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James Cocks was a Whig politician who sat in the House of Commons. | Whig(james) ∧ Politician(james) ∧ SatInHouseOfCommons(james) |
A British is a European. | ∀x (British(x) → European(x)) |
Any lawyer is familiar with laws. | ∀x (Lawyer(x) → FamiliarWithLaws(x)) |
Some Whigs speak French. | ∃x ∃y (Whig(x) ∧ SpeakFrench(x)) ∧ (¬(x=y)) ∧ (Whig(y) ∧ SpeakFrench(y)) |
No lawyer ever sat in the House of Commons. | ∀x (Lawyer(x) → ¬SatInHouseOfCommons(x)) |
Some European was familiar with laws. | ∃x (European(x) ∧ FamiliarWithLaws(x)) |
James Cocks speaks French. | SpeakFrench(james) |
Beasts of Prey is a fantasy novel or a science fiction novel, or both. | Novel(beastsOfPrey) → (Fantasy(beastsOfPrey) ∨ ScienceFiction(beastsOfPrey)) |
Science fiction novels are not about mythological creatures | ∀x ∀y (ScienceFiction(x) ∧ Mythological(y) ∧ Creature(y) → ¬About(x, y)) |
Beasts of Prey Is about a creature known as the Shetani. | About(beastsOfPrey, shetani) ∧ Creature(shetani) |
Shetanis are mythological. | Mythological(shetani) |
Beasts of prey is a fantasy novel. | Fantasy(beastsOfpPrey) ∧ Novel(beastsOfPrey) |
Beasts of prey isn't a science fiction novel. | ¬ScienceFiction(beastsofprey) ∧ Novel(beastsOfPrey) |
A shetani is either mythological or a creature. | Mythological(shetani) ⊕ Creature(shetani) |
Odell is an English surname originating in Odell, Bedfordshire. | Surname(nameODell) ∧ From(nameODell, oDellBedfordshire) |
In some families, Odell is spelled O'Dell in a mistaken Irish adaptation. | MistakenSpellingOf(nameO'Dell, nameODell) ∧ (∃x∃y(Family(x) ∧ Named(x, nameO'Dell) ∧ (¬(x=y)) ∧ Family(y) ∧ Named(y, nameO'Dell)) |
Notable people with surnames include Amy Odell, Jack Odell, and Mats Odell. | Named(amyODell, nameODell) ∧ NotablePerson(amyODell) ∧ Named(jackODell, nameODell) ∧ NotablePerson(jackODell) ∧ Named(matsODell, nameODell) ∧ NotablePerson(matsODell) |
Amy Odell is a British singer-songwriter. | British(amyODell) ∧ Singer(amyODell) ∧ SongWriter(amyODell) |
Jack Odell is an English toy inventor. | English(jackODell) ∧ ToyInventor(jackODell) |
Jack Odell is a notable person. | NotablePerson(jackODell) |
Odell is Amy Odell's surname. | Named(amyODell, nameODell) |
Amy Odell is an English toy inventor. | English(amyODell) ∧ ToyInventor(amyODell) |
Amy Odell is also Amy O'Dell. | Named(amyODell, nameODell) ∧ Named(amyODell, nameO'Dell) |
If you go somewhere by train, you will not lose time. | ∀x (GoByTrain(x) → ¬LoseTime(x)) |
If you go somewhere by car and meet a traffic jam, you will lose time. | ∀x((GoByCar(x) ∧ Meet(x, trafficJam)) → LoseTime(x)) |
If you lose time, you will be late for work. | ∀x (LoseTime(x) → LateForWork(x)) |
Mary can get from New Haven to New York City either by train or car. | FromAndTo(newHaven, newYork) ∧ (GoByTrain(mary) ⊕ GoByCar(mary)) |
Mary is late for work. | LateForWork(mary) |
Mary gets from New Haven to New York City by train. | FromAndTo(newHaven, newYork) ∧ GoByTrain(mary) |
Mary gets from New Haven to New York City by car. | FromAndTo(newHaven, newYork) ∧ GoByCar(mary) |
Mary meets a traffic jam. | Meet(mary, trafficJam) |
If a person is hungry, the person is uncomfortable. | ∀x (Hungry(x) → Uncomfortable(x)) |
If a person is uncomfortable, the person is unhappy. | ∀x (Uncomfortable(x) → ¬Happy(x)) |
If a person is not hungry, the person is unhappy. | ∀x (¬Hungry(x) → ¬Happy(x)) |
