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 either not generous or not brave then susan is both kind and calm. If fred is not rich then someone is either kind or not tall and vice versa. Everyone who is not happy or not kind is both not tall and calm. Everyone who is either not patient or tall is old and vice versa. Everyone who is both happy and not patient is either curious or not old and vice versa. If alice is curious then someone is both not strong and not creative. If mary is either not humble or curious then susan is humble and vice versa. Everyone who is both creative and not tall is both funny and not quiet. Everyone who is happy is strong or not rich. Everyone who is either patient or humble is either strong or not happy and vice versa. Everyone who is kind or wise is not kind and vice versa. If someone is both not rich and old then someone is tall or not kind and vice versa. Everyone who is both old and calm is both brave and not funny. Everyone who is either not brave or not old is not funny or not brave. If paul is curious then mary is both wise and tall. If fred is not rich then someone is both calm and curious and vice versa. Lucy is either happy or not happy. Someone is either not rich or not patient. Someone is brave or not rich. Someone is not happy or not old. Alice is both not patient and not funny. Someone is either not generous or happy. | Mary is not rich. | neutral | ((?[X]:((~generous(X)<~>~brave(X))))=>((kind(susan)&calm(susan))))&
((~rich(fred))<=>(?[X]:((kind(X)<~>~tall(X)))))&
(![X]:((~happy(X)|~kind(X))=>(~tall(X)&calm(X))))&
(![X]:((~patient(X)<~>tall(X))<=>old(X)))&
(![X]:((happy(X)&~patient(X))<=>(curious(X)<~>~old(X))))&
((curious(alice))=>(?[X]:((~strong(X)&~creative(X)))))&
(((~humble(mary)<~>curious(mary)))<=>(humble(susan)))&
(![X]:((creative(X)&~tall(X))=>(funny(X)&~quiet(X))))&
(![X]:(happy(X)=>(strong(X)|~rich(X))))&
(![X]:((patient(X)<~>humble(X))<=>(strong(X)<~>~happy(X))))&
(![X]:((kind(X)|wise(X))<=>~kind(X)))&
((?[X]:((~rich(X)&old(X))))<=>(?[X]:((tall(X)|~kind(X)))))&
(![X]:((old(X)&calm(X))=>(brave(X)&~funny(X))))&
(![X]:((~brave(X)<~>~old(X))=>(~funny(X)|~brave(X))))&
((curious(paul))=>((wise(mary)&tall(mary))))&
((~rich(fred))<=>(?[X]:((calm(X)&curious(X)))))&
((happy(lucy)<~>~happy(lucy)))&
(?[X]:((~rich(X)<~>~patient(X))))&
(?[X]:((brave(X)|~rich(X))))&
(?[X]:((~happy(X)|~old(X))))&
((~patient(alice)&~funny(alice)))&
(?[X]:((~generous(X)<~>happy(X)))) | ~rich(mary) | [] | null | 0 |
If someone is both not creative and not calm then someone is quiet or not curious and vice versa.
Everyone who is not calm is rich or strong.
Everyone who is quiet or not wise is not wise or not funny.
If john is not creative or not generous then someone is not rich or not quiet and vice versa.
If someone is strong then paul is not quiet or not curious and vice versa.
If someone is old or kind then someone is both brave and not brave.
If alice is not kind then someone is not generous or humble and vice versa.
If john is curious then someone is not brave or not kind.
Everyone who is kind is generous or not patient and vice versa.
Everyone who is strong is either curious or rich and vice versa.
If lucy is generous then paul is either curious or not patient.
If mary is not brave or strong then lucy is not quiet and vice versa.
If susan is not strong then john is both curious and not patient and vice versa.
If susan is not strong or creative then someone is either strong or old.
Everyone who is both wise and not happy is curious or not curious and vice versa.
Everyone who is either not brave or generous is not wise and vice versa.
Someone is either not tall or humble.
Lucy is curious.
Someone is both strong and not tall.
Fred is both not kind and not humble.
Alice is either not brave or calm.
Lucy is rich or not strong. | Susan is not generous. | entailment | ((?[X]:((~creative(X)&~calm(X))))<=>(?[X]:((quiet(X)|~curious(X)))))&
(![X]:(~calm(X)=>(rich(X)|strong(X))))&
(![X]:((quiet(X)|~wise(X))=>(~wise(X)|~funny(X))))&
(((~creative(john)|~generous(john)))<=>(?[X]:((~rich(X)|~quiet(X)))))&
((?[X]:(strong(X)))<=>((~quiet(paul)|~curious(paul))))&
((?[X]:((old(X)|kind(X))))=>(?[X]:((brave(X)&~brave(X)))))&
((~kind(alice))<=>(?[X]:((~generous(X)|humble(X)))))&
((curious(john))=>(?[X]:((~brave(X)|~kind(X)))))&
(![X]:(kind(X)<=>(generous(X)|~patient(X))))&
(![X]:(strong(X)<=>(curious(X)<~>rich(X))))&
((generous(lucy))=>((curious(paul)<~>~patient(paul))))&
(((~brave(mary)|strong(mary)))<=>(~quiet(lucy)))&
((~strong(susan))<=>((curious(john)&~patient(john))))&
(((~strong(susan)|creative(susan)))=>(?[X]:((strong(X)<~>old(X)))))&
(![X]:((wise(X)&~happy(X))<=>(curious(X)|~curious(X))))&
(![X]:((~brave(X)<~>generous(X))<=>~wise(X)))&
(?[X]:((~tall(X)<~>humble(X))))&
(curious(lucy))&
(?[X]:((strong(X)&~tall(X))))&
((~kind(fred)&~humble(fred)))&
((~brave(alice)<~>calm(alice)))&
((rich(lucy)|~strong(lucy))) | ~generous(susan) | [
"p5",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 8542042167860902367925514
% SZS output start Proof for 8542042167860902367925514
6. ? [X0] : (kind(X0) | old(X0)) => ? [X0] : (~brave(X0) & brave(X0)) [input p5]
9. ! [X0] : (kind(X0) <=> (~patient(X0) | generous(X0))) [input p8]
23. generous(susan) [input hypothesis]
25. ? [X0] : (kind(X0) | old(X0)) => ? [X1] : (~brave(X1) & brave(X1)) [rectify 6]
29. ? [X1] : (~brave(X1) & brave(X1)) | ! [X0] : (~kind(X0) & ~old(X0)) [ennf transformation 25]
48. ? [X0] : (~brave(X0) & brave(X0)) | ! [X1] : (~kind(X1) & ~old(X1)) [rectify 29]
49. ? [X0] : (~brave(X0) & brave(X0)) => (~brave(sK4) & brave(sK4)) [choice axiom]
50. (~brave(sK4) & brave(sK4)) | ! [X1] : (~kind(X1) & ~old(X1)) [skolemisation 48,49]
57. ! [X0] : ((kind(X0) | (patient(X0) & ~generous(X0))) & ((~patient(X0) | generous(X0)) | ~kind(X0))) [nnf transformation 9]
58. ! [X0] : ((kind(X0) | (patient(X0) & ~generous(X0))) & (~patient(X0) | generous(X0) | ~kind(X0))) [flattening 57]
91. brave(sK4) | ~kind(X1) [cnf transformation 50]
93. ~brave(sK4) | ~kind(X1) [cnf transformation 50]
99. ~generous(X0) | kind(X0) [cnf transformation 58]
136. generous(susan) [cnf transformation 23]
212. 18 <=> ! [X1] : ~kind(X1) [avatar definition]
213. ~kind(X1) <- (18) [avatar component clause 212]
215. 19 <=> brave(sK4) [avatar definition]
218. 18 | ~19 [avatar split clause 93,215,212]
223. 18 | 19 [avatar split clause 91,215,212]
344. kind(susan) [resolution 99,136]
345. $false <- (18) [subsumption resolution 344,213]
346. ~18 [avatar contradiction clause 345]
347. $false [avatar sat refutation 218,223,346]
% SZS output end Proof for 8542042167860902367925514
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either tall or wise is both not quiet and not generous.
Everyone who is both not calm and not funny is both not funny and not old and vice versa.
Everyone who is not kind or not happy is both patient and not patient.
If john is brave or not generous then fred is both not generous and not funny and vice versa.
Everyone who is both not old and tall is either brave or not kind and vice versa.
If someone is quiet then someone is either humble or tall.
If someone is both curious and kind then someone is either old or humble.
If lucy is rich or not old then paul is both generous and quiet and vice versa.
Everyone who is either wise or not generous is happy or not brave.
Everyone who is either not tall or not humble is humble or not rich.
Everyone who is not quiet is both not strong and not tall.
Everyone who is either not calm or not strong is quiet and vice versa.
Everyone who is not brave is generous or not brave and vice versa.
If alice is kind then someone is kind and vice versa.
Everyone who is not kind or not calm is humble and vice versa.
Everyone who is not calm or not rich is not humble or not kind and vice versa.
Someone is not creative or wise.
Someone is calm.
Mary is not humble or not wise.
Someone is quiet or strong.
Alice is happy or creative.
Lucy is either not funny or not quiet.
Someone is curious or calm. | Paul is not curious. | neutral | (![X]:((tall(X)<~>wise(X))=>(~quiet(X)&~generous(X))))&
(![X]:((~calm(X)&~funny(X))<=>(~funny(X)&~old(X))))&
(![X]:((~kind(X)|~happy(X))=>(patient(X)&~patient(X))))&
(((brave(john)|~generous(john)))<=>((~generous(fred)&~funny(fred))))&
(![X]:((~old(X)&tall(X))<=>(brave(X)<~>~kind(X))))&
((?[X]:(quiet(X)))=>(?[X]:((humble(X)<~>tall(X)))))&
((?[X]:((curious(X)&kind(X))))=>(?[X]:((old(X)<~>humble(X)))))&
(((rich(lucy)|~old(lucy)))<=>((generous(paul)&quiet(paul))))&
(![X]:((wise(X)<~>~generous(X))=>(happy(X)|~brave(X))))&
(![X]:((~tall(X)<~>~humble(X))=>(humble(X)|~rich(X))))&
(![X]:(~quiet(X)=>(~strong(X)&~tall(X))))&
(![X]:((~calm(X)<~>~strong(X))<=>quiet(X)))&
(![X]:(~brave(X)<=>(generous(X)|~brave(X))))&
((kind(alice))<=>(?[X]:(kind(X))))&
(![X]:((~kind(X)|~calm(X))<=>humble(X)))&
(![X]:((~calm(X)|~rich(X))<=>(~humble(X)|~kind(X))))&
(?[X]:((~creative(X)|wise(X))))&
(?[X]:(calm(X)))&
((~humble(mary)|~wise(mary)))&
(?[X]:((quiet(X)|strong(X))))&
((happy(alice)|creative(alice)))&
((~funny(lucy)<~>~quiet(lucy)))&
(?[X]:((curious(X)|calm(X)))) | ~curious(paul) | [] | null | 0 |
Everyone who is both funny and not creative is both brave and not tall and vice versa.
If someone is both not rich and patient then someone is either not generous or not kind.
Everyone who is not old or not brave is not tall or not happy and vice versa.
If someone is creative or patient then someone is both not humble and creative.
Everyone who is both not quiet and not old is quiet.
Everyone who is creative or old is not generous or not curious and vice versa.
Everyone who is rich or not strong is both not rich and creative.
Everyone who is humble or not patient is not quiet and vice versa.
If someone is both patient and not strong then alice is either wise or generous and vice versa.
If alice is either curious or not strong then paul is either not happy or not generous.
Everyone who is either not wise or not rich is rich and vice versa.
If susan is not patient or not tall then someone is both not calm and not old and vice versa.
If someone is not generous then mary is both not brave and not funny and vice versa.
If john is curious or not quiet then john is both not curious and not strong.
If someone is both not tall and not curious then mary is either not strong or not calm and vice versa.
If someone is not generous or not kind then alice is either curious or strong.
Lucy is not brave.
Someone is tall.
Someone is happy or not kind.
Someone is either funny or tall.
Someone is either calm or not quiet.
Susan is either not humble or happy.
John is not generous or curious.
Someone is kind. | Mary is not funny. | entailment | (![X]:((funny(X)&~creative(X))<=>(brave(X)&~tall(X))))&
((?[X]:((~rich(X)&patient(X))))=>(?[X]:((~generous(X)<~>~kind(X)))))&
(![X]:((~old(X)|~brave(X))<=>(~tall(X)|~happy(X))))&
((?[X]:((creative(X)|patient(X))))=>(?[X]:((~humble(X)&creative(X)))))&
(![X]:((~quiet(X)&~old(X))=>quiet(X)))&
(![X]:((creative(X)|old(X))<=>(~generous(X)|~curious(X))))&
(![X]:((rich(X)|~strong(X))=>(~rich(X)&creative(X))))&
(![X]:((humble(X)|~patient(X))<=>~quiet(X)))&
((?[X]:((patient(X)&~strong(X))))<=>((wise(alice)<~>generous(alice))))&
(((curious(alice)<~>~strong(alice)))=>((~happy(paul)<~>~generous(paul))))&
(![X]:((~wise(X)<~>~rich(X))<=>rich(X)))&
(((~patient(susan)|~tall(susan)))<=>(?[X]:((~calm(X)&~old(X)))))&
((?[X]:(~generous(X)))<=>((~brave(mary)&~funny(mary))))&
(((curious(john)|~quiet(john)))=>((~curious(john)&~strong(john))))&
((?[X]:((~tall(X)&~curious(X))))<=>((~strong(mary)<~>~calm(mary))))&
((?[X]:((~generous(X)|~kind(X))))=>((curious(alice)<~>strong(alice))))&
(~brave(lucy))&
(?[X]:(tall(X)))&
(?[X]:((happy(X)|~kind(X))))&
(?[X]:((funny(X)<~>tall(X))))&
(?[X]:((calm(X)<~>~quiet(X))))&
((~humble(susan)<~>happy(susan)))&
((~generous(john)|curious(john)))&
(?[X]:(kind(X))) | ~funny(mary) | [
"p12",
"p13",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 2041483710881138397562687
% SZS output start Proof for 2041483710881138397562687
13. ? [X0] : ~generous(X0) <=> (~funny(mary) & ~brave(mary)) [input p12]
14. (~quiet(john) | curious(john)) => (~strong(john) & ~curious(john)) [input p13]
23. curious(john) | ~generous(john) [input p22]
25. funny(mary) [input hypothesis]
34. (~strong(john) & ~curious(john)) | (quiet(john) & ~curious(john)) [ennf transformation 14]
62. (? [X0] : ~generous(X0) | (funny(mary) | brave(mary))) & ((~funny(mary) & ~brave(mary)) | ! [X0] : generous(X0)) [nnf transformation 13]
63. (? [X0] : ~generous(X0) | funny(mary) | brave(mary)) & ((~funny(mary) & ~brave(mary)) | ! [X0] : generous(X0)) [flattening 62]
64. (? [X0] : ~generous(X0) | funny(mary) | brave(mary)) & ((~funny(mary) & ~brave(mary)) | ! [X1] : generous(X1)) [rectify 63]
65. ? [X0] : ~generous(X0) => ~generous(sK4) [choice axiom]
66. (~generous(sK4) | funny(mary) | brave(mary)) & ((~funny(mary) & ~brave(mary)) | ! [X1] : generous(X1)) [skolemisation 64,65]
131. ~funny(mary) | generous(X1) [cnf transformation 66]
133. ~curious(john) | ~curious(john) [cnf transformation 34]
156. curious(john) | ~generous(john) [cnf transformation 23]
158. funny(mary) [cnf transformation 25]
159. ~curious(john) [duplicate literal removal 133]
270. 23 <=> funny(mary) [avatar definition]
279. 25 <=> ! [X1] : generous(X1) [avatar definition]
280. generous(X1) <- (25) [avatar component clause 279]
281. 25 | ~23 [avatar split clause 131,270,279]
293. 28 <=> curious(john) [avatar definition]
298. ~28 [avatar split clause 159,293]
371. 43 <=> generous(john) [avatar definition]
373. ~generous(john) <- (~43) [avatar component clause 371]
374. ~43 | 28 [avatar split clause 156,293,371]
375. 23 [avatar split clause 158,270]
378. $false <- (25, ~43) [resolution 373,280]
379. ~25 | 43 [avatar contradiction clause 378]
380. $false [avatar sat refutation 281,298,374,375,379]
% SZS output end Proof for 2041483710881138397562687
% ------------------------------
% 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 |
Everyone who is not humble or not wise is not funny or quiet and vice versa. Everyone who is not strong or not humble is both not strong and not calm and vice versa. Everyone who is both humble and not strong is both not happy and humble. Everyone who is tall is either not rich or not funny and vice versa. Everyone who is both brave and not generous is humble and vice versa. If lucy is wise or not happy then fred is brave or not kind and vice versa. Everyone who is strong is both humble and not brave and vice versa. Everyone who is not generous is not wise or strong and vice versa. If mary is both brave and not quiet then john is both funny and not kind. Everyone who is wise is either humble or strong and vice versa. If lucy is both not quiet and not happy then someone is either wise or not rich and vice versa. If someone is not kind then john is either not kind or not tall. If alice is not creative or calm then someone is not rich or old. If someone is both tall and generous then lucy is quiet and vice versa. Everyone who is creative is not generous or not patient. Paul is either not patient or not curious. Alice is either creative or not creative. Someone is either not humble or brave. Someone is tall or humble. John is either not strong or quiet. Someone is patient. | Mary is brave. | contradiction | (![X]:((~humble(X)|~wise(X))<=>(~funny(X)|quiet(X))))&
(![X]:((~strong(X)|~humble(X))<=>(~strong(X)&~calm(X))))&
(![X]:((humble(X)&~strong(X))=>(~happy(X)&humble(X))))&
(![X]:(tall(X)<=>(~rich(X)<~>~funny(X))))&
(![X]:((brave(X)&~generous(X))<=>humble(X)))&
(((wise(lucy)|~happy(lucy)))<=>((brave(fred)|~kind(fred))))&
(![X]:(strong(X)<=>(humble(X)&~brave(X))))&
(![X]:(~generous(X)<=>(~wise(X)|strong(X))))&
(((brave(mary)&~quiet(mary)))=>((funny(john)&~kind(john))))&
(![X]:(wise(X)<=>(humble(X)<~>strong(X))))&
(((~quiet(lucy)&~happy(lucy)))<=>(?[X]:((wise(X)<~>~rich(X)))))&
((?[X]:(~kind(X)))=>((~kind(john)<~>~tall(john))))&
(((~creative(alice)|calm(alice)))=>(?[X]:((~rich(X)|old(X)))))&
((?[X]:((tall(X)&generous(X))))<=>(quiet(lucy)))&
(![X]:(creative(X)=>(~generous(X)|~patient(X))))&
((~patient(paul)<~>~curious(paul)))&
((creative(alice)<~>~creative(alice)))&
(?[X]:((~humble(X)<~>brave(X))))&
(?[X]:((tall(X)|humble(X))))&
((~strong(john)<~>quiet(john)))&
(?[X]:(patient(X))) | brave(mary) | [
"p1",
"p4",
"p6",
"p7",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 6462103395637061578456991
% SZS output start Proof for 6462103395637061578456991
2. ! [X0] : ((~humble(X0) | ~strong(X0)) <=> (~calm(X0) & ~strong(X0))) [input p1]
5. ! [X0] : ((~generous(X0) & brave(X0)) <=> humble(X0)) [input p4]
7. ! [X0] : (strong(X0) <=> (~brave(X0) & humble(X0))) [input p6]
8. ! [X0] : (~generous(X0) <=> (strong(X0) | ~wise(X0))) [input p7]
10. ! [X0] : (wise(X0) <=> (humble(X0) <~> strong(X0))) [input p9]
22. brave(mary) [input hypothesis]
33. ! [X0] : (((~humble(X0) | ~strong(X0)) | (calm(X0) | strong(X0))) & ((~calm(X0) & ~strong(X0)) | (humble(X0) & strong(X0)))) [nnf transformation 2]
34. ! [X0] : ((~humble(X0) | ~strong(X0) | calm(X0) | strong(X0)) & ((~calm(X0) & ~strong(X0)) | (humble(X0) & strong(X0)))) [flattening 33]
36. ! [X0] : (((~generous(X0) & brave(X0)) | ~humble(X0)) & (humble(X0) | (generous(X0) | ~brave(X0)))) [nnf transformation 5]
37. ! [X0] : (((~generous(X0) & brave(X0)) | ~humble(X0)) & (humble(X0) | generous(X0) | ~brave(X0))) [flattening 36]
40. ! [X0] : ((strong(X0) | (brave(X0) | ~humble(X0))) & ((~brave(X0) & humble(X0)) | ~strong(X0))) [nnf transformation 7]
41. ! [X0] : ((strong(X0) | brave(X0) | ~humble(X0)) & ((~brave(X0) & humble(X0)) | ~strong(X0))) [flattening 40]
42. ! [X0] : ((~generous(X0) | (~strong(X0) & wise(X0))) & ((strong(X0) | ~wise(X0)) | generous(X0))) [nnf transformation 8]
43. ! [X0] : ((~generous(X0) | (~strong(X0) & wise(X0))) & (strong(X0) | ~wise(X0) | generous(X0))) [flattening 42]
44. ! [X0] : ((wise(X0) | ((humble(X0) | ~strong(X0)) & (strong(X0) | ~humble(X0)))) & (((~strong(X0) | ~humble(X0)) & (strong(X0) | humble(X0))) | ~wise(X0))) [nnf transformation 10]
70. ~strong(X0) | humble(X0) [cnf transformation 34]
80. ~brave(X0) | generous(X0) | humble(X0) [cnf transformation 37]
82. ~generous(X0) | ~humble(X0) [cnf transformation 37]
88. ~brave(X0) | ~strong(X0) [cnf transformation 41]
90. ~wise(X0) | strong(X0) | generous(X0) [cnf transformation 43]
91. ~generous(X0) | wise(X0) [cnf transformation 43]
95. strong(X0) | humble(X0) | ~wise(X0) [cnf transformation 44]
96. ~strong(X0) | ~humble(X0) | ~wise(X0) [cnf transformation 44]
97. ~humble(X0) | strong(X0) | wise(X0) [cnf transformation 44]
121. brave(mary) [cnf transformation 22]
143. 5 <=> brave(mary) [avatar definition]
144. brave(mary) <- (5) [avatar component clause 143]
160. ~strong(X0) | ~wise(X0) [subsumption resolution 96,70]
161. ~wise(X0) | humble(X0) [subsumption resolution 95,160]
247. 5 [avatar split clause 121,143]
249. ~strong(mary) <- (5) [resolution 88,144]
314. generous(mary) | humble(mary) <- (5) [resolution 80,144]
317. 33 <=> humble(mary) [avatar definition]
318. ~humble(mary) <- (~33) [avatar component clause 317]
319. humble(mary) <- (33) [avatar component clause 317]
321. 34 <=> generous(mary) [avatar definition]
322. ~generous(mary) <- (~34) [avatar component clause 321]
323. generous(mary) <- (34) [avatar component clause 321]
324. 33 | 34 | ~5 [avatar split clause 314,143,321,317]
333. ~humble(mary) <- (34) [resolution 323,82]
336. ~33 | ~34 [avatar split clause 333,321,317]
372. wise(mary) <- (34) [resolution 323,91]
440. humble(mary) <- (34) [resolution 372,161]
441. $false <- (~33, 34) [subsumption resolution 440,318]
442. 33 | ~34 [avatar contradiction clause 441]
443. strong(mary) | wise(mary) <- (33) [resolution 319,97]
445. wise(mary) <- (5, 33) [subsumption resolution 443,249]
470. strong(mary) | generous(mary) <- (5, 33) [resolution 445,90]
473. generous(mary) <- (5, 33) [subsumption resolution 470,249]
474. $false <- (5, 33, ~34) [subsumption resolution 473,322]
475. ~5 | ~33 | 34 [avatar contradiction clause 474]
477. $false [avatar sat refutation 247,324,336,442,475]
% SZS output end Proof for 6462103395637061578456991
% ------------------------------
% 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 |
Everyone who is both not tall and happy is creative or rich.
If someone is not creative then someone is both humble and not kind.
If someone is either rich or not wise then susan is rich or not wise and vice versa.
If someone is wise or not generous then someone is both not rich and patient and vice versa.
Everyone who is both calm and curious is both not humble and wise and vice versa.
Everyone who is not funny or not patient is not calm and vice versa.
If mary is not creative or not tall then susan is both patient and not kind and vice versa.
Everyone who is not rich is either wise or not tall.
Everyone who is both not funny and funny is patient.
If someone is humble or not creative then someone is not wise.
Everyone who is not wise is either not kind or humble and vice versa.
If someone is both funny and not rich then mary is both humble and not happy.
Everyone who is generous is either humble or quiet and vice versa.
Everyone who is not strong or curious is not wise and vice versa.
If john is either not funny or not quiet then mary is happy and vice versa.
Everyone who is patient or not calm is creative and vice versa.
Alice is not generous.
Alice is either humble or old.
Someone is either not patient or creative.
Mary is curious or not curious.
Lucy is kind.
Mary is not generous.
Someone is funny or creative.
Someone is either not wise or creative. | Lucy is not wise. | entailment | (![X]:((~tall(X)&happy(X))=>(creative(X)|rich(X))))&
((?[X]:(~creative(X)))=>(?[X]:((humble(X)&~kind(X)))))&
((?[X]:((rich(X)<~>~wise(X))))<=>((rich(susan)|~wise(susan))))&
((?[X]:((wise(X)|~generous(X))))<=>(?[X]:((~rich(X)&patient(X)))))&
(![X]:((calm(X)&curious(X))<=>(~humble(X)&wise(X))))&
(![X]:((~funny(X)|~patient(X))<=>~calm(X)))&
(((~creative(mary)|~tall(mary)))<=>((patient(susan)&~kind(susan))))&
(![X]:(~rich(X)=>(wise(X)<~>~tall(X))))&
(![X]:((~funny(X)&funny(X))=>patient(X)))&
((?[X]:((humble(X)|~creative(X))))=>(?[X]:(~wise(X))))&
(![X]:(~wise(X)<=>(~kind(X)<~>humble(X))))&
((?[X]:((funny(X)&~rich(X))))=>((humble(mary)&~happy(mary))))&
(![X]:(generous(X)<=>(humble(X)<~>quiet(X))))&
(![X]:((~strong(X)|curious(X))<=>~wise(X)))&
(((~funny(john)<~>~quiet(john)))<=>(happy(mary)))&
(![X]:((patient(X)|~calm(X))<=>creative(X)))&
(~generous(alice))&
((humble(alice)<~>old(alice)))&
(?[X]:((~patient(X)<~>creative(X))))&
((curious(mary)|~curious(mary)))&
(kind(lucy))&
(~generous(mary))&
(?[X]:((funny(X)|creative(X))))&
(?[X]:((~wise(X)<~>creative(X)))) | ~wise(lucy) | [
"p4",
"p10",
"p13",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 4071359403734458588310026
% SZS output start Proof for 4071359403734458588310026
5. ! [X0] : ((curious(X0) & calm(X0)) <=> (wise(X0) & ~humble(X0))) [input p4]
11. ! [X0] : (~wise(X0) <=> (~kind(X0) <~> humble(X0))) [input p10]
14. ! [X0] : ((curious(X0) | ~strong(X0)) <=> ~wise(X0)) [input p13]
21. kind(lucy) [input p20]
25. wise(lucy) [input hypothesis]
50. ! [X0] : (((curious(X0) & calm(X0)) | (~wise(X0) | humble(X0))) & ((wise(X0) & ~humble(X0)) | (~curious(X0) | ~calm(X0)))) [nnf transformation 5]
51. ! [X0] : (((curious(X0) & calm(X0)) | ~wise(X0) | humble(X0)) & ((wise(X0) & ~humble(X0)) | ~curious(X0) | ~calm(X0))) [flattening 50]
60. ! [X0] : ((~wise(X0) | ((~kind(X0) | ~humble(X0)) & (humble(X0) | kind(X0)))) & (((~humble(X0) | kind(X0)) & (humble(X0) | ~kind(X0))) | wise(X0))) [nnf transformation 11]
62. ! [X0] : (((curious(X0) | ~strong(X0)) | wise(X0)) & (~wise(X0) | (~curious(X0) & strong(X0)))) [nnf transformation 14]
63. ! [X0] : ((curious(X0) | ~strong(X0) | wise(X0)) & (~wise(X0) | (~curious(X0) & strong(X0)))) [flattening 62]
93. ~wise(X0) | curious(X0) | humble(X0) [cnf transformation 51]
110. ~wise(X0) | ~kind(X0) | ~humble(X0) [cnf transformation 60]
118. ~curious(X0) | ~wise(X0) [cnf transformation 63]
133. kind(lucy) [cnf transformation 21]
138. wise(lucy) [cnf transformation 25]
320. 36 <=> humble(lucy) [avatar definition]
337. curious(lucy) | humble(lucy) [resolution 93,138]
408. ~kind(lucy) | ~humble(lucy) [resolution 110,138]
410. ~humble(lucy) [subsumption resolution 408,133]
414. ~36 [avatar split clause 410,320]
416. 51 <=> curious(lucy) [avatar definition]
418. curious(lucy) <- (51) [avatar component clause 416]
419. 36 | 51 [avatar split clause 337,416,320]
471. ~wise(lucy) <- (51) [resolution 418,118]
472. $false <- (51) [subsumption resolution 471,138]
473. ~51 [avatar contradiction clause 472]
474. $false [avatar sat refutation 414,419,473]
% SZS output end Proof for 4071359403734458588310026
% ------------------------------
% 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 |
If lucy is old or patient then lucy is either quiet or not humble. If paul is both not quiet and humble then someone is either not calm or quiet. If lucy is rich then someone is either not happy or not curious and vice versa. Everyone who is not strong is either not happy or wise and vice versa. If susan is either not funny or generous then paul is happy and vice versa. Everyone who is either strong or not kind is not funny or not humble and vice versa. Everyone who is both not calm and not patient is both generous and tall. Everyone who is curious is rich. If paul is both kind and not wise then mary is both not strong and generous and vice versa. Everyone who is not happy or brave is either not rich or tall and vice versa. Everyone who is not old or strong is both creative and curious and vice versa. If fred is either quiet or not quiet then someone is kind or not wise and vice versa. Everyone who is generous or tall is brave or calm. If someone is not happy then susan is tall. If fred is rich or brave then susan is either patient or not brave and vice versa. Everyone who is both not creative and not quiet is either generous or not tall. Fred is either not rich or not old. Susan is not rich or not brave. Someone is not wise. John is not old. Fred is both not funny and not humble. Someone is either funny or strong. Lucy is old. John is either not tall or funny. | John is rich. | entailment | (((old(lucy)|patient(lucy)))=>((quiet(lucy)<~>~humble(lucy))))&
(((~quiet(paul)&humble(paul)))=>(?[X]:((~calm(X)<~>quiet(X)))))&
((rich(lucy))<=>(?[X]:((~happy(X)<~>~curious(X)))))&
(![X]:(~strong(X)<=>(~happy(X)<~>wise(X))))&
(((~funny(susan)<~>generous(susan)))<=>(happy(paul)))&
(![X]:((strong(X)<~>~kind(X))<=>(~funny(X)|~humble(X))))&
(![X]:((~calm(X)&~patient(X))=>(generous(X)&tall(X))))&
(![X]:(curious(X)=>rich(X)))&
(((kind(paul)&~wise(paul)))<=>((~strong(mary)&generous(mary))))&
(![X]:((~happy(X)|brave(X))<=>(~rich(X)<~>tall(X))))&
(![X]:((~old(X)|strong(X))<=>(creative(X)&curious(X))))&
(((quiet(fred)<~>~quiet(fred)))<=>(?[X]:((kind(X)|~wise(X)))))&
(![X]:((generous(X)|tall(X))=>(brave(X)|calm(X))))&
((?[X]:(~happy(X)))=>(tall(susan)))&
(((rich(fred)|brave(fred)))<=>((patient(susan)<~>~brave(susan))))&
(![X]:((~creative(X)&~quiet(X))=>(generous(X)<~>~tall(X))))&
((~rich(fred)<~>~old(fred)))&
((~rich(susan)|~brave(susan)))&
(?[X]:(~wise(X)))&
(~old(john))&
((~funny(fred)&~humble(fred)))&
(?[X]:((funny(X)<~>strong(X))))&
(old(lucy))&
((~tall(john)<~>funny(john))) | rich(john) | [
"p7",
"p10",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 9042473750212279823847972
% SZS output start Proof for 9042473750212279823847972
8. ! [X0] : (curious(X0) => rich(X0)) [input p7]
11. ! [X0] : ((strong(X0) | ~old(X0)) <=> (curious(X0) & creative(X0))) [input p10]
20. ~old(john) [input p19]
25. ~rich(john) [input hypothesis]
31. ! [X0] : (rich(X0) | ~curious(X0)) [ennf transformation 8]
53. ! [X0] : (((strong(X0) | ~old(X0)) | (~curious(X0) | ~creative(X0))) & ((curious(X0) & creative(X0)) | (~strong(X0) & old(X0)))) [nnf transformation 11]
54. ! [X0] : ((strong(X0) | ~old(X0) | ~curious(X0) | ~creative(X0)) & ((curious(X0) & creative(X0)) | (~strong(X0) & old(X0)))) [flattening 53]
95. ~curious(X0) | rich(X0) [cnf transformation 31]
108. curious(X0) | old(X0) [cnf transformation 54]
132. ~old(john) [cnf transformation 20]
140. ~rich(john) [cnf transformation 25]
321. rich(X0) | old(X0) [resolution 108,95]
324. old(john) [resolution 321,140]
325. $false [subsumption resolution 324,132]
% SZS output end Proof for 9042473750212279823847972
% ------------------------------
% 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 mary is strong then fred is both not strong and not curious.
If paul is both not patient and quiet then fred is either rich or not brave.
If someone is either happy or not old then susan is either not funny or not strong.
Everyone who is either brave or strong is either not strong or not rich.
Everyone who is tall is both not rich and happy.
Everyone who is not funny or strong is both creative and not brave.
Everyone who is not brave or not quiet is both not humble and not calm and vice versa.
If someone is either humble or not kind then someone is both not humble and rich and vice versa.
If someone is not strong or not calm then someone is not generous.
If fred is wise or quiet then john is wise.
If fred is creative or not rich then susan is either calm or not quiet.
Everyone who is either not rich or not humble is not tall or not quiet.
Everyone who is either tall or generous is not quiet and vice versa.
Everyone who is both not kind and not creative is either rich or wise and vice versa.
Everyone who is kind is patient.
Someone is funny.
Alice is creative or not old.
Paul is either not patient or not creative.
Mary is either not strong or not kind. | Susan is tall. | neutral | ((strong(mary))=>((~strong(fred)&~curious(fred))))&
(((~patient(paul)&quiet(paul)))=>((rich(fred)<~>~brave(fred))))&
((?[X]:((happy(X)<~>~old(X))))=>((~funny(susan)<~>~strong(susan))))&
(![X]:((brave(X)<~>strong(X))=>(~strong(X)<~>~rich(X))))&
(![X]:(tall(X)=>(~rich(X)&happy(X))))&
(![X]:((~funny(X)|strong(X))=>(creative(X)&~brave(X))))&
(![X]:((~brave(X)|~quiet(X))<=>(~humble(X)&~calm(X))))&
((?[X]:((humble(X)<~>~kind(X))))<=>(?[X]:((~humble(X)&rich(X)))))&
((?[X]:((~strong(X)|~calm(X))))=>(?[X]:(~generous(X))))&
(((wise(fred)|quiet(fred)))=>(wise(john)))&
(((creative(fred)|~rich(fred)))=>((calm(susan)<~>~quiet(susan))))&
(![X]:((~rich(X)<~>~humble(X))=>(~tall(X)|~quiet(X))))&
(![X]:((tall(X)<~>generous(X))<=>~quiet(X)))&
(![X]:((~kind(X)&~creative(X))<=>(rich(X)<~>wise(X))))&
(![X]:(kind(X)=>patient(X)))&
(?[X]:(funny(X)))&
((creative(alice)|~old(alice)))&
((~patient(paul)<~>~creative(paul)))&
((~strong(mary)<~>~kind(mary))) | tall(susan) | [] | null | 0 |
If john is quiet or not tall then mary is either not wise or creative and vice versa.
Everyone who is both quiet and rich is generous or funny and vice versa.
If mary is both wise and rich then someone is both not quiet and brave and vice versa.
Everyone who is curious or funny is not rich.
If someone is either not old or wise then someone is both not humble and tall and vice versa.
If someone is both generous and not generous then paul is both creative and strong and vice versa.
Everyone who is rich is either not wise or not patient.
Everyone who is wise or curious is both curious and generous and vice versa.
Everyone who is not rich or generous is not generous or wise and vice versa.
If susan is either wise or not happy then someone is not humble.
If alice is patient or funny then lucy is patient or creative.
Everyone who is both not brave and not funny is curious or not curious and vice versa.
If someone is brave then john is both wise and not calm and vice versa.
If mary is humble then lucy is old or not calm.
If someone is either brave or not old then fred is either not calm or not strong.
If someone is either not wise or tall then someone is both patient and not calm and vice versa.
Someone is not tall.
Someone is creative.
Fred is either humble or rich.
Fred is either curious or not creative.
Someone is either not calm or generous. | John is not patient. | neutral | (((quiet(john)|~tall(john)))<=>((~wise(mary)<~>creative(mary))))&
(![X]:((quiet(X)&rich(X))<=>(generous(X)|funny(X))))&
(((wise(mary)&rich(mary)))<=>(?[X]:((~quiet(X)&brave(X)))))&
(![X]:((curious(X)|funny(X))=>~rich(X)))&
((?[X]:((~old(X)<~>wise(X))))<=>(?[X]:((~humble(X)&tall(X)))))&
((?[X]:((generous(X)&~generous(X))))<=>((creative(paul)&strong(paul))))&
(![X]:(rich(X)=>(~wise(X)<~>~patient(X))))&
(![X]:((wise(X)|curious(X))<=>(curious(X)&generous(X))))&
(![X]:((~rich(X)|generous(X))<=>(~generous(X)|wise(X))))&
(((wise(susan)<~>~happy(susan)))=>(?[X]:(~humble(X))))&
(((patient(alice)|funny(alice)))=>((patient(lucy)|creative(lucy))))&
(![X]:((~brave(X)&~funny(X))<=>(curious(X)|~curious(X))))&
((?[X]:(brave(X)))<=>((wise(john)&~calm(john))))&
((humble(mary))=>((old(lucy)|~calm(lucy))))&
((?[X]:((brave(X)<~>~old(X))))=>((~calm(fred)<~>~strong(fred))))&
((?[X]:((~wise(X)<~>tall(X))))<=>(?[X]:((patient(X)&~calm(X)))))&
(?[X]:(~tall(X)))&
(?[X]:(creative(X)))&
((humble(fred)<~>rich(fred)))&
((curious(fred)<~>~creative(fred)))&
(?[X]:((~calm(X)<~>generous(X)))) | ~patient(john) | [] | null | 0 |
If mary is generous or not calm then someone is both humble and not kind and vice versa.
If someone is either generous or not curious then john is either not strong or kind and vice versa.
If someone is both not humble and tall then paul is either humble or not generous and vice versa.
If someone is both happy and rich then someone is both not patient and not strong.
If susan is both not creative and not kind then someone is creative.
If someone is both not patient and not rich then mary is both not wise and patient.
If john is rich or not happy then someone is either calm or funny.
Everyone who is old or wise is either not patient or not brave.
Everyone who is not tall or not old is not rich.
If someone is either not wise or generous then susan is tall or generous and vice versa.
If mary is either funny or not happy then paul is curious and vice versa.
Everyone who is generous is either funny or not calm and vice versa.
Everyone who is humble or not strong is either curious or not strong and vice versa.
Everyone who is either not rich or not strong is not patient and vice versa.
If john is either not curious or patient then someone is both not funny and not rich.
Everyone who is both not tall and curious is not curious or creative and vice versa.
Someone is brave or happy.
Someone is either not humble or quiet.
Fred is both funny and not tall.
Susan is happy. | Mary is funny. | contradiction | (((generous(mary)|~calm(mary)))<=>(?[X]:((humble(X)&~kind(X)))))&
((?[X]:((generous(X)<~>~curious(X))))<=>((~strong(john)<~>kind(john))))&
((?[X]:((~humble(X)&tall(X))))<=>((humble(paul)<~>~generous(paul))))&
((?[X]:((happy(X)&rich(X))))=>(?[X]:((~patient(X)&~strong(X)))))&
(((~creative(susan)&~kind(susan)))=>(?[X]:(creative(X))))&
((?[X]:((~patient(X)&~rich(X))))=>((~wise(mary)&patient(mary))))&
(((rich(john)|~happy(john)))=>(?[X]:((calm(X)<~>funny(X)))))&
(![X]:((old(X)|wise(X))=>(~patient(X)<~>~brave(X))))&
(![X]:((~tall(X)|~old(X))=>~rich(X)))&
((?[X]:((~wise(X)<~>generous(X))))<=>((tall(susan)|generous(susan))))&
(((funny(mary)<~>~happy(mary)))<=>(curious(paul)))&
(![X]:(generous(X)<=>(funny(X)<~>~calm(X))))&
(![X]:((humble(X)|~strong(X))<=>(curious(X)<~>~strong(X))))&
(![X]:((~rich(X)<~>~strong(X))<=>~patient(X)))&
(((~curious(john)<~>patient(john)))=>(?[X]:((~funny(X)&~rich(X)))))&
(![X]:((~tall(X)&curious(X))<=>(~curious(X)|creative(X))))&
(?[X]:((brave(X)|happy(X))))&
(?[X]:((~humble(X)<~>quiet(X))))&
((funny(fred)&~tall(fred)))&
(happy(susan)) | funny(mary) | [
"p3",
"p5",
"p10",
"p12",
"p13",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 849545445540520004451789
% SZS output start Proof for 849545445540520004451789
4. ? [X0] : (rich(X0) & happy(X0)) => ? [X0] : (~strong(X0) & ~patient(X0)) [input p3]
6. ? [X0] : (~rich(X0) & ~patient(X0)) => (patient(mary) & ~wise(mary)) [input p5]
11. (funny(mary) <~> ~happy(mary)) <=> curious(paul) [input p10]
13. ! [X0] : ((~strong(X0) | humble(X0)) <=> (curious(X0) <~> ~strong(X0))) [input p12]
14. ! [X0] : ((~rich(X0) <~> ~strong(X0)) <=> ~patient(X0)) [input p13]
15. (~curious(john) <~> patient(john)) => ? [X0] : (~rich(X0) & ~funny(X0)) [input p14]
16. ! [X0] : ((curious(X0) & ~tall(X0)) <=> (creative(X0) | ~curious(X0))) [input p15]
21. funny(mary) [input hypothesis]
22. ? [X0] : (rich(X0) & happy(X0)) => ? [X1] : (~strong(X1) & ~patient(X1)) [rectify 4]
23. ? [X1] : (~strong(X1) & ~patient(X1)) | ! [X0] : (~rich(X0) | ~happy(X0)) [ennf transformation 22]
26. (patient(mary) & ~wise(mary)) | ! [X0] : (rich(X0) | patient(X0)) [ennf transformation 6]
30. ? [X0] : (~rich(X0) & ~funny(X0)) | (~curious(john) <=> patient(john)) [ennf transformation 15]
44. ? [X0] : (~strong(X0) & ~patient(X0)) | ! [X1] : (~rich(X1) | ~happy(X1)) [rectify 23]
45. ? [X0] : (~strong(X0) & ~patient(X0)) => (~strong(sK3) & ~patient(sK3)) [choice axiom]
46. (~strong(sK3) & ~patient(sK3)) | ! [X1] : (~rich(X1) | ~happy(X1)) [skolemisation 44,45]
58. (((happy(mary) | ~funny(mary)) & (~happy(mary) | funny(mary))) | ~curious(paul)) & (curious(paul) | ((funny(mary) | happy(mary)) & (~happy(mary) | ~funny(mary)))) [nnf transformation 11]
60. ! [X0] : (((~strong(X0) | humble(X0)) | ((curious(X0) | strong(X0)) & (~strong(X0) | ~curious(X0)))) & (((strong(X0) | ~curious(X0)) & (~strong(X0) | curious(X0))) | (strong(X0) & ~humble(X0)))) [nnf transformation 13]
61. ! [X0] : ((~strong(X0) | humble(X0) | ((curious(X0) | strong(X0)) & (~strong(X0) | ~curious(X0)))) & (((strong(X0) | ~curious(X0)) & (~strong(X0) | curious(X0))) | (strong(X0) & ~humble(X0)))) [flattening 60]
62. ! [X0] : ((((strong(X0) | rich(X0)) & (~strong(X0) | ~rich(X0))) | patient(X0)) & (~patient(X0) | ((~rich(X0) | strong(X0)) & (~strong(X0) | rich(X0))))) [nnf transformation 14]
63. ? [X0] : (~rich(X0) & ~funny(X0)) | ((~curious(john) | ~patient(john)) & (patient(john) | curious(john))) [nnf transformation 30]
64. ? [X0] : (~rich(X0) & ~funny(X0)) => (~rich(sK7) & ~funny(sK7)) [choice axiom]
65. (~rich(sK7) & ~funny(sK7)) | ((~curious(john) | ~patient(john)) & (patient(john) | curious(john))) [skolemisation 63,64]
66. ! [X0] : (((curious(X0) & ~tall(X0)) | (~creative(X0) & curious(X0))) & ((creative(X0) | ~curious(X0)) | (~curious(X0) | tall(X0)))) [nnf transformation 16]
67. ! [X0] : (((curious(X0) & ~tall(X0)) | (~creative(X0) & curious(X0))) & (creative(X0) | ~curious(X0) | ~curious(X0) | tall(X0))) [flattening 66]
93. ~strong(sK3) | ~rich(X1) | ~happy(X1) [cnf transformation 46]
96. patient(mary) | rich(X0) | patient(X0) [cnf transformation 26]
116. happy(mary) | ~funny(mary) | ~curious(paul) [cnf transformation 58]
124. strong(X0) | ~curious(X0) | strong(X0) [cnf transformation 61]
127. ~patient(X0) | ~strong(X0) | rich(X0) [cnf transformation 62]
129. ~rich(X0) | ~strong(X0) | patient(X0) [cnf transformation 62]
134. ~rich(sK7) | ~curious(john) | ~patient(john) [cnf transformation 65]
138. curious(X0) | curious(X0) [cnf transformation 67]
146. funny(mary) [cnf transformation 21]
148. curious(X0) [duplicate literal removal 138]
149. ~curious(X0) | strong(X0) [duplicate literal removal 124]
231. 17 <=> ! [X1] : (~rich(X1) | ~happy(X1)) [avatar definition]
232. ~rich(X1) | ~happy(X1) <- (17) [avatar component clause 231]
234. 18 <=> strong(sK3) [avatar definition]
236. ~strong(sK3) <- (~18) [avatar component clause 234]
237. 17 | ~18 [avatar split clause 93,234,231]
257. 23 <=> ! [X0] : (rich(X0) | patient(X0)) [avatar definition]
258. patient(X0) | rich(X0) <- (23) [avatar component clause 257]
260. 24 <=> patient(mary) [avatar definition]
262. patient(mary) <- (24) [avatar component clause 260]
263. 23 | 24 [avatar split clause 96,260,257]
283. 29 <=> rich(john) [avatar definition]
284. rich(john) <- (29) [avatar component clause 283]
285. ~rich(john) <- (~29) [avatar component clause 283]
318. 36 <=> curious(paul) [avatar definition]
320. ~curious(paul) <- (~36) [avatar component clause 318]
322. 37 <=> funny(mary) [avatar definition]
326. 38 <=> happy(mary) [avatar definition]
328. happy(mary) <- (38) [avatar component clause 326]
329. ~36 | ~37 | 38 [avatar split clause 116,326,322,318]
334. 39 <=> patient(john) [avatar definition]
336. ~patient(john) <- (~39) [avatar component clause 334]
338. 40 <=> curious(john) [avatar definition]
340. ~curious(john) <- (~40) [avatar component clause 338]
342. 41 <=> rich(sK7) [avatar definition]
344. ~rich(sK7) <- (~41) [avatar component clause 342]
345. ~39 | ~40 | ~41 [avatar split clause 134,342,338,334]
373. 37 [avatar split clause 146,322]
374. $false <- (~36) [subsumption resolution 320,148]
375. 36 [avatar contradiction clause 374]
384. strong(X0) [resolution 149,148]
386. $false <- (~18) [resolution 384,236]
387. 18 [avatar contradiction clause 386]
433. ~strong(X0) | rich(X0) | rich(X0) <- (23) [resolution 127,258]
435. ~strong(X0) | rich(X0) <- (23) [duplicate literal removal 433]
436. rich(X0) <- (23) [subsumption resolution 435,384]
437. $false <- (23, ~29) [resolution 436,285]
438. $false <- (23, ~41) [resolution 436,344]
442. ~23 | 41 [avatar contradiction clause 438]
443. ~23 | 29 [avatar contradiction clause 437]
445. ~strong(mary) | rich(mary) <- (24) [resolution 262,127]
446. rich(mary) <- (24) [subsumption resolution 445,384]
449. ~happy(mary) <- (17, 24) [resolution 446,232]
452. $false <- (17, 24, 38) [subsumption resolution 449,328]
453. ~17 | ~24 | ~38 [avatar contradiction clause 452]
454. $false <- (~40) [subsumption resolution 340,148]
455. 40 [avatar contradiction clause 454]
476. ~strong(john) | patient(john) <- (29) [resolution 129,284]
482. patient(john) <- (29) [subsumption resolution 476,384]
483. $false <- (29, ~39) [subsumption resolution 482,336]
484. ~29 | 39 [avatar contradiction clause 483]
489. $false [avatar sat refutation 237,263,329,345,373,375,387,442,443,453,455,484]
% SZS output end Proof for 849545445540520004451789
% ------------------------------
% 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 not quiet then someone is both not brave and generous and vice versa. If fred is either creative or humble then someone is either not kind or happy. Everyone who is either brave or creative is not wise. If someone is both not rich and kind then paul is both generous and quiet and vice versa. If someone is both not calm and not patient then someone is not kind or not calm. Everyone who is not calm is humble or old. Everyone who is not happy or old is not funny. Everyone who is either patient or not brave is both not calm and not tall. If john is old then someone is not old and vice versa. Everyone who is either wise or not happy is happy and vice versa. If someone is either not kind or patient then paul is either generous or not rich and vice versa. Everyone who is either kind or not tall is either tall or not humble. If someone is either not rich or generous then someone is both not happy and brave and vice versa. If someone is either tall or not rich then someone is not patient or strong. If alice is not brave or happy then susan is either brave or not funny and vice versa. Everyone who is either not kind or happy is both curious and old. Lucy is both not old and curious. Susan is wise or not happy. Someone is not calm or curious. Lucy is wise or not calm. Mary is patient or not generous. Someone is tall. Someone is either not humble or not generous. Someone is patient or not calm. | Lucy is old. | contradiction | ((?[X]:(~quiet(X)))<=>(?[X]:((~brave(X)&generous(X)))))&
(((creative(fred)<~>humble(fred)))=>(?[X]:((~kind(X)<~>happy(X)))))&
(![X]:((brave(X)<~>creative(X))=>~wise(X)))&
((?[X]:((~rich(X)&kind(X))))<=>((generous(paul)&quiet(paul))))&
((?[X]:((~calm(X)&~patient(X))))=>(?[X]:((~kind(X)|~calm(X)))))&
(![X]:(~calm(X)=>(humble(X)|old(X))))&
(![X]:((~happy(X)|old(X))=>~funny(X)))&
(![X]:((patient(X)<~>~brave(X))=>(~calm(X)&~tall(X))))&
((old(john))<=>(?[X]:(~old(X))))&
(![X]:((wise(X)<~>~happy(X))<=>happy(X)))&
((?[X]:((~kind(X)<~>patient(X))))<=>((generous(paul)<~>~rich(paul))))&
(![X]:((kind(X)<~>~tall(X))=>(tall(X)<~>~humble(X))))&
((?[X]:((~rich(X)<~>generous(X))))<=>(?[X]:((~happy(X)&brave(X)))))&
((?[X]:((tall(X)<~>~rich(X))))=>(?[X]:((~patient(X)|strong(X)))))&
(((~brave(alice)|happy(alice)))<=>((brave(susan)<~>~funny(susan))))&
(![X]:((~kind(X)<~>happy(X))=>(curious(X)&old(X))))&
((~old(lucy)&curious(lucy)))&
((wise(susan)|~happy(susan)))&
(?[X]:((~calm(X)|curious(X))))&
((wise(lucy)|~calm(lucy)))&
((patient(mary)|~generous(mary)))&
(?[X]:(tall(X)))&
(?[X]:((~humble(X)<~>~generous(X))))&
(?[X]:((patient(X)|~calm(X)))) | old(lucy) | [
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 766836178050784573663572
% SZS output start Proof for 766836178050784573663572
17. curious(lucy) & ~old(lucy) [input p16]
25. old(lucy) [input hypothesis]
32. ~old(lucy) [pure predicate removal 17]
139. ~old(lucy) [cnf transformation 32]
147. old(lucy) [cnf transformation 25]
349. $false [subsumption resolution 147,139]
% SZS output end Proof for 766836178050784573663572
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If susan is both not happy and kind then someone is either not calm or wise and vice versa.
Everyone who is either happy or not humble is humble or tall and vice versa.
Everyone who is kind or calm is both patient and not quiet and vice versa.
Everyone who is not rich or happy is not kind.
Everyone who is either patient or generous is both kind and happy and vice versa.
If john is either not rich or old then paul is either humble or rich and vice versa.
If someone is both creative and quiet then someone is rich and vice versa.
Everyone who is calm is kind.
If someone is either not funny or happy then paul is both rich and not old and vice versa.
If someone is both not old and tall then paul is generous and vice versa.
If someone is not humble or brave then susan is rich or not curious.
Everyone who is happy is calm and vice versa.
Everyone who is both not patient and old is strong and vice versa.
Everyone who is not strong is both funny and not strong.
If paul is either not kind or not creative then fred is both calm and tall.
If someone is old then john is both kind and strong and vice versa.
Someone is not strong or quiet.
Someone is not brave or not tall.
Lucy is either not wise or not happy.
Mary is not happy.
Someone is not wise. | Lucy is old. | contradiction | (((~happy(susan)&kind(susan)))<=>(?[X]:((~calm(X)<~>wise(X)))))&
(![X]:((happy(X)<~>~humble(X))<=>(humble(X)|tall(X))))&
(![X]:((kind(X)|calm(X))<=>(patient(X)&~quiet(X))))&
(![X]:((~rich(X)|happy(X))=>~kind(X)))&
(![X]:((patient(X)<~>generous(X))<=>(kind(X)&happy(X))))&
(((~rich(john)<~>old(john)))<=>((humble(paul)<~>rich(paul))))&
((?[X]:((creative(X)&quiet(X))))<=>(?[X]:(rich(X))))&
(![X]:(calm(X)=>kind(X)))&
((?[X]:((~funny(X)<~>happy(X))))<=>((rich(paul)&~old(paul))))&
((?[X]:((~old(X)&tall(X))))<=>(generous(paul)))&
((?[X]:((~humble(X)|brave(X))))=>((rich(susan)|~curious(susan))))&
(![X]:(happy(X)<=>calm(X)))&
(![X]:((~patient(X)&old(X))<=>strong(X)))&
(![X]:(~strong(X)=>(funny(X)&~strong(X))))&
(((~kind(paul)<~>~creative(paul)))=>((calm(fred)&tall(fred))))&
((?[X]:(old(X)))<=>((kind(john)&strong(john))))&
(?[X]:((~strong(X)|quiet(X))))&
(?[X]:((~brave(X)|~tall(X))))&
((~wise(lucy)<~>~happy(lucy)))&
(~happy(mary))&
(?[X]:(~wise(X))) | old(lucy) | [
"p2",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8953797195530621681566963
% SZS output start Proof for 8953797195530621681566963
3. ! [X0] : ((calm(X0) | kind(X0)) <=> (~quiet(X0) & patient(X0))) [input p2]
13. ! [X0] : ((old(X0) & ~patient(X0)) <=> strong(X0)) [input p12]
16. ? [X0] : old(X0) <=> (strong(john) & kind(john)) [input p15]
22. old(lucy) [input hypothesis]
37. ! [X0] : (((calm(X0) | kind(X0)) | (quiet(X0) | ~patient(X0))) & ((~quiet(X0) & patient(X0)) | (~calm(X0) & ~kind(X0)))) [nnf transformation 3]
38. ! [X0] : ((calm(X0) | kind(X0) | quiet(X0) | ~patient(X0)) & ((~quiet(X0) & patient(X0)) | (~calm(X0) & ~kind(X0)))) [flattening 37]
57. ! [X0] : (((old(X0) & ~patient(X0)) | ~strong(X0)) & (strong(X0) | (~old(X0) | patient(X0)))) [nnf transformation 13]
58. ! [X0] : (((old(X0) & ~patient(X0)) | ~strong(X0)) & (strong(X0) | ~old(X0) | patient(X0))) [flattening 57]
60. (? [X0] : old(X0) | (~strong(john) | ~kind(john))) & ((strong(john) & kind(john)) | ! [X0] : ~old(X0)) [nnf transformation 16]
61. (? [X0] : old(X0) | ~strong(john) | ~kind(john)) & ((strong(john) & kind(john)) | ! [X0] : ~old(X0)) [flattening 60]
62. (? [X0] : old(X0) | ~strong(john) | ~kind(john)) & ((strong(john) & kind(john)) | ! [X1] : ~old(X1)) [rectify 61]
63. ? [X0] : old(X0) => old(sK5) [choice axiom]
64. (old(sK5) | ~strong(john) | ~kind(john)) & ((strong(john) & kind(john)) | ! [X1] : ~old(X1)) [skolemisation 62,63]
82. ~kind(X0) | patient(X0) [cnf transformation 38]
119. ~strong(X0) | ~patient(X0) [cnf transformation 58]
127. kind(john) | ~old(X1) [cnf transformation 64]
128. strong(john) | ~old(X1) [cnf transformation 64]
135. old(lucy) [cnf transformation 22]
276. 29 <=> kind(john) [avatar definition]
277. kind(john) <- (29) [avatar component clause 276]
280. 30 <=> strong(john) [avatar definition]
281. strong(john) <- (30) [avatar component clause 280]
289. 32 <=> ! [X1] : ~old(X1) [avatar definition]
290. ~old(X1) <- (32) [avatar component clause 289]
291. 32 | 30 [avatar split clause 128,280,289]
292. 32 | 29 [avatar split clause 127,276,289]
315. patient(john) <- (29) [resolution 82,277]
325. ~patient(john) <- (30) [resolution 119,281]
326. $false <- (29, 30) [subsumption resolution 325,315]
327. ~29 | ~30 [avatar contradiction clause 326]
328. $false <- (32) [resolution 290,135]
331. ~32 [avatar contradiction clause 328]
332. $false [avatar sat refutation 291,292,327,331]
% SZS output end Proof for 8953797195530621681566963
% ------------------------------
% 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 humble then someone is both happy and creative.
If someone is both not old and not quiet then someone is either wise or not tall and vice versa.
If paul is quiet then someone is both not wise and not funny.
If mary is both brave and rich then paul is not curious.
Everyone who is both curious and brave is funny and vice versa.
If lucy is tall then lucy is kind and vice versa.
If john is both not creative and not happy then susan is both creative and kind and vice versa.
If someone is not quiet then susan is either not tall or not creative and vice versa.
Everyone who is either not kind or generous is rich.
Everyone who is curious is either not generous or brave.
If someone is both quiet and curious then someone is both creative and brave and vice versa.
Everyone who is not rich is either humble or not old.
If someone is either not happy or generous then someone is both not rich and curious.
If mary is not creative or not curious then someone is creative and vice versa.
If mary is either not happy or calm then john is both not tall and not kind and vice versa.
Everyone who is either old or not curious is curious and vice versa.
Paul is tall.
Susan is not brave.
Someone is not old or tall.
Someone is patient or not funny.
Susan is either wise or not strong.
Someone is either tall or generous.
Lucy is both not brave and not patient. | Paul is wise. | contradiction | ((?[X]:(humble(X)))=>(?[X]:((happy(X)&creative(X)))))&
((?[X]:((~old(X)&~quiet(X))))<=>(?[X]:((wise(X)<~>~tall(X)))))&
((quiet(paul))=>(?[X]:((~wise(X)&~funny(X)))))&
(((brave(mary)&rich(mary)))=>(~curious(paul)))&
(![X]:((curious(X)&brave(X))<=>funny(X)))&
((tall(lucy))<=>(kind(lucy)))&
(((~creative(john)&~happy(john)))<=>((creative(susan)&kind(susan))))&
((?[X]:(~quiet(X)))<=>((~tall(susan)<~>~creative(susan))))&
(![X]:((~kind(X)<~>generous(X))=>rich(X)))&
(![X]:(curious(X)=>(~generous(X)<~>brave(X))))&
((?[X]:((quiet(X)&curious(X))))<=>(?[X]:((creative(X)&brave(X)))))&
(![X]:(~rich(X)=>(humble(X)<~>~old(X))))&
((?[X]:((~happy(X)<~>generous(X))))=>(?[X]:((~rich(X)&curious(X)))))&
(((~creative(mary)|~curious(mary)))<=>(?[X]:(creative(X))))&
(((~happy(mary)<~>calm(mary)))<=>((~tall(john)&~kind(john))))&
(![X]:((old(X)<~>~curious(X))<=>curious(X)))&
(tall(paul))&
(~brave(susan))&
(?[X]:((~old(X)|tall(X))))&
(?[X]:((patient(X)|~funny(X))))&
((wise(susan)<~>~strong(susan)))&
(?[X]:((tall(X)<~>generous(X))))&
((~brave(lucy)&~patient(lucy))) | wise(paul) | [
"p1",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 8649272860843777588453587
% SZS output start Proof for 8649272860843777588453587
2. ? [X0] : (~quiet(X0) & ~old(X0)) <=> ? [X0] : (wise(X0) <~> ~tall(X0)) [input p1]
16. ! [X0] : ((old(X0) <~> ~curious(X0)) <=> curious(X0)) [input p15]
17. tall(paul) [input p16]
24. wise(paul) [input hypothesis]
26. ? [X0] : (~quiet(X0) & ~old(X0)) <=> ? [X1] : (wise(X1) <~> ~tall(X1)) [rectify 2]
43. (? [X0] : (~quiet(X0) & ~old(X0)) | ! [X1] : ((wise(X1) | tall(X1)) & (~tall(X1) | ~wise(X1)))) & (? [X1] : ((tall(X1) | ~wise(X1)) & (~tall(X1) | wise(X1))) | ! [X0] : (quiet(X0) | old(X0))) [nnf transformation 26]
44. (? [X0] : (~quiet(X0) & ~old(X0)) | ! [X1] : ((wise(X1) | tall(X1)) & (~tall(X1) | ~wise(X1)))) & (? [X2] : ((tall(X2) | ~wise(X2)) & (~tall(X2) | wise(X2))) | ! [X3] : (quiet(X3) | old(X3))) [rectify 43]
45. ? [X0] : (~quiet(X0) & ~old(X0)) => (~quiet(sK1) & ~old(sK1)) [choice axiom]
46. ? [X2] : ((tall(X2) | ~wise(X2)) & (~tall(X2) | wise(X2))) => ((tall(sK2) | ~wise(sK2)) & (~tall(sK2) | wise(sK2))) [choice axiom]
47. ((~quiet(sK1) & ~old(sK1)) | ! [X1] : ((wise(X1) | tall(X1)) & (~tall(X1) | ~wise(X1)))) & (((tall(sK2) | ~wise(sK2)) & (~tall(sK2) | wise(sK2))) | ! [X3] : (quiet(X3) | old(X3))) [skolemisation 44,46,45]
76. ! [X0] : ((((curious(X0) | ~old(X0)) & (~curious(X0) | old(X0))) | ~curious(X0)) & (curious(X0) | ((old(X0) | curious(X0)) & (~curious(X0) | ~old(X0))))) [nnf transformation 16]
89. ~old(sK1) | ~tall(X1) | ~wise(X1) [cnf transformation 47]
131. curious(X0) | old(X0) | curious(X0) [cnf transformation 76]
132. ~curious(X0) | old(X0) | ~curious(X0) [cnf transformation 76]
134. tall(paul) [cnf transformation 17]
144. wise(paul) [cnf transformation 24]
145. curious(X0) | old(X0) [duplicate literal removal 131]
146. ~curious(X0) | old(X0) [duplicate literal removal 132]
169. 6 <=> ! [X1] : (~tall(X1) | ~wise(X1)) [avatar definition]
170. ~tall(X1) | ~wise(X1) <- (6) [avatar component clause 169]
173. 7 <=> old(sK1) [avatar definition]
175. ~old(sK1) <- (~7) [avatar component clause 173]
177. 6 | ~7 [avatar split clause 89,173,169]
347. old(X0) [subsumption resolution 145,146]
380. $false <- (~7) [subsumption resolution 175,347]
381. 7 [avatar contradiction clause 380]
401. ~wise(paul) <- (6) [resolution 170,134]
405. $false <- (6) [subsumption resolution 401,144]
406. ~6 [avatar contradiction clause 405]
407. $false [avatar sat refutation 177,381,406]
% SZS output end Proof for 8649272860843777588453587
% ------------------------------
% 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 humble or not old is not calm or happy.
Everyone who is both curious and not brave is either not funny or not strong and vice versa.
Everyone who is not calm or not generous is either not strong or not patient.
If someone is either not old or not curious then someone is both not kind and not curious.
Everyone who is either not happy or creative is either not kind or not generous.
Everyone who is both tall and not calm is tall or rich.
