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
|
|---|---|---|---|---|---|---|---|
Everyone who is calm or not rich is either quiet or not curious.
Everyone who is not kind is both not wise and not curious and vice versa.
Everyone who is either old or not happy is both not wise and kind.
Everyone who is happy is curious or not curious.
Everyone who is strong or not generous is both patient and not happy.
Everyone who is both not wise and generous is either patient or not kind and vice versa.
Everyone who is either kind or not kind is either not funny or not tall and vice versa.
If someone is strong or not curious then john is not kind.
Everyone who is either not patient or not rich is brave and vice versa.
Everyone who is not strong is not old or funny.
Everyone who is both not creative and not funny is quiet or not rich and vice versa.
If alice is not quiet then someone is both humble and kind.
If someone is either tall or rich then lucy is both not strong and patient.
Everyone who is either curious or not happy is both funny and old and vice versa.
If someone is either not tall or curious then someone is not humble.
Everyone who is not humble is both not generous and not rich and vice versa.
Paul is strong or not happy. | Lucy is not rich. | contradiction | (![X]:((calm(X)|~rich(X))=>(quiet(X)<~>~curious(X))))&
(![X]:(~kind(X)<=>(~wise(X)&~curious(X))))&
(![X]:((old(X)<~>~happy(X))=>(~wise(X)&kind(X))))&
(![X]:(happy(X)=>(curious(X)|~curious(X))))&
(![X]:((strong(X)|~generous(X))=>(patient(X)&~happy(X))))&
(![X]:((~wise(X)&generous(X))<=>(patient(X)<~>~kind(X))))&
(![X]:((kind(X)<~>~kind(X))<=>(~funny(X)<~>~tall(X))))&
((?[X]:((strong(X)|~curious(X))))=>(~kind(john)))&
(![X]:((~patient(X)<~>~rich(X))<=>brave(X)))&
(![X]:(~strong(X)=>(~old(X)|funny(X))))&
(![X]:((~creative(X)&~funny(X))<=>(quiet(X)|~rich(X))))&
((~quiet(alice))=>(?[X]:((humble(X)&kind(X)))))&
((?[X]:((tall(X)<~>rich(X))))=>((~strong(lucy)&patient(lucy))))&
(![X]:((curious(X)<~>~happy(X))<=>(funny(X)&old(X))))&
((?[X]:((~tall(X)<~>curious(X))))=>(?[X]:(~humble(X))))&
(![X]:(~humble(X)<=>(~generous(X)&~rich(X))))&
((strong(paul)|~happy(paul))) | ~rich(lucy) | [
"p0",
"p1",
"p2",
"p4",
"p5",
"p6",
"p10",
"p12",
"p13",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3967813592415305723631285
% SZS output start Proof for 3967813592415305723631285
1. ! [X0] : ((~rich(X0) | calm(X0)) => (quiet(X0) <~> ~curious(X0))) [input p0]
2. ! [X0] : (~kind(X0) <=> (~curious(X0) & ~wise(X0))) [input p1]
3. ! [X0] : ((old(X0) <~> ~happy(X0)) => (kind(X0) & ~wise(X0))) [input p2]
5. ! [X0] : ((~generous(X0) | strong(X0)) => (~happy(X0) & patient(X0))) [input p4]
6. ! [X0] : ((generous(X0) & ~wise(X0)) <=> (patient(X0) <~> ~kind(X0))) [input p5]
7. ! [X0] : ((kind(X0) <~> ~kind(X0)) <=> (~funny(X0) <~> ~tall(X0))) [input p6]
11. ! [X0] : ((~funny(X0) & ~creative(X0)) <=> (~rich(X0) | quiet(X0))) [input p10]
13. ? [X0] : (tall(X0) <~> rich(X0)) => (patient(lucy) & ~strong(lucy)) [input p12]
14. ! [X0] : ((curious(X0) <~> ~happy(X0)) <=> (old(X0) & funny(X0))) [input p13]
15. ? [X0] : (~tall(X0) <~> curious(X0)) => ? [X0] : ~humble(X0) [input p14]
16. ! [X0] : (~humble(X0) <=> (~rich(X0) & ~generous(X0))) [input p15]
18. ~rich(lucy) [input hypothesis]
19. ? [X0] : (~tall(X0) <~> curious(X0)) => ? [X1] : ~humble(X1) [rectify 15]
20. ! [X0] : (~rich(X0) => (quiet(X0) <~> ~curious(X0))) [pure predicate removal 1]
21. ! [X0] : ((quiet(X0) <~> ~curious(X0)) | rich(X0)) [ennf transformation 20]
22. ! [X0] : ((kind(X0) & ~wise(X0)) | (old(X0) <=> ~happy(X0))) [ennf transformation 3]
25. ! [X0] : ((~happy(X0) & patient(X0)) | (generous(X0) & ~strong(X0))) [ennf transformation 5]
30. (patient(lucy) & ~strong(lucy)) | ! [X0] : (tall(X0) <=> rich(X0)) [ennf transformation 13]
31. ? [X1] : ~humble(X1) | ! [X0] : (~tall(X0) <=> curious(X0)) [ennf transformation 19]
32. ! [X0] : (((curious(X0) | ~quiet(X0)) & (~curious(X0) | quiet(X0))) | rich(X0)) [nnf transformation 21]
33. ! [X0] : ((~kind(X0) | (curious(X0) | wise(X0))) & ((~curious(X0) & ~wise(X0)) | kind(X0))) [nnf transformation 2]
34. ! [X0] : ((~kind(X0) | curious(X0) | wise(X0)) & ((~curious(X0) & ~wise(X0)) | kind(X0))) [flattening 33]
35. ! [X0] : ((kind(X0) & ~wise(X0)) | ((old(X0) | happy(X0)) & (~happy(X0) | ~old(X0)))) [nnf transformation 22]
36. ! [X0] : (((generous(X0) & ~wise(X0)) | ((patient(X0) | kind(X0)) & (~kind(X0) | ~patient(X0)))) & (((kind(X0) | ~patient(X0)) & (~kind(X0) | patient(X0))) | (~generous(X0) | wise(X0)))) [nnf transformation 6]
37. ! [X0] : (((generous(X0) & ~wise(X0)) | ((patient(X0) | kind(X0)) & (~kind(X0) | ~patient(X0)))) & (((kind(X0) | ~patient(X0)) & (~kind(X0) | patient(X0))) | ~generous(X0) | wise(X0))) [flattening 36]
38. ! [X0] : ((((kind(X0) | ~kind(X0)) & (~kind(X0) | kind(X0))) | ((~funny(X0) | tall(X0)) & (~tall(X0) | funny(X0)))) & (((tall(X0) | funny(X0)) & (~tall(X0) | ~funny(X0))) | ((kind(X0) | kind(X0)) & (~kind(X0) | ~kind(X0))))) [nnf transformation 7]
39. ! [X0] : (((~funny(X0) & ~creative(X0)) | (rich(X0) & ~quiet(X0))) & ((~rich(X0) | quiet(X0)) | (funny(X0) | creative(X0)))) [nnf transformation 11]
40. ! [X0] : (((~funny(X0) & ~creative(X0)) | (rich(X0) & ~quiet(X0))) & (~rich(X0) | quiet(X0) | funny(X0) | creative(X0))) [flattening 39]
43. (patient(lucy) & ~strong(lucy)) | ! [X0] : ((tall(X0) | ~rich(X0)) & (rich(X0) | ~tall(X0))) [nnf transformation 30]
44. ! [X0] : ((((happy(X0) | ~curious(X0)) & (~happy(X0) | curious(X0))) | (~old(X0) | ~funny(X0))) & ((old(X0) & funny(X0)) | ((curious(X0) | happy(X0)) & (~happy(X0) | ~curious(X0))))) [nnf transformation 14]
45. ! [X0] : ((((happy(X0) | ~curious(X0)) & (~happy(X0) | curious(X0))) | ~old(X0) | ~funny(X0)) & ((old(X0) & funny(X0)) | ((curious(X0) | happy(X0)) & (~happy(X0) | ~curious(X0))))) [flattening 44]
46. ? [X1] : ~humble(X1) | ! [X0] : ((~tall(X0) | ~curious(X0)) & (curious(X0) | tall(X0))) [nnf transformation 31]
47. ? [X0] : ~humble(X0) | ! [X1] : ((~tall(X1) | ~curious(X1)) & (curious(X1) | tall(X1))) [rectify 46]
48. ? [X0] : ~humble(X0) => ~humble(sK1) [choice axiom]
49. ~humble(sK1) | ! [X1] : ((~tall(X1) | ~curious(X1)) & (curious(X1) | tall(X1))) [skolemisation 47,48]
50. ! [X0] : ((~humble(X0) | (rich(X0) | generous(X0))) & ((~rich(X0) & ~generous(X0)) | humble(X0))) [nnf transformation 16]
51. ! [X0] : ((~humble(X0) | rich(X0) | generous(X0)) & ((~rich(X0) & ~generous(X0)) | humble(X0))) [flattening 50]
52. ~curious(X0) | quiet(X0) | rich(X0) [cnf transformation 32]
54. ~wise(X0) | kind(X0) [cnf transformation 34]
55. ~curious(X0) | kind(X0) [cnf transformation 34]
56. ~kind(X0) | curious(X0) | wise(X0) [cnf transformation 34]
59. ~happy(X0) | kind(X0) | ~old(X0) [cnf transformation 35]
60. happy(X0) | old(X0) | kind(X0) [cnf transformation 35]
63. patient(X0) | generous(X0) [cnf transformation 25]
65. ~happy(X0) | generous(X0) [cnf transformation 25]
67. kind(X0) | ~patient(X0) | ~generous(X0) | wise(X0) [cnf transformation 37]
68. ~wise(X0) | ~kind(X0) | ~patient(X0) [cnf transformation 37]
70. generous(X0) | ~kind(X0) | ~patient(X0) [cnf transformation 37]
74. tall(X0) | funny(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 38]
75. tall(X0) | funny(X0) | kind(X0) | kind(X0) [cnf transformation 38]
86. ~funny(X0) | ~quiet(X0) [cnf transformation 40]
87. ~funny(X0) | rich(X0) [cnf transformation 40]
92. patient(lucy) | rich(X0) | ~tall(X0) [cnf transformation 43]
95. funny(X0) | curious(X0) | happy(X0) [cnf transformation 45]
101. ~humble(sK1) | ~tall(X1) | ~curious(X1) [cnf transformation 49]
102. ~generous(X0) | humble(X0) [cnf transformation 51]
103. ~rich(X0) | humble(X0) [cnf transformation 51]
106. ~rich(lucy) [cnf transformation 18]
109. tall(X0) | funny(X0) | ~kind(X0) [duplicate literal removal 74]
110. tall(X0) | funny(X0) | kind(X0) [duplicate literal removal 75]
111. ~kind(X0) | generous(X0) [subsumption resolution 70,63]
112. ~patient(X0) | ~wise(X0) [subsumption resolution 68,54]
113. ~patient(X0) | kind(X0) | ~generous(X0) [subsumption resolution 67,112]
115. tall(X0) | funny(X0) [subsumption resolution 109,110]
147. 8 <=> patient(lucy) [avatar definition]
149. patient(lucy) <- (8) [avatar component clause 147]
152. 9 <=> ! [X0] : (rich(X0) | ~tall(X0)) [avatar definition]
153. ~tall(X0) | rich(X0) <- (9) [avatar component clause 152]
154. 9 | 8 [avatar split clause 92,147,152]
162. 11 <=> ! [X1] : (~tall(X1) | ~curious(X1)) [avatar definition]
163. ~tall(X1) | ~curious(X1) <- (11) [avatar component clause 162]
165. 12 <=> humble(sK1) [avatar definition]
167. ~humble(sK1) <- (~12) [avatar component clause 165]
168. 11 | ~12 [avatar split clause 101,165,162]
204. old(X2) | kind(X2) | generous(X2) [resolution 60,65]
215. generous(X2) | old(X2) [subsumption resolution 204,111]
238. happy(X0) | curious(X0) | rich(X0) [resolution 95,87]
287. kind(lucy) | ~generous(lucy) <- (8) [resolution 113,149]
290. 28 <=> generous(lucy) [avatar definition]
292. ~generous(lucy) <- (~28) [avatar component clause 290]
294. 29 <=> kind(lucy) [avatar definition]
296. kind(lucy) <- (29) [avatar component clause 294]
297. ~28 | 29 | ~8 [avatar split clause 287,147,294,290]
310. humble(X0) | old(X0) [resolution 215,102]
311. old(lucy) <- (~28) [resolution 215,292]
316. curious(X2) | rich(X2) | kind(X2) | ~old(X2) [resolution 238,59]
321. ~old(X2) | kind(X2) | rich(X2) [subsumption resolution 316,55]
362. old(sK1) <- (~12) [resolution 310,167]
380. kind(lucy) | rich(lucy) <- (~28) [resolution 321,311]
381. kind(lucy) <- (~28) [subsumption resolution 380,106]
382. 29 | 28 [avatar split clause 381,290,294]
388. rich(X1) | funny(X1) <- (9) [resolution 153,115]
390. rich(X1) <- (9) [subsumption resolution 388,87]
391. $false <- (9) [resolution 390,106]
395. ~9 [avatar contradiction clause 391]
397. ~wise(lucy) <- (8) [resolution 149,112]
399. curious(lucy) | wise(lucy) <- (29) [resolution 296,56]
401. curious(lucy) <- (8, 29) [subsumption resolution 399,397]
407. quiet(lucy) | rich(lucy) <- (8, 29) [resolution 401,52]
409. quiet(lucy) <- (8, 29) [subsumption resolution 407,106]
415. kind(sK1) | rich(sK1) <- (~12) [resolution 362,321]
426. 38 <=> rich(sK1) [avatar definition]
428. rich(sK1) <- (38) [avatar component clause 426]
431. 39 <=> kind(sK1) [avatar definition]
433. kind(sK1) <- (39) [avatar component clause 431]
434. 38 | 39 | 12 [avatar split clause 415,165,431,426]
531. humble(sK1) <- (38) [resolution 428,103]
537. $false <- (~12, 38) [subsumption resolution 531,167]
538. 12 | ~38 [avatar contradiction clause 537]
541. generous(sK1) <- (39) [resolution 433,111]
552. humble(sK1) <- (39) [resolution 541,102]
553. $false <- (~12, 39) [subsumption resolution 552,167]
554. 12 | ~39 [avatar contradiction clause 553]
564. ~curious(X1) | funny(X1) <- (11) [resolution 163,115]
569. funny(lucy) <- (8, 11, 29) [resolution 564,401]
577. ~quiet(lucy) <- (8, 11, 29) [resolution 569,86]
590. $false <- (8, 11, 29) [subsumption resolution 577,409]
591. ~8 | ~11 | ~29 [avatar contradiction clause 590]
592. $false [avatar sat refutation 154,168,297,382,395,434,538,554,591]
% SZS output end Proof for 3967813592415305723631285
% ------------------------------
% 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 curious or creative is not curious and vice versa. If someone is either curious or not funny then paul is curious or not wise. If someone is either not wise or not humble then someone is both not quiet and not old and vice versa. Everyone who is not creative or not brave is either old or not humble. If susan is rich or not quiet then susan is either not creative or not kind and vice versa. Everyone who is not calm is rich or generous. Everyone who is both not calm and humble is both generous and not old. Everyone who is either quiet or happy is creative. If someone is generous or creative then someone is not calm and vice versa. If fred is both not strong and not rich then mary is not quiet. If mary is both not patient and old then someone is not curious or curious and vice versa. Everyone who is either not kind or not funny is both not humble and not patient and vice versa. Everyone who is not funny or kind is either patient or not tall. Everyone who is not creative is not rich or patient. Everyone who is not humble is either not patient or creative and vice versa. If susan is not quiet or rich then john is curious or old and vice versa. Someone is not funny. Fred is not tall. Someone is not curious. John is both humble and not happy. Susan is both kind and not tall. Someone is old. Someone is patient or not kind. Paul is both humble and not generous. | Mary is not calm. | contradiction | (![X]:((~curious(X)|creative(X))<=>~curious(X)))&
((?[X]:((curious(X)<~>~funny(X))))=>((curious(paul)|~wise(paul))))&
((?[X]:((~wise(X)<~>~humble(X))))<=>(?[X]:((~quiet(X)&~old(X)))))&
(![X]:((~creative(X)|~brave(X))=>(old(X)<~>~humble(X))))&
(((rich(susan)|~quiet(susan)))<=>((~creative(susan)<~>~kind(susan))))&
(![X]:(~calm(X)=>(rich(X)|generous(X))))&
(![X]:((~calm(X)&humble(X))=>(generous(X)&~old(X))))&
(![X]:((quiet(X)<~>happy(X))=>creative(X)))&
((?[X]:((generous(X)|creative(X))))<=>(?[X]:(~calm(X))))&
(((~strong(fred)&~rich(fred)))=>(~quiet(mary)))&
(((~patient(mary)&old(mary)))<=>(?[X]:((~curious(X)|curious(X)))))&
(![X]:((~kind(X)<~>~funny(X))<=>(~humble(X)&~patient(X))))&
(![X]:((~funny(X)|kind(X))=>(patient(X)<~>~tall(X))))&
(![X]:(~creative(X)=>(~rich(X)|patient(X))))&
(![X]:(~humble(X)<=>(~patient(X)<~>creative(X))))&
(((~quiet(susan)|rich(susan)))<=>((curious(john)|old(john))))&
(?[X]:(~funny(X)))&
(~tall(fred))&
(?[X]:(~curious(X)))&
((humble(john)&~happy(john)))&
((kind(susan)&~tall(susan)))&
(?[X]:(old(X)))&
(?[X]:((patient(X)|~kind(X))))&
((humble(paul)&~generous(paul))) | ~calm(mary) | [
"p3",
"p6",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4590341071134033208109426
% SZS output start Proof for 4590341071134033208109426
4. ! [X0] : ((~brave(X0) | ~creative(X0)) => (old(X0) <~> ~humble(X0))) [input p3]
7. ! [X0] : ((humble(X0) & ~calm(X0)) => (~old(X0) & generous(X0))) [input p6]
11. (old(mary) & ~patient(mary)) <=> ? [X0] : (curious(X0) | ~curious(X0)) [input p10]
15. ! [X0] : (~humble(X0) <=> (~patient(X0) <~> creative(X0))) [input p14]
25. ~calm(mary) [input hypothesis]
29. ! [X0] : (~creative(X0) => (old(X0) <~> ~humble(X0))) [pure predicate removal 4]
32. ! [X0] : ((old(X0) <~> ~humble(X0)) | creative(X0)) [ennf transformation 29]
35. ! [X0] : ((~old(X0) & generous(X0)) | (~humble(X0) | calm(X0))) [ennf transformation 7]
36. ! [X0] : ((~old(X0) & generous(X0)) | ~humble(X0) | calm(X0)) [flattening 35]
49. ! [X0] : (((humble(X0) | ~old(X0)) & (~humble(X0) | old(X0))) | creative(X0)) [nnf transformation 32]
58. ((old(mary) & ~patient(mary)) | ! [X0] : (~curious(X0) & curious(X0))) & (? [X0] : (curious(X0) | ~curious(X0)) | (~old(mary) | patient(mary))) [nnf transformation 11]
59. ((old(mary) & ~patient(mary)) | ! [X0] : (~curious(X0) & curious(X0))) & (? [X0] : (curious(X0) | ~curious(X0)) | ~old(mary) | patient(mary)) [flattening 58]
60. ((old(mary) & ~patient(mary)) | ! [X0] : (~curious(X0) & curious(X0))) & (? [X1] : (curious(X1) | ~curious(X1)) | ~old(mary) | patient(mary)) [rectify 59]
61. ? [X1] : (curious(X1) | ~curious(X1)) => (curious(sK4) | ~curious(sK4)) [choice axiom]
62. ((old(mary) & ~patient(mary)) | ! [X0] : (~curious(X0) & curious(X0))) & ((curious(sK4) | ~curious(sK4)) | ~old(mary) | patient(mary)) [skolemisation 60,61]
66. ! [X0] : ((~humble(X0) | ((~patient(X0) | ~creative(X0)) & (creative(X0) | patient(X0)))) & (((~creative(X0) | patient(X0)) & (creative(X0) | ~patient(X0))) | humble(X0))) [nnf transformation 15]
89. ~old(X0) | humble(X0) | creative(X0) [cnf transformation 49]
98. ~old(X0) | ~humble(X0) | calm(X0) [cnf transformation 36]
105. ~patient(mary) | curious(X0) [cnf transformation 62]
106. ~patient(mary) | ~curious(X0) [cnf transformation 62]
107. old(mary) | curious(X0) [cnf transformation 62]
108. old(mary) | ~curious(X0) [cnf transformation 62]
121. ~creative(X0) | patient(X0) | humble(X0) [cnf transformation 66]
139. ~calm(mary) [cnf transformation 25]
234. 22 <=> ! [X0] : ~curious(X0) [avatar definition]
235. ~curious(X0) <- (22) [avatar component clause 234]
237. 23 <=> old(mary) [avatar definition]
239. old(mary) <- (23) [avatar component clause 237]
240. 22 | 23 [avatar split clause 108,237,234]
242. 24 <=> ! [X0] : curious(X0) [avatar definition]
243. curious(X0) <- (24) [avatar component clause 242]
244. 24 | 23 [avatar split clause 107,237,242]
246. 25 <=> patient(mary) [avatar definition]
248. ~patient(mary) <- (~25) [avatar component clause 246]
249. 22 | ~25 [avatar split clause 106,246,234]
250. 24 | ~25 [avatar split clause 105,246,242]
293. humble(mary) | creative(mary) <- (23) [resolution 89,239]
304. 34 <=> creative(mary) [avatar definition]
306. creative(mary) <- (34) [avatar component clause 304]
308. 35 <=> humble(mary) [avatar definition]
309. ~humble(mary) <- (~35) [avatar component clause 308]
311. 34 | 35 | ~23 [avatar split clause 293,237,308,304]
312. $false <- (22, 24) [subsumption resolution 235,243]
313. ~22 | ~24 [avatar contradiction clause 312]
342. ~humble(mary) | calm(mary) <- (23) [resolution 98,239]
351. ~humble(mary) <- (23) [subsumption resolution 342,139]
352. ~35 | ~23 [avatar split clause 351,237,308]
389. patient(mary) | humble(mary) <- (34) [resolution 121,306]
393. humble(mary) <- (~25, 34) [subsumption resolution 389,248]
394. $false <- (~25, 34, ~35) [subsumption resolution 393,309]
395. 25 | ~34 | 35 [avatar contradiction clause 394]
397. $false [avatar sat refutation 240,244,249,250,311,313,352,395]
% SZS output end Proof for 4590341071134033208109426
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both strong and not wise is either not curious or strong and vice versa.
If someone is quiet then lucy is both not wise and not creative and vice versa.
Everyone who is both not happy and happy is not old or quiet.
Everyone who is not patient is not curious and vice versa.
Everyone who is funny or curious is not humble and vice versa.
Everyone who is either not wise or kind is wise or rich and vice versa.
Everyone who is not strong or not quiet is not strong and vice versa.
Everyone who is either not quiet or not funny is brave.
Everyone who is either wise or not tall is not kind or not creative.
If lucy is wise then someone is funny and vice versa.
If someone is curious or not old then someone is not tall and vice versa.
Everyone who is either not calm or strong is quiet and vice versa.
If paul is either not generous or not calm then someone is either not quiet or not humble.
Everyone who is creative is either curious or not rich.
If lucy is both not calm and not old then fred is either wise or not calm.
If alice is both brave and not old then john is not creative or happy.
Mary is not quiet or old.
Alice is happy or not funny.
Someone is rich or calm.
Susan is not wise or not curious.
Lucy is both wise and not funny.
Paul is kind or not old.
Someone is either not tall or generous.
Paul is not humble or patient. | Fred is not humble. | entailment | (![X]:((strong(X)&~wise(X))<=>(~curious(X)<~>strong(X))))&
((?[X]:(quiet(X)))<=>((~wise(lucy)&~creative(lucy))))&
(![X]:((~happy(X)&happy(X))=>(~old(X)|quiet(X))))&
(![X]:(~patient(X)<=>~curious(X)))&
(![X]:((funny(X)|curious(X))<=>~humble(X)))&
(![X]:((~wise(X)<~>kind(X))<=>(wise(X)|rich(X))))&
(![X]:((~strong(X)|~quiet(X))<=>~strong(X)))&
(![X]:((~quiet(X)<~>~funny(X))=>brave(X)))&
(![X]:((wise(X)<~>~tall(X))=>(~kind(X)|~creative(X))))&
((wise(lucy))<=>(?[X]:(funny(X))))&
((?[X]:((curious(X)|~old(X))))<=>(?[X]:(~tall(X))))&
(![X]:((~calm(X)<~>strong(X))<=>quiet(X)))&
(((~generous(paul)<~>~calm(paul)))=>(?[X]:((~quiet(X)<~>~humble(X)))))&
(![X]:(creative(X)=>(curious(X)<~>~rich(X))))&
(((~calm(lucy)&~old(lucy)))=>((wise(fred)<~>~calm(fred))))&
(((brave(alice)&~old(alice)))=>((~creative(john)|happy(john))))&
((~quiet(mary)|old(mary)))&
((happy(alice)|~funny(alice)))&
(?[X]:((rich(X)|calm(X))))&
((~wise(susan)|~curious(susan)))&
((wise(lucy)&~funny(lucy)))&
((kind(paul)|~old(paul)))&
(?[X]:((~tall(X)<~>generous(X))))&
((~humble(paul)|patient(paul))) | ~humble(fred) | [
"p0",
"p1",
"p4",
"p6",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 1304471867734250781932418
% SZS output start Proof for 1304471867734250781932418
1. ! [X0] : ((~wise(X0) & strong(X0)) <=> (~curious(X0) <~> strong(X0))) [input p0]
2. ? [X0] : quiet(X0) <=> (~creative(lucy) & ~wise(lucy)) [input p1]
5. ! [X0] : ((curious(X0) | funny(X0)) <=> ~humble(X0)) [input p4]
7. ! [X0] : ((~quiet(X0) | ~strong(X0)) <=> ~strong(X0)) [input p6]
21. ~funny(lucy) & wise(lucy) [input p20]
25. humble(fred) [input hypothesis]
40. ! [X0] : (((~wise(X0) & strong(X0)) | ((~curious(X0) | ~strong(X0)) & (strong(X0) | curious(X0)))) & (((~strong(X0) | curious(X0)) & (strong(X0) | ~curious(X0))) | (wise(X0) | ~strong(X0)))) [nnf transformation 1]
41. ! [X0] : (((~wise(X0) & strong(X0)) | ((~curious(X0) | ~strong(X0)) & (strong(X0) | curious(X0)))) & (((~strong(X0) | curious(X0)) & (strong(X0) | ~curious(X0))) | wise(X0) | ~strong(X0))) [flattening 40]
42. (? [X0] : quiet(X0) | (creative(lucy) | wise(lucy))) & ((~creative(lucy) & ~wise(lucy)) | ! [X0] : ~quiet(X0)) [nnf transformation 2]
43. (? [X0] : quiet(X0) | creative(lucy) | wise(lucy)) & ((~creative(lucy) & ~wise(lucy)) | ! [X0] : ~quiet(X0)) [flattening 42]
44. (? [X0] : quiet(X0) | creative(lucy) | wise(lucy)) & ((~creative(lucy) & ~wise(lucy)) | ! [X1] : ~quiet(X1)) [rectify 43]
45. ? [X0] : quiet(X0) => quiet(sK0) [choice axiom]
46. (quiet(sK0) | creative(lucy) | wise(lucy)) & ((~creative(lucy) & ~wise(lucy)) | ! [X1] : ~quiet(X1)) [skolemisation 44,45]
47. ! [X0] : (((curious(X0) | funny(X0)) | humble(X0)) & (~humble(X0) | (~curious(X0) & ~funny(X0)))) [nnf transformation 5]
48. ! [X0] : ((curious(X0) | funny(X0) | humble(X0)) & (~humble(X0) | (~curious(X0) & ~funny(X0)))) [flattening 47]
51. ! [X0] : (((~quiet(X0) | ~strong(X0)) | strong(X0)) & (~strong(X0) | (quiet(X0) & strong(X0)))) [nnf transformation 7]
52. ! [X0] : ((~quiet(X0) | ~strong(X0) | strong(X0)) & (~strong(X0) | (quiet(X0) & strong(X0)))) [flattening 51]
77. strong(X0) | strong(X0) | curious(X0) [cnf transformation 41]
81. ~wise(lucy) | ~quiet(X1) [cnf transformation 46]
87. ~humble(X0) | ~curious(X0) [cnf transformation 48]
96. ~strong(X0) | quiet(X0) [cnf transformation 52]
124. wise(lucy) [cnf transformation 21]
130. humble(fred) [cnf transformation 25]
134. curious(X0) | strong(X0) [duplicate literal removal 77]
137. 1 <=> wise(lucy) [avatar definition]
150. 4 <=> ! [X1] : ~quiet(X1) [avatar definition]
151. ~quiet(X1) <- (4) [avatar component clause 150]
153. 4 | ~1 [avatar split clause 81,137,150]
282. 1 [avatar split clause 124,137]
312. ~curious(fred) [resolution 87,130]
315. strong(fred) [resolution 134,312]
336. quiet(fred) [resolution 315,96]
337. $false <- (4) [subsumption resolution 336,151]
338. ~4 [avatar contradiction clause 337]
339. $false [avatar sat refutation 153,282,338]
% SZS output end Proof for 1304471867734250781932418
% ------------------------------
% 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 creative or not happy is both not tall and calm and vice versa.
Everyone who is not funny or not humble is not generous or curious and vice versa.
If someone is humble then mary is either not happy or not brave and vice versa.
Everyone who is curious is not generous or not creative.
Everyone who is either not calm or not brave is both patient and not kind.
Everyone who is not patient is either not wise or humble and vice versa.
If someone is either not happy or not strong then alice is funny.
Everyone who is not funny is either not patient or wise and vice versa.
If someone is either not patient or not funny then someone is either calm or old and vice versa.
If fred is both not funny and not kind then lucy is not brave.
If john is humble then someone is either not strong or not old.
Everyone who is not tall or quiet is not funny or wise.
Everyone who is either happy or not humble is generous or strong and vice versa.
If lucy is either not generous or not happy then someone is funny and vice versa.
Everyone who is generous or not rich is not brave or happy and vice versa.
Everyone who is both funny and not tall is both generous and strong and vice versa.
Fred is either not rich or not humble.
Someone is either funny or rich.
Someone is either humble or not rich.
Someone is not brave.
Someone is not curious.
Alice is either not strong or tall.
Fred is patient or not tall.
Someone is both creative and wise. | Lucy is calm. | entailment | (![X]:((creative(X)|~happy(X))<=>(~tall(X)&calm(X))))&
(![X]:((~funny(X)|~humble(X))<=>(~generous(X)|curious(X))))&
((?[X]:(humble(X)))<=>((~happy(mary)<~>~brave(mary))))&
(![X]:(curious(X)=>(~generous(X)|~creative(X))))&
(![X]:((~calm(X)<~>~brave(X))=>(patient(X)&~kind(X))))&
(![X]:(~patient(X)<=>(~wise(X)<~>humble(X))))&
((?[X]:((~happy(X)<~>~strong(X))))=>(funny(alice)))&
(![X]:(~funny(X)<=>(~patient(X)<~>wise(X))))&
((?[X]:((~patient(X)<~>~funny(X))))<=>(?[X]:((calm(X)<~>old(X)))))&
(((~funny(fred)&~kind(fred)))=>(~brave(lucy)))&
((humble(john))=>(?[X]:((~strong(X)<~>~old(X)))))&
(![X]:((~tall(X)|quiet(X))=>(~funny(X)|wise(X))))&
(![X]:((happy(X)<~>~humble(X))<=>(generous(X)|strong(X))))&
(((~generous(lucy)<~>~happy(lucy)))<=>(?[X]:(funny(X))))&
(![X]:((generous(X)|~rich(X))<=>(~brave(X)|happy(X))))&
(![X]:((funny(X)&~tall(X))<=>(generous(X)&strong(X))))&
((~rich(fred)<~>~humble(fred)))&
(?[X]:((funny(X)<~>rich(X))))&
(?[X]:((humble(X)<~>~rich(X))))&
(?[X]:(~brave(X)))&
(?[X]:(~curious(X)))&
((~strong(alice)<~>tall(alice)))&
((patient(fred)|~tall(fred)))&
(?[X]:((creative(X)&wise(X)))) | calm(lucy) | [
"p0",
"p1",
"p2",
"p5",
"p6",
"p7",
"p12",
"p13",
"p15",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 7554217429601066806741841
% SZS output start Proof for 7554217429601066806741841
1. ! [X0] : ((~happy(X0) | creative(X0)) <=> (calm(X0) & ~tall(X0))) [input p0]
2. ! [X0] : ((~humble(X0) | ~funny(X0)) <=> (curious(X0) | ~generous(X0))) [input p1]
3. ? [X0] : humble(X0) <=> (~happy(mary) <~> ~brave(mary)) [input p2]
6. ! [X0] : (~patient(X0) <=> (~wise(X0) <~> humble(X0))) [input p5]
7. ? [X0] : (~happy(X0) <~> ~strong(X0)) => funny(alice) [input p6]
8. ! [X0] : (~funny(X0) <=> (~patient(X0) <~> wise(X0))) [input p7]
13. ! [X0] : ((happy(X0) <~> ~humble(X0)) <=> (strong(X0) | generous(X0))) [input p12]
14. (~generous(lucy) <~> ~happy(lucy)) <=> ? [X0] : funny(X0) [input p13]
16. ! [X0] : ((~tall(X0) & funny(X0)) <=> (strong(X0) & generous(X0))) [input p15]
22. ~strong(alice) <~> tall(alice) [input p21]
25. ~calm(lucy) [input hypothesis]
31. funny(alice) | ! [X0] : (~happy(X0) <=> ~strong(X0)) [ennf transformation 7]
37. ! [X0] : (((~happy(X0) | creative(X0)) | (~calm(X0) | tall(X0))) & ((calm(X0) & ~tall(X0)) | (happy(X0) & ~creative(X0)))) [nnf transformation 1]
38. ! [X0] : ((~happy(X0) | creative(X0) | ~calm(X0) | tall(X0)) & ((calm(X0) & ~tall(X0)) | (happy(X0) & ~creative(X0)))) [flattening 37]
39. ! [X0] : (((~humble(X0) | ~funny(X0)) | (~curious(X0) & generous(X0))) & ((curious(X0) | ~generous(X0)) | (humble(X0) & funny(X0)))) [nnf transformation 2]
40. ! [X0] : ((~humble(X0) | ~funny(X0) | (~curious(X0) & generous(X0))) & (curious(X0) | ~generous(X0) | (humble(X0) & funny(X0)))) [flattening 39]
41. (? [X0] : humble(X0) | ((~happy(mary) | brave(mary)) & (~brave(mary) | happy(mary)))) & (((brave(mary) | happy(mary)) & (~brave(mary) | ~happy(mary))) | ! [X0] : ~humble(X0)) [nnf transformation 3]
42. (? [X0] : humble(X0) | ((~happy(mary) | brave(mary)) & (~brave(mary) | happy(mary)))) & (((brave(mary) | happy(mary)) & (~brave(mary) | ~happy(mary))) | ! [X1] : ~humble(X1)) [rectify 41]
43. ? [X0] : humble(X0) => humble(sK0) [choice axiom]
44. (humble(sK0) | ((~happy(mary) | brave(mary)) & (~brave(mary) | happy(mary)))) & (((brave(mary) | happy(mary)) & (~brave(mary) | ~happy(mary))) | ! [X1] : ~humble(X1)) [skolemisation 42,43]
46. ! [X0] : ((~patient(X0) | ((~wise(X0) | ~humble(X0)) & (humble(X0) | wise(X0)))) & (((~humble(X0) | wise(X0)) & (humble(X0) | ~wise(X0))) | patient(X0))) [nnf transformation 6]
47. funny(alice) | ! [X0] : ((~happy(X0) | strong(X0)) & (~strong(X0) | happy(X0))) [nnf transformation 31]
48. ! [X0] : ((~funny(X0) | ((~patient(X0) | ~wise(X0)) & (wise(X0) | patient(X0)))) & (((~wise(X0) | patient(X0)) & (wise(X0) | ~patient(X0))) | funny(X0))) [nnf transformation 8]
57. ! [X0] : ((((humble(X0) | ~happy(X0)) & (~humble(X0) | happy(X0))) | (~strong(X0) & ~generous(X0))) & ((strong(X0) | generous(X0)) | ((happy(X0) | humble(X0)) & (~humble(X0) | ~happy(X0))))) [nnf transformation 13]
58. ! [X0] : ((((humble(X0) | ~happy(X0)) & (~humble(X0) | happy(X0))) | (~strong(X0) & ~generous(X0))) & (strong(X0) | generous(X0) | ((happy(X0) | humble(X0)) & (~humble(X0) | ~happy(X0))))) [flattening 57]
59. (((happy(lucy) | generous(lucy)) & (~happy(lucy) | ~generous(lucy))) | ! [X0] : ~funny(X0)) & (? [X0] : funny(X0) | ((~generous(lucy) | happy(lucy)) & (~happy(lucy) | generous(lucy)))) [nnf transformation 14]
60. (((happy(lucy) | generous(lucy)) & (~happy(lucy) | ~generous(lucy))) | ! [X0] : ~funny(X0)) & (? [X1] : funny(X1) | ((~generous(lucy) | happy(lucy)) & (~happy(lucy) | generous(lucy)))) [rectify 59]
61. ? [X1] : funny(X1) => funny(sK4) [choice axiom]
62. (((happy(lucy) | generous(lucy)) & (~happy(lucy) | ~generous(lucy))) | ! [X0] : ~funny(X0)) & (funny(sK4) | ((~generous(lucy) | happy(lucy)) & (~happy(lucy) | generous(lucy)))) [skolemisation 60,61]
65. ! [X0] : (((~tall(X0) & funny(X0)) | (~strong(X0) | ~generous(X0))) & ((strong(X0) & generous(X0)) | (tall(X0) | ~funny(X0)))) [nnf transformation 16]
66. ! [X0] : (((~tall(X0) & funny(X0)) | ~strong(X0) | ~generous(X0)) & ((strong(X0) & generous(X0)) | tall(X0) | ~funny(X0))) [flattening 65]
78. (~tall(alice) | strong(alice)) & (tall(alice) | ~strong(alice)) [nnf transformation 22]
82. ~tall(X0) | happy(X0) [cnf transformation 38]
84. calm(X0) | happy(X0) [cnf transformation 38]
88. ~humble(X0) | ~funny(X0) | generous(X0) [cnf transformation 40]
91. brave(mary) | happy(mary) | ~humble(X1) [cnf transformation 44]
92. humble(sK0) | ~brave(mary) | happy(mary) [cnf transformation 44]
100. ~humble(X0) | wise(X0) | patient(X0) [cnf transformation 46]
102. ~wise(X0) | ~patient(X0) | ~humble(X0) [cnf transformation 46]
104. funny(alice) | ~happy(X0) | strong(X0) [cnf transformation 47]
105. ~patient(X0) | wise(X0) | funny(X0) [cnf transformation 48]
106. ~wise(X0) | patient(X0) | funny(X0) [cnf transformation 48]
126. ~strong(X0) | ~happy(X0) | humble(X0) [cnf transformation 58]
129. ~happy(lucy) | ~generous(lucy) | ~funny(X0) [cnf transformation 62]
136. ~funny(X0) | tall(X0) | strong(X0) [cnf transformation 66]
138. ~strong(X0) | ~tall(X0) | ~generous(X0) [cnf transformation 66]
147. tall(alice) | ~strong(alice) [cnf transformation 78]
148. ~tall(alice) | strong(alice) [cnf transformation 78]
152. ~calm(lucy) [cnf transformation 25]
154. 1 <=> brave(mary) [avatar definition]
158. 2 <=> happy(mary) [avatar definition]
159. happy(mary) <- (2) [avatar component clause 158]
162. 3 <=> humble(sK0) [avatar definition]
164. humble(sK0) <- (3) [avatar component clause 162]
166. 2 | ~1 | 3 [avatar split clause 92,162,154,158]
168. 4 <=> ! [X1] : ~humble(X1) [avatar definition]
169. ~humble(X1) <- (4) [avatar component clause 168]
170. 4 | 2 | 1 [avatar split clause 91,154,158,168]
173. 5 <=> ! [X0] : (~happy(X0) | strong(X0)) [avatar definition]
174. ~happy(X0) | strong(X0) <- (5) [avatar component clause 173]
176. 6 <=> funny(alice) [avatar definition]
178. funny(alice) <- (6) [avatar component clause 176]
179. 5 | 6 [avatar split clause 104,176,173]
248. 22 <=> ! [X0] : ~funny(X0) [avatar definition]
249. ~funny(X0) <- (22) [avatar component clause 248]
251. 23 <=> generous(lucy) [avatar definition]
252. ~generous(lucy) <- (~23) [avatar component clause 251]
255. 24 <=> happy(lucy) [avatar definition]
257. happy(lucy) <- (24) [avatar component clause 255]
259. 22 | ~23 | ~24 [avatar split clause 129,255,251,248]
297. 32 <=> strong(alice) [avatar definition]
298. ~strong(alice) <- (~32) [avatar component clause 297]
299. strong(alice) <- (32) [avatar component clause 297]
301. 33 <=> tall(alice) [avatar definition]
302. tall(alice) <- (33) [avatar component clause 301]
303. ~tall(alice) <- (~33) [avatar component clause 301]
304. 32 | ~33 [avatar split clause 148,301,297]
305. ~32 | 33 [avatar split clause 147,301,297]
320. happy(lucy) [resolution 84,152]
323. 24 [avatar split clause 320,255]
324. strong(mary) <- (2, 5) [resolution 174,159]
334. 37 <=> funny(sK0) [avatar definition]
335. funny(sK0) <- (37) [avatar component clause 334]
336. ~funny(sK0) <- (~37) [avatar component clause 334]
379. wise(sK0) | patient(sK0) <- (3) [resolution 100,164]
382. 45 <=> patient(sK0) [avatar definition]
383. ~patient(sK0) <- (~45) [avatar component clause 382]
384. patient(sK0) <- (45) [avatar component clause 382]
386. 46 <=> wise(sK0) [avatar definition]
388. wise(sK0) <- (46) [avatar component clause 386]
389. 45 | 46 | ~3 [avatar split clause 379,162,386,382]
409. wise(sK0) | funny(sK0) <- (45) [resolution 105,384]
410. wise(sK0) <- (~37, 45) [subsumption resolution 409,336]
411. 46 | 37 | ~45 [avatar split clause 410,382,334,386]
412. ~patient(sK0) | ~humble(sK0) <- (46) [resolution 388,102]
414. ~patient(sK0) <- (3, 46) [subsumption resolution 412,164]
415. ~45 | ~3 | ~46 [avatar split clause 414,386,162,382]
418. patient(sK0) | funny(sK0) <- (46) [resolution 106,388]
422. funny(sK0) <- (~45, 46) [subsumption resolution 418,383]
423. $false <- (~37, ~45, 46) [subsumption resolution 422,336]
424. 37 | 45 | ~46 [avatar contradiction clause 423]
493. ~happy(mary) | humble(mary) <- (2, 5) [resolution 126,324]
496. humble(mary) <- (2, 5) [subsumption resolution 493,159]
579. 62 <=> funny(mary) [avatar definition]
580. ~funny(mary) <- (~62) [avatar component clause 579]
581. funny(mary) <- (62) [avatar component clause 579]
613. 65 <=> humble(alice) [avatar definition]
614. ~humble(alice) <- (~65) [avatar component clause 613]
615. humble(alice) <- (65) [avatar component clause 613]
617. 66 <=> happy(alice) [avatar definition]
618. ~happy(alice) <- (~66) [avatar component clause 617]
621. 67 <=> generous(alice) [avatar definition]
630. ~funny(alice) | generous(alice) <- (65) [resolution 615,88]
670. 67 | ~6 | ~65 [avatar split clause 630,613,176,621]
671. tall(alice) | strong(alice) <- (6) [resolution 178,136]
675. strong(alice) <- (6, ~33) [subsumption resolution 671,303]
676. $false <- (6, ~32, ~33) [subsumption resolution 675,298]
677. ~6 | 32 | 33 [avatar contradiction clause 676]
728. wise(mary) | patient(mary) <- (2, 5) [resolution 496,100]
731. 72 <=> patient(mary) [avatar definition]
732. ~patient(mary) <- (~72) [avatar component clause 731]
733. patient(mary) <- (72) [avatar component clause 731]
735. 73 <=> wise(mary) [avatar definition]
737. wise(mary) <- (73) [avatar component clause 735]
738. 72 | 73 | ~2 | ~5 [avatar split clause 728,173,158,735,731]
745. 74 <=> patient(lucy) [avatar definition]
747. patient(lucy) <- (74) [avatar component clause 745]
749. 75 <=> wise(lucy) [avatar definition]
750. ~wise(lucy) <- (~75) [avatar component clause 749]
751. wise(lucy) <- (75) [avatar component clause 749]
866. ~tall(alice) | ~generous(alice) <- (32) [resolution 299,138]
868. ~happy(alice) | humble(alice) <- (32) [resolution 299,126]
872. ~generous(alice) <- (32, 33) [subsumption resolution 866,302]
875. ~happy(alice) <- (32, ~65) [subsumption resolution 868,614]
876. ~66 | ~32 | 65 [avatar split clause 875,613,297,617]
883. ~67 | ~32 | ~33 [avatar split clause 872,301,297,621]
884. happy(alice) <- (33) [resolution 302,82]
886. $false <- (33, ~66) [subsumption resolution 884,618]
887. ~33 | 66 [avatar contradiction clause 886]
900. strong(mary) <- (2, 5) [resolution 174,159]
901. strong(lucy) <- (5, 24) [resolution 174,257]
922. ~happy(mary) | humble(mary) <- (2, 5) [resolution 900,126]
924. humble(mary) <- (2, 5) [subsumption resolution 922,159]
928. ~happy(lucy) | humble(lucy) <- (5, 24) [resolution 901,126]
930. humble(lucy) <- (5, 24) [subsumption resolution 928,257]
971. wise(lucy) | patient(lucy) <- (5, 24) [resolution 930,100]
972. ~funny(lucy) | generous(lucy) <- (5, 24) [resolution 930,88]
973. ~funny(lucy) <- (5, ~23, 24) [subsumption resolution 972,252]
982. wise(mary) | funny(mary) <- (72) [resolution 733,105]
984. wise(mary) <- (~62, 72) [subsumption resolution 982,580]
985. 73 | 62 | ~72 [avatar split clause 984,731,579,735]
987. patient(mary) | funny(mary) <- (73) [resolution 737,106]
988. ~patient(mary) | ~humble(mary) <- (73) [resolution 737,102]
993. ~patient(mary) <- (2, 5, 73) [subsumption resolution 988,924]
994. ~72 | ~2 | ~5 | ~73 [avatar split clause 993,735,173,158,731]
1003. funny(mary) <- (~72, 73) [subsumption resolution 987,732]
1004. 62 | 72 | ~73 [avatar split clause 1003,735,731,579]
1016. patient(lucy) | funny(lucy) <- (75) [resolution 751,106]
1017. ~patient(lucy) | ~humble(lucy) <- (75) [resolution 751,102]
1019. patient(lucy) <- (5, ~23, 24, 75) [subsumption resolution 1016,973]
1020. 74 | ~5 | 23 | ~24 | ~75 [avatar split clause 1019,749,255,251,173,745]
1021. ~patient(lucy) <- (5, 24, 75) [subsumption resolution 1017,930]
1022. ~74 | ~5 | ~24 | ~75 [avatar split clause 1021,749,255,173,745]
1023. 74 | 75 | ~5 | ~24 [avatar split clause 971,255,173,749,745]
1024. wise(lucy) | funny(lucy) <- (74) [resolution 747,105]
1026. funny(lucy) <- (74, ~75) [subsumption resolution 1024,750]
1029. generous(lucy) <- (5, 24, 74, ~75) [subsumption resolution 972,1026]
1030. 23 | ~5 | ~24 | ~74 | 75 [avatar split clause 1029,749,745,255,173,251]
1044. $false <- (22, 62) [resolution 249,581]
1045. $false <- (22, 37) [resolution 249,335]
1050. ~22 | ~37 [avatar contradiction clause 1045]
1051. ~22 | ~62 [avatar contradiction clause 1044]
1122. $false <- (4, 5, 24) [resolution 169,930]
1125. ~4 | ~5 | ~24 [avatar contradiction clause 1122]
1126. $false [avatar sat refutation 166,170,179,259,304,305,323,389,411,415,424,670,677,738,876,883,887,985,994,1004,1020,1022,1023,1030,1050,1051,1125]
% SZS output end Proof for 7554217429601066806741841
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5500
% Time elapsed: 0.042 s
% ------------------------------
% ------------------------------
| 0 |
If someone is old then paul is both not calm and quiet and vice versa. Everyone who is not tall or old is quiet. If someone is both not quiet and quiet then someone is strong or not humble and vice versa. If john is either not patient or wise then alice is kind. Everyone who is curious is kind or old. Everyone who is not humble or happy is not patient and vice versa. Everyone who is either curious or not rich is both funny and old and vice versa. Everyone who is quiet or not happy is both strong and not quiet and vice versa. Everyone who is not old is not patient or not funny and vice versa. If fred is humble then someone is either tall or not creative. If paul is either not happy or wise then someone is not rich and vice versa. If someone is either generous or not kind then someone is not patient or not kind and vice versa. Everyone who is either calm or curious is either tall or funny. If paul is either not calm or not wise then someone is not tall or not patient and vice versa. Everyone who is either not curious or not kind is either creative or not quiet. If susan is not curious or not funny then lucy is kind or humble and vice versa. Alice is creative or curious. Someone is either not tall or tall. John is tall or creative. Someone is either not quiet or not calm. John is either happy or not kind. Lucy is wise or not rich. Someone is either calm or not quiet. | Susan is happy. | entailment | ((?[X]:(old(X)))<=>((~calm(paul)&quiet(paul))))&
(![X]:((~tall(X)|old(X))=>quiet(X)))&
((?[X]:((~quiet(X)&quiet(X))))<=>(?[X]:((strong(X)|~humble(X)))))&
(((~patient(john)<~>wise(john)))=>(kind(alice)))&
(![X]:(curious(X)=>(kind(X)|old(X))))&
(![X]:((~humble(X)|happy(X))<=>~patient(X)))&
(![X]:((curious(X)<~>~rich(X))<=>(funny(X)&old(X))))&
(![X]:((quiet(X)|~happy(X))<=>(strong(X)&~quiet(X))))&
(![X]:(~old(X)<=>(~patient(X)|~funny(X))))&
((humble(fred))=>(?[X]:((tall(X)<~>~creative(X)))))&
(((~happy(paul)<~>wise(paul)))<=>(?[X]:(~rich(X))))&
((?[X]:((generous(X)<~>~kind(X))))<=>(?[X]:((~patient(X)|~kind(X)))))&
(![X]:((calm(X)<~>curious(X))=>(tall(X)<~>funny(X))))&
(((~calm(paul)<~>~wise(paul)))<=>(?[X]:((~tall(X)|~patient(X)))))&
(![X]:((~curious(X)<~>~kind(X))=>(creative(X)<~>~quiet(X))))&
(((~curious(susan)|~funny(susan)))<=>((kind(lucy)|humble(lucy))))&
((creative(alice)|curious(alice)))&
(?[X]:((~tall(X)<~>tall(X))))&
((tall(john)|creative(john)))&
(?[X]:((~quiet(X)<~>~calm(X))))&
((happy(john)<~>~kind(john)))&
((wise(lucy)|~rich(lucy)))&
(?[X]:((calm(X)<~>~quiet(X)))) | happy(susan) | [
"p2",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 4571736997069275871264531
% SZS output start Proof for 4571736997069275871264531
3. ? [X0] : (quiet(X0) & ~quiet(X0)) <=> ? [X0] : (~humble(X0) | strong(X0)) [input p2]
8. ! [X0] : ((~happy(X0) | quiet(X0)) <=> (~quiet(X0) & strong(X0))) [input p7]
24. ~happy(susan) [input hypothesis]
25. ? [X0] : (quiet(X0) & ~quiet(X0)) <=> ? [X1] : (~humble(X1) | strong(X1)) [rectify 3]
39. (? [X0] : (quiet(X0) & ~quiet(X0)) | ! [X1] : (humble(X1) & ~strong(X1))) & (? [X1] : (~humble(X1) | strong(X1)) | ! [X0] : (~quiet(X0) | quiet(X0))) [nnf transformation 25]
40. (? [X0] : (quiet(X0) & ~quiet(X0)) | ! [X1] : (humble(X1) & ~strong(X1))) & (? [X2] : (~humble(X2) | strong(X2)) | ! [X3] : (~quiet(X3) | quiet(X3))) [rectify 39]
41. ? [X0] : (quiet(X0) & ~quiet(X0)) => (quiet(sK1) & ~quiet(sK1)) [choice axiom]
42. ? [X2] : (~humble(X2) | strong(X2)) => (~humble(sK2) | strong(sK2)) [choice axiom]
43. ((quiet(sK1) & ~quiet(sK1)) | ! [X1] : (humble(X1) & ~strong(X1))) & ((~humble(sK2) | strong(sK2)) | ! [X3] : (~quiet(X3) | quiet(X3))) [skolemisation 40,42,41]
49. ! [X0] : (((~happy(X0) | quiet(X0)) | (quiet(X0) | ~strong(X0))) & ((~quiet(X0) & strong(X0)) | (happy(X0) & ~quiet(X0)))) [nnf transformation 8]
50. ! [X0] : ((~happy(X0) | quiet(X0) | quiet(X0) | ~strong(X0)) & ((~quiet(X0) & strong(X0)) | (happy(X0) & ~quiet(X0)))) [flattening 49]
89. ~quiet(sK1) | ~strong(X1) [cnf transformation 43]
91. quiet(sK1) | ~strong(X1) [cnf transformation 43]
106. happy(X0) | strong(X0) [cnf transformation 50]
154. ~happy(susan) [cnf transformation 24]
179. 6 <=> quiet(sK1) [avatar definition]
184. 7 <=> ! [X1] : ~strong(X1) [avatar definition]
185. ~strong(X1) <- (7) [avatar component clause 184]
186. 7 | 6 [avatar split clause 91,179,184]
188. 7 | ~6 [avatar split clause 89,179,184]
359. strong(susan) [resolution 106,154]
362. $false <- (7) [subsumption resolution 359,185]
363. ~7 [avatar contradiction clause 362]
367. $false [avatar sat refutation 186,188,363]
% SZS output end Proof for 4571736997069275871264531
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not happy is either not curious or rich and vice versa.
Everyone who is not curious or not kind is either not brave or curious and vice versa.
If someone is either not generous or tall then someone is generous and vice versa.
Everyone who is either calm or old is patient and vice versa.
Everyone who is either not creative or wise is patient or brave.
If fred is brave then someone is either not old or not curious.
If john is either not old or not strong then someone is tall.
If someone is both not patient and tall then paul is not wise or not funny.
If fred is generous then someone is either happy or calm and vice versa.
Everyone who is not funny or strong is either happy or not funny.
If susan is tall then paul is not humble and vice versa.
Everyone who is not patient is either not tall or rich and vice versa.
Everyone who is both not brave and not generous is kind or not rich.
If someone is either calm or humble then paul is either not funny or not generous.
Everyone who is both not generous and funny is both happy and creative.
Everyone who is not patient is either not strong or not brave.
Someone is either rich or brave.
Lucy is not curious or not generous.
Susan is funny.
Paul is not happy or not strong.
Lucy is calm or curious.
Mary is quiet or old. | Fred is tall. | neutral | (![X]:(~happy(X)<=>(~curious(X)<~>rich(X))))&
(![X]:((~curious(X)|~kind(X))<=>(~brave(X)<~>curious(X))))&
((?[X]:((~generous(X)<~>tall(X))))<=>(?[X]:(generous(X))))&
(![X]:((calm(X)<~>old(X))<=>patient(X)))&
(![X]:((~creative(X)<~>wise(X))=>(patient(X)|brave(X))))&
((brave(fred))=>(?[X]:((~old(X)<~>~curious(X)))))&
(((~old(john)<~>~strong(john)))=>(?[X]:(tall(X))))&
((?[X]:((~patient(X)&tall(X))))=>((~wise(paul)|~funny(paul))))&
((generous(fred))<=>(?[X]:((happy(X)<~>calm(X)))))&
(![X]:((~funny(X)|strong(X))=>(happy(X)<~>~funny(X))))&
((tall(susan))<=>(~humble(paul)))&
(![X]:(~patient(X)<=>(~tall(X)<~>rich(X))))&
(![X]:((~brave(X)&~generous(X))=>(kind(X)|~rich(X))))&
((?[X]:((calm(X)<~>humble(X))))=>((~funny(paul)<~>~generous(paul))))&
(![X]:((~generous(X)&funny(X))=>(happy(X)&creative(X))))&
(![X]:(~patient(X)=>(~strong(X)<~>~brave(X))))&
(?[X]:((rich(X)<~>brave(X))))&
((~curious(lucy)|~generous(lucy)))&
(funny(susan))&
((~happy(paul)|~strong(paul)))&
((calm(lucy)|curious(lucy)))&
((quiet(mary)|old(mary))) | tall(fred) | [] | null | 0 |
Everyone who is patient or creative is not patient and vice versa. If someone is generous then someone is brave and vice versa. Everyone who is both old and happy is both not patient and not strong. Everyone who is not patient is both not rich and curious. Everyone who is happy is either not strong or not generous. If john is both brave and not humble then someone is both not rich and not humble and vice versa. If someone is strong or happy then someone is humble and vice versa. Everyone who is either wise or not generous is both not generous and calm. If someone is both not curious and wise then mary is not quiet or generous and vice versa. Everyone who is both not humble and not kind is not curious or generous. If john is happy then alice is not generous. If fred is not strong then lucy is not old or not tall. Everyone who is tall or old is both humble and not old. Everyone who is both wise and brave is either not funny or not calm. Everyone who is wise is not old or brave and vice versa. Everyone who is either not happy or funny is either quiet or not humble. Someone is both funny and creative. Paul is calm. Susan is either old or not tall. Paul is patient or not strong. Lucy is curious or old. | John is not old. | entailment | (![X]:((patient(X)|creative(X))<=>~patient(X)))&
((?[X]:(generous(X)))<=>(?[X]:(brave(X))))&
(![X]:((old(X)&happy(X))=>(~patient(X)&~strong(X))))&
(![X]:(~patient(X)=>(~rich(X)&curious(X))))&
(![X]:(happy(X)=>(~strong(X)<~>~generous(X))))&
(((brave(john)&~humble(john)))<=>(?[X]:((~rich(X)&~humble(X)))))&
((?[X]:((strong(X)|happy(X))))<=>(?[X]:(humble(X))))&
(![X]:((wise(X)<~>~generous(X))=>(~generous(X)&calm(X))))&
((?[X]:((~curious(X)&wise(X))))<=>((~quiet(mary)|generous(mary))))&
(![X]:((~humble(X)&~kind(X))=>(~curious(X)|generous(X))))&
((happy(john))=>(~generous(alice)))&
((~strong(fred))=>((~old(lucy)|~tall(lucy))))&
(![X]:((tall(X)|old(X))=>(humble(X)&~old(X))))&
(![X]:((wise(X)&brave(X))=>(~funny(X)<~>~calm(X))))&
(![X]:(wise(X)<=>(~old(X)|brave(X))))&
(![X]:((~happy(X)<~>funny(X))=>(quiet(X)<~>~humble(X))))&
(?[X]:((funny(X)&creative(X))))&
(calm(paul))&
((old(susan)<~>~tall(susan)))&
((patient(paul)|~strong(paul)))&
((curious(lucy)|old(lucy))) | ~old(john) | [
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 5289160446191122694103034
% SZS output start Proof for 5289160446191122694103034
13. ! [X0] : ((old(X0) | tall(X0)) => (~old(X0) & humble(X0))) [input p12]
22. old(john) [input hypothesis]
34. ! [X0] : ((~old(X0) & humble(X0)) | (~old(X0) & ~tall(X0))) [ennf transformation 13]
101. ~old(X0) | ~old(X0) [cnf transformation 34]
118. old(john) [cnf transformation 22]
119. ~old(X0) [duplicate literal removal 101]
228. $false [subsumption resolution 118,119]
% SZS output end Proof for 5289160446191122694103034
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not calm is not funny or not patient and vice versa.
If john is either not quiet or not patient then lucy is tall or not tall and vice versa.
If someone is not brave then fred is not rich or not wise.
If fred is calm or tall then someone is both wise and calm and vice versa.
If susan is both quiet and not quiet then someone is both not strong and curious.
If someone is generous or funny then someone is not creative and vice versa.
Everyone who is not generous or not strong is patient and vice versa.
If someone is either not happy or kind then john is not funny or strong and vice versa.
Everyone who is both not kind and generous is both not rich and not old and vice versa.
Everyone who is wise is creative.
Everyone who is creative is either not strong or creative and vice versa.
If someone is both patient and not funny then john is either patient or tall and vice versa.
If someone is both not calm and kind then someone is not generous or curious and vice versa.
If john is wise or not strong then someone is either not quiet or humble and vice versa.
If susan is not generous then someone is not funny.
Everyone who is generous or tall is not wise or not old.
Someone is not brave or not calm.
Mary is not curious.
Fred is either curious or funny.
Someone is not calm or tall.
Someone is either not creative or not old.
Someone is not rich or patient.
Mary is either not curious or not funny. | Fred is not kind. | neutral | (![X]:(~calm(X)<=>(~funny(X)|~patient(X))))&
(((~quiet(john)<~>~patient(john)))<=>((tall(lucy)|~tall(lucy))))&
((?[X]:(~brave(X)))=>((~rich(fred)|~wise(fred))))&
(((calm(fred)|tall(fred)))<=>(?[X]:((wise(X)&calm(X)))))&
(((quiet(susan)&~quiet(susan)))=>(?[X]:((~strong(X)&curious(X)))))&
((?[X]:((generous(X)|funny(X))))<=>(?[X]:(~creative(X))))&
(![X]:((~generous(X)|~strong(X))<=>patient(X)))&
((?[X]:((~happy(X)<~>kind(X))))<=>((~funny(john)|strong(john))))&
(![X]:((~kind(X)&generous(X))<=>(~rich(X)&~old(X))))&
(![X]:(wise(X)=>creative(X)))&
(![X]:(creative(X)<=>(~strong(X)<~>creative(X))))&
((?[X]:((patient(X)&~funny(X))))<=>((patient(john)<~>tall(john))))&
((?[X]:((~calm(X)&kind(X))))<=>(?[X]:((~generous(X)|curious(X)))))&
(((wise(john)|~strong(john)))<=>(?[X]:((~quiet(X)<~>humble(X)))))&
((~generous(susan))=>(?[X]:(~funny(X))))&
(![X]:((generous(X)|tall(X))=>(~wise(X)|~old(X))))&
(?[X]:((~brave(X)|~calm(X))))&
(~curious(mary))&
((curious(fred)<~>funny(fred)))&
(?[X]:((~calm(X)|tall(X))))&
(?[X]:((~creative(X)<~>~old(X))))&
(?[X]:((~rich(X)|patient(X))))&
((~curious(mary)<~>~funny(mary))) | ~kind(fred) | [] | null | 0 |
Everyone who is rich is both creative and old and vice versa.
