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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.

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))

Asa Hoffmann does not live in New York.

¬LiveIn(asaHoffmann, newYorkCity)

False

Some of those who apply for a Schengen visa get it. To apply for a Schengen Visa, you need to provide financial guarantees. If you need to provide financial guarantees, you must request documents from the bank. Do not close your bank account if you request documents from the bank. Philip closed his bank account.

∃x (Apply(x, schengenVisa) → Get(x, schengenVisa)) ∀x (Apply(x, schengenVisa) → Provide(x, financialGuarantees)) ∀x (Provide(x, financialGuarantees) → Request(x, documentsFromBank)) ∀x (Request(x, documentsFromBank) → ¬Close(x, bankAccount)) Close(philip, bankAccount)

Philip got a Schengen visa.

Get(philip, schengenVisa)

Uncertain

Some of those who apply for a Schengen visa get it. To apply for a Schengen Visa, you need to provide financial guarantees. If you need to provide financial guarantees, you must request documents from the bank. Do not close your bank account if you request documents from the bank. Philip closed his bank account.

∃x (Apply(x, schengenVisa) → Get(x, schengenVisa)) ∀x (Apply(x, schengenVisa) → Provide(x, financialGuarantees)) ∀x (Provide(x, financialGuarantees) → Request(x, documentsFromBank)) ∀x (Request(x, documentsFromBank) → ¬Close(x, bankAccount)) Close(philip, bankAccount)

Philip applied for a Schengen visa and got it.

Apply(philip, schengenVisa) ∧ Get(philip, schengenVisa)

False

Some of those who apply for a Schengen visa get it. To apply for a Schengen Visa, you need to provide financial guarantees. If you need to provide financial guarantees, you must request documents from the bank. Do not close your bank account if you request documents from the bank. Philip closed his bank account.

∃x (Apply(x, schengenVisa) → Get(x, schengenVisa)) ∀x (Apply(x, schengenVisa) → Provide(x, financialGuarantees)) ∀x (Provide(x, financialGuarantees) → Request(x, documentsFromBank)) ∀x (Request(x, documentsFromBank) → ¬Close(x, bankAccount)) Close(philip, bankAccount)

If Philip did not request documents from the bank or get a Schengen visa, he didn’t apply for a Schengen visa.

(¬Request(philip, documentsFromBank) ∧ ¬Get(x, schengenVisa)) → Apply(x, schengenVisa)

True

Some fears lead to anxiety. Some anxiety leads to terror.

∃x ∃y (Fear(x) ∧ Anxiety(y) ∧ LeadTo(x, y) ∧ ¬(x=y)) ∃x ∃y (Anxiety(x) ∧ Terror(y) ∧ LeadTo(x, y))

No fears lead to terror.

∀x ∀y (Fear(x) → ¬(Terror(y) ∧ LeadTo(x, y)))

Uncertain

The Great Lakes are Lake Superior, Lake Michigan, Lake Huron, Lake Erie, and Lake Ontario. Some major settlements of Lake Erie are in NY, PA, OH, and MI. NY, PA, OH, and MI are states in the US. ON is a state of Canada. There is a major settlement of Lake Huron in ON. All states are in their country. The US is in North America. The Great Lakes began to form at the end of the Last Glacial Period.

∀x (GreatLake(x) → Superior(x) ⊕ Michigan(x) ⊕ Huron(x) ⊕ Erie(x) ⊕ Ontario(x)) ∀x (Erie (x) ∧ MajorSettlement(x) → In(x, nY) ∨ In(x, pA) ∨ In(x, oH) ∨ In(x, mI)) StateOf(nY, uS) ∧ StateOf(pA, uS) ∧ StateOf(oH, uS) ∧ StateOf(mI, uS) StateOf(oN, canada) ∃x (Huron(x) ∧ MajorSettlement(x) ∧ In(x, oN)) ∀x ∀y (StateOf(x, y) → In(x, y)) In(us, northAmerica) ∀x (GreatLake(x) → FormAtEndOf(x, lastGlacialPeriod))

Lake Erie has a major settlement.

∃x ∃y (Erie(y) ∧ MajorSettlementOf(x, y))

True

The Great Lakes are Lake Superior, Lake Michigan, Lake Huron, Lake Erie, and Lake Ontario. Some major settlements of Lake Erie are in NY, PA, OH, and MI. NY, PA, OH, and MI are states in the US. ON is a state of Canada. There is a major settlement of Lake Huron in ON. All states are in their country. The US is in North America. The Great Lakes began to form at the end of the Last Glacial Period.

∀x (GreatLake(x) → Superior(x) ⊕ Michigan(x) ⊕ Huron(x) ⊕ Erie(x) ⊕ Ontario(x)) ∀x (Erie (x) ∧ MajorSettlement(x) → In(x, nY) ∨ In(x, pA) ∨ In(x, oH) ∨ In(x, mI)) StateOf(nY, uS) ∧ StateOf(pA, uS) ∧ StateOf(oH, uS) ∧ StateOf(mI, uS) StateOf(oN, canada) ∃x (Huron(x) ∧ MajorSettlement(x) ∧ In(x, oN)) ∀x ∀y (StateOf(x, y) → In(x, y)) In(us, northAmerica) ∀x (GreatLake(x) → FormAtEndOf(x, lastGlacialPeriod))

There is a great lake that did not form at the end of the Last Glacial Period.

∃x (GreatLake(x) ∧ ¬FormAtEndOf(x, lastGlacialPeriod))

False

All professional soccer defenders are professional soccer players. No professional soccer players are professional basketball players. All professional centerbacks are professional soccer defenders. All NBA players are professional basketball players. Stephen Curry is an NBA player.

∀x ((Professional(x) ∧ Defender(x)) → (Professional(x) ∧ SoccerPlayer(x))) ∀x ((Professional(x) ∧ SoccerPlayer(x)) → ¬(Professional(x) ∧ BasketballPlayer(x))) ∀x ((Professional(x) ∧ CenterBack(x)) → (Professional(x) ∧ Defender(x)) ∀x (NBAPlayer(x) → (Professional(x) ∧ BasketballPlayer(x))) NBAPlayer(stephenCurry)

Stephen Curry is a professional basketball player.

Professional(stephenCurry) ∧ BasketballPlayer(stephenCurry)

Uncertain

All professional soccer defenders are professional soccer players. No professional soccer players are professional basketball players. All professional centerbacks are professional soccer defenders. All NBA players are professional basketball players. Stephen Curry is an NBA player.

∀x ((Professional(x) ∧ Defender(x)) → (Professional(x) ∧ SoccerPlayer(x))) ∀x ((Professional(x) ∧ SoccerPlayer(x)) → ¬(Professional(x) ∧ BasketballPlayer(x))) ∀x ((Professional(x) ∧ CenterBack(x)) → (Professional(x) ∧ Defender(x)) ∀x (NBAPlayer(x) → (Professional(x) ∧ BasketballPlayer(x))) NBAPlayer(stephenCurry)

Stephen Curry is a professional centerback.

Professional(stephenCurry) ∧ CenterBack(stephenCurry)

False

All professional soccer defenders are professional soccer players. No professional soccer players are professional basketball players. All professional centerbacks are professional soccer defenders. All NBA players are professional basketball players. Stephen Curry is an NBA player.

∀x ((Professional(x) ∧ Defender(x)) → (Professional(x) ∧ SoccerPlayer(x))) ∀x ((Professional(x) ∧ SoccerPlayer(x)) → ¬(Professional(x) ∧ BasketballPlayer(x))) ∀x ((Professional(x) ∧ CenterBack(x)) → (Professional(x) ∧ Defender(x)) ∀x (NBAPlayer(x) → (Professional(x) ∧ BasketballPlayer(x))) NBAPlayer(stephenCurry)

Stephen Curry is not a centerback.

¬(Professional(stephenCurry) ∧ CenterBack(stephenCurry))

True

Naive cynicism was proposed by Justin Kruger and a colleague. Thomas Gilovich is a colleague of Justin Kruger. Naive cynicism is a philosophy of mind.

Proposed(justinKruger, naiveCynicism) ∧ ∃y (colleagueOfJustinKruger(y) ∧ Proposed(y, naiveCynicism)) Colleagues(thomasGilovich, justinKruger) PhilosophyOfMind(naiveCynicism)

Thomas Gilovich proposed naive cynicism.

Proposed(thomasGilovich, naiveCynicism)

Uncertain

Naive cynicism was proposed by Justin Kruger and a colleague. Thomas Gilovich is a colleague of Justin Kruger. Naive cynicism is a philosophy of mind.

Proposed(justinKruger, naiveCynicism) ∧ ∃y (colleagueOfJustinKruger(y) ∧ Proposed(y, naiveCynicism)) Colleagues(thomasGilovich, justinKruger) PhilosophyOfMind(naiveCynicism)

Justin Kruger proposed a philosophy of mind.

∃x (Proposed(justinKruger, x) ∧ PhilosophyOfMind(x))

True

Naive cynicism was proposed by Justin Kruger and a colleague. Thomas Gilovich is a colleague of Justin Kruger. Naive cynicism is a philosophy of mind.

Proposed(justinKruger, naiveCynicism) ∧ ∃y (colleagueOfJustinKruger(y) ∧ Proposed(y, naiveCynicism)) Colleagues(thomasGilovich, justinKruger) PhilosophyOfMind(naiveCynicism)

Thomas Gilovich worked on philosophies of mind.

