premise stringlengths 940 1.64k | hypothesis stringclasses 224
values | label stringclasses 3
values | premise_tptp stringlengths 721 1.28k | hypothesis_tptp stringclasses 224
values | proof_inputs listlengths 0 15 | proof stringlengths 684 15.9k ⌀ | rule_concentration int64 0 0 |
|---|---|---|---|---|---|---|---|
If fred is either not curious or patient then lucy is not tall. Everyone who is both not rich and not old is not old. Everyone who is not humble or not patient is funny or brave. Everyone who is not funny or not old is either not curious or not rich. Everyone who is not rich is not humble. Everyone who is both not funn... | John is brave. | entailment | (((~curious(fred)<~>patient(fred)))=>(~tall(lucy)))&
(![X]:((~rich(X)&~old(X))=>~old(X)))&
(![X]:((~humble(X)|~patient(X))=>(funny(X)|brave(X))))&
(![X]:((~funny(X)|~old(X))=>(~curious(X)<~>~rich(X))))&
(![X]:(~rich(X)=>~humble(X)))&
(![X]:((~funny(X)&rich(X))=>tall(X)))&
(((funny(fred)|~wise(fred)))=>(?[X]:((calm(X)<~... | brave(john) | [
"p11",
"p13",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 475551141223024031369291
% SZS output start Proof for 475551141223024031369291
12. ! [X0] : ((~rich(X0) | kind(X0)) => (~wise(X0) | brave(X0))) [input p11]
14. ! [X0] : ((~wise(X0) | brave(X0)) => (brave(X0) | rich(X0))) [input p13]
17. ~creative(john) & ~rich(john) [input p16]
25. ~brave... | 0 |
If john is either kind or not tall then alice is not wise or strong and vice versa.
If mary is not generous or creative then someone is not old.
If fred is curious or kind then someone is either not generous or not creative.
Everyone who is both kind and not wise is tall.
Everyone who is either calm or happy is both no... | Alice is kind. | neutral | (((kind(john)<~>~tall(john)))<=>((~wise(alice)|strong(alice))))&
(((~generous(mary)|creative(mary)))=>(?[X]:(~old(X))))&
(((curious(fred)|kind(fred)))=>(?[X]:((~generous(X)<~>~creative(X)))))&
(![X]:((kind(X)&~wise(X))=>tall(X)))&
(![X]:((calm(X)<~>happy(X))<=>(~wise(X)&~curious(X))))&
(![X]:((tall(X)&~old(X))<=>(~kind... | kind(alice) | [] | null | 0 |
Everyone who is either brave or not funny is either old or not funny.
Everyone who is both not rich and not quiet is both wise and creative and vice versa.
If someone is either not wise or brave then someone is either humble or happy and vice versa.
Everyone who is tall or strong is not funny and vice versa.
If someone... | Lucy is not rich. | neutral | (![X]:((brave(X)<~>~funny(X))=>(old(X)<~>~funny(X))))&
(![X]:((~rich(X)&~quiet(X))<=>(wise(X)&creative(X))))&
((?[X]:((~wise(X)<~>brave(X))))<=>(?[X]:((humble(X)<~>happy(X)))))&
(![X]:((tall(X)|strong(X))<=>~funny(X)))&
((?[X]:((wise(X)|~rich(X))))=>(?[X]:((~funny(X)|rich(X)))))&
((?[X]:((~happy(X)|patient(X))))<=>((qu... | ~rich(lucy) | [] | null | 0 |
Everyone who is creative or tall is both funny and not funny. Everyone who is not strong or not generous is rich. Everyone who is not humble is both brave and not tall and vice versa. Everyone who is either happy or not quiet is not brave or calm and vice versa. Everyone who is not calm is both not curious and patient ... | Alice is patient. | entailment | (![X]:((creative(X)|tall(X))=>(funny(X)&~funny(X))))&
(![X]:((~strong(X)|~generous(X))=>rich(X)))&
(![X]:(~humble(X)<=>(brave(X)&~tall(X))))&
(![X]:((happy(X)<~>~quiet(X))<=>(~brave(X)|calm(X))))&
(![X]:(~calm(X)<=>(~curious(X)&patient(X))))&
(![X]:((curious(X)&~generous(X))<=>(~wise(X)&~kind(X))))&
((?[X]:((~calm(X)&w... | patient(alice) | [
"p0",
"p4",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 7473027473208306314529203
% SZS output start Proof for 7473027473208306314529203
1. ! [X0] : ((tall(X0) | creative(X0)) => (~funny(X0) & funny(X0))) [input p0]
5. ! [X0] : (~calm(X0) <=> (patient(X0) & ~curious(X0))) [input p4]
13. ? [X0] : calm(X0) => ? [X0] : creative(X0) [input p12]
21... | 0 |
Everyone who is not happy or not calm is either not old or not rich and vice versa. If someone is not calm then someone is happy or not rich and vice versa. Everyone who is either not old or tall is not generous or not calm. Everyone who is both strong and not tall is both generous and not funny and vice versa. Everyon... | Lucy is calm. | entailment | (![X]:((~happy(X)|~calm(X))<=>(~old(X)<~>~rich(X))))&
((?[X]:(~calm(X)))<=>(?[X]:((happy(X)|~rich(X)))))&
(![X]:((~old(X)<~>tall(X))=>(~generous(X)|~calm(X))))&
(![X]:((strong(X)&~tall(X))<=>(generous(X)&~funny(X))))&
(![X]:((old(X)|happy(X))<=>(~calm(X)<~>~curious(X))))&
(![X]:((patient(X)<~>brave(X))=>quiet(X)))&
(![... | calm(lucy) | [
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 6230822056698153587129748
% SZS output start Proof for 6230822056698153587129748
24. calm(lucy) [input p23]
25. ~calm(lucy) [input hypothesis]
146. calm(lucy) [cnf transformation 24]
147. ~calm(lucy) [cnf transformation 25]
196. 12 <=> calm(lucy) [avatar definition]
278. 12 [avatar split ... | 0 |
Everyone who is both calm and not creative is not strong or rich and vice versa.
If someone is either brave or humble then mary is either not rich or not patient.
If fred is not strong or tall then susan is curious or kind.
Everyone who is either not calm or not humble is creative or not humble and vice versa.
Everyone... | Mary is humble. | neutral | (![X]:((calm(X)&~creative(X))<=>(~strong(X)|rich(X))))&
((?[X]:((brave(X)<~>humble(X))))=>((~rich(mary)<~>~patient(mary))))&
(((~strong(fred)|tall(fred)))=>((curious(susan)|kind(susan))))&
(![X]:((~calm(X)<~>~humble(X))<=>(creative(X)|~humble(X))))&
(![X]:((~wise(X)&generous(X))<=>(~happy(X)&happy(X))))&
(((~strong(luc... | humble(mary) | [] | null | 0 |
If john is both brave and curious then someone is both curious and tall and vice versa.
If susan is both happy and not funny then someone is either generous or rich.
Everyone who is both not strong and tall is tall and vice versa.
Everyone who is either calm or not happy is either humble or not generous and vice versa.... | Paul is not creative. | neutral | (((brave(john)&curious(john)))<=>(?[X]:((curious(X)&tall(X)))))&
(((happy(susan)&~funny(susan)))=>(?[X]:((generous(X)<~>rich(X)))))&
(![X]:((~strong(X)&tall(X))<=>tall(X)))&
(![X]:((calm(X)<~>~happy(X))<=>(humble(X)<~>~generous(X))))&
(![X]:((quiet(X)&happy(X))<=>(~generous(X)<~>rich(X))))&
((?[X]:((~strong(X)|~creativ... | ~creative(paul) | [] | null | 0 |
If someone is not funny or old then someone is either generous or not curious.
Everyone who is curious or not quiet is not calm or not happy and vice versa.
If someone is either not generous or kind then someone is either old or calm.
Everyone who is not generous is old.
Everyone who is not kind or kind is not happy an... | John is not old. | entailment | ((?[X]:((~funny(X)|old(X))))=>(?[X]:((generous(X)<~>~curious(X)))))&
(![X]:((curious(X)|~quiet(X))<=>(~calm(X)|~happy(X))))&
((?[X]:((~generous(X)<~>kind(X))))=>(?[X]:((old(X)<~>calm(X)))))&
(![X]:(~generous(X)=>old(X)))&
(![X]:((~kind(X)|kind(X))<=>~happy(X)))&
(((humble(paul)|happy(paul)))<=>((old(john)|~patient(john... | ~old(john) | [
"p4",
"p5",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 3057805875219791834837931
% SZS output start Proof for 3057805875219791834837931
5. ! [X0] : ((kind(X0) | ~kind(X0)) <=> ~happy(X0)) [input p4]
6. (happy(paul) | humble(paul)) <=> (~patient(john) | old(john)) [input p5]
8. ! [X0] : (~happy(X0) => (quiet(X0) & ~humble(X0))) [input p7]
24. ... | 0 |
Everyone who is both not creative and not tall is both brave and wise and vice versa.
Everyone who is not rich or strong is both not generous and not brave.
If someone is strong then someone is both not strong and not tall and vice versa.
Everyone who is both not tall and not generous is kind or strong and vice versa.
... | Alice is wise. | contradiction | (![X]:((~creative(X)&~tall(X))<=>(brave(X)&wise(X))))&
(![X]:((~rich(X)|strong(X))=>(~generous(X)&~brave(X))))&
((?[X]:(strong(X)))<=>(?[X]:((~strong(X)&~tall(X)))))&
(![X]:((~tall(X)&~generous(X))<=>(kind(X)|strong(X))))&
(![X]:((creative(X)&wise(X))=>(~tall(X)&tall(X))))&
((?[X]:((~brave(X)|kind(X))))=>(?[X]:((~rich(... | wise(alice) | [
"p0",
"p1",
"p5",
"p14",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 3521149428896916941175928
% SZS output start Proof for 3521149428896916941175928
1. ! [X0] : ((~tall(X0) & ~creative(X0)) <=> (wise(X0) & brave(X0))) [input p0]
2. ! [X0] : ((strong(X0) | ~rich(X0)) => (~brave(X0) & ~generous(X0))) [input p1]
6. ? [X0] : (kind(X0) | ~brave(X0)) => ? [X0] ... | 0 |
Everyone who is curious is either not generous or not rich and vice versa.
Everyone who is humble is both not wise and generous.
If susan is tall or creative then someone is both generous and patient.
If someone is both curious and not generous then someone is both not funny and creative.
Everyone who is both not creat... | Paul is not brave. | entailment | (![X]:(curious(X)<=>(~generous(X)<~>~rich(X))))&
(![X]:(humble(X)=>(~wise(X)&generous(X))))&
(((tall(susan)|creative(susan)))=>(?[X]:((generous(X)&patient(X)))))&
((?[X]:((curious(X)&~generous(X))))=>(?[X]:((~funny(X)&creative(X)))))&
(![X]:((~creative(X)&~calm(X))=>(~humble(X)<~>generous(X))))&
(![X]:((~patient(X)&ric... | ~brave(paul) | [
"p6",
"p7",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 8950720951373667102512933
% SZS output start Proof for 8950720951373667102512933
7. ! [X0] : ((brave(X0) <~> ~strong(X0)) => (~funny(X0) & wise(X0))) [input p6]
8. ! [X0] : ((funny(X0) <~> ~strong(X0)) <=> (strong(X0) | ~wise(X0))) [input p7]
9. ! [X0] : ((~calm(X0) | ~strong(X0)) <=> ~br... | 0 |
Everyone who is patient is generous.
Everyone who is both not tall and brave is rich.
If mary is both not kind and patient then someone is either not generous or not wise.
If someone is both not wise and not brave then mary is calm or creative.
Everyone who is either tall or not funny is either not rich or quiet.
If so... | Mary is not kind. | entailment | (![X]:(patient(X)=>generous(X)))&
(![X]:((~tall(X)&brave(X))=>rich(X)))&
(((~kind(mary)&patient(mary)))=>(?[X]:((~generous(X)<~>~wise(X)))))&
((?[X]:((~wise(X)&~brave(X))))=>((calm(mary)|creative(mary))))&
(![X]:((tall(X)<~>~funny(X))=>(~rich(X)<~>quiet(X))))&
((?[X]:(happy(X)))<=>((~generous(susan)&brave(susan))))&
(!... | ~kind(mary) | [
"p0",
"p5",
"p6",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 9105232002249397970753005
% SZS output start Proof for 9105232002249397970753005
1. ! [X0] : (patient(X0) => generous(X0)) [input p0]
6. ? [X0] : happy(X0) <=> (brave(susan) & ~generous(susan)) [input p5]
7. ! [X0] : ((~old(X0) <~> patient(X0)) => (~brave(X0) & wise(X0))) [input p6]
13. !... | 0 |
Everyone who is either strong or not calm is not happy. If someone is both not wise and not happy then fred is not old and vice versa. If fred is not generous or not kind then someone is either brave or not creative and vice versa. If mary is creative then someone is either not creative or brave. If alice is both patie... | Fred is curious. | entailment | (![X]:((strong(X)<~>~calm(X))=>~happy(X)))&
((?[X]:((~wise(X)&~happy(X))))<=>(~old(fred)))&
(((~generous(fred)|~kind(fred)))<=>(?[X]:((brave(X)<~>~creative(X)))))&
((creative(mary))=>(?[X]:((~creative(X)<~>brave(X)))))&
(((patient(alice)&calm(alice)))<=>(?[X]:((tall(X)|calm(X)))))&
((?[X]:(~old(X)))=>(?[X]:((happy(X)|~... | curious(fred) | [
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 7727914594403504605124024
% SZS output start Proof for 7727914594403504605124024
15. ! [X0] : ((curious(X0) | strong(X0)) <=> ~strong(X0)) [input p14]
21. ~curious(fred) [input hypothesis]
69. ! [X0] : (((curious(X0) | strong(X0)) | strong(X0)) & (~strong(X0) | (~curious(X0) & ~strong(X0)... | 0 |
Everyone who is kind is both not wise and strong and vice versa.
Everyone who is both patient and rich is curious and vice versa.
Everyone who is not rich is generous and vice versa.
Everyone who is quiet or kind is both curious and not humble.
Everyone who is tall is either patient or happy.
Everyone who is both not b... | Fred is not calm. | entailment | (![X]:(kind(X)<=>(~wise(X)&strong(X))))&
(![X]:((patient(X)&rich(X))<=>curious(X)))&
(![X]:(~rich(X)<=>generous(X)))&
(![X]:((quiet(X)|kind(X))=>(curious(X)&~humble(X))))&
(![X]:(tall(X)=>(patient(X)<~>happy(X))))&
(![X]:((~brave(X)&~kind(X))<=>wise(X)))&
(![X]:((~old(X)<~>~funny(X))=>(kind(X)&quiet(X))))&
((?[X]:((cal... | ~calm(fred) | [
"p12",
"p13",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 1464077875566887917966554
% SZS output start Proof for 1464077875566887917966554
13. ! [X0] : (calm(X0) => rich(X0)) [input p12]
14. ! [X0] : ((rich(X0) | strong(X0)) => (creative(X0) & ~brave(X0))) [input p13]
23. ~brave(fred) <~> calm(fred) [input p22]
24. calm(fred) [input hypothesis]
... | 0 |
If fred is not rich then john is tall.
Everyone who is not creative is both not patient and not humble and vice versa.
If someone is either wise or not creative then lucy is not old.
If someone is both old and calm then john is brave or not funny and vice versa.
Everyone who is either not wise or not humble is either n... | Susan is creative. | entailment | ((~rich(fred))=>(tall(john)))&
(![X]:(~creative(X)<=>(~patient(X)&~humble(X))))&
((?[X]:((wise(X)<~>~creative(X))))=>(~old(lucy)))&
((?[X]:((old(X)&calm(X))))<=>((brave(john)|~funny(john))))&
(![X]:((~wise(X)<~>~humble(X))<=>(~creative(X)<~>humble(X))))&
(![X]:((calm(X)|quiet(X))=>(~tall(X)&tall(X))))&
(![X]:(kind(X)=>... | creative(susan) | [
"p1",
"p4",
"p5",
"p9",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 1074510848696188291628408
% SZS output start Proof for 1074510848696188291628408
2. ! [X0] : (~creative(X0) <=> (~humble(X0) & ~patient(X0))) [input p1]
5. ! [X0] : ((~wise(X0) <~> ~humble(X0)) <=> (~creative(X0) <~> humble(X0))) [input p4]
6. ! [X0] : ((quiet(X0) | calm(X0)) => (tall(X0)... | 0 |
Everyone who is creative or not quiet is either generous or not creative and vice versa.
If someone is both brave and not old then lucy is either not calm or calm and vice versa.
If mary is not patient then alice is not calm.
If lucy is both not tall and calm then someone is quiet and vice versa.
If someone is not happ... | Alice is funny. | neutral | (![X]:((creative(X)|~quiet(X))<=>(generous(X)<~>~creative(X))))&
((?[X]:((brave(X)&~old(X))))<=>((~calm(lucy)<~>calm(lucy))))&
((~patient(mary))=>(~calm(alice)))&
(((~tall(lucy)&calm(lucy)))<=>(?[X]:(quiet(X))))&
((?[X]:(~happy(X)))=>(?[X]:((~wise(X)|patient(X)))))&
(![X]:((~brave(X)&~wise(X))<=>(happy(X)<~>~wise(X))))... | funny(alice) | [] | null | 0 |
If alice is not calm or not creative then someone is either old or wise.
Everyone who is both not happy and not patient is either old or not happy and vice versa.
If mary is either not brave or brave then lucy is not funny.
If someone is either generous or old then someone is either creative or wise and vice versa.
Eve... | Alice is creative. | contradiction | (((~calm(alice)|~creative(alice)))=>(?[X]:((old(X)<~>wise(X)))))&
(![X]:((~happy(X)&~patient(X))<=>(old(X)<~>~happy(X))))&
(((~brave(mary)<~>brave(mary)))=>(~funny(lucy)))&
((?[X]:((generous(X)<~>old(X))))<=>(?[X]:((creative(X)<~>wise(X)))))&
(![X]:((~kind(X)|~curious(X))=>(~generous(X)<~>~happy(X))))&
(![X]:((~old(X)|... | creative(alice) | [
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 4004127512784437641965629
% SZS output start Proof for 4004127512784437641965629
9. kind(alice) <=> (creative(alice) <~> kind(alice)) [input p8]
24. creative(alice) [input hypothesis]
57. (kind(alice) | ((creative(alice) | ~kind(alice)) & (kind(alice) | ~creative(alice)))) & (((~kind(alic... | 0 |
If alice is both not curious and not funny then lucy is either generous or not funny.
If someone is both not brave and not calm then someone is wise or creative and vice versa.
If someone is either not patient or not kind then fred is tall.
Everyone who is both humble and kind is both not funny and tall and vice versa.... | Susan is not funny. | entailment | (((~curious(alice)&~funny(alice)))=>((generous(lucy)<~>~funny(lucy))))&
((?[X]:((~brave(X)&~calm(X))))<=>(?[X]:((wise(X)|creative(X)))))&
((?[X]:((~patient(X)<~>~kind(X))))=>(tall(fred)))&
(![X]:((humble(X)&kind(X))<=>(~funny(X)&tall(X))))&
(![X]:((old(X)&~old(X))<=>(rich(X)&funny(X))))&
((?[X]:((~wise(X)<~>~funny(X)))... | ~funny(susan) | [
"p2",
"p4",
"p6",
"p13",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 8954062569025376043730684
% SZS output start Proof for 8954062569025376043730684
3. ? [X0] : (~patient(X0) <~> ~kind(X0)) => tall(fred) [input p2]
5. ! [X0] : ((~old(X0) & old(X0)) <=> (funny(X0) & rich(X0))) [input p4]
7. ? [X0] : (tall(X0) | kind(X0)) <=> (~patient(susan) <~> ~happy(sus... | 0 |
If fred is either strong or curious then alice is both not quiet and not old and vice versa.
Everyone who is strong is kind or not strong and vice versa.
Everyone who is patient or not humble is not creative or not tall and vice versa.
If lucy is both not patient and not happy then someone is either patient or not calm... | Alice is brave. | entailment | (((strong(fred)<~>curious(fred)))<=>((~quiet(alice)&~old(alice))))&
(![X]:(strong(X)<=>(kind(X)|~strong(X))))&
(![X]:((patient(X)|~humble(X))<=>(~creative(X)|~tall(X))))&
(((~patient(lucy)&~happy(lucy)))=>(?[X]:((patient(X)<~>~calm(X)))))&
(![X]:((~humble(X)|~rich(X))<=>(~wise(X)<~>happy(X))))&
(((calm(john)|quiet(john... | brave(alice) | [
"p1",
"p8",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 4578446273626256915199422
% SZS output start Proof for 4578446273626256915199422
2. ! [X0] : (strong(X0) <=> (~strong(X0) | kind(X0))) [input p1]
9. ? [X0] : ~old(X0) <=> ? [X0] : (~brave(X0) | patient(X0)) [input p8]
10. ! [X0] : ((kind(X0) & ~old(X0)) <=> (~strong(X0) & ~calm(X0))) [inp... | 0 |
If paul is either not quiet or kind then fred is both creative and not wise and vice versa. If paul is calm or not old then susan is both generous and humble and vice versa. If john is humble then lucy is both curious and not patient. If alice is either wise or rich then susan is not rich or not calm. If fred is happy ... | John is not curious. | neutral | (((~quiet(paul)<~>kind(paul)))<=>((creative(fred)&~wise(fred))))&
(((calm(paul)|~old(paul)))<=>((generous(susan)&humble(susan))))&
((humble(john))=>((curious(lucy)&~patient(lucy))))&
(((wise(alice)<~>rich(alice)))=>((~rich(susan)|~calm(susan))))&
(((happy(fred)|patient(fred)))<=>(?[X]:((~generous(X)&calm(X)))))&
(![X]:... | ~curious(john) | [] | null | 0 |
Everyone who is funny is both not strong and not happy.
Everyone who is both wise and not kind is either old or not creative and vice versa.
If someone is not strong or not wise then john is kind or not calm and vice versa.
Everyone who is not tall or quiet is not quiet.
If someone is either not strong or kind then som... | John is kind. | entailment | (![X]:(funny(X)=>(~strong(X)&~happy(X))))&
(![X]:((wise(X)&~kind(X))<=>(old(X)<~>~creative(X))))&
((?[X]:((~strong(X)|~wise(X))))<=>((kind(john)|~calm(john))))&
(![X]:((~tall(X)|quiet(X))=>~quiet(X)))&
((?[X]:((~strong(X)<~>kind(X))))<=>(?[X]:((funny(X)&brave(X)))))&
(![X]:((~wise(X)<~>~strong(X))<=>(~happy(X)<~>quiet(... | kind(john) | [
"p0",
"p2",
"p3",
"p5",
"p9",
"p11",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 7959504968933427595692481
% SZS output start Proof for 7959504968933427595692481
1. ! [X0] : (funny(X0) => (~happy(X0) & ~strong(X0))) [input p0]
3. ? [X0] : (~wise(X0) | ~strong(X0)) <=> (~calm(john) | kind(john)) [input p2]
4. ! [X0] : ((quiet(X0) | ~tall(X0)) => ~quiet(X0)) [input p3]
... | 0 |
If someone is patient then john is both rich and not tall and vice versa. Everyone who is both rich and humble is kind and vice versa. Everyone who is both not wise and not tall is curious or tall and vice versa. Everyone who is either not happy or happy is both brave and strong and vice versa. If susan is not patient ... | Fred is not patient. | entailment | ((?[X]:(patient(X)))<=>((rich(john)&~tall(john))))&
(![X]:((rich(X)&humble(X))<=>kind(X)))&
(![X]:((~wise(X)&~tall(X))<=>(curious(X)|tall(X))))&
(![X]:((~happy(X)<~>happy(X))<=>(brave(X)&strong(X))))&
(((~patient(susan)|tall(susan)))<=>(?[X]:(tall(X))))&
(![X]:(~creative(X)=>(~old(X)|wise(X))))&
(((~strong(fred)&~brave... | ~patient(fred) | [
"p2",
"p10",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 3251783540114630508340285
% SZS output start Proof for 3251783540114630508340285
3. ! [X0] : ((~tall(X0) & ~wise(X0)) <=> (tall(X0) | curious(X0))) [input p2]
11. ! [X0] : ((rich(X0) & ~patient(X0)) <=> (curious(X0) | ~quiet(X0))) [input p10]
18. wise(fred) <~> quiet(fred) [input p17]
23.... | 0 |
Everyone who is not generous or creative is both not generous and not happy and vice versa.
Everyone who is either not calm or calm is either not patient or not funny.
Everyone who is not curious or kind is either not creative or strong.
If someone is rich or not humble then someone is both not wise and patient and vic... | Fred is humble. | entailment | (![X]:((~generous(X)|creative(X))<=>(~generous(X)&~happy(X))))&
(![X]:((~calm(X)<~>calm(X))=>(~patient(X)<~>~funny(X))))&
(![X]:((~curious(X)|kind(X))=>(~creative(X)<~>strong(X))))&
((?[X]:((rich(X)|~humble(X))))<=>(?[X]:((~wise(X)&patient(X)))))&
((?[X]:((happy(X)<~>funny(X))))=>(~calm(paul)))&
(((~humble(fred)<~>~tal... | humble(fred) | [
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 8346725261906962061658328
% SZS output start Proof for 8346725261906962061658328
20. humble(fred) [input p19]
25. ~humble(fred) [input hypothesis]
134. humble(fred) [cnf transformation 20]
140. ~humble(fred) [cnf transformation 25]
196. 12 <=> humble(fred) [avatar definition]
303. 12 [ava... | 0 |
Everyone who is either curious or not kind is both not generous and not wise.
Everyone who is not calm or not strong is either kind or not curious.
Everyone who is both not calm and not patient is either brave or calm.
Everyone who is both calm and curious is wise.
If someone is either rich or not kind then susan is ei... | Alice is brave. | neutral | (![X]:((curious(X)<~>~kind(X))=>(~generous(X)&~wise(X))))&
(![X]:((~calm(X)|~strong(X))=>(kind(X)<~>~curious(X))))&
(![X]:((~calm(X)&~patient(X))=>(brave(X)<~>calm(X))))&
(![X]:((calm(X)&curious(X))=>wise(X)))&
((?[X]:((rich(X)<~>~kind(X))))<=>((old(susan)<~>~humble(susan))))&
(![X]:((funny(X)<~>~humble(X))=>(generous(... | brave(alice) | [] | null | 0 |
If paul is either not curious or quiet then someone is both not humble and calm and vice versa.
Everyone who is strong or not curious is both not strong and wise.
Everyone who is rich or not generous is not brave.
If john is wise or not generous then paul is happy or not generous and vice versa.
If someone is patient t... | Mary is not old. | neutral | (((~curious(paul)<~>quiet(paul)))<=>(?[X]:((~humble(X)&calm(X)))))&
(![X]:((strong(X)|~curious(X))=>(~strong(X)&wise(X))))&
(![X]:((rich(X)|~generous(X))=>~brave(X)))&
(((wise(john)|~generous(john)))<=>((happy(paul)|~generous(paul))))&
((?[X]:(patient(X)))=>(?[X]:((~rich(X)&rich(X)))))&
((?[X]:((~brave(X)<~>~patient(X)... | ~old(mary) | [] | null | 0 |
If someone is not kind then someone is either not humble or tall.
If john is kind then someone is either happy or calm and vice versa.
Everyone who is not creative or brave is calm.
If john is old or quiet then mary is not wise or creative.
Everyone who is tall or generous is either not humble or not funny and vice ver... | Fred is funny. | contradiction | ((?[X]:(~kind(X)))=>(?[X]:((~humble(X)<~>tall(X)))))&
((kind(john))<=>(?[X]:((happy(X)<~>calm(X)))))&
(![X]:((~creative(X)|brave(X))=>calm(X)))&
(((old(john)|quiet(john)))=>((~wise(mary)|creative(mary))))&
(![X]:((tall(X)|generous(X))<=>(~humble(X)<~>~funny(X))))&
(![X]:((~brave(X)|generous(X))=>~brave(X)))&
(![X]:((~c... | funny(fred) | [
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 6417450967585571094739749
% SZS output start Proof for 6417450967585571094739749
8. ! [X0] : (patient(X0) <=> (~funny(X0) | ~patient(X0))) [input p7]
23. funny(fred) [input hypothesis]
49. ! [X0] : ((patient(X0) | (funny(X0) & patient(X0))) & ((~funny(X0) | ~patient(X0)) | ~patient(X0))) ... | 0 |
If someone is either wise or not generous then fred is rich or not generous and vice versa.
Everyone who is generous is either not old or not humble and vice versa.
If susan is either humble or strong then someone is both not kind and not old.
Everyone who is not tall or old is both wise and kind.
