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All of Michael's neighbors who grow their own fresh vegetables in their home gardens also have ample space. All of Michael's neighbors who are young working professionals and live in large cities, do not have ample space. All of Michael's neighbors who order takeout from delivery services often grow their own fresh vegetables in their home garden. All of Michael's neighbors who enjoy going out often to restaurants with friends order takeout from delivery services often. All of Michael's neighbors who regularly tout the benefits of homegrown and homecooked meals over fast food enjoy going out often to restaurants with friends. Peter, Michael's neighbor, grows his own fresh vegetables in his home garden, or regularly touts the benefits of homegrown and homecooked meals over fast food, or both.

∀x (MichaelsNeightbor(x) ∧ GrowIn(x, vegetable, garden) → Have(x, ampleSpace)) ∀x (MichaelsNeightbor(x) ∧ YoungWorkingProfession(x) ∧ LiveIn(x, largeCity) → ¬Have(x, ampleSpace)) ∀x (MichaelsNeightbor(x) ∧ OrderOften(x, takeout) → Grow(x, vegetable, garden)) ∀x (MichaelsNeightbor(x) ∧ EnjoyGoingOutOftenToWith(x, restaurant, friend) → OrderOften(x, takeout)) ∀x (MichaelsNeightbor(x) ∧ ToutOver(x, homecookedMeals, fastFood) → EnjoyGoingOutOftenToWith(x, restaurant, friend)) MichaelsNeightbor(peter) ∧ (GrowIn(peter, vegetable, garden) ∨ ToutOver(peter, homecookedMeals, fastFood))

Peter enjoys going out often to restaurants with friends.

EnjoyGoingOutOftenTo(peter, restaurant, friend)

Uncertain

All of Michael's neighbors who grow their own fresh vegetables in their home gardens also have ample space. All of Michael's neighbors who are young working professionals and live in large cities, do not have ample space. All of Michael's neighbors who order takeout from delivery services often grow their own fresh vegetables in their home garden. All of Michael's neighbors who enjoy going out often to restaurants with friends order takeout from delivery services often. All of Michael's neighbors who regularly tout the benefits of homegrown and homecooked meals over fast food enjoy going out often to restaurants with friends. Peter, Michael's neighbor, grows his own fresh vegetables in his home garden, or regularly touts the benefits of homegrown and homecooked meals over fast food, or both.

∀x (MichaelsNeightbor(x) ∧ GrowIn(x, vegetable, garden) → Have(x, ampleSpace)) ∀x (MichaelsNeightbor(x) ∧ YoungWorkingProfession(x) ∧ LiveIn(x, largeCity) → ¬Have(x, ampleSpace)) ∀x (MichaelsNeightbor(x) ∧ OrderOften(x, takeout) → Grow(x, vegetable, garden)) ∀x (MichaelsNeightbor(x) ∧ EnjoyGoingOutOftenToWith(x, restaurant, friend) → OrderOften(x, takeout)) ∀x (MichaelsNeightbor(x) ∧ ToutOver(x, homecookedMeals, fastFood) → EnjoyGoingOutOftenToWith(x, restaurant, friend)) MichaelsNeightbor(peter) ∧ (GrowIn(peter, vegetable, garden) ∨ ToutOver(peter, homecookedMeals, fastFood))

Peter is a young working professional who lives in large cities.

YoungWorkingProfession(peter) ∧ LiveIn(peter, largeCity)

False

All of Michael's neighbors who grow their own fresh vegetables in their home gardens also have ample space. All of Michael's neighbors who are young working professionals and live in large cities, do not have ample space. All of Michael's neighbors who order takeout from delivery services often grow their own fresh vegetables in their home garden. All of Michael's neighbors who enjoy going out often to restaurants with friends order takeout from delivery services often. All of Michael's neighbors who regularly tout the benefits of homegrown and homecooked meals over fast food enjoy going out often to restaurants with friends. Peter, Michael's neighbor, grows his own fresh vegetables in his home garden, or regularly touts the benefits of homegrown and homecooked meals over fast food, or both.

∀x (MichaelsNeightbor(x) ∧ GrowIn(x, vegetable, garden) → Have(x, ampleSpace)) ∀x (MichaelsNeightbor(x) ∧ YoungWorkingProfession(x) ∧ LiveIn(x, largeCity) → ¬Have(x, ampleSpace)) ∀x (MichaelsNeightbor(x) ∧ OrderOften(x, takeout) → Grow(x, vegetable, garden)) ∀x (MichaelsNeightbor(x) ∧ EnjoyGoingOutOftenToWith(x, restaurant, friend) → OrderOften(x, takeout)) ∀x (MichaelsNeightbor(x) ∧ ToutOver(x, homecookedMeals, fastFood) → EnjoyGoingOutOftenToWith(x, restaurant, friend)) MichaelsNeightbor(peter) ∧ (GrowIn(peter, vegetable, garden) ∨ ToutOver(peter, homecookedMeals, fastFood))

Peter grows his own fresh vegetables in their home garden or is a young working professional who lives in large cities.

GrowIn(peter, vegetable, garden) ∨ (YoungWorkingProfession(peter) ∧ LiveIn(peter, largeCity))

True

All devices belonging to the company are connected to Google Home. All devices belonging to employees are connected to the company's wifi. All devices connected to Google Home are controlled by the managers. All devices that connect to the company's wifi are easy to operate. ModelXX belongs to employees.

∀x (OwnedBy(x, company) → ConnectedTo(x, googleHome)) ∀x (OwnedBy(x, employee) → ConnectedTo(x, companyWiFi)) ∀x (ConnectedTo(x, googleHome) → ControlledBy(x, managers)) ∀x (ConnectedTo(x, companyWiFi) → EasyToOperate(x)) OwnedBy(modelXX, employee)

ModelXX is easy to operate.

EasyToOperate(modelXX)

True

All devices belonging to the company are connected to Google Home. All devices belonging to employees are connected to the company's wifi. All devices connected to Google Home are controlled by the managers. All devices that connect to the company's wifi are easy to operate. ModelXX belongs to employees.

∀x (OwnedBy(x, company) → ConnectedTo(x, googleHome)) ∀x (OwnedBy(x, employee) → ConnectedTo(x, companyWiFi)) ∀x (ConnectedTo(x, googleHome) → ControlledBy(x, managers)) ∀x (ConnectedTo(x, companyWiFi) → EasyToOperate(x)) OwnedBy(modelXX, employee)

ModelXX is controlled by managers.

ControlledBy(modelXX, managers)

Uncertain

All devices belonging to the company are connected to Google Home. All devices belonging to employees are connected to the company's wifi. All devices connected to Google Home are controlled by the managers. All devices that connect to the company's wifi are easy to operate. ModelXX belongs to employees.

∀x (OwnedBy(x, company) → ConnectedTo(x, googleHome)) ∀x (OwnedBy(x, employee) → ConnectedTo(x, companyWiFi)) ∀x (ConnectedTo(x, googleHome) → ControlledBy(x, managers)) ∀x (ConnectedTo(x, companyWiFi) → EasyToOperate(x)) OwnedBy(modelXX, employee)

ModelXX is connected to Google Home.

ConnectedTo(modelXX, googleHome)

Uncertain

No touring musicians who perform at the New Haven Symphony Orchestra are permanent members of the orchestra. Musicians who perform at the New Haven Symphony Orchestra are permanent members of an orchestra, or they have temporary roles at the orchestra. All touring musicians who perform at the New Haven Symphony Orchestra have temporary roles at the orchestra. All musicians performing at the New Haven Symphony Orchestra who have temporary roles at the orchestra are interesting soloists. All musicians performing at New Haven Symphony Orchestra who are interesting soloists are capable of attracting audiences. Ryan is performing at New Haven Symphony Orchestra. If Ryan is an interesting soloist and has a temporary role at the orchestra, then he is capable of attracting large audiences if and only if he is a touring soloist musician.

∀x ((PerformAt(x, newHavenSymphonyOrchestra) ∧ TouringMusician(x)) → ¬PermanentMemberOf(x, theOrchestra)) ∀x (PerformAt(x, newHavenSymphonyOrchestra) → (PermanentMemberOf(x, theOrchestra) ∨ HaveTemporaryRoleAt(x, theOrchestra))) ∀x ((PerformAt(x, newHavenSymphonyOrchestra) ∧ TouringMusicians(x)) → HaveTemporaryRoleAt(x, theOrchestra)) ∀x ((PerformAt(x, newHavenSymphonyOrchestra) ∧ HaveTemporaryRoleAt(x, theOrchestra)) → InterestingSoloist(x)) ∀x ((PerformAt(x, newHavenSymphonyOrchestra) ∧ InterestingSoloist(x)) → CapableOfAttractingAudiences(x)) PerformAt(ryan, newHavenSymphonyOrchestra) (InterestingSoloist(ryan) ∧ HaveTemporaryRoleAt(ryan, theOrchestra)) → ¬(TouringMusician(ryan) ⊕ CapableOfAttractingAudiences(ryan))

Ryan is an interesting soloist.

InterestingSoloist(ryan)

Uncertain

No touring musicians who perform at the New Haven Symphony Orchestra are permanent members of the orchestra. Musicians who perform at the New Haven Symphony Orchestra are permanent members of an orchestra, or they have temporary roles at the orchestra. All touring musicians who perform at the New Haven Symphony Orchestra have temporary roles at the orchestra. All musicians performing at the New Haven Symphony Orchestra who have temporary roles at the orchestra are interesting soloists. All musicians performing at New Haven Symphony Orchestra who are interesting soloists are capable of attracting audiences. Ryan is performing at New Haven Symphony Orchestra. If Ryan is an interesting soloist and has a temporary role at the orchestra, then he is capable of attracting large audiences if and only if he is a touring soloist musician.

∀x ((PerformAt(x, newHavenSymphonyOrchestra) ∧ TouringMusician(x)) → ¬PermanentMemberOf(x, theOrchestra)) ∀x (PerformAt(x, newHavenSymphonyOrchestra) → (PermanentMemberOf(x, theOrchestra) ∨ HaveTemporaryRoleAt(x, theOrchestra))) ∀x ((PerformAt(x, newHavenSymphonyOrchestra) ∧ TouringMusicians(x)) → HaveTemporaryRoleAt(x, theOrchestra)) ∀x ((PerformAt(x, newHavenSymphonyOrchestra) ∧ HaveTemporaryRoleAt(x, theOrchestra)) → InterestingSoloist(x)) ∀x ((PerformAt(x, newHavenSymphonyOrchestra) ∧ InterestingSoloist(x)) → CapableOfAttractingAudiences(x)) PerformAt(ryan, newHavenSymphonyOrchestra) (InterestingSoloist(ryan) ∧ HaveTemporaryRoleAt(ryan, theOrchestra)) → ¬(TouringMusician(ryan) ⊕ CapableOfAttractingAudiences(ryan))

Ryan is either a permanent member of an orchestra or a touring soloist musician.

(PermanentMemberOf(ryan, orchestra) ⊕ TouringMusician(ryan))

True

No touring musicians who perform at the New Haven Symphony Orchestra are permanent members of the orchestra. Musicians who perform at the New Haven Symphony Orchestra are permanent members of an orchestra, or they have temporary roles at the orchestra. All touring musicians who perform at the New Haven Symphony Orchestra have temporary roles at the orchestra. All musicians performing at the New Haven Symphony Orchestra who have temporary roles at the orchestra are interesting soloists. All musicians performing at New Haven Symphony Orchestra who are interesting soloists are capable of attracting audiences. Ryan is performing at New Haven Symphony Orchestra. If Ryan is an interesting soloist and has a temporary role at the orchestra, then he is capable of attracting large audiences if and only if he is a touring soloist musician.

∀x ((PerformAt(x, newHavenSymphonyOrchestra) ∧ TouringMusician(x)) → ¬PermanentMemberOf(x, theOrchestra)) ∀x (PerformAt(x, newHavenSymphonyOrchestra) → (PermanentMemberOf(x, theOrchestra) ∨ HaveTemporaryRoleAt(x, theOrchestra))) ∀x ((PerformAt(x, newHavenSymphonyOrchestra) ∧ TouringMusicians(x)) → HaveTemporaryRoleAt(x, theOrchestra)) ∀x ((PerformAt(x, newHavenSymphonyOrchestra) ∧ HaveTemporaryRoleAt(x, theOrchestra)) → InterestingSoloist(x)) ∀x ((PerformAt(x, newHavenSymphonyOrchestra) ∧ InterestingSoloist(x)) → CapableOfAttractingAudiences(x)) PerformAt(ryan, newHavenSymphonyOrchestra) (InterestingSoloist(ryan) ∧ HaveTemporaryRoleAt(ryan, theOrchestra)) → ¬(TouringMusician(ryan) ⊕ CapableOfAttractingAudiences(ryan))

Ryan is either a permanent member of an orchestra or has a temporary role at the orchestra.

(PermanentMemberOf(ryan, orchestra) ⊕ HaveTemporaryRoleAt(ryan, orchestra))

True

If someone in Potterville yells, then they are not cool. If someone in Potterville is angry, then they yell. If someone in Potterville flies, then they are cool. Every person in Potterville that knows magic flies. All wizards in Potterville know magic. Harry, who lives in Potterville either yells or flies. Potter, who lives in Potterville, is a wizard and flies.

∀x (In(x, potterville) ∧ Yell(x) → ¬Cool(x)) ∀x (In(x, potterville) ∧ Angry(x) → Yell(x)) ∀x (In(x, potterville) ∧ Fly(x) → Cool(x)) ∀x (In(x, potterville) ∧ Know(x, magic) → Fly(x)) ∀x (In(x, potterville) ∧ Wizard(x) → Know(x, magic)) In(harry, potterville) ∧ (Yell(harry) ⊕ Fly(harry)) Wizard(potter) ∧ Fly(potter)

Harry is cool.

Cool(harry)

Uncertain

If someone in Potterville yells, then they are not cool. If someone in Potterville is angry, then they yell. If someone in Potterville flies, then they are cool. Every person in Potterville that knows magic flies. All wizards in Potterville know magic. Harry, who lives in Potterville either yells or flies. Potter, who lives in Potterville, is a wizard and flies.

∀x (In(x, potterville) ∧ Yell(x) → ¬Cool(x)) ∀x (In(x, potterville) ∧ Angry(x) → Yell(x)) ∀x (In(x, potterville) ∧ Fly(x) → Cool(x)) ∀x (In(x, potterville) ∧ Know(x, magic) → Fly(x)) ∀x (In(x, potterville) ∧ Wizard(x) → Know(x, magic)) In(harry, potterville) ∧ (Yell(harry) ⊕ Fly(harry)) Wizard(potter) ∧ Fly(potter)

Harry is not cool.

¬Cool(harry)

Uncertain

If someone in Potterville yells, then they are not cool. If someone in Potterville is angry, then they yell. If someone in Potterville flies, then they are cool. Every person in Potterville that knows magic flies. All wizards in Potterville know magic. Harry, who lives in Potterville either yells or flies. Potter, who lives in Potterville, is a wizard and flies.

∀x (In(x, potterville) ∧ Yell(x) → ¬Cool(x)) ∀x (In(x, potterville) ∧ Angry(x) → Yell(x)) ∀x (In(x, potterville) ∧ Fly(x) → Cool(x)) ∀x (In(x, potterville) ∧ Know(x, magic) → Fly(x)) ∀x (In(x, potterville) ∧ Wizard(x) → Know(x, magic)) In(harry, potterville) ∧ (Yell(harry) ⊕ Fly(harry)) Wizard(potter) ∧ Fly(potter)

Harry is a wizard or angry.

Wizard(harry) ∨ Angry(harry)

False

If someone in Potterville yells, then they are not cool. If someone in Potterville is angry, then they yell. If someone in Potterville flies, then they are cool. Every person in Potterville that knows magic flies. All wizards in Potterville know magic. Harry, who lives in Potterville either yells or flies. Potter, who lives in Potterville, is a wizard and flies.

∀x (In(x, potterville) ∧ Yell(x) → ¬Cool(x)) ∀x (In(x, potterville) ∧ Angry(x) → Yell(x)) ∀x (In(x, potterville) ∧ Fly(x) → Cool(x)) ∀x (In(x, potterville) ∧ Know(x, magic) → Fly(x)) ∀x (In(x, potterville) ∧ Wizard(x) → Know(x, magic)) In(harry, potterville) ∧ (Yell(harry) ⊕ Fly(harry)) Wizard(potter) ∧ Fly(potter)

Harry is neither a wizard nor angry.

¬Wizard(harry) ∧ ¬Angry(harry)

True

All of this brand's products are either produced in China or in the US. All of this brand's products produced in China are labeled. All of this brand's products produced in the US are sold in the US. The products of this brand that are labeled are cheaper. All of this brand's products sold in the US are sold at Walmart. All products of this brand displayed on the homepage are sold at Walmart. None of this brand's products that are returned by customers are sold at Walmart. G-910 is a product of this brand, and it is either displayed on the homepage and is cheaper, or it is neither displayed on the homepage nor is it cheaper.

∀x (ThisBrand(x) ∧ Product(x) → (ProducedIn(x, china) ⊕ ProducedIn(x, uS))) ∀x ((ThisBrand(x) ∧ Product(x) ∧ ProducedIn(x, china)) → Labeled(x)) ∀x ((ThisBrand(x) ∧ Product(x) ∧ ProducedIn(x, us)) → SoldIn(x, us)) ∀x ((ThisBrand(x) ∧ Product(x) ∧ Labeled(x)) → Cheaper(x)) ∀x ((ThisBrand(x) ∧ Product(x) ∧ SoldIn(x, us)) → SoldIn(x, walmart)) ∀x (ThisBrand(x) ∧ Product(x) ∧ DisplayedIn(x, homepage) → SoldIn(x, walmart)) ∀x (ThisBrand(x) ∧ Product(x) ∧ ReturnedBy(x, customer) → ¬SoldIn(x, walmart)) Product(g910) ∧ ThisBrand(g910) ∧ (¬(DisplayedIn(g910, homepage) ⊕ Cheaper(g910)))

G-910 is displayed on the homepage.

DisplayedIn(g910, homepage)

Uncertain

All of this brand's products are either produced in China or in the US. All of this brand's products produced in China are labeled. All of this brand's products produced in the US are sold in the US. The products of this brand that are labeled are cheaper. All of this brand's products sold in the US are sold at Walmart. All products of this brand displayed on the homepage are sold at Walmart. None of this brand's products that are returned by customers are sold at Walmart. G-910 is a product of this brand, and it is either displayed on the homepage and is cheaper, or it is neither displayed on the homepage nor is it cheaper.

∀x (ThisBrand(x) ∧ Product(x) → (ProducedIn(x, china) ⊕ ProducedIn(x, uS))) ∀x ((ThisBrand(x) ∧ Product(x) ∧ ProducedIn(x, china)) → Labeled(x)) ∀x ((ThisBrand(x) ∧ Product(x) ∧ ProducedIn(x, us)) → SoldIn(x, us)) ∀x ((ThisBrand(x) ∧ Product(x) ∧ Labeled(x)) → Cheaper(x)) ∀x ((ThisBrand(x) ∧ Product(x) ∧ SoldIn(x, us)) → SoldIn(x, walmart)) ∀x (ThisBrand(x) ∧ Product(x) ∧ DisplayedIn(x, homepage) → SoldIn(x, walmart)) ∀x (ThisBrand(x) ∧ Product(x) ∧ ReturnedBy(x, customer) → ¬SoldIn(x, walmart)) Product(g910) ∧ ThisBrand(g910) ∧ (¬(DisplayedIn(g910, homepage) ⊕ Cheaper(g910)))

G-910 is not displayed on the homepage.

¬DisplayedIn(g910, homepage)

Uncertain

All of this brand's products are either produced in China or in the US. All of this brand's products produced in China are labeled. All of this brand's products produced in the US are sold in the US. The products of this brand that are labeled are cheaper. All of this brand's products sold in the US are sold at Walmart. All products of this brand displayed on the homepage are sold at Walmart. None of this brand's products that are returned by customers are sold at Walmart. G-910 is a product of this brand, and it is either displayed on the homepage and is cheaper, or it is neither displayed on the homepage nor is it cheaper.

∀x (ThisBrand(x) ∧ Product(x) → (ProducedIn(x, china) ⊕ ProducedIn(x, uS))) ∀x ((ThisBrand(x) ∧ Product(x) ∧ ProducedIn(x, china)) → Labeled(x)) ∀x ((ThisBrand(x) ∧ Product(x) ∧ ProducedIn(x, us)) → SoldIn(x, us)) ∀x ((ThisBrand(x) ∧ Product(x) ∧ Labeled(x)) → Cheaper(x)) ∀x ((ThisBrand(x) ∧ Product(x) ∧ SoldIn(x, us)) → SoldIn(x, walmart)) ∀x (ThisBrand(x) ∧ Product(x) ∧ DisplayedIn(x, homepage) → SoldIn(x, walmart)) ∀x (ThisBrand(x) ∧ Product(x) ∧ ReturnedBy(x, customer) → ¬SoldIn(x, walmart)) Product(g910) ∧ ThisBrand(g910) ∧ (¬(DisplayedIn(g910, homepage) ⊕ Cheaper(g910)))

G-910 is a product returned by customers.

ThisBrand(g910) ∧ ReturnedBy(g910, customer)

False

All of this brand's products are either produced in China or in the US. All of this brand's products produced in China are labeled. All of this brand's products produced in the US are sold in the US. The products of this brand that are labeled are cheaper. All of this brand's products sold in the US are sold at Walmart. All products of this brand displayed on the homepage are sold at Walmart. None of this brand's products that are returned by customers are sold at Walmart. G-910 is a product of this brand, and it is either displayed on the homepage and is cheaper, or it is neither displayed on the homepage nor is it cheaper.

∀x (ThisBrand(x) ∧ Product(x) → (ProducedIn(x, china) ⊕ ProducedIn(x, uS))) ∀x ((ThisBrand(x) ∧ Product(x) ∧ ProducedIn(x, china)) → Labeled(x)) ∀x ((ThisBrand(x) ∧ Product(x) ∧ ProducedIn(x, us)) → SoldIn(x, us)) ∀x ((ThisBrand(x) ∧ Product(x) ∧ Labeled(x)) → Cheaper(x)) ∀x ((ThisBrand(x) ∧ Product(x) ∧ SoldIn(x, us)) → SoldIn(x, walmart)) ∀x (ThisBrand(x) ∧ Product(x) ∧ DisplayedIn(x, homepage) → SoldIn(x, walmart)) ∀x (ThisBrand(x) ∧ Product(x) ∧ ReturnedBy(x, customer) → ¬SoldIn(x, walmart)) Product(g910) ∧ ThisBrand(g910) ∧ (¬(DisplayedIn(g910, homepage) ⊕ Cheaper(g910)))

G-910 is a product returned by customers or sold in Walmart.

ThisBrand(g910) ∧ (ReturnedBy(g910, customer) ∨ SoldIn(g910, walmart))

True

All of this brand's products are either produced in China or in the US. All of this brand's products produced in China are labeled. All of this brand's products produced in the US are sold in the US. The products of this brand that are labeled are cheaper. All of this brand's products sold in the US are sold at Walmart. All products of this brand displayed on the homepage are sold at Walmart. None of this brand's products that are returned by customers are sold at Walmart. G-910 is a product of this brand, and it is either displayed on the homepage and is cheaper, or it is neither displayed on the homepage nor is it cheaper.

∀x (ThisBrand(x) ∧ Product(x) → (ProducedIn(x, china) ⊕ ProducedIn(x, uS))) ∀x ((ThisBrand(x) ∧ Product(x) ∧ ProducedIn(x, china)) → Labeled(x)) ∀x ((ThisBrand(x) ∧ Product(x) ∧ ProducedIn(x, us)) → SoldIn(x, us)) ∀x ((ThisBrand(x) ∧ Product(x) ∧ Labeled(x)) → Cheaper(x)) ∀x ((ThisBrand(x) ∧ Product(x) ∧ SoldIn(x, us)) → SoldIn(x, walmart)) ∀x (ThisBrand(x) ∧ Product(x) ∧ DisplayedIn(x, homepage) → SoldIn(x, walmart)) ∀x (ThisBrand(x) ∧ Product(x) ∧ ReturnedBy(x, customer) → ¬SoldIn(x, walmart)) Product(g910) ∧ ThisBrand(g910) ∧ (¬(DisplayedIn(g910, homepage) ⊕ Cheaper(g910)))

G-910 is either returned by customers or sold in Walmart.

ReturnedBy(g910, customer) ⊕ SoldIn(g910, walmart)

True

People either believe in Santa Claus, or think he is made up. People who believe in Santa Claus expect to get presents on Christmas morning. People who think Santa Claus is made up, then they would be surprised to see him in their house. People who expect presents on Christmas morning are excited for it to be Christmas. If people would be surprised to see Santa Claus in their house, then they don't leave out cookies on Chrismtas Eve. Mercy is not someone who expects presents Christmas morning, is excited for Chrismtas, and believes in Santa Claus.

∀x (BelieveIn(x, santaClaus) ⊕ ThinkMadeUp(x, santaClaus)) ∀x (BelieveIn(x, santaClaus) → Expect(x, present, christmasMorning)) ∀x (ThinkMadeUp(x, santaClaus) → WouldBeSurprisedToSeeIn(x, santaClaus, house)) ∀x (Expect(x, present, christmasMorning) → ExcitedFor(x, christmas)) ∀x (WouldBeSurprisedToSeeIn(x, santaClaus, house) → ¬LeaveOut(x, cookies)) ¬(Expect(marcy, present, christmasMorning) ∧ ExcitedFor(marcy, christmas) ∧ BelieveIn(marcy, santaClaus))

Marcy either believes in Santa Claus or doesn't leave cookies out on Christmas Eve.

