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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|---|---|---|---|---|---|---|---|
If someone is both brave and not strong then lucy is not kind and vice versa. Everyone who is either not rich or not happy is not strong and vice versa. Everyone who is both not tall and not kind is both funny and not happy. Everyone who is not tall is either not rich or brave. Everyone who is either kind or not quiet is not quiet or not curious and vice versa. If fred is curious or not strong then someone is both kind and rich. If someone is not wise or kind then someone is rich. If someone is either tall or not strong then susan is both brave and not brave. Everyone who is generous is humble or calm and vice versa. Everyone who is happy or rich is both not calm and quiet. Everyone who is both tall and quiet is both wise and old and vice versa. Everyone who is both old and wise is either not calm or brave and vice versa. If susan is not humble then fred is either not tall or calm and vice versa. If someone is humble then susan is rich or not kind. Everyone who is both not happy and not quiet is either patient or not funny and vice versa. If someone is both creative and calm then someone is not generous. Mary is strong. Alice is either kind or not tall. Someone is not old or old. Susan is either wise or tall. Someone is not funny or humble. Mary is not rich or not wise. Someone is either not rich or patient. Someone is either not tall or rich. | Susan is tall. | contradiction | ((?[X]:((brave(X)&~strong(X))))<=>(~kind(lucy)))&
(![X]:((~rich(X)<~>~happy(X))<=>~strong(X)))&
(![X]:((~tall(X)&~kind(X))=>(funny(X)&~happy(X))))&
(![X]:(~tall(X)=>(~rich(X)<~>brave(X))))&
(![X]:((kind(X)<~>~quiet(X))<=>(~quiet(X)|~curious(X))))&
(((curious(fred)|~strong(fred)))=>(?[X]:((kind(X)&rich(X)))))&
((?[X]:((~wise(X)|kind(X))))=>(?[X]:(rich(X))))&
((?[X]:((tall(X)<~>~strong(X))))=>((brave(susan)&~brave(susan))))&
(![X]:(generous(X)<=>(humble(X)|calm(X))))&
(![X]:((happy(X)|rich(X))=>(~calm(X)&quiet(X))))&
(![X]:((tall(X)&quiet(X))<=>(wise(X)&old(X))))&
(![X]:((old(X)&wise(X))<=>(~calm(X)<~>brave(X))))&
((~humble(susan))<=>((~tall(fred)<~>calm(fred))))&
((?[X]:(humble(X)))=>((rich(susan)|~kind(susan))))&
(![X]:((~happy(X)&~quiet(X))<=>(patient(X)<~>~funny(X))))&
((?[X]:((creative(X)&calm(X))))=>(?[X]:(~generous(X))))&
(strong(mary))&
((kind(alice)<~>~tall(alice)))&
(?[X]:((~old(X)|old(X))))&
((wise(susan)<~>tall(susan)))&
(?[X]:((~funny(X)|humble(X))))&
((~rich(mary)|~wise(mary)))&
(?[X]:((~rich(X)<~>patient(X))))&
(?[X]:((~tall(X)<~>rich(X)))) | tall(susan) | [
"p1",
"p7",
"p9",
"p10",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 9024398951153252343955098
% SZS output start Proof for 9024398951153252343955098
2. ! [X0] : ((~rich(X0) <~> ~happy(X0)) <=> ~strong(X0)) [input p1]
8. ? [X0] : (tall(X0) <~> ~strong(X0)) => (~brave(susan) & brave(susan)) [input p7]
10. ! [X0] : ((rich(X0) | happy(X0)) => (quiet(X0) & ~calm(X0))) [input p9]
11. ! [X0] : ((quiet(X0) & tall(X0)) <=> (old(X0) & wise(X0))) [input p10]
20. wise(susan) <~> tall(susan) [input p19]
25. tall(susan) [input hypothesis]
36. (~brave(susan) & brave(susan)) | ! [X0] : (tall(X0) <=> ~strong(X0)) [ennf transformation 8]
37. ! [X0] : ((quiet(X0) & ~calm(X0)) | (~rich(X0) & ~happy(X0))) [ennf transformation 10]
44. ! [X0] : ((((happy(X0) | rich(X0)) & (~happy(X0) | ~rich(X0))) | strong(X0)) & (~strong(X0) | ((~rich(X0) | happy(X0)) & (~happy(X0) | rich(X0))))) [nnf transformation 2]
53. (~brave(susan) & brave(susan)) | ! [X0] : ((tall(X0) | strong(X0)) & (~strong(X0) | ~tall(X0))) [nnf transformation 36]
54. ! [X0] : (((quiet(X0) & tall(X0)) | (~old(X0) | ~wise(X0))) & ((old(X0) & wise(X0)) | (~quiet(X0) | ~tall(X0)))) [nnf transformation 11]
55. ! [X0] : (((quiet(X0) & tall(X0)) | ~old(X0) | ~wise(X0)) & ((old(X0) & wise(X0)) | ~quiet(X0) | ~tall(X0))) [flattening 54]
64. (~tall(susan) | ~wise(susan)) & (tall(susan) | wise(susan)) [nnf transformation 20]
79. happy(X0) | rich(X0) | strong(X0) [cnf transformation 44]
96. brave(susan) | ~strong(X0) | ~tall(X0) [cnf transformation 53]
98. ~brave(susan) | ~strong(X0) | ~tall(X0) [cnf transformation 53]
102. ~happy(X0) | quiet(X0) [cnf transformation 37]
103. ~rich(X0) | quiet(X0) [cnf transformation 37]
104. ~quiet(X0) | wise(X0) | ~tall(X0) [cnf transformation 55]
130. ~tall(susan) | ~wise(susan) [cnf transformation 64]
137. tall(susan) [cnf transformation 25]
195. 13 <=> brave(susan) [avatar definition]
200. 14 <=> ! [X0] : (~strong(X0) | ~tall(X0)) [avatar definition]
201. ~tall(X0) | ~strong(X0) <- (14) [avatar component clause 200]
202. 14 | ~13 [avatar split clause 98,195,200]
204. 14 | 13 [avatar split clause 96,195,200]
246. 23 <=> wise(susan) [avatar definition]
248. ~wise(susan) <- (~23) [avatar component clause 246]
250. 24 <=> tall(susan) [avatar definition]
251. tall(susan) <- (24) [avatar component clause 250]
253. ~23 | ~24 [avatar split clause 130,250,246]
293. 24 [avatar split clause 137,250]
312. rich(X2) | strong(X2) | quiet(X2) [resolution 79,102]
315. quiet(X2) | strong(X2) [subsumption resolution 312,103]
373. wise(X0) | ~tall(X0) | strong(X0) [resolution 104,315]
376. ~tall(X0) | wise(X0) <- (14) [subsumption resolution 373,201]
377. wise(susan) <- (14, 24) [resolution 376,251]
380. $false <- (14, ~23, 24) [subsumption resolution 377,248]
381. ~14 | 23 | ~24 [avatar contradiction clause 380]
382. $false [avatar sat refutation 202,204,253,293,381]
% SZS output end Proof for 9024398951153252343955098
% ------------------------------
% 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 susan is not generous or not funny then someone is both patient and generous.
Everyone who is either strong or kind is both not creative and not quiet.
If alice is either not old or not creative then someone is quiet and vice versa.
If mary is either not generous or not quiet then someone is either curious or not strong and vice versa.
If paul is both not calm and not kind then someone is both rich and brave and vice versa.
Everyone who is either generous or not funny is either strong or happy and vice versa.
Everyone who is both rich and not wise is not wise or generous and vice versa.
Everyone who is both kind and brave is strong and vice versa.
If someone is generous or not old then john is happy.
Everyone who is both curious and calm is not funny.
Everyone who is not generous is either not generous or kind and vice versa.
Everyone who is quiet or not old is not old and vice versa.
If alice is both humble and not calm then paul is either strong or not calm.
Everyone who is both humble and tall is kind and vice versa.
Everyone who is either not creative or brave is not humble and vice versa.
If alice is not wise then john is rich.
Someone is tall.
Someone is both not patient and not calm.
Fred is not curious or not humble.
Lucy is either happy or calm.
Susan is both happy and not old.
Someone is patient or strong.
Someone is not quiet or not wise. | Mary is not humble. | neutral | (((~generous(susan)|~funny(susan)))=>(?[X]:((patient(X)&generous(X)))))&
(![X]:((strong(X)<~>kind(X))=>(~creative(X)&~quiet(X))))&
(((~old(alice)<~>~creative(alice)))<=>(?[X]:(quiet(X))))&
(((~generous(mary)<~>~quiet(mary)))<=>(?[X]:((curious(X)<~>~strong(X)))))&
(((~calm(paul)&~kind(paul)))<=>(?[X]:((rich(X)&brave(X)))))&
(![X]:((generous(X)<~>~funny(X))<=>(strong(X)<~>happy(X))))&
(![X]:((rich(X)&~wise(X))<=>(~wise(X)|generous(X))))&
(![X]:((kind(X)&brave(X))<=>strong(X)))&
((?[X]:((generous(X)|~old(X))))=>(happy(john)))&
(![X]:((curious(X)&calm(X))=>~funny(X)))&
(![X]:(~generous(X)<=>(~generous(X)<~>kind(X))))&
(![X]:((quiet(X)|~old(X))<=>~old(X)))&
(((humble(alice)&~calm(alice)))=>((strong(paul)<~>~calm(paul))))&
(![X]:((humble(X)&tall(X))<=>kind(X)))&
(![X]:((~creative(X)<~>brave(X))<=>~humble(X)))&
((~wise(alice))=>(rich(john)))&
(?[X]:(tall(X)))&
(?[X]:((~patient(X)&~calm(X))))&
((~curious(fred)|~humble(fred)))&
((happy(lucy)<~>calm(lucy)))&
((happy(susan)&~old(susan)))&
(?[X]:((patient(X)|strong(X))))&
(?[X]:((~quiet(X)|~wise(X)))) | ~humble(mary) | [] | null | 0 |
If lucy is both not rich and creative then alice is both not patient and not calm and vice versa. Everyone who is not tall or not creative is either not old or not happy and vice versa. If someone is both wise and patient then susan is brave or not generous and vice versa. If someone is happy or not strong then someone is both quiet and rich. If john is either funny or not funny then someone is not patient or not brave and vice versa. If mary is not patient then someone is not curious or calm. Everyone who is not generous is not kind or creative and vice versa. Everyone who is happy is not happy or not funny. Everyone who is not rich is either humble or patient and vice versa. If someone is both calm and not funny then john is humble or not humble and vice versa. Everyone who is not funny or not tall is both calm and kind and vice versa. Everyone who is both not curious and kind is kind. Everyone who is either creative or calm is either not calm or not creative. Everyone who is either not patient or not wise is not creative and vice versa. Everyone who is either patient or not patient is either not tall or not brave. If someone is tall then fred is either not tall or brave. Someone is not old. Alice is either not happy or generous. Susan is not happy or not tall. John is either not kind or not patient. Someone is not quiet or old. Someone is both creative and kind. Susan is creative. | Fred is not funny. | neutral | (((~rich(lucy)&creative(lucy)))<=>((~patient(alice)&~calm(alice))))&
(![X]:((~tall(X)|~creative(X))<=>(~old(X)<~>~happy(X))))&
((?[X]:((wise(X)&patient(X))))<=>((brave(susan)|~generous(susan))))&
((?[X]:((happy(X)|~strong(X))))=>(?[X]:((quiet(X)&rich(X)))))&
(((funny(john)<~>~funny(john)))<=>(?[X]:((~patient(X)|~brave(X)))))&
((~patient(mary))=>(?[X]:((~curious(X)|calm(X)))))&
(![X]:(~generous(X)<=>(~kind(X)|creative(X))))&
(![X]:(happy(X)=>(~happy(X)|~funny(X))))&
(![X]:(~rich(X)<=>(humble(X)<~>patient(X))))&
((?[X]:((calm(X)&~funny(X))))<=>((humble(john)|~humble(john))))&
(![X]:((~funny(X)|~tall(X))<=>(calm(X)&kind(X))))&
(![X]:((~curious(X)&kind(X))=>kind(X)))&
(![X]:((creative(X)<~>calm(X))=>(~calm(X)<~>~creative(X))))&
(![X]:((~patient(X)<~>~wise(X))<=>~creative(X)))&
(![X]:((patient(X)<~>~patient(X))=>(~tall(X)<~>~brave(X))))&
((?[X]:(tall(X)))=>((~tall(fred)<~>brave(fred))))&
(?[X]:(~old(X)))&
((~happy(alice)<~>generous(alice)))&
((~happy(susan)|~tall(susan)))&
((~kind(john)<~>~patient(john)))&
(?[X]:((~quiet(X)|old(X))))&
(?[X]:((creative(X)&kind(X))))&
(creative(susan)) | ~funny(fred) | [] | null | 0 |
Everyone who is both not kind and patient is both not calm and patient and vice versa. If paul is not funny or calm then alice is both not quiet and rich and vice versa. If mary is either not creative or not patient then john is both calm and happy and vice versa. Everyone who is both not calm and rich is both not kind and not quiet. Everyone who is either funny or not brave is both not creative and not humble. Everyone who is either not quiet or not calm is not generous. If someone is humble or kind then john is either not funny or not wise and vice versa. Everyone who is not generous or not rich is either not old or not humble. If paul is either old or kind then someone is either curious or happy. If someone is not wise then susan is both tall and not tall and vice versa. Everyone who is tall is either not brave or not patient and vice versa. Everyone who is both not quiet and not brave is not happy and vice versa. If mary is either not happy or not generous then fred is strong or not rich and vice versa. Everyone who is happy is both not generous and not quiet and vice versa. Everyone who is both quiet and not old is either not generous or curious. If mary is not calm then john is both happy and not funny. John is both rich and not creative. Lucy is both kind and patient. Paul is both not creative and not calm. Fred is both generous and patient. Someone is rich or not kind. Someone is not patient. Someone is not brave or calm. Someone is both rich and not brave. | Alice is wise. | entailment | (![X]:((~kind(X)&patient(X))<=>(~calm(X)&patient(X))))&
(((~funny(paul)|calm(paul)))<=>((~quiet(alice)&rich(alice))))&
(((~creative(mary)<~>~patient(mary)))<=>((calm(john)&happy(john))))&
(![X]:((~calm(X)&rich(X))=>(~kind(X)&~quiet(X))))&
(![X]:((funny(X)<~>~brave(X))=>(~creative(X)&~humble(X))))&
(![X]:((~quiet(X)<~>~calm(X))=>~generous(X)))&
((?[X]:((humble(X)|kind(X))))<=>((~funny(john)<~>~wise(john))))&
(![X]:((~generous(X)|~rich(X))=>(~old(X)<~>~humble(X))))&
(((old(paul)<~>kind(paul)))=>(?[X]:((curious(X)<~>happy(X)))))&
((?[X]:(~wise(X)))<=>((tall(susan)&~tall(susan))))&
(![X]:(tall(X)<=>(~brave(X)<~>~patient(X))))&
(![X]:((~quiet(X)&~brave(X))<=>~happy(X)))&
(((~happy(mary)<~>~generous(mary)))<=>((strong(fred)|~rich(fred))))&
(![X]:(happy(X)<=>(~generous(X)&~quiet(X))))&
(![X]:((quiet(X)&~old(X))=>(~generous(X)<~>curious(X))))&
((~calm(mary))=>((happy(john)&~funny(john))))&
((rich(john)&~creative(john)))&
((kind(lucy)&patient(lucy)))&
((~creative(paul)&~calm(paul)))&
((generous(fred)&patient(fred)))&
(?[X]:((rich(X)|~kind(X))))&
(?[X]:(~patient(X)))&
(?[X]:((~brave(X)|calm(X))))&
(?[X]:((rich(X)&~brave(X)))) | wise(alice) | [
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 4645188282903871154964112
% SZS output start Proof for 4645188282903871154964112
10. ? [X0] : ~wise(X0) <=> (~tall(susan) & tall(susan)) [input p9]
25. ~wise(alice) [input hypothesis]
51. (? [X0] : ~wise(X0) | (tall(susan) | ~tall(susan))) & ((~tall(susan) & tall(susan)) | ! [X0] : wise(X0)) [nnf transformation 10]
52. (? [X0] : ~wise(X0) | tall(susan) | ~tall(susan)) & ((~tall(susan) & tall(susan)) | ! [X0] : wise(X0)) [flattening 51]
53. (? [X0] : ~wise(X0) | tall(susan) | ~tall(susan)) & ((~tall(susan) & tall(susan)) | ! [X1] : wise(X1)) [rectify 52]
54. ? [X0] : ~wise(X0) => ~wise(sK2) [choice axiom]
55. (~wise(sK2) | tall(susan) | ~tall(susan)) & ((~tall(susan) & tall(susan)) | ! [X1] : wise(X1)) [skolemisation 53,54]
109. tall(susan) | wise(X1) [cnf transformation 55]
110. ~tall(susan) | wise(X1) [cnf transformation 55]
145. ~wise(alice) [cnf transformation 25]
238. 19 <=> ! [X1] : wise(X1) [avatar definition]
239. wise(X1) <- (19) [avatar component clause 238]
241. 20 <=> tall(susan) [avatar definition]
244. 19 | ~20 [avatar split clause 110,241,238]
245. 19 | 20 [avatar split clause 109,241,238]
295. $false <- (19) [resolution 239,145]
296. ~19 [avatar contradiction clause 295]
297. $false [avatar sat refutation 244,245,296]
% SZS output end Proof for 4645188282903871154964112
% ------------------------------
% 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 happy and not kind is happy and vice versa.
If lucy is not calm or not curious then susan is kind and vice versa.
Everyone who is both not generous and creative is rich or quiet and vice versa.
If paul is both patient and not wise then someone is either quiet or not happy and vice versa.
If someone is not humble then alice is not creative or not rich and vice versa.
Everyone who is both old and not kind is quiet or not humble.
If alice is not wise then mary is generous.
Everyone who is either not funny or not rich is either not generous or brave.
Everyone who is either not happy or not curious is either not kind or funny and vice versa.
Everyone who is old is strong or not old and vice versa.
Everyone who is kind is either not tall or not happy.
If alice is either patient or not quiet then lucy is both happy and not strong and vice versa.
Everyone who is not wise is not funny or not kind and vice versa.
Everyone who is both funny and not generous is kind and vice versa.
If someone is wise or rich then susan is curious and vice versa.
If john is both funny and not happy then someone is calm.
Lucy is not rich.
Someone is either curious or rich. | Mary is tall. | entailment | (![X]:((~happy(X)&~kind(X))<=>happy(X)))&
(((~calm(lucy)|~curious(lucy)))<=>(kind(susan)))&
(![X]:((~generous(X)&creative(X))<=>(rich(X)|quiet(X))))&
(((patient(paul)&~wise(paul)))<=>(?[X]:((quiet(X)<~>~happy(X)))))&
((?[X]:(~humble(X)))<=>((~creative(alice)|~rich(alice))))&
(![X]:((old(X)&~kind(X))=>(quiet(X)|~humble(X))))&
((~wise(alice))=>(generous(mary)))&
(![X]:((~funny(X)<~>~rich(X))=>(~generous(X)<~>brave(X))))&
(![X]:((~happy(X)<~>~curious(X))<=>(~kind(X)<~>funny(X))))&
(![X]:(old(X)<=>(strong(X)|~old(X))))&
(![X]:(kind(X)=>(~tall(X)<~>~happy(X))))&
(((patient(alice)<~>~quiet(alice)))<=>((happy(lucy)&~strong(lucy))))&
(![X]:(~wise(X)<=>(~funny(X)|~kind(X))))&
(![X]:((funny(X)&~generous(X))<=>kind(X)))&
((?[X]:((wise(X)|rich(X))))<=>(curious(susan)))&
(((funny(john)&~happy(john)))=>(?[X]:(calm(X))))&
(~rich(lucy))&
(?[X]:((curious(X)<~>rich(X)))) | tall(mary) | [
"p0",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 2077931501800781608477334
% SZS output start Proof for 2077931501800781608477334
1. ! [X0] : ((~kind(X0) & ~happy(X0)) <=> happy(X0)) [input p0]
11. ! [X0] : (kind(X0) => (~tall(X0) <~> ~happy(X0))) [input p10]
19. ~tall(mary) [input hypothesis]
24. ! [X0] : ((~tall(X0) <~> ~happy(X0)) | ~kind(X0)) [ennf transformation 11]
27. ! [X0] : (((~kind(X0) & ~happy(X0)) | ~happy(X0)) & (happy(X0) | (kind(X0) | happy(X0)))) [nnf transformation 1]
28. ! [X0] : (((~kind(X0) & ~happy(X0)) | ~happy(X0)) & (happy(X0) | kind(X0) | happy(X0))) [flattening 27]
47. ! [X0] : (((happy(X0) | tall(X0)) & (~happy(X0) | ~tall(X0))) | ~kind(X0)) [nnf transformation 24]
63. happy(X0) | kind(X0) | happy(X0) [cnf transformation 28]
64. ~happy(X0) | ~happy(X0) [cnf transformation 28]
101. happy(X0) | tall(X0) | ~kind(X0) [cnf transformation 47]
121. ~tall(mary) [cnf transformation 19]
124. happy(X0) | kind(X0) [duplicate literal removal 63]
125. ~happy(X0) [duplicate literal removal 64]
126. kind(X0) [subsumption resolution 124,125]
193. tall(X0) | ~kind(X0) [subsumption resolution 101,125]
194. tall(X0) [subsumption resolution 193,126]
247. $false [subsumption resolution 121,194]
% SZS output end Proof for 2077931501800781608477334
% ------------------------------
% 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 either not funny or creative then fred is either not funny or quiet. Everyone who is both not generous and strong is both wise and old and vice versa. If john is not old or not creative then mary is either tall or happy and vice versa. If john is either generous or not strong then someone is both not quiet and quiet. Everyone who is either not creative or not kind is funny or not generous. If john is generous then john is either not creative or happy. If someone is wise then someone is both not funny and not wise and vice versa. If susan is either wise or creative then john is not patient or humble. Everyone who is not calm is both not humble and creative. If paul is not wise or creative then john is creative. If someone is both wise and not curious then someone is not curious. If someone is either old or not brave then someone is both not humble and not rich and vice versa. If someone is kind or funny then someone is both old and kind. If someone is not happy or not tall then paul is both creative and curious and vice versa. Everyone who is quiet is not generous. Everyone who is either humble or strong is both tall and not old and vice versa. Fred is not funny or not happy. Someone is either quiet or not old. Mary is both not quiet and not calm. Someone is not wise or not funny. Someone is not humble. Someone is not funny. Someone is not wise or not happy. | John is not creative. | contradiction | ((?[X]:((~funny(X)<~>creative(X))))=>((~funny(fred)<~>quiet(fred))))&
(![X]:((~generous(X)&strong(X))<=>(wise(X)&old(X))))&
(((~old(john)|~creative(john)))<=>((tall(mary)<~>happy(mary))))&
(((generous(john)<~>~strong(john)))=>(?[X]:((~quiet(X)&quiet(X)))))&
(![X]:((~creative(X)<~>~kind(X))=>(funny(X)|~generous(X))))&
((generous(john))=>((~creative(john)<~>happy(john))))&
((?[X]:(wise(X)))<=>(?[X]:((~funny(X)&~wise(X)))))&
(((wise(susan)<~>creative(susan)))=>((~patient(john)|humble(john))))&
(![X]:(~calm(X)=>(~humble(X)&creative(X))))&
(((~wise(paul)|creative(paul)))=>(creative(john)))&
((?[X]:((wise(X)&~curious(X))))=>(?[X]:(~curious(X))))&
((?[X]:((old(X)<~>~brave(X))))<=>(?[X]:((~humble(X)&~rich(X)))))&
((?[X]:((kind(X)|funny(X))))=>(?[X]:((old(X)&kind(X)))))&
((?[X]:((~happy(X)|~tall(X))))<=>((creative(paul)&curious(paul))))&
(![X]:(quiet(X)=>~generous(X)))&
(![X]:((humble(X)<~>strong(X))<=>(tall(X)&~old(X))))&
((~funny(fred)|~happy(fred)))&
(?[X]:((quiet(X)<~>~old(X))))&
((~quiet(mary)&~calm(mary)))&
(?[X]:((~wise(X)|~funny(X))))&
(?[X]:(~humble(X)))&
(?[X]:(~funny(X)))&
(?[X]:((~wise(X)|~happy(X)))) | ~creative(john) | [
"p2",
"p9",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 4764180551379142064231772
% SZS output start Proof for 4764180551379142064231772
3. (~creative(john) | ~old(john)) <=> (tall(mary) <~> happy(mary)) [input p2]
10. (creative(paul) | ~wise(paul)) => creative(john) [input p9]
14. ? [X0] : (~tall(X0) | ~happy(X0)) <=> (curious(paul) & creative(paul)) [input p13]
24. ~creative(john) [input hypothesis]
36. creative(john) | (~creative(paul) & wise(paul)) [ennf transformation 10]
43. ((~creative(john) | ~old(john)) | ((tall(mary) | ~happy(mary)) & (happy(mary) | ~tall(mary)))) & (((~happy(mary) | ~tall(mary)) & (happy(mary) | tall(mary))) | (creative(john) & old(john))) [nnf transformation 3]
44. (~creative(john) | ~old(john) | ((tall(mary) | ~happy(mary)) & (happy(mary) | ~tall(mary)))) & (((~happy(mary) | ~tall(mary)) & (happy(mary) | tall(mary))) | (creative(john) & old(john))) [flattening 43]
66. (? [X0] : (~tall(X0) | ~happy(X0)) | (~curious(paul) | ~creative(paul))) & ((curious(paul) & creative(paul)) | ! [X0] : (tall(X0) & happy(X0))) [nnf transformation 14]
67. (? [X0] : (~tall(X0) | ~happy(X0)) | ~curious(paul) | ~creative(paul)) & ((curious(paul) & creative(paul)) | ! [X0] : (tall(X0) & happy(X0))) [flattening 66]
68. (? [X0] : (~tall(X0) | ~happy(X0)) | ~curious(paul) | ~creative(paul)) & ((curious(paul) & creative(paul)) | ! [X1] : (tall(X1) & happy(X1))) [rectify 67]
69. ? [X0] : (~tall(X0) | ~happy(X0)) => (~tall(sK7) | ~happy(sK7)) [choice axiom]
70. ((~tall(sK7) | ~happy(sK7)) | ~curious(paul) | ~creative(paul)) & ((curious(paul) & creative(paul)) | ! [X1] : (tall(X1) & happy(X1))) [skolemisation 68,69]
95. ~happy(mary) | ~tall(mary) | creative(john) [cnf transformation 44]
112. creative(john) | ~creative(paul) [cnf transformation 36]
124. creative(paul) | happy(X1) [cnf transformation 70]
125. creative(paul) | tall(X1) [cnf transformation 70]
145. ~creative(john) [cnf transformation 24]
165. 5 <=> happy(mary) [avatar definition]
167. ~happy(mary) <- (~5) [avatar component clause 165]
169. 6 <=> tall(mary) [avatar definition]
170. ~tall(mary) <- (~6) [avatar component clause 169]
177. 8 <=> creative(john) [avatar definition]
182. 8 | ~6 | ~5 [avatar split clause 95,165,169,177]
230. 18 <=> creative(paul) [avatar definition]
233. ~18 | 8 [avatar split clause 112,177,230]
310. 36 <=> ! [X1] : tall(X1) [avatar definition]
311. tall(X1) <- (36) [avatar component clause 310]
314. 37 <=> ! [X1] : happy(X1) [avatar definition]
315. happy(X1) <- (37) [avatar component clause 314]
317. 36 | 18 [avatar split clause 125,230,310]
318. 37 | 18 [avatar split clause 124,230,314]
352. ~8 [avatar split clause 145,177]
354. $false <- (~6, 36) [subsumption resolution 170,311]
355. 6 | ~36 [avatar contradiction clause 354]
356. $false <- (~5, 37) [subsumption resolution 167,315]
357. 5 | ~37 [avatar contradiction clause 356]
358. $false [avatar sat refutation 182,233,317,318,352,355,357]
% SZS output end Proof for 4764180551379142064231772
% ------------------------------
% 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 |
If fred is either humble or not wise then mary is both not curious and curious and vice versa. If paul is not humble then lucy is humble or not curious. If fred is not tall or not brave then someone is not old or humble and vice versa. If someone is both humble and not generous then lucy is both not humble and not tall and vice versa. Everyone who is both not tall and not patient is either not humble or patient and vice versa. Everyone who is both not patient and not creative is both not patient and calm and vice versa. If mary is either not kind or not strong then someone is brave and vice versa. Everyone who is old or not calm is both brave and not humble and vice versa. Everyone who is both not kind and not quiet is either not curious or not brave. If mary is not wise then someone is not calm and vice versa. If fred is not happy or kind then mary is both not generous and calm. If paul is calm then paul is either patient or not quiet and vice versa. If paul is either old or patient then alice is both creative and not creative. Everyone who is not patient is not happy or kind and vice versa. If fred is both not humble and quiet then paul is either not generous or not curious. Everyone who is not curious or patient is either not humble or strong and vice versa. Mary is both curious and not calm. Susan is both not old and not funny. Someone is both funny and not kind. Someone is generous. John is not brave. Paul is not happy or not funny. John is either not kind or wise. | Mary is not quiet. | contradiction | (((humble(fred)<~>~wise(fred)))<=>((~curious(mary)&curious(mary))))&
((~humble(paul))=>((humble(lucy)|~curious(lucy))))&
(((~tall(fred)|~brave(fred)))<=>(?[X]:((~old(X)|humble(X)))))&
((?[X]:((humble(X)&~generous(X))))<=>((~humble(lucy)&~tall(lucy))))&
(![X]:((~tall(X)&~patient(X))<=>(~humble(X)<~>patient(X))))&
(![X]:((~patient(X)&~creative(X))<=>(~patient(X)&calm(X))))&
(((~kind(mary)<~>~strong(mary)))<=>(?[X]:(brave(X))))&
(![X]:((old(X)|~calm(X))<=>(brave(X)&~humble(X))))&
(![X]:((~kind(X)&~quiet(X))=>(~curious(X)<~>~brave(X))))&
((~wise(mary))<=>(?[X]:(~calm(X))))&
(((~happy(fred)|kind(fred)))=>((~generous(mary)&calm(mary))))&
((calm(paul))<=>((patient(paul)<~>~quiet(paul))))&
(((old(paul)<~>patient(paul)))=>((creative(alice)&~creative(alice))))&
(![X]:(~patient(X)<=>(~happy(X)|kind(X))))&
(((~humble(fred)&quiet(fred)))=>((~generous(paul)<~>~curious(paul))))&
(![X]:((~curious(X)|patient(X))<=>(~humble(X)<~>strong(X))))&
((curious(mary)&~calm(mary)))&
((~old(susan)&~funny(susan)))&
(?[X]:((funny(X)&~kind(X))))&
(?[X]:(generous(X)))&
(~brave(john))&
((~happy(paul)|~funny(paul)))&
((~kind(john)<~>wise(john))) | ~quiet(mary) | [
"p6",
"p7",
"p8",
"p13",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 6949581488404702299450681
% SZS output start Proof for 6949581488404702299450681
7. (~kind(mary) <~> ~strong(mary)) <=> ? [X0] : brave(X0) [input p6]
8. ! [X0] : ((~calm(X0) | old(X0)) <=> (~humble(X0) & brave(X0))) [input p7]
9. ! [X0] : ((~quiet(X0) & ~kind(X0)) => (~curious(X0) <~> ~brave(X0))) [input p8]
14. ! [X0] : (~patient(X0) <=> (kind(X0) | ~happy(X0))) [input p13]
16. ! [X0] : ((patient(X0) | ~curious(X0)) <=> (~humble(X0) <~> strong(X0))) [input p15]
17. ~calm(mary) & curious(mary) [input p16]
24. ~quiet(mary) [input hypothesis]
27. ! [X0] : ((~curious(X0) <~> ~brave(X0)) | (quiet(X0) | kind(X0))) [ennf transformation 9]
28. ! [X0] : ((~curious(X0) <~> ~brave(X0)) | quiet(X0) | kind(X0)) [flattening 27]
49. (((strong(mary) | kind(mary)) & (~strong(mary) | ~kind(mary))) | ! [X0] : ~brave(X0)) & (? [X0] : brave(X0) | ((~kind(mary) | strong(mary)) & (~strong(mary) | kind(mary)))) [nnf transformation 7]
50. (((strong(mary) | kind(mary)) & (~strong(mary) | ~kind(mary))) | ! [X0] : ~brave(X0)) & (? [X1] : brave(X1) | ((~kind(mary) | strong(mary)) & (~strong(mary) | kind(mary)))) [rectify 49]
51. ? [X1] : brave(X1) => brave(sK2) [choice axiom]
52. (((strong(mary) | kind(mary)) & (~strong(mary) | ~kind(mary))) | ! [X0] : ~brave(X0)) & (brave(sK2) | ((~kind(mary) | strong(mary)) & (~strong(mary) | kind(mary)))) [skolemisation 50,51]
53. ! [X0] : (((~calm(X0) | old(X0)) | (humble(X0) | ~brave(X0))) & ((~humble(X0) & brave(X0)) | (calm(X0) & ~old(X0)))) [nnf transformation 8]
54. ! [X0] : ((~calm(X0) | old(X0) | humble(X0) | ~brave(X0)) & ((~humble(X0) & brave(X0)) | (calm(X0) & ~old(X0)))) [flattening 53]
55. ! [X0] : (((brave(X0) | curious(X0)) & (~brave(X0) | ~curious(X0))) | quiet(X0) | kind(X0)) [nnf transformation 28]
62. ! [X0] : ((~patient(X0) | (~kind(X0) & happy(X0))) & ((kind(X0) | ~happy(X0)) | patient(X0))) [nnf transformation 14]
63. ! [X0] : ((~patient(X0) | (~kind(X0) & happy(X0))) & (kind(X0) | ~happy(X0) | patient(X0))) [flattening 62]
65. ! [X0] : (((patient(X0) | ~curious(X0)) | ((~humble(X0) | ~strong(X0)) & (strong(X0) | humble(X0)))) & (((~strong(X0) | humble(X0)) & (strong(X0) | ~humble(X0))) | (~patient(X0) & curious(X0)))) [nnf transformation 16]
66. ! [X0] : ((patient(X0) | ~curious(X0) | ((~humble(X0) | ~strong(X0)) & (strong(X0) | humble(X0)))) & (((~strong(X0) | humble(X0)) & (strong(X0) | ~humble(X0))) | (~patient(X0) & curious(X0)))) [flattening 65]
99. ~strong(mary) | ~kind(mary) | ~brave(X0) [cnf transformation 52]
102. calm(X0) | brave(X0) [cnf transformation 54]
104. ~humble(X0) | calm(X0) [cnf transformation 54]
106. ~brave(X0) | ~curious(X0) | quiet(X0) | kind(X0) [cnf transformation 55]
124. ~kind(X0) | ~patient(X0) [cnf transformation 63]
131. ~curious(X0) | patient(X0) | strong(X0) | humble(X0) [cnf transformation 66]
133. curious(mary) [cnf transformation 17]
134. ~calm(mary) [cnf transformation 17]
144. ~quiet(mary) [cnf transformation 24]
156. 3 <=> curious(mary) [avatar definition]
158. curious(mary) <- (3) [avatar component clause 156]
223. 17 <=> ! [X0] : ~brave(X0) [avatar definition]
224. ~brave(X0) <- (17) [avatar component clause 223]
226. 18 <=> kind(mary) [avatar definition]
228. kind(mary) <- (18) [avatar component clause 226]
230. 19 <=> strong(mary) [avatar definition]
231. ~strong(mary) <- (~19) [avatar component clause 230]
234. 17 | ~18 | ~19 [avatar split clause 99,230,226,223]
259. 25 <=> calm(mary) [avatar definition]
260. ~calm(mary) <- (~25) [avatar component clause 259]
318. ~25 [avatar split clause 134,259]
319. 3 [avatar split clause 133,156]
340. brave(mary) <- (~25) [resolution 102,260]
344. $false <- (17, ~25) [subsumption resolution 340,224]
345. ~17 | 25 [avatar contradiction clause 344]
350. ~patient(mary) <- (18) [resolution 124,228]
429. ~curious(mary) | quiet(mary) | kind(mary) <- (~25) [resolution 106,340]
481. patient(mary) | strong(mary) | humble(mary) <- (3) [resolution 131,158]
482. strong(mary) | humble(mary) <- (3, 18) [subsumption resolution 481,350]
483. humble(mary) <- (3, 18, ~19) [subsumption resolution 482,231]
486. calm(mary) <- (3, 18, ~19) [resolution 483,104]
487. $false <- (3, 18, ~19, ~25) [subsumption resolution 486,260]
488. ~3 | ~18 | 19 | 25 [avatar contradiction clause 487]
498. quiet(mary) | kind(mary) <- (3, ~25) [subsumption resolution 429,158]
499. kind(mary) <- (3, ~25) [subsumption resolution 498,144]
500. 18 | ~3 | 25 [avatar split clause 499,259,156,226]
506. $false [avatar sat refutation 234,318,319,345,488,500]
% SZS output end Proof for 6949581488404702299450681
% ------------------------------
% 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: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is generous or curious is not curious or quiet and vice versa.
Everyone who is either funny or tall is creative.
If mary is calm then someone is not old.
If someone is wise or not calm then someone is patient and vice versa.
Everyone who is not quiet or not creative is either not tall or quiet.
If mary is both creative and brave then susan is both not curious and brave and vice versa.
Everyone who is not old or not brave is either not tall or old.
If someone is not quiet then fred is not rich.
Everyone who is either curious or kind is not humble and vice versa.
If someone is both humble and brave then john is not creative or not kind.
If someone is quiet or not strong then someone is either not strong or happy.
Everyone who is either not creative or generous is either not patient or not old and vice versa.
Everyone who is not quiet is old or kind and vice versa.
Everyone who is both humble and tall is both creative and rich and vice versa.
If someone is either tall or old then someone is either not creative or wise and vice versa.
Everyone who is both not tall and not humble is quiet and vice versa.
Someone is both not quiet and wise.
Someone is calm.
Fred is curious.
John is not tall or curious.
Someone is not generous or not creative.
Someone is calm or not wise.
Mary is both patient and not humble. | Susan is not kind. | entailment | (![X]:((generous(X)|curious(X))<=>(~curious(X)|quiet(X))))&
(![X]:((funny(X)<~>tall(X))=>creative(X)))&
((calm(mary))=>(?[X]:(~old(X))))&
((?[X]:((wise(X)|~calm(X))))<=>(?[X]:(patient(X))))&
(![X]:((~quiet(X)|~creative(X))=>(~tall(X)<~>quiet(X))))&
(((creative(mary)&brave(mary)))<=>((~curious(susan)&brave(susan))))&
(![X]:((~old(X)|~brave(X))=>(~tall(X)<~>old(X))))&
((?[X]:(~quiet(X)))=>(~rich(fred)))&
(![X]:((curious(X)<~>kind(X))<=>~humble(X)))&
((?[X]:((humble(X)&brave(X))))=>((~creative(john)|~kind(john))))&
((?[X]:((quiet(X)|~strong(X))))=>(?[X]:((~strong(X)<~>happy(X)))))&
(![X]:((~creative(X)<~>generous(X))<=>(~patient(X)<~>~old(X))))&
(![X]:(~quiet(X)<=>(old(X)|kind(X))))&
(![X]:((humble(X)&tall(X))<=>(creative(X)&rich(X))))&
((?[X]:((tall(X)<~>old(X))))<=>(?[X]:((~creative(X)<~>wise(X)))))&
(![X]:((~tall(X)&~humble(X))<=>quiet(X)))&
(?[X]:((~quiet(X)&wise(X))))&
(?[X]:(calm(X)))&
(curious(fred))&
((~tall(john)|curious(john)))&
(?[X]:((~generous(X)|~creative(X))))&
(?[X]:((calm(X)|~wise(X))))&
((patient(mary)&~humble(mary))) | ~kind(susan) | [
"p0",
"p4",
"p8",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8540555166234038420736567
% SZS output start Proof for 8540555166234038420736567
1. ! [X0] : ((curious(X0) | generous(X0)) <=> (quiet(X0) | ~curious(X0))) [input p0]
5. ! [X0] : ((~creative(X0) | ~quiet(X0)) => (~tall(X0) <~> quiet(X0))) [input p4]
9. ! [X0] : ((curious(X0) <~> kind(X0)) <=> ~humble(X0)) [input p8]
13. ! [X0] : (~quiet(X0) <=> (kind(X0) | old(X0))) [input p12]
16. ! [X0] : ((~humble(X0) & ~tall(X0)) <=> quiet(X0)) [input p15]
24. kind(susan) [input hypothesis]
30. ! [X0] : ((~tall(X0) <~> quiet(X0)) | (creative(X0) & quiet(X0))) [ennf transformation 5]
36. ! [X0] : (((curious(X0) | generous(X0)) | (~quiet(X0) & curious(X0))) & ((quiet(X0) | ~curious(X0)) | (~curious(X0) & ~generous(X0)))) [nnf transformation 1]
37. ! [X0] : ((curious(X0) | generous(X0) | (~quiet(X0) & curious(X0))) & (quiet(X0) | ~curious(X0) | (~curious(X0) & ~generous(X0)))) [flattening 36]
46. ! [X0] : (((~quiet(X0) | tall(X0)) & (quiet(X0) | ~tall(X0))) | (creative(X0) & quiet(X0))) [nnf transformation 30]
50. ! [X0] : ((((~kind(X0) | ~curious(X0)) & (kind(X0) | curious(X0))) | humble(X0)) & (~humble(X0) | ((curious(X0) | ~kind(X0)) & (kind(X0) | ~curious(X0))))) [nnf transformation 9]
56. ! [X0] : ((~quiet(X0) | (~kind(X0) & ~old(X0))) & ((kind(X0) | old(X0)) | quiet(X0))) [nnf transformation 13]
57. ! [X0] : ((~quiet(X0) | (~kind(X0) & ~old(X0))) & (kind(X0) | old(X0) | quiet(X0))) [flattening 56]
65. ! [X0] : (((~humble(X0) & ~tall(X0)) | ~quiet(X0)) & (quiet(X0) | (humble(X0) | tall(X0)))) [nnf transformation 16]
66. ! [X0] : (((~humble(X0) & ~tall(X0)) | ~quiet(X0)) & (quiet(X0) | humble(X0) | tall(X0))) [flattening 65]
76. quiet(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 37]
85. quiet(X0) | ~tall(X0) | quiet(X0) [cnf transformation 46]
99. ~humble(X0) | curious(X0) | ~kind(X0) [cnf transformation 50]
117. ~kind(X0) | ~quiet(X0) [cnf transformation 57]
130. quiet(X0) | humble(X0) | tall(X0) [cnf transformation 66]
131. ~tall(X0) | ~quiet(X0) [cnf transformation 66]
142. kind(susan) [cnf transformation 24]
144. ~tall(X0) | quiet(X0) [duplicate literal removal 85]
145. ~curious(X0) | quiet(X0) [duplicate literal removal 76]
273. ~tall(X0) [subsumption resolution 131,144]
274. humble(X0) | quiet(X0) [subsumption resolution 130,273]
324. curious(X0) | ~kind(X0) | quiet(X0) [resolution 99,274]
325. ~kind(X0) | quiet(X0) [subsumption resolution 324,145]
326. ~kind(X0) [subsumption resolution 325,117]
327. $false [resolution 326,142]
% SZS output end Proof for 8540555166234038420736567
% ------------------------------
% 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 calm is both curious and not calm.
Everyone who is old or generous is not old or not quiet.
If susan is both brave and old then alice is rich and vice versa.
If someone is either brave or not generous then someone is both not funny and not happy.
Everyone who is not funny is both not kind and not patient and vice versa.
If someone is not calm then john is either patient or not brave and vice versa.
If paul is either not funny or not generous then john is both not funny and patient and vice versa.
If someone is not curious then someone is either not old or not creative and vice versa.
Everyone who is either not kind or not humble is not brave and vice versa.
Everyone who is not patient is both not funny and not curious.
If someone is either not calm or not kind then john is both wise and not funny.
If someone is both funny and humble then someone is not patient and vice versa.
Everyone who is both patient and not tall is either funny or not kind and vice versa.
If fred is funny or not rich then someone is not patient or rich and vice versa.
Everyone who is quiet or humble is both wise and not calm and vice versa.
If alice is not tall then john is not strong or not tall.
Lucy is both not old and not quiet.
Someone is not rich.
John is either strong or generous.
Mary is happy or calm.
Lucy is not kind or not humble.
Paul is not quiet or quiet.
Alice is either quiet or creative. | John is not old. | neutral | (![X]:(~calm(X)=>(curious(X)&~calm(X))))&
(![X]:((old(X)|generous(X))=>(~old(X)|~quiet(X))))&
(((brave(susan)&old(susan)))<=>(rich(alice)))&
((?[X]:((brave(X)<~>~generous(X))))=>(?[X]:((~funny(X)&~happy(X)))))&
(![X]:(~funny(X)<=>(~kind(X)&~patient(X))))&
((?[X]:(~calm(X)))<=>((patient(john)<~>~brave(john))))&
(((~funny(paul)<~>~generous(paul)))<=>((~funny(john)&patient(john))))&
((?[X]:(~curious(X)))<=>(?[X]:((~old(X)<~>~creative(X)))))&
(![X]:((~kind(X)<~>~humble(X))<=>~brave(X)))&
(![X]:(~patient(X)=>(~funny(X)&~curious(X))))&
((?[X]:((~calm(X)<~>~kind(X))))=>((wise(john)&~funny(john))))&
((?[X]:((funny(X)&humble(X))))<=>(?[X]:(~patient(X))))&
(![X]:((patient(X)&~tall(X))<=>(funny(X)<~>~kind(X))))&
(((funny(fred)|~rich(fred)))<=>(?[X]:((~patient(X)|rich(X)))))&
(![X]:((quiet(X)|humble(X))<=>(wise(X)&~calm(X))))&
((~tall(alice))=>((~strong(john)|~tall(john))))&
((~old(lucy)&~quiet(lucy)))&
(?[X]:(~rich(X)))&
((strong(john)<~>generous(john)))&
((happy(mary)|calm(mary)))&
((~kind(lucy)|~humble(lucy)))&
((~quiet(paul)|quiet(paul)))&
((quiet(alice)<~>creative(alice))) | ~old(john) | [] | null | 0 |
If someone is both not humble and not old then mary is not happy.
If paul is both not calm and happy then someone is strong and vice versa.
If paul is not quiet or curious then someone is both brave and not humble.
Everyone who is not happy or happy is patient and vice versa.
Everyone who is either creative or funny is either not happy or not creative and vice versa.
Everyone who is creative is either creative or not quiet.
Everyone who is not creative is not funny.
Everyone who is calm is both not patient and not happy and vice versa.
Everyone who is either creative or old is either not humble or not quiet and vice versa.
Everyone who is both not wise and quiet is either not calm or tall.
Everyone who is both curious and not quiet is both not creative and not brave and vice versa.
Everyone who is both not brave and not funny is not humble.
If someone is either not patient or old then john is either wise or not rich and vice versa.
If someone is either brave or not kind then alice is both generous and patient and vice versa.
If someone is either not patient or happy then someone is generous or strong and vice versa.
Everyone who is curious or not creative is not humble or not rich and vice versa.
Mary is both not strong and not tall.
Mary is either not strong or not curious.
Alice is either not creative or old.
Mary is creative.
Paul is either curious or rich.
John is creative or not creative.
Susan is either not calm or not happy.
Someone is both not calm and creative. | Susan is not quiet. | contradiction | ((?[X]:((~humble(X)&~old(X))))=>(~happy(mary)))&
(((~calm(paul)&happy(paul)))<=>(?[X]:(strong(X))))&
(((~quiet(paul)|curious(paul)))=>(?[X]:((brave(X)&~humble(X)))))&
(![X]:((~happy(X)|happy(X))<=>patient(X)))&
(![X]:((creative(X)<~>funny(X))<=>(~happy(X)<~>~creative(X))))&
(![X]:(creative(X)=>(creative(X)<~>~quiet(X))))&
(![X]:(~creative(X)=>~funny(X)))&
(![X]:(calm(X)<=>(~patient(X)&~happy(X))))&
(![X]:((creative(X)<~>old(X))<=>(~humble(X)<~>~quiet(X))))&
(![X]:((~wise(X)&quiet(X))=>(~calm(X)<~>tall(X))))&
(![X]:((curious(X)&~quiet(X))<=>(~creative(X)&~brave(X))))&
(![X]:((~brave(X)&~funny(X))=>~humble(X)))&
((?[X]:((~patient(X)<~>old(X))))<=>((wise(john)<~>~rich(john))))&
((?[X]:((brave(X)<~>~kind(X))))<=>((generous(alice)&patient(alice))))&
((?[X]:((~patient(X)<~>happy(X))))<=>(?[X]:((generous(X)|strong(X)))))&
(![X]:((curious(X)|~creative(X))<=>(~humble(X)|~rich(X))))&
((~strong(mary)&~tall(mary)))&
((~strong(mary)<~>~curious(mary)))&
((~creative(alice)<~>old(alice)))&
(creative(mary))&
((curious(paul)<~>rich(paul)))&
((creative(john)|~creative(john)))&
((~calm(susan)<~>~happy(susan)))&
(?[X]:((~calm(X)&creative(X)))) | ~quiet(susan) | [
"p3",
"p4",
"p5",
"p6",
"p7",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 4836659443582397137232224
% SZS output start Proof for 4836659443582397137232224
4. ! [X0] : ((happy(X0) | ~happy(X0)) <=> patient(X0)) [input p3]
5. ! [X0] : ((creative(X0) <~> funny(X0)) <=> (~happy(X0) <~> ~creative(X0))) [input p4]
6. ! [X0] : (creative(X0) => (creative(X0) <~> ~quiet(X0))) [input p5]
7. ! [X0] : (~creative(X0) => ~funny(X0)) [input p6]
8. ! [X0] : (calm(X0) <=> (~happy(X0) & ~patient(X0))) [input p7]
23. ~calm(susan) <~> ~happy(susan) [input p22]
25. ~quiet(susan) [input hypothesis]
29. ! [X0] : ((creative(X0) <~> ~quiet(X0)) | ~creative(X0)) [ennf transformation 6]
30. ! [X0] : (~funny(X0) | creative(X0)) [ennf transformation 7]
42. ! [X0] : (((happy(X0) | ~happy(X0)) | ~patient(X0)) & (patient(X0) | (~happy(X0) & happy(X0)))) [nnf transformation 4]
43. ! [X0] : ((happy(X0) | ~happy(X0) | ~patient(X0)) & (patient(X0) | (~happy(X0) & happy(X0)))) [flattening 42]
44. ! [X0] : ((((~funny(X0) | ~creative(X0)) & (funny(X0) | creative(X0))) | ((~happy(X0) | creative(X0)) & (~creative(X0) | happy(X0)))) & (((creative(X0) | happy(X0)) & (~creative(X0) | ~happy(X0))) | ((creative(X0) | ~funny(X0)) & (funny(X0) | ~creative(X0))))) [nnf transformation 5]
45. ! [X0] : (((quiet(X0) | ~creative(X0)) & (~quiet(X0) | creative(X0))) | ~creative(X0)) [nnf transformation 29]
46. ! [X0] : ((calm(X0) | (happy(X0) | patient(X0))) & ((~happy(X0) & ~patient(X0)) | ~calm(X0))) [nnf transformation 8]
47. ! [X0] : ((calm(X0) | happy(X0) | patient(X0)) & ((~happy(X0) & ~patient(X0)) | ~calm(X0))) [flattening 46]
71. (happy(susan) | calm(susan)) & (~happy(susan) | ~calm(susan)) [nnf transformation 23]
82. patient(X0) | happy(X0) [cnf transformation 43]
83. ~happy(X0) | patient(X0) [cnf transformation 43]
85. ~creative(X0) | ~happy(X0) | funny(X0) | ~creative(X0) [cnf transformation 44]
90. funny(X0) | creative(X0) | ~happy(X0) | creative(X0) [cnf transformation 44]
94. quiet(X0) | ~creative(X0) | ~creative(X0) [cnf transformation 45]
95. ~funny(X0) | creative(X0) [cnf transformation 30]
96. ~patient(X0) | ~calm(X0) [cnf transformation 47]
149. happy(susan) | calm(susan) [cnf transformation 71]
152. ~quiet(susan) [cnf transformation 25]
153. ~creative(X0) | quiet(X0) [duplicate literal removal 94]
154. ~creative(X0) | ~happy(X0) | funny(X0) [duplicate literal removal 85]
156. funny(X0) | creative(X0) | ~happy(X0) [duplicate literal removal 90]
204. patient(X0) [subsumption resolution 82,83]
206. ~happy(X0) | funny(X0) [subsumption resolution 154,156]
207. ~calm(X0) [subsumption resolution 96,204]
301. happy(susan) [subsumption resolution 149,207]
318. funny(susan) [resolution 206,301]
321. creative(susan) [resolution 318,95]
362. quiet(susan) [resolution 321,153]
363. $false [subsumption resolution 362,152]
% SZS output end Proof for 4836659443582397137232224
% ------------------------------
% 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 |
Everyone who is not calm is either old or not strong. Everyone who is either not kind or quiet is patient or not wise. Everyone who is patient is brave or tall. Everyone who is not generous is both not humble and not brave. Everyone who is both kind and not kind is brave and vice versa. If someone is both funny and not kind then alice is humble or not generous and vice versa. If someone is both happy and not old then fred is rich. Everyone who is tall or quiet is either quiet or not curious and vice versa. If someone is not wise or rich then someone is creative and vice versa. Everyone who is either calm or not strong is not generous or not brave and vice versa. If alice is wise then someone is both generous and not brave and vice versa. Everyone who is tall or funny is both not strong and calm and vice versa. If fred is not brave then someone is happy or not happy. Everyone who is not kind or quiet is not kind or not funny and vice versa. Everyone who is generous or not rich is creative or kind. If someone is generous or not tall then someone is both curious and not old. Someone is creative or not rich. Someone is either humble or not patient. Lucy is both not old and not funny. John is either not generous or not patient. Someone is not calm. Lucy is both not kind and calm. Fred is both not humble and not creative. | Lucy is curious. | entailment | (![X]:(~calm(X)=>(old(X)<~>~strong(X))))&
(![X]:((~kind(X)<~>quiet(X))=>(patient(X)|~wise(X))))&
(![X]:(patient(X)=>(brave(X)|tall(X))))&
(![X]:(~generous(X)=>(~humble(X)&~brave(X))))&
(![X]:((kind(X)&~kind(X))<=>brave(X)))&
((?[X]:((funny(X)&~kind(X))))<=>((humble(alice)|~generous(alice))))&
((?[X]:((happy(X)&~old(X))))=>(rich(fred)))&
(![X]:((tall(X)|quiet(X))<=>(quiet(X)<~>~curious(X))))&
((?[X]:((~wise(X)|rich(X))))<=>(?[X]:(creative(X))))&
(![X]:((calm(X)<~>~strong(X))<=>(~generous(X)|~brave(X))))&
((wise(alice))<=>(?[X]:((generous(X)&~brave(X)))))&
(![X]:((tall(X)|funny(X))<=>(~strong(X)&calm(X))))&
((~brave(fred))=>(?[X]:((happy(X)|~happy(X)))))&
(![X]:((~kind(X)|quiet(X))<=>(~kind(X)|~funny(X))))&
(![X]:((generous(X)|~rich(X))=>(creative(X)|kind(X))))&
((?[X]:((generous(X)|~tall(X))))=>(?[X]:((curious(X)&~old(X)))))&
(?[X]:((creative(X)|~rich(X))))&
(?[X]:((humble(X)<~>~patient(X))))&
((~old(lucy)&~funny(lucy)))&
((~generous(john)<~>~patient(john)))&
(?[X]:(~calm(X)))&
((~kind(lucy)&calm(lucy)))&
((~humble(fred)&~creative(fred))) | curious(lucy) | [
"p4",
"p7",
"p9",
"p11",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 6953818662294381354114492
% SZS output start Proof for 6953818662294381354114492
5. ! [X0] : ((~kind(X0) & kind(X0)) <=> brave(X0)) [input p4]
8. ! [X0] : ((quiet(X0) | tall(X0)) <=> (quiet(X0) <~> ~curious(X0))) [input p7]
10. ! [X0] : ((calm(X0) <~> ~strong(X0)) <=> (~brave(X0) | ~generous(X0))) [input p9]
12. ! [X0] : ((funny(X0) | tall(X0)) <=> (calm(X0) & ~strong(X0))) [input p11]
22. calm(lucy) & ~kind(lucy) [input p21]
24. ~curious(lucy) [input hypothesis]
40. ! [X0] : (((~kind(X0) & kind(X0)) | ~brave(X0)) & (brave(X0) | (kind(X0) | ~kind(X0)))) [nnf transformation 5]
41. ! [X0] : (((~kind(X0) & kind(X0)) | ~brave(X0)) & (brave(X0) | kind(X0) | ~kind(X0))) [flattening 40]
47. ! [X0] : (((quiet(X0) | tall(X0)) | ((quiet(X0) | curious(X0)) & (~curious(X0) | ~quiet(X0)))) & (((curious(X0) | ~quiet(X0)) & (~curious(X0) | quiet(X0))) | (~quiet(X0) & ~tall(X0)))) [nnf transformation 8]
48. ! [X0] : ((quiet(X0) | tall(X0) | ((quiet(X0) | curious(X0)) & (~curious(X0) | ~quiet(X0)))) & (((curious(X0) | ~quiet(X0)) & (~curious(X0) | quiet(X0))) | (~quiet(X0) & ~tall(X0)))) [flattening 47]
54. ! [X0] : ((((strong(X0) | ~calm(X0)) & (~strong(X0) | calm(X0))) | (brave(X0) & generous(X0))) & ((~brave(X0) | ~generous(X0)) | ((calm(X0) | strong(X0)) & (~strong(X0) | ~calm(X0))))) [nnf transformation 10]
55. ! [X0] : ((((strong(X0) | ~calm(X0)) & (~strong(X0) | calm(X0))) | (brave(X0) & generous(X0))) & (~brave(X0) | ~generous(X0) | ((calm(X0) | strong(X0)) & (~strong(X0) | ~calm(X0))))) [flattening 54]
60. ! [X0] : (((funny(X0) | tall(X0)) | (~calm(X0) | strong(X0))) & ((calm(X0) & ~strong(X0)) | (~funny(X0) & ~tall(X0)))) [nnf transformation 12]
61. ! [X0] : ((funny(X0) | tall(X0) | ~calm(X0) | strong(X0)) & ((calm(X0) & ~strong(X0)) | (~funny(X0) & ~tall(X0)))) [flattening 60]
85. kind(X0) | ~brave(X0) [cnf transformation 41]
86. ~brave(X0) | ~kind(X0) [cnf transformation 41]
96. curious(X0) | ~quiet(X0) | ~quiet(X0) [cnf transformation 48]
98. quiet(X0) | tall(X0) | quiet(X0) | curious(X0) [cnf transformation 48]
107. strong(X0) | ~calm(X0) | brave(X0) [cnf transformation 55]
111. ~tall(X0) | ~strong(X0) [cnf transformation 61]
136. calm(lucy) [cnf transformation 22]
139. ~curious(lucy) [cnf transformation 24]
140. ~quiet(X0) | curious(X0) [duplicate literal removal 96]
141. curious(X0) | tall(X0) | quiet(X0) [duplicate literal removal 98]
142. ~brave(X0) [subsumption resolution 85,86]
199. ~calm(X0) | strong(X0) [subsumption resolution 107,142]
267. strong(lucy) [resolution 199,136]
324. tall(lucy) | quiet(lucy) [resolution 141,139]
328. 35 <=> quiet(lucy) [avatar definition]
330. quiet(lucy) <- (35) [avatar component clause 328]
332. 36 <=> tall(lucy) [avatar definition]
334. tall(lucy) <- (36) [avatar component clause 332]
335. 35 | 36 [avatar split clause 324,332,328]
363. curious(lucy) <- (35) [resolution 330,140]
364. $false <- (35) [subsumption resolution 363,139]
365. ~35 [avatar contradiction clause 364]
367. ~strong(lucy) <- (36) [resolution 334,111]
368. $false <- (36) [subsumption resolution 367,267]
369. ~36 [avatar contradiction clause 368]
370. $false [avatar sat refutation 335,365,369]
% SZS output end Proof for 6953818662294381354114492
% ------------------------------
% 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: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is rich is brave. Everyone who is both curious and not kind is not rich or happy. Everyone who is generous is not rich. Everyone who is strong is both not humble and not brave and vice versa. Everyone who is both creative and not curious is both funny and not calm and vice versa. If fred is not happy then someone is calm or curious and vice versa. If john is not creative or humble then someone is wise or patient and vice versa. Everyone who is both not quiet and not creative is happy and vice versa. Everyone who is both not old and not strong is curious or not patient. If someone is not happy or not curious then someone is both kind and quiet. If fred is either wise or quiet then someone is brave or not humble. If susan is either not quiet or old then someone is kind or curious and vice versa. Everyone who is either generous or old is either brave or not generous and vice versa. Everyone who is both not tall and not kind is strong and vice versa. Everyone who is not curious or wise is rich or not old and vice versa. Everyone who is not quiet is not creative or strong and vice versa. Someone is either tall or creative. Alice is rich or not brave. Someone is both not calm and not generous. Paul is either rich or kind. Someone is either creative or not wise. Someone is not humble or not quiet. Someone is not creative. | Alice is happy. | neutral | (![X]:(rich(X)=>brave(X)))&
(![X]:((curious(X)&~kind(X))=>(~rich(X)|happy(X))))&
(![X]:(generous(X)=>~rich(X)))&
(![X]:(strong(X)<=>(~humble(X)&~brave(X))))&
(![X]:((creative(X)&~curious(X))<=>(funny(X)&~calm(X))))&
((~happy(fred))<=>(?[X]:((calm(X)|curious(X)))))&
(((~creative(john)|humble(john)))<=>(?[X]:((wise(X)|patient(X)))))&
(![X]:((~quiet(X)&~creative(X))<=>happy(X)))&
(![X]:((~old(X)&~strong(X))=>(curious(X)|~patient(X))))&
((?[X]:((~happy(X)|~curious(X))))=>(?[X]:((kind(X)&quiet(X)))))&
(((wise(fred)<~>quiet(fred)))=>(?[X]:((brave(X)|~humble(X)))))&
(((~quiet(susan)<~>old(susan)))<=>(?[X]:((kind(X)|curious(X)))))&
(![X]:((generous(X)<~>old(X))<=>(brave(X)<~>~generous(X))))&
(![X]:((~tall(X)&~kind(X))<=>strong(X)))&
(![X]:((~curious(X)|wise(X))<=>(rich(X)|~old(X))))&
(![X]:(~quiet(X)<=>(~creative(X)|strong(X))))&
(?[X]:((tall(X)<~>creative(X))))&
((rich(alice)|~brave(alice)))&
(?[X]:((~calm(X)&~generous(X))))&
((rich(paul)<~>kind(paul)))&
(?[X]:((creative(X)<~>~wise(X))))&
(?[X]:((~humble(X)|~quiet(X))))&
(?[X]:(~creative(X))) | happy(alice) | [] | null | 0 |
Everyone who is funny is both quiet and not old.
