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
sequencelengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
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|---|---|---|---|---|---|---|---|
Everyone who is either quiet or curious is not wise or old.
Everyone who is curious is both not tall and not rich and vice versa.
If susan is not funny or wise then fred is kind or not patient and vice versa.
If fred is either not patient or creative then john is brave and vice versa.
If someone is either not wise or calm then lucy is either not creative or not funny and vice versa.
If lucy is either not old or not humble then lucy is not strong or not curious.
Everyone who is not calm or not rich is patient or humble and vice versa.
If someone is either not brave or not generous then someone is both generous and not patient.
If lucy is both not old and curious then someone is both not kind and tall.
If alice is either rich or not calm then john is not kind and vice versa.
If someone is both happy and not kind then lucy is both not rich and happy and vice versa.
Everyone who is not patient is both curious and patient.
If susan is both not tall and tall then mary is not kind.
If john is patient then someone is both humble and rich.
If fred is brave or creative then susan is not curious.
Someone is not wise.
Someone is both patient and generous.
Paul is both not wise and generous.
Someone is curious or not tall.
John is either not curious or happy.
Mary is both creative and not kind. | Alice is not funny. | neutral | (![X]:((quiet(X)<~>curious(X))=>(~wise(X)|old(X))))&
(![X]:(curious(X)<=>(~tall(X)&~rich(X))))&
(((~funny(susan)|wise(susan)))<=>((kind(fred)|~patient(fred))))&
(((~patient(fred)<~>creative(fred)))<=>(brave(john)))&
((?[X]:((~wise(X)<~>calm(X))))<=>((~creative(lucy)<~>~funny(lucy))))&
(((~old(lucy)<~>~humble(lucy)))=>((~strong(lucy)|~curious(lucy))))&
(![X]:((~calm(X)|~rich(X))<=>(patient(X)|humble(X))))&
((?[X]:((~brave(X)<~>~generous(X))))=>(?[X]:((generous(X)&~patient(X)))))&
(((~old(lucy)&curious(lucy)))=>(?[X]:((~kind(X)&tall(X)))))&
(((rich(alice)<~>~calm(alice)))<=>(~kind(john)))&
((?[X]:((happy(X)&~kind(X))))<=>((~rich(lucy)&happy(lucy))))&
(![X]:(~patient(X)=>(curious(X)&patient(X))))&
(((~tall(susan)&tall(susan)))=>(~kind(mary)))&
((patient(john))=>(?[X]:((humble(X)&rich(X)))))&
(((brave(fred)|creative(fred)))=>(~curious(susan)))&
(?[X]:(~wise(X)))&
(?[X]:((patient(X)&generous(X))))&
((~wise(paul)&generous(paul)))&
(?[X]:((curious(X)|~tall(X))))&
((~curious(john)<~>happy(john)))&
((creative(mary)&~kind(mary))) | ~funny(alice) | [] | null | 0 |
If mary is not generous then susan is either old or not curious and vice versa.
If someone is patient or not old then alice is strong or not old and vice versa.
Everyone who is not brave is curious or wise.
Everyone who is not brave or kind is quiet and vice versa.
If fred is funny or not humble then someone is both not rich and humble.
Everyone who is not calm or happy is not calm and vice versa.
If fred is both not quiet and not rich then someone is either not happy or strong.
If paul is not funny or brave then lucy is both strong and not quiet and vice versa.
If someone is either not old or tall then alice is both wise and calm and vice versa.
If someone is either brave or old then someone is not tall and vice versa.
If mary is either humble or brave then someone is either not quiet or wise.
Everyone who is humble is either humble or not wise and vice versa.
Everyone who is either not happy or not quiet is either creative or not curious and vice versa.
If someone is not calm or brave then fred is either strong or not kind and vice versa.
Everyone who is not patient or kind is either wise or old.
If someone is both wise and not calm then susan is both not creative and creative and vice versa.
Mary is funny.
Fred is patient.
Someone is generous.
Paul is curious or wise.
Someone is both tall and quiet.
Someone is generous or not generous.
Someone is either generous or not generous.
John is not patient. | Susan is not wise. | contradiction | ((~generous(mary))<=>((old(susan)<~>~curious(susan))))&
((?[X]:((patient(X)|~old(X))))<=>((strong(alice)|~old(alice))))&
(![X]:(~brave(X)=>(curious(X)|wise(X))))&
(![X]:((~brave(X)|kind(X))<=>quiet(X)))&
(((funny(fred)|~humble(fred)))=>(?[X]:((~rich(X)&humble(X)))))&
(![X]:((~calm(X)|happy(X))<=>~calm(X)))&
(((~quiet(fred)&~rich(fred)))=>(?[X]:((~happy(X)<~>strong(X)))))&
(((~funny(paul)|brave(paul)))<=>((strong(lucy)&~quiet(lucy))))&
((?[X]:((~old(X)<~>tall(X))))<=>((wise(alice)&calm(alice))))&
((?[X]:((brave(X)<~>old(X))))<=>(?[X]:(~tall(X))))&
(((humble(mary)<~>brave(mary)))=>(?[X]:((~quiet(X)<~>wise(X)))))&
(![X]:(humble(X)<=>(humble(X)<~>~wise(X))))&
(![X]:((~happy(X)<~>~quiet(X))<=>(creative(X)<~>~curious(X))))&
((?[X]:((~calm(X)|brave(X))))<=>((strong(fred)<~>~kind(fred))))&
(![X]:((~patient(X)|kind(X))=>(wise(X)<~>old(X))))&
((?[X]:((wise(X)&~calm(X))))<=>((~creative(susan)&creative(susan))))&
(funny(mary))&
(patient(fred))&
(?[X]:(generous(X)))&
((curious(paul)|wise(paul)))&
(?[X]:((tall(X)&quiet(X))))&
(?[X]:((generous(X)|~generous(X))))&
(?[X]:((generous(X)<~>~generous(X))))&
(~patient(john)) | ~wise(susan) | [
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 880425141526283789511247
% SZS output start Proof for 880425141526283789511247
12. ! [X0] : (humble(X0) <=> (humble(X0) <~> ~wise(X0))) [input p11]
25. ~wise(susan) [input hypothesis]
64. ! [X0] : ((humble(X0) | ((humble(X0) | wise(X0)) & (~wise(X0) | ~humble(X0)))) & (((wise(X0) | ~humble(X0)) & (~wise(X0) | humble(X0))) | ~humble(X0))) [nnf transformation 12]
126. wise(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 64]
128. humble(X0) | humble(X0) | wise(X0) [cnf transformation 64]
161. ~wise(susan) [cnf transformation 25]
162. wise(X0) | ~humble(X0) [duplicate literal removal 126]
163. humble(X0) | wise(X0) [duplicate literal removal 128]
338. wise(X0) [subsumption resolution 162,163]
377. $false [subsumption resolution 161,338]
% SZS output end Proof for 880425141526283789511247
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is not rich or not generous then someone is not brave and vice versa.
Everyone who is both not patient and strong is tall or not funny and vice versa.
If fred is funny or wise then someone is either patient or not generous and vice versa.
If someone is not quiet or brave then fred is curious or old and vice versa.
If paul is not patient then someone is brave.
Everyone who is both curious and rich is not brave.
If alice is wise then lucy is both not curious and kind and vice versa.
Everyone who is patient or not happy is either not calm or brave.
If someone is either not patient or quiet then fred is not humble or calm.
If someone is generous then someone is both tall and not curious and vice versa.
Everyone who is both wise and not tall is either strong or funny and vice versa.
If fred is strong or not tall then mary is both wise and funny.
If susan is kind then someone is either not quiet or strong.
If someone is not creative or brave then someone is both not tall and tall.
Everyone who is not brave or not curious is humble or not humble and vice versa.
If someone is not patient then someone is either curious or not strong.
Paul is both not rich and old.
Someone is not patient or quiet.
Someone is both not old and wise.
John is not wise or strong.
Someone is happy or strong.
Someone is either generous or strong.
Someone is either not rich or not generous. | Paul is not funny. | contradiction | (((~rich(lucy)|~generous(lucy)))<=>(?[X]:(~brave(X))))&
(![X]:((~patient(X)&strong(X))<=>(tall(X)|~funny(X))))&
(((funny(fred)|wise(fred)))<=>(?[X]:((patient(X)<~>~generous(X)))))&
((?[X]:((~quiet(X)|brave(X))))<=>((curious(fred)|old(fred))))&
((~patient(paul))=>(?[X]:(brave(X))))&
(![X]:((curious(X)&rich(X))=>~brave(X)))&
((wise(alice))<=>((~curious(lucy)&kind(lucy))))&
(![X]:((patient(X)|~happy(X))=>(~calm(X)<~>brave(X))))&
((?[X]:((~patient(X)<~>quiet(X))))=>((~humble(fred)|calm(fred))))&
((?[X]:(generous(X)))<=>(?[X]:((tall(X)&~curious(X)))))&
(![X]:((wise(X)&~tall(X))<=>(strong(X)<~>funny(X))))&
(((strong(fred)|~tall(fred)))=>((wise(mary)&funny(mary))))&
((kind(susan))=>(?[X]:((~quiet(X)<~>strong(X)))))&
((?[X]:((~creative(X)|brave(X))))=>(?[X]:((~tall(X)&tall(X)))))&
(![X]:((~brave(X)|~curious(X))<=>(humble(X)|~humble(X))))&
((?[X]:(~patient(X)))=>(?[X]:((curious(X)<~>~strong(X)))))&
((~rich(paul)&old(paul)))&
(?[X]:((~patient(X)|quiet(X))))&
(?[X]:((~old(X)&wise(X))))&
((~wise(john)|strong(john)))&
(?[X]:((happy(X)|strong(X))))&
(?[X]:((generous(X)<~>strong(X))))&
(?[X]:((~rich(X)<~>~generous(X)))) | ~funny(paul) | [
"p1",
"p4",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 5820197522342451405980242
% SZS output start Proof for 5820197522342451405980242
2. ! [X0] : ((strong(X0) & ~patient(X0)) <=> (~funny(X0) | tall(X0))) [input p1]
5. ~patient(paul) => ? [X0] : brave(X0) [input p4]
14. ? [X0] : (brave(X0) | ~creative(X0)) => ? [X0] : (tall(X0) & ~tall(X0)) [input p13]
24. ~funny(paul) [input hypothesis]
26. ? [X0] : (brave(X0) | ~creative(X0)) => ? [X1] : (tall(X1) & ~tall(X1)) [rectify 14]
28. ? [X0] : brave(X0) => ? [X1] : (tall(X1) & ~tall(X1)) [pure predicate removal 26]
31. ? [X0] : brave(X0) | patient(paul) [ennf transformation 5]
39. ? [X1] : (tall(X1) & ~tall(X1)) | ! [X0] : ~brave(X0) [ennf transformation 28]
46. ! [X0] : (((strong(X0) & ~patient(X0)) | (funny(X0) & ~tall(X0))) & ((~funny(X0) | tall(X0)) | (~strong(X0) | patient(X0)))) [nnf transformation 2]
47. ! [X0] : (((strong(X0) & ~patient(X0)) | (funny(X0) & ~tall(X0))) & (~funny(X0) | tall(X0) | ~strong(X0) | patient(X0))) [flattening 46]
58. ? [X0] : brave(X0) => brave(sK3) [choice axiom]
59. brave(sK3) | patient(paul) [skolemisation 31,58]
74. ? [X0] : (tall(X0) & ~tall(X0)) | ! [X1] : ~brave(X1) [rectify 39]
75. ? [X0] : (tall(X0) & ~tall(X0)) => (tall(sK7) & ~tall(sK7)) [choice axiom]
76. (tall(sK7) & ~tall(sK7)) | ! [X1] : ~brave(X1) [skolemisation 74,75]
98. ~patient(X0) | funny(X0) [cnf transformation 47]
111. brave(sK3) | patient(paul) [cnf transformation 59]
135. ~tall(sK7) | ~brave(X1) [cnf transformation 76]
136. tall(sK7) | ~brave(X1) [cnf transformation 76]
153. ~funny(paul) [cnf transformation 24]
219. 15 <=> ! [X1] : ~brave(X1) [avatar definition]
220. ~brave(X1) <- (15) [avatar component clause 219]
227. 17 <=> patient(paul) [avatar definition]
229. patient(paul) <- (17) [avatar component clause 227]
231. 18 <=> brave(sK3) [avatar definition]
233. brave(sK3) <- (18) [avatar component clause 231]
234. 17 | 18 [avatar split clause 111,231,227]
325. 38 <=> tall(sK7) [avatar definition]
328. 15 | 38 [avatar split clause 136,325,219]
329. 15 | ~38 [avatar split clause 135,325,219]
378. funny(paul) <- (17) [resolution 98,229]
379. $false <- (17) [subsumption resolution 378,153]
380. ~17 [avatar contradiction clause 379]
381. $false <- (15, 18) [subsumption resolution 233,220]
382. ~15 | ~18 [avatar contradiction clause 381]
383. $false [avatar sat refutation 234,328,329,380,382]
% SZS output end Proof for 5820197522342451405980242
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not strong and creative is not quiet or not old and vice versa. If someone is not calm then someone is calm and vice versa. Everyone who is both not rich and brave is not patient and vice versa. Everyone who is either rich or old is not tall or not brave and vice versa. If someone is brave then someone is funny and vice versa. If someone is both quiet and not patient then paul is both not strong and funny. If someone is both rich and not strong then someone is both wise and funny and vice versa. If someone is not humble then mary is either patient or not tall and vice versa. Everyone who is not patient or not tall is calm or humble and vice versa. If someone is either calm or humble then someone is both not quiet and rich. If mary is humble or old then john is humble or not kind. Everyone who is either strong or brave is not rich. Everyone who is strong or not creative is either not curious or not calm. Everyone who is either not curious or not strong is not rich or not old. If mary is not kind then someone is quiet and vice versa. Everyone who is both generous and happy is either quiet or patient. Paul is happy or humble. Someone is either not kind or not old. Someone is either not curious or not generous. Someone is not funny. Alice is both not generous and quiet. John is not tall or calm. Someone is both curious and wise. John is both not wise and quiet. | Mary is old. | neutral | (![X]:((~strong(X)&creative(X))<=>(~quiet(X)|~old(X))))&
((?[X]:(~calm(X)))<=>(?[X]:(calm(X))))&
(![X]:((~rich(X)&brave(X))<=>~patient(X)))&
(![X]:((rich(X)<~>old(X))<=>(~tall(X)|~brave(X))))&
((?[X]:(brave(X)))<=>(?[X]:(funny(X))))&
((?[X]:((quiet(X)&~patient(X))))=>((~strong(paul)&funny(paul))))&
((?[X]:((rich(X)&~strong(X))))<=>(?[X]:((wise(X)&funny(X)))))&
((?[X]:(~humble(X)))<=>((patient(mary)<~>~tall(mary))))&
(![X]:((~patient(X)|~tall(X))<=>(calm(X)|humble(X))))&
((?[X]:((calm(X)<~>humble(X))))=>(?[X]:((~quiet(X)&rich(X)))))&
(((humble(mary)|old(mary)))=>((humble(john)|~kind(john))))&
(![X]:((strong(X)<~>brave(X))=>~rich(X)))&
(![X]:((strong(X)|~creative(X))=>(~curious(X)<~>~calm(X))))&
(![X]:((~curious(X)<~>~strong(X))=>(~rich(X)|~old(X))))&
((~kind(mary))<=>(?[X]:(quiet(X))))&
(![X]:((generous(X)&happy(X))=>(quiet(X)<~>patient(X))))&
((happy(paul)|humble(paul)))&
(?[X]:((~kind(X)<~>~old(X))))&
(?[X]:((~curious(X)<~>~generous(X))))&
(?[X]:(~funny(X)))&
((~generous(alice)&quiet(alice)))&
((~tall(john)|calm(john)))&
(?[X]:((curious(X)&wise(X))))&
((~wise(john)&quiet(john))) | old(mary) | [] | null | 0 |
If john is both not wise and not kind then paul is either not curious or old. If someone is either funny or not strong then lucy is both humble and calm and vice versa. If john is both brave and not brave then alice is either not wise or not tall and vice versa. If someone is curious or not kind then john is not kind or not happy. Everyone who is both creative and not wise is either not brave or not patient and vice versa. Everyone who is both rich and kind is calm or patient and vice versa. If someone is both not calm and not curious then susan is not quiet or tall. If fred is curious then paul is not tall. Everyone who is either wise or curious is not funny or tall. Everyone who is both not old and not strong is either tall or brave. If someone is either not wise or not curious then paul is not creative. Everyone who is either not kind or patient is both patient and calm and vice versa. Everyone who is not patient is both tall and not funny and vice versa. Everyone who is either not humble or calm is both not curious and not creative and vice versa. Everyone who is not curious or not patient is either not wise or not quiet. Everyone who is not creative or not humble is either not quiet or wise and vice versa. Someone is either brave or generous. Alice is not patient or not tall. Someone is not rich. Someone is either strong or funny. Alice is generous or wise. John is either brave or creative. | Susan is not generous. | neutral | (((~wise(john)&~kind(john)))=>((~curious(paul)<~>old(paul))))&
((?[X]:((funny(X)<~>~strong(X))))<=>((humble(lucy)&calm(lucy))))&
(((brave(john)&~brave(john)))<=>((~wise(alice)<~>~tall(alice))))&
((?[X]:((curious(X)|~kind(X))))=>((~kind(john)|~happy(john))))&
(![X]:((creative(X)&~wise(X))<=>(~brave(X)<~>~patient(X))))&
(![X]:((rich(X)&kind(X))<=>(calm(X)|patient(X))))&
((?[X]:((~calm(X)&~curious(X))))=>((~quiet(susan)|tall(susan))))&
((curious(fred))=>(~tall(paul)))&
(![X]:((wise(X)<~>curious(X))=>(~funny(X)|tall(X))))&
(![X]:((~old(X)&~strong(X))=>(tall(X)<~>brave(X))))&
((?[X]:((~wise(X)<~>~curious(X))))=>(~creative(paul)))&
(![X]:((~kind(X)<~>patient(X))<=>(patient(X)&calm(X))))&
(![X]:(~patient(X)<=>(tall(X)&~funny(X))))&
(![X]:((~humble(X)<~>calm(X))<=>(~curious(X)&~creative(X))))&
(![X]:((~curious(X)|~patient(X))=>(~wise(X)<~>~quiet(X))))&
(![X]:((~creative(X)|~humble(X))<=>(~quiet(X)<~>wise(X))))&
(?[X]:((brave(X)<~>generous(X))))&
((~patient(alice)|~tall(alice)))&
(?[X]:(~rich(X)))&
(?[X]:((strong(X)<~>funny(X))))&
((generous(alice)|wise(alice)))&
((brave(john)<~>creative(john))) | ~generous(susan) | [] | null | 0 |
If someone is either not generous or calm then susan is both not rich and rich and vice versa.
If paul is either humble or not happy then someone is not old and vice versa.
Everyone who is not funny or creative is rich or wise.
If someone is either not happy or not humble then someone is both funny and not wise and vice versa.
Everyone who is both not quiet and creative is funny or curious.
Everyone who is brave or wise is both generous and not brave and vice versa.
If john is not funny or kind then paul is both wise and creative.
Everyone who is creative is not generous and vice versa.
If mary is both strong and not funny then someone is either not wise or not humble.
Everyone who is either not brave or not humble is both not brave and creative.
If john is both not happy and creative then paul is both not funny and not calm.
Everyone who is either not humble or not patient is both wise and not humble.
If paul is generous or strong then paul is not patient or not kind and vice versa.
If someone is both not rich and not funny then john is not kind.
If someone is not wise or not old then someone is both happy and not tall and vice versa.
If susan is patient or not tall then susan is either quiet or kind and vice versa.
Susan is either rich or not tall.
Fred is funny.
Someone is humble or not humble.
Paul is wise.
Fred is tall or not wise.
Susan is not patient.
Fred is not generous.
Someone is strong. | John is kind. | contradiction | ((?[X]:((~generous(X)<~>calm(X))))<=>((~rich(susan)&rich(susan))))&
(((humble(paul)<~>~happy(paul)))<=>(?[X]:(~old(X))))&
(![X]:((~funny(X)|creative(X))=>(rich(X)|wise(X))))&
((?[X]:((~happy(X)<~>~humble(X))))<=>(?[X]:((funny(X)&~wise(X)))))&
(![X]:((~quiet(X)&creative(X))=>(funny(X)|curious(X))))&
(![X]:((brave(X)|wise(X))<=>(generous(X)&~brave(X))))&
(((~funny(john)|kind(john)))=>((wise(paul)&creative(paul))))&
(![X]:(creative(X)<=>~generous(X)))&
(((strong(mary)&~funny(mary)))=>(?[X]:((~wise(X)<~>~humble(X)))))&
(![X]:((~brave(X)<~>~humble(X))=>(~brave(X)&creative(X))))&
(((~happy(john)&creative(john)))=>((~funny(paul)&~calm(paul))))&
(![X]:((~humble(X)<~>~patient(X))=>(wise(X)&~humble(X))))&
(((generous(paul)|strong(paul)))<=>((~patient(paul)|~kind(paul))))&
((?[X]:((~rich(X)&~funny(X))))=>(~kind(john)))&
((?[X]:((~wise(X)|~old(X))))<=>(?[X]:((happy(X)&~tall(X)))))&
(((patient(susan)|~tall(susan)))<=>((quiet(susan)<~>kind(susan))))&
((rich(susan)<~>~tall(susan)))&
(funny(fred))&
(?[X]:((humble(X)|~humble(X))))&
(wise(paul))&
((tall(fred)|~wise(fred)))&
(~patient(susan))&
(~generous(fred))&
(?[X]:(strong(X))) | kind(john) | [
"p5",
"p6",
"p7",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 8921482297048996699831774
% SZS output start Proof for 8921482297048996699831774
6. ! [X0] : ((wise(X0) | brave(X0)) <=> (~brave(X0) & generous(X0))) [input p5]
7. (kind(john) | ~funny(john)) => (creative(paul) & wise(paul)) [input p6]
8. ! [X0] : (creative(X0) <=> ~generous(X0)) [input p7]
20. wise(paul) [input p19]
25. kind(john) [input hypothesis]
31. (creative(paul) & wise(paul)) | (~kind(john) & funny(john)) [ennf transformation 7]
53. ! [X0] : (((wise(X0) | brave(X0)) | (brave(X0) | ~generous(X0))) & ((~brave(X0) & generous(X0)) | (~wise(X0) & ~brave(X0)))) [nnf transformation 6]
54. ! [X0] : ((wise(X0) | brave(X0) | brave(X0) | ~generous(X0)) & ((~brave(X0) & generous(X0)) | (~wise(X0) & ~brave(X0)))) [flattening 53]
55. ! [X0] : ((creative(X0) | generous(X0)) & (~generous(X0) | ~creative(X0))) [nnf transformation 8]
94. ~wise(X0) | generous(X0) [cnf transformation 54]
101. creative(paul) | ~kind(john) [cnf transformation 31]
102. ~creative(X0) | ~generous(X0) [cnf transformation 55]
136. wise(paul) [cnf transformation 20]
141. kind(john) [cnf transformation 25]
211. 15 <=> kind(john) [avatar definition]
215. 16 <=> creative(paul) [avatar definition]
217. creative(paul) <- (16) [avatar component clause 215]
218. ~15 | 16 [avatar split clause 101,215,211]
225. 18 <=> wise(paul) [avatar definition]
227. wise(paul) <- (18) [avatar component clause 225]
272. 28 <=> generous(paul) [avatar definition]
342. 18 [avatar split clause 136,225]
353. 15 [avatar split clause 141,211]
362. generous(paul) <- (18) [resolution 94,227]
364. ~generous(paul) <- (16) [resolution 102,217]
367. ~28 | ~16 [avatar split clause 364,215,272]
368. 28 | ~18 [avatar split clause 362,225,272]
369. $false [avatar sat refutation 218,342,353,367,368]
% SZS output end Proof for 8921482297048996699831774
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not kind is both kind and quiet.
If someone is old or not creative then john is both patient and creative and vice versa.
If lucy is either not patient or brave then lucy is curious.
Everyone who is not brave is rich or humble and vice versa.
Everyone who is either not curious or rich is either wise or creative.
If someone is either generous or not patient then someone is wise or not calm and vice versa.
Everyone who is curious is both old and not patient.
If fred is not humble then fred is not creative.
If someone is both funny and not generous then someone is not old or rich and vice versa.
If paul is either creative or happy then someone is either quiet or brave.
Everyone who is both not curious and happy is either not creative or not curious.
If mary is both quiet and tall then someone is either not wise or not humble and vice versa.
Everyone who is not patient is either not generous or not humble.
Everyone who is not old or not kind is funny or quiet.
Everyone who is wise or kind is both not generous and quiet and vice versa.
If mary is not quiet or humble then lucy is both not funny and not calm and vice versa.
Mary is not calm or strong.
Someone is kind or not tall.
Paul is not calm or not old.
Someone is either quiet or not strong.
Paul is not calm.
Fred is not wise.
Someone is not rich or not happy. | John is not generous. | entailment | (![X]:(~kind(X)=>(kind(X)&quiet(X))))&
((?[X]:((old(X)|~creative(X))))<=>((patient(john)&creative(john))))&
(((~patient(lucy)<~>brave(lucy)))=>(curious(lucy)))&
(![X]:(~brave(X)<=>(rich(X)|humble(X))))&
(![X]:((~curious(X)<~>rich(X))=>(wise(X)<~>creative(X))))&
((?[X]:((generous(X)<~>~patient(X))))<=>(?[X]:((wise(X)|~calm(X)))))&
(![X]:(curious(X)=>(old(X)&~patient(X))))&
((~humble(fred))=>(~creative(fred)))&
((?[X]:((funny(X)&~generous(X))))<=>(?[X]:((~old(X)|rich(X)))))&
(((creative(paul)<~>happy(paul)))=>(?[X]:((quiet(X)<~>brave(X)))))&
(![X]:((~curious(X)&happy(X))=>(~creative(X)<~>~curious(X))))&
(((quiet(mary)&tall(mary)))<=>(?[X]:((~wise(X)<~>~humble(X)))))&
(![X]:(~patient(X)=>(~generous(X)<~>~humble(X))))&
(![X]:((~old(X)|~kind(X))=>(funny(X)|quiet(X))))&
(![X]:((wise(X)|kind(X))<=>(~generous(X)&quiet(X))))&
(((~quiet(mary)|humble(mary)))<=>((~funny(lucy)&~calm(lucy))))&
((~calm(mary)|strong(mary)))&
(?[X]:((kind(X)|~tall(X))))&
((~calm(paul)|~old(paul)))&
(?[X]:((quiet(X)<~>~strong(X))))&
(~calm(paul))&
(~wise(fred))&
(?[X]:((~rich(X)|~happy(X)))) | ~generous(john) | [
"p0",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 921745229326543817502438
% SZS output start Proof for 921745229326543817502438
1. ! [X0] : (~kind(X0) => (quiet(X0) & kind(X0))) [input p0]
15. ! [X0] : ((kind(X0) | wise(X0)) <=> (quiet(X0) & ~generous(X0))) [input p14]
24. generous(john) [input hypothesis]
27. ! [X0] : ((quiet(X0) & kind(X0)) | kind(X0)) [ennf transformation 1]
67. ! [X0] : (((kind(X0) | wise(X0)) | (~quiet(X0) | generous(X0))) & ((quiet(X0) & ~generous(X0)) | (~kind(X0) & ~wise(X0)))) [nnf transformation 15]
68. ! [X0] : ((kind(X0) | wise(X0) | ~quiet(X0) | generous(X0)) & ((quiet(X0) & ~generous(X0)) | (~kind(X0) & ~wise(X0)))) [flattening 67]
78. kind(X0) | kind(X0) [cnf transformation 27]
125. ~generous(X0) | ~kind(X0) [cnf transformation 68]
142. generous(john) [cnf transformation 24]
144. kind(X0) [duplicate literal removal 78]
308. ~generous(X0) [subsumption resolution 125,144]
354. $false [subsumption resolution 142,308]
% SZS output end Proof for 921745229326543817502438
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not strong is strong or calm. Everyone who is not brave is either not rich or brave and vice versa. Everyone who is either not brave or old is tall or not happy. Everyone who is creative is either not quiet or not patient and vice versa. If fred is either not happy or funny then mary is calm or patient. If someone is either wise or not wise then lucy is not kind or old and vice versa. Everyone who is not strong or not curious is both strong and wise. If someone is either not patient or not rich then someone is wise and vice versa. If alice is both not brave and not kind then someone is not humble or not happy. Everyone who is not funny or not generous is both brave and generous. Everyone who is either not generous or kind is both calm and patient. Everyone who is rich is both not tall and kind and vice versa. If someone is strong then susan is old or calm and vice versa. Everyone who is both curious and calm is funny. If someone is funny or not happy then someone is either not quiet or tall and vice versa. Everyone who is brave is either creative or tall. Someone is not wise. Someone is either not generous or not humble. Someone is strong. Someone is both not tall and not kind. Someone is both generous and not humble. Someone is both not quiet and strong. Someone is calm or strong. | Susan is rich. | contradiction | (![X]:(~strong(X)=>(strong(X)|calm(X))))&
(![X]:(~brave(X)<=>(~rich(X)<~>brave(X))))&
(![X]:((~brave(X)<~>old(X))=>(tall(X)|~happy(X))))&
(![X]:(creative(X)<=>(~quiet(X)<~>~patient(X))))&
(((~happy(fred)<~>funny(fred)))=>((calm(mary)|patient(mary))))&
((?[X]:((wise(X)<~>~wise(X))))<=>((~kind(lucy)|old(lucy))))&
(![X]:((~strong(X)|~curious(X))=>(strong(X)&wise(X))))&
((?[X]:((~patient(X)<~>~rich(X))))<=>(?[X]:(wise(X))))&
(((~brave(alice)&~kind(alice)))=>(?[X]:((~humble(X)|~happy(X)))))&
(![X]:((~funny(X)|~generous(X))=>(brave(X)&generous(X))))&
(![X]:((~generous(X)<~>kind(X))=>(calm(X)&patient(X))))&
(![X]:(rich(X)<=>(~tall(X)&kind(X))))&
((?[X]:(strong(X)))<=>((old(susan)|calm(susan))))&
(![X]:((curious(X)&calm(X))=>funny(X)))&
((?[X]:((funny(X)|~happy(X))))<=>(?[X]:((~quiet(X)<~>tall(X)))))&
(![X]:(brave(X)=>(creative(X)<~>tall(X))))&
(?[X]:(~wise(X)))&
(?[X]:((~generous(X)<~>~humble(X))))&
(?[X]:(strong(X)))&
(?[X]:((~tall(X)&~kind(X))))&
(?[X]:((generous(X)&~humble(X))))&
(?[X]:((~quiet(X)&strong(X))))&
(?[X]:((calm(X)|strong(X)))) | rich(susan) | [
"p1",
"hypothesis"
] | % SZS status Unsatisfiable for 7947381877319571341344364
% SZS output start Proof for 7947381877319571341344364
2. ! [X0] : (~brave(X0) <=> (~rich(X0) <~> brave(X0))) [input p1]
24. rich(susan) [input hypothesis]
41. ! [X0] : ((~brave(X0) | ((~rich(X0) | ~brave(X0)) & (brave(X0) | rich(X0)))) & (((~brave(X0) | rich(X0)) & (brave(X0) | ~rich(X0))) | brave(X0))) [nnf transformation 2]
87. brave(X0) | ~rich(X0) | brave(X0) [cnf transformation 41]
90. ~brave(X0) | ~rich(X0) | ~brave(X0) [cnf transformation 41]
148. rich(susan) [cnf transformation 24]
153. brave(X0) | ~rich(X0) [duplicate literal removal 87]
154. ~brave(X0) | ~rich(X0) [duplicate literal removal 90]
156. ~rich(X0) [subsumption resolution 153,154]
271. $false [subsumption resolution 148,156]
% SZS output end Proof for 7947381877319571341344364
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
If someone is generous or not quiet then susan is not brave or old and vice versa.
If someone is patient or generous then someone is either not kind or not funny and vice versa.
Everyone who is not quiet is both not old and tall and vice versa.
Everyone who is tall or not curious is either happy or not brave and vice versa.
If john is strong or not brave then john is either funny or patient and vice versa.
Everyone who is either not calm or kind is not rich or not generous and vice versa.
If lucy is either generous or not creative then paul is generous.
Everyone who is both kind and not calm is both kind and rich.
Everyone who is either not happy or creative is patient or not quiet.
Everyone who is not old is not strong and vice versa.
Everyone who is rich is either happy or tall and vice versa.
If someone is both not quiet and not tall then someone is not old.
Everyone who is not patient or brave is either patient or not strong.
If someone is not rich or not happy then paul is not happy and vice versa.
Everyone who is both not kind and calm is either not strong or happy.
If paul is tall or not humble then someone is both quiet and not strong.
Fred is either old or curious.
Lucy is either not calm or not happy.
Alice is both calm and not old.
Alice is either not rich or not tall.
Someone is both strong and not generous.
Paul is both rich and not humble.
Fred is either not brave or not happy. | Alice is kind. | entailment | ((?[X]:((generous(X)|~quiet(X))))<=>((~brave(susan)|old(susan))))&
((?[X]:((patient(X)|generous(X))))<=>(?[X]:((~kind(X)<~>~funny(X)))))&
(![X]:(~quiet(X)<=>(~old(X)&tall(X))))&
(![X]:((tall(X)|~curious(X))<=>(happy(X)<~>~brave(X))))&
(((strong(john)|~brave(john)))<=>((funny(john)<~>patient(john))))&
(![X]:((~calm(X)<~>kind(X))<=>(~rich(X)|~generous(X))))&
(((generous(lucy)<~>~creative(lucy)))=>(generous(paul)))&
(![X]:((kind(X)&~calm(X))=>(kind(X)&rich(X))))&
(![X]:((~happy(X)<~>creative(X))=>(patient(X)|~quiet(X))))&
(![X]:(~old(X)<=>~strong(X)))&
(![X]:(rich(X)<=>(happy(X)<~>tall(X))))&
((?[X]:((~quiet(X)&~tall(X))))=>(?[X]:(~old(X))))&
(![X]:((~patient(X)|brave(X))=>(patient(X)<~>~strong(X))))&
((?[X]:((~rich(X)|~happy(X))))<=>(~happy(paul)))&
(![X]:((~kind(X)&calm(X))=>(~strong(X)<~>happy(X))))&
(((tall(paul)|~humble(paul)))=>(?[X]:((quiet(X)&~strong(X)))))&
((old(fred)<~>curious(fred)))&
((~calm(lucy)<~>~happy(lucy)))&
((calm(alice)&~old(alice)))&
((~rich(alice)<~>~tall(alice)))&
(?[X]:((strong(X)&~generous(X))))&
((rich(paul)&~humble(paul)))&
((~brave(fred)<~>~happy(fred))) | kind(alice) | [
"p5",
"p9",
"p10",
"p14",
"p18",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 7446604694455626023880177
% SZS output start Proof for 7446604694455626023880177
6. ! [X0] : ((~calm(X0) <~> kind(X0)) <=> (~generous(X0) | ~rich(X0))) [input p5]
10. ! [X0] : (~old(X0) <=> ~strong(X0)) [input p9]
11. ! [X0] : (rich(X0) <=> (happy(X0) <~> tall(X0))) [input p10]
15. ! [X0] : ((calm(X0) & ~kind(X0)) => (~strong(X0) <~> happy(X0))) [input p14]
19. ~old(alice) & calm(alice) [input p18]
20. ~rich(alice) <~> ~tall(alice) [input p19]
24. ~kind(alice) [input hypothesis]
34. ! [X0] : ((~strong(X0) <~> happy(X0)) | (~calm(X0) | kind(X0))) [ennf transformation 15]
35. ! [X0] : ((~strong(X0) <~> happy(X0)) | ~calm(X0) | kind(X0)) [flattening 34]
53. ! [X0] : ((((~kind(X0) | calm(X0)) & (kind(X0) | ~calm(X0))) | (generous(X0) & rich(X0))) & ((~generous(X0) | ~rich(X0)) | ((~calm(X0) | ~kind(X0)) & (kind(X0) | calm(X0))))) [nnf transformation 6]
54. ! [X0] : ((((~kind(X0) | calm(X0)) & (kind(X0) | ~calm(X0))) | (generous(X0) & rich(X0))) & (~generous(X0) | ~rich(X0) | ((~calm(X0) | ~kind(X0)) & (kind(X0) | calm(X0))))) [flattening 53]
57. ! [X0] : ((~old(X0) | strong(X0)) & (~strong(X0) | old(X0))) [nnf transformation 10]
58. ! [X0] : ((rich(X0) | ((happy(X0) | ~tall(X0)) & (tall(X0) | ~happy(X0)))) & (((~tall(X0) | ~happy(X0)) & (tall(X0) | happy(X0))) | ~rich(X0))) [nnf transformation 11]
67. ! [X0] : (((~happy(X0) | strong(X0)) & (happy(X0) | ~strong(X0))) | ~calm(X0) | kind(X0)) [nnf transformation 35]
72. (tall(alice) | rich(alice)) & (~tall(alice) | ~rich(alice)) [nnf transformation 20]
103. ~calm(X0) | kind(X0) | rich(X0) [cnf transformation 54]
113. ~strong(X0) | old(X0) [cnf transformation 57]
115. ~rich(X0) | happy(X0) | tall(X0) [cnf transformation 58]
128. ~calm(X0) | strong(X0) | ~happy(X0) | kind(X0) [cnf transformation 67]
137. calm(alice) [cnf transformation 19]
138. ~old(alice) [cnf transformation 19]
139. ~tall(alice) | ~rich(alice) [cnf transformation 72]
147. ~kind(alice) [cnf transformation 24]
304. 34 <=> rich(alice) [avatar definition]
306. rich(alice) <- (34) [avatar component clause 304]
308. 35 <=> tall(alice) [avatar definition]
309. ~tall(alice) <- (~35) [avatar component clause 308]
312. ~34 | ~35 [avatar split clause 139,308,304]
340. kind(alice) | rich(alice) [resolution 103,137]
436. rich(alice) [subsumption resolution 340,147]
437. 34 [avatar split clause 436,304]
439. happy(alice) | tall(alice) <- (34) [resolution 306,115]
440. happy(alice) <- (34, ~35) [subsumption resolution 439,309]
497. strong(alice) | ~happy(alice) | kind(alice) [resolution 128,137]
499. strong(alice) | kind(alice) <- (34, ~35) [subsumption resolution 497,440]
500. strong(alice) <- (34, ~35) [subsumption resolution 499,147]
503. old(alice) <- (34, ~35) [resolution 500,113]
505. $false <- (34, ~35) [subsumption resolution 503,138]
506. ~34 | 35 [avatar contradiction clause 505]
507. $false [avatar sat refutation 312,437,506]
% SZS output end Proof for 7446604694455626023880177
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
If someone is happy or not wise then someone is old and vice versa.
Everyone who is both not curious and not wise is both not generous and old.
If susan is not generous then someone is rich.
Everyone who is either not curious or curious is not quiet.
If fred is either quiet or not generous then fred is either old or tall.
If someone is both not funny and tall then someone is either tall or humble and vice versa.
Everyone who is not kind or not strong is both not happy and wise and vice versa.
If someone is either generous or not creative then someone is both funny and humble and vice versa.
Everyone who is not generous is both not brave and not rich.
If someone is either generous or not kind then mary is wise or not wise.
If someone is not rich then john is not quiet.
Everyone who is both funny and quiet is not happy and vice versa.
Everyone who is either not old or happy is brave and vice versa.
If alice is curious then alice is both generous and not happy and vice versa.
Everyone who is creative or strong is both not funny and happy and vice versa.
Everyone who is not quiet is not curious.
Susan is not kind or not brave.
Someone is happy or not creative.
Someone is either quiet or not patient.
Someone is brave or not kind.
Someone is funny or not quiet.
Alice is not old or quiet. | Susan is not kind. | contradiction | ((?[X]:((happy(X)|~wise(X))))<=>(?[X]:(old(X))))&
(![X]:((~curious(X)&~wise(X))=>(~generous(X)&old(X))))&
((~generous(susan))=>(?[X]:(rich(X))))&
(![X]:((~curious(X)<~>curious(X))=>~quiet(X)))&
(((quiet(fred)<~>~generous(fred)))=>((old(fred)<~>tall(fred))))&
((?[X]:((~funny(X)&tall(X))))<=>(?[X]:((tall(X)<~>humble(X)))))&
(![X]:((~kind(X)|~strong(X))<=>(~happy(X)&wise(X))))&
((?[X]:((generous(X)<~>~creative(X))))<=>(?[X]:((funny(X)&humble(X)))))&
(![X]:(~generous(X)=>(~brave(X)&~rich(X))))&
((?[X]:((generous(X)<~>~kind(X))))=>((wise(mary)|~wise(mary))))&
((?[X]:(~rich(X)))=>(~quiet(john)))&
(![X]:((funny(X)&quiet(X))<=>~happy(X)))&
(![X]:((~old(X)<~>happy(X))<=>brave(X)))&
((curious(alice))<=>((generous(alice)&~happy(alice))))&
(![X]:((creative(X)|strong(X))<=>(~funny(X)&happy(X))))&
(![X]:(~quiet(X)=>~curious(X)))&
((~kind(susan)|~brave(susan)))&
(?[X]:((happy(X)|~creative(X))))&
(?[X]:((quiet(X)<~>~patient(X))))&
(?[X]:((brave(X)|~kind(X))))&
(?[X]:((funny(X)|~quiet(X))))&
((~old(alice)|quiet(alice))) | ~kind(susan) | [
"p3",
"p6",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 704195314794187017615169
% SZS output start Proof for 704195314794187017615169
4. ! [X0] : ((~curious(X0) <~> curious(X0)) => ~quiet(X0)) [input p3]
7. ! [X0] : ((~strong(X0) | ~kind(X0)) <=> (wise(X0) & ~happy(X0))) [input p6]
12. ! [X0] : ((quiet(X0) & funny(X0)) <=> ~happy(X0)) [input p11]
23. ~kind(susan) [input hypothesis]
30. ! [X0] : (~quiet(X0) | (~curious(X0) <=> curious(X0))) [ennf transformation 4]
44. ! [X0] : (~quiet(X0) | ((~curious(X0) | ~curious(X0)) & (curious(X0) | curious(X0)))) [nnf transformation 30]
51. ! [X0] : (((~strong(X0) | ~kind(X0)) | (~wise(X0) | happy(X0))) & ((wise(X0) & ~happy(X0)) | (strong(X0) & kind(X0)))) [nnf transformation 7]
52. ! [X0] : ((~strong(X0) | ~kind(X0) | ~wise(X0) | happy(X0)) & ((wise(X0) & ~happy(X0)) | (strong(X0) & kind(X0)))) [flattening 51]
59. ! [X0] : (((quiet(X0) & funny(X0)) | happy(X0)) & (~happy(X0) | (~quiet(X0) | ~funny(X0)))) [nnf transformation 12]
60. ! [X0] : (((quiet(X0) & funny(X0)) | happy(X0)) & (~happy(X0) | ~quiet(X0) | ~funny(X0))) [flattening 59]
81. ~quiet(X0) | curious(X0) | curious(X0) [cnf transformation 44]
82. ~quiet(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 44]
93. ~happy(X0) | kind(X0) [cnf transformation 52]
111. quiet(X0) | happy(X0) [cnf transformation 60]
132. ~kind(susan) [cnf transformation 23]
133. ~quiet(X0) | curious(X0) [duplicate literal removal 81]
134. ~quiet(X0) | ~curious(X0) [duplicate literal removal 82]
168. ~quiet(X0) [subsumption resolution 133,134]
247. happy(X0) [subsumption resolution 111,168]
253. 26 <=> kind(susan) [avatar definition]
255. ~kind(susan) <- (~26) [avatar component clause 253]
272. ~26 [avatar split clause 132,253]
273. kind(X0) [resolution 93,247]
275. $false <- (~26) [resolution 273,255]
278. 26 [avatar contradiction clause 275]
279. $false [avatar sat refutation 272,278]
% SZS output end Proof for 704195314794187017615169
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either strong or not generous is both creative and generous and vice versa.
Everyone who is both not old and rich is generous.
Everyone who is either not strong or not creative is either not funny or not quiet.
If lucy is not old or not rich then someone is both tall and brave.
If someone is either calm or not happy then someone is either calm or creative.
If john is not calm then fred is either strong or funny and vice versa.
Everyone who is either not brave or not tall is not brave.
If john is either humble or quiet then susan is rich or not old.
Everyone who is not brave or not humble is tall or happy.
Everyone who is brave is either brave or not rich.
If john is generous then lucy is not quiet.
Everyone who is either quiet or not quiet is both not old and rich and vice versa.
Everyone who is not curious is both not funny and not brave.
Everyone who is not wise is either creative or not funny.
If someone is both not wise and not patient then someone is wise or kind.
Someone is curious.
Someone is curious or not generous.
Fred is either not generous or not curious.
Someone is either strong or wise.
Someone is both not old and calm.
Someone is patient.
Alice is not rich or not tall. | Fred is brave. | contradiction | (![X]:((strong(X)<~>~generous(X))<=>(creative(X)&generous(X))))&
(![X]:((~old(X)&rich(X))=>generous(X)))&
(![X]:((~strong(X)<~>~creative(X))=>(~funny(X)<~>~quiet(X))))&
(((~old(lucy)|~rich(lucy)))=>(?[X]:((tall(X)&brave(X)))))&
((?[X]:((calm(X)<~>~happy(X))))=>(?[X]:((calm(X)<~>creative(X)))))&
((~calm(john))<=>((strong(fred)<~>funny(fred))))&
(![X]:((~brave(X)<~>~tall(X))=>~brave(X)))&
(((humble(john)<~>quiet(john)))=>((rich(susan)|~old(susan))))&
(![X]:((~brave(X)|~humble(X))=>(tall(X)|happy(X))))&
(![X]:(brave(X)=>(brave(X)<~>~rich(X))))&
((generous(john))=>(~quiet(lucy)))&
(![X]:((quiet(X)<~>~quiet(X))<=>(~old(X)&rich(X))))&
(![X]:(~curious(X)=>(~funny(X)&~brave(X))))&
(![X]:(~wise(X)=>(creative(X)<~>~funny(X))))&
((?[X]:((~wise(X)&~patient(X))))=>(?[X]:((wise(X)|kind(X)))))&
(?[X]:(curious(X)))&
(?[X]:((curious(X)|~generous(X))))&
((~generous(fred)<~>~curious(fred)))&
(?[X]:((strong(X)<~>wise(X))))&
(?[X]:((~old(X)&calm(X))))&
(?[X]:(patient(X)))&
((~rich(alice)|~tall(alice))) | brave(fred) | [
"p1",
"p11",
"p12",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 1755789313411043583708791
% SZS output start Proof for 1755789313411043583708791
2. ! [X0] : ((rich(X0) & ~old(X0)) => generous(X0)) [input p1]
12. ! [X0] : ((quiet(X0) <~> ~quiet(X0)) <=> (rich(X0) & ~old(X0))) [input p11]
13. ! [X0] : (~curious(X0) => (~brave(X0) & ~funny(X0))) [input p12]
18. ~generous(fred) <~> ~curious(fred) [input p17]
23. brave(fred) [input hypothesis]
28. ! [X0] : (generous(X0) | (~rich(X0) | old(X0))) [ennf transformation 2]
29. ! [X0] : (generous(X0) | ~rich(X0) | old(X0)) [flattening 28]
40. ! [X0] : ((~brave(X0) & ~funny(X0)) | curious(X0)) [ennf transformation 13]
55. ! [X0] : ((((quiet(X0) | ~quiet(X0)) & (~quiet(X0) | quiet(X0))) | (~rich(X0) | old(X0))) & ((rich(X0) & ~old(X0)) | ((quiet(X0) | quiet(X0)) & (~quiet(X0) | ~quiet(X0))))) [nnf transformation 12]
56. ! [X0] : ((((quiet(X0) | ~quiet(X0)) & (~quiet(X0) | quiet(X0))) | ~rich(X0) | old(X0)) & ((rich(X0) & ~old(X0)) | ((quiet(X0) | quiet(X0)) & (~quiet(X0) | ~quiet(X0))))) [flattening 55]
62. (curious(fred) | generous(fred)) & (~curious(fred) | ~generous(fred)) [nnf transformation 18]
74. ~rich(X0) | generous(X0) | old(X0) [cnf transformation 29]
100. ~old(X0) | ~quiet(X0) | ~quiet(X0) [cnf transformation 56]
101. ~old(X0) | quiet(X0) | quiet(X0) [cnf transformation 56]
102. rich(X0) | ~quiet(X0) | ~quiet(X0) [cnf transformation 56]
103. rich(X0) | quiet(X0) | quiet(X0) [cnf transformation 56]
107. ~brave(X0) | curious(X0) [cnf transformation 40]
112. ~curious(fred) | ~generous(fred) [cnf transformation 62]
119. brave(fred) [cnf transformation 23]
120. ~old(X0) | ~quiet(X0) [duplicate literal removal 100]
121. ~old(X0) | quiet(X0) [duplicate literal removal 101]
122. rich(X0) | ~quiet(X0) [duplicate literal removal 102]
123. quiet(X0) | rich(X0) [duplicate literal removal 103]
210. rich(X0) [subsumption resolution 122,123]
211. ~old(X0) [subsumption resolution 120,121]
222. 20 <=> generous(fred) [avatar definition]
223. ~generous(fred) <- (~20) [avatar component clause 222]
226. 21 <=> curious(fred) [avatar definition]
230. ~20 | ~21 [avatar split clause 112,226,222]
245. curious(fred) [resolution 107,119]
249. 21 [avatar split clause 245,226]
258. generous(X0) | old(X0) [resolution 74,210]
259. generous(X0) [subsumption resolution 258,211]
261. $false <- (~20) [resolution 259,223]
263. 20 [avatar contradiction clause 261]
265. $false [avatar sat refutation 230,249,263]
% SZS output end Proof for 1755789313411043583708791
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is funny or old is either tall or not rich. Everyone who is both wise and humble is wise. Everyone who is not tall or brave is brave and vice versa. If susan is either not curious or not wise then john is both patient and not calm and vice versa. If fred is not wise then someone is kind or not funny and vice versa. If someone is both wise and patient then someone is both not calm and not tall and vice versa. If someone is not happy then mary is either old or not rich and vice versa. Everyone who is either patient or tall is both old and calm. Everyone who is both happy and not tall is either not kind or not funny. Everyone who is either not humble or not kind is tall and vice versa. Everyone who is not old is quiet or calm. Everyone who is humble or not happy is both not old and kind and vice versa. Everyone who is not generous is either wise or curious. Everyone who is either not humble or not tall is both strong and not old. Everyone who is kind or not funny is rich or not strong and vice versa. Everyone who is either not brave or strong is tall or not patient and vice versa. Mary is either rich or not humble. Someone is not generous or tall. Fred is both wise and old. Someone is either not brave or happy. Alice is either wise or not tall. Someone is both not old and brave. Paul is either not quiet or not generous. Someone is either not quiet or not brave. | Mary is not brave. | contradiction | (![X]:((funny(X)|old(X))=>(tall(X)<~>~rich(X))))&
(![X]:((wise(X)&humble(X))=>wise(X)))&
(![X]:((~tall(X)|brave(X))<=>brave(X)))&
(((~curious(susan)<~>~wise(susan)))<=>((patient(john)&~calm(john))))&
((~wise(fred))<=>(?[X]:((kind(X)|~funny(X)))))&
((?[X]:((wise(X)&patient(X))))<=>(?[X]:((~calm(X)&~tall(X)))))&
((?[X]:(~happy(X)))<=>((old(mary)<~>~rich(mary))))&
(![X]:((patient(X)<~>tall(X))=>(old(X)&calm(X))))&
(![X]:((happy(X)&~tall(X))=>(~kind(X)<~>~funny(X))))&
(![X]:((~humble(X)<~>~kind(X))<=>tall(X)))&
(![X]:(~old(X)=>(quiet(X)|calm(X))))&
(![X]:((humble(X)|~happy(X))<=>(~old(X)&kind(X))))&
(![X]:(~generous(X)=>(wise(X)<~>curious(X))))&
(![X]:((~humble(X)<~>~tall(X))=>(strong(X)&~old(X))))&
(![X]:((kind(X)|~funny(X))<=>(rich(X)|~strong(X))))&
(![X]:((~brave(X)<~>strong(X))<=>(tall(X)|~patient(X))))&
((rich(mary)<~>~humble(mary)))&
(?[X]:((~generous(X)|tall(X))))&
((wise(fred)&old(fred)))&
(?[X]:((~brave(X)<~>happy(X))))&
((wise(alice)<~>~tall(alice)))&
(?[X]:((~old(X)&brave(X))))&
((~quiet(paul)<~>~generous(paul)))&
(?[X]:((~quiet(X)<~>~brave(X)))) | ~brave(mary) | [
"p2",
"p4",
"p6",
"p11",
"p13",
"p16",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 7811994604996372625650599
% SZS output start Proof for 7811994604996372625650599
3. ! [X0] : ((brave(X0) | ~tall(X0)) <=> brave(X0)) [input p2]
5. ~wise(fred) <=> ? [X0] : (~funny(X0) | kind(X0)) [input p4]
7. ? [X0] : ~happy(X0) <=> (old(mary) <~> ~rich(mary)) [input p6]
12. ! [X0] : ((~happy(X0) | humble(X0)) <=> (kind(X0) & ~old(X0))) [input p11]
14. ! [X0] : ((~humble(X0) <~> ~tall(X0)) => (~old(X0) & strong(X0))) [input p13]
17. rich(mary) <~> ~humble(mary) [input p16]
19. old(fred) & wise(fred) [input p18]
25. ~brave(mary) [input hypothesis]
36. ! [X0] : ((~old(X0) & strong(X0)) | (~humble(X0) <=> ~tall(X0))) [ennf transformation 14]
38. ! [X0] : (((brave(X0) | ~tall(X0)) | ~brave(X0)) & (brave(X0) | (~brave(X0) & tall(X0)))) [nnf transformation 3]
39. ! [X0] : ((brave(X0) | ~tall(X0) | ~brave(X0)) & (brave(X0) | (~brave(X0) & tall(X0)))) [flattening 38]
42. (~wise(fred) | ! [X0] : (funny(X0) & ~kind(X0))) & (? [X0] : (~funny(X0) | kind(X0)) | wise(fred)) [nnf transformation 5]
43. (~wise(fred) | ! [X0] : (funny(X0) & ~kind(X0))) & (? [X1] : (~funny(X1) | kind(X1)) | wise(fred)) [rectify 42]
44. ? [X1] : (~funny(X1) | kind(X1)) => (~funny(sK0) | kind(sK0)) [choice axiom]
45. (~wise(fred) | ! [X0] : (funny(X0) & ~kind(X0))) & ((~funny(sK0) | kind(sK0)) | wise(fred)) [skolemisation 43,44]
51. (? [X0] : ~happy(X0) | ((old(mary) | rich(mary)) & (~rich(mary) | ~old(mary)))) & (((rich(mary) | ~old(mary)) & (~rich(mary) | old(mary))) | ! [X0] : happy(X0)) [nnf transformation 7]
52. (? [X0] : ~happy(X0) | ((old(mary) | rich(mary)) & (~rich(mary) | ~old(mary)))) & (((rich(mary) | ~old(mary)) & (~rich(mary) | old(mary))) | ! [X1] : happy(X1)) [rectify 51]
53. ? [X0] : ~happy(X0) => ~happy(sK3) [choice axiom]
54. (~happy(sK3) | ((old(mary) | rich(mary)) & (~rich(mary) | ~old(mary)))) & (((rich(mary) | ~old(mary)) & (~rich(mary) | old(mary))) | ! [X1] : happy(X1)) [skolemisation 52,53]
58. ! [X0] : (((~happy(X0) | humble(X0)) | (~kind(X0) | old(X0))) & ((kind(X0) & ~old(X0)) | (happy(X0) & ~humble(X0)))) [nnf transformation 12]
59. ! [X0] : ((~happy(X0) | humble(X0) | ~kind(X0) | old(X0)) & ((kind(X0) & ~old(X0)) | (happy(X0) & ~humble(X0)))) [flattening 58]
61. ! [X0] : ((~old(X0) & strong(X0)) | ((~humble(X0) | tall(X0)) & (~tall(X0) | humble(X0)))) [nnf transformation 36]
66. (humble(mary) | ~rich(mary)) & (~humble(mary) | rich(mary)) [nnf transformation 17]
84. brave(X0) | tall(X0) [cnf transformation 39]
94. ~wise(fred) | ~kind(X0) [cnf transformation 45]
103. ~happy(sK3) | old(mary) | rich(mary) [cnf transformation 54]
115. ~humble(X0) | ~old(X0) [cnf transformation 59]
117. ~humble(X0) | kind(X0) [cnf transformation 59]
118. happy(X0) | kind(X0) [cnf transformation 59]
124. ~old(X0) | ~tall(X0) | humble(X0) [cnf transformation 61]
137. humble(mary) | ~rich(mary) [cnf transformation 66]
139. wise(fred) [cnf transformation 19]
151. ~brave(mary) [cnf transformation 25]
178. 6 <=> wise(fred) [avatar definition]
183. 7 <=> ! [X0] : ~kind(X0) [avatar definition]
184. ~kind(X0) <- (7) [avatar component clause 183]
185. 7 | ~6 [avatar split clause 94,178,183]
222. 16 <=> rich(mary) [avatar definition]
226. 17 <=> old(mary) [avatar definition]
230. 18 <=> happy(sK3) [avatar definition]
232. ~happy(sK3) <- (~18) [avatar component clause 230]
233. 16 | 17 | ~18 [avatar split clause 103,230,226,222]
240. ~tall(X0) | ~old(X0) [subsumption resolution 124,115]
244. 20 <=> humble(mary) [avatar definition]
246. humble(mary) <- (20) [avatar component clause 244]
247. ~16 | 20 [avatar split clause 137,244,222]
258. 6 [avatar split clause 139,178]
299. tall(mary) [resolution 84,151]
303. kind(sK3) <- (~18) [resolution 118,232]
305. $false <- (7, ~18) [subsumption resolution 303,184]
306. ~7 | 18 [avatar contradiction clause 305]
313. ~old(mary) [resolution 240,299]
317. ~17 [avatar split clause 313,226]
318. kind(mary) <- (20) [resolution 246,117]
320. $false <- (7, 20) [subsumption resolution 318,184]
321. ~7 | ~20 [avatar contradiction clause 320]
322. $false [avatar sat refutation 185,233,247,258,306,317,321]
% SZS output end Proof for 7811994604996372625650599
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not rich or not humble is either patient or not creative. Everyone who is both not strong and rich is not humble. Everyone who is calm is not patient or not strong. If someone is quiet or brave then susan is tall. Everyone who is patient or not patient is happy or humble and vice versa. Everyone who is both not strong and patient is strong or not strong and vice versa. Everyone who is either not calm or not humble is wise and vice versa. Everyone who is both not strong and generous is quiet or not brave and vice versa. If fred is either patient or generous then fred is either not patient or not tall. Everyone who is not calm is both calm and not creative. Everyone who is generous is strong or wise and vice versa. Everyone who is either generous or not calm is both patient and funny. Everyone who is not brave is not wise or rich and vice versa. If susan is funny or humble then paul is either curious or strong. If fred is either strong or happy then fred is either tall or not quiet and vice versa. Everyone who is rich is both humble and brave. Someone is both not old and not tall. Someone is not humble or not creative. Someone is either not curious or old. Someone is either not brave or calm. Someone is not funny or not rich. Mary is either not generous or curious. Alice is either not tall or not wise. Someone is either not funny or calm. | Fred is not brave. | contradiction | (![X]:((~rich(X)<~>~humble(X))=>(patient(X)<~>~creative(X))))&
(![X]:((~strong(X)&rich(X))=>~humble(X)))&
(![X]:(calm(X)=>(~patient(X)|~strong(X))))&
((?[X]:((quiet(X)|brave(X))))=>(tall(susan)))&
(![X]:((patient(X)|~patient(X))<=>(happy(X)|humble(X))))&
(![X]:((~strong(X)&patient(X))<=>(strong(X)|~strong(X))))&
(![X]:((~calm(X)<~>~humble(X))<=>wise(X)))&
(![X]:((~strong(X)&generous(X))<=>(quiet(X)|~brave(X))))&
(((patient(fred)<~>generous(fred)))=>((~patient(fred)<~>~tall(fred))))&
(![X]:(~calm(X)=>(calm(X)&~creative(X))))&
(![X]:(generous(X)<=>(strong(X)|wise(X))))&
(![X]:((generous(X)<~>~calm(X))=>(patient(X)&funny(X))))&
(![X]:(~brave(X)<=>(~wise(X)|rich(X))))&
(((funny(susan)|humble(susan)))=>((curious(paul)<~>strong(paul))))&
(((strong(fred)<~>happy(fred)))<=>((tall(fred)<~>~quiet(fred))))&
(![X]:(rich(X)=>(humble(X)&brave(X))))&
(?[X]:((~old(X)&~tall(X))))&
(?[X]:((~humble(X)|~creative(X))))&
(?[X]:((~curious(X)<~>old(X))))&
(?[X]:((~brave(X)<~>calm(X))))&
(?[X]:((~funny(X)|~rich(X))))&
((~generous(mary)<~>curious(mary)))&
((~tall(alice)<~>~wise(alice)))&
(?[X]:((~funny(X)<~>calm(X)))) | ~brave(fred) | [
"p5",
"p7",
"p10",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6011323006715193921876564
% SZS output start Proof for 6011323006715193921876564
6. ! [X0] : ((patient(X0) & ~strong(X0)) <=> (~strong(X0) | strong(X0))) [input p5]
8. ! [X0] : ((generous(X0) & ~strong(X0)) <=> (~brave(X0) | quiet(X0))) [input p7]
11. ! [X0] : (generous(X0) <=> (wise(X0) | strong(X0))) [input p10]
13. ! [X0] : (~brave(X0) <=> (rich(X0) | ~wise(X0))) [input p12]
16. ! [X0] : (rich(X0) => (brave(X0) & humble(X0))) [input p15]
25. ~brave(fred) [input hypothesis]
36. ! [X0] : ((brave(X0) & humble(X0)) | ~rich(X0)) [ennf transformation 16]
40. ! [X0] : (((patient(X0) & ~strong(X0)) | (strong(X0) & ~strong(X0))) & ((~strong(X0) | strong(X0)) | (~patient(X0) | strong(X0)))) [nnf transformation 6]
41. ! [X0] : (((patient(X0) & ~strong(X0)) | (strong(X0) & ~strong(X0))) & (~strong(X0) | strong(X0) | ~patient(X0) | strong(X0))) [flattening 40]
43. ! [X0] : (((generous(X0) & ~strong(X0)) | (brave(X0) & ~quiet(X0))) & ((~brave(X0) | quiet(X0)) | (~generous(X0) | strong(X0)))) [nnf transformation 8]
44. ! [X0] : (((generous(X0) & ~strong(X0)) | (brave(X0) & ~quiet(X0))) & (~brave(X0) | quiet(X0) | ~generous(X0) | strong(X0))) [flattening 43]
46. ! [X0] : ((generous(X0) | (~wise(X0) & ~strong(X0))) & ((wise(X0) | strong(X0)) | ~generous(X0))) [nnf transformation 11]
47. ! [X0] : ((generous(X0) | (~wise(X0) & ~strong(X0))) & (wise(X0) | strong(X0) | ~generous(X0))) [flattening 46]
49. ! [X0] : ((~brave(X0) | (~rich(X0) & wise(X0))) & ((rich(X0) | ~wise(X0)) | brave(X0))) [nnf transformation 13]
50. ! [X0] : ((~brave(X0) | (~rich(X0) & wise(X0))) & (rich(X0) | ~wise(X0) | brave(X0))) [flattening 49]
83. ~strong(X0) | ~strong(X0) [cnf transformation 41]
95. generous(X0) | brave(X0) [cnf transformation 44]
102. wise(X0) | strong(X0) | ~generous(X0) [cnf transformation 47]
109. ~wise(X0) | rich(X0) | brave(X0) [cnf transformation 50]
110. ~brave(X0) | wise(X0) [cnf transformation 50]
111. ~brave(X0) | ~rich(X0) [cnf transformation 50]
125. brave(X0) | ~rich(X0) [cnf transformation 36]
140. ~brave(fred) [cnf transformation 25]
145. ~strong(X0) [duplicate literal removal 83]
171. ~generous(X0) | wise(X0) [subsumption resolution 102,145]
205. ~rich(X0) [subsumption resolution 125,111]
259. wise(X0) | brave(X0) [resolution 171,95]
261. wise(X0) [subsumption resolution 259,110]
293. rich(X0) | brave(X0) [resolution 109,261]
294. brave(X0) [subsumption resolution 293,205]
300. $false [resolution 294,140]
% SZS output end Proof for 6011323006715193921876564
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either happy or patient is either not strong or not quiet. If someone is not creative then someone is either tall or funny. If someone is both funny and strong then alice is both quiet and not curious and vice versa. If someone is not old then someone is curious and vice versa. Everyone who is kind is not kind. If someone is either not curious or quiet then someone is tall or brave and vice versa. Everyone who is both not quiet and kind is humble or not curious and vice versa. If mary is either creative or tall then alice is not creative or rich and vice versa. If someone is not quiet or quiet then lucy is either not humble or creative. If someone is either not rich or tall then fred is curious or not happy. If someone is either not old or humble then someone is either kind or calm. Everyone who is humble is wise. If someone is not brave or not humble then alice is both tall and curious. If someone is not happy then someone is not tall or brave and vice versa. If someone is not humble then someone is either rich or quiet. Mary is either strong or not wise. Alice is either not happy or not patient. Someone is tall. Someone is both not funny and creative. Susan is either not quiet or strong. | Susan is kind. | contradiction | (![X]:((happy(X)<~>patient(X))=>(~strong(X)<~>~quiet(X))))&
((?[X]:(~creative(X)))=>(?[X]:((tall(X)<~>funny(X)))))&
((?[X]:((funny(X)&strong(X))))<=>((quiet(alice)&~curious(alice))))&
((?[X]:(~old(X)))<=>(?[X]:(curious(X))))&
(![X]:(kind(X)=>~kind(X)))&
((?[X]:((~curious(X)<~>quiet(X))))<=>(?[X]:((tall(X)|brave(X)))))&
(![X]:((~quiet(X)&kind(X))<=>(humble(X)|~curious(X))))&
(((creative(mary)<~>tall(mary)))<=>((~creative(alice)|rich(alice))))&
((?[X]:((~quiet(X)|quiet(X))))=>((~humble(lucy)<~>creative(lucy))))&
((?[X]:((~rich(X)<~>tall(X))))=>((curious(fred)|~happy(fred))))&
((?[X]:((~old(X)<~>humble(X))))=>(?[X]:((kind(X)<~>calm(X)))))&
(![X]:(humble(X)=>wise(X)))&
((?[X]:((~brave(X)|~humble(X))))=>((tall(alice)&curious(alice))))&
((?[X]:(~happy(X)))<=>(?[X]:((~tall(X)|brave(X)))))&
((?[X]:(~humble(X)))=>(?[X]:((rich(X)<~>quiet(X)))))&
((strong(mary)<~>~wise(mary)))&
((~happy(alice)<~>~patient(alice)))&
(?[X]:(tall(X)))&
(?[X]:((~funny(X)&creative(X))))&
((~quiet(susan)<~>strong(susan))) | kind(susan) | [
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 39370666341487159341347
% SZS output start Proof for 39370666341487159341347
5. ! [X0] : (kind(X0) => ~kind(X0)) [input p4]
21. kind(susan) [input hypothesis]
30. ! [X0] : (~kind(X0) | ~kind(X0)) [ennf transformation 5]
96. ~kind(X0) | ~kind(X0) [cnf transformation 30]
143. kind(susan) [cnf transformation 21]
144. ~kind(X0) [duplicate literal removal 96]
340. $false [subsumption resolution 143,144]
% SZS output end Proof for 39370666341487159341347
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not curious or not patient is not happy and vice versa. If paul is either old or creative then paul is not calm. Everyone who is either not wise or wise is both not happy and wise. Everyone who is either quiet or tall is not funny or not kind and vice versa. Everyone who is not strong is both patient and creative and vice versa. Everyone who is not patient is both wise and tall. If someone is either not kind or creative then fred is brave and vice versa. Everyone who is not wise or calm is both old and funny. If paul is either kind or calm then someone is both curious and not humble and vice versa. Everyone who is both humble and wise is happy or kind. If fred is both not calm and not creative then someone is both not humble and rich. If john is quiet or not happy then mary is not creative and vice versa. If someone is either creative or funny then someone is not strong or not humble. If someone is either not calm or not happy then paul is both not tall and not rich and vice versa. Everyone who is creative or patient is not kind and vice versa. Everyone who is either tall or wise is not wise and vice versa. Alice is either not rich or not wise. Fred is not calm or not generous. Mary is not humble. Someone is either humble or wise. Susan is not old or strong. Someone is not generous. Susan is both wise and tall. Paul is both not curious and not funny. | Fred is calm. | contradiction | (![X]:((~curious(X)<~>~patient(X))<=>~happy(X)))&
(((old(paul)<~>creative(paul)))=>(~calm(paul)))&
(![X]:((~wise(X)<~>wise(X))=>(~happy(X)&wise(X))))&
(![X]:((quiet(X)<~>tall(X))<=>(~funny(X)|~kind(X))))&
(![X]:(~strong(X)<=>(patient(X)&creative(X))))&
(![X]:(~patient(X)=>(wise(X)&tall(X))))&
((?[X]:((~kind(X)<~>creative(X))))<=>(brave(fred)))&
(![X]:((~wise(X)|calm(X))=>(old(X)&funny(X))))&
(((kind(paul)<~>calm(paul)))<=>(?[X]:((curious(X)&~humble(X)))))&
(![X]:((humble(X)&wise(X))=>(happy(X)|kind(X))))&
(((~calm(fred)&~creative(fred)))=>(?[X]:((~humble(X)&rich(X)))))&
(((quiet(john)|~happy(john)))<=>(~creative(mary)))&
((?[X]:((creative(X)<~>funny(X))))=>(?[X]:((~strong(X)|~humble(X)))))&
((?[X]:((~calm(X)<~>~happy(X))))<=>((~tall(paul)&~rich(paul))))&
(![X]:((creative(X)|patient(X))<=>~kind(X)))&
(![X]:((tall(X)<~>wise(X))<=>~wise(X)))&
((~rich(alice)<~>~wise(alice)))&
((~calm(fred)|~generous(fred)))&
(~humble(mary))&
(?[X]:((humble(X)<~>wise(X))))&
((~old(susan)|strong(susan)))&
(?[X]:(~generous(X)))&
((wise(susan)&tall(susan)))&
((~curious(paul)&~funny(paul))) | calm(fred) | [
"p2",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3985786282357598103462012
% SZS output start Proof for 3985786282357598103462012
3. ! [X0] : ((~wise(X0) <~> wise(X0)) => (wise(X0) & ~happy(X0))) [input p2]
14. ? [X0] : (~calm(X0) <~> ~happy(X0)) <=> (~rich(paul) & ~tall(paul)) [input p13]
16. ! [X0] : ((tall(X0) <~> wise(X0)) <=> ~wise(X0)) [input p15]
25. calm(fred) [input hypothesis]
30. ! [X0] : ((wise(X0) & ~happy(X0)) | (~wise(X0) <=> wise(X0))) [ennf transformation 3]
40. ! [X0] : ((wise(X0) & ~happy(X0)) | ((~wise(X0) | ~wise(X0)) & (wise(X0) | wise(X0)))) [nnf transformation 30]
61. (? [X0] : ((happy(X0) | calm(X0)) & (~happy(X0) | ~calm(X0))) | (rich(paul) | tall(paul))) & ((~rich(paul) & ~tall(paul)) | ! [X0] : ((~calm(X0) | happy(X0)) & (~happy(X0) | calm(X0)))) [nnf transformation 14]
62. (? [X0] : ((happy(X0) | calm(X0)) & (~happy(X0) | ~calm(X0))) | rich(paul) | tall(paul)) & ((~rich(paul) & ~tall(paul)) | ! [X0] : ((~calm(X0) | happy(X0)) & (~happy(X0) | calm(X0)))) [flattening 61]
63. (? [X0] : ((happy(X0) | calm(X0)) & (~happy(X0) | ~calm(X0))) | rich(paul) | tall(paul)) & ((~rich(paul) & ~tall(paul)) | ! [X1] : ((~calm(X1) | happy(X1)) & (~happy(X1) | calm(X1)))) [rectify 62]
64. ? [X0] : ((happy(X0) | calm(X0)) & (~happy(X0) | ~calm(X0))) => ((happy(sK4) | calm(sK4)) & (~happy(sK4) | ~calm(sK4))) [choice axiom]
65. (((happy(sK4) | calm(sK4)) & (~happy(sK4) | ~calm(sK4))) | rich(paul) | tall(paul)) & ((~rich(paul) & ~tall(paul)) | ! [X1] : ((~calm(X1) | happy(X1)) & (~happy(X1) | calm(X1)))) [skolemisation 63,64]
68. ! [X0] : ((((~wise(X0) | ~tall(X0)) & (wise(X0) | tall(X0))) | wise(X0)) & (~wise(X0) | ((tall(X0) | ~wise(X0)) & (wise(X0) | ~tall(X0))))) [nnf transformation 16]
80. ~happy(X0) | ~wise(X0) | ~wise(X0) [cnf transformation 40]
81. wise(X0) | wise(X0) | wise(X0) [cnf transformation 40]
117. ~tall(paul) | ~calm(X1) | happy(X1) [cnf transformation 65]
126. ~wise(X0) | tall(X0) | ~wise(X0) [cnf transformation 68]
139. calm(fred) [cnf transformation 25]
140. ~wise(X0) | tall(X0) [duplicate literal removal 126]
143. ~happy(X0) | ~wise(X0) [duplicate literal removal 80]
144. wise(X0) [duplicate literal removal 81]
160. ~happy(X0) [subsumption resolution 143,144]
207. 13 <=> calm(fred) [avatar definition]
209. calm(fred) <- (13) [avatar component clause 207]
243. 21 <=> tall(paul) [avatar definition]
244. ~tall(paul) <- (~21) [avatar component clause 243]
257. 24 <=> ! [X1] : ~calm(X1) [avatar definition]
258. ~calm(X1) <- (24) [avatar component clause 257]
260. ~tall(paul) | ~calm(X1) [subsumption resolution 117,160]
261. 24 | ~21 [avatar split clause 260,243,257]
263. tall(X0) [subsumption resolution 140,144]
275. 13 [avatar split clause 139,207]
276. $false <- (~21) [subsumption resolution 244,263]
277. 21 [avatar contradiction clause 276]
278. $false <- (13, 24) [resolution 258,209]
281. ~13 | ~24 [avatar contradiction clause 278]
282. $false [avatar sat refutation 261,275,277,281]
% SZS output end Proof for 3985786282357598103462012
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If fred is both wise and quiet then someone is not wise and vice versa.