Everyone who is either wise or creative is either not kind or not generous and vice versa.
Everyone who is generous is both brave and old and vice versa.
If someone is either tall or not curious then someone is either strong or humble.
Everyone who is either not kind or not funny is funny and vice versa.
Everyone who is not quiet or not brave is both not wise and creative.
Everyone who is not quiet is not generous or not brave and vice versa.
Everyone who is both strong and humble is not strong or humble and vice versa.
If someone is funny then alice is either strong or creative and vice versa.
Everyone who is creative is either not patient or not kind.
Alice is old.
Alice is calm.
Someone is not quiet or not kind.
Fred is happy or not old.
Someone is both patient and brave.
Mary is happy or not funny. | Fred is generous. | entailment | (![X]:((humble(X)|~old(X))=>(~calm(X)|happy(X))))&
(![X]:((curious(X)&~brave(X))<=>(~funny(X)<~>~strong(X))))&
(![X]:((~calm(X)|~generous(X))=>(~strong(X)<~>~patient(X))))&
((?[X]:((~old(X)<~>~curious(X))))=>(?[X]:((~kind(X)&~curious(X)))))&
(![X]:((~happy(X)<~>creative(X))=>(~kind(X)<~>~generous(X))))&
(![X]:((tall(X)&~calm(X))=>(tall(X)|rich(X))))&
(![X]:((wise(X)<~>creative(X))<=>(~kind(X)<~>~generous(X))))&
(![X]:(generous(X)<=>(brave(X)&old(X))))&
((?[X]:((tall(X)<~>~curious(X))))=>(?[X]:((strong(X)<~>humble(X)))))&
(![X]:((~kind(X)<~>~funny(X))<=>funny(X)))&
(![X]:((~quiet(X)|~brave(X))=>(~wise(X)&creative(X))))&
(![X]:(~quiet(X)<=>(~generous(X)|~brave(X))))&
(![X]:((strong(X)&humble(X))<=>(~strong(X)|humble(X))))&
((?[X]:(funny(X)))<=>((strong(alice)<~>creative(alice))))&
(![X]:(creative(X)=>(~patient(X)<~>~kind(X))))&
(old(alice))&
(calm(alice))&
(?[X]:((~quiet(X)|~kind(X))))&
((happy(fred)|~old(fred)))&
(?[X]:((patient(X)&brave(X))))&
((happy(mary)|~funny(mary))) | generous(fred) | [
"p2",
"p9",
"p10",
"p11",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5007430318803728771801969
% SZS output start Proof for 5007430318803728771801969
3. ! [X0] : ((~generous(X0) | ~calm(X0)) => (~strong(X0) <~> ~patient(X0))) [input p2]
10. ! [X0] : ((~kind(X0) <~> ~funny(X0)) <=> funny(X0)) [input p9]
11. ! [X0] : ((~brave(X0) | ~quiet(X0)) => (creative(X0) & ~wise(X0))) [input p10]
12. ! [X0] : (~quiet(X0) <=> (~brave(X0) | ~generous(X0))) [input p11]
13. ! [X0] : ((humble(X0) & strong(X0)) <=> (humble(X0) | ~strong(X0))) [input p12]
15. ! [X0] : (creative(X0) => (~patient(X0) <~> ~kind(X0))) [input p14]
22. ~generous(fred) [input hypothesis]
28. ! [X0] : ((~strong(X0) <~> ~patient(X0)) | (generous(X0) & calm(X0))) [ennf transformation 3]
32. ! [X0] : ((creative(X0) & ~wise(X0)) | (brave(X0) & quiet(X0))) [ennf transformation 11]
33. ! [X0] : ((~patient(X0) <~> ~kind(X0)) | ~creative(X0)) [ennf transformation 15]
36. ! [X0] : (((patient(X0) | strong(X0)) & (~patient(X0) | ~strong(X0))) | (generous(X0) & calm(X0))) [nnf transformation 28]
49. ! [X0] : ((((funny(X0) | kind(X0)) & (~funny(X0) | ~kind(X0))) | ~funny(X0)) & (funny(X0) | ((~kind(X0) | funny(X0)) & (~funny(X0) | kind(X0))))) [nnf transformation 10]
50. ! [X0] : ((~quiet(X0) | (brave(X0) & generous(X0))) & ((~brave(X0) | ~generous(X0)) | quiet(X0))) [nnf transformation 12]
51. ! [X0] : ((~quiet(X0) | (brave(X0) & generous(X0))) & (~brave(X0) | ~generous(X0) | quiet(X0))) [flattening 50]
52. ! [X0] : (((humble(X0) & strong(X0)) | (~humble(X0) & strong(X0))) & ((humble(X0) | ~strong(X0)) | (~humble(X0) | ~strong(X0)))) [nnf transformation 13]
53. ! [X0] : (((humble(X0) & strong(X0)) | (~humble(X0) & strong(X0))) & (humble(X0) | ~strong(X0) | ~humble(X0) | ~strong(X0))) [flattening 52]
58. ! [X0] : (((kind(X0) | patient(X0)) & (~kind(X0) | ~patient(X0))) | ~creative(X0)) [nnf transformation 33]
72. ~patient(X0) | ~strong(X0) | generous(X0) [cnf transformation 36]
99. funny(X0) | ~kind(X0) | funny(X0) [cnf transformation 49]
100. ~funny(X0) | ~kind(X0) | ~funny(X0) [cnf transformation 49]
104. quiet(X0) | creative(X0) [cnf transformation 32]
107. ~quiet(X0) | generous(X0) [cnf transformation 51]
111. strong(X0) | ~humble(X0) [cnf transformation 53]
112. strong(X0) | humble(X0) [cnf transformation 53]
119. kind(X0) | patient(X0) | ~creative(X0) [cnf transformation 58]
127. ~generous(fred) [cnf transformation 22]
130. funny(X0) | ~kind(X0) [duplicate literal removal 99]
131. ~kind(X0) | ~funny(X0) [duplicate literal removal 100]
168. ~kind(X0) [subsumption resolution 130,131]
170. strong(X0) [subsumption resolution 111,112]
186. ~creative(X0) | patient(X0) [subsumption resolution 119,168]
206. creative(X0) | generous(X0) [resolution 107,104]
210. patient(X0) | generous(X0) [resolution 206,186]
295. generous(X0) | ~strong(X0) | generous(X0) [resolution 210,72]
297. generous(X0) | ~strong(X0) [duplicate literal removal 295]
298. generous(X0) [subsumption resolution 297,170]
304. $false [resolution 298,127]
% SZS output end Proof for 5007430318803728771801969
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either old or wise then lucy is old.
If fred is both not creative and not happy then susan is either not patient or curious and vice versa.
Everyone who is both not quiet and curious is either wise or kind and vice versa.
If someone is calm then alice is both creative and tall and vice versa.
Everyone who is both not patient and funny is either brave or funny.
Everyone who is either tall or not generous is not calm or not happy.
Everyone who is either not humble or strong is rich.
Everyone who is quiet or not patient is creative.
If john is not patient then someone is both wise and not kind and vice versa.
If fred is not humble then someone is curious.
If alice is not patient then fred is either not strong or not quiet and vice versa.
Everyone who is strong or not rich is both creative and not patient.
Everyone who is both not happy and quiet is either not old or not happy and vice versa.
Everyone who is both funny and not creative is not quiet or not wise and vice versa.
If someone is quiet or not wise then someone is both not old and not rich and vice versa.
Everyone who is either strong or old is not kind or humble.
Someone is humble or not happy.
John is either not humble or humble.
Paul is both not calm and not creative.
Mary is not calm or not funny. | Lucy is rich. | entailment | ((?[X]:((old(X)<~>wise(X))))=>(old(lucy)))&
(((~creative(fred)&~happy(fred)))<=>((~patient(susan)<~>curious(susan))))&
(![X]:((~quiet(X)&curious(X))<=>(wise(X)<~>kind(X))))&
((?[X]:(calm(X)))<=>((creative(alice)&tall(alice))))&
(![X]:((~patient(X)&funny(X))=>(brave(X)<~>funny(X))))&
(![X]:((tall(X)<~>~generous(X))=>(~calm(X)|~happy(X))))&
(![X]:((~humble(X)<~>strong(X))=>rich(X)))&
(![X]:((quiet(X)|~patient(X))=>creative(X)))&
((~patient(john))<=>(?[X]:((wise(X)&~kind(X)))))&
((~humble(fred))=>(?[X]:(curious(X))))&
((~patient(alice))<=>((~strong(fred)<~>~quiet(fred))))&
(![X]:((strong(X)|~rich(X))=>(creative(X)&~patient(X))))&
(![X]:((~happy(X)&quiet(X))<=>(~old(X)<~>~happy(X))))&
(![X]:((funny(X)&~creative(X))<=>(~quiet(X)|~wise(X))))&
((?[X]:((quiet(X)|~wise(X))))<=>(?[X]:((~old(X)&~rich(X)))))&
(![X]:((strong(X)<~>old(X))=>(~kind(X)|humble(X))))&
(?[X]:((humble(X)|~happy(X))))&
((~humble(john)<~>humble(john)))&
((~calm(paul)&~creative(paul)))&
((~calm(mary)|~funny(mary))) | rich(lucy) | [
"p11",
"p12",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2449697121209340070589851
% SZS output start Proof for 2449697121209340070589851
12. ! [X0] : ((~rich(X0) | strong(X0)) => (~patient(X0) & creative(X0))) [input p11]
13. ! [X0] : ((quiet(X0) & ~happy(X0)) <=> (~old(X0) <~> ~happy(X0))) [input p12]
14. ! [X0] : ((~creative(X0) & funny(X0)) <=> (~wise(X0) | ~quiet(X0))) [input p13]
15. ? [X0] : (~wise(X0) | quiet(X0)) <=> ? [X0] : (~rich(X0) & ~old(X0)) [input p14]
21. ~rich(lucy) [input hypothesis]
22. ? [X0] : (~wise(X0) | quiet(X0)) <=> ? [X1] : (~rich(X1) & ~old(X1)) [rectify 15]
31. ! [X0] : ((~patient(X0) & creative(X0)) | (rich(X0) & ~strong(X0))) [ennf transformation 12]
54. ! [X0] : (((quiet(X0) & ~happy(X0)) | ((~old(X0) | happy(X0)) & (~happy(X0) | old(X0)))) & (((happy(X0) | old(X0)) & (~happy(X0) | ~old(X0))) | (~quiet(X0) | happy(X0)))) [nnf transformation 13]
55. ! [X0] : (((quiet(X0) & ~happy(X0)) | ((~old(X0) | happy(X0)) & (~happy(X0) | old(X0)))) & (((happy(X0) | old(X0)) & (~happy(X0) | ~old(X0))) | ~quiet(X0) | happy(X0))) [flattening 54]
56. ! [X0] : (((~creative(X0) & funny(X0)) | (wise(X0) & quiet(X0))) & ((~wise(X0) | ~quiet(X0)) | (creative(X0) | ~funny(X0)))) [nnf transformation 14]
57. ! [X0] : (((~creative(X0) & funny(X0)) | (wise(X0) & quiet(X0))) & (~wise(X0) | ~quiet(X0) | creative(X0) | ~funny(X0))) [flattening 56]
58. (? [X0] : (~wise(X0) | quiet(X0)) | ! [X1] : (rich(X1) | old(X1))) & (? [X1] : (~rich(X1) & ~old(X1)) | ! [X0] : (wise(X0) & ~quiet(X0))) [nnf transformation 22]
59. (? [X0] : (~wise(X0) | quiet(X0)) | ! [X1] : (rich(X1) | old(X1))) & (? [X2] : (~rich(X2) & ~old(X2)) | ! [X3] : (wise(X3) & ~quiet(X3))) [rectify 58]
60. ? [X0] : (~wise(X0) | quiet(X0)) => (~wise(sK3) | quiet(sK3)) [choice axiom]
61. ? [X2] : (~rich(X2) & ~old(X2)) => (~rich(sK4) & ~old(sK4)) [choice axiom]
62. ((~wise(sK3) | quiet(sK3)) | ! [X1] : (rich(X1) | old(X1))) & ((~rich(sK4) & ~old(sK4)) | ! [X3] : (wise(X3) & ~quiet(X3))) [skolemisation 59,61,60]
101. rich(X0) | creative(X0) [cnf transformation 31]
105. happy(X0) | old(X0) | ~quiet(X0) | happy(X0) [cnf transformation 55]
106. ~happy(X0) | ~happy(X0) | old(X0) [cnf transformation 55]
113. ~creative(X0) | quiet(X0) [cnf transformation 57]
115. ~old(sK4) | ~quiet(X3) [cnf transformation 62]
117. ~rich(sK4) | ~quiet(X3) [cnf transformation 62]
128. ~rich(lucy) [cnf transformation 21]
129. happy(X0) | old(X0) | ~quiet(X0) [duplicate literal removal 105]
130. ~happy(X0) | old(X0) [duplicate literal removal 106]
227. ~quiet(X0) | old(X0) [subsumption resolution 129,130]
244. 25 <=> rich(sK4) [avatar definition]
246. ~rich(sK4) <- (~25) [avatar component clause 244]
249. 26 <=> ! [X3] : ~quiet(X3) [avatar definition]
250. ~quiet(X3) <- (26) [avatar component clause 249]
251. 26 | ~25 [avatar split clause 117,244,249]
253. 27 <=> old(sK4) [avatar definition]
255. ~old(sK4) <- (~27) [avatar component clause 253]
257. 26 | ~27 [avatar split clause 115,253,249]
282. creative(lucy) [resolution 101,128]
283. creative(sK4) <- (~25) [resolution 101,246]
286. quiet(lucy) [resolution 113,282]
290. quiet(sK4) <- (~25) [resolution 113,283]
310. old(sK4) <- (~25) [resolution 290,227]
312. $false <- (~25, ~27) [subsumption resolution 310,255]
313. 25 | 27 [avatar contradiction clause 312]
317. $false <- (26) [resolution 250,286]
324. ~26 [avatar contradiction clause 317]
325. $false [avatar sat refutation 251,257,313,324]
% SZS output end Proof for 2449697121209340070589851
% ------------------------------
% 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 rich is kind and vice versa. Everyone who is both not rich and not strong is quiet and vice versa. If susan is not curious then paul is not generous or not wise. Everyone who is not creative is not tall and vice versa. Everyone who is either not humble or tall is not strong or not happy. Everyone who is creative or quiet is either calm or brave. If lucy is either not quiet or not funny then someone is both not quiet and not old and vice versa. Everyone who is not wise is either not curious or old and vice versa. Everyone who is patient is either quiet or not strong and vice versa. Everyone who is either not patient or brave is creative or not generous and vice versa. Everyone who is either not patient or not tall is creative and vice versa. Everyone who is either tall or brave is not rich and vice versa. If someone is rich then someone is either humble or not creative and vice versa. Everyone who is either not kind or not calm is kind and vice versa. If fred is patient then someone is either humble or tall. Everyone who is either rich or not calm is calm or strong and vice versa. Fred is either happy or not tall. Someone is either happy or old. Someone is either kind or not curious. Paul is both curious and old. | Susan is not kind. | entailment | (![X]:(rich(X)<=>kind(X)))&
(![X]:((~rich(X)&~strong(X))<=>quiet(X)))&
((~curious(susan))=>((~generous(paul)|~wise(paul))))&
(![X]:(~creative(X)<=>~tall(X)))&
(![X]:((~humble(X)<~>tall(X))=>(~strong(X)|~happy(X))))&
(![X]:((creative(X)|quiet(X))=>(calm(X)<~>brave(X))))&
(((~quiet(lucy)<~>~funny(lucy)))<=>(?[X]:((~quiet(X)&~old(X)))))&
(![X]:(~wise(X)<=>(~curious(X)<~>old(X))))&
(![X]:(patient(X)<=>(quiet(X)<~>~strong(X))))&
(![X]:((~patient(X)<~>brave(X))<=>(creative(X)|~generous(X))))&
(![X]:((~patient(X)<~>~tall(X))<=>creative(X)))&
(![X]:((tall(X)<~>brave(X))<=>~rich(X)))&
((?[X]:(rich(X)))<=>(?[X]:((humble(X)<~>~creative(X)))))&
(![X]:((~kind(X)<~>~calm(X))<=>kind(X)))&
((patient(fred))=>(?[X]:((humble(X)<~>tall(X)))))&
(![X]:((rich(X)<~>~calm(X))<=>(calm(X)|strong(X))))&
((happy(fred)<~>~tall(fred)))&
(?[X]:((happy(X)<~>old(X))))&
(?[X]:((kind(X)<~>~curious(X))))&
((curious(paul)&old(paul))) | ~kind(susan) | [
"p0",
"p1",
"p3",
"p8",
"p10",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4143016278058149239113360
% SZS output start Proof for 4143016278058149239113360
1. ! [X0] : (rich(X0) <=> kind(X0)) [input p0]
2. ! [X0] : ((~strong(X0) & ~rich(X0)) <=> quiet(X0)) [input p1]
4. ! [X0] : (~creative(X0) <=> ~tall(X0)) [input p3]
9. ! [X0] : (patient(X0) <=> (quiet(X0) <~> ~strong(X0))) [input p8]
11. ! [X0] : ((~patient(X0) <~> ~tall(X0)) <=> creative(X0)) [input p10]
14. ! [X0] : ((~kind(X0) <~> ~calm(X0)) <=> kind(X0)) [input p13]
16. ! [X0] : ((rich(X0) <~> ~calm(X0)) <=> (strong(X0) | calm(X0))) [input p15]
21. kind(susan) [input hypothesis]
31. ! [X0] : ((rich(X0) | ~kind(X0)) & (kind(X0) | ~rich(X0))) [nnf transformation 1]
32. ! [X0] : (((~strong(X0) & ~rich(X0)) | ~quiet(X0)) & (quiet(X0) | (strong(X0) | rich(X0)))) [nnf transformation 2]
33. ! [X0] : (((~strong(X0) & ~rich(X0)) | ~quiet(X0)) & (quiet(X0) | strong(X0) | rich(X0))) [flattening 32]
34. ! [X0] : ((~creative(X0) | tall(X0)) & (~tall(X0) | creative(X0))) [nnf transformation 4]
42. ! [X0] : ((patient(X0) | ((quiet(X0) | strong(X0)) & (~strong(X0) | ~quiet(X0)))) & (((strong(X0) | ~quiet(X0)) & (~strong(X0) | quiet(X0))) | ~patient(X0))) [nnf transformation 9]
45. ! [X0] : ((((tall(X0) | patient(X0)) & (~tall(X0) | ~patient(X0))) | ~creative(X0)) & (creative(X0) | ((~patient(X0) | tall(X0)) & (~tall(X0) | patient(X0))))) [nnf transformation 11]
52. ! [X0] : ((((calm(X0) | kind(X0)) & (~calm(X0) | ~kind(X0))) | ~kind(X0)) & (kind(X0) | ((~kind(X0) | calm(X0)) & (~calm(X0) | kind(X0))))) [nnf transformation 14]
56. ! [X0] : ((((calm(X0) | ~rich(X0)) & (~calm(X0) | rich(X0))) | (~strong(X0) & ~calm(X0))) & ((strong(X0) | calm(X0)) | ((rich(X0) | calm(X0)) & (~calm(X0) | ~rich(X0))))) [nnf transformation 16]
57. ! [X0] : ((((calm(X0) | ~rich(X0)) & (~calm(X0) | rich(X0))) | (~strong(X0) & ~calm(X0))) & (strong(X0) | calm(X0) | ((rich(X0) | calm(X0)) & (~calm(X0) | ~rich(X0))))) [flattening 56]
66. ~kind(X0) | rich(X0) [cnf transformation 31]
68. ~quiet(X0) | ~rich(X0) [cnf transformation 33]
71. ~tall(X0) | creative(X0) [cnf transformation 34]
72. ~creative(X0) | tall(X0) [cnf transformation 34]
90. patient(X0) | quiet(X0) | strong(X0) [cnf transformation 42]
98. creative(X0) | ~patient(X0) | tall(X0) [cnf transformation 45]
99. ~tall(X0) | ~patient(X0) | ~creative(X0) [cnf transformation 45]
109. kind(X0) | ~calm(X0) | kind(X0) [cnf transformation 52]
111. ~calm(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 52]
116. strong(X0) | calm(X0) | rich(X0) | calm(X0) [cnf transformation 57]
120. calm(X0) | ~rich(X0) | ~strong(X0) [cnf transformation 57]
129. kind(susan) [cnf transformation 21]
130. strong(X0) | calm(X0) | rich(X0) [duplicate literal removal 116]
132. kind(X0) | ~calm(X0) [duplicate literal removal 109]
133. ~calm(X0) | ~kind(X0) [duplicate literal removal 111]
174. ~patient(X0) | ~tall(X0) [subsumption resolution 99,71]
175. ~patient(X0) | tall(X0) [subsumption resolution 98,72]
176. ~patient(X0) [subsumption resolution 175,174]
190. 12 <=> ! [X3] : ~rich(X3) [avatar definition]
191. ~rich(X3) <- (12) [avatar component clause 190]
202. ~calm(X0) [subsumption resolution 132,133]
203. ~strong(X0) | ~rich(X0) [subsumption resolution 120,202]
204. strong(X0) | rich(X0) [subsumption resolution 130,202]
236. rich(susan) [resolution 66,129]
261. quiet(X3) | strong(X3) [resolution 90,176]
265. strong(X2) | ~rich(X2) [resolution 261,68]
269. strong(X2) [subsumption resolution 265,204]
271. ~rich(X0) [resolution 269,203]
272. 12 [avatar split clause 271,190]
274. $false <- (12) [resolution 191,236]
275. ~12 [avatar contradiction clause 274]
277. $false [avatar sat refutation 272,275]
% SZS output end Proof for 4143016278058149239113360
% ------------------------------
% 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 john is both patient and rich then john is quiet or not happy and vice versa.
If someone is both not generous and patient then someone is not patient or not generous and vice versa.
Everyone who is both not patient and rich is both generous and happy.
Everyone who is both not tall and tall is either not humble or not generous and vice versa.
If fred is not tall then susan is both not old and not curious.
Everyone who is funny is not kind or curious.
If lucy is kind or not happy then someone is curious and vice versa.
If alice is both quiet and not generous then someone is not patient or patient and vice versa.
If lucy is not funny then mary is either not calm or quiet.
Everyone who is both old and not quiet is not calm.
If john is creative then someone is both not curious and not patient and vice versa.
If susan is both not strong and not calm then someone is tall or not brave and vice versa.
Everyone who is either not brave or not happy is either funny or happy.
If john is both not calm and not tall then john is both humble and wise and vice versa.
Everyone who is both brave and not generous is wise.
If someone is both not strong and humble then someone is not strong or not kind and vice versa.
Someone is not humble.
Someone is not happy or humble.
Paul is either kind or not old.
Someone is not quiet.
Someone is both not brave and not calm.
Someone is both not rich and not happy.
Someone is either kind or happy. | Susan is not kind. | neutral | (((patient(john)&rich(john)))<=>((quiet(john)|~happy(john))))&
((?[X]:((~generous(X)&patient(X))))<=>(?[X]:((~patient(X)|~generous(X)))))&
(![X]:((~patient(X)&rich(X))=>(generous(X)&happy(X))))&
(![X]:((~tall(X)&tall(X))<=>(~humble(X)<~>~generous(X))))&
((~tall(fred))=>((~old(susan)&~curious(susan))))&
(![X]:(funny(X)=>(~kind(X)|curious(X))))&
(((kind(lucy)|~happy(lucy)))<=>(?[X]:(curious(X))))&
(((quiet(alice)&~generous(alice)))<=>(?[X]:((~patient(X)|patient(X)))))&
((~funny(lucy))=>((~calm(mary)<~>quiet(mary))))&
(![X]:((old(X)&~quiet(X))=>~calm(X)))&
((creative(john))<=>(?[X]:((~curious(X)&~patient(X)))))&
(((~strong(susan)&~calm(susan)))<=>(?[X]:((tall(X)|~brave(X)))))&
(![X]:((~brave(X)<~>~happy(X))=>(funny(X)<~>happy(X))))&
(((~calm(john)&~tall(john)))<=>((humble(john)&wise(john))))&
(![X]:((brave(X)&~generous(X))=>wise(X)))&
((?[X]:((~strong(X)&humble(X))))<=>(?[X]:((~strong(X)|~kind(X)))))&
(?[X]:(~humble(X)))&
(?[X]:((~happy(X)|humble(X))))&
((kind(paul)<~>~old(paul)))&
(?[X]:(~quiet(X)))&
(?[X]:((~brave(X)&~calm(X))))&
(?[X]:((~rich(X)&~happy(X))))&
(?[X]:((kind(X)<~>happy(X)))) | ~kind(susan) | [] | null | 0 |
Everyone who is both not quiet and generous is not happy or creative and vice versa.
Everyone who is calm is quiet and vice versa.
Everyone who is tall is either not happy or funny.
Everyone who is either brave or not patient is patient.
Everyone who is both quiet and not happy is either kind or not generous.
Everyone who is not brave is not creative and vice versa.
Everyone who is either not calm or happy is brave and vice versa.
If mary is not patient or not creative then someone is both not curious and not humble.
If alice is not brave or not funny then lucy is either not patient or curious.
Everyone who is creative or funny is both humble and strong and vice versa.
Everyone who is brave or not curious is both tall and not curious and vice versa.
If someone is calm then someone is both not curious and not calm.
If someone is both wise and generous then someone is either happy or not strong.
Everyone who is humble is either not patient or wise.
If someone is not kind then susan is both tall and not funny and vice versa.
Everyone who is either strong or not brave is kind.
Someone is generous or calm.
Alice is not creative or not generous.
Someone is either patient or generous.
Someone is either not funny or not old.
Alice is both not wise and not calm.
Alice is either not rich or not quiet.
Someone is both not kind and not humble. | Alice is not curious. | contradiction | (![X]:((~quiet(X)&generous(X))<=>(~happy(X)|creative(X))))&
(![X]:(calm(X)<=>quiet(X)))&
(![X]:(tall(X)=>(~happy(X)<~>funny(X))))&
(![X]:((brave(X)<~>~patient(X))=>patient(X)))&
(![X]:((quiet(X)&~happy(X))=>(kind(X)<~>~generous(X))))&
(![X]:(~brave(X)<=>~creative(X)))&
(![X]:((~calm(X)<~>happy(X))<=>brave(X)))&
(((~patient(mary)|~creative(mary)))=>(?[X]:((~curious(X)&~humble(X)))))&
(((~brave(alice)|~funny(alice)))=>((~patient(lucy)<~>curious(lucy))))&
(![X]:((creative(X)|funny(X))<=>(humble(X)&strong(X))))&
(![X]:((brave(X)|~curious(X))<=>(tall(X)&~curious(X))))&
((?[X]:(calm(X)))=>(?[X]:((~curious(X)&~calm(X)))))&
((?[X]:((wise(X)&generous(X))))=>(?[X]:((happy(X)<~>~strong(X)))))&
(![X]:(humble(X)=>(~patient(X)<~>wise(X))))&
((?[X]:(~kind(X)))<=>((tall(susan)&~funny(susan))))&
(![X]:((strong(X)<~>~brave(X))=>kind(X)))&
(?[X]:((generous(X)|calm(X))))&
((~creative(alice)|~generous(alice)))&
(?[X]:((patient(X)<~>generous(X))))&
(?[X]:((~funny(X)<~>~old(X))))&
((~wise(alice)&~calm(alice)))&
((~rich(alice)<~>~quiet(alice)))&
(?[X]:((~kind(X)&~humble(X)))) | ~curious(alice) | [
"p0",
"p2",
"p3",
"p5",
"p6",
"p9",
"p10",
"p13",
"p17",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 8374150567152451130314940
% SZS output start Proof for 8374150567152451130314940
1. ! [X0] : ((generous(X0) & ~quiet(X0)) <=> (creative(X0) | ~happy(X0))) [input p0]
3. ! [X0] : (tall(X0) => (~happy(X0) <~> funny(X0))) [input p2]
4. ! [X0] : ((brave(X0) <~> ~patient(X0)) => patient(X0)) [input p3]
6. ! [X0] : (~brave(X0) <=> ~creative(X0)) [input p5]
7. ! [X0] : ((~calm(X0) <~> happy(X0)) <=> brave(X0)) [input p6]
10. ! [X0] : ((funny(X0) | creative(X0)) <=> (strong(X0) & humble(X0))) [input p9]
11. ! [X0] : ((~curious(X0) | brave(X0)) <=> (~curious(X0) & tall(X0))) [input p10]
14. ! [X0] : (humble(X0) => (~patient(X0) <~> wise(X0))) [input p13]
18. ~generous(alice) | ~creative(alice) [input p17]
21. ~calm(alice) & ~wise(alice) [input p20]
24. ~curious(alice) [input hypothesis]
27. ! [X0] : ((~happy(X0) <~> funny(X0)) | ~tall(X0)) [ennf transformation 3]
28. ! [X0] : (patient(X0) | (brave(X0) <=> ~patient(X0))) [ennf transformation 4]
35. ! [X0] : ((~patient(X0) <~> wise(X0)) | ~humble(X0)) [ennf transformation 14]
37. ! [X0] : (((generous(X0) & ~quiet(X0)) | (~creative(X0) & happy(X0))) & ((creative(X0) | ~happy(X0)) | (~generous(X0) | quiet(X0)))) [nnf transformation 1]
38. ! [X0] : (((generous(X0) & ~quiet(X0)) | (~creative(X0) & happy(X0))) & (creative(X0) | ~happy(X0) | ~generous(X0) | quiet(X0))) [flattening 37]
40. ! [X0] : (((~funny(X0) | happy(X0)) & (funny(X0) | ~happy(X0))) | ~tall(X0)) [nnf transformation 27]
41. ! [X0] : (patient(X0) | ((brave(X0) | patient(X0)) & (~patient(X0) | ~brave(X0)))) [nnf transformation 28]
43. ! [X0] : ((~brave(X0) | creative(X0)) & (~creative(X0) | brave(X0))) [nnf transformation 6]
44. ! [X0] : ((((~happy(X0) | calm(X0)) & (happy(X0) | ~calm(X0))) | ~brave(X0)) & (brave(X0) | ((~calm(X0) | ~happy(X0)) & (happy(X0) | calm(X0))))) [nnf transformation 7]
48. ! [X0] : (((funny(X0) | creative(X0)) | (~strong(X0) | ~humble(X0))) & ((strong(X0) & humble(X0)) | (~funny(X0) & ~creative(X0)))) [nnf transformation 10]
49. ! [X0] : ((funny(X0) | creative(X0) | ~strong(X0) | ~humble(X0)) & ((strong(X0) & humble(X0)) | (~funny(X0) & ~creative(X0)))) [flattening 48]
50. ! [X0] : (((~curious(X0) | brave(X0)) | (curious(X0) | ~tall(X0))) & ((~curious(X0) & tall(X0)) | (curious(X0) & ~brave(X0)))) [nnf transformation 11]
51. ! [X0] : ((~curious(X0) | brave(X0) | curious(X0) | ~tall(X0)) & ((~curious(X0) & tall(X0)) | (curious(X0) & ~brave(X0)))) [flattening 50]
59. ! [X0] : (((~wise(X0) | patient(X0)) & (wise(X0) | ~patient(X0))) | ~humble(X0)) [nnf transformation 35]
81. ~creative(X0) | generous(X0) [cnf transformation 38]
84. ~tall(X0) | ~happy(X0) | funny(X0) [cnf transformation 40]
87. patient(X0) | brave(X0) | patient(X0) [cnf transformation 41]
91. ~brave(X0) | creative(X0) [cnf transformation 43]
92. brave(X0) | happy(X0) | calm(X0) [cnf transformation 44]
105. ~funny(X0) | humble(X0) [cnf transformation 49]
110. curious(X0) | tall(X0) [cnf transformation 51]
118. ~humble(X0) | ~patient(X0) | wise(X0) [cnf transformation 59]
126. ~generous(alice) | ~creative(alice) [cnf transformation 18]
131. ~wise(alice) [cnf transformation 21]
132. ~calm(alice) [cnf transformation 21]
137. ~curious(alice) [cnf transformation 24]
138. patient(X0) | brave(X0) [duplicate literal removal 87]
160. 5 <=> funny(alice) [avatar definition]
162. funny(alice) <- (5) [avatar component clause 160]
173. 8 <=> brave(alice) [avatar definition]
175. brave(alice) <- (8) [avatar component clause 173]
232. ~creative(alice) [subsumption resolution 126,81]
266. tall(alice) [resolution 110,137]
273. ~happy(alice) | funny(alice) [resolution 84,266]
277. 27 <=> happy(alice) [avatar definition]
279. ~happy(alice) <- (~27) [avatar component clause 277]
280. 5 | ~27 [avatar split clause 273,277,160]
321. calm(X1) | happy(X1) | creative(X1) [resolution 92,91]
406. happy(alice) | creative(alice) [resolution 321,132]
410. creative(alice) <- (~27) [subsumption resolution 406,279]
411. $false <- (~27) [subsumption resolution 410,232]
412. 27 [avatar contradiction clause 411]
417. humble(alice) <- (5) [resolution 162,105]
426. ~patient(alice) | wise(alice) <- (5) [resolution 417,118]
427. ~patient(alice) <- (5) [subsumption resolution 426,131]
462. brave(alice) <- (5) [resolution 427,138]
465. 8 | ~5 [avatar split clause 462,160,173]
469. creative(alice) <- (8) [resolution 175,91]
473. $false <- (8) [subsumption resolution 469,232]
474. ~8 [avatar contradiction clause 473]
475. $false [avatar sat refutation 280,412,465,474]
% SZS output end Proof for 8374150567152451130314940
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
If john is humble then john is old.
If mary is not kind or not humble then someone is not brave and vice versa.
If mary is either wise or not generous then mary is not kind or not brave.
Everyone who is quiet or funny is not funny.
If someone is both generous and wise then fred is either not humble or not patient.
Everyone who is not rich is both funny and not quiet.
Everyone who is both patient and not generous is either humble or not wise.
If alice is patient or not quiet then fred is patient.
Everyone who is both quiet and tall is either calm or not calm and vice versa.
Everyone who is tall is not patient.
If john is not funny then alice is both not patient and not calm.
Everyone who is brave is not quiet or humble and vice versa.
If someone is not tall or not rich then susan is both generous and tall and vice versa.
If fred is either not brave or funny then paul is not old and vice versa.
Someone is not patient or not curious.
Paul is not tall or calm.
Paul is kind.
Someone is not curious or not strong.
Someone is humble or generous.
Someone is both strong and calm. | Alice is not funny. | entailment | ((humble(john))=>(old(john)))&
(((~kind(mary)|~humble(mary)))<=>(?[X]:(~brave(X))))&
(((wise(mary)<~>~generous(mary)))=>((~kind(mary)|~brave(mary))))&
(![X]:((quiet(X)|funny(X))=>~funny(X)))&
((?[X]:((generous(X)&wise(X))))=>((~humble(fred)<~>~patient(fred))))&
(![X]:(~rich(X)=>(funny(X)&~quiet(X))))&
(![X]:((patient(X)&~generous(X))=>(humble(X)<~>~wise(X))))&
(((patient(alice)|~quiet(alice)))=>(patient(fred)))&
(![X]:((quiet(X)&tall(X))<=>(calm(X)<~>~calm(X))))&
(![X]:(tall(X)=>~patient(X)))&
((~funny(john))=>((~patient(alice)&~calm(alice))))&
(![X]:(brave(X)<=>(~quiet(X)|humble(X))))&
((?[X]:((~tall(X)|~rich(X))))<=>((generous(susan)&tall(susan))))&
(((~brave(fred)<~>funny(fred)))<=>(~old(paul)))&
(?[X]:((~patient(X)|~curious(X))))&
((~tall(paul)|calm(paul)))&
(kind(paul))&
(?[X]:((~curious(X)|~strong(X))))&
(?[X]:((humble(X)|generous(X))))&
(?[X]:((strong(X)&calm(X)))) | ~funny(alice) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 6150452028806593801519950
% SZS output start Proof for 6150452028806593801519950
4. ! [X0] : ((funny(X0) | quiet(X0)) => ~funny(X0)) [input p3]
21. funny(alice) [input hypothesis]
28. ! [X0] : (~funny(X0) | (~funny(X0) & ~quiet(X0))) [ennf transformation 4]
65. ~funny(X0) | ~funny(X0) [cnf transformation 28]
99. funny(alice) [cnf transformation 21]
104. ~funny(X0) [duplicate literal removal 65]
200. $false [subsumption resolution 99,104]
% SZS output end Proof for 6150452028806593801519950
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 4989
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not generous or not brave is brave or not wise and vice versa.
Everyone who is both old and generous is both not happy and not quiet and vice versa.
Everyone who is not tall or not strong is either not curious or kind and vice versa.
Everyone who is kind or not quiet is both creative and old.
If john is not old then paul is tall or happy.
Everyone who is both strong and not kind is funny.
Everyone who is either happy or not old is either strong or not curious.
If someone is quiet then someone is both curious and not calm and vice versa.
Everyone who is not patient or not happy is brave or not funny.
Everyone who is old is not curious.
Everyone who is not creative or not quiet is both old and not tall and vice versa.
If john is not old then fred is both not generous and not humble and vice versa.
Everyone who is both humble and not humble is both calm and patient and vice versa.
If mary is not creative then someone is either wise or rich and vice versa.
If john is both not kind and happy then someone is not happy or not humble and vice versa.
Everyone who is either calm or not tall is either quiet or patient and vice versa.
Lucy is not wise or happy.
Someone is both not calm and rich.
Someone is strong or generous.
Mary is not old or quiet.
Susan is both not brave and not kind.
John is generous or not tall.
Someone is either not patient or not kind. | Lucy is not wise. | neutral | (![X]:((~generous(X)<~>~brave(X))<=>(brave(X)|~wise(X))))&
(![X]:((old(X)&generous(X))<=>(~happy(X)&~quiet(X))))&
(![X]:((~tall(X)|~strong(X))<=>(~curious(X)<~>kind(X))))&
(![X]:((kind(X)|~quiet(X))=>(creative(X)&old(X))))&
((~old(john))=>((tall(paul)|happy(paul))))&
(![X]:((strong(X)&~kind(X))=>funny(X)))&
(![X]:((happy(X)<~>~old(X))=>(strong(X)<~>~curious(X))))&
((?[X]:(quiet(X)))<=>(?[X]:((curious(X)&~calm(X)))))&
(![X]:((~patient(X)|~happy(X))=>(brave(X)|~funny(X))))&
(![X]:(old(X)=>~curious(X)))&
(![X]:((~creative(X)|~quiet(X))<=>(old(X)&~tall(X))))&
((~old(john))<=>((~generous(fred)&~humble(fred))))&
(![X]:((humble(X)&~humble(X))<=>(calm(X)&patient(X))))&
((~creative(mary))<=>(?[X]:((wise(X)<~>rich(X)))))&
(((~kind(john)&happy(john)))<=>(?[X]:((~happy(X)|~humble(X)))))&
(![X]:((calm(X)<~>~tall(X))<=>(quiet(X)<~>patient(X))))&
((~wise(lucy)|happy(lucy)))&
(?[X]:((~calm(X)&rich(X))))&
(?[X]:((strong(X)|generous(X))))&
((~old(mary)|quiet(mary)))&
((~brave(susan)&~kind(susan)))&
((generous(john)|~tall(john)))&
(?[X]:((~patient(X)<~>~kind(X)))) | ~wise(lucy) | [] | null | 0 |
If alice is old then lucy is kind and vice versa. If someone is not calm or not happy then someone is either strong or not old and vice versa. If someone is not brave then someone is humble and vice versa. If someone is either wise or not strong then someone is calm or rich. Everyone who is not rich is not rich or happy and vice versa. Everyone who is not generous is either curious or not curious and vice versa. Everyone who is either rich or not calm is not old or happy and vice versa. Everyone who is humble or not happy is not humble. If alice is not curious then someone is both creative and not old. Everyone who is not happy or not tall is not wise or wise and vice versa. Everyone who is either not funny or patient is either not calm or not rich. If susan is either not happy or not brave then fred is either humble or not tall and vice versa. Everyone who is either not rich or tall is both not brave and generous. If someone is both not creative and rich then someone is both happy and rich. Everyone who is strong or kind is not curious. Someone is not strong. Susan is both kind and creative. Mary is not funny or not creative. Paul is not calm. Someone is both not generous and tall. Someone is either generous or not humble. Fred is tall or brave. | Paul is happy. | contradiction | ((old(alice))<=>(kind(lucy)))&
((?[X]:((~calm(X)|~happy(X))))<=>(?[X]:((strong(X)<~>~old(X)))))&
((?[X]:(~brave(X)))<=>(?[X]:(humble(X))))&
((?[X]:((wise(X)<~>~strong(X))))=>(?[X]:((calm(X)|rich(X)))))&
(![X]:(~rich(X)<=>(~rich(X)|happy(X))))&
(![X]:(~generous(X)<=>(curious(X)<~>~curious(X))))&
(![X]:((rich(X)<~>~calm(X))<=>(~old(X)|happy(X))))&
(![X]:((humble(X)|~happy(X))=>~humble(X)))&
((~curious(alice))=>(?[X]:((creative(X)&~old(X)))))&
(![X]:((~happy(X)|~tall(X))<=>(~wise(X)|wise(X))))&
(![X]:((~funny(X)<~>patient(X))=>(~calm(X)<~>~rich(X))))&
(((~happy(susan)<~>~brave(susan)))<=>((humble(fred)<~>~tall(fred))))&
(![X]:((~rich(X)<~>tall(X))=>(~brave(X)&generous(X))))&
((?[X]:((~creative(X)&rich(X))))=>(?[X]:((happy(X)&rich(X)))))&
(![X]:((strong(X)|kind(X))=>~curious(X)))&
(?[X]:(~strong(X)))&
((kind(susan)&creative(susan)))&
((~funny(mary)|~creative(mary)))&
(~calm(paul))&
(?[X]:((~generous(X)&tall(X))))&
(?[X]:((generous(X)<~>~humble(X))))&
((tall(fred)|brave(fred))) | happy(paul) | [
"p4",
"p5",
"p9",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 5221429726719049360139237
% SZS output start Proof for 5221429726719049360139237
5. ! [X0] : (~rich(X0) <=> (happy(X0) | ~rich(X0))) [input p4]
6. ! [X0] : (~generous(X0) <=> (curious(X0) <~> ~curious(X0))) [input p5]
10. ! [X0] : ((~tall(X0) | ~happy(X0)) <=> (wise(X0) | ~wise(X0))) [input p9]
13. ! [X0] : ((~rich(X0) <~> tall(X0)) => (generous(X0) & ~brave(X0))) [input p12]
23. happy(paul) [input hypothesis]
32. ! [X0] : ((generous(X0) & ~brave(X0)) | (~rich(X0) <=> tall(X0))) [ennf transformation 13]
50. ! [X0] : ((~rich(X0) | (~happy(X0) & rich(X0))) & ((happy(X0) | ~rich(X0)) | rich(X0))) [nnf transformation 5]
51. ! [X0] : ((~rich(X0) | (~happy(X0) & rich(X0))) & (happy(X0) | ~rich(X0) | rich(X0))) [flattening 50]
52. ! [X0] : ((~generous(X0) | ((curious(X0) | curious(X0)) & (~curious(X0) | ~curious(X0)))) & (((curious(X0) | ~curious(X0)) & (~curious(X0) | curious(X0))) | generous(X0))) [nnf transformation 6]
57. ! [X0] : (((~tall(X0) | ~happy(X0)) | (~wise(X0) & wise(X0))) & ((wise(X0) | ~wise(X0)) | (tall(X0) & happy(X0)))) [nnf transformation 10]
58. ! [X0] : ((~tall(X0) | ~happy(X0) | (~wise(X0) & wise(X0))) & (wise(X0) | ~wise(X0) | (tall(X0) & happy(X0)))) [flattening 57]
61. ! [X0] : ((generous(X0) & ~brave(X0)) | ((~rich(X0) | ~tall(X0)) & (tall(X0) | rich(X0)))) [nnf transformation 32]
86. ~rich(X0) | ~happy(X0) [cnf transformation 51]
89. ~generous(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 52]
90. ~generous(X0) | curious(X0) | curious(X0) [cnf transformation 52]
103. ~tall(X0) | ~happy(X0) | wise(X0) [cnf transformation 58]
104. ~tall(X0) | ~happy(X0) | ~wise(X0) [cnf transformation 58]
119. generous(X0) | tall(X0) | rich(X0) [cnf transformation 61]
135. happy(paul) [cnf transformation 23]
137. ~generous(X0) | ~curious(X0) [duplicate literal removal 89]
138. ~generous(X0) | curious(X0) [duplicate literal removal 90]
215. ~generous(X0) [subsumption resolution 137,138]
233. ~tall(X0) | ~happy(X0) [subsumption resolution 103,104]
259. tall(X0) | rich(X0) [subsumption resolution 119,215]
303. rich(X1) | ~happy(X1) [resolution 259,233]
304. ~happy(X1) [subsumption resolution 303,86]
317. $false [resolution 304,135]
% SZS output end Proof for 5221429726719049360139237
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not brave or not tall then mary is either generous or curious and vice versa.
Everyone who is both not rich and happy is both funny and not kind and vice versa.
Everyone who is both calm and kind is both kind and not happy and vice versa.
Everyone who is both not old and not creative is not patient or not strong and vice versa.
Everyone who is either not generous or kind is both creative and not generous and vice versa.
Everyone who is not calm or wise is calm and vice versa.
Everyone who is patient is rich and vice versa.
Everyone who is happy or not happy is funny or quiet.
If someone is either strong or not calm then alice is either not kind or rich.
If mary is either not patient or wise then someone is either not wise or humble.
Everyone who is brave or not wise is both brave and creative.
Everyone who is not humble or kind is not old and vice versa.
If someone is both humble and not old then mary is humble or curious and vice versa.
Everyone who is not calm or brave is not strong or brave and vice versa.
If someone is both not brave and quiet then lucy is not kind.
Everyone who is either generous or funny is both humble and not generous and vice versa.
Lucy is either quiet or tall.
Someone is both generous and not old.
Someone is both not rich and not kind.
Someone is quiet.
Someone is either not happy or strong.
Someone is rich.
Paul is either not patient or kind.
Lucy is both rich and not tall. | Paul is not tall. | neutral | ((?[X]:((~brave(X)|~tall(X))))<=>((generous(mary)<~>curious(mary))))&
(![X]:((~rich(X)&happy(X))<=>(funny(X)&~kind(X))))&
(![X]:((calm(X)&kind(X))<=>(kind(X)&~happy(X))))&
(![X]:((~old(X)&~creative(X))<=>(~patient(X)|~strong(X))))&
(![X]:((~generous(X)<~>kind(X))<=>(creative(X)&~generous(X))))&
(![X]:((~calm(X)|wise(X))<=>calm(X)))&
(![X]:(patient(X)<=>rich(X)))&
(![X]:((happy(X)|~happy(X))=>(funny(X)|quiet(X))))&
((?[X]:((strong(X)<~>~calm(X))))=>((~kind(alice)<~>rich(alice))))&
(((~patient(mary)<~>wise(mary)))=>(?[X]:((~wise(X)<~>humble(X)))))&
(![X]:((brave(X)|~wise(X))=>(brave(X)&creative(X))))&
(![X]:((~humble(X)|kind(X))<=>~old(X)))&
((?[X]:((humble(X)&~old(X))))<=>((humble(mary)|curious(mary))))&
(![X]:((~calm(X)|brave(X))<=>(~strong(X)|brave(X))))&
((?[X]:((~brave(X)&quiet(X))))=>(~kind(lucy)))&
(![X]:((generous(X)<~>funny(X))<=>(humble(X)&~generous(X))))&
((quiet(lucy)<~>tall(lucy)))&
(?[X]:((generous(X)&~old(X))))&
(?[X]:((~rich(X)&~kind(X))))&
(?[X]:(quiet(X)))&
(?[X]:((~happy(X)<~>strong(X))))&
(?[X]:(rich(X)))&
((~patient(paul)<~>kind(paul)))&
((rich(lucy)&~tall(lucy))) | ~tall(paul) | [] | null | 0 |
If mary is not kind then someone is either not strong or kind and vice versa.
Everyone who is creative is both not happy and curious and vice versa.
Everyone who is not rich is both not quiet and not calm and vice versa.
Everyone who is tall or curious is either calm or not kind.
Everyone who is strong or not calm is either curious or strong.
If someone is not patient then someone is generous.
If john is rich or patient then someone is calm or quiet and vice versa.
Everyone who is either not humble or funny is both not wise and not brave and vice versa.
Everyone who is not old or not quiet is kind or generous.
Everyone who is both not curious and kind is curious or patient and vice versa.
If fred is both wise and rich then someone is rich and vice versa.
If susan is both creative and not happy then john is both not tall and not humble and vice versa.
Everyone who is not wise or not rich is not tall.
Everyone who is either brave or calm is either not creative or not humble and vice versa.
Everyone who is both creative and strong is both patient and rich and vice versa.
Everyone who is curious is funny and vice versa.
John is not brave.
Someone is either not generous or not happy.
Someone is either quiet or not old.
Someone is either happy or not generous.
Fred is both not generous and not patient. | Mary is not tall. | neutral | ((~kind(mary))<=>(?[X]:((~strong(X)<~>kind(X)))))&
(![X]:(creative(X)<=>(~happy(X)&curious(X))))&
(![X]:(~rich(X)<=>(~quiet(X)&~calm(X))))&
(![X]:((tall(X)|curious(X))=>(calm(X)<~>~kind(X))))&
(![X]:((strong(X)|~calm(X))=>(curious(X)<~>strong(X))))&
((?[X]:(~patient(X)))=>(?[X]:(generous(X))))&
(((rich(john)|patient(john)))<=>(?[X]:((calm(X)|quiet(X)))))&
(![X]:((~humble(X)<~>funny(X))<=>(~wise(X)&~brave(X))))&
(![X]:((~old(X)|~quiet(X))=>(kind(X)|generous(X))))&
(![X]:((~curious(X)&kind(X))<=>(curious(X)|patient(X))))&
(((wise(fred)&rich(fred)))<=>(?[X]:(rich(X))))&
(((creative(susan)&~happy(susan)))<=>((~tall(john)&~humble(john))))&
(![X]:((~wise(X)|~rich(X))=>~tall(X)))&
(![X]:((brave(X)<~>calm(X))<=>(~creative(X)<~>~humble(X))))&
(![X]:((creative(X)&strong(X))<=>(patient(X)&rich(X))))&
(![X]:(curious(X)<=>funny(X)))&
(~brave(john))&
(?[X]:((~generous(X)<~>~happy(X))))&
(?[X]:((quiet(X)<~>~old(X))))&
(?[X]:((happy(X)<~>~generous(X))))&
((~generous(fred)&~patient(fred))) | ~tall(mary) | [] | null | 0 |
Everyone who is both strong and calm is not generous or not strong and vice versa.
Everyone who is happy is both not tall and old and vice versa.
If someone is both not humble and tall then alice is either tall or not happy.
Everyone who is both not wise and not rich is not calm.
If fred is either not kind or old then someone is both not quiet and creative and vice versa.
Everyone who is tall or old is not patient or brave.
Everyone who is either funny or not happy is either not tall or patient and vice versa.
Everyone who is not curious is either tall or happy.
If alice is both not happy and old then john is both rich and brave and vice versa.
If someone is either not strong or not patient then someone is not strong and vice versa.
If john is either not tall or not creative then john is humble or not calm and vice versa.
Everyone who is not wise or calm is funny.
Everyone who is either quiet or not strong is not patient or not old and vice versa.
Everyone who is both not generous and strong is not humble or not calm and vice versa.
Everyone who is both not brave and calm is either wise or tall.
Lucy is not creative.
Someone is either not quiet or not kind.
Someone is either brave or curious.
Susan is kind.
Someone is either not kind or generous. | Alice is not patient. | contradiction | (![X]:((strong(X)&calm(X))<=>(~generous(X)|~strong(X))))&
(![X]:(happy(X)<=>(~tall(X)&old(X))))&
((?[X]:((~humble(X)&tall(X))))=>((tall(alice)<~>~happy(alice))))&
(![X]:((~wise(X)&~rich(X))=>~calm(X)))&
(((~kind(fred)<~>old(fred)))<=>(?[X]:((~quiet(X)&creative(X)))))&
(![X]:((tall(X)|old(X))=>(~patient(X)|brave(X))))&
(![X]:((funny(X)<~>~happy(X))<=>(~tall(X)<~>patient(X))))&
(![X]:(~curious(X)=>(tall(X)<~>happy(X))))&
(((~happy(alice)&old(alice)))<=>((rich(john)&brave(john))))&
((?[X]:((~strong(X)<~>~patient(X))))<=>(?[X]:(~strong(X))))&
(((~tall(john)<~>~creative(john)))<=>((humble(john)|~calm(john))))&
(![X]:((~wise(X)|calm(X))=>funny(X)))&
(![X]:((quiet(X)<~>~strong(X))<=>(~patient(X)|~old(X))))&
(![X]:((~generous(X)&strong(X))<=>(~humble(X)|~calm(X))))&
(![X]:((~brave(X)&calm(X))=>(wise(X)<~>tall(X))))&
(~creative(lucy))&
(?[X]:((~quiet(X)<~>~kind(X))))&
(?[X]:((brave(X)<~>curious(X))))&
(kind(susan))&
(?[X]:((~kind(X)<~>generous(X)))) | ~patient(alice) | [
"p0",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 136615385980346960021385
% SZS output start Proof for 136615385980346960021385
1. ! [X0] : ((calm(X0) & strong(X0)) <=> (~strong(X0) | ~generous(X0))) [input p0]
10. ? [X0] : (~strong(X0) <~> ~patient(X0)) <=> ? [X0] : ~strong(X0) [input p9]
21. ~patient(alice) [input hypothesis]
22. ? [X0] : (~strong(X0) <~> ~patient(X0)) <=> ? [X1] : ~strong(X1) [rectify 10]
32. ! [X0] : (((calm(X0) & strong(X0)) | (strong(X0) & generous(X0))) & ((~strong(X0) | ~generous(X0)) | (~calm(X0) | ~strong(X0)))) [nnf transformation 1]
33. ! [X0] : (((calm(X0) & strong(X0)) | (strong(X0) & generous(X0))) & (~strong(X0) | ~generous(X0) | ~calm(X0) | ~strong(X0))) [flattening 32]
45. (? [X0] : ((patient(X0) | strong(X0)) & (~patient(X0) | ~strong(X0))) | ! [X1] : strong(X1)) & (? [X1] : ~strong(X1) | ! [X0] : ((~strong(X0) | patient(X0)) & (~patient(X0) | strong(X0)))) [nnf transformation 22]
46. (? [X0] : ((patient(X0) | strong(X0)) & (~patient(X0) | ~strong(X0))) | ! [X1] : strong(X1)) & (? [X2] : ~strong(X2) | ! [X3] : ((~strong(X3) | patient(X3)) & (~patient(X3) | strong(X3)))) [rectify 45]
47. ? [X0] : ((patient(X0) | strong(X0)) & (~patient(X0) | ~strong(X0))) => ((patient(sK1) | strong(sK1)) & (~patient(sK1) | ~strong(sK1))) [choice axiom]
48. ? [X2] : ~strong(X2) => ~strong(sK2) [choice axiom]
49. (((patient(sK1) | strong(sK1)) & (~patient(sK1) | ~strong(sK1))) | ! [X1] : strong(X1)) & (~strong(sK2) | ! [X3] : ((~strong(X3) | patient(X3)) & (~patient(X3) | strong(X3)))) [skolemisation 46,48,47]
68. strong(X0) | strong(X0) [cnf transformation 33]
100. ~strong(sK2) | ~strong(X3) | patient(X3) [cnf transformation 49]
132. ~patient(alice) [cnf transformation 21]
134. strong(X0) [duplicate literal removal 68]
196. ~strong(X3) | patient(X3) [subsumption resolution 100,134]
197. patient(X3) [subsumption resolution 196,134]
258. $false [subsumption resolution 132,197]
% SZS output end Proof for 136615385980346960021385
% ------------------------------
% 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 funny is not brave or curious. If someone is quiet then fred is not rich and vice versa. If someone is not happy then someone is rich or funny. Everyone who is patient or not brave is both curious and not wise and vice versa. Everyone who is either not funny or rich is rich or not patient. Everyone who is both not happy and not tall is kind or not patient and vice versa. Everyone who is either not old or not wise is brave and vice versa. Everyone who is not humble is not rich. Everyone who is quiet or not funny is both not kind and kind and vice versa. If someone is not old then fred is happy. If someone is calm then someone is either wise or not quiet and vice versa. Everyone who is not brave or funny is either happy or not generous and vice versa. Everyone who is both happy and generous is not tall or not humble and vice versa. If mary is either not wise or quiet then someone is not old or not humble and vice versa. Everyone who is rich is not generous and vice versa. Someone is either not rich or curious. Someone is patient. Someone is wise or not calm. Someone is either old or kind. Alice is tall or not kind. Lucy is not creative or not happy. Paul is not calm. | Lucy is not old. | contradiction | (![X]:((humble(X)|~funny(X))=>(~brave(X)|curious(X))))&
((?[X]:(quiet(X)))<=>(~rich(fred)))&
((?[X]:(~happy(X)))=>(?[X]:((rich(X)|funny(X)))))&
(![X]:((patient(X)|~brave(X))<=>(curious(X)&~wise(X))))&
(![X]:((~funny(X)<~>rich(X))=>(rich(X)|~patient(X))))&
(![X]:((~happy(X)&~tall(X))<=>(kind(X)|~patient(X))))&
(![X]:((~old(X)<~>~wise(X))<=>brave(X)))&
(![X]:(~humble(X)=>~rich(X)))&
(![X]:((quiet(X)|~funny(X))<=>(~kind(X)&kind(X))))&
((?[X]:(~old(X)))=>(happy(fred)))&
((?[X]:(calm(X)))<=>(?[X]:((wise(X)<~>~quiet(X)))))&
(![X]:((~brave(X)|funny(X))<=>(happy(X)<~>~generous(X))))&
(![X]:((happy(X)&generous(X))<=>(~tall(X)|~humble(X))))&
(((~wise(mary)<~>quiet(mary)))<=>(?[X]:((~old(X)|~humble(X)))))&
(![X]:(rich(X)<=>~generous(X)))&
(?[X]:((~rich(X)<~>curious(X))))&
(?[X]:(patient(X)))&
(?[X]:((wise(X)|~calm(X))))&
(?[X]:((old(X)<~>kind(X))))&
((tall(alice)|~kind(alice)))&
((~creative(lucy)|~happy(lucy)))&
(~calm(paul)) | ~old(lucy) | [
"p1",
"p8",
"p9",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5602876385915549796461677
% SZS output start Proof for 5602876385915549796461677
2. ? [X0] : quiet(X0) <=> ~rich(fred) [input p1]
9. ! [X0] : ((~funny(X0) | quiet(X0)) <=> (kind(X0) & ~kind(X0))) [input p8]
10. ? [X0] : ~old(X0) => happy(fred) [input p9]
12. ! [X0] : ((funny(X0) | ~brave(X0)) <=> (happy(X0) <~> ~generous(X0))) [input p11]
15. ! [X0] : (rich(X0) <=> ~generous(X0)) [input p14]
23. ~old(lucy) [input hypothesis]
33. happy(fred) | ! [X0] : old(X0) [ennf transformation 10]
34. (? [X0] : quiet(X0) | rich(fred)) & (~rich(fred) | ! [X0] : ~quiet(X0)) [nnf transformation 2]
35. (? [X0] : quiet(X0) | rich(fred)) & (~rich(fred) | ! [X1] : ~quiet(X1)) [rectify 34]
36. ? [X0] : quiet(X0) => quiet(sK0) [choice axiom]
37. (quiet(sK0) | rich(fred)) & (~rich(fred) | ! [X1] : ~quiet(X1)) [skolemisation 35,36]
47. ! [X0] : (((~funny(X0) | quiet(X0)) | (~kind(X0) | kind(X0))) & ((kind(X0) & ~kind(X0)) | (funny(X0) & ~quiet(X0)))) [nnf transformation 9]
48. ! [X0] : ((~funny(X0) | quiet(X0) | ~kind(X0) | kind(X0)) & ((kind(X0) & ~kind(X0)) | (funny(X0) & ~quiet(X0)))) [flattening 47]
54. ! [X0] : (((funny(X0) | ~brave(X0)) | ((happy(X0) | generous(X0)) & (~generous(X0) | ~happy(X0)))) & (((generous(X0) | ~happy(X0)) & (~generous(X0) | happy(X0))) | (~funny(X0) & brave(X0)))) [nnf transformation 12]
55. ! [X0] : ((funny(X0) | ~brave(X0) | ((happy(X0) | generous(X0)) & (~generous(X0) | ~happy(X0)))) & (((generous(X0) | ~happy(X0)) & (~generous(X0) | happy(X0))) | (~funny(X0) & brave(X0)))) [flattening 54]
62. ! [X0] : ((rich(X0) | generous(X0)) & (~generous(X0) | ~rich(X0))) [nnf transformation 15]
76. quiet(sK0) | rich(fred) [cnf transformation 37]
95. ~kind(X0) | ~quiet(X0) [cnf transformation 48]
96. ~kind(X0) | funny(X0) [cnf transformation 48]
97. ~quiet(X0) | kind(X0) [cnf transformation 48]
98. kind(X0) | funny(X0) [cnf transformation 48]
100. happy(fred) | old(X0) [cnf transformation 33]
108. generous(X0) | ~happy(X0) | ~funny(X0) [cnf transformation 55]
122. ~generous(X0) | ~rich(X0) [cnf transformation 62]
132. ~old(lucy) [cnf transformation 23]
135. 1 <=> rich(fred) [avatar definition]
137. rich(fred) <- (1) [avatar component clause 135]
139. 2 <=> quiet(sK0) [avatar definition]
141. quiet(sK0) <- (2) [avatar component clause 139]
142. 1 | 2 [avatar split clause 76,139,135]
144. 3 <=> ! [X1] : ~quiet(X1) [avatar definition]
145. ~quiet(X1) <- (3) [avatar component clause 144]
161. funny(X0) [subsumption resolution 96,98]
162. ~quiet(X0) [subsumption resolution 95,97]
163. 3 [avatar split clause 162,144]
165. 7 <=> ! [X0] : old(X0) [avatar definition]
166. old(X0) <- (7) [avatar component clause 165]
168. 8 <=> happy(fred) [avatar definition]
170. happy(fred) <- (8) [avatar component clause 168]
171. 7 | 8 [avatar split clause 100,168,165]
197. ~happy(X0) | generous(X0) [subsumption resolution 108,161]
255. $false <- (2, 3) [subsumption resolution 141,145]
256. ~2 | ~3 [avatar contradiction clause 255]
257. $false <- (7) [resolution 166,132]
258. ~7 [avatar contradiction clause 257]
301. generous(fred) <- (8) [resolution 170,197]
307. ~rich(fred) <- (8) [resolution 301,122]
308. $false <- (1, 8) [subsumption resolution 307,137]
309. ~1 | ~8 [avatar contradiction clause 308]
310. $false [avatar sat refutation 142,163,171,256,258,309]
% SZS output end Proof for 5602876385915549796461677
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not wise and not kind is not curious or not creative and vice versa.
Everyone who is not rich is not rich or not funny.
Everyone who is happy is kind or rich.
Everyone who is either kind or not funny is both curious and not tall and vice versa.
If mary is not generous or not patient then john is both tall and happy.
Everyone who is not calm is not calm or old and vice versa.
If someone is both funny and humble then someone is both not quiet and quiet and vice versa.
Everyone who is both curious and not tall is patient or not rich and vice versa.
If mary is either not tall or strong then lucy is both not tall and generous.
If alice is rich then alice is happy.
Everyone who is both not brave and not generous is not strong or generous.
If someone is not quiet then susan is either curious or rich.
If susan is tall then someone is either tall or not tall and vice versa.
Everyone who is humble or curious is not brave or funny and vice versa.
Everyone who is either not kind or rich is both not brave and not patient and vice versa.
Everyone who is both happy and not old is not kind or not calm.
Susan is generous or not patient.
Someone is both not patient and not wise.
Mary is tall or patient.
Someone is not brave.
Alice is either tall or not happy.
Someone is either strong or generous.
Someone is both quiet and brave.
Fred is both old and quiet. | Susan is not generous. | neutral | (![X]:((~wise(X)&~kind(X))<=>(~curious(X)|~creative(X))))&
(![X]:(~rich(X)=>(~rich(X)|~funny(X))))&
(![X]:(happy(X)=>(kind(X)|rich(X))))&
(![X]:((kind(X)<~>~funny(X))<=>(curious(X)&~tall(X))))&
(((~generous(mary)|~patient(mary)))=>((tall(john)&happy(john))))&
(![X]:(~calm(X)<=>(~calm(X)|old(X))))&
((?[X]:((funny(X)&humble(X))))<=>(?[X]:((~quiet(X)&quiet(X)))))&
(![X]:((curious(X)&~tall(X))<=>(patient(X)|~rich(X))))&
(((~tall(mary)<~>strong(mary)))=>((~tall(lucy)&generous(lucy))))&
((rich(alice))=>(happy(alice)))&
(![X]:((~brave(X)&~generous(X))=>(~strong(X)|generous(X))))&
((?[X]:(~quiet(X)))=>((curious(susan)<~>rich(susan))))&
((tall(susan))<=>(?[X]:((tall(X)<~>~tall(X)))))&
(![X]:((humble(X)|curious(X))<=>(~brave(X)|funny(X))))&
(![X]:((~kind(X)<~>rich(X))<=>(~brave(X)&~patient(X))))&
(![X]:((happy(X)&~old(X))=>(~kind(X)|~calm(X))))&
((generous(susan)|~patient(susan)))&
(?[X]:((~patient(X)&~wise(X))))&
((tall(mary)|patient(mary)))&
(?[X]:(~brave(X)))&
((tall(alice)<~>~happy(alice)))&
(?[X]:((strong(X)<~>generous(X))))&
(?[X]:((quiet(X)&brave(X))))&
((old(fred)&quiet(fred))) | ~generous(susan) | [] | null | 0 |
If someone is funny or not strong then john is not humble and vice versa.