If someone is both happy and not funny then someone is not creative and vice versa.
Everyone who is either not quiet or calm is not creative.
Everyone who is quiet is both curious and not generous.
Everyone who is strong or rich is old or not calm.
Everyone who is rich or tall is generous.
If mary is both not wise and funny then alice is not humble and vice versa.
If susan is either curious or not creative then paul is not humble or brave and vice versa.
If someone is either not patient or patient then john is not curious or brave.
Everyone who is strong or quiet is either not wise or not strong and vice versa.
Everyone who is both not old and not wise is both not strong and not quiet and vice versa.
Everyone who is both happy and brave is both not creative and not wise.
Everyone who is both funny and not quiet is either not quiet or not curious.
If john is both not wise and strong then fred is tall and vice versa.
If paul is not generous or not humble then someone is not patient.
If alice is either funny or not wise then someone is both not strong and humble and vice versa.
Susan is not tall.
Paul is tall or strong.
Paul is kind or not patient.
Someone is either not rich or calm.
Susan is quiet or calm.
Someone is either kind or not strong. | Fred is happy. | neutral | (![X]:(rich(X)<=>(creative(X)&old(X))))&
((?[X]:((happy(X)&~funny(X))))<=>(?[X]:(~creative(X))))&
(![X]:((~quiet(X)<~>calm(X))=>~creative(X)))&
(![X]:(quiet(X)=>(curious(X)&~generous(X))))&
(![X]:((strong(X)|rich(X))=>(old(X)|~calm(X))))&
(![X]:((rich(X)|tall(X))=>generous(X)))&
(((~wise(mary)&funny(mary)))<=>(~humble(alice)))&
(((curious(susan)<~>~creative(susan)))<=>((~humble(paul)|brave(paul))))&
((?[X]:((~patient(X)<~>patient(X))))=>((~curious(john)|brave(john))))&
(![X]:((strong(X)|quiet(X))<=>(~wise(X)<~>~strong(X))))&
(![X]:((~old(X)&~wise(X))<=>(~strong(X)&~quiet(X))))&
(![X]:((happy(X)&brave(X))=>(~creative(X)&~wise(X))))&
(![X]:((funny(X)&~quiet(X))=>(~quiet(X)<~>~curious(X))))&
(((~wise(john)&strong(john)))<=>(tall(fred)))&
(((~generous(paul)|~humble(paul)))=>(?[X]:(~patient(X))))&
(((funny(alice)<~>~wise(alice)))<=>(?[X]:((~strong(X)&humble(X)))))&
(~tall(susan))&
((tall(paul)|strong(paul)))&
((kind(paul)|~patient(paul)))&
(?[X]:((~rich(X)<~>calm(X))))&
((quiet(susan)|calm(susan)))&
(?[X]:((kind(X)<~>~strong(X)))) | happy(fred) | [] | null | 0 |
Everyone who is quiet or not quiet is both not generous and humble and vice versa. If mary is rich then lucy is not old. Everyone who is not happy or creative is either calm or old. Everyone who is creative or not creative is both not brave and not calm. If someone is either not quiet or tall then someone is either humble or not kind and vice versa. If someone is brave or funny then fred is either brave or not funny. If someone is happy or humble then paul is tall and vice versa. Everyone who is calm or not generous is creative and vice versa. If someone is either not patient or funny then someone is kind. If susan is not old or strong then lucy is not curious or rich and vice versa. If someone is either wise or not humble then someone is not funny or not patient. If someone is both brave and not creative then fred is wise and vice versa. Everyone who is not funny or not quiet is either funny or not generous. Everyone who is both not happy and funny is quiet or rich and vice versa. If alice is generous then someone is either quiet or not happy. Someone is both not patient and wise. Alice is creative. Susan is funny or curious. Someone is both not patient and not rich. Lucy is not happy. Alice is either not wise or wise. | Fred is generous. | contradiction | (![X]:((quiet(X)|~quiet(X))<=>(~generous(X)&humble(X))))&
((rich(mary))=>(~old(lucy)))&
(![X]:((~happy(X)|creative(X))=>(calm(X)<~>old(X))))&
(![X]:((creative(X)|~creative(X))=>(~brave(X)&~calm(X))))&
((?[X]:((~quiet(X)<~>tall(X))))<=>(?[X]:((humble(X)<~>~kind(X)))))&
((?[X]:((brave(X)|funny(X))))=>((brave(fred)<~>~funny(fred))))&
((?[X]:((happy(X)|humble(X))))<=>(tall(paul)))&
(![X]:((calm(X)|~generous(X))<=>creative(X)))&
((?[X]:((~patient(X)<~>funny(X))))=>(?[X]:(kind(X))))&
(((~old(susan)|strong(susan)))<=>((~curious(lucy)|rich(lucy))))&
((?[X]:((wise(X)<~>~humble(X))))=>(?[X]:((~funny(X)|~patient(X)))))&
((?[X]:((brave(X)&~creative(X))))<=>(wise(fred)))&
(![X]:((~funny(X)|~quiet(X))=>(funny(X)<~>~generous(X))))&
(![X]:((~happy(X)&funny(X))<=>(quiet(X)|rich(X))))&
((generous(alice))=>(?[X]:((quiet(X)<~>~happy(X)))))&
(?[X]:((~patient(X)&wise(X))))&
(creative(alice))&
((funny(susan)|curious(susan)))&
(?[X]:((~patient(X)&~rich(X))))&
(~happy(lucy))&
((~wise(alice)<~>wise(alice))) | generous(fred) | [
"p0",
"hypothesis"
] | % SZS status Unsatisfiable for 2165953084487930496269851
% SZS output start Proof for 2165953084487930496269851
1. ! [X0] : ((~quiet(X0) | quiet(X0)) <=> (humble(X0) & ~generous(X0))) [input p0]
22. generous(fred) [input hypothesis]
34. ! [X0] : (((~quiet(X0) | quiet(X0)) | (~humble(X0) | generous(X0))) & ((humble(X0) & ~generous(X0)) | (quiet(X0) & ~quiet(X0)))) [nnf transformation 1]
35. ! [X0] : ((~quiet(X0) | quiet(X0) | ~humble(X0) | generous(X0)) & ((humble(X0) & ~generous(X0)) | (quiet(X0) & ~quiet(X0)))) [flattening 34]
74. ~generous(X0) | ~quiet(X0) [cnf transformation 35]
75. ~generous(X0) | quiet(X0) [cnf transformation 35]
137. generous(fred) [cnf transformation 22]
140. ~generous(X0) [subsumption resolution 74,75]
248. $false [subsumption resolution 137,140]
% SZS output end Proof for 2165953084487930496269851
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not wise then fred is not kind or strong and vice versa.
If lucy is either not wise or patient then mary is not generous.
Everyone who is not calm is both not brave and kind and vice versa.
If someone is either funny or creative then alice is either not curious or wise and vice versa.
If someone is not kind then john is both humble and not humble.
Everyone who is either not funny or quiet is not wise.
If someone is not creative or kind then fred is either not rich or strong and vice versa.
If alice is old or not old then paul is kind or not brave and vice versa.
Everyone who is either rich or not happy is not generous and vice versa.
Everyone who is both not humble and not kind is either wise or quiet and vice versa.
If someone is both not quiet and not strong then someone is not strong or humble.
If someone is both not humble and not quiet then john is not old or not happy and vice versa.
If alice is either not generous or not humble then someone is either not rich or brave and vice versa.
Everyone who is quiet or calm is either not calm or not quiet and vice versa.
If someone is either creative or not creative then lucy is rich or wise.
Everyone who is not wise is old or curious and vice versa.
Someone is either not calm or not old.
Someone is both brave and not patient.
Paul is either not calm or not strong.
Someone is not generous or not tall.
Lucy is both tall and not brave.
Alice is either generous or patient.
Someone is not patient or not funny. | Paul is not humble. | neutral | ((?[X]:(~wise(X)))<=>((~kind(fred)|strong(fred))))&
(((~wise(lucy)<~>patient(lucy)))=>(~generous(mary)))&
(![X]:(~calm(X)<=>(~brave(X)&kind(X))))&
((?[X]:((funny(X)<~>creative(X))))<=>((~curious(alice)<~>wise(alice))))&
((?[X]:(~kind(X)))=>((humble(john)&~humble(john))))&
(![X]:((~funny(X)<~>quiet(X))=>~wise(X)))&
((?[X]:((~creative(X)|kind(X))))<=>((~rich(fred)<~>strong(fred))))&
(((old(alice)|~old(alice)))<=>((kind(paul)|~brave(paul))))&
(![X]:((rich(X)<~>~happy(X))<=>~generous(X)))&
(![X]:((~humble(X)&~kind(X))<=>(wise(X)<~>quiet(X))))&
((?[X]:((~quiet(X)&~strong(X))))=>(?[X]:((~strong(X)|humble(X)))))&
((?[X]:((~humble(X)&~quiet(X))))<=>((~old(john)|~happy(john))))&
(((~generous(alice)<~>~humble(alice)))<=>(?[X]:((~rich(X)<~>brave(X)))))&
(![X]:((quiet(X)|calm(X))<=>(~calm(X)<~>~quiet(X))))&
((?[X]:((creative(X)<~>~creative(X))))=>((rich(lucy)|wise(lucy))))&
(![X]:(~wise(X)<=>(old(X)|curious(X))))&
(?[X]:((~calm(X)<~>~old(X))))&
(?[X]:((brave(X)&~patient(X))))&
((~calm(paul)<~>~strong(paul)))&
(?[X]:((~generous(X)|~tall(X))))&
((tall(lucy)&~brave(lucy)))&
((generous(alice)<~>patient(alice)))&
(?[X]:((~patient(X)|~funny(X)))) | ~humble(paul) | [] | null | 0 |
If someone is not funny then alice is not generous or not brave and vice versa.
If someone is not brave then someone is either happy or quiet and vice versa.
If john is both not old and not happy then mary is not quiet or creative.
If fred is tall or not tall then someone is not humble and vice versa.
If someone is either not old or not curious then someone is not wise.
If someone is happy or curious then paul is either not wise or calm.
If someone is both not patient and creative then someone is either not brave or not patient.
If someone is either not curious or not quiet then someone is not tall or calm and vice versa.
Everyone who is curious is rich or creative and vice versa.
If someone is tall or brave then someone is not generous.
If paul is not curious or rich then someone is not creative or generous and vice versa.
Everyone who is either not strong or humble is not patient or funny and vice versa.
Everyone who is either not rich or patient is either strong or not kind and vice versa.
Everyone who is both patient and brave is humble or not happy and vice versa.
Everyone who is tall or kind is strong or not tall and vice versa.
Everyone who is either strong or happy is either not curious or old.
Someone is calm.
Fred is either not generous or curious.
Lucy is either not kind or not old.
Susan is not rich.
Paul is both tall and strong.
Susan is either not rich or not quiet.
Mary is funny or strong.
Paul is both not happy and not quiet. | Lucy is patient. | entailment | ((?[X]:(~funny(X)))<=>((~generous(alice)|~brave(alice))))&
((?[X]:(~brave(X)))<=>(?[X]:((happy(X)<~>quiet(X)))))&
(((~old(john)&~happy(john)))=>((~quiet(mary)|creative(mary))))&
(((tall(fred)|~tall(fred)))<=>(?[X]:(~humble(X))))&
((?[X]:((~old(X)<~>~curious(X))))=>(?[X]:(~wise(X))))&
((?[X]:((happy(X)|curious(X))))=>((~wise(paul)<~>calm(paul))))&
((?[X]:((~patient(X)&creative(X))))=>(?[X]:((~brave(X)<~>~patient(X)))))&
((?[X]:((~curious(X)<~>~quiet(X))))<=>(?[X]:((~tall(X)|calm(X)))))&
(![X]:(curious(X)<=>(rich(X)|creative(X))))&
((?[X]:((tall(X)|brave(X))))=>(?[X]:(~generous(X))))&
(((~curious(paul)|rich(paul)))<=>(?[X]:((~creative(X)|generous(X)))))&
(![X]:((~strong(X)<~>humble(X))<=>(~patient(X)|funny(X))))&
(![X]:((~rich(X)<~>patient(X))<=>(strong(X)<~>~kind(X))))&
(![X]:((patient(X)&brave(X))<=>(humble(X)|~happy(X))))&
(![X]:((tall(X)|kind(X))<=>(strong(X)|~tall(X))))&
(![X]:((strong(X)<~>happy(X))=>(~curious(X)<~>old(X))))&
(?[X]:(calm(X)))&
((~generous(fred)<~>curious(fred)))&
((~kind(lucy)<~>~old(lucy)))&
(~rich(susan))&
((tall(paul)&strong(paul)))&
((~rich(susan)<~>~quiet(susan)))&
((funny(mary)|strong(mary)))&
((~happy(paul)&~quiet(paul))) | patient(lucy) | [
"p8",
"p11",
"p12",
"p13",
"p14",
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 8881140399980732581158461
% SZS output start Proof for 8881140399980732581158461
9. ! [X0] : (curious(X0) <=> (creative(X0) | rich(X0))) [input p8]
12. ! [X0] : ((~strong(X0) <~> humble(X0)) <=> (funny(X0) | ~patient(X0))) [input p11]
13. ! [X0] : ((~rich(X0) <~> patient(X0)) <=> (strong(X0) <~> ~kind(X0))) [input p12]
14. ! [X0] : ((brave(X0) & patient(X0)) <=> (~happy(X0) | humble(X0))) [input p13]
15. ! [X0] : ((kind(X0) | tall(X0)) <=> (~tall(X0) | strong(X0))) [input p14]
16. ! [X0] : ((strong(X0) <~> happy(X0)) => (~curious(X0) <~> old(X0))) [input p15]
19. ~kind(lucy) <~> ~old(lucy) [input p18]
25. ~patient(lucy) [input hypothesis]
37. ! [X0] : ((~curious(X0) <~> old(X0)) | (strong(X0) <=> happy(X0))) [ennf transformation 16]
67. ! [X0] : ((curious(X0) | (~creative(X0) & ~rich(X0))) & ((creative(X0) | rich(X0)) | ~curious(X0))) [nnf transformation 9]
68. ! [X0] : ((curious(X0) | (~creative(X0) & ~rich(X0))) & (creative(X0) | rich(X0) | ~curious(X0))) [flattening 67]
77. ! [X0] : ((((~humble(X0) | strong(X0)) & (humble(X0) | ~strong(X0))) | (~funny(X0) & patient(X0))) & ((funny(X0) | ~patient(X0)) | ((~strong(X0) | ~humble(X0)) & (humble(X0) | strong(X0))))) [nnf transformation 12]
78. ! [X0] : ((((~humble(X0) | strong(X0)) & (humble(X0) | ~strong(X0))) | (~funny(X0) & patient(X0))) & (funny(X0) | ~patient(X0) | ((~strong(X0) | ~humble(X0)) & (humble(X0) | strong(X0))))) [flattening 77]
79. ! [X0] : ((((~patient(X0) | rich(X0)) & (patient(X0) | ~rich(X0))) | ((strong(X0) | kind(X0)) & (~kind(X0) | ~strong(X0)))) & (((kind(X0) | ~strong(X0)) & (~kind(X0) | strong(X0))) | ((~rich(X0) | ~patient(X0)) & (patient(X0) | rich(X0))))) [nnf transformation 13]
80. ! [X0] : (((brave(X0) & patient(X0)) | (happy(X0) & ~humble(X0))) & ((~happy(X0) | humble(X0)) | (~brave(X0) | ~patient(X0)))) [nnf transformation 14]
81. ! [X0] : (((brave(X0) & patient(X0)) | (happy(X0) & ~humble(X0))) & (~happy(X0) | humble(X0) | ~brave(X0) | ~patient(X0))) [flattening 80]
82. ! [X0] : (((kind(X0) | tall(X0)) | (tall(X0) & ~strong(X0))) & ((~tall(X0) | strong(X0)) | (~kind(X0) & ~tall(X0)))) [nnf transformation 15]
83. ! [X0] : ((kind(X0) | tall(X0) | (tall(X0) & ~strong(X0))) & (~tall(X0) | strong(X0) | (~kind(X0) & ~tall(X0)))) [flattening 82]
84. ! [X0] : (((~old(X0) | curious(X0)) & (old(X0) | ~curious(X0))) | ((strong(X0) | ~happy(X0)) & (happy(X0) | ~strong(X0)))) [nnf transformation 37]
88. (old(lucy) | kind(lucy)) & (~old(lucy) | ~kind(lucy)) [nnf transformation 19]
116. ~rich(X0) | curious(X0) [cnf transformation 68]
126. ~strong(X0) | humble(X0) | patient(X0) [cnf transformation 78]
130. ~kind(X0) | strong(X0) | patient(X0) | rich(X0) [cnf transformation 79]
139. ~humble(X0) | patient(X0) [cnf transformation 81]
140. patient(X0) | happy(X0) [cnf transformation 81]
143. ~tall(X0) | strong(X0) | ~tall(X0) [cnf transformation 83]
146. kind(X0) | tall(X0) | tall(X0) [cnf transformation 83]
148. ~curious(X0) | old(X0) | strong(X0) | ~happy(X0) [cnf transformation 84]
154. ~old(lucy) | ~kind(lucy) [cnf transformation 88]
164. ~patient(lucy) [cnf transformation 25]
165. ~tall(X0) | strong(X0) [duplicate literal removal 143]
166. kind(X0) | tall(X0) [duplicate literal removal 146]
363. 46 <=> kind(lucy) [avatar definition]
364. ~kind(lucy) <- (~46) [avatar component clause 363]
367. 47 <=> old(lucy) [avatar definition]
368. ~old(lucy) <- (~47) [avatar component clause 367]
371. ~46 | ~47 [avatar split clause 154,367,363]
386. happy(lucy) [resolution 140,164]
420. strong(X0) | patient(X0) | rich(X0) | tall(X0) [resolution 130,166]
423. 54 <=> rich(lucy) [avatar definition]
424. ~rich(lucy) <- (~54) [avatar component clause 423]
425. rich(lucy) <- (54) [avatar component clause 423]
427. 55 <=> strong(lucy) [avatar definition]
428. ~strong(lucy) <- (~55) [avatar component clause 427]
429. strong(lucy) <- (55) [avatar component clause 427]
431. strong(X0) | patient(X0) | rich(X0) [subsumption resolution 420,165]
432. tall(lucy) <- (~46) [resolution 364,166]
433. strong(lucy) <- (~46) [resolution 432,165]
434. 55 | 46 [avatar split clause 433,363,427]
440. curious(lucy) <- (54) [resolution 425,116]
460. patient(X4) | rich(X4) | humble(X4) | patient(X4) [resolution 431,126]
462. patient(X4) | rich(X4) | humble(X4) [duplicate literal removal 460]
465. rich(X4) | patient(X4) [subsumption resolution 462,139]
530. old(lucy) | strong(lucy) | ~happy(lucy) <- (54) [resolution 148,440]
531. strong(lucy) | ~happy(lucy) <- (~47, 54) [subsumption resolution 530,368]
532. ~happy(lucy) <- (~47, 54, ~55) [subsumption resolution 531,428]
533. $false <- (~47, 54, ~55) [subsumption resolution 532,386]
534. 47 | ~54 | 55 [avatar contradiction clause 533]
537. patient(lucy) <- (~54) [resolution 424,465]
538. $false <- (~54) [subsumption resolution 537,164]
539. 54 [avatar contradiction clause 538]
553. humble(lucy) | patient(lucy) <- (55) [resolution 429,126]
559. humble(lucy) <- (55) [subsumption resolution 553,164]
574. patient(lucy) <- (55) [resolution 559,139]
575. $false <- (55) [subsumption resolution 574,164]
576. ~55 [avatar contradiction clause 575]
577. $false [avatar sat refutation 371,434,534,539,576]
% SZS output end Proof for 8881140399980732581158461
% ------------------------------
% 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 both not funny and not rich then susan is either quiet or strong and vice versa.
If someone is either not brave or humble then susan is both not kind and not old and vice versa.
Everyone who is quiet or not quiet is both generous and old.
If someone is both not generous and not tall then someone is either not happy or not curious.
If fred is both not funny and humble then someone is either not patient or not funny and vice versa.
Everyone who is both wise and funny is both humble and not old.
Everyone who is brave or wise is humble or old and vice versa.
Everyone who is either happy or not humble is funny.
If lucy is not funny or humble then lucy is either not rich or not tall.
If someone is not curious then someone is both not rich and brave and vice versa.
If john is both rich and funny then someone is curious and vice versa.
If someone is rich or not rich then mary is both kind and not humble and vice versa.
If someone is either not brave or not patient then john is not humble or brave.
Everyone who is both not funny and patient is not humble or not generous and vice versa.
If someone is not quiet or not brave then paul is either not old or not rich and vice versa.
If someone is humble or creative then someone is not strong.
Susan is not rich.
Someone is patient or not generous.
Mary is generous.
Mary is both old and strong.
Alice is both creative and kind.
Someone is either not generous or patient.
Someone is not humble. | John is not curious. | entailment | ((?[X]:((~funny(X)&~rich(X))))<=>((quiet(susan)<~>strong(susan))))&
((?[X]:((~brave(X)<~>humble(X))))<=>((~kind(susan)&~old(susan))))&
(![X]:((quiet(X)|~quiet(X))=>(generous(X)&old(X))))&
((?[X]:((~generous(X)&~tall(X))))=>(?[X]:((~happy(X)<~>~curious(X)))))&
(((~funny(fred)&humble(fred)))<=>(?[X]:((~patient(X)<~>~funny(X)))))&
(![X]:((wise(X)&funny(X))=>(humble(X)&~old(X))))&
(![X]:((brave(X)|wise(X))<=>(humble(X)|old(X))))&
(![X]:((happy(X)<~>~humble(X))=>funny(X)))&
(((~funny(lucy)|humble(lucy)))=>((~rich(lucy)<~>~tall(lucy))))&
((?[X]:(~curious(X)))<=>(?[X]:((~rich(X)&brave(X)))))&
(((rich(john)&funny(john)))<=>(?[X]:(curious(X))))&
((?[X]:((rich(X)|~rich(X))))<=>((kind(mary)&~humble(mary))))&
((?[X]:((~brave(X)<~>~patient(X))))=>((~humble(john)|brave(john))))&
(![X]:((~funny(X)&patient(X))<=>(~humble(X)|~generous(X))))&
((?[X]:((~quiet(X)|~brave(X))))<=>((~old(paul)<~>~rich(paul))))&
((?[X]:((humble(X)|creative(X))))=>(?[X]:(~strong(X))))&
(~rich(susan))&
(?[X]:((patient(X)|~generous(X))))&
(generous(mary))&
((old(mary)&strong(mary)))&
((creative(alice)&kind(alice)))&
(?[X]:((~generous(X)<~>patient(X))))&
(?[X]:(~humble(X))) | ~curious(john) | [
"p1",
"p2",
"p5",
"p6",
"p10",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 6125028640219219231521231
% SZS output start Proof for 6125028640219219231521231
2. ? [X0] : (~brave(X0) <~> humble(X0)) <=> (~old(susan) & ~kind(susan)) [input p1]
3. ! [X0] : ((~quiet(X0) | quiet(X0)) => (old(X0) & generous(X0))) [input p2]
6. ! [X0] : ((funny(X0) & wise(X0)) => (~old(X0) & humble(X0))) [input p5]
7. ! [X0] : ((wise(X0) | brave(X0)) <=> (old(X0) | humble(X0))) [input p6]
11. (funny(john) & rich(john)) <=> ? [X0] : curious(X0) [input p10]
14. ! [X0] : ((patient(X0) & ~funny(X0)) <=> (~generous(X0) | ~humble(X0))) [input p13]
24. curious(john) [input hypothesis]
28. ! [X0] : ((old(X0) & generous(X0)) | (quiet(X0) & ~quiet(X0))) [ennf transformation 3]
30. ! [X0] : ((~old(X0) & humble(X0)) | (~funny(X0) | ~wise(X0))) [ennf transformation 6]
31. ! [X0] : ((~old(X0) & humble(X0)) | ~funny(X0) | ~wise(X0)) [flattening 30]
41. (? [X0] : ((~humble(X0) | brave(X0)) & (humble(X0) | ~brave(X0))) | (old(susan) | kind(susan))) & ((~old(susan) & ~kind(susan)) | ! [X0] : ((~brave(X0) | ~humble(X0)) & (humble(X0) | brave(X0)))) [nnf transformation 2]
42. (? [X0] : ((~humble(X0) | brave(X0)) & (humble(X0) | ~brave(X0))) | old(susan) | kind(susan)) & ((~old(susan) & ~kind(susan)) | ! [X0] : ((~brave(X0) | ~humble(X0)) & (humble(X0) | brave(X0)))) [flattening 41]
43. (? [X0] : ((~humble(X0) | brave(X0)) & (humble(X0) | ~brave(X0))) | old(susan) | kind(susan)) & ((~old(susan) & ~kind(susan)) | ! [X1] : ((~brave(X1) | ~humble(X1)) & (humble(X1) | brave(X1)))) [rectify 42]
44. ? [X0] : ((~humble(X0) | brave(X0)) & (humble(X0) | ~brave(X0))) => ((~humble(sK1) | brave(sK1)) & (humble(sK1) | ~brave(sK1))) [choice axiom]
45. (((~humble(sK1) | brave(sK1)) & (humble(sK1) | ~brave(sK1))) | old(susan) | kind(susan)) & ((~old(susan) & ~kind(susan)) | ! [X1] : ((~brave(X1) | ~humble(X1)) & (humble(X1) | brave(X1)))) [skolemisation 43,44]
55. ! [X0] : (((wise(X0) | brave(X0)) | (~old(X0) & ~humble(X0))) & ((old(X0) | humble(X0)) | (~wise(X0) & ~brave(X0)))) [nnf transformation 7]
56. ! [X0] : ((wise(X0) | brave(X0) | (~old(X0) & ~humble(X0))) & (old(X0) | humble(X0) | (~wise(X0) & ~brave(X0)))) [flattening 55]
64. ((funny(john) & rich(john)) | ! [X0] : ~curious(X0)) & (? [X0] : curious(X0) | (~funny(john) | ~rich(john))) [nnf transformation 11]
65. ((funny(john) & rich(john)) | ! [X0] : ~curious(X0)) & (? [X0] : curious(X0) | ~funny(john) | ~rich(john)) [flattening 64]
66. ((funny(john) & rich(john)) | ! [X0] : ~curious(X0)) & (? [X1] : curious(X1) | ~funny(john) | ~rich(john)) [rectify 65]
67. ? [X1] : curious(X1) => curious(sK6) [choice axiom]
68. ((funny(john) & rich(john)) | ! [X0] : ~curious(X0)) & (curious(sK6) | ~funny(john) | ~rich(john)) [skolemisation 66,67]
75. ! [X0] : (((patient(X0) & ~funny(X0)) | (generous(X0) & humble(X0))) & ((~generous(X0) | ~humble(X0)) | (~patient(X0) | funny(X0)))) [nnf transformation 14]
76. ! [X0] : (((patient(X0) & ~funny(X0)) | (generous(X0) & humble(X0))) & (~generous(X0) | ~humble(X0) | ~patient(X0) | funny(X0))) [flattening 75]
100. ~old(susan) | ~brave(X1) | ~humble(X1) [cnf transformation 45]
105. old(X0) | ~quiet(X0) [cnf transformation 28]
106. old(X0) | quiet(X0) [cnf transformation 28]
116. ~old(X0) | ~funny(X0) | ~wise(X0) [cnf transformation 31]
120. wise(X0) | brave(X0) | ~old(X0) [cnf transformation 56]
132. funny(john) | ~curious(X0) [cnf transformation 68]
141. ~funny(X0) | humble(X0) [cnf transformation 76]
163. curious(john) [cnf transformation 24]
194. 7 <=> old(susan) [avatar definition]
195. ~old(susan) <- (~7) [avatar component clause 194]
208. 10 <=> ! [X1] : (~brave(X1) | ~humble(X1)) [avatar definition]
209. ~humble(X1) | ~brave(X1) <- (10) [avatar component clause 208]
210. 10 | ~7 [avatar split clause 100,194,208]
217. old(X0) [subsumption resolution 105,106]
247. ~wise(X0) | ~funny(X0) [subsumption resolution 116,217]
248. wise(X0) | brave(X0) [subsumption resolution 120,217]
291. 27 <=> ! [X0] : ~curious(X0) [avatar definition]
292. ~curious(X0) <- (27) [avatar component clause 291]
294. 28 <=> funny(john) [avatar definition]
296. funny(john) <- (28) [avatar component clause 294]
297. 27 | 28 [avatar split clause 132,294,291]
330. 36 <=> humble(john) [avatar definition]
331. humble(john) <- (36) [avatar component clause 330]
334. 37 <=> brave(john) [avatar definition]
335. ~brave(john) <- (~37) [avatar component clause 334]
387. $false <- (~7) [subsumption resolution 195,217]
388. 7 [avatar contradiction clause 387]
389. $false <- (27) [resolution 292,163]
390. ~27 [avatar contradiction clause 389]
393. humble(john) <- (28) [resolution 141,296]
396. 36 | ~28 [avatar split clause 393,294,330]
397. ~brave(john) <- (10, 36) [resolution 209,331]
400. ~37 | ~10 | ~36 [avatar split clause 397,330,208,334]
414. ~funny(X0) | brave(X0) [resolution 248,247]
485. brave(john) <- (28) [resolution 414,296]
487. $false <- (28, ~37) [subsumption resolution 485,335]
488. ~28 | 37 [avatar contradiction clause 487]
491. $false [avatar sat refutation 210,297,388,390,396,400,488]
% SZS output end Proof for 6125028640219219231521231
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not brave and not humble is quiet or not tall and vice versa. Everyone who is either not brave or patient is both old and kind and vice versa. Everyone who is not curious is not quiet. Everyone who is not brave or not humble is either patient or not humble and vice versa. Everyone who is happy or not calm is either not wise or not old and vice versa. Everyone who is not wise or humble is happy. Everyone who is strong or not generous is calm. Everyone who is both not funny and not tall is not brave or not rich. If someone is not creative or not curious then someone is both not calm and kind and vice versa. Everyone who is patient or not kind is funny or not calm. Everyone who is wise is funny or rich and vice versa. If susan is both kind and rich then paul is both not patient and not quiet. Everyone who is old or strong is tall and vice versa. If someone is not wise or not strong then someone is either not old or happy and vice versa. Everyone who is not funny or not quiet is both not old and not brave and vice versa. If mary is either not patient or curious then john is either old or not kind. Alice is either old or rich. Someone is not old or not curious. John is not rich or curious. | Alice is not creative. | contradiction | (![X]:((~brave(X)&~humble(X))<=>(quiet(X)|~tall(X))))&
(![X]:((~brave(X)<~>patient(X))<=>(old(X)&kind(X))))&
(![X]:(~curious(X)=>~quiet(X)))&
(![X]:((~brave(X)|~humble(X))<=>(patient(X)<~>~humble(X))))&
(![X]:((happy(X)|~calm(X))<=>(~wise(X)<~>~old(X))))&
(![X]:((~wise(X)|humble(X))=>happy(X)))&
(![X]:((strong(X)|~generous(X))=>calm(X)))&
(![X]:((~funny(X)&~tall(X))=>(~brave(X)|~rich(X))))&
((?[X]:((~creative(X)|~curious(X))))<=>(?[X]:((~calm(X)&kind(X)))))&
(![X]:((patient(X)|~kind(X))=>(funny(X)|~calm(X))))&
(![X]:(wise(X)<=>(funny(X)|rich(X))))&
(((kind(susan)&rich(susan)))=>((~patient(paul)&~quiet(paul))))&
(![X]:((old(X)|strong(X))<=>tall(X)))&
((?[X]:((~wise(X)|~strong(X))))<=>(?[X]:((~old(X)<~>happy(X)))))&
(![X]:((~funny(X)|~quiet(X))<=>(~old(X)&~brave(X))))&
(((~patient(mary)<~>curious(mary)))=>((old(john)<~>~kind(john))))&
((old(alice)<~>rich(alice)))&
(?[X]:((~old(X)|~curious(X))))&
((~rich(john)|curious(john))) | ~creative(alice) | [
"p0",
"p1",
"p3",
"p4",
"p5",
"p6",
"p8",
"p10",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5815079463962235717786634
% SZS output start Proof for 5815079463962235717786634
1. ! [X0] : ((~humble(X0) & ~brave(X0)) <=> (~tall(X0) | quiet(X0))) [input p0]
2. ! [X0] : ((~brave(X0) <~> patient(X0)) <=> (kind(X0) & old(X0))) [input p1]
4. ! [X0] : ((~humble(X0) | ~brave(X0)) <=> (patient(X0) <~> ~humble(X0))) [input p3]
5. ! [X0] : ((~calm(X0) | happy(X0)) <=> (~wise(X0) <~> ~old(X0))) [input p4]
6. ! [X0] : ((humble(X0) | ~wise(X0)) => happy(X0)) [input p5]
7. ! [X0] : ((~generous(X0) | strong(X0)) => calm(X0)) [input p6]
9. ? [X0] : (~curious(X0) | ~creative(X0)) <=> ? [X0] : (kind(X0) & ~calm(X0)) [input p8]
11. ! [X0] : (wise(X0) <=> (rich(X0) | funny(X0))) [input p10]
14. ? [X0] : (~strong(X0) | ~wise(X0)) <=> ? [X0] : (~old(X0) <~> happy(X0)) [input p13]
15. ! [X0] : ((~quiet(X0) | ~funny(X0)) <=> (~brave(X0) & ~old(X0))) [input p14]
20. ~creative(alice) [input hypothesis]
21. ? [X0] : (~curious(X0) | ~creative(X0)) <=> ? [X1] : (kind(X1) & ~calm(X1)) [rectify 9]
22. ? [X0] : (~strong(X0) | ~wise(X0)) <=> ? [X1] : (~old(X1) <~> happy(X1)) [rectify 14]
23. ! [X0] : (strong(X0) => calm(X0)) [pure predicate removal 7]
25. ! [X0] : (happy(X0) | (~humble(X0) & wise(X0))) [ennf transformation 6]
26. ! [X0] : (calm(X0) | ~strong(X0)) [ennf transformation 23]
34. ! [X0] : (((~humble(X0) & ~brave(X0)) | (tall(X0) & ~quiet(X0))) & ((~tall(X0) | quiet(X0)) | (humble(X0) | brave(X0)))) [nnf transformation 1]
35. ! [X0] : (((~humble(X0) & ~brave(X0)) | (tall(X0) & ~quiet(X0))) & (~tall(X0) | quiet(X0) | humble(X0) | brave(X0))) [flattening 34]
36. ! [X0] : ((((~patient(X0) | brave(X0)) & (patient(X0) | ~brave(X0))) | (~kind(X0) | ~old(X0))) & ((kind(X0) & old(X0)) | ((~brave(X0) | ~patient(X0)) & (patient(X0) | brave(X0))))) [nnf transformation 2]
37. ! [X0] : ((((~patient(X0) | brave(X0)) & (patient(X0) | ~brave(X0))) | ~kind(X0) | ~old(X0)) & ((kind(X0) & old(X0)) | ((~brave(X0) | ~patient(X0)) & (patient(X0) | brave(X0))))) [flattening 36]
38. ! [X0] : (((~humble(X0) | ~brave(X0)) | ((patient(X0) | humble(X0)) & (~humble(X0) | ~patient(X0)))) & (((humble(X0) | ~patient(X0)) & (~humble(X0) | patient(X0))) | (humble(X0) & brave(X0)))) [nnf transformation 4]
39. ! [X0] : ((~humble(X0) | ~brave(X0) | ((patient(X0) | humble(X0)) & (~humble(X0) | ~patient(X0)))) & (((humble(X0) | ~patient(X0)) & (~humble(X0) | patient(X0))) | (humble(X0) & brave(X0)))) [flattening 38]
40. ! [X0] : (((~calm(X0) | happy(X0)) | ((~wise(X0) | old(X0)) & (~old(X0) | wise(X0)))) & (((old(X0) | wise(X0)) & (~old(X0) | ~wise(X0))) | (calm(X0) & ~happy(X0)))) [nnf transformation 5]
41. ! [X0] : ((~calm(X0) | happy(X0) | ((~wise(X0) | old(X0)) & (~old(X0) | wise(X0)))) & (((old(X0) | wise(X0)) & (~old(X0) | ~wise(X0))) | (calm(X0) & ~happy(X0)))) [flattening 40]
42. (? [X0] : (~curious(X0) | ~creative(X0)) | ! [X1] : (~kind(X1) | calm(X1))) & (? [X1] : (kind(X1) & ~calm(X1)) | ! [X0] : (curious(X0) & creative(X0))) [nnf transformation 21]
43. (? [X0] : (~curious(X0) | ~creative(X0)) | ! [X1] : (~kind(X1) | calm(X1))) & (? [X2] : (kind(X2) & ~calm(X2)) | ! [X3] : (curious(X3) & creative(X3))) [rectify 42]
44. ? [X0] : (~curious(X0) | ~creative(X0)) => (~curious(sK0) | ~creative(sK0)) [choice axiom]
45. ? [X2] : (kind(X2) & ~calm(X2)) => (kind(sK1) & ~calm(sK1)) [choice axiom]
46. ((~curious(sK0) | ~creative(sK0)) | ! [X1] : (~kind(X1) | calm(X1))) & ((kind(sK1) & ~calm(sK1)) | ! [X3] : (curious(X3) & creative(X3))) [skolemisation 43,45,44]
47. ! [X0] : ((wise(X0) | (~rich(X0) & ~funny(X0))) & ((rich(X0) | funny(X0)) | ~wise(X0))) [nnf transformation 11]
48. ! [X0] : ((wise(X0) | (~rich(X0) & ~funny(X0))) & (rich(X0) | funny(X0) | ~wise(X0))) [flattening 47]
51. (? [X0] : (~strong(X0) | ~wise(X0)) | ! [X1] : ((~old(X1) | ~happy(X1)) & (happy(X1) | old(X1)))) & (? [X1] : ((~happy(X1) | old(X1)) & (happy(X1) | ~old(X1))) | ! [X0] : (strong(X0) & wise(X0))) [nnf transformation 22]
52. (? [X0] : (~strong(X0) | ~wise(X0)) | ! [X1] : ((~old(X1) | ~happy(X1)) & (happy(X1) | old(X1)))) & (? [X2] : ((~happy(X2) | old(X2)) & (happy(X2) | ~old(X2))) | ! [X3] : (strong(X3) & wise(X3))) [rectify 51]
53. ? [X0] : (~strong(X0) | ~wise(X0)) => (~strong(sK2) | ~wise(sK2)) [choice axiom]
54. ? [X2] : ((~happy(X2) | old(X2)) & (happy(X2) | ~old(X2))) => ((~happy(sK3) | old(sK3)) & (happy(sK3) | ~old(sK3))) [choice axiom]
55. ((~strong(sK2) | ~wise(sK2)) | ! [X1] : ((~old(X1) | ~happy(X1)) & (happy(X1) | old(X1)))) & (((~happy(sK3) | old(sK3)) & (happy(sK3) | ~old(sK3))) | ! [X3] : (strong(X3) & wise(X3))) [skolemisation 52,54,53]
56. ! [X0] : (((~quiet(X0) | ~funny(X0)) | (brave(X0) | old(X0))) & ((~brave(X0) & ~old(X0)) | (quiet(X0) & funny(X0)))) [nnf transformation 15]
57. ! [X0] : ((~quiet(X0) | ~funny(X0) | brave(X0) | old(X0)) & ((~brave(X0) & ~old(X0)) | (quiet(X0) & funny(X0)))) [flattening 56]
63. ~quiet(X0) | ~brave(X0) [cnf transformation 35]
67. old(X0) | patient(X0) | brave(X0) [cnf transformation 37]
77. humble(X0) | ~patient(X0) | humble(X0) [cnf transformation 39]
80. ~wise(X0) | ~old(X0) | ~happy(X0) [cnf transformation 41]
87. ~humble(X0) | happy(X0) [cnf transformation 25]
88. ~strong(X0) | calm(X0) [cnf transformation 26]
90. ~calm(sK1) | creative(X3) [cnf transformation 46]
98. ~funny(X0) | wise(X0) [cnf transformation 48]
106. happy(sK3) | ~old(sK3) | strong(X3) [cnf transformation 55]
108. ~happy(sK3) | old(sK3) | strong(X3) [cnf transformation 55]
111. ~old(X0) | funny(X0) [cnf transformation 57]
114. ~brave(X0) | quiet(X0) [cnf transformation 57]
124. ~creative(alice) [cnf transformation 20]
125. ~patient(X0) | humble(X0) [duplicate literal removal 77]
148. 6 <=> ! [X3] : creative(X3) [avatar definition]
149. creative(X3) <- (6) [avatar component clause 148]
152. 7 <=> calm(sK1) [avatar definition]
154. ~calm(sK1) <- (~7) [avatar component clause 152]
156. 6 | ~7 [avatar split clause 90,152,148]
192. 16 <=> ! [X3] : strong(X3) [avatar definition]
193. strong(X3) <- (16) [avatar component clause 192]
195. 17 <=> old(sK3) [avatar definition]
196. ~old(sK3) <- (~17) [avatar component clause 195]
197. old(sK3) <- (17) [avatar component clause 195]
199. 18 <=> happy(sK3) [avatar definition]
201. ~happy(sK3) <- (~18) [avatar component clause 199]
202. 16 | 17 | ~18 [avatar split clause 108,199,195,192]
207. 16 | ~17 | 18 [avatar split clause 106,199,195,192]
210. ~brave(X0) [subsumption resolution 114,63]
271. patient(sK3) | brave(sK3) <- (~17) [resolution 67,196]
277. patient(sK3) <- (~17) [subsumption resolution 271,210]
282. humble(sK3) <- (~17) [resolution 277,125]
306. happy(sK3) <- (~17) [resolution 282,87]
308. $false <- (~17, ~18) [subsumption resolution 306,201]
309. 17 | 18 [avatar contradiction clause 308]
311. funny(sK3) <- (17) [resolution 197,111]
321. wise(sK3) <- (17) [resolution 311,98]
349. ~old(sK3) | ~happy(sK3) <- (17) [resolution 321,80]
351. ~happy(sK3) <- (17) [subsumption resolution 349,197]
354. ~18 | ~17 [avatar split clause 351,195,199]
356. calm(X1) <- (16) [resolution 193,88]
368. $false <- (~7, 16) [resolution 356,154]
371. 7 | ~16 [avatar contradiction clause 368]
377. $false <- (6) [resolution 149,124]
378. ~6 [avatar contradiction clause 377]
379. $false [avatar sat refutation 156,202,207,309,354,371,378]
% SZS output end Proof for 5815079463962235717786634
% ------------------------------
% 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 both not generous and wise is either not curious or happy and vice versa. Everyone who is not happy or rich is not funny or rich. Everyone who is both not kind and old is both creative and not quiet and vice versa. Everyone who is not calm or not happy is either not strong or funny and vice versa. Everyone who is rich or not old is not tall or not calm. Everyone who is old or not curious is creative. Everyone who is creative or patient is rich or not brave and vice versa. If john is both generous and brave then someone is not curious and vice versa. If john is not funny then someone is both generous and not strong. Everyone who is both brave and strong is both not calm and not tall and vice versa. Everyone who is both not happy and funny is humble or brave. If someone is both humble and kind then mary is not wise or curious. If lucy is not calm or not generous then someone is not old or generous and vice versa. If lucy is both wise and kind then someone is old and vice versa. If someone is both patient and not happy then alice is not happy and vice versa. If someone is not kind or rich then john is both humble and not wise. Someone is both strong and not quiet. Lucy is not funny. Fred is not patient or not old. Someone is either quiet or wise. Someone is both brave and curious. Lucy is brave. Someone is happy or not happy. Someone is either happy or not brave. | Mary is not wise. | neutral | (![X]:((~generous(X)&wise(X))<=>(~curious(X)<~>happy(X))))&
(![X]:((~happy(X)|rich(X))=>(~funny(X)|rich(X))))&
(![X]:((~kind(X)&old(X))<=>(creative(X)&~quiet(X))))&
(![X]:((~calm(X)|~happy(X))<=>(~strong(X)<~>funny(X))))&
(![X]:((rich(X)|~old(X))=>(~tall(X)|~calm(X))))&
(![X]:((old(X)|~curious(X))=>creative(X)))&
(![X]:((creative(X)|patient(X))<=>(rich(X)|~brave(X))))&
(((generous(john)&brave(john)))<=>(?[X]:(~curious(X))))&
((~funny(john))=>(?[X]:((generous(X)&~strong(X)))))&
(![X]:((brave(X)&strong(X))<=>(~calm(X)&~tall(X))))&
(![X]:((~happy(X)&funny(X))=>(humble(X)|brave(X))))&
((?[X]:((humble(X)&kind(X))))=>((~wise(mary)|curious(mary))))&
(((~calm(lucy)|~generous(lucy)))<=>(?[X]:((~old(X)|generous(X)))))&
(((wise(lucy)&kind(lucy)))<=>(?[X]:(old(X))))&
((?[X]:((patient(X)&~happy(X))))<=>(~happy(alice)))&
((?[X]:((~kind(X)|rich(X))))=>((humble(john)&~wise(john))))&
(?[X]:((strong(X)&~quiet(X))))&
(~funny(lucy))&
((~patient(fred)|~old(fred)))&
(?[X]:((quiet(X)<~>wise(X))))&
(?[X]:((brave(X)&curious(X))))&
(brave(lucy))&
(?[X]:((happy(X)|~happy(X))))&
(?[X]:((happy(X)<~>~brave(X)))) | ~wise(mary) | [] | null | 0 |
If paul is not strong or not generous then fred is not patient and vice versa.
Everyone who is both not curious and humble is old or not rich and vice versa.
Everyone who is happy is not humble and vice versa.
Everyone who is generous or not creative is either not rich or calm.
If someone is either tall or not calm then someone is not generous or not tall.
Everyone who is creative or not humble is either not funny or old.
Everyone who is either quiet or not rich is both calm and patient and vice versa.
Everyone who is calm is not curious.
If fred is either calm or not curious then alice is both not humble and creative and vice versa.
If someone is not old or not calm then john is both not creative and old and vice versa.
Everyone who is generous or humble is creative.
Everyone who is both patient and rich is not curious or not rich and vice versa.
If someone is both old and funny then john is either kind or patient and vice versa.
If lucy is both not kind and not tall then someone is either not quiet or quiet.
Everyone who is kind or not rich is either curious or not strong.
Mary is calm or not funny.
Someone is not wise.
Someone is brave. | Alice is not old. | contradiction | (((~strong(paul)|~generous(paul)))<=>(~patient(fred)))&
(![X]:((~curious(X)&humble(X))<=>(old(X)|~rich(X))))&
(![X]:(happy(X)<=>~humble(X)))&
(![X]:((generous(X)|~creative(X))=>(~rich(X)<~>calm(X))))&
((?[X]:((tall(X)<~>~calm(X))))=>(?[X]:((~generous(X)|~tall(X)))))&
(![X]:((creative(X)|~humble(X))=>(~funny(X)<~>old(X))))&
(![X]:((quiet(X)<~>~rich(X))<=>(calm(X)&patient(X))))&
(![X]:(calm(X)=>~curious(X)))&
(((calm(fred)<~>~curious(fred)))<=>((~humble(alice)&creative(alice))))&
((?[X]:((~old(X)|~calm(X))))<=>((~creative(john)&old(john))))&
(![X]:((generous(X)|humble(X))=>creative(X)))&
(![X]:((patient(X)&rich(X))<=>(~curious(X)|~rich(X))))&
((?[X]:((old(X)&funny(X))))<=>((kind(john)<~>patient(john))))&
(((~kind(lucy)&~tall(lucy)))=>(?[X]:((~quiet(X)<~>quiet(X)))))&
(![X]:((kind(X)|~rich(X))=>(curious(X)<~>~strong(X))))&
((calm(mary)|~funny(mary)))&
(?[X]:(~wise(X)))&
(?[X]:(brave(X))) | ~old(alice) | [
"p1",
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 3437204444163731771349688
% SZS output start Proof for 3437204444163731771349688
2. ! [X0] : ((humble(X0) & ~curious(X0)) <=> (~rich(X0) | old(X0))) [input p1]
10. ? [X0] : (~calm(X0) | ~old(X0)) <=> (old(john) & ~creative(john)) [input p9]
11. ! [X0] : ((humble(X0) | generous(X0)) => creative(X0)) [input p10]
19. ~old(alice) [input hypothesis]
27. ! [X0] : (creative(X0) | (~humble(X0) & ~generous(X0))) [ennf transformation 11]
33. ! [X0] : (((humble(X0) & ~curious(X0)) | (rich(X0) & ~old(X0))) & ((~rich(X0) | old(X0)) | (~humble(X0) | curious(X0)))) [nnf transformation 2]
34. ! [X0] : (((humble(X0) & ~curious(X0)) | (rich(X0) & ~old(X0))) & (~rich(X0) | old(X0) | ~humble(X0) | curious(X0))) [flattening 33]
45. (? [X0] : (~calm(X0) | ~old(X0)) | (~old(john) | creative(john))) & ((old(john) & ~creative(john)) | ! [X0] : (calm(X0) & old(X0))) [nnf transformation 10]
46. (? [X0] : (~calm(X0) | ~old(X0)) | ~old(john) | creative(john)) & ((old(john) & ~creative(john)) | ! [X0] : (calm(X0) & old(X0))) [flattening 45]
47. (? [X0] : (~calm(X0) | ~old(X0)) | ~old(john) | creative(john)) & ((old(john) & ~creative(john)) | ! [X1] : (calm(X1) & old(X1))) [rectify 46]
48. ? [X0] : (~calm(X0) | ~old(X0)) => (~calm(sK1) | ~old(sK1)) [choice axiom]
49. ((~calm(sK1) | ~old(sK1)) | ~old(john) | creative(john)) & ((old(john) & ~creative(john)) | ! [X1] : (calm(X1) & old(X1))) [skolemisation 47,48]
66. ~old(X0) | humble(X0) [cnf transformation 34]
91. ~creative(john) | old(X1) [cnf transformation 49]
93. old(john) | old(X1) [cnf transformation 49]
97. ~humble(X0) | creative(X0) [cnf transformation 27]
116. ~old(alice) [cnf transformation 19]
174. 12 <=> creative(john) [avatar definition]
175. ~creative(john) <- (~12) [avatar component clause 174]
178. 13 <=> old(john) [avatar definition]
179. old(john) <- (13) [avatar component clause 178]
195. 17 <=> ! [X1] : old(X1) [avatar definition]
196. old(X1) <- (17) [avatar component clause 195]
197. 17 | 13 [avatar split clause 93,178,195]
199. 17 | ~12 [avatar split clause 91,174,195]
237. humble(john) <- (13) [resolution 66,179]
241. creative(john) <- (13) [resolution 97,237]
243. $false <- (~12, 13) [subsumption resolution 241,175]
244. 12 | ~13 [avatar contradiction clause 243]
250. $false <- (17) [resolution 196,116]
253. ~17 [avatar contradiction clause 250]
254. $false [avatar sat refutation 197,199,244,253]
% SZS output end Proof for 3437204444163731771349688
% ------------------------------
% 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 someone is not generous then fred is either not patient or not kind and vice versa.
If someone is not generous then paul is both calm and not tall.
Everyone who is not old is calm or not rich and vice versa.
If someone is not patient then alice is creative or not funny and vice versa.
If someone is either old or creative then fred is old.
Everyone who is both humble and wise is curious or creative and vice versa.
Everyone who is funny is not tall or not rich and vice versa.
Everyone who is not wise or not patient is both generous and kind.
If susan is either happy or not creative then someone is generous.
If paul is creative then someone is patient or not wise.
If someone is kind then someone is brave.
If someone is brave then someone is either not strong or not kind.
Everyone who is not patient or not wise is not generous.
If paul is both not strong and not curious then john is not rich or rich and vice versa.
Everyone who is either generous or brave is either calm or not generous and vice versa.
If susan is generous then someone is both old and not wise and vice versa.
Fred is not happy or kind.
Someone is both funny and not rich.
John is either creative or not happy.
Someone is either not quiet or not brave.
Someone is both rich and not brave.
Mary is both not humble and not kind.
Someone is not calm or not old.
Lucy is either funny or not strong. | Lucy is wise. | entailment | ((?[X]:(~generous(X)))<=>((~patient(fred)<~>~kind(fred))))&
((?[X]:(~generous(X)))=>((calm(paul)&~tall(paul))))&
(![X]:(~old(X)<=>(calm(X)|~rich(X))))&
((?[X]:(~patient(X)))<=>((creative(alice)|~funny(alice))))&
((?[X]:((old(X)<~>creative(X))))=>(old(fred)))&
(![X]:((humble(X)&wise(X))<=>(curious(X)|creative(X))))&
(![X]:(funny(X)<=>(~tall(X)|~rich(X))))&
(![X]:((~wise(X)|~patient(X))=>(generous(X)&kind(X))))&
(((happy(susan)<~>~creative(susan)))=>(?[X]:(generous(X))))&
((creative(paul))=>(?[X]:((patient(X)|~wise(X)))))&
((?[X]:(kind(X)))=>(?[X]:(brave(X))))&
((?[X]:(brave(X)))=>(?[X]:((~strong(X)<~>~kind(X)))))&
(![X]:((~patient(X)|~wise(X))=>~generous(X)))&
(((~strong(paul)&~curious(paul)))<=>((~rich(john)|rich(john))))&
(![X]:((generous(X)<~>brave(X))<=>(calm(X)<~>~generous(X))))&
((generous(susan))<=>(?[X]:((old(X)&~wise(X)))))&
((~happy(fred)|kind(fred)))&
(?[X]:((funny(X)&~rich(X))))&
((creative(john)<~>~happy(john)))&
(?[X]:((~quiet(X)<~>~brave(X))))&
(?[X]:((rich(X)&~brave(X))))&
((~humble(mary)&~kind(mary)))&
(?[X]:((~calm(X)|~old(X))))&
((funny(lucy)<~>~strong(lucy))) | wise(lucy) | [
"p7",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 6871493563986900040478551
% SZS output start Proof for 6871493563986900040478551
8. ! [X0] : ((~patient(X0) | ~wise(X0)) => (kind(X0) & generous(X0))) [input p7]
13. ! [X0] : ((~wise(X0) | ~patient(X0)) => ~generous(X0)) [input p12]
25. ~wise(lucy) [input hypothesis]
30. ! [X0] : ((kind(X0) & generous(X0)) | (patient(X0) & wise(X0))) [ennf transformation 8]
35. ! [X0] : (~generous(X0) | (wise(X0) & patient(X0))) [ennf transformation 13]
104. generous(X0) | wise(X0) [cnf transformation 30]
115. ~generous(X0) | wise(X0) [cnf transformation 35]
146. ~wise(lucy) [cnf transformation 25]
258. wise(X0) [subsumption resolution 115,104]
315. $false [subsumption resolution 146,258]
% SZS output end Proof for 6871493563986900040478551
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is calm is either not patient or not strong and vice versa.
Everyone who is either humble or not happy is creative and vice versa.
Everyone who is both creative and curious is both not calm and not brave and vice versa.
If lucy is kind or old then susan is wise and vice versa.
If paul is not brave then john is not generous and vice versa.
If alice is not brave then susan is not kind or not tall.
Everyone who is both rich and creative is calm.
Everyone who is either not brave or calm is either not patient or not strong and vice versa.
If someone is strong then fred is not calm.
Everyone who is strong is not curious or kind and vice versa.
Everyone who is happy or curious is both old and not calm and vice versa.
Everyone who is humble is not strong.
Everyone who is both not happy and not humble is not tall and vice versa.
If john is not brave or generous then someone is either tall or creative.
Everyone who is not calm or wise is either not generous or kind.
Everyone who is both brave and strong is not funny or tall and vice versa.
Someone is either not brave or not happy.
Someone is either calm or funny.
Someone is not curious or not humble.
Fred is both not kind and patient.
Paul is wise.
Fred is either creative or not generous.
Susan is not quiet.
Mary is either quiet or not rich. | Fred is not old. | contradiction | (![X]:(calm(X)<=>(~patient(X)<~>~strong(X))))&
(![X]:((humble(X)<~>~happy(X))<=>creative(X)))&
(![X]:((creative(X)&curious(X))<=>(~calm(X)&~brave(X))))&
(((kind(lucy)|old(lucy)))<=>(wise(susan)))&
((~brave(paul))<=>(~generous(john)))&
((~brave(alice))=>((~kind(susan)|~tall(susan))))&
(![X]:((rich(X)&creative(X))=>calm(X)))&
(![X]:((~brave(X)<~>calm(X))<=>(~patient(X)<~>~strong(X))))&
((?[X]:(strong(X)))=>(~calm(fred)))&
(![X]:(strong(X)<=>(~curious(X)|kind(X))))&
(![X]:((happy(X)|curious(X))<=>(old(X)&~calm(X))))&
(![X]:(humble(X)=>~strong(X)))&
(![X]:((~happy(X)&~humble(X))<=>~tall(X)))&
(((~brave(john)|generous(john)))=>(?[X]:((tall(X)<~>creative(X)))))&
(![X]:((~calm(X)|wise(X))=>(~generous(X)<~>kind(X))))&
(![X]:((brave(X)&strong(X))<=>(~funny(X)|tall(X))))&
(?[X]:((~brave(X)<~>~happy(X))))&
(?[X]:((calm(X)<~>funny(X))))&
(?[X]:((~curious(X)|~humble(X))))&
((~kind(fred)&patient(fred)))&
(wise(paul))&
((creative(fred)<~>~generous(fred)))&
(~quiet(susan))&
((quiet(mary)<~>~rich(mary))) | ~old(fred) | [
"p0",
"p1",
"p9",
"p10",
"p11",
"p14",
"p19",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 2667489288308525139204580
% SZS output start Proof for 2667489288308525139204580
1. ! [X0] : (calm(X0) <=> (~patient(X0) <~> ~strong(X0))) [input p0]
2. ! [X0] : ((humble(X0) <~> ~happy(X0)) <=> creative(X0)) [input p1]
10. ! [X0] : (strong(X0) <=> (kind(X0) | ~curious(X0))) [input p9]
11. ! [X0] : ((curious(X0) | happy(X0)) <=> (~calm(X0) & old(X0))) [input p10]
12. ! [X0] : (humble(X0) => ~strong(X0)) [input p11]
15. ! [X0] : ((wise(X0) | ~calm(X0)) => (~generous(X0) <~> kind(X0))) [input p14]
20. patient(fred) & ~kind(fred) [input p19]
22. creative(fred) <~> ~generous(fred) [input p21]
25. ~old(fred) [input hypothesis]
31. ! [X0] : (~strong(X0) | ~humble(X0)) [ennf transformation 12]
33. ! [X0] : ((~generous(X0) <~> kind(X0)) | (~wise(X0) & calm(X0))) [ennf transformation 15]
34. ! [X0] : ((calm(X0) | ((~patient(X0) | strong(X0)) & (~strong(X0) | patient(X0)))) & (((strong(X0) | patient(X0)) & (~strong(X0) | ~patient(X0))) | ~calm(X0))) [nnf transformation 1]
35. ! [X0] : ((((happy(X0) | ~humble(X0)) & (~happy(X0) | humble(X0))) | ~creative(X0)) & (creative(X0) | ((humble(X0) | happy(X0)) & (~happy(X0) | ~humble(X0))))) [nnf transformation 2]
42. ! [X0] : ((strong(X0) | (~kind(X0) & curious(X0))) & ((kind(X0) | ~curious(X0)) | ~strong(X0))) [nnf transformation 10]
43. ! [X0] : ((strong(X0) | (~kind(X0) & curious(X0))) & (kind(X0) | ~curious(X0) | ~strong(X0))) [flattening 42]
44. ! [X0] : (((curious(X0) | happy(X0)) | (calm(X0) | ~old(X0))) & ((~calm(X0) & old(X0)) | (~curious(X0) & ~happy(X0)))) [nnf transformation 11]
45. ! [X0] : ((curious(X0) | happy(X0) | calm(X0) | ~old(X0)) & ((~calm(X0) & old(X0)) | (~curious(X0) & ~happy(X0)))) [flattening 44]
51. ! [X0] : (((~kind(X0) | generous(X0)) & (kind(X0) | ~generous(X0))) | (~wise(X0) & calm(X0))) [nnf transformation 33]
62. (generous(fred) | ~creative(fred)) & (~generous(fred) | creative(fred)) [nnf transformation 22]
64. ~strong(X0) | ~patient(X0) | ~calm(X0) [cnf transformation 34]
69. creative(X0) | humble(X0) | happy(X0) [cnf transformation 35]
93. curious(X0) | strong(X0) [cnf transformation 43]
95. ~happy(X0) | old(X0) [cnf transformation 45]
96. ~curious(X0) | old(X0) [cnf transformation 45]
100. ~humble(X0) | ~strong(X0) [cnf transformation 31]
108. ~generous(X0) | kind(X0) | calm(X0) [cnf transformation 51]
122. ~kind(fred) [cnf transformation 20]
123. patient(fred) [cnf transformation 20]
126. generous(fred) | ~creative(fred) [cnf transformation 62]
130. ~old(fred) [cnf transformation 25]
177. 10 <=> calm(fred) [avatar definition]
178. calm(fred) <- (10) [avatar component clause 177]
179. ~calm(fred) <- (~10) [avatar component clause 177]
227. 20 <=> creative(fred) [avatar definition]
229. ~creative(fred) <- (~20) [avatar component clause 227]
231. 21 <=> generous(fred) [avatar definition]
233. generous(fred) <- (21) [avatar component clause 231]
234. ~20 | 21 [avatar split clause 126,231,227]
246. old(X0) | strong(X0) [resolution 96,93]
273. strong(fred) [resolution 246,130]
275. humble(fred) | happy(fred) <- (~20) [resolution 69,229]
277. 26 <=> happy(fred) [avatar definition]
279. happy(fred) <- (26) [avatar component clause 277]
281. 27 <=> humble(fred) [avatar definition]
283. humble(fred) <- (27) [avatar component clause 281]
284. 26 | 27 | 20 [avatar split clause 275,227,281,277]
377. kind(fred) | calm(fred) <- (21) [resolution 108,233]
379. calm(fred) <- (21) [subsumption resolution 377,122]
380. $false <- (~10, 21) [subsumption resolution 379,179]
381. 10 | ~21 [avatar contradiction clause 380]
399. old(fred) <- (26) [resolution 279,95]
400. $false <- (26) [subsumption resolution 399,130]
401. ~26 [avatar contradiction clause 400]
408. ~strong(fred) <- (27) [resolution 283,100]
409. $false <- (27) [subsumption resolution 408,273]
410. ~27 [avatar contradiction clause 409]
454. ~patient(fred) | ~calm(fred) [resolution 273,64]
456. ~calm(fred) [subsumption resolution 454,123]
457. $false <- (10) [subsumption resolution 456,178]
458. ~10 [avatar contradiction clause 457]
459. $false [avatar sat refutation 234,284,381,401,410,458]
% SZS output end Proof for 2667489288308525139204580
% ------------------------------
% 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: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either kind or not strong then someone is happy or not quiet.
