yuansui/folio huggingface dataset:
Premises:
Shafaq-Asiman is a large complex of offshore geological structures in the Caspian Sea.
Baku is northwest of Shafaq-Asiman.
If place A is northwest of place B, then place B is southeast of place A.

Premises in first-order logic:
LargeComplex(shafaq-asiman) ∧ LargeComplex(shafaq-asiman) ∧ Offshore(shafaq-asiman) ∧ GeologicalStructures(shafaq-asiman) ∧ In(shafaq-asiman, caspiansea)
NorthwestOf(baku, shafaq-asiman)
∀x ∀y (NorthwestOf(x, y) → SoutheastOf(y, x))

Conclusions:
Baku is southeast of Shafaq-Asiman.
A large complex is southeast of Baku.
Baku is not northwest of offshore geological structures.

Conclusions in first-order logic:
SoutheastOf(baku, shafaq-asiman)
∃x (LargeComplex(x) ∧ SoutheastOf(x, baku))
∀x (GeologicalStructures(x) ∧ Offshore(x) → ¬NorthwestOf(baku, x))

Truth value of each conclusion (T = true, F = false, U = unknown):
U
T
F
Premises:
A roundel is a rounded artillery fortification.
A roundel is not higher than adjacent walls. 
Cannons can be deployed on artillery fortifications. 
Roundels are the oldest artillery fortifications.
Battery towers are artillery fortifications.

Premises in first-order logic:
∀x (Roundel(x) → (Rounded(x) ∧ ArtilleryFortification(x)))
∀x ∀y ((Roundel(x) ∧ AdjacentWalls(x,y)) → ¬Higher(x, y))
∀x (ArtilleryFortification(x) → DeployCannons(x))
∀x ∀y ((Roundel(x) ∧ ArtilleryFortification(y)) → Older(x, y))
∀x (BatteryTower(x) → ArtilleryFortification(x))

Conclusions:
Cannons can be deployed on battery towers. 
Roundels are older than battery towers.
Battery towers are higher than adjacent walls.
Cannons can be deployed on roundels.

Conclusions in first-order logic:
∀x (BatteryTower(x) → DeployCannons(x))
∀x ∀y ((Roundel(x) ∧ BatteryTower(y)) → Older(x, y))
∀x ∀y ((BatteryTower(x) ∧ AdjacentWall(x,y)) → Higher(x, y))
∀x (Roundel(x) → DeployCannons(x))

Truth value of each conclusion (T = true, F = false, U = unknown):
T
T
U
T
Premises:
No television stars are certified public accountants.
All certified public accountants have good business sense.

Premises in first-order logic:
∀x (TelevisionStar(x) → ¬CertifiedPublicAccoutant(x))
∀x (CertifiedPublicAccoutant(x) → Have(x, goodBusinessSense))

Conclusions:
All television stars have good business sense.

Conclusions in first-order logic:
∀x (TelevisionStar(x) → Have(x, goodBusinessSense))

Truth value of each conclusion (T = true, F = false, U = unknown):
U
Premises:
All devices belonging to the company are connected to Google Home. 
All devices belonging to employees are connected to the company's wifi. 
All devices connected to Google Home are controlled by the managers. 
All devices that connect to the company's wifi are easy to operate. 
ModelXX belongs to employees. 

Premises in first-order logic:
∀x (OwnedBy(x, company) → ConnectedTo(x, googleHome))
∀x (OwnedBy(x, employee) → ConnectedTo(x, companyWiFi))
∀x (ConnectedTo(x, googleHome) → ControlledBy(x, managers))
∀x (ConnectedTo(x, companyWiFi) → EasyToOperate(x))
OwnedBy(modelXX, employee)

Conclusions:
ModelXX is easy to operate. 
ModelXX is controlled by managers. 
ModelXX is connected to Google Home.

Conclusions in first-order logic:
EasyToOperate(modelXX)
ControlledBy(modelXX, managers)
ConnectedTo(modelXX, googleHome)

Truth value of each conclusion (T = true, F = false, U = unknown):
T
U
U
Premises:
A cutman is responsible for preventing and treating physical damage to a fighter.
Cutmen appear in boxing matches, kickboxing matches, or mixed martial arts matches bout. 
Cutmen handle swelling, nosebleeds and lacerations. 
Jack is a cutman.

