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
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⌀ | rule_concentration
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Everyone who is either kind or not happy is both patient and quiet. Everyone who is not humble or funny is both not quiet and not humble. If someone is old or quiet then someone is generous or not wise. Everyone who is either creative or not happy is not calm and vice versa. Everyone who is both patient and not strong is either not wise or brave. If lucy is not happy then someone is not creative or not calm. Everyone who is either not humble or not strong is old and vice versa. Everyone who is either not tall or not creative is not curious or not funny and vice versa. Everyone who is patient or not tall is both old and tall. If someone is either strong or not happy then mary is either quiet or curious. Everyone who is funny or tall is not generous and vice versa. Everyone who is calm is not kind or quiet. Everyone who is not funny or old is generous or funny. Everyone who is either rich or not humble is kind. Everyone who is tall or not brave is both patient and not generous. Someone is generous or kind. John is rich. Susan is both funny and not generous. Alice is both wise and tall. | John is not generous. | entailment | (![X]:((kind(X)<~>~happy(X))=>(patient(X)&quiet(X))))&
(![X]:((~humble(X)|funny(X))=>(~quiet(X)&~humble(X))))&
((?[X]:((old(X)|quiet(X))))=>(?[X]:((generous(X)|~wise(X)))))&
(![X]:((creative(X)<~>~happy(X))<=>~calm(X)))&
(![X]:((patient(X)&~strong(X))=>(~wise(X)<~>brave(X))))&
((~happy(lucy))=>(?[X]:((~creative(X)|~calm(X)))))&
(![X]:((~humble(X)<~>~strong(X))<=>old(X)))&
(![X]:((~tall(X)<~>~creative(X))<=>(~curious(X)|~funny(X))))&
(![X]:((patient(X)|~tall(X))=>(old(X)&tall(X))))&
((?[X]:((strong(X)<~>~happy(X))))=>((quiet(mary)<~>curious(mary))))&
(![X]:((funny(X)|tall(X))<=>~generous(X)))&
(![X]:(calm(X)=>(~kind(X)|quiet(X))))&
(![X]:((~funny(X)|old(X))=>(generous(X)|funny(X))))&
(![X]:((rich(X)<~>~humble(X))=>kind(X)))&
(![X]:((tall(X)|~brave(X))=>(patient(X)&~generous(X))))&
(?[X]:((generous(X)|kind(X))))&
(rich(john))&
((funny(susan)&~generous(susan)))&
((wise(alice)&tall(alice))) | ~generous(john) | [
"p8",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 7486199419623664974902677
% SZS output start Proof for 7486199419623664974902677
9. ! [X0] : ((~tall(X0) | patient(X0)) => (tall(X0) & old(X0))) [input p8]
11. ! [X0] : ((tall(X0) | funny(X0)) <=> ~generous(X0)) [input p10]
20. generous(john) [input hypothesis]
30. ! [X0] : ((tall(X0) & old(X0)) | (tall(X0) & ~patient(X0))) [ennf transformation 9]
50. ! [X0] : (((tall(X0) | funny(X0)) | generous(X0)) & (~generous(X0) | (~tall(X0) & ~funny(X0)))) [nnf transformation 11]
51. ! [X0] : ((tall(X0) | funny(X0) | generous(X0)) & (~generous(X0) | (~tall(X0) & ~funny(X0)))) [flattening 50]
83. tall(X0) | tall(X0) [cnf transformation 30]
89. ~generous(X0) | ~tall(X0) [cnf transformation 51]
106. generous(john) [cnf transformation 20]
108. tall(X0) [duplicate literal removal 83]
156. ~generous(X0) [subsumption resolution 89,108]
161. $false [subsumption resolution 106,156]
% SZS output end Proof for 7486199419623664974902677
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 4989
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If fred is both tall and not calm then someone is both happy and not tall. If paul is both tall and not happy then someone is both calm and happy. Everyone who is creative is both not funny and rich. If lucy is either generous or not rich then someone is happy or not funny and vice versa. Everyone who is either humble or not calm is not happy. Everyone who is happy is humble and vice versa. Everyone who is either not curious or not funny is strong and vice versa. Everyone who is either not kind or not rich is either not happy or brave and vice versa. Everyone who is both not calm and not humble is not rich or wise and vice versa. If alice is not calm then someone is not strong or not brave and vice versa. Everyone who is happy is not curious or not happy and vice versa. If lucy is not tall then mary is not kind or not funny and vice versa. Everyone who is either creative or not old is kind and vice versa. If someone is either generous or not calm then paul is either tall or not kind and vice versa. Everyone who is either not happy or not strong is both not creative and strong. If mary is not kind then fred is not old and vice versa. Fred is both not calm and not brave. Fred is either not tall or not quiet. Alice is not wise or quiet. Susan is not generous. Someone is strong or not humble. Mary is quiet or not happy. Someone is creative or not curious. | Mary is not wise. | entailment | (((tall(fred)&~calm(fred)))=>(?[X]:((happy(X)&~tall(X)))))&
(((tall(paul)&~happy(paul)))=>(?[X]:((calm(X)&happy(X)))))&
(![X]:(creative(X)=>(~funny(X)&rich(X))))&
(((generous(lucy)<~>~rich(lucy)))<=>(?[X]:((happy(X)|~funny(X)))))&
(![X]:((humble(X)<~>~calm(X))=>~happy(X)))&
(![X]:(happy(X)<=>humble(X)))&
(![X]:((~curious(X)<~>~funny(X))<=>strong(X)))&
(![X]:((~kind(X)<~>~rich(X))<=>(~happy(X)<~>brave(X))))&
(![X]:((~calm(X)&~humble(X))<=>(~rich(X)|wise(X))))&
((~calm(alice))<=>(?[X]:((~strong(X)|~brave(X)))))&
(![X]:(happy(X)<=>(~curious(X)|~happy(X))))&
((~tall(lucy))<=>((~kind(mary)|~funny(mary))))&
(![X]:((creative(X)<~>~old(X))<=>kind(X)))&
((?[X]:((generous(X)<~>~calm(X))))<=>((tall(paul)<~>~kind(paul))))&
(![X]:((~happy(X)<~>~strong(X))=>(~creative(X)&strong(X))))&
((~kind(mary))<=>(~old(fred)))&
((~calm(fred)&~brave(fred)))&
((~tall(fred)<~>~quiet(fred)))&
((~wise(alice)|quiet(alice)))&
(~generous(susan))&
(?[X]:((strong(X)|~humble(X))))&
((quiet(mary)|~happy(mary)))&
(?[X]:((creative(X)|~curious(X)))) | ~wise(mary) | [
"p5",
"p8",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 8881886456369638541205993
% SZS output start Proof for 8881886456369638541205993
6. ! [X0] : (happy(X0) <=> humble(X0)) [input p5]
9. ! [X0] : ((~humble(X0) & ~calm(X0)) <=> (wise(X0) | ~rich(X0))) [input p8]
11. ! [X0] : (happy(X0) <=> (~happy(X0) | ~curious(X0))) [input p10]
24. wise(mary) [input hypothesis]
41. ! [X0] : ((happy(X0) | ~humble(X0)) & (humble(X0) | ~happy(X0))) [nnf transformation 6]
44. ! [X0] : (((~humble(X0) & ~calm(X0)) | (~wise(X0) & rich(X0))) & ((wise(X0) | ~rich(X0)) | (humble(X0) | calm(X0)))) [nnf transformation 9]
45. ! [X0] : (((~humble(X0) & ~calm(X0)) | (~wise(X0) & rich(X0))) & (wise(X0) | ~rich(X0) | humble(X0) | calm(X0))) [flattening 44]
50. ! [X0] : ((happy(X0) | (happy(X0) & curious(X0))) & ((~happy(X0) | ~curious(X0)) | ~happy(X0))) [nnf transformation 11]
51. ! [X0] : ((happy(X0) | (happy(X0) & curious(X0))) & (~happy(X0) | ~curious(X0) | ~happy(X0))) [flattening 50]
80. ~happy(X0) | humble(X0) [cnf transformation 41]
98. ~wise(X0) | ~humble(X0) [cnf transformation 45]
104. happy(X0) | happy(X0) [cnf transformation 51]
135. wise(mary) [cnf transformation 24]
138. happy(X0) [duplicate literal removal 104]
303. humble(X0) [resolution 80,138]
311. ~humble(mary) [resolution 98,135]
312. $false [subsumption resolution 311,303]
% SZS output end Proof for 8881886456369638541205993
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not humble then mary is either calm or curious and vice versa. Everyone who is not generous or not strong is not wise and vice versa. Everyone who is humble is kind or not tall. If fred is either not funny or patient then someone is both not creative and not kind. If someone is either not humble or not generous then mary is brave. Everyone who is both not patient and not wise is happy or not quiet and vice versa. If someone is both not wise and brave then mary is both old and not patient. Everyone who is either not creative or not strong is rich. Everyone who is kind is both wise and not rich and vice versa. Everyone who is either not tall or not strong is kind or not funny and vice versa. If someone is both rich and not creative then paul is not patient or humble and vice versa. If someone is both kind and quiet then someone is both happy and not funny and vice versa. Everyone who is both curious and not strong is not calm and vice versa. If john is either calm or wise then mary is humble. Everyone who is tall is not strong or not kind and vice versa. If mary is both not generous and not wise then someone is both not patient and tall and vice versa. Mary is curious or not generous. Fred is not quiet or not kind. Fred is either not strong or tall. Someone is kind or not wise. Someone is either not happy or patient. Susan is either not brave or not creative. Someone is not kind or kind. | Mary is not generous. | entailment | ((?[X]:(~humble(X)))<=>((calm(mary)<~>curious(mary))))&
(![X]:((~generous(X)|~strong(X))<=>~wise(X)))&
(![X]:(humble(X)=>(kind(X)|~tall(X))))&
(((~funny(fred)<~>patient(fred)))=>(?[X]:((~creative(X)&~kind(X)))))&
((?[X]:((~humble(X)<~>~generous(X))))=>(brave(mary)))&
(![X]:((~patient(X)&~wise(X))<=>(happy(X)|~quiet(X))))&
((?[X]:((~wise(X)&brave(X))))=>((old(mary)&~patient(mary))))&
(![X]:((~creative(X)<~>~strong(X))=>rich(X)))&
(![X]:(kind(X)<=>(wise(X)&~rich(X))))&
(![X]:((~tall(X)<~>~strong(X))<=>(kind(X)|~funny(X))))&
((?[X]:((rich(X)&~creative(X))))<=>((~patient(paul)|humble(paul))))&
((?[X]:((kind(X)&quiet(X))))<=>(?[X]:((happy(X)&~funny(X)))))&
(![X]:((curious(X)&~strong(X))<=>~calm(X)))&
(((calm(john)<~>wise(john)))=>(humble(mary)))&
(![X]:(tall(X)<=>(~strong(X)|~kind(X))))&
(((~generous(mary)&~wise(mary)))<=>(?[X]:((~patient(X)&tall(X)))))&
((curious(mary)|~generous(mary)))&
((~quiet(fred)|~kind(fred)))&
((~strong(fred)<~>tall(fred)))&
(?[X]:((kind(X)|~wise(X))))&
(?[X]:((~happy(X)<~>patient(X))))&
((~brave(susan)<~>~creative(susan)))&
(?[X]:((~kind(X)|kind(X)))) | ~generous(mary) | [
"p0",
"p1",
"p2",
"p4",
"p5",
"p6",
"p8",
"p11",
"p12",
"p14",
"p15",
"p16",
"p17",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 8236032182890752665755936
% SZS output start Proof for 8236032182890752665755936
1. ? [X0] : ~humble(X0) <=> (calm(mary) <~> curious(mary)) [input p0]
2. ! [X0] : ((~strong(X0) | ~generous(X0)) <=> ~wise(X0)) [input p1]
3. ! [X0] : (humble(X0) => (~tall(X0) | kind(X0))) [input p2]
5. ? [X0] : (~humble(X0) <~> ~generous(X0)) => brave(mary) [input p4]
6. ! [X0] : ((~wise(X0) & ~patient(X0)) <=> (~quiet(X0) | happy(X0))) [input p5]
7. ? [X0] : (brave(X0) & ~wise(X0)) => (~patient(mary) & old(mary)) [input p6]
9. ! [X0] : (kind(X0) <=> (~rich(X0) & wise(X0))) [input p8]
12. ? [X0] : (quiet(X0) & kind(X0)) <=> ? [X0] : (~funny(X0) & happy(X0)) [input p11]
13. ! [X0] : ((~strong(X0) & curious(X0)) <=> ~calm(X0)) [input p12]
15. ! [X0] : (tall(X0) <=> (~kind(X0) | ~strong(X0))) [input p14]
16. (~wise(mary) & ~generous(mary)) <=> ? [X0] : (tall(X0) & ~patient(X0)) [input p15]
17. ~generous(mary) | curious(mary) [input p16]
18. ~kind(fred) | ~quiet(fred) [input p17]
19. ~strong(fred) <~> tall(fred) [input p18]
24. generous(mary) [input hypothesis]
25. ? [X0] : (quiet(X0) & kind(X0)) <=> ? [X1] : (~funny(X1) & happy(X1)) [rectify 12]
26. ? [X0] : (brave(X0) & ~wise(X0)) => ~patient(mary) [pure predicate removal 7]
27. ! [X0] : ((~tall(X0) | kind(X0)) | ~humble(X0)) [ennf transformation 3]
28. ! [X0] : (~tall(X0) | kind(X0) | ~humble(X0)) [flattening 27]
30. brave(mary) | ! [X0] : (~humble(X0) <=> ~generous(X0)) [ennf transformation 5]
31. ~patient(mary) | ! [X0] : (~brave(X0) | wise(X0)) [ennf transformation 26]
34. (? [X0] : ~humble(X0) | ((calm(mary) | ~curious(mary)) & (curious(mary) | ~calm(mary)))) & (((~curious(mary) | ~calm(mary)) & (curious(mary) | calm(mary))) | ! [X0] : humble(X0)) [nnf transformation 1]
35. (? [X0] : ~humble(X0) | ((calm(mary) | ~curious(mary)) & (curious(mary) | ~calm(mary)))) & (((~curious(mary) | ~calm(mary)) & (curious(mary) | calm(mary))) | ! [X1] : humble(X1)) [rectify 34]
36. ? [X0] : ~humble(X0) => ~humble(sK0) [choice axiom]
37. (~humble(sK0) | ((calm(mary) | ~curious(mary)) & (curious(mary) | ~calm(mary)))) & (((~curious(mary) | ~calm(mary)) & (curious(mary) | calm(mary))) | ! [X1] : humble(X1)) [skolemisation 35,36]
38. ! [X0] : (((~strong(X0) | ~generous(X0)) | wise(X0)) & (~wise(X0) | (strong(X0) & generous(X0)))) [nnf transformation 2]
39. ! [X0] : ((~strong(X0) | ~generous(X0) | wise(X0)) & (~wise(X0) | (strong(X0) & generous(X0)))) [flattening 38]
43. brave(mary) | ! [X0] : ((~humble(X0) | generous(X0)) & (~generous(X0) | humble(X0))) [nnf transformation 30]
44. ! [X0] : (((~wise(X0) & ~patient(X0)) | (quiet(X0) & ~happy(X0))) & ((~quiet(X0) | happy(X0)) | (wise(X0) | patient(X0)))) [nnf transformation 6]
45. ! [X0] : (((~wise(X0) & ~patient(X0)) | (quiet(X0) & ~happy(X0))) & (~quiet(X0) | happy(X0) | wise(X0) | patient(X0))) [flattening 44]
47. ! [X0] : ((kind(X0) | (rich(X0) | ~wise(X0))) & ((~rich(X0) & wise(X0)) | ~kind(X0))) [nnf transformation 9]
48. ! [X0] : ((kind(X0) | rich(X0) | ~wise(X0)) & ((~rich(X0) & wise(X0)) | ~kind(X0))) [flattening 47]
56. (? [X0] : (quiet(X0) & kind(X0)) | ! [X1] : (funny(X1) | ~happy(X1))) & (? [X1] : (~funny(X1) & happy(X1)) | ! [X0] : (~quiet(X0) | ~kind(X0))) [nnf transformation 25]
57. (? [X0] : (quiet(X0) & kind(X0)) | ! [X1] : (funny(X1) | ~happy(X1))) & (? [X2] : (~funny(X2) & happy(X2)) | ! [X3] : (~quiet(X3) | ~kind(X3))) [rectify 56]
58. ? [X0] : (quiet(X0) & kind(X0)) => (quiet(sK3) & kind(sK3)) [choice axiom]
59. ? [X2] : (~funny(X2) & happy(X2)) => (~funny(sK4) & happy(sK4)) [choice axiom]
60. ((quiet(sK3) & kind(sK3)) | ! [X1] : (funny(X1) | ~happy(X1))) & ((~funny(sK4) & happy(sK4)) | ! [X3] : (~quiet(X3) | ~kind(X3))) [skolemisation 57,59,58]
61. ! [X0] : (((~strong(X0) & curious(X0)) | calm(X0)) & (~calm(X0) | (strong(X0) | ~curious(X0)))) [nnf transformation 13]
62. ! [X0] : (((~strong(X0) & curious(X0)) | calm(X0)) & (~calm(X0) | strong(X0) | ~curious(X0))) [flattening 61]
64. ! [X0] : ((tall(X0) | (kind(X0) & strong(X0))) & ((~kind(X0) | ~strong(X0)) | ~tall(X0))) [nnf transformation 15]
65. ! [X0] : ((tall(X0) | (kind(X0) & strong(X0))) & (~kind(X0) | ~strong(X0) | ~tall(X0))) [flattening 64]
66. ((~wise(mary) & ~generous(mary)) | ! [X0] : (~tall(X0) | patient(X0))) & (? [X0] : (tall(X0) & ~patient(X0)) | (wise(mary) | generous(mary))) [nnf transformation 16]
67. ((~wise(mary) & ~generous(mary)) | ! [X0] : (~tall(X0) | patient(X0))) & (? [X0] : (tall(X0) & ~patient(X0)) | wise(mary) | generous(mary)) [flattening 66]
68. ((~wise(mary) & ~generous(mary)) | ! [X0] : (~tall(X0) | patient(X0))) & (? [X1] : (tall(X1) & ~patient(X1)) | wise(mary) | generous(mary)) [rectify 67]
69. ? [X1] : (tall(X1) & ~patient(X1)) => (tall(sK5) & ~patient(sK5)) [choice axiom]
70. ((~wise(mary) & ~generous(mary)) | ! [X0] : (~tall(X0) | patient(X0))) & ((tall(sK5) & ~patient(sK5)) | wise(mary) | generous(mary)) [skolemisation 68,69]
71. (~tall(fred) | strong(fred)) & (tall(fred) | ~strong(fred)) [nnf transformation 19]
81. ~curious(mary) | ~calm(mary) | humble(X1) [cnf transformation 37]
85. ~wise(X0) | strong(X0) [cnf transformation 39]
87. ~tall(X0) | kind(X0) | ~humble(X0) [cnf transformation 28]
92. brave(mary) | ~generous(X0) | humble(X0) [cnf transformation 43]
95. ~happy(X0) | ~patient(X0) [cnf transformation 45]
96. ~patient(X0) | quiet(X0) [cnf transformation 45]
97. ~happy(X0) | ~wise(X0) [cnf transformation 45]
99. ~patient(mary) | ~brave(X0) | wise(X0) [cnf transformation 31]
102. ~kind(X0) | wise(X0) [cnf transformation 48]
116. happy(sK4) | ~quiet(X3) | ~kind(X3) [cnf transformation 60]
122. ~strong(X0) | calm(X0) [cnf transformation 62]
126. tall(X0) | strong(X0) [cnf transformation 65]
127. tall(X0) | kind(X0) [cnf transformation 65]
130. ~generous(mary) | ~tall(X0) | patient(X0) [cnf transformation 70]
132. ~generous(mary) | curious(mary) [cnf transformation 17]
133. ~kind(fred) | ~quiet(fred) [cnf transformation 18]
134. tall(fred) | ~strong(fred) [cnf transformation 71]
135. ~tall(fred) | strong(fred) [cnf transformation 71]
142. generous(mary) [cnf transformation 24]
144. 1 <=> curious(mary) [avatar definition]
148. 2 <=> calm(mary) [avatar definition]
158. 4 <=> ! [X1] : humble(X1) [avatar definition]
159. humble(X1) <- (4) [avatar component clause 158]
160. 4 | ~2 | ~1 [avatar split clause 81,144,148,158]
163. 5 <=> patient(fred) [avatar definition]
164. patient(fred) <- (5) [avatar component clause 163]
186. 10 <=> brave(mary) [avatar definition]
188. brave(mary) <- (10) [avatar component clause 186]
191. 11 <=> ! [X0] : (~generous(X0) | humble(X0)) [avatar definition]
192. ~generous(X0) | humble(X0) <- (11) [avatar component clause 191]
193. 11 | 10 [avatar split clause 92,186,191]
195. 12 <=> ! [X0] : (~brave(X0) | wise(X0)) [avatar definition]
196. ~brave(X0) | wise(X0) <- (12) [avatar component clause 195]
198. 13 <=> patient(mary) [avatar definition]
199. patient(mary) <- (13) [avatar component clause 198]
200. ~patient(mary) <- (~13) [avatar component clause 198]
201. 12 | ~13 [avatar split clause 99,198,195]
240. 22 <=> ! [X3] : (~quiet(X3) | ~kind(X3)) [avatar definition]
241. ~quiet(X3) | ~kind(X3) <- (22) [avatar component clause 240]
248. 24 <=> happy(sK4) [avatar definition]
250. happy(sK4) <- (24) [avatar component clause 248]
251. 22 | 24 [avatar split clause 116,248,240]
261. 27 <=> humble(mary) [avatar definition]
263. humble(mary) <- (27) [avatar component clause 261]
267. 28 <=> ! [X0] : (~tall(X0) | patient(X0)) [avatar definition]
268. ~tall(X0) | patient(X0) <- (28) [avatar component clause 267]
270. 29 <=> wise(mary) [avatar definition]
271. wise(mary) <- (29) [avatar component clause 270]
275. 30 <=> generous(mary) [avatar definition]
276. generous(mary) <- (30) [avatar component clause 275]
278. 28 | ~30 [avatar split clause 130,275,267]
291. 1 | ~30 [avatar split clause 132,275,144]
293. 33 <=> quiet(fred) [avatar definition]
297. 34 <=> kind(fred) [avatar definition]
299. ~kind(fred) <- (~34) [avatar component clause 297]
300. ~33 | ~34 [avatar split clause 133,297,293]
301. strong(fred) [subsumption resolution 135,126]
302. tall(fred) [subsumption resolution 134,301]
324. 30 [avatar split clause 142,275]
327. patient(fred) <- (28) [resolution 268,302]
328. patient(X0) | kind(X0) <- (28) [resolution 268,127]
330. 5 | ~28 [avatar split clause 327,267,163]
331. quiet(fred) <- (5) [resolution 164,96]
332. 33 | ~5 [avatar split clause 331,163,293]
344. kind(fred) | ~humble(fred) [resolution 87,302]
345. kind(X0) | ~humble(X0) | kind(X0) [resolution 87,127]
347. ~humble(X0) | kind(X0) [duplicate literal removal 345]
348. ~humble(fred) <- (~34) [subsumption resolution 344,299]
360. kind(mary) <- (~13, 28) [resolution 328,200]
363. wise(mary) <- (~13, 28) [resolution 360,102]
364. 29 | 13 | ~28 [avatar split clause 363,267,198,270]
365. quiet(mary) <- (13) [resolution 199,96]
367. wise(mary) <- (10, 12) [resolution 196,188]
369. 29 | ~10 | ~12 [avatar split clause 367,195,186,270]
384. humble(mary) <- (11, 30) [resolution 192,276]
385. 27 | ~11 | ~30 [avatar split clause 384,275,191,261]
407. ~wise(sK4) <- (24) [resolution 250,97]
408. ~patient(sK4) <- (24) [resolution 250,95]
413. ~kind(mary) <- (13, 22) [resolution 241,365]
415. kind(sK4) <- (24, 28) [resolution 408,328]
436. kind(mary) <- (27) [resolution 347,263]
437. $false <- (13, 22, 27) [subsumption resolution 436,413]
438. ~13 | ~22 | ~27 [avatar contradiction clause 437]
443. strong(mary) <- (29) [resolution 271,85]
453. calm(mary) <- (29) [resolution 443,122]
456. 2 | ~29 [avatar split clause 453,270,148]
460. $false <- (4, ~34) [resolution 159,348]
463. ~4 | 34 [avatar contradiction clause 460]
501. wise(sK4) <- (24, 28) [resolution 415,102]
502. $false <- (24, 28) [subsumption resolution 501,407]
503. ~24 | ~28 [avatar contradiction clause 502]
504. $false [avatar sat refutation 160,193,201,251,278,291,300,324,330,332,364,369,385,438,456,463,503]
% SZS output end Proof for 8236032182890752665755936
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is brave then john is rich. If paul is either tall or humble then someone is both generous and not rich and vice versa. If someone is rich or happy then mary is tall or funny and vice versa. If paul is either not wise or not brave then someone is not old or not tall. If someone is either kind or quiet then alice is humble or not old and vice versa. If someone is either rich or not curious then someone is both not old and not strong and vice versa. Everyone who is not calm or creative is either rich or wise. Everyone who is creative is either calm or not calm and vice versa. If mary is both happy and brave then fred is either kind or not tall. Everyone who is not kind or tall is both not brave and patient. Everyone who is not tall or not happy is both not funny and not calm. Everyone who is both brave and strong is both not brave and not patient and vice versa. If someone is not quiet or not calm then someone is not generous. If john is not tall or not old then john is either not humble or not patient and vice versa. If alice is old or not happy then someone is not kind or creative and vice versa. Everyone who is not rich or not kind is strong or not creative and vice versa. Susan is humble. Fred is happy or not patient. Someone is both not calm and not quiet. Susan is either not happy or tall. Lucy is either not happy or not funny. Someone is not kind or not brave. Paul is not happy. | Paul is not rich. | neutral | ((brave(lucy))=>(rich(john)))&
(((tall(paul)<~>humble(paul)))<=>(?[X]:((generous(X)&~rich(X)))))&
((?[X]:((rich(X)|happy(X))))<=>((tall(mary)|funny(mary))))&
(((~wise(paul)<~>~brave(paul)))=>(?[X]:((~old(X)|~tall(X)))))&
((?[X]:((kind(X)<~>quiet(X))))<=>((humble(alice)|~old(alice))))&
((?[X]:((rich(X)<~>~curious(X))))<=>(?[X]:((~old(X)&~strong(X)))))&
(![X]:((~calm(X)|creative(X))=>(rich(X)<~>wise(X))))&
(![X]:(creative(X)<=>(calm(X)<~>~calm(X))))&
(((happy(mary)&brave(mary)))=>((kind(fred)<~>~tall(fred))))&
(![X]:((~kind(X)|tall(X))=>(~brave(X)&patient(X))))&
(![X]:((~tall(X)|~happy(X))=>(~funny(X)&~calm(X))))&
(![X]:((brave(X)&strong(X))<=>(~brave(X)&~patient(X))))&
((?[X]:((~quiet(X)|~calm(X))))=>(?[X]:(~generous(X))))&
(((~tall(john)|~old(john)))<=>((~humble(john)<~>~patient(john))))&
(((old(alice)|~happy(alice)))<=>(?[X]:((~kind(X)|creative(X)))))&
(![X]:((~rich(X)|~kind(X))<=>(strong(X)|~creative(X))))&
(humble(susan))&
((happy(fred)|~patient(fred)))&
(?[X]:((~calm(X)&~quiet(X))))&
((~happy(susan)<~>tall(susan)))&
((~happy(lucy)<~>~funny(lucy)))&
(?[X]:((~kind(X)|~brave(X))))&
(~happy(paul)) | ~rich(paul) | [] | null | 0 |
Everyone who is quiet or generous is both tall and creative.
Everyone who is not old or not curious is not quiet.
If someone is not brave then alice is patient and vice versa.
Everyone who is either not tall or quiet is not kind or kind and vice versa.
Everyone who is not curious is not happy or quiet.
If someone is not tall then alice is rich and vice versa.
If someone is both wise and creative then someone is not brave or not curious and vice versa.
If someone is not creative then lucy is either funny or generous.
Everyone who is either not happy or old is both not rich and creative.
Everyone who is not happy or not strong is both calm and not curious.
Everyone who is both funny and patient is not brave.
Everyone who is not rich is not strong or not rich and vice versa.
Everyone who is both funny and calm is not brave and vice versa.
If someone is brave or kind then someone is not calm or not kind and vice versa.
If lucy is either patient or rich then mary is either not rich or not brave.
Everyone who is both wise and not calm is not generous or rich and vice versa.
Alice is humble.
Lucy is either not kind or happy.
Fred is either happy or not patient.
Lucy is not patient.
John is either humble or not kind.
Someone is not patient or tall.
Someone is both not calm and wise. | Mary is kind. | neutral | (![X]:((quiet(X)|generous(X))=>(tall(X)&creative(X))))&
(![X]:((~old(X)|~curious(X))=>~quiet(X)))&
((?[X]:(~brave(X)))<=>(patient(alice)))&
(![X]:((~tall(X)<~>quiet(X))<=>(~kind(X)|kind(X))))&
(![X]:(~curious(X)=>(~happy(X)|quiet(X))))&
((?[X]:(~tall(X)))<=>(rich(alice)))&
((?[X]:((wise(X)&creative(X))))<=>(?[X]:((~brave(X)|~curious(X)))))&
((?[X]:(~creative(X)))=>((funny(lucy)<~>generous(lucy))))&
(![X]:((~happy(X)<~>old(X))=>(~rich(X)&creative(X))))&
(![X]:((~happy(X)|~strong(X))=>(calm(X)&~curious(X))))&
(![X]:((funny(X)&patient(X))=>~brave(X)))&
(![X]:(~rich(X)<=>(~strong(X)|~rich(X))))&
(![X]:((funny(X)&calm(X))<=>~brave(X)))&
((?[X]:((brave(X)|kind(X))))<=>(?[X]:((~calm(X)|~kind(X)))))&
(((patient(lucy)<~>rich(lucy)))=>((~rich(mary)<~>~brave(mary))))&
(![X]:((wise(X)&~calm(X))<=>(~generous(X)|rich(X))))&
(humble(alice))&
((~kind(lucy)<~>happy(lucy)))&
((happy(fred)<~>~patient(fred)))&
(~patient(lucy))&
((humble(john)<~>~kind(john)))&
(?[X]:((~patient(X)|tall(X))))&
(?[X]:((~calm(X)&wise(X)))) | kind(mary) | [] | null | 0 |
Everyone who is happy is strong and vice versa.
Everyone who is not wise is either not tall or not patient and vice versa.
If mary is both quiet and happy then someone is both tall and generous.
Everyone who is either humble or patient is curious or not wise.
If susan is both humble and patient then fred is both quiet and rich and vice versa.
Everyone who is either generous or not old is humble and vice versa.
If paul is tall or patient then someone is not generous and vice versa.
If someone is not rich or curious then someone is quiet or not strong.
Everyone who is not old is not generous or brave and vice versa.
If john is both not humble and not calm then someone is patient or tall.
Everyone who is not patient is not old or generous.
Everyone who is not kind is not calm or not rich.
Everyone who is both not happy and not wise is not humble or generous.
If john is wise or not curious then someone is wise.
Everyone who is either not happy or quiet is not tall and vice versa.
Someone is strong or humble.
Someone is kind or funny.
Someone is not calm.
Susan is either not calm or not patient.
Fred is not funny.
Someone is curious.
Paul is both not calm and not old.
Lucy is curious. | Mary is happy. | neutral | (![X]:(happy(X)<=>strong(X)))&
(![X]:(~wise(X)<=>(~tall(X)<~>~patient(X))))&
(((quiet(mary)&happy(mary)))=>(?[X]:((tall(X)&generous(X)))))&
(![X]:((humble(X)<~>patient(X))=>(curious(X)|~wise(X))))&
(((humble(susan)&patient(susan)))<=>((quiet(fred)&rich(fred))))&
(![X]:((generous(X)<~>~old(X))<=>humble(X)))&
(((tall(paul)|patient(paul)))<=>(?[X]:(~generous(X))))&
((?[X]:((~rich(X)|curious(X))))=>(?[X]:((quiet(X)|~strong(X)))))&
(![X]:(~old(X)<=>(~generous(X)|brave(X))))&
(((~humble(john)&~calm(john)))=>(?[X]:((patient(X)|tall(X)))))&
(![X]:(~patient(X)=>(~old(X)|generous(X))))&
(![X]:(~kind(X)=>(~calm(X)|~rich(X))))&
(![X]:((~happy(X)&~wise(X))=>(~humble(X)|generous(X))))&
(((wise(john)|~curious(john)))=>(?[X]:(wise(X))))&
(![X]:((~happy(X)<~>quiet(X))<=>~tall(X)))&
(?[X]:((strong(X)|humble(X))))&
(?[X]:((kind(X)|funny(X))))&
(?[X]:(~calm(X)))&
((~calm(susan)<~>~patient(susan)))&
(~funny(fred))&
(?[X]:(curious(X)))&
((~calm(paul)&~old(paul)))&
(curious(lucy)) | happy(mary) | [] | null | 0 |
Everyone who is both not strong and not calm is either patient or calm.
Everyone who is curious or not patient is either not generous or not calm and vice versa.
Everyone who is both curious and patient is not creative.
Everyone who is not kind is funny.
If john is either not creative or not wise then someone is either not calm or tall.
Everyone who is creative is both old and creative and vice versa.
Everyone who is either funny or not rich is either creative or not curious and vice versa.
Everyone who is generous or creative is both rich and not kind and vice versa.
Everyone who is both generous and not creative is wise or not creative and vice versa.
Everyone who is both kind and not wise is both not generous and strong.
Everyone who is not calm is not old or not humble and vice versa.
Everyone who is both funny and not strong is creative and vice versa.
Everyone who is not funny is wise.
If someone is both happy and humble then someone is both strong and funny.
Everyone who is both humble and generous is not quiet and vice versa.
If susan is either not happy or not tall then lucy is either not strong or not patient and vice versa.
Fred is not quiet or patient.
Paul is not brave or not funny.
Someone is either wise or humble.
Alice is curious.
Susan is brave or kind.
Someone is either not rich or not kind.
Paul is not quiet.
John is not old. | Alice is not humble. | contradiction | (![X]:((~strong(X)&~calm(X))=>(patient(X)<~>calm(X))))&
(![X]:((curious(X)|~patient(X))<=>(~generous(X)<~>~calm(X))))&
(![X]:((curious(X)&patient(X))=>~creative(X)))&
(![X]:(~kind(X)=>funny(X)))&
(((~creative(john)<~>~wise(john)))=>(?[X]:((~calm(X)<~>tall(X)))))&
(![X]:(creative(X)<=>(old(X)&creative(X))))&
(![X]:((funny(X)<~>~rich(X))<=>(creative(X)<~>~curious(X))))&
(![X]:((generous(X)|creative(X))<=>(rich(X)&~kind(X))))&
(![X]:((generous(X)&~creative(X))<=>(wise(X)|~creative(X))))&
(![X]:((kind(X)&~wise(X))=>(~generous(X)&strong(X))))&
(![X]:(~calm(X)<=>(~old(X)|~humble(X))))&
(![X]:((funny(X)&~strong(X))<=>creative(X)))&
(![X]:(~funny(X)=>wise(X)))&
((?[X]:((happy(X)&humble(X))))=>(?[X]:((strong(X)&funny(X)))))&
(![X]:((humble(X)&generous(X))<=>~quiet(X)))&
(((~happy(susan)<~>~tall(susan)))<=>((~strong(lucy)<~>~patient(lucy))))&
((~quiet(fred)|patient(fred)))&
((~brave(paul)|~funny(paul)))&
(?[X]:((wise(X)<~>humble(X))))&
(curious(alice))&
((brave(susan)|kind(susan)))&
(?[X]:((~rich(X)<~>~kind(X))))&
(~quiet(paul))&
(~old(john)) | ~humble(alice) | [
"p0",
"p1",
"p2",
"p3",
"p6",
"p7",
"p8",
"p10",
"p11",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 7340858182073399832305945
% SZS output start Proof for 7340858182073399832305945
1. ! [X0] : ((~calm(X0) & ~strong(X0)) => (patient(X0) <~> calm(X0))) [input p0]
2. ! [X0] : ((~patient(X0) | curious(X0)) <=> (~generous(X0) <~> ~calm(X0))) [input p1]
3. ! [X0] : ((patient(X0) & curious(X0)) => ~creative(X0)) [input p2]
4. ! [X0] : (~kind(X0) => funny(X0)) [input p3]
7. ! [X0] : ((funny(X0) <~> ~rich(X0)) <=> (creative(X0) <~> ~curious(X0))) [input p6]
8. ! [X0] : ((creative(X0) | generous(X0)) <=> (~kind(X0) & rich(X0))) [input p7]
9. ! [X0] : ((~creative(X0) & generous(X0)) <=> (~creative(X0) | wise(X0))) [input p8]
11. ! [X0] : (~calm(X0) <=> (~humble(X0) | ~old(X0))) [input p10]
12. ! [X0] : ((~strong(X0) & funny(X0)) <=> creative(X0)) [input p11]
20. curious(alice) [input p19]
25. ~humble(alice) [input hypothesis]
28. ! [X0] : ((patient(X0) <~> calm(X0)) | (calm(X0) | strong(X0))) [ennf transformation 1]
29. ! [X0] : ((patient(X0) <~> calm(X0)) | calm(X0) | strong(X0)) [flattening 28]
30. ! [X0] : (~creative(X0) | (~patient(X0) | ~curious(X0))) [ennf transformation 3]
31. ! [X0] : (~creative(X0) | ~patient(X0) | ~curious(X0)) [flattening 30]
32. ! [X0] : (funny(X0) | kind(X0)) [ennf transformation 4]
39. ! [X0] : (((~calm(X0) | ~patient(X0)) & (calm(X0) | patient(X0))) | calm(X0) | strong(X0)) [nnf transformation 29]
40. ! [X0] : (((~patient(X0) | curious(X0)) | ((~generous(X0) | calm(X0)) & (~calm(X0) | generous(X0)))) & (((calm(X0) | generous(X0)) & (~calm(X0) | ~generous(X0))) | (patient(X0) & ~curious(X0)))) [nnf transformation 2]
41. ! [X0] : ((~patient(X0) | curious(X0) | ((~generous(X0) | calm(X0)) & (~calm(X0) | generous(X0)))) & (((calm(X0) | generous(X0)) & (~calm(X0) | ~generous(X0))) | (patient(X0) & ~curious(X0)))) [flattening 40]
47. ! [X0] : ((((rich(X0) | ~funny(X0)) & (~rich(X0) | funny(X0))) | ((creative(X0) | curious(X0)) & (~curious(X0) | ~creative(X0)))) & (((curious(X0) | ~creative(X0)) & (~curious(X0) | creative(X0))) | ((funny(X0) | rich(X0)) & (~rich(X0) | ~funny(X0))))) [nnf transformation 7]
48. ! [X0] : (((creative(X0) | generous(X0)) | (kind(X0) | ~rich(X0))) & ((~kind(X0) & rich(X0)) | (~creative(X0) & ~generous(X0)))) [nnf transformation 8]
49. ! [X0] : ((creative(X0) | generous(X0) | kind(X0) | ~rich(X0)) & ((~kind(X0) & rich(X0)) | (~creative(X0) & ~generous(X0)))) [flattening 48]
50. ! [X0] : (((~creative(X0) & generous(X0)) | (creative(X0) & ~wise(X0))) & ((~creative(X0) | wise(X0)) | (creative(X0) | ~generous(X0)))) [nnf transformation 9]
51. ! [X0] : (((~creative(X0) & generous(X0)) | (creative(X0) & ~wise(X0))) & (~creative(X0) | wise(X0) | creative(X0) | ~generous(X0))) [flattening 50]
52. ! [X0] : ((~calm(X0) | (humble(X0) & old(X0))) & ((~humble(X0) | ~old(X0)) | calm(X0))) [nnf transformation 11]
53. ! [X0] : ((~calm(X0) | (humble(X0) & old(X0))) & (~humble(X0) | ~old(X0) | calm(X0))) [flattening 52]
54. ! [X0] : (((~strong(X0) & funny(X0)) | ~creative(X0)) & (creative(X0) | (strong(X0) | ~funny(X0)))) [nnf transformation 12]
55. ! [X0] : (((~strong(X0) & funny(X0)) | ~creative(X0)) & (creative(X0) | strong(X0) | ~funny(X0))) [flattening 54]
66. calm(X0) | patient(X0) | calm(X0) | strong(X0) [cnf transformation 39]
70. ~curious(X0) | generous(X0) | calm(X0) [cnf transformation 41]
74. ~creative(X0) | ~patient(X0) | ~curious(X0) [cnf transformation 31]
75. funny(X0) | kind(X0) [cnf transformation 32]
83. ~rich(X0) | creative(X0) | ~curious(X0) | ~funny(X0) [cnf transformation 47]
91. ~generous(X0) | rich(X0) [cnf transformation 49]
92. ~creative(X0) | rich(X0) [cnf transformation 49]
93. ~kind(X0) | ~generous(X0) [cnf transformation 49]
98. creative(X0) | generous(X0) [cnf transformation 51]
105. ~calm(X0) | humble(X0) [cnf transformation 53]
106. ~funny(X0) | strong(X0) | creative(X0) [cnf transformation 55]
108. ~creative(X0) | ~strong(X0) [cnf transformation 55]
126. curious(alice) [cnf transformation 20]
132. ~humble(alice) [cnf transformation 25]
133. patient(X0) | calm(X0) | strong(X0) [duplicate literal removal 66]
241. generous(X0) | rich(X0) [resolution 98,92]
243. rich(X0) [subsumption resolution 241,91]
308. generous(alice) | calm(alice) [resolution 70,126]
310. 31 <=> calm(alice) [avatar definition]
311. ~calm(alice) <- (~31) [avatar component clause 310]
312. calm(alice) <- (31) [avatar component clause 310]
314. 32 <=> generous(alice) [avatar definition]
316. generous(alice) <- (32) [avatar component clause 314]
317. 31 | 32 [avatar split clause 308,314,310]
318. humble(alice) <- (31) [resolution 312,105]
320. $false <- (31) [subsumption resolution 318,132]
321. ~31 [avatar contradiction clause 320]
334. kind(X0) | creative(X0) | strong(X0) [resolution 106,75]
370. ~funny(X0) | ~curious(X0) | creative(X0) [resolution 83,243]
441. creative(X2) | strong(X2) | ~generous(X2) [resolution 334,93]
444. creative(X2) | strong(X2) [subsumption resolution 441,98]
490. ~curious(X0) | ~patient(X0) | strong(X0) [resolution 444,74]
502. ~curious(X2) | creative(X2) | kind(X2) [resolution 370,75]
533. ~patient(alice) | strong(alice) [resolution 490,126]
538. 42 <=> strong(alice) [avatar definition]
540. strong(alice) <- (42) [avatar component clause 538]
542. 43 <=> patient(alice) [avatar definition]
544. ~patient(alice) <- (~43) [avatar component clause 542]
545. 42 | ~43 [avatar split clause 533,542,538]
546. calm(alice) | strong(alice) <- (~43) [resolution 544,133]
547. strong(alice) <- (~31, ~43) [subsumption resolution 546,311]
548. 42 | 31 | 43 [avatar split clause 547,542,310,538]
549. creative(alice) | kind(alice) [resolution 502,126]
553. 44 <=> kind(alice) [avatar definition]
555. kind(alice) <- (44) [avatar component clause 553]
557. 45 <=> creative(alice) [avatar definition]
559. creative(alice) <- (45) [avatar component clause 557]
560. 44 | 45 [avatar split clause 549,557,553]
564. ~generous(alice) <- (44) [resolution 555,93]
566. $false <- (32, 44) [subsumption resolution 564,316]
567. ~32 | ~44 [avatar contradiction clause 566]
574. ~strong(alice) <- (45) [resolution 559,108]
576. $false <- (42, 45) [subsumption resolution 574,540]
577. ~42 | ~45 [avatar contradiction clause 576]
578. $false [avatar sat refutation 317,321,545,548,560,567,577]
% SZS output end Proof for 7340858182073399832305945
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.021 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not brave is either curious or not wise and vice versa.
If john is both not kind and not funny then someone is both quiet and not kind and vice versa.
If someone is either wise or not rich then someone is creative or not rich.
If john is brave or not old then lucy is not quiet.
If paul is both curious and not funny then paul is both creative and wise and vice versa.
Everyone who is both not rich and not kind is humble.
If susan is quiet then someone is not patient or not strong.
Everyone who is not rich or generous is either happy or creative.
If susan is not calm or generous then someone is not creative or not funny and vice versa.
If alice is either patient or not strong then paul is not quiet and vice versa.
Everyone who is either not brave or not funny is not funny or tall and vice versa.
Everyone who is either humble or calm is happy or humble and vice versa.
Everyone who is either curious or not rich is both quiet and kind and vice versa.
Everyone who is not wise or wise is not curious or not creative.
Everyone who is either not kind or kind is both not wise and tall.
Someone is patient or not kind.
Mary is not rich or quiet.
Mary is not generous or strong.
Someone is not quiet.
Lucy is either not kind or not creative.
Mary is brave or not funny.
Lucy is both generous and not humble. | Paul is not curious. | entailment | (![X]:(~brave(X)<=>(curious(X)<~>~wise(X))))&
(((~kind(john)&~funny(john)))<=>(?[X]:((quiet(X)&~kind(X)))))&
((?[X]:((wise(X)<~>~rich(X))))=>(?[X]:((creative(X)|~rich(X)))))&
(((brave(john)|~old(john)))=>(~quiet(lucy)))&
(((curious(paul)&~funny(paul)))<=>((creative(paul)&wise(paul))))&
(![X]:((~rich(X)&~kind(X))=>humble(X)))&
((quiet(susan))=>(?[X]:((~patient(X)|~strong(X)))))&
(![X]:((~rich(X)|generous(X))=>(happy(X)<~>creative(X))))&
(((~calm(susan)|generous(susan)))<=>(?[X]:((~creative(X)|~funny(X)))))&
(((patient(alice)<~>~strong(alice)))<=>(~quiet(paul)))&
(![X]:((~brave(X)<~>~funny(X))<=>(~funny(X)|tall(X))))&
(![X]:((humble(X)<~>calm(X))<=>(happy(X)|humble(X))))&
(![X]:((curious(X)<~>~rich(X))<=>(quiet(X)&kind(X))))&
(![X]:((~wise(X)|wise(X))=>(~curious(X)|~creative(X))))&
(![X]:((~kind(X)<~>kind(X))=>(~wise(X)&tall(X))))&
(?[X]:((patient(X)|~kind(X))))&
((~rich(mary)|quiet(mary)))&
((~generous(mary)|strong(mary)))&
(?[X]:(~quiet(X)))&
((~kind(lucy)<~>~creative(lucy)))&
((brave(mary)|~funny(mary)))&
((generous(lucy)&~humble(lucy))) | ~curious(paul) | [
"p0",
"p4",
"p10",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6530419666698131411955726
% SZS output start Proof for 6530419666698131411955726
1. ! [X0] : (~brave(X0) <=> (curious(X0) <~> ~wise(X0))) [input p0]
5. (~funny(paul) & curious(paul)) <=> (wise(paul) & creative(paul)) [input p4]
11. ! [X0] : ((~brave(X0) <~> ~funny(X0)) <=> (tall(X0) | ~funny(X0))) [input p10]
14. ! [X0] : ((wise(X0) | ~wise(X0)) => (~creative(X0) | ~curious(X0))) [input p13]
15. ! [X0] : ((~kind(X0) <~> kind(X0)) => (tall(X0) & ~wise(X0))) [input p14]
23. curious(paul) [input hypothesis]
32. ! [X0] : ((~creative(X0) | ~curious(X0)) | (~wise(X0) & wise(X0))) [ennf transformation 14]
33. ! [X0] : (~creative(X0) | ~curious(X0) | (~wise(X0) & wise(X0))) [flattening 32]
34. ! [X0] : ((tall(X0) & ~wise(X0)) | (~kind(X0) <=> kind(X0))) [ennf transformation 15]
35. ! [X0] : ((~brave(X0) | ((curious(X0) | wise(X0)) & (~wise(X0) | ~curious(X0)))) & (((wise(X0) | ~curious(X0)) & (~wise(X0) | curious(X0))) | brave(X0))) [nnf transformation 1]
45. ((~funny(paul) & curious(paul)) | (~wise(paul) | ~creative(paul))) & ((wise(paul) & creative(paul)) | (funny(paul) | ~curious(paul))) [nnf transformation 5]
46. ((~funny(paul) & curious(paul)) | ~wise(paul) | ~creative(paul)) & ((wise(paul) & creative(paul)) | funny(paul) | ~curious(paul)) [flattening 45]
56. ! [X0] : ((((funny(X0) | brave(X0)) & (~funny(X0) | ~brave(X0))) | (~tall(X0) & funny(X0))) & ((tall(X0) | ~funny(X0)) | ((~brave(X0) | funny(X0)) & (~funny(X0) | brave(X0))))) [nnf transformation 11]
57. ! [X0] : ((((funny(X0) | brave(X0)) & (~funny(X0) | ~brave(X0))) | (~tall(X0) & funny(X0))) & (tall(X0) | ~funny(X0) | ((~brave(X0) | funny(X0)) & (~funny(X0) | brave(X0))))) [flattening 56]
62. ! [X0] : ((tall(X0) & ~wise(X0)) | ((~kind(X0) | ~kind(X0)) & (kind(X0) | kind(X0)))) [nnf transformation 34]
69. ~curious(X0) | wise(X0) | brave(X0) [cnf transformation 35]
79. creative(paul) | funny(paul) | ~curious(paul) [cnf transformation 46]
100. ~tall(X0) | ~brave(X0) | ~funny(X0) [cnf transformation 57]
115. ~creative(X0) | ~curious(X0) | wise(X0) [cnf transformation 33]
116. ~creative(X0) | ~curious(X0) | ~wise(X0) [cnf transformation 33]
117. ~wise(X0) | kind(X0) | kind(X0) [cnf transformation 62]
118. ~wise(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 62]
119. tall(X0) | kind(X0) | kind(X0) [cnf transformation 62]
120. tall(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 62]
130. curious(paul) [cnf transformation 23]
131. ~wise(X0) | kind(X0) [duplicate literal removal 117]
132. ~kind(X0) | ~wise(X0) [duplicate literal removal 118]
133. tall(X0) | kind(X0) [duplicate literal removal 119]
134. ~kind(X0) | tall(X0) [duplicate literal removal 120]
188. 12 <=> creative(paul) [avatar definition]
189. creative(paul) <- (12) [avatar component clause 188]
196. 14 <=> funny(paul) [avatar definition]
197. funny(paul) <- (14) [avatar component clause 196]
201. 15 <=> curious(paul) [avatar definition]
203. curious(paul) <- (15) [avatar component clause 201]
206. ~15 | 14 | 12 [avatar split clause 79,188,196,201]
264. ~creative(X0) | ~curious(X0) [subsumption resolution 115,116]
265. tall(X0) [subsumption resolution 133,134]
266. ~wise(X0) [subsumption resolution 131,132]
305. 15 [avatar split clause 130,201]
312. ~curious(paul) <- (12) [resolution 264,189]
313. $false <- (12, 15) [subsumption resolution 312,203]
314. ~12 | ~15 [avatar contradiction clause 313]
315. wise(paul) | brave(paul) <- (15) [resolution 69,203]
316. brave(paul) <- (15) [subsumption resolution 315,266]
333. ~funny(X1) | ~brave(X1) [resolution 100,265]
337. ~brave(paul) <- (14) [resolution 333,197]
339. $false <- (14, 15) [subsumption resolution 337,316]
340. ~14 | ~15 [avatar contradiction clause 339]
341. $false [avatar sat refutation 206,305,314,340]
% SZS output end Proof for 6530419666698131411955726
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is not old or old then john is tall and vice versa. Everyone who is both not old and not patient is either quiet or not old. If someone is not funny or old then someone is either curious or rich. If alice is both old and rich then lucy is not rich and vice versa. Everyone who is both not patient and not rich is either creative or humble and vice versa. Everyone who is funny or generous is both not strong and not kind. If paul is either not old or not rich then paul is not creative and vice versa. Everyone who is not old is both rich and patient and vice versa. Everyone who is not calm is happy and vice versa. Everyone who is both not patient and not happy is both not funny and quiet and vice versa. Everyone who is calm is both not old and not kind and vice versa. If john is both not kind and creative then lucy is both brave and creative and vice versa. If lucy is not wise then paul is quiet. Everyone who is old is either not old or quiet. Everyone who is happy or calm is both creative and not wise. If someone is not rich then john is both not kind and not quiet and vice versa. Susan is not calm. Someone is either curious or not funny. Someone is either not creative or humble. Fred is both curious and not strong. Someone is either brave or generous. Someone is both old and not curious. John is both quiet and generous. | Paul is not funny. | contradiction | (((~old(lucy)|old(lucy)))<=>(tall(john)))&
(![X]:((~old(X)&~patient(X))=>(quiet(X)<~>~old(X))))&
((?[X]:((~funny(X)|old(X))))=>(?[X]:((curious(X)<~>rich(X)))))&
(((old(alice)&rich(alice)))<=>(~rich(lucy)))&
(![X]:((~patient(X)&~rich(X))<=>(creative(X)<~>humble(X))))&
(![X]:((funny(X)|generous(X))=>(~strong(X)&~kind(X))))&
(((~old(paul)<~>~rich(paul)))<=>(~creative(paul)))&
(![X]:(~old(X)<=>(rich(X)&patient(X))))&
(![X]:(~calm(X)<=>happy(X)))&
(![X]:((~patient(X)&~happy(X))<=>(~funny(X)&quiet(X))))&
(![X]:(calm(X)<=>(~old(X)&~kind(X))))&
(((~kind(john)&creative(john)))<=>((brave(lucy)&creative(lucy))))&
((~wise(lucy))=>(quiet(paul)))&
(![X]:(old(X)=>(~old(X)<~>quiet(X))))&
(![X]:((happy(X)|calm(X))=>(creative(X)&~wise(X))))&
((?[X]:(~rich(X)))<=>((~kind(john)&~quiet(john))))&
(~calm(susan))&
(?[X]:((curious(X)<~>~funny(X))))&
(?[X]:((~creative(X)<~>humble(X))))&
((curious(fred)&~strong(fred)))&
(?[X]:((brave(X)<~>generous(X))))&
(?[X]:((old(X)&~curious(X))))&
((quiet(john)&generous(john))) | ~funny(paul) | [
"p6",
"p8",
"p9",
"p10",
"p12",
"p14",
"p15",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 221478574391275414186992
% SZS output start Proof for 221478574391275414186992
7. (~old(paul) <~> ~rich(paul)) <=> ~creative(paul) [input p6]
9. ! [X0] : (~calm(X0) <=> happy(X0)) [input p8]
10. ! [X0] : ((~happy(X0) & ~patient(X0)) <=> (quiet(X0) & ~funny(X0))) [input p9]
11. ! [X0] : (calm(X0) <=> (~kind(X0) & ~old(X0))) [input p10]
13. ~wise(lucy) => quiet(paul) [input p12]
15. ! [X0] : ((calm(X0) | happy(X0)) => (~wise(X0) & creative(X0))) [input p14]
16. ? [X0] : ~rich(X0) <=> (~quiet(john) & ~kind(john)) [input p15]
23. generous(john) & quiet(john) [input p22]
24. ~funny(paul) [input hypothesis]
32. quiet(paul) | wise(lucy) [ennf transformation 13]
34. ! [X0] : ((~wise(X0) & creative(X0)) | (~calm(X0) & ~happy(X0))) [ennf transformation 15]
46. (((rich(paul) | old(paul)) & (~rich(paul) | ~old(paul))) | creative(paul)) & (~creative(paul) | ((~old(paul) | rich(paul)) & (~rich(paul) | old(paul)))) [nnf transformation 7]
49. ! [X0] : ((~calm(X0) | ~happy(X0)) & (happy(X0) | calm(X0))) [nnf transformation 9]
50. ! [X0] : (((~happy(X0) & ~patient(X0)) | (~quiet(X0) | funny(X0))) & ((quiet(X0) & ~funny(X0)) | (happy(X0) | patient(X0)))) [nnf transformation 10]
51. ! [X0] : (((~happy(X0) & ~patient(X0)) | ~quiet(X0) | funny(X0)) & ((quiet(X0) & ~funny(X0)) | happy(X0) | patient(X0))) [flattening 50]
52. ! [X0] : ((calm(X0) | (kind(X0) | old(X0))) & ((~kind(X0) & ~old(X0)) | ~calm(X0))) [nnf transformation 11]
53. ! [X0] : ((calm(X0) | kind(X0) | old(X0)) & ((~kind(X0) & ~old(X0)) | ~calm(X0))) [flattening 52]
57. (? [X0] : ~rich(X0) | (quiet(john) | kind(john))) & ((~quiet(john) & ~kind(john)) | ! [X0] : rich(X0)) [nnf transformation 16]
58. (? [X0] : ~rich(X0) | quiet(john) | kind(john)) & ((~quiet(john) & ~kind(john)) | ! [X0] : rich(X0)) [flattening 57]
59. (? [X0] : ~rich(X0) | quiet(john) | kind(john)) & ((~quiet(john) & ~kind(john)) | ! [X1] : rich(X1)) [rectify 58]
60. ? [X0] : ~rich(X0) => ~rich(sK1) [choice axiom]
61. (~rich(sK1) | quiet(john) | kind(john)) & ((~quiet(john) & ~kind(john)) | ! [X1] : rich(X1)) [skolemisation 59,60]
93. ~creative(paul) | ~rich(paul) | old(paul) [cnf transformation 46]
100. happy(X0) | calm(X0) [cnf transformation 49]
105. ~happy(X0) | ~quiet(X0) | funny(X0) [cnf transformation 51]
106. ~calm(X0) | ~old(X0) [cnf transformation 53]
113. quiet(paul) | wise(lucy) [cnf transformation 32]
116. ~happy(X0) | creative(X0) [cnf transformation 34]
117. ~calm(X0) | creative(X0) [cnf transformation 34]
118. ~wise(X0) | ~happy(X0) [cnf transformation 34]
119. ~wise(X0) | ~calm(X0) [cnf transformation 34]
121. ~quiet(john) | rich(X1) [cnf transformation 61]
133. quiet(john) [cnf transformation 23]
135. ~funny(paul) [cnf transformation 24]
182. 10 <=> creative(paul) [avatar definition]
183. ~creative(paul) <- (~10) [avatar component clause 182]
186. 11 <=> old(paul) [avatar definition]
188. old(paul) <- (11) [avatar component clause 186]
190. 12 <=> rich(paul) [avatar definition]
191. ~rich(paul) <- (~12) [avatar component clause 190]
196. 11 | ~12 | ~10 [avatar split clause 93,182,190,186]
218. 17 <=> wise(lucy) [avatar definition]
220. wise(lucy) <- (17) [avatar component clause 218]
222. 18 <=> quiet(paul) [avatar definition]
224. quiet(paul) <- (18) [avatar component clause 222]
225. 17 | 18 [avatar split clause 113,222,218]
227. 19 <=> quiet(john) [avatar definition]
236. 21 <=> ! [X1] : rich(X1) [avatar definition]
237. rich(X1) <- (21) [avatar component clause 236]
238. 21 | ~19 [avatar split clause 121,227,236]
270. 19 [avatar split clause 133,227]
271. $false <- (~12, 21) [subsumption resolution 191,237]
272. 12 | ~21 [avatar contradiction clause 271]
276. creative(X0) | calm(X0) [resolution 116,100]
277. creative(X0) [subsumption resolution 276,117]
278. $false <- (~10) [resolution 277,183]
283. 10 [avatar contradiction clause 278]
284. ~happy(lucy) <- (17) [resolution 118,220]
285. calm(lucy) <- (17) [resolution 284,100]
286. ~calm(lucy) <- (17) [resolution 119,220]
287. $false <- (17) [subsumption resolution 286,285]
288. ~17 [avatar contradiction clause 287]
330. ~quiet(X1) | funny(X1) | calm(X1) [resolution 105,100]
374. funny(paul) | calm(paul) <- (18) [resolution 330,224]
382. calm(paul) <- (18) [subsumption resolution 374,135]
403. ~old(paul) <- (18) [resolution 382,106]
404. $false <- (11, 18) [subsumption resolution 403,188]
405. ~11 | ~18 [avatar contradiction clause 404]
406. $false [avatar sat refutation 196,225,238,270,272,283,288,405]
% SZS output end Proof for 221478574391275414186992
% ------------------------------
% 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: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
If paul is not generous then susan is not generous.
If someone is both not strong and wise then someone is not creative and vice versa.
Everyone who is both calm and quiet is brave or not brave.
Everyone who is either not strong or not rich is not strong or patient and vice versa.
Everyone who is either funny or not curious is either generous or happy.
Everyone who is either not happy or not funny is both wise and rich and vice versa.
If fred is either rich or funny then someone is calm.
Everyone who is not generous or not creative is both creative and not humble and vice versa.
Everyone who is tall is old or not funny and vice versa.
If someone is either not curious or brave then john is patient and vice versa.
If someone is humble then someone is funny.
If someone is patient or funny then fred is not strong and vice versa.
Everyone who is both old and not happy is either rich or calm.
If someone is not old then fred is brave and vice versa.
Everyone who is creative or generous is either happy or not old and vice versa.
Fred is either not rich or not brave.
John is not patient.
Alice is either not generous or not curious.
Someone is wise or strong.
Someone is either generous or not quiet.
Fred is not brave or not quiet.
Lucy is not generous or not quiet.
Someone is either humble or not wise. | Alice is happy. | entailment | ((~generous(paul))=>(~generous(susan)))&
((?[X]:((~strong(X)&wise(X))))<=>(?[X]:(~creative(X))))&
(![X]:((calm(X)&quiet(X))=>(brave(X)|~brave(X))))&
(![X]:((~strong(X)<~>~rich(X))<=>(~strong(X)|patient(X))))&
(![X]:((funny(X)<~>~curious(X))=>(generous(X)<~>happy(X))))&
(![X]:((~happy(X)<~>~funny(X))<=>(wise(X)&rich(X))))&
(((rich(fred)<~>funny(fred)))=>(?[X]:(calm(X))))&
(![X]:((~generous(X)|~creative(X))<=>(creative(X)&~humble(X))))&
(![X]:(tall(X)<=>(old(X)|~funny(X))))&
((?[X]:((~curious(X)<~>brave(X))))<=>(patient(john)))&
((?[X]:(humble(X)))=>(?[X]:(funny(X))))&
((?[X]:((patient(X)|funny(X))))<=>(~strong(fred)))&
(![X]:((old(X)&~happy(X))=>(rich(X)<~>calm(X))))&
((?[X]:(~old(X)))<=>(brave(fred)))&
(![X]:((creative(X)|generous(X))<=>(happy(X)<~>~old(X))))&
((~rich(fred)<~>~brave(fred)))&
(~patient(john))&
((~generous(alice)<~>~curious(alice)))&
(?[X]:((wise(X)|strong(X))))&
(?[X]:((generous(X)<~>~quiet(X))))&
((~brave(fred)|~quiet(fred)))&
((~generous(lucy)|~quiet(lucy)))&
(?[X]:((humble(X)<~>~wise(X)))) | happy(alice) | [
"p3",
"p7",
"p11",
"p13",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 5676541964665822355250782
% SZS output start Proof for 5676541964665822355250782
4. ! [X0] : ((~strong(X0) <~> ~rich(X0)) <=> (patient(X0) | ~strong(X0))) [input p3]
8. ! [X0] : ((~creative(X0) | ~generous(X0)) <=> (~humble(X0) & creative(X0))) [input p7]
12. ? [X0] : (funny(X0) | patient(X0)) <=> ~strong(fred) [input p11]
14. ? [X0] : ~old(X0) <=> brave(fred) [input p13]
15. ! [X0] : ((generous(X0) | creative(X0)) <=> (happy(X0) <~> ~old(X0))) [input p14]
16. ~rich(fred) <~> ~brave(fred) [input p15]
24. ~happy(alice) [input hypothesis]
40. ! [X0] : ((((rich(X0) | strong(X0)) & (~rich(X0) | ~strong(X0))) | (~patient(X0) & strong(X0))) & ((patient(X0) | ~strong(X0)) | ((~strong(X0) | rich(X0)) & (~rich(X0) | strong(X0))))) [nnf transformation 4]
41. ! [X0] : ((((rich(X0) | strong(X0)) & (~rich(X0) | ~strong(X0))) | (~patient(X0) & strong(X0))) & (patient(X0) | ~strong(X0) | ((~strong(X0) | rich(X0)) & (~rich(X0) | strong(X0))))) [flattening 40]
48. ! [X0] : (((~creative(X0) | ~generous(X0)) | (humble(X0) | ~creative(X0))) & ((~humble(X0) & creative(X0)) | (creative(X0) & generous(X0)))) [nnf transformation 8]
49. ! [X0] : ((~creative(X0) | ~generous(X0) | humble(X0) | ~creative(X0)) & ((~humble(X0) & creative(X0)) | (creative(X0) & generous(X0)))) [flattening 48]
57. (? [X0] : (funny(X0) | patient(X0)) | strong(fred)) & (~strong(fred) | ! [X0] : (~funny(X0) & ~patient(X0))) [nnf transformation 12]
58. (? [X0] : (funny(X0) | patient(X0)) | strong(fred)) & (~strong(fred) | ! [X1] : (~funny(X1) & ~patient(X1))) [rectify 57]
59. ? [X0] : (funny(X0) | patient(X0)) => (funny(sK5) | patient(sK5)) [choice axiom]
60. ((funny(sK5) | patient(sK5)) | strong(fred)) & (~strong(fred) | ! [X1] : (~funny(X1) & ~patient(X1))) [skolemisation 58,59]
62. (? [X0] : ~old(X0) | ~brave(fred)) & (brave(fred) | ! [X0] : old(X0)) [nnf transformation 14]
63. (? [X0] : ~old(X0) | ~brave(fred)) & (brave(fred) | ! [X1] : old(X1)) [rectify 62]
64. ? [X0] : ~old(X0) => ~old(sK6) [choice axiom]
65. (~old(sK6) | ~brave(fred)) & (brave(fred) | ! [X1] : old(X1)) [skolemisation 63,64]
66. ! [X0] : (((generous(X0) | creative(X0)) | ((happy(X0) | old(X0)) & (~old(X0) | ~happy(X0)))) & (((old(X0) | ~happy(X0)) & (~old(X0) | happy(X0))) | (~generous(X0) & ~creative(X0)))) [nnf transformation 15]
67. ! [X0] : ((generous(X0) | creative(X0) | ((happy(X0) | old(X0)) & (~old(X0) | ~happy(X0)))) & (((old(X0) | ~happy(X0)) & (~old(X0) | happy(X0))) | (~generous(X0) & ~creative(X0)))) [flattening 66]
68. (brave(fred) | rich(fred)) & (~brave(fred) | ~rich(fred)) [nnf transformation 16]
84. patient(X0) | ~strong(X0) | ~strong(X0) | rich(X0) [cnf transformation 41]
87. rich(X0) | strong(X0) | strong(X0) [cnf transformation 41]
102. creative(X0) | creative(X0) [cnf transformation 49]
111. ~strong(fred) | ~patient(X1) [cnf transformation 60]
116. brave(fred) | old(X1) [cnf transformation 65]
118. ~old(X0) | happy(X0) | ~creative(X0) [cnf transformation 67]
124. ~brave(fred) | ~rich(fred) [cnf transformation 68]
136. ~happy(alice) [cnf transformation 24]
137. creative(X0) [duplicate literal removal 102]
139. patient(X0) | ~strong(X0) | rich(X0) [duplicate literal removal 84]
140. rich(X0) | strong(X0) [duplicate literal removal 87]
151. 3 <=> ! [X1] : creative(X1) [avatar definition]
152. creative(X1) <- (3) [avatar component clause 151]
171. patient(X0) | rich(X0) [subsumption resolution 139,140]
177. 9 <=> rich(fred) [avatar definition]
178. ~rich(fred) <- (~9) [avatar component clause 177]
186. 3 [avatar split clause 137,151]
218. 18 <=> strong(fred) [avatar definition]
235. 22 <=> ! [X1] : ~patient(X1) [avatar definition]
236. ~patient(X1) <- (22) [avatar component clause 235]
237. 22 | ~18 [avatar split clause 111,218,235]
239. 23 <=> brave(fred) [avatar definition]
248. 25 <=> ! [X1] : old(X1) [avatar definition]
249. old(X1) <- (25) [avatar component clause 248]
250. 25 | 23 [avatar split clause 116,239,248]
252. ~9 | ~23 [avatar split clause 124,239,177]
309. strong(fred) <- (~9) [resolution 140,178]
312. 18 | 9 [avatar split clause 309,177,218]
318. rich(X0) <- (22) [resolution 171,236]
321. $false <- (~9, 22) [resolution 318,178]
322. 9 | ~22 [avatar contradiction clause 321]
345. happy(X0) | ~creative(X0) <- (25) [resolution 118,249]
346. happy(X0) <- (3, 25) [subsumption resolution 345,152]
348. $false <- (3, 25) [resolution 346,136]
351. ~3 | ~25 [avatar contradiction clause 348]
354. $false [avatar sat refutation 186,237,250,252,312,322,351]
% SZS output end Proof for 5676541964665822355250782
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either kind or not tall then john is both tall and calm.
If someone is not brave then someone is both not happy and calm and vice versa.
Everyone who is not humble or brave is either not funny or not brave.
Everyone who is old or kind is funny and vice versa.
Everyone who is both rich and not tall is not funny or kind and vice versa.
Everyone who is both not old and rich is both not rich and not curious.
If mary is both not calm and creative then susan is brave or curious and vice versa.
Everyone who is either not tall or generous is not generous or creative.
Everyone who is either not humble or funny is strong.
Everyone who is either brave or generous is both brave and quiet.
Everyone who is funny is either humble or tall.
If mary is either not kind or not creative then john is both not creative and not generous and vice versa.
If someone is both not funny and curious then lucy is both not creative and not happy and vice versa.
Everyone who is not curious or brave is not patient or not generous.
Mary is either patient or funny.
Someone is old or strong.
Alice is calm or not creative.
Someone is both creative and strong. | Mary is strong. | neutral | ((?[X]:((kind(X)<~>~tall(X))))=>((tall(john)&calm(john))))&
((?[X]:(~brave(X)))<=>(?[X]:((~happy(X)&calm(X)))))&
(![X]:((~humble(X)|brave(X))=>(~funny(X)<~>~brave(X))))&
(![X]:((old(X)|kind(X))<=>funny(X)))&
(![X]:((rich(X)&~tall(X))<=>(~funny(X)|kind(X))))&
(![X]:((~old(X)&rich(X))=>(~rich(X)&~curious(X))))&
(((~calm(mary)&creative(mary)))<=>((brave(susan)|curious(susan))))&
(![X]:((~tall(X)<~>generous(X))=>(~generous(X)|creative(X))))&
(![X]:((~humble(X)<~>funny(X))=>strong(X)))&
(![X]:((brave(X)<~>generous(X))=>(brave(X)&quiet(X))))&
(![X]:(funny(X)=>(humble(X)<~>tall(X))))&
(((~kind(mary)<~>~creative(mary)))<=>((~creative(john)&~generous(john))))&
((?[X]:((~funny(X)&curious(X))))<=>((~creative(lucy)&~happy(lucy))))&
(![X]:((~curious(X)|brave(X))=>(~patient(X)|~generous(X))))&
((patient(mary)<~>funny(mary)))&
(?[X]:((old(X)|strong(X))))&
((calm(alice)|~creative(alice)))&
(?[X]:((creative(X)&strong(X)))) | strong(mary) | [] | null | 0 |
Everyone who is not humble is not quiet. If john is funny or not creative then john is both happy and curious and vice versa. If someone is either strong or tall then alice is both not quiet and not old. If lucy is not creative or rich then john is not tall or not kind and vice versa. If susan is either not humble or wise then alice is calm and vice versa. If someone is not strong or tall then alice is either not rich or not creative. Everyone who is both not strong and rich is not quiet or not creative and vice versa. If someone is curious or not calm then someone is not old. If someone is happy then susan is old or tall. If john is quiet then mary is not generous or tall. Everyone who is both humble and tall is brave and vice versa. Everyone who is both not patient and tall is either curious or brave and vice versa. Everyone who is either not curious or not old is either happy or not strong. If john is both not old and patient then fred is generous or not generous and vice versa. Everyone who is either not funny or funny is not kind. If lucy is not curious then someone is not calm and vice versa. Susan is both not funny and not old. Someone is not wise or not funny. Alice is both not patient and not kind. Someone is calm. Someone is not brave. Paul is both not generous and patient. John is not tall. Someone is not funny or brave. | Mary is not kind. | entailment | (![X]:(~humble(X)=>~quiet(X)))&
(((funny(john)|~creative(john)))<=>((happy(john)&curious(john))))&
((?[X]:((strong(X)<~>tall(X))))=>((~quiet(alice)&~old(alice))))&
(((~creative(lucy)|rich(lucy)))<=>((~tall(john)|~kind(john))))&
(((~humble(susan)<~>wise(susan)))<=>(calm(alice)))&
((?[X]:((~strong(X)|tall(X))))=>((~rich(alice)<~>~creative(alice))))&
(![X]:((~strong(X)&rich(X))<=>(~quiet(X)|~creative(X))))&
((?[X]:((curious(X)|~calm(X))))=>(?[X]:(~old(X))))&
((?[X]:(happy(X)))=>((old(susan)|tall(susan))))&
((quiet(john))=>((~generous(mary)|tall(mary))))&
(![X]:((humble(X)&tall(X))<=>brave(X)))&
(![X]:((~patient(X)&tall(X))<=>(curious(X)<~>brave(X))))&
(![X]:((~curious(X)<~>~old(X))=>(happy(X)<~>~strong(X))))&
(((~old(john)&patient(john)))<=>((generous(fred)|~generous(fred))))&
(![X]:((~funny(X)<~>funny(X))=>~kind(X)))&
((~curious(lucy))<=>(?[X]:(~calm(X))))&
((~funny(susan)&~old(susan)))&
(?[X]:((~wise(X)|~funny(X))))&
((~patient(alice)&~kind(alice)))&
(?[X]:(calm(X)))&
(?[X]:(~brave(X)))&
((~generous(paul)&patient(paul)))&
(~tall(john))&
(?[X]:((~funny(X)|brave(X)))) | ~kind(mary) | [
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3871584996133552711574320
% SZS output start Proof for 3871584996133552711574320
15. ! [X0] : ((~funny(X0) <~> funny(X0)) => ~kind(X0)) [input p14]
25. kind(mary) [input hypothesis]
36. ! [X0] : (~kind(X0) | (~funny(X0) <=> funny(X0))) [ennf transformation 15]
56. ! [X0] : (~kind(X0) | ((~funny(X0) | ~funny(X0)) & (funny(X0) | funny(X0)))) [nnf transformation 36]
118. ~kind(X0) | funny(X0) | funny(X0) [cnf transformation 56]
119. ~kind(X0) | ~funny(X0) | ~funny(X0) [cnf transformation 56]
133. kind(mary) [cnf transformation 25]
134. ~kind(X0) | funny(X0) [duplicate literal removal 118]
135. ~kind(X0) | ~funny(X0) [duplicate literal removal 119]
284. ~kind(X0) [subsumption resolution 134,135]
315. $false [subsumption resolution 133,284]
% SZS output end Proof for 3871584996133552711574320
% ------------------------------
% 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 both calm and rich then fred is either rich or not brave.
If lucy is both wise and quiet then paul is both strong and not tall.
Everyone who is either not strong or brave is curious or generous and vice versa.
If susan is patient or quiet then john is either not humble or not happy.
Everyone who is not creative or quiet is both curious and not creative.
Everyone who is either patient or strong is both not kind and creative and vice versa.
If someone is either not strong or patient then someone is strong or wise and vice versa.
Everyone who is either happy or not creative is either tall or brave.
If mary is generous or not curious then john is either not generous or curious.
Everyone who is strong or not generous is either not humble or not generous and vice versa.
Everyone who is both not humble and not wise is both not wise and not rich and vice versa.
Everyone who is not brave is quiet or kind.
Everyone who is brave is not strong and vice versa.
If someone is brave then someone is both not wise and funny and vice versa.
Everyone who is both patient and kind is both rich and wise and vice versa.
Everyone who is not brave or brave is brave or not creative and vice versa.
Paul is not strong.
Someone is either creative or not funny.
Someone is happy or creative.
Paul is both creative and not tall.
Alice is rich or strong.
Someone is either generous or patient. | Alice is creative. | entailment | (((calm(john)&rich(john)))=>((rich(fred)<~>~brave(fred))))&
(((wise(lucy)&quiet(lucy)))=>((strong(paul)&~tall(paul))))&
(![X]:((~strong(X)<~>brave(X))<=>(curious(X)|generous(X))))&
(((patient(susan)|quiet(susan)))=>((~humble(john)<~>~happy(john))))&
(![X]:((~creative(X)|quiet(X))=>(curious(X)&~creative(X))))&
(![X]:((patient(X)<~>strong(X))<=>(~kind(X)&creative(X))))&
((?[X]:((~strong(X)<~>patient(X))))<=>(?[X]:((strong(X)|wise(X)))))&
(![X]:((happy(X)<~>~creative(X))=>(tall(X)<~>brave(X))))&
(((generous(mary)|~curious(mary)))=>((~generous(john)<~>curious(john))))&
(![X]:((strong(X)|~generous(X))<=>(~humble(X)<~>~generous(X))))&
(![X]:((~humble(X)&~wise(X))<=>(~wise(X)&~rich(X))))&
(![X]:(~brave(X)=>(quiet(X)|kind(X))))&
(![X]:(brave(X)<=>~strong(X)))&
((?[X]:(brave(X)))<=>(?[X]:((~wise(X)&funny(X)))))&
(![X]:((patient(X)&kind(X))<=>(rich(X)&wise(X))))&
(![X]:((~brave(X)|brave(X))<=>(brave(X)|~creative(X))))&
(~strong(paul))&
(?[X]:((creative(X)<~>~funny(X))))&
(?[X]:((happy(X)|creative(X))))&
((creative(paul)&~tall(paul)))&
((rich(alice)|strong(alice)))&
(?[X]:((generous(X)<~>patient(X)))) | creative(alice) | [
"p2",
"p4",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 821916898739788009739667
% SZS output start Proof for 821916898739788009739667
3. ! [X0] : ((~strong(X0) <~> brave(X0)) <=> (generous(X0) | curious(X0))) [input p2]
5. ! [X0] : ((quiet(X0) | ~creative(X0)) => (~creative(X0) & curious(X0))) [input p4]
13. ! [X0] : (brave(X0) <=> ~strong(X0)) [input p12]
23. ~creative(alice) [input hypothesis]
30. ! [X0] : ((~creative(X0) & curious(X0)) | (~quiet(X0) & creative(X0))) [ennf transformation 5]
35. ! [X0] : ((((~brave(X0) | strong(X0)) & (brave(X0) | ~strong(X0))) | (~generous(X0) & ~curious(X0))) & ((generous(X0) | curious(X0)) | ((~strong(X0) | ~brave(X0)) & (brave(X0) | strong(X0))))) [nnf transformation 3]
36. ! [X0] : ((((~brave(X0) | strong(X0)) & (brave(X0) | ~strong(X0))) | (~generous(X0) & ~curious(X0))) & (generous(X0) | curious(X0) | ((~strong(X0) | ~brave(X0)) & (brave(X0) | strong(X0))))) [flattening 35]
51. ! [X0] : ((brave(X0) | strong(X0)) & (~strong(X0) | ~brave(X0))) [nnf transformation 13]
73. ~curious(X0) | ~strong(X0) | brave(X0) [cnf transformation 36]
75. ~curious(X0) | strong(X0) | ~brave(X0) [cnf transformation 36]
81. creative(X0) | curious(X0) [cnf transformation 30]
116. ~strong(X0) | ~brave(X0) [cnf transformation 51]
117. strong(X0) | brave(X0) [cnf transformation 51]
138. ~creative(alice) [cnf transformation 23]
282. 31 <=> strong(alice) [avatar definition]
284. strong(alice) <- (31) [avatar component clause 282]
296. curious(alice) [resolution 81,138]
316. ~strong(alice) | brave(alice) [resolution 73,296]
318. brave(alice) [subsumption resolution 316,117]
322. strong(alice) | ~brave(alice) [resolution 75,296]
324. strong(alice) [subsumption resolution 322,318]
325. 31 [avatar split clause 324,282]
327. ~brave(alice) <- (31) [resolution 284,116]
328. $false <- (31) [subsumption resolution 327,318]
329. ~31 [avatar contradiction clause 328]
330. $false [avatar sat refutation 325,329]
% SZS output end Proof for 821916898739788009739667
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not generous or kind is either not curious or tall. If someone is not kind or not patient then someone is either calm or not curious and vice versa. If fred is both not kind and creative then john is not wise or not curious and vice versa. Everyone who is tall is not tall or not wise and vice versa. If someone is both not quiet and not strong then mary is either not funny or not calm and vice versa. Everyone who is not generous is not creative or wise. If someone is either calm or not quiet then someone is both kind and not generous and vice versa. Everyone who is either happy or quiet is both brave and quiet. If susan is either not funny or happy then someone is either not humble or curious and vice versa. Everyone who is both not creative and not brave is both not happy and not wise. If lucy is not old then someone is not rich or creative and vice versa. If john is both wise and not patient then someone is either not patient or wise and vice versa. If susan is funny then someone is not creative or strong. Everyone who is not funny is either curious or not humble and vice versa. Everyone who is either patient or not creative is not calm or tall and vice versa. Someone is not quiet or not curious. Fred is rich. Alice is either humble or not strong. Someone is both kind and not brave. Someone is patient or not strong. Someone is rich. Someone is either not brave or funny. Someone is not calm. | Susan is wise. | contradiction | (![X]:((~generous(X)<~>kind(X))=>(~curious(X)<~>tall(X))))&
((?[X]:((~kind(X)|~patient(X))))<=>(?[X]:((calm(X)<~>~curious(X)))))&
(((~kind(fred)&creative(fred)))<=>((~wise(john)|~curious(john))))&
(![X]:(tall(X)<=>(~tall(X)|~wise(X))))&
((?[X]:((~quiet(X)&~strong(X))))<=>((~funny(mary)<~>~calm(mary))))&
(![X]:(~generous(X)=>(~creative(X)|wise(X))))&
((?[X]:((calm(X)<~>~quiet(X))))<=>(?[X]:((kind(X)&~generous(X)))))&
(![X]:((happy(X)<~>quiet(X))=>(brave(X)&quiet(X))))&
(((~funny(susan)<~>happy(susan)))<=>(?[X]:((~humble(X)<~>curious(X)))))&
(![X]:((~creative(X)&~brave(X))=>(~happy(X)&~wise(X))))&
((~old(lucy))<=>(?[X]:((~rich(X)|creative(X)))))&
(((wise(john)&~patient(john)))<=>(?[X]:((~patient(X)<~>wise(X)))))&
((funny(susan))=>(?[X]:((~creative(X)|strong(X)))))&
(![X]:(~funny(X)<=>(curious(X)<~>~humble(X))))&
(![X]:((patient(X)<~>~creative(X))<=>(~calm(X)|tall(X))))&
(?[X]:((~quiet(X)|~curious(X))))&
(rich(fred))&
((humble(alice)<~>~strong(alice)))&
(?[X]:((kind(X)&~brave(X))))&
(?[X]:((patient(X)|~strong(X))))&
(?[X]:(rich(X)))&
(?[X]:((~brave(X)<~>funny(X))))&
(?[X]:(~calm(X))) | wise(susan) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 3015442047263471508453543
% SZS output start Proof for 3015442047263471508453543
4. ! [X0] : (tall(X0) <=> (~wise(X0) | ~tall(X0))) [input p3]
24. wise(susan) [input hypothesis]
42. ! [X0] : ((tall(X0) | (wise(X0) & tall(X0))) & ((~wise(X0) | ~tall(X0)) | ~tall(X0))) [nnf transformation 4]
43. ! [X0] : ((tall(X0) | (wise(X0) & tall(X0))) & (~wise(X0) | ~tall(X0) | ~tall(X0))) [flattening 42]
101. ~wise(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 43]
102. tall(X0) | tall(X0) [cnf transformation 43]
162. wise(susan) [cnf transformation 24]
164. ~wise(X0) | ~tall(X0) [duplicate literal removal 101]
165. tall(X0) [duplicate literal removal 102]
221. ~wise(X0) [subsumption resolution 164,165]
388. $false [subsumption resolution 162,221]
% SZS output end Proof for 3015442047263471508453543
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not wise or not kind then someone is both quiet and calm.
If fred is not generous or quiet then someone is either not strong or calm and vice versa.
If someone is not generous then someone is both not curious and calm and vice versa.
Everyone who is generous is not curious and vice versa.
Everyone who is not old or not rich is old or not generous.
Everyone who is not calm or curious is calm.
If someone is creative then someone is either calm or not generous and vice versa.
Everyone who is tall or not generous is not calm or brave.
Everyone who is both curious and kind is both tall and not wise and vice versa.
If mary is not curious or brave then alice is either curious or creative and vice versa.
Everyone who is either quiet or not funny is both not patient and strong and vice versa.
Everyone who is strong is either not quiet or not curious.
Everyone who is not patient or not tall is patient and vice versa.
If someone is not strong then someone is both patient and not calm and vice versa.
Everyone who is either funny or quiet is both not rich and wise and vice versa.
If someone is both wise and not curious then someone is patient.
Someone is not rich.
Alice is funny or not creative.
Someone is not generous.
Paul is both strong and old.
Lucy is quiet. | Mary is creative. | neutral | ((?[X]:((~wise(X)|~kind(X))))=>(?[X]:((quiet(X)&calm(X)))))&
(((~generous(fred)|quiet(fred)))<=>(?[X]:((~strong(X)<~>calm(X)))))&
((?[X]:(~generous(X)))<=>(?[X]:((~curious(X)&calm(X)))))&
(![X]:(generous(X)<=>~curious(X)))&
(![X]:((~old(X)|~rich(X))=>(old(X)|~generous(X))))&
(![X]:((~calm(X)|curious(X))=>calm(X)))&
((?[X]:(creative(X)))<=>(?[X]:((calm(X)<~>~generous(X)))))&
(![X]:((tall(X)|~generous(X))=>(~calm(X)|brave(X))))&
(![X]:((curious(X)&kind(X))<=>(tall(X)&~wise(X))))&
(((~curious(mary)|brave(mary)))<=>((curious(alice)<~>creative(alice))))&
(![X]:((quiet(X)<~>~funny(X))<=>(~patient(X)&strong(X))))&
(![X]:(strong(X)=>(~quiet(X)<~>~curious(X))))&
(![X]:((~patient(X)|~tall(X))<=>patient(X)))&
((?[X]:(~strong(X)))<=>(?[X]:((patient(X)&~calm(X)))))&
(![X]:((funny(X)<~>quiet(X))<=>(~rich(X)&wise(X))))&
((?[X]:((wise(X)&~curious(X))))=>(?[X]:(patient(X))))&
(?[X]:(~rich(X)))&
((funny(alice)|~creative(alice)))&
(?[X]:(~generous(X)))&
((strong(paul)&old(paul)))&
(quiet(lucy)) | creative(mary) | [] | null | 0 |
Everyone who is generous is both not happy and not patient and vice versa.
If someone is either wise or not quiet then fred is both tall and calm and vice versa.
If alice is either not quiet or not old then someone is both rich and not calm and vice versa.
Everyone who is both curious and not humble is either kind or not happy and vice versa.
Everyone who is not kind or tall is humble or not rich and vice versa.
If someone is not brave then paul is both not rich and humble and vice versa.
Everyone who is either not calm or not tall is not brave.
If someone is not humble or funny then lucy is not kind or wise.
If someone is both not wise and generous then someone is not kind and vice versa.
Everyone who is either not brave or not tall is either happy or not wise.
Everyone who is either rich or not funny is both creative and rich and vice versa.
If susan is both patient and not patient then someone is patient and vice versa.
If someone is generous then paul is creative or not funny.
If susan is both rich and old then paul is either generous or not humble.
Everyone who is not patient is not curious or not patient and vice versa.
If someone is not brave then susan is either generous or not quiet and vice versa.
Paul is calm or not happy.
Alice is both not curious and not rich.
Someone is not quiet.
Mary is brave or quiet.
Someone is both calm and humble.
Lucy is not rich. | Alice is not curious. | entailment | (![X]:(generous(X)<=>(~happy(X)&~patient(X))))&
((?[X]:((wise(X)<~>~quiet(X))))<=>((tall(fred)&calm(fred))))&
(((~quiet(alice)<~>~old(alice)))<=>(?[X]:((rich(X)&~calm(X)))))&
(![X]:((curious(X)&~humble(X))<=>(kind(X)<~>~happy(X))))&
(![X]:((~kind(X)|tall(X))<=>(humble(X)|~rich(X))))&
((?[X]:(~brave(X)))<=>((~rich(paul)&humble(paul))))&
(![X]:((~calm(X)<~>~tall(X))=>~brave(X)))&
((?[X]:((~humble(X)|funny(X))))=>((~kind(lucy)|wise(lucy))))&
((?[X]:((~wise(X)&generous(X))))<=>(?[X]:(~kind(X))))&
(![X]:((~brave(X)<~>~tall(X))=>(happy(X)<~>~wise(X))))&
(![X]:((rich(X)<~>~funny(X))<=>(creative(X)&rich(X))))&
(((patient(susan)&~patient(susan)))<=>(?[X]:(patient(X))))&
((?[X]:(generous(X)))=>((creative(paul)|~funny(paul))))&
(((rich(susan)&old(susan)))=>((generous(paul)<~>~humble(paul))))&
(![X]:(~patient(X)<=>(~curious(X)|~patient(X))))&
((?[X]:(~brave(X)))<=>((generous(susan)<~>~quiet(susan))))&
((calm(paul)|~happy(paul)))&
((~curious(alice)&~rich(alice)))&
(?[X]:(~quiet(X)))&
((brave(mary)|quiet(mary)))&
(?[X]:((calm(X)&humble(X))))&
(~rich(lucy)) | ~curious(alice) | [
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 7192026612568952630348358
% SZS output start Proof for 7192026612568952630348358
18. ~rich(alice) & ~curious(alice) [input p17]
23. curious(alice) [input hypothesis]
137. ~curious(alice) [cnf transformation 18]
144. curious(alice) [cnf transformation 23]
324. $false [subsumption resolution 144,137]
% SZS output end Proof for 7192026612568952630348358
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If susan is both not rich and not tall then someone is both not rich and not creative.
If someone is not humble or patient then john is either not rich or old and vice versa.
Everyone who is not brave is both not happy and rich and vice versa.
Everyone who is either not generous or old is either creative or not humble.
Everyone who is both tall and rich is patient or not patient and vice versa.
If paul is either humble or not wise then john is quiet.
Everyone who is not happy is both not funny and not happy.
Everyone who is either not wise or kind is not wise or not calm and vice versa.
Everyone who is either not humble or wise is generous or not kind.
Everyone who is both not calm and funny is not rich or not creative.
If mary is either quiet or not happy then mary is either patient or not patient.
Everyone who is not brave or generous is either not calm or not old and vice versa.
If someone is both not funny and not curious then someone is either generous or not humble and vice versa.
If someone is both kind and not strong then susan is both not kind and old.
Everyone who is both kind and not patient is either not quiet or not wise and vice versa.
Everyone who is not wise or kind is either humble or funny.
Someone is both wise and happy.
Paul is both not calm and not patient.
Paul is old or not strong.
Mary is both not kind and funny.
Paul is either creative or not brave.
Lucy is patient or not quiet.
Alice is not old or funny. | Susan is not quiet. | neutral | (((~rich(susan)&~tall(susan)))=>(?[X]:((~rich(X)&~creative(X)))))&
((?[X]:((~humble(X)|patient(X))))<=>((~rich(john)<~>old(john))))&
(![X]:(~brave(X)<=>(~happy(X)&rich(X))))&
(![X]:((~generous(X)<~>old(X))=>(creative(X)<~>~humble(X))))&
(![X]:((tall(X)&rich(X))<=>(patient(X)|~patient(X))))&
(((humble(paul)<~>~wise(paul)))=>(quiet(john)))&
(![X]:(~happy(X)=>(~funny(X)&~happy(X))))&
(![X]:((~wise(X)<~>kind(X))<=>(~wise(X)|~calm(X))))&
(![X]:((~humble(X)<~>wise(X))=>(generous(X)|~kind(X))))&
(![X]:((~calm(X)&funny(X))=>(~rich(X)|~creative(X))))&
(((quiet(mary)<~>~happy(mary)))=>((patient(mary)<~>~patient(mary))))&
(![X]:((~brave(X)|generous(X))<=>(~calm(X)<~>~old(X))))&
((?[X]:((~funny(X)&~curious(X))))<=>(?[X]:((generous(X)<~>~humble(X)))))&
((?[X]:((kind(X)&~strong(X))))=>((~kind(susan)&old(susan))))&
(![X]:((kind(X)&~patient(X))<=>(~quiet(X)<~>~wise(X))))&
(![X]:((~wise(X)|kind(X))=>(humble(X)<~>funny(X))))&
(?[X]:((wise(X)&happy(X))))&
((~calm(paul)&~patient(paul)))&
((old(paul)|~strong(paul)))&
((~kind(mary)&funny(mary)))&
((creative(paul)<~>~brave(paul)))&
((patient(lucy)|~quiet(lucy)))&
((~old(alice)|funny(alice))) | ~quiet(susan) | [] | null | 0 |
If someone is either not calm or creative then alice is both quiet and tall. Everyone who is not quiet or not rich is not calm. If alice is either quiet or not tall then john is either not old or creative. If someone is curious then mary is happy or patient and vice versa. Everyone who is both not calm and kind is not generous or curious and vice versa. Everyone who is calm is either not rich or not kind. Everyone who is not wise is creative and vice versa. Everyone who is both not happy and not kind is not generous or not creative. Everyone who is both rich and kind is either calm or not wise. Everyone who is brave is both not patient and not rich. Everyone who is both not tall and not old is not quiet or not kind. Everyone who is both brave and old is funny or rich. If alice is both not happy and wise then someone is not rich and vice versa. Everyone who is not quiet or generous is quiet and vice versa. If someone is brave or not wise then alice is not brave. Everyone who is both not wise and tall is either curious or not kind and vice versa. Someone is either not kind or rich. Mary is not curious or not funny. Someone is not kind or creative. John is patient or old. Someone is calm or rich. Someone is curious. John is either humble or brave. | Alice is tall. | entailment | ((?[X]:((~calm(X)<~>creative(X))))=>((quiet(alice)&tall(alice))))&
(![X]:((~quiet(X)|~rich(X))=>~calm(X)))&
(((quiet(alice)<~>~tall(alice)))=>((~old(john)<~>creative(john))))&
((?[X]:(curious(X)))<=>((happy(mary)|patient(mary))))&
(![X]:((~calm(X)&kind(X))<=>(~generous(X)|curious(X))))&
(![X]:(calm(X)=>(~rich(X)<~>~kind(X))))&
(![X]:(~wise(X)<=>creative(X)))&
(![X]:((~happy(X)&~kind(X))=>(~generous(X)|~creative(X))))&
(![X]:((rich(X)&kind(X))=>(calm(X)<~>~wise(X))))&
(![X]:(brave(X)=>(~patient(X)&~rich(X))))&
(![X]:((~tall(X)&~old(X))=>(~quiet(X)|~kind(X))))&
(![X]:((brave(X)&old(X))=>(funny(X)|rich(X))))&
(((~happy(alice)&wise(alice)))<=>(?[X]:(~rich(X))))&
(![X]:((~quiet(X)|generous(X))<=>quiet(X)))&
((?[X]:((brave(X)|~wise(X))))=>(~brave(alice)))&
(![X]:((~wise(X)&tall(X))<=>(curious(X)<~>~kind(X))))&
(?[X]:((~kind(X)<~>rich(X))))&
((~curious(mary)|~funny(mary)))&
(?[X]:((~kind(X)|creative(X))))&
((patient(john)|old(john)))&
(?[X]:((calm(X)|rich(X))))&
(?[X]:(curious(X)))&
((humble(john)<~>brave(john))) | tall(alice) | [
"p1",
"p4",
"p5",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 139403284322624060241219
% SZS output start Proof for 139403284322624060241219
2. ! [X0] : ((~rich(X0) | ~quiet(X0)) => ~calm(X0)) [input p1]
5. ! [X0] : ((kind(X0) & ~calm(X0)) <=> (curious(X0) | ~generous(X0))) [input p4]
6. ! [X0] : (calm(X0) => (~rich(X0) <~> ~kind(X0))) [input p5]
14. ! [X0] : ((generous(X0) | ~quiet(X0)) <=> quiet(X0)) [input p13]
16. ! [X0] : ((tall(X0) & ~wise(X0)) <=> (curious(X0) <~> ~kind(X0))) [input p15]
24. ~tall(alice) [input hypothesis]
26. ! [X0] : (~calm(X0) | (rich(X0) & quiet(X0))) [ennf transformation 2]
28. ! [X0] : ((~rich(X0) <~> ~kind(X0)) | ~calm(X0)) [ennf transformation 6]
46. ! [X0] : (((kind(X0) & ~calm(X0)) | (~curious(X0) & generous(X0))) & ((curious(X0) | ~generous(X0)) | (~kind(X0) | calm(X0)))) [nnf transformation 5]
47. ! [X0] : (((kind(X0) & ~calm(X0)) | (~curious(X0) & generous(X0))) & (curious(X0) | ~generous(X0) | ~kind(X0) | calm(X0))) [flattening 46]
48. ! [X0] : (((kind(X0) | rich(X0)) & (~kind(X0) | ~rich(X0))) | ~calm(X0)) [nnf transformation 28]
56. ! [X0] : (((generous(X0) | ~quiet(X0)) | ~quiet(X0)) & (quiet(X0) | (~generous(X0) & quiet(X0)))) [nnf transformation 14]
57. ! [X0] : ((generous(X0) | ~quiet(X0) | ~quiet(X0)) & (quiet(X0) | (~generous(X0) & quiet(X0)))) [flattening 56]
58. ! [X0] : (((tall(X0) & ~wise(X0)) | ((curious(X0) | kind(X0)) & (~kind(X0) | ~curious(X0)))) & (((kind(X0) | ~curious(X0)) & (~kind(X0) | curious(X0))) | (~tall(X0) | wise(X0)))) [nnf transformation 16]
59. ! [X0] : (((tall(X0) & ~wise(X0)) | ((curious(X0) | kind(X0)) & (~kind(X0) | ~curious(X0)))) & (((kind(X0) | ~curious(X0)) & (~kind(X0) | curious(X0))) | ~tall(X0) | wise(X0))) [flattening 58]
75. ~calm(X0) | rich(X0) [cnf transformation 26]
83. ~generous(X0) | curious(X0) | ~kind(X0) | calm(X0) [cnf transformation 47]
87. ~curious(X0) | kind(X0) [cnf transformation 47]
88. ~kind(X0) | ~rich(X0) | ~calm(X0) [cnf transformation 48]
102. quiet(X0) | quiet(X0) [cnf transformation 57]
104. generous(X0) | ~quiet(X0) | ~quiet(X0) [cnf transformation 57]
111. tall(X0) | ~kind(X0) | ~curious(X0) [cnf transformation 59]
112. tall(X0) | curious(X0) | kind(X0) [cnf transformation 59]
122. ~tall(alice) [cnf transformation 24]
123. quiet(X0) [duplicate literal removal 102]
124. ~quiet(X0) | generous(X0) [duplicate literal removal 104]
129. 2 <=> tall(alice) [avatar definition]
130. ~tall(alice) <- (~2) [avatar component clause 129]
173. ~kind(X0) | ~calm(X0) [subsumption resolution 88,75]
207. kind(X0) | tall(X0) [subsumption resolution 112,87]
208. ~curious(X0) | tall(X0) [subsumption resolution 111,87]
255. ~2 [avatar split clause 122,129]
265. generous(X0) [resolution 124,123]
312. curious(X0) | ~kind(X0) | calm(X0) [resolution 83,265]
314. ~kind(X0) | curious(X0) [subsumption resolution 312,173]
357. curious(X1) | tall(X1) [resolution 314,207]
362. tall(X1) [subsumption resolution 357,208]
379. $false <- (~2) [resolution 362,130]
382. 2 [avatar contradiction clause 379]
383. $false [avatar sat refutation 255,382]
% SZS output end Proof for 139403284322624060241219
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not old or tall then susan is both humble and not quiet. Everyone who is either kind or not strong is humble or not rich and vice versa. Everyone who is either generous or not calm is both not curious and not old and vice versa. If paul is both kind and creative then fred is not calm. Everyone who is either happy or creative is either not old or not curious and vice versa. Everyone who is both rich and not wise is both not rich and not calm and vice versa. If paul is not generous then susan is not creative and vice versa. Everyone who is kind is not strong and vice versa. If someone is either kind or curious then fred is tall and vice versa. If someone is both not brave and rich then alice is either not brave or not happy and vice versa. Everyone who is rich is either not brave or old and vice versa. If someone is not generous or not funny then someone is either quiet or tall. If someone is either not kind or old then someone is not creative or creative. Everyone who is either quiet or funny is both happy and humble. Everyone who is not strong is both not strong and brave and vice versa. Lucy is either not tall or curious. John is not calm or not creative. John is happy. Someone is not quiet or not creative. Fred is creative or not rich. Paul is either wise or happy. Susan is not patient. | Lucy is not brave. | contradiction | ((?[X]:((~old(X)|tall(X))))=>((humble(susan)&~quiet(susan))))&
(![X]:((kind(X)<~>~strong(X))<=>(humble(X)|~rich(X))))&
(![X]:((generous(X)<~>~calm(X))<=>(~curious(X)&~old(X))))&
(((kind(paul)&creative(paul)))=>(~calm(fred)))&
(![X]:((happy(X)<~>creative(X))<=>(~old(X)<~>~curious(X))))&
(![X]:((rich(X)&~wise(X))<=>(~rich(X)&~calm(X))))&
((~generous(paul))<=>(~creative(susan)))&
(![X]:(kind(X)<=>~strong(X)))&
((?[X]:((kind(X)<~>curious(X))))<=>(tall(fred)))&
((?[X]:((~brave(X)&rich(X))))<=>((~brave(alice)<~>~happy(alice))))&
(![X]:(rich(X)<=>(~brave(X)<~>old(X))))&
((?[X]:((~generous(X)|~funny(X))))=>(?[X]:((quiet(X)<~>tall(X)))))&
((?[X]:((~kind(X)<~>old(X))))=>(?[X]:((~creative(X)|creative(X)))))&
(![X]:((quiet(X)<~>funny(X))=>(happy(X)&humble(X))))&
(![X]:(~strong(X)<=>(~strong(X)&brave(X))))&
((~tall(lucy)<~>curious(lucy)))&
((~calm(john)|~creative(john)))&
(happy(john))&
(?[X]:((~quiet(X)|~creative(X))))&
((creative(fred)|~rich(fred)))&
((wise(paul)<~>happy(paul)))&
(~patient(susan)) | ~brave(lucy) | [
"p0",
"p1",
"p7",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5552398847894812179881582
% SZS output start Proof for 5552398847894812179881582
1. ? [X0] : (tall(X0) | ~old(X0)) => (~quiet(susan) & humble(susan)) [input p0]
2. ! [X0] : ((kind(X0) <~> ~strong(X0)) <=> (~rich(X0) | humble(X0))) [input p1]
8. ! [X0] : (kind(X0) <=> ~strong(X0)) [input p7]
11. ! [X0] : (rich(X0) <=> (~brave(X0) <~> old(X0))) [input p10]
15. ! [X0] : (~strong(X0) <=> (brave(X0) & ~strong(X0))) [input p14]
23. ~brave(lucy) [input hypothesis]
27. (~quiet(susan) & humble(susan)) | ! [X0] : (~tall(X0) & old(X0)) [ennf transformation 1]
33. ! [X0] : ((((strong(X0) | ~kind(X0)) & (~strong(X0) | kind(X0))) | (rich(X0) & ~humble(X0))) & ((~rich(X0) | humble(X0)) | ((kind(X0) | strong(X0)) & (~strong(X0) | ~kind(X0))))) [nnf transformation 2]
34. ! [X0] : ((((strong(X0) | ~kind(X0)) & (~strong(X0) | kind(X0))) | (rich(X0) & ~humble(X0))) & (~rich(X0) | humble(X0) | ((kind(X0) | strong(X0)) & (~strong(X0) | ~kind(X0))))) [flattening 33]
41. ! [X0] : ((kind(X0) | strong(X0)) & (~strong(X0) | ~kind(X0))) [nnf transformation 8]
50. ! [X0] : ((rich(X0) | ((~brave(X0) | ~old(X0)) & (old(X0) | brave(X0)))) & (((~old(X0) | brave(X0)) & (old(X0) | ~brave(X0))) | ~rich(X0))) [nnf transformation 11]
60. ! [X0] : ((~strong(X0) | (~brave(X0) | strong(X0))) & ((brave(X0) & ~strong(X0)) | strong(X0))) [nnf transformation 15]
61. ! [X0] : ((~strong(X0) | ~brave(X0) | strong(X0)) & ((brave(X0) & ~strong(X0)) | strong(X0))) [flattening 60]
66. humble(susan) | old(X0) [cnf transformation 27]
72. ~strong(X0) | kind(X0) | ~humble(X0) [cnf transformation 34]
73. ~strong(X0) | kind(X0) | rich(X0) [cnf transformation 34]
74. ~kind(X0) | strong(X0) | ~humble(X0) [cnf transformation 34]
97. ~strong(X0) | ~kind(X0) [cnf transformation 41]
98. strong(X0) | kind(X0) [cnf transformation 41]
110. ~rich(X0) | brave(X0) | ~old(X0) [cnf transformation 50]
124. brave(X0) | strong(X0) [cnf transformation 61]
134. ~brave(lucy) [cnf transformation 23]
146. 3 <=> ! [X0] : old(X0) [avatar definition]
147. old(X0) <- (3) [avatar component clause 146]
150. 4 <=> humble(susan) [avatar definition]
152. humble(susan) <- (4) [avatar component clause 150]
154. 3 | 4 [avatar split clause 66,150,146]
291. strong(lucy) [resolution 124,134]
294. ~kind(lucy) [resolution 291,97]
298. kind(X0) | ~humble(X0) | kind(X0) [resolution 72,98]
302. ~humble(X0) | kind(X0) [duplicate literal removal 298]
303. kind(X0) | rich(X0) | kind(X0) [resolution 73,98]
307. rich(X0) | kind(X0) [duplicate literal removal 303]
326. kind(susan) <- (4) [resolution 302,152]
329. strong(susan) | ~humble(susan) <- (4) [resolution 326,74]
335. 38 <=> strong(susan) [avatar definition]
337. strong(susan) <- (38) [avatar component clause 335]
339. strong(susan) <- (4) [subsumption resolution 329,152]
340. 38 | ~4 [avatar split clause 339,150,335]
346. ~kind(susan) <- (38) [resolution 337,97]
347. $false <- (4, 38) [subsumption resolution 346,326]
348. ~4 | ~38 [avatar contradiction clause 347]
373. brave(X0) | ~old(X0) | kind(X0) [resolution 110,307]
378. brave(X0) | kind(X0) <- (3) [subsumption resolution 373,147]
495. kind(lucy) <- (3) [resolution 378,134]
498. $false <- (3) [subsumption resolution 495,294]
499. ~3 [avatar contradiction clause 498]
500. $false [avatar sat refutation 154,340,348,499]
% SZS output end Proof for 5552398847894812179881582
% ------------------------------
% 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 quiet is not tall.
If mary is both not rich and not calm then lucy is either not rich or not kind and vice versa.
If john is kind or patient then someone is brave or strong and vice versa.
Everyone who is both not strong and rich is kind.
Everyone who is not quiet or old is both not tall and quiet and vice versa.
If someone is either strong or not brave then someone is both not old and brave and vice versa.
Everyone who is either not curious or not tall is both not strong and generous and vice versa.
Everyone who is either calm or quiet is happy or not brave.
Everyone who is old is not humble or not tall.
If lucy is not humble then susan is not brave or not quiet.
If paul is not funny or not quiet then someone is not old or generous.
Everyone who is either creative or not funny is either not generous or tall.
If someone is not old or not calm then someone is both not tall and tall.
If lucy is either not patient or not funny then someone is wise.
If someone is both curious and not curious then lucy is not wise or funny and vice versa.
Everyone who is humble is creative or calm and vice versa.
Paul is strong or not brave.
Susan is quiet or not quiet.
Susan is either funny or not kind.
Someone is either not tall or happy.
Fred is either calm or not happy.
Someone is strong.
Lucy is either generous or patient. | Mary is not rich. | neutral | (![X]:(~quiet(X)=>~tall(X)))&
(((~rich(mary)&~calm(mary)))<=>((~rich(lucy)<~>~kind(lucy))))&
(((kind(john)|patient(john)))<=>(?[X]:((brave(X)|strong(X)))))&
(![X]:((~strong(X)&rich(X))=>kind(X)))&
(![X]:((~quiet(X)|old(X))<=>(~tall(X)&quiet(X))))&
((?[X]:((strong(X)<~>~brave(X))))<=>(?[X]:((~old(X)&brave(X)))))&
(![X]:((~curious(X)<~>~tall(X))<=>(~strong(X)&generous(X))))&
(![X]:((calm(X)<~>quiet(X))=>(happy(X)|~brave(X))))&
(![X]:(old(X)=>(~humble(X)|~tall(X))))&
((~humble(lucy))=>((~brave(susan)|~quiet(susan))))&
(((~funny(paul)|~quiet(paul)))=>(?[X]:((~old(X)|generous(X)))))&
(![X]:((creative(X)<~>~funny(X))=>(~generous(X)<~>tall(X))))&
((?[X]:((~old(X)|~calm(X))))=>(?[X]:((~tall(X)&tall(X)))))&
(((~patient(lucy)<~>~funny(lucy)))=>(?[X]:(wise(X))))&
((?[X]:((curious(X)&~curious(X))))<=>((~wise(lucy)|funny(lucy))))&
(![X]:(humble(X)<=>(creative(X)|calm(X))))&
((strong(paul)|~brave(paul)))&
((quiet(susan)|~quiet(susan)))&
((funny(susan)<~>~kind(susan)))&
(?[X]:((~tall(X)<~>happy(X))))&
((calm(fred)<~>~happy(fred)))&
(?[X]:(strong(X)))&
((generous(lucy)<~>patient(lucy))) | ~rich(mary) | [] | null | 0 |
Everyone who is not patient or tall is not generous and vice versa. Everyone who is not quiet or not happy is either not happy or tall. If someone is creative then susan is old and vice versa. If paul is generous then mary is tall and vice versa. Everyone who is quiet or not tall is kind. Everyone who is both rich and not curious is both old and not old and vice versa. Everyone who is kind or old is happy. Everyone who is both not curious and not calm is either not happy or brave and vice versa. Everyone who is strong or tall is both humble and brave. If lucy is either generous or not strong then someone is old or not calm and vice versa. Everyone who is generous is rich or not happy and vice versa. Everyone who is either not calm or curious is not quiet or humble. Everyone who is not kind or funny is not brave. Everyone who is either not creative or tall is either calm or not generous and vice versa. Everyone who is either not wise or quiet is either not generous or wise. Paul is either not brave or tall. Someone is strong. Someone is not tall or not generous. Fred is not tall or not old. Lucy is either humble or old. Someone is not curious or not patient. Mary is either not creative or tall. | Lucy is rich. | contradiction | (![X]:((~patient(X)|tall(X))<=>~generous(X)))&
(![X]:((~quiet(X)|~happy(X))=>(~happy(X)<~>tall(X))))&
((?[X]:(creative(X)))<=>(old(susan)))&
((generous(paul))<=>(tall(mary)))&
(![X]:((quiet(X)|~tall(X))=>kind(X)))&
(![X]:((rich(X)&~curious(X))<=>(old(X)&~old(X))))&
(![X]:((kind(X)|old(X))=>happy(X)))&
(![X]:((~curious(X)&~calm(X))<=>(~happy(X)<~>brave(X))))&
(![X]:((strong(X)|tall(X))=>(humble(X)&brave(X))))&
(((generous(lucy)<~>~strong(lucy)))<=>(?[X]:((old(X)|~calm(X)))))&
(![X]:(generous(X)<=>(rich(X)|~happy(X))))&
(![X]:((~calm(X)<~>curious(X))=>(~quiet(X)|humble(X))))&
(![X]:((~kind(X)|funny(X))=>~brave(X)))&
(![X]:((~creative(X)<~>tall(X))<=>(calm(X)<~>~generous(X))))&
(![X]:((~wise(X)<~>quiet(X))=>(~generous(X)<~>wise(X))))&
((~brave(paul)<~>tall(paul)))&
(?[X]:(strong(X)))&
(?[X]:((~tall(X)|~generous(X))))&
((~tall(fred)|~old(fred)))&
((humble(lucy)<~>old(lucy)))&
(?[X]:((~curious(X)|~patient(X))))&
((~creative(mary)<~>tall(mary))) | rich(lucy) | [
"p1",
"p4",
"p5",
"p6",
"p7",
"p8",
"p9",
"p10",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 8547150478243786403273627
% SZS output start Proof for 8547150478243786403273627
2. ! [X0] : ((~happy(X0) | ~quiet(X0)) => (~happy(X0) <~> tall(X0))) [input p1]
5. ! [X0] : ((~tall(X0) | quiet(X0)) => kind(X0)) [input p4]
6. ! [X0] : ((~curious(X0) & rich(X0)) <=> (~old(X0) & old(X0))) [input p5]
7. ! [X0] : ((old(X0) | kind(X0)) => happy(X0)) [input p6]
8. ! [X0] : ((~calm(X0) & ~curious(X0)) <=> (~happy(X0) <~> brave(X0))) [input p7]
9. ! [X0] : ((tall(X0) | strong(X0)) => (brave(X0) & humble(X0))) [input p8]
10. (generous(lucy) <~> ~strong(lucy)) <=> ? [X0] : (~calm(X0) | old(X0)) [input p9]
11. ! [X0] : (generous(X0) <=> (~happy(X0) | rich(X0))) [input p10]
17. ? [X0] : strong(X0) [input p16]
23. rich(lucy) [input hypothesis]
25. ! [X0] : ((~happy(X0) <~> tall(X0)) | (happy(X0) & quiet(X0))) [ennf transformation 2]
26. ! [X0] : (kind(X0) | (tall(X0) & ~quiet(X0))) [ennf transformation 5]
27. ! [X0] : (happy(X0) | (~old(X0) & ~kind(X0))) [ennf transformation 7]
28. ! [X0] : ((brave(X0) & humble(X0)) | (~tall(X0) & ~strong(X0))) [ennf transformation 9]
35. ! [X0] : (((~tall(X0) | happy(X0)) & (tall(X0) | ~happy(X0))) | (happy(X0) & quiet(X0))) [nnf transformation 25]
41. ! [X0] : (((~curious(X0) & rich(X0)) | (old(X0) | ~old(X0))) & ((~old(X0) & old(X0)) | (curious(X0) | ~rich(X0)))) [nnf transformation 6]
42. ! [X0] : (((~curious(X0) & rich(X0)) | old(X0) | ~old(X0)) & ((~old(X0) & old(X0)) | curious(X0) | ~rich(X0))) [flattening 41]
43. ! [X0] : (((~calm(X0) & ~curious(X0)) | ((~happy(X0) | ~brave(X0)) & (brave(X0) | happy(X0)))) & (((~brave(X0) | happy(X0)) & (brave(X0) | ~happy(X0))) | (calm(X0) | curious(X0)))) [nnf transformation 8]
44. ! [X0] : (((~calm(X0) & ~curious(X0)) | ((~happy(X0) | ~brave(X0)) & (brave(X0) | happy(X0)))) & (((~brave(X0) | happy(X0)) & (brave(X0) | ~happy(X0))) | calm(X0) | curious(X0))) [flattening 43]
45. (((strong(lucy) | ~generous(lucy)) & (~strong(lucy) | generous(lucy))) | ! [X0] : (calm(X0) & ~old(X0))) & (? [X0] : (~calm(X0) | old(X0)) | ((generous(lucy) | strong(lucy)) & (~strong(lucy) | ~generous(lucy)))) [nnf transformation 10]
46. (((strong(lucy) | ~generous(lucy)) & (~strong(lucy) | generous(lucy))) | ! [X0] : (calm(X0) & ~old(X0))) & (? [X1] : (~calm(X1) | old(X1)) | ((generous(lucy) | strong(lucy)) & (~strong(lucy) | ~generous(lucy)))) [rectify 45]
47. ? [X1] : (~calm(X1) | old(X1)) => (~calm(sK1) | old(sK1)) [choice axiom]
48. (((strong(lucy) | ~generous(lucy)) & (~strong(lucy) | generous(lucy))) | ! [X0] : (calm(X0) & ~old(X0))) & ((~calm(sK1) | old(sK1)) | ((generous(lucy) | strong(lucy)) & (~strong(lucy) | ~generous(lucy)))) [skolemisation 46,47]
49. ! [X0] : ((generous(X0) | (happy(X0) & ~rich(X0))) & ((~happy(X0) | rich(X0)) | ~generous(X0))) [nnf transformation 11]
50. ! [X0] : ((generous(X0) | (happy(X0) & ~rich(X0))) & (~happy(X0) | rich(X0) | ~generous(X0))) [flattening 49]
55. ? [X0] : strong(X0) => strong(sK2) [choice axiom]
56. strong(sK2) [skolemisation 17,55]
69. ~tall(X0) | happy(X0) | happy(X0) [cnf transformation 35]
75. kind(X0) | tall(X0) [cnf transformation 26]
76. old(X0) | curious(X0) | ~rich(X0) [cnf transformation 42]
77. ~rich(X0) | curious(X0) | ~old(X0) [cnf transformation 42]
80. ~kind(X0) | happy(X0) [cnf transformation 27]
85. ~brave(X0) | ~happy(X0) | ~curious(X0) [cnf transformation 44]
87. ~brave(X0) | ~happy(X0) | ~calm(X0) [cnf transformation 44]
90. ~strong(X0) | brave(X0) [cnf transformation 28]
97. strong(lucy) | ~generous(lucy) | calm(X0) [cnf transformation 48]
99. ~rich(X0) | generous(X0) [cnf transformation 50]
118. strong(sK2) [cnf transformation 56]
126. rich(lucy) [cnf transformation 23]
129. ~tall(X0) | happy(X0) [duplicate literal removal 69]
153. ~rich(X0) | curious(X0) [subsumption resolution 76,77]
155. 6 <=> ! [X0] : calm(X0) [avatar definition]
156. calm(X0) <- (6) [avatar component clause 155]
158. 7 <=> generous(lucy) [avatar definition]
162. 8 <=> strong(lucy) [avatar definition]
164. strong(lucy) <- (8) [avatar component clause 162]
165. 6 | ~7 | 8 [avatar split clause 97,162,158,155]
229. happy(X0) | tall(X0) [resolution 80,75]
230. happy(X0) [subsumption resolution 229,129]
232. brave(sK2) [resolution 90,118]
233. generous(lucy) [resolution 99,126]
236. 7 [avatar split clause 233,158]
239. brave(lucy) <- (8) [resolution 164,90]
243. curious(lucy) [resolution 153,126]
253. ~happy(lucy) | ~curious(lucy) <- (8) [resolution 85,239]
255. ~curious(lucy) <- (8) [subsumption resolution 253,230]
256. $false <- (8) [subsumption resolution 255,243]
257. ~8 [avatar contradiction clause 256]
261. ~happy(sK2) | ~calm(sK2) [resolution 87,232]
262. ~calm(sK2) [subsumption resolution 261,230]
263. $false <- (6) [subsumption resolution 262,156]
264. ~6 [avatar contradiction clause 263]
265. $false [avatar sat refutation 165,236,257,264]
% SZS output end Proof for 8547150478243786403273627
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not humble then someone is either funny or happy and vice versa.
Everyone who is not patient is both old and funny and vice versa.
Everyone who is both not generous and strong is both rich and wise.
If someone is old then fred is both curious and not quiet and vice versa.
Everyone who is generous or not happy is both creative and not generous.
Everyone who is both funny and rich is both not wise and not happy and vice versa.
If someone is not tall or not calm then someone is either curious or not creative.
Everyone who is not generous is either wise or brave and vice versa.
If someone is not brave then susan is happy and vice versa.
If someone is both not curious and not wise then mary is creative.
If someone is old or not creative then someone is both not strong and not old.
If someone is both happy and humble then someone is both not happy and generous and vice versa.
Everyone who is either not humble or strong is both not old and not tall and vice versa.
If someone is both happy and not happy then someone is both humble and curious.
Everyone who is both not tall and not generous is both not happy and patient and vice versa.
If someone is both not humble and kind then someone is not tall or creative and vice versa.
Mary is not brave or not kind.
Someone is either not rich or tall.
Fred is either not wise or not generous.
Someone is wise.
Someone is either not humble or not curious.
Someone is both rich and not strong.
Someone is either calm or brave. | Susan is humble. | contradiction | