yuansui/folio huggingface dataset:
Premises:
No iPhones are standalone desktops. 
All Apple-made cellphones are iPhones.  
All phones with A15 Bionic chips are Apple-made cell phones. 
All phones equipped with four core-GPU made by Apple are phones with A15 Bionic chips. 
If an unannounced Huawei phone is either a phone with A15 Bionic chips or equipped with four core-GPU made by Apple, then unannounced Huawei phone is neither a phone with A15 Bionic chips nor a standalone desktop.

Premises in first-order logic:
∀x (IPhone(x) → ¬StandaloneDesktop(x))
∀x (AppleMade(x) ∧ Cellphone(x) → IPhone(x))
∀x (Phone(x) ∧ With(x, a15BionicChip) → AppleMade(x) ∧ Cellphone(x))
∀x (Phone(x) ∧ EquippedWith(x, fourCoreGPU) ∧ MadeBy(x, apple) → Phone(x) ∧ With(x, a15BionicChip))
(Phone(unannouncedHuaweiPhone) ∧ With(unannouncedHuaweiPhone, a15BionicChip)) ⊕ (Phone(unannouncedHuaweiPhone) ∧ EquippedWith(unannouncedHuaweiPhone, fourCoreGPU) ∧ MadeBy(unannouncedHuaweiPhone, apple)) → ¬(Phone(unannouncedHuaweiPhone) ∧ With(unannouncedHuaweiPhone, a15BionicChip) ∧ StandaloneDesktop(unannouncedHuaweiPhone))

Conclusions:
Joe is a person taking classes. 
Joe is a PhD student. 
Joe is not a PhD student. 

Conclusions in first-order logic:
AppleMade(unannouncedHuaweiPhone) ∧ Cellphone(unannouncedHuaweiPhone)
Phone(unannouncedHuaweiPhone) ∧ EquippedWith(unannouncedHuaweiPhone, fourCoreGPU) ∧ MadeByApple(unannouncedHuaweiPhone)
¬(Phone(unannouncedHuaweiPhone) ∧ EquippedWith(unannouncedHuaweiPhone, fourCoreGPU) ∧ MadeByApple(unannouncedHuaweiPhone))

Truth value of each conclusion (T = true, F = false, U = unknown):
U
F
T
Premises:
A Unix operating system used in the lab computers is a piece of software.
All versions of MacOS used in the lab computer are based on Unix operating systems.
A lab computer uses either MacOS or Linux. 
All Linux computers in the lab are convenient.
All software used in the lab computers is written with code.
If something is convenient in the lab computer, then it is popular.
Burger is used in the lab computer, and it is written with code and a new version of MacOS.
PyTorch is used in the lab computer, and PyTorch is neither a Linux system nor a piece of software.

Premises in first-order logic:
∀x (UsedIn(x, labComputer) ∧ UnixOperatingSystem(x) → Software(x))
∀x (UsedIn(x, labComputer) ∧ MacOS(x) → UnixOperatingSystem(x))
∀x (UsedIn(x, labComputer) → MacOS(x) ⊕ Linux(x))
∀x (UsedIn(x, labComputer) ∧ Linux(x) → Convenient(x))
∀x (UsedIn(x, labComputer) ∧ Software(x) → WrittenWithCode(x))
∀x (UsedIn(x, labComputer) ∧ Convenient(x) → Popular(x))
UsedIn(burger, labComputer) ∧ WrittenWithCode(burger) ∧ MacOS(burger))
UsedIn(pytorch, labComputer) ∧ ¬(Linux(pytorch) ⊕ Software(pytorch))

Conclusions:
Burger is popular.
Burger is not popular.
PyTorch is popular and written with code.
PyTorch is not popular and it is not written with code.

Conclusions in first-order logic:
Popular(burger)
¬Popular(burger)
Popular(pytorch) ∧ WrittenWithCode(pytorch)
¬(Popular(pytorch) ∧ WrittenWithCode(pytorch))

Truth value of each conclusion (T = true, F = false, U = unknown):
U
U
T
F
Premises:
Hermès bags are not made in Italy.
All Birkin bags are Hermès bags. 
All Ferraris are made in Italy. 
All cars that carry a Ferrari V12 engine are Ferraris. 
All cars that are made in Maranello carry a Ferrari V12 engine.
A Lamborghini SUV is not both a Ferrari and made in Maranello. 
A Kelly bag is a Hermès bag, or it is a car that carries a Ferrari V12 engine. 