Everyone who is both not funny and not tall is not strong or not calm.
If fred is either generous or funny then someone is funny or not tall and vice versa.
If someone is not tall then someone is both calm and quiet and vice versa.
If someone is either patient or not generous then someone is both funny and not brave.
Everyone who is either not creative or not patient is not patient and vice versa.
Everyone who is strong or not patient is either not generous or not humble and vice versa.
Everyone who is not calm or kind is both not patient and not tall.
Everyone who is not tall is both brave and happy.
Everyone who is curious is both not rich and curious and vice versa.
Everyone who is both calm and creative is both curious and tall.
If someone is both not quiet and wise then john is not wise or creative.
If someone is both tall and not curious then someone is not calm or curious.
Everyone who is not tall is not calm and vice versa.
Everyone who is either not generous or not happy is old or humble and vice versa.
If lucy is not patient then someone is both not curious and not strong and vice versa.
Alice is not calm.
Susan is kind.
Someone is both calm and not happy.
John is both not curious and happy.
Fred is either not tall or strong.
Someone is not kind or not wise. | Susan is not happy. | contradiction | ((?[X]:((funny(X)|~strong(X))))<=>(~humble(john)))&
(![X]:((~funny(X)&~tall(X))=>(~strong(X)|~calm(X))))&
(((generous(fred)<~>funny(fred)))<=>(?[X]:((funny(X)|~tall(X)))))&
((?[X]:(~tall(X)))<=>(?[X]:((calm(X)&quiet(X)))))&
((?[X]:((patient(X)<~>~generous(X))))=>(?[X]:((funny(X)&~brave(X)))))&
(![X]:((~creative(X)<~>~patient(X))<=>~patient(X)))&
(![X]:((strong(X)|~patient(X))<=>(~generous(X)<~>~humble(X))))&
(![X]:((~calm(X)|kind(X))=>(~patient(X)&~tall(X))))&
(![X]:(~tall(X)=>(brave(X)&happy(X))))&
(![X]:(curious(X)<=>(~rich(X)&curious(X))))&
(![X]:((calm(X)&creative(X))=>(curious(X)&tall(X))))&
((?[X]:((~quiet(X)&wise(X))))=>((~wise(john)|creative(john))))&
((?[X]:((tall(X)&~curious(X))))=>(?[X]:((~calm(X)|curious(X)))))&
(![X]:(~tall(X)<=>~calm(X)))&
(![X]:((~generous(X)<~>~happy(X))<=>(old(X)|humble(X))))&
((~patient(lucy))<=>(?[X]:((~curious(X)&~strong(X)))))&
(~calm(alice))&
(kind(susan))&
(?[X]:((calm(X)&~happy(X))))&
((~curious(john)&happy(john)))&
((~tall(fred)<~>strong(fred)))&
(?[X]:((~kind(X)|~wise(X)))) | ~happy(susan) | [
"p7",
"p8",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 2384154383071196610753243
% SZS output start Proof for 2384154383071196610753243
8. ! [X0] : ((kind(X0) | ~calm(X0)) => (~tall(X0) & ~patient(X0))) [input p7]
9. ! [X0] : (~tall(X0) => (happy(X0) & brave(X0))) [input p8]
18. kind(susan) [input p17]
23. ~happy(susan) [input hypothesis]
32. ! [X0] : ((~tall(X0) & ~patient(X0)) | (~kind(X0) & calm(X0))) [ennf transformation 8]
33. ! [X0] : ((happy(X0) & brave(X0)) | tall(X0)) [ennf transformation 9]
102. ~kind(X0) | ~tall(X0) [cnf transformation 32]
104. happy(X0) | tall(X0) [cnf transformation 33]
123. kind(susan) [cnf transformation 18]
130. ~happy(susan) [cnf transformation 23]
257. ~tall(susan) [resolution 102,123]
259. tall(susan) [resolution 104,130]
260. $false [subsumption resolution 259,257]
% SZS output end Proof for 2384154383071196610753243
% ------------------------------
% 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 brave or kind is either wise or not old and vice versa.
Everyone who is either not happy or not calm is both not patient and calm and vice versa.
If someone is patient or tall then someone is either not curious or kind and vice versa.
If john is quiet or not strong then someone is not rich.
If someone is either funny or not calm then alice is not calm or not wise and vice versa.
Everyone who is both brave and calm is curious and vice versa.
If mary is either funny or not creative then someone is both humble and not creative.
Everyone who is brave is not strong or not rich and vice versa.
Everyone who is both strong and quiet is humble or not humble.
Everyone who is funny or not generous is not kind and vice versa.
If paul is old or happy then someone is either strong or brave and vice versa.
If paul is either old or rich then someone is curious or humble and vice versa.
If mary is happy then someone is either tall or not quiet.
If paul is happy then someone is both not calm and funny and vice versa.
Everyone who is kind is not creative or generous.
Everyone who is not patient is wise or quiet and vice versa.
Alice is happy.
Someone is happy.
Paul is funny or patient.
Paul is tall.
Susan is either funny or brave. | Paul is not kind. | neutral | (![X]:((brave(X)|kind(X))<=>(wise(X)<~>~old(X))))&
(![X]:((~happy(X)<~>~calm(X))<=>(~patient(X)&calm(X))))&
((?[X]:((patient(X)|tall(X))))<=>(?[X]:((~curious(X)<~>kind(X)))))&
(((quiet(john)|~strong(john)))=>(?[X]:(~rich(X))))&
((?[X]:((funny(X)<~>~calm(X))))<=>((~calm(alice)|~wise(alice))))&
(![X]:((brave(X)&calm(X))<=>curious(X)))&
(((funny(mary)<~>~creative(mary)))=>(?[X]:((humble(X)&~creative(X)))))&
(![X]:(brave(X)<=>(~strong(X)|~rich(X))))&
(![X]:((strong(X)&quiet(X))=>(humble(X)|~humble(X))))&
(![X]:((funny(X)|~generous(X))<=>~kind(X)))&
(((old(paul)|happy(paul)))<=>(?[X]:((strong(X)<~>brave(X)))))&
(((old(paul)<~>rich(paul)))<=>(?[X]:((curious(X)|humble(X)))))&
((happy(mary))=>(?[X]:((tall(X)<~>~quiet(X)))))&
((happy(paul))<=>(?[X]:((~calm(X)&funny(X)))))&
(![X]:(kind(X)=>(~creative(X)|generous(X))))&
(![X]:(~patient(X)<=>(wise(X)|quiet(X))))&
(happy(alice))&
(?[X]:(happy(X)))&
((funny(paul)|patient(paul)))&
(tall(paul))&
((funny(susan)<~>brave(susan))) | ~kind(paul) | [] | null | 0 |
If someone is humble then fred is either not creative or not kind and vice versa. If alice is not curious or not patient then someone is either generous or brave. If someone is either not creative or funny then mary is both not curious and not calm and vice versa. Everyone who is brave or not humble is both not brave and curious. If someone is either brave or quiet then someone is either patient or not creative. If susan is wise or not tall then someone is either patient or kind. Everyone who is either not curious or not quiet is either not tall or quiet. Everyone who is calm or humble is not patient and vice versa. Everyone who is curious or generous is both happy and old and vice versa. Everyone who is either curious or humble is not calm or funny. Everyone who is both not strong and not tall is either not patient or brave and vice versa. Everyone who is both not quiet and not tall is either not generous or not old and vice versa. If someone is calm or patient then someone is quiet and vice versa. If paul is either not calm or not strong then someone is both not patient and calm and vice versa. Everyone who is either not humble or funny is creative or not tall and vice versa. If someone is both tall and not funny then john is not happy. Lucy is patient or not wise. John is not patient or not curious. Paul is either patient or curious. Alice is not patient or not wise. John is either tall or not curious. Susan is both not patient and wise. | Susan is humble. | entailment | ((?[X]:(humble(X)))<=>((~creative(fred)<~>~kind(fred))))&
(((~curious(alice)|~patient(alice)))=>(?[X]:((generous(X)<~>brave(X)))))&
((?[X]:((~creative(X)<~>funny(X))))<=>((~curious(mary)&~calm(mary))))&
(![X]:((brave(X)|~humble(X))=>(~brave(X)&curious(X))))&
((?[X]:((brave(X)<~>quiet(X))))=>(?[X]:((patient(X)<~>~creative(X)))))&
(((wise(susan)|~tall(susan)))=>(?[X]:((patient(X)<~>kind(X)))))&
(![X]:((~curious(X)<~>~quiet(X))=>(~tall(X)<~>quiet(X))))&
(![X]:((calm(X)|humble(X))<=>~patient(X)))&
(![X]:((curious(X)|generous(X))<=>(happy(X)&old(X))))&
(![X]:((curious(X)<~>humble(X))=>(~calm(X)|funny(X))))&
(![X]:((~strong(X)&~tall(X))<=>(~patient(X)<~>brave(X))))&
(![X]:((~quiet(X)&~tall(X))<=>(~generous(X)<~>~old(X))))&
((?[X]:((calm(X)|patient(X))))<=>(?[X]:(quiet(X))))&
(((~calm(paul)<~>~strong(paul)))<=>(?[X]:((~patient(X)&calm(X)))))&
(![X]:((~humble(X)<~>funny(X))<=>(creative(X)|~tall(X))))&
((?[X]:((tall(X)&~funny(X))))=>(~happy(john)))&
((patient(lucy)|~wise(lucy)))&
((~patient(john)|~curious(john)))&
((patient(paul)<~>curious(paul)))&
((~patient(alice)|~wise(alice)))&
((tall(john)<~>~curious(john)))&
((~patient(susan)&wise(susan))) | humble(susan) | [
"p3",
"p7",
"p9",
"p10",
"p14",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 6985912797134729535429600
% SZS output start Proof for 6985912797134729535429600
4. ! [X0] : ((~humble(X0) | brave(X0)) => (curious(X0) & ~brave(X0))) [input p3]
8. ! [X0] : ((humble(X0) | calm(X0)) <=> ~patient(X0)) [input p7]
10. ! [X0] : ((curious(X0) <~> humble(X0)) => (funny(X0) | ~calm(X0))) [input p9]
11. ! [X0] : ((~tall(X0) & ~strong(X0)) <=> (~patient(X0) <~> brave(X0))) [input p10]
15. ! [X0] : ((~humble(X0) <~> funny(X0)) <=> (~tall(X0) | creative(X0))) [input p14]
22. wise(susan) & ~patient(susan) [input p21]
23. ~humble(susan) [input hypothesis]
27. ! [X0] : ((curious(X0) & ~brave(X0)) | (humble(X0) & ~brave(X0))) [ennf transformation 4]
31. ! [X0] : ((funny(X0) | ~calm(X0)) | (curious(X0) <=> humble(X0))) [ennf transformation 10]
32. ! [X0] : (funny(X0) | ~calm(X0) | (curious(X0) <=> humble(X0))) [flattening 31]
54. ! [X0] : (((humble(X0) | calm(X0)) | patient(X0)) & (~patient(X0) | (~humble(X0) & ~calm(X0)))) [nnf transformation 8]
55. ! [X0] : ((humble(X0) | calm(X0) | patient(X0)) & (~patient(X0) | (~humble(X0) & ~calm(X0)))) [flattening 54]
58. ! [X0] : (funny(X0) | ~calm(X0) | ((curious(X0) | ~humble(X0)) & (humble(X0) | ~curious(X0)))) [nnf transformation 32]
59. ! [X0] : (((~tall(X0) & ~strong(X0)) | ((~patient(X0) | ~brave(X0)) & (brave(X0) | patient(X0)))) & (((~brave(X0) | patient(X0)) & (brave(X0) | ~patient(X0))) | (tall(X0) | strong(X0)))) [nnf transformation 11]
60. ! [X0] : (((~tall(X0) & ~strong(X0)) | ((~patient(X0) | ~brave(X0)) & (brave(X0) | patient(X0)))) & (((~brave(X0) | patient(X0)) & (brave(X0) | ~patient(X0))) | tall(X0) | strong(X0))) [flattening 59]
72. ! [X0] : ((((~funny(X0) | humble(X0)) & (funny(X0) | ~humble(X0))) | (tall(X0) & ~creative(X0))) & ((~tall(X0) | creative(X0)) | ((~humble(X0) | ~funny(X0)) & (funny(X0) | humble(X0))))) [nnf transformation 15]
73. ! [X0] : ((((~funny(X0) | humble(X0)) & (funny(X0) | ~humble(X0))) | (tall(X0) & ~creative(X0))) & (~tall(X0) | creative(X0) | ((~humble(X0) | ~funny(X0)) & (funny(X0) | humble(X0))))) [flattening 72]
90. ~brave(X0) | ~brave(X0) [cnf transformation 27]
93. curious(X0) | humble(X0) [cnf transformation 27]
108. calm(X0) | humble(X0) | patient(X0) [cnf transformation 55]
114. funny(X0) | ~calm(X0) | humble(X0) | ~curious(X0) [cnf transformation 58]
115. funny(X0) | ~calm(X0) | curious(X0) | ~humble(X0) [cnf transformation 58]
120. ~tall(X0) | brave(X0) | patient(X0) [cnf transformation 60]
142. ~funny(X0) | humble(X0) | tall(X0) [cnf transformation 73]
151. ~patient(susan) [cnf transformation 22]
153. ~humble(susan) [cnf transformation 23]
156. ~brave(X0) [duplicate literal removal 90]
259. ~calm(X0) | funny(X0) | curious(X0) [subsumption resolution 115,93]
260. ~calm(X0) | funny(X0) | humble(X0) [subsumption resolution 114,259]
261. ~tall(X0) | patient(X0) [subsumption resolution 120,156]
498. funny(X0) | humble(X0) | humble(X0) | patient(X0) [resolution 260,108]
499. funny(X0) | humble(X0) | patient(X0) [duplicate literal removal 498]
656. humble(X0) | patient(X0) | humble(X0) | tall(X0) [resolution 499,142]
660. humble(X0) | patient(X0) | tall(X0) [duplicate literal removal 656]
662. patient(X0) | humble(X0) [subsumption resolution 660,261]
715. humble(susan) [resolution 662,151]
721. $false [subsumption resolution 715,153]
% SZS output end Proof for 6985912797134729535429600
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not calm is not quiet or brave.
Everyone who is both generous and not generous is either not calm or curious.
Everyone who is brave or curious is wise or not strong.
Everyone who is funny or happy is either rich or tall and vice versa.
Everyone who is kind or not humble is not humble and vice versa.
Everyone who is either not happy or not rich is either brave or happy and vice versa.
If someone is both not wise and not strong then paul is both wise and tall and vice versa.
Everyone who is either brave or not creative is either not rich or not wise and vice versa.
Everyone who is either curious or old is creative and vice versa.
Everyone who is rich is either not kind or curious and vice versa.
Everyone who is either not wise or curious is either not happy or quiet and vice versa.
Everyone who is not quiet is quiet or not humble and vice versa.
Everyone who is either not tall or creative is either generous or quiet and vice versa.
If paul is both not generous and not wise then someone is both curious and creative and vice versa.
Everyone who is not creative or calm is not calm or humble and vice versa.
Everyone who is either humble or calm is not humble or kind.
Someone is either not patient or curious.
Paul is both strong and not quiet.
Fred is calm or not rich.
Someone is generous.
John is not strong or not creative.
Alice is patient or not rich.
Someone is either not kind or funny. | Fred is not tall. | neutral | (![X]:(~calm(X)=>(~quiet(X)|brave(X))))&
(![X]:((generous(X)&~generous(X))=>(~calm(X)<~>curious(X))))&
(![X]:((brave(X)|curious(X))=>(wise(X)|~strong(X))))&
(![X]:((funny(X)|happy(X))<=>(rich(X)<~>tall(X))))&
(![X]:((kind(X)|~humble(X))<=>~humble(X)))&
(![X]:((~happy(X)<~>~rich(X))<=>(brave(X)<~>happy(X))))&
((?[X]:((~wise(X)&~strong(X))))<=>((wise(paul)&tall(paul))))&
(![X]:((brave(X)<~>~creative(X))<=>(~rich(X)<~>~wise(X))))&
(![X]:((curious(X)<~>old(X))<=>creative(X)))&
(![X]:(rich(X)<=>(~kind(X)<~>curious(X))))&
(![X]:((~wise(X)<~>curious(X))<=>(~happy(X)<~>quiet(X))))&
(![X]:(~quiet(X)<=>(quiet(X)|~humble(X))))&
(![X]:((~tall(X)<~>creative(X))<=>(generous(X)<~>quiet(X))))&
(((~generous(paul)&~wise(paul)))<=>(?[X]:((curious(X)&creative(X)))))&
(![X]:((~creative(X)|calm(X))<=>(~calm(X)|humble(X))))&
(![X]:((humble(X)<~>calm(X))=>(~humble(X)|kind(X))))&
(?[X]:((~patient(X)<~>curious(X))))&
((strong(paul)&~quiet(paul)))&
((calm(fred)|~rich(fred)))&
(?[X]:(generous(X)))&
((~strong(john)|~creative(john)))&
((patient(alice)|~rich(alice)))&
(?[X]:((~kind(X)<~>funny(X)))) | ~tall(fred) | [] | null | 0 |
If paul is either not curious or not humble then someone is not funny or not curious and vice versa. If paul is not creative then john is both creative and not old. Everyone who is both quiet and not curious is old or not humble and vice versa. If someone is both tall and not curious then alice is funny or not curious. Everyone who is either not curious or old is not strong. Everyone who is creative is not funny. Everyone who is funny or not strong is both not strong and old. If alice is strong then mary is not funny or patient and vice versa. If someone is not calm then someone is humble or not calm. Everyone who is patient is kind or not wise and vice versa. If someone is not rich or rich then someone is both curious and not quiet and vice versa. Everyone who is both not generous and not tall is either not strong or happy. Everyone who is both not brave and funny is not funny or generous. Everyone who is either not patient or kind is both curious and not rich and vice versa. Everyone who is rich is patient or old and vice versa. If someone is either not old or strong then john is both quiet and not quiet. Alice is not wise. Someone is rich or not tall. Someone is both not calm and not patient. Paul is brave. Someone is either not brave or strong. Susan is not funny or not tall. Mary is both funny and not brave. Someone is patient or curious. | Paul is not strong. | entailment | (((~curious(paul)<~>~humble(paul)))<=>(?[X]:((~funny(X)|~curious(X)))))&
((~creative(paul))=>((creative(john)&~old(john))))&
(![X]:((quiet(X)&~curious(X))<=>(old(X)|~humble(X))))&
((?[X]:((tall(X)&~curious(X))))=>((funny(alice)|~curious(alice))))&
(![X]:((~curious(X)<~>old(X))=>~strong(X)))&
(![X]:(creative(X)=>~funny(X)))&
(![X]:((funny(X)|~strong(X))=>(~strong(X)&old(X))))&
((strong(alice))<=>((~funny(mary)|patient(mary))))&
((?[X]:(~calm(X)))=>(?[X]:((humble(X)|~calm(X)))))&
(![X]:(patient(X)<=>(kind(X)|~wise(X))))&
((?[X]:((~rich(X)|rich(X))))<=>(?[X]:((curious(X)&~quiet(X)))))&
(![X]:((~generous(X)&~tall(X))=>(~strong(X)<~>happy(X))))&
(![X]:((~brave(X)&funny(X))=>(~funny(X)|generous(X))))&
(![X]:((~patient(X)<~>kind(X))<=>(curious(X)&~rich(X))))&
(![X]:(rich(X)<=>(patient(X)|old(X))))&
((?[X]:((~old(X)<~>strong(X))))=>((quiet(john)&~quiet(john))))&
(~wise(alice))&
(?[X]:((rich(X)|~tall(X))))&
(?[X]:((~calm(X)&~patient(X))))&
(brave(paul))&
(?[X]:((~brave(X)<~>strong(X))))&
((~funny(susan)|~tall(susan)))&
((funny(mary)&~brave(mary)))&
(?[X]:((patient(X)|curious(X)))) | ~strong(paul) | [
"p0",
"p2",
"p4",
"p6",
"p15",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 7585417462591481455610095
% SZS output start Proof for 7585417462591481455610095
1. (~curious(paul) <~> ~humble(paul)) <=> ? [X0] : (~curious(X0) | ~funny(X0)) [input p0]
3. ! [X0] : ((~curious(X0) & quiet(X0)) <=> (~humble(X0) | old(X0))) [input p2]
5. ! [X0] : ((~curious(X0) <~> old(X0)) => ~strong(X0)) [input p4]
7. ! [X0] : ((~strong(X0) | funny(X0)) => (old(X0) & ~strong(X0))) [input p6]
16. ? [X0] : (~old(X0) <~> strong(X0)) => (~quiet(john) & quiet(john)) [input p15]
23. ~brave(mary) & funny(mary) [input p22]
25. strong(paul) [input hypothesis]
34. ! [X0] : (~strong(X0) | (~curious(X0) <=> old(X0))) [ennf transformation 5]
36. ! [X0] : ((old(X0) & ~strong(X0)) | (strong(X0) & ~funny(X0))) [ennf transformation 7]
38. (~quiet(john) & quiet(john)) | ! [X0] : (~old(X0) <=> strong(X0)) [ennf transformation 16]
39. (((humble(paul) | curious(paul)) & (~humble(paul) | ~curious(paul))) | ! [X0] : (curious(X0) & funny(X0))) & (? [X0] : (~curious(X0) | ~funny(X0)) | ((~curious(paul) | humble(paul)) & (~humble(paul) | curious(paul)))) [nnf transformation 1]
40. (((humble(paul) | curious(paul)) & (~humble(paul) | ~curious(paul))) | ! [X0] : (curious(X0) & funny(X0))) & (? [X1] : (~curious(X1) | ~funny(X1)) | ((~curious(paul) | humble(paul)) & (~humble(paul) | curious(paul)))) [rectify 39]
41. ? [X1] : (~curious(X1) | ~funny(X1)) => (~curious(sK0) | ~funny(sK0)) [choice axiom]
42. (((humble(paul) | curious(paul)) & (~humble(paul) | ~curious(paul))) | ! [X0] : (curious(X0) & funny(X0))) & ((~curious(sK0) | ~funny(sK0)) | ((~curious(paul) | humble(paul)) & (~humble(paul) | curious(paul)))) [skolemisation 40,41]
43. ! [X0] : (((~curious(X0) & quiet(X0)) | (humble(X0) & ~old(X0))) & ((~humble(X0) | old(X0)) | (curious(X0) | ~quiet(X0)))) [nnf transformation 3]
44. ! [X0] : (((~curious(X0) & quiet(X0)) | (humble(X0) & ~old(X0))) & (~humble(X0) | old(X0) | curious(X0) | ~quiet(X0))) [flattening 43]
45. ! [X0] : (~strong(X0) | ((~curious(X0) | ~old(X0)) & (old(X0) | curious(X0)))) [nnf transformation 34]
62. (~quiet(john) & quiet(john)) | ! [X0] : ((~old(X0) | ~strong(X0)) & (strong(X0) | old(X0))) [nnf transformation 38]
73. ~humble(paul) | ~curious(paul) | curious(X0) [cnf transformation 42]
81. ~old(X0) | ~curious(X0) [cnf transformation 44]
82. ~curious(X0) | humble(X0) [cnf transformation 44]
83. ~strong(X0) | old(X0) | curious(X0) [cnf transformation 45]
88. ~funny(X0) | old(X0) [cnf transformation 36]
112. quiet(john) | ~old(X0) | ~strong(X0) [cnf transformation 62]
114. ~quiet(john) | ~old(X0) | ~strong(X0) [cnf transformation 62]
121. funny(mary) [cnf transformation 23]
124. strong(paul) [cnf transformation 25]
126. 1 <=> ! [X0] : curious(X0) [avatar definition]
127. curious(X0) <- (1) [avatar component clause 126]
129. 2 <=> curious(paul) [avatar definition]
131. curious(paul) <- (2) [avatar component clause 129]
133. 3 <=> humble(paul) [avatar definition]
134. ~humble(paul) <- (~3) [avatar component clause 133]
141. 1 | ~2 | ~3 [avatar split clause 73,133,129,126]
177. 12 <=> funny(mary) [avatar definition]
179. funny(mary) <- (12) [avatar component clause 177]
217. 20 <=> ! [X0] : (~old(X0) | ~strong(X0)) [avatar definition]
218. ~strong(X0) | ~old(X0) <- (20) [avatar component clause 217]
220. 21 <=> quiet(john) [avatar definition]
223. 20 | ~21 [avatar split clause 114,220,217]
224. 20 | 21 [avatar split clause 112,220,217]
235. 12 [avatar split clause 121,177]
239. humble(paul) <- (2) [resolution 82,131]
241. $false <- (2, ~3) [subsumption resolution 239,134]
242. ~2 | 3 [avatar contradiction clause 241]
245. old(mary) <- (12) [resolution 88,179]
246. ~curious(mary) <- (12) [resolution 245,81]
275. ~old(paul) <- (20) [resolution 218,124]
278. old(paul) | curious(paul) [resolution 83,124]
282. curious(paul) <- (20) [subsumption resolution 278,275]
285. 2 | ~20 [avatar split clause 282,217,129]
287. $false <- (1, 12) [resolution 127,246]
288. ~1 | ~12 [avatar contradiction clause 287]
289. $false [avatar sat refutation 141,223,224,235,242,285,288]
% SZS output end Proof for 7585417462591481455610095
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.022 s
% ------------------------------
% ------------------------------
| 0 |
If fred is either not curious or strong then someone is old or not curious.
If someone is curious then mary is both not old and generous and vice versa.
Everyone who is not curious is both not generous and not old and vice versa.
Everyone who is not kind or wise is funny.
Everyone who is either brave or rich is tall.
Everyone who is not old is both not generous and not calm.
If susan is either old or not strong then fred is strong or funny.
If paul is not generous then john is not kind and vice versa.
If someone is either not brave or wise then mary is both not old and generous.
If alice is humble or patient then paul is not generous and vice versa.
If someone is not kind then someone is happy.
If someone is either rich or tall then someone is not quiet or humble.
Everyone who is both generous and happy is either brave or tall and vice versa.
Everyone who is both not happy and curious is either not calm or happy and vice versa.
Everyone who is not creative is either not humble or not brave and vice versa.
Everyone who is either not quiet or generous is not humble or curious.
Mary is either not rich or not strong.
Paul is both not brave and not old.
Fred is kind.
Someone is patient or not rich.
John is not old or strong.
Lucy is not wise.
Alice is not generous. | Alice is not happy. | contradiction | (((~curious(fred)<~>strong(fred)))=>(?[X]:((old(X)|~curious(X)))))&
((?[X]:(curious(X)))<=>((~old(mary)&generous(mary))))&
(![X]:(~curious(X)<=>(~generous(X)&~old(X))))&
(![X]:((~kind(X)|wise(X))=>funny(X)))&
(![X]:((brave(X)<~>rich(X))=>tall(X)))&
(![X]:(~old(X)=>(~generous(X)&~calm(X))))&
(((old(susan)<~>~strong(susan)))=>((strong(fred)|funny(fred))))&
((~generous(paul))<=>(~kind(john)))&
((?[X]:((~brave(X)<~>wise(X))))=>((~old(mary)&generous(mary))))&
(((humble(alice)|patient(alice)))<=>(~generous(paul)))&
((?[X]:(~kind(X)))=>(?[X]:(happy(X))))&
((?[X]:((rich(X)<~>tall(X))))=>(?[X]:((~quiet(X)|humble(X)))))&
(![X]:((generous(X)&happy(X))<=>(brave(X)<~>tall(X))))&
(![X]:((~happy(X)&curious(X))<=>(~calm(X)<~>happy(X))))&
(![X]:(~creative(X)<=>(~humble(X)<~>~brave(X))))&
(![X]:((~quiet(X)<~>generous(X))=>(~humble(X)|curious(X))))&
((~rich(mary)<~>~strong(mary)))&
((~brave(paul)&~old(paul)))&
(kind(fred))&
(?[X]:((patient(X)|~rich(X))))&
((~old(john)|strong(john)))&
(~wise(lucy))&
(~generous(alice)) | ~happy(alice) | [
"p1",
"p2",
"p5",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 6394691199442064162167328
% SZS output start Proof for 6394691199442064162167328
2. ? [X0] : curious(X0) <=> (generous(mary) & ~old(mary)) [input p1]
3. ! [X0] : (~curious(X0) <=> (~old(X0) & ~generous(X0))) [input p2]
6. ! [X0] : (~old(X0) => (~calm(X0) & ~generous(X0))) [input p5]
14. ! [X0] : ((curious(X0) & ~happy(X0)) <=> (~calm(X0) <~> happy(X0))) [input p13]
24. ~happy(alice) [input hypothesis]
31. ! [X0] : ((~calm(X0) & ~generous(X0)) | old(X0)) [ennf transformation 6]
40. (? [X0] : curious(X0) | (~generous(mary) | old(mary))) & ((generous(mary) & ~old(mary)) | ! [X0] : ~curious(X0)) [nnf transformation 2]
41. (? [X0] : curious(X0) | ~generous(mary) | old(mary)) & ((generous(mary) & ~old(mary)) | ! [X0] : ~curious(X0)) [flattening 40]
42. (? [X0] : curious(X0) | ~generous(mary) | old(mary)) & ((generous(mary) & ~old(mary)) | ! [X1] : ~curious(X1)) [rectify 41]
43. ? [X0] : curious(X0) => curious(sK1) [choice axiom]
44. (curious(sK1) | ~generous(mary) | old(mary)) & ((generous(mary) & ~old(mary)) | ! [X1] : ~curious(X1)) [skolemisation 42,43]
45. ! [X0] : ((~curious(X0) | (old(X0) | generous(X0))) & ((~old(X0) & ~generous(X0)) | curious(X0))) [nnf transformation 3]
46. ! [X0] : ((~curious(X0) | old(X0) | generous(X0)) & ((~old(X0) & ~generous(X0)) | curious(X0))) [flattening 45]
61. ! [X0] : (((curious(X0) & ~happy(X0)) | ((~calm(X0) | ~happy(X0)) & (happy(X0) | calm(X0)))) & (((~happy(X0) | calm(X0)) & (happy(X0) | ~calm(X0))) | (~curious(X0) | happy(X0)))) [nnf transformation 14]
62. ! [X0] : (((curious(X0) & ~happy(X0)) | ((~calm(X0) | ~happy(X0)) & (happy(X0) | calm(X0)))) & (((~happy(X0) | calm(X0)) & (happy(X0) | ~calm(X0))) | ~curious(X0) | happy(X0))) [flattening 61]
69. ~old(mary) | ~curious(X1) [cnf transformation 44]
70. generous(mary) | ~curious(X1) [cnf transformation 44]
73. ~old(X0) | curious(X0) [cnf transformation 46]
77. ~generous(X0) | old(X0) [cnf transformation 31]
78. ~calm(X0) | old(X0) [cnf transformation 31]
101. happy(X0) | curious(X0) | calm(X0) [cnf transformation 62]
114. ~happy(alice) [cnf transformation 24]
136. 5 <=> old(mary) [avatar definition]
137. ~old(mary) <- (~5) [avatar component clause 136]
140. 6 <=> generous(mary) [avatar definition]
141. generous(mary) <- (6) [avatar component clause 140]
149. 8 <=> ! [X1] : ~curious(X1) [avatar definition]
150. ~curious(X1) <- (8) [avatar component clause 149]
151. 8 | 6 [avatar split clause 70,140,149]
152. 8 | ~5 [avatar split clause 69,136,149]
240. old(mary) <- (6) [resolution 77,141]
242. $false <- (~5, 6) [subsumption resolution 240,137]
243. 5 | ~6 [avatar contradiction clause 242]
275. curious(alice) | calm(alice) [resolution 101,114]
277. calm(alice) <- (8) [subsumption resolution 275,150]
279. old(alice) <- (8) [resolution 277,78]
283. curious(alice) <- (8) [resolution 279,73]
284. $false <- (8) [subsumption resolution 283,150]
285. ~8 [avatar contradiction clause 284]
286. $false [avatar sat refutation 151,152,243,285]
% SZS output end Proof for 6394691199442064162167328
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both kind and tall is either brave or not wise and vice versa.
If someone is not humble or creative then lucy is both not kind and creative and vice versa.
If someone is either funny or not rich then lucy is not curious or tall.
If fred is either not patient or funny then someone is either not curious or not patient.
Everyone who is not calm is not wise.
Everyone who is both humble and not rich is either quiet or not creative and vice versa.
Everyone who is not happy is quiet or not generous.
Everyone who is generous or humble is both not old and not tall.
Everyone who is not generous is either calm or rich and vice versa.
If someone is either not curious or curious then someone is creative or curious and vice versa.
Everyone who is both not creative and not humble is creative or funny and vice versa.
If someone is both not generous and generous then paul is not kind.
If someone is either quiet or strong then paul is not patient and vice versa.
Everyone who is not creative or not strong is both not old and not happy and vice versa.
If lucy is strong then someone is both not curious and rich and vice versa.
If someone is either brave or strong then someone is either kind or tall and vice versa.
Lucy is either generous or not old.
John is not patient.
Someone is not patient.
Someone is not quiet or creative.
Someone is not old or not kind. | Lucy is not old. | entailment | (![X]:((kind(X)&tall(X))<=>(brave(X)<~>~wise(X))))&
((?[X]:((~humble(X)|creative(X))))<=>((~kind(lucy)&creative(lucy))))&
((?[X]:((funny(X)<~>~rich(X))))=>((~curious(lucy)|tall(lucy))))&
(((~patient(fred)<~>funny(fred)))=>(?[X]:((~curious(X)<~>~patient(X)))))&
(![X]:(~calm(X)=>~wise(X)))&
(![X]:((humble(X)&~rich(X))<=>(quiet(X)<~>~creative(X))))&
(![X]:(~happy(X)=>(quiet(X)|~generous(X))))&
(![X]:((generous(X)|humble(X))=>(~old(X)&~tall(X))))&
(![X]:(~generous(X)<=>(calm(X)<~>rich(X))))&
((?[X]:((~curious(X)<~>curious(X))))<=>(?[X]:((creative(X)|curious(X)))))&
(![X]:((~creative(X)&~humble(X))<=>(creative(X)|funny(X))))&
((?[X]:((~generous(X)&generous(X))))=>(~kind(paul)))&
((?[X]:((quiet(X)<~>strong(X))))<=>(~patient(paul)))&
(![X]:((~creative(X)|~strong(X))<=>(~old(X)&~happy(X))))&
((strong(lucy))<=>(?[X]:((~curious(X)&rich(X)))))&
((?[X]:((brave(X)<~>strong(X))))<=>(?[X]:((kind(X)<~>tall(X)))))&
((generous(lucy)<~>~old(lucy)))&
(~patient(john))&
(?[X]:(~patient(X)))&
(?[X]:((~quiet(X)|creative(X))))&
(?[X]:((~old(X)|~kind(X)))) | ~old(lucy) | [
"p7",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 849625106758529300259822
% SZS output start Proof for 849625106758529300259822
8. ! [X0] : ((humble(X0) | generous(X0)) => (~tall(X0) & ~old(X0))) [input p7]
17. generous(lucy) <~> ~old(lucy) [input p16]
22. old(lucy) [input hypothesis]
31. ! [X0] : ((~tall(X0) & ~old(X0)) | (~humble(X0) & ~generous(X0))) [ennf transformation 8]
69. (old(lucy) | ~generous(lucy)) & (~old(lucy) | generous(lucy)) [nnf transformation 17]
101. ~old(X0) | ~generous(X0) [cnf transformation 31]
141. ~old(lucy) | generous(lucy) [cnf transformation 69]
142. old(lucy) | ~generous(lucy) [cnf transformation 69]
147. old(lucy) [cnf transformation 22]
308. ~generous(lucy) [subsumption resolution 142,101]
309. ~old(lucy) [subsumption resolution 141,308]
328. $false [subsumption resolution 147,309]
% SZS output end Proof for 849625106758529300259822
% ------------------------------
% 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 lucy is not strong then susan is creative or not creative and vice versa. Everyone who is both brave and not old is strong or patient and vice versa. If someone is rich then paul is either humble or happy. If mary is both not happy and creative then someone is both not creative and generous and vice versa. If someone is either not curious or generous then john is either funny or calm. If someone is both not generous and tall then paul is either not funny or creative and vice versa. Everyone who is humble is either generous or brave. Everyone who is either brave or creative is not humble and vice versa. Everyone who is not generous is either not creative or happy and vice versa. If someone is both tall and not patient then fred is not brave and vice versa. If john is either patient or not old then someone is wise or funny and vice versa. Everyone who is either kind or not generous is either not wise or not humble. If alice is both not funny and old then someone is both not brave and tall. Everyone who is both not generous and happy is either tall or funny. Everyone who is either not funny or not tall is not creative and vice versa. Everyone who is not curious or not old is humble and vice versa. Someone is either not tall or generous. Someone is either not brave or not tall. Someone is not patient or not generous. Fred is either strong or old. Susan is either not old or not calm. Lucy is old or not calm. | John is not creative. | neutral | ((~strong(lucy))<=>((creative(susan)|~creative(susan))))&
(![X]:((brave(X)&~old(X))<=>(strong(X)|patient(X))))&
((?[X]:(rich(X)))=>((humble(paul)<~>happy(paul))))&
(((~happy(mary)&creative(mary)))<=>(?[X]:((~creative(X)&generous(X)))))&
((?[X]:((~curious(X)<~>generous(X))))=>((funny(john)<~>calm(john))))&
((?[X]:((~generous(X)&tall(X))))<=>((~funny(paul)<~>creative(paul))))&
(![X]:(humble(X)=>(generous(X)<~>brave(X))))&
(![X]:((brave(X)<~>creative(X))<=>~humble(X)))&
(![X]:(~generous(X)<=>(~creative(X)<~>happy(X))))&
((?[X]:((tall(X)&~patient(X))))<=>(~brave(fred)))&
(((patient(john)<~>~old(john)))<=>(?[X]:((wise(X)|funny(X)))))&
(![X]:((kind(X)<~>~generous(X))=>(~wise(X)<~>~humble(X))))&
(((~funny(alice)&old(alice)))=>(?[X]:((~brave(X)&tall(X)))))&
(![X]:((~generous(X)&happy(X))=>(tall(X)<~>funny(X))))&
(![X]:((~funny(X)<~>~tall(X))<=>~creative(X)))&
(![X]:((~curious(X)|~old(X))<=>humble(X)))&
(?[X]:((~tall(X)<~>generous(X))))&
(?[X]:((~brave(X)<~>~tall(X))))&
(?[X]:((~patient(X)|~generous(X))))&
((strong(fred)<~>old(fred)))&
((~old(susan)<~>~calm(susan)))&
((old(lucy)|~calm(lucy))) | ~creative(john) | [] | null | 0 |
If someone is old then john is not brave or creative. Everyone who is curious or not old is either not creative or not wise. Everyone who is both not strong and wise is not curious or creative. Everyone who is old or not brave is both not curious and tall. Everyone who is not happy or not strong is generous. Everyone who is humble is kind or not funny. If mary is patient or not wise then someone is kind or calm. Everyone who is rich or tall is strong or humble. Everyone who is rich or not humble is either creative or old. If someone is not old then someone is both not curious and kind and vice versa. Everyone who is both patient and funny is either patient or not humble. Everyone who is both not rich and wise is either not wise or generous. If someone is happy then mary is humble and vice versa. Everyone who is both rich and old is either not humble or humble and vice versa. Everyone who is both not calm and patient is both not rich and strong and vice versa. If someone is either strong or not quiet then paul is not patient and vice versa. Someone is calm or not calm. Mary is funny or humble. Fred is either kind or not funny. Someone is both happy and tall. Someone is not calm. Someone is rich or generous. | Paul is not calm. | neutral | ((?[X]:(old(X)))=>((~brave(john)|creative(john))))&
(![X]:((curious(X)|~old(X))=>(~creative(X)<~>~wise(X))))&
(![X]:((~strong(X)&wise(X))=>(~curious(X)|creative(X))))&
(![X]:((old(X)|~brave(X))=>(~curious(X)&tall(X))))&
(![X]:((~happy(X)|~strong(X))=>generous(X)))&
(![X]:(humble(X)=>(kind(X)|~funny(X))))&
(((patient(mary)|~wise(mary)))=>(?[X]:((kind(X)|calm(X)))))&
(![X]:((rich(X)|tall(X))=>(strong(X)|humble(X))))&
(![X]:((rich(X)|~humble(X))=>(creative(X)<~>old(X))))&
((?[X]:(~old(X)))<=>(?[X]:((~curious(X)&kind(X)))))&
(![X]:((patient(X)&funny(X))=>(patient(X)<~>~humble(X))))&
(![X]:((~rich(X)&wise(X))=>(~wise(X)<~>generous(X))))&
((?[X]:(happy(X)))<=>(humble(mary)))&
(![X]:((rich(X)&old(X))<=>(~humble(X)<~>humble(X))))&
(![X]:((~calm(X)&patient(X))<=>(~rich(X)&strong(X))))&
((?[X]:((strong(X)<~>~quiet(X))))<=>(~patient(paul)))&
(?[X]:((calm(X)|~calm(X))))&
((funny(mary)|humble(mary)))&
((kind(fred)<~>~funny(fred)))&
(?[X]:((happy(X)&tall(X))))&
(?[X]:(~calm(X)))&
(?[X]:((rich(X)|generous(X)))) | ~calm(paul) | [] | null | 0 |
Everyone who is either not happy or happy is tall and vice versa. Everyone who is either not patient or not tall is old or happy. If someone is not old or kind then susan is both wise and tall and vice versa. Everyone who is both not kind and old is not creative. Everyone who is creative or not strong is both strong and curious. If lucy is either not strong or not creative then someone is both not happy and not patient and vice versa. If someone is either quiet or not wise then someone is kind and vice versa. Everyone who is either generous or old is not humble or not wise and vice versa. Everyone who is either patient or curious is either not generous or humble. If fred is not happy then someone is wise or not calm. Everyone who is not patient is not happy and vice versa. Everyone who is both tall and not creative is not generous or not humble and vice versa. If susan is both happy and not strong then someone is either not old or curious and vice versa. Everyone who is either not generous or humble is either not happy or not creative and vice versa. If fred is both not rich and not old then lucy is either not calm or not humble and vice versa. Everyone who is not wise is both calm and old and vice versa. Someone is not humble. Someone is quiet. Fred is either not happy or not quiet. Mary is either not curious or not strong. Susan is not funny. Someone is funny. Alice is both not curious and humble. Susan is brave. | Alice is wise. | contradiction | (![X]:((~happy(X)<~>happy(X))<=>tall(X)))&
(![X]:((~patient(X)<~>~tall(X))=>(old(X)|happy(X))))&
((?[X]:((~old(X)|kind(X))))<=>((wise(susan)&tall(susan))))&
(![X]:((~kind(X)&old(X))=>~creative(X)))&
(![X]:((creative(X)|~strong(X))=>(strong(X)&curious(X))))&
(((~strong(lucy)<~>~creative(lucy)))<=>(?[X]:((~happy(X)&~patient(X)))))&
((?[X]:((quiet(X)<~>~wise(X))))<=>(?[X]:(kind(X))))&
(![X]:((generous(X)<~>old(X))<=>(~humble(X)|~wise(X))))&
(![X]:((patient(X)<~>curious(X))=>(~generous(X)<~>humble(X))))&
((~happy(fred))=>(?[X]:((wise(X)|~calm(X)))))&
(![X]:(~patient(X)<=>~happy(X)))&
(![X]:((tall(X)&~creative(X))<=>(~generous(X)|~humble(X))))&
(((happy(susan)&~strong(susan)))<=>(?[X]:((~old(X)<~>curious(X)))))&
(![X]:((~generous(X)<~>humble(X))<=>(~happy(X)<~>~creative(X))))&
(((~rich(fred)&~old(fred)))<=>((~calm(lucy)<~>~humble(lucy))))&
(![X]:(~wise(X)<=>(calm(X)&old(X))))&
(?[X]:(~humble(X)))&
(?[X]:(quiet(X)))&
((~happy(fred)<~>~quiet(fred)))&
((~curious(mary)<~>~strong(mary)))&
(~funny(susan))&
(?[X]:(funny(X)))&
((~curious(alice)&humble(alice)))&
(brave(susan)) | wise(alice) | [
"p0",
"p4",
"p7",
"p11",
"p12",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 5064272315701938693925375
% SZS output start Proof for 5064272315701938693925375
1. ! [X0] : ((~happy(X0) <~> happy(X0)) <=> tall(X0)) [input p0]
5. ! [X0] : ((~strong(X0) | creative(X0)) => (curious(X0) & strong(X0))) [input p4]
8. ! [X0] : ((generous(X0) <~> old(X0)) <=> (~wise(X0) | ~humble(X0))) [input p7]
12. ! [X0] : ((~creative(X0) & tall(X0)) <=> (~humble(X0) | ~generous(X0))) [input p11]
13. (~strong(susan) & happy(susan)) <=> ? [X0] : (~old(X0) <~> curious(X0)) [input p12]
23. humble(alice) & ~curious(alice) [input p22]
25. wise(alice) [input hypothesis]
32. ! [X0] : ((curious(X0) & strong(X0)) | (strong(X0) & ~creative(X0))) [ennf transformation 5]
35. ! [X0] : ((((~happy(X0) | happy(X0)) & (happy(X0) | ~happy(X0))) | ~tall(X0)) & (tall(X0) | ((~happy(X0) | ~happy(X0)) & (happy(X0) | happy(X0))))) [nnf transformation 1]
51. ! [X0] : ((((~old(X0) | ~generous(X0)) & (old(X0) | generous(X0))) | (wise(X0) & humble(X0))) & ((~wise(X0) | ~humble(X0)) | ((generous(X0) | ~old(X0)) & (old(X0) | ~generous(X0))))) [nnf transformation 8]
52. ! [X0] : ((((~old(X0) | ~generous(X0)) & (old(X0) | generous(X0))) | (wise(X0) & humble(X0))) & (~wise(X0) | ~humble(X0) | ((generous(X0) | ~old(X0)) & (old(X0) | ~generous(X0))))) [flattening 51]
57. ! [X0] : (((~creative(X0) & tall(X0)) | (humble(X0) & generous(X0))) & ((~humble(X0) | ~generous(X0)) | (creative(X0) | ~tall(X0)))) [nnf transformation 12]
58. ! [X0] : (((~creative(X0) & tall(X0)) | (humble(X0) & generous(X0))) & (~humble(X0) | ~generous(X0) | creative(X0) | ~tall(X0))) [flattening 57]
59. ((~strong(susan) & happy(susan)) | ! [X0] : ((~old(X0) | ~curious(X0)) & (curious(X0) | old(X0)))) & (? [X0] : ((~curious(X0) | old(X0)) & (curious(X0) | ~old(X0))) | (strong(susan) | ~happy(susan))) [nnf transformation 13]
60. ((~strong(susan) & happy(susan)) | ! [X0] : ((~old(X0) | ~curious(X0)) & (curious(X0) | old(X0)))) & (? [X0] : ((~curious(X0) | old(X0)) & (curious(X0) | ~old(X0))) | strong(susan) | ~happy(susan)) [flattening 59]
61. ((~strong(susan) & happy(susan)) | ! [X0] : ((~old(X0) | ~curious(X0)) & (curious(X0) | old(X0)))) & (? [X1] : ((~curious(X1) | old(X1)) & (curious(X1) | ~old(X1))) | strong(susan) | ~happy(susan)) [rectify 60]
62. ? [X1] : ((~curious(X1) | old(X1)) & (curious(X1) | ~old(X1))) => ((~curious(sK5) | old(sK5)) & (curious(sK5) | ~old(sK5))) [choice axiom]
63. ((~strong(susan) & happy(susan)) | ! [X0] : ((~old(X0) | ~curious(X0)) & (curious(X0) | old(X0)))) & (((~curious(sK5) | old(sK5)) & (curious(sK5) | ~old(sK5))) | strong(susan) | ~happy(susan)) [skolemisation 61,62]
77. tall(X0) | happy(X0) | happy(X0) [cnf transformation 35]
78. tall(X0) | ~happy(X0) | ~happy(X0) [cnf transformation 35]
90. strong(X0) | strong(X0) [cnf transformation 32]
91. ~creative(X0) | curious(X0) [cnf transformation 32]
104. ~humble(X0) | ~wise(X0) | generous(X0) | ~old(X0) [cnf transformation 52]
116. ~humble(X0) | ~generous(X0) | creative(X0) | ~tall(X0) [cnf transformation 58]
125. ~strong(susan) | curious(X0) | old(X0) [cnf transformation 63]
152. ~curious(alice) [cnf transformation 23]
153. humble(alice) [cnf transformation 23]
154. wise(alice) [cnf transformation 25]
155. strong(X0) [duplicate literal removal 90]
156. tall(X0) | happy(X0) [duplicate literal removal 77]
157. ~happy(X0) | tall(X0) [duplicate literal removal 78]
158. tall(X0) [subsumption resolution 156,157]
238. ~humble(X0) | ~generous(X0) | creative(X0) [subsumption resolution 116,158]
240. curious(X0) | old(X0) [subsumption resolution 125,155]
290. old(alice) [resolution 240,152]
311. ~generous(alice) | creative(alice) [resolution 238,153]
315. 25 <=> creative(alice) [avatar definition]
317. creative(alice) <- (25) [avatar component clause 315]
319. 26 <=> generous(alice) [avatar definition]
322. 25 | ~26 [avatar split clause 311,319,315]
361. ~wise(alice) | generous(alice) | ~old(alice) [resolution 104,153]
367. generous(alice) | ~old(alice) [subsumption resolution 361,154]
373. generous(alice) [subsumption resolution 367,290]
374. 26 [avatar split clause 373,319]
384. curious(alice) <- (25) [resolution 317,91]
389. $false <- (25) [subsumption resolution 384,152]
390. ~25 [avatar contradiction clause 389]
391. $false [avatar sat refutation 322,374,390]
% SZS output end Proof for 5064272315701938693925375
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not humble then someone is both calm and not happy.
If fred is tall then paul is either old or not happy.
Everyone who is either not brave or quiet is curious or not funny and vice versa.
If paul is not humble or old then someone is creative or not humble and vice versa.
If someone is either not creative or not old then someone is both not old and strong and vice versa.
Everyone who is not rich is humble or not generous.
Everyone who is not generous is not strong and vice versa.
Everyone who is both strong and not happy is old and vice versa.
Everyone who is old is not tall or not humble and vice versa.
Everyone who is both funny and not patient is both not funny and not strong.
If someone is happy then someone is both not kind and patient and vice versa.
Everyone who is quiet or calm is not funny and vice versa.
Everyone who is either funny or strong is kind or brave.
If someone is either not old or humble then paul is either happy or not curious.
If someone is both not patient and not rich then paul is funny.
Everyone who is not generous or quiet is either old or rich and vice versa.
Someone is not humble or funny.
Someone is both rich and not creative.
John is rich.
Someone is wise.
Someone is either old or brave. | Paul is not kind. | neutral | ((?[X]:(~humble(X)))=>(?[X]:((calm(X)&~happy(X)))))&
((tall(fred))=>((old(paul)<~>~happy(paul))))&
(![X]:((~brave(X)<~>quiet(X))<=>(curious(X)|~funny(X))))&
(((~humble(paul)|old(paul)))<=>(?[X]:((creative(X)|~humble(X)))))&
((?[X]:((~creative(X)<~>~old(X))))<=>(?[X]:((~old(X)&strong(X)))))&
(![X]:(~rich(X)=>(humble(X)|~generous(X))))&
(![X]:(~generous(X)<=>~strong(X)))&
(![X]:((strong(X)&~happy(X))<=>old(X)))&
(![X]:(old(X)<=>(~tall(X)|~humble(X))))&
(![X]:((funny(X)&~patient(X))=>(~funny(X)&~strong(X))))&
((?[X]:(happy(X)))<=>(?[X]:((~kind(X)&patient(X)))))&
(![X]:((quiet(X)|calm(X))<=>~funny(X)))&
(![X]:((funny(X)<~>strong(X))=>(kind(X)|brave(X))))&
((?[X]:((~old(X)<~>humble(X))))=>((happy(paul)<~>~curious(paul))))&
((?[X]:((~patient(X)&~rich(X))))=>(funny(paul)))&
(![X]:((~generous(X)|quiet(X))<=>(old(X)<~>rich(X))))&
(?[X]:((~humble(X)|funny(X))))&
(?[X]:((rich(X)&~creative(X))))&
(rich(john))&
(?[X]:(wise(X)))&
(?[X]:((old(X)<~>brave(X)))) | ~kind(paul) | [] | null | 0 |
If lucy is brave or wise then alice is both generous and not happy.
If mary is either not generous or not old then alice is both not patient and not quiet and vice versa.
If alice is not strong then someone is creative.
Everyone who is not tall or not kind is not creative and vice versa.
If john is both wise and not brave then mary is both calm and humble.
Everyone who is humble or quiet is wise or happy.
If someone is both not humble and not wise then someone is not old or not tall and vice versa.
Everyone who is not strong or not creative is both not generous and creative and vice versa.
Everyone who is not quiet is both calm and not curious.
If john is both not happy and calm then mary is both happy and wise.
Everyone who is both generous and not rich is not kind or patient.
Everyone who is either wise or generous is kind.
Everyone who is either brave or patient is both not funny and funny and vice versa.
Everyone who is both not curious and old is not tall.
If fred is happy or not happy then mary is either not old or brave.
Everyone who is not funny is either not happy or not rich and vice versa.
Someone is both tall and not quiet.
Someone is not wise.
Someone is both not funny and not wise.
John is not tall or rich.
Someone is both not funny and rich.
Someone is both not brave and not rich.
Mary is patient or happy. | Lucy is quiet. | neutral | (((brave(lucy)|wise(lucy)))=>((generous(alice)&~happy(alice))))&
(((~generous(mary)<~>~old(mary)))<=>((~patient(alice)&~quiet(alice))))&
((~strong(alice))=>(?[X]:(creative(X))))&
(![X]:((~tall(X)|~kind(X))<=>~creative(X)))&
(((wise(john)&~brave(john)))=>((calm(mary)&humble(mary))))&
(![X]:((humble(X)|quiet(X))=>(wise(X)|happy(X))))&
((?[X]:((~humble(X)&~wise(X))))<=>(?[X]:((~old(X)|~tall(X)))))&
(![X]:((~strong(X)|~creative(X))<=>(~generous(X)&creative(X))))&
(![X]:(~quiet(X)=>(calm(X)&~curious(X))))&
(((~happy(john)&calm(john)))=>((happy(mary)&wise(mary))))&
(![X]:((generous(X)&~rich(X))=>(~kind(X)|patient(X))))&
(![X]:((wise(X)<~>generous(X))=>kind(X)))&
(![X]:((brave(X)<~>patient(X))<=>(~funny(X)&funny(X))))&
(![X]:((~curious(X)&old(X))=>~tall(X)))&
(((happy(fred)|~happy(fred)))=>((~old(mary)<~>brave(mary))))&
(![X]:(~funny(X)<=>(~happy(X)<~>~rich(X))))&
(?[X]:((tall(X)&~quiet(X))))&
(?[X]:(~wise(X)))&
(?[X]:((~funny(X)&~wise(X))))&
((~tall(john)|rich(john)))&
(?[X]:((~funny(X)&rich(X))))&
(?[X]:((~brave(X)&~rich(X))))&
((patient(mary)|happy(mary))) | quiet(lucy) | [] | null | 0 |
Everyone who is calm or not quiet is kind or rich and vice versa.
Everyone who is generous or not funny is either creative or not rich.
If someone is either happy or not humble then lucy is not brave or not generous and vice versa.
Everyone who is both brave and not calm is either patient or not brave.
Everyone who is not rich or kind is strong.
If someone is not brave then paul is creative or humble and vice versa.
If someone is either funny or tall then lucy is either happy or rich.
Everyone who is either brave or not rich is either funny or strong.
Everyone who is not quiet or patient is not rich.
Everyone who is rich or not rich is not funny and vice versa.
Everyone who is quiet is both humble and generous and vice versa.
If lucy is not happy then fred is either not creative or rich and vice versa.
Everyone who is creative is kind or patient and vice versa.
Everyone who is both wise and generous is both rich and not happy.
If someone is rich then paul is kind.
Everyone who is not happy is rich and vice versa.
Someone is curious.
Someone is either not old or not kind.
Susan is not wise.
Someone is either funny or not funny.
Someone is both not calm and not curious.
Fred is not strong or not creative.
Someone is generous or not kind. | Paul is not humble. | contradiction | (![X]:((calm(X)|~quiet(X))<=>(kind(X)|rich(X))))&
(![X]:((generous(X)|~funny(X))=>(creative(X)<~>~rich(X))))&
((?[X]:((happy(X)<~>~humble(X))))<=>((~brave(lucy)|~generous(lucy))))&
(![X]:((brave(X)&~calm(X))=>(patient(X)<~>~brave(X))))&
(![X]:((~rich(X)|kind(X))=>strong(X)))&
((?[X]:(~brave(X)))<=>((creative(paul)|humble(paul))))&
((?[X]:((funny(X)<~>tall(X))))=>((happy(lucy)<~>rich(lucy))))&
(![X]:((brave(X)<~>~rich(X))=>(funny(X)<~>strong(X))))&
(![X]:((~quiet(X)|patient(X))=>~rich(X)))&
(![X]:((rich(X)|~rich(X))<=>~funny(X)))&
(![X]:(quiet(X)<=>(humble(X)&generous(X))))&
((~happy(lucy))<=>((~creative(fred)<~>rich(fred))))&
(![X]:(creative(X)<=>(kind(X)|patient(X))))&
(![X]:((wise(X)&generous(X))=>(rich(X)&~happy(X))))&
((?[X]:(rich(X)))=>(kind(paul)))&
(![X]:(~happy(X)<=>rich(X)))&
(?[X]:(curious(X)))&
(?[X]:((~old(X)<~>~kind(X))))&
(~wise(susan))&
(?[X]:((funny(X)<~>~funny(X))))&
(?[X]:((~calm(X)&~curious(X))))&
((~strong(fred)|~creative(fred)))&
(?[X]:((generous(X)|~kind(X)))) | ~humble(paul) | [
"p1",
"p4",
"p8",
"p9",
"p10",
"p11",
"p12",
"p14",
"p15",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 70148062988375210932621
% SZS output start Proof for 70148062988375210932621
2. ! [X0] : ((~funny(X0) | generous(X0)) => (creative(X0) <~> ~rich(X0))) [input p1]
5. ! [X0] : ((kind(X0) | ~rich(X0)) => strong(X0)) [input p4]
9. ! [X0] : ((patient(X0) | ~quiet(X0)) => ~rich(X0)) [input p8]
10. ! [X0] : ((~rich(X0) | rich(X0)) <=> ~funny(X0)) [input p9]
11. ! [X0] : (quiet(X0) <=> (generous(X0) & humble(X0))) [input p10]
12. ~happy(lucy) <=> (~creative(fred) <~> rich(fred)) [input p11]
13. ! [X0] : (creative(X0) <=> (patient(X0) | kind(X0))) [input p12]
15. ? [X0] : rich(X0) => kind(paul) [input p14]
16. ! [X0] : (~happy(X0) <=> rich(X0)) [input p15]
22. ~creative(fred) | ~strong(fred) [input p21]
24. ~humble(paul) [input hypothesis]
27. ! [X0] : ((creative(X0) <~> ~rich(X0)) | (funny(X0) & ~generous(X0))) [ennf transformation 2]
30. ! [X0] : (strong(X0) | (~kind(X0) & rich(X0))) [ennf transformation 5]
33. ! [X0] : (~rich(X0) | (~patient(X0) & quiet(X0))) [ennf transformation 9]
34. kind(paul) | ! [X0] : ~rich(X0) [ennf transformation 15]
37. ! [X0] : (((rich(X0) | ~creative(X0)) & (~rich(X0) | creative(X0))) | (funny(X0) & ~generous(X0))) [nnf transformation 27]
51. ! [X0] : (((~rich(X0) | rich(X0)) | funny(X0)) & (~funny(X0) | (rich(X0) & ~rich(X0)))) [nnf transformation 10]
52. ! [X0] : ((~rich(X0) | rich(X0) | funny(X0)) & (~funny(X0) | (rich(X0) & ~rich(X0)))) [flattening 51]
53. ! [X0] : ((quiet(X0) | (~generous(X0) | ~humble(X0))) & ((generous(X0) & humble(X0)) | ~quiet(X0))) [nnf transformation 11]
54. ! [X0] : ((quiet(X0) | ~generous(X0) | ~humble(X0)) & ((generous(X0) & humble(X0)) | ~quiet(X0))) [flattening 53]
55. (~happy(lucy) | ((~creative(fred) | ~rich(fred)) & (rich(fred) | creative(fred)))) & (((~rich(fred) | creative(fred)) & (rich(fred) | ~creative(fred))) | happy(lucy)) [nnf transformation 12]
56. ! [X0] : ((creative(X0) | (~patient(X0) & ~kind(X0))) & ((patient(X0) | kind(X0)) | ~creative(X0))) [nnf transformation 13]
57. ! [X0] : ((creative(X0) | (~patient(X0) & ~kind(X0))) & (patient(X0) | kind(X0) | ~creative(X0))) [flattening 56]
58. ! [X0] : ((~happy(X0) | ~rich(X0)) & (rich(X0) | happy(X0))) [nnf transformation 16]
76. ~rich(X0) | creative(X0) | funny(X0) [cnf transformation 37]
78. ~creative(X0) | rich(X0) | funny(X0) [cnf transformation 37]
87. strong(X0) | rich(X0) [cnf transformation 30]
100. ~rich(X0) | quiet(X0) [cnf transformation 33]
102. ~funny(X0) | ~rich(X0) [cnf transformation 52]
103. ~funny(X0) | rich(X0) [cnf transformation 52]
105. ~quiet(X0) | humble(X0) [cnf transformation 54]
110. ~happy(lucy) | rich(fred) | creative(fred) [cnf transformation 55]
111. ~happy(lucy) | ~creative(fred) | ~rich(fred) [cnf transformation 55]
113. ~kind(X0) | creative(X0) [cnf transformation 57]
115. kind(paul) | ~rich(X0) [cnf transformation 34]
116. happy(X0) | rich(X0) [cnf transformation 58]
125. ~creative(fred) | ~strong(fred) [cnf transformation 22]
127. ~humble(paul) [cnf transformation 24]
158. 7 <=> humble(paul) [avatar definition]
160. ~humble(paul) <- (~7) [avatar component clause 158]
167. 9 <=> creative(paul) [avatar definition]
168. creative(paul) <- (9) [avatar component clause 167]
179. 12 <=> happy(lucy) [avatar definition]
181. ~happy(lucy) <- (~12) [avatar component clause 179]
195. ~funny(X0) [subsumption resolution 102,103]
197. 15 <=> rich(fred) [avatar definition]
198. rich(fred) <- (15) [avatar component clause 197]
199. ~rich(fred) <- (~15) [avatar component clause 197]
201. 16 <=> creative(fred) [avatar definition]
203. ~creative(fred) <- (~16) [avatar component clause 201]
204. ~15 | ~16 | ~12 [avatar split clause 111,179,201,197]
205. 16 | 15 | ~12 [avatar split clause 110,179,197,201]
209. 17 <=> ! [X0] : ~rich(X0) [avatar definition]
210. ~rich(X0) <- (17) [avatar component clause 209]
212. 18 <=> kind(paul) [avatar definition]
214. kind(paul) <- (18) [avatar component clause 212]
215. 17 | 18 [avatar split clause 115,212,209]
227. 21 <=> strong(fred) [avatar definition]
229. ~strong(fred) <- (~21) [avatar component clause 227]
230. ~21 | ~16 [avatar split clause 125,201,227]
240. ~7 [avatar split clause 127,158]
245. rich(lucy) <- (~12) [resolution 116,181]
248. $false <- (~12, 17) [subsumption resolution 245,210]
249. 12 | ~17 [avatar contradiction clause 248]
252. creative(paul) <- (18) [resolution 214,113]
264. 24 <=> quiet(paul) [avatar definition]
265. quiet(paul) <- (24) [avatar component clause 264]
283. creative(fred) | funny(fred) <- (15) [resolution 76,198]
285. funny(fred) <- (15, ~16) [subsumption resolution 283,203]
286. $false <- (15, ~16) [subsumption resolution 285,195]
287. ~15 | 16 [avatar contradiction clause 286]
289. rich(fred) <- (~21) [resolution 229,87]
290. $false <- (~15, ~21) [subsumption resolution 289,199]
291. 15 | 21 [avatar contradiction clause 290]
313. 29 <=> rich(paul) [avatar definition]
315. rich(paul) <- (29) [avatar component clause 313]
318. rich(paul) | funny(paul) <- (9) [resolution 78,168]
319. rich(paul) <- (9) [subsumption resolution 318,195]
320. 29 | ~9 [avatar split clause 319,167,313]
351. quiet(paul) <- (29) [resolution 315,100]
354. 24 | ~29 [avatar split clause 351,313,264]
357. humble(paul) <- (24) [resolution 265,105]
360. $false <- (~7, 24) [subsumption resolution 357,160]
361. 7 | ~24 [avatar contradiction clause 360]
362. 9 | ~18 [avatar split clause 252,212,167]
363. $false [avatar sat refutation 204,205,215,230,240,249,287,291,320,354,361,362]
% SZS output end Proof for 70148062988375210932621
% ------------------------------
% 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 |
If someone is either brave or not curious then someone is strong or curious.