Everyone who is both ... | Fred is not funny. | neutral | ((?[X]:((wise(X)<~>~generous(X))))<=>((rich(fred)|~generous(fred))))&
(![X]:(generous(X)<=>(~old(X)<~>~humble(X))))&
(((humble(susan)<~>strong(susan)))=>(?[X]:((~kind(X)&~old(X)))))&
(![X]:((~tall(X)|old(X))=>(wise(X)&kind(X))))&
(![X]:((~funny(X)&~brave(X))=>(~old(X)<~>old(X))))&
((?[X]:(funny(X)))<=>((~rich(paul)&~ge... | ~funny(fred) | [] | null | 0 |
Everyone who is either not old or not funny is patient and vice versa.
Everyone who is either not curious or not rich is either not calm or not tall.
If alice is not brave or quiet then john is either happy or not humble and vice versa.
If someone is not patient or quiet then alice is curious or creative and vice versa... | Paul is funny. | neutral | (![X]:((~old(X)<~>~funny(X))<=>patient(X)))&
(![X]:((~curious(X)<~>~rich(X))=>(~calm(X)<~>~tall(X))))&
(((~brave(alice)|quiet(alice)))<=>((happy(john)<~>~humble(john))))&
((?[X]:((~patient(X)|quiet(X))))<=>((curious(alice)|creative(alice))))&
(((strong(alice)&~kind(alice)))=>(?[X]:((quiet(X)<~>~curious(X)))))&
(![X]:((... | funny(paul) | [] | null | 0 |
Everyone who is strong or not curious is either happy or not curious and vice versa.
If alice is not generous then lucy is not wise or curious.
Everyone who is both old and not strong is either not funny or not happy and vice versa.
Everyone who is not curious is creative or tall and vice versa.
If someone is not wise ... | Mary is not curious. | entailment | (![X]:((strong(X)|~curious(X))<=>(happy(X)<~>~curious(X))))&
((~generous(alice))=>((~wise(lucy)|curious(lucy))))&
(![X]:((old(X)&~strong(X))<=>(~funny(X)<~>~happy(X))))&
(![X]:(~curious(X)<=>(creative(X)|tall(X))))&
((?[X]:((~wise(X)|~creative(X))))<=>((~humble(john)&curious(john))))&
((?[X]:((funny(X)<~>creative(X))))... | ~curious(mary) | [
"p0",
"p2",
"p3",
"p4",
"p6",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 9184584933404005170244292
% SZS output start Proof for 9184584933404005170244292
1. ! [X0] : ((~curious(X0) | strong(X0)) <=> (happy(X0) <~> ~curious(X0))) [input p0]
3. ! [X0] : ((~strong(X0) & old(X0)) <=> (~funny(X0) <~> ~happy(X0))) [input p2]
4. ! [X0] : (~curious(X0) <=> (tall(X0) |... | 0 |
If someone is either not curious or not old then paul is not curious or not humble and vice versa.
If alice is not brave or curious then someone is not strong and vice versa.
Everyone who is not tall is both not kind and brave.
Everyone who is either strong or patient is not tall or not kind and vice versa.
If someone ... | John is generous. | contradiction | ((?[X]:((~curious(X)<~>~old(X))))<=>((~curious(paul)|~humble(paul))))&
(((~brave(alice)|curious(alice)))<=>(?[X]:(~strong(X))))&
(![X]:(~tall(X)=>(~kind(X)&brave(X))))&
(![X]:((strong(X)<~>patient(X))<=>(~tall(X)|~kind(X))))&
((?[X]:((~curious(X)|funny(X))))<=>((old(fred)|quiet(fred))))&
(![X]:(creative(X)<=>(curious(X... | generous(john) | [
"p2",
"p7",
"p12",
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 5676562654766781979382619
% SZS output start Proof for 5676562654766781979382619
3. ! [X0] : (~tall(X0) => (brave(X0) & ~kind(X0))) [input p2]
8. ! [X0] : ((brave(X0) & ~quiet(X0)) <=> (~quiet(X0) <~> ~kind(X0))) [input p7]
13. ! [X0] : ((humble(X0) | ~generous(X0)) <=> ~brave(X0)) [input... | 0 |
Everyone who is either humble or not quiet is curious and vice versa.
If alice is either not happy or not rich then susan is both not quiet and not humble.
Everyone who is wise is either not patient or wise and vice versa.
If someone is not wise then someone is not strong or not quiet.
Everyone who is both brave and ri... | John is not patient. | contradiction | (![X]:((humble(X)<~>~quiet(X))<=>curious(X)))&
(((~happy(alice)<~>~rich(alice)))=>((~quiet(susan)&~humble(susan))))&
(![X]:(wise(X)<=>(~patient(X)<~>wise(X))))&
((?[X]:(~wise(X)))=>(?[X]:((~strong(X)|~quiet(X)))))&
(![X]:((brave(X)&rich(X))<=>(curious(X)<~>generous(X))))&
(![X]:((strong(X)<~>wise(X))<=>(wise(X)|creativ... | ~patient(john) | [
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 5156217559952621913633038
% SZS output start Proof for 5156217559952621913633038
3. ! [X0] : (wise(X0) <=> (~patient(X0) <~> wise(X0))) [input p2]
24. ~patient(john) [input hypothesis]
38. ! [X0] : ((wise(X0) | ((~patient(X0) | ~wise(X0)) & (wise(X0) | patient(X0)))) & (((~wise(X0) | pati... | 0 |
Everyone who is either not tall or not calm is not patient or calm and vice versa.
If paul is either strong or funny then lucy is funny and vice versa.
Everyone who is either calm or not wise is not wise and vice versa.
Everyone who is tall is either rich or tall.
Everyone who is both funny and not tall is either funny... | Alice is brave. | entailment | (![X]:((~tall(X)<~>~calm(X))<=>(~patient(X)|calm(X))))&
(((strong(paul)<~>funny(paul)))<=>(funny(lucy)))&
(![X]:((calm(X)<~>~wise(X))<=>~wise(X)))&
(![X]:(tall(X)=>(rich(X)<~>tall(X))))&
(![X]:((funny(X)&~tall(X))<=>(funny(X)<~>~creative(X))))&
(![X]:((~curious(X)&creative(X))=>(strong(X)&~patient(X))))&
((?[X]:(~funny... | brave(alice) | [
"p0",
"p4",
"p5",
"p7",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 5681134190965142605886701
% SZS output start Proof for 5681134190965142605886701
1. ! [X0] : ((~tall(X0) <~> ~calm(X0)) <=> (calm(X0) | ~patient(X0))) [input p0]
5. ! [X0] : ((~tall(X0) & funny(X0)) <=> (funny(X0) <~> ~creative(X0))) [input p4]
6. ! [X0] : ((creative(X0) & ~curious(X0)) =... | 0 |
Everyone who is either happy or brave is wise and vice versa. If alice is not rich or not generous then mary is rich and vice versa. Everyone who is curious or patient is both not kind and wise and vice versa. If someone is not wise then susan is not wise. If someone is both generous and not kind then john is not quiet... | Susan is not tall. | contradiction | (![X]:((happy(X)<~>brave(X))<=>wise(X)))&
(((~rich(alice)|~generous(alice)))<=>(rich(mary)))&
(![X]:((curious(X)|patient(X))<=>(~kind(X)&wise(X))))&
((?[X]:(~wise(X)))=>(~wise(susan)))&
((?[X]:((generous(X)&~kind(X))))=>((~quiet(john)|~happy(john))))&
(((~brave(susan)|funny(susan)))=>((~curious(alice)<~>funny(alice))))... | ~tall(susan) | [
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 462473365818183849373455
% SZS output start Proof for 462473365818183849373455
13. ! [X0] : (~tall(X0) => (tall(X0) & ~creative(X0))) [input p12]
25. ~tall(susan) [input hypothesis]
41. ! [X0] : ((tall(X0) & ~creative(X0)) | tall(X0)) [ennf transformation 13]
107. tall(X0) | tall(X0) [cnf... | 0 |
Everyone who is either not calm or funny is both not generous and not kind and vice versa. If lucy is not humble then mary is not old or funny. If someone is happy or not patient then someone is either not brave or rich and vice versa. If someone is both not strong and not quiet then someone is brave or not humble. Eve... | John is not brave. | contradiction | (![X]:((~calm(X)<~>funny(X))<=>(~generous(X)&~kind(X))))&
((~humble(lucy))=>((~old(mary)|funny(mary))))&
((?[X]:((happy(X)|~patient(X))))<=>(?[X]:((~brave(X)<~>rich(X)))))&
((?[X]:((~strong(X)&~quiet(X))))=>(?[X]:((brave(X)|~humble(X)))))&
(![X]:((quiet(X)&curious(X))<=>(~generous(X)<~>~quiet(X))))&
(![X]:((happy(X)|~b... | ~brave(john) | [
"p5",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 2081675011056225989813319
% SZS output start Proof for 2081675011056225989813319
6. ! [X0] : ((~brave(X0) | happy(X0)) => ~kind(X0)) [input p5]
12. ! [X0] : ((~generous(X0) | ~kind(X0)) <=> (kind(X0) & tall(X0))) [input p11]
23. ~brave(john) [input hypothesis]
29. ! [X0] : (~kind(X0) | (b... | 0 |
If someone is either happy or not quiet then john is both not kind and happy and vice versa.
Everyone who is either brave or curious is either calm or curious and vice versa.
Everyone who is not humble or creative is both not quiet and rich and vice versa.
If paul is both tall and not humble then alice is strong or not... | John is not brave. | contradiction | ((?[X]:((happy(X)<~>~quiet(X))))<=>((~kind(john)&happy(john))))&
(![X]:((brave(X)<~>curious(X))<=>(calm(X)<~>curious(X))))&
(![X]:((~humble(X)|creative(X))<=>(~quiet(X)&rich(X))))&
(((tall(paul)&~humble(paul)))=>((strong(alice)|~kind(alice))))&
(((~tall(paul)<~>~generous(paul)))<=>((~creative(mary)&old(mary))))&
(![X]:... | ~brave(john) | [
"p1",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 249028556472613092638804
% SZS output start Proof for 249028556472613092638804
2. ! [X0] : ((brave(X0) <~> curious(X0)) <=> (calm(X0) <~> curious(X0))) [input p1]
6. ! [X0] : ((brave(X0) & ~tall(X0)) <=> (~calm(X0) | patient(X0))) [input p5]
24. ~brave(john) [input hypothesis]
39. ! [X0] ... | 0 |
If alice is both not tall and not patient then someone is not kind.
If someone is curious then someone is both generous and not funny and vice versa.
If someone is both curious and creative then someone is both generous and tall.
Everyone who is either not curious or quiet is either not tall or humble.
If someone is ei... | Mary is quiet. | contradiction | (((~tall(alice)&~patient(alice)))=>(?[X]:(~kind(X))))&
((?[X]:(curious(X)))<=>(?[X]:((generous(X)&~funny(X)))))&
((?[X]:((curious(X)&creative(X))))=>(?[X]:((generous(X)&tall(X)))))&
(![X]:((~curious(X)<~>quiet(X))=>(~tall(X)<~>humble(X))))&
((?[X]:((patient(X)<~>~brave(X))))<=>((~calm(john)&~humble(john))))&
(![X]:((~s... | quiet(mary) | [
"p7",
"p11",
"p13",
"p14",
"p17",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 4321747213949338533693752
% SZS output start Proof for 4321747213949338533693752
8. ! [X0] : ((tall(X0) <~> ~humble(X0)) => (~strong(X0) <~> wise(X0))) [input p7]
12. ! [X0] : (~quiet(X0) <=> ~humble(X0)) [input p11]
14. ! [X0] : ((happy(X0) | ~kind(X0)) => (~calm(X0) <~> kind(X0))) [inpu... | 0 |
Everyone who is not curious is kind.
If someone is quiet or not wise then someone is both not calm and creative and vice versa.
If lucy is not kind then susan is either patient or not creative.
If john is either not patient or not creative then alice is both not rich and rich.
If someone is either creative or not creat... | John is not old. | entailment | (![X]:(~curious(X)=>kind(X)))&
((?[X]:((quiet(X)|~wise(X))))<=>(?[X]:((~calm(X)&creative(X)))))&
((~kind(lucy))=>((patient(susan)<~>~creative(susan))))&
(((~patient(john)<~>~creative(john)))=>((~rich(alice)&rich(alice))))&
((?[X]:((creative(X)<~>~creative(X))))<=>(patient(lucy)))&
(![X]:((~patient(X)|~tall(X))=>(~tall(... | ~old(john) | [
"p8",
"p9",
"p14",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 537887533330165482921941
% SZS output start Proof for 537887533330165482921941
9. ! [X0] : ((~wise(X0) | patient(X0)) <=> ~old(X0)) [input p8]
10. ! [X0] : ((calm(X0) | generous(X0)) <=> (~funny(X0) & wise(X0))) [input p9]
15. ! [X0] : ((~patient(X0) | ~quiet(X0)) <=> (funny(X0) & ~genero... | 0 |
If someone is both brave and happy then susan is kind or not humble.
Everyone who is both creative and not generous is generous.
Everyone who is both tall and wise is both not creative and generous.
Everyone who is funny or not generous is both calm and creative.
If someone is generous then lucy is either patient or cr... | Paul is not generous. | contradiction | ((?[X]:((brave(X)&happy(X))))=>((kind(susan)|~humble(susan))))&
(![X]:((creative(X)&~generous(X))=>generous(X)))&
(![X]:((tall(X)&wise(X))=>(~creative(X)&generous(X))))&
(![X]:((funny(X)|~generous(X))=>(calm(X)&creative(X))))&
((?[X]:(generous(X)))=>((patient(lucy)<~>creative(lucy))))&
(![X]:(humble(X)=>(brave(X)&~curi... | ~generous(paul) | [
"p1",
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 7007927625113521912230534
% SZS output start Proof for 7007927625113521912230534
2. ! [X0] : ((~generous(X0) & creative(X0)) => generous(X0)) [input p1]
4. ! [X0] : ((~generous(X0) | funny(X0)) => (creative(X0) & calm(X0))) [input p3]
24. ~generous(paul) [input hypothesis]
30. ! [X0] : (g... | 0 |
Everyone who is both happy and not rich is generous or not kind.
If someone is calm or not creative then paul is either not happy or not strong and vice versa.
If lucy is both not generous and not strong then fred is kind or calm and vice versa.
Everyone who is brave or not rich is not calm or not rich.