BelieveIn(marcy, santaClaus) ⊕ LeaveOut(marcy, cookies)

True

People either believe in Santa Claus, or think he is made up. People who believe in Santa Claus expect to get presents on Christmas morning. People who think Santa Claus is made up, then they would be surprised to see him in their house. People who expect presents on Christmas morning are excited for it to be Christmas. If people would be surprised to see Santa Claus in their house, then they don't leave out cookies on Chrismtas Eve. Mercy is not someone who expects presents Christmas morning, is excited for Chrismtas, and believes in Santa Claus.

∀x (BelieveIn(x, santaClaus) ⊕ ThinkMadeUp(x, santaClaus)) ∀x (BelieveIn(x, santaClaus) → Expect(x, present, christmasMorning)) ∀x (ThinkMadeUp(x, santaClaus) → WouldBeSurprisedToSeeIn(x, santaClaus, house)) ∀x (Expect(x, present, christmasMorning) → ExcitedFor(x, christmas)) ∀x (WouldBeSurprisedToSeeIn(x, santaClaus, house) → ¬LeaveOut(x, cookies)) ¬(Expect(marcy, present, christmasMorning) ∧ ExcitedFor(marcy, christmas) ∧ BelieveIn(marcy, santaClaus))

Marcy is not someone who both leaves out cookies on Chrismtas eve and thinks Santa Claus is made up, or Marcy believes in Santa Claus.

¬(LeaveOut(marcy, cookies) ∧ ThinkMadeUp(marcy, santaClaus)) ∨ BelieveIn(marcy, santaClaus)

False

Indonesia is a country. In Indonesia, the prosecutor only personally investigates cases of some special crimes. Corruption is a type of crime. Once the police complete crime investigations, the evidence is handed to the prosecutor. Evidence can be either satisfactory or unsatisfactory. If the evidence is handed to the prosecutor and the evidence is satisfactory, the prosecutor will prosecute the offender in an appropriate court.

Country(indonesia) ∀x ∃y (In(indonesia) ∧ Prosecutor(x) ∧ SpecialCrime(y) → InvestigatePersonally(x, y)) Crime(corruption) ∀x ∀y ∀z (Crime(y) ∧ PoliceCompleteInvestigation(y) ∧ Prosecutor(x) → Evidence(z) ∧ HandedTo(z, x)) ∀x (Evidence(x) ∧ (Satisfactory(x) ⊕ Unsatisfactory(x))) ∀x ∀y (Evidence(y) ∧ Prosecutor(x) ∧ HandedTo(x) ∧ Satisfactory(y) → ProsecuteInAppropriateCourt(x, theOffender))

When the police complete investigations, the prosecutor will prosecute the offender at an appropriate court.

∀x ∀y (Crime(y) ∧ PoliceCompleteInvestigation(y) ∧ Prosecutor(x) → ProsecuteInAppropriateCourt(x, theOffender))

Uncertain

Indonesia is a country. In Indonesia, the prosecutor only personally investigates cases of some special crimes. Corruption is a type of crime. Once the police complete crime investigations, the evidence is handed to the prosecutor. Evidence can be either satisfactory or unsatisfactory. If the evidence is handed to the prosecutor and the evidence is satisfactory, the prosecutor will prosecute the offender in an appropriate court.

Country(indonesia) ∀x ∃y (In(indonesia) ∧ Prosecutor(x) ∧ SpecialCrime(y) → InvestigatePersonally(x, y)) Crime(corruption) ∀x ∀y ∀z (Crime(y) ∧ PoliceCompleteInvestigation(y) ∧ Prosecutor(x) → Evidence(z) ∧ HandedTo(z, x)) ∀x (Evidence(x) ∧ (Satisfactory(x) ⊕ Unsatisfactory(x))) ∀x ∀y (Evidence(y) ∧ Prosecutor(x) ∧ HandedTo(x) ∧ Satisfactory(y) → ProsecuteInAppropriateCourt(x, theOffender))

In Indonesia, the prosecutor personally investigates cases of corruption.

∀x (Country(indonesia) ∧ Prosecutor(x) ∧ Crime(corruption) → InvestigatePersonally(x, corruption))

Uncertain

Indonesia is a country. In Indonesia, the prosecutor only personally investigates cases of some special crimes. Corruption is a type of crime. Once the police complete crime investigations, the evidence is handed to the prosecutor. Evidence can be either satisfactory or unsatisfactory. If the evidence is handed to the prosecutor and the evidence is satisfactory, the prosecutor will prosecute the offender in an appropriate court.

Country(indonesia) ∀x ∃y (In(indonesia) ∧ Prosecutor(x) ∧ SpecialCrime(y) → InvestigatePersonally(x, y)) Crime(corruption) ∀x ∀y ∀z (Crime(y) ∧ PoliceCompleteInvestigation(y) ∧ Prosecutor(x) → Evidence(z) ∧ HandedTo(z, x)) ∀x (Evidence(x) ∧ (Satisfactory(x) ⊕ Unsatisfactory(x))) ∀x ∀y (Evidence(y) ∧ Prosecutor(x) ∧ HandedTo(x) ∧ Satisfactory(y) → ProsecuteInAppropriateCourt(x, theOffender))

When the police complete investigations, the prosecutor investigates personally.

∀x ∀y (Crime(y) ∧ PoliceCompleteInvestigation(y) ∧ Prosecutor(x) → InvestigatePersonally(x, y))

Uncertain

No battery-powered watch is automatic. All digital watches are battery-powered. Some mechanical watches are automatic. All smart watches are digital. Moonwatch is either a digital watch and an automatic, or it is neither.

∀x (BatteryPoweredWatch(x) → ¬AutomaticWatch(x)) ∀x (DigitalWatch(x) → BatteryPoweredWatch(x)) ∃x (MechanicalWatch(x) ∧ AutomaticWatch(x)) ∀x (SmartWatch(x) → DigitalWatch(x)) ¬(DigitalWatch(moonwatch) ⊕ AutomaticWatch(moonwatch))

Moonwatch is a mechanical watch.

MechanicalWatch(moonWatch)

Uncertain

No battery-powered watch is automatic. All digital watches are battery-powered. Some mechanical watches are automatic. All smart watches are digital. Moonwatch is either a digital watch and an automatic, or it is neither.

∀x (BatteryPoweredWatch(x) → ¬AutomaticWatch(x)) ∀x (DigitalWatch(x) → BatteryPoweredWatch(x)) ∃x (MechanicalWatch(x) ∧ AutomaticWatch(x)) ∀x (SmartWatch(x) → DigitalWatch(x)) ¬(DigitalWatch(moonwatch) ⊕ AutomaticWatch(moonwatch))

Moonwatch is a smartwatch and a mechanical watch.

SmartWatch(moonwatch) ∧ MechanicalWatch(moonwatch)

False

No battery-powered watch is automatic. All digital watches are battery-powered. Some mechanical watches are automatic. All smart watches are digital. Moonwatch is either a digital watch and an automatic, or it is neither.

∀x (BatteryPoweredWatch(x) → ¬AutomaticWatch(x)) ∀x (DigitalWatch(x) → BatteryPoweredWatch(x)) ∃x (MechanicalWatch(x) ∧ AutomaticWatch(x)) ∀x (SmartWatch(x) → DigitalWatch(x)) ¬(DigitalWatch(moonwatch) ⊕ AutomaticWatch(moonwatch))

If Moonwatch is a smartwatch and a mechanical watch, then Moonwatch is not a mechanical watch.

SmartWatch(moonwatch) ∧ MechanicalWatch(moonwatch) → ¬MechanicalWatch(moonwatch)

True

No battery-powered watch is automatic. All digital watches are battery-powered. Some mechanical watches are automatic. All smart watches are digital. Moonwatch is either a digital watch and an automatic, or it is neither.

∀x (BatteryPoweredWatch(x) → ¬AutomaticWatch(x)) ∀x (DigitalWatch(x) → BatteryPoweredWatch(x)) ∃x (MechanicalWatch(x) ∧ AutomaticWatch(x)) ∀x (SmartWatch(x) → DigitalWatch(x)) ¬(DigitalWatch(moonwatch) ⊕ AutomaticWatch(moonwatch))

If Moonwatch is a mechanical or battery-powered watch, then Moonwatch is not a smartwatch.

MechanicalWatch(moonwatch)) ∨ BatteryPoweredWatch(moonwatch) → ¬SmartWatch(moonwatch)

True

If a person can distinguish the taste of different condiments, then they can also use different condiments for cooking. People who have a talent of cooking can distinguish the taste of different condiments. Only people with the talent of cooking can make delicious meals. If the meal is popular at the party, then it is delicious. John can make meals which are popular at the party.

∀x (Person(x) ∧ Can(x, distinguishTheTasteOfDifferentCondiments) → Can(x, useDifferentCondimentsToCook)) ∀x (Person(x) ∧ Has(x, talentOfCooking) → Can(x, distinguishTheTasteOfDifferentCondiments)) ∀x ∀y (CanMake(x, y) ∧ Meal(y) ∧ Delicious(y) ∧ Person(x) → Has(x, talentOfCooking)) ∀x ∀y (Meal(y) ∧ PopularAt(y, party) → Delicious(y)) ∃x (Person(john) ∧ MakeMeal(john, x) ∧ Meal(x) ∧ PopularAt(x, party))

John cannot use different condiments for cooking.

¬Can(john, useDifferentCondimentsToCook)

False

For a country, if effective monetary policy is possible, it must have successful inflation control and a strong national currency. A country cannot simultaneously regulate the exchange rate and successfully control inflation. The introduction of an embargo on foreign trade goods in a country leads to a sharp decrease in exports. If exports fall sharply, this country's national currency cannot be strong. Inflation control is required to have a strong national currency. There is an embargo on Russian foreign trade goods.

∀x (Country(x) ∧ PossibleEffectiveMonetaryPolicy(x) → SuccessfulInflationControl(x) ∧ StongNationalCurrency(x)) ¬(∃x (Country(x) ∧ SuccessfulInflationControl(x) ∧ RegulateExchangeRate(x))) ∀x (IntroductionOfOn(x, embargo, foreightTradeGoods) → SharpDecreasesInExport(x)) ∀x (SharpDecreasesInExport(x) → ¬StongNationalCurrency(x)) ∀x (InflationControl(x) → StongNationalCurrency(x)) IntroductionOfOn(russia, embargo, foreightTradeGoods)

In Russia, an effective monetary policy is possible.

PossibleEffectiveMonetaryPolicy(russia)

False

Video Gag is a French television series that airs weekly. Video Gag airs on the French broadcast channel TF1. If viewers send funny videos to the French broadcast channel TF1, then Video Gag airs them weekly. All videos aired on Video Gag are in French.

FrenchTelevision(videoGag) ∧ AirWeekly(videoGag) AirOn(videoGag, frenchBroadcastChannelTF1) ∀x (Funny(x) ∧ Video(x) ∧ SendIn(viewers, x, frenchBroadcastChannelTF1) → AirWeekly(x) ) ∧ AirOn(videoGag, x)) ∀x (Video(x) ∧ AirOn(videoGag, x) → In(x, french))

Viewers send funny videos to the French broadcast channel TF1 that are in French.

∃x (SendIn(viewers, x, frenchBroadcastChannelTF1) ∧ French(x))

Uncertain

Video Gag is a French television series that airs weekly. Video Gag airs on the French broadcast channel TF1. If viewers send funny videos to the French broadcast channel TF1, then Video Gag airs them weekly. All videos aired on Video Gag are in French.

FrenchTelevision(videoGag) ∧ AirWeekly(videoGag) AirOn(videoGag, frenchBroadcastChannelTF1) ∀x (Funny(x) ∧ Video(x) ∧ SendIn(viewers, x, frenchBroadcastChannelTF1) → AirWeekly(x) ) ∧ AirOn(videoGag, x)) ∀x (Video(x) ∧ AirOn(videoGag, x) → In(x, french))

Viewers send funny videos to the French broadcast channel that are in English.

∃x (SendIn(viewers, x, frenchBroadcastChannelTF1) ∧ English(x))

Uncertain

All phones are things. All cell phones are phones. All iPhones are cell phones. All employees are wage earners. All wage earners are human. Jack is either an employee or a wage earner. Jack is either a human or a phone.

∀x (Phone(x) → Thing(x)) ∀x (Cellphone(x) → Phone(x)) ∀x (Iphone(x) → Cellphone(x)) ∀x (Employee(x) → WageEarner(x)) ∀x (WageEarner(x) → Human(x)) Employee(jack) ⊕ WageEarner(jack) Human(jack) ⊕ Phone(jack)

Jack is a thing.