If someone is either generous or calm then fred is both not kind and rich and vice versa.
Everyone who is either wise or not strong is either calm or not calm.
If lucy is humble or not wise then susan is not funny or strong.
Everyone who is either not tall or curious is not tall.
If susan is generous then mary is quiet or not funny and vice versa.
Everyone who is patient is strong and vice versa.
Everyone who is either rich or calm is not quiet.
Everyone who is both not creative and patient is not brave and vice versa.
Everyone who is quiet is kind or strong and vice versa.
If someone is either quiet or not tall then someone is both not creative and not curious and vice versa.
If someone is either wise or not old then someone is either not tall or not happy and vice versa.
Everyone who is not brave or not old is both kind and not generous.
Everyone who is brave or happy is both humble and strong and vice versa.
Everyone who is both not generous and tall is both not patient and brave.
If someone is either quiet or not tall then fred is not old and vice versa.
Someone is kind or brave.
Someone is not happy or not brave.
Someone is funny.
Someone is either not brave or kind.
Paul is either not curious or tall. | Fred is quiet. | entailment | ((?[X]:((brave(X)<~>~curious(X))))=>(?[X]:((strong(X)|curious(X)))))&
((?[X]:((generous(X)<~>calm(X))))<=>((~kind(fred)&rich(fred))))&
(![X]:((wise(X)<~>~strong(X))=>(calm(X)<~>~calm(X))))&
(((humble(lucy)|~wise(lucy)))=>((~funny(susan)|strong(susan))))&
(![X]:((~tall(X)<~>curious(X))=>~tall(X)))&
((generous(susan))<=>((quiet(mary)|~funny(mary))))&
(![X]:(patient(X)<=>strong(X)))&
(![X]:((rich(X)<~>calm(X))=>~quiet(X)))&
(![X]:((~creative(X)&patient(X))<=>~brave(X)))&
(![X]:(quiet(X)<=>(kind(X)|strong(X))))&
((?[X]:((quiet(X)<~>~tall(X))))<=>(?[X]:((~creative(X)&~curious(X)))))&
((?[X]:((wise(X)<~>~old(X))))<=>(?[X]:((~tall(X)<~>~happy(X)))))&
(![X]:((~brave(X)|~old(X))=>(kind(X)&~generous(X))))&
(![X]:((brave(X)|happy(X))<=>(humble(X)&strong(X))))&
(![X]:((~generous(X)&tall(X))=>(~patient(X)&brave(X))))&
((?[X]:((quiet(X)<~>~tall(X))))<=>(~old(fred)))&
(?[X]:((kind(X)|brave(X))))&
(?[X]:((~happy(X)|~brave(X))))&
(?[X]:(funny(X)))&
(?[X]:((~brave(X)<~>kind(X))))&
((~curious(paul)<~>tall(paul))) | quiet(fred) | [
"p6",
"p8",
"p9",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 5443686794861476211284139
% SZS output start Proof for 5443686794861476211284139
7. ! [X0] : (patient(X0) <=> strong(X0)) [input p6]
9. ! [X0] : ((patient(X0) & ~creative(X0)) <=> ~brave(X0)) [input p8]
10. ! [X0] : (quiet(X0) <=> (strong(X0) | kind(X0))) [input p9]
14. ! [X0] : ((happy(X0) | brave(X0)) <=> (strong(X0) & humble(X0))) [input p13]
22. ~quiet(fred) [input hypothesis]
48. ! [X0] : ((patient(X0) | ~strong(X0)) & (strong(X0) | ~patient(X0))) [nnf transformation 7]
50. ! [X0] : (((patient(X0) & ~creative(X0)) | brave(X0)) & (~brave(X0) | (~patient(X0) | creative(X0)))) [nnf transformation 9]
51. ! [X0] : (((patient(X0) & ~creative(X0)) | brave(X0)) & (~brave(X0) | ~patient(X0) | creative(X0))) [flattening 50]
52. ! [X0] : ((quiet(X0) | (~strong(X0) & ~kind(X0))) & ((strong(X0) | kind(X0)) | ~quiet(X0))) [nnf transformation 10]
53. ! [X0] : ((quiet(X0) | (~strong(X0) & ~kind(X0))) & (strong(X0) | kind(X0) | ~quiet(X0))) [flattening 52]
64. ! [X0] : (((happy(X0) | brave(X0)) | (~strong(X0) | ~humble(X0))) & ((strong(X0) & humble(X0)) | (~happy(X0) & ~brave(X0)))) [nnf transformation 14]
65. ! [X0] : ((happy(X0) | brave(X0) | ~strong(X0) | ~humble(X0)) & ((strong(X0) & humble(X0)) | (~happy(X0) & ~brave(X0)))) [flattening 64]
99. ~patient(X0) | strong(X0) [cnf transformation 48]
105. patient(X0) | brave(X0) [cnf transformation 51]
108. ~strong(X0) | quiet(X0) [cnf transformation 53]
129. ~brave(X0) | strong(X0) [cnf transformation 65]
145. ~quiet(fred) [cnf transformation 22]
323. brave(X0) | strong(X0) [resolution 105,99]
324. strong(X0) [subsumption resolution 323,129]
328. quiet(X0) [resolution 108,324]
345. $false [resolution 328,145]
% SZS output end Proof for 5443686794861476211284139
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is not calm then john is both humble and tall.
If someone is both not brave and happy then alice is both not strong and quiet.
If alice is humble then someone is patient or rich and vice versa.
Everyone who is either not kind or calm is both not tall and not rich and vice versa.
If someone is not tall then someone is either not rich or not brave.
If someone is not generous then someone is not old.
Everyone who is both quiet and not tall is not quiet and vice versa.
Everyone who is both not rich and curious is either tall or not quiet and vice versa.
If lucy is both not kind and not old then someone is either not kind or wise.
If alice is either not old or not wise then alice is quiet or patient and vice versa.
If alice is brave or strong then paul is not patient and vice versa.
Everyone who is either not generous or kind is not strong.
If someone is patient then someone is calm or not generous.
Everyone who is both generous and not wise is either old or happy.
Everyone who is not funny is both funny and not patient and vice versa.
Everyone who is generous or not calm is both not quiet and funny and vice versa.
Fred is either not strong or not brave.
John is tall or not curious.
Someone is not wise.
Someone is either brave or not brave.
Someone is quiet. | Alice is not happy. | neutral | ((~calm(lucy))=>((humble(john)&tall(john))))&
((?[X]:((~brave(X)&happy(X))))=>((~strong(alice)&quiet(alice))))&
((humble(alice))<=>(?[X]:((patient(X)|rich(X)))))&
(![X]:((~kind(X)<~>calm(X))<=>(~tall(X)&~rich(X))))&
((?[X]:(~tall(X)))=>(?[X]:((~rich(X)<~>~brave(X)))))&
((?[X]:(~generous(X)))=>(?[X]:(~old(X))))&
(![X]:((quiet(X)&~tall(X))<=>~quiet(X)))&
(![X]:((~rich(X)&curious(X))<=>(tall(X)<~>~quiet(X))))&
(((~kind(lucy)&~old(lucy)))=>(?[X]:((~kind(X)<~>wise(X)))))&
(((~old(alice)<~>~wise(alice)))<=>((quiet(alice)|patient(alice))))&
(((brave(alice)|strong(alice)))<=>(~patient(paul)))&
(![X]:((~generous(X)<~>kind(X))=>~strong(X)))&
((?[X]:(patient(X)))=>(?[X]:((calm(X)|~generous(X)))))&
(![X]:((generous(X)&~wise(X))=>(old(X)<~>happy(X))))&
(![X]:(~funny(X)<=>(funny(X)&~patient(X))))&
(![X]:((generous(X)|~calm(X))<=>(~quiet(X)&funny(X))))&
((~strong(fred)<~>~brave(fred)))&
((tall(john)|~curious(john)))&
(?[X]:(~wise(X)))&
(?[X]:((brave(X)<~>~brave(X))))&
(?[X]:(quiet(X))) | ~happy(alice) | [] | null | 0 |
If someone is not calm then paul is either not generous or wise. Everyone who is either not strong or humble is either tall or kind. Everyone who is both calm and not happy is not humble. If someone is both funny and not curious then someone is not old or creative and vice versa. Everyone who is both not creative and tall is calm and vice versa. If susan is either wise or not happy then alice is funny or kind and vice versa. If someone is either not quiet or generous then mary is quiet or strong and vice versa. Everyone who is both not rich and calm is brave or not strong and vice versa. Everyone who is humble is calm and vice versa. If someone is not old or not quiet then someone is both generous and patient. Everyone who is not happy is both not curious and old and vice versa. If mary is not calm or not happy then alice is strong or quiet and vice versa. Everyone who is not calm or not curious is either not patient or quiet. Everyone who is strong or not curious is not strong. Everyone who is either creative or not generous is either kind or creative and vice versa. If someone is both wise and happy then someone is either not patient or funny. Someone is not patient or patient. Someone is both kind and curious. Lucy is patient. Someone is not quiet. Paul is generous or not happy. Alice is both humble and wise. Someone is either not rich or kind. Someone is tall or not old. | Mary is creative. | contradiction | ((?[X]:(~calm(X)))=>((~generous(paul)<~>wise(paul))))&
(![X]:((~strong(X)<~>humble(X))=>(tall(X)<~>kind(X))))&
(![X]:((calm(X)&~happy(X))=>~humble(X)))&
((?[X]:((funny(X)&~curious(X))))<=>(?[X]:((~old(X)|creative(X)))))&
(![X]:((~creative(X)&tall(X))<=>calm(X)))&
(((wise(susan)<~>~happy(susan)))<=>((funny(alice)|kind(alice))))&
((?[X]:((~quiet(X)<~>generous(X))))<=>((quiet(mary)|strong(mary))))&
(![X]:((~rich(X)&calm(X))<=>(brave(X)|~strong(X))))&
(![X]:(humble(X)<=>calm(X)))&
((?[X]:((~old(X)|~quiet(X))))=>(?[X]:((generous(X)&patient(X)))))&
(![X]:(~happy(X)<=>(~curious(X)&old(X))))&
(((~calm(mary)|~happy(mary)))<=>((strong(alice)|quiet(alice))))&
(![X]:((~calm(X)|~curious(X))=>(~patient(X)<~>quiet(X))))&
(![X]:((strong(X)|~curious(X))=>~strong(X)))&
(![X]:((creative(X)<~>~generous(X))<=>(kind(X)<~>creative(X))))&
((?[X]:((wise(X)&happy(X))))=>(?[X]:((~patient(X)<~>funny(X)))))&
(?[X]:((~patient(X)|patient(X))))&
(?[X]:((kind(X)&curious(X))))&
(patient(lucy))&
(?[X]:(~quiet(X)))&
((generous(paul)|~happy(paul)))&
((humble(alice)&wise(alice)))&
(?[X]:((~rich(X)<~>kind(X))))&
(?[X]:((tall(X)|~old(X)))) | creative(mary) | [
"p4",
"p7",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 2942405060581826952808265
% SZS output start Proof for 2942405060581826952808265
5. ! [X0] : ((tall(X0) & ~creative(X0)) <=> calm(X0)) [input p4]
8. ! [X0] : ((calm(X0) & ~rich(X0)) <=> (~strong(X0) | brave(X0))) [input p7]
14. ! [X0] : ((~curious(X0) | strong(X0)) => ~strong(X0)) [input p13]
25. creative(mary) [input hypothesis]
35. ! [X0] : (~strong(X0) | (curious(X0) & ~strong(X0))) [ennf transformation 14]
44. ! [X0] : (((tall(X0) & ~creative(X0)) | ~calm(X0)) & (calm(X0) | (~tall(X0) | creative(X0)))) [nnf transformation 5]
45. ! [X0] : (((tall(X0) & ~creative(X0)) | ~calm(X0)) & (calm(X0) | ~tall(X0) | creative(X0))) [flattening 44]
53. ! [X0] : (((calm(X0) & ~rich(X0)) | (strong(X0) & ~brave(X0))) & ((~strong(X0) | brave(X0)) | (~calm(X0) | rich(X0)))) [nnf transformation 8]
54. ! [X0] : (((calm(X0) & ~rich(X0)) | (strong(X0) & ~brave(X0))) & (~strong(X0) | brave(X0) | ~calm(X0) | rich(X0))) [flattening 53]
93. ~creative(X0) | ~calm(X0) [cnf transformation 45]
111. strong(X0) | calm(X0) [cnf transformation 54]
129. ~strong(X0) | ~strong(X0) [cnf transformation 35]
152. creative(mary) [cnf transformation 25]
157. ~strong(X0) [duplicate literal removal 129]
159. 1 <=> ! [X0] : calm(X0) [avatar definition]
160. calm(X0) <- (1) [avatar component clause 159]
337. ~calm(mary) [resolution 93,152]
338. calm(X0) [resolution 111,157]
339. 1 [avatar split clause 338,159]
343. $false <- (1) [subsumption resolution 337,160]
344. ~1 [avatar contradiction clause 343]
345. $false [avatar sat refutation 339,344]
% SZS output end Proof for 2942405060581826952808265
% ------------------------------
% 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 both humble and not rich is either not calm or not brave.
If someone is either creative or not old then paul is both wise and not calm.
If someone is patient then someone is not wise and vice versa.
Everyone who is not funny or humble is both not happy and not tall.
Everyone who is not rich or strong is either curious or patient and vice versa.
Everyone who is not kind or not creative is both humble and not kind and vice versa.
Everyone who is both not creative and not old is not wise and vice versa.
If john is both not patient and funny then someone is either creative or not calm.
Everyone who is either quiet or not rich is both rich and generous and vice versa.
Everyone who is generous or not rich is either tall or not patient and vice versa.
If someone is humble or tall then someone is not humble or not strong.
If fred is both not funny and generous then someone is patient or not humble and vice versa.
Everyone who is both tall and quiet is not funny or not curious and vice versa.
Everyone who is either generous or happy is either humble or not strong.
If someone is both not wise and rich then susan is not rich.
Someone is humble.
Lucy is either not rich or not wise.
Someone is either not brave or funny.
Someone is calm.
Someone is both not calm and not rich.
Someone is funny or not funny. | Fred is not curious. | contradiction | (![X]:((humble(X)&~rich(X))=>(~calm(X)<~>~brave(X))))&
((?[X]:((creative(X)<~>~old(X))))=>((wise(paul)&~calm(paul))))&
((?[X]:(patient(X)))<=>(?[X]:(~wise(X))))&
(![X]:((~funny(X)|humble(X))=>(~happy(X)&~tall(X))))&
(![X]:((~rich(X)|strong(X))<=>(curious(X)<~>patient(X))))&
(![X]:((~kind(X)|~creative(X))<=>(humble(X)&~kind(X))))&
(![X]:((~creative(X)&~old(X))<=>~wise(X)))&
(((~patient(john)&funny(john)))=>(?[X]:((creative(X)<~>~calm(X)))))&
(![X]:((quiet(X)<~>~rich(X))<=>(rich(X)&generous(X))))&
(![X]:((generous(X)|~rich(X))<=>(tall(X)<~>~patient(X))))&
((?[X]:((humble(X)|tall(X))))=>(?[X]:((~humble(X)|~strong(X)))))&
(((~funny(fred)&generous(fred)))<=>(?[X]:((patient(X)|~humble(X)))))&
(![X]:((tall(X)&quiet(X))<=>(~funny(X)|~curious(X))))&
(![X]:((generous(X)<~>happy(X))=>(humble(X)<~>~strong(X))))&
((?[X]:((~wise(X)&rich(X))))=>(~rich(susan)))&
(?[X]:(humble(X)))&
((~rich(lucy)<~>~wise(lucy)))&
(?[X]:((~brave(X)<~>funny(X))))&
(?[X]:(calm(X)))&
(?[X]:((~calm(X)&~rich(X))))&
(?[X]:((funny(X)|~funny(X)))) | ~curious(fred) | [
"p3",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 7613576670659104746875871
% SZS output start Proof for 7613576670659104746875871
4. ! [X0] : ((humble(X0) | ~funny(X0)) => (~tall(X0) & ~happy(X0))) [input p3]
12. (generous(fred) & ~funny(fred)) <=> ? [X0] : (~humble(X0) | patient(X0)) [input p11]
13. ! [X0] : ((quiet(X0) & tall(X0)) <=> (~curious(X0) | ~funny(X0))) [input p12]
22. ~curious(fred) [input hypothesis]
28. ! [X0] : ((~tall(X0) & ~happy(X0)) | (~humble(X0) & funny(X0))) [ennf transformation 4]
57. ((generous(fred) & ~funny(fred)) | ! [X0] : (humble(X0) & ~patient(X0))) & (? [X0] : (~humble(X0) | patient(X0)) | (~generous(fred) | funny(fred))) [nnf transformation 12]
58. ((generous(fred) & ~funny(fred)) | ! [X0] : (humble(X0) & ~patient(X0))) & (? [X0] : (~humble(X0) | patient(X0)) | ~generous(fred) | funny(fred)) [flattening 57]
59. ((generous(fred) & ~funny(fred)) | ! [X0] : (humble(X0) & ~patient(X0))) & (? [X1] : (~humble(X1) | patient(X1)) | ~generous(fred) | funny(fred)) [rectify 58]
60. ? [X1] : (~humble(X1) | patient(X1)) => (~humble(sK4) | patient(sK4)) [choice axiom]
61. ((generous(fred) & ~funny(fred)) | ! [X0] : (humble(X0) & ~patient(X0))) & ((~humble(sK4) | patient(sK4)) | ~generous(fred) | funny(fred)) [skolemisation 59,60]
62. ! [X0] : (((quiet(X0) & tall(X0)) | (curious(X0) & funny(X0))) & ((~curious(X0) | ~funny(X0)) | (~quiet(X0) | ~tall(X0)))) [nnf transformation 13]
63. ! [X0] : (((quiet(X0) & tall(X0)) | (curious(X0) & funny(X0))) & (~curious(X0) | ~funny(X0) | ~quiet(X0) | ~tall(X0))) [flattening 62]
87. ~tall(X0) | funny(X0) [cnf transformation 28]
88. ~tall(X0) | ~humble(X0) [cnf transformation 28]
121. ~funny(fred) | humble(X0) [cnf transformation 61]
125. tall(X0) | funny(X0) [cnf transformation 63]
126. curious(X0) | tall(X0) [cnf transformation 63]
143. ~curious(fred) [cnf transformation 22]
215. 17 <=> ! [X0] : humble(X0) [avatar definition]
216. humble(X0) <- (17) [avatar component clause 215]
224. 19 <=> funny(fred) [avatar definition]
226. ~funny(fred) <- (~19) [avatar component clause 224]
227. 17 | ~19 [avatar split clause 121,224,215]
238. funny(X0) [subsumption resolution 125,87]
267. $false <- (~19) [subsumption resolution 226,238]
268. 19 [avatar contradiction clause 267]
276. tall(fred) [resolution 126,143]
277. ~humble(fred) [resolution 276,88]
279. $false <- (17) [subsumption resolution 277,216]
280. ~17 [avatar contradiction clause 279]
281. $false [avatar sat refutation 227,268,280]
% SZS output end Proof for 7613576670659104746875871
% ------------------------------
% 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 wise or old is both not rich and old. If susan is kind or tall then mary is both not calm and happy and vice versa. Everyone who is either generous or not tall is humble or strong. If someone is humble or creative then someone is patient. Everyone who is not calm or strong is tall. Everyone who is both curious and not generous is rich and vice versa. If someone is both wise and not tall then someone is either wise or not strong and vice versa. If fred is either not calm or wise then lucy is not strong. Everyone who is both old and patient is either not tall or patient and vice versa. If someone is not calm or not happy then john is both curious and not patient. Everyone who is both not brave and not old is old. Everyone who is old or not rich is both not tall and rich. Everyone who is both not generous and not humble is not tall or tall and vice versa. Everyone who is patient is curious or brave. Everyone who is both not brave and brave is either not tall or generous. Lucy is not calm. Someone is not patient. Someone is both curious and not kind. Alice is calm. Someone is not calm. Alice is not creative or not strong. | Alice is creative. | contradiction | (![X]:((wise(X)<~>old(X))=>(~rich(X)&old(X))))&
(((kind(susan)|tall(susan)))<=>((~calm(mary)&happy(mary))))&
(![X]:((generous(X)<~>~tall(X))=>(humble(X)|strong(X))))&
((?[X]:((humble(X)|creative(X))))=>(?[X]:(patient(X))))&
(![X]:((~calm(X)|strong(X))=>tall(X)))&
(![X]:((curious(X)&~generous(X))<=>rich(X)))&
((?[X]:((wise(X)&~tall(X))))<=>(?[X]:((wise(X)<~>~strong(X)))))&
(((~calm(fred)<~>wise(fred)))=>(~strong(lucy)))&
(![X]:((old(X)&patient(X))<=>(~tall(X)<~>patient(X))))&
((?[X]:((~calm(X)|~happy(X))))=>((curious(john)&~patient(john))))&
(![X]:((~brave(X)&~old(X))=>old(X)))&
(![X]:((old(X)|~rich(X))=>(~tall(X)&rich(X))))&
(![X]:((~generous(X)&~humble(X))<=>(~tall(X)|tall(X))))&
(![X]:(patient(X)=>(curious(X)|brave(X))))&
(![X]:((~brave(X)&brave(X))=>(~tall(X)<~>generous(X))))&
(~calm(lucy))&
(?[X]:(~patient(X)))&
(?[X]:((curious(X)&~kind(X))))&
(calm(alice))&
(?[X]:(~calm(X)))&
((~creative(alice)|~strong(alice))) | creative(alice) | [
"p0",
"p6",
"p8",
"p11",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 5865098114973426753731652
% SZS output start Proof for 5865098114973426753731652
1. ! [X0] : ((wise(X0) <~> old(X0)) => (old(X0) & ~rich(X0))) [input p0]
7. ? [X0] : (~tall(X0) & wise(X0)) <=> ? [X0] : (wise(X0) <~> ~strong(X0)) [input p6]
9. ! [X0] : ((patient(X0) & old(X0)) <=> (~tall(X0) <~> patient(X0))) [input p8]
12. ! [X0] : ((~rich(X0) | old(X0)) => (rich(X0) & ~tall(X0))) [input p11]
21. ~strong(alice) | ~creative(alice) [input p20]
22. creative(alice) [input hypothesis]
24. ? [X0] : (~tall(X0) & wise(X0)) <=> ? [X1] : (wise(X1) <~> ~strong(X1)) [rectify 7]
25. ! [X0] : ((old(X0) & ~rich(X0)) | (wise(X0) <=> old(X0))) [ennf transformation 1]
34. ! [X0] : ((rich(X0) & ~tall(X0)) | (rich(X0) & ~old(X0))) [ennf transformation 12]
39. ! [X0] : ((old(X0) & ~rich(X0)) | ((wise(X0) | ~old(X0)) & (old(X0) | ~wise(X0)))) [nnf transformation 25]
48. (? [X0] : (~tall(X0) & wise(X0)) | ! [X1] : ((wise(X1) | strong(X1)) & (~strong(X1) | ~wise(X1)))) & (? [X1] : ((strong(X1) | ~wise(X1)) & (~strong(X1) | wise(X1))) | ! [X0] : (tall(X0) | ~wise(X0))) [nnf transformation 24]
49. (? [X0] : (~tall(X0) & wise(X0)) | ! [X1] : ((wise(X1) | strong(X1)) & (~strong(X1) | ~wise(X1)))) & (? [X2] : ((strong(X2) | ~wise(X2)) & (~strong(X2) | wise(X2))) | ! [X3] : (tall(X3) | ~wise(X3))) [rectify 48]
50. ? [X0] : (~tall(X0) & wise(X0)) => (~tall(sK1) & wise(sK1)) [choice axiom]
51. ? [X2] : ((strong(X2) | ~wise(X2)) & (~strong(X2) | wise(X2))) => ((strong(sK2) | ~wise(sK2)) & (~strong(sK2) | wise(sK2))) [choice axiom]
52. ((~tall(sK1) & wise(sK1)) | ! [X1] : ((wise(X1) | strong(X1)) & (~strong(X1) | ~wise(X1)))) & (((strong(sK2) | ~wise(sK2)) & (~strong(sK2) | wise(sK2))) | ! [X3] : (tall(X3) | ~wise(X3))) [skolemisation 49,51,50]
54. ! [X0] : (((patient(X0) & old(X0)) | ((~tall(X0) | ~patient(X0)) & (patient(X0) | tall(X0)))) & (((~patient(X0) | tall(X0)) & (patient(X0) | ~tall(X0))) | (~patient(X0) | ~old(X0)))) [nnf transformation 9]
55. ! [X0] : (((patient(X0) & old(X0)) | ((~tall(X0) | ~patient(X0)) & (patient(X0) | tall(X0)))) & (((~patient(X0) | tall(X0)) & (patient(X0) | ~tall(X0))) | ~patient(X0) | ~old(X0))) [flattening 54]
67. old(X0) | old(X0) | ~wise(X0) [cnf transformation 39]
86. wise(sK1) | wise(X1) | strong(X1) [cnf transformation 52]
92. ~patient(X0) | tall(X0) | ~patient(X0) | ~old(X0) [cnf transformation 55]
95. patient(X0) | patient(X0) | tall(X0) [cnf transformation 55]
102. ~tall(X0) | ~old(X0) [cnf transformation 34]
120. ~strong(alice) | ~creative(alice) [cnf transformation 21]
121. creative(alice) [cnf transformation 22]
124. ~patient(X0) | tall(X0) | ~old(X0) [duplicate literal removal 92]
125. patient(X0) | tall(X0) [duplicate literal removal 95]
126. ~wise(X0) | old(X0) [duplicate literal removal 67]
161. 8 <=> ! [X1] : (wise(X1) | strong(X1)) [avatar definition]
162. strong(X1) | wise(X1) <- (8) [avatar component clause 161]
173. 11 <=> wise(sK1) [avatar definition]
175. wise(sK1) <- (11) [avatar component clause 173]
176. 8 | 11 [avatar split clause 86,173,161]
205. tall(X0) | ~old(X0) [subsumption resolution 124,125]
224. ~old(X0) [subsumption resolution 102,205]
229. 22 <=> creative(alice) [avatar definition]
233. 23 <=> strong(alice) [avatar definition]
235. ~strong(alice) <- (~23) [avatar component clause 233]
236. ~22 | ~23 [avatar split clause 120,233,229]
237. 22 [avatar split clause 121,229]
256. old(sK1) <- (11) [resolution 175,126]
257. $false <- (11) [subsumption resolution 256,224]
258. ~11 [avatar contradiction clause 257]
265. wise(alice) <- (8, ~23) [resolution 162,235]
278. old(alice) <- (8, ~23) [resolution 265,126]
279. $false <- (8, ~23) [subsumption resolution 278,224]
280. ~8 | 23 [avatar contradiction clause 279]
281. $false [avatar sat refutation 176,236,237,258,280]
% SZS output end Proof for 5865098114973426753731652
% ------------------------------
% 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 susan is either strong or funny then someone is not wise or not tall. Everyone who is brave is either wise or not happy and vice versa. Everyone who is both not tall and happy is kind or not curious and vice versa. Everyone who is not tall is both not tall and funny and vice versa. If lucy is not calm or not creative then someone is calm and vice versa. Everyone who is either tall or kind is humble and vice versa. If lucy is not brave or calm then someone is not kind or wise. Everyone who is either not quiet or curious is either old or not patient. Everyone who is both rich and not happy is either not quiet or not calm. Everyone who is kind or happy is either not rich or not funny and vice versa. If john is not patient then lucy is happy. Everyone who is funny is not humble and vice versa. Everyone who is brave is not curious. Everyone who is not rich is both rich and patient and vice versa. Everyone who is both not kind and funny is not creative and vice versa. If someone is not rich then lucy is either calm or not humble. Alice is both not strong and not wise. Mary is old or not humble. Someone is not curious or not old. Fred is generous. Fred is not brave or strong. Alice is generous. | Susan is not wise. | neutral | (((strong(susan)<~>funny(susan)))=>(?[X]:((~wise(X)|~tall(X)))))&
(![X]:(brave(X)<=>(wise(X)<~>~happy(X))))&
(![X]:((~tall(X)&happy(X))<=>(kind(X)|~curious(X))))&
(![X]:(~tall(X)<=>(~tall(X)&funny(X))))&
(((~calm(lucy)|~creative(lucy)))<=>(?[X]:(calm(X))))&
(![X]:((tall(X)<~>kind(X))<=>humble(X)))&
(((~brave(lucy)|calm(lucy)))=>(?[X]:((~kind(X)|wise(X)))))&
(![X]:((~quiet(X)<~>curious(X))=>(old(X)<~>~patient(X))))&
(![X]:((rich(X)&~happy(X))=>(~quiet(X)<~>~calm(X))))&
(![X]:((kind(X)|happy(X))<=>(~rich(X)<~>~funny(X))))&
((~patient(john))=>(happy(lucy)))&
(![X]:(funny(X)<=>~humble(X)))&
(![X]:(brave(X)=>~curious(X)))&
(![X]:(~rich(X)<=>(rich(X)&patient(X))))&
(![X]:((~kind(X)&funny(X))<=>~creative(X)))&
((?[X]:(~rich(X)))=>((calm(lucy)<~>~humble(lucy))))&
((~strong(alice)&~wise(alice)))&
((old(mary)|~humble(mary)))&
(?[X]:((~curious(X)|~old(X))))&
(generous(fred))&
((~brave(fred)|strong(fred)))&
(generous(alice)) | ~wise(susan) | [] | null | 0 |
Everyone who is generous or patient is both not calm and curious.
If someone is either not curious or strong then susan is either quiet or not curious.
Everyone who is not brave is either not funny or not patient and vice versa.
Everyone who is both not humble and not brave is not patient and vice versa.
If someone is not brave then someone is either brave or not creative.
Everyone who is brave is both not humble and not curious.
If lucy is either not curious or not brave then john is not quiet or not creative.
If someone is both not wise and not rich then someone is either not tall or not happy.
Everyone who is not wise or calm is strong or not curious.
If susan is both humble and kind then lucy is not rich or patient.
If mary is funny or old then someone is both not calm and not patient.
Everyone who is both not creative and not patient is not happy or strong and vice versa.
Everyone who is either not tall or rich is either patient or old and vice versa.
Everyone who is happy or not generous is not creative and vice versa.
If mary is creative then someone is either rich or not humble and vice versa.
Someone is generous or not quiet.
Alice is both tall and not brave.
Someone is kind.
Susan is not tall.
John is old. | Lucy is not brave. | entailment | (![X]:((generous(X)|patient(X))=>(~calm(X)&curious(X))))&
((?[X]:((~curious(X)<~>strong(X))))=>((quiet(susan)<~>~curious(susan))))&
(![X]:(~brave(X)<=>(~funny(X)<~>~patient(X))))&
(![X]:((~humble(X)&~brave(X))<=>~patient(X)))&
((?[X]:(~brave(X)))=>(?[X]:((brave(X)<~>~creative(X)))))&
(![X]:(brave(X)=>(~humble(X)&~curious(X))))&
(((~curious(lucy)<~>~brave(lucy)))=>((~quiet(john)|~creative(john))))&
((?[X]:((~wise(X)&~rich(X))))=>(?[X]:((~tall(X)<~>~happy(X)))))&
(![X]:((~wise(X)|calm(X))=>(strong(X)|~curious(X))))&
(((humble(susan)&kind(susan)))=>((~rich(lucy)|patient(lucy))))&
(((funny(mary)|old(mary)))=>(?[X]:((~calm(X)&~patient(X)))))&
(![X]:((~creative(X)&~patient(X))<=>(~happy(X)|strong(X))))&
(![X]:((~tall(X)<~>rich(X))<=>(patient(X)<~>old(X))))&
(![X]:((happy(X)|~generous(X))<=>~creative(X)))&
((creative(mary))<=>(?[X]:((rich(X)<~>~humble(X)))))&
(?[X]:((generous(X)|~quiet(X))))&
((tall(alice)&~brave(alice)))&
(?[X]:(kind(X)))&
(~tall(susan))&
(old(john)) | ~brave(lucy) | [
"p0",
"p3",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 901543174547095204518372
% SZS output start Proof for 901543174547095204518372
1. ! [X0] : ((patient(X0) | generous(X0)) => (curious(X0) & ~calm(X0))) [input p0]
4. ! [X0] : ((~brave(X0) & ~humble(X0)) <=> ~patient(X0)) [input p3]
6. ! [X0] : (brave(X0) => (~curious(X0) & ~humble(X0))) [input p5]
21. brave(lucy) [input hypothesis]
27. ! [X0] : ((patient(X0) | generous(X0)) => curious(X0)) [pure predicate removal 1]
29. ! [X0] : (curious(X0) | (~patient(X0) & ~generous(X0))) [ennf transformation 27]
32. ! [X0] : ((~curious(X0) & ~humble(X0)) | ~brave(X0)) [ennf transformation 6]
40. ! [X0] : (((~brave(X0) & ~humble(X0)) | patient(X0)) & (~patient(X0) | (brave(X0) | humble(X0)))) [nnf transformation 4]
41. ! [X0] : (((~brave(X0) & ~humble(X0)) | patient(X0)) & (~patient(X0) | brave(X0) | humble(X0))) [flattening 40]
63. ~patient(X0) | curious(X0) [cnf transformation 29]
74. ~brave(X0) | patient(X0) [cnf transformation 41]
78. ~brave(X0) | ~curious(X0) [cnf transformation 32]
110. brave(lucy) [cnf transformation 21]
144. 8 <=> curious(lucy) [avatar definition]
145. curious(lucy) <- (8) [avatar component clause 144]
158. 11 <=> brave(lucy) [avatar definition]
159. brave(lucy) <- (11) [avatar component clause 158]
175. 15 <=> patient(lucy) [avatar definition]
177. patient(lucy) <- (15) [avatar component clause 175]
206. 11 [avatar split clause 110,158]
207. patient(lucy) <- (11) [resolution 74,159]
208. 15 | ~11 [avatar split clause 207,158,175]
209. curious(lucy) <- (15) [resolution 177,63]
210. 8 | ~15 [avatar split clause 209,175,144]
211. ~curious(lucy) <- (11) [resolution 78,159]
212. $false <- (8, 11) [subsumption resolution 211,145]
213. ~8 | ~11 [avatar contradiction clause 212]
214. $false [avatar sat refutation 206,208,210,213]
% SZS output end Proof for 901543174547095204518372
% ------------------------------
% 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 both rich and not humble then paul is both not old and not calm and vice versa. If lucy is not kind then someone is not rich. Everyone who is both not rich and not generous is either old or curious and vice versa. Everyone who is curious is curious or kind and vice versa. Everyone who is either not generous or happy is either not funny or generous. Everyone who is either not kind or rich is not kind or tall and vice versa. If someone is both not funny and not humble then someone is either generous or not wise. If john is not humble or curious then someone is not rich or not old. Everyone who is rich is either not humble or not curious and vice versa. If lucy is not strong or not generous then paul is either not old or generous and vice versa. Everyone who is not creative or not strong is not patient or calm and vice versa. If someone is not quiet then mary is tall or not happy and vice versa. If lucy is curious or happy then paul is either not funny or rich. If someone is curious then someone is not tall and vice versa. If paul is humble or not tall then paul is funny. If paul is generous then fred is not calm or not patient and vice versa. Someone is rich. Someone is calm or not strong. Someone is either generous or humble. Susan is both wise and not happy. Someone is either not curious or not quiet. Fred is tall or patient. Fred is rich or not kind. | John is curious. | neutral | ((?[X]:((rich(X)&~humble(X))))<=>((~old(paul)&~calm(paul))))&
((~kind(lucy))=>(?[X]:(~rich(X))))&
(![X]:((~rich(X)&~generous(X))<=>(old(X)<~>curious(X))))&
(![X]:(curious(X)<=>(curious(X)|kind(X))))&
(![X]:((~generous(X)<~>happy(X))=>(~funny(X)<~>generous(X))))&
(![X]:((~kind(X)<~>rich(X))<=>(~kind(X)|tall(X))))&
((?[X]:((~funny(X)&~humble(X))))=>(?[X]:((generous(X)<~>~wise(X)))))&
(((~humble(john)|curious(john)))=>(?[X]:((~rich(X)|~old(X)))))&
(![X]:(rich(X)<=>(~humble(X)<~>~curious(X))))&
(((~strong(lucy)|~generous(lucy)))<=>((~old(paul)<~>generous(paul))))&
(![X]:((~creative(X)|~strong(X))<=>(~patient(X)|calm(X))))&
((?[X]:(~quiet(X)))<=>((tall(mary)|~happy(mary))))&
(((curious(lucy)|happy(lucy)))=>((~funny(paul)<~>rich(paul))))&
((?[X]:(curious(X)))<=>(?[X]:(~tall(X))))&
(((humble(paul)|~tall(paul)))=>(funny(paul)))&
((generous(paul))<=>((~calm(fred)|~patient(fred))))&
(?[X]:(rich(X)))&
(?[X]:((calm(X)|~strong(X))))&
(?[X]:((generous(X)<~>humble(X))))&
((wise(susan)&~happy(susan)))&
(?[X]:((~curious(X)<~>~quiet(X))))&
((tall(fred)|patient(fred)))&
((rich(fred)|~kind(fred))) | curious(john) | [] | null | 0 |
If someone is not generous then lucy is creative and vice versa.
If fred is both not happy and not calm then john is curious or wise and vice versa.
Everyone who is both creative and curious is both happy and tall and vice versa.
Everyone who is either not brave or rich is both not wise and not brave and vice versa.
Everyone who is not tall is not wise or rich.
If alice is either not strong or not kind then fred is both brave and tall and vice versa.
If someone is patient or wise then john is either not strong or not tall.
Everyone who is not curious is generous or not old.
If alice is either brave or not rich then someone is both brave and funny and vice versa.
If alice is curious or generous then someone is both patient and quiet.
Everyone who is wise or rich is patient and vice versa.
If mary is either funny or not patient then lucy is either not tall or kind.
Everyone who is not rich is funny.
Everyone who is either humble or brave is not happy.
If john is either not curious or creative then susan is both calm and tall and vice versa.
If someone is both generous and curious then fred is both calm and not generous and vice versa.
Someone is both not funny and not kind.
Lucy is either not happy or humble.
Someone is both wise and not humble.
Someone is both curious and quiet.
John is not wise.
Fred is both not calm and brave.
Someone is both rich and not humble.
Mary is either kind or creative. | John is happy. | neutral | ((?[X]:(~generous(X)))<=>(creative(lucy)))&
(((~happy(fred)&~calm(fred)))<=>((curious(john)|wise(john))))&
(![X]:((creative(X)&curious(X))<=>(happy(X)&tall(X))))&
(![X]:((~brave(X)<~>rich(X))<=>(~wise(X)&~brave(X))))&
(![X]:(~tall(X)=>(~wise(X)|rich(X))))&
(((~strong(alice)<~>~kind(alice)))<=>((brave(fred)&tall(fred))))&
((?[X]:((patient(X)|wise(X))))=>((~strong(john)<~>~tall(john))))&
(![X]:(~curious(X)=>(generous(X)|~old(X))))&
(((brave(alice)<~>~rich(alice)))<=>(?[X]:((brave(X)&funny(X)))))&
(((curious(alice)|generous(alice)))=>(?[X]:((patient(X)&quiet(X)))))&
(![X]:((wise(X)|rich(X))<=>patient(X)))&
(((funny(mary)<~>~patient(mary)))=>((~tall(lucy)<~>kind(lucy))))&
(![X]:(~rich(X)=>funny(X)))&
(![X]:((humble(X)<~>brave(X))=>~happy(X)))&
(((~curious(john)<~>creative(john)))<=>((calm(susan)&tall(susan))))&
((?[X]:((generous(X)&curious(X))))<=>((calm(fred)&~generous(fred))))&
(?[X]:((~funny(X)&~kind(X))))&
((~happy(lucy)<~>humble(lucy)))&
(?[X]:((wise(X)&~humble(X))))&
(?[X]:((curious(X)&quiet(X))))&
(~wise(john))&
((~calm(fred)&brave(fred)))&
(?[X]:((rich(X)&~humble(X))))&
((kind(mary)<~>creative(mary))) | happy(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. | Lucy is wise. | neutral | (![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))) | wise(lucy) | [] | null | 0 |
Everyone who is not wise or calm is tall or not brave. If someone is both not tall and rich then john is either not kind or not creative. Everyone who is not strong or quiet is not brave and vice versa. Everyone who is not quiet or not humble is kind or creative. Everyone who is both not humble and strong is curious and vice versa. Everyone who is brave is both creative and not strong and vice versa. Everyone who is happy or not patient is either quiet or not strong. Everyone who is either wise or kind is either not funny or not brave. Everyone who is not tall is not wise. If someone is both not funny and not patient then someone is either humble or calm and vice versa. If someone is either not strong or not patient then someone is both not old and old. If susan is either kind or brave then someone is not curious and vice versa. Everyone who is either quiet or generous is both generous and creative. If mary is not creative then alice is both wise and not wise. Everyone who is not humble is either not calm or not patient. If someone is not happy or not calm then alice is not brave. Someone is either not generous or rich. Someone is not generous or curious. Someone is happy or wise. Someone is either not happy or not old. Someone is creative or curious. Someone is both not patient and kind. Alice is either not happy or creative. Someone is either rich or not patient. | Alice is generous. | neutral | (![X]:((~wise(X)|calm(X))=>(tall(X)|~brave(X))))&
((?[X]:((~tall(X)&rich(X))))=>((~kind(john)<~>~creative(john))))&
(![X]:((~strong(X)|quiet(X))<=>~brave(X)))&
(![X]:((~quiet(X)|~humble(X))=>(kind(X)|creative(X))))&
(![X]:((~humble(X)&strong(X))<=>curious(X)))&
(![X]:(brave(X)<=>(creative(X)&~strong(X))))&
(![X]:((happy(X)|~patient(X))=>(quiet(X)<~>~strong(X))))&
(![X]:((wise(X)<~>kind(X))=>(~funny(X)<~>~brave(X))))&
(![X]:(~tall(X)=>~wise(X)))&
((?[X]:((~funny(X)&~patient(X))))<=>(?[X]:((humble(X)<~>calm(X)))))&
((?[X]:((~strong(X)<~>~patient(X))))=>(?[X]:((~old(X)&old(X)))))&
(((kind(susan)<~>brave(susan)))<=>(?[X]:(~curious(X))))&
(![X]:((quiet(X)<~>generous(X))=>(generous(X)&creative(X))))&
((~creative(mary))=>((wise(alice)&~wise(alice))))&
(![X]:(~humble(X)=>(~calm(X)<~>~patient(X))))&
((?[X]:((~happy(X)|~calm(X))))=>(~brave(alice)))&
(?[X]:((~generous(X)<~>rich(X))))&
(?[X]:((~generous(X)|curious(X))))&
(?[X]:((happy(X)|wise(X))))&
(?[X]:((~happy(X)<~>~old(X))))&
(?[X]:((creative(X)|curious(X))))&
(?[X]:((~patient(X)&kind(X))))&
((~happy(alice)<~>creative(alice)))&
(?[X]:((rich(X)<~>~patient(X)))) | generous(alice) | [] | null | 0 |
If someone is not happy or not tall then susan is either not quiet or kind and vice versa.
Everyone who is both tall and humble is rich.
Everyone who is happy is old or not wise and vice versa.
Everyone who is curious is both not kind and not strong and vice versa.
Everyone who is not curious is either not calm or not old.
Everyone who is both not funny and kind is tall or not patient.
Everyone who is both not generous and tall is either not strong or not quiet.
Everyone who is happy or tall is either curious or wise.
Everyone who is either not creative or not humble is generous or not brave and vice versa.
If someone is both wise and not humble then mary is creative.
If susan is either rich or generous then someone is not humble and vice versa.
Everyone who is strong or not old is both not happy and kind and vice versa.
Everyone who is either not kind or not generous is either calm or happy and vice versa.
Everyone who is quiet is both quiet and humble and vice versa.
Everyone who is not rich or happy is both wise and strong and vice versa.
Everyone who is not calm or not funny is either not wise or not tall and vice versa.
Someone is either patient or not funny.
Someone is either not tall or patient.
Lucy is either creative or calm.
Paul is not generous. | Mary is not tall. | neutral | ((?[X]:((~happy(X)|~tall(X))))<=>((~quiet(susan)<~>kind(susan))))&
(![X]:((tall(X)&humble(X))=>rich(X)))&
(![X]:(happy(X)<=>(old(X)|~wise(X))))&
(![X]:(curious(X)<=>(~kind(X)&~strong(X))))&
(![X]:(~curious(X)=>(~calm(X)<~>~old(X))))&
(![X]:((~funny(X)&kind(X))=>(tall(X)|~patient(X))))&
(![X]:((~generous(X)&tall(X))=>(~strong(X)<~>~quiet(X))))&
(![X]:((happy(X)|tall(X))=>(curious(X)<~>wise(X))))&
(![X]:((~creative(X)<~>~humble(X))<=>(generous(X)|~brave(X))))&
((?[X]:((wise(X)&~humble(X))))=>(creative(mary)))&
(((rich(susan)<~>generous(susan)))<=>(?[X]:(~humble(X))))&
(![X]:((strong(X)|~old(X))<=>(~happy(X)&kind(X))))&
(![X]:((~kind(X)<~>~generous(X))<=>(calm(X)<~>happy(X))))&
(![X]:(quiet(X)<=>(quiet(X)&humble(X))))&
(![X]:((~rich(X)|happy(X))<=>(wise(X)&strong(X))))&
(![X]:((~calm(X)|~funny(X))<=>(~wise(X)<~>~tall(X))))&
(?[X]:((patient(X)<~>~funny(X))))&
(?[X]:((~tall(X)<~>patient(X))))&
((creative(lucy)<~>calm(lucy)))&
(~generous(paul)) | ~tall(mary) | [] | null | 0 |
Everyone who is not tall is creative or not funny and vice versa. If someone is not calm or not funny then mary is both funny and curious. Everyone who is not funny or not wise is calm and vice versa. Everyone who is not tall or not wise is both not wise and creative. Everyone who is strong is either calm or wise and vice versa. Everyone who is creative is not funny. Everyone who is both curious and not humble is both calm and curious and vice versa. Everyone who is either not patient or not wise is either old or not calm and vice versa. Everyone who is humble is either quiet or old. Everyone who is not wise is both not kind and not patient and vice versa. Everyone who is both not old and curious is both tall and calm and vice versa. If someone is humble or not creative then someone is not old or kind. Everyone who is either not creative or not wise is either not brave or not wise and vice versa. If someone is kind or not funny then someone is not patient or not humble. Everyone who is either old or not calm is both quiet and not generous and vice versa. Everyone who is not tall is happy. Paul is creative or patient. Lucy is quiet or patient. Someone is happy or not creative. Someone is both not generous and not tall. Lucy is happy. Someone is both not humble and not happy. Someone is either humble or not funny. Someone is either not rich or strong. | Mary is not rich. | neutral | (![X]:(~tall(X)<=>(creative(X)|~funny(X))))&
((?[X]:((~calm(X)|~funny(X))))=>((funny(mary)&curious(mary))))&
(![X]:((~funny(X)|~wise(X))<=>calm(X)))&
(![X]:((~tall(X)|~wise(X))=>(~wise(X)&creative(X))))&
(![X]:(strong(X)<=>(calm(X)<~>wise(X))))&
(![X]:(creative(X)=>~funny(X)))&
(![X]:((curious(X)&~humble(X))<=>(calm(X)&curious(X))))&
(![X]:((~patient(X)<~>~wise(X))<=>(old(X)<~>~calm(X))))&
(![X]:(humble(X)=>(quiet(X)<~>old(X))))&
(![X]:(~wise(X)<=>(~kind(X)&~patient(X))))&
(![X]:((~old(X)&curious(X))<=>(tall(X)&calm(X))))&
((?[X]:((humble(X)|~creative(X))))=>(?[X]:((~old(X)|kind(X)))))&
(![X]:((~creative(X)<~>~wise(X))<=>(~brave(X)<~>~wise(X))))&
((?[X]:((kind(X)|~funny(X))))=>(?[X]:((~patient(X)|~humble(X)))))&
(![X]:((old(X)<~>~calm(X))<=>(quiet(X)&~generous(X))))&
(![X]:(~tall(X)=>happy(X)))&
((creative(paul)|patient(paul)))&
((quiet(lucy)|patient(lucy)))&
(?[X]:((happy(X)|~creative(X))))&
(?[X]:((~generous(X)&~tall(X))))&
(happy(lucy))&
(?[X]:((~humble(X)&~happy(X))))&
(?[X]:((humble(X)<~>~funny(X))))&
(?[X]:((~rich(X)<~>strong(X)))) | ~rich(mary) | [] | null | 0 |
Everyone who is both curious and not old is happy. Everyone who is not tall is not patient. If lucy is not strong then mary is funny and vice versa. Everyone who is kind or not quiet is not brave or happy and vice versa. Everyone who is either not curious or happy is either humble or not happy. If someone is tall or curious then alice is either not quiet or calm. Everyone who is both patient and not happy is either kind or humble and vice versa. Everyone who is both not funny and not strong is not kind and vice versa. Everyone who is both not old and not kind is generous or not wise and vice versa. If someone is not calm or not kind then paul is both humble and generous. If someone is either funny or not tall then paul is strong. If someone is old then alice is either not funny or wise and vice versa. Everyone who is both not curious and not brave is calm or not quiet. If someone is calm then susan is happy or tall and vice versa. Everyone who is curious is both not strong and tall. Everyone who is rich is both wise and strong and vice versa. Someone is strong or not wise. John is either not humble or happy. Someone is quiet. Fred is not humble or not generous. Someone is not generous. Someone is not old. Someone is either generous or tall. | Susan is kind. | entailment | (![X]:((curious(X)&~old(X))=>happy(X)))&
(![X]:(~tall(X)=>~patient(X)))&
((~strong(lucy))<=>(funny(mary)))&
(![X]:((kind(X)|~quiet(X))<=>(~brave(X)|happy(X))))&
(![X]:((~curious(X)<~>happy(X))=>(humble(X)<~>~happy(X))))&
((?[X]:((tall(X)|curious(X))))=>((~quiet(alice)<~>calm(alice))))&
(![X]:((patient(X)&~happy(X))<=>(kind(X)<~>humble(X))))&
(![X]:((~funny(X)&~strong(X))<=>~kind(X)))&
(![X]:((~old(X)&~kind(X))<=>(generous(X)|~wise(X))))&
((?[X]:((~calm(X)|~kind(X))))=>((humble(paul)&generous(paul))))&
((?[X]:((funny(X)<~>~tall(X))))=>(strong(paul)))&
((?[X]:(old(X)))<=>((~funny(alice)<~>wise(alice))))&
(![X]:((~curious(X)&~brave(X))=>(calm(X)|~quiet(X))))&
((?[X]:(calm(X)))<=>((happy(susan)|tall(susan))))&
(![X]:(curious(X)=>(~strong(X)&tall(X))))&
(![X]:(rich(X)<=>(wise(X)&strong(X))))&
(?[X]:((strong(X)|~wise(X))))&
((~humble(john)<~>happy(john)))&
(?[X]:(quiet(X)))&
((~humble(fred)|~generous(fred)))&
(?[X]:(~generous(X)))&
(?[X]:(~old(X)))&
(?[X]:((generous(X)<~>tall(X)))) | kind(susan) | [
"p0",
"p4",
"p6",
"p8",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 6304271989167059167237538
% SZS output start Proof for 6304271989167059167237538
1. ! [X0] : ((~old(X0) & curious(X0)) => happy(X0)) [input p0]
5. ! [X0] : ((~curious(X0) <~> happy(X0)) => (humble(X0) <~> ~happy(X0))) [input p4]
7. ! [X0] : ((~happy(X0) & patient(X0)) <=> (kind(X0) <~> humble(X0))) [input p6]
9. ! [X0] : ((~kind(X0) & ~old(X0)) <=> (~wise(X0) | generous(X0))) [input p8]
10. ? [X0] : (~kind(X0) | ~calm(X0)) => (generous(paul) & humble(paul)) [input p9]
24. ~kind(susan) [input hypothesis]
25. ! [X0] : (happy(X0) | (old(X0) | ~curious(X0))) [ennf transformation 1]
26. ! [X0] : (happy(X0) | old(X0) | ~curious(X0)) [flattening 25]
28. ! [X0] : ((humble(X0) <~> ~happy(X0)) | (~curious(X0) <=> happy(X0))) [ennf transformation 5]
30. (generous(paul) & humble(paul)) | ! [X0] : (kind(X0) & calm(X0)) [ennf transformation 10]
38. ! [X0] : (((happy(X0) | ~humble(X0)) & (~happy(X0) | humble(X0))) | ((~curious(X0) | ~happy(X0)) & (happy(X0) | curious(X0)))) [nnf transformation 28]
40. ! [X0] : (((~happy(X0) & patient(X0)) | ((kind(X0) | ~humble(X0)) & (humble(X0) | ~kind(X0)))) & (((~humble(X0) | ~kind(X0)) & (humble(X0) | kind(X0))) | (happy(X0) | ~patient(X0)))) [nnf transformation 7]
41. ! [X0] : (((~happy(X0) & patient(X0)) | ((kind(X0) | ~humble(X0)) & (humble(X0) | ~kind(X0)))) & (((~humble(X0) | ~kind(X0)) & (humble(X0) | kind(X0))) | happy(X0) | ~patient(X0))) [flattening 40]
44. ! [X0] : (((~kind(X0) & ~old(X0)) | (wise(X0) & ~generous(X0))) & ((~wise(X0) | generous(X0)) | (kind(X0) | old(X0)))) [nnf transformation 9]
45. ! [X0] : (((~kind(X0) & ~old(X0)) | (wise(X0) & ~generous(X0))) & (~wise(X0) | generous(X0) | kind(X0) | old(X0))) [flattening 44]
68. ~curious(X0) | old(X0) | happy(X0) [cnf transformation 26]
78. happy(X0) | ~humble(X0) | happy(X0) | curious(X0) [cnf transformation 38]
89. ~humble(X0) | kind(X0) | ~happy(X0) [cnf transformation 41]
94. ~generous(X0) | ~old(X0) [cnf transformation 45]
96. ~generous(X0) | ~kind(X0) [cnf transformation 45]
99. humble(paul) | kind(X0) [cnf transformation 30]
101. generous(paul) | kind(X0) [cnf transformation 30]
123. ~kind(susan) [cnf transformation 24]
125. ~humble(X0) | happy(X0) | curious(X0) [duplicate literal removal 78]
155. 7 <=> ! [X0] : kind(X0) [avatar definition]
156. kind(X0) <- (7) [avatar component clause 155]
158. 8 <=> generous(paul) [avatar definition]
160. generous(paul) <- (8) [avatar component clause 158]
161. 7 | 8 [avatar split clause 101,158,155]
167. 10 <=> humble(paul) [avatar definition]
169. humble(paul) <- (10) [avatar component clause 167]
170. 7 | 10 [avatar split clause 99,167,155]
261. $false <- (7) [resolution 156,123]
262. ~7 [avatar contradiction clause 261]
265. ~old(paul) <- (8) [resolution 94,160]
268. ~kind(paul) <- (8) [resolution 96,160]
335. kind(paul) | ~happy(paul) <- (10) [resolution 89,169]
336. ~happy(paul) <- (8, 10) [subsumption resolution 335,268]
350. happy(paul) | curious(paul) <- (10) [resolution 125,169]
352. curious(paul) <- (8, 10) [subsumption resolution 350,336]
354. old(paul) | happy(paul) <- (8, 10) [resolution 352,68]
356. happy(paul) <- (8, 10) [subsumption resolution 354,265]
357. $false <- (8, 10) [subsumption resolution 356,336]
358. ~8 | ~10 [avatar contradiction clause 357]
359. $false [avatar sat refutation 161,170,262,358]
% SZS output end Proof for 6304271989167059167237538
% ------------------------------
% 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 not generous then paul is funny. Everyone who is both not humble and not strong is humble and vice versa. Everyone who is either wise or not generous is either funny or tall. If someone is both not wise and not rich then paul is both tall and rich. If paul is not quiet or kind then someone is happy or curious and vice versa. Everyone who is not patient or not wise is not curious or curious. Everyone who is both quiet and not patient is either tall or rich and vice versa. Everyone who is either tall or not old is not strong or not happy. If paul is either creative or happy then someone is either not humble or creative and vice versa. If mary is both patient and not curious then paul is not calm and vice versa. Everyone who is curious is both patient and old and vice versa. Everyone who is funny is either not strong or not happy and vice versa. If someone is either kind or not patient then someone is not old. If someone is either not quiet or rich then someone is not happy or generous and vice versa. If someone is not humble then someone is creative or funny and vice versa. Everyone who is either not curious or not tall is both strong and not tall and vice versa. Susan is not curious or rich. Someone is not curious or old. Alice is either not brave or not humble. Mary is not calm. Someone is either not quiet or funny. Someone is not wise or generous. Someone is funny. | Paul is not strong. | contradiction | ((?[X]:(~generous(X)))=>(funny(paul)))&
(![X]:((~humble(X)&~strong(X))<=>humble(X)))&
(![X]:((wise(X)<~>~generous(X))=>(funny(X)<~>tall(X))))&
((?[X]:((~wise(X)&~rich(X))))=>((tall(paul)&rich(paul))))&
(((~quiet(paul)|kind(paul)))<=>(?[X]:((happy(X)|curious(X)))))&
(![X]:((~patient(X)|~wise(X))=>(~curious(X)|curious(X))))&
(![X]:((quiet(X)&~patient(X))<=>(tall(X)<~>rich(X))))&
(![X]:((tall(X)<~>~old(X))=>(~strong(X)|~happy(X))))&
(((creative(paul)<~>happy(paul)))<=>(?[X]:((~humble(X)<~>creative(X)))))&
(((patient(mary)&~curious(mary)))<=>(~calm(paul)))&
(![X]:(curious(X)<=>(patient(X)&old(X))))&
(![X]:(funny(X)<=>(~strong(X)<~>~happy(X))))&
((?[X]:((kind(X)<~>~patient(X))))=>(?[X]:(~old(X))))&
((?[X]:((~quiet(X)<~>rich(X))))<=>(?[X]:((~happy(X)|generous(X)))))&
((?[X]:(~humble(X)))<=>(?[X]:((creative(X)|funny(X)))))&
(![X]:((~curious(X)<~>~tall(X))<=>(strong(X)&~tall(X))))&
((~curious(susan)|rich(susan)))&
(?[X]:((~curious(X)|old(X))))&
((~brave(alice)<~>~humble(alice)))&
(~calm(mary))&
(?[X]:((~quiet(X)<~>funny(X))))&
(?[X]:((~wise(X)|generous(X))))&
(?[X]:(funny(X))) | ~strong(paul) | [
"p1",
"hypothesis"
] | % SZS status Unsatisfiable for 1498839214249178884817778
% SZS output start Proof for 1498839214249178884817778
2. ! [X0] : ((~strong(X0) & ~humble(X0)) <=> humble(X0)) [input p1]
24. ~strong(paul) [input hypothesis]
36. ! [X0] : (((~strong(X0) & ~humble(X0)) | ~humble(X0)) & (humble(X0) | (strong(X0) | humble(X0)))) [nnf transformation 2]
37. ! [X0] : (((~strong(X0) & ~humble(X0)) | ~humble(X0)) & (humble(X0) | strong(X0) | humble(X0))) [flattening 36]
83. humble(X0) | strong(X0) | humble(X0) [cnf transformation 37]
84. ~humble(X0) | ~humble(X0) [cnf transformation 37]
150. ~strong(paul) [cnf transformation 24]
153. humble(X0) | strong(X0) [duplicate literal removal 83]
154. ~humble(X0) [duplicate literal removal 84]
163. strong(X0) [subsumption resolution 153,154]
324. $false [subsumption resolution 150,163]
% SZS output end Proof for 1498839214249178884817778
% ------------------------------
% 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 lucy is not funny or not calm then someone is either old or not strong.
Everyone who is not generous is humble.
If someone is either brave or not creative then susan is both not wise and not happy.
Everyone who is not patient is not creative or kind and vice versa.
Everyone who is not funny or not creative is curious and vice versa.
Everyone who is not rich or not happy is creative or not patient.
Everyone who is either not quiet or not calm is either not patient or calm and vice versa.
Everyone who is not happy or not curious is both not brave and generous.
Everyone who is both not creative and not happy is both not kind and funny and vice versa.
Everyone who is both funny and not brave is either not old or not strong.
If someone is not curious then someone is both quiet and patient.
If alice is both happy and funny then someone is patient.
Everyone who is either kind or not tall is rich and vice versa.
Everyone who is either not funny or brave is both not curious and not generous.
If someone is both happy and calm then alice is either not brave or curious and vice versa.
If someone is either not brave or generous then fred is quiet and vice versa.
Someone is either quiet or not funny.
Someone is funny.
Alice is either not tall or not patient.
Someone is both quiet and not creative.
Susan is not brave.
Someone is humble or calm.
Someone is creative.