Tipped employees are not entitled to be paid the federal minimum wage by their employees. | ∀x (TippedEmployee(x) → ¬EntitledTo(x, federalMinimumWage)) |
If a person is a white-collar worker, they are entitled to be paid the federal minimum wage by their employees. | ∀x (WhiteCollarWorker(x) → EntitledTo(x, federalMinimumWage)) |
All lawyers are white-collar workers. | ∀x (Lawyer(x) → WhiteCollarWorker(x)) |
Every advocate is a lawyer. | ∀x (Advocate(x) → Lawyer(x)) |
Mary is not a lawyer or a tipped employee. | ¬(Lawyer(mary) ⊕ TippedEmployee(mary)) |
Mary is a white-collar worker. | WhiteCollarWorker(mary) |
Mary is an advocate. | Advocate(mary) |
Mary is not an advocate. | ¬Advocate(mary) |
Mary is either an advocate or a tipped employee. | Advocate(mary) ⊕ TippedEmployee(mary) |
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. | (¬(Advocate(mary) ∧ EntitledTo(mary, federalMinimumWage))) → ¬TippedEmployee(mary) |
If Mary is either an advocate or a tipped employee, she is an advocate. | (Advocate(mary) ⊕ TippedEmployee(mary)) → Advocate(mary) |
Asa Hoffmann was born in New York City. | BornIn(asaHoffmann, newYorkCity) |
Asa Hoffman lives in Manhattan. | LiveIn(asaHoffmann, manhattan) |
Asa Hoffman is a chess player. | ChessPlayer(asaHoffmann) |
Some chess players are grandmasters. | ∃x ∃y (ChessPlayer(x) ∧ GrandMaster(x) ∧ (¬(x=y)) ∧ ChessPlayer(y) ∧ GrandMaster(y)) |
People born and living in New York City are New Yorkers. | ∀x ((BornIn(x, newYorkCity) ∧ LiveIn(x, newYorkCity)) → NewYorker(x)) |
People living in Manhattan live in New York City. | ∀x (LiveIn(x, manhattan) → LiveIn(x, newYorkCity)) |
Asa Hoffmann is a New Yorker. | NewYorker(asaHoffmann) |
Asa Hoffmann is a grandmaster. | GrandMaster(asaHoffmann) |
Asa Hoffmann does not live in New York. | ¬LiveIn(asaHoffmann, newYorkCity) |
Some of those who apply for a Schengen visa get it. | ∃x (Apply(x, schengenVisa) → Get(x, schengenVisa)) |
To apply for a Schengen Visa, you need to provide financial guarantees. | ∀x (Apply(x, schengenVisa) → Provide(x, financialGuarantees)) |
If you need to provide financial guarantees, you must request documents from the bank. | ∀x (Provide(x, financialGuarantees) → Request(x, documentsFromBank)) |
Do not close your bank account if you request documents from the bank. | ∀x (Request(x, documentsFromBank) → ¬Close(x, bankAccount)) |
Philip closed his bank account. | Close(philip, bankAccount) |
Philip got a Schengen visa. | Get(philip, schengenVisa) |
Philip applied for a Schengen visa and got it. | Apply(philip, schengenVisa) ∧ Get(philip, schengenVisa) |
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) |
Some fears lead to anxiety. | ∃x ∃y (Fear(x) ∧ Anxiety(y) ∧ LeadTo(x, y) ∧ ¬(x=y)) |
Some anxiety leads to terror. | ∃x ∃y (Anxiety(x) ∧ Terror(y) ∧ LeadTo(x, y)) |
No fears lead to terror. | ∀x ∀y (Fear(x) → ¬(Terror(y) ∧ LeadTo(x, y))) |
The Great Lakes are Lake Superior, Lake Michigan, Lake Huron, Lake Erie, and Lake Ontario. | ∀x (GreatLake(x) → Superior(x) ⊕ Michigan(x) ⊕ Huron(x) ⊕ Erie(x) ⊕ Ontario(x)) |
Some major settlements of Lake Erie are in NY, PA, OH, and MI. | ∀x (Erie (x) ∧ MajorSettlement(x) → In(x, nY) ∨ In(x, pA) ∨ In(x, oH) ∨ In(x, mI)) |
NY, PA, OH, and MI are states in the US. | StateOf(nY, uS) ∧ StateOf(pA, uS) ∧ StateOf(oH, uS) ∧ StateOf(mI, uS) |
ON is a state of Canada. | StateOf(oN, canada) |
There is a major settlement of Lake Huron in ON. | ∃x (Huron(x) ∧ MajorSettlement(x) ∧ In(x, oN)) |