Thing(jack)

Uncertain

All phones are things. All cell phones are phones. All iPhones are cell phones. All employees are wage earners. All wage earners are human. Jack is either an employee or a wage earner. Jack is either a human or a phone.

∀x (Phone(x) → Thing(x)) ∀x (Cellphone(x) → Phone(x)) ∀x (Iphone(x) → Cellphone(x)) ∀x (Employee(x) → WageEarner(x)) ∀x (WageEarner(x) → Human(x)) Employee(jack) ⊕ WageEarner(jack) Human(jack) ⊕ Phone(jack)

Jack is not a thing.

¬Thing(jack)

Uncertain

All phones are things. All cell phones are phones. All iPhones are cell phones. All employees are wage earners. All wage earners are human. Jack is either an employee or a wage earner. Jack is either a human or a phone.

∀x (Phone(x) → Thing(x)) ∀x (Cellphone(x) → Phone(x)) ∀x (Iphone(x) → Cellphone(x)) ∀x (Employee(x) → WageEarner(x)) ∀x (WageEarner(x) → Human(x)) Employee(jack) ⊕ WageEarner(jack) Human(jack) ⊕ Phone(jack)

Jack is a thing and an iPhone.

Thing(jack) ∧ Iphone(jack)

False

All phones are things. All cell phones are phones. All iPhones are cell phones. All employees are wage earners. All wage earners are human. Jack is either an employee or a wage earner. Jack is either a human or a phone.

∀x (Phone(x) → Thing(x)) ∀x (Cellphone(x) → Phone(x)) ∀x (Iphone(x) → Cellphone(x)) ∀x (Employee(x) → WageEarner(x)) ∀x (WageEarner(x) → Human(x)) Employee(jack) ⊕ WageEarner(jack) Human(jack) ⊕ Phone(jack)

Jack is not both a thing and an iPhone.

¬(Thing(jack) ∧ Iphone(jack))

True

All iPhones are electronic. Some phones are iPhones.

∀x (IPhone(x) → Electronic(x)) ∃x ∃y (Phone(x) ∧ Phone(y) ∧ IPhone(x) ∧ IPhone(y) ∧ ¬(x=y))

No phones are electronic.

∀x (Phone(x) → ¬Electronic(x))

False

The Metropolitan Museum of Art is a museum in NYC. Whitney Museum of American Art is a museum in NYC. The Museum of Modern Art (MoMA) is a museum in NYC. The Metropolitan Museum of Art includes Byzantine and Islamic Art. Whitney Museum of American Art includes American art.

Museum(metropolitanMuseumOfArt) ∧ In(metropolitanMuseumOfArt, nYC) Museum(whitneyMuseumOfAmericanArt) ∧ In(metropolitanMuseumOfArt, nYC) Museum(museumOfModernArt) ∧ In(museumOfModernArt, nYC) Include(metropolitanMuseumOfArt, byzantineArt) ∧ Include(metropolitanMuseumOfArt, islamicArt) Include(whitneyMuseumOfAmericanArt, americanArt)

A museum in NYC includes Byzantine and Islamic Art.

∃x (Museum(x) ∧ In(x, nYC) ∧ Include(x, byzantineArt) ∧ Include(x, islamicArt))

True

The Metropolitan Museum of Art is a museum in NYC. Whitney Museum of American Art is a museum in NYC. The Museum of Modern Art (MoMA) is a museum in NYC. The Metropolitan Museum of Art includes Byzantine and Islamic Art. Whitney Museum of American Art includes American art.

Museum(metropolitanMuseumOfArt) ∧ In(metropolitanMuseumOfArt, nYC) Museum(whitneyMuseumOfAmericanArt) ∧ In(metropolitanMuseumOfArt, nYC) Museum(museumOfModernArt) ∧ In(museumOfModernArt, nYC) Include(metropolitanMuseumOfArt, byzantineArt) ∧ Include(metropolitanMuseumOfArt, islamicArt) Include(whitneyMuseumOfAmericanArt, americanArt)

A museum in NYC includes American art.

∃x (Museum(x) ∧ In(x, nYC) ∧ Include(x, americanArt))

True

The Metropolitan Museum of Art is a museum in NYC. Whitney Museum of American Art is a museum in NYC. The Museum of Modern Art (MoMA) is a museum in NYC. The Metropolitan Museum of Art includes Byzantine and Islamic Art. Whitney Museum of American Art includes American art.

Museum(metropolitanMuseumOfArt) ∧ In(metropolitanMuseumOfArt, nYC) Museum(whitneyMuseumOfAmericanArt) ∧ In(metropolitanMuseumOfArt, nYC) Museum(museumOfModernArt) ∧ In(museumOfModernArt, nYC) Include(metropolitanMuseumOfArt, byzantineArt) ∧ Include(metropolitanMuseumOfArt, islamicArt) Include(whitneyMuseumOfAmericanArt, americanArt)

A museum in NYC includes Greek art.

∃x (Museum(x) ∧ In(x, nYC) ∧ Include(x, greekArt))

Uncertain

There's a person in Benji's family who likes eating cheese or is a francophile. There is no francophile in Benji's family whose favorite country is Spain. There is a person in Benji's family who likes eating cheese or whose favorite country is Spain. Fabien is in Benji's family and does not both study Spanish and also like eating cheese. Fabien studies Spanish.

∃x (InBenjiSFamily(x) → (LikeEating(x, cheese) ∨ Francophile(x))) ∀x ((InBenjiSFamily(x) ∧ Francophile(x)) → ¬Favor(x, spain)) ∃x (InBenjiSFamily(x) ∧ (Favor(x, spain) ∨ LikeEating(x, cheese))) InBenjiSFamily(fabien) ∧ (¬(LikeEating(fabien, cheese) ∧ Study(fabien, spanish))) Study(fabien, spanish)

Fabien is a person who likes eating cheese.

LikeEating(fabien, cheese)

Uncertain

There's a person in Benji's family who likes eating cheese or is a francophile. There is no francophile in Benji's family whose favorite country is Spain. There is a person in Benji's family who likes eating cheese or whose favorite country is Spain. Fabien is in Benji's family and does not both study Spanish and also like eating cheese. Fabien studies Spanish.

∃x (InBenjiSFamily(x) → (LikeEating(x, cheese) ∨ Francophile(x))) ∀x ((InBenjiSFamily(x) ∧ Francophile(x)) → ¬Favor(x, spain)) ∃x (InBenjiSFamily(x) ∧ (Favor(x, spain) ∨ LikeEating(x, cheese))) InBenjiSFamily(fabien) ∧ (¬(LikeEating(fabien, cheese) ∧ Study(fabien, spanish))) Study(fabien, spanish)

If Fabien is either a person who likes eating cheese or a francophile, then Fabien is neither a person who studies Spanish nor a person who is a francophile.

(LikeEating(fabien, cheese) ⊕ Francophile(fabien)) → (¬(Study(fabien, spanish) ∨ Francophile(fabien)))

True

There's a person in Benji's family who likes eating cheese or is a francophile. There is no francophile in Benji's family whose favorite country is Spain. There is a person in Benji's family who likes eating cheese or whose favorite country is Spain. Fabien is in Benji's family and does not both study Spanish and also like eating cheese. Fabien studies Spanish.

∃x (InBenjiSFamily(x) → (LikeEating(x, cheese) ∨ Francophile(x))) ∀x ((InBenjiSFamily(x) ∧ Francophile(x)) → ¬Favor(x, spain)) ∃x (InBenjiSFamily(x) ∧ (Favor(x, spain) ∨ LikeEating(x, cheese))) InBenjiSFamily(fabien) ∧ (¬(LikeEating(fabien, cheese) ∧ Study(fabien, spanish))) Study(fabien, spanish)

If Fabien is a person who likes Spain as their favorite country or is a francophile, then Fabien is either a person who studies Spanish or a person who likes Spain as their favorite country.

(Favor(fabien, spain) ∨ Francophile(fabien)) → (Study(fabien, spanish) ⊕ Favor(fabien, spain))

False

Gasteren is a village located in the province of Drenthe. Drenthe is a Dutch province. No cities are villages. The population of a village in Drenthe was 155 people.

Village(gasteren) ∧ Province(drenthe) ∧ In(gasteren, drenthe) Province(drenthe) ∧ In(drenthe, netherlands) ∀x (City(x) → ¬Village(x)) ∃x (Population(x, num155) ∧ Village(x) ∧ In(x, drenthe))

Gasteren is a Dutch village.

Village(gasteren) ∧ In(gasteren, netherlands)

Uncertain

Gasteren is a village located in the province of Drenthe. Drenthe is a Dutch province. No cities are villages. The population of a village in Drenthe was 155 people.

Village(gasteren) ∧ Province(drenthe) ∧ In(gasteren, drenthe) Province(drenthe) ∧ In(drenthe, netherlands) ∀x (City(x) → ¬Village(x)) ∃x (Population(x, num155) ∧ Village(x) ∧ In(x, drenthe))

Gasteren is a city.

City(gasteren)

False

Gasteren is a village located in the province of Drenthe. Drenthe is a Dutch province. No cities are villages. The population of a village in Drenthe was 155 people.

Village(gasteren) ∧ Province(drenthe) ∧ In(gasteren, drenthe) Province(drenthe) ∧ In(drenthe, netherlands) ∀x (City(x) → ¬Village(x)) ∃x (Population(x, num155) ∧ Village(x) ∧ In(x, drenthe))

Gasteren has a population of 155.

Population(gasteren, num155)

Uncertain

The only types of mammals that lay eggs are either platypuses or echidnas. Platypuses are not hyrax. Echidnas are not hyrax. No mammals are invertebrates. All animals are either vertebrates or invertebrates. Mammals are animals. Hyraxes are mammals. Grebes lay eggs. Grebes are not platypuses and also not echidnas.

∀x ((Mammal(x) ∧ LayEgg(x)) → (Platypus(x) ⊕ Echidna(x))) ∀x (Platypuses(x) → ¬Hyrax(x)) ∀x (Echidnas(x) → ¬Hyrax(x)) ∀x (Mammal(x) → ¬Invertebrate(x)) ∀x (Animal(x) → (Vertebrate(x) ∨ Invertebrate(x))) ∀x (Mammal(x) → Animal(x)) ∀x (Hyrax(x) → Mammal(x)) ∀x (Grebes(x) → LayEgg(x)) ∀x (Grebes(x) → (¬Platypuses(x) ∧ ¬Echidnas(x)))

Hyraxes lay eggs.

∃x (Hyrax(x) ∧ LayEgg(x))

False

The only types of mammals that lay eggs are either platypuses or echidnas. Platypuses are not hyrax. Echidnas are not hyrax. No mammals are invertebrates. All animals are either vertebrates or invertebrates. Mammals are animals. Hyraxes are mammals. Grebes lay eggs. Grebes are not platypuses and also not echidnas.

∀x ((Mammal(x) ∧ LayEgg(x)) → (Platypus(x) ⊕ Echidna(x))) ∀x (Platypuses(x) → ¬Hyrax(x)) ∀x (Echidnas(x) → ¬Hyrax(x)) ∀x (Mammal(x) → ¬Invertebrate(x)) ∀x (Animal(x) → (Vertebrate(x) ∨ Invertebrate(x))) ∀x (Mammal(x) → Animal(x)) ∀x (Hyrax(x) → Mammal(x)) ∀x (Grebes(x) → LayEgg(x)) ∀x (Grebes(x) → (¬Platypuses(x) ∧ ¬Echidnas(x)))

Grebes are not mammals.

∀x (Grebes(x) → ¬Mammal(x))

True

The only types of mammals that lay eggs are either platypuses or echidnas. Platypuses are not hyrax. Echidnas are not hyrax. No mammals are invertebrates. All animals are either vertebrates or invertebrates. Mammals are animals. Hyraxes are mammals. Grebes lay eggs. Grebes are not platypuses and also not echidnas.

∀x ((Mammal(x) ∧ LayEgg(x)) → (Platypus(x) ⊕ Echidna(x))) ∀x (Platypuses(x) → ¬Hyrax(x)) ∀x (Echidnas(x) → ¬Hyrax(x)) ∀x (Mammal(x) → ¬Invertebrate(x)) ∀x (Animal(x) → (Vertebrate(x) ∨ Invertebrate(x))) ∀x (Mammal(x) → Animal(x)) ∀x (Hyrax(x) → Mammal(x)) ∀x (Grebes(x) → LayEgg(x)) ∀x (Grebes(x) → (¬Platypuses(x) ∧ ¬Echidnas(x)))

Platypuses are vertebrates.

∀x (Platypuses(x) → Vertebrate(x))

Uncertain

Bobby Flynn is a singer-songwriter. Bobby Flynn finished 7th while competing on Australian Idol. Australian Idol competitors are Australian citizens. The Omega Three band made a nationwide tour in 2007. Bobby Flynn is a member of The Omega Three band. Bobby Flynn was born in Queensland.

Singer(bobbyFlynn) ∧ SongWriter(bobbyFlynn) FinishesIn(bobbyFlynn, number7) ∧ CompetesOnAustralianIdol(bobbyFlynn) ∀x (CompetesOnAustralianIdol(x) → AustralianCitizen(x)) NationWideTourIn(theOmegaThreeBand, year2007) Member(bobbyFlynn, theOmegaThreeBand) BornIn(bobbyFlynn, queensland)

Bobby Flynn is an Australian citizen.

AustralianCitizen(bobbyFlynn)

True

Bobby Flynn is a singer-songwriter. Bobby Flynn finished 7th while competing on Australian Idol. Australian Idol competitors are Australian citizens. The Omega Three band made a nationwide tour in 2007. Bobby Flynn is a member of The Omega Three band. Bobby Flynn was born in Queensland.

Singer(bobbyFlynn) ∧ SongWriter(bobbyFlynn) FinishesIn(bobbyFlynn, number7) ∧ CompetesOnAustralianIdol(bobbyFlynn) ∀x (CompetesOnAustralianIdol(x) → AustralianCitizen(x)) NationWideTourIn(theOmegaThreeBand, year2007) Member(bobbyFlynn, theOmegaThreeBand) BornIn(bobbyFlynn, queensland)

Bobby Flynn flew to America in 2007.

FlewToIn(bobbyFlynn, america, year2007)

Uncertain

Bobby Flynn is a singer-songwriter. Bobby Flynn finished 7th while competing on Australian Idol. Australian Idol competitors are Australian citizens. The Omega Three band made a nationwide tour in 2007. Bobby Flynn is a member of The Omega Three band. Bobby Flynn was born in Queensland.

Singer(bobbyFlynn) ∧ SongWriter(bobbyFlynn) FinishesIn(bobbyFlynn, number7) ∧ CompetesOnAustralianIdol(bobbyFlynn) ∀x (CompetesOnAustralianIdol(x) → AustralianCitizen(x)) NationWideTourIn(theOmegaThreeBand, year2007) Member(bobbyFlynn, theOmegaThreeBand) BornIn(bobbyFlynn, queensland)

Bobby Flynn was born in Queens.

BornIn(bobbyFlynn, queens)

Uncertain

All proteins are organic compounds. All enzymes are organic compounds.

∀x (Protein(x) → OrganicCompound(x)) ∀x (Enzyme(x) → OrganicCompound(x))

All enzymes are proteins.

∀x (Enzyme(x) → Protein(x))

Uncertain

Maggie Friedman is an American screenwriter and producer. Maggie Friedman was the showrunner and executive producer of the lifetime television series Witches of East End. Witches of East End is a fantasy-drama series. Maggie Friedman produced and developed Eastwick. Eastwick is a series by ABC.

American(maggieFriedman) ∧ Screenwriter(maggieFriedman) ∧ Producer(maggieFriedman) ShowRunnerOf(maggieFriedman, witchesOfEastEnd) ∧ ExecutiveProducerOf(maggieFriedman, witchesOfEastEnd) ∧ LifetimeTelevisionSeries(maggieFriedman) FantasyDrama(witchesOfEastEnd) ∧ Series(witchesOfEastEnd) Produces(maggieFriedman, eastwick) ∧ Develops(maggieFriedman, eastwick) Series(eastwick) ∧ AiredOn(eastwick, aBC)

There is a series by ABC that was developed by the showrunner of Witches of East End.

∃x ∃y (Series(x) ∧ AiredOn(x, aBC) ∧ Develops(y, x) ∧ ShowRunnerOf(y, witchesOfEastEnd))

True

Maggie Friedman is an American screenwriter and producer. Maggie Friedman was the showrunner and executive producer of the lifetime television series Witches of East End. Witches of East End is a fantasy-drama series. Maggie Friedman produced and developed Eastwick. Eastwick is a series by ABC.

American(maggieFriedman) ∧ Screenwriter(maggieFriedman) ∧ Producer(maggieFriedman) ShowRunnerOf(maggieFriedman, witchesOfEastEnd) ∧ ExecutiveProducerOf(maggieFriedman, witchesOfEastEnd) ∧ LifetimeTelevisionSeries(maggieFriedman) FantasyDrama(witchesOfEastEnd) ∧ Series(witchesOfEastEnd) Produces(maggieFriedman, eastwick) ∧ Develops(maggieFriedman, eastwick) Series(eastwick) ∧ AiredOn(eastwick, aBC)

No series by ABC was developed by the showrunner of Witches of East End.

∀x (Series(x) ∧ AiredOn(x, aBC) ∧ ∃y(ShowRunnerOf(y, witchesOfEastEnd)) → ¬Develops(y, x))

False

Maggie Friedman is an American screenwriter and producer. Maggie Friedman was the showrunner and executive producer of the lifetime television series Witches of East End. Witches of East End is a fantasy-drama series. Maggie Friedman produced and developed Eastwick. Eastwick is a series by ABC.

American(maggieFriedman) ∧ Screenwriter(maggieFriedman) ∧ Producer(maggieFriedman) ShowRunnerOf(maggieFriedman, witchesOfEastEnd) ∧ ExecutiveProducerOf(maggieFriedman, witchesOfEastEnd) ∧ LifetimeTelevisionSeries(maggieFriedman) FantasyDrama(witchesOfEastEnd) ∧ Series(witchesOfEastEnd) Produces(maggieFriedman, eastwick) ∧ Develops(maggieFriedman, eastwick) Series(eastwick) ∧ AiredOn(eastwick, aBC)

Maggie Friedman developed Witches of East End.

Develops(maggieFriedman, witchesOfEastEnd)

Uncertain

Evangelos Eleftheriou is a Greek electrical engineer. Evangelos Eleftheriou worked for IBM in Zurich. If a company has employees working for them somewhere, then they have an office there. IBM is a company.

Greek(evangelosEleftheriou) ∧ ElectricalEngineer(evangelosEleftheriou) WorkForIn(evangelosEleftheriou, iBM, zurich) ∀x ∀x ∀z (Company(x) ∧ WorkForIn(y, x, z) → HaveOfficeIn(x, z)) Company(ibm)

IBM has an office in London or Zurich or both.

HaveOfficeIn(ibm, london) ∨ HaveOfficeIn(ibm, zurich)

True

Evangelos Eleftheriou is a Greek electrical engineer. Evangelos Eleftheriou worked for IBM in Zurich. If a company has employees working for them somewhere, then they have an office there. IBM is a company.

Greek(evangelosEleftheriou) ∧ ElectricalEngineer(evangelosEleftheriou) WorkForIn(evangelosEleftheriou, iBM, zurich) ∀x ∀x ∀z (Company(x) ∧ WorkForIn(y, x, z) → HaveOfficeIn(x, z)) Company(ibm)

No Greeks have worked for IBM.

∀x (Greek(x) → ¬WorkFor(x, ibm))

False

Boney M. had several German #1 singles. "Hooray! Hooray! It's a Holi-Holiday!" was a big hit all over Europe. "Hooray! Hooray! It's a Holi-Holiday!" was not in German #1 singles. A song that peaks below #1 on the german charts is also a song that is not the #1 single in Germany.

∃x (Song(x) ∧ By(x, boneym,) ∧ Number1GermanSingle(x)) Song(hoorayHoorayItsAHoliHoliday) ∧ HitAllOverEurope(hoorayHoorayItsAHoliHoliday) Song(hoorayHoorayItsAHoliHoliday) ∧ ¬Number1GermanSingle(hoorayHoorayItsAHoliHoliday) ∀x (PeakBelowOn(x, number1, germanChart) → ¬Number1GermanSingle(x))

"Hooray! Hooray! It's a Holi-Holiday!" was the #1 hit in Germany.

Song(hoorayHoorayItsAHoliHoliday) ∧ Number1GermanSingle(hoorayHoorayItsAHoliHoliday)

False

Boney M. had several German #1 singles. "Hooray! Hooray! It's a Holi-Holiday!" was a big hit all over Europe. "Hooray! Hooray! It's a Holi-Holiday!" was not in German #1 singles. A song that peaks below #1 on the german charts is also a song that is not the #1 single in Germany.

∃x (Song(x) ∧ By(x, boneym,) ∧ Number1GermanSingle(x)) Song(hoorayHoorayItsAHoliHoliday) ∧ HitAllOverEurope(hoorayHoorayItsAHoliHoliday) Song(hoorayHoorayItsAHoliHoliday) ∧ ¬Number1GermanSingle(hoorayHoorayItsAHoliHoliday) ∀x (PeakBelowOn(x, number1, germanChart) → ¬Number1GermanSingle(x))

"Hooray! Hooray! It's a Holi-Holiday!" peaked below #1 on the German charts.

PeaksBelowOn(hoorayHoorayItsAHoliHoliday, number1, germanChart)

True

Boney M. had several German #1 singles. "Hooray! Hooray! It's a Holi-Holiday!" was a big hit all over Europe. "Hooray! Hooray! It's a Holi-Holiday!" was not in German #1 singles. A song that peaks below #1 on the german charts is also a song that is not the #1 single in Germany.

∃x (Song(x) ∧ By(x, boneym,) ∧ Number1GermanSingle(x)) Song(hoorayHoorayItsAHoliHoliday) ∧ HitAllOverEurope(hoorayHoorayItsAHoliHoliday) Song(hoorayHoorayItsAHoliHoliday) ∧ ¬Number1GermanSingle(hoorayHoorayItsAHoliHoliday) ∀x (PeakBelowOn(x, number1, germanChart) → ¬Number1GermanSingle(x))

"Hooray! Hooray! It's a Holi-Holiday!" peaked at #3 on the UK charts.

PeaksAtOn(hoorayHoorayItsAHoliHoliday, number3, germanChart)

Uncertain

Every chef can cook. Some people who aren’t chefs can cook. People who cook can make scrambled eggs and pasta. If someone can make cookies and muffins, they are a baker. Bakers who can also make scrambled eggs can make a good breakfast. Luke can make cookies, scrambled eggs, and muffins, but not pasta.

∀x (Chef(x) → Can(x, cook)) ∃x (¬Chef(x) ∧ Can(x, cook)) ∀x (Can(x, cook) → (CanMake(x, scrambledEggs) ∧ CanMake(x, pasta))) ∀x (CanMake(x, cookies) ∧ CanMake(x, muffins) → Baker(x)) ∀x ((Baker(x) ∧ CanMake(x, scrambledEggs)) → CanMake(x, goodBreakfast)) CanMake(luke, cookies) ∧ (CanMake(luke, scrambledEggs) ∧ CanMake(luke, muffins) ∧ ¬CanMake(luke, pasta)

Luke can make a good breakfast.

CanMake(luke, goodBreakfast)

True

Every chef can cook. Some people who aren’t chefs can cook. People who cook can make scrambled eggs and pasta. If someone can make cookies and muffins, they are a baker. Bakers who can also make scrambled eggs can make a good breakfast. Luke can make cookies, scrambled eggs, and muffins, but not pasta.

∀x (Chef(x) → Can(x, cook)) ∃x (¬Chef(x) ∧ Can(x, cook)) ∀x (Can(x, cook) → (CanMake(x, scrambledEggs) ∧ CanMake(x, pasta))) ∀x (CanMake(x, cookies) ∧ CanMake(x, muffins) → Baker(x)) ∀x ((Baker(x) ∧ CanMake(x, scrambledEggs)) → CanMake(x, goodBreakfast)) CanMake(luke, cookies) ∧ (CanMake(luke, scrambledEggs) ∧ CanMake(luke, muffins) ∧ ¬CanMake(luke, pasta)

Luke is a chef.

Chef(luke)

False

ETS develops various standardized tests primarily in the United States for K-12 and higher education. ETS administers international tests, including the TOEFL, TOEIC, GRE, and subject tests. Many of the assessments ETS develops are associated with entry to the US tertiary and quaternary education institutions. ETS also develops K-12 statewide assessments used for accountability testing in many states.

∃x ∃y (Develop(eTS, x) ∧ Develop(eTS, y) ∧ StandardizedTest(x) ∧ StandardizedTest(y) ∧ In(x, unitedState) ∧ In(y, unitedState) ∧ For(x, k12AndHigherEducation) ∧ For(y, k12AndHigherEducation)) ∃x (Administer(eTS, x) ∧ InternationalTest(x) ∧ (TOEFL(x) ∨ TOEIC(x) ∨ GRE(x) ∨ SubjectTest(x))) ∃x (Develop(eTS, x) ∧ AssociatedWith(x, entryToUSEducationInstitution)) ∃x (Develop(eTS, x) ∧ StateWideAssesment(x) ∧ UsedFor(x, accountabilityTesting))

ETS develops assessments for K-12 statewide as well as entry to US tertiary and quaternary education institutions.