If paul is both not creative and not happy then someone is either not generous or happy.
Everyone who is both kind and not brave is either rich or creative and vice versa.
Everyone who is both not wise and creative is either not humble or quiet and vice versa.
If paul is patient or not humble then fred is not calm or not creative and vice versa.
Everyone who is not kind or not generous is creative.
Everyone who is either humble or strong is brave or not tall.
If susan is either not patient or not generous then john is strong and vice versa.
If john is either humble or wise then someone is either not rich or not happy.
Everyone who is either funny or old is both not creative and strong and vice versa.
If lucy is both wise and quiet then mary is both generous and not humble and vice versa.
Everyone who is either creative or not humble is not happy or patient.
If someone is not wise or not curious then mary is either kind or curious.
Everyone who is patient or not patient is creative and vice versa.
If someone is both old and not patient then john is generous or wise and vice versa.
Everyone who is both not humble and quiet is not humble or not brave.
Someone is generous or kind.
Susan is both not brave and not tall.
Fred is either brave or not rich.
Lucy is happy.
Alice is brave or generous. | Fred is not old. | entailment | (![X]:(funny(X)=>(quiet(X)&~old(X))))&
(((~creative(paul)&~happy(paul)))=>(?[X]:((~generous(X)<~>happy(X)))))&
(![X]:((kind(X)&~brave(X))<=>(rich(X)<~>creative(X))))&
(![X]:((~wise(X)&creative(X))<=>(~humble(X)<~>quiet(X))))&
(((patient(paul)|~humble(paul)))<=>((~calm(fred)|~creative(fred))))&
(![X]:((~kind(X)|~generous(X))=>creative(X)))&
(![X]:((humble(X)<~>strong(X))=>(brave(X)|~tall(X))))&
(((~patient(susan)<~>~generous(susan)))<=>(strong(john)))&
(((humble(john)<~>wise(john)))=>(?[X]:((~rich(X)<~>~happy(X)))))&
(![X]:((funny(X)<~>old(X))<=>(~creative(X)&strong(X))))&
(((wise(lucy)&quiet(lucy)))<=>((generous(mary)&~humble(mary))))&
(![X]:((creative(X)<~>~humble(X))=>(~happy(X)|patient(X))))&
((?[X]:((~wise(X)|~curious(X))))=>((kind(mary)<~>curious(mary))))&
(![X]:((patient(X)|~patient(X))<=>creative(X)))&
((?[X]:((old(X)&~patient(X))))<=>((generous(john)|wise(john))))&
(![X]:((~humble(X)&quiet(X))=>(~humble(X)|~brave(X))))&
(?[X]:((generous(X)|kind(X))))&
((~brave(susan)&~tall(susan)))&
((brave(fred)<~>~rich(fred)))&
(happy(lucy))&
((brave(alice)|generous(alice))) | ~old(fred) | [
"p0",
"p9",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 2992891996968991010412540
% SZS output start Proof for 2992891996968991010412540
1. ! [X0] : (funny(X0) => (~old(X0) & quiet(X0))) [input p0]
10. ! [X0] : ((funny(X0) <~> old(X0)) <=> (strong(X0) & ~creative(X0))) [input p9]
14. ! [X0] : ((~patient(X0) | patient(X0)) <=> creative(X0)) [input p13]
22. old(fred) [input hypothesis]
25. ! [X0] : ((~old(X0) & quiet(X0)) | ~funny(X0)) [ennf transformation 1]
48. ! [X0] : ((((~old(X0) | ~funny(X0)) & (old(X0) | funny(X0))) | (~strong(X0) | creative(X0))) & ((strong(X0) & ~creative(X0)) | ((funny(X0) | ~old(X0)) & (old(X0) | ~funny(X0))))) [nnf transformation 10]
49. ! [X0] : ((((~old(X0) | ~funny(X0)) & (old(X0) | funny(X0))) | ~strong(X0) | creative(X0)) & ((strong(X0) & ~creative(X0)) | ((funny(X0) | ~old(X0)) & (old(X0) | ~funny(X0))))) [flattening 48]
54. ! [X0] : (((~patient(X0) | patient(X0)) | ~creative(X0)) & (creative(X0) | (patient(X0) & ~patient(X0)))) [nnf transformation 14]
55. ! [X0] : ((~patient(X0) | patient(X0) | ~creative(X0)) & (creative(X0) | (patient(X0) & ~patient(X0)))) [flattening 54]
65. ~old(X0) | ~funny(X0) [cnf transformation 25]
95. ~creative(X0) | funny(X0) | ~old(X0) [cnf transformation 49]
110. creative(X0) | ~patient(X0) [cnf transformation 55]
111. patient(X0) | creative(X0) [cnf transformation 55]
125. old(fred) [cnf transformation 22]
202. ~creative(X0) | ~old(X0) [subsumption resolution 95,65]
242. creative(X0) [subsumption resolution 110,111]
302. ~old(X0) [resolution 202,242]
304. $false [resolution 302,125]
% SZS output end Proof for 2992891996968991010412540
% ------------------------------
% 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 wise is either not funny or kind and vice versa.
Everyone who is both not calm and creative is both not happy and not patient and vice versa.
Everyone who is not tall or not calm is either not strong or curious and vice versa.
If alice is strong or happy then someone is not humble or humble and vice versa.
If someone is not brave then mary is either creative or strong and vice versa.
Everyone who is both strong and calm is not happy and vice versa.
Everyone who is calm is either not wise or not humble.
Everyone who is either curious or brave is both not kind and rich and vice versa.
Everyone who is kind or not funny is both not strong and happy.
Everyone who is not curious is either not generous or not patient.
Everyone who is either not funny or quiet is humble or not creative and vice versa.
Everyone who is not funny or not calm is both kind and not strong.
Everyone who is either not brave or happy is either not brave or curious.
If someone is both rich and not humble then mary is both wise and not funny and vice versa.
Everyone who is creative or funny is both happy and not humble and vice versa.
If someone is both not happy and humble then someone is not rich or curious and vice versa.
Someone is either creative or brave.
Someone is either not tall or not calm.
Paul is old.
Someone is not brave or not humble.
Mary is quiet or old.
Mary is creative or rich.
Someone is humble. | Mary is tall. | contradiction | (![X]:((~curious(X)<~>wise(X))<=>(~funny(X)<~>kind(X))))&
(![X]:((~calm(X)&creative(X))<=>(~happy(X)&~patient(X))))&
(![X]:((~tall(X)|~calm(X))<=>(~strong(X)<~>curious(X))))&
(((strong(alice)|happy(alice)))<=>(?[X]:((~humble(X)|humble(X)))))&
((?[X]:(~brave(X)))<=>((creative(mary)<~>strong(mary))))&
(![X]:((strong(X)&calm(X))<=>~happy(X)))&
(![X]:(calm(X)=>(~wise(X)<~>~humble(X))))&
(![X]:((curious(X)<~>brave(X))<=>(~kind(X)&rich(X))))&
(![X]:((kind(X)|~funny(X))=>(~strong(X)&happy(X))))&
(![X]:(~curious(X)=>(~generous(X)<~>~patient(X))))&
(![X]:((~funny(X)<~>quiet(X))<=>(humble(X)|~creative(X))))&
(![X]:((~funny(X)|~calm(X))=>(kind(X)&~strong(X))))&
(![X]:((~brave(X)<~>happy(X))=>(~brave(X)<~>curious(X))))&
((?[X]:((rich(X)&~humble(X))))<=>((wise(mary)&~funny(mary))))&
(![X]:((creative(X)|funny(X))<=>(happy(X)&~humble(X))))&
((?[X]:((~happy(X)&humble(X))))<=>(?[X]:((~rich(X)|curious(X)))))&
(?[X]:((creative(X)<~>brave(X))))&
(?[X]:((~tall(X)<~>~calm(X))))&
(old(paul))&
(?[X]:((~brave(X)|~humble(X))))&
((quiet(mary)|old(mary)))&
((creative(mary)|rich(mary)))&
(?[X]:(humble(X))) | tall(mary) | [
"p1",
"p2",
"p4",
"p5",
"p8",
"p12",
"p13",
"p14",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 9170188065226849937351544
% SZS output start Proof for 9170188065226849937351544
2. ! [X0] : ((creative(X0) & ~calm(X0)) <=> (~patient(X0) & ~happy(X0))) [input p1]
3. ! [X0] : ((~calm(X0) | ~tall(X0)) <=> (~strong(X0) <~> curious(X0))) [input p2]
5. ? [X0] : ~brave(X0) <=> (creative(mary) <~> strong(mary)) [input p4]
6. ! [X0] : ((calm(X0) & strong(X0)) <=> ~happy(X0)) [input p5]
9. ! [X0] : ((~funny(X0) | kind(X0)) => (happy(X0) & ~strong(X0))) [input p8]
13. ! [X0] : ((~brave(X0) <~> happy(X0)) => (~brave(X0) <~> curious(X0))) [input p12]
14. ? [X0] : (~humble(X0) & rich(X0)) <=> (~funny(mary) & wise(mary)) [input p13]
15. ! [X0] : ((funny(X0) | creative(X0)) <=> (~humble(X0) & happy(X0))) [input p14]
16. ? [X0] : (humble(X0) & ~happy(X0)) <=> ? [X0] : (curious(X0) | ~rich(X0)) [input p15]
17. ? [X0] : (creative(X0) <~> brave(X0)) [input p16]
24. tall(mary) [input hypothesis]
25. ? [X0] : (humble(X0) & ~happy(X0)) <=> ? [X1] : (curious(X1) | ~rich(X1)) [rectify 16]
29. ! [X0] : ((happy(X0) & ~strong(X0)) | (funny(X0) & ~kind(X0))) [ennf transformation 9]
32. ! [X0] : ((~brave(X0) <~> curious(X0)) | (~brave(X0) <=> happy(X0))) [ennf transformation 13]
34. ! [X0] : (((creative(X0) & ~calm(X0)) | (patient(X0) | happy(X0))) & ((~patient(X0) & ~happy(X0)) | (~creative(X0) | calm(X0)))) [nnf transformation 2]
35. ! [X0] : (((creative(X0) & ~calm(X0)) | patient(X0) | happy(X0)) & ((~patient(X0) & ~happy(X0)) | ~creative(X0) | calm(X0))) [flattening 34]
36. ! [X0] : (((~calm(X0) | ~tall(X0)) | ((~strong(X0) | ~curious(X0)) & (curious(X0) | strong(X0)))) & (((~curious(X0) | strong(X0)) & (curious(X0) | ~strong(X0))) | (calm(X0) & tall(X0)))) [nnf transformation 3]
37. ! [X0] : ((~calm(X0) | ~tall(X0) | ((~strong(X0) | ~curious(X0)) & (curious(X0) | strong(X0)))) & (((~curious(X0) | strong(X0)) & (curious(X0) | ~strong(X0))) | (calm(X0) & tall(X0)))) [flattening 36]
43. (? [X0] : ~brave(X0) | ((creative(mary) | ~strong(mary)) & (strong(mary) | ~creative(mary)))) & (((~strong(mary) | ~creative(mary)) & (strong(mary) | creative(mary))) | ! [X0] : brave(X0)) [nnf transformation 5]
44. (? [X0] : ~brave(X0) | ((creative(mary) | ~strong(mary)) & (strong(mary) | ~creative(mary)))) & (((~strong(mary) | ~creative(mary)) & (strong(mary) | creative(mary))) | ! [X1] : brave(X1)) [rectify 43]
45. ? [X0] : ~brave(X0) => ~brave(sK1) [choice axiom]
46. (~brave(sK1) | ((creative(mary) | ~strong(mary)) & (strong(mary) | ~creative(mary)))) & (((~strong(mary) | ~creative(mary)) & (strong(mary) | creative(mary))) | ! [X1] : brave(X1)) [skolemisation 44,45]
47. ! [X0] : (((calm(X0) & strong(X0)) | happy(X0)) & (~happy(X0) | (~calm(X0) | ~strong(X0)))) [nnf transformation 6]
48. ! [X0] : (((calm(X0) & strong(X0)) | happy(X0)) & (~happy(X0) | ~calm(X0) | ~strong(X0))) [flattening 47]
55. ! [X0] : (((~curious(X0) | brave(X0)) & (curious(X0) | ~brave(X0))) | ((~brave(X0) | ~happy(X0)) & (happy(X0) | brave(X0)))) [nnf transformation 32]
56. (? [X0] : (~humble(X0) & rich(X0)) | (funny(mary) | ~wise(mary))) & ((~funny(mary) & wise(mary)) | ! [X0] : (humble(X0) | ~rich(X0))) [nnf transformation 14]
57. (? [X0] : (~humble(X0) & rich(X0)) | funny(mary) | ~wise(mary)) & ((~funny(mary) & wise(mary)) | ! [X0] : (humble(X0) | ~rich(X0))) [flattening 56]
58. (? [X0] : (~humble(X0) & rich(X0)) | funny(mary) | ~wise(mary)) & ((~funny(mary) & wise(mary)) | ! [X1] : (humble(X1) | ~rich(X1))) [rectify 57]
59. ? [X0] : (~humble(X0) & rich(X0)) => (~humble(sK2) & rich(sK2)) [choice axiom]
60. ((~humble(sK2) & rich(sK2)) | funny(mary) | ~wise(mary)) & ((~funny(mary) & wise(mary)) | ! [X1] : (humble(X1) | ~rich(X1))) [skolemisation 58,59]
61. ! [X0] : (((funny(X0) | creative(X0)) | (humble(X0) | ~happy(X0))) & ((~humble(X0) & happy(X0)) | (~funny(X0) & ~creative(X0)))) [nnf transformation 15]
62. ! [X0] : ((funny(X0) | creative(X0) | humble(X0) | ~happy(X0)) & ((~humble(X0) & happy(X0)) | (~funny(X0) & ~creative(X0)))) [flattening 61]
63. (? [X0] : (humble(X0) & ~happy(X0)) | ! [X1] : (~curious(X1) & rich(X1))) & (? [X1] : (curious(X1) | ~rich(X1)) | ! [X0] : (~humble(X0) | happy(X0))) [nnf transformation 25]
64. (? [X0] : (humble(X0) & ~happy(X0)) | ! [X1] : (~curious(X1) & rich(X1))) & (? [X2] : (curious(X2) | ~rich(X2)) | ! [X3] : (~humble(X3) | happy(X3))) [rectify 63]
65. ? [X0] : (humble(X0) & ~happy(X0)) => (humble(sK3) & ~happy(sK3)) [choice axiom]
66. ? [X2] : (curious(X2) | ~rich(X2)) => (curious(sK4) | ~rich(sK4)) [choice axiom]
67. ((humble(sK3) & ~happy(sK3)) | ! [X1] : (~curious(X1) & rich(X1))) & ((curious(sK4) | ~rich(sK4)) | ! [X3] : (~humble(X3) | happy(X3))) [skolemisation 64,66,65]
68. ? [X0] : ((~brave(X0) | ~creative(X0)) & (brave(X0) | creative(X0))) [nnf transformation 17]
69. ? [X0] : ((~brave(X0) | ~creative(X0)) & (brave(X0) | creative(X0))) => ((~brave(sK5) | ~creative(sK5)) & (brave(sK5) | creative(sK5))) [choice axiom]
70. (~brave(sK5) | ~creative(sK5)) & (brave(sK5) | creative(sK5)) [skolemisation 68,69]
86. ~happy(X0) | ~creative(X0) | calm(X0) [cnf transformation 35]
94. ~tall(X0) | ~calm(X0) | curious(X0) | strong(X0) [cnf transformation 37]
100. strong(mary) | creative(mary) | brave(X1) [cnf transformation 46]
106. happy(X0) | calm(X0) [cnf transformation 48]
116. ~strong(X0) | funny(X0) [cnf transformation 29]
118. happy(X0) | funny(X0) [cnf transformation 29]
132. curious(X0) | ~brave(X0) | ~brave(X0) | ~happy(X0) [cnf transformation 55]
136. ~funny(mary) | humble(X1) | ~rich(X1) [cnf transformation 60]
140. happy(X0) | ~funny(X0) [cnf transformation 62]
141. ~humble(X0) | ~creative(X0) [cnf transformation 62]
145. ~happy(sK3) | rich(X1) [cnf transformation 67]
146. ~happy(sK3) | ~curious(X1) [cnf transformation 67]
149. brave(sK5) | creative(sK5) [cnf transformation 70]
156. tall(mary) [cnf transformation 24]
157. ~brave(X0) | curious(X0) | ~happy(X0) [duplicate literal removal 132]
172. 4 <=> ! [X0] : humble(X0) [avatar definition]
173. humble(X0) <- (4) [avatar component clause 172]
176. 5 <=> strong(mary) [avatar definition]
177. strong(mary) <- (5) [avatar component clause 176]
178. ~strong(mary) <- (~5) [avatar component clause 176]
180. 6 <=> creative(mary) [avatar definition]
182. creative(mary) <- (6) [avatar component clause 180]
190. 8 <=> ! [X1] : brave(X1) [avatar definition]
191. brave(X1) <- (8) [avatar component clause 190]
193. 8 | 6 | 5 [avatar split clause 100,176,180,190]
199. 10 <=> funny(mary) [avatar definition]
200. ~funny(mary) <- (~10) [avatar component clause 199]
213. 13 <=> ! [X1] : (humble(X1) | ~rich(X1)) [avatar definition]
214. humble(X1) | ~rich(X1) <- (13) [avatar component clause 213]
215. 13 | ~10 [avatar split clause 136,199,213]
218. happy(X0) [subsumption resolution 140,118]
220. 14 <=> ! [X1] : ~curious(X1) [avatar definition]
221. ~curious(X1) <- (14) [avatar component clause 220]
228. 16 <=> ! [X1] : rich(X1) [avatar definition]
229. rich(X1) <- (16) [avatar component clause 228]
231. ~curious(X1) [subsumption resolution 146,218]
232. 14 [avatar split clause 231,220]
233. rich(X1) [subsumption resolution 145,218]
234. 16 [avatar split clause 233,228]
236. 17 <=> creative(sK5) [avatar definition]
237. creative(sK5) <- (17) [avatar component clause 236]
240. 18 <=> brave(sK5) [avatar definition]
241. brave(sK5) <- (18) [avatar component clause 240]
244. 17 | 18 [avatar split clause 149,240,236]
283. ~creative(X1) | calm(X1) | calm(X1) [resolution 86,106]
285. ~creative(X1) | calm(X1) [duplicate literal removal 283]
286. calm(mary) <- (6) [resolution 285,182]
342. curious(sK5) | ~happy(sK5) <- (18) [resolution 157,241]
343. ~happy(sK5) <- (14, 18) [subsumption resolution 342,221]
344. $false <- (14, 18) [subsumption resolution 343,218]
345. ~14 | ~18 [avatar contradiction clause 344]
382. humble(X1) <- (13, 16) [subsumption resolution 214,229]
383. 4 | ~13 | ~16 [avatar split clause 382,228,213,172]
387. ~creative(X3) <- (4) [resolution 173,141]
397. $false <- (4, 17) [resolution 387,237]
398. ~4 | ~17 [avatar contradiction clause 397]
458. ~calm(mary) | curious(mary) | strong(mary) [resolution 94,156]
460. curious(mary) | strong(mary) <- (6) [subsumption resolution 458,286]
461. strong(mary) <- (6, 14) [subsumption resolution 460,221]
462. $false <- (~5, 6, 14) [subsumption resolution 461,178]
463. 5 | ~6 | ~14 [avatar contradiction clause 462]
466. curious(X0) | ~happy(X0) <- (8) [resolution 191,157]
475. ~happy(X0) <- (8, 14) [subsumption resolution 466,221]
476. $false <- (8, 14) [subsumption resolution 475,218]
477. ~8 | ~14 [avatar contradiction clause 476]
488. funny(mary) <- (5) [resolution 177,116]
495. $false <- (5, ~10) [subsumption resolution 488,200]
496. ~5 | 10 [avatar contradiction clause 495]
497. $false [avatar sat refutation 193,215,232,234,244,345,383,398,463,477,496]
% SZS output end Proof for 9170188065226849937351544
% ------------------------------
% 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: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
If john is either not wise or not rich then john is both calm and not patient. Everyone who is not creative is both not calm and rich. Everyone who is strong or funny is both wise and creative and vice versa. Everyone who is not patient or not strong is either kind or rich. Everyone who is not quiet or curious is both humble and not funny. If someone is both rich and tall then someone is not wise and vice versa. Everyone who is creative is either not creative or not old. Everyone who is either not calm or not rich is not tall or old. Everyone who is both creative and not old is either not creative or not old and vice versa. If someone is either not tall or tall then fred is both not patient and not creative. If susan is either not funny or creative then someone is both not brave and kind. If lucy is both not creative and rich then paul is not tall or kind. If someone is not old then john is not old. If someone is not curious or not humble then someone is either not curious or generous and vice versa. If lucy is either funny or not old then mary is not generous or creative and vice versa. If someone is not strong or old then paul is either not patient or not wise and vice versa. Mary is either not humble or not calm. Alice is generous or not curious. Someone is not calm or not creative. Alice is calm. Susan is either quiet or not quiet. Fred is not quiet or patient. Susan is both not humble and calm. Someone is old or humble. | Alice is not creative. | contradiction | (((~wise(john)<~>~rich(john)))=>((calm(john)&~patient(john))))&
(![X]:(~creative(X)=>(~calm(X)&rich(X))))&
(![X]:((strong(X)|funny(X))<=>(wise(X)&creative(X))))&
(![X]:((~patient(X)|~strong(X))=>(kind(X)<~>rich(X))))&
(![X]:((~quiet(X)|curious(X))=>(humble(X)&~funny(X))))&
((?[X]:((rich(X)&tall(X))))<=>(?[X]:(~wise(X))))&
(![X]:(creative(X)=>(~creative(X)<~>~old(X))))&
(![X]:((~calm(X)<~>~rich(X))=>(~tall(X)|old(X))))&
(![X]:((creative(X)&~old(X))<=>(~creative(X)<~>~old(X))))&
((?[X]:((~tall(X)<~>tall(X))))=>((~patient(fred)&~creative(fred))))&
(((~funny(susan)<~>creative(susan)))=>(?[X]:((~brave(X)&kind(X)))))&
(((~creative(lucy)&rich(lucy)))=>((~tall(paul)|kind(paul))))&
((?[X]:(~old(X)))=>(~old(john)))&
((?[X]:((~curious(X)|~humble(X))))<=>(?[X]:((~curious(X)<~>generous(X)))))&
(((funny(lucy)<~>~old(lucy)))<=>((~generous(mary)|creative(mary))))&
((?[X]:((~strong(X)|old(X))))<=>((~patient(paul)<~>~wise(paul))))&
((~humble(mary)<~>~calm(mary)))&
((generous(alice)|~curious(alice)))&
(?[X]:((~calm(X)|~creative(X))))&
(calm(alice))&
((quiet(susan)<~>~quiet(susan)))&
((~quiet(fred)|patient(fred)))&
((~humble(susan)&calm(susan)))&
(?[X]:((old(X)|humble(X)))) | ~creative(alice) | [
"p1",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 8915416388834179754668574
% SZS output start Proof for 8915416388834179754668574
2. ! [X0] : (~creative(X0) => (rich(X0) & ~calm(X0))) [input p1]
20. calm(alice) [input p19]
25. ~creative(alice) [input hypothesis]
30. ! [X0] : ((rich(X0) & ~calm(X0)) | creative(X0)) [ennf transformation 2]
79. ~calm(X0) | creative(X0) [cnf transformation 30]
137. calm(alice) [cnf transformation 20]
144. ~creative(alice) [cnf transformation 25]
345. creative(alice) [resolution 79,137]
348. $false [subsumption resolution 345,144]
% SZS output end Proof for 8915416388834179754668574
% ------------------------------
% 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 calm is either not creative or not calm and vice versa.
If someone is quiet or humble then alice is both old and not brave and vice versa.
Everyone who is patient is both kind and not kind and vice versa.
If someone is either not kind or calm then alice is either kind or not generous.
If someone is not funny then someone is both not funny and not quiet.
Everyone who is not rich is either generous or happy.
Everyone who is humble is not humble.
If alice is brave or kind then paul is both not brave and not rich.
If john is not funny then john is either patient or not calm and vice versa.
Everyone who is kind or strong is curious and vice versa.
If someone is patient then someone is not generous.
If john is both happy and not quiet then fred is not quiet and vice versa.
Everyone who is either not strong or generous is funny.
If someone is either funny or kind then someone is both kind and not quiet.
Everyone who is humble is both humble and not kind.
Everyone who is not quiet or not patient is either curious or happy and vice versa.
Someone is either not wise or creative.
Someone is wise.
Paul is both not creative and not patient.
Mary is rich.
Susan is not rich or quiet.
Someone is either generous or tall.
Someone is either not rich or brave.
Someone is not kind. | Mary is not humble. | entailment | (![X]:(calm(X)<=>(~creative(X)<~>~calm(X))))&
((?[X]:((quiet(X)|humble(X))))<=>((old(alice)&~brave(alice))))&
(![X]:(patient(X)<=>(kind(X)&~kind(X))))&
((?[X]:((~kind(X)<~>calm(X))))=>((kind(alice)<~>~generous(alice))))&
((?[X]:(~funny(X)))=>(?[X]:((~funny(X)&~quiet(X)))))&
(![X]:(~rich(X)=>(generous(X)<~>happy(X))))&
(![X]:(humble(X)=>~humble(X)))&
(((brave(alice)|kind(alice)))=>((~brave(paul)&~rich(paul))))&
((~funny(john))<=>((patient(john)<~>~calm(john))))&
(![X]:((kind(X)|strong(X))<=>curious(X)))&
((?[X]:(patient(X)))=>(?[X]:(~generous(X))))&
(((happy(john)&~quiet(john)))<=>(~quiet(fred)))&
(![X]:((~strong(X)<~>generous(X))=>funny(X)))&
((?[X]:((funny(X)<~>kind(X))))=>(?[X]:((kind(X)&~quiet(X)))))&
(![X]:(humble(X)=>(humble(X)&~kind(X))))&
(![X]:((~quiet(X)|~patient(X))<=>(curious(X)<~>happy(X))))&
(?[X]:((~wise(X)<~>creative(X))))&
(?[X]:(wise(X)))&
((~creative(paul)&~patient(paul)))&
(rich(mary))&
((~rich(susan)|quiet(susan)))&
(?[X]:((generous(X)<~>tall(X))))&
(?[X]:((~rich(X)<~>brave(X))))&
(?[X]:(~kind(X))) | ~humble(mary) | [
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 6804860723361766780213769
% SZS output start Proof for 6804860723361766780213769
7. ! [X0] : (humble(X0) => ~humble(X0)) [input p6]
25. humble(mary) [input hypothesis]
32. ! [X0] : (~humble(X0) | ~humble(X0)) [ennf transformation 7]
99. ~humble(X0) | ~humble(X0) [cnf transformation 32]
141. humble(mary) [cnf transformation 25]
142. ~humble(X0) [duplicate literal removal 99]
164. 5 <=> ! [X1] : ~humble(X1) [avatar definition]
165. ~humble(X1) <- (5) [avatar component clause 164]
205. 5 [avatar split clause 142,164]
295. $false <- (5) [resolution 165,141]
296. ~5 [avatar contradiction clause 295]
297. $false [avatar sat refutation 205,296]
% SZS output end Proof for 6804860723361766780213769
% ------------------------------
% 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 both happy and not happy then someone is both curious and patient.
Everyone who is old or humble is both wise and funny.
Everyone who is happy is not humble.
Everyone who is both quiet and humble is either not brave or not curious and vice versa.
Everyone who is both calm and brave is not happy and vice versa.
If someone is either quiet or wise then alice is both generous and strong.
If someone is either funny or humble then someone is both not tall and not quiet and vice versa.
Everyone who is old is wise and vice versa.
Everyone who is wise or not kind is not quiet.
If someone is tall then someone is both strong and brave and vice versa.
Everyone who is either old or not strong is both not kind and patient.
If susan is happy then someone is both quiet and generous and vice versa.
If someone is quiet then someone is strong.
Everyone who is calm is not quiet.
If someone is not old or humble then paul is wise and vice versa.
If someone is both humble and patient then paul is both not quiet and not happy and vice versa.
Someone is not wise or not quiet.
John is not curious or wise.
Someone is happy or humble.
Someone is not generous or calm.
Paul is both tall and strong.
Fred is both not patient and not funny.
Someone is not old or not kind. | Alice is not funny. | neutral | ((?[X]:((happy(X)&~happy(X))))=>(?[X]:((curious(X)&patient(X)))))&
(![X]:((old(X)|humble(X))=>(wise(X)&funny(X))))&
(![X]:(happy(X)=>~humble(X)))&
(![X]:((quiet(X)&humble(X))<=>(~brave(X)<~>~curious(X))))&
(![X]:((calm(X)&brave(X))<=>~happy(X)))&
((?[X]:((quiet(X)<~>wise(X))))=>((generous(alice)&strong(alice))))&
((?[X]:((funny(X)<~>humble(X))))<=>(?[X]:((~tall(X)&~quiet(X)))))&
(![X]:(old(X)<=>wise(X)))&
(![X]:((wise(X)|~kind(X))=>~quiet(X)))&
((?[X]:(tall(X)))<=>(?[X]:((strong(X)&brave(X)))))&
(![X]:((old(X)<~>~strong(X))=>(~kind(X)&patient(X))))&
((happy(susan))<=>(?[X]:((quiet(X)&generous(X)))))&
((?[X]:(quiet(X)))=>(?[X]:(strong(X))))&
(![X]:(calm(X)=>~quiet(X)))&
((?[X]:((~old(X)|humble(X))))<=>(wise(paul)))&
((?[X]:((humble(X)&patient(X))))<=>((~quiet(paul)&~happy(paul))))&
(?[X]:((~wise(X)|~quiet(X))))&
((~curious(john)|wise(john)))&
(?[X]:((happy(X)|humble(X))))&
(?[X]:((~generous(X)|calm(X))))&
((tall(paul)&strong(paul)))&
((~patient(fred)&~funny(fred)))&
(?[X]:((~old(X)|~kind(X)))) | ~funny(alice) | [] | null | 0 |
Everyone who is either not calm or funny is both not generous and not kind and vice versa. If john is both not humble and not old then fred is tall. If lucy is not quiet then someone is both not wise and funny. If someone is not kind or not generous then someone is either not generous or generous. 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. Someone is both rich and old. Alice is not happy or old. Someone is either generous or brave. Someone is curious or quiet. John is both humble and not patient. Fred is old. Someone is not generous. John is not kind or not quiet. | Lucy is not kind. | contradiction | (![X]:((~calm(X)<~>funny(X))<=>(~generous(X)&~kind(X))))&
(((~humble(john)&~old(john)))=>(tall(fred)))&
((~quiet(lucy))=>(?[X]:((~wise(X)&funny(X)))))&
((?[X]:((~kind(X)|~generous(X))))=>(?[X]:((~generous(X)<~>generous(X)))))&
(![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)&old(X))))&
((~happy(alice)|old(alice)))&
(?[X]:((generous(X)<~>brave(X))))&
(?[X]:((curious(X)|quiet(X))))&
((humble(john)&~patient(john)))&
(old(fred))&
(?[X]:(~generous(X)))&
((~kind(john)|~quiet(john))) | ~kind(lucy) | [
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 2332779241431645951419811
% SZS output start Proof for 2332779241431645951419811
12. ! [X0] : ((~generous(X0) | ~kind(X0)) <=> (kind(X0) & tall(X0))) [input p11]
25. ~kind(lucy) [input hypothesis]
55. ! [X0] : (((~generous(X0) | ~kind(X0)) | (~kind(X0) | ~tall(X0))) & ((kind(X0) & tall(X0)) | (generous(X0) & kind(X0)))) [nnf transformation 12]
56. ! [X0] : ((~generous(X0) | ~kind(X0) | ~kind(X0) | ~tall(X0)) & ((kind(X0) & tall(X0)) | (generous(X0) & kind(X0)))) [flattening 55]
118. kind(X0) | kind(X0) [cnf transformation 56]
152. ~kind(lucy) [cnf transformation 25]
157. kind(X0) [duplicate literal removal 118]
300. $false [subsumption resolution 152,157]
% SZS output end Proof for 2332779241431645951419811
% ------------------------------
% 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 old is not funny or tall and vice versa. Everyone who is creative or kind is not kind or not rich. Everyone who is either curious or kind is either not happy or calm and vice versa. If someone is both not calm and curious then fred is both not tall and calm and vice versa. If fred is strong then someone is either humble or not happy. If lucy is either generous or not rich then someone is both not happy and brave. If someone is not humble then someone is humble and vice versa. If fred is not curious or strong then someone is both not happy and not funny and vice versa. Everyone who is both tall and not kind is not funny and vice versa. If lucy is both rich and happy then mary is both rich and quiet and vice versa. Everyone who is patient or kind is both rich and quiet and vice versa. If someone is either quiet or not patient then susan is both calm and patient. If paul is not creative then someone is not quiet or curious. Everyone who is either tall or not kind is rich and vice versa. If alice is old then someone is wise or old. If someone is not funny or rich then susan is rich. Alice is happy. Lucy is happy. John is strong. Someone is creative or not calm. Someone is either quiet or not old. | Susan is not calm. | contradiction | (![X]:(old(X)<=>(~funny(X)|tall(X))))&
(![X]:((creative(X)|kind(X))=>(~kind(X)|~rich(X))))&
(![X]:((curious(X)<~>kind(X))<=>(~happy(X)<~>calm(X))))&
((?[X]:((~calm(X)&curious(X))))<=>((~tall(fred)&calm(fred))))&
((strong(fred))=>(?[X]:((humble(X)<~>~happy(X)))))&
(((generous(lucy)<~>~rich(lucy)))=>(?[X]:((~happy(X)&brave(X)))))&
((?[X]:(~humble(X)))<=>(?[X]:(humble(X))))&
(((~curious(fred)|strong(fred)))<=>(?[X]:((~happy(X)&~funny(X)))))&
(![X]:((tall(X)&~kind(X))<=>~funny(X)))&
(((rich(lucy)&happy(lucy)))<=>((rich(mary)&quiet(mary))))&
(![X]:((patient(X)|kind(X))<=>(rich(X)&quiet(X))))&
((?[X]:((quiet(X)<~>~patient(X))))=>((calm(susan)&patient(susan))))&
((~creative(paul))=>(?[X]:((~quiet(X)|curious(X)))))&
(![X]:((tall(X)<~>~kind(X))<=>rich(X)))&
((old(alice))=>(?[X]:((wise(X)|old(X)))))&
((?[X]:((~funny(X)|rich(X))))=>(rich(susan)))&
(happy(alice))&
(happy(lucy))&
(strong(john))&
(?[X]:((creative(X)|~calm(X))))&
(?[X]:((quiet(X)<~>~old(X)))) | ~calm(susan) | [
"p1",
"p8",
"p10",
"p11",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 667342532626885389985040
% SZS output start Proof for 667342532626885389985040
2. ! [X0] : ((kind(X0) | creative(X0)) => (~rich(X0) | ~kind(X0))) [input p1]
9. ! [X0] : ((~kind(X0) & tall(X0)) <=> ~funny(X0)) [input p8]
11. ! [X0] : ((kind(X0) | patient(X0)) <=> (quiet(X0) & rich(X0))) [input p10]
12. ? [X0] : (quiet(X0) <~> ~patient(X0)) => (patient(susan) & calm(susan)) [input p11]
14. ! [X0] : ((tall(X0) <~> ~kind(X0)) <=> rich(X0)) [input p13]
16. ? [X0] : (rich(X0) | ~funny(X0)) => rich(susan) [input p15]
22. ~calm(susan) [input hypothesis]
26. ! [X0] : ((~rich(X0) | ~kind(X0)) | (~kind(X0) & ~creative(X0))) [ennf transformation 2]
27. ! [X0] : (~rich(X0) | ~kind(X0) | (~kind(X0) & ~creative(X0))) [flattening 26]
30. (patient(susan) & calm(susan)) | ! [X0] : (quiet(X0) <=> ~patient(X0)) [ennf transformation 12]
32. rich(susan) | ! [X0] : (~rich(X0) & funny(X0)) [ennf transformation 16]
57. ! [X0] : (((~kind(X0) & tall(X0)) | funny(X0)) & (~funny(X0) | (kind(X0) | ~tall(X0)))) [nnf transformation 9]
58. ! [X0] : (((~kind(X0) & tall(X0)) | funny(X0)) & (~funny(X0) | kind(X0) | ~tall(X0))) [flattening 57]
61. ! [X0] : (((kind(X0) | patient(X0)) | (~quiet(X0) | ~rich(X0))) & ((quiet(X0) & rich(X0)) | (~kind(X0) & ~patient(X0)))) [nnf transformation 11]
62. ! [X0] : ((kind(X0) | patient(X0) | ~quiet(X0) | ~rich(X0)) & ((quiet(X0) & rich(X0)) | (~kind(X0) & ~patient(X0)))) [flattening 61]
63. (patient(susan) & calm(susan)) | ! [X0] : ((quiet(X0) | patient(X0)) & (~patient(X0) | ~quiet(X0))) [nnf transformation 30]
66. ! [X0] : ((((kind(X0) | ~tall(X0)) & (~kind(X0) | tall(X0))) | ~rich(X0)) & (rich(X0) | ((tall(X0) | kind(X0)) & (~kind(X0) | ~tall(X0))))) [nnf transformation 14]
76. ~rich(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 27]
100. ~tall(X0) | kind(X0) | ~funny(X0) [cnf transformation 58]
108. rich(X0) | ~kind(X0) [cnf transformation 62]
109. ~patient(X0) | quiet(X0) [cnf transformation 62]
111. kind(X0) | patient(X0) | ~quiet(X0) | ~rich(X0) [cnf transformation 62]
112. calm(susan) | ~patient(X0) | ~quiet(X0) [cnf transformation 63]
113. calm(susan) | quiet(X0) | patient(X0) [cnf transformation 63]
118. rich(X0) | tall(X0) | kind(X0) [cnf transformation 66]
121. rich(susan) | funny(X0) [cnf transformation 32]
129. ~calm(susan) [cnf transformation 22]
130. ~rich(X0) | ~kind(X0) [duplicate literal removal 76]
234. ~quiet(X0) | patient(X0) | ~rich(X0) [subsumption resolution 111,130]
235. ~kind(X0) [subsumption resolution 108,130]
238. 23 <=> ! [X0] : quiet(X0) [avatar definition]
239. quiet(X0) <- (23) [avatar component clause 238]
247. 25 <=> ! [X0] : ~patient(X0) [avatar definition]
248. ~patient(X0) <- (25) [avatar component clause 247]
250. calm(susan) | quiet(X0) [subsumption resolution 113,109]
252. 26 <=> calm(susan) [avatar definition]
255. 23 | 26 [avatar split clause 250,252,238]
256. calm(susan) | ~patient(X0) [subsumption resolution 112,109]
257. 25 | 26 [avatar split clause 256,252,247]
272. rich(X0) | tall(X0) [subsumption resolution 118,235]
274. 30 <=> ! [X0] : ~rich(X0) [avatar definition]
275. ~rich(X0) <- (30) [avatar component clause 274]
277. 31 <=> rich(susan) [avatar definition]
279. rich(susan) <- (31) [avatar component clause 277]
282. 32 <=> ! [X0] : funny(X0) [avatar definition]
283. funny(X0) <- (32) [avatar component clause 282]
284. 32 | 31 [avatar split clause 121,277,282]
305. ~26 [avatar split clause 129,252]
336. patient(X0) | ~rich(X0) <- (23) [resolution 234,239]
337. ~rich(X0) <- (23, 25) [subsumption resolution 336,248]
338. 30 | ~23 | ~25 [avatar split clause 337,247,238,274]
339. $false <- (30, 31) [resolution 275,279]
340. tall(X0) <- (30) [resolution 275,272]
341. ~30 | ~31 [avatar contradiction clause 339]
368. kind(X0) | ~funny(X0) <- (30) [resolution 340,100]
371. ~funny(X0) <- (30) [subsumption resolution 368,235]
372. $false <- (30, 32) [subsumption resolution 371,283]
373. ~30 | ~32 [avatar contradiction clause 372]
374. $false [avatar sat refutation 255,257,284,305,338,341,373]
% SZS output end Proof for 667342532626885389985040
% ------------------------------
% 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 susan is both not generous and tall then someone is not rich or not generous. Everyone who is either not kind or not tall is not wise or not curious. If someone is not generous then susan is both not kind and happy and vice versa. Everyone who is both funny and not kind is both not wise and not brave. If someone is either not curious or patient then mary is not humble and vice versa. Everyone who is quiet or not kind is not patient or happy and vice versa. If john is calm then john is generous and vice versa. Everyone who is either old or not humble is rich or not happy and vice versa. If john is tall or not funny then someone is not generous. Everyone who is not happy is curious or not old. Everyone who is brave is not generous. If mary is not humble then someone is old or curious. If someone is either not generous or not happy then susan is quiet or not curious and vice versa. If fred is both not calm and not tall then susan is creative or humble. Everyone who is either creative or calm is both kind and not tall and vice versa. Everyone who is both strong and brave is either not strong or old and vice versa. Someone is not wise or humble. Someone is either patient or not strong. Susan is either patient or funny. Someone is both not kind and quiet. Fred is either patient or brave. Someone is generous. Someone is both not happy and not patient. Someone is kind or humble. | Susan is generous. | neutral | (((~generous(susan)&tall(susan)))=>(?[X]:((~rich(X)|~generous(X)))))&
(![X]:((~kind(X)<~>~tall(X))=>(~wise(X)|~curious(X))))&
((?[X]:(~generous(X)))<=>((~kind(susan)&happy(susan))))&
(![X]:((funny(X)&~kind(X))=>(~wise(X)&~brave(X))))&
((?[X]:((~curious(X)<~>patient(X))))<=>(~humble(mary)))&
(![X]:((quiet(X)|~kind(X))<=>(~patient(X)|happy(X))))&
((calm(john))<=>(generous(john)))&
(![X]:((old(X)<~>~humble(X))<=>(rich(X)|~happy(X))))&
(((tall(john)|~funny(john)))=>(?[X]:(~generous(X))))&
(![X]:(~happy(X)=>(curious(X)|~old(X))))&
(![X]:(brave(X)=>~generous(X)))&
((~humble(mary))=>(?[X]:((old(X)|curious(X)))))&
((?[X]:((~generous(X)<~>~happy(X))))<=>((quiet(susan)|~curious(susan))))&
(((~calm(fred)&~tall(fred)))=>((creative(susan)|humble(susan))))&
(![X]:((creative(X)<~>calm(X))<=>(kind(X)&~tall(X))))&
(![X]:((strong(X)&brave(X))<=>(~strong(X)<~>old(X))))&
(?[X]:((~wise(X)|humble(X))))&
(?[X]:((patient(X)<~>~strong(X))))&
((patient(susan)<~>funny(susan)))&
(?[X]:((~kind(X)&quiet(X))))&
((patient(fred)<~>brave(fred)))&
(?[X]:(generous(X)))&
(?[X]:((~happy(X)&~patient(X))))&
(?[X]:((kind(X)|humble(X)))) | generous(susan) | [] | null | 0 |
Everyone who is both not creative and brave is happy and vice versa.
Everyone who is not rich or strong is both not generous and not brave and vice versa.
If someone is strong then someone is both not strong and not tall and vice versa.
Everyone who is both not tall and not generous is kind or strong and vice versa.
Everyone who is both creative and wise is both not tall and tall.
If someone is not brave or kind then someone is both not rich and generous.
If someone is both creative and not old then susan is both brave and not tall and vice versa.
If paul is kind then john is not rich or not wise.
If lucy is not quiet or not brave then alice is not calm or generous and vice versa.
Everyone who is not funny or not old is either not curious or tall.
If someone is both quiet and tall then paul is both rich and humble.
Everyone who is not patient is not kind and vice versa.
Everyone who is either patient or kind is either not old or happy and vice versa.
Everyone who is both not happy and generous is either wise or calm.
Everyone who is both not generous and tall is not humble and vice versa.
Everyone who is not curious or not calm is both old and not patient and vice versa.
Someone is creative or not humble.
Susan is not calm or quiet.
Someone is both wise and curious.
John is both not patient and quiet.
John is either not curious or not humble.
Alice is not humble.
Mary is not strong or funny. | Susan is not brave. | contradiction | (![X]:((~creative(X)&brave(X))<=>happy(X)))&
(![X]:((~rich(X)|strong(X))<=>(~generous(X)&~brave(X))))&
((?[X]:(strong(X)))<=>(?[X]:((~strong(X)&~tall(X)))))&
(![X]:((~tall(X)&~generous(X))<=>(kind(X)|strong(X))))&
(![X]:((creative(X)&wise(X))=>(~tall(X)&tall(X))))&
((?[X]:((~brave(X)|kind(X))))=>(?[X]:((~rich(X)&generous(X)))))&
((?[X]:((creative(X)&~old(X))))<=>((brave(susan)&~tall(susan))))&
((kind(paul))=>((~rich(john)|~wise(john))))&
(((~quiet(lucy)|~brave(lucy)))<=>((~calm(alice)|generous(alice))))&
(![X]:((~funny(X)|~old(X))=>(~curious(X)<~>tall(X))))&
((?[X]:((quiet(X)&tall(X))))=>((rich(paul)&humble(paul))))&
(![X]:(~patient(X)<=>~kind(X)))&
(![X]:((patient(X)<~>kind(X))<=>(~old(X)<~>happy(X))))&
(![X]:((~happy(X)&generous(X))=>(wise(X)<~>calm(X))))&
(![X]:((~generous(X)&tall(X))<=>~humble(X)))&
(![X]:((~curious(X)|~calm(X))<=>(old(X)&~patient(X))))&
(?[X]:((creative(X)|~humble(X))))&
((~calm(susan)|quiet(susan)))&
(?[X]:((wise(X)&curious(X))))&
((~patient(john)&quiet(john)))&
((~curious(john)<~>~humble(john)))&
(~humble(alice))&
((~strong(mary)|funny(mary))) | ~brave(susan) | [
"p1",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 469997530670963495066627
% SZS output start Proof for 469997530670963495066627
2. ! [X0] : ((strong(X0) | ~rich(X0)) <=> (~brave(X0) & ~generous(X0))) [input p1]
6. ? [X0] : (kind(X0) | ~brave(X0)) => ? [X0] : (generous(X0) & ~rich(X0)) [input p5]
24. ~brave(susan) [input hypothesis]
26. ? [X0] : (kind(X0) | ~brave(X0)) => ? [X1] : (generous(X1) & ~rich(X1)) [rectify 6]
31. ? [X1] : (generous(X1) & ~rich(X1)) | ! [X0] : (~kind(X0) & brave(X0)) [ennf transformation 26]
40. ! [X0] : (((strong(X0) | ~rich(X0)) | (brave(X0) | generous(X0))) & ((~brave(X0) & ~generous(X0)) | (~strong(X0) & rich(X0)))) [nnf transformation 2]
41. ! [X0] : ((strong(X0) | ~rich(X0) | brave(X0) | generous(X0)) & ((~brave(X0) & ~generous(X0)) | (~strong(X0) & rich(X0)))) [flattening 40]
49. ? [X0] : (generous(X0) & ~rich(X0)) | ! [X1] : (~kind(X1) & brave(X1)) [rectify 31]
50. ? [X0] : (generous(X0) & ~rich(X0)) => (generous(sK2) & ~rich(sK2)) [choice axiom]
51. (generous(sK2) & ~rich(sK2)) | ! [X1] : (~kind(X1) & brave(X1)) [skolemisation 49,50]
75. ~generous(X0) | rich(X0) [cnf transformation 41]
90. ~rich(sK2) | brave(X1) [cnf transformation 51]
92. generous(sK2) | brave(X1) [cnf transformation 51]
136. ~brave(susan) [cnf transformation 24]
163. 7 <=> generous(sK2) [avatar definition]
165. generous(sK2) <- (7) [avatar component clause 163]
168. 8 <=> ! [X1] : brave(X1) [avatar definition]
169. brave(X1) <- (8) [avatar component clause 168]
170. 8 | 7 [avatar split clause 92,163,168]
172. 9 <=> rich(sK2) [avatar definition]
174. ~rich(sK2) <- (~9) [avatar component clause 172]
176. 8 | ~9 [avatar split clause 90,172,168]
178. 10 <=> brave(susan) [avatar definition]
180. ~brave(susan) <- (~10) [avatar component clause 178]
279. ~10 [avatar split clause 136,178]
280. rich(sK2) <- (7) [resolution 75,165]
281. $false <- (7, ~9) [subsumption resolution 280,174]
282. ~7 | 9 [avatar contradiction clause 281]
283. $false <- (8, ~10) [resolution 169,180]
284. ~8 | 10 [avatar contradiction clause 283]
285. $false [avatar sat refutation 170,176,279,282,284]
% SZS output end Proof for 469997530670963495066627
% ------------------------------
% 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 happy or not rich is either quiet or happy and vice versa.
Everyone who is strong or not wise is either calm or rich and vice versa.
Everyone who is humble is happy and vice versa.
Everyone who is not patient is either not tall or funny and vice versa.
If someone is patient or happy then fred is not strong.
Everyone who is both tall and not generous is calm.
If someone is not wise or creative then someone is patient and vice versa.
Everyone who is not strong or not generous is both kind and not rich and vice versa.
Everyone who is either not patient or not happy is not strong or patient and vice versa.
Everyone who is funny is not quiet or not kind.
Everyone who is either not strong or not generous is humble.
Everyone who is either not curious or curious is not happy and vice versa.
Everyone who is both brave and not tall is patient or wise and vice versa.
Everyone who is both not happy and curious is both curious and not tall and vice versa.
Everyone who is either strong or generous is not calm.
If paul is funny or humble then fred is either rich or kind.
Someone is not curious.
John is not old or rich.
Someone is both not old and kind.
Someone is either not wise or quiet.
Someone is either not rich or brave.
Someone is calm.
John is either not old or rich. | John is old. | neutral | (![X]:((~happy(X)|~rich(X))<=>(quiet(X)<~>happy(X))))&
(![X]:((strong(X)|~wise(X))<=>(calm(X)<~>rich(X))))&
(![X]:(humble(X)<=>happy(X)))&
(![X]:(~patient(X)<=>(~tall(X)<~>funny(X))))&
((?[X]:((patient(X)|happy(X))))=>(~strong(fred)))&
(![X]:((tall(X)&~generous(X))=>calm(X)))&
((?[X]:((~wise(X)|creative(X))))<=>(?[X]:(patient(X))))&
(![X]:((~strong(X)|~generous(X))<=>(kind(X)&~rich(X))))&
(![X]:((~patient(X)<~>~happy(X))<=>(~strong(X)|patient(X))))&
(![X]:(funny(X)=>(~quiet(X)|~kind(X))))&
(![X]:((~strong(X)<~>~generous(X))=>humble(X)))&
(![X]:((~curious(X)<~>curious(X))<=>~happy(X)))&
(![X]:((brave(X)&~tall(X))<=>(patient(X)|wise(X))))&
(![X]:((~happy(X)&curious(X))<=>(curious(X)&~tall(X))))&
(![X]:((strong(X)<~>generous(X))=>~calm(X)))&
(((funny(paul)|humble(paul)))=>((rich(fred)<~>kind(fred))))&
(?[X]:(~curious(X)))&
((~old(john)|rich(john)))&
(?[X]:((~old(X)&kind(X))))&
(?[X]:((~wise(X)<~>quiet(X))))&
(?[X]:((~rich(X)<~>brave(X))))&
(?[X]:(calm(X)))&
((~old(john)<~>rich(john))) | old(john) | [] | null | 0 |
If someone is humble then alice is not curious or humble and vice versa.
If someone is either not tall or calm then paul is both funny and rich and vice versa.
If alice is kind then lucy is happy and vice versa.
If paul is not creative then fred is either quiet or not happy and vice versa.
Everyone who is both happy and funny is both happy and strong and vice versa.
If mary is old then someone is curious or patient.
Everyone who is strong is both tall and humble and vice versa.
If john is creative then susan is not creative.
Everyone who is both wise and happy is not old.
Everyone who is either happy or quiet is not brave.
If someone is brave or rich then john is both not funny and not happy.
Everyone who is tall is not brave and vice versa.
Everyone who is generous is not happy and vice versa.
Everyone who is either not strong or funny is both generous and humble and vice versa.
If paul is both not kind and not brave then mary is either not wise or not curious and vice versa.
Everyone who is not curious is both old and not kind and vice versa.
John is both tall and not strong.
Someone is either not patient or not happy.
Fred is both not wise and strong.
Fred is humble.
Mary is both not patient and not kind.
Someone is either creative or old.
Susan is curious.
Someone is either calm or tall. | Alice is not humble. | neutral | ((?[X]:(humble(X)))<=>((~curious(alice)|humble(alice))))&
((?[X]:((~tall(X)<~>calm(X))))<=>((funny(paul)&rich(paul))))&
((kind(alice))<=>(happy(lucy)))&
((~creative(paul))<=>((quiet(fred)<~>~happy(fred))))&
(![X]:((happy(X)&funny(X))<=>(happy(X)&strong(X))))&
((old(mary))=>(?[X]:((curious(X)|patient(X)))))&
(![X]:(strong(X)<=>(tall(X)&humble(X))))&
((creative(john))=>(~creative(susan)))&
(![X]:((wise(X)&happy(X))=>~old(X)))&
(![X]:((happy(X)<~>quiet(X))=>~brave(X)))&
((?[X]:((brave(X)|rich(X))))=>((~funny(john)&~happy(john))))&
(![X]:(tall(X)<=>~brave(X)))&
(![X]:(generous(X)<=>~happy(X)))&
(![X]:((~strong(X)<~>funny(X))<=>(generous(X)&humble(X))))&
(((~kind(paul)&~brave(paul)))<=>((~wise(mary)<~>~curious(mary))))&
(![X]:(~curious(X)<=>(old(X)&~kind(X))))&
((tall(john)&~strong(john)))&
(?[X]:((~patient(X)<~>~happy(X))))&
((~wise(fred)&strong(fred)))&
(humble(fred))&
((~patient(mary)&~kind(mary)))&
(?[X]:((creative(X)<~>old(X))))&
(curious(susan))&
(?[X]:((calm(X)<~>tall(X)))) | ~humble(alice) | [] | null | 0 |
If someone is not generous or not kind then someone is both humble and not strong.
Everyone who is both not creative and funny is curious.
Everyone who is kind or happy is patient or wise and vice versa.
Everyone who is both calm and not wise is both humble and not generous and vice versa.
If someone is either old or not strong then someone is either quiet or not brave.
If someone is tall then someone is rich or not happy and vice versa.
Everyone who is not strong is both kind and not kind and vice versa.
Everyone who is not tall or funny is both generous and kind.
Everyone who is either wise or not rich is not wise or strong and vice versa.
If someone is not calm then someone is funny and vice versa.
Everyone who is either not kind or not quiet is not curious.
Everyone who is both not rich and wise is both quiet and patient.
Everyone who is both not quiet and creative is both wise and not quiet.
If alice is both patient and not kind then john is calm or curious.
If someone is both not brave and not patient then lucy is both not quiet and creative and vice versa.
If lucy is not happy or not curious then alice is calm or happy.
Lucy is not happy or not curious.
Someone is either not kind or not old.
Fred is both not quiet and not tall.
John is either quiet or calm.
Someone is not kind or patient.
Susan is not brave.
Someone is not brave.
Someone is humble or not happy. | Lucy is tall. | neutral | ((?[X]:((~generous(X)|~kind(X))))=>(?[X]:((humble(X)&~strong(X)))))&
(![X]:((~creative(X)&funny(X))=>curious(X)))&
(![X]:((kind(X)|happy(X))<=>(patient(X)|wise(X))))&
(![X]:((calm(X)&~wise(X))<=>(humble(X)&~generous(X))))&
((?[X]:((old(X)<~>~strong(X))))=>(?[X]:((quiet(X)<~>~brave(X)))))&
((?[X]:(tall(X)))<=>(?[X]:((rich(X)|~happy(X)))))&
(![X]:(~strong(X)<=>(kind(X)&~kind(X))))&
(![X]:((~tall(X)|funny(X))=>(generous(X)&kind(X))))&
(![X]:((wise(X)<~>~rich(X))<=>(~wise(X)|strong(X))))&
((?[X]:(~calm(X)))<=>(?[X]:(funny(X))))&
(![X]:((~kind(X)<~>~quiet(X))=>~curious(X)))&
(![X]:((~rich(X)&wise(X))=>(quiet(X)&patient(X))))&
(![X]:((~quiet(X)&creative(X))=>(wise(X)&~quiet(X))))&
(((patient(alice)&~kind(alice)))=>((calm(john)|curious(john))))&
((?[X]:((~brave(X)&~patient(X))))<=>((~quiet(lucy)&creative(lucy))))&
(((~happy(lucy)|~curious(lucy)))=>((calm(alice)|happy(alice))))&
((~happy(lucy)|~curious(lucy)))&
(?[X]:((~kind(X)<~>~old(X))))&
((~quiet(fred)&~tall(fred)))&
((quiet(john)<~>calm(john)))&
(?[X]:((~kind(X)|patient(X))))&
(~brave(susan))&
(?[X]:(~brave(X)))&
(?[X]:((humble(X)|~happy(X)))) | tall(lucy) | [] | null | 0 |
Everyone who is not patient or not brave is both strong and not strong and vice versa.
If alice is curious or not tall then john is both quiet and not curious and vice versa.
Everyone who is either not patient or not brave is either tall or creative.
If someone is not curious or not strong then lucy is brave and vice versa.
If fred is not old then someone is not funny or humble.
Everyone who is either humble or not quiet is not generous or rich and vice versa.
Everyone who is either not quiet or not brave is either not rich or not calm.
If someone is strong or quiet then someone is either wise or not rich.
Everyone who is both not brave and not happy is wise or not humble and vice versa.
Everyone who is either not generous or not rich is both not patient and not wise and vice versa.
Everyone who is both not generous and happy is not funny or not happy and vice versa.
Everyone who is either humble or happy is either funny or not creative.
If someone is generous or funny then mary is quiet or not strong and vice versa.
If someone is either not strong or generous then someone is either old or not tall and vice versa.
Everyone who is both not curious and patient is either not tall or not calm.
Someone is either kind or not strong.
Someone is tall or not rich.
Someone is not humble or curious.
Someone is old or funny.
Susan is not rich or not humble. | Susan is tall. | neutral | (![X]:((~patient(X)|~brave(X))<=>(strong(X)&~strong(X))))&
(((curious(alice)|~tall(alice)))<=>((quiet(john)&~curious(john))))&
(![X]:((~patient(X)<~>~brave(X))=>(tall(X)<~>creative(X))))&
((?[X]:((~curious(X)|~strong(X))))<=>(brave(lucy)))&
((~old(fred))=>(?[X]:((~funny(X)|humble(X)))))&
(![X]:((humble(X)<~>~quiet(X))<=>(~generous(X)|rich(X))))&
(![X]:((~quiet(X)<~>~brave(X))=>(~rich(X)<~>~calm(X))))&
((?[X]:((strong(X)|quiet(X))))=>(?[X]:((wise(X)<~>~rich(X)))))&
(![X]:((~brave(X)&~happy(X))<=>(wise(X)|~humble(X))))&
(![X]:((~generous(X)<~>~rich(X))<=>(~patient(X)&~wise(X))))&
(![X]:((~generous(X)&happy(X))<=>(~funny(X)|~happy(X))))&
(![X]:((humble(X)<~>happy(X))=>(funny(X)<~>~creative(X))))&
((?[X]:((generous(X)|funny(X))))<=>((quiet(mary)|~strong(mary))))&
((?[X]:((~strong(X)<~>generous(X))))<=>(?[X]:((old(X)<~>~tall(X)))))&
(![X]:((~curious(X)&patient(X))=>(~tall(X)<~>~calm(X))))&
(?[X]:((kind(X)<~>~strong(X))))&
(?[X]:((tall(X)|~rich(X))))&
(?[X]:((~humble(X)|curious(X))))&
(?[X]:((old(X)|funny(X))))&
((~rich(susan)|~humble(susan))) | tall(susan) | [] | null | 0 |
If someone is brave then someone is either generous or quiet and vice versa.