Someone is not humble or not patient. | Susan is kind. | contradiction | (((~funny(lucy)|~calm(lucy)))=>(?[X]:((old(X)<~>~strong(X)))))&
(![X]:(~generous(X)=>humble(X)))&
((?[X]:((brave(X)<~>~creative(X))))=>((~wise(susan)&~happy(susan))))&
(![X]:(~patient(X)<=>(~creative(X)|kind(X))))&
(![X]:((~funny(X)|~creative(X))<=>curious(X)))&
(![X]:((~rich(X)|~happy(X))=>(creative(X)|~patient(X))))&
(![X]:((~quiet(X)<~>~calm(X))<=>(~patient(X)<~>calm(X))))&
(![X]:((~happy(X)|~curious(X))=>(~brave(X)&generous(X))))&
(![X]:((~creative(X)&~happy(X))<=>(~kind(X)&funny(X))))&
(![X]:((funny(X)&~brave(X))=>(~old(X)<~>~strong(X))))&
((?[X]:(~curious(X)))=>(?[X]:((quiet(X)&patient(X)))))&
(((happy(alice)&funny(alice)))=>(?[X]:(patient(X))))&
(![X]:((kind(X)<~>~tall(X))<=>rich(X)))&
(![X]:((~funny(X)<~>brave(X))=>(~curious(X)&~generous(X))))&
((?[X]:((happy(X)&calm(X))))<=>((~brave(alice)<~>curious(alice))))&
((?[X]:((~brave(X)<~>generous(X))))<=>(quiet(fred)))&
(?[X]:((quiet(X)<~>~funny(X))))&
(?[X]:(funny(X)))&
((~tall(alice)<~>~patient(alice)))&
(?[X]:((quiet(X)&~creative(X))))&
(~brave(susan))&
(?[X]:((humble(X)|calm(X))))&
(?[X]:(creative(X)))&
(?[X]:((~humble(X)|~patient(X)))) | kind(susan) | [
"p2",
"p4",
"p6",
"p7",
"p8",
"p10",
"p13",
"p20",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 5072565438644203671438600
% SZS output start Proof for 5072565438644203671438600
3. ? [X0] : (brave(X0) <~> ~creative(X0)) => (~happy(susan) & ~wise(susan)) [input p2]
5. ! [X0] : ((~creative(X0) | ~funny(X0)) <=> curious(X0)) [input p4]
7. ! [X0] : ((~quiet(X0) <~> ~calm(X0)) <=> (~patient(X0) <~> calm(X0))) [input p6]
8. ! [X0] : ((~curious(X0) | ~happy(X0)) => (generous(X0) & ~brave(X0))) [input p7]
9. ! [X0] : ((~happy(X0) & ~creative(X0)) <=> (funny(X0) & ~kind(X0))) [input p8]
11. ? [X0] : ~curious(X0) => ? [X0] : (patient(X0) & quiet(X0)) [input p10]
14. ! [X0] : ((~funny(X0) <~> brave(X0)) => (~generous(X0) & ~curious(X0))) [input p13]
21. ~brave(susan) [input p20]
23. ? [X0] : creative(X0) [input p22]
25. kind(susan) [input hypothesis]
26. ? [X0] : ~curious(X0) => ? [X1] : (patient(X1) & quiet(X1)) [rectify 11]
28. ? [X0] : (brave(X0) <~> ~creative(X0)) => ~happy(susan) [pure predicate removal 3]
31. ~happy(susan) | ! [X0] : (brave(X0) <=> ~creative(X0)) [ennf transformation 28]
34. ! [X0] : ((generous(X0) & ~brave(X0)) | (curious(X0) & happy(X0))) [ennf transformation 8]
37. ? [X1] : (patient(X1) & quiet(X1)) | ! [X0] : curious(X0) [ennf transformation 26]
41. ! [X0] : ((~generous(X0) & ~curious(X0)) | (~funny(X0) <=> brave(X0))) [ennf transformation 14]
45. ~happy(susan) | ! [X0] : ((brave(X0) | creative(X0)) & (~creative(X0) | ~brave(X0))) [nnf transformation 31]
48. ! [X0] : (((~creative(X0) | ~funny(X0)) | ~curious(X0)) & (curious(X0) | (creative(X0) & funny(X0)))) [nnf transformation 5]
49. ! [X0] : ((~creative(X0) | ~funny(X0) | ~curious(X0)) & (curious(X0) | (creative(X0) & funny(X0)))) [flattening 48]
50. ! [X0] : ((((calm(X0) | quiet(X0)) & (~calm(X0) | ~quiet(X0))) | ((~patient(X0) | ~calm(X0)) & (calm(X0) | patient(X0)))) & (((~calm(X0) | patient(X0)) & (calm(X0) | ~patient(X0))) | ((~quiet(X0) | calm(X0)) & (~calm(X0) | quiet(X0))))) [nnf transformation 7]
51. ! [X0] : (((~happy(X0) & ~creative(X0)) | (~funny(X0) | kind(X0))) & ((funny(X0) & ~kind(X0)) | (happy(X0) | creative(X0)))) [nnf transformation 9]
52. ! [X0] : (((~happy(X0) & ~creative(X0)) | ~funny(X0) | kind(X0)) & ((funny(X0) & ~kind(X0)) | happy(X0) | creative(X0))) [flattening 51]
54. ? [X0] : (patient(X0) & quiet(X0)) | ! [X1] : curious(X1) [rectify 37]
55. ? [X0] : (patient(X0) & quiet(X0)) => (patient(sK1) & quiet(sK1)) [choice axiom]
56. (patient(sK1) & quiet(sK1)) | ! [X1] : curious(X1) [skolemisation 54,55]
60. ! [X0] : ((~generous(X0) & ~curious(X0)) | ((~funny(X0) | ~brave(X0)) & (brave(X0) | funny(X0)))) [nnf transformation 41]
79. ? [X0] : creative(X0) => creative(sK9) [choice axiom]
80. creative(sK9) [skolemisation 23,79]
88. ~happy(susan) | ~creative(X0) | ~brave(X0) [cnf transformation 45]
89. ~happy(susan) | brave(X0) | creative(X0) [cnf transformation 45]
93. curious(X0) | funny(X0) [cnf transformation 49]
95. ~curious(X0) | ~funny(X0) | ~creative(X0) [cnf transformation 49]
99. calm(X0) | ~patient(X0) | ~quiet(X0) | calm(X0) [cnf transformation 50]
103. ~calm(X0) | ~quiet(X0) | ~patient(X0) | ~calm(X0) [cnf transformation 50]
107. ~brave(X0) | curious(X0) [cnf transformation 34]
110. ~kind(X0) | happy(X0) | creative(X0) [cnf transformation 52]
116. quiet(sK1) | curious(X1) [cnf transformation 56]
117. patient(sK1) | curious(X1) [cnf transformation 56]
121. ~curious(X0) | brave(X0) | funny(X0) [cnf transformation 60]
122. ~curious(X0) | ~funny(X0) | ~brave(X0) [cnf transformation 60]
142. ~brave(susan) [cnf transformation 21]
144. creative(sK9) [cnf transformation 80]
146. kind(susan) [cnf transformation 25]
147. calm(X0) | ~patient(X0) | ~quiet(X0) [duplicate literal removal 99]
149. ~quiet(X0) | ~calm(X0) | ~patient(X0) [duplicate literal removal 103]
172. 5 <=> ! [X0] : (brave(X0) | creative(X0)) [avatar definition]
173. creative(X0) | brave(X0) <- (5) [avatar component clause 172]
175. 6 <=> happy(susan) [avatar definition]
177. ~happy(susan) <- (~6) [avatar component clause 175]
178. 5 | ~6 [avatar split clause 89,175,172]
180. 7 <=> ! [X0] : (~creative(X0) | ~brave(X0)) [avatar definition]
181. ~creative(X0) | ~brave(X0) <- (7) [avatar component clause 180]
182. 7 | ~6 [avatar split clause 88,175,180]
184. ~quiet(X0) | ~patient(X0) [subsumption resolution 147,149]
186. 8 <=> ! [X1] : curious(X1) [avatar definition]
187. curious(X1) <- (8) [avatar component clause 186]
189. 9 <=> patient(sK1) [avatar definition]
191. patient(sK1) <- (9) [avatar component clause 189]
192. 8 | 9 [avatar split clause 117,189,186]
194. 10 <=> quiet(sK1) [avatar definition]
196. quiet(sK1) <- (10) [avatar component clause 194]
197. 8 | 10 [avatar split clause 116,194,186]
211. ~brave(X0) | ~funny(X0) [subsumption resolution 122,107]
212. brave(X0) | funny(X0) [subsumption resolution 121,93]
313. funny(susan) [resolution 212,142]
331. ~creative(X3) | ~funny(X3) <- (8) [resolution 95,187]
332. happy(susan) | creative(susan) [resolution 110,146]
333. creative(susan) <- (~6) [subsumption resolution 332,177]
376. ~funny(susan) <- (~6, 8) [resolution 331,333]
378. $false <- (~6, 8) [subsumption resolution 376,313]
379. 6 | ~8 [avatar contradiction clause 378]
387. brave(X0) | ~funny(X0) <- (5, 8) [resolution 173,331]
390. ~funny(X0) <- (5, 8) [subsumption resolution 387,211]
391. ~brave(sK9) <- (7) [resolution 181,144]
401. funny(sK9) <- (7) [resolution 391,212]
404. $false <- (5, 7, 8) [subsumption resolution 401,390]
405. ~5 | ~7 | ~8 [avatar contradiction clause 404]
414. ~patient(sK1) <- (10) [resolution 196,184]
416. $false <- (9, 10) [subsumption resolution 414,191]
417. ~9 | ~10 [avatar contradiction clause 416]
418. $false [avatar sat refutation 178,182,192,197,379,405,417]
% SZS output end Proof for 5072565438644203671438600
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either strong or not calm is both calm and funny and vice versa. Everyone who is either not wise or not patient is patient or curious and vice versa. If someone is not happy or tall then paul is not brave or happy. If someone is creative then alice is curious or not rich. If someone is either not humble or not quiet then fred is funny or not old. If someone is patient or rich then mary is either tall or kind. Everyone who is both not generous and not strong is both creative and not strong. If john is both curious and strong then alice is not generous or not brave. Everyone who is both calm and generous is either not kind or not happy and vice versa. Everyone who is not brave is both calm and strong and vice versa. If paul is strong or kind then someone is tall and vice versa. Everyone who is strong is tall and vice versa. Everyone who is either not wise or not quiet is either humble or tall and vice versa. If someone is quiet then john is either not tall or tall and vice versa. If john is either happy or not happy then mary is both humble and not kind and vice versa. Everyone who is old or funny is both strong and brave and vice versa. Someone is both patient and not quiet. Susan is not generous. Alice is either quiet or patient. Someone is not generous or creative. Fred is either not quiet or not happy. Paul is strong. Someone is funny. Mary is happy or wise. | Mary is not happy. | entailment | (![X]:((strong(X)<~>~calm(X))<=>(calm(X)&funny(X))))&
(![X]:((~wise(X)<~>~patient(X))<=>(patient(X)|curious(X))))&
((?[X]:((~happy(X)|tall(X))))=>((~brave(paul)|happy(paul))))&
((?[X]:(creative(X)))=>((curious(alice)|~rich(alice))))&
((?[X]:((~humble(X)<~>~quiet(X))))=>((funny(fred)|~old(fred))))&
((?[X]:((patient(X)|rich(X))))=>((tall(mary)<~>kind(mary))))&
(![X]:((~generous(X)&~strong(X))=>(creative(X)&~strong(X))))&
(((curious(john)&strong(john)))=>((~generous(alice)|~brave(alice))))&
(![X]:((calm(X)&generous(X))<=>(~kind(X)<~>~happy(X))))&
(![X]:(~brave(X)<=>(calm(X)&strong(X))))&
(((strong(paul)|kind(paul)))<=>(?[X]:(tall(X))))&
(![X]:(strong(X)<=>tall(X)))&
(![X]:((~wise(X)<~>~quiet(X))<=>(humble(X)<~>tall(X))))&
((?[X]:(quiet(X)))<=>((~tall(john)<~>tall(john))))&
(((happy(john)<~>~happy(john)))<=>((humble(mary)&~kind(mary))))&
(![X]:((old(X)|funny(X))<=>(strong(X)&brave(X))))&
(?[X]:((patient(X)&~quiet(X))))&
(~generous(susan))&
((quiet(alice)<~>patient(alice)))&
(?[X]:((~generous(X)|creative(X))))&
((~quiet(fred)<~>~happy(fred)))&
(strong(paul))&
(?[X]:(funny(X)))&
((happy(mary)|wise(mary))) | ~happy(mary) | [
"p0",
"p5",
"p8",
"p9",
"p11",
"p14",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 2241415115174440596602688
% SZS output start Proof for 2241415115174440596602688
1. ! [X0] : ((strong(X0) <~> ~calm(X0)) <=> (funny(X0) & calm(X0))) [input p0]
6. ? [X0] : (rich(X0) | patient(X0)) => (tall(mary) <~> kind(mary)) [input p5]
9. ! [X0] : ((generous(X0) & calm(X0)) <=> (~kind(X0) <~> ~happy(X0))) [input p8]
10. ! [X0] : (~brave(X0) <=> (strong(X0) & calm(X0))) [input p9]
12. ! [X0] : (strong(X0) <=> tall(X0)) [input p11]
15. (happy(john) <~> ~happy(john)) <=> (~kind(mary) & humble(mary)) [input p14]
16. ! [X0] : ((funny(X0) | old(X0)) <=> (brave(X0) & strong(X0))) [input p15]
17. ? [X0] : (~quiet(X0) & patient(X0)) [input p16]
25. happy(mary) [input hypothesis]
26. ? [X0] : patient(X0) => (tall(mary) <~> kind(mary)) [pure predicate removal 6]
34. (tall(mary) <~> kind(mary)) | ! [X0] : ~patient(X0) [ennf transformation 26]
39. ! [X0] : ((((calm(X0) | ~strong(X0)) & (~calm(X0) | strong(X0))) | (~funny(X0) | ~calm(X0))) & ((funny(X0) & calm(X0)) | ((strong(X0) | calm(X0)) & (~calm(X0) | ~strong(X0))))) [nnf transformation 1]
40. ! [X0] : ((((calm(X0) | ~strong(X0)) & (~calm(X0) | strong(X0))) | ~funny(X0) | ~calm(X0)) & ((funny(X0) & calm(X0)) | ((strong(X0) | calm(X0)) & (~calm(X0) | ~strong(X0))))) [flattening 39]
44. ((~kind(mary) | ~tall(mary)) & (kind(mary) | tall(mary))) | ! [X0] : ~patient(X0) [nnf transformation 34]
45. ! [X0] : (((generous(X0) & calm(X0)) | ((~kind(X0) | happy(X0)) & (~happy(X0) | kind(X0)))) & (((happy(X0) | kind(X0)) & (~happy(X0) | ~kind(X0))) | (~generous(X0) | ~calm(X0)))) [nnf transformation 9]
46. ! [X0] : (((generous(X0) & calm(X0)) | ((~kind(X0) | happy(X0)) & (~happy(X0) | kind(X0)))) & (((happy(X0) | kind(X0)) & (~happy(X0) | ~kind(X0))) | ~generous(X0) | ~calm(X0))) [flattening 45]
47. ! [X0] : ((~brave(X0) | (~strong(X0) | ~calm(X0))) & ((strong(X0) & calm(X0)) | brave(X0))) [nnf transformation 10]
48. ! [X0] : ((~brave(X0) | ~strong(X0) | ~calm(X0)) & ((strong(X0) & calm(X0)) | brave(X0))) [flattening 47]
54. ! [X0] : ((strong(X0) | ~tall(X0)) & (tall(X0) | ~strong(X0))) [nnf transformation 12]
60. (((happy(john) | ~happy(john)) & (~happy(john) | happy(john))) | (kind(mary) | ~humble(mary))) & ((~kind(mary) & humble(mary)) | ((happy(john) | happy(john)) & (~happy(john) | ~happy(john)))) [nnf transformation 15]
61. (((happy(john) | ~happy(john)) & (~happy(john) | happy(john))) | kind(mary) | ~humble(mary)) & ((~kind(mary) & humble(mary)) | ((happy(john) | happy(john)) & (~happy(john) | ~happy(john)))) [flattening 60]
62. ! [X0] : (((funny(X0) | old(X0)) | (~brave(X0) | ~strong(X0))) & ((brave(X0) & strong(X0)) | (~funny(X0) & ~old(X0)))) [nnf transformation 16]
63. ! [X0] : ((funny(X0) | old(X0) | ~brave(X0) | ~strong(X0)) & ((brave(X0) & strong(X0)) | (~funny(X0) & ~old(X0)))) [flattening 62]
64. ? [X0] : (~quiet(X0) & patient(X0)) => (~quiet(sK2) & patient(sK2)) [choice axiom]
65. ~quiet(sK2) & patient(sK2) [skolemisation 17,64]
72. ~calm(X0) | funny(X0) | ~strong(X0) [cnf transformation 40]
86. kind(mary) | tall(mary) | ~patient(X0) [cnf transformation 44]
92. ~happy(X0) | calm(X0) | kind(X0) [cnf transformation 46]
98. ~brave(X0) | ~strong(X0) | ~calm(X0) [cnf transformation 48]
103. ~tall(X0) | strong(X0) [cnf transformation 54]
118. ~kind(mary) | ~happy(john) | ~happy(john) [cnf transformation 61]
119. ~kind(mary) | happy(john) | happy(john) [cnf transformation 61]
125. ~funny(X0) | brave(X0) [cnf transformation 63]
127. patient(sK2) [cnf transformation 65]
137. happy(mary) [cnf transformation 25]
140. ~kind(mary) | ~happy(john) [duplicate literal removal 118]
141. ~kind(mary) | happy(john) [duplicate literal removal 119]
182. 9 <=> ! [X0] : ~patient(X0) [avatar definition]
183. ~patient(X0) <- (9) [avatar component clause 182]
185. 10 <=> tall(mary) [avatar definition]
186. tall(mary) <- (10) [avatar component clause 185]
189. 11 <=> kind(mary) [avatar definition]
191. ~kind(mary) <- (~11) [avatar component clause 189]
193. 9 | 10 | 11 [avatar split clause 86,189,185,182]
237. 21 <=> happy(john) [avatar definition]
240. 21 | ~11 [avatar split clause 141,189,237]
241. ~21 | ~11 [avatar split clause 140,189,237]
270. 27 <=> happy(mary) [avatar definition]
272. happy(mary) <- (27) [avatar component clause 270]
278. 27 [avatar split clause 137,270]
282. strong(mary) <- (10) [resolution 103,186]
312. calm(mary) | kind(mary) <- (27) [resolution 92,272]
314. calm(mary) <- (~11, 27) [subsumption resolution 312,191]
320. funny(mary) | ~strong(mary) <- (~11, 27) [resolution 314,72]
321. funny(mary) <- (10, ~11, 27) [subsumption resolution 320,282]
352. brave(mary) <- (10, ~11, 27) [resolution 321,125]
520. ~strong(mary) | ~calm(mary) <- (10, ~11, 27) [resolution 352,98]
521. ~calm(mary) <- (10, ~11, 27) [subsumption resolution 520,282]
522. $false <- (10, ~11, 27) [subsumption resolution 521,314]
523. ~10 | 11 | ~27 [avatar contradiction clause 522]
535. $false <- (9) [resolution 183,127]
538. ~9 [avatar contradiction clause 535]
539. $false [avatar sat refutation 193,240,241,278,523,538]
% SZS output end Proof for 2241415115174440596602688
% ------------------------------
% 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: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
If someone is creative then someone is either brave or generous. If someone is either rich or not happy then paul is either not kind or patient. If someone is both not old and humble then lucy is patient and vice versa. Everyone who is both not patient and funny is either not humble or wise. If paul is both not rich and not brave then someone is both not calm and calm and vice versa. If someone is both not creative and not rich then someone is happy and vice versa. If alice is either not curious or not humble then susan is not wise and vice versa. If someone is both patient and creative then lucy is both not funny and not old. If john is both not calm and creative then lucy is both strong and not calm and vice versa. Everyone who is both not kind and not old is both not tall and not rich. If someone is brave or happy then mary is either not generous or not tall and vice versa. If paul is both not patient and not wise then fred is not kind. Everyone who is not funny is either not calm or quiet. Everyone who is either brave or funny is either tall or not humble. Everyone who is both quiet and generous is kind and vice versa. Everyone who is generous or not strong is not funny or not quiet. Someone is not old. Someone is happy. Someone is both funny and rich. Someone is wise. Lucy is not curious or not quiet. Someone is not funny or kind. Fred is both brave and calm. Someone is either strong or not brave. | Paul is humble. | neutral | ((?[X]:(creative(X)))=>(?[X]:((brave(X)<~>generous(X)))))&
((?[X]:((rich(X)<~>~happy(X))))=>((~kind(paul)<~>patient(paul))))&
((?[X]:((~old(X)&humble(X))))<=>(patient(lucy)))&
(![X]:((~patient(X)&funny(X))=>(~humble(X)<~>wise(X))))&
(((~rich(paul)&~brave(paul)))<=>(?[X]:((~calm(X)&calm(X)))))&
((?[X]:((~creative(X)&~rich(X))))<=>(?[X]:(happy(X))))&
(((~curious(alice)<~>~humble(alice)))<=>(~wise(susan)))&
((?[X]:((patient(X)&creative(X))))=>((~funny(lucy)&~old(lucy))))&
(((~calm(john)&creative(john)))<=>((strong(lucy)&~calm(lucy))))&
(![X]:((~kind(X)&~old(X))=>(~tall(X)&~rich(X))))&
((?[X]:((brave(X)|happy(X))))<=>((~generous(mary)<~>~tall(mary))))&
(((~patient(paul)&~wise(paul)))=>(~kind(fred)))&
(![X]:(~funny(X)=>(~calm(X)<~>quiet(X))))&
(![X]:((brave(X)<~>funny(X))=>(tall(X)<~>~humble(X))))&
(![X]:((quiet(X)&generous(X))<=>kind(X)))&
(![X]:((generous(X)|~strong(X))=>(~funny(X)|~quiet(X))))&
(?[X]:(~old(X)))&
(?[X]:(happy(X)))&
(?[X]:((funny(X)&rich(X))))&
(?[X]:(wise(X)))&
((~curious(lucy)|~quiet(lucy)))&
(?[X]:((~funny(X)|kind(X))))&
((brave(fred)&calm(fred)))&
(?[X]:((strong(X)<~>~brave(X)))) | humble(paul) | [] | null | 0 |
If someone is not strong then someone is brave and vice versa. If fred is not brave then someone is wise and vice versa. If someone is kind then lucy is calm. Everyone who is both not calm and not funny is not old or happy. Everyone who is either not quiet or not wise is both tall and strong and vice versa. Everyone who is both not tall and tall is either not wise or humble. If someone is either old or quiet then john is creative or brave. Everyone who is not kind or not quiet is brave or kind and vice versa. Everyone who is rich is kind. Everyone who is either not happy or not rich is either not happy or not kind and vice versa. If fred is both not old and brave then someone is rich. Everyone who is either not brave or humble is happy or kind and vice versa. If paul is both wise and patient then someone is either rich or not generous. If someone is both kind and creative then paul is patient. Everyone who is both brave and strong is both patient and not humble. Everyone who is kind or not humble is both humble and tall. Someone is both funny and not calm. Paul is not funny or rich. Paul is either not patient or happy. Someone is not patient or not quiet. Someone is curious or not creative. Paul is both not happy and not funny. Someone is not happy or tall. | Lucy is old. | neutral | ((?[X]:(~strong(X)))<=>(?[X]:(brave(X))))&
((~brave(fred))<=>(?[X]:(wise(X))))&
((?[X]:(kind(X)))=>(calm(lucy)))&
(![X]:((~calm(X)&~funny(X))=>(~old(X)|happy(X))))&
(![X]:((~quiet(X)<~>~wise(X))<=>(tall(X)&strong(X))))&
(![X]:((~tall(X)&tall(X))=>(~wise(X)<~>humble(X))))&
((?[X]:((old(X)<~>quiet(X))))=>((creative(john)|brave(john))))&
(![X]:((~kind(X)|~quiet(X))<=>(brave(X)|kind(X))))&
(![X]:(rich(X)=>kind(X)))&
(![X]:((~happy(X)<~>~rich(X))<=>(~happy(X)<~>~kind(X))))&
(((~old(fred)&brave(fred)))=>(?[X]:(rich(X))))&
(![X]:((~brave(X)<~>humble(X))<=>(happy(X)|kind(X))))&
(((wise(paul)&patient(paul)))=>(?[X]:((rich(X)<~>~generous(X)))))&
((?[X]:((kind(X)&creative(X))))=>(patient(paul)))&
(![X]:((brave(X)&strong(X))=>(patient(X)&~humble(X))))&
(![X]:((kind(X)|~humble(X))=>(humble(X)&tall(X))))&
(?[X]:((funny(X)&~calm(X))))&
((~funny(paul)|rich(paul)))&
((~patient(paul)<~>happy(paul)))&
(?[X]:((~patient(X)|~quiet(X))))&
(?[X]:((curious(X)|~creative(X))))&
((~happy(paul)&~funny(paul)))&
(?[X]:((~happy(X)|tall(X)))) | old(lucy) | [] | null | 0 |
Everyone who is either happy or strong is not rich or wise and vice versa. If mary is both not funny and curious then someone is not funny or strong and vice versa. Everyone who is either calm or wise is tall and vice versa. Everyone who is both not curious and wise is not funny. Everyone who is not wise or not kind is quiet or not wise and vice versa. Everyone who is either humble or not curious is creative. Everyone who is both rich and curious is either old or funny and vice versa. Everyone who is not funny or not calm is funny or patient and vice versa. If paul is both kind and not kind then fred is both not kind and not calm. If someone is not kind or tall then john is not happy or kind. Everyone who is both brave and tall is not funny or creative and vice versa. If someone is old or not creative then someone is humble. Everyone who is not brave or kind is quiet or kind and vice versa. If lucy is both not patient and happy then someone is curious or not curious. If alice is not brave then susan is not wise and vice versa. Everyone who is either wise or tall is generous or rich and vice versa. Fred is not rich. Fred is happy. Someone is either generous or rich. Alice is both happy and not generous. John is not wise. Susan is either quiet or happy. Paul is calm or rich. Alice is both not creative and funny. | John is strong. | neutral | (![X]:((happy(X)<~>strong(X))<=>(~rich(X)|wise(X))))&
(((~funny(mary)&curious(mary)))<=>(?[X]:((~funny(X)|strong(X)))))&
(![X]:((calm(X)<~>wise(X))<=>tall(X)))&
(![X]:((~curious(X)&wise(X))=>~funny(X)))&
(![X]:((~wise(X)|~kind(X))<=>(quiet(X)|~wise(X))))&
(![X]:((humble(X)<~>~curious(X))=>creative(X)))&
(![X]:((rich(X)&curious(X))<=>(old(X)<~>funny(X))))&
(![X]:((~funny(X)|~calm(X))<=>(funny(X)|patient(X))))&
(((kind(paul)&~kind(paul)))=>((~kind(fred)&~calm(fred))))&
((?[X]:((~kind(X)|tall(X))))=>((~happy(john)|kind(john))))&
(![X]:((brave(X)&tall(X))<=>(~funny(X)|creative(X))))&
((?[X]:((old(X)|~creative(X))))=>(?[X]:(humble(X))))&
(![X]:((~brave(X)|kind(X))<=>(quiet(X)|kind(X))))&
(((~patient(lucy)&happy(lucy)))=>(?[X]:((curious(X)|~curious(X)))))&
((~brave(alice))<=>(~wise(susan)))&
(![X]:((wise(X)<~>tall(X))<=>(generous(X)|rich(X))))&
(~rich(fred))&
(happy(fred))&
(?[X]:((generous(X)<~>rich(X))))&
((happy(alice)&~generous(alice)))&
(~wise(john))&
((quiet(susan)<~>happy(susan)))&
((calm(paul)|rich(paul)))&
((~creative(alice)&funny(alice))) | strong(john) | [] | null | 0 |
Everyone who is either not patient or not generous is rich or not wise. Everyone who is either not quiet or not kind is not generous and vice versa. Everyone who is not patient or not tall is generous. If someone is either not humble or curious then someone is both not brave and not humble. If fred is creative or not creative then fred is both not calm and brave and vice versa. Everyone who is both tall and not generous is either calm or funny and vice versa. If someone is curious then someone is both not old and not wise and vice versa. Everyone who is either patient or rich is both rich and not rich. Everyone who is tall or old is either not generous or not calm. If someone is not humble then someone is both funny and not wise. If someone is both wise and not tall then susan is not happy. Everyone who is not calm or strong is both not quiet and not rich. Everyone who is not old is not quiet or patient. If someone is both not happy and not kind then lucy is both old and not strong and vice versa. If someone is either not tall or not brave then someone is both not generous and calm and vice versa. If someone is either wise or kind then someone is both brave and not quiet and vice versa. Someone is both curious and old. Someone is both curious and not rich. Someone is either not old or creative. Mary is not old. Someone is both humble and wise. John is not calm or rich. Someone is either happy or patient. | Fred is not curious. | neutral | (![X]:((~patient(X)<~>~generous(X))=>(rich(X)|~wise(X))))&
(![X]:((~quiet(X)<~>~kind(X))<=>~generous(X)))&
(![X]:((~patient(X)|~tall(X))=>generous(X)))&
((?[X]:((~humble(X)<~>curious(X))))=>(?[X]:((~brave(X)&~humble(X)))))&
(((creative(fred)|~creative(fred)))<=>((~calm(fred)&brave(fred))))&
(![X]:((tall(X)&~generous(X))<=>(calm(X)<~>funny(X))))&
((?[X]:(curious(X)))<=>(?[X]:((~old(X)&~wise(X)))))&
(![X]:((patient(X)<~>rich(X))=>(rich(X)&~rich(X))))&
(![X]:((tall(X)|old(X))=>(~generous(X)<~>~calm(X))))&
((?[X]:(~humble(X)))=>(?[X]:((funny(X)&~wise(X)))))&
((?[X]:((wise(X)&~tall(X))))=>(~happy(susan)))&
(![X]:((~calm(X)|strong(X))=>(~quiet(X)&~rich(X))))&
(![X]:(~old(X)=>(~quiet(X)|patient(X))))&
((?[X]:((~happy(X)&~kind(X))))<=>((old(lucy)&~strong(lucy))))&
((?[X]:((~tall(X)<~>~brave(X))))<=>(?[X]:((~generous(X)&calm(X)))))&
((?[X]:((wise(X)<~>kind(X))))<=>(?[X]:((brave(X)&~quiet(X)))))&
(?[X]:((curious(X)&old(X))))&
(?[X]:((curious(X)&~rich(X))))&
(?[X]:((~old(X)<~>creative(X))))&
(~old(mary))&
(?[X]:((humble(X)&wise(X))))&
((~calm(john)|rich(john)))&
(?[X]:((happy(X)<~>patient(X)))) | ~curious(fred) | [] | null | 0 |
If paul is both funny and not generous then susan is either wise or creative. Everyone who is kind is both not calm and tall and vice versa. Everyone who is not brave or creative is not happy. Everyone who is both brave and rich is quiet or not old and vice versa. Everyone who is both not quiet and funny is quiet or humble. Everyone who is not quiet or calm is creative or not patient and vice versa. If mary is not generous then someone is not old and vice versa. Everyone who is old is quiet. Everyone who is not strong or generous is not happy. If fred is either old or wise then alice is both not calm and not happy. If john is either happy or not brave then someone is not curious or not rich and vice versa. If alice is either creative or not wise then someone is curious and vice versa. Everyone who is rich is not strong or not humble. Everyone who is both strong and rich is not generous or not kind. If susan is funny then someone is not wise or happy and vice versa. Everyone who is both not curious and humble is old or not strong and vice versa. Lucy is either humble or not wise. Alice is both brave and not creative. Someone is either old or not calm. | Alice is calm. | neutral | (((funny(paul)&~generous(paul)))=>((wise(susan)<~>creative(susan))))&
(![X]:(kind(X)<=>(~calm(X)&tall(X))))&
(![X]:((~brave(X)|creative(X))=>~happy(X)))&
(![X]:((brave(X)&rich(X))<=>(quiet(X)|~old(X))))&
(![X]:((~quiet(X)&funny(X))=>(quiet(X)|humble(X))))&
(![X]:((~quiet(X)|calm(X))<=>(creative(X)|~patient(X))))&
((~generous(mary))<=>(?[X]:(~old(X))))&
(![X]:(old(X)=>quiet(X)))&
(![X]:((~strong(X)|generous(X))=>~happy(X)))&
(((old(fred)<~>wise(fred)))=>((~calm(alice)&~happy(alice))))&
(((happy(john)<~>~brave(john)))<=>(?[X]:((~curious(X)|~rich(X)))))&
(((creative(alice)<~>~wise(alice)))<=>(?[X]:(curious(X))))&
(![X]:(rich(X)=>(~strong(X)|~humble(X))))&
(![X]:((strong(X)&rich(X))=>(~generous(X)|~kind(X))))&
((funny(susan))<=>(?[X]:((~wise(X)|happy(X)))))&
(![X]:((~curious(X)&humble(X))<=>(old(X)|~strong(X))))&
((humble(lucy)<~>~wise(lucy)))&
((brave(alice)&~creative(alice)))&
(?[X]:((old(X)<~>~calm(X)))) | calm(alice) | [] | null | 0 |
Everyone who is not creative or quiet is both not creative and quiet and vice versa. Everyone who is brave or not wise is both not rich and creative and vice versa. Everyone who is curious is either curious or humble and vice versa. If alice is either not creative or curious then mary is quiet. If someone is either not humble or not kind then lucy is both generous and not quiet and vice versa. Everyone who is both calm and strong is both quiet and wise. If lucy is both rich and not generous then paul is either creative or not tall and vice versa. If someone is rich then paul is both not old and strong. If someone is not creative or wise then fred is humble. Everyone who is not kind or funny is either patient or tall and vice versa. If alice is not patient then someone is brave. Everyone who is either not funny or funny is either not kind or quiet and vice versa. If lucy is both funny and tall then someone is either quiet or kind. If fred is humble then john is both brave and happy and vice versa. If lucy is either rich or brave then john is both not strong and humble and vice versa. If mary is calm then fred is either kind or rich. Someone is both brave and not rich. Someone is happy or not humble. Someone is not generous. Susan is not old or generous. Someone is either strong or funny. Susan is either not calm or funny. | Fred is funny. | neutral | (![X]:((~creative(X)|quiet(X))<=>(~creative(X)&quiet(X))))&
(![X]:((brave(X)|~wise(X))<=>(~rich(X)&creative(X))))&
(![X]:(curious(X)<=>(curious(X)<~>humble(X))))&
(((~creative(alice)<~>curious(alice)))=>(quiet(mary)))&
((?[X]:((~humble(X)<~>~kind(X))))<=>((generous(lucy)&~quiet(lucy))))&
(![X]:((calm(X)&strong(X))=>(quiet(X)&wise(X))))&
(((rich(lucy)&~generous(lucy)))<=>((creative(paul)<~>~tall(paul))))&
((?[X]:(rich(X)))=>((~old(paul)&strong(paul))))&
((?[X]:((~creative(X)|wise(X))))=>(humble(fred)))&
(![X]:((~kind(X)|funny(X))<=>(patient(X)<~>tall(X))))&
((~patient(alice))=>(?[X]:(brave(X))))&
(![X]:((~funny(X)<~>funny(X))<=>(~kind(X)<~>quiet(X))))&
(((funny(lucy)&tall(lucy)))=>(?[X]:((quiet(X)<~>kind(X)))))&
((humble(fred))<=>((brave(john)&happy(john))))&
(((rich(lucy)<~>brave(lucy)))<=>((~strong(john)&humble(john))))&
((calm(mary))=>((kind(fred)<~>rich(fred))))&
(?[X]:((brave(X)&~rich(X))))&
(?[X]:((happy(X)|~humble(X))))&
(?[X]:(~generous(X)))&
((~old(susan)|generous(susan)))&
(?[X]:((strong(X)<~>funny(X))))&
((~calm(susan)<~>funny(susan))) | funny(fred) | [] | null | 0 |
If someone is either strong or happy then fred is not calm and vice versa.
If someone is rich then someone is both not funny and strong and vice versa.
Everyone who is not curious is either not kind or happy and vice versa.
Everyone who is not quiet or not humble is wise.
If someone is either not happy or calm then someone is kind or creative.
If someone is both brave and not patient then someone is both calm and brave and vice versa.
If lucy is both happy and not generous then lucy is both not funny and wise.
Everyone who is not strong or brave is not humble and vice versa.
If someone is brave or not wise then someone is not calm or not creative.
If someone is not calm then someone is humble or not calm.
If alice is brave or generous then someone is both humble and not happy.
Everyone who is either not tall or kind is curious.
Everyone who is both not curious and old is both curious and not strong.
If lucy is either funny or curious then someone is generous and vice versa.
If someone is kind or not curious then lucy is both not curious and humble and vice versa.
Everyone who is patient is both not patient and quiet and vice versa.
Someone is either quiet or not rich.
John is either not funny or generous.
Paul is both not calm and not rich.
Alice is not generous or brave.
Susan is both strong and not kind.
Someone is rich or funny.
Someone is not happy or curious. | John is quiet. | contradiction | ((?[X]:((strong(X)<~>happy(X))))<=>(~calm(fred)))&
((?[X]:(rich(X)))<=>(?[X]:((~funny(X)&strong(X)))))&
(![X]:(~curious(X)<=>(~kind(X)<~>happy(X))))&
(![X]:((~quiet(X)|~humble(X))=>wise(X)))&
((?[X]:((~happy(X)<~>calm(X))))=>(?[X]:((kind(X)|creative(X)))))&
((?[X]:((brave(X)&~patient(X))))<=>(?[X]:((calm(X)&brave(X)))))&
(((happy(lucy)&~generous(lucy)))=>((~funny(lucy)&wise(lucy))))&
(![X]:((~strong(X)|brave(X))<=>~humble(X)))&
((?[X]:((brave(X)|~wise(X))))=>(?[X]:((~calm(X)|~creative(X)))))&
((?[X]:(~calm(X)))=>(?[X]:((humble(X)|~calm(X)))))&
(((brave(alice)|generous(alice)))=>(?[X]:((humble(X)&~happy(X)))))&
(![X]:((~tall(X)<~>kind(X))=>curious(X)))&
(![X]:((~curious(X)&old(X))=>(curious(X)&~strong(X))))&
(((funny(lucy)<~>curious(lucy)))<=>(?[X]:(generous(X))))&
((?[X]:((kind(X)|~curious(X))))<=>((~curious(lucy)&humble(lucy))))&
(![X]:(patient(X)<=>(~patient(X)&quiet(X))))&
(?[X]:((quiet(X)<~>~rich(X))))&
((~funny(john)<~>generous(john)))&
((~calm(paul)&~rich(paul)))&
((~generous(alice)|brave(alice)))&
((strong(susan)&~kind(susan)))&
(?[X]:((rich(X)|funny(X))))&
(?[X]:((~happy(X)|curious(X)))) | quiet(john) | [
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4442738788318995870115096
% SZS output start Proof for 4442738788318995870115096
16. ! [X0] : (patient(X0) <=> (quiet(X0) & ~patient(X0))) [input p15]
24. quiet(john) [input hypothesis]
80. ! [X0] : ((patient(X0) | (~quiet(X0) | patient(X0))) & ((quiet(X0) & ~patient(X0)) | ~patient(X0))) [nnf transformation 16]
81. ! [X0] : ((patient(X0) | ~quiet(X0) | patient(X0)) & ((quiet(X0) & ~patient(X0)) | ~patient(X0))) [flattening 80]
128. ~patient(X0) | ~patient(X0) [cnf transformation 81]
130. patient(X0) | ~quiet(X0) | patient(X0) [cnf transformation 81]
142. quiet(john) [cnf transformation 24]
143. ~patient(X0) [duplicate literal removal 128]
144. ~quiet(X0) | patient(X0) [duplicate literal removal 130]
370. patient(john) [resolution 144,142]
371. $false [subsumption resolution 370,143]
% SZS output end Proof for 4442738788318995870115096
% ------------------------------
% 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 calm and not rich is patient or not kind.
If someone is not rich or not generous then fred is not brave or patient and vice versa.
If someone is not brave or not rich then fred is either not rich or not curious.
Everyone who is calm is humble or strong and vice versa.
Everyone who is calm or happy is not quiet or wise and vice versa.
If lucy is either not old or not calm then alice is both not brave and not curious and vice versa.
Everyone who is either not humble or funny is rich or not tall and vice versa.
If someone is old then paul is strong and vice versa.
If someone is either rich or curious then lucy is both quiet and humble and vice versa.
If lucy is funny or not calm then fred is either not curious or happy.
If susan is not curious or wise then mary is both not generous and funny and vice versa.
Everyone who is not strong or humble is not curious or brave and vice versa.
Everyone who is humble is either calm or generous.
Everyone who is both happy and rich is humble.
Everyone who is either not curious or not old is either quiet or not strong.
Everyone who is quiet is both not generous and curious.
Paul is funny.
Someone is brave.
Alice is either calm or humble.
Someone is both not wise and not tall.
John is kind or not wise.
Someone is old.
Someone is wise or not funny. | Fred is patient. | neutral | (![X]:((~calm(X)&~rich(X))=>(patient(X)|~kind(X))))&
((?[X]:((~rich(X)|~generous(X))))<=>((~brave(fred)|patient(fred))))&
((?[X]:((~brave(X)|~rich(X))))=>((~rich(fred)<~>~curious(fred))))&
(![X]:(calm(X)<=>(humble(X)|strong(X))))&
(![X]:((calm(X)|happy(X))<=>(~quiet(X)|wise(X))))&
(((~old(lucy)<~>~calm(lucy)))<=>((~brave(alice)&~curious(alice))))&
(![X]:((~humble(X)<~>funny(X))<=>(rich(X)|~tall(X))))&
((?[X]:(old(X)))<=>(strong(paul)))&
((?[X]:((rich(X)<~>curious(X))))<=>((quiet(lucy)&humble(lucy))))&
(((funny(lucy)|~calm(lucy)))=>((~curious(fred)<~>happy(fred))))&
(((~curious(susan)|wise(susan)))<=>((~generous(mary)&funny(mary))))&
(![X]:((~strong(X)|humble(X))<=>(~curious(X)|brave(X))))&
(![X]:(humble(X)=>(calm(X)<~>generous(X))))&
(![X]:((happy(X)&rich(X))=>humble(X)))&
(![X]:((~curious(X)<~>~old(X))=>(quiet(X)<~>~strong(X))))&
(![X]:(quiet(X)=>(~generous(X)&curious(X))))&
(funny(paul))&
(?[X]:(brave(X)))&
((calm(alice)<~>humble(alice)))&
(?[X]:((~wise(X)&~tall(X))))&
((kind(john)|~wise(john)))&
(?[X]:(old(X)))&
(?[X]:((wise(X)|~funny(X)))) | patient(fred) | [] | null | 0 |
If paul is both curious and rich then john is not happy or not humble and vice versa.
Everyone who is calm or not creative is both patient and not kind.
Everyone who is both not funny and not brave is creative or not tall and vice versa.
If fred is both not happy and not tall then someone is either kind or happy and vice versa.
If john is both tall and rich then someone is both not humble and funny and vice versa.
Everyone who is both not calm and old is either happy or calm and vice versa.
If someone is not humble or tall then someone is both strong and not patient and vice versa.
If someone is both not strong and brave then someone is either not quiet or not old.
If susan is both not generous and not patient then john is both quiet and curious.
If someone is both happy and funny then someone is calm.
If fred is both creative and curious then lucy is not strong or not funny and vice versa.
If someone is both happy and not old then mary is not kind or brave and vice versa.
Everyone who is brave is both not quiet and not old and vice versa.
Everyone who is funny or curious is brave or not creative and vice versa.
Everyone who is both curious and creative is not rich and vice versa.
Everyone who is both kind and not curious is old or happy.
Someone is old.
Fred is strong.
Alice is both humble and not happy.
Susan is either not tall or not patient.
John is humble or rich.
John is rich or not brave.
Lucy is either old or creative. | Fred is not happy. | entailment | (((curious(paul)&rich(paul)))<=>((~happy(john)|~humble(john))))&
(![X]:((calm(X)|~creative(X))=>(patient(X)&~kind(X))))&
(![X]:((~funny(X)&~brave(X))<=>(creative(X)|~tall(X))))&
(((~happy(fred)&~tall(fred)))<=>(?[X]:((kind(X)<~>happy(X)))))&
(((tall(john)&rich(john)))<=>(?[X]:((~humble(X)&funny(X)))))&
(![X]:((~calm(X)&old(X))<=>(happy(X)<~>calm(X))))&
((?[X]:((~humble(X)|tall(X))))<=>(?[X]:((strong(X)&~patient(X)))))&
((?[X]:((~strong(X)&brave(X))))=>(?[X]:((~quiet(X)<~>~old(X)))))&
(((~generous(susan)&~patient(susan)))=>((quiet(john)&curious(john))))&
((?[X]:((happy(X)&funny(X))))=>(?[X]:(calm(X))))&
(((creative(fred)&curious(fred)))<=>((~strong(lucy)|~funny(lucy))))&
((?[X]:((happy(X)&~old(X))))<=>((~kind(mary)|brave(mary))))&
(![X]:(brave(X)<=>(~quiet(X)&~old(X))))&
(![X]:((funny(X)|curious(X))<=>(brave(X)|~creative(X))))&
(![X]:((curious(X)&creative(X))<=>~rich(X)))&
(![X]:((kind(X)&~curious(X))=>(old(X)|happy(X))))&
(?[X]:(old(X)))&
(strong(fred))&
((humble(alice)&~happy(alice)))&
((~tall(susan)<~>~patient(susan)))&
((humble(john)|rich(john)))&
((rich(john)|~brave(john)))&
((old(lucy)<~>creative(lucy))) | ~happy(fred) | [
"p1",
"p2",
"p3",
"p5",
"p10",
"p13",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 6119905981776661238353137
% SZS output start Proof for 6119905981776661238353137
2. ! [X0] : ((~creative(X0) | calm(X0)) => (~kind(X0) & patient(X0))) [input p1]
3. ! [X0] : ((~brave(X0) & ~funny(X0)) <=> (~tall(X0) | creative(X0))) [input p2]
4. (~tall(fred) & ~happy(fred)) <=> ? [X0] : (kind(X0) <~> happy(X0)) [input p3]
6. ! [X0] : ((old(X0) & ~calm(X0)) <=> (happy(X0) <~> calm(X0))) [input p5]
11. (curious(fred) & creative(fred)) <=> (~funny(lucy) | ~strong(lucy)) [input p10]
14. ! [X0] : ((curious(X0) | funny(X0)) <=> (~creative(X0) | brave(X0))) [input p13]
23. old(lucy) <~> creative(lucy) [input p22]
24. happy(fred) [input hypothesis]
29. ! [X0] : ((~kind(X0) & patient(X0)) | (creative(X0) & ~calm(X0))) [ennf transformation 2]
36. ! [X0] : (((~brave(X0) & ~funny(X0)) | (tall(X0) & ~creative(X0))) & ((~tall(X0) | creative(X0)) | (brave(X0) | funny(X0)))) [nnf transformation 3]
37. ! [X0] : (((~brave(X0) & ~funny(X0)) | (tall(X0) & ~creative(X0))) & (~tall(X0) | creative(X0) | brave(X0) | funny(X0))) [flattening 36]
38. ((~tall(fred) & ~happy(fred)) | ! [X0] : ((kind(X0) | ~happy(X0)) & (happy(X0) | ~kind(X0)))) & (? [X0] : ((~happy(X0) | ~kind(X0)) & (happy(X0) | kind(X0))) | (tall(fred) | happy(fred))) [nnf transformation 4]
39. ((~tall(fred) & ~happy(fred)) | ! [X0] : ((kind(X0) | ~happy(X0)) & (happy(X0) | ~kind(X0)))) & (? [X0] : ((~happy(X0) | ~kind(X0)) & (happy(X0) | kind(X0))) | tall(fred) | happy(fred)) [flattening 38]
40. ((~tall(fred) & ~happy(fred)) | ! [X0] : ((kind(X0) | ~happy(X0)) & (happy(X0) | ~kind(X0)))) & (? [X1] : ((~happy(X1) | ~kind(X1)) & (happy(X1) | kind(X1))) | tall(fred) | happy(fred)) [rectify 39]
41. ? [X1] : ((~happy(X1) | ~kind(X1)) & (happy(X1) | kind(X1))) => ((~happy(sK0) | ~kind(sK0)) & (happy(sK0) | kind(sK0))) [choice axiom]
42. ((~tall(fred) & ~happy(fred)) | ! [X0] : ((kind(X0) | ~happy(X0)) & (happy(X0) | ~kind(X0)))) & (((~happy(sK0) | ~kind(sK0)) & (happy(sK0) | kind(sK0))) | tall(fred) | happy(fred)) [skolemisation 40,41]
48. ! [X0] : (((old(X0) & ~calm(X0)) | ((happy(X0) | ~calm(X0)) & (calm(X0) | ~happy(X0)))) & (((~calm(X0) | ~happy(X0)) & (calm(X0) | happy(X0))) | (~old(X0) | calm(X0)))) [nnf transformation 6]
49. ! [X0] : (((old(X0) & ~calm(X0)) | ((happy(X0) | ~calm(X0)) & (calm(X0) | ~happy(X0)))) & (((~calm(X0) | ~happy(X0)) & (calm(X0) | happy(X0))) | ~old(X0) | calm(X0))) [flattening 48]
62. ((curious(fred) & creative(fred)) | (funny(lucy) & strong(lucy))) & ((~funny(lucy) | ~strong(lucy)) | (~curious(fred) | ~creative(fred))) [nnf transformation 11]
63. ((curious(fred) & creative(fred)) | (funny(lucy) & strong(lucy))) & (~funny(lucy) | ~strong(lucy) | ~curious(fred) | ~creative(fred)) [flattening 62]
71. ! [X0] : (((curious(X0) | funny(X0)) | (creative(X0) & ~brave(X0))) & ((~creative(X0) | brave(X0)) | (~curious(X0) & ~funny(X0)))) [nnf transformation 14]
72. ! [X0] : ((curious(X0) | funny(X0) | (creative(X0) & ~brave(X0))) & (~creative(X0) | brave(X0) | (~curious(X0) & ~funny(X0)))) [flattening 71]
78. (~creative(lucy) | ~old(lucy)) & (creative(lucy) | old(lucy)) [nnf transformation 23]
87. ~kind(X0) | creative(X0) [cnf transformation 29]
89. ~funny(X0) | ~creative(X0) [cnf transformation 37]
91. ~brave(X0) | ~creative(X0) [cnf transformation 37]
96. ~happy(fred) | kind(X0) | ~happy(X0) [cnf transformation 42]
103. calm(X0) | happy(X0) | ~old(X0) | calm(X0) [cnf transformation 49]
106. ~calm(X0) | happy(X0) | ~calm(X0) [cnf transformation 49]
121. curious(fred) | funny(lucy) [cnf transformation 63]
131. ~creative(X0) | brave(X0) | ~curious(X0) [cnf transformation 72]
146. creative(lucy) | old(lucy) [cnf transformation 78]
148. happy(fred) [cnf transformation 24]
149. calm(X0) | happy(X0) | ~old(X0) [duplicate literal removal 103]
150. ~calm(X0) | happy(X0) [duplicate literal removal 106]
173. 5 <=> ! [X0] : (kind(X0) | ~happy(X0)) [avatar definition]
174. ~happy(X0) | kind(X0) <- (5) [avatar component clause 173]
185. 8 <=> happy(fred) [avatar definition]
186. happy(fred) <- (8) [avatar component clause 185]
188. 5 | ~8 [avatar split clause 96,185,173]
223. ~old(X0) | happy(X0) [subsumption resolution 149,150]
276. 28 <=> funny(lucy) [avatar definition]
278. funny(lucy) <- (28) [avatar component clause 276]
280. 29 <=> curious(fred) [avatar definition]
283. 28 | 29 [avatar split clause 121,280,276]
290. 31 <=> creative(fred) [avatar definition]
292. creative(fred) <- (31) [avatar component clause 290]
320. ~creative(X0) | ~curious(X0) [subsumption resolution 131,91]
339. 40 <=> old(lucy) [avatar definition]
340. old(lucy) <- (40) [avatar component clause 339]
343. 41 <=> creative(lucy) [avatar definition]
345. ~creative(lucy) <- (~41) [avatar component clause 343]
347. 40 | 41 [avatar split clause 146,343,339]
348. 8 [avatar split clause 148,185]
355. ~creative(lucy) <- (28) [resolution 89,278]
363. kind(fred) <- (5, 8) [resolution 174,186]
365. creative(fred) <- (5, 8) [resolution 363,87]
367. 31 | ~5 | ~8 [avatar split clause 365,185,173,290]
373. happy(lucy) <- (40) [resolution 223,340]
381. kind(lucy) <- (5, 40) [resolution 373,174]
389. ~curious(fred) <- (31) [resolution 320,292]
451. creative(lucy) <- (5, 40) [resolution 381,87]
453. $false <- (5, 40, ~41) [subsumption resolution 451,345]
454. ~5 | ~40 | 41 [avatar contradiction clause 453]
455. ~41 | ~28 [avatar split clause 355,276,343]
456. ~29 | ~31 [avatar split clause 389,290,280]
457. $false [avatar sat refutation 188,283,347,348,367,454,455,456]
% SZS output end Proof for 6119905981776661238353137
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both happy and not funny is not patient or not humble. If john is either wise or not kind then john is not patient. Everyone who is curious is not humble and vice versa. Everyone who is not humble is either rich or not humble. If john is wise or not brave then lucy is not humble. Everyone who is both happy and wise is either not calm or old and vice versa. If someone is not happy then mary is either tall or kind and vice versa. If fred is both happy and not happy then someone is patient or not brave. Everyone who is not patient or not funny is either not wise or not patient and vice versa. Everyone who is either not kind or tall is not generous. Everyone who is not quiet is either rich or not old and vice versa. Everyone who is both funny and calm is not wise or humble and vice versa. If paul is either strong or not old then someone is not funny. Everyone who is not tall is both not wise and not funny and vice versa. If someone is both strong and happy then paul is either happy or wise. Everyone who is curious is patient. Susan is not old. Someone is not patient or tall. Lucy is not brave. Someone is either old or rich. Someone is either kind or not patient. Someone is not patient or patient. Someone is kind. Someone is not quiet or humble. | Mary is not funny. | contradiction | (![X]:((happy(X)&~funny(X))=>(~patient(X)|~humble(X))))&
(((wise(john)<~>~kind(john)))=>(~patient(john)))&
(![X]:(curious(X)<=>~humble(X)))&
(![X]:(~humble(X)=>(rich(X)<~>~humble(X))))&
(((wise(john)|~brave(john)))=>(~humble(lucy)))&
(![X]:((happy(X)&wise(X))<=>(~calm(X)<~>old(X))))&
((?[X]:(~happy(X)))<=>((tall(mary)<~>kind(mary))))&
(((happy(fred)&~happy(fred)))=>(?[X]:((patient(X)|~brave(X)))))&
(![X]:((~patient(X)|~funny(X))<=>(~wise(X)<~>~patient(X))))&
(![X]:((~kind(X)<~>tall(X))=>~generous(X)))&
(![X]:(~quiet(X)<=>(rich(X)<~>~old(X))))&
(![X]:((funny(X)&calm(X))<=>(~wise(X)|humble(X))))&
(((strong(paul)<~>~old(paul)))=>(?[X]:(~funny(X))))&
(![X]:(~tall(X)<=>(~wise(X)&~funny(X))))&
((?[X]:((strong(X)&happy(X))))=>((happy(paul)<~>wise(paul))))&
(![X]:(curious(X)=>patient(X)))&
(~old(susan))&
(?[X]:((~patient(X)|tall(X))))&
(~brave(lucy))&
(?[X]:((old(X)<~>rich(X))))&
(?[X]:((kind(X)<~>~patient(X))))&
(?[X]:((~patient(X)|patient(X))))&
(?[X]:(kind(X)))&
(?[X]:((~quiet(X)|humble(X)))) | ~funny(mary) | [
"p2",
"p8",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3065525193048875834444967
% SZS output start Proof for 3065525193048875834444967
3. ! [X0] : (curious(X0) <=> ~humble(X0)) [input p2]
9. ! [X0] : ((~funny(X0) | ~patient(X0)) <=> (~wise(X0) <~> ~patient(X0))) [input p8]
12. ! [X0] : ((calm(X0) & funny(X0)) <=> (humble(X0) | ~wise(X0))) [input p11]
16. ! [X0] : (curious(X0) => patient(X0)) [input p15]
25. ~funny(mary) [input hypothesis]
27. ! [X0] : (~humble(X0) => curious(X0)) [unused predicate definition removal 3]
32. ! [X0] : (curious(X0) | humble(X0)) [ennf transformation 27]
40. ! [X0] : (patient(X0) | ~curious(X0)) [ennf transformation 16]
51. ! [X0] : (((~funny(X0) | ~patient(X0)) | ((~wise(X0) | patient(X0)) & (~patient(X0) | wise(X0)))) & (((patient(X0) | wise(X0)) & (~patient(X0) | ~wise(X0))) | (funny(X0) & patient(X0)))) [nnf transformation 9]
52. ! [X0] : ((~funny(X0) | ~patient(X0) | ((~wise(X0) | patient(X0)) & (~patient(X0) | wise(X0)))) & (((patient(X0) | wise(X0)) & (~patient(X0) | ~wise(X0))) | (funny(X0) & patient(X0)))) [flattening 51]
54. ! [X0] : (((calm(X0) & funny(X0)) | (~humble(X0) & wise(X0))) & ((humble(X0) | ~wise(X0)) | (~calm(X0) | ~funny(X0)))) [nnf transformation 12]
55. ! [X0] : (((calm(X0) & funny(X0)) | (~humble(X0) & wise(X0))) & (humble(X0) | ~wise(X0) | ~calm(X0) | ~funny(X0))) [flattening 54]
79. curious(X0) | humble(X0) [cnf transformation 32]
96. ~wise(X0) | ~patient(X0) | funny(X0) [cnf transformation 52]
104. wise(X0) | funny(X0) [cnf transformation 55]
105. ~humble(X0) | funny(X0) [cnf transformation 55]
115. ~curious(X0) | patient(X0) [cnf transformation 40]
126. ~funny(mary) [cnf transformation 25]
244. humble(X0) | patient(X0) [resolution 115,79]
252. patient(X1) | funny(X1) [resolution 244,105]
284. ~patient(X1) | funny(X1) | funny(X1) [resolution 96,104]
287. ~patient(X1) | funny(X1) [duplicate literal removal 284]
288. funny(X1) [subsumption resolution 287,252]
289. $false [resolution 288,126]
% SZS output end Proof for 3065525193048875834444967
% ------------------------------
% 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 paul is either not generous or not wise then mary is both funny and not old and vice versa.
If lucy is both calm and curious then someone is either not old or not curious and vice versa.
Everyone who is both tall and not generous is rich or curious.
Everyone who is either not generous or not strong is not generous and vice versa.
Everyone who is rich is not curious or humble and vice versa.
If susan is not kind or not humble then alice is not strong and vice versa.
If alice is both not curious and not tall then alice is either not tall or not funny and vice versa.
Everyone who is either not humble or not wise is funny or curious.
Everyone who is brave or not brave is both happy and funny.
Everyone who is both not curious and not funny is not calm.
Everyone who is both not generous and generous is either not tall or not strong and vice versa.
If mary is either humble or creative then susan is not generous or creative and vice versa.
If lucy is not wise then susan is wise and vice versa.
Everyone who is both old and not wise is rich or not kind and vice versa.
If someone is calm or not creative then someone is both brave and patient and vice versa.
If paul is not kind then someone is both not old and kind and vice versa.
Mary is both not kind and old.
John is wise.
Someone is wise.
Mary is either happy or not happy.
Alice is either creative or not brave.
Someone is both old and not creative.
Someone is tall or not wise.
John is both strong and brave. | Lucy is not kind. | contradiction | (((~generous(paul)<~>~wise(paul)))<=>((funny(mary)&~old(mary))))&
(((calm(lucy)&curious(lucy)))<=>(?[X]:((~old(X)<~>~curious(X)))))&
(![X]:((tall(X)&~generous(X))=>(rich(X)|curious(X))))&
(![X]:((~generous(X)<~>~strong(X))<=>~generous(X)))&
(![X]:(rich(X)<=>(~curious(X)|humble(X))))&
(((~kind(susan)|~humble(susan)))<=>(~strong(alice)))&
(((~curious(alice)&~tall(alice)))<=>((~tall(alice)<~>~funny(alice))))&
(![X]:((~humble(X)<~>~wise(X))=>(funny(X)|curious(X))))&
(![X]:((brave(X)|~brave(X))=>(happy(X)&funny(X))))&
(![X]:((~curious(X)&~funny(X))=>~calm(X)))&
(![X]:((~generous(X)&generous(X))<=>(~tall(X)<~>~strong(X))))&
(((humble(mary)<~>creative(mary)))<=>((~generous(susan)|creative(susan))))&
((~wise(lucy))<=>(wise(susan)))&
(![X]:((old(X)&~wise(X))<=>(rich(X)|~kind(X))))&
((?[X]:((calm(X)|~creative(X))))<=>(?[X]:((brave(X)&patient(X)))))&
((~kind(paul))<=>(?[X]:((~old(X)&kind(X)))))&
((~kind(mary)&old(mary)))&
(wise(john))&
(?[X]:(wise(X)))&
((happy(mary)<~>~happy(mary)))&
((creative(alice)<~>~brave(alice)))&
(?[X]:((old(X)&~creative(X))))&
(?[X]:((tall(X)|~wise(X))))&
((strong(john)&brave(john))) | ~kind(lucy) | [
"p3",
"p4",
"p5",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 7148050679924546494522008
% SZS output start Proof for 7148050679924546494522008
4. ! [X0] : ((~generous(X0) <~> ~strong(X0)) <=> ~generous(X0)) [input p3]
5. ! [X0] : (rich(X0) <=> (humble(X0) | ~curious(X0))) [input p4]
6. (~humble(susan) | ~kind(susan)) <=> ~strong(alice) [input p5]
13. ~wise(lucy) <=> wise(susan) [input p12]
14. ! [X0] : ((~wise(X0) & old(X0)) <=> (~kind(X0) | rich(X0))) [input p13]
25. ~kind(lucy) [input hypothesis]
41. ! [X0] : ((((strong(X0) | generous(X0)) & (~strong(X0) | ~generous(X0))) | generous(X0)) & (~generous(X0) | ((~generous(X0) | strong(X0)) & (~strong(X0) | generous(X0))))) [nnf transformation 4]
42. ! [X0] : ((rich(X0) | (~humble(X0) & curious(X0))) & ((humble(X0) | ~curious(X0)) | ~rich(X0))) [nnf transformation 5]
43. ! [X0] : ((rich(X0) | (~humble(X0) & curious(X0))) & (humble(X0) | ~curious(X0) | ~rich(X0))) [flattening 42]
44. ((~humble(susan) | ~kind(susan)) | strong(alice)) & (~strong(alice) | (humble(susan) & kind(susan))) [nnf transformation 6]
45. (~humble(susan) | ~kind(susan) | strong(alice)) & (~strong(alice) | (humble(susan) & kind(susan))) [flattening 44]
53. (~wise(lucy) | ~wise(susan)) & (wise(susan) | wise(lucy)) [nnf transformation 13]
54. ! [X0] : (((~wise(X0) & old(X0)) | (kind(X0) & ~rich(X0))) & ((~kind(X0) | rich(X0)) | (wise(X0) | ~old(X0)))) [nnf transformation 14]
55. ! [X0] : (((~wise(X0) & old(X0)) | (kind(X0) & ~rich(X0))) & (~kind(X0) | rich(X0) | wise(X0) | ~old(X0))) [flattening 54]
87. ~generous(X0) | ~generous(X0) | strong(X0) [cnf transformation 41]
89. strong(X0) | generous(X0) | generous(X0) [cnf transformation 41]
92. ~humble(X0) | rich(X0) [cnf transformation 43]
94. ~strong(alice) | humble(susan) [cnf transformation 45]
121. wise(susan) | wise(lucy) [cnf transformation 53]
126. ~rich(X0) | ~wise(X0) [cnf transformation 55]
127. ~wise(X0) | kind(X0) [cnf transformation 55]
149. ~kind(lucy) [cnf transformation 25]
152. ~generous(X0) | strong(X0) [duplicate literal removal 87]
153. strong(X0) | generous(X0) [duplicate literal removal 89]
204. strong(X0) [subsumption resolution 152,153]
205. humble(susan) [subsumption resolution 94,204]
251. 18 <=> wise(susan) [avatar definition]
255. 19 <=> wise(lucy) [avatar definition]
256. wise(lucy) <- (19) [avatar component clause 255]
259. 19 | 18 [avatar split clause 121,251,255]
340. rich(susan) [resolution 92,205]
347. ~wise(susan) [resolution 126,340]
350. ~18 [avatar split clause 347,251]
353. kind(lucy) <- (19) [resolution 127,256]
354. $false <- (19) [subsumption resolution 353,149]
355. ~19 [avatar contradiction clause 354]
356. $false [avatar sat refutation 259,350,355]
% SZS output end Proof for 7148050679924546494522008
% ------------------------------
% 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 both not rich and not kind is either not tall or patient.
Everyone who is both not curious and not calm is not generous and vice versa.
Everyone who is not rich is either not wise or not calm and vice versa.
If someone is both not curious and not generous then someone is both calm and not patient.
If paul is both not humble and brave then someone is funny and vice versa.
Everyone who is either calm or happy is both not generous and not tall and vice versa.
Everyone who is rich or brave is either not brave or kind and vice versa.
Everyone who is either old or not funny is both not brave and quiet.
If lucy is not brave or not strong then mary is not patient and vice versa.
Everyone who is not curious is strong and vice versa.
Everyone who is both wise and tall is old or tall.
Everyone who is either old or happy is either not rich or not wise and vice versa.
Everyone who is either funny or quiet is either not brave or calm and vice versa.
Everyone who is either not wise or not brave is old and vice versa.
Everyone who is both not humble and not funny is either old or quiet.
If john is either not generous or not quiet then someone is either wise or patient.
Someone is both generous and not tall.
Someone is patient.
Lucy is either old or not funny.
Someone is calm.
Alice is either old or happy.
Someone is old or kind.
Someone is both patient and not calm.
Paul is not curious or kind. | Lucy is brave. | contradiction | (![X]:((~rich(X)&~kind(X))=>(~tall(X)<~>patient(X))))&
(![X]:((~curious(X)&~calm(X))<=>~generous(X)))&
(![X]:(~rich(X)<=>(~wise(X)<~>~calm(X))))&
((?[X]:((~curious(X)&~generous(X))))=>(?[X]:((calm(X)&~patient(X)))))&
(((~humble(paul)&brave(paul)))<=>(?[X]:(funny(X))))&
(![X]:((calm(X)<~>happy(X))<=>(~generous(X)&~tall(X))))&
(![X]:((rich(X)|brave(X))<=>(~brave(X)<~>kind(X))))&
(![X]:((old(X)<~>~funny(X))=>(~brave(X)&quiet(X))))&
(((~brave(lucy)|~strong(lucy)))<=>(~patient(mary)))&
(![X]:(~curious(X)<=>strong(X)))&
(![X]:((wise(X)&tall(X))=>(old(X)|tall(X))))&
(![X]:((old(X)<~>happy(X))<=>(~rich(X)<~>~wise(X))))&
(![X]:((funny(X)<~>quiet(X))<=>(~brave(X)<~>calm(X))))&
(![X]:((~wise(X)<~>~brave(X))<=>old(X)))&
(![X]:((~humble(X)&~funny(X))=>(old(X)<~>quiet(X))))&
(((~generous(john)<~>~quiet(john)))=>(?[X]:((wise(X)<~>patient(X)))))&
(?[X]:((generous(X)&~tall(X))))&
(?[X]:(patient(X)))&
((old(lucy)<~>~funny(lucy)))&
(?[X]:(calm(X)))&
((old(alice)<~>happy(alice)))&
(?[X]:((old(X)|kind(X))))&
(?[X]:((patient(X)&~calm(X))))&
((~curious(paul)|kind(paul))) | brave(lucy) | [
"p7",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 8683510989880972366539499
% SZS output start Proof for 8683510989880972366539499
8. ! [X0] : ((old(X0) <~> ~funny(X0)) => (quiet(X0) & ~brave(X0))) [input p7]
19. old(lucy) <~> ~funny(lucy) [input p18]
25. brave(lucy) [input hypothesis]
30. ! [X0] : ((quiet(X0) & ~brave(X0)) | (old(X0) <=> ~funny(X0))) [ennf transformation 8]
52. ! [X0] : ((quiet(X0) & ~brave(X0)) | ((old(X0) | funny(X0)) & (~funny(X0) | ~old(X0)))) [nnf transformation 30]
67. (funny(lucy) | ~old(lucy)) & (~funny(lucy) | old(lucy)) [nnf transformation 19]
101. ~old(X0) | ~funny(X0) | ~brave(X0) [cnf transformation 52]
102. ~brave(X0) | old(X0) | funny(X0) [cnf transformation 52]
140. ~funny(lucy) | old(lucy) [cnf transformation 67]
141. funny(lucy) | ~old(lucy) [cnf transformation 67]
149. brave(lucy) [cnf transformation 25]
192. 9 <=> brave(lucy) [avatar definition]
193. brave(lucy) <- (9) [avatar component clause 192]
223. 15 <=> old(lucy) [avatar definition]
224. old(lucy) <- (15) [avatar component clause 223]
225. ~old(lucy) <- (~15) [avatar component clause 223]
227. 16 <=> funny(lucy) [avatar definition]
228. ~funny(lucy) <- (~16) [avatar component clause 227]
229. funny(lucy) <- (16) [avatar component clause 227]
230. ~15 | 16 [avatar split clause 141,227,223]
231. 15 | ~16 [avatar split clause 140,227,223]
260. 9 [avatar split clause 149,192]
316. old(lucy) | funny(lucy) <- (9) [resolution 102,193]
317. funny(lucy) <- (9, ~15) [subsumption resolution 316,225]
318. $false <- (9, ~15, ~16) [subsumption resolution 317,228]
319. ~9 | 15 | 16 [avatar contradiction clause 318]
354. ~funny(lucy) | ~brave(lucy) <- (15) [resolution 224,101]
355. ~brave(lucy) <- (15, 16) [subsumption resolution 354,229]
356. $false <- (9, 15, 16) [subsumption resolution 355,193]
357. ~9 | ~15 | ~16 [avatar contradiction clause 356]
358. $false [avatar sat refutation 230,231,260,319,357]
% SZS output end Proof for 8683510989880972366539499
% ------------------------------
% 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 lucy is either curious or not rich then someone is rich or not creative.
If someone is not strong then someone is both not creative and not kind and vice versa.
If mary is both wise and not tall then alice is either not generous or not humble.
Everyone who is both old and kind is both not creative and not rich.
Everyone who is either tall or wise is either not kind or tall and vice versa.
Everyone who is both quiet and not calm is strong or not wise and vice versa.
If susan is not rich or not humble then someone is either not funny or not kind.
Everyone who is not strong is either not kind or curious and vice versa.
Everyone who is either not patient or patient is creative or strong.
If fred is both not tall and strong then someone is both brave and not tall.
Everyone who is generous or not happy is not humble.
Everyone who is old is not patient and vice versa.
Everyone who is both not rich and not curious is not happy or curious and vice versa.
If someone is not old then someone is not humble or tall and vice versa.
Everyone who is either strong or tall is not rich and vice versa.
If lucy is not quiet then someone is funny and vice versa.
Someone is generous or not strong.
John is either not quiet or not creative.
Someone is generous or strong.
Someone is either not curious or not happy.
Someone is happy or not strong.
Someone is not brave.
Someone is either not kind or not humble. | Fred is funny. | contradiction | (((curious(lucy)<~>~rich(lucy)))=>(?[X]:((rich(X)|~creative(X)))))&
((?[X]:(~strong(X)))<=>(?[X]:((~creative(X)&~kind(X)))))&
(((wise(mary)&~tall(mary)))=>((~generous(alice)<~>~humble(alice))))&
(![X]:((old(X)&kind(X))=>(~creative(X)&~rich(X))))&
(![X]:((tall(X)<~>wise(X))<=>(~kind(X)<~>tall(X))))&
(![X]:((quiet(X)&~calm(X))<=>(strong(X)|~wise(X))))&
(((~rich(susan)|~humble(susan)))=>(?[X]:((~funny(X)<~>~kind(X)))))&
(![X]:(~strong(X)<=>(~kind(X)<~>curious(X))))&
(![X]:((~patient(X)<~>patient(X))=>(creative(X)|strong(X))))&
(((~tall(fred)&strong(fred)))=>(?[X]:((brave(X)&~tall(X)))))&
(![X]:((generous(X)|~happy(X))=>~humble(X)))&
(![X]:(old(X)<=>~patient(X)))&
(![X]:((~rich(X)&~curious(X))<=>(~happy(X)|curious(X))))&
((?[X]:(~old(X)))<=>(?[X]:((~humble(X)|tall(X)))))&
(![X]:((strong(X)<~>tall(X))<=>~rich(X)))&
((~quiet(lucy))<=>(?[X]:(funny(X))))&
(?[X]:((generous(X)|~strong(X))))&
((~quiet(john)<~>~creative(john)))&
(?[X]:((generous(X)|strong(X))))&
(?[X]:((~curious(X)<~>~happy(X))))&
(?[X]:((happy(X)|~strong(X))))&
(?[X]:(~brave(X)))&
(?[X]:((~kind(X)<~>~humble(X)))) | funny(fred) | [
"p1",
"p5",
"p7",
"p8",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 211977524936192470539621
% SZS output start Proof for 211977524936192470539621
2. ? [X0] : ~strong(X0) <=> ? [X0] : (~kind(X0) & ~creative(X0)) [input p1]
6. ! [X0] : ((~calm(X0) & quiet(X0)) <=> (~wise(X0) | strong(X0))) [input p5]
8. ! [X0] : (~strong(X0) <=> (~kind(X0) <~> curious(X0))) [input p7]
9. ! [X0] : ((~patient(X0) <~> patient(X0)) => (strong(X0) | creative(X0))) [input p8]
13. ! [X0] : ((~curious(X0) & ~rich(X0)) <=> (curious(X0) | ~happy(X0))) [input p12]
16. ~quiet(lucy) <=> ? [X0] : funny(X0) [input p15]
24. funny(fred) [input hypothesis]
25. ? [X0] : ~strong(X0) <=> ? [X1] : (~kind(X1) & ~creative(X1)) [rectify 2]
33. ! [X0] : ((strong(X0) | creative(X0)) | (~patient(X0) <=> patient(X0))) [ennf transformation 9]
34. ! [X0] : (strong(X0) | creative(X0) | (~patient(X0) <=> patient(X0))) [flattening 33]
41. (? [X0] : ~strong(X0) | ! [X1] : (kind(X1) | creative(X1))) & (? [X1] : (~kind(X1) & ~creative(X1)) | ! [X0] : strong(X0)) [nnf transformation 25]
42. (? [X0] : ~strong(X0) | ! [X1] : (kind(X1) | creative(X1))) & (? [X2] : (~kind(X2) & ~creative(X2)) | ! [X3] : strong(X3)) [rectify 41]
43. ? [X0] : ~strong(X0) => ~strong(sK1) [choice axiom]
44. ? [X2] : (~kind(X2) & ~creative(X2)) => (~kind(sK2) & ~creative(sK2)) [choice axiom]
45. (~strong(sK1) | ! [X1] : (kind(X1) | creative(X1))) & ((~kind(sK2) & ~creative(sK2)) | ! [X3] : strong(X3)) [skolemisation 42,44,43]
48. ! [X0] : (((~calm(X0) & quiet(X0)) | (wise(X0) & ~strong(X0))) & ((~wise(X0) | strong(X0)) | (calm(X0) | ~quiet(X0)))) [nnf transformation 6]
49. ! [X0] : (((~calm(X0) & quiet(X0)) | (wise(X0) & ~strong(X0))) & (~wise(X0) | strong(X0) | calm(X0) | ~quiet(X0))) [flattening 48]
53. ! [X0] : ((~strong(X0) | ((~kind(X0) | ~curious(X0)) & (curious(X0) | kind(X0)))) & (((~curious(X0) | kind(X0)) & (curious(X0) | ~kind(X0))) | strong(X0))) [nnf transformation 8]
54. ! [X0] : (strong(X0) | creative(X0) | ((~patient(X0) | ~patient(X0)) & (patient(X0) | patient(X0)))) [nnf transformation 34]
58. ! [X0] : (((~curious(X0) & ~rich(X0)) | (~curious(X0) & happy(X0))) & ((curious(X0) | ~happy(X0)) | (curious(X0) | rich(X0)))) [nnf transformation 13]
59. ! [X0] : (((~curious(X0) & ~rich(X0)) | (~curious(X0) & happy(X0))) & (curious(X0) | ~happy(X0) | curious(X0) | rich(X0))) [flattening 58]
66. (~quiet(lucy) | ! [X0] : ~funny(X0)) & (? [X0] : funny(X0) | quiet(lucy)) [nnf transformation 16]
67. (~quiet(lucy) | ! [X0] : ~funny(X0)) & (? [X1] : funny(X1) | quiet(lucy)) [rectify 66]
68. ? [X1] : funny(X1) => funny(sK7) [choice axiom]
69. (~quiet(lucy) | ! [X0] : ~funny(X0)) & (funny(sK7) | quiet(lucy)) [skolemisation 67,68]
87. ~creative(sK2) | strong(X3) [cnf transformation 45]
88. ~kind(sK2) | strong(X3) [cnf transformation 45]
103. ~strong(X0) | quiet(X0) [cnf transformation 49]
113. ~strong(X0) | curious(X0) | kind(X0) [cnf transformation 53]
115. strong(X0) | creative(X0) | patient(X0) | patient(X0) [cnf transformation 54]
116. strong(X0) | creative(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 54]
127. ~curious(X0) | ~curious(X0) [cnf transformation 59]
136. ~quiet(lucy) | ~funny(X0) [cnf transformation 69]
147. funny(fred) [cnf transformation 24]
149. ~curious(X0) [duplicate literal removal 127]
150. strong(X0) | creative(X0) | patient(X0) [duplicate literal removal 115]
151. strong(X0) | creative(X0) | ~patient(X0) [duplicate literal removal 116]
175. 5 <=> ! [X1] : (kind(X1) | creative(X1)) [avatar definition]
176. kind(X1) | creative(X1) <- (5) [avatar component clause 175]
183. 7 <=> ! [X3] : strong(X3) [avatar definition]
184. strong(X3) <- (7) [avatar component clause 183]
186. 8 <=> kind(sK2) [avatar definition]
188. ~kind(sK2) <- (~8) [avatar component clause 186]
189. 7 | ~8 [avatar split clause 88,186,183]
191. 9 <=> creative(sK2) [avatar definition]
193. ~creative(sK2) <- (~9) [avatar component clause 191]
194. 7 | ~9 [avatar split clause 87,191,183]
235. strong(X0) | creative(X0) [subsumption resolution 150,151]
280. 28 <=> ! [X0] : ~funny(X0) [avatar definition]
281. ~funny(X0) <- (28) [avatar component clause 280]
283. 29 <=> quiet(lucy) [avatar definition]
285. ~quiet(lucy) <- (~29) [avatar component clause 283]
286. 28 | ~29 [avatar split clause 136,283,280]
342. $false <- (28) [resolution 281,147]
343. ~28 [avatar contradiction clause 342]
363. curious(X0) | kind(X0) | creative(X0) [resolution 113,235]
365. kind(X0) | creative(X0) [subsumption resolution 363,149]
366. 5 [avatar split clause 365,175]
369. creative(sK2) <- (5, ~8) [resolution 176,188]
371. $false <- (5, ~8, ~9) [subsumption resolution 369,193]
372. ~5 | 8 | 9 [avatar contradiction clause 371]
374. quiet(X1) <- (7) [resolution 184,103]
391. $false <- (7, ~29) [resolution 374,285]
392. ~7 | 29 [avatar contradiction clause 391]
393. $false [avatar sat refutation 189,194,286,343,366,372,392]
% SZS output end Proof for 211977524936192470539621
% ------------------------------
% 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 |
If someone is either not calm or creative then someone is both old and brave. Everyone who is not wise is both humble and quiet and vice versa. If someone is generous or not patient then someone is creative or not funny and vice versa. If susan is brave then mary is generous. Everyone who is both not rich and rich is both quiet and happy and vice versa. Everyone who is both not kind and not wise is brave and vice versa. If someone is both not humble and not kind then someone is both brave and not creative. Everyone who is either strong or rich is not quiet or creative and vice versa. Everyone who is both brave and old is either wise or kind and vice versa. If mary is either not brave or not calm then paul is both not generous and kind and vice versa. Everyone who is not humble or curious is funny or wise. If fred is either creative or not wise then someone is either not rich or not kind. Everyone who is either kind or humble is both tall and not wise. If lucy is both not funny and kind then mary is either not happy or tall and vice versa. Everyone who is humble or generous is creative or not kind and vice versa. Everyone who is not calm or not curious is either not curious or not tall and vice versa. Someone is either creative or generous. Paul is generous. John is calm. Paul is both brave and not calm. Someone is either not curious or not patient. Someone is not generous. Fred is either not old or old. | John is not kind. | entailment | ((?[X]:((~calm(X)<~>creative(X))))=>(?[X]:((old(X)&brave(X)))))&
(![X]:(~wise(X)<=>(humble(X)&quiet(X))))&
((?[X]:((generous(X)|~patient(X))))<=>(?[X]:((creative(X)|~funny(X)))))&
((brave(susan))=>(generous(mary)))&
(![X]:((~rich(X)&rich(X))<=>(quiet(X)&happy(X))))&
(![X]:((~kind(X)&~wise(X))<=>brave(X)))&
((?[X]:((~humble(X)&~kind(X))))=>(?[X]:((brave(X)&~creative(X)))))&
(![X]:((strong(X)<~>rich(X))<=>(~quiet(X)|creative(X))))&
(![X]:((brave(X)&old(X))<=>(wise(X)<~>kind(X))))&
(((~brave(mary)<~>~calm(mary)))<=>((~generous(paul)&kind(paul))))&
(![X]:((~humble(X)|curious(X))=>(funny(X)|wise(X))))&
(((creative(fred)<~>~wise(fred)))=>(?[X]:((~rich(X)<~>~kind(X)))))&
(![X]:((kind(X)<~>humble(X))=>(tall(X)&~wise(X))))&
(((~funny(lucy)&kind(lucy)))<=>((~happy(mary)<~>tall(mary))))&
(![X]:((humble(X)|generous(X))<=>(creative(X)|~kind(X))))&
(![X]:((~calm(X)|~curious(X))<=>(~curious(X)<~>~tall(X))))&
(?[X]:((creative(X)<~>generous(X))))&
(generous(paul))&
(calm(john))&
((brave(paul)&~calm(paul)))&
(?[X]:((~curious(X)<~>~patient(X))))&
(?[X]:(~generous(X)))&
((~old(fred)<~>old(fred))) | ~kind(john) | [
"p0",
"p5",
"p8",
"p12",
"p14",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 1658499550944598544984878
% SZS output start Proof for 1658499550944598544984878
1. ? [X0] : (~calm(X0) <~> creative(X0)) => ? [X0] : (brave(X0) & old(X0)) [input p0]
6. ! [X0] : ((~wise(X0) & ~kind(X0)) <=> brave(X0)) [input p5]
9. ! [X0] : ((old(X0) & brave(X0)) <=> (wise(X0) <~> kind(X0))) [input p8]
13. ! [X0] : ((kind(X0) <~> humble(X0)) => (~wise(X0) & tall(X0))) [input p12]
15. ! [X0] : ((generous(X0) | humble(X0)) <=> (~kind(X0) | creative(X0))) [input p14]
19. calm(john) [input p18]
24. kind(john) [input hypothesis]
25. ? [X0] : (~calm(X0) <~> creative(X0)) => ? [X1] : (brave(X1) & old(X1)) [rectify 1]
28. ? [X1] : (brave(X1) & old(X1)) | ! [X0] : (~calm(X0) <=> creative(X0)) [ennf transformation 25]
34. ! [X0] : ((~wise(X0) & tall(X0)) | (kind(X0) <=> humble(X0))) [ennf transformation 13]
35. ? [X1] : (brave(X1) & old(X1)) | ! [X0] : ((~calm(X0) | ~creative(X0)) & (creative(X0) | calm(X0))) [nnf transformation 28]
36. ? [X0] : (brave(X0) & old(X0)) | ! [X1] : ((~calm(X1) | ~creative(X1)) & (creative(X1) | calm(X1))) [rectify 35]
37. ? [X0] : (brave(X0) & old(X0)) => (brave(sK0) & old(sK0)) [choice axiom]
38. (brave(sK0) & old(sK0)) | ! [X1] : ((~calm(X1) | ~creative(X1)) & (creative(X1) | calm(X1))) [skolemisation 36,37]
48. ! [X0] : (((~wise(X0) & ~kind(X0)) | ~brave(X0)) & (brave(X0) | (wise(X0) | kind(X0)))) [nnf transformation 6]
49. ! [X0] : (((~wise(X0) & ~kind(X0)) | ~brave(X0)) & (brave(X0) | wise(X0) | kind(X0))) [flattening 48]
55. ! [X0] : (((old(X0) & brave(X0)) | ((wise(X0) | ~kind(X0)) & (kind(X0) | ~wise(X0)))) & (((~kind(X0) | ~wise(X0)) & (kind(X0) | wise(X0))) | (~old(X0) | ~brave(X0)))) [nnf transformation 9]
56. ! [X0] : (((old(X0) & brave(X0)) | ((wise(X0) | ~kind(X0)) & (kind(X0) | ~wise(X0)))) & (((~kind(X0) | ~wise(X0)) & (kind(X0) | wise(X0))) | ~old(X0) | ~brave(X0))) [flattening 55]
62. ! [X0] : ((~wise(X0) & tall(X0)) | ((kind(X0) | ~humble(X0)) & (humble(X0) | ~kind(X0)))) [nnf transformation 34]
65. ! [X0] : (((generous(X0) | humble(X0)) | (kind(X0) & ~creative(X0))) & ((~kind(X0) | creative(X0)) | (~generous(X0) & ~humble(X0)))) [nnf transformation 15]
66. ! [X0] : ((generous(X0) | humble(X0) | (kind(X0) & ~creative(X0))) & (~kind(X0) | creative(X0) | (~generous(X0) & ~humble(X0)))) [flattening 65]
79. old(sK0) | ~calm(X1) | ~creative(X1) [cnf transformation 38]
81. brave(sK0) | ~calm(X1) | ~creative(X1) [cnf transformation 38]
95. ~kind(X0) | ~brave(X0) [cnf transformation 49]
96. ~wise(X0) | ~brave(X0) [cnf transformation 49]
105. kind(X0) | wise(X0) | ~old(X0) | ~brave(X0) [cnf transformation 56]
108. brave(X0) | wise(X0) | ~kind(X0) [cnf transformation 56]
125. ~wise(X0) | humble(X0) | ~kind(X0) [cnf transformation 62]
133. ~kind(X0) | creative(X0) | ~humble(X0) [cnf transformation 66]
146. calm(john) [cnf transformation 19]
154. kind(john) [cnf transformation 24]
158. 1 <=> ! [X1] : (~calm(X1) | ~creative(X1)) [avatar definition]
159. ~creative(X1) | ~calm(X1) <- (1) [avatar component clause 158]
161. 2 <=> brave(sK0) [avatar definition]
163. brave(sK0) <- (2) [avatar component clause 161]
164. 1 | 2 [avatar split clause 81,161,158]
170. 4 <=> old(sK0) [avatar definition]
172. old(sK0) <- (4) [avatar component clause 170]
173. 1 | 4 [avatar split clause 79,170,158]
230. ~kind(X0) | wise(X0) [subsumption resolution 108,95]
232. kind(X0) | ~old(X0) | ~brave(X0) [subsumption resolution 105,96]
233. ~brave(X0) | ~old(X0) [subsumption resolution 232,95]
276. ~kind(X0) | humble(X0) [subsumption resolution 125,230]
300. ~kind(X0) | creative(X0) [subsumption resolution 133,276]
331. ~old(sK0) <- (2) [resolution 233,163]
333. $false <- (2, 4) [subsumption resolution 331,172]
334. ~2 | ~4 [avatar contradiction clause 333]
342. creative(john) [resolution 300,154]
344. ~calm(john) <- (1) [resolution 342,159]
345. $false <- (1) [subsumption resolution 344,146]
346. ~1 [avatar contradiction clause 345]
347. $false [avatar sat refutation 164,173,334,346]
% SZS output end Proof for 1658499550944598544984878
% ------------------------------
% 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 not strong then susan is either kind or patient and vice versa.
Everyone who is both wise and not generous is either not funny or not wise and vice versa.
Everyone who is not humble is happy.
Everyone who is not humble is not curious.
Everyone who is both not creative and not strong is strong or not funny.
Everyone who is generous or creative is not strong or not funny and vice versa.
Everyone who is kind or not funny is not creative and vice versa.
If someone is either calm or humble then someone is generous or creative and vice versa.
Everyone who is strong or rich is not quiet and vice versa.
Everyone who is both not patient and creative is both happy and not wise.
Everyone who is not happy or not tall is not strong and vice versa.
Everyone who is patient is either not tall or not brave and vice versa.
If lucy is either not humble or calm then someone is both not generous and not tall and vice versa.
Everyone who is not curious is both happy and not kind and vice versa.
If susan is both not old and not humble then mary is generous or not humble and vice versa.
Everyone who is not quiet is not funny or not brave and vice versa.
Someone is either not calm or not tall.
Someone is not kind or kind.
Fred is either funny or not happy.
Someone is not humble or brave.
Paul is both not quiet and kind.
John is not tall.
Alice is both not funny and strong.
Alice is not humble. | Mary is not generous. | contradiction | ((~strong(lucy))<=>((kind(susan)<~>patient(susan))))&
(![X]:((wise(X)&~generous(X))<=>(~funny(X)<~>~wise(X))))&
(![X]:(~humble(X)=>happy(X)))&
(![X]:(~humble(X)=>~curious(X)))&
(![X]:((~creative(X)&~strong(X))=>(strong(X)|~funny(X))))&
(![X]:((generous(X)|creative(X))<=>(~strong(X)|~funny(X))))&
(![X]:((kind(X)|~funny(X))<=>~creative(X)))&
((?[X]:((calm(X)<~>humble(X))))<=>(?[X]:((generous(X)|creative(X)))))&
(![X]:((strong(X)|rich(X))<=>~quiet(X)))&
(![X]:((~patient(X)&creative(X))=>(happy(X)&~wise(X))))&
(![X]:((~happy(X)|~tall(X))<=>~strong(X)))&
(![X]:(patient(X)<=>(~tall(X)<~>~brave(X))))&
(((~humble(lucy)<~>calm(lucy)))<=>(?[X]:((~generous(X)&~tall(X)))))&
(![X]:(~curious(X)<=>(happy(X)&~kind(X))))&
(((~old(susan)&~humble(susan)))<=>((generous(mary)|~humble(mary))))&
(![X]:(~quiet(X)<=>(~funny(X)|~brave(X))))&
(?[X]:((~calm(X)<~>~tall(X))))&
(?[X]:((~kind(X)|kind(X))))&
((funny(fred)<~>~happy(fred)))&
(?[X]:((~humble(X)|brave(X))))&
((~quiet(paul)&kind(paul)))&
(~tall(john))&
((~funny(alice)&strong(alice)))&
(~humble(alice)) | ~generous(mary) | [
"p1",
"p5",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 4019759100851062167540120
% SZS output start Proof for 4019759100851062167540120
2. ! [X0] : ((~generous(X0) & wise(X0)) <=> (~funny(X0) <~> ~wise(X0))) [input p1]
6. ! [X0] : ((creative(X0) | generous(X0)) <=> (~funny(X0) | ~strong(X0))) [input p5]
7. ! [X0] : ((~funny(X0) | kind(X0)) <=> ~creative(X0)) [input p6]
25. ~generous(mary) [input hypothesis]
36. ! [X0] : (((~generous(X0) & wise(X0)) | ((~funny(X0) | wise(X0)) & (~wise(X0) | funny(X0)))) & (((wise(X0) | funny(X0)) & (~wise(X0) | ~funny(X0))) | (generous(X0) | ~wise(X0)))) [nnf transformation 2]
37. ! [X0] : (((~generous(X0) & wise(X0)) | ((~funny(X0) | wise(X0)) & (~wise(X0) | funny(X0)))) & (((wise(X0) | funny(X0)) & (~wise(X0) | ~funny(X0))) | generous(X0) | ~wise(X0))) [flattening 36]
38. ! [X0] : (((creative(X0) | generous(X0)) | (funny(X0) & strong(X0))) & ((~funny(X0) | ~strong(X0)) | (~creative(X0) & ~generous(X0)))) [nnf transformation 6]
39. ! [X0] : ((creative(X0) | generous(X0) | (funny(X0) & strong(X0))) & (~funny(X0) | ~strong(X0) | (~creative(X0) & ~generous(X0)))) [flattening 38]
40. ! [X0] : (((~funny(X0) | kind(X0)) | creative(X0)) & (~creative(X0) | (funny(X0) & ~kind(X0)))) [nnf transformation 7]
41. ! [X0] : ((~funny(X0) | kind(X0) | creative(X0)) & (~creative(X0) | (funny(X0) & ~kind(X0)))) [flattening 40]
72. ~wise(X0) | ~funny(X0) | generous(X0) | ~wise(X0) [cnf transformation 37]
75. wise(X0) | ~funny(X0) | wise(X0) [cnf transformation 37]
84. creative(X0) | generous(X0) | funny(X0) [cnf transformation 39]
86. ~creative(X0) | funny(X0) [cnf transformation 41]
134. ~generous(mary) [cnf transformation 25]
136. ~wise(X0) | ~funny(X0) | generous(X0) [duplicate literal removal 72]
137. ~funny(X0) | wise(X0) [duplicate literal removal 75]
154. ~funny(X0) | generous(X0) [subsumption resolution 136,137]
155. creative(X0) | generous(X0) [subsumption resolution 84,154]
210. 15 <=> generous(mary) [avatar definition]
212. ~generous(mary) <- (~15) [avatar component clause 210]
250. ~15 [avatar split clause 134,210]
262. generous(X0) | funny(X0) [resolution 155,86]
264. generous(X0) [subsumption resolution 262,154]
266. $false <- (~15) [resolution 264,212]
267. 15 [avatar contradiction clause 266]
269. $false [avatar sat refutation 250,267]
% SZS output end Proof for 4019759100851062167540120
% ------------------------------
% 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 creative is both not quiet and not calm and vice versa.
If paul is not creative then someone is either strong or calm.
Everyone who is either humble or not funny is tall or not generous and vice versa.
Everyone who is not kind is rich.
If paul is patient or not generous then someone is either not rich or kind and vice versa.
Everyone who is happy is both quiet and wise.
If someone is both not happy and tall then someone is not creative or patient.
Everyone who is tall or funny is happy or not kind and vice versa.
If fred is both not calm and not generous then someone is both not calm and wise and vice versa.
Everyone who is funny is rich and vice versa.
Everyone who is either not kind or funny is not old and vice versa.
Everyone who is not calm is either quiet or happy and vice versa.
If alice is not kind then alice is either not humble or funny and vice versa.
Everyone who is not old or not calm is not brave and vice versa.
Everyone who is both kind and not brave is kind or funny and vice versa.
If alice is either humble or calm then someone is either strong or patient and vice versa.
Lucy is rich.
Mary is both old and not happy.
Someone is both not strong and humble.
Someone is either not old or wise.
Someone is not patient.
Someone is tall or curious. | Lucy is quiet. | entailment | (![X]:(creative(X)<=>(~quiet(X)&~calm(X))))&
((~creative(paul))=>(?[X]:((strong(X)<~>calm(X)))))&
(![X]:((humble(X)<~>~funny(X))<=>(tall(X)|~generous(X))))&
(![X]:(~kind(X)=>rich(X)))&
(((patient(paul)|~generous(paul)))<=>(?[X]:((~rich(X)<~>kind(X)))))&
(![X]:(happy(X)=>(quiet(X)&wise(X))))&
((?[X]:((~happy(X)&tall(X))))=>(?[X]:((~creative(X)|patient(X)))))&
(![X]:((tall(X)|funny(X))<=>(happy(X)|~kind(X))))&
(((~calm(fred)&~generous(fred)))<=>(?[X]:((~calm(X)&wise(X)))))&
(![X]:(funny(X)<=>rich(X)))&
(![X]:((~kind(X)<~>funny(X))<=>~old(X)))&
(![X]:(~calm(X)<=>(quiet(X)<~>happy(X))))&
((~kind(alice))<=>((~humble(alice)<~>funny(alice))))&
(![X]:((~old(X)|~calm(X))<=>~brave(X)))&
(![X]:((kind(X)&~brave(X))<=>(kind(X)|funny(X))))&
(((humble(alice)<~>calm(alice)))<=>(?[X]:((strong(X)<~>patient(X)))))&
(rich(lucy))&
((old(mary)&~happy(mary)))&
(?[X]:((~strong(X)&humble(X))))&
(?[X]:((~old(X)<~>wise(X))))&
(?[X]:(~patient(X)))&
(?[X]:((tall(X)|curious(X)))) | quiet(lucy) | [
"p3",
"p5",
"p7",
"p9",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 3152744214753605285933464
% SZS output start Proof for 3152744214753605285933464
4. ! [X0] : (~kind(X0) => rich(X0)) [input p3]
6. ! [X0] : (happy(X0) => (wise(X0) & quiet(X0))) [input p5]
8. ! [X0] : ((funny(X0) | tall(X0)) <=> (~kind(X0) | happy(X0))) [input p7]
10. ! [X0] : (funny(X0) <=> rich(X0)) [input p9]
15. ! [X0] : ((~brave(X0) & kind(X0)) <=> (funny(X0) | kind(X0))) [input p14]
17. rich(lucy) [input p16]
23. ~quiet(lucy) [input hypothesis]
27. ! [X0] : (rich(X0) | kind(X0)) [ennf transformation 4]
28. ! [X0] : ((wise(X0) & quiet(X0)) | ~happy(X0)) [ennf transformation 6]
45. ! [X0] : (((funny(X0) | tall(X0)) | (kind(X0) & ~happy(X0))) & ((~kind(X0) | happy(X0)) | (~funny(X0) & ~tall(X0)))) [nnf transformation 8]
46. ! [X0] : ((funny(X0) | tall(X0) | (kind(X0) & ~happy(X0))) & (~kind(X0) | happy(X0) | (~funny(X0) & ~tall(X0)))) [flattening 45]
52. ! [X0] : ((funny(X0) | ~rich(X0)) & (rich(X0) | ~funny(X0))) [nnf transformation 10]
58. ! [X0] : (((~brave(X0) & kind(X0)) | (~funny(X0) & ~kind(X0))) & ((funny(X0) | kind(X0)) | (brave(X0) | ~kind(X0)))) [nnf transformation 15]
59. ! [X0] : (((~brave(X0) & kind(X0)) | (~funny(X0) & ~kind(X0))) & (funny(X0) | kind(X0) | brave(X0) | ~kind(X0))) [flattening 58]
82. rich(X0) | kind(X0) [cnf transformation 27]
89. ~happy(X0) | quiet(X0) [cnf transformation 28]
93. ~kind(X0) | happy(X0) | ~funny(X0) [cnf transformation 46]
101. ~rich(X0) | funny(X0) [cnf transformation 52]
119. ~funny(X0) | kind(X0) [cnf transformation 59]
130. rich(lucy) [cnf transformation 17]
138. ~quiet(lucy) [cnf transformation 23]
271. funny(lucy) [resolution 101,130]
273. funny(X0) | kind(X0) [resolution 101,82]
274. kind(X0) [subsumption resolution 273,119]
335. ~funny(X0) | happy(X0) [resolution 93,274]
354. happy(lucy) [resolution 335,271]
363. quiet(lucy) [resolution 354,89]
364. $false [subsumption resolution 363,138]
% SZS output end Proof for 3152744214753605285933464
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not curious is both not tall and generous.
If someone is not rich or not brave then alice is not curious or tall.
Everyone who is both funny and brave is not tall and vice versa.
Everyone who is both kind and funny is both curious and generous.
Everyone who is not patient is both not kind and not wise and vice versa.
If susan is curious then alice is not happy or not funny.
If john is wise then someone is either not funny or not generous.
Everyone who is brave or calm is either not humble or not generous.
If mary is generous then someone is either not strong or quiet and vice versa.
Everyone who is old is either strong or not strong.
If paul is not curious then someone is both not happy and funny and vice versa.
If fred is not curious or not tall then someone is humble.
Everyone who is either not creative or creative is not wise or patient.
Everyone who is either not generous or not old is not curious and vice versa.
If fred is not strong or humble then john is both wise and not funny and vice versa.
If paul is both not calm and not old then someone is calm.
Someone is either kind or not patient.
Mary is both creative and rich.
Someone is not happy or not wise.
Susan is not funny or strong.
Fred is either calm or rich.
Alice is happy.
Alice is either not tall or brave.
Paul is either patient or happy. | Mary is rich. | entailment | (![X]:(~curious(X)=>(~tall(X)&generous(X))))&
((?[X]:((~rich(X)|~brave(X))))=>((~curious(alice)|tall(alice))))&
(![X]:((funny(X)&brave(X))<=>~tall(X)))&
(![X]:((kind(X)&funny(X))=>(curious(X)&generous(X))))&
(![X]:(~patient(X)<=>(~kind(X)&~wise(X))))&
((curious(susan))=>((~happy(alice)|~funny(alice))))&
((wise(john))=>(?[X]:((~funny(X)<~>~generous(X)))))&
(![X]:((brave(X)|calm(X))=>(~humble(X)<~>~generous(X))))&
((generous(mary))<=>(?[X]:((~strong(X)<~>quiet(X)))))&
(![X]:(old(X)=>(strong(X)<~>~strong(X))))&
((~curious(paul))<=>(?[X]:((~happy(X)&funny(X)))))&
(((~curious(fred)|~tall(fred)))=>(?[X]:(humble(X))))&
(![X]:((~creative(X)<~>creative(X))=>(~wise(X)|patient(X))))&
(![X]:((~generous(X)<~>~old(X))<=>~curious(X)))&
(((~strong(fred)|humble(fred)))<=>((wise(john)&~funny(john))))&
(((~calm(paul)&~old(paul)))=>(?[X]:(calm(X))))&
(?[X]:((kind(X)<~>~patient(X))))&
((creative(mary)&rich(mary)))&
(?[X]:((~happy(X)|~wise(X))))&
((~funny(susan)|strong(susan)))&
((calm(fred)<~>rich(fred)))&
(happy(alice))&
((~tall(alice)<~>brave(alice)))&
((patient(paul)<~>happy(paul))) | rich(mary) | [
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 906578440931801914338829
% SZS output start Proof for 906578440931801914338829
18. rich(mary) & creative(mary) [input p17]
25. ~rich(mary) [input hypothesis]
119. rich(mary) [cnf transformation 18]
129. ~rich(mary) [cnf transformation 25]
312. $false [subsumption resolution 129,119]
% SZS output end Proof for 906578440931801914338829
% ------------------------------
% 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 humble or happy is either not wise or wise.
If someone is either creative or not funny then john is kind and vice versa.
Everyone who is strong or quiet is not strong.
If someone is funny then lucy is both happy and not humble and vice versa.
If someone is either not generous or not quiet then fred is both not curious and not quiet and vice versa.
If john is either not old or not rich then someone is both quiet and not old and vice versa.
Everyone who is patient is humble or not patient and vice versa.
Everyone who is happy is either quiet or not generous.
If someone is funny then someone is both funny and rich and vice versa.
Everyone who is not rich or creative is both humble and kind and vice versa.
Everyone who is generous is not calm or curious.
If someone is both not creative and not calm then someone is not patient or wise and vice versa.
Everyone who is rich is calm or rich and vice versa.
Everyone who is rich is generous or not patient and vice versa.
Everyone who is either old or not happy is both not generous and not strong and vice versa.
Everyone who is old or not generous is humble and vice versa.
Someone is both generous and creative.
Someone is either humble or not tall.
Fred is either kind or generous.
Paul is both patient and not strong.
Susan is either curious or not strong.
Someone is not strong or not patient.
Someone is either not humble or quiet. | Lucy is not old. | neutral | (![X]:((humble(X)<~>happy(X))=>(~wise(X)<~>wise(X))))&
((?[X]:((creative(X)<~>~funny(X))))<=>(kind(john)))&
(![X]:((strong(X)|quiet(X))=>~strong(X)))&
((?[X]:(funny(X)))<=>((happy(lucy)&~humble(lucy))))&
((?[X]:((~generous(X)<~>~quiet(X))))<=>((~curious(fred)&~quiet(fred))))&
(((~old(john)<~>~rich(john)))<=>(?[X]:((quiet(X)&~old(X)))))&
(![X]:(patient(X)<=>(humble(X)|~patient(X))))&
(![X]:(happy(X)=>(quiet(X)<~>~generous(X))))&
((?[X]:(funny(X)))<=>(?[X]:((funny(X)&rich(X)))))&
(![X]:((~rich(X)|creative(X))<=>(humble(X)&kind(X))))&
(![X]:(generous(X)=>(~calm(X)|curious(X))))&
((?[X]:((~creative(X)&~calm(X))))<=>(?[X]:((~patient(X)|wise(X)))))&
(![X]:(rich(X)<=>(calm(X)|rich(X))))&
(![X]:(rich(X)<=>(generous(X)|~patient(X))))&
(![X]:((old(X)<~>~happy(X))<=>(~generous(X)&~strong(X))))&
(![X]:((old(X)|~generous(X))<=>humble(X)))&
(?[X]:((generous(X)&creative(X))))&
(?[X]:((humble(X)<~>~tall(X))))&
((kind(fred)<~>generous(fred)))&
((patient(paul)&~strong(paul)))&
((curious(susan)<~>~strong(susan)))&
(?[X]:((~strong(X)|~patient(X))))&
(?[X]:((~humble(X)<~>quiet(X)))) | ~old(lucy) | [] | null | 0 |
If someone is not humble then someone is either humble or not curious.
Everyone who is not curious is calm or patient and vice versa.
Everyone who is both old and not brave is either creative or not old and vice versa.
Everyone who is both creative and not generous is old and vice versa.
Everyone who is either old or not happy is not creative and vice versa.
If someone is kind then fred is both not happy and calm.
Everyone who is not calm is both not rich and creative.
If susan is strong or tall then someone is tall.
Everyone who is not curious or kind is either not kind or not wise.
Everyone who is either rich or not quiet is either kind or not old and vice versa.
If lucy is either wise or not quiet then lucy is not funny and vice versa.
If someone is both patient and rich then someone is both not quiet and not funny.
If someone is not humble or happy then someone is either not generous or not creative.
Everyone who is either not brave or humble is both curious and not rich.
Everyone who is curious or not funny is patient or not quiet.
Everyone who is either not humble or wise is both humble and not humble and vice versa.
Someone is calm.
Someone is both humble and not old.
Someone is humble or strong.
Paul is not patient or curious.
Someone is either not humble or not happy.
Mary is not rich. | Fred is not curious. | entailment | ((?[X]:(~humble(X)))=>(?[X]:((humble(X)<~>~curious(X)))))&
(![X]:(~curious(X)<=>(calm(X)|patient(X))))&
(![X]:((old(X)&~brave(X))<=>(creative(X)<~>~old(X))))&
(![X]:((creative(X)&~generous(X))<=>old(X)))&
(![X]:((old(X)<~>~happy(X))<=>~creative(X)))&
((?[X]:(kind(X)))=>((~happy(fred)&calm(fred))))&
(![X]:(~calm(X)=>(~rich(X)&creative(X))))&
(((strong(susan)|tall(susan)))=>(?[X]:(tall(X))))&
(![X]:((~curious(X)|kind(X))=>(~kind(X)<~>~wise(X))))&
(![X]:((rich(X)<~>~quiet(X))<=>(kind(X)<~>~old(X))))&
(((wise(lucy)<~>~quiet(lucy)))<=>(~funny(lucy)))&
((?[X]:((patient(X)&rich(X))))=>(?[X]:((~quiet(X)&~funny(X)))))&
((?[X]:((~humble(X)|happy(X))))=>(?[X]:((~generous(X)<~>~creative(X)))))&
(![X]:((~brave(X)<~>humble(X))=>(curious(X)&~rich(X))))&
(![X]:((curious(X)|~funny(X))=>(patient(X)|~quiet(X))))&
(![X]:((~humble(X)<~>wise(X))<=>(humble(X)&~humble(X))))&
(?[X]:(calm(X)))&
(?[X]:((humble(X)&~old(X))))&
(?[X]:((humble(X)|strong(X))))&
((~patient(paul)|curious(paul)))&
(?[X]:((~humble(X)<~>~happy(X))))&
(~rich(mary)) | ~curious(fred) | [
"p1",
"p2",
"p3",
"p4",
"p5",
"p6",
"p8",
"p9",
"p12",
"p13",
"p14",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 1917964229633658750260100
% SZS output start Proof for 1917964229633658750260100
2. ! [X0] : (~curious(X0) <=> (patient(X0) | calm(X0))) [input p1]
3. ! [X0] : ((~brave(X0) & old(X0)) <=> (creative(X0) <~> ~old(X0))) [input p2]
4. ! [X0] : ((~generous(X0) & creative(X0)) <=> old(X0)) [input p3]
5. ! [X0] : ((old(X0) <~> ~happy(X0)) <=> ~creative(X0)) [input p4]
6. ? [X0] : kind(X0) => (calm(fred) & ~happy(fred)) [input p5]
7. ! [X0] : (~calm(X0) => (creative(X0) & ~rich(X0))) [input p6]
9. ! [X0] : ((kind(X0) | ~curious(X0)) => (~kind(X0) <~> ~wise(X0))) [input p8]
10. ! [X0] : ((rich(X0) <~> ~quiet(X0)) <=> (kind(X0) <~> ~old(X0))) [input p9]
13. ? [X0] : (happy(X0) | ~humble(X0)) => ? [X0] : (~generous(X0) <~> ~creative(X0)) [input p12]
14. ! [X0] : ((~brave(X0) <~> humble(X0)) => (~rich(X0) & curious(X0))) [input p13]
15. ! [X0] : ((~funny(X0) | curious(X0)) => (~quiet(X0) | patient(X0))) [input p14]
16. ! [X0] : ((~humble(X0) <~> wise(X0)) <=> (~humble(X0) & humble(X0))) [input p15]
18. ? [X0] : (~old(X0) & humble(X0)) [input p17]
23. curious(fred) [input hypothesis]
26. ? [X0] : (happy(X0) | ~humble(X0)) => ? [X1] : (~generous(X1) <~> ~creative(X1)) [rectify 13]
28. (calm(fred) & ~happy(fred)) | ! [X0] : ~kind(X0) [ennf transformation 6]
29. ! [X0] : ((creative(X0) & ~rich(X0)) | calm(X0)) [ennf transformation 7]
31. ! [X0] : ((~kind(X0) <~> ~wise(X0)) | (~kind(X0) & curious(X0))) [ennf transformation 9]
33. ? [X1] : (~generous(X1) <~> ~creative(X1)) | ! [X0] : (~happy(X0) & humble(X0)) [ennf transformation 26]
34. ! [X0] : ((~rich(X0) & curious(X0)) | (~brave(X0) <=> humble(X0))) [ennf transformation 14]
35. ! [X0] : ((~quiet(X0) | patient(X0)) | (funny(X0) & ~curious(X0))) [ennf transformation 15]
36. ! [X0] : (~quiet(X0) | patient(X0) | (funny(X0) & ~curious(X0))) [flattening 35]
41. ! [X0] : ((~curious(X0) | (~patient(X0) & ~calm(X0))) & ((patient(X0) | calm(X0)) | curious(X0))) [nnf transformation 2]
42. ! [X0] : ((~curious(X0) | (~patient(X0) & ~calm(X0))) & (patient(X0) | calm(X0) | curious(X0))) [flattening 41]
43. ! [X0] : (((~brave(X0) & old(X0)) | ((creative(X0) | old(X0)) & (~old(X0) | ~creative(X0)))) & (((old(X0) | ~creative(X0)) & (~old(X0) | creative(X0))) | (brave(X0) | ~old(X0)))) [nnf transformation 3]
44. ! [X0] : (((~brave(X0) & old(X0)) | ((creative(X0) | old(X0)) & (~old(X0) | ~creative(X0)))) & (((old(X0) | ~creative(X0)) & (~old(X0) | creative(X0))) | brave(X0) | ~old(X0))) [flattening 43]
45. ! [X0] : (((~generous(X0) & creative(X0)) | ~old(X0)) & (old(X0) | (generous(X0) | ~creative(X0)))) [nnf transformation 4]
46. ! [X0] : (((~generous(X0) & creative(X0)) | ~old(X0)) & (old(X0) | generous(X0) | ~creative(X0))) [flattening 45]
47. ! [X0] : ((((happy(X0) | ~old(X0)) & (~happy(X0) | old(X0))) | creative(X0)) & (~creative(X0) | ((old(X0) | happy(X0)) & (~happy(X0) | ~old(X0))))) [nnf transformation 5]
50. ! [X0] : (((wise(X0) | kind(X0)) & (~wise(X0) | ~kind(X0))) | (~kind(X0) & curious(X0))) [nnf transformation 31]
51. ! [X0] : ((((quiet(X0) | ~rich(X0)) & (~quiet(X0) | rich(X0))) | ((kind(X0) | old(X0)) & (~old(X0) | ~kind(X0)))) & (((old(X0) | ~kind(X0)) & (~old(X0) | kind(X0))) | ((rich(X0) | quiet(X0)) & (~quiet(X0) | ~rich(X0))))) [nnf transformation 10]
56. ? [X1] : ((creative(X1) | generous(X1)) & (~creative(X1) | ~generous(X1))) | ! [X0] : (~happy(X0) & humble(X0)) [nnf transformation 33]
57. ? [X0] : ((creative(X0) | generous(X0)) & (~creative(X0) | ~generous(X0))) | ! [X1] : (~happy(X1) & humble(X1)) [rectify 56]
58. ? [X0] : ((creative(X0) | generous(X0)) & (~creative(X0) | ~generous(X0))) => ((creative(sK3) | generous(sK3)) & (~creative(sK3) | ~generous(sK3))) [choice axiom]
59. ((creative(sK3) | generous(sK3)) & (~creative(sK3) | ~generous(sK3))) | ! [X1] : (~happy(X1) & humble(X1)) [skolemisation 57,58]
60. ! [X0] : ((~rich(X0) & curious(X0)) | ((~brave(X0) | ~humble(X0)) & (humble(X0) | brave(X0)))) [nnf transformation 34]
61. ! [X0] : ((((~wise(X0) | humble(X0)) & (wise(X0) | ~humble(X0))) | (humble(X0) | ~humble(X0))) & ((~humble(X0) & humble(X0)) | ((~humble(X0) | ~wise(X0)) & (wise(X0) | humble(X0))))) [nnf transformation 16]
62. ! [X0] : ((((~wise(X0) | humble(X0)) & (wise(X0) | ~humble(X0))) | humble(X0) | ~humble(X0)) & ((~humble(X0) & humble(X0)) | ((~humble(X0) | ~wise(X0)) & (wise(X0) | humble(X0))))) [flattening 61]
65. ? [X0] : (~old(X0) & humble(X0)) => (~old(sK5) & humble(sK5)) [choice axiom]
66. ~old(sK5) & humble(sK5) [skolemisation 18,65]
75. ~calm(X0) | ~curious(X0) [cnf transformation 42]
76. ~patient(X0) | ~curious(X0) [cnf transformation 42]
80. old(X0) | creative(X0) | old(X0) [cnf transformation 44]
81. ~creative(X0) | ~old(X0) | ~brave(X0) [cnf transformation 44]
83. old(X0) | generous(X0) | ~creative(X0) [cnf transformation 46]
84. creative(X0) | ~old(X0) [cnf transformation 46]
87. ~creative(X0) | old(X0) | happy(X0) [cnf transformation 47]
91. calm(fred) | ~kind(X0) [cnf transformation 28]
92. ~rich(X0) | calm(X0) [cnf transformation 29]
98. wise(X0) | kind(X0) | curious(X0) [cnf transformation 50]
101. ~old(X0) | kind(X0) | rich(X0) | quiet(X0) [cnf transformation 51]
115. ~creative(sK3) | ~generous(sK3) | ~happy(X1) [cnf transformation 59]
118. brave(X0) | humble(X0) | curious(X0) [cnf transformation 60]
122. ~quiet(X0) | patient(X0) | ~curious(X0) [cnf transformation 36]
127. ~humble(X0) | ~humble(X0) | ~wise(X0) [cnf transformation 62]
132. ~old(sK5) [cnf transformation 66]
138. curious(fred) [cnf transformation 23]
140. ~wise(X0) | ~humble(X0) [duplicate literal removal 127]
145. creative(X0) | old(X0) [duplicate literal removal 80]
160. creative(X0) [subsumption resolution 84,145]
161. generous(X0) | old(X0) [subsumption resolution 83,160]
162. happy(X0) | old(X0) [subsumption resolution 87,160]
165. 4 <=> ! [X0] : ~kind(X0) [avatar definition]
166. ~kind(X0) <- (4) [avatar component clause 165]
168. 5 <=> calm(fred) [avatar definition]
170. calm(fred) <- (5) [avatar component clause 168]
171. 4 | 5 [avatar split clause 91,168,165]
220. ~generous(sK3) | ~happy(X1) [subsumption resolution 115,160]
222. 16 <=> ! [X1] : ~happy(X1) [avatar definition]
223. ~happy(X1) <- (16) [avatar component clause 222]
225. 17 <=> generous(sK3) [avatar definition]
227. ~generous(sK3) <- (~17) [avatar component clause 225]
228. 16 | ~17 [avatar split clause 220,225,222]
231. ~quiet(X0) | ~curious(X0) [subsumption resolution 122,76]
273. ~brave(X2) | ~old(X2) [resolution 81,160]
276. kind(X1) | curious(X1) | ~humble(X1) [resolution 98,140]
279. humble(X0) | curious(X0) | ~old(X0) [resolution 118,273]
294. 24 <=> quiet(sK3) [avatar definition]
296. quiet(sK3) <- (24) [avatar component clause 294]
298. 25 <=> rich(sK3) [avatar definition]
300. rich(sK3) <- (25) [avatar component clause 298]
315. old(X0) <- (16) [resolution 223,162]
320. ~curious(fred) <- (5) [resolution 170,75]
321. $false <- (5) [subsumption resolution 320,138]
322. ~5 [avatar contradiction clause 321]
323. old(sK3) <- (~17) [resolution 227,161]
327. ~humble(X1) | curious(X1) <- (4) [subsumption resolution 276,166]
335. $false <- (16) [resolution 315,132]
337. ~16 [avatar contradiction clause 335]
339. ~old(X0) | curious(X0) <- (4) [subsumption resolution 279,327]
342. kind(sK3) | rich(sK3) | quiet(sK3) <- (~17) [resolution 323,101]
374. rich(sK3) | quiet(sK3) <- (4, ~17) [subsumption resolution 342,166]
375. 24 | 25 | ~4 | 17 [avatar split clause 374,225,165,298,294]
400. ~curious(sK3) <- (24) [resolution 296,231]
422. curious(sK3) <- (4, ~17) [resolution 339,323]
423. $false <- (4, ~17, 24) [subsumption resolution 422,400]
424. ~4 | 17 | ~24 [avatar contradiction clause 423]
429. calm(sK3) <- (25) [resolution 300,92]
432. ~curious(sK3) <- (25) [resolution 429,75]
433. $false <- (4, ~17, 25) [subsumption resolution 432,422]
434. ~4 | 17 | ~25 [avatar contradiction clause 433]
435. $false [avatar sat refutation 171,228,322,337,375,424,434]
% SZS output end Proof for 1917964229633658750260100
% ------------------------------
% 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 creative or not funny is not humble or rich.
Everyone who is not calm is either quiet or not brave and vice versa.
Everyone who is not tall is both not creative and not humble.
If someone is not kind then someone is both not rich and old and vice versa.
If someone is both not brave and kind then someone is either not rich or not brave.
If alice is either quiet or rich then someone is generous and vice versa.
If someone is not brave or patient then alice is either kind or brave.
Everyone who is either not generous or not curious is both quiet and brave.
If someone is not tall then paul is both brave and patient and vice versa.
Everyone who is either not tall or not funny is both strong and patient and vice versa.
If someone is not rich then someone is not quiet or not generous.
If fred is calm then susan is both wise and not brave.
Everyone who is not wise is both not funny and old.
If someone is either not calm or funny then john is not kind or rich.
Everyone who is both not wise and not generous is not strong or curious and vice versa.
Everyone who is tall or funny is either humble or curious.
Someone is quiet or not brave.
Alice is not brave.
Lucy is not quiet.
Someone is not strong.
Someone is not tall or not wise.
Someone is either not happy or not kind.
Someone is both not old and patient. | Paul is funny. | contradiction | (![X]:((~creative(X)<~>~funny(X))=>(~humble(X)|rich(X))))&
(![X]:(~calm(X)<=>(quiet(X)<~>~brave(X))))&
(![X]:(~tall(X)=>(~creative(X)&~humble(X))))&
((?[X]:(~kind(X)))<=>(?[X]:((~rich(X)&old(X)))))&
((?[X]:((~brave(X)&kind(X))))=>(?[X]:((~rich(X)<~>~brave(X)))))&
(((quiet(alice)<~>rich(alice)))<=>(?[X]:(generous(X))))&
((?[X]:((~brave(X)|patient(X))))=>((kind(alice)<~>brave(alice))))&
(![X]:((~generous(X)<~>~curious(X))=>(quiet(X)&brave(X))))&
((?[X]:(~tall(X)))<=>((brave(paul)&patient(paul))))&
(![X]:((~tall(X)<~>~funny(X))<=>(strong(X)&patient(X))))&
((?[X]:(~rich(X)))=>(?[X]:((~quiet(X)|~generous(X)))))&
((calm(fred))=>((wise(susan)&~brave(susan))))&
(![X]:(~wise(X)=>(~funny(X)&old(X))))&
((?[X]:((~calm(X)<~>funny(X))))=>((~kind(john)|rich(john))))&
(![X]:((~wise(X)&~generous(X))<=>(~strong(X)|curious(X))))&
(![X]:((tall(X)|funny(X))=>(humble(X)<~>curious(X))))&
(?[X]:((quiet(X)|~brave(X))))&
(~brave(alice))&
(~quiet(lucy))&
(?[X]:(~strong(X)))&
(?[X]:((~tall(X)|~wise(X))))&
(?[X]:((~happy(X)<~>~kind(X))))&
(?[X]:((~old(X)&patient(X)))) | funny(paul) | [
"p2",
"p8",
"p9",
"p12",
"p14",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 585409235875727174544692
% SZS output start Proof for 585409235875727174544692
3. ! [X0] : (~tall(X0) => (~humble(X0) & ~creative(X0))) [input p2]
9. ? [X0] : ~tall(X0) <=> (patient(paul) & brave(paul)) [input p8]
10. ! [X0] : ((~tall(X0) <~> ~funny(X0)) <=> (patient(X0) & strong(X0))) [input p9]
13. ! [X0] : (~wise(X0) => (old(X0) & ~funny(X0))) [input p12]
15. ! [X0] : ((~generous(X0) & ~wise(X0)) <=> (curious(X0) | ~strong(X0))) [input p14]
16. ! [X0] : ((funny(X0) | tall(X0)) => (humble(X0) <~> curious(X0))) [input p15]
20. ? [X0] : ~strong(X0) [input p19]
24. funny(paul) [input hypothesis]
30. ! [X0] : ((~humble(X0) & ~creative(X0)) | tall(X0)) [ennf transformation 3]
36. ! [X0] : ((old(X0) & ~funny(X0)) | wise(X0)) [ennf transformation 13]
39. ! [X0] : ((humble(X0) <~> curious(X0)) | (~funny(X0) & ~tall(X0))) [ennf transformation 16]
57. (? [X0] : ~tall(X0) | (~patient(paul) | ~brave(paul))) & ((patient(paul) & brave(paul)) | ! [X0] : tall(X0)) [nnf transformation 9]
58. (? [X0] : ~tall(X0) | ~patient(paul) | ~brave(paul)) & ((patient(paul) & brave(paul)) | ! [X0] : tall(X0)) [flattening 57]
59. (? [X0] : ~tall(X0) | ~patient(paul) | ~brave(paul)) & ((patient(paul) & brave(paul)) | ! [X1] : tall(X1)) [rectify 58]
60. ? [X0] : ~tall(X0) => ~tall(sK4) [choice axiom]
61. (~tall(sK4) | ~patient(paul) | ~brave(paul)) & ((patient(paul) & brave(paul)) | ! [X1] : tall(X1)) [skolemisation 59,60]
62. ! [X0] : ((((funny(X0) | tall(X0)) & (~funny(X0) | ~tall(X0))) | (~patient(X0) | ~strong(X0))) & ((patient(X0) & strong(X0)) | ((~tall(X0) | funny(X0)) & (~funny(X0) | tall(X0))))) [nnf transformation 10]
63. ! [X0] : ((((funny(X0) | tall(X0)) & (~funny(X0) | ~tall(X0))) | ~patient(X0) | ~strong(X0)) & ((patient(X0) & strong(X0)) | ((~tall(X0) | funny(X0)) & (~funny(X0) | tall(X0))))) [flattening 62]
68. ! [X0] : (((~generous(X0) & ~wise(X0)) | (~curious(X0) & strong(X0))) & ((curious(X0) | ~strong(X0)) | (generous(X0) | wise(X0)))) [nnf transformation 15]
69. ! [X0] : (((~generous(X0) & ~wise(X0)) | (~curious(X0) & strong(X0))) & (curious(X0) | ~strong(X0) | generous(X0) | wise(X0))) [flattening 68]
70. ! [X0] : (((~curious(X0) | ~humble(X0)) & (curious(X0) | humble(X0))) | (~funny(X0) & ~tall(X0))) [nnf transformation 39]
73. ? [X0] : ~strong(X0) => ~strong(sK7) [choice axiom]
74. ~strong(sK7) [skolemisation 20,73]
89. ~humble(X0) | tall(X0) [cnf transformation 30]
108. patient(paul) | tall(X1) [cnf transformation 61]
111. ~tall(X0) | strong(X0) | funny(X0) [cnf transformation 63]
114. ~strong(X0) | ~tall(X0) | ~patient(X0) | ~funny(X0) [cnf transformation 63]
119. ~funny(X0) | wise(X0) [cnf transformation 36]
124. ~wise(X0) | strong(X0) [cnf transformation 69]
125. ~wise(X0) | ~curious(X0) [cnf transformation 69]
129. ~funny(X0) | humble(X0) | curious(X0) [cnf transformation 70]
135. ~strong(sK7) [cnf transformation 74]
141. funny(paul) [cnf transformation 24]
218. 18 <=> patient(paul) [avatar definition]
219. patient(paul) <- (18) [avatar component clause 218]
227. 20 <=> ! [X1] : tall(X1) [avatar definition]
228. tall(X1) <- (20) [avatar component clause 227]
229. 20 | 18 [avatar split clause 108,218,227]
309. wise(paul) [resolution 119,141]
311. strong(paul) [resolution 124,309]
313. ~curious(paul) [resolution 125,309]
347. strong(X0) | funny(X0) <- (20) [resolution 111,228]
348. funny(sK7) <- (20) [resolution 347,135]
352. wise(sK7) <- (20) [resolution 348,119]
355. strong(sK7) <- (20) [resolution 352,124]
356. $false <- (20) [subsumption resolution 355,135]
357. ~20 [avatar contradiction clause 356]
363. humble(paul) | curious(paul) [resolution 129,141]
364. humble(paul) [subsumption resolution 363,313]
365. tall(paul) [resolution 364,89]
382. ~tall(paul) | ~patient(paul) | ~funny(paul) [resolution 114,311]
384. ~patient(paul) | ~funny(paul) [subsumption resolution 382,365]
385. ~funny(paul) <- (18) [subsumption resolution 384,219]
386. $false <- (18) [subsumption resolution 385,141]
387. ~18 [avatar contradiction clause 386]
388. $false [avatar sat refutation 229,357,387]
% SZS output end Proof for 585409235875727174544692
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either brave or funny then someone is happy or strong and vice versa.
Everyone who is either old or rich is either strong or brave and vice versa.
If someone is either not old or quiet then someone is either not kind or not patient and vice versa.
Everyone who is generous or rich is not humble or generous.
Everyone who is either not funny or not brave is either happy or quiet and vice versa.
Everyone who is both curious and not wise is quiet or not funny.
If someone is both not calm and calm then someone is either not funny or brave.
Everyone who is curious is calm or not strong.
If mary is either calm or tall then someone is either not patient or calm and vice versa.
Everyone who is strong is both generous and tall and vice versa.
Everyone who is either old or not tall is either not rich or funny and vice versa.
If someone is quiet or brave then mary is not quiet.
Everyone who is either tall or curious is not curious or creative.
If someone is not generous then paul is not rich and vice versa.
If alice is both not patient and not funny then someone is either curious or quiet and vice versa.
Everyone who is both not generous and not strong is not tall.
Someone is either patient or not rich.
Someone is either humble or not rich.
Lucy is not happy.
Paul is not quiet or not tall.
Fred is both generous and old.
Someone is funny.