If alice is tal... | Mary is old. | neutral | (![X]:((happy(X)&~rich(X))=>(generous(X)|~kind(X))))&
((?[X]:((calm(X)|~creative(X))))<=>((~happy(paul)<~>~strong(paul))))&
(((~generous(lucy)&~strong(lucy)))<=>((kind(fred)|calm(fred))))&
(![X]:((brave(X)|~rich(X))=>(~calm(X)|~rich(X))))&
((tall(alice))<=>((rich(john)&~patient(john))))&
(((happy(alice)&~kind(alice)))=... | old(mary) | [] | null | 0 |
Everyone who is not tall or not old is both not funny and wise. Everyone who is humble or not wise is both not brave and not curious and vice versa. If someone is either kind or rich then fred is wise or not strong. Everyone who is both not happy and calm is both not tall and old and vice versa. Everyone who is curious... | Fred is not humble. | neutral | (![X]:((~tall(X)|~old(X))=>(~funny(X)&wise(X))))&
(![X]:((humble(X)|~wise(X))<=>(~brave(X)&~curious(X))))&
((?[X]:((kind(X)<~>rich(X))))=>((wise(fred)|~strong(fred))))&
(![X]:((~happy(X)&calm(X))<=>(~tall(X)&old(X))))&
(![X]:(curious(X)=>patient(X)))&
(![X]:((patient(X)|~humble(X))<=>(strong(X)<~>~curious(X))))&
((?[X]... | ~humble(fred) | [] | null | 0 |
If lucy is both quiet and curious then fred is patient and vice versa.
Everyone who is not tall is both not humble and creative.
If john is both quiet and not patient then someone is either not quiet or not patient and vice versa.
If someone is both quiet and kind then someone is kind or not happy and vice versa.
If pa... | Paul is strong. | contradiction | (((quiet(lucy)&curious(lucy)))<=>(patient(fred)))&
(![X]:(~tall(X)=>(~humble(X)&creative(X))))&
(((quiet(john)&~patient(john)))<=>(?[X]:((~quiet(X)<~>~patient(X)))))&
((?[X]:((quiet(X)&kind(X))))<=>(?[X]:((kind(X)|~happy(X)))))&
(((~old(paul)<~>creative(paul)))=>((kind(john)|quiet(john))))&
(![X]:((~tall(X)|old(X))<=>(... | strong(paul) | [
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 7241529210636501126536534
% SZS output start Proof for 7241529210636501126536534
15. ! [X0] : ((~strong(X0) & ~old(X0)) <=> (~strong(X0) | strong(X0))) [input p14]
24. strong(paul) [input hypothesis]
67. ! [X0] : (((~strong(X0) & ~old(X0)) | (strong(X0) & ~strong(X0))) & ((~strong(X0) | s... | 0 |
Everyone who is both not curious and rich is either strong or not generous and vice versa. If someone is both rich and not calm then lucy is either strong or curious. If mary is not wise then someone is not tall or kind. Everyone who is not humble is tall or not happy. If someone is both strong and quiet then susan is ... | Alice is kind. | contradiction | (![X]:((~curious(X)&rich(X))<=>(strong(X)<~>~generous(X))))&
((?[X]:((rich(X)&~calm(X))))=>((strong(lucy)<~>curious(lucy))))&
((~wise(mary))=>(?[X]:((~tall(X)|kind(X)))))&
(![X]:(~humble(X)=>(tall(X)|~happy(X))))&
((?[X]:((strong(X)&quiet(X))))<=>(happy(susan)))&
(![X]:(quiet(X)=>(~wise(X)|~rich(X))))&
(![X]:((~rich(X)... | kind(alice) | [
"p7",
"p8",
"p9",
"p13",
"p14",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 6725360586608013504436690
% SZS output start Proof for 6725360586608013504436690
8. ! [X0] : (brave(X0) <=> patient(X0)) [input p7]
9. ! [X0] : ((patient(X0) <~> ~strong(X0)) <=> (brave(X0) & ~calm(X0))) [input p8]
10. ! [X0] : (~strong(X0) <=> (~calm(X0) | kind(X0))) [input p9]
14. ! [X0... | 0 |
If paul is brave then someone is both not calm and brave and vice versa. Everyone who is quiet or not happy is quiet or old and vice versa. If mary is not wise or creative then someone is either not rich or not quiet and vice versa. Everyone who is kind is either not kind or not curious and vice versa. If someone is cr... | Alice is not calm. | entailment | ((brave(paul))<=>(?[X]:((~calm(X)&brave(X)))))&
(![X]:((quiet(X)|~happy(X))<=>(quiet(X)|old(X))))&
(((~wise(mary)|creative(mary)))<=>(?[X]:((~rich(X)<~>~quiet(X)))))&
(![X]:(kind(X)<=>(~kind(X)<~>~curious(X))))&
((?[X]:((creative(X)|~kind(X))))<=>(?[X]:(strong(X))))&
(((quiet(paul)|creative(paul)))=>(?[X]:((creative(X)... | ~calm(alice) | [
"p10",
"p13",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 844755367508486820075393
% SZS output start Proof for 844755367508486820075393
11. ! [X0] : (creative(X0) <=> (tall(X0) <~> ~creative(X0))) [input p10]
14. ! [X0] : ((brave(X0) | ~old(X0)) => (~generous(X0) & ~calm(X0))) [input p13]
20. brave(alice) <~> ~tall(alice) [input p19]
24. calm(a... | 0 |
If someone is both brave and curious then susan is not humble or curious and vice versa. Everyone who is generous is generous or not kind and vice versa. If someone is both kind and quiet then someone is strong or not old. Everyone who is both old and not calm is not rich or not funny and vice versa. Everyone who is bo... | Mary is not kind. | neutral | ((?[X]:((brave(X)&curious(X))))<=>((~humble(susan)|curious(susan))))&
(![X]:(generous(X)<=>(generous(X)|~kind(X))))&
((?[X]:((kind(X)&quiet(X))))=>(?[X]:((strong(X)|~old(X)))))&
(![X]:((old(X)&~calm(X))<=>(~rich(X)|~funny(X))))&
(![X]:((rich(X)&~wise(X))=>(curious(X)&quiet(X))))&
(((curious(john)&old(john)))<=>(rich(su... | ~kind(mary) | [] | null | 0 |
Everyone who is calm is either not creative or not calm and vice versa.
If someone is quiet or humble then alice is both old and not brave and vice versa.
Everyone who is patient is both kind and not kind and vice versa.
If someone is either not kind or calm then alice is either kind or not generous.
If someone is not ... | Alice is not humble. | entailment | (![X]:(calm(X)<=>(~creative(X)<~>~calm(X))))&
((?[X]:((quiet(X)|humble(X))))<=>((old(alice)&~brave(alice))))&
(![X]:(patient(X)<=>(kind(X)&~kind(X))))&
((?[X]:((~kind(X)<~>calm(X))))=>((kind(alice)<~>~generous(alice))))&
((?[X]:(~funny(X)))=>(?[X]:((~funny(X)&~quiet(X)))))&
(![X]:(~rich(X)=>(generous(X)<~>happy(X))))&
... | ~humble(alice) | [
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 8258181528718086292768179
% SZS output start Proof for 8258181528718086292768179
7. ! [X0] : (humble(X0) => ~humble(X0)) [input p6]
25. humble(alice) [input hypothesis]
32. ! [X0] : (~humble(X0) | ~humble(X0)) [ennf transformation 7]
99. ~humble(X0) | ~humble(X0) [cnf transformation 32]
1... | 0 |
Everyone who is either happy or old is both calm and not brave and vice versa. Everyone who is both humble and calm is both wise and rich. Everyone who is not rich or not patient is creative. Everyone who is humble or not humble is both not strong and not tall. Everyone who is brave or not old is tall. If someone is ei... | Alice is old. | entailment | (![X]:((happy(X)<~>old(X))<=>(calm(X)&~brave(X))))&
(![X]:((humble(X)&calm(X))=>(wise(X)&rich(X))))&
(![X]:((~rich(X)|~patient(X))=>creative(X)))&
(![X]:((humble(X)|~humble(X))=>(~strong(X)&~tall(X))))&
(![X]:((brave(X)|~old(X))=>tall(X)))&
((?[X]:((~funny(X)<~>~creative(X))))=>((strong(paul)|old(paul))))&
((?[X]:(~wis... | old(alice) | [
"p3",
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 7626434595904860489175236
% SZS output start Proof for 7626434595904860489175236
4. ! [X0] : ((~humble(X0) | humble(X0)) => (~tall(X0) & ~strong(X0))) [input p3]
5. ! [X0] : ((~old(X0) | brave(X0)) => tall(X0)) [input p4]
24. ~old(alice) [input hypothesis]
31. ! [X0] : ((~tall(X0) & ~stro... | 0 |
Everyone who is either quiet or not tall is not brave or not wise and vice versa. Everyone who is happy or not creative is not kind. If someone is either not happy or kind then someone is either kind or patient and vice versa. If paul is both happy and strong then fred is not quiet or old and vice versa. If alice is ei... | John is not rich. | contradiction | (![X]:((quiet(X)<~>~tall(X))<=>(~brave(X)|~wise(X))))&
(![X]:((happy(X)|~creative(X))=>~kind(X)))&
((?[X]:((~happy(X)<~>kind(X))))<=>(?[X]:((kind(X)<~>patient(X)))))&
(((happy(paul)&strong(paul)))<=>((~quiet(fred)|old(fred))))&
(((~old(alice)<~>curious(alice)))=>(~old(lucy)))&
((?[X]:((happy(X)<~>~old(X))))<=>(?[X]:((r... | ~rich(john) | [
"p1",
"p11",
"p13",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 802728255048696726122099
% SZS output start Proof for 802728255048696726122099
2. ! [X0] : ((~creative(X0) | happy(X0)) => ~kind(X0)) [input p1]
12. ! [X0] : (~strong(X0) => strong(X0)) [input p11]
14. ! [X0] : ((rich(X0) <~> ~creative(X0)) <=> (~generous(X0) | creative(X0))) [input p13]
... | 0 |
If someone is kind or funny then lucy is both strong and wise and vice versa.
Everyone who is either not strong or not patient is either kind or calm and vice versa.
If susan is either old or not patient then fred is either quiet or not funny and vice versa.
Everyone who is either old or not humble is not quiet or quie... | Lucy is not funny. | contradiction | ((?[X]:((kind(X)|funny(X))))<=>((strong(lucy)&wise(lucy))))&
(![X]:((~strong(X)<~>~patient(X))<=>(kind(X)<~>calm(X))))&
(((old(susan)<~>~patient(susan)))<=>((quiet(fred)<~>~funny(fred))))&
(![X]:((old(X)<~>~humble(X))=>(~quiet(X)|quiet(X))))&
(![X]:(humble(X)<=>(calm(X)&tall(X))))&
((?[X]:(quiet(X)))<=>((~strong(susan)... | ~funny(lucy) | [
"p0",
"p7",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 864407004952093701190800
% SZS output start Proof for 864407004952093701190800
1. ? [X0] : (funny(X0) | kind(X0)) <=> (wise(lucy) & strong(lucy)) [input p0]
8. ! [X0] : (funny(X0) <=> (~kind(X0) | ~old(X0))) [input p7]
16. ! [X0] : (funny(X0) <=> (wise(X0) | ~rich(X0))) [input p15]
25. ~f... | 0 |
Everyone who is not brave is both old and kind and vice versa.
If someone is funny or not kind then john is both not creative and brave and vice versa.
If someone is not curious or rich then fred is both patient and not patient and vice versa.
Everyone who is not happy is both not quiet and not strong and vice versa.
E... | John is not quiet. | neutral | (![X]:(~brave(X)<=>(old(X)&kind(X))))&
((?[X]:((funny(X)|~kind(X))))<=>((~creative(john)&brave(john))))&
((?[X]:((~curious(X)|rich(X))))<=>((patient(fred)&~patient(fred))))&
(![X]:(~happy(X)<=>(~quiet(X)&~strong(X))))&
(![X]:((kind(X)<~>~brave(X))<=>(~patient(X)&kind(X))))&
(![X]:(~funny(X)<=>(~patient(X)<~>brave(X))))... | ~quiet(john) | [] | null | 0 |
Everyone who is both happy and not calm is not wise and vice versa. Everyone who is either generous or old is either curious or rich. Everyone who is not calm or not strong is both not funny and not tall. If lucy is either not tall or creative then john is both not curious and not funny and vice versa. If susan is not ... | Paul is not old. | entailment | (![X]:((happy(X)&~calm(X))<=>~wise(X)))&
(![X]:((generous(X)<~>old(X))=>(curious(X)<~>rich(X))))&
(![X]:((~calm(X)|~strong(X))=>(~funny(X)&~tall(X))))&
(((~tall(lucy)<~>creative(lucy)))<=>((~curious(john)&~funny(john))))&
((~brave(susan))=>(?[X]:(~humble(X))))&
((?[X]:((creative(X)&~patient(X))))<=>((~humble(lucy)|gene... | ~old(paul) | [
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 913806776685812599110078
% SZS output start Proof for 913806776685812599110078
8. ! [X0] : ((~old(X0) & ~rich(X0)) <=> old(X0)) [input p7]
21. old(paul) [input hypothesis]
46. ! [X0] : (((~old(X0) & ~rich(X0)) | ~old(X0)) & (old(X0) | (old(X0) | rich(X0)))) [nnf transformation 8]
47. ! [X... | 0 |
Everyone who is either not tall or not humble is old or not happy and vice versa.
Everyone who is quiet is either quiet or brave.
If someone is both kind and quiet then someone is both curious and creative and vice versa.
If susan is kind then someone is patient or rich and vice versa.
Everyone who is happy is both not... | Susan is humble. | contradiction | (![X]:((~tall(X)<~>~humble(X))<=>(old(X)|~happy(X))))&
(![X]:(quiet(X)=>(quiet(X)<~>brave(X))))&
((?[X]:((kind(X)&quiet(X))))<=>(?[X]:((curious(X)&creative(X)))))&
((kind(susan))<=>(?[X]:((patient(X)|rich(X)))))&
(![X]:(happy(X)<=>(~humble(X)&brave(X))))&
(![X]:((~strong(X)|tall(X))<=>(strong(X)&humble(X))))&
(((old(jo... | humble(susan) | [
"p0",
"p4",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 1915794616524615321960648
% SZS output start Proof for 1915794616524615321960648
1. ! [X0] : ((~tall(X0) <~> ~humble(X0)) <=> (~happy(X0) | old(X0))) [input p0]
5. ! [X0] : (happy(X0) <=> (brave(X0) & ~humble(X0))) [input p4]
6. ! [X0] : ((tall(X0) | ~strong(X0)) <=> (humble(X0) & strong(... | 0 |
If fred is patient then someone is not old and vice versa.
Everyone who is not old or generous is not curious and vice versa.
Everyone who is calm or funny is calm and vice versa.
Everyone who is not tall is either funny or strong and vice versa.
If john is not creative then someone is patient and vice versa.
Everyone ... | Lucy is old. | entailment | ((patient(fred))<=>(?[X]:(~old(X))))&
(![X]:((~old(X)|generous(X))<=>~curious(X)))&
(![X]:((calm(X)|funny(X))<=>calm(X)))&
(![X]:(~tall(X)<=>(funny(X)<~>strong(X))))&
((~creative(john))<=>(?[X]:(patient(X))))&
(![X]:(~calm(X)<=>(~rich(X)&tall(X))))&
(![X]:((~generous(X)|~funny(X))<=>(~brave(X)|~strong(X))))&
((?[X]:((o... | old(lucy) | [
"p0",
"p1",
"p7",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 8866438770465535996973984
% SZS output start Proof for 8866438770465535996973984
1. patient(fred) <=> ? [X0] : ~old(X0) [input p0]
2. ! [X0] : ((generous(X0) | ~old(X0)) <=> ~curious(X0)) [input p1]
8. ? [X0] : (creative(X0) | old(X0)) => ~patient(fred) [input p7]
21. ? [X0] : curious(X0)... | 0 |
Everyone who is brave or rich is both not wise and not brave and vice versa.
Everyone who is both old and generous is not tall or calm.
Everyone who is either not humble or calm is not happy or not kind and vice versa.
If someone is wise then susan is both rich and quiet.
Everyone who is not rich or not quiet is not ca... | Alice is old. | entailment | (![X]:((brave(X)|rich(X))<=>(~wise(X)&~brave(X))))&
(![X]:((old(X)&generous(X))=>(~tall(X)|calm(X))))&
(![X]:((~humble(X)<~>calm(X))<=>(~happy(X)|~kind(X))))&
((?[X]:(wise(X)))=>((rich(susan)&quiet(susan))))&
(![X]:((~rich(X)|~quiet(X))<=>(~calm(X)|~brave(X))))&
(![X]:(~calm(X)<=>(~old(X)|~happy(X))))&
(![X]:((strong(X... | old(alice) | [
"p0",
"p2",
"p5",
"p6",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 293862244198528194023462
% SZS output start Proof for 293862244198528194023462
1. ! [X0] : ((rich(X0) | brave(X0)) <=> (~brave(X0) & ~wise(X0))) [input p0]
3. ! [X0] : ((~humble(X0) <~> calm(X0)) <=> (~kind(X0) | ~happy(X0))) [input p2]
6. ! [X0] : (~calm(X0) <=> (~happy(X0) | ~old(X0))) ... | 0 |
If susan is not curious or not happy then susan is either not old or tall and vice versa.
Everyone who is either calm or not creative is not curious or strong.
Everyone who is not tall is curious or brave and vice versa.
Everyone who is not curious or not generous is curious.
If lucy is both not wise and not quiet then... | Lucy is not quiet. | contradiction | (((~curious(susan)|~happy(susan)))<=>((~old(susan)<~>tall(susan))))&
(![X]:((calm(X)<~>~creative(X))=>(~curious(X)|strong(X))))&
(![X]:(~tall(X)<=>(curious(X)|brave(X))))&
(![X]:((~curious(X)|~generous(X))=>curious(X)))&
(((~wise(lucy)&~quiet(lucy)))=>((~curious(john)&quiet(john))))&
(![X]:((funny(X)&~old(X))=>(~strong... | ~quiet(lucy) | [
"p2",
"p3",
"p4",
"p9",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 656042956184790215844045
% SZS output start Proof for 656042956184790215844045
3. ! [X0] : (~tall(X0) <=> (brave(X0) | curious(X0))) [input p2]
4. ! [X0] : ((~generous(X0) | ~curious(X0)) => curious(X0)) [input p3]
5. (~quiet(lucy) & ~wise(lucy)) => (quiet(john) & ~curious(john)) [input p... | 0 |
If someone is both kind and not patient then someone is either funny or not funny and vice versa.
Everyone who is both quiet and not humble is not happy or not humble.
If someone is both not generous and rich then someone is not rich.
If someone is not kind or kind then someone is not kind and vice versa.
Everyone who ... | Susan is not wise. | contradiction | ((?[X]:((kind(X)&~patient(X))))<=>(?[X]:((funny(X)<~>~funny(X)))))&
(![X]:((quiet(X)&~humble(X))=>(~happy(X)|~humble(X))))&
((?[X]:((~generous(X)&rich(X))))=>(?[X]:(~rich(X))))&
((?[X]:((~kind(X)|kind(X))))<=>(?[X]:(~kind(X))))&
(![X]:(calm(X)<=>(strong(X)<~>~strong(X))))&
(![X]:((~generous(X)|~happy(X))<=>(brave(X)<~>... | ~wise(susan) | [
"p4",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4205659890423123790915862
% SZS output start Proof for 4205659890423123790915862
5. ! [X0] : (calm(X0) <=> (strong(X0) <~> ~strong(X0))) [input p4]
16. ! [X0] : ((~humble(X0) <~> calm(X0)) <=> (~wise(X0) & ~humble(X0))) [input p15]
24. ~wise(susan) [input hypothesis]
55. ! [X0] : ((calm(X... | 0 |
Everyone who is both funny and not wise is either not old or not humble. If fred is both calm and not kind then susan is not tall. Everyone who is not generous is brave and vice versa. Everyone who is both patient and creative is not curious. If someone is both not happy and funny then someone is both not wise and rich... | Lucy is curious. | neutral | (![X]:((funny(X)&~wise(X))=>(~old(X)<~>~humble(X))))&
(((calm(fred)&~kind(fred)))=>(~tall(susan)))&
(![X]:(~generous(X)<=>brave(X)))&
(![X]:((patient(X)&creative(X))=>~curious(X)))&
((?[X]:((~happy(X)&funny(X))))<=>(?[X]:((~wise(X)&rich(X)))))&
((?[X]:(funny(X)))=>(wise(mary)))&
(((brave(paul)|~strong(paul)))=>(?[X]:((... | curious(lucy) | [] | null | 0 |
If someone is patient or not calm then fred is either not creative or not patient.
Everyone who is both not kind and calm is both not tall and not humble and vice versa.
If someone is not kind then fred is not humble and vice versa.
Everyone who is both humble and tall is not patient or wise.
Everyone who is tall is pa... | Paul is not strong. | neutral | ((?[X]:((patient(X)|~calm(X))))=>((~creative(fred)<~>~patient(fred))))&
(![X]:((~kind(X)&calm(X))<=>(~tall(X)&~humble(X))))&
((?[X]:(~kind(X)))<=>(~humble(fred)))&
(![X]:((humble(X)&tall(X))=>(~patient(X)|wise(X))))&
(![X]:(tall(X)<=>(patient(X)|funny(X))))&
(![X]:((funny(X)&creative(X))<=>~calm(X)))&
(![X]:((~humble(X... | ~strong(paul) | [] | null | 0 |
If alice is not rich then someone is not wise and vice versa. If someone is either funny or tall then someone is either not calm or generous. If lucy is kind then susan is either brave or tall and vice versa. If susan is both old and not happy then someone is humble and vice versa. If someone is strong then alice is no... | John is humble. | contradiction | ((~rich(alice))<=>(?[X]:(~wise(X))))&
((?[X]:((funny(X)<~>tall(X))))=>(?[X]:((~calm(X)<~>generous(X)))))&
((kind(lucy))<=>((brave(susan)<~>tall(susan))))&
(((old(susan)&~happy(susan)))<=>(?[X]:(humble(X))))&
((?[X]:(strong(X)))=>((~humble(alice)|~kind(alice))))&
((?[X]:(brave(X)))=>((~humble(alice)|quiet(alice))))&
(![... | humble(john) | [
"p3",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 3898352636276524634648055
% SZS output start Proof for 3898352636276524634648055
4. (~happy(susan) & old(susan)) <=> ? [X0] : humble(X0) [input p3]
19. ~old(susan) & calm(susan) [input p18]
25. humble(john) [input hypothesis]
50. ((~happy(susan) & old(susan)) | ! [X0] : ~humble(X0)) & (? ... | 0 |
If mary is not funny or quiet then someone is not generous or old. If fred is both not old and not happy then john is not brave or not curious and vice versa. If someone is not brave or wise then fred is not strong or happy. If lucy is not humble or not curious then someone is calm and vice versa. Everyone who is eithe... | Fred is funny. | neutral | (((~funny(mary)|quiet(mary)))=>(?[X]:((~generous(X)|old(X)))))&
(((~old(fred)&~happy(fred)))<=>((~brave(john)|~curious(john))))&
((?[X]:((~brave(X)|wise(X))))=>((~strong(fred)|happy(fred))))&
(((~humble(lucy)|~curious(lucy)))<=>(?[X]:(calm(X))))&
(![X]:((strong(X)<~>~wise(X))=>(happy(X)|~brave(X))))&
(![X]:((~quiet(X)|... | funny(fred) | [] | null | 0 |
If someone is either humble or not kind then someone is both tall and not creative.
If mary is not curious then someone is not wise or generous and vice versa.
Everyone who is either wise or patient is both not old and happy and vice versa.
Everyone who is not kind is not creative or not quiet and vice versa.
If someon... | Paul is generous. | contradiction | ((?[X]:((humble(X)<~>~kind(X))))=>(?[X]:((tall(X)&~creative(X)))))&
((~curious(mary))<=>(?[X]:((~wise(X)|generous(X)))))&
(![X]:((wise(X)<~>patient(X))<=>(~old(X)&happy(X))))&
(![X]:(~kind(X)<=>(~creative(X)|~quiet(X))))&
((?[X]:(calm(X)))=>(?[X]:((~creative(X)&quiet(X)))))&
(![X]:((calm(X)|~happy(X))=>(humble(X)&~quie... | generous(paul) | [
"p7",
"p8",
"p10",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 263055639467125087265451
% SZS output start Proof for 263055639467125087265451
8. ! [X0] : ((wise(X0) <~> brave(X0)) <=> (tall(X0) | brave(X0))) [input p7]
9. ! [X0] : ((~strong(X0) | funny(X0)) <=> (~funny(X0) | wise(X0))) [input p8]
11. ! [X0] : ((~generous(X0) & wise(X0)) <=> tall(X0))... | 0 |
If someone is kind or brave then someone is not strong or not funny.
If mary is both brave and patient then alice is both not generous and not quiet.
Everyone who is either generous or not curious is both not humble and creative and vice versa.
If susan is both not humble and calm then susan is funny or calm and vice v... | Susan is kind. | neutral | ((?[X]:((kind(X)|brave(X))))=>(?[X]:((~strong(X)|~funny(X)))))&
(((brave(mary)&patient(mary)))=>((~generous(alice)&~quiet(alice))))&
(![X]:((generous(X)<~>~curious(X))<=>(~humble(X)&creative(X))))&
(((~humble(susan)&calm(susan)))<=>((funny(susan)|calm(susan))))&
(![X]:(~patient(X)<=>~happy(X)))&
((~quiet(fred))<=>(?[X]... | kind(susan) | [] | null | 0 |
Everyone who is not happy is either not humble or old.
If someone is either happy or tall then someone is both not wise and not calm and vice versa.
If alice is either not old or humble then someone is not patient or not quiet.
Everyone who is either happy or not creative is either not calm or not brave and vice versa.... | Lucy is rich. | contradiction | (![X]:(~happy(X)=>(~humble(X)<~>old(X))))&
((?[X]:((happy(X)<~>tall(X))))<=>(?[X]:((~wise(X)&~calm(X)))))&
(((~old(alice)<~>humble(alice)))=>(?[X]:((~patient(X)|~quiet(X)))))&
(![X]:((happy(X)<~>~creative(X))<=>(~calm(X)<~>~brave(X))))&
(![X]:((~quiet(X)|~happy(X))=>(rich(X)<~>~generous(X))))&
((?[X]:(generous(X)))=>((... | rich(lucy) | [
"p8",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 780844184361360850991876
% SZS output start Proof for 780844184361360850991876
9. ? [X0] : ~wise(X0) <=> (tall(lucy) & ~rich(lucy)) [input p8]
22. ~rich(alice) & ~wise(alice) [input p21]
25. rich(lucy) [input hypothesis]
54. (? [X0] : ~wise(X0) | (~tall(lucy) | rich(lucy))) & ((tall(lucy)... | 0 |
If paul is not rich then lucy is either creative or calm and vice versa. Everyone who is both not curious and not humble is not strong or not patient and vice versa. If someone is both not happy and old then john is humble or happy. If mary is kind or creative then someone is not calm or not curious. If someone is eith... | Paul is not quiet. | entailment | ((~rich(paul))<=>((creative(lucy)<~>calm(lucy))))&
(![X]:((~curious(X)&~humble(X))<=>(~strong(X)|~patient(X))))&
((?[X]:((~happy(X)&old(X))))=>((humble(john)|happy(john))))&
(((kind(mary)|creative(mary)))=>(?[X]:((~calm(X)|~curious(X)))))&
((?[X]:((~kind(X)<~>~curious(X))))<=>(?[X]:(~tall(X))))&
(![X]:(~humble(X)<=>(~q... | ~quiet(paul) | [
"p1",
"p5",
"p7",
"p8",
"p9",
"p10",
"p11",
"p12",
"p13",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1773508444932026950527608
% SZS output start Proof for 1773508444932026950527608
2. ! [X0] : ((~humble(X0) & ~curious(X0)) <=> (~patient(X0) | ~strong(X0))) [input p1]
6. ! [X0] : (~humble(X0) <=> (~kind(X0) | ~quiet(X0))) [input p5]
8. ! [X0] : ((happy(X0) <~> strong(X0)) => (~funny(X0) ... | 0 |
If alice is curious or brave then alice is not kind and vice versa.
Everyone who is not generous or wise is both not calm and not old and vice versa.
If paul is not kind then someone is both not happy and not calm and vice versa.
Everyone who is funny or not humble is kind or old and vice versa.