If someone is either humble or not brave then lucy is rich or brave.
Everyone who is patient is not generous or kind and vice versa.
Everyone who is either quiet or not curious is both not strong and not quiet.
Everyone who is not happy is either tall or generous and vice versa.
If someone is either curious or not rich then susan is both creative and wise and vice versa.
Everyone who is not rich is both old and happy and vice versa.
Everyone who is both not curious and old is not tall.
If someone is strong then lucy is both kind and generous and vice versa.
Everyone who is either not rich or not calm is calm or tall and vice versa.
If susan is patient then someone is not curious or brave.
If someone is either old or not wise then someone is either quiet or not funny.
Everyone who is not generous is both strong and not happy and vice versa.
If someone is either not quiet or not curious then someone is not tall and vice versa.
Everyone who is either curious or not happy is either not humble or funny and vice versa.
Everyone who is both not calm and not brave is both humble and kind and vice versa.
Someone is either wise or not curious.
Someone is patient.
Alice is funny or not creative.
Alice is either wise or patient. | Alice is rich. | entailment | ((?[X]:(brave(X)))<=>(?[X]:((generous(X)<~>quiet(X)))))&
((?[X]:((humble(X)<~>~brave(X))))=>((rich(lucy)|brave(lucy))))&
(![X]:(patient(X)<=>(~generous(X)|kind(X))))&
(![X]:((quiet(X)<~>~curious(X))=>(~strong(X)&~quiet(X))))&
(![X]:(~happy(X)<=>(tall(X)<~>generous(X))))&
((?[X]:((curious(X)<~>~rich(X))))<=>((creative(susan)&wise(susan))))&
(![X]:(~rich(X)<=>(old(X)&happy(X))))&
(![X]:((~curious(X)&old(X))=>~tall(X)))&
((?[X]:(strong(X)))<=>((kind(lucy)&generous(lucy))))&
(![X]:((~rich(X)<~>~calm(X))<=>(calm(X)|tall(X))))&
((patient(susan))=>(?[X]:((~curious(X)|brave(X)))))&
((?[X]:((old(X)<~>~wise(X))))=>(?[X]:((quiet(X)<~>~funny(X)))))&
(![X]:(~generous(X)<=>(strong(X)&~happy(X))))&
((?[X]:((~quiet(X)<~>~curious(X))))<=>(?[X]:(~tall(X))))&
(![X]:((curious(X)<~>~happy(X))<=>(~humble(X)<~>funny(X))))&
(![X]:((~calm(X)&~brave(X))<=>(humble(X)&kind(X))))&
(?[X]:((wise(X)<~>~curious(X))))&
(?[X]:(patient(X)))&
((funny(alice)|~creative(alice)))&
((wise(alice)<~>patient(alice))) | rich(alice) | [
"p3",
"p4",
"p6",
"p7",
"p9",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 6798354547611508955920318
% SZS output start Proof for 6798354547611508955920318
4. ! [X0] : ((quiet(X0) <~> ~curious(X0)) => (~quiet(X0) & ~strong(X0))) [input p3]
5. ! [X0] : (~happy(X0) <=> (tall(X0) <~> generous(X0))) [input p4]
7. ! [X0] : (~rich(X0) <=> (happy(X0) & old(X0))) [input p6]
8. ! [X0] : ((old(X0) & ~curious(X0)) => ~tall(X0)) [input p7]
10. ! [X0] : ((~rich(X0) <~> ~calm(X0)) <=> (tall(X0) | calm(X0))) [input p9]
13. ! [X0] : (~generous(X0) <=> (~happy(X0) & strong(X0))) [input p12]
14. ? [X0] : (~quiet(X0) <~> ~curious(X0)) <=> ? [X0] : ~tall(X0) [input p13]
21. ~rich(alice) [input hypothesis]
24. ? [X0] : (~quiet(X0) <~> ~curious(X0)) <=> ? [X1] : ~tall(X1) [rectify 14]
27. ! [X0] : ((~quiet(X0) & ~strong(X0)) | (quiet(X0) <=> ~curious(X0))) [ennf transformation 4]
28. ! [X0] : (~tall(X0) | (~old(X0) | curious(X0))) [ennf transformation 8]
29. ! [X0] : (~tall(X0) | ~old(X0) | curious(X0)) [flattening 28]
40. ! [X0] : ((~quiet(X0) & ~strong(X0)) | ((quiet(X0) | curious(X0)) & (~curious(X0) | ~quiet(X0)))) [nnf transformation 27]
41. ! [X0] : ((~happy(X0) | ((tall(X0) | ~generous(X0)) & (generous(X0) | ~tall(X0)))) & (((~generous(X0) | ~tall(X0)) & (generous(X0) | tall(X0))) | happy(X0))) [nnf transformation 5]
47. ! [X0] : ((~rich(X0) | (~happy(X0) | ~old(X0))) & ((happy(X0) & old(X0)) | rich(X0))) [nnf transformation 7]
48. ! [X0] : ((~rich(X0) | ~happy(X0) | ~old(X0)) & ((happy(X0) & old(X0)) | rich(X0))) [flattening 47]
54. ! [X0] : ((((calm(X0) | rich(X0)) & (~calm(X0) | ~rich(X0))) | (~tall(X0) & ~calm(X0))) & ((tall(X0) | calm(X0)) | ((~rich(X0) | calm(X0)) & (~calm(X0) | rich(X0))))) [nnf transformation 10]
55. ! [X0] : ((((calm(X0) | rich(X0)) & (~calm(X0) | ~rich(X0))) | (~tall(X0) & ~calm(X0))) & (tall(X0) | calm(X0) | ((~rich(X0) | calm(X0)) & (~calm(X0) | rich(X0))))) [flattening 54]
62. ! [X0] : ((~generous(X0) | (happy(X0) | ~strong(X0))) & ((~happy(X0) & strong(X0)) | generous(X0))) [nnf transformation 13]
63. ! [X0] : ((~generous(X0) | happy(X0) | ~strong(X0)) & ((~happy(X0) & strong(X0)) | generous(X0))) [flattening 62]
64. (? [X0] : ((curious(X0) | quiet(X0)) & (~curious(X0) | ~quiet(X0))) | ! [X1] : tall(X1)) & (? [X1] : ~tall(X1) | ! [X0] : ((~quiet(X0) | curious(X0)) & (~curious(X0) | quiet(X0)))) [nnf transformation 24]
65. (? [X0] : ((curious(X0) | quiet(X0)) & (~curious(X0) | ~quiet(X0))) | ! [X1] : tall(X1)) & (? [X2] : ~tall(X2) | ! [X3] : ((~quiet(X3) | curious(X3)) & (~curious(X3) | quiet(X3)))) [rectify 64]
66. ? [X0] : ((curious(X0) | quiet(X0)) & (~curious(X0) | ~quiet(X0))) => ((curious(sK6) | quiet(sK6)) & (~curious(sK6) | ~quiet(sK6))) [choice axiom]
67. ? [X2] : ~tall(X2) => ~tall(sK7) [choice axiom]
68. (((curious(sK6) | quiet(sK6)) & (~curious(sK6) | ~quiet(sK6))) | ! [X1] : tall(X1)) & (~tall(sK7) | ! [X3] : ((~quiet(X3) | curious(X3)) & (~curious(X3) | quiet(X3)))) [skolemisation 65,67,66]
89. ~quiet(X0) | ~curious(X0) | ~quiet(X0) [cnf transformation 40]
94. ~happy(X0) | tall(X0) | ~generous(X0) [cnf transformation 41]
101. old(X0) | rich(X0) [cnf transformation 48]
102. happy(X0) | rich(X0) [cnf transformation 48]
104. ~old(X0) | ~tall(X0) | curious(X0) [cnf transformation 29]
109. tall(X0) | calm(X0) | ~rich(X0) | calm(X0) [cnf transformation 55]
110. ~calm(X0) | ~rich(X0) | ~calm(X0) [cnf transformation 55]
120. ~happy(X0) | generous(X0) [cnf transformation 63]
122. ~tall(sK7) | ~curious(X3) | quiet(X3) [cnf transformation 68]
144. ~rich(alice) [cnf transformation 21]
145. tall(X0) | calm(X0) | ~rich(X0) [duplicate literal removal 109]
146. ~calm(X0) | ~rich(X0) [duplicate literal removal 110]
147. ~curious(X0) | ~quiet(X0) [duplicate literal removal 89]
235. ~rich(X0) | tall(X0) [subsumption resolution 145,146]
268. 28 <=> ! [X1] : tall(X1) [avatar definition]
269. tall(X1) <- (28) [avatar component clause 268]
284. 32 <=> tall(sK7) [avatar definition]
286. ~tall(sK7) <- (~32) [avatar component clause 284]
288. ~tall(sK7) | ~curious(X3) [subsumption resolution 122,147]
290. 33 <=> ! [X3] : ~curious(X3) [avatar definition]
291. ~curious(X3) <- (33) [avatar component clause 290]
292. 33 | ~32 [avatar split clause 288,284,290]
324. $false <- (28, ~32) [resolution 286,269]
325. ~28 | 32 [avatar contradiction clause 324]
328. generous(X0) | rich(X0) [resolution 120,102]
371. tall(X0) | ~generous(X0) | rich(X0) [resolution 94,102]
389. ~tall(X0) | curious(X0) | rich(X0) [resolution 104,101]
390. curious(X0) | rich(X0) <- (28) [subsumption resolution 389,269]
391. rich(X0) <- (28, 33) [subsumption resolution 390,291]
392. $false <- (28, 33) [resolution 391,144]
396. ~28 | ~33 [avatar contradiction clause 392]
406. tall(X0) | rich(X0) [subsumption resolution 371,328]
407. tall(X0) [subsumption resolution 406,235]
408. 28 [avatar split clause 407,268]
419. $false [avatar sat refutation 292,325,396,408]
% SZS output end Proof for 6798354547611508955920318
% ------------------------------
% 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 generous or not humble is not patient or calm and vice versa. Everyone who is either patient or not quiet is happy or not kind and vice versa. If someone is both tall and not tall then someone is either humble or rich and vice versa. If someone is happy or generous then susan is not generous or not quiet. If someone is kind then susan is creative. Everyone who is either generous or calm is humble and vice versa. Everyone who is not strong or brave is either brave or wise. Everyone who is not brave or not kind is both strong and not quiet. Everyone who is either not tall or not wise is strong or creative and vice versa. Everyone who is both creative and not tall is either generous or quiet and vice versa. If someone is both not rich and not humble then someone is not happy or not tall and vice versa. If someone is rich or strong then someone is not calm and vice versa. If someone is quiet or humble then mary is not humble or not brave. If fred is both not patient and not generous then someone is either not quiet or humble and vice versa. Everyone who is not strong is happy and vice versa. Everyone who is rich is curious or not old and vice versa. Someone is wise. Alice is happy. Someone is rich or not happy. Paul is not wise. Someone is patient or not tall. Someone is both not wise and not creative. Alice is not patient. | Alice is tall. | neutral | (![X]:((~generous(X)<~>~humble(X))<=>(~patient(X)|calm(X))))&
(![X]:((patient(X)<~>~quiet(X))<=>(happy(X)|~kind(X))))&
((?[X]:((tall(X)&~tall(X))))<=>(?[X]:((humble(X)<~>rich(X)))))&
((?[X]:((happy(X)|generous(X))))=>((~generous(susan)|~quiet(susan))))&
((?[X]:(kind(X)))=>(creative(susan)))&
(![X]:((generous(X)<~>calm(X))<=>humble(X)))&
(![X]:((~strong(X)|brave(X))=>(brave(X)<~>wise(X))))&
(![X]:((~brave(X)|~kind(X))=>(strong(X)&~quiet(X))))&
(![X]:((~tall(X)<~>~wise(X))<=>(strong(X)|creative(X))))&
(![X]:((creative(X)&~tall(X))<=>(generous(X)<~>quiet(X))))&
((?[X]:((~rich(X)&~humble(X))))<=>(?[X]:((~happy(X)|~tall(X)))))&
((?[X]:((rich(X)|strong(X))))<=>(?[X]:(~calm(X))))&
((?[X]:((quiet(X)|humble(X))))=>((~humble(mary)|~brave(mary))))&
(((~patient(fred)&~generous(fred)))<=>(?[X]:((~quiet(X)<~>humble(X)))))&
(![X]:(~strong(X)<=>happy(X)))&
(![X]:(rich(X)<=>(curious(X)|~old(X))))&
(?[X]:(wise(X)))&
(happy(alice))&
(?[X]:((rich(X)|~happy(X))))&
(~wise(paul))&
(?[X]:((patient(X)|~tall(X))))&
(?[X]:((~wise(X)&~creative(X))))&
(~patient(alice)) | tall(alice) | [] | null | 0 |
If someone is not curious or not strong then lucy is not old and vice versa.
Everyone who is both not patient and not humble is patient and vice versa.
Everyone who is generous is either not patient or humble.
Everyone who is both not happy and not old is tall and vice versa.
Everyone who is either creative or rich is generous or not rich and vice versa.
If someone is not humble or not wise then someone is quiet.
If someone is either wise or old then someone is not rich.
If someone is not old or generous then paul is both brave and kind and vice versa.
If lucy is both happy and not brave then someone is not rich or not calm and vice versa.
If someone is either not old or not brave then someone is not brave.
Everyone who is old is not rich and vice versa.
If susan is both not happy and curious then alice is not calm or wise and vice versa.
Everyone who is both generous and not happy is old or not funny and vice versa.
If fred is old or not strong then someone is happy or kind and vice versa.
If someone is brave or not creative then lucy is either tall or funny and vice versa.
If alice is quiet or not patient then someone is both tall and strong and vice versa.
Mary is curious or not funny.
Someone is not quiet.
John is both not calm and not brave.
Mary is both not patient and kind.
Someone is not happy or not generous. | Paul is not quiet. | neutral | ((?[X]:((~curious(X)|~strong(X))))<=>(~old(lucy)))&
(![X]:((~patient(X)&~humble(X))<=>patient(X)))&
(![X]:(generous(X)=>(~patient(X)<~>humble(X))))&
(![X]:((~happy(X)&~old(X))<=>tall(X)))&
(![X]:((creative(X)<~>rich(X))<=>(generous(X)|~rich(X))))&
((?[X]:((~humble(X)|~wise(X))))=>(?[X]:(quiet(X))))&
((?[X]:((wise(X)<~>old(X))))=>(?[X]:(~rich(X))))&
((?[X]:((~old(X)|generous(X))))<=>((brave(paul)&kind(paul))))&
(((happy(lucy)&~brave(lucy)))<=>(?[X]:((~rich(X)|~calm(X)))))&
((?[X]:((~old(X)<~>~brave(X))))=>(?[X]:(~brave(X))))&
(![X]:(old(X)<=>~rich(X)))&
(((~happy(susan)&curious(susan)))<=>((~calm(alice)|wise(alice))))&
(![X]:((generous(X)&~happy(X))<=>(old(X)|~funny(X))))&
(((old(fred)|~strong(fred)))<=>(?[X]:((happy(X)|kind(X)))))&
((?[X]:((brave(X)|~creative(X))))<=>((tall(lucy)<~>funny(lucy))))&
(((quiet(alice)|~patient(alice)))<=>(?[X]:((tall(X)&strong(X)))))&
((curious(mary)|~funny(mary)))&
(?[X]:(~quiet(X)))&
((~calm(john)&~brave(john)))&
((~patient(mary)&kind(mary)))&
(?[X]:((~happy(X)|~generous(X)))) | ~quiet(paul) | [] | null | 0 |
Everyone who is calm or not rich is either quiet or not curious.
Everyone who is not kind is both not wise and not curious and vice versa.
Everyone who is either old or not happy is both not wise and kind.
Everyone who is happy is curious or not curious.
Everyone who is strong or not generous is both patient and not happy.
Everyone who is both not wise and generous is either patient or not kind and vice versa.
Everyone who is either kind or not kind is either not funny or not tall and vice versa.
If someone is strong or not curious then john is not kind.
Everyone who is either not patient or not rich is brave and vice versa.
Everyone who is not strong is not old or funny.
Everyone who is both not creative and not funny is quiet or not rich and vice versa.
If alice is not quiet then someone is both humble and kind.
If someone is either tall or rich then lucy is both not strong and patient.
Everyone who is either curious or not happy is both funny and old and vice versa.
If someone is either not tall or curious then someone is not humble.
Everyone who is not humble is both not generous and not rich and vice versa.
Paul is strong or not happy. | John is not generous. | contradiction | (![X]:((calm(X)|~rich(X))=>(quiet(X)<~>~curious(X))))&
(![X]:(~kind(X)<=>(~wise(X)&~curious(X))))&
(![X]:((old(X)<~>~happy(X))=>(~wise(X)&kind(X))))&
(![X]:(happy(X)=>(curious(X)|~curious(X))))&
(![X]:((strong(X)|~generous(X))=>(patient(X)&~happy(X))))&
(![X]:((~wise(X)&generous(X))<=>(patient(X)<~>~kind(X))))&
(![X]:((kind(X)<~>~kind(X))<=>(~funny(X)<~>~tall(X))))&
((?[X]:((strong(X)|~curious(X))))=>(~kind(john)))&
(![X]:((~patient(X)<~>~rich(X))<=>brave(X)))&
(![X]:(~strong(X)=>(~old(X)|funny(X))))&
(![X]:((~creative(X)&~funny(X))<=>(quiet(X)|~rich(X))))&
((~quiet(alice))=>(?[X]:((humble(X)&kind(X)))))&
((?[X]:((tall(X)<~>rich(X))))=>((~strong(lucy)&patient(lucy))))&
(![X]:((curious(X)<~>~happy(X))<=>(funny(X)&old(X))))&
((?[X]:((~tall(X)<~>curious(X))))=>(?[X]:(~humble(X))))&
(![X]:(~humble(X)<=>(~generous(X)&~rich(X))))&
((strong(paul)|~happy(paul))) | ~generous(john) | [
"p1",
"p2",
"p4",
"p5",
"p6",
"p9",
"p10",
"p13",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 5645178091147118423954525
% SZS output start Proof for 5645178091147118423954525
2. ! [X0] : (~kind(X0) <=> (~curious(X0) & ~wise(X0))) [input p1]
3. ! [X0] : ((old(X0) <~> ~happy(X0)) => (kind(X0) & ~wise(X0))) [input p2]
5. ! [X0] : ((~generous(X0) | strong(X0)) => (~happy(X0) & patient(X0))) [input p4]
6. ! [X0] : ((generous(X0) & ~wise(X0)) <=> (patient(X0) <~> ~kind(X0))) [input p5]
7. ! [X0] : ((kind(X0) <~> ~kind(X0)) <=> (~funny(X0) <~> ~tall(X0))) [input p6]
10. ! [X0] : (~strong(X0) => (funny(X0) | ~old(X0))) [input p9]
11. ! [X0] : ((~funny(X0) & ~creative(X0)) <=> (~rich(X0) | quiet(X0))) [input p10]
14. ! [X0] : ((curious(X0) <~> ~happy(X0)) <=> (old(X0) & funny(X0))) [input p13]
15. ? [X0] : (~tall(X0) <~> curious(X0)) => ? [X0] : ~humble(X0) [input p14]
16. ! [X0] : (~humble(X0) <=> (~rich(X0) & ~generous(X0))) [input p15]
18. ~generous(john) [input hypothesis]
19. ? [X0] : (~tall(X0) <~> curious(X0)) => ? [X1] : ~humble(X1) [rectify 15]
22. ! [X0] : ((kind(X0) & ~wise(X0)) | (old(X0) <=> ~happy(X0))) [ennf transformation 3]
25. ! [X0] : ((~happy(X0) & patient(X0)) | (generous(X0) & ~strong(X0))) [ennf transformation 5]
27. ! [X0] : ((funny(X0) | ~old(X0)) | strong(X0)) [ennf transformation 10]
28. ! [X0] : (funny(X0) | ~old(X0) | strong(X0)) [flattening 27]
31. ? [X1] : ~humble(X1) | ! [X0] : (~tall(X0) <=> curious(X0)) [ennf transformation 19]
33. ! [X0] : ((~kind(X0) | (curious(X0) | wise(X0))) & ((~curious(X0) & ~wise(X0)) | kind(X0))) [nnf transformation 2]
34. ! [X0] : ((~kind(X0) | curious(X0) | wise(X0)) & ((~curious(X0) & ~wise(X0)) | kind(X0))) [flattening 33]
35. ! [X0] : ((kind(X0) & ~wise(X0)) | ((old(X0) | happy(X0)) & (~happy(X0) | ~old(X0)))) [nnf transformation 22]
36. ! [X0] : (((generous(X0) & ~wise(X0)) | ((patient(X0) | kind(X0)) & (~kind(X0) | ~patient(X0)))) & (((kind(X0) | ~patient(X0)) & (~kind(X0) | patient(X0))) | (~generous(X0) | wise(X0)))) [nnf transformation 6]
37. ! [X0] : (((generous(X0) & ~wise(X0)) | ((patient(X0) | kind(X0)) & (~kind(X0) | ~patient(X0)))) & (((kind(X0) | ~patient(X0)) & (~kind(X0) | patient(X0))) | ~generous(X0) | wise(X0))) [flattening 36]
38. ! [X0] : ((((kind(X0) | ~kind(X0)) & (~kind(X0) | kind(X0))) | ((~funny(X0) | tall(X0)) & (~tall(X0) | funny(X0)))) & (((tall(X0) | funny(X0)) & (~tall(X0) | ~funny(X0))) | ((kind(X0) | kind(X0)) & (~kind(X0) | ~kind(X0))))) [nnf transformation 7]
39. ! [X0] : (((~funny(X0) & ~creative(X0)) | (rich(X0) & ~quiet(X0))) & ((~rich(X0) | quiet(X0)) | (funny(X0) | creative(X0)))) [nnf transformation 11]
40. ! [X0] : (((~funny(X0) & ~creative(X0)) | (rich(X0) & ~quiet(X0))) & (~rich(X0) | quiet(X0) | funny(X0) | creative(X0))) [flattening 39]
44. ! [X0] : ((((happy(X0) | ~curious(X0)) & (~happy(X0) | curious(X0))) | (~old(X0) | ~funny(X0))) & ((old(X0) & funny(X0)) | ((curious(X0) | happy(X0)) & (~happy(X0) | ~curious(X0))))) [nnf transformation 14]
45. ! [X0] : ((((happy(X0) | ~curious(X0)) & (~happy(X0) | curious(X0))) | ~old(X0) | ~funny(X0)) & ((old(X0) & funny(X0)) | ((curious(X0) | happy(X0)) & (~happy(X0) | ~curious(X0))))) [flattening 44]
46. ? [X1] : ~humble(X1) | ! [X0] : ((~tall(X0) | ~curious(X0)) & (curious(X0) | tall(X0))) [nnf transformation 31]
47. ? [X0] : ~humble(X0) | ! [X1] : ((~tall(X1) | ~curious(X1)) & (curious(X1) | tall(X1))) [rectify 46]
48. ? [X0] : ~humble(X0) => ~humble(sK1) [choice axiom]
49. ~humble(sK1) | ! [X1] : ((~tall(X1) | ~curious(X1)) & (curious(X1) | tall(X1))) [skolemisation 47,48]
50. ! [X0] : ((~humble(X0) | (rich(X0) | generous(X0))) & ((~rich(X0) & ~generous(X0)) | humble(X0))) [nnf transformation 16]
51. ! [X0] : ((~humble(X0) | rich(X0) | generous(X0)) & ((~rich(X0) & ~generous(X0)) | humble(X0))) [flattening 50]
55. ~curious(X0) | kind(X0) [cnf transformation 34]
59. ~happy(X0) | kind(X0) | ~old(X0) [cnf transformation 35]
60. happy(X0) | old(X0) | kind(X0) [cnf transformation 35]
63. patient(X0) | generous(X0) [cnf transformation 25]
64. ~strong(X0) | ~happy(X0) [cnf transformation 25]
65. ~happy(X0) | generous(X0) [cnf transformation 25]
70. generous(X0) | ~kind(X0) | ~patient(X0) [cnf transformation 37]
72. ~tall(X0) | ~funny(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 38]
73. ~tall(X0) | ~funny(X0) | kind(X0) | kind(X0) [cnf transformation 38]
82. ~old(X0) | funny(X0) | strong(X0) [cnf transformation 28]
87. ~funny(X0) | rich(X0) [cnf transformation 40]
95. funny(X0) | curious(X0) | happy(X0) [cnf transformation 45]
100. ~humble(sK1) | curious(X1) | tall(X1) [cnf transformation 49]
102. ~generous(X0) | humble(X0) [cnf transformation 51]
103. ~rich(X0) | humble(X0) [cnf transformation 51]
106. ~generous(john) [cnf transformation 18]
107. ~tall(X0) | ~funny(X0) | ~kind(X0) [duplicate literal removal 72]
108. ~tall(X0) | ~funny(X0) | kind(X0) [duplicate literal removal 73]
111. ~kind(X0) | generous(X0) [subsumption resolution 70,63]
116. ~tall(X0) | ~funny(X0) [subsumption resolution 107,108]
121. 2 <=> kind(john) [avatar definition]
122. kind(john) <- (2) [avatar component clause 121]
123. ~kind(john) <- (~2) [avatar component clause 121]
165. 12 <=> humble(sK1) [avatar definition]
167. ~humble(sK1) <- (~12) [avatar component clause 165]
170. 13 <=> ! [X1] : (curious(X1) | tall(X1)) [avatar definition]
171. tall(X1) | curious(X1) <- (13) [avatar component clause 170]
172. 13 | ~12 [avatar split clause 100,165,170]
204. old(X2) | kind(X2) | generous(X2) [resolution 60,65]
215. generous(X2) | old(X2) [subsumption resolution 204,111]
238. happy(X0) | curious(X0) | rich(X0) [resolution 95,87]
310. old(john) [resolution 215,106]
311. humble(X0) | old(X0) [resolution 215,102]
317. curious(X2) | rich(X2) | kind(X2) | ~old(X2) [resolution 238,59]
322. ~old(X2) | kind(X2) | rich(X2) [subsumption resolution 317,55]
323. funny(john) | strong(john) [resolution 310,82]
325. 30 <=> strong(john) [avatar definition]
327. strong(john) <- (30) [avatar component clause 325]
329. 31 <=> funny(john) [avatar definition]
331. funny(john) <- (31) [avatar component clause 329]
332. 30 | 31 [avatar split clause 323,329,325]
366. old(sK1) <- (~12) [resolution 311,167]
380. 38 <=> curious(john) [avatar definition]
381. ~curious(john) <- (~38) [avatar component clause 380]
382. curious(john) <- (38) [avatar component clause 380]
451. kind(sK1) | rich(sK1) <- (~12) [resolution 366,322]
462. 45 <=> rich(sK1) [avatar definition]
464. rich(sK1) <- (45) [avatar component clause 462]
467. 46 <=> kind(sK1) [avatar definition]
469. kind(sK1) <- (46) [avatar component clause 467]
470. 45 | 46 | 12 [avatar split clause 451,165,467,462]
510. kind(john) <- (38) [resolution 382,55]
511. $false <- (~2, 38) [subsumption resolution 510,123]
512. 2 | ~38 [avatar contradiction clause 511]
515. 51 <=> happy(john) [avatar definition]
516. happy(john) <- (51) [avatar component clause 515]
517. ~happy(john) <- (~51) [avatar component clause 515]
556. humble(sK1) <- (45) [resolution 464,103]
557. $false <- (~12, 45) [subsumption resolution 556,167]
558. 12 | ~45 [avatar contradiction clause 557]
566. generous(sK1) <- (46) [resolution 469,111]
602. ~funny(X2) | curious(X2) <- (13) [resolution 171,116]
610. curious(john) <- (13, 31) [resolution 602,331]
614. $false <- (13, 31, ~38) [subsumption resolution 610,381]
615. ~13 | ~31 | 38 [avatar contradiction clause 614]
626. humble(sK1) <- (46) [resolution 566,102]
643. 12 | ~46 [avatar split clause 626,467,165]
681. ~funny(X2) | curious(X2) <- (13) [resolution 171,116]
684. curious(X0) | curious(X0) | happy(X0) <- (13) [resolution 681,95]
685. happy(X0) | curious(X0) <- (13) [duplicate literal removal 684]
702. curious(john) <- (13, ~51) [resolution 685,517]
705. $false <- (13, ~38, ~51) [subsumption resolution 702,381]
706. ~13 | 38 | 51 [avatar contradiction clause 705]
737. ~happy(john) <- (30) [resolution 327,64]
739. $false <- (30, 51) [subsumption resolution 737,516]
740. ~30 | ~51 [avatar contradiction clause 739]
759. generous(john) <- (2) [resolution 122,111]
769. $false <- (2) [subsumption resolution 759,106]
770. ~2 [avatar contradiction clause 769]
771. $false [avatar sat refutation 172,332,470,512,558,615,643,706,740,770]
% SZS output end Proof for 5645178091147118423954525
% ------------------------------
% 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: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is not calm then paul is not strong. Everyone who is either wise or not old is either creative or not creative and vice versa. Everyone who is either tall or not old is not strong or not old and vice versa. Everyone who is either rich or creative is not kind or patient and vice versa. Everyone who is both not strong and not happy is calm or not humble and vice versa. If someone is strong then someone is either curious or not brave and vice versa. If mary is strong then john is either brave or quiet and vice versa. Everyone who is not strong or generous is either wise or kind and vice versa. Everyone who is both generous and strong is not calm or not brave and vice versa. Everyone who is both not creative and wise is kind. Everyone who is quiet or not funny is not curious and vice versa. Everyone who is not patient or not happy is both not funny and not humble and vice versa. If someone is either old or not quiet then mary is both not creative and not old. Everyone who is both happy and not brave is both wise and brave. Everyone who is not calm or not wise is either generous or not brave. If fred is both happy and not kind then someone is both not quiet and generous and vice versa. Someone is both not creative and not humble. Fred is not creative. Mary is either generous or not curious. Paul is wise. Someone is brave or not strong. Someone is either patient or not funny. | Mary is not creative. | contradiction | ((~calm(lucy))=>(~strong(paul)))&
(![X]:((wise(X)<~>~old(X))<=>(creative(X)<~>~creative(X))))&
(![X]:((tall(X)<~>~old(X))<=>(~strong(X)|~old(X))))&
(![X]:((rich(X)<~>creative(X))<=>(~kind(X)|patient(X))))&
(![X]:((~strong(X)&~happy(X))<=>(calm(X)|~humble(X))))&
((?[X]:(strong(X)))<=>(?[X]:((curious(X)<~>~brave(X)))))&
((strong(mary))<=>((brave(john)<~>quiet(john))))&
(![X]:((~strong(X)|generous(X))<=>(wise(X)<~>kind(X))))&
(![X]:((generous(X)&strong(X))<=>(~calm(X)|~brave(X))))&
(![X]:((~creative(X)&wise(X))=>kind(X)))&
(![X]:((quiet(X)|~funny(X))<=>~curious(X)))&
(![X]:((~patient(X)|~happy(X))<=>(~funny(X)&~humble(X))))&
((?[X]:((old(X)<~>~quiet(X))))=>((~creative(mary)&~old(mary))))&
(![X]:((happy(X)&~brave(X))=>(wise(X)&brave(X))))&
(![X]:((~calm(X)|~wise(X))=>(generous(X)<~>~brave(X))))&
(((happy(fred)&~kind(fred)))<=>(?[X]:((~quiet(X)&generous(X)))))&
(?[X]:((~creative(X)&~humble(X))))&
(~creative(fred))&
((generous(mary)<~>~curious(mary)))&
(wise(paul))&
(?[X]:((brave(X)|~strong(X))))&
(?[X]:((patient(X)<~>~funny(X)))) | ~creative(mary) | [
"p4",
"p7",
"p8",
"p9",
"p10",
"p14",
"p15",
"p17",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 5860149282157856346734041
% SZS output start Proof for 5860149282157856346734041
5. ! [X0] : ((~happy(X0) & ~strong(X0)) <=> (~humble(X0) | calm(X0))) [input p4]
8. ! [X0] : ((generous(X0) | ~strong(X0)) <=> (wise(X0) <~> kind(X0))) [input p7]
9. ! [X0] : ((strong(X0) & generous(X0)) <=> (~brave(X0) | ~calm(X0))) [input p8]
10. ! [X0] : ((wise(X0) & ~creative(X0)) => kind(X0)) [input p9]
11. ! [X0] : ((~funny(X0) | quiet(X0)) <=> ~curious(X0)) [input p10]
15. ! [X0] : ((~wise(X0) | ~calm(X0)) => (generous(X0) <~> ~brave(X0))) [input p14]
16. (~kind(fred) & happy(fred)) <=> ? [X0] : (generous(X0) & ~quiet(X0)) [input p15]
18. ~creative(fred) [input p17]
19. generous(mary) <~> ~curious(mary) [input p18]
23. ~creative(mary) [input hypothesis]
26. ! [X0] : (kind(X0) | (~wise(X0) | creative(X0))) [ennf transformation 10]
27. ! [X0] : (kind(X0) | ~wise(X0) | creative(X0)) [flattening 26]
31. ! [X0] : ((generous(X0) <~> ~brave(X0)) | (wise(X0) & calm(X0))) [ennf transformation 15]
37. ! [X0] : (((~happy(X0) & ~strong(X0)) | (humble(X0) & ~calm(X0))) & ((~humble(X0) | calm(X0)) | (happy(X0) | strong(X0)))) [nnf transformation 5]
38. ! [X0] : (((~happy(X0) & ~strong(X0)) | (humble(X0) & ~calm(X0))) & (~humble(X0) | calm(X0) | happy(X0) | strong(X0))) [flattening 37]
45. ! [X0] : (((generous(X0) | ~strong(X0)) | ((wise(X0) | ~kind(X0)) & (kind(X0) | ~wise(X0)))) & (((~kind(X0) | ~wise(X0)) & (kind(X0) | wise(X0))) | (~generous(X0) & strong(X0)))) [nnf transformation 8]
46. ! [X0] : ((generous(X0) | ~strong(X0) | ((wise(X0) | ~kind(X0)) & (kind(X0) | ~wise(X0)))) & (((~kind(X0) | ~wise(X0)) & (kind(X0) | wise(X0))) | (~generous(X0) & strong(X0)))) [flattening 45]
47. ! [X0] : (((strong(X0) & generous(X0)) | (brave(X0) & calm(X0))) & ((~brave(X0) | ~calm(X0)) | (~strong(X0) | ~generous(X0)))) [nnf transformation 9]
48. ! [X0] : (((strong(X0) & generous(X0)) | (brave(X0) & calm(X0))) & (~brave(X0) | ~calm(X0) | ~strong(X0) | ~generous(X0))) [flattening 47]
49. ! [X0] : (((~funny(X0) | quiet(X0)) | curious(X0)) & (~curious(X0) | (funny(X0) & ~quiet(X0)))) [nnf transformation 11]
50. ! [X0] : ((~funny(X0) | quiet(X0) | curious(X0)) & (~curious(X0) | (funny(X0) & ~quiet(X0)))) [flattening 49]
54. ! [X0] : (((brave(X0) | ~generous(X0)) & (~brave(X0) | generous(X0))) | (wise(X0) & calm(X0))) [nnf transformation 31]
55. ((~kind(fred) & happy(fred)) | ! [X0] : (~generous(X0) | quiet(X0))) & (? [X0] : (generous(X0) & ~quiet(X0)) | (kind(fred) | ~happy(fred))) [nnf transformation 16]
56. ((~kind(fred) & happy(fred)) | ! [X0] : (~generous(X0) | quiet(X0))) & (? [X0] : (generous(X0) & ~quiet(X0)) | kind(fred) | ~happy(fred)) [flattening 55]
57. ((~kind(fred) & happy(fred)) | ! [X0] : (~generous(X0) | quiet(X0))) & (? [X1] : (generous(X1) & ~quiet(X1)) | kind(fred) | ~happy(fred)) [rectify 56]
58. ? [X1] : (generous(X1) & ~quiet(X1)) => (generous(sK2) & ~quiet(sK2)) [choice axiom]
59. ((~kind(fred) & happy(fred)) | ! [X0] : (~generous(X0) | quiet(X0))) & ((generous(sK2) & ~quiet(sK2)) | kind(fred) | ~happy(fred)) [skolemisation 57,58]
62. (curious(mary) | ~generous(mary)) & (~curious(mary) | generous(mary)) [nnf transformation 19]
90. ~strong(X0) | ~calm(X0) [cnf transformation 38]
103. ~generous(X0) | wise(X0) | kind(X0) [cnf transformation 46]
104. ~kind(X0) | ~wise(X0) | strong(X0) [cnf transformation 46]
109. generous(X0) | calm(X0) [cnf transformation 48]
110. generous(X0) | brave(X0) [cnf transformation 48]
113. ~wise(X0) | kind(X0) | creative(X0) [cnf transformation 27]
114. ~quiet(X0) | ~curious(X0) [cnf transformation 50]
129. ~brave(X0) | generous(X0) | wise(X0) [cnf transformation 54]
135. ~kind(fred) | ~generous(X0) | quiet(X0) [cnf transformation 59]
138. ~creative(fred) [cnf transformation 18]
140. curious(mary) | ~generous(mary) [cnf transformation 62]
145. ~creative(mary) [cnf transformation 23]
199. 11 <=> strong(mary) [avatar definition]
200. ~strong(mary) <- (~11) [avatar component clause 199]
201. strong(mary) <- (11) [avatar component clause 199]
219. 15 <=> creative(mary) [avatar definition]
221. ~creative(mary) <- (~15) [avatar component clause 219]
226. generous(X0) | wise(X0) [subsumption resolution 129,110]
228. 16 <=> ! [X0] : (~generous(X0) | quiet(X0)) [avatar definition]
229. ~generous(X0) | quiet(X0) <- (16) [avatar component clause 228]
231. 17 <=> kind(fred) [avatar definition]
233. ~kind(fred) <- (~17) [avatar component clause 231]
234. 16 | ~17 [avatar split clause 135,231,228]
251. 21 <=> generous(mary) [avatar definition]
252. generous(mary) <- (21) [avatar component clause 251]
253. ~generous(mary) <- (~21) [avatar component clause 251]
255. 22 <=> curious(mary) [avatar definition]
257. curious(mary) <- (22) [avatar component clause 255]
258. ~21 | 22 [avatar split clause 140,255,251]
270. ~15 [avatar split clause 145,219]
318. wise(mary) <- (~21) [resolution 226,253]
347. wise(X0) | kind(X0) | wise(X0) [resolution 103,226]
350. kind(X0) | wise(X0) [duplicate literal removal 347]
365. kind(mary) | creative(mary) <- (~21) [resolution 113,318]
375. kind(mary) <- (~15, ~21) [subsumption resolution 365,221]
377. ~wise(mary) | strong(mary) <- (~15, ~21) [resolution 375,104]
378. strong(mary) <- (~15, ~21) [subsumption resolution 377,318]
379. $false <- (~11, ~15, ~21) [subsumption resolution 378,200]
380. 11 | 15 | 21 [avatar contradiction clause 379]
502. 35 <=> wise(fred) [avatar definition]
503. wise(fred) <- (35) [avatar component clause 502]
525. quiet(mary) <- (16, 21) [resolution 229,252]
545. ~curious(mary) <- (16, 21) [resolution 525,114]
546. $false <- (16, 21, 22) [subsumption resolution 545,257]
547. ~16 | ~21 | ~22 [avatar contradiction clause 546]
560. ~calm(mary) <- (11) [resolution 201,90]
574. calm(mary) <- (~21) [resolution 253,109]
575. $false <- (11, ~21) [subsumption resolution 574,560]
576. ~11 | 21 [avatar contradiction clause 575]
579. wise(fred) <- (~17) [resolution 233,350]
588. 35 | 17 [avatar split clause 579,231,502]
608. kind(fred) | creative(fred) <- (35) [resolution 503,113]
617. creative(fred) <- (~17, 35) [subsumption resolution 608,233]
618. $false <- (~17, 35) [subsumption resolution 617,138]
619. 17 | ~35 [avatar contradiction clause 618]
620. $false [avatar sat refutation 234,258,270,380,547,576,588,619]
% SZS output end Proof for 5860149282157856346734041
% ------------------------------
% 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: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both calm and rich is not strong or not calm and vice versa.
Everyone who is not creative or not humble is old.
If someone is both calm and not patient then john is creative.
Everyone who is humble is either not creative or funny.
Everyone who is not tall or funny is either calm or not happy.
Everyone who is both creative and brave is both creative and not kind and vice versa.
If someone is both happy and not calm then john is both not humble and not rich.
Everyone who is calm is both old and patient and vice versa.
Everyone who is both generous and quiet is either not brave or tall.
Everyone who is both kind and brave is both not patient and not tall.
Everyone who is either not funny or rich is either not curious or not kind.
Everyone who is not brave or not quiet is funny or not calm and vice versa.
Everyone who is not rich or humble is strong or humble.
Everyone who is both funny and not curious is curious and vice versa.
If someone is both not strong and wise then alice is happy and vice versa.
Alice is both humble and old.
Someone is not creative or not happy.
Someone is either not kind or not wise.
Lucy is not curious.
Someone is either not kind or creative.
Susan is happy or not tall. | Lucy is not funny. | entailment | (![X]:((calm(X)&rich(X))<=>(~strong(X)|~calm(X))))&
(![X]:((~creative(X)|~humble(X))=>old(X)))&
((?[X]:((calm(X)&~patient(X))))=>(creative(john)))&
(![X]:(humble(X)=>(~creative(X)<~>funny(X))))&
(![X]:((~tall(X)|funny(X))=>(calm(X)<~>~happy(X))))&
(![X]:((creative(X)&brave(X))<=>(creative(X)&~kind(X))))&
((?[X]:((happy(X)&~calm(X))))=>((~humble(john)&~rich(john))))&
(![X]:(calm(X)<=>(old(X)&patient(X))))&
(![X]:((generous(X)&quiet(X))=>(~brave(X)<~>tall(X))))&
(![X]:((kind(X)&brave(X))=>(~patient(X)&~tall(X))))&
(![X]:((~funny(X)<~>rich(X))=>(~curious(X)<~>~kind(X))))&
(![X]:((~brave(X)|~quiet(X))<=>(funny(X)|~calm(X))))&
(![X]:((~rich(X)|humble(X))=>(strong(X)|humble(X))))&
(![X]:((funny(X)&~curious(X))<=>curious(X)))&
((?[X]:((~strong(X)&wise(X))))<=>(happy(alice)))&
((humble(alice)&old(alice)))&
(?[X]:((~creative(X)|~happy(X))))&
(?[X]:((~kind(X)<~>~wise(X))))&
(~curious(lucy))&
(?[X]:((~kind(X)<~>creative(X))))&
((happy(susan)|~tall(susan))) | ~funny(lucy) | [
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 161135215749630905561176
% SZS output start Proof for 161135215749630905561176
14. ! [X0] : ((~curious(X0) & funny(X0)) <=> curious(X0)) [input p13]
22. funny(lucy) [input hypothesis]
45. ! [X0] : (((~curious(X0) & funny(X0)) | ~curious(X0)) & (curious(X0) | (curious(X0) | ~funny(X0)))) [nnf transformation 14]
46. ! [X0] : (((~curious(X0) & funny(X0)) | ~curious(X0)) & (curious(X0) | curious(X0) | ~funny(X0))) [flattening 45]
94. curious(X0) | curious(X0) | ~funny(X0) [cnf transformation 46]
96. ~curious(X0) | ~curious(X0) [cnf transformation 46]
109. funny(lucy) [cnf transformation 22]
110. curious(X0) | ~funny(X0) [duplicate literal removal 94]
111. ~curious(X0) [duplicate literal removal 96]
131. ~funny(X0) [subsumption resolution 110,111]
180. $false [subsumption resolution 109,131]
% SZS output end Proof for 161135215749630905561176
% ------------------------------
% 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: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If paul is either not happy or happy then john is rich or not quiet and vice versa. Everyone who is either not creative or not rich is both happy and not quiet and vice versa. If paul is not tall then someone is not rich and vice versa. If susan is not old then alice is not creative or not generous. If alice is either not wise or not funny then someone is curious or tall. If paul is either not rich or not creative then someone is either rich or humble and vice versa. Everyone who is not brave or not happy is creative or not curious. Everyone who is either not curious or quiet is not calm. If paul is both not tall and happy then someone is generous and vice versa. If someone is humble or curious then someone is both not creative and strong and vice versa. Everyone who is both not creative and not generous is either creative or rich. Everyone who is not kind is not old. If someone is not calm or strong then someone is not rich or not quiet and vice versa. Everyone who is funny or not rich is both old and tall. If lucy is not happy then someone is not kind and vice versa. Everyone who is quiet or happy is either not humble or creative. Someone is either not tall or humble. Susan is humble or not generous. Someone is generous or not patient. Susan is either not kind or tall. Someone is not quiet or calm. Fred is either happy or not rich. Susan is not tall or not happy. | Paul is not tall. | neutral | (((~happy(paul)<~>happy(paul)))<=>((rich(john)|~quiet(john))))&
(![X]:((~creative(X)<~>~rich(X))<=>(happy(X)&~quiet(X))))&
((~tall(paul))<=>(?[X]:(~rich(X))))&
((~old(susan))=>((~creative(alice)|~generous(alice))))&
(((~wise(alice)<~>~funny(alice)))=>(?[X]:((curious(X)|tall(X)))))&
(((~rich(paul)<~>~creative(paul)))<=>(?[X]:((rich(X)<~>humble(X)))))&
(![X]:((~brave(X)|~happy(X))=>(creative(X)|~curious(X))))&
(![X]:((~curious(X)<~>quiet(X))=>~calm(X)))&
(((~tall(paul)&happy(paul)))<=>(?[X]:(generous(X))))&
((?[X]:((humble(X)|curious(X))))<=>(?[X]:((~creative(X)&strong(X)))))&
(![X]:((~creative(X)&~generous(X))=>(creative(X)<~>rich(X))))&
(![X]:(~kind(X)=>~old(X)))&
((?[X]:((~calm(X)|strong(X))))<=>(?[X]:((~rich(X)|~quiet(X)))))&
(![X]:((funny(X)|~rich(X))=>(old(X)&tall(X))))&
((~happy(lucy))<=>(?[X]:(~kind(X))))&
(![X]:((quiet(X)|happy(X))=>(~humble(X)<~>creative(X))))&
(?[X]:((~tall(X)<~>humble(X))))&
((humble(susan)|~generous(susan)))&
(?[X]:((generous(X)|~patient(X))))&
((~kind(susan)<~>tall(susan)))&
(?[X]:((~quiet(X)|calm(X))))&
((happy(fred)<~>~rich(fred)))&
((~tall(susan)|~happy(susan))) | ~tall(paul) | [] | null | 0 |
Everyone who is either quiet or not brave is either calm or not quiet and vice versa. Everyone who is both brave and not happy is either not brave or curious and vice versa. If paul is not calm or not creative then paul is curious or old. If someone is either brave or not rich then someone is both strong and not quiet. If someone is either calm or curious then someone is generous and vice versa. If someone is either not strong or wise then john is either not wise or not strong and vice versa. If someone is either not patient or generous then fred is both strong and creative and vice versa. If susan is calm or not humble then fred is not wise and vice versa. Everyone who is not creative or not happy is both not patient and not kind. If someone is either not quiet or not funny then someone is curious. If someone is either not creative or not happy then susan is not old and vice versa. Everyone who is either not happy or not funny is not creative. If someone is not brave or funny then paul is kind or not happy. Everyone who is either funny or generous is both patient and generous and vice versa. Everyone who is not wise or not strong is either not rich or not old and vice versa. Everyone who is not old is curious and vice versa. Mary is tall or not generous. Paul is not curious. Alice is not generous. Someone is either brave or tall. Someone is either not funny or patient. Someone is creative. Someone is strong or not strong. Fred is both brave and funny. | John is not patient. | entailment | (![X]:((quiet(X)<~>~brave(X))<=>(calm(X)<~>~quiet(X))))&
(![X]:((brave(X)&~happy(X))<=>(~brave(X)<~>curious(X))))&
(((~calm(paul)|~creative(paul)))=>((curious(paul)|old(paul))))&
((?[X]:((brave(X)<~>~rich(X))))=>(?[X]:((strong(X)&~quiet(X)))))&
((?[X]:((calm(X)<~>curious(X))))<=>(?[X]:(generous(X))))&
((?[X]:((~strong(X)<~>wise(X))))<=>((~wise(john)<~>~strong(john))))&
((?[X]:((~patient(X)<~>generous(X))))<=>((strong(fred)&creative(fred))))&
(((calm(susan)|~humble(susan)))<=>(~wise(fred)))&
(![X]:((~creative(X)|~happy(X))=>(~patient(X)&~kind(X))))&
((?[X]:((~quiet(X)<~>~funny(X))))=>(?[X]:(curious(X))))&
((?[X]:((~creative(X)<~>~happy(X))))<=>(~old(susan)))&
(![X]:((~happy(X)<~>~funny(X))=>~creative(X)))&
((?[X]:((~brave(X)|funny(X))))=>((kind(paul)|~happy(paul))))&
(![X]:((funny(X)<~>generous(X))<=>(patient(X)&generous(X))))&
(![X]:((~wise(X)|~strong(X))<=>(~rich(X)<~>~old(X))))&
(![X]:(~old(X)<=>curious(X)))&
((tall(mary)|~generous(mary)))&
(~curious(paul))&
(~generous(alice))&
(?[X]:((brave(X)<~>tall(X))))&
(?[X]:((~funny(X)<~>patient(X))))&
(?[X]:(creative(X)))&
(?[X]:((strong(X)|~strong(X))))&
((brave(fred)&funny(fred))) | ~patient(john) | [
"p8",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 48598930470132641019026
% SZS output start Proof for 48598930470132641019026
9. ! [X0] : ((~happy(X0) | ~creative(X0)) => (~kind(X0) & ~patient(X0))) [input p8]
12. ! [X0] : ((~happy(X0) <~> ~funny(X0)) => ~creative(X0)) [input p11]
14. ! [X0] : ((funny(X0) <~> generous(X0)) <=> (generous(X0) & patient(X0))) [input p13]
25. patient(john) [input hypothesis]
32. ! [X0] : ((~kind(X0) & ~patient(X0)) | (happy(X0) & creative(X0))) [ennf transformation 9]
34. ! [X0] : (~creative(X0) | (~happy(X0) <=> ~funny(X0))) [ennf transformation 12]
68. ! [X0] : (~creative(X0) | ((~happy(X0) | funny(X0)) & (~funny(X0) | happy(X0)))) [nnf transformation 34]
69. ! [X0] : ((((~generous(X0) | ~funny(X0)) & (generous(X0) | funny(X0))) | (~generous(X0) | ~patient(X0))) & ((generous(X0) & patient(X0)) | ((funny(X0) | ~generous(X0)) & (generous(X0) | ~funny(X0))))) [nnf transformation 14]
70. ! [X0] : ((((~generous(X0) | ~funny(X0)) & (generous(X0) | funny(X0))) | ~generous(X0) | ~patient(X0)) & ((generous(X0) & patient(X0)) | ((funny(X0) | ~generous(X0)) & (generous(X0) | ~funny(X0))))) [flattening 69]
125. ~patient(X0) | creative(X0) [cnf transformation 32]
126. ~patient(X0) | happy(X0) [cnf transformation 32]
136. ~creative(X0) | ~happy(X0) | funny(X0) [cnf transformation 68]
141. generous(X0) | generous(X0) | ~funny(X0) [cnf transformation 70]
144. ~generous(X0) | ~funny(X0) | ~generous(X0) | ~patient(X0) [cnf transformation 70]
164. patient(john) [cnf transformation 25]
165. ~funny(X0) | generous(X0) [duplicate literal removal 141]
166. ~funny(X0) | ~generous(X0) | ~patient(X0) [duplicate literal removal 144]
392. creative(john) [resolution 125,164]
393. happy(john) [resolution 126,164]
436. ~happy(john) | funny(john) [resolution 136,392]
441. funny(john) [subsumption resolution 436,393]
621. ~generous(john) | ~patient(john) [resolution 441,166]
623. generous(john) [resolution 441,165]
624. ~generous(john) [subsumption resolution 621,164]
625. $false [subsumption resolution 623,624]
% SZS output end Proof for 48598930470132641019026
% ------------------------------
% 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 old or rich is calm or strong.
If alice is not brave or creative then someone is either not curious or not humble.
If mary is funny then someone is wise.
If john is patient then someone is either not old or not quiet.
Everyone who is not funny is not happy.
If someone is both patient and brave then someone is not wise or strong and vice versa.
If someone is not brave then someone is not generous and vice versa.
Everyone who is both not strong and not calm is either funny or old and vice versa.
Everyone who is not brave is patient or not rich and vice versa.
If someone is either tall or calm then someone is either humble or generous and vice versa.
If lucy is either tall or not creative then susan is not strong and vice versa.
If someone is strong then susan is not brave or not curious and vice versa.
Everyone who is not quiet or brave is either old or not brave.
Everyone who is brave is not happy or kind.
Everyone who is either curious or not generous is both not kind and humble.
If susan is both humble and funny then fred is either humble or generous and vice versa.
Someone is both not brave and not strong.
Alice is either generous or old.
Mary is either funny or not strong.
Someone is not generous.
Someone is old or wise.
Mary is wise.
Paul is tall. | Lucy is strong. | contradiction | (![X]:((~old(X)<~>rich(X))=>(calm(X)|strong(X))))&
(((~brave(alice)|creative(alice)))=>(?[X]:((~curious(X)<~>~humble(X)))))&
((funny(mary))=>(?[X]:(wise(X))))&
((patient(john))=>(?[X]:((~old(X)<~>~quiet(X)))))&
(![X]:(~funny(X)=>~happy(X)))&
((?[X]:((patient(X)&brave(X))))<=>(?[X]:((~wise(X)|strong(X)))))&
((?[X]:(~brave(X)))<=>(?[X]:(~generous(X))))&
(![X]:((~strong(X)&~calm(X))<=>(funny(X)<~>old(X))))&
(![X]:(~brave(X)<=>(patient(X)|~rich(X))))&
((?[X]:((tall(X)<~>calm(X))))<=>(?[X]:((humble(X)<~>generous(X)))))&
(((tall(lucy)<~>~creative(lucy)))<=>(~strong(susan)))&
((?[X]:(strong(X)))<=>((~brave(susan)|~curious(susan))))&
(![X]:((~quiet(X)|brave(X))=>(old(X)<~>~brave(X))))&
(![X]:(brave(X)=>(~happy(X)|kind(X))))&
(![X]:((curious(X)<~>~generous(X))=>(~kind(X)&humble(X))))&
(((humble(susan)&funny(susan)))<=>((humble(fred)<~>generous(fred))))&
(?[X]:((~brave(X)&~strong(X))))&
((generous(alice)<~>old(alice)))&
((funny(mary)<~>~strong(mary)))&
(?[X]:(~generous(X)))&
(?[X]:((old(X)|wise(X))))&
(wise(mary))&
(tall(paul)) | strong(lucy) | [
"p5",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 7041649645572082210212000
% SZS output start Proof for 7041649645572082210212000
6. ? [X0] : (brave(X0) & patient(X0)) <=> ? [X0] : (strong(X0) | ~wise(X0)) [input p5]
9. ! [X0] : (~brave(X0) <=> (~rich(X0) | patient(X0))) [input p8]
24. strong(lucy) [input hypothesis]
25. ? [X0] : (brave(X0) & patient(X0)) <=> ? [X1] : (strong(X1) | ~wise(X1)) [rectify 6]
47. (? [X0] : (brave(X0) & patient(X0)) | ! [X1] : (~strong(X1) & wise(X1))) & (? [X1] : (strong(X1) | ~wise(X1)) | ! [X0] : (~brave(X0) | ~patient(X0))) [nnf transformation 25]
48. (? [X0] : (brave(X0) & patient(X0)) | ! [X1] : (~strong(X1) & wise(X1))) & (? [X2] : (strong(X2) | ~wise(X2)) | ! [X3] : (~brave(X3) | ~patient(X3))) [rectify 47]
49. ? [X0] : (brave(X0) & patient(X0)) => (brave(sK3) & patient(sK3)) [choice axiom]
50. ? [X2] : (strong(X2) | ~wise(X2)) => (strong(sK4) | ~wise(sK4)) [choice axiom]
51. ((brave(sK3) & patient(sK3)) | ! [X1] : (~strong(X1) & wise(X1))) & ((strong(sK4) | ~wise(sK4)) | ! [X3] : (~brave(X3) | ~patient(X3))) [skolemisation 48,50,49]
59. ! [X0] : ((~brave(X0) | (rich(X0) & ~patient(X0))) & ((~rich(X0) | patient(X0)) | brave(X0))) [nnf transformation 9]
60. ! [X0] : ((~brave(X0) | (rich(X0) & ~patient(X0))) & (~rich(X0) | patient(X0) | brave(X0))) [flattening 59]
95. patient(sK3) | ~strong(X1) [cnf transformation 51]
97. brave(sK3) | ~strong(X1) [cnf transformation 51]
107. ~brave(X0) | ~patient(X0) [cnf transformation 60]
146. strong(lucy) [cnf transformation 24]
192. 10 <=> ! [X1] : ~strong(X1) [avatar definition]
193. ~strong(X1) <- (10) [avatar component clause 192]
195. 11 <=> brave(sK3) [avatar definition]
197. brave(sK3) <- (11) [avatar component clause 195]
198. 10 | 11 [avatar split clause 97,195,192]
204. 13 <=> patient(sK3) [avatar definition]
206. patient(sK3) <- (13) [avatar component clause 204]
207. 10 | 13 [avatar split clause 95,204,192]
210. 14 <=> ! [X3] : (~brave(X3) | ~patient(X3)) [avatar definition]
211. ~patient(X3) | ~brave(X3) <- (14) [avatar component clause 210]
237. 14 [avatar split clause 107,210]
352. $false <- (10) [resolution 193,146]
353. ~10 [avatar contradiction clause 352]
356. ~brave(sK3) <- (13, 14) [resolution 211,206]
357. $false <- (11, 13, 14) [subsumption resolution 356,197]
358. ~11 | ~13 | ~14 [avatar contradiction clause 357]
359. $false [avatar sat refutation 198,207,237,353,358]
% SZS output end Proof for 7041649645572082210212000
% ------------------------------
% 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: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either funny or not wise is not funny or humble and vice versa. If paul is both not rich and not curious then someone is creative or kind. Everyone who is not kind is either not humble or not tall. If someone is not creative or not calm then someone is not patient or funny. If fred is both strong and funny then someone is either not brave or funny. Everyone who is either not generous or patient is patient and vice versa. If someone is both not humble and not strong then someone is both not creative and calm. Everyone who is either patient or brave is not curious and vice versa. If someone is either not wise or humble then someone is both not happy and rich and vice versa. Everyone who is funny is not strong. If someone is creative then paul is humble or happy and vice versa. If someone is either funny or not kind then paul is both not brave and not old and vice versa. If john is both patient and generous then lucy is generous or quiet and vice versa. If paul is both not tall and not generous then lucy is both brave and not creative. Everyone who is not strong is not patient or not tall. If paul is both not strong and brave then lucy is calm or not kind. Someone is both wise and happy. Someone is both strong and generous. Mary is either not happy or not calm. Someone is patient. Susan is both calm and kind. Someone is not kind or patient. John is either brave or not generous. Someone is old. | John is curious. | entailment | (![X]:((funny(X)<~>~wise(X))<=>(~funny(X)|humble(X))))&
(((~rich(paul)&~curious(paul)))=>(?[X]:((creative(X)|kind(X)))))&
(![X]:(~kind(X)=>(~humble(X)<~>~tall(X))))&
((?[X]:((~creative(X)|~calm(X))))=>(?[X]:((~patient(X)|funny(X)))))&
(((strong(fred)&funny(fred)))=>(?[X]:((~brave(X)<~>funny(X)))))&
(![X]:((~generous(X)<~>patient(X))<=>patient(X)))&
((?[X]:((~humble(X)&~strong(X))))=>(?[X]:((~creative(X)&calm(X)))))&
(![X]:((patient(X)<~>brave(X))<=>~curious(X)))&
((?[X]:((~wise(X)<~>humble(X))))<=>(?[X]:((~happy(X)&rich(X)))))&
(![X]:(funny(X)=>~strong(X)))&
((?[X]:(creative(X)))<=>((humble(paul)|happy(paul))))&
((?[X]:((funny(X)<~>~kind(X))))<=>((~brave(paul)&~old(paul))))&
(((patient(john)&generous(john)))<=>((generous(lucy)|quiet(lucy))))&
(((~tall(paul)&~generous(paul)))=>((brave(lucy)&~creative(lucy))))&
(![X]:(~strong(X)=>(~patient(X)|~tall(X))))&
(((~strong(paul)&brave(paul)))=>((calm(lucy)|~kind(lucy))))&
(?[X]:((wise(X)&happy(X))))&
(?[X]:((strong(X)&generous(X))))&
((~happy(mary)<~>~calm(mary)))&
(?[X]:(patient(X)))&
((calm(susan)&kind(susan)))&
(?[X]:((~kind(X)|patient(X))))&
((brave(john)<~>~generous(john)))&
(?[X]:(old(X))) | curious(john) | [
"p5",
"p7",
"p12",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 9113546054309487841585430
% SZS output start Proof for 9113546054309487841585430
6. ! [X0] : ((~generous(X0) <~> patient(X0)) <=> patient(X0)) [input p5]
8. ! [X0] : ((patient(X0) <~> brave(X0)) <=> ~curious(X0)) [input p7]
13. (generous(john) & patient(john)) <=> (quiet(lucy) | generous(lucy)) [input p12]
23. brave(john) <~> ~generous(john) [input p22]
25. ~curious(john) [input hypothesis]
54. ! [X0] : ((((~patient(X0) | generous(X0)) & (patient(X0) | ~generous(X0))) | ~patient(X0)) & (patient(X0) | ((~generous(X0) | ~patient(X0)) & (patient(X0) | generous(X0))))) [nnf transformation 6]
58. ! [X0] : ((((~brave(X0) | ~patient(X0)) & (brave(X0) | patient(X0))) | curious(X0)) & (~curious(X0) | ((patient(X0) | ~brave(X0)) & (brave(X0) | ~patient(X0))))) [nnf transformation 8]
74. ((generous(john) & patient(john)) | (~quiet(lucy) & ~generous(lucy))) & ((quiet(lucy) | generous(lucy)) | (~generous(john) | ~patient(john))) [nnf transformation 13]
75. ((generous(john) & patient(john)) | (~quiet(lucy) & ~generous(lucy))) & (quiet(lucy) | generous(lucy) | ~generous(john) | ~patient(john)) [flattening 74]
85. (generous(john) | ~brave(john)) & (~generous(john) | brave(john)) [nnf transformation 23]
101. patient(X0) | patient(X0) | generous(X0) [cnf transformation 54]
104. ~patient(X0) | generous(X0) | ~patient(X0) [cnf transformation 54]
110. ~brave(X0) | ~patient(X0) | curious(X0) [cnf transformation 58]
128. patient(john) | ~generous(lucy) [cnf transformation 75]
146. ~generous(john) | brave(john) [cnf transformation 85]
149. ~curious(john) [cnf transformation 25]
150. patient(X0) | generous(X0) [duplicate literal removal 101]
151. ~patient(X0) | generous(X0) [duplicate literal removal 104]
206. generous(X0) [subsumption resolution 150,151]
305. 34 <=> patient(john) [avatar definition]
307. patient(john) <- (34) [avatar component clause 305]
309. patient(john) [subsumption resolution 128,206]
310. 34 [avatar split clause 309,305]
343. brave(john) [subsumption resolution 146,206]
370. ~patient(john) | curious(john) [resolution 110,343]
373. curious(john) <- (34) [subsumption resolution 370,307]
374. $false <- (34) [subsumption resolution 373,149]
375. ~34 [avatar contradiction clause 374]
376. $false [avatar sat refutation 310,375]
% SZS output end Proof for 9113546054309487841585430
% ------------------------------
% 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 creative or kind is both curious and not generous and vice versa.