∃x (WorkedOn(thomasGilovich, x) ∧ PhilosophyOfMind(x))

Uncertain

The Turing Award has been awarded to Donald Knuth, Marvin Minsky, Richard Hamming, and John McCarthy. Donald Knuth made contributions to the analysis of algorithms. Marvin Minsky is recognized for his contributions to the field of artificial intelligence. Richard Hamming researched numerical methods. John McCarthy made contributions to the field of artificial intelligence.

AwardedTo(turingAward, donaldKnuth) ∧ AwardedTo(turingAward, marvinMinsky) ∧ AwardedTo(turingAward, richardHamming) ∧ AwardedTo(turingAward, johnMccarthy) ContributedTo(donaldKnuth, analysisOfAlgorithms) ContributedTo(marvinMinsky, artificialIntelligence) ContributedTo(richardHamming, numericalMethods) ContributedTo(johnMccarthy, artificialIntelligence)

At least two people who have won the Turing Award worked in artificial intelligence.

∃x ∃y (¬(x=y) ∧ AwardedTo(turingAward, x) ∧ AwardedTo(turingAward, y) ∧ ContributedTo(x, artificialIntelligence) ∧ ContributedTo(y, artificialIntelligence))

True

The Turing Award has been awarded to Donald Knuth, Marvin Minsky, Richard Hamming, and John McCarthy. Donald Knuth made contributions to the analysis of algorithms. Marvin Minsky is recognized for his contributions to the field of artificial intelligence. Richard Hamming researched numerical methods. John McCarthy made contributions to the field of artificial intelligence.

AwardedTo(turingAward, donaldKnuth) ∧ AwardedTo(turingAward, marvinMinsky) ∧ AwardedTo(turingAward, richardHamming) ∧ AwardedTo(turingAward, johnMccarthy) ContributedTo(donaldKnuth, analysisOfAlgorithms) ContributedTo(marvinMinsky, artificialIntelligence) ContributedTo(richardHamming, numericalMethods) ContributedTo(johnMccarthy, artificialIntelligence)

At least two people who worked in artificial intelligence have won the Turing Award.

∃x ∃y (¬(x=y) ∧ ContributedTo(x, artificialIntelligence) ∧ ContributedTo(x, artificialIntelligence) ∧ AwardedTo(turingAward, x) ∧ AwardedTo(turingAward, y))

True

The Turing Award has been awarded to Donald Knuth, Marvin Minsky, Richard Hamming, and John McCarthy. Donald Knuth made contributions to the analysis of algorithms. Marvin Minsky is recognized for his contributions to the field of artificial intelligence. Richard Hamming researched numerical methods. John McCarthy made contributions to the field of artificial intelligence.

AwardedTo(turingAward, donaldKnuth) ∧ AwardedTo(turingAward, marvinMinsky) ∧ AwardedTo(turingAward, richardHamming) ∧ AwardedTo(turingAward, johnMccarthy) ContributedTo(donaldKnuth, analysisOfAlgorithms) ContributedTo(marvinMinsky, artificialIntelligence) ContributedTo(richardHamming, numericalMethods) ContributedTo(johnMccarthy, artificialIntelligence)

Only one person who won the Turing Award made significant contributions to the analysis of algorithms.

∃x ∀y ((AwardedTo(turingAward, x) ∧ AwardedTo(turingAward, y) ∧ ContributedTo(y, algorithms) ∧ ¬(x=y)) → ¬ContributedTo(y, algorithms))

Uncertain

The Turing Award has been awarded to Donald Knuth, Marvin Minsky, Richard Hamming, and John McCarthy. Donald Knuth made contributions to the analysis of algorithms. Marvin Minsky is recognized for his contributions to the field of artificial intelligence. Richard Hamming researched numerical methods. John McCarthy made contributions to the field of artificial intelligence.

AwardedTo(turingAward, donaldKnuth) ∧ AwardedTo(turingAward, marvinMinsky) ∧ AwardedTo(turingAward, richardHamming) ∧ AwardedTo(turingAward, johnMccarthy) ContributedTo(donaldKnuth, analysisOfAlgorithms) ContributedTo(marvinMinsky, artificialIntelligence) ContributedTo(richardHamming, numericalMethods) ContributedTo(johnMccarthy, artificialIntelligence)

No Turing Award winners worked in the field of numerical methods.

∀x (AwardedTo(turingAward, x) → ¬ContributedTo(x, numericalMethods))

False

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.

∀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)

2Sum is an easy Leetcode problem.

LeetcodeProblems(twosum) ∧ Easy(twosum)

Uncertain

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.

∀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)

2Sum is not an easy Leetcode problem.

¬(LeetcodeProblems(twosum) ∧ Easy(twosum))

Uncertain

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.

∀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)

4Sum is recommended to novices or is hard.

RecommendedTo(foursum, novices) ∨ Hard(foursum)

False

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.

∀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)

4Sum is neither recommended to the novice nor a Leetcode problem that's hard.

¬RecommendedTo(foursum, novices) ∧ ¬Hard(foursum)

True

Show Your Love is a song recorded by the South Korean boy band BtoB 4u. The lead single of the extended play Inside is Show Your Love. Show Your Love contains a hopeful message. BtoB 4u member Hyunsik wrote Show Your Love. There is a music video for Show Your Love.

Song(showYourLove) ∧ RecordedBy(showYourLove, bToB4u) ∧ SouthKorean(bToB4u) ∧ BoyBand(bToB4u) ExtendedPlay(inside) ∧ LeadSingleOf(showYourLove, inside) Contains(showYourLove, hopefulMessage) Member(hyunsik, btob4u) ∧ Wrote(hyunsik, showYourLove) Have(showYourLove, musicVideo)

Show Your Love wasn't written by a member of a boy band.

∀x ∀y (Wrote(x, showYourLove) → ¬(BoyBand(y) ∧ MemberOf(x, y)))

False

Show Your Love is a song recorded by the South Korean boy band BtoB 4u. The lead single of the extended play Inside is Show Your Love. Show Your Love contains a hopeful message. BtoB 4u member Hyunsik wrote Show Your Love. There is a music video for Show Your Love.

Song(showYourLove) ∧ RecordedBy(showYourLove, bToB4u) ∧ SouthKorean(bToB4u) ∧ BoyBand(bToB4u) ExtendedPlay(inside) ∧ LeadSingleOf(showYourLove, inside) Contains(showYourLove, hopefulMessage) Member(hyunsik, btob4u) ∧ Wrote(hyunsik, showYourLove) Have(showYourLove, musicVideo)

A lead single of Inside contains a hopeful message.

∃x (LeadSingleOf(x, inside) ∧ Contains(x, hopefulMessage))

True

Show Your Love is a song recorded by the South Korean boy band BtoB 4u. The lead single of the extended play Inside is Show Your Love. Show Your Love contains a hopeful message. BtoB 4u member Hyunsik wrote Show Your Love. There is a music video for Show Your Love.

Song(showYourLove) ∧ RecordedBy(showYourLove, bToB4u) ∧ SouthKorean(bToB4u) ∧ BoyBand(bToB4u) ExtendedPlay(inside) ∧ LeadSingleOf(showYourLove, inside) Contains(showYourLove, hopefulMessage) Member(hyunsik, btob4u) ∧ Wrote(hyunsik, showYourLove) Have(showYourLove, musicVideo)

Hyunsik is Korean.

Korean(hyunsik)

Uncertain

All tables are round. Some pieces of furniture are tables.

∀x (Table(x) → Round(x)) ∃x ∃y (Furniture(x) ∧ Furniture(y) ∧ Table(x) ∧ Table(y) ∧ ¬(x=y))

Some pieces of furniture are round.

∃x ∃y (Furniture(x) ∧ Furniture(y) ∧ Round(x) ∧ Round(y) ∧ ¬(x=y))

True

All juvenile delinquents have committed a crime. Some juvenile delinquents are products of broken homes.

∀x (JuvenileDelinquent(x) → Commited(x, crime)) ∃x ∃y (JuvenileDelinquent(x) ∧ JuvenileDelinquent(y) ∧ ProductOf(x, brokenHome) ∧ ProductOf(y, brokenHome) ∧ ¬(x=y))

Some people who have committed a crime are products of broken homes.

∃x ∃y (Commited(x, crime) ∧ Commited(y, crime) ∧ ProductOf(x, brokenHome) ∧ ProductOf(y, brokenHome) ∧ ¬(x=y))

True

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.

∀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)

Multivoxel (pattern) analysis is a brain decoding.

MindReading(multivoxelPatternAnalysis) ∧ BrainDecoding(multivoxelPatternAnalysis)

Uncertain

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.

∀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)

Multivoxel (pattern) analysis is the writing of a novel.

MindReading(multivoxelPatternAnalysis) ∧ NovelWriting(multivoxelPatternAnalysis)

False

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.

∀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)

Multivoxel (pattern) analysis is without statistical pattern analysis and writing a novel.

¬(Uses(multivoxelPatternAnalysis, statisticalPatternAnalysis) ∧ NovelWriting(multivoxelPatternAnalysis))

False

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.

∀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)

Multivoxel (pattern) analysis is without statistical pattern analysis or writing a novel.

¬(Uses(multivoxelPatternAnalysis, statisticalPatternAnalysis) ∨ NovelWriting(multivoxelPatternAnalysis))

False

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.

∀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)

Multivoxel (pattern) analysis is either without statistical pattern analysis or writing a novel.

¬Uses(multivoxelPatternAnalysis, statisticalPatternAnalysis) ⊕ Writing(multivoxelPatternAnalysis, aNovel)

False

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.

∀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)

If multivoxel (pattern) analysis is writing a novel, then multivoxel (pattern) analysis is neither without statistical pattern analysis nor writing a novel.