If susan is both not generous and strong then mary is not tall and vice versa.
Everyone who is not happy or patient is both curious and not creative.
If john is not strong then lucy is not old or not generous.
Everyone who is happy is either not strong or not funny and vice versa.
Everyone who is curious or not old is curious.
Everyone who is not happy or happy is strong.
If someone is not strong or not quiet then someone is both not funny and patient.
Everyone who is not tall or kind is curious and vice versa.
Everyone who is both brave and not quiet is both quiet and not rich and vice versa.
Everyone who is happy is not happy or not kind and vice versa.
If someone is both kind and generous then someone is both wise and not tall and vice versa.
Everyone who is not creative or not rich is wise or not happy.
Everyone who is either not funny or humble is patient.
If paul is either not tall or humble then someone is either happy or not humble.
If lucy is not wise then lucy is either not kind or rich and vice versa.
Lucy is not funny or not strong.
Fred is both happy and not tall.
Someone is happy.
Paul is either funny or not curious.
Someone is not generous or not happy.
Fred is not old.
Someone is either generous or wise.
Someone is creative. | Fred is creative. | entailment | ((?[X]:((kind(X)<~>~strong(X))))=>(?[X]:((happy(X)|~quiet(X)))))&
(((~generous(susan)&strong(susan)))<=>(~tall(mary)))&
(![X]:((~happy(X)|patient(X))=>(curious(X)&~creative(X))))&
((~strong(john))=>((~old(lucy)|~generous(lucy))))&
(![X]:(happy(X)<=>(~strong(X)<~>~funny(X))))&
(![X]:((curious(X)|~old(X))=>curious(X)))&
(![X]:((~happy(X)|happy(X))=>strong(X)))&
((?[X]:((~strong(X)|~quiet(X))))=>(?[X]:((~funny(X)&patient(X)))))&
(![X]:((~tall(X)|kind(X))<=>curious(X)))&
(![X]:((brave(X)&~quiet(X))<=>(quiet(X)&~rich(X))))&
(![X]:(happy(X)<=>(~happy(X)|~kind(X))))&
((?[X]:((kind(X)&generous(X))))<=>(?[X]:((wise(X)&~tall(X)))))&
(![X]:((~creative(X)|~rich(X))=>(wise(X)|~happy(X))))&
(![X]:((~funny(X)<~>humble(X))=>patient(X)))&
(((~tall(paul)<~>humble(paul)))=>(?[X]:((happy(X)<~>~humble(X)))))&
((~wise(lucy))<=>((~kind(lucy)<~>rich(lucy))))&
((~funny(lucy)|~strong(lucy)))&
((happy(fred)&~tall(fred)))&
(?[X]:(happy(X)))&
((funny(paul)<~>~curious(paul)))&
(?[X]:((~generous(X)|~happy(X))))&
(~old(fred))&
(?[X]:((generous(X)<~>wise(X))))&
(?[X]:(creative(X))) | creative(fred) | [
"p10",
"p11",
"p12",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 3707625226946630064636342
% SZS output start Proof for 3707625226946630064636342
11. ! [X0] : (happy(X0) <=> (~kind(X0) | ~happy(X0))) [input p10]
12. ? [X0] : (generous(X0) & kind(X0)) <=> ? [X0] : (~tall(X0) & wise(X0)) [input p11]
13. ! [X0] : ((~rich(X0) | ~creative(X0)) => (~happy(X0) | wise(X0))) [input p12]
18. ~tall(fred) & happy(fred) [input p17]
25. ~creative(fred) [input hypothesis]
28. ? [X0] : (generous(X0) & kind(X0)) <=> ? [X1] : (~tall(X1) & wise(X1)) [rectify 12]
36. ! [X0] : ((~happy(X0) | wise(X0)) | (rich(X0) & creative(X0))) [ennf transformation 13]
37. ! [X0] : (~happy(X0) | wise(X0) | (rich(X0) & creative(X0))) [flattening 36]
54. ! [X0] : ((happy(X0) | (kind(X0) & happy(X0))) & ((~kind(X0) | ~happy(X0)) | ~happy(X0))) [nnf transformation 11]
55. ! [X0] : ((happy(X0) | (kind(X0) & happy(X0))) & (~kind(X0) | ~happy(X0) | ~happy(X0))) [flattening 54]
56. (? [X0] : (generous(X0) & kind(X0)) | ! [X1] : (tall(X1) | ~wise(X1))) & (? [X1] : (~tall(X1) & wise(X1)) | ! [X0] : (~generous(X0) | ~kind(X0))) [nnf transformation 28]
57. (? [X0] : (generous(X0) & kind(X0)) | ! [X1] : (tall(X1) | ~wise(X1))) & (? [X2] : (~tall(X2) & wise(X2)) | ! [X3] : (~generous(X3) | ~kind(X3))) [rectify 56]
58. ? [X0] : (generous(X0) & kind(X0)) => (generous(sK2) & kind(sK2)) [choice axiom]
59. ? [X2] : (~tall(X2) & wise(X2)) => (~tall(sK3) & wise(sK3)) [choice axiom]
60. ((generous(sK2) & kind(sK2)) | ! [X1] : (tall(X1) | ~wise(X1))) & ((~tall(sK3) & wise(sK3)) | ! [X3] : (~generous(X3) | ~kind(X3))) [skolemisation 57,59,58]
105. ~kind(X0) | ~happy(X0) | ~happy(X0) [cnf transformation 55]
106. happy(X0) | happy(X0) [cnf transformation 55]
110. kind(sK2) | tall(X1) | ~wise(X1) [cnf transformation 60]
112. ~happy(X0) | wise(X0) | creative(X0) [cnf transformation 37]
126. ~tall(fred) [cnf transformation 18]
135. ~creative(fred) [cnf transformation 25]
136. ~kind(X0) | ~happy(X0) [duplicate literal removal 105]
137. happy(X0) [duplicate literal removal 106]
198. ~kind(X0) [subsumption resolution 136,137]
200. 14 <=> ! [X1] : (tall(X1) | ~wise(X1)) [avatar definition]
201. ~wise(X1) | tall(X1) <- (14) [avatar component clause 200]
207. tall(X1) | ~wise(X1) [subsumption resolution 110,198]
208. 14 [avatar split clause 207,200]
210. wise(X0) | creative(X0) [subsumption resolution 112,137]
272. creative(X0) | tall(X0) <- (14) [resolution 210,201]
277. tall(fred) <- (14) [resolution 272,135]
280. $false <- (14) [subsumption resolution 277,126]
281. ~14 [avatar contradiction clause 280]
282. $false [avatar sat refutation 208,281]
% SZS output end Proof for 3707625226946630064636342
% ------------------------------
% 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 patient and not wise is both not happy and old.
Everyone who is both not creative and tall is both not generous and happy and vice versa.
Everyone who is kind or rich is not rich.
Everyone who is either not calm or humble is not old and vice versa.
Everyone who is rich is not tall.
If alice is either calm or brave then someone is rich.
Everyone who is either brave or patient is not rich and vice versa.
Everyone who is not tall is not happy.
Everyone who is either calm or tall is both not rich and not tall and vice versa.
Everyone who is not kind is both not kind and kind.
Everyone who is either not happy or creative is either old or not calm and vice versa.
Everyone who is either creative or not kind is patient.
Everyone who is humble is wise or happy and vice versa.
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.
Someone is not calm or generous.
Someone is either not calm or not wise.
Someone is both not quiet and generous.
Someone is either wise or curious.
Someone is brave or not quiet.
Paul is old.
Someone is kind or rich. | Alice is not old. | neutral | (![X]:((~patient(X)&~wise(X))=>(~happy(X)&old(X))))&
(![X]:((~creative(X)&tall(X))<=>(~generous(X)&happy(X))))&
(![X]:((kind(X)|rich(X))=>~rich(X)))&
(![X]:((~calm(X)<~>humble(X))<=>~old(X)))&
(![X]:(rich(X)=>~tall(X)))&
(((calm(alice)<~>brave(alice)))=>(?[X]:(rich(X))))&
(![X]:((brave(X)<~>patient(X))<=>~rich(X)))&
(![X]:(~tall(X)=>~happy(X)))&
(![X]:((calm(X)<~>tall(X))<=>(~rich(X)&~tall(X))))&
(![X]:(~kind(X)=>(~kind(X)&kind(X))))&
(![X]:((~happy(X)<~>creative(X))<=>(old(X)<~>~calm(X))))&
(![X]:((creative(X)<~>~kind(X))=>patient(X)))&
(![X]:(humble(X)<=>(wise(X)|happy(X))))&
(((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]:((~calm(X)|generous(X))))&
(?[X]:((~calm(X)<~>~wise(X))))&
(?[X]:((~quiet(X)&generous(X))))&
(?[X]:((wise(X)<~>curious(X))))&
(?[X]:((brave(X)|~quiet(X))))&
(old(paul))&
(?[X]:((kind(X)|rich(X)))) | ~old(alice) | [] | null | 0 |
Everyone who is tall or not strong is not brave. Everyone who is both old and tall is both not calm and not strong. Everyone who is both not patient and creative is either not happy or kind and vice versa. Everyone who is both not tall and not strong is both creative and quiet and vice versa. Everyone who is rich or not brave is both not generous and tall and vice versa. If alice is not creative or not brave then someone is creative or generous and vice versa. Everyone who is both not rich and not humble is not brave or kind and vice versa. Everyone who is both not patient and happy is not patient and vice versa. Everyone who is humble or not patient is both creative and not wise. Everyone who is either creative or old is old. If mary is curious or not old then someone is either brave or not kind. Everyone who is not happy or brave is not calm. Everyone who is either not happy or generous is either old or curious and vice versa. If someone is not calm or wise then alice is either generous or strong and vice versa. Everyone who is either funny or not quiet is both wise and not kind and vice versa. Everyone who is either not patient or not quiet is both not brave and kind and vice versa. Fred is either brave or not patient. Paul is quiet. Fred is generous or not old. Paul is generous. Someone is both not tall and happy. Paul is both not creative and generous. Someone is tall. | Paul is not kind. | contradiction | (![X]:((tall(X)|~strong(X))=>~brave(X)))&
(![X]:((old(X)&tall(X))=>(~calm(X)&~strong(X))))&
(![X]:((~patient(X)&creative(X))<=>(~happy(X)<~>kind(X))))&
(![X]:((~tall(X)&~strong(X))<=>(creative(X)&quiet(X))))&
(![X]:((rich(X)|~brave(X))<=>(~generous(X)&tall(X))))&
(((~creative(alice)|~brave(alice)))<=>(?[X]:((creative(X)|generous(X)))))&
(![X]:((~rich(X)&~humble(X))<=>(~brave(X)|kind(X))))&
(![X]:((~patient(X)&happy(X))<=>~patient(X)))&
(![X]:((humble(X)|~patient(X))=>(creative(X)&~wise(X))))&
(![X]:((creative(X)<~>old(X))=>old(X)))&
(((curious(mary)|~old(mary)))=>(?[X]:((brave(X)<~>~kind(X)))))&
(![X]:((~happy(X)|brave(X))=>~calm(X)))&
(![X]:((~happy(X)<~>generous(X))<=>(old(X)<~>curious(X))))&
((?[X]:((~calm(X)|wise(X))))<=>((generous(alice)<~>strong(alice))))&
(![X]:((funny(X)<~>~quiet(X))<=>(wise(X)&~kind(X))))&
(![X]:((~patient(X)<~>~quiet(X))<=>(~brave(X)&kind(X))))&
((brave(fred)<~>~patient(fred)))&
(quiet(paul))&
((generous(fred)|~old(fred)))&
(generous(paul))&
(?[X]:((~tall(X)&happy(X))))&
((~creative(paul)&generous(paul)))&
(?[X]:(tall(X))) | ~kind(paul) | [
"p4",
"p6",
"p8",
"p19",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 4721496040268349395481781
% SZS output start Proof for 4721496040268349395481781
5. ! [X0] : ((~brave(X0) | rich(X0)) <=> (tall(X0) & ~generous(X0))) [input p4]
7. ! [X0] : ((~humble(X0) & ~rich(X0)) <=> (kind(X0) | ~brave(X0))) [input p6]
9. ! [X0] : ((~patient(X0) | humble(X0)) => (~wise(X0) & creative(X0))) [input p8]
20. generous(paul) [input p19]
22. generous(paul) & ~creative(paul) [input p21]
24. ~kind(paul) [input hypothesis]
28. ! [X0] : ((~wise(X0) & creative(X0)) | (patient(X0) & ~humble(X0))) [ennf transformation 9]
36. ! [X0] : (((~brave(X0) | rich(X0)) | (~tall(X0) | generous(X0))) & ((tall(X0) & ~generous(X0)) | (brave(X0) & ~rich(X0)))) [nnf transformation 5]
37. ! [X0] : ((~brave(X0) | rich(X0) | ~tall(X0) | generous(X0)) & ((tall(X0) & ~generous(X0)) | (brave(X0) & ~rich(X0)))) [flattening 36]
43. ! [X0] : (((~humble(X0) & ~rich(X0)) | (~kind(X0) & brave(X0))) & ((kind(X0) | ~brave(X0)) | (humble(X0) | rich(X0)))) [nnf transformation 7]
44. ! [X0] : (((~humble(X0) & ~rich(X0)) | (~kind(X0) & brave(X0))) & (kind(X0) | ~brave(X0) | humble(X0) | rich(X0))) [flattening 43]
79. ~generous(X0) | ~rich(X0) [cnf transformation 37]
80. ~generous(X0) | brave(X0) [cnf transformation 37]
88. ~brave(X0) | kind(X0) | humble(X0) | rich(X0) [cnf transformation 44]
96. ~humble(X0) | creative(X0) [cnf transformation 28]
138. generous(paul) [cnf transformation 20]
141. ~creative(paul) [cnf transformation 22]
144. ~kind(paul) [cnf transformation 24]
239. ~rich(paul) [resolution 79,138]
240. brave(paul) [resolution 80,138]
348. kind(paul) | humble(paul) | rich(paul) [resolution 88,240]
351. humble(paul) | rich(paul) [subsumption resolution 348,144]
352. humble(paul) [subsumption resolution 351,239]
455. creative(paul) [resolution 352,96]
458. $false [subsumption resolution 455,141]
% SZS output end Proof for 4721496040268349395481781
% ------------------------------
% 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 rich is either not funny or not curious and vice versa.
If someone is both not rich and not tall then someone is both curious and not generous.
If someone is both happy and curious then susan is wise or curious.
Everyone who is happy or curious is either curious or tall and vice versa.
Everyone who is both not calm and old is both funny and brave and vice versa.
Everyone who is either tall or not old is either calm or not wise.
If someone is both not kind and quiet then someone is not funny and vice versa.
Everyone who is brave or funny is not curious.
If someone is both quiet and curious then someone is either not wise or strong.
Everyone who is generous or old is patient or not calm and vice versa.
Everyone who is happy or not old is either not brave or not calm.
Everyone who is either not patient or not creative is not strong and vice versa.
Everyone who is both not calm and kind is both not generous and not funny and vice versa.
Everyone who is not quiet or not strong is not generous.
If susan is not brave or not wise then someone is both not creative and not calm and vice versa.
Everyone who is both not brave and rich is both not brave and not kind and vice versa.
Alice is either not patient or tall.
Paul is not funny.
Someone is wise.
Someone is not quiet or not brave.
Fred is not patient.
Paul is not curious or rich.
Someone is funny or strong.
Paul is not calm or tall. | Alice is not patient. | neutral | (![X]:(rich(X)<=>(~funny(X)<~>~curious(X))))&
((?[X]:((~rich(X)&~tall(X))))=>(?[X]:((curious(X)&~generous(X)))))&
((?[X]:((happy(X)&curious(X))))=>((wise(susan)|curious(susan))))&
(![X]:((happy(X)|curious(X))<=>(curious(X)<~>tall(X))))&
(![X]:((~calm(X)&old(X))<=>(funny(X)&brave(X))))&
(![X]:((tall(X)<~>~old(X))=>(calm(X)<~>~wise(X))))&
((?[X]:((~kind(X)&quiet(X))))<=>(?[X]:(~funny(X))))&
(![X]:((brave(X)|funny(X))=>~curious(X)))&
((?[X]:((quiet(X)&curious(X))))=>(?[X]:((~wise(X)<~>strong(X)))))&
(![X]:((generous(X)|old(X))<=>(patient(X)|~calm(X))))&
(![X]:((happy(X)|~old(X))=>(~brave(X)<~>~calm(X))))&
(![X]:((~patient(X)<~>~creative(X))<=>~strong(X)))&
(![X]:((~calm(X)&kind(X))<=>(~generous(X)&~funny(X))))&
(![X]:((~quiet(X)|~strong(X))=>~generous(X)))&
(((~brave(susan)|~wise(susan)))<=>(?[X]:((~creative(X)&~calm(X)))))&
(![X]:((~brave(X)&rich(X))<=>(~brave(X)&~kind(X))))&
((~patient(alice)<~>tall(alice)))&
(~funny(paul))&
(?[X]:(wise(X)))&
(?[X]:((~quiet(X)|~brave(X))))&
(~patient(fred))&
((~curious(paul)|rich(paul)))&
(?[X]:((funny(X)|strong(X))))&
((~calm(paul)|tall(paul))) | ~patient(alice) | [] | null | 0 |
Everyone who is either old or generous is not calm and vice versa.
If someone is both not old and not rich then someone is brave and vice versa.
Everyone who is kind is not quiet.
Everyone who is both not rich and not patient is both brave and not generous.
If susan is creative or wise then someone is not calm.
If someone is not kind or brave then someone is calm or funny and vice versa.
If someone is either wise or humble then someone is not kind or not happy and vice versa.
If mary is both not wise and funny then alice is either not happy or old and vice versa.
Everyone who is not quiet is either not creative or not kind.
Everyone who is both not happy and brave is wise or brave.
Everyone who is brave is not calm or patient and vice versa.
Everyone who is not humble is both not quiet and old.
Everyone who is generous or curious is not curious.
If someone is funny then someone is old or strong.
Everyone who is either rich or creative is either not quiet or calm and vice versa.
Everyone who is both not tall and not humble is not kind or humble.
Mary is either funny or creative.
Mary is both not calm and rich.
Mary is calm or not wise.
Someone is both not kind and tall.
Someone is either calm or quiet.
Someone is kind or creative.
Susan is both tall and calm.
Someone is either not happy or generous. | Mary is creative. | neutral | (![X]:((old(X)<~>generous(X))<=>~calm(X)))&
((?[X]:((~old(X)&~rich(X))))<=>(?[X]:(brave(X))))&
(![X]:(kind(X)=>~quiet(X)))&
(![X]:((~rich(X)&~patient(X))=>(brave(X)&~generous(X))))&
(((creative(susan)|wise(susan)))=>(?[X]:(~calm(X))))&
((?[X]:((~kind(X)|brave(X))))<=>(?[X]:((calm(X)|funny(X)))))&
((?[X]:((wise(X)<~>humble(X))))<=>(?[X]:((~kind(X)|~happy(X)))))&
(((~wise(mary)&funny(mary)))<=>((~happy(alice)<~>old(alice))))&
(![X]:(~quiet(X)=>(~creative(X)<~>~kind(X))))&
(![X]:((~happy(X)&brave(X))=>(wise(X)|brave(X))))&
(![X]:(brave(X)<=>(~calm(X)|patient(X))))&
(![X]:(~humble(X)=>(~quiet(X)&old(X))))&
(![X]:((generous(X)|curious(X))=>~curious(X)))&
((?[X]:(funny(X)))=>(?[X]:((old(X)|strong(X)))))&
(![X]:((rich(X)<~>creative(X))<=>(~quiet(X)<~>calm(X))))&
(![X]:((~tall(X)&~humble(X))=>(~kind(X)|humble(X))))&
((funny(mary)<~>creative(mary)))&
((~calm(mary)&rich(mary)))&
((calm(mary)|~wise(mary)))&
(?[X]:((~kind(X)&tall(X))))&
(?[X]:((calm(X)<~>quiet(X))))&
(?[X]:((kind(X)|creative(X))))&
((tall(susan)&calm(susan)))&
(?[X]:((~happy(X)<~>generous(X)))) | creative(mary) | [] | null | 0 |
Everyone who is patient is either brave or not humble and vice versa.
If john is both brave and humble then someone is not strong or not creative.
If fred is not kind then mary is funny or not funny and vice versa.
Everyone who is both not old and not kind is not patient or tall and vice versa.
If someone is humble or not happy then someone is rich.
If someone is not generous then someone is not funny and vice versa.
If someone is either not brave or not old then someone is not strong or kind and vice versa.
Everyone who is strong is tall or humble.
Everyone who is both not generous and tall is generous or quiet and vice versa.
Everyone who is not humble is happy or not funny and vice versa.
Everyone who is both not kind and rich is not calm and vice versa.
Everyone who is humble is humble or happy.
If susan is either not creative or wise then someone is either creative or not strong.
Everyone who is quiet or not rich is not tall or curious and vice versa.
Everyone who is either not tall or creative is both not humble and not curious.
Mary is either not rich or not generous.
Someone is not curious or not creative.
Someone is either not creative or not kind.
John is not strong or curious.
Fred is both funny and curious.
Susan is either strong or not kind.
Someone is strong.
Alice is either tall or curious. | Alice is not calm. | contradiction | (![X]:(patient(X)<=>(brave(X)<~>~humble(X))))&
(((brave(john)&humble(john)))=>(?[X]:((~strong(X)|~creative(X)))))&
((~kind(fred))<=>((funny(mary)|~funny(mary))))&
(![X]:((~old(X)&~kind(X))<=>(~patient(X)|tall(X))))&
((?[X]:((humble(X)|~happy(X))))=>(?[X]:(rich(X))))&
((?[X]:(~generous(X)))<=>(?[X]:(~funny(X))))&
((?[X]:((~brave(X)<~>~old(X))))<=>(?[X]:((~strong(X)|kind(X)))))&
(![X]:(strong(X)=>(tall(X)|humble(X))))&
(![X]:((~generous(X)&tall(X))<=>(generous(X)|quiet(X))))&
(![X]:(~humble(X)<=>(happy(X)|~funny(X))))&
(![X]:((~kind(X)&rich(X))<=>~calm(X)))&
(![X]:(humble(X)=>(humble(X)|happy(X))))&
(((~creative(susan)<~>wise(susan)))=>(?[X]:((creative(X)<~>~strong(X)))))&
(![X]:((quiet(X)|~rich(X))<=>(~tall(X)|curious(X))))&
(![X]:((~tall(X)<~>creative(X))=>(~humble(X)&~curious(X))))&
((~rich(mary)<~>~generous(mary)))&
(?[X]:((~curious(X)|~creative(X))))&
(?[X]:((~creative(X)<~>~kind(X))))&
((~strong(john)|curious(john)))&
((funny(fred)&curious(fred)))&
((strong(susan)<~>~kind(susan)))&
(?[X]:(strong(X)))&
((tall(alice)<~>curious(alice))) | ~calm(alice) | [
"p8",
"p10",
"p13",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 3913686180791935232797855
% SZS output start Proof for 3913686180791935232797855
9. ! [X0] : ((tall(X0) & ~generous(X0)) <=> (quiet(X0) | generous(X0))) [input p8]
11. ! [X0] : ((rich(X0) & ~kind(X0)) <=> ~calm(X0)) [input p10]
14. ! [X0] : ((~rich(X0) | quiet(X0)) <=> (curious(X0) | ~tall(X0))) [input p13]
23. tall(alice) <~> curious(alice) [input p22]
24. ~calm(alice) [input hypothesis]
28. ! [X0] : (~calm(X0) => (rich(X0) & ~kind(X0))) [unused predicate definition removal 11]
34. ! [X0] : ((rich(X0) & ~kind(X0)) | calm(X0)) [ennf transformation 28]
59. ! [X0] : (((tall(X0) & ~generous(X0)) | (~quiet(X0) & ~generous(X0))) & ((quiet(X0) | generous(X0)) | (~tall(X0) | generous(X0)))) [nnf transformation 9]
60. ! [X0] : (((tall(X0) & ~generous(X0)) | (~quiet(X0) & ~generous(X0))) & (quiet(X0) | generous(X0) | ~tall(X0) | generous(X0))) [flattening 59]
66. ! [X0] : (((~rich(X0) | quiet(X0)) | (~curious(X0) & tall(X0))) & ((curious(X0) | ~tall(X0)) | (rich(X0) & ~quiet(X0)))) [nnf transformation 14]
67. ! [X0] : ((~rich(X0) | quiet(X0) | (~curious(X0) & tall(X0))) & (curious(X0) | ~tall(X0) | (rich(X0) & ~quiet(X0)))) [flattening 66]
78. (~curious(alice) | ~tall(alice)) & (curious(alice) | tall(alice)) [nnf transformation 23]
103. quiet(X0) | generous(X0) | ~tall(X0) | generous(X0) [cnf transformation 60]
104. ~generous(X0) | ~generous(X0) [cnf transformation 60]
107. ~quiet(X0) | tall(X0) [cnf transformation 60]
112. calm(X0) | rich(X0) [cnf transformation 34]
118. curious(X0) | ~tall(X0) | ~quiet(X0) [cnf transformation 67]
120. ~rich(X0) | quiet(X0) | tall(X0) [cnf transformation 67]
138. ~curious(alice) | ~tall(alice) [cnf transformation 78]
139. ~calm(alice) [cnf transformation 24]
140. quiet(X0) | generous(X0) | ~tall(X0) [duplicate literal removal 103]
141. ~generous(X0) [duplicate literal removal 104]
231. ~tall(X0) | quiet(X0) [subsumption resolution 140,141]
252. ~rich(X0) | tall(X0) [subsumption resolution 120,107]
253. ~quiet(X0) | curious(X0) [subsumption resolution 118,107]
294. 34 <=> tall(alice) [avatar definition]
295. tall(alice) <- (34) [avatar component clause 294]
298. 35 <=> curious(alice) [avatar definition]
300. ~curious(alice) <- (~35) [avatar component clause 298]
301. ~34 | ~35 [avatar split clause 138,298,294]
305. rich(alice) [resolution 112,139]
306. quiet(alice) <- (34) [resolution 231,295]
311. tall(alice) [resolution 252,305]
315. curious(alice) <- (34) [resolution 253,306]
316. $false <- (34, ~35) [subsumption resolution 315,300]
317. ~34 | 35 [avatar contradiction clause 316]
318. 34 [avatar split clause 311,294]
319. $false [avatar sat refutation 301,317,318]
% SZS output end Proof for 3913686180791935232797855
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If fred is both not creative and creative then someone is not tall or not happy and vice versa.
Everyone who is not quiet is not quiet or not patient.
Everyone who is funny or not happy is kind and vice versa.
If someone is both not patient and not happy then lucy is either wise or not funny.
Everyone who is both not strong and not funny is creative or humble.
Everyone who is calm is both quiet and curious.
If lucy is not generous then john is humble and vice versa.
If someone is not curious then john is not wise or not tall.
If someone is either not quiet or not old then someone is generous.
If someone is kind or not rich then mary is not brave or not happy and vice versa.
Everyone who is tall or not funny is tall or strong and vice versa.
If john is rich or not humble then john is both happy and tall and vice versa.
If someone is either creative or curious then alice is not funny and vice versa.
Everyone who is wise or kind is not calm or not creative.
Everyone who is either calm or not curious is not generous or not kind and vice versa.
Everyone who is curious or old is both strong and funny and vice versa.
Mary is either tall or not calm.
Someone is strong or quiet.
Mary is happy.
Someone is not rich or calm.
Lucy is either happy or funny.
Someone is either quiet or calm. | Mary is not tall. | contradiction | (((~creative(fred)&creative(fred)))<=>(?[X]:((~tall(X)|~happy(X)))))&
(![X]:(~quiet(X)=>(~quiet(X)|~patient(X))))&
(![X]:((funny(X)|~happy(X))<=>kind(X)))&
((?[X]:((~patient(X)&~happy(X))))=>((wise(lucy)<~>~funny(lucy))))&
(![X]:((~strong(X)&~funny(X))=>(creative(X)|humble(X))))&
(![X]:(calm(X)=>(quiet(X)&curious(X))))&
((~generous(lucy))<=>(humble(john)))&
((?[X]:(~curious(X)))=>((~wise(john)|~tall(john))))&
((?[X]:((~quiet(X)<~>~old(X))))=>(?[X]:(generous(X))))&
((?[X]:((kind(X)|~rich(X))))<=>((~brave(mary)|~happy(mary))))&
(![X]:((tall(X)|~funny(X))<=>(tall(X)|strong(X))))&
(((rich(john)|~humble(john)))<=>((happy(john)&tall(john))))&
((?[X]:((creative(X)<~>curious(X))))<=>(~funny(alice)))&
(![X]:((wise(X)|kind(X))=>(~calm(X)|~creative(X))))&
(![X]:((calm(X)<~>~curious(X))<=>(~generous(X)|~kind(X))))&
(![X]:((curious(X)|old(X))<=>(strong(X)&funny(X))))&
((tall(mary)<~>~calm(mary)))&
(?[X]:((strong(X)|quiet(X))))&
(happy(mary))&
(?[X]:((~rich(X)|calm(X))))&
((happy(lucy)<~>funny(lucy)))&
(?[X]:((quiet(X)<~>calm(X)))) | ~tall(mary) | [
"p0",
"hypothesis"
] | % SZS status Unsatisfiable for 7379462972069140108420929
% SZS output start Proof for 7379462972069140108420929
1. (creative(fred) & ~creative(fred)) <=> ? [X0] : (~happy(X0) | ~tall(X0)) [input p0]
23. ~tall(mary) [input hypothesis]
36. ((creative(fred) & ~creative(fred)) | ! [X0] : (happy(X0) & tall(X0))) & (? [X0] : (~happy(X0) | ~tall(X0)) | (~creative(fred) | creative(fred))) [nnf transformation 1]
37. ((creative(fred) & ~creative(fred)) | ! [X0] : (happy(X0) & tall(X0))) & (? [X0] : (~happy(X0) | ~tall(X0)) | ~creative(fred) | creative(fred)) [flattening 36]
38. ((creative(fred) & ~creative(fred)) | ! [X0] : (happy(X0) & tall(X0))) & (? [X1] : (~happy(X1) | ~tall(X1)) | ~creative(fred) | creative(fred)) [rectify 37]
39. ? [X1] : (~happy(X1) | ~tall(X1)) => (~happy(sK0) | ~tall(sK0)) [choice axiom]
40. ((creative(fred) & ~creative(fred)) | ! [X0] : (happy(X0) & tall(X0))) & ((~happy(sK0) | ~tall(sK0)) | ~creative(fred) | creative(fred)) [skolemisation 38,39]
76. ~creative(fred) | tall(X0) [cnf transformation 40]
78. creative(fred) | tall(X0) [cnf transformation 40]
133. ~tall(mary) [cnf transformation 23]
138. 2 <=> creative(fred) [avatar definition]
143. 3 <=> ! [X0] : tall(X0) [avatar definition]
144. tall(X0) <- (3) [avatar component clause 143]
145. 3 | 2 [avatar split clause 78,138,143]
147. 3 | ~2 [avatar split clause 76,138,143]
259. 28 <=> tall(mary) [avatar definition]
261. ~tall(mary) <- (~28) [avatar component clause 259]
295. ~28 [avatar split clause 133,259]
300. $false <- (3, ~28) [resolution 261,144]
301. ~3 | 28 [avatar contradiction clause 300]
302. $false [avatar sat refutation 145,147,295,301]
% SZS output end Proof for 7379462972069140108420929
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not patient is tall or kind. If someone is both not brave and not strong then someone is wise. Everyone who is either not old or creative is both brave and not wise and vice versa. Everyone who is creative is wise and vice versa. If someone is both brave and not strong then someone is either not happy or tall and vice versa. Everyone who is either not brave or not patient is quiet. Everyone who is wise is either not curious or tall and vice versa. Everyone who is not wise is happy and vice versa. Everyone who is happy is not quiet and vice versa. If someone is brave or old then lucy is not old or wise and vice versa. 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. If john is brave then paul is patient or quiet and vice versa. If paul is either humble or brave then someone is either quiet or not happy and vice versa. If someone is both not tall and tall then lucy is happy and vice versa. Someone is either not tall or not strong. Someone is wise or not generous. Fred is either not wise or rich. Alice is both not creative and happy. Someone is either not funny or not creative. Paul is both creative and not tall. John is either not quiet or rich. Paul is humble or funny. | Lucy is quiet. | entailment | (![X]:(~patient(X)=>(tall(X)|kind(X))))&
((?[X]:((~brave(X)&~strong(X))))=>(?[X]:(wise(X))))&
(![X]:((~old(X)<~>creative(X))<=>(brave(X)&~wise(X))))&
(![X]:(creative(X)<=>wise(X)))&
((?[X]:((brave(X)&~strong(X))))<=>(?[X]:((~happy(X)<~>tall(X)))))&
(![X]:((~brave(X)<~>~patient(X))=>quiet(X)))&
(![X]:(wise(X)<=>(~curious(X)<~>tall(X))))&
(![X]:(~wise(X)<=>happy(X)))&
(![X]:(happy(X)<=>~quiet(X)))&
((?[X]:((brave(X)|old(X))))<=>((~old(lucy)|wise(lucy))))&
(((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)))))&
((brave(john))<=>((patient(paul)|quiet(paul))))&
(((humble(paul)<~>brave(paul)))<=>(?[X]:((quiet(X)<~>~happy(X)))))&
((?[X]:((~tall(X)&tall(X))))<=>(happy(lucy)))&
(?[X]:((~tall(X)<~>~strong(X))))&
(?[X]:((wise(X)|~generous(X))))&
((~wise(fred)<~>rich(fred)))&
((~creative(alice)&happy(alice)))&
(?[X]:((~funny(X)<~>~creative(X))))&
((creative(paul)&~tall(paul)))&
((~quiet(john)<~>rich(john)))&
((humble(paul)|funny(paul))) | quiet(lucy) | [
"p8",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4636324468382988581405300
% SZS output start Proof for 4636324468382988581405300
9. ! [X0] : (happy(X0) <=> ~quiet(X0)) [input p8]
16. ? [X0] : (tall(X0) & ~tall(X0)) <=> happy(lucy) [input p15]
25. ~quiet(lucy) [input hypothesis]
50. ! [X0] : ((happy(X0) | quiet(X0)) & (~quiet(X0) | ~happy(X0))) [nnf transformation 9]
68. (? [X0] : (tall(X0) & ~tall(X0)) | ~happy(lucy)) & (happy(lucy) | ! [X0] : (~tall(X0) | tall(X0))) [nnf transformation 16]
69. (? [X0] : (tall(X0) & ~tall(X0)) | ~happy(lucy)) & (happy(lucy) | ! [X1] : (~tall(X1) | tall(X1))) [rectify 68]
70. ? [X0] : (tall(X0) & ~tall(X0)) => (tall(sK6) & ~tall(sK6)) [choice axiom]
71. ((tall(sK6) & ~tall(sK6)) | ~happy(lucy)) & (happy(lucy) | ! [X1] : (~tall(X1) | tall(X1))) [skolemisation 69,70]
105. quiet(X0) | happy(X0) [cnf transformation 50]
128. ~tall(sK6) | ~happy(lucy) [cnf transformation 71]
129. tall(sK6) | ~happy(lucy) [cnf transformation 71]
143. ~quiet(lucy) [cnf transformation 25]
277. 29 <=> happy(lucy) [avatar definition]
279. ~happy(lucy) <- (~29) [avatar component clause 277]
281. 30 <=> tall(sK6) [avatar definition]
284. ~29 | 30 [avatar split clause 129,281,277]
285. ~29 | ~30 [avatar split clause 128,281,277]
345. happy(lucy) [resolution 105,143]
348. $false <- (~29) [subsumption resolution 345,279]
349. 29 [avatar contradiction clause 348]
350. $false [avatar sat refutation 284,285,349]
% SZS output end Proof for 4636324468382988581405300
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not old is either wise or patient.
If someone is either patient or not kind then mary is both not humble and not creative and vice versa.
If someone is either funny or not wise then alice is happy and vice versa.
Everyone who is both not quiet and wise is not curious and vice versa.
If someone is both not brave and humble then mary is old or not happy.
If mary is strong then someone is not kind or not tall and vice versa.
Everyone who is not brave is both tall and not rich and vice versa.
Everyone who is not calm or not patient is creative and vice versa.
If someone is either not calm or generous then mary is both not patient and not funny and vice versa.
If someone is not rich or strong then mary is either not kind or humble and vice versa.
If mary is both not funny and strong then john is not rich or not creative and vice versa.
If someone is funny then someone is either humble or tall and vice versa.
Everyone who is either generous or not humble is both not funny and rich and vice versa.
Everyone who is either not happy or not patient is tall or wise.
Everyone who is quiet or humble is humble.
If someone is quiet then alice is curious.
Mary is both quiet and rich.
Paul is not tall or old.
Someone is not wise.
Mary is either not generous or strong.
John is not funny. | Mary is not patient. | entailment | (![X]:(~old(X)=>(wise(X)<~>patient(X))))&
((?[X]:((patient(X)<~>~kind(X))))<=>((~humble(mary)&~creative(mary))))&
((?[X]:((funny(X)<~>~wise(X))))<=>(happy(alice)))&
(![X]:((~quiet(X)&wise(X))<=>~curious(X)))&
((?[X]:((~brave(X)&humble(X))))=>((old(mary)|~happy(mary))))&
((strong(mary))<=>(?[X]:((~kind(X)|~tall(X)))))&
(![X]:(~brave(X)<=>(tall(X)&~rich(X))))&
(![X]:((~calm(X)|~patient(X))<=>creative(X)))&
((?[X]:((~calm(X)<~>generous(X))))<=>((~patient(mary)&~funny(mary))))&
((?[X]:((~rich(X)|strong(X))))<=>((~kind(mary)<~>humble(mary))))&
(((~funny(mary)&strong(mary)))<=>((~rich(john)|~creative(john))))&
((?[X]:(funny(X)))<=>(?[X]:((humble(X)<~>tall(X)))))&
(![X]:((generous(X)<~>~humble(X))<=>(~funny(X)&rich(X))))&
(![X]:((~happy(X)<~>~patient(X))=>(tall(X)|wise(X))))&
(![X]:((quiet(X)|humble(X))=>humble(X)))&
((?[X]:(quiet(X)))=>(curious(alice)))&
((quiet(mary)&rich(mary)))&
((~tall(paul)|old(paul)))&
(?[X]:(~wise(X)))&
((~generous(mary)<~>strong(mary)))&
(~funny(john)) | ~patient(mary) | [
"p1",
"p5",
"p9",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 279249768693331942553221
% SZS output start Proof for 279249768693331942553221
2. ? [X0] : (patient(X0) <~> ~kind(X0)) <=> (~creative(mary) & ~humble(mary)) [input p1]
6. strong(mary) <=> ? [X0] : (~tall(X0) | ~kind(X0)) [input p5]
10. ? [X0] : (strong(X0) | ~rich(X0)) <=> (~kind(mary) <~> humble(mary)) [input p9]
15. ! [X0] : ((humble(X0) | quiet(X0)) => humble(X0)) [input p14]
17. rich(mary) & quiet(mary) [input p16]
22. patient(mary) [input hypothesis]
34. ! [X0] : (humble(X0) | (~humble(X0) & ~quiet(X0))) [ennf transformation 15]
36. (? [X0] : ((kind(X0) | ~patient(X0)) & (~kind(X0) | patient(X0))) | (creative(mary) | humble(mary))) & ((~creative(mary) & ~humble(mary)) | ! [X0] : ((patient(X0) | kind(X0)) & (~kind(X0) | ~patient(X0)))) [nnf transformation 2]
37. (? [X0] : ((kind(X0) | ~patient(X0)) & (~kind(X0) | patient(X0))) | creative(mary) | humble(mary)) & ((~creative(mary) & ~humble(mary)) | ! [X0] : ((patient(X0) | kind(X0)) & (~kind(X0) | ~patient(X0)))) [flattening 36]
38. (? [X0] : ((kind(X0) | ~patient(X0)) & (~kind(X0) | patient(X0))) | creative(mary) | humble(mary)) & ((~creative(mary) & ~humble(mary)) | ! [X1] : ((patient(X1) | kind(X1)) & (~kind(X1) | ~patient(X1)))) [rectify 37]
39. ? [X0] : ((kind(X0) | ~patient(X0)) & (~kind(X0) | patient(X0))) => ((kind(sK0) | ~patient(sK0)) & (~kind(sK0) | patient(sK0))) [choice axiom]
40. (((kind(sK0) | ~patient(sK0)) & (~kind(sK0) | patient(sK0))) | creative(mary) | humble(mary)) & ((~creative(mary) & ~humble(mary)) | ! [X1] : ((patient(X1) | kind(X1)) & (~kind(X1) | ~patient(X1)))) [skolemisation 38,39]
45. (strong(mary) | ! [X0] : (tall(X0) & kind(X0))) & (? [X0] : (~tall(X0) | ~kind(X0)) | ~strong(mary)) [nnf transformation 6]
46. (strong(mary) | ! [X0] : (tall(X0) & kind(X0))) & (? [X1] : (~tall(X1) | ~kind(X1)) | ~strong(mary)) [rectify 45]
47. ? [X1] : (~tall(X1) | ~kind(X1)) => (~tall(sK2) | ~kind(sK2)) [choice axiom]
48. (strong(mary) | ! [X0] : (tall(X0) & kind(X0))) & ((~tall(sK2) | ~kind(sK2)) | ~strong(mary)) [skolemisation 46,47]
56. (? [X0] : (strong(X0) | ~rich(X0)) | ((~kind(mary) | ~humble(mary)) & (humble(mary) | kind(mary)))) & (((~humble(mary) | kind(mary)) & (humble(mary) | ~kind(mary))) | ! [X0] : (~strong(X0) & rich(X0))) [nnf transformation 10]
57. (? [X0] : (strong(X0) | ~rich(X0)) | ((~kind(mary) | ~humble(mary)) & (humble(mary) | kind(mary)))) & (((~humble(mary) | kind(mary)) & (humble(mary) | ~kind(mary))) | ! [X1] : (~strong(X1) & rich(X1))) [rectify 56]
58. ? [X0] : (strong(X0) | ~rich(X0)) => (strong(sK4) | ~rich(sK4)) [choice axiom]
59. ((strong(sK4) | ~rich(sK4)) | ((~kind(mary) | ~humble(mary)) & (humble(mary) | kind(mary)))) & (((~humble(mary) | kind(mary)) & (humble(mary) | ~kind(mary))) | ! [X1] : (~strong(X1) & rich(X1))) [skolemisation 57,58]
73. ~humble(mary) | ~kind(X1) | ~patient(X1) [cnf transformation 40]
85. strong(mary) | kind(X0) [cnf transformation 48]
99. ~humble(mary) | kind(mary) | ~strong(X1) [cnf transformation 59]
119. ~quiet(X0) | humble(X0) [cnf transformation 34]
122. quiet(mary) [cnf transformation 17]
128. patient(mary) [cnf transformation 22]
130. 1 <=> humble(mary) [avatar definition]
152. 6 <=> ! [X1] : (~kind(X1) | ~patient(X1)) [avatar definition]
153. ~kind(X1) | ~patient(X1) <- (6) [avatar component clause 152]
156. 6 | ~1 [avatar split clause 73,130,152]
183. 13 <=> strong(mary) [avatar definition]
185. strong(mary) <- (13) [avatar component clause 183]
188. 14 <=> ! [X0] : kind(X0) [avatar definition]
189. kind(X0) <- (14) [avatar component clause 188]
190. 14 | 13 [avatar split clause 85,183,188]
201. 17 <=> patient(mary) [avatar definition]
203. patient(mary) <- (17) [avatar component clause 201]
229. 23 <=> kind(mary) [avatar definition]
230. kind(mary) <- (23) [avatar component clause 229]
243. 26 <=> ! [X1] : ~strong(X1) [avatar definition]
244. ~strong(X1) <- (26) [avatar component clause 243]
245. 26 | 23 | ~1 [avatar split clause 99,130,229,243]
304. 17 [avatar split clause 128,201]
310. ~patient(X1) <- (6, 14) [subsumption resolution 153,189]
321. $false <- (6, 14, 17) [resolution 310,203]
322. ~6 | ~14 | ~17 [avatar contradiction clause 321]
325. $false <- (13, 26) [subsumption resolution 185,244]
326. ~13 | ~26 [avatar contradiction clause 325]
327. humble(mary) [resolution 119,122]
330. 1 [avatar split clause 327,130]
333. ~patient(mary) <- (6, 23) [resolution 153,230]
335. $false <- (6, 17, 23) [subsumption resolution 333,203]
336. ~6 | ~17 | ~23 [avatar contradiction clause 335]
337. $false [avatar sat refutation 156,190,245,304,322,326,330,336]
% SZS output end Proof for 279249768693331942553221
% ------------------------------
% 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 creative or happy is either not brave or calm. Everyone who is not old is either not quiet or not generous and vice versa. If someone is either not quiet or not rich then susan is both not rich and curious and vice versa. If someone is both not funny and patient then alice is not humble and vice versa. Everyone who is happy or old is wise or not generous and vice versa. If someone is happy or tall then someone is both not old and calm and vice versa. Everyone who is both curious and not curious is either not humble or brave. If someone is happy then someone is both not strong and wise. If john is not brave then someone is not patient or humble. Everyone who is both not tall and not strong is not brave or not kind. If someone is both not humble and not happy then someone is brave or not patient and vice versa. If someone is both not quiet and patient then alice is either funny or not humble and vice versa. Everyone who is tall is patient and vice versa. Everyone who is strong or wise is both not quiet and not creative and vice versa. Everyone who is strong or creative is either calm or creative and vice versa. If someone is patient then john is both not wise and not funny and vice versa. Someone is not generous or not happy. Someone is not happy. Mary is brave. Susan is not strong or strong. Someone is both not happy and creative. Paul is old or curious. Someone is not tall or generous. Fred is generous or curious. | John is happy. | neutral | (![X]:((creative(X)<~>happy(X))=>(~brave(X)<~>calm(X))))&
(![X]:(~old(X)<=>(~quiet(X)<~>~generous(X))))&
((?[X]:((~quiet(X)<~>~rich(X))))<=>((~rich(susan)&curious(susan))))&
((?[X]:((~funny(X)&patient(X))))<=>(~humble(alice)))&
(![X]:((happy(X)|old(X))<=>(wise(X)|~generous(X))))&
((?[X]:((happy(X)|tall(X))))<=>(?[X]:((~old(X)&calm(X)))))&
(![X]:((curious(X)&~curious(X))=>(~humble(X)<~>brave(X))))&
((?[X]:(happy(X)))=>(?[X]:((~strong(X)&wise(X)))))&
((~brave(john))=>(?[X]:((~patient(X)|humble(X)))))&
(![X]:((~tall(X)&~strong(X))=>(~brave(X)|~kind(X))))&
((?[X]:((~humble(X)&~happy(X))))<=>(?[X]:((brave(X)|~patient(X)))))&
((?[X]:((~quiet(X)&patient(X))))<=>((funny(alice)<~>~humble(alice))))&
(![X]:(tall(X)<=>patient(X)))&
(![X]:((strong(X)|wise(X))<=>(~quiet(X)&~creative(X))))&
(![X]:((strong(X)|creative(X))<=>(calm(X)<~>creative(X))))&
((?[X]:(patient(X)))<=>((~wise(john)&~funny(john))))&
(?[X]:((~generous(X)|~happy(X))))&
(?[X]:(~happy(X)))&
(brave(mary))&
((~strong(susan)|strong(susan)))&
(?[X]:((~happy(X)&creative(X))))&
((old(paul)|curious(paul)))&
(?[X]:((~tall(X)|generous(X))))&
((generous(fred)|curious(fred))) | happy(john) | [] | null | 0 |
Everyone who is not quiet or humble is either not quiet or calm and vice versa. Everyone who is either wise or not humble is either not generous or wise and vice versa. Everyone who is not old or generous is either tall or wise and vice versa. Everyone who is not generous or generous is not old and vice versa. Everyone who is either patient or not kind is either quiet or not wise and vice versa. Everyone who is either generous or calm is either not kind or quiet and vice versa. If paul is either not rich or happy then someone is both not quiet and quiet. Everyone who is either not patient or patient is both not old and not quiet. Everyone who is not patient is either not creative or funny and vice versa. If susan is either not happy or kind then susan is either not tall or not old and vice versa. Everyone who is either old or not generous is calm or happy. If someone is not happy or tall then someone is either patient or not kind. If fred is not happy then fred is either brave or not quiet and vice versa. Everyone who is strong is both strong and not quiet and vice versa. If susan is old or patient then alice is both not curious and curious. Someone is both curious and not brave. Someone is not tall or not humble. Paul is not kind. Mary is not creative. Susan is either brave or not happy. | Alice is not wise. | neutral | (![X]:((~quiet(X)|humble(X))<=>(~quiet(X)<~>calm(X))))&
(![X]:((wise(X)<~>~humble(X))<=>(~generous(X)<~>wise(X))))&
(![X]:((~old(X)|generous(X))<=>(tall(X)<~>wise(X))))&
(![X]:((~generous(X)|generous(X))<=>~old(X)))&
(![X]:((patient(X)<~>~kind(X))<=>(quiet(X)<~>~wise(X))))&
(![X]:((generous(X)<~>calm(X))<=>(~kind(X)<~>quiet(X))))&
(((~rich(paul)<~>happy(paul)))=>(?[X]:((~quiet(X)&quiet(X)))))&
(![X]:((~patient(X)<~>patient(X))=>(~old(X)&~quiet(X))))&
(![X]:(~patient(X)<=>(~creative(X)<~>funny(X))))&
(((~happy(susan)<~>kind(susan)))<=>((~tall(susan)<~>~old(susan))))&
(![X]:((old(X)<~>~generous(X))=>(calm(X)|happy(X))))&
((?[X]:((~happy(X)|tall(X))))=>(?[X]:((patient(X)<~>~kind(X)))))&
((~happy(fred))<=>((brave(fred)<~>~quiet(fred))))&
(![X]:(strong(X)<=>(strong(X)&~quiet(X))))&
(((old(susan)|patient(susan)))=>((~curious(alice)&curious(alice))))&
(?[X]:((curious(X)&~brave(X))))&
(?[X]:((~tall(X)|~humble(X))))&
(~kind(paul))&
(~creative(mary))&
((brave(susan)<~>~happy(susan))) | ~wise(alice) | [] | null | 0 |
Everyone who is both humble and brave is not patient or old and vice versa.
If someone is both tall and generous then someone is either humble or not funny and vice versa.
If mary is both funny and not patient then mary is both patient and not brave.
If someone is patient then alice is both not brave and kind and vice versa.
If susan is not generous then someone is either not calm or strong.
Everyone who is not kind is either not brave or not kind and vice versa.
Everyone who is either humble or kind is either not quiet or brave.
If someone is quiet or not brave then alice is both not curious and happy.
Everyone who is calm is both strong and not generous.
Everyone who is happy or quiet is either humble or quiet.
If john is not humble or not curious then mary is kind or not generous.
Everyone who is both not strong and old is calm or not kind.
Everyone who is humble or strong is both wise and not curious and vice versa.
If someone is rich or not curious then john is not funny and vice versa.
Everyone who is not tall is not wise and vice versa.
Everyone who is either humble or not generous is rich.
Fred is either brave or quiet.
Someone is not brave or tall.
Someone is not old or kind.
Someone is either curious or not creative.
Alice is both not funny and not quiet. | Susan is quiet. | contradiction | (![X]:((humble(X)&brave(X))<=>(~patient(X)|old(X))))&
((?[X]:((tall(X)&generous(X))))<=>(?[X]:((humble(X)<~>~funny(X)))))&
(((funny(mary)&~patient(mary)))=>((patient(mary)&~brave(mary))))&
((?[X]:(patient(X)))<=>((~brave(alice)&kind(alice))))&
((~generous(susan))=>(?[X]:((~calm(X)<~>strong(X)))))&
(![X]:(~kind(X)<=>(~brave(X)<~>~kind(X))))&
(![X]:((humble(X)<~>kind(X))=>(~quiet(X)<~>brave(X))))&
((?[X]:((quiet(X)|~brave(X))))=>((~curious(alice)&happy(alice))))&
(![X]:(calm(X)=>(strong(X)&~generous(X))))&
(![X]:((happy(X)|quiet(X))=>(humble(X)<~>quiet(X))))&
(((~humble(john)|~curious(john)))=>((kind(mary)|~generous(mary))))&
(![X]:((~strong(X)&old(X))=>(calm(X)|~kind(X))))&
(![X]:((humble(X)|strong(X))<=>(wise(X)&~curious(X))))&
((?[X]:((rich(X)|~curious(X))))<=>(~funny(john)))&
(![X]:(~tall(X)<=>~wise(X)))&
(![X]:((humble(X)<~>~generous(X))=>rich(X)))&
((brave(fred)<~>quiet(fred)))&
(?[X]:((~brave(X)|tall(X))))&
(?[X]:((~old(X)|kind(X))))&
(?[X]:((curious(X)<~>~creative(X))))&
((~funny(alice)&~quiet(alice))) | quiet(susan) | [
"p0",
"p3",
"p5",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 6134936621115705108320633
% SZS output start Proof for 6134936621115705108320633
1. ! [X0] : ((brave(X0) & humble(X0)) <=> (old(X0) | ~patient(X0))) [input p0]
4. ? [X0] : patient(X0) <=> (kind(alice) & ~brave(alice)) [input p3]
6. ! [X0] : (~kind(X0) <=> (~brave(X0) <~> ~kind(X0))) [input p5]
10. ! [X0] : ((quiet(X0) | happy(X0)) => (humble(X0) <~> quiet(X0))) [input p9]
22. quiet(susan) [input hypothesis]
30. ! [X0] : ((humble(X0) <~> quiet(X0)) | (~quiet(X0) & ~happy(X0))) [ennf transformation 10]
36. ! [X0] : (((brave(X0) & humble(X0)) | (~old(X0) & patient(X0))) & ((old(X0) | ~patient(X0)) | (~brave(X0) | ~humble(X0)))) [nnf transformation 1]
37. ! [X0] : (((brave(X0) & humble(X0)) | (~old(X0) & patient(X0))) & (old(X0) | ~patient(X0) | ~brave(X0) | ~humble(X0))) [flattening 36]
43. (? [X0] : patient(X0) | (~kind(alice) | brave(alice))) & ((kind(alice) & ~brave(alice)) | ! [X0] : ~patient(X0)) [nnf transformation 4]
44. (? [X0] : patient(X0) | ~kind(alice) | brave(alice)) & ((kind(alice) & ~brave(alice)) | ! [X0] : ~patient(X0)) [flattening 43]
45. (? [X0] : patient(X0) | ~kind(alice) | brave(alice)) & ((kind(alice) & ~brave(alice)) | ! [X1] : ~patient(X1)) [rectify 44]
46. ? [X0] : patient(X0) => patient(sK2) [choice axiom]
47. (patient(sK2) | ~kind(alice) | brave(alice)) & ((kind(alice) & ~brave(alice)) | ! [X1] : ~patient(X1)) [skolemisation 45,46]
51. ! [X0] : ((~kind(X0) | ((~brave(X0) | kind(X0)) & (~kind(X0) | brave(X0)))) & (((kind(X0) | brave(X0)) & (~kind(X0) | ~brave(X0))) | kind(X0))) [nnf transformation 6]
53. ! [X0] : (((~quiet(X0) | ~humble(X0)) & (quiet(X0) | humble(X0))) | (~quiet(X0) & ~happy(X0))) [nnf transformation 30]
71. patient(X0) | humble(X0) [cnf transformation 37]
83. ~brave(alice) | ~patient(X1) [cnf transformation 47]
89. kind(X0) | brave(X0) | kind(X0) [cnf transformation 51]
90. ~kind(X0) | ~kind(X0) | brave(X0) [cnf transformation 51]
105. ~quiet(X0) | ~humble(X0) | ~quiet(X0) [cnf transformation 53]
129. quiet(susan) [cnf transformation 22]
130. ~quiet(X0) | ~humble(X0) [duplicate literal removal 105]
131. kind(X0) | brave(X0) [duplicate literal removal 89]
132. ~kind(X0) | brave(X0) [duplicate literal removal 90]
177. 10 <=> brave(alice) [avatar definition]
178. ~brave(alice) <- (~10) [avatar component clause 177]
190. 13 <=> ! [X1] : ~patient(X1) [avatar definition]
191. ~patient(X1) <- (13) [avatar component clause 190]
193. 13 | ~10 [avatar split clause 83,177,190]
208. brave(X0) [subsumption resolution 131,132]
285. $false <- (~10) [subsumption resolution 178,208]
286. 10 [avatar contradiction clause 285]
291. humble(X0) <- (13) [resolution 71,191]
300. ~humble(susan) [resolution 130,129]
301. $false <- (13) [subsumption resolution 300,291]
302. ~13 [avatar contradiction clause 301]
303. $false [avatar sat refutation 193,286,302]
% SZS output end Proof for 6134936621115705108320633
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not funny is both strong and not quiet and vice versa.
Everyone who is either rich or humble is both strong and not creative.
Everyone who is curious or not calm is not quiet or not happy.
If someone is patient or kind then paul is kind.
Everyone who is humble or tall is tall or funny.
Everyone who is either not brave or rich is not rich or patient and vice versa.
Everyone who is wise or not patient is both curious and humble.
Everyone who is generous or not quiet is both not patient and wise.
If lucy is funny or not creative then someone is either not curious or not brave and vice versa.
Everyone who is either creative or rich is not funny or old and vice versa.
Everyone who is either not tall or not kind is both not strong and not patient and vice versa.
If susan is both curious and generous then someone is curious and vice versa.
Everyone who is both generous and not humble is not strong and vice versa.
Everyone who is either creative or old is both tall and humble and vice versa.
Everyone who is either strong or creative is both generous and curious.
If someone is not tall then fred is not wise or not rich and vice versa.
Someone is curious.
Someone is not curious or happy.
Fred is either not happy or not rich.
Someone is not happy or happy.
Someone is either brave or kind.
Mary is either brave or not generous.
Susan is either not quiet or not old.
Someone is either creative or strong. | Mary is funny. | entailment | (![X]:(~funny(X)<=>(strong(X)&~quiet(X))))&
(![X]:((rich(X)<~>humble(X))=>(strong(X)&~creative(X))))&
(![X]:((curious(X)|~calm(X))=>(~quiet(X)|~happy(X))))&
((?[X]:((patient(X)|kind(X))))=>(kind(paul)))&
(![X]:((humble(X)|tall(X))=>(tall(X)|funny(X))))&
(![X]:((~brave(X)<~>rich(X))<=>(~rich(X)|patient(X))))&
(![X]:((wise(X)|~patient(X))=>(curious(X)&humble(X))))&
(![X]:((generous(X)|~quiet(X))=>(~patient(X)&wise(X))))&
(((funny(lucy)|~creative(lucy)))<=>(?[X]:((~curious(X)<~>~brave(X)))))&
(![X]:((creative(X)<~>rich(X))<=>(~funny(X)|old(X))))&
(![X]:((~tall(X)<~>~kind(X))<=>(~strong(X)&~patient(X))))&
(((curious(susan)&generous(susan)))<=>(?[X]:(curious(X))))&
(![X]:((generous(X)&~humble(X))<=>~strong(X)))&
(![X]:((creative(X)<~>old(X))<=>(tall(X)&humble(X))))&
(![X]:((strong(X)<~>creative(X))=>(generous(X)&curious(X))))&
((?[X]:(~tall(X)))<=>((~wise(fred)|~rich(fred))))&
(?[X]:(curious(X)))&
(?[X]:((~curious(X)|happy(X))))&
((~happy(fred)<~>~rich(fred)))&
(?[X]:((~happy(X)|happy(X))))&
(?[X]:((brave(X)<~>kind(X))))&
((brave(mary)<~>~generous(mary)))&
((~quiet(susan)<~>~old(susan)))&
(?[X]:((creative(X)<~>strong(X)))) | funny(mary) | [
"p0",
"p1",
"p5",
"p6",
"p7",
"p9",
"p12",
"p14",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 7729819005773817929123171
% SZS output start Proof for 7729819005773817929123171
1. ! [X0] : (~funny(X0) <=> (~quiet(X0) & strong(X0))) [input p0]
2. ! [X0] : ((rich(X0) <~> humble(X0)) => (~creative(X0) & strong(X0))) [input p1]
6. ! [X0] : ((~brave(X0) <~> rich(X0)) <=> (patient(X0) | ~rich(X0))) [input p5]
7. ! [X0] : ((~patient(X0) | wise(X0)) => (humble(X0) & curious(X0))) [input p6]
8. ! [X0] : ((~quiet(X0) | generous(X0)) => (wise(X0) & ~patient(X0))) [input p7]
10. ! [X0] : ((creative(X0) <~> rich(X0)) <=> (old(X0) | ~funny(X0))) [input p9]
13. ! [X0] : ((~humble(X0) & generous(X0)) <=> ~strong(X0)) [input p12]
15. ! [X0] : ((strong(X0) <~> creative(X0)) => (curious(X0) & generous(X0))) [input p14]
22. brave(mary) <~> ~generous(mary) [input p21]
25. ~funny(mary) [input hypothesis]
27. ! [X0] : ((~creative(X0) & strong(X0)) | (rich(X0) <=> humble(X0))) [ennf transformation 2]
33. ! [X0] : ((humble(X0) & curious(X0)) | (patient(X0) & ~wise(X0))) [ennf transformation 7]
34. ! [X0] : ((wise(X0) & ~patient(X0)) | (quiet(X0) & ~generous(X0))) [ennf transformation 8]
35. ! [X0] : ((curious(X0) & generous(X0)) | (strong(X0) <=> creative(X0))) [ennf transformation 15]
36. ! [X0] : ((~funny(X0) | (quiet(X0) | ~strong(X0))) & ((~quiet(X0) & strong(X0)) | funny(X0))) [nnf transformation 1]
37. ! [X0] : ((~funny(X0) | quiet(X0) | ~strong(X0)) & ((~quiet(X0) & strong(X0)) | funny(X0))) [flattening 36]
38. ! [X0] : ((~creative(X0) & strong(X0)) | ((rich(X0) | ~humble(X0)) & (humble(X0) | ~rich(X0)))) [nnf transformation 27]
39. ! [X0] : ((((~rich(X0) | brave(X0)) & (rich(X0) | ~brave(X0))) | (~patient(X0) & rich(X0))) & ((patient(X0) | ~rich(X0)) | ((~brave(X0) | ~rich(X0)) & (rich(X0) | brave(X0))))) [nnf transformation 6]
40. ! [X0] : ((((~rich(X0) | brave(X0)) & (rich(X0) | ~brave(X0))) | (~patient(X0) & rich(X0))) & (patient(X0) | ~rich(X0) | ((~brave(X0) | ~rich(X0)) & (rich(X0) | brave(X0))))) [flattening 39]
46. ! [X0] : ((((~rich(X0) | ~creative(X0)) & (rich(X0) | creative(X0))) | (~old(X0) & funny(X0))) & ((old(X0) | ~funny(X0)) | ((creative(X0) | ~rich(X0)) & (rich(X0) | ~creative(X0))))) [nnf transformation 10]
47. ! [X0] : ((((~rich(X0) | ~creative(X0)) & (rich(X0) | creative(X0))) | (~old(X0) & funny(X0))) & (old(X0) | ~funny(X0) | ((creative(X0) | ~rich(X0)) & (rich(X0) | ~creative(X0))))) [flattening 46]
55. ! [X0] : (((~humble(X0) & generous(X0)) | strong(X0)) & (~strong(X0) | (humble(X0) | ~generous(X0)))) [nnf transformation 13]
56. ! [X0] : (((~humble(X0) & generous(X0)) | strong(X0)) & (~strong(X0) | humble(X0) | ~generous(X0))) [flattening 55]
59. ! [X0] : ((curious(X0) & generous(X0)) | ((strong(X0) | ~creative(X0)) & (creative(X0) | ~strong(X0)))) [nnf transformation 35]
75. (generous(mary) | ~brave(mary)) & (~generous(mary) | brave(mary)) [nnf transformation 22]
81. ~quiet(X0) | funny(X0) [cnf transformation 37]
86. ~creative(X0) | rich(X0) | ~humble(X0) [cnf transformation 38]
93. patient(X0) | ~rich(X0) | ~brave(X0) | ~rich(X0) [cnf transformation 40]
94. rich(X0) | ~brave(X0) | rich(X0) [cnf transformation 40]
101. patient(X0) | humble(X0) [cnf transformation 33]
102. ~generous(X0) | ~patient(X0) [cnf transformation 34]
103. ~patient(X0) | quiet(X0) [cnf transformation 34]
116. ~creative(X0) | ~rich(X0) | funny(X0) [cnf transformation 47]
128. generous(X0) | strong(X0) [cnf transformation 56]
136. generous(X0) | creative(X0) | ~strong(X0) [cnf transformation 59]
150. ~generous(mary) | brave(mary) [cnf transformation 75]
156. ~funny(mary) [cnf transformation 25]
157. patient(X0) | ~rich(X0) | ~brave(X0) [duplicate literal removal 93]
158. ~brave(X0) | rich(X0) [duplicate literal removal 94]
171. ~brave(X0) | patient(X0) [subsumption resolution 157,158]
218. generous(X0) | creative(X0) [subsumption resolution 136,128]
263. 23 <=> brave(mary) [avatar definition]
264. brave(mary) <- (23) [avatar component clause 263]
267. 24 <=> generous(mary) [avatar definition]
268. ~generous(mary) <- (~24) [avatar component clause 267]
269. generous(mary) <- (24) [avatar component clause 267]
271. 23 | ~24 [avatar split clause 150,267,263]
298. humble(X0) | quiet(X0) [resolution 103,101]
328. creative(mary) <- (~24) [resolution 218,268]
352. 31 <=> rich(mary) [avatar definition]
353. rich(mary) <- (31) [avatar component clause 352]
354. ~rich(mary) <- (~31) [avatar component clause 352]
356. 32 <=> humble(mary) [avatar definition]
357. ~humble(mary) <- (~32) [avatar component clause 356]
361. rich(mary) | ~humble(mary) <- (~24) [resolution 86,328]
364. ~humble(mary) <- (~24, ~31) [subsumption resolution 361,354]
365. ~32 | 24 | 31 [avatar split clause 364,352,267,356]
390. quiet(mary) <- (~32) [resolution 298,357]
494. 46 <=> patient(mary) [avatar definition]
495. patient(mary) <- (46) [avatar component clause 494]
826. funny(mary) <- (~32) [resolution 390,81]
827. $false <- (~32) [subsumption resolution 826,156]
828. 32 [avatar contradiction clause 827]
832. patient(mary) <- (23) [resolution 264,171]
836. 46 | ~23 [avatar split clause 832,263,494]
845. creative(mary) <- (~24) [resolution 268,218]
852. ~rich(mary) | funny(mary) <- (~24) [resolution 845,116]
856. funny(mary) <- (~24, 31) [subsumption resolution 852,353]
857. $false <- (~24, 31) [subsumption resolution 856,156]
858. 24 | ~31 [avatar contradiction clause 857]
865. ~patient(mary) <- (24) [resolution 269,102]
866. $false <- (24, 46) [subsumption resolution 865,495]
867. ~24 | ~46 [avatar contradiction clause 866]
868. $false [avatar sat refutation 271,365,828,836,858,867]
% SZS output end Proof for 7729819005773817929123171
% ------------------------------
% 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 tall or not tall is both quiet and not wise and vice versa.
Everyone who is either not kind or not curious is old.
If someone is not old or not brave then alice is either creative or tall.
Everyone who is not old is not brave or kind and vice versa.
If susan is either creative or not happy then someone is both happy and generous.
Everyone who is not old is both humble and not happy.
If someone is quiet then mary is either brave or not tall.
If mary is humble then someone is not rich or wise.
Everyone who is not rich or not creative is calm or wise and vice versa.
Everyone who is either not rich or not strong is both not funny and creative.
Everyone who is not calm is both not calm and humble and vice versa.
If someone is not old then someone is brave.
Everyone who is both not patient and humble is not happy or tall and vice versa.
Everyone who is either calm or creative is either strong or tall.
Everyone who is rich is either not wise or creative.
Mary is either happy or not calm.
Someone is either not wise or not tall.
Susan is either not funny or not generous.
Susan is not funny or humble.
Someone is either generous or not rich.
John is either patient or wise.
Someone is either not happy or not generous.
Mary is both not generous and funny. | Mary is rich. | contradiction | (![X]:((tall(X)|~tall(X))<=>(quiet(X)&~wise(X))))&
(![X]:((~kind(X)<~>~curious(X))=>old(X)))&
((?[X]:((~old(X)|~brave(X))))=>((creative(alice)<~>tall(alice))))&
(![X]:(~old(X)<=>(~brave(X)|kind(X))))&
(((creative(susan)<~>~happy(susan)))=>(?[X]:((happy(X)&generous(X)))))&
(![X]:(~old(X)=>(humble(X)&~happy(X))))&
((?[X]:(quiet(X)))=>((brave(mary)<~>~tall(mary))))&
((humble(mary))=>(?[X]:((~rich(X)|wise(X)))))&
(![X]:((~rich(X)|~creative(X))<=>(calm(X)|wise(X))))&
(![X]:((~rich(X)<~>~strong(X))=>(~funny(X)&creative(X))))&
(![X]:(~calm(X)<=>(~calm(X)&humble(X))))&
((?[X]:(~old(X)))=>(?[X]:(brave(X))))&
(![X]:((~patient(X)&humble(X))<=>(~happy(X)|tall(X))))&
(![X]:((calm(X)<~>creative(X))=>(strong(X)<~>tall(X))))&
(![X]:(rich(X)=>(~wise(X)<~>creative(X))))&
((happy(mary)<~>~calm(mary)))&
(?[X]:((~wise(X)<~>~tall(X))))&
((~funny(susan)<~>~generous(susan)))&
((~funny(susan)|humble(susan)))&
(?[X]:((generous(X)<~>~rich(X))))&
((patient(john)<~>wise(john)))&
(?[X]:((~happy(X)<~>~generous(X))))&
((~generous(mary)&funny(mary))) | rich(mary) | [
"p0",
"p3",
"p5",
"p6",
"p8",
"p9",
"p13",
"p14",
"p15",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 6306619349412184742323521
% SZS output start Proof for 6306619349412184742323521
1. ! [X0] : ((~tall(X0) | tall(X0)) <=> (~wise(X0) & quiet(X0))) [input p0]
4. ! [X0] : (~old(X0) <=> (kind(X0) | ~brave(X0))) [input p3]
6. ! [X0] : (~old(X0) => (~happy(X0) & humble(X0))) [input p5]
7. ? [X0] : quiet(X0) => (brave(mary) <~> ~tall(mary)) [input p6]
9. ! [X0] : ((~creative(X0) | ~rich(X0)) <=> (wise(X0) | calm(X0))) [input p8]
10. ! [X0] : ((~rich(X0) <~> ~strong(X0)) => (creative(X0) & ~funny(X0))) [input p9]
14. ! [X0] : ((calm(X0) <~> creative(X0)) => (strong(X0) <~> tall(X0))) [input p13]
15. ! [X0] : (rich(X0) => (~wise(X0) <~> creative(X0))) [input p14]
16. happy(mary) <~> ~calm(mary) [input p15]
23. funny(mary) & ~generous(mary) [input p22]
24. rich(mary) [input hypothesis]
26. ! [X0] : ((kind(X0) | ~brave(X0)) => ~old(X0)) [unused predicate definition removal 4]
29. ! [X0] : (~old(X0) | (~kind(X0) & brave(X0))) [ennf transformation 26]
31. ! [X0] : ((~happy(X0) & humble(X0)) | old(X0)) [ennf transformation 6]
32. (brave(mary) <~> ~tall(mary)) | ! [X0] : ~quiet(X0) [ennf transformation 7]
34. ! [X0] : ((creative(X0) & ~funny(X0)) | (~rich(X0) <=> ~strong(X0))) [ennf transformation 10]
36. ! [X0] : ((strong(X0) <~> tall(X0)) | (calm(X0) <=> creative(X0))) [ennf transformation 14]
37. ! [X0] : ((~wise(X0) <~> creative(X0)) | ~rich(X0)) [ennf transformation 15]
38. ! [X0] : (((~tall(X0) | tall(X0)) | (wise(X0) | ~quiet(X0))) & ((~wise(X0) & quiet(X0)) | (tall(X0) & ~tall(X0)))) [nnf transformation 1]
39. ! [X0] : ((~tall(X0) | tall(X0) | wise(X0) | ~quiet(X0)) & ((~wise(X0) & quiet(X0)) | (tall(X0) & ~tall(X0)))) [flattening 38]
45. ((tall(mary) | ~brave(mary)) & (~tall(mary) | brave(mary))) | ! [X0] : ~quiet(X0) [nnf transformation 32]
48. ! [X0] : (((~creative(X0) | ~rich(X0)) | (~wise(X0) & ~calm(X0))) & ((wise(X0) | calm(X0)) | (creative(X0) & rich(X0)))) [nnf transformation 9]
49. ! [X0] : ((~creative(X0) | ~rich(X0) | (~wise(X0) & ~calm(X0))) & (wise(X0) | calm(X0) | (creative(X0) & rich(X0)))) [flattening 48]
50. ! [X0] : ((creative(X0) & ~funny(X0)) | ((~rich(X0) | strong(X0)) & (~strong(X0) | rich(X0)))) [nnf transformation 34]
58. ! [X0] : (((~tall(X0) | ~strong(X0)) & (tall(X0) | strong(X0))) | ((calm(X0) | ~creative(X0)) & (creative(X0) | ~calm(X0)))) [nnf transformation 36]
59. ! [X0] : (((~creative(X0) | wise(X0)) & (creative(X0) | ~wise(X0))) | ~rich(X0)) [nnf transformation 37]
60. (calm(mary) | ~happy(mary)) & (~calm(mary) | happy(mary)) [nnf transformation 16]
72. quiet(X0) | ~tall(X0) [cnf transformation 39]
73. quiet(X0) | tall(X0) [cnf transformation 39]
74. ~wise(X0) | ~tall(X0) [cnf transformation 39]
75. ~wise(X0) | tall(X0) [cnf transformation 39]
83. ~old(X0) | brave(X0) [cnf transformation 29]
90. ~happy(X0) | old(X0) [cnf transformation 31]
92. tall(mary) | ~brave(mary) | ~quiet(X0) [cnf transformation 45]
95. wise(X0) | calm(X0) | creative(X0) [cnf transformation 49]
99. ~funny(X0) | ~rich(X0) | strong(X0) [cnf transformation 50]
113. ~tall(X0) | ~strong(X0) | creative(X0) | ~calm(X0) [cnf transformation 58]
114. ~tall(X0) | ~strong(X0) | calm(X0) | ~creative(X0) [cnf transformation 58]
116. ~creative(X0) | wise(X0) | ~rich(X0) [cnf transformation 59]
117. ~calm(mary) | happy(mary) [cnf transformation 60]
131. funny(mary) [cnf transformation 23]
132. rich(mary) [cnf transformation 24]
133. ~wise(X0) [subsumption resolution 74,75]
134. quiet(X0) [subsumption resolution 72,73]
173. tall(mary) | ~brave(mary) [subsumption resolution 92,134]
175. 9 <=> brave(mary) [avatar definition]
179. 10 <=> tall(mary) [avatar definition]
181. tall(mary) <- (10) [avatar component clause 179]
182. ~9 | 10 [avatar split clause 173,179,175]
195. calm(X0) | creative(X0) [subsumption resolution 95,133]
202. ~strong(X0) | ~tall(X0) | calm(X0) [subsumption resolution 114,195]
203. ~strong(X0) | ~tall(X0) | creative(X0) [subsumption resolution 113,202]
206. ~rich(X0) | ~creative(X0) [subsumption resolution 116,133]
208. 14 <=> happy(mary) [avatar definition]
209. happy(mary) <- (14) [avatar component clause 208]
212. 15 <=> calm(mary) [avatar definition]
213. ~calm(mary) <- (~15) [avatar component clause 212]
216. 14 | ~15 [avatar split clause 117,212,208]
268. creative(mary) <- (~15) [resolution 195,213]
270. ~creative(mary) [resolution 206,132]
271. $false <- (~15) [subsumption resolution 270,268]
272. 15 [avatar contradiction clause 271]
273. old(mary) <- (14) [resolution 209,90]
275. brave(mary) <- (14) [resolution 273,83]
278. 9 | ~14 [avatar split clause 275,208,175]
285. ~rich(mary) | strong(mary) [resolution 99,131]
286. strong(mary) [subsumption resolution 285,132]
292. ~tall(mary) | creative(mary) [resolution 203,286]
293. creative(mary) <- (10) [subsumption resolution 292,181]
294. $false <- (10) [subsumption resolution 293,270]
295. ~10 [avatar contradiction clause 294]
296. $false [avatar sat refutation 182,216,272,278,295]
% SZS output end Proof for 6306619349412184742323521
% ------------------------------
% 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 john is strong or not wise then john is either funny or not humble and vice versa.
Everyone who is not strong is both not kind and not brave and vice versa.
If fred is either old or not brave then someone is quiet and vice versa.
Everyone who is kind or calm is both patient and happy and vice versa.
If alice is happy or brave then someone is not kind and vice versa.
Everyone who is both not humble and not tall is not wise or funny and vice versa.
If someone is both creative and not creative then someone is either creative or not wise.
If someone is curious then someone is old.
Everyone who is not calm is strong or not wise and vice versa.
Everyone who is not happy is either patient or not creative.
Everyone who is not generous or not brave is both not happy and not quiet.
Everyone who is not brave or quiet is either not old or not tall and vice versa.
Everyone who is not kind or not generous is either wise or humble.
If someone is both curious and patient then someone is strong and vice versa.
If someone is not generous or not funny then lucy is not happy or not quiet.
Everyone who is both strong and not quiet is either tall or brave.
John is either not brave or patient.
Someone is not generous or not kind.
Susan is not generous or humble.
Someone is both funny and not humble.
Someone is not old.
Someone is not humble.
Someone is humble or calm. | Alice is brave. | entailment | (((strong(john)|~wise(john)))<=>((funny(john)<~>~humble(john))))&
(![X]:(~strong(X)<=>(~kind(X)&~brave(X))))&
(((old(fred)<~>~brave(fred)))<=>(?[X]:(quiet(X))))&
(![X]:((kind(X)|calm(X))<=>(patient(X)&happy(X))))&
(((happy(alice)|brave(alice)))<=>(?[X]:(~kind(X))))&
(![X]:((~humble(X)&~tall(X))<=>(~wise(X)|funny(X))))&
((?[X]:((creative(X)&~creative(X))))=>(?[X]:((creative(X)<~>~wise(X)))))&
((?[X]:(curious(X)))=>(?[X]:(old(X))))&
(![X]:(~calm(X)<=>(strong(X)|~wise(X))))&
(![X]:(~happy(X)=>(patient(X)<~>~creative(X))))&
(![X]:((~generous(X)|~brave(X))=>(~happy(X)&~quiet(X))))&
(![X]:((~brave(X)|quiet(X))<=>(~old(X)<~>~tall(X))))&
(![X]:((~kind(X)|~generous(X))=>(wise(X)<~>humble(X))))&
((?[X]:((curious(X)&patient(X))))<=>(?[X]:(strong(X))))&
((?[X]:((~generous(X)|~funny(X))))=>((~happy(lucy)|~quiet(lucy))))&
(![X]:((strong(X)&~quiet(X))=>(tall(X)<~>brave(X))))&
((~brave(john)<~>patient(john)))&
(?[X]:((~generous(X)|~kind(X))))&
((~generous(susan)|humble(susan)))&
(?[X]:((funny(X)&~humble(X))))&
(?[X]:(~old(X)))&
(?[X]:(~humble(X)))&
(?[X]:((humble(X)|calm(X)))) | brave(alice) | [
"p3",
"p4",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 7567619497309015350275907
% SZS output start Proof for 7567619497309015350275907
4. ! [X0] : ((calm(X0) | kind(X0)) <=> (happy(X0) & patient(X0))) [input p3]
5. (brave(alice) | happy(alice)) <=> ? [X0] : ~kind(X0) [input p4]
11. ! [X0] : ((~brave(X0) | ~generous(X0)) => (~quiet(X0) & ~happy(X0))) [input p10]
24. ~brave(alice) [input hypothesis]
31. ! [X0] : ((~quiet(X0) & ~happy(X0)) | (brave(X0) & generous(X0))) [ennf transformation 11]
45. ! [X0] : (((calm(X0) | kind(X0)) | (~happy(X0) | ~patient(X0))) & ((happy(X0) & patient(X0)) | (~calm(X0) & ~kind(X0)))) [nnf transformation 4]
46. ! [X0] : ((calm(X0) | kind(X0) | ~happy(X0) | ~patient(X0)) & ((happy(X0) & patient(X0)) | (~calm(X0) & ~kind(X0)))) [flattening 45]
47. ((brave(alice) | happy(alice)) | ! [X0] : kind(X0)) & (? [X0] : ~kind(X0) | (~brave(alice) & ~happy(alice))) [nnf transformation 5]
48. (brave(alice) | happy(alice) | ! [X0] : kind(X0)) & (? [X0] : ~kind(X0) | (~brave(alice) & ~happy(alice))) [flattening 47]
49. (brave(alice) | happy(alice) | ! [X0] : kind(X0)) & (? [X1] : ~kind(X1) | (~brave(alice) & ~happy(alice))) [rectify 48]
50. ? [X1] : ~kind(X1) => ~kind(sK1) [choice axiom]
51. (brave(alice) | happy(alice) | ! [X0] : kind(X0)) & (~kind(sK1) | (~brave(alice) & ~happy(alice))) [skolemisation 49,50]
99. ~kind(X0) | happy(X0) [cnf transformation 46]
104. brave(alice) | happy(alice) | kind(X0) [cnf transformation 51]
119. ~happy(X0) | brave(X0) [cnf transformation 31]
148. ~brave(alice) [cnf transformation 24]
191. 9 <=> ! [X0] : kind(X0) [avatar definition]
192. kind(X0) <- (9) [avatar component clause 191]
194. 10 <=> happy(alice) [avatar definition]
195. ~happy(alice) <- (~10) [avatar component clause 194]
196. happy(alice) <- (10) [avatar component clause 194]
198. 11 <=> brave(alice) [avatar definition]
199. ~brave(alice) <- (~11) [avatar component clause 198]
201. 9 | 10 | 11 [avatar split clause 104,198,194,191]
296. ~11 [avatar split clause 148,198]
302. brave(alice) <- (10) [resolution 119,196]
303. $false <- (10, ~11) [subsumption resolution 302,199]
304. ~10 | 11 [avatar contradiction clause 303]
305. happy(X0) <- (9) [resolution 192,99]
318. $false <- (9, ~10) [resolution 305,195]
319. ~9 | 10 [avatar contradiction clause 318]
322. $false [avatar sat refutation 201,296,304,319]
% SZS output end Proof for 7567619497309015350275907
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is wise is either not brave or not happy.
If fred is not patient then alice is humble or not quiet and vice versa.
Everyone who is either creative or tall is not funny or humble and vice versa.
Everyone who is not patient or humble is not humble.
If susan is both creative and not calm then someone is funny and vice versa.
Everyone who is rich is brave or not patient.
Everyone who is not humble or wise is both not curious and patient.
Everyone who is calm is either patient or wise and vice versa.
Everyone who is either humble or brave is both not funny and not calm.
Everyone who is not tall is both tall and not brave.
Everyone who is either kind or not generous is both not humble and quiet and vice versa.
If john is happy or not humble then someone is both creative and not rich.
Everyone who is not quiet or not kind is either kind or brave.
If fred is not patient then susan is not rich or not generous.
Everyone who is both patient and not patient is either kind or happy and vice versa.
Someone is wise or not curious.
Susan is either not old or rich.
Someone is not happy or not kind.
Someone is either not kind or curious.
Mary is not brave or not old.
Someone is not strong. | John is not rich. | neutral | (![X]:(wise(X)=>(~brave(X)<~>~happy(X))))&
((~patient(fred))<=>((humble(alice)|~quiet(alice))))&
(![X]:((creative(X)<~>tall(X))<=>(~funny(X)|humble(X))))&
(![X]:((~patient(X)|humble(X))=>~humble(X)))&
(((creative(susan)&~calm(susan)))<=>(?[X]:(funny(X))))&
(![X]:(rich(X)=>(brave(X)|~patient(X))))&
(![X]:((~humble(X)|wise(X))=>(~curious(X)&patient(X))))&
(![X]:(calm(X)<=>(patient(X)<~>wise(X))))&
(![X]:((humble(X)<~>brave(X))=>(~funny(X)&~calm(X))))&
(![X]:(~tall(X)=>(tall(X)&~brave(X))))&
(![X]:((kind(X)<~>~generous(X))<=>(~humble(X)&quiet(X))))&
(((happy(john)|~humble(john)))=>(?[X]:((creative(X)&~rich(X)))))&
(![X]:((~quiet(X)|~kind(X))=>(kind(X)<~>brave(X))))&
((~patient(fred))=>((~rich(susan)|~generous(susan))))&
(![X]:((patient(X)&~patient(X))<=>(kind(X)<~>happy(X))))&
(?[X]:((wise(X)|~curious(X))))&
((~old(susan)<~>rich(susan)))&
(?[X]:((~happy(X)|~kind(X))))&
(?[X]:((~kind(X)<~>curious(X))))&
((~brave(mary)|~old(mary)))&
(?[X]:(~strong(X))) | ~rich(john) | [] | null | 0 |
If someone is happy then alice is both not generous and not brave and vice versa. Everyone who is either generous or funny is calm or creative and vice versa. If susan is generous or not wise then someone is both rich and not generous. Everyone who is either not brave or not funny is wise or creative and vice versa. If lucy is calm then someone is generous or calm and vice versa. Everyone who is not humble is either not generous or old and vice versa. Everyone who is not curious or tall is humble and vice versa. Everyone who is not funny or rich is happy or not funny. Everyone who is brave or not quiet is both not rich and humble. If mary is not humble then mary is not curious or patient. If paul is either kind or not rich then someone is quiet. Everyone who is not creative or patient is happy or not patient. If someone is not rich or wise then someone is generous or happy and vice versa. Everyone who is not tall or not patient is calm or humble and vice versa. If lucy is both not creative and brave then fred is strong and vice versa. Everyone who is either happy or not generous is both not curious and not calm. Susan is not happy or not humble. Fred is either not calm or quiet. Someone is strong. Alice is both not strong and not quiet. Someone is not funny or creative. Alice is not rich. Susan is either not generous or not happy. Someone is not tall. | Susan is not generous. | neutral | ((?[X]:(happy(X)))<=>((~generous(alice)&~brave(alice))))&
(![X]:((generous(X)<~>funny(X))<=>(calm(X)|creative(X))))&
(((generous(susan)|~wise(susan)))=>(?[X]:((rich(X)&~generous(X)))))&
(![X]:((~brave(X)<~>~funny(X))<=>(wise(X)|creative(X))))&
((calm(lucy))<=>(?[X]:((generous(X)|calm(X)))))&
(![X]:(~humble(X)<=>(~generous(X)<~>old(X))))&
(![X]:((~curious(X)|tall(X))<=>humble(X)))&
(![X]:((~funny(X)|rich(X))=>(happy(X)|~funny(X))))&
(![X]:((brave(X)|~quiet(X))=>(~rich(X)&humble(X))))&
((~humble(mary))=>((~curious(mary)|patient(mary))))&
(((kind(paul)<~>~rich(paul)))=>(?[X]:(quiet(X))))&
(![X]:((~creative(X)|patient(X))=>(happy(X)|~patient(X))))&
((?[X]:((~rich(X)|wise(X))))<=>(?[X]:((generous(X)|happy(X)))))&
(![X]:((~tall(X)|~patient(X))<=>(calm(X)|humble(X))))&
(((~creative(lucy)&brave(lucy)))<=>(strong(fred)))&
(![X]:((happy(X)<~>~generous(X))=>(~curious(X)&~calm(X))))&
((~happy(susan)|~humble(susan)))&
((~calm(fred)<~>quiet(fred)))&
(?[X]:(strong(X)))&
((~strong(alice)&~quiet(alice)))&
(?[X]:((~funny(X)|creative(X))))&
(~rich(alice))&
((~generous(susan)<~>~happy(susan)))&
(?[X]:(~tall(X))) | ~generous(susan) | [] | null | 0 |
If alice is not funny then someone is both not funny and not rich and vice versa. Everyone who is both generous and not brave is either happy or curious. Everyone who is either calm or not quiet is either wise or not wise and vice versa. If someone is not humble then paul is both humble and strong and vice versa. Everyone who is not creative or curious is both happy and curious. If someone is not humble or not happy then someone is rich or creative. Everyone who is not generous is either strong or brave. Everyone who is both not tall and happy is not generous or not humble and vice versa. Everyone who is either wise or not funny is strong and vice versa. If someone is both not humble and not brave then john is not brave. If paul is not generous or happy then alice is either wise or not rich. Everyone who is calm or humble is both not brave and not rich and vice versa. Everyone who is not rich is either not old or not creative. If alice is calm then paul is either not wise or not rich and vice versa. If someone is either not wise or not generous then someone is both not funny and not strong. If someone is not rich then lucy is both kind and not generous. Someone is either not creative or not wise. Alice is kind. Fred is humble. Alice is curious or not rich. Someone is either quiet or wise. Mary is not strong or humble. Someone is either funny or creative. Someone is not old. | Fred is rich. | contradiction | ((~funny(alice))<=>(?[X]:((~funny(X)&~rich(X)))))&
(![X]:((generous(X)&~brave(X))=>(happy(X)<~>curious(X))))&
(![X]:((calm(X)<~>~quiet(X))<=>(wise(X)<~>~wise(X))))&
((?[X]:(~humble(X)))<=>((humble(paul)&strong(paul))))&
(![X]:((~creative(X)|curious(X))=>(happy(X)&curious(X))))&
((?[X]:((~humble(X)|~happy(X))))=>(?[X]:((rich(X)|creative(X)))))&
(![X]:(~generous(X)=>(strong(X)<~>brave(X))))&
(![X]:((~tall(X)&happy(X))<=>(~generous(X)|~humble(X))))&
(![X]:((wise(X)<~>~funny(X))<=>strong(X)))&
((?[X]:((~humble(X)&~brave(X))))=>(~brave(john)))&
(((~generous(paul)|happy(paul)))=>((wise(alice)<~>~rich(alice))))&
(![X]:((calm(X)|humble(X))<=>(~brave(X)&~rich(X))))&
(![X]:(~rich(X)=>(~old(X)<~>~creative(X))))&
((calm(alice))<=>((~wise(paul)<~>~rich(paul))))&
((?[X]:((~wise(X)<~>~generous(X))))=>(?[X]:((~funny(X)&~strong(X)))))&
((?[X]:(~rich(X)))=>((kind(lucy)&~generous(lucy))))&
(?[X]:((~creative(X)<~>~wise(X))))&
(kind(alice))&
(humble(fred))&
((curious(alice)|~rich(alice)))&
(?[X]:((quiet(X)<~>wise(X))))&
((~strong(mary)|humble(mary)))&
(?[X]:((funny(X)<~>creative(X))))&
(?[X]:(~old(X))) | rich(fred) | [
"p11",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 7245404932998363851327047
% SZS output start Proof for 7245404932998363851327047
12. ! [X0] : ((humble(X0) | calm(X0)) <=> (~rich(X0) & ~brave(X0))) [input p11]
19. humble(fred) [input p18]
25. rich(fred) [input hypothesis]
59. ! [X0] : (((humble(X0) | calm(X0)) | (rich(X0) | brave(X0))) & ((~rich(X0) & ~brave(X0)) | (~humble(X0) & ~calm(X0)))) [nnf transformation 12]
60. ! [X0] : ((humble(X0) | calm(X0) | rich(X0) | brave(X0)) & ((~rich(X0) & ~brave(X0)) | (~humble(X0) & ~calm(X0)))) [flattening 59]
119. ~humble(X0) | ~rich(X0) [cnf transformation 60]
134. humble(fred) [cnf transformation 19]
142. rich(fred) [cnf transformation 25]
320. ~rich(fred) [resolution 119,134]
323. $false [subsumption resolution 320,142]
% SZS output end Proof for 7245404932998363851327047
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not quiet and generous is old or not creative and vice versa. Everyone who is both not old and not generous is either not happy or not generous. Everyone who is either brave or not tall is either not old or not rich and vice versa. Everyone who is creative is not strong or kind. If alice is not funny or rich then fred is patient. If alice is both old and not creative then someone is happy or not kind and vice versa. Everyone who is either not calm or generous is not old and vice versa. If alice is both not calm and creative then someone is not rich or strong and vice versa. Everyone who is both not kind and not creative is curious or kind and vice versa. If paul is not strong or not brave then alice is not quiet or happy and vice versa. If lucy is both kind and not curious then susan is brave or not curious. If someone is not wise then someone is both brave and quiet and vice versa. If susan is not wise then someone is both kind and not generous and vice versa. If john is either calm or not funny then mary is kind and vice versa. Someone is both not old and wise. Mary is both quiet and creative. Someone is either funny or not wise. Someone is either humble or not creative. | Lucy is not calm. | neutral | (![X]:((~quiet(X)&generous(X))<=>(old(X)|~creative(X))))&
(![X]:((~old(X)&~generous(X))=>(~happy(X)<~>~generous(X))))&
(![X]:((brave(X)<~>~tall(X))<=>(~old(X)<~>~rich(X))))&
(![X]:(creative(X)=>(~strong(X)|kind(X))))&
(((~funny(alice)|rich(alice)))=>(patient(fred)))&
(((old(alice)&~creative(alice)))<=>(?[X]:((happy(X)|~kind(X)))))&
(![X]:((~calm(X)<~>generous(X))<=>~old(X)))&
(((~calm(alice)&creative(alice)))<=>(?[X]:((~rich(X)|strong(X)))))&
(![X]:((~kind(X)&~creative(X))<=>(curious(X)|kind(X))))&
(((~strong(paul)|~brave(paul)))<=>((~quiet(alice)|happy(alice))))&
(((kind(lucy)&~curious(lucy)))=>((brave(susan)|~curious(susan))))&
((?[X]:(~wise(X)))<=>(?[X]:((brave(X)&quiet(X)))))&
((~wise(susan))<=>(?[X]:((kind(X)&~generous(X)))))&
(((calm(john)<~>~funny(john)))<=>(kind(mary)))&
(?[X]:((~old(X)&wise(X))))&
((quiet(mary)&creative(mary)))&
(?[X]:((funny(X)<~>~wise(X))))&
(?[X]:((humble(X)<~>~creative(X)))) | ~calm(lucy) | [] | null | 0 |
Everyone who is not patient is both funny and not calm and vice versa.
Everyone who is either rich or not patient is patient and vice versa.
If someone is both not humble and not kind then someone is both not funny and calm.
If someone is both not tall and generous then john is either not quiet or tall and vice versa.
Everyone who is not tall is not tall or curious and vice versa.
Everyone who is not funny or not patient is funny.
Everyone who is either not old or curious is not tall and vice versa.
If john is rich or not brave then someone is either not calm or quiet and vice versa.
Everyone who is generous is calm or patient and vice versa.
If john is either not kind or humble then someone is not wise or not strong and vice versa.
If someone is both not old and not patient then john is not brave.
Everyone who is not funny or strong is not calm or calm and vice versa.
Everyone who is either not generous or not strong is not patient or not generous and vice versa.
If susan is either not rich or tall then someone is not curious or not humble and vice versa.
If john is both not strong and quiet then someone is not humble.
If someone is rich or humble then fred is old or not kind.
Someone is either not old or calm.
Someone is both brave and funny.
Lucy is both creative and humble.
John is either not creative or not rich.
Alice is brave.
Fred is not funny or strong.
Susan is either strong or humble. | John is not kind. | neutral | (![X]:(~patient(X)<=>(funny(X)&~calm(X))))&
(![X]:((rich(X)<~>~patient(X))<=>patient(X)))&
((?[X]:((~humble(X)&~kind(X))))=>(?[X]:((~funny(X)&calm(X)))))&
((?[X]:((~tall(X)&generous(X))))<=>((~quiet(john)<~>tall(john))))&
(![X]:(~tall(X)<=>(~tall(X)|curious(X))))&
(![X]:((~funny(X)|~patient(X))=>funny(X)))&
(![X]:((~old(X)<~>curious(X))<=>~tall(X)))&
(((rich(john)|~brave(john)))<=>(?[X]:((~calm(X)<~>quiet(X)))))&
(![X]:(generous(X)<=>(calm(X)|patient(X))))&
(((~kind(john)<~>humble(john)))<=>(?[X]:((~wise(X)|~strong(X)))))&
((?[X]:((~old(X)&~patient(X))))=>(~brave(john)))&
(![X]:((~funny(X)|strong(X))<=>(~calm(X)|calm(X))))&
(![X]:((~generous(X)<~>~strong(X))<=>(~patient(X)|~generous(X))))&
(((~rich(susan)<~>tall(susan)))<=>(?[X]:((~curious(X)|~humble(X)))))&
(((~strong(john)&quiet(john)))=>(?[X]:(~humble(X))))&
((?[X]:((rich(X)|humble(X))))=>((old(fred)|~kind(fred))))&
(?[X]:((~old(X)<~>calm(X))))&
(?[X]:((brave(X)&funny(X))))&
((creative(lucy)&humble(lucy)))&
((~creative(john)<~>~rich(john)))&
(brave(alice))&
((~funny(fred)|strong(fred)))&
((strong(susan)<~>humble(susan))) | ~kind(john) | [] | null | 0 |
Everyone who is not kind is rich or not calm and vice versa.
Everyone who is both curious and quiet is not tall and vice versa.
Everyone who is either happy or old is happy or quiet and vice versa.
Everyone who is either wise or creative is both not patient and not happy.
Everyone who is both not curious and not strong is not old and vice versa.
If someone is patient then someone is either funny or not brave and vice versa.
Everyone who is not patient or rich is either calm or old.
Everyone who is patient is either old or calm and vice versa.
If alice is both happy and not rich then someone is both rich and funny and vice versa.
If someone is rich or patient then someone is humble.
If mary is happy or not wise then fred is not curious or old and vice versa.
If mary is either not rich or not patient then susan is curious or quiet and vice versa.
If john is not tall then john is not wise or not tall and vice versa.
Everyone who is both funny and not calm is either not funny or not quiet.
Everyone who is both not quiet and wise is either not curious or not creative and vice versa.
If someone is both funny and not creative then someone is either curious or not tall.
Someone is both happy and wise.
Someone is either not funny or curious.
Fred is curious.
Someone is not curious.
Someone is old or tall.
Someone is both wise and patient.
Someone is either not quiet or not creative.
Mary is strong. | Mary is not wise. | entailment | (![X]:(~kind(X)<=>(rich(X)|~calm(X))))&
(![X]:((curious(X)&quiet(X))<=>~tall(X)))&
(![X]:((happy(X)<~>old(X))<=>(happy(X)|quiet(X))))&
(![X]:((wise(X)<~>creative(X))=>(~patient(X)&~happy(X))))&
(![X]:((~curious(X)&~strong(X))<=>~old(X)))&
((?[X]:(patient(X)))<=>(?[X]:((funny(X)<~>~brave(X)))))&
(![X]:((~patient(X)|rich(X))=>(calm(X)<~>old(X))))&
(![X]:(patient(X)<=>(old(X)<~>calm(X))))&
(((happy(alice)&~rich(alice)))<=>(?[X]:((rich(X)&funny(X)))))&
((?[X]:((rich(X)|patient(X))))=>(?[X]:(humble(X))))&
(((happy(mary)|~wise(mary)))<=>((~curious(fred)|old(fred))))&
(((~rich(mary)<~>~patient(mary)))<=>((curious(susan)|quiet(susan))))&
((~tall(john))<=>((~wise(john)|~tall(john))))&
(![X]:((funny(X)&~calm(X))=>(~funny(X)<~>~quiet(X))))&
(![X]:((~quiet(X)&wise(X))<=>(~curious(X)<~>~creative(X))))&
((?[X]:((funny(X)&~creative(X))))=>(?[X]:((curious(X)<~>~tall(X)))))&
(?[X]:((happy(X)&wise(X))))&
(?[X]:((~funny(X)<~>curious(X))))&
(curious(fred))&
(?[X]:(~curious(X)))&
(?[X]:((old(X)|tall(X))))&
(?[X]:((wise(X)&patient(X))))&
(?[X]:((~quiet(X)<~>~creative(X))))&
(strong(mary)) | ~wise(mary) | [
"p2",
"p4",
"p10",
"p18",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 3617997532460838010557593
% SZS output start Proof for 3617997532460838010557593
3. ! [X0] : ((happy(X0) <~> old(X0)) <=> (quiet(X0) | happy(X0))) [input p2]
5. ! [X0] : ((~strong(X0) & ~curious(X0)) <=> ~old(X0)) [input p4]
11. (~wise(mary) | happy(mary)) <=> (old(fred) | ~curious(fred)) [input p10]
19. curious(fred) [input p18]
24. strong(mary) [input p23]
25. wise(mary) [input hypothesis]
37. ! [X0] : ((((~old(X0) | ~happy(X0)) & (old(X0) | happy(X0))) | (~quiet(X0) & ~happy(X0))) & ((quiet(X0) | happy(X0)) | ((happy(X0) | ~old(X0)) & (old(X0) | ~happy(X0))))) [nnf transformation 3]
38. ! [X0] : ((((~old(X0) | ~happy(X0)) & (old(X0) | happy(X0))) | (~quiet(X0) & ~happy(X0))) & (quiet(X0) | happy(X0) | ((happy(X0) | ~old(X0)) & (old(X0) | ~happy(X0))))) [flattening 37]
40. ! [X0] : (((~strong(X0) & ~curious(X0)) | old(X0)) & (~old(X0) | (strong(X0) | curious(X0)))) [nnf transformation 5]
41. ! [X0] : (((~strong(X0) & ~curious(X0)) | old(X0)) & (~old(X0) | strong(X0) | curious(X0))) [flattening 40]
54. ((~wise(mary) | happy(mary)) | (~old(fred) & curious(fred))) & ((old(fred) | ~curious(fred)) | (wise(mary) & ~happy(mary))) [nnf transformation 11]
55. (~wise(mary) | happy(mary) | (~old(fred) & curious(fred))) & (old(fred) | ~curious(fred) | (wise(mary) & ~happy(mary))) [flattening 54]
88. ~old(X0) | ~happy(X0) | ~happy(X0) [cnf transformation 38]
95. ~curious(X0) | old(X0) [cnf transformation 41]
96. ~strong(X0) | old(X0) [cnf transformation 41]
116. ~wise(mary) | happy(mary) | ~old(fred) [cnf transformation 55]
140. curious(fred) [cnf transformation 19]
147. strong(mary) [cnf transformation 24]
148. wise(mary) [cnf transformation 25]
151. ~old(X0) | ~happy(X0) [duplicate literal removal 88]
207. 12 <=> old(fred) [avatar definition]
211. 13 <=> happy(mary) [avatar definition]
213. happy(mary) <- (13) [avatar component clause 211]
215. 14 <=> wise(mary) [avatar definition]
218. ~12 | 13 | ~14 [avatar split clause 116,215,211,207]
220. 15 <=> curious(fred) [avatar definition]
222. curious(fred) <- (15) [avatar component clause 220]
276. 15 [avatar split clause 140,220]
296. 14 [avatar split clause 148,215]
299. old(fred) <- (15) [resolution 95,222]
303. 12 | ~15 [avatar split clause 299,220,207]
304. old(mary) [resolution 96,147]
307. ~happy(mary) [resolution 151,304]
308. $false <- (13) [subsumption resolution 307,213]
309. ~13 [avatar contradiction clause 308]
310. $false [avatar sat refutation 218,276,296,303,309]
% SZS output end Proof for 3617997532460838010557593
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not tall or not humble is both old and not brave and vice versa. Everyone who is not generous is both not happy and not creative and vice versa. If alice is not strong or not funny then someone is either not strong or not humble and vice versa. Everyone who is either tall or calm is happy and vice versa. Everyone who is both humble and not funny is happy. Everyone who is not curious or curious is not humble and vice versa. If someone is wise then someone is not old. Everyone who is not wise or not happy is not curious or not creative. Everyone who is not brave is either not strong or happy. If someone is not wise or not curious then someone is either not wise or curious. If alice is both not rich and happy then someone is not rich. Everyone who is both rich and not creative is strong or not old. If alice is kind then paul is both not calm and not humble. If mary is not happy or not wise then someone is either not funny or not quiet. Alice is both curious and not kind. Someone is either not generous or old. Someone is generous. Someone is either rich or brave. Someone is both old and happy. Someone is either not quiet or not creative. | Mary is not tall. | neutral | (![X]:((~tall(X)|~humble(X))<=>(old(X)&~brave(X))))&
(![X]:(~generous(X)<=>(~happy(X)&~creative(X))))&
(((~strong(alice)|~funny(alice)))<=>(?[X]:((~strong(X)<~>~humble(X)))))&
(![X]:((tall(X)<~>calm(X))<=>happy(X)))&
(![X]:((humble(X)&~funny(X))=>happy(X)))&
(![X]:((~curious(X)|curious(X))<=>~humble(X)))&
((?[X]:(wise(X)))=>(?[X]:(~old(X))))&
(![X]:((~wise(X)|~happy(X))=>(~curious(X)|~creative(X))))&
(![X]:(~brave(X)=>(~strong(X)<~>happy(X))))&
((?[X]:((~wise(X)|~curious(X))))=>(?[X]:((~wise(X)<~>curious(X)))))&
(((~rich(alice)&happy(alice)))=>(?[X]:(~rich(X))))&
(![X]:((rich(X)&~creative(X))=>(strong(X)|~old(X))))&
((kind(alice))=>((~calm(paul)&~humble(paul))))&
(((~happy(mary)|~wise(mary)))=>(?[X]:((~funny(X)<~>~quiet(X)))))&
((curious(alice)&~kind(alice)))&
(?[X]:((~generous(X)<~>old(X))))&
(?[X]:(generous(X)))&
(?[X]:((rich(X)<~>brave(X))))&
(?[X]:((old(X)&happy(X))))&
(?[X]:((~quiet(X)<~>~creative(X)))) | ~tall(mary) | [] | null | 0 |
Everyone who is humble is not generous or creative. If someone is either not brave or strong then someone is not strong or quiet and vice versa. Everyone who is not generous is not funny and vice versa. Everyone who is kind or quiet is not curious or funny and vice versa. Everyone who is either not quiet or humble is quiet and vice versa. Everyone who is both quiet and brave is not tall and vice versa. If fred is not curious or not tall then someone is patient and vice versa. If susan is either not kind or quiet then someone is both not quiet and patient. Everyone who is either not curious or not wise is both strong and not quiet and vice versa. If lucy is both not calm and not kind then someone is happy or not rich and vice versa. If someone is patient then paul is not wise and vice versa. If mary is rich then someone is either not funny or patient and vice versa. Everyone who is not strong or not humble is not brave and vice versa. Everyone who is not funny is brave. If someone is either patient or rich then someone is strong or brave. If someone is either not rich or creative then susan is calm or not brave. Mary is not funny. John is quiet or humble. Lucy is either not strong or not old. Someone is either happy or wise. Susan is not tall. Someone is either rich or not strong. Susan is both calm and strong. | John is not old. | neutral | (![X]:(humble(X)=>(~generous(X)|creative(X))))&
((?[X]:((~brave(X)<~>strong(X))))<=>(?[X]:((~strong(X)|quiet(X)))))&
(![X]:(~generous(X)<=>~funny(X)))&
(![X]:((kind(X)|quiet(X))<=>(~curious(X)|funny(X))))&
(![X]:((~quiet(X)<~>humble(X))<=>quiet(X)))&
(![X]:((quiet(X)&brave(X))<=>~tall(X)))&
(((~curious(fred)|~tall(fred)))<=>(?[X]:(patient(X))))&
(((~kind(susan)<~>quiet(susan)))=>(?[X]:((~quiet(X)&patient(X)))))&
(![X]:((~curious(X)<~>~wise(X))<=>(strong(X)&~quiet(X))))&
(((~calm(lucy)&~kind(lucy)))<=>(?[X]:((happy(X)|~rich(X)))))&
((?[X]:(patient(X)))<=>(~wise(paul)))&
((rich(mary))<=>(?[X]:((~funny(X)<~>patient(X)))))&
(![X]:((~strong(X)|~humble(X))<=>~brave(X)))&
(![X]:(~funny(X)=>brave(X)))&
((?[X]:((patient(X)<~>rich(X))))=>(?[X]:((strong(X)|brave(X)))))&
((?[X]:((~rich(X)<~>creative(X))))=>((calm(susan)|~brave(susan))))&
(~funny(mary))&
((quiet(john)|humble(john)))&
((~strong(lucy)<~>~old(lucy)))&
(?[X]:((happy(X)<~>wise(X))))&
(~tall(susan))&
(?[X]:((rich(X)<~>~strong(X))))&
((calm(susan)&strong(susan))) | ~old(john) | [] | null | 0 |
If fred is not tall or rich then someone is both not humble and wise and vice versa. Everyone who is both quiet and not patient is both wise and brave and vice versa. Everyone who is either not kind or not funny is either not strong or not creative. If paul is both old and not calm then susan is humble. Everyone who is either funny or not brave is not curious and vice versa. If someone is both not generous and not wise then someone is either not humble or humble and vice versa. If someone is strong or not quiet then someone is both old and quiet. If someone is not quiet or calm then paul is brave. Everyone who is both curious and funny is either patient or generous and vice versa. If paul is tall then someone is both not brave and not generous. If someone is both not creative and wise then susan is either funny or rich and vice versa. If someone is both curious and not generous then lucy is kind or patient. Everyone who is both humble and not kind is both calm and old. If someone is creative then john is calm and vice versa. Everyone who is calm is either not tall or curious and vice versa. If mary is either not generous or not wise then susan is old. Someone is both not calm and not happy. Fred is not tall or rich. Alice is not creative. Paul is both not generous and patient. Someone is both not old and not wise. Someone is strong or old. Someone is quiet or wise. | Susan is creative. | contradiction | (((~tall(fred)|rich(fred)))<=>(?[X]:((~humble(X)&wise(X)))))&
(![X]:((quiet(X)&~patient(X))<=>(wise(X)&brave(X))))&
(![X]:((~kind(X)<~>~funny(X))=>(~strong(X)<~>~creative(X))))&
(((old(paul)&~calm(paul)))=>(humble(susan)))&
(![X]:((funny(X)<~>~brave(X))<=>~curious(X)))&
((?[X]:((~generous(X)&~wise(X))))<=>(?[X]:((~humble(X)<~>humble(X)))))&
((?[X]:((strong(X)|~quiet(X))))=>(?[X]:((old(X)&quiet(X)))))&
((?[X]:((~quiet(X)|calm(X))))=>(brave(paul)))&
(![X]:((curious(X)&funny(X))<=>(patient(X)<~>generous(X))))&
((tall(paul))=>(?[X]:((~brave(X)&~generous(X)))))&
((?[X]:((~creative(X)&wise(X))))<=>((funny(susan)<~>rich(susan))))&
((?[X]:((curious(X)&~generous(X))))=>((kind(lucy)|patient(lucy))))&
(![X]:((humble(X)&~kind(X))=>(calm(X)&old(X))))&
((?[X]:(creative(X)))<=>(calm(john)))&
(![X]:(calm(X)<=>(~tall(X)<~>curious(X))))&
(((~generous(mary)<~>~wise(mary)))=>(old(susan)))&
(?[X]:((~calm(X)&~happy(X))))&
((~tall(fred)|rich(fred)))&
(~creative(alice))&
((~generous(paul)&patient(paul)))&
(?[X]:((~old(X)&~wise(X))))&
(?[X]:((strong(X)|old(X))))&
(?[X]:((quiet(X)|wise(X)))) | creative(susan) | [
"p4",
"p7",
"p8",
"p13",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 493646061150657133326853
% SZS output start Proof for 493646061150657133326853
5. ! [X0] : ((funny(X0) <~> ~brave(X0)) <=> ~curious(X0)) [input p4]
8. ? [X0] : (calm(X0) | ~quiet(X0)) => brave(paul) [input p7]
9. ! [X0] : ((funny(X0) & curious(X0)) <=> (patient(X0) <~> generous(X0))) [input p8]
14. ? [X0] : creative(X0) <=> calm(john) [input p13]
20. patient(paul) & ~generous(paul) [input p19]
24. creative(susan) [input hypothesis]
32. brave(paul) | ! [X0] : (~calm(X0) & quiet(X0)) [ennf transformation 8]
47. ! [X0] : ((((brave(X0) | ~funny(X0)) & (~brave(X0) | funny(X0))) | curious(X0)) & (~curious(X0) | ((funny(X0) | brave(X0)) & (~brave(X0) | ~funny(X0))))) [nnf transformation 5]
56. ! [X0] : (((funny(X0) & curious(X0)) | ((patient(X0) | ~generous(X0)) & (generous(X0) | ~patient(X0)))) & (((~generous(X0) | ~patient(X0)) & (generous(X0) | patient(X0))) | (~funny(X0) | ~curious(X0)))) [nnf transformation 9]
57. ! [X0] : (((funny(X0) & curious(X0)) | ((patient(X0) | ~generous(X0)) & (generous(X0) | ~patient(X0)))) & (((~generous(X0) | ~patient(X0)) & (generous(X0) | patient(X0))) | ~funny(X0) | ~curious(X0))) [flattening 56]
64. (? [X0] : creative(X0) | ~calm(john)) & (calm(john) | ! [X0] : ~creative(X0)) [nnf transformation 14]
65. (? [X0] : creative(X0) | ~calm(john)) & (calm(john) | ! [X1] : ~creative(X1)) [rectify 64]
66. ? [X0] : creative(X0) => creative(sK6) [choice axiom]
67. (creative(sK6) | ~calm(john)) & (calm(john) | ! [X1] : ~creative(X1)) [skolemisation 65,66]
92. ~curious(X0) | ~brave(X0) | ~funny(X0) [cnf transformation 47]
107. brave(paul) | ~calm(X0) [cnf transformation 32]
110. ~patient(X0) | generous(X0) | curious(X0) [cnf transformation 57]
112. ~patient(X0) | generous(X0) | funny(X0) [cnf transformation 57]
125. calm(john) | ~creative(X1) [cnf transformation 67]
136. ~generous(paul) [cnf transformation 20]
137. patient(paul) [cnf transformation 20]
142. creative(susan) [cnf transformation 24]
221. 17 <=> ! [X0] : ~calm(X0) [avatar definition]
222. ~calm(X0) <- (17) [avatar component clause 221]
224. 18 <=> brave(paul) [avatar definition]
227. 17 | 18 [avatar split clause 107,224,221]
281. 30 <=> calm(john) [avatar definition]
282. calm(john) <- (30) [avatar component clause 281]
290. 32 <=> ! [X1] : ~creative(X1) [avatar definition]
291. ~creative(X1) <- (32) [avatar component clause 290]
292. 32 | 30 [avatar split clause 125,281,290]
326. $false <- (17, 30) [resolution 282,222]
327. ~17 | ~30 [avatar contradiction clause 326]
342. 40 <=> curious(paul) [avatar definition]
344. curious(paul) <- (40) [avatar component clause 342]
346. 41 <=> funny(paul) [avatar definition]
357. generous(paul) | curious(paul) [resolution 110,137]
359. curious(paul) [subsumption resolution 357,136]
363. 40 [avatar split clause 359,342]
365. ~brave(paul) | ~funny(paul) <- (40) [resolution 344,92]
366. generous(paul) | funny(paul) [resolution 112,137]
368. funny(paul) [subsumption resolution 366,136]
372. 41 [avatar split clause 368,346]
373. ~41 | ~18 | ~40 [avatar split clause 365,342,224,346]
375. $false <- (32) [resolution 291,142]
378. ~32 [avatar contradiction clause 375]
379. $false [avatar sat refutation 227,292,327,363,372,373,378]
% SZS output end Proof for 493646061150657133326853
% ------------------------------
% 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: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not patient then alice is humble and vice versa.
If fred is not kind then someone is brave.
Everyone who is both generous and rich is not quiet or calm and vice versa.
If fred is either generous or humble then someone is both not generous and happy.
Everyone who is both funny and not creative is not rich or not happy and vice versa.
If someone is not tall then someone is both not funny and tall and vice versa.
Everyone who is either tall or kind is curious or not creative.
Everyone who is either not funny or not patient is both not wise and not patient and vice versa.
Everyone who is not tall is rich.
If someone is either calm or not funny then someone is patient.
If someone is either happy or strong then someone is happy.
If alice is funny then someone is either humble or wise and vice versa.
Everyone who is not tall is both not quiet and not patient.
Everyone who is either calm or patient is not quiet and vice versa.
Everyone who is not old is humble or not patient and vice versa.
If fred is either happy or humble then alice is not patient or brave.
Someone is not creative.
Someone is either not humble or not funny.
Someone is brave.
Someone is both calm and not quiet.
Mary is patient.
Someone is both not patient and not funny.
John is both not quiet and not tall.
Fred is rich. | Alice is not patient. | neutral | ((?[X]:(~patient(X)))<=>(humble(alice)))&
((~kind(fred))=>(?[X]:(brave(X))))&
(![X]:((generous(X)&rich(X))<=>(~quiet(X)|calm(X))))&
(((generous(fred)<~>humble(fred)))=>(?[X]:((~generous(X)&happy(X)))))&
(![X]:((funny(X)&~creative(X))<=>(~rich(X)|~happy(X))))&
((?[X]:(~tall(X)))<=>(?[X]:((~funny(X)&tall(X)))))&
(![X]:((tall(X)<~>kind(X))=>(curious(X)|~creative(X))))&
(![X]:((~funny(X)<~>~patient(X))<=>(~wise(X)&~patient(X))))&
(![X]:(~tall(X)=>rich(X)))&
((?[X]:((calm(X)<~>~funny(X))))=>(?[X]:(patient(X))))&
((?[X]:((happy(X)<~>strong(X))))=>(?[X]:(happy(X))))&
((funny(alice))<=>(?[X]:((humble(X)<~>wise(X)))))&
(![X]:(~tall(X)=>(~quiet(X)&~patient(X))))&
(![X]:((calm(X)<~>patient(X))<=>~quiet(X)))&
(![X]:(~old(X)<=>(humble(X)|~patient(X))))&
(((happy(fred)<~>humble(fred)))=>((~patient(alice)|brave(alice))))&
(?[X]:(~creative(X)))&
(?[X]:((~humble(X)<~>~funny(X))))&
(?[X]:(brave(X)))&
(?[X]:((calm(X)&~quiet(X))))&
(patient(mary))&
(?[X]:((~patient(X)&~funny(X))))&
((~quiet(john)&~tall(john)))&
(rich(fred)) | ~patient(alice) | [] | null | 0 |
Everyone who is both kind and not kind is both not tall and not brave and vice versa. If someone is either brave or not wise then someone is not patient and vice versa. Everyone who is not funny or funny is either wise or strong and vice versa. Everyone who is both tall and strong is either not calm or tall and vice versa. If someone is either funny or old then susan is brave or happy. Everyone who is either brave or tall is either quiet or not kind and vice versa. Everyone who is happy is both not wise and patient. Everyone who is either not old or not quiet is either not old or not curious and vice versa. If paul is both kind and not kind then someone is not generous or not tall. Everyone who is either not rich or not curious is old or not old and vice versa. Everyone who is either kind or brave is generous and vice versa. Everyone who is rich or funny is humble and vice versa. If someone is both happy and not patient then john is both generous and not funny. If someone is both not rich and happy then alice is both patient and calm. Everyone who is both not wise and not strong is both creative and not tall. If paul is strong or not kind then someone is either brave or not curious. Lucy is both tall and not kind. Mary is either not generous or tall. Fred is either not humble or wise. Someone is both not generous and not wise. Someone is quiet. Someone is both quiet and not old. Mary is not wise or curious. | John is wise. | neutral | (![X]:((kind(X)&~kind(X))<=>(~tall(X)&~brave(X))))&
((?[X]:((brave(X)<~>~wise(X))))<=>(?[X]:(~patient(X))))&
(![X]:((~funny(X)|funny(X))<=>(wise(X)<~>strong(X))))&
(![X]:((tall(X)&strong(X))<=>(~calm(X)<~>tall(X))))&
((?[X]:((funny(X)<~>old(X))))=>((brave(susan)|happy(susan))))&
(![X]:((brave(X)<~>tall(X))<=>(quiet(X)<~>~kind(X))))&
(![X]:(happy(X)=>(~wise(X)&patient(X))))&
(![X]:((~old(X)<~>~quiet(X))<=>(~old(X)<~>~curious(X))))&
(((kind(paul)&~kind(paul)))=>(?[X]:((~generous(X)|~tall(X)))))&
(![X]:((~rich(X)<~>~curious(X))<=>(old(X)|~old(X))))&
(![X]:((kind(X)<~>brave(X))<=>generous(X)))&
(![X]:((rich(X)|funny(X))<=>humble(X)))&
((?[X]:((happy(X)&~patient(X))))=>((generous(john)&~funny(john))))&
((?[X]:((~rich(X)&happy(X))))=>((patient(alice)&calm(alice))))&
(![X]:((~wise(X)&~strong(X))=>(creative(X)&~tall(X))))&
(((strong(paul)|~kind(paul)))=>(?[X]:((brave(X)<~>~curious(X)))))&
((tall(lucy)&~kind(lucy)))&
((~generous(mary)<~>tall(mary)))&
((~humble(fred)<~>wise(fred)))&
(?[X]:((~generous(X)&~wise(X))))&
(?[X]:(quiet(X)))&
(?[X]:((quiet(X)&~old(X))))&
((~wise(mary)|curious(mary))) | wise(john) | [] | null | 0 |
If someone is either creative or patient then someone is generous or not kind.
Everyone who is not brave is both calm and not calm.
Everyone who is both not humble and not strong is either not wise or not calm.
Everyone who is either creative or quiet is either not rich or humble and vice versa.
Everyone who is either curious or not funny is curious or not wise and vice versa.
Everyone who is happy is not happy or funny.
Everyone who is rich or not creative is either not tall or curious.
If someone is not happy then someone is both old and funny and vice versa.
Everyone who is either not tall or calm is not funny and vice versa.
If someone is either strong or old then someone is not patient and vice versa.
Everyone who is not wise is both kind and not funny and vice versa.
Everyone who is both creative and kind is both not kind and not wise.
Everyone who is both funny and not tall is either not kind or not strong and vice versa.
Everyone who is either happy or kind is not strong or not wise.
Everyone who is either old or funny is both not kind and strong.
Everyone who is not old or strong is either calm or old and vice versa.
Someone is rich.
Someone is either not strong or brave.
Someone is patient or not tall.
Lucy is both not patient and not old.
Someone is not kind or humble.
Susan is either not humble or not creative.
Someone is either not generous or not brave.
Someone is both not old and not curious. | Lucy is happy. | contradiction | ((?[X]:((creative(X)<~>patient(X))))=>(?[X]:((generous(X)|~kind(X)))))&
(![X]:(~brave(X)=>(calm(X)&~calm(X))))&
(![X]:((~humble(X)&~strong(X))=>(~wise(X)<~>~calm(X))))&
(![X]:((creative(X)<~>quiet(X))<=>(~rich(X)<~>humble(X))))&
(![X]:((curious(X)<~>~funny(X))<=>(curious(X)|~wise(X))))&
(![X]:(happy(X)=>(~happy(X)|funny(X))))&
(![X]:((rich(X)|~creative(X))=>(~tall(X)<~>curious(X))))&
((?[X]:(~happy(X)))<=>(?[X]:((old(X)&funny(X)))))&
(![X]:((~tall(X)<~>calm(X))<=>~funny(X)))&
((?[X]:((strong(X)<~>old(X))))<=>(?[X]:(~patient(X))))&
(![X]:(~wise(X)<=>(kind(X)&~funny(X))))&
(![X]:((creative(X)&kind(X))=>(~kind(X)&~wise(X))))&
(![X]:((funny(X)&~tall(X))<=>(~kind(X)<~>~strong(X))))&
(![X]:((happy(X)<~>kind(X))=>(~strong(X)|~wise(X))))&
(![X]:((old(X)<~>funny(X))=>(~kind(X)&strong(X))))&
(![X]:((~old(X)|strong(X))<=>(calm(X)<~>old(X))))&
(?[X]:(rich(X)))&
(?[X]:((~strong(X)<~>brave(X))))&
(?[X]:((patient(X)|~tall(X))))&
((~patient(lucy)&~old(lucy)))&
(?[X]:((~kind(X)|humble(X))))&
((~humble(susan)<~>~creative(susan)))&
(?[X]:((~generous(X)<~>~brave(X))))&
(?[X]:((~old(X)&~curious(X)))) | happy(lucy) | [
"p5",
"p10",
"p13",
"p14",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 7657023129503445239530821
% SZS output start Proof for 7657023129503445239530821
6. ! [X0] : (happy(X0) => (funny(X0) | ~happy(X0))) [input p5]
11. ! [X0] : (~wise(X0) <=> (~funny(X0) & kind(X0))) [input p10]
14. ! [X0] : ((happy(X0) <~> kind(X0)) => (~wise(X0) | ~strong(X0))) [input p13]
15. ! [X0] : ((old(X0) <~> funny(X0)) => (strong(X0) & ~kind(X0))) [input p14]
20. ~old(lucy) & ~patient(lucy) [input p19]
25. happy(lucy) [input hypothesis]
33. ! [X0] : ((funny(X0) | ~happy(X0)) | ~happy(X0)) [ennf transformation 6]
34. ! [X0] : (funny(X0) | ~happy(X0) | ~happy(X0)) [flattening 33]
38. ! [X0] : ((~wise(X0) | ~strong(X0)) | (happy(X0) <=> kind(X0))) [ennf transformation 14]
39. ! [X0] : (~wise(X0) | ~strong(X0) | (happy(X0) <=> kind(X0))) [flattening 38]
40. ! [X0] : ((strong(X0) & ~kind(X0)) | (old(X0) <=> funny(X0))) [ennf transformation 15]
61. ! [X0] : ((~wise(X0) | (funny(X0) | ~kind(X0))) & ((~funny(X0) & kind(X0)) | wise(X0))) [nnf transformation 11]
62. ! [X0] : ((~wise(X0) | funny(X0) | ~kind(X0)) & ((~funny(X0) & kind(X0)) | wise(X0))) [flattening 61]
65. ! [X0] : (~wise(X0) | ~strong(X0) | ((happy(X0) | ~kind(X0)) & (kind(X0) | ~happy(X0)))) [nnf transformation 39]
66. ! [X0] : ((strong(X0) & ~kind(X0)) | ((old(X0) | ~funny(X0)) & (funny(X0) | ~old(X0)))) [nnf transformation 40]
104. funny(X0) | ~happy(X0) | ~happy(X0) [cnf transformation 34]
120. wise(X0) | kind(X0) [cnf transformation 62]
131. ~wise(X0) | ~strong(X0) | kind(X0) | ~happy(X0) [cnf transformation 65]
134. ~funny(X0) | old(X0) | ~kind(X0) [cnf transformation 66]
136. ~funny(X0) | old(X0) | strong(X0) [cnf transformation 66]
148. ~old(lucy) [cnf transformation 20]
156. happy(lucy) [cnf transformation 25]
160. ~happy(X0) | funny(X0) [duplicate literal removal 104]
227. ~happy(X0) | kind(X0) | ~strong(X0) [subsumption resolution 131,120]
266. funny(lucy) [resolution 160,156]
292. old(lucy) | ~kind(lucy) [resolution 134,266]
294. ~kind(lucy) [subsumption resolution 292,148]
296. old(lucy) | strong(lucy) [resolution 136,266]
298. strong(lucy) [subsumption resolution 296,148]
319. kind(lucy) | ~strong(lucy) [resolution 227,156]
321. ~strong(lucy) [subsumption resolution 319,294]
322. $false [subsumption resolution 321,298]
% SZS output end Proof for 7657023129503445239530821
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not kind or not wise is not happy or not strong.
Everyone who is humble is patient or humble.
Everyone who is kind or not humble is either kind or tall and vice versa.
If someone is patient then someone is both not creative and not happy and vice versa.
Everyone who is both wise and not patient is happy and vice versa.
If someone is kind then someone is both not humble and curious and vice versa.
If paul is generous then someone is either brave or not tall and vice versa.
Everyone who is not kind or strong is either not calm or brave and vice versa.
Everyone who is both not curious and humble is either not funny or not old and vice versa.
Everyone who is both humble and not calm is patient.
If alice is not humble or patient then someone is calm or not patient.
If someone is both quiet and not patient then lucy is either creative or not humble and vice versa.
Everyone who is not humble or tall is patient.
If paul is both not rich and quiet then lucy is either brave or wise.
Everyone who is not brave is tall.
Everyone who is old is either humble or not humble and vice versa.
Fred is either tall or wise.
Someone is both not patient and generous.
John is humble or patient.
Someone is not creative or not brave.
Someone is quiet.
Someone is not creative or wise.
Fred is either wise or funny.
John is either not creative or not humble. | Fred is funny. | neutral | (![X]:((~kind(X)|~wise(X))=>(~happy(X)|~strong(X))))&
(![X]:(humble(X)=>(patient(X)|humble(X))))&
(![X]:((kind(X)|~humble(X))<=>(kind(X)<~>tall(X))))&
((?[X]:(patient(X)))<=>(?[X]:((~creative(X)&~happy(X)))))&
(![X]:((wise(X)&~patient(X))<=>happy(X)))&
((?[X]:(kind(X)))<=>(?[X]:((~humble(X)&curious(X)))))&
((generous(paul))<=>(?[X]:((brave(X)<~>~tall(X)))))&
(![X]:((~kind(X)|strong(X))<=>(~calm(X)<~>brave(X))))&
(![X]:((~curious(X)&humble(X))<=>(~funny(X)<~>~old(X))))&
(![X]:((humble(X)&~calm(X))=>patient(X)))&
(((~humble(alice)|patient(alice)))=>(?[X]:((calm(X)|~patient(X)))))&
((?[X]:((quiet(X)&~patient(X))))<=>((creative(lucy)<~>~humble(lucy))))&
(![X]:((~humble(X)|tall(X))=>patient(X)))&
(((~rich(paul)&quiet(paul)))=>((brave(lucy)<~>wise(lucy))))&
(![X]:(~brave(X)=>tall(X)))&
(![X]:(old(X)<=>(humble(X)<~>~humble(X))))&
((tall(fred)<~>wise(fred)))&
(?[X]:((~patient(X)&generous(X))))&
((humble(john)|patient(john)))&
(?[X]:((~creative(X)|~brave(X))))&
(?[X]:(quiet(X)))&
(?[X]:((~creative(X)|wise(X))))&
((wise(fred)<~>funny(fred)))&
((~creative(john)<~>~humble(john))) | funny(fred) | [] | null | 0 |
If susan is either not humble or old then mary is both not humble and not wise and vice versa.
Everyone who is either creative or not generous is quiet and vice versa.
Everyone who is not curious or not generous is kind.
Everyone who is not wise or not quiet is both not rich and generous.
Everyone who is either patient or not strong is generous and vice versa.
If someone is both strong and tall then someone is either not old or not rich and vice versa.
If john is either not old or not tall then someone is quiet or not curious.
If mary is tall or happy then fred is both not calm and creative and vice versa.
If susan is either not strong or not generous then someone is either not creative or happy and vice versa.
Everyone who is happy or not creative is both patient and not quiet and vice versa.
If someone is either old or not wise then someone is both curious and kind.
Everyone who is either humble or creative is both funny and not curious and vice versa.
If susan is both rich and not kind then susan is either old or not humble and vice versa.
Everyone who is either funny or not humble is generous or not happy.
If susan is not happy then someone is either not strong or not humble and vice versa.
If susan is generous then someone is both not creative and kind and vice versa.
Someone is either not funny or not wise.
Paul is not creative or old.
Mary is both not creative and not wise.
Someone is kind or curious.
Lucy is old or happy.
Lucy is either tall or curious.
Lucy is both calm and not happy.
Lucy is not calm or curious. | Mary is not wise. | entailment | (((~humble(susan)<~>old(susan)))<=>((~humble(mary)&~wise(mary))))&
(![X]:((creative(X)<~>~generous(X))<=>quiet(X)))&
(![X]:((~curious(X)|~generous(X))=>kind(X)))&
(![X]:((~wise(X)|~quiet(X))=>(~rich(X)&generous(X))))&
(![X]:((patient(X)<~>~strong(X))<=>generous(X)))&
((?[X]:((strong(X)&tall(X))))<=>(?[X]:((~old(X)<~>~rich(X)))))&
(((~old(john)<~>~tall(john)))=>(?[X]:((quiet(X)|~curious(X)))))&
(((tall(mary)|happy(mary)))<=>((~calm(fred)&creative(fred))))&
(((~strong(susan)<~>~generous(susan)))<=>(?[X]:((~creative(X)<~>happy(X)))))&
(![X]:((happy(X)|~creative(X))<=>(patient(X)&~quiet(X))))&
((?[X]:((old(X)<~>~wise(X))))=>(?[X]:((curious(X)&kind(X)))))&
(![X]:((humble(X)<~>creative(X))<=>(funny(X)&~curious(X))))&
(((rich(susan)&~kind(susan)))<=>((old(susan)<~>~humble(susan))))&
(![X]:((funny(X)<~>~humble(X))=>(generous(X)|~happy(X))))&
((~happy(susan))<=>(?[X]:((~strong(X)<~>~humble(X)))))&
((generous(susan))<=>(?[X]:((~creative(X)&kind(X)))))&
(?[X]:((~funny(X)<~>~wise(X))))&
((~creative(paul)|old(paul)))&
((~creative(mary)&~wise(mary)))&
(?[X]:((kind(X)|curious(X))))&
((old(lucy)|happy(lucy)))&
((tall(lucy)<~>curious(lucy)))&
((calm(lucy)&~happy(lucy)))&
((~calm(lucy)|curious(lucy))) | ~wise(mary) | [
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 4544882434168457749161609
% SZS output start Proof for 4544882434168457749161609
19. ~wise(mary) & ~creative(mary) [input p18]
25. wise(mary) [input hypothesis]
152. ~wise(mary) [cnf transformation 19]
160. wise(mary) [cnf transformation 25]
166. 2 <=> wise(mary) [avatar definition]
370. ~2 [avatar split clause 152,166]
393. 2 [avatar split clause 160,166]
394. $false [avatar sat refutation 370,393]
% SZS output end Proof for 4544882434168457749161609
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not old is both not calm and brave. Everyone who is either happy or wise is both not brave and not funny and vice versa. Everyone who is not patient is both not rich and not curious and vice versa. If someone is not tall or not humble then someone is creative. Everyone who is either not happy or strong is quiet and vice versa. Everyone who is strong or humble is both not creative and kind and vice versa. Everyone who is both creative and calm is both funny and not calm. Everyone who is patient or not kind is either generous or strong. Everyone who is not rich is creative or not creative and vice versa. Everyone who is either curious or kind is either not generous or creative and vice versa. If paul is both tall and calm then paul is not patient or not wise. Everyone who is both not brave and not calm is both kind and tall and vice versa. Everyone who is both curious and happy is either happy or strong and vice versa. Everyone who is both wise and not humble is patient and vice versa. Everyone who is both not funny and not rich is not rich or not patient. If susan is not strong or happy then someone is not rich. Someone is funny. Someone is not kind. Paul is both not strong and calm. Someone is kind or not creative. Someone is old. Susan is not humble. Susan is both not tall and not brave. | Susan is calm. | entailment | (![X]:(~old(X)=>(~calm(X)&brave(X))))&
(![X]:((happy(X)<~>wise(X))<=>(~brave(X)&~funny(X))))&
(![X]:(~patient(X)<=>(~rich(X)&~curious(X))))&
((?[X]:((~tall(X)|~humble(X))))=>(?[X]:(creative(X))))&
(![X]:((~happy(X)<~>strong(X))<=>quiet(X)))&
(![X]:((strong(X)|humble(X))<=>(~creative(X)&kind(X))))&
(![X]:((creative(X)&calm(X))=>(funny(X)&~calm(X))))&
(![X]:((patient(X)|~kind(X))=>(generous(X)<~>strong(X))))&
(![X]:(~rich(X)<=>(creative(X)|~creative(X))))&
(![X]:((curious(X)<~>kind(X))<=>(~generous(X)<~>creative(X))))&
(((tall(paul)&calm(paul)))=>((~patient(paul)|~wise(paul))))&
(![X]:((~brave(X)&~calm(X))<=>(kind(X)&tall(X))))&
(![X]:((curious(X)&happy(X))<=>(happy(X)<~>strong(X))))&
(![X]:((wise(X)&~humble(X))<=>patient(X)))&
(![X]:((~funny(X)&~rich(X))=>(~rich(X)|~patient(X))))&
(((~strong(susan)|happy(susan)))=>(?[X]:(~rich(X))))&
(?[X]:(funny(X)))&
(?[X]:(~kind(X)))&
((~strong(paul)&calm(paul)))&
(?[X]:((kind(X)|~creative(X))))&
(?[X]:(old(X)))&
(~humble(susan))&
((~tall(susan)&~brave(susan))) | calm(susan) | [
"p11",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 1914600017380645195127945
% SZS output start Proof for 1914600017380645195127945
12. ! [X0] : ((~calm(X0) & ~brave(X0)) <=> (tall(X0) & kind(X0))) [input p11]
23. ~brave(susan) & ~tall(susan) [input p22]
24. ~calm(susan) [input hypothesis]
50. ! [X0] : (((~calm(X0) & ~brave(X0)) | (~tall(X0) | ~kind(X0))) & ((tall(X0) & kind(X0)) | (calm(X0) | brave(X0)))) [nnf transformation 12]
51. ! [X0] : (((~calm(X0) & ~brave(X0)) | ~tall(X0) | ~kind(X0)) & ((tall(X0) & kind(X0)) | calm(X0) | brave(X0))) [flattening 50]
99. tall(X0) | calm(X0) | brave(X0) [cnf transformation 51]
120. ~tall(susan) [cnf transformation 23]
121. ~brave(susan) [cnf transformation 23]
122. ~calm(susan) [cnf transformation 24]
198. calm(susan) | brave(susan) [resolution 99,120]
199. brave(susan) [subsumption resolution 198,122]
200. $false [subsumption resolution 199,121]
% SZS output end Proof for 1914600017380645195127945
% ------------------------------
% 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 mary is both quiet and not creative then paul is both old and happy and vice versa.
Everyone who is both not quiet and not funny is both old and not rich and vice versa.
Everyone who is not tall or not strong is either happy or not strong and vice versa.
Everyone who is not generous or tall is either not rich or tall.
If john is both curious and not generous then someone is not happy or kind.
If fred is rich then someone is both not generous and not happy.
Everyone who is not strong is both not patient and not generous and vice versa.
If someone is not wise then alice is not happy and vice versa.
Everyone who is both funny and not happy is both old and happy and vice versa.
Everyone who is brave is not happy.
Everyone who is happy is either wise or rich.
If someone is not creative or not generous then paul is both not kind and tall.
Everyone who is not happy or quiet is either quiet or not quiet.
Everyone who is either old or not humble is either tall or quiet and vice versa.
If mary is both not patient and not kind then susan is not kind and vice versa.
Everyone who is either not tall or not curious is both rich and happy and vice versa.
Fred is tall.
Lucy is both not happy and not brave.
John is either not wise or not calm.
Paul is both quiet and humble.
Someone is creative.
Paul is not calm.
Alice is both not creative and not kind.
Someone is not happy. | Lucy is happy. | contradiction | (((quiet(mary)&~creative(mary)))<=>((old(paul)&happy(paul))))&
(![X]:((~quiet(X)&~funny(X))<=>(old(X)&~rich(X))))&
(![X]:((~tall(X)|~strong(X))<=>(happy(X)<~>~strong(X))))&
(![X]:((~generous(X)|tall(X))=>(~rich(X)<~>tall(X))))&
(((curious(john)&~generous(john)))=>(?[X]:((~happy(X)|kind(X)))))&
((rich(fred))=>(?[X]:((~generous(X)&~happy(X)))))&
(![X]:(~strong(X)<=>(~patient(X)&~generous(X))))&
((?[X]:(~wise(X)))<=>(~happy(alice)))&
(![X]:((funny(X)&~happy(X))<=>(old(X)&happy(X))))&
(![X]:(brave(X)=>~happy(X)))&
(![X]:(happy(X)=>(wise(X)<~>rich(X))))&
((?[X]:((~creative(X)|~generous(X))))=>((~kind(paul)&tall(paul))))&
(![X]:((~happy(X)|quiet(X))=>(quiet(X)<~>~quiet(X))))&
(![X]:((old(X)<~>~humble(X))<=>(tall(X)<~>quiet(X))))&
(((~patient(mary)&~kind(mary)))<=>(~kind(susan)))&
(![X]:((~tall(X)<~>~curious(X))<=>(rich(X)&happy(X))))&
(tall(fred))&
((~happy(lucy)&~brave(lucy)))&
((~wise(john)<~>~calm(john)))&
((quiet(paul)&humble(paul)))&
(?[X]:(creative(X)))&
(~calm(paul))&
((~creative(alice)&~kind(alice)))&
(?[X]:(~happy(X))) | happy(lucy) | [
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 8669828318513046864902194
% SZS output start Proof for 8669828318513046864902194
18. ~brave(lucy) & ~happy(lucy) [input p17]
25. happy(lucy) [input hypothesis]
27. ~happy(lucy) [pure predicate removal 18]
124. ~happy(lucy) [cnf transformation 27]
134. happy(lucy) [cnf transformation 25]
251. $false [subsumption resolution 134,124]
% SZS output end Proof for 8669828318513046864902194
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is humble is both not calm and curious and vice versa.
Everyone who is both happy and calm is not strong or strong and vice versa.
If someone is either not humble or not brave then someone is both funny and not wise and vice versa.
If alice is happy then lucy is either not brave or not rich and vice versa.
If someone is curious or not old then someone is both happy and calm.
If someone is either not wise or not calm then someone is not wise or not curious.
Everyone who is rich is either not creative or patient.
Everyone who is both not generous and not strong is strong or not curious.
Everyone who is either happy or old is both not tall and calm and vice versa.
Everyone who is generous or not funny is either brave or patient.
Everyone who is both not tall and not quiet is not old and vice versa.
If john is either happy or not wise then someone is old.
Everyone who is either kind or quiet is both not strong and humble.
If paul is quiet or not wise then susan is both not generous and rich.
Everyone who is not strong is either old or not tall and vice versa.
Everyone who is not creative is both curious and calm and vice versa.
Mary is both not creative and not brave.
Susan is not patient or curious.
John is either not curious or happy.
Lucy is either patient or quiet.
Paul is either not tall or strong.
Paul is both not quiet and brave. | Lucy is rich. | neutral | (![X]:(humble(X)<=>(~calm(X)&curious(X))))&
(![X]:((happy(X)&calm(X))<=>(~strong(X)|strong(X))))&
((?[X]:((~humble(X)<~>~brave(X))))<=>(?[X]:((funny(X)&~wise(X)))))&
((happy(alice))<=>((~brave(lucy)<~>~rich(lucy))))&
((?[X]:((curious(X)|~old(X))))=>(?[X]:((happy(X)&calm(X)))))&
((?[X]:((~wise(X)<~>~calm(X))))=>(?[X]:((~wise(X)|~curious(X)))))&
(![X]:(rich(X)=>(~creative(X)<~>patient(X))))&
(![X]:((~generous(X)&~strong(X))=>(strong(X)|~curious(X))))&
(![X]:((happy(X)<~>old(X))<=>(~tall(X)&calm(X))))&
(![X]:((generous(X)|~funny(X))=>(brave(X)<~>patient(X))))&
(![X]:((~tall(X)&~quiet(X))<=>~old(X)))&
(((happy(john)<~>~wise(john)))=>(?[X]:(old(X))))&
(![X]:((kind(X)<~>quiet(X))=>(~strong(X)&humble(X))))&
(((quiet(paul)|~wise(paul)))=>((~generous(susan)&rich(susan))))&
(![X]:(~strong(X)<=>(old(X)<~>~tall(X))))&
(![X]:(~creative(X)<=>(curious(X)&calm(X))))&
((~creative(mary)&~brave(mary)))&
((~patient(susan)|curious(susan)))&
((~curious(john)<~>happy(john)))&
((patient(lucy)<~>quiet(lucy)))&
((~tall(paul)<~>strong(paul)))&
((~quiet(paul)&brave(paul))) | rich(lucy) | [] | null | 0 |
If alice is both not old and patient then someone is brave. If susan is either not generous or not strong then someone is not rich and vice versa. If someone is either tall or wise then someone is both not old and strong. Everyone who is either calm or not generous is not happy or not strong and vice versa. If someone is not wise then john is both not funny and generous and vice versa. Everyone who is either strong or patient is both brave and not calm. Everyone who is both strong and happy is both not wise and not brave. If someone is either not happy or not tall then lucy is wise. If john is tall then someone is not kind or not happy and vice versa. If someone is not patient or not happy then susan is happy. Everyone who is either generous or not brave is either not creative or not brave and vice versa. If susan is not rich or old then susan is both not rich and kind. Everyone who is both not old and not quiet is both patient and not wise and vice versa. If someone is not strong or generous then someone is both not tall and not wise and vice versa. Everyone who is either not creative or not generous is not wise and vice versa. If someone is either wise or kind then someone is either quiet or not wise. Alice is both not calm and not patient. Paul is not curious or not happy. Alice is not kind or quiet. Lucy is old or wise. Susan is either not generous or not humble. Someone is either curious or kind. Someone is not strong. Alice is either curious or rich. | John is happy. | entailment | (((~old(alice)&patient(alice)))=>(?[X]:(brave(X))))&
(((~generous(susan)<~>~strong(susan)))<=>(?[X]:(~rich(X))))&
((?[X]:((tall(X)<~>wise(X))))=>(?[X]:((~old(X)&strong(X)))))&
(![X]:((calm(X)<~>~generous(X))<=>(~happy(X)|~strong(X))))&
((?[X]:(~wise(X)))<=>((~funny(john)&generous(john))))&
(![X]:((strong(X)<~>patient(X))=>(brave(X)&~calm(X))))&
(![X]:((strong(X)&happy(X))=>(~wise(X)&~brave(X))))&
((?[X]:((~happy(X)<~>~tall(X))))=>(wise(lucy)))&
((tall(john))<=>(?[X]:((~kind(X)|~happy(X)))))&
((?[X]:((~patient(X)|~happy(X))))=>(happy(susan)))&
(![X]:((generous(X)<~>~brave(X))<=>(~creative(X)<~>~brave(X))))&
(((~rich(susan)|old(susan)))=>((~rich(susan)&kind(susan))))&
(![X]:((~old(X)&~quiet(X))<=>(patient(X)&~wise(X))))&
((?[X]:((~strong(X)|generous(X))))<=>(?[X]:((~tall(X)&~wise(X)))))&
(![X]:((~creative(X)<~>~generous(X))<=>~wise(X)))&
((?[X]:((wise(X)<~>kind(X))))=>(?[X]:((quiet(X)<~>~wise(X)))))&
((~calm(alice)&~patient(alice)))&
((~curious(paul)|~happy(paul)))&
((~kind(alice)|quiet(alice)))&
((old(lucy)|wise(lucy)))&
((~generous(susan)<~>~humble(susan)))&
(?[X]:((curious(X)<~>kind(X))))&
(?[X]:(~strong(X)))&
((curious(alice)<~>rich(alice))) | happy(john) | [
"p7",
"p8",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 1645863193275042026834769
% SZS output start Proof for 1645863193275042026834769
8. ? [X0] : (~happy(X0) <~> ~tall(X0)) => wise(lucy) [input p7]
9. tall(john) <=> ? [X0] : (~happy(X0) | ~kind(X0)) [input p8]
11. ! [X0] : ((generous(X0) <~> ~brave(X0)) <=> (~creative(X0) <~> ~brave(X0))) [input p10]
15. ! [X0] : ((~creative(X0) <~> ~generous(X0)) <=> ~wise(X0)) [input p14]
25. ~happy(john) [input hypothesis]
35. wise(lucy) | ! [X0] : (~happy(X0) <=> ~tall(X0)) [ennf transformation 8]
57. wise(lucy) | ! [X0] : ((~happy(X0) | tall(X0)) & (~tall(X0) | happy(X0))) [nnf transformation 35]
58. (tall(john) | ! [X0] : (happy(X0) & kind(X0))) & (? [X0] : (~happy(X0) | ~kind(X0)) | ~tall(john)) [nnf transformation 9]
59. (tall(john) | ! [X0] : (happy(X0) & kind(X0))) & (? [X1] : (~happy(X1) | ~kind(X1)) | ~tall(john)) [rectify 58]
60. ? [X1] : (~happy(X1) | ~kind(X1)) => (~happy(sK4) | ~kind(sK4)) [choice axiom]
61. (tall(john) | ! [X0] : (happy(X0) & kind(X0))) & ((~happy(sK4) | ~kind(sK4)) | ~tall(john)) [skolemisation 59,60]
62. ! [X0] : ((((brave(X0) | ~generous(X0)) & (~brave(X0) | generous(X0))) | ((~creative(X0) | brave(X0)) & (~brave(X0) | creative(X0)))) & (((brave(X0) | creative(X0)) & (~brave(X0) | ~creative(X0))) | ((generous(X0) | brave(X0)) & (~brave(X0) | ~generous(X0))))) [nnf transformation 11]
70. ! [X0] : ((((generous(X0) | creative(X0)) & (~generous(X0) | ~creative(X0))) | wise(X0)) & (~wise(X0) | ((~creative(X0) | generous(X0)) & (~generous(X0) | creative(X0))))) [nnf transformation 15]
106. wise(lucy) | ~tall(X0) | happy(X0) [cnf transformation 57]
110. tall(john) | happy(X0) [cnf transformation 61]
113. ~brave(X0) | ~creative(X0) | ~brave(X0) | ~generous(X0) [cnf transformation 62]
116. brave(X0) | creative(X0) | generous(X0) | brave(X0) [cnf transformation 62]
117. ~brave(X0) | generous(X0) | ~brave(X0) | creative(X0) [cnf transformation 62]
120. brave(X0) | ~generous(X0) | ~creative(X0) | brave(X0) [cnf transformation 62]
134. ~wise(X0) | ~generous(X0) | creative(X0) [cnf transformation 70]
135. ~wise(X0) | ~creative(X0) | generous(X0) [cnf transformation 70]
154. ~happy(john) [cnf transformation 25]
155. ~brave(X0) | ~creative(X0) | ~generous(X0) [duplicate literal removal 113]
156. brave(X0) | creative(X0) | generous(X0) [duplicate literal removal 116]
157. ~brave(X0) | generous(X0) | creative(X0) [duplicate literal removal 117]
158. brave(X0) | ~generous(X0) | ~creative(X0) [duplicate literal removal 120]
231. 17 <=> wise(lucy) [avatar definition]
233. wise(lucy) <- (17) [avatar component clause 231]
236. 18 <=> ! [X0] : (~tall(X0) | happy(X0)) [avatar definition]
237. ~tall(X0) | happy(X0) <- (18) [avatar component clause 236]
238. 18 | 17 [avatar split clause 106,231,236]
240. 19 <=> ! [X0] : happy(X0) [avatar definition]
241. happy(X0) <- (19) [avatar component clause 240]
243. 20 <=> tall(john) [avatar definition]
245. tall(john) <- (20) [avatar component clause 243]
246. 19 | 20 [avatar split clause 110,243,240]
269. creative(X0) | generous(X0) [subsumption resolution 156,157]
270. ~creative(X0) | ~generous(X0) [subsumption resolution 155,158]
316. ~wise(X0) | ~creative(X0) [subsumption resolution 135,270]
317. ~wise(X0) | creative(X0) [subsumption resolution 134,269]
318. ~wise(X0) [subsumption resolution 317,316]
375. $false <- (17) [subsumption resolution 233,318]
376. ~17 [avatar contradiction clause 375]
378. happy(john) <- (18, 20) [resolution 237,245]
379. $false <- (18, 20) [subsumption resolution 378,154]
380. ~18 | ~20 [avatar contradiction clause 379]
382. $false <- (19) [resolution 241,154]
387. ~19 [avatar contradiction clause 382]
388. $false [avatar sat refutation 238,246,376,380,387]
% SZS output end Proof for 1645863193275042026834769
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not brave or calm then someone is either not curious or quiet and vice versa.
Everyone who is not funny is brave.
Everyone who is either not rich or creative is both curious and not funny and vice versa.
If someone is both not tall and not quiet then paul is either not calm or wise and vice versa.
If susan is both not calm and not kind then someone is calm and vice versa.
If susan is not patient then john is either tall or not old and vice versa.
Everyone who is generous is happy and vice versa.
Everyone who is not rich is creative and vice versa.
If mary is not quiet or kind then someone is both funny and calm and vice versa.
Everyone who is patient is not quiet.
If someone is either funny or wise then susan is not calm.
Everyone who is both not happy and old is rich and vice versa.
Everyone who is both not old and funny is both not tall and not wise and vice versa.
If fred is either curious or rich then someone is both generous and creative.
Everyone who is both not brave and old is either not brave or rich and vice versa.
If someone is not quiet or not patient then someone is not creative or humble.
John is not quiet.
Someone is either humble or not rich.
John is either not wise or patient.
Susan is rich or wise.
Paul is either calm or old.
Paul is funny or not old.
Fred is either not tall or generous. | Susan is not kind. | neutral | ((?[X]:((~brave(X)<~>calm(X))))<=>(?[X]:((~curious(X)<~>quiet(X)))))&
(![X]:(~funny(X)=>brave(X)))&
(![X]:((~rich(X)<~>creative(X))<=>(curious(X)&~funny(X))))&
((?[X]:((~tall(X)&~quiet(X))))<=>((~calm(paul)<~>wise(paul))))&
(((~calm(susan)&~kind(susan)))<=>(?[X]:(calm(X))))&
((~patient(susan))<=>((tall(john)<~>~old(john))))&
(![X]:(generous(X)<=>happy(X)))&
(![X]:(~rich(X)<=>creative(X)))&
(((~quiet(mary)|kind(mary)))<=>(?[X]:((funny(X)&calm(X)))))&
(![X]:(patient(X)=>~quiet(X)))&
((?[X]:((funny(X)<~>wise(X))))=>(~calm(susan)))&
(![X]:((~happy(X)&old(X))<=>rich(X)))&
(![X]:((~old(X)&funny(X))<=>(~tall(X)&~wise(X))))&
(((curious(fred)<~>rich(fred)))=>(?[X]:((generous(X)&creative(X)))))&
(![X]:((~brave(X)&old(X))<=>(~brave(X)<~>rich(X))))&
((?[X]:((~quiet(X)|~patient(X))))=>(?[X]:((~creative(X)|humble(X)))))&
(~quiet(john))&
(?[X]:((humble(X)<~>~rich(X))))&
((~wise(john)<~>patient(john)))&
((rich(susan)|wise(susan)))&
((calm(paul)<~>old(paul)))&
((funny(paul)|~old(paul)))&
((~tall(fred)<~>generous(fred))) | ~kind(susan) | [] | null | 0 |
Everyone who is tall or not brave is both old and not patient. If alice is either patient or not generous then fred is not funny. If someone is not creative then john is humble and vice versa. Everyone who is not curious is not quiet. If someone is either tall or not wise then someone is tall or not happy. Everyone who is both creative and quiet is both creative and not strong and vice versa. Everyone who is brave is not curious and vice versa. Everyone who is not brave or not funny is not humble. If someone is not humble or not strong then alice is not humble. Everyone who is not happy or not brave is both quiet and not happy. If someone is not brave or not wise then someone is both generous and strong. If john is both not happy and creative then someone is generous and vice versa. Everyone who is wise is strong. If someone is both not calm and brave then fred is both old and not funny. If someone is both old and quiet then mary is not happy or humble and vice versa. If john is either not brave or generous then susan is kind and vice versa. Fred is brave. Someone is tall. Mary is both not funny and generous. Paul is both humble and calm. Someone is either old or brave. Alice is either not old or not brave. Susan is not calm or not funny. | Fred is not strong. | contradiction | (![X]:((tall(X)|~brave(X))=>(old(X)&~patient(X))))&
(((patient(alice)<~>~generous(alice)))=>(~funny(fred)))&
((?[X]:(~creative(X)))<=>(humble(john)))&
(![X]:(~curious(X)=>~quiet(X)))&
((?[X]:((tall(X)<~>~wise(X))))=>(?[X]:((tall(X)|~happy(X)))))&
(![X]:((creative(X)&quiet(X))<=>(creative(X)&~strong(X))))&
(![X]:(brave(X)<=>~curious(X)))&
(![X]:((~brave(X)|~funny(X))=>~humble(X)))&
((?[X]:((~humble(X)|~strong(X))))=>(~humble(alice)))&
(![X]:((~happy(X)|~brave(X))=>(quiet(X)&~happy(X))))&
((?[X]:((~brave(X)|~wise(X))))=>(?[X]:((generous(X)&strong(X)))))&
(((~happy(john)&creative(john)))<=>(?[X]:(generous(X))))&
(![X]:(wise(X)=>strong(X)))&
((?[X]:((~calm(X)&brave(X))))=>((old(fred)&~funny(fred))))&
((?[X]:((old(X)&quiet(X))))<=>((~happy(mary)|humble(mary))))&
(((~brave(john)<~>generous(john)))<=>(kind(susan)))&
(brave(fred))&
(?[X]:(tall(X)))&
((~funny(mary)&generous(mary)))&
((humble(paul)&calm(paul)))&
(?[X]:((old(X)<~>brave(X))))&
((~old(alice)<~>~brave(alice)))&
((~calm(susan)|~funny(susan))) | ~strong(fred) | [
"p2",
"p3",
"p5",
"p6",
"p7",
"p9",
"p11",
"p16",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 389771434289475452219213
% SZS output start Proof for 389771434289475452219213
3. ? [X0] : ~creative(X0) <=> humble(john) [input p2]
4. ! [X0] : (~curious(X0) => ~quiet(X0)) [input p3]
6. ! [X0] : ((quiet(X0) & creative(X0)) <=> (~strong(X0) & creative(X0))) [input p5]
7. ! [X0] : (brave(X0) <=> ~curious(X0)) [input p6]
8. ! [X0] : ((~funny(X0) | ~brave(X0)) => ~humble(X0)) [input p7]
10. ! [X0] : ((~brave(X0) | ~happy(X0)) => (~happy(X0) & quiet(X0))) [input p9]
12. (creative(john) & ~happy(john)) <=> ? [X0] : generous(X0) [input p11]
17. brave(fred) [input p16]
19. generous(mary) & ~funny(mary) [input p18]
24. ~strong(fred) [input hypothesis]
29. ! [X0] : (~quiet(X0) | curious(X0)) [ennf transformation 4]
31. ! [X0] : (~humble(X0) | (funny(X0) & brave(X0))) [ennf transformation 8]
33. ! [X0] : ((~happy(X0) & quiet(X0)) | (brave(X0) & happy(X0))) [ennf transformation 10]
38. (? [X0] : ~creative(X0) | ~humble(john)) & (humble(john) | ! [X0] : creative(X0)) [nnf transformation 3]
39. (? [X0] : ~creative(X0) | ~humble(john)) & (humble(john) | ! [X1] : creative(X1)) [rectify 38]
40. ? [X0] : ~creative(X0) => ~creative(sK0) [choice axiom]
41. (~creative(sK0) | ~humble(john)) & (humble(john) | ! [X1] : creative(X1)) [skolemisation 39,40]
46. ! [X0] : (((quiet(X0) & creative(X0)) | (strong(X0) | ~creative(X0))) & ((~strong(X0) & creative(X0)) | (~quiet(X0) | ~creative(X0)))) [nnf transformation 6]
47. ! [X0] : (((quiet(X0) & creative(X0)) | strong(X0) | ~creative(X0)) & ((~strong(X0) & creative(X0)) | ~quiet(X0) | ~creative(X0))) [flattening 46]
48. ! [X0] : ((brave(X0) | curious(X0)) & (~curious(X0) | ~brave(X0))) [nnf transformation 7]
52. ((creative(john) & ~happy(john)) | ! [X0] : ~generous(X0)) & (? [X0] : generous(X0) | (~creative(john) | happy(john))) [nnf transformation 12]
53. ((creative(john) & ~happy(john)) | ! [X0] : ~generous(X0)) & (? [X0] : generous(X0) | ~creative(john) | happy(john)) [flattening 52]
54. ((creative(john) & ~happy(john)) | ! [X0] : ~generous(X0)) & (? [X1] : generous(X1) | ~creative(john) | happy(john)) [rectify 53]
55. ? [X1] : generous(X1) => generous(sK3) [choice axiom]
56. ((creative(john) & ~happy(john)) | ! [X0] : ~generous(X0)) & (generous(sK3) | ~creative(john) | happy(john)) [skolemisation 54,55]
75. humble(john) | creative(X1) [cnf transformation 41]
77. ~quiet(X0) | curious(X0) [cnf transformation 29]
83. ~creative(X0) | strong(X0) | quiet(X0) [cnf transformation 47]
84. ~curious(X0) | ~brave(X0) [cnf transformation 48]
86. ~humble(X0) | brave(X0) [cnf transformation 31]
90. happy(X0) | quiet(X0) [cnf transformation 33]
99. ~happy(john) | ~generous(X0) [cnf transformation 56]
113. brave(fred) [cnf transformation 17]
116. generous(mary) [cnf transformation 19]
124. ~strong(fred) [cnf transformation 24]
140. 4 <=> humble(john) [avatar definition]
141. humble(john) <- (4) [avatar component clause 140]
149. 6 <=> ! [X1] : creative(X1) [avatar definition]
150. creative(X1) <- (6) [avatar component clause 149]
151. 6 | 4 [avatar split clause 75,140,149]
199. 18 <=> ! [X0] : ~generous(X0) [avatar definition]
200. ~generous(X0) <- (18) [avatar component clause 199]
207. 20 <=> happy(john) [avatar definition]
209. ~happy(john) <- (~20) [avatar component clause 207]
210. 18 | ~20 [avatar split clause 99,207,199]
254. 30 <=> brave(john) [avatar definition]
255. ~brave(john) <- (~30) [avatar component clause 254]
292. $false <- (18) [resolution 200,116]
293. ~18 [avatar contradiction clause 292]
301. brave(john) <- (4) [resolution 86,141]
303. $false <- (4, ~30) [subsumption resolution 301,255]
304. ~4 | 30 [avatar contradiction clause 303]
312. quiet(john) <- (~20) [resolution 90,209]
319. curious(john) <- (~20) [resolution 312,77]
346. strong(X0) | quiet(X0) <- (6) [resolution 83,150]
352. ~brave(john) <- (~20) [resolution 319,84]
357. ~30 | 20 [avatar split clause 352,207,254]
365. quiet(fred) <- (6) [resolution 346,124]
369. curious(fred) <- (6) [resolution 365,77]
370. ~brave(fred) <- (6) [resolution 369,84]
371. $false <- (6) [subsumption resolution 370,113]
372. ~6 [avatar contradiction clause 371]
373. $false [avatar sat refutation 151,210,293,304,357,372]
% SZS output end Proof for 389771434289475452219213
% ------------------------------
% 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: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not humble or old then mary is old. Everyone who is not quiet is both not creative and not humble. Everyone who is both not kind and curious is not old. If someone is either tall or generous then someone is kind or calm and vice versa. Everyone who is either quiet or old is both tall and not humble. Everyone who is either brave or funny is generous or not patient and vice versa. Everyone who is not old or not happy is either not kind or tall and vice versa. Everyone who is curious is strong. If paul is both not strong and not brave then someone is both not funny and calm. If alice is both not calm and not old then paul is not old and vice versa. Everyone who is both patient and not patient is not happy or curious. Everyone who is funny is not generous and vice versa. If paul is either not curious or not humble then john is not strong or not humble and vice versa. If fred is either not quiet or not funny then someone is either not wise or not strong. If lucy is not creative or not funny then someone is kind. If alice is old or not quiet then john is wise. Someone is either not tall or not brave. Someone is both rich and not quiet. Someone is brave or humble. Someone is both not brave and creative. Someone is either wise or brave. John is tall. Someone is both not brave and calm. | Paul is brave. | neutral | ((?[X]:((~humble(X)<~>old(X))))=>(old(mary)))&
(![X]:(~quiet(X)=>(~creative(X)&~humble(X))))&
(![X]:((~kind(X)&curious(X))=>~old(X)))&
((?[X]:((tall(X)<~>generous(X))))<=>(?[X]:((kind(X)|calm(X)))))&
(![X]:((quiet(X)<~>old(X))=>(tall(X)&~humble(X))))&
(![X]:((brave(X)<~>funny(X))<=>(generous(X)|~patient(X))))&
(![X]:((~old(X)|~happy(X))<=>(~kind(X)<~>tall(X))))&
(![X]:(curious(X)=>strong(X)))&
(((~strong(paul)&~brave(paul)))=>(?[X]:((~funny(X)&calm(X)))))&
(((~calm(alice)&~old(alice)))<=>(~old(paul)))&
(![X]:((patient(X)&~patient(X))=>(~happy(X)|curious(X))))&
(![X]:(funny(X)<=>~generous(X)))&
(((~curious(paul)<~>~humble(paul)))<=>((~strong(john)|~humble(john))))&
(((~quiet(fred)<~>~funny(fred)))=>(?[X]:((~wise(X)<~>~strong(X)))))&
(((~creative(lucy)|~funny(lucy)))=>(?[X]:(kind(X))))&
(((old(alice)|~quiet(alice)))=>(wise(john)))&
(?[X]:((~tall(X)<~>~brave(X))))&
(?[X]:((rich(X)&~quiet(X))))&
(?[X]:((brave(X)|humble(X))))&
(?[X]:((~brave(X)&creative(X))))&
(?[X]:((wise(X)<~>brave(X))))&
(tall(john))&
(?[X]:((~brave(X)&calm(X)))) | brave(paul) | [] | null | 0 |
Everyone who is both not old and not tall is not creative or funny.
If someone is not old or tall then fred is funny or not rich and vice versa.
If someone is creative then someone is happy and vice versa.
Everyone who is either not strong or wise is not curious or wise and vice versa.
If someone is either wise or brave then someone is either not happy or not rich and vice versa.
Everyone who is not brave is wise.
Everyone who is either curious or not humble is old and vice versa.
If paul is happy or old then someone is either happy or not strong.
Everyone who is both humble and not tall is either wise or brave.
Everyone who is not curious is not kind.
If john is either not curious or happy then someone is strong or not humble and vice versa.
Everyone who is both funny and humble is patient or not kind and vice versa.
If someone is brave then someone is not tall or not humble and vice versa.
If alice is patient then mary is both not brave and not humble.
If someone is kind then alice is either not kind or not happy.
Everyone who is either quiet or not tall is curious and vice versa.
Someone is brave.
Mary is both not rich and wise.
Susan is both not curious and strong.
Someone is not humble.
John is wise.
Mary is both not humble and funny.
Someone is either wise or not quiet.
Fred is either not wise or old. | Mary is rich. | contradiction | (![X]:((~old(X)&~tall(X))=>(~creative(X)|funny(X))))&
((?[X]:((~old(X)|tall(X))))<=>((funny(fred)|~rich(fred))))&
((?[X]:(creative(X)))<=>(?[X]:(happy(X))))&
(![X]:((~strong(X)<~>wise(X))<=>(~curious(X)|wise(X))))&
((?[X]:((wise(X)<~>brave(X))))<=>(?[X]:((~happy(X)<~>~rich(X)))))&
(![X]:(~brave(X)=>wise(X)))&
(![X]:((curious(X)<~>~humble(X))<=>old(X)))&
(((happy(paul)|old(paul)))=>(?[X]:((happy(X)<~>~strong(X)))))&
(![X]:((humble(X)&~tall(X))=>(wise(X)<~>brave(X))))&
(![X]:(~curious(X)=>~kind(X)))&
(((~curious(john)<~>happy(john)))<=>(?[X]:((strong(X)|~humble(X)))))&
(![X]:((funny(X)&humble(X))<=>(patient(X)|~kind(X))))&
((?[X]:(brave(X)))<=>(?[X]:((~tall(X)|~humble(X)))))&
((patient(alice))=>((~brave(mary)&~humble(mary))))&
((?[X]:(kind(X)))=>((~kind(alice)<~>~happy(alice))))&
(![X]:((quiet(X)<~>~tall(X))<=>curious(X)))&
(?[X]:(brave(X)))&
((~rich(mary)&wise(mary)))&
((~curious(susan)&strong(susan)))&
(?[X]:(~humble(X)))&
(wise(john))&
((~humble(mary)&funny(mary)))&
(?[X]:((wise(X)<~>~quiet(X))))&
((~wise(fred)<~>old(fred))) | rich(mary) | [
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 5229500457787470842437808
% SZS output start Proof for 5229500457787470842437808
18. wise(mary) & ~rich(mary) [input p17]
25. rich(mary) [input hypothesis]
137. ~rich(mary) [cnf transformation 18]
149. rich(mary) [cnf transformation 25]
348. $false [subsumption resolution 149,137]
% SZS output end Proof for 5229500457787470842437808
% ------------------------------
% 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 either creative or wise is both not happy and creative and vice versa.
Everyone who is both not humble and funny is both not strong and kind.
If alice is calm then someone is both calm and generous.
If alice is humble or happy then someone is both humble and not old.
Everyone who is both not wise and not humble is either rich or strong.
Everyone who is both not happy and wise is both not strong and old and vice versa.
If alice is either not wise or patient then alice is funny and vice versa.
Everyone who is either not tall or calm is both old and rich.
If alice is both funny and happy then paul is both rich and creative and vice versa.
If mary is not kind then mary is funny or not patient and vice versa.
If john is either wise or tall then paul is not humble and vice versa.
Everyone who is creative is not strong or happy.
Everyone who is either not generous or brave is both brave and not brave.
Everyone who is both patient and not brave is not calm or wise and vice versa.
If lucy is strong then john is both not patient and not old.
If someone is both not strong and rich then john is both not humble and not strong.
Someone is not creative or curious.
Mary is both not curious and not quiet.
Someone is kind or generous.
Susan is generous or humble.
Mary is not patient.
John is not quiet.
Someone is quiet or old.
Susan is both curious and funny. | Mary is creative. | neutral | (![X]:((creative(X)<~>wise(X))<=>(~happy(X)&creative(X))))&
(![X]:((~humble(X)&funny(X))=>(~strong(X)&kind(X))))&
((calm(alice))=>(?[X]:((calm(X)&generous(X)))))&
(((humble(alice)|happy(alice)))=>(?[X]:((humble(X)&~old(X)))))&
(![X]:((~wise(X)&~humble(X))=>(rich(X)<~>strong(X))))&
(![X]:((~happy(X)&wise(X))<=>(~strong(X)&old(X))))&
(((~wise(alice)<~>patient(alice)))<=>(funny(alice)))&
(![X]:((~tall(X)<~>calm(X))=>(old(X)&rich(X))))&
(((funny(alice)&happy(alice)))<=>((rich(paul)&creative(paul))))&
((~kind(mary))<=>((funny(mary)|~patient(mary))))&
(((wise(john)<~>tall(john)))<=>(~humble(paul)))&
(![X]:(creative(X)=>(~strong(X)|happy(X))))&
(![X]:((~generous(X)<~>brave(X))=>(brave(X)&~brave(X))))&
(![X]:((patient(X)&~brave(X))<=>(~calm(X)|wise(X))))&
((strong(lucy))=>((~patient(john)&~old(john))))&
((?[X]:((~strong(X)&rich(X))))=>((~humble(john)&~strong(john))))&
(?[X]:((~creative(X)|curious(X))))&
((~curious(mary)&~quiet(mary)))&
(?[X]:((kind(X)|generous(X))))&
((generous(susan)|humble(susan)))&
(~patient(mary))&
(~quiet(john))&
(?[X]:((quiet(X)|old(X))))&
((curious(susan)&funny(susan))) | creative(mary) | [] | null | 0 |
If mary is either not kind or humble then john is wise.
Everyone who is not curious is both quiet and curious and vice versa.
Everyone who is both not strong and not happy is calm or creative.
If susan is either not funny or kind then someone is both not strong and kind and vice versa.
Everyone who is either old or funny is calm and vice versa.
Everyone who is generous is not happy and vice versa.
Everyone who is not patient is quiet.
If john is both happy and quiet then someone is either not old or happy.
If someone is either not strong or not generous then someone is quiet and vice versa.
Everyone who is not funny is creative and vice versa.
Everyone who is not funny or not happy is not old or happy and vice versa.
Everyone who is not generous or not funny is both not strong and humble.
Everyone who is both not strong and not creative is quiet or not calm and vice versa.
Everyone who is both not tall and not rich is not creative or not kind and vice versa.
Everyone who is patient or generous is funny or not old and vice versa.
Fred is either quiet or not wise.
Lucy is either kind or not curious.
Someone is either brave or patient.
Someone is humble. | Susan is patient. | entailment | (((~kind(mary)<~>humble(mary)))=>(wise(john)))&
(![X]:(~curious(X)<=>(quiet(X)&curious(X))))&
(![X]:((~strong(X)&~happy(X))=>(calm(X)|creative(X))))&
(((~funny(susan)<~>kind(susan)))<=>(?[X]:((~strong(X)&kind(X)))))&
(![X]:((old(X)<~>funny(X))<=>calm(X)))&
(![X]:(generous(X)<=>~happy(X)))&
(![X]:(~patient(X)=>quiet(X)))&
(((happy(john)&quiet(john)))=>(?[X]:((~old(X)<~>happy(X)))))&
((?[X]:((~strong(X)<~>~generous(X))))<=>(?[X]:(quiet(X))))&
(![X]:(~funny(X)<=>creative(X)))&
(![X]:((~funny(X)|~happy(X))<=>(~old(X)|happy(X))))&
(![X]:((~generous(X)|~funny(X))=>(~strong(X)&humble(X))))&
(![X]:((~strong(X)&~creative(X))<=>(quiet(X)|~calm(X))))&
(![X]:((~tall(X)&~rich(X))<=>(~creative(X)|~kind(X))))&
(![X]:((patient(X)|generous(X))<=>(funny(X)|~old(X))))&
((quiet(fred)<~>~wise(fred)))&
((kind(lucy)<~>~curious(lucy)))&
(?[X]:((brave(X)<~>patient(X))))&
(?[X]:(humble(X))) | patient(susan) | [
"p1",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 706378899648013963541273
% SZS output start Proof for 706378899648013963541273
2. ! [X0] : (~curious(X0) <=> (curious(X0) & quiet(X0))) [input p1]
7. ! [X0] : (~patient(X0) => quiet(X0)) [input p6]
20. ~patient(susan) [input hypothesis]
25. ! [X0] : (quiet(X0) | patient(X0)) [ennf transformation 7]
30. ! [X0] : ((~curious(X0) | (~curious(X0) | ~quiet(X0))) & ((curious(X0) & quiet(X0)) | curious(X0))) [nnf transformation 2]
31. ! [X0] : ((~curious(X0) | ~curious(X0) | ~quiet(X0)) & ((curious(X0) & quiet(X0)) | curious(X0))) [flattening 30]
65. curious(X0) | curious(X0) [cnf transformation 31]
66. ~curious(X0) | ~curious(X0) | ~quiet(X0) [cnf transformation 31]
80. patient(X0) | quiet(X0) [cnf transformation 25]
118. ~patient(susan) [cnf transformation 20]
121. curious(X0) [duplicate literal removal 65]
122. ~quiet(X0) | ~curious(X0) [duplicate literal removal 66]
231. quiet(susan) [resolution 80,118]
250. ~curious(susan) [resolution 122,231]
254. $false [subsumption resolution 250,121]
% SZS output end Proof for 706378899648013963541273
% ------------------------------
% 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 strong and not happy then susan is not brave. Everyone who is either brave or not creative is kind and vice versa. Everyone who is both not old and quiet is happy. If lucy is both quiet and not wise then mary is both wise and not patient. Everyone who is creative or humble is either not patient or rich. Everyone who is either not creative or generous is not brave. Everyone who is brave is not calm or humble and vice versa. If fred is either not strong or not wise then paul is both strong and old. Everyone who is old is either not funny or not brave. Everyone who is both not brave and patient is both not wise and brave and vice versa. If someone is not quiet or not brave then someone is both not kind and humble. Everyone who is patient or not tall is either not humble or wise. Everyone who is both kind and not funny is not patient and vice versa. If someone is not calm or patient then paul is generous. Everyone who is either not wise or not strong is either not rich or strong and vice versa. Someone is brave. Mary is either funny or curious. Someone is creative. Someone is not patient or wise. Someone is either happy or not old. Mary is not tall or not kind. | Paul is quiet. | entailment | ((?[X]:((strong(X)&~happy(X))))=>(~brave(susan)))&
(![X]:((brave(X)<~>~creative(X))<=>kind(X)))&
(![X]:((~old(X)&quiet(X))=>happy(X)))&
(((quiet(lucy)&~wise(lucy)))=>((wise(mary)&~patient(mary))))&
(![X]:((creative(X)|humble(X))=>(~patient(X)<~>rich(X))))&
(![X]:((~creative(X)<~>generous(X))=>~brave(X)))&
(![X]:(brave(X)<=>(~calm(X)|humble(X))))&
(((~strong(fred)<~>~wise(fred)))=>((strong(paul)&old(paul))))&
(![X]:(old(X)=>(~funny(X)<~>~brave(X))))&
(![X]:((~brave(X)&patient(X))<=>(~wise(X)&brave(X))))&
((?[X]:((~quiet(X)|~brave(X))))=>(?[X]:((~kind(X)&humble(X)))))&
(![X]:((patient(X)|~tall(X))=>(~humble(X)<~>wise(X))))&
(![X]:((kind(X)&~funny(X))<=>~patient(X)))&
((?[X]:((~calm(X)|patient(X))))=>(generous(paul)))&
(![X]:((~wise(X)<~>~strong(X))<=>(~rich(X)<~>strong(X))))&
(?[X]:(brave(X)))&
((funny(mary)<~>curious(mary)))&
(?[X]:(creative(X)))&
(?[X]:((~patient(X)|wise(X))))&
(?[X]:((happy(X)<~>~old(X))))&
((~tall(mary)|~kind(mary))) | quiet(paul) | [
"p4",
"p6",
"p9",
"p10",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2111343696807591623277141
% SZS output start Proof for 2111343696807591623277141
5. ! [X0] : ((humble(X0) | creative(X0)) => (~patient(X0) <~> rich(X0))) [input p4]
7. ! [X0] : (brave(X0) <=> (humble(X0) | ~calm(X0))) [input p6]
10. ! [X0] : ((patient(X0) & ~brave(X0)) <=> (brave(X0) & ~wise(X0))) [input p9]
11. ? [X0] : (~brave(X0) | ~quiet(X0)) => ? [X0] : (humble(X0) & ~kind(X0)) [input p10]
13. ! [X0] : ((~funny(X0) & kind(X0)) <=> ~patient(X0)) [input p12]
15. ! [X0] : ((~wise(X0) <~> ~strong(X0)) <=> (~rich(X0) <~> strong(X0))) [input p14]
22. ~quiet(paul) [input hypothesis]
23. ? [X0] : (~brave(X0) | ~quiet(X0)) => ? [X1] : (humble(X1) & ~kind(X1)) [rectify 11]
29. ! [X0] : ((~patient(X0) <~> rich(X0)) | (~humble(X0) & ~creative(X0))) [ennf transformation 5]
33. ? [X1] : (humble(X1) & ~kind(X1)) | ! [X0] : (brave(X0) & quiet(X0)) [ennf transformation 23]
37. ! [X0] : (((~rich(X0) | patient(X0)) & (rich(X0) | ~patient(X0))) | (~humble(X0) & ~creative(X0))) [nnf transformation 29]
39. ! [X0] : ((brave(X0) | (~humble(X0) & calm(X0))) & ((humble(X0) | ~calm(X0)) | ~brave(X0))) [nnf transformation 7]
40. ! [X0] : ((brave(X0) | (~humble(X0) & calm(X0))) & (humble(X0) | ~calm(X0) | ~brave(X0))) [flattening 39]
43. ! [X0] : (((patient(X0) & ~brave(X0)) | (~brave(X0) | wise(X0))) & ((brave(X0) & ~wise(X0)) | (~patient(X0) | brave(X0)))) [nnf transformation 10]
44. ! [X0] : (((patient(X0) & ~brave(X0)) | ~brave(X0) | wise(X0)) & ((brave(X0) & ~wise(X0)) | ~patient(X0) | brave(X0))) [flattening 43]
45. ? [X0] : (humble(X0) & ~kind(X0)) | ! [X1] : (brave(X1) & quiet(X1)) [rectify 33]
46. ? [X0] : (humble(X0) & ~kind(X0)) => (humble(sK0) & ~kind(sK0)) [choice axiom]
47. (humble(sK0) & ~kind(sK0)) | ! [X1] : (brave(X1) & quiet(X1)) [skolemisation 45,46]
49. ! [X0] : (((~funny(X0) & kind(X0)) | patient(X0)) & (~patient(X0) | (funny(X0) | ~kind(X0)))) [nnf transformation 13]
50. ! [X0] : (((~funny(X0) & kind(X0)) | patient(X0)) & (~patient(X0) | funny(X0) | ~kind(X0))) [flattening 49]
51. ! [X0] : ((((strong(X0) | wise(X0)) & (~strong(X0) | ~wise(X0))) | ((~rich(X0) | ~strong(X0)) & (strong(X0) | rich(X0)))) & (((~strong(X0) | rich(X0)) & (strong(X0) | ~rich(X0))) | ((~wise(X0) | strong(X0)) & (~strong(X0) | wise(X0))))) [nnf transformation 15]
71. ~humble(X0) | ~patient(X0) | rich(X0) [cnf transformation 37]
78. ~humble(X0) | brave(X0) [cnf transformation 40]
87. ~brave(X0) | ~brave(X0) | wise(X0) [cnf transformation 44]
89. ~kind(sK0) | quiet(X1) [cnf transformation 47]
91. humble(sK0) | quiet(X1) [cnf transformation 47]
98. patient(X0) | kind(X0) [cnf transformation 50]
103. strong(X0) | ~rich(X0) | ~wise(X0) | strong(X0) [cnf transformation 51]
107. ~strong(X0) | ~wise(X0) | ~rich(X0) | ~strong(X0) [cnf transformation 51]
118. ~quiet(paul) [cnf transformation 22]
119. strong(X0) | ~rich(X0) | ~wise(X0) [duplicate literal removal 103]
121. ~strong(X0) | ~wise(X0) | ~rich(X0) [duplicate literal removal 107]
124. ~brave(X0) | wise(X0) [duplicate literal removal 87]
175. 12 <=> humble(sK0) [avatar definition]
177. humble(sK0) <- (12) [avatar component clause 175]
180. 13 <=> ! [X1] : quiet(X1) [avatar definition]
181. quiet(X1) <- (13) [avatar component clause 180]
182. 13 | 12 [avatar split clause 91,175,180]
184. 14 <=> kind(sK0) [avatar definition]
186. ~kind(sK0) <- (~14) [avatar component clause 184]
188. 13 | ~14 [avatar split clause 89,184,180]
202. ~rich(X0) | ~wise(X0) [subsumption resolution 119,121]
241. brave(sK0) <- (12) [resolution 78,177]
248. wise(sK0) <- (12) [resolution 124,241]
291. ~patient(sK0) | rich(sK0) <- (12) [resolution 71,177]
293. 30 <=> rich(sK0) [avatar definition]
295. rich(sK0) <- (30) [avatar component clause 293]
297. 31 <=> patient(sK0) [avatar definition]
299. ~patient(sK0) <- (~31) [avatar component clause 297]
300. 30 | ~31 | ~12 [avatar split clause 291,175,297,293]
301. kind(sK0) <- (~31) [resolution 299,98]
302. $false <- (~14, ~31) [subsumption resolution 301,186]
303. 14 | 31 [avatar contradiction clause 302]
306. ~wise(sK0) <- (30) [resolution 295,202]
307. $false <- (12, 30) [subsumption resolution 306,248]
308. ~12 | ~30 [avatar contradiction clause 307]
314. $false <- (13) [resolution 181,118]
318. ~13 [avatar contradiction clause 314]
319. $false [avatar sat refutation 182,188,300,303,308,318]
% SZS output end Proof for 2111343696807591623277141
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not wise is both not brave and wise and vice versa.
Everyone who is not calm or old is either patient or not quiet.
Everyone who is curious or not strong is not tall.
Everyone who is both calm and not patient is either humble or not humble and vice versa.
Everyone who is creative is humble.
Everyone who is not generous or tall is either not happy or calm.
Everyone who is either not kind or wise is strong.
If mary is both not tall and humble then mary is both kind and not brave.
If susan is strong then john is both old and not old and vice versa.
Everyone who is both not creative and creative is both not strong and kind and vice versa.
If john is either brave or not old then someone is either old or not brave.
Everyone who is funny or generous is either quiet or not humble.
If fred is generous then lucy is either brave or creative.
Everyone who is not rich is both not humble and happy and vice versa.
If someone is rich or humble then susan is both tall and not curious.
If lucy is both old and happy then alice is both happy and quiet.
Alice is not tall.
Someone is both brave and strong.
Fred is not creative.
Someone is kind.
Paul is old or not wise. | John is generous. | neutral | (![X]:(~wise(X)<=>(~brave(X)&wise(X))))&
(![X]:((~calm(X)|old(X))=>(patient(X)<~>~quiet(X))))&
(![X]:((curious(X)|~strong(X))=>~tall(X)))&
(![X]:((calm(X)&~patient(X))<=>(humble(X)<~>~humble(X))))&
(![X]:(creative(X)=>humble(X)))&
(![X]:((~generous(X)|tall(X))=>(~happy(X)<~>calm(X))))&
(![X]:((~kind(X)<~>wise(X))=>strong(X)))&
(((~tall(mary)&humble(mary)))=>((kind(mary)&~brave(mary))))&
((strong(susan))<=>((old(john)&~old(john))))&
(![X]:((~creative(X)&creative(X))<=>(~strong(X)&kind(X))))&
(((brave(john)<~>~old(john)))=>(?[X]:((old(X)<~>~brave(X)))))&
(![X]:((funny(X)|generous(X))=>(quiet(X)<~>~humble(X))))&
((generous(fred))=>((brave(lucy)<~>creative(lucy))))&
(![X]:(~rich(X)<=>(~humble(X)&happy(X))))&
((?[X]:((rich(X)|humble(X))))=>((tall(susan)&~curious(susan))))&
(((old(lucy)&happy(lucy)))=>((happy(alice)&quiet(alice))))&
(~tall(alice))&
(?[X]:((brave(X)&strong(X))))&
(~creative(fred))&
(?[X]:(kind(X)))&
((old(paul)|~wise(paul))) | generous(john) | [] | null | 0 |
Everyone who is patient or creative is either rich or not strong and vice versa.
Everyone who is funny or curious is creative or not quiet and vice versa.
Everyone who is both not curious and tall is either creative or not quiet and vice versa.
If fred is funny then john is not curious or rich and vice versa.
Everyone who is both not rich and not happy is not brave and vice versa.
If john is quiet then someone is not tall or not generous.
If paul is curious or patient then someone is both not humble and tall.
Everyone who is both not calm and brave is both not patient and not funny and vice versa.
Everyone who is both not happy and calm is both not quiet and patient.
If someone is brave then john is both funny and not rich and vice versa.
Everyone who is not funny is either not rich or strong.
Everyone who is not patient is both not strong and humble.
Everyone who is not humble or not kind is not old or generous.
If alice is both not quiet and not rich then someone is not creative and vice versa.
Everyone who is wise is old and vice versa.
If alice is either not quiet or curious then mary is either old or curious.
Someone is quiet.
Mary is either strong or rich.
Fred is not generous or patient.
Someone is either generous or old.
Someone is not patient.
Someone is creative.
Someone is either not old or funny.
Someone is both happy and not funny. | Mary is quiet. | contradiction | (![X]:((patient(X)|creative(X))<=>(rich(X)<~>~strong(X))))&
(![X]:((funny(X)|curious(X))<=>(creative(X)|~quiet(X))))&
(![X]:((~curious(X)&tall(X))<=>(creative(X)<~>~quiet(X))))&
((funny(fred))<=>((~curious(john)|rich(john))))&
(![X]:((~rich(X)&~happy(X))<=>~brave(X)))&
((quiet(john))=>(?[X]:((~tall(X)|~generous(X)))))&
(((curious(paul)|patient(paul)))=>(?[X]:((~humble(X)&tall(X)))))&
(![X]:((~calm(X)&brave(X))<=>(~patient(X)&~funny(X))))&
(![X]:((~happy(X)&calm(X))=>(~quiet(X)&patient(X))))&
((?[X]:(brave(X)))<=>((funny(john)&~rich(john))))&
(![X]:(~funny(X)=>(~rich(X)<~>strong(X))))&
(![X]:(~patient(X)=>(~strong(X)&humble(X))))&
(![X]:((~humble(X)|~kind(X))=>(~old(X)|generous(X))))&
(((~quiet(alice)&~rich(alice)))<=>(?[X]:(~creative(X))))&
(![X]:(wise(X)<=>old(X)))&
(((~quiet(alice)<~>curious(alice)))=>((old(mary)<~>curious(mary))))&
(?[X]:(quiet(X)))&
((strong(mary)<~>rich(mary)))&
((~generous(fred)|patient(fred)))&
(?[X]:((generous(X)<~>old(X))))&
(?[X]:(~patient(X)))&
(?[X]:(creative(X)))&
(?[X]:((~old(X)<~>funny(X))))&
(?[X]:((happy(X)&~funny(X)))) | quiet(mary) | [
"p0",
"p1",
"p10",
"p11",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 1144968402258637657811073
% SZS output start Proof for 1144968402258637657811073
1. ! [X0] : ((creative(X0) | patient(X0)) <=> (rich(X0) <~> ~strong(X0))) [input p0]
2. ! [X0] : ((curious(X0) | funny(X0)) <=> (~quiet(X0) | creative(X0))) [input p1]
11. ! [X0] : (~funny(X0) => (~rich(X0) <~> strong(X0))) [input p10]
12. ! [X0] : (~patient(X0) => (humble(X0) & ~strong(X0))) [input p11]
18. strong(mary) <~> rich(mary) [input p17]
25. quiet(mary) [input hypothesis]
31. ! [X0] : ((~rich(X0) <~> strong(X0)) | funny(X0)) [ennf transformation 11]
32. ! [X0] : ((humble(X0) & ~strong(X0)) | patient(X0)) [ennf transformation 12]
36. ! [X0] : (((creative(X0) | patient(X0)) | ((rich(X0) | strong(X0)) & (~strong(X0) | ~rich(X0)))) & (((strong(X0) | ~rich(X0)) & (~strong(X0) | rich(X0))) | (~creative(X0) & ~patient(X0)))) [nnf transformation 1]
37. ! [X0] : ((creative(X0) | patient(X0) | ((rich(X0) | strong(X0)) & (~strong(X0) | ~rich(X0)))) & (((strong(X0) | ~rich(X0)) & (~strong(X0) | rich(X0))) | (~creative(X0) & ~patient(X0)))) [flattening 36]
38. ! [X0] : (((curious(X0) | funny(X0)) | (quiet(X0) & ~creative(X0))) & ((~quiet(X0) | creative(X0)) | (~curious(X0) & ~funny(X0)))) [nnf transformation 2]
39. ! [X0] : ((curious(X0) | funny(X0) | (quiet(X0) & ~creative(X0))) & (~quiet(X0) | creative(X0) | (~curious(X0) & ~funny(X0)))) [flattening 38]
57. ! [X0] : (((~strong(X0) | rich(X0)) & (strong(X0) | ~rich(X0))) | funny(X0)) [nnf transformation 31]
66. (~rich(mary) | ~strong(mary)) & (rich(mary) | strong(mary)) [nnf transformation 18]
79. ~strong(X0) | rich(X0) | ~patient(X0) [cnf transformation 37]
82. ~rich(X0) | strong(X0) | ~creative(X0) [cnf transformation 37]
85. ~quiet(X0) | creative(X0) | ~funny(X0) [cnf transformation 39]
115. ~rich(X0) | strong(X0) | funny(X0) [cnf transformation 57]
117. ~strong(X0) | patient(X0) [cnf transformation 32]
128. rich(mary) | strong(mary) [cnf transformation 66]
129. ~rich(mary) | ~strong(mary) [cnf transformation 66]
139. quiet(mary) [cnf transformation 25]
238. 21 <=> strong(mary) [avatar definition]
239. strong(mary) <- (21) [avatar component clause 238]
240. ~strong(mary) <- (~21) [avatar component clause 238]
242. 22 <=> rich(mary) [avatar definition]
243. rich(mary) <- (22) [avatar component clause 242]
244. ~rich(mary) <- (~22) [avatar component clause 242]
245. ~21 | ~22 [avatar split clause 129,242,238]
246. 21 | 22 [avatar split clause 128,242,238]
277. patient(mary) <- (21) [resolution 117,239]
283. rich(mary) | ~patient(mary) <- (21) [resolution 79,239]
284. ~patient(mary) <- (21, ~22) [subsumption resolution 283,244]
285. $false <- (21, ~22) [subsumption resolution 284,277]
286. ~21 | 22 [avatar contradiction clause 285]
290. strong(mary) | ~creative(mary) <- (22) [resolution 82,243]
291. ~creative(mary) <- (~21, 22) [subsumption resolution 290,240]
296. creative(mary) | ~funny(mary) [resolution 85,139]
306. ~funny(mary) <- (~21, 22) [subsumption resolution 296,291]
421. strong(mary) | funny(mary) <- (22) [resolution 115,243]
423. funny(mary) <- (~21, 22) [subsumption resolution 421,240]
424. $false <- (~21, 22) [subsumption resolution 423,306]
425. 21 | ~22 [avatar contradiction clause 424]
428. $false [avatar sat refutation 245,246,286,425]
% SZS output end Proof for 1144968402258637657811073
% ------------------------------
% 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: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not funny or not patient is either brave or tall and vice versa.
Everyone who is not humble is not tall and vice versa.
Everyone who is not strong or not happy is calm or not brave.
Everyone who is either curious or humble is both kind and not humble.
Everyone who is both rich and wise is either quiet or strong and vice versa.
If alice is both not tall and old then someone is not patient or kind.
Everyone who is not calm is both humble and not strong and vice versa.
Everyone who is wise is old.
Everyone who is not brave is not quiet or creative.
Everyone who is not quiet is either calm or not happy.
If fred is both calm and tall then someone is both rich and creative and vice versa.
Everyone who is quiet or not quiet is not funny and vice versa.
Everyone who is both creative and humble is both not quiet and humble.
Everyone who is either not creative or not quiet is not rich or calm and vice versa.
Everyone who is not creative is both not strong and curious.
Everyone who is not quiet is not rich and vice versa.
Paul is both creative and wise.
Someone is curious or not rich.
Someone is not patient.
Someone is rich or not kind.
Susan is not kind.
Someone is not generous. | Alice is humble. | neutral | (![X]:((~funny(X)<~>~patient(X))<=>(brave(X)<~>tall(X))))&
(![X]:(~humble(X)<=>~tall(X)))&
(![X]:((~strong(X)|~happy(X))=>(calm(X)|~brave(X))))&
(![X]:((curious(X)<~>humble(X))=>(kind(X)&~humble(X))))&
(![X]:((rich(X)&wise(X))<=>(quiet(X)<~>strong(X))))&
(((~tall(alice)&old(alice)))=>(?[X]:((~patient(X)|kind(X)))))&
(![X]:(~calm(X)<=>(humble(X)&~strong(X))))&
(![X]:(wise(X)=>old(X)))&
(![X]:(~brave(X)=>(~quiet(X)|creative(X))))&
(![X]:(~quiet(X)=>(calm(X)<~>~happy(X))))&
(((calm(fred)&tall(fred)))<=>(?[X]:((rich(X)&creative(X)))))&
(![X]:((quiet(X)|~quiet(X))<=>~funny(X)))&
(![X]:((creative(X)&humble(X))=>(~quiet(X)&humble(X))))&
(![X]:((~creative(X)<~>~quiet(X))<=>(~rich(X)|calm(X))))&
(![X]:(~creative(X)=>(~strong(X)&curious(X))))&
(![X]:(~quiet(X)<=>~rich(X)))&
((creative(paul)&wise(paul)))&
(?[X]:((curious(X)|~rich(X))))&
(?[X]:(~patient(X)))&
(?[X]:((rich(X)|~kind(X))))&
(~kind(susan))&
(?[X]:(~generous(X))) | humble(alice) | [] | null | 0 |
Everyone who is old or not old is not humble and vice versa.
Everyone who is both not generous and curious is either not curious or generous and vice versa.
Everyone who is patient is wise or not rich and vice versa.
If susan is not generous then someone is both old and not creative.
Everyone who is either quiet or creative is old or not funny and vice versa.
Everyone who is either not strong or not humble is kind.
Everyone who is both generous and not brave is either curious or not wise.
Everyone who is either not old or calm is not generous or kind and vice versa.
Everyone who is either not quiet or rich is either not brave or not tall and vice versa.
Everyone who is generous is not brave.
Everyone who is either not strong or not old is old or kind and vice versa.
Everyone who is either wise or humble is both curious and strong.
If john is either tall or calm then someone is wise and vice versa.
If lucy is either not generous or quiet then someone is either creative or not happy.
Everyone who is either not humble or kind is not curious and vice versa.
Everyone who is not rich is not patient or not creative and vice versa.
Someone is quiet.
Someone is not humble or funny.
Someone is both not calm and quiet.
Paul is not quiet.
Fred is generous.
Lucy is either not patient or quiet. | Lucy is tall. | contradiction | (![X]:((old(X)|~old(X))<=>~humble(X)))&
(![X]:((~generous(X)&curious(X))<=>(~curious(X)<~>generous(X))))&
(![X]:(patient(X)<=>(wise(X)|~rich(X))))&
((~generous(susan))=>(?[X]:((old(X)&~creative(X)))))&
(![X]:((quiet(X)<~>creative(X))<=>(old(X)|~funny(X))))&
(![X]:((~strong(X)<~>~humble(X))=>kind(X)))&
(![X]:((generous(X)&~brave(X))=>(curious(X)<~>~wise(X))))&
(![X]:((~old(X)<~>calm(X))<=>(~generous(X)|kind(X))))&
(![X]:((~quiet(X)<~>rich(X))<=>(~brave(X)<~>~tall(X))))&
(![X]:(generous(X)=>~brave(X)))&
(![X]:((~strong(X)<~>~old(X))<=>(old(X)|kind(X))))&
(![X]:((wise(X)<~>humble(X))=>(curious(X)&strong(X))))&
(((tall(john)<~>calm(john)))<=>(?[X]:(wise(X))))&
(((~generous(lucy)<~>quiet(lucy)))=>(?[X]:((creative(X)<~>~happy(X)))))&
(![X]:((~humble(X)<~>kind(X))<=>~curious(X)))&
(![X]:(~rich(X)<=>(~patient(X)|~creative(X))))&
(?[X]:(quiet(X)))&
(?[X]:((~humble(X)|funny(X))))&
(?[X]:((~calm(X)&quiet(X))))&
(~quiet(paul))&
(generous(fred))&
((~patient(lucy)<~>quiet(lucy))) | tall(lucy) | [
"p0",
"p1",
"p2",
"p8",
"p9",
"p11",
"p15",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 7949446660952558360232698
% SZS output start Proof for 7949446660952558360232698
1. ! [X0] : ((~old(X0) | old(X0)) <=> ~humble(X0)) [input p0]
2. ! [X0] : ((curious(X0) & ~generous(X0)) <=> (~curious(X0) <~> generous(X0))) [input p1]
3. ! [X0] : (patient(X0) <=> (~rich(X0) | wise(X0))) [input p2]
9. ! [X0] : ((~quiet(X0) <~> rich(X0)) <=> (~brave(X0) <~> ~tall(X0))) [input p8]
10. ! [X0] : (generous(X0) => ~brave(X0)) [input p9]
12. ! [X0] : ((wise(X0) <~> humble(X0)) => (strong(X0) & curious(X0))) [input p11]
16. ! [X0] : (~rich(X0) <=> (~creative(X0) | ~patient(X0))) [input p15]
22. ~patient(lucy) <~> quiet(lucy) [input p21]
23. tall(lucy) [input hypothesis]
28. ! [X0] : (~brave(X0) | ~generous(X0)) [ennf transformation 10]
29. ! [X0] : ((strong(X0) & curious(X0)) | (wise(X0) <=> humble(X0))) [ennf transformation 12]
31. ! [X0] : (((~old(X0) | old(X0)) | humble(X0)) & (~humble(X0) | (old(X0) & ~old(X0)))) [nnf transformation 1]
32. ! [X0] : ((~old(X0) | old(X0) | humble(X0)) & (~humble(X0) | (old(X0) & ~old(X0)))) [flattening 31]
33. ! [X0] : (((curious(X0) & ~generous(X0)) | ((~curious(X0) | ~generous(X0)) & (generous(X0) | curious(X0)))) & (((~generous(X0) | curious(X0)) & (generous(X0) | ~curious(X0))) | (~curious(X0) | generous(X0)))) [nnf transformation 2]
34. ! [X0] : (((curious(X0) & ~generous(X0)) | ((~curious(X0) | ~generous(X0)) & (generous(X0) | curious(X0)))) & (((~generous(X0) | curious(X0)) & (generous(X0) | ~curious(X0))) | ~curious(X0) | generous(X0))) [flattening 33]
35. ! [X0] : ((patient(X0) | (rich(X0) & ~wise(X0))) & ((~rich(X0) | wise(X0)) | ~patient(X0))) [nnf transformation 3]
36. ! [X0] : ((patient(X0) | (rich(X0) & ~wise(X0))) & (~rich(X0) | wise(X0) | ~patient(X0))) [flattening 35]
45. ! [X0] : ((((~rich(X0) | quiet(X0)) & (rich(X0) | ~quiet(X0))) | ((~brave(X0) | tall(X0)) & (~tall(X0) | brave(X0)))) & (((tall(X0) | brave(X0)) & (~tall(X0) | ~brave(X0))) | ((~quiet(X0) | ~rich(X0)) & (rich(X0) | quiet(X0))))) [nnf transformation 9]
48. ! [X0] : ((strong(X0) & curious(X0)) | ((wise(X0) | ~humble(X0)) & (humble(X0) | ~wise(X0)))) [nnf transformation 29]
57. ! [X0] : ((~rich(X0) | (creative(X0) & patient(X0))) & ((~creative(X0) | ~patient(X0)) | rich(X0))) [nnf transformation 16]
58. ! [X0] : ((~rich(X0) | (creative(X0) & patient(X0))) & (~creative(X0) | ~patient(X0) | rich(X0))) [flattening 57]
65. (~quiet(lucy) | patient(lucy)) & (quiet(lucy) | ~patient(lucy)) [nnf transformation 22]
66. ~humble(X0) | ~old(X0) [cnf transformation 32]
67. ~humble(X0) | old(X0) [cnf transformation 32]
69. generous(X0) | ~curious(X0) | ~curious(X0) | generous(X0) [cnf transformation 34]
72. ~generous(X0) | ~curious(X0) | ~generous(X0) [cnf transformation 34]
73. curious(X0) | generous(X0) | curious(X0) [cnf transformation 34]
75. ~rich(X0) | wise(X0) | ~patient(X0) [cnf transformation 36]
77. rich(X0) | patient(X0) [cnf transformation 36]
100. ~tall(X0) | ~quiet(X0) | rich(X0) | brave(X0) [cnf transformation 45]
104. ~brave(X0) | ~generous(X0) [cnf transformation 28]
111. curious(X0) | humble(X0) | ~wise(X0) [cnf transformation 48]
128. ~rich(X0) | patient(X0) [cnf transformation 58]
136. quiet(lucy) | ~patient(lucy) [cnf transformation 65]
138. tall(lucy) [cnf transformation 23]
141. generous(X0) | ~curious(X0) [duplicate literal removal 69]
142. ~curious(X0) | ~generous(X0) [duplicate literal removal 72]
143. curious(X0) | generous(X0) [duplicate literal removal 73]
144. ~humble(X0) [subsumption resolution 66,67]
145. ~curious(X0) [subsumption resolution 141,142]
164. humble(X0) | ~wise(X0) [subsumption resolution 111,145]
165. ~wise(X0) [subsumption resolution 164,144]
179. 6 <=> quiet(lucy) [avatar definition]
180. quiet(lucy) <- (6) [avatar component clause 179]
200. patient(X0) [subsumption resolution 128,77]
202. quiet(lucy) [subsumption resolution 136,200]
203. 6 [avatar split clause 202,179]
206. generous(X1) [resolution 143,145]
288. 21 <=> rich(lucy) [avatar definition]
289. rich(lucy) <- (21) [avatar component clause 288]
292. 22 <=> brave(lucy) [avatar definition]
293. brave(lucy) <- (22) [avatar component clause 292]
366. ~quiet(lucy) | rich(lucy) | brave(lucy) [resolution 100,138]
370. rich(lucy) | brave(lucy) <- (6) [subsumption resolution 366,180]
375. 22 | 21 | ~6 [avatar split clause 370,179,288,292]
376. wise(lucy) | ~patient(lucy) <- (21) [resolution 289,75]
378. ~patient(lucy) <- (21) [subsumption resolution 376,165]
379. $false <- (21) [subsumption resolution 378,200]
380. ~21 [avatar contradiction clause 379]
392. ~generous(lucy) <- (22) [resolution 293,104]
393. $false <- (22) [subsumption resolution 392,206]
394. ~22 [avatar contradiction clause 393]
395. $false [avatar sat refutation 203,375,380,394]
% SZS output end Proof for 7949446660952558360232698
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not generous or wise then someone is both not creative and funny and vice versa.
If someone is either brave or not happy then mary is either not happy or curious.
Everyone who is both strong and not creative is creative or kind and vice versa.
If someone is kind or not kind then someone is not creative and vice versa.
Everyone who is both not happy and tall is happy and vice versa.
Everyone who is curious or humble is not happy.
If someone is either not funny or generous then fred is both rich and not happy and vice versa.
Everyone who is calm is either patient or not creative and vice versa.
If lucy is both not funny and not generous then someone is both wise and not patient and vice versa.
If paul is humble or kind then someone is both not kind and kind.
If someone is not funny or not wise then someone is generous and vice versa.
If mary is either not old or creative then paul is not calm.
If someone is either not kind or strong then lucy is not curious.
Everyone who is not funny or quiet is either kind or patient and vice versa.
Everyone who is not brave is rich.
Someone is either old or wise.
Someone is either funny or not generous.
Paul is not quiet.
Fred is not brave or not kind.
Someone is humble.
Someone is both not happy and not wise.
Someone is either not brave or wise. | Paul is not kind. | entailment | ((?[X]:((~generous(X)<~>wise(X))))<=>(?[X]:((~creative(X)&funny(X)))))&
((?[X]:((brave(X)<~>~happy(X))))=>((~happy(mary)<~>curious(mary))))&
(![X]:((strong(X)&~creative(X))<=>(creative(X)|kind(X))))&
((?[X]:((kind(X)|~kind(X))))<=>(?[X]:(~creative(X))))&
(![X]:((~happy(X)&tall(X))<=>happy(X)))&
(![X]:((curious(X)|humble(X))=>~happy(X)))&
((?[X]:((~funny(X)<~>generous(X))))<=>((rich(fred)&~happy(fred))))&
(![X]:(calm(X)<=>(patient(X)<~>~creative(X))))&
(((~funny(lucy)&~generous(lucy)))<=>(?[X]:((wise(X)&~patient(X)))))&
(((humble(paul)|kind(paul)))=>(?[X]:((~kind(X)&kind(X)))))&
((?[X]:((~funny(X)|~wise(X))))<=>(?[X]:(generous(X))))&
(((~old(mary)<~>creative(mary)))=>(~calm(paul)))&
((?[X]:((~kind(X)<~>strong(X))))=>(~curious(lucy)))&
(![X]:((~funny(X)|quiet(X))<=>(kind(X)<~>patient(X))))&
(![X]:(~brave(X)=>rich(X)))&
(?[X]:((old(X)<~>wise(X))))&
(?[X]:((funny(X)<~>~generous(X))))&
(~quiet(paul))&
((~brave(fred)|~kind(fred)))&
(?[X]:(humble(X)))&
(?[X]:((~happy(X)&~wise(X))))&
(?[X]:((~brave(X)<~>wise(X)))) | ~kind(paul) | [
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 6445123127610181759701072
% SZS output start Proof for 6445123127610181759701072
10. (kind(paul) | humble(paul)) => ? [X0] : (kind(X0) & ~kind(X0)) [input p9]
23. kind(paul) [input hypothesis]
31. ? [X0] : (kind(X0) & ~kind(X0)) | (~kind(paul) & ~humble(paul)) [ennf transformation 10]
61. ? [X0] : (kind(X0) & ~kind(X0)) => (kind(sK6) & ~kind(sK6)) [choice axiom]
62. (kind(sK6) & ~kind(sK6)) | (~kind(paul) & ~humble(paul)) [skolemisation 31,61]
121. ~kind(sK6) | ~kind(paul) [cnf transformation 62]
123. kind(sK6) | ~kind(paul) [cnf transformation 62]
149. kind(paul) [cnf transformation 23]
254. 22 <=> kind(paul) [avatar definition]
258. 23 <=> kind(sK6) [avatar definition]
261. ~22 | 23 [avatar split clause 123,258,254]
267. ~22 | ~23 [avatar split clause 121,258,254]
356. 22 [avatar split clause 149,254]
357. $false [avatar sat refutation 261,267,356]
% SZS output end Proof for 6445123127610181759701072
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not happy and not kind is not strong.
If mary is either not humble or funny then fred is either old or not curious and vice versa.
If someone is either not wise or not happy then fred is either not calm or generous.
Everyone who is rich is both wise and not curious and vice versa.
If someone is rich or tall then someone is either not creative or not tall and vice versa.
Everyone who is either happy or not patient is not happy or creative and vice versa.
If john is funny then someone is either not rich or rich and vice versa.
If fred is not brave then john is calm or wise and vice versa.
If lucy is patient or calm then paul is either quiet or calm.
If someone is not quiet or creative then alice is not humble.
Everyone who is either humble or kind is either not calm or not rich.
Everyone who is either not strong or curious is not creative and vice versa.
Everyone who is rich is either old or tall and vice versa.
Everyone who is either not happy or not quiet is not humble or funny and vice versa.
Everyone who is not curious or generous is generous or wise.
Everyone who is either creative or not quiet is not tall.
Someone is both not brave and funny.
Someone is both not quiet and not wise.
Someone is either not happy or calm.
Fred is curious or calm.
Lucy is rich.
Someone is happy.
Someone is calm. | Paul is not patient. | neutral | (![X]:((~happy(X)&~kind(X))=>~strong(X)))&
(((~humble(mary)<~>funny(mary)))<=>((old(fred)<~>~curious(fred))))&
((?[X]:((~wise(X)<~>~happy(X))))=>((~calm(fred)<~>generous(fred))))&
(![X]:(rich(X)<=>(wise(X)&~curious(X))))&
((?[X]:((rich(X)|tall(X))))<=>(?[X]:((~creative(X)<~>~tall(X)))))&
(![X]:((happy(X)<~>~patient(X))<=>(~happy(X)|creative(X))))&
((funny(john))<=>(?[X]:((~rich(X)<~>rich(X)))))&
((~brave(fred))<=>((calm(john)|wise(john))))&
(((patient(lucy)|calm(lucy)))=>((quiet(paul)<~>calm(paul))))&
((?[X]:((~quiet(X)|creative(X))))=>(~humble(alice)))&
(![X]:((humble(X)<~>kind(X))=>(~calm(X)<~>~rich(X))))&
(![X]:((~strong(X)<~>curious(X))<=>~creative(X)))&
(![X]:(rich(X)<=>(old(X)<~>tall(X))))&
(![X]:((~happy(X)<~>~quiet(X))<=>(~humble(X)|funny(X))))&
(![X]:((~curious(X)|generous(X))=>(generous(X)|wise(X))))&
(![X]:((creative(X)<~>~quiet(X))=>~tall(X)))&
(?[X]:((~brave(X)&funny(X))))&
(?[X]:((~quiet(X)&~wise(X))))&
(?[X]:((~happy(X)<~>calm(X))))&
((curious(fred)|calm(fred)))&
(rich(lucy))&
(?[X]:(happy(X)))&
(?[X]:(calm(X))) | ~patient(paul) | [] | null | 0 |
Everyone who is both not rich and not funny is both rich and not curious and vice versa.
Everyone who is either not wise or not patient is not calm or kind and vice versa.
Everyone who is either not calm or calm is both not rich and quiet and vice versa.
Everyone who is not wise is both not patient and not wise and vice versa.
If paul is both not creative and not quiet then someone is rich or not happy and vice versa.
Everyone who is not funny is kind or not kind.
Everyone who is quiet is not tall or wise and vice versa.
Everyone who is either funny or strong is not generous or humble.
If someone is either wise or not patient then mary is either kind or not tall and vice versa.
Everyone who is both not old and not generous is happy or patient.
If someone is both not wise and not generous then paul is curious.
Everyone who is not quiet or tall is generous and vice versa.
Everyone who is humble is both old and not happy.
Everyone who is either not wise or kind is either not wise or generous and vice versa.
Everyone who is either not tall or not humble is both calm and not quiet and vice versa.
If someone is not wise or not curious then mary is not curious and vice versa.
Susan is not curious.
Someone is both brave and not humble.
Alice is either not patient or not humble.
Lucy is either tall or not humble.
Someone is either not wise or not generous. | Alice is not happy. | contradiction | (![X]:((~rich(X)&~funny(X))<=>(rich(X)&~curious(X))))&
(![X]:((~wise(X)<~>~patient(X))<=>(~calm(X)|kind(X))))&
(![X]:((~calm(X)<~>calm(X))<=>(~rich(X)&quiet(X))))&
(![X]:(~wise(X)<=>(~patient(X)&~wise(X))))&
(((~creative(paul)&~quiet(paul)))<=>(?[X]:((rich(X)|~happy(X)))))&
(![X]:(~funny(X)=>(kind(X)|~kind(X))))&
(![X]:(quiet(X)<=>(~tall(X)|wise(X))))&
(![X]:((funny(X)<~>strong(X))=>(~generous(X)|humble(X))))&
((?[X]:((wise(X)<~>~patient(X))))<=>((kind(mary)<~>~tall(mary))))&
(![X]:((~old(X)&~generous(X))=>(happy(X)|patient(X))))&
((?[X]:((~wise(X)&~generous(X))))=>(curious(paul)))&
(![X]:((~quiet(X)|tall(X))<=>generous(X)))&
(![X]:(humble(X)=>(old(X)&~happy(X))))&
(![X]:((~wise(X)<~>kind(X))<=>(~wise(X)<~>generous(X))))&
(![X]:((~tall(X)<~>~humble(X))<=>(calm(X)&~quiet(X))))&
((?[X]:((~wise(X)|~curious(X))))<=>(~curious(mary)))&
(~curious(susan))&
(?[X]:((brave(X)&~humble(X))))&
((~patient(alice)<~>~humble(alice)))&
((tall(lucy)<~>~humble(lucy)))&
(?[X]:((~wise(X)<~>~generous(X)))) | ~happy(alice) | [
"p2",
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 1253293869049657803708418
% SZS output start Proof for 1253293869049657803708418
3. ! [X0] : ((~calm(X0) <~> calm(X0)) <=> (quiet(X0) & ~rich(X0))) [input p2]
5. (~quiet(paul) & ~creative(paul)) <=> ? [X0] : (~happy(X0) | rich(X0)) [input p4]
22. ~happy(alice) [input hypothesis]
36. ! [X0] : ((((~calm(X0) | calm(X0)) & (calm(X0) | ~calm(X0))) | (~quiet(X0) | rich(X0))) & ((quiet(X0) & ~rich(X0)) | ((~calm(X0) | ~calm(X0)) & (calm(X0) | calm(X0))))) [nnf transformation 3]
37. ! [X0] : ((((~calm(X0) | calm(X0)) & (calm(X0) | ~calm(X0))) | ~quiet(X0) | rich(X0)) & ((quiet(X0) & ~rich(X0)) | ((~calm(X0) | ~calm(X0)) & (calm(X0) | calm(X0))))) [flattening 36]
40. ((~quiet(paul) & ~creative(paul)) | ! [X0] : (happy(X0) & ~rich(X0))) & (? [X0] : (~happy(X0) | rich(X0)) | (quiet(paul) | creative(paul))) [nnf transformation 5]
41. ((~quiet(paul) & ~creative(paul)) | ! [X0] : (happy(X0) & ~rich(X0))) & (? [X0] : (~happy(X0) | rich(X0)) | quiet(paul) | creative(paul)) [flattening 40]
42. ((~quiet(paul) & ~creative(paul)) | ! [X0] : (happy(X0) & ~rich(X0))) & (? [X1] : (~happy(X1) | rich(X1)) | quiet(paul) | creative(paul)) [rectify 41]
43. ? [X1] : (~happy(X1) | rich(X1)) => (~happy(sK0) | rich(sK0)) [choice axiom]
44. ((~quiet(paul) & ~creative(paul)) | ! [X0] : (happy(X0) & ~rich(X0))) & ((~happy(sK0) | rich(sK0)) | quiet(paul) | creative(paul)) [skolemisation 42,43]
80. quiet(X0) | calm(X0) | calm(X0) [cnf transformation 37]
81. quiet(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 37]
91. ~quiet(paul) | happy(X0) [cnf transformation 44]
136. ~happy(alice) [cnf transformation 22]
143. quiet(X0) | calm(X0) [duplicate literal removal 80]
144. quiet(X0) | ~calm(X0) [duplicate literal removal 81]
147. quiet(X0) [subsumption resolution 143,144]
149. happy(X0) [subsumption resolution 91,147]
226. $false [subsumption resolution 136,149]
% SZS output end Proof for 1253293869049657803708418
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either quiet or not humble is kind.
If someone is not creative then john is either funny or not wise and vice versa.
If someone is both not quiet and brave then fred is wise or not curious.
If someone is curious then alice is both not humble and not kind.
Everyone who is humble is creative and vice versa.
If mary is either generous or brave then someone is curious or quiet.
Everyone who is both wise and quiet is either not patient or strong and vice versa.
Everyone who is tall or not wise is tall or not curious.
If john is both strong and not strong then someone is both curious and quiet and vice versa.
Everyone who is either tall or funny is both not calm and not curious and vice versa.
Everyone who is either quiet or strong is calm or not wise.
If someone is not wise or not humble then alice is both funny and quiet.
Everyone who is not rich is either tall or creative and vice versa.
If someone is not kind or generous then alice is brave or not quiet.
If paul is not creative then lucy is brave or quiet and vice versa.
If john is curious or not curious then someone is both happy and curious and vice versa.
Someone is quiet.
Paul is old.
Someone is both not calm and not strong.
Someone is old or not funny.
Someone is brave or wise.
Paul is rich or patient. | Alice is strong. | neutral | (![X]:((quiet(X)<~>~humble(X))=>kind(X)))&
((?[X]:(~creative(X)))<=>((funny(john)<~>~wise(john))))&
((?[X]:((~quiet(X)&brave(X))))=>((wise(fred)|~curious(fred))))&
((?[X]:(curious(X)))=>((~humble(alice)&~kind(alice))))&
(![X]:(humble(X)<=>creative(X)))&
(((generous(mary)<~>brave(mary)))=>(?[X]:((curious(X)|quiet(X)))))&
(![X]:((wise(X)&quiet(X))<=>(~patient(X)<~>strong(X))))&
(![X]:((tall(X)|~wise(X))=>(tall(X)|~curious(X))))&
(((strong(john)&~strong(john)))<=>(?[X]:((curious(X)&quiet(X)))))&
(![X]:((tall(X)<~>funny(X))<=>(~calm(X)&~curious(X))))&
(![X]:((quiet(X)<~>strong(X))=>(calm(X)|~wise(X))))&
((?[X]:((~wise(X)|~humble(X))))=>((funny(alice)&quiet(alice))))&
(![X]:(~rich(X)<=>(tall(X)<~>creative(X))))&
((?[X]:((~kind(X)|generous(X))))=>((brave(alice)|~quiet(alice))))&
((~creative(paul))<=>((brave(lucy)|quiet(lucy))))&
(((curious(john)|~curious(john)))<=>(?[X]:((happy(X)&curious(X)))))&
(?[X]:(quiet(X)))&
(old(paul))&
(?[X]:((~calm(X)&~strong(X))))&
(?[X]:((old(X)|~funny(X))))&
(?[X]:((brave(X)|wise(X))))&
((rich(paul)|patient(paul))) | strong(alice) | [] | null | 0 |
If lucy is funny then someone is both not rich and tall. Everyone who is tall or curious is both generous and not calm and vice versa. Everyone who is not strong is either strong or not rich. If lucy is either not brave or not rich then someone is not brave and vice versa. Everyone who is either not brave or patient is creative. Everyone who is happy is both curious and not kind and vice versa. If someone is both curious and not happy then lucy is both generous and patient. If someone is old then fred is kind or not strong. Everyone who is both not old and not kind is not curious or strong and vice versa. If lucy is both tall and not wise then mary is not old or not creative and vice versa. Everyone who is not patient is either kind or not brave. Everyone who is both not rich and quiet is happy or not funny. Everyone who is both funny and not wise is not humble or not generous and vice versa. If mary is either not curious or not tall then someone is either rich or brave and vice versa. If paul is both curious and happy then someone is both creative and calm. If someone is calm or not brave then someone is rich and vice versa. John is not curious. Someone is either happy or not creative. Someone is both wise and not strong. Someone is not funny. Someone is not happy. Fred is both not kind and not rich. Someone is either kind or calm. | Mary is creative. | neutral | ((funny(lucy))=>(?[X]:((~rich(X)&tall(X)))))&
(![X]:((tall(X)|curious(X))<=>(generous(X)&~calm(X))))&
(![X]:(~strong(X)=>(strong(X)<~>~rich(X))))&
(((~brave(lucy)<~>~rich(lucy)))<=>(?[X]:(~brave(X))))&
(![X]:((~brave(X)<~>patient(X))=>creative(X)))&
(![X]:(happy(X)<=>(curious(X)&~kind(X))))&
((?[X]:((curious(X)&~happy(X))))=>((generous(lucy)&patient(lucy))))&
((?[X]:(old(X)))=>((kind(fred)|~strong(fred))))&
(![X]:((~old(X)&~kind(X))<=>(~curious(X)|strong(X))))&
(((tall(lucy)&~wise(lucy)))<=>((~old(mary)|~creative(mary))))&
(![X]:(~patient(X)=>(kind(X)<~>~brave(X))))&
(![X]:((~rich(X)&quiet(X))=>(happy(X)|~funny(X))))&
(![X]:((funny(X)&~wise(X))<=>(~humble(X)|~generous(X))))&
(((~curious(mary)<~>~tall(mary)))<=>(?[X]:((rich(X)<~>brave(X)))))&
(((curious(paul)&happy(paul)))=>(?[X]:((creative(X)&calm(X)))))&
((?[X]:((calm(X)|~brave(X))))<=>(?[X]:(rich(X))))&
(~curious(john))&
(?[X]:((happy(X)<~>~creative(X))))&
(?[X]:((wise(X)&~strong(X))))&
(?[X]:(~funny(X)))&
(?[X]:(~happy(X)))&
((~kind(fred)&~rich(fred)))&
(?[X]:((kind(X)<~>calm(X)))) | creative(mary) | [] | null | 0 |
Everyone who is not wise or funny is either not wise or not curious.
If john is not kind or humble then john is strong and vice versa.
If alice is either not kind or brave then someone is strong or not patient and vice versa.
If someone is both not curious and curious then alice is not funny or rich.
Everyone who is funny is not funny or rich.
Everyone who is both humble and patient is both not creative and old and vice versa.
Everyone who is both old and not funny is not old or not happy.
Everyone who is not kind or funny is happy.
Everyone who is either happy or not strong is not strong or not happy and vice versa.
Everyone who is not rich is quiet and vice versa.
If someone is either tall or happy then fred is not old or not tall and vice versa.
If alice is not brave or not old then someone is both rich and not patient.
Everyone who is kind or curious is not calm or happy and vice versa.
Everyone who is not generous or not brave is patient or not brave and vice versa.
If lucy is either not happy or quiet then someone is either quiet or not funny.
If someone is wise then lucy is both not tall and not patient and vice versa.
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.
Paul is either not patient or strong.
Fred is calm or tall. | Paul is funny. | contradiction | (![X]:((~wise(X)|funny(X))=>(~wise(X)<~>~curious(X))))&
(((~kind(john)|humble(john)))<=>(strong(john)))&
(((~kind(alice)<~>brave(alice)))<=>(?[X]:((strong(X)|~patient(X)))))&
((?[X]:((~curious(X)&curious(X))))=>((~funny(alice)|rich(alice))))&
(![X]:(funny(X)=>(~funny(X)|rich(X))))&
(![X]:((humble(X)&patient(X))<=>(~creative(X)&old(X))))&
(![X]:((old(X)&~funny(X))=>(~old(X)|~happy(X))))&
(![X]:((~kind(X)|funny(X))=>happy(X)))&
(![X]:((happy(X)<~>~strong(X))<=>(~strong(X)|~happy(X))))&
(![X]:(~rich(X)<=>quiet(X)))&
((?[X]:((tall(X)<~>happy(X))))<=>((~old(fred)|~tall(fred))))&
(((~brave(alice)|~old(alice)))=>(?[X]:((rich(X)&~patient(X)))))&
(![X]:((kind(X)|curious(X))<=>(~calm(X)|happy(X))))&
(![X]:((~generous(X)|~brave(X))<=>(patient(X)|~brave(X))))&
(((~happy(lucy)<~>quiet(lucy)))=>(?[X]:((quiet(X)<~>~funny(X)))))&
((?[X]:(wise(X)))<=>((~tall(lucy)&~patient(lucy))))&
(?[X]:((quiet(X)&~creative(X))))&
(~brave(susan))&
(?[X]:((humble(X)|calm(X))))&
(?[X]:(creative(X)))&
(?[X]:((~humble(X)|~patient(X))))&
((~patient(paul)<~>strong(paul)))&
((calm(fred)|tall(fred))) | funny(paul) | [
"p7",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 4197251627303942322744118
% SZS output start Proof for 4197251627303942322744118
8. ! [X0] : ((funny(X0) | ~kind(X0)) => happy(X0)) [input p7]
9. ! [X0] : ((happy(X0) <~> ~strong(X0)) <=> (~happy(X0) | ~strong(X0))) [input p8]
24. funny(paul) [input hypothesis]
33. ! [X0] : (happy(X0) | (~funny(X0) & kind(X0))) [ennf transformation 8]
46. ! [X0] : ((((strong(X0) | ~happy(X0)) & (~strong(X0) | happy(X0))) | (happy(X0) & strong(X0))) & ((~happy(X0) | ~strong(X0)) | ((happy(X0) | strong(X0)) & (~strong(X0) | ~happy(X0))))) [nnf transformation 9]
47. ! [X0] : ((((strong(X0) | ~happy(X0)) & (~strong(X0) | happy(X0))) | (happy(X0) & strong(X0))) & (~happy(X0) | ~strong(X0) | ((happy(X0) | strong(X0)) & (~strong(X0) | ~happy(X0))))) [flattening 46]
97. ~funny(X0) | happy(X0) [cnf transformation 33]
98. ~happy(X0) | ~strong(X0) | ~strong(X0) | ~happy(X0) [cnf transformation 47]
101. ~strong(X0) | happy(X0) | happy(X0) [cnf transformation 47]
102. strong(X0) | ~happy(X0) | strong(X0) [cnf transformation 47]
139. funny(paul) [cnf transformation 24]
140. ~happy(X0) | ~strong(X0) [duplicate literal removal 98]
141. ~strong(X0) | happy(X0) [duplicate literal removal 101]
142. ~happy(X0) | strong(X0) [duplicate literal removal 102]
174. 7 <=> ! [X0] : ~strong(X0) [avatar definition]
175. ~strong(X0) <- (7) [avatar component clause 174]
189. ~strong(X0) [subsumption resolution 140,141]
190. 7 [avatar split clause 189,174]
317. happy(paul) [resolution 97,139]
320. strong(paul) [resolution 142,317]
322. $false <- (7) [subsumption resolution 320,175]
323. ~7 [avatar contradiction clause 322]
324. $false [avatar sat refutation 190,323]
% SZS output end Proof for 4197251627303942322744118
% ------------------------------
% 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 brave or calm is brave or not funny and vice versa. Everyone who is not creative is rich or patient. If someone is both generous and not brave then someone is both creative and quiet. If fred is not strong or not funny then paul is old and vice versa. Everyone who is not happy is both wise and not old and vice versa. Everyone who is rich is strong and vice versa. Everyone who is either not brave or wise is either not creative or brave and vice versa. If someone is not happy then someone is both kind and not happy. If susan is both not creative and patient then someone is not strong or quiet and vice versa. If susan is either strong or kind then alice is both humble and not creative and vice versa. Everyone who is either not generous or not rich is either not happy or not calm and vice versa. Everyone who is not tall or happy is brave and vice versa. Everyone who is strong is humble or not rich and vice versa. If someone is either brave or strong then someone is both not wise and old. If fred is either not generous or not old then someone is not old. Everyone who is not kind or not creative is not happy or creative. Someone is both old and patient. Susan is either quiet or brave. Someone is either quiet or funny. Susan is either patient or not calm. Paul is wise. Someone is old or not generous. | Alice is strong. | entailment | (![X]:((~brave(X)|calm(X))<=>(brave(X)|~funny(X))))&
(![X]:(~creative(X)=>(rich(X)|patient(X))))&
((?[X]:((generous(X)&~brave(X))))=>(?[X]:((creative(X)&quiet(X)))))&
(((~strong(fred)|~funny(fred)))<=>(old(paul)))&
(![X]:(~happy(X)<=>(wise(X)&~old(X))))&
(![X]:(rich(X)<=>strong(X)))&
(![X]:((~brave(X)<~>wise(X))<=>(~creative(X)<~>brave(X))))&
((?[X]:(~happy(X)))=>(?[X]:((kind(X)&~happy(X)))))&
(((~creative(susan)&patient(susan)))<=>(?[X]:((~strong(X)|quiet(X)))))&
(((strong(susan)<~>kind(susan)))<=>((humble(alice)&~creative(alice))))&
(![X]:((~generous(X)<~>~rich(X))<=>(~happy(X)<~>~calm(X))))&
(![X]:((~tall(X)|happy(X))<=>brave(X)))&
(![X]:(strong(X)<=>(humble(X)|~rich(X))))&
((?[X]:((brave(X)<~>strong(X))))=>(?[X]:((~wise(X)&old(X)))))&
(((~generous(fred)<~>~old(fred)))=>(?[X]:(~old(X))))&
(![X]:((~kind(X)|~creative(X))=>(~happy(X)|creative(X))))&
(?[X]:((old(X)&patient(X))))&
((quiet(susan)<~>brave(susan)))&
(?[X]:((quiet(X)<~>funny(X))))&
((patient(susan)<~>~calm(susan)))&
(wise(paul))&
(?[X]:((old(X)|~generous(X)))) | strong(alice) | [
"p5",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 7552041085357009324921958
% SZS output start Proof for 7552041085357009324921958
6. ! [X0] : (rich(X0) <=> strong(X0)) [input p5]
13. ! [X0] : (strong(X0) <=> (~rich(X0) | humble(X0))) [input p12]
23. ~strong(alice) [input hypothesis]
44. ! [X0] : ((rich(X0) | ~strong(X0)) & (strong(X0) | ~rich(X0))) [nnf transformation 6]
59. ! [X0] : ((strong(X0) | (rich(X0) & ~humble(X0))) & ((~rich(X0) | humble(X0)) | ~strong(X0))) [nnf transformation 13]
60. ! [X0] : ((strong(X0) | (rich(X0) & ~humble(X0))) & (~rich(X0) | humble(X0) | ~strong(X0))) [flattening 59]
90. ~rich(X0) | strong(X0) [cnf transformation 44]
91. rich(X0) | ~strong(X0) [cnf transformation 44]
126. strong(X0) | rich(X0) [cnf transformation 60]
145. ~strong(alice) [cnf transformation 23]
205. 12 <=> ! [X0] : strong(X0) [avatar definition]
206. strong(X0) <- (12) [avatar component clause 205]
245. rich(X0) [subsumption resolution 126,91]
322. strong(X0) [resolution 90,245]
323. 12 [avatar split clause 322,205]
325. $false <- (12) [resolution 206,145]
328. ~12 [avatar contradiction clause 325]
330. $false [avatar sat refutation 323,328]
% SZS output end Proof for 7552041085357009324921958
% ------------------------------
% 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 susan is both not wise and not rich then lucy is not calm and vice versa. Everyone who is either not quiet or not tall is funny and vice versa. Everyone who is not strong is not wise. If john is strong then john is either not quiet or tall. If mary is both not patient and not quiet then someone is both calm and not generous and vice versa. Everyone who is either curious or not generous is both calm and rich and vice versa. Everyone who is both calm and rich is both brave and not kind. If someone is both not creative and not happy then someone is either creative or not kind and vice versa. Everyone who is kind is not quiet or strong and vice versa. If someone is both calm and not brave then mary is either not tall or wise. Everyone who is wise is happy or not patient and vice versa. Everyone who is creative or humble is either quiet or kind and vice versa. Everyone who is not quiet or generous is either not creative or funny and vice versa. If someone is both not old and not brave then paul is both wise and not tall. Everyone who is not quiet or generous is either not funny or not old. Everyone who is not wise is either not happy or not funny and vice versa. Someone is not curious. Someone is either calm or not brave. Lucy is not strong or quiet. Someone is either rich or not happy. Someone is both old and rich. Mary is both not tall and creative. Someone is either generous or patient. Susan is either not strong or patient. | John is happy. | contradiction | (((~wise(susan)&~rich(susan)))<=>(~calm(lucy)))&
(![X]:((~quiet(X)<~>~tall(X))<=>funny(X)))&
(![X]:(~strong(X)=>~wise(X)))&
((strong(john))=>((~quiet(john)<~>tall(john))))&
(((~patient(mary)&~quiet(mary)))<=>(?[X]:((calm(X)&~generous(X)))))&
(![X]:((curious(X)<~>~generous(X))<=>(calm(X)&rich(X))))&
(![X]:((calm(X)&rich(X))=>(brave(X)&~kind(X))))&
((?[X]:((~creative(X)&~happy(X))))<=>(?[X]:((creative(X)<~>~kind(X)))))&
(![X]:(kind(X)<=>(~quiet(X)|strong(X))))&
((?[X]:((calm(X)&~brave(X))))=>((~tall(mary)<~>wise(mary))))&
(![X]:(wise(X)<=>(happy(X)|~patient(X))))&
(![X]:((creative(X)|humble(X))<=>(quiet(X)<~>kind(X))))&
(![X]:((~quiet(X)|generous(X))<=>(~creative(X)<~>funny(X))))&
((?[X]:((~old(X)&~brave(X))))=>((wise(paul)&~tall(paul))))&
(![X]:((~quiet(X)|generous(X))=>(~funny(X)<~>~old(X))))&
(![X]:(~wise(X)<=>(~happy(X)<~>~funny(X))))&
(?[X]:(~curious(X)))&
(?[X]:((calm(X)<~>~brave(X))))&
((~strong(lucy)|quiet(lucy)))&
(?[X]:((rich(X)<~>~happy(X))))&
(?[X]:((old(X)&rich(X))))&
((~tall(mary)&creative(mary)))&
(?[X]:((generous(X)<~>patient(X))))&
((~strong(susan)<~>patient(susan))) | happy(john) | [
"p1",
"p2",
"p3",
"p10",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3982991767952239615206059
% SZS output start Proof for 3982991767952239615206059
2. ! [X0] : ((~quiet(X0) <~> ~tall(X0)) <=> funny(X0)) [input p1]
3. ! [X0] : (~strong(X0) => ~wise(X0)) [input p2]
4. strong(john) => (~quiet(john) <~> tall(john)) [input p3]
11. ! [X0] : (wise(X0) <=> (~patient(X0) | happy(X0))) [input p10]
16. ! [X0] : (~wise(X0) <=> (~happy(X0) <~> ~funny(X0))) [input p15]
25. happy(john) [input hypothesis]
27. ! [X0] : (~wise(X0) | strong(X0)) [ennf transformation 3]
28. (~quiet(john) <~> tall(john)) | ~strong(john) [ennf transformation 4]
36. ! [X0] : ((((tall(X0) | quiet(X0)) & (~tall(X0) | ~quiet(X0))) | ~funny(X0)) & (funny(X0) | ((~quiet(X0) | tall(X0)) & (~tall(X0) | quiet(X0))))) [nnf transformation 2]
37. ((~tall(john) | quiet(john)) & (tall(john) | ~quiet(john))) | ~strong(john) [nnf transformation 28]
53. ! [X0] : ((wise(X0) | (patient(X0) & ~happy(X0))) & ((~patient(X0) | happy(X0)) | ~wise(X0))) [nnf transformation 11]
54. ! [X0] : ((wise(X0) | (patient(X0) & ~happy(X0))) & (~patient(X0) | happy(X0) | ~wise(X0))) [flattening 53]
60. ! [X0] : ((~wise(X0) | ((~happy(X0) | funny(X0)) & (~funny(X0) | happy(X0)))) & (((funny(X0) | happy(X0)) & (~funny(X0) | ~happy(X0))) | wise(X0))) [nnf transformation 16]
80. ~funny(X0) | ~quiet(X0) | ~tall(X0) [cnf transformation 36]
81. ~funny(X0) | quiet(X0) | tall(X0) [cnf transformation 36]
82. ~wise(X0) | strong(X0) [cnf transformation 27]
83. tall(john) | ~quiet(john) | ~strong(john) [cnf transformation 37]
84. ~tall(john) | quiet(john) | ~strong(john) [cnf transformation 37]
109. ~happy(X0) | wise(X0) [cnf transformation 54]
132. ~wise(X0) | ~happy(X0) | funny(X0) [cnf transformation 60]
147. happy(john) [cnf transformation 25]
164. 4 <=> strong(john) [avatar definition]
168. 5 <=> quiet(john) [avatar definition]
172. 6 <=> tall(john) [avatar definition]
175. ~4 | 5 | ~6 [avatar split clause 84,172,168,164]
176. ~4 | ~5 | 6 [avatar split clause 83,172,168,164]
259. ~happy(X0) | funny(X0) [subsumption resolution 132,109]
312. wise(john) [resolution 109,147]
313. strong(john) [resolution 312,82]
316. 4 [avatar split clause 313,164]
325. funny(john) [resolution 259,147]
352. ~quiet(john) | ~tall(john) [resolution 80,325]
366. quiet(john) | tall(john) [resolution 81,325]
374. 6 | 5 [avatar split clause 366,168,172]
375. ~6 | ~5 [avatar split clause 352,168,172]
376. $false [avatar sat refutation 175,176,316,374,375]
% SZS output end Proof for 3982991767952239615206059
% ------------------------------
% 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: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not curious or patient is not old or rich and vice versa. If someone is generous then someone is both old and not strong. If someone is not quiet then lucy is either not old or not brave and vice versa. Everyone who is curious is not strong and vice versa. If mary is both curious and not calm then someone is not tall and vice versa. Everyone who is both rich and not funny is either tall or not brave and vice versa. Everyone who is not old or not tall is both generous and rich and vice versa. Everyone who is curious or not old is either not kind or not patient and vice versa. If someone is not generous or kind then susan is both curious and strong. If someone is both not old and wise then john is not calm or not curious and vice versa. If mary is both generous and not creative then someone is either not rich or not patient. If someone is both not kind and not strong then someone is curious or not quiet. Everyone who is either not tall or not quiet is not strong or not calm. Everyone who is both tall and not old is either not brave or not humble and vice versa. Everyone who is either patient or not patient is quiet or happy. If someone is curious or funny then someone is either brave or humble and vice versa. Paul is either strong or patient. Fred is strong or not old. Someone is either not wise or generous. Someone is not brave. Lucy is rich or not strong. Lucy is not creative. Someone is both not happy and tall. | Mary is patient. | entailment | (![X]:((~curious(X)<~>patient(X))<=>(~old(X)|rich(X))))&
((?[X]:(generous(X)))=>(?[X]:((old(X)&~strong(X)))))&
((?[X]:(~quiet(X)))<=>((~old(lucy)<~>~brave(lucy))))&
(![X]:(curious(X)<=>~strong(X)))&
(((curious(mary)&~calm(mary)))<=>(?[X]:(~tall(X))))&
(![X]:((rich(X)&~funny(X))<=>(tall(X)<~>~brave(X))))&
(![X]:((~old(X)|~tall(X))<=>(generous(X)&rich(X))))&
(![X]:((curious(X)|~old(X))<=>(~kind(X)<~>~patient(X))))&
((?[X]:((~generous(X)|kind(X))))=>((curious(susan)&strong(susan))))&
((?[X]:((~old(X)&wise(X))))<=>((~calm(john)|~curious(john))))&
(((generous(mary)&~creative(mary)))=>(?[X]:((~rich(X)<~>~patient(X)))))&
((?[X]:((~kind(X)&~strong(X))))=>(?[X]:((curious(X)|~quiet(X)))))&
(![X]:((~tall(X)<~>~quiet(X))=>(~strong(X)|~calm(X))))&
(![X]:((tall(X)&~old(X))<=>(~brave(X)<~>~humble(X))))&
(![X]:((patient(X)<~>~patient(X))=>(quiet(X)|happy(X))))&
((?[X]:((curious(X)|funny(X))))<=>(?[X]:((brave(X)<~>humble(X)))))&
((strong(paul)<~>patient(paul)))&
((strong(fred)|~old(fred)))&
(?[X]:((~wise(X)<~>generous(X))))&
(?[X]:(~brave(X)))&
((rich(lucy)|~strong(lucy)))&
(~creative(lucy))&
(?[X]:((~happy(X)&tall(X)))) | patient(mary) | [
"p0",
"p1",
"p3",
"p4",
"p6",
"p7",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 8800718634829082992902917
% SZS output start Proof for 8800718634829082992902917
1. ! [X0] : ((~curious(X0) <~> patient(X0)) <=> (rich(X0) | ~old(X0))) [input p0]
2. ? [X0] : generous(X0) => ? [X0] : (~strong(X0) & old(X0)) [input p1]
4. ! [X0] : (curious(X0) <=> ~strong(X0)) [input p3]
5. (~calm(mary) & curious(mary)) <=> ? [X0] : ~tall(X0) [input p4]
7. ! [X0] : ((~tall(X0) | ~old(X0)) <=> (rich(X0) & generous(X0))) [input p6]
8. ! [X0] : ((~old(X0) | curious(X0)) <=> (~kind(X0) <~> ~patient(X0))) [input p7]
9. ? [X0] : (kind(X0) | ~generous(X0)) => (strong(susan) & curious(susan)) [input p8]
24. ~patient(mary) [input hypothesis]
25. ? [X0] : generous(X0) => ? [X1] : (~strong(X1) & old(X1)) [rectify 2]
28. ? [X1] : (~strong(X1) & old(X1)) | ! [X0] : ~generous(X0) [ennf transformation 25]
29. (strong(susan) & curious(susan)) | ! [X0] : (~kind(X0) & generous(X0)) [ennf transformation 9]
37. ! [X0] : ((((~patient(X0) | curious(X0)) & (patient(X0) | ~curious(X0))) | (~rich(X0) & old(X0))) & ((rich(X0) | ~old(X0)) | ((~curious(X0) | ~patient(X0)) & (patient(X0) | curious(X0))))) [nnf transformation 1]
38. ! [X0] : ((((~patient(X0) | curious(X0)) & (patient(X0) | ~curious(X0))) | (~rich(X0) & old(X0))) & (rich(X0) | ~old(X0) | ((~curious(X0) | ~patient(X0)) & (patient(X0) | curious(X0))))) [flattening 37]
39. ? [X0] : (~strong(X0) & old(X0)) | ! [X1] : ~generous(X1) [rectify 28]
40. ? [X0] : (~strong(X0) & old(X0)) => (~strong(sK0) & old(sK0)) [choice axiom]
41. (~strong(sK0) & old(sK0)) | ! [X1] : ~generous(X1) [skolemisation 39,40]
46. ! [X0] : ((curious(X0) | strong(X0)) & (~strong(X0) | ~curious(X0))) [nnf transformation 4]
47. ((~calm(mary) & curious(mary)) | ! [X0] : tall(X0)) & (? [X0] : ~tall(X0) | (calm(mary) | ~curious(mary))) [nnf transformation 5]
48. ((~calm(mary) & curious(mary)) | ! [X0] : tall(X0)) & (? [X0] : ~tall(X0) | calm(mary) | ~curious(mary)) [flattening 47]
49. ((~calm(mary) & curious(mary)) | ! [X0] : tall(X0)) & (? [X1] : ~tall(X1) | calm(mary) | ~curious(mary)) [rectify 48]
50. ? [X1] : ~tall(X1) => ~tall(sK2) [choice axiom]
51. ((~calm(mary) & curious(mary)) | ! [X0] : tall(X0)) & (~tall(sK2) | calm(mary) | ~curious(mary)) [skolemisation 49,50]
54. ! [X0] : (((~tall(X0) | ~old(X0)) | (~rich(X0) | ~generous(X0))) & ((rich(X0) & generous(X0)) | (tall(X0) & old(X0)))) [nnf transformation 7]
55. ! [X0] : ((~tall(X0) | ~old(X0) | ~rich(X0) | ~generous(X0)) & ((rich(X0) & generous(X0)) | (tall(X0) & old(X0)))) [flattening 54]
56. ! [X0] : (((~old(X0) | curious(X0)) | ((~kind(X0) | patient(X0)) & (~patient(X0) | kind(X0)))) & (((patient(X0) | kind(X0)) & (~patient(X0) | ~kind(X0))) | (old(X0) & ~curious(X0)))) [nnf transformation 8]
57. ! [X0] : ((~old(X0) | curious(X0) | ((~kind(X0) | patient(X0)) & (~patient(X0) | kind(X0)))) & (((patient(X0) | kind(X0)) & (~patient(X0) | ~kind(X0))) | (old(X0) & ~curious(X0)))) [flattening 56]
87. ~old(X0) | rich(X0) | ~curious(X0) | ~patient(X0) [cnf transformation 38]
92. old(sK0) | ~generous(X1) [cnf transformation 41]
93. ~strong(sK0) | ~generous(X1) [cnf transformation 41]
98. ~strong(X0) | ~curious(X0) [cnf transformation 46]
99. strong(X0) | curious(X0) [cnf transformation 46]
101. curious(mary) | tall(X0) [cnf transformation 51]
113. ~tall(X0) | ~old(X0) | ~rich(X0) | ~generous(X0) [cnf transformation 55]
116. ~curious(X0) | kind(X0) | patient(X0) [cnf transformation 57]
120. curious(susan) | generous(X0) [cnf transformation 29]
121. curious(susan) | ~kind(X0) [cnf transformation 29]
122. strong(susan) | generous(X0) [cnf transformation 29]
123. strong(susan) | ~kind(X0) [cnf transformation 29]
158. ~patient(mary) [cnf transformation 24]
162. 1 <=> ! [X1] : ~generous(X1) [avatar definition]
163. ~generous(X1) <- (1) [avatar component clause 162]
165. 2 <=> strong(sK0) [avatar definition]
167. ~strong(sK0) <- (~2) [avatar component clause 165]
168. 1 | ~2 [avatar split clause 93,165,162]
170. 3 <=> old(sK0) [avatar definition]
172. old(sK0) <- (3) [avatar component clause 170]
173. 1 | 3 [avatar split clause 92,170,162]
194. 8 <=> ! [X0] : tall(X0) [avatar definition]
195. tall(X0) <- (8) [avatar component clause 194]
202. 10 <=> curious(mary) [avatar definition]
204. curious(mary) <- (10) [avatar component clause 202]
205. 8 | 10 [avatar split clause 101,202,194]
213. 12 <=> ! [X0] : ~kind(X0) [avatar definition]
214. ~kind(X0) <- (12) [avatar component clause 213]
216. 13 <=> strong(susan) [avatar definition]
218. strong(susan) <- (13) [avatar component clause 216]
219. 12 | 13 [avatar split clause 123,216,213]
221. 14 <=> ! [X0] : generous(X0) [avatar definition]
222. generous(X0) <- (14) [avatar component clause 221]
223. 14 | 13 [avatar split clause 122,216,221]
225. 15 <=> curious(susan) [avatar definition]
228. 12 | 15 [avatar split clause 121,225,213]
229. 14 | 15 [avatar split clause 120,225,221]
359. ~curious(susan) <- (13) [resolution 98,218]
363. ~15 | ~13 [avatar split clause 359,216,225]
465. $false <- (1, 14) [subsumption resolution 163,222]
466. ~1 | ~14 [avatar contradiction clause 465]
467. curious(sK0) <- (~2) [resolution 167,99]
481. kind(sK0) | patient(sK0) <- (~2) [resolution 467,116]
483. patient(sK0) <- (~2, 12) [subsumption resolution 481,214]
491. rich(sK0) | ~curious(sK0) | ~patient(sK0) <- (3) [resolution 87,172]
494. rich(sK0) | ~patient(sK0) <- (~2, 3) [subsumption resolution 491,467]
495. rich(sK0) <- (~2, 3, 12) [subsumption resolution 494,483]
513. ~old(X3) | ~rich(X3) | ~generous(X3) <- (8) [resolution 113,195]
514. ~rich(X3) | ~old(X3) <- (8, 14) [subsumption resolution 513,222]
570. ~old(sK0) <- (~2, 3, 8, 12, 14) [resolution 514,495]
573. $false <- (~2, 3, 8, 12, 14) [subsumption resolution 570,172]
574. 2 | ~3 | ~8 | ~12 | ~14 [avatar contradiction clause 573]
576. kind(mary) | patient(mary) <- (10) [resolution 204,116]
578. patient(mary) <- (10, 12) [subsumption resolution 576,214]
579. $false <- (10, 12) [subsumption resolution 578,158]
580. ~10 | ~12 [avatar contradiction clause 579]
581. $false [avatar sat refutation 168,173,205,219,223,228,229,363,466,574,580]
% SZS output end Proof for 8800718634829082992902917
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both wise and kind is rich and vice versa. Everyone who is both not rich and not quiet is not tall or patient. If someone is both not kind and generous then mary is both not happy and not generous and vice versa. If lucy is not generous then mary is calm and vice versa. Everyone who is funny is rich or not calm and vice versa. If mary is not rich or not strong then alice is both not wise and brave. Everyone who is not kind or not strong is either funny or quiet and vice versa. If fred is both not generous and not tall then paul is not strong. Everyone who is both old and rich is both not old and not curious. Everyone who is both calm and kind is old or not rich and vice versa. If someone is both not generous and strong then fred is strong. Everyone who is either not humble or not old is either wise or patient. Everyone who is happy or not rich is either not calm or not quiet and vice versa. Everyone who is either not brave or not wise is both not happy and funny and vice versa. If alice is both curious and not humble then mary is brave and vice versa. If someone is both curious and rich then john is humble. Someone is brave or not tall. Someone is either kind or not wise. Someone is both not curious and funny. Someone is quiet. Someone is not happy. Someone is rich. Someone is either not brave or not humble. | Paul is rich. | neutral | (![X]:((wise(X)&kind(X))<=>rich(X)))&
(![X]:((~rich(X)&~quiet(X))=>(~tall(X)|patient(X))))&
((?[X]:((~kind(X)&generous(X))))<=>((~happy(mary)&~generous(mary))))&
((~generous(lucy))<=>(calm(mary)))&
(![X]:(funny(X)<=>(rich(X)|~calm(X))))&
(((~rich(mary)|~strong(mary)))=>((~wise(alice)&brave(alice))))&
(![X]:((~kind(X)|~strong(X))<=>(funny(X)<~>quiet(X))))&
(((~generous(fred)&~tall(fred)))=>(~strong(paul)))&
(![X]:((old(X)&rich(X))=>(~old(X)&~curious(X))))&
(![X]:((calm(X)&kind(X))<=>(old(X)|~rich(X))))&
((?[X]:((~generous(X)&strong(X))))=>(strong(fred)))&
(![X]:((~humble(X)<~>~old(X))=>(wise(X)<~>patient(X))))&
(![X]:((happy(X)|~rich(X))<=>(~calm(X)<~>~quiet(X))))&
(![X]:((~brave(X)<~>~wise(X))<=>(~happy(X)&funny(X))))&
(((curious(alice)&~humble(alice)))<=>(brave(mary)))&
((?[X]:((curious(X)&rich(X))))=>(humble(john)))&
(?[X]:((brave(X)|~tall(X))))&
(?[X]:((kind(X)<~>~wise(X))))&
(?[X]:((~curious(X)&funny(X))))&
(?[X]:(quiet(X)))&
(?[X]:(~happy(X)))&
(?[X]:(rich(X)))&
(?[X]:((~brave(X)<~>~humble(X)))) | rich(paul) | [] | null | 0 |
If susan is either not rich or wise then someone is either quiet or not calm. If mary is calm then someone is happy or rich and vice versa. If john is either brave or old then someone is either old or not curious and vice versa. Everyone who is old or not brave is both not patient and curious. If someone is not creative or calm then someone is both strong and not creative. Everyone who is not tall or funny is either calm or not happy. Everyone who is both creative and brave is both creative and not kind and vice versa. If someone is both happy and not calm then john is both not humble and not rich. Everyone who is calm is both old and patient and vice versa. Everyone who is both generous and quiet is either not brave or tall. Everyone who is both kind and brave is both not patient and not tall. Everyone who is either not funny or rich is either not curious or not kind. Everyone who is not brave or not quiet is funny or not calm and vice versa. Everyone who is not rich or humble is strong or humble. Everyone who is both funny and not curious is curious and vice versa. If someone is both not strong and wise then alice is happy and vice versa. John is both not curious and not funny. Someone is not creative or not happy. Someone is either not kind or not wise. Lucy is not curious. Someone is not calm. | Alice is tall. | contradiction | (((~rich(susan)<~>wise(susan)))=>(?[X]:((quiet(X)<~>~calm(X)))))&
((calm(mary))<=>(?[X]:((happy(X)|rich(X)))))&
(((brave(john)<~>old(john)))<=>(?[X]:((old(X)<~>~curious(X)))))&
(![X]:((old(X)|~brave(X))=>(~patient(X)&curious(X))))&
((?[X]:((~creative(X)|calm(X))))=>(?[X]:((strong(X)&~creative(X)))))&
(![X]:((~tall(X)|funny(X))=>(calm(X)<~>~happy(X))))&
(![X]:((creative(X)&brave(X))<=>(creative(X)&~kind(X))))&
((?[X]:((happy(X)&~calm(X))))=>((~humble(john)&~rich(john))))&
(![X]:(calm(X)<=>(old(X)&patient(X))))&
(![X]:((generous(X)&quiet(X))=>(~brave(X)<~>tall(X))))&
(![X]:((kind(X)&brave(X))=>(~patient(X)&~tall(X))))&
(![X]:((~funny(X)<~>rich(X))=>(~curious(X)<~>~kind(X))))&
(![X]:((~brave(X)|~quiet(X))<=>(funny(X)|~calm(X))))&
(![X]:((~rich(X)|humble(X))=>(strong(X)|humble(X))))&
(![X]:((funny(X)&~curious(X))<=>curious(X)))&
((?[X]:((~strong(X)&wise(X))))<=>(happy(alice)))&
((~curious(john)&~funny(john)))&
(?[X]:((~creative(X)|~happy(X))))&
(?[X]:((~kind(X)<~>~wise(X))))&
(~curious(lucy))&
(?[X]:(~calm(X))) | tall(alice) | [
"p1",
"p3",
"p8",
"p10",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 621116113925337879192341
% SZS output start Proof for 621116113925337879192341
2. calm(mary) <=> ? [X0] : (rich(X0) | happy(X0)) [input p1]
4. ! [X0] : ((~brave(X0) | old(X0)) => (curious(X0) & ~patient(X0))) [input p3]
9. ! [X0] : (calm(X0) <=> (patient(X0) & old(X0))) [input p8]
11. ! [X0] : ((brave(X0) & kind(X0)) => (~tall(X0) & ~patient(X0))) [input p10]
12. ! [X0] : ((~funny(X0) <~> rich(X0)) => (~curious(X0) <~> ~kind(X0))) [input p11]
15. ! [X0] : ((~curious(X0) & funny(X0)) <=> curious(X0)) [input p14]
22. tall(alice) [input hypothesis]
26. ! [X0] : ((curious(X0) & ~patient(X0)) | (brave(X0) & ~old(X0))) [ennf transformation 4]
30. ! [X0] : ((~tall(X0) & ~patient(X0)) | (~brave(X0) | ~kind(X0))) [ennf transformation 11]
31. ! [X0] : ((~tall(X0) & ~patient(X0)) | ~brave(X0) | ~kind(X0)) [flattening 30]
32. ! [X0] : ((~curious(X0) <~> ~kind(X0)) | (~funny(X0) <=> rich(X0))) [ennf transformation 12]
38. (calm(mary) | ! [X0] : (~rich(X0) & ~happy(X0))) & (? [X0] : (rich(X0) | happy(X0)) | ~calm(mary)) [nnf transformation 2]
39. (calm(mary) | ! [X0] : (~rich(X0) & ~happy(X0))) & (? [X1] : (rich(X1) | happy(X1)) | ~calm(mary)) [rectify 38]
40. ? [X1] : (rich(X1) | happy(X1)) => (rich(sK1) | happy(sK1)) [choice axiom]
41. (calm(mary) | ! [X0] : (~rich(X0) & ~happy(X0))) & ((rich(sK1) | happy(sK1)) | ~calm(mary)) [skolemisation 39,40]
52. ! [X0] : ((calm(X0) | (~patient(X0) | ~old(X0))) & ((patient(X0) & old(X0)) | ~calm(X0))) [nnf transformation 9]
53. ! [X0] : ((calm(X0) | ~patient(X0) | ~old(X0)) & ((patient(X0) & old(X0)) | ~calm(X0))) [flattening 52]
54. ! [X0] : (((kind(X0) | curious(X0)) & (~kind(X0) | ~curious(X0))) | ((~funny(X0) | ~rich(X0)) & (rich(X0) | funny(X0)))) [nnf transformation 32]
57. ! [X0] : (((~curious(X0) & funny(X0)) | ~curious(X0)) & (curious(X0) | (curious(X0) | ~funny(X0)))) [nnf transformation 15]
58. ! [X0] : (((~curious(X0) & funny(X0)) | ~curious(X0)) & (curious(X0) | curious(X0) | ~funny(X0))) [flattening 57]
76. calm(mary) | ~rich(X0) [cnf transformation 41]
87. ~old(X0) | curious(X0) [cnf transformation 26]
88. curious(X0) | brave(X0) [cnf transformation 26]
103. ~calm(X0) | old(X0) [cnf transformation 53]
107. ~kind(X0) | ~brave(X0) | ~tall(X0) [cnf transformation 31]
110. kind(X0) | curious(X0) | rich(X0) | funny(X0) [cnf transformation 54]
118. curious(X0) | curious(X0) | ~funny(X0) [cnf transformation 58]
120. ~curious(X0) | ~curious(X0) [cnf transformation 58]
131. tall(alice) [cnf transformation 22]
132. curious(X0) | ~funny(X0) [duplicate literal removal 118]
133. ~curious(X0) [duplicate literal removal 120]
155. 5 <=> ! [X0] : ~rich(X0) [avatar definition]
156. ~rich(X0) <- (5) [avatar component clause 155]
158. 6 <=> calm(mary) [avatar definition]
160. calm(mary) <- (6) [avatar component clause 158]
161. 5 | 6 [avatar split clause 76,158,155]
237. ~funny(X0) [subsumption resolution 132,133]
281. brave(X0) [resolution 88,133]
282. old(mary) <- (6) [resolution 103,160]
283. curious(mary) <- (6) [resolution 282,87]
284. $false <- (6) [subsumption resolution 283,133]
285. ~6 [avatar contradiction clause 284]
313. curious(X2) | rich(X2) | funny(X2) | ~brave(X2) | ~tall(X2) [resolution 110,107]
317. rich(X2) | funny(X2) | ~brave(X2) | ~tall(X2) [subsumption resolution 313,133]
318. funny(X2) | ~brave(X2) | ~tall(X2) <- (5) [subsumption resolution 317,156]
319. ~brave(X2) | ~tall(X2) <- (5) [subsumption resolution 318,237]
320. ~tall(X2) <- (5) [subsumption resolution 319,281]
328. $false <- (5) [resolution 320,131]
329. ~5 [avatar contradiction clause 328]
330. $false [avatar sat refutation 161,285,329]
% SZS output end Proof for 621116113925337879192341
% ------------------------------
% 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: 0.018 s
% ------------------------------
% ------------------------------
| 0 |
If mary is either not generous or humble then fred is both not patient and not strong.
Everyone who is happy or not curious is either brave or not humble and vice versa.
If lucy is quiet or not wise then someone is not brave or kind.
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.
Someone is both calm and brave.
Someone is not funny.
Someone is both curious and patient.
Fred is not kind or quiet. | Mary is strong. | neutral | (((~generous(mary)<~>humble(mary)))=>((~patient(fred)&~strong(fred))))&
(![X]:((happy(X)|~curious(X))<=>(brave(X)<~>~humble(X))))&
(((quiet(lucy)|~wise(lucy)))=>(?[X]:((~brave(X)|kind(X)))))&
(![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)))))&
(?[X]:((calm(X)&brave(X))))&
(?[X]:(~funny(X)))&
(?[X]:((curious(X)&patient(X))))&
((~kind(fred)|quiet(fred))) | strong(mary) | [] | null | 0 |
Everyone who is both generous and not brave is either not rich or not quiet and vice versa.
Everyone who is either quiet or kind is not strong or not creative and vice versa.
If lucy is not patient or not funny then someone is both tall and not quiet.
Everyone who is not calm or not patient is not kind or wise.
Everyone who is not wise or humble is not wise or tall and vice versa.
Everyone who is not kind is happy or old and vice versa.
If mary is not calm or rich then someone is either not kind or not calm.
If alice is either curious or not old then someone is either not rich or not strong.
Everyone who is curious or wise is either calm or humble.
If someone is both not quiet and not rich then alice is both patient and old and vice versa.
Everyone who is not old or creative is both not calm and not tall and vice versa.
Everyone who is either not rich or brave is both not brave and not happy and vice versa.
If john is not creative or humble then mary is not calm.
Everyone who is both rich and humble is both not kind and funny and vice versa.
If someone is either strong or tall then john is tall or kind.
Everyone who is both not creative and not calm is both happy and not quiet and vice versa.
Susan is not old.
Someone is quiet.
Someone is both not strong and not patient.
Someone is both not generous and tall.
Someone is both strong and happy.
Paul is both tall and not kind.
Someone is both not brave and not funny. | Lucy is not happy. | contradiction | (![X]:((generous(X)&~brave(X))<=>(~rich(X)<~>~quiet(X))))&
(![X]:((quiet(X)<~>kind(X))<=>(~strong(X)|~creative(X))))&
(((~patient(lucy)|~funny(lucy)))=>(?[X]:((tall(X)&~quiet(X)))))&
(![X]:((~calm(X)|~patient(X))=>(~kind(X)|wise(X))))&
(![X]:((~wise(X)|humble(X))<=>(~wise(X)|tall(X))))&
(![X]:(~kind(X)<=>(happy(X)|old(X))))&
(((~calm(mary)|rich(mary)))=>(?[X]:((~kind(X)<~>~calm(X)))))&
(((curious(alice)<~>~old(alice)))=>(?[X]:((~rich(X)<~>~strong(X)))))&
(![X]:((curious(X)|wise(X))=>(calm(X)<~>humble(X))))&
((?[X]:((~quiet(X)&~rich(X))))<=>((patient(alice)&old(alice))))&
(![X]:((~old(X)|creative(X))<=>(~calm(X)&~tall(X))))&
(![X]:((~rich(X)<~>brave(X))<=>(~brave(X)&~happy(X))))&
(((~creative(john)|humble(john)))=>(~calm(mary)))&
(![X]:((rich(X)&humble(X))<=>(~kind(X)&funny(X))))&
((?[X]:((strong(X)<~>tall(X))))=>((tall(john)|kind(john))))&
(![X]:((~creative(X)&~calm(X))<=>(happy(X)&~quiet(X))))&
(~old(susan))&
(?[X]:(quiet(X)))&
(?[X]:((~strong(X)&~patient(X))))&
(?[X]:((~generous(X)&tall(X))))&
(?[X]:((strong(X)&happy(X))))&
((tall(paul)&~kind(paul)))&
(?[X]:((~brave(X)&~funny(X)))) | ~happy(lucy) | [
"p1",
"p2",
"p3",
"p4",
"p5",
"p8",
"p10",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 29664152536857910413980
% SZS output start Proof for 29664152536857910413980
2. ! [X0] : ((quiet(X0) <~> kind(X0)) <=> (~creative(X0) | ~strong(X0))) [input p1]
3. (~funny(lucy) | ~patient(lucy)) => ? [X0] : (~quiet(X0) & tall(X0)) [input p2]
4. ! [X0] : ((~patient(X0) | ~calm(X0)) => (wise(X0) | ~kind(X0))) [input p3]
5. ! [X0] : ((humble(X0) | ~wise(X0)) <=> (tall(X0) | ~wise(X0))) [input p4]
6. ! [X0] : (~kind(X0) <=> (old(X0) | happy(X0))) [input p5]
9. ! [X0] : ((wise(X0) | curious(X0)) => (calm(X0) <~> humble(X0))) [input p8]
11. ! [X0] : ((creative(X0) | ~old(X0)) <=> (~tall(X0) & ~calm(X0))) [input p10]
12. ! [X0] : ((~rich(X0) <~> brave(X0)) <=> (~happy(X0) & ~brave(X0))) [input p11]
14. ! [X0] : ((humble(X0) & rich(X0)) <=> (funny(X0) & ~kind(X0))) [input p13]
24. ~happy(lucy) [input hypothesis]
25. ? [X0] : (~quiet(X0) & tall(X0)) | (funny(lucy) & patient(lucy)) [ennf transformation 3]
26. ! [X0] : ((wise(X0) | ~kind(X0)) | (patient(X0) & calm(X0))) [ennf transformation 4]
27. ! [X0] : (wise(X0) | ~kind(X0) | (patient(X0) & calm(X0))) [flattening 26]
30. ! [X0] : ((calm(X0) <~> humble(X0)) | (~wise(X0) & ~curious(X0))) [ennf transformation 9]
36. ! [X0] : ((((~kind(X0) | ~quiet(X0)) & (kind(X0) | quiet(X0))) | (creative(X0) & strong(X0))) & ((~creative(X0) | ~strong(X0)) | ((quiet(X0) | ~kind(X0)) & (kind(X0) | ~quiet(X0))))) [nnf transformation 2]
37. ! [X0] : ((((~kind(X0) | ~quiet(X0)) & (kind(X0) | quiet(X0))) | (creative(X0) & strong(X0))) & (~creative(X0) | ~strong(X0) | ((quiet(X0) | ~kind(X0)) & (kind(X0) | ~quiet(X0))))) [flattening 36]
38. ? [X0] : (~quiet(X0) & tall(X0)) => (~quiet(sK0) & tall(sK0)) [choice axiom]
39. (~quiet(sK0) & tall(sK0)) | (funny(lucy) & patient(lucy)) [skolemisation 25,38]
40. ! [X0] : (((humble(X0) | ~wise(X0)) | (~tall(X0) & wise(X0))) & ((tall(X0) | ~wise(X0)) | (~humble(X0) & wise(X0)))) [nnf transformation 5]
41. ! [X0] : ((humble(X0) | ~wise(X0) | (~tall(X0) & wise(X0))) & (tall(X0) | ~wise(X0) | (~humble(X0) & wise(X0)))) [flattening 40]
42. ! [X0] : ((~kind(X0) | (~old(X0) & ~happy(X0))) & ((old(X0) | happy(X0)) | kind(X0))) [nnf transformation 6]
43. ! [X0] : ((~kind(X0) | (~old(X0) & ~happy(X0))) & (old(X0) | happy(X0) | kind(X0))) [flattening 42]
50. ! [X0] : (((~humble(X0) | ~calm(X0)) & (humble(X0) | calm(X0))) | (~wise(X0) & ~curious(X0))) [nnf transformation 30]
56. ! [X0] : (((creative(X0) | ~old(X0)) | (tall(X0) | calm(X0))) & ((~tall(X0) & ~calm(X0)) | (~creative(X0) & old(X0)))) [nnf transformation 11]
57. ! [X0] : ((creative(X0) | ~old(X0) | tall(X0) | calm(X0)) & ((~tall(X0) & ~calm(X0)) | (~creative(X0) & old(X0)))) [flattening 56]
58. ! [X0] : ((((~brave(X0) | rich(X0)) & (brave(X0) | ~rich(X0))) | (happy(X0) | brave(X0))) & ((~happy(X0) & ~brave(X0)) | ((~rich(X0) | ~brave(X0)) & (brave(X0) | rich(X0))))) [nnf transformation 12]
59. ! [X0] : ((((~brave(X0) | rich(X0)) & (brave(X0) | ~rich(X0))) | happy(X0) | brave(X0)) & ((~happy(X0) & ~brave(X0)) | ((~rich(X0) | ~brave(X0)) & (brave(X0) | rich(X0))))) [flattening 58]
60. ! [X0] : (((humble(X0) & rich(X0)) | (~funny(X0) | kind(X0))) & ((funny(X0) & ~kind(X0)) | (~humble(X0) | ~rich(X0)))) [nnf transformation 14]
61. ! [X0] : (((humble(X0) & rich(X0)) | ~funny(X0) | kind(X0)) & ((funny(X0) & ~kind(X0)) | ~humble(X0) | ~rich(X0))) [flattening 60]
84. creative(X0) | quiet(X0) | kind(X0) [cnf transformation 37]
88. tall(sK0) | funny(lucy) [cnf transformation 39]
90. ~quiet(sK0) | funny(lucy) [cnf transformation 39]
91. ~kind(X0) | wise(X0) | calm(X0) [cnf transformation 27]
94. ~humble(X0) | ~wise(X0) | tall(X0) [cnf transformation 41]
99. ~old(X0) | ~kind(X0) [cnf transformation 43]
109. ~wise(X0) | calm(X0) | humble(X0) [cnf transformation 50]
116. ~calm(X0) | old(X0) [cnf transformation 57]
118. ~tall(X0) | old(X0) [cnf transformation 57]
119. ~tall(X0) | ~creative(X0) [cnf transformation 57]
122. ~brave(X0) | ~rich(X0) | ~brave(X0) [cnf transformation 59]
125. brave(X0) | ~rich(X0) | happy(X0) | brave(X0) [cnf transformation 59]
131. ~funny(X0) | rich(X0) | kind(X0) [cnf transformation 61]
151. ~happy(lucy) [cnf transformation 24]
152. ~rich(X0) | ~brave(X0) [duplicate literal removal 122]
153. ~rich(X0) | brave(X0) | happy(X0) [duplicate literal removal 125]
155. 1 <=> funny(lucy) [avatar definition]
157. funny(lucy) <- (1) [avatar component clause 155]
159. 2 <=> quiet(sK0) [avatar definition]
161. ~quiet(sK0) <- (~2) [avatar component clause 159]
162. 1 | ~2 [avatar split clause 90,159,155]
169. 4 <=> tall(sK0) [avatar definition]
171. tall(sK0) <- (4) [avatar component clause 169]
172. 1 | 4 [avatar split clause 88,169,155]
263. old(sK0) <- (4) [resolution 118,171]
267. ~creative(sK0) <- (4) [resolution 119,171]
283. ~kind(sK0) <- (4) [resolution 263,99]
298. quiet(sK0) | kind(sK0) <- (4) [resolution 84,267]
302. kind(sK0) <- (~2, 4) [subsumption resolution 298,161]
303. $false <- (~2, 4) [subsumption resolution 302,283]
304. 2 | ~4 [avatar contradiction clause 303]
445. rich(lucy) | kind(lucy) <- (1) [resolution 131,157]
447. 48 <=> kind(lucy) [avatar definition]
449. kind(lucy) <- (48) [avatar component clause 447]
451. 49 <=> rich(lucy) [avatar definition]
453. rich(lucy) <- (49) [avatar component clause 451]
454. 48 | 49 | ~1 [avatar split clause 445,155,451,447]
457. 50 <=> humble(lucy) [avatar definition]
459. humble(lucy) <- (50) [avatar component clause 457]
482. 54 <=> calm(lucy) [avatar definition]
483. ~calm(lucy) <- (~54) [avatar component clause 482]
484. calm(lucy) <- (54) [avatar component clause 482]
488. ~brave(lucy) <- (49) [resolution 453,152]
494. 56 <=> brave(lucy) [avatar definition]
496. ~brave(lucy) <- (~56) [avatar component clause 494]
503. ~56 | ~49 [avatar split clause 488,451,494]
525. ~wise(lucy) | tall(lucy) <- (50) [resolution 459,94]
564. brave(lucy) | happy(lucy) <- (49) [resolution 153,453]
566. happy(lucy) <- (49, ~56) [subsumption resolution 564,496]
567. $false <- (49, ~56) [subsumption resolution 566,151]
568. ~49 | 56 [avatar contradiction clause 567]
571. wise(lucy) | calm(lucy) <- (48) [resolution 449,91]
791. 81 <=> wise(lucy) [avatar definition]
793. wise(lucy) <- (81) [avatar component clause 791]
794. 54 | 81 | ~48 [avatar split clause 571,447,791,482]
796. 82 <=> tall(lucy) [avatar definition]
798. tall(lucy) <- (82) [avatar component clause 796]
799. 82 | ~81 | ~50 [avatar split clause 525,457,791,796]
936. calm(lucy) | humble(lucy) <- (81) [resolution 793,109]
938. humble(lucy) <- (~54, 81) [subsumption resolution 936,483]
946. 50 | 54 | ~81 [avatar split clause 938,791,482,457]
953. old(lucy) <- (82) [resolution 798,118]
960. old(lucy) <- (54) [resolution 484,116]
1030. ~kind(lucy) <- (82) [resolution 953,99]
1031. $false <- (48, 82) [subsumption resolution 1030,449]
1032. ~48 | ~82 [avatar contradiction clause 1031]
1036. ~kind(lucy) <- (54) [resolution 960,99]
1037. $false <- (48, 54) [subsumption resolution 1036,449]
1038. ~48 | ~54 [avatar contradiction clause 1037]
1039. $false [avatar sat refutation 162,172,304,454,503,568,794,799,946,1032,1038]
% SZS output end Proof for 29664152536857910413980
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5500
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is creative or old is not wise and vice versa. If lucy is not generous then fred is generous or tall. Everyone who is either creative or old is either calm or old and vice versa. Everyone who is not kind or not brave is tall and vice versa. Everyone who is either not strong or not rich is both not humble and creative. Everyone who is both strong and not wise is generous or calm. If susan is either rich or not wise then someone is either quiet or rich and vice versa. Everyone who is both wise and happy is either not quiet or not brave. Everyone who is kind is either not kind or funny and vice versa. Everyone who is either calm or not creative is both funny and not wise and vice versa. If someone is both not patient and tall then someone is either kind or tall. If someone is not calm then john is not quiet or not old. Everyone who is either not wise or funny is not humble and vice versa. Everyone who is both curious and not funny is humble. If alice is either old or strong then someone is not old or patient and vice versa. If someone is not strong then lucy is either not happy or not brave and vice versa. Someone is both not brave and kind. Fred is both not tall and not quiet. Mary is humble or not patient. Someone is not brave or not funny. Someone is wise or generous. Someone is funny. | Mary is not humble. | contradiction | (![X]:((creative(X)|old(X))<=>~wise(X)))&
((~generous(lucy))=>((generous(fred)|tall(fred))))&
(![X]:((creative(X)<~>old(X))<=>(calm(X)<~>old(X))))&
(![X]:((~kind(X)|~brave(X))<=>tall(X)))&
(![X]:((~strong(X)<~>~rich(X))=>(~humble(X)&creative(X))))&
(![X]:((strong(X)&~wise(X))=>(generous(X)|calm(X))))&
(((rich(susan)<~>~wise(susan)))<=>(?[X]:((quiet(X)<~>rich(X)))))&
(![X]:((wise(X)&happy(X))=>(~quiet(X)<~>~brave(X))))&
(![X]:(kind(X)<=>(~kind(X)<~>funny(X))))&
(![X]:((calm(X)<~>~creative(X))<=>(funny(X)&~wise(X))))&
((?[X]:((~patient(X)&tall(X))))=>(?[X]:((kind(X)<~>tall(X)))))&
((?[X]:(~calm(X)))=>((~quiet(john)|~old(john))))&
(![X]:((~wise(X)<~>funny(X))<=>~humble(X)))&
(![X]:((curious(X)&~funny(X))=>humble(X)))&
(((old(alice)<~>strong(alice)))<=>(?[X]:((~old(X)|patient(X)))))&
((?[X]:(~strong(X)))<=>((~happy(lucy)<~>~brave(lucy))))&
(?[X]:((~brave(X)&kind(X))))&
((~tall(fred)&~quiet(fred)))&
((humble(mary)|~patient(mary)))&
(?[X]:((~brave(X)|~funny(X))))&
(?[X]:((wise(X)|generous(X))))&
(?[X]:(funny(X))) | ~humble(mary) | [
"p0",
"p2",
"p8",
"p9",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 566086890867084379959186
% SZS output start Proof for 566086890867084379959186
1. ! [X0] : ((old(X0) | creative(X0)) <=> ~wise(X0)) [input p0]
3. ! [X0] : ((creative(X0) <~> old(X0)) <=> (calm(X0) <~> old(X0))) [input p2]
9. ! [X0] : (kind(X0) <=> (~kind(X0) <~> funny(X0))) [input p8]
10. ! [X0] : ((calm(X0) <~> ~creative(X0)) <=> (~wise(X0) & funny(X0))) [input p9]
13. ! [X0] : ((~wise(X0) <~> funny(X0)) <=> ~humble(X0)) [input p12]
23. ~humble(mary) [input hypothesis]
35. ! [X0] : (((old(X0) | creative(X0)) | wise(X0)) & (~wise(X0) | (~old(X0) & ~creative(X0)))) [nnf transformation 1]
36. ! [X0] : ((old(X0) | creative(X0) | wise(X0)) & (~wise(X0) | (~old(X0) & ~creative(X0)))) [flattening 35]
37. ! [X0] : ((((~old(X0) | ~creative(X0)) & (old(X0) | creative(X0))) | ((calm(X0) | ~old(X0)) & (old(X0) | ~calm(X0)))) & (((~old(X0) | ~calm(X0)) & (old(X0) | calm(X0))) | ((creative(X0) | ~old(X0)) & (old(X0) | ~creative(X0))))) [nnf transformation 3]
46. ! [X0] : ((kind(X0) | ((~kind(X0) | ~funny(X0)) & (funny(X0) | kind(X0)))) & (((~funny(X0) | kind(X0)) & (funny(X0) | ~kind(X0))) | ~kind(X0))) [nnf transformation 9]
47. ! [X0] : ((((creative(X0) | ~calm(X0)) & (~creative(X0) | calm(X0))) | (wise(X0) | ~funny(X0))) & ((~wise(X0) & funny(X0)) | ((calm(X0) | creative(X0)) & (~creative(X0) | ~calm(X0))))) [nnf transformation 10]
48. ! [X0] : ((((creative(X0) | ~calm(X0)) & (~creative(X0) | calm(X0))) | wise(X0) | ~funny(X0)) & ((~wise(X0) & funny(X0)) | ((calm(X0) | creative(X0)) & (~creative(X0) | ~calm(X0))))) [flattening 47]
53. ! [X0] : ((((~funny(X0) | wise(X0)) & (funny(X0) | ~wise(X0))) | humble(X0)) & (~humble(X0) | ((~wise(X0) | ~funny(X0)) & (funny(X0) | wise(X0))))) [nnf transformation 13]
68. ~wise(X0) | ~creative(X0) [cnf transformation 36]
74. ~old(X0) | ~calm(X0) | creative(X0) | ~old(X0) [cnf transformation 37]
75. old(X0) | creative(X0) | old(X0) | ~calm(X0) [cnf transformation 37]
96. funny(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 46]
98. kind(X0) | funny(X0) | kind(X0) [cnf transformation 46]
103. ~wise(X0) | calm(X0) | creative(X0) [cnf transformation 48]
112. ~funny(X0) | wise(X0) | humble(X0) [cnf transformation 53]
130. ~humble(mary) [cnf transformation 23]
131. funny(X0) | ~kind(X0) [duplicate literal removal 96]
132. kind(X0) | funny(X0) [duplicate literal removal 98]
134. ~old(X0) | ~calm(X0) | creative(X0) [duplicate literal removal 74]
135. old(X0) | creative(X0) | ~calm(X0) [duplicate literal removal 75]
137. ~calm(X0) | creative(X0) [subsumption resolution 134,135]
169. funny(X0) [subsumption resolution 131,132]
170. ~wise(X0) | creative(X0) [subsumption resolution 103,137]
171. ~wise(X0) [subsumption resolution 170,68]
196. wise(X0) | humble(X0) [subsumption resolution 112,169]
197. humble(X0) [subsumption resolution 196,171]
246. $false [subsumption resolution 130,197]
% SZS output end Proof for 566086890867084379959186
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both generous and not kind is creative or brave. Everyone who is either not strong or not happy is not generous and vice versa. If john is not creative then someone is not old and vice versa. If susan is patient or not old then someone is both not calm and happy and vice versa. If susan is both not patient and not humble then lucy is both calm and not happy and vice versa. Everyone who is not calm is not tall and vice versa. If someone is old or creative then someone is both not humble and patient and vice versa. Everyone who is both rich and old is both quiet and humble. If someone is kind or not old then mary is not rich. Everyone who is both strong and patient is not rich or wise. Everyone who is either not kind or not generous is either wise or not funny. Everyone who is both not brave and curious is strong or brave and vice versa. If someone is patient or not calm then mary is either happy or humble and vice versa. If someone is both humble and not old then someone is both wise and not old and vice versa. If someone is happy then lucy is both not wise and curious and vice versa. Everyone who is both strong and not patient is not wise or not calm and vice versa. Lucy is either tall or not funny. Someone is either tall or not humble. Someone is not kind or strong. Someone is both not curious and quiet. Fred is not curious or brave. Mary is both not patient and not creative. Fred is not patient or humble. Someone is both wise and not rich. | Fred is not calm. | contradiction | (![X]:((generous(X)&~kind(X))=>(creative(X)|brave(X))))&
(![X]:((~strong(X)<~>~happy(X))<=>~generous(X)))&
((~creative(john))<=>(?[X]:(~old(X))))&
(((patient(susan)|~old(susan)))<=>(?[X]:((~calm(X)&happy(X)))))&
(((~patient(susan)&~humble(susan)))<=>((calm(lucy)&~happy(lucy))))&
(![X]:(~calm(X)<=>~tall(X)))&
((?[X]:((old(X)|creative(X))))<=>(?[X]:((~humble(X)&patient(X)))))&
(![X]:((rich(X)&old(X))=>(quiet(X)&humble(X))))&
((?[X]:((kind(X)|~old(X))))=>(~rich(mary)))&
(![X]:((strong(X)&patient(X))=>(~rich(X)|wise(X))))&
(![X]:((~kind(X)<~>~generous(X))=>(wise(X)<~>~funny(X))))&
(![X]:((~brave(X)&curious(X))<=>(strong(X)|brave(X))))&
((?[X]:((patient(X)|~calm(X))))<=>((happy(mary)<~>humble(mary))))&
((?[X]:((humble(X)&~old(X))))<=>(?[X]:((wise(X)&~old(X)))))&
((?[X]:(happy(X)))<=>((~wise(lucy)&curious(lucy))))&
(![X]:((strong(X)&~patient(X))<=>(~wise(X)|~calm(X))))&
((tall(lucy)<~>~funny(lucy)))&
(?[X]:((tall(X)<~>~humble(X))))&
(?[X]:((~kind(X)|strong(X))))&
(?[X]:((~curious(X)&quiet(X))))&
((~curious(fred)|brave(fred)))&
((~patient(mary)&~creative(mary)))&
((~patient(fred)|humble(fred)))&
(?[X]:((wise(X)&~rich(X)))) | ~calm(fred) | [
"p11",
"p15",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 4939478255277153806408727
% SZS output start Proof for 4939478255277153806408727
12. ! [X0] : ((curious(X0) & ~brave(X0)) <=> (brave(X0) | strong(X0))) [input p11]
16. ! [X0] : ((~patient(X0) & strong(X0)) <=> (~calm(X0) | ~wise(X0))) [input p15]
21. brave(fred) | ~curious(fred) [input p20]
25. ~calm(fred) [input hypothesis]
56. ! [X0] : (((curious(X0) & ~brave(X0)) | (~brave(X0) & ~strong(X0))) & ((brave(X0) | strong(X0)) | (~curious(X0) | brave(X0)))) [nnf transformation 12]
57. ! [X0] : (((curious(X0) & ~brave(X0)) | (~brave(X0) & ~strong(X0))) & (brave(X0) | strong(X0) | ~curious(X0) | brave(X0))) [flattening 56]
72. ! [X0] : (((~patient(X0) & strong(X0)) | (calm(X0) & wise(X0))) & ((~calm(X0) | ~wise(X0)) | (patient(X0) | ~strong(X0)))) [nnf transformation 16]
73. ! [X0] : (((~patient(X0) & strong(X0)) | (calm(X0) & wise(X0))) & (~calm(X0) | ~wise(X0) | patient(X0) | ~strong(X0))) [flattening 72]
113. ~brave(X0) | ~brave(X0) [cnf transformation 57]
114. ~strong(X0) | curious(X0) [cnf transformation 57]
131. calm(X0) | strong(X0) [cnf transformation 73]
140. brave(fred) | ~curious(fred) [cnf transformation 21]
145. ~calm(fred) [cnf transformation 25]
147. ~brave(X0) [duplicate literal removal 113]
333. ~curious(fred) [subsumption resolution 140,147]
347. strong(fred) [resolution 131,145]
350. curious(fred) [resolution 347,114]
351. $false [subsumption resolution 350,333]
% SZS output end Proof for 4939478255277153806408727
% ------------------------------
% 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 funny or kind then someone is curious or not creative.
If someone is both old and wise then paul is happy or not strong.
If someone is both calm and happy then someone is both not quiet and kind and vice versa.
If someone is both rich and curious then lucy is brave or calm.
If alice is either not quiet or not rich then susan is not curious and vice versa.
If someone is either strong or not funny then mary is not old and vice versa.
If someone is not generous then someone is tall or not kind.
If someone is not calm or kind then mary is either generous or not funny.
Everyone who is quiet or not tall is not quiet or calm.
Everyone who is funny is both not wise and not rich.
Everyone who is funny is old.
If someone is not funny then someone is both tall and not kind.
If mary is both not patient and not calm then someone is tall or happy and vice versa.
If someone is both not generous and brave then someone is not funny or brave and vice versa.
Everyone who is either not tall or not curious is not brave and vice versa.
Everyone who is calm or old is not tall or humble and vice versa.
Someone is both patient and not wise.
Alice is not happy.
Someone is both not patient and rich.
Mary is either not tall or quiet.
Lucy is not creative or happy.
Someone is either generous or not generous.
Someone is both happy and not rich.
John is either not wise or tall. | Mary is quiet. | contradiction | ((?[X]:((funny(X)|kind(X))))=>(?[X]:((curious(X)|~creative(X)))))&
((?[X]:((old(X)&wise(X))))=>((happy(paul)|~strong(paul))))&
((?[X]:((calm(X)&happy(X))))<=>(?[X]:((~quiet(X)&kind(X)))))&
((?[X]:((rich(X)&curious(X))))=>((brave(lucy)|calm(lucy))))&
(((~quiet(alice)<~>~rich(alice)))<=>(~curious(susan)))&
((?[X]:((strong(X)<~>~funny(X))))<=>(~old(mary)))&
((?[X]:(~generous(X)))=>(?[X]:((tall(X)|~kind(X)))))&
((?[X]:((~calm(X)|kind(X))))=>((generous(mary)<~>~funny(mary))))&
(![X]:((quiet(X)|~tall(X))=>(~quiet(X)|calm(X))))&
(![X]:(funny(X)=>(~wise(X)&~rich(X))))&
(![X]:(funny(X)=>old(X)))&
((?[X]:(~funny(X)))=>(?[X]:((tall(X)&~kind(X)))))&
(((~patient(mary)&~calm(mary)))<=>(?[X]:((tall(X)|happy(X)))))&
((?[X]:((~generous(X)&brave(X))))<=>(?[X]:((~funny(X)|brave(X)))))&
(![X]:((~tall(X)<~>~curious(X))<=>~brave(X)))&
(![X]:((calm(X)|old(X))<=>(~tall(X)|humble(X))))&
(?[X]:((patient(X)&~wise(X))))&
(~happy(alice))&
(?[X]:((~patient(X)&rich(X))))&
((~tall(mary)<~>quiet(mary)))&
((~creative(lucy)|happy(lucy)))&
(?[X]:((generous(X)<~>~generous(X))))&
(?[X]:((happy(X)&~rich(X))))&
((~wise(john)<~>tall(john))) | quiet(mary) | [
"p8",
"p12",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 7587496291695224554759061
% SZS output start Proof for 7587496291695224554759061
9. ! [X0] : ((~tall(X0) | quiet(X0)) => (calm(X0) | ~quiet(X0))) [input p8]
13. (~calm(mary) & ~patient(mary)) <=> ? [X0] : (happy(X0) | tall(X0)) [input p12]
23. ? [X0] : (~rich(X0) & happy(X0)) [input p22]
25. quiet(mary) [input hypothesis]
39. ! [X0] : ((calm(X0) | ~quiet(X0)) | (tall(X0) & ~quiet(X0))) [ennf transformation 9]
40. ! [X0] : (calm(X0) | ~quiet(X0) | (tall(X0) & ~quiet(X0))) [flattening 39]
61. ((~calm(mary) & ~patient(mary)) | ! [X0] : (~happy(X0) & ~tall(X0))) & (? [X0] : (happy(X0) | tall(X0)) | (calm(mary) | patient(mary))) [nnf transformation 13]
62. ((~calm(mary) & ~patient(mary)) | ! [X0] : (~happy(X0) & ~tall(X0))) & (? [X0] : (happy(X0) | tall(X0)) | calm(mary) | patient(mary)) [flattening 61]
63. ((~calm(mary) & ~patient(mary)) | ! [X0] : (~happy(X0) & ~tall(X0))) & (? [X1] : (happy(X1) | tall(X1)) | calm(mary) | patient(mary)) [rectify 62]
64. ? [X1] : (happy(X1) | tall(X1)) => (happy(sK5) | tall(sK5)) [choice axiom]
65. ((~calm(mary) & ~patient(mary)) | ! [X0] : (~happy(X0) & ~tall(X0))) & ((happy(sK5) | tall(sK5)) | calm(mary) | patient(mary)) [skolemisation 63,64]
82. ? [X0] : (~rich(X0) & happy(X0)) => (~rich(sK11) & happy(sK11)) [choice axiom]
83. ~rich(sK11) & happy(sK11) [skolemisation 23,82]
104. calm(X0) | ~quiet(X0) | ~quiet(X0) [cnf transformation 40]
115. ~calm(mary) | ~happy(X0) [cnf transformation 65]
138. happy(sK11) [cnf transformation 83]
142. quiet(mary) [cnf transformation 25]
143. ~quiet(X0) | calm(X0) [duplicate literal removal 104]
276. 31 <=> ! [X0] : ~happy(X0) [avatar definition]
277. ~happy(X0) <- (31) [avatar component clause 276]
279. 32 <=> calm(mary) [avatar definition]
281. ~calm(mary) <- (~32) [avatar component clause 279]
282. 31 | ~32 [avatar split clause 115,279,276]
334. 44 <=> quiet(mary) [avatar definition]
335. quiet(mary) <- (44) [avatar component clause 334]
349. 44 [avatar split clause 142,334]
354. $false <- (31) [resolution 277,138]
355. ~31 [avatar contradiction clause 354]
368. calm(mary) <- (44) [resolution 143,335]
369. $false <- (~32, 44) [subsumption resolution 368,281]
370. 32 | ~44 [avatar contradiction clause 369]
371. $false [avatar sat refutation 282,349,355,370]
% SZS output end Proof for 7587496291695224554759061
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not humble or not creative then someone is both happy and not quiet and vice versa.
If john is strong then lucy is generous or not tall and vice versa.
Everyone who is quiet is both brave and patient and vice versa.
Everyone who is not happy or kind is not old and vice versa.
Everyone who is brave or not strong is both generous and not kind and vice versa.
If alice is old or not patient then someone is both not quiet and generous.
Everyone who is not happy is not brave or creative and vice versa.
If someone is not tall then alice is not tall.
Everyone who is both not humble and not happy is both creative and not rich.
Everyone who is either creative or funny is not funny or not kind.
Everyone who is not wise or calm is wise.
If someone is not strong then paul is not wise and vice versa.
If someone is tall then someone is both not old and patient and vice versa.
If someone is quiet then someone is both not rich and rich and vice versa.
Everyone who is tall or funny is both not happy and not quiet.
If someone is either not strong or generous then paul is both generous and not tall and vice versa.
Someone is not creative.
Lucy is funny or not strong.
Someone is either not calm or not tall.
Someone is both humble and strong.
Someone is both not brave and strong.
Susan is curious.
Someone is either not funny or generous. | Lucy is strong. | entailment | ((?[X]:((~humble(X)|~creative(X))))<=>(?[X]:((happy(X)&~quiet(X)))))&
((strong(john))<=>((generous(lucy)|~tall(lucy))))&
(![X]:(quiet(X)<=>(brave(X)&patient(X))))&
(![X]:((~happy(X)|kind(X))<=>~old(X)))&
(![X]:((brave(X)|~strong(X))<=>(generous(X)&~kind(X))))&
(((old(alice)|~patient(alice)))=>(?[X]:((~quiet(X)&generous(X)))))&
(![X]:(~happy(X)<=>(~brave(X)|creative(X))))&
((?[X]:(~tall(X)))=>(~tall(alice)))&
(![X]:((~humble(X)&~happy(X))=>(creative(X)&~rich(X))))&
(![X]:((creative(X)<~>funny(X))=>(~funny(X)|~kind(X))))&
(![X]:((~wise(X)|calm(X))=>wise(X)))&
((?[X]:(~strong(X)))<=>(~wise(paul)))&
((?[X]:(tall(X)))<=>(?[X]:((~old(X)&patient(X)))))&
((?[X]:(quiet(X)))<=>(?[X]:((~rich(X)&rich(X)))))&
(![X]:((tall(X)|funny(X))=>(~happy(X)&~quiet(X))))&
((?[X]:((~strong(X)<~>generous(X))))<=>((generous(paul)&~tall(paul))))&
(?[X]:(~creative(X)))&
((funny(lucy)|~strong(lucy)))&
(?[X]:((~calm(X)<~>~tall(X))))&
(?[X]:((humble(X)&strong(X))))&
(?[X]:((~brave(X)&strong(X))))&
(curious(susan))&
(?[X]:((~funny(X)<~>generous(X)))) | strong(lucy) | [
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 8051061308708580635479203
% SZS output start Proof for 8051061308708580635479203
11. ! [X0] : ((calm(X0) | ~wise(X0)) => wise(X0)) [input p10]
12. ? [X0] : ~strong(X0) <=> ~wise(paul) [input p11]
24. ~strong(lucy) [input hypothesis]
35. ! [X0] : (wise(X0) | (~calm(X0) & wise(X0))) [ennf transformation 11]
55. (? [X0] : ~strong(X0) | wise(paul)) & (~wise(paul) | ! [X0] : strong(X0)) [nnf transformation 12]
56. (? [X0] : ~strong(X0) | wise(paul)) & (~wise(paul) | ! [X1] : strong(X1)) [rectify 55]
57. ? [X0] : ~strong(X0) => ~strong(sK3) [choice axiom]
58. (~strong(sK3) | wise(paul)) & (~wise(paul) | ! [X1] : strong(X1)) [skolemisation 56,57]
117. wise(X0) | wise(X0) [cnf transformation 35]
119. ~wise(paul) | strong(X1) [cnf transformation 58]
147. ~strong(lucy) [cnf transformation 24]
148. wise(X0) [duplicate literal removal 117]
223. strong(X1) [subsumption resolution 119,148]
296. $false [subsumption resolution 147,223]
% SZS output end Proof for 8051061308708580635479203
% ------------------------------
% 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 mary is both happy and rich then fred is not humble.
If someone is not curious then someone is not humble or quiet.
If someone is generous or brave then lucy is not calm.
Everyone who is quiet is either wise or not funny.
If someone is wise or not generous then lucy is not happy.
If john is both not humble and not rich then lucy is either funny or creative.
Everyone who is both funny and not patient is strong and vice versa.
Everyone who is not strong is both not calm and not strong.
Everyone who is both not creative and not kind is not rich and vice versa.
If someone is not kind or not rich then alice is happy and vice versa.
If someone is both patient and brave then someone is not happy or not strong.
Everyone who is both not kind and not creative is either rich or wise and vice versa.
If lucy is both calm and tall then someone is not generous and vice versa.
Everyone who is kind is patient.
If mary is old then susan is not wise or not calm.
Everyone who is not generous is not kind and vice versa.
Paul is funny.
Someone is calm.
Someone is not humble or not curious.
Lucy is not rich or not kind.
John is not kind or not creative.
Someone is not funny.
Susan is humble.
John is curious. | Lucy is patient. | contradiction | (((happy(mary)&rich(mary)))=>(~humble(fred)))&
((?[X]:(~curious(X)))=>(?[X]:((~humble(X)|quiet(X)))))&
((?[X]:((generous(X)|brave(X))))=>(~calm(lucy)))&
(![X]:(quiet(X)=>(wise(X)<~>~funny(X))))&
((?[X]:((wise(X)|~generous(X))))=>(~happy(lucy)))&
(((~humble(john)&~rich(john)))=>((funny(lucy)<~>creative(lucy))))&
(![X]:((funny(X)&~patient(X))<=>strong(X)))&
(![X]:(~strong(X)=>(~calm(X)&~strong(X))))&
(![X]:((~creative(X)&~kind(X))<=>~rich(X)))&
((?[X]:((~kind(X)|~rich(X))))<=>(happy(alice)))&
((?[X]:((patient(X)&brave(X))))=>(?[X]:((~happy(X)|~strong(X)))))&
(![X]:((~kind(X)&~creative(X))<=>(rich(X)<~>wise(X))))&
(((calm(lucy)&tall(lucy)))<=>(?[X]:(~generous(X))))&
(![X]:(kind(X)=>patient(X)))&
((old(mary))=>((~wise(susan)|~calm(susan))))&
(![X]:(~generous(X)<=>~kind(X)))&
(funny(paul))&
(?[X]:(calm(X)))&
(?[X]:((~humble(X)|~curious(X))))&
((~rich(lucy)|~kind(lucy)))&
((~kind(john)|~creative(john)))&
(?[X]:(~funny(X)))&
(humble(susan))&
(curious(john)) | patient(lucy) | [
"p6",
"p7",
"p8",
"p12",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 3759765489505694027877281
% SZS output start Proof for 3759765489505694027877281
7. ! [X0] : ((~patient(X0) & funny(X0)) <=> strong(X0)) [input p6]
8. ! [X0] : (~strong(X0) => (~strong(X0) & ~calm(X0))) [input p7]
9. ! [X0] : ((~kind(X0) & ~creative(X0)) <=> ~rich(X0)) [input p8]
13. (tall(lucy) & calm(lucy)) <=> ? [X0] : ~generous(X0) [input p12]
16. ! [X0] : (~generous(X0) <=> ~kind(X0)) [input p15]
20. ~kind(lucy) | ~rich(lucy) [input p19]
25. patient(lucy) [input hypothesis]
39. ! [X0] : ((~strong(X0) & ~calm(X0)) | strong(X0)) [ennf transformation 8]
46. ! [X0] : (((~patient(X0) & funny(X0)) | ~strong(X0)) & (strong(X0) | (patient(X0) | ~funny(X0)))) [nnf transformation 7]
47. ! [X0] : (((~patient(X0) & funny(X0)) | ~strong(X0)) & (strong(X0) | patient(X0) | ~funny(X0))) [flattening 46]
48. ! [X0] : (((~kind(X0) & ~creative(X0)) | rich(X0)) & (~rich(X0) | (kind(X0) | creative(X0)))) [nnf transformation 9]
49. ! [X0] : (((~kind(X0) & ~creative(X0)) | rich(X0)) & (~rich(X0) | kind(X0) | creative(X0))) [flattening 48]
56. ((tall(lucy) & calm(lucy)) | ! [X0] : generous(X0)) & (? [X0] : ~generous(X0) | (~tall(lucy) | ~calm(lucy))) [nnf transformation 13]
57. ((tall(lucy) & calm(lucy)) | ! [X0] : generous(X0)) & (? [X0] : ~generous(X0) | ~tall(lucy) | ~calm(lucy)) [flattening 56]
58. ((tall(lucy) & calm(lucy)) | ! [X0] : generous(X0)) & (? [X1] : ~generous(X1) | ~tall(lucy) | ~calm(lucy)) [rectify 57]
59. ? [X1] : ~generous(X1) => ~generous(sK2) [choice axiom]
60. ((tall(lucy) & calm(lucy)) | ! [X0] : generous(X0)) & (~generous(sK2) | ~tall(lucy) | ~calm(lucy)) [skolemisation 58,59]
61. ! [X0] : ((~generous(X0) | kind(X0)) & (~kind(X0) | generous(X0))) [nnf transformation 16]
79. ~strong(X0) | ~patient(X0) [cnf transformation 47]
80. ~calm(X0) | strong(X0) [cnf transformation 39]
84. ~kind(X0) | rich(X0) [cnf transformation 49]
95. calm(lucy) | generous(X0) [cnf transformation 60]
99. ~generous(X0) | kind(X0) [cnf transformation 61]
103. ~kind(lucy) | ~rich(lucy) [cnf transformation 20]
108. patient(lucy) [cnf transformation 25]
138. 8 <=> calm(lucy) [avatar definition]
139. calm(lucy) <- (8) [avatar component clause 138]
143. 9 <=> ! [X0] : generous(X0) [avatar definition]
144. generous(X0) <- (9) [avatar component clause 143]
187. 19 <=> ! [X1] : kind(X1) [avatar definition]
188. kind(X1) <- (19) [avatar component clause 187]
199. 9 | 8 [avatar split clause 95,138,143]
214. ~kind(lucy) [subsumption resolution 103,84]
227. kind(X0) <- (9) [resolution 99,144]
228. 19 | ~9 [avatar split clause 227,143,187]
232. $false <- (19) [resolution 188,214]
237. ~19 [avatar contradiction clause 232]
239. strong(lucy) <- (8) [resolution 139,80]
240. ~patient(lucy) <- (8) [resolution 239,79]
242. $false <- (8) [subsumption resolution 240,108]
243. ~8 [avatar contradiction clause 242]
245. $false [avatar sat refutation 199,228,237,243]
% SZS output end Proof for 3759765489505694027877281
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is happy or not patient is not humble and vice versa.
If someone is creative then alice is strong and vice versa.
If lucy is not wise or generous then john is curious and vice versa.
If paul is not tall or tall then paul is not wise or happy.
If someone is not tall then susan is not old or not generous.
Everyone who is either humble or tall is both not generous and not strong and vice versa.
Everyone who is not humble is not brave and vice versa.
If someone is both not patient and not humble then someone is both not quiet and tall and vice versa.
Everyone who is rich is not generous.
Everyone who is both kind and not brave is not kind or not strong.
If john is not creative or not funny then someone is both not tall and kind.
Everyone who is not happy or brave is not patient and vice versa.
If mary is curious or not rich then fred is either not calm or humble and vice versa.
Everyone who is either not patient or generous is either tall or wise and vice versa.
If someone is both calm and not generous then fred is both patient and funny.
Everyone who is either not generous or happy is not tall and vice versa.
Fred is tall or not brave.
Someone is both patient and not brave.
Someone is funny or not calm.
Alice is not strong.
Mary is not happy or funny.
Mary is either not funny or humble.
Paul is either creative or not quiet. | Lucy is not brave. | entailment | (![X]:((happy(X)|~patient(X))<=>~humble(X)))&
((?[X]:(creative(X)))<=>(strong(alice)))&
(((~wise(lucy)|generous(lucy)))<=>(curious(john)))&
(((~tall(paul)|tall(paul)))=>((~wise(paul)|happy(paul))))&
((?[X]:(~tall(X)))=>((~old(susan)|~generous(susan))))&
(![X]:((humble(X)<~>tall(X))<=>(~generous(X)&~strong(X))))&
(![X]:(~humble(X)<=>~brave(X)))&
((?[X]:((~patient(X)&~humble(X))))<=>(?[X]:((~quiet(X)&tall(X)))))&
(![X]:(rich(X)=>~generous(X)))&
(![X]:((kind(X)&~brave(X))=>(~kind(X)|~strong(X))))&
(((~creative(john)|~funny(john)))=>(?[X]:((~tall(X)&kind(X)))))&
(![X]:((~happy(X)|brave(X))<=>~patient(X)))&
(((curious(mary)|~rich(mary)))<=>((~calm(fred)<~>humble(fred))))&
(![X]:((~patient(X)<~>generous(X))<=>(tall(X)<~>wise(X))))&
((?[X]:((calm(X)&~generous(X))))=>((patient(fred)&funny(fred))))&
(![X]:((~generous(X)<~>happy(X))<=>~tall(X)))&
((tall(fred)|~brave(fred)))&
(?[X]:((patient(X)&~brave(X))))&
(?[X]:((funny(X)|~calm(X))))&
(~strong(alice))&
((~happy(mary)|funny(mary)))&
((~funny(mary)<~>humble(mary)))&
((creative(paul)<~>~quiet(paul))) | ~brave(lucy) | [
"p0",
"p6",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 1316289273372391610531775
% SZS output start Proof for 1316289273372391610531775
1. ! [X0] : ((~patient(X0) | happy(X0)) <=> ~humble(X0)) [input p0]
7. ! [X0] : (~humble(X0) <=> ~brave(X0)) [input p6]
12. ! [X0] : ((brave(X0) | ~happy(X0)) <=> ~patient(X0)) [input p11]
24. brave(lucy) [input hypothesis]
34. ! [X0] : (((~patient(X0) | happy(X0)) | humble(X0)) & (~humble(X0) | (patient(X0) & ~happy(X0)))) [nnf transformation 1]
35. ! [X0] : ((~patient(X0) | happy(X0) | humble(X0)) & (~humble(X0) | (patient(X0) & ~happy(X0)))) [flattening 34]
44. ! [X0] : ((~humble(X0) | brave(X0)) & (~brave(X0) | humble(X0))) [nnf transformation 7]
52. ! [X0] : (((brave(X0) | ~happy(X0)) | patient(X0)) & (~patient(X0) | (~brave(X0) & happy(X0)))) [nnf transformation 12]
53. ! [X0] : ((brave(X0) | ~happy(X0) | patient(X0)) & (~patient(X0) | (~brave(X0) & happy(X0)))) [flattening 52]
65. ~humble(X0) | patient(X0) [cnf transformation 35]
80. ~brave(X0) | humble(X0) [cnf transformation 44]
93. ~brave(X0) | ~patient(X0) [cnf transformation 53]
125. brave(lucy) [cnf transformation 24]
298. humble(lucy) [resolution 80,125]
300. patient(lucy) [resolution 298,65]
304. ~patient(lucy) [resolution 93,125]
307. $false [subsumption resolution 300,304]
% SZS output end Proof for 1316289273372391610531775
% ------------------------------
% 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 wise then susan is both calm and not patient and vice versa.
Everyone who is both not creative and tall is both not creative and strong.
If paul is both not calm and old then fred is not tall or not brave and vice versa.
Everyone who is not rich is both not curious and not strong.
If someone is both not rich and curious then fred is not generous and vice versa.
If someone is both creative and tall then paul is both not calm and not rich and vice versa.
If someone is curious then john is either not kind or not creative.
If john is both not wise and calm then paul is not patient or brave.
Everyone who is both creative and brave is not funny.
If paul is either rich or not brave then lucy is not strong and vice versa.
Everyone who is either quiet or not wise is not generous or curious and vice versa.
If mary is not creative then someone is either patient or kind and vice versa.
If lucy is both tall and not funny then fred is creative and vice versa.
If susan is not generous or curious then someone is curious.
If someone is humble then someone is not creative and vice versa.
Everyone who is brave or not funny is calm and vice versa.
Alice is both not kind and not wise.
John is both quiet and happy.
John is either old or patient.
Mary is either creative or not creative.
Paul is both creative and curious.
Fred is humble.
Susan is both not curious and not wise.
Someone is both not strong and not kind. | Alice is not kind. | entailment | ((?[X]:(wise(X)))<=>((calm(susan)&~patient(susan))))&
(![X]:((~creative(X)&tall(X))=>(~creative(X)&strong(X))))&
(((~calm(paul)&old(paul)))<=>((~tall(fred)|~brave(fred))))&
(![X]:(~rich(X)=>(~curious(X)&~strong(X))))&
((?[X]:((~rich(X)&curious(X))))<=>(~generous(fred)))&
((?[X]:((creative(X)&tall(X))))<=>((~calm(paul)&~rich(paul))))&
((?[X]:(curious(X)))=>((~kind(john)<~>~creative(john))))&
(((~wise(john)&calm(john)))=>((~patient(paul)|brave(paul))))&
(![X]:((creative(X)&brave(X))=>~funny(X)))&
(((rich(paul)<~>~brave(paul)))<=>(~strong(lucy)))&
(![X]:((quiet(X)<~>~wise(X))<=>(~generous(X)|curious(X))))&
((~creative(mary))<=>(?[X]:((patient(X)<~>kind(X)))))&
(((tall(lucy)&~funny(lucy)))<=>(creative(fred)))&
(((~generous(susan)|curious(susan)))=>(?[X]:(curious(X))))&
((?[X]:(humble(X)))<=>(?[X]:(~creative(X))))&
(![X]:((brave(X)|~funny(X))<=>calm(X)))&
((~kind(alice)&~wise(alice)))&
((quiet(john)&happy(john)))&
((old(john)<~>patient(john)))&
((creative(mary)<~>~creative(mary)))&
((creative(paul)&curious(paul)))&
(humble(fred))&
((~curious(susan)&~wise(susan)))&
(?[X]:((~strong(X)&~kind(X)))) | ~kind(alice) | [
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 83752638140933641649866
% SZS output start Proof for 83752638140933641649866
17. ~wise(alice) & ~kind(alice) [input p16]
25. kind(alice) [input hypothesis]
123. ~kind(alice) [cnf transformation 17]
137. kind(alice) [cnf transformation 25]
326. $false [subsumption resolution 137,123]
% SZS output end Proof for 83752638140933641649866
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not old or quiet then someone is either not kind or wise.
Everyone who is patient is both not patient and quiet and vice versa.
If paul is strong then someone is strong.
Everyone who is old or not quiet is both curious and not brave.
If paul is either wise or not old then fred is tall.
Everyone who is both not quiet and not patient is both not tall and old.
Everyone who is both not quiet and quiet is either not generous or not curious and vice versa.
If someone is not creative then alice is either not brave or not curious.
If alice is curious then someone is either not humble or not creative and vice versa.
Everyone who is both creative and not creative is both not strong and strong.
Everyone who is both not strong and generous is quiet and vice versa.
Everyone who is both kind and not old is either not strong or not funny and vice versa.
If john is either kind or quiet then paul is either kind or tall.
Everyone who is both not brave and happy is both tall and wise.
Everyone who is either old or tall is old and vice versa.
Everyone who is not humble or tall is not wise.
Someone is kind or not happy.
Someone is not kind.
Lucy is either calm or happy.
Paul is not funny or generous.
Someone is generous. | Fred is not humble. | neutral | ((?[X]:((~old(X)<~>quiet(X))))=>(?[X]:((~kind(X)<~>wise(X)))))&
(![X]:(patient(X)<=>(~patient(X)&quiet(X))))&
((strong(paul))=>(?[X]:(strong(X))))&
(![X]:((old(X)|~quiet(X))=>(curious(X)&~brave(X))))&
(((wise(paul)<~>~old(paul)))=>(tall(fred)))&
(![X]:((~quiet(X)&~patient(X))=>(~tall(X)&old(X))))&
(![X]:((~quiet(X)&quiet(X))<=>(~generous(X)<~>~curious(X))))&
((?[X]:(~creative(X)))=>((~brave(alice)<~>~curious(alice))))&
((curious(alice))<=>(?[X]:((~humble(X)<~>~creative(X)))))&
(![X]:((creative(X)&~creative(X))=>(~strong(X)&strong(X))))&
(![X]:((~strong(X)&generous(X))<=>quiet(X)))&
(![X]:((kind(X)&~old(X))<=>(~strong(X)<~>~funny(X))))&
(((kind(john)<~>quiet(john)))=>((kind(paul)<~>tall(paul))))&
(![X]:((~brave(X)&happy(X))=>(tall(X)&wise(X))))&
(![X]:((old(X)<~>tall(X))<=>old(X)))&
(![X]:((~humble(X)|tall(X))=>~wise(X)))&
(?[X]:((kind(X)|~happy(X))))&
(?[X]:(~kind(X)))&
((calm(lucy)<~>happy(lucy)))&
((~funny(paul)|generous(paul)))&
(?[X]:(generous(X))) | ~humble(fred) | [] | null | 0 |
If paul is either strong or creative then someone is either rich or not patient and vice versa. If mary is both quiet and not wise then susan is not generous and vice versa. If someone is brave then susan is either creative or calm and vice versa. If fred is not brave or brave then someone is strong and vice versa. If someone is not rich then someone is either not happy or wise and vice versa. If someone is both tall and not wise then mary is either funny or not happy and vice versa. If someone is rich then john is both wise and not calm. Everyone who is rich is either not rich or strong and vice versa. Everyone who is calm or not creative is not strong or happy. Everyone who is brave or patient is either not wise or not old. Everyone who is either happy or humble is patient. Everyone who is not creative or not humble is both not generous and not quiet. Everyone who is either not brave or not rich is either generous or curious. Everyone who is wise or not brave is not rich and vice versa. Everyone who is both not quiet and quiet is either humble or brave. Alice is curious or not happy. Paul is either calm or not tall. Alice is not patient. Someone is both not old and not quiet. Alice is not generous or not calm. Someone is calm. | Susan is not patient. | neutral | (((strong(paul)<~>creative(paul)))<=>(?[X]:((rich(X)<~>~patient(X)))))&
(((quiet(mary)&~wise(mary)))<=>(~generous(susan)))&
((?[X]:(brave(X)))<=>((creative(susan)<~>calm(susan))))&
(((~brave(fred)|brave(fred)))<=>(?[X]:(strong(X))))&
((?[X]:(~rich(X)))<=>(?[X]:((~happy(X)<~>wise(X)))))&
((?[X]:((tall(X)&~wise(X))))<=>((funny(mary)<~>~happy(mary))))&
((?[X]:(rich(X)))=>((wise(john)&~calm(john))))&
(![X]:(rich(X)<=>(~rich(X)<~>strong(X))))&
(![X]:((calm(X)|~creative(X))=>(~strong(X)|happy(X))))&
(![X]:((brave(X)|patient(X))=>(~wise(X)<~>~old(X))))&
(![X]:((happy(X)<~>humble(X))=>patient(X)))&
(![X]:((~creative(X)|~humble(X))=>(~generous(X)&~quiet(X))))&
(![X]:((~brave(X)<~>~rich(X))=>(generous(X)<~>curious(X))))&
(![X]:((wise(X)|~brave(X))<=>~rich(X)))&
(![X]:((~quiet(X)&quiet(X))=>(humble(X)<~>brave(X))))&
((curious(alice)|~happy(alice)))&
((calm(paul)<~>~tall(paul)))&
(~patient(alice))&
(?[X]:((~old(X)&~quiet(X))))&
((~generous(alice)|~calm(alice)))&
(?[X]:(calm(X))) | ~patient(susan) | [] | null | 0 |
If someone is both strong and not funny then paul is wise or not kind.