Everyone who is either tall or not humble is either brave or not calm and vice versa.
Everyone who is either creative or not funny is humble.
Everyone who is happy or wise is both not calm and not patient.
If alice is happy then fred is not patient or not creative.
If someone is either not funny or curious then someone is either rich or not generous.
If john is either not old or not generous then alice is both strong and not happy and vice versa.
Everyone who is both strong and not calm is humble and vice versa.
Everyone who is either funny or not happy is either not curious or not creative and vice versa.
Everyone who is both not happy and not generous is curious and vice versa.
Everyone who is not quiet or not creative is not tall and vice versa.
If susan is either old or not calm then fred is either not strong or not tall.
If mary is either not happy or not strong then someone is not humble and vice versa.
If someone is funny or not happy then someone is either kind or brave and vice versa.
Everyone who is funny or brave is either not old or not creative and vice versa.
Everyone who is either not brave or strong is quiet and vice versa.
Someone is calm or old.
Someone is both not generous and brave.
Alice is either old or not rich.
Fred is both not tall and kind.
Someone is curious or not strong.
Someone is old or calm.
Someone is generous. | John is not curious. | neutral | (![X]:((creative(X)<~>kind(X))<=>(curious(X)&~generous(X))))&
(![X]:((tall(X)<~>~humble(X))<=>(brave(X)<~>~calm(X))))&
(![X]:((creative(X)<~>~funny(X))=>humble(X)))&
(![X]:((happy(X)|wise(X))=>(~calm(X)&~patient(X))))&
((happy(alice))=>((~patient(fred)|~creative(fred))))&
((?[X]:((~funny(X)<~>curious(X))))=>(?[X]:((rich(X)<~>~generous(X)))))&
(((~old(john)<~>~generous(john)))<=>((strong(alice)&~happy(alice))))&
(![X]:((strong(X)&~calm(X))<=>humble(X)))&
(![X]:((funny(X)<~>~happy(X))<=>(~curious(X)<~>~creative(X))))&
(![X]:((~happy(X)&~generous(X))<=>curious(X)))&
(![X]:((~quiet(X)|~creative(X))<=>~tall(X)))&
(((old(susan)<~>~calm(susan)))=>((~strong(fred)<~>~tall(fred))))&
(((~happy(mary)<~>~strong(mary)))<=>(?[X]:(~humble(X))))&
((?[X]:((funny(X)|~happy(X))))<=>(?[X]:((kind(X)<~>brave(X)))))&
(![X]:((funny(X)|brave(X))<=>(~old(X)<~>~creative(X))))&
(![X]:((~brave(X)<~>strong(X))<=>quiet(X)))&
(?[X]:((calm(X)|old(X))))&
(?[X]:((~generous(X)&brave(X))))&
((old(alice)<~>~rich(alice)))&
((~tall(fred)&kind(fred)))&
(?[X]:((curious(X)|~strong(X))))&
(?[X]:((old(X)|calm(X))))&
(?[X]:(generous(X))) | ~curious(john) | [] | null | 0 |
Everyone who is not humble or not curious is both not strong and calm. Everyone who is not happy or patient is not strong or kind. Everyone who is either brave or not old is either tall or not old and vice versa. Everyone who is tall or not quiet is both happy and not brave and vice versa. If susan is both not humble and calm then someone is rich and vice versa. If someone is both brave and creative then someone is both not tall and not wise. Everyone who is not happy is both quiet and not generous. Everyone who is happy or rich is not curious or humble and vice versa. If susan is either tall or patient then someone is either happy or tall and vice versa. If john is not old or not patient then someone is calm or wise. If lucy is old then someone is either not wise or not creative and vice versa. If someone is not calm or rich then someone is not curious or not kind and vice versa. Everyone who is both not tall and not generous is not calm and vice versa. Everyone who is not happy is both not old and not funny. Everyone who is calm is not brave. Everyone who is either not brave or brave is rich and vice versa. John is not patient. Susan is not happy or not brave. Someone is either not patient or generous. Someone is either kind or not curious. Mary is not humble. Someone is happy. Someone is not patient. | Mary is not calm. | contradiction | (![X]:((~humble(X)|~curious(X))=>(~strong(X)&calm(X))))&
(![X]:((~happy(X)|patient(X))=>(~strong(X)|kind(X))))&
(![X]:((brave(X)<~>~old(X))<=>(tall(X)<~>~old(X))))&
(![X]:((tall(X)|~quiet(X))<=>(happy(X)&~brave(X))))&
(((~humble(susan)&calm(susan)))<=>(?[X]:(rich(X))))&
((?[X]:((brave(X)&creative(X))))=>(?[X]:((~tall(X)&~wise(X)))))&
(![X]:(~happy(X)=>(quiet(X)&~generous(X))))&
(![X]:((happy(X)|rich(X))<=>(~curious(X)|humble(X))))&
(((tall(susan)<~>patient(susan)))<=>(?[X]:((happy(X)<~>tall(X)))))&
(((~old(john)|~patient(john)))=>(?[X]:((calm(X)|wise(X)))))&
((old(lucy))<=>(?[X]:((~wise(X)<~>~creative(X)))))&
((?[X]:((~calm(X)|rich(X))))<=>(?[X]:((~curious(X)|~kind(X)))))&
(![X]:((~tall(X)&~generous(X))<=>~calm(X)))&
(![X]:(~happy(X)=>(~old(X)&~funny(X))))&
(![X]:(calm(X)=>~brave(X)))&
(![X]:((~brave(X)<~>brave(X))<=>rich(X)))&
(~patient(john))&
((~happy(susan)|~brave(susan)))&
(?[X]:((~patient(X)<~>generous(X))))&
(?[X]:((kind(X)<~>~curious(X))))&
(~humble(mary))&
(?[X]:(happy(X)))&
(?[X]:(~patient(X))) | ~calm(mary) | [
"p0",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 3915524635593182024477559
% SZS output start Proof for 3915524635593182024477559
1. ! [X0] : ((~curious(X0) | ~humble(X0)) => (calm(X0) & ~strong(X0))) [input p0]
21. ~humble(mary) [input p20]
24. ~calm(mary) [input hypothesis]
29. ! [X0] : ((~curious(X0) | ~humble(X0)) => calm(X0)) [pure predicate removal 1]
30. ! [X0] : (calm(X0) | (curious(X0) & humble(X0))) [ennf transformation 29]
77. calm(X0) | humble(X0) [cnf transformation 30]
136. ~humble(mary) [cnf transformation 21]
139. ~calm(mary) [cnf transformation 24]
297. humble(mary) [resolution 77,139]
299. $false [subsumption resolution 297,136]
% SZS output end Proof for 3915524635593182024477559
% ------------------------------
% 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 generous is wise or not funny and vice versa. If paul is not strong then someone is both not patient and not brave and vice versa. If alice is curious then someone is both generous and not generous. Everyone who is both strong and not old is either tall or strong and vice versa. If mary is both creative and old then someone is either not quiet or not calm and vice versa. If someone is kind then susan is either humble or not calm and vice versa. If alice is wise then someone is either not brave or not patient and vice versa. Everyone who is patient or not rich is either patient or not creative and vice versa. If paul is happy then someone is both old and not patient. If someone is both not funny and brave then susan is both not wise and quiet and vice versa. If paul is not happy then someone is not rich or funny. If someone is not humble or funny then susan is both not humble and not creative. Everyone who is not funny is both funny and kind and vice versa. Everyone who is generous or calm is either brave or tall. Everyone who is not kind is not tall or wise and vice versa. Someone is wise. Fred is not creative or not calm. Someone is either generous or patient. Lucy is either not humble or not rich. Someone is either funny or not old. Lucy is either creative or not humble. Someone is either not old or kind. Someone is funny. | Paul is happy. | neutral | (![X]:(generous(X)<=>(wise(X)|~funny(X))))&
((~strong(paul))<=>(?[X]:((~patient(X)&~brave(X)))))&
((curious(alice))=>(?[X]:((generous(X)&~generous(X)))))&
(![X]:((strong(X)&~old(X))<=>(tall(X)<~>strong(X))))&
(((creative(mary)&old(mary)))<=>(?[X]:((~quiet(X)<~>~calm(X)))))&
((?[X]:(kind(X)))<=>((humble(susan)<~>~calm(susan))))&
((wise(alice))<=>(?[X]:((~brave(X)<~>~patient(X)))))&
(![X]:((patient(X)|~rich(X))<=>(patient(X)<~>~creative(X))))&
((happy(paul))=>(?[X]:((old(X)&~patient(X)))))&
((?[X]:((~funny(X)&brave(X))))<=>((~wise(susan)&quiet(susan))))&
((~happy(paul))=>(?[X]:((~rich(X)|funny(X)))))&
((?[X]:((~humble(X)|funny(X))))=>((~humble(susan)&~creative(susan))))&
(![X]:(~funny(X)<=>(funny(X)&kind(X))))&
(![X]:((generous(X)|calm(X))=>(brave(X)<~>tall(X))))&
(![X]:(~kind(X)<=>(~tall(X)|wise(X))))&
(?[X]:(wise(X)))&
((~creative(fred)|~calm(fred)))&
(?[X]:((generous(X)<~>patient(X))))&
((~humble(lucy)<~>~rich(lucy)))&
(?[X]:((funny(X)<~>~old(X))))&
((creative(lucy)<~>~humble(lucy)))&
(?[X]:((~old(X)<~>kind(X))))&
(?[X]:(funny(X))) | happy(paul) | [] | null | 0 |
If someone is both creative and happy then someone is both not rich and not funny and vice versa.
Everyone who is quiet is not generous.
Everyone who is both creative and rich is either not rich or curious.
Everyone who is creative is either not old or funny and vice versa.
If someone is patient or not quiet then john is either curious or not humble and vice versa.
If someone is not rich or generous then alice is generous.
If someone is both not kind and not old then lucy is generous.
If someone is either funny or not calm then paul is either funny or kind and vice versa.
Everyone who is both kind and not old is not generous or curious and vice versa.
Everyone who is both patient and not quiet is either not patient or patient.
Everyone who is either not kind or not tall is either calm or not happy.
If someone is either old or not creative then someone is both not wise and not humble.
Everyone who is either generous or strong is not creative or not calm and vice versa.
Everyone who is not tall is not generous or funny.
If john is both quiet and not creative then someone is either brave or not generous.
Everyone who is either not curious or strong is both curious and rich and vice versa.
Someone is generous or not funny.
Alice is kind or creative.
Mary is not wise.
Paul is not rich.
Susan is rich or not happy.
Someone is kind or old.
Someone is either not creative or tall. | John is creative. | neutral | ((?[X]:((creative(X)&happy(X))))<=>(?[X]:((~rich(X)&~funny(X)))))&
(![X]:(quiet(X)=>~generous(X)))&
(![X]:((creative(X)&rich(X))=>(~rich(X)<~>curious(X))))&
(![X]:(creative(X)<=>(~old(X)<~>funny(X))))&
((?[X]:((patient(X)|~quiet(X))))<=>((curious(john)<~>~humble(john))))&
((?[X]:((~rich(X)|generous(X))))=>(generous(alice)))&
((?[X]:((~kind(X)&~old(X))))=>(generous(lucy)))&
((?[X]:((funny(X)<~>~calm(X))))<=>((funny(paul)<~>kind(paul))))&
(![X]:((kind(X)&~old(X))<=>(~generous(X)|curious(X))))&
(![X]:((patient(X)&~quiet(X))=>(~patient(X)<~>patient(X))))&
(![X]:((~kind(X)<~>~tall(X))=>(calm(X)<~>~happy(X))))&
((?[X]:((old(X)<~>~creative(X))))=>(?[X]:((~wise(X)&~humble(X)))))&
(![X]:((generous(X)<~>strong(X))<=>(~creative(X)|~calm(X))))&
(![X]:(~tall(X)=>(~generous(X)|funny(X))))&
(((quiet(john)&~creative(john)))=>(?[X]:((brave(X)<~>~generous(X)))))&
(![X]:((~curious(X)<~>strong(X))<=>(curious(X)&rich(X))))&
(?[X]:((generous(X)|~funny(X))))&
((kind(alice)|creative(alice)))&
(~wise(mary))&
(~rich(paul))&
((rich(susan)|~happy(susan)))&
(?[X]:((kind(X)|old(X))))&
(?[X]:((~creative(X)<~>tall(X)))) | creative(john) | [] | null | 0 |
Everyone who is both not brave and patient is not happy or humble and vice versa.
Everyone who is both happy and tall is not calm and vice versa.
Everyone who is funny is humble and vice versa.
Everyone who is humble or quiet is either old or not happy and vice versa.
Everyone who is quiet is either calm or tall.
If mary is old then someone is either not kind or not strong and vice versa.
Everyone who is both not patient and generous is either not old or not calm.
Everyone who is either not happy or old is calm or not wise and vice versa.
Everyone who is both patient and not tall is wise or funny.
If someone is either not brave or not happy then john is not funny or calm.
If alice is tall or kind then someone is not kind and vice versa.
If lucy is both quiet and not curious then paul is either not quiet or tall and vice versa.
If mary is either not quiet or not humble then someone is either not happy or kind.
Everyone who is both not brave and curious is both not happy and not generous.
If fred is brave then paul is either old or not old.
Everyone who is not creative is both wise and not humble and vice versa.
Someone is tall.
Fred is either not tall or not brave.
Someone is not generous or not tall.
Susan is humble.
Mary is both rich and not patient.
Alice is both not creative and strong. | Alice is brave. | neutral | (![X]:((~brave(X)&patient(X))<=>(~happy(X)|humble(X))))&
(![X]:((happy(X)&tall(X))<=>~calm(X)))&
(![X]:(funny(X)<=>humble(X)))&
(![X]:((humble(X)|quiet(X))<=>(old(X)<~>~happy(X))))&
(![X]:(quiet(X)=>(calm(X)<~>tall(X))))&
((old(mary))<=>(?[X]:((~kind(X)<~>~strong(X)))))&
(![X]:((~patient(X)&generous(X))=>(~old(X)<~>~calm(X))))&
(![X]:((~happy(X)<~>old(X))<=>(calm(X)|~wise(X))))&
(![X]:((patient(X)&~tall(X))=>(wise(X)|funny(X))))&
((?[X]:((~brave(X)<~>~happy(X))))=>((~funny(john)|calm(john))))&
(((tall(alice)|kind(alice)))<=>(?[X]:(~kind(X))))&
(((quiet(lucy)&~curious(lucy)))<=>((~quiet(paul)<~>tall(paul))))&
(((~quiet(mary)<~>~humble(mary)))=>(?[X]:((~happy(X)<~>kind(X)))))&
(![X]:((~brave(X)&curious(X))=>(~happy(X)&~generous(X))))&
((brave(fred))=>((old(paul)<~>~old(paul))))&
(![X]:(~creative(X)<=>(wise(X)&~humble(X))))&
(?[X]:(tall(X)))&
((~tall(fred)<~>~brave(fred)))&
(?[X]:((~generous(X)|~tall(X))))&
(humble(susan))&
((rich(mary)&~patient(mary)))&
((~creative(alice)&strong(alice))) | brave(alice) | [] | null | 0 |
Everyone who is creative or not strong is both not kind and not funny. If lucy is both kind and not generous then alice is both not curious and rich. If someone is not happy or not funny then mary is either not curious or rich. Everyone who is patient or happy is not generous. Everyone who is both not happy and not wise is not patient and vice versa. If mary is not brave then someone is both kind and not happy and vice versa. If someone is both not kind and not calm then john is not happy or calm and vice versa. If fred is not calm or not curious then someone is both humble and not creative. If john is not strong then lucy is not old or not generous. Everyone who is happy is either not strong or not funny and vice versa. Everyone who is curious or not old is curious. Everyone who is not happy or happy is strong. If someone is not strong or not quiet then someone is both not funny and patient. Everyone who is not tall or kind is curious and vice versa. Everyone who is both brave and not quiet is both quiet and not rich and vice versa. Everyone who is happy is not happy or not kind and vice versa. Someone is both wise and creative. Fred is brave or not curious. Paul is not kind or generous. John is not quiet or patient. Someone is both brave and old. Someone is not old. | John is not funny. | entailment | (![X]:((creative(X)|~strong(X))=>(~kind(X)&~funny(X))))&
(((kind(lucy)&~generous(lucy)))=>((~curious(alice)&rich(alice))))&
((?[X]:((~happy(X)|~funny(X))))=>((~curious(mary)<~>rich(mary))))&
(![X]:((patient(X)|happy(X))=>~generous(X)))&
(![X]:((~happy(X)&~wise(X))<=>~patient(X)))&
((~brave(mary))<=>(?[X]:((kind(X)&~happy(X)))))&
((?[X]:((~kind(X)&~calm(X))))<=>((~happy(john)|calm(john))))&
(((~calm(fred)|~curious(fred)))=>(?[X]:((humble(X)&~creative(X)))))&
((~strong(john))=>((~old(lucy)|~generous(lucy))))&
(![X]:(happy(X)<=>(~strong(X)<~>~funny(X))))&
(![X]:((curious(X)|~old(X))=>curious(X)))&
(![X]:((~happy(X)|happy(X))=>strong(X)))&
((?[X]:((~strong(X)|~quiet(X))))=>(?[X]:((~funny(X)&patient(X)))))&
(![X]:((~tall(X)|kind(X))<=>curious(X)))&
(![X]:((brave(X)&~quiet(X))<=>(quiet(X)&~rich(X))))&
(![X]:(happy(X)<=>(~happy(X)|~kind(X))))&
(?[X]:((wise(X)&creative(X))))&
((brave(fred)|~curious(fred)))&
((~kind(paul)|generous(paul)))&
((~quiet(john)|patient(john)))&
(?[X]:((brave(X)&old(X))))&
(?[X]:(~old(X))) | ~funny(john) | [
"p0",
"p9",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1544793323144817191271106
% SZS output start Proof for 1544793323144817191271106
1. ! [X0] : ((~strong(X0) | creative(X0)) => (~funny(X0) & ~kind(X0))) [input p0]
10. ! [X0] : (happy(X0) <=> (~strong(X0) <~> ~funny(X0))) [input p9]
16. ! [X0] : (happy(X0) <=> (~kind(X0) | ~happy(X0))) [input p15]
23. funny(john) [input hypothesis]
26. ! [X0] : ((~funny(X0) & ~kind(X0)) | (strong(X0) & ~creative(X0))) [ennf transformation 1]
51. ! [X0] : ((happy(X0) | ((~strong(X0) | funny(X0)) & (~funny(X0) | strong(X0)))) & (((funny(X0) | strong(X0)) & (~funny(X0) | ~strong(X0))) | ~happy(X0))) [nnf transformation 10]
59. ! [X0] : ((happy(X0) | (kind(X0) & happy(X0))) & ((~kind(X0) | ~happy(X0)) | ~happy(X0))) [nnf transformation 16]
60. ! [X0] : ((happy(X0) | (kind(X0) & happy(X0))) & (~kind(X0) | ~happy(X0) | ~happy(X0))) [flattening 59]
70. ~funny(X0) | strong(X0) [cnf transformation 26]
93. ~funny(X0) | ~strong(X0) | ~happy(X0) [cnf transformation 51]
94. funny(X0) | strong(X0) | ~happy(X0) [cnf transformation 51]
112. ~kind(X0) | ~happy(X0) | ~happy(X0) [cnf transformation 60]
113. happy(X0) | happy(X0) [cnf transformation 60]
114. happy(X0) | kind(X0) [cnf transformation 60]
123. funny(john) [cnf transformation 23]
124. ~happy(X0) | ~kind(X0) [duplicate literal removal 112]
125. happy(X0) [duplicate literal removal 113]
159. 8 <=> ! [X0] : happy(X0) [avatar definition]
160. happy(X0) <- (8) [avatar component clause 159]
229. ~happy(X0) | strong(X0) [subsumption resolution 94,70]
230. ~happy(X0) | ~funny(X0) [subsumption resolution 93,229]
245. 8 [avatar split clause 125,159]
287. ~kind(X1) <- (8) [resolution 124,160]
307. ~funny(X0) | kind(X0) [resolution 230,114]
309. ~funny(X0) <- (8) [subsumption resolution 307,287]
313. $false <- (8) [resolution 309,123]
316. ~8 [avatar contradiction clause 313]
317. $false [avatar sat refutation 245,316]
% SZS output end Proof for 1544793323144817191271106
% ------------------------------
% 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: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
If mary is creative or not funny then someone is either patient or not brave and vice versa. Everyone who is humble or not wise is quiet. Everyone who is either strong or not funny is not generous or not old and vice versa. Everyone who is both calm and not patient is rich. Everyone who is not old is either calm or not generous and vice versa. Everyone who is not happy is creative. If someone is calm then someone is not rich or kind. Everyone who is both not patient and creative is both not old and creative and vice versa. If someone is both humble and quiet then someone is not funny or tall and vice versa. Everyone who is either not strong or happy is not funny or not rich. Everyone who is quiet or creative is both tall and not humble. If john is both not quiet and not happy then mary is both old and quiet. Everyone who is both not happy and not strong is both strong and not rich. Everyone who is either not happy or kind is both brave and rich. Everyone who is both not tall and calm is both humble and not brave. Everyone who is either old or rich is not wise or not quiet. Lucy is not old. Fred is either not happy or kind. Paul is both not kind and not calm. Someone is not tall or not patient. Paul is both not brave and happy. Someone is either patient or not calm. | Fred is not calm. | entailment | (((creative(mary)|~funny(mary)))<=>(?[X]:((patient(X)<~>~brave(X)))))&
(![X]:((humble(X)|~wise(X))=>quiet(X)))&
(![X]:((strong(X)<~>~funny(X))<=>(~generous(X)|~old(X))))&
(![X]:((calm(X)&~patient(X))=>rich(X)))&
(![X]:(~old(X)<=>(calm(X)<~>~generous(X))))&
(![X]:(~happy(X)=>creative(X)))&
((?[X]:(calm(X)))=>(?[X]:((~rich(X)|kind(X)))))&
(![X]:((~patient(X)&creative(X))<=>(~old(X)&creative(X))))&
((?[X]:((humble(X)&quiet(X))))<=>(?[X]:((~funny(X)|tall(X)))))&
(![X]:((~strong(X)<~>happy(X))=>(~funny(X)|~rich(X))))&
(![X]:((quiet(X)|creative(X))=>(tall(X)&~humble(X))))&
(((~quiet(john)&~happy(john)))=>((old(mary)&quiet(mary))))&
(![X]:((~happy(X)&~strong(X))=>(strong(X)&~rich(X))))&
(![X]:((~happy(X)<~>kind(X))=>(brave(X)&rich(X))))&
(![X]:((~tall(X)&calm(X))=>(humble(X)&~brave(X))))&
(![X]:((old(X)<~>rich(X))=>(~wise(X)|~quiet(X))))&
(~old(lucy))&
((~happy(fred)<~>kind(fred)))&
((~kind(paul)&~calm(paul)))&
(?[X]:((~tall(X)|~patient(X))))&
((~brave(paul)&happy(paul)))&
(?[X]:((patient(X)<~>~calm(X)))) | ~calm(fred) | [
"p1",
"p8",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8499271180060420944147685
% SZS output start Proof for 8499271180060420944147685
2. ! [X0] : ((~wise(X0) | humble(X0)) => quiet(X0)) [input p1]
9. ? [X0] : (quiet(X0) & humble(X0)) <=> ? [X0] : (tall(X0) | ~funny(X0)) [input p8]
11. ! [X0] : ((creative(X0) | quiet(X0)) => (~humble(X0) & tall(X0))) [input p10]
15. ! [X0] : ((calm(X0) & ~tall(X0)) => (~brave(X0) & humble(X0))) [input p14]
23. calm(fred) [input hypothesis]
25. ? [X0] : (quiet(X0) & humble(X0)) <=> ? [X1] : (tall(X1) | ~funny(X1)) [rectify 9]
26. ! [X0] : (quiet(X0) | (wise(X0) & ~humble(X0))) [ennf transformation 2]
33. ! [X0] : ((~humble(X0) & tall(X0)) | (~creative(X0) & ~quiet(X0))) [ennf transformation 11]
39. ! [X0] : ((~brave(X0) & humble(X0)) | (~calm(X0) | tall(X0))) [ennf transformation 15]
40. ! [X0] : ((~brave(X0) & humble(X0)) | ~calm(X0) | tall(X0)) [flattening 39]
56. (? [X0] : (quiet(X0) & humble(X0)) | ! [X1] : (~tall(X1) & funny(X1))) & (? [X1] : (tall(X1) | ~funny(X1)) | ! [X0] : (~quiet(X0) | ~humble(X0))) [nnf transformation 25]
57. (? [X0] : (quiet(X0) & humble(X0)) | ! [X1] : (~tall(X1) & funny(X1))) & (? [X2] : (tall(X2) | ~funny(X2)) | ! [X3] : (~quiet(X3) | ~humble(X3))) [rectify 56]
58. ? [X0] : (quiet(X0) & humble(X0)) => (quiet(sK2) & humble(sK2)) [choice axiom]
59. ? [X2] : (tall(X2) | ~funny(X2)) => (tall(sK3) | ~funny(sK3)) [choice axiom]
60. ((quiet(sK2) & humble(sK2)) | ! [X1] : (~tall(X1) & funny(X1))) & ((tall(sK3) | ~funny(sK3)) | ! [X3] : (~quiet(X3) | ~humble(X3))) [skolemisation 57,59,58]
76. ~humble(X0) | quiet(X0) [cnf transformation 26]
97. humble(sK2) | ~tall(X1) [cnf transformation 60]
104. ~humble(X0) | ~quiet(X0) [cnf transformation 33]
114. ~calm(X0) | humble(X0) | tall(X0) [cnf transformation 40]
128. calm(fred) [cnf transformation 23]
171. 10 <=> ! [X1] : ~tall(X1) [avatar definition]
172. ~tall(X1) <- (10) [avatar component clause 171]
183. 13 <=> humble(sK2) [avatar definition]
185. humble(sK2) <- (13) [avatar component clause 183]
186. 10 | 13 [avatar split clause 97,183,171]
190. 14 <=> ! [X3] : ~humble(X3) [avatar definition]
191. ~humble(X3) <- (14) [avatar component clause 190]
201. ~humble(X0) [subsumption resolution 104,76]
202. 14 [avatar split clause 201,190]
252. $false <- (13, 14) [subsumption resolution 185,191]
253. ~13 | ~14 [avatar contradiction clause 252]
342. humble(fred) | tall(fred) [resolution 114,128]
343. tall(fred) <- (14) [subsumption resolution 342,191]
344. $false <- (10, 14) [subsumption resolution 343,172]
345. ~10 | ~14 [avatar contradiction clause 344]
346. $false [avatar sat refutation 186,202,253,345]
% SZS output end Proof for 8499271180060420944147685
% ------------------------------
% 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 lucy is both not funny and generous then someone is curious and vice versa. If susan is both humble and not creative then fred is both generous and creative. If fred is either not tall or not generous then someone is either funny or not rich and vice versa. If john is humble or not patient then lucy is both not happy and tall and vice versa. Everyone who is not calm is either creative or humble. If someone is both not calm and happy then someone is either humble or not strong. Everyone who is either happy or generous is both not happy and strong. If someone is either not strong or brave then someone is curious or not old and vice versa. If paul is either not strong or wise then paul is rich or not calm and vice versa. If john is either not rich or not curious then someone is either not wise or not happy and vice versa. Everyone who is brave is both funny and not strong and vice versa. Everyone who is either brave or not quiet is not curious or old and vice versa. If susan is not old or tall then alice is either not old or not creative and vice versa. If mary is either happy or rich then fred is not creative or strong and vice versa. If susan is not wise or calm then someone is not kind or not rich. Everyone who is both generous and not tall is not curious and vice versa. Lucy is either quiet or not creative. Fred is strong. Lucy is not happy. Fred is either calm or brave. Someone is not funny or humble. Mary is kind. Someone is either patient or not quiet. | Fred is not calm. | contradiction | (((~funny(lucy)&generous(lucy)))<=>(?[X]:(curious(X))))&
(((humble(susan)&~creative(susan)))=>((generous(fred)&creative(fred))))&
(((~tall(fred)<~>~generous(fred)))<=>(?[X]:((funny(X)<~>~rich(X)))))&
(((humble(john)|~patient(john)))<=>((~happy(lucy)&tall(lucy))))&
(![X]:(~calm(X)=>(creative(X)<~>humble(X))))&
((?[X]:((~calm(X)&happy(X))))=>(?[X]:((humble(X)<~>~strong(X)))))&
(![X]:((happy(X)<~>generous(X))=>(~happy(X)&strong(X))))&
((?[X]:((~strong(X)<~>brave(X))))<=>(?[X]:((curious(X)|~old(X)))))&
(((~strong(paul)<~>wise(paul)))<=>((rich(paul)|~calm(paul))))&
(((~rich(john)<~>~curious(john)))<=>(?[X]:((~wise(X)<~>~happy(X)))))&
(![X]:(brave(X)<=>(funny(X)&~strong(X))))&
(![X]:((brave(X)<~>~quiet(X))<=>(~curious(X)|old(X))))&
(((~old(susan)|tall(susan)))<=>((~old(alice)<~>~creative(alice))))&
(((happy(mary)<~>rich(mary)))<=>((~creative(fred)|strong(fred))))&
(((~wise(susan)|calm(susan)))=>(?[X]:((~kind(X)|~rich(X)))))&
(![X]:((generous(X)&~tall(X))<=>~curious(X)))&
((quiet(lucy)<~>~creative(lucy)))&
(strong(fred))&
(~happy(lucy))&
((calm(fred)<~>brave(fred)))&
(?[X]:((~funny(X)|humble(X))))&
(kind(mary))&
(?[X]:((patient(X)<~>~quiet(X)))) | ~calm(fred) | [
"p10",
"p17",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 6888610696542167972280609
% SZS output start Proof for 6888610696542167972280609
11. ! [X0] : (brave(X0) <=> (~strong(X0) & funny(X0))) [input p10]
18. strong(fred) [input p17]
20. calm(fred) <~> brave(fred) [input p19]
24. ~calm(fred) [input hypothesis]
61. ! [X0] : ((brave(X0) | (strong(X0) | ~funny(X0))) & ((~strong(X0) & funny(X0)) | ~brave(X0))) [nnf transformation 11]
62. ! [X0] : ((brave(X0) | strong(X0) | ~funny(X0)) & ((~strong(X0) & funny(X0)) | ~brave(X0))) [flattening 61]
74. (~brave(fred) | ~calm(fred)) & (brave(fred) | calm(fred)) [nnf transformation 20]
127. ~strong(X0) | ~brave(X0) [cnf transformation 62]
154. strong(fred) [cnf transformation 18]
156. brave(fred) | calm(fred) [cnf transformation 74]
162. ~calm(fred) [cnf transformation 24]
276. 24 <=> ! [X3] : (~strong(X3) | ~brave(X3)) [avatar definition]
277. ~brave(X3) | ~strong(X3) <- (24) [avatar component clause 276]
343. 24 [avatar split clause 127,276]
367. 42 <=> strong(fred) [avatar definition]
368. strong(fred) <- (42) [avatar component clause 367]
412. 42 [avatar split clause 154,367]
415. 51 <=> calm(fred) [avatar definition]
419. 52 <=> brave(fred) [avatar definition]
420. brave(fred) <- (52) [avatar component clause 419]
423. 51 | 52 [avatar split clause 156,419,415]
443. ~51 [avatar split clause 162,415]
448. ~strong(fred) <- (24, 52) [resolution 277,420]
449. $false <- (24, 42, 52) [subsumption resolution 448,368]
450. ~24 | ~42 | ~52 [avatar contradiction clause 449]
451. $false [avatar sat refutation 343,412,423,443,450]
% SZS output end Proof for 6888610696542167972280609
% ------------------------------
% 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 paul is either not calm or not funny then susan is not wise or brave. Everyone who is both rich and kind is both not creative and rich and vice versa. Everyone who is not quiet is wise or not calm and vice versa. Everyone who is either tall or calm is not quiet and vice versa. Everyone who is tall is not funny or not rich and vice versa. Everyone who is not strong is either rich or wise. Everyone who is not old is not kind. If paul is either calm or not rich then john is not humble or kind. If lucy is not funny then someone is rich. Everyone who is rich or not tall is both tall and old. Everyone who is both happy and humble is not generous. Everyone who is both generous and not creative is not old or not humble. Everyone who is either generous or not generous is either not curious or funny and vice versa. Everyone who is both not strong and humble is not humble and vice versa. If someone is either tall or funny then someone is both kind and strong. If someone is old or not patient then fred is not patient. Someone is both humble and not creative. Someone is not funny or patient. Someone is either not curious or funny. Someone is not calm. Lucy is curious. Susan is kind or not funny. Fred is either not curious or not kind. Alice is not calm. | Paul is tall. | entailment | (((~calm(paul)<~>~funny(paul)))=>((~wise(susan)|brave(susan))))&
(![X]:((rich(X)&kind(X))<=>(~creative(X)&rich(X))))&
(![X]:(~quiet(X)<=>(wise(X)|~calm(X))))&
(![X]:((tall(X)<~>calm(X))<=>~quiet(X)))&
(![X]:(tall(X)<=>(~funny(X)|~rich(X))))&
(![X]:(~strong(X)=>(rich(X)<~>wise(X))))&
(![X]:(~old(X)=>~kind(X)))&
(((calm(paul)<~>~rich(paul)))=>((~humble(john)|kind(john))))&
((~funny(lucy))=>(?[X]:(rich(X))))&
(![X]:((rich(X)|~tall(X))=>(tall(X)&old(X))))&
(![X]:((happy(X)&humble(X))=>~generous(X)))&
(![X]:((generous(X)&~creative(X))=>(~old(X)|~humble(X))))&
(![X]:((generous(X)<~>~generous(X))<=>(~curious(X)<~>funny(X))))&
(![X]:((~strong(X)&humble(X))<=>~humble(X)))&
((?[X]:((tall(X)<~>funny(X))))=>(?[X]:((kind(X)&strong(X)))))&
((?[X]:((old(X)|~patient(X))))=>(~patient(fred)))&
(?[X]:((humble(X)&~creative(X))))&
(?[X]:((~funny(X)|patient(X))))&
(?[X]:((~curious(X)<~>funny(X))))&
(?[X]:(~calm(X)))&
(curious(lucy))&
((kind(susan)|~funny(susan)))&
((~curious(fred)<~>~kind(fred)))&
(~calm(alice)) | tall(paul) | [
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 3110367960077175660236393
% SZS output start Proof for 3110367960077175660236393
10. ! [X0] : ((~tall(X0) | rich(X0)) => (old(X0) & tall(X0))) [input p9]
25. ~tall(paul) [input hypothesis]
34. ! [X0] : ((old(X0) & tall(X0)) | (tall(X0) & ~rich(X0))) [ennf transformation 10]
88. tall(X0) | tall(X0) [cnf transformation 34]
120. ~tall(paul) [cnf transformation 25]
127. tall(X0) [duplicate literal removal 88]
209. $false [subsumption resolution 120,127]
% SZS output end Proof for 3110367960077175660236393
% ------------------------------
% 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 |
Everyone who is either tall or not strong is either not calm or not patient. Everyone who is funny or brave is curious and vice versa. If fred is either curious or not rich then someone is either patient or happy. If lucy is rich or brave then lucy is either kind or not quiet and vice versa. Everyone who is not creative is not wise or not tall. Everyone who is both not humble and generous is old or funny. If lucy is both creative and old then someone is wise. If someone is both not patient and strong then lucy is not curious and vice versa. If someone is not tall then mary is either old or not patient and vice versa. If someone is not patient then susan is not curious and vice versa. Everyone who is both not happy and patient is both quiet and not wise and vice versa. Everyone who is not kind is brave or not humble and vice versa. Everyone who is not generous or not creative is not kind. Everyone who is both quiet and not tall is not old or not brave and vice versa. If someone is both kind and creative then paul is not creative or funny and vice versa. Lucy is both strong and not patient. Susan is calm or funny. Alice is happy or kind. Someone is wise. Mary is either not generous or not happy. Someone is both quiet and calm. Lucy is humble. | Lucy is humble. | entailment | (![X]:((tall(X)<~>~strong(X))=>(~calm(X)<~>~patient(X))))&
(![X]:((funny(X)|brave(X))<=>curious(X)))&
(((curious(fred)<~>~rich(fred)))=>(?[X]:((patient(X)<~>happy(X)))))&
(((rich(lucy)|brave(lucy)))<=>((kind(lucy)<~>~quiet(lucy))))&
(![X]:(~creative(X)=>(~wise(X)|~tall(X))))&
(![X]:((~humble(X)&generous(X))=>(old(X)|funny(X))))&
(((creative(lucy)&old(lucy)))=>(?[X]:(wise(X))))&
((?[X]:((~patient(X)&strong(X))))<=>(~curious(lucy)))&
((?[X]:(~tall(X)))<=>((old(mary)<~>~patient(mary))))&
((?[X]:(~patient(X)))<=>(~curious(susan)))&
(![X]:((~happy(X)&patient(X))<=>(quiet(X)&~wise(X))))&
(![X]:(~kind(X)<=>(brave(X)|~humble(X))))&
(![X]:((~generous(X)|~creative(X))=>~kind(X)))&
(![X]:((quiet(X)&~tall(X))<=>(~old(X)|~brave(X))))&
((?[X]:((kind(X)&creative(X))))<=>((~creative(paul)|funny(paul))))&
((strong(lucy)&~patient(lucy)))&
((calm(susan)|funny(susan)))&
((happy(alice)|kind(alice)))&
(?[X]:(wise(X)))&
((~generous(mary)<~>~happy(mary)))&
(?[X]:((quiet(X)&calm(X))))&
(humble(lucy)) | humble(lucy) | [
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 3859648226308961376440371
% SZS output start Proof for 3859648226308961376440371
22. humble(lucy) [input p21]
23. ~humble(lucy) [input hypothesis]
128. humble(lucy) [cnf transformation 22]
129. ~humble(lucy) [cnf transformation 23]
288. $false [subsumption resolution 129,128]
% SZS output end Proof for 3859648226308961376440371
% ------------------------------
% 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 brave is not old. Everyone who is both brave and calm is both patient and generous and vice versa. Everyone who is old is not wise or happy and vice versa. Everyone who is not generous or not quiet is both strong and not humble and vice versa. Everyone who is not quiet or tall is either not brave or not strong and vice versa. Everyone who is not quiet or rich is both not rich and kind. If someone is both not strong and not rich then lucy is both not kind and old and vice versa. Everyone who is not rich is either brave or not tall. 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. Mary is either not humble or not patient. Paul is either rich or not calm. John is curious. John is curious or old. Susan is patient. | Mary is not brave. | contradiction | (![X]:(~brave(X)=>~old(X)))&
(![X]:((brave(X)&calm(X))<=>(patient(X)&generous(X))))&
(![X]:(old(X)<=>(~wise(X)|happy(X))))&
(![X]:((~generous(X)|~quiet(X))<=>(strong(X)&~humble(X))))&
(![X]:((~quiet(X)|tall(X))<=>(~brave(X)<~>~strong(X))))&
(![X]:((~quiet(X)|rich(X))=>(~rich(X)&kind(X))))&
((?[X]:((~strong(X)&~rich(X))))<=>((~kind(lucy)&old(lucy))))&
(![X]:(~rich(X)=>(brave(X)<~>~tall(X))))&
(((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))))&
((~humble(mary)<~>~patient(mary)))&
((rich(paul)<~>~calm(paul)))&
(curious(john))&
((curious(john)|old(john)))&
(patient(susan)) | ~brave(mary) | [
"p3",
"p4",
"p5",
"p7",
"p9",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5628544324683091924500627
% SZS output start Proof for 5628544324683091924500627
4. ! [X0] : ((~quiet(X0) | ~generous(X0)) <=> (~humble(X0) & strong(X0))) [input p3]
5. ! [X0] : ((tall(X0) | ~quiet(X0)) <=> (~brave(X0) <~> ~strong(X0))) [input p4]
6. ! [X0] : ((rich(X0) | ~quiet(X0)) => (kind(X0) & ~rich(X0))) [input p5]
8. ! [X0] : (~rich(X0) => (brave(X0) <~> ~tall(X0))) [input p7]
10. ! [X0] : ((~happy(X0) <~> ~quiet(X0)) => (~creative(X0) & tall(X0))) [input p9]
13. ! [X0] : (~tall(X0) => (~strong(X0) & ~curious(X0))) [input p12]
15. ! [X0] : ((generous(X0) <~> ~happy(X0)) <=> ~generous(X0)) [input p14]
22. ~brave(mary) [input hypothesis]
23. ! [X0] : ((~happy(X0) <~> ~quiet(X0)) => tall(X0)) [pure predicate removal 10]
26. ! [X0] : ((kind(X0) & ~rich(X0)) | (~rich(X0) & quiet(X0))) [ennf transformation 6]
27. ! [X0] : ((brave(X0) <~> ~tall(X0)) | rich(X0)) [ennf transformation 8]
28. ! [X0] : (tall(X0) | (~happy(X0) <=> ~quiet(X0))) [ennf transformation 23]
31. ! [X0] : ((~strong(X0) & ~curious(X0)) | tall(X0)) [ennf transformation 13]
37. ! [X0] : (((~quiet(X0) | ~generous(X0)) | (humble(X0) | ~strong(X0))) & ((~humble(X0) & strong(X0)) | (quiet(X0) & generous(X0)))) [nnf transformation 4]
38. ! [X0] : ((~quiet(X0) | ~generous(X0) | humble(X0) | ~strong(X0)) & ((~humble(X0) & strong(X0)) | (quiet(X0) & generous(X0)))) [flattening 37]
39. ! [X0] : (((tall(X0) | ~quiet(X0)) | ((~brave(X0) | strong(X0)) & (~strong(X0) | brave(X0)))) & (((strong(X0) | brave(X0)) & (~strong(X0) | ~brave(X0))) | (~tall(X0) & quiet(X0)))) [nnf transformation 5]
40. ! [X0] : ((tall(X0) | ~quiet(X0) | ((~brave(X0) | strong(X0)) & (~strong(X0) | brave(X0)))) & (((strong(X0) | brave(X0)) & (~strong(X0) | ~brave(X0))) | (~tall(X0) & quiet(X0)))) [flattening 39]
46. ! [X0] : (((tall(X0) | ~brave(X0)) & (~tall(X0) | brave(X0))) | rich(X0)) [nnf transformation 27]
47. ! [X0] : (tall(X0) | ((~happy(X0) | quiet(X0)) & (~quiet(X0) | happy(X0)))) [nnf transformation 28]
53. ! [X0] : ((((happy(X0) | ~generous(X0)) & (~happy(X0) | generous(X0))) | generous(X0)) & (~generous(X0) | ((generous(X0) | happy(X0)) & (~happy(X0) | ~generous(X0))))) [nnf transformation 15]
67. strong(X0) | quiet(X0) [cnf transformation 38]
71. ~strong(X0) | ~brave(X0) | quiet(X0) [cnf transformation 40]
78. ~rich(X0) | ~rich(X0) [cnf transformation 26]
85. ~tall(X0) | brave(X0) | rich(X0) [cnf transformation 46]
87. ~quiet(X0) | tall(X0) | happy(X0) [cnf transformation 47]
99. ~strong(X0) | tall(X0) [cnf transformation 31]
104. ~generous(X0) | ~happy(X0) | ~generous(X0) [cnf transformation 53]
106. ~happy(X0) | generous(X0) | generous(X0) [cnf transformation 53]
118. ~brave(mary) [cnf transformation 22]
119. ~generous(X0) | ~happy(X0) [duplicate literal removal 104]
120. ~happy(X0) | generous(X0) [duplicate literal removal 106]
121. ~rich(X0) [duplicate literal removal 78]
123. ~brave(X0) | quiet(X0) [subsumption resolution 71,67]
145. ~tall(X0) | brave(X0) [subsumption resolution 85,121]
180. ~happy(X0) [subsumption resolution 119,120]
200. tall(X0) | quiet(X0) [resolution 99,67]
324. quiet(X2) | brave(X2) [resolution 200,145]
325. quiet(X2) [subsumption resolution 324,123]
332. tall(X0) | happy(X0) [resolution 325,87]
334. tall(X0) [subsumption resolution 332,180]
352. brave(X2) [resolution 334,145]
359. $false [resolution 352,118]
% SZS output end Proof for 5628544324683091924500627
% ------------------------------
% 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 generous is both not generous and not quiet.
Everyone who is either old or not kind is both calm and not patient and vice versa.
If someone is both rich and not generous then lucy is both not calm and brave.
Everyone who is both wise and strong is not generous and vice versa.
If mary is either not humble or not quiet then john is either kind or funny.
If alice is either creative or happy then someone is not strong or not brave and vice versa.
Everyone who is either strong or curious is not quiet and vice versa.
Everyone who is not happy is either not generous or quiet and vice versa.
If mary is wise or calm then someone is either generous or not strong.
If someone is both brave and quiet then someone is funny or patient and vice versa.
If lucy is not humble or not creative then mary is not creative or curious and vice versa.
Everyone who is strong or not strong is creative or not humble.
If mary is rich or not old then lucy is both not generous and patient.
Everyone who is quiet is not tall or patient.
If someone is not old or tall then john is wise or funny.
Everyone who is not patient is not kind and vice versa.
Someone is not quiet.
Someone is both old and not generous.
Lucy is wise or not patient.
Alice is not old.
Someone is either not rich or not old.
Someone is both not creative and tall.
Someone is either not strong or quiet.
Someone is not kind or not patient. | Mary is kind. | neutral | (![X]:(~generous(X)=>(~generous(X)&~quiet(X))))&
(![X]:((old(X)<~>~kind(X))<=>(calm(X)&~patient(X))))&
((?[X]:((rich(X)&~generous(X))))=>((~calm(lucy)&brave(lucy))))&
(![X]:((wise(X)&strong(X))<=>~generous(X)))&
(((~humble(mary)<~>~quiet(mary)))=>((kind(john)<~>funny(john))))&
(((creative(alice)<~>happy(alice)))<=>(?[X]:((~strong(X)|~brave(X)))))&
(![X]:((strong(X)<~>curious(X))<=>~quiet(X)))&
(![X]:(~happy(X)<=>(~generous(X)<~>quiet(X))))&
(((wise(mary)|calm(mary)))=>(?[X]:((generous(X)<~>~strong(X)))))&
((?[X]:((brave(X)&quiet(X))))<=>(?[X]:((funny(X)|patient(X)))))&
(((~humble(lucy)|~creative(lucy)))<=>((~creative(mary)|curious(mary))))&
(![X]:((strong(X)|~strong(X))=>(creative(X)|~humble(X))))&
(((rich(mary)|~old(mary)))=>((~generous(lucy)&patient(lucy))))&
(![X]:(quiet(X)=>(~tall(X)|patient(X))))&
((?[X]:((~old(X)|tall(X))))=>((wise(john)|funny(john))))&
(![X]:(~patient(X)<=>~kind(X)))&
(?[X]:(~quiet(X)))&
(?[X]:((old(X)&~generous(X))))&
((wise(lucy)|~patient(lucy)))&
(~old(alice))&
(?[X]:((~rich(X)<~>~old(X))))&
(?[X]:((~creative(X)&tall(X))))&
(?[X]:((~strong(X)<~>quiet(X))))&
(?[X]:((~kind(X)|~patient(X)))) | kind(mary) | [] | null | 0 |
Everyone who is patient or quiet is patient.
If lucy is creative or patient then someone is strong or happy and vice versa.
Everyone who is both curious and humble is either quiet or brave.
Everyone who is either happy or calm is curious or not rich and vice versa.
If alice is both not creative and tall then someone is both not funny and generous and vice versa.
Everyone who is both not brave and not generous is both wise and not strong.
If someone is not generous then someone is both not funny and not old.
If mary is curious or not funny then someone is both wise and curious and vice versa.
Everyone who is either generous or happy is either not rich or not curious.
Everyone who is wise or not happy is creative or not strong.
If mary is both creative and not funny then susan is patient or not quiet and vice versa.
If alice is either not generous or not old then someone is not humble or calm.
If mary is both not strong and patient then someone is both patient and not wise.
If someone is both old and not patient then someone is both calm and not old and vice versa.
If someone is not creative or funny then someone is kind or funny.
If alice is either patient or quiet then someone is curious or not calm.
Susan is not generous.
Fred is not old.
Alice is either humble or calm.
Someone is kind.
Lucy is both kind and creative.
Someone is not humble.
Alice is not curious.
Mary is both rich and not happy. | Mary is not creative. | contradiction | (![X]:((patient(X)|quiet(X))=>patient(X)))&
(((creative(lucy)|patient(lucy)))<=>(?[X]:((strong(X)|happy(X)))))&
(![X]:((curious(X)&humble(X))=>(quiet(X)<~>brave(X))))&
(![X]:((happy(X)<~>calm(X))<=>(curious(X)|~rich(X))))&
(((~creative(alice)&tall(alice)))<=>(?[X]:((~funny(X)&generous(X)))))&
(![X]:((~brave(X)&~generous(X))=>(wise(X)&~strong(X))))&
((?[X]:(~generous(X)))=>(?[X]:((~funny(X)&~old(X)))))&
(((curious(mary)|~funny(mary)))<=>(?[X]:((wise(X)&curious(X)))))&
(![X]:((generous(X)<~>happy(X))=>(~rich(X)<~>~curious(X))))&
(![X]:((wise(X)|~happy(X))=>(creative(X)|~strong(X))))&
(((creative(mary)&~funny(mary)))<=>((patient(susan)|~quiet(susan))))&
(((~generous(alice)<~>~old(alice)))=>(?[X]:((~humble(X)|calm(X)))))&
(((~strong(mary)&patient(mary)))=>(?[X]:((patient(X)&~wise(X)))))&
((?[X]:((old(X)&~patient(X))))<=>(?[X]:((calm(X)&~old(X)))))&
((?[X]:((~creative(X)|funny(X))))=>(?[X]:((kind(X)|funny(X)))))&
(((patient(alice)<~>quiet(alice)))=>(?[X]:((curious(X)|~calm(X)))))&
(~generous(susan))&
(~old(fred))&
((humble(alice)<~>calm(alice)))&
(?[X]:(kind(X)))&
((kind(lucy)&creative(lucy)))&
(?[X]:(~humble(X)))&
(~curious(alice))&
((rich(mary)&~happy(mary))) | ~creative(mary) | [
"p0",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 699511691371787919633736
% SZS output start Proof for 699511691371787919633736
1. ! [X0] : ((quiet(X0) | patient(X0)) => patient(X0)) [input p0]
11. (~funny(mary) & creative(mary)) <=> (~quiet(susan) | patient(susan)) [input p10]
25. ~creative(mary) [input hypothesis]
32. ! [X0] : (patient(X0) | (~quiet(X0) & ~patient(X0))) [ennf transformation 1]
67. ((~funny(mary) & creative(mary)) | (quiet(susan) & ~patient(susan))) & ((~quiet(susan) | patient(susan)) | (funny(mary) | ~creative(mary))) [nnf transformation 11]
68. ((~funny(mary) & creative(mary)) | (quiet(susan) & ~patient(susan))) & (~quiet(susan) | patient(susan) | funny(mary) | ~creative(mary)) [flattening 67]
86. ~quiet(X0) | patient(X0) [cnf transformation 32]
119. creative(mary) | ~patient(susan) [cnf transformation 68]
120. creative(mary) | quiet(susan) [cnf transformation 68]
142. ~creative(mary) [cnf transformation 25]
230. 20 <=> quiet(susan) [avatar definition]
232. quiet(susan) <- (20) [avatar component clause 230]
235. 21 <=> patient(susan) [avatar definition]
237. ~patient(susan) <- (~21) [avatar component clause 235]
240. 22 <=> creative(mary) [avatar definition]
243. 20 | 22 [avatar split clause 120,240,230]
244. ~21 | 22 [avatar split clause 119,240,235]
335. ~22 [avatar split clause 142,240]
336. patient(susan) <- (20) [resolution 86,232]
337. $false <- (20, ~21) [subsumption resolution 336,237]
338. ~20 | 21 [avatar contradiction clause 337]
339. $false [avatar sat refutation 243,244,335,338]
% SZS output end Proof for 699511691371787919633736
% ------------------------------
% 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 strong or not calm then mary is either not creative or not happy and vice versa.
Everyone who is tall or curious is both strong and not creative.
If fred is creative or quiet then john is either not strong or curious.
If mary is calm then lucy is not quiet and vice versa.
Everyone who is both quiet and not happy is not happy and vice versa.
Everyone who is creative is not wise or tall and vice versa.
If john is not patient then susan is either not curious or creative and vice versa.
If someone is both not funny and not generous then paul is strong or brave and vice versa.
If someone is humble then someone is both kind and not funny and vice versa.
Everyone who is not happy or strong is either not strong or not patient.
Everyone who is not funny is either not patient or strong.
Everyone who is not humble is calm or wise.
Everyone who is brave is not creative.
Everyone who is not happy is not strong or not calm and vice versa.
Everyone who is both brave and not patient is wise or brave.
If someone is not humble then someone is rich or generous.
Mary is either calm or not patient.
Someone is not patient.
Someone is either not calm or not old.
Someone is both funny and not wise. | Fred is not kind. | neutral | ((?[X]:((strong(X)|~calm(X))))<=>((~creative(mary)<~>~happy(mary))))&
(![X]:((tall(X)|curious(X))=>(strong(X)&~creative(X))))&
(((creative(fred)|quiet(fred)))=>((~strong(john)<~>curious(john))))&
((calm(mary))<=>(~quiet(lucy)))&
(![X]:((quiet(X)&~happy(X))<=>~happy(X)))&
(![X]:(creative(X)<=>(~wise(X)|tall(X))))&
((~patient(john))<=>((~curious(susan)<~>creative(susan))))&
((?[X]:((~funny(X)&~generous(X))))<=>((strong(paul)|brave(paul))))&
((?[X]:(humble(X)))<=>(?[X]:((kind(X)&~funny(X)))))&
(![X]:((~happy(X)|strong(X))=>(~strong(X)<~>~patient(X))))&
(![X]:(~funny(X)=>(~patient(X)<~>strong(X))))&
(![X]:(~humble(X)=>(calm(X)|wise(X))))&
(![X]:(brave(X)=>~creative(X)))&
(![X]:(~happy(X)<=>(~strong(X)|~calm(X))))&
(![X]:((brave(X)&~patient(X))=>(wise(X)|brave(X))))&
((?[X]:(~humble(X)))=>(?[X]:((rich(X)|generous(X)))))&
((calm(mary)<~>~patient(mary)))&
(?[X]:(~patient(X)))&
(?[X]:((~calm(X)<~>~old(X))))&
(?[X]:((funny(X)&~wise(X)))) | ~kind(fred) | [] | null | 0 |
Everyone who is strong or not rich is not generous and vice versa.
Everyone who is calm is either not strong or humble and vice versa.
Everyone who is either generous or not rich is both old and kind and vice versa.
Everyone who is generous or kind is strong and vice versa.
Everyone who is not patient or humble is funny and vice versa.
If someone is both creative and old then someone is both old and creative.
Everyone who is generous or happy is either not tall or rich and vice versa.
Everyone who is either not generous or happy is creative.
Everyone who is either not wise or quiet is not rich or creative.
Everyone who is both not patient and creative is wise and vice versa.
Everyone who is either happy or not old is creative and vice versa.
Everyone who is both rich and not kind is wise or quiet and vice versa.
Everyone who is not curious or strong is either humble or kind.
If someone is patient or brave then susan is not old and vice versa.
If someone is either not happy or not humble then fred is both old and creative and vice versa.
Susan is quiet or not humble.
John is either wise or not rich.
Someone is either brave or tall.
Lucy is either wise or not quiet.