All states are in their country. | ∀x ∀y (StateOf(x, y) → In(x, y)) |
The US is in North America. | In(us, northAmerica) |
The Great Lakes began to form at the end of the Last Glacial Period. | ∀x (GreatLake(x) → FormAtEndOf(x, lastGlacialPeriod)) |
Lake Erie has a major settlement. | ∃x ∃y (Erie(y) ∧ MajorSettlementOf(x, y)) |
There is a great lake that did not form at the end of the Last Glacial Period. | ∃x (GreatLake(x) ∧ ¬FormAtEndOf(x, lastGlacialPeriod)) |
All professional soccer defenders are professional soccer players. | ∀x ((Professional(x) ∧ Defender(x)) → (Professional(x) ∧ SoccerPlayer(x))) |
No professional soccer players are professional basketball players. | ∀x ((Professional(x) ∧ SoccerPlayer(x)) → ¬(Professional(x) ∧ BasketballPlayer(x))) |
All professional centerbacks are professional soccer defenders. | ∀x ((Professional(x) ∧ CenterBack(x)) → (Professional(x) ∧ Defender(x)) |
Stephen Curry is a professional basketball player. | Professional(stephenCurry) ∧ BasketballPlayer(stephenCurry) |
Stephen Curry is a professional centerback. | Professional(stephenCurry) ∧ CenterBack(stephenCurry) |
Stephen Curry is not a centerback. | ¬(Professional(stephenCurry) ∧ CenterBack(stephenCurry)) |
Naive cynicism was proposed by Justin Kruger and a colleague. | Proposed(justinKruger, naiveCynicism) ∧ ∃y (colleagueOfJustinKruger(y) ∧ Proposed(y, naiveCynicism)) |
Thomas Gilovich is a colleague of Justin Kruger. | Colleagues(thomasGilovich, justinKruger) |
Naive cynicism is a philosophy of mind. | PhilosophyOfMind(naiveCynicism) |
Thomas Gilovich proposed naive cynicism. | Proposed(thomasGilovich, naiveCynicism) |
Justin Kruger proposed a philosophy of mind. | ∃x (Proposed(justinKruger, x) ∧ PhilosophyOfMind(x)) |
Thomas Gilovich worked on philosophies of mind. | ∃x (WorkedOn(thomasGilovich, x) ∧ PhilosophyOfMind(x)) |
The Turing Award has been awarded to Donald Knuth, Marvin Minsky, Richard Hamming, and John McCarthy. | AwardedTo(turingAward, donaldKnuth) ∧ AwardedTo(turingAward, marvinMinsky) ∧ AwardedTo(turingAward, richardHamming) ∧ AwardedTo(turingAward, johnMccarthy) |
Donald Knuth made contributions to the analysis of algorithms. | ContributedTo(donaldKnuth, analysisOfAlgorithms) |
Marvin Minsky is recognized for his contributions to the field of artificial intelligence. | ContributedTo(marvinMinsky, artificialIntelligence) |
Richard Hamming researched numerical methods. | ContributedTo(richardHamming, numericalMethods) |
John McCarthy made contributions to the field of artificial intelligence. | 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)) |
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)) |
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)) |
No Turing Award winners worked in the field of numerical methods. | ∀x (AwardedTo(turingAward, x) → ¬ContributedTo(x, numericalMethods)) |
None of the easy Leetcode problems have an AC rate lower than 20 percent. | ∀x ((LeetcodeProblems(x) ∧ Easy(x)) → ¬HaveAnACRateLowerThan(x, percent20)) |
All Leetcode problems recommended to novices are easy. | ∀x ((LeetcodeProblems(x) ∧ RecommendedTo(x, novices)) → Easy(x)) |
Leetcode problems either have an AC rate lower than 20 percent or are starred by more than 1 thousand users. | ∀x (LeetcodeProblems(x) → HaveAnACRateLowerThan(x, percent20) ⊕ StarredByMoreThan(x, num1000)) |
All hard Leetcode problems are starred by more than 1,000 users. | ∀x ((LeetcodeProblems(x) ∧ Hard(x)) → StarredByMoreThan(x, num1000)) |