle will be uncomfortable.

Conclusions in first-order logic:
∃x (TravelingTo(x, seattle) ∧ TravelingFrom(x, newYorkCity) ∧ uncomfortable(x))

Truth value of each conclusion (T = true, F = false, U = unknown):
T
Premises:
Thomas Barber was an English professional footballer.
Thomas Barber played in the Football League for Aston Villa.
Thomas Barber played as a halfback and inside left.
Thomas Barber scored the winning goal in the 1913 FA Cup Final.

Premises in first-order logic:
English(thomasBarber) ∧ ProfessionalFootballer(thomasBarber)
PlayedFor(thomasBarber, astonVilla) ∧ PlayedIn(astonVilla,theFootballLeague)
PlayedAs(thomasBarber, halfBack) ∧ PlayedAs(thomasBarber, insideLeft)
ScoredTheWinningGoalIn(thomasBarber, facupfinal1913)

Conclusions:
Thomas Barber played in the Football League for Bolton Wanderers
Thomas Barber played as an inside left.
An English professional footballer scored the winning goal in the 1913 FA Cup Final.

Conclusions in first-order logic:
PlayedFor(thomasBarber, boltonWanderers) ∧ PlayedIn(boltonWanderers,theFootballLeague)
PlayedAs(thomasBarber, insideLeft)
∃x (English(x) ∧ ProfessionalFootballer(x) ∧ ScoredTheWinningGoalIn(x, facupfinal1913))

Truth value of each conclusion (T = true, F = false, U = unknown):
U
T
T
Premises:
All high-quality scarves are made of wool, cashmere, or alpaca.
If a scarf is high quality, then it will be expensive. 
Some expensive products are not worth their prices. 
Experienced shoppers do not buy products that are not worth their prices.
Scarves are products. 

Premises in first-order logic:
∀x (Scarf(x) ∧ HighQuality(x) → (MadeOf(x, wool) ∨ MadeOf(x, cashmere) ∨ MadeOf(x, alpaca))
∀x ((Scarf(x) ∧ HighQuality(x)) → Expensive(x))
∃x (Expensive(x) ∧ ¬WorthTheirPrice(x))
∀x ((¬WorthTheirPrice(x) ∧ Product(x)) → ¬BoughtBy(x, experiencedShopper))
∀x (Scarf(x) → Product(x))

Conclusions:
Some scarves made of alpaca are not bought by experienced shoppers.

Conclusions in first-order logic:
∃x (Scarf(x) ∧ Alpaca(x) ∧ ¬BoughtBy(x, experiencedShopper))

Truth value of each conclusion (T = true, F = false, U = unknown):
U
Premises:
Events are either happy or sad.
At least one event is happy. 

Premises in first-order logic:
∀x (Event(x) → Happy(x) ⊕ Sad(x))
∃x (Event(x) ∧ Happy(x)) 

Conclusions:
All events are sad.

Conclusions in first-order logic:
∀x (Event(x) → Sad(x))

Truth value of each conclusion (T = true, F = false, U = unknown):
F
Premises:
All rabbits have fur
Some pets are rabbits.

Premises in first-order logic:
∀x (Rabbit(x) → Have(x, fur))
∃x (Pet(x) ∧ Rabbit(x))

Conclusions:
Some pets do not have fur.

Conclusions in first-order logic:
∃x ∃y (Pet(x) ∧ Pet(y) ∧ ¬Have(x, fur) ∧ ¬Have(y, fur))

Truth value of each conclusion (T = true, F = false, U = unknown):
U
Premises:
When the Monkeypox virus occurs in a being, it may get Monkeypox. 
Monkeypox virus can occur in certain animals.
Humans are mammals.
Mammals are animals.
Symptoms of Monkeypox include fever, headache, muscle pains, and tiredness. 
People feel tired when they get the flu.

Premises in first-order logic:
∃x (OccurIn(monkeypoxVirus, x) ∧ Get(x, monkeypoxVirus))
∃x (Animal(x) ∧ OccurIn(monkeypoxVirus, x))
∀x (Human(x) → Mammal(x))
∀x (Mammal(x) → Animal(x))
∃x (SymptonOf(x, monkeypoxVirus) ∧ (Fever(x) ∨ Headache(x) ∨ MusclePain(x) ∨ Tired(x)))
∀x (Human(x) ∧ Get(x, flu) → Feel(x, tired))

Conclusions:
There is an animal.
No one gets the flu.
Symptoms of Monkeypox include coughing.