Someone is either not patient or not funny. | Fred is not happy. | contradiction | (![X]:((strong(X)|~rich(X))<=>~generous(X)))&
(![X]:(calm(X)<=>(~strong(X)<~>humble(X))))&
(![X]:((generous(X)<~>~rich(X))<=>(old(X)&kind(X))))&
(![X]:((generous(X)|kind(X))<=>strong(X)))&
(![X]:((~patient(X)|humble(X))<=>funny(X)))&
((?[X]:((creative(X)&old(X))))=>(?[X]:((old(X)&creative(X)))))&
(![X]:((generous(X)|happy(X))<=>(~tall(X)<~>rich(X))))&
(![X]:((~generous(X)<~>happy(X))=>creative(X)))&
(![X]:((~wise(X)<~>quiet(X))=>(~rich(X)|creative(X))))&
(![X]:((~patient(X)&creative(X))<=>wise(X)))&
(![X]:((happy(X)<~>~old(X))<=>creative(X)))&
(![X]:((rich(X)&~kind(X))<=>(wise(X)|quiet(X))))&
(![X]:((~curious(X)|strong(X))=>(humble(X)<~>kind(X))))&
((?[X]:((patient(X)|brave(X))))<=>(~old(susan)))&
((?[X]:((~happy(X)<~>~humble(X))))<=>((old(fred)&creative(fred))))&
((quiet(susan)|~humble(susan)))&
((wise(john)<~>~rich(john)))&
(?[X]:((brave(X)<~>tall(X))))&
((wise(lucy)<~>~quiet(lucy)))&
(?[X]:((~patient(X)<~>~funny(X)))) | ~happy(fred) | [
"p0",
"p2",
"p3",
"p7",
"p10",
"p11",
"p12",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 6297386917061359152823400
% SZS output start Proof for 6297386917061359152823400
1. ! [X0] : ((~rich(X0) | strong(X0)) <=> ~generous(X0)) [input p0]
3. ! [X0] : ((generous(X0) <~> ~rich(X0)) <=> (kind(X0) & old(X0))) [input p2]
4. ! [X0] : ((kind(X0) | generous(X0)) <=> strong(X0)) [input p3]
8. ! [X0] : ((~generous(X0) <~> happy(X0)) => creative(X0)) [input p7]
11. ! [X0] : ((happy(X0) <~> ~old(X0)) <=> creative(X0)) [input p10]
12. ! [X0] : ((~kind(X0) & rich(X0)) <=> (quiet(X0) | wise(X0))) [input p11]
13. ! [X0] : ((strong(X0) | ~curious(X0)) => (humble(X0) <~> kind(X0))) [input p12]
15. ? [X0] : (~happy(X0) <~> ~humble(X0)) <=> (creative(fred) & old(fred)) [input p14]
17. wise(john) <~> ~rich(john) [input p16]
21. ~happy(fred) [input hypothesis]
23. ! [X0] : (strong(X0) => (humble(X0) <~> kind(X0))) [pure predicate removal 13]
25. ! [X0] : (creative(X0) | (~generous(X0) <=> happy(X0))) [ennf transformation 8]
28. ! [X0] : ((humble(X0) <~> kind(X0)) | ~strong(X0)) [ennf transformation 23]
29. ! [X0] : (((~rich(X0) | strong(X0)) | generous(X0)) & (~generous(X0) | (rich(X0) & ~strong(X0)))) [nnf transformation 1]
30. ! [X0] : ((~rich(X0) | strong(X0) | generous(X0)) & (~generous(X0) | (rich(X0) & ~strong(X0)))) [flattening 29]
31. ! [X0] : ((((rich(X0) | ~generous(X0)) & (~rich(X0) | generous(X0))) | (~kind(X0) | ~old(X0))) & ((kind(X0) & old(X0)) | ((generous(X0) | rich(X0)) & (~rich(X0) | ~generous(X0))))) [nnf transformation 3]
32. ! [X0] : ((((rich(X0) | ~generous(X0)) & (~rich(X0) | generous(X0))) | ~kind(X0) | ~old(X0)) & ((kind(X0) & old(X0)) | ((generous(X0) | rich(X0)) & (~rich(X0) | ~generous(X0))))) [flattening 31]
33. ! [X0] : (((kind(X0) | generous(X0)) | ~strong(X0)) & (strong(X0) | (~kind(X0) & ~generous(X0)))) [nnf transformation 4]
34. ! [X0] : ((kind(X0) | generous(X0) | ~strong(X0)) & (strong(X0) | (~kind(X0) & ~generous(X0)))) [flattening 33]
42. ! [X0] : (creative(X0) | ((~generous(X0) | ~happy(X0)) & (happy(X0) | generous(X0)))) [nnf transformation 25]
46. ! [X0] : ((((old(X0) | ~happy(X0)) & (~old(X0) | happy(X0))) | ~creative(X0)) & (creative(X0) | ((happy(X0) | old(X0)) & (~old(X0) | ~happy(X0))))) [nnf transformation 11]
47. ! [X0] : (((~kind(X0) & rich(X0)) | (~quiet(X0) & ~wise(X0))) & ((quiet(X0) | wise(X0)) | (kind(X0) | ~rich(X0)))) [nnf transformation 12]
48. ! [X0] : (((~kind(X0) & rich(X0)) | (~quiet(X0) & ~wise(X0))) & (quiet(X0) | wise(X0) | kind(X0) | ~rich(X0))) [flattening 47]
49. ! [X0] : (((~kind(X0) | ~humble(X0)) & (kind(X0) | humble(X0))) | ~strong(X0)) [nnf transformation 28]
54. (? [X0] : ((humble(X0) | happy(X0)) & (~humble(X0) | ~happy(X0))) | (~creative(fred) | ~old(fred))) & ((creative(fred) & old(fred)) | ! [X0] : ((~happy(X0) | humble(X0)) & (~humble(X0) | happy(X0)))) [nnf transformation 15]
55. (? [X0] : ((humble(X0) | happy(X0)) & (~humble(X0) | ~happy(X0))) | ~creative(fred) | ~old(fred)) & ((creative(fred) & old(fred)) | ! [X0] : ((~happy(X0) | humble(X0)) & (~humble(X0) | happy(X0)))) [flattening 54]
56. (? [X0] : ((humble(X0) | happy(X0)) & (~humble(X0) | ~happy(X0))) | ~creative(fred) | ~old(fred)) & ((creative(fred) & old(fred)) | ! [X1] : ((~happy(X1) | humble(X1)) & (~humble(X1) | happy(X1)))) [rectify 55]
57. ? [X0] : ((humble(X0) | happy(X0)) & (~humble(X0) | ~happy(X0))) => ((humble(sK2) | happy(sK2)) & (~humble(sK2) | ~happy(sK2))) [choice axiom]
58. (((humble(sK2) | happy(sK2)) & (~humble(sK2) | ~happy(sK2))) | ~creative(fred) | ~old(fred)) & ((creative(fred) & old(fred)) | ! [X1] : ((~happy(X1) | humble(X1)) & (~humble(X1) | happy(X1)))) [skolemisation 56,57]
59. (rich(john) | ~wise(john)) & (~rich(john) | wise(john)) [nnf transformation 17]
67. ~generous(X0) | ~strong(X0) [cnf transformation 30]
68. ~generous(X0) | rich(X0) [cnf transformation 30]
69. ~rich(X0) | strong(X0) | generous(X0) [cnf transformation 30]
71. old(X0) | generous(X0) | rich(X0) [cnf transformation 32]
73. kind(X0) | generous(X0) | rich(X0) [cnf transformation 32]
76. strong(X0) | ~generous(X0) [cnf transformation 34]
77. ~kind(X0) | strong(X0) [cnf transformation 34]
78. kind(X0) | generous(X0) | ~strong(X0) [cnf transformation 34]
90. creative(X0) | happy(X0) | generous(X0) [cnf transformation 42]
99. ~old(X0) | happy(X0) | ~creative(X0) [cnf transformation 46]
104. ~wise(X0) | ~kind(X0) [cnf transformation 48]
107. ~kind(X0) | ~humble(X0) | ~strong(X0) [cnf transformation 49]
112. old(fred) | ~happy(X1) | humble(X1) [cnf transformation 58]
118. ~rich(john) | wise(john) [cnf transformation 59]
126. ~happy(fred) [cnf transformation 21]
127. kind(X0) | rich(X0) [subsumption resolution 73,68]
129. old(X0) | rich(X0) [subsumption resolution 71,68]
131. ~strong(X0) | kind(X0) [subsumption resolution 78,67]
132. ~generous(X0) [subsumption resolution 76,67]
148. happy(X0) | creative(X0) [subsumption resolution 90,132]
149. ~old(X0) | happy(X0) [subsumption resolution 99,148]
152. ~kind(X0) | ~humble(X0) [subsumption resolution 107,77]
176. 9 <=> old(fred) [avatar definition]
177. old(fred) <- (9) [avatar component clause 176]
191. 12 <=> ! [X1] : (~happy(X1) | humble(X1)) [avatar definition]
192. ~happy(X1) | humble(X1) <- (12) [avatar component clause 191]
202. 12 | 9 [avatar split clause 112,176,191]
214. 17 <=> wise(john) [avatar definition]
216. wise(john) <- (17) [avatar component clause 214]
218. 18 <=> rich(john) [avatar definition]
220. ~rich(john) <- (~18) [avatar component clause 218]
221. 17 | ~18 [avatar split clause 118,218,214]
251. rich(X0) | strong(X0) [resolution 127,77]
255. happy(fred) <- (9) [resolution 149,177]
256. happy(X0) | rich(X0) [resolution 149,129]
257. $false <- (9) [subsumption resolution 255,126]
258. ~9 [avatar contradiction clause 257]
262. ~humble(X0) | rich(X0) [resolution 152,127]
493. strong(X1) | strong(X1) | generous(X1) [resolution 251,69]
496. strong(X1) | generous(X1) [duplicate literal removal 493]
498. strong(X1) [subsumption resolution 496,132]
504. rich(X2) | humble(X2) <- (12) [resolution 256,192]
505. rich(X2) <- (12) [subsumption resolution 504,262]
564. kind(X0) [resolution 498,131]
567. $false <- (12, ~18) [resolution 505,220]
570. ~12 | 18 [avatar contradiction clause 567]
576. ~kind(john) <- (17) [resolution 216,104]
580. $false <- (17) [subsumption resolution 576,564]
581. ~17 [avatar contradiction clause 580]
582. $false [avatar sat refutation 202,221,258,570,581]
% SZS output end Proof for 6297386917061359152823400
% ------------------------------
% 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 creative is not strong.
If lucy is not wise then someone is both happy and not wise.
Everyone who is either not brave or old is both wise and strong and vice versa.
Everyone who is either not brave or not humble is both not strong and not calm and vice versa.
Everyone who is not quiet is either strong or old.
Everyone who is either old or not humble is not creative or not tall.
Everyone who is not brave is either creative or not strong and vice versa.
Everyone who is generous is both not funny and funny.
Everyone who is not tall is kind or strong.
If fred is not calm then mary is not patient or happy.
If someone is both not happy and not old then fred is not brave and vice versa.
Everyone who is rich is not brave and vice versa.
Everyone who is patient or not brave is either tall or not wise and vice versa.
If lucy is generous then someone is not happy or calm.
Everyone who is either not brave or not strong is patient or not wise and vice versa.
Everyone who is both not happy and not tall is either not calm or quiet.
Someone is either wise or funny.
John is not calm or creative.
Someone is both not quiet and happy.
Someone is both brave and humble.
Alice is both tall and not generous.
Mary is not kind or not strong.
Someone is both old and tall.
Someone is not generous. | Mary is tall. | neutral | (![X]:(creative(X)=>~strong(X)))&
((~wise(lucy))=>(?[X]:((happy(X)&~wise(X)))))&
(![X]:((~brave(X)<~>old(X))<=>(wise(X)&strong(X))))&
(![X]:((~brave(X)<~>~humble(X))<=>(~strong(X)&~calm(X))))&
(![X]:(~quiet(X)=>(strong(X)<~>old(X))))&
(![X]:((old(X)<~>~humble(X))=>(~creative(X)|~tall(X))))&
(![X]:(~brave(X)<=>(creative(X)<~>~strong(X))))&
(![X]:(generous(X)=>(~funny(X)&funny(X))))&
(![X]:(~tall(X)=>(kind(X)|strong(X))))&
((~calm(fred))=>((~patient(mary)|happy(mary))))&
((?[X]:((~happy(X)&~old(X))))<=>(~brave(fred)))&
(![X]:(rich(X)<=>~brave(X)))&
(![X]:((patient(X)|~brave(X))<=>(tall(X)<~>~wise(X))))&
((generous(lucy))=>(?[X]:((~happy(X)|calm(X)))))&
(![X]:((~brave(X)<~>~strong(X))<=>(patient(X)|~wise(X))))&
(![X]:((~happy(X)&~tall(X))=>(~calm(X)<~>quiet(X))))&
(?[X]:((wise(X)<~>funny(X))))&
((~calm(john)|creative(john)))&
(?[X]:((~quiet(X)&happy(X))))&
(?[X]:((brave(X)&humble(X))))&
((tall(alice)&~generous(alice)))&
((~kind(mary)|~strong(mary)))&
(?[X]:((old(X)&tall(X))))&
(?[X]:(~generous(X))) | tall(mary) | [] | null | 0 |
If alice is either not creative or brave then someone is not tall and vice versa. Everyone who is either strong or quiet is not strong and vice versa. Everyone who is either calm or not quiet is either not humble or not calm and vice versa. If fred is both not creative and calm then fred is either not rich or not tall. Everyone who is either humble or funny is rich or not quiet and vice versa. If someone is not kind or not quiet then someone is either strong or tall and vice versa. If alice is not happy or not quiet then someone is old or quiet and vice versa. Everyone who is both generous and creative is both tall and rich. Everyone who is either not calm or funny is quiet. Everyone who is both not generous and calm is not happy and vice versa. If paul is either generous or not curious then john is brave. Everyone who is not brave or not kind is both brave and creative. If someone is either patient or not wise then susan is happy or not wise and vice versa. If fred is both not wise and rich then fred is calm or not tall and vice versa. Everyone who is quiet or not kind is curious. Someone is both not strong and not rich. Someone is either not wise or not patient. Mary is funny or not curious. Someone is not quiet or curious. Someone is not patient or not calm. Someone is either not patient or not tall. Susan is creative. | Mary is humble. | contradiction | (((~creative(alice)<~>brave(alice)))<=>(?[X]:(~tall(X))))&
(![X]:((strong(X)<~>quiet(X))<=>~strong(X)))&
(![X]:((calm(X)<~>~quiet(X))<=>(~humble(X)<~>~calm(X))))&
(((~creative(fred)&calm(fred)))=>((~rich(fred)<~>~tall(fred))))&
(![X]:((humble(X)<~>funny(X))<=>(rich(X)|~quiet(X))))&
((?[X]:((~kind(X)|~quiet(X))))<=>(?[X]:((strong(X)<~>tall(X)))))&
(((~happy(alice)|~quiet(alice)))<=>(?[X]:((old(X)|quiet(X)))))&
(![X]:((generous(X)&creative(X))=>(tall(X)&rich(X))))&
(![X]:((~calm(X)<~>funny(X))=>quiet(X)))&
(![X]:((~generous(X)&calm(X))<=>~happy(X)))&
(((generous(paul)<~>~curious(paul)))=>(brave(john)))&
(![X]:((~brave(X)|~kind(X))=>(brave(X)&creative(X))))&
((?[X]:((patient(X)<~>~wise(X))))<=>((happy(susan)|~wise(susan))))&
(((~wise(fred)&rich(fred)))<=>((calm(fred)|~tall(fred))))&
(![X]:((quiet(X)|~kind(X))=>curious(X)))&
(?[X]:((~strong(X)&~rich(X))))&
(?[X]:((~wise(X)<~>~patient(X))))&
((funny(mary)|~curious(mary)))&
(?[X]:((~quiet(X)|curious(X))))&
(?[X]:((~patient(X)|~calm(X))))&
(?[X]:((~patient(X)<~>~tall(X))))&
(creative(susan)) | humble(mary) | [
"p1",
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 944787869884464089223072
% SZS output start Proof for 944787869884464089223072
2. ! [X0] : ((strong(X0) <~> quiet(X0)) <=> ~strong(X0)) [input p1]
3. ! [X0] : ((calm(X0) <~> ~quiet(X0)) <=> (~humble(X0) <~> ~calm(X0))) [input p2]
23. humble(mary) [input hypothesis]
37. ! [X0] : ((((~quiet(X0) | ~strong(X0)) & (quiet(X0) | strong(X0))) | strong(X0)) & (~strong(X0) | ((strong(X0) | ~quiet(X0)) & (quiet(X0) | ~strong(X0))))) [nnf transformation 2]
38. ! [X0] : ((((quiet(X0) | ~calm(X0)) & (~quiet(X0) | calm(X0))) | ((~humble(X0) | calm(X0)) & (~calm(X0) | humble(X0)))) & (((calm(X0) | humble(X0)) & (~calm(X0) | ~humble(X0))) | ((calm(X0) | quiet(X0)) & (~quiet(X0) | ~calm(X0))))) [nnf transformation 3]
79. ~strong(X0) | quiet(X0) | ~strong(X0) [cnf transformation 37]
81. quiet(X0) | strong(X0) | strong(X0) [cnf transformation 37]
83. ~calm(X0) | ~humble(X0) | ~quiet(X0) | ~calm(X0) [cnf transformation 38]
88. ~quiet(X0) | calm(X0) | ~humble(X0) | calm(X0) [cnf transformation 38]
145. humble(mary) [cnf transformation 23]
147. ~calm(X0) | ~humble(X0) | ~quiet(X0) [duplicate literal removal 83]
149. ~quiet(X0) | calm(X0) | ~humble(X0) [duplicate literal removal 88]
151. ~strong(X0) | quiet(X0) [duplicate literal removal 79]
152. quiet(X0) | strong(X0) [duplicate literal removal 81]
172. quiet(X0) [subsumption resolution 151,152]
173. calm(X0) | ~humble(X0) [subsumption resolution 149,172]
174. ~calm(X0) | ~humble(X0) [subsumption resolution 147,172]
175. ~humble(X0) [subsumption resolution 174,173]
308. $false [subsumption resolution 145,175]
% SZS output end Proof for 944787869884464089223072
% ------------------------------
% 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: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
If someone is happy or calm then someone is not kind and vice versa.
If mary is curious then john is either brave or old and vice versa.
Everyone who is both not tall and not kind is not happy or not patient and vice versa.
Everyone who is generous is old or calm and vice versa.
If someone is not wise or not creative then someone is both happy and not old.
If someone is not strong or not funny then fred is brave or not rich.
Everyone who is both calm and not tall is funny and vice versa.
If someone is either happy or tall then someone is both curious and not calm.
If john is both not kind and humble then john is patient or not rich.
Everyone who is either not generous or strong is not brave or quiet and vice versa.
Everyone who is either generous or strong is not old or not tall.
If someone is calm or not rich then someone is quiet or generous and vice versa.
Everyone who is either calm or not brave is both old and not curious and vice versa.
Everyone who is not patient is either not humble or not patient and vice versa.
Everyone who is either not wise or not strong is both not humble and not happy.
Everyone who is wise is not old or calm.
Alice is curious.
Someone is either not wise or not patient.
Someone is either not patient or old.
Someone is not curious.
Someone is not kind.
Alice is calm or not creative.
Someone is not creative or not brave.
Fred is either not rich or old. | John is old. | neutral | ((?[X]:((happy(X)|calm(X))))<=>(?[X]:(~kind(X))))&
((curious(mary))<=>((brave(john)<~>old(john))))&
(![X]:((~tall(X)&~kind(X))<=>(~happy(X)|~patient(X))))&
(![X]:(generous(X)<=>(old(X)|calm(X))))&
((?[X]:((~wise(X)|~creative(X))))=>(?[X]:((happy(X)&~old(X)))))&
((?[X]:((~strong(X)|~funny(X))))=>((brave(fred)|~rich(fred))))&
(![X]:((calm(X)&~tall(X))<=>funny(X)))&
((?[X]:((happy(X)<~>tall(X))))=>(?[X]:((curious(X)&~calm(X)))))&
(((~kind(john)&humble(john)))=>((patient(john)|~rich(john))))&
(![X]:((~generous(X)<~>strong(X))<=>(~brave(X)|quiet(X))))&
(![X]:((generous(X)<~>strong(X))=>(~old(X)|~tall(X))))&
((?[X]:((calm(X)|~rich(X))))<=>(?[X]:((quiet(X)|generous(X)))))&
(![X]:((calm(X)<~>~brave(X))<=>(old(X)&~curious(X))))&
(![X]:(~patient(X)<=>(~humble(X)<~>~patient(X))))&
(![X]:((~wise(X)<~>~strong(X))=>(~humble(X)&~happy(X))))&
(![X]:(wise(X)=>(~old(X)|calm(X))))&
(curious(alice))&
(?[X]:((~wise(X)<~>~patient(X))))&
(?[X]:((~patient(X)<~>old(X))))&
(?[X]:(~curious(X)))&
(?[X]:(~kind(X)))&
((calm(alice)|~creative(alice)))&
(?[X]:((~creative(X)|~brave(X))))&
((~rich(fred)<~>old(fred))) | old(john) | [] | null | 0 |
Everyone who is not funny is happy or generous. If susan is not wise then someone is funny and vice versa. Everyone who is either not old or not patient is both quiet and calm and vice versa. If someone is both not quiet and not wise then lucy is curious or patient and vice versa. Everyone who is wise or not funny is both brave and not creative. If someone is either tall or not humble then susan is rich. Everyone who is not rich is both generous and kind and vice versa. Everyone who is calm or quiet is both not funny and creative and vice versa. If someone is either quiet or not curious then someone is quiet or not patient. If someone is kind or not old then alice is happy. Everyone who is not calm or not old is either brave or rich and vice versa. If someone is not tall then someone is both kind and not curious and vice versa. If lucy is both wise and calm then fred is strong or humble. If someone is both not funny and funny then someone is both not brave and happy. If someone is calm or tall then someone is either quiet or not rich. Everyone who is either calm or patient is calm. Mary is either calm or not quiet. Mary is either happy or not humble. Mary is not funny or not curious. Someone is patient or not strong. Someone is not humble. John is not rich. Someone is strong. Someone is either wise or not old. | Mary is not calm. | entailment | (![X]:(~funny(X)=>(happy(X)|generous(X))))&
((~wise(susan))<=>(?[X]:(funny(X))))&
(![X]:((~old(X)<~>~patient(X))<=>(quiet(X)&calm(X))))&
((?[X]:((~quiet(X)&~wise(X))))<=>((curious(lucy)|patient(lucy))))&
(![X]:((wise(X)|~funny(X))=>(brave(X)&~creative(X))))&
((?[X]:((tall(X)<~>~humble(X))))=>(rich(susan)))&
(![X]:(~rich(X)<=>(generous(X)&kind(X))))&
(![X]:((calm(X)|quiet(X))<=>(~funny(X)&creative(X))))&
((?[X]:((quiet(X)<~>~curious(X))))=>(?[X]:((quiet(X)|~patient(X)))))&
((?[X]:((kind(X)|~old(X))))=>(happy(alice)))&
(![X]:((~calm(X)|~old(X))<=>(brave(X)<~>rich(X))))&
((?[X]:(~tall(X)))<=>(?[X]:((kind(X)&~curious(X)))))&
(((wise(lucy)&calm(lucy)))=>((strong(fred)|humble(fred))))&
((?[X]:((~funny(X)&funny(X))))=>(?[X]:((~brave(X)&happy(X)))))&
((?[X]:((calm(X)|tall(X))))=>(?[X]:((quiet(X)<~>~rich(X)))))&
(![X]:((calm(X)<~>patient(X))=>calm(X)))&
((calm(mary)<~>~quiet(mary)))&
((happy(mary)<~>~humble(mary)))&
((~funny(mary)|~curious(mary)))&
(?[X]:((patient(X)|~strong(X))))&
(?[X]:(~humble(X)))&
(~rich(john))&
(?[X]:(strong(X)))&
(?[X]:((wise(X)<~>~old(X)))) | ~calm(mary) | [
"p4",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 580256597114449852799161
% SZS output start Proof for 580256597114449852799161
5. ! [X0] : ((~funny(X0) | wise(X0)) => (~creative(X0) & brave(X0))) [input p4]
8. ! [X0] : ((quiet(X0) | calm(X0)) <=> (creative(X0) & ~funny(X0))) [input p7]
25. calm(mary) [input hypothesis]
32. ! [X0] : ((~creative(X0) & brave(X0)) | (funny(X0) & ~wise(X0))) [ennf transformation 5]
55. ! [X0] : (((quiet(X0) | calm(X0)) | (~creative(X0) | funny(X0))) & ((creative(X0) & ~funny(X0)) | (~quiet(X0) & ~calm(X0)))) [nnf transformation 8]
56. ! [X0] : ((quiet(X0) | calm(X0) | ~creative(X0) | funny(X0)) & ((creative(X0) & ~funny(X0)) | (~quiet(X0) & ~calm(X0)))) [flattening 55]
104. ~creative(X0) | funny(X0) [cnf transformation 32]
110. ~calm(X0) | ~funny(X0) [cnf transformation 56]
112. ~calm(X0) | creative(X0) [cnf transformation 56]
148. calm(mary) [cnf transformation 25]
284. 32 <=> calm(mary) [avatar definition]
285. calm(mary) <- (32) [avatar component clause 284]
304. 36 <=> funny(mary) [avatar definition]
331. 32 [avatar split clause 148,284]
336. ~funny(mary) <- (32) [resolution 110,285]
338. creative(mary) <- (32) [resolution 112,285]
339. funny(mary) <- (32) [resolution 338,104]
343. 36 | ~32 [avatar split clause 339,284,304]
345. ~36 | ~32 [avatar split clause 336,284,304]
346. $false [avatar sat refutation 331,343,345]
% SZS output end Proof for 580256597114449852799161
% ------------------------------
% 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 rich then someone is not generous or curious and vice versa.
Everyone who is both quiet and creative is rich.
If lucy is both creative and not curious then paul is both happy and not old and vice versa.
If someone is both curious and not creative then someone is both happy and brave and vice versa.
If lucy is either old or kind then someone is brave.
Everyone who is not rich or curious is both funny and not quiet and vice versa.
If someone is either not strong or generous then susan is tall and vice versa.
Everyone who is curious or not calm is patient or not patient and vice versa.
Everyone who is both not strong and patient is either humble or not rich and vice versa.
Everyone who is either not old or not funny is generous.
Everyone who is either not curious or happy is both not calm and not strong.
Everyone who is generous or brave is both not old and happy.
If paul is both creative and not brave then paul is tall and vice versa.
If alice is patient or humble then someone is both generous and not quiet and vice versa.
Everyone who is either brave or not patient is either tall or not old and vice versa.
If someone is not humble or patient then paul is quiet or not rich.
Someone is not strong or patient.
Someone is humble or not old.
Susan is either not calm or rich.
Paul is either not quiet or wise.
Someone is humble or old.
Paul is either not patient or patient.
Someone is not brave. | Paul is not old. | neutral | ((?[X]:(~rich(X)))<=>(?[X]:((~generous(X)|curious(X)))))&
(![X]:((quiet(X)&creative(X))=>rich(X)))&
(((creative(lucy)&~curious(lucy)))<=>((happy(paul)&~old(paul))))&
((?[X]:((curious(X)&~creative(X))))<=>(?[X]:((happy(X)&brave(X)))))&
(((old(lucy)<~>kind(lucy)))=>(?[X]:(brave(X))))&
(![X]:((~rich(X)|curious(X))<=>(funny(X)&~quiet(X))))&
((?[X]:((~strong(X)<~>generous(X))))<=>(tall(susan)))&
(![X]:((curious(X)|~calm(X))<=>(patient(X)|~patient(X))))&
(![X]:((~strong(X)&patient(X))<=>(humble(X)<~>~rich(X))))&
(![X]:((~old(X)<~>~funny(X))=>generous(X)))&
(![X]:((~curious(X)<~>happy(X))=>(~calm(X)&~strong(X))))&
(![X]:((generous(X)|brave(X))=>(~old(X)&happy(X))))&
(((creative(paul)&~brave(paul)))<=>(tall(paul)))&
(((patient(alice)|humble(alice)))<=>(?[X]:((generous(X)&~quiet(X)))))&
(![X]:((brave(X)<~>~patient(X))<=>(tall(X)<~>~old(X))))&
((?[X]:((~humble(X)|patient(X))))=>((quiet(paul)|~rich(paul))))&
(?[X]:((~strong(X)|patient(X))))&
(?[X]:((humble(X)|~old(X))))&
((~calm(susan)<~>rich(susan)))&
((~quiet(paul)<~>wise(paul)))&
(?[X]:((humble(X)|old(X))))&
((~patient(paul)<~>patient(paul)))&
(?[X]:(~brave(X))) | ~old(paul) | [] | null | 0 |
Everyone who is creative or brave is either curious or not creative and vice versa. If someone is calm then john is not humble and vice versa. If someone is quiet or old then someone is both not tall and calm. Everyone who is not wise is either strong or not quiet and vice versa. Everyone who is both curious and generous is funny or not strong and vice versa. Everyone who is either not tall or strong is both not curious and funny. If john is not rich or not old then mary is both quiet and not calm and vice versa. Everyone who is both not creative and old is quiet or not humble and vice versa. Everyone who is kind or not wise is both wise and not strong and vice versa. If someone is kind or not creative then someone is both not happy and strong and vice versa. Everyone who is not tall is not strong or calm. If someone is both patient and curious then john is patient. Everyone who is both not strong and not funny is either not funny or brave. Everyone who is not brave is either not old or humble. Everyone who is either old or funny is either creative or wise. If someone is not humble or not generous then someone is happy and vice versa. Paul is funny. Someone is not old or not strong. Someone is either not strong or not wise. Paul is not rich or not generous. Someone is not patient or not quiet. Someone is either not generous or not patient. Paul is creative. | John is not tall. | entailment | (![X]:((creative(X)|brave(X))<=>(curious(X)<~>~creative(X))))&
((?[X]:(calm(X)))<=>(~humble(john)))&
((?[X]:((quiet(X)|old(X))))=>(?[X]:((~tall(X)&calm(X)))))&
(![X]:(~wise(X)<=>(strong(X)<~>~quiet(X))))&
(![X]:((curious(X)&generous(X))<=>(funny(X)|~strong(X))))&
(![X]:((~tall(X)<~>strong(X))=>(~curious(X)&funny(X))))&
(((~rich(john)|~old(john)))<=>((quiet(mary)&~calm(mary))))&
(![X]:((~creative(X)&old(X))<=>(quiet(X)|~humble(X))))&
(![X]:((kind(X)|~wise(X))<=>(wise(X)&~strong(X))))&
((?[X]:((kind(X)|~creative(X))))<=>(?[X]:((~happy(X)&strong(X)))))&
(![X]:(~tall(X)=>(~strong(X)|calm(X))))&
((?[X]:((patient(X)&curious(X))))=>(patient(john)))&
(![X]:((~strong(X)&~funny(X))=>(~funny(X)<~>brave(X))))&
(![X]:(~brave(X)=>(~old(X)<~>humble(X))))&
(![X]:((old(X)<~>funny(X))=>(creative(X)<~>wise(X))))&
((?[X]:((~humble(X)|~generous(X))))<=>(?[X]:(happy(X))))&
(funny(paul))&
(?[X]:((~old(X)|~strong(X))))&
(?[X]:((~strong(X)<~>~wise(X))))&
((~rich(paul)|~generous(paul)))&
(?[X]:((~patient(X)|~quiet(X))))&
(?[X]:((~generous(X)<~>~patient(X))))&
(creative(paul)) | ~tall(john) | [
"p0",
"p1",
"p4",
"p5",
"p7",
"p8",
"p9",
"p10",
"p12",
"p13",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 7808345351792497759687115
% SZS output start Proof for 7808345351792497759687115
1. ! [X0] : ((brave(X0) | creative(X0)) <=> (curious(X0) <~> ~creative(X0))) [input p0]
2. ? [X0] : calm(X0) <=> ~humble(john) [input p1]
5. ! [X0] : ((generous(X0) & curious(X0)) <=> (~strong(X0) | funny(X0))) [input p4]
6. ! [X0] : ((~tall(X0) <~> strong(X0)) => (funny(X0) & ~curious(X0))) [input p5]
8. ! [X0] : ((old(X0) & ~creative(X0)) <=> (~humble(X0) | quiet(X0))) [input p7]
9. ! [X0] : ((~wise(X0) | kind(X0)) <=> (~strong(X0) & wise(X0))) [input p8]
10. ? [X0] : (~creative(X0) | kind(X0)) <=> ? [X0] : (strong(X0) & ~happy(X0)) [input p9]
11. ! [X0] : (~tall(X0) => (calm(X0) | ~strong(X0))) [input p10]
13. ! [X0] : ((~funny(X0) & ~strong(X0)) => (~funny(X0) <~> brave(X0))) [input p12]
14. ! [X0] : (~brave(X0) => (~old(X0) <~> humble(X0))) [input p13]
19. ? [X0] : (~strong(X0) <~> ~wise(X0)) [input p18]
24. tall(john) [input hypothesis]
26. ? [X0] : (~creative(X0) | kind(X0)) <=> ? [X1] : (strong(X1) & ~happy(X1)) [rectify 10]
29. ! [X0] : ((funny(X0) & ~curious(X0)) | (~tall(X0) <=> strong(X0))) [ennf transformation 6]
30. ! [X0] : ((calm(X0) | ~strong(X0)) | tall(X0)) [ennf transformation 11]
31. ! [X0] : (calm(X0) | ~strong(X0) | tall(X0)) [flattening 30]
33. ! [X0] : ((~funny(X0) <~> brave(X0)) | (funny(X0) | strong(X0))) [ennf transformation 13]
34. ! [X0] : ((~funny(X0) <~> brave(X0)) | funny(X0) | strong(X0)) [flattening 33]
35. ! [X0] : ((~old(X0) <~> humble(X0)) | brave(X0)) [ennf transformation 14]
37. ! [X0] : (((brave(X0) | creative(X0)) | ((curious(X0) | creative(X0)) & (~creative(X0) | ~curious(X0)))) & (((creative(X0) | ~curious(X0)) & (~creative(X0) | curious(X0))) | (~brave(X0) & ~creative(X0)))) [nnf transformation 1]
38. ! [X0] : ((brave(X0) | creative(X0) | ((curious(X0) | creative(X0)) & (~creative(X0) | ~curious(X0)))) & (((creative(X0) | ~curious(X0)) & (~creative(X0) | curious(X0))) | (~brave(X0) & ~creative(X0)))) [flattening 37]
39. (? [X0] : calm(X0) | humble(john)) & (~humble(john) | ! [X0] : ~calm(X0)) [nnf transformation 2]
40. (? [X0] : calm(X0) | humble(john)) & (~humble(john) | ! [X1] : ~calm(X1)) [rectify 39]
41. ? [X0] : calm(X0) => calm(sK0) [choice axiom]
42. (calm(sK0) | humble(john)) & (~humble(john) | ! [X1] : ~calm(X1)) [skolemisation 40,41]
47. ! [X0] : (((generous(X0) & curious(X0)) | (strong(X0) & ~funny(X0))) & ((~strong(X0) | funny(X0)) | (~generous(X0) | ~curious(X0)))) [nnf transformation 5]
48. ! [X0] : (((generous(X0) & curious(X0)) | (strong(X0) & ~funny(X0))) & (~strong(X0) | funny(X0) | ~generous(X0) | ~curious(X0))) [flattening 47]
49. ! [X0] : ((funny(X0) & ~curious(X0)) | ((~tall(X0) | ~strong(X0)) & (strong(X0) | tall(X0)))) [nnf transformation 29]
52. ! [X0] : (((old(X0) & ~creative(X0)) | (humble(X0) & ~quiet(X0))) & ((~humble(X0) | quiet(X0)) | (~old(X0) | creative(X0)))) [nnf transformation 8]
53. ! [X0] : (((old(X0) & ~creative(X0)) | (humble(X0) & ~quiet(X0))) & (~humble(X0) | quiet(X0) | ~old(X0) | creative(X0))) [flattening 52]
54. ! [X0] : (((~wise(X0) | kind(X0)) | (strong(X0) | ~wise(X0))) & ((~strong(X0) & wise(X0)) | (wise(X0) & ~kind(X0)))) [nnf transformation 9]
55. ! [X0] : ((~wise(X0) | kind(X0) | strong(X0) | ~wise(X0)) & ((~strong(X0) & wise(X0)) | (wise(X0) & ~kind(X0)))) [flattening 54]
56. (? [X0] : (~creative(X0) | kind(X0)) | ! [X1] : (~strong(X1) | happy(X1))) & (? [X1] : (strong(X1) & ~happy(X1)) | ! [X0] : (creative(X0) & ~kind(X0))) [nnf transformation 26]
57. (? [X0] : (~creative(X0) | kind(X0)) | ! [X1] : (~strong(X1) | happy(X1))) & (? [X2] : (strong(X2) & ~happy(X2)) | ! [X3] : (creative(X3) & ~kind(X3))) [rectify 56]
58. ? [X0] : (~creative(X0) | kind(X0)) => (~creative(sK2) | kind(sK2)) [choice axiom]
59. ? [X2] : (strong(X2) & ~happy(X2)) => (strong(sK3) & ~happy(sK3)) [choice axiom]
60. ((~creative(sK2) | kind(sK2)) | ! [X1] : (~strong(X1) | happy(X1))) & ((strong(sK3) & ~happy(sK3)) | ! [X3] : (creative(X3) & ~kind(X3))) [skolemisation 57,59,58]
61. ! [X0] : (((~brave(X0) | funny(X0)) & (brave(X0) | ~funny(X0))) | funny(X0) | strong(X0)) [nnf transformation 34]
62. ! [X0] : (((~humble(X0) | old(X0)) & (humble(X0) | ~old(X0))) | brave(X0)) [nnf transformation 35]
71. ? [X0] : ((wise(X0) | strong(X0)) & (~wise(X0) | ~strong(X0))) [nnf transformation 19]
72. ? [X0] : ((wise(X0) | strong(X0)) & (~wise(X0) | ~strong(X0))) => ((wise(sK7) | strong(sK7)) & (~wise(sK7) | ~strong(sK7))) [choice axiom]
73. (wise(sK7) | strong(sK7)) & (~wise(sK7) | ~strong(sK7)) [skolemisation 71,72]
82. ~curious(X0) | creative(X0) | ~brave(X0) [cnf transformation 38]
85. ~humble(john) | ~calm(X1) [cnf transformation 42]
96. ~funny(X0) | curious(X0) [cnf transformation 48]
97. strong(X0) | curious(X0) [cnf transformation 48]
100. ~curious(X0) | strong(X0) | tall(X0) [cnf transformation 49]
101. ~strong(X0) | ~tall(X0) | ~curious(X0) [cnf transformation 49]
103. ~strong(X0) | ~tall(X0) | funny(X0) [cnf transformation 49]
111. ~creative(X0) | humble(X0) [cnf transformation 53]
113. old(X0) | humble(X0) [cnf transformation 53]
115. wise(X0) | wise(X0) [cnf transformation 55]
118. ~wise(X0) | kind(X0) | strong(X0) | ~wise(X0) [cnf transformation 55]
121. strong(sK3) | ~kind(X3) [cnf transformation 60]
124. calm(X0) | ~strong(X0) | tall(X0) [cnf transformation 31]
127. ~brave(X0) | funny(X0) | funny(X0) | strong(X0) [cnf transformation 61]
128. humble(X0) | ~old(X0) | brave(X0) [cnf transformation 62]
139. ~wise(sK7) | ~strong(sK7) [cnf transformation 73]
146. tall(john) [cnf transformation 24]
147. ~brave(X0) | funny(X0) | strong(X0) [duplicate literal removal 127]
148. wise(X0) [duplicate literal removal 115]
149. ~wise(X0) | kind(X0) | strong(X0) [duplicate literal removal 118]
153. 1 <=> humble(john) [avatar definition]
154. ~humble(john) <- (~1) [avatar component clause 153]
162. 3 <=> ! [X1] : ~calm(X1) [avatar definition]
163. ~calm(X1) <- (3) [avatar component clause 162]
164. 3 | ~1 [avatar split clause 85,153,162]
183. strong(X0) | tall(X0) [subsumption resolution 100,97]
221. 16 <=> strong(sK3) [avatar definition]
223. strong(sK3) <- (16) [avatar component clause 221]
226. 17 <=> ! [X3] : ~kind(X3) [avatar definition]
227. ~kind(X3) <- (17) [avatar component clause 226]
228. 17 | 16 [avatar split clause 121,221,226]
235. tall(X0) | calm(X0) [subsumption resolution 124,183]
245. humble(X0) | brave(X0) [subsumption resolution 128,113]
281. ~strong(sK7) [subsumption resolution 139,148]
327. brave(john) <- (~1) [resolution 245,154]
364. ~tall(sK3) | ~curious(sK3) <- (16) [resolution 101,223]
369. 39 <=> curious(sK3) [avatar definition]
371. ~curious(sK3) <- (~39) [avatar component clause 369]
373. 40 <=> tall(sK3) [avatar definition]
374. tall(sK3) <- (40) [avatar component clause 373]
375. ~tall(sK3) <- (~40) [avatar component clause 373]
376. ~39 | ~40 | ~16 [avatar split clause 364,221,373,369]
391. ~tall(X1) | funny(X1) | curious(X1) [resolution 103,97]
398. ~tall(X1) | curious(X1) [subsumption resolution 391,96]
400. funny(john) | strong(john) <- (~1) [resolution 147,327]
402. 44 <=> strong(john) [avatar definition]
404. strong(john) <- (44) [avatar component clause 402]
406. 45 <=> funny(john) [avatar definition]
408. funny(john) <- (45) [avatar component clause 406]
409. 44 | 45 | 1 [avatar split clause 400,153,406,402]
414. brave(john) <- (~1) [resolution 154,245]
415. kind(X0) | strong(X0) [resolution 149,148]
474. ~tall(john) | funny(john) <- (44) [resolution 404,103]
479. funny(john) <- (44) [subsumption resolution 474,146]
480. 45 | ~44 [avatar split clause 479,402,406]
486. curious(john) <- (45) [resolution 408,96]
488. 53 <=> creative(john) [avatar definition]
489. creative(john) <- (53) [avatar component clause 488]
561. strong(X0) <- (17) [resolution 227,415]
601. curious(sK3) <- (40) [resolution 374,398]
602. $false <- (~39, 40) [subsumption resolution 601,371]
603. 39 | ~40 [avatar contradiction clause 602]
604. calm(sK3) <- (~40) [resolution 375,235]
659. $false <- (17) [resolution 561,281]
662. ~17 [avatar contradiction clause 659]
695. creative(john) | ~brave(john) <- (45) [resolution 486,82]
699. creative(john) <- (~1, 45) [subsumption resolution 695,414]
700. 53 | 1 | ~45 [avatar split clause 699,406,153,488]
708. humble(john) <- (53) [resolution 489,111]
711. 1 | ~53 [avatar split clause 708,488,153]
714. $false <- (3, ~40) [resolution 163,604]
717. ~3 | 40 [avatar contradiction clause 714]
718. $false [avatar sat refutation 164,228,376,409,480,603,662,700,711,717]
% SZS output end Proof for 7808345351792497759687115
% ------------------------------
% 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: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is brave is either not tall or generous.
Everyone who is not humble or wise is both not wise and not happy and vice versa.
If lucy is creative then alice is both not patient and not calm.
If john is both not humble and strong then paul is either humble or kind.
If john is either not tall or not humble then susan is either kind or tall.
If someone is both patient and old then someone is either not brave or not rich and vice versa.
Everyone who is not generous is both not brave and quiet.
Everyone who is not humble is creative.
Everyone who is creative is not generous or not old.
Everyone who is humble is not generous and vice versa.
Everyone who is both happy and not humble is not quiet or curious and vice versa.
Everyone who is both tall and old is both tall and not happy.
If someone is both kind and not brave then someone is not happy or funny.
Everyone who is not quiet or strong is happy and vice versa.
Everyone who is either not quiet or creative is both old and not calm.
Fred is not wise.
Someone is not old or not strong.
Alice is both tall and not rich.
Someone is kind or generous.
Someone is brave or not curious.
Susan is both tall and not wise.
Mary is both not creative and rich. | Paul is patient. | neutral | (![X]:(brave(X)=>(~tall(X)<~>generous(X))))&
(![X]:((~humble(X)|wise(X))<=>(~wise(X)&~happy(X))))&
((creative(lucy))=>((~patient(alice)&~calm(alice))))&
(((~humble(john)&strong(john)))=>((humble(paul)<~>kind(paul))))&
(((~tall(john)<~>~humble(john)))=>((kind(susan)<~>tall(susan))))&
((?[X]:((patient(X)&old(X))))<=>(?[X]:((~brave(X)<~>~rich(X)))))&
(![X]:(~generous(X)=>(~brave(X)&quiet(X))))&
(![X]:(~humble(X)=>creative(X)))&
(![X]:(creative(X)=>(~generous(X)|~old(X))))&
(![X]:(humble(X)<=>~generous(X)))&
(![X]:((happy(X)&~humble(X))<=>(~quiet(X)|curious(X))))&
(![X]:((tall(X)&old(X))=>(tall(X)&~happy(X))))&
((?[X]:((kind(X)&~brave(X))))=>(?[X]:((~happy(X)|funny(X)))))&
(![X]:((~quiet(X)|strong(X))<=>happy(X)))&
(![X]:((~quiet(X)<~>creative(X))=>(old(X)&~calm(X))))&
(~wise(fred))&
(?[X]:((~old(X)|~strong(X))))&
((tall(alice)&~rich(alice)))&
(?[X]:((kind(X)|generous(X))))&
(?[X]:((brave(X)|~curious(X))))&
((tall(susan)&~wise(susan)))&
((~creative(mary)&rich(mary))) | patient(paul) | [] | null | 0 |
If susan is curious or not generous then paul is both generous and not wise. Everyone who is either not calm or not quiet is kind and vice versa. If someone is calm or not patient then alice is both calm and humble and vice versa. If someone is tall or brave then someone is both not humble and not kind. Everyone who is not tall or not brave is not old and vice versa. If fred is either not curious or not tall then fred is both not rich and not humble. If someone is patient then someone is not happy. Everyone who is either tall or funny is strong or quiet. Everyone who is not tall or not brave is both not kind and not humble and vice versa. If fred is not rich then someone is either rich or funny. If someone is not strong or not tall then susan is both not old and not patient and vice versa. Everyone who is either not calm or not funny is not tall. If alice is both humble and not curious then someone is both strong and tall and vice versa. If someone is either wise or old then alice is either not tall or not calm and vice versa. If someone is both kind and humble then someone is either generous or not happy. Everyone who is both not patient and strong is both not calm and quiet and vice versa. Mary is patient or not strong. Someone is both not quiet and not strong. Someone is either not rich or wise. Susan is not humble or funny. Someone is wise or calm. Someone is not humble or humble. Someone is both old and wise. Someone is either not humble or not calm. | Alice is brave. | entailment | (((curious(susan)|~generous(susan)))=>((generous(paul)&~wise(paul))))&
(![X]:((~calm(X)<~>~quiet(X))<=>kind(X)))&
((?[X]:((calm(X)|~patient(X))))<=>((calm(alice)&humble(alice))))&
((?[X]:((tall(X)|brave(X))))=>(?[X]:((~humble(X)&~kind(X)))))&
(![X]:((~tall(X)|~brave(X))<=>~old(X)))&
(((~curious(fred)<~>~tall(fred)))=>((~rich(fred)&~humble(fred))))&
((?[X]:(patient(X)))=>(?[X]:(~happy(X))))&
(![X]:((tall(X)<~>funny(X))=>(strong(X)|quiet(X))))&
(![X]:((~tall(X)|~brave(X))<=>(~kind(X)&~humble(X))))&
((~rich(fred))=>(?[X]:((rich(X)<~>funny(X)))))&
((?[X]:((~strong(X)|~tall(X))))<=>((~old(susan)&~patient(susan))))&
(![X]:((~calm(X)<~>~funny(X))=>~tall(X)))&
(((humble(alice)&~curious(alice)))<=>(?[X]:((strong(X)&tall(X)))))&
((?[X]:((wise(X)<~>old(X))))<=>((~tall(alice)<~>~calm(alice))))&
((?[X]:((kind(X)&humble(X))))=>(?[X]:((generous(X)<~>~happy(X)))))&
(![X]:((~patient(X)&strong(X))<=>(~calm(X)&quiet(X))))&
((patient(mary)|~strong(mary)))&
(?[X]:((~quiet(X)&~strong(X))))&
(?[X]:((~rich(X)<~>wise(X))))&
((~humble(susan)|funny(susan)))&
(?[X]:((wise(X)|calm(X))))&
(?[X]:((~humble(X)|humble(X))))&
(?[X]:((old(X)&wise(X))))&
(?[X]:((~humble(X)<~>~calm(X)))) | brave(alice) | [
"p2",
"p8",
"p10",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 291695156856999064812634
% SZS output start Proof for 291695156856999064812634
3. ? [X0] : (~patient(X0) | calm(X0)) <=> (humble(alice) & calm(alice)) [input p2]
9. ! [X0] : ((~brave(X0) | ~tall(X0)) <=> (~humble(X0) & ~kind(X0))) [input p8]
11. ? [X0] : (~tall(X0) | ~strong(X0)) <=> (~patient(susan) & ~old(susan)) [input p10]
18. ? [X0] : (~strong(X0) & ~quiet(X0)) [input p17]
25. ~brave(alice) [input hypothesis]
39. (? [X0] : (~patient(X0) | calm(X0)) | (~humble(alice) | ~calm(alice))) & ((humble(alice) & calm(alice)) | ! [X0] : (patient(X0) & ~calm(X0))) [nnf transformation 3]
40. (? [X0] : (~patient(X0) | calm(X0)) | ~humble(alice) | ~calm(alice)) & ((humble(alice) & calm(alice)) | ! [X0] : (patient(X0) & ~calm(X0))) [flattening 39]
41. (? [X0] : (~patient(X0) | calm(X0)) | ~humble(alice) | ~calm(alice)) & ((humble(alice) & calm(alice)) | ! [X1] : (patient(X1) & ~calm(X1))) [rectify 40]
42. ? [X0] : (~patient(X0) | calm(X0)) => (~patient(sK0) | calm(sK0)) [choice axiom]
43. ((~patient(sK0) | calm(sK0)) | ~humble(alice) | ~calm(alice)) & ((humble(alice) & calm(alice)) | ! [X1] : (patient(X1) & ~calm(X1))) [skolemisation 41,42]
54. ! [X0] : (((~brave(X0) | ~tall(X0)) | (humble(X0) | kind(X0))) & ((~humble(X0) & ~kind(X0)) | (brave(X0) & tall(X0)))) [nnf transformation 9]
55. ! [X0] : ((~brave(X0) | ~tall(X0) | humble(X0) | kind(X0)) & ((~humble(X0) & ~kind(X0)) | (brave(X0) & tall(X0)))) [flattening 54]
59. (? [X0] : (~tall(X0) | ~strong(X0)) | (patient(susan) | old(susan))) & ((~patient(susan) & ~old(susan)) | ! [X0] : (tall(X0) & strong(X0))) [nnf transformation 11]
60. (? [X0] : (~tall(X0) | ~strong(X0)) | patient(susan) | old(susan)) & ((~patient(susan) & ~old(susan)) | ! [X0] : (tall(X0) & strong(X0))) [flattening 59]
61. (? [X0] : (~tall(X0) | ~strong(X0)) | patient(susan) | old(susan)) & ((~patient(susan) & ~old(susan)) | ! [X1] : (tall(X1) & strong(X1))) [rectify 60]
62. ? [X0] : (~tall(X0) | ~strong(X0)) => (~tall(sK4) | ~strong(sK4)) [choice axiom]
63. ((~tall(sK4) | ~strong(sK4)) | patient(susan) | old(susan)) & ((~patient(susan) & ~old(susan)) | ! [X1] : (tall(X1) & strong(X1))) [skolemisation 61,62]
80. ? [X0] : (~strong(X0) & ~quiet(X0)) => (~strong(sK8) & ~quiet(sK8)) [choice axiom]
81. ~strong(sK8) & ~quiet(sK8) [skolemisation 18,80]
103. calm(alice) | patient(X1) [cnf transformation 43]
104. humble(alice) | ~calm(X1) [cnf transformation 43]
124. ~humble(X0) | brave(X0) [cnf transformation 55]
130. ~patient(susan) | strong(X1) [cnf transformation 63]
155. ~strong(sK8) [cnf transformation 81]
165. ~brave(alice) [cnf transformation 25]
187. 5 <=> calm(alice) [avatar definition]
188. calm(alice) <- (5) [avatar component clause 187]
191. 6 <=> humble(alice) [avatar definition]
192. humble(alice) <- (6) [avatar component clause 191]
204. 9 <=> ! [X1] : patient(X1) [avatar definition]
205. patient(X1) <- (9) [avatar component clause 204]
208. 10 <=> ! [X1] : ~calm(X1) [avatar definition]
209. ~calm(X1) <- (10) [avatar component clause 208]
210. 10 | 6 [avatar split clause 104,191,208]
211. 9 | 5 [avatar split clause 103,187,204]
274. 24 <=> patient(susan) [avatar definition]
275. ~patient(susan) <- (~24) [avatar component clause 274]
291. 28 <=> ! [X1] : strong(X1) [avatar definition]
292. strong(X1) <- (28) [avatar component clause 291]
293. 28 | ~24 [avatar split clause 130,274,291]
401. $false <- (5, 10) [subsumption resolution 188,209]
402. ~5 | ~10 [avatar contradiction clause 401]
411. $false <- (9, ~24) [resolution 205,275]
412. ~9 | 24 [avatar contradiction clause 411]
419. $false <- (28) [resolution 292,155]
422. ~28 [avatar contradiction clause 419]
425. brave(alice) <- (6) [resolution 124,192]
426. $false <- (6) [subsumption resolution 425,165]
427. ~6 [avatar contradiction clause 426]
428. $false [avatar sat refutation 210,211,293,402,412,422,427]
% SZS output end Proof for 291695156856999064812634
% ------------------------------
% 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 paul is brave or not tall then someone is brave or happy. Everyone who is not curious is patient and vice versa. Everyone who is not generous is curious and vice versa. Everyone who is not strong or old is both funny and not tall. Everyone who is not creative or not brave is both tall and curious and vice versa. Everyone who is both funny and not patient is either rich or not calm and vice versa. If someone is not generous or funny then someone is funny and vice versa. Everyone who is either not old or not calm is not strong or strong and vice versa. Everyone who is both curious and tall is both not patient and creative. Everyone who is either not quiet or generous is rich or creative and vice versa. Everyone who is either not patient or not rich is both quiet and calm. Everyone who is either not brave or not wise is either not funny or curious. Everyone who is funny is either not brave or wise and vice versa. Everyone who is both patient and strong is strong and vice versa. If someone is either not patient or not humble then someone is both creative and not creative. Everyone who is both patient and not funny is both not funny and funny and vice versa. Fred is not quiet or not strong. Lucy is either kind or funny. Susan is either not tall or not wise. Susan is not calm. Paul is creative or old. Someone is happy or tall. Someone is generous. | Fred is wise. | entailment | (((brave(paul)|~tall(paul)))=>(?[X]:((brave(X)|happy(X)))))&
(![X]:(~curious(X)<=>patient(X)))&
(![X]:(~generous(X)<=>curious(X)))&
(![X]:((~strong(X)|old(X))=>(funny(X)&~tall(X))))&
(![X]:((~creative(X)|~brave(X))<=>(tall(X)&curious(X))))&
(![X]:((funny(X)&~patient(X))<=>(rich(X)<~>~calm(X))))&
((?[X]:((~generous(X)|funny(X))))<=>(?[X]:(funny(X))))&
(![X]:((~old(X)<~>~calm(X))<=>(~strong(X)|strong(X))))&
(![X]:((curious(X)&tall(X))=>(~patient(X)&creative(X))))&
(![X]:((~quiet(X)<~>generous(X))<=>(rich(X)|creative(X))))&
(![X]:((~patient(X)<~>~rich(X))=>(quiet(X)&calm(X))))&
(![X]:((~brave(X)<~>~wise(X))=>(~funny(X)<~>curious(X))))&
(![X]:(funny(X)<=>(~brave(X)<~>wise(X))))&
(![X]:((patient(X)&strong(X))<=>strong(X)))&
((?[X]:((~patient(X)<~>~humble(X))))=>(?[X]:((creative(X)&~creative(X)))))&
(![X]:((patient(X)&~funny(X))<=>(~funny(X)&funny(X))))&
((~quiet(fred)|~strong(fred)))&
((kind(lucy)<~>funny(lucy)))&
((~tall(susan)<~>~wise(susan)))&
(~calm(susan))&
((creative(paul)|old(paul)))&
(?[X]:((happy(X)|tall(X))))&
(?[X]:(generous(X))) | wise(fred) | [
"p1",
"p2",
"p3",
"p4",
"p8",
"p9",
"p12",
"p13",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 7011172813684363222141612
% SZS output start Proof for 7011172813684363222141612
2. ! [X0] : (~curious(X0) <=> patient(X0)) [input p1]
3. ! [X0] : (~generous(X0) <=> curious(X0)) [input p2]
4. ! [X0] : ((old(X0) | ~strong(X0)) => (~tall(X0) & funny(X0))) [input p3]
5. ! [X0] : ((~brave(X0) | ~creative(X0)) <=> (curious(X0) & tall(X0))) [input p4]
9. ! [X0] : ((tall(X0) & curious(X0)) => (creative(X0) & ~patient(X0))) [input p8]
10. ! [X0] : ((~quiet(X0) <~> generous(X0)) <=> (creative(X0) | rich(X0))) [input p9]
13. ! [X0] : (funny(X0) <=> (~brave(X0) <~> wise(X0))) [input p12]
14. ! [X0] : ((strong(X0) & patient(X0)) <=> strong(X0)) [input p13]
17. ~strong(fred) | ~quiet(fred) [input p16]
24. ~wise(fred) [input hypothesis]
29. ! [X0] : ((~tall(X0) & funny(X0)) | (~old(X0) & strong(X0))) [ennf transformation 4]
30. ! [X0] : ((creative(X0) & ~patient(X0)) | (~tall(X0) | ~curious(X0))) [ennf transformation 9]
31. ! [X0] : ((creative(X0) & ~patient(X0)) | ~tall(X0) | ~curious(X0)) [flattening 30]
35. ! [X0] : ((~curious(X0) | ~patient(X0)) & (patient(X0) | curious(X0))) [nnf transformation 2]
36. ! [X0] : ((~generous(X0) | ~curious(X0)) & (curious(X0) | generous(X0))) [nnf transformation 3]
37. ! [X0] : (((~brave(X0) | ~creative(X0)) | (~curious(X0) | ~tall(X0))) & ((curious(X0) & tall(X0)) | (brave(X0) & creative(X0)))) [nnf transformation 5]
38. ! [X0] : ((~brave(X0) | ~creative(X0) | ~curious(X0) | ~tall(X0)) & ((curious(X0) & tall(X0)) | (brave(X0) & creative(X0)))) [flattening 37]
48. ! [X0] : ((((~generous(X0) | quiet(X0)) & (generous(X0) | ~quiet(X0))) | (~creative(X0) & ~rich(X0))) & ((creative(X0) | rich(X0)) | ((~quiet(X0) | ~generous(X0)) & (generous(X0) | quiet(X0))))) [nnf transformation 10]
49. ! [X0] : ((((~generous(X0) | quiet(X0)) & (generous(X0) | ~quiet(X0))) | (~creative(X0) & ~rich(X0))) & (creative(X0) | rich(X0) | ((~quiet(X0) | ~generous(X0)) & (generous(X0) | quiet(X0))))) [flattening 48]
52. ! [X0] : ((funny(X0) | ((~brave(X0) | ~wise(X0)) & (wise(X0) | brave(X0)))) & (((~wise(X0) | brave(X0)) & (wise(X0) | ~brave(X0))) | ~funny(X0))) [nnf transformation 13]
53. ! [X0] : (((strong(X0) & patient(X0)) | ~strong(X0)) & (strong(X0) | (~strong(X0) | ~patient(X0)))) [nnf transformation 14]
54. ! [X0] : (((strong(X0) & patient(X0)) | ~strong(X0)) & (strong(X0) | ~strong(X0) | ~patient(X0))) [flattening 53]
66. ~patient(X0) | ~curious(X0) [cnf transformation 35]
67. generous(X0) | curious(X0) [cnf transformation 36]
69. funny(X0) | strong(X0) [cnf transformation 29]
71. ~tall(X0) | strong(X0) [cnf transformation 29]
73. creative(X0) | tall(X0) [cnf transformation 38]
74. tall(X0) | brave(X0) [cnf transformation 38]
75. creative(X0) | curious(X0) [cnf transformation 38]
76. curious(X0) | brave(X0) [cnf transformation 38]
94. creative(X0) | ~tall(X0) | ~curious(X0) [cnf transformation 31]
100. ~generous(X0) | quiet(X0) | ~creative(X0) [cnf transformation 49]
109. ~funny(X0) | ~brave(X0) | wise(X0) [cnf transformation 52]
114. ~strong(X0) | patient(X0) [cnf transformation 54]
124. ~strong(fred) | ~quiet(fred) [cnf transformation 17]
132. ~wise(fred) [cnf transformation 24]
158. creative(X0) | ~tall(X0) [subsumption resolution 94,75]
159. creative(X0) [subsumption resolution 158,73]
160. ~generous(X0) | quiet(X0) [subsumption resolution 100,159]
170. 6 <=> quiet(fred) [avatar definition]
172. ~quiet(fred) <- (~6) [avatar component clause 170]
174. 7 <=> strong(fred) [avatar definition]
175. strong(fred) <- (7) [avatar component clause 174]
177. ~6 | ~7 [avatar split clause 124,174,170]
204. strong(X0) | brave(X0) [resolution 74,71]
222. quiet(X0) | curious(X0) [resolution 160,67]
228. patient(X0) | brave(X0) [resolution 204,114]
246. brave(X3) | ~curious(X3) [resolution 228,66]
247. brave(X3) [subsumption resolution 246,76]
253. ~brave(X2) | wise(X2) | strong(X2) [resolution 109,69]
258. wise(X2) | strong(X2) [subsumption resolution 253,247]
279. strong(fred) [resolution 258,132]
285. 7 [avatar split clause 279,174]
286. curious(fred) <- (~6) [resolution 172,222]
288. patient(fred) <- (7) [resolution 175,114]
296. ~curious(fred) <- (7) [resolution 288,66]
298. $false <- (~6, 7) [subsumption resolution 296,286]
299. 6 | ~7 [avatar contradiction clause 298]
300. $false [avatar sat refutation 177,285,299]
% SZS output end Proof for 7011172813684363222141612
% ------------------------------
% 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 |
If someone is both not wise and not calm then alice is both old and not humble. If someone is both not tall and rich then someone is not rich or not happy. If fred is kind then alice is brave and vice versa. Everyone who is not brave or happy is both not calm and generous. If fred is either not kind or not patient then someone is not quiet or brave. Everyone who is not creative is curious. Everyone who is strong or not generous is not strong or happy and vice versa. Everyone who is funny is both not generous and not quiet. If someone is both not creative and calm then alice is either calm or tall. Everyone who is generous or quiet is funny. Everyone who is both not humble and strong is not funny or curious. Everyone who is both funny and not kind is both not calm and not funny. Everyone who is both funny and patient is both not curious and not calm and vice versa. If mary is funny then someone is both generous and not funny. If someone is creative or not wise then someone is both not kind and not wise and vice versa. Everyone who is funny is both happy and not patient and vice versa. Mary is either not funny or old. Paul is rich or patient. Paul is both tall and kind. Fred is not quiet. Someone is both not wise and calm. Susan is creative or not old. Fred is both not curious and not tall. | Fred is not quiet. | entailment | ((?[X]:((~wise(X)&~calm(X))))=>((old(alice)&~humble(alice))))&
((?[X]:((~tall(X)&rich(X))))=>(?[X]:((~rich(X)|~happy(X)))))&
((kind(fred))<=>(brave(alice)))&
(![X]:((~brave(X)|happy(X))=>(~calm(X)&generous(X))))&
(((~kind(fred)<~>~patient(fred)))=>(?[X]:((~quiet(X)|brave(X)))))&
(![X]:(~creative(X)=>curious(X)))&
(![X]:((strong(X)|~generous(X))<=>(~strong(X)|happy(X))))&
(![X]:(funny(X)=>(~generous(X)&~quiet(X))))&
((?[X]:((~creative(X)&calm(X))))=>((calm(alice)<~>tall(alice))))&
(![X]:((generous(X)|quiet(X))=>funny(X)))&
(![X]:((~humble(X)&strong(X))=>(~funny(X)|curious(X))))&
(![X]:((funny(X)&~kind(X))=>(~calm(X)&~funny(X))))&
(![X]:((funny(X)&patient(X))<=>(~curious(X)&~calm(X))))&
((funny(mary))=>(?[X]:((generous(X)&~funny(X)))))&
((?[X]:((creative(X)|~wise(X))))<=>(?[X]:((~kind(X)&~wise(X)))))&
(![X]:(funny(X)<=>(happy(X)&~patient(X))))&
((~funny(mary)<~>old(mary)))&
((rich(paul)|patient(paul)))&
((tall(paul)&kind(paul)))&
(~quiet(fred))&
(?[X]:((~wise(X)&calm(X))))&
((creative(susan)|~old(susan)))&
((~curious(fred)&~tall(fred))) | ~quiet(fred) | [
"p7",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 556714425860667878617128
% SZS output start Proof for 556714425860667878617128
8. ! [X0] : (funny(X0) => (~quiet(X0) & ~generous(X0))) [input p7]
10. ! [X0] : ((quiet(X0) | generous(X0)) => funny(X0)) [input p9]
24. quiet(fred) [input hypothesis]
32. ! [X0] : ((~quiet(X0) & ~generous(X0)) | ~funny(X0)) [ennf transformation 8]
34. ! [X0] : (funny(X0) | (~quiet(X0) & ~generous(X0))) [ennf transformation 10]
81. ~quiet(X0) | ~funny(X0) [cnf transformation 32]
85. funny(X0) | ~quiet(X0) [cnf transformation 34]
114. quiet(fred) [cnf transformation 24]
182. ~quiet(X0) [subsumption resolution 85,81]
249. $false [subsumption resolution 114,182]
% SZS output end Proof for 556714425860667878617128
% ------------------------------
% 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 curious is either not tall or creative and vice versa. Everyone who is not rich or quiet is both strong and not funny and vice versa. Everyone who is tall or brave is both not tall and funny and vice versa. If someone is not funny then susan is not generous or funny and vice versa. If paul is quiet then someone is brave. If mary is happy or not strong then someone is not tall or not quiet and vice versa. Everyone who is brave or tall is either not kind or old. Everyone who is not generous is either strong or not creative and vice versa. If someone is strong then someone is both rich and kind and vice versa. If susan is tall then someone is either calm or not happy. If someone is not rich or not kind then someone is both calm and not wise and vice versa. Everyone who is either not wise or not creative is either rich or curious and vice versa. Everyone who is not patient is both strong and not wise and vice versa. If paul is either generous or funny then paul is not quiet or tall and vice versa. Everyone who is both not generous and not funny is happy. Everyone who is both happy and not curious is both calm and not humble. Susan is old. Someone is patient or brave. Paul is either not strong or not tall. Susan is either curious or not old. Alice is strong. Someone is not curious. Someone is not kind. | Paul is quiet. | neutral | (![X]:(~curious(X)<=>(~tall(X)<~>creative(X))))&
(![X]:((~rich(X)|quiet(X))<=>(strong(X)&~funny(X))))&
(![X]:((tall(X)|brave(X))<=>(~tall(X)&funny(X))))&
((?[X]:(~funny(X)))<=>((~generous(susan)|funny(susan))))&
((quiet(paul))=>(?[X]:(brave(X))))&
(((happy(mary)|~strong(mary)))<=>(?[X]:((~tall(X)|~quiet(X)))))&
(![X]:((brave(X)|tall(X))=>(~kind(X)<~>old(X))))&
(![X]:(~generous(X)<=>(strong(X)<~>~creative(X))))&
((?[X]:(strong(X)))<=>(?[X]:((rich(X)&kind(X)))))&
((tall(susan))=>(?[X]:((calm(X)<~>~happy(X)))))&
((?[X]:((~rich(X)|~kind(X))))<=>(?[X]:((calm(X)&~wise(X)))))&
(![X]:((~wise(X)<~>~creative(X))<=>(rich(X)<~>curious(X))))&
(![X]:(~patient(X)<=>(strong(X)&~wise(X))))&
(((generous(paul)<~>funny(paul)))<=>((~quiet(paul)|tall(paul))))&
(![X]:((~generous(X)&~funny(X))=>happy(X)))&
(![X]:((happy(X)&~curious(X))=>(calm(X)&~humble(X))))&
(old(susan))&
(?[X]:((patient(X)|brave(X))))&
((~strong(paul)<~>~tall(paul)))&
((curious(susan)<~>~old(susan)))&
(strong(alice))&
(?[X]:(~curious(X)))&
(?[X]:(~kind(X))) | quiet(paul) | [] | null | 0 |
If someone is quiet then lucy is generous or not patient and vice versa.