Premises in first-order logic:
∀x (Cutman(x) → Prevent(x, physicalDamageToAFighter) ∧ Treat(x, physicalDamageToAFighter))
∀x (Cutman(x) → AppearIn(x, boxingMatch) ∨ AppearIn(x, kickboxingMatch) ∨ AppearIn(x, mixedMartialArtsMatchBout))
∀x (Cutman(x) → Handle(x, swelling) ∧ Handle(x, nosebleed) ∧ Handle(x, laceration))
Cutman(jack)

Conclusions:
No cutmen appear in boxing matches.
If someone is not a cutman, then they cannot handle nosebleeds.
Jack is responsible for treating physical damage to a fighter.

Conclusions in first-order logic:
¬(∃x (Cutman(x) ∧ AppearIn(x, boxingMatch)))
∀x (¬Cutman(x) → ¬Handle(x, nosebleed))
Treat(jack, physicalDamageToAFighter)

Truth value of each conclusion (T = true, F = false, U = unknown):
U
U
T
Premises:
Everyone who rents a car spends money.
Whenever Sarah goes to Vermont, Sarah drives there.
Someone who does not own a car to drive somewhere must either borrow a car or rent a car.
Sarah doesn’t own a car.
Sarah never borrows a car to go camping.
Sarah is going to go camping in Vermont.
To go camping somewhere, you must go to that place.

Premises in first-order logic:
∀x (Rent(x, car) → Spend(x, money))
GoTo(sarah, vermont) → DriveTo(sarah, vermont)
∀x ∀y (¬Own(x, car) ∧ DriveTo(x, y) → Borrow(x, car) ⊕ Rent(x, car))
¬Own(sarah, car)
∀x (Camping(sarah, x) → ¬(Borrow(sarah, car)))
Camping(sarah, vermont)
∀x ∀y (Camping(x, y) → GoTo(x, y))

Conclusions:
Sarah will spend money this weekend.

Conclusions in first-order logic:
Spend(sarah, money)

Truth value of each conclusion (T = true, F = false, U = unknown):
T
Premises:
If a person doesn't have enough money to buy a product, then that person can't buy it.
Monitors are products.
4k monitors are more expensive than 1080 monitors and 2k monitors.
John is a person.
John doesn't have enough money to buy a 2k monitor.

Premises in first-order logic:
∀x ∀y (Person(x) ∧ Product(y) ∧ ¬HaveEnoughMoneyFor(x, y) → ¬Buy(x, y))
∀x (Monitor(x) → Product(x))
∀x ∀y ∀z (Monitor(x) ∧ Monitor(y) ∧ Monitor(z) ∧ FourK(x) ∧ OneOEightO(y) ∧ TwoK(z) → MoreExpensive(x, y) ∧ MoreExpensive(x, z))
Person(john)
∀x (Monitor(x) ∧ TwoK(x) → ¬HaveEnoughMoneyFor(john, x))

Conclusions:
John can't buy a 1080 monitor.
John can't buy a 2k monitor.

Conclusions in first-order logic:
∀x (Monitor(x) ∧ OneOEightO(x) → ¬Buy(john, x))
∀x (Monitor(x) ∧ TwoK(x) → ¬Buy(john, x))

Truth value of each conclusion (T = true, F = false, U = unknown):
U
T
Premises:
Books contain tons of knowledge.
When a person reads a book, that person gains knowledge. 
If a person gains knowledge, they become smarter.
Harry read the book “Walden” by Henry Thoreau.

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

Conclusions:
Walden contains knowledge.
Harry is smarter than before. 
A smarter person has gained knowledge. 

Conclusions in first-order logic:
Gains(harry, knowledge)
Smarter(harry)
∀x (Smarter(x) → GainKnowledge(x))

Truth value of each conclusion (T = true, F = false, U = unknown):
T
T
U
Premises:
The Mona Lisa is a world's best-known painting.
The Mona Lisa is a portrait painted by Leonardo da Vinci.
Leonardo da Vinci was a scientist and painter.
Painting genres can be history, portrait, animal, landscape, and still life.

Premises in first-order logic:
Painting(monaLisa) ∧ TheWorldsBestKnown(monaLisa)
PaintedBy(monaLisa, leonardodaVinci) ∧ Portrait(monaLisa)
Scientist(leonardodaVinci) ∧ Painter(leonardodaVinci)
∀x (Painting(x) → (History(x) ∨ Portrait(x) ∨ Animal(x) ∨ Landscape(x) ∨ StillLife(x)))

Conclusions:
A world's best-known artwork is painted by a scientist.
Leonardo da Vinci has artworks in the landscape genre.
No world's best-known artworks are portraits.

Conclusions in first-order logic:
∃x ∃y (Painting(x) ∧ TheWorldsBestKnown(x) ∧ PaintedBy(x, y) ∧ Scientist(y))
∃x (PaintedBy(x, leonardodaVinci) ∧ Landscape(x))
∀x (WorldsBestKnown(x)  → ¬Portrait(x))

Truth value of each conclusion (T = true, F = false, U = unknown):
T
U
F
Premises:
Elation is pleasant.
If something is pleasant, it is positive.

Premises in first-order logic:
∀x (Elation(x) → Pleasant(x))
∀x (Pleasant(x) → Positive(x))

Conclusions:
Elation is not positive.

Conclusions in first-order logic:
∀x (Elation(x) → ¬Positive(x))

Truth value of each conclusion (T = true, F = false, U = unknown):
F
Premises:
Fort Ticonderoga is the current name for Fort Carillon.
Pierre de Rigaud de Vaudreuil built Fort Carillon.
Fort Carillon was located in New France.
New France is not in Europe.

Premises in first-order logic:
RenamedAs(fortCarillon, fortTiconderoga)
Built(pierredeRigauddeVaudreuil, fortCarillon)
LocatedIn(fortCarillon, newFrance)
¬LocatedIn(newFrance, europe) 

Conclusions:
Pierre de Rigaud de Vaudreuil built a fort in New France.
Pierre de Rigaud de Vaudreuil built a fort in New England.
Fort Carillon was located in Europe.

Conclusions in first-order logic:
∃x (Built(pierredeRigauddeVaudreuil, x) ∧ LocatedIn(x, newFrance))
∃x (Built(pierredeRigauddeVaudreuil, x) ∧ LocatedIn(x, newEngland))
LocatedIn(fortCarillon, europe)

Truth value of each conclusion (T = true, F = false, U = unknown):
T
U
U
Premises:
Soccer players have a right foot and a left foot.
Top soccer players are soccer players who can use both the left foot and right foot very efficiently.
If a soccer player can score many goals using the left foot, they can use that foot very efficiently.
If a soccer player can score many goals using the right foot, they can use that foot very efficiently.
Cristiano Ronaldo is a soccer player.
Cristiano Ronaldo can use his right foot very efficiently.
Cristiano Ronaldo has scored many goals using his left foot.

Premises in first-order logic:
∀x (SoccerPlayer(x) → Have(x, leftFoot) ∧ Have(x, rightFoot))
∀x (SoccerPlayer(x) ∧ UseEfficiently(x, leftFoot) ∧ UseEfficiently(x, rightFoot) → TopSoccerPlayer(x))
∀x (SoccerPlayer(x) ∧ ScoreUsing(x, manyGoals, leftFoot) → UseEfficiently(x, leftFoot))
∀x (SoccerPlayer(x) ∧ ScoreUsing(x, manyGoals, rightFoot) → UseEfficiently(x, rightFoot))
SoccerPlayer(ronaldo)
UseEfficiently(ronaldo, rightFoot)
ScoreUsing(ronaldo, manyGoals, leftFoot)

Conclusions:
Cristiano Ronaldo is a top soccer player. 
Cristiano Ronaldo is not a top soccer player. 

Conclusions in first-order logic:
TopSoccerPlayer(ronaldo)
¬TopSoccerPlayer(ronaldo)

Truth value of each conclusion (T = true, F = false, U = unknown):
T
F
Premises:
Lana Wilson directed After Tiller, The Departure, and Miss Americana.
If a film is directed by a person, the person is a filmmaker.
After Tiller is a documentary.
The documentary is a type of film.
Lana Wilson is from Kirkland.
Kirkland is a US city.
If a person is from a city in a country, the person is from the country.
After Tiller is nominated for the Independent Spirit Award for Best Documentary.

Premises in first-order logic:
DirectedBy(afterTiller, lanaWilson) ∧ DirectedBy(theDeparture, lanaWilson) ∧ DirectedBy(missAmericana, lanaWilson)
∀x ∀y (DirectedBy(x, y) → Filmmaker(y))
Documentary(afterTiller)
∀x (Documentary(x) → Film(x))
From(lanaWilson, kirkland)
In(kirkland, unitedStates)
∀x ∀y ∀z ((From(x, y) ∧ In(y, z)) → From(x, z))
Nomination(afterTiller, theIndependentSpiritAwardForBestDocumentary)

Conclusions:
Lana Wilson is a US filmmaker.
Miss Americana is not directed by a filmmaker from Kirkland.
Lana Wilson has won the Independent Spirit Award.

Conclusions in first-order logic:
From(lanaWilson, unitedStates) ∧ Filmmaker(lanaWilson)
¬(∃x(Filmmaker(x) ∧ From(x, kirkland) ∧ DirectedBy(missAmericana, x)))
FilmmakerAward(lanaWilson, theIndependentSpiritAwardForBestDocumentary)

Truth value of each conclusion (T = true, F = false, U = unknown):
T
F
U
Premises:
No man can run faster than Bolt. 
Superman is not a man.

Premises in first-order logic:
∀x (Man(x) → ¬RunFasterThan(xm bolt))
¬Man(superman)

Conclusions:
Superman can run faster than Bolt.

Conclusions in first-order logic:
RunFasterThan(superman, bolt) 

Truth value of each conclusion (T = true, F = false, U = unknown):
U
Premises:
Trees are plants. 
Some living things are trees.

Premises in first-order logic:
∀x (Tree(x) → Plant(x))
∃x ∃y (Living(x) ∧ Living(y) ∧ Tree(x) ∧ Tree(y) ∧ ¬(x=y))

Conclusions:
Some living things are plants.

Conclusions in first-order logic:
∃x ∃y (Living(x) ∧ Living(y) ∧ Plant(x) ∧ Plant(y) ∧ ¬(x=y))

Truth value of each conclusion (T = true, F = false, U = unknown):
T
Premises:
LanguageA is a universal language
If a universal language exists, then for every two people if they both know the same universal language they can communicate.
Katya cannot communicate with Danil.
Katya knows LanguageA. 

Premises in first-order logic:
UniversalLanguage(languageA)
∀x ∀y (∃z (¬(x=y) ∧ Know(x, z) ∧ Know(y, z) ∧ UniversalLanguage(z)) → CanCommunicateWith(x, y) ∧ CanCommunicateWith(y, x))
¬CanCommunicateWith(katya, danil)
Know(katya, languageA)

Conclusions:
Danil knows LanguageA.

Conclusions in first-order logic:
Know(danil, languageA)

Truth value of each conclusion (T = true, F = false, U = unknown):
F
Premises:
A hawk never swims. 
Some birds are hawks.

Premises in first-order logic:
∀x (Hawk(x) → ¬Swim(x))
∃x ∃y (Bird(x) ∧ Bird(y) ∧ Hawk(x) ∧ Hawk(y) ∧ ¬(x=y))

Conclusions:
All birds swim.

Conclusions in first-order logic:
∀x (Bird(x) → Swim(x))

Truth value of each conclusion (T = true, F = false, U = unknown):
F
Premises:
A podcast is not a novel.
If a person is born in American City, the person is American.
If a book is a novel and it is written by a person, then the person is a novel writer.
Dani Shapiro is an American writer.
Family History is written by Dani Shapiro.
Family History is a novel written in 2003.
Dani Shapiro created a podcast called Family Secrets.
Boston is an American city.

Premises in first-order logic:
∀x (Podcast(x) → ¬Novel(x))
∀x((∃y (BornIn(x, y) ∧ City(y) ∧ LocatedIn(y,america)) → American(x))
∀x ∀y ((Novel(x) ∧ WrittenBy(x, y)) → WritesNovel(y))
American(dani_Shapiro) ∧ Writer(dani_Shapiro)
WrittenBy(family_History, dani_Shapiro)
Novel(family_History) ∧ WrittenIn(family_History, yr2003)
Podcast(family_Secrets) ∧ CreatedBy(family_Secrets, dani_Shapiro)
City(boston) ∧ American(boston)

Conclusions:
Dani Shapiro is a novel writer.   
Family Secrets is a novel.        
Dani Shapiro was born in Boston.  