Everyone who is not generous is not humble or strong and vice versa.
If paul is either tall or calm then john is either not calm or brave.
Everyone who is not generous is either not creative or kind and vice versa.
Everyone who is either creative or not patient is both not calm and strong and vice versa.
Everyone who is not kind is wise or funny.
Everyone who is calm or brave is calm or rich and vice versa.
Everyone who is kind or not wise is either not quiet or patient and vice versa.
Everyone who is both funny and not kind is both not rich and not curious.
Everyone who is either not wise or kind is both not happy and old and vice versa.
If lucy is patient then mary is both not patient and not old.
If someone is both not calm and not rich then someone is both old and not strong and vice versa.
Everyone who is humble or strong is not funny or not wise and vice versa.
Everyone who is either not creative or not kind is either not generous or happy and vice versa.
Everyone who is not funny is either creative or not kind and vice versa.
If fred is either not calm or tall then mary is generous.
Someone is either strong or tall.
Someone is either creative or not happy.
John is either not happy or patient.
Someone is either not quiet or not creative.
Mary is not brave or not happy.
Paul is both not quiet and not generous.
Paul is not funny or not kind.
Someone is both not kind and wise. | Paul is strong. | entailment | (((wise(fred)&quiet(fred)))<=>(?[X]:(~wise(X))))&
(![X]:(~generous(X)<=>(~humble(X)|strong(X))))&
(((tall(paul)<~>calm(paul)))=>((~calm(john)<~>brave(john))))&
(![X]:(~generous(X)<=>(~creative(X)<~>kind(X))))&
(![X]:((creative(X)<~>~patient(X))<=>(~calm(X)&strong(X))))&
(![X]:(~kind(X)=>(wise(X)|funny(X))))&
(![X]:((calm(X)|brave(X))<=>(calm(X)|rich(X))))&
(![X]:((kind(X)|~wise(X))<=>(~quiet(X)<~>patient(X))))&
(![X]:((funny(X)&~kind(X))=>(~rich(X)&~curious(X))))&
(![X]:((~wise(X)<~>kind(X))<=>(~happy(X)&old(X))))&
((patient(lucy))=>((~patient(mary)&~old(mary))))&
((?[X]:((~calm(X)&~rich(X))))<=>(?[X]:((old(X)&~strong(X)))))&
(![X]:((humble(X)|strong(X))<=>(~funny(X)|~wise(X))))&
(![X]:((~creative(X)<~>~kind(X))<=>(~generous(X)<~>happy(X))))&
(![X]:(~funny(X)<=>(creative(X)<~>~kind(X))))&
(((~calm(fred)<~>tall(fred)))=>(generous(mary)))&
(?[X]:((strong(X)<~>tall(X))))&
(?[X]:((creative(X)<~>~happy(X))))&
((~happy(john)<~>patient(john)))&
(?[X]:((~quiet(X)<~>~creative(X))))&
((~brave(mary)|~happy(mary)))&
((~quiet(paul)&~generous(paul)))&
((~funny(paul)|~kind(paul)))&
(?[X]:((~kind(X)&wise(X)))) | strong(paul) | [
"p1",
"p3",
"p12",
"p14",
"p21",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 2704738457521905126370810
% SZS output start Proof for 2704738457521905126370810
2. ! [X0] : (~generous(X0) <=> (strong(X0) | ~humble(X0))) [input p1]
4. ! [X0] : (~generous(X0) <=> (~creative(X0) <~> kind(X0))) [input p3]
13. ! [X0] : ((strong(X0) | humble(X0)) <=> (~wise(X0) | ~funny(X0))) [input p12]
15. ! [X0] : (~funny(X0) <=> (creative(X0) <~> ~kind(X0))) [input p14]
22. ~generous(paul) & ~quiet(paul) [input p21]
23. ~kind(paul) | ~funny(paul) [input p22]
25. ~strong(paul) [input hypothesis]
40. ! [X0] : ((~generous(X0) | (~strong(X0) & humble(X0))) & ((strong(X0) | ~humble(X0)) | generous(X0))) [nnf transformation 2]
41. ! [X0] : ((~generous(X0) | (~strong(X0) & humble(X0))) & (strong(X0) | ~humble(X0) | generous(X0))) [flattening 40]
43. ! [X0] : ((~generous(X0) | ((~creative(X0) | ~kind(X0)) & (kind(X0) | creative(X0)))) & (((~kind(X0) | creative(X0)) & (kind(X0) | ~creative(X0))) | generous(X0))) [nnf transformation 4]
57. ! [X0] : (((strong(X0) | humble(X0)) | (wise(X0) & funny(X0))) & ((~wise(X0) | ~funny(X0)) | (~strong(X0) & ~humble(X0)))) [nnf transformation 13]
58. ! [X0] : ((strong(X0) | humble(X0) | (wise(X0) & funny(X0))) & (~wise(X0) | ~funny(X0) | (~strong(X0) & ~humble(X0)))) [flattening 57]
60. ! [X0] : ((~funny(X0) | ((creative(X0) | kind(X0)) & (~kind(X0) | ~creative(X0)))) & (((kind(X0) | ~creative(X0)) & (~kind(X0) | creative(X0))) | funny(X0))) [nnf transformation 15]
77. ~humble(X0) | strong(X0) | generous(X0) [cnf transformation 41]
84. ~creative(X0) | kind(X0) | generous(X0) [cnf transformation 43]
120. funny(X0) | humble(X0) | strong(X0) [cnf transformation 58]
133. ~funny(X0) | creative(X0) | kind(X0) [cnf transformation 60]
146. ~generous(paul) [cnf transformation 22]
147. ~kind(paul) | ~funny(paul) [cnf transformation 23]
150. ~strong(paul) [cnf transformation 25]
298. 31 <=> funny(paul) [avatar definition]
299. funny(paul) <- (31) [avatar component clause 298]
300. ~funny(paul) <- (~31) [avatar component clause 298]
302. 32 <=> kind(paul) [avatar definition]
304. ~kind(paul) <- (~32) [avatar component clause 302]
305. ~31 | ~32 [avatar split clause 147,302,298]
473. 57 <=> humble(paul) [avatar definition]
474. humble(paul) <- (57) [avatar component clause 473]
540. creative(paul) | kind(paul) <- (31) [resolution 133,299]
543. creative(paul) <- (31, ~32) [subsumption resolution 540,304]
545. kind(paul) | generous(paul) <- (31, ~32) [resolution 543,84]
546. generous(paul) <- (31, ~32) [subsumption resolution 545,304]
547. $false <- (31, ~32) [subsumption resolution 546,146]
548. ~31 | 32 [avatar contradiction clause 547]
549. humble(paul) | strong(paul) <- (~31) [resolution 300,120]
554. humble(paul) <- (~31) [subsumption resolution 549,150]
555. 57 | 31 [avatar split clause 554,298,473]
556. strong(paul) | generous(paul) <- (57) [resolution 474,77]
557. generous(paul) <- (57) [subsumption resolution 556,150]
558. $false <- (57) [subsumption resolution 557,146]
559. ~57 [avatar contradiction clause 558]
560. $false [avatar sat refutation 305,548,555,559]
% SZS output end Proof for 2704738457521905126370810
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not happy or tall is tall and vice versa.
Everyone who is either not quiet or not patient is both not tall and rich.
If someone is both not brave and kind then susan is brave.
If someone is either not calm or quiet then someone is wise or not tall and vice versa.
If mary is either tall or kind then mary is patient and vice versa.
Everyone who is not patient is not kind or not tall.
If someone is both quiet and humble then someone is not humble or creative.
Everyone who is not calm is not funny or rich and vice versa.
If mary is not curious or not rich then mary is not creative.
If someone is both funny and not patient then someone is old.
Everyone who is not old is not creative or not kind.
Everyone who is brave is either not rich or not quiet.
Everyone who is happy or tall is both not funny and not quiet and vice versa.
Everyone who is not brave or not happy is strong.
Everyone who is both tall and not tall is either not funny or not creative.
Susan is both not quiet and old.
John is both brave and not wise.
Mary is either not rich or calm.
Someone is humble or not strong.
Susan is not funny.
Someone is not humble or tall.
Someone is not humble. | Mary is not quiet. | entailment | (![X]:((~happy(X)<~>tall(X))<=>tall(X)))&
(![X]:((~quiet(X)<~>~patient(X))=>(~tall(X)&rich(X))))&
((?[X]:((~brave(X)&kind(X))))=>(brave(susan)))&
((?[X]:((~calm(X)<~>quiet(X))))<=>(?[X]:((wise(X)|~tall(X)))))&
(((tall(mary)<~>kind(mary)))<=>(patient(mary)))&
(![X]:(~patient(X)=>(~kind(X)|~tall(X))))&
((?[X]:((quiet(X)&humble(X))))=>(?[X]:((~humble(X)|creative(X)))))&
(![X]:(~calm(X)<=>(~funny(X)|rich(X))))&
(((~curious(mary)|~rich(mary)))=>(~creative(mary)))&
((?[X]:((funny(X)&~patient(X))))=>(?[X]:(old(X))))&
(![X]:(~old(X)=>(~creative(X)|~kind(X))))&
(![X]:(brave(X)=>(~rich(X)<~>~quiet(X))))&
(![X]:((happy(X)|tall(X))<=>(~funny(X)&~quiet(X))))&
(![X]:((~brave(X)|~happy(X))=>strong(X)))&
(![X]:((tall(X)&~tall(X))=>(~funny(X)<~>~creative(X))))&
((~quiet(susan)&old(susan)))&
((brave(john)&~wise(john)))&
((~rich(mary)<~>calm(mary)))&
(?[X]:((humble(X)|~strong(X))))&
(~funny(susan))&
(?[X]:((~humble(X)|tall(X))))&
(?[X]:(~humble(X))) | ~quiet(mary) | [
"p0",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 918349218826078975994361
% SZS output start Proof for 918349218826078975994361
1. ! [X0] : ((~happy(X0) <~> tall(X0)) <=> tall(X0)) [input p0]
13. ! [X0] : ((tall(X0) | happy(X0)) <=> (~quiet(X0) & ~funny(X0))) [input p12]
23. quiet(mary) [input hypothesis]
41. ! [X0] : ((((~tall(X0) | happy(X0)) & (tall(X0) | ~happy(X0))) | ~tall(X0)) & (tall(X0) | ((~happy(X0) | ~tall(X0)) & (tall(X0) | happy(X0))))) [nnf transformation 1]
55. ! [X0] : (((tall(X0) | happy(X0)) | (quiet(X0) | funny(X0))) & ((~quiet(X0) & ~funny(X0)) | (~tall(X0) & ~happy(X0)))) [nnf transformation 13]
56. ! [X0] : ((tall(X0) | happy(X0) | quiet(X0) | funny(X0)) & ((~quiet(X0) & ~funny(X0)) | (~tall(X0) & ~happy(X0)))) [flattening 55]
65. tall(X0) | tall(X0) | happy(X0) [cnf transformation 41]
68. ~tall(X0) | happy(X0) | ~tall(X0) [cnf transformation 41]
94. ~quiet(X0) | ~happy(X0) [cnf transformation 56]
110. quiet(mary) [cnf transformation 23]
111. tall(X0) | happy(X0) [duplicate literal removal 65]
112. ~tall(X0) | happy(X0) [duplicate literal removal 68]
113. happy(X0) [subsumption resolution 111,112]
193. ~quiet(X0) [subsumption resolution 94,113]
216. $false [subsumption resolution 110,193]
% SZS output end Proof for 918349218826078975994361
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is patient is strong and vice versa.
Everyone who is either happy or creative is either humble or rich.
Everyone who is calm is not generous and vice versa.
Everyone who is both not curious and happy is both not quiet and rich.
Everyone who is strong or curious is both not generous and quiet.
Everyone who is not curious is not wise.
If someone is both not generous and quiet then someone is happy or old.
Everyone who is either creative or rich is not wise or wise.
Everyone who is either not old or not generous is quiet or not rich and vice versa.
Everyone who is both not kind and strong is both strong and calm.
If someone is either kind or not quiet then alice is not calm and vice versa.
Everyone who is either patient or not creative is not humble or patient.
If susan is either not patient or patient then lucy is not old or not quiet.
Everyone who is both not old and quiet is not creative.
Everyone who is funny is generous or not generous.
Everyone who is either wise or not old is both not curious and not strong and vice versa.
Someone is either not old or not creative.
Someone is not curious.
Someone is not rich or not tall.
Someone is both humble and not tall.
Someone is rich.
Lucy is both quiet and not tall.
Susan is not happy.
Someone is not quiet. | Lucy is not wise. | entailment | (![X]:(patient(X)<=>strong(X)))&
(![X]:((happy(X)<~>creative(X))=>(humble(X)<~>rich(X))))&
(![X]:(calm(X)<=>~generous(X)))&
(![X]:((~curious(X)&happy(X))=>(~quiet(X)&rich(X))))&
(![X]:((strong(X)|curious(X))=>(~generous(X)&quiet(X))))&
(![X]:(~curious(X)=>~wise(X)))&
((?[X]:((~generous(X)&quiet(X))))=>(?[X]:((happy(X)|old(X)))))&
(![X]:((creative(X)<~>rich(X))=>(~wise(X)|wise(X))))&
(![X]:((~old(X)<~>~generous(X))<=>(quiet(X)|~rich(X))))&
(![X]:((~kind(X)&strong(X))=>(strong(X)&calm(X))))&
((?[X]:((kind(X)<~>~quiet(X))))<=>(~calm(alice)))&
(![X]:((patient(X)<~>~creative(X))=>(~humble(X)|patient(X))))&
(((~patient(susan)<~>patient(susan)))=>((~old(lucy)|~quiet(lucy))))&
(![X]:((~old(X)&quiet(X))=>~creative(X)))&
(![X]:(funny(X)=>(generous(X)|~generous(X))))&
(![X]:((wise(X)<~>~old(X))<=>(~curious(X)&~strong(X))))&
(?[X]:((~old(X)<~>~creative(X))))&
(?[X]:(~curious(X)))&
(?[X]:((~rich(X)|~tall(X))))&
(?[X]:((humble(X)&~tall(X))))&
(?[X]:(rich(X)))&
((quiet(lucy)&~tall(lucy)))&
(~happy(susan))&
(?[X]:(~quiet(X))) | ~wise(lucy) | [
"p4",
"p5",
"p8",
"p12",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 3154657269622617036824406
% SZS output start Proof for 3154657269622617036824406
5. ! [X0] : ((curious(X0) | strong(X0)) => (quiet(X0) & ~generous(X0))) [input p4]
6. ! [X0] : (~curious(X0) => ~wise(X0)) [input p5]
9. ! [X0] : ((~old(X0) <~> ~generous(X0)) <=> (~rich(X0) | quiet(X0))) [input p8]
13. (~patient(susan) <~> patient(susan)) => (~quiet(lucy) | ~old(lucy)) [input p12]
22. ~tall(lucy) & quiet(lucy) [input p21]
25. wise(lucy) [input hypothesis]
28. quiet(lucy) [pure predicate removal 22]
34. ! [X0] : ((quiet(X0) & ~generous(X0)) | (~curious(X0) & ~strong(X0))) [ennf transformation 5]
35. ! [X0] : (~wise(X0) | curious(X0)) [ennf transformation 6]
43. (~quiet(lucy) | ~old(lucy)) | (~patient(susan) <=> patient(susan)) [ennf transformation 13]
44. ~quiet(lucy) | ~old(lucy) | (~patient(susan) <=> patient(susan)) [flattening 43]
54. ! [X0] : ((((generous(X0) | old(X0)) & (~generous(X0) | ~old(X0))) | (rich(X0) & ~quiet(X0))) & ((~rich(X0) | quiet(X0)) | ((~old(X0) | generous(X0)) & (~generous(X0) | old(X0))))) [nnf transformation 9]
55. ! [X0] : ((((generous(X0) | old(X0)) & (~generous(X0) | ~old(X0))) | (rich(X0) & ~quiet(X0))) & (~rich(X0) | quiet(X0) | ((~old(X0) | generous(X0)) & (~generous(X0) | old(X0))))) [flattening 54]
61. ~quiet(lucy) | ~old(lucy) | ((~patient(susan) | ~patient(susan)) & (patient(susan) | patient(susan))) [nnf transformation 44]
86. ~curious(X0) | ~generous(X0) [cnf transformation 34]
89. ~wise(X0) | curious(X0) [cnf transformation 35]
97. ~quiet(X0) | old(X0) | generous(X0) [cnf transformation 55]
107. ~quiet(lucy) | ~old(lucy) | patient(susan) | patient(susan) [cnf transformation 61]
108. ~quiet(lucy) | ~old(lucy) | ~patient(susan) | ~patient(susan) [cnf transformation 61]
121. quiet(lucy) [cnf transformation 28]
124. wise(lucy) [cnf transformation 25]
125. ~quiet(lucy) | ~old(lucy) | patient(susan) [duplicate literal removal 107]
126. ~quiet(lucy) | ~old(lucy) | ~patient(susan) [duplicate literal removal 108]
163. 9 <=> patient(susan) [avatar definition]
167. 10 <=> old(lucy) [avatar definition]
169. ~old(lucy) <- (~10) [avatar component clause 167]
171. 11 <=> quiet(lucy) [avatar definition]
172. quiet(lucy) <- (11) [avatar component clause 171]
174. ~9 | ~10 | ~11 [avatar split clause 126,171,167,163]
175. 9 | ~10 | ~11 [avatar split clause 125,171,167,163]
188. 11 [avatar split clause 121,171]
191. curious(lucy) [resolution 89,124]
194. ~generous(lucy) [resolution 191,86]
225. old(lucy) | generous(lucy) <- (11) [resolution 97,172]
226. generous(lucy) <- (~10, 11) [subsumption resolution 225,169]
227. $false <- (~10, 11) [subsumption resolution 226,194]
228. 10 | ~11 [avatar contradiction clause 227]
229. $false [avatar sat refutation 174,175,188,228]
% SZS output end Proof for 3154657269622617036824406
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not humble or not wise is both calm and humble and vice versa.
Everyone who is not happy is both patient and not curious.
Everyone who is not old is both generous and not brave and vice versa.
Everyone who is old or not funny is either old or calm.
Everyone who is either rich or not tall is either patient or not brave and vice versa.
Everyone who is both funny and rich is both not calm and not generous and vice versa.
Everyone who is both not calm and curious is either not calm or calm and vice versa.
If fred is both not old and brave then someone is both wise and not quiet.
Everyone who is creative is either not humble or wise.
If someone is old or patient then someone is creative.
If susan is not quiet then someone is either generous or calm and vice versa.
Everyone who is not brave or humble is wise and vice versa.
Everyone who is both not strong and old is either not strong or curious.
If paul is either not kind or quiet then someone is both quiet and patient.
If john is funny then susan is both not curious and creative and vice versa.
If someone is funny or rich then alice is tall or rich.
Someone is not patient.
Mary is not brave.
Someone is not wise or patient.
John is generous.
Someone is kind.
Someone is either creative or curious.
Paul is either not curious or not tall. | John is not strong. | contradiction | (![X]:((~humble(X)|~wise(X))<=>(calm(X)&humble(X))))&
(![X]:(~happy(X)=>(patient(X)&~curious(X))))&
(![X]:(~old(X)<=>(generous(X)&~brave(X))))&
(![X]:((old(X)|~funny(X))=>(old(X)<~>calm(X))))&
(![X]:((rich(X)<~>~tall(X))<=>(patient(X)<~>~brave(X))))&
(![X]:((funny(X)&rich(X))<=>(~calm(X)&~generous(X))))&
(![X]:((~calm(X)&curious(X))<=>(~calm(X)<~>calm(X))))&
(((~old(fred)&brave(fred)))=>(?[X]:((wise(X)&~quiet(X)))))&
(![X]:(creative(X)=>(~humble(X)<~>wise(X))))&
((?[X]:((old(X)|patient(X))))=>(?[X]:(creative(X))))&
((~quiet(susan))<=>(?[X]:((generous(X)<~>calm(X)))))&
(![X]:((~brave(X)|humble(X))<=>wise(X)))&
(![X]:((~strong(X)&old(X))=>(~strong(X)<~>curious(X))))&
(((~kind(paul)<~>quiet(paul)))=>(?[X]:((quiet(X)&patient(X)))))&
((funny(john))<=>((~curious(susan)&creative(susan))))&
((?[X]:((funny(X)|rich(X))))=>((tall(alice)|rich(alice))))&
(?[X]:(~patient(X)))&
(~brave(mary))&
(?[X]:((~wise(X)|patient(X))))&
(generous(john))&
(?[X]:(kind(X)))&
(?[X]:((creative(X)<~>curious(X))))&
((~curious(paul)<~>~tall(paul))) | ~strong(john) | [
"p3",
"p6",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 1040052472524722267232528
% SZS output start Proof for 1040052472524722267232528
4. ! [X0] : ((~funny(X0) | old(X0)) => (old(X0) <~> calm(X0))) [input p3]
7. ! [X0] : ((curious(X0) & ~calm(X0)) <=> (~calm(X0) <~> calm(X0))) [input p6]
13. ! [X0] : ((old(X0) & ~strong(X0)) => (~strong(X0) <~> curious(X0))) [input p12]
15. funny(john) <=> (creative(susan) & ~curious(susan)) [input p14]
24. ~strong(john) [input hypothesis]
27. ! [X0] : ((old(X0) <~> calm(X0)) | (funny(X0) & ~old(X0))) [ennf transformation 4]
32. ! [X0] : ((~strong(X0) <~> curious(X0)) | (~old(X0) | strong(X0))) [ennf transformation 13]
33. ! [X0] : ((~strong(X0) <~> curious(X0)) | ~old(X0) | strong(X0)) [flattening 32]
41. ! [X0] : (((~calm(X0) | ~old(X0)) & (calm(X0) | old(X0))) | (funny(X0) & ~old(X0))) [nnf transformation 27]
45. ! [X0] : (((curious(X0) & ~calm(X0)) | ((~calm(X0) | ~calm(X0)) & (calm(X0) | calm(X0)))) & (((~calm(X0) | calm(X0)) & (calm(X0) | ~calm(X0))) | (~curious(X0) | calm(X0)))) [nnf transformation 7]
46. ! [X0] : (((curious(X0) & ~calm(X0)) | ((~calm(X0) | ~calm(X0)) & (calm(X0) | calm(X0)))) & (((~calm(X0) | calm(X0)) & (calm(X0) | ~calm(X0))) | ~curious(X0) | calm(X0))) [flattening 45]
59. ! [X0] : (((~curious(X0) | strong(X0)) & (curious(X0) | ~strong(X0))) | ~old(X0) | strong(X0)) [nnf transformation 33]
63. (funny(john) | (~creative(susan) | curious(susan))) & ((creative(susan) & ~curious(susan)) | ~funny(john)) [nnf transformation 15]
64. (funny(john) | ~creative(susan) | curious(susan)) & ((creative(susan) & ~curious(susan)) | ~funny(john)) [flattening 63]
84. funny(X0) | old(X0) | calm(X0) [cnf transformation 41]
102. ~calm(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 46]
103. curious(X0) | calm(X0) | calm(X0) [cnf transformation 46]
104. curious(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 46]
119. ~curious(X0) | strong(X0) | ~old(X0) | strong(X0) [cnf transformation 59]
124. ~curious(susan) | ~funny(john) [cnf transformation 64]
138. ~strong(john) [cnf transformation 24]
139. ~curious(X0) | strong(X0) | ~old(X0) [duplicate literal removal 119]
143. ~calm(X0) [duplicate literal removal 102]
144. curious(X0) | calm(X0) [duplicate literal removal 103]
145. ~calm(X0) | curious(X0) [duplicate literal removal 104]
149. curious(X0) [subsumption resolution 144,145]
179. ~old(X0) | strong(X0) [subsumption resolution 139,149]
201. 11 <=> funny(john) [avatar definition]
203. ~funny(john) <- (~11) [avatar component clause 201]
209. ~funny(john) [subsumption resolution 124,149]
210. ~11 [avatar split clause 209,201]
239. 17 <=> old(john) [avatar definition]
240. old(john) <- (17) [avatar component clause 239]
256. old(john) | calm(john) <- (~11) [resolution 84,203]
260. old(john) <- (~11) [subsumption resolution 256,143]
261. 17 | 11 [avatar split clause 260,201,239]
262. strong(john) <- (17) [resolution 240,179]
264. $false <- (17) [subsumption resolution 262,138]
265. ~17 [avatar contradiction clause 264]
266. $false [avatar sat refutation 210,261,265]
% SZS output end Proof for 1040052472524722267232528
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not rich and not kind is not humble and vice versa. If someone is not curious then someone is either funny or not generous. Everyone who is both not kind and not curious is not patient. Everyone who is both not humble and not creative is either not curious or not patient. Everyone who is old or rich is not rich or strong and vice versa. If alice is both old and not generous then someone is both old and not creative. Everyone who is not quiet or patient is not patient. Everyone who is funny is wise. If someone is either not patient or wise then someone is both not quiet and not old. If mary is both not curious and tall then someone is old or wise and vice versa. Everyone who is not curious is funny and vice versa. If someone is both not tall and wise then lucy is either patient or not curious and vice versa. If someone is both wise and not curious then someone is both not humble and patient. If someone is generous or wise then someone is either not quiet or wise and vice versa. If someone is either not creative or patient then mary is both strong and not strong and vice versa. Someone is calm. Someone is creative or curious. Alice is not funny. Susan is either brave or tall. | Susan is funny. | contradiction | (![X]:((~rich(X)&~kind(X))<=>~humble(X)))&
((?[X]:(~curious(X)))=>(?[X]:((funny(X)<~>~generous(X)))))&
(![X]:((~kind(X)&~curious(X))=>~patient(X)))&
(![X]:((~humble(X)&~creative(X))=>(~curious(X)<~>~patient(X))))&
(![X]:((old(X)|rich(X))<=>(~rich(X)|strong(X))))&
(((old(alice)&~generous(alice)))=>(?[X]:((old(X)&~creative(X)))))&
(![X]:((~quiet(X)|patient(X))=>~patient(X)))&
(![X]:(funny(X)=>wise(X)))&
((?[X]:((~patient(X)<~>wise(X))))=>(?[X]:((~quiet(X)&~old(X)))))&
(((~curious(mary)&tall(mary)))<=>(?[X]:((old(X)|wise(X)))))&
(![X]:(~curious(X)<=>funny(X)))&
((?[X]:((~tall(X)&wise(X))))<=>((patient(lucy)<~>~curious(lucy))))&
((?[X]:((wise(X)&~curious(X))))=>(?[X]:((~humble(X)&patient(X)))))&
((?[X]:((generous(X)|wise(X))))<=>(?[X]:((~quiet(X)<~>wise(X)))))&
((?[X]:((~creative(X)<~>patient(X))))<=>((strong(mary)&~strong(mary))))&
(?[X]:(calm(X)))&
(?[X]:((creative(X)|curious(X))))&
(~funny(alice))&
((brave(susan)<~>tall(susan))) | funny(susan) | [
"p6",
"p7",
"p10",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 3342304499659649306125150
% SZS output start Proof for 3342304499659649306125150
7. ! [X0] : ((patient(X0) | ~quiet(X0)) => ~patient(X0)) [input p6]
8. ! [X0] : (funny(X0) => wise(X0)) [input p7]
11. ! [X0] : (~curious(X0) <=> funny(X0)) [input p10]
13. ? [X0] : (~curious(X0) & wise(X0)) => ? [X0] : (patient(X0) & ~humble(X0)) [input p12]
20. funny(susan) [input hypothesis]
23. ? [X0] : (~curious(X0) & wise(X0)) => ? [X1] : (patient(X1) & ~humble(X1)) [rectify 13]
33. ! [X0] : (~patient(X0) | (~patient(X0) & quiet(X0))) [ennf transformation 7]
34. ! [X0] : (wise(X0) | ~funny(X0)) [ennf transformation 8]
36. ? [X1] : (patient(X1) & ~humble(X1)) | ! [X0] : (curious(X0) | ~wise(X0)) [ennf transformation 23]
57. ! [X0] : ((~curious(X0) | ~funny(X0)) & (funny(X0) | curious(X0))) [nnf transformation 11]
62. ? [X0] : (patient(X0) & ~humble(X0)) | ! [X1] : (curious(X1) | ~wise(X1)) [rectify 36]
63. ? [X0] : (patient(X0) & ~humble(X0)) => (patient(sK5) & ~humble(sK5)) [choice axiom]
64. (patient(sK5) & ~humble(sK5)) | ! [X1] : (curious(X1) | ~wise(X1)) [skolemisation 62,63]
93. ~patient(X0) | ~patient(X0) [cnf transformation 33]
94. ~funny(X0) | wise(X0) [cnf transformation 34]
104. funny(X0) | curious(X0) [cnf transformation 57]
105. ~funny(X0) | ~curious(X0) [cnf transformation 57]
113. patient(sK5) | curious(X1) | ~wise(X1) [cnf transformation 64]
130. funny(susan) [cnf transformation 20]
131. ~patient(X0) [duplicate literal removal 93]
135. 1 <=> ! [X1] : curious(X1) [avatar definition]
136. curious(X1) <- (1) [avatar component clause 135]
228. curious(X1) | ~wise(X1) [subsumption resolution 113,131]
297. curious(X0) | wise(X0) [resolution 104,94]
298. curious(X0) [subsumption resolution 297,228]
299. 1 [avatar split clause 298,135]
304. ~curious(susan) [resolution 105,130]
306. $false <- (1) [subsumption resolution 304,136]
307. ~1 [avatar contradiction clause 306]
308. $false [avatar sat refutation 299,307]
% SZS output end Proof for 3342304499659649306125150
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not humble or not creative then someone is both happy and not quiet and vice versa.
If john is strong then lucy is generous or not tall and vice versa.
Everyone who is quiet is both brave and patient and vice versa.
Everyone who is not happy or kind is not old and vice versa.
Everyone who is brave or not strong is both generous and not kind and vice versa.
If alice is old or not patient then someone is both not quiet and generous.
Everyone who is not happy is not brave or creative and vice versa.
If someone is not tall then alice is not tall.
Everyone who is both not humble and not happy is both creative and not rich.
Everyone who is either creative or funny is not funny or not kind.
Everyone who is not wise or calm is wise.
If someone is not strong then paul is not wise and vice versa.
If someone is tall then someone is both not old and patient and vice versa.
If someone is quiet then someone is both not rich and rich and vice versa.
Everyone who is tall or funny is both not happy and not quiet.
If someone is either not strong or generous then paul is both generous and not tall and vice versa.
Someone is not creative.
Lucy is funny or not strong.
Someone is either not calm or not tall.
Someone is both humble and strong.
Someone is both not brave and strong.
Susan is curious.
Someone is either not funny or generous. | Lucy is strong. | entailment | ((?[X]:((~humble(X)|~creative(X))))<=>(?[X]:((happy(X)&~quiet(X)))))&
((strong(john))<=>((generous(lucy)|~tall(lucy))))&
(![X]:(quiet(X)<=>(brave(X)&patient(X))))&
(![X]:((~happy(X)|kind(X))<=>~old(X)))&
(![X]:((brave(X)|~strong(X))<=>(generous(X)&~kind(X))))&
(((old(alice)|~patient(alice)))=>(?[X]:((~quiet(X)&generous(X)))))&
(![X]:(~happy(X)<=>(~brave(X)|creative(X))))&
((?[X]:(~tall(X)))=>(~tall(alice)))&
(![X]:((~humble(X)&~happy(X))=>(creative(X)&~rich(X))))&
(![X]:((creative(X)<~>funny(X))=>(~funny(X)|~kind(X))))&
(![X]:((~wise(X)|calm(X))=>wise(X)))&
((?[X]:(~strong(X)))<=>(~wise(paul)))&
((?[X]:(tall(X)))<=>(?[X]:((~old(X)&patient(X)))))&
((?[X]:(quiet(X)))<=>(?[X]:((~rich(X)&rich(X)))))&
(![X]:((tall(X)|funny(X))=>(~happy(X)&~quiet(X))))&
((?[X]:((~strong(X)<~>generous(X))))<=>((generous(paul)&~tall(paul))))&
(?[X]:(~creative(X)))&
((funny(lucy)|~strong(lucy)))&
(?[X]:((~calm(X)<~>~tall(X))))&
(?[X]:((humble(X)&strong(X))))&
(?[X]:((~brave(X)&strong(X))))&
(curious(susan))&
(?[X]:((~funny(X)<~>generous(X)))) | strong(lucy) | [
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 8051061308708580635358920
% SZS output start Proof for 8051061308708580635358920
11. ! [X0] : ((calm(X0) | ~wise(X0)) => wise(X0)) [input p10]
12. ? [X0] : ~strong(X0) <=> ~wise(paul) [input p11]
24. ~strong(lucy) [input hypothesis]
35. ! [X0] : (wise(X0) | (~calm(X0) & wise(X0))) [ennf transformation 11]
55. (? [X0] : ~strong(X0) | wise(paul)) & (~wise(paul) | ! [X0] : strong(X0)) [nnf transformation 12]
56. (? [X0] : ~strong(X0) | wise(paul)) & (~wise(paul) | ! [X1] : strong(X1)) [rectify 55]
57. ? [X0] : ~strong(X0) => ~strong(sK3) [choice axiom]
58. (~strong(sK3) | wise(paul)) & (~wise(paul) | ! [X1] : strong(X1)) [skolemisation 56,57]
117. wise(X0) | wise(X0) [cnf transformation 35]
119. ~wise(paul) | strong(X1) [cnf transformation 58]
147. ~strong(lucy) [cnf transformation 24]
148. wise(X0) [duplicate literal removal 117]
223. strong(X1) [subsumption resolution 119,148]
296. $false [subsumption resolution 147,223]
% SZS output end Proof for 8051061308708580635358920
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is humble then someone is both happy and creative.
If someone is both not old and not quiet then someone is either wise or not tall and vice versa.
If paul is quiet then someone is both not wise and not funny.
If mary is both brave and rich then paul is not curious.
Everyone who is both curious and brave is funny and vice versa.
If lucy is tall then lucy is kind and vice versa.
If john is both not creative and not happy then susan is both creative and kind and vice versa.
If someone is not quiet then susan is either not tall or not creative and vice versa.
Everyone who is either not kind or generous is rich.
Everyone who is curious is either not generous or brave.
If someone is both quiet and curious then someone is both creative and brave and vice versa.
Everyone who is not rich is either humble or not old.
If someone is either not happy or generous then someone is both not rich and curious.
If mary is not creative or not curious then someone is creative and vice versa.
If mary is either not happy or calm then john is both not tall and not kind and vice versa.
Everyone who is either old or not curious is curious and vice versa.
Paul is tall.
Susan is not brave.
Someone is not old or tall.
Someone is patient or not funny.
Susan is either wise or not strong.
Someone is either tall or generous.
Lucy is both not brave and not patient. | John is old. | entailment | ((?[X]:(humble(X)))=>(?[X]:((happy(X)&creative(X)))))&
((?[X]:((~old(X)&~quiet(X))))<=>(?[X]:((wise(X)<~>~tall(X)))))&
((quiet(paul))=>(?[X]:((~wise(X)&~funny(X)))))&
(((brave(mary)&rich(mary)))=>(~curious(paul)))&
(![X]:((curious(X)&brave(X))<=>funny(X)))&
((tall(lucy))<=>(kind(lucy)))&
(((~creative(john)&~happy(john)))<=>((creative(susan)&kind(susan))))&
((?[X]:(~quiet(X)))<=>((~tall(susan)<~>~creative(susan))))&
(![X]:((~kind(X)<~>generous(X))=>rich(X)))&
(![X]:(curious(X)=>(~generous(X)<~>brave(X))))&
((?[X]:((quiet(X)&curious(X))))<=>(?[X]:((creative(X)&brave(X)))))&
(![X]:(~rich(X)=>(humble(X)<~>~old(X))))&
((?[X]:((~happy(X)<~>generous(X))))=>(?[X]:((~rich(X)&curious(X)))))&
(((~creative(mary)|~curious(mary)))<=>(?[X]:(creative(X))))&
(((~happy(mary)<~>calm(mary)))<=>((~tall(john)&~kind(john))))&
(![X]:((old(X)<~>~curious(X))<=>curious(X)))&
(tall(paul))&
(~brave(susan))&
(?[X]:((~old(X)|tall(X))))&
(?[X]:((patient(X)|~funny(X))))&
((wise(susan)<~>~strong(susan)))&
(?[X]:((tall(X)<~>generous(X))))&
((~brave(lucy)&~patient(lucy))) | old(john) | [
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 217862893450946590411850
% SZS output start Proof for 217862893450946590411850
16. ! [X0] : ((old(X0) <~> ~curious(X0)) <=> curious(X0)) [input p15]
24. ~old(john) [input hypothesis]
76. ! [X0] : ((((curious(X0) | ~old(X0)) & (~curious(X0) | old(X0))) | ~curious(X0)) & (curious(X0) | ((old(X0) | curious(X0)) & (~curious(X0) | ~old(X0))))) [nnf transformation 16]
131. curious(X0) | old(X0) | curious(X0) [cnf transformation 76]
132. ~curious(X0) | old(X0) | ~curious(X0) [cnf transformation 76]
144. ~old(john) [cnf transformation 24]
145. curious(X0) | old(X0) [duplicate literal removal 131]
146. ~curious(X0) | old(X0) [duplicate literal removal 132]
347. old(X0) [subsumption resolution 145,146]
378. $false [subsumption resolution 144,347]
% SZS output end Proof for 217862893450946590411850
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If susan is both patient and strong then someone is not humble. Everyone who is curious or not calm is both calm and brave and vice versa. If mary is rich then someone is both old and not generous and vice versa. If fred is not wise then mary is tall or humble and vice versa. If someone is both tall and generous then susan is not rich or not funny and vice versa. Everyone who is either not happy or patient is both creative and humble and vice versa. If someone is both not strong and not brave then someone is either tall or not quiet and vice versa. If someone is not strong then someone is kind or wise. If mary is both not generous and brave then someone is brave or not calm and vice versa. Everyone who is either generous or not generous is both not happy and not quiet and vice versa. Everyone who is either curious or not quiet is happy. Everyone who is both not funny and not patient is not funny. If paul is not quiet then someone is humble or quiet. If fred is both happy and not generous then someone is both strong and calm. Everyone who is not strong is happy and vice versa. Everyone who is not funny is humble. Alice is either calm or rich. Paul is both not patient and brave. Someone is kind. Susan is not funny. John is either not creative or kind. Paul is wise. Someone is tall or happy. | Fred is not calm. | contradiction | (((patient(susan)&strong(susan)))=>(?[X]:(~humble(X))))&
(![X]:((curious(X)|~calm(X))<=>(calm(X)&brave(X))))&
((rich(mary))<=>(?[X]:((old(X)&~generous(X)))))&
((~wise(fred))<=>((tall(mary)|humble(mary))))&
((?[X]:((tall(X)&generous(X))))<=>((~rich(susan)|~funny(susan))))&
(![X]:((~happy(X)<~>patient(X))<=>(creative(X)&humble(X))))&
((?[X]:((~strong(X)&~brave(X))))<=>(?[X]:((tall(X)<~>~quiet(X)))))&
((?[X]:(~strong(X)))=>(?[X]:((kind(X)|wise(X)))))&
(((~generous(mary)&brave(mary)))<=>(?[X]:((brave(X)|~calm(X)))))&
(![X]:((generous(X)<~>~generous(X))<=>(~happy(X)&~quiet(X))))&
(![X]:((curious(X)<~>~quiet(X))=>happy(X)))&
(![X]:((~funny(X)&~patient(X))=>~funny(X)))&
((~quiet(paul))=>(?[X]:((humble(X)|quiet(X)))))&
(((happy(fred)&~generous(fred)))=>(?[X]:((strong(X)&calm(X)))))&
(![X]:(~strong(X)<=>happy(X)))&
(![X]:(~funny(X)=>humble(X)))&
((calm(alice)<~>rich(alice)))&
((~patient(paul)&brave(paul)))&
(?[X]:(kind(X)))&
(~funny(susan))&
((~creative(john)<~>kind(john)))&
(wise(paul))&
(?[X]:((tall(X)|happy(X)))) | ~calm(fred) | [
"p1",
"hypothesis"
] | % SZS status Unsatisfiable for 1453927273171782877553408
% SZS output start Proof for 1453927273171782877553408
2. ! [X0] : ((~calm(X0) | curious(X0)) <=> (brave(X0) & calm(X0))) [input p1]
24. ~calm(fred) [input hypothesis]
39. ! [X0] : (((~calm(X0) | curious(X0)) | (~brave(X0) | ~calm(X0))) & ((brave(X0) & calm(X0)) | (calm(X0) & ~curious(X0)))) [nnf transformation 2]
40. ! [X0] : ((~calm(X0) | curious(X0) | ~brave(X0) | ~calm(X0)) & ((brave(X0) & calm(X0)) | (calm(X0) & ~curious(X0)))) [flattening 39]
83. calm(X0) | calm(X0) [cnf transformation 40]
141. ~calm(fred) [cnf transformation 24]
146. calm(X0) [duplicate literal removal 83]
301. $false [subsumption resolution 141,146]
% SZS output end Proof for 1453927273171782877553408
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either wise or generous is either creative or not rich. Everyone who is both not funny and patient is both wise and patient. Everyone who is patient or not happy is both creative and not tall. If john is either strong or not tall then alice is not humble and vice versa. If someone is either not happy or not old then someone is either patient or not wise and vice versa. If fred is both wise and not tall then someone is either not curious or not generous. If someone is either strong or rich then susan is both wise and happy and vice versa. Everyone who is not wise or happy is wise and vice versa. If someone is either wise or not strong then someone is either creative or not calm and vice versa. If someone is not patient then someone is either not curious or quiet. Everyone who is either not happy or tall is not strong or brave and vice versa. If alice is generous or not patient then john is curious. If lucy is kind then someone is not patient and vice versa. If someone is patient or quiet then someone is brave and vice versa. If fred is not humble or kind then someone is either funny or tall and vice versa. Everyone who is both generous and happy is both not rich and generous. Susan is not kind. John is both brave and not patient. Someone is not tall. Paul is brave or not generous. Someone is not generous. Someone is both not creative and calm. | John is not patient. | entailment | (![X]:((wise(X)<~>generous(X))=>(creative(X)<~>~rich(X))))&
(![X]:((~funny(X)&patient(X))=>(wise(X)&patient(X))))&
(![X]:((patient(X)|~happy(X))=>(creative(X)&~tall(X))))&
(((strong(john)<~>~tall(john)))<=>(~humble(alice)))&
((?[X]:((~happy(X)<~>~old(X))))<=>(?[X]:((patient(X)<~>~wise(X)))))&
(((wise(fred)&~tall(fred)))=>(?[X]:((~curious(X)<~>~generous(X)))))&
((?[X]:((strong(X)<~>rich(X))))<=>((wise(susan)&happy(susan))))&
(![X]:((~wise(X)|happy(X))<=>wise(X)))&
((?[X]:((wise(X)<~>~strong(X))))<=>(?[X]:((creative(X)<~>~calm(X)))))&
((?[X]:(~patient(X)))=>(?[X]:((~curious(X)<~>quiet(X)))))&
(![X]:((~happy(X)<~>tall(X))<=>(~strong(X)|brave(X))))&
(((generous(alice)|~patient(alice)))=>(curious(john)))&
((kind(lucy))<=>(?[X]:(~patient(X))))&
((?[X]:((patient(X)|quiet(X))))<=>(?[X]:(brave(X))))&
(((~humble(fred)|kind(fred)))<=>(?[X]:((funny(X)<~>tall(X)))))&
(![X]:((generous(X)&happy(X))=>(~rich(X)&generous(X))))&
(~kind(susan))&
((brave(john)&~patient(john)))&
(?[X]:(~tall(X)))&
((brave(paul)|~generous(paul)))&
(?[X]:(~generous(X)))&
(?[X]:((~creative(X)&calm(X)))) | ~patient(john) | [
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 7541479348951911105594908
% SZS output start Proof for 7541479348951911105594908
18. ~patient(john) & brave(john) [input p17]
23. patient(john) [input hypothesis]
152. ~patient(john) [cnf transformation 18]
158. patient(john) [cnf transformation 23]
388. $false [subsumption resolution 158,152]
% SZS output end Proof for 7541479348951911105594908
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not rich or calm is funny or not funny and vice versa. If mary is either happy or not happy then paul is strong or not funny and vice versa. Everyone who is humble is both curious and not calm and vice versa. Everyone who is either not tall or wise is not creative or patient. Everyone who is both not rich and tall is both happy and rich. If someone is kind or funny then someone is either not humble or wise and vice versa. If fred is either not kind or kind then someone is both not curious and not patient and vice versa. If susan is creative or not wise then susan is not funny or not wise. Everyone who is either not rich or happy is not generous or not tall and vice versa. Everyone who is both wise and humble is both wise and not happy and vice versa. Everyone who is both curious and not generous is either not funny or calm and vice versa. If john is not brave then alice is not funny and vice versa. Everyone who is brave or kind is either happy or not creative and vice versa. If paul is tall then someone is not happy. Everyone who is tall is not old or not rich and vice versa. Someone is either generous or not kind. Someone is either creative or not curious. Someone is creative or not creative. Paul is either humble or not curious. Someone is either not brave or old. John is both funny and not brave. Someone is not wise or creative. | Fred is calm. | entailment | (![X]:((~rich(X)<~>calm(X))<=>(funny(X)|~funny(X))))&
(((happy(mary)<~>~happy(mary)))<=>((strong(paul)|~funny(paul))))&
(![X]:(humble(X)<=>(curious(X)&~calm(X))))&
(![X]:((~tall(X)<~>wise(X))=>(~creative(X)|patient(X))))&
(![X]:((~rich(X)&tall(X))=>(happy(X)&rich(X))))&
((?[X]:((kind(X)|funny(X))))<=>(?[X]:((~humble(X)<~>wise(X)))))&
(((~kind(fred)<~>kind(fred)))<=>(?[X]:((~curious(X)&~patient(X)))))&
(((creative(susan)|~wise(susan)))=>((~funny(susan)|~wise(susan))))&
(![X]:((~rich(X)<~>happy(X))<=>(~generous(X)|~tall(X))))&
(![X]:((wise(X)&humble(X))<=>(wise(X)&~happy(X))))&
(![X]:((curious(X)&~generous(X))<=>(~funny(X)<~>calm(X))))&
((~brave(john))<=>(~funny(alice)))&
(![X]:((brave(X)|kind(X))<=>(happy(X)<~>~creative(X))))&
((tall(paul))=>(?[X]:(~happy(X))))&
(![X]:(tall(X)<=>(~old(X)|~rich(X))))&
(?[X]:((generous(X)<~>~kind(X))))&
(?[X]:((creative(X)<~>~curious(X))))&
(?[X]:((creative(X)|~creative(X))))&
((humble(paul)<~>~curious(paul)))&
(?[X]:((~brave(X)<~>old(X))))&
((funny(john)&~brave(john)))&
(?[X]:((~wise(X)|creative(X)))) | calm(fred) | [
"p0",
"p4",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3646496873657999316653859
% SZS output start Proof for 3646496873657999316653859
1. ! [X0] : ((~rich(X0) <~> calm(X0)) <=> (~funny(X0) | funny(X0))) [input p0]
5. ! [X0] : ((tall(X0) & ~rich(X0)) => (rich(X0) & happy(X0))) [input p4]
15. ! [X0] : (tall(X0) <=> (~rich(X0) | ~old(X0))) [input p14]
23. ~calm(fred) [input hypothesis]
27. ! [X0] : ((rich(X0) & happy(X0)) | (~tall(X0) | rich(X0))) [ennf transformation 5]
28. ! [X0] : ((rich(X0) & happy(X0)) | ~tall(X0) | rich(X0)) [flattening 27]
32. ! [X0] : ((((~calm(X0) | rich(X0)) & (calm(X0) | ~rich(X0))) | (funny(X0) & ~funny(X0))) & ((~funny(X0) | funny(X0)) | ((~rich(X0) | ~calm(X0)) & (calm(X0) | rich(X0))))) [nnf transformation 1]
33. ! [X0] : ((((~calm(X0) | rich(X0)) & (calm(X0) | ~rich(X0))) | (funny(X0) & ~funny(X0))) & (~funny(X0) | funny(X0) | ((~rich(X0) | ~calm(X0)) & (calm(X0) | rich(X0))))) [flattening 32]
59. ! [X0] : ((tall(X0) | (rich(X0) & old(X0))) & ((~rich(X0) | ~old(X0)) | ~tall(X0))) [nnf transformation 15]
60. ! [X0] : ((tall(X0) | (rich(X0) & old(X0))) & (~rich(X0) | ~old(X0) | ~tall(X0))) [flattening 59]
77. calm(X0) | ~rich(X0) | ~funny(X0) [cnf transformation 33]
78. calm(X0) | ~rich(X0) | funny(X0) [cnf transformation 33]
93. rich(X0) | ~tall(X0) | rich(X0) [cnf transformation 28]
135. tall(X0) | rich(X0) [cnf transformation 60]
148. ~calm(fred) [cnf transformation 23]
153. ~tall(X0) | rich(X0) [duplicate literal removal 93]
157. ~rich(X0) | calm(X0) [subsumption resolution 77,78]
256. rich(X0) [subsumption resolution 135,153]
309. calm(X0) [resolution 157,256]
310. $false [resolution 309,148]
% SZS output end Proof for 3646496873657999316653859
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.022 s
% ------------------------------
% ------------------------------
| 0 |
If mary is not strong or not old then someone is not quiet.
Everyone who is wise or kind is curious and vice versa.
If someone is both calm and tall then someone is both patient and not strong and vice versa.
If someone is funny or not brave then fred is not rich or strong and vice versa.
Everyone who is either not curious or funny is happy or generous and vice versa.
Everyone who is generous is strong or creative and vice versa.
Everyone who is not calm is both generous and calm and vice versa.
Everyone who is both brave and not humble is either not quiet or wise.
Everyone who is not curious is not rich or not quiet.
If someone is either not tall or not wise then paul is not tall or kind and vice versa.
If someone is both not old and not kind then fred is not quiet and vice versa.
If someone is rich or old then someone is either old or not rich.
If someone is both not strong and not brave then mary is both creative and not curious and vice versa.
If someone is old then lucy is either calm or humble and vice versa.
Everyone who is either not curious or quiet is old and vice versa.
Everyone who is not curious or kind is not wise or not creative and vice versa.
Someone is either wise or not brave.
Someone is humble.
Someone is brave or not generous.
Someone is either strong or rich.
Someone is either not humble or funny.