Everyone who is both hu... | Fred is not happy. | entailment | (((curious(alice)|brave(alice)))<=>(~kind(alice)))&
(![X]:((~generous(X)|wise(X))<=>(~calm(X)&~old(X))))&
((~kind(paul))<=>(?[X]:((~happy(X)&~calm(X)))))&
(![X]:((funny(X)|~humble(X))<=>(kind(X)|old(X))))&
(![X]:((humble(X)&patient(X))<=>~calm(X)))&
((?[X]:((~happy(X)<~>~rich(X))))<=>(?[X]:((generous(X)|funny(X)))))&
(... | ~happy(fred) | [
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 835456482692307866436499
% SZS output start Proof for 835456482692307866436499
19. ~happy(fred) & rich(fred) [input p18]
23. happy(fred) [input hypothesis]
141. ~happy(fred) [cnf transformation 19]
144. happy(fred) [cnf transformation 23]
272. 30 <=> happy(fred) [avatar definition]
357. ~... | 0 |
If mary is both not kind and not wise then someone is both not strong and not quiet and vice versa.
Everyone who is kind is not creative.
If mary is not happy then someone is not curious.
Everyone who is brave or not generous is not old and vice versa.
If someone is rich or not patient then someone is not funny or not ... | John is curious. | entailment | (((~kind(mary)&~wise(mary)))<=>(?[X]:((~strong(X)&~quiet(X)))))&
(![X]:(kind(X)=>~creative(X)))&
((~happy(mary))=>(?[X]:(~curious(X))))&
(![X]:((brave(X)|~generous(X))<=>~old(X)))&
((?[X]:((rich(X)|~patient(X))))=>(?[X]:((~funny(X)|~wise(X)))))&
(![X]:((~curious(X)|patient(X))=>(~generous(X)&kind(X))))&
((?[X]:((patien... | curious(john) | [
"p3",
"p5",
"p7",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 42023042688609770260303
% SZS output start Proof for 42023042688609770260303
4. ! [X0] : ((~generous(X0) | brave(X0)) <=> ~old(X0)) [input p3]
6. ! [X0] : ((patient(X0) | ~curious(X0)) => (kind(X0) & ~generous(X0))) [input p5]
8. ! [X0] : ((~funny(X0) | humble(X0)) => (wise(X0) & old(X0))... | 0 |
Everyone who is either tall or not kind is either not rich or calm. If someone is both not kind and not calm then alice is not brave or not rich. If someone is either not rich or not happy then someone is humble or calm. If lucy is both not quiet and not brave then someone is either not old or calm and vice versa. Ever... | Alice is tall. | contradiction | (![X]:((tall(X)<~>~kind(X))=>(~rich(X)<~>calm(X))))&
((?[X]:((~kind(X)&~calm(X))))=>((~brave(alice)|~rich(alice))))&
((?[X]:((~rich(X)<~>~happy(X))))=>(?[X]:((humble(X)|calm(X)))))&
(((~quiet(lucy)&~brave(lucy)))<=>(?[X]:((~old(X)<~>calm(X)))))&
(![X]:((~humble(X)|tall(X))=>~rich(X)))&
((?[X]:((~quiet(X)<~>kind(X))))<=... | tall(alice) | [
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 6454046368181375759712845
% SZS output start Proof for 6454046368181375759712845
8. ! [X0] : ((tall(X0) | calm(X0)) => (~tall(X0) & ~strong(X0))) [input p7]
25. tall(alice) [input hypothesis]
33. ! [X0] : ((~tall(X0) & ~strong(X0)) | (~tall(X0) & ~calm(X0))) [ennf transformation 8]
112. ~... | 0 |
Everyone who is either not brave or brave is rich.
If mary is patient or strong then paul is both brave and strong.
If fred is either not strong or funny then susan is either happy or kind.
Everyone who is not strong is either not creative or not patient.
If mary is either creative or not strong then someone is either ... | Mary is rich. | entailment | (![X]:((~brave(X)<~>brave(X))=>rich(X)))&
(((patient(mary)|strong(mary)))=>((brave(paul)&strong(paul))))&
(((~strong(fred)<~>funny(fred)))=>((happy(susan)<~>kind(susan))))&
(![X]:(~strong(X)=>(~creative(X)<~>~patient(X))))&
(((creative(mary)<~>~strong(mary)))=>(?[X]:((funny(X)<~>kind(X)))))&
(![X]:((~old(X)|kind(X))<=>... | rich(mary) | [
"p0",
"hypothesis"
] | % SZS status Unsatisfiable for 7440146600292801366620083
% SZS output start Proof for 7440146600292801366620083
1. ! [X0] : ((~brave(X0) <~> brave(X0)) => rich(X0)) [input p0]
22. ~rich(mary) [input hypothesis]
24. ! [X0] : (rich(X0) | (~brave(X0) <=> brave(X0))) [ennf transformation 1]
32. ! [X0] : (rich(X0) | ((~brav... | 0 |
Everyone who is either generous or curious is wise.
If paul is either brave or not brave then someone is not wise or old.
If someone is not curious or quiet then alice is either humble or not kind and vice versa.
If someone is not happy then someone is humble.
If someone is not tall or not brave then someone is both no... | Mary is humble. | entailment | (![X]:((generous(X)<~>curious(X))=>wise(X)))&
(((brave(paul)<~>~brave(paul)))=>(?[X]:((~wise(X)|old(X)))))&
((?[X]:((~curious(X)|quiet(X))))<=>((humble(alice)<~>~kind(alice))))&
((?[X]:(~happy(X)))=>(?[X]:(humble(X))))&
((?[X]:((~tall(X)|~brave(X))))<=>(?[X]:((~tall(X)&wise(X)))))&
(![X]:((creative(X)|wise(X))=>quiet(X... | humble(mary) | [
"p4",
"p5",
"p7",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 3202648980898636728450634
% SZS output start Proof for 3202648980898636728450634
5. ? [X0] : (~brave(X0) | ~tall(X0)) <=> ? [X0] : (wise(X0) & ~tall(X0)) [input p4]
6. ! [X0] : ((wise(X0) | creative(X0)) => quiet(X0)) [input p5]
8. ! [X0] : ((~tall(X0) | ~humble(X0)) <=> (~brave(X0) & ~pa... | 0 |
Everyone who is either not patient or funny is either not generous or not happy and vice versa.
If someone is funny then paul is humble or not brave.
Everyone who is both not tall and happy is not humble and vice versa.
Everyone who is not patient is rich.
Everyone who is calm or not calm is both not humble and curious... | Fred is not happy. | contradiction | (![X]:((~patient(X)<~>funny(X))<=>(~generous(X)<~>~happy(X))))&
((?[X]:(funny(X)))=>((humble(paul)|~brave(paul))))&
(![X]:((~tall(X)&happy(X))<=>~humble(X)))&
(![X]:(~patient(X)=>rich(X)))&
(![X]:((calm(X)|~calm(X))<=>(~humble(X)&curious(X))))&
(![X]:(generous(X)<=>~quiet(X)))&
((?[X]:((calm(X)|~rich(X))))<=>(?[X]:((wi... | ~happy(fred) | [
"p2",
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 1098697620821103179766792
% SZS output start Proof for 1098697620821103179766792
3. ! [X0] : ((happy(X0) & ~tall(X0)) <=> ~humble(X0)) [input p2]
5. ! [X0] : ((~calm(X0) | calm(X0)) <=> (curious(X0) & ~humble(X0))) [input p4]
24. ~happy(fred) [input hypothesis]
39. ! [X0] : (((happy(X0) &... | 0 |
Everyone who is rich or strong is not tall or not creative.
Everyone who is strong is generous or not creative and vice versa.
Everyone who is either not strong or patient is both humble and brave and vice versa.
If susan is not kind or patient then someone is both not old and funny and vice versa.
Everyone who is both... | Alice is not brave. | entailment | (![X]:((rich(X)|strong(X))=>(~tall(X)|~creative(X))))&
(![X]:(strong(X)<=>(generous(X)|~creative(X))))&
(![X]:((~strong(X)<~>patient(X))<=>(humble(X)&brave(X))))&
(((~kind(susan)|patient(susan)))<=>(?[X]:((~old(X)&funny(X)))))&
(![X]:((humble(X)&creative(X))=>(~quiet(X)<~>~old(X))))&
(![X]:((~patient(X)|~creative(X))=>... | ~brave(alice) | [
"p0",
"p1",
"p2",
"p5",
"p7",
"p12",
"p13",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 5786043772695689442375289
% SZS output start Proof for 5786043772695689442375289
1. ! [X0] : ((strong(X0) | rich(X0)) => (~creative(X0) | ~tall(X0))) [input p0]
2. ! [X0] : (strong(X0) <=> (~creative(X0) | generous(X0))) [input p1]
3. ! [X0] : ((~strong(X0) <~> patient(X0)) <=> (brave(X0)... | 0 |
Everyone who is both old and curious is not kind or not happy and vice versa.
If paul is either strong or calm then someone is both brave and generous.
If someone is both not humble and quiet then susan is kind and vice versa.
Everyone who is not calm or not kind is not brave.
Everyone who is both tall and not rich is ... | Susan is not strong. | entailment | (![X]:((old(X)&curious(X))<=>(~kind(X)|~happy(X))))&
(((strong(paul)<~>calm(paul)))=>(?[X]:((brave(X)&generous(X)))))&
((?[X]:((~humble(X)&quiet(X))))<=>(kind(susan)))&
(![X]:((~calm(X)|~kind(X))=>~brave(X)))&
(![X]:((tall(X)&~rich(X))<=>(humble(X)<~>~old(X))))&
((~humble(alice))<=>(?[X]:(~curious(X))))&
(![X]:((humble... | ~strong(susan) | [
"p0",
"p4",
"p6",
"p7",
"p12",
"p15",
"p16",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 2723795831688446368370378
% SZS output start Proof for 2723795831688446368370378
1. ! [X0] : ((curious(X0) & old(X0)) <=> (~happy(X0) | ~kind(X0))) [input p0]
5. ! [X0] : ((~rich(X0) & tall(X0)) <=> (humble(X0) <~> ~old(X0))) [input p4]
7. ! [X0] : ((humble(X0) <~> rich(X0)) <=> (wise(X0)... | 0 |
If paul is not kind or not calm then someone is not patient or not kind and vice versa.
If someone is either not patient or not wise then someone is not kind or not wise.
Everyone who is either old or brave is both happy and not brave and vice versa.
Everyone who is either kind or calm is both not tall and not humble a... | Lucy is not rich. | contradiction | (((~kind(paul)|~calm(paul)))<=>(?[X]:((~patient(X)|~kind(X)))))&
((?[X]:((~patient(X)<~>~wise(X))))=>(?[X]:((~kind(X)|~wise(X)))))&
(![X]:((old(X)<~>brave(X))<=>(happy(X)&~brave(X))))&
(![X]:((kind(X)<~>calm(X))<=>(~tall(X)&~humble(X))))&
(![X]:(~humble(X)=>(~kind(X)<~>kind(X))))&
(((rich(mary)<~>tall(mary)))<=>(?[X]:(... | ~rich(lucy) | [
"p7",
"p9",
"p10",
"p12",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 5583895839964411210281834
% SZS output start Proof for 5583895839964411210281834
8. ! [X0] : ((rich(X0) | old(X0)) <=> (strong(X0) | ~rich(X0))) [input p7]
10. ! [X0] : ((patient(X0) | ~quiet(X0)) => ~patient(X0)) [input p9]
11. ! [X0] : (funny(X0) => wise(X0)) [input p10]
13. (tall(mary)... | 0 |
If mary is either quiet or brave then someone is happy or patient. If john is either happy or calm then fred is not happy or not old and vice versa. Everyone who is either not brave or not generous is either not patient or not creative and vice versa. If fred is either not happy or not tall then fred is either strong o... | John is not wise. | entailment | (((quiet(mary)<~>brave(mary)))=>(?[X]:((happy(X)|patient(X)))))&
(((happy(john)<~>calm(john)))<=>((~happy(fred)|~old(fred))))&
(![X]:((~brave(X)<~>~generous(X))<=>(~patient(X)<~>~creative(X))))&
(((~happy(fred)<~>~tall(fred)))<=>((strong(fred)<~>~generous(fred))))&
((?[X]:((brave(X)|generous(X))))=>(?[X]:((~generous(X)... | ~wise(john) | [
"p1",
"p7",
"p10",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 4195679516500482168583621
% SZS output start Proof for 4195679516500482168583621
2. (happy(john) <~> calm(john)) <=> (~old(fred) | ~happy(fred)) [input p1]
8. ! [X0] : ((creative(X0) | ~calm(X0)) => (~wise(X0) <~> ~happy(X0))) [input p7]
11. ! [X0] : (patient(X0) <=> (~patient(X0) <~> ~ca... | 0 |
If someone is both not curious and patient then someone is either rich or not funny.
Everyone who is not curious or not patient is both not old and not brave and vice versa.
If lucy is wise or not happy then john is happy and vice versa.
If alice is both not rich and calm then someone is either not creative or not calm... | John is rich. | neutral | ((?[X]:((~curious(X)&patient(X))))=>(?[X]:((rich(X)<~>~funny(X)))))&
(![X]:((~curious(X)|~patient(X))<=>(~old(X)&~brave(X))))&
(((wise(lucy)|~happy(lucy)))<=>(happy(john)))&
(((~rich(alice)&calm(alice)))=>(?[X]:((~creative(X)<~>~calm(X)))))&
(![X]:((~strong(X)|~brave(X))<=>~strong(X)))&
((~funny(lucy))=>((~calm(mary)<~... | rich(john) | [] | null | 0 |
If susan is both patient and quiet then someone is not rich or tall.
If john is either patient or not patient then susan is not strong or not curious and vice versa.
If someone is either kind or strong then someone is both not creative and not patient.
If john is either wise or generous then someone is not wise or not ... | Mary is kind. | entailment | (((patient(susan)&quiet(susan)))=>(?[X]:((~rich(X)|tall(X)))))&
(((patient(john)<~>~patient(john)))<=>((~strong(susan)|~curious(susan))))&
((?[X]:((kind(X)<~>strong(X))))=>(?[X]:((~creative(X)&~patient(X)))))&
(((wise(john)<~>generous(john)))<=>(?[X]:((~wise(X)|~calm(X)))))&
(![X]:((~wise(X)|creative(X))=>(~happy(X)&~r... | kind(mary) | [
"p2",
"p3",
"p4",
"p5",
"p7",
"p8",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 1849878695405105102363991
% SZS output start Proof for 1849878695405105102363991
3. ? [X0] : (kind(X0) <~> strong(X0)) => ? [X0] : (~patient(X0) & ~creative(X0)) [input p2]
4. (wise(john) <~> generous(john)) <=> ? [X0] : (~calm(X0) | ~wise(X0)) [input p3]
5. ! [X0] : ((creative(X0) | ~wis... | 0 |
If someone is not curious or not funny then fred is both happy and creative.
If john is not creative then someone is either not happy or not patient and vice versa.
If someone is not kind or not curious then someone is quiet and vice versa.
If paul is both not creative and rich then someone is not happy.
If paul is not... | Alice is not wise. | contradiction | ((?[X]:((~curious(X)|~funny(X))))=>((happy(fred)&creative(fred))))&
((~creative(john))<=>(?[X]:((~happy(X)<~>~patient(X)))))&
((?[X]:((~kind(X)|~curious(X))))<=>(?[X]:(quiet(X))))&
(((~creative(paul)&rich(paul)))=>(?[X]:(~happy(X))))&
(((~kind(paul)|~happy(paul)))<=>(?[X]:((creative(X)<~>~quiet(X)))))&
((?[X]:((~humble... | ~wise(alice) | [
"p7",
"p10",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2931762589962529409493029
% SZS output start Proof for 2931762589962529409493029
8. ! [X0] : ((strong(X0) <~> brave(X0)) <=> (generous(X0) & ~curious(X0))) [input p7]
11. ? [X0] : (wise(X0) | rich(X0)) => (~generous(alice) & ~strong(alice)) [input p10]
15. (rich(fred) <~> wise(fred)) <=> ... | 0 |
Everyone who is not generous is both generous and not brave.
Everyone who is not curious or not brave is both wise and not generous.
Everyone who is tall or brave is not curious or not rich.
If alice is calm or patient then alice is quiet or calm.
Everyone who is not brave or funny is either rich or kind and vice versa... | Susan is funny. | entailment | (![X]:(~generous(X)=>(generous(X)&~brave(X))))&
(![X]:((~curious(X)|~brave(X))=>(wise(X)&~generous(X))))&
(![X]:((tall(X)|brave(X))=>(~curious(X)|~rich(X))))&
(((calm(alice)|patient(alice)))=>((quiet(alice)|calm(alice))))&
(![X]:((~brave(X)|funny(X))<=>(rich(X)<~>kind(X))))&
((?[X]:(humble(X)))=>((patient(alice)|~happy... | funny(susan) | [
"p0",
"p1",
"p2",
"p7",
"p8",
"p13",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 1609307538593566629962635
% SZS output start Proof for 1609307538593566629962635
1. ! [X0] : (~generous(X0) => (~brave(X0) & generous(X0))) [input p0]
2. ! [X0] : ((~brave(X0) | ~curious(X0)) => (~generous(X0) & wise(X0))) [input p1]
3. ! [X0] : ((brave(X0) | tall(X0)) => (~rich(X0) | ~cu... | 0 |
Everyone who is both happy and not tall is not humble. If someone is happy then someone is both not patient and not wise and vice versa. Everyone who is not generous is both not tall and strong. Everyone who is either happy or not quiet is not tall and vice versa. Everyone who is both not old and strong is wise. Everyo... | Paul is patient. | entailment | (![X]:((happy(X)&~tall(X))=>~humble(X)))&
((?[X]:(happy(X)))<=>(?[X]:((~patient(X)&~wise(X)))))&
(![X]:(~generous(X)=>(~tall(X)&strong(X))))&
(![X]:((happy(X)<~>~quiet(X))<=>~tall(X)))&
(![X]:((~old(X)&strong(X))=>wise(X)))&
(![X]:(quiet(X)<=>(~quiet(X)&~creative(X))))&
((?[X]:(rich(X)))=>((curious(paul)&calm(paul))))&... | patient(paul) | [
"p5",
"p11",
"p19",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 5606878472520667692186453
% SZS output start Proof for 5606878472520667692186453
6. ! [X0] : (quiet(X0) <=> (~creative(X0) & ~quiet(X0))) [input p5]
12. ! [X0] : (calm(X0) <=> patient(X0)) [input p11]
20. old(paul) <~> quiet(paul) [input p19]
22. calm(paul) | ~old(paul) [input p21]
23. ~p... | 0 |
Everyone who is not wise is both not wise and not humble and vice versa.
Everyone who is either not rich or not quiet is either wise or brave.
Everyone who is either not calm or not strong is curious or old and vice versa.
Everyone who is humble is either funny or humble and vice versa.
If alice is either brave or not ... | Paul is not generous. | neutral | (![X]:(~wise(X)<=>(~wise(X)&~humble(X))))&
(![X]:((~rich(X)<~>~quiet(X))=>(wise(X)<~>brave(X))))&
(![X]:((~calm(X)<~>~strong(X))<=>(curious(X)|old(X))))&
(![X]:(humble(X)<=>(funny(X)<~>humble(X))))&
(((brave(alice)<~>~generous(alice)))=>(?[X]:(~wise(X))))&
(![X]:((~funny(X)|~wise(X))<=>(patient(X)<~>~old(X))))&
(![X]:(... | ~generous(paul) | [] | null | 0 |
Everyone who is either strong or quiet is both patient and funny and vice versa.
Everyone who is either curious or brave is either not creative or funny.
Everyone who is not brave is either wise or not generous and vice versa.
If someone is wise or not wise then paul is either not funny or not creative.
Everyone who is... | Alice is old. | neutral | (![X]:((strong(X)<~>quiet(X))<=>(patient(X)&funny(X))))&
(![X]:((curious(X)<~>brave(X))=>(~creative(X)<~>funny(X))))&
(![X]:(~brave(X)<=>(wise(X)<~>~generous(X))))&
((?[X]:((wise(X)|~wise(X))))=>((~funny(paul)<~>~creative(paul))))&
(![X]:((~calm(X)|brave(X))=>(~tall(X)|kind(X))))&
(![X]:((~funny(X)|calm(X))<=>(humble(X... | old(alice) | [] | null | 0 |
If someone is not creative then alice is either not tall or not patient.
If someone is not calm then paul is both not rich and kind.
If fred is happy or calm then someone is not old or happy.
Everyone who is either not strong or calm is happy.
Everyone who is either not old or wise is either kind or wise.
If someone is... | Lucy is not humble. | entailment | ((?[X]:(~creative(X)))=>((~tall(alice)<~>~patient(alice))))&
((?[X]:(~calm(X)))=>((~rich(paul)&kind(paul))))&
(((happy(fred)|calm(fred)))=>(?[X]:((~old(X)|happy(X)))))&
(![X]:((~strong(X)<~>calm(X))=>happy(X)))&
(![X]:((~old(X)<~>wise(X))=>(kind(X)<~>wise(X))))&
((?[X]:((~patient(X)|humble(X))))<=>((happy(lucy)&~calm(l... | ~humble(lucy) | [
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 6596244738142687172856560
% SZS output start Proof for 6596244738142687172856560
7. ! [X0] : ((~kind(X0) <~> kind(X0)) => (patient(X0) & ~humble(X0))) [input p6]
24. humble(lucy) [input hypothesis]
30. ! [X0] : ((patient(X0) & ~humble(X0)) | (~kind(X0) <=> kind(X0))) [ennf transformation ... | 0 |
If someone is either not brave or not rich then paul is both not wise and not generous. Everyone who is quiet is either not curious or not creative and vice versa. If someone is generous or curious then someone is rich or patient and vice versa. If fred is not rich then someone is either tall or not wise and vice versa... | John is not curious. | neutral | ((?[X]:((~brave(X)<~>~rich(X))))=>((~wise(paul)&~generous(paul))))&
(![X]:(quiet(X)<=>(~curious(X)<~>~creative(X))))&
((?[X]:((generous(X)|curious(X))))<=>(?[X]:((rich(X)|patient(X)))))&
((~rich(fred))<=>(?[X]:((tall(X)<~>~wise(X)))))&
(![X]:((~happy(X)&~humble(X))=>funny(X)))&
(((quiet(mary)&wise(mary)))=>(?[X]:((curi... | ~curious(john) | [] | null | 0 |
Everyone who is either not strong or not patient is rich.
If someone is either tall or not patient then someone is strong.
If paul is old or not calm then someone is not quiet or creative and vice versa.
Everyone who is both not curious and old is creative.
If someone is both humble and not kind then lucy is either not... | Susan is not happy. | neutral | (![X]:((~strong(X)<~>~patient(X))=>rich(X)))&
((?[X]:((tall(X)<~>~patient(X))))=>(?[X]:(strong(X))))&
(((old(paul)|~calm(paul)))<=>(?[X]:((~quiet(X)|creative(X)))))&
(![X]:((~curious(X)&old(X))=>creative(X)))&
((?[X]:((humble(X)&~kind(X))))=>((~creative(lucy)<~>kind(lucy))))&
(![X]:((wise(X)&patient(X))<=>(~calm(X)|cur... | ~happy(susan) | [] | null | 0 |
Everyone who is both not generous and creative is either not patient or not generous and vice versa.
If mary is either patient or kind then someone is both brave and strong.
If someone is creative or not generous then mary is both not brave and not creative and vice versa.
If someone is not happy then alice is both hap... | Mary is generous. | contradiction | (![X]:((~generous(X)&creative(X))<=>(~patient(X)<~>~generous(X))))&
(((patient(mary)<~>kind(mary)))=>(?[X]:((brave(X)&strong(X)))))&
((?[X]:((creative(X)|~generous(X))))<=>((~brave(mary)&~creative(mary))))&
((?[X]:(~happy(X)))<=>((happy(alice)&~quiet(alice))))&
(![X]:((~happy(X)|patient(X))=>(quiet(X)&~quiet(X))))&
((?... | generous(mary) | [
"p2",
"p16",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 6216536910818401071639844
% SZS output start Proof for 6216536910818401071639844
3. ? [X0] : (~generous(X0) | creative(X0)) <=> (~creative(mary) & ~brave(mary)) [input p2]
17. brave(mary) <~> ~generous(mary) [input p16]
18. ? [X0] : (~generous(X0) & kind(X0)) [input p17]
23. generous(mary... | 0 |
Everyone who is generous is brave.
Everyone who is both not wise and humble is generous.
Everyone who is both curious and not wise is both creative and not generous.
Everyone who is either patient or quiet is either not creative or not brave and vice versa.
If someone is either not kind or not quiet then mary is not ca... | Paul is not rich. | entailment | (![X]:(generous(X)=>brave(X)))&
(![X]:((~wise(X)&humble(X))=>generous(X)))&
(![X]:((curious(X)&~wise(X))=>(creative(X)&~generous(X))))&
(![X]:((patient(X)<~>quiet(X))<=>(~creative(X)<~>~brave(X))))&
((?[X]:((~kind(X)<~>~quiet(X))))=>(~calm(mary)))&
(![X]:(tall(X)<=>(rich(X)|wise(X))))&
((?[X]:((humble(X)|quiet(X))))=>(... | ~rich(paul) | [
"p7",
"p10",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 8883796526308734250331165
% SZS output start Proof for 8883796526308734250331165
8. ! [X0] : ((~happy(X0) & calm(X0)) <=> (strong(X0) | brave(X0))) [input p7]
11. ! [X0] : (rich(X0) => (brave(X0) | calm(X0))) [input p10]
21. ~calm(paul) [input p20]
25. rich(paul) [input hypothesis]
35. ! ... | 0 |
If paul is quiet or not kind then someone is either wise or not kind and vice versa. Everyone who is both patient and not wise is strong. Everyone who is both rich and not quiet is not old or creative and vice versa. Everyone who is both happy and not kind is not humble or not tall and vice versa. Everyone who is both ... | Fred is not curious. | entailment | (((quiet(paul)|~kind(paul)))<=>(?[X]:((wise(X)<~>~kind(X)))))&
(![X]:((patient(X)&~wise(X))=>strong(X)))&
(![X]:((rich(X)&~quiet(X))<=>(~old(X)|creative(X))))&
(![X]:((happy(X)&~kind(X))<=>(~humble(X)|~tall(X))))&
(![X]:((calm(X)&tall(X))<=>(humble(X)|old(X))))&
(![X]:(~funny(X)<=>rich(X)))&
(![X]:((~kind(X)&~quiet(X))... | ~curious(fred) | [
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 8816892841181373760784791
% SZS output start Proof for 8816892841181373760784791
8. ! [X0] : (curious(X0) => (~curious(X0) & rich(X0))) [input p7]
24. curious(fred) [input hypothesis]
28. ! [X0] : ((~curious(X0) & rich(X0)) | ~curious(X0)) [ennf transformation 8]
107. ~curious(X0) | ~curi... | 0 |
If someone is both not generous and brave then john is quiet and vice versa.
Everyone who is funny is either calm or not curious and vice versa.
Everyone who is both not quiet and not brave is either humble or not happy and vice versa.
Everyone who is both not generous and patient is either rich or not old and vice ver... | Lucy is humble. | contradiction | ((?[X]:((~generous(X)&brave(X))))<=>(quiet(john)))&
(![X]:(funny(X)<=>(calm(X)<~>~curious(X))))&
(![X]:((~quiet(X)&~brave(X))<=>(humble(X)<~>~happy(X))))&
(![X]:((~generous(X)&patient(X))<=>(rich(X)<~>~old(X))))&
((?[X]:((~kind(X)<~>~happy(X))))<=>(?[X]:((calm(X)|strong(X)))))&
(![X]:(~creative(X)<=>rich(X)))&
((~gener... | humble(lucy) | [
"p2",
"p7",
"p8",
"p9",
"p10",
"p11",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 5638858086510221084410022
% SZS output start Proof for 5638858086510221084410022
3. ! [X0] : ((~brave(X0) & ~quiet(X0)) <=> (humble(X0) <~> ~happy(X0))) [input p2]
8. ! [X0] : ((calm(X0) <~> kind(X0)) => calm(X0)) [input p7]
9. ! [X0] : ((~quiet(X0) | brave(X0)) => (humble(X0) & kind(X0))... | 0 |
If someone is quiet or patient then someone is both wise and strong and vice versa. Everyone who is not calm is both generous and not brave and vice versa. If fred is either not happy or quiet then someone is both not rich and tall. If someone is both patient and kind then alice is wise or not old. Everyone who is eith... | Mary is not calm. | contradiction | ((?[X]:((quiet(X)|patient(X))))<=>(?[X]:((wise(X)&strong(X)))))&
(![X]:(~calm(X)<=>(generous(X)&~brave(X))))&
(((~happy(fred)<~>quiet(fred)))=>(?[X]:((~rich(X)&tall(X)))))&
((?[X]:((patient(X)&kind(X))))=>((wise(alice)|~old(alice))))&
(![X]:((~happy(X)<~>rich(X))=>(generous(X)&~old(X))))&
(((~wise(paul)<~>quiet(paul)))... | ~calm(mary) | [
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 6084044090091080096504648
% SZS output start Proof for 6084044090091080096504648
9. ? [X0] : (rich(X0) | ~calm(X0)) => (~calm(lucy) & calm(lucy)) [input p8]
23. ~calm(mary) [input hypothesis]
37. (~calm(lucy) & calm(lucy)) | ! [X0] : (~rich(X0) & calm(X0)) [ennf transformation 9]
94. calm... | 0 |
Everyone who is old is both not curious and not kind and vice versa.
If someone is both not strong and not creative then someone is not strong or rich.
If paul is either not tall or rich then someone is either not curious or kind and vice versa.
Everyone who is not patient is funny or creative and vice versa.
Everyone ... | John is quiet. | neutral | (![X]:(old(X)<=>(~curious(X)&~kind(X))))&
((?[X]:((~strong(X)&~creative(X))))=>(?[X]:((~strong(X)|rich(X)))))&
(((~tall(paul)<~>rich(paul)))<=>(?[X]:((~curious(X)<~>kind(X)))))&
(![X]:(~patient(X)<=>(funny(X)|creative(X))))&
(![X]:((happy(X)|~curious(X))<=>~strong(X)))&
((?[X]:((~strong(X)|funny(X))))=>((~strong(john)&... | quiet(john) | [] | null | 0 |
If paul is either patient or curious then lucy is both funny and tall and vice versa.
Everyone who is both creative and not quiet is both not wise and brave and vice versa.
If lucy is either quiet or not wise then alice is not brave and vice versa.
Everyone who is both not creative and quiet is both not funny and kind.... | Alice is brave. | contradiction | (((patient(paul)<~>curious(paul)))<=>((funny(lucy)&tall(lucy))))&
(![X]:((creative(X)&~quiet(X))<=>(~wise(X)&brave(X))))&
(((quiet(lucy)<~>~wise(lucy)))<=>(~brave(alice)))&
(![X]:((~creative(X)&quiet(X))=>(~funny(X)&kind(X))))&
((?[X]:((~calm(X)<~>~tall(X))))=>((~strong(mary)&kind(mary))))&
((?[X]:((~brave(X)&~patient(... | brave(alice) | [
"p1",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 1235114290128297826621547
% SZS output start Proof for 1235114290128297826621547
2. ! [X0] : ((~quiet(X0) & creative(X0)) <=> (brave(X0) & ~wise(X0))) [input p1]
16. ! [X0] : ((funny(X0) & ~wise(X0)) <=> (brave(X0) | tall(X0))) [input p15]
18. wise(alice) | ~creative(alice) [input p17]
25... | 0 |
If lucy is either not strong or not humble then someone is not kind or not patient.
Everyone who is either not funny or creative is wise and vice versa.
Everyone who is both not rich and humble is not funny or not quiet and vice versa.
Everyone who is not creative is not rich and vice versa.
Everyone who is not humble ... | Alice is not funny. | entailment | (((~strong(lucy)<~>~humble(lucy)))=>(?[X]:((~kind(X)|~patient(X)))))&
(![X]:((~funny(X)<~>creative(X))<=>wise(X)))&
(![X]:((~rich(X)&humble(X))<=>(~funny(X)|~quiet(X))))&
(![X]:(~creative(X)<=>~rich(X)))&
(![X]:(~humble(X)<=>~wise(X)))&
(![X]:((creative(X)<~>~kind(X))=>(curious(X)<~>wise(X))))&
((?[X]:((~rich(X)<~>~wis... | ~funny(alice) | [
"p1",
"p2",
"p3",
"p4",
"p9",
"p11",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 3672939005935618114925010
% SZS output start Proof for 3672939005935618114925010
2. ! [X0] : ((~funny(X0) <~> creative(X0)) <=> wise(X0)) [input p1]
3. ! [X0] : ((humble(X0) & ~rich(X0)) <=> (~quiet(X0) | ~funny(X0))) [input p2]
4. ! [X0] : (~creative(X0) <=> ~rich(X0)) [input p3]
5. ! [X... | 0 |
If paul is either not funny or humble then alice is both not creative and strong.
Everyone who is not tall is both not quiet and creative.
If susan is not tall or brave then fred is brave or not creative.
If lucy is both not brave and creative then someone is either not brave or calm and vice versa.
If someone is rich ... | John is not old. | neutral | (((~funny(paul)<~>humble(paul)))=>((~creative(alice)&strong(alice))))&
(![X]:(~tall(X)=>(~quiet(X)&creative(X))))&
(((~tall(susan)|brave(susan)))=>((brave(fred)|~creative(fred))))&
(((~brave(lucy)&creative(lucy)))<=>(?[X]:((~brave(X)<~>calm(X)))))&
((?[X]:(rich(X)))<=>((~brave(lucy)<~>~kind(lucy))))&
((?[X]:((generous(... | ~old(john) | [] | null | 0 |
Everyone who is both strong and kind is not strong and vice versa.
If someone is either not curious or not quiet then paul is funny or not tall and vice versa.
If fred is not rich or not brave then mary is either rich or old.
Everyone who is not creative is not rich or not generous and vice versa.
If alice is both not ... | Mary is not strong. | contradiction | (![X]:((strong(X)&kind(X))<=>~strong(X)))&
((?[X]:((~curious(X)<~>~quiet(X))))<=>((funny(paul)|~tall(paul))))&
(((~rich(fred)|~brave(fred)))=>((rich(mary)<~>old(mary))))&
(![X]:(~creative(X)<=>(~rich(X)|~generous(X))))&
(((~quiet(alice)&~happy(alice)))<=>(?[X]:((calm(X)|~strong(X)))))&
(![X]:((~calm(X)|happy(X))<=>(~fu... | ~strong(mary) | [
"p0",
"hypothesis"
] | % SZS status Unsatisfiable for 1072865270172442235238022
% SZS output start Proof for 1072865270172442235238022
1. ! [X0] : ((kind(X0) & strong(X0)) <=> ~strong(X0)) [input p0]
20. ~strong(mary) [input hypothesis]
29. ! [X0] : (((kind(X0) & strong(X0)) | strong(X0)) & (~strong(X0) | (~kind(X0) | ~strong(X0)))) [nnf tra... | 0 |
If someone is brave or tall then someone is either rich or kind. If someone is either not calm or not quiet then fred is either humble or not kind and vice versa. If someone is humble or generous then someone is both not tall and wise. Everyone who is either not generous or not happy is both not curious and humble. Eve... | Paul is not tall. | contradiction | ((?[X]:((brave(X)|tall(X))))=>(?[X]:((rich(X)<~>kind(X)))))&
((?[X]:((~calm(X)<~>~quiet(X))))<=>((humble(fred)<~>~kind(fred))))&
((?[X]:((humble(X)|generous(X))))=>(?[X]:((~tall(X)&wise(X)))))&
(![X]:((~generous(X)<~>~happy(X))=>(~curious(X)&humble(X))))&
(![X]:((~happy(X)|~kind(X))<=>(~curious(X)|curious(X))))&
(![X]:... | ~tall(paul) | [
"p13",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 538469143603020656775696
% SZS output start Proof for 538469143603020656775696
14. ! [X0] : (~tall(X0) => (~creative(X0) & patient(X0))) [input p13]
24. brave(paul) & ~patient(paul) [input p23]
25. ~tall(paul) [input hypothesis]
37. ! [X0] : ((~creative(X0) & patient(X0)) | tall(X0)) [enn... | 0 |
Everyone who is not happy is either quiet or not curious. If someone is old or kind then someone is funny and vice versa. If someone is brave or generous then someone is either not patient or kind. Everyone who is strong or patient is calm. Everyone who is either humble or wise is not calm. If mary is either quiet or n... | Paul is rich. | neutral | (![X]:(~happy(X)=>(quiet(X)<~>~curious(X))))&
((?[X]:((old(X)|kind(X))))<=>(?[X]:(funny(X))))&
((?[X]:((brave(X)|generous(X))))=>(?[X]:((~patient(X)<~>kind(X)))))&
(![X]:((strong(X)|patient(X))=>calm(X)))&
(![X]:((humble(X)<~>wise(X))=>~calm(X)))&
(((quiet(mary)<~>~calm(mary)))<=>(?[X]:((~generous(X)&brave(X)))))&
(![X... | rich(paul) | [] | null | 0 |
Everyone who is rich or generous is quiet or not tall. Everyone who is either happy or kind is either not quiet or not happy and vice versa. If alice is not generous then someone is either old or not happy. Everyone who is either brave or not generous is either not curious or rich. Everyone who is both strong and brave... | Alice is not rich. | neutral | (![X]:((rich(X)|generous(X))=>(quiet(X)|~tall(X))))&
(![X]:((happy(X)<~>kind(X))<=>(~quiet(X)<~>~happy(X))))&
((~generous(alice))=>(?[X]:((old(X)<~>~happy(X)))))&
(![X]:((brave(X)<~>~generous(X))=>(~curious(X)<~>rich(X))))&
(![X]:((strong(X)&brave(X))<=>brave(X)))&
((?[X]:((~wise(X)<~>strong(X))))<=>(?[X]:(~calm(X))))&... | ~rich(alice) | [] | null | 0 |
If someone is both tall and not brave then someone is not tall and vice versa.
If someone is either creative or not curious then someone is either not creative or wise.
Everyone who is both not kind and generous is rich.
Everyone who is either creative or not calm is both not kind and not wise and vice versa.
If someon... | Mary is happy. | neutral | ((?[X]:((tall(X)&~brave(X))))<=>(?[X]:(~tall(X))))&
((?[X]:((creative(X)<~>~curious(X))))=>(?[X]:((~creative(X)<~>wise(X)))))&
(![X]:((~kind(X)&generous(X))=>rich(X)))&
(![X]:((creative(X)<~>~calm(X))<=>(~kind(X)&~wise(X))))&
((?[X]:(patient(X)))=>(?[X]:((~tall(X)&patient(X)))))&
(![X]:(funny(X)=>(happy(X)&creative(X))... | happy(mary) | [] | null | 0 |
Everyone who is both not humble and quiet is either not humble or quiet and vice versa.
If someone is either humble or not happy then someone is old and vice versa.
If someone is both strong and not patient then paul is rich or not wise.
If someone is not happy then someone is happy or calm and vice versa.
Everyone who... | Paul is patient. | contradiction | (![X]:((~humble(X)&quiet(X))<=>(~humble(X)<~>quiet(X))))&
((?[X]:((humble(X)<~>~happy(X))))<=>(?[X]:(old(X))))&
((?[X]:((strong(X)&~patient(X))))=>((rich(paul)|~wise(paul))))&
((?[X]:(~happy(X)))<=>(?[X]:((happy(X)|calm(X)))))&
(![X]:((funny(X)<~>calm(X))<=>(~funny(X)<~>wise(X))))&
((?[X]:((patient(X)&rich(X))))=>(?[X]... | patient(paul) | [
"p4",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 6964475471900760462418946
% SZS output start Proof for 6964475471900760462418946
5. ! [X0] : ((funny(X0) <~> calm(X0)) <=> (~funny(X0) <~> wise(X0))) [input p4]
12. ! [X0] : (~calm(X0) <=> (~patient(X0) <~> ~wise(X0))) [input p11]
19. patient(paul) [input hypothesis]
46. ! [X0] : ((((~cal... | 0 |
If someone is not kind or not humble then someone is both not quiet and kind and vice versa. If paul is either not strong or not wise then fred is either not creative or old and vice versa. Everyone who is not generous or not happy is either not humble or kind. Everyone who is either happy or not creative is not quiet ... | Paul is not strong. | neutral | ((?[X]:((~kind(X)|~humble(X))))<=>(?[X]:((~quiet(X)&kind(X)))))&
(((~strong(paul)<~>~wise(paul)))<=>((~creative(fred)<~>old(fred))))&
(![X]:((~generous(X)|~happy(X))=>(~humble(X)<~>kind(X))))&
(![X]:((happy(X)<~>~creative(X))<=>~quiet(X)))&
(![X]:((kind(X)<~>~wise(X))=>(~curious(X)&~funny(X))))&
(![X]:((generous(X)|~cu... | ~strong(paul) | [] | null | 0 |
If someone is calm then alice is both creative and tall and vice versa. Everyone who is both not patient and funny is either brave or funny. Everyone who is either tall or not generous is not calm or not happy. Everyone who is either not humble or strong is rich. Everyone who is quiet or not patient is creative. If joh... | John is not happy. | entailment | ((?[X]:(calm(X)))<=>((creative(alice)&tall(alice))))&
(![X]:((~patient(X)&funny(X))=>(brave(X)<~>funny(X))))&
(![X]:((tall(X)<~>~generous(X))=>(~calm(X)|~happy(X))))&
(![X]:((~humble(X)<~>strong(X))=>rich(X)))&
(![X]:((quiet(X)|~patient(X))=>creative(X)))&
((~patient(john))<=>(?[X]:((wise(X)&~kind(X)))))&
((~humble(fre... | ~happy(john) | [
"p8",
"p9",
"p10",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 4156446111287752915612320
% SZS output start Proof for 4156446111287752915612320
9. ! [X0] : ((~rich(X0) | strong(X0)) => (~patient(X0) & creative(X0))) [input p8]
10. ! [X0] : ((quiet(X0) & ~happy(X0)) <=> (~old(X0) <~> ~happy(X0))) [input p9]
11. ! [X0] : ((~creative(X0) & funny(X0)) <=... | 0 |
If someone is happy then alice is either wise or not generous and vice versa.
If fred is calm then someone is not kind.
Everyone who is generous is both not brave and not rich and vice versa.
If john is not rich then lucy is both not generous and creative and vice versa.
Everyone who is calm or not quiet is not old or ... | Lucy is happy. | entailment | ((?[X]:(happy(X)))<=>((wise(alice)<~>~generous(alice))))&
((calm(fred))=>(?[X]:(~kind(X))))&
(![X]:(generous(X)<=>(~brave(X)&~rich(X))))&
((~rich(john))<=>((~generous(lucy)&creative(lucy))))&
(![X]:((calm(X)|~quiet(X))<=>(~old(X)|wise(X))))&
(![X]:((~happy(X)<~>rich(X))<=>(~old(X)<~>~generous(X))))&
(((tall(alice)<~>~f... | happy(lucy) | [
"p2",
"p5",
"p9",
"p11",
"p13",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 8148968973482234842158977
% SZS output start Proof for 8148968973482234842158977
3. ! [X0] : (generous(X0) <=> (~rich(X0) & ~brave(X0))) [input p2]
6. ! [X0] : ((~happy(X0) <~> rich(X0)) <=> (~old(X0) <~> ~generous(X0))) [input p5]
10. ! [X0] : (~kind(X0) <=> (creative(X0) & patient(X0)))... | 0 |
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