Premises in first-order logic:
∀x ((Bag(x) ∧ Hermès(x)) → ¬MadeIn(x, italy))
∀x ((Bag(x) ∧ Birkin(x)) → Hermès(x))
∀x (Ferrari(x) → MadeIn(x, italy))
∀x ((Car(x) ∧ Carry(x, ferrariV12Engine)) → Ferrrari(x))
∀x ((Car(x) ∧ MadeIn(x, maranello)) → Carry(x, ferrariV12Engine))
¬(Ferrari(lamborghiniSUV) ∧ MadeIn(lamborghiniSUV, maranello))
(Bag(kelly) ∧ Hermès(kelly)) ∨ (Bag(kelly) ∧ Car(kelly) ∧ Carry(kelly, ferrariV12Engine))

Conclusions:
A Lamborghini SUV is made in Italy.
A Lamborghini SUV is not made in Italy.
A Kelly bag is a Birkin bag made in Maranello.
A Kelly bag is not both made in Maranello and a Birkin bag.

Conclusions in first-order logic:
MadeIn(lamborghiniSUV, italy)
¬MadeIn(lamborghiniSUV, italy)
Bag(kelly) ∧ MadeIn(kelly, maranello) ∧ Birkin(kelly)
Bag(kelly) ∧ ¬(MadeIn(kelly, maranello) ∧ Birkin(kelly))

Truth value of each conclusion (T = true, F = false, U = unknown):
U
U
F
T
Premises:
All imaginative processes that Dan knows are results of creative processes.
All science fiction that Dan knows comes from an imaginative process.
Everthing that Dan knows comes from either science-fiction or realistic fiction.
No facts that Dan knows have proven to be false.
Dan knows that Dune is science fiction or has proven to be false.

Premises in first-order logic:
∀x ((Knows(dan, x) ∧ ImaginativeProcess(x)) → ResultOf(x, creativeProcess))
∀x ((Knows(dan, x) ∧ ScienceFiction(x)) → ImaginativeProcess(x)) 
∀x (Knows(dan, x) → (ScienceFiction(x) ⊕ RealisticFiction(x)))
∀x ((Knows(dan, x) ∧ Fact(x)) → ¬ProvedToBe(x, false)) 
(Knows(dan, dune) ∧ ScienceFiction(dune)) ∨ ProvedToBe(dune, false))

Conclusions:
Dune is realistic fiction.
Dune is a result of creative and imaginative process. 
Dune is either a result of creative processes or came from an imaginative process. 
Dune is a result of creative processes and is science fiction. 
Dune is either a result of creative processes or is science fiction. 
If Dune is a result of creative and imaginative processes, then Dune is not a result of creative processes and science-fiction. 
If Dune is either a fact and a result of creative processes, or neither a fact nor a result of creative processes, then Dune is a result of creative processes and science-fiction. 
If Dune is science-fiction, then Dune is not a result of creative processes and science-fiction. 
If Dune is not a result of creative processes and science-fiction, then Dune neither came from an imaginative process nor proved to be false. 
If Dune is did not come from imaginative process and is not science-fiction, then Dune is neither a result of creative processes nor came from an imaginative process.

Conclusions in first-order logic:
RealisticFiction(dune)
ResultOf(dune, creativeProcess) ∧ ImaginativeProcess(dune)
ResultOf(dune, creativeProcess) ⊕ ImaginativeProcess(dune)
ResultOf(dune, creativeProcess) ∧ ScienceFiction(dune))
Knows(dan, dune) ∧ (ResultOf(dune, creativeProcess)  ⊕ ScienceFiction(dune)) 
(ResultOf(dune, creativeProcess)  ∧ ImaginativeProcess(dune)) → (¬ResultOf(dune, creativeProcess) ∧ ¬ScienceFiction(dune))
Knows(dan, dune) ∧ (¬(Fact(dune) ⊕ ResultOf(dune, creativeProcess))) → (ResultOf(dune, creativeProcess) ∧ ScienceFiction(dune))
Knows(dan, dune) ∧ (ScienceFiction(dune)) → (¬(ResultOf(dune, creativeProcess)  ∧ ScienceFiction(dune)))
Knows(dan, dune) ∧ (¬(ResultOf(dune, creativeProcess)  ∧ ScienceFiction(dune))) → (¬(ImaginativeProcess(dune) ∨ ProvedToBe(dune, false)))
Knows(dan, dune) ∧ (¬(ImaginativeProcess(dune) ∧ ScienceFiction(dune))) → (¬(ResultOf(dune, creativeProcess)  ∨ ImaginativeProcess(dune)))