Someone is both rich and not quiet. | Mary is not calm. | contradiction | (((~strong(mary)|~old(mary)))=>(?[X]:(~quiet(X))))&
(![X]:((wise(X)|kind(X))<=>curious(X)))&
((?[X]:((calm(X)&tall(X))))<=>(?[X]:((patient(X)&~strong(X)))))&
((?[X]:((funny(X)|~brave(X))))<=>((~rich(fred)|strong(fred))))&
(![X]:((~curious(X)<~>funny(X))<=>(happy(X)|generous(X))))&
(![X]:(generous(X)<=>(strong(X)|creative(X))))&
(![X]:(~calm(X)<=>(generous(X)&calm(X))))&
(![X]:((brave(X)&~humble(X))=>(~quiet(X)<~>wise(X))))&
(![X]:(~curious(X)=>(~rich(X)|~quiet(X))))&
((?[X]:((~tall(X)<~>~wise(X))))<=>((~tall(paul)|kind(paul))))&
((?[X]:((~old(X)&~kind(X))))<=>(~quiet(fred)))&
((?[X]:((rich(X)|old(X))))=>(?[X]:((old(X)<~>~rich(X)))))&
((?[X]:((~strong(X)&~brave(X))))<=>((creative(mary)&~curious(mary))))&
((?[X]:(old(X)))<=>((calm(lucy)<~>humble(lucy))))&
(![X]:((~curious(X)<~>quiet(X))<=>old(X)))&
(![X]:((~curious(X)|kind(X))<=>(~wise(X)|~creative(X))))&
(?[X]:((wise(X)<~>~brave(X))))&
(?[X]:(humble(X)))&
(?[X]:((brave(X)|~generous(X))))&
(?[X]:((strong(X)<~>rich(X))))&
(?[X]:((~humble(X)<~>funny(X))))&
(?[X]:((rich(X)&~quiet(X)))) | ~calm(mary) | [
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 2151676762306696764453251
% SZS output start Proof for 2151676762306696764453251
7. ! [X0] : (~calm(X0) <=> (calm(X0) & generous(X0))) [input p6]
23. ~calm(mary) [input hypothesis]
50. ! [X0] : ((~calm(X0) | (~calm(X0) | ~generous(X0))) & ((calm(X0) & generous(X0)) | calm(X0))) [nnf transformation 7]
51. ! [X0] : ((~calm(X0) | ~calm(X0) | ~generous(X0)) & ((calm(X0) & generous(X0)) | calm(X0))) [flattening 50]
116. calm(X0) | calm(X0) [cnf transformation 51]
160. ~calm(mary) [cnf transformation 23]
161. calm(X0) [duplicate literal removal 116]
367. $false [subsumption resolution 160,161]
% SZS output end Proof for 2151676762306696764453251
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If susan is either not kind or not quiet then someone is both not rich and not tall. Everyone who is either not strong or generous is rich. If mary is not strong then john is either patient or not rich and vice versa. Everyone who is either not funny or curious is rich or not tall. If someone is calm or strong then someone is both wise and not patient and vice versa. If someone is calm or not patient then susan is both not wise and not brave. If someone is either humble or creative then john is wise and vice versa. Everyone who is rich or not quiet is both humble and not quiet. Everyone who is not old is both brave and not old. If someone is funny or not creative then fred is strong or kind and vice versa. If someone is tall or calm then someone is not patient or not humble and vice versa. Everyone who is both not patient and funny is kind or not generous and vice versa. If fred is either brave or not humble then john is either not patient or not kind and vice versa. If alice is either quiet or strong then john is both patient and not old. If someone is either not humble or curious then alice is both humble and creative and vice versa. Everyone who is both tall and not happy is not tall or not wise. Fred is both not curious and not humble. Susan is curious or not creative. John is old. Someone is not old. Paul is both patient and not curious. Someone is funny. Someone is not generous or curious. Someone is creative. | Fred is patient. | contradiction | (((~kind(susan)<~>~quiet(susan)))=>(?[X]:((~rich(X)&~tall(X)))))&
(![X]:((~strong(X)<~>generous(X))=>rich(X)))&
((~strong(mary))<=>((patient(john)<~>~rich(john))))&
(![X]:((~funny(X)<~>curious(X))=>(rich(X)|~tall(X))))&
((?[X]:((calm(X)|strong(X))))<=>(?[X]:((wise(X)&~patient(X)))))&
((?[X]:((calm(X)|~patient(X))))=>((~wise(susan)&~brave(susan))))&
((?[X]:((humble(X)<~>creative(X))))<=>(wise(john)))&
(![X]:((rich(X)|~quiet(X))=>(humble(X)&~quiet(X))))&
(![X]:(~old(X)=>(brave(X)&~old(X))))&
((?[X]:((funny(X)|~creative(X))))<=>((strong(fred)|kind(fred))))&
((?[X]:((tall(X)|calm(X))))<=>(?[X]:((~patient(X)|~humble(X)))))&
(![X]:((~patient(X)&funny(X))<=>(kind(X)|~generous(X))))&
(((brave(fred)<~>~humble(fred)))<=>((~patient(john)<~>~kind(john))))&
(((quiet(alice)<~>strong(alice)))=>((patient(john)&~old(john))))&
((?[X]:((~humble(X)<~>curious(X))))<=>((humble(alice)&creative(alice))))&
(![X]:((tall(X)&~happy(X))=>(~tall(X)|~wise(X))))&
((~curious(fred)&~humble(fred)))&
((curious(susan)|~creative(susan)))&
(old(john))&
(?[X]:(~old(X)))&
((patient(paul)&~curious(paul)))&
(?[X]:(funny(X)))&
(?[X]:((~generous(X)|curious(X))))&
(?[X]:(creative(X))) | patient(fred) | [
"p1",
"p7",
"p9",
"p11",
"p16",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 5211377684949296539648134
% SZS output start Proof for 5211377684949296539648134
2. ! [X0] : ((~strong(X0) <~> generous(X0)) => rich(X0)) [input p1]
8. ! [X0] : ((~quiet(X0) | rich(X0)) => (~quiet(X0) & humble(X0))) [input p7]
10. ? [X0] : (~creative(X0) | funny(X0)) <=> (kind(fred) | strong(fred)) [input p9]
12. ! [X0] : ((funny(X0) & ~patient(X0)) <=> (~generous(X0) | kind(X0))) [input p11]
17. ~humble(fred) & ~curious(fred) [input p16]
22. ? [X0] : funny(X0) [input p21]
25. patient(fred) [input hypothesis]
30. ! [X0] : (rich(X0) | (~strong(X0) <=> generous(X0))) [ennf transformation 2]
34. ! [X0] : ((~quiet(X0) & humble(X0)) | (quiet(X0) & ~rich(X0))) [ennf transformation 8]
40. ! [X0] : (rich(X0) | ((~strong(X0) | ~generous(X0)) & (generous(X0) | strong(X0)))) [nnf transformation 30]
52. (? [X0] : (~creative(X0) | funny(X0)) | (~kind(fred) & ~strong(fred))) & ((kind(fred) | strong(fred)) | ! [X0] : (creative(X0) & ~funny(X0))) [nnf transformation 10]
53. (? [X0] : (~creative(X0) | funny(X0)) | (~kind(fred) & ~strong(fred))) & (kind(fred) | strong(fred) | ! [X0] : (creative(X0) & ~funny(X0))) [flattening 52]
54. (? [X0] : (~creative(X0) | funny(X0)) | (~kind(fred) & ~strong(fred))) & (kind(fred) | strong(fred) | ! [X1] : (creative(X1) & ~funny(X1))) [rectify 53]
55. ? [X0] : (~creative(X0) | funny(X0)) => (~creative(sK4) | funny(sK4)) [choice axiom]
56. ((~creative(sK4) | funny(sK4)) | (~kind(fred) & ~strong(fred))) & (kind(fred) | strong(fred) | ! [X1] : (creative(X1) & ~funny(X1))) [skolemisation 54,55]
62. ! [X0] : (((funny(X0) & ~patient(X0)) | (generous(X0) & ~kind(X0))) & ((~generous(X0) | kind(X0)) | (~funny(X0) | patient(X0)))) [nnf transformation 12]
63. ! [X0] : (((funny(X0) & ~patient(X0)) | (generous(X0) & ~kind(X0))) & (~generous(X0) | kind(X0) | ~funny(X0) | patient(X0))) [flattening 62]
73. ? [X0] : funny(X0) => funny(sK9) [choice axiom]
74. funny(sK9) [skolemisation 22,73]
84. ~generous(X0) | ~strong(X0) | rich(X0) [cnf transformation 40]
104. ~rich(X0) | humble(X0) [cnf transformation 34]
110. kind(fred) | strong(fred) | ~funny(X1) [cnf transformation 56]
119. ~patient(X0) | ~kind(X0) [cnf transformation 63]
120. ~patient(X0) | generous(X0) [cnf transformation 63]
142. ~humble(fred) [cnf transformation 17]
148. funny(sK9) [cnf transformation 74]
151. patient(fred) [cnf transformation 25]
256. 23 <=> kind(fred) [avatar definition]
269. 26 <=> strong(fred) [avatar definition]
270. strong(fred) <- (26) [avatar component clause 269]
278. 28 <=> ! [X1] : ~funny(X1) [avatar definition]
279. ~funny(X1) <- (28) [avatar component clause 278]
280. 28 | 26 | 23 [avatar split clause 110,256,269,278]
313. 36 <=> humble(fred) [avatar definition]
314. ~humble(fred) <- (~36) [avatar component clause 313]
373. ~36 [avatar split clause 142,313]
403. ~kind(fred) [resolution 119,151]
408. ~23 [avatar split clause 403,256]
412. generous(fred) [resolution 120,151]
432. ~strong(fred) | rich(fred) [resolution 84,412]
436. rich(fred) <- (26) [subsumption resolution 432,270]
519. humble(fred) <- (26) [resolution 436,104]
522. $false <- (26, ~36) [subsumption resolution 519,314]
523. ~26 | 36 [avatar contradiction clause 522]
536. $false <- (28) [resolution 279,148]
540. ~28 [avatar contradiction clause 536]
541. $false [avatar sat refutation 280,373,408,523,540]
% SZS output end Proof for 5211377684949296539648134
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not rich or not brave is not patient and vice versa.
Everyone who is either kind or patient is not brave.
If someone is either rich or happy then someone is either brave or not patient and vice versa.
If someone is not happy then someone is both generous and not brave and vice versa.
If someone is either brave or curious then someone is not tall.
If mary is not brave or wise then paul is both kind and not wise.
If lucy is funny or humble then someone is either strong or not brave and vice versa.
Everyone who is both generous and not calm is both quiet and old.
Everyone who is calm is both not calm and not funny.
Everyone who is either brave or not funny is either not creative or not wise.
Everyone who is curious or patient is both calm and not wise and vice versa.
Everyone who is either not calm or not generous is not happy or not old.
If lucy is funny or not tall then mary is old and vice versa.
Everyone who is either rich or not patient is patient.
If someone is both humble and rich then paul is both kind and not brave and vice versa.
Everyone who is humble is not creative.
John is patient or humble.
Alice is both not creative and not old.
Lucy is not creative.
Fred is both kind and not funny. | Mary is rich. | entailment | (![X]:((~rich(X)|~brave(X))<=>~patient(X)))&
(![X]:((kind(X)<~>patient(X))=>~brave(X)))&
((?[X]:((rich(X)<~>happy(X))))<=>(?[X]:((brave(X)<~>~patient(X)))))&
((?[X]:(~happy(X)))<=>(?[X]:((generous(X)&~brave(X)))))&
((?[X]:((brave(X)<~>curious(X))))=>(?[X]:(~tall(X))))&
(((~brave(mary)|wise(mary)))=>((kind(paul)&~wise(paul))))&
(((funny(lucy)|humble(lucy)))<=>(?[X]:((strong(X)<~>~brave(X)))))&
(![X]:((generous(X)&~calm(X))=>(quiet(X)&old(X))))&
(![X]:(calm(X)=>(~calm(X)&~funny(X))))&
(![X]:((brave(X)<~>~funny(X))=>(~creative(X)<~>~wise(X))))&
(![X]:((curious(X)|patient(X))<=>(calm(X)&~wise(X))))&
(![X]:((~calm(X)<~>~generous(X))=>(~happy(X)|~old(X))))&
(((funny(lucy)|~tall(lucy)))<=>(old(mary)))&
(![X]:((rich(X)<~>~patient(X))=>patient(X)))&
((?[X]:((humble(X)&rich(X))))<=>((kind(paul)&~brave(paul))))&
(![X]:(humble(X)=>~creative(X)))&
((patient(john)|humble(john)))&
((~creative(alice)&~old(alice)))&
(~creative(lucy))&
((kind(fred)&~funny(fred))) | rich(mary) | [
"p0",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 8922406087694259143911750
% SZS output start Proof for 8922406087694259143911750
1. ! [X0] : ((~brave(X0) | ~rich(X0)) <=> ~patient(X0)) [input p0]
14. ! [X0] : ((rich(X0) <~> ~patient(X0)) => patient(X0)) [input p13]
21. ~rich(mary) [input hypothesis]
35. ! [X0] : (patient(X0) | (rich(X0) <=> ~patient(X0))) [ennf transformation 14]
37. ! [X0] : (((~brave(X0) | ~rich(X0)) | patient(X0)) & (~patient(X0) | (brave(X0) & rich(X0)))) [nnf transformation 1]
38. ! [X0] : ((~brave(X0) | ~rich(X0) | patient(X0)) & (~patient(X0) | (brave(X0) & rich(X0)))) [flattening 37]
65. ! [X0] : (patient(X0) | ((rich(X0) | patient(X0)) & (~patient(X0) | ~rich(X0)))) [nnf transformation 35]
71. ~patient(X0) | rich(X0) [cnf transformation 38]
117. patient(X0) | rich(X0) | patient(X0) [cnf transformation 65]
129. ~rich(mary) [cnf transformation 21]
130. patient(X0) | rich(X0) [duplicate literal removal 117]
267. rich(X0) [subsumption resolution 130,71]
293. $false [subsumption resolution 129,267]
% SZS output end Proof for 8922406087694259143911750
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not calm or not funny is strong.
If lucy is brave or humble then someone is not generous or humble and vice versa.
Everyone who is patient or not old is both not quiet and tall.
Everyone who is rich is strong or not strong.
If mary is both calm and not creative then susan is both old and not generous.
Everyone who is not rich is brave and vice versa.
If paul is both not generous and not curious then lucy is both not creative and not strong and vice versa.
If someone is happy or not kind then john is old or not generous.
If susan is either not generous or rich then mary is not strong and vice versa.
Everyone who is old or not happy is not kind or quiet.
If john is both strong and not generous then someone is either not calm or not tall and vice versa.
If someone is either not tall or generous then paul is either generous or not kind.
If susan is not kind or not quiet then someone is creative or rich and vice versa.
If someone is not happy or funny then paul is not calm or happy.
If someone is both not old and not funny then paul is not creative.
Everyone who is both not brave and rich is funny and vice versa.
Fred is both not curious and funny.
Someone is not patient.
Someone is either not brave or not creative.
Someone is both patient and not creative.
Someone is either not rich or not happy.
Mary is both not rich and not wise.
Lucy is either not tall or rich.
Someone is either not kind or not calm. | Mary is funny. | contradiction | (![X]:((~calm(X)<~>~funny(X))=>strong(X)))&
(((brave(lucy)|humble(lucy)))<=>(?[X]:((~generous(X)|humble(X)))))&
(![X]:((patient(X)|~old(X))=>(~quiet(X)&tall(X))))&
(![X]:(rich(X)=>(strong(X)|~strong(X))))&
(((calm(mary)&~creative(mary)))=>((old(susan)&~generous(susan))))&
(![X]:(~rich(X)<=>brave(X)))&
(((~generous(paul)&~curious(paul)))<=>((~creative(lucy)&~strong(lucy))))&
((?[X]:((happy(X)|~kind(X))))=>((old(john)|~generous(john))))&
(((~generous(susan)<~>rich(susan)))<=>(~strong(mary)))&
(![X]:((old(X)|~happy(X))=>(~kind(X)|quiet(X))))&
(((strong(john)&~generous(john)))<=>(?[X]:((~calm(X)<~>~tall(X)))))&
((?[X]:((~tall(X)<~>generous(X))))=>((generous(paul)<~>~kind(paul))))&
(((~kind(susan)|~quiet(susan)))<=>(?[X]:((creative(X)|rich(X)))))&
((?[X]:((~happy(X)|funny(X))))=>((~calm(paul)|happy(paul))))&
((?[X]:((~old(X)&~funny(X))))=>(~creative(paul)))&
(![X]:((~brave(X)&rich(X))<=>funny(X)))&
((~curious(fred)&funny(fred)))&
(?[X]:(~patient(X)))&
(?[X]:((~brave(X)<~>~creative(X))))&
(?[X]:((patient(X)&~creative(X))))&
(?[X]:((~rich(X)<~>~happy(X))))&
((~rich(mary)&~wise(mary)))&
((~tall(lucy)<~>rich(lucy)))&
(?[X]:((~kind(X)<~>~calm(X)))) | funny(mary) | [
"p5",
"p15",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 9462330856862875655986
% SZS output start Proof for 9462330856862875655986
6. ! [X0] : (~rich(X0) <=> brave(X0)) [input p5]
16. ! [X0] : ((rich(X0) & ~brave(X0)) <=> funny(X0)) [input p15]
22. ~wise(mary) & ~rich(mary) [input p21]
25. funny(mary) [input hypothesis]
26. ~rich(mary) [pure predicate removal 22]
47. ! [X0] : ((~rich(X0) | ~brave(X0)) & (brave(X0) | rich(X0))) [nnf transformation 6]
62. ! [X0] : (((rich(X0) & ~brave(X0)) | ~funny(X0)) & (funny(X0) | (~rich(X0) | brave(X0)))) [nnf transformation 16]
63. ! [X0] : (((rich(X0) & ~brave(X0)) | ~funny(X0)) & (funny(X0) | ~rich(X0) | brave(X0))) [flattening 62]
91. rich(X0) | brave(X0) [cnf transformation 47]
123. ~brave(X0) | ~funny(X0) [cnf transformation 63]
134. ~rich(mary) [cnf transformation 26]
139. funny(mary) [cnf transformation 25]
367. brave(mary) [resolution 91,134]
374. ~funny(mary) [resolution 123,367]
375. $false [subsumption resolution 374,139]
% SZS output end Proof for 9462330856862875655986
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either curious or brave is tall or humble.
If john is both not generous and not patient then alice is not rich.
Everyone who is both not happy and not tall is both humble and old.
Everyone who is both not generous and calm is either not kind or old and vice versa.
Everyone who is not generous is both kind and not quiet and vice versa.
Everyone who is humble or generous is not wise or not happy and vice versa.
If alice is not creative or not kind then someone is not funny or old and vice versa.
If paul is not calm or not generous then lucy is not old or not tall and vice versa.
If someone is not calm then fred is not curious or strong and vice versa.
If john is both old and rich then someone is both not wise and not kind.
Everyone who is not brave is both funny and not wise and vice versa.
Everyone who is happy or not quiet is quiet and vice versa.
Everyone who is kind or not rich is brave or not wise.
Everyone who is quiet or not happy is both kind and not tall.
Everyone who is brave or not wise is rich or brave.
Everyone who is both not quiet and curious is either curious or funny.
Someone is both generous and not creative.
Alice is rich or creative.
Fred is either old or funny.
Susan is not funny.
Alice is not wise. | Lucy is not patient. | neutral | (![X]:((curious(X)<~>brave(X))=>(tall(X)|humble(X))))&
(((~generous(john)&~patient(john)))=>(~rich(alice)))&
(![X]:((~happy(X)&~tall(X))=>(humble(X)&old(X))))&
(![X]:((~generous(X)&calm(X))<=>(~kind(X)<~>old(X))))&
(![X]:(~generous(X)<=>(kind(X)&~quiet(X))))&
(![X]:((humble(X)|generous(X))<=>(~wise(X)|~happy(X))))&
(((~creative(alice)|~kind(alice)))<=>(?[X]:((~funny(X)|old(X)))))&
(((~calm(paul)|~generous(paul)))<=>((~old(lucy)|~tall(lucy))))&
((?[X]:(~calm(X)))<=>((~curious(fred)|strong(fred))))&
(((old(john)&rich(john)))=>(?[X]:((~wise(X)&~kind(X)))))&
(![X]:(~brave(X)<=>(funny(X)&~wise(X))))&
(![X]:((happy(X)|~quiet(X))<=>quiet(X)))&
(![X]:((kind(X)|~rich(X))=>(brave(X)|~wise(X))))&
(![X]:((quiet(X)|~happy(X))=>(kind(X)&~tall(X))))&
(![X]:((brave(X)|~wise(X))=>(rich(X)|brave(X))))&
(![X]:((~quiet(X)&curious(X))=>(curious(X)<~>funny(X))))&
(?[X]:((generous(X)&~creative(X))))&
((rich(alice)|creative(alice)))&
((old(fred)<~>funny(fred)))&
(~funny(susan))&
(~wise(alice)) | ~patient(lucy) | [] | null | 0 |
Everyone who is both old and not creative is not rich or not generous and vice versa.
If someone is either not happy or not kind then someone is either not funny or curious.
If someone is quiet or not calm then paul is humble and vice versa.
If someone is not old then fred is both humble and not kind.
Everyone who is both not calm and strong is both quiet and not quiet and vice versa.
If someone is either not curious or not old then lucy is both not old and not humble and vice versa.
Everyone who is either not quiet or not strong is brave.
If fred is both not quiet and strong then someone is both tall and not funny and vice versa.
If someone is either not old or not wise then paul is not old and vice versa.
Everyone who is not brave is either not happy or strong.
Everyone who is not humble is generous.
Everyone who is either not strong or not old is not calm or happy.
If john is wise or not creative then someone is patient and vice versa.
Everyone who is not happy or not curious is not old or not quiet and vice versa.
Everyone who is not creative is either calm or not wise and vice versa.
If fred is both not rich and old then someone is rich.
Paul is kind.
Paul is not humble or old.
Lucy is wise or quiet.
Someone is either calm or not strong.
Alice is both humble and not funny.
Fred is either not quiet or not happy.
Someone is humble. | Fred is quiet. | neutral | (![X]:((old(X)&~creative(X))<=>(~rich(X)|~generous(X))))&
((?[X]:((~happy(X)<~>~kind(X))))=>(?[X]:((~funny(X)<~>curious(X)))))&
((?[X]:((quiet(X)|~calm(X))))<=>(humble(paul)))&
((?[X]:(~old(X)))=>((humble(fred)&~kind(fred))))&
(![X]:((~calm(X)&strong(X))<=>(quiet(X)&~quiet(X))))&
((?[X]:((~curious(X)<~>~old(X))))<=>((~old(lucy)&~humble(lucy))))&
(![X]:((~quiet(X)<~>~strong(X))=>brave(X)))&
(((~quiet(fred)&strong(fred)))<=>(?[X]:((tall(X)&~funny(X)))))&
((?[X]:((~old(X)<~>~wise(X))))<=>(~old(paul)))&
(![X]:(~brave(X)=>(~happy(X)<~>strong(X))))&
(![X]:(~humble(X)=>generous(X)))&
(![X]:((~strong(X)<~>~old(X))=>(~calm(X)|happy(X))))&
(((wise(john)|~creative(john)))<=>(?[X]:(patient(X))))&
(![X]:((~happy(X)|~curious(X))<=>(~old(X)|~quiet(X))))&
(![X]:(~creative(X)<=>(calm(X)<~>~wise(X))))&
(((~rich(fred)&old(fred)))=>(?[X]:(rich(X))))&
(kind(paul))&
((~humble(paul)|old(paul)))&
((wise(lucy)|quiet(lucy)))&
(?[X]:((calm(X)<~>~strong(X))))&
((humble(alice)&~funny(alice)))&
((~quiet(fred)<~>~happy(fred)))&
(?[X]:(humble(X))) | quiet(fred) | [] | null | 0 |
If john is both kind and not funny then someone is not creative. Everyone who is either not happy or not quiet is both tall and not creative. Everyone who is quiet is not rich or not calm. If john is either strong or generous then someone is either not brave or not humble and vice versa. Everyone who is not tall is both not curious and not strong. Everyone who is either rich or wise is both not quiet and not humble. Everyone who is either generous or not happy is not generous and vice versa. Everyone who is curious is not kind or humble and vice versa. Everyone who is patient or strong is happy or not kind. If fred is either not curious or old then someone is both not creative and patient and vice versa. Everyone who is humble is not brave or old and vice versa. If susan is both not wise and not rich then alice is generous or not calm and vice versa. If someone is not rich or curious then someone is both not generous and old. If someone is both rich and happy then mary is quiet and vice versa. If john is not happy or curious then susan is old or strong and vice versa. Everyone who is both happy and kind is either not curious or not tall and vice versa. Someone is either not patient or wise. Someone is both calm and humble. Paul is both humble and rich. John is not creative or happy. Someone is either not humble or generous. Alice is calm. Someone is either not generous or funny. | Susan is patient. | neutral | (((kind(john)&~funny(john)))=>(?[X]:(~creative(X))))&
(![X]:((~happy(X)<~>~quiet(X))=>(tall(X)&~creative(X))))&
(![X]:(quiet(X)=>(~rich(X)|~calm(X))))&
(((strong(john)<~>generous(john)))<=>(?[X]:((~brave(X)<~>~humble(X)))))&
(![X]:(~tall(X)=>(~curious(X)&~strong(X))))&
(![X]:((rich(X)<~>wise(X))=>(~quiet(X)&~humble(X))))&
(![X]:((generous(X)<~>~happy(X))<=>~generous(X)))&
(![X]:(curious(X)<=>(~kind(X)|humble(X))))&
(![X]:((patient(X)|strong(X))=>(happy(X)|~kind(X))))&
(((~curious(fred)<~>old(fred)))<=>(?[X]:((~creative(X)&patient(X)))))&
(![X]:(humble(X)<=>(~brave(X)|old(X))))&
(((~wise(susan)&~rich(susan)))<=>((generous(alice)|~calm(alice))))&
((?[X]:((~rich(X)|curious(X))))=>(?[X]:((~generous(X)&old(X)))))&
((?[X]:((rich(X)&happy(X))))<=>(quiet(mary)))&
(((~happy(john)|curious(john)))<=>((old(susan)|strong(susan))))&
(![X]:((happy(X)&kind(X))<=>(~curious(X)<~>~tall(X))))&
(?[X]:((~patient(X)<~>wise(X))))&
(?[X]:((calm(X)&humble(X))))&
((humble(paul)&rich(paul)))&
((~creative(john)|happy(john)))&
(?[X]:((~humble(X)<~>generous(X))))&
(calm(alice))&
(?[X]:((~generous(X)<~>funny(X)))) | patient(susan) | [] | null | 0 |
If someone is either tall or not kind then someone is both happy and calm and vice versa. Everyone who is strong or rich is not kind or not rich. Everyone who is not rich or funny is either not curious or kind. If alice is both patient and not happy then someone is either not curious or not old. Everyone who is not wise or not old is both rich and not wise and vice versa. If john is not brave or not kind then alice is either not humble or not kind. Everyone who is humble or creative is either not humble or brave. Everyone who is not creative or creative is funny. If someone is patient then someone is both not curious and not generous and vice versa. If someone is both brave and not old then someone is kind or not strong. If someone is both old and not funny then someone is rich and vice versa. Everyone who is both not strong and not wise is both not wise and not calm. Everyone who is not calm is not quiet or old and vice versa. Everyone who is patient is either not old or not wise and vice versa. If lucy is both old and not tall then alice is either not curious or curious and vice versa. Everyone who is rich or quiet is not generous. Someone is rich or not happy. Someone is not happy. Alice is not wise or tall. Lucy is either not kind or not tall. Alice is both tall and not happy. | Alice is rich. | contradiction | ((?[X]:((tall(X)<~>~kind(X))))<=>(?[X]:((happy(X)&calm(X)))))&
(![X]:((strong(X)|rich(X))=>(~kind(X)|~rich(X))))&
(![X]:((~rich(X)|funny(X))=>(~curious(X)<~>kind(X))))&
(((patient(alice)&~happy(alice)))=>(?[X]:((~curious(X)<~>~old(X)))))&
(![X]:((~wise(X)|~old(X))<=>(rich(X)&~wise(X))))&
(((~brave(john)|~kind(john)))=>((~humble(alice)<~>~kind(alice))))&
(![X]:((humble(X)|creative(X))=>(~humble(X)<~>brave(X))))&
(![X]:((~creative(X)|creative(X))=>funny(X)))&
((?[X]:(patient(X)))<=>(?[X]:((~curious(X)&~generous(X)))))&
((?[X]:((brave(X)&~old(X))))=>(?[X]:((kind(X)|~strong(X)))))&
((?[X]:((old(X)&~funny(X))))<=>(?[X]:(rich(X))))&
(![X]:((~strong(X)&~wise(X))=>(~wise(X)&~calm(X))))&
(![X]:(~calm(X)<=>(~quiet(X)|old(X))))&
(![X]:(patient(X)<=>(~old(X)<~>~wise(X))))&
(((old(lucy)&~tall(lucy)))<=>((~curious(alice)<~>curious(alice))))&
(![X]:((rich(X)|quiet(X))=>~generous(X)))&
(?[X]:((rich(X)|~happy(X))))&
(?[X]:(~happy(X)))&
((~wise(alice)|tall(alice)))&
((~kind(lucy)<~>~tall(lucy)))&
((tall(alice)&~happy(alice))) | rich(alice) | [
"p7",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 7652744548693845375390023
% SZS output start Proof for 7652744548693845375390023
8. ! [X0] : ((creative(X0) | ~creative(X0)) => funny(X0)) [input p7]
11. ? [X0] : (~funny(X0) & old(X0)) <=> ? [X0] : rich(X0) [input p10]
22. rich(alice) [input hypothesis]
26. ? [X0] : (~funny(X0) & old(X0)) <=> ? [X1] : rich(X1) [rectify 11]
34. ! [X0] : (funny(X0) | (~creative(X0) & creative(X0))) [ennf transformation 8]
60. (? [X0] : (~funny(X0) & old(X0)) | ! [X1] : ~rich(X1)) & (? [X1] : rich(X1) | ! [X0] : (funny(X0) | ~old(X0))) [nnf transformation 26]
61. (? [X0] : (~funny(X0) & old(X0)) | ! [X1] : ~rich(X1)) & (? [X2] : rich(X2) | ! [X3] : (funny(X3) | ~old(X3))) [rectify 60]
62. ? [X0] : (~funny(X0) & old(X0)) => (~funny(sK6) & old(sK6)) [choice axiom]
63. ? [X2] : rich(X2) => rich(sK7) [choice axiom]
64. ((~funny(sK6) & old(sK6)) | ! [X1] : ~rich(X1)) & (rich(sK7) | ! [X3] : (funny(X3) | ~old(X3))) [skolemisation 61,63,62]
102. funny(X0) | creative(X0) [cnf transformation 34]
103. funny(X0) | ~creative(X0) [cnf transformation 34]
110. ~funny(sK6) | ~rich(X1) [cnf transformation 64]
135. rich(alice) [cnf transformation 22]
212. funny(X0) [subsumption resolution 102,103]
246. ~rich(X1) [subsumption resolution 110,212]
283. $false [subsumption resolution 135,246]
% SZS output end Proof for 7652744548693845375390023
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not strong and calm then fred is not creative and vice versa.
Everyone who is quiet is either curious or strong and vice versa.
Everyone who is both not rich and brave is either tall or not funny and vice versa.
Everyone who is strong is either not strong or happy.
Everyone who is tall is both rich and creative and vice versa.
Everyone who is either not generous or not happy is both humble and not calm and vice versa.
Everyone who is both not tall and not brave is not patient or patient and vice versa.
Everyone who is both not patient and not wise is either quiet or funny.
If someone is either strong or old then someone is not strong and vice versa.
Everyone who is not rich or not happy is wise or not funny.
Everyone who is both happy and tall is both not kind and not brave.
If someone is both curious and not quiet then mary is strong.
If susan is both not tall and not brave then susan is either not creative or rich and vice versa.
Everyone who is rich or curious is both not generous and not calm.
If mary is both not generous and humble then someone is not curious or not calm.
If someone is not tall or patient then someone is not tall and vice versa.
Alice is not generous.
Someone is not generous.
Someone is generous or not quiet.
Someone is both patient and not tall.
Fred is both creative and not rich.
Someone is either not humble or not wise.
Mary is not strong.
Lucy is not kind or old. | Susan is generous. | neutral | ((?[X]:((~strong(X)&calm(X))))<=>(~creative(fred)))&
(![X]:(quiet(X)<=>(curious(X)<~>strong(X))))&
(![X]:((~rich(X)&brave(X))<=>(tall(X)<~>~funny(X))))&
(![X]:(strong(X)=>(~strong(X)<~>happy(X))))&
(![X]:(tall(X)<=>(rich(X)&creative(X))))&
(![X]:((~generous(X)<~>~happy(X))<=>(humble(X)&~calm(X))))&
(![X]:((~tall(X)&~brave(X))<=>(~patient(X)|patient(X))))&
(![X]:((~patient(X)&~wise(X))=>(quiet(X)<~>funny(X))))&
((?[X]:((strong(X)<~>old(X))))<=>(?[X]:(~strong(X))))&
(![X]:((~rich(X)|~happy(X))=>(wise(X)|~funny(X))))&
(![X]:((happy(X)&tall(X))=>(~kind(X)&~brave(X))))&
((?[X]:((curious(X)&~quiet(X))))=>(strong(mary)))&
(((~tall(susan)&~brave(susan)))<=>((~creative(susan)<~>rich(susan))))&
(![X]:((rich(X)|curious(X))=>(~generous(X)&~calm(X))))&
(((~generous(mary)&humble(mary)))=>(?[X]:((~curious(X)|~calm(X)))))&
((?[X]:((~tall(X)|patient(X))))<=>(?[X]:(~tall(X))))&
(~generous(alice))&
(?[X]:(~generous(X)))&
(?[X]:((generous(X)|~quiet(X))))&
(?[X]:((patient(X)&~tall(X))))&
((creative(fred)&~rich(fred)))&
(?[X]:((~humble(X)<~>~wise(X))))&
(~strong(mary))&
((~kind(lucy)|old(lucy))) | generous(susan) | [] | null | 0 |
Everyone who is either not curious or generous is humble and vice versa. Everyone who is old is either happy or not creative. Everyone who is both wise and rich is not curious and vice versa. Everyone who is both not strong and rich is not patient or not humble and vice versa. Everyone who is kind or not patient is not creative or wise and vice versa. Everyone who is not old is either not calm or not wise and vice versa. Everyone who is wise is happy or brave and vice versa. Everyone who is both not generous and not quiet is not tall or not old. If someone is not wise then fred is both creative and not funny and vice versa. If alice is rich or not creative then fred is both not patient and brave and vice versa. If mary is both tall and not patient then someone is either not strong or not funny. If john is not patient or not rich then someone is both not kind and kind and vice versa. If someone is not wise then someone is either not calm or not quiet and vice versa. Everyone who is creative is both strong and not creative. If paul is either patient or not kind then someone is both tall and not creative. Everyone who is either not happy or rich is not calm or rich and vice versa. Fred is both not tall and not humble. Someone is wise. Someone is not brave or patient. Susan is not generous. | John is not quiet. | entailment | (![X]:((~curious(X)<~>generous(X))<=>humble(X)))&
(![X]:(old(X)=>(happy(X)<~>~creative(X))))&
(![X]:((wise(X)&rich(X))<=>~curious(X)))&
(![X]:((~strong(X)&rich(X))<=>(~patient(X)|~humble(X))))&
(![X]:((kind(X)|~patient(X))<=>(~creative(X)|wise(X))))&
(![X]:(~old(X)<=>(~calm(X)<~>~wise(X))))&
(![X]:(wise(X)<=>(happy(X)|brave(X))))&
(![X]:((~generous(X)&~quiet(X))=>(~tall(X)|~old(X))))&
((?[X]:(~wise(X)))<=>((creative(fred)&~funny(fred))))&
(((rich(alice)|~creative(alice)))<=>((~patient(fred)&brave(fred))))&
(((tall(mary)&~patient(mary)))=>(?[X]:((~strong(X)<~>~funny(X)))))&
(((~patient(john)|~rich(john)))<=>(?[X]:((~kind(X)&kind(X)))))&
((?[X]:(~wise(X)))<=>(?[X]:((~calm(X)<~>~quiet(X)))))&
(![X]:(creative(X)=>(strong(X)&~creative(X))))&
(((patient(paul)<~>~kind(paul)))=>(?[X]:((tall(X)&~creative(X)))))&
(![X]:((~happy(X)<~>rich(X))<=>(~calm(X)|rich(X))))&
((~tall(fred)&~humble(fred)))&
(?[X]:(wise(X)))&
(?[X]:((~brave(X)|patient(X))))&
(~generous(susan)) | ~quiet(john) | [
"p1",
"p5",
"p8",
"p11",
"p12",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4655601805042322684769454
% SZS output start Proof for 4655601805042322684769454
2. ! [X0] : (old(X0) => (happy(X0) <~> ~creative(X0))) [input p1]
6. ! [X0] : (~old(X0) <=> (~calm(X0) <~> ~wise(X0))) [input p5]
9. ? [X0] : ~wise(X0) <=> (~funny(fred) & creative(fred)) [input p8]
12. (~rich(john) | ~patient(john)) <=> ? [X0] : (kind(X0) & ~kind(X0)) [input p11]
13. ? [X0] : ~wise(X0) <=> ? [X0] : (~calm(X0) <~> ~quiet(X0)) [input p12]
14. ! [X0] : (creative(X0) => (~creative(X0) & strong(X0))) [input p13]
16. ! [X0] : ((~happy(X0) <~> rich(X0)) <=> (rich(X0) | ~calm(X0))) [input p15]
21. quiet(john) [input hypothesis]
22. ? [X0] : ~wise(X0) <=> ? [X1] : (~calm(X1) <~> ~quiet(X1)) [rectify 13]
23. ! [X0] : (~old(X0) => (~calm(X0) <~> ~wise(X0))) [unused predicate definition removal 6]
24. ! [X0] : ((happy(X0) <~> ~creative(X0)) | ~old(X0)) [ennf transformation 2]
25. ! [X0] : ((~calm(X0) <~> ~wise(X0)) | old(X0)) [ennf transformation 23]
30. ! [X0] : ((~creative(X0) & strong(X0)) | ~creative(X0)) [ennf transformation 14]
33. ! [X0] : (((creative(X0) | ~happy(X0)) & (~creative(X0) | happy(X0))) | ~old(X0)) [nnf transformation 24]
40. ! [X0] : (((wise(X0) | calm(X0)) & (~wise(X0) | ~calm(X0))) | old(X0)) [nnf transformation 25]
43. (? [X0] : ~wise(X0) | (funny(fred) | ~creative(fred))) & ((~funny(fred) & creative(fred)) | ! [X0] : wise(X0)) [nnf transformation 9]
44. (? [X0] : ~wise(X0) | funny(fred) | ~creative(fred)) & ((~funny(fred) & creative(fred)) | ! [X0] : wise(X0)) [flattening 43]
45. (? [X0] : ~wise(X0) | funny(fred) | ~creative(fred)) & ((~funny(fred) & creative(fred)) | ! [X1] : wise(X1)) [rectify 44]
46. ? [X0] : ~wise(X0) => ~wise(sK0) [choice axiom]
47. (~wise(sK0) | funny(fred) | ~creative(fred)) & ((~funny(fred) & creative(fred)) | ! [X1] : wise(X1)) [skolemisation 45,46]
53. ((~rich(john) | ~patient(john)) | ! [X0] : (~kind(X0) | kind(X0))) & (? [X0] : (kind(X0) & ~kind(X0)) | (rich(john) & patient(john))) [nnf transformation 12]
54. (~rich(john) | ~patient(john) | ! [X0] : (~kind(X0) | kind(X0))) & (? [X0] : (kind(X0) & ~kind(X0)) | (rich(john) & patient(john))) [flattening 53]
55. (~rich(john) | ~patient(john) | ! [X0] : (~kind(X0) | kind(X0))) & (? [X1] : (kind(X1) & ~kind(X1)) | (rich(john) & patient(john))) [rectify 54]
56. ? [X1] : (kind(X1) & ~kind(X1)) => (kind(sK2) & ~kind(sK2)) [choice axiom]
57. (~rich(john) | ~patient(john) | ! [X0] : (~kind(X0) | kind(X0))) & ((kind(sK2) & ~kind(sK2)) | (rich(john) & patient(john))) [skolemisation 55,56]
58. (? [X0] : ~wise(X0) | ! [X1] : ((~calm(X1) | quiet(X1)) & (~quiet(X1) | calm(X1)))) & (? [X1] : ((quiet(X1) | calm(X1)) & (~quiet(X1) | ~calm(X1))) | ! [X0] : wise(X0)) [nnf transformation 22]
59. (? [X0] : ~wise(X0) | ! [X1] : ((~calm(X1) | quiet(X1)) & (~quiet(X1) | calm(X1)))) & (? [X2] : ((quiet(X2) | calm(X2)) & (~quiet(X2) | ~calm(X2))) | ! [X3] : wise(X3)) [rectify 58]
60. ? [X0] : ~wise(X0) => ~wise(sK3) [choice axiom]
61. ? [X2] : ((quiet(X2) | calm(X2)) & (~quiet(X2) | ~calm(X2))) => ((quiet(sK4) | calm(sK4)) & (~quiet(sK4) | ~calm(sK4))) [choice axiom]
62. (~wise(sK3) | ! [X1] : ((~calm(X1) | quiet(X1)) & (~quiet(X1) | calm(X1)))) & (((quiet(sK4) | calm(sK4)) & (~quiet(sK4) | ~calm(sK4))) | ! [X3] : wise(X3)) [skolemisation 59,61,60]
66. ! [X0] : ((((~rich(X0) | happy(X0)) & (rich(X0) | ~happy(X0))) | (~rich(X0) & calm(X0))) & ((rich(X0) | ~calm(X0)) | ((~happy(X0) | ~rich(X0)) & (rich(X0) | happy(X0))))) [nnf transformation 16]
67. ! [X0] : ((((~rich(X0) | happy(X0)) & (rich(X0) | ~happy(X0))) | (~rich(X0) & calm(X0))) & (rich(X0) | ~calm(X0) | ((~happy(X0) | ~rich(X0)) & (rich(X0) | happy(X0))))) [flattening 66]
77. ~happy(X0) | creative(X0) | ~old(X0) [cnf transformation 33]
90. ~calm(X0) | ~wise(X0) | old(X0) [cnf transformation 40]
96. creative(fred) | wise(X1) [cnf transformation 47]
107. ~kind(sK2) | rich(john) [cnf transformation 57]
109. kind(sK2) | rich(john) [cnf transformation 57]
113. ~wise(sK3) | ~quiet(X1) | calm(X1) [cnf transformation 62]
116. ~creative(X0) | ~creative(X0) [cnf transformation 30]
126. ~rich(X0) | happy(X0) | ~rich(X0) [cnf transformation 67]
132. quiet(john) [cnf transformation 21]
134. ~rich(X0) | happy(X0) [duplicate literal removal 126]
135. ~creative(X0) [duplicate literal removal 116]
137. 1 <=> creative(fred) [avatar definition]
138. creative(fred) <- (1) [avatar component clause 137]
150. 4 <=> ! [X1] : wise(X1) [avatar definition]
151. wise(X1) <- (4) [avatar component clause 150]
153. 4 | 1 [avatar split clause 96,137,150]
194. 13 <=> rich(john) [avatar definition]
196. rich(john) <- (13) [avatar component clause 194]
198. 14 <=> kind(sK2) [avatar definition]
201. 13 | 14 [avatar split clause 109,198,194]
207. 13 | ~14 [avatar split clause 107,198,194]
213. 17 <=> wise(sK3) [avatar definition]
215. ~wise(sK3) <- (~17) [avatar component clause 213]
218. 18 <=> ! [X1] : (~quiet(X1) | calm(X1)) [avatar definition]
219. ~quiet(X1) | calm(X1) <- (18) [avatar component clause 218]
220. 18 | ~17 [avatar split clause 113,213,218]
255. $false <- (4, ~17) [resolution 215,151]
256. ~4 | 17 [avatar contradiction clause 255]
257. $false <- (1) [subsumption resolution 138,135]
258. ~1 [avatar contradiction clause 257]
267. happy(john) <- (13) [resolution 134,196]
272. calm(john) <- (18) [resolution 219,132]
297. creative(john) | ~old(john) <- (13) [resolution 77,267]
302. ~old(john) <- (13) [subsumption resolution 297,135]
333. ~wise(john) | old(john) <- (18) [resolution 90,272]
334. old(john) <- (4, 18) [subsumption resolution 333,151]
335. $false <- (4, 13, 18) [subsumption resolution 334,302]
336. ~4 | ~13 | ~18 [avatar contradiction clause 335]
337. $false [avatar sat refutation 153,201,207,220,256,258,336]
% SZS output end Proof for 4655601805042322684769454
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not tall or not curious is both rich and happy and vice versa.
Everyone who is either not funny or not tall is not brave.
If someone is either not strong or not calm then paul is both quiet and humble.
If someone is both not happy and not curious then someone is curious or not kind and vice versa.
Everyone who is not curious or not happy is either not kind or not patient.
Everyone who is humble is old or happy.
If fred is either brave or quiet then someone is either not tall or not generous.
Everyone who is not happy or not humble is not brave or not funny and vice versa.
Everyone who is either quiet or tall is either not patient or funny and vice versa.
Everyone who is patient or humble is not old and vice versa.
If someone is tall then someone is either not strong or tall and vice versa.
If susan is rich or generous then paul is humble or not funny.
If someone is either not rich or not humble then someone is both curious and not tall and vice versa.
If alice is curious or not funny then fred is happy or not strong and vice versa.
Everyone who is either not tall or not patient is both not happy and not curious and vice versa.
If someone is both generous and not humble then fred is either kind or not humble and vice versa.
Lucy is both not curious and strong.
Susan is either not rich or happy.
Someone is not rich or not tall.
John is not funny or rich.
Susan is both patient and not funny.
Paul is curious or not curious.
Someone is either not calm or not kind. | Susan is not funny. | entailment | (![X]:((~tall(X)<~>~curious(X))<=>(rich(X)&happy(X))))&
(![X]:((~funny(X)<~>~tall(X))=>~brave(X)))&
((?[X]:((~strong(X)<~>~calm(X))))=>((quiet(paul)&humble(paul))))&
((?[X]:((~happy(X)&~curious(X))))<=>(?[X]:((curious(X)|~kind(X)))))&
(![X]:((~curious(X)|~happy(X))=>(~kind(X)<~>~patient(X))))&
(![X]:(humble(X)=>(old(X)|happy(X))))&
(((brave(fred)<~>quiet(fred)))=>(?[X]:((~tall(X)<~>~generous(X)))))&
(![X]:((~happy(X)|~humble(X))<=>(~brave(X)|~funny(X))))&
(![X]:((quiet(X)<~>tall(X))<=>(~patient(X)<~>funny(X))))&
(![X]:((patient(X)|humble(X))<=>~old(X)))&
((?[X]:(tall(X)))<=>(?[X]:((~strong(X)<~>tall(X)))))&
(((rich(susan)|generous(susan)))=>((humble(paul)|~funny(paul))))&
((?[X]:((~rich(X)<~>~humble(X))))<=>(?[X]:((curious(X)&~tall(X)))))&
(((curious(alice)|~funny(alice)))<=>((happy(fred)|~strong(fred))))&
(![X]:((~tall(X)<~>~patient(X))<=>(~happy(X)&~curious(X))))&
((?[X]:((generous(X)&~humble(X))))<=>((kind(fred)<~>~humble(fred))))&
((~curious(lucy)&strong(lucy)))&
((~rich(susan)<~>happy(susan)))&
(?[X]:((~rich(X)|~tall(X))))&
((~funny(john)|rich(john)))&
((patient(susan)&~funny(susan)))&
((curious(paul)|~curious(paul)))&
(?[X]:((~calm(X)<~>~kind(X)))) | ~funny(susan) | [
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 5833338904552485481432270
% SZS output start Proof for 5833338904552485481432270
21. ~funny(susan) & patient(susan) [input p20]
24. funny(susan) [input hypothesis]
153. ~funny(susan) [cnf transformation 21]
157. funny(susan) [cnf transformation 24]
376. $false [subsumption resolution 157,153]
% SZS output end Proof for 5833338904552485481432270
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is strong or not rich is not patient and vice versa.
If alice is either not happy or creative then susan is either generous or not funny.
Everyone who is funny or not strong is not humble.
Everyone who is both not quiet and not calm is strong.
Everyone who is either not happy or not strong is wise or not tall and vice versa.
Everyone who is strong is either not kind or creative.
Everyone who is either old or quiet is either not creative or calm and vice versa.
If paul is either not generous or not creative then someone is either not generous or rich.
Everyone who is tall or not funny is both not kind and generous and vice versa.
If paul is wise or not strong then john is not generous and vice versa.
Everyone who is not rich or kind is not old or creative.
Everyone who is strong is not brave or not rich and vice versa.
If paul is both calm and patient then someone is patient.
If someone is either not kind or not brave then someone is both quiet and creative.
Everyone who is either wise or not quiet is not rich or not patient.
Everyone who is not tall is not funny and vice versa.
Susan is either rich or generous.
Someone is not old or tall.
Someone is either curious or calm.
John is either not generous or creative.
Someone is not creative.
Paul is patient or rich.
Someone is not strong or not tall.
Someone is quiet or not curious. | John is brave. | entailment | (![X]:((strong(X)|~rich(X))<=>~patient(X)))&
(((~happy(alice)<~>creative(alice)))=>((generous(susan)<~>~funny(susan))))&
(![X]:((funny(X)|~strong(X))=>~humble(X)))&
(![X]:((~quiet(X)&~calm(X))=>strong(X)))&
(![X]:((~happy(X)<~>~strong(X))<=>(wise(X)|~tall(X))))&
(![X]:(strong(X)=>(~kind(X)<~>creative(X))))&
(![X]:((old(X)<~>quiet(X))<=>(~creative(X)<~>calm(X))))&
(((~generous(paul)<~>~creative(paul)))=>(?[X]:((~generous(X)<~>rich(X)))))&
(![X]:((tall(X)|~funny(X))<=>(~kind(X)&generous(X))))&
(((wise(paul)|~strong(paul)))<=>(~generous(john)))&
(![X]:((~rich(X)|kind(X))=>(~old(X)|creative(X))))&
(![X]:(strong(X)<=>(~brave(X)|~rich(X))))&
(((calm(paul)&patient(paul)))=>(?[X]:(patient(X))))&
((?[X]:((~kind(X)<~>~brave(X))))=>(?[X]:((quiet(X)&creative(X)))))&
(![X]:((wise(X)<~>~quiet(X))=>(~rich(X)|~patient(X))))&
(![X]:(~tall(X)<=>~funny(X)))&
((rich(susan)<~>generous(susan)))&
(?[X]:((~old(X)|tall(X))))&
(?[X]:((curious(X)<~>calm(X))))&
((~generous(john)<~>creative(john)))&
(?[X]:(~creative(X)))&
((patient(paul)|rich(paul)))&
(?[X]:((~strong(X)|~tall(X))))&
(?[X]:((quiet(X)|~curious(X)))) | brave(john) | [
"p5",
"p8",
"p11",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 2775156286076592813981002
% SZS output start Proof for 2775156286076592813981002
6. ! [X0] : (strong(X0) => (~kind(X0) <~> creative(X0))) [input p5]
9. ! [X0] : ((~funny(X0) | tall(X0)) <=> (generous(X0) & ~kind(X0))) [input p8]
12. ! [X0] : (strong(X0) <=> (~rich(X0) | ~brave(X0))) [input p11]
16. ! [X0] : (~tall(X0) <=> ~funny(X0)) [input p15]
20. ~generous(john) <~> creative(john) [input p19]
25. ~brave(john) [input hypothesis]
31. ! [X0] : ((~kind(X0) <~> creative(X0)) | ~strong(X0)) [ennf transformation 6]
45. ! [X0] : (((~creative(X0) | kind(X0)) & (creative(X0) | ~kind(X0))) | ~strong(X0)) [nnf transformation 31]
50. ! [X0] : (((~funny(X0) | tall(X0)) | (~generous(X0) | kind(X0))) & ((generous(X0) & ~kind(X0)) | (funny(X0) & ~tall(X0)))) [nnf transformation 9]
51. ! [X0] : ((~funny(X0) | tall(X0) | ~generous(X0) | kind(X0)) & ((generous(X0) & ~kind(X0)) | (funny(X0) & ~tall(X0)))) [flattening 50]
54. ! [X0] : ((strong(X0) | (rich(X0) & brave(X0))) & ((~rich(X0) | ~brave(X0)) | ~strong(X0))) [nnf transformation 12]
55. ! [X0] : ((strong(X0) | (rich(X0) & brave(X0))) & (~rich(X0) | ~brave(X0) | ~strong(X0))) [flattening 54]
63. ! [X0] : ((~tall(X0) | funny(X0)) & (~funny(X0) | tall(X0))) [nnf transformation 16]
70. (~creative(john) | generous(john)) & (creative(john) | ~generous(john)) [nnf transformation 20]
92. ~creative(X0) | kind(X0) | ~strong(X0) [cnf transformation 45]
105. ~kind(X0) | ~tall(X0) [cnf transformation 51]
106. ~kind(X0) | funny(X0) [cnf transformation 51]
107. ~tall(X0) | generous(X0) [cnf transformation 51]
108. funny(X0) | generous(X0) [cnf transformation 51]
116. brave(X0) | strong(X0) [cnf transformation 55]
125. ~funny(X0) | tall(X0) [cnf transformation 63]
132. creative(john) | ~generous(john) [cnf transformation 70]
138. ~brave(john) [cnf transformation 25]
180. 9 <=> generous(john) [avatar definition]
181. ~generous(john) <- (~9) [avatar component clause 180]
253. 24 <=> creative(john) [avatar definition]
254. creative(john) <- (24) [avatar component clause 253]
257. ~9 | 24 [avatar split clause 132,253,180]
277. strong(john) [resolution 116,138]
280. tall(X0) | generous(X0) [resolution 125,108]
281. generous(X0) [subsumption resolution 280,107]
283. $false <- (~9) [resolution 281,181]
284. 9 [avatar contradiction clause 283]
325. kind(john) | ~strong(john) <- (24) [resolution 92,254]
328. kind(john) <- (24) [subsumption resolution 325,277]
344. funny(john) <- (24) [resolution 328,106]
345. ~tall(john) <- (24) [resolution 328,105]
354. tall(john) <- (24) [resolution 344,125]
355. $false <- (24) [subsumption resolution 354,345]
356. ~24 [avatar contradiction clause 355]
357. $false [avatar sat refutation 257,284,356]
% SZS output end Proof for 2775156286076592813981002
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both old and not wise is humble or not brave and vice versa.
Everyone who is either not brave or happy is not patient and vice versa.
If susan is either not patient or old then someone is not generous and vice versa.
Everyone who is not curious is curious or creative.
If someone is not brave then john is either generous or calm.
Everyone who is both creative and not patient is kind.
If someone is either not kind or not old then someone is not funny.
Everyone who is both not funny and not tall is either not happy or not patient and vice versa.
Everyone who is both creative and kind is patient.
If mary is either not creative or wise then someone is not tall or wise and vice versa.
Everyone who is either quiet or not curious is not kind.
If john is not happy then someone is both humble and not wise.
Everyone who is not old is either happy or not happy.
Everyone who is not quiet is either not happy or tall and vice versa.
Everyone who is both not tall and not patient is humble or curious and vice versa.
Everyone who is both not generous and not humble is not wise or not funny and vice versa.
Lucy is both not humble and wise.
Lucy is rich or funny.
Someone is either brave or not old.
Fred is both not old and not strong.
Someone is curious or calm.
Paul is both brave and not rich.
Alice is either not generous or brave.
Someone is wise or generous. | Mary is not tall. | entailment | (![X]:((old(X)&~wise(X))<=>(humble(X)|~brave(X))))&
(![X]:((~brave(X)<~>happy(X))<=>~patient(X)))&
(((~patient(susan)<~>old(susan)))<=>(?[X]:(~generous(X))))&
(![X]:(~curious(X)=>(curious(X)|creative(X))))&
((?[X]:(~brave(X)))=>((generous(john)<~>calm(john))))&
(![X]:((creative(X)&~patient(X))=>kind(X)))&
((?[X]:((~kind(X)<~>~old(X))))=>(?[X]:(~funny(X))))&
(![X]:((~funny(X)&~tall(X))<=>(~happy(X)<~>~patient(X))))&
(![X]:((creative(X)&kind(X))=>patient(X)))&
(((~creative(mary)<~>wise(mary)))<=>(?[X]:((~tall(X)|wise(X)))))&
(![X]:((quiet(X)<~>~curious(X))=>~kind(X)))&
((~happy(john))=>(?[X]:((humble(X)&~wise(X)))))&
(![X]:(~old(X)=>(happy(X)<~>~happy(X))))&
(![X]:(~quiet(X)<=>(~happy(X)<~>tall(X))))&
(![X]:((~tall(X)&~patient(X))<=>(humble(X)|curious(X))))&
(![X]:((~generous(X)&~humble(X))<=>(~wise(X)|~funny(X))))&
((~humble(lucy)&wise(lucy)))&
((rich(lucy)|funny(lucy)))&
(?[X]:((brave(X)<~>~old(X))))&
((~old(fred)&~strong(fred)))&
(?[X]:((curious(X)|calm(X))))&
((brave(paul)&~rich(paul)))&
((~generous(alice)<~>brave(alice)))&
(?[X]:((wise(X)|generous(X)))) | ~tall(mary) | [
"p0",
"p1",
"p3",
"p5",
"p7",
"p8",
"p9",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 61025223863462326502037
% SZS output start Proof for 61025223863462326502037
1. ! [X0] : ((~wise(X0) & old(X0)) <=> (~brave(X0) | humble(X0))) [input p0]
2. ! [X0] : ((~brave(X0) <~> happy(X0)) <=> ~patient(X0)) [input p1]
4. ! [X0] : (~curious(X0) => (creative(X0) | curious(X0))) [input p3]
6. ! [X0] : ((~patient(X0) & creative(X0)) => kind(X0)) [input p5]
8. ! [X0] : ((~tall(X0) & ~funny(X0)) <=> (~happy(X0) <~> ~patient(X0))) [input p7]
9. ! [X0] : ((kind(X0) & creative(X0)) => patient(X0)) [input p8]
10. (~creative(mary) <~> wise(mary)) <=> ? [X0] : (wise(X0) | ~tall(X0)) [input p9]
15. ! [X0] : ((~patient(X0) & ~tall(X0)) <=> (curious(X0) | humble(X0))) [input p14]
17. wise(lucy) & ~humble(lucy) [input p16]
25. tall(mary) [input hypothesis]
28. ! [X0] : ((creative(X0) | curious(X0)) | curious(X0)) [ennf transformation 4]
29. ! [X0] : (creative(X0) | curious(X0) | curious(X0)) [flattening 28]
31. ! [X0] : (kind(X0) | (patient(X0) | ~creative(X0))) [ennf transformation 6]
32. ! [X0] : (kind(X0) | patient(X0) | ~creative(X0)) [flattening 31]
34. ! [X0] : (patient(X0) | (~kind(X0) | ~creative(X0))) [ennf transformation 9]
35. ! [X0] : (patient(X0) | ~kind(X0) | ~creative(X0)) [flattening 34]
39. ! [X0] : (((~wise(X0) & old(X0)) | (brave(X0) & ~humble(X0))) & ((~brave(X0) | humble(X0)) | (wise(X0) | ~old(X0)))) [nnf transformation 1]
40. ! [X0] : (((~wise(X0) & old(X0)) | (brave(X0) & ~humble(X0))) & (~brave(X0) | humble(X0) | wise(X0) | ~old(X0))) [flattening 39]
41. ! [X0] : ((((~happy(X0) | brave(X0)) & (happy(X0) | ~brave(X0))) | patient(X0)) & (~patient(X0) | ((~brave(X0) | ~happy(X0)) & (happy(X0) | brave(X0))))) [nnf transformation 2]
51. ! [X0] : (((~tall(X0) & ~funny(X0)) | ((~happy(X0) | patient(X0)) & (~patient(X0) | happy(X0)))) & (((patient(X0) | happy(X0)) & (~patient(X0) | ~happy(X0))) | (tall(X0) | funny(X0)))) [nnf transformation 8]
52. ! [X0] : (((~tall(X0) & ~funny(X0)) | ((~happy(X0) | patient(X0)) & (~patient(X0) | happy(X0)))) & (((patient(X0) | happy(X0)) & (~patient(X0) | ~happy(X0))) | tall(X0) | funny(X0))) [flattening 51]
53. (((~wise(mary) | creative(mary)) & (wise(mary) | ~creative(mary))) | ! [X0] : (~wise(X0) & tall(X0))) & (? [X0] : (wise(X0) | ~tall(X0)) | ((~creative(mary) | ~wise(mary)) & (wise(mary) | creative(mary)))) [nnf transformation 10]
54. (((~wise(mary) | creative(mary)) & (wise(mary) | ~creative(mary))) | ! [X0] : (~wise(X0) & tall(X0))) & (? [X1] : (wise(X1) | ~tall(X1)) | ((~creative(mary) | ~wise(mary)) & (wise(mary) | creative(mary)))) [rectify 53]
55. ? [X1] : (wise(X1) | ~tall(X1)) => (wise(sK2) | ~tall(sK2)) [choice axiom]
56. (((~wise(mary) | creative(mary)) & (wise(mary) | ~creative(mary))) | ! [X0] : (~wise(X0) & tall(X0))) & ((wise(sK2) | ~tall(sK2)) | ((~creative(mary) | ~wise(mary)) & (wise(mary) | creative(mary)))) [skolemisation 54,55]
62. ! [X0] : (((~patient(X0) & ~tall(X0)) | (~curious(X0) & ~humble(X0))) & ((curious(X0) | humble(X0)) | (patient(X0) | tall(X0)))) [nnf transformation 15]
63. ! [X0] : (((~patient(X0) & ~tall(X0)) | (~curious(X0) & ~humble(X0))) & (curious(X0) | humble(X0) | patient(X0) | tall(X0))) [flattening 62]
78. ~wise(X0) | brave(X0) [cnf transformation 40]
80. ~patient(X0) | ~brave(X0) | ~happy(X0) [cnf transformation 41]
87. creative(X0) | curious(X0) | curious(X0) [cnf transformation 29]
90. ~creative(X0) | patient(X0) | kind(X0) [cnf transformation 32]
97. ~tall(X0) | ~patient(X0) | happy(X0) [cnf transformation 52]
99. patient(X0) | ~kind(X0) | ~creative(X0) [cnf transformation 35]
103. wise(mary) | ~creative(mary) | ~wise(X0) [cnf transformation 56]
118. ~tall(X0) | ~curious(X0) [cnf transformation 63]
127. wise(lucy) [cnf transformation 17]
138. tall(mary) [cnf transformation 25]
139. creative(X0) | curious(X0) [duplicate literal removal 87]
184. ~creative(X0) | patient(X0) [subsumption resolution 99,90]
186. 11 <=> ! [X0] : ~wise(X0) [avatar definition]
187. ~wise(X0) <- (11) [avatar component clause 186]
189. 12 <=> creative(mary) [avatar definition]
190. ~creative(mary) <- (~12) [avatar component clause 189]
191. creative(mary) <- (12) [avatar component clause 189]
193. 13 <=> wise(mary) [avatar definition]
194. wise(mary) <- (13) [avatar component clause 193]
201. 11 | ~12 | 13 [avatar split clause 103,193,189,186]
266. ~curious(mary) [resolution 118,138]
271. curious(mary) <- (~12) [resolution 139,190]
272. $false <- (~12) [subsumption resolution 271,266]
273. 12 [avatar contradiction clause 272]
274. brave(mary) <- (13) [resolution 194,78]
276. patient(mary) <- (12) [resolution 184,191]
281. ~brave(mary) | ~happy(mary) <- (12) [resolution 80,276]
282. ~happy(mary) <- (12, 13) [subsumption resolution 281,274]
347. ~patient(mary) | happy(mary) [resolution 97,138]
348. happy(mary) <- (12) [subsumption resolution 347,276]
349. $false <- (12, 13) [subsumption resolution 348,282]
350. ~12 | ~13 [avatar contradiction clause 349]
353. $false <- (11) [resolution 187,127]
356. ~11 [avatar contradiction clause 353]
358. $false [avatar sat refutation 201,273,350,356]
% SZS output end Proof for 61025223863462326502037
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not happy and not strong is not quiet or tall.
Everyone who is not generous or not quiet is both humble and curious and vice versa.
If mary is both rich and kind then someone is either not quiet or not generous and vice versa.
Everyone who is curious is not happy.
Everyone who is both not curious and wise is both not kind and happy.
If john is both not old and not calm then john is not tall or not generous and vice versa.
If someone is not kind then john is either not quiet or happy and vice versa.
Everyone who is both strong and patient is happy or wise.
Everyone who is both not curious and curious is generous or creative and vice versa.
Everyone who is both calm and not brave is rich.
Everyone who is not brave or not creative is not patient.
If lucy is not strong or tall then someone is either not creative or not patient and vice versa.
If paul is happy or not strong then someone is both not calm and curious and vice versa.
Everyone who is wise is not humble or generous.
Everyone who is both funny and tall is not strong.
Everyone who is calm is both curious and generous.
Lucy is either quiet or humble.
Fred is not kind.
Alice is not kind.
John is either funny or patient.
Mary is either quiet or funny. | John is rich. | neutral | (![X]:((~happy(X)&~strong(X))=>(~quiet(X)|tall(X))))&
(![X]:((~generous(X)|~quiet(X))<=>(humble(X)&curious(X))))&
(((rich(mary)&kind(mary)))<=>(?[X]:((~quiet(X)<~>~generous(X)))))&
(![X]:(curious(X)=>~happy(X)))&
(![X]:((~curious(X)&wise(X))=>(~kind(X)&happy(X))))&
(((~old(john)&~calm(john)))<=>((~tall(john)|~generous(john))))&
((?[X]:(~kind(X)))<=>((~quiet(john)<~>happy(john))))&
(![X]:((strong(X)&patient(X))=>(happy(X)|wise(X))))&
(![X]:((~curious(X)&curious(X))<=>(generous(X)|creative(X))))&
(![X]:((calm(X)&~brave(X))=>rich(X)))&
(![X]:((~brave(X)|~creative(X))=>~patient(X)))&
(((~strong(lucy)|tall(lucy)))<=>(?[X]:((~creative(X)<~>~patient(X)))))&
(((happy(paul)|~strong(paul)))<=>(?[X]:((~calm(X)&curious(X)))))&
(![X]:(wise(X)=>(~humble(X)|generous(X))))&
(![X]:((funny(X)&tall(X))=>~strong(X)))&
(![X]:(calm(X)=>(curious(X)&generous(X))))&
((quiet(lucy)<~>humble(lucy)))&
(~kind(fred))&
(~kind(alice))&
((funny(john)<~>patient(john)))&
((quiet(mary)<~>funny(mary))) | rich(john) | [] | null | 0 |
If john is either curious or old then someone is curious or kind and vice versa.
Everyone who is not humble or creative is either not calm or humble.
Everyone who is both calm and funny is both humble and kind.
Everyone who is funny or not rich is not humble.
If someone is not creative or generous then someone is curious or rich and vice versa.
Everyone who is both creative and old is creative and vice versa.
Everyone who is not calm or not humble is either calm or not wise and vice versa.
If mary is strong or not curious then fred is both rich and happy.
Everyone who is not brave or not wise is calm and vice versa.
Everyone who is either not funny or generous is not tall or curious.
If someone is either not curious or wise then lucy is not quiet and vice versa.
Everyone who is both happy and not strong is both brave and not kind.
If susan is either generous or quiet then someone is old or not generous.
Everyone who is not brave or not happy is both not quiet and generous.
Everyone who is either not wise or not humble is happy.
Everyone who is calm is quiet or not calm.
Fred is quiet.
Susan is calm or not old.
Someone is patient.
Lucy is not generous or not curious.
John is either generous or old.
Paul is generous or not calm.
Mary is either not funny or not calm. | Paul is rich. | entailment | (((curious(john)<~>old(john)))<=>(?[X]:((curious(X)|kind(X)))))&
(![X]:((~humble(X)|creative(X))=>(~calm(X)<~>humble(X))))&
(![X]:((calm(X)&funny(X))=>(humble(X)&kind(X))))&
(![X]:((funny(X)|~rich(X))=>~humble(X)))&
((?[X]:((~creative(X)|generous(X))))<=>(?[X]:((curious(X)|rich(X)))))&
(![X]:((creative(X)&old(X))<=>creative(X)))&
(![X]:((~calm(X)|~humble(X))<=>(calm(X)<~>~wise(X))))&
(((strong(mary)|~curious(mary)))=>((rich(fred)&happy(fred))))&
(![X]:((~brave(X)|~wise(X))<=>calm(X)))&
(![X]:((~funny(X)<~>generous(X))=>(~tall(X)|curious(X))))&
((?[X]:((~curious(X)<~>wise(X))))<=>(~quiet(lucy)))&
(![X]:((happy(X)&~strong(X))=>(brave(X)&~kind(X))))&
(((generous(susan)<~>quiet(susan)))=>(?[X]:((old(X)|~generous(X)))))&
(![X]:((~brave(X)|~happy(X))=>(~quiet(X)&generous(X))))&
(![X]:((~wise(X)<~>~humble(X))=>happy(X)))&
(![X]:(calm(X)=>(quiet(X)|~calm(X))))&
(quiet(fred))&
((calm(susan)|~old(susan)))&
(?[X]:(patient(X)))&
((~generous(lucy)|~curious(lucy)))&
((generous(john)<~>old(john)))&
((generous(paul)|~calm(paul)))&
((~funny(mary)<~>~calm(mary))) | rich(paul) | [
"p1",
"p3",
"p6",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 1902918550287379894628150
% SZS output start Proof for 1902918550287379894628150
2. ! [X0] : ((creative(X0) | ~humble(X0)) => (~calm(X0) <~> humble(X0))) [input p1]
4. ! [X0] : ((~rich(X0) | funny(X0)) => ~humble(X0)) [input p3]
7. ! [X0] : ((~humble(X0) | ~calm(X0)) <=> (calm(X0) <~> ~wise(X0))) [input p6]
9. ! [X0] : ((~wise(X0) | ~brave(X0)) <=> calm(X0)) [input p8]
24. ~rich(paul) [input hypothesis]
28. ! [X0] : ((~calm(X0) <~> humble(X0)) | (~creative(X0) & humble(X0))) [ennf transformation 2]
31. ! [X0] : (~humble(X0) | (rich(X0) & ~funny(X0))) [ennf transformation 4]
44. ! [X0] : (((~humble(X0) | calm(X0)) & (humble(X0) | ~calm(X0))) | (~creative(X0) & humble(X0))) [nnf transformation 28]
52. ! [X0] : (((~humble(X0) | ~calm(X0)) | ((calm(X0) | wise(X0)) & (~wise(X0) | ~calm(X0)))) & (((wise(X0) | ~calm(X0)) & (~wise(X0) | calm(X0))) | (humble(X0) & calm(X0)))) [nnf transformation 7]
53. ! [X0] : ((~humble(X0) | ~calm(X0) | ((calm(X0) | wise(X0)) & (~wise(X0) | ~calm(X0)))) & (((wise(X0) | ~calm(X0)) & (~wise(X0) | calm(X0))) | (humble(X0) & calm(X0)))) [flattening 52]
54. ! [X0] : (((~wise(X0) | ~brave(X0)) | ~calm(X0)) & (calm(X0) | (wise(X0) & brave(X0)))) [nnf transformation 9]
55. ! [X0] : ((~wise(X0) | ~brave(X0) | ~calm(X0)) & (calm(X0) | (wise(X0) & brave(X0)))) [flattening 54]
72. humble(X0) | ~calm(X0) | humble(X0) [cnf transformation 44]
79. ~humble(X0) | rich(X0) [cnf transformation 31]
87. ~wise(X0) | calm(X0) | calm(X0) [cnf transformation 53]
91. ~humble(X0) | ~calm(X0) | ~wise(X0) | ~calm(X0) [cnf transformation 53]
98. calm(X0) | wise(X0) [cnf transformation 55]
123. ~rich(paul) [cnf transformation 24]
125. ~wise(X0) | calm(X0) [duplicate literal removal 87]
126. ~humble(X0) | ~calm(X0) | ~wise(X0) [duplicate literal removal 91]
127. ~calm(X0) | humble(X0) [duplicate literal removal 72]
185. ~wise(X0) | ~calm(X0) [subsumption resolution 126,127]
187. ~wise(X0) [subsumption resolution 125,185]
208. calm(X0) [subsumption resolution 98,187]
269. humble(X0) [resolution 127,208]
270. rich(X0) [resolution 269,79]
271. $false [resolution 270,123]
% SZS output end Proof for 1902918550287379894628150
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both strong and not brave then someone is generous or not rich and vice versa.
Everyone who is both not funny and not happy is tall and vice versa.
Everyone who is both not creative and happy is both not quiet and calm and vice versa.
Everyone who is not creative or tall is both rich and old and vice versa.
Everyone who is not curious or not rich is both not quiet and patient and vice versa.
If someone is either not curious or old then mary is curious and vice versa.
If someone is not tall then someone is both not happy and not kind and vice versa.
Everyone who is not strong is not curious or happy.
If mary is both not rich and not humble then lucy is either wise or patient and vice versa.
Everyone who is tall or not humble is not generous.
Everyone who is either not generous or old is both not kind and patient.
Everyone who is both not patient and not quiet is funny or not strong and vice versa.
Everyone who is both patient and not quiet is tall or kind.
Everyone who is either not happy or wise is both wise and brave.
If lucy is either not strong or not curious then someone is not humble or not kind and vice versa.
If someone is generous then someone is either not kind or wise.
Someone is either not patient or not calm.
Someone is either tall or happy.
Fred is not old.
Mary is either humble or quiet.
Susan is either not generous or humble.
Lucy is wise or happy.
Mary is calm. | Mary is not generous. | entailment | ((?[X]:((strong(X)&~brave(X))))<=>(?[X]:((generous(X)|~rich(X)))))&
(![X]:((~funny(X)&~happy(X))<=>tall(X)))&
(![X]:((~creative(X)&happy(X))<=>(~quiet(X)&calm(X))))&
(![X]:((~creative(X)|tall(X))<=>(rich(X)&old(X))))&
(![X]:((~curious(X)|~rich(X))<=>(~quiet(X)&patient(X))))&
((?[X]:((~curious(X)<~>old(X))))<=>(curious(mary)))&
((?[X]:(~tall(X)))<=>(?[X]:((~happy(X)&~kind(X)))))&
(![X]:(~strong(X)=>(~curious(X)|happy(X))))&
(((~rich(mary)&~humble(mary)))<=>((wise(lucy)<~>patient(lucy))))&
(![X]:((tall(X)|~humble(X))=>~generous(X)))&
(![X]:((~generous(X)<~>old(X))=>(~kind(X)&patient(X))))&
(![X]:((~patient(X)&~quiet(X))<=>(funny(X)|~strong(X))))&
(![X]:((patient(X)&~quiet(X))=>(tall(X)|kind(X))))&
(![X]:((~happy(X)<~>wise(X))=>(wise(X)&brave(X))))&
(((~strong(lucy)<~>~curious(lucy)))<=>(?[X]:((~humble(X)|~kind(X)))))&
((?[X]:(generous(X)))=>(?[X]:((~kind(X)<~>wise(X)))))&
(?[X]:((~patient(X)<~>~calm(X))))&
(?[X]:((tall(X)<~>happy(X))))&
(~old(fred))&
((humble(mary)<~>quiet(mary)))&
((~generous(susan)<~>humble(susan)))&
((wise(lucy)|happy(lucy)))&
(calm(mary)) | ~generous(mary) | [
"p2",
"p3",
"p4",
"p5",
"p9",
"p10",
"p12",
"p19",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 3717766619154148026370507
% SZS output start Proof for 3717766619154148026370507
3. ! [X0] : ((happy(X0) & ~creative(X0)) <=> (calm(X0) & ~quiet(X0))) [input p2]
4. ! [X0] : ((tall(X0) | ~creative(X0)) <=> (old(X0) & rich(X0))) [input p3]
5. ! [X0] : ((~rich(X0) | ~curious(X0)) <=> (patient(X0) & ~quiet(X0))) [input p4]
6. ? [X0] : (~curious(X0) <~> old(X0)) <=> curious(mary) [input p5]
10. ! [X0] : ((~humble(X0) | tall(X0)) => ~generous(X0)) [input p9]
11. ! [X0] : ((~generous(X0) <~> old(X0)) => (patient(X0) & ~kind(X0))) [input p10]
13. ! [X0] : ((~quiet(X0) & patient(X0)) => (kind(X0) | tall(X0))) [input p12]
20. humble(mary) <~> quiet(mary) [input p19]
23. calm(mary) [input p22]
24. generous(mary) [input hypothesis]
30. ! [X0] : (~generous(X0) | (humble(X0) & ~tall(X0))) [ennf transformation 10]
31. ! [X0] : ((patient(X0) & ~kind(X0)) | (~generous(X0) <=> old(X0))) [ennf transformation 11]
32. ! [X0] : ((kind(X0) | tall(X0)) | (quiet(X0) | ~patient(X0))) [ennf transformation 13]
33. ! [X0] : (kind(X0) | tall(X0) | quiet(X0) | ~patient(X0)) [flattening 32]
43. ! [X0] : (((happy(X0) & ~creative(X0)) | (~calm(X0) | quiet(X0))) & ((calm(X0) & ~quiet(X0)) | (~happy(X0) | creative(X0)))) [nnf transformation 3]
44. ! [X0] : (((happy(X0) & ~creative(X0)) | ~calm(X0) | quiet(X0)) & ((calm(X0) & ~quiet(X0)) | ~happy(X0) | creative(X0))) [flattening 43]
45. ! [X0] : (((tall(X0) | ~creative(X0)) | (~old(X0) | ~rich(X0))) & ((old(X0) & rich(X0)) | (~tall(X0) & creative(X0)))) [nnf transformation 4]
46. ! [X0] : ((tall(X0) | ~creative(X0) | ~old(X0) | ~rich(X0)) & ((old(X0) & rich(X0)) | (~tall(X0) & creative(X0)))) [flattening 45]
47. ! [X0] : (((~rich(X0) | ~curious(X0)) | (~patient(X0) | quiet(X0))) & ((patient(X0) & ~quiet(X0)) | (rich(X0) & curious(X0)))) [nnf transformation 5]
48. ! [X0] : ((~rich(X0) | ~curious(X0) | ~patient(X0) | quiet(X0)) & ((patient(X0) & ~quiet(X0)) | (rich(X0) & curious(X0)))) [flattening 47]
49. (? [X0] : ((~old(X0) | curious(X0)) & (old(X0) | ~curious(X0))) | ~curious(mary)) & (curious(mary) | ! [X0] : ((~curious(X0) | ~old(X0)) & (old(X0) | curious(X0)))) [nnf transformation 6]
50. (? [X0] : ((~old(X0) | curious(X0)) & (old(X0) | ~curious(X0))) | ~curious(mary)) & (curious(mary) | ! [X1] : ((~curious(X1) | ~old(X1)) & (old(X1) | curious(X1)))) [rectify 49]
51. ? [X0] : ((~old(X0) | curious(X0)) & (old(X0) | ~curious(X0))) => ((~old(sK2) | curious(sK2)) & (old(sK2) | ~curious(sK2))) [choice axiom]
52. (((~old(sK2) | curious(sK2)) & (old(sK2) | ~curious(sK2))) | ~curious(mary)) & (curious(mary) | ! [X1] : ((~curious(X1) | ~old(X1)) & (old(X1) | curious(X1)))) [skolemisation 50,51]
60. ! [X0] : ((patient(X0) & ~kind(X0)) | ((~generous(X0) | ~old(X0)) & (old(X0) | generous(X0)))) [nnf transformation 31]
78. (~quiet(mary) | ~humble(mary)) & (quiet(mary) | humble(mary)) [nnf transformation 20]
90. ~calm(X0) | ~creative(X0) | quiet(X0) [cnf transformation 44]
92. creative(X0) | rich(X0) [cnf transformation 46]
94. old(X0) | creative(X0) [cnf transformation 46]
97. ~quiet(X0) | curious(X0) [cnf transformation 48]
99. patient(X0) | curious(X0) [cnf transformation 48]
101. ~patient(X0) | ~curious(X0) | ~rich(X0) | quiet(X0) [cnf transformation 48]
102. curious(mary) | old(X1) | curious(X1) [cnf transformation 52]
116. ~tall(X0) | ~generous(X0) [cnf transformation 30]
117. ~generous(X0) | humble(X0) [cnf transformation 30]
119. ~kind(X0) | ~generous(X0) | ~old(X0) [cnf transformation 60]
121. ~old(X0) | ~generous(X0) | patient(X0) [cnf transformation 60]
127. ~patient(X0) | tall(X0) | quiet(X0) | kind(X0) [cnf transformation 33]
146. ~quiet(mary) | ~humble(mary) [cnf transformation 78]
150. calm(mary) [cnf transformation 23]
151. generous(mary) [cnf transformation 24]
184. 8 <=> curious(mary) [avatar definition]
186. ~curious(mary) <- (~8) [avatar component clause 184]
202. 12 <=> ! [X1] : (old(X1) | curious(X1)) [avatar definition]
203. curious(X1) | old(X1) <- (12) [avatar component clause 202]
204. 12 | 8 [avatar split clause 102,184,202]
235. 20 <=> humble(mary) [avatar definition]
241. 21 <=> rich(mary) [avatar definition]
242. rich(mary) <- (21) [avatar component clause 241]
306. 34 <=> quiet(mary) [avatar definition]
308. ~quiet(mary) <- (~34) [avatar component clause 306]
309. ~20 | ~34 [avatar split clause 146,306,235]
331. humble(mary) [resolution 117,151]
396. ~creative(mary) | quiet(mary) [resolution 90,150]
418. ~generous(X0) | patient(X0) | creative(X0) [resolution 121,94]
484. tall(X2) | quiet(X2) | kind(X2) | curious(X2) [resolution 127,99]
490. kind(X2) | tall(X2) | curious(X2) [subsumption resolution 484,97]
540. 20 [avatar split clause 331,235]
552. 62 <=> creative(mary) [avatar definition]
554. ~creative(mary) <- (~62) [avatar component clause 552]
555. 34 | ~62 [avatar split clause 396,552,306]
634. rich(mary) <- (~62) [resolution 554,92]
637. 21 | 62 [avatar split clause 634,552,241]
752. patient(mary) | creative(mary) [resolution 418,151]
754. patient(mary) <- (~62) [subsumption resolution 752,554]
774. tall(X0) | curious(X0) | ~generous(X0) | ~old(X0) [resolution 490,119]
786. ~old(X0) | ~generous(X0) | curious(X0) [subsumption resolution 774,116]
816. ~curious(mary) | ~rich(mary) | quiet(mary) <- (~62) [resolution 754,101]
834. ~curious(mary) | quiet(mary) <- (21, ~62) [subsumption resolution 816,242]
835. ~curious(mary) <- (21, ~34, ~62) [subsumption resolution 834,308]
836. ~8 | ~21 | 34 | 62 [avatar split clause 835,552,306,241,184]
866. old(mary) <- (~8, 12) [resolution 203,186]
971. ~generous(mary) | curious(mary) <- (~8, 12) [resolution 786,866]
976. curious(mary) <- (~8, 12) [subsumption resolution 971,151]
977. $false <- (~8, 12) [subsumption resolution 976,186]
978. 8 | ~12 [avatar contradiction clause 977]
979. $false [avatar sat refutation 204,309,540,555,637,836,978]
% SZS output end Proof for 3717766619154148026370507
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5500
% Time elapsed: 0.041 s
% ------------------------------
% ------------------------------
| 0 |
If someone is kind then someone is generous or creative.
Everyone who is both not curious and old is both kind and creative and vice versa.
If someone is tall or not old then paul is not patient and vice versa.
If someone is not brave then john is funny and vice versa.
Everyone who is kind is rich or not funny.
Everyone who is strong is not wise.
Everyone who is both wise and creative is either strong or not generous.
Everyone who is funny is not kind or not funny and vice versa.
Everyone who is both quiet and patient is not kind or wise and vice versa.
If someone is both not rich and not strong then someone is either not creative or brave.
If mary is either not happy or generous then lucy is both not old and not creative and vice versa.
Everyone who is either creative or not strong is funny.
If alice is quiet or not curious then someone is not tall and vice versa.
Everyone who is not wise is both curious and quiet.
If someone is generous or not creative then someone is rich or funny and vice versa.
Someone is happy.
John is both not calm and not generous.
Someone is either happy or not quiet.
Someone is both brave and not happy.
Someone is wise or generous.
Someone is both rich and wise.
Fred is not creative or quiet. | Alice is curious. | entailment | ((?[X]:(kind(X)))=>(?[X]:((generous(X)|creative(X)))))&
(![X]:((~curious(X)&old(X))<=>(kind(X)&creative(X))))&
((?[X]:((tall(X)|~old(X))))<=>(~patient(paul)))&
((?[X]:(~brave(X)))<=>(funny(john)))&
(![X]:(kind(X)=>(rich(X)|~funny(X))))&
(![X]:(strong(X)=>~wise(X)))&
(![X]:((wise(X)&creative(X))=>(strong(X)<~>~generous(X))))&
(![X]:(funny(X)<=>(~kind(X)|~funny(X))))&
(![X]:((quiet(X)&patient(X))<=>(~kind(X)|wise(X))))&
((?[X]:((~rich(X)&~strong(X))))=>(?[X]:((~creative(X)<~>brave(X)))))&
(((~happy(mary)<~>generous(mary)))<=>((~old(lucy)&~creative(lucy))))&
(![X]:((creative(X)<~>~strong(X))=>funny(X)))&
(((quiet(alice)|~curious(alice)))<=>(?[X]:(~tall(X))))&
(![X]:(~wise(X)=>(curious(X)&quiet(X))))&
((?[X]:((generous(X)|~creative(X))))<=>(?[X]:((rich(X)|funny(X)))))&
(?[X]:(happy(X)))&
((~calm(john)&~generous(john)))&
(?[X]:((happy(X)<~>~quiet(X))))&
(?[X]:((brave(X)&~happy(X))))&
(?[X]:((wise(X)|generous(X))))&
(?[X]:((rich(X)&wise(X))))&
((~creative(fred)|quiet(fred))) | curious(alice) | [
"p1",
"p2",
"p7",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 5462363673438536196520561
% SZS output start Proof for 5462363673438536196520561
2. ! [X0] : ((old(X0) & ~curious(X0)) <=> (creative(X0) & kind(X0))) [input p1]
3. ? [X0] : (~old(X0) | tall(X0)) <=> ~patient(paul) [input p2]
8. ! [X0] : (funny(X0) <=> (~funny(X0) | ~kind(X0))) [input p7]
9. ! [X0] : ((patient(X0) & quiet(X0)) <=> (wise(X0) | ~kind(X0))) [input p8]
23. ~curious(alice) [input hypothesis]
40. ! [X0] : (((old(X0) & ~curious(X0)) | (~creative(X0) | ~kind(X0))) & ((creative(X0) & kind(X0)) | (~old(X0) | curious(X0)))) [nnf transformation 2]
41. ! [X0] : (((old(X0) & ~curious(X0)) | ~creative(X0) | ~kind(X0)) & ((creative(X0) & kind(X0)) | ~old(X0) | curious(X0))) [flattening 40]
42. (? [X0] : (~old(X0) | tall(X0)) | patient(paul)) & (~patient(paul) | ! [X0] : (old(X0) & ~tall(X0))) [nnf transformation 3]
43. (? [X0] : (~old(X0) | tall(X0)) | patient(paul)) & (~patient(paul) | ! [X1] : (old(X1) & ~tall(X1))) [rectify 42]
44. ? [X0] : (~old(X0) | tall(X0)) => (~old(sK1) | tall(sK1)) [choice axiom]
45. ((~old(sK1) | tall(sK1)) | patient(paul)) & (~patient(paul) | ! [X1] : (old(X1) & ~tall(X1))) [skolemisation 43,44]
51. ! [X0] : ((funny(X0) | (funny(X0) & kind(X0))) & ((~funny(X0) | ~kind(X0)) | ~funny(X0))) [nnf transformation 8]
52. ! [X0] : ((funny(X0) | (funny(X0) & kind(X0))) & (~funny(X0) | ~kind(X0) | ~funny(X0))) [flattening 51]
53. ! [X0] : (((patient(X0) & quiet(X0)) | (~wise(X0) & kind(X0))) & ((wise(X0) | ~kind(X0)) | (~patient(X0) | ~quiet(X0)))) [nnf transformation 9]
54. ! [X0] : (((patient(X0) & quiet(X0)) | (~wise(X0) & kind(X0))) & (wise(X0) | ~kind(X0) | ~patient(X0) | ~quiet(X0))) [flattening 53]
84. ~old(X0) | kind(X0) | curious(X0) [cnf transformation 41]
89. ~patient(paul) | old(X1) [cnf transformation 45]
97. ~funny(X0) | ~kind(X0) | ~funny(X0) [cnf transformation 52]
99. funny(X0) | funny(X0) [cnf transformation 52]
103. patient(X0) | kind(X0) [cnf transformation 54]
134. ~curious(alice) [cnf transformation 23]
135. ~funny(X0) | ~kind(X0) [duplicate literal removal 97]
136. funny(X0) [duplicate literal removal 99]
138. 1 <=> ! [X1] : ~kind(X1) [avatar definition]
139. ~kind(X1) <- (1) [avatar component clause 138]
150. 4 <=> patient(paul) [avatar definition]
151. ~patient(paul) <- (~4) [avatar component clause 150]
163. 7 <=> ! [X1] : old(X1) [avatar definition]
164. old(X1) <- (7) [avatar component clause 163]
165. 7 | ~4 [avatar split clause 89,150,163]
184. ~kind(X0) [subsumption resolution 135,136]
185. 1 [avatar split clause 184,138]
229. 21 <=> curious(alice) [avatar definition]
231. ~curious(alice) <- (~21) [avatar component clause 229]
264. ~21 [avatar split clause 134,229]
269. kind(paul) <- (~4) [resolution 103,151]
270. $false <- (1, ~4) [subsumption resolution 269,139]
271. ~1 | 4 [avatar contradiction clause 270]
281. kind(X0) | curious(X0) <- (7) [resolution 84,164]
282. curious(X0) <- (1, 7) [subsumption resolution 281,139]
283. $false <- (1, 7, ~21) [resolution 282,231]
284. ~1 | ~7 | 21 [avatar contradiction clause 283]
285. $false [avatar sat refutation 165,185,264,271,284]
% SZS output end Proof for 5462363673438536196520561
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both brave and happy then lucy is not kind or not happy and vice versa.
Everyone who is both happy and rich is either happy or generous.
If alice is creative or not quiet then lucy is not quiet.
If fred is both not old and not rich then someone is brave and vice versa.
Everyone who is both not generous and wise is either not generous or not patient and vice versa.
If someone is not strong or kind then john is not rich.
Everyone who is either not wise or kind is both not funny and not wise and vice versa.
Everyone who is not generous is curious or not patient.
Everyone who is both not brave and funny is not creative and vice versa.
If john is either old or not funny then someone is either not brave or tall.
Everyone who is brave is either not tall or not creative and vice versa.
Everyone who is curious or creative is either humble or happy and vice versa.
If someone is either not curious or old then john is creative and vice versa.
Everyone who is both not old and not brave is not tall and vice versa.
Everyone who is creative or not wise is either quiet or creative.
If someone is both not strong and humble then someone is both calm and not tall.
Someone is either not quiet or not patient.
Someone is not generous or not quiet.
Susan is happy or tall.
Susan is tall.
Susan is both not curious and rich.
Someone is either funny or not wise.
Someone is either not wise or funny.
Someone is not generous. | Lucy is funny. | entailment | ((?[X]:((brave(X)&happy(X))))<=>((~kind(lucy)|~happy(lucy))))&
(![X]:((happy(X)&rich(X))=>(happy(X)<~>generous(X))))&
(((creative(alice)|~quiet(alice)))=>(~quiet(lucy)))&
(((~old(fred)&~rich(fred)))<=>(?[X]:(brave(X))))&
(![X]:((~generous(X)&wise(X))<=>(~generous(X)<~>~patient(X))))&
((?[X]:((~strong(X)|kind(X))))=>(~rich(john)))&
(![X]:((~wise(X)<~>kind(X))<=>(~funny(X)&~wise(X))))&
(![X]:(~generous(X)=>(curious(X)|~patient(X))))&
(![X]:((~brave(X)&funny(X))<=>~creative(X)))&
(((old(john)<~>~funny(john)))=>(?[X]:((~brave(X)<~>tall(X)))))&
(![X]:(brave(X)<=>(~tall(X)<~>~creative(X))))&
(![X]:((curious(X)|creative(X))<=>(humble(X)<~>happy(X))))&
((?[X]:((~curious(X)<~>old(X))))<=>(creative(john)))&
(![X]:((~old(X)&~brave(X))<=>~tall(X)))&
(![X]:((creative(X)|~wise(X))=>(quiet(X)<~>creative(X))))&
((?[X]:((~strong(X)&humble(X))))=>(?[X]:((calm(X)&~tall(X)))))&
(?[X]:((~quiet(X)<~>~patient(X))))&
(?[X]:((~generous(X)|~quiet(X))))&
((happy(susan)|tall(susan)))&
(tall(susan))&
((~curious(susan)&rich(susan)))&
(?[X]:((funny(X)<~>~wise(X))))&
(?[X]:((~wise(X)<~>funny(X))))&
(?[X]:(~generous(X))) | funny(lucy) | [
"p0",
"p6",
"p8",
"p10",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 4529480664051184087369127
% SZS output start Proof for 4529480664051184087369127
1. ? [X0] : (happy(X0) & brave(X0)) <=> (~happy(lucy) | ~kind(lucy)) [input p0]
7. ! [X0] : ((~wise(X0) <~> kind(X0)) <=> (~wise(X0) & ~funny(X0))) [input p6]
9. ! [X0] : ((funny(X0) & ~brave(X0)) <=> ~creative(X0)) [input p8]
11. ! [X0] : (brave(X0) <=> (~tall(X0) <~> ~creative(X0))) [input p10]
14. ! [X0] : ((~brave(X0) & ~old(X0)) <=> ~tall(X0)) [input p13]
25. ~funny(lucy) [input hypothesis]
38. (? [X0] : (happy(X0) & brave(X0)) | (happy(lucy) & kind(lucy))) & ((~happy(lucy) | ~kind(lucy)) | ! [X0] : (~happy(X0) | ~brave(X0))) [nnf transformation 1]
39. (? [X0] : (happy(X0) & brave(X0)) | (happy(lucy) & kind(lucy))) & (~happy(lucy) | ~kind(lucy) | ! [X0] : (~happy(X0) | ~brave(X0))) [flattening 38]
40. (? [X0] : (happy(X0) & brave(X0)) | (happy(lucy) & kind(lucy))) & (~happy(lucy) | ~kind(lucy) | ! [X1] : (~happy(X1) | ~brave(X1))) [rectify 39]
41. ? [X0] : (happy(X0) & brave(X0)) => (happy(sK0) & brave(sK0)) [choice axiom]
42. ((happy(sK0) & brave(sK0)) | (happy(lucy) & kind(lucy))) & (~happy(lucy) | ~kind(lucy) | ! [X1] : (~happy(X1) | ~brave(X1))) [skolemisation 40,41]
51. ! [X0] : ((((~kind(X0) | wise(X0)) & (kind(X0) | ~wise(X0))) | (wise(X0) | funny(X0))) & ((~wise(X0) & ~funny(X0)) | ((~wise(X0) | ~kind(X0)) & (kind(X0) | wise(X0))))) [nnf transformation 7]
52. ! [X0] : ((((~kind(X0) | wise(X0)) & (kind(X0) | ~wise(X0))) | wise(X0) | funny(X0)) & ((~wise(X0) & ~funny(X0)) | ((~wise(X0) | ~kind(X0)) & (kind(X0) | wise(X0))))) [flattening 51]
53. ! [X0] : (((funny(X0) & ~brave(X0)) | creative(X0)) & (~creative(X0) | (~funny(X0) | brave(X0)))) [nnf transformation 9]
54. ! [X0] : (((funny(X0) & ~brave(X0)) | creative(X0)) & (~creative(X0) | ~funny(X0) | brave(X0))) [flattening 53]
58. ! [X0] : ((brave(X0) | ((~tall(X0) | creative(X0)) & (~creative(X0) | tall(X0)))) & (((creative(X0) | tall(X0)) & (~creative(X0) | ~tall(X0))) | ~brave(X0))) [nnf transformation 11]
65. ! [X0] : (((~brave(X0) & ~old(X0)) | tall(X0)) & (~tall(X0) | (brave(X0) | old(X0)))) [nnf transformation 14]
66. ! [X0] : (((~brave(X0) & ~old(X0)) | tall(X0)) & (~tall(X0) | brave(X0) | old(X0))) [flattening 65]
82. brave(sK0) | kind(lucy) [cnf transformation 42]
103. ~wise(X0) | ~wise(X0) | ~kind(X0) [cnf transformation 52]
105. ~kind(X0) | wise(X0) | wise(X0) | funny(X0) [cnf transformation 52]
108. ~brave(X0) | creative(X0) [cnf transformation 54]
114. ~creative(X0) | ~tall(X0) | ~brave(X0) [cnf transformation 58]
117. brave(X0) | ~tall(X0) | creative(X0) [cnf transformation 58]
130. ~brave(X0) | tall(X0) [cnf transformation 66]
147. ~funny(lucy) [cnf transformation 25]
149. ~wise(X0) | ~kind(X0) [duplicate literal removal 103]
150. ~kind(X0) | wise(X0) | funny(X0) [duplicate literal removal 105]
164. 3 <=> kind(lucy) [avatar definition]
166. kind(lucy) <- (3) [avatar component clause 164]
169. 4 <=> brave(sK0) [avatar definition]
171. brave(sK0) <- (4) [avatar component clause 169]
173. 3 | 4 [avatar split clause 82,169,164]
193. 9 <=> ! [X0] : ~brave(X0) [avatar definition]
194. ~brave(X0) <- (9) [avatar component clause 193]
239. ~tall(X0) | creative(X0) [subsumption resolution 117,108]
240. ~tall(X0) | ~brave(X0) [subsumption resolution 114,239]
263. ~brave(X0) [subsumption resolution 130,240]
264. 9 [avatar split clause 263,193]
315. $false <- (4, 9) [subsumption resolution 171,194]
316. ~4 | ~9 [avatar contradiction clause 315]
455. wise(lucy) | funny(lucy) <- (3) [resolution 150,166]
456. wise(lucy) <- (3) [subsumption resolution 455,147]
489. ~kind(lucy) <- (3) [resolution 456,149]
490. $false <- (3) [subsumption resolution 489,166]
491. ~3 [avatar contradiction clause 490]
492. $false [avatar sat refutation 173,264,316,491]
% SZS output end Proof for 4529480664051184087369127
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both strong and not quiet is either not old or patient and vice versa.
If paul is not calm or not generous then alice is not generous or not tall and vice versa.
If lucy is not patient then fred is either kind or tall.
If someone is both not humble and not creative then alice is tall and vice versa.
If someone is both strong and not tall then someone is creative and vice versa.
Everyone who is either quiet or not old is brave and vice versa.
If susan is both not curious and not quiet then mary is happy and vice versa.
Everyone who is tall is not funny and vice versa.
If someone is not old or not funny then mary is both kind and rich and vice versa.
Everyone who is either not brave or old is not wise or quiet and vice versa.
Everyone who is either generous or kind is both not rich and not brave.
Everyone who is both not calm and creative is not funny.
If someone is humble or tall then someone is creative.
Everyone who is not patient is either not quiet or creative and vice versa.
If alice is tall or wise then susan is creative or not strong.
Someone is either not patient or generous.
John is not curious or not old.
Someone is either tall or not generous.
Susan is either patient or rich.
Susan is both not kind and not patient.
Paul is both not brave and not quiet.
Alice is both generous and not curious. | Fred is not wise. | neutral | (![X]:((strong(X)&~quiet(X))<=>(~old(X)<~>patient(X))))&
(((~calm(paul)|~generous(paul)))<=>((~generous(alice)|~tall(alice))))&
((~patient(lucy))=>((kind(fred)<~>tall(fred))))&
((?[X]:((~humble(X)&~creative(X))))<=>(tall(alice)))&
((?[X]:((strong(X)&~tall(X))))<=>(?[X]:(creative(X))))&
(![X]:((quiet(X)<~>~old(X))<=>brave(X)))&
(((~curious(susan)&~quiet(susan)))<=>(happy(mary)))&
(![X]:(tall(X)<=>~funny(X)))&
((?[X]:((~old(X)|~funny(X))))<=>((kind(mary)&rich(mary))))&
(![X]:((~brave(X)<~>old(X))<=>(~wise(X)|quiet(X))))&
(![X]:((generous(X)<~>kind(X))=>(~rich(X)&~brave(X))))&
(![X]:((~calm(X)&creative(X))=>~funny(X)))&
((?[X]:((humble(X)|tall(X))))=>(?[X]:(creative(X))))&
(![X]:(~patient(X)<=>(~quiet(X)<~>creative(X))))&
(((tall(alice)|wise(alice)))=>((creative(susan)|~strong(susan))))&
(?[X]:((~patient(X)<~>generous(X))))&
((~curious(john)|~old(john)))&
(?[X]:((tall(X)<~>~generous(X))))&
((patient(susan)<~>rich(susan)))&
((~kind(susan)&~patient(susan)))&
((~brave(paul)&~quiet(paul)))&
((generous(alice)&~curious(alice))) | ~wise(fred) | [] | null | 0 |
If someone is rich then someone is either old or not rich and vice versa. If someone is both not funny and strong then someone is both not humble and not funny. If someone is both not tall and tall then alice is not creative or not brave. Everyone who is not humble is both quiet and not curious and vice versa. Everyone who is not brave or curious is strong and vice versa. If someone is not rich or curious then someone is not happy. If paul is not old then someone is not patient. Everyone who is both quiet and not happy is not tall or not calm. Everyone who is either happy or quiet is quiet and vice versa. Everyone who is both not patient and not curious is either not old or humble and vice versa. Everyone who is either not rich or curious is patient and vice versa. If someone is not strong or wise then mary is either not patient or not quiet and vice versa. If someone is both humble and not rich then someone is both not brave and not old. Everyone who is either quiet or not quiet is both strong and patient. If someone is funny then someone is both kind and calm and vice versa. If someone is both not humble and not strong then someone is curious or not calm. Susan is old. Paul is tall. Lucy is not happy or strong. Someone is funny. Lucy is not patient or quiet. Mary is either not generous or funny. | Mary is generous. | neutral | ((?[X]:(rich(X)))<=>(?[X]:((old(X)<~>~rich(X)))))&
((?[X]:((~funny(X)&strong(X))))=>(?[X]:((~humble(X)&~funny(X)))))&
((?[X]:((~tall(X)&tall(X))))=>((~creative(alice)|~brave(alice))))&
(![X]:(~humble(X)<=>(quiet(X)&~curious(X))))&
(![X]:((~brave(X)|curious(X))<=>strong(X)))&
((?[X]:((~rich(X)|curious(X))))=>(?[X]:(~happy(X))))&
((~old(paul))=>(?[X]:(~patient(X))))&
(![X]:((quiet(X)&~happy(X))=>(~tall(X)|~calm(X))))&
(![X]:((happy(X)<~>quiet(X))<=>quiet(X)))&
(![X]:((~patient(X)&~curious(X))<=>(~old(X)<~>humble(X))))&
(![X]:((~rich(X)<~>curious(X))<=>patient(X)))&
((?[X]:((~strong(X)|wise(X))))<=>((~patient(mary)<~>~quiet(mary))))&
((?[X]:((humble(X)&~rich(X))))=>(?[X]:((~brave(X)&~old(X)))))&
(![X]:((quiet(X)<~>~quiet(X))=>(strong(X)&patient(X))))&
((?[X]:(funny(X)))<=>(?[X]:((kind(X)&calm(X)))))&
((?[X]:((~humble(X)&~strong(X))))=>(?[X]:((curious(X)|~calm(X)))))&
(old(susan))&
(tall(paul))&
((~happy(lucy)|strong(lucy)))&
(?[X]:(funny(X)))&
((~patient(lucy)|quiet(lucy)))&
((~generous(mary)<~>funny(mary))) | generous(mary) | [] | null | 0 |
If someone is not brave then someone is both not humble and rich. If someone is either happy or brave then someone is either not calm or tall. Everyone who is both not happy and not humble is not creative and vice versa. Everyone who is not kind is not old or kind and vice versa. Everyone who is generous or not curious is either not calm or not kind. Everyone who is not generous is both humble and not strong. If someone is kind or happy then john is both generous and not kind. Everyone who is both quiet and wise is creative. Everyone who is both generous and kind is not humble and vice versa. Everyone who is wise is strong. If someone is creative or curious then lucy is not funny or brave. Everyone who is either not funny or brave is both not curious and not rich. Everyone who is both wise and not rich is both not generous and not curious. Everyone who is not quiet or not funny is funny and vice versa. Everyone who is either not tall or happy is not old or kind. Someone is not happy. Someone is both not kind and funny. Lucy is old or not strong. Someone is generous. Susan is quiet or not kind. Paul is not quiet or not calm. | Lucy is not calm. | contradiction | ((?[X]:(~brave(X)))=>(?[X]:((~humble(X)&rich(X)))))&
((?[X]:((happy(X)<~>brave(X))))=>(?[X]:((~calm(X)<~>tall(X)))))&
(![X]:((~happy(X)&~humble(X))<=>~creative(X)))&
(![X]:(~kind(X)<=>(~old(X)|kind(X))))&
(![X]:((generous(X)|~curious(X))=>(~calm(X)<~>~kind(X))))&
(![X]:(~generous(X)=>(humble(X)&~strong(X))))&
((?[X]:((kind(X)|happy(X))))=>((generous(john)&~kind(john))))&
(![X]:((quiet(X)&wise(X))=>creative(X)))&
(![X]:((generous(X)&kind(X))<=>~humble(X)))&
(![X]:(wise(X)=>strong(X)))&
((?[X]:((creative(X)|curious(X))))=>((~funny(lucy)|brave(lucy))))&
(![X]:((~funny(X)<~>brave(X))=>(~curious(X)&~rich(X))))&
(![X]:((wise(X)&~rich(X))=>(~generous(X)&~curious(X))))&
(![X]:((~quiet(X)|~funny(X))<=>funny(X)))&
(![X]:((~tall(X)<~>happy(X))=>(~old(X)|kind(X))))&
(?[X]:(~happy(X)))&
(?[X]:((~kind(X)&funny(X))))&
((old(lucy)|~strong(lucy)))&
(?[X]:(generous(X)))&
((quiet(susan)|~kind(susan)))&
((~quiet(paul)|~calm(paul))) | ~calm(lucy) | [
"p0",
"p3",
"p4",
"p8",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 2466293443231146599809903
% SZS output start Proof for 2466293443231146599809903
1. ? [X0] : ~brave(X0) => ? [X0] : (rich(X0) & ~humble(X0)) [input p0]
4. ! [X0] : (~kind(X0) <=> (kind(X0) | ~old(X0))) [input p3]
5. ! [X0] : ((~curious(X0) | generous(X0)) => (~calm(X0) <~> ~kind(X0))) [input p4]
9. ! [X0] : ((kind(X0) & generous(X0)) <=> ~humble(X0)) [input p8]
12. ! [X0] : ((~funny(X0) <~> brave(X0)) => (~rich(X0) & ~curious(X0))) [input p11]
14. ! [X0] : ((~funny(X0) | ~quiet(X0)) <=> funny(X0)) [input p13]
22. ~calm(lucy) [input hypothesis]
23. ? [X0] : ~brave(X0) => ? [X1] : (rich(X1) & ~humble(X1)) [rectify 1]
31. ? [X1] : (rich(X1) & ~humble(X1)) | ! [X0] : brave(X0) [ennf transformation 23]
34. ! [X0] : ((~calm(X0) <~> ~kind(X0)) | (curious(X0) & ~generous(X0))) [ennf transformation 5]
39. ! [X0] : ((~rich(X0) & ~curious(X0)) | (~funny(X0) <=> brave(X0))) [ennf transformation 12]
42. ? [X0] : (rich(X0) & ~humble(X0)) | ! [X1] : brave(X1) [rectify 31]
43. ? [X0] : (rich(X0) & ~humble(X0)) => (rich(sK0) & ~humble(sK0)) [choice axiom]
44. (rich(sK0) & ~humble(sK0)) | ! [X1] : brave(X1) [skolemisation 42,43]
49. ! [X0] : ((~kind(X0) | (~kind(X0) & old(X0))) & ((kind(X0) | ~old(X0)) | kind(X0))) [nnf transformation 4]
50. ! [X0] : ((~kind(X0) | (~kind(X0) & old(X0))) & (kind(X0) | ~old(X0) | kind(X0))) [flattening 49]
51. ! [X0] : (((kind(X0) | calm(X0)) & (~kind(X0) | ~calm(X0))) | (curious(X0) & ~generous(X0))) [nnf transformation 34]
52. ! [X0] : (((kind(X0) & generous(X0)) | humble(X0)) & (~humble(X0) | (~kind(X0) | ~generous(X0)))) [nnf transformation 9]
53. ! [X0] : (((kind(X0) & generous(X0)) | humble(X0)) & (~humble(X0) | ~kind(X0) | ~generous(X0))) [flattening 52]
54. ! [X0] : ((~rich(X0) & ~curious(X0)) | ((~funny(X0) | ~brave(X0)) & (brave(X0) | funny(X0)))) [nnf transformation 39]
55. ! [X0] : (((~funny(X0) | ~quiet(X0)) | ~funny(X0)) & (funny(X0) | (funny(X0) & quiet(X0)))) [nnf transformation 14]
56. ! [X0] : ((~funny(X0) | ~quiet(X0) | ~funny(X0)) & (funny(X0) | (funny(X0) & quiet(X0)))) [flattening 55]
64. ~humble(sK0) | brave(X1) [cnf transformation 44]
74. ~kind(X0) | ~kind(X0) [cnf transformation 50]
78. kind(X0) | calm(X0) | curious(X0) [cnf transformation 51]
86. kind(X0) | humble(X0) [cnf transformation 53]
90. ~funny(X0) | ~curious(X0) | ~brave(X0) [cnf transformation 54]
94. funny(X0) | funny(X0) [cnf transformation 56]
104. ~calm(lucy) [cnf transformation 22]
105. funny(X0) [duplicate literal removal 94]
108. ~kind(X0) [duplicate literal removal 74]
110. 1 <=> ! [X1] : brave(X1) [avatar definition]
111. brave(X1) <- (1) [avatar component clause 110]
118. 3 <=> humble(sK0) [avatar definition]
120. ~humble(sK0) <- (~3) [avatar component clause 118]
121. 1 | ~3 [avatar split clause 64,118,110]
141. curious(X0) | calm(X0) [subsumption resolution 78,108]
151. humble(X0) [subsumption resolution 86,108]
153. 10 <=> ! [X0] : ~curious(X0) [avatar definition]
154. ~curious(X0) <- (10) [avatar component clause 153]
179. $false <- (~3) [subsumption resolution 120,151]
180. 3 [avatar contradiction clause 179]
186. ~curious(X0) | ~brave(X0) [resolution 90,105]
187. ~curious(X0) <- (1) [subsumption resolution 186,111]
188. 10 | ~1 [avatar split clause 187,110,153]
189. calm(X0) <- (10) [resolution 154,141]
190. $false <- (10) [resolution 189,104]
195. ~10 [avatar contradiction clause 190]
196. $false [avatar sat refutation 121,180,188,195]
% SZS output end Proof for 2466293443231146599809903
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not humble is generous or humble and vice versa.
Everyone who is tall is both generous and strong and vice versa.
Everyone who is either not humble or not happy is both not patient and not happy and vice versa.
If someone is both calm and patient then someone is not calm and vice versa.
Everyone who is either calm or funny is both not creative and not humble.
Everyone who is either old or brave is either not generous or rich.
If someone is either not strong or generous then someone is not strong and vice versa.
Everyone who is both patient and strong is either wise or not quiet.
If lucy is either calm or humble then someone is either rich or not kind and vice versa.
Everyone who is both not old and strong is brave or not creative.
Everyone who is both creative and brave is wise or brave and vice versa.
If fred is both not happy and humble then susan is creative and vice versa.
Everyone who is not brave is not calm or tall.
If paul is not rich or creative then someone is either brave or tall and vice versa.
Everyone who is both humble and brave is both tall and humble and vice versa.
Susan is either curious or not tall.
Susan is either not generous or patient.
Fred is not old.
Paul is either rich or quiet.
Paul is either not curious or not brave.
John is both kind and tall.
Someone is either not creative or not brave.
Mary is either not creative or calm. | Lucy is not patient. | contradiction | (![X]:(~humble(X)<=>(generous(X)|humble(X))))&
(![X]:(tall(X)<=>(generous(X)&strong(X))))&
(![X]:((~humble(X)<~>~happy(X))<=>(~patient(X)&~happy(X))))&
((?[X]:((calm(X)&patient(X))))<=>(?[X]:(~calm(X))))&
(![X]:((calm(X)<~>funny(X))=>(~creative(X)&~humble(X))))&
(![X]:((old(X)<~>brave(X))=>(~generous(X)<~>rich(X))))&
((?[X]:((~strong(X)<~>generous(X))))<=>(?[X]:(~strong(X))))&
(![X]:((patient(X)&strong(X))=>(wise(X)<~>~quiet(X))))&
(((calm(lucy)<~>humble(lucy)))<=>(?[X]:((rich(X)<~>~kind(X)))))&
(![X]:((~old(X)&strong(X))=>(brave(X)|~creative(X))))&
(![X]:((creative(X)&brave(X))<=>(wise(X)|brave(X))))&
(((~happy(fred)&humble(fred)))<=>(creative(susan)))&
(![X]:(~brave(X)=>(~calm(X)|tall(X))))&
(((~rich(paul)|creative(paul)))<=>(?[X]:((brave(X)<~>tall(X)))))&
(![X]:((humble(X)&brave(X))<=>(tall(X)&humble(X))))&
((curious(susan)<~>~tall(susan)))&
((~generous(susan)<~>patient(susan)))&
(~old(fred))&
((rich(paul)<~>quiet(paul)))&
((~curious(paul)<~>~brave(paul)))&
((kind(john)&tall(john)))&
(?[X]:((~creative(X)<~>~brave(X))))&
((~creative(mary)<~>calm(mary))) | ~patient(lucy) | [
"p0",
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 7601884756645424619463865
% SZS output start Proof for 7601884756645424619463865
1. ! [X0] : (~humble(X0) <=> (humble(X0) | generous(X0))) [input p0]
3. ! [X0] : ((~humble(X0) <~> ~happy(X0)) <=> (~happy(X0) & ~patient(X0))) [input p2]
24. ~patient(lucy) [input hypothesis]
35. ! [X0] : ((~humble(X0) | (~humble(X0) & ~generous(X0))) & ((humble(X0) | generous(X0)) | humble(X0))) [nnf transformation 1]
36. ! [X0] : ((~humble(X0) | (~humble(X0) & ~generous(X0))) & (humble(X0) | generous(X0) | humble(X0))) [flattening 35]
39. ! [X0] : ((((happy(X0) | humble(X0)) & (~happy(X0) | ~humble(X0))) | (happy(X0) | patient(X0))) & ((~happy(X0) & ~patient(X0)) | ((~humble(X0) | happy(X0)) & (~happy(X0) | humble(X0))))) [nnf transformation 3]
40. ! [X0] : ((((happy(X0) | humble(X0)) & (~happy(X0) | ~humble(X0))) | happy(X0) | patient(X0)) & ((~happy(X0) & ~patient(X0)) | ((~humble(X0) | happy(X0)) & (~happy(X0) | humble(X0))))) [flattening 39]
79. ~humble(X0) | ~humble(X0) [cnf transformation 36]
85. ~happy(X0) | ~happy(X0) | humble(X0) [cnf transformation 40]
88. happy(X0) | humble(X0) | happy(X0) | patient(X0) [cnf transformation 40]
149. ~patient(lucy) [cnf transformation 24]
150. ~happy(X0) | humble(X0) [duplicate literal removal 85]
151. happy(X0) | humble(X0) | patient(X0) [duplicate literal removal 88]
153. ~humble(X0) [duplicate literal removal 79]
156. patient(X0) | happy(X0) [subsumption resolution 151,153]
157. ~happy(X0) [subsumption resolution 150,153]
298. happy(lucy) [resolution 156,149]
299. $false [subsumption resolution 298,157]
% SZS output end Proof for 7601884756645424619463865
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not curious or kind is either not patient or creative. If someone is not rich or humble then alice is funny or brave and vice versa. If fred is either not calm or happy then someone is both not tall and funny and vice versa. If fred is either tall or not strong then someone is not funny or not brave and vice versa. If someone is happy then someone is both not strong and generous and vice versa. Everyone who is either patient or not calm is both not quiet and not happy. Everyone who is not old is generous and vice versa. Everyone who is both not wise and rich is generous or not humble and vice versa. Everyone who is either quiet or generous is either happy or not quiet and vice versa. Everyone who is either not kind or kind is not humble or generous and vice versa. Everyone who is both patient and not funny is not patient or happy and vice versa. Everyone who is either brave or not rich is not creative and vice versa. If john is old or humble then someone is both quiet and not patient. Everyone who is either patient or kind is both brave and not funny and vice versa. If someone is generous or calm then someone is kind and vice versa. If someone is either tall or old then fred is humble. Lucy is humble or not quiet. Someone is kind. Someone is not happy or not quiet. Someone is both kind and strong. John is not creative or not funny. Someone is not rich or not tall. Someone is either kind or not happy. | Fred is happy. | contradiction | (![X]:((~curious(X)<~>kind(X))=>(~patient(X)<~>creative(X))))&
((?[X]:((~rich(X)|humble(X))))<=>((funny(alice)|brave(alice))))&
(((~calm(fred)<~>happy(fred)))<=>(?[X]:((~tall(X)&funny(X)))))&
(((tall(fred)<~>~strong(fred)))<=>(?[X]:((~funny(X)|~brave(X)))))&
((?[X]:(happy(X)))<=>(?[X]:((~strong(X)&generous(X)))))&
(![X]:((patient(X)<~>~calm(X))=>(~quiet(X)&~happy(X))))&
(![X]:(~old(X)<=>generous(X)))&
(![X]:((~wise(X)&rich(X))<=>(generous(X)|~humble(X))))&
(![X]:((quiet(X)<~>generous(X))<=>(happy(X)<~>~quiet(X))))&
(![X]:((~kind(X)<~>kind(X))<=>(~humble(X)|generous(X))))&
(![X]:((patient(X)&~funny(X))<=>(~patient(X)|happy(X))))&
(![X]:((brave(X)<~>~rich(X))<=>~creative(X)))&
(((old(john)|humble(john)))=>(?[X]:((quiet(X)&~patient(X)))))&
(![X]:((patient(X)<~>kind(X))<=>(brave(X)&~funny(X))))&
((?[X]:((generous(X)|calm(X))))<=>(?[X]:(kind(X))))&
((?[X]:((tall(X)<~>old(X))))=>(humble(fred)))&
((humble(lucy)|~quiet(lucy)))&
(?[X]:(kind(X)))&
(?[X]:((~happy(X)|~quiet(X))))&
(?[X]:((kind(X)&strong(X))))&
((~creative(john)|~funny(john)))&
(?[X]:((~rich(X)|~tall(X))))&
(?[X]:((kind(X)<~>~happy(X)))) | happy(fred) | [
"p2",
"p5",
"p6",
"p8",
"p9",
"p10",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8218817800158575975246934
% SZS output start Proof for 8218817800158575975246934
3. (~calm(fred) <~> happy(fred)) <=> ? [X0] : (funny(X0) & ~tall(X0)) [input p2]
6. ! [X0] : ((patient(X0) <~> ~calm(X0)) => (~happy(X0) & ~quiet(X0))) [input p5]
7. ! [X0] : (~old(X0) <=> generous(X0)) [input p6]
9. ! [X0] : ((quiet(X0) <~> generous(X0)) <=> (happy(X0) <~> ~quiet(X0))) [input p8]
10. ! [X0] : ((~kind(X0) <~> kind(X0)) <=> (generous(X0) | ~humble(X0))) [input p9]
11. ! [X0] : ((~funny(X0) & patient(X0)) <=> (happy(X0) | ~patient(X0))) [input p10]
13. (humble(john) | old(john)) => ? [X0] : (~patient(X0) & quiet(X0)) [input p12]
16. ? [X0] : (tall(X0) <~> old(X0)) => humble(fred) [input p15]
24. happy(fred) [input hypothesis]
28. ! [X0] : ((~happy(X0) & ~quiet(X0)) | (patient(X0) <=> ~calm(X0))) [ennf transformation 6]
29. ? [X0] : (~patient(X0) & quiet(X0)) | (~humble(john) & ~old(john)) [ennf transformation 13]
30. humble(fred) | ! [X0] : (tall(X0) <=> old(X0)) [ennf transformation 16]
37. (((~happy(fred) | calm(fred)) & (happy(fred) | ~calm(fred))) | ! [X0] : (~funny(X0) | tall(X0))) & (? [X0] : (funny(X0) & ~tall(X0)) | ((~calm(fred) | ~happy(fred)) & (happy(fred) | calm(fred)))) [nnf transformation 3]
38. (((~happy(fred) | calm(fred)) & (happy(fred) | ~calm(fred))) | ! [X0] : (~funny(X0) | tall(X0))) & (? [X1] : (funny(X1) & ~tall(X1)) | ((~calm(fred) | ~happy(fred)) & (happy(fred) | calm(fred)))) [rectify 37]
39. ? [X1] : (funny(X1) & ~tall(X1)) => (funny(sK1) & ~tall(sK1)) [choice axiom]
40. (((~happy(fred) | calm(fred)) & (happy(fred) | ~calm(fred))) | ! [X0] : (~funny(X0) | tall(X0))) & ((funny(sK1) & ~tall(sK1)) | ((~calm(fred) | ~happy(fred)) & (happy(fred) | calm(fred)))) [skolemisation 38,39]
50. ! [X0] : ((~happy(X0) & ~quiet(X0)) | ((patient(X0) | calm(X0)) & (~calm(X0) | ~patient(X0)))) [nnf transformation 28]
51. ! [X0] : ((~old(X0) | ~generous(X0)) & (generous(X0) | old(X0))) [nnf transformation 7]
54. ! [X0] : ((((~generous(X0) | ~quiet(X0)) & (generous(X0) | quiet(X0))) | ((happy(X0) | quiet(X0)) & (~quiet(X0) | ~happy(X0)))) & (((quiet(X0) | ~happy(X0)) & (~quiet(X0) | happy(X0))) | ((quiet(X0) | ~generous(X0)) & (generous(X0) | ~quiet(X0))))) [nnf transformation 9]
55. ! [X0] : ((((~kind(X0) | kind(X0)) & (kind(X0) | ~kind(X0))) | (~generous(X0) & humble(X0))) & ((generous(X0) | ~humble(X0)) | ((~kind(X0) | ~kind(X0)) & (kind(X0) | kind(X0))))) [nnf transformation 10]
56. ! [X0] : ((((~kind(X0) | kind(X0)) & (kind(X0) | ~kind(X0))) | (~generous(X0) & humble(X0))) & (generous(X0) | ~humble(X0) | ((~kind(X0) | ~kind(X0)) & (kind(X0) | kind(X0))))) [flattening 55]
57. ! [X0] : (((~funny(X0) & patient(X0)) | (~happy(X0) & patient(X0))) & ((happy(X0) | ~patient(X0)) | (funny(X0) | ~patient(X0)))) [nnf transformation 11]
58. ! [X0] : (((~funny(X0) & patient(X0)) | (~happy(X0) & patient(X0))) & (happy(X0) | ~patient(X0) | funny(X0) | ~patient(X0))) [flattening 57]
60. ? [X0] : (~patient(X0) & quiet(X0)) => (~patient(sK5) & quiet(sK5)) [choice axiom]
61. (~patient(sK5) & quiet(sK5)) | (~humble(john) & ~old(john)) [skolemisation 29,60]
69. humble(fred) | ! [X0] : ((tall(X0) | ~old(X0)) & (old(X0) | ~tall(X0))) [nnf transformation 30]
94. ~happy(fred) | calm(fred) | ~funny(X0) | tall(X0) [cnf transformation 40]
106. ~happy(X0) | ~calm(X0) | ~patient(X0) [cnf transformation 50]
108. old(X0) | generous(X0) [cnf transformation 51]
118. quiet(X0) | ~happy(X0) | quiet(X0) | ~generous(X0) [cnf transformation 54]
121. ~generous(X0) | ~quiet(X0) | ~quiet(X0) | ~happy(X0) [cnf transformation 54]
123. generous(X0) | ~humble(X0) | kind(X0) | kind(X0) [cnf transformation 56]
124. generous(X0) | ~humble(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 56]
129. happy(X0) | ~patient(X0) | funny(X0) | ~patient(X0) [cnf transformation 58]
130. patient(X0) | patient(X0) [cnf transformation 58]
140. ~patient(sK5) | ~old(john) [cnf transformation 61]
151. humble(fred) | old(X0) | ~tall(X0) [cnf transformation 69]
162. happy(fred) [cnf transformation 24]
163. happy(X0) | ~patient(X0) | funny(X0) [duplicate literal removal 129]
164. patient(X0) [duplicate literal removal 130]
165. generous(X0) | ~humble(X0) | kind(X0) [duplicate literal removal 123]
166. generous(X0) | ~humble(X0) | ~kind(X0) [duplicate literal removal 124]
168. quiet(X0) | ~happy(X0) | ~generous(X0) [duplicate literal removal 118]
170. ~generous(X0) | ~quiet(X0) | ~happy(X0) [duplicate literal removal 121]
198. 7 <=> ! [X0] : (~funny(X0) | tall(X0)) [avatar definition]
199. ~funny(X0) | tall(X0) <- (7) [avatar component clause 198]
201. 8 <=> calm(fred) [avatar definition]
205. 9 <=> happy(fred) [avatar definition]
206. happy(fred) <- (9) [avatar component clause 205]
208. 7 | 8 | ~9 [avatar split clause 94,205,201,198]
271. ~generous(X0) | ~happy(X0) [subsumption resolution 168,170]
273. ~humble(X0) | generous(X0) [subsumption resolution 165,166]
274. happy(X0) | funny(X0) [subsumption resolution 163,164]
276. ~old(john) [subsumption resolution 140,164]
308. 30 <=> humble(fred) [avatar definition]
310. humble(fred) <- (30) [avatar component clause 308]
313. 31 <=> ! [X0] : (old(X0) | ~tall(X0)) [avatar definition]
314. ~tall(X0) | old(X0) <- (31) [avatar component clause 313]
315. 31 | 30 [avatar split clause 151,308,313]
339. 37 <=> funny(john) [avatar definition]
340. funny(john) <- (37) [avatar component clause 339]
362. 9 [avatar split clause 162,205]
369. generous(john) [resolution 108,276]
388. ~happy(john) [resolution 271,369]
391. generous(fred) <- (30) [resolution 273,310]
407. ~happy(fred) <- (30) [resolution 391,271]
409. $false <- (9, 30) [subsumption resolution 407,206]
410. ~9 | ~30 [avatar contradiction clause 409]
426. funny(john) [resolution 388,274]
429. 37 [avatar split clause 426,339]
431. tall(john) <- (7, 37) [resolution 340,199]
434. ~calm(fred) | ~patient(fred) <- (9) [resolution 106,206]
444. old(john) <- (7, 31, 37) [resolution 431,314]
445. $false <- (7, 31, 37) [subsumption resolution 444,276]
446. ~7 | ~31 | ~37 [avatar contradiction clause 445]
447. ~calm(fred) <- (9) [subsumption resolution 434,164]
448. ~8 | ~9 [avatar split clause 447,205,201]
449. $false [avatar sat refutation 208,315,362,410,429,446,448]
% SZS output end Proof for 8218817800158575975246934
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not generous or funny then someone is either not curious or kind and vice versa.