(MindReading(multivoxelPatternAnalysis) ∧ NovelWriting(multivoxelPatternAnalysis)) → (Uses(multivoxelPatternAnalysis, statisticalPatternAnalysis) ∨ ¬NovelWriting(multivoxelPatternAnalysis))

True

If you have room for dessert, you have room for broccoli. Everyone at Luis's dinner party has room for dessert, including Luis. Mauricia does not have room for broccoli. Luis's dinner party is the first ever dinner party that Allison has attended. Gustave has room for both broccoli and asparagus. Broccoli and asparagus are both vegetables.

∀x (RoomFor(x, dessert) → RoomFor(x, broccoli)) ∀x (AtLuisParty(x) → RoomFor(x, dessert)) ¬RoomFor(mauricia, broccoli) AtLuisParty(allison) ∧ FirstDinnerPartyFor(luisparty, allison) RoomFor(gustave, broccoli) ∧ RoomFor(gustave, asparagus) Vegetable(broccoli) ∧ Vegetable(asparagus)

Allison has room for broccoli.

RoomFor(allison, broccoli)

True

If you have room for dessert, you have room for broccoli. Everyone at Luis's dinner party has room for dessert, including Luis. Mauricia does not have room for broccoli. Luis's dinner party is the first ever dinner party that Allison has attended. Gustave has room for both broccoli and asparagus. Broccoli and asparagus are both vegetables.

∀x (RoomFor(x, dessert) → RoomFor(x, broccoli)) ∀x (AtLuisParty(x) → RoomFor(x, dessert)) ¬RoomFor(mauricia, broccoli) AtLuisParty(allison) ∧ FirstDinnerPartyFor(luisparty, allison) RoomFor(gustave, broccoli) ∧ RoomFor(gustave, asparagus) Vegetable(broccoli) ∧ Vegetable(asparagus)

Mauricia is at Luis's dinner party.

AtLuisParty(mauricia)

False

If you have room for dessert, you have room for broccoli. Everyone at Luis's dinner party has room for dessert, including Luis. Mauricia does not have room for broccoli. Luis's dinner party is the first ever dinner party that Allison has attended. Gustave has room for both broccoli and asparagus. Broccoli and asparagus are both vegetables.

∀x (RoomFor(x, dessert) → RoomFor(x, broccoli)) ∀x (AtLuisParty(x) → RoomFor(x, dessert)) ¬RoomFor(mauricia, broccoli) AtLuisParty(allison) ∧ FirstDinnerPartyFor(luisparty, allison) RoomFor(gustave, broccoli) ∧ RoomFor(gustave, asparagus) Vegetable(broccoli) ∧ Vegetable(asparagus)

Gustav has room for dessert.

RoomFor(gustave, dessert)

Uncertain

Imagine Dragons are an American pop-rock band. The lead singer of Imagine Dragons is Dan. Dan is also a songwriter. All lead singers are singers. All singers are musicians. Demons is one of the most popular singles of Imagine Dragons. Some singles of Imagine Dragons have been on Billboard Hot 100.

American(imagineDragon) ∧ RockBand(imagineDragon) LeadSinger(imagineDragon, dan) SongWriter(dan) ∀x ∀y (LeadSinger(x, y) → Singer(y)) ∀x (Singer(x) → Musician(x)) PopularSingle(imagineDragon, demons) ∃x ∃y (PopularSingle(imagineDragon, x) ∧ BillboardHot100(x)) ∧ (¬(x=y)) ∧ (PopularSingle(imagineDragon, y) ∧ BillboardHot100(y))

Some rock band has a lead singer who is also a songwriter.

∃x ∃y (RockBand(x) ∧ LeadSinger(x, y) ∧ SongWriter(y))

True

Imagine Dragons are an American pop-rock band. The lead singer of Imagine Dragons is Dan. Dan is also a songwriter. All lead singers are singers. All singers are musicians. Demons is one of the most popular singles of Imagine Dragons. Some singles of Imagine Dragons have been on Billboard Hot 100.

American(imagineDragon) ∧ RockBand(imagineDragon) LeadSinger(imagineDragon, dan) SongWriter(dan) ∀x ∀y (LeadSinger(x, y) → Singer(y)) ∀x (Singer(x) → Musician(x)) PopularSingle(imagineDragon, demons) ∃x ∃y (PopularSingle(imagineDragon, x) ∧ BillboardHot100(x)) ∧ (¬(x=y)) ∧ (PopularSingle(imagineDragon, y) ∧ BillboardHot100(y))

Dan is not a musician.

¬Musician(dan)

False

Imagine Dragons are an American pop-rock band. The lead singer of Imagine Dragons is Dan. Dan is also a songwriter. All lead singers are singers. All singers are musicians. Demons is one of the most popular singles of Imagine Dragons. Some singles of Imagine Dragons have been on Billboard Hot 100.

American(imagineDragon) ∧ RockBand(imagineDragon) LeadSinger(imagineDragon, dan) SongWriter(dan) ∀x ∀y (LeadSinger(x, y) → Singer(y)) ∀x (Singer(x) → Musician(x)) PopularSingle(imagineDragon, demons) ∃x ∃y (PopularSingle(imagineDragon, x) ∧ BillboardHot100(x)) ∧ (¬(x=y)) ∧ (PopularSingle(imagineDragon, y) ∧ BillboardHot100(y))

Demons has been on Billboard Hot 100.

BillboardHot100(demons)

Uncertain

All philosophers reason. Some sophists reason. All who can reason can distinguish truth from falsehood. Nobody who can distinguish truth from falsehood is morally perfect. The theistic God is morally perfect.

∀x (Philosopher(x) → Reason(x)) ∃x (Sophist(x) ∧ Reason(x)) ∀x (Reason(x) → CanDistinguishFrom(x, truth, falsehood)) ∀x (CanDistinguishFrom(x, truth, falsehood) → ¬MorallyPerfect(x)) MorallyPerfect(theisticGod)

The theistic God is a sophist.

Sophist(theisticGod)

Uncertain

All philosophers reason. Some sophists reason. All who can reason can distinguish truth from falsehood. Nobody who can distinguish truth from falsehood is morally perfect. The theistic God is morally perfect.

∀x (Philosopher(x) → Reason(x)) ∃x (Sophist(x) ∧ Reason(x)) ∀x (Reason(x) → CanDistinguishFrom(x, truth, falsehood)) ∀x (CanDistinguishFrom(x, truth, falsehood) → ¬MorallyPerfect(x)) MorallyPerfect(theisticGod)

The theistic God is a sophist and a philosopher.

Sophist(theisticGod) ∧ Philosopher(theisticGod)

False

All philosophers reason. Some sophists reason. All who can reason can distinguish truth from falsehood. Nobody who can distinguish truth from falsehood is morally perfect. The theistic God is morally perfect.

∀x (Philosopher(x) → Reason(x)) ∃x (Sophist(x) ∧ Reason(x)) ∀x (Reason(x) → CanDistinguishFrom(x, truth, falsehood)) ∀x (CanDistinguishFrom(x, truth, falsehood) → ¬MorallyPerfect(x)) MorallyPerfect(theisticGod)

if the theistic God is a philosopher, then he is not a sophist.

Philosopher(theisticGod) → ¬Sophist(theisticGod)

True

Common utilities include water, electricity, gas, heating, sewer, trash, and recycling. Many apartment rents cover the cost of water and electricity. Susan lives in an apartment where the rent covers all utilities. The rent of the apartment where Ava lives does not cover any utility expenses. Noah lives in an apartment where the rent does not cover heating.

CommonUtilities(water) ∧ CommonUtilities(electricity) ∧ CommonUtilities(gas) ∧ CommonUtilities(heating) ∃x (Apartment(x) ∧ Cover(x, water) ∧ Cover(x, electricity)) ∀x (Apartment(x) ∧ LiveIn(susan, x) ∧ Cover(x, water) ∧ Cover(x, electricity) ∧ Cover(x, gas) ∧ Cover(x, heating)) ∀x (Apartment(x) ∧ LiveIn(ava, x) ∧ ¬Cover(x, water) ∧ ¬Cover(x, electricity) ∧ ¬Cover(x, gas) ∧ ¬Cover(x, heating)) ∀x (Apartment(x) ∧ LiveIn(noah, x) ∧ ¬Cover(x, heating))

Noah needs to pay the water bill.

∀x (Apartment(x) ∧ LiveIn(noah, x) ∧ ¬Cover(x, water))

Uncertain

Common utilities include water, electricity, gas, heating, sewer, trash, and recycling. Many apartment rents cover the cost of water and electricity. Susan lives in an apartment where the rent covers all utilities. The rent of the apartment where Ava lives does not cover any utility expenses. Noah lives in an apartment where the rent does not cover heating.

CommonUtilities(water) ∧ CommonUtilities(electricity) ∧ CommonUtilities(gas) ∧ CommonUtilities(heating) ∃x (Apartment(x) ∧ Cover(x, water) ∧ Cover(x, electricity)) ∀x (Apartment(x) ∧ LiveIn(susan, x) ∧ Cover(x, water) ∧ Cover(x, electricity) ∧ Cover(x, gas) ∧ Cover(x, heating)) ∀x (Apartment(x) ∧ LiveIn(ava, x) ∧ ¬Cover(x, water) ∧ ¬Cover(x, electricity) ∧ ¬Cover(x, gas) ∧ ¬Cover(x, heating)) ∀x (Apartment(x) ∧ LiveIn(noah, x) ∧ ¬Cover(x, heating))

Noah and Ava both need to pay the heating bill.