Lucy is tall or not happy. | Paul is quiet. | contradiction | ((?[X]:((brave(X)<~>funny(X))))<=>(?[X]:((happy(X)|strong(X)))))&
(![X]:((old(X)<~>rich(X))<=>(strong(X)<~>brave(X))))&
((?[X]:((~old(X)<~>quiet(X))))<=>(?[X]:((~kind(X)<~>~patient(X)))))&
(![X]:((generous(X)|rich(X))=>(~humble(X)|generous(X))))&
(![X]:((~funny(X)<~>~brave(X))<=>(happy(X)<~>quiet(X))))&
(![X]:((curious(X)&~wise(X))=>(quiet(X)|~funny(X))))&
((?[X]:((~calm(X)&calm(X))))=>(?[X]:((~funny(X)<~>brave(X)))))&
(![X]:(curious(X)=>(calm(X)|~strong(X))))&
(((calm(mary)<~>tall(mary)))<=>(?[X]:((~patient(X)<~>calm(X)))))&
(![X]:(strong(X)<=>(generous(X)&tall(X))))&
(![X]:((old(X)<~>~tall(X))<=>(~rich(X)<~>funny(X))))&
((?[X]:((quiet(X)|brave(X))))=>(~quiet(mary)))&
(![X]:((tall(X)<~>curious(X))=>(~curious(X)|creative(X))))&
((?[X]:(~generous(X)))<=>(~rich(paul)))&
(((~patient(alice)&~funny(alice)))<=>(?[X]:((curious(X)<~>quiet(X)))))&
(![X]:((~generous(X)&~strong(X))=>~tall(X)))&
(?[X]:((patient(X)<~>~rich(X))))&
(?[X]:((humble(X)<~>~rich(X))))&
(~happy(lucy))&
((~quiet(paul)|~tall(paul)))&
((generous(fred)&old(fred)))&
(?[X]:(funny(X)))&
((tall(lucy)|~happy(lucy))) | quiet(paul) | [
"p0",
"p1",
"p4",
"p9",
"p10",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 5588413491499742955156948
% SZS output start Proof for 5588413491499742955156948
1. ? [X0] : (brave(X0) <~> funny(X0)) <=> ? [X0] : (strong(X0) | happy(X0)) [input p0]
2. ! [X0] : ((old(X0) <~> rich(X0)) <=> (strong(X0) <~> brave(X0))) [input p1]
5. ! [X0] : ((~funny(X0) <~> ~brave(X0)) <=> (happy(X0) <~> quiet(X0))) [input p4]
10. ! [X0] : (strong(X0) <=> (tall(X0) & generous(X0))) [input p9]
11. ! [X0] : ((old(X0) <~> ~tall(X0)) <=> (~rich(X0) <~> funny(X0))) [input p10]
16. ! [X0] : ((~strong(X0) & ~generous(X0)) => ~tall(X0)) [input p15]
24. quiet(paul) [input hypothesis]
25. ? [X0] : (brave(X0) <~> funny(X0)) <=> ? [X1] : (strong(X1) | happy(X1)) [rectify 1]
36. ! [X0] : (~tall(X0) | (strong(X0) | generous(X0))) [ennf transformation 16]
37. ! [X0] : (~tall(X0) | strong(X0) | generous(X0)) [flattening 36]
38. (? [X0] : ((~funny(X0) | ~brave(X0)) & (funny(X0) | brave(X0))) | ! [X1] : (~strong(X1) & ~happy(X1))) & (? [X1] : (strong(X1) | happy(X1)) | ! [X0] : ((brave(X0) | ~funny(X0)) & (funny(X0) | ~brave(X0)))) [nnf transformation 25]
39. (? [X0] : ((~funny(X0) | ~brave(X0)) & (funny(X0) | brave(X0))) | ! [X1] : (~strong(X1) & ~happy(X1))) & (? [X2] : (strong(X2) | happy(X2)) | ! [X3] : ((brave(X3) | ~funny(X3)) & (funny(X3) | ~brave(X3)))) [rectify 38]
40. ? [X0] : ((~funny(X0) | ~brave(X0)) & (funny(X0) | brave(X0))) => ((~funny(sK0) | ~brave(sK0)) & (funny(sK0) | brave(sK0))) [choice axiom]
41. ? [X2] : (strong(X2) | happy(X2)) => (strong(sK1) | happy(sK1)) [choice axiom]
42. (((~funny(sK0) | ~brave(sK0)) & (funny(sK0) | brave(sK0))) | ! [X1] : (~strong(X1) & ~happy(X1))) & ((strong(sK1) | happy(sK1)) | ! [X3] : ((brave(X3) | ~funny(X3)) & (funny(X3) | ~brave(X3)))) [skolemisation 39,41,40]
43. ! [X0] : ((((~rich(X0) | ~old(X0)) & (rich(X0) | old(X0))) | ((strong(X0) | ~brave(X0)) & (brave(X0) | ~strong(X0)))) & (((~brave(X0) | ~strong(X0)) & (brave(X0) | strong(X0))) | ((old(X0) | ~rich(X0)) & (rich(X0) | ~old(X0))))) [nnf transformation 2]
49. ! [X0] : ((((brave(X0) | funny(X0)) & (~brave(X0) | ~funny(X0))) | ((happy(X0) | ~quiet(X0)) & (quiet(X0) | ~happy(X0)))) & (((~quiet(X0) | ~happy(X0)) & (quiet(X0) | happy(X0))) | ((~funny(X0) | brave(X0)) & (~brave(X0) | funny(X0))))) [nnf transformation 5]
58. ! [X0] : ((strong(X0) | (~tall(X0) | ~generous(X0))) & ((tall(X0) & generous(X0)) | ~strong(X0))) [nnf transformation 10]
59. ! [X0] : ((strong(X0) | ~tall(X0) | ~generous(X0)) & ((tall(X0) & generous(X0)) | ~strong(X0))) [flattening 58]
60. ! [X0] : ((((tall(X0) | ~old(X0)) & (~tall(X0) | old(X0))) | ((~rich(X0) | ~funny(X0)) & (funny(X0) | rich(X0)))) & (((~funny(X0) | rich(X0)) & (funny(X0) | ~rich(X0))) | ((old(X0) | tall(X0)) & (~tall(X0) | ~old(X0))))) [nnf transformation 11]
78. strong(sK1) | happy(sK1) | funny(X3) | ~brave(X3) [cnf transformation 42]
79. strong(sK1) | happy(sK1) | brave(X3) | ~funny(X3) [cnf transformation 42]
80. funny(sK0) | brave(sK0) | ~happy(X1) [cnf transformation 42]
81. funny(sK0) | brave(sK0) | ~strong(X1) [cnf transformation 42]
82. ~funny(sK0) | ~brave(sK0) | ~happy(X1) [cnf transformation 42]
83. ~funny(sK0) | ~brave(sK0) | ~strong(X1) [cnf transformation 42]
84. ~old(X0) | strong(X0) | rich(X0) | brave(X0) [cnf transformation 43]
85. ~rich(X0) | strong(X0) | old(X0) | brave(X0) [cnf transformation 43]
86. ~old(X0) | ~strong(X0) | rich(X0) | ~brave(X0) [cnf transformation 43]
87. ~rich(X0) | ~strong(X0) | old(X0) | ~brave(X0) [cnf transformation 43]
88. ~strong(X0) | old(X0) | brave(X0) | rich(X0) [cnf transformation 43]
89. ~brave(X0) | old(X0) | strong(X0) | rich(X0) [cnf transformation 43]
90. ~rich(X0) | ~old(X0) | brave(X0) | ~strong(X0) [cnf transformation 43]
91. ~rich(X0) | ~old(X0) | strong(X0) | ~brave(X0) [cnf transformation 43]
107. ~quiet(X0) | ~funny(X0) | happy(X0) | ~brave(X0) [cnf transformation 49]
109. ~quiet(X0) | funny(X0) | happy(X0) | brave(X0) [cnf transformation 49]
121. ~strong(X0) | generous(X0) [cnf transformation 59]
122. ~strong(X0) | tall(X0) [cnf transformation 59]
123. ~tall(X0) | strong(X0) | ~generous(X0) [cnf transformation 59]
124. ~tall(X0) | ~rich(X0) | funny(X0) | ~old(X0) [cnf transformation 60]
125. ~rich(X0) | funny(X0) | old(X0) | tall(X0) [cnf transformation 60]
126. ~tall(X0) | rich(X0) | ~funny(X0) | ~old(X0) [cnf transformation 60]
127. ~funny(X0) | rich(X0) | old(X0) | tall(X0) [cnf transformation 60]
128. ~tall(X0) | old(X0) | funny(X0) | rich(X0) [cnf transformation 60]
129. ~tall(X0) | old(X0) | ~rich(X0) | ~funny(X0) [cnf transformation 60]
130. ~old(X0) | tall(X0) | funny(X0) | rich(X0) [cnf transformation 60]
131. ~rich(X0) | ~old(X0) | tall(X0) | ~funny(X0) [cnf transformation 60]
142. ~tall(X0) | strong(X0) | generous(X0) [cnf transformation 37]
153. quiet(paul) [cnf transformation 24]
155. 1 <=> ! [X1] : ~strong(X1) [avatar definition]
156. ~strong(X1) <- (1) [avatar component clause 155]
158. 2 <=> brave(sK0) [avatar definition]
159. brave(sK0) <- (2) [avatar component clause 158]
160. ~brave(sK0) <- (~2) [avatar component clause 158]
162. 3 <=> funny(sK0) [avatar definition]
163. funny(sK0) <- (3) [avatar component clause 162]
164. ~funny(sK0) <- (~3) [avatar component clause 162]
165. 1 | ~2 | ~3 [avatar split clause 83,162,158,155]
167. 4 <=> ! [X1] : ~happy(X1) [avatar definition]
168. ~happy(X1) <- (4) [avatar component clause 167]
169. 4 | ~2 | ~3 [avatar split clause 82,162,158,167]
170. 1 | 2 | 3 [avatar split clause 81,162,158,155]
171. 4 | 2 | 3 [avatar split clause 80,162,158,167]
173. 5 <=> ! [X3] : (brave(X3) | ~funny(X3)) [avatar definition]
174. ~funny(X3) | brave(X3) <- (5) [avatar component clause 173]
176. 6 <=> happy(sK1) [avatar definition]
178. happy(sK1) <- (6) [avatar component clause 176]
180. 7 <=> strong(sK1) [avatar definition]
182. strong(sK1) <- (7) [avatar component clause 180]
183. 5 | 6 | 7 [avatar split clause 79,180,176,173]
185. 8 <=> ! [X3] : (funny(X3) | ~brave(X3)) [avatar definition]
186. ~brave(X3) | funny(X3) <- (8) [avatar component clause 185]
187. 8 | 6 | 7 [avatar split clause 78,180,176,185]
307. ~tall(X0) | generous(X0) [subsumption resolution 142,121]
329. 39 <=> quiet(paul) [avatar definition]
330. quiet(paul) <- (39) [avatar component clause 329]
337. 39 [avatar split clause 153,329]
370. 46 <=> rich(sK0) [avatar definition]
371. ~rich(sK0) <- (~46) [avatar component clause 370]
372. rich(sK0) <- (46) [avatar component clause 370]
374. 47 <=> strong(sK0) [avatar definition]
375. ~strong(sK0) <- (~47) [avatar component clause 374]
376. strong(sK0) <- (47) [avatar component clause 374]
378. 48 <=> old(sK0) [avatar definition]
379. ~old(sK0) <- (~48) [avatar component clause 378]
380. old(sK0) <- (48) [avatar component clause 378]
435. $false <- (4, 6) [resolution 168,178]
436. ~4 | ~6 [avatar contradiction clause 435]
438. old(sK0) | strong(sK0) | rich(sK0) <- (2) [resolution 159,89]
447. 60 <=> funny(paul) [avatar definition]
448. ~funny(paul) <- (~60) [avatar component clause 447]
449. funny(paul) <- (60) [avatar component clause 447]
451. 61 <=> brave(paul) [avatar definition]
452. brave(paul) <- (61) [avatar component clause 451]
453. ~brave(paul) <- (~61) [avatar component clause 451]
455. 62 <=> happy(paul) [avatar definition]
456. happy(paul) <- (62) [avatar component clause 455]
461. ~strong(sK0) | old(sK0) | ~brave(sK0) <- (46) [resolution 372,87]
500. ~strong(sK0) | ~brave(sK0) <- (46, ~48) [subsumption resolution 461,379]
501. ~strong(sK0) <- (2, 46, ~48) [subsumption resolution 500,159]
502. ~47 | ~2 | ~46 | 48 [avatar split clause 501,378,370,158,374]
503. ~funny(paul) | happy(paul) | ~brave(paul) <- (39) [resolution 107,330]
509. funny(paul) | happy(paul) | brave(paul) <- (39) [resolution 109,330]
510. happy(paul) | brave(paul) <- (39, ~60) [subsumption resolution 509,448]
511. happy(paul) <- (39, ~60, ~61) [subsumption resolution 510,453]
512. 62 | ~39 | 60 | 61 [avatar split clause 511,451,447,329,455]
514. funny(sK0) | old(sK0) | tall(sK0) <- (46) [resolution 125,372]
515. old(sK0) | tall(sK0) <- (~3, 46) [subsumption resolution 514,164]
516. tall(sK0) <- (~3, 46, ~48) [subsumption resolution 515,379]
567. strong(sK0) | ~generous(sK0) <- (~3, 46, ~48) [resolution 516,123]
568. generous(sK0) <- (~3, 46, ~48) [resolution 516,307]
569. ~generous(sK0) <- (~3, 46, ~47, ~48) [subsumption resolution 567,375]
570. $false <- (~3, 46, ~47, ~48) [subsumption resolution 568,569]
571. 3 | ~46 | 47 | 48 [avatar contradiction clause 570]
575. tall(sK0) <- (47) [resolution 376,122]
603. old(sK0) | funny(sK0) | rich(sK0) <- (47) [resolution 575,128]
605. ~rich(sK0) | funny(sK0) | ~old(sK0) <- (47) [resolution 575,124]
612. old(sK0) | rich(sK0) <- (~3, 47) [subsumption resolution 603,164]
613. old(sK0) <- (~3, ~46, 47) [subsumption resolution 612,371]
614. 48 | 3 | 46 | ~47 [avatar split clause 613,374,370,162,378]
615. tall(sK0) | funny(sK0) | rich(sK0) <- (48) [resolution 380,130]
616. ~strong(sK0) | rich(sK0) | ~brave(sK0) <- (48) [resolution 380,86]
618. rich(sK0) | ~brave(sK0) <- (47, 48) [subsumption resolution 616,376]
622. rich(sK0) <- (2, 47, 48) [subsumption resolution 618,159]
623. 46 | ~2 | ~47 | ~48 [avatar split clause 622,378,374,158,370]
624. ~rich(sK0) | ~old(sK0) <- (~3, 47) [subsumption resolution 605,164]
625. ~rich(sK0) <- (~3, 47, 48) [subsumption resolution 624,380]
626. ~46 | 3 | ~47 | ~48 [avatar split clause 625,378,374,162,370]
629. ~old(sK0) | strong(sK0) | ~brave(sK0) <- (46) [resolution 372,91]
633. strong(sK0) | ~brave(sK0) <- (46, 48) [subsumption resolution 629,380]
634. ~brave(sK0) <- (46, ~47, 48) [subsumption resolution 633,375]
635. $false <- (2, 46, ~47, 48) [subsumption resolution 634,159]
636. ~2 | ~46 | 47 | ~48 [avatar contradiction clause 635]
637. tall(sK0) | rich(sK0) <- (~3, 48) [subsumption resolution 615,164]
639. 75 <=> tall(sK0) [avatar definition]
641. tall(sK0) <- (75) [avatar component clause 639]
642. 46 | 75 | 3 | ~48 [avatar split clause 637,378,162,639,370]
654. strong(sK0) | ~generous(sK0) <- (75) [resolution 641,123]
655. generous(sK0) <- (75) [resolution 641,307]
656. ~generous(sK0) <- (~47, 75) [subsumption resolution 654,375]
657. $false <- (~47, 75) [subsumption resolution 655,656]
658. 47 | ~75 [avatar contradiction clause 657]
664. old(sK0) | rich(sK0) <- (2, ~47) [subsumption resolution 438,375]
665. 46 | 48 | ~2 | 47 [avatar split clause 664,374,158,378,370]
670. rich(sK0) | old(sK0) | tall(sK0) <- (3) [resolution 163,127]
672. $false <- (4, 62) [resolution 168,456]
673. ~4 | ~62 [avatar contradiction clause 672]
682. strong(sK0) | old(sK0) | brave(sK0) <- (46) [resolution 372,85]
687. brave(paul) <- (5, 60) [resolution 449,174]
694. 61 | ~5 | ~60 [avatar split clause 687,447,173,451]
698. $false <- (1, 7) [subsumption resolution 182,156]
699. ~1 | ~7 [avatar contradiction clause 698]
705. old(sK0) | brave(sK0) <- (46, ~47) [subsumption resolution 682,375]
706. brave(sK0) <- (46, ~47, ~48) [subsumption resolution 705,379]
707. 2 | ~46 | 47 | 48 [avatar split clause 706,378,374,370,158]
709. ~funny(paul) | happy(paul) <- (39, 61) [subsumption resolution 503,452]
710. 62 | ~60 | ~39 | ~61 [avatar split clause 709,451,329,447,455]
718. brave(sK0) <- (3, 5) [resolution 174,163]
719. $false <- (~2, 3, 5) [subsumption resolution 718,160]
720. 2 | ~3 | ~5 [avatar contradiction clause 719]
730. strong(sK0) | rich(sK0) | brave(sK0) <- (48) [resolution 380,84]
731. rich(sK0) | brave(sK0) <- (~47, 48) [subsumption resolution 730,375]
735. rich(sK0) <- (~2, ~47, 48) [subsumption resolution 731,160]
736. 46 | 2 | 47 | ~48 [avatar split clause 735,378,374,158,370]
737. ~old(sK0) | tall(sK0) | ~funny(sK0) <- (46) [resolution 372,131]
740. ~old(sK0) | brave(sK0) | ~strong(sK0) <- (46) [resolution 372,90]
743. tall(sK0) | ~funny(sK0) <- (46, 48) [subsumption resolution 737,380]
750. tall(sK0) <- (3, 46, 48) [subsumption resolution 743,163]
751. 75 | ~3 | ~46 | ~48 [avatar split clause 750,378,370,162,639]
752. ~old(sK0) | ~strong(sK0) <- (~2, 46) [subsumption resolution 740,160]
753. ~old(sK0) <- (~2, 46, 47) [subsumption resolution 752,376]
754. ~48 | 2 | ~46 | ~47 [avatar split clause 753,374,370,158,378]
755. old(sK0) | brave(sK0) | rich(sK0) <- (47) [resolution 376,88]
756. tall(sK0) <- (47) [resolution 376,122]
760. funny(paul) <- (8, 61) [resolution 452,186]
763. $false <- (8, ~60, 61) [subsumption resolution 760,448]
764. ~8 | 60 | ~61 [avatar contradiction clause 763]
785. old(sK0) | ~rich(sK0) | ~funny(sK0) <- (75) [resolution 641,129]
791. ~rich(sK0) | ~funny(sK0) <- (~48, 75) [subsumption resolution 785,379]
792. ~funny(sK0) <- (46, ~48, 75) [subsumption resolution 791,372]
793. $false <- (3, 46, ~48, 75) [subsumption resolution 792,163]
794. ~3 | ~46 | 48 | ~75 [avatar contradiction clause 793]
795. 75 | ~47 [avatar split clause 756,374,639]
799. rich(sK0) | tall(sK0) <- (3, ~48) [subsumption resolution 670,379]
800. 75 | 46 | ~3 | 48 [avatar split clause 799,378,162,370,639]
801. old(sK0) | rich(sK0) <- (~2, 47) [subsumption resolution 755,160]
802. old(sK0) <- (~2, ~46, 47) [subsumption resolution 801,371]
803. 48 | 2 | 46 | ~47 [avatar split clause 802,374,370,158,378]
809. rich(sK0) | ~funny(sK0) | ~old(sK0) <- (75) [resolution 641,126]
813. ~funny(sK0) | ~old(sK0) <- (~46, 75) [subsumption resolution 809,371]
814. ~old(sK0) <- (3, ~46, 75) [subsumption resolution 813,163]
815. $false <- (3, ~46, 48, 75) [subsumption resolution 814,380]
816. ~3 | 46 | ~48 | ~75 [avatar contradiction clause 815]
817. $false [avatar sat refutation 165,169,170,171,183,187,337,436,502,512,571,614,623,626,636,642,658,665,673,694,699,707,710,720,736,751,754,764,794,795,800,803,816]
% SZS output end Proof for 5588413491499742955156948
% ------------------------------
% 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: 0.041 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both creative and happy then someone is either brave or creative. Everyone who is either funny or old is tall. Everyone who is funny is either not quiet or happy and vice versa. If someone is not rich then someone is either kind or old and vice versa. If someone is not brave then someone is not quiet. If someone is both curious and wise then someone is not generous or funny and vice versa. Everyone who is not brave or generous is not kind. Everyone who is both not strong and not kind is kind. Everyone who is strong is not funny or rich. If susan is both old and not kind then someone is both not brave and not patient. If someone is not funny then susan is not old. If someone is both not creative and not happy then mary is either calm or funny. If susan is either not humble or not old then someone is not calm and vice versa. If fred is patient then someone is humble or quiet. Everyone who is not creative or funny is not patient or not tall and vice versa. Everyone who is both not kind and not curious is not patient and vice versa. Alice is creative. Susan is not rich. Someone is both not calm and old. Someone is both not kind and not tall. John is both not funny and not strong. Someone is both generous and not patient. Someone is generous or calm. Mary is either curious or generous. | Susan is humble. | entailment | ((?[X]:((creative(X)&happy(X))))=>(?[X]:((brave(X)<~>creative(X)))))&
(![X]:((funny(X)<~>old(X))=>tall(X)))&
(![X]:(funny(X)<=>(~quiet(X)<~>happy(X))))&
((?[X]:(~rich(X)))<=>(?[X]:((kind(X)<~>old(X)))))&
((?[X]:(~brave(X)))=>(?[X]:(~quiet(X))))&
((?[X]:((curious(X)&wise(X))))<=>(?[X]:((~generous(X)|funny(X)))))&
(![X]:((~brave(X)|generous(X))=>~kind(X)))&
(![X]:((~strong(X)&~kind(X))=>kind(X)))&
(![X]:(strong(X)=>(~funny(X)|rich(X))))&
(((old(susan)&~kind(susan)))=>(?[X]:((~brave(X)&~patient(X)))))&
((?[X]:(~funny(X)))=>(~old(susan)))&
((?[X]:((~creative(X)&~happy(X))))=>((calm(mary)<~>funny(mary))))&
(((~humble(susan)<~>~old(susan)))<=>(?[X]:(~calm(X))))&
((patient(fred))=>(?[X]:((humble(X)|quiet(X)))))&
(![X]:((~creative(X)|funny(X))<=>(~patient(X)|~tall(X))))&
(![X]:((~kind(X)&~curious(X))<=>~patient(X)))&
(creative(alice))&
(~rich(susan))&
(?[X]:((~calm(X)&old(X))))&
(?[X]:((~kind(X)&~tall(X))))&
((~funny(john)&~strong(john)))&
(?[X]:((generous(X)&~patient(X))))&
(?[X]:((generous(X)|calm(X))))&
((curious(mary)<~>generous(mary))) | humble(susan) | [
"p10",
"p12",
"p18",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 5596056337288616404404019
% SZS output start Proof for 5596056337288616404404019
11. ? [X0] : ~funny(X0) => ~old(susan) [input p10]
13. (~humble(susan) <~> ~old(susan)) <=> ? [X0] : ~calm(X0) [input p12]
19. ? [X0] : (old(X0) & ~calm(X0)) [input p18]
21. ~strong(john) & ~funny(john) [input p20]
25. ~humble(susan) [input hypothesis]
40. ~old(susan) | ! [X0] : funny(X0) [ennf transformation 11]
65. (((old(susan) | humble(susan)) & (~old(susan) | ~humble(susan))) | ! [X0] : calm(X0)) & (? [X0] : ~calm(X0) | ((~humble(susan) | old(susan)) & (~old(susan) | humble(susan)))) [nnf transformation 13]
66. (((old(susan) | humble(susan)) & (~old(susan) | ~humble(susan))) | ! [X0] : calm(X0)) & (? [X1] : ~calm(X1) | ((~humble(susan) | old(susan)) & (~old(susan) | humble(susan)))) [rectify 65]
67. ? [X1] : ~calm(X1) => ~calm(sK7) [choice axiom]
68. (((old(susan) | humble(susan)) & (~old(susan) | ~humble(susan))) | ! [X0] : calm(X0)) & (~calm(sK7) | ((~humble(susan) | old(susan)) & (~old(susan) | humble(susan)))) [skolemisation 66,67]
75. ? [X0] : (old(X0) & ~calm(X0)) => (old(sK9) & ~calm(sK9)) [choice axiom]
76. old(sK9) & ~calm(sK9) [skolemisation 19,75]
108. ~old(susan) | funny(X0) [cnf transformation 40]
114. old(susan) | humble(susan) | calm(X0) [cnf transformation 68]
125. ~calm(sK9) [cnf transformation 76]
129. ~funny(john) [cnf transformation 21]
136. ~humble(susan) [cnf transformation 25]
215. 19 <=> old(susan) [avatar definition]
233. 23 <=> ! [X0] : funny(X0) [avatar definition]
234. funny(X0) <- (23) [avatar component clause 233]
235. 23 | ~19 [avatar split clause 108,215,233]
250. 27 <=> ! [X0] : calm(X0) [avatar definition]
251. calm(X0) <- (27) [avatar component clause 250]
253. 28 <=> humble(susan) [avatar definition]
256. 27 | 28 | 19 [avatar split clause 114,215,253,250]
296. ~28 [avatar split clause 136,253]
305. $false <- (23) [resolution 234,129]
306. ~23 [avatar contradiction clause 305]
307. $false <- (27) [resolution 251,125]
308. ~27 [avatar contradiction clause 307]
309. $false [avatar sat refutation 235,256,296,306,308]
% SZS output end Proof for 5596056337288616404404019
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If alice is not kind or not curious then someone is tall.
If someone is either rich or wise then someone is patient and vice versa.
If mary is both not humble and curious then someone is both not strong and not rich and vice versa.
Everyone who is not curious or patient is generous or not creative and vice versa.
Everyone who is not kind is both not funny and not old.
Everyone who is not humble or wise is not brave or rich and vice versa.
Everyone who is either not calm or generous is both patient and not curious and vice versa.
Everyone who is both not rich and brave is not calm or generous.
Everyone who is either not patient or wise is either happy or not creative.
If fred is not curious then someone is both brave and not old and vice versa.
Everyone who is strong or not funny is both not humble and not quiet and vice versa.
Everyone who is both not kind and tall is both calm and not wise.
Everyone who is not patient or not funny is both patient and not rich and vice versa.
Everyone who is brave is creative or patient and vice versa.
If fred is tall then someone is not funny or not calm and vice versa.
Everyone who is either not strong or happy is not tall or calm.
Alice is patient.
Susan is not strong.
Someone is either tall or not brave.
Paul is either creative or not rich.
Fred is not curious or not happy.
Fred is tall or not old. | Mary is brave. | entailment | (((~kind(alice)|~curious(alice)))=>(?[X]:(tall(X))))&
((?[X]:((rich(X)<~>wise(X))))<=>(?[X]:(patient(X))))&
(((~humble(mary)&curious(mary)))<=>(?[X]:((~strong(X)&~rich(X)))))&
(![X]:((~curious(X)|patient(X))<=>(generous(X)|~creative(X))))&
(![X]:(~kind(X)=>(~funny(X)&~old(X))))&
(![X]:((~humble(X)|wise(X))<=>(~brave(X)|rich(X))))&
(![X]:((~calm(X)<~>generous(X))<=>(patient(X)&~curious(X))))&
(![X]:((~rich(X)&brave(X))=>(~calm(X)|generous(X))))&
(![X]:((~patient(X)<~>wise(X))=>(happy(X)<~>~creative(X))))&
((~curious(fred))<=>(?[X]:((brave(X)&~old(X)))))&
(![X]:((strong(X)|~funny(X))<=>(~humble(X)&~quiet(X))))&
(![X]:((~kind(X)&tall(X))=>(calm(X)&~wise(X))))&
(![X]:((~patient(X)|~funny(X))<=>(patient(X)&~rich(X))))&
(![X]:(brave(X)<=>(creative(X)|patient(X))))&
((tall(fred))<=>(?[X]:((~funny(X)|~calm(X)))))&
(![X]:((~strong(X)<~>happy(X))=>(~tall(X)|calm(X))))&
(patient(alice))&
(~strong(susan))&
(?[X]:((tall(X)<~>~brave(X))))&
((creative(paul)<~>~rich(paul)))&
((~curious(fred)|~happy(fred)))&
((tall(fred)|~old(fred))) | brave(mary) | [
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 301972327544759334153861
% SZS output start Proof for 301972327544759334153861
13. ! [X0] : ((~funny(X0) | ~patient(X0)) <=> (~rich(X0) & patient(X0))) [input p12]
14. ! [X0] : (brave(X0) <=> (patient(X0) | creative(X0))) [input p13]
23. ~brave(mary) [input hypothesis]
59. ! [X0] : (((~funny(X0) | ~patient(X0)) | (rich(X0) | ~patient(X0))) & ((~rich(X0) & patient(X0)) | (funny(X0) & patient(X0)))) [nnf transformation 13]
60. ! [X0] : ((~funny(X0) | ~patient(X0) | rich(X0) | ~patient(X0)) & ((~rich(X0) & patient(X0)) | (funny(X0) & patient(X0)))) [flattening 59]
61. ! [X0] : ((brave(X0) | (~patient(X0) & ~creative(X0))) & ((patient(X0) | creative(X0)) | ~brave(X0))) [nnf transformation 14]
62. ! [X0] : ((brave(X0) | (~patient(X0) & ~creative(X0))) & (patient(X0) | creative(X0) | ~brave(X0))) [flattening 61]
108. patient(X0) | patient(X0) [cnf transformation 60]
115. brave(X0) | ~patient(X0) [cnf transformation 62]
129. ~brave(mary) [cnf transformation 23]
130. patient(X0) [duplicate literal removal 108]
207. brave(X0) [subsumption resolution 115,130]
250. $false [subsumption resolution 129,207]
% SZS output end Proof for 301972327544759334153861
% ------------------------------
% 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 wise is either creative or not funny.
Everyone who is wise is either not calm or not strong and vice versa.
If someone is both funny and not rich then someone is not wise.
Everyone who is not quiet is either calm or funny and vice versa.
If mary is either happy or quiet then someone is not quiet or calm and vice versa.
Everyone who is both happy and not old is both not funny and humble.
Everyone who is not calm is curious or not patient and vice versa.
Everyone who is kind or not quiet is not quiet or not kind.
If someone is not calm or not creative then someone is not old or happy and vice versa.
If fred is not kind or funny then susan is both not brave and tall.
Everyone who is not tall or not generous is both not happy and curious.
Everyone who is either not humble or not generous is not patient or not kind and vice versa.
Everyone who is both patient and kind is not tall or not kind and vice versa.
If susan is either patient or calm then someone is both not kind and not patient.
Everyone who is not wise or generous is not calm or not rich and vice versa.
If susan is both patient and not rich then john is not creative.
Someone is not humble or funny.
Someone is strong.
Alice is humble.
Someone is curious.
Mary is not creative or funny.
Lucy is creative or old. | Lucy is not generous. | neutral | (![X]:(wise(X)=>(creative(X)<~>~funny(X))))&
(![X]:(wise(X)<=>(~calm(X)<~>~strong(X))))&
((?[X]:((funny(X)&~rich(X))))=>(?[X]:(~wise(X))))&
(![X]:(~quiet(X)<=>(calm(X)<~>funny(X))))&
(((happy(mary)<~>quiet(mary)))<=>(?[X]:((~quiet(X)|calm(X)))))&
(![X]:((happy(X)&~old(X))=>(~funny(X)&humble(X))))&
(![X]:(~calm(X)<=>(curious(X)|~patient(X))))&
(![X]:((kind(X)|~quiet(X))=>(~quiet(X)|~kind(X))))&
((?[X]:((~calm(X)|~creative(X))))<=>(?[X]:((~old(X)|happy(X)))))&
(((~kind(fred)|funny(fred)))=>((~brave(susan)&tall(susan))))&
(![X]:((~tall(X)|~generous(X))=>(~happy(X)&curious(X))))&
(![X]:((~humble(X)<~>~generous(X))<=>(~patient(X)|~kind(X))))&
(![X]:((patient(X)&kind(X))<=>(~tall(X)|~kind(X))))&
(((patient(susan)<~>calm(susan)))=>(?[X]:((~kind(X)&~patient(X)))))&
(![X]:((~wise(X)|generous(X))<=>(~calm(X)|~rich(X))))&
(((patient(susan)&~rich(susan)))=>(~creative(john)))&
(?[X]:((~humble(X)|funny(X))))&
(?[X]:(strong(X)))&
(humble(alice))&
(?[X]:(curious(X)))&
((~creative(mary)|funny(mary)))&
((creative(lucy)|old(lucy))) | ~generous(lucy) | [] | null | 0 |
If lucy is either wise or creative then fred is either tall or rich.
If someone is funny then john is generous and vice versa.
If mary is kind or not curious then john is both not humble and creative and vice versa.
Everyone who is both old and not funny is not funny.
Everyone who is not funny is creative or calm and vice versa.
If fred is both curious and not old then susan is either not quiet or generous and vice versa.
Everyone who is not quiet or not generous is not patient.
Everyone who is either generous or not patient is not happy or not rich and vice versa.
Everyone who is not kind is quiet and vice versa.
If john is both old and kind then someone is not curious or old.
If john is brave then someone is both not creative and not kind.
If john is both creative and not strong then mary is either not quiet or happy.
If john is both not quiet and rich then someone is brave and vice versa.
Everyone who is both brave and not brave is both kind and not generous and vice versa.
Everyone who is not strong or old is both not kind and not tall and vice versa.
Everyone who is both not strong and curious is kind or not generous.
Mary is either generous or humble.
Someone is either kind or not strong.
Paul is either creative or not curious.
Alice is both generous and wise.
Alice is not quiet.
Alice is either rich or not kind.
Someone is not kind.
Someone is rich. | Alice is happy. | entailment | (((wise(lucy)<~>creative(lucy)))=>((tall(fred)<~>rich(fred))))&
((?[X]:(funny(X)))<=>(generous(john)))&
(((kind(mary)|~curious(mary)))<=>((~humble(john)&creative(john))))&
(![X]:((old(X)&~funny(X))=>~funny(X)))&
(![X]:(~funny(X)<=>(creative(X)|calm(X))))&
(((curious(fred)&~old(fred)))<=>((~quiet(susan)<~>generous(susan))))&
(![X]:((~quiet(X)|~generous(X))=>~patient(X)))&
(![X]:((generous(X)<~>~patient(X))<=>(~happy(X)|~rich(X))))&
(![X]:(~kind(X)<=>quiet(X)))&
(((old(john)&kind(john)))=>(?[X]:((~curious(X)|old(X)))))&
((brave(john))=>(?[X]:((~creative(X)&~kind(X)))))&
(((creative(john)&~strong(john)))=>((~quiet(mary)<~>happy(mary))))&
(((~quiet(john)&rich(john)))<=>(?[X]:(brave(X))))&
(![X]:((brave(X)&~brave(X))<=>(kind(X)&~generous(X))))&
(![X]:((~strong(X)|old(X))<=>(~kind(X)&~tall(X))))&
(![X]:((~strong(X)&curious(X))=>(kind(X)|~generous(X))))&
((generous(mary)<~>humble(mary)))&
(?[X]:((kind(X)<~>~strong(X))))&
((creative(paul)<~>~curious(paul)))&
((generous(alice)&wise(alice)))&
(~quiet(alice))&
((rich(alice)<~>~kind(alice)))&
(?[X]:(~kind(X)))&
(?[X]:(rich(X))) | happy(alice) | [
"p6",
"p7",
"p19",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 7716839788987420339907180
% SZS output start Proof for 7716839788987420339907180
7. ! [X0] : ((~generous(X0) | ~quiet(X0)) => ~patient(X0)) [input p6]
8. ! [X0] : ((generous(X0) <~> ~patient(X0)) <=> (~rich(X0) | ~happy(X0))) [input p7]
20. wise(alice) & generous(alice) [input p19]
21. ~quiet(alice) [input p20]
25. ~happy(alice) [input hypothesis]
29. ! [X0] : (~patient(X0) | (generous(X0) & quiet(X0))) [ennf transformation 7]
48. ! [X0] : ((((patient(X0) | ~generous(X0)) & (~patient(X0) | generous(X0))) | (rich(X0) & happy(X0))) & ((~rich(X0) | ~happy(X0)) | ((generous(X0) | patient(X0)) & (~patient(X0) | ~generous(X0))))) [nnf transformation 8]
49. ! [X0] : ((((patient(X0) | ~generous(X0)) & (~patient(X0) | generous(X0))) | (rich(X0) & happy(X0))) & (~rich(X0) | ~happy(X0) | ((generous(X0) | patient(X0)) & (~patient(X0) | ~generous(X0))))) [flattening 48]
96. ~patient(X0) | quiet(X0) [cnf transformation 29]
102. ~generous(X0) | patient(X0) | happy(X0) [cnf transformation 49]
130. generous(alice) [cnf transformation 20]
132. ~quiet(alice) [cnf transformation 21]
137. ~happy(alice) [cnf transformation 25]
339. patient(alice) | happy(alice) [resolution 102,130]
359. patient(alice) [subsumption resolution 339,137]
375. quiet(alice) [resolution 359,96]
376. $false [subsumption resolution 375,132]
% SZS output end Proof for 7716839788987420339907180
% ------------------------------
% 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 happy or not happy is rich or strong and vice versa. If lucy is both quiet and generous then someone is both not kind and not quiet and vice versa. If mary is generous then someone is patient and vice versa. Everyone who is not generous or not calm is both not old and not calm. Everyone who is rich is not old or wise and vice versa. Everyone who is patient is either not quiet or strong and vice versa. Everyone who is either not strong or not wise is either not generous or not humble. Everyone who is not curious is both quiet and tall and vice versa. If someone is either not tall or curious then someone is not happy or funny. If someone is not generous or wise then lucy is not brave. If someone is wise then someone is not happy or funny and vice versa. Everyone who is calm or tall is not funny and vice versa. Everyone who is either not tall or brave is tall and vice versa. Everyone who is not calm is both brave and not quiet. If someone is not quiet or not old then someone is humble and vice versa. If john is both kind and creative then someone is both not funny and not curious and vice versa. Someone is happy or humble. Alice is generous or happy. Someone is calm or not happy. Paul is not generous or quiet. Someone is both not kind and brave. Paul is not calm or curious. | John is not calm. | contradiction | (![X]:((happy(X)|~happy(X))<=>(rich(X)|strong(X))))&
(((quiet(lucy)&generous(lucy)))<=>(?[X]:((~kind(X)&~quiet(X)))))&
((generous(mary))<=>(?[X]:(patient(X))))&
(![X]:((~generous(X)|~calm(X))=>(~old(X)&~calm(X))))&
(![X]:(rich(X)<=>(~old(X)|wise(X))))&
(![X]:(patient(X)<=>(~quiet(X)<~>strong(X))))&
(![X]:((~strong(X)<~>~wise(X))=>(~generous(X)<~>~humble(X))))&
(![X]:(~curious(X)<=>(quiet(X)&tall(X))))&
((?[X]:((~tall(X)<~>curious(X))))=>(?[X]:((~happy(X)|funny(X)))))&
((?[X]:((~generous(X)|wise(X))))=>(~brave(lucy)))&
((?[X]:(wise(X)))<=>(?[X]:((~happy(X)|funny(X)))))&
(![X]:((calm(X)|tall(X))<=>~funny(X)))&
(![X]:((~tall(X)<~>brave(X))<=>tall(X)))&
(![X]:(~calm(X)=>(brave(X)&~quiet(X))))&
((?[X]:((~quiet(X)|~old(X))))<=>(?[X]:(humble(X))))&
(((kind(john)&creative(john)))<=>(?[X]:((~funny(X)&~curious(X)))))&
(?[X]:((happy(X)|humble(X))))&
((generous(alice)|happy(alice)))&
(?[X]:((calm(X)|~happy(X))))&
((~generous(paul)|quiet(paul)))&
(?[X]:((~kind(X)&brave(X))))&
((~calm(paul)|curious(paul))) | ~calm(john) | [
"p7",
"p8",
"p9",
"p10",
"p11",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 2817805092005011892667900
% SZS output start Proof for 2817805092005011892667900
8. ! [X0] : (~curious(X0) <=> (tall(X0) & quiet(X0))) [input p7]
9. ? [X0] : (~tall(X0) <~> curious(X0)) => ? [X0] : (funny(X0) | ~happy(X0)) [input p8]
10. ? [X0] : (wise(X0) | ~generous(X0)) => ~brave(lucy) [input p9]
11. ? [X0] : wise(X0) <=> ? [X0] : (funny(X0) | ~happy(X0)) [input p10]
12. ! [X0] : ((tall(X0) | calm(X0)) <=> ~funny(X0)) [input p11]
13. ! [X0] : ((~tall(X0) <~> brave(X0)) <=> tall(X0)) [input p12]
14. ! [X0] : (~calm(X0) => (~quiet(X0) & brave(X0))) [input p13]
23. ~calm(john) [input hypothesis]
24. ? [X0] : (~tall(X0) <~> curious(X0)) => ? [X1] : (funny(X1) | ~happy(X1)) [rectify 9]
25. ? [X0] : wise(X0) <=> ? [X1] : (funny(X1) | ~happy(X1)) [rectify 11]
29. ? [X1] : (funny(X1) | ~happy(X1)) | ! [X0] : (~tall(X0) <=> curious(X0)) [ennf transformation 24]
30. ~brave(lucy) | ! [X0] : (~wise(X0) & generous(X0)) [ennf transformation 10]
31. ! [X0] : ((~quiet(X0) & brave(X0)) | calm(X0)) [ennf transformation 14]
47. ! [X0] : ((~curious(X0) | (~tall(X0) | ~quiet(X0))) & ((tall(X0) & quiet(X0)) | curious(X0))) [nnf transformation 8]
48. ! [X0] : ((~curious(X0) | ~tall(X0) | ~quiet(X0)) & ((tall(X0) & quiet(X0)) | curious(X0))) [flattening 47]
49. ? [X1] : (funny(X1) | ~happy(X1)) | ! [X0] : ((~tall(X0) | ~curious(X0)) & (curious(X0) | tall(X0))) [nnf transformation 29]
50. ? [X0] : (funny(X0) | ~happy(X0)) | ! [X1] : ((~tall(X1) | ~curious(X1)) & (curious(X1) | tall(X1))) [rectify 49]
51. ? [X0] : (funny(X0) | ~happy(X0)) => (funny(sK2) | ~happy(sK2)) [choice axiom]
52. (funny(sK2) | ~happy(sK2)) | ! [X1] : ((~tall(X1) | ~curious(X1)) & (curious(X1) | tall(X1))) [skolemisation 50,51]
53. (? [X0] : wise(X0) | ! [X1] : (~funny(X1) & happy(X1))) & (? [X1] : (funny(X1) | ~happy(X1)) | ! [X0] : ~wise(X0)) [nnf transformation 25]
54. (? [X0] : wise(X0) | ! [X1] : (~funny(X1) & happy(X1))) & (? [X2] : (funny(X2) | ~happy(X2)) | ! [X3] : ~wise(X3)) [rectify 53]
55. ? [X0] : wise(X0) => wise(sK3) [choice axiom]
56. ? [X2] : (funny(X2) | ~happy(X2)) => (funny(sK4) | ~happy(sK4)) [choice axiom]
57. (wise(sK3) | ! [X1] : (~funny(X1) & happy(X1))) & ((funny(sK4) | ~happy(sK4)) | ! [X3] : ~wise(X3)) [skolemisation 54,56,55]
58. ! [X0] : (((tall(X0) | calm(X0)) | funny(X0)) & (~funny(X0) | (~tall(X0) & ~calm(X0)))) [nnf transformation 12]
59. ! [X0] : ((tall(X0) | calm(X0) | funny(X0)) & (~funny(X0) | (~tall(X0) & ~calm(X0)))) [flattening 58]
60. ! [X0] : ((((~brave(X0) | tall(X0)) & (brave(X0) | ~tall(X0))) | ~tall(X0)) & (tall(X0) | ((~tall(X0) | ~brave(X0)) & (brave(X0) | tall(X0))))) [nnf transformation 13]
102. curious(X0) | quiet(X0) [cnf transformation 48]
106. funny(sK2) | ~happy(sK2) | ~tall(X1) | ~curious(X1) [cnf transformation 52]
108. ~brave(lucy) | ~wise(X0) [cnf transformation 30]
110. wise(sK3) | happy(X1) [cnf transformation 57]
111. wise(sK3) | ~funny(X1) [cnf transformation 57]
114. funny(X0) | calm(X0) | tall(X0) [cnf transformation 59]
115. tall(X0) | brave(X0) | tall(X0) [cnf transformation 60]
117. brave(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 60]
120. ~quiet(X0) | calm(X0) [cnf transformation 31]
135. ~calm(john) [cnf transformation 23]
136. tall(X0) | brave(X0) [duplicate literal removal 115]
137. ~tall(X0) | brave(X0) [duplicate literal removal 117]
176. 9 <=> ! [X1] : (~tall(X1) | ~curious(X1)) [avatar definition]
177. ~tall(X1) | ~curious(X1) <- (9) [avatar component clause 176]
179. 10 <=> happy(sK2) [avatar definition]
181. ~happy(sK2) <- (~10) [avatar component clause 179]
183. 11 <=> funny(sK2) [avatar definition]
185. funny(sK2) <- (11) [avatar component clause 183]
186. 9 | ~10 | 11 [avatar split clause 106,183,179,176]
188. 12 <=> ! [X0] : ~wise(X0) [avatar definition]
189. ~wise(X0) <- (12) [avatar component clause 188]
191. 13 <=> brave(lucy) [avatar definition]
193. ~brave(lucy) <- (~13) [avatar component clause 191]
194. 12 | ~13 [avatar split clause 108,191,188]
200. 15 <=> ! [X1] : ~funny(X1) [avatar definition]
201. ~funny(X1) <- (15) [avatar component clause 200]
203. 16 <=> wise(sK3) [avatar definition]
205. wise(sK3) <- (16) [avatar component clause 203]
206. 15 | 16 [avatar split clause 111,203,200]
208. 17 <=> ! [X1] : happy(X1) [avatar definition]
209. happy(X1) <- (17) [avatar component clause 208]
210. 17 | 16 [avatar split clause 110,203,208]
220. brave(X0) [subsumption resolution 136,137]
313. $false <- (~13) [subsumption resolution 193,220]
314. 13 [avatar contradiction clause 313]
319. $false <- (12, 16) [resolution 205,189]
320. ~12 | ~16 [avatar contradiction clause 319]
321. $false <- (~10, 17) [resolution 209,181]
322. 10 | ~17 [avatar contradiction clause 321]
323. $false <- (11, 15) [subsumption resolution 185,201]
324. ~11 | ~15 [avatar contradiction clause 323]
396. tall(X2) | calm(X2) <- (15) [resolution 114,201]
427. ~curious(X1) | calm(X1) <- (9, 15) [resolution 396,177]
429. calm(X0) | quiet(X0) <- (9, 15) [resolution 427,102]
431. calm(X0) <- (9, 15) [subsumption resolution 429,120]
432. $false <- (9, 15) [resolution 431,135]
434. ~9 | ~15 [avatar contradiction clause 432]
435. $false [avatar sat refutation 186,194,206,210,314,320,322,324,434]
% SZS output end Proof for 2817805092005011892667900
% ------------------------------
% 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 strong is not strong or quiet.
Everyone who is either not happy or creative is old or generous.
Everyone who is quiet or rich is either patient or not kind.
Everyone who is either generous or not rich is not calm or not brave.
If someone is either creative or calm then someone is either wise or calm and vice versa.
Everyone who is both tall and funny is either not happy or not humble and vice versa.
Everyone who is either happy or humble is either quiet or not curious and vice versa.
Everyone who is not rich or not calm is old or not old.
If someone is either generous or rich then paul is both generous and not curious.
Everyone who is not quiet is either not curious or not creative.
Everyone who is both curious and not humble is not brave or old and vice versa.
Everyone who is kind is both not patient and not creative.
Everyone who is calm is both not humble and not rich.
Everyone who is either calm or kind is not calm or not happy and vice versa.
If paul is both not tall and tall then someone is strong.
Everyone who is either not creative or not brave is not patient.
Mary is generous or not curious.
Paul is not kind or wise.
Someone is strong or not happy.
Someone is both not curious and not kind.
Lucy is both tall and kind.
Mary is not old.
Someone is either funny or strong. | Mary is rich. | contradiction | (![X]:(strong(X)=>(~strong(X)|quiet(X))))&
(![X]:((~happy(X)<~>creative(X))=>(old(X)|generous(X))))&
(![X]:((quiet(X)|rich(X))=>(patient(X)<~>~kind(X))))&
(![X]:((generous(X)<~>~rich(X))=>(~calm(X)|~brave(X))))&
((?[X]:((creative(X)<~>calm(X))))<=>(?[X]:((wise(X)<~>calm(X)))))&
(![X]:((tall(X)&funny(X))<=>(~happy(X)<~>~humble(X))))&
(![X]:((happy(X)<~>humble(X))<=>(quiet(X)<~>~curious(X))))&
(![X]:((~rich(X)|~calm(X))=>(old(X)|~old(X))))&
((?[X]:((generous(X)<~>rich(X))))=>((generous(paul)&~curious(paul))))&
(![X]:(~quiet(X)=>(~curious(X)<~>~creative(X))))&
(![X]:((curious(X)&~humble(X))<=>(~brave(X)|old(X))))&
(![X]:(kind(X)=>(~patient(X)&~creative(X))))&
(![X]:(calm(X)=>(~humble(X)&~rich(X))))&
(![X]:((calm(X)<~>kind(X))<=>(~calm(X)|~happy(X))))&
(((~tall(paul)&tall(paul)))=>(?[X]:(strong(X))))&
(![X]:((~creative(X)<~>~brave(X))=>~patient(X)))&
((generous(mary)|~curious(mary)))&
((~kind(paul)|wise(paul)))&
(?[X]:((strong(X)|~happy(X))))&
(?[X]:((~curious(X)&~kind(X))))&
((tall(lucy)&kind(lucy)))&
(~old(mary))&
(?[X]:((funny(X)<~>strong(X)))) | rich(mary) | [
"p2",
"p11",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 3366666965937647996195172
% SZS output start Proof for 3366666965937647996195172
3. ! [X0] : ((rich(X0) | quiet(X0)) => (patient(X0) <~> ~kind(X0))) [input p2]
12. ! [X0] : (kind(X0) => (~creative(X0) & ~patient(X0))) [input p11]
13. ! [X0] : (calm(X0) => (~rich(X0) & ~humble(X0))) [input p12]
14. ! [X0] : ((calm(X0) <~> kind(X0)) <=> (~happy(X0) | ~calm(X0))) [input p13]
24. rich(mary) [input hypothesis]
30. ! [X0] : ((patient(X0) <~> ~kind(X0)) | (~rich(X0) & ~quiet(X0))) [ennf transformation 3]
37. ! [X0] : ((~creative(X0) & ~patient(X0)) | ~kind(X0)) [ennf transformation 12]
38. ! [X0] : ((~rich(X0) & ~humble(X0)) | ~calm(X0)) [ennf transformation 13]
43. ! [X0] : (((kind(X0) | ~patient(X0)) & (~kind(X0) | patient(X0))) | (~rich(X0) & ~quiet(X0))) [nnf transformation 30]
57. ! [X0] : ((((~kind(X0) | ~calm(X0)) & (kind(X0) | calm(X0))) | (happy(X0) & calm(X0))) & ((~happy(X0) | ~calm(X0)) | ((calm(X0) | ~kind(X0)) & (kind(X0) | ~calm(X0))))) [nnf transformation 14]
58. ! [X0] : ((((~kind(X0) | ~calm(X0)) & (kind(X0) | calm(X0))) | (happy(X0) & calm(X0))) & (~happy(X0) | ~calm(X0) | ((calm(X0) | ~kind(X0)) & (kind(X0) | ~calm(X0))))) [flattening 57]
73. ~kind(X0) | patient(X0) | ~rich(X0) [cnf transformation 43]
113. ~kind(X0) | ~patient(X0) [cnf transformation 37]
116. ~calm(X0) | ~rich(X0) [cnf transformation 38]
119. kind(X0) | calm(X0) | calm(X0) [cnf transformation 58]
136. rich(mary) [cnf transformation 24]
138. calm(X0) | kind(X0) [duplicate literal removal 119]
238. ~rich(X0) | kind(X0) [resolution 138,116]
264. kind(mary) [resolution 238,136]
270. patient(mary) | ~rich(mary) [resolution 264,73]
273. ~patient(mary) [resolution 264,113]
274. patient(mary) [subsumption resolution 270,136]
275. $false [subsumption resolution 273,274]
% SZS output end Proof for 3366666965937647996195172
% ------------------------------
% 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 not humble or quiet then someone is either not creative or tall.
Everyone who is old or curious is wise or creative.
If mary is not tall then someone is not kind and vice versa.
If someone is either curious or not strong then someone is not generous or calm and vice versa.
If lucy is either not kind or humble then someone is curious or quiet.
If john is both not rich and not creative then someone is creative or strong.
Everyone who is kind is both not old and not generous.
If alice is both creative and funny then someone is either funny or tall and vice versa.
Everyone who is both not wise and not brave is curious or creative and vice versa.
If alice is funny or calm then someone is kind or not wise.
Everyone who is either not generous or generous is not quiet or quiet and vice versa.
Everyone who is either curious or not wise is not creative and vice versa.
If paul is both patient and not old then fred is both brave and generous and vice versa.
If john is wise then someone is either not generous or not rich.
Everyone who is both strong and not tall is both funny and not funny.
Everyone who is funny is quiet.
Lucy is either tall or not strong.
Paul is both not wise and humble.
Alice is not funny.
Mary is kind.
Someone is patient or not calm.
John is both funny and not kind.
Someone is either wise or not happy.
Someone is either not tall or creative. | Alice is strong. | contradiction | ((?[X]:((~humble(X)|quiet(X))))=>(?[X]:((~creative(X)<~>tall(X)))))&
(![X]:((old(X)|curious(X))=>(wise(X)|creative(X))))&
((~tall(mary))<=>(?[X]:(~kind(X))))&
((?[X]:((curious(X)<~>~strong(X))))<=>(?[X]:((~generous(X)|calm(X)))))&
(((~kind(lucy)<~>humble(lucy)))=>(?[X]:((curious(X)|quiet(X)))))&
(((~rich(john)&~creative(john)))=>(?[X]:((creative(X)|strong(X)))))&
(![X]:(kind(X)=>(~old(X)&~generous(X))))&
(((creative(alice)&funny(alice)))<=>(?[X]:((funny(X)<~>tall(X)))))&
(![X]:((~wise(X)&~brave(X))<=>(curious(X)|creative(X))))&
(((funny(alice)|calm(alice)))=>(?[X]:((kind(X)|~wise(X)))))&
(![X]:((~generous(X)<~>generous(X))<=>(~quiet(X)|quiet(X))))&
(![X]:((curious(X)<~>~wise(X))<=>~creative(X)))&
(((patient(paul)&~old(paul)))<=>((brave(fred)&generous(fred))))&
((wise(john))=>(?[X]:((~generous(X)<~>~rich(X)))))&
(![X]:((strong(X)&~tall(X))=>(funny(X)&~funny(X))))&
(![X]:(funny(X)=>quiet(X)))&
((tall(lucy)<~>~strong(lucy)))&
((~wise(paul)&humble(paul)))&
(~funny(alice))&
(kind(mary))&
(?[X]:((patient(X)|~calm(X))))&
((funny(john)&~kind(john)))&
(?[X]:((wise(X)<~>~happy(X))))&
(?[X]:((~tall(X)<~>creative(X)))) | strong(alice) | [
"p7",
"p14",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 4230491557083860666388726
% SZS output start Proof for 4230491557083860666388726
8. (funny(alice) & creative(alice)) <=> ? [X0] : (funny(X0) <~> tall(X0)) [input p7]
15. ! [X0] : ((~tall(X0) & strong(X0)) => (~funny(X0) & funny(X0))) [input p14]
19. ~funny(alice) [input p18]
25. strong(alice) [input hypothesis]
37. ! [X0] : ((~funny(X0) & funny(X0)) | (tall(X0) | ~strong(X0))) [ennf transformation 15]
38. ! [X0] : ((~funny(X0) & funny(X0)) | tall(X0) | ~strong(X0)) [flattening 37]
58. ((funny(alice) & creative(alice)) | ! [X0] : ((funny(X0) | ~tall(X0)) & (tall(X0) | ~funny(X0)))) & (? [X0] : ((~tall(X0) | ~funny(X0)) & (tall(X0) | funny(X0))) | (~funny(alice) | ~creative(alice))) [nnf transformation 8]
59. ((funny(alice) & creative(alice)) | ! [X0] : ((funny(X0) | ~tall(X0)) & (tall(X0) | ~funny(X0)))) & (? [X0] : ((~tall(X0) | ~funny(X0)) & (tall(X0) | funny(X0))) | ~funny(alice) | ~creative(alice)) [flattening 58]
60. ((funny(alice) & creative(alice)) | ! [X0] : ((funny(X0) | ~tall(X0)) & (tall(X0) | ~funny(X0)))) & (? [X1] : ((~tall(X1) | ~funny(X1)) & (tall(X1) | funny(X1))) | ~funny(alice) | ~creative(alice)) [rectify 59]
61. ? [X1] : ((~tall(X1) | ~funny(X1)) & (tall(X1) | funny(X1))) => ((~tall(sK6) | ~funny(sK6)) & (tall(sK6) | funny(sK6))) [choice axiom]
62. ((funny(alice) & creative(alice)) | ! [X0] : ((funny(X0) | ~tall(X0)) & (tall(X0) | ~funny(X0)))) & (((~tall(sK6) | ~funny(sK6)) & (tall(sK6) | funny(sK6))) | ~funny(alice) | ~creative(alice)) [skolemisation 60,61]
108. funny(alice) | funny(X0) | ~tall(X0) [cnf transformation 62]
132. funny(X0) | tall(X0) | ~strong(X0) [cnf transformation 38]
133. ~funny(X0) | tall(X0) | ~strong(X0) [cnf transformation 38]
139. ~funny(alice) [cnf transformation 19]
148. strong(alice) [cnf transformation 25]
252. 24 <=> ! [X0] : (funny(X0) | ~tall(X0)) [avatar definition]
253. ~tall(X0) | funny(X0) <- (24) [avatar component clause 252]
255. 25 <=> funny(alice) [avatar definition]
256. ~funny(alice) <- (~25) [avatar component clause 255]
258. 24 | 25 [avatar split clause 108,255,252]
317. ~strong(X0) | tall(X0) [subsumption resolution 132,133]
327. ~25 [avatar split clause 139,255]
352. tall(alice) [resolution 317,148]
353. funny(alice) <- (24) [resolution 352,253]
354. $false <- (24, ~25) [subsumption resolution 353,256]
355. ~24 | 25 [avatar contradiction clause 354]
356. $false [avatar sat refutation 258,327,355]
% SZS output end Proof for 4230491557083860666388726
% ------------------------------
% 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 both not generous and not creative is kind or curious.
If someone is either not funny or wise then someone is either not curious or humble.
If john is either not curious or brave then paul is both wise and not kind.
If someone is quiet then someone is wise or old and vice versa.
Everyone who is kind is not wise.
If john is either creative or happy then someone is quiet and vice versa.
Everyone who is not patient is humble.
If someone is not patient then someone is strong and vice versa.
If someone is not calm then mary is not rich.
Everyone who is both not rich and not wise is funny and vice versa.
If someone is either creative or wise then someone is generous or not funny.
If fred is both calm and not happy then susan is strong and vice versa.
Everyone who is both rich and curious is both not rich and not patient and vice versa.
If john is either wise or not brave then someone is both not generous and not calm.
If someone is curious or not humble then someone is either not rich or not strong and vice versa.
Everyone who is either not old or generous is either curious or not generous.
Lucy is not strong.
Paul is either creative or calm.
Someone is creative.
Lucy is funny.
Someone is quiet or not generous.
Mary is not tall.
Someone is either not tall or not kind.
Paul is not generous. | John is brave. | neutral | (![X]:((~generous(X)&~creative(X))=>(kind(X)|curious(X))))&
((?[X]:((~funny(X)<~>wise(X))))=>(?[X]:((~curious(X)<~>humble(X)))))&
(((~curious(john)<~>brave(john)))=>((wise(paul)&~kind(paul))))&
((?[X]:(quiet(X)))<=>(?[X]:((wise(X)|old(X)))))&
(![X]:(kind(X)=>~wise(X)))&
(((creative(john)<~>happy(john)))<=>(?[X]:(quiet(X))))&
(![X]:(~patient(X)=>humble(X)))&
((?[X]:(~patient(X)))<=>(?[X]:(strong(X))))&
((?[X]:(~calm(X)))=>(~rich(mary)))&
(![X]:((~rich(X)&~wise(X))<=>funny(X)))&
((?[X]:((creative(X)<~>wise(X))))=>(?[X]:((generous(X)|~funny(X)))))&
(((calm(fred)&~happy(fred)))<=>(strong(susan)))&
(![X]:((rich(X)&curious(X))<=>(~rich(X)&~patient(X))))&
(((wise(john)<~>~brave(john)))=>(?[X]:((~generous(X)&~calm(X)))))&
((?[X]:((curious(X)|~humble(X))))<=>(?[X]:((~rich(X)<~>~strong(X)))))&
(![X]:((~old(X)<~>generous(X))=>(curious(X)<~>~generous(X))))&
(~strong(lucy))&
((creative(paul)<~>calm(paul)))&
(?[X]:(creative(X)))&
(funny(lucy))&
(?[X]:((quiet(X)|~generous(X))))&
(~tall(mary))&
(?[X]:((~tall(X)<~>~kind(X))))&
(~generous(paul)) | brave(john) | [] | null | 0 |
If fred is both happy and tall then paul is either wise or not wise.
If alice is not rich then susan is both not quiet and funny.
Everyone who is happy is happy or quiet.
If john is tall or not humble then someone is kind and vice versa.
Everyone who is not tall or generous is not quiet.
Everyone who is either not generous or old is both happy and not patient and vice versa.
If someone is either not quiet or not curious then mary is funny and vice versa.
If mary is kind or funny then someone is not humble and vice versa.
If someone is either generous or not happy then mary is either strong or patient and vice versa.
If alice is wise then someone is either not curious or brave.
If paul is either kind or funny then someone is either curious or old.
If susan is both generous and wise then someone is generous or not calm and vice versa.
If someone is humble then someone is either not quiet or quiet and vice versa.
Everyone who is old is both not kind and not wise.
If lucy is not quiet then lucy is not generous.
If someone is both not happy and calm then alice is either not generous or creative and vice versa.
Someone is tall or generous.
Susan is strong or old.
Someone is both not quiet and calm.
John is both humble and curious.
Someone is rich.
Paul is not funny.
Someone is both not calm and not wise.
Someone is both tall and not creative. | John is not humble. | contradiction | (((happy(fred)&tall(fred)))=>((wise(paul)<~>~wise(paul))))&
((~rich(alice))=>((~quiet(susan)&funny(susan))))&
(![X]:(happy(X)=>(happy(X)|quiet(X))))&
(((tall(john)|~humble(john)))<=>(?[X]:(kind(X))))&
(![X]:((~tall(X)|generous(X))=>~quiet(X)))&
(![X]:((~generous(X)<~>old(X))<=>(happy(X)&~patient(X))))&
((?[X]:((~quiet(X)<~>~curious(X))))<=>(funny(mary)))&
(((kind(mary)|funny(mary)))<=>(?[X]:(~humble(X))))&
((?[X]:((generous(X)<~>~happy(X))))<=>((strong(mary)<~>patient(mary))))&
((wise(alice))=>(?[X]:((~curious(X)<~>brave(X)))))&
(((kind(paul)<~>funny(paul)))=>(?[X]:((curious(X)<~>old(X)))))&
(((generous(susan)&wise(susan)))<=>(?[X]:((generous(X)|~calm(X)))))&
((?[X]:(humble(X)))<=>(?[X]:((~quiet(X)<~>quiet(X)))))&
(![X]:(old(X)=>(~kind(X)&~wise(X))))&
((~quiet(lucy))=>(~generous(lucy)))&
((?[X]:((~happy(X)&calm(X))))<=>((~generous(alice)<~>creative(alice))))&
(?[X]:((tall(X)|generous(X))))&
((strong(susan)|old(susan)))&
(?[X]:((~quiet(X)&calm(X))))&
((humble(john)&curious(john)))&
(?[X]:(rich(X)))&
(~funny(paul))&
(?[X]:((~calm(X)&~wise(X))))&
(?[X]:((tall(X)&~creative(X)))) | ~humble(john) | [
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 8896759300021777586369128
% SZS output start Proof for 8896759300021777586369128
20. curious(john) & humble(john) [input p19]
25. ~humble(john) [input hypothesis]
144. humble(john) [cnf transformation 20]
151. ~humble(john) [cnf transformation 25]
162. 3 <=> humble(john) [avatar definition]
355. 3 [avatar split clause 144,162]
357. ~3 [avatar split clause 151,162]
358. $false [avatar sat refutation 355,357]
% SZS output end Proof for 8896759300021777586369128
% ------------------------------
% 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 happy then paul is not old. Everyone who is both not tall and quiet is wise or humble and vice versa. Everyone who is not humble or not quiet is both tall and funny. Everyone who is either not strong or tall is both brave and not brave and vice versa. If mary is both not patient and not quiet then paul is not creative or not quiet and vice versa. If someone is either not patient or not happy then someone is not curious and vice versa. Everyone who is curious is either brave or not rich and vice versa. Everyone who is quiet is not kind and vice versa. Everyone who is either not rich or generous is wise or quiet and vice versa. Everyone who is both not brave and strong is either not curious or not quiet. Everyone who is both kind and not patient is brave or happy and vice versa. If alice is not strong or patient then someone is either not quiet or not patient and vice versa. If fred is not strong or kind then paul is either old or not patient. Everyone who is not quiet is not tall or old. Everyone who is both wise and tall is both quiet and generous and vice versa. If someone is not wise then lucy is either happy or not humble and vice versa. Someone is not curious or calm. Lucy is not happy. Someone is quiet or humble. Someone is both quiet and not brave. Alice is either not creative or generous. | Alice is funny. | entailment | ((?[X]:(~happy(X)))=>(~old(paul)))&
(![X]:((~tall(X)&quiet(X))<=>(wise(X)|humble(X))))&
(![X]:((~humble(X)|~quiet(X))=>(tall(X)&funny(X))))&
(![X]:((~strong(X)<~>tall(X))<=>(brave(X)&~brave(X))))&
(((~patient(mary)&~quiet(mary)))<=>((~creative(paul)|~quiet(paul))))&
((?[X]:((~patient(X)<~>~happy(X))))<=>(?[X]:(~curious(X))))&
(![X]:(curious(X)<=>(brave(X)<~>~rich(X))))&
(![X]:(quiet(X)<=>~kind(X)))&
(![X]:((~rich(X)<~>generous(X))<=>(wise(X)|quiet(X))))&
(![X]:((~brave(X)&strong(X))=>(~curious(X)<~>~quiet(X))))&
(![X]:((kind(X)&~patient(X))<=>(brave(X)|happy(X))))&
(((~strong(alice)|patient(alice)))<=>(?[X]:((~quiet(X)<~>~patient(X)))))&
(((~strong(fred)|kind(fred)))=>((old(paul)<~>~patient(paul))))&
(![X]:(~quiet(X)=>(~tall(X)|old(X))))&
(![X]:((wise(X)&tall(X))<=>(quiet(X)&generous(X))))&
((?[X]:(~wise(X)))<=>((happy(lucy)<~>~humble(lucy))))&
(?[X]:((~curious(X)|calm(X))))&
(~happy(lucy))&
(?[X]:((quiet(X)|humble(X))))&
(?[X]:((quiet(X)&~brave(X))))&
((~creative(alice)<~>generous(alice))) | funny(alice) | [
"p1",
"p2",
"p3",
"p6",
"p8",
"p9",
"p10",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8267345434667988910937450
% SZS output start Proof for 8267345434667988910937450
2. ! [X0] : ((quiet(X0) & ~tall(X0)) <=> (humble(X0) | wise(X0))) [input p1]
3. ! [X0] : ((~quiet(X0) | ~humble(X0)) => (funny(X0) & tall(X0))) [input p2]
4. ! [X0] : ((~strong(X0) <~> tall(X0)) <=> (~brave(X0) & brave(X0))) [input p3]
7. ! [X0] : (curious(X0) <=> (brave(X0) <~> ~rich(X0))) [input p6]
9. ! [X0] : ((~rich(X0) <~> generous(X0)) <=> (quiet(X0) | wise(X0))) [input p8]
10. ! [X0] : ((strong(X0) & ~brave(X0)) => (~curious(X0) <~> ~quiet(X0))) [input p9]
11. ! [X0] : ((~patient(X0) & kind(X0)) <=> (happy(X0) | brave(X0))) [input p10]
12. (patient(alice) | ~strong(alice)) <=> ? [X0] : (~quiet(X0) <~> ~patient(X0)) [input p11]
15. ! [X0] : ((tall(X0) & wise(X0)) <=> (generous(X0) & quiet(X0))) [input p14]
22. ~funny(alice) [input hypothesis]
26. ! [X0] : ((funny(X0) & tall(X0)) | (quiet(X0) & humble(X0))) [ennf transformation 3]
27. ! [X0] : ((~curious(X0) <~> ~quiet(X0)) | (~strong(X0) | brave(X0))) [ennf transformation 10]
28. ! [X0] : ((~curious(X0) <~> ~quiet(X0)) | ~strong(X0) | brave(X0)) [flattening 27]
32. ! [X0] : (((quiet(X0) & ~tall(X0)) | (~humble(X0) & ~wise(X0))) & ((humble(X0) | wise(X0)) | (~quiet(X0) | tall(X0)))) [nnf transformation 2]
33. ! [X0] : (((quiet(X0) & ~tall(X0)) | (~humble(X0) & ~wise(X0))) & (humble(X0) | wise(X0) | ~quiet(X0) | tall(X0))) [flattening 32]
34. ! [X0] : ((((~tall(X0) | strong(X0)) & (tall(X0) | ~strong(X0))) | (brave(X0) | ~brave(X0))) & ((~brave(X0) & brave(X0)) | ((~strong(X0) | ~tall(X0)) & (tall(X0) | strong(X0))))) [nnf transformation 4]
35. ! [X0] : ((((~tall(X0) | strong(X0)) & (tall(X0) | ~strong(X0))) | brave(X0) | ~brave(X0)) & ((~brave(X0) & brave(X0)) | ((~strong(X0) | ~tall(X0)) & (tall(X0) | strong(X0))))) [flattening 34]
43. ! [X0] : ((curious(X0) | ((brave(X0) | rich(X0)) & (~rich(X0) | ~brave(X0)))) & (((rich(X0) | ~brave(X0)) & (~rich(X0) | brave(X0))) | ~curious(X0))) [nnf transformation 7]
45. ! [X0] : ((((~generous(X0) | rich(X0)) & (generous(X0) | ~rich(X0))) | (~quiet(X0) & ~wise(X0))) & ((quiet(X0) | wise(X0)) | ((~rich(X0) | ~generous(X0)) & (generous(X0) | rich(X0))))) [nnf transformation 9]
46. ! [X0] : ((((~generous(X0) | rich(X0)) & (generous(X0) | ~rich(X0))) | (~quiet(X0) & ~wise(X0))) & (quiet(X0) | wise(X0) | ((~rich(X0) | ~generous(X0)) & (generous(X0) | rich(X0))))) [flattening 45]
47. ! [X0] : (((quiet(X0) | curious(X0)) & (~quiet(X0) | ~curious(X0))) | ~strong(X0) | brave(X0)) [nnf transformation 28]
48. ! [X0] : (((~patient(X0) & kind(X0)) | (~happy(X0) & ~brave(X0))) & ((happy(X0) | brave(X0)) | (patient(X0) | ~kind(X0)))) [nnf transformation 11]
49. ! [X0] : (((~patient(X0) & kind(X0)) | (~happy(X0) & ~brave(X0))) & (happy(X0) | brave(X0) | patient(X0) | ~kind(X0))) [flattening 48]
50. ((patient(alice) | ~strong(alice)) | ! [X0] : ((~quiet(X0) | patient(X0)) & (~patient(X0) | quiet(X0)))) & (? [X0] : ((patient(X0) | quiet(X0)) & (~patient(X0) | ~quiet(X0))) | (~patient(alice) & strong(alice))) [nnf transformation 12]
51. (patient(alice) | ~strong(alice) | ! [X0] : ((~quiet(X0) | patient(X0)) & (~patient(X0) | quiet(X0)))) & (? [X0] : ((patient(X0) | quiet(X0)) & (~patient(X0) | ~quiet(X0))) | (~patient(alice) & strong(alice))) [flattening 50]
52. (patient(alice) | ~strong(alice) | ! [X0] : ((~quiet(X0) | patient(X0)) & (~patient(X0) | quiet(X0)))) & (? [X1] : ((patient(X1) | quiet(X1)) & (~patient(X1) | ~quiet(X1))) | (~patient(alice) & strong(alice))) [rectify 51]
53. ? [X1] : ((patient(X1) | quiet(X1)) & (~patient(X1) | ~quiet(X1))) => ((patient(sK2) | quiet(sK2)) & (~patient(sK2) | ~quiet(sK2))) [choice axiom]
54. (patient(alice) | ~strong(alice) | ! [X0] : ((~quiet(X0) | patient(X0)) & (~patient(X0) | quiet(X0)))) & (((patient(sK2) | quiet(sK2)) & (~patient(sK2) | ~quiet(sK2))) | (~patient(alice) & strong(alice))) [skolemisation 52,53]
56. ! [X0] : (((tall(X0) & wise(X0)) | (~generous(X0) | ~quiet(X0))) & ((generous(X0) & quiet(X0)) | (~tall(X0) | ~wise(X0)))) [nnf transformation 15]
57. ! [X0] : (((tall(X0) & wise(X0)) | ~generous(X0) | ~quiet(X0)) & ((generous(X0) & quiet(X0)) | ~tall(X0) | ~wise(X0))) [flattening 56]
70. ~humble(X0) | ~tall(X0) [cnf transformation 33]
74. quiet(X0) | tall(X0) [cnf transformation 26]
75. funny(X0) | humble(X0) [cnf transformation 26]
76. funny(X0) | quiet(X0) [cnf transformation 26]
77. brave(X0) | tall(X0) | strong(X0) [cnf transformation 35]
79. ~brave(X0) | tall(X0) | strong(X0) [cnf transformation 35]
95. rich(X0) | brave(X0) | curious(X0) [cnf transformation 43]
101. ~rich(X0) | generous(X0) | ~quiet(X0) [cnf transformation 46]
104. ~curious(X0) | ~quiet(X0) | ~strong(X0) | brave(X0) [cnf transformation 47]
109. ~patient(X0) | ~brave(X0) [cnf transformation 49]
116. patient(alice) | ~strong(alice) | ~quiet(X0) | patient(X0) [cnf transformation 54]
125. tall(X0) | ~generous(X0) | ~quiet(X0) [cnf transformation 57]
136. ~funny(alice) [cnf transformation 22]
146. strong(X0) | tall(X0) [subsumption resolution 77,79]
196. 13 <=> ! [X0] : (~quiet(X0) | patient(X0)) [avatar definition]
197. ~quiet(X0) | patient(X0) <- (13) [avatar component clause 196]
199. 14 <=> strong(alice) [avatar definition]
200. strong(alice) <- (14) [avatar component clause 199]
201. ~strong(alice) <- (~14) [avatar component clause 199]
203. 15 <=> patient(alice) [avatar definition]
204. ~patient(alice) <- (~15) [avatar component clause 203]
205. patient(alice) <- (15) [avatar component clause 203]
206. 13 | ~14 | 15 [avatar split clause 116,203,199,196]
240. ~generous(X0) | tall(X0) [subsumption resolution 125,74]
267. 27 <=> generous(alice) [avatar definition]
268. generous(alice) <- (27) [avatar component clause 267]
269. ~generous(alice) <- (~27) [avatar component clause 267]
279. humble(alice) [resolution 75,136]
280. quiet(alice) [resolution 76,136]
282. ~tall(alice) [resolution 279,70]
289. patient(alice) <- (13) [resolution 197,280]
292. $false <- (13, ~15) [subsumption resolution 289,204]
293. ~13 | 15 [avatar contradiction clause 292]
295. ~brave(alice) <- (15) [resolution 205,109]
307. ~quiet(X0) | generous(X0) | brave(X0) | curious(X0) [resolution 101,95]
339. generous(alice) | brave(alice) | curious(alice) [resolution 307,280]
358. brave(alice) | curious(alice) <- (~27) [subsumption resolution 339,269]
359. curious(alice) <- (15, ~27) [subsumption resolution 358,295]
443. ~quiet(alice) | ~strong(alice) | brave(alice) <- (15, ~27) [resolution 359,104]
445. ~strong(alice) | brave(alice) <- (15, ~27) [subsumption resolution 443,280]
446. brave(alice) <- (14, 15, ~27) [subsumption resolution 445,200]
447. $false <- (14, 15, ~27) [subsumption resolution 446,295]
448. ~14 | ~15 | 27 [avatar contradiction clause 447]
459. tall(alice) <- (27) [resolution 268,240]
462. $false <- (27) [subsumption resolution 459,282]
463. ~27 [avatar contradiction clause 462]
464. tall(alice) <- (~14) [resolution 201,146]
465. $false <- (~14) [subsumption resolution 464,282]
466. 14 [avatar contradiction clause 465]
467. $false [avatar sat refutation 206,293,448,463,466]
% SZS output end Proof for 8267345434667988910937450
% ------------------------------
% 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 not tall and curious is either not brave or old and vice versa.
If someone is not calm then someone is not tall or wise and vice versa.
If john is rich then john is either brave or not quiet.
Everyone who is either not kind or not wise is either wise or not quiet and vice versa.
Everyone who is both not patient and not wise is not funny or rich.
Everyone who is both not curious and not calm is not creative and vice versa.
Everyone who is either not calm or not happy is not patient.
If paul is not kind or curious then someone is brave or not kind and vice versa.
If alice is not tall then someone is brave.
Everyone who is rich or calm is both not funny and not tall.
Everyone who is not quiet is patient.
If susan is both not wise and brave then fred is strong or wise.
If susan is both not generous and quiet then someone is not funny.
Everyone who is both not happy and brave is curious and vice versa.
Everyone who is either happy or tall is either not quiet or not tall.
Mary is patient.
Someone is both brave and kind.
Someone is both humble and not patient.
Someone is happy.
John is not humble or not creative.
Fred is kind. | Fred is happy. | contradiction | (![X]:((~tall(X)&curious(X))<=>(~brave(X)<~>old(X))))&
((?[X]:(~calm(X)))<=>(?[X]:((~tall(X)|wise(X)))))&
((rich(john))=>((brave(john)<~>~quiet(john))))&
(![X]:((~kind(X)<~>~wise(X))<=>(wise(X)<~>~quiet(X))))&
(![X]:((~patient(X)&~wise(X))=>(~funny(X)|rich(X))))&
(![X]:((~curious(X)&~calm(X))<=>~creative(X)))&
(![X]:((~calm(X)<~>~happy(X))=>~patient(X)))&
(((~kind(paul)|curious(paul)))<=>(?[X]:((brave(X)|~kind(X)))))&
((~tall(alice))=>(?[X]:(brave(X))))&
(![X]:((rich(X)|calm(X))=>(~funny(X)&~tall(X))))&
(![X]:(~quiet(X)=>patient(X)))&
(((~wise(susan)&brave(susan)))=>((strong(fred)|wise(fred))))&
(((~generous(susan)&quiet(susan)))=>(?[X]:(~funny(X))))&
(![X]:((~happy(X)&brave(X))<=>curious(X)))&
(![X]:((happy(X)<~>tall(X))=>(~quiet(X)<~>~tall(X))))&
(patient(mary))&
(?[X]:((brave(X)&kind(X))))&
(?[X]:((humble(X)&~patient(X))))&
(?[X]:(happy(X)))&
((~humble(john)|~creative(john)))&
(kind(fred)) | happy(fred) | [
"p3",
"p6",
"p9",
"p10",
"p14",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 4472980009724243857338929
% SZS output start Proof for 4472980009724243857338929
4. ! [X0] : ((~kind(X0) <~> ~wise(X0)) <=> (wise(X0) <~> ~quiet(X0))) [input p3]
7. ! [X0] : ((~calm(X0) <~> ~happy(X0)) => ~patient(X0)) [input p6]
10. ! [X0] : ((calm(X0) | rich(X0)) => (~tall(X0) & ~funny(X0))) [input p9]
11. ! [X0] : (~quiet(X0) => patient(X0)) [input p10]
15. ! [X0] : ((happy(X0) <~> tall(X0)) => (~quiet(X0) <~> ~tall(X0))) [input p14]
21. kind(fred) [input p20]
22. happy(fred) [input hypothesis]
27. ! [X0] : ((calm(X0) | rich(X0)) => ~tall(X0)) [pure predicate removal 10]
30. ! [X0] : (calm(X0) => ~tall(X0)) [pure predicate removal 27]
32. ! [X0] : (~patient(X0) | (~calm(X0) <=> ~happy(X0))) [ennf transformation 7]
34. ! [X0] : (~tall(X0) | ~calm(X0)) [ennf transformation 30]
35. ! [X0] : (patient(X0) | quiet(X0)) [ennf transformation 11]
36. ! [X0] : ((~quiet(X0) <~> ~tall(X0)) | (happy(X0) <=> tall(X0))) [ennf transformation 15]
44. ! [X0] : ((((wise(X0) | kind(X0)) & (~wise(X0) | ~kind(X0))) | ((wise(X0) | quiet(X0)) & (~quiet(X0) | ~wise(X0)))) & (((quiet(X0) | ~wise(X0)) & (~quiet(X0) | wise(X0))) | ((~kind(X0) | wise(X0)) & (~wise(X0) | kind(X0))))) [nnf transformation 4]
45. ! [X0] : (~patient(X0) | ((~calm(X0) | happy(X0)) & (~happy(X0) | calm(X0)))) [nnf transformation 32]
55. ! [X0] : (((tall(X0) | quiet(X0)) & (~tall(X0) | ~quiet(X0))) | ((happy(X0) | ~tall(X0)) & (tall(X0) | ~happy(X0)))) [nnf transformation 36]
72. ~quiet(X0) | wise(X0) | ~kind(X0) | wise(X0) [cnf transformation 44]
75. ~wise(X0) | ~kind(X0) | ~quiet(X0) | ~wise(X0) [cnf transformation 44]
81. ~happy(X0) | ~patient(X0) | calm(X0) [cnf transformation 45]
88. ~calm(X0) | ~tall(X0) [cnf transformation 34]
89. patient(X0) | quiet(X0) [cnf transformation 35]
95. tall(X0) | quiet(X0) | tall(X0) | ~happy(X0) [cnf transformation 55]
104. kind(fred) [cnf transformation 21]
105. happy(fred) [cnf transformation 22]
107. ~happy(X0) | quiet(X0) | tall(X0) [duplicate literal removal 95]
108. ~quiet(X0) | wise(X0) | ~kind(X0) [duplicate literal removal 72]
110. ~kind(X0) | ~wise(X0) | ~quiet(X0) [duplicate literal removal 75]
137. ~kind(X0) | ~quiet(X0) [subsumption resolution 108,110]
188. ~quiet(fred) [resolution 137,104]
204. ~patient(fred) | calm(fred) [resolution 81,105]
215. 21 <=> calm(fred) [avatar definition]
217. calm(fred) <- (21) [avatar component clause 215]
219. 22 <=> patient(fred) [avatar definition]
221. ~patient(fred) <- (~22) [avatar component clause 219]
222. 21 | ~22 [avatar split clause 204,219,215]
235. quiet(fred) <- (~22) [resolution 221,89]
236. $false <- (~22) [subsumption resolution 235,188]
237. 22 [avatar contradiction clause 236]
301. quiet(fred) | tall(fred) [resolution 107,105]
302. tall(fred) [subsumption resolution 301,188]
308. ~tall(fred) <- (21) [resolution 217,88]
310. $false <- (21) [subsumption resolution 308,302]
311. ~21 [avatar contradiction clause 310]
312. $false [avatar sat refutation 222,237,311]
% SZS output end Proof for 4472980009724243857338929
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either old or wise then lucy is old.
If fred is both not creative and not happy then susan is either not patient or curious and vice versa.
Everyone who is both not quiet and curious is either wise or kind and vice versa.
If someone is calm then alice is both creative and tall and vice versa.
Everyone who is both not patient and funny is either brave or funny.
Everyone who is either tall or not generous is not calm or not happy.
Everyone who is either not humble or strong is rich.
Everyone who is quiet or not patient is creative.
If john is not patient then someone is both wise and not kind and vice versa.
If fred is not humble then someone is curious.
If alice is not patient then fred is either not strong or not quiet and vice versa.
Everyone who is strong or not rich is both creative and not patient.
Everyone who is both not happy and quiet is either not old or not happy and vice versa.
Everyone who is both funny and not creative is not quiet or not wise and vice versa.
If someone is quiet or not wise then someone is both not old and not rich and vice versa.
Everyone who is either strong or old is not kind or humble.
Someone is humble or not happy.
John is either not humble or humble.
Paul is both not calm and not creative.
Mary is not calm or not funny. | Lucy is not brave. | neutral | ((?[X]:((old(X)<~>wise(X))))=>(old(lucy)))&
(((~creative(fred)&~happy(fred)))<=>((~patient(susan)<~>curious(susan))))&
(![X]:((~quiet(X)&curious(X))<=>(wise(X)<~>kind(X))))&
((?[X]:(calm(X)))<=>((creative(alice)&tall(alice))))&
(![X]:((~patient(X)&funny(X))=>(brave(X)<~>funny(X))))&
(![X]:((tall(X)<~>~generous(X))=>(~calm(X)|~happy(X))))&
(![X]:((~humble(X)<~>strong(X))=>rich(X)))&
(![X]:((quiet(X)|~patient(X))=>creative(X)))&
((~patient(john))<=>(?[X]:((wise(X)&~kind(X)))))&
((~humble(fred))=>(?[X]:(curious(X))))&
((~patient(alice))<=>((~strong(fred)<~>~quiet(fred))))&
(![X]:((strong(X)|~rich(X))=>(creative(X)&~patient(X))))&
(![X]:((~happy(X)&quiet(X))<=>(~old(X)<~>~happy(X))))&
(![X]:((funny(X)&~creative(X))<=>(~quiet(X)|~wise(X))))&
((?[X]:((quiet(X)|~wise(X))))<=>(?[X]:((~old(X)&~rich(X)))))&
(![X]:((strong(X)<~>old(X))=>(~kind(X)|humble(X))))&
(?[X]:((humble(X)|~happy(X))))&
((~humble(john)<~>humble(john)))&
((~calm(paul)&~creative(paul)))&
((~calm(mary)|~funny(mary))) | ~brave(lucy) | [] | null | 0 |
If someone is both not funny and kind then someone is old.
Everyone who is not tall or generous is brave and vice versa.
Everyone who is both not kind and brave is kind and vice versa.
If someone is curious then someone is not strong or strong and vice versa.
If paul is both kind and not tall then someone is either brave or not generous.
Everyone who is old or not strong is not patient.
If alice is both not brave and kind then someone is not funny or kind.
If john is either not creative or calm then someone is both not kind and quiet and vice versa.
If lucy is not strong then john is brave or kind.
Everyone who is both not happy and quiet is either calm or creative.
Everyone who is both not wise and not kind is not kind and vice versa.
If susan is not rich or generous then john is brave.
If someone is either not happy or not funny then fred is not strong.
If someone is not wise then someone is not humble.
If someone is generous then john is either not strong or creative and vice versa.
If paul is not humble or wise then alice is either not curious or not quiet.
Someone is calm or old.
Susan is calm or not calm.
Someone is not old or curious.
Someone is either humble or not humble.
John is either not humble or not tall. | Lucy is not brave. | entailment | ((?[X]:((~funny(X)&kind(X))))=>(?[X]:(old(X))))&
(![X]:((~tall(X)|generous(X))<=>brave(X)))&
(![X]:((~kind(X)&brave(X))<=>kind(X)))&
((?[X]:(curious(X)))<=>(?[X]:((~strong(X)|strong(X)))))&
(((kind(paul)&~tall(paul)))=>(?[X]:((brave(X)<~>~generous(X)))))&
(![X]:((old(X)|~strong(X))=>~patient(X)))&
(((~brave(alice)&kind(alice)))=>(?[X]:((~funny(X)|kind(X)))))&
(((~creative(john)<~>calm(john)))<=>(?[X]:((~kind(X)&quiet(X)))))&
((~strong(lucy))=>((brave(john)|kind(john))))&
(![X]:((~happy(X)&quiet(X))=>(calm(X)<~>creative(X))))&
(![X]:((~wise(X)&~kind(X))<=>~kind(X)))&
(((~rich(susan)|generous(susan)))=>(brave(john)))&
((?[X]:((~happy(X)<~>~funny(X))))=>(~strong(fred)))&
((?[X]:(~wise(X)))=>(?[X]:(~humble(X))))&
((?[X]:(generous(X)))<=>((~strong(john)<~>creative(john))))&
(((~humble(paul)|wise(paul)))=>((~curious(alice)<~>~quiet(alice))))&
(?[X]:((calm(X)|old(X))))&
((calm(susan)|~calm(susan)))&
(?[X]:((~old(X)|curious(X))))&
(?[X]:((humble(X)<~>~humble(X))))&
((~humble(john)<~>~tall(john))) | ~brave(lucy) | [
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 8940715393764126076132238
% SZS output start Proof for 8940715393764126076132238
3. ! [X0] : ((brave(X0) & ~kind(X0)) <=> kind(X0)) [input p2]
22. brave(lucy) [input hypothesis]
46. ! [X0] : (((brave(X0) & ~kind(X0)) | ~kind(X0)) & (kind(X0) | (~brave(X0) | kind(X0)))) [nnf transformation 3]
47. ! [X0] : (((brave(X0) & ~kind(X0)) | ~kind(X0)) & (kind(X0) | ~brave(X0) | kind(X0))) [flattening 46]
86. kind(X0) | ~brave(X0) | kind(X0) [cnf transformation 47]
87. ~kind(X0) | ~kind(X0) [cnf transformation 47]
126. brave(lucy) [cnf transformation 22]
127. kind(X0) | ~brave(X0) [duplicate literal removal 86]
128. ~kind(X0) [duplicate literal removal 87]
137. ~brave(X0) [subsumption resolution 127,128]
245. $false [subsumption resolution 126,137]
% SZS output end Proof for 8940715393764126076132238
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If susan is quiet then paul is happy. If alice is either quiet or not creative then someone is not strong. Everyone who is generous or not rich is either not curious or creative. If someone is not humble or curious then paul is either not humble or not generous. Everyone who is either not rich or humble is either generous or not tall and vice versa. Everyone who is wise is either not tall or happy. Everyone who is humble or not humble is both not rich and brave and vice versa. If someone is either not quiet or not wise then someone is not quiet and vice versa. If mary is not humble then someone is generous and vice versa. If someone is not quiet then paul is not wise. If lucy is not curious or not funny then lucy is either not funny or kind and vice versa. If someone is either strong or curious then someone is not curious or not brave. If fred is not patient then john is not old or wise. If john is funny or brave then mary is not happy or old and vice versa. If someone is both not wise and not calm then alice is both not humble and not old. If someone is either kind or patient then someone is not kind or tall. Someone is both tall and creative. Fred is both quiet and generous. Someone is either not curious or brave. Someone is either quiet or not happy. Someone is not curious. Someone is either tall or not kind. Alice is not old. Someone is either wise or not creative. | Fred is not quiet. | contradiction | ((quiet(susan))=>(happy(paul)))&
(((quiet(alice)<~>~creative(alice)))=>(?[X]:(~strong(X))))&
(![X]:((generous(X)|~rich(X))=>(~curious(X)<~>creative(X))))&
((?[X]:((~humble(X)|curious(X))))=>((~humble(paul)<~>~generous(paul))))&
(![X]:((~rich(X)<~>humble(X))<=>(generous(X)<~>~tall(X))))&
(![X]:(wise(X)=>(~tall(X)<~>happy(X))))&
(![X]:((humble(X)|~humble(X))<=>(~rich(X)&brave(X))))&
((?[X]:((~quiet(X)<~>~wise(X))))<=>(?[X]:(~quiet(X))))&
((~humble(mary))<=>(?[X]:(generous(X))))&
((?[X]:(~quiet(X)))=>(~wise(paul)))&
(((~curious(lucy)|~funny(lucy)))<=>((~funny(lucy)<~>kind(lucy))))&
((?[X]:((strong(X)<~>curious(X))))=>(?[X]:((~curious(X)|~brave(X)))))&
((~patient(fred))=>((~old(john)|wise(john))))&
(((funny(john)|brave(john)))<=>((~happy(mary)|old(mary))))&
((?[X]:((~wise(X)&~calm(X))))=>((~humble(alice)&~old(alice))))&
((?[X]:((kind(X)<~>patient(X))))=>(?[X]:((~kind(X)|tall(X)))))&
(?[X]:((tall(X)&creative(X))))&
((quiet(fred)&generous(fred)))&
(?[X]:((~curious(X)<~>brave(X))))&
(?[X]:((quiet(X)<~>~happy(X))))&
(?[X]:(~curious(X)))&
(?[X]:((tall(X)<~>~kind(X))))&
(~old(alice))&
(?[X]:((wise(X)<~>~creative(X)))) | ~quiet(fred) | [
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 145642444310057259864349
% SZS output start Proof for 145642444310057259864349
18. generous(fred) & quiet(fred) [input p17]
25. ~quiet(fred) [input hypothesis]
136. quiet(fred) [cnf transformation 18]
148. ~quiet(fred) [cnf transformation 25]
342. $false [subsumption resolution 148,136]
% SZS output end Proof for 145642444310057259864349
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not calm then susan is either not kind or happy and vice versa.
If paul is not wise then mary is not tall and vice versa.
If fred is either humble or old then someone is not brave and vice versa.
If someone is both old and not rich then someone is either not brave or strong and vice versa.
Everyone who is both patient and not kind is both calm and not kind.
Everyone who is either brave or not rich is creative or happy and vice versa.
If lucy is both curious and not tall then someone is both funny and not creative.
If someone is either not kind or creative then mary is not brave or curious.
Everyone who is curious is either not creative or not tall and vice versa.
Everyone who is not humble is not kind or not wise and vice versa.
Everyone who is either humble or not happy is both not brave and not generous and vice versa.
Everyone who is either not strong or brave is not old and vice versa.
If someone is both not old and not humble then someone is both creative and wise and vice versa.
If someone is not kind then lucy is both brave and not creative.
Everyone who is either strong or not patient is either generous or not quiet and vice versa.
Everyone who is both not strong and not humble is not kind or not old.
Alice is curious or not funny.
Paul is either not rich or not quiet.
Paul is either curious or creative.
Someone is not old or generous.
Lucy is curious.
Paul is not brave.
Susan is not generous.
Mary is either curious or not tall. | Mary is not quiet. | neutral | ((?[X]:(~calm(X)))<=>((~kind(susan)<~>happy(susan))))&
((~wise(paul))<=>(~tall(mary)))&
(((humble(fred)<~>old(fred)))<=>(?[X]:(~brave(X))))&
((?[X]:((old(X)&~rich(X))))<=>(?[X]:((~brave(X)<~>strong(X)))))&
(![X]:((patient(X)&~kind(X))=>(calm(X)&~kind(X))))&
(![X]:((brave(X)<~>~rich(X))<=>(creative(X)|happy(X))))&
(((curious(lucy)&~tall(lucy)))=>(?[X]:((funny(X)&~creative(X)))))&
((?[X]:((~kind(X)<~>creative(X))))=>((~brave(mary)|curious(mary))))&
(![X]:(curious(X)<=>(~creative(X)<~>~tall(X))))&
(![X]:(~humble(X)<=>(~kind(X)|~wise(X))))&
(![X]:((humble(X)<~>~happy(X))<=>(~brave(X)&~generous(X))))&
(![X]:((~strong(X)<~>brave(X))<=>~old(X)))&
((?[X]:((~old(X)&~humble(X))))<=>(?[X]:((creative(X)&wise(X)))))&
((?[X]:(~kind(X)))=>((brave(lucy)&~creative(lucy))))&
(![X]:((strong(X)<~>~patient(X))<=>(generous(X)<~>~quiet(X))))&
(![X]:((~strong(X)&~humble(X))=>(~kind(X)|~old(X))))&
((curious(alice)|~funny(alice)))&
((~rich(paul)<~>~quiet(paul)))&
((curious(paul)<~>creative(paul)))&
(?[X]:((~old(X)|generous(X))))&
(curious(lucy))&
(~brave(paul))&
(~generous(susan))&
((curious(mary)<~>~tall(mary))) | ~quiet(mary) | [] | null | 0 |
If fred is calm then lucy is either not patient or humble and vice versa.
Everyone who is not humble or not rich is both creative and kind and vice versa.
If someone is not creative then fred is either not tall or not brave.
If someone is either brave or creative then someone is not quiet or not brave.
If someone is not humble then someone is either not wise or generous and vice versa.
Everyone who is not funny or not generous is not brave.
If john is both not happy and not generous then john is either brave or not quiet.
Everyone who is either tall or not rich is either quiet or not brave and vice versa.
Everyone who is not curious or curious is either not generous or rich and vice versa.
Everyone who is either not tall or not quiet is both quiet and not quiet.
Everyone who is either not calm or not old is not happy and vice versa.
Everyone who is both not kind and not funny is strong or generous and vice versa.
If someone is not strong or not old then someone is both not brave and not humble.
If someone is either not wise or tall then someone is generous or not tall and vice versa.
If mary is both funny and curious then someone is quiet.
If someone is brave or not calm then paul is both brave and creative.
Susan is either not generous or not kind.
John is kind.
John is tall.
Someone is either not creative or not rich.
Someone is funny or not quiet.
Mary is not tall. | Lucy is not strong. | entailment | ((calm(fred))<=>((~patient(lucy)<~>humble(lucy))))&
(![X]:((~humble(X)|~rich(X))<=>(creative(X)&kind(X))))&
((?[X]:(~creative(X)))=>((~tall(fred)<~>~brave(fred))))&
((?[X]:((brave(X)<~>creative(X))))=>(?[X]:((~quiet(X)|~brave(X)))))&
((?[X]:(~humble(X)))<=>(?[X]:((~wise(X)<~>generous(X)))))&
(![X]:((~funny(X)|~generous(X))=>~brave(X)))&
(((~happy(john)&~generous(john)))=>((brave(john)<~>~quiet(john))))&
(![X]:((tall(X)<~>~rich(X))<=>(quiet(X)<~>~brave(X))))&
(![X]:((~curious(X)|curious(X))<=>(~generous(X)<~>rich(X))))&
(![X]:((~tall(X)<~>~quiet(X))=>(quiet(X)&~quiet(X))))&
(![X]:((~calm(X)<~>~old(X))<=>~happy(X)))&
(![X]:((~kind(X)&~funny(X))<=>(strong(X)|generous(X))))&
((?[X]:((~strong(X)|~old(X))))=>(?[X]:((~brave(X)&~humble(X)))))&
((?[X]:((~wise(X)<~>tall(X))))<=>(?[X]:((generous(X)|~tall(X)))))&
(((funny(mary)&curious(mary)))=>(?[X]:(quiet(X))))&
((?[X]:((brave(X)|~calm(X))))=>((brave(paul)&creative(paul))))&
((~generous(susan)<~>~kind(susan)))&
(kind(john))&
(tall(john))&
(?[X]:((~creative(X)<~>~rich(X))))&
(?[X]:((funny(X)|~quiet(X))))&
(~tall(mary)) | ~strong(lucy) | [
"p1",
"p5",
"p7",
"p9",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4500040602956014882408034
% SZS output start Proof for 4500040602956014882408034
2. ! [X0] : ((~rich(X0) | ~humble(X0)) <=> (kind(X0) & creative(X0))) [input p1]
6. ! [X0] : ((~generous(X0) | ~funny(X0)) => ~brave(X0)) [input p5]
8. ! [X0] : ((tall(X0) <~> ~rich(X0)) <=> (quiet(X0) <~> ~brave(X0))) [input p7]
10. ! [X0] : ((~tall(X0) <~> ~quiet(X0)) => (~quiet(X0) & quiet(X0))) [input p9]
12. ! [X0] : ((~funny(X0) & ~kind(X0)) <=> (generous(X0) | strong(X0))) [input p11]
16. ? [X0] : (~calm(X0) | brave(X0)) => (creative(paul) & brave(paul)) [input p15]
23. strong(lucy) [input hypothesis]
31. ! [X0] : (~brave(X0) | (generous(X0) & funny(X0))) [ennf transformation 6]
34. ! [X0] : ((~quiet(X0) & quiet(X0)) | (~tall(X0) <=> ~quiet(X0))) [ennf transformation 10]
39. (creative(paul) & brave(paul)) | ! [X0] : (calm(X0) & ~brave(X0)) [ennf transformation 16]
41. ! [X0] : (((~rich(X0) | ~humble(X0)) | (~kind(X0) | ~creative(X0))) & ((kind(X0) & creative(X0)) | (rich(X0) & humble(X0)))) [nnf transformation 2]
42. ! [X0] : ((~rich(X0) | ~humble(X0) | ~kind(X0) | ~creative(X0)) & ((kind(X0) & creative(X0)) | (rich(X0) & humble(X0)))) [flattening 41]
54. ! [X0] : ((((rich(X0) | ~tall(X0)) & (~rich(X0) | tall(X0))) | ((quiet(X0) | brave(X0)) & (~brave(X0) | ~quiet(X0)))) & (((brave(X0) | ~quiet(X0)) & (~brave(X0) | quiet(X0))) | ((tall(X0) | rich(X0)) & (~rich(X0) | ~tall(X0))))) [nnf transformation 8]
57. ! [X0] : ((~quiet(X0) & quiet(X0)) | ((~tall(X0) | quiet(X0)) & (~quiet(X0) | tall(X0)))) [nnf transformation 34]
59. ! [X0] : (((~funny(X0) & ~kind(X0)) | (~generous(X0) & ~strong(X0))) & ((generous(X0) | strong(X0)) | (funny(X0) | kind(X0)))) [nnf transformation 12]
60. ! [X0] : (((~funny(X0) & ~kind(X0)) | (~generous(X0) & ~strong(X0))) & (generous(X0) | strong(X0) | funny(X0) | kind(X0))) [flattening 59]
84. kind(X0) | rich(X0) [cnf transformation 42]
94. ~brave(X0) | funny(X0) [cnf transformation 31]
95. ~brave(X0) | generous(X0) [cnf transformation 31]
100. ~quiet(X0) | brave(X0) | ~rich(X0) | ~tall(X0) [cnf transformation 54]
103. ~rich(X0) | tall(X0) | quiet(X0) | brave(X0) [cnf transformation 54]
113. quiet(X0) | ~tall(X0) | quiet(X0) [cnf transformation 57]
114. ~quiet(X0) | ~quiet(X0) | tall(X0) [cnf transformation 57]
119. ~strong(X0) | ~kind(X0) [cnf transformation 60]
122. ~funny(X0) | ~generous(X0) [cnf transformation 60]
134. brave(paul) | ~brave(X0) [cnf transformation 39]
146. strong(lucy) [cnf transformation 23]
147. ~tall(X0) | quiet(X0) [duplicate literal removal 113]
148. ~quiet(X0) | tall(X0) [duplicate literal removal 114]
309. 37 <=> ! [X0] : ~brave(X0) [avatar definition]
310. ~brave(X0) <- (37) [avatar component clause 309]
313. 38 <=> brave(paul) [avatar definition]
315. brave(paul) <- (38) [avatar component clause 313]
317. 37 | 38 [avatar split clause 134,313,309]
349. funny(paul) <- (38) [resolution 94,315]
350. generous(paul) <- (38) [resolution 95,315]
351. ~kind(lucy) [resolution 119,146]
352. rich(lucy) [resolution 351,84]
363. ~generous(paul) <- (38) [resolution 122,349]
364. $false <- (38) [subsumption resolution 363,350]
365. ~38 [avatar contradiction clause 364]
396. tall(lucy) | quiet(lucy) | brave(lucy) [resolution 103,352]
399. tall(lucy) | quiet(lucy) <- (37) [subsumption resolution 396,310]
400. tall(lucy) <- (37) [subsumption resolution 399,148]
403. quiet(lucy) <- (37) [resolution 400,147]
432. brave(lucy) | ~rich(lucy) | ~tall(lucy) <- (37) [resolution 403,100]
434. ~rich(lucy) | ~tall(lucy) <- (37) [subsumption resolution 432,310]
435. ~tall(lucy) <- (37) [subsumption resolution 434,352]
436. $false <- (37) [subsumption resolution 435,400]
437. ~37 [avatar contradiction clause 436]
438. $false [avatar sat refutation 317,365,437]
% SZS output end Proof for 4500040602956014882408034
% ------------------------------
% 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: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not funny or not humble then someone is not happy and vice versa. Everyone who is not kind or old is both not tall and curious. If alice is either generous or not patient then someone is either tall or not wise. Everyone who is not curious is not generous or creative and vice versa. Everyone who is both patient and not old is not kind. Everyone who is both not patient and not calm is both calm and not tall. Everyone who is both not old and kind is happy or not generous and vice versa. If someone is both not patient and not quiet then someone is old and vice versa. If someone is either not generous or not calm then someone is not rich or calm. Everyone who is strong or not old is kind. Everyone who is creative or kind is not old or not creative. Everyone who is generous or not tall is not generous and vice versa. If someone is both generous and not creative then someone is not quiet and vice versa. If john is generous or wise then someone is rich and vice versa. If alice is brave or not creative then someone is both generous and calm and vice versa. Someone is either not generous or brave. Paul is kind. Someone is either strong or kind. Someone is not funny or curious. Someone is brave. Someone is not humble. Someone is humble or rich. | John is not generous. | entailment | ((?[X]:((~funny(X)|~humble(X))))<=>(?[X]:(~happy(X))))&
(![X]:((~kind(X)|old(X))=>(~tall(X)&curious(X))))&
(((generous(alice)<~>~patient(alice)))=>(?[X]:((tall(X)<~>~wise(X)))))&
(![X]:(~curious(X)<=>(~generous(X)|creative(X))))&
(![X]:((patient(X)&~old(X))=>~kind(X)))&
(![X]:((~patient(X)&~calm(X))=>(calm(X)&~tall(X))))&
(![X]:((~old(X)&kind(X))<=>(happy(X)|~generous(X))))&
((?[X]:((~patient(X)&~quiet(X))))<=>(?[X]:(old(X))))&
((?[X]:((~generous(X)<~>~calm(X))))=>(?[X]:((~rich(X)|calm(X)))))&
(![X]:((strong(X)|~old(X))=>kind(X)))&
(![X]:((creative(X)|kind(X))=>(~old(X)|~creative(X))))&
(![X]:((generous(X)|~tall(X))<=>~generous(X)))&
((?[X]:((generous(X)&~creative(X))))<=>(?[X]:(~quiet(X))))&
(((generous(john)|wise(john)))<=>(?[X]:(rich(X))))&
(((brave(alice)|~creative(alice)))<=>(?[X]:((generous(X)&calm(X)))))&
(?[X]:((~generous(X)<~>brave(X))))&
(kind(paul))&
(?[X]:((strong(X)<~>kind(X))))&
(?[X]:((~funny(X)|curious(X))))&
(?[X]:(brave(X)))&
(?[X]:(~humble(X)))&
(?[X]:((humble(X)|rich(X)))) | ~generous(john) | [
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 5753560299244368001921598
% SZS output start Proof for 5753560299244368001921598
12. ! [X0] : ((~tall(X0) | generous(X0)) <=> ~generous(X0)) [input p11]
23. generous(john) [input hypothesis]
59. ! [X0] : (((~tall(X0) | generous(X0)) | generous(X0)) & (~generous(X0) | (tall(X0) & ~generous(X0)))) [nnf transformation 12]
60. ! [X0] : ((~tall(X0) | generous(X0) | generous(X0)) & (~generous(X0) | (tall(X0) & ~generous(X0)))) [flattening 59]
120. ~generous(X0) | ~generous(X0) [cnf transformation 60]
143. generous(john) [cnf transformation 23]
144. ~generous(X0) [duplicate literal removal 120]
292. $false [subsumption resolution 143,144]
% SZS output end Proof for 5753560299244368001921598
% ------------------------------
% 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 humble or not funny is curious or not strong and vice versa.
Everyone who is either old or not kind is not brave or wise and vice versa.
Everyone who is either happy or not humble is either not happy or rich and vice versa.
Everyone who is either not funny or kind is curious.
If fred is either wise or not funny then someone is funny or not wise and vice versa.
Everyone who is curious is either not quiet or not calm and vice versa.
If someone is either generous or not humble then alice is not brave.
If someone is both not kind and funny then susan is brave or not creative and vice versa.
Everyone who is not rich or humble is both not funny and not tall.
If someone is either not rich or strong then someone is not humble and vice versa.
Everyone who is both not old and not calm is both strong and not creative and vice versa.
Everyone who is either wise or old is not tall and vice versa.
Everyone who is strong or not quiet is both funny and strong.
If paul is either not humble or rich then john is strong or patient and vice versa.
If lucy is both not curious and not humble then someone is both not patient and not curious.
If someone is not brave then john is creative.
Lucy is not wise or calm.
Someone is quiet.
Someone is either brave or not quiet.
Susan is not wise.
Alice is not generous or not old.
Lucy is creative. | Paul is rich. | contradiction | (![X]:((humble(X)<~>~funny(X))<=>(curious(X)|~strong(X))))&
(![X]:((old(X)<~>~kind(X))<=>(~brave(X)|wise(X))))&
(![X]:((happy(X)<~>~humble(X))<=>(~happy(X)<~>rich(X))))&
(![X]:((~funny(X)<~>kind(X))=>curious(X)))&
(((wise(fred)<~>~funny(fred)))<=>(?[X]:((funny(X)|~wise(X)))))&
(![X]:(curious(X)<=>(~quiet(X)<~>~calm(X))))&
((?[X]:((generous(X)<~>~humble(X))))=>(~brave(alice)))&
((?[X]:((~kind(X)&funny(X))))<=>((brave(susan)|~creative(susan))))&
(![X]:((~rich(X)|humble(X))=>(~funny(X)&~tall(X))))&
((?[X]:((~rich(X)<~>strong(X))))<=>(?[X]:(~humble(X))))&
(![X]:((~old(X)&~calm(X))<=>(strong(X)&~creative(X))))&
(![X]:((wise(X)<~>old(X))<=>~tall(X)))&
(![X]:((strong(X)|~quiet(X))=>(funny(X)&strong(X))))&
(((~humble(paul)<~>rich(paul)))<=>((strong(john)|patient(john))))&
(((~curious(lucy)&~humble(lucy)))=>(?[X]:((~patient(X)&~curious(X)))))&
((?[X]:(~brave(X)))=>(creative(john)))&
((~wise(lucy)|calm(lucy)))&
(?[X]:(quiet(X)))&
(?[X]:((brave(X)<~>~quiet(X))))&
(~wise(susan))&
((~generous(alice)|~old(alice)))&
(creative(lucy)) | rich(paul) | [
"p0",
"p2",
"p8",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 9029316422915360341292577
% SZS output start Proof for 9029316422915360341292577
1. ! [X0] : ((humble(X0) <~> ~funny(X0)) <=> (~strong(X0) | curious(X0))) [input p0]
3. ! [X0] : ((happy(X0) <~> ~humble(X0)) <=> (~happy(X0) <~> rich(X0))) [input p2]
9. ! [X0] : ((humble(X0) | ~rich(X0)) => (~tall(X0) & ~funny(X0))) [input p8]
13. ! [X0] : ((~quiet(X0) | strong(X0)) => (strong(X0) & funny(X0))) [input p12]
23. rich(paul) [input hypothesis]
28. ! [X0] : ((~tall(X0) & ~funny(X0)) | (~humble(X0) & rich(X0))) [ennf transformation 9]
30. ! [X0] : ((strong(X0) & funny(X0)) | (quiet(X0) & ~strong(X0))) [ennf transformation 13]
34. ! [X0] : ((((funny(X0) | ~humble(X0)) & (~funny(X0) | humble(X0))) | (strong(X0) & ~curious(X0))) & ((~strong(X0) | curious(X0)) | ((humble(X0) | funny(X0)) & (~funny(X0) | ~humble(X0))))) [nnf transformation 1]
35. ! [X0] : ((((funny(X0) | ~humble(X0)) & (~funny(X0) | humble(X0))) | (strong(X0) & ~curious(X0))) & (~strong(X0) | curious(X0) | ((humble(X0) | funny(X0)) & (~funny(X0) | ~humble(X0))))) [flattening 34]
38. ! [X0] : ((((humble(X0) | ~happy(X0)) & (~humble(X0) | happy(X0))) | ((~happy(X0) | ~rich(X0)) & (rich(X0) | happy(X0)))) & (((~rich(X0) | happy(X0)) & (rich(X0) | ~happy(X0))) | ((happy(X0) | humble(X0)) & (~humble(X0) | ~happy(X0))))) [nnf transformation 3]
73. ~humble(X0) | funny(X0) | strong(X0) [cnf transformation 35]
83. ~rich(X0) | happy(X0) | happy(X0) | humble(X0) [cnf transformation 38]
87. humble(X0) | ~happy(X0) | ~happy(X0) | ~rich(X0) [cnf transformation 38]
108. ~funny(X0) | ~humble(X0) [cnf transformation 28]
121. ~strong(X0) | funny(X0) [cnf transformation 30]
141. rich(paul) [cnf transformation 23]
143. ~rich(X0) | happy(X0) | humble(X0) [duplicate literal removal 83]
145. humble(X0) | ~happy(X0) | ~rich(X0) [duplicate literal removal 87]
146. ~rich(X0) | humble(X0) [subsumption resolution 143,145]
239. 21 <=> rich(paul) [avatar definition]
240. rich(paul) <- (21) [avatar component clause 239]
307. 21 [avatar split clause 141,239]
322. humble(paul) <- (21) [resolution 146,240]
340. funny(paul) | strong(paul) <- (21) [resolution 73,322]
342. funny(paul) <- (21) [subsumption resolution 340,121]
346. ~humble(paul) <- (21) [resolution 342,108]
348. $false <- (21) [subsumption resolution 346,322]
349. ~21 [avatar contradiction clause 348]
350. $false [avatar sat refutation 307,349]
% SZS output end Proof for 9029316422915360341292577
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is wise or not wise is funny.
Everyone who is not patient or quiet is humble and vice versa.
Everyone who is wise is not wise.
Everyone who is either not old or not generous is either not strong or tall.
If someone is either calm or not wise then susan is kind or old.
Everyone who is not calm or not rich is both humble and quiet and vice versa.
Everyone who is not tall or happy is not kind.
Everyone who is either quiet or wise is either not strong or curious and vice versa.
Everyone who is either humble or not creative is not curious.
If lucy is tall or not kind then mary is wise or quiet.
Everyone who is not funny or not quiet is quiet or not wise.
If someone is not wise then someone is either not tall or brave.
If john is either tall or funny then someone is both not creative and calm and vice versa.
If someone is either wise or not old then someone is both not kind and old and vice versa.
Everyone who is either calm or not old is both kind and not old and vice versa.
Everyone who is not kind or not rich is not strong.
Paul is either not strong or creative.
Someone is not calm.
Susan is humble or funny.
Someone is kind.
Someone is not old or rich.
Someone is both old and tall.
Someone is patient or wise.
Someone is both not creative and tall. | Susan is not quiet. | contradiction | (![X]:((wise(X)|~wise(X))=>funny(X)))&
(![X]:((~patient(X)|quiet(X))<=>humble(X)))&
(![X]:(wise(X)=>~wise(X)))&
(![X]:((~old(X)<~>~generous(X))=>(~strong(X)<~>tall(X))))&
((?[X]:((calm(X)<~>~wise(X))))=>((kind(susan)|old(susan))))&
(![X]:((~calm(X)|~rich(X))<=>(humble(X)&quiet(X))))&
(![X]:((~tall(X)|happy(X))=>~kind(X)))&
(![X]:((quiet(X)<~>wise(X))<=>(~strong(X)<~>curious(X))))&
(![X]:((humble(X)<~>~creative(X))=>~curious(X)))&
(((tall(lucy)|~kind(lucy)))=>((wise(mary)|quiet(mary))))&
(![X]:((~funny(X)|~quiet(X))=>(quiet(X)|~wise(X))))&
((?[X]:(~wise(X)))=>(?[X]:((~tall(X)<~>brave(X)))))&
(((tall(john)<~>funny(john)))<=>(?[X]:((~creative(X)&calm(X)))))&
((?[X]:((wise(X)<~>~old(X))))<=>(?[X]:((~kind(X)&old(X)))))&
(![X]:((calm(X)<~>~old(X))<=>(kind(X)&~old(X))))&
(![X]:((~kind(X)|~rich(X))=>~strong(X)))&
((~strong(paul)<~>creative(paul)))&
(?[X]:(~calm(X)))&
((humble(susan)|funny(susan)))&
(?[X]:(kind(X)))&
(?[X]:((~old(X)|rich(X))))&
(?[X]:((old(X)&tall(X))))&
(?[X]:((patient(X)|wise(X))))&
(?[X]:((~creative(X)&tall(X)))) | ~quiet(susan) | [
"p2",
"p4",
"p5",
"p14",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 819998385093889800086861
% SZS output start Proof for 819998385093889800086861
3. ! [X0] : (wise(X0) => ~wise(X0)) [input p2]
5. ? [X0] : (calm(X0) <~> ~wise(X0)) => (old(susan) | kind(susan)) [input p4]
6. ! [X0] : ((~rich(X0) | ~calm(X0)) <=> (quiet(X0) & humble(X0))) [input p5]
15. ! [X0] : ((calm(X0) <~> ~old(X0)) <=> (~old(X0) & kind(X0))) [input p14]
18. ? [X0] : ~calm(X0) [input p17]
25. ~quiet(susan) [input hypothesis]
30. ! [X0] : (~wise(X0) | ~wise(X0)) [ennf transformation 3]
32. (old(susan) | kind(susan)) | ! [X0] : (calm(X0) <=> ~wise(X0)) [ennf transformation 5]
33. old(susan) | kind(susan) | ! [X0] : (calm(X0) <=> ~wise(X0)) [flattening 32]
45. old(susan) | kind(susan) | ! [X0] : ((calm(X0) | wise(X0)) & (~wise(X0) | ~calm(X0))) [nnf transformation 33]
46. ! [X0] : (((~rich(X0) | ~calm(X0)) | (~quiet(X0) | ~humble(X0))) & ((quiet(X0) & humble(X0)) | (rich(X0) & calm(X0)))) [nnf transformation 6]
47. ! [X0] : ((~rich(X0) | ~calm(X0) | ~quiet(X0) | ~humble(X0)) & ((quiet(X0) & humble(X0)) | (rich(X0) & calm(X0)))) [flattening 46]
63. ! [X0] : ((((old(X0) | ~calm(X0)) & (~old(X0) | calm(X0))) | (old(X0) | ~kind(X0))) & ((~old(X0) & kind(X0)) | ((calm(X0) | old(X0)) & (~old(X0) | ~calm(X0))))) [nnf transformation 15]
64. ! [X0] : ((((old(X0) | ~calm(X0)) & (~old(X0) | calm(X0))) | old(X0) | ~kind(X0)) & ((~old(X0) & kind(X0)) | ((calm(X0) | old(X0)) & (~old(X0) | ~calm(X0))))) [flattening 63]
66. ? [X0] : ~calm(X0) => ~calm(sK4) [choice axiom]
67. ~calm(sK4) [skolemisation 18,66]
83. ~wise(X0) | ~wise(X0) [cnf transformation 30]
89. old(susan) | kind(susan) | calm(X0) | wise(X0) [cnf transformation 45]
92. calm(X0) | quiet(X0) [cnf transformation 47]
126. ~old(X0) | ~old(X0) | ~calm(X0) [cnf transformation 64]
129. old(X0) | ~calm(X0) | old(X0) | ~kind(X0) [cnf transformation 64]
134. ~calm(sK4) [cnf transformation 67]
143. ~quiet(susan) [cnf transformation 25]
144. ~calm(X0) | ~old(X0) [duplicate literal removal 126]
145. ~kind(X0) | ~calm(X0) | old(X0) [duplicate literal removal 129]
147. ~wise(X0) [duplicate literal removal 83]
149. old(susan) | kind(susan) | calm(X0) [subsumption resolution 89,147]
151. 1 <=> ! [X0] : calm(X0) [avatar definition]
152. calm(X0) <- (1) [avatar component clause 151]
154. 2 <=> kind(susan) [avatar definition]
156. kind(susan) <- (2) [avatar component clause 154]
158. 3 <=> old(susan) [avatar definition]
160. old(susan) <- (3) [avatar component clause 158]
161. 1 | 2 | 3 [avatar split clause 149,158,154,151]
275. ~old(X0) | quiet(X0) [resolution 144,92]
296. ~calm(susan) | old(susan) <- (2) [resolution 145,156]
300. ~calm(susan) <- (2) [subsumption resolution 296,144]
303. quiet(susan) <- (2) [resolution 300,92]
305. $false <- (2) [subsumption resolution 303,143]
306. ~2 [avatar contradiction clause 305]
308. quiet(susan) <- (3) [resolution 160,275]
309. $false <- (3) [subsumption resolution 308,143]
310. ~3 [avatar contradiction clause 309]
316. $false <- (1) [resolution 152,134]
319. ~1 [avatar contradiction clause 316]
320. $false [avatar sat refutation 161,306,310,319]
% SZS output end Proof for 819998385093889800086861
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If fred is not humble or not quiet then john is not creative and vice versa.
If susan is both not funny and not patient then susan is both patient and brave and vice versa.
Everyone who is either calm or not brave is patient or humble.
If alice is either not happy or old then paul is not creative or rich.
Everyone who is not generous is either happy or not wise.
If someone is not kind or calm then someone is either quiet or wise.
Everyone who is both not happy and not generous is not humble or not generous.
Everyone who is not creative or not rich is strong and vice versa.
Everyone who is both not humble and quiet is not funny or generous and vice versa.
If lucy is both curious and patient then someone is old.
Everyone who is happy is not happy.
Everyone who is not calm or not generous is either calm or not happy and vice versa.
Everyone who is not tall or not rich is not humble or tall and vice versa.
If someone is quiet or kind then fred is calm and vice versa.
If someone is patient then john is either not creative or not quiet and vice versa.
If fred is both not happy and not generous then someone is either not tall or not kind and vice versa.
Fred is rich or creative.
Susan is either generous or rich.
Someone is not brave or brave.
Paul is both calm and not curious.
Someone is either funny or kind. | John is not generous. | neutral | (((~humble(fred)|~quiet(fred)))<=>(~creative(john)))&
(((~funny(susan)&~patient(susan)))<=>((patient(susan)&brave(susan))))&
(![X]:((calm(X)<~>~brave(X))=>(patient(X)|humble(X))))&
(((~happy(alice)<~>old(alice)))=>((~creative(paul)|rich(paul))))&
(![X]:(~generous(X)=>(happy(X)<~>~wise(X))))&
((?[X]:((~kind(X)|calm(X))))=>(?[X]:((quiet(X)<~>wise(X)))))&
(![X]:((~happy(X)&~generous(X))=>(~humble(X)|~generous(X))))&
(![X]:((~creative(X)|~rich(X))<=>strong(X)))&
(![X]:((~humble(X)&quiet(X))<=>(~funny(X)|generous(X))))&
(((curious(lucy)&patient(lucy)))=>(?[X]:(old(X))))&
(![X]:(happy(X)=>~happy(X)))&
(![X]:((~calm(X)|~generous(X))<=>(calm(X)<~>~happy(X))))&
(![X]:((~tall(X)|~rich(X))<=>(~humble(X)|tall(X))))&
((?[X]:((quiet(X)|kind(X))))<=>(calm(fred)))&
((?[X]:(patient(X)))<=>((~creative(john)<~>~quiet(john))))&
(((~happy(fred)&~generous(fred)))<=>(?[X]:((~tall(X)<~>~kind(X)))))&
((rich(fred)|creative(fred)))&
((generous(susan)<~>rich(susan)))&
(?[X]:((~brave(X)|brave(X))))&
((calm(paul)&~curious(paul)))&
(?[X]:((funny(X)<~>kind(X)))) | ~generous(john) | [] | null | 0 |
Everyone who is either not happy or not curious is curious.
If someone is either rich or funny then someone is both humble and creative and vice versa.
If john is both not generous and generous then someone is either humble or tall.
Everyone who is not kind or creative is not calm or old and vice versa.
If alice is funny or kind then alice is not quiet or quiet and vice versa.
Everyone who is both quiet and rich is both curious and kind.
Everyone who is not tall or creative is creative and vice versa.
If paul is either happy or not wise then someone is humble and vice versa.
If lucy is either not funny or not strong then someone is either not curious or not rich and vice versa.
Everyone who is curious is both not patient and not curious and vice versa.
If someone is not happy then someone is wise or creative and vice versa.
Everyone who is both wise and not funny is rich or not happy and vice versa.
If someone is old or not brave then susan is both humble and not quiet and vice versa.
If mary is not calm or humble then someone is brave or not funny and vice versa.
Everyone who is either not tall or quiet is either not curious or not quiet and vice versa.
Fred is either curious or not calm.
Someone is calm or tall.
Fred is either quiet or not patient.
Someone is either not brave or not calm.
Someone is brave or creative. | Susan is curious. | contradiction | (![X]:((~happy(X)<~>~curious(X))=>curious(X)))&
((?[X]:((rich(X)<~>funny(X))))<=>(?[X]:((humble(X)&creative(X)))))&
(((~generous(john)&generous(john)))=>(?[X]:((humble(X)<~>tall(X)))))&
(![X]:((~kind(X)|creative(X))<=>(~calm(X)|old(X))))&
(((funny(alice)|kind(alice)))<=>((~quiet(alice)|quiet(alice))))&
(![X]:((quiet(X)&rich(X))=>(curious(X)&kind(X))))&
(![X]:((~tall(X)|creative(X))<=>creative(X)))&
(((happy(paul)<~>~wise(paul)))<=>(?[X]:(humble(X))))&
(((~funny(lucy)<~>~strong(lucy)))<=>(?[X]:((~curious(X)<~>~rich(X)))))&
(![X]:(curious(X)<=>(~patient(X)&~curious(X))))&
((?[X]:(~happy(X)))<=>(?[X]:((wise(X)|creative(X)))))&
(![X]:((wise(X)&~funny(X))<=>(rich(X)|~happy(X))))&
((?[X]:((old(X)|~brave(X))))<=>((humble(susan)&~quiet(susan))))&
(((~calm(mary)|humble(mary)))<=>(?[X]:((brave(X)|~funny(X)))))&
(![X]:((~tall(X)<~>quiet(X))<=>(~curious(X)<~>~quiet(X))))&
((curious(fred)<~>~calm(fred)))&
(?[X]:((calm(X)|tall(X))))&
((quiet(fred)<~>~patient(fred)))&
(?[X]:((~brave(X)<~>~calm(X))))&
(?[X]:((brave(X)|creative(X)))) | curious(susan) | [
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 1869222417505195095308032
% SZS output start Proof for 1869222417505195095308032
10. ! [X0] : (curious(X0) <=> (~curious(X0) & ~patient(X0))) [input p9]
21. curious(susan) [input hypothesis]
52. ! [X0] : ((curious(X0) | (curious(X0) | patient(X0))) & ((~curious(X0) & ~patient(X0)) | ~curious(X0))) [nnf transformation 10]
53. ! [X0] : ((curious(X0) | curious(X0) | patient(X0)) & ((~curious(X0) & ~patient(X0)) | ~curious(X0))) [flattening 52]
117. ~curious(X0) | ~curious(X0) [cnf transformation 53]
152. curious(susan) [cnf transformation 21]
157. ~curious(X0) [duplicate literal removal 117]
364. $false [subsumption resolution 152,157]
% SZS output end Proof for 1869222417505195095308032
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not kind and wise then someone is either brave or not rich. Everyone who is not quiet is both not brave and curious. If susan is both not curious and calm then someone is both not patient and not rich and vice versa. If someone is both creative and curious then someone is patient or not funny and vice versa. If someone is humble or not quiet then someone is both rich and old and vice versa. If susan is either not funny or not generous then fred is both not calm and not happy. Everyone who is creative or not strong is not creative. Everyone who is creative is tall. Everyone who is both patient and not kind is kind or not generous and vice versa. Everyone who is both not kind and not creative is either curious or not humble and vice versa. If someone is quiet or not kind then someone is either not humble or not patient and vice versa. Everyone who is both brave and not rich is either curious or not wise and vice versa. Everyone who is both wise and not rich is both not happy and not kind. Everyone who is either curious or kind is not old and vice versa. If mary is both not happy and not humble then fred is both calm and not strong. If lucy is both not happy and not strong then someone is both not wise and not kind and vice versa. Mary is strong. Someone is either not rich or not brave. Paul is both not old and not quiet. Alice is humble or not tall. Fred is not patient. Lucy is not curious or patient. Lucy is not creative or humble. John is not tall or not patient. | Susan is not patient. | entailment | ((?[X]:((~kind(X)&wise(X))))=>(?[X]:((brave(X)<~>~rich(X)))))&
(![X]:(~quiet(X)=>(~brave(X)&curious(X))))&
(((~curious(susan)&calm(susan)))<=>(?[X]:((~patient(X)&~rich(X)))))&
((?[X]:((creative(X)&curious(X))))<=>(?[X]:((patient(X)|~funny(X)))))&
((?[X]:((humble(X)|~quiet(X))))<=>(?[X]:((rich(X)&old(X)))))&
(((~funny(susan)<~>~generous(susan)))=>((~calm(fred)&~happy(fred))))&
(![X]:((creative(X)|~strong(X))=>~creative(X)))&
(![X]:(creative(X)=>tall(X)))&
(![X]:((patient(X)&~kind(X))<=>(kind(X)|~generous(X))))&
(![X]:((~kind(X)&~creative(X))<=>(curious(X)<~>~humble(X))))&
((?[X]:((quiet(X)|~kind(X))))<=>(?[X]:((~humble(X)<~>~patient(X)))))&
(![X]:((brave(X)&~rich(X))<=>(curious(X)<~>~wise(X))))&
(![X]:((wise(X)&~rich(X))=>(~happy(X)&~kind(X))))&
(![X]:((curious(X)<~>kind(X))<=>~old(X)))&
(((~happy(mary)&~humble(mary)))=>((calm(fred)&~strong(fred))))&
(((~happy(lucy)&~strong(lucy)))<=>(?[X]:((~wise(X)&~kind(X)))))&
(strong(mary))&
(?[X]:((~rich(X)<~>~brave(X))))&
((~old(paul)&~quiet(paul)))&
((humble(alice)|~tall(alice)))&
(~patient(fred))&
((~curious(lucy)|patient(lucy)))&
((~creative(lucy)|humble(lucy)))&
((~tall(john)|~patient(john))) | ~patient(susan) | [
"p3",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 7381081208771282724111412
% SZS output start Proof for 7381081208771282724111412
4. ? [X0] : (curious(X0) & creative(X0)) <=> ? [X0] : (~funny(X0) | patient(X0)) [input p3]
7. ! [X0] : ((~strong(X0) | creative(X0)) => ~creative(X0)) [input p6]
25. patient(susan) [input hypothesis]
27. ? [X0] : (curious(X0) & creative(X0)) <=> ? [X1] : (~funny(X1) | patient(X1)) [rectify 4]
33. ! [X0] : (~creative(X0) | (strong(X0) & ~creative(X0))) [ennf transformation 7]
48. (? [X0] : (curious(X0) & creative(X0)) | ! [X1] : (funny(X1) & ~patient(X1))) & (? [X1] : (~funny(X1) | patient(X1)) | ! [X0] : (~curious(X0) | ~creative(X0))) [nnf transformation 27]
49. (? [X0] : (curious(X0) & creative(X0)) | ! [X1] : (funny(X1) & ~patient(X1))) & (? [X2] : (~funny(X2) | patient(X2)) | ! [X3] : (~curious(X3) | ~creative(X3))) [rectify 48]
50. ? [X0] : (curious(X0) & creative(X0)) => (curious(sK2) & creative(sK2)) [choice axiom]
51. ? [X2] : (~funny(X2) | patient(X2)) => (~funny(sK3) | patient(sK3)) [choice axiom]
52. ((curious(sK2) & creative(sK2)) | ! [X1] : (funny(X1) & ~patient(X1))) & ((~funny(sK3) | patient(sK3)) | ! [X3] : (~curious(X3) | ~creative(X3))) [skolemisation 49,51,50]
88. creative(sK2) | ~patient(X1) [cnf transformation 52]
101. ~creative(X0) | ~creative(X0) [cnf transformation 33]
149. patient(susan) [cnf transformation 25]
152. ~creative(X0) [duplicate literal removal 101]
198. 11 <=> ! [X1] : ~patient(X1) [avatar definition]
199. ~patient(X1) <- (11) [avatar component clause 198]
202. 12 <=> creative(sK2) [avatar definition]
204. creative(sK2) <- (12) [avatar component clause 202]
206. 11 | 12 [avatar split clause 88,202,198]
369. $false <- (11) [resolution 199,149]
370. ~11 [avatar contradiction clause 369]
371. $false <- (12) [subsumption resolution 204,152]
372. ~12 [avatar contradiction clause 371]
373. $false [avatar sat refutation 206,370,372]
% SZS output end Proof for 7381081208771282724111412
% ------------------------------
% 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 both curious and patient is both not creative and happy.
If someone is happy or not curious then susan is both kind and not humble and vice versa.
Everyone who is both not happy and not funny is either not generous or not happy.
Everyone who is both quiet and kind is not brave or funny and vice versa.
If alice is curious or creative then someone is both creative and quiet.
Everyone who is not curious or tall is both not old and funny and vice versa.
If someone is not rich or not strong then someone is both not calm and not old.
If alice is either wise or funny then someone is strong and vice versa.
Everyone who is both not calm and not quiet is either not patient or not creative and vice versa.
If someone is either not tall or not funny then someone is either strong or not calm and vice versa.
Everyone who is wise or happy is not kind.
Everyone who is not kind or funny is either not happy or not tall.
Everyone who is either not strong or not kind is both not old and not patient.
If alice is either not rich or not tall then lucy is both brave and not rich.
If someone is both kind and not rich then someone is both old and not strong and vice versa.
If someone is either generous or not wise then paul is not curious.
Paul is strong.
Lucy is not humble.
Mary is not strong.
Someone is either happy or brave.
Someone is both funny and not rich.
Someone is either not happy or humble.
Paul is not strong or tall. | Susan is not creative. | neutral | (![X]:((curious(X)&patient(X))=>(~creative(X)&happy(X))))&
((?[X]:((happy(X)|~curious(X))))<=>((kind(susan)&~humble(susan))))&
(![X]:((~happy(X)&~funny(X))=>(~generous(X)<~>~happy(X))))&
(![X]:((quiet(X)&kind(X))<=>(~brave(X)|funny(X))))&
(((curious(alice)|creative(alice)))=>(?[X]:((creative(X)&quiet(X)))))&
(![X]:((~curious(X)|tall(X))<=>(~old(X)&funny(X))))&
((?[X]:((~rich(X)|~strong(X))))=>(?[X]:((~calm(X)&~old(X)))))&
(((wise(alice)<~>funny(alice)))<=>(?[X]:(strong(X))))&
(![X]:((~calm(X)&~quiet(X))<=>(~patient(X)<~>~creative(X))))&
((?[X]:((~tall(X)<~>~funny(X))))<=>(?[X]:((strong(X)<~>~calm(X)))))&
(![X]:((wise(X)|happy(X))=>~kind(X)))&
(![X]:((~kind(X)|funny(X))=>(~happy(X)<~>~tall(X))))&
(![X]:((~strong(X)<~>~kind(X))=>(~old(X)&~patient(X))))&
(((~rich(alice)<~>~tall(alice)))=>((brave(lucy)&~rich(lucy))))&
((?[X]:((kind(X)&~rich(X))))<=>(?[X]:((old(X)&~strong(X)))))&
((?[X]:((generous(X)<~>~wise(X))))=>(~curious(paul)))&
(strong(paul))&
(~humble(lucy))&
(~strong(mary))&
(?[X]:((happy(X)<~>brave(X))))&
(?[X]:((funny(X)&~rich(X))))&
(?[X]:((~happy(X)<~>humble(X))))&
((~strong(paul)|tall(paul))) | ~creative(susan) | [] | null | 0 |
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