∃x ∃y (Develop(eTS, x) ∧ StateWideAssesment(x) ∧ Develop(eTS, y) ∧ AssociatedWith(y, entryToUSEducationInstitution))

True

ETS develops various standardized tests primarily in the United States for K-12 and higher education. ETS administers international tests, including the TOEFL, TOEIC, GRE, and subject tests. Many of the assessments ETS develops are associated with entry to the US tertiary and quaternary education institutions. ETS also develops K-12 statewide assessments used for accountability testing in many states.

∃x ∃y (Develop(eTS, x) ∧ Develop(eTS, y) ∧ StandardizedTest(x) ∧ StandardizedTest(y) ∧ In(x, unitedState) ∧ In(y, unitedState) ∧ For(x, k12AndHigherEducation) ∧ For(y, k12AndHigherEducation)) ∃x (Administer(eTS, x) ∧ InternationalTest(x) ∧ (TOEFL(x) ∨ TOEIC(x) ∨ GRE(x) ∨ SubjectTest(x))) ∃x (Develop(eTS, x) ∧ AssociatedWith(x, entryToUSEducationInstitution)) ∃x (Develop(eTS, x) ∧ StateWideAssesment(x) ∧ UsedFor(x, accountabilityTesting))

ETS doesn't administer tests internationally.

∀x (Administer(eTS, x) → ¬InternationalTest(x))

False

ETS develops various standardized tests primarily in the United States for K-12 and higher education. ETS administers international tests, including the TOEFL, TOEIC, GRE, and subject tests. Many of the assessments ETS develops are associated with entry to the US tertiary and quaternary education institutions. ETS also develops K-12 statewide assessments used for accountability testing in many states.

∃x ∃y (Develop(eTS, x) ∧ Develop(eTS, y) ∧ StandardizedTest(x) ∧ StandardizedTest(y) ∧ In(x, unitedState) ∧ In(y, unitedState) ∧ For(x, k12AndHigherEducation) ∧ For(y, k12AndHigherEducation)) ∃x (Administer(eTS, x) ∧ InternationalTest(x) ∧ (TOEFL(x) ∨ TOEIC(x) ∨ GRE(x) ∨ SubjectTest(x))) ∃x (Develop(eTS, x) ∧ AssociatedWith(x, entryToUSEducationInstitution)) ∃x (Develop(eTS, x) ∧ StateWideAssesment(x) ∧ UsedFor(x, accountabilityTesting))

ETS administers international tests including the TOEFL, GRE and subject tests in China.

∃x (Administer(eTS, x) ∧ InChina(x) ∧ (TOEFL(x) ∨ TOEIC(x) ∨ GRE(x) ∨ SubjectTest(x)))

Uncertain

All hodophiles who enjoy eating gelato ice cream would enjoy a vacation to Italy. No hodophiles can resist the hallmark delectable desserts famous in Italy. Hodophiles enjoy eating gelato ice cream or love to travel and vacation often, or both. No hodophiles who study abroad in Europe regret their college experiences. If hodophiles love to travel and vacation often, then they study abroad in Europe. Robert is a hodophile, and he either enjoys eating gelato ice cream and loves to travel and vacation often, or does not enjoy eating gelato ice cream and does not love to travel and vacation often.

∀x (Hodophiles(x) ∧ EnjoyEating(x, gelato) → Enjoy(x, vacationToItaly)) ∀x (Hodophiles(x) ∧ ¬(∃y (Resist(x, y) ∧ Hallmark(y) ∧ Delectabl(y) ∧ Dessert(y) ∧ FamousIn(y, italy)))) ∀x (Hodophiles(x) → (EnjoyEating(x, gelato) ∨ LoveToTravelOften(x)) ∀x (Hodophiles(x) ∧ TakeIn(x, studyAbroadSemester, europe) → ¬Regret(x, collegeExperience)) ∀x (Hodophiles(x) ∧ LoveToTravelOften(x) → TakeIn(x, studyAbroadSemester, europe)) Hodophiles(robert) ∧ ¬(EnjoyEating(robert, gelato) ⊕ LoveToTravelOften(robert))

Robert can resist the hallmark delectable desserts that are famous in Italy.

∃y (Resist(robert, y) ∧ Hallmark(y) ∧ Delectabl(y) ∧ Dessert(y) ∧ FamousIn(y, italy))

False

All hodophiles who enjoy eating gelato ice cream would enjoy a vacation to Italy. No hodophiles can resist the hallmark delectable desserts famous in Italy. Hodophiles enjoy eating gelato ice cream or love to travel and vacation often, or both. No hodophiles who study abroad in Europe regret their college experiences. If hodophiles love to travel and vacation often, then they study abroad in Europe. Robert is a hodophile, and he either enjoys eating gelato ice cream and loves to travel and vacation often, or does not enjoy eating gelato ice cream and does not love to travel and vacation often.

∀x (Hodophiles(x) ∧ EnjoyEating(x, gelato) → Enjoy(x, vacationToItaly)) ∀x (Hodophiles(x) ∧ ¬(∃y (Resist(x, y) ∧ Hallmark(y) ∧ Delectabl(y) ∧ Dessert(y) ∧ FamousIn(y, italy)))) ∀x (Hodophiles(x) → (EnjoyEating(x, gelato) ∨ LoveToTravelOften(x)) ∀x (Hodophiles(x) ∧ TakeIn(x, studyAbroadSemester, europe) → ¬Regret(x, collegeExperience)) ∀x (Hodophiles(x) ∧ LoveToTravelOften(x) → TakeIn(x, studyAbroadSemester, europe)) Hodophiles(robert) ∧ ¬(EnjoyEating(robert, gelato) ⊕ LoveToTravelOften(robert))

If Robert either would both enjoy a vacation to Italy and regrets his college experiences or neither would enjoy a vacation to Italy nor regrets his college experiences, then Robert would either enjoy a vacation to Italy or he can resist the hallmark delectable desserts that are famous in Italy.

¬((Enjoy(robert, vacation) ∧ In(vacation, italy)) ⊕ Regret(x, collegeExperiences)) → Enjoy(robert, vacation) ∧ In(vacation, italy) ⊕ (∃y (Resist(robert, y) ∧ Hallmark(y) ∧ Delectabl(y) ∧ Dessert(y) ∧ FamousIn(y, italy))

True

All hodophiles who enjoy eating gelato ice cream would enjoy a vacation to Italy. No hodophiles can resist the hallmark delectable desserts famous in Italy. Hodophiles enjoy eating gelato ice cream or love to travel and vacation often, or both. No hodophiles who study abroad in Europe regret their college experiences. If hodophiles love to travel and vacation often, then they study abroad in Europe. Robert is a hodophile, and he either enjoys eating gelato ice cream and loves to travel and vacation often, or does not enjoy eating gelato ice cream and does not love to travel and vacation often.

∀x (Hodophiles(x) ∧ EnjoyEating(x, gelato) → Enjoy(x, vacationToItaly)) ∀x (Hodophiles(x) ∧ ¬(∃y (Resist(x, y) ∧ Hallmark(y) ∧ Delectabl(y) ∧ Dessert(y) ∧ FamousIn(y, italy)))) ∀x (Hodophiles(x) → (EnjoyEating(x, gelato) ∨ LoveToTravelOften(x)) ∀x (Hodophiles(x) ∧ TakeIn(x, studyAbroadSemester, europe) → ¬Regret(x, collegeExperience)) ∀x (Hodophiles(x) ∧ LoveToTravelOften(x) → TakeIn(x, studyAbroadSemester, europe)) Hodophiles(robert) ∧ ¬(EnjoyEating(robert, gelato) ⊕ LoveToTravelOften(robert))

If Robert is not both a person who can resist the hallmark delectable desserts that are famous in Italy and regrets his college experiences, then Robert either enjoys eating gelato ice cream or would enjoy a vacation to Italy.

(∃y (Resist(robert, y) ∧ Hallmark(y) ∧ Delectabl(y) ∧ Dessert(y) ∧ FamousIn(y, italy))) ∧ Regret(robert, collegeExperience)) → (EnjoyEating(robert, gelato) ⊕ (Enjoy(robert, vacation) ∧ In(vacation, italy))

False

To have the authorization to study in the United States as a foreigner, you must be enrolled in an academic program. Those who are enrolled in an academic program can not work full-time. Every who studies in the United States as a foreigner has the authorization to study in the U.S. All PhD graduate can work full-time. If Tom does not study in the United States as a foreigner, he is enrolled in an academic program.

∀x (Have(x, authorization, studyIn, unitedStates) → EnrolledIn(x, academicProgram)) ∀x (EnrolledIn(x, academicProgram) → ¬Work(x, fullTime)) ∀x (StudyIn(x, unitedStates) → Have(x, authorization, studyIn, unitedStates)) ∀x (PhDGraduate(x) → Work(x, fullTime)) ¬StudyIn(x, unitedStates) → EnrolledIn(x, academicProgram)

Tom is a PhD graduate.

PhdGraduate(tom)

False

To have the authorization to study in the United States as a foreigner, you must be enrolled in an academic program. Those who are enrolled in an academic program can not work full-time. Every who studies in the United States as a foreigner has the authorization to study in the U.S. All PhD graduate can work full-time. If Tom does not study in the United States as a foreigner, he is enrolled in an academic program.

∀x (Have(x, authorization, studyIn, unitedStates) → EnrolledIn(x, academicProgram)) ∀x (EnrolledIn(x, academicProgram) → ¬Work(x, fullTime)) ∀x (StudyIn(x, unitedStates) → Have(x, authorization, studyIn, unitedStates)) ∀x (PhDGraduate(x) → Work(x, fullTime)) ¬StudyIn(x, unitedStates) → EnrolledIn(x, academicProgram)

Tom is not a PhD graduate.

¬PhdGraduate(tom)

True

To have the authorization to study in the United States as a foreigner, you must be enrolled in an academic program. Those who are enrolled in an academic program can not work full-time. Every who studies in the United States as a foreigner has the authorization to study in the U.S. All PhD graduate can work full-time. If Tom does not study in the United States as a foreigner, he is enrolled in an academic program.

∀x (Have(x, authorization, studyIn, unitedStates) → EnrolledIn(x, academicProgram)) ∀x (EnrolledIn(x, academicProgram) → ¬Work(x, fullTime)) ∀x (StudyIn(x, unitedStates) → Have(x, authorization, studyIn, unitedStates)) ∀x (PhDGraduate(x) → Work(x, fullTime)) ¬StudyIn(x, unitedStates) → EnrolledIn(x, academicProgram)

Tom wants to study abroad.

StudyIn(tom, unitedStates)

Uncertain

Islip Speedway is the smallest race track. There was a demolition derby on the smallest race track. Islip is either demolished or still being used. Speedways that are still being used have races held at them. Islip doesn't have races held at it.

Speedway(islip) ∧ SmallestRaceTrack(islip) ∃x ∃y (DemolitionDerby(x) ∧ SmallestRaceTrack(y) ∧ On(x, y)) Demolished(islip) ⊕ StillUsed(islip) ∀x (Speedway(x) ∧ StillUsed(x) → Have(races, heldAt, x)) ¬Have(races, heldAt, islip)

There has been a demolition derby somewhere that has since been demolished.

∃x ∃y (DemolitionDerby(x) ∧ On(x, y) ∧ Demolished(y))

True

Islip Speedway is the smallest race track. There was a demolition derby on the smallest race track. Islip is either demolished or still being used. Speedways that are still being used have races held at them. Islip doesn't have races held at it.

Speedway(islip) ∧ SmallestRaceTrack(islip) ∃x ∃y (DemolitionDerby(x) ∧ SmallestRaceTrack(y) ∧ On(x, y)) Demolished(islip) ⊕ StillUsed(islip) ∀x (Speedway(x) ∧ StillUsed(x) → Have(races, heldAt, x)) ¬Have(races, heldAt, islip)

Islip was demolished.

Demolished(islip)

True

Islip Speedway is the smallest race track. There was a demolition derby on the smallest race track. Islip is either demolished or still being used. Speedways that are still being used have races held at them. Islip doesn't have races held at it.

Speedway(islip) ∧ SmallestRaceTrack(islip) ∃x ∃y (DemolitionDerby(x) ∧ SmallestRaceTrack(y) ∧ On(x, y)) Demolished(islip) ⊕ StillUsed(islip) ∀x (Speedway(x) ∧ StillUsed(x) → Have(races, heldAt, x)) ¬Have(races, heldAt, islip)

Islip is still being used.

StillUsed(islip)

False

If a person pays their taxes, then they contribute to the country. Everyone who works for a government department pays a tax on their salary. Everyone in the army is an employee of a government department. Everyone convicted of murder goes to prison. Everyone who has been to prison has a criminal record. James was either once convicted of murder, or spent time in prison. James either has a criminal record, or pays his taxes.

∀x (Taxpayer(x) → ContributeTo(x, country)) ∀x (WorkFor(x, governmentAgency) → Taxpayer(x)) ∀x (ServesIn(x, theArmy) → WorkFor(x, governmentAgency)) ∀x (SentencedForMurder(x) → Imprisoned(x)) ∀x (Imprisoned((x) → Has(x, criminalRecord)) SentencedForMurder(james) ⊕ Imprisoned(james) Has(james, criminalRecord) ⊕ Taxpayer(james)

James contributes to the country.

