FOL

Every child loves Santa.

∀ x (CHILD(x) → LOVES(x,Santa))

Everyone who loves Santa loves any reindeer.

∀ x (LOVES(x,Santa) → ∀ y (REINDEER(y) → LOVES(x,y)))

Rudolph is a reindeer, and Rudolph has a red nose.

REINDEER(Rudolph) ∧ REDNOSE(Rudolph)

Anything which has a red nose is weird or is a clown.

∀ x (REDNOSE(x) → WEIRD(x) ∨ CLOWN(x))

No reindeer is a clown.

¬ ∃ x (REINDEER(x) ∧ CLOWN(x))

Scrooge does not love anything which is weird.

∀ x (WEIRD(x) → ¬ LOVES(Scrooge,x))

(Conclusion) Scrooge is not a child.

¬ CHILD(Scrooge)

Anyone who buys carrots by the bushel owns either a rabbit or a grocery store.

∀ x (BUY(x) → ∃ y (OWNS(x,y) ∧ (RABBIT(y) ∨ GROCERY(y))))

Every dog chases some rabbit.

∀ x (DOG(x) → ∃ y (RABBIT(y) ∧ CHASE(x,y)))

Mary buys carrots by the bushel.

BUY(Mary)

Anyone who owns a rabbit hates anything that chases any rabbit.

∀ x ∀ y (OWNS(x,y) ∧ RABBIT(y) → ∀ z ∀ w (RABBIT(w) ∧ CHASE(z,w) → HATES(x,z)))

John owns a dog.

∃ x (DOG(x) ∧ OWNS(John,x))

Someone who hates something owned by another person will not date that person.

∀ x ∀ y ∀ z (OWNS(y,z) ∧ HATES(x,z) → ¬ DATE(x,y))

(Conclusion) If Mary does not own a grocery store, she will not date John.

(( ¬ ∃ x (GROCERY(x) ∧ OWN(Mary,x))) → ¬ DATE(Mary,John))

Every Austinite who is not conservative loves some armadillo.

∀ x (AUSTINITE(x) ∧ ¬ CONSERVATIVE(x) → ∃ y (ARMADILLO(y) ∧ LOVES(x,y)))

Anyone who wears maroon-and-white shirts is an Aggie.

∀ x (WEARS(x) → AGGIE(x))

Every Aggie loves every dog.

∀ x (AGGIE(x) → ∀ y (DOG(y) → LOVES(x,y)))

Nobody who loves every dog loves any armadillo.

¬ ∃ x ((∀ y (DOG(y) → LOVES(x,y))) ∧ ∃ z (ARMADILLO(z) ∧ LOVES(x,z)))

Clem is an Austinite, and Clem wears maroon-and-white shirts.

AUSTINITE(Clem) ∧ WEARS(Clem)

(Conclusion) Is there a conservative Austinite?

∃ x (AUSTINITE(x) ∧ CONSERVATIVE(x)).

Anyone whom Mary loves is a football star.

∀ x (LOVES(Mary,x) → STAR(x))

Any student who does not pass does not play.

∀ x (STUDENT(x) ∧ ¬ PASS(x) → ¬ PLAY(x))

John is a student.

STUDENT(John)

Any student who does not study does not pass.

∀ x (STUDENT(x) ∧ ¬ STUDY(x) → ¬ PASS(x))

Anyone who does not play is not a football star.

∀ x (¬ PLAY(x) → ¬ STAR(x))

(Conclusion) If John does not study, then Mary does not love John.

¬ STUDY(John) → ¬ LOVES(Mary,John)

Every coyote chases some roadrunner.

∀ x (COYOTE(x) → ∃ y (RR(y) ∧ CHASE(x,y)))

Every roadrunner who says ``beep-beep'' is smart.

∀ x (RR(x) ∧ BEEP(x) → SMART(x))

No coyote catches any smart roadrunner.

¬ ∃ x ∃ y (COYOTE(x) ∧ RR(y) ∧ SMART(y) ∧ CATCH(x,y))

Any coyote who chases some roadrunner but does not catch it is frustrated.

∀ x (COYOTE(x) ∧ ∃ y (RR(y) ∧ CHASE(x,y) ∧ ¬ CATCH(x,y)) → FRUSTRATED(x))

(Conclusion) If all roadrunners say ``beep-beep'', then all coyotes are frustrated.