¬Cover(noah, heating) ∧ ¬Cover(ava, heating)

True

Common utilities include water, electricity, gas, heating, sewer, trash, and recycling. Many apartment rents cover the cost of water and electricity. Susan lives in an apartment where the rent covers all utilities. The rent of the apartment where Ava lives does not cover any utility expenses. Noah lives in an apartment where the rent does not cover heating.

CommonUtilities(water) ∧ CommonUtilities(electricity) ∧ CommonUtilities(gas) ∧ CommonUtilities(heating) ∃x (Apartment(x) ∧ Cover(x, water) ∧ Cover(x, electricity)) ∀x (Apartment(x) ∧ LiveIn(susan, x) ∧ Cover(x, water) ∧ Cover(x, electricity) ∧ Cover(x, gas) ∧ Cover(x, heating)) ∀x (Apartment(x) ∧ LiveIn(ava, x) ∧ ¬Cover(x, water) ∧ ¬Cover(x, electricity) ∧ ¬Cover(x, gas) ∧ ¬Cover(x, heating)) ∀x (Apartment(x) ∧ LiveIn(noah, x) ∧ ¬Cover(x, heating))

Susan does not need to pay the water bill.

∀x (Apartment(x) ∧ LiveIn(susan, x) ∧ Cover(x, water))

True

All clothes are products. No products are perfect. All dresses are clothes. All skirts are dresses. If the fabric bundle is a piece of clothing, then the fabric bundle is a perfect dress.

∀x (Clothes(x) → Product(x)) ∀x (Product(x) → ¬Perfect(x)) ∀x (Dress(x) → Clothes(x)) ∀x (Skirt(x) → Dress(x)) Clothes(fabricBundle) → Perfect(fabricBundle) ∧ Dress(fabricBundle)

The fabric bundle is perfect.

Perfect(fabricbundle)

Uncertain

All clothes are products. No products are perfect. All dresses are clothes. All skirts are dresses. If the fabric bundle is a piece of clothing, then the fabric bundle is a perfect dress.

∀x (Clothes(x) → Product(x)) ∀x (Product(x) → ¬Perfect(x)) ∀x (Dress(x) → Clothes(x)) ∀x (Skirt(x) → Dress(x)) Clothes(fabricBundle) → Perfect(fabricBundle) ∧ Dress(fabricBundle)

The fabric bundle is a skirt.

Skirt(fabricbundle)

False

All clothes are products. No products are perfect. All dresses are clothes. All skirts are dresses. If the fabric bundle is a piece of clothing, then the fabric bundle is a perfect dress.

∀x (Clothes(x) → Product(x)) ∀x (Product(x) → ¬Perfect(x)) ∀x (Dress(x) → Clothes(x)) ∀x (Skirt(x) → Dress(x)) Clothes(fabricBundle) → Perfect(fabricBundle) ∧ Dress(fabricBundle)

The fabric bundle is not a skirt.

¬Skirt(fabricbundle)

True

All pets are animals. Pets can be either a dog or a cat. If a person has a pet, they care for that pet. Dogs and cats can be naughty. Pets who are naughty are not liked as much. Charlie has a naughty pet dog named Leo.

∀x (Pet(x) → Animal(x)) ∀x (Pet(x) → (Dog(x) ⊕ Cat(x))) ∀x ∀y ((Pet(y) ∧ OwnedBy(x,y)) → Cares(x, y)) ∃x ∃y (Cat(x) ∧ Naughty(x) ∧ (¬(x=y)) ∧ Dog(y) ∧ Naughty(y)) ∀x ∀y ((Pet(x) ∧ Naughty(x) ∧ OwnedBy(x,y)) → ¬Liked(x, y)) OwnedBy(leo, charlie) ∧ Pet(leo) ∧ Dog(leo) ∧ Naughty(leo)

Leo is an animal.

Animal(leo)

True

All pets are animals. Pets can be either a dog or a cat. If a person has a pet, they care for that pet. Dogs and cats can be naughty. Pets who are naughty are not liked as much. Charlie has a naughty pet dog named Leo.

∀x (Pet(x) → Animal(x)) ∀x (Pet(x) → (Dog(x) ⊕ Cat(x))) ∀x ∀y ((Pet(y) ∧ OwnedBy(x,y)) → Cares(x, y)) ∃x ∃y (Cat(x) ∧ Naughty(x) ∧ (¬(x=y)) ∧ Dog(y) ∧ Naughty(y)) ∀x ∀y ((Pet(x) ∧ Naughty(x) ∧ OwnedBy(x,y)) → ¬Liked(x, y)) OwnedBy(leo, charlie) ∧ Pet(leo) ∧ Dog(leo) ∧ Naughty(leo)

Charlie does not like Leo and does not care for Leo.

¬Liked(leo, charlie) ∧ ¬Cares(charlie, leo)

False

All pets are animals. Pets can be either a dog or a cat. If a person has a pet, they care for that pet. Dogs and cats can be naughty. Pets who are naughty are not liked as much. Charlie has a naughty pet dog named Leo.

∀x (Pet(x) → Animal(x)) ∀x (Pet(x) → (Dog(x) ⊕ Cat(x))) ∀x ∀y ((Pet(y) ∧ OwnedBy(x,y)) → Cares(x, y)) ∃x ∃y (Cat(x) ∧ Naughty(x) ∧ (¬(x=y)) ∧ Dog(y) ∧ Naughty(y)) ∀x ∀y ((Pet(x) ∧ Naughty(x) ∧ OwnedBy(x,y)) → ¬Liked(x, y)) OwnedBy(leo, charlie) ∧ Pet(leo) ∧ Dog(leo) ∧ Naughty(leo)

Dogs are not always naughty.

∀x (Dog(x) → ¬Naughty(x))

False

Surprises are either fun or dreadful. All scares are surprises.

∀x (Surprise(x) → (Fun(x) ⊕ Dreadful(x))) ∀x (Scare(x) → Surprise(x))

All scares are fun.

∀x (Scare(x) → Fun(x))

Uncertain

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.

∀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) ∧ ∃y(MoreThan(y, oneMillion) ∧ Sold(threeBodyProblem,y)) AboutFuture(threeBodyProblem)

The Three-Body Problem won the Hugo Award.

Won(threeBodyProblem, hugoAward)

Uncertain

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.

∀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) ∧ ∃y(MoreThan(y, oneMillion) ∧ Sold(threeBodyProblem,y)) AboutFuture(threeBodyProblem)

The Three-Body Problem is forward-looking.

AboutFuture(threeBodyProblem)

True

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.

∀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) ∧ ∃y(MoreThan(y, oneMillion) ∧ Sold(threeBodyProblem,y)) AboutFuture(threeBodyProblem)

The Three-Body Problem was written by Cixin Liu.

WrittenBy(threeBodyProblem, cixinLiu)

Uncertain

Some people are both late-night and early-morning people. If a person is an earl- morning person, they have early-morning habits. Everyone who has early-morning habits gets up early. Everyone who gets up early catches the sunrise. James doesn't catch the sunrise.

∃x (LateNightPerson(x) ∧ EarlyMorningPerson(x)) ∀x (EarlyMorningPerson(x) → Have(x, earlyMorningHabit)) ∀x (Have(x, earlyMorningHabit) → GetUpEarly(x)) ∀x (GetUpEarly(x) → CatchTheSunrise(x)) ¬CatchTheSunrise(james)

James is a late night person.

LateNightPerson(james)

Uncertain

Some people are both late-night and early-morning people. If a person is an earl- morning person, they have early-morning habits. Everyone who has early-morning habits gets up early. Everyone who gets up early catches the sunrise. James doesn't catch the sunrise.

∃x (LateNightPerson(x) ∧ EarlyMorningPerson(x)) ∀x (EarlyMorningPerson(x) → Have(x, earlyMorningHabit)) ∀x (Have(x, earlyMorningHabit) → GetUpEarly(x)) ∀x (GetUpEarly(x) → CatchTheSunrise(x)) ¬CatchTheSunrise(james)

James is a late night person and an early-morning person.

LateNightPerson(james) ∧ EarlyMorningPerson(james)

False

Some people are both late-night and early-morning people. If a person is an earl- morning person, they have early-morning habits. Everyone who has early-morning habits gets up early. Everyone who gets up early catches the sunrise. James doesn't catch the sunrise.

∃x (LateNightPerson(x) ∧ EarlyMorningPerson(x)) ∀x (EarlyMorningPerson(x) → Have(x, earlyMorningHabit)) ∀x (Have(x, earlyMorningHabit) → GetUpEarly(x)) ∀x (GetUpEarly(x) → CatchTheSunrise(x)) ¬CatchTheSunrise(james)

If James is an early-morning person, then he is a late night person.

EarlyMorningPerson(james) → LateNightPerson(james)

True

There is no dog on the roof. If there is a dog on the roof, something went wrong.

∀x (Dog(x) → ¬OnRoof(x))) ∀x ∃y ((Dog(x) ∧ OnRoof(x)) → GoWrong(y))

Something went wrong.

∃x (GoWrong(x))

Uncertain

Elephantopus is a genus of perennial plants in the daisy family. Elephantopus is widespread over much of Africa, southern Asia, Australia, and the Americas. Several species of Elephantopus are native to the southeastern United States. Elephantopus scaber is a traditional medicine.

∀x (Elephantopus(x) → (Genus(x, perennialplants) ∧ BelongTo(x, daisyfamily))) ∃x ∃y ∃z(Elephantopus(x) ∧ In(x,africa) ∧ (¬(x=y)) ∧ Elephantopus(y) ∧ In(y, southernasia) ∧ (¬(x=z)) ∧ (¬(y=z)) ∧ Elephantopus(z) ∧ In(z, australia)) ∃x ∃y (Elephantopus(x) ∧ NativeTo(x, southeasternunitedstates) ∧ (¬(x=y)) ∧ Elephantopus(y) ∧ NativeTo(y, southeasternunitedstates)) ∀x (ElephantopusScaber(x) → TraditionalMedicine(x))

Elephantopus is found in Australia and Southern Asia.

∃x∃y(Elephantopus(x) ∧ In(x,africa) ∧ Elephantopus(y) ∧ In(y,africa))

True

Elephantopus is a genus of perennial plants in the daisy family. Elephantopus is widespread over much of Africa, southern Asia, Australia, and the Americas. Several species of Elephantopus are native to the southeastern United States. Elephantopus scaber is a traditional medicine.

∀x (Elephantopus(x) → (Genus(x, perennialplants) ∧ BelongTo(x, daisyfamily))) ∃x ∃y ∃z(Elephantopus(x) ∧ In(x,africa) ∧ (¬(x=y)) ∧ Elephantopus(y) ∧ In(y, southernasia) ∧ (¬(x=z)) ∧ (¬(y=z)) ∧ Elephantopus(z) ∧ In(z, australia)) ∃x ∃y (Elephantopus(x) ∧ NativeTo(x, southeasternunitedstates) ∧ (¬(x=y)) ∧ Elephantopus(y) ∧ NativeTo(y, southeasternunitedstates)) ∀x (ElephantopusScaber(x) → TraditionalMedicine(x))

No Elephantopus is native to the southeastern United States.

∀x (Elephantopus(x) → ¬NativeTo(x, southeasternunitedstates))

False

Elephantopus is a genus of perennial plants in the daisy family. Elephantopus is widespread over much of Africa, southern Asia, Australia, and the Americas. Several species of Elephantopus are native to the southeastern United States. Elephantopus scaber is a traditional medicine.

∀x (Elephantopus(x) → (Genus(x, perennialplants) ∧ BelongTo(x, daisyfamily))) ∃x ∃y ∃z(Elephantopus(x) ∧ In(x,africa) ∧ (¬(x=y)) ∧ Elephantopus(y) ∧ In(y, southernasia) ∧ (¬(x=z)) ∧ (¬(y=z)) ∧ Elephantopus(z) ∧ In(z, australia)) ∃x ∃y (Elephantopus(x) ∧ NativeTo(x, southeasternunitedstates) ∧ (¬(x=y)) ∧ Elephantopus(y) ∧ NativeTo(y, southeasternunitedstates)) ∀x (ElephantopusScaber(x) → TraditionalMedicine(x))

Elephantopus is a traditional medicine.

∀x (Elephantopus(x) → TraditionalMedicine(x))

Uncertain

All Yale dormitories are located on the Yale campus. All Yale buildings managed by Yale Housing are dormitories. All Yale buildings operated by Yale Housing staff are managed by Yale Housing. None of the Yale buildings open to students were built before 1701. All Yale buildings located on the Yale campus are open to students. Harkness is either a Yale building operated by Yale Housing staff, or it is located on York Street.

∀x (YaleDormitory(x) → LocatedOn(x, yaleCampus)) ∀x ((YaleBuildings(x) ∧ ManagedBy(x, yaleHousing)) → YaleDormitory(x)) ∀x ((YaleBuildings(x) ∧ OperatedBy(x, yaleHousingStaff)) → ManagedBy(x, yaleHousing)) ∀x ((YaleBuildings(x) ∧ OpenToStudents(x)) → (¬∃y(Before(y, yr1701) ∧ Established(x, y)))) ∀x ((YaleBuildings(x) ∧ LocatedOn(x, yaleCampus)) → OpenToStudents(x)) YaleBuildings(harkness) ∧ (OperatedBy(x, harkness) ⊕ LocatedOn(harkness, yaleCampus))

Harkness is a Yale dormitory.

YaleDormitory(harkness)

Uncertain

All Yale dormitories are located on the Yale campus. All Yale buildings managed by Yale Housing are dormitories. All Yale buildings operated by Yale Housing staff are managed by Yale Housing. None of the Yale buildings open to students were built before 1701. All Yale buildings located on the Yale campus are open to students. Harkness is either a Yale building operated by Yale Housing staff, or it is located on York Street.

∀x (YaleDormitory(x) → LocatedOn(x, yaleCampus)) ∀x ((YaleBuildings(x) ∧ ManagedBy(x, yaleHousing)) → YaleDormitory(x)) ∀x ((YaleBuildings(x) ∧ OperatedBy(x, yaleHousingStaff)) → ManagedBy(x, yaleHousing)) ∀x ((YaleBuildings(x) ∧ OpenToStudents(x)) → (¬∃y(Before(y, yr1701) ∧ Established(x, y)))) ∀x ((YaleBuildings(x) ∧ LocatedOn(x, yaleCampus)) → OpenToStudents(x)) YaleBuildings(harkness) ∧ (OperatedBy(x, harkness) ⊕ LocatedOn(harkness, yaleCampus))

Harkness is not a Yale dormitory.

¬YaleDormitory(harkness)

Uncertain

All Yale dormitories are located on the Yale campus. All Yale buildings managed by Yale Housing are dormitories. All Yale buildings operated by Yale Housing staff are managed by Yale Housing. None of the Yale buildings open to students were built before 1701. All Yale buildings located on the Yale campus are open to students. Harkness is either a Yale building operated by Yale Housing staff, or it is located on York Street.

∀x (YaleDormitory(x) → LocatedOn(x, yaleCampus)) ∀x ((YaleBuildings(x) ∧ ManagedBy(x, yaleHousing)) → YaleDormitory(x)) ∀x ((YaleBuildings(x) ∧ OperatedBy(x, yaleHousingStaff)) → ManagedBy(x, yaleHousing)) ∀x ((YaleBuildings(x) ∧ OpenToStudents(x)) → (¬∃y(Before(y, yr1701) ∧ Established(x, y)))) ∀x ((YaleBuildings(x) ∧ LocatedOn(x, yaleCampus)) → OpenToStudents(x)) YaleBuildings(harkness) ∧ (OperatedBy(x, harkness) ⊕ LocatedOn(harkness, yaleCampus))

Harkness is established before 1701.

∃y(Before(y, year1701) ∧ Established(x, y))

False

All Yale dormitories are located on the Yale campus. All Yale buildings managed by Yale Housing are dormitories. All Yale buildings operated by Yale Housing staff are managed by Yale Housing. None of the Yale buildings open to students were built before 1701. All Yale buildings located on the Yale campus are open to students. Harkness is either a Yale building operated by Yale Housing staff, or it is located on York Street.

∀x (YaleDormitory(x) → LocatedOn(x, yaleCampus)) ∀x ((YaleBuildings(x) ∧ ManagedBy(x, yaleHousing)) → YaleDormitory(x)) ∀x ((YaleBuildings(x) ∧ OperatedBy(x, yaleHousingStaff)) → ManagedBy(x, yaleHousing)) ∀x ((YaleBuildings(x) ∧ OpenToStudents(x)) → (¬∃y(Before(y, yr1701) ∧ Established(x, y)))) ∀x ((YaleBuildings(x) ∧ LocatedOn(x, yaleCampus)) → OpenToStudents(x)) YaleBuildings(harkness) ∧ (OperatedBy(x, harkness) ⊕ LocatedOn(harkness, yaleCampus))

Harkness is not established before 1701.

¬∃y(Before(y, year1701) ∧ Established(x, y))

True

There are no mansion houses in an urban area. All skyscrapers are in urban areas. Every creepy haunted house is a mansion house. Every terrifying building on Halloween is a creepy haunted house. The LaLaurie House is a creepy haunted house or a terrifying building on Halloween.

∀x (InUrbanArea(x) → ¬MansionHouse(x)) ∀x (Skyscraper(x) → InUrbanArea(x)) ∀x (CreepyHauntedHouse(x) → MansionHouse(x)) ∀x (TerrifyingBuilding(x) ∧ OnHalloween(x) → CreepyHauntedHouse(x)) CreepyHauntedHouse(laLaurieHouse) ∨ TerrifyingBuilding(laLaurieHouse) ∧ OnHalloween(laLaurieHouse)

The LaLaurie House is a skyscraper.

Skyscraper(laLaurieHouse)

False

There are no mansion houses in an urban area. All skyscrapers are in urban areas. Every creepy haunted house is a mansion house. Every terrifying building on Halloween is a creepy haunted house. The LaLaurie House is a creepy haunted house or a terrifying building on Halloween.

∀x (InUrbanArea(x) → ¬MansionHouse(x)) ∀x (Skyscraper(x) → InUrbanArea(x)) ∀x (CreepyHauntedHouse(x) → MansionHouse(x)) ∀x (TerrifyingBuilding(x) ∧ OnHalloween(x) → CreepyHauntedHouse(x)) CreepyHauntedHouse(laLaurieHouse) ∨ TerrifyingBuilding(laLaurieHouse) ∧ OnHalloween(laLaurieHouse)

The LaLaurie House is not a skyscraper.

¬Skyscraper(laLaurieHouse)

True

There are no mansion houses in an urban area. All skyscrapers are in urban areas. Every creepy haunted house is a mansion house. Every terrifying building on Halloween is a creepy haunted house. The LaLaurie House is a creepy haunted house or a terrifying building on Halloween.

∀x (InUrbanArea(x) → ¬MansionHouse(x)) ∀x (Skyscraper(x) → InUrbanArea(x)) ∀x (CreepyHauntedHouse(x) → MansionHouse(x)) ∀x (TerrifyingBuilding(x) ∧ OnHalloween(x) → CreepyHauntedHouse(x)) CreepyHauntedHouse(laLaurieHouse) ∨ TerrifyingBuilding(laLaurieHouse) ∧ OnHalloween(laLaurieHouse)

The LaLaurie House is a terrifying building on Halloween.