ContributeToCountry(james)

Uncertain

If a person pays their taxes, then they contribute to the country. Everyone who works for a government department pays a tax on their salary. Everyone in the army is an employee of a government department. Everyone convicted of murder goes to prison. Everyone who has been to prison has a criminal record. James was either once convicted of murder, or spent time in prison. James either has a criminal record, or pays his taxes.

∀x (Taxpayer(x) → ContributeTo(x, country)) ∀x (WorkFor(x, governmentAgency) → Taxpayer(x)) ∀x (ServesIn(x, theArmy) → WorkFor(x, governmentAgency)) ∀x (SentencedForMurder(x) → Imprisoned(x)) ∀x (Imprisoned((x) → Has(x, criminalRecord)) SentencedForMurder(james) ⊕ Imprisoned(james) Has(james, criminalRecord) ⊕ Taxpayer(james)

James does not contribute to the country.

¬ContributeTo(james, country)

Uncertain

If a person pays their taxes, then they contribute to the country. Everyone who works for a government department pays a tax on their salary. Everyone in the army is an employee of a government department. Everyone convicted of murder goes to prison. Everyone who has been to prison has a criminal record. James was either once convicted of murder, or spent time in prison. James either has a criminal record, or pays his taxes.

∀x (Taxpayer(x) → ContributeTo(x, country)) ∀x (WorkFor(x, governmentAgency) → Taxpayer(x)) ∀x (ServesIn(x, theArmy) → WorkFor(x, governmentAgency)) ∀x (SentencedForMurder(x) → Imprisoned(x)) ∀x (Imprisoned((x) → Has(x, criminalRecord)) SentencedForMurder(james) ⊕ Imprisoned(james) Has(james, criminalRecord) ⊕ Taxpayer(james)

James contributes to the country and he serves in the army.

ContributeTo(james, country) ∧ ServesIn(james, army)

False

If a person pays their taxes, then they contribute to the country. Everyone who works for a government department pays a tax on their salary. Everyone in the army is an employee of a government department. Everyone convicted of murder goes to prison. Everyone who has been to prison has a criminal record. James was either once convicted of murder, or spent time in prison. James either has a criminal record, or pays his taxes.

∀x (Taxpayer(x) → ContributeTo(x, country)) ∀x (WorkFor(x, governmentAgency) → Taxpayer(x)) ∀x (ServesIn(x, theArmy) → WorkFor(x, governmentAgency)) ∀x (SentencedForMurder(x) → Imprisoned(x)) ∀x (Imprisoned((x) → Has(x, criminalRecord)) SentencedForMurder(james) ⊕ Imprisoned(james) Has(james, criminalRecord) ⊕ Taxpayer(james)

James does not contribute to the country and does not serve in the army.

¬(ContributeTo(james, country) ∧ ServesIn(james, army))

True

The Croton River watershed is the drainage basin of the Croton River. The Croton River is in southwestern New York. Water from the Croton River watershed flows to the Bronx. The Bronx is in New York.

DrainageBasinOf(crotonRiverWatershed, crotonRiver) In(crotonRiver, southwesternNewYork) ∀x ((Water(x) ∧ In(x, crotonRiverWatershed)) → FlowsTo(x, bronx)) In(bronx, newYork)

Water from the Croton River watershed flows to somewhere in New York.

∀x ((Water(x) ∧ From(x, crotonRiverWatershed)) → ∃y(FlowsTo(x, y) ∧ In(y, newYork)))

True

The Croton River watershed is the drainage basin of the Croton River. The Croton River is in southwestern New York. Water from the Croton River watershed flows to the Bronx. The Bronx is in New York.

DrainageBasinOf(crotonRiverWatershed, crotonRiver) In(crotonRiver, southwesternNewYork) ∀x ((Water(x) ∧ In(x, crotonRiverWatershed)) → FlowsTo(x, bronx)) In(bronx, newYork)

The Croton River watershed is in the Bronx.

In(crotonRiverWatershed, bronx)

Uncertain

The Croton River watershed is the drainage basin of the Croton River. The Croton River is in southwestern New York. Water from the Croton River watershed flows to the Bronx. The Bronx is in New York.

DrainageBasinOf(crotonRiverWatershed, crotonRiver) In(crotonRiver, southwesternNewYork) ∀x ((Water(x) ∧ In(x, crotonRiverWatershed)) → FlowsTo(x, bronx)) In(bronx, newYork)

Water from the Croton River flows to the Bronx.

∀x (Water(x) ∧ From(x, crotonRiver) → FlowsTo(x, bronx))

Uncertain

All nuclear-powered submarines are warships. No nuclear-powered submarines are commercial vessels.

∀x (NuclearPoweredSubmarine(x) → Warship(x)) ∀x (NuclearPoweredSubmarine(x) → ¬CommercialVessel(x))

No warships are commercial vessels.

∀x (Warship(x) → ¬CommercialVessel(x))

Uncertain

If an album is written by a rock band, then the genre of the album is rock. If a band writes an album winning an award, then this band wins this award. Trouble at the Henhouse is an album by The Tragically Hip. The Tragically Hip is a Canadian rock band. The song "Butts Wigglin'" is in Trouble at the Henhouse. Trouble at the Henhouse won the Album of the Year award. A song in Trouble at the Henhouse appeared in a film.

∀x ∀y ∀z (AlbumByBand(x, y) ∧ RockBand(y, z) → Genre(x, rock)) ∀x ∀y ∀z (AlbumByBand(x, y) ∧ AlbumAward(x, z) → RockBandAward(y, z)) AlbumByBand(trouble_at_the_Henhouse, the_Tragically_Hip) RockBand(the_Tragically_Hip, canada) SongInAlbum(butts_Wigglin, trouble_at_the_Henhouse) AlbumAward(trouble_at_the_Henhouse, the_Album_of_the_Year) ∃x (SongInFilm(x) ∧ SongInAlbum(x, trouble_at_the_Henhouse))

The genre of Trouble at the Henhouse is rock.

Genre(troubleAtTheHenhouse, rock)

True

If an album is written by a rock band, then the genre of the album is rock. If a band writes an album winning an award, then this band wins this award. Trouble at the Henhouse is an album by The Tragically Hip. The Tragically Hip is a Canadian rock band. The song "Butts Wigglin'" is in Trouble at the Henhouse. Trouble at the Henhouse won the Album of the Year award. A song in Trouble at the Henhouse appeared in a film.

∀x ∀y ∀z (AlbumByBand(x, y) ∧ RockBand(y, z) → Genre(x, rock)) ∀x ∀y ∀z (AlbumByBand(x, y) ∧ AlbumAward(x, z) → RockBandAward(y, z)) AlbumByBand(trouble_at_the_Henhouse, the_Tragically_Hip) RockBand(the_Tragically_Hip, canada) SongInAlbum(butts_Wigglin, trouble_at_the_Henhouse) AlbumAward(trouble_at_the_Henhouse, the_Album_of_the_Year) ∃x (SongInFilm(x) ∧ SongInAlbum(x, trouble_at_the_Henhouse))

No Canadian rock band has won the Album of the Year award.

¬∃x(RockBand(x, canada) ∧ Award(x, theAlbumOfTheYear))

False

If an album is written by a rock band, then the genre of the album is rock. If a band writes an album winning an award, then this band wins this award. Trouble at the Henhouse is an album by The Tragically Hip. The Tragically Hip is a Canadian rock band. The song "Butts Wigglin'" is in Trouble at the Henhouse. Trouble at the Henhouse won the Album of the Year award. A song in Trouble at the Henhouse appeared in a film.

∀x ∀y ∀z (AlbumByBand(x, y) ∧ RockBand(y, z) → Genre(x, rock)) ∀x ∀y ∀z (AlbumByBand(x, y) ∧ AlbumAward(x, z) → RockBandAward(y, z)) AlbumByBand(trouble_at_the_Henhouse, the_Tragically_Hip) RockBand(the_Tragically_Hip, canada) SongInAlbum(butts_Wigglin, trouble_at_the_Henhouse) AlbumAward(trouble_at_the_Henhouse, the_Album_of_the_Year) ∃x (SongInFilm(x) ∧ SongInAlbum(x, trouble_at_the_Henhouse))

"Butts Wigglin'" appeared in a film.

SongInFilm(buttsWigglin)

Uncertain

Daniel is a software engineer, and he works at Palantir Technologies. Daniel studied bioengineering during his undergraduate at Rice University. Daniel’s older sister works at Meta as a technical sourcer. Daniel’s dad and older sister both graduated from Stanford University. Daniel’s dad is a doctor practicing internal medicine at a veteran’s hospital in Minneapolis.

SoftwareEngineer(daniel) ∧ WorksAt(daniel, palantirTechnologies) Studied(daniel, bioengineering) ∧ UndergraduateAt(daniel, riceUniversity) WorksAtMeta(danielsOlderSister) ∧ TechnicalSourcer(danielsOlderSister) GraduatedFromStanfordUniversity(danielsOlderSister) ∧ GraduatedFromStanfordUniversity(danielsDad) Doctor(danielsDad) ∧ Practicing(danielsDad, internalMedicine) ∧ PracticingAt(danielsDad, veteransHospital) ∧ In(veteransHospital, minneapolis)

Daniel once applied to Stanford University, but he couldn’t get in even though he has family members who are Stanford alumni.

AppliedTo(daniel, stanfordUniversity) ∧ ¬GotInto(daniel, stanfordUniversity) ∧ Alumni(danielsFamilyMembers, stanfordUniversity)

Uncertain

Daniel is a software engineer, and he works at Palantir Technologies. Daniel studied bioengineering during his undergraduate at Rice University. Daniel’s older sister works at Meta as a technical sourcer. Daniel’s dad and older sister both graduated from Stanford University. Daniel’s dad is a doctor practicing internal medicine at a veteran’s hospital in Minneapolis.

SoftwareEngineer(daniel) ∧ WorksAt(daniel, palantirTechnologies) Studied(daniel, bioengineering) ∧ UndergraduateAt(daniel, riceUniversity) WorksAtMeta(danielsOlderSister) ∧ TechnicalSourcer(danielsOlderSister) GraduatedFromStanfordUniversity(danielsOlderSister) ∧ GraduatedFromStanfordUniversity(danielsDad) Doctor(danielsDad) ∧ Practicing(danielsDad, internalMedicine) ∧ PracticingAt(danielsDad, veteransHospital) ∧ In(veteransHospital, minneapolis)

Daniel studied bioengineering as an undergraduate at Rice University.

Studied(daniel, bioengineering) ∧ UndergraduateAt(daniel, riceUniversity)

True

Daniel is a software engineer, and he works at Palantir Technologies. Daniel studied bioengineering during his undergraduate at Rice University. Daniel’s older sister works at Meta as a technical sourcer. Daniel’s dad and older sister both graduated from Stanford University. Daniel’s dad is a doctor practicing internal medicine at a veteran’s hospital in Minneapolis.

SoftwareEngineer(daniel) ∧ WorksAt(daniel, palantirTechnologies) Studied(daniel, bioengineering) ∧ UndergraduateAt(daniel, riceUniversity) WorksAtMeta(danielsOlderSister) ∧ TechnicalSourcer(danielsOlderSister) GraduatedFromStanfordUniversity(danielsOlderSister) ∧ GraduatedFromStanfordUniversity(danielsDad) Doctor(danielsDad) ∧ Practicing(danielsDad, internalMedicine) ∧ PracticingAt(danielsDad, veteransHospital) ∧ In(veteransHospital, minneapolis)

Daniel and his sister grew up in Minneapolis, Minnesota.

GrewUpIn(daniel, minneapolis) ∧ GrewUpIn(danielsOlderSister, minneapolis)

Uncertain

The world's only major large passenger aircraft manufacturers are Boeing and Airbus. All American Airlines planes are from the world's major large passenger aircraft manufacturers. Airbus made more revenue than Boeing last year.

∀x (WorldMajorLargePassengerAircraftManufacturer(x) → x=boeing ⊕ x=airbus) ∀x (AmericanAirlinesAircraft(x) → WorldMajorLargePassengerAircraftManufacturer(x)) MoreInRevenue(airbus, boeing)

An American Airlines plane is either a Boeing or Airbus plane.

∀x (AmericanAirlinesPlane(x) → x=boeing ⊕ x=airbus)

True

The world's only major large passenger aircraft manufacturers are Boeing and Airbus. All American Airlines planes are from the world's major large passenger aircraft manufacturers. Airbus made more revenue than Boeing last year.

∀x (WorldMajorLargePassengerAircraftManufacturer(x) → x=boeing ⊕ x=airbus) ∀x (AmericanAirlinesAircraft(x) → WorldMajorLargePassengerAircraftManufacturer(x)) MoreInRevenue(airbus, boeing)

There exists a SpaceX commercial aircraft.