Conclusions in first-order logic:
WritesNovel(dani_Shapiro)
IsNovel(family_Secrets)
BornIn(dani_Shapiro, boston)

Truth value of each conclusion (T = true, F = false, U = unknown):
T
F
U
Premises:
A summarization model is always faithful if it uses content from the input documents.
Extractive models are summarization models.
An extractive model can only use content from the input documents.

Premises in first-order logic:
∀x (Model(x) ∧ Summarization(x) ∧ OnlyUseInputDocument(x) → Faithful(x))
∀x (Model(x) ∧ Extractive(x) → Model(x) ∧ Summarization(x))
∀x (Model(x) ∧ Extractive(x) → OnlyUseInputDocument(x))

Conclusions:
Extractive models are always faithful.
Extractive models are not always faithful.

Conclusions in first-order logic:
∀x (Model(x) ∧ Extractive(x) → Faithful(x))
∃x (Model(x) ∧ Extractive(x) ∧ ¬Faithful(x))

Truth value of each conclusion (T = true, F = false, U = unknown):
T
F
Premises:
Maggie Friedman is an American screenwriter and producer.
Maggie Friedman was the showrunner and executive producer of the lifetime television series Witches of East End.
Witches of East End is a fantasy-drama series.
Maggie Friedman produced and developed Eastwick.
Eastwick is a series by ABC.

Premises in first-order logic:
American(maggieFriedman) ∧ Screenwriter(maggieFriedman) ∧ Producer(maggieFriedman)
ShowRunnerOf(maggieFriedman, witchesOfEastEnd) ∧ ExecutiveProducerOf(maggieFriedman, witchesOfEastEnd) ∧ LifetimeTelevisionSeries(maggieFriedman)
FantasyDrama(witchesOfEastEnd) ∧ Series(witchesOfEastEnd)
Produces(maggieFriedman, eastwick) ∧ Develops(maggieFriedman, eastwick)
Series(eastwick) ∧ AiredOn(eastwick, aBC)

Conclusions:
There is a series by ABC that was developed by the showrunner of Witches of East End.
No series by ABC was developed by the showrunner of Witches of East End.
Maggie Friedman developed Witches of East End.

Conclusions in first-order logic:
∃x ∃y (Series(x) ∧ AiredOn(x, aBC) ∧ Develops(y, x) ∧ ShowRunnerOf(y, witchesOfEastEnd))
∀x (Series(x) ∧ AiredOn(x, aBC) ∧ ∃y (ShowRunnerOf(y, witchesOfEastEnd)) → ¬Develops(y, x))
Develops(maggieFriedman, witchesOfEastEnd)

Truth value of each conclusion (T = true, F = false, U = unknown):
T
F
U
Premises:
SR 287 is in Alabama.
Alabama is in the United States.
US 31 intersects with SR 287.
CR 47 intersects with SR 287.
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:
In(sR287, alabama)
In(alabama, unitedStates)
Intersect(uS31, sR287)
Intersect(cR47, sR287)
∀x ∀y ∀z ((In(x, y) ∧ In(y, z)) → In(x, z))

Conclusions:
US 31 is in Alabama.
CR 47 is not in Alabama.
SR 287 is in the United States.

Conclusions in first-order logic:
In(uS31, alabama)
¬In(cR47, alabama)
In(sR287, unitedStates)

Truth value of each conclusion (T = true, F = false, U = unknown):
U
U
T
Premises:
All nuclear-powered submarines are warships.
No nuclear-powered submarines are commercial vessels.

Premises in first-order logic:
∀x (NuclearPoweredSubmarine(x) → Warship(x))
∀x (NuclearPoweredSubmarine(x) → ¬CommercialVessel(x))

Conclusions:
No warships are commercial vessels.

Conclusions in first-order logic:
∀x (Warship(x) → ¬CommercialVessel(x))

Truth value of each conclusion (T = true, F = false, U = unknown):
U
Premises:
Six, seven and eight are real numbers.
If a real number equals another real number added by one, the first number is larger.
If the number x is larger than the number y, then y is not larger than x.
Seven equals six plus one.
Eight equals seven plus one.
Two is positive.
If a number is positive, then the double of it is also positive.
Eight is the double of four.
Four is the double of two.