Everyone who is both humble and calm is either humble or not old.
Everyone who is calm or not strong is both calm and quiet and vice versa.
Everyone who is either not strong or funny is strong or calm and vice versa.
If susan is tall then someone is not calm and vice versa.
If mary is not generous then lucy is either not rich or wise and vice versa.
Everyone who is both not curious and not quiet is either not funny or not wise and vice versa.
If lucy is not generous then someone is both not generous and not quiet and vice versa.
If someone is not happy then fred is calm.
If alice is not curious or not creative then alice is funny or not funny.
If lucy is both not funny and curious then someone is tall or not strong and vice versa.
Everyone who is not happy is strong and vice versa.
Everyone who is either old or not tall is rich or patient.
Everyone who is generous or tall is not kind or not rich and vice versa.
Everyone who is not tall or kind is both kind and not quiet.
Everyone who is either not funny or not creative is both not creative and not rich.
Someone is not kind.
John is not kind or not old.
Someone is both rich and brave.
Someone is either kind or tall.
Fred is old.
Mary is not curious. | Susan is not creative. | neutral | ((?[X]:((strong(X)&~funny(X))))=>((wise(paul)|~kind(paul))))&
(![X]:((humble(X)&calm(X))=>(humble(X)<~>~old(X))))&
(![X]:((calm(X)|~strong(X))<=>(calm(X)&quiet(X))))&
(![X]:((~strong(X)<~>funny(X))<=>(strong(X)|calm(X))))&
((tall(susan))<=>(?[X]:(~calm(X))))&
((~generous(mary))<=>((~rich(lucy)<~>wise(lucy))))&
(![X]:((~curious(X)&~quiet(X))<=>(~funny(X)<~>~wise(X))))&
((~generous(lucy))<=>(?[X]:((~generous(X)&~quiet(X)))))&
((?[X]:(~happy(X)))=>(calm(fred)))&
(((~curious(alice)|~creative(alice)))=>((funny(alice)|~funny(alice))))&
(((~funny(lucy)&curious(lucy)))<=>(?[X]:((tall(X)|~strong(X)))))&
(![X]:(~happy(X)<=>strong(X)))&
(![X]:((old(X)<~>~tall(X))=>(rich(X)|patient(X))))&
(![X]:((generous(X)|tall(X))<=>(~kind(X)|~rich(X))))&
(![X]:((~tall(X)|kind(X))=>(kind(X)&~quiet(X))))&
(![X]:((~funny(X)<~>~creative(X))=>(~creative(X)&~rich(X))))&
(?[X]:(~kind(X)))&
((~kind(john)|~old(john)))&
(?[X]:((rich(X)&brave(X))))&
(?[X]:((kind(X)<~>tall(X))))&
(old(fred))&
(~curious(mary)) | ~creative(susan) | [] | null | 0 |
If someone is generous then someone is both quiet and not tall.
Everyone who is not curious is not kind or creative.
Everyone who is not curious or rich is either not curious or humble.
Everyone who is happy is not happy.
Everyone who is calm or tall is either funny or not humble and vice versa.
If someone is either not happy or not generous then fred is creative and vice versa.
Everyone who is not humble or not happy is either kind or not old.
If someone is rich or not strong then someone is not funny and vice versa.
Everyone who is quiet or not creative is either not calm or humble and vice versa.
If john is happy or kind then someone is either happy or not strong.
Everyone who is either kind or not happy is both generous and wise and vice versa.
Everyone who is both not quiet and not old is both strong and not curious and vice versa.
If fred is humble or tall then someone is both happy and not generous.
Everyone who is either not strong or not tall is happy or curious.
Everyone who is funny or not happy is funny or creative and vice versa.
If fred is both generous and wise then paul is either not creative or patient.
Someone is old.
Alice is both not creative and old.
Someone is happy or not patient.
Someone is both brave and not wise.
Lucy is either tall or funny.
Alice is brave or humble. | Fred is not kind. | neutral | ((?[X]:(generous(X)))=>(?[X]:((quiet(X)&~tall(X)))))&
(![X]:(~curious(X)=>(~kind(X)|creative(X))))&
(![X]:((~curious(X)|rich(X))=>(~curious(X)<~>humble(X))))&
(![X]:(happy(X)=>~happy(X)))&
(![X]:((calm(X)|tall(X))<=>(funny(X)<~>~humble(X))))&
((?[X]:((~happy(X)<~>~generous(X))))<=>(creative(fred)))&
(![X]:((~humble(X)|~happy(X))=>(kind(X)<~>~old(X))))&
((?[X]:((rich(X)|~strong(X))))<=>(?[X]:(~funny(X))))&
(![X]:((quiet(X)|~creative(X))<=>(~calm(X)<~>humble(X))))&
(((happy(john)|kind(john)))=>(?[X]:((happy(X)<~>~strong(X)))))&
(![X]:((kind(X)<~>~happy(X))<=>(generous(X)&wise(X))))&
(![X]:((~quiet(X)&~old(X))<=>(strong(X)&~curious(X))))&
(((humble(fred)|tall(fred)))=>(?[X]:((happy(X)&~generous(X)))))&
(![X]:((~strong(X)<~>~tall(X))=>(happy(X)|curious(X))))&
(![X]:((funny(X)|~happy(X))<=>(funny(X)|creative(X))))&
(((generous(fred)&wise(fred)))=>((~creative(paul)<~>patient(paul))))&
(?[X]:(old(X)))&
((~creative(alice)&old(alice)))&
(?[X]:((happy(X)|~patient(X))))&
(?[X]:((brave(X)&~wise(X))))&
((tall(lucy)<~>funny(lucy)))&
((brave(alice)|humble(alice))) | ~kind(fred) | [] | null | 0 |
If paul is either rich or not curious then fred is not curious or not creative.
Everyone who is not tall or brave is not quiet and vice versa.
If someone is old or quiet then fred is rich or curious and vice versa.
Everyone who is curious is either rich or humble and vice versa.
Everyone who is both brave and tall is not tall or not curious.
Everyone who is humble is either old or not patient and vice versa.
Everyone who is not wise or not funny is either not humble or not brave and vice versa.
Everyone who is both rich and not funny is either patient or funny and vice versa.
If john is either not humble or not generous then alice is tall.
If paul is both not generous and not funny then john is either creative or not brave.
Everyone who is not funny is either patient or not calm and vice versa.
Everyone who is either not wise or curious is either rich or not generous and vice versa.
Everyone who is either curious or not humble is not rich.
If someone is either funny or not curious then someone is both funny and not quiet and vice versa.
Everyone who is both not humble and not kind is kind.
Everyone who is both not creative and not tall is curious.
Paul is old or quiet.
Alice is either not tall or generous.
Someone is either not rich or not calm.
Someone is either not creative or happy.
Susan is happy.
Someone is not kind or not happy.
Someone is not calm. | Paul is not humble. | neutral | (((rich(paul)<~>~curious(paul)))=>((~curious(fred)|~creative(fred))))&
(![X]:((~tall(X)|brave(X))<=>~quiet(X)))&
((?[X]:((old(X)|quiet(X))))<=>((rich(fred)|curious(fred))))&
(![X]:(curious(X)<=>(rich(X)<~>humble(X))))&
(![X]:((brave(X)&tall(X))=>(~tall(X)|~curious(X))))&
(![X]:(humble(X)<=>(old(X)<~>~patient(X))))&
(![X]:((~wise(X)|~funny(X))<=>(~humble(X)<~>~brave(X))))&
(![X]:((rich(X)&~funny(X))<=>(patient(X)<~>funny(X))))&
(((~humble(john)<~>~generous(john)))=>(tall(alice)))&
(((~generous(paul)&~funny(paul)))=>((creative(john)<~>~brave(john))))&
(![X]:(~funny(X)<=>(patient(X)<~>~calm(X))))&
(![X]:((~wise(X)<~>curious(X))<=>(rich(X)<~>~generous(X))))&
(![X]:((curious(X)<~>~humble(X))=>~rich(X)))&
((?[X]:((funny(X)<~>~curious(X))))<=>(?[X]:((funny(X)&~quiet(X)))))&
(![X]:((~humble(X)&~kind(X))=>kind(X)))&
(![X]:((~creative(X)&~tall(X))=>curious(X)))&
((old(paul)|quiet(paul)))&
((~tall(alice)<~>generous(alice)))&
(?[X]:((~rich(X)<~>~calm(X))))&
(?[X]:((~creative(X)<~>happy(X))))&
(happy(susan))&
(?[X]:((~kind(X)|~happy(X))))&
(?[X]:(~calm(X))) | ~humble(paul) | [] | null | 0 |
Everyone who is old or not wise is wise and vice versa.
Everyone who is not curious is both not funny and not brave.
If susan is generous or not patient then mary is either strong or tall and vice versa.
Everyone who is not wise or calm is either not creative or calm.
If john is both brave and tall then susan is not patient and vice versa.
Everyone who is either not humble or not rich is either not creative or not generous and vice versa.
If someone is not quiet or not generous then someone is not old or not strong and vice versa.
If someone is funny then fred is brave.
Everyone who is both generous and wise is not wise or tall and vice versa.
If lucy is both calm and creative then susan is not calm.
Everyone who is both funny and quiet is both humble and brave and vice versa.
If someone is both old and generous then fred is curious or old and vice versa.
If someone is not tall or rich then fred is both wise and not calm and vice versa.
If mary is tall or not curious then susan is either strong or happy and vice versa.
If someone is both tall and kind then lucy is both not creative and not rich and vice versa.
If paul is not quiet or not happy then someone is strong.
Alice is funny or not creative.
Susan is both not humble and kind.
Someone is curious or not creative.
Someone is old or not funny.
John is either not kind or quiet. | John is quiet. | neutral | (![X]:((old(X)|~wise(X))<=>wise(X)))&
(![X]:(~curious(X)=>(~funny(X)&~brave(X))))&
(((generous(susan)|~patient(susan)))<=>((strong(mary)<~>tall(mary))))&
(![X]:((~wise(X)|calm(X))=>(~creative(X)<~>calm(X))))&
(((brave(john)&tall(john)))<=>(~patient(susan)))&
(![X]:((~humble(X)<~>~rich(X))<=>(~creative(X)<~>~generous(X))))&
((?[X]:((~quiet(X)|~generous(X))))<=>(?[X]:((~old(X)|~strong(X)))))&
((?[X]:(funny(X)))=>(brave(fred)))&
(![X]:((generous(X)&wise(X))<=>(~wise(X)|tall(X))))&
(((calm(lucy)&creative(lucy)))=>(~calm(susan)))&
(![X]:((funny(X)&quiet(X))<=>(humble(X)&brave(X))))&
((?[X]:((old(X)&generous(X))))<=>((curious(fred)|old(fred))))&
((?[X]:((~tall(X)|rich(X))))<=>((wise(fred)&~calm(fred))))&
(((tall(mary)|~curious(mary)))<=>((strong(susan)<~>happy(susan))))&
((?[X]:((tall(X)&kind(X))))<=>((~creative(lucy)&~rich(lucy))))&
(((~quiet(paul)|~happy(paul)))=>(?[X]:(strong(X))))&
((funny(alice)|~creative(alice)))&
((~humble(susan)&kind(susan)))&
(?[X]:((curious(X)|~creative(X))))&
(?[X]:((old(X)|~funny(X))))&
((~kind(john)<~>quiet(john))) | quiet(john) | [] | null | 0 |
If paul is both rich and wise then susan is either generous or not rich.
Everyone who is both not happy and not curious is not happy and vice versa.
Everyone who is both wise and not generous is tall or not wise and vice versa.
Everyone who is wise or humble is not wise or generous and vice versa.
If susan is not happy then someone is both funny and not funny.
Everyone who is either calm or quiet is funny or patient.
If alice is rich or not generous then susan is not strong.
Everyone who is not quiet or not wise is strong and vice versa.
Everyone who is either brave or happy is not patient or wise and vice versa.
If someone is kind then paul is quiet and vice versa.
Everyone who is both not strong and kind is either not creative or not curious.
If someone is either kind or not brave then someone is both not generous and not patient and vice versa.
If susan is not funny or not generous then someone is brave and vice versa.
Everyone who is rich or wise is either calm or generous and vice versa.
Everyone who is both not strong and creative is brave or humble.
Alice is either not calm or quiet.
Someone is not old or not calm.
Fred is both not tall and wise.
Someone is either not patient or not wise.
John is not patient or not calm.
John is humble.
Someone is not funny or happy. | Alice is strong. | entailment | (((rich(paul)&wise(paul)))=>((generous(susan)<~>~rich(susan))))&
(![X]:((~happy(X)&~curious(X))<=>~happy(X)))&
(![X]:((wise(X)&~generous(X))<=>(tall(X)|~wise(X))))&
(![X]:((wise(X)|humble(X))<=>(~wise(X)|generous(X))))&
((~happy(susan))=>(?[X]:((funny(X)&~funny(X)))))&
(![X]:((calm(X)<~>quiet(X))=>(funny(X)|patient(X))))&
(((rich(alice)|~generous(alice)))=>(~strong(susan)))&
(![X]:((~quiet(X)|~wise(X))<=>strong(X)))&
(![X]:((brave(X)<~>happy(X))<=>(~patient(X)|wise(X))))&
((?[X]:(kind(X)))<=>(quiet(paul)))&
(![X]:((~strong(X)&kind(X))=>(~creative(X)<~>~curious(X))))&
((?[X]:((kind(X)<~>~brave(X))))<=>(?[X]:((~generous(X)&~patient(X)))))&
(((~funny(susan)|~generous(susan)))<=>(?[X]:(brave(X))))&
(![X]:((rich(X)|wise(X))<=>(calm(X)<~>generous(X))))&
(![X]:((~strong(X)&creative(X))=>(brave(X)|humble(X))))&
((~calm(alice)<~>quiet(alice)))&
(?[X]:((~old(X)|~calm(X))))&
((~tall(fred)&wise(fred)))&
(?[X]:((~patient(X)<~>~wise(X))))&
((~patient(john)|~calm(john)))&
(humble(john))&
(?[X]:((~funny(X)|happy(X)))) | strong(alice) | [
"p2",
"p3",
"p7",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3265644839505449771231320
% SZS output start Proof for 3265644839505449771231320
3. ! [X0] : ((~generous(X0) & wise(X0)) <=> (~wise(X0) | tall(X0))) [input p2]
4. ! [X0] : ((humble(X0) | wise(X0)) <=> (generous(X0) | ~wise(X0))) [input p3]
8. ! [X0] : ((~wise(X0) | ~quiet(X0)) <=> strong(X0)) [input p7]
14. ! [X0] : ((wise(X0) | rich(X0)) <=> (calm(X0) <~> generous(X0))) [input p13]
16. ~calm(alice) <~> quiet(alice) [input p15]
23. ~strong(alice) [input hypothesis]
39. ! [X0] : (((~generous(X0) & wise(X0)) | (wise(X0) & ~tall(X0))) & ((~wise(X0) | tall(X0)) | (generous(X0) | ~wise(X0)))) [nnf transformation 3]
40. ! [X0] : (((~generous(X0) & wise(X0)) | (wise(X0) & ~tall(X0))) & (~wise(X0) | tall(X0) | generous(X0) | ~wise(X0))) [flattening 39]
41. ! [X0] : (((humble(X0) | wise(X0)) | (~generous(X0) & wise(X0))) & ((generous(X0) | ~wise(X0)) | (~humble(X0) & ~wise(X0)))) [nnf transformation 4]
42. ! [X0] : ((humble(X0) | wise(X0) | (~generous(X0) & wise(X0))) & (generous(X0) | ~wise(X0) | (~humble(X0) & ~wise(X0)))) [flattening 41]
46. ! [X0] : (((~wise(X0) | ~quiet(X0)) | ~strong(X0)) & (strong(X0) | (wise(X0) & quiet(X0)))) [nnf transformation 8]
47. ! [X0] : ((~wise(X0) | ~quiet(X0) | ~strong(X0)) & (strong(X0) | (wise(X0) & quiet(X0)))) [flattening 46]
65. ! [X0] : (((wise(X0) | rich(X0)) | ((calm(X0) | ~generous(X0)) & (generous(X0) | ~calm(X0)))) & (((~generous(X0) | ~calm(X0)) & (generous(X0) | calm(X0))) | (~wise(X0) & ~rich(X0)))) [nnf transformation 14]
66. ! [X0] : ((wise(X0) | rich(X0) | ((calm(X0) | ~generous(X0)) & (generous(X0) | ~calm(X0)))) & (((~generous(X0) | ~calm(X0)) & (generous(X0) | calm(X0))) | (~wise(X0) & ~rich(X0)))) [flattening 65]
67. (~quiet(alice) | calm(alice)) & (quiet(alice) | ~calm(alice)) [nnf transformation 16]
80. wise(X0) | wise(X0) [cnf transformation 40]
83. generous(X0) | ~wise(X0) | ~wise(X0) [cnf transformation 42]
93. strong(X0) | quiet(X0) [cnf transformation 47]
118. ~generous(X0) | ~calm(X0) | ~wise(X0) [cnf transformation 66]
123. ~quiet(alice) | calm(alice) [cnf transformation 67]
131. ~strong(alice) [cnf transformation 23]
132. generous(X0) | ~wise(X0) [duplicate literal removal 83]
135. wise(X0) [duplicate literal removal 80]
156. generous(X0) [subsumption resolution 132,135]
222. ~calm(X0) | ~wise(X0) [subsumption resolution 118,156]
223. ~calm(X0) [subsumption resolution 222,135]
224. ~quiet(alice) [subsumption resolution 123,223]
237. quiet(alice) [resolution 93,131]
239. $false [subsumption resolution 237,224]
% SZS output end Proof for 3265644839505449771231320
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not curious or not patient is either calm or not creative and vice versa.
If someone is not kind then someone is funny or patient and vice versa.
Everyone who is both wise and quiet is either not quiet or calm and vice versa.
If someone is not old or curious then lucy is either not kind or old and vice versa.
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.
If fred is rich or creative then someone is both humble and not kind.
If someone is either funny or rich then someone is not brave or brave and vice versa.
If someone is tall or not happy then someone is either calm or not happy and vice versa.
If someone is funny or not creative then someone is either curious or calm and vice versa.
Everyone who is either not patient or not wise is kind or not strong.
If someone is not happy then john is both not happy and funny.
Mary is not rich.
Someone is both humble and not curious.
Mary is old.
Lucy is either not calm or generous.
John is either not strong or not old.
Someone is not curious or not patient. | Fred is patient. | neutral | (![X]:((~curious(X)<~>~patient(X))<=>(calm(X)<~>~creative(X))))&
((?[X]:(~kind(X)))<=>(?[X]:((funny(X)|patient(X)))))&
(![X]:((wise(X)&quiet(X))<=>(~quiet(X)<~>calm(X))))&
((?[X]:((~old(X)|curious(X))))<=>((~kind(lucy)<~>old(lucy))))&
(![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)))=>(?[X]:((humble(X)&~kind(X)))))&
((?[X]:((funny(X)<~>rich(X))))<=>(?[X]:((~brave(X)|brave(X)))))&
((?[X]:((tall(X)|~happy(X))))<=>(?[X]:((calm(X)<~>~happy(X)))))&
((?[X]:((funny(X)|~creative(X))))<=>(?[X]:((curious(X)<~>calm(X)))))&
(![X]:((~patient(X)<~>~wise(X))=>(kind(X)|~strong(X))))&
((?[X]:(~happy(X)))=>((~happy(john)&funny(john))))&
(~rich(mary))&
(?[X]:((humble(X)&~curious(X))))&
(old(mary))&
((~calm(lucy)<~>generous(lucy)))&
((~strong(john)<~>~old(john)))&
(?[X]:((~curious(X)|~patient(X)))) | patient(fred) | [] | null | 0 |
If someone is either humble or brave then mary is not rich or not tall. Everyone who is not patient or not quiet is either not strong or not humble and vice versa. If fred is either not patient or not strong then susan is either strong or not quiet and vice versa. Everyone who is creative is both calm and strong and vice versa. Everyone who is both not quiet and not creative is rich or not happy and vice versa. Everyone who is both brave and not strong is either not tall or not creative and vice versa. If someone is both kind and brave then someone is not curious or not humble and vice versa. If fred is both not patient and generous then someone is curious. If someone is both not generous and not creative then someone is not patient or humble. If mary is patient or not wise then john is not happy. Everyone who is either not calm or wise is not brave and vice versa. If someone is either not humble or not funny then mary is both not creative and tall and vice versa. If john is either not patient or rich then someone is either not kind or not brave. Everyone who is not brave or rich is not rich and vice versa. Everyone who is either not humble or brave is either not patient or happy. If fred is old or not curious then someone is either quiet or not brave. Lucy is funny or happy. Susan is not generous. Someone is either not creative or calm. Someone is not brave or wise. John is not creative or funny. Paul is not tall or not old. | Paul is generous. | neutral | ((?[X]:((humble(X)<~>brave(X))))=>((~rich(mary)|~tall(mary))))&
(![X]:((~patient(X)|~quiet(X))<=>(~strong(X)<~>~humble(X))))&
(((~patient(fred)<~>~strong(fred)))<=>((strong(susan)<~>~quiet(susan))))&
(![X]:(creative(X)<=>(calm(X)&strong(X))))&
(![X]:((~quiet(X)&~creative(X))<=>(rich(X)|~happy(X))))&
(![X]:((brave(X)&~strong(X))<=>(~tall(X)<~>~creative(X))))&
((?[X]:((kind(X)&brave(X))))<=>(?[X]:((~curious(X)|~humble(X)))))&
(((~patient(fred)&generous(fred)))=>(?[X]:(curious(X))))&
((?[X]:((~generous(X)&~creative(X))))=>(?[X]:((~patient(X)|humble(X)))))&
(((patient(mary)|~wise(mary)))=>(~happy(john)))&
(![X]:((~calm(X)<~>wise(X))<=>~brave(X)))&
((?[X]:((~humble(X)<~>~funny(X))))<=>((~creative(mary)&tall(mary))))&
(((~patient(john)<~>rich(john)))=>(?[X]:((~kind(X)<~>~brave(X)))))&
(![X]:((~brave(X)|rich(X))<=>~rich(X)))&
(![X]:((~humble(X)<~>brave(X))=>(~patient(X)<~>happy(X))))&
(((old(fred)|~curious(fred)))=>(?[X]:((quiet(X)<~>~brave(X)))))&
((funny(lucy)|happy(lucy)))&
(~generous(susan))&
(?[X]:((~creative(X)<~>calm(X))))&
(?[X]:((~brave(X)|wise(X))))&
((~creative(john)|funny(john)))&
((~tall(paul)|~old(paul))) | generous(paul) | [] | null | 0 |
Everyone who is calm is either not rich or brave and vice versa.
If mary is both not tall and tall then someone is not brave or not kind.
If someone is both not tall and calm then lucy is either creative or not old.
If fred is not wise or not rich then someone is rich and vice versa.
Everyone who is both not old and strong is not wise or wise.
If someone is either not old or tall then someone is not quiet.
If fred is either not quiet or generous then someone is both old and not quiet.
If alice is both generous and curious then susan is either brave or humble and vice versa.
If someone is both happy and kind then mary is brave and vice versa.
Everyone who is quiet is both curious and not calm.
If someone is happy or not humble then mary is both calm and wise.
If john is not kind then fred is not brave or calm.
Everyone who is quiet is both not quiet and not rich and vice versa.
Everyone who is not brave is not rich.
If someone is either brave or calm then someone is both not strong and not quiet and vice versa.
If mary is humble or patient then john is patient or humble and vice versa.
Lucy is either curious or tall.
Someone is both patient and humble.
Someone is humble.
Someone is not generous.
Mary is funny or not strong.
Someone is either not brave or not generous. | Lucy is not quiet. | entailment | (![X]:(calm(X)<=>(~rich(X)<~>brave(X))))&
(((~tall(mary)&tall(mary)))=>(?[X]:((~brave(X)|~kind(X)))))&
((?[X]:((~tall(X)&calm(X))))=>((creative(lucy)<~>~old(lucy))))&
(((~wise(fred)|~rich(fred)))<=>(?[X]:(rich(X))))&
(![X]:((~old(X)&strong(X))=>(~wise(X)|wise(X))))&
((?[X]:((~old(X)<~>tall(X))))=>(?[X]:(~quiet(X))))&
(((~quiet(fred)<~>generous(fred)))=>(?[X]:((old(X)&~quiet(X)))))&
(((generous(alice)&curious(alice)))<=>((brave(susan)<~>humble(susan))))&
((?[X]:((happy(X)&kind(X))))<=>(brave(mary)))&
(![X]:(quiet(X)=>(curious(X)&~calm(X))))&
((?[X]:((happy(X)|~humble(X))))=>((calm(mary)&wise(mary))))&
((~kind(john))=>((~brave(fred)|calm(fred))))&
(![X]:(quiet(X)<=>(~quiet(X)&~rich(X))))&
(![X]:(~brave(X)=>~rich(X)))&
((?[X]:((brave(X)<~>calm(X))))<=>(?[X]:((~strong(X)&~quiet(X)))))&
(((humble(mary)|patient(mary)))<=>((patient(john)|humble(john))))&
((curious(lucy)<~>tall(lucy)))&
(?[X]:((patient(X)&humble(X))))&
(?[X]:(humble(X)))&
(?[X]:(~generous(X)))&
((funny(mary)|~strong(mary)))&
(?[X]:((~brave(X)<~>~generous(X)))) | ~quiet(lucy) | [
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 1090662303841291647488259
% SZS output start Proof for 1090662303841291647488259
13. ! [X0] : (quiet(X0) <=> (~rich(X0) & ~quiet(X0))) [input p12]
23. quiet(lucy) [input hypothesis]
61. ! [X0] : ((quiet(X0) | (rich(X0) | quiet(X0))) & ((~rich(X0) & ~quiet(X0)) | ~quiet(X0))) [nnf transformation 13]
62. ! [X0] : ((quiet(X0) | rich(X0) | quiet(X0)) & ((~rich(X0) & ~quiet(X0)) | ~quiet(X0))) [flattening 61]
113. ~quiet(X0) | ~quiet(X0) [cnf transformation 62]
135. quiet(lucy) [cnf transformation 23]
136. ~quiet(X0) [duplicate literal removal 113]
339. $false [subsumption resolution 135,136]
% SZS output end Proof for 1090662303841291647488259
% ------------------------------
% 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 mary is both not brave and quiet then someone is tall and vice versa.
Everyone who is both kind and not quiet is old.
Everyone who is both not patient and wise is either not rich or wise and vice versa.
If someone is not brave or not kind then susan is not calm and vice versa.
Everyone who is not funny or funny is either not calm or not tall and vice versa.
If someone is not kind then someone is not strong and vice versa.
Everyone who is either wise or not wise is not tall.
If someone is not quiet or happy then someone is not tall or not kind.
If susan is either not old or not creative then someone is either curious or funny.
If lucy is wise then mary is either not patient or happy and vice versa.
Everyone who is either not curious or quiet is either old or calm and vice versa.
If john is both strong and patient then someone is calm and vice versa.
If someone is calm or curious then fred is either not humble or not calm and vice versa.
If someone is both tall and not strong then someone is both calm and rich.
Someone is either strong or old.
Someone is both not generous and strong.
Someone is either kind or not funny.
Paul is either not creative or curious.
Someone is quiet or not funny.
Someone is either creative or not curious.
Someone is either not curious or brave. | Mary is strong. | entailment | (((~brave(mary)&quiet(mary)))<=>(?[X]:(tall(X))))&
(![X]:((kind(X)&~quiet(X))=>old(X)))&
(![X]:((~patient(X)&wise(X))<=>(~rich(X)<~>wise(X))))&
((?[X]:((~brave(X)|~kind(X))))<=>(~calm(susan)))&
(![X]:((~funny(X)|funny(X))<=>(~calm(X)<~>~tall(X))))&
((?[X]:(~kind(X)))<=>(?[X]:(~strong(X))))&
(![X]:((wise(X)<~>~wise(X))=>~tall(X)))&
((?[X]:((~quiet(X)|happy(X))))=>(?[X]:((~tall(X)|~kind(X)))))&
(((~old(susan)<~>~creative(susan)))=>(?[X]:((curious(X)<~>funny(X)))))&
((wise(lucy))<=>((~patient(mary)<~>happy(mary))))&
(![X]:((~curious(X)<~>quiet(X))<=>(old(X)<~>calm(X))))&
(((strong(john)&patient(john)))<=>(?[X]:(calm(X))))&
((?[X]:((calm(X)|curious(X))))<=>((~humble(fred)<~>~calm(fred))))&
((?[X]:((tall(X)&~strong(X))))=>(?[X]:((calm(X)&rich(X)))))&
(?[X]:((strong(X)<~>old(X))))&
(?[X]:((~generous(X)&strong(X))))&
(?[X]:((kind(X)<~>~funny(X))))&
((~creative(paul)<~>curious(paul)))&
(?[X]:((quiet(X)|~funny(X))))&
(?[X]:((creative(X)<~>~curious(X))))&
(?[X]:((~curious(X)<~>brave(X)))) | strong(mary) | [
"p3",
"p4",
"p5",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 7920977675786437188766707
% SZS output start Proof for 7920977675786437188766707
4. ? [X0] : (~kind(X0) | ~brave(X0)) <=> ~calm(susan) [input p3]
5. ! [X0] : ((funny(X0) | ~funny(X0)) <=> (~calm(X0) <~> ~tall(X0))) [input p4]
6. ? [X0] : ~kind(X0) <=> ? [X0] : ~strong(X0) [input p5]
7. ! [X0] : ((wise(X0) <~> ~wise(X0)) => ~tall(X0)) [input p6]
22. ~strong(mary) [input hypothesis]
23. ? [X0] : ~kind(X0) <=> ? [X1] : ~strong(X1) [rectify 6]
29. ! [X0] : (~tall(X0) | (wise(X0) <=> ~wise(X0))) [ennf transformation 7]
40. (? [X0] : (~kind(X0) | ~brave(X0)) | calm(susan)) & (~calm(susan) | ! [X0] : (kind(X0) & brave(X0))) [nnf transformation 4]
41. (? [X0] : (~kind(X0) | ~brave(X0)) | calm(susan)) & (~calm(susan) | ! [X1] : (kind(X1) & brave(X1))) [rectify 40]
42. ? [X0] : (~kind(X0) | ~brave(X0)) => (~kind(sK1) | ~brave(sK1)) [choice axiom]
43. ((~kind(sK1) | ~brave(sK1)) | calm(susan)) & (~calm(susan) | ! [X1] : (kind(X1) & brave(X1))) [skolemisation 41,42]
44. ! [X0] : (((funny(X0) | ~funny(X0)) | ((~calm(X0) | tall(X0)) & (~tall(X0) | calm(X0)))) & (((tall(X0) | calm(X0)) & (~tall(X0) | ~calm(X0))) | (~funny(X0) & funny(X0)))) [nnf transformation 5]
45. ! [X0] : ((funny(X0) | ~funny(X0) | ((~calm(X0) | tall(X0)) & (~tall(X0) | calm(X0)))) & (((tall(X0) | calm(X0)) & (~tall(X0) | ~calm(X0))) | (~funny(X0) & funny(X0)))) [flattening 44]
46. (? [X0] : ~kind(X0) | ! [X1] : strong(X1)) & (? [X1] : ~strong(X1) | ! [X0] : kind(X0)) [nnf transformation 23]
47. (? [X0] : ~kind(X0) | ! [X1] : strong(X1)) & (? [X2] : ~strong(X2) | ! [X3] : kind(X3)) [rectify 46]
48. ? [X0] : ~kind(X0) => ~kind(sK2) [choice axiom]
49. ? [X2] : ~strong(X2) => ~strong(sK3) [choice axiom]
50. (~kind(sK2) | ! [X1] : strong(X1)) & (~strong(sK3) | ! [X3] : kind(X3)) [skolemisation 47,49,48]
51. ! [X0] : (~tall(X0) | ((wise(X0) | wise(X0)) & (~wise(X0) | ~wise(X0)))) [nnf transformation 29]
100. ~calm(susan) | kind(X1) [cnf transformation 43]
104. tall(X0) | calm(X0) | funny(X0) [cnf transformation 45]
105. tall(X0) | calm(X0) | ~funny(X0) [cnf transformation 45]
109. ~kind(sK2) | strong(X1) [cnf transformation 50]
110. ~tall(X0) | ~wise(X0) | ~wise(X0) [cnf transformation 51]
111. ~tall(X0) | wise(X0) | wise(X0) [cnf transformation 51]
153. ~strong(mary) [cnf transformation 22]
154. ~tall(X0) | ~wise(X0) [duplicate literal removal 110]
155. ~tall(X0) | wise(X0) [duplicate literal removal 111]
159. 1 <=> ! [X0] : ~tall(X0) [avatar definition]
160. ~tall(X0) <- (1) [avatar component clause 159]
178. 5 <=> calm(susan) [avatar definition]
179. ~calm(susan) <- (~5) [avatar component clause 178]
191. 8 <=> ! [X1] : kind(X1) [avatar definition]
192. kind(X1) <- (8) [avatar component clause 191]
193. 8 | ~5 [avatar split clause 100,178,191]
198. calm(X0) | tall(X0) [subsumption resolution 104,105]
201. 10 <=> ! [X1] : strong(X1) [avatar definition]
202. strong(X1) <- (10) [avatar component clause 201]
204. 11 <=> kind(sK2) [avatar definition]
206. ~kind(sK2) <- (~11) [avatar component clause 204]
207. 10 | ~11 [avatar split clause 109,204,201]
213. ~tall(X0) [subsumption resolution 154,155]
214. 1 [avatar split clause 213,159]
384. tall(susan) <- (~5) [resolution 198,179]
385. $false <- (1, ~5) [subsumption resolution 384,160]
386. ~1 | 5 [avatar contradiction clause 385]
388. $false <- (8, ~11) [resolution 192,206]
393. ~8 | 11 [avatar contradiction clause 388]
397. $false <- (10) [resolution 202,153]
400. ~10 [avatar contradiction clause 397]
401. $false [avatar sat refutation 193,207,214,386,393,400]
% SZS output end Proof for 7920977675786437188766707
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If john is both not quiet and not generous then alice is kind or not curious and vice versa.
If john is both not strong and not rich then susan is funny or not patient and vice versa.
Everyone who is humble or happy is funny or happy.
Everyone who is either quiet or calm is tall or not quiet and vice versa.
If alice is either not quiet or curious then someone is either not wise or funny and vice versa.
If fred is tall then fred is both brave and strong.
Everyone who is wise or not tall is kind and vice versa.
Everyone who is rich is either strong or old and vice versa.
Everyone who is kind or generous is both humble and wise.
Everyone who is either not funny or not brave is either not old or not rich and vice versa.
Everyone who is humble is both not kind and creative and vice versa.
Everyone who is either not happy or rich is either not generous or quiet and vice versa.
Everyone who is not patient or humble is both not kind and brave and vice versa.
If alice is kind or humble then someone is both not humble and brave.
Everyone who is both strong and calm is either not curious or rich and vice versa.
Everyone who is both strong and brave is brave and vice versa.
Someone is both tall and strong.
Someone is not calm.
Someone is both strong and curious.
Paul is calm or kind.
Mary is not curious or old.
John is patient or quiet.
Someone is tall or not calm.
Someone is not generous or not funny. | Mary is not wise. | entailment | (((~quiet(john)&~generous(john)))<=>((kind(alice)|~curious(alice))))&
(((~strong(john)&~rich(john)))<=>((funny(susan)|~patient(susan))))&
(![X]:((humble(X)|happy(X))=>(funny(X)|happy(X))))&
(![X]:((quiet(X)<~>calm(X))<=>(tall(X)|~quiet(X))))&
(((~quiet(alice)<~>curious(alice)))<=>(?[X]:((~wise(X)<~>funny(X)))))&
((tall(fred))=>((brave(fred)&strong(fred))))&
(![X]:((wise(X)|~tall(X))<=>kind(X)))&
(![X]:(rich(X)<=>(strong(X)<~>old(X))))&
(![X]:((kind(X)|generous(X))=>(humble(X)&wise(X))))&
(![X]:((~funny(X)<~>~brave(X))<=>(~old(X)<~>~rich(X))))&
(![X]:(humble(X)<=>(~kind(X)&creative(X))))&
(![X]:((~happy(X)<~>rich(X))<=>(~generous(X)<~>quiet(X))))&
(![X]:((~patient(X)|humble(X))<=>(~kind(X)&brave(X))))&
(((kind(alice)|humble(alice)))=>(?[X]:((~humble(X)&brave(X)))))&
(![X]:((strong(X)&calm(X))<=>(~curious(X)<~>rich(X))))&
(![X]:((strong(X)&brave(X))<=>brave(X)))&
(?[X]:((tall(X)&strong(X))))&
(?[X]:(~calm(X)))&
(?[X]:((strong(X)&curious(X))))&
((calm(paul)|kind(paul)))&
((~curious(mary)|old(mary)))&
((patient(john)|quiet(john)))&
(?[X]:((tall(X)|~calm(X))))&
(?[X]:((~generous(X)|~funny(X)))) | ~wise(mary) | [
"p6",
"p8",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 483380030934865793979803
% SZS output start Proof for 483380030934865793979803
7. ! [X0] : ((~tall(X0) | wise(X0)) <=> kind(X0)) [input p6]
9. ! [X0] : ((generous(X0) | kind(X0)) => (wise(X0) & humble(X0))) [input p8]
11. ! [X0] : (humble(X0) <=> (creative(X0) & ~kind(X0))) [input p10]
25. wise(mary) [input hypothesis]
29. ! [X0] : ((wise(X0) & humble(X0)) | (~generous(X0) & ~kind(X0))) [ennf transformation 9]
41. ! [X0] : (((~tall(X0) | wise(X0)) | ~kind(X0)) & (kind(X0) | (tall(X0) & ~wise(X0)))) [nnf transformation 7]
42. ! [X0] : ((~tall(X0) | wise(X0) | ~kind(X0)) & (kind(X0) | (tall(X0) & ~wise(X0)))) [flattening 41]
45. ! [X0] : ((humble(X0) | (~creative(X0) | kind(X0))) & ((creative(X0) & ~kind(X0)) | ~humble(X0))) [nnf transformation 11]
46. ! [X0] : ((humble(X0) | ~creative(X0) | kind(X0)) & ((creative(X0) & ~kind(X0)) | ~humble(X0))) [flattening 45]
94. ~wise(X0) | kind(X0) [cnf transformation 42]
101. humble(X0) | ~kind(X0) [cnf transformation 29]
113. ~kind(X0) | ~humble(X0) [cnf transformation 46]
152. wise(mary) [cnf transformation 25]
239. ~kind(X0) [subsumption resolution 113,101]
280. kind(mary) [resolution 94,152]
281. $false [subsumption resolution 280,239]
% SZS output end Proof for 483380030934865793979803
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not tall or not creative is generous or not generous.
Everyone who is old or quiet is both not rich and not happy and vice versa.
Everyone who is not strong is both strong and kind and vice versa.
Everyone who is not rich is both brave and not creative.
If mary is either creative or calm then alice is either not old or not tall.
Everyone who is not strong or not creative is both not quiet and not curious.
Everyone who is both kind and generous is wise or patient.
Everyone who is not humble or happy is either curious or funny.
Everyone who is both humble and calm is both happy and kind.
If someone is not calm or old then alice is either not wise or generous.
Everyone who is not funny is either rich or not calm.
Everyone who is both not calm and happy is strong and vice versa.
If someone is either kind or not wise then fred is both not rich and not patient and vice versa.
If someone is either not funny or kind then someone is both generous and not kind and vice versa.
Everyone who is either not kind or not calm is both rich and old.
Everyone who is not old or kind is humble and vice versa.
Someone is not creative.
Alice is both strong and creative.
Susan is either wise or quiet.
Mary is both patient and funny.
Someone is either brave or not old. | Susan is curious. | contradiction | (![X]:((~tall(X)|~creative(X))=>(generous(X)|~generous(X))))&
(![X]:((old(X)|quiet(X))<=>(~rich(X)&~happy(X))))&
(![X]:(~strong(X)<=>(strong(X)&kind(X))))&
(![X]:(~rich(X)=>(brave(X)&~creative(X))))&
(((creative(mary)<~>calm(mary)))=>((~old(alice)<~>~tall(alice))))&
(![X]:((~strong(X)|~creative(X))=>(~quiet(X)&~curious(X))))&
(![X]:((kind(X)&generous(X))=>(wise(X)|patient(X))))&
(![X]:((~humble(X)|happy(X))=>(curious(X)<~>funny(X))))&
(![X]:((humble(X)&calm(X))=>(happy(X)&kind(X))))&
((?[X]:((~calm(X)|old(X))))=>((~wise(alice)<~>generous(alice))))&
(![X]:(~funny(X)=>(rich(X)<~>~calm(X))))&
(![X]:((~calm(X)&happy(X))<=>strong(X)))&
((?[X]:((kind(X)<~>~wise(X))))<=>((~rich(fred)&~patient(fred))))&
((?[X]:((~funny(X)<~>kind(X))))<=>(?[X]:((generous(X)&~kind(X)))))&
(![X]:((~kind(X)<~>~calm(X))=>(rich(X)&old(X))))&
(![X]:((~old(X)|kind(X))<=>humble(X)))&
(?[X]:(~creative(X)))&
((strong(alice)&creative(alice)))&
((wise(susan)<~>quiet(susan)))&
((patient(mary)&funny(mary)))&
(?[X]:((brave(X)<~>~old(X)))) | curious(susan) | [
"p2",
"p3",
"p5",
"p7",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 7052620350678992369982761
% SZS output start Proof for 7052620350678992369982761
3. ! [X0] : (~strong(X0) <=> (kind(X0) & strong(X0))) [input p2]
4. ! [X0] : (~rich(X0) => (~creative(X0) & brave(X0))) [input p3]
6. ! [X0] : ((~creative(X0) | ~strong(X0)) => (~curious(X0) & ~quiet(X0))) [input p5]
8. ! [X0] : ((happy(X0) | ~humble(X0)) => (curious(X0) <~> funny(X0))) [input p7]
11. ! [X0] : (~funny(X0) => (rich(X0) <~> ~calm(X0))) [input p10]
12. ! [X0] : ((happy(X0) & ~calm(X0)) <=> strong(X0)) [input p11]
22. curious(susan) [input hypothesis]
26. ! [X0] : ((~creative(X0) & brave(X0)) | rich(X0)) [ennf transformation 4]
28. ! [X0] : ((~curious(X0) & ~quiet(X0)) | (creative(X0) & strong(X0))) [ennf transformation 6]
31. ! [X0] : ((curious(X0) <~> funny(X0)) | (~happy(X0) & humble(X0))) [ennf transformation 8]
35. ! [X0] : ((rich(X0) <~> ~calm(X0)) | funny(X0)) [ennf transformation 11]
39. ! [X0] : ((~strong(X0) | (~kind(X0) | ~strong(X0))) & ((kind(X0) & strong(X0)) | strong(X0))) [nnf transformation 3]
40. ! [X0] : ((~strong(X0) | ~kind(X0) | ~strong(X0)) & ((kind(X0) & strong(X0)) | strong(X0))) [flattening 39]
42. ! [X0] : (((~funny(X0) | ~curious(X0)) & (funny(X0) | curious(X0))) | (~happy(X0) & humble(X0))) [nnf transformation 31]
44. ! [X0] : (((calm(X0) | ~rich(X0)) & (~calm(X0) | rich(X0))) | funny(X0)) [nnf transformation 35]
45. ! [X0] : (((happy(X0) & ~calm(X0)) | ~strong(X0)) & (strong(X0) | (~happy(X0) | calm(X0)))) [nnf transformation 12]
46. ! [X0] : (((happy(X0) & ~calm(X0)) | ~strong(X0)) & (strong(X0) | ~happy(X0) | calm(X0))) [flattening 45]
73. strong(X0) | strong(X0) [cnf transformation 40]
77. ~creative(X0) | rich(X0) [cnf transformation 26]
85. ~curious(X0) | creative(X0) [cnf transformation 28]
90. ~funny(X0) | ~curious(X0) | ~happy(X0) [cnf transformation 42]
98. ~rich(X0) | calm(X0) | funny(X0) [cnf transformation 44]
100. ~calm(X0) | ~strong(X0) [cnf transformation 46]
101. happy(X0) | ~strong(X0) [cnf transformation 46]
130. curious(susan) [cnf transformation 22]
131. strong(X0) [duplicate literal removal 73]
171. happy(X0) [subsumption resolution 101,131]
172. ~calm(X0) [subsumption resolution 100,131]
265. creative(susan) [resolution 85,130]
266. rich(susan) [resolution 265,77]
314. calm(susan) | funny(susan) [resolution 98,266]
317. funny(susan) [subsumption resolution 314,172]
346. ~curious(susan) | ~happy(susan) [resolution 317,90]
349. ~happy(susan) [subsumption resolution 346,130]
350. $false [subsumption resolution 349,171]
% SZS output end Proof for 7052620350678992369982761
% ------------------------------
% 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 kind is wise and vice versa.
If someone is both rich and happy then alice is not funny or brave.
Everyone who is either not kind or not curious is curious and vice versa.
If fred is kind or happy then someone is both curious and generous.
Everyone who is either rich or calm is not calm.
If mary is both kind and tall then someone is not tall or not calm and vice versa.
If someone is not rich then someone is both not strong and not quiet and vice versa.
Everyone who is wise or not funny is tall and vice versa.
If john is either not calm or creative then susan is either calm or happy.
Everyone who is not wise or curious is not quiet or curious.
Everyone who is both not strong and not humble is patient.
If alice is old then someone is not kind or funny.
Everyone who is both not old and tall is either curious or not humble.
If fred is tall or not old then john is both not happy and quiet.
Everyone who is not quiet or tall is quiet or not quiet and vice versa.
If someone is either not creative or rich then paul is not kind.
Someone is quiet.
Alice is not kind or tall.
Fred is not happy.
John is not curious or old.
Alice is either generous or quiet.
Lucy is either strong or old.
Paul is not old or not quiet. | Susan is calm. | entailment | (![X]:(kind(X)<=>wise(X)))&
((?[X]:((rich(X)&happy(X))))=>((~funny(alice)|brave(alice))))&
(![X]:((~kind(X)<~>~curious(X))<=>curious(X)))&
(((kind(fred)|happy(fred)))=>(?[X]:((curious(X)&generous(X)))))&
(![X]:((rich(X)<~>calm(X))=>~calm(X)))&
(((kind(mary)&tall(mary)))<=>(?[X]:((~tall(X)|~calm(X)))))&
((?[X]:(~rich(X)))<=>(?[X]:((~strong(X)&~quiet(X)))))&
(![X]:((wise(X)|~funny(X))<=>tall(X)))&
(((~calm(john)<~>creative(john)))=>((calm(susan)<~>happy(susan))))&
(![X]:((~wise(X)|curious(X))=>(~quiet(X)|curious(X))))&
(![X]:((~strong(X)&~humble(X))=>patient(X)))&
((old(alice))=>(?[X]:((~kind(X)|funny(X)))))&
(![X]:((~old(X)&tall(X))=>(curious(X)<~>~humble(X))))&
(((tall(fred)|~old(fred)))=>((~happy(john)&quiet(john))))&
(![X]:((~quiet(X)|tall(X))<=>(quiet(X)|~quiet(X))))&
((?[X]:((~creative(X)<~>rich(X))))=>(~kind(paul)))&
(?[X]:(quiet(X)))&
((~kind(alice)|tall(alice)))&
(~happy(fred))&
((~curious(john)|old(john)))&
((generous(alice)<~>quiet(alice)))&
((strong(lucy)<~>old(lucy)))&
((~old(paul)|~quiet(paul))) | calm(susan) | [
"p2",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 7858460294486318070543005
% SZS output start Proof for 7858460294486318070543005
3. ! [X0] : ((~kind(X0) <~> ~curious(X0)) <=> curious(X0)) [input p2]
6. (tall(mary) & kind(mary)) <=> ? [X0] : (~calm(X0) | ~tall(X0)) [input p5]
24. ~calm(susan) [input hypothesis]
39. ! [X0] : ((((curious(X0) | kind(X0)) & (~curious(X0) | ~kind(X0))) | ~curious(X0)) & (curious(X0) | ((~kind(X0) | curious(X0)) & (~curious(X0) | kind(X0))))) [nnf transformation 3]
43. ((tall(mary) & kind(mary)) | ! [X0] : (calm(X0) & tall(X0))) & (? [X0] : (~calm(X0) | ~tall(X0)) | (~tall(mary) | ~kind(mary))) [nnf transformation 6]
44. ((tall(mary) & kind(mary)) | ! [X0] : (calm(X0) & tall(X0))) & (? [X0] : (~calm(X0) | ~tall(X0)) | ~tall(mary) | ~kind(mary)) [flattening 43]
45. ((tall(mary) & kind(mary)) | ! [X0] : (calm(X0) & tall(X0))) & (? [X1] : (~calm(X1) | ~tall(X1)) | ~tall(mary) | ~kind(mary)) [rectify 44]
46. ? [X1] : (~calm(X1) | ~tall(X1)) => (~calm(sK1) | ~tall(sK1)) [choice axiom]
47. ((tall(mary) & kind(mary)) | ! [X0] : (calm(X0) & tall(X0))) & ((~calm(sK1) | ~tall(sK1)) | ~tall(mary) | ~kind(mary)) [skolemisation 45,46]
69. curious(X0) | ~kind(X0) | curious(X0) [cnf transformation 39]
70. ~curious(X0) | ~kind(X0) | ~curious(X0) [cnf transformation 39]
80. kind(mary) | calm(X0) [cnf transformation 47]
117. ~calm(susan) [cnf transformation 24]
121. curious(X0) | ~kind(X0) [duplicate literal removal 69]
122. ~curious(X0) | ~kind(X0) [duplicate literal removal 70]
123. ~kind(X0) [subsumption resolution 121,122]
139. 4 <=> ! [X0] : calm(X0) [avatar definition]
140. calm(X0) <- (4) [avatar component clause 139]
150. calm(X0) [subsumption resolution 80,123]
151. 4 [avatar split clause 150,139]
184. 14 <=> calm(susan) [avatar definition]
186. ~calm(susan) <- (~14) [avatar component clause 184]
254. ~14 [avatar split clause 117,184]
257. $false <- (4, ~14) [resolution 186,140]
258. ~4 | 14 [avatar contradiction clause 257]
259. $false [avatar sat refutation 151,254,258]
% SZS output end Proof for 7858460294486318070543005
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either wise or not generous then fred is rich or not generous and vice versa.
Everyone who is generous is either not old or not humble and vice versa.
If susan is either humble or strong then someone is both not kind and not old.
Everyone who is not tall or old is both wise and kind.
Everyone who is both not funny and not brave is either not old or old.
If someone is funny then paul is both not rich and not generous and vice versa.
Everyone who is tall is either not tall or not rich.
Everyone who is both generous and wise is both not tall and not patient.
Everyone who is creative is curious or not generous and vice versa.
If susan is both not rich and not curious then alice is not happy or not funny and vice versa.
Everyone who is wise or not happy is not tall or rich and vice versa.
If someone is not humble then someone is either not tall or not rich and vice versa.
Everyone who is curious or not funny is both generous and rich and vice versa.
Everyone who is humble or strong is not creative.
If john is both not wise and not rich then john is quiet or curious.
If someone is both rich and happy then fred is curious or not funny and vice versa.
Alice is not rich or not humble.
Susan is both quiet and brave.
Someone is either not humble or rich.
Someone is not rich or patient.
Paul is kind or not strong.
Mary is either rich or not curious.
Someone is generous.
Alice is both funny and not old. | Fred is not funny. | neutral | ((?[X]:((wise(X)<~>~generous(X))))<=>((rich(fred)|~generous(fred))))&
(![X]:(generous(X)<=>(~old(X)<~>~humble(X))))&
(((humble(susan)<~>strong(susan)))=>(?[X]:((~kind(X)&~old(X)))))&
(![X]:((~tall(X)|old(X))=>(wise(X)&kind(X))))&
(![X]:((~funny(X)&~brave(X))=>(~old(X)<~>old(X))))&
((?[X]:(funny(X)))<=>((~rich(paul)&~generous(paul))))&
(![X]:(tall(X)=>(~tall(X)<~>~rich(X))))&
(![X]:((generous(X)&wise(X))=>(~tall(X)&~patient(X))))&
(![X]:(creative(X)<=>(curious(X)|~generous(X))))&
(((~rich(susan)&~curious(susan)))<=>((~happy(alice)|~funny(alice))))&
(![X]:((wise(X)|~happy(X))<=>(~tall(X)|rich(X))))&
((?[X]:(~humble(X)))<=>(?[X]:((~tall(X)<~>~rich(X)))))&
(![X]:((curious(X)|~funny(X))<=>(generous(X)&rich(X))))&
(![X]:((humble(X)|strong(X))=>~creative(X)))&
(((~wise(john)&~rich(john)))=>((quiet(john)|curious(john))))&
((?[X]:((rich(X)&happy(X))))<=>((curious(fred)|~funny(fred))))&
((~rich(alice)|~humble(alice)))&
((quiet(susan)&brave(susan)))&
(?[X]:((~humble(X)<~>rich(X))))&
(?[X]:((~rich(X)|patient(X))))&
((kind(paul)|~strong(paul)))&
((rich(mary)<~>~curious(mary)))&
(?[X]:(generous(X)))&
((funny(alice)&~old(alice))) | ~funny(fred) | [] | null | 0 |
Everyone who is not patient is both not rich and not patient.
If someone is both curious and humble then paul is not brave.
If mary is calm or rich then someone is humble or wise.
Everyone who is not calm or tall is both humble and rich and vice versa.
If someone is not creative or not happy then someone is wise.
Everyone who is not humble is humble.
If lucy is tall then someone is both quiet and wise and vice versa.
Everyone who is either creative or quiet is both not rich and happy.
If alice is curious or quiet then someone is both strong and not tall and vice versa.
If someone is not curious or rich then alice is both not rich and humble.
If someone is both not creative and not rich then fred is calm and vice versa.
Everyone who is quiet or not tall is generous.
If someone is not tall then john is either not kind or calm and vice versa.
Everyone who is not kind or curious is humble.
Everyone who is curious is both not rich and calm and vice versa.
Lucy is not tall or not patient.
Alice is either patient or not brave.
Someone is either not wise or not tall.
Someone is both not brave and curious.
Someone is either not old or not kind.
John is either not patient or not quiet.
Someone is brave. | Alice is humble. | entailment | (![X]:(~patient(X)=>(~rich(X)&~patient(X))))&
((?[X]:((curious(X)&humble(X))))=>(~brave(paul)))&
(((calm(mary)|rich(mary)))=>(?[X]:((humble(X)|wise(X)))))&
(![X]:((~calm(X)|tall(X))<=>(humble(X)&rich(X))))&
((?[X]:((~creative(X)|~happy(X))))=>(?[X]:(wise(X))))&
(![X]:(~humble(X)=>humble(X)))&
((tall(lucy))<=>(?[X]:((quiet(X)&wise(X)))))&
(![X]:((creative(X)<~>quiet(X))=>(~rich(X)&happy(X))))&
(((curious(alice)|quiet(alice)))<=>(?[X]:((strong(X)&~tall(X)))))&
((?[X]:((~curious(X)|rich(X))))=>((~rich(alice)&humble(alice))))&
((?[X]:((~creative(X)&~rich(X))))<=>(calm(fred)))&
(![X]:((quiet(X)|~tall(X))=>generous(X)))&
((?[X]:(~tall(X)))<=>((~kind(john)<~>calm(john))))&
(![X]:((~kind(X)|curious(X))=>humble(X)))&
(![X]:(curious(X)<=>(~rich(X)&calm(X))))&
((~tall(lucy)|~patient(lucy)))&
((patient(alice)<~>~brave(alice)))&
(?[X]:((~wise(X)<~>~tall(X))))&
(?[X]:((~brave(X)&curious(X))))&
(?[X]:((~old(X)<~>~kind(X))))&
((~patient(john)<~>~quiet(john)))&
(?[X]:(brave(X))) | humble(alice) | [
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 6913427417253680668615825
% SZS output start Proof for 6913427417253680668615825
6. ! [X0] : (~humble(X0) => humble(X0)) [input p5]
23. ~humble(alice) [input hypothesis]
32. ! [X0] : (humble(X0) | humble(X0)) [ennf transformation 6]
86. humble(X0) | humble(X0) [cnf transformation 32]
125. ~humble(alice) [cnf transformation 23]
126. humble(X0) [duplicate literal removal 86]
298. $false [subsumption resolution 125,126]
% SZS output end Proof for 6913427417253680668615825
% ------------------------------
% 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 quiet and not strong is not curious.
Everyone who is not generous or not kind is strong or happy and vice versa.
If someone is both brave and not wise then someone is both not happy and not funny and vice versa.
If john is not humble then fred is not tall or not creative and vice versa.
Everyone who is not funny is either not quiet or not generous and vice versa.
If someone is both not patient and brave then someone is not wise and vice versa.
Everyone who is either curious or not generous is either not happy or humble.
Everyone who is not brave is not calm or not creative and vice versa.
If mary is not calm or not brave then lucy is not generous.
If lucy is strong then lucy is both quiet and not curious.
If fred is both not brave and creative then paul is strong or not creative.
If lucy is rich or not wise then someone is not calm or happy.
Everyone who is curious is tall.
Everyone who is either not kind or strong is not funny.
If someone is both not wise and patient then susan is tall.
Everyone who is not brave is funny or tall.
Someone is not brave or rich.
Someone is rich or curious.
Someone is curious.
John is either curious or not rich.
Susan is funny or not humble.
Someone is brave.
Fred is both creative and humble.
Someone is both not generous and curious. | Fred is brave. | neutral | (![X]:((~quiet(X)&~strong(X))=>~curious(X)))&
(![X]:((~generous(X)|~kind(X))<=>(strong(X)|happy(X))))&
((?[X]:((brave(X)&~wise(X))))<=>(?[X]:((~happy(X)&~funny(X)))))&
((~humble(john))<=>((~tall(fred)|~creative(fred))))&
(![X]:(~funny(X)<=>(~quiet(X)<~>~generous(X))))&
((?[X]:((~patient(X)&brave(X))))<=>(?[X]:(~wise(X))))&
(![X]:((curious(X)<~>~generous(X))=>(~happy(X)<~>humble(X))))&
(![X]:(~brave(X)<=>(~calm(X)|~creative(X))))&
(((~calm(mary)|~brave(mary)))=>(~generous(lucy)))&
((strong(lucy))=>((quiet(lucy)&~curious(lucy))))&
(((~brave(fred)&creative(fred)))=>((strong(paul)|~creative(paul))))&
(((rich(lucy)|~wise(lucy)))=>(?[X]:((~calm(X)|happy(X)))))&
(![X]:(curious(X)=>tall(X)))&
(![X]:((~kind(X)<~>strong(X))=>~funny(X)))&
((?[X]:((~wise(X)&patient(X))))=>(tall(susan)))&
(![X]:(~brave(X)=>(funny(X)|tall(X))))&
(?[X]:((~brave(X)|rich(X))))&
(?[X]:((rich(X)|curious(X))))&
(?[X]:(curious(X)))&
((curious(john)<~>~rich(john)))&
((funny(susan)|~humble(susan)))&
(?[X]:(brave(X)))&
((creative(fred)&humble(fred)))&
(?[X]:((~generous(X)&curious(X)))) | brave(fred) | [] | null | 0 |
Everyone who is old is both not curious and not old.
Everyone who is not happy is kind or not wise and vice versa.
If fred is either not tall or not funny then paul is either rich or humble and vice versa.
Everyone who is either generous or not creative is either not patient or creative and vice versa.
If someone is creative or not funny then someone is both not generous and humble.
If mary is either calm or old then someone is either patient or happy and vice versa.
If someone is both calm and not humble then someone is not rich or wise and vice versa.
If someone is generous or happy then someone is either not tall or creative and vice versa.
Everyone who is either generous or not kind is either not happy or happy and vice versa.
Everyone who is not kind is not happy and vice versa.
If mary is both funny and not generous then john is curious and vice versa.
Everyone who is not generous or not calm is not rich or not curious and vice versa.
Everyone who is either not humble or not strong is not generous or not kind.
Everyone who is not humble is either not creative or not funny.
If someone is either strong or humble then lucy is not curious or not rich and vice versa.
Everyone who is kind is generous and vice versa.
Someone is either not strong or not humble.
Someone is either not curious or funny.
John is not creative or not happy.
Paul is brave.
Mary is either kind or humble.
John is not generous. | Paul is humble. | neutral | (![X]:(old(X)=>(~curious(X)&~old(X))))&
(![X]:(~happy(X)<=>(kind(X)|~wise(X))))&
(((~tall(fred)<~>~funny(fred)))<=>((rich(paul)<~>humble(paul))))&
(![X]:((generous(X)<~>~creative(X))<=>(~patient(X)<~>creative(X))))&
((?[X]:((creative(X)|~funny(X))))=>(?[X]:((~generous(X)&humble(X)))))&
(((calm(mary)<~>old(mary)))<=>(?[X]:((patient(X)<~>happy(X)))))&
((?[X]:((calm(X)&~humble(X))))<=>(?[X]:((~rich(X)|wise(X)))))&
((?[X]:((generous(X)|happy(X))))<=>(?[X]:((~tall(X)<~>creative(X)))))&
(![X]:((generous(X)<~>~kind(X))<=>(~happy(X)<~>happy(X))))&
(![X]:(~kind(X)<=>~happy(X)))&
(((funny(mary)&~generous(mary)))<=>(curious(john)))&
(![X]:((~generous(X)|~calm(X))<=>(~rich(X)|~curious(X))))&
(![X]:((~humble(X)<~>~strong(X))=>(~generous(X)|~kind(X))))&
(![X]:(~humble(X)=>(~creative(X)<~>~funny(X))))&
((?[X]:((strong(X)<~>humble(X))))<=>((~curious(lucy)|~rich(lucy))))&
(![X]:(kind(X)<=>generous(X)))&
(?[X]:((~strong(X)<~>~humble(X))))&
(?[X]:((~curious(X)<~>funny(X))))&
((~creative(john)|~happy(john)))&
(brave(paul))&
((kind(mary)<~>humble(mary)))&
(~generous(john)) | humble(paul) | [] | null | 0 |
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