(∀ x (RR(x) → BEEP(x)) → (∀ y (COYOTE(y) → FRUSTRATED(y)))

Anyone who rides any Harley is a rough character.

∀ x ((∃ y (HARLEY(y) ∧ RIDES(x,y))) → ROUGH(x))

Every biker rides [something that is] either a Harley or a BMW.

∀ x (BIKER(x) → ∃ y ((HARLEY(y) ∨ BMW(y)) ∧ RIDES(x,y)))

Anyone who rides any BMW is a yuppie.

∀ x ∀ y (RIDES(x,y) ∧ BMW(y) → YUPPIE(x))

Every yuppie is a lawyer.

∀ x (YUPPIE(x) → LAWYER(x))

Any nice girl does not date anyone who is a rough character.

∀ x ∀ y (NICE(x) ∧ ROUGH(y) → ¬ DATE(x,y))

Mary is a nice girl, and John is a biker.

NICE(Mary) ∧ BIKER(John)

(Conclusion) If John is not a lawyer, then Mary does not date John.

¬ LAWYER(John) → ¬ DATE(Mary,John)

Every child loves anyone who gives the child any present.

∀ x ∀ y ∀ z (CHILD(x) ∧ PRESENT(y) ∧ GIVE(z,y,x) → LOVES(x,z)

Every child will be given some present by Santa if Santa can travel on Christmas eve.

TRAVEL(Santa,Christmas) → ∀ x (CHILD(x) → ∃ y (PRESENT(y) ∧ GIVE(Santa,y,x)))

It is foggy on Christmas eve.

FOGGY(Christmas)

Anytime it is foggy, anyone can travel if he has some source of light.

∀ x ∀ t (FOGGY(t) → ( ∃ y (LIGHT(y) ∧ HAS(x,y)) → TRAVEL(x,t)))

Any reindeer with a red nose is a source of light.

∀ x (RNR(x) → LIGHT(x))

(Conclusion) If Santa has some reindeer with a red nose, then every child loves Santa.

( ∃ x (RNR(x) ∧ HAS(Santa,x))) → ∀ y (CHILD(y) → LOVES(y,Santa))

Every investor bought [something that is] stocks or bonds.

∀ x (INVESTOR(x) → ∃ y ((STOCK(y) ∨ BOND(y)) ∧ BUY(x,y)))

If the Dow-Jones Average crashes, then all stocks that are not gold stocks fall.

DJCRASH → ∀ x ((STOCK(x) ∧ ¬ GOLD(x)) → FALL(x))

If the T-Bill interest rate rises, then all bonds fall.

TBRISE → ∀ x (BOND(x) → FALL(x))

Every investor who bought something that falls is not happy.

∀ x ∀ y (INVESTOR(x) ∧ BUY(x,y) ∧ FALL(y) &rarrm; ¬ HAPPY(x))

(Conclusion) If the Dow-Jones Average crashes and the T-Bill interest rate rises, then any investor who is happy bought some gold stock.

( DJCRASH ∧ TBRISE ) → ∀ x (INVESTOR(x) ∧ HAPPY(x) → ∃ y (GOLD(y) ∧ BUY(x,y)))

Every child loves every candy.

∀ x ∀ y (CHILD(x) ∧ CANDY(y) → LOVES(x,y))

Anyone who loves some candy is not a nutrition fanatic.

∀ x ( (∃ y (CANDY(y) ∧ LOVES(x,y))) → ¬ FANATIC(x))

Anyone who eats any pumpkin is a nutrition fanatic.

∀ x ((∃ y (PUMPKIN(y) ∧ EAT(x,y))) → FANATIC(x))

Anyone who buys any pumpkin either carves it or eats it.

∀ x ∀ y (PUMPKIN(y) ∧ BUY(x,y) → CARVE(x,y) ∨ EAT(x,y))

John buys a pumpkin.

∃ x (PUMPKIN(x) ∧ BUY(John,x))

Lifesavers is a candy.

CANDY(Lifesavers)

(Conclusion) If John is a child, then John carves some pumpkin.

CHILD(John) → ∃ x (PUMPKIN(x) ∧ CARVE(John,x))

REF:::https://www.cs.utexas.edu/