∃x (CommercialAircraft(x) ∧ x=spaceX)

Uncertain

The world's only major large passenger aircraft manufacturers are Boeing and Airbus. All American Airlines planes are from the world's major large passenger aircraft manufacturers. Airbus made more revenue than Boeing last year.

∀x (WorldMajorLargePassengerAircraftManufacturer(x) → x=boeing ⊕ x=airbus) ∀x (AmericanAirlinesAircraft(x) → WorldMajorLargePassengerAircraftManufacturer(x)) MoreInRevenue(airbus, boeing)

There does not exist a United Airlines plane produced by Boeing.

∀x (UnitedAirlinesAircraft(x) → ¬(x=boeing))

Uncertain

The world's only major large passenger aircraft manufacturers are Boeing and Airbus. All American Airlines planes are from the world's major large passenger aircraft manufacturers. Airbus made more revenue than Boeing last year.

∀x (WorldMajorLargePassengerAircraftManufacturer(x) → x=boeing ⊕ x=airbus) ∀x (AmericanAirlinesAircraft(x) → WorldMajorLargePassengerAircraftManufacturer(x)) MoreInRevenue(airbus, boeing)

There is a commercial plane made by both Airbus and Boeing.

∃x (WorldMajorLargePassengerAircraftManufacturer(x) ∧ ProducedBy(x, airbus) ∧ ProducedBy(x, boeing))

False

Luzon is an island in the Philippines. In December 1999, an earthquake struck Luzon. People died in the December 1999 earthquake in Luzon.

Island(luzon) ∧ In(luzon, philippines) ∃x (Earthquake(x) ∧ StrikeInYr(x, year1999) ∧ StrikeInMo(x, december) ∧ StrikeInCity(x, luzon)) ∃x (Earthquake(x) ∧ StrikeInYr(x, year1999) ∧ StrikeInMo(x, december) ∧ StrikeInCity(x, luzon) ∧ Deadly(x))

Leyte is an island in the Philippines.

Island(leyte) ∧ In(leyte, philippines)

Uncertain

Luzon is an island in the Philippines. In December 1999, an earthquake struck Luzon. People died in the December 1999 earthquake in Luzon.

Island(luzon) ∧ In(luzon, philippines) ∃x (Earthquake(x) ∧ StrikeInYr(x, year1999) ∧ StrikeInMo(x, december) ∧ StrikeInCity(x, luzon)) ∃x (Earthquake(x) ∧ StrikeInYr(x, year1999) ∧ StrikeInMo(x, december) ∧ StrikeInCity(x, luzon) ∧ Deadly(x))

No one has ever died in an earthquake that struck the Philippines.

∀x ∀y ((Earthquake(x) ∧ StrikeInCity(x, y) ∧ In(y, philippines)) → ¬Deadly(x))

False

Luzon is an island in the Philippines. In December 1999, an earthquake struck Luzon. People died in the December 1999 earthquake in Luzon.

Island(luzon) ∧ In(luzon, philippines) ∃x (Earthquake(x) ∧ StrikeInYr(x, year1999) ∧ StrikeInMo(x, december) ∧ StrikeInCity(x, luzon)) ∃x (Earthquake(x) ∧ StrikeInYr(x, year1999) ∧ StrikeInMo(x, december) ∧ StrikeInCity(x, luzon) ∧ Deadly(x))

In 1999, there was at least one earthquake in the Philippines.

∃x ∃y (Earthquake(x) ∧ StrikeInYr(x, year1999) ∧ StrikeInMo(x, december) ∧ StrikeInCity(x, y) ∧ In(y, philippines))

True

People who like financial risks invest in the public stock market regularly or enjoy gambling regularly. If people invest in the public stock market regularly, then they read the Wall Street Journal and other newspapers regularly to keep updated on financial metrics. All people who enjoy enjoy gambling regularly spend a lot of money at casinos or other betting games. People who spend a lot of money at casinos and other betting games would enjoy visiting the Las Vegas Strip. People who spend a lot of money at casinos and other betting games are at risk of gambling addiction. Matt does not invest in the public stock market regularly. Matt likes financial risks.

∀x (Like(x, financialRisk) → InvestInRegularly(x, publicStockMarket) ∨ EnjoyRegularly(x, gambling)) ∀x (InvestInRegularly(x, publicStockMarket) → ReadToKeepUpdatedOn(x, theWallStreetJournal, financialMetric) ∨ (∃y (¬(y=theWallStreetJournal) ∧ NewsPaper(y) ∧ ReadToKeepUpdatedOn(x, y, financialMetric)))) ∀x (EnjoyRegularly(x, gambling) → SpendAt(x, alotOfMoney, casino) ∨ (∃y (¬(y=casino) ∧ BettingGame(y) ∧ SpendAt(x, aLotOfMoney, y))) ∀x (SpendAt(x, alotOfMoney, casino) ∨ (∃y (¬(y=casino) ∧ BettingGame(y) ∧ SpendAt(x, aLotOfMoney, y))) → EnjoyVisiting(x, theLasVegasStrip)) ∀x (SpendAt(x, alotOfMoney, casino) ∨ (∃y (¬(y=casino) ∧ BettingGame(y) ∧ SpendAt(x, aLotOfMoney, y)) → AtRiskOf(x, gamblingAddiction)) InvestInRegularly(matt, publicStockMarket) Like(matt, financialRisk)

Matt reads the Wall Street Journal and other newspapers regularly to keep updated on financial metrics.

Newspapers(matt)

Uncertain

People who like financial risks invest in the public stock market regularly or enjoy gambling regularly. If people invest in the public stock market regularly, then they read the Wall Street Journal and other newspapers regularly to keep updated on financial metrics. All people who enjoy enjoy gambling regularly spend a lot of money at casinos or other betting games. People who spend a lot of money at casinos and other betting games would enjoy visiting the Las Vegas Strip. People who spend a lot of money at casinos and other betting games are at risk of gambling addiction. Matt does not invest in the public stock market regularly. Matt likes financial risks.

∀x (Like(x, financialRisk) → InvestInRegularly(x, publicStockMarket) ∨ EnjoyRegularly(x, gambling)) ∀x (InvestInRegularly(x, publicStockMarket) → ReadToKeepUpdatedOn(x, theWallStreetJournal, financialMetric) ∨ (∃y (¬(y=theWallStreetJournal) ∧ NewsPaper(y) ∧ ReadToKeepUpdatedOn(x, y, financialMetric)))) ∀x (EnjoyRegularly(x, gambling) → SpendAt(x, alotOfMoney, casino) ∨ (∃y (¬(y=casino) ∧ BettingGame(y) ∧ SpendAt(x, aLotOfMoney, y))) ∀x (SpendAt(x, alotOfMoney, casino) ∨ (∃y (¬(y=casino) ∧ BettingGame(y) ∧ SpendAt(x, aLotOfMoney, y))) → EnjoyVisiting(x, theLasVegasStrip)) ∀x (SpendAt(x, alotOfMoney, casino) ∨ (∃y (¬(y=casino) ∧ BettingGame(y) ∧ SpendAt(x, aLotOfMoney, y)) → AtRiskOf(x, gamblingAddiction)) InvestInRegularly(matt, publicStockMarket) Like(matt, financialRisk)

If Matt is either both a person who is at risk of a gambling addiction and invests in the public stock market regularly, or neither is at risk of a gambling addiction nor invests in the public stock market regularly, then Matt neither visits the Las Vegas Strip regularly nor reads the Wall Street Journal and other newspapers regularly to keep updated on the financial metrics.

AtRiskOf(matt, gamblingAddiction) ⊕ InvestInRegularly(matt, publicStockMarket) → ¬EnjoyVisiting(matt, theLasVegasStrip) ∧ ¬(ReadToKeepUpdatedOn(matt, theWallStreetJournal, financialMetric) ∨ (∃y (¬(y=theWallStreetJournal) ∧ NewsPaper(y) ∧ ReadToKeepUpdatedOn(matt, y, financialMetric))))

True

People who like financial risks invest in the public stock market regularly or enjoy gambling regularly. If people invest in the public stock market regularly, then they read the Wall Street Journal and other newspapers regularly to keep updated on financial metrics. All people who enjoy enjoy gambling regularly spend a lot of money at casinos or other betting games. People who spend a lot of money at casinos and other betting games would enjoy visiting the Las Vegas Strip. People who spend a lot of money at casinos and other betting games are at risk of gambling addiction. Matt does not invest in the public stock market regularly. Matt likes financial risks.

∀x (Like(x, financialRisk) → InvestInRegularly(x, publicStockMarket) ∨ EnjoyRegularly(x, gambling)) ∀x (InvestInRegularly(x, publicStockMarket) → ReadToKeepUpdatedOn(x, theWallStreetJournal, financialMetric) ∨ (∃y (¬(y=theWallStreetJournal) ∧ NewsPaper(y) ∧ ReadToKeepUpdatedOn(x, y, financialMetric)))) ∀x (EnjoyRegularly(x, gambling) → SpendAt(x, alotOfMoney, casino) ∨ (∃y (¬(y=casino) ∧ BettingGame(y) ∧ SpendAt(x, aLotOfMoney, y))) ∀x (SpendAt(x, alotOfMoney, casino) ∨ (∃y (¬(y=casino) ∧ BettingGame(y) ∧ SpendAt(x, aLotOfMoney, y))) → EnjoyVisiting(x, theLasVegasStrip)) ∀x (SpendAt(x, alotOfMoney, casino) ∨ (∃y (¬(y=casino) ∧ BettingGame(y) ∧ SpendAt(x, aLotOfMoney, y)) → AtRiskOf(x, gamblingAddiction)) InvestInRegularly(matt, publicStockMarket) Like(matt, financialRisk)

Matt is not at risk of a gambling addiction and Mike does not both read the Wall Street Journal and other newspapers regularly and visits the Las Vegas Strip regularly.

¬AtRiskOf(matt, gamblingAddiction) ∧ ¬(ReadToKeepUpdatedOn(x, theWallStreetJournal, financialMetric) ∨ (∃y (¬(y=theWallStreetJournal) ∧ NewsPaper(y) ∧ ReadToKeepUpdatedOn(x, y, financialMetric))) ∧ EnjoyVisiting(matt, theLasVegasStrip))

False

All students learning piano can strike the right notes. All students who can strike the right note can get the rhythms right. If a student can get the rhythms right, he will start working on coordination between the left and the right hands. Some students who start working on coordination between the left and the right hands become good at it, while other students find it challenging. If John can strike the right notes, get the rhythms right, and is good at coordination between right and left hands, then he puts emotions into his playing. John is a student learning piano. John does not find coordination between the left and the right hands challenging.

∀x (Student(x) ∧ LearningPiano(x) → Can(x, strike, rightNote)) ∀x (Student(x) ∧ Can(x, strike, rightNote) → Can(x, getTheRhythmRight)) ∀x (Student(x) ∧ Can(x, getTheRhythmRight) → Start(x, workingOnCoordinationBetweenTheLeftAndRightHands)) ∀x (Student(x) ∧ Start(x, workingOnCoordinationBetweenTheLeftAndRightHands) → Become(x, goodAtCoordination) ⊕ Find(x, coordinationChallenging)) (Can(john, getTheRhythmRight) ∧ Can(john, getTheRhythmRight)) ∧ Become(john, goodAtCoordination) → PutEmotionInto(john, hisPlaying) Student(john) ∧ LearningPiano(john) ¬Find(john, coordinationChallenging)

John can get the rhythms right.

Can(john, getTheRhythmRight)

True

All students learning piano can strike the right notes. All students who can strike the right note can get the rhythms right. If a student can get the rhythms right, he will start working on coordination between the left and the right hands. Some students who start working on coordination between the left and the right hands become good at it, while other students find it challenging. If John can strike the right notes, get the rhythms right, and is good at coordination between right and left hands, then he puts emotions into his playing. John is a student learning piano. John does not find coordination between the left and the right hands challenging.

∀x (Student(x) ∧ LearningPiano(x) → Can(x, strike, rightNote)) ∀x (Student(x) ∧ Can(x, strike, rightNote) → Can(x, getTheRhythmRight)) ∀x (Student(x) ∧ Can(x, getTheRhythmRight) → Start(x, workingOnCoordinationBetweenTheLeftAndRightHands)) ∀x (Student(x) ∧ Start(x, workingOnCoordinationBetweenTheLeftAndRightHands) → Become(x, goodAtCoordination) ⊕ Find(x, coordinationChallenging)) (Can(john, getTheRhythmRight) ∧ Can(john, getTheRhythmRight)) ∧ Become(john, goodAtCoordination) → PutEmotionInto(john, hisPlaying) Student(john) ∧ LearningPiano(john) ¬Find(john, coordinationChallenging)

John does not put emotions into his playing.

PutEmotionInto(john, hisPlaying)

False