TerrifyingBuilding(laLaurieHouse) ∧ OnHalloween(laLaurieHouse)

Uncertain

There are no mansion houses in an urban area. All skyscrapers are in urban areas. Every creepy haunted house is a mansion house. Every terrifying building on Halloween is a creepy haunted house. The LaLaurie House is a creepy haunted house or a terrifying building on Halloween.

∀x (InUrbanArea(x) → ¬MansionHouse(x)) ∀x (Skyscraper(x) → InUrbanArea(x)) ∀x (CreepyHauntedHouse(x) → MansionHouse(x)) ∀x (TerrifyingBuilding(x) ∧ OnHalloween(x) → CreepyHauntedHouse(x)) CreepyHauntedHouse(laLaurieHouse) ∨ TerrifyingBuilding(laLaurieHouse) ∧ OnHalloween(laLaurieHouse)

The LaLaurie House is either a skyscraper or a mansion house.

Skyscraper(laLaurieHouse) ⊕ MansionHouse(laLaurieHouse)

True

There are no mansion houses in an urban area. All skyscrapers are in urban areas. Every creepy haunted house is a mansion house. Every terrifying building on Halloween is a creepy haunted house. The LaLaurie House is a creepy haunted house or a terrifying building on Halloween.

∀x (InUrbanArea(x) → ¬MansionHouse(x)) ∀x (Skyscraper(x) → InUrbanArea(x)) ∀x (CreepyHauntedHouse(x) → MansionHouse(x)) ∀x (TerrifyingBuilding(x) ∧ OnHalloween(x) → CreepyHauntedHouse(x)) CreepyHauntedHouse(laLaurieHouse) ∨ TerrifyingBuilding(laLaurieHouse) ∧ OnHalloween(laLaurieHouse)

The LaLaurie House is either a skyscraper or in an urban area.

Skyscraper(laLaurieHouse) ⊕ UrbanArea(laLaurieHouse)

False

There are no mansion houses in an urban area. All skyscrapers are in urban areas. Every creepy haunted house is a mansion house. Every terrifying building on Halloween is a creepy haunted house. The LaLaurie House is a creepy haunted house or a terrifying building on Halloween.

∀x (InUrbanArea(x) → ¬MansionHouse(x)) ∀x (Skyscraper(x) → InUrbanArea(x)) ∀x (CreepyHauntedHouse(x) → MansionHouse(x)) ∀x (TerrifyingBuilding(x) ∧ OnHalloween(x) → CreepyHauntedHouse(x)) CreepyHauntedHouse(laLaurieHouse) ∨ TerrifyingBuilding(laLaurieHouse) ∧ OnHalloween(laLaurieHouse)

The LaLaurie House is either a skyscraper or a creepy haunted house.

Skyscraper(laLaurieHouse) ⊕ CreepyHauntedHouse(laLaurieHouse)

True

There are no mansion houses in an urban area. All skyscrapers are in urban areas. Every creepy haunted house is a mansion house. Every terrifying building on Halloween is a creepy haunted house. The LaLaurie House is a creepy haunted house or a terrifying building on Halloween.

∀x (InUrbanArea(x) → ¬MansionHouse(x)) ∀x (Skyscraper(x) → InUrbanArea(x)) ∀x (CreepyHauntedHouse(x) → MansionHouse(x)) ∀x (TerrifyingBuilding(x) ∧ OnHalloween(x) → CreepyHauntedHouse(x)) CreepyHauntedHouse(laLaurieHouse) ∨ TerrifyingBuilding(laLaurieHouse) ∧ OnHalloween(laLaurieHouse)

If the LaLaurie House is not a mansion or not in an urban area, then it is either a skyscraper or in an urban area.

¬(MansionHouse(laLaurieHouse) ∧ InUrbanArea(laLaurieHouse)) → (Skyscraper(laLaurieHouse) ⊕ InUrbanArea(laLaurieHouse))

False

There are no mansion houses in an urban area. All skyscrapers are in urban areas. Every creepy haunted house is a mansion house. Every terrifying building on Halloween is a creepy haunted house. The LaLaurie House is a creepy haunted house or a terrifying building on Halloween.

∀x (InUrbanArea(x) → ¬MansionHouse(x)) ∀x (Skyscraper(x) → InUrbanArea(x)) ∀x (CreepyHauntedHouse(x) → MansionHouse(x)) ∀x (TerrifyingBuilding(x) ∧ OnHalloween(x) → CreepyHauntedHouse(x)) CreepyHauntedHouse(laLaurieHouse) ∨ TerrifyingBuilding(laLaurieHouse) ∧ OnHalloween(laLaurieHouse)

If the LaLaurie House is either a skyscraper or a mansion house, then it is in an urban area.

Skyscraper(laLaurieHouse) ⊕ MansionHouse(laLaurieHouse) → InUrbanArea(laLaurieHouse)

False

There are no mansion houses in an urban area. All skyscrapers are in urban areas. Every creepy haunted house is a mansion house. Every terrifying building on Halloween is a creepy haunted house. The LaLaurie House is a creepy haunted house or a terrifying building on Halloween.

∀x (InUrbanArea(x) → ¬MansionHouse(x)) ∀x (Skyscraper(x) → InUrbanArea(x)) ∀x (CreepyHauntedHouse(x) → MansionHouse(x)) ∀x (TerrifyingBuilding(x) ∧ OnHalloween(x) → CreepyHauntedHouse(x)) CreepyHauntedHouse(laLaurieHouse) ∨ TerrifyingBuilding(laLaurieHouse) ∧ OnHalloween(laLaurieHouse)

If the LaLaurie House is either a skyscraper or a mansion house, then it is neither a creepy haunted house nor a terrifying building on Halloween.

Skyscraper(laLaurieHouse) ⊕ MansionHouse(laLaurieHouse) → ¬(CreepyHauntedHouse(laLaurieHouse) ∨ TerrifyingBuilding(laLaurieHouse) ∧ OnHalloween(laLaurieHouse))

False

There are no mansion houses in an urban area. All skyscrapers are in urban areas. Every creepy haunted house is a mansion house. Every terrifying building on Halloween is a creepy haunted house. The LaLaurie House is a creepy haunted house or a terrifying building on Halloween.

∀x (InUrbanArea(x) → ¬MansionHouse(x)) ∀x (Skyscraper(x) → InUrbanArea(x)) ∀x (CreepyHauntedHouse(x) → MansionHouse(x)) ∀x (TerrifyingBuilding(x) ∧ OnHalloween(x) → CreepyHauntedHouse(x)) CreepyHauntedHouse(laLaurieHouse) ∨ TerrifyingBuilding(laLaurieHouse) ∧ OnHalloween(laLaurieHouse)

If the LaLaurie House is either a skyscraper or a creepy haunted house, then it is not a mansion house.

Skyscraper(laLaurieHouse) ⊕ CreepyHauntedHouse(laLaurieHouse) → ¬MansionHouse(laLaurieHouse)

False

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.

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)

There is a nature reserve in Vietnam.

∃x (NatureReserve(x) ∧ LocatedIn(x, vietnam))

True

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.

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)

Phuoc Binh is a UNESCO Heritage Site.

UNESCOWorldHeritageSite(phuocBinh))

Uncertain

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.

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)

Phuoc Binh is managed by the People's Committee.

Mangedby(phuocBinh, peoplesCommittee)

True

Greyhound racing is a competitive sport where spectators bet on greyhounds. Greyhound racing involves coursing. Some competitive sports where spectators bet on things are banned. Coursing involves spectators betting on a hare being pursued by greyhounds. Spectators betting on a hare is a small game. If a competitive sport involves spectators betting on small games, then it is banned.

∀x (GreyhoundRacing(x) → ∃y (CompetitiveSport(x) ∧ Greyhound(y) ∧ BetOn(spectators, y, x))) ∀x (GreyhoundRacing(x) → Coursing(x)) ∃x ∃y (CompetitiveSport(x) ∧ BetOn(spectators, y, x) ∧ Banned(x)) ∀x ∃y ∃z (Coursing(x) → Hare(y) ∧ BetOn(spectators, y, x) ∧ GreyHound(z) ∧ PursuedBy(y, z)) ∃x ∀y (Hare(x) ∧ BetOn(spectators, x, y) → SmallGame(y)) ∀x ∃y (CompetitiveSport(x) ∧ SmallGame(y) ∧ BetOn(spectators, y, x) → Banned(x))

No coursing is banned.

∀x (Coursing(x) ∧ ¬Banned(x))

False

Greyhound racing is a competitive sport where spectators bet on greyhounds. Greyhound racing involves coursing. Some competitive sports where spectators bet on things are banned. Coursing involves spectators betting on a hare being pursued by greyhounds. Spectators betting on a hare is a small game. If a competitive sport involves spectators betting on small games, then it is banned.

∀x (GreyhoundRacing(x) → ∃y (CompetitiveSport(x) ∧ Greyhound(y) ∧ BetOn(spectators, y, x))) ∀x (GreyhoundRacing(x) → Coursing(x)) ∃x ∃y (CompetitiveSport(x) ∧ BetOn(spectators, y, x) ∧ Banned(x)) ∀x ∃y ∃z (Coursing(x) → Hare(y) ∧ BetOn(spectators, y, x) ∧ GreyHound(z) ∧ PursuedBy(y, z)) ∃x ∀y (Hare(x) ∧ BetOn(spectators, x, y) → SmallGame(y)) ∀x ∃y (CompetitiveSport(x) ∧ SmallGame(y) ∧ BetOn(spectators, y, x) → Banned(x))

Greyhound racing is a competitive sport.