Everyone who is tall is curious or not patient and vice versa.
If someone is either rich or patient then john is both not kind and not creative and vice versa.
If someone is both happy and not happy then lucy is either not happy or generous and vice versa.
Everyone who is either not rich or not patient is either not quiet or creative and vice versa.
Everyone who is both not curious and not tall is both generous and not happy and vice versa.
If john is calm or happy then susan is either happy or not strong and vice versa.
Everyone who is not old is both not creative and not kind.
Everyone who is calm is not brave or generous and vice versa.
Everyone who is not calm is generous.
Everyone who is either not wise or not generous is calm or not brave.
Everyone who is not calm is either not patient or old.
If alice is either happy or not old then susan is not curious or not rich.
Everyone who is patient or not funny is rich.
Everyone who is brave is not humble or funny and vice versa.
Everyone who is either tall or creative is quiet and vice versa.
John is both not patient and not kind.
Mary is not generous.
Susan is either not rich or not creative.
Someone is either quiet or not humble.
Someone is both not brave and not funny.
Paul is either wise or not old.
Fred is not creative or not old. | Mary is not curious. | contradiction | ((?[X]:((~generous(X)<~>funny(X))))<=>(?[X]:((~curious(X)<~>kind(X)))))&
(![X]:(tall(X)<=>(curious(X)|~patient(X))))&
((?[X]:((rich(X)<~>patient(X))))<=>((~kind(john)&~creative(john))))&
((?[X]:((happy(X)&~happy(X))))<=>((~happy(lucy)<~>generous(lucy))))&
(![X]:((~rich(X)<~>~patient(X))<=>(~quiet(X)<~>creative(X))))&
(![X]:((~curious(X)&~tall(X))<=>(generous(X)&~happy(X))))&
(((calm(john)|happy(john)))<=>((happy(susan)<~>~strong(susan))))&
(![X]:(~old(X)=>(~creative(X)&~kind(X))))&
(![X]:(calm(X)<=>(~brave(X)|generous(X))))&
(![X]:(~calm(X)=>generous(X)))&
(![X]:((~wise(X)<~>~generous(X))=>(calm(X)|~brave(X))))&
(![X]:(~calm(X)=>(~patient(X)<~>old(X))))&
(((happy(alice)<~>~old(alice)))=>((~curious(susan)|~rich(susan))))&
(![X]:((patient(X)|~funny(X))=>rich(X)))&
(![X]:(brave(X)<=>(~humble(X)|funny(X))))&
(![X]:((tall(X)<~>creative(X))<=>quiet(X)))&
((~patient(john)&~kind(john)))&
(~generous(mary))&
((~rich(susan)<~>~creative(susan)))&
(?[X]:((quiet(X)<~>~humble(X))))&
(?[X]:((~brave(X)&~funny(X))))&
((wise(paul)<~>~old(paul)))&
((~creative(fred)|~old(fred))) | ~curious(mary) | [
"p1",
"p2",
"p4",
"p5",
"p8",
"p9",
"p13",
"p14",
"p15",
"p16",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 155586108310229123116374
% SZS output start Proof for 155586108310229123116374
2. ! [X0] : (tall(X0) <=> (~patient(X0) | curious(X0))) [input p1]
3. ? [X0] : (rich(X0) <~> patient(X0)) <=> (~creative(john) & ~kind(john)) [input p2]
5. ! [X0] : ((~rich(X0) <~> ~patient(X0)) <=> (~quiet(X0) <~> creative(X0))) [input p4]
6. ! [X0] : ((~tall(X0) & ~curious(X0)) <=> (~happy(X0) & generous(X0))) [input p5]
9. ! [X0] : (calm(X0) <=> (generous(X0) | ~brave(X0))) [input p8]
10. ! [X0] : (~calm(X0) => generous(X0)) [input p9]
14. ! [X0] : ((~funny(X0) | patient(X0)) => rich(X0)) [input p13]
15. ! [X0] : (brave(X0) <=> (funny(X0) | ~humble(X0))) [input p14]
16. ! [X0] : ((tall(X0) <~> creative(X0)) <=> quiet(X0)) [input p15]
17. ~kind(john) & ~patient(john) [input p16]
18. ~generous(mary) [input p17]
24. ~curious(mary) [input hypothesis]
27. ! [X0] : (generous(X0) | calm(X0)) [ennf transformation 10]
33. ! [X0] : (rich(X0) | (funny(X0) & ~patient(X0))) [ennf transformation 14]
39. ! [X0] : ((tall(X0) | (patient(X0) & ~curious(X0))) & ((~patient(X0) | curious(X0)) | ~tall(X0))) [nnf transformation 2]
40. ! [X0] : ((tall(X0) | (patient(X0) & ~curious(X0))) & (~patient(X0) | curious(X0) | ~tall(X0))) [flattening 39]
41. (? [X0] : ((~patient(X0) | ~rich(X0)) & (patient(X0) | rich(X0))) | (creative(john) | kind(john))) & ((~creative(john) & ~kind(john)) | ! [X0] : ((rich(X0) | ~patient(X0)) & (patient(X0) | ~rich(X0)))) [nnf transformation 3]
42. (? [X0] : ((~patient(X0) | ~rich(X0)) & (patient(X0) | rich(X0))) | creative(john) | kind(john)) & ((~creative(john) & ~kind(john)) | ! [X0] : ((rich(X0) | ~patient(X0)) & (patient(X0) | ~rich(X0)))) [flattening 41]
43. (? [X0] : ((~patient(X0) | ~rich(X0)) & (patient(X0) | rich(X0))) | creative(john) | kind(john)) & ((~creative(john) & ~kind(john)) | ! [X1] : ((rich(X1) | ~patient(X1)) & (patient(X1) | ~rich(X1)))) [rectify 42]
44. ? [X0] : ((~patient(X0) | ~rich(X0)) & (patient(X0) | rich(X0))) => ((~patient(sK2) | ~rich(sK2)) & (patient(sK2) | rich(sK2))) [choice axiom]
45. (((~patient(sK2) | ~rich(sK2)) & (patient(sK2) | rich(sK2))) | creative(john) | kind(john)) & ((~creative(john) & ~kind(john)) | ! [X1] : ((rich(X1) | ~patient(X1)) & (patient(X1) | ~rich(X1)))) [skolemisation 43,44]
50. ! [X0] : ((((patient(X0) | rich(X0)) & (~patient(X0) | ~rich(X0))) | ((~quiet(X0) | ~creative(X0)) & (creative(X0) | quiet(X0)))) & (((~creative(X0) | quiet(X0)) & (creative(X0) | ~quiet(X0))) | ((~rich(X0) | patient(X0)) & (~patient(X0) | rich(X0))))) [nnf transformation 5]
51. ! [X0] : (((~tall(X0) & ~curious(X0)) | (happy(X0) | ~generous(X0))) & ((~happy(X0) & generous(X0)) | (tall(X0) | curious(X0)))) [nnf transformation 6]
52. ! [X0] : (((~tall(X0) & ~curious(X0)) | happy(X0) | ~generous(X0)) & ((~happy(X0) & generous(X0)) | tall(X0) | curious(X0))) [flattening 51]
55. ! [X0] : ((calm(X0) | (~generous(X0) & brave(X0))) & ((generous(X0) | ~brave(X0)) | ~calm(X0))) [nnf transformation 9]
56. ! [X0] : ((calm(X0) | (~generous(X0) & brave(X0))) & (generous(X0) | ~brave(X0) | ~calm(X0))) [flattening 55]
60. ! [X0] : ((brave(X0) | (~funny(X0) & humble(X0))) & ((funny(X0) | ~humble(X0)) | ~brave(X0))) [nnf transformation 15]
61. ! [X0] : ((brave(X0) | (~funny(X0) & humble(X0))) & (funny(X0) | ~humble(X0) | ~brave(X0))) [flattening 60]
62. ! [X0] : ((((~creative(X0) | ~tall(X0)) & (creative(X0) | tall(X0))) | ~quiet(X0)) & (quiet(X0) | ((tall(X0) | ~creative(X0)) & (creative(X0) | ~tall(X0))))) [nnf transformation 16]
78. ~patient(X0) | curious(X0) | ~tall(X0) [cnf transformation 40]
79. ~curious(X0) | tall(X0) [cnf transformation 40]
80. patient(X0) | tall(X0) [cnf transformation 40]
83. ~creative(john) | patient(X1) | ~rich(X1) [cnf transformation 45]
85. patient(sK2) | rich(sK2) | creative(john) | kind(john) [cnf transformation 45]
86. ~patient(sK2) | ~rich(sK2) | creative(john) | kind(john) [cnf transformation 45]
94. ~quiet(X0) | creative(X0) | ~rich(X0) | patient(X0) [cnf transformation 50]
96. ~creative(X0) | quiet(X0) | ~rich(X0) | patient(X0) [cnf transformation 50]
97. ~rich(X0) | ~patient(X0) | creative(X0) | quiet(X0) [cnf transformation 50]
98. ~quiet(X0) | ~rich(X0) | ~patient(X0) | ~creative(X0) [cnf transformation 50]
101. generous(X0) | tall(X0) | curious(X0) [cnf transformation 52]
113. ~brave(X0) | generous(X0) | ~calm(X0) [cnf transformation 56]
115. ~generous(X0) | calm(X0) [cnf transformation 56]
116. generous(X0) | calm(X0) [cnf transformation 27]
123. rich(X0) | ~patient(X0) [cnf transformation 33]
124. rich(X0) | funny(X0) [cnf transformation 33]
127. ~funny(X0) | brave(X0) [cnf transformation 61]
128. ~tall(X0) | creative(X0) | quiet(X0) [cnf transformation 62]
129. ~creative(X0) | tall(X0) | quiet(X0) [cnf transformation 62]
130. ~quiet(X0) | tall(X0) | creative(X0) [cnf transformation 62]
131. ~quiet(X0) | ~tall(X0) | ~creative(X0) [cnf transformation 62]
133. ~kind(john) [cnf transformation 17]
134. ~generous(mary) [cnf transformation 18]
144. ~curious(mary) [cnf transformation 24]
182. 9 <=> kind(john) [avatar definition]
186. 10 <=> creative(john) [avatar definition]
190. 11 <=> rich(sK2) [avatar definition]
191. rich(sK2) <- (11) [avatar component clause 190]
194. 12 <=> patient(sK2) [avatar definition]
195. patient(sK2) <- (12) [avatar component clause 194]
196. ~patient(sK2) <- (~12) [avatar component clause 194]
197. 9 | 10 | ~11 | ~12 [avatar split clause 86,194,190,186,182]
198. 9 | 10 | 11 | 12 [avatar split clause 85,194,190,186,182]
200. 13 <=> ! [X1] : (rich(X1) | ~patient(X1)) [avatar definition]
201. ~patient(X1) | rich(X1) <- (13) [avatar component clause 200]
204. 14 <=> ! [X1] : (patient(X1) | ~rich(X1)) [avatar definition]
205. ~rich(X1) | patient(X1) <- (14) [avatar component clause 204]
206. 14 | ~10 [avatar split clause 83,186,204]
226. tall(X0) | generous(X0) [subsumption resolution 101,79]
249. calm(X0) [subsumption resolution 116,115]
268. 13 [avatar split clause 123,200]
269. ~9 [avatar split clause 133,182]
300. tall(sK2) <- (~12) [resolution 80,196]
304. rich(X0) | tall(X0) <- (13) [resolution 201,80]
325. creative(sK2) | quiet(sK2) <- (~12) [resolution 128,300]
329. 33 <=> quiet(sK2) [avatar definition]
330. ~quiet(sK2) <- (~33) [avatar component clause 329]
331. quiet(sK2) <- (33) [avatar component clause 329]
333. 34 <=> creative(sK2) [avatar definition]
335. creative(sK2) <- (34) [avatar component clause 333]
336. 33 | 34 | 12 [avatar split clause 325,194,333,329]
340. rich(sK2) <- (12, 13) [resolution 195,201]
349. 11 | ~12 | ~13 [avatar split clause 340,200,194,190]
351. 36 <=> tall(sK2) [avatar definition]
352. tall(sK2) <- (36) [avatar component clause 351]
353. ~tall(sK2) <- (~36) [avatar component clause 351]
365. patient(X1) | funny(X1) <- (14) [resolution 205,124]
376. ~tall(X0) | curious(X0) | funny(X0) <- (14) [resolution 365,78]
390. ~patient(X0) | creative(X0) | quiet(X0) | tall(X0) <- (13) [resolution 97,304]
394. ~patient(X0) | creative(X0) | tall(X0) <- (13) [subsumption resolution 390,130]
395. creative(X0) | tall(X0) <- (13) [subsumption resolution 394,80]
407. creative(sK2) | ~rich(sK2) | patient(sK2) <- (33) [resolution 331,94]
409. ~tall(sK2) | ~creative(sK2) <- (33) [resolution 331,131]
496. tall(X2) | tall(X2) | quiet(X2) <- (13) [resolution 395,129]
502. quiet(X2) | tall(X2) <- (13) [duplicate literal removal 496]
554. curious(X0) | funny(X0) | generous(X0) <- (14) [resolution 376,226]
586. tall(X1) | ~rich(X1) | ~patient(X1) | ~creative(X1) <- (13) [resolution 502,98]
592. tall(X1) | ~patient(X1) | ~creative(X1) <- (13) [subsumption resolution 586,201]
593. tall(X1) | ~creative(X1) <- (13) [subsumption resolution 592,80]
594. tall(X1) <- (13) [subsumption resolution 593,395]
604. funny(mary) | generous(mary) <- (14) [resolution 554,144]
606. funny(mary) <- (14) [subsumption resolution 604,134]
649. brave(mary) <- (14) [resolution 606,127]
676. generous(mary) | ~calm(mary) <- (14) [resolution 649,113]
677. ~calm(mary) <- (14) [subsumption resolution 676,134]
678. $false <- (14) [subsumption resolution 677,249]
679. ~14 [avatar contradiction clause 678]
701. creative(sK2) | patient(sK2) <- (11, 33) [subsumption resolution 407,191]
702. creative(sK2) <- (11, ~12, 33) [subsumption resolution 701,196]
703. 34 | ~11 | 12 | ~33 [avatar split clause 702,329,194,190,333]
704. ~creative(sK2) <- (33, 36) [subsumption resolution 409,352]
705. ~34 | ~33 | ~36 [avatar split clause 704,351,329,333]
709. $false <- (13, ~36) [subsumption resolution 353,594]
710. ~13 | 36 [avatar contradiction clause 709]
720. quiet(sK2) | ~rich(sK2) | patient(sK2) <- (34) [resolution 335,96]
724. ~rich(sK2) | patient(sK2) <- (~33, 34) [subsumption resolution 720,330]
725. patient(sK2) <- (11, ~33, 34) [subsumption resolution 724,191]
726. $false <- (11, ~12, ~33, 34) [subsumption resolution 725,196]
727. ~11 | 12 | 33 | ~34 [avatar contradiction clause 726]
728. $false [avatar sat refutation 197,198,206,268,269,336,349,679,703,705,710,727]
% SZS output end Proof for 155586108310229123116374
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either humble or not quiet is not wise and vice versa. If someone is not tall then someone is either old or quiet and vice versa. If someone is both rich and funny then susan is happy. If john is not strong then someone is tall or not curious. Everyone who is kind is both humble and not kind. If mary is patient or happy then mary is either quiet or strong. Everyone who is either happy or old is either happy or not brave. Everyone who is not brave is tall or brave and vice versa. Everyone who is calm is not curious and vice versa. If susan is either old or not patient then john is not calm or curious and vice versa. Everyone who is old is either not rich or quiet and vice versa. Everyone who is not generous or creative is humble. Everyone who is not calm is not rich. Everyone who is wise is both creative and not calm and vice versa. If someone is both not patient and not kind then someone is either not kind or tall and vice versa. Everyone who is either not brave or calm is either not brave or strong and vice versa. Someone is not creative. Fred is rich. Alice is either wise or not creative. Alice is generous or rich. Someone is not wise or not rich. Someone is not old. | John is happy. | neutral | (![X]:((humble(X)<~>~quiet(X))<=>~wise(X)))&
((?[X]:(~tall(X)))<=>(?[X]:((old(X)<~>quiet(X)))))&
((?[X]:((rich(X)&funny(X))))=>(happy(susan)))&
((~strong(john))=>(?[X]:((tall(X)|~curious(X)))))&
(![X]:(kind(X)=>(humble(X)&~kind(X))))&
(((patient(mary)|happy(mary)))=>((quiet(mary)<~>strong(mary))))&
(![X]:((happy(X)<~>old(X))=>(happy(X)<~>~brave(X))))&
(![X]:(~brave(X)<=>(tall(X)|brave(X))))&
(![X]:(calm(X)<=>~curious(X)))&
(((old(susan)<~>~patient(susan)))<=>((~calm(john)|curious(john))))&
(![X]:(old(X)<=>(~rich(X)<~>quiet(X))))&
(![X]:((~generous(X)|creative(X))=>humble(X)))&
(![X]:(~calm(X)=>~rich(X)))&
(![X]:(wise(X)<=>(creative(X)&~calm(X))))&
((?[X]:((~patient(X)&~kind(X))))<=>(?[X]:((~kind(X)<~>tall(X)))))&
(![X]:((~brave(X)<~>calm(X))<=>(~brave(X)<~>strong(X))))&
(?[X]:(~creative(X)))&
(rich(fred))&
((wise(alice)<~>~creative(alice)))&
((generous(alice)|rich(alice)))&
(?[X]:((~wise(X)|~rich(X))))&
(?[X]:(~old(X))) | happy(john) | [] | null | 0 |
Everyone who is kind is either curious or not funny. If someone is either not generous or tall then someone is both happy and calm. If alice is either not rich or tall then fred is both happy and rich and vice versa. Everyone who is both not brave and quiet is not generous or curious. Everyone who is not kind or not humble is both not happy and rich and vice versa. Everyone who is either not calm or not creative is not kind or tall and vice versa. Everyone who is either not happy or not patient is not brave. Everyone who is not patient or brave is humble or not calm and vice versa. Everyone who is not old or wise is curious. Everyone who is both not humble and not rich is rich. Everyone who is not funny is either not generous or curious. Everyone who is not rich or tall is patient or not old. Everyone who is strong or old is generous or not strong. If paul is tall or not creative then lucy is not calm. Everyone who is both not strong and not brave is either not happy or brave. If alice is either wise or old then susan is not tall or not generous and vice versa. Someone is rich. John is kind. Lucy is calm or not old. Paul is either not humble or happy. John is not patient or happy. Fred is not kind or not funny. Fred is not rich. Someone is humble or not strong. | Fred is old. | entailment | (![X]:(kind(X)=>(curious(X)<~>~funny(X))))&
((?[X]:((~generous(X)<~>tall(X))))=>(?[X]:((happy(X)&calm(X)))))&
(((~rich(alice)<~>tall(alice)))<=>((happy(fred)&rich(fred))))&
(![X]:((~brave(X)&quiet(X))=>(~generous(X)|curious(X))))&
(![X]:((~kind(X)|~humble(X))<=>(~happy(X)&rich(X))))&
(![X]:((~calm(X)<~>~creative(X))<=>(~kind(X)|tall(X))))&
(![X]:((~happy(X)<~>~patient(X))=>~brave(X)))&
(![X]:((~patient(X)|brave(X))<=>(humble(X)|~calm(X))))&
(![X]:((~old(X)|wise(X))=>curious(X)))&
(![X]:((~humble(X)&~rich(X))=>rich(X)))&
(![X]:(~funny(X)=>(~generous(X)<~>curious(X))))&
(![X]:((~rich(X)|tall(X))=>(patient(X)|~old(X))))&
(![X]:((strong(X)|old(X))=>(generous(X)|~strong(X))))&
(((tall(paul)|~creative(paul)))=>(~calm(lucy)))&
(![X]:((~strong(X)&~brave(X))=>(~happy(X)<~>brave(X))))&
(((wise(alice)<~>old(alice)))<=>((~tall(susan)|~generous(susan))))&
(?[X]:(rich(X)))&
(kind(john))&
((calm(lucy)|~old(lucy)))&
((~humble(paul)<~>happy(paul)))&
((~patient(john)|happy(john)))&
((~kind(fred)|~funny(fred)))&
(~rich(fred))&
(?[X]:((humble(X)|~strong(X)))) | old(fred) | [
"p0",
"p4",
"p8",
"p21",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 6221627448817095058752180
% SZS output start Proof for 6221627448817095058752180
1. ! [X0] : (kind(X0) => (curious(X0) <~> ~funny(X0))) [input p0]
5. ! [X0] : ((~humble(X0) | ~kind(X0)) <=> (rich(X0) & ~happy(X0))) [input p4]
9. ! [X0] : ((wise(X0) | ~old(X0)) => curious(X0)) [input p8]
22. ~funny(fred) | ~kind(fred) [input p21]
23. ~rich(fred) [input p22]
25. ~old(fred) [input hypothesis]
28. ! [X0] : ((curious(X0) <~> ~funny(X0)) | ~kind(X0)) [ennf transformation 1]
31. ! [X0] : (curious(X0) | (~wise(X0) & old(X0))) [ennf transformation 9]
42. ! [X0] : (((funny(X0) | ~curious(X0)) & (~funny(X0) | curious(X0))) | ~kind(X0)) [nnf transformation 28]
49. ! [X0] : (((~humble(X0) | ~kind(X0)) | (~rich(X0) | happy(X0))) & ((rich(X0) & ~happy(X0)) | (humble(X0) & kind(X0)))) [nnf transformation 5]
50. ! [X0] : ((~humble(X0) | ~kind(X0) | ~rich(X0) | happy(X0)) & ((rich(X0) & ~happy(X0)) | (humble(X0) & kind(X0)))) [flattening 49]
66. ~curious(X0) | funny(X0) | ~kind(X0) [cnf transformation 42]
79. rich(X0) | kind(X0) [cnf transformation 50]
94. old(X0) | curious(X0) [cnf transformation 31]
119. ~funny(fred) | ~kind(fred) [cnf transformation 22]
120. ~rich(fred) [cnf transformation 23]
122. ~old(fred) [cnf transformation 25]
149. 6 <=> rich(fred) [avatar definition]
151. ~rich(fred) <- (~6) [avatar component clause 149]
226. 21 <=> kind(fred) [avatar definition]
227. kind(fred) <- (21) [avatar component clause 226]
230. 22 <=> funny(fred) [avatar definition]
232. ~funny(fred) <- (~22) [avatar component clause 230]
233. ~21 | ~22 [avatar split clause 119,230,226]
234. ~6 [avatar split clause 120,149]
246. kind(fred) <- (~6) [resolution 79,151]
247. 21 | 6 [avatar split clause 246,149,226]
249. curious(fred) [resolution 94,122]
253. funny(fred) | ~kind(fred) [resolution 66,249]
256. ~kind(fred) <- (~22) [subsumption resolution 253,232]
257. $false <- (21, ~22) [subsumption resolution 256,227]
258. ~21 | 22 [avatar contradiction clause 257]
277. $false [avatar sat refutation 233,234,247,258]
% SZS output end Proof for 6221627448817095058752180
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If alice is either not quiet or kind then someone is kind or not humble.
Everyone who is either funny or not humble is rich or brave and vice versa.
If someone is not old then john is not humble or generous and vice versa.
If someone is calm or not strong then someone is curious.
Everyone who is not quiet or generous is either not creative or not wise.
Everyone who is not strong or old is not brave or curious.
If paul is humble then john is both not patient and generous.
Everyone who is patient or wise is both strong and not tall.
If john is not humble or patient then lucy is curious or patient.
Everyone who is both not tall and wise is not happy or not creative.
Everyone who is both not rich and happy is not tall and vice versa.
Everyone who is curious or calm is curious or happy and vice versa.
If someone is either tall or curious then someone is either creative or not funny and vice versa.
If someone is both not old and not rich then paul is either not old or old and vice versa.
Everyone who is old or not rich is both funny and not wise.
Everyone who is creative or not happy is not kind or quiet and vice versa.
Someone is not tall.
Someone is either not rich or not patient.
Someone is both not funny and generous.
Someone is both not quiet and not calm.
Someone is not funny or not wise.
Paul is both generous and not funny.
Someone is generous or not kind. | Alice is happy. | neutral | (((~quiet(alice)<~>kind(alice)))=>(?[X]:((kind(X)|~humble(X)))))&
(![X]:((funny(X)<~>~humble(X))<=>(rich(X)|brave(X))))&
((?[X]:(~old(X)))<=>((~humble(john)|generous(john))))&
((?[X]:((calm(X)|~strong(X))))=>(?[X]:(curious(X))))&
(![X]:((~quiet(X)|generous(X))=>(~creative(X)<~>~wise(X))))&
(![X]:((~strong(X)|old(X))=>(~brave(X)|curious(X))))&
((humble(paul))=>((~patient(john)&generous(john))))&
(![X]:((patient(X)|wise(X))=>(strong(X)&~tall(X))))&
(((~humble(john)|patient(john)))=>((curious(lucy)|patient(lucy))))&
(![X]:((~tall(X)&wise(X))=>(~happy(X)|~creative(X))))&
(![X]:((~rich(X)&happy(X))<=>~tall(X)))&
(![X]:((curious(X)|calm(X))<=>(curious(X)|happy(X))))&
((?[X]:((tall(X)<~>curious(X))))<=>(?[X]:((creative(X)<~>~funny(X)))))&
((?[X]:((~old(X)&~rich(X))))<=>((~old(paul)<~>old(paul))))&
(![X]:((old(X)|~rich(X))=>(funny(X)&~wise(X))))&
(![X]:((creative(X)|~happy(X))<=>(~kind(X)|quiet(X))))&
(?[X]:(~tall(X)))&
(?[X]:((~rich(X)<~>~patient(X))))&
(?[X]:((~funny(X)&generous(X))))&
(?[X]:((~quiet(X)&~calm(X))))&
(?[X]:((~funny(X)|~wise(X))))&
((generous(paul)&~funny(paul)))&
(?[X]:((generous(X)|~kind(X)))) | happy(alice) | [] | null | 0 |
If mary is calm or patient then john is humble and vice versa.
Everyone who is not happy is not calm or calm and vice versa.
If alice is both calm and not rich then fred is both patient and old and vice versa.
If someone is not patient or brave then someone is both generous and happy.
If someone is curious then someone is either funny or not calm.
Everyone who is not calm is both not kind and not quiet.
If susan is either not calm or not generous then paul is either not strong or tall and vice versa.
If susan is not tall then someone is either humble or not strong and vice versa.
Everyone who is rich is patient or kind and vice versa.
Everyone who is either not generous or not quiet is patient or not calm.
Everyone who is not wise is either not kind or rich and vice versa.
If someone is both not funny and not kind then someone is either not curious or not creative.
Everyone who is not kind is both not patient and not wise and vice versa.
If paul is either not rich or brave then someone is old.
Someone is not creative.
Someone is not rich or humble.
Susan is both curious and not old.
Someone is both tall and not humble.
Susan is either patient or funny.
Lucy is both not curious and not strong. | Paul is not rich. | contradiction | (((calm(mary)|patient(mary)))<=>(humble(john)))&
(![X]:(~happy(X)<=>(~calm(X)|calm(X))))&
(((calm(alice)&~rich(alice)))<=>((patient(fred)&old(fred))))&
((?[X]:((~patient(X)|brave(X))))=>(?[X]:((generous(X)&happy(X)))))&
((?[X]:(curious(X)))=>(?[X]:((funny(X)<~>~calm(X)))))&
(![X]:(~calm(X)=>(~kind(X)&~quiet(X))))&
(((~calm(susan)<~>~generous(susan)))<=>((~strong(paul)<~>tall(paul))))&
((~tall(susan))<=>(?[X]:((humble(X)<~>~strong(X)))))&
(![X]:(rich(X)<=>(patient(X)|kind(X))))&
(![X]:((~generous(X)<~>~quiet(X))=>(patient(X)|~calm(X))))&
(![X]:(~wise(X)<=>(~kind(X)<~>rich(X))))&
((?[X]:((~funny(X)&~kind(X))))=>(?[X]:((~curious(X)<~>~creative(X)))))&
(![X]:(~kind(X)<=>(~patient(X)&~wise(X))))&
(((~rich(paul)<~>brave(paul)))=>(?[X]:(old(X))))&
(?[X]:(~creative(X)))&
(?[X]:((~rich(X)|humble(X))))&
((curious(susan)&~old(susan)))&
(?[X]:((tall(X)&~humble(X))))&
((patient(susan)<~>funny(susan)))&
((~curious(lucy)&~strong(lucy))) | ~rich(paul) | [
"p1",
"p3",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 4233152514055782554931084
% SZS output start Proof for 4233152514055782554931084
2. ! [X0] : (~happy(X0) <=> (calm(X0) | ~calm(X0))) [input p1]
4. ? [X0] : (brave(X0) | ~patient(X0)) => ? [X0] : (happy(X0) & generous(X0)) [input p3]
9. ! [X0] : (rich(X0) <=> (kind(X0) | patient(X0))) [input p8]
21. ~rich(paul) [input hypothesis]
22. ? [X0] : (brave(X0) | ~patient(X0)) => ? [X1] : (happy(X1) & generous(X1)) [rectify 4]
25. ! [X0] : ((calm(X0) | ~calm(X0)) => ~happy(X0)) [unused predicate definition removal 2]
26. ! [X0] : (~happy(X0) | (~calm(X0) & calm(X0))) [ennf transformation 25]
27. ? [X1] : (happy(X1) & generous(X1)) | ! [X0] : (~brave(X0) & patient(X0)) [ennf transformation 22]
38. ? [X0] : (happy(X0) & generous(X0)) | ! [X1] : (~brave(X1) & patient(X1)) [rectify 27]
39. ? [X0] : (happy(X0) & generous(X0)) => (happy(sK0) & generous(sK0)) [choice axiom]
40. (happy(sK0) & generous(sK0)) | ! [X1] : (~brave(X1) & patient(X1)) [skolemisation 38,39]
50. ! [X0] : ((rich(X0) | (~kind(X0) & ~patient(X0))) & ((kind(X0) | patient(X0)) | ~rich(X0))) [nnf transformation 9]
51. ! [X0] : ((rich(X0) | (~kind(X0) & ~patient(X0))) & (kind(X0) | patient(X0) | ~rich(X0))) [flattening 50]
73. ~happy(X0) | calm(X0) [cnf transformation 26]
74. ~happy(X0) | ~calm(X0) [cnf transformation 26]
81. happy(sK0) | patient(X1) [cnf transformation 40]
100. rich(X0) | ~patient(X0) [cnf transformation 51]
125. ~rich(paul) [cnf transformation 21]
141. ~happy(X0) [subsumption resolution 73,74]
163. patient(X1) [subsumption resolution 81,141]
223. rich(X0) [subsumption resolution 100,163]
243. $false [subsumption resolution 125,223]
% SZS output end Proof for 4233152514055782554931084
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not old is either not tall or not brave and vice versa.
If someone is funny then someone is quiet or curious and vice versa.
Everyone who is old is either happy or patient and vice versa.
If susan is not wise or not creative then susan is either not rich or kind.
If paul is both not rich and tall then john is either not funny or not generous.
If lucy is not humble or not tall then someone is generous or brave and vice versa.
If someone is both not kind and not quiet then someone is both wise and strong and vice versa.
If lucy is both not kind and not old then someone is both not tall and not funny.
Everyone who is humble or quiet is both patient and not quiet.
Everyone who is both not curious and not brave is not curious.
Everyone who is humble or not old is both calm and patient.
Everyone who is happy or patient is calm.
If someone is generous or not curious then someone is humble.
If someone is not humble or not brave then someone is tall.
If lucy is not tall or humble then paul is not kind and vice versa.
Everyone who is not strong is either not funny or not tall.
Someone is curious or not patient.
Someone is patient or strong.
John is either not generous or creative.
Mary is not curious or generous.
Someone is either wise or rich.
Mary is strong or not tall.
Mary is old or not funny.
Someone is not old. | Paul is quiet. | contradiction | (![X]:(~old(X)<=>(~tall(X)<~>~brave(X))))&
((?[X]:(funny(X)))<=>(?[X]:((quiet(X)|curious(X)))))&
(![X]:(old(X)<=>(happy(X)<~>patient(X))))&
(((~wise(susan)|~creative(susan)))=>((~rich(susan)<~>kind(susan))))&
(((~rich(paul)&tall(paul)))=>((~funny(john)<~>~generous(john))))&
(((~humble(lucy)|~tall(lucy)))<=>(?[X]:((generous(X)|brave(X)))))&
((?[X]:((~kind(X)&~quiet(X))))<=>(?[X]:((wise(X)&strong(X)))))&
(((~kind(lucy)&~old(lucy)))=>(?[X]:((~tall(X)&~funny(X)))))&
(![X]:((humble(X)|quiet(X))=>(patient(X)&~quiet(X))))&
(![X]:((~curious(X)&~brave(X))=>~curious(X)))&
(![X]:((humble(X)|~old(X))=>(calm(X)&patient(X))))&
(![X]:((happy(X)|patient(X))=>calm(X)))&
((?[X]:((generous(X)|~curious(X))))=>(?[X]:(humble(X))))&
((?[X]:((~humble(X)|~brave(X))))=>(?[X]:(tall(X))))&
(((~tall(lucy)|humble(lucy)))<=>(~kind(paul)))&
(![X]:(~strong(X)=>(~funny(X)<~>~tall(X))))&
(?[X]:((curious(X)|~patient(X))))&
(?[X]:((patient(X)|strong(X))))&
((~generous(john)<~>creative(john)))&
((~curious(mary)|generous(mary)))&
(?[X]:((wise(X)<~>rich(X))))&
((strong(mary)|~tall(mary)))&
((old(mary)|~funny(mary)))&
(?[X]:(~old(X))) | quiet(paul) | [
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 1604055091390951056331007
% SZS output start Proof for 1604055091390951056331007
9. ! [X0] : ((quiet(X0) | humble(X0)) => (~quiet(X0) & patient(X0))) [input p8]
25. quiet(paul) [input hypothesis]
37. ! [X0] : ((~quiet(X0) & patient(X0)) | (~quiet(X0) & ~humble(X0))) [ennf transformation 9]
114. ~quiet(X0) | ~quiet(X0) [cnf transformation 37]
137. quiet(paul) [cnf transformation 25]
138. ~quiet(X0) [duplicate literal removal 114]
148. 3 <=> ! [X1] : ~quiet(X1) [avatar definition]
149. ~quiet(X1) <- (3) [avatar component clause 148]
271. 3 [avatar split clause 138,148]
365. $false <- (3) [resolution 149,137]
366. ~3 [avatar contradiction clause 365]
367. $false [avatar sat refutation 271,366]
% SZS output end Proof for 1604055091390951056331007
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both quiet and brave is not curious or creative and vice versa. Everyone who is not humble is not brave. If someone is not calm or strong then someone is not strong. Everyone who is both not wise and not strong is either kind or not patient. Everyone who is not strong is happy or not patient. Everyone who is either not curious or not tall is both not generous and quiet and vice versa. Everyone who is not humble is both not calm and happy. If someone is not quiet then someone is either old or not creative. Everyone who is not creative or rich is either curious or kind. Everyone who is both not kind and not curious is not funny or curious and vice versa. If someone is both funny and not creative then susan is not patient and vice versa. Everyone who is either generous or not funny is either tall or strong and vice versa. If someone is brave then paul is either rich or strong and vice versa. If someone is either funny or not quiet then john is either not humble or not generous. Everyone who is not wise or strong is both calm and generous. Mary is either not brave or old. Susan is both not tall and humble. Alice is brave or not tall. Lucy is both not funny and humble. Someone is either not humble or not calm. | Alice is old. | neutral | (![X]:((quiet(X)&brave(X))<=>(~curious(X)|creative(X))))&
(![X]:(~humble(X)=>~brave(X)))&
((?[X]:((~calm(X)|strong(X))))=>(?[X]:(~strong(X))))&
(![X]:((~wise(X)&~strong(X))=>(kind(X)<~>~patient(X))))&
(![X]:(~strong(X)=>(happy(X)|~patient(X))))&
(![X]:((~curious(X)<~>~tall(X))<=>(~generous(X)&quiet(X))))&
(![X]:(~humble(X)=>(~calm(X)&happy(X))))&
((?[X]:(~quiet(X)))=>(?[X]:((old(X)<~>~creative(X)))))&
(![X]:((~creative(X)|rich(X))=>(curious(X)<~>kind(X))))&
(![X]:((~kind(X)&~curious(X))<=>(~funny(X)|curious(X))))&
((?[X]:((funny(X)&~creative(X))))<=>(~patient(susan)))&
(![X]:((generous(X)<~>~funny(X))<=>(tall(X)<~>strong(X))))&
((?[X]:(brave(X)))<=>((rich(paul)<~>strong(paul))))&
((?[X]:((funny(X)<~>~quiet(X))))=>((~humble(john)<~>~generous(john))))&
(![X]:((~wise(X)|strong(X))=>(calm(X)&generous(X))))&
((~brave(mary)<~>old(mary)))&
((~tall(susan)&humble(susan)))&
((brave(alice)|~tall(alice)))&
((~funny(lucy)&humble(lucy)))&
(?[X]:((~humble(X)<~>~calm(X)))) | old(alice) | [] | null | 0 |
Everyone who is not happy is humble or not strong and vice versa. If john is not humble then paul is both not humble and kind. Everyone who is tall is curious. If someone is not calm then lucy is wise and vice versa. Everyone who is both not humble and patient is either not curious or not calm. Everyone who is both humble and not creative is both not strong and brave. Everyone who is humble or happy is both not tall and generous. Everyone who is both strong and generous is either not happy or not generous. Everyone who is both strong and not strong is both old and wise. If mary is not creative or patient then lucy is either humble or not tall and vice versa. Everyone who is wise or not strong is not wise and vice versa. If john is either not happy or not rich then mary is not happy or not curious. Everyone who is not old is rich. If paul is kind then john is both old and not tall and vice versa. Everyone who is not quiet is both generous and not happy and vice versa. Everyone who is both creative and happy is both creative and not generous and vice versa. Fred is both not rich and tall. John is either rich or quiet. Alice is not happy or not brave. Someone is either not old or humble. Someone is not patient or wise. Someone is not happy. | Paul is not happy. | entailment | (![X]:(~happy(X)<=>(humble(X)|~strong(X))))&
((~humble(john))=>((~humble(paul)&kind(paul))))&
(![X]:(tall(X)=>curious(X)))&
((?[X]:(~calm(X)))<=>(wise(lucy)))&
(![X]:((~humble(X)&patient(X))=>(~curious(X)<~>~calm(X))))&
(![X]:((humble(X)&~creative(X))=>(~strong(X)&brave(X))))&
(![X]:((humble(X)|happy(X))=>(~tall(X)&generous(X))))&
(![X]:((strong(X)&generous(X))=>(~happy(X)<~>~generous(X))))&
(![X]:((strong(X)&~strong(X))=>(old(X)&wise(X))))&
(((~creative(mary)|patient(mary)))<=>((humble(lucy)<~>~tall(lucy))))&
(![X]:((wise(X)|~strong(X))<=>~wise(X)))&
(((~happy(john)<~>~rich(john)))=>((~happy(mary)|~curious(mary))))&
(![X]:(~old(X)=>rich(X)))&
((kind(paul))<=>((old(john)&~tall(john))))&
(![X]:(~quiet(X)<=>(generous(X)&~happy(X))))&
(![X]:((creative(X)&happy(X))<=>(creative(X)&~generous(X))))&
((~rich(fred)&tall(fred)))&
((rich(john)<~>quiet(john)))&
((~happy(alice)|~brave(alice)))&
(?[X]:((~old(X)<~>humble(X))))&
(?[X]:((~patient(X)|wise(X))))&
(?[X]:(~happy(X))) | ~happy(paul) | [
"p0",
"p6",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 2297235181438796123294445
% SZS output start Proof for 2297235181438796123294445
1. ! [X0] : (~happy(X0) <=> (~strong(X0) | humble(X0))) [input p0]
7. ! [X0] : ((happy(X0) | humble(X0)) => (generous(X0) & ~tall(X0))) [input p6]
8. ! [X0] : ((generous(X0) & strong(X0)) => (~happy(X0) <~> ~generous(X0))) [input p7]
23. happy(paul) [input hypothesis]
30. ! [X0] : ((generous(X0) & ~tall(X0)) | (~happy(X0) & ~humble(X0))) [ennf transformation 7]
31. ! [X0] : ((~happy(X0) <~> ~generous(X0)) | (~generous(X0) | ~strong(X0))) [ennf transformation 8]
32. ! [X0] : ((~happy(X0) <~> ~generous(X0)) | ~generous(X0) | ~strong(X0)) [flattening 31]
38. ! [X0] : ((~happy(X0) | (strong(X0) & ~humble(X0))) & ((~strong(X0) | humble(X0)) | happy(X0))) [nnf transformation 1]
39. ! [X0] : ((~happy(X0) | (strong(X0) & ~humble(X0))) & (~strong(X0) | humble(X0) | happy(X0))) [flattening 38]
45. ! [X0] : (((generous(X0) | happy(X0)) & (~generous(X0) | ~happy(X0))) | ~generous(X0) | ~strong(X0)) [nnf transformation 32]
67. ~happy(X0) | strong(X0) [cnf transformation 39]
80. generous(X0) | ~happy(X0) [cnf transformation 30]
81. ~generous(X0) | ~happy(X0) | ~generous(X0) | ~strong(X0) [cnf transformation 45]
116. happy(paul) [cnf transformation 23]
119. ~generous(X0) | ~happy(X0) | ~strong(X0) [duplicate literal removal 81]
147. ~happy(X0) | ~strong(X0) [subsumption resolution 119,80]
148. ~happy(X0) [subsumption resolution 147,67]
208. $false [subsumption resolution 116,148]
% SZS output end Proof for 2297235181438796123294445
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 4989
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either generous or not calm is both rich and quiet.
Everyone who is not quiet is either not humble or wise.
If someone is tall then someone is happy and vice versa.
If someone is both not creative and not patient then someone is curious or old.
If susan is either not kind or not calm then alice is either not happy or strong.
If mary is tall or not tall then paul is not wise and vice versa.
Everyone who is either patient or generous is not curious or not funny and vice versa.
If someone is either not old or not happy then john is either kind or funny and vice versa.
Everyone who is either not humble or not patient is either rich or not rich and vice versa.
Everyone who is not old or not tall is both rich and kind.
Everyone who is humble or wise is strong.
Everyone who is wise is creative or not generous and vice versa.
Everyone who is not old is either happy or calm and vice versa.
If paul is both not happy and not patient then john is not funny.
If alice is not calm then fred is patient.
If someone is both funny and strong then someone is not funny and vice versa.
Mary is either not generous or funny.
Someone is creative or happy.
Alice is either curious or strong.
Alice is both curious and not calm.
Paul is not curious.
Someone is either patient or not wise.
Someone is not strong.
Paul is not creative or brave. | Alice is patient. | entailment | (![X]:((generous(X)<~>~calm(X))=>(rich(X)&quiet(X))))&
(![X]:(~quiet(X)=>(~humble(X)<~>wise(X))))&
((?[X]:(tall(X)))<=>(?[X]:(happy(X))))&
((?[X]:((~creative(X)&~patient(X))))=>(?[X]:((curious(X)|old(X)))))&
(((~kind(susan)<~>~calm(susan)))=>((~happy(alice)<~>strong(alice))))&
(((tall(mary)|~tall(mary)))<=>(~wise(paul)))&
(![X]:((patient(X)<~>generous(X))<=>(~curious(X)|~funny(X))))&
((?[X]:((~old(X)<~>~happy(X))))<=>((kind(john)<~>funny(john))))&
(![X]:((~humble(X)<~>~patient(X))<=>(rich(X)<~>~rich(X))))&
(![X]:((~old(X)|~tall(X))=>(rich(X)&kind(X))))&
(![X]:((humble(X)|wise(X))=>strong(X)))&
(![X]:(wise(X)<=>(creative(X)|~generous(X))))&
(![X]:(~old(X)<=>(happy(X)<~>calm(X))))&
(((~happy(paul)&~patient(paul)))=>(~funny(john)))&
((~calm(alice))=>(patient(fred)))&
((?[X]:((funny(X)&strong(X))))<=>(?[X]:(~funny(X))))&
((~generous(mary)<~>funny(mary)))&
(?[X]:((creative(X)|happy(X))))&
((curious(alice)<~>strong(alice)))&
((curious(alice)&~calm(alice)))&
(~curious(paul))&
(?[X]:((patient(X)<~>~wise(X))))&
(?[X]:(~strong(X)))&
((~creative(paul)|brave(paul))) | patient(alice) | [
"p8",
"p10",
"p18",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 47872548093653969132567
% SZS output start Proof for 47872548093653969132567
9. ! [X0] : ((~humble(X0) <~> ~patient(X0)) <=> (rich(X0) <~> ~rich(X0))) [input p8]
11. ! [X0] : ((wise(X0) | humble(X0)) => strong(X0)) [input p10]
19. curious(alice) <~> strong(alice) [input p18]
20. ~calm(alice) & curious(alice) [input p19]
25. ~patient(alice) [input hypothesis]
36. ! [X0] : (strong(X0) | (~wise(X0) & ~humble(X0))) [ennf transformation 11]
58. ! [X0] : ((((patient(X0) | humble(X0)) & (~patient(X0) | ~humble(X0))) | ((rich(X0) | rich(X0)) & (~rich(X0) | ~rich(X0)))) & (((rich(X0) | ~rich(X0)) & (~rich(X0) | rich(X0))) | ((~humble(X0) | patient(X0)) & (~patient(X0) | humble(X0))))) [nnf transformation 9]
70. (~strong(alice) | ~curious(alice)) & (strong(alice) | curious(alice)) [nnf transformation 19]
108. patient(X0) | humble(X0) | ~rich(X0) | ~rich(X0) [cnf transformation 58]
109. patient(X0) | humble(X0) | rich(X0) | rich(X0) [cnf transformation 58]
114. ~humble(X0) | strong(X0) [cnf transformation 36]
132. ~strong(alice) | ~curious(alice) [cnf transformation 70]
133. curious(alice) [cnf transformation 20]
139. ~patient(alice) [cnf transformation 25]
142. patient(X0) | humble(X0) | ~rich(X0) [duplicate literal removal 108]
143. patient(X0) | humble(X0) | rich(X0) [duplicate literal removal 109]
185. 11 <=> strong(alice) [avatar definition]
187. ~strong(alice) <- (~11) [avatar component clause 185]
232. patient(X0) | humble(X0) [subsumption resolution 142,143]
293. 33 <=> curious(alice) [avatar definition]
296. ~33 | ~11 [avatar split clause 132,185,293]
299. 33 [avatar split clause 133,293]
334. humble(alice) [resolution 232,139]
346. strong(alice) [resolution 334,114]
347. $false <- (~11) [subsumption resolution 346,187]
348. 11 [avatar contradiction clause 347]
349. $false [avatar sat refutation 296,299,348]
% SZS output end Proof for 47872548093653969132567
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is creative or not strong is both funny and generous. Everyone who is not curious is not old and vice versa. If john is not old then fred is either not humble or not happy. If lucy is either generous or not funny then someone is quiet. If lucy is rich then someone is both wise and not brave. Everyone who is happy or not strong is either quiet or curious and vice versa. If someone is creative then john is strong or generous and vice versa. If fred is both curious and generous then someone is not quiet and vice versa. Everyone who is both not wise and happy is either not kind or tall. Everyone who is not wise or not happy is not curious or not rich and vice versa. Everyone who is quiet or brave is either curious or kind. Everyone who is not happy is not curious or not funny. If fred is either not generous or humble then susan is patient or not old and vice versa. Everyone who is quiet or strong is either not humble or not brave and vice versa. Everyone who is tall is either rich or not old and vice versa. Everyone who is kind is either not old or not rich. Fred is calm. Alice is not old. Paul is not curious. Mary is not creative. Lucy is rich or not brave. Fred is not curious. Someone is either not wise or quiet. Someone is not humble. | Fred is rich. | entailment | (![X]:((creative(X)|~strong(X))=>(funny(X)&generous(X))))&
(![X]:(~curious(X)<=>~old(X)))&
((~old(john))=>((~humble(fred)<~>~happy(fred))))&
(((generous(lucy)<~>~funny(lucy)))=>(?[X]:(quiet(X))))&
((rich(lucy))=>(?[X]:((wise(X)&~brave(X)))))&
(![X]:((happy(X)|~strong(X))<=>(quiet(X)<~>curious(X))))&
((?[X]:(creative(X)))<=>((strong(john)|generous(john))))&
(((curious(fred)&generous(fred)))<=>(?[X]:(~quiet(X))))&
(![X]:((~wise(X)&happy(X))=>(~kind(X)<~>tall(X))))&
(![X]:((~wise(X)|~happy(X))<=>(~curious(X)|~rich(X))))&
(![X]:((quiet(X)|brave(X))=>(curious(X)<~>kind(X))))&
(![X]:(~happy(X)=>(~curious(X)|~funny(X))))&
(((~generous(fred)<~>humble(fred)))<=>((patient(susan)|~old(susan))))&
(![X]:((quiet(X)|strong(X))<=>(~humble(X)<~>~brave(X))))&
(![X]:(tall(X)<=>(rich(X)<~>~old(X))))&
(![X]:(kind(X)=>(~old(X)<~>~rich(X))))&
(calm(fred))&
(~old(alice))&
(~curious(paul))&
(~creative(mary))&
((rich(lucy)|~brave(lucy)))&
(~curious(fred))&
(?[X]:((~wise(X)<~>quiet(X))))&
(?[X]:(~humble(X))) | rich(fred) | [
"p1",
"p7",
"p10",
"p15",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 8549736688218376880664512
% SZS output start Proof for 8549736688218376880664512
2. ! [X0] : (~curious(X0) <=> ~old(X0)) [input p1]
8. (generous(fred) & curious(fred)) <=> ? [X0] : ~quiet(X0) [input p7]
11. ! [X0] : ((brave(X0) | quiet(X0)) => (curious(X0) <~> kind(X0))) [input p10]
16. ! [X0] : (kind(X0) => (~old(X0) <~> ~rich(X0))) [input p15]
22. ~curious(fred) [input p21]
25. ~rich(fred) [input hypothesis]
33. ! [X0] : ((curious(X0) <~> kind(X0)) | (~brave(X0) & ~quiet(X0))) [ennf transformation 11]
36. ! [X0] : ((~old(X0) <~> ~rich(X0)) | ~kind(X0)) [ennf transformation 16]
37. ! [X0] : ((~curious(X0) | old(X0)) & (~old(X0) | curious(X0))) [nnf transformation 2]
51. ((generous(fred) & curious(fred)) | ! [X0] : quiet(X0)) & (? [X0] : ~quiet(X0) | (~generous(fred) | ~curious(fred))) [nnf transformation 8]
52. ((generous(fred) & curious(fred)) | ! [X0] : quiet(X0)) & (? [X0] : ~quiet(X0) | ~generous(fred) | ~curious(fred)) [flattening 51]
53. ((generous(fred) & curious(fred)) | ! [X0] : quiet(X0)) & (? [X1] : ~quiet(X1) | ~generous(fred) | ~curious(fred)) [rectify 52]
54. ? [X1] : ~quiet(X1) => ~quiet(sK3) [choice axiom]
55. ((generous(fred) & curious(fred)) | ! [X0] : quiet(X0)) & (~quiet(sK3) | ~generous(fred) | ~curious(fred)) [skolemisation 53,54]
59. ! [X0] : (((~kind(X0) | ~curious(X0)) & (kind(X0) | curious(X0))) | (~brave(X0) & ~quiet(X0))) [nnf transformation 33]
65. ! [X0] : (((rich(X0) | old(X0)) & (~rich(X0) | ~old(X0))) | ~kind(X0)) [nnf transformation 36]
75. ~old(X0) | curious(X0) [cnf transformation 37]
76. ~curious(X0) | old(X0) [cnf transformation 37]
93. curious(fred) | quiet(X0) [cnf transformation 55]
101. ~quiet(X0) | curious(X0) | kind(X0) [cnf transformation 59]
123. ~kind(X0) | old(X0) | rich(X0) [cnf transformation 65]
128. ~curious(fred) [cnf transformation 22]
132. ~rich(fred) [cnf transformation 25]
190. 13 <=> ! [X0] : quiet(X0) [avatar definition]
191. quiet(X0) <- (13) [avatar component clause 190]
198. 15 <=> curious(fred) [avatar definition]
199. ~curious(fred) <- (~15) [avatar component clause 198]
201. 13 | 15 [avatar split clause 93,198,190]
226. ~15 [avatar split clause 128,198]
257. kind(X1) | curious(X1) <- (13) [resolution 101,191]
281. old(X1) | rich(X1) | curious(X1) <- (13) [resolution 123,257]
282. rich(X1) | old(X1) <- (13) [subsumption resolution 281,76]
283. old(fred) <- (13) [resolution 282,132]
291. curious(fred) <- (13) [resolution 283,75]
292. $false <- (13, ~15) [subsumption resolution 291,199]
293. ~13 | 15 [avatar contradiction clause 292]
294. $false [avatar sat refutation 201,226,293]
% SZS output end Proof for 8549736688218376880664512
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If paul is humble or not wise then lucy is strong or not happy and vice versa.
If alice is either old or rich then someone is old or not strong and vice versa.
Everyone who is not calm is not strong and vice versa.
Everyone who is either not quiet or rich is not quiet.
Everyone who is curious is both not old and old.
Everyone who is patient is both not brave and not tall.
If paul is either tall or creative then fred is either not patient or humble.
Everyone who is both patient and generous is tall and vice versa.
Everyone who is patient or tall is brave and vice versa.
If paul is quiet or patient then someone is rich and vice versa.
If john is both happy and old then susan is both kind and strong and vice versa.
If susan is both generous and funny then someone is either not happy or generous and vice versa.
Everyone who is not humble or strong is quiet.
Everyone who is either creative or not patient is both not brave and rich.
If john is both not calm and not wise then someone is either funny or not strong and vice versa.
Paul is either strong or kind.
John is curious or not tall.
John is either not strong or not funny.
Someone is either not rich or not creative.
Someone is both happy and generous.
Susan is not humble or humble.
Mary is not rich.
Paul is both quiet and old. | Alice is creative. | neutral | (((humble(paul)|~wise(paul)))<=>((strong(lucy)|~happy(lucy))))&
(((old(alice)<~>rich(alice)))<=>(?[X]:((old(X)|~strong(X)))))&
(![X]:(~calm(X)<=>~strong(X)))&
(![X]:((~quiet(X)<~>rich(X))=>~quiet(X)))&
(![X]:(curious(X)=>(~old(X)&old(X))))&
(![X]:(patient(X)=>(~brave(X)&~tall(X))))&
(((tall(paul)<~>creative(paul)))=>((~patient(fred)<~>humble(fred))))&
(![X]:((patient(X)&generous(X))<=>tall(X)))&
(![X]:((patient(X)|tall(X))<=>brave(X)))&
(((quiet(paul)|patient(paul)))<=>(?[X]:(rich(X))))&
(((happy(john)&old(john)))<=>((kind(susan)&strong(susan))))&
(((generous(susan)&funny(susan)))<=>(?[X]:((~happy(X)<~>generous(X)))))&
(![X]:((~humble(X)|strong(X))=>quiet(X)))&
(![X]:((creative(X)<~>~patient(X))=>(~brave(X)&rich(X))))&
(((~calm(john)&~wise(john)))<=>(?[X]:((funny(X)<~>~strong(X)))))&
((strong(paul)<~>kind(paul)))&
((curious(john)|~tall(john)))&
((~strong(john)<~>~funny(john)))&
(?[X]:((~rich(X)<~>~creative(X))))&
(?[X]:((happy(X)&generous(X))))&
((~humble(susan)|humble(susan)))&
(~rich(mary))&
((quiet(paul)&old(paul))) | creative(alice) | [] | null | 0 |
Everyone who is either wise or not kind is kind. Everyone who is not curious is brave and vice versa. If someone is old or strong then someone is patient or wise. If susan is both calm and not creative then paul is strong or not calm and vice versa. Everyone who is either not brave or funny is either not patient or old and vice versa. If john is patient or not patient then mary is tall or generous and vice versa. Everyone who is either rich or calm is both not wise and not brave. Everyone who is both humble and rich is not curious or rich. If alice is both not humble and quiet then someone is not rich or not humble and vice versa. If someone is either happy or calm then someone is either not old or calm. Everyone who is either not humble or creative is creative and vice versa. Everyone who is generous is either not tall or not quiet. Everyone who is either not generous or strong is tall. If lucy is either not old or not brave then someone is either old or happy and vice versa. If john is either not kind or not humble then someone is both not strong and humble. If alice is funny or not wise then fred is not wise. Someone is happy. Someone is not humble or not old. Susan is either not old or curious. Lucy is curious or wise. Mary is either creative or funny. Someone is not generous. Alice is creative or old. | Paul is humble. | entailment | (![X]:((wise(X)<~>~kind(X))=>kind(X)))&
(![X]:(~curious(X)<=>brave(X)))&
((?[X]:((old(X)|strong(X))))=>(?[X]:((patient(X)|wise(X)))))&
(((calm(susan)&~creative(susan)))<=>((strong(paul)|~calm(paul))))&
(![X]:((~brave(X)<~>funny(X))<=>(~patient(X)<~>old(X))))&
(((patient(john)|~patient(john)))<=>((tall(mary)|generous(mary))))&
(![X]:((rich(X)<~>calm(X))=>(~wise(X)&~brave(X))))&
(![X]:((humble(X)&rich(X))=>(~curious(X)|rich(X))))&
(((~humble(alice)&quiet(alice)))<=>(?[X]:((~rich(X)|~humble(X)))))&
((?[X]:((happy(X)<~>calm(X))))=>(?[X]:((~old(X)<~>calm(X)))))&
(![X]:((~humble(X)<~>creative(X))<=>creative(X)))&
(![X]:(generous(X)=>(~tall(X)<~>~quiet(X))))&
(![X]:((~generous(X)<~>strong(X))=>tall(X)))&
(((~old(lucy)<~>~brave(lucy)))<=>(?[X]:((old(X)<~>happy(X)))))&
(((~kind(john)<~>~humble(john)))=>(?[X]:((~strong(X)&humble(X)))))&
(((funny(alice)|~wise(alice)))=>(~wise(fred)))&
(?[X]:(happy(X)))&
(?[X]:((~humble(X)|~old(X))))&
((~old(susan)<~>curious(susan)))&
((curious(lucy)|wise(lucy)))&
((creative(mary)<~>funny(mary)))&
(?[X]:(~generous(X)))&
((creative(alice)|old(alice))) | humble(paul) | [
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 693687693082273300652458
% SZS output start Proof for 693687693082273300652458
11. ! [X0] : ((~humble(X0) <~> creative(X0)) <=> creative(X0)) [input p10]
24. ~humble(paul) [input hypothesis]
57. ! [X0] : ((((~creative(X0) | humble(X0)) & (creative(X0) | ~humble(X0))) | ~creative(X0)) & (creative(X0) | ((~humble(X0) | ~creative(X0)) & (creative(X0) | humble(X0))))) [nnf transformation 11]
112. creative(X0) | creative(X0) | humble(X0) [cnf transformation 57]
115. ~creative(X0) | humble(X0) | ~creative(X0) [cnf transformation 57]
143. ~humble(paul) [cnf transformation 24]
144. creative(X0) | humble(X0) [duplicate literal removal 112]
145. ~creative(X0) | humble(X0) [duplicate literal removal 115]
199. 12 <=> ! [X0] : humble(X0) [avatar definition]
200. humble(X0) <- (12) [avatar component clause 199]
243. humble(X0) [subsumption resolution 144,145]
244. 12 [avatar split clause 243,199]
356. $false <- (12) [resolution 200,143]
357. ~12 [avatar contradiction clause 356]
358. $false [avatar sat refutation 244,357]
% SZS output end Proof for 693687693082273300652458
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.021 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not old or kind is brave.
Everyone who is either not rich or brave is both funny and not brave.
If mary is either not creative or tall then someone is either not patient or strong.
If mary is quiet or wise then paul is old.
Everyone who is generous is funny and vice versa.
If someone is creative then susan is both tall and not quiet.
Everyone who is either not rich or brave is not funny and vice versa.
If fred is not happy then lucy is both not strong and funny and vice versa.
If mary is not old then someone is calm or not kind.
Everyone who is not wise is either not patient or wise and vice versa.
If mary is calm then alice is either old or not strong and vice versa.
Everyone who is both curious and calm is not strong.
Everyone who is both patient and not happy is both generous and not patient.
Everyone who is not quiet is funny or not quiet and vice versa.
If someone is tall or not creative then someone is either happy or curious.
Everyone who is either quiet or strong is humble and vice versa.
Mary is either calm or not curious.
Mary is either not funny or tall.
Someone is old.
Someone is curious.
Someone is either not old or not quiet. | Mary is strong. | neutral | (![X]:((~old(X)<~>kind(X))=>brave(X)))&
(![X]:((~rich(X)<~>brave(X))=>(funny(X)&~brave(X))))&
(((~creative(mary)<~>tall(mary)))=>(?[X]:((~patient(X)<~>strong(X)))))&
(((quiet(mary)|wise(mary)))=>(old(paul)))&
(![X]:(generous(X)<=>funny(X)))&
((?[X]:(creative(X)))=>((tall(susan)&~quiet(susan))))&
(![X]:((~rich(X)<~>brave(X))<=>~funny(X)))&
((~happy(fred))<=>((~strong(lucy)&funny(lucy))))&
((~old(mary))=>(?[X]:((calm(X)|~kind(X)))))&
(![X]:(~wise(X)<=>(~patient(X)<~>wise(X))))&
((calm(mary))<=>((old(alice)<~>~strong(alice))))&
(![X]:((curious(X)&calm(X))=>~strong(X)))&
(![X]:((patient(X)&~happy(X))=>(generous(X)&~patient(X))))&
(![X]:(~quiet(X)<=>(funny(X)|~quiet(X))))&
((?[X]:((tall(X)|~creative(X))))=>(?[X]:((happy(X)<~>curious(X)))))&
(![X]:((quiet(X)<~>strong(X))<=>humble(X)))&
((calm(mary)<~>~curious(mary)))&
((~funny(mary)<~>tall(mary)))&
(?[X]:(old(X)))&
(?[X]:(curious(X)))&
(?[X]:((~old(X)<~>~quiet(X)))) | strong(mary) | [] | null | 0 |
If someone is not quiet then someone is not old or kind and vice versa.
If lucy is funny or kind then alice is both patient and not humble and vice versa.
If mary is either not curious or not kind then paul is patient or tall and vice versa.
If someone is not wise or humble then someone is either not happy or not strong and vice versa.
If someone is patient or brave then john is not old or not curious and vice versa.
Everyone who is not strong is rich and vice versa.
Everyone who is either wise or generous is not patient or calm and vice versa.
Everyone who is quiet is not generous or not tall and vice versa.
If alice is curious then lucy is humble.
If someone is either not old or funny then someone is curious or not calm.
If someone is not strong then susan is either not quiet or not calm and vice versa.
Everyone who is both not curious and brave is not brave or rich.
If someone is either happy or funny then paul is not funny.
Everyone who is not generous is either funny or not creative and vice versa.
Everyone who is not rich is humble and vice versa.
Everyone who is not humble is creative.
Lucy is either wise or brave.
Paul is not calm or not creative.
John is both brave and not quiet.
Someone is humble or strong.
Someone is generous.
Fred is brave or tall.