Truth value of each conclusion (T = true, F = false, U = unknown):
U
T
F
T
F
F
T
F
T
T
Premises:
If people work well in teams in the workplace, then they get along with all their colleagues at their work.
If people come to work every day with a positive attitude, then they work well in teams in the workplace.
People either come to work every day with a positive attitude or are always tired every morning.
If people are always tired in the morning, then they are criticized by their boss.
If people are criticized by their boss, then they do not receive positive feedback from teams at work.
Kat either is a person who works well in teams in the workplac and is always tired every morning, or she is neither.

Premises in first-order logic:
∀x (WorkWellInTeamsIn(x, workPlace) → ∀y (Colleague(y) ∧ GetAlongWithAtWork(x, y)))
∀x (ComeToWorkWithEveryDay(x, positiveAttitude) → WorkWellInTeamsIn(x, workPlace))
∀x (ComeToWorkWithEveryDay(x, positiveAttitude) ⊕ AlwaysTiredInMorning(x))
∀x (AlwaysTiredInMorning(x) → CriticizedBy(x, boss))
∀x (CriticizedBy(x, boss) → ¬ReceiveFromAtWork(x, positiveFeedback, team))
¬(WorkWellInTeamsIn(kat, workPlace) ⊕ Tired(kat))

Conclusions:
Kat is a person who comes to work every day with a positive attitude.
Kat gets along with her colleagues at her work and receives positive feedback from teams at her work.
Kat either gets along with her colleagues at her work or receives positive feedback from teams at her work.

Conclusions in first-order logic:
ComeToWorkWithEveryDay(kat, positiveAttitude)
(∀y (Colleague(y) ∧ GetAlongWithAtWork(kat, y))) ∧ ReceiveFromAtWork(kat, positiveFeedback, team)
(∀y (Colleague(y) ∧ GetAlongWithAtWork(kat, y))) ⊕ ReceiveFromAtWork(kat, positiveFeedback, team)

Truth value of each conclusion (T = true, F = false, U = unknown):
U
F 
T
Premises:
People on the payroll are being paid by the school.
If someone has a job at a school, then they are on the payroll.
All faculty members have a job at a school.
If someone teaches students, they are a faculty member or a teacher.
Every teacher has students.
If Nancy is a teacher, then they are on the payroll.
If Nancy is not a teacher, then they are not paid by the school.
Nancy teaches students.

Premises in first-order logic:
∀x (OnPayroll(x) → PaidBy(x, school))
∀x (HaveJobAt(x, school) → OnPayroll(x))
∀x (FacultyMember(x) → HaveJobAt(x, school))
∀x (Teach(x, student) → FacultyMember(x) ∨ Teacher(x))
∀x (Teacher(x) → Have(x, student))
Teacher(nancy) → OnPayroll(nancy)
¬Teacher(nancy) → ¬OnPayroll(nancy)
Teach(nancy, student)

Conclusions:
Nancy is a faculty member.
Nancy is paid by the school and has students.
Nancy is not paid by the school or does not have students.

Conclusions in first-order logic:
FacultyMember(nancy)
PaidBy(nancy, school) ∧ Have(nancy, student)
¬PaidBy(nancy, school) ∨ ¬Have(nancy, student))

Truth value of each conclusion (T = true, F = false, U = unknown):
U
T
F
Premises:
None of the easy Leetcode problems have an AC rate lower than 20 percent. 
All Leetcode problems recommended to novices are easy. 
Leetcode problems either have an AC rate lower than 20 percent or are starred by more than 1 thousand users. 
All hard Leetcode problems are starred by more than 1,000 users. 
No Leetcode problems published after 2022 are starred by more than 1,000 users. 
'2Sum' is not both hard and also recommended to novices.
'4Sum' is either starred by more than 1,000 users and published after 2022, or it is neither. 