If someone is calm or not tall then someone is either strong or patient.
Everyone who is either not patient or rich is not humble and vice versa.
Everyone who is not tall or funny is not funny.
Everyone who is strong is not funny or not brave.
Everyone who is not old is happy or kind.
Everyone who is both humble and not strong is both rich and tall.
If paul is not funny then someone is rich or wise.
If alice is not old or calm then mary is quiet.
If lucy is not quiet then susan is either not kind or not happy and vice versa.
If someone is happy or not old then someone is both not strong and patient.
Everyone who is not creative or happy is either tall or not quiet and vice versa.
If someone is both not funny and old then someone is not brave or not kind.
Everyone who is both not strong and old is not humble or not wise and vice versa.
If mary is both not creative and old then someone is not kind or creative and vice versa.
Everyone who is not strong or calm is both old and funny and vice versa.
Paul is either not creative or rich.
Someone is either not happy or patient.
Someone is calm or not kind.
Lucy is strong.
Someone is not humble or patient. | Paul is funny. | contradiction | ((?[X]:(quiet(X)))<=>((generous(lucy)|~patient(lucy))))&
((?[X]:((calm(X)|~tall(X))))=>(?[X]:((strong(X)<~>patient(X)))))&
(![X]:((~patient(X)<~>rich(X))<=>~humble(X)))&
(![X]:((~tall(X)|funny(X))=>~funny(X)))&
(![X]:(strong(X)=>(~funny(X)|~brave(X))))&
(![X]:(~old(X)=>(happy(X)|kind(X))))&
(![X]:((humble(X)&~strong(X))=>(rich(X)&tall(X))))&
((~funny(paul))=>(?[X]:((rich(X)|wise(X)))))&
(((~old(alice)|calm(alice)))=>(quiet(mary)))&
((~quiet(lucy))<=>((~kind(susan)<~>~happy(susan))))&
((?[X]:((happy(X)|~old(X))))=>(?[X]:((~strong(X)&patient(X)))))&
(![X]:((~creative(X)|happy(X))<=>(tall(X)<~>~quiet(X))))&
((?[X]:((~funny(X)&old(X))))=>(?[X]:((~brave(X)|~kind(X)))))&
(![X]:((~strong(X)&old(X))<=>(~humble(X)|~wise(X))))&
(((~creative(mary)&old(mary)))<=>(?[X]:((~kind(X)|creative(X)))))&
(![X]:((~strong(X)|calm(X))<=>(old(X)&funny(X))))&
((~creative(paul)<~>rich(paul)))&
(?[X]:((~happy(X)<~>patient(X))))&
(?[X]:((calm(X)|~kind(X))))&
(strong(lucy))&
(?[X]:((~humble(X)|patient(X)))) | funny(paul) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 6338305414914171071800929
% SZS output start Proof for 6338305414914171071800929
4. ! [X0] : ((funny(X0) | ~tall(X0)) => ~funny(X0)) [input p3]
22. funny(paul) [input hypothesis]
29. ! [X0] : (~funny(X0) | (~funny(X0) & tall(X0))) [ennf transformation 4]
84. ~funny(X0) | ~funny(X0) [cnf transformation 29]
127. funny(paul) [cnf transformation 22]
128. ~funny(X0) [duplicate literal removal 84]
291. $false [subsumption resolution 127,128]
% SZS output end Proof for 6338305414914171071800929
% ------------------------------
% 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 funny or not calm is humble or old and vice versa. If someone is wise or tall then someone is either not wise or not rich and vice versa. Everyone who is wise is not curious and vice versa. Everyone who is both not wise and not rich is not wise or not rich and vice versa. Everyone who is not wise or not generous is curious. Everyone who is either old or not kind is both quiet and not wise and vice versa. If someone is not happy then someone is either not creative or calm and vice versa. If someone is humble or not curious then susan is old and vice versa. Everyone who is either happy or not rich is brave. Everyone who is happy or not tall is either rich or brave and vice versa. Everyone who is either not quiet or not kind is both strong and brave. Everyone who is either quiet or old is either not happy or not calm and vice versa. If lucy is wise then someone is not old. If someone is both not humble and not calm then someone is both old and tall. If someone is quiet or generous then someone is either not calm or humble and vice versa. If someone is either calm or not old then someone is strong. Someone is either not tall or not generous. Someone is not quiet or not creative. Alice is not creative or quiet. Fred is both not humble and not wise. Someone is either brave or not kind. Someone is either generous or calm. John is tall or not rich. | Fred is not tall. | entailment | (![X]:((funny(X)|~calm(X))<=>(humble(X)|old(X))))&
((?[X]:((wise(X)|tall(X))))<=>(?[X]:((~wise(X)<~>~rich(X)))))&
(![X]:(wise(X)<=>~curious(X)))&
(![X]:((~wise(X)&~rich(X))<=>(~wise(X)|~rich(X))))&
(![X]:((~wise(X)|~generous(X))=>curious(X)))&
(![X]:((old(X)<~>~kind(X))<=>(quiet(X)&~wise(X))))&
((?[X]:(~happy(X)))<=>(?[X]:((~creative(X)<~>calm(X)))))&
((?[X]:((humble(X)|~curious(X))))<=>(old(susan)))&
(![X]:((happy(X)<~>~rich(X))=>brave(X)))&
(![X]:((happy(X)|~tall(X))<=>(rich(X)<~>brave(X))))&
(![X]:((~quiet(X)<~>~kind(X))=>(strong(X)&brave(X))))&
(![X]:((quiet(X)<~>old(X))<=>(~happy(X)<~>~calm(X))))&
((wise(lucy))=>(?[X]:(~old(X))))&
((?[X]:((~humble(X)&~calm(X))))=>(?[X]:((old(X)&tall(X)))))&
((?[X]:((quiet(X)|generous(X))))<=>(?[X]:((~calm(X)<~>humble(X)))))&
((?[X]:((calm(X)<~>~old(X))))=>(?[X]:(strong(X))))&
(?[X]:((~tall(X)<~>~generous(X))))&
(?[X]:((~quiet(X)|~creative(X))))&
((~creative(alice)|quiet(alice)))&
((~humble(fred)&~wise(fred)))&
(?[X]:((brave(X)<~>~kind(X))))&
(?[X]:((generous(X)<~>calm(X))))&
((tall(john)|~rich(john))) | ~tall(fred) | [
"p1",
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 7952607346352367723129867
% SZS output start Proof for 7952607346352367723129867
2. ? [X0] : (tall(X0) | wise(X0)) <=> ? [X0] : (~wise(X0) <~> ~rich(X0)) [input p1]
4. ! [X0] : ((~rich(X0) & ~wise(X0)) <=> (~rich(X0) | ~wise(X0))) [input p3]
24. tall(fred) [input hypothesis]
25. ? [X0] : (tall(X0) | wise(X0)) <=> ? [X1] : (~wise(X1) <~> ~rich(X1)) [rectify 2]
39. (? [X0] : (tall(X0) | wise(X0)) | ! [X1] : ((~wise(X1) | rich(X1)) & (~rich(X1) | wise(X1)))) & (? [X1] : ((rich(X1) | wise(X1)) & (~rich(X1) | ~wise(X1))) | ! [X0] : (~tall(X0) & ~wise(X0))) [nnf transformation 25]
40. (? [X0] : (tall(X0) | wise(X0)) | ! [X1] : ((~wise(X1) | rich(X1)) & (~rich(X1) | wise(X1)))) & (? [X2] : ((rich(X2) | wise(X2)) & (~rich(X2) | ~wise(X2))) | ! [X3] : (~tall(X3) & ~wise(X3))) [rectify 39]
41. ? [X0] : (tall(X0) | wise(X0)) => (tall(sK0) | wise(sK0)) [choice axiom]
42. ? [X2] : ((rich(X2) | wise(X2)) & (~rich(X2) | ~wise(X2))) => ((rich(sK1) | wise(sK1)) & (~rich(sK1) | ~wise(sK1))) [choice axiom]
43. ((tall(sK0) | wise(sK0)) | ! [X1] : ((~wise(X1) | rich(X1)) & (~rich(X1) | wise(X1)))) & (((rich(sK1) | wise(sK1)) & (~rich(sK1) | ~wise(sK1))) | ! [X3] : (~tall(X3) & ~wise(X3))) [skolemisation 40,42,41]
45. ! [X0] : (((~rich(X0) & ~wise(X0)) | (rich(X0) & wise(X0))) & ((~rich(X0) | ~wise(X0)) | (rich(X0) | wise(X0)))) [nnf transformation 4]
46. ! [X0] : (((~rich(X0) & ~wise(X0)) | (rich(X0) & wise(X0))) & (~rich(X0) | ~wise(X0) | rich(X0) | wise(X0))) [flattening 45]
89. ~rich(sK1) | ~wise(sK1) | ~tall(X3) [cnf transformation 43]
91. rich(sK1) | wise(sK1) | ~tall(X3) [cnf transformation 43]
98. ~wise(X0) | rich(X0) [cnf transformation 46]
99. ~rich(X0) | wise(X0) [cnf transformation 46]
154. tall(fred) [cnf transformation 24]
156. 1 <=> ! [X1] : (~wise(X1) | rich(X1)) [avatar definition]
157. ~wise(X1) | rich(X1) <- (1) [avatar component clause 156]
168. 4 <=> ! [X1] : (~rich(X1) | wise(X1)) [avatar definition]
169. ~rich(X1) | wise(X1) <- (4) [avatar component clause 168]
172. 5 <=> ! [X3] : ~tall(X3) [avatar definition]
173. ~tall(X3) <- (5) [avatar component clause 172]
175. 6 <=> wise(sK1) [avatar definition]
176. ~wise(sK1) <- (~6) [avatar component clause 175]
177. wise(sK1) <- (6) [avatar component clause 175]
179. 7 <=> rich(sK1) [avatar definition]
180. ~rich(sK1) <- (~7) [avatar component clause 179]
181. rich(sK1) <- (7) [avatar component clause 179]
182. 5 | 6 | 7 [avatar split clause 91,179,175,172]
187. 5 | ~6 | ~7 [avatar split clause 89,179,175,172]
189. 4 [avatar split clause 99,168]
190. 1 [avatar split clause 98,156]
355. rich(sK1) <- (1, 6) [resolution 157,177]
357. $false <- (1, 6, ~7) [subsumption resolution 355,180]
358. ~1 | ~6 | 7 [avatar contradiction clause 357]
359. wise(sK1) <- (4, 7) [resolution 169,181]
360. $false <- (4, ~6, 7) [subsumption resolution 359,176]
361. ~4 | 6 | ~7 [avatar contradiction clause 360]
362. $false <- (5) [resolution 173,154]
365. ~5 [avatar contradiction clause 362]
366. $false [avatar sat refutation 182,187,189,190,358,361,365]
% SZS output end Proof for 7952607346352367723129867
% ------------------------------
% 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 alice is either humble or not old then someone is funny. If paul is either curious or not creative then someone is not wise. Everyone who is not brave is both not tall and creative and vice versa. Everyone who is both calm and not quiet is either not quiet or not happy. If john is not old or not quiet then paul is tall or not happy and vice versa. Everyone who is old is not tall or humble and vice versa. Everyone who is not generous is both humble and happy. Everyone who is either not wise or not generous is funny. Everyone who is wise is funny and vice versa. Everyone who is not humble is not strong. If someone is either not funny or not brave then susan is not brave. Everyone who is either not wise or calm is both old and kind and vice versa. Everyone who is both not wise and wise is brave or not happy. If someone is both patient and not quiet then lucy is generous or not brave. If someone is both funny and not patient then paul is either tall or happy and vice versa. If alice is either not curious or not funny then someone is not wise and vice versa. Paul is not kind or not tall. Someone is wise. Someone is either not wise or not rich. Paul is both not happy and not strong. Someone is not rich. Someone is not tall or rich. John is not wise or not creative. | Lucy is not brave. | neutral | (((humble(alice)<~>~old(alice)))=>(?[X]:(funny(X))))&
(((curious(paul)<~>~creative(paul)))=>(?[X]:(~wise(X))))&
(![X]:(~brave(X)<=>(~tall(X)&creative(X))))&
(![X]:((calm(X)&~quiet(X))=>(~quiet(X)<~>~happy(X))))&
(((~old(john)|~quiet(john)))<=>((tall(paul)|~happy(paul))))&
(![X]:(old(X)<=>(~tall(X)|humble(X))))&
(![X]:(~generous(X)=>(humble(X)&happy(X))))&
(![X]:((~wise(X)<~>~generous(X))=>funny(X)))&
(![X]:(wise(X)<=>funny(X)))&
(![X]:(~humble(X)=>~strong(X)))&
((?[X]:((~funny(X)<~>~brave(X))))=>(~brave(susan)))&
(![X]:((~wise(X)<~>calm(X))<=>(old(X)&kind(X))))&
(![X]:((~wise(X)&wise(X))=>(brave(X)|~happy(X))))&
((?[X]:((patient(X)&~quiet(X))))=>((generous(lucy)|~brave(lucy))))&
((?[X]:((funny(X)&~patient(X))))<=>((tall(paul)<~>happy(paul))))&
(((~curious(alice)<~>~funny(alice)))<=>(?[X]:(~wise(X))))&
((~kind(paul)|~tall(paul)))&
(?[X]:(wise(X)))&
(?[X]:((~wise(X)<~>~rich(X))))&
((~happy(paul)&~strong(paul)))&
(?[X]:(~rich(X)))&
(?[X]:((~tall(X)|rich(X))))&
((~wise(john)|~creative(john))) | ~brave(lucy) | [] | null | 0 |
If lucy is not brave or strong then susan is both not generous and wise and vice versa.
Everyone who is either not humble or strong is happy.
If someone is funny or curious then someone is not humble or not generous and vice versa.
Everyone who is either not wise or not brave is not quiet.
Everyone who is both happy and old is not happy or quiet.
If someone is both not kind and not tall then someone is either curious or not creative.
Everyone who is both not happy and rich is rich or curious and vice versa.
If someone is either humble or old then paul is either patient or happy.
If someone is calm or generous then someone is not old.
Everyone who is quiet or funny is either not patient or not calm.
If someone is kind then paul is curious and vice versa.
If someone is both not curious and brave then someone is not old or not funny.
Everyone who is old or not humble is not humble or not patient and vice versa.
Everyone who is both humble and not calm is both happy and kind.
Everyone who is tall is either kind or not brave and vice versa.
Everyone who is not old or quiet is both brave and patient and vice versa.
Someone is both not wise and kind.
Someone is either not old or not funny.
Someone is funny.
Someone is both patient and not curious.
Someone is either calm or kind.
Someone is not brave or happy.
Someone is not strong.
Someone is funny or not creative. | Susan is not generous. | neutral | (((~brave(lucy)|strong(lucy)))<=>((~generous(susan)&wise(susan))))&
(![X]:((~humble(X)<~>strong(X))=>happy(X)))&
((?[X]:((funny(X)|curious(X))))<=>(?[X]:((~humble(X)|~generous(X)))))&
(![X]:((~wise(X)<~>~brave(X))=>~quiet(X)))&
(![X]:((happy(X)&old(X))=>(~happy(X)|quiet(X))))&
((?[X]:((~kind(X)&~tall(X))))=>(?[X]:((curious(X)<~>~creative(X)))))&
(![X]:((~happy(X)&rich(X))<=>(rich(X)|curious(X))))&
((?[X]:((humble(X)<~>old(X))))=>((patient(paul)<~>happy(paul))))&
((?[X]:((calm(X)|generous(X))))=>(?[X]:(~old(X))))&
(![X]:((quiet(X)|funny(X))=>(~patient(X)<~>~calm(X))))&
((?[X]:(kind(X)))<=>(curious(paul)))&
((?[X]:((~curious(X)&brave(X))))=>(?[X]:((~old(X)|~funny(X)))))&
(![X]:((old(X)|~humble(X))<=>(~humble(X)|~patient(X))))&
(![X]:((humble(X)&~calm(X))=>(happy(X)&kind(X))))&
(![X]:(tall(X)<=>(kind(X)<~>~brave(X))))&
(![X]:((~old(X)|quiet(X))<=>(brave(X)&patient(X))))&
(?[X]:((~wise(X)&kind(X))))&
(?[X]:((~old(X)<~>~funny(X))))&
(?[X]:(funny(X)))&
(?[X]:((patient(X)&~curious(X))))&
(?[X]:((calm(X)<~>kind(X))))&
(?[X]:((~brave(X)|happy(X))))&
(?[X]:(~strong(X)))&
(?[X]:((funny(X)|~creative(X)))) | ~generous(susan) | [] | null | 0 |
Everyone who is not strong or not brave is happy and vice versa.
If paul is both not curious and strong then someone is both not humble and happy.
If paul is both calm and not old then someone is curious and vice versa.
Everyone who is not wise is not quiet.
If someone is quiet or not strong then someone is both not quiet and not calm and vice versa.
If paul is humble or not kind then someone is either funny or old and vice versa.
If someone is not calm then susan is not curious and vice versa.
Everyone who is both not wise and not happy is both not curious and curious and vice versa.
Everyone who is not patient is kind and vice versa.
If mary is kind or not quiet then someone is both creative and humble.
Everyone who is both rich and brave is both funny and not curious and vice versa.
Everyone who is either curious or not curious is both not generous and not happy and vice versa.
If lucy is generous or not rich then paul is either not humble or strong.
If lucy is both funny and not rich then mary is either kind or curious and vice versa.
If someone is both wise and not calm then someone is wise or curious and vice versa.
If lucy is either not happy or not rich then someone is both not wise and not generous.
Someone is kind.
Someone is both humble and creative.
Someone is not strong or not kind.
Someone is creative or not calm.
Someone is both quiet and calm.
Someone is old.
Mary is both not generous and not tall.
Mary is not quiet. | Paul is not generous. | entailment | (![X]:((~strong(X)|~brave(X))<=>happy(X)))&
(((~curious(paul)&strong(paul)))=>(?[X]:((~humble(X)&happy(X)))))&
(((calm(paul)&~old(paul)))<=>(?[X]:(curious(X))))&
(![X]:(~wise(X)=>~quiet(X)))&
((?[X]:((quiet(X)|~strong(X))))<=>(?[X]:((~quiet(X)&~calm(X)))))&
(((humble(paul)|~kind(paul)))<=>(?[X]:((funny(X)<~>old(X)))))&
((?[X]:(~calm(X)))<=>(~curious(susan)))&
(![X]:((~wise(X)&~happy(X))<=>(~curious(X)&curious(X))))&
(![X]:(~patient(X)<=>kind(X)))&
(((kind(mary)|~quiet(mary)))=>(?[X]:((creative(X)&humble(X)))))&
(![X]:((rich(X)&brave(X))<=>(funny(X)&~curious(X))))&
(![X]:((curious(X)<~>~curious(X))<=>(~generous(X)&~happy(X))))&
(((generous(lucy)|~rich(lucy)))=>((~humble(paul)<~>strong(paul))))&
(((funny(lucy)&~rich(lucy)))<=>((kind(mary)<~>curious(mary))))&
((?[X]:((wise(X)&~calm(X))))<=>(?[X]:((wise(X)|curious(X)))))&
(((~happy(lucy)<~>~rich(lucy)))=>(?[X]:((~wise(X)&~generous(X)))))&
(?[X]:(kind(X)))&
(?[X]:((humble(X)&creative(X))))&
(?[X]:((~strong(X)|~kind(X))))&
(?[X]:((creative(X)|~calm(X))))&
(?[X]:((quiet(X)&calm(X))))&
(?[X]:(old(X)))&
((~generous(mary)&~tall(mary)))&
(~quiet(mary)) | ~generous(paul) | [
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 646356962453032609768758
% SZS output start Proof for 646356962453032609768758
12. ! [X0] : ((curious(X0) <~> ~curious(X0)) <=> (~happy(X0) & ~generous(X0))) [input p11]
25. generous(paul) [input hypothesis]
67. ! [X0] : ((((curious(X0) | ~curious(X0)) & (~curious(X0) | curious(X0))) | (happy(X0) | generous(X0))) & ((~happy(X0) & ~generous(X0)) | ((curious(X0) | curious(X0)) & (~curious(X0) | ~curious(X0))))) [nnf transformation 12]
68. ! [X0] : ((((curious(X0) | ~curious(X0)) & (~curious(X0) | curious(X0))) | happy(X0) | generous(X0)) & ((~happy(X0) & ~generous(X0)) | ((curious(X0) | curious(X0)) & (~curious(X0) | ~curious(X0))))) [flattening 67]
122. ~generous(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 68]
123. ~generous(X0) | curious(X0) | curious(X0) [cnf transformation 68]
155. generous(paul) [cnf transformation 25]
156. ~generous(X0) | ~curious(X0) [duplicate literal removal 122]
157. ~generous(X0) | curious(X0) [duplicate literal removal 123]
283. ~generous(X0) [subsumption resolution 156,157]
347. $false [subsumption resolution 155,283]
% SZS output end Proof for 646356962453032609768758
% ------------------------------
% 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 alice is not creative or old then lucy is tall or patient and vice versa. If alice is wise or not rich then susan is not old or tall. Everyone who is not happy or not kind is both not strong and tall. Everyone who is either not old or not quiet is either not creative or strong and vice versa. If susan is generous then fred is either not old or not brave and vice versa. Everyone who is both not generous and strong is not rich or old and vice versa. If someone is not kind then susan is either rich or not rich and vice versa. If someone is both quiet and rich then someone is creative and vice versa. If lucy is not brave or not creative then someone is tall or not creative and vice versa. If someone is happy or wise then fred is not calm and vice versa. Everyone who is not quiet is either not tall or not calm and vice versa. Everyone who is patient is both not old and generous. Everyone who is both happy and funny is either funny or not kind and vice versa. Everyone who is either calm or not funny is either rich or curious and vice versa. Everyone who is not kind is rich. If someone is creative then someone is old or not calm and vice versa. Someone is either not old or not creative. Someone is not calm. Fred is both not curious and funny. Mary is either quiet or wise. John is calm or patient. Fred is both creative and not rich. Someone is calm. Someone is both wise and happy. | Fred is happy. | entailment | (((~creative(alice)|old(alice)))<=>((tall(lucy)|patient(lucy))))&
(((wise(alice)|~rich(alice)))=>((~old(susan)|tall(susan))))&
(![X]:((~happy(X)|~kind(X))=>(~strong(X)&tall(X))))&
(![X]:((~old(X)<~>~quiet(X))<=>(~creative(X)<~>strong(X))))&
((generous(susan))<=>((~old(fred)<~>~brave(fred))))&
(![X]:((~generous(X)&strong(X))<=>(~rich(X)|old(X))))&
((?[X]:(~kind(X)))<=>((rich(susan)<~>~rich(susan))))&
((?[X]:((quiet(X)&rich(X))))<=>(?[X]:(creative(X))))&
(((~brave(lucy)|~creative(lucy)))<=>(?[X]:((tall(X)|~creative(X)))))&
((?[X]:((happy(X)|wise(X))))<=>(~calm(fred)))&
(![X]:(~quiet(X)<=>(~tall(X)<~>~calm(X))))&
(![X]:(patient(X)=>(~old(X)&generous(X))))&
(![X]:((happy(X)&funny(X))<=>(funny(X)<~>~kind(X))))&
(![X]:((calm(X)<~>~funny(X))<=>(rich(X)<~>curious(X))))&
(![X]:(~kind(X)=>rich(X)))&
((?[X]:(creative(X)))<=>(?[X]:((old(X)|~calm(X)))))&
(?[X]:((~old(X)<~>~creative(X))))&
(?[X]:(~calm(X)))&
((~curious(fred)&funny(fred)))&
((quiet(mary)<~>wise(mary)))&
((calm(john)|patient(john)))&
((creative(fred)&~rich(fred)))&
(?[X]:(calm(X)))&
(?[X]:((wise(X)&happy(X)))) | happy(fred) | [
"p12",
"p14",
"p18",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 5703620361068358415815978
% SZS output start Proof for 5703620361068358415815978
13. ! [X0] : ((funny(X0) & happy(X0)) <=> (funny(X0) <~> ~kind(X0))) [input p12]
15. ! [X0] : (~kind(X0) => rich(X0)) [input p14]
19. funny(fred) & ~curious(fred) [input p18]
22. ~rich(fred) & creative(fred) [input p21]
25. ~happy(fred) [input hypothesis]
32. ! [X0] : (rich(X0) | kind(X0)) [ennf transformation 15]
58. ! [X0] : (((funny(X0) & happy(X0)) | ((funny(X0) | kind(X0)) & (~kind(X0) | ~funny(X0)))) & (((kind(X0) | ~funny(X0)) & (~kind(X0) | funny(X0))) | (~funny(X0) | ~happy(X0)))) [nnf transformation 13]
59. ! [X0] : (((funny(X0) & happy(X0)) | ((funny(X0) | kind(X0)) & (~kind(X0) | ~funny(X0)))) & (((kind(X0) | ~funny(X0)) & (~kind(X0) | funny(X0))) | ~funny(X0) | ~happy(X0))) [flattening 58]
125. ~funny(X0) | ~kind(X0) | happy(X0) [cnf transformation 59]
137. kind(X0) | rich(X0) [cnf transformation 32]
145. funny(fred) [cnf transformation 19]
150. ~rich(fred) [cnf transformation 22]
154. ~happy(fred) [cnf transformation 25]
437. ~kind(fred) | happy(fred) [resolution 125,145]
439. ~kind(fred) [subsumption resolution 437,154]
581. rich(fred) [resolution 439,137]
583. $false [subsumption resolution 581,150]
% SZS output end Proof for 5703620361068358415815978
% ------------------------------
% 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 either wise or not patient is either not calm or old and vice versa.
Everyone who is both funny and tall is both not funny and happy and vice versa.
Everyone who is both brave and kind is old and vice versa.
If john is both brave and curious then mary is creative.
If john is wise or not quiet then lucy is quiet.
Everyone who is strong or not old is either humble or not rich.
Everyone who is old or not funny is not tall.
If someone is both not creative and quiet then someone is patient or brave.
Everyone who is not generous or rich is either generous or not quiet.
Everyone who is brave or tall is either calm or patient.
If mary is both wise and humble then someone is either creative or not strong and vice versa.
If mary is either not generous or quiet then someone is kind or not humble.
Everyone who is either wise or not funny is not curious.
If john is either not old or kind then someone is not generous or not brave and vice versa.
If someone is not strong then someone is both tall and not curious.
If someone is not patient or not old then someone is both not kind and not strong and vice versa.
Alice is either not rich or not strong.
Someone is not creative.
Someone is either strong or not brave.
Fred is both not curious and not wise. | Lucy is not old. | contradiction | (![X]:((wise(X)<~>~patient(X))<=>(~calm(X)<~>old(X))))&
(![X]:((funny(X)&tall(X))<=>(~funny(X)&happy(X))))&
(![X]:((brave(X)&kind(X))<=>old(X)))&
(((brave(john)&curious(john)))=>(creative(mary)))&
(((wise(john)|~quiet(john)))=>(quiet(lucy)))&
(![X]:((strong(X)|~old(X))=>(humble(X)<~>~rich(X))))&
(![X]:((old(X)|~funny(X))=>~tall(X)))&
((?[X]:((~creative(X)&quiet(X))))=>(?[X]:((patient(X)|brave(X)))))&
(![X]:((~generous(X)|rich(X))=>(generous(X)<~>~quiet(X))))&
(![X]:((brave(X)|tall(X))=>(calm(X)<~>patient(X))))&
(((wise(mary)&humble(mary)))<=>(?[X]:((creative(X)<~>~strong(X)))))&
(((~generous(mary)<~>quiet(mary)))=>(?[X]:((kind(X)|~humble(X)))))&
(![X]:((wise(X)<~>~funny(X))=>~curious(X)))&
(((~old(john)<~>kind(john)))<=>(?[X]:((~generous(X)|~brave(X)))))&
((?[X]:(~strong(X)))=>(?[X]:((tall(X)&~curious(X)))))&
((?[X]:((~patient(X)|~old(X))))<=>(?[X]:((~kind(X)&~strong(X)))))&
((~rich(alice)<~>~strong(alice)))&
(?[X]:(~creative(X)))&
(?[X]:((strong(X)<~>~brave(X))))&
((~curious(fred)&~wise(fred))) | ~old(lucy) | [
"p1",
"p6",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3430598752117877544160284
% SZS output start Proof for 3430598752117877544160284
2. ! [X0] : ((tall(X0) & funny(X0)) <=> (happy(X0) & ~funny(X0))) [input p1]
7. ! [X0] : ((~funny(X0) | old(X0)) => ~tall(X0)) [input p6]
15. ? [X0] : ~strong(X0) => ? [X0] : (~curious(X0) & tall(X0)) [input p14]
16. ? [X0] : (~old(X0) | ~patient(X0)) <=> ? [X0] : (~strong(X0) & ~kind(X0)) [input p15]
21. ~old(lucy) [input hypothesis]
23. ? [X0] : ~strong(X0) => ? [X1] : (~curious(X1) & tall(X1)) [rectify 15]
24. ? [X0] : (~old(X0) | ~patient(X0)) <=> ? [X1] : (~strong(X1) & ~kind(X1)) [rectify 16]
26. ? [X0] : ~strong(X0) => ? [X1] : tall(X1) [pure predicate removal 23]
31. ! [X0] : (~tall(X0) | (funny(X0) & ~old(X0))) [ennf transformation 7]
36. ? [X1] : tall(X1) | ! [X0] : strong(X0) [ennf transformation 26]
38. ! [X0] : (((tall(X0) & funny(X0)) | (~happy(X0) | funny(X0))) & ((happy(X0) & ~funny(X0)) | (~tall(X0) | ~funny(X0)))) [nnf transformation 2]
39. ! [X0] : (((tall(X0) & funny(X0)) | ~happy(X0) | funny(X0)) & ((happy(X0) & ~funny(X0)) | ~tall(X0) | ~funny(X0))) [flattening 38]
60. ? [X0] : tall(X0) | ! [X1] : strong(X1) [rectify 36]
61. ? [X0] : tall(X0) => tall(sK4) [choice axiom]
62. tall(sK4) | ! [X1] : strong(X1) [skolemisation 60,61]
63. (? [X0] : (~old(X0) | ~patient(X0)) | ! [X1] : (strong(X1) | kind(X1))) & (? [X1] : (~strong(X1) & ~kind(X1)) | ! [X0] : (old(X0) & patient(X0))) [nnf transformation 24]
64. (? [X0] : (~old(X0) | ~patient(X0)) | ! [X1] : (strong(X1) | kind(X1))) & (? [X2] : (~strong(X2) & ~kind(X2)) | ! [X3] : (old(X3) & patient(X3))) [rectify 63]
65. ? [X0] : (~old(X0) | ~patient(X0)) => (~old(sK5) | ~patient(sK5)) [choice axiom]
66. ? [X2] : (~strong(X2) & ~kind(X2)) => (~strong(sK6) & ~kind(sK6)) [choice axiom]
67. ((~old(sK5) | ~patient(sK5)) | ! [X1] : (strong(X1) | kind(X1))) & ((~strong(sK6) & ~kind(sK6)) | ! [X3] : (old(X3) & patient(X3))) [skolemisation 64,66,65]
82. ~funny(X0) | ~tall(X0) | ~funny(X0) [cnf transformation 39]
96. ~tall(X0) | funny(X0) [cnf transformation 31]
120. tall(sK4) | strong(X1) [cnf transformation 62]
124. ~strong(sK6) | old(X3) [cnf transformation 67]
132. ~old(lucy) [cnf transformation 21]
134. ~funny(X0) | ~tall(X0) [duplicate literal removal 82]
150. ~tall(X0) [subsumption resolution 96,134]
239. strong(X1) [subsumption resolution 120,150]
240. old(X3) [subsumption resolution 124,239]
244. $false [subsumption resolution 132,240]
% SZS output end Proof for 3430598752117877544160284
% ------------------------------
% 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 old and tall then someone is strong or not generous. Everyone who is both creative and not generous is kind or happy. If someone is either not tall or not quiet then someone is funny or creative and vice versa. Everyone who is either not humble or strong is not happy or not kind. Everyone who is not kind is both creative and not kind. If someone is either not creative or not rich then lucy is wise and vice versa. Everyone who is not patient or funny is either not generous or creative. Everyone who is either humble or not happy is both kind and calm. If someone is both kind and not tall then someone is either not quiet or not rich and vice versa. Everyone who is not strong or not rich is both generous and not patient. Everyone who is both not funny and not tall is wise. If mary is either calm or not wise then someone is not kind. If someone is not strong then john is not happy or tall and vice versa. Everyone who is wise or calm is not creative. Everyone who is both not quiet and not strong is both kind and not wise and vice versa. If someone is either not wise or not quiet then paul is both not patient and brave. Someone is both humble and old. Someone is not funny or quiet. Fred is both not humble and not kind. Someone is either happy or not happy. Someone is not curious or curious. Someone is both creative and not quiet. Paul is wise. Mary is either kind or wise. | Mary is not generous. | contradiction | ((?[X]:((old(X)&tall(X))))=>(?[X]:((strong(X)|~generous(X)))))&
(![X]:((creative(X)&~generous(X))=>(kind(X)|happy(X))))&
((?[X]:((~tall(X)<~>~quiet(X))))<=>(?[X]:((funny(X)|creative(X)))))&
(![X]:((~humble(X)<~>strong(X))=>(~happy(X)|~kind(X))))&
(![X]:(~kind(X)=>(creative(X)&~kind(X))))&
((?[X]:((~creative(X)<~>~rich(X))))<=>(wise(lucy)))&
(![X]:((~patient(X)|funny(X))=>(~generous(X)<~>creative(X))))&
(![X]:((humble(X)<~>~happy(X))=>(kind(X)&calm(X))))&
((?[X]:((kind(X)&~tall(X))))<=>(?[X]:((~quiet(X)<~>~rich(X)))))&
(![X]:((~strong(X)|~rich(X))=>(generous(X)&~patient(X))))&
(![X]:((~funny(X)&~tall(X))=>wise(X)))&
(((calm(mary)<~>~wise(mary)))=>(?[X]:(~kind(X))))&
((?[X]:(~strong(X)))<=>((~happy(john)|tall(john))))&
(![X]:((wise(X)|calm(X))=>~creative(X)))&
(![X]:((~quiet(X)&~strong(X))<=>(kind(X)&~wise(X))))&
((?[X]:((~wise(X)<~>~quiet(X))))=>((~patient(paul)&brave(paul))))&
(?[X]:((humble(X)&old(X))))&
(?[X]:((~funny(X)|quiet(X))))&
((~humble(fred)&~kind(fred)))&
(?[X]:((happy(X)<~>~happy(X))))&
(?[X]:((~curious(X)|curious(X))))&
(?[X]:((creative(X)&~quiet(X))))&
(wise(paul))&
((kind(mary)<~>wise(mary))) | ~generous(mary) | [
"p4",
"p9",
"p13",
"p14",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 155782744415860153138658
% SZS output start Proof for 155782744415860153138658
5. ! [X0] : (~kind(X0) => (~kind(X0) & creative(X0))) [input p4]
10. ! [X0] : ((~rich(X0) | ~strong(X0)) => (~patient(X0) & generous(X0))) [input p9]
14. ! [X0] : ((calm(X0) | wise(X0)) => ~creative(X0)) [input p13]
15. ! [X0] : ((~strong(X0) & ~quiet(X0)) <=> (~wise(X0) & kind(X0))) [input p14]
24. kind(mary) <~> wise(mary) [input p23]
25. ~generous(mary) [input hypothesis]
35. ! [X0] : ((~kind(X0) & creative(X0)) | kind(X0)) [ennf transformation 5]
38. ! [X0] : ((~patient(X0) & generous(X0)) | (rich(X0) & strong(X0))) [ennf transformation 10]
42. ! [X0] : (~creative(X0) | (~calm(X0) & ~wise(X0))) [ennf transformation 14]
72. ! [X0] : (((~strong(X0) & ~quiet(X0)) | (wise(X0) | ~kind(X0))) & ((~wise(X0) & kind(X0)) | (strong(X0) | quiet(X0)))) [nnf transformation 15]
73. ! [X0] : (((~strong(X0) & ~quiet(X0)) | wise(X0) | ~kind(X0)) & ((~wise(X0) & kind(X0)) | strong(X0) | quiet(X0))) [flattening 72]
86. (~wise(mary) | ~kind(mary)) & (wise(mary) | kind(mary)) [nnf transformation 24]
97. kind(X0) | creative(X0) [cnf transformation 35]
117. generous(X0) | strong(X0) [cnf transformation 38]
127. ~wise(X0) | ~creative(X0) [cnf transformation 42]
132. ~kind(X0) | wise(X0) | ~strong(X0) [cnf transformation 73]
146. wise(mary) | kind(mary) [cnf transformation 86]
147. ~wise(mary) | ~kind(mary) [cnf transformation 86]
148. ~generous(mary) [cnf transformation 25]
249. 24 <=> wise(mary) [avatar definition]
250. ~wise(mary) <- (~24) [avatar component clause 249]
251. wise(mary) <- (24) [avatar component clause 249]
302. 36 <=> kind(mary) [avatar definition]
303. kind(mary) <- (36) [avatar component clause 302]
304. ~kind(mary) <- (~36) [avatar component clause 302]
305. ~36 | ~24 [avatar split clause 147,249,302]
306. 36 | 24 [avatar split clause 146,249,302]
309. creative(mary) <- (~36) [resolution 97,304]
310. strong(mary) [resolution 117,148]
316. ~creative(mary) <- (24) [resolution 127,251]
317. $false <- (24, ~36) [subsumption resolution 316,309]
318. ~24 | 36 [avatar contradiction clause 317]
462. wise(mary) | ~strong(mary) <- (36) [resolution 132,303]
465. ~strong(mary) <- (~24, 36) [subsumption resolution 462,250]
466. $false <- (~24, 36) [subsumption resolution 465,310]
467. 24 | ~36 [avatar contradiction clause 466]
477. $false [avatar sat refutation 305,306,318,467]
% SZS output end Proof for 155782744415860153138658
% ------------------------------
% 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 humble or not quiet then someone is not strong and vice versa. Everyone who is either brave or quiet is creative or brave and vice versa. If susan is not creative then fred is both not curious and quiet and vice versa. Everyone who is both not quiet and not rich is both not humble and quiet and vice versa. If mary is calm then someone is both calm and not curious and vice versa. Everyone who is either patient or not calm is quiet or creative and vice versa. Everyone who is not humble is both not old and not generous and vice versa. If fred is not tall or not kind then susan is either curious or not calm. Everyone who is both not kind and generous is both not calm and not generous. Everyone who is both not rich and not calm is both not funny and creative and vice versa. If susan is both not funny and tall then someone is either kind or not happy and vice versa. If john is not funny or curious then lucy is either patient or old and vice versa. If someone is old or not quiet then susan is either creative or funny and vice versa. If someone is not funny or wise then someone is not old. If fred is not strong or not kind then someone is both rich and tall and vice versa. Everyone who is patient or calm is both not kind and not tall and vice versa. Someone is both brave and humble. Someone is either not old or not strong. Someone is not humble or not patient. Fred is both not generous and brave. Someone is creative. Someone is curious. Paul is either not strong or tall. Someone is either not rich or not wise. | Susan is not funny. | entailment | ((?[X]:((~humble(X)|~quiet(X))))<=>(?[X]:(~strong(X))))&
(![X]:((brave(X)<~>quiet(X))<=>(creative(X)|brave(X))))&
((~creative(susan))<=>((~curious(fred)&quiet(fred))))&
(![X]:((~quiet(X)&~rich(X))<=>(~humble(X)&quiet(X))))&
((calm(mary))<=>(?[X]:((calm(X)&~curious(X)))))&
(![X]:((patient(X)<~>~calm(X))<=>(quiet(X)|creative(X))))&
(![X]:(~humble(X)<=>(~old(X)&~generous(X))))&
(((~tall(fred)|~kind(fred)))=>((curious(susan)<~>~calm(susan))))&
(![X]:((~kind(X)&generous(X))=>(~calm(X)&~generous(X))))&
(![X]:((~rich(X)&~calm(X))<=>(~funny(X)&creative(X))))&
(((~funny(susan)&tall(susan)))<=>(?[X]:((kind(X)<~>~happy(X)))))&
(((~funny(john)|curious(john)))<=>((patient(lucy)<~>old(lucy))))&
((?[X]:((old(X)|~quiet(X))))<=>((creative(susan)<~>funny(susan))))&
((?[X]:((~funny(X)|wise(X))))=>(?[X]:(~old(X))))&
(((~strong(fred)|~kind(fred)))<=>(?[X]:((rich(X)&tall(X)))))&
(![X]:((patient(X)|calm(X))<=>(~kind(X)&~tall(X))))&
(?[X]:((brave(X)&humble(X))))&
(?[X]:((~old(X)<~>~strong(X))))&
(?[X]:((~humble(X)|~patient(X))))&
((~generous(fred)&brave(fred)))&
(?[X]:(creative(X)))&
(?[X]:(curious(X)))&
((~strong(paul)<~>tall(paul)))&
(?[X]:((~rich(X)<~>~wise(X)))) | ~funny(susan) | [
"p1",
"p2",
"p12",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 5358850419210143078614350
% SZS output start Proof for 5358850419210143078614350
2. ! [X0] : ((brave(X0) <~> quiet(X0)) <=> (brave(X0) | creative(X0))) [input p1]
3. ~creative(susan) <=> (quiet(fred) & ~curious(fred)) [input p2]
13. ? [X0] : (~quiet(X0) | old(X0)) <=> (creative(susan) <~> funny(susan)) [input p12]
20. brave(fred) & ~generous(fred) [input p19]
25. funny(susan) [input hypothesis]
37. ! [X0] : ((((~quiet(X0) | ~brave(X0)) & (quiet(X0) | brave(X0))) | (~brave(X0) & ~creative(X0))) & ((brave(X0) | creative(X0)) | ((brave(X0) | ~quiet(X0)) & (quiet(X0) | ~brave(X0))))) [nnf transformation 2]
38. ! [X0] : ((((~quiet(X0) | ~brave(X0)) & (quiet(X0) | brave(X0))) | (~brave(X0) & ~creative(X0))) & (brave(X0) | creative(X0) | ((brave(X0) | ~quiet(X0)) & (quiet(X0) | ~brave(X0))))) [flattening 37]
39. (~creative(susan) | (~quiet(fred) | curious(fred))) & ((quiet(fred) & ~curious(fred)) | creative(susan)) [nnf transformation 3]
40. (~creative(susan) | ~quiet(fred) | curious(fred)) & ((quiet(fred) & ~curious(fred)) | creative(susan)) [flattening 39]
61. (? [X0] : (~quiet(X0) | old(X0)) | ((creative(susan) | ~funny(susan)) & (funny(susan) | ~creative(susan)))) & (((~funny(susan) | ~creative(susan)) & (funny(susan) | creative(susan))) | ! [X0] : (quiet(X0) & ~old(X0))) [nnf transformation 13]
62. (? [X0] : (~quiet(X0) | old(X0)) | ((creative(susan) | ~funny(susan)) & (funny(susan) | ~creative(susan)))) & (((~funny(susan) | ~creative(susan)) & (funny(susan) | creative(susan))) | ! [X1] : (quiet(X1) & ~old(X1))) [rectify 61]
63. ? [X0] : (~quiet(X0) | old(X0)) => (~quiet(sK4) | old(sK4)) [choice axiom]
64. ((~quiet(sK4) | old(sK4)) | ((creative(susan) | ~funny(susan)) & (funny(susan) | ~creative(susan)))) & (((~funny(susan) | ~creative(susan)) & (funny(susan) | creative(susan))) | ! [X1] : (quiet(X1) & ~old(X1))) [skolemisation 62,63]
98. ~quiet(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 38]
100. quiet(fred) | creative(susan) [cnf transformation 40]
143. ~funny(susan) | ~creative(susan) | quiet(X1) [cnf transformation 64]
164. brave(fred) [cnf transformation 20]
171. funny(susan) [cnf transformation 25]
176. ~brave(X0) | ~quiet(X0) [duplicate literal removal 98]
190. 4 <=> ! [X3] : quiet(X3) [avatar definition]
191. quiet(X3) <- (4) [avatar component clause 190]
207. 8 <=> quiet(fred) [avatar definition]
209. ~quiet(fred) <- (~8) [avatar component clause 207]
211. 9 <=> creative(susan) [avatar definition]
215. 9 | 8 [avatar split clause 100,207,211]
270. 21 <=> funny(susan) [avatar definition]
317. 4 | ~9 | ~21 [avatar split clause 143,270,211,190]
395. 21 [avatar split clause 171,270]
402. ~quiet(fred) [resolution 176,164]
405. ~8 [avatar split clause 402,207]
422. $false <- (4, ~8) [resolution 209,191]
423. ~4 | 8 [avatar contradiction clause 422]
424. $false [avatar sat refutation 215,317,395,405,423]
% SZS output end Proof for 5358850419210143078614350
% ------------------------------
% 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: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both patient and not funny is not kind or creative.
If fred is both generous and rich then paul is either funny or wise and vice versa.
If alice is either old or not calm then john is curious.
Everyone who is both not wise and not funny is either funny or generous and vice versa.
If mary is funny then someone is either patient or not funny and vice versa.
If someone is kind or not wise then paul is brave or not tall.
Everyone who is both not wise and quiet is not calm.
If someone is not generous then someone is either rich or not patient and vice versa.
Everyone who is calm or not generous is rich.
Everyone who is both not happy and not brave is either not calm or tall.
If john is not generous or not happy then paul is tall or not wise.
If someone is either curious or not kind then susan is wise or creative and vice versa.
Everyone who is creative is not creative.
Everyone who is both not happy and tall is calm or not old and vice versa.
Everyone who is either rich or not generous is both happy and not curious and vice versa.
Everyone who is curious is either not brave or curious.
Paul is both kind and not funny.
Susan is both not happy and not wise.
Someone is both not funny and humble.
Paul is either funny or calm.
Someone is funny or not rich.
Lucy is either not kind or quiet.
Someone is not patient or not tall. | Fred is rich. | entailment | (![X]:((patient(X)&~funny(X))=>(~kind(X)|creative(X))))&
(((generous(fred)&rich(fred)))<=>((funny(paul)<~>wise(paul))))&
(((old(alice)<~>~calm(alice)))=>(curious(john)))&
(![X]:((~wise(X)&~funny(X))<=>(funny(X)<~>generous(X))))&
((funny(mary))<=>(?[X]:((patient(X)<~>~funny(X)))))&
((?[X]:((kind(X)|~wise(X))))=>((brave(paul)|~tall(paul))))&
(![X]:((~wise(X)&quiet(X))=>~calm(X)))&
((?[X]:(~generous(X)))<=>(?[X]:((rich(X)<~>~patient(X)))))&
(![X]:((calm(X)|~generous(X))=>rich(X)))&
(![X]:((~happy(X)&~brave(X))=>(~calm(X)<~>tall(X))))&
(((~generous(john)|~happy(john)))=>((tall(paul)|~wise(paul))))&
((?[X]:((curious(X)<~>~kind(X))))<=>((wise(susan)|creative(susan))))&
(![X]:(creative(X)=>~creative(X)))&
(![X]:((~happy(X)&tall(X))<=>(calm(X)|~old(X))))&
(![X]:((rich(X)<~>~generous(X))<=>(happy(X)&~curious(X))))&
(![X]:(curious(X)=>(~brave(X)<~>curious(X))))&
((kind(paul)&~funny(paul)))&
((~happy(susan)&~wise(susan)))&
(?[X]:((~funny(X)&humble(X))))&
((funny(paul)<~>calm(paul)))&
(?[X]:((funny(X)|~rich(X))))&
((~kind(lucy)<~>quiet(lucy)))&
(?[X]:((~patient(X)|~tall(X)))) | rich(fred) | [
"p1",
"p3",
"p8",
"p13",
"p14",
"p16",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 7337341890492613613868220
% SZS output start Proof for 7337341890492613613868220
2. (rich(fred) & generous(fred)) <=> (funny(paul) <~> wise(paul)) [input p1]
4. ! [X0] : ((~funny(X0) & ~wise(X0)) <=> (funny(X0) <~> generous(X0))) [input p3]
9. ! [X0] : ((~generous(X0) | calm(X0)) => rich(X0)) [input p8]
14. ! [X0] : ((tall(X0) & ~happy(X0)) <=> (~old(X0) | calm(X0))) [input p13]
15. ! [X0] : ((rich(X0) <~> ~generous(X0)) <=> (~curious(X0) & happy(X0))) [input p14]
17. ~funny(paul) & kind(paul) [input p16]
20. funny(paul) <~> calm(paul) [input p19]
24. ~rich(fred) [input hypothesis]
34. ! [X0] : (rich(X0) | (generous(X0) & ~calm(X0))) [ennf transformation 9]
41. ((rich(fred) & generous(fred)) | ((funny(paul) | ~wise(paul)) & (wise(paul) | ~funny(paul)))) & (((~wise(paul) | ~funny(paul)) & (wise(paul) | funny(paul))) | (~rich(fred) | ~generous(fred))) [nnf transformation 2]
42. ((rich(fred) & generous(fred)) | ((funny(paul) | ~wise(paul)) & (wise(paul) | ~funny(paul)))) & (((~wise(paul) | ~funny(paul)) & (wise(paul) | funny(paul))) | ~rich(fred) | ~generous(fred)) [flattening 41]
44. ! [X0] : (((~funny(X0) & ~wise(X0)) | ((funny(X0) | ~generous(X0)) & (generous(X0) | ~funny(X0)))) & (((~generous(X0) | ~funny(X0)) & (generous(X0) | funny(X0))) | (funny(X0) | wise(X0)))) [nnf transformation 4]
45. ! [X0] : (((~funny(X0) & ~wise(X0)) | ((funny(X0) | ~generous(X0)) & (generous(X0) | ~funny(X0)))) & (((~generous(X0) | ~funny(X0)) & (generous(X0) | funny(X0))) | funny(X0) | wise(X0))) [flattening 44]
61. ! [X0] : (((tall(X0) & ~happy(X0)) | (old(X0) & ~calm(X0))) & ((~old(X0) | calm(X0)) | (~tall(X0) | happy(X0)))) [nnf transformation 14]
62. ! [X0] : (((tall(X0) & ~happy(X0)) | (old(X0) & ~calm(X0))) & (~old(X0) | calm(X0) | ~tall(X0) | happy(X0))) [flattening 61]
63. ! [X0] : ((((generous(X0) | ~rich(X0)) & (~generous(X0) | rich(X0))) | (curious(X0) | ~happy(X0))) & ((~curious(X0) & happy(X0)) | ((rich(X0) | generous(X0)) & (~generous(X0) | ~rich(X0))))) [nnf transformation 15]
64. ! [X0] : ((((generous(X0) | ~rich(X0)) & (~generous(X0) | rich(X0))) | curious(X0) | ~happy(X0)) & ((~curious(X0) & happy(X0)) | ((rich(X0) | generous(X0)) & (~generous(X0) | ~rich(X0))))) [flattening 63]
68. (~calm(paul) | ~funny(paul)) & (calm(paul) | funny(paul)) [nnf transformation 20]
80. rich(fred) | funny(paul) | ~wise(paul) [cnf transformation 42]
83. generous(X0) | funny(X0) | funny(X0) | wise(X0) [cnf transformation 45]
87. ~funny(X0) | generous(X0) | ~funny(X0) [cnf transformation 45]
100. ~calm(X0) | rich(X0) [cnf transformation 34]
114. ~happy(X0) | ~calm(X0) [cnf transformation 62]
118. ~rich(X0) | ~generous(X0) | happy(X0) [cnf transformation 64]
127. ~funny(paul) [cnf transformation 17]
131. calm(paul) | funny(paul) [cnf transformation 68]
137. ~rich(fred) [cnf transformation 24]
140. generous(X0) | funny(X0) | wise(X0) [duplicate literal removal 83]
141. ~funny(X0) | generous(X0) [duplicate literal removal 87]
143. 1 <=> wise(paul) [avatar definition]
145. ~wise(paul) <- (~1) [avatar component clause 143]
147. 2 <=> funny(paul) [avatar definition]
151. 3 <=> rich(fred) [avatar definition]
154. ~1 | 2 | 3 [avatar split clause 80,151,147,143]
178. wise(X0) | generous(X0) [subsumption resolution 140,141]
282. ~2 [avatar split clause 127,147]
285. 31 <=> calm(paul) [avatar definition]
286. calm(paul) <- (31) [avatar component clause 285]
289. 2 | 31 [avatar split clause 131,285,147]
318. ~3 [avatar split clause 137,151]
322. rich(paul) <- (31) [resolution 100,286]
333. generous(paul) <- (~1) [resolution 178,145]
345. ~generous(paul) | happy(paul) <- (31) [resolution 118,322]
355. happy(paul) <- (~1, 31) [subsumption resolution 345,333]
378. ~calm(paul) <- (~1, 31) [resolution 355,114]
379. $false <- (~1, 31) [subsumption resolution 378,286]
380. 1 | ~31 [avatar contradiction clause 379]
381. $false [avatar sat refutation 154,282,289,318,380]
% SZS output end Proof for 7337341890492613613868220
% ------------------------------
% 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 |
If someone is funny then someone is happy or not happy and vice versa. Everyone who is rich or creative is either not generous or humble and vice versa. If someone is either creative or happy then fred is either curious or not patient and vice versa. Everyone who is old is either funny or not tall. Everyone who is calm or not funny is both not brave and not rich. If alice is either not quiet or kind then john is not funny or rich and vice versa. Everyone who is not rich is both funny and calm and vice versa. Everyone who is brave is not generous and vice versa. If someone is rich or not patient then someone is generous or not happy and vice versa. If fred is creative or not wise then lucy is tall. If someone is either not humble or not creative then mary is either funny or brave. Everyone who is not brave or calm is wise or not generous and vice versa. If alice is both rich and strong then susan is not curious. Everyone who is not old or not patient is both not patient and not old and vice versa. If paul is not kind or generous then someone is generous or quiet and vice versa. If susan is either calm or strong then someone is both not humble and not quiet and vice versa. Someone is curious or creative. Someone is either not tall or generous. Alice is not creative or creative. Someone is either patient or not creative. John is not curious. Alice is either patient or kind. | Mary is curious. | neutral | ((?[X]:(funny(X)))<=>(?[X]:((happy(X)|~happy(X)))))&
(![X]:((rich(X)|creative(X))<=>(~generous(X)<~>humble(X))))&
((?[X]:((creative(X)<~>happy(X))))<=>((curious(fred)<~>~patient(fred))))&
(![X]:(old(X)=>(funny(X)<~>~tall(X))))&
(![X]:((calm(X)|~funny(X))=>(~brave(X)&~rich(X))))&
(((~quiet(alice)<~>kind(alice)))<=>((~funny(john)|rich(john))))&
(![X]:(~rich(X)<=>(funny(X)&calm(X))))&
(![X]:(brave(X)<=>~generous(X)))&
((?[X]:((rich(X)|~patient(X))))<=>(?[X]:((generous(X)|~happy(X)))))&
(((creative(fred)|~wise(fred)))=>(tall(lucy)))&
((?[X]:((~humble(X)<~>~creative(X))))=>((funny(mary)<~>brave(mary))))&
(![X]:((~brave(X)|calm(X))<=>(wise(X)|~generous(X))))&
(((rich(alice)&strong(alice)))=>(~curious(susan)))&
(![X]:((~old(X)|~patient(X))<=>(~patient(X)&~old(X))))&
(((~kind(paul)|generous(paul)))<=>(?[X]:((generous(X)|quiet(X)))))&
(((calm(susan)<~>strong(susan)))<=>(?[X]:((~humble(X)&~quiet(X)))))&
(?[X]:((curious(X)|creative(X))))&
(?[X]:((~tall(X)<~>generous(X))))&
((~creative(alice)|creative(alice)))&
(?[X]:((patient(X)<~>~creative(X))))&
(~curious(john))&
((patient(alice)<~>kind(alice))) | curious(mary) | [] | null | 0 |
Everyone who is either humble or brave is both calm and not happy.
If someone is both calm and not old then someone is both not old and not brave.
Everyone who is both generous and not quiet is not rich and vice versa.
Everyone who is both patient and old is creative.
If someone is either not happy or curious then paul is either calm or not generous.
Everyone who is both not old and not tall is either strong or tall and vice versa.
Everyone who is both tall and not patient is both generous and rich and vice versa.
Everyone who is patient is both not quiet and not generous.
Everyone who is either brave or not calm is curious or rich.
Everyone who is rich is both generous and strong and vice versa.
If someone is not funny or not generous then lucy is not brave and vice versa.
Everyone who is curious is not calm or creative and vice versa.