Paul is not humble or old. | Alice is curious. | neutral | ((?[X]:(~quiet(X)))<=>(?[X]:((~old(X)|kind(X)))))&
(((funny(lucy)|kind(lucy)))<=>((patient(alice)&~humble(alice))))&
(((~curious(mary)<~>~kind(mary)))<=>((patient(paul)|tall(paul))))&
((?[X]:((~wise(X)|humble(X))))<=>(?[X]:((~happy(X)<~>~strong(X)))))&
((?[X]:((patient(X)|brave(X))))<=>((~old(john)|~curious(john))))&
(![X]:(~strong(X)<=>rich(X)))&
(![X]:((wise(X)<~>generous(X))<=>(~patient(X)|calm(X))))&
(![X]:(quiet(X)<=>(~generous(X)|~tall(X))))&
((curious(alice))=>(humble(lucy)))&
((?[X]:((~old(X)<~>funny(X))))=>(?[X]:((curious(X)|~calm(X)))))&
((?[X]:(~strong(X)))<=>((~quiet(susan)<~>~calm(susan))))&
(![X]:((~curious(X)&brave(X))=>(~brave(X)|rich(X))))&
((?[X]:((happy(X)<~>funny(X))))=>(~funny(paul)))&
(![X]:(~generous(X)<=>(funny(X)<~>~creative(X))))&
(![X]:(~rich(X)<=>humble(X)))&
(![X]:(~humble(X)=>creative(X)))&
((wise(lucy)<~>brave(lucy)))&
((~calm(paul)|~creative(paul)))&
((brave(john)&~quiet(john)))&
(?[X]:((humble(X)|strong(X))))&
(?[X]:(generous(X)))&
((brave(fred)|tall(fred)))&
((~humble(paul)|old(paul))) | curious(alice) | [] | null | 0 |
Everyone who is not generous is patient and vice versa.
If susan is both patient and happy then john is either not happy or brave.
If someone is both patient and generous then john is both old and not humble.
If someone is both kind and patient then alice is both strong and old.
Everyone who is generous or creative is not humble.
If someone is either not curious or kind then someone is both old and not humble and vice versa.
Everyone who is either curious or old is not curious and vice versa.
Everyone who is both rich and tall is both not old and not patient.
Everyone who is either old or kind is not kind or tall.
If someone is not strong or creative then someone is patient or not humble.
Everyone who is quiet is both tall and not happy and vice versa.
Everyone who is either patient or creative is not kind and vice versa.
If fred is both not happy and not kind then someone is not rich and vice versa.
Everyone who is either not funny or calm is kind or humble.
If someone is not humble or not kind then paul is both generous and rich and vice versa.
If someone is generous or wise then someone is either not quiet or not wise.
Susan is both creative and happy.
Paul is strong or not calm.
Fred is not creative or strong.
Alice is wise.
Someone is not quiet. | John is not kind. | neutral | (![X]:(~generous(X)<=>patient(X)))&
(((patient(susan)&happy(susan)))=>((~happy(john)<~>brave(john))))&
((?[X]:((patient(X)&generous(X))))=>((old(john)&~humble(john))))&
((?[X]:((kind(X)&patient(X))))=>((strong(alice)&old(alice))))&
(![X]:((generous(X)|creative(X))=>~humble(X)))&
((?[X]:((~curious(X)<~>kind(X))))<=>(?[X]:((old(X)&~humble(X)))))&
(![X]:((curious(X)<~>old(X))<=>~curious(X)))&
(![X]:((rich(X)&tall(X))=>(~old(X)&~patient(X))))&
(![X]:((old(X)<~>kind(X))=>(~kind(X)|tall(X))))&
((?[X]:((~strong(X)|creative(X))))=>(?[X]:((patient(X)|~humble(X)))))&
(![X]:(quiet(X)<=>(tall(X)&~happy(X))))&
(![X]:((patient(X)<~>creative(X))<=>~kind(X)))&
(((~happy(fred)&~kind(fred)))<=>(?[X]:(~rich(X))))&
(![X]:((~funny(X)<~>calm(X))=>(kind(X)|humble(X))))&
((?[X]:((~humble(X)|~kind(X))))<=>((generous(paul)&rich(paul))))&
((?[X]:((generous(X)|wise(X))))=>(?[X]:((~quiet(X)<~>~wise(X)))))&
((creative(susan)&happy(susan)))&
((strong(paul)|~calm(paul)))&
((~creative(fred)|strong(fred)))&
(wise(alice))&
(?[X]:(~quiet(X))) | ~kind(john) | [] | null | 0 |
If someone is either old or not funny then mary is both patient and happy and vice versa.
Everyone who is funny or not rich is both calm and not strong.
Everyone who is not curious is old or not brave and vice versa.
If john is calm or brave then someone is patient or generous and vice versa.
If susan is both wise and brave then paul is both not strong and not wise and vice versa.
If someone is old or quiet then someone is not kind.
Everyone who is not kind or creative is kind and vice versa.
If someone is either patient or curious then alice is both generous and not kind.
If someone is brave or kind then someone is both kind and wise.
Everyone who is rich or not brave is either generous or humble and vice versa.
If john is both strong and not calm then someone is not kind or patient.
Everyone who is both calm and not funny is either not old or not strong.
Everyone who is generous or kind is not humble or calm.
If alice is not brave or calm then someone is either old or not brave.
If john is either kind or happy then someone is either kind or not brave.
Everyone who is not generous is either not kind or not tall.
Mary is not kind or funny.
Someone is not old.
Paul is rich.
Susan is not humble.
Paul is either not humble or not tall.
Fred is not generous.
Someone is not kind or tall. | Paul is humble. | neutral | ((?[X]:((old(X)<~>~funny(X))))<=>((patient(mary)&happy(mary))))&
(![X]:((funny(X)|~rich(X))=>(calm(X)&~strong(X))))&
(![X]:(~curious(X)<=>(old(X)|~brave(X))))&
(((calm(john)|brave(john)))<=>(?[X]:((patient(X)|generous(X)))))&
(((wise(susan)&brave(susan)))<=>((~strong(paul)&~wise(paul))))&
((?[X]:((old(X)|quiet(X))))=>(?[X]:(~kind(X))))&
(![X]:((~kind(X)|creative(X))<=>kind(X)))&
((?[X]:((patient(X)<~>curious(X))))=>((generous(alice)&~kind(alice))))&
((?[X]:((brave(X)|kind(X))))=>(?[X]:((kind(X)&wise(X)))))&
(![X]:((rich(X)|~brave(X))<=>(generous(X)<~>humble(X))))&
(((strong(john)&~calm(john)))=>(?[X]:((~kind(X)|patient(X)))))&
(![X]:((calm(X)&~funny(X))=>(~old(X)<~>~strong(X))))&
(![X]:((generous(X)|kind(X))=>(~humble(X)|calm(X))))&
(((~brave(alice)|calm(alice)))=>(?[X]:((old(X)<~>~brave(X)))))&
(((kind(john)<~>happy(john)))=>(?[X]:((kind(X)<~>~brave(X)))))&
(![X]:(~generous(X)=>(~kind(X)<~>~tall(X))))&
((~kind(mary)|funny(mary)))&
(?[X]:(~old(X)))&
(rich(paul))&
(~humble(susan))&
((~humble(paul)<~>~tall(paul)))&
(~generous(fred))&
(?[X]:((~kind(X)|tall(X)))) | humble(paul) | [] | null | 0 |
Everyone who is either strong or generous is both not curious and not wise.
If someone is not happy then someone is both not patient and not calm and vice versa.
Everyone who is not funny is both humble and funny and vice versa.
If fred is either old or not calm then fred is curious or funny.
Everyone who is generous is wise.
If lucy is either not kind or not generous then john is not happy or not funny and vice versa.
Everyone who is either not creative or old is either not humble or patient and vice versa.
Everyone who is curious or calm is brave.
If mary is either not calm or not rich then someone is either old or not quiet.
Everyone who is either not happy or not generous is either happy or strong and vice versa.
Everyone who is either kind or not happy is both not quiet and not calm and vice versa.
If mary is either not rich or not quiet then john is not funny or quiet.
If someone is not generous or strong then someone is generous or not generous and vice versa.
Everyone who is old or quiet is both not rich and not happy and vice versa.
Everyone who is not strong is both strong and kind and vice versa.
Everyone who is not rich is both brave and not creative.
Someone is either kind or not creative.
Alice is either not old or not tall.
Someone is not patient.
Someone is happy.
Someone is not quiet. | Mary is not rich. | entailment | (![X]:((strong(X)<~>generous(X))=>(~curious(X)&~wise(X))))&
((?[X]:(~happy(X)))<=>(?[X]:((~patient(X)&~calm(X)))))&
(![X]:(~funny(X)<=>(humble(X)&funny(X))))&
(((old(fred)<~>~calm(fred)))=>((curious(fred)|funny(fred))))&
(![X]:(generous(X)=>wise(X)))&
(((~kind(lucy)<~>~generous(lucy)))<=>((~happy(john)|~funny(john))))&
(![X]:((~creative(X)<~>old(X))<=>(~humble(X)<~>patient(X))))&
(![X]:((curious(X)|calm(X))=>brave(X)))&
(((~calm(mary)<~>~rich(mary)))=>(?[X]:((old(X)<~>~quiet(X)))))&
(![X]:((~happy(X)<~>~generous(X))<=>(happy(X)<~>strong(X))))&
(![X]:((kind(X)<~>~happy(X))<=>(~quiet(X)&~calm(X))))&
(((~rich(mary)<~>~quiet(mary)))=>((~funny(john)|quiet(john))))&
((?[X]:((~generous(X)|strong(X))))<=>(?[X]:((generous(X)|~generous(X)))))&
(![X]:((old(X)|quiet(X))<=>(~rich(X)&~happy(X))))&
(![X]:(~strong(X)<=>(strong(X)&kind(X))))&
(![X]:(~rich(X)=>(brave(X)&~creative(X))))&
(?[X]:((kind(X)<~>~creative(X))))&
((~old(alice)<~>~tall(alice)))&
(?[X]:(~patient(X)))&
(?[X]:(happy(X)))&
(?[X]:(~quiet(X))) | ~rich(mary) | [
"p2",
"p10",
"p11",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4835272230089568454188326
% SZS output start Proof for 4835272230089568454188326
3. ! [X0] : (~funny(X0) <=> (funny(X0) & humble(X0))) [input p2]
11. ! [X0] : ((kind(X0) <~> ~happy(X0)) <=> (~calm(X0) & ~quiet(X0))) [input p10]
12. (~rich(mary) <~> ~quiet(mary)) => (quiet(john) | ~funny(john)) [input p11]
14. ! [X0] : ((quiet(X0) | old(X0)) <=> (~happy(X0) & ~rich(X0))) [input p13]
15. ! [X0] : (~strong(X0) <=> (kind(X0) & strong(X0))) [input p14]
22. rich(mary) [input hypothesis]
32. (quiet(john) | ~funny(john)) | (~rich(mary) <=> ~quiet(mary)) [ennf transformation 12]
33. quiet(john) | ~funny(john) | (~rich(mary) <=> ~quiet(mary)) [flattening 32]
41. ! [X0] : ((~funny(X0) | (~funny(X0) | ~humble(X0))) & ((funny(X0) & humble(X0)) | funny(X0))) [nnf transformation 3]
42. ! [X0] : ((~funny(X0) | ~funny(X0) | ~humble(X0)) & ((funny(X0) & humble(X0)) | funny(X0))) [flattening 41]
51. ! [X0] : ((((happy(X0) | ~kind(X0)) & (~happy(X0) | kind(X0))) | (calm(X0) | quiet(X0))) & ((~calm(X0) & ~quiet(X0)) | ((kind(X0) | happy(X0)) & (~happy(X0) | ~kind(X0))))) [nnf transformation 11]
52. ! [X0] : ((((happy(X0) | ~kind(X0)) & (~happy(X0) | kind(X0))) | calm(X0) | quiet(X0)) & ((~calm(X0) & ~quiet(X0)) | ((kind(X0) | happy(X0)) & (~happy(X0) | ~kind(X0))))) [flattening 51]
53. quiet(john) | ~funny(john) | ((~rich(mary) | quiet(mary)) & (~quiet(mary) | rich(mary))) [nnf transformation 33]
59. ! [X0] : (((quiet(X0) | old(X0)) | (happy(X0) | rich(X0))) & ((~happy(X0) & ~rich(X0)) | (~quiet(X0) & ~old(X0)))) [nnf transformation 14]
60. ! [X0] : ((quiet(X0) | old(X0) | happy(X0) | rich(X0)) & ((~happy(X0) & ~rich(X0)) | (~quiet(X0) & ~old(X0)))) [flattening 59]
61. ! [X0] : ((~strong(X0) | (~kind(X0) | ~strong(X0))) & ((kind(X0) & strong(X0)) | strong(X0))) [nnf transformation 15]
62. ! [X0] : ((~strong(X0) | ~kind(X0) | ~strong(X0)) & ((kind(X0) & strong(X0)) | strong(X0))) [flattening 61]
81. funny(X0) | funny(X0) [cnf transformation 42]
113. ~quiet(X0) | kind(X0) | happy(X0) [cnf transformation 52]
119. quiet(john) | ~funny(john) | ~rich(mary) | quiet(mary) [cnf transformation 53]
125. ~quiet(X0) | ~rich(X0) [cnf transformation 60]
127. ~quiet(X0) | ~happy(X0) [cnf transformation 60]
129. strong(X0) | strong(X0) [cnf transformation 62]
131. ~strong(X0) | ~kind(X0) | ~strong(X0) [cnf transformation 62]
140. rich(mary) [cnf transformation 22]
141. strong(X0) [duplicate literal removal 129]
142. ~kind(X0) | ~strong(X0) [duplicate literal removal 131]
147. funny(X0) [duplicate literal removal 81]
171. 6 <=> happy(john) [avatar definition]
172. ~happy(john) <- (~6) [avatar component clause 171]
189. 9 <=> rich(mary) [avatar definition]
191. rich(mary) <- (9) [avatar component clause 189]
210. quiet(john) | ~rich(mary) | quiet(mary) [subsumption resolution 119,147]
212. 13 <=> quiet(mary) [avatar definition]
214. quiet(mary) <- (13) [avatar component clause 212]
216. 14 <=> quiet(john) [avatar definition]
218. quiet(john) <- (14) [avatar component clause 216]
219. 13 | ~9 | 14 [avatar split clause 210,216,189,212]
242. 9 [avatar split clause 140,189]
244. ~rich(mary) <- (13) [resolution 125,214]
245. $false <- (9, 13) [subsumption resolution 244,191]
246. ~9 | ~13 [avatar contradiction clause 245]
249. ~happy(john) <- (14) [resolution 127,218]
252. ~6 | ~14 [avatar split clause 249,216,171]
269. kind(john) | happy(john) <- (14) [resolution 113,218]
270. kind(john) <- (~6, 14) [subsumption resolution 269,172]
271. ~strong(john) <- (~6, 14) [resolution 270,142]
272. $false <- (~6, 14) [subsumption resolution 271,141]
273. 6 | ~14 [avatar contradiction clause 272]
274. $false [avatar sat refutation 219,242,246,252,273]
% SZS output end Proof for 4835272230089568454188326
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not generous and funny is either generous or not funny. Everyone who is either kind or not funny is not calm or funny and vice versa. If someone is not humble or old then someone is creative. If john is either not curious or not happy then susan is either not generous or not humble. Everyone who is both strong and not quiet is not tall. Everyone who is both humble and not curious is either generous or strong and vice versa. If paul is not quiet or not patient then someone is rich or not brave and vice versa. If someone is calm or not generous then someone is either not quiet or not kind. Everyone who is either funny or not strong is generous or curious and vice versa. Everyone who is curious is either patient or not wise and vice versa. If someone is not old then someone is happy or quiet. If someone is either not humble or not funny then susan is either not curious or happy and vice versa. Everyone who is strong is not funny or tall and vice versa. Everyone who is not quiet is both not wise and not generous. Everyone who is either not humble or not generous is either curious or not happy and vice versa. If mary is either curious or not happy then someone is either funny or tall. Fred is either not creative or funny. Susan is not calm or curious. Someone is happy or not creative. Mary is either not strong or quiet. Someone is wise. Fred is both not quiet and rich. | John is not patient. | neutral | (![X]:((~generous(X)&funny(X))=>(generous(X)<~>~funny(X))))&
(![X]:((kind(X)<~>~funny(X))<=>(~calm(X)|funny(X))))&
((?[X]:((~humble(X)|old(X))))=>(?[X]:(creative(X))))&
(((~curious(john)<~>~happy(john)))=>((~generous(susan)<~>~humble(susan))))&
(![X]:((strong(X)&~quiet(X))=>~tall(X)))&
(![X]:((humble(X)&~curious(X))<=>(generous(X)<~>strong(X))))&
(((~quiet(paul)|~patient(paul)))<=>(?[X]:((rich(X)|~brave(X)))))&
((?[X]:((calm(X)|~generous(X))))=>(?[X]:((~quiet(X)<~>~kind(X)))))&
(![X]:((funny(X)<~>~strong(X))<=>(generous(X)|curious(X))))&
(![X]:(curious(X)<=>(patient(X)<~>~wise(X))))&
((?[X]:(~old(X)))=>(?[X]:((happy(X)|quiet(X)))))&
((?[X]:((~humble(X)<~>~funny(X))))<=>((~curious(susan)<~>happy(susan))))&
(![X]:(strong(X)<=>(~funny(X)|tall(X))))&
(![X]:(~quiet(X)=>(~wise(X)&~generous(X))))&
(![X]:((~humble(X)<~>~generous(X))<=>(curious(X)<~>~happy(X))))&
(((curious(mary)<~>~happy(mary)))=>(?[X]:((funny(X)<~>tall(X)))))&
((~creative(fred)<~>funny(fred)))&
((~calm(susan)|curious(susan)))&
(?[X]:((happy(X)|~creative(X))))&
((~strong(mary)<~>quiet(mary)))&
(?[X]:(wise(X)))&
((~quiet(fred)&rich(fred))) | ~patient(john) | [] | null | 0 |
If someone is creative or rich then mary is both not funny and brave and vice versa. If fred is either old or strong then john is both patient and curious. If alice is both not funny and humble then fred is curious. If someone is either funny or not patient then paul is both curious and tall and vice versa. Everyone who is not calm is both brave and not kind and vice versa. Everyone who is both humble and tall is not creative or kind and vice versa. If alice is not wise or patient then someone is both not kind and not happy. Everyone who is happy or humble is old and vice versa. Everyone who is either tall or rich is not quiet or not brave and vice versa. Everyone who is either creative or not creative is curious or old and vice versa. Everyone who is quiet or humble is rich or not happy and vice versa. Everyone who is both strong and calm is either humble or happy and vice versa. Everyone who is curious is not patient or quiet and vice versa. If someone is not kind or old then alice is creative or not old and vice versa. Everyone who is funny is creative. Everyone who is either not strong or kind is either strong or not happy and vice versa. John is either not brave or kind. Someone is both not kind and funny. Susan is not brave. Susan is either not brave or happy. Someone is quiet. Someone is creative or kind. Paul is either brave or not patient. Someone is patient or not funny. | Paul is tall. | neutral | ((?[X]:((creative(X)|rich(X))))<=>((~funny(mary)&brave(mary))))&
(((old(fred)<~>strong(fred)))=>((patient(john)&curious(john))))&
(((~funny(alice)&humble(alice)))=>(curious(fred)))&
((?[X]:((funny(X)<~>~patient(X))))<=>((curious(paul)&tall(paul))))&
(![X]:(~calm(X)<=>(brave(X)&~kind(X))))&
(![X]:((humble(X)&tall(X))<=>(~creative(X)|kind(X))))&
(((~wise(alice)|patient(alice)))=>(?[X]:((~kind(X)&~happy(X)))))&
(![X]:((happy(X)|humble(X))<=>old(X)))&
(![X]:((tall(X)<~>rich(X))<=>(~quiet(X)|~brave(X))))&
(![X]:((creative(X)<~>~creative(X))<=>(curious(X)|old(X))))&
(![X]:((quiet(X)|humble(X))<=>(rich(X)|~happy(X))))&
(![X]:((strong(X)&calm(X))<=>(humble(X)<~>happy(X))))&
(![X]:(curious(X)<=>(~patient(X)|quiet(X))))&
((?[X]:((~kind(X)|old(X))))<=>((creative(alice)|~old(alice))))&
(![X]:(funny(X)=>creative(X)))&
(![X]:((~strong(X)<~>kind(X))<=>(strong(X)<~>~happy(X))))&
((~brave(john)<~>kind(john)))&
(?[X]:((~kind(X)&funny(X))))&
(~brave(susan))&
((~brave(susan)<~>happy(susan)))&
(?[X]:(quiet(X)))&
(?[X]:((creative(X)|kind(X))))&
((brave(paul)<~>~patient(paul)))&
(?[X]:((patient(X)|~funny(X)))) | tall(paul) | [] | null | 0 |
Everyone who is both not old and not calm is either not tall or not happy and vice versa.
Everyone who is not kind or not funny is either wise or not funny and vice versa.
Everyone who is either quiet or not kind is quiet or kind.
If alice is not patient then mary is either creative or not brave.
Everyone who is both tall and strong is both brave and generous and vice versa.
Everyone who is funny or not wise is both tall and rich and vice versa.
Everyone who is happy or not patient is patient.
Everyone who is tall is both strong and humble and vice versa.
If someone is either happy or brave then someone is not patient and vice versa.
If someone is not kind then someone is brave or not creative.
If lucy is brave or old then someone is either not strong or patient and vice versa.
If alice is both not brave and humble then alice is either quiet or calm.
If someone is either happy or not creative then someone is either not humble or patient.
If paul is curious then susan is either not humble or old and vice versa.
Everyone who is both rich and not creative is either not happy or curious.
Everyone who is rich is not curious or creative.
Someone is not rich or calm.
Lucy is funny.
Someone is either not old or not rich.
Someone is not creative or happy.
Someone is creative or patient.
John is either happy or not wise.
Alice is either not kind or humble.
Someone is either tall or not wise. | Mary is not generous. | contradiction | (![X]:((~old(X)&~calm(X))<=>(~tall(X)<~>~happy(X))))&
(![X]:((~kind(X)|~funny(X))<=>(wise(X)<~>~funny(X))))&
(![X]:((quiet(X)<~>~kind(X))=>(quiet(X)|kind(X))))&
((~patient(alice))=>((creative(mary)<~>~brave(mary))))&
(![X]:((tall(X)&strong(X))<=>(brave(X)&generous(X))))&
(![X]:((funny(X)|~wise(X))<=>(tall(X)&rich(X))))&
(![X]:((happy(X)|~patient(X))=>patient(X)))&
(![X]:(tall(X)<=>(strong(X)&humble(X))))&
((?[X]:((happy(X)<~>brave(X))))<=>(?[X]:(~patient(X))))&
((?[X]:(~kind(X)))=>(?[X]:((brave(X)|~creative(X)))))&
(((brave(lucy)|old(lucy)))<=>(?[X]:((~strong(X)<~>patient(X)))))&
(((~brave(alice)&humble(alice)))=>((quiet(alice)<~>calm(alice))))&
((?[X]:((happy(X)<~>~creative(X))))=>(?[X]:((~humble(X)<~>patient(X)))))&
((curious(paul))<=>((~humble(susan)<~>old(susan))))&
(![X]:((rich(X)&~creative(X))=>(~happy(X)<~>curious(X))))&
(![X]:(rich(X)=>(~curious(X)|creative(X))))&
(?[X]:((~rich(X)|calm(X))))&
(funny(lucy))&
(?[X]:((~old(X)<~>~rich(X))))&
(?[X]:((~creative(X)|happy(X))))&
(?[X]:((creative(X)|patient(X))))&
((happy(john)<~>~wise(john)))&
((~kind(alice)<~>humble(alice)))&
(?[X]:((tall(X)<~>~wise(X)))) | ~generous(mary) | [
"p1",
"p4",
"p5",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 900460798916005508567113
% SZS output start Proof for 900460798916005508567113
2. ! [X0] : ((~funny(X0) | ~kind(X0)) <=> (wise(X0) <~> ~funny(X0))) [input p1]
5. ! [X0] : ((strong(X0) & tall(X0)) <=> (generous(X0) & brave(X0))) [input p4]
6. ! [X0] : ((~wise(X0) | funny(X0)) <=> (rich(X0) & tall(X0))) [input p5]
8. ! [X0] : (tall(X0) <=> (humble(X0) & strong(X0))) [input p7]
25. ~generous(mary) [input hypothesis]
43. ! [X0] : (((~funny(X0) | ~kind(X0)) | ((wise(X0) | funny(X0)) & (~funny(X0) | ~wise(X0)))) & (((funny(X0) | ~wise(X0)) & (~funny(X0) | wise(X0))) | (funny(X0) & kind(X0)))) [nnf transformation 2]
44. ! [X0] : ((~funny(X0) | ~kind(X0) | ((wise(X0) | funny(X0)) & (~funny(X0) | ~wise(X0)))) & (((funny(X0) | ~wise(X0)) & (~funny(X0) | wise(X0))) | (funny(X0) & kind(X0)))) [flattening 43]
47. ! [X0] : (((strong(X0) & tall(X0)) | (~generous(X0) | ~brave(X0))) & ((generous(X0) & brave(X0)) | (~strong(X0) | ~tall(X0)))) [nnf transformation 5]
48. ! [X0] : (((strong(X0) & tall(X0)) | ~generous(X0) | ~brave(X0)) & ((generous(X0) & brave(X0)) | ~strong(X0) | ~tall(X0))) [flattening 47]
49. ! [X0] : (((~wise(X0) | funny(X0)) | (~rich(X0) | ~tall(X0))) & ((rich(X0) & tall(X0)) | (wise(X0) & ~funny(X0)))) [nnf transformation 6]
50. ! [X0] : ((~wise(X0) | funny(X0) | ~rich(X0) | ~tall(X0)) & ((rich(X0) & tall(X0)) | (wise(X0) & ~funny(X0)))) [flattening 49]
51. ! [X0] : ((tall(X0) | (~humble(X0) | ~strong(X0))) & ((humble(X0) & strong(X0)) | ~tall(X0))) [nnf transformation 8]
52. ! [X0] : ((tall(X0) | ~humble(X0) | ~strong(X0)) & ((humble(X0) & strong(X0)) | ~tall(X0))) [flattening 51]
96. funny(X0) | ~wise(X0) | funny(X0) [cnf transformation 44]
104. ~strong(X0) | generous(X0) | ~tall(X0) [cnf transformation 48]
107. ~funny(X0) | tall(X0) [cnf transformation 50]
108. wise(X0) | tall(X0) [cnf transformation 50]
114. ~tall(X0) | strong(X0) [cnf transformation 52]
153. ~generous(mary) [cnf transformation 25]
156. ~wise(X0) | funny(X0) [duplicate literal removal 96]
318. funny(X0) | tall(X0) [resolution 156,108]
322. tall(X0) [subsumption resolution 318,107]
326. strong(X1) [resolution 322,114]
418. generous(X0) | ~tall(X0) [resolution 326,104]
420. generous(X0) [subsumption resolution 418,322]
579. $false [resolution 420,153]
% SZS output end Proof for 900460798916005508567113
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not brave and not kind is not generous or patient.
Everyone who is either curious or not rich is either tall or rich.
If mary is not generous or patient then john is not kind.
If someone is happy then alice is creative or funny.
Everyone who is either creative or not brave is not brave or not tall.
If mary is either curious or not generous then paul is either not generous or not wise.
Everyone who is not funny or not happy is generous.
Everyone who is either funny or not creative is both creative and not wise and vice versa.
Everyone who is not wise is quiet or not patient.
Everyone who is both not wise and not old is strong and vice versa.
Everyone who is either not creative or not brave is either not strong or strong and vice versa.
Everyone who is patient or calm is both creative and not tall and vice versa.
Everyone who is both not wise and not kind is rich or not creative.
Everyone who is not calm or not tall is happy and vice versa.
If alice is both not kind and not tall then alice is not brave.
If paul is not happy or not tall then someone is both not quiet and rich.
Lucy is not calm or not funny.
Someone is rich.
Someone is either not quiet or not kind.
Someone is both strong and calm.
Someone is both not brave and strong.
John is kind or wise.
Alice is brave.
Someone is either not rich or quiet. | Mary is quiet. | neutral | (![X]:((~brave(X)&~kind(X))=>(~generous(X)|patient(X))))&
(![X]:((curious(X)<~>~rich(X))=>(tall(X)<~>rich(X))))&
(((~generous(mary)|patient(mary)))=>(~kind(john)))&
((?[X]:(happy(X)))=>((creative(alice)|funny(alice))))&
(![X]:((creative(X)<~>~brave(X))=>(~brave(X)|~tall(X))))&
(((curious(mary)<~>~generous(mary)))=>((~generous(paul)<~>~wise(paul))))&
(![X]:((~funny(X)|~happy(X))=>generous(X)))&
(![X]:((funny(X)<~>~creative(X))<=>(creative(X)&~wise(X))))&
(![X]:(~wise(X)=>(quiet(X)|~patient(X))))&
(![X]:((~wise(X)&~old(X))<=>strong(X)))&
(![X]:((~creative(X)<~>~brave(X))<=>(~strong(X)<~>strong(X))))&
(![X]:((patient(X)|calm(X))<=>(creative(X)&~tall(X))))&
(![X]:((~wise(X)&~kind(X))=>(rich(X)|~creative(X))))&
(![X]:((~calm(X)|~tall(X))<=>happy(X)))&
(((~kind(alice)&~tall(alice)))=>(~brave(alice)))&
(((~happy(paul)|~tall(paul)))=>(?[X]:((~quiet(X)&rich(X)))))&
((~calm(lucy)|~funny(lucy)))&
(?[X]:(rich(X)))&
(?[X]:((~quiet(X)<~>~kind(X))))&
(?[X]:((strong(X)&calm(X))))&
(?[X]:((~brave(X)&strong(X))))&
((kind(john)|wise(john)))&
(brave(alice))&
(?[X]:((~rich(X)<~>quiet(X)))) | quiet(mary) | [] | null | 0 |
Everyone who is rich is either quiet or not humble. If someone is not quiet then someone is both rich and not wise and vice versa. Everyone who is both humble and not happy is funny. If fred is curious or calm then fred is both not happy and not funny. Everyone who is both not patient and not wise is not rich. If someone is wise then paul is not generous or strong and vice versa. Everyone who is either not strong or not patient is both not rich and not calm and vice versa. If someone is both creative and rich then someone is either not humble or brave and vice versa. Everyone who is not generous or happy is not happy and vice versa. Everyone who is not creative is either not strong or creative. Everyone who is patient or calm is not humble. If fred is either not quiet or kind then someone is not rich. Everyone who is either not patient or not strong is either kind or not tall. Everyone who is both not curious and not brave is not generous and vice versa. If paul is both not tall and old then susan is either quiet or not calm and vice versa. If someone is both happy and not rich then someone is tall or not patient. Someone is either not calm or curious. Paul is funny or calm. Someone is either creative or humble. Someone is happy or not brave. Someone is not brave. John is both funny and calm. Someone is either not calm or quiet. Someone is not old. | John is not brave. | entailment | (![X]:(rich(X)=>(quiet(X)<~>~humble(X))))&
((?[X]:(~quiet(X)))<=>(?[X]:((rich(X)&~wise(X)))))&
(![X]:((humble(X)&~happy(X))=>funny(X)))&
(((curious(fred)|calm(fred)))=>((~happy(fred)&~funny(fred))))&
(![X]:((~patient(X)&~wise(X))=>~rich(X)))&
((?[X]:(wise(X)))<=>((~generous(paul)|strong(paul))))&
(![X]:((~strong(X)<~>~patient(X))<=>(~rich(X)&~calm(X))))&
((?[X]:((creative(X)&rich(X))))<=>(?[X]:((~humble(X)<~>brave(X)))))&
(![X]:((~generous(X)|happy(X))<=>~happy(X)))&
(![X]:(~creative(X)=>(~strong(X)<~>creative(X))))&
(![X]:((patient(X)|calm(X))=>~humble(X)))&
(((~quiet(fred)<~>kind(fred)))=>(?[X]:(~rich(X))))&
(![X]:((~patient(X)<~>~strong(X))=>(kind(X)<~>~tall(X))))&
(![X]:((~curious(X)&~brave(X))<=>~generous(X)))&
(((~tall(paul)&old(paul)))<=>((quiet(susan)<~>~calm(susan))))&
((?[X]:((happy(X)&~rich(X))))=>(?[X]:((tall(X)|~patient(X)))))&
(?[X]:((~calm(X)<~>curious(X))))&
((funny(paul)|calm(paul)))&
(?[X]:((creative(X)<~>humble(X))))&
(?[X]:((happy(X)|~brave(X))))&
(?[X]:(~brave(X)))&
((funny(john)&calm(john)))&
(?[X]:((~calm(X)<~>quiet(X))))&
(?[X]:(~old(X))) | ~brave(john) | [
"p8",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 4132119737005865134516281
% SZS output start Proof for 4132119737005865134516281
9. ! [X0] : ((happy(X0) | ~generous(X0)) <=> ~happy(X0)) [input p8]
14. ! [X0] : ((~brave(X0) & ~curious(X0)) <=> ~generous(X0)) [input p13]
25. brave(john) [input hypothesis]
58. ! [X0] : (((happy(X0) | ~generous(X0)) | happy(X0)) & (~happy(X0) | (~happy(X0) & generous(X0)))) [nnf transformation 9]
59. ! [X0] : ((happy(X0) | ~generous(X0) | happy(X0)) & (~happy(X0) | (~happy(X0) & generous(X0)))) [flattening 58]
65. ! [X0] : (((~brave(X0) & ~curious(X0)) | generous(X0)) & (~generous(X0) | (brave(X0) | curious(X0)))) [nnf transformation 14]
66. ! [X0] : (((~brave(X0) & ~curious(X0)) | generous(X0)) & (~generous(X0) | brave(X0) | curious(X0))) [flattening 65]
114. ~happy(X0) | ~happy(X0) [cnf transformation 59]
115. happy(X0) | ~generous(X0) | happy(X0) [cnf transformation 59]
128. ~brave(X0) | generous(X0) [cnf transformation 66]
148. brave(john) [cnf transformation 25]
150. ~happy(X0) [duplicate literal removal 114]
151. ~generous(X0) | happy(X0) [duplicate literal removal 115]
322. generous(john) [resolution 128,148]
323. happy(john) [resolution 151,322]
324. $false [subsumption resolution 323,150]
% SZS output end Proof for 4132119737005865134516281
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both wise and funny is wise or patient. Everyone who is both creative and kind is not happy. If someone is strong then someone is creative and vice versa. If someone is either quiet or calm then someone is either not wise or not curious and vice versa. Everyone who is either tall or funny is both not curious and not funny. Everyone who is not calm or not rich is either rich or tall and vice versa. If someone is not wise then fred is not old and vice versa. Everyone who is both curious and not rich is not creative or not calm and vice versa. If paul is either not tall or not brave then john is either not creative or not tall. Everyone who is either generous or not happy is old or generous and vice versa. Everyone who is both humble and brave is either happy or tall and vice versa. If someone is calm then someone is strong or patient and vice versa. If alice is either creative or brave then mary is either not generous or kind. Everyone who is both old and not curious is brave. Everyone who is not humble or quiet is both not funny and not kind. Everyone who is both rich and not patient is humble or rich and vice versa. Someone is not strong. Alice is brave. Paul is both not kind and old. Paul is quiet. Someone is creative. Someone is not funny. Someone is both not strong and not rich. Susan is both not humble and tall. | John is not calm. | contradiction | (![X]:((wise(X)&funny(X))=>(wise(X)|patient(X))))&
(![X]:((creative(X)&kind(X))=>~happy(X)))&
((?[X]:(strong(X)))<=>(?[X]:(creative(X))))&
((?[X]:((quiet(X)<~>calm(X))))<=>(?[X]:((~wise(X)<~>~curious(X)))))&
(![X]:((tall(X)<~>funny(X))=>(~curious(X)&~funny(X))))&
(![X]:((~calm(X)|~rich(X))<=>(rich(X)<~>tall(X))))&
((?[X]:(~wise(X)))<=>(~old(fred)))&
(![X]:((curious(X)&~rich(X))<=>(~creative(X)|~calm(X))))&
(((~tall(paul)<~>~brave(paul)))=>((~creative(john)<~>~tall(john))))&
(![X]:((generous(X)<~>~happy(X))<=>(old(X)|generous(X))))&
(![X]:((humble(X)&brave(X))<=>(happy(X)<~>tall(X))))&
((?[X]:(calm(X)))<=>(?[X]:((strong(X)|patient(X)))))&
(((creative(alice)<~>brave(alice)))=>((~generous(mary)<~>kind(mary))))&
(![X]:((old(X)&~curious(X))=>brave(X)))&
(![X]:((~humble(X)|quiet(X))=>(~funny(X)&~kind(X))))&
(![X]:((rich(X)&~patient(X))<=>(humble(X)|rich(X))))&
(?[X]:(~strong(X)))&
(brave(alice))&
((~kind(paul)&old(paul)))&
(quiet(paul))&
(?[X]:(creative(X)))&
(?[X]:(~funny(X)))&
(?[X]:((~strong(X)&~rich(X))))&
((~humble(susan)&tall(susan))) | ~calm(john) | [
"p4",
"p5",
"p7",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7265823684606168454493947
% SZS output start Proof for 7265823684606168454493947
5. ! [X0] : ((tall(X0) <~> funny(X0)) => (~funny(X0) & ~curious(X0))) [input p4]
6. ! [X0] : ((~rich(X0) | ~calm(X0)) <=> (rich(X0) <~> tall(X0))) [input p5]
8. ! [X0] : ((~rich(X0) & curious(X0)) <=> (~calm(X0) | ~creative(X0))) [input p7]
15. ! [X0] : ((quiet(X0) | ~humble(X0)) => (~kind(X0) & ~funny(X0))) [input p14]
16. ! [X0] : ((~patient(X0) & rich(X0)) <=> (rich(X0) | humble(X0))) [input p15]
25. ~calm(john) [input hypothesis]
33. ! [X0] : ((~funny(X0) & ~curious(X0)) | (tall(X0) <=> funny(X0))) [ennf transformation 5]
38. ! [X0] : ((~kind(X0) & ~funny(X0)) | (~quiet(X0) & humble(X0))) [ennf transformation 15]
49. ! [X0] : ((~funny(X0) & ~curious(X0)) | ((tall(X0) | ~funny(X0)) & (funny(X0) | ~tall(X0)))) [nnf transformation 33]
50. ! [X0] : (((~rich(X0) | ~calm(X0)) | ((rich(X0) | ~tall(X0)) & (tall(X0) | ~rich(X0)))) & (((~tall(X0) | ~rich(X0)) & (tall(X0) | rich(X0))) | (rich(X0) & calm(X0)))) [nnf transformation 6]
51. ! [X0] : ((~rich(X0) | ~calm(X0) | ((rich(X0) | ~tall(X0)) & (tall(X0) | ~rich(X0)))) & (((~tall(X0) | ~rich(X0)) & (tall(X0) | rich(X0))) | (rich(X0) & calm(X0)))) [flattening 50]
56. ! [X0] : (((~rich(X0) & curious(X0)) | (calm(X0) & creative(X0))) & ((~calm(X0) | ~creative(X0)) | (rich(X0) | ~curious(X0)))) [nnf transformation 8]
57. ! [X0] : (((~rich(X0) & curious(X0)) | (calm(X0) & creative(X0))) & (~calm(X0) | ~creative(X0) | rich(X0) | ~curious(X0))) [flattening 56]
69. ! [X0] : (((~patient(X0) & rich(X0)) | (~rich(X0) & ~humble(X0))) & ((rich(X0) | humble(X0)) | (patient(X0) | ~rich(X0)))) [nnf transformation 16]
70. ! [X0] : (((~patient(X0) & rich(X0)) | (~rich(X0) & ~humble(X0))) & (rich(X0) | humble(X0) | patient(X0) | ~rich(X0))) [flattening 69]
91. ~tall(X0) | funny(X0) | ~curious(X0) [cnf transformation 49]
96. tall(X0) | rich(X0) | rich(X0) [cnf transformation 51]
97. ~rich(X0) | ~tall(X0) | calm(X0) [cnf transformation 51]
99. ~rich(X0) | ~calm(X0) | tall(X0) | ~rich(X0) [cnf transformation 51]
105. curious(X0) | calm(X0) [cnf transformation 57]
107. ~rich(X0) | calm(X0) [cnf transformation 57]
132. ~funny(X0) | humble(X0) [cnf transformation 38]
137. ~humble(X0) | rich(X0) [cnf transformation 70]
152. ~calm(john) [cnf transformation 25]
155. rich(X0) | tall(X0) [duplicate literal removal 96]
156. ~rich(X0) | ~calm(X0) | tall(X0) [duplicate literal removal 99]
300. tall(X1) | calm(X1) [resolution 155,107]
409. ~calm(X0) | tall(X0) | tall(X0) [resolution 156,155]
410. ~calm(X0) | tall(X0) [duplicate literal removal 409]
411. tall(X0) [subsumption resolution 410,300]
415. ~curious(X2) | funny(X2) [resolution 411,91]
462. calm(X0) | funny(X0) [resolution 415,105]
481. funny(john) [resolution 462,152]
486. humble(john) [resolution 481,132]
494. rich(john) [resolution 486,137]
508. ~tall(john) | calm(john) [resolution 494,97]
512. calm(john) [subsumption resolution 508,411]
513. $false [subsumption resolution 512,152]
% SZS output end Proof for 7265823684606168454493947
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not patient or not quiet then lucy is curious or strong.
If someone is either not old or not strong then someone is old or wise and vice versa.
If mary is wise then someone is either not funny or not old.
Everyone who is either not curious or not calm is not creative.
Everyone who is not funny is not old or not kind.
Everyone who is not tall or rich is either not tall or not old and vice versa.
If someone is either tall or not kind then someone is funny or brave and vice versa.
If someone is generous then someone is creative or old.
Everyone who is not generous is quiet and vice versa.
If someone is either brave or rich then paul is both kind and not funny and vice versa.
Everyone who is not happy or wise is tall or old and vice versa.
Everyone who is not calm or not strong is both kind and not brave.
Everyone who is calm or not tall is funny or strong and vice versa.
Everyone who is either strong or happy is both not happy and not patient and vice versa.
If alice is both not creative and happy then mary is happy or tall and vice versa.
If lucy is either humble or tall then john is both brave and calm and vice versa.
Someone is either not curious or not old.
Someone is generous or old.
Someone is quiet.
Mary is both not creative and funny.
Lucy is both not happy and rich.
Someone is either tall or not humble.
Susan is patient or not kind. | Mary is rich. | neutral | ((?[X]:((~patient(X)|~quiet(X))))=>((curious(lucy)|strong(lucy))))&
((?[X]:((~old(X)<~>~strong(X))))<=>(?[X]:((old(X)|wise(X)))))&
((wise(mary))=>(?[X]:((~funny(X)<~>~old(X)))))&
(![X]:((~curious(X)<~>~calm(X))=>~creative(X)))&
(![X]:(~funny(X)=>(~old(X)|~kind(X))))&
(![X]:((~tall(X)|rich(X))<=>(~tall(X)<~>~old(X))))&
((?[X]:((tall(X)<~>~kind(X))))<=>(?[X]:((funny(X)|brave(X)))))&
((?[X]:(generous(X)))=>(?[X]:((creative(X)|old(X)))))&
(![X]:(~generous(X)<=>quiet(X)))&
((?[X]:((brave(X)<~>rich(X))))<=>((kind(paul)&~funny(paul))))&
(![X]:((~happy(X)|wise(X))<=>(tall(X)|old(X))))&
(![X]:((~calm(X)|~strong(X))=>(kind(X)&~brave(X))))&
(![X]:((calm(X)|~tall(X))<=>(funny(X)|strong(X))))&
(![X]:((strong(X)<~>happy(X))<=>(~happy(X)&~patient(X))))&
(((~creative(alice)&happy(alice)))<=>((happy(mary)|tall(mary))))&
(((humble(lucy)<~>tall(lucy)))<=>((brave(john)&calm(john))))&
(?[X]:((~curious(X)<~>~old(X))))&
(?[X]:((generous(X)|old(X))))&
(?[X]:(quiet(X)))&
((~creative(mary)&funny(mary)))&
((~happy(lucy)&rich(lucy)))&
(?[X]:((tall(X)<~>~humble(X))))&
((patient(susan)|~kind(susan))) | rich(mary) | [] | null | 0 |
Everyone who is calm or creative is not funny or not calm and vice versa.
If someone is either not calm or curious then someone is not tall or not strong and vice versa.
Everyone who is not old or wise is not patient or not humble.
Everyone who is wise or not funny is wise and vice versa.
If paul is both not creative and patient then someone is either patient or not happy and vice versa.
Everyone who is both brave and not rich is either brave or not rich.
If someone is either not happy or not curious then someone is not kind or not happy.
Everyone who is creative is not happy.
Everyone who is either not tall or not creative is both not rich and not kind and vice versa.
If someone is both kind and not creative then someone is not rich and vice versa.
Everyone who is kind is not rich or rich.
Everyone who is either not creative or not old is not old or not strong.
If someone is patient or not strong then someone is either generous or not old and vice versa.
Everyone who is either patient or calm is both brave and not strong.
Everyone who is not quiet is both humble and not quiet.
If someone is either happy or not creative then alice is both not creative and curious.
Someone is not patient.
Someone is both not calm and patient.
Paul is either calm or not tall.
Someone is not calm.
Someone is either wise or humble.
Someone is both not tall and not creative.
Alice is not generous or rich.
Paul is both not strong and not old. | Paul is quiet. | entailment | (![X]:((calm(X)|creative(X))<=>(~funny(X)|~calm(X))))&
((?[X]:((~calm(X)<~>curious(X))))<=>(?[X]:((~tall(X)|~strong(X)))))&
(![X]:((~old(X)|wise(X))=>(~patient(X)|~humble(X))))&
(![X]:((wise(X)|~funny(X))<=>wise(X)))&
(((~creative(paul)&patient(paul)))<=>(?[X]:((patient(X)<~>~happy(X)))))&
(![X]:((brave(X)&~rich(X))=>(brave(X)<~>~rich(X))))&
((?[X]:((~happy(X)<~>~curious(X))))=>(?[X]:((~kind(X)|~happy(X)))))&
(![X]:(creative(X)=>~happy(X)))&
(![X]:((~tall(X)<~>~creative(X))<=>(~rich(X)&~kind(X))))&
((?[X]:((kind(X)&~creative(X))))<=>(?[X]:(~rich(X))))&
(![X]:(kind(X)=>(~rich(X)|rich(X))))&
(![X]:((~creative(X)<~>~old(X))=>(~old(X)|~strong(X))))&
((?[X]:((patient(X)|~strong(X))))<=>(?[X]:((generous(X)<~>~old(X)))))&
(![X]:((patient(X)<~>calm(X))=>(brave(X)&~strong(X))))&
(![X]:(~quiet(X)=>(humble(X)&~quiet(X))))&
((?[X]:((happy(X)<~>~creative(X))))=>((~creative(alice)&curious(alice))))&
(?[X]:(~patient(X)))&
(?[X]:((~calm(X)&patient(X))))&
((calm(paul)<~>~tall(paul)))&
(?[X]:(~calm(X)))&
(?[X]:((wise(X)<~>humble(X))))&
(?[X]:((~tall(X)&~creative(X))))&
((~generous(alice)|rich(alice)))&
((~strong(paul)&~old(paul))) | quiet(paul) | [
"p0",
"p2",
"p4",
"p5",
"p7",
"p8",
"p13",
"p14",
"p18",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 2364729171373170442142598
% SZS output start Proof for 2364729171373170442142598
1. ! [X0] : ((creative(X0) | calm(X0)) <=> (~calm(X0) | ~funny(X0))) [input p0]
3. ! [X0] : ((wise(X0) | ~old(X0)) => (~humble(X0) | ~patient(X0))) [input p2]
5. (patient(paul) & ~creative(paul)) <=> ? [X0] : (patient(X0) <~> ~happy(X0)) [input p4]
6. ! [X0] : ((~rich(X0) & brave(X0)) => (brave(X0) <~> ~rich(X0))) [input p5]
8. ! [X0] : (creative(X0) => ~happy(X0)) [input p7]
9. ! [X0] : ((~tall(X0) <~> ~creative(X0)) <=> (~kind(X0) & ~rich(X0))) [input p8]
14. ! [X0] : ((patient(X0) <~> calm(X0)) => (~strong(X0) & brave(X0))) [input p13]
15. ! [X0] : (~quiet(X0) => (~quiet(X0) & humble(X0))) [input p14]
19. calm(paul) <~> ~tall(paul) [input p18]
24. ~old(paul) & ~strong(paul) [input p23]
25. ~quiet(paul) [input hypothesis]
30. ! [X0] : ((~humble(X0) | ~patient(X0)) | (~wise(X0) & old(X0))) [ennf transformation 3]
31. ! [X0] : (~humble(X0) | ~patient(X0) | (~wise(X0) & old(X0))) [flattening 30]
32. ! [X0] : ((brave(X0) <~> ~rich(X0)) | (rich(X0) | ~brave(X0))) [ennf transformation 6]
33. ! [X0] : ((brave(X0) <~> ~rich(X0)) | rich(X0) | ~brave(X0)) [flattening 32]
35. ! [X0] : (~happy(X0) | ~creative(X0)) [ennf transformation 8]
40. ! [X0] : ((~strong(X0) & brave(X0)) | (patient(X0) <=> calm(X0))) [ennf transformation 14]
41. ! [X0] : ((~quiet(X0) & humble(X0)) | quiet(X0)) [ennf transformation 15]
43. ! [X0] : (((creative(X0) | calm(X0)) | (calm(X0) & funny(X0))) & ((~calm(X0) | ~funny(X0)) | (~creative(X0) & ~calm(X0)))) [nnf transformation 1]
44. ! [X0] : ((creative(X0) | calm(X0) | (calm(X0) & funny(X0))) & (~calm(X0) | ~funny(X0) | (~creative(X0) & ~calm(X0)))) [flattening 43]
52. ((patient(paul) & ~creative(paul)) | ! [X0] : ((patient(X0) | happy(X0)) & (~happy(X0) | ~patient(X0)))) & (? [X0] : ((happy(X0) | ~patient(X0)) & (~happy(X0) | patient(X0))) | (~patient(paul) | creative(paul))) [nnf transformation 5]
53. ((patient(paul) & ~creative(paul)) | ! [X0] : ((patient(X0) | happy(X0)) & (~happy(X0) | ~patient(X0)))) & (? [X0] : ((happy(X0) | ~patient(X0)) & (~happy(X0) | patient(X0))) | ~patient(paul) | creative(paul)) [flattening 52]
54. ((patient(paul) & ~creative(paul)) | ! [X0] : ((patient(X0) | happy(X0)) & (~happy(X0) | ~patient(X0)))) & (? [X1] : ((happy(X1) | ~patient(X1)) & (~happy(X1) | patient(X1))) | ~patient(paul) | creative(paul)) [rectify 53]
55. ? [X1] : ((happy(X1) | ~patient(X1)) & (~happy(X1) | patient(X1))) => ((happy(sK2) | ~patient(sK2)) & (~happy(sK2) | patient(sK2))) [choice axiom]
56. ((patient(paul) & ~creative(paul)) | ! [X0] : ((patient(X0) | happy(X0)) & (~happy(X0) | ~patient(X0)))) & (((happy(sK2) | ~patient(sK2)) & (~happy(sK2) | patient(sK2))) | ~patient(paul) | creative(paul)) [skolemisation 54,55]
57. ! [X0] : (((rich(X0) | ~brave(X0)) & (~rich(X0) | brave(X0))) | rich(X0) | ~brave(X0)) [nnf transformation 33]
62. ! [X0] : ((((creative(X0) | tall(X0)) & (~creative(X0) | ~tall(X0))) | (kind(X0) | rich(X0))) & ((~kind(X0) & ~rich(X0)) | ((~tall(X0) | creative(X0)) & (~creative(X0) | tall(X0))))) [nnf transformation 9]
63. ! [X0] : ((((creative(X0) | tall(X0)) & (~creative(X0) | ~tall(X0))) | kind(X0) | rich(X0)) & ((~kind(X0) & ~rich(X0)) | ((~tall(X0) | creative(X0)) & (~creative(X0) | tall(X0))))) [flattening 62]
75. ! [X0] : ((~strong(X0) & brave(X0)) | ((patient(X0) | ~calm(X0)) & (calm(X0) | ~patient(X0)))) [nnf transformation 40]
81. (tall(paul) | ~calm(paul)) & (~tall(paul) | calm(paul)) [nnf transformation 19]
92. creative(X0) | calm(X0) | calm(X0) [cnf transformation 44]
99. ~humble(X0) | ~patient(X0) | old(X0) [cnf transformation 31]
107. ~creative(paul) | patient(X0) | happy(X0) [cnf transformation 56]
111. rich(X0) | ~brave(X0) | rich(X0) | ~brave(X0) [cnf transformation 57]
114. ~happy(X0) | ~creative(X0) [cnf transformation 35]
116. ~rich(X0) | ~tall(X0) | creative(X0) [cnf transformation 63]
134. ~calm(X0) | patient(X0) | brave(X0) [cnf transformation 75]
137. quiet(X0) | humble(X0) [cnf transformation 41]
147. tall(paul) | ~calm(paul) [cnf transformation 81]
155. ~old(paul) [cnf transformation 24]
156. ~quiet(paul) [cnf transformation 25]
158. ~brave(X0) | rich(X0) [duplicate literal removal 111]
160. creative(X0) | calm(X0) [duplicate literal removal 92]
196. 9 <=> ! [X0] : (patient(X0) | happy(X0)) [avatar definition]
197. happy(X0) | patient(X0) <- (9) [avatar component clause 196]
199. 10 <=> patient(paul) [avatar definition]
200. ~patient(paul) <- (~10) [avatar component clause 199]
208. 12 <=> creative(paul) [avatar definition]
209. creative(paul) <- (12) [avatar component clause 208]
210. ~creative(paul) <- (~12) [avatar component clause 208]
211. 9 | ~12 [avatar split clause 107,208,196]
305. 34 <=> calm(paul) [avatar definition]
306. calm(paul) <- (34) [avatar component clause 305]
307. ~calm(paul) <- (~34) [avatar component clause 305]
309. 35 <=> tall(paul) [avatar definition]
311. tall(paul) <- (35) [avatar component clause 309]
312. ~34 | 35 [avatar split clause 147,309,305]
335. humble(paul) [resolution 137,156]
337. calm(paul) <- (~12) [resolution 160,210]
339. $false <- (~12, ~34) [subsumption resolution 337,307]
340. 12 | 34 [avatar contradiction clause 339]
342. ~creative(X0) | patient(X0) <- (9) [resolution 197,114]
350. ~patient(paul) | old(paul) [resolution 99,335]
354. ~patient(paul) [subsumption resolution 350,155]
355. ~10 [avatar split clause 354,199]
358. patient(paul) <- (9, 12) [resolution 342,209]
360. $false <- (9, ~10, 12) [subsumption resolution 358,200]
361. ~9 | 10 | ~12 [avatar contradiction clause 360]
399. patient(paul) | brave(paul) <- (34) [resolution 134,306]
403. brave(paul) <- (~10, 34) [subsumption resolution 399,200]
442. rich(paul) <- (~10, 34) [resolution 403,158]
518. ~tall(paul) | creative(paul) <- (~10, 34) [resolution 442,116]
520. creative(paul) <- (~10, 34, 35) [subsumption resolution 518,311]
521. $false <- (~10, ~12, 34, 35) [subsumption resolution 520,210]
522. 10 | 12 | ~34 | ~35 [avatar contradiction clause 521]
523. $false [avatar sat refutation 211,312,340,355,361,522]
% SZS output end Proof for 2364729171373170442142598
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If mary is not generous then someone is not old or tall and vice versa. If paul is not wise or not patient then someone is kind or calm. Everyone who is strong or generous is not tall or not wise and vice versa. Everyone who is both not creative and not wise is patient and vice versa. Everyone who is either not creative or generous is both generous and not quiet. Everyone who is either kind or not wise is patient or tall and vice versa. Everyone who is not old is either not creative or not strong and vice versa. If john is not strong or not quiet then paul is both not tall and patient. Everyone who is both not kind and not curious is either not happy or funny and vice versa. Everyone who is both not generous and not humble is both generous and not humble and vice versa. If susan is both not happy and rich then fred is calm or old and vice versa. If someone is funny then lucy is humble and vice versa. Everyone who is either not calm or not happy is creative and vice versa. If mary is both tall and not kind then someone is either not tall or quiet and vice versa. Everyone who is either not patient or not tall is either not happy or not kind and vice versa. If someone is calm then someone is not patient and vice versa. Someone is not rich. Susan is not creative or tall. John is both not tall and quiet. Lucy is either brave or not strong. Someone is humble. Susan is either not tall or not creative. Lucy is not rich or brave. Someone is either not kind or old. | Susan is not kind. | entailment | ((~generous(mary))<=>(?[X]:((~old(X)|tall(X)))))&
(((~wise(paul)|~patient(paul)))=>(?[X]:((kind(X)|calm(X)))))&
(![X]:((strong(X)|generous(X))<=>(~tall(X)|~wise(X))))&
(![X]:((~creative(X)&~wise(X))<=>patient(X)))&
(![X]:((~creative(X)<~>generous(X))=>(generous(X)&~quiet(X))))&
(![X]:((kind(X)<~>~wise(X))<=>(patient(X)|tall(X))))&
(![X]:(~old(X)<=>(~creative(X)<~>~strong(X))))&
(((~strong(john)|~quiet(john)))=>((~tall(paul)&patient(paul))))&
(![X]:((~kind(X)&~curious(X))<=>(~happy(X)<~>funny(X))))&
(![X]:((~generous(X)&~humble(X))<=>(generous(X)&~humble(X))))&
(((~happy(susan)&rich(susan)))<=>((calm(fred)|old(fred))))&
((?[X]:(funny(X)))<=>(humble(lucy)))&
(![X]:((~calm(X)<~>~happy(X))<=>creative(X)))&
(((tall(mary)&~kind(mary)))<=>(?[X]:((~tall(X)<~>quiet(X)))))&
(![X]:((~patient(X)<~>~tall(X))<=>(~happy(X)<~>~kind(X))))&
((?[X]:(calm(X)))<=>(?[X]:(~patient(X))))&
(?[X]:(~rich(X)))&
((~creative(susan)|tall(susan)))&
((~tall(john)&quiet(john)))&
((brave(lucy)<~>~strong(lucy)))&
(?[X]:(humble(X)))&
((~tall(susan)<~>~creative(susan)))&
((~rich(lucy)|brave(lucy)))&
(?[X]:((~kind(X)<~>old(X)))) | ~kind(susan) | [
"p2",
"p3",
"p4",
"p5",
"p17",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 349562399153519327662423
% SZS output start Proof for 349562399153519327662423
3. ! [X0] : ((generous(X0) | strong(X0)) <=> (~wise(X0) | ~tall(X0))) [input p2]
4. ! [X0] : ((~wise(X0) & ~creative(X0)) <=> patient(X0)) [input p3]
5. ! [X0] : ((~creative(X0) <~> generous(X0)) => (~quiet(X0) & generous(X0))) [input p4]
6. ! [X0] : ((kind(X0) <~> ~wise(X0)) <=> (tall(X0) | patient(X0))) [input p5]
18. tall(susan) | ~creative(susan) [input p17]
22. ~tall(susan) <~> ~creative(susan) [input p21]
25. kind(susan) [input hypothesis]
28. ! [X0] : ((~quiet(X0) & generous(X0)) | (~creative(X0) <=> generous(X0))) [ennf transformation 5]
36. ! [X0] : (((generous(X0) | strong(X0)) | (wise(X0) & tall(X0))) & ((~wise(X0) | ~tall(X0)) | (~generous(X0) & ~strong(X0)))) [nnf transformation 3]
37. ! [X0] : ((generous(X0) | strong(X0) | (wise(X0) & tall(X0))) & (~wise(X0) | ~tall(X0) | (~generous(X0) & ~strong(X0)))) [flattening 36]
38. ! [X0] : (((~wise(X0) & ~creative(X0)) | ~patient(X0)) & (patient(X0) | (wise(X0) | creative(X0)))) [nnf transformation 4]
39. ! [X0] : (((~wise(X0) & ~creative(X0)) | ~patient(X0)) & (patient(X0) | wise(X0) | creative(X0))) [flattening 38]
40. ! [X0] : ((~quiet(X0) & generous(X0)) | ((~creative(X0) | ~generous(X0)) & (generous(X0) | creative(X0)))) [nnf transformation 28]
41. ! [X0] : ((((wise(X0) | ~kind(X0)) & (~wise(X0) | kind(X0))) | (~tall(X0) & ~patient(X0))) & ((tall(X0) | patient(X0)) | ((kind(X0) | wise(X0)) & (~wise(X0) | ~kind(X0))))) [nnf transformation 6]
42. ! [X0] : ((((wise(X0) | ~kind(X0)) & (~wise(X0) | kind(X0))) | (~tall(X0) & ~patient(X0))) & (tall(X0) | patient(X0) | ((kind(X0) | wise(X0)) & (~wise(X0) | ~kind(X0))))) [flattening 41]
71. (creative(susan) | tall(susan)) & (~creative(susan) | ~tall(susan)) [nnf transformation 22]
81. ~wise(X0) | ~tall(X0) | ~generous(X0) [cnf transformation 37]
84. creative(X0) | wise(X0) | patient(X0) [cnf transformation 39]
86. ~patient(X0) | ~wise(X0) [cnf transformation 39]
87. generous(X0) | generous(X0) | creative(X0) [cnf transformation 40]
95. wise(X0) | ~kind(X0) | ~patient(X0) [cnf transformation 42]
143. tall(susan) | ~creative(susan) [cnf transformation 18]
149. ~creative(susan) | ~tall(susan) [cnf transformation 71]
150. creative(susan) | tall(susan) [cnf transformation 71]
154. kind(susan) [cnf transformation 25]
157. creative(X0) | generous(X0) [duplicate literal removal 87]
197. ~kind(X0) | ~patient(X0) [subsumption resolution 95,86]
287. 27 <=> creative(susan) [avatar definition]
289. ~creative(susan) <- (~27) [avatar component clause 287]
291. 28 <=> tall(susan) [avatar definition]
293. tall(susan) <- (28) [avatar component clause 291]
294. ~27 | 28 [avatar split clause 143,291,287]
306. 28 | 27 [avatar split clause 150,287,291]
307. ~28 | ~27 [avatar split clause 149,287,291]
325. generous(susan) <- (~27) [resolution 157,289]
328. ~patient(susan) [resolution 197,154]
351. wise(susan) | patient(susan) <- (~27) [resolution 84,289]
353. wise(susan) <- (~27) [subsumption resolution 351,328]
356. ~tall(susan) | ~generous(susan) <- (~27) [resolution 353,81]
357. ~generous(susan) <- (~27, 28) [subsumption resolution 356,293]
358. $false <- (~27, 28) [subsumption resolution 357,325]
359. 27 | ~28 [avatar contradiction clause 358]
360. $false [avatar sat refutation 294,306,307,359]
% SZS output end Proof for 349562399153519327662423
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not happy or not strong then mary is both not humble and not brave.
If someone is either old or wise then alice is not curious and vice versa.
Everyone who is generous is either not tall or old and vice versa.
Everyone who is wise or creative is both funny and not old and vice versa.
If paul is not humble or not tall then mary is not patient.
If paul is not happy or generous then fred is both not quiet and not strong and vice versa.