Premises in first-order logic:
∀x ((LeetcodeProblems(x) ∧ Easy(x)) → ¬HaveAnACRateLowerThan(x, percent20))
∀x ((LeetcodeProblems(x) ∧ RecommendedTo(x, novices)) → Easy(x))
∀x (LeetcodeProblems(x) → HaveAnACRateLowerThan(x, percent20) ⊕ StarredByMoreThan(x, num1000))
∀x ((LeetcodeProblems(x) ∧ Hard(x)) → StarredByMoreThan(x, num1000))
∀x ((LeetcodeProblems(x) ∧ PublishedAfter(x, yr2022)) → (¬StarredByMoreThan(x, num1000)))
¬(RecommendedTo(twosum, novices) ∧ Hard(twosum)) ∧ LeetcodeProblems(twosum)
¬(StarredByMoreThan(foursum, num1000) ⊕ PublishedAfter(foursum, yr2022)) ∧ LeetcodeProblems(twosum)

Conclusions:
2Sum is an easy Leetcode problem. 
2Sum is not an easy Leetcode problem. 
4Sum is recommended to novices or is hard. 
4Sum is neither recommended to the novice nor a Leetcode problem that's hard.

Conclusions in first-order logic:
LeetcodeProblems(twosum) ∧ Easy(twosum)
¬(LeetcodeProblems(twosum) ∧ Easy(twosum))
RecommendedTo(foursum, novices) ∨ Hard(foursum)
¬RecommendedTo(foursum, novices) ∧ ¬Hard(foursum)

Truth value of each conclusion (T = true, F = false, U = unknown):
U
U
F
T
Premises:
Every instrument in the percussion section is either an idiophone or a membranophone.
Idiophones in the percussion section vibrate their primary body.
Membranophones in the percussion section vibrate a stretched membrane.
Every instrument in the percussion section that vibrates its primary body also tunes by sanding.
Every instrument in the percussion section that vibrates a stretched membrane also tunes by tightening.
Timpani in the percussion section are tuned by tightening.
Xylophones in the percussion section are not tuned by tightening.
The snare drum is in the percussion section; and either is both a timpani and is tuned by standing, or neither. 

Premises in first-order logic:
∀x (Instrument(x) ∧ In(x, percussionSection) → Idiophone(x) ⊕ Membranophone(x))
∀x (Instrument(x) ∧ In(x, percussionSection) ∧ Idiophone(x) → Vibrate(x, primaryBody))
∀x (Instrument(x) ∧ In(x, percussionSection) ∧ Membranophone(x) → Vibrate(x, stretchedMembrane))
∀x (Instrument(x) ∧ In(x, percussionSection) ∧ Vibrate(x, primaryBody) → TuneBySanding(x))
∀x (Instrument(x) ∧ In(x, percussionSection) ∧ Vibrate(x, stretchedMembrane) → TuneByTightening(x))
∀x (Instrument(x) ∧ In(x, percussionSection) ∧ Timpani(x) → TunedByTightening(x))
∀x (Instrument(x) ∧ In(x, percussionSection) ∧ Xylophone(x) → ¬TunedByTightening(x))
Instrument(snareDrum) ∧ In(snareDrum, percussionSection) ∧ ¬(Timpani(snareDrum) ⊕ TunedBySanding(snareDrum))

Conclusions:
The snare drum is a timpani.
The snare drum is not a timpani.
The snare drum is a xylophone.
The snare drum is a xylophone or tuned by tightening.
The snare drum is either a xylophone or tuned by tightening.

Conclusions in first-order logic:
Timpani(snareDrum)
¬Timpani(snareDrum)
Xylophone(snareDrum)
Xylophone(snareDrum) ∨ TunedByTightening(snareDrum)
Xylophone(snareDrum) ⊕ TunedByTightening(snareDrum)

Truth value of each conclusion (T = true, F = false, U = unknown):
U
U
F
T
T
Premises:
All pets in my house are either cats or dogs.
All the dogs in my house bark.
Ghosts do not exist.
If some pet in my house barks, then it is not dead.
All of the pets in my house are either dead or alive.
Jojo is a pet in my house, and it is not alive.