Premises in first-order logic:
RealNum(num6) ∧ RealNum(num7) ∧ RealNum(num8)
∀x ∀y ((RealNum(x) ∧ RealNum(y) ∧ IsSuccessorOf(x, y)) → Larger(x, y))
∀x ∀y (Larger(x, y) → ¬Larger(y, x))
∃x (IsSuccessorOf(x, num6) ∧ Equals(num7, x))
∃x (IsSuccessorOf(x, num7) ∧ Equals(num8, x))
Positive(num2)
∀x ∀y ((Positive(x) ∧ IsDouble(y, x)) → Positive(y))
IsDouble(num8, num4)
IsDouble(num4, num2)

Conclusions:
Eight is larger than seven.
Eight is positive.
Six is larger than seven.

Conclusions in first-order logic:
Larger(eight, seven)
Positive(eight)
Larger(six, seven)

Truth value of each conclusion (T = true, F = false, U = unknown):
T
T
F
Premises:
Wildfeed exists as an unannounced program.
Wildfeed can be sporting events, news, or syndicated shows.
Pre-recorded content is a copyright violation.
Programs are pre-recorded.

Premises in first-order logic:
∃x (Wildfeed(x) ∧ Unannounced(x) ∧ Program(x))
∀x (Wildfeed(x) → SportingEvent(x) ∨ News(x) ∨ SyndicatedShow(x))
∀x (Prerecorded(x) → CopyrightViolation(x))
∀x (Program(x) → Prerecorded(x))

Conclusions:
Some wildfeed is violating copyright laws.
Wildfeed can be prerecorded. 
Syndicated shows are copyright violations.

Conclusions in first-order logic:
∃x (Wildfeed(x) ∧ CopyrightViolation(x))
∃x (Wildfeed(x) ∧ Prerecorded(x))
∃x (SyndicatedShows(x) ∧ CopyrightViolation(x))

Truth value of each conclusion (T = true, F = false, U = unknown):
T
T
U
Premises:
Beijing is the capital of the People's Republic of China. 
Beijing is the capital city of the world's most populous nation.
Beijing is located in Northern China.
Beijing hosted the 2008 Summer Olympics and 2008 Summer Paralympics Games.
Beijing has hosted the Summer and Winter Olympics and the Summer and Winter Paralympics.
Many of Beijing's 91 universities consistently rank among the best universities in the world.

Premises in first-order logic:
CapitalOf(beijing, peoplesRepublicOfChina)
∃x (CapitalOf(beijing, x) → WorldsMostPopulousNation(x))
LocatedIn(beijing, northernChina)
Hosted(beijing, 2008SummerOlympics) ∧ Hosted(beijing, 2008SummerParalympicGames)
Hosted(beijing, summerOlympics) ∧ Hosted(beijing, winterOlympics) ∧ Hosted(beijing, summerParalympicGames)  ∧ Hosted(beijing, winterParalympicGames)
∃x (University(x) ∧ InBeijing(x) ∧ ConsistentlyRankAmongTheBestIn(x, theWorld))

Conclusions:
Beijing hosted both the 2008 Summer Olympics and the Winter Olympics. 
Beijing is located in southern China.
Beijing is the second largest Chinese city.

Conclusions in first-order logic:
Hosted(beijing, summerOlympics) ∧ Hosted(beijing, winterOlympics)
LocatedIn(beijing, southernChina)
SecondLargestChineseCity(beijing)

Truth value of each conclusion (T = true, F = false, U = unknown):
T
U
U
Premises:
All CD players are delicate mechanisms.
No delicate mechanisms are suitable toys for children.

Premises in first-order logic:
∀x (CDPlayer(x) → DelicateMechanism(x))
∀x (DelicateMechanism(x) → ¬(Toy(x) ∧ SuitableFor(x, children)))

Conclusions:
Some CD players are suitable toys for children.

Conclusions in first-order logic:
∃x ∃y (CDPlayer(x) ∧ CDPlayer(y) ∧ Toy(x) ∧ Toy(y) ∧ SuitableFor(x, children) ∧ SuitableFor(y, children) ∧ ¬(x=y))

Truth value of each conclusion (T = true, F = false, U = unknown):
U
Premises:
John will go to the cinema if and only if Jack goes to the cinema today.
Jack will go to the cinema if and only if Iron Man is on and the weather is not bad today.
Some days in March have bad weather.
Iron Man is on.
It's March now.

Premises in first-order logic:
(GoTo(john, theCinema) ∧ GoTo(john, today)) ↔ GoTo(jack, theCinema) ∧ GoTo(jack, today)
(GoTo(john, theCinema) ∧ GoTo(john, today)) ↔ (On(ironman) ∧ ¬Bad(weather, today))
∃x (Day(x) ∧ March(x) → ¬Bad(weather, x))
On(ironman)
Day(presentMoment) ∧ March(presentMoment)

Conclusions:
John will go to the cinema. 
The weather is good today. 

Conclusions in first-order logic:
GoTo(john, theCinema) ∧ GoTo(john, today)
¬Bad(weather, today)

Truth value of each conclusion (T = true, F = false, U = unknown):
U
U
Premises:
Phuoc Binh national park is a national park in Vietnam. 
Any national park in Vietnam is classified as a nature reserve. 
There is a national park in Vietnam classified as a UNESCO World Heritage Site.
All national parks in Vietnam are either managed by the Ministry of Agriculture or managed by the People's Committee. 
Phuoc Binh is not managed by the Ministry of Agriculture.

Premises in first-order logic:
NationalPark(phuocBinh) ∧ Locatedin(phuocBinh, vietnam)
∀x ((NationalPark(x) ∧ Locatedin(x, vietnam)) → NatureReserve(x))
∃x (NationalPark(x) ∧ Locatedin(x, vietnam) ∧ UNESCOWorldHeritageSite(x))
∀x ((NationalPark(x) ∧ Locatedin(x, vietnam)) → (Mangedby(x, ministryofAgriculture) ⊕ Managedby(x, peoplesCommittee)))
¬Mangedby(phuocBinh, ministryofAgriculture)

Conclusions:
There is a nature reserve in Vietnam. 
Phuoc Binh is a UNESCO Heritage Site. 
Phuoc Binh is managed by the People's Committee. 

Conclusions in first-order logic:
∃x (NatureReserve(x) ∧ LocatedIn(x, vietnam))
UNESCOWorldHeritageSite(phuocBinh))
Mangedby(phuocBinh, peoplesCommittee)

Truth value of each conclusion (T = true, F = false, U = unknown):
T
U
T
Premises:
Ailton Silva, born in 1995, is commonly known as Ailton.
Ailton is a football player who was loaned out to Braga.
Ailton Silva is a Brazilian footballer who plays for Náutico.
Náutico is a football club along with Braga.
Fluminense is a football club.

Premises in first-order logic:
BornIn(ailtonSilva, year1995) ∧ CommonlyKnownAs(ailtonSilva, ailton)
FootballPlayer(ailton) ∧ LoanedTo(ailton, braga)
Brazilian(ailtonSilva) ∧ Footballplayer(ailtonSilva) ∧ PlayFor(ailtonSilva, nautico)
FootballClub(nautico) ∧ FootballClub(braga)
FootballClub(fluminense)

Conclusions:
No one playing for Nautico is Brazilian.
Ailton Silva does not play for a football club.
Ailton was not loaned out to a football club.
Ailton Silva played for Fluminense.
Ailton Silva was loaned out to a football club.

Conclusions in first-order logic:
∀x (PlayFor(x, nautico) → ¬Brazilian(x))
∀x (FootballClub(x) → ¬PlayFor(ailtonSilva, x))
∀x (FootballClub(x) → ¬LoanedTo(ailton, x))
PlayFor(ailtonSilva, fluminense)
∃x (FootballClub(x) ∧ LoanedTo(ailtonSilva, x))

Truth value of each conclusion (T = true, F = false, U = unknown):
F
F
F
U
U
Premises:
All squares are four-sided.
All four-sided things are shapes. 

Premises in first-order logic:
∀x (Square(x) → FourSided(x))
∀x (FourSided(x) → Shape(x))

Conclusions:
All squares are shapes.

Conclusions in first-order logic:
∀x (Square(x) → Shape(x))

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