∀x (GreyhoundRacing(x) → CompetitiveSport(x))

True

If a soccer player receives two yellow cards in one game, this player will be ejected from the rest of the game. If a soccer player receives one red card in one game, this player will be ejected from the rest of the game. Henry is a soccer player. In one game, Henry receives one yellow card and one red card.

∀x (SoccerPlayer(x) ∧ Receive(x, twoYellowCard) → EjectFromRestOfGame(x)) ∀x (SoccerPlayer(x) ∧ Receive(x, oneRedCard)) → EjectFromRestOfGame(x)) SoccerPlayer(henry) Receive(henry, oneYellowCard) ∧ Receive(x, oneRedCard)

Henry will be ejected from the rest of the game.

EjectFromRestOfGame(henry)

True

If a soccer player receives two yellow cards in one game, this player will be ejected from the rest of the game. If a soccer player receives one red card in one game, this player will be ejected from the rest of the game. Henry is a soccer player. In one game, Henry receives one yellow card and one red card.

∀x (SoccerPlayer(x) ∧ Receive(x, twoYellowCard) → EjectFromRestOfGame(x)) ∀x (SoccerPlayer(x) ∧ Receive(x, oneRedCard)) → EjectFromRestOfGame(x)) SoccerPlayer(henry) Receive(henry, oneYellowCard) ∧ Receive(x, oneRedCard)

Henry will not be ejected from the rest of the game.

¬EjectFromRestOfGame(henry)

False

Trees are plants. Some living things are trees.

∀x (Tree(x) → Plant(x)) ∃x ∃y (Living(x) ∧ Living(y) ∧ Tree(x) ∧ Tree(y) ∧ ¬(x=y))

Some living things are plants.

∃x ∃y (Living(x) ∧ Living(y) ∧ Plant(x) ∧ Plant(y) ∧ ¬(x=y))

True

Notable people with the given name include Dagfinn Aarskog, Dagfinn Bakke and Dagfinn Dahl. Dagfinn Aarskog is a Norwegian physician. Dagfinn Dahl is a Norwegian barrister.

GivenName(nameDagfinn) ∧ Named(dagfinnAarskog, nameDagfinn) ∧ NotablePerson(dagfinnAarskog) ∧ Named(dagfinnBakke, nameDagfinn) ∧ NotablePerson(dagfinnBakke) ∧ Named(dagfinnDahl, nameDagfinn) ∧ NotablePerson(dagfinnDahl) Norwegian(dagfinnAarskog) ∧ Physician(dagfinnAarskog) Norwegian(dagfinnDahl) ∧ Barrister(dagfinnDahl)

Dagfinn Aarskog is a notable person.

NotablePerson(dagfinnAarskog)

True

Notable people with the given name include Dagfinn Aarskog, Dagfinn Bakke and Dagfinn Dahl. Dagfinn Aarskog is a Norwegian physician. Dagfinn Dahl is a Norwegian barrister.

GivenName(nameDagfinn) ∧ Named(dagfinnAarskog, nameDagfinn) ∧ NotablePerson(dagfinnAarskog) ∧ Named(dagfinnBakke, nameDagfinn) ∧ NotablePerson(dagfinnBakke) ∧ Named(dagfinnDahl, nameDagfinn) ∧ NotablePerson(dagfinnDahl) Norwegian(dagfinnAarskog) ∧ Physician(dagfinnAarskog) Norwegian(dagfinnDahl) ∧ Barrister(dagfinnDahl)

Dagfinn is Dagfinn Aarskog's given name.

Named(dagfinnAarskog, nameDagfinn)

True

Notable people with the given name include Dagfinn Aarskog, Dagfinn Bakke and Dagfinn Dahl. Dagfinn Aarskog is a Norwegian physician. Dagfinn Dahl is a Norwegian barrister.

GivenName(nameDagfinn) ∧ Named(dagfinnAarskog, nameDagfinn) ∧ NotablePerson(dagfinnAarskog) ∧ Named(dagfinnBakke, nameDagfinn) ∧ NotablePerson(dagfinnBakke) ∧ Named(dagfinnDahl, nameDagfinn) ∧ NotablePerson(dagfinnDahl) Norwegian(dagfinnAarskog) ∧ Physician(dagfinnAarskog) Norwegian(dagfinnDahl) ∧ Barrister(dagfinnDahl)

Dagfinn Dahl is a Norwegian physician.

Norwegian(dagfinnDahl) ∧ Physician(dagfinnDahl)

Uncertain

If a movie is popular, some people enjoy watching it. All things that some people enjoy attract attention.

∀x (Movie(x) ∧ Popular(x) → ∃y ∃z (Person(y) ∧ EnjoyWatching(y, x) ∧ Person(z) ∧ EnjoyWatching(z, x) ∧ ¬(y=z))) ∀x (∃y ∃z (Person(y) ∧ EnjoyWatching(y, x) ∧ Person(z) ∧ EnjoyWatching(z, x)) → Attract(x, attention))

If a movie is popular, then it attracts attention.

∀x (Movie(x) ∧ Popular(x) → Attract(x, attention))

True

It is not true that some giant language models do not have good performance. All language models with good performance are used by some researchers. If a language model is used by some researchers, it is popular. If BERT is a giant language model, then GPT-3 is also a giant language model. BERT is a giant language model.

¬(∃x (LanguageModel(x) ∧ Giant(x) ∧ ¬GoodPerformance(x))) ∀x ∃y ∃z (LanguageModel(x) ∧ GoodPerformance(x) → ¬(x=y) ∧ Researcher(y) ∧ UsedBy(x, y) ∧ Researcher(z) ∧ UsedBy(x, z)) ∀x ∃y ∃z (LanguageModel(x) ∧ ¬(x=y) ∧ Researcher(y) ∧ UsedBy(x, y) ∧ Researcher(z) ∧ UsedBy(x, z) → Popular(x)) (LanguageModel(bert) ∧ Giant(bert)) → (LanguageModel(gpt-3) ∧ Giant(gpt-3)). LanguageModel(bert) ∧ Giant(bert)

GPT-3 is popular.

Popular(gpt-3)

True

St Johnstone is a Scottish team. St Johnstone is part of the Scottish Premiership league. If a team is part of the league, it has joined the league. St Johnstone and Minsk are different teams. For two teams, either one team wins, or the other team wins. Minsk won against St Johnstone.

Scottish(stJohnstone) ∧ Team(stJohnstone) PartOf(stJohnstone, scottishPremiership) ∧ League(scottishPremiership) ∀x ∀y (Team(x) ∧ League(y) ∧ PartOf(x, y) → Joined(x, y)) ¬(misnk=stJohnstone) ∀x ∀y (¬(x=y) → WonAgainst(x, y) ⊕ WonAgainst(y, x)) WonAgainst(minsk, stJohnstone)

At least one Scottish team has joined the Scottish Premiership.

∃x (Scottish(x) ∧ Joined(x, scottishPremiership))

True

St Johnstone is a Scottish team. St Johnstone is part of the Scottish Premiership league. If a team is part of the league, it has joined the league. St Johnstone and Minsk are different teams. For two teams, either one team wins, or the other team wins. Minsk won against St Johnstone.

Scottish(stJohnstone) ∧ Team(stJohnstone) PartOf(stJohnstone, scottishPremiership) ∧ League(scottishPremiership) ∀x ∀y (Team(x) ∧ League(y) ∧ PartOf(x, y) → Joined(x, y)) ¬(misnk=stJohnstone) ∀x ∀y (¬(x=y) → WonAgainst(x, y) ⊕ WonAgainst(y, x)) WonAgainst(minsk, stJohnstone)

St Johnstone won against Minsk.

WonGame(stJohnstone, minsk)

False

St Johnstone is a Scottish team. St Johnstone is part of the Scottish Premiership league. If a team is part of the league, it has joined the league. St Johnstone and Minsk are different teams. For two teams, either one team wins, or the other team wins. Minsk won against St Johnstone.

Scottish(stJohnstone) ∧ Team(stJohnstone) PartOf(stJohnstone, scottishPremiership) ∧ League(scottishPremiership) ∀x ∀y (Team(x) ∧ League(y) ∧ PartOf(x, y) → Joined(x, y)) ¬(misnk=stJohnstone) ∀x ∀y (¬(x=y) → WonAgainst(x, y) ⊕ WonAgainst(y, x)) WonAgainst(minsk, stJohnstone)

Minsk joined the Scottish Premiership.

Joined(minsk, scottishPremiership))

Uncertain

No Boeing-737 plane has more than 300 seats. All of the planes acquired by Delta in this batch are Boeing-737. Planes either have more than 300 seats or have a capacity of 100 passengers. All planes with a capacity of 100 passengers are scheduled for a short-distance flight. All planes with a capacity of 100 passengers are produced before 2010. Jake32 is either a Boeing-737 plane or a plane acquired by Delta in this batch. T10 is either both a Boeing-737 plane and acquired by Delta in this batch, or it is neither.

∀x (Plane(x) ∧ Boeing737(x) → (¬∃y(GreaterThan(y, num300) ∧ EquippedWithSeats(x,y))) ∀x (Plane(x) ∧ AcquiredBy(x, delta) → Boeing737(x)) ∀x (Plane(x) → ((∃y(GreaterThan(y, num300) ∧ EquippedWithSeats(x,y))) ⊕ (∃y(Equals(y, num100) ∧ EquippedWithSeats(x,y)))) ∀x (Plane(x) ∧ ∃y(Equals(y, num100) ∧ EquippedWithSeats(x,y)) → ScheduledFor(x, shortdistanceflight)) ∀x (Plane(x) ∧ ∃y(Equals(y, num100) ∧ EquippedWithSeats(x,y)) → ∃z(Before(z, yr2010) ∧ Produced(x, z)) (Boeing737(jake32) ∧ Plane(jake32)) ⊕ (AcquiredByDeltaInThisBatch(jake32) ∧ Plane(jake32)) ¬((Boeing737(t10) ∧ Plane(t10)) ⊕ (AcquiredByDeltaInThisBatch(t10) ∧ Plane(t10)))

Jake32 was produced before 2010 and is scheduled for a short-distance flight.

∃z(Before(z, year2010) ∧ Produced(jake32, z)) ∧ ScheduledFor(jake32, shortdistanceflight))

True

No Boeing-737 plane has more than 300 seats. All of the planes acquired by Delta in this batch are Boeing-737. Planes either have more than 300 seats or have a capacity of 100 passengers. All planes with a capacity of 100 passengers are scheduled for a short-distance flight. All planes with a capacity of 100 passengers are produced before 2010. Jake32 is either a Boeing-737 plane or a plane acquired by Delta in this batch. T10 is either both a Boeing-737 plane and acquired by Delta in this batch, or it is neither.

∀x (Plane(x) ∧ Boeing737(x) → (¬∃y(GreaterThan(y, num300) ∧ EquippedWithSeats(x,y))) ∀x (Plane(x) ∧ AcquiredBy(x, delta) → Boeing737(x)) ∀x (Plane(x) → ((∃y(GreaterThan(y, num300) ∧ EquippedWithSeats(x,y))) ⊕ (∃y(Equals(y, num100) ∧ EquippedWithSeats(x,y)))) ∀x (Plane(x) ∧ ∃y(Equals(y, num100) ∧ EquippedWithSeats(x,y)) → ScheduledFor(x, shortdistanceflight)) ∀x (Plane(x) ∧ ∃y(Equals(y, num100) ∧ EquippedWithSeats(x,y)) → ∃z(Before(z, yr2010) ∧ Produced(x, z)) (Boeing737(jake32) ∧ Plane(jake32)) ⊕ (AcquiredByDeltaInThisBatch(jake32) ∧ Plane(jake32)) ¬((Boeing737(t10) ∧ Plane(t10)) ⊕ (AcquiredByDeltaInThisBatch(t10) ∧ Plane(t10)))

Jake32 is not produced before 2010 and is not scheduled for a short-distance flight.

¬(∃z(Before(z, year2010) ∧ Produced(jake32, z)) ∧ ScheduledFor(jake32, shortdistanceflight)))

False

No Boeing-737 plane has more than 300 seats. All of the planes acquired by Delta in this batch are Boeing-737. Planes either have more than 300 seats or have a capacity of 100 passengers. All planes with a capacity of 100 passengers are scheduled for a short-distance flight. All planes with a capacity of 100 passengers are produced before 2010. Jake32 is either a Boeing-737 plane or a plane acquired by Delta in this batch. T10 is either both a Boeing-737 plane and acquired by Delta in this batch, or it is neither.

∀x (Plane(x) ∧ Boeing737(x) → (¬∃y(GreaterThan(y, num300) ∧ EquippedWithSeats(x,y))) ∀x (Plane(x) ∧ AcquiredBy(x, delta) → Boeing737(x)) ∀x (Plane(x) → ((∃y(GreaterThan(y, num300) ∧ EquippedWithSeats(x,y))) ⊕ (∃y(Equals(y, num100) ∧ EquippedWithSeats(x,y)))) ∀x (Plane(x) ∧ ∃y(Equals(y, num100) ∧ EquippedWithSeats(x,y)) → ScheduledFor(x, shortdistanceflight)) ∀x (Plane(x) ∧ ∃y(Equals(y, num100) ∧ EquippedWithSeats(x,y)) → ∃z(Before(z, yr2010) ∧ Produced(x, z)) (Boeing737(jake32) ∧ Plane(jake32)) ⊕ (AcquiredByDeltaInThisBatch(jake32) ∧ Plane(jake32)) ¬((Boeing737(t10) ∧ Plane(t10)) ⊕ (AcquiredByDeltaInThisBatch(t10) ∧ Plane(t10)))

Jake32 is produced before 2010 or scheduled for a short-distance flight.

∃z(Before(z, year2010) ∧ Produced(jake32, z)) ∨ ScheduledFor(jake32, shortdistanceflight))

True

No Boeing-737 plane has more than 300 seats. All of the planes acquired by Delta in this batch are Boeing-737. Planes either have more than 300 seats or have a capacity of 100 passengers. All planes with a capacity of 100 passengers are scheduled for a short-distance flight. All planes with a capacity of 100 passengers are produced before 2010. Jake32 is either a Boeing-737 plane or a plane acquired by Delta in this batch. T10 is either both a Boeing-737 plane and acquired by Delta in this batch, or it is neither.

∀x (Plane(x) ∧ Boeing737(x) → (¬∃y(GreaterThan(y, num300) ∧ EquippedWithSeats(x,y))) ∀x (Plane(x) ∧ AcquiredBy(x, delta) → Boeing737(x)) ∀x (Plane(x) → ((∃y(GreaterThan(y, num300) ∧ EquippedWithSeats(x,y))) ⊕ (∃y(Equals(y, num100) ∧ EquippedWithSeats(x,y)))) ∀x (Plane(x) ∧ ∃y(Equals(y, num100) ∧ EquippedWithSeats(x,y)) → ScheduledFor(x, shortdistanceflight)) ∀x (Plane(x) ∧ ∃y(Equals(y, num100) ∧ EquippedWithSeats(x,y)) → ∃z(Before(z, yr2010) ∧ Produced(x, z)) (Boeing737(jake32) ∧ Plane(jake32)) ⊕ (AcquiredByDeltaInThisBatch(jake32) ∧ Plane(jake32)) ¬((Boeing737(t10) ∧ Plane(t10)) ⊕ (AcquiredByDeltaInThisBatch(t10) ∧ Plane(t10)))

Jake32 is neither produced before 2010 nor scheduled for a short-distance flight.

¬∃z(Before(z, year2010) ∧ Produced(jake32, z)) ∧ ¬ScheduledFor(jake32, shortdistanceflight))

False

The SAT test is wholly owned and developed by the College Board. The SAT test is intended to assess students' readiness for college. The SAT was originally designed not to be aligned with high school curricula. Several adjustments were made to the version of the SAT introduced in 2016 to align with the high school curriculum.

OwnedBy(sAT, collegeBoard) ∧ DevelopedBy(sAT, collegeBoard) ∧ ¬(∃y (¬(y=collegeBoard) ∧ (OwnedBy(sAT, y) ∨ DevelopedBy(sAT, y))) IntendedToAssess(sAT, studentsReadinessForCollege) OriginallyDesignedToBeAlignedWith(sAT, highSchoolCurricula) AdjustmentMadeIn(sAT, 2016, toAlignWithHighSchoolCurriculum)

The SAT test is owned by the College Board and other third parties.

OwnedBy(sAT, collegeBoard) ∧ OwnedBy(sAT, otherThirdParties)

False

The SAT test is wholly owned and developed by the College Board. The SAT test is intended to assess students' readiness for college. The SAT was originally designed not to be aligned with high school curricula. Several adjustments were made to the version of the SAT introduced in 2016 to align with the high school curriculum.

OwnedBy(sAT, collegeBoard) ∧ DevelopedBy(sAT, collegeBoard) ∧ ¬(∃y (¬(y=collegeBoard) ∧ (OwnedBy(sAT, y) ∨ DevelopedBy(sAT, y))) IntendedToAssess(sAT, studentsReadinessForCollege) OriginallyDesignedToBeAlignedWith(sAT, highSchoolCurricula) AdjustmentMadeIn(sAT, 2016, toAlignWithHighSchoolCurriculum)

The SAT test assesses students' math skills.

IntendedToAssess(sAT, studentsMathSkill)

Uncertain

Rafa Nadal was born in Mallorca. Rafa Nadal is a professional tennis player. Nadal's win ratio is high. All players in the Big 3 are professionals who have a high win ratio.

BornIn(rafaNadal, mallorca) ProfessionalTennisPlayer(rafaNadal) HighWinRatio(rafaNadal) ∀x ((ProfessionalTennisPlayer(x) ∧ HighWinRatio(x)) → InBig3(x))

Nadal was not born in Mallorca.

¬BornIn(rafaNadal, mallorca)

False

Rafa Nadal was born in Mallorca. Rafa Nadal is a professional tennis player. Nadal's win ratio is high. All players in the Big 3 are professionals who have a high win ratio.

BornIn(rafaNadal, mallorca) ProfessionalTennisPlayer(rafaNadal) HighWinRatio(rafaNadal) ∀x ((ProfessionalTennisPlayer(x) ∧ HighWinRatio(x)) → InBig3(x))

Nadal is in the Big 3.

InBig3(rafaNadal)

True

Rafa Nadal was born in Mallorca. Rafa Nadal is a professional tennis player. Nadal's win ratio is high. All players in the Big 3 are professionals who have a high win ratio.

BornIn(rafaNadal, mallorca) ProfessionalTennisPlayer(rafaNadal) HighWinRatio(rafaNadal) ∀x ((ProfessionalTennisPlayer(x) ∧ HighWinRatio(x)) → InBig3(x))

Nadal is the greatest player of all time.

GreatestOfAllTime(rafaNadal)

Uncertain