Premises in first-order logic:
∀x (Pet(x) ∧ In(x, myHouse) → Cat(x) ⊕ Dog(x))
∀x (Dog(x) ∧ In(x, myHouse) → Bark(x))
∀x (¬Ghost(x))
∀x (Bark(x) ∧ Pet(x) ∧ In(x, myHouse) → ¬Dead(x))
∀x (Pet(x) ∧ In(x, myHouse) → Dead(x) ⊕ Alive(x))
Pet(jojo) ∧ InMyHouse(jojo)∧ ¬Alive(jojo)

Conclusions:
Jojo is a ghost.
Jojo is a cat or a ghost.
If Jojo is a cat or a ghost, then Jojo either barks or is a dog.

Conclusions in first-order logic:
Ghost(jojo)
Cat(jojo) ∨ Ghost(jojo)
Cat(jojo) ∨ Ghost(jojo) → Bark(jojo) ⊕ Dog(jojo)

Truth value of each conclusion (T = true, F = false, U = unknown):
F
T
F
Premises:
All mind-reading is either brain reading or brain decoding. 
All brain decoding that is mind-reading is extracting information from BOLD signals.
No studies that are mind-reading and extract information from BOLD signals are without statistical pattern analysis. 
Writing a novel is without statistical pattern analysis.
If multivoxel (pattern) analysis is without statistical pattern analysis and a brain reading, then multivoxel (pattern) analysis is without statistical pattern analysis and brain decoding.
Multivoxel (pattern) analysis is a type of mind-reading.

Premises in first-order logic:
∀x (MindReading(x) ∧ (BrainReading(x) ⊕ BrainDecoding(x)))
∀x ((MindReading(x) ∧ BrainDecoding(x)) → ExtractingFrom(x, information, bOLDSignals))
∀x ((MindReading(x) ∧ ExtractingFrom(x, information, bOLDSignals)) → Uses(x, statisticalPatternAnalysis))
∀x (NovelWriting(x) → ¬Uses(x, statisticalPatternAnalysis)) 
MindReading(multivoxelPatternAnalysis) ∧ (¬Uses(multivoxelPatternAnalysis, statisticalPatternAnalysis) ∧ BrainReading(multivoxelPatternAnalysis)) →  (¬Uses(multivoxelPatternAnalysis, statisticalPatternAnalysis) ∧ (¬BrainDecoding(multivoxelPatternAnalysis)))
MindReading(multivoxelPatternAnalysis) 

Conclusions:
Multivoxel (pattern) analysis is a brain decoding. 
Multivoxel (pattern) analysis is the writing of a novel. 
Multivoxel (pattern) analysis is without statistical pattern analysis and writing a novel. 
Multivoxel (pattern) analysis is without statistical pattern analysis or writing a novel. 
Multivoxel (pattern) analysis is either without statistical pattern analysis or writing a novel. 
If multivoxel (pattern) analysis is writing a novel, then multivoxel (pattern) analysis is neither without statistical pattern analysis nor writing a novel.

Conclusions in first-order logic:
MindReading(multivoxelPatternAnalysis) ∧ BrainDecoding(multivoxelPatternAnalysis)
MindReading(multivoxelPatternAnalysis) ∧ NovelWriting(multivoxelPatternAnalysis)
¬(Uses(multivoxelPatternAnalysis, statisticalPatternAnalysis) ∧ NovelWriting(multivoxelPatternAnalysis))
¬(Uses(multivoxelPatternAnalysis, statisticalPatternAnalysis) ∨ NovelWriting(multivoxelPatternAnalysis))
¬Uses(multivoxelPatternAnalysis, statisticalPatternAnalysis) ⊕ Writing(multivoxelPatternAnalysis, aNovel)
(MindReading(multivoxelPatternAnalysis) ∧ NovelWriting(multivoxelPatternAnalysis)) → (Uses(multivoxelPatternAnalysis, statisticalPatternAnalysis) ∨ ¬NovelWriting(multivoxelPatternAnalysis))

Truth value of each conclusion (T = true, F = false, U = unknown):
U
F
F
F
F
T
Premises:
If people play competitive equestrian polo, then they are not expected to prepare for standardized exams.
If people are world-class at horse riding and polo, then they play competitive equestrian polo.
If people are expected to become a doctor or lawyers after school, then they are expected to prepare for standardized exams.
If people are expected to get high-paying and stable careers, then they are expected to become a doctor or a lawyer after school.
People who are nominated the CRA reward during the undergraduate study are expected to get high paying, stable careers. 
Riley either both is expected to get a high paying, stable career and expected to prepare for standardized exams, or she neither is expected to get a high paying, stable career nor expected to prepare for standardized exams.

Premises in first-order logic:
∀x (Play(x, competitiveEquestrianPolo) → ¬ExpectedToPrepareFor(x, standardizedExam))
∀x (WorldClassAt(x, horseRiding) ∧ WorldClassAt(x, polo) → Play(riley, competitiveEquestrianPolo))
∀x (ExpectedToBecome(x, doctor) ∨ ExpectedToBecome(x, lawyer) → ExpectedToPrepareFor(x, standardizedExam))
∀x (ExpectedToGet(x, highPayingCareer) ∧ ExpectedToGet(x, stableCareer) → ExpectedToBe(x, doctor) ∨ ExpectedToBe(x, lawyer))
∀x (Nominated(x, cRAAward) → ExpectedToGet(x, highPayingCareer) ∧ ExpectedToGet(x, stableCareer))
¬((ExpectedToGet(riley, highPayingCareer) ∧ ExpectedToGet(riley, stableCareer)) ⊕ ExpectedToPrepareFor(riley, standardizedExam))

Conclusions:
Riley is world-class at horse riding and polo.
Riley is nominated the CRA reward during the undergraduate study.
Riley either plays competitive equestrian polo or, if she does not, then she is nominated the CRA reward during the undergraduate study.

Conclusions in first-order logic:
WorldClassAt(x, horseRiding) ∧ WorldClassAt(x, polo)
Nominated(riley, cRAAward)
Play(riley, competitiveEquestrianPolo) ⊕ Nominated(riley, cRAAward)

Truth value of each conclusion (T = true, F = false, U = unknown):
U
U
U
Premises:
Tipped employees are not entitled to be paid the federal minimum wage by their employees. 
If a person is a white-collar worker, they are entitled to be paid the federal minimum wage by their employees. 
All lawyers are white-collar workers.
Every advocate is a lawyer.
Mary is not a lawyer or a tipped employee.

Premises in first-order logic:
∀x (TippedEmployee(x) → ¬EntitledTo(x, federalMinimumWage))
∀x (WhiteCollarWorker(x) → EntitledTo(x, federalMinimumWage))
∀x (Lawyer(x) → WhiteCollarWorker(x))
∀x (Advocate(x) → Lawyer(x))
¬(Lawyer(mary) ⊕ TippedEmployee(mary))

Conclusions:
Mary is a white-collar worker.
Mary is an advocate.
Mary is not an advocate.
Mary is either an advocate or a tipped employee.
If Mary is not both an advocate and is entitled to be paid the federal minimum wage by their employees, she is not a tipped employee.
If Mary is either an advocate or a tipped employee, she is an advocate.

Conclusions in first-order logic:
WhiteCollarWorker(mary)
Advocate(mary)
¬Advocate(mary)
Advocate(mary) ⊕ TippedEmployee(mary)
(¬(Advocate(mary) ∧ EntitledTo(mary, federalMinimumWage))) → ¬TippedEmployee(mary)
(Advocate(mary) ⊕ TippedEmployee(mary)) → Advocate(mary)

Truth value of each conclusion (T = true, F = false, U = unknown):
U
F
T
F
T
T
Premises:
No professional basketball players are soccer players.
All NBA players are professional basketball players.
All soccer defenders are soccer players.
All centerbacks are soccer defenders.
Roger Federer is either both an NBA player and a soccer defender, or neither.

Premises in first-order logic:
∀x (ProfessionalBasketballPlayer(x) → ¬ProfessionalSoccerPlayer(x))
∀x (NBAPlayer(x) → ProfessionalBasketballPlayer(x))
∀x (ProfessionalSoccerDefender(x) → ProfessionalSoccerPlayer(x))
∀x (ProfessionalCenterback(x) → ProfessionalSoccerDefender(x))
¬(NBAPlayer(rogerfederer) ⊕ ProfessionalSoccerDefender(rogerfederer))

Conclusions:
Roger Federer is a centerback.
Roger Federer is not a centerback.
Roger Federer is a soccer player.

Conclusions in first-order logic:
ProfessionalCenterback(rogerFederer) 
¬ProfessionalCenterback(rogerFederer)
ProfessionalSoccerPlayer(rogerFederer)

Truth value of each conclusion (T = true, F = false, U = unknown):
F
T
U
Premises:
Those who can fly over a vast distance glide in the air. 
Flightless birds cannot fly over a vast distance. 
Penguins are flightless birds. 
Nonflying birds in Antarctica are penguins. 
Fido is a penguin, or flies over a vast distance. 

Premises in first-order logic:
∀x (FlyOver(x, vastDistance) → GlideInAir(x))
∀x (Flightless(x) ∧ Bird(x) → ¬FlyOver(x, vastDistance))
∀x (Penguin(x) → Flightless(x) ∧ Bird(x))
∀x (NonFlying(x) ∧ Bird(x) ∧ In(x, antarctica) → Penguin(x))
Penguin(fido) ∨ FlyOver(fido, vastDistance)

Conclusions:
Fido is a flightless bird
Fido is not a nonflying bird in Antarctica, and he cannot glid in the air.
If Fido either can fly over a vast distance or cannot fly over a vast distance, then Fido is a nonflying bird in Antartica.

Conclusions in first-order logic:
Flightless(fido) ∧ Bird(fido)
¬(NonFlying(fido) ∧ Bird(fido) ∧ In(fido, antarctica)) ∧ ¬GlideInAir(fido)
(FlyOver(fido, vastDistance) ⊕ ¬FlyOver(fido, vastDistance)) → (NonFlying(fido) ∧ Bird(fido) ∧ In(fido, antarctica))

Truth value of each conclusion (T = true, F = false, U = unknown):
U
F
T
Premises:
All young adults at the event like independence.
All college students at the event are young adults.
All Yale students at the event are college students.
Everyone at the event is a Yale student or a Harvard student.
All Harvard students at the event are diligent.
Susan is at the event, and if Susan is a Harvard student, then she is a young adult.
If Susan is a Yale student, then she does not like independence.

Premises in first-order logic:
∀x (At(x, event) ∧ YoungAdult(x) → Like(x, independence))
∀x (At(x, event) ∧ CollegeStudent(x) → YoungAdult(x))
∀x (At(x, event) ∧ YaleStudent(x) → CollegeStudent(x))
∀x (At(x, event) → (YaleStudent(x) ⊕ HarvardStudent(x)))
∀x (At(x, event) ∧ HarvardStudent(x) → Diligent(x))
At(susan, event) ∧ (HarvardStudent(susan) → YoungAdult(susan))
YaleStudent(susan) → ¬Like(susan, independence)

Conclusions:
Susan is a college student.
Susan likes independence and is diligent.
Susan is not both diligent and likes independence.

Conclusions in first-order logic:
CollegeStudent(susan)
Like(susan, independence) ∧ Diligent(susan)
¬(Like(susan, independence) ∧ Diligent(susan))

Truth value of each conclusion (T = true, F = false, U = unknown):
U
T
F
Premises:
Animals who need large territory travel far.
Every animal that eats a lot needs a large territory.
If something is a big animal, then it will eat a lot.
Bears are big animals.
Larry is a big animal.

Premises in first-order logic:
∀x (Animal(x) ∧ Need(x, largeTerritory) → TravelFar(x))
∀x (EatALot(x) → Need(x, largeTerritory))
∀x (Big(x) ∧ Animal(x) → EatALot(x))
∀x (Bear(x) → Big(x) ∧ Animal(x))
Big(larry) ∧ Animal(larry)

Conclusions:
Larry is a bear.
Larry is not a bear and does not travel far.
If Larry either travels far or needs a large territory, then Larry is a bear.

Conclusions in first-order logic:
Bear(larry)
¬Bear(larry) ∧ ¬TravelFar(larry)
TravelFar(larry) ⊕ Need(larry, largeTerritory) → Bear(larry)

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