Conclusions in first-order logic:
∃x (Animal(x))
∀x (Human(x) → ¬Get(x, flu))
∃x (SymptonOf(x, monkeypoxVirus) ∧ Coughing(x))

Truth value of each conclusion (T = true, F = false, U = unknown):
T
U
U
Premises:
Robert Zimmer was a philosopher born in Germany.
Robert Zimmer is an essayist.
Robert Zimmer was born in 1953.
Every essayist is a writer.

Premises in first-order logic:
BornIn(robertZimmer, germany) ∧ Philosopher(robertZimmer)
Essayist(robertZimmer)
BornIn(robertZimmer, yr1953)
∀x (Essayist(x) → Writer(x))

Conclusions:
Robert Zimmer is German.
Robert Zimmer is not a writer.
Robert Zimmer is a biographer.

Conclusions in first-order logic:
BornIn(robertZimmer, germany)
¬Writer(robertZimmer)
Biographer(robertZimmer)

Truth value of each conclusion (T = true, F = false, U = unknown):
U
F
U
Premises:
No reptile has fur.
All snakes are reptiles.

Premises in first-order logic:
∀x (Reptile(x) → ¬Have(x, fur))
∀x (Snake(x) → Reptile(x))

Conclusions:
Some snake has fur.

Conclusions in first-order logic:
∃x (Snake(x) ∧ Have(x, fur))

Truth value of each conclusion (T = true, F = false, U = unknown):
F
Premises:
All students who attend in person have registered for the conference. 
Students either attend the conference in person or remotely. 
No students from China attend the conference remotely. 
James attends the conference, but he does not attend the conference remotely.
Jack attends the conference, and he is a student from China.

Premises in first-order logic:
∀x (AttendInPerson(x) → Registered(x))
∀x (Attend(x) → (AttendInPerson(x) ⊕ AttendRemotely(x)))
∀x ((Attend(x) ∧ FromChina(x)) → ¬AttendRemotely(x))
Attend(james) ∧ (¬AttendRemotely(james))
FromChina(jack) ∧ Attend(jack)

Conclusions:
James attends the conference but not in person. 
Jack attends the conference in person.
Jack has registered for the conference.

Conclusions in first-order logic:
Attend(james) ∧ (¬AttendInPerson(james))
Attend(jack) ∧ AttendInPerson(jack)
Registered(jack)

Truth value of each conclusion (T = true, F = false, U = unknown):
F
T
T
Premises:
Ralph Hammerthaler was born in Wasserburg am Inn.
Wasserburg am Inn is in Germany.
Germany is in Europe.
Ralph Hammerthaler is a German writer.
Ralph Hammerthaler was born in 1965. 

Premises in first-order logic:
BornIn(ralphHammerthaler, wasserburgamInn)
LocatedIn(wasserbAmInn, germany)
LocatedIn(germany, europe)
Writer(ralphHammerthaler) ∧ German(ralphHammerthaler)
BornIn1965(ralphHammerthaler)

Conclusions:
Ralph Hammerthaler is a writer born in Asia.
Ralph Hammerthaler lives in Germany. 

Conclusions in first-order logic:
Writer(ralphHammerthaler) ∧ BornIn(ralphHammerthaler, asia)
LivesIn(ralphHammerthaler, germany)

Truth value of each conclusion (T = true, F = false, U = unknown):
U
U
Premises:
No flower is noisy.
Roses are flowers.

Premises in first-order logic:
∀x (Flower(x) → ¬Noisy(x))
∀x (Rose(x) → Flower(x))

Conclusions:
Some roses are noisy.

Conclusions in first-order logic:
∃x ∃y (Rose(x) ∧ Rose(y) ∧ Noisy(x) ∧ Noisy(y) ∧ ¬(x=y))

Truth value of each conclusion (T = true, F = false, U = unknown):
F
Premises:
Xiufeng, Xiangshan, Diecai, Qixing are districts in the city of Guilin.
Yangshuo is not a district in Guilin. 

Premises in first-order logic:
DistrictIn(xiufeng, guilin) ∧ DistrictIn(xiangshan, guilin) ∧ DistrictIn(diecai, guilin) ∧ DistrictIn(qixing, guilin) ∧ City(guilin)
¬DistrictIn(yangshuo, guilin)

Conclusions:
Xiangshan and Diecai are districts in the same city. 
Xiufeng is a district in Guilin. 
Kowloon District is in Hong Kong. 

Conclusions in first-order logic:
∃x (DistrictIn(xiangshan, x) ∧ DistrictIn(diecai, x) ∧ City(x))
DistrictIn(xiufeng, guilin)
DistrictIn(kowloon, hongKong)

Truth value of each conclusion (T = true, F = false, U = unknown):
T
T
U