Everyone who is either not kind or funny is either calm or funny and vice versa.
Everyone who is kind is happy or not brave.
Everyone who is not curious or humble is both not brave and happy and vice versa.
Everyone who is not wise or not brave is creative and vice versa.
Everyone who is either not patient or not strong is both quiet and happy.
Everyone who is either creative or not happy is not generous and vice versa.
If someone is both not quiet and not happy then john is either creative or quiet and vice versa.
If fred is happy then someone is both not calm and not generous.
Everyone who is patient is both not curious and not strong and vice versa.
If someone is humble then susan is both brave and patient and vice versa.
Someone is either patient or not curious.
Lucy is happy.
Someone is not quiet or not rich.
Someone is not strong.
Susan is not generous or not funny.
Lucy is not old or not rich. | John is kind. | neutral | ((?[X]:((~happy(X)<~>~strong(X))))=>((~humble(mary)&~brave(mary))))&
((?[X]:((old(X)<~>wise(X))))<=>(~curious(alice)))&
(![X]:(generous(X)<=>(~tall(X)<~>old(X))))&
(![X]:((wise(X)|creative(X))<=>(funny(X)&~old(X))))&
(((~humble(paul)|~tall(paul)))=>(~patient(mary)))&
(((~happy(paul)|generous(paul)))<=>((~quiet(fred)&~strong(fred))))&
(![X]:((~kind(X)<~>funny(X))<=>(calm(X)<~>funny(X))))&
(![X]:(kind(X)=>(happy(X)|~brave(X))))&
(![X]:((~curious(X)|humble(X))<=>(~brave(X)&happy(X))))&
(![X]:((~wise(X)|~brave(X))<=>creative(X)))&
(![X]:((~patient(X)<~>~strong(X))=>(quiet(X)&happy(X))))&
(![X]:((creative(X)<~>~happy(X))<=>~generous(X)))&
((?[X]:((~quiet(X)&~happy(X))))<=>((creative(john)<~>quiet(john))))&
((happy(fred))=>(?[X]:((~calm(X)&~generous(X)))))&
(![X]:(patient(X)<=>(~curious(X)&~strong(X))))&
((?[X]:(humble(X)))<=>((brave(susan)&patient(susan))))&
(?[X]:((patient(X)<~>~curious(X))))&
(happy(lucy))&
(?[X]:((~quiet(X)|~rich(X))))&
(?[X]:(~strong(X)))&
((~generous(susan)|~funny(susan)))&
((~old(lucy)|~rich(lucy))) | kind(john) | [] | null | 0 |
If someone is both rich and curious then someone is both happy and quiet. If susan is both not old and generous then susan is strong or not humble. Everyone who is not patient or not calm is strong or old and vice versa. If someone is either not kind or not strong then someone is not creative. If susan is both not tall and not brave then someone is either not humble or not calm and vice versa. If lucy is either not humble or not brave then john is funny. If alice is quiet then susan is not calm and vice versa. Everyone who is both not funny and creative is humble or not brave and vice versa. Everyone who is calm or creative is both not curious and not brave and vice versa. Everyone who is either creative or quiet is both happy and tall and vice versa. Everyone who is either patient or not curious is either rich or brave. If mary is both not humble and not creative then mary is strong. Everyone who is either brave or not creative is brave or not wise and vice versa. Everyone who is either strong or not kind is either kind or wise. If someone is calm or funny then someone is not humble. If someone is happy then someone is not tall and vice versa. Fred is both not patient and not humble. Susan is both not brave and not strong. Someone is either not curious or humble. Mary is either not curious or quiet. Someone is either calm or tall. | John is not funny. | entailment | ((?[X]:((rich(X)&curious(X))))=>(?[X]:((happy(X)&quiet(X)))))&
(((~old(susan)&generous(susan)))=>((strong(susan)|~humble(susan))))&
(![X]:((~patient(X)|~calm(X))<=>(strong(X)|old(X))))&
((?[X]:((~kind(X)<~>~strong(X))))=>(?[X]:(~creative(X))))&
(((~tall(susan)&~brave(susan)))<=>(?[X]:((~humble(X)<~>~calm(X)))))&
(((~humble(lucy)<~>~brave(lucy)))=>(funny(john)))&
((quiet(alice))<=>(~calm(susan)))&
(![X]:((~funny(X)&creative(X))<=>(humble(X)|~brave(X))))&
(![X]:((calm(X)|creative(X))<=>(~curious(X)&~brave(X))))&
(![X]:((creative(X)<~>quiet(X))<=>(happy(X)&tall(X))))&
(![X]:((patient(X)<~>~curious(X))=>(rich(X)<~>brave(X))))&
(((~humble(mary)&~creative(mary)))=>(strong(mary)))&
(![X]:((brave(X)<~>~creative(X))<=>(brave(X)|~wise(X))))&
(![X]:((strong(X)<~>~kind(X))=>(kind(X)<~>wise(X))))&
((?[X]:((calm(X)|funny(X))))=>(?[X]:(~humble(X))))&
((?[X]:(happy(X)))<=>(?[X]:(~tall(X))))&
((~patient(fred)&~humble(fred)))&
((~brave(susan)&~strong(susan)))&
(?[X]:((~curious(X)<~>humble(X))))&
((~curious(mary)<~>quiet(mary)))&
(?[X]:((calm(X)<~>tall(X)))) | ~funny(john) | [
"p7",
"p8",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 8232048174926888161388180
% SZS output start Proof for 8232048174926888161388180
8. ! [X0] : ((creative(X0) & ~funny(X0)) <=> (~brave(X0) | humble(X0))) [input p7]
9. ! [X0] : ((creative(X0) | calm(X0)) <=> (~brave(X0) & ~curious(X0))) [input p8]
13. ! [X0] : ((brave(X0) <~> ~creative(X0)) <=> (~wise(X0) | brave(X0))) [input p12]
22. funny(john) [input hypothesis]
52. ! [X0] : (((creative(X0) & ~funny(X0)) | (brave(X0) & ~humble(X0))) & ((~brave(X0) | humble(X0)) | (~creative(X0) | funny(X0)))) [nnf transformation 8]
53. ! [X0] : (((creative(X0) & ~funny(X0)) | (brave(X0) & ~humble(X0))) & (~brave(X0) | humble(X0) | ~creative(X0) | funny(X0))) [flattening 52]
54. ! [X0] : (((creative(X0) | calm(X0)) | (brave(X0) | curious(X0))) & ((~brave(X0) & ~curious(X0)) | (~creative(X0) & ~calm(X0)))) [nnf transformation 9]
55. ! [X0] : ((creative(X0) | calm(X0) | brave(X0) | curious(X0)) & ((~brave(X0) & ~curious(X0)) | (~creative(X0) & ~calm(X0)))) [flattening 54]
59. ! [X0] : ((((creative(X0) | ~brave(X0)) & (~creative(X0) | brave(X0))) | (wise(X0) & ~brave(X0))) & ((~wise(X0) | brave(X0)) | ((brave(X0) | creative(X0)) & (~creative(X0) | ~brave(X0))))) [nnf transformation 13]
60. ! [X0] : ((((creative(X0) | ~brave(X0)) & (~creative(X0) | brave(X0))) | (wise(X0) & ~brave(X0))) & (~wise(X0) | brave(X0) | ((brave(X0) | creative(X0)) & (~creative(X0) | ~brave(X0))))) [flattening 59]
97. ~funny(X0) | brave(X0) [cnf transformation 53]
103. ~brave(X0) | ~creative(X0) [cnf transformation 55]
120. creative(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 60]
140. funny(john) [cnf transformation 22]
144. creative(X0) | ~brave(X0) [duplicate literal removal 120]
207. 15 <=> funny(john) [avatar definition]
209. funny(john) <- (15) [avatar component clause 207]
233. ~brave(X0) [subsumption resolution 144,103]
293. 15 [avatar split clause 140,207]
299. brave(john) <- (15) [resolution 97,209]
300. $false <- (15) [subsumption resolution 299,233]
301. ~15 [avatar contradiction clause 300]
302. $false [avatar sat refutation 293,301]
% SZS output end Proof for 8232048174926888161388180
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not calm is kind or not wise and vice versa.
Everyone who is both not generous and not strong is quiet and vice versa.
If someone is either wise or kind then paul is both not brave and not patient.
Everyone who is either not curious or happy is either not humble or not rich.
Everyone who is creative or old is wise or quiet.
If mary is both curious and kind then someone is wise and vice versa.
Everyone who is generous is brave and vice versa.
If lucy is funny then paul is wise or not curious.
If someone is not wise then john is not wise and vice versa.
Everyone who is both not funny and not patient is either rich or wise.
Everyone who is not patient or not creative is not creative.
If mary is either not calm or wise then someone is either strong or not wise and vice versa.
If fred is either creative or not calm then paul is old.
Everyone who is wise or not happy is brave and vice versa.
Everyone who is quiet or not calm is either quiet or calm and vice versa.
Everyone who is not happy is both tall and kind.
Someone is both kind and not tall.
Paul is either kind or wise.
Paul is both old and not curious.
Fred is not tall or rich.
Someone is not humble or not wise. | Lucy is curious. | neutral | (![X]:(~calm(X)<=>(kind(X)|~wise(X))))&
(![X]:((~generous(X)&~strong(X))<=>quiet(X)))&
((?[X]:((wise(X)<~>kind(X))))=>((~brave(paul)&~patient(paul))))&
(![X]:((~curious(X)<~>happy(X))=>(~humble(X)<~>~rich(X))))&
(![X]:((creative(X)|old(X))=>(wise(X)|quiet(X))))&
(((curious(mary)&kind(mary)))<=>(?[X]:(wise(X))))&
(![X]:(generous(X)<=>brave(X)))&
((funny(lucy))=>((wise(paul)|~curious(paul))))&
((?[X]:(~wise(X)))<=>(~wise(john)))&
(![X]:((~funny(X)&~patient(X))=>(rich(X)<~>wise(X))))&
(![X]:((~patient(X)|~creative(X))=>~creative(X)))&
(((~calm(mary)<~>wise(mary)))<=>(?[X]:((strong(X)<~>~wise(X)))))&
(((creative(fred)<~>~calm(fred)))=>(old(paul)))&
(![X]:((wise(X)|~happy(X))<=>brave(X)))&
(![X]:((quiet(X)|~calm(X))<=>(quiet(X)<~>calm(X))))&
(![X]:(~happy(X)=>(tall(X)&kind(X))))&
(?[X]:((kind(X)&~tall(X))))&
((kind(paul)<~>wise(paul)))&
((old(paul)&~curious(paul)))&
((~tall(fred)|rich(fred)))&
(?[X]:((~humble(X)|~wise(X)))) | curious(lucy) | [] | null | 0 |
If someone is tall then someone is either rich or creative and vice versa.
Everyone who is both kind and not humble is quiet.
Everyone who is calm or not tall is either not humble or not strong and vice versa.
If someone is both not old and not patient then mary is both not generous and humble.
If someone is brave or not old then someone is either not brave or not humble.
Everyone who is not wise is either quiet or funny.
Everyone who is calm or rich is rich.
Everyone who is quiet or not strong is calm and vice versa.
If susan is either patient or happy then john is either not creative or rich and vice versa.
Everyone who is not creative or not tall is either not quiet or creative and vice versa.
Everyone who is both old and brave is both generous and not funny.
Everyone who is either not wise or wise is either not quiet or not wise and vice versa.
Everyone who is rich or not funny is both not rich and not curious.
If someone is both patient and not kind then lucy is either not old or not kind.
If someone is both not quiet and kind then susan is rich or tall.
Alice is funny or not brave.
Someone is either not patient or humble.
Someone is both creative and not old.
Fred is not generous.
Alice is not funny. | John is not calm. | entailment | ((?[X]:(tall(X)))<=>(?[X]:((rich(X)<~>creative(X)))))&
(![X]:((kind(X)&~humble(X))=>quiet(X)))&
(![X]:((calm(X)|~tall(X))<=>(~humble(X)<~>~strong(X))))&
((?[X]:((~old(X)&~patient(X))))=>((~generous(mary)&humble(mary))))&
((?[X]:((brave(X)|~old(X))))=>(?[X]:((~brave(X)<~>~humble(X)))))&
(![X]:(~wise(X)=>(quiet(X)<~>funny(X))))&
(![X]:((calm(X)|rich(X))=>rich(X)))&
(![X]:((quiet(X)|~strong(X))<=>calm(X)))&
(((patient(susan)<~>happy(susan)))<=>((~creative(john)<~>rich(john))))&
(![X]:((~creative(X)|~tall(X))<=>(~quiet(X)<~>creative(X))))&
(![X]:((old(X)&brave(X))=>(generous(X)&~funny(X))))&
(![X]:((~wise(X)<~>wise(X))<=>(~quiet(X)<~>~wise(X))))&
(![X]:((rich(X)|~funny(X))=>(~rich(X)&~curious(X))))&
((?[X]:((patient(X)&~kind(X))))=>((~old(lucy)<~>~kind(lucy))))&
((?[X]:((~quiet(X)&kind(X))))=>((rich(susan)|tall(susan))))&
((funny(alice)|~brave(alice)))&
(?[X]:((~patient(X)<~>humble(X))))&
(?[X]:((creative(X)&~old(X))))&
(~generous(fred))&
(~funny(alice)) | ~calm(john) | [
"p6",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 2577705598687698970921226
% SZS output start Proof for 2577705598687698970921226
7. ! [X0] : ((rich(X0) | calm(X0)) => rich(X0)) [input p6]
13. ! [X0] : ((~funny(X0) | rich(X0)) => (~curious(X0) & ~rich(X0))) [input p12]
21. calm(john) [input hypothesis]
24. ! [X0] : ((~funny(X0) | rich(X0)) => ~rich(X0)) [pure predicate removal 13]
30. ! [X0] : (rich(X0) | (~rich(X0) & ~calm(X0))) [ennf transformation 7]
33. ! [X0] : (~rich(X0) | (funny(X0) & ~rich(X0))) [ennf transformation 24]
80. ~calm(X0) | rich(X0) [cnf transformation 30]
109. ~rich(X0) | ~rich(X0) [cnf transformation 33]
121. calm(john) [cnf transformation 21]
122. ~rich(X0) [duplicate literal removal 109]
261. rich(john) [resolution 80,121]
262. $false [subsumption resolution 261,122]
% SZS output end Proof for 2577705598687698970921226
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not calm or not wise then someone is both not brave and tall and vice versa. If mary is brave or not humble then someone is either generous or kind and vice versa. Everyone who is not quiet or not creative is not old or humble and vice versa. Everyone who is both not old and not curious is both not curious and not quiet. Everyone who is both not creative and rich is both kind and not kind. If susan is not strong then someone is both kind and creative. If someone is not patient then someone is either not wise or not generous. Everyone who is tall is creative and vice versa. Everyone who is not happy or not humble is not brave or strong and vice versa. If paul is not brave or creative then susan is calm and vice versa. Everyone who is funny or not rich is both rich and not happy. Everyone who is wise is both not generous and not rich and vice versa. If someone is calm then fred is not strong. Everyone who is either funny or not patient is not brave and vice versa. Everyone who is either calm or not rich is either not quiet or not rich and vice versa. Everyone who is either patient or not rich is not kind and vice versa. Someone is both creative and not funny. Lucy is quiet. Someone is not rich or generous. Susan is not wise or funny. Susan is wise or not humble. Mary is either not creative or creative. | Susan is not strong. | neutral | ((?[X]:((~calm(X)<~>~wise(X))))<=>(?[X]:((~brave(X)&tall(X)))))&
(((brave(mary)|~humble(mary)))<=>(?[X]:((generous(X)<~>kind(X)))))&
(![X]:((~quiet(X)|~creative(X))<=>(~old(X)|humble(X))))&
(![X]:((~old(X)&~curious(X))=>(~curious(X)&~quiet(X))))&
(![X]:((~creative(X)&rich(X))=>(kind(X)&~kind(X))))&
((~strong(susan))=>(?[X]:((kind(X)&creative(X)))))&
((?[X]:(~patient(X)))=>(?[X]:((~wise(X)<~>~generous(X)))))&
(![X]:(tall(X)<=>creative(X)))&
(![X]:((~happy(X)|~humble(X))<=>(~brave(X)|strong(X))))&
(((~brave(paul)|creative(paul)))<=>(calm(susan)))&
(![X]:((funny(X)|~rich(X))=>(rich(X)&~happy(X))))&
(![X]:(wise(X)<=>(~generous(X)&~rich(X))))&
((?[X]:(calm(X)))=>(~strong(fred)))&
(![X]:((funny(X)<~>~patient(X))<=>~brave(X)))&
(![X]:((calm(X)<~>~rich(X))<=>(~quiet(X)<~>~rich(X))))&
(![X]:((patient(X)<~>~rich(X))<=>~kind(X)))&
(?[X]:((creative(X)&~funny(X))))&
(quiet(lucy))&
(?[X]:((~rich(X)|generous(X))))&
((~wise(susan)|funny(susan)))&
((wise(susan)|~humble(susan)))&
((~creative(mary)<~>creative(mary))) | ~strong(susan) | [] | null | 0 |
Everyone who is not quiet is both not rich and not generous.
Everyone who is old is both generous and not creative.
If fred is not funny then lucy is either old or curious.
Everyone who is not happy is either not humble or not quiet and vice versa.
Everyone who is either not humble or humble is both not wise and not happy and vice versa.
Everyone who is not patient is not creative or kind and vice versa.
Everyone who is not funny or not creative is curious and vice versa.
Everyone who is not rich or not happy is creative or not patient.
Everyone who is either not quiet or not calm is either not patient or calm and vice versa.
Everyone who is not happy or not curious is both not brave and generous.
Everyone who is both not creative and not happy is both not kind and funny and vice versa.
Everyone who is both funny and not brave is either not old or not strong.
If someone is not curious then someone is both quiet and patient.
If alice is both happy and funny then someone is patient.
Everyone who is either kind or not tall is rich and vice versa.
Everyone who is either not funny or brave is both not curious and not generous.
Someone is tall or not kind.
Someone is not brave.
Someone is either rich or wise.
Someone is not old.
Alice is either not tall or not patient. | Fred is humble. | contradiction | (![X]:(~quiet(X)=>(~rich(X)&~generous(X))))&
(![X]:(old(X)=>(generous(X)&~creative(X))))&
((~funny(fred))=>((old(lucy)<~>curious(lucy))))&
(![X]:(~happy(X)<=>(~humble(X)<~>~quiet(X))))&
(![X]:((~humble(X)<~>humble(X))<=>(~wise(X)&~happy(X))))&
(![X]:(~patient(X)<=>(~creative(X)|kind(X))))&
(![X]:((~funny(X)|~creative(X))<=>curious(X)))&
(![X]:((~rich(X)|~happy(X))=>(creative(X)|~patient(X))))&
(![X]:((~quiet(X)<~>~calm(X))<=>(~patient(X)<~>calm(X))))&
(![X]:((~happy(X)|~curious(X))=>(~brave(X)&generous(X))))&
(![X]:((~creative(X)&~happy(X))<=>(~kind(X)&funny(X))))&
(![X]:((funny(X)&~brave(X))=>(~old(X)<~>~strong(X))))&
((?[X]:(~curious(X)))=>(?[X]:((quiet(X)&patient(X)))))&
(((happy(alice)&funny(alice)))=>(?[X]:(patient(X))))&
(![X]:((kind(X)<~>~tall(X))<=>rich(X)))&
(![X]:((~funny(X)<~>brave(X))=>(~curious(X)&~generous(X))))&
(?[X]:((tall(X)|~kind(X))))&
(?[X]:(~brave(X)))&
(?[X]:((rich(X)<~>wise(X))))&
(?[X]:(~old(X)))&
((~tall(alice)<~>~patient(alice))) | humble(fred) | [
"p0",
"p3",
"p4",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 3900401605821222963548294
% SZS output start Proof for 3900401605821222963548294
1. ! [X0] : (~quiet(X0) => (~generous(X0) & ~rich(X0))) [input p0]
4. ! [X0] : (~happy(X0) <=> (~humble(X0) <~> ~quiet(X0))) [input p3]
5. ! [X0] : ((~humble(X0) <~> humble(X0)) <=> (~happy(X0) & ~wise(X0))) [input p4]
10. ! [X0] : ((~curious(X0) | ~happy(X0)) => (generous(X0) & ~brave(X0))) [input p9]
22. humble(fred) [input hypothesis]
24. ! [X0] : ((~generous(X0) & ~rich(X0)) | quiet(X0)) [ennf transformation 1]
29. ! [X0] : ((generous(X0) & ~brave(X0)) | (curious(X0) & happy(X0))) [ennf transformation 10]
37. ! [X0] : ((~happy(X0) | ((~humble(X0) | quiet(X0)) & (~quiet(X0) | humble(X0)))) & (((quiet(X0) | humble(X0)) & (~quiet(X0) | ~humble(X0))) | happy(X0))) [nnf transformation 4]
38. ! [X0] : ((((~humble(X0) | humble(X0)) & (humble(X0) | ~humble(X0))) | (happy(X0) | wise(X0))) & ((~happy(X0) & ~wise(X0)) | ((~humble(X0) | ~humble(X0)) & (humble(X0) | humble(X0))))) [nnf transformation 5]
39. ! [X0] : ((((~humble(X0) | humble(X0)) & (humble(X0) | ~humble(X0))) | happy(X0) | wise(X0)) & ((~happy(X0) & ~wise(X0)) | ((~humble(X0) | ~humble(X0)) & (humble(X0) | humble(X0))))) [flattening 38]
66. ~generous(X0) | quiet(X0) [cnf transformation 24]
71. ~humble(X0) | ~quiet(X0) | happy(X0) [cnf transformation 37]
77. ~happy(X0) | humble(X0) | humble(X0) [cnf transformation 39]
78. ~happy(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 39]
99. generous(X0) | happy(X0) [cnf transformation 29]
125. humble(fred) [cnf transformation 22]
132. ~happy(X0) | humble(X0) [duplicate literal removal 77]
133. ~humble(X0) | ~happy(X0) [duplicate literal removal 78]
148. ~happy(X0) [subsumption resolution 132,133]
152. generous(X0) [subsumption resolution 99,148]
196. quiet(X0) [resolution 66,152]
213. ~quiet(fred) | happy(fred) [resolution 71,125]
214. happy(fred) [subsumption resolution 213,196]
215. $false [subsumption resolution 214,148]
% SZS output end Proof for 3900401605821222963548294
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not rich is either not old or not rich and vice versa.
Everyone who is either not rich or not kind is either not brave or not funny and vice versa.
Everyone who is not kind or not funny is old or funny and vice versa.
If someone is funny then someone is either curious or not kind.
Everyone who is not strong or not funny is either not creative or tall and vice versa.
Everyone who is not tall or patient is both tall and not calm and vice versa.
Everyone who is either not strong or old is either not tall or kind and vice versa.
If john is both strong and not patient then lucy is either not tall or not kind.
Everyone who is not old is both tall and curious and vice versa.
If someone is not creative then someone is funny or rich and vice versa.
Everyone who is both not strong and not rich is either not wise or not funny.
Everyone who is not strong is both old and not patient and vice versa.
If susan is either not strong or quiet then alice is not tall or wise and vice versa.
Everyone who is either kind or not creative is generous or kind.
Everyone who is either wise or not brave is either calm or not calm.
If susan is calm then someone is either not patient or not kind.
Alice is not happy.
Someone is both not quiet and brave.
John is both creative and not curious.
Someone is either old or generous.
Someone is tall.
John is not rich.
Someone is not brave. | Alice is not kind. | neutral | (![X]:(~rich(X)<=>(~old(X)<~>~rich(X))))&
(![X]:((~rich(X)<~>~kind(X))<=>(~brave(X)<~>~funny(X))))&
(![X]:((~kind(X)|~funny(X))<=>(old(X)|funny(X))))&
((?[X]:(funny(X)))=>(?[X]:((curious(X)<~>~kind(X)))))&
(![X]:((~strong(X)|~funny(X))<=>(~creative(X)<~>tall(X))))&
(![X]:((~tall(X)|patient(X))<=>(tall(X)&~calm(X))))&
(![X]:((~strong(X)<~>old(X))<=>(~tall(X)<~>kind(X))))&
(((strong(john)&~patient(john)))=>((~tall(lucy)<~>~kind(lucy))))&
(![X]:(~old(X)<=>(tall(X)&curious(X))))&
((?[X]:(~creative(X)))<=>(?[X]:((funny(X)|rich(X)))))&
(![X]:((~strong(X)&~rich(X))=>(~wise(X)<~>~funny(X))))&
(![X]:(~strong(X)<=>(old(X)&~patient(X))))&
(((~strong(susan)<~>quiet(susan)))<=>((~tall(alice)|wise(alice))))&
(![X]:((kind(X)<~>~creative(X))=>(generous(X)|kind(X))))&
(![X]:((wise(X)<~>~brave(X))=>(calm(X)<~>~calm(X))))&
((calm(susan))=>(?[X]:((~patient(X)<~>~kind(X)))))&
(~happy(alice))&
(?[X]:((~quiet(X)&brave(X))))&
((creative(john)&~curious(john)))&
(?[X]:((old(X)<~>generous(X))))&
(?[X]:(tall(X)))&
(~rich(john))&
(?[X]:(~brave(X))) | ~kind(alice) | [] | null | 0 |
Everyone who is not wise or tall is both not rich and not humble and vice versa. Everyone who is either not strong or generous is both funny and brave. If john is brave then someone is either brave or not tall and vice versa. If someone is either patient or not humble then someone is humble or brave. If someone is either old or curious then someone is calm. Everyone who is happy is generous and vice versa. Everyone who is either not curious or patient is not old or rich and vice versa. If someone is generous then someone is both old and not strong. If someone is not quiet then lucy is either not old or not brave and vice versa. Everyone who is curious is not strong and vice versa. If mary is both curious and not calm then someone is not tall and vice versa. Everyone who is both rich and not funny is either tall or not brave and vice versa. Everyone who is not old or not tall is both generous and rich and vice versa. Everyone who is curious or not old is either not kind or not patient and vice versa. If someone is not generous or kind then susan is both curious and strong. If someone is both not old and wise then john is not calm or not curious and vice versa. Someone is not quiet or creative. Someone is funny or tall. Someone is either not calm or tall. | Mary is not curious. | contradiction | (![X]:((~wise(X)|tall(X))<=>(~rich(X)&~humble(X))))&
(![X]:((~strong(X)<~>generous(X))=>(funny(X)&brave(X))))&
((brave(john))<=>(?[X]:((brave(X)<~>~tall(X)))))&
((?[X]:((patient(X)<~>~humble(X))))=>(?[X]:((humble(X)|brave(X)))))&
((?[X]:((old(X)<~>curious(X))))=>(?[X]:(calm(X))))&
(![X]:(happy(X)<=>generous(X)))&
(![X]:((~curious(X)<~>patient(X))<=>(~old(X)|rich(X))))&
((?[X]:(generous(X)))=>(?[X]:((old(X)&~strong(X)))))&
((?[X]:(~quiet(X)))<=>((~old(lucy)<~>~brave(lucy))))&
(![X]:(curious(X)<=>~strong(X)))&
(((curious(mary)&~calm(mary)))<=>(?[X]:(~tall(X))))&
(![X]:((rich(X)&~funny(X))<=>(tall(X)<~>~brave(X))))&
(![X]:((~old(X)|~tall(X))<=>(generous(X)&rich(X))))&
(![X]:((curious(X)|~old(X))<=>(~kind(X)<~>~patient(X))))&
((?[X]:((~generous(X)|kind(X))))=>((curious(susan)&strong(susan))))&
((?[X]:((~old(X)&wise(X))))<=>((~calm(john)|~curious(john))))&
(?[X]:((~quiet(X)|creative(X))))&
(?[X]:((funny(X)|tall(X))))&
(?[X]:((~calm(X)<~>tall(X)))) | ~curious(mary) | [
"p0",
"p1",
"p9",
"p10",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 7095903649856584575497985
% SZS output start Proof for 7095903649856584575497985
1. ! [X0] : ((tall(X0) | ~wise(X0)) <=> (~humble(X0) & ~rich(X0))) [input p0]
2. ! [X0] : ((~strong(X0) <~> generous(X0)) => (brave(X0) & funny(X0))) [input p1]
10. ! [X0] : (curious(X0) <=> ~strong(X0)) [input p9]
11. (~calm(mary) & curious(mary)) <=> ? [X0] : ~tall(X0) [input p10]
12. ! [X0] : ((~funny(X0) & rich(X0)) <=> (tall(X0) <~> ~brave(X0))) [input p11]
15. ? [X0] : (kind(X0) | ~generous(X0)) => (strong(susan) & curious(susan)) [input p14]
20. ~curious(mary) [input hypothesis]
25. ! [X0] : ((brave(X0) & funny(X0)) | (~strong(X0) <=> generous(X0))) [ennf transformation 2]
29. (strong(susan) & curious(susan)) | ! [X0] : (~kind(X0) & generous(X0)) [ennf transformation 15]
30. ! [X0] : (((tall(X0) | ~wise(X0)) | (humble(X0) | rich(X0))) & ((~humble(X0) & ~rich(X0)) | (~tall(X0) & wise(X0)))) [nnf transformation 1]
31. ! [X0] : ((tall(X0) | ~wise(X0) | humble(X0) | rich(X0)) & ((~humble(X0) & ~rich(X0)) | (~tall(X0) & wise(X0)))) [flattening 30]
32. ! [X0] : ((brave(X0) & funny(X0)) | ((~strong(X0) | ~generous(X0)) & (generous(X0) | strong(X0)))) [nnf transformation 25]
54. ! [X0] : ((curious(X0) | strong(X0)) & (~strong(X0) | ~curious(X0))) [nnf transformation 10]
55. ((~calm(mary) & curious(mary)) | ! [X0] : tall(X0)) & (? [X0] : ~tall(X0) | (calm(mary) | ~curious(mary))) [nnf transformation 11]
56. ((~calm(mary) & curious(mary)) | ! [X0] : tall(X0)) & (? [X0] : ~tall(X0) | calm(mary) | ~curious(mary)) [flattening 55]
57. ((~calm(mary) & curious(mary)) | ! [X0] : tall(X0)) & (? [X1] : ~tall(X1) | calm(mary) | ~curious(mary)) [rectify 56]
58. ? [X1] : ~tall(X1) => ~tall(sK5) [choice axiom]
59. ((~calm(mary) & curious(mary)) | ! [X0] : tall(X0)) & (~tall(sK5) | calm(mary) | ~curious(mary)) [skolemisation 57,58]
60. ! [X0] : (((~funny(X0) & rich(X0)) | ((tall(X0) | brave(X0)) & (~brave(X0) | ~tall(X0)))) & (((brave(X0) | ~tall(X0)) & (~brave(X0) | tall(X0))) | (funny(X0) | ~rich(X0)))) [nnf transformation 12]
61. ! [X0] : (((~funny(X0) & rich(X0)) | ((tall(X0) | brave(X0)) & (~brave(X0) | ~tall(X0)))) & (((brave(X0) | ~tall(X0)) & (~brave(X0) | tall(X0))) | funny(X0) | ~rich(X0))) [flattening 60]
77. ~rich(X0) | ~tall(X0) [cnf transformation 31]
84. ~generous(X0) | ~strong(X0) | brave(X0) [cnf transformation 32]
105. ~curious(X0) | ~strong(X0) [cnf transformation 54]
106. curious(X0) | strong(X0) [cnf transformation 54]
108. curious(mary) | tall(X0) [cnf transformation 59]
112. rich(X0) | ~brave(X0) | ~tall(X0) [cnf transformation 61]
127. curious(susan) | generous(X0) [cnf transformation 29]
129. strong(susan) | generous(X0) [cnf transformation 29]
139. ~curious(mary) [cnf transformation 20]
149. 3 <=> ! [X0] : (~tall(X0) | ~brave(X0)) [avatar definition]
150. ~tall(X0) | ~brave(X0) <- (3) [avatar component clause 149]
223. 20 <=> ! [X0] : tall(X0) [avatar definition]
224. tall(X0) <- (20) [avatar component clause 223]
231. 22 <=> curious(mary) [avatar definition]
232. ~curious(mary) <- (~22) [avatar component clause 231]
234. 20 | 22 [avatar split clause 108,231,223]
240. ~brave(X0) | ~tall(X0) [subsumption resolution 112,77]
241. 3 [avatar split clause 240,149]
248. 25 <=> strong(susan) [avatar definition]
250. strong(susan) <- (25) [avatar component clause 248]
253. 26 <=> ! [X0] : generous(X0) [avatar definition]
254. generous(X0) <- (26) [avatar component clause 253]
255. 26 | 25 [avatar split clause 129,248,253]
257. 27 <=> curious(susan) [avatar definition]
259. curious(susan) <- (27) [avatar component clause 257]
261. 26 | 27 [avatar split clause 127,257,253]
305. ~22 [avatar split clause 139,231]
310. ~brave(X0) <- (3, 20) [subsumption resolution 150,224]
323. strong(mary) <- (~22) [resolution 106,232]
342. ~strong(X1) | brave(X1) <- (26) [resolution 84,254]
343. ~strong(X1) <- (3, 20, 26) [subsumption resolution 342,310]
344. $false <- (3, 20, ~22, 26) [resolution 343,323]
345. ~3 | ~20 | 22 | ~26 [avatar contradiction clause 344]
346. ~strong(susan) <- (27) [resolution 259,105]
347. $false <- (25, 27) [subsumption resolution 346,250]
348. ~25 | ~27 [avatar contradiction clause 347]
349. $false [avatar sat refutation 234,241,255,261,305,345,348]
% SZS output end Proof for 7095903649856584575497985
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both curious and not generous is either old or tall and vice versa.
Everyone who is either not happy or not brave is both not wise and not brave.
Everyone who is both not humble and happy is either not funny or not generous.
If someone is either curious or rich then susan is either not humble or not rich and vice versa.
If someone is quiet then alice is rich and vice versa.
If lucy is creative then someone is not brave or not rich and vice versa.
Everyone who is both funny and not creative is either not rich or strong and vice versa.
If someone is either not generous or not kind then mary is either wise or not calm and vice versa.
Everyone who is both quiet and kind is not funny and vice versa.
Everyone who is either not kind or not strong is not creative or not happy.
Everyone who is both not calm and not strong is either not patient or not generous and vice versa.
Everyone who is either not tall or not generous is curious or not generous and vice versa.
If susan is not quiet or humble then someone is both not rich and not generous and vice versa.
Everyone who is quiet or calm is not calm.
Everyone who is old or not happy is creative or not creative and vice versa.
If mary is both not curious and quiet then someone is kind.
Someone is either happy or not generous.
Paul is either creative or not brave.
John is not old or not funny.
Someone is both patient and quiet.
Someone is funny.
Someone is quiet.
Someone is not tall or not brave. | Alice is patient. | neutral | (![X]:((curious(X)&~generous(X))<=>(old(X)<~>tall(X))))&
(![X]:((~happy(X)<~>~brave(X))=>(~wise(X)&~brave(X))))&
(![X]:((~humble(X)&happy(X))=>(~funny(X)<~>~generous(X))))&
((?[X]:((curious(X)<~>rich(X))))<=>((~humble(susan)<~>~rich(susan))))&
((?[X]:(quiet(X)))<=>(rich(alice)))&
((creative(lucy))<=>(?[X]:((~brave(X)|~rich(X)))))&
(![X]:((funny(X)&~creative(X))<=>(~rich(X)<~>strong(X))))&
((?[X]:((~generous(X)<~>~kind(X))))<=>((wise(mary)<~>~calm(mary))))&
(![X]:((quiet(X)&kind(X))<=>~funny(X)))&
(![X]:((~kind(X)<~>~strong(X))=>(~creative(X)|~happy(X))))&
(![X]:((~calm(X)&~strong(X))<=>(~patient(X)<~>~generous(X))))&
(![X]:((~tall(X)<~>~generous(X))<=>(curious(X)|~generous(X))))&
(((~quiet(susan)|humble(susan)))<=>(?[X]:((~rich(X)&~generous(X)))))&
(![X]:((quiet(X)|calm(X))=>~calm(X)))&
(![X]:((old(X)|~happy(X))<=>(creative(X)|~creative(X))))&
(((~curious(mary)&quiet(mary)))=>(?[X]:(kind(X))))&
(?[X]:((happy(X)<~>~generous(X))))&
((creative(paul)<~>~brave(paul)))&
((~old(john)|~funny(john)))&
(?[X]:((patient(X)&quiet(X))))&
(?[X]:(funny(X)))&
(?[X]:(quiet(X)))&
(?[X]:((~tall(X)|~brave(X)))) | patient(alice) | [] | null | 0 |
If lucy is creative or wise then fred is either calm or not kind.
Everyone who is either creative or happy is both not creative and not rich and vice versa.
If someone is both strong and kind then alice is kind or not curious.
If alice is both generous and brave then someone is either curious or not generous and vice versa.
If mary is either not humble or creative then fred is not kind.
Everyone who is both not funny and not old is both not funny and old and vice versa.
If someone is either not happy or not calm then someone is both patient and not humble and vice versa.
Everyone who is not curious is both patient and not calm.
Everyone who is both humble and patient is either not calm or not rich.
Everyone who is not creative is both not curious and kind and vice versa.
If alice is both not creative and not generous then someone is either calm or happy.
Everyone who is either curious or not kind is quiet.
If someone is both not calm and happy then someone is patient or not wise and vice versa.
If someone is not happy or brave then someone is both not curious and not patient.
If mary is patient or not old then lucy is happy or not kind and vice versa.
John is either not rich or strong.
Susan is both rich and wise.
Susan is not kind or rich.
Mary is curious.
Someone is either tall or not kind.
Someone is tall. | John is funny. | entailment | (((creative(lucy)|wise(lucy)))=>((calm(fred)<~>~kind(fred))))&
(![X]:((creative(X)<~>happy(X))<=>(~creative(X)&~rich(X))))&
((?[X]:((strong(X)&kind(X))))=>((kind(alice)|~curious(alice))))&
(((generous(alice)&brave(alice)))<=>(?[X]:((curious(X)<~>~generous(X)))))&
(((~humble(mary)<~>creative(mary)))=>(~kind(fred)))&
(![X]:((~funny(X)&~old(X))<=>(~funny(X)&old(X))))&
((?[X]:((~happy(X)<~>~calm(X))))<=>(?[X]:((patient(X)&~humble(X)))))&
(![X]:(~curious(X)=>(patient(X)&~calm(X))))&
(![X]:((humble(X)&patient(X))=>(~calm(X)<~>~rich(X))))&
(![X]:(~creative(X)<=>(~curious(X)&kind(X))))&
(((~creative(alice)&~generous(alice)))=>(?[X]:((calm(X)<~>happy(X)))))&
(![X]:((curious(X)<~>~kind(X))=>quiet(X)))&
((?[X]:((~calm(X)&happy(X))))<=>(?[X]:((patient(X)|~wise(X)))))&
((?[X]:((~happy(X)|brave(X))))=>(?[X]:((~curious(X)&~patient(X)))))&
(((patient(mary)|~old(mary)))<=>((happy(lucy)|~kind(lucy))))&
((~rich(john)<~>strong(john)))&
((rich(susan)&wise(susan)))&
((~kind(susan)|rich(susan)))&
(curious(mary))&
(?[X]:((tall(X)<~>~kind(X))))&
(?[X]:(tall(X))) | funny(john) | [
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 6484926934433959580215948
% SZS output start Proof for 6484926934433959580215948
6. ! [X0] : ((~old(X0) & ~funny(X0)) <=> (old(X0) & ~funny(X0))) [input p5]
22. ~funny(john) [input hypothesis]
46. ! [X0] : (((~old(X0) & ~funny(X0)) | (~old(X0) | funny(X0))) & ((old(X0) & ~funny(X0)) | (old(X0) | funny(X0)))) [nnf transformation 6]
47. ! [X0] : (((~old(X0) & ~funny(X0)) | ~old(X0) | funny(X0)) & ((old(X0) & ~funny(X0)) | old(X0) | funny(X0))) [flattening 46]
95. old(X0) | old(X0) | funny(X0) [cnf transformation 47]
97. ~old(X0) | ~old(X0) | funny(X0) [cnf transformation 47]
135. ~funny(john) [cnf transformation 22]
136. old(X0) | funny(X0) [duplicate literal removal 95]
137. ~old(X0) | funny(X0) [duplicate literal removal 97]
210. funny(X0) [subsumption resolution 136,137]
341. $false [subsumption resolution 135,210]
% SZS output end Proof for 6484926934433959580215948
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not creative and not generous is both generous and not patient. If someone is both not curious and quiet then someone is both funny and calm. Everyone who is quiet is either not tall or quiet and vice versa. If someone is quiet or not kind then fred is either not creative or curious and vice versa. Everyone who is either creative or not happy is either not tall or not brave and vice versa. Everyone who is generous is not humble or not quiet and vice versa. If mary is humble then someone is not tall. Everyone who is both not happy and calm is not kind. Everyone who is both not strong and not patient is not creative and vice versa. Everyone who is happy or not tall is both curious and not generous. Everyone who is strong is not tall and vice versa. If paul is strong or not strong then fred is either not quiet or strong. Everyone who is patient or happy is both not creative and not brave. If someone is both not funny and generous then someone is either tall or not curious and vice versa. If someone is happy then alice is wise and vice versa. If fred is not funny then lucy is both not happy and rich. Someone is both wise and not calm. Alice is either not humble or not happy. Alice is not brave or not happy. Someone is either not old or curious. Someone is either not old or not patient. Someone is not kind. Someone is not brave. | Lucy is not tall. | contradiction | (![X]:((~creative(X)&~generous(X))=>(generous(X)&~patient(X))))&
((?[X]:((~curious(X)&quiet(X))))=>(?[X]:((funny(X)&calm(X)))))&
(![X]:(quiet(X)<=>(~tall(X)<~>quiet(X))))&
((?[X]:((quiet(X)|~kind(X))))<=>((~creative(fred)<~>curious(fred))))&
(![X]:((creative(X)<~>~happy(X))<=>(~tall(X)<~>~brave(X))))&
(![X]:(generous(X)<=>(~humble(X)|~quiet(X))))&
((humble(mary))=>(?[X]:(~tall(X))))&
(![X]:((~happy(X)&calm(X))=>~kind(X)))&
(![X]:((~strong(X)&~patient(X))<=>~creative(X)))&
(![X]:((happy(X)|~tall(X))=>(curious(X)&~generous(X))))&
(![X]:(strong(X)<=>~tall(X)))&
(((strong(paul)|~strong(paul)))=>((~quiet(fred)<~>strong(fred))))&
(![X]:((patient(X)|happy(X))=>(~creative(X)&~brave(X))))&
((?[X]:((~funny(X)&generous(X))))<=>(?[X]:((tall(X)<~>~curious(X)))))&
((?[X]:(happy(X)))<=>(wise(alice)))&
((~funny(fred))=>((~happy(lucy)&rich(lucy))))&
(?[X]:((wise(X)&~calm(X))))&
((~humble(alice)<~>~happy(alice)))&
((~brave(alice)|~happy(alice)))&
(?[X]:((~old(X)<~>curious(X))))&
(?[X]:((~old(X)<~>~patient(X))))&
(?[X]:(~kind(X)))&
(?[X]:(~brave(X))) | ~tall(lucy) | [
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 7662617860330325114381005
% SZS output start Proof for 7662617860330325114381005
3. ! [X0] : (quiet(X0) <=> (~tall(X0) <~> quiet(X0))) [input p2]
24. ~tall(lucy) [input hypothesis]
41. ! [X0] : ((quiet(X0) | ((~tall(X0) | ~quiet(X0)) & (quiet(X0) | tall(X0)))) & (((~quiet(X0) | tall(X0)) & (quiet(X0) | ~tall(X0))) | ~quiet(X0))) [nnf transformation 3]
82. ~quiet(X0) | tall(X0) | ~quiet(X0) [cnf transformation 41]
83. quiet(X0) | quiet(X0) | tall(X0) [cnf transformation 41]
141. ~tall(lucy) [cnf transformation 24]
142. ~quiet(X0) | tall(X0) [duplicate literal removal 82]
143. quiet(X0) | tall(X0) [duplicate literal removal 83]
158. tall(X0) [subsumption resolution 142,143]
263. $false [subsumption resolution 141,158]
% SZS output end Proof for 7662617860330325114381005
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not calm and not funny is both not strong and not funny. Everyone who is curious is quiet. Everyone who is not old is happy or rich and vice versa. If mary is not curious or patient then alice is tall or strong. If someone is either tall or brave then susan is kind or not brave and vice versa. Everyone who is not tall is either calm or not funny and vice versa. If someone is calm then john is rich or not quiet. Everyone who is not curious is old. Everyone who is kind is not brave or not funny and vice versa. If fred is not kind then someone is not humble and vice versa. If someone is not tall or curious then someone is either strong or not kind and vice versa. Everyone who is either calm or not kind is either wise or humble and vice versa. If someone is not old then someone is not happy. If john is either not kind or creative then fred is both patient and not quiet. If someone is both not old and not calm then someone is either not rich or strong. Everyone who is either not funny or not wise is not strong. Someone is not funny or not tall. Someone is both old and not creative. Lucy is not kind or not wise. Someone is quiet or curious. Someone is not brave or strong. Someone is both not wise and not calm. Someone is patient. Mary is calm. | Mary is not curious. | neutral | (![X]:((~calm(X)&~funny(X))=>(~strong(X)&~funny(X))))&
(![X]:(curious(X)=>quiet(X)))&
(![X]:(~old(X)<=>(happy(X)|rich(X))))&
(((~curious(mary)|patient(mary)))=>((tall(alice)|strong(alice))))&
((?[X]:((tall(X)<~>brave(X))))<=>((kind(susan)|~brave(susan))))&
(![X]:(~tall(X)<=>(calm(X)<~>~funny(X))))&
((?[X]:(calm(X)))=>((rich(john)|~quiet(john))))&
(![X]:(~curious(X)=>old(X)))&
(![X]:(kind(X)<=>(~brave(X)|~funny(X))))&
((~kind(fred))<=>(?[X]:(~humble(X))))&
((?[X]:((~tall(X)|curious(X))))<=>(?[X]:((strong(X)<~>~kind(X)))))&
(![X]:((calm(X)<~>~kind(X))<=>(wise(X)<~>humble(X))))&
((?[X]:(~old(X)))=>(?[X]:(~happy(X))))&
(((~kind(john)<~>creative(john)))=>((patient(fred)&~quiet(fred))))&
((?[X]:((~old(X)&~calm(X))))=>(?[X]:((~rich(X)<~>strong(X)))))&
(![X]:((~funny(X)<~>~wise(X))=>~strong(X)))&
(?[X]:((~funny(X)|~tall(X))))&
(?[X]:((old(X)&~creative(X))))&
((~kind(lucy)|~wise(lucy)))&
(?[X]:((quiet(X)|curious(X))))&
(?[X]:((~brave(X)|strong(X))))&
(?[X]:((~wise(X)&~calm(X))))&
(?[X]:(patient(X)))&
(calm(mary)) | ~curious(mary) | [] | null | 0 |
Everyone who is both wise and not rich is quiet and vice versa.
Everyone who is not rich or rich is not calm and vice versa.
If alice is either not calm or rich then someone is both not humble and funny.
If alice is old or not tall then paul is not wise.
If someone is either not patient or rich then lucy is tall or not humble.
If someone is patient then lucy is kind.
If someone is not patient or kind then john is both not rich and not curious and vice versa.
If someone is patient then alice is either creative or happy.
If susan is calm then alice is kind.
If lucy is either not calm or not old then someone is both not tall and not strong and vice versa.
If fred is either tall or not tall then paul is not rich or not curious and vice versa.
If alice is curious or not wise then lucy is not kind.
If someone is not strong or quiet then someone is either not creative or patient.
If someone is funny then mary is happy.
Everyone who is either brave or tall is not rich and vice versa.
Someone is both funny and curious.
Someone is either not rich or not quiet.
Someone is both not creative and brave.
Someone is not humble.
Someone is wise.
Someone is both kind and curious. | Alice is old. | neutral | (![X]:((wise(X)&~rich(X))<=>quiet(X)))&
(![X]:((~rich(X)|rich(X))<=>~calm(X)))&
(((~calm(alice)<~>rich(alice)))=>(?[X]:((~humble(X)&funny(X)))))&
(((old(alice)|~tall(alice)))=>(~wise(paul)))&
((?[X]:((~patient(X)<~>rich(X))))=>((tall(lucy)|~humble(lucy))))&
((?[X]:(patient(X)))=>(kind(lucy)))&
((?[X]:((~patient(X)|kind(X))))<=>((~rich(john)&~curious(john))))&
((?[X]:(patient(X)))=>((creative(alice)<~>happy(alice))))&
((calm(susan))=>(kind(alice)))&
(((~calm(lucy)<~>~old(lucy)))<=>(?[X]:((~tall(X)&~strong(X)))))&
(((tall(fred)<~>~tall(fred)))<=>((~rich(paul)|~curious(paul))))&
(((curious(alice)|~wise(alice)))=>(~kind(lucy)))&
((?[X]:((~strong(X)|quiet(X))))=>(?[X]:((~creative(X)<~>patient(X)))))&
((?[X]:(funny(X)))=>(happy(mary)))&
(![X]:((brave(X)<~>tall(X))<=>~rich(X)))&
(?[X]:((funny(X)&curious(X))))&
(?[X]:((~rich(X)<~>~quiet(X))))&
(?[X]:((~creative(X)&brave(X))))&
(?[X]:(~humble(X)))&
(?[X]:(wise(X)))&
(?[X]:((kind(X)&curious(X)))) | old(alice) | [] | null | 0 |
If john is not brave or not strong then someone is funny.
Everyone who is either strong or curious is not strong or brave and vice versa.
Everyone who is creative or kind is not happy.
If someone is both not generous and not curious then lucy is not generous or not wise.
Everyone who is either calm or not brave is not creative or not calm.
If someone is both not brave and quiet then lucy is either not old or not creative and vice versa.
Everyone who is humble is either rich or kind and vice versa.
If someone is not old or strong then someone is not wise or not strong.
If someone is humble then someone is not quiet.
If someone is rich or not funny then susan is not rich or not calm.
Everyone who is both not humble and strong is either kind or strong.
If someone is humble or strong then john is both not wise and rich.
Everyone who is happy or brave is both not rich and happy.
If someone is not quiet or not kind then alice is not humble or quiet.
If someone is either calm or happy then alice is not quiet or not rich and vice versa.
Everyone who is both happy and curious is wise or rich and vice versa.
Someone is either not old or not generous.
John is either brave or not curious.
Someone is not wise or not curious.
Someone is both not creative and not funny.
Someone is either strong or not rich.
Someone is both curious and not rich.
Someone is brave or not kind. | John is not creative. | entailment | (((~brave(john)|~strong(john)))=>(?[X]:(funny(X))))&
(![X]:((strong(X)<~>curious(X))<=>(~strong(X)|brave(X))))&
(![X]:((creative(X)|kind(X))=>~happy(X)))&
((?[X]:((~generous(X)&~curious(X))))=>((~generous(lucy)|~wise(lucy))))&
(![X]:((calm(X)<~>~brave(X))=>(~creative(X)|~calm(X))))&
((?[X]:((~brave(X)&quiet(X))))<=>((~old(lucy)<~>~creative(lucy))))&
(![X]:(humble(X)<=>(rich(X)<~>kind(X))))&
((?[X]:((~old(X)|strong(X))))=>(?[X]:((~wise(X)|~strong(X)))))&
((?[X]:(humble(X)))=>(?[X]:(~quiet(X))))&
((?[X]:((rich(X)|~funny(X))))=>((~rich(susan)|~calm(susan))))&
(![X]:((~humble(X)&strong(X))=>(kind(X)<~>strong(X))))&
((?[X]:((humble(X)|strong(X))))=>((~wise(john)&rich(john))))&
(![X]:((happy(X)|brave(X))=>(~rich(X)&happy(X))))&
((?[X]:((~quiet(X)|~kind(X))))=>((~humble(alice)|quiet(alice))))&
((?[X]:((calm(X)<~>happy(X))))<=>((~quiet(alice)|~rich(alice))))&
(![X]:((happy(X)&curious(X))<=>(wise(X)|rich(X))))&
(?[X]:((~old(X)<~>~generous(X))))&
((brave(john)<~>~curious(john)))&
(?[X]:((~wise(X)|~curious(X))))&
(?[X]:((~creative(X)&~funny(X))))&
(?[X]:((strong(X)<~>~rich(X))))&
(?[X]:((curious(X)&~rich(X))))&
(?[X]:((brave(X)|~kind(X)))) | ~creative(john) | [
"p1",
"p2",
"p12",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 741139129589794078344598
% SZS output start Proof for 741139129589794078344598
2. ! [X0] : ((strong(X0) <~> curious(X0)) <=> (brave(X0) | ~strong(X0))) [input p1]
3. ! [X0] : ((kind(X0) | creative(X0)) => ~happy(X0)) [input p2]
13. ! [X0] : ((brave(X0) | happy(X0)) => (happy(X0) & ~rich(X0))) [input p12]
18. brave(john) <~> ~curious(john) [input p17]
24. creative(john) [input hypothesis]
28. ! [X0] : (~happy(X0) | (~kind(X0) & ~creative(X0))) [ennf transformation 3]
40. ! [X0] : ((happy(X0) & ~rich(X0)) | (~brave(X0) & ~happy(X0))) [ennf transformation 13]
45. ! [X0] : ((((~curious(X0) | ~strong(X0)) & (curious(X0) | strong(X0))) | (~brave(X0) & strong(X0))) & ((brave(X0) | ~strong(X0)) | ((strong(X0) | ~curious(X0)) & (curious(X0) | ~strong(X0))))) [nnf transformation 2]
46. ! [X0] : ((((~curious(X0) | ~strong(X0)) & (curious(X0) | strong(X0))) | (~brave(X0) & strong(X0))) & (brave(X0) | ~strong(X0) | ((strong(X0) | ~curious(X0)) & (curious(X0) | ~strong(X0))))) [flattening 45]
70. (curious(john) | ~brave(john)) & (~curious(john) | brave(john)) [nnf transformation 18]
84. brave(X0) | ~strong(X0) | curious(X0) | ~strong(X0) [cnf transformation 46]
86. curious(X0) | strong(X0) | strong(X0) [cnf transformation 46]
90. ~happy(X0) | ~creative(X0) [cnf transformation 28]
119. ~brave(X0) | happy(X0) [cnf transformation 40]
135. ~curious(john) | brave(john) [cnf transformation 70]
136. curious(john) | ~brave(john) [cnf transformation 70]
145. creative(john) [cnf transformation 24]
148. brave(X0) | ~strong(X0) | curious(X0) [duplicate literal removal 84]
149. curious(X0) | strong(X0) [duplicate literal removal 86]
160. 3 <=> brave(john) [avatar definition]
162. brave(john) <- (3) [avatar component clause 160]
164. brave(X0) | curious(X0) [subsumption resolution 148,149]
307. curious(john) [subsumption resolution 136,164]
308. brave(john) [subsumption resolution 135,307]
309. 3 [avatar split clause 308,160]
330. happy(john) <- (3) [resolution 119,162]
332. ~creative(john) <- (3) [resolution 330,90]
333. $false <- (3) [subsumption resolution 332,145]
334. ~3 [avatar contradiction clause 333]
335. $false [avatar sat refutation 309,334]
% SZS output end Proof for 741139129589794078344598
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not creative then someone is both quiet and tall.
Everyone who is either not old or not funny is strong or not generous.
Everyone who is either not humble or not funny is either calm or creative and vice versa.
Everyone who is not patient or not humble is either humble or not happy and vice versa.
If someone is both not strong and calm then someone is patient.
If mary is kind or not brave then fred is both old and not kind.
Everyone who is both not calm and not curious is both not patient and calm.
If someone is either kind or tall then someone is not quiet or brave.
If mary is either curious or not humble then mary is both not tall and not humble and vice versa.
Everyone who is quiet or kind is both not creative and not rich.
If susan is either tall or not wise then someone is rich or not quiet.
Everyone who is both not calm and not creative is either funny or not quiet and vice versa.
Everyone who is both not happy and strong is either brave or rich and vice versa.
Everyone who is curious or not rich is not humble.
If fred is brave or not funny then someone is both patient and wise.
Everyone who is creative is either not generous or not funny.
Someone is either not old or humble.
Lucy is either quiet or curious.
Susan is both calm and not quiet.
Fred is either not strong or funny.
Someone is either happy or rich.
Someone is wise.
Mary is either rich or brave. | Susan is generous. | contradiction | ((?[X]:(~creative(X)))=>(?[X]:((quiet(X)&tall(X)))))&
(![X]:((~old(X)<~>~funny(X))=>(strong(X)|~generous(X))))&
(![X]:((~humble(X)<~>~funny(X))<=>(calm(X)<~>creative(X))))&
(![X]:((~patient(X)|~humble(X))<=>(humble(X)<~>~happy(X))))&
((?[X]:((~strong(X)&calm(X))))=>(?[X]:(patient(X))))&
(((kind(mary)|~brave(mary)))=>((old(fred)&~kind(fred))))&
(![X]:((~calm(X)&~curious(X))=>(~patient(X)&calm(X))))&
((?[X]:((kind(X)<~>tall(X))))=>(?[X]:((~quiet(X)|brave(X)))))&
(((curious(mary)<~>~humble(mary)))<=>((~tall(mary)&~humble(mary))))&
(![X]:((quiet(X)|kind(X))=>(~creative(X)&~rich(X))))&
(((tall(susan)<~>~wise(susan)))=>(?[X]:((rich(X)|~quiet(X)))))&
(![X]:((~calm(X)&~creative(X))<=>(funny(X)<~>~quiet(X))))&
(![X]:((~happy(X)&strong(X))<=>(brave(X)<~>rich(X))))&
(![X]:((curious(X)|~rich(X))=>~humble(X)))&
(((brave(fred)|~funny(fred)))=>(?[X]:((patient(X)&wise(X)))))&
(![X]:(creative(X)=>(~generous(X)<~>~funny(X))))&
(?[X]:((~old(X)<~>humble(X))))&
((quiet(lucy)<~>curious(lucy)))&
((calm(susan)&~quiet(susan)))&
((~strong(fred)<~>funny(fred)))&
(?[X]:((happy(X)<~>rich(X))))&
(?[X]:(wise(X)))&
((rich(mary)<~>brave(mary))) | generous(susan) | [
"p0",
"p2",
"p6",
"p9",
"p11",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1218668802375364206375609
% SZS output start Proof for 1218668802375364206375609
1. ? [X0] : ~creative(X0) => ? [X0] : (tall(X0) & quiet(X0)) [input p0]
3. ! [X0] : ((~humble(X0) <~> ~funny(X0)) <=> (calm(X0) <~> creative(X0))) [input p2]
7. ! [X0] : ((~curious(X0) & ~calm(X0)) => (calm(X0) & ~patient(X0))) [input p6]
10. ! [X0] : ((kind(X0) | quiet(X0)) => (~rich(X0) & ~creative(X0))) [input p9]
12. ! [X0] : ((~creative(X0) & ~calm(X0)) <=> (funny(X0) <~> ~quiet(X0))) [input p11]
14. ! [X0] : ((~rich(X0) | curious(X0)) => ~humble(X0)) [input p13]
16. ! [X0] : (creative(X0) => (~generous(X0) <~> ~funny(X0))) [input p15]
24. generous(susan) [input hypothesis]
25. ? [X0] : ~creative(X0) => ? [X1] : (tall(X1) & quiet(X1)) [rectify 1]
28. ? [X1] : (tall(X1) & quiet(X1)) | ! [X0] : creative(X0) [ennf transformation 25]
33. ! [X0] : ((calm(X0) & ~patient(X0)) | (curious(X0) | calm(X0))) [ennf transformation 7]
34. ! [X0] : ((calm(X0) & ~patient(X0)) | curious(X0) | calm(X0)) [flattening 33]
36. ! [X0] : ((~rich(X0) & ~creative(X0)) | (~kind(X0) & ~quiet(X0))) [ennf transformation 10]
38. ! [X0] : (~humble(X0) | (rich(X0) & ~curious(X0))) [ennf transformation 14]
40. ! [X0] : ((~generous(X0) <~> ~funny(X0)) | ~creative(X0)) [ennf transformation 16]
41. ? [X0] : (tall(X0) & quiet(X0)) | ! [X1] : creative(X1) [rectify 28]
42. ? [X0] : (tall(X0) & quiet(X0)) => (tall(sK0) & quiet(sK0)) [choice axiom]
43. (tall(sK0) & quiet(sK0)) | ! [X1] : creative(X1) [skolemisation 41,42]
45. ! [X0] : ((((funny(X0) | humble(X0)) & (~funny(X0) | ~humble(X0))) | ((calm(X0) | ~creative(X0)) & (creative(X0) | ~calm(X0)))) & (((~creative(X0) | ~calm(X0)) & (creative(X0) | calm(X0))) | ((~humble(X0) | funny(X0)) & (~funny(X0) | humble(X0))))) [nnf transformation 3]
60. ! [X0] : (((~creative(X0) & ~calm(X0)) | ((funny(X0) | quiet(X0)) & (~quiet(X0) | ~funny(X0)))) & (((quiet(X0) | ~funny(X0)) & (~quiet(X0) | funny(X0))) | (creative(X0) | calm(X0)))) [nnf transformation 12]
61. ! [X0] : (((~creative(X0) & ~calm(X0)) | ((funny(X0) | quiet(X0)) & (~quiet(X0) | ~funny(X0)))) & (((quiet(X0) | ~funny(X0)) & (~quiet(X0) | funny(X0))) | creative(X0) | calm(X0))) [flattening 60]
66. ! [X0] : (((funny(X0) | generous(X0)) & (~funny(X0) | ~generous(X0))) | ~creative(X0)) [nnf transformation 40]
78. quiet(sK0) | creative(X1) [cnf transformation 43]
82. ~funny(X0) | calm(X0) | creative(X0) | humble(X0) [cnf transformation 45]
88. ~calm(X0) | humble(X0) | creative(X0) | funny(X0) [cnf transformation 45]
102. calm(X0) | curious(X0) | calm(X0) [cnf transformation 34]
111. ~quiet(X0) | ~creative(X0) [cnf transformation 36]
113. ~rich(X0) | ~quiet(X0) [cnf transformation 36]
117. ~quiet(X0) | funny(X0) | creative(X0) | calm(X0) [cnf transformation 61]
119. ~calm(X0) | ~quiet(X0) | ~funny(X0) [cnf transformation 61]
122. ~creative(X0) | funny(X0) | quiet(X0) [cnf transformation 61]
129. ~curious(X0) | ~humble(X0) [cnf transformation 38]
130. ~humble(X0) | rich(X0) [cnf transformation 38]
135. ~funny(X0) | ~generous(X0) | ~creative(X0) [cnf transformation 66]
150. generous(susan) [cnf transformation 24]
153. curious(X0) | calm(X0) [duplicate literal removal 102]
157. 1 <=> ! [X1] : creative(X1) [avatar definition]
158. creative(X1) <- (1) [avatar component clause 157]
165. 3 <=> quiet(sK0) [avatar definition]
167. quiet(sK0) <- (3) [avatar component clause 165]
168. 1 | 3 [avatar split clause 78,165,157]
245. ~creative(X0) | funny(X0) [subsumption resolution 122,111]
246. ~quiet(X0) | funny(X0) | calm(X0) [subsumption resolution 117,245]
267. ~generous(X0) | ~creative(X0) [subsumption resolution 135,245]
314. ~humble(X0) | calm(X0) [resolution 153,129]
324. ~creative(susan) [resolution 267,150]
363. 36 <=> calm(sK0) [avatar definition]
364. ~calm(sK0) <- (~36) [avatar component clause 363]
365. calm(sK0) <- (36) [avatar component clause 363]
367. 37 <=> funny(sK0) [avatar definition]
368. ~funny(sK0) <- (~37) [avatar component clause 367]
369. funny(sK0) <- (37) [avatar component clause 367]
372. $false <- (1) [resolution 158,324]
375. ~1 [avatar contradiction clause 372]
376. funny(sK0) | calm(sK0) <- (3) [resolution 167,246]
377. ~creative(sK0) <- (3) [resolution 167,111]
379. ~quiet(sK0) | ~funny(sK0) <- (36) [resolution 365,119]
381. ~funny(sK0) <- (3, 36) [subsumption resolution 379,167]
382. ~37 | ~3 | ~36 [avatar split clause 381,363,165,367]
399. humble(sK0) | creative(sK0) | funny(sK0) <- (36) [resolution 88,365]
402. humble(sK0) | funny(sK0) <- (3, 36) [subsumption resolution 399,377]
403. humble(sK0) <- (3, 36, ~37) [subsumption resolution 402,368]
424. rich(sK0) <- (3, 36, ~37) [resolution 403,130]
471. ~quiet(sK0) <- (3, 36, ~37) [resolution 424,113]
479. $false <- (3, 36, ~37) [subsumption resolution 471,167]
480. ~3 | ~36 | 37 [avatar contradiction clause 479]
481. 36 | 37 | ~3 [avatar split clause 376,165,367,363]
483. calm(sK0) | creative(sK0) | humble(sK0) <- (37) [resolution 369,82]
484. creative(sK0) | humble(sK0) <- (~36, 37) [subsumption resolution 483,364]
485. humble(sK0) <- (3, ~36, 37) [subsumption resolution 484,377]
486. calm(sK0) <- (3, ~36, 37) [resolution 485,314]
491. $false <- (3, ~36, 37) [subsumption resolution 486,364]
492. ~3 | 36 | ~37 [avatar contradiction clause 491]
493. $false [avatar sat refutation 168,375,382,480,481,492]
% SZS output end Proof for 1218668802375364206375609
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
If fred is not happy or not old then someone is either not brave or not generous and vice versa. If someone is happy or not creative then alice is not old. If someone is not tall or not generous then someone is both kind and curious. Everyone who is not happy or brave is not creative and vice versa. Everyone who is either not creative or funny is both kind and patient. If someone is not patient then someone is not calm. If mary is not kind or not patient then someone is old or patient and vice versa. If someone is both quiet and not funny then someone is both wise and not wise. Everyone who is not kind or old is both not quiet and not wise. If someone is both not calm and calm then someone is either not quiet or patient and vice versa. Everyone who is both humble and quiet is either not rich or humble. Everyone who is wise is either brave or rich. Everyone who is both not tall and old is either happy or not rich. If mary is both not curious and tall then fred is not old and vice versa. If someone is funny then someone is both rich and not generous. Everyone who is kind is both brave and creative. Someone is either not wise or kind. Susan is either old or not strong. Alice is either not brave or not happy. Someone is either not kind or not humble. Lucy is not calm or kind. Someone is not rich. | Mary is not funny. | entailment | (((~happy(fred)|~old(fred)))<=>(?[X]:((~brave(X)<~>~generous(X)))))&
((?[X]:((happy(X)|~creative(X))))=>(~old(alice)))&
((?[X]:((~tall(X)|~generous(X))))=>(?[X]:((kind(X)&curious(X)))))&
(![X]:((~happy(X)|brave(X))<=>~creative(X)))&
(![X]:((~creative(X)<~>funny(X))=>(kind(X)&patient(X))))&
((?[X]:(~patient(X)))=>(?[X]:(~calm(X))))&
(((~kind(mary)|~patient(mary)))<=>(?[X]:((old(X)|patient(X)))))&
((?[X]:((quiet(X)&~funny(X))))=>(?[X]:((wise(X)&~wise(X)))))&
(![X]:((~kind(X)|old(X))=>(~quiet(X)&~wise(X))))&
((?[X]:((~calm(X)&calm(X))))<=>(?[X]:((~quiet(X)<~>patient(X)))))&
(![X]:((humble(X)&quiet(X))=>(~rich(X)<~>humble(X))))&
(![X]:(wise(X)=>(brave(X)<~>rich(X))))&
(![X]:((~tall(X)&old(X))=>(happy(X)<~>~rich(X))))&
(((~curious(mary)&tall(mary)))<=>(~old(fred)))&
((?[X]:(funny(X)))=>(?[X]:((rich(X)&~generous(X)))))&
(![X]:(kind(X)=>(brave(X)&creative(X))))&
(?[X]:((~wise(X)<~>kind(X))))&
((old(susan)<~>~strong(susan)))&
((~brave(alice)<~>~happy(alice)))&
(?[X]:((~kind(X)<~>~humble(X))))&
((~calm(lucy)|kind(lucy)))&
(?[X]:(~rich(X))) | ~funny(mary) | [
"p2",
"p3",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4060474975450443556497176
% SZS output start Proof for 4060474975450443556497176
3. ? [X0] : (~generous(X0) | ~tall(X0)) => ? [X0] : (curious(X0) & kind(X0)) [input p2]
4. ! [X0] : ((brave(X0) | ~happy(X0)) <=> ~creative(X0)) [input p3]
15. ? [X0] : funny(X0) => ? [X0] : (~generous(X0) & rich(X0)) [input p14]
16. ! [X0] : (kind(X0) => (creative(X0) & brave(X0))) [input p15]
23. funny(mary) [input hypothesis]
24. ? [X0] : (~generous(X0) | ~tall(X0)) => ? [X1] : (curious(X1) & kind(X1)) [rectify 3]
28. ? [X0] : funny(X0) => ? [X1] : (~generous(X1) & rich(X1)) [rectify 15]
30. ? [X1] : (curious(X1) & kind(X1)) | ! [X0] : (generous(X0) & tall(X0)) [ennf transformation 24]
40. ? [X1] : (~generous(X1) & rich(X1)) | ! [X0] : ~funny(X0) [ennf transformation 28]
41. ! [X0] : ((creative(X0) & brave(X0)) | ~kind(X0)) [ennf transformation 16]
47. ? [X0] : (curious(X0) & kind(X0)) | ! [X1] : (generous(X1) & tall(X1)) [rectify 30]
48. ? [X0] : (curious(X0) & kind(X0)) => (curious(sK1) & kind(sK1)) [choice axiom]
49. (curious(sK1) & kind(sK1)) | ! [X1] : (generous(X1) & tall(X1)) [skolemisation 47,48]
50. ! [X0] : (((brave(X0) | ~happy(X0)) | creative(X0)) & (~creative(X0) | (~brave(X0) & happy(X0)))) [nnf transformation 4]
51. ! [X0] : ((brave(X0) | ~happy(X0) | creative(X0)) & (~creative(X0) | (~brave(X0) & happy(X0)))) [flattening 50]
74. ? [X0] : (~generous(X0) & rich(X0)) | ! [X1] : ~funny(X1) [rectify 40]
75. ? [X0] : (~generous(X0) & rich(X0)) => (~generous(sK7) & rich(sK7)) [choice axiom]
76. (~generous(sK7) & rich(sK7)) | ! [X1] : ~funny(X1) [skolemisation 74,75]
96. kind(sK1) | generous(X1) [cnf transformation 49]
100. ~creative(X0) | ~brave(X0) [cnf transformation 51]
133. ~generous(sK7) | ~funny(X1) [cnf transformation 76]
134. ~kind(X0) | brave(X0) [cnf transformation 41]
135. ~kind(X0) | creative(X0) [cnf transformation 41]
146. funny(mary) [cnf transformation 23]
189. 10 <=> ! [X1] : generous(X1) [avatar definition]
190. generous(X1) <- (10) [avatar component clause 189]
201. 13 <=> kind(sK1) [avatar definition]
203. kind(sK1) <- (13) [avatar component clause 201]
204. 10 | 13 [avatar split clause 96,201,189]
275. 29 <=> ! [X1] : ~funny(X1) [avatar definition]
276. ~funny(X1) <- (29) [avatar component clause 275]
278. 30 <=> generous(sK7) [avatar definition]
280. ~generous(sK7) <- (~30) [avatar component clause 278]
281. 29 | ~30 [avatar split clause 133,278,275]
338. $false <- (29) [resolution 276,146]
339. ~29 [avatar contradiction clause 338]
340. brave(sK1) <- (13) [resolution 134,203]
343. creative(sK1) <- (13) [resolution 135,203]
350. ~brave(sK1) <- (13) [resolution 343,100]
352. $false <- (13) [subsumption resolution 350,340]
353. ~13 [avatar contradiction clause 352]
354. $false <- (10, ~30) [resolution 190,280]
356. ~10 | 30 [avatar contradiction clause 354]
357. $false [avatar sat refutation 204,281,339,353,356]
% SZS output end Proof for 4060474975450443556497176
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If fred is both rich and not calm then someone is both patient and not funny and vice versa.
Everyone who is either kind or generous is kind.
Everyone who is not humble is not brave and vice versa.
If fred is old or quiet then someone is both tall and strong.
Everyone who is both brave and not generous is tall or generous and vice versa.
Everyone who is patient is both not curious and not patient and vice versa.
Everyone who is either quiet or funny is either wise or strong.
Everyone who is either curious or not creative is not quiet.
Everyone who is both not rich and generous is rich.
Everyone who is not old or not patient is both happy and rich.
Everyone who is either calm or old is both not funny and humble.
If someone is both not funny and strong then someone is both kind and patient.
Everyone who is either not wise or not rich is either not strong or not curious.
If someone is not kind or not creative then lucy is either not curious or not tall and vice versa.
Someone is not old.
Someone is either not brave or happy.
Mary is both calm and not tall.
Someone is funny or patient.
Someone is curious or kind.
Mary is old.
Someone is creative or rich.
Lucy is kind. | Fred is generous. | contradiction | (((rich(fred)&~calm(fred)))<=>(?[X]:((patient(X)&~funny(X)))))&
(![X]:((kind(X)<~>generous(X))=>kind(X)))&
(![X]:(~humble(X)<=>~brave(X)))&
(((old(fred)|quiet(fred)))=>(?[X]:((tall(X)&strong(X)))))&
(![X]:((brave(X)&~generous(X))<=>(tall(X)|generous(X))))&
(![X]:(patient(X)<=>(~curious(X)&~patient(X))))&
(![X]:((quiet(X)<~>funny(X))=>(wise(X)<~>strong(X))))&
(![X]:((curious(X)<~>~creative(X))=>~quiet(X)))&
(![X]:((~rich(X)&generous(X))=>rich(X)))&
(![X]:((~old(X)|~patient(X))=>(happy(X)&rich(X))))&
(![X]:((calm(X)<~>old(X))=>(~funny(X)&humble(X))))&
((?[X]:((~funny(X)&strong(X))))=>(?[X]:((kind(X)&patient(X)))))&
(![X]:((~wise(X)<~>~rich(X))=>(~strong(X)<~>~curious(X))))&
((?[X]:((~kind(X)|~creative(X))))<=>((~curious(lucy)<~>~tall(lucy))))&
(?[X]:(~old(X)))&
(?[X]:((~brave(X)<~>happy(X))))&
((calm(mary)&~tall(mary)))&
(?[X]:((funny(X)|patient(X))))&
(?[X]:((curious(X)|kind(X))))&
(old(mary))&
(?[X]:((creative(X)|rich(X))))&
(kind(lucy)) | generous(fred) | [
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 3036135037723744419859238
% SZS output start Proof for 3036135037723744419859238
5. ! [X0] : ((~generous(X0) & brave(X0)) <=> (generous(X0) | tall(X0))) [input p4]
23. generous(fred) [input hypothesis]
45. ! [X0] : (((~generous(X0) & brave(X0)) | (~generous(X0) & ~tall(X0))) & ((generous(X0) | tall(X0)) | (generous(X0) | ~brave(X0)))) [nnf transformation 5]
46. ! [X0] : (((~generous(X0) & brave(X0)) | (~generous(X0) & ~tall(X0))) & (generous(X0) | tall(X0) | generous(X0) | ~brave(X0))) [flattening 45]
86. ~generous(X0) | ~generous(X0) [cnf transformation 46]
127. generous(fred) [cnf transformation 23]
132. ~generous(X0) [duplicate literal removal 86]
222. $false [subsumption resolution 127,132]
% SZS output end Proof for 3036135037723744419859238
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not humble is not funny.
If mary is either curious or not creative then john is brave and vice versa.
Everyone who is either not quiet or calm is not brave or happy and vice versa.
If someone is quiet or happy then someone is both not wise and kind.
If alice is not old or not kind then someone is both not strong and not funny and vice versa.
If john is both not patient and curious then someone is either rich or not old and vice versa.
Everyone who is patient or not old is both not strong and not calm and vice versa.
Everyone who is both humble and not kind is either not calm or kind.
Everyone who is either quiet or calm is not quiet or kind and vice versa.
If someone is either not funny or creative then someone is either not curious or funny.
Everyone who is either not wise or calm is both quiet and not brave.
If mary is both not old and not calm then someone is either wise or not tall and vice versa.
If lucy is not creative then someone is both not calm and generous.
If someone is either funny or not happy then someone is both tall and happy.
Everyone who is either brave or not strong is wise and vice versa.
Everyone who is not wise is old and vice versa.
John is either old or not old.
Fred is either not calm or not brave.
Someone is either not generous or quiet.
Alice is both not rich and not strong.
Someone is not strong.
Lucy is both not humble and old. | John is patient. | contradiction | (![X]:(~humble(X)=>~funny(X)))&
(((curious(mary)<~>~creative(mary)))<=>(brave(john)))&
(![X]:((~quiet(X)<~>calm(X))<=>(~brave(X)|happy(X))))&
((?[X]:((quiet(X)|happy(X))))=>(?[X]:((~wise(X)&kind(X)))))&
(((~old(alice)|~kind(alice)))<=>(?[X]:((~strong(X)&~funny(X)))))&
(((~patient(john)&curious(john)))<=>(?[X]:((rich(X)<~>~old(X)))))&
(![X]:((patient(X)|~old(X))<=>(~strong(X)&~calm(X))))&
(![X]:((humble(X)&~kind(X))=>(~calm(X)<~>kind(X))))&
(![X]:((quiet(X)<~>calm(X))<=>(~quiet(X)|kind(X))))&
((?[X]:((~funny(X)<~>creative(X))))=>(?[X]:((~curious(X)<~>funny(X)))))&
(![X]:((~wise(X)<~>calm(X))=>(quiet(X)&~brave(X))))&
(((~old(mary)&~calm(mary)))<=>(?[X]:((wise(X)<~>~tall(X)))))&
((~creative(lucy))=>(?[X]:((~calm(X)&generous(X)))))&
((?[X]:((funny(X)<~>~happy(X))))=>(?[X]:((tall(X)&happy(X)))))&
(![X]:((brave(X)<~>~strong(X))<=>wise(X)))&
(![X]:(~wise(X)<=>old(X)))&
((old(john)<~>~old(john)))&
((~calm(fred)<~>~brave(fred)))&
(?[X]:((~generous(X)<~>quiet(X))))&
((~rich(alice)&~strong(alice)))&
(?[X]:(~strong(X)))&
((~humble(lucy)&old(lucy))) | patient(john) | [
"p2",
"p6",
"p8",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3616871428568174241702507
% SZS output start Proof for 3616871428568174241702507
3. ! [X0] : ((~quiet(X0) <~> calm(X0)) <=> (happy(X0) | ~brave(X0))) [input p2]
7. ! [X0] : ((~old(X0) | patient(X0)) <=> (~calm(X0) & ~strong(X0))) [input p6]
9. ! [X0] : ((quiet(X0) <~> calm(X0)) <=> (kind(X0) | ~quiet(X0))) [input p8]
11. ! [X0] : ((~wise(X0) <~> calm(X0)) => (~brave(X0) & quiet(X0))) [input p10]
15. ! [X0] : ((brave(X0) <~> ~strong(X0)) <=> wise(X0)) [input p14]
23. patient(john) [input hypothesis]
32. ! [X0] : ((~brave(X0) & quiet(X0)) | (~wise(X0) <=> calm(X0))) [ennf transformation 11]
36. ! [X0] : ((((~calm(X0) | quiet(X0)) & (calm(X0) | ~quiet(X0))) | (~happy(X0) & brave(X0))) & ((happy(X0) | ~brave(X0)) | ((~quiet(X0) | ~calm(X0)) & (calm(X0) | quiet(X0))))) [nnf transformation 3]
37. ! [X0] : ((((~calm(X0) | quiet(X0)) & (calm(X0) | ~quiet(X0))) | (~happy(X0) & brave(X0))) & (happy(X0) | ~brave(X0) | ((~quiet(X0) | ~calm(X0)) & (calm(X0) | quiet(X0))))) [flattening 36]
51. ! [X0] : (((~old(X0) | patient(X0)) | (calm(X0) | strong(X0))) & ((~calm(X0) & ~strong(X0)) | (old(X0) & ~patient(X0)))) [nnf transformation 7]
52. ! [X0] : ((~old(X0) | patient(X0) | calm(X0) | strong(X0)) & ((~calm(X0) & ~strong(X0)) | (old(X0) & ~patient(X0)))) [flattening 51]
54. ! [X0] : ((((~calm(X0) | ~quiet(X0)) & (calm(X0) | quiet(X0))) | (~kind(X0) & quiet(X0))) & ((kind(X0) | ~quiet(X0)) | ((quiet(X0) | ~calm(X0)) & (calm(X0) | ~quiet(X0))))) [nnf transformation 9]
55. ! [X0] : ((((~calm(X0) | ~quiet(X0)) & (calm(X0) | quiet(X0))) | (~kind(X0) & quiet(X0))) & (kind(X0) | ~quiet(X0) | ((quiet(X0) | ~calm(X0)) & (calm(X0) | ~quiet(X0))))) [flattening 54]
60. ! [X0] : ((~brave(X0) & quiet(X0)) | ((~wise(X0) | ~calm(X0)) & (calm(X0) | wise(X0)))) [nnf transformation 32]
72. ! [X0] : ((((strong(X0) | ~brave(X0)) & (~strong(X0) | brave(X0))) | ~wise(X0)) & (wise(X0) | ((brave(X0) | strong(X0)) & (~strong(X0) | ~brave(X0))))) [nnf transformation 15]
88. ~quiet(X0) | calm(X0) | brave(X0) [cnf transformation 37]
107. ~patient(X0) | ~strong(X0) [cnf transformation 52]
109. ~patient(X0) | ~calm(X0) [cnf transformation 52]
116. calm(X0) | quiet(X0) | quiet(X0) [cnf transformation 55]
126. ~brave(X0) | calm(X0) | wise(X0) [cnf transformation 60]
143. ~wise(X0) | ~brave(X0) | strong(X0) [cnf transformation 72]
157. patient(john) [cnf transformation 23]
159. calm(X0) | quiet(X0) [duplicate literal removal 116]
162. 1 <=> brave(john) [avatar definition]
163. brave(john) <- (1) [avatar component clause 162]
232. 16 <=> patient(john) [avatar definition]
233. patient(john) <- (16) [avatar component clause 232]
349. 16 [avatar split clause 157,232]
350. ~strong(john) <- (16) [resolution 107,233]
351. ~calm(john) <- (16) [resolution 109,233]
359. quiet(john) <- (16) [resolution 159,351]
374. calm(john) | brave(john) <- (16) [resolution 88,359]
376. brave(john) <- (16) [subsumption resolution 374,351]
379. 1 | ~16 [avatar split clause 376,232,162]
413. calm(john) | wise(john) <- (1) [resolution 126,163]
415. wise(john) <- (1, 16) [subsumption resolution 413,351]
479. ~brave(john) | strong(john) <- (1, 16) [resolution 143,415]
481. strong(john) <- (1, 16) [subsumption resolution 479,163]
482. $false <- (1, 16) [subsumption resolution 481,350]
483. ~1 | ~16 [avatar contradiction clause 482]
484. $false [avatar sat refutation 349,379,483]
% SZS output end Proof for 3616871428568174241702507
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not calm or funny is both not humble and not old and vice versa.
Everyone who is either not generous or not kind is both not curious and tall and vice versa.
If paul is both not strong and not wise then mary is either not old or generous and vice versa.
Everyone who is either not old or strong is either patient or funny and vice versa.
Everyone who is patient or not old is both not strong and not humble.
If someone is both not quiet and humble then someone is not wise.
If susan is patient or generous then someone is both not brave and not quiet.
If alice is either happy or calm then susan is both not quiet and quiet.
If john is either humble or not humble then someone is not generous and vice versa.
Everyone who is not old is both funny and not patient.
Everyone who is not kind or not generous is both tall and kind and vice versa.
If someone is either tall or calm then mary is creative or not strong and vice versa.
Everyone who is quiet is not generous or not kind and vice versa.
If someone is either brave or not humble then mary is creative and vice versa.
Everyone who is either old or curious is either calm or curious and vice versa.
Everyone who is rich is either not brave or wise.
Paul is not rich or not patient.
Susan is either brave or not quiet.
Alice is not humble.
Someone is either not old or old.
Fred is old or not patient.
John is not kind or not quiet.
Paul is wise.
Someone is either not quiet or not strong. | Mary is not calm. | contradiction | (![X]:((~calm(X)<~>funny(X))<=>(~humble(X)&~old(X))))&
(![X]:((~generous(X)<~>~kind(X))<=>(~curious(X)&tall(X))))&
(((~strong(paul)&~wise(paul)))<=>((~old(mary)<~>generous(mary))))&
(![X]:((~old(X)<~>strong(X))<=>(patient(X)<~>funny(X))))&
(![X]:((patient(X)|~old(X))=>(~strong(X)&~humble(X))))&
((?[X]:((~quiet(X)&humble(X))))=>(?[X]:(~wise(X))))&
(((patient(susan)|generous(susan)))=>(?[X]:((~brave(X)&~quiet(X)))))&
(((happy(alice)<~>calm(alice)))=>((~quiet(susan)&quiet(susan))))&
(((humble(john)<~>~humble(john)))<=>(?[X]:(~generous(X))))&
(![X]:(~old(X)=>(funny(X)&~patient(X))))&
(![X]:((~kind(X)|~generous(X))<=>(tall(X)&kind(X))))&
((?[X]:((tall(X)<~>calm(X))))<=>((creative(mary)|~strong(mary))))&
(![X]:(quiet(X)<=>(~generous(X)|~kind(X))))&
((?[X]:((brave(X)<~>~humble(X))))<=>(creative(mary)))&
(![X]:((old(X)<~>curious(X))<=>(calm(X)<~>curious(X))))&
(![X]:(rich(X)=>(~brave(X)<~>wise(X))))&
((~rich(paul)|~patient(paul)))&
((brave(susan)<~>~quiet(susan)))&
(~humble(alice))&
(?[X]:((~old(X)<~>old(X))))&
((old(fred)|~patient(fred)))&
((~kind(john)|~quiet(john)))&
(wise(paul))&
(?[X]:((~quiet(X)<~>~strong(X)))) | ~calm(mary) | [
"p0",
"p4",
"p9",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4832912977270194069703775
% SZS output start Proof for 4832912977270194069703775
1. ! [X0] : ((~calm(X0) <~> funny(X0)) <=> (~old(X0) & ~humble(X0))) [input p0]
5. ! [X0] : ((~old(X0) | patient(X0)) => (~humble(X0) & ~strong(X0))) [input p4]
10. ! [X0] : (~old(X0) => (~patient(X0) & funny(X0))) [input p9]
15. ! [X0] : ((old(X0) <~> curious(X0)) <=> (calm(X0) <~> curious(X0))) [input p14]
25. ~calm(mary) [input hypothesis]
29. ! [X0] : ((~humble(X0) & ~strong(X0)) | (old(X0) & ~patient(X0))) [ennf transformation 5]
33. ! [X0] : ((~patient(X0) & funny(X0)) | old(X0)) [ennf transformation 10]
34. ! [X0] : ((((~funny(X0) | calm(X0)) & (funny(X0) | ~calm(X0))) | (old(X0) | humble(X0))) & ((~old(X0) & ~humble(X0)) | ((~calm(X0) | ~funny(X0)) & (funny(X0) | calm(X0))))) [nnf transformation 1]
35. ! [X0] : ((((~funny(X0) | calm(X0)) & (funny(X0) | ~calm(X0))) | old(X0) | humble(X0)) & ((~old(X0) & ~humble(X0)) | ((~calm(X0) | ~funny(X0)) & (funny(X0) | calm(X0))))) [flattening 34]
64. ! [X0] : ((((~curious(X0) | ~old(X0)) & (curious(X0) | old(X0))) | ((calm(X0) | ~curious(X0)) & (curious(X0) | ~calm(X0)))) & (((~curious(X0) | ~calm(X0)) & (curious(X0) | calm(X0))) | ((old(X0) | ~curious(X0)) & (curious(X0) | ~old(X0))))) [nnf transformation 15]
77. ~funny(X0) | calm(X0) | old(X0) | humble(X0) [cnf transformation 35]
101. ~humble(X0) | old(X0) [cnf transformation 29]
115. old(X0) | funny(X0) [cnf transformation 33]
135. curious(X0) | calm(X0) | curious(X0) | ~old(X0) [cnf transformation 64]
138. ~curious(X0) | ~calm(X0) | old(X0) | ~curious(X0) [cnf transformation 64]
139. curious(X0) | old(X0) | curious(X0) | ~calm(X0) [cnf transformation 64]
142. ~curious(X0) | ~old(X0) | calm(X0) | ~curious(X0) [cnf transformation 64]
153. ~calm(mary) [cnf transformation 25]
154. curious(X0) | calm(X0) | ~old(X0) [duplicate literal removal 135]
155. ~curious(X0) | ~calm(X0) | old(X0) [duplicate literal removal 138]
156. ~calm(X0) | old(X0) | curious(X0) [duplicate literal removal 139]
157. ~curious(X0) | ~old(X0) | calm(X0) [duplicate literal removal 142]
167. 2 <=> old(mary) [avatar definition]
168. old(mary) <- (2) [avatar component clause 167]
169. ~old(mary) <- (~2) [avatar component clause 167]
285. ~calm(X0) | old(X0) [subsumption resolution 155,156]
286. ~old(X0) | calm(X0) [subsumption resolution 154,157]
311. calm(mary) <- (2) [resolution 286,168]
312. funny(X0) | calm(X0) [resolution 286,115]
313. $false <- (2) [subsumption resolution 311,153]
314. ~2 [avatar contradiction clause 313]
330. calm(X0) | old(X0) | humble(X0) | calm(X0) [resolution 77,312]
331. calm(X0) | old(X0) | humble(X0) [duplicate literal removal 330]
334. calm(X0) | old(X0) [subsumption resolution 331,101]
335. old(X0) [subsumption resolution 334,285]
344. $false <- (~2) [resolution 335,169]
345. 2 [avatar contradiction clause 344]
346. $false [avatar sat refutation 314,345]
% SZS output end Proof for 4832912977270194069703775
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not happy or not quiet then someone is calm or not calm.
Everyone who is not humble is not wise and vice versa.
Everyone who is either creative or not kind is either curious or wise.
If someone is either not rich or not wise then lucy is patient or not humble and vice versa.
If mary is brave then john is both not kind and not brave.
Everyone who is both not tall and not brave is not creative or rich and vice versa.
Everyone who is not wise is not patient and vice versa.
Everyone who is not old is both not funny and patient.
Everyone who is calm or funny is patient.
Everyone who is both wise and not kind is rich and vice versa.
Everyone who is both funny and not wise is tall or brave and vice versa.
If someone is both happy and not happy then paul is either not quiet or humble and vice versa.
If someone is wise or not creative then someone is not strong or generous.
If fred is kind then john is both humble and not brave.
Everyone who is not wise is not kind and vice versa.
Everyone who is both calm and wise is kind or rich.
Susan is either rich or funny.
Susan is both not tall and old.
Someone is both calm and quiet.
Someone is both old and curious.
Lucy is either quiet or generous.
Fred is either not wise or brave.
Someone is either wise or tall. | Fred is curious. | entailment | ((?[X]:((~happy(X)|~quiet(X))))=>(?[X]:((calm(X)|~calm(X)))))&
(![X]:(~humble(X)<=>~wise(X)))&
(![X]:((creative(X)<~>~kind(X))=>(curious(X)<~>wise(X))))&
((?[X]:((~rich(X)<~>~wise(X))))<=>((patient(lucy)|~humble(lucy))))&
((brave(mary))=>((~kind(john)&~brave(john))))&
(![X]:((~tall(X)&~brave(X))<=>(~creative(X)|rich(X))))&
(![X]:(~wise(X)<=>~patient(X)))&
(![X]:(~old(X)=>(~funny(X)&patient(X))))&
(![X]:((calm(X)|funny(X))=>patient(X)))&
(![X]:((wise(X)&~kind(X))<=>rich(X)))&
(![X]:((funny(X)&~wise(X))<=>(tall(X)|brave(X))))&
((?[X]:((happy(X)&~happy(X))))<=>((~quiet(paul)<~>humble(paul))))&
((?[X]:((wise(X)|~creative(X))))=>(?[X]:((~strong(X)|generous(X)))))&
((kind(fred))=>((humble(john)&~brave(john))))&
(![X]:(~wise(X)<=>~kind(X)))&
(![X]:((calm(X)&wise(X))=>(kind(X)|rich(X))))&
((rich(susan)<~>funny(susan)))&
((~tall(susan)&old(susan)))&
(?[X]:((calm(X)&quiet(X))))&
(?[X]:((old(X)&curious(X))))&
((quiet(lucy)<~>generous(lucy)))&
((~wise(fred)<~>brave(fred)))&
(?[X]:((wise(X)<~>tall(X)))) | curious(fred) | [
"p2",
"p5",
"p6",
"p8",
"p9",
"p10",
"p14",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 3487539965881235858666561
% SZS output start Proof for 3487539965881235858666561
3. ! [X0] : ((creative(X0) <~> ~kind(X0)) => (curious(X0) <~> wise(X0))) [input p2]
6. ! [X0] : ((~brave(X0) & ~tall(X0)) <=> (rich(X0) | ~creative(X0))) [input p5]
7. ! [X0] : (~wise(X0) <=> ~patient(X0)) [input p6]
9. ! [X0] : ((funny(X0) | calm(X0)) => patient(X0)) [input p8]
10. ! [X0] : ((~kind(X0) & wise(X0)) <=> rich(X0)) [input p9]
11. ! [X0] : ((~wise(X0) & funny(X0)) <=> (brave(X0) | tall(X0))) [input p10]
15. ! [X0] : (~wise(X0) <=> ~kind(X0)) [input p14]
22. ~wise(fred) <~> brave(fred) [input p21]
24. ~curious(fred) [input hypothesis]
32. ! [X0] : ((curious(X0) <~> wise(X0)) | (creative(X0) <=> ~kind(X0))) [ennf transformation 3]
34. ! [X0] : (patient(X0) | (~funny(X0) & ~calm(X0))) [ennf transformation 9]
42. ! [X0] : (((~wise(X0) | ~curious(X0)) & (wise(X0) | curious(X0))) | ((creative(X0) | kind(X0)) & (~kind(X0) | ~creative(X0)))) [nnf transformation 32]
48. ! [X0] : (((~brave(X0) & ~tall(X0)) | (~rich(X0) & creative(X0))) & ((rich(X0) | ~creative(X0)) | (brave(X0) | tall(X0)))) [nnf transformation 6]
49. ! [X0] : (((~brave(X0) & ~tall(X0)) | (~rich(X0) & creative(X0))) & (rich(X0) | ~creative(X0) | brave(X0) | tall(X0))) [flattening 48]
50. ! [X0] : ((~wise(X0) | patient(X0)) & (~patient(X0) | wise(X0))) [nnf transformation 7]
51. ! [X0] : (((~kind(X0) & wise(X0)) | ~rich(X0)) & (rich(X0) | (kind(X0) | ~wise(X0)))) [nnf transformation 10]
52. ! [X0] : (((~kind(X0) & wise(X0)) | ~rich(X0)) & (rich(X0) | kind(X0) | ~wise(X0))) [flattening 51]
53. ! [X0] : (((~wise(X0) & funny(X0)) | (~brave(X0) & ~tall(X0))) & ((brave(X0) | tall(X0)) | (wise(X0) | ~funny(X0)))) [nnf transformation 11]
54. ! [X0] : (((~wise(X0) & funny(X0)) | (~brave(X0) & ~tall(X0))) & (brave(X0) | tall(X0) | wise(X0) | ~funny(X0))) [flattening 53]
59. ! [X0] : ((~wise(X0) | kind(X0)) & (~kind(X0) | wise(X0))) [nnf transformation 15]
66. (~brave(fred) | wise(fred)) & (brave(fred) | ~wise(fred)) [nnf transformation 22]
75. curious(X0) | wise(X0) | creative(X0) | kind(X0) [cnf transformation 42]
86. ~creative(X0) | rich(X0) | brave(X0) | tall(X0) [cnf transformation 49]
91. ~patient(X0) | wise(X0) [cnf transformation 50]
94. ~funny(X0) | patient(X0) [cnf transformation 34]
96. wise(X0) | ~rich(X0) [cnf transformation 52]
99. ~tall(X0) | funny(X0) [cnf transformation 54]
102. ~brave(X0) | ~wise(X0) [cnf transformation 54]
111. ~kind(X0) | wise(X0) [cnf transformation 59]
122. brave(fred) | ~wise(fred) [cnf transformation 66]
123. ~brave(fred) | wise(fred) [cnf transformation 66]
126. ~curious(fred) [cnf transformation 24]
148. 5 <=> ! [X1] : (~rich(X1) | wise(X1)) [avatar definition]
149. ~rich(X1) | wise(X1) <- (5) [avatar component clause 148]
169. 5 [avatar split clause 96,148]
187. 13 <=> kind(fred) [avatar definition]
188. kind(fred) <- (13) [avatar component clause 187]
216. ~brave(fred) [subsumption resolution 123,102]
217. ~wise(fred) [subsumption resolution 122,216]
277. wise(fred) | creative(fred) | kind(fred) [resolution 75,126]
278. creative(fred) | kind(fred) [subsumption resolution 277,217]
301. 23 <=> tall(fred) [avatar definition]
303. tall(fred) <- (23) [avatar component clause 301]
305. 24 <=> rich(fred) [avatar definition]
307. rich(fred) <- (24) [avatar component clause 305]
310. 25 <=> creative(fred) [avatar definition]
312. creative(fred) <- (25) [avatar component clause 310]
313. 13 | 25 [avatar split clause 278,310,187]
315. wise(fred) <- (13) [resolution 188,111]
319. $false <- (13) [subsumption resolution 315,217]
320. ~13 [avatar contradiction clause 319]
323. rich(fred) | brave(fred) | tall(fred) <- (25) [resolution 312,86]
344. funny(fred) <- (23) [resolution 303,99]
355. patient(fred) <- (23) [resolution 344,94]
356. wise(fred) <- (23) [resolution 355,91]
357. $false <- (23) [subsumption resolution 356,217]
358. ~23 [avatar contradiction clause 357]
359. rich(fred) | tall(fred) <- (25) [subsumption resolution 323,216]
360. 23 | 24 | ~25 [avatar split clause 359,310,305,301]
361. wise(fred) <- (5, 24) [resolution 307,149]
363. $false <- (5, 24) [subsumption resolution 361,217]
364. ~5 | ~24 [avatar contradiction clause 363]
365. $false [avatar sat refutation 169,313,320,358,360,364]
% SZS output end Proof for 3487539965881235858666561
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both funny and strong then someone is both creative and not tall and vice versa.
If someone is not strong then john is creative and vice versa.
If paul is tall or not patient then someone is tall or not humble.
Everyone who is both humble and not wise is either creative or humble and vice versa.
If someone is not funny or funny then susan is either brave or creative.
If paul is either not quiet or quiet then susan is strong.
Everyone who is either not quiet or calm is generous.
Everyone who is both brave and not quiet is funny or wise and vice versa.
If someone is calm then someone is both strong and wise.
Everyone who is either funny or tall is either generous or not kind.
If someone is both happy and not curious then paul is humble.
Everyone who is either not tall or quiet is either not funny or patient and vice versa.
Everyone who is both brave and tall is both old and not funny.
John is both not curious and tall.
Someone is either not humble or not wise.
Susan is not rich.
Alice is happy or not rich.
Someone is either not funny or humble.
Alice is not tall. | Paul is not wise. | neutral | ((?[X]:((funny(X)&strong(X))))<=>(?[X]:((creative(X)&~tall(X)))))&
((?[X]:(~strong(X)))<=>(creative(john)))&
(((tall(paul)|~patient(paul)))=>(?[X]:((tall(X)|~humble(X)))))&
(![X]:((humble(X)&~wise(X))<=>(creative(X)<~>humble(X))))&
((?[X]:((~funny(X)|funny(X))))=>((brave(susan)<~>creative(susan))))&
(((~quiet(paul)<~>quiet(paul)))=>(strong(susan)))&
(![X]:((~quiet(X)<~>calm(X))=>generous(X)))&
(![X]:((brave(X)&~quiet(X))<=>(funny(X)|wise(X))))&
((?[X]:(calm(X)))=>(?[X]:((strong(X)&wise(X)))))&
(![X]:((funny(X)<~>tall(X))=>(generous(X)<~>~kind(X))))&
((?[X]:((happy(X)&~curious(X))))=>(humble(paul)))&
(![X]:((~tall(X)<~>quiet(X))<=>(~funny(X)<~>patient(X))))&
(![X]:((brave(X)&tall(X))=>(old(X)&~funny(X))))&
((~curious(john)&tall(john)))&
(?[X]:((~humble(X)<~>~wise(X))))&
(~rich(susan))&
((happy(alice)|~rich(alice)))&
(?[X]:((~funny(X)<~>humble(X))))&
(~tall(alice)) | ~wise(paul) | [] | null | 0 |
Everyone who is both not humble and quiet is patient or quiet.
Everyone who is not creative or kind is patient and vice versa.
If fred is creative or not generous then john is not creative.
Everyone who is calm or curious is both not curious and not happy and vice versa.
If fred is either calm or not calm then someone is not kind or patient and vice versa.
Everyone who is rich is not brave and vice versa.
If someone is not rich or not curious then someone is not quiet and vice versa.
Everyone who is both funny and generous is happy.
If susan is wise then lucy is both kind and not patient.
Everyone who is both generous and not humble is both not happy and calm.
If lucy is creative or not rich then someone is both brave and not funny.
Everyone who is either creative or not wise is not old and vice versa.
If paul is both not kind and funny then someone is not old or not quiet and vice versa.
Everyone who is brave is creative or patient.
If susan is old then someone is both not kind and happy and vice versa.
If someone is tall then paul is not rich or not old.
Someone is either not patient or funny.
Someone is both not creative and brave.
Someone is not humble or not generous.
Someone is either not wise or humble.
Someone is not kind.
Someone is old or humble.
Lucy is old.
John is happy or kind. | Susan is not wise. | entailment | (![X]:((~humble(X)&quiet(X))=>(patient(X)|quiet(X))))&
(![X]:((~creative(X)|kind(X))<=>patient(X)))&
(((creative(fred)|~generous(fred)))=>(~creative(john)))&
(![X]:((calm(X)|curious(X))<=>(~curious(X)&~happy(X))))&
(((calm(fred)<~>~calm(fred)))<=>(?[X]:((~kind(X)|patient(X)))))&
(![X]:(rich(X)<=>~brave(X)))&
((?[X]:((~rich(X)|~curious(X))))<=>(?[X]:(~quiet(X))))&
(![X]:((funny(X)&generous(X))=>happy(X)))&
((wise(susan))=>((kind(lucy)&~patient(lucy))))&
(![X]:((generous(X)&~humble(X))=>(~happy(X)&calm(X))))&
(((creative(lucy)|~rich(lucy)))=>(?[X]:((brave(X)&~funny(X)))))&
(![X]:((creative(X)<~>~wise(X))<=>~old(X)))&
(((~kind(paul)&funny(paul)))<=>(?[X]:((~old(X)|~quiet(X)))))&
(![X]:(brave(X)=>(creative(X)|patient(X))))&
((old(susan))<=>(?[X]:((~kind(X)&happy(X)))))&
((?[X]:(tall(X)))=>((~rich(paul)|~old(paul))))&
(?[X]:((~patient(X)<~>funny(X))))&
(?[X]:((~creative(X)&brave(X))))&
(?[X]:((~humble(X)|~generous(X))))&
(?[X]:((~wise(X)<~>humble(X))))&
(?[X]:(~kind(X)))&
(?[X]:((old(X)|humble(X))))&
(old(lucy))&
((happy(john)|kind(john))) | ~wise(susan) | [
"p1",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 4347846288733951221192841
% SZS output start Proof for 4347846288733951221192841
2. ! [X0] : ((kind(X0) | ~creative(X0)) <=> patient(X0)) [input p1]
9. wise(susan) => (~patient(lucy) & kind(lucy)) [input p8]
25. wise(susan) [input hypothesis]
33. (~patient(lucy) & kind(lucy)) | ~wise(susan) [ennf transformation 9]
39. ! [X0] : (((kind(X0) | ~creative(X0)) | ~patient(X0)) & (patient(X0) | (~kind(X0) & creative(X0)))) [nnf transformation 2]
40. ! [X0] : ((kind(X0) | ~creative(X0) | ~patient(X0)) & (patient(X0) | (~kind(X0) & creative(X0)))) [flattening 39]
81. ~kind(X0) | patient(X0) [cnf transformation 40]
102. kind(lucy) | ~wise(susan) [cnf transformation 33]
103. ~patient(lucy) | ~wise(susan) [cnf transformation 33]
134. wise(susan) [cnf transformation 25]
155. 4 <=> wise(susan) [avatar definition]
159. 5 <=> patient(lucy) [avatar definition]
161. ~patient(lucy) <- (~5) [avatar component clause 159]
162. ~4 | ~5 [avatar split clause 103,159,155]
164. 6 <=> kind(lucy) [avatar definition]
166. kind(lucy) <- (6) [avatar component clause 164]
167. ~4 | 6 [avatar split clause 102,164,155]
280. 4 [avatar split clause 134,155]
286. patient(lucy) <- (6) [resolution 81,166]
287. $false <- (~5, 6) [subsumption resolution 286,161]
288. 5 | ~6 [avatar contradiction clause 287]
289. $false [avatar sat refutation 162,167,280,288]
% SZS output end Proof for 4347846288733951221192841
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both tall and not wise is either curious or not generous and vice versa.
Everyone who is either patient or not generous is not wise or old.
If someone is old then fred is not funny and vice versa.
If mary is either not wise or not kind then susan is not quiet or not calm and vice versa.
Everyone who is not generous or quiet is both patient and not tall and vice versa.
Everyone who is either not curious or not funny is kind and vice versa.
If someone is both not calm and patient then someone is not calm and vice versa.
If someone is not quiet then someone is either not generous or rich and vice versa.
If john is both brave and kind then paul is patient or not curious.
If someone is not tall or not strong then john is humble and vice versa.
Everyone who is either patient or creative is not calm or not generous and vice versa.
If someone is either not calm or not creative then someone is either not quiet or brave and vice versa.
If someone is quiet or not old then john is both not creative and not humble.
If alice is not patient then alice is tall or not wise and vice versa.
If someone is humble then john is not humble.
Everyone who is strong is both calm and not funny and vice versa.
Someone is both creative and old.
Lucy is wise.
Fred is strong or not quiet.
Someone is not humble. | Lucy is strong. | entailment | (![X]:((tall(X)&~wise(X))<=>(curious(X)<~>~generous(X))))&
(![X]:((patient(X)<~>~generous(X))=>(~wise(X)|old(X))))&
((?[X]:(old(X)))<=>(~funny(fred)))&
(((~wise(mary)<~>~kind(mary)))<=>((~quiet(susan)|~calm(susan))))&
(![X]:((~generous(X)|quiet(X))<=>(patient(X)&~tall(X))))&
(![X]:((~curious(X)<~>~funny(X))<=>kind(X)))&
((?[X]:((~calm(X)&patient(X))))<=>(?[X]:(~calm(X))))&
((?[X]:(~quiet(X)))<=>(?[X]:((~generous(X)<~>rich(X)))))&
(((brave(john)&kind(john)))=>((patient(paul)|~curious(paul))))&
((?[X]:((~tall(X)|~strong(X))))<=>(humble(john)))&
(![X]:((patient(X)<~>creative(X))<=>(~calm(X)|~generous(X))))&
((?[X]:((~calm(X)<~>~creative(X))))<=>(?[X]:((~quiet(X)<~>brave(X)))))&
((?[X]:((quiet(X)|~old(X))))=>((~creative(john)&~humble(john))))&
((~patient(alice))<=>((tall(alice)|~wise(alice))))&
((?[X]:(humble(X)))=>(~humble(john)))&
(![X]:(strong(X)<=>(calm(X)&~funny(X))))&
(?[X]:((creative(X)&old(X))))&
(wise(lucy))&
((strong(fred)|~quiet(fred)))&
(?[X]:(~humble(X))) | strong(lucy) | [
"p9",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 1234166540848218776816032
% SZS output start Proof for 1234166540848218776816032
10. ? [X0] : (~strong(X0) | ~tall(X0)) <=> humble(john) [input p9]
15. ? [X0] : humble(X0) => ~humble(john) [input p14]
21. ~strong(lucy) [input hypothesis]
30. ~humble(john) | ! [X0] : ~humble(X0) [ennf transformation 15]
53. (? [X0] : (~strong(X0) | ~tall(X0)) | ~humble(john)) & (humble(john) | ! [X0] : (strong(X0) & tall(X0))) [nnf transformation 10]
54. (? [X0] : (~strong(X0) | ~tall(X0)) | ~humble(john)) & (humble(john) | ! [X1] : (strong(X1) & tall(X1))) [rectify 53]
55. ? [X0] : (~strong(X0) | ~tall(X0)) => (~strong(sK5) | ~tall(sK5)) [choice axiom]
56. ((~strong(sK5) | ~tall(sK5)) | ~humble(john)) & (humble(john) | ! [X1] : (strong(X1) & tall(X1))) [skolemisation 54,55]
106. humble(john) | strong(X1) [cnf transformation 56]
129. ~humble(john) | ~humble(X0) [cnf transformation 30]
138. ~strong(lucy) [cnf transformation 21]
238. 23 <=> humble(john) [avatar definition]
239. humble(john) <- (23) [avatar component clause 238]
251. 26 <=> ! [X1] : strong(X1) [avatar definition]
252. strong(X1) <- (26) [avatar component clause 251]
253. 26 | 23 [avatar split clause 106,238,251]
326. 42 <=> ! [X0] : ~humble(X0) [avatar definition]
327. ~humble(X0) <- (42) [avatar component clause 326]
328. 42 | ~23 [avatar split clause 129,238,326]
340. $false <- (26) [resolution 252,138]
341. ~26 [avatar contradiction clause 340]
344. $false <- (23, 42) [subsumption resolution 239,327]
345. ~23 | ~42 [avatar contradiction clause 344]
346. $false [avatar sat refutation 253,328,341,345]
% SZS output end Proof for 1234166540848218776816032
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If susan is both funny and quiet then someone is either brave or not tall and vice versa.
Everyone who is not calm is either not wise or not brave and vice versa.
If lucy is either humble or happy then susan is not rich or creative.
If susan is not calm or not generous then someone is both generous and quiet and vice versa.
Everyone who is not rich is not generous or creative and vice versa.
If susan is humble or creative then someone is creative and vice versa.
Everyone who is both brave and generous is not calm and vice versa.
Everyone who is not patient is both funny and strong.
If fred is generous then john is funny and vice versa.
Everyone who is not strong is creative or not generous and vice versa.
If someone is either kind or not old then mary is both tall and not calm.
Everyone who is both strong and not old is not happy or not generous and vice versa.
Everyone who is calm is not quiet.
Everyone who is both happy and not creative is not quiet or generous and vice versa.
Everyone who is not calm is not funny or old and vice versa.
Paul is either not happy or funny.
Lucy is not humble or not kind.
Someone is either not calm or not quiet. | Susan is not humble. | entailment | (((funny(susan)&quiet(susan)))<=>(?[X]:((brave(X)<~>~tall(X)))))&
(![X]:(~calm(X)<=>(~wise(X)<~>~brave(X))))&
(((humble(lucy)<~>happy(lucy)))=>((~rich(susan)|creative(susan))))&
(((~calm(susan)|~generous(susan)))<=>(?[X]:((generous(X)&quiet(X)))))&
(![X]:(~rich(X)<=>(~generous(X)|creative(X))))&
(((humble(susan)|creative(susan)))<=>(?[X]:(creative(X))))&
(![X]:((brave(X)&generous(X))<=>~calm(X)))&
(![X]:(~patient(X)=>(funny(X)&strong(X))))&
((generous(fred))<=>(funny(john)))&
(![X]:(~strong(X)<=>(creative(X)|~generous(X))))&
((?[X]:((kind(X)<~>~old(X))))=>((tall(mary)&~calm(mary))))&
(![X]:((strong(X)&~old(X))<=>(~happy(X)|~generous(X))))&
(![X]:(calm(X)=>~quiet(X)))&
(![X]:((happy(X)&~creative(X))<=>(~quiet(X)|generous(X))))&
(![X]:(~calm(X)<=>(~funny(X)|old(X))))&
((~happy(paul)<~>funny(paul)))&
((~humble(lucy)|~kind(lucy)))&
(?[X]:((~calm(X)<~>~quiet(X)))) | ~humble(susan) | [
"p5",
"p9",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 1646698130747443876673372
% SZS output start Proof for 1646698130747443876673372
6. (creative(susan) | humble(susan)) <=> ? [X0] : creative(X0) [input p5]
10. ! [X0] : (~strong(X0) <=> (~generous(X0) | creative(X0))) [input p9]
12. ! [X0] : ((~old(X0) & strong(X0)) <=> (~generous(X0) | ~happy(X0))) [input p11]
14. ! [X0] : ((~creative(X0) & happy(X0)) <=> (generous(X0) | ~quiet(X0))) [input p13]
19. humble(susan) [input hypothesis]
40. ((creative(susan) | humble(susan)) | ! [X0] : ~creative(X0)) & (? [X0] : creative(X0) | (~creative(susan) & ~humble(susan))) [nnf transformation 6]
41. (creative(susan) | humble(susan) | ! [X0] : ~creative(X0)) & (? [X0] : creative(X0) | (~creative(susan) & ~humble(susan))) [flattening 40]
42. (creative(susan) | humble(susan) | ! [X0] : ~creative(X0)) & (? [X1] : creative(X1) | (~creative(susan) & ~humble(susan))) [rectify 41]
43. ? [X1] : creative(X1) => creative(sK2) [choice axiom]
44. (creative(susan) | humble(susan) | ! [X0] : ~creative(X0)) & (creative(sK2) | (~creative(susan) & ~humble(susan))) [skolemisation 42,43]
48. ! [X0] : ((~strong(X0) | (generous(X0) & ~creative(X0))) & ((~generous(X0) | creative(X0)) | strong(X0))) [nnf transformation 10]
49. ! [X0] : ((~strong(X0) | (generous(X0) & ~creative(X0))) & (~generous(X0) | creative(X0) | strong(X0))) [flattening 48]
51. ! [X0] : (((~old(X0) & strong(X0)) | (generous(X0) & happy(X0))) & ((~generous(X0) | ~happy(X0)) | (old(X0) | ~strong(X0)))) [nnf transformation 12]
52. ! [X0] : (((~old(X0) & strong(X0)) | (generous(X0) & happy(X0))) & (~generous(X0) | ~happy(X0) | old(X0) | ~strong(X0))) [flattening 51]
53. ! [X0] : (((~creative(X0) & happy(X0)) | (~generous(X0) & quiet(X0))) & ((generous(X0) | ~quiet(X0)) | (creative(X0) | ~happy(X0)))) [nnf transformation 14]
54. ! [X0] : (((~creative(X0) & happy(X0)) | (~generous(X0) & quiet(X0))) & (generous(X0) | ~quiet(X0) | creative(X0) | ~happy(X0))) [flattening 53]
79. creative(sK2) | ~humble(susan) [cnf transformation 44]
89. ~strong(X0) | generous(X0) [cnf transformation 49]
96. strong(X0) | generous(X0) [cnf transformation 52]
104. ~creative(X0) | ~generous(X0) [cnf transformation 54]
113. humble(susan) [cnf transformation 19]
185. 16 <=> ! [X0] : ~creative(X0) [avatar definition]
186. ~creative(X0) <- (16) [avatar component clause 185]
188. 17 <=> humble(susan) [avatar definition]
193. 18 <=> creative(sK2) [avatar definition]
195. creative(sK2) <- (18) [avatar component clause 193]
197. ~17 | 18 [avatar split clause 79,193,188]
226. generous(X0) [subsumption resolution 96,89]
228. ~creative(X0) [subsumption resolution 104,226]
229. 16 [avatar split clause 228,185]
246. 17 [avatar split clause 113,188]
256. $false <- (16, 18) [resolution 195,186]
257. ~16 | ~18 [avatar contradiction clause 256]
258. $false [avatar sat refutation 197,229,246,257]
% SZS output end Proof for 1646698130747443876673372
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is quiet or generous is both tall and creative.
Everyone who is not old or not curious is not quiet.
If someone is not brave then alice is patient and vice versa.
Everyone who is either not tall or quiet is not kind or kind and vice versa.
Everyone who is not curious is not happy or quiet.
If someone is not tall then alice is rich and vice versa.
If someone is both wise and creative then someone is not brave or not curious and vice versa.
If someone is not creative then lucy is either funny or generous.
Everyone who is either not happy or old is both not rich and creative.
Everyone who is not happy or not strong is both calm and not curious.
Everyone who is both funny and patient is not brave.
Everyone who is not rich is not strong or not rich and vice versa.
Everyone who is both funny and calm is not brave and vice versa.
If someone is brave or kind then someone is not calm or not kind and vice versa.
If lucy is either patient or rich then mary is either not rich or not brave.
Everyone who is both wise and not calm is not generous or rich and vice versa.
Alice is humble.
Lucy is either not kind or happy.
Fred is either happy or not patient.
Lucy is not patient.
John is either humble or not kind.
Someone is not patient or tall.
Someone is both not calm and wise. | Lucy is strong. | entailment | (![X]:((quiet(X)|generous(X))=>(tall(X)&creative(X))))&
(![X]:((~old(X)|~curious(X))=>~quiet(X)))&
((?[X]:(~brave(X)))<=>(patient(alice)))&
(![X]:((~tall(X)<~>quiet(X))<=>(~kind(X)|kind(X))))&
(![X]:(~curious(X)=>(~happy(X)|quiet(X))))&
((?[X]:(~tall(X)))<=>(rich(alice)))&
((?[X]:((wise(X)&creative(X))))<=>(?[X]:((~brave(X)|~curious(X)))))&
((?[X]:(~creative(X)))=>((funny(lucy)<~>generous(lucy))))&
(![X]:((~happy(X)<~>old(X))=>(~rich(X)&creative(X))))&
(![X]:((~happy(X)|~strong(X))=>(calm(X)&~curious(X))))&
(![X]:((funny(X)&patient(X))=>~brave(X)))&
(![X]:(~rich(X)<=>(~strong(X)|~rich(X))))&
(![X]:((funny(X)&calm(X))<=>~brave(X)))&
((?[X]:((brave(X)|kind(X))))<=>(?[X]:((~calm(X)|~kind(X)))))&
(((patient(lucy)<~>rich(lucy)))=>((~rich(mary)<~>~brave(mary))))&
(![X]:((wise(X)&~calm(X))<=>(~generous(X)|rich(X))))&
(humble(alice))&
((~kind(lucy)<~>happy(lucy)))&
((happy(fred)<~>~patient(fred)))&
(~patient(lucy))&
((humble(john)<~>~kind(john)))&
(?[X]:((~patient(X)|tall(X))))&
(?[X]:((~calm(X)&wise(X)))) | strong(lucy) | [
"p0",
"p1",
"p3",
"p9",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3666446823455500244434057
% SZS output start Proof for 3666446823455500244434057
1. ! [X0] : ((generous(X0) | quiet(X0)) => (creative(X0) & tall(X0))) [input p0]
2. ! [X0] : ((~curious(X0) | ~old(X0)) => ~quiet(X0)) [input p1]
4. ! [X0] : ((~tall(X0) <~> quiet(X0)) <=> (kind(X0) | ~kind(X0))) [input p3]
10. ! [X0] : ((~strong(X0) | ~happy(X0)) => (~curious(X0) & calm(X0))) [input p9]
16. ! [X0] : ((~calm(X0) & wise(X0)) <=> (rich(X0) | ~generous(X0))) [input p15]
24. ~strong(lucy) [input hypothesis]
27. ! [X0] : ((creative(X0) & tall(X0)) | (~generous(X0) & ~quiet(X0))) [ennf transformation 1]
28. ! [X0] : (~quiet(X0) | (curious(X0) & old(X0))) [ennf transformation 2]
33. ! [X0] : ((~curious(X0) & calm(X0)) | (strong(X0) & happy(X0))) [ennf transformation 10]
41. ! [X0] : ((((~quiet(X0) | tall(X0)) & (quiet(X0) | ~tall(X0))) | (~kind(X0) & kind(X0))) & ((kind(X0) | ~kind(X0)) | ((~tall(X0) | ~quiet(X0)) & (quiet(X0) | tall(X0))))) [nnf transformation 4]
42. ! [X0] : ((((~quiet(X0) | tall(X0)) & (quiet(X0) | ~tall(X0))) | (~kind(X0) & kind(X0))) & (kind(X0) | ~kind(X0) | ((~tall(X0) | ~quiet(X0)) & (quiet(X0) | tall(X0))))) [flattening 41]
64. ! [X0] : (((~calm(X0) & wise(X0)) | (~rich(X0) & generous(X0))) & ((rich(X0) | ~generous(X0)) | (calm(X0) | ~wise(X0)))) [nnf transformation 16]
65. ! [X0] : (((~calm(X0) & wise(X0)) | (~rich(X0) & generous(X0))) & (rich(X0) | ~generous(X0) | calm(X0) | ~wise(X0))) [flattening 64]
74. ~generous(X0) | tall(X0) [cnf transformation 27]
78. ~quiet(X0) | curious(X0) [cnf transformation 28]
83. quiet(X0) | ~tall(X0) | kind(X0) [cnf transformation 42]
84. ~kind(X0) | ~tall(X0) | quiet(X0) [cnf transformation 42]
102. calm(X0) | strong(X0) [cnf transformation 33]
104. ~curious(X0) | strong(X0) [cnf transformation 33]
123. ~calm(X0) | generous(X0) [cnf transformation 65]
136. ~strong(lucy) [cnf transformation 24]
150. ~tall(X0) | quiet(X0) [subsumption resolution 83,84]
200. 15 <=> generous(lucy) [avatar definition]
201. generous(lucy) <- (15) [avatar component clause 200]
310. strong(X1) | generous(X1) [resolution 123,102]
384. generous(lucy) [resolution 310,136]
385. 15 [avatar split clause 384,200]
387. tall(lucy) <- (15) [resolution 201,74]
388. quiet(lucy) <- (15) [resolution 387,150]
389. curious(lucy) <- (15) [resolution 388,78]
401. strong(lucy) <- (15) [resolution 389,104]
403. $false <- (15) [subsumption resolution 401,136]
404. ~15 [avatar contradiction clause 403]
407. $false [avatar sat refutation 385,404]
% SZS output end Proof for 3666446823455500244434057
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.021 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either happy or not creative is not brave and vice versa.
Everyone who is not humble is both old and not patient.
If someone is both not generous and quiet then john is both not brave and not patient.
Everyone who is not rich is either not curious or wise.
If someone is either calm or rich then susan is both not calm and happy and vice versa.
If fred is both not patient and rich then someone is either humble or quiet.
If john is not funny or not tall then john is either rich or not rich and vice versa.
Everyone who is old is both patient and generous and vice versa.
Everyone who is both not kind and not humble is either tall or kind and vice versa.
If someone is humble then lucy is not patient or old and vice versa.
Everyone who is generous or kind is not happy or creative.
If paul is not happy or not funny then someone is either not curious or generous.
If someone is brave or wise then fred is calm or wise.
Everyone who is not funny or not strong is not funny or tall.
If someone is either wise or not brave then susan is either generous or patient.
Everyone who is not old or not curious is humble and vice versa.
Someone is either not wise or not calm.
Someone is humble.
Mary is both not creative and calm.
Someone is calm.
John is old or not curious.
Mary is either not tall or not funny.
Someone is not funny or not happy. | John is humble. | entailment | (![X]:((happy(X)<~>~creative(X))<=>~brave(X)))&
(![X]:(~humble(X)=>(old(X)&~patient(X))))&
((?[X]:((~generous(X)&quiet(X))))=>((~brave(john)&~patient(john))))&
(![X]:(~rich(X)=>(~curious(X)<~>wise(X))))&
((?[X]:((calm(X)<~>rich(X))))<=>((~calm(susan)&happy(susan))))&
(((~patient(fred)&rich(fred)))=>(?[X]:((humble(X)<~>quiet(X)))))&
(((~funny(john)|~tall(john)))<=>((rich(john)<~>~rich(john))))&
(![X]:(old(X)<=>(patient(X)&generous(X))))&
(![X]:((~kind(X)&~humble(X))<=>(tall(X)<~>kind(X))))&
((?[X]:(humble(X)))<=>((~patient(lucy)|old(lucy))))&
(![X]:((generous(X)|kind(X))=>(~happy(X)|creative(X))))&
(((~happy(paul)|~funny(paul)))=>(?[X]:((~curious(X)<~>generous(X)))))&
((?[X]:((brave(X)|wise(X))))=>((calm(fred)|wise(fred))))&
(![X]:((~funny(X)|~strong(X))=>(~funny(X)|tall(X))))&
((?[X]:((wise(X)<~>~brave(X))))=>((generous(susan)<~>patient(susan))))&
(![X]:((~old(X)|~curious(X))<=>humble(X)))&
(?[X]:((~wise(X)<~>~calm(X))))&
(?[X]:(humble(X)))&
((~creative(mary)&calm(mary)))&
(?[X]:(calm(X)))&
((old(john)|~curious(john)))&
((~tall(mary)<~>~funny(mary)))&
(?[X]:((~funny(X)|~happy(X)))) | humble(john) | [
"p1",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 3067545669395715264907640
% SZS output start Proof for 3067545669395715264907640
2. ! [X0] : (~humble(X0) => (~patient(X0) & old(X0))) [input p1]
8. ! [X0] : (old(X0) <=> (generous(X0) & patient(X0))) [input p7]
24. ~humble(john) [input hypothesis]
26. ! [X0] : ((~patient(X0) & old(X0)) | humble(X0)) [ennf transformation 2]
51. ! [X0] : ((old(X0) | (~generous(X0) | ~patient(X0))) & ((generous(X0) & patient(X0)) | ~old(X0))) [nnf transformation 8]
52. ! [X0] : ((old(X0) | ~generous(X0) | ~patient(X0)) & ((generous(X0) & patient(X0)) | ~old(X0))) [flattening 51]
80. old(X0) | humble(X0) [cnf transformation 26]
81. ~patient(X0) | humble(X0) [cnf transformation 26]
100. ~old(X0) | patient(X0) [cnf transformation 52]
138. ~humble(john) [cnf transformation 24]
327. patient(X0) | humble(X0) [resolution 100,80]
328. humble(X0) [subsumption resolution 327,81]
330. $false [resolution 328,138]
% SZS output end Proof for 3067545669395715264907640
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
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