If fred is both wise and not strong then susan is both not patient and happy.
If susan is both not generous and not rich then someone is funny and vice versa.
If someone is funny then someone is tall or wise and vice versa.
Fred is not brave or strong.
Someone is either wise or not funny.
Paul is not happy or not calm.
Fred is humble.
Susan is both calm and curious.
Someone is creative. | Fred is not wise. | entailment | (![X]:((humble(X)<~>brave(X))=>(calm(X)&~happy(X))))&
((?[X]:((calm(X)&~old(X))))=>(?[X]:((~old(X)&~brave(X)))))&
(![X]:((generous(X)&~quiet(X))<=>~rich(X)))&
(![X]:((patient(X)&old(X))=>creative(X)))&
((?[X]:((~happy(X)<~>curious(X))))=>((calm(paul)<~>~generous(paul))))&
(![X]:((~old(X)&~tall(X))<=>(strong(X)<~>tall(X))))&
(![X]:((tall(X)&~patient(X))<=>(generous(X)&rich(X))))&
(![X]:(patient(X)=>(~quiet(X)&~generous(X))))&
(![X]:((brave(X)<~>~calm(X))=>(curious(X)|rich(X))))&
(![X]:(rich(X)<=>(generous(X)&strong(X))))&
((?[X]:((~funny(X)|~generous(X))))<=>(~brave(lucy)))&
(![X]:(curious(X)<=>(~calm(X)|creative(X))))&
(((wise(fred)&~strong(fred)))=>((~patient(susan)&happy(susan))))&
(((~generous(susan)&~rich(susan)))<=>(?[X]:(funny(X))))&
((?[X]:(funny(X)))<=>(?[X]:((tall(X)|wise(X)))))&
((~brave(fred)|strong(fred)))&
(?[X]:((wise(X)<~>~funny(X))))&
((~happy(paul)|~calm(paul)))&
(humble(fred))&
((calm(susan)&curious(susan)))&
(?[X]:(creative(X))) | ~wise(fred) | [
"p2",
"p9",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 496595130362951342420350
% SZS output start Proof for 496595130362951342420350
3. ! [X0] : ((~quiet(X0) & generous(X0)) <=> ~rich(X0)) [input p2]
10. ! [X0] : (rich(X0) <=> (strong(X0) & generous(X0))) [input p9]
14. (~rich(susan) & ~generous(susan)) <=> ? [X0] : funny(X0) [input p13]
15. ? [X0] : funny(X0) <=> ? [X0] : (wise(X0) | tall(X0)) [input p14]
22. wise(fred) [input hypothesis]
24. ? [X0] : funny(X0) <=> ? [X1] : (wise(X1) | tall(X1)) [rectify 15]
39. ! [X0] : (((~quiet(X0) & generous(X0)) | rich(X0)) & (~rich(X0) | (quiet(X0) | ~generous(X0)))) [nnf transformation 3]
40. ! [X0] : (((~quiet(X0) & generous(X0)) | rich(X0)) & (~rich(X0) | quiet(X0) | ~generous(X0))) [flattening 39]
47. ! [X0] : ((rich(X0) | (~strong(X0) | ~generous(X0))) & ((strong(X0) & generous(X0)) | ~rich(X0))) [nnf transformation 10]
48. ! [X0] : ((rich(X0) | ~strong(X0) | ~generous(X0)) & ((strong(X0) & generous(X0)) | ~rich(X0))) [flattening 47]
55. ((~rich(susan) & ~generous(susan)) | ! [X0] : ~funny(X0)) & (? [X0] : funny(X0) | (rich(susan) | generous(susan))) [nnf transformation 14]
56. ((~rich(susan) & ~generous(susan)) | ! [X0] : ~funny(X0)) & (? [X0] : funny(X0) | rich(susan) | generous(susan)) [flattening 55]
57. ((~rich(susan) & ~generous(susan)) | ! [X0] : ~funny(X0)) & (? [X1] : funny(X1) | rich(susan) | generous(susan)) [rectify 56]
58. ? [X1] : funny(X1) => funny(sK2) [choice axiom]
59. ((~rich(susan) & ~generous(susan)) | ! [X0] : ~funny(X0)) & (funny(sK2) | rich(susan) | generous(susan)) [skolemisation 57,58]
60. (? [X0] : funny(X0) | ! [X1] : (~wise(X1) & ~tall(X1))) & (? [X1] : (wise(X1) | tall(X1)) | ! [X0] : ~funny(X0)) [nnf transformation 24]
61. (? [X0] : funny(X0) | ! [X1] : (~wise(X1) & ~tall(X1))) & (? [X2] : (wise(X2) | tall(X2)) | ! [X3] : ~funny(X3)) [rectify 60]
62. ? [X0] : funny(X0) => funny(sK3) [choice axiom]
63. ? [X2] : (wise(X2) | tall(X2)) => (wise(sK4) | tall(sK4)) [choice axiom]
64. (funny(sK3) | ! [X1] : (~wise(X1) & ~tall(X1))) & ((wise(sK4) | tall(sK4)) | ! [X3] : ~funny(X3)) [skolemisation 61,63,62]
77. generous(X0) | rich(X0) [cnf transformation 40]
98. generous(X0) | ~rich(X0) [cnf transformation 48]
110. ~generous(susan) | ~funny(X0) [cnf transformation 59]
114. funny(sK3) | ~wise(X1) [cnf transformation 64]
123. wise(fred) [cnf transformation 22]
159. generous(X0) [subsumption resolution 98,77]
175. 11 <=> wise(fred) [avatar definition]
176. wise(fred) <- (11) [avatar component clause 175]
193. 15 <=> ! [X0] : ~funny(X0) [avatar definition]
194. ~funny(X0) <- (15) [avatar component clause 193]
200. ~funny(X0) [subsumption resolution 110,159]
201. 15 [avatar split clause 200,193]
203. 17 <=> ! [X1] : ~wise(X1) [avatar definition]
204. ~wise(X1) <- (17) [avatar component clause 203]
206. 18 <=> funny(sK3) [avatar definition]
208. funny(sK3) <- (18) [avatar component clause 206]
209. 17 | 18 [avatar split clause 114,206,203]
243. 11 [avatar split clause 123,175]
246. $false <- (15, 18) [resolution 208,194]
247. ~15 | ~18 [avatar contradiction clause 246]
248. $false <- (11, 17) [resolution 204,176]
249. ~11 | ~17 [avatar contradiction clause 248]
250. $false [avatar sat refutation 201,209,243,247,249]
% SZS output end Proof for 496595130362951342420350
% ------------------------------
% 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 |
If fred is not quiet then mary is brave or creative. If fred is either patient or not brave then someone is both not tall and tall. If john is both not creative and happy then someone is either not creative or not strong and vice versa. If alice is not funny or not strong then fred is both kind and not rich. Everyone who is either not tall or not kind is creative and vice versa. If someone is either not brave or brave then someone is both not calm and old and vice versa. Everyone who is not humble or not rich is rich. If someone is either not happy or not humble then someone is both not quiet and humble and vice versa. Everyone who is either not brave or not calm is either not generous or wise and vice versa. Everyone who is humble or strong is wise. Everyone who is not rich is both not funny and not rich. If someone is humble or not rich then someone is either strong or not funny and vice versa. Everyone who is not happy is generous and vice versa. Everyone who is either quiet or old is both happy and rich and vice versa. Everyone who is both not calm and not rich is either not brave or calm and vice versa. If paul is not tall or not calm then someone is either kind or not happy and vice versa. Someone is creative or happy. Alice is not funny or not quiet. Someone is both generous and not kind. Alice is creative or old. Fred is both not happy and brave. Someone is either not happy or not wise. Alice is both wise and not tall. | Alice is not creative. | contradiction | ((~quiet(fred))=>((brave(mary)|creative(mary))))&
(((patient(fred)<~>~brave(fred)))=>(?[X]:((~tall(X)&tall(X)))))&
(((~creative(john)&happy(john)))<=>(?[X]:((~creative(X)<~>~strong(X)))))&
(((~funny(alice)|~strong(alice)))=>((kind(fred)&~rich(fred))))&
(![X]:((~tall(X)<~>~kind(X))<=>creative(X)))&
((?[X]:((~brave(X)<~>brave(X))))<=>(?[X]:((~calm(X)&old(X)))))&
(![X]:((~humble(X)|~rich(X))=>rich(X)))&
((?[X]:((~happy(X)<~>~humble(X))))<=>(?[X]:((~quiet(X)&humble(X)))))&
(![X]:((~brave(X)<~>~calm(X))<=>(~generous(X)<~>wise(X))))&
(![X]:((humble(X)|strong(X))=>wise(X)))&
(![X]:(~rich(X)=>(~funny(X)&~rich(X))))&
((?[X]:((humble(X)|~rich(X))))<=>(?[X]:((strong(X)<~>~funny(X)))))&
(![X]:(~happy(X)<=>generous(X)))&
(![X]:((quiet(X)<~>old(X))<=>(happy(X)&rich(X))))&
(![X]:((~calm(X)&~rich(X))<=>(~brave(X)<~>calm(X))))&
(((~tall(paul)|~calm(paul)))<=>(?[X]:((kind(X)<~>~happy(X)))))&
(?[X]:((creative(X)|happy(X))))&
((~funny(alice)|~quiet(alice)))&
(?[X]:((generous(X)&~kind(X))))&
((creative(alice)|old(alice)))&
((~happy(fred)&brave(fred)))&
(?[X]:((~happy(X)<~>~wise(X))))&
((wise(alice)&~tall(alice))) | ~creative(alice) | [
"p3",
"p6",
"p8",
"p12",
"p13",
"p14",
"p17",
"p19",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 2212194555461538714990505
% SZS output start Proof for 2212194555461538714990505
4. (~strong(alice) | ~funny(alice)) => (~rich(fred) & kind(fred)) [input p3]
7. ! [X0] : ((~rich(X0) | ~humble(X0)) => rich(X0)) [input p6]
9. ! [X0] : ((~brave(X0) <~> ~calm(X0)) <=> (~generous(X0) <~> wise(X0))) [input p8]
13. ! [X0] : (~happy(X0) <=> generous(X0)) [input p12]
14. ! [X0] : ((quiet(X0) <~> old(X0)) <=> (rich(X0) & happy(X0))) [input p13]
15. ! [X0] : ((~rich(X0) & ~calm(X0)) <=> (~brave(X0) <~> calm(X0))) [input p14]
18. ~quiet(alice) | ~funny(alice) [input p17]
20. old(alice) | creative(alice) [input p19]
23. ~tall(alice) & wise(alice) [input p22]
24. ~creative(alice) [input hypothesis]
31. (~rich(fred) & kind(fred)) | (strong(alice) & funny(alice)) [ennf transformation 4]
32. ! [X0] : (rich(X0) | (rich(X0) & humble(X0))) [ennf transformation 7]
54. ! [X0] : ((((calm(X0) | brave(X0)) & (~calm(X0) | ~brave(X0))) | ((~generous(X0) | ~wise(X0)) & (wise(X0) | generous(X0)))) & (((~wise(X0) | generous(X0)) & (wise(X0) | ~generous(X0))) | ((~brave(X0) | calm(X0)) & (~calm(X0) | brave(X0))))) [nnf transformation 9]
60. ! [X0] : ((~happy(X0) | ~generous(X0)) & (generous(X0) | happy(X0))) [nnf transformation 13]
61. ! [X0] : ((((~old(X0) | ~quiet(X0)) & (old(X0) | quiet(X0))) | (~rich(X0) | ~happy(X0))) & ((rich(X0) & happy(X0)) | ((quiet(X0) | ~old(X0)) & (old(X0) | ~quiet(X0))))) [nnf transformation 14]
62. ! [X0] : ((((~old(X0) | ~quiet(X0)) & (old(X0) | quiet(X0))) | ~rich(X0) | ~happy(X0)) & ((rich(X0) & happy(X0)) | ((quiet(X0) | ~old(X0)) & (old(X0) | ~quiet(X0))))) [flattening 61]
63. ! [X0] : (((~rich(X0) & ~calm(X0)) | ((~brave(X0) | ~calm(X0)) & (calm(X0) | brave(X0)))) & (((~calm(X0) | brave(X0)) & (calm(X0) | ~brave(X0))) | (rich(X0) | calm(X0)))) [nnf transformation 15]
64. ! [X0] : (((~rich(X0) & ~calm(X0)) | ((~brave(X0) | ~calm(X0)) & (calm(X0) | brave(X0)))) & (((~calm(X0) | brave(X0)) & (calm(X0) | ~brave(X0))) | rich(X0) | calm(X0))) [flattening 63]
90. ~rich(fred) | funny(alice) [cnf transformation 31]
103. rich(X0) | rich(X0) [cnf transformation 32]
112. ~wise(X0) | generous(X0) | ~calm(X0) | brave(X0) [cnf transformation 54]
113. ~wise(X0) | generous(X0) | ~brave(X0) | calm(X0) [cnf transformation 54]
129. ~generous(X0) | ~happy(X0) [cnf transformation 60]
131. ~old(X0) | quiet(X0) | happy(X0) [cnf transformation 62]
140. ~rich(X0) | calm(X0) | brave(X0) [cnf transformation 64]
141. ~rich(X0) | ~brave(X0) | ~calm(X0) [cnf transformation 64]
149. ~quiet(alice) | ~funny(alice) [cnf transformation 18]
152. old(alice) | creative(alice) [cnf transformation 20]
157. wise(alice) [cnf transformation 23]
159. ~creative(alice) [cnf transformation 24]
162. rich(X0) [duplicate literal removal 103]
229. 14 <=> rich(fred) [avatar definition]
231. ~rich(fred) <- (~14) [avatar component clause 229]
234. 15 <=> funny(alice) [avatar definition]
237. 15 | ~14 [avatar split clause 90,229,234]
322. ~calm(X0) | ~brave(X0) [subsumption resolution 141,162]
323. calm(X0) | brave(X0) [subsumption resolution 140,162]
362. 42 <=> quiet(alice) [avatar definition]
364. ~quiet(alice) <- (~42) [avatar component clause 362]
365. ~15 | ~42 [avatar split clause 149,362,234]
367. 43 <=> creative(alice) [avatar definition]
371. 44 <=> old(alice) [avatar definition]
373. old(alice) <- (44) [avatar component clause 371]
374. 43 | 44 [avatar split clause 152,371,367]
386. ~43 [avatar split clause 159,367]
429. quiet(alice) | happy(alice) <- (44) [resolution 131,373]
439. happy(alice) <- (~42, 44) [subsumption resolution 429,364]
493. $false <- (~14) [subsumption resolution 231,162]
494. 14 [avatar contradiction clause 493]
541. generous(alice) | ~calm(alice) | brave(alice) [resolution 112,157]
546. generous(alice) | ~calm(alice) [subsumption resolution 541,322]
548. 66 <=> calm(alice) [avatar definition]
550. ~calm(alice) <- (~66) [avatar component clause 548]
552. 67 <=> generous(alice) [avatar definition]
554. generous(alice) <- (67) [avatar component clause 552]
555. ~66 | 67 [avatar split clause 546,552,548]
600. generous(alice) | ~brave(alice) | calm(alice) [resolution 113,157]
605. generous(alice) | ~brave(alice) <- (~66) [subsumption resolution 600,550]
607. 76 <=> brave(alice) [avatar definition]
609. ~brave(alice) <- (~76) [avatar component clause 607]
610. ~76 | 67 | 66 [avatar split clause 605,548,552,607]
679. brave(alice) <- (~66) [resolution 550,323]
680. $false <- (~66, ~76) [subsumption resolution 679,609]
681. 66 | 76 [avatar contradiction clause 680]
686. ~happy(alice) <- (67) [resolution 554,129]
687. $false <- (~42, 44, 67) [subsumption resolution 686,439]
688. 42 | ~44 | ~67 [avatar contradiction clause 687]
689. $false [avatar sat refutation 237,365,374,386,494,555,610,681,688]
% SZS output end Proof for 2212194555461538714990505
% ------------------------------
% 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: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is kind is both not quiet and kind and vice versa.
Everyone who is calm or humble is not brave and vice versa.
Everyone who is both calm and not quiet is not brave.
If someone is not old or curious then mary is both calm and humble.
Everyone who is either patient or not old is both happy and curious and vice versa.
Everyone who is both not curious and not happy is not happy and vice versa.
Everyone who is either quiet or not kind is not kind and vice versa.
Everyone who is not quiet or not brave is either humble or happy and vice versa.
Everyone who is not happy or not curious is either not calm or humble.
If someone is curious or not wise then someone is not strong or not generous and vice versa.
If mary is both not curious and not humble then mary is either generous or not happy and vice versa.
Everyone who is not generous or not funny is not generous.
Everyone who is both not funny and not old is happy.
If paul is brave then someone is both not quiet and not tall.
Lucy is either funny or not strong.
Someone is either not old or not creative.
John is funny or tall.
Mary is either not quiet or not old. | Mary is kind. | neutral | (![X]:(kind(X)<=>(~quiet(X)&kind(X))))&
(![X]:((calm(X)|humble(X))<=>~brave(X)))&
(![X]:((calm(X)&~quiet(X))=>~brave(X)))&
((?[X]:((~old(X)|curious(X))))=>((calm(mary)&humble(mary))))&
(![X]:((patient(X)<~>~old(X))<=>(happy(X)&curious(X))))&
(![X]:((~curious(X)&~happy(X))<=>~happy(X)))&
(![X]:((quiet(X)<~>~kind(X))<=>~kind(X)))&
(![X]:((~quiet(X)|~brave(X))<=>(humble(X)<~>happy(X))))&
(![X]:((~happy(X)|~curious(X))=>(~calm(X)<~>humble(X))))&
((?[X]:((curious(X)|~wise(X))))<=>(?[X]:((~strong(X)|~generous(X)))))&
(((~curious(mary)&~humble(mary)))<=>((generous(mary)<~>~happy(mary))))&
(![X]:((~generous(X)|~funny(X))=>~generous(X)))&
(![X]:((~funny(X)&~old(X))=>happy(X)))&
((brave(paul))=>(?[X]:((~quiet(X)&~tall(X)))))&
((funny(lucy)<~>~strong(lucy)))&
(?[X]:((~old(X)<~>~creative(X))))&
((funny(john)|tall(john)))&
((~quiet(mary)<~>~old(mary))) | kind(mary) | [] | null | 0 |
Everyone who is not rich or kind is patient.
Everyone who is either quiet or not generous is rich and vice versa.
If mary is either not calm or generous then someone is humble or not humble and vice versa.
Everyone who is tall is both happy and not curious and vice versa.
Everyone who is generous or not strong is brave.
Everyone who is not quiet is kind and vice versa.
Everyone who is both happy and not humble is old or not funny and vice versa.
If paul is both not brave and not patient then paul is humble and vice versa.
If someone is not funny then someone is either not old or strong.
If alice is both kind and rich then someone is either not kind or not humble.
If someone is both strong and not old then susan is both not humble and patient and vice versa.
If someone is both not creative and creative then someone is both not kind and brave.
Everyone who is not brave or curious is quiet or not quiet.
If someone is humble or not rich then john is tall or not brave and vice versa.
If fred is both patient and not quiet then someone is not happy and vice versa.
Everyone who is not old or generous is either not creative or not rich.
Someone is strong.
Someone is not rich.
Someone is either brave or old.
Someone is either old or not happy.
Fred is either not happy or not generous.
Someone is either not old or tall.
Someone is both not humble and brave.
Someone is not patient. | Fred is not patient. | contradiction | (![X]:((~rich(X)|kind(X))=>patient(X)))&
(![X]:((quiet(X)<~>~generous(X))<=>rich(X)))&
(((~calm(mary)<~>generous(mary)))<=>(?[X]:((humble(X)|~humble(X)))))&
(![X]:(tall(X)<=>(happy(X)&~curious(X))))&
(![X]:((generous(X)|~strong(X))=>brave(X)))&
(![X]:(~quiet(X)<=>kind(X)))&
(![X]:((happy(X)&~humble(X))<=>(old(X)|~funny(X))))&
(((~brave(paul)&~patient(paul)))<=>(humble(paul)))&
((?[X]:(~funny(X)))=>(?[X]:((~old(X)<~>strong(X)))))&
(((kind(alice)&rich(alice)))=>(?[X]:((~kind(X)<~>~humble(X)))))&
((?[X]:((strong(X)&~old(X))))<=>((~humble(susan)&patient(susan))))&
((?[X]:((~creative(X)&creative(X))))=>(?[X]:((~kind(X)&brave(X)))))&
(![X]:((~brave(X)|curious(X))=>(quiet(X)|~quiet(X))))&
((?[X]:((humble(X)|~rich(X))))<=>((tall(john)|~brave(john))))&
(((patient(fred)&~quiet(fred)))<=>(?[X]:(~happy(X))))&
(![X]:((~old(X)|generous(X))=>(~creative(X)<~>~rich(X))))&
(?[X]:(strong(X)))&
(?[X]:(~rich(X)))&
(?[X]:((brave(X)<~>old(X))))&
(?[X]:((old(X)<~>~happy(X))))&
((~happy(fred)<~>~generous(fred)))&
(?[X]:((~old(X)<~>tall(X))))&
(?[X]:((~humble(X)&brave(X))))&
(?[X]:(~patient(X))) | ~patient(fred) | [
"p0",
"p1",
"p5",
"p14",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 693721327371663237389198
% SZS output start Proof for 693721327371663237389198
1. ! [X0] : ((kind(X0) | ~rich(X0)) => patient(X0)) [input p0]
2. ! [X0] : ((quiet(X0) <~> ~generous(X0)) <=> rich(X0)) [input p1]
6. ! [X0] : (~quiet(X0) <=> kind(X0)) [input p5]
15. (~quiet(fred) & patient(fred)) <=> ? [X0] : ~happy(X0) [input p14]
21. ~happy(fred) <~> ~generous(fred) [input p20]
25. ~patient(fred) [input hypothesis]
28. ! [X0] : (patient(X0) | (~kind(X0) & rich(X0))) [ennf transformation 1]
37. ! [X0] : ((((generous(X0) | ~quiet(X0)) & (~generous(X0) | quiet(X0))) | ~rich(X0)) & (rich(X0) | ((quiet(X0) | generous(X0)) & (~generous(X0) | ~quiet(X0))))) [nnf transformation 2]
44. ! [X0] : ((~quiet(X0) | ~kind(X0)) & (kind(X0) | quiet(X0))) [nnf transformation 6]
69. ((~quiet(fred) & patient(fred)) | ! [X0] : happy(X0)) & (? [X0] : ~happy(X0) | (quiet(fred) | ~patient(fred))) [nnf transformation 15]
70. ((~quiet(fred) & patient(fred)) | ! [X0] : happy(X0)) & (? [X0] : ~happy(X0) | quiet(fred) | ~patient(fred)) [flattening 69]
71. ((~quiet(fred) & patient(fred)) | ! [X0] : happy(X0)) & (? [X1] : ~happy(X1) | quiet(fred) | ~patient(fred)) [rectify 70]
72. ? [X1] : ~happy(X1) => ~happy(sK6) [choice axiom]
73. ((~quiet(fred) & patient(fred)) | ! [X0] : happy(X0)) & (~happy(sK6) | quiet(fred) | ~patient(fred)) [skolemisation 71,72]
85. (generous(fred) | happy(fred)) & (~generous(fred) | ~happy(fred)) [nnf transformation 21]
93. patient(X0) | rich(X0) [cnf transformation 28]
94. ~kind(X0) | patient(X0) [cnf transformation 28]
98. ~quiet(X0) | generous(X0) | ~rich(X0) [cnf transformation 37]
110. quiet(X0) | kind(X0) [cnf transformation 44]
137. patient(fred) | happy(X0) [cnf transformation 73]
149. ~generous(fred) | ~happy(fred) [cnf transformation 85]
156. ~patient(fred) [cnf transformation 25]
268. 25 <=> ! [X0] : happy(X0) [avatar definition]
269. happy(X0) <- (25) [avatar component clause 268]
276. 27 <=> patient(fred) [avatar definition]
277. ~patient(fred) <- (~27) [avatar component clause 276]
279. 25 | 27 [avatar split clause 137,276,268]
305. 33 <=> happy(fred) [avatar definition]
306. ~happy(fred) <- (~33) [avatar component clause 305]
309. 34 <=> generous(fred) [avatar definition]
310. ~generous(fred) <- (~34) [avatar component clause 309]
313. ~33 | ~34 [avatar split clause 149,309,305]
324. ~27 [avatar split clause 156,276]
329. rich(fred) <- (~27) [resolution 93,277]
359. ~rich(X0) | generous(X0) | kind(X0) [resolution 98,110]
389. generous(fred) | kind(fred) <- (~27) [resolution 359,329]
408. kind(fred) <- (~27, ~34) [subsumption resolution 389,310]
428. patient(fred) <- (~27, ~34) [resolution 408,94]
429. $false <- (~27, ~34) [subsumption resolution 428,277]
430. 27 | 34 [avatar contradiction clause 429]
436. $false <- (25, ~33) [subsumption resolution 306,269]
437. ~25 | 33 [avatar contradiction clause 436]
438. $false [avatar sat refutation 279,313,324,430,437]
% SZS output end Proof for 693721327371663237389198
% ------------------------------
% 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: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If fred is not generous then someone is either tall or not calm and vice versa. If fred is both kind and strong then mary is tall. If fred is either funny or not creative then someone is brave. Everyone who is kind is either generous or kind. Everyone who is both patient and not curious is both strong and calm. Everyone who is patient or not brave is rich or not tall. If someone is not strong or not curious then john is not rich and vice versa. If someone is either kind or not funny then someone is either wise or kind and vice versa. Everyone who is creative is not happy or not strong and vice versa. Everyone who is not rich is either not brave or tall. Everyone who is either not calm or strong is patient and vice versa. Everyone who is patient or strong is not quiet. If someone is both not calm and tall then paul is both kind and curious. If john is not creative then someone is either strong or not quiet. If someone is both happy and not quiet then someone is not creative or not happy. Everyone who is either not funny or humble is either not creative or not brave. Susan is calm or strong. Mary is creative or not creative. Someone is not humble or not happy. John is both wise and strong. John is funny. Someone is not calm. Susan is either not tall or not wise. | Susan is calm. | neutral | ((~generous(fred))<=>(?[X]:((tall(X)<~>~calm(X)))))&
(((kind(fred)&strong(fred)))=>(tall(mary)))&
(((funny(fred)<~>~creative(fred)))=>(?[X]:(brave(X))))&
(![X]:(kind(X)=>(generous(X)<~>kind(X))))&
(![X]:((patient(X)&~curious(X))=>(strong(X)&calm(X))))&
(![X]:((patient(X)|~brave(X))=>(rich(X)|~tall(X))))&
((?[X]:((~strong(X)|~curious(X))))<=>(~rich(john)))&
((?[X]:((kind(X)<~>~funny(X))))<=>(?[X]:((wise(X)<~>kind(X)))))&
(![X]:(creative(X)<=>(~happy(X)|~strong(X))))&
(![X]:(~rich(X)=>(~brave(X)<~>tall(X))))&
(![X]:((~calm(X)<~>strong(X))<=>patient(X)))&
(![X]:((patient(X)|strong(X))=>~quiet(X)))&
((?[X]:((~calm(X)&tall(X))))=>((kind(paul)&curious(paul))))&
((~creative(john))=>(?[X]:((strong(X)<~>~quiet(X)))))&
((?[X]:((happy(X)&~quiet(X))))=>(?[X]:((~creative(X)|~happy(X)))))&
(![X]:((~funny(X)<~>humble(X))=>(~creative(X)<~>~brave(X))))&
((calm(susan)|strong(susan)))&
((creative(mary)|~creative(mary)))&
(?[X]:((~humble(X)|~happy(X))))&
((wise(john)&strong(john)))&
(funny(john))&
(?[X]:(~calm(X)))&
((~tall(susan)<~>~wise(susan))) | calm(susan) | [] | null | 0 |
Everyone who is both quiet and not funny is either old or not old and vice versa. If someone is either not old or not calm then someone is either not funny or not humble. If someone is either not curious or tall then alice is either not strong or curious. If someone is both not humble and tall then someone is both happy and tall and vice versa. Everyone who is not humble is both quiet and not curious. If someone is either not humble or tall then john is quiet and vice versa. Everyone who is not funny is not humble or not rich and vice versa. Everyone who is kind or not generous is both creative and not funny and vice versa. Everyone who is not happy or calm is both humble and not quiet. Everyone who is either happy or old is not generous or not funny and vice versa. Everyone who is not patient or not creative is either generous or not humble. Everyone who is wise is tall and vice versa. Everyone who is not patient or patient is not old and vice versa. If someone is either rich or not happy then fred is either not funny or not kind and vice versa. Someone is not strong or calm. Susan is both not funny and brave. Paul is not wise. Lucy is either creative or not tall. | Lucy is not patient. | neutral | (![X]:((quiet(X)&~funny(X))<=>(old(X)<~>~old(X))))&
((?[X]:((~old(X)<~>~calm(X))))=>(?[X]:((~funny(X)<~>~humble(X)))))&
((?[X]:((~curious(X)<~>tall(X))))=>((~strong(alice)<~>curious(alice))))&
((?[X]:((~humble(X)&tall(X))))<=>(?[X]:((happy(X)&tall(X)))))&
(![X]:(~humble(X)=>(quiet(X)&~curious(X))))&
((?[X]:((~humble(X)<~>tall(X))))<=>(quiet(john)))&
(![X]:(~funny(X)<=>(~humble(X)|~rich(X))))&
(![X]:((kind(X)|~generous(X))<=>(creative(X)&~funny(X))))&
(![X]:((~happy(X)|calm(X))=>(humble(X)&~quiet(X))))&
(![X]:((happy(X)<~>old(X))<=>(~generous(X)|~funny(X))))&
(![X]:((~patient(X)|~creative(X))=>(generous(X)<~>~humble(X))))&
(![X]:(wise(X)<=>tall(X)))&
(![X]:((~patient(X)|patient(X))<=>~old(X)))&
((?[X]:((rich(X)<~>~happy(X))))<=>((~funny(fred)<~>~kind(fred))))&
(?[X]:((~strong(X)|calm(X))))&
((~funny(susan)&brave(susan)))&
(~wise(paul))&
((creative(lucy)<~>~tall(lucy))) | ~patient(lucy) | [] | null | 0 |
Everyone who is rich is rich or not humble and vice versa. Everyone who is humble is old or not rich. If someone is either strong or not strong then susan is creative or not generous and vice versa. Everyone who is either quiet or not generous is not kind. Everyone who is both not generous and wise is not calm or not patient and vice versa. Everyone who is strong or not creative is strong or not curious. Everyone who is tall is old or not creative. Everyone who is not strong is either not strong or tall. Everyone who is both generous and happy is both not calm and generous. Everyone who is both humble and not old is not humble or not happy and vice versa. Everyone who is tall or curious is either not tall or brave and vice versa. Everyone who is either strong or rich is either not quiet or not wise. If someone is not old then someone is not quiet and vice versa. Everyone who is brave or quiet is not rich. Everyone who is not quiet is not funny or happy. Everyone who is both kind and not calm is not strong. Lucy is both happy and not wise. Mary is not old or not generous. Someone is either not strong or not tall. Someone is creative. Someone is both quiet and not strong. Paul is not calm or not tall. Alice is either tall or not calm. | Mary is old. | neutral | (![X]:(rich(X)<=>(rich(X)|~humble(X))))&
(![X]:(humble(X)=>(old(X)|~rich(X))))&
((?[X]:((strong(X)<~>~strong(X))))<=>((creative(susan)|~generous(susan))))&
(![X]:((quiet(X)<~>~generous(X))=>~kind(X)))&
(![X]:((~generous(X)&wise(X))<=>(~calm(X)|~patient(X))))&
(![X]:((strong(X)|~creative(X))=>(strong(X)|~curious(X))))&
(![X]:(tall(X)=>(old(X)|~creative(X))))&
(![X]:(~strong(X)=>(~strong(X)<~>tall(X))))&
(![X]:((generous(X)&happy(X))=>(~calm(X)&generous(X))))&
(![X]:((humble(X)&~old(X))<=>(~humble(X)|~happy(X))))&
(![X]:((tall(X)|curious(X))<=>(~tall(X)<~>brave(X))))&
(![X]:((strong(X)<~>rich(X))=>(~quiet(X)<~>~wise(X))))&
((?[X]:(~old(X)))<=>(?[X]:(~quiet(X))))&
(![X]:((brave(X)|quiet(X))=>~rich(X)))&
(![X]:(~quiet(X)=>(~funny(X)|happy(X))))&
(![X]:((kind(X)&~calm(X))=>~strong(X)))&
((happy(lucy)&~wise(lucy)))&
((~old(mary)|~generous(mary)))&
(?[X]:((~strong(X)<~>~tall(X))))&
(?[X]:(creative(X)))&
(?[X]:((quiet(X)&~strong(X))))&
((~calm(paul)|~tall(paul)))&
((tall(alice)<~>~calm(alice))) | old(mary) | [] | null | 0 |
Everyone who is brave is not calm or rich and vice versa.
Everyone who is not creative or not brave is wise or funny and vice versa.
If fred is not quiet then paul is rich and vice versa.
Everyone who is patient or not funny is curious.
Everyone who is both not tall and not creative is both brave and happy.
Everyone who is both humble and kind is not happy and vice versa.
Everyone who is brave is rich or not wise and vice versa.
Everyone who is creative is creative or not quiet.
Everyone who is not brave is both not calm and calm and vice versa.
Everyone who is not old is both brave and not funny and vice versa.
Everyone who is either not patient or kind is both not funny and quiet and vice versa.
Everyone who is either old or not rich is both generous and not kind.
Everyone who is either not funny or kind is both strong and old.
If mary is either funny or not strong then someone is not creative or not old.
If susan is either humble or strong then someone is kind and vice versa.
Everyone who is calm or not rich is not generous and vice versa.
Someone is calm or not quiet.
Mary is either quiet or not funny.
Someone is not calm or not rich.
Fred is wise or strong.
Paul is tall or old.
Paul is either not calm or not wise.
Lucy is either not humble or not curious.
Someone is creative. | Lucy is not happy. | neutral | (![X]:(brave(X)<=>(~calm(X)|rich(X))))&
(![X]:((~creative(X)|~brave(X))<=>(wise(X)|funny(X))))&
((~quiet(fred))<=>(rich(paul)))&
(![X]:((patient(X)|~funny(X))=>curious(X)))&
(![X]:((~tall(X)&~creative(X))=>(brave(X)&happy(X))))&
(![X]:((humble(X)&kind(X))<=>~happy(X)))&
(![X]:(brave(X)<=>(rich(X)|~wise(X))))&
(![X]:(creative(X)=>(creative(X)|~quiet(X))))&
(![X]:(~brave(X)<=>(~calm(X)&calm(X))))&
(![X]:(~old(X)<=>(brave(X)&~funny(X))))&
(![X]:((~patient(X)<~>kind(X))<=>(~funny(X)&quiet(X))))&
(![X]:((old(X)<~>~rich(X))=>(generous(X)&~kind(X))))&
(![X]:((~funny(X)<~>kind(X))=>(strong(X)&old(X))))&
(((funny(mary)<~>~strong(mary)))=>(?[X]:((~creative(X)|~old(X)))))&
(((humble(susan)<~>strong(susan)))<=>(?[X]:(kind(X))))&
(![X]:((calm(X)|~rich(X))<=>~generous(X)))&
(?[X]:((calm(X)|~quiet(X))))&
((quiet(mary)<~>~funny(mary)))&
(?[X]:((~calm(X)|~rich(X))))&
((wise(fred)|strong(fred)))&
((tall(paul)|old(paul)))&
((~calm(paul)<~>~wise(paul)))&
((~humble(lucy)<~>~curious(lucy)))&
(?[X]:(creative(X))) | ~happy(lucy) | [] | null | 0 |
Everyone who is not strong is not wise. Everyone who is both strong and not creative is not humble. Everyone who is both curious and not funny is curious. Everyone who is either not patient or wise is both not rich and humble. If someone is not rich then someone is both curious and old. Everyone who is both not old and funny is not strong or patient. If lucy is curious or not creative then john is both not calm and not curious and vice versa. If someone is wise then someone is curious or not humble and vice versa. Everyone who is tall or calm is either not humble or funny. Everyone who is either strong or kind is both not generous and not kind. Everyone who is humble or not calm is either not curious or not strong. Everyone who is both not creative and not kind is either tall or happy and vice versa. If fred is both not wise and wise then mary is either wise or not strong and vice versa. Everyone who is wise or old is either rich or tall. Everyone who is patient or old is not patient and vice versa. If someone is both rich and not old then susan is brave and vice versa. Someone is both funny and not creative. Someone is either not wise or not humble. Alice is not generous. Someone is not tall. Fred is not kind. Fred is both not curious and not kind. Someone is not calm. | Mary is not curious. | entailment | (![X]:(~strong(X)=>~wise(X)))&
(![X]:((strong(X)&~creative(X))=>~humble(X)))&
(![X]:((curious(X)&~funny(X))=>curious(X)))&
(![X]:((~patient(X)<~>wise(X))=>(~rich(X)&humble(X))))&
((?[X]:(~rich(X)))=>(?[X]:((curious(X)&old(X)))))&
(![X]:((~old(X)&funny(X))=>(~strong(X)|patient(X))))&
(((curious(lucy)|~creative(lucy)))<=>((~calm(john)&~curious(john))))&
((?[X]:(wise(X)))<=>(?[X]:((curious(X)|~humble(X)))))&
(![X]:((tall(X)|calm(X))=>(~humble(X)<~>funny(X))))&
(![X]:((strong(X)<~>kind(X))=>(~generous(X)&~kind(X))))&
(![X]:((humble(X)|~calm(X))=>(~curious(X)<~>~strong(X))))&
(![X]:((~creative(X)&~kind(X))<=>(tall(X)<~>happy(X))))&
(((~wise(fred)&wise(fred)))<=>((wise(mary)<~>~strong(mary))))&
(![X]:((wise(X)|old(X))=>(rich(X)<~>tall(X))))&
(![X]:((patient(X)|old(X))<=>~patient(X)))&
((?[X]:((rich(X)&~old(X))))<=>(brave(susan)))&
(?[X]:((funny(X)&~creative(X))))&
(?[X]:((~wise(X)<~>~humble(X))))&
(~generous(alice))&
(?[X]:(~tall(X)))&
(~kind(fred))&
((~curious(fred)&~kind(fred)))&
(?[X]:(~calm(X))) | ~curious(mary) | [
"p0",
"p3",
"p10",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4440317749373806524568865
% SZS output start Proof for 4440317749373806524568865
1. ! [X0] : (~strong(X0) => ~wise(X0)) [input p0]
4. ! [X0] : ((~patient(X0) <~> wise(X0)) => (humble(X0) & ~rich(X0))) [input p3]
11. ! [X0] : ((~calm(X0) | humble(X0)) => (~curious(X0) <~> ~strong(X0))) [input p10]
13. (wise(fred) & ~wise(fred)) <=> (wise(mary) <~> ~strong(mary)) [input p12]
15. ! [X0] : ((old(X0) | patient(X0)) <=> ~patient(X0)) [input p14]
24. curious(mary) [input hypothesis]
29. ! [X0] : (~wise(X0) | strong(X0)) [ennf transformation 1]
34. ! [X0] : ((humble(X0) & ~rich(X0)) | (~patient(X0) <=> wise(X0))) [ennf transformation 4]
40. ! [X0] : ((~curious(X0) <~> ~strong(X0)) | (calm(X0) & ~humble(X0))) [ennf transformation 11]
42. ! [X0] : ((humble(X0) & ~rich(X0)) | ((~patient(X0) | ~wise(X0)) & (wise(X0) | patient(X0)))) [nnf transformation 34]
55. ! [X0] : (((strong(X0) | curious(X0)) & (~strong(X0) | ~curious(X0))) | (calm(X0) & ~humble(X0))) [nnf transformation 40]
58. ((wise(fred) & ~wise(fred)) | ((wise(mary) | strong(mary)) & (~strong(mary) | ~wise(mary)))) & (((strong(mary) | ~wise(mary)) & (~strong(mary) | wise(mary))) | (~wise(fred) | wise(fred))) [nnf transformation 13]
59. ((wise(fred) & ~wise(fred)) | ((wise(mary) | strong(mary)) & (~strong(mary) | ~wise(mary)))) & (((strong(mary) | ~wise(mary)) & (~strong(mary) | wise(mary))) | ~wise(fred) | wise(fred)) [flattening 58]
61. ! [X0] : (((old(X0) | patient(X0)) | patient(X0)) & (~patient(X0) | (~old(X0) & ~patient(X0)))) [nnf transformation 15]
62. ! [X0] : ((old(X0) | patient(X0) | patient(X0)) & (~patient(X0) | (~old(X0) & ~patient(X0)))) [flattening 61]
76. ~wise(X0) | strong(X0) [cnf transformation 29]
81. patient(X0) | wise(X0) | humble(X0) [cnf transformation 42]
100. ~curious(X0) | ~strong(X0) | ~humble(X0) [cnf transformation 55]
112. ~wise(fred) | ~strong(mary) | ~wise(mary) [cnf transformation 59]
113. ~wise(fred) | wise(mary) | strong(mary) [cnf transformation 59]
114. wise(fred) | ~strong(mary) | ~wise(mary) [cnf transformation 59]
115. wise(fred) | wise(mary) | strong(mary) [cnf transformation 59]
120. ~patient(X0) | ~patient(X0) [cnf transformation 62]
135. curious(mary) [cnf transformation 24]
136. ~patient(X0) [duplicate literal removal 120]
197. wise(fred) | strong(mary) [subsumption resolution 115,76]
199. 14 <=> strong(mary) [avatar definition]
201. strong(mary) <- (14) [avatar component clause 199]
203. 15 <=> wise(fred) [avatar definition]
206. 14 | 15 [avatar split clause 197,203,199]
207. wise(fred) | ~wise(mary) [subsumption resolution 114,76]
209. 16 <=> wise(mary) [avatar definition]
211. ~wise(mary) <- (~16) [avatar component clause 209]
212. ~16 | 15 [avatar split clause 207,203,209]
213. ~wise(fred) | strong(mary) [subsumption resolution 113,76]
214. 14 | ~15 [avatar split clause 213,203,199]
215. ~wise(fred) | ~wise(mary) [subsumption resolution 112,76]
216. ~16 | ~15 [avatar split clause 215,203,209]
258. humble(X0) | wise(X0) [resolution 81,136]
265. ~strong(mary) | ~humble(mary) [resolution 100,135]
267. ~humble(mary) <- (14) [subsumption resolution 265,201]
277. wise(mary) <- (14) [resolution 267,258]
278. $false <- (14, ~16) [subsumption resolution 277,211]
279. ~14 | 16 [avatar contradiction clause 278]
280. $false [avatar sat refutation 206,212,214,216,279]
% SZS output end Proof for 4440317749373806524568865
% ------------------------------
% 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 |
If alice is not wise then someone is not wise or not tall.
Everyone who is curious or strong is both not quiet and not curious.
If john is kind or not happy then someone is not patient.
If mary is both not strong and tall then paul is not brave and vice versa.
Everyone who is patient is curious or not old and vice versa.
Everyone who is not creative is both not rich and wise and vice versa.
Everyone who is not wise is either not rich or patient.
Everyone who is not happy or patient is humble or old and vice versa.
Everyone who is both not curious and not rich is both not tall and not brave and vice versa.
Everyone who is not generous is not wise or not strong.
If mary is not kind then john is not calm or not wise.
If john is either curious or not brave then susan is either calm or kind and vice versa.
If someone is not calm or calm then someone is tall or rich.
Everyone who is either not curious or creative is both tall and not rich and vice versa.
Everyone who is both wise and not old is either kind or rich and vice versa.
If alice is both rich and not rich then alice is not quiet or not kind and vice versa.
Someone is both not quiet and not humble.
Someone is both not generous and not curious.
Someone is either curious or kind.
Paul is not patient.
Someone is quiet or not creative.
Mary is either not tall or curious.
Someone is either not happy or happy.
Someone is happy. | Susan is not patient. | neutral | ((~wise(alice))=>(?[X]:((~wise(X)|~tall(X)))))&
(![X]:((curious(X)|strong(X))=>(~quiet(X)&~curious(X))))&
(((kind(john)|~happy(john)))=>(?[X]:(~patient(X))))&
(((~strong(mary)&tall(mary)))<=>(~brave(paul)))&
(![X]:(patient(X)<=>(curious(X)|~old(X))))&
(![X]:(~creative(X)<=>(~rich(X)&wise(X))))&
(![X]:(~wise(X)=>(~rich(X)<~>patient(X))))&
(![X]:((~happy(X)|patient(X))<=>(humble(X)|old(X))))&
(![X]:((~curious(X)&~rich(X))<=>(~tall(X)&~brave(X))))&
(![X]:(~generous(X)=>(~wise(X)|~strong(X))))&
((~kind(mary))=>((~calm(john)|~wise(john))))&
(((curious(john)<~>~brave(john)))<=>((calm(susan)<~>kind(susan))))&
((?[X]:((~calm(X)|calm(X))))=>(?[X]:((tall(X)|rich(X)))))&
(![X]:((~curious(X)<~>creative(X))<=>(tall(X)&~rich(X))))&
(![X]:((wise(X)&~old(X))<=>(kind(X)<~>rich(X))))&
(((rich(alice)&~rich(alice)))<=>((~quiet(alice)|~kind(alice))))&
(?[X]:((~quiet(X)&~humble(X))))&
(?[X]:((~generous(X)&~curious(X))))&
(?[X]:((curious(X)<~>kind(X))))&
(~patient(paul))&
(?[X]:((quiet(X)|~creative(X))))&
((~tall(mary)<~>curious(mary)))&
(?[X]:((~happy(X)<~>happy(X))))&
(?[X]:(happy(X))) | ~patient(susan) | [] | null | 0 |
If someone is not brave then someone is both strong and not curious and vice versa. If paul is funny then lucy is both strong and quiet. Everyone who is not strong is happy or not curious and vice versa. Everyone who is funny is wise or not rich and vice versa. If someone is either not happy or not rich then paul is both not rich and strong. Everyone who is not creative or not old is either not tall or not patient. Everyone who is either strong or calm is both curious and not happy. Everyone who is not strong or happy is old or not generous. Everyone who is not quiet is not rich or not brave. Everyone who is either rich or creative is either not generous or funny and vice versa. Everyone who is both not patient and not quiet is either not tall or not creative. Everyone who is both not generous and creative is either not creative or not tall. Everyone who is not quiet is quiet. Everyone who is either not humble or creative is either not tall or not old and vice versa. If someone is wise or not wise then someone is tall or generous. Everyone who is not happy is both not strong and not tall. Lucy is not happy or not generous. Someone is not brave or brave. Someone is not creative. Someone is not happy or not quiet. Someone is humble or not happy. Someone is not wise or not patient. Mary is either not creative or old. | Mary is quiet. | entailment | ((?[X]:(~brave(X)))<=>(?[X]:((strong(X)&~curious(X)))))&
((funny(paul))=>((strong(lucy)&quiet(lucy))))&
(![X]:(~strong(X)<=>(happy(X)|~curious(X))))&
(![X]:(funny(X)<=>(wise(X)|~rich(X))))&
((?[X]:((~happy(X)<~>~rich(X))))=>((~rich(paul)&strong(paul))))&
(![X]:((~creative(X)|~old(X))=>(~tall(X)<~>~patient(X))))&
(![X]:((strong(X)<~>calm(X))=>(curious(X)&~happy(X))))&
(![X]:((~strong(X)|happy(X))=>(old(X)|~generous(X))))&
(![X]:(~quiet(X)=>(~rich(X)|~brave(X))))&
(![X]:((rich(X)<~>creative(X))<=>(~generous(X)<~>funny(X))))&
(![X]:((~patient(X)&~quiet(X))=>(~tall(X)<~>~creative(X))))&
(![X]:((~generous(X)&creative(X))=>(~creative(X)<~>~tall(X))))&
(![X]:(~quiet(X)=>quiet(X)))&
(![X]:((~humble(X)<~>creative(X))<=>(~tall(X)<~>~old(X))))&
((?[X]:((wise(X)|~wise(X))))=>(?[X]:((tall(X)|generous(X)))))&
(![X]:(~happy(X)=>(~strong(X)&~tall(X))))&
((~happy(lucy)|~generous(lucy)))&
(?[X]:((~brave(X)|brave(X))))&
(?[X]:(~creative(X)))&
(?[X]:((~happy(X)|~quiet(X))))&
(?[X]:((humble(X)|~happy(X))))&
(?[X]:((~wise(X)|~patient(X))))&
((~creative(mary)<~>old(mary))) | quiet(mary) | [
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 7058946304735707355593510
% SZS output start Proof for 7058946304735707355593510
13. ! [X0] : (~quiet(X0) => quiet(X0)) [input p12]
24. ~quiet(mary) [input hypothesis]
39. ! [X0] : (quiet(X0) | quiet(X0)) [ennf transformation 13]
110. quiet(X0) | quiet(X0) [cnf transformation 39]
131. ~quiet(mary) [cnf transformation 24]
132. quiet(X0) [duplicate literal removal 110]
248. $false [subsumption resolution 131,132]
% SZS output end Proof for 7058946304735707355593510
% ------------------------------
% 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 not generous and humble then john is both not wise and not old.
If lucy is old then someone is either curious or not quiet.
Everyone who is not generous is either strong or generous.
If lucy is not brave then someone is not humble and vice versa.
Everyone who is either brave or not calm is not kind or calm and vice versa.
Everyone who is humble or curious is humble or wise and vice versa.
If fred is both quiet and not rich then someone is wise or not humble.
Everyone who is either not patient or not creative is either rich or patient and vice versa.
If someone is either generous or brave then someone is funny or not generous and vice versa.
If paul is either patient or humble then someone is both kind and not patient and vice versa.
If susan is not curious or wise then someone is both wise and not curious and vice versa.
Everyone who is either rich or brave is not happy.
Everyone who is tall or not humble is not generous or quiet and vice versa.
Everyone who is rich or brave is either not wise or not old.
Everyone who is not quiet is curious and vice versa.
If paul is either not happy or strong then someone is either not kind or not patient.
Someone is both tall and curious.
John is both happy and wise.
Fred is not creative or wise.
Someone is creative.
Someone is not old.
Someone is either not funny or not generous.
Someone is creative or not strong.
Paul is funny or not quiet. | John is old. | neutral | ((?[X]:((~generous(X)&humble(X))))=>((~wise(john)&~old(john))))&
((old(lucy))=>(?[X]:((curious(X)<~>~quiet(X)))))&
(![X]:(~generous(X)=>(strong(X)<~>generous(X))))&
((~brave(lucy))<=>(?[X]:(~humble(X))))&
(![X]:((brave(X)<~>~calm(X))<=>(~kind(X)|calm(X))))&
(![X]:((humble(X)|curious(X))<=>(humble(X)|wise(X))))&
(((quiet(fred)&~rich(fred)))=>(?[X]:((wise(X)|~humble(X)))))&
(![X]:((~patient(X)<~>~creative(X))<=>(rich(X)<~>patient(X))))&
((?[X]:((generous(X)<~>brave(X))))<=>(?[X]:((funny(X)|~generous(X)))))&
(((patient(paul)<~>humble(paul)))<=>(?[X]:((kind(X)&~patient(X)))))&
(((~curious(susan)|wise(susan)))<=>(?[X]:((wise(X)&~curious(X)))))&
(![X]:((rich(X)<~>brave(X))=>~happy(X)))&
(![X]:((tall(X)|~humble(X))<=>(~generous(X)|quiet(X))))&
(![X]:((rich(X)|brave(X))=>(~wise(X)<~>~old(X))))&
(![X]:(~quiet(X)<=>curious(X)))&
(((~happy(paul)<~>strong(paul)))=>(?[X]:((~kind(X)<~>~patient(X)))))&
(?[X]:((tall(X)&curious(X))))&
((happy(john)&wise(john)))&
((~creative(fred)|wise(fred)))&
(?[X]:(creative(X)))&
(?[X]:(~old(X)))&
(?[X]:((~funny(X)<~>~generous(X))))&
(?[X]:((creative(X)|~strong(X))))&
((funny(paul)|~quiet(paul))) | old(john) | [] | null | 0 |
If susan is old then someone is both happy and patient.
Everyone who is both not funny and not patient is both not kind and old and vice versa.
Everyone who is not humble is both funny and curious.
Everyone who is not generous or funny is both not creative and not quiet.
Everyone who is brave or curious is not humble or not tall and vice versa.
Everyone who is not patient is old or happy.
If john is strong or not brave then someone is either not happy or not strong.
Everyone who is not quiet is patient.
If someone is curious then alice is both creative and generous.
Everyone who is not funny is both not wise and patient and vice versa.
If someone is either calm or quiet then mary is curious or not creative.
Everyone who is both not patient and not rich is both tall and creative.
If john is not happy then someone is happy and vice versa.
Everyone who is both creative and wise is not funny or strong and vice versa.
Everyone who is either creative or brave is either rich or not happy and vice versa.
Paul is either not strong or not calm.
John is either funny or brave.
Mary is both not calm and not rich.
Paul is either not wise or calm. | Mary is not patient. | contradiction | ((old(susan))=>(?[X]:((happy(X)&patient(X)))))&
(![X]:((~funny(X)&~patient(X))<=>(~kind(X)&old(X))))&
(![X]:(~humble(X)=>(funny(X)&curious(X))))&
(![X]:((~generous(X)|funny(X))=>(~creative(X)&~quiet(X))))&
(![X]:((brave(X)|curious(X))<=>(~humble(X)|~tall(X))))&
(![X]:(~patient(X)=>(old(X)|happy(X))))&
(((strong(john)|~brave(john)))=>(?[X]:((~happy(X)<~>~strong(X)))))&
(![X]:(~quiet(X)=>patient(X)))&
((?[X]:(curious(X)))=>((creative(alice)&generous(alice))))&
(![X]:(~funny(X)<=>(~wise(X)&patient(X))))&
((?[X]:((calm(X)<~>quiet(X))))=>((curious(mary)|~creative(mary))))&
(![X]:((~patient(X)&~rich(X))=>(tall(X)&creative(X))))&
((~happy(john))<=>(?[X]:(happy(X))))&
(![X]:((creative(X)&wise(X))<=>(~funny(X)|strong(X))))&
(![X]:((creative(X)<~>brave(X))<=>(rich(X)<~>~happy(X))))&
((~strong(paul)<~>~calm(paul)))&
((funny(john)<~>brave(john)))&
((~calm(mary)&~rich(mary)))&
((~wise(paul)<~>calm(paul))) | ~patient(mary) | [
"p3",
"p7",
"p9",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 3460650473948975949204311
% SZS output start Proof for 3460650473948975949204311
4. ! [X0] : ((funny(X0) | ~generous(X0)) => (~quiet(X0) & ~creative(X0))) [input p3]
8. ! [X0] : (~quiet(X0) => patient(X0)) [input p7]
10. ! [X0] : (~funny(X0) <=> (patient(X0) & ~wise(X0))) [input p9]
14. ! [X0] : ((wise(X0) & creative(X0)) <=> (strong(X0) | ~funny(X0))) [input p13]
20. ~patient(mary) [input hypothesis]
22. ! [X0] : (funny(X0) => (~quiet(X0) & ~creative(X0))) [pure predicate removal 4]
25. ! [X0] : ((~quiet(X0) & ~creative(X0)) | ~funny(X0)) [ennf transformation 22]
29. ! [X0] : (patient(X0) | quiet(X0)) [ennf transformation 8]
44. ! [X0] : ((~funny(X0) | (~patient(X0) | wise(X0))) & ((patient(X0) & ~wise(X0)) | funny(X0))) [nnf transformation 10]
45. ! [X0] : ((~funny(X0) | ~patient(X0) | wise(X0)) & ((patient(X0) & ~wise(X0)) | funny(X0))) [flattening 44]
51. ! [X0] : (((wise(X0) & creative(X0)) | (~strong(X0) & funny(X0))) & ((strong(X0) | ~funny(X0)) | (~wise(X0) | ~creative(X0)))) [nnf transformation 14]
52. ! [X0] : (((wise(X0) & creative(X0)) | (~strong(X0) & funny(X0))) & (strong(X0) | ~funny(X0) | ~wise(X0) | ~creative(X0))) [flattening 51]
66. ~quiet(X0) | ~funny(X0) [cnf transformation 25]
76. quiet(X0) | patient(X0) [cnf transformation 29]
78. ~wise(X0) | funny(X0) [cnf transformation 45]
90. wise(X0) | funny(X0) [cnf transformation 52]
108. ~patient(mary) [cnf transformation 20]
180. funny(X0) [subsumption resolution 90,78]
206. patient(X0) | ~funny(X0) [resolution 76,66]
207. patient(X0) [subsumption resolution 206,180]
208. $false [resolution 207,108]
% SZS output end Proof for 3460650473948975949204311
% ------------------------------
% 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 humble or not wise is quiet. Everyone who is either not happy or not calm is either not creative or not funny and vice versa. Everyone who is not wise or not happy is both curious and tall. If lucy is either patient or not patient then fred is either not curious or creative. If someone is humble then someone is both not tall and strong and vice versa. Everyone who is both not kind and not creative is either not patient or not funny and vice versa. Everyone who is either not happy or generous is both not quiet and brave. If paul is both not creative and quiet then john is strong or rich and vice versa. If susan is quiet then alice is not rich. Everyone who is both rich and not brave is not brave or not strong. Everyone who is kind is either brave or not brave and vice versa. Everyone who is humble is either not patient or kind and vice versa. Everyone who is curious or not generous is both not calm and strong and vice versa. Everyone who is not generous or not wise is both tall and not brave. Everyone who is not wise or humble is not curious and vice versa. If someone is both curious and tall then john is not patient or not tall and vice versa. Someone is either not curious or not happy. Someone is both creative and not patient. Alice is either calm or not patient. Someone is either patient or calm. | Fred is not rich. | neutral | (![X]:((humble(X)|~wise(X))=>quiet(X)))&
(![X]:((~happy(X)<~>~calm(X))<=>(~creative(X)<~>~funny(X))))&
(![X]:((~wise(X)|~happy(X))=>(curious(X)&tall(X))))&
(((patient(lucy)<~>~patient(lucy)))=>((~curious(fred)<~>creative(fred))))&
((?[X]:(humble(X)))<=>(?[X]:((~tall(X)&strong(X)))))&
(![X]:((~kind(X)&~creative(X))<=>(~patient(X)<~>~funny(X))))&
(![X]:((~happy(X)<~>generous(X))=>(~quiet(X)&brave(X))))&
(((~creative(paul)&quiet(paul)))<=>((strong(john)|rich(john))))&
((quiet(susan))=>(~rich(alice)))&
(![X]:((rich(X)&~brave(X))=>(~brave(X)|~strong(X))))&
(![X]:(kind(X)<=>(brave(X)<~>~brave(X))))&
(![X]:(humble(X)<=>(~patient(X)<~>kind(X))))&
(![X]:((curious(X)|~generous(X))<=>(~calm(X)&strong(X))))&
(![X]:((~generous(X)|~wise(X))=>(tall(X)&~brave(X))))&
(![X]:((~wise(X)|humble(X))<=>~curious(X)))&
((?[X]:((curious(X)&tall(X))))<=>((~patient(john)|~tall(john))))&
(?[X]:((~curious(X)<~>~happy(X))))&
(?[X]:((creative(X)&~patient(X))))&
((calm(alice)<~>~patient(alice)))&
(?[X]:((patient(X)<~>calm(X)))) | ~rich(fred) | [] | null | 0 |
If someone is either generous or not patient then alice is both not tall and not wise and vice versa.
Everyone who is both not curious and kind is not quiet.
If fred is not patient or not brave then alice is both not patient and curious and vice versa.
Everyone who is either not kind or not funny is either curious or not wise and vice versa.
If someone is either not calm or not patient then susan is not tall and vice versa.
If someone is not generous or wise then someone is not quiet or tall.
Everyone who is old is not wise or wise and vice versa.
If paul is patient then lucy is patient or humble.
Everyone who is strong is both generous and not funny.
If someone is either not funny or not calm then someone is either not brave or generous.
Everyone who is both generous and curious is both not tall and tall.
Everyone who is old or not funny is not calm and vice versa.
Everyone who is either not patient or not old is wise or not creative.
If someone is not curious then lucy is not generous or not rich and vice versa.
If someone is either not funny or patient then someone is either not calm or not creative.
Someone is kind or not brave.
Paul is humble.
Someone is not rich or calm.
Alice is both kind and tall.
Mary is not brave. | Susan is generous. | neutral | ((?[X]:((generous(X)<~>~patient(X))))<=>((~tall(alice)&~wise(alice))))&
(![X]:((~curious(X)&kind(X))=>~quiet(X)))&
(((~patient(fred)|~brave(fred)))<=>((~patient(alice)&curious(alice))))&
(![X]:((~kind(X)<~>~funny(X))<=>(curious(X)<~>~wise(X))))&
((?[X]:((~calm(X)<~>~patient(X))))<=>(~tall(susan)))&
((?[X]:((~generous(X)|wise(X))))=>(?[X]:((~quiet(X)|tall(X)))))&
(![X]:(old(X)<=>(~wise(X)|wise(X))))&
((patient(paul))=>((patient(lucy)|humble(lucy))))&
(![X]:(strong(X)=>(generous(X)&~funny(X))))&
((?[X]:((~funny(X)<~>~calm(X))))=>(?[X]:((~brave(X)<~>generous(X)))))&
(![X]:((generous(X)&curious(X))=>(~tall(X)&tall(X))))&
(![X]:((old(X)|~funny(X))<=>~calm(X)))&
(![X]:((~patient(X)<~>~old(X))=>(wise(X)|~creative(X))))&
((?[X]:(~curious(X)))<=>((~generous(lucy)|~rich(lucy))))&
((?[X]:((~funny(X)<~>patient(X))))=>(?[X]:((~calm(X)<~>~creative(X)))))&
(?[X]:((kind(X)|~brave(X))))&
(humble(paul))&
(?[X]:((~rich(X)|calm(X))))&
((kind(alice)&tall(alice)))&
(~brave(mary)) | generous(susan) | [] | null | 0 |
Everyone who is both strong and creative is both not kind and humble and vice versa. Everyone who is not curious or strong is both not curious and wise. Everyone who is not curious is funny and vice versa. Everyone who is quiet is either funny or old and vice versa. Everyone who is either not generous or wise is both not patient and brave. If someone is either patient or wise then someone is both not happy and curious and vice versa. If susan is either strong or kind then someone is either not tall or rich. Everyone who is both not curious and quiet is both patient and not tall. Everyone who is wise is either kind or not creative. Everyone who is both not brave and kind is either kind or quiet and vice versa. Everyone who is not patient or not kind is calm or strong and vice versa. If someone is funny or not funny then susan is both generous and not tall. Everyone who is funny is both not old and not funny and vice versa. If someone is both not creative and not brave then someone is both old and not creative and vice versa. If john is not generous then someone is either not curious or kind and vice versa. Everyone who is both not calm and not patient is funny and vice versa. John is either not happy or not funny. Fred is not funny. John is either calm or tall. Someone is creative or not brave. Someone is not wise. Paul is both not tall and quiet. | Fred is kind. | entailment | (![X]:((strong(X)&creative(X))<=>(~kind(X)&humble(X))))&
(![X]:((~curious(X)|strong(X))=>(~curious(X)&wise(X))))&
(![X]:(~curious(X)<=>funny(X)))&
(![X]:(quiet(X)<=>(funny(X)<~>old(X))))&
(![X]:((~generous(X)<~>wise(X))=>(~patient(X)&brave(X))))&
((?[X]:((patient(X)<~>wise(X))))<=>(?[X]:((~happy(X)&curious(X)))))&
(((strong(susan)<~>kind(susan)))=>(?[X]:((~tall(X)<~>rich(X)))))&
(![X]:((~curious(X)&quiet(X))=>(patient(X)&~tall(X))))&
(![X]:(wise(X)=>(kind(X)<~>~creative(X))))&
(![X]:((~brave(X)&kind(X))<=>(kind(X)<~>quiet(X))))&
(![X]:((~patient(X)|~kind(X))<=>(calm(X)|strong(X))))&
((?[X]:((funny(X)|~funny(X))))=>((generous(susan)&~tall(susan))))&
(![X]:(funny(X)<=>(~old(X)&~funny(X))))&
((?[X]:((~creative(X)&~brave(X))))<=>(?[X]:((old(X)&~creative(X)))))&
((~generous(john))<=>(?[X]:((~curious(X)<~>kind(X)))))&
(![X]:((~calm(X)&~patient(X))<=>funny(X)))&
((~happy(john)<~>~funny(john)))&
(~funny(fred))&
((calm(john)<~>tall(john)))&
(?[X]:((creative(X)|~brave(X))))&
(?[X]:(~wise(X)))&
((~tall(paul)&quiet(paul))) | kind(fred) | [
"p3",
"p9",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 6538467821899926093528865
% SZS output start Proof for 6538467821899926093528865
4. ! [X0] : (quiet(X0) <=> (funny(X0) <~> old(X0))) [input p3]
10. ! [X0] : ((kind(X0) & ~brave(X0)) <=> (kind(X0) <~> quiet(X0))) [input p9]
13. ! [X0] : (funny(X0) <=> (~funny(X0) & ~old(X0))) [input p12]
23. ~kind(fred) [input hypothesis]
36. ! [X0] : ((quiet(X0) | ((funny(X0) | ~old(X0)) & (old(X0) | ~funny(X0)))) & (((~old(X0) | ~funny(X0)) & (old(X0) | funny(X0))) | ~quiet(X0))) [nnf transformation 4]
47. ! [X0] : (((kind(X0) & ~brave(X0)) | ((kind(X0) | ~quiet(X0)) & (quiet(X0) | ~kind(X0)))) & (((~quiet(X0) | ~kind(X0)) & (quiet(X0) | kind(X0))) | (~kind(X0) | brave(X0)))) [nnf transformation 10]
48. ! [X0] : (((kind(X0) & ~brave(X0)) | ((kind(X0) | ~quiet(X0)) & (quiet(X0) | ~kind(X0)))) & (((~quiet(X0) | ~kind(X0)) & (quiet(X0) | kind(X0))) | ~kind(X0) | brave(X0))) [flattening 47]
51. ! [X0] : ((funny(X0) | (funny(X0) | old(X0))) & ((~funny(X0) & ~old(X0)) | ~funny(X0))) [nnf transformation 13]
52. ! [X0] : ((funny(X0) | funny(X0) | old(X0)) & ((~funny(X0) & ~old(X0)) | ~funny(X0))) [flattening 51]
83. ~old(X0) | funny(X0) | quiet(X0) [cnf transformation 36]
107. kind(X0) | kind(X0) | ~quiet(X0) [cnf transformation 48]
117. ~funny(X0) | ~funny(X0) [cnf transformation 52]
118. funny(X0) | funny(X0) | old(X0) [cnf transformation 52]
139. ~kind(fred) [cnf transformation 23]
140. ~funny(X0) [duplicate literal removal 117]
141. old(X0) | funny(X0) [duplicate literal removal 118]
143. ~quiet(X0) | kind(X0) [duplicate literal removal 107]
205. 14 <=> ! [X0] : ~funny(X0) [avatar definition]
206. ~funny(X0) <- (14) [avatar component clause 205]
214. 14 [avatar split clause 140,205]
327. funny(X0) | quiet(X0) | funny(X0) [resolution 83,141]
329. funny(X0) | quiet(X0) [duplicate literal removal 327]
330. quiet(X0) <- (14) [subsumption resolution 329,206]
335. kind(X2) <- (14) [resolution 330,143]
370. $false <- (14) [resolution 335,139]
372. ~14 [avatar contradiction clause 370]
373. $false [avatar sat refutation 214,372]
% SZS output end Proof for 6538467821899926093528865
% ------------------------------
% 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: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If fred is not quiet or humble then susan is patient or happy. If someone is not kind or kind then someone is both not calm and not happy and vice versa. If someone is both tall and quiet then someone is either patient or strong and vice versa. Everyone who is rich is not tall or not wise. Everyone who is either not creative or patient is both patient and not generous. If someone is both not creative and brave then someone is brave and vice versa. If someone is both not rich and not strong then someone is not generous and vice versa. Everyone who is both not rich and not creative is either brave or not generous. If someone is either quiet or not kind then someone is both funny and not funny and vice versa. Everyone who is not tall is not humble and vice versa. If someone is either not tall or not strong then alice is happy or generous and vice versa. Everyone who is not curious is not strong. If someone is wise then mary is happy or not funny. If fred is generous or wise then alice is either not happy or not funny and vice versa. Everyone who is not brave is not creative and vice versa. Everyone who is calm or humble is both calm and humble. Lucy is creative or not strong. Lucy is not curious. Susan is generous or tall. Mary is not tall or quiet. Someone is both curious and humble. Someone is not creative or not funny. Lucy is not rich. | Susan is not rich. | neutral | (((~quiet(fred)|humble(fred)))=>((patient(susan)|happy(susan))))&
((?[X]:((~kind(X)|kind(X))))<=>(?[X]:((~calm(X)&~happy(X)))))&
((?[X]:((tall(X)&quiet(X))))<=>(?[X]:((patient(X)<~>strong(X)))))&
(![X]:(rich(X)=>(~tall(X)|~wise(X))))&
(![X]:((~creative(X)<~>patient(X))=>(patient(X)&~generous(X))))&
((?[X]:((~creative(X)&brave(X))))<=>(?[X]:(brave(X))))&
((?[X]:((~rich(X)&~strong(X))))<=>(?[X]:(~generous(X))))&
(![X]:((~rich(X)&~creative(X))=>(brave(X)<~>~generous(X))))&
((?[X]:((quiet(X)<~>~kind(X))))<=>(?[X]:((funny(X)&~funny(X)))))&
(![X]:(~tall(X)<=>~humble(X)))&
((?[X]:((~tall(X)<~>~strong(X))))<=>((happy(alice)|generous(alice))))&
(![X]:(~curious(X)=>~strong(X)))&
((?[X]:(wise(X)))=>((happy(mary)|~funny(mary))))&
(((generous(fred)|wise(fred)))<=>((~happy(alice)<~>~funny(alice))))&
(![X]:(~brave(X)<=>~creative(X)))&
(![X]:((calm(X)|humble(X))=>(calm(X)&humble(X))))&
((creative(lucy)|~strong(lucy)))&
(~curious(lucy))&
((generous(susan)|tall(susan)))&
((~tall(mary)|quiet(mary)))&
(?[X]:((curious(X)&humble(X))))&
(?[X]:((~creative(X)|~funny(X))))&
(~rich(lucy)) | ~rich(susan) | [] | null | 0 |
Everyone who is either not curious or rich is both brave and not happy and vice versa. Everyone who is funny or curious is not humble. Everyone who is calm or not generous is both not strong and humble and vice versa. If someone is both not kind and not happy then mary is funny or happy and vice versa. Everyone who is both tall and humble is patient. Everyone who is both not strong and not creative is both calm and tall. If lucy is either generous or not generous then paul is patient and vice versa. If mary is either not kind or calm then paul is either not generous or not old. If someone is humble then alice is creative or not wise. If someone is both funny and not calm then lucy is either wise or patient and vice versa. Everyone who is either creative or not calm is either creative or not funny and vice versa. If someone is not tall or not creative then someone is both generous and quiet and vice versa. Everyone who is either not old or not funny is not humble and vice versa. If someone is calm then someone is not brave and vice versa. Everyone who is either not kind or not generous is either humble or creative. Mary is either strong or not quiet. Alice is rich or curious. Someone is either curious or not wise. Someone is not kind or not strong. Fred is not quiet. Someone is either brave or wise. Someone is generous or not funny. | Alice is not happy. | neutral | (![X]:((~curious(X)<~>rich(X))<=>(brave(X)&~happy(X))))&
(![X]:((funny(X)|curious(X))=>~humble(X)))&
(![X]:((calm(X)|~generous(X))<=>(~strong(X)&humble(X))))&
((?[X]:((~kind(X)&~happy(X))))<=>((funny(mary)|happy(mary))))&
(![X]:((tall(X)&humble(X))=>patient(X)))&
(![X]:((~strong(X)&~creative(X))=>(calm(X)&tall(X))))&
(((generous(lucy)<~>~generous(lucy)))<=>(patient(paul)))&
(((~kind(mary)<~>calm(mary)))=>((~generous(paul)<~>~old(paul))))&
((?[X]:(humble(X)))=>((creative(alice)|~wise(alice))))&
((?[X]:((funny(X)&~calm(X))))<=>((wise(lucy)<~>patient(lucy))))&
(![X]:((creative(X)<~>~calm(X))<=>(creative(X)<~>~funny(X))))&
((?[X]:((~tall(X)|~creative(X))))<=>(?[X]:((generous(X)&quiet(X)))))&
(![X]:((~old(X)<~>~funny(X))<=>~humble(X)))&
((?[X]:(calm(X)))<=>(?[X]:(~brave(X))))&
(![X]:((~kind(X)<~>~generous(X))=>(humble(X)<~>creative(X))))&
((strong(mary)<~>~quiet(mary)))&
((rich(alice)|curious(alice)))&
(?[X]:((curious(X)<~>~wise(X))))&
(?[X]:((~kind(X)|~strong(X))))&
(~quiet(fred))&
(?[X]:((brave(X)<~>wise(X))))&
(?[X]:((generous(X)|~funny(X)))) | ~happy(alice) | [] | null | 0 |
If someone is not wise or kind then someone is not humble.
If someone is both not happy and not funny then someone is both wise and not kind and vice versa.
If mary is not happy then alice is either not tall or humble.
Everyone who is either quiet or kind is not wise and vice versa.
If paul is not curious or funny then someone is not quiet and vice versa.
Everyone who is happy is both creative and not strong and vice versa.
Everyone who is quiet is creative or not generous.
If paul is not kind then fred is both curious and not happy.
If someone is quiet or not generous then someone is both not old and not tall and vice versa.
Everyone who is curious or strong is both not wise and not humble and vice versa.
If someone is both not generous and not humble then susan is not generous.
If paul is creative or wise then lucy is rich or happy and vice versa.
Everyone who is both calm and not quiet is not rich or not wise.
Everyone who is patient or wise is quiet and vice versa.
Everyone who is both tall and generous is not tall or not creative and vice versa.
Mary is funny or not wise.
Someone is not curious.
Mary is both not wise and kind.
Mary is not quiet or curious.
Someone is kind or not rich.
John is not curious or old.
Someone is either strong or not kind. | John is wise. | contradiction | ((?[X]:((~wise(X)|kind(X))))=>(?[X]:(~humble(X))))&
((?[X]:((~happy(X)&~funny(X))))<=>(?[X]:((wise(X)&~kind(X)))))&
((~happy(mary))=>((~tall(alice)<~>humble(alice))))&
(![X]:((quiet(X)<~>kind(X))<=>~wise(X)))&
(((~curious(paul)|funny(paul)))<=>(?[X]:(~quiet(X))))&
(![X]:(happy(X)<=>(creative(X)&~strong(X))))&
(![X]:(quiet(X)=>(creative(X)|~generous(X))))&
((~kind(paul))=>((curious(fred)&~happy(fred))))&
((?[X]:((quiet(X)|~generous(X))))<=>(?[X]:((~old(X)&~tall(X)))))&
(![X]:((curious(X)|strong(X))<=>(~wise(X)&~humble(X))))&
((?[X]:((~generous(X)&~humble(X))))=>(~generous(susan)))&
(((creative(paul)|wise(paul)))<=>((rich(lucy)|happy(lucy))))&
(![X]:((calm(X)&~quiet(X))=>(~rich(X)|~wise(X))))&
(![X]:((patient(X)|wise(X))<=>quiet(X)))&
(![X]:((tall(X)&generous(X))<=>(~tall(X)|~creative(X))))&
((funny(mary)|~wise(mary)))&
(?[X]:(~curious(X)))&
((~wise(mary)&kind(mary)))&
((~quiet(mary)|curious(mary)))&
(?[X]:((kind(X)|~rich(X))))&
((~curious(john)|old(john)))&
(?[X]:((strong(X)<~>~kind(X)))) | wise(john) | [
"p8",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 312468117227607972167069
% SZS output start Proof for 312468117227607972167069
9. ? [X0] : (~generous(X0) | quiet(X0)) <=> ? [X0] : (~tall(X0) & ~old(X0)) [input p8]
14. ! [X0] : ((wise(X0) | patient(X0)) <=> quiet(X0)) [input p13]
15. ! [X0] : ((generous(X0) & tall(X0)) <=> (~creative(X0) | ~tall(X0))) [input p14]
23. wise(john) [input hypothesis]
26. ? [X0] : (~generous(X0) | quiet(X0)) <=> ? [X1] : (~tall(X1) & ~old(X1)) [rectify 9]
51. (? [X0] : (~generous(X0) | quiet(X0)) | ! [X1] : (tall(X1) | old(X1))) & (? [X1] : (~tall(X1) & ~old(X1)) | ! [X0] : (generous(X0) & ~quiet(X0))) [nnf transformation 26]
52. (? [X0] : (~generous(X0) | quiet(X0)) | ! [X1] : (tall(X1) | old(X1))) & (? [X2] : (~tall(X2) & ~old(X2)) | ! [X3] : (generous(X3) & ~quiet(X3))) [rectify 51]
53. ? [X0] : (~generous(X0) | quiet(X0)) => (~generous(sK4) | quiet(sK4)) [choice axiom]
54. ? [X2] : (~tall(X2) & ~old(X2)) => (~tall(sK5) & ~old(sK5)) [choice axiom]
55. ((~generous(sK4) | quiet(sK4)) | ! [X1] : (tall(X1) | old(X1))) & ((~tall(sK5) & ~old(sK5)) | ! [X3] : (generous(X3) & ~quiet(X3))) [skolemisation 52,54,53]
60. ! [X0] : (((wise(X0) | patient(X0)) | ~quiet(X0)) & (quiet(X0) | (~wise(X0) & ~patient(X0)))) [nnf transformation 14]
61. ! [X0] : ((wise(X0) | patient(X0) | ~quiet(X0)) & (quiet(X0) | (~wise(X0) & ~patient(X0)))) [flattening 60]
62. ! [X0] : (((generous(X0) & tall(X0)) | (creative(X0) & tall(X0))) & ((~creative(X0) | ~tall(X0)) | (~generous(X0) | ~tall(X0)))) [nnf transformation 15]
63. ! [X0] : (((generous(X0) & tall(X0)) | (creative(X0) & tall(X0))) & (~creative(X0) | ~tall(X0) | ~generous(X0) | ~tall(X0))) [flattening 62]
94. ~tall(sK5) | ~quiet(X3) [cnf transformation 55]
108. ~wise(X0) | quiet(X0) [cnf transformation 61]
111. tall(X0) | tall(X0) [cnf transformation 63]
124. wise(john) [cnf transformation 23]
126. tall(X0) [duplicate literal removal 111]
227. 24 <=> tall(sK5) [avatar definition]
229. ~tall(sK5) <- (~24) [avatar component clause 227]
232. 25 <=> ! [X3] : ~quiet(X3) [avatar definition]
233. ~quiet(X3) <- (25) [avatar component clause 232]
234. 25 | ~24 [avatar split clause 94,227,232]
317. $false <- (~24) [subsumption resolution 229,126]
318. 24 [avatar contradiction clause 317]
326. quiet(john) [resolution 108,124]
327. $false <- (25) [subsumption resolution 326,233]
328. ~25 [avatar contradiction clause 327]
329. $false [avatar sat refutation 234,318,328]
% SZS output end Proof for 312468117227607972167069
% ------------------------------
% 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 alice is calm or wise then someone is both curious and not kind and vice versa.
Everyone who is not calm is not quiet.
Everyone who is either not curious or not tall is either not creative or curious and vice versa.
If someone is either patient or curious then paul is not strong or not wise.
Everyone who is either not curious or brave is tall.
Everyone who is both not rich and quiet is not brave or wise.
Everyone who is either not quiet or not generous is old or quiet and vice versa.
Everyone who is not humble or kind is either not patient or not rich.
If someone is not quiet then someone is not patient or not happy.
Everyone who is not quiet is both not humble and strong and vice versa.
Everyone who is not quiet is curious or not wise and vice versa.
Everyone who is both not kind and not wise is curious or old and vice versa.
Everyone who is both not patient and not tall is both happy and not creative and vice versa.
Everyone who is tall or not tall is old or not tall.
Everyone who is either humble or creative is creative or kind.
If mary is tall or not curious then john is tall.
Someone is both strong and not kind.
Fred is either not strong or rich.
Mary is either happy or not tall.
Mary is either not creative or quiet.
Someone is both brave and happy.
Alice is wise.
Someone is not strong. | Mary is not curious. | entailment | (((calm(alice)|wise(alice)))<=>(?[X]:((curious(X)&~kind(X)))))&
(![X]:(~calm(X)=>~quiet(X)))&
(![X]:((~curious(X)<~>~tall(X))<=>(~creative(X)<~>curious(X))))&
((?[X]:((patient(X)<~>curious(X))))=>((~strong(paul)|~wise(paul))))&
(![X]:((~curious(X)<~>brave(X))=>tall(X)))&
(![X]:((~rich(X)&quiet(X))=>(~brave(X)|wise(X))))&
(![X]:((~quiet(X)<~>~generous(X))<=>(old(X)|quiet(X))))&
(![X]:((~humble(X)|kind(X))=>(~patient(X)<~>~rich(X))))&
((?[X]:(~quiet(X)))=>(?[X]:((~patient(X)|~happy(X)))))&
(![X]:(~quiet(X)<=>(~humble(X)&strong(X))))&
(![X]:(~quiet(X)<=>(curious(X)|~wise(X))))&
(![X]:((~kind(X)&~wise(X))<=>(curious(X)|old(X))))&
(![X]:((~patient(X)&~tall(X))<=>(happy(X)&~creative(X))))&
(![X]:((tall(X)|~tall(X))=>(old(X)|~tall(X))))&
(![X]:((humble(X)<~>creative(X))=>(creative(X)|kind(X))))&
(((tall(mary)|~curious(mary)))=>(tall(john)))&
(?[X]:((strong(X)&~kind(X))))&
((~strong(fred)<~>rich(fred)))&
((happy(mary)<~>~tall(mary)))&
((~creative(mary)<~>quiet(mary)))&
(?[X]:((brave(X)&happy(X))))&
(wise(alice))&
(?[X]:(~strong(X))) | ~curious(mary) | [
"p2",
"p10",
"p12",
"p18",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 857591153606040142820222
% SZS output start Proof for 857591153606040142820222
3. ! [X0] : ((~curious(X0) <~> ~tall(X0)) <=> (~creative(X0) <~> curious(X0))) [input p2]
11. ! [X0] : (~quiet(X0) <=> (~wise(X0) | curious(X0))) [input p10]
13. ! [X0] : ((~tall(X0) & ~patient(X0)) <=> (~creative(X0) & happy(X0))) [input p12]
19. happy(mary) <~> ~tall(mary) [input p18]
20. ~creative(mary) <~> quiet(mary) [input p19]
24. curious(mary) [input hypothesis]
44. ! [X0] : ((((tall(X0) | curious(X0)) & (~tall(X0) | ~curious(X0))) | ((~creative(X0) | ~curious(X0)) & (curious(X0) | creative(X0)))) & (((~curious(X0) | creative(X0)) & (curious(X0) | ~creative(X0))) | ((~curious(X0) | tall(X0)) & (~tall(X0) | curious(X0))))) [nnf transformation 3]
55. ! [X0] : ((~quiet(X0) | (wise(X0) & ~curious(X0))) & ((~wise(X0) | curious(X0)) | quiet(X0))) [nnf transformation 11]
56. ! [X0] : ((~quiet(X0) | (wise(X0) & ~curious(X0))) & (~wise(X0) | curious(X0) | quiet(X0))) [flattening 55]
59. ! [X0] : (((~tall(X0) & ~patient(X0)) | (creative(X0) | ~happy(X0))) & ((~creative(X0) & happy(X0)) | (tall(X0) | patient(X0)))) [nnf transformation 13]
60. ! [X0] : (((~tall(X0) & ~patient(X0)) | creative(X0) | ~happy(X0)) & ((~creative(X0) & happy(X0)) | tall(X0) | patient(X0))) [flattening 59]
65. (tall(mary) | ~happy(mary)) & (~tall(mary) | happy(mary)) [nnf transformation 19]
66. (~quiet(mary) | creative(mary)) & (quiet(mary) | ~creative(mary)) [nnf transformation 20]
80. ~curious(X0) | creative(X0) | ~curious(X0) | tall(X0) [cnf transformation 44]
83. tall(X0) | curious(X0) | curious(X0) | creative(X0) [cnf transformation 44]
105. ~quiet(X0) | ~curious(X0) [cnf transformation 56]
115. ~tall(X0) | creative(X0) | ~happy(X0) [cnf transformation 60]
126. ~tall(mary) | happy(mary) [cnf transformation 65]
128. quiet(mary) | ~creative(mary) [cnf transformation 66]
134. curious(mary) [cnf transformation 24]
140. ~curious(X0) | creative(X0) | tall(X0) [duplicate literal removal 80]
142. tall(X0) | curious(X0) | creative(X0) [duplicate literal removal 83]
167. creative(X0) | tall(X0) [subsumption resolution 140,142]
198. ~happy(X0) | creative(X0) [subsumption resolution 115,167]
201. 13 <=> curious(mary) [avatar definition]
203. curious(mary) <- (13) [avatar component clause 201]
210. 15 <=> tall(mary) [avatar definition]
225. 18 <=> happy(mary) [avatar definition]
226. happy(mary) <- (18) [avatar component clause 225]
229. 18 | ~15 [avatar split clause 126,210,225]
231. 19 <=> creative(mary) [avatar definition]
232. ~creative(mary) <- (~19) [avatar component clause 231]
235. 20 <=> quiet(mary) [avatar definition]
236. quiet(mary) <- (20) [avatar component clause 235]
239. ~19 | 20 [avatar split clause 128,235,231]
241. 13 [avatar split clause 134,201]
257. tall(mary) <- (~19) [resolution 167,232]
260. 15 | 19 [avatar split clause 257,231,210]
269. creative(mary) <- (18) [resolution 198,226]
272. 19 | ~18 [avatar split clause 269,225,231]
278. ~curious(mary) <- (20) [resolution 236,105]
282. $false <- (13, 20) [subsumption resolution 278,203]
283. ~13 | ~20 [avatar contradiction clause 282]
284. $false [avatar sat refutation 229,239,241,260,272,283]
% SZS output end Proof for 857591153606040142820222
% ------------------------------
% 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 or not funny is happy and vice versa. If someone is not humble then someone is both not generous and not calm and vice versa. Everyone who is not generous or not tall is tall and vice versa. Everyone who is either happy or not humble is both not tall and not curious. If susan is not patient then alice is either rich or not tall. If alice is both old and not calm then someone is either strong or funny and vice versa. Everyone who is either creative or happy is either not brave or not calm. If someone is rich then someone is either not old or calm and vice versa. If someone is not strong then mary is either curious or not funny. Everyone who is both not curious and wise is funny and vice versa. Everyone who is either not happy or not quiet is either generous or not patient. If someone is not generous or not calm then fred is both not quiet and funny and vice versa. Everyone who is patient or happy is both patient and humble and vice versa. If someone is not old then someone is either humble or funny. Everyone who is not wise or not kind is not kind and vice versa. Someone is either not tall or not kind. Lucy is not patient. Alice is either strong or not creative. Fred is not quiet or strong. | Alice is not strong. | contradiction | (![X]:((~humble(X)|~funny(X))<=>happy(X)))&
((?[X]:(~humble(X)))<=>(?[X]:((~generous(X)&~calm(X)))))&
(![X]:((~generous(X)|~tall(X))<=>tall(X)))&
(![X]:((happy(X)<~>~humble(X))=>(~tall(X)&~curious(X))))&
((~patient(susan))=>((rich(alice)<~>~tall(alice))))&
(((old(alice)&~calm(alice)))<=>(?[X]:((strong(X)<~>funny(X)))))&
(![X]:((creative(X)<~>happy(X))=>(~brave(X)<~>~calm(X))))&
((?[X]:(rich(X)))<=>(?[X]:((~old(X)<~>calm(X)))))&
((?[X]:(~strong(X)))=>((curious(mary)<~>~funny(mary))))&
(![X]:((~curious(X)&wise(X))<=>funny(X)))&
(![X]:((~happy(X)<~>~quiet(X))=>(generous(X)<~>~patient(X))))&
((?[X]:((~generous(X)|~calm(X))))<=>((~quiet(fred)&funny(fred))))&
(![X]:((patient(X)|happy(X))<=>(patient(X)&humble(X))))&
((?[X]:(~old(X)))=>(?[X]:((humble(X)<~>funny(X)))))&
(![X]:((~wise(X)|~kind(X))<=>~kind(X)))&
(?[X]:((~tall(X)<~>~kind(X))))&
(~patient(lucy))&
((strong(alice)<~>~creative(alice)))&
((~quiet(fred)|strong(fred))) | ~strong(alice) | [
"p0",
"p2",
"p3",
"p8",
"p9",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 1556439396056134382267891
% SZS output start Proof for 1556439396056134382267891
1. ! [X0] : ((~funny(X0) | ~humble(X0)) <=> happy(X0)) [input p0]
3. ! [X0] : ((~tall(X0) | ~generous(X0)) <=> tall(X0)) [input p2]
4. ! [X0] : ((happy(X0) <~> ~humble(X0)) => (~curious(X0) & ~tall(X0))) [input p3]
9. ? [X0] : ~strong(X0) => (curious(mary) <~> ~funny(mary)) [input p8]
10. ! [X0] : ((wise(X0) & ~curious(X0)) <=> funny(X0)) [input p9]
13. ! [X0] : ((happy(X0) | patient(X0)) <=> (humble(X0) & patient(X0))) [input p12]
20. ~strong(alice) [input hypothesis]
24. ! [X0] : ((~curious(X0) & ~tall(X0)) | (happy(X0) <=> ~humble(X0))) [ennf transformation 4]
27. (curious(mary) <~> ~funny(mary)) | ! [X0] : strong(X0) [ennf transformation 9]
30. ! [X0] : (((~funny(X0) | ~humble(X0)) | ~happy(X0)) & (happy(X0) | (funny(X0) & humble(X0)))) [nnf transformation 1]
31. ! [X0] : ((~funny(X0) | ~humble(X0) | ~happy(X0)) & (happy(X0) | (funny(X0) & humble(X0)))) [flattening 30]
37. ! [X0] : (((~tall(X0) | ~generous(X0)) | ~tall(X0)) & (tall(X0) | (tall(X0) & generous(X0)))) [nnf transformation 3]
38. ! [X0] : ((~tall(X0) | ~generous(X0) | ~tall(X0)) & (tall(X0) | (tall(X0) & generous(X0)))) [flattening 37]
39. ! [X0] : ((~curious(X0) & ~tall(X0)) | ((happy(X0) | humble(X0)) & (~humble(X0) | ~happy(X0)))) [nnf transformation 24]
52. ((funny(mary) | ~curious(mary)) & (~funny(mary) | curious(mary))) | ! [X0] : strong(X0) [nnf transformation 27]
53. ! [X0] : (((wise(X0) & ~curious(X0)) | ~funny(X0)) & (funny(X0) | (~wise(X0) | curious(X0)))) [nnf transformation 10]
54. ! [X0] : (((wise(X0) & ~curious(X0)) | ~funny(X0)) & (funny(X0) | ~wise(X0) | curious(X0))) [flattening 53]
61. ! [X0] : (((happy(X0) | patient(X0)) | (~humble(X0) | ~patient(X0))) & ((humble(X0) & patient(X0)) | (~happy(X0) & ~patient(X0)))) [nnf transformation 13]
62. ! [X0] : ((happy(X0) | patient(X0) | ~humble(X0) | ~patient(X0)) & ((humble(X0) & patient(X0)) | (~happy(X0) & ~patient(X0)))) [flattening 61]
74. happy(X0) | funny(X0) [cnf transformation 31]
80. tall(X0) | tall(X0) [cnf transformation 38]
82. ~tall(X0) | ~humble(X0) | ~happy(X0) [cnf transformation 39]
102. ~funny(mary) | curious(mary) | strong(X0) [cnf transformation 52]
105. ~curious(X0) | ~funny(X0) [cnf transformation 54]
119. humble(X0) | ~happy(X0) [cnf transformation 62]
132. ~strong(alice) [cnf transformation 20]
133. tall(X0) [duplicate literal removal 80]
156. ~humble(X0) | ~happy(X0) [subsumption resolution 82,133]
221. 20 <=> ! [X0] : strong(X0) [avatar definition]
222. strong(X0) <- (20) [avatar component clause 221]
224. 21 <=> curious(mary) [avatar definition]
225. curious(mary) <- (21) [avatar component clause 224]
228. 22 <=> funny(mary) [avatar definition]
229. ~funny(mary) <- (~22) [avatar component clause 228]
232. 20 | 21 | ~22 [avatar split clause 102,228,224,221]
260. ~happy(X0) [subsumption resolution 119,156]
276. 32 <=> strong(alice) [avatar definition]
278. ~strong(alice) <- (~32) [avatar component clause 276]
290. ~32 [avatar split clause 132,276]
306. funny(X0) [resolution 74,260]
307. $false <- (~22) [resolution 306,229]
310. 22 [avatar contradiction clause 307]
311. $false <- (20, ~32) [resolution 222,278]
312. ~20 | 32 [avatar contradiction clause 311]
313. ~funny(mary) <- (21) [resolution 225,105]
314. $false <- (21) [subsumption resolution 313,306]
315. ~21 [avatar contradiction clause 314]
316. $false [avatar sat refutation 232,290,310,312,315]
% SZS output end Proof for 1556439396056134382267891
% ------------------------------
% 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 brave and not generous then john is either not creative or generous and vice versa.
Everyone who is patient is both not humble and not creative.
Everyone who is quiet or tall is calm.
Everyone who is old or creative is calm or funny.
If fred is rich or not happy then susan is both not calm and funny.
Everyone who is both rich and not strong is both old and not curious.
If someone is both not strong and brave then someone is creative and vice versa.
Everyone who is funny is either not humble or strong and vice versa.
Everyone who is not brave or patient is either not calm or not patient and vice versa.
Everyone who is funny or not creative is not funny.
Everyone who is not kind or patient is creative or funny and vice versa.
If john is both patient and tall then alice is not quiet.
If fred is not rich then lucy is either not creative or not old.
Everyone who is not happy or creative is tall and vice versa.
Everyone who is not rich or quiet is either kind or not calm.
If someone is both rich and not curious then alice is humble and vice versa.
Someone is happy or not funny.
Susan is not brave.
Someone is quiet.
Alice is not generous or not brave.
Someone is strong or tall.
Alice is not tall.
Someone is not creative. | Fred is not kind. | contradiction | ((?[X]:((brave(X)&~generous(X))))<=>((~creative(john)<~>generous(john))))&
(![X]:(patient(X)=>(~humble(X)&~creative(X))))&
(![X]:((quiet(X)|tall(X))=>calm(X)))&
(![X]:((old(X)|creative(X))=>(calm(X)|funny(X))))&
(((rich(fred)|~happy(fred)))=>((~calm(susan)&funny(susan))))&
(![X]:((rich(X)&~strong(X))=>(old(X)&~curious(X))))&
((?[X]:((~strong(X)&brave(X))))<=>(?[X]:(creative(X))))&
(![X]:(funny(X)<=>(~humble(X)<~>strong(X))))&
(![X]:((~brave(X)|patient(X))<=>(~calm(X)<~>~patient(X))))&
(![X]:((funny(X)|~creative(X))=>~funny(X)))&
(![X]:((~kind(X)|patient(X))<=>(creative(X)|funny(X))))&
(((patient(john)&tall(john)))=>(~quiet(alice)))&
((~rich(fred))=>((~creative(lucy)<~>~old(lucy))))&
(![X]:((~happy(X)|creative(X))<=>tall(X)))&
(![X]:((~rich(X)|quiet(X))=>(kind(X)<~>~calm(X))))&
((?[X]:((rich(X)&~curious(X))))<=>(humble(alice)))&
(?[X]:((happy(X)|~funny(X))))&
(~brave(susan))&
(?[X]:(quiet(X)))&
((~generous(alice)|~brave(alice)))&
(?[X]:((strong(X)|tall(X))))&
(~tall(alice))&
(?[X]:(~creative(X))) | ~kind(fred) | [
"p1",
"p3",
"p4",
"p8",
"p9",
"p10",
"p14",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 7035075265512903843926354
% SZS output start Proof for 7035075265512903843926354
2. ! [X0] : (patient(X0) => (~creative(X0) & ~humble(X0))) [input p1]
4. ! [X0] : ((creative(X0) | old(X0)) => (funny(X0) | calm(X0))) [input p3]
5. (~happy(fred) | rich(fred)) => (funny(susan) & ~calm(susan)) [input p4]
9. ! [X0] : ((patient(X0) | ~brave(X0)) <=> (~calm(X0) <~> ~patient(X0))) [input p8]
10. ! [X0] : ((~creative(X0) | funny(X0)) => ~funny(X0)) [input p9]
11. ! [X0] : ((patient(X0) | ~kind(X0)) <=> (funny(X0) | creative(X0))) [input p10]
15. ! [X0] : ((quiet(X0) | ~rich(X0)) => (kind(X0) <~> ~calm(X0))) [input p14]
18. ~brave(susan) [input p17]
24. ~kind(fred) [input hypothesis]
26. ! [X0] : ((~creative(X0) & ~humble(X0)) | ~patient(X0)) [ennf transformation 2]
28. ! [X0] : ((funny(X0) | calm(X0)) | (~creative(X0) & ~old(X0))) [ennf transformation 4]
29. ! [X0] : (funny(X0) | calm(X0) | (~creative(X0) & ~old(X0))) [flattening 28]
30. (funny(susan) & ~calm(susan)) | (happy(fred) & ~rich(fred)) [ennf transformation 5]
33. ! [X0] : (~funny(X0) | (creative(X0) & ~funny(X0))) [ennf transformation 10]
37. ! [X0] : ((kind(X0) <~> ~calm(X0)) | (~quiet(X0) & rich(X0))) [ennf transformation 15]
48. ! [X0] : (((patient(X0) | ~brave(X0)) | ((~calm(X0) | patient(X0)) & (~patient(X0) | calm(X0)))) & (((patient(X0) | calm(X0)) & (~patient(X0) | ~calm(X0))) | (~patient(X0) & brave(X0)))) [nnf transformation 9]
49. ! [X0] : ((patient(X0) | ~brave(X0) | ((~calm(X0) | patient(X0)) & (~patient(X0) | calm(X0)))) & (((patient(X0) | calm(X0)) & (~patient(X0) | ~calm(X0))) | (~patient(X0) & brave(X0)))) [flattening 48]
50. ! [X0] : (((patient(X0) | ~kind(X0)) | (~funny(X0) & ~creative(X0))) & ((funny(X0) | creative(X0)) | (~patient(X0) & kind(X0)))) [nnf transformation 11]
51. ! [X0] : ((patient(X0) | ~kind(X0) | (~funny(X0) & ~creative(X0))) & (funny(X0) | creative(X0) | (~patient(X0) & kind(X0)))) [flattening 50]
55. ! [X0] : (((calm(X0) | ~kind(X0)) & (~calm(X0) | kind(X0))) | (~quiet(X0) & rich(X0))) [nnf transformation 37]
75. ~patient(X0) | ~creative(X0) [cnf transformation 26]
79. ~creative(X0) | calm(X0) | funny(X0) [cnf transformation 29]
80. ~calm(susan) | ~rich(fred) [cnf transformation 30]
95. calm(X0) | patient(X0) | brave(X0) [cnf transformation 49]
99. ~funny(X0) | ~funny(X0) [cnf transformation 33]
101. funny(X0) | creative(X0) | kind(X0) [cnf transformation 51]
102. funny(X0) | creative(X0) | ~patient(X0) [cnf transformation 51]
111. ~calm(X0) | kind(X0) | rich(X0) [cnf transformation 55]
119. ~brave(susan) [cnf transformation 18]
125. ~kind(fred) [cnf transformation 24]
126. ~funny(X0) [duplicate literal removal 99]
164. 8 <=> rich(fred) [avatar definition]
166. ~rich(fred) <- (~8) [avatar component clause 164]
169. 9 <=> calm(susan) [avatar definition]
171. ~calm(susan) <- (~9) [avatar component clause 169]
173. ~8 | ~9 [avatar split clause 80,169,164]
196. creative(X0) | ~patient(X0) [subsumption resolution 102,126]
197. ~patient(X0) [subsumption resolution 196,75]
198. kind(X0) | creative(X0) [subsumption resolution 101,126]
261. creative(fred) [resolution 198,125]
269. calm(fred) | funny(fred) [resolution 79,261]
270. calm(fred) [subsumption resolution 269,126]
294. patient(susan) | brave(susan) <- (~9) [resolution 95,171]
296. brave(susan) <- (~9) [subsumption resolution 294,197]
297. $false <- (~9) [subsumption resolution 296,119]
298. 9 [avatar contradiction clause 297]
303. kind(fred) | rich(fred) [resolution 111,270]
309. rich(fred) [subsumption resolution 303,125]
310. $false <- (~8) [subsumption resolution 309,166]
311. 8 [avatar contradiction clause 310]
339. $false [avatar sat refutation 173,298,311]
% SZS output end Proof for 7035075265512903843926354
% ------------------------------
% 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 wise or kind is both creative and calm and vice versa.
If someone is both wise and calm then someone is not calm.
If alice is both kind and not brave then alice is both old and not strong and vice versa.
If someone is patient then john is rich.
If mary is funny then someone is not wise or not strong.
Everyone who is curious or not old is brave or not wise.
Everyone who is tall is not generous and vice versa.
Everyone who is brave is patient and vice versa.
Everyone who is either patient or not strong is both not calm and brave and vice versa.
Everyone who is not strong is kind or not calm and vice versa.
If susan is old or not tall then someone is quiet.
If someone is both quiet and happy then fred is happy or generous and vice versa.
Everyone who is not wise or not rich is both not happy and not brave.
Everyone who is either not curious or not brave is curious or funny and vice versa.
Everyone who is not curious or not calm is not calm and vice versa.
Everyone who is either rich or curious is brave or not quiet and vice versa.
Paul is both not humble and not generous.
Someone is either not funny or not wise.
Someone is either not brave or not funny.
Alice is both calm and not tall.
Susan is not funny or funny.
Someone is both not tall and not wise. | Paul is curious. | entailment | (![X]:((~wise(X)<~>kind(X))<=>(creative(X)&calm(X))))&
((?[X]:((wise(X)&calm(X))))=>(?[X]:(~calm(X))))&
(((kind(alice)&~brave(alice)))<=>((old(alice)&~strong(alice))))&
((?[X]:(patient(X)))=>(rich(john)))&
((funny(mary))=>(?[X]:((~wise(X)|~strong(X)))))&
(![X]:((curious(X)|~old(X))=>(brave(X)|~wise(X))))&
(![X]:(tall(X)<=>~generous(X)))&
(![X]:(brave(X)<=>patient(X)))&
(![X]:((patient(X)<~>~strong(X))<=>(~calm(X)&brave(X))))&
(![X]:(~strong(X)<=>(kind(X)|~calm(X))))&
(((old(susan)|~tall(susan)))=>(?[X]:(quiet(X))))&
((?[X]:((quiet(X)&happy(X))))<=>((happy(fred)|generous(fred))))&
(![X]:((~wise(X)|~rich(X))=>(~happy(X)&~brave(X))))&
(![X]:((~curious(X)<~>~brave(X))<=>(curious(X)|funny(X))))&
(![X]:((~curious(X)|~calm(X))<=>~calm(X)))&
(![X]:((rich(X)<~>curious(X))<=>(brave(X)|~quiet(X))))&
((~humble(paul)&~generous(paul)))&
(?[X]:((~funny(X)<~>~wise(X))))&
(?[X]:((~brave(X)<~>~funny(X))))&
((calm(alice)&~tall(alice)))&
((~funny(susan)|funny(susan)))&
(?[X]:((~tall(X)&~wise(X)))) | curious(paul) | [
"p7",
"p8",
"p9",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3342937417163126743447257
% SZS output start Proof for 3342937417163126743447257
8. ! [X0] : (brave(X0) <=> patient(X0)) [input p7]
9. ! [X0] : ((patient(X0) <~> ~strong(X0)) <=> (brave(X0) & ~calm(X0))) [input p8]
10. ! [X0] : (~strong(X0) <=> (~calm(X0) | kind(X0))) [input p9]
15. ! [X0] : ((~calm(X0) | ~curious(X0)) <=> ~calm(X0)) [input p14]
23. ~curious(paul) [input hypothesis]
43. ! [X0] : ((brave(X0) | ~patient(X0)) & (patient(X0) | ~brave(X0))) [nnf transformation 8]
44. ! [X0] : ((((strong(X0) | ~patient(X0)) & (~strong(X0) | patient(X0))) | (~brave(X0) | calm(X0))) & ((brave(X0) & ~calm(X0)) | ((patient(X0) | strong(X0)) & (~strong(X0) | ~patient(X0))))) [nnf transformation 9]
45. ! [X0] : ((((strong(X0) | ~patient(X0)) & (~strong(X0) | patient(X0))) | ~brave(X0) | calm(X0)) & ((brave(X0) & ~calm(X0)) | ((patient(X0) | strong(X0)) & (~strong(X0) | ~patient(X0))))) [flattening 44]
46. ! [X0] : ((~strong(X0) | (calm(X0) & ~kind(X0))) & ((~calm(X0) | kind(X0)) | strong(X0))) [nnf transformation 10]
47. ! [X0] : ((~strong(X0) | (calm(X0) & ~kind(X0))) & (~calm(X0) | kind(X0) | strong(X0))) [flattening 46]
57. ! [X0] : (((~calm(X0) | ~curious(X0)) | calm(X0)) & (~calm(X0) | (calm(X0) & curious(X0)))) [nnf transformation 15]
58. ! [X0] : ((~calm(X0) | ~curious(X0) | calm(X0)) & (~calm(X0) | (calm(X0) & curious(X0)))) [flattening 57]
86. ~brave(X0) | patient(X0) [cnf transformation 43]
87. ~patient(X0) | brave(X0) [cnf transformation 43]
91. brave(X0) | patient(X0) | strong(X0) [cnf transformation 45]
93. strong(X0) | ~patient(X0) | ~brave(X0) | calm(X0) [cnf transformation 45]
96. ~strong(X0) | calm(X0) [cnf transformation 47]
114. ~calm(X0) | curious(X0) [cnf transformation 58]
133. ~curious(paul) [cnf transformation 23]
185. ~brave(X0) | strong(X0) | calm(X0) [subsumption resolution 93,86]
186. patient(X0) | strong(X0) [subsumption resolution 91,86]
247. strong(X0) | brave(X0) [resolution 186,87]
248. brave(X0) | calm(X0) [resolution 247,96]
368. strong(X0) | calm(X0) | calm(X0) [resolution 185,248]
370. strong(X0) | calm(X0) [duplicate literal removal 368]
371. calm(X0) [subsumption resolution 370,96]
374. curious(X1) [resolution 371,114]
411. $false [resolution 374,133]
% SZS output end Proof for 3342937417163126743447257
% ------------------------------
% 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 wise or not funny is either rich or patient and vice versa.
If john is not humble or happy then paul is both not kind and not generous and vice versa.
Everyone who is strong is not rich or not patient and vice versa.
If someone is old then paul is either not wise or curious.
Everyone who is generous is either calm or tall.
If someone is humble then alice is either happy or not quiet and vice versa.
If mary is brave then john is not generous.
Everyone who is either not funny or not creative is not strong and vice versa.
Everyone who is either not humble or curious is quiet or patient and vice versa.
Everyone who is both quiet and not kind is both creative and strong and vice versa.
If someone is either calm or patient then someone is quiet or not quiet and vice versa.
If alice is either not old or not calm then susan is not calm and vice versa.
If someone is both creative and rich then fred is either not strong or brave and vice versa.
If john is not calm then someone is not strong or humble.
Everyone who is both rich and creative is quiet.
Everyone who is not strong or humble is quiet.
Someone is not generous.
Paul is both not quiet and not old.
Someone is either patient or old.
John is either not curious or not quiet.
Someone is wise.
Someone is either not wise or not quiet.
Someone is not patient.
Susan is not patient. | Paul is not old. | entailment | (![X]:((wise(X)<~>~funny(X))<=>(rich(X)<~>patient(X))))&
(((~humble(john)|happy(john)))<=>((~kind(paul)&~generous(paul))))&
(![X]:(strong(X)<=>(~rich(X)|~patient(X))))&
((?[X]:(old(X)))=>((~wise(paul)<~>curious(paul))))&
(![X]:(generous(X)=>(calm(X)<~>tall(X))))&
((?[X]:(humble(X)))<=>((happy(alice)<~>~quiet(alice))))&
((brave(mary))=>(~generous(john)))&
(![X]:((~funny(X)<~>~creative(X))<=>~strong(X)))&
(![X]:((~humble(X)<~>curious(X))<=>(quiet(X)|patient(X))))&
(![X]:((quiet(X)&~kind(X))<=>(creative(X)&strong(X))))&
((?[X]:((calm(X)<~>patient(X))))<=>(?[X]:((quiet(X)|~quiet(X)))))&
(((~old(alice)<~>~calm(alice)))<=>(~calm(susan)))&
((?[X]:((creative(X)&rich(X))))<=>((~strong(fred)<~>brave(fred))))&
((~calm(john))=>(?[X]:((~strong(X)|humble(X)))))&
(![X]:((rich(X)&creative(X))=>quiet(X)))&
(![X]:((~strong(X)|humble(X))=>quiet(X)))&
(?[X]:(~generous(X)))&
((~quiet(paul)&~old(paul)))&
(?[X]:((patient(X)<~>old(X))))&
((~curious(john)<~>~quiet(john)))&
(?[X]:(wise(X)))&
(?[X]:((~wise(X)<~>~quiet(X))))&
(?[X]:(~patient(X)))&
(~patient(susan)) | ~old(paul) | [
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 5577044644864267791847674
% SZS output start Proof for 5577044644864267791847674
18. ~old(paul) & ~quiet(paul) [input p17]
25. old(paul) [input hypothesis]
136. ~old(paul) [cnf transformation 18]
146. old(paul) [cnf transformation 25]
311. $false [subsumption resolution 146,136]
% SZS output end Proof for 5577044644864267791847674
% ------------------------------
% 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 |
Everyone who is either old or happy is either old or wise and vice versa. Everyone who is not old is not generous and vice versa. Everyone who is patient is both patient and wise. If someone is either not patient or not creative then fred is either creative or not creative and vice versa. If someone is calm then fred is either not funny or funny and vice versa. Everyone who is not humble or tall is quiet or tall and vice versa. If fred is curious or humble then fred is not generous. Everyone who is tall is not patient or calm. If someone is not strong or rich then someone is humble or tall. Everyone who is rich or happy is either tall or brave. If lucy is humble then fred is either tall or not brave. If lucy is both kind and creative then someone is generous or curious. If mary is either humble or creative then susan is curious or not funny. Everyone who is either not curious or creative is generous. If someone is both strong and rich then paul is not strong or old and vice versa. Everyone who is both kind and wise is both creative and not patient and vice versa. Someone is funny or tall. Someone is both patient and not creative. Someone is generous or quiet. Susan is happy. Mary is creative. Someone is curious or not creative. Alice is both happy and brave. Lucy is either not calm or not happy. | Susan is not curious. | neutral | (![X]:((old(X)<~>happy(X))<=>(old(X)<~>wise(X))))&
(![X]:(~old(X)<=>~generous(X)))&
(![X]:(patient(X)=>(patient(X)&wise(X))))&
((?[X]:((~patient(X)<~>~creative(X))))<=>((creative(fred)<~>~creative(fred))))&
((?[X]:(calm(X)))<=>((~funny(fred)<~>funny(fred))))&
(![X]:((~humble(X)|tall(X))<=>(quiet(X)|tall(X))))&
(((curious(fred)|humble(fred)))=>(~generous(fred)))&
(![X]:(tall(X)=>(~patient(X)|calm(X))))&
((?[X]:((~strong(X)|rich(X))))=>(?[X]:((humble(X)|tall(X)))))&
(![X]:((rich(X)|happy(X))=>(tall(X)<~>brave(X))))&
((humble(lucy))=>((tall(fred)<~>~brave(fred))))&
(((kind(lucy)&creative(lucy)))=>(?[X]:((generous(X)|curious(X)))))&
(((humble(mary)<~>creative(mary)))=>((curious(susan)|~funny(susan))))&
(![X]:((~curious(X)<~>creative(X))=>generous(X)))&
((?[X]:((strong(X)&rich(X))))<=>((~strong(paul)|old(paul))))&
(![X]:((kind(X)&wise(X))<=>(creative(X)&~patient(X))))&
(?[X]:((funny(X)|tall(X))))&
(?[X]:((patient(X)&~creative(X))))&
(?[X]:((generous(X)|quiet(X))))&
(happy(susan))&
(creative(mary))&
(?[X]:((curious(X)|~creative(X))))&
((happy(alice)&brave(alice)))&
((~calm(lucy)<~>~happy(lucy))) | ~curious(susan) | [] | null | 0 |
Everyone who is not old is creative or not patient and vice versa.
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.
If someone is not calm or humble then susan is not strong.
Someone is brave.
Someone is generous.
Susan is wise.
Mary is wise or not funny.
Someone is calm or happy.
Someone is not calm.
Someone is brave or not quiet.
Someone is either generous or funny. | John is patient. | entailment | (![X]:(~old(X)<=>(creative(X)|~patient(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]:((~calm(X)|humble(X))))=>(~strong(susan)))&
(?[X]:(brave(X)))&
(?[X]:(generous(X)))&
(wise(susan))&
((wise(mary)|~funny(mary)))&
(?[X]:((calm(X)|happy(X))))&
(?[X]:(~calm(X)))&
(?[X]:((brave(X)|~quiet(X))))&
(?[X]:((generous(X)<~>funny(X)))) | patient(john) | [
"p0",
"p2",
"p5",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 4909461610446697274941368
% SZS output start Proof for 4909461610446697274941368
1. ! [X0] : (~old(X0) <=> (~patient(X0) | creative(X0))) [input p0]
3. ! [X0] : ((~funny(X0) | old(X0)) => (old(X0) <~> calm(X0))) [input p2]
6. ! [X0] : ((curious(X0) & ~calm(X0)) <=> (~calm(X0) <~> calm(X0))) [input p5]
14. funny(john) <=> (creative(susan) & ~curious(susan)) [input p13]
25. ~patient(john) [input hypothesis]
28. ! [X0] : ((old(X0) <~> calm(X0)) | (funny(X0) & ~old(X0))) [ennf transformation 3]
39. ! [X0] : ((~old(X0) | (patient(X0) & ~creative(X0))) & ((~patient(X0) | creative(X0)) | old(X0))) [nnf transformation 1]
40. ! [X0] : ((~old(X0) | (patient(X0) & ~creative(X0))) & (~patient(X0) | creative(X0) | old(X0))) [flattening 39]
43. ! [X0] : (((~calm(X0) | ~old(X0)) & (calm(X0) | old(X0))) | (funny(X0) & ~old(X0))) [nnf transformation 28]
47. ! [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 6]
48. ! [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 47]
65. (funny(john) | (~creative(susan) | curious(susan))) & ((creative(susan) & ~curious(susan)) | ~funny(john)) [nnf transformation 14]
66. (funny(john) | ~creative(susan) | curious(susan)) & ((creative(susan) & ~curious(susan)) | ~funny(john)) [flattening 65]
80. ~old(X0) | patient(X0) [cnf transformation 40]
85. calm(X0) | old(X0) | funny(X0) [cnf transformation 43]
103. ~calm(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 48]
104. curious(X0) | calm(X0) | calm(X0) [cnf transformation 48]
105. curious(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 48]
125. ~curious(susan) | ~funny(john) [cnf transformation 66]
140. ~patient(john) [cnf transformation 25]
145. ~calm(X0) [duplicate literal removal 103]
146. curious(X0) | calm(X0) [duplicate literal removal 104]
147. ~calm(X0) | curious(X0) [duplicate literal removal 105]
149. curious(X0) [subsumption resolution 146,147]
199. 11 <=> funny(john) [avatar definition]
201. ~funny(john) <- (~11) [avatar component clause 199]
207. ~funny(john) [subsumption resolution 125,149]
208. ~11 [avatar split clause 207,199]
303. funny(X2) | old(X2) [resolution 85,145]
306. old(john) <- (~11) [resolution 303,201]
326. patient(john) <- (~11) [resolution 306,80]
327. $false <- (~11) [subsumption resolution 326,140]
328. 11 [avatar contradiction clause 327]
329. $false [avatar sat refutation 208,328]
% SZS output end Proof for 4909461610446697274941368
% ------------------------------
% 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 brave or not old is funny or not happy.
If mary is either not kind or not old then someone is either not rich or not old.
If someone is kind or creative then mary is either strong or not funny and vice versa.
Everyone who is patient or humble is strong or not strong and vice versa.
Everyone who is both not generous and wise is either humble or patient and vice versa.
Everyone who is patient is either funny or not quiet.
If someone is either wise or not humble then someone is funny or kind and vice versa.
If susan is either quiet or not brave then someone is not happy or not calm and vice versa.
Everyone who is either not calm or quiet is not curious and vice versa.
Everyone who is not quiet is either brave or kind and vice versa.
Everyone who is either generous or not funny is not brave or not generous and vice versa.
Everyone who is not curious or tall is either humble or not curious.
Everyone who is curious is both patient and not quiet.
Everyone who is not wise is both kind and creative and vice versa.
If john is creative then someone is either not kind or tall and vice versa.
If someone is both old and rich then someone is both not rich and not wise.
John is wise or not calm.
Someone is either not patient or generous.
Paul is either not kind or not funny.
Mary is strong or calm.
Lucy is not kind or not strong.
Someone is generous. | John is not kind. | neutral | (![X]:((~brave(X)<~>~old(X))=>(funny(X)|~happy(X))))&
(((~kind(mary)<~>~old(mary)))=>(?[X]:((~rich(X)<~>~old(X)))))&
((?[X]:((kind(X)|creative(X))))<=>((strong(mary)<~>~funny(mary))))&
(![X]:((patient(X)|humble(X))<=>(strong(X)|~strong(X))))&
(![X]:((~generous(X)&wise(X))<=>(humble(X)<~>patient(X))))&
(![X]:(patient(X)=>(funny(X)<~>~quiet(X))))&
((?[X]:((wise(X)<~>~humble(X))))<=>(?[X]:((funny(X)|kind(X)))))&
(((quiet(susan)<~>~brave(susan)))<=>(?[X]:((~happy(X)|~calm(X)))))&
(![X]:((~calm(X)<~>quiet(X))<=>~curious(X)))&
(![X]:(~quiet(X)<=>(brave(X)<~>kind(X))))&
(![X]:((generous(X)<~>~funny(X))<=>(~brave(X)|~generous(X))))&
(![X]:((~curious(X)|tall(X))=>(humble(X)<~>~curious(X))))&
(![X]:(curious(X)=>(patient(X)&~quiet(X))))&
(![X]:(~wise(X)<=>(kind(X)&creative(X))))&
((creative(john))<=>(?[X]:((~kind(X)<~>tall(X)))))&
((?[X]:((old(X)&rich(X))))=>(?[X]:((~rich(X)&~wise(X)))))&
((wise(john)|~calm(john)))&
(?[X]:((~patient(X)<~>generous(X))))&
((~kind(paul)<~>~funny(paul)))&
((strong(mary)|calm(mary)))&
((~kind(lucy)|~strong(lucy)))&
(?[X]:(generous(X))) | ~kind(john) | [] | null | 0 |
Everyone who is either not humble or not rich is either not humble or not kind and vice versa.
If lucy is both not patient and not tall then lucy is both not creative and brave and vice versa.
If someone is both not humble and not tall then someone is not creative or not quiet.
Everyone who is wise is calm or curious and vice versa.
If someone is both happy and not kind then alice is either kind or not generous and vice versa.
Everyone who is either not curious or wise is both patient and strong and vice versa.
If someone is both tall and not patient then someone is creative and vice versa.
If someone is old or not creative then mary is both old and humble.
Everyone who is both calm and not humble is creative.
Everyone who is calm is not brave.
Everyone who is both generous and kind is not generous and vice versa.
Everyone who is curious or kind is both brave and not wise.
Everyone who is both not quiet and not humble is either not creative or not brave and vice versa.
Everyone who is not quiet is either brave or generous.
Everyone who is not funny is both patient and rich and vice versa.
Everyone who is creative or not rich is either not strong or not rich.
Someone is not strong or not quiet.
Someone is either generous or not generous.
Someone is quiet or not tall.
Someone is both funny and not patient.
Lucy is not brave or not funny.
Alice is not brave or not creative.
Someone is either creative or kind.
Someone is either not funny or quiet. | Mary is not quiet. | neutral | (![X]:((~humble(X)<~>~rich(X))<=>(~humble(X)<~>~kind(X))))&
(((~patient(lucy)&~tall(lucy)))<=>((~creative(lucy)&brave(lucy))))&
((?[X]:((~humble(X)&~tall(X))))=>(?[X]:((~creative(X)|~quiet(X)))))&
(![X]:(wise(X)<=>(calm(X)|curious(X))))&
((?[X]:((happy(X)&~kind(X))))<=>((kind(alice)<~>~generous(alice))))&
(![X]:((~curious(X)<~>wise(X))<=>(patient(X)&strong(X))))&
((?[X]:((tall(X)&~patient(X))))<=>(?[X]:(creative(X))))&
((?[X]:((old(X)|~creative(X))))=>((old(mary)&humble(mary))))&
(![X]:((calm(X)&~humble(X))=>creative(X)))&
(![X]:(calm(X)=>~brave(X)))&
(![X]:((generous(X)&kind(X))<=>~generous(X)))&
(![X]:((curious(X)|kind(X))=>(brave(X)&~wise(X))))&
(![X]:((~quiet(X)&~humble(X))<=>(~creative(X)<~>~brave(X))))&
(![X]:(~quiet(X)=>(brave(X)<~>generous(X))))&
(![X]:(~funny(X)<=>(patient(X)&rich(X))))&
(![X]:((creative(X)|~rich(X))=>(~strong(X)<~>~rich(X))))&
(?[X]:((~strong(X)|~quiet(X))))&
(?[X]:((generous(X)<~>~generous(X))))&
(?[X]:((quiet(X)|~tall(X))))&
(?[X]:((funny(X)&~patient(X))))&
((~brave(lucy)|~funny(lucy)))&
((~brave(alice)|~creative(alice)))&
(?[X]:((creative(X)<~>kind(X))))&
(?[X]:((~funny(X)<~>quiet(X)))) | ~quiet(mary) | [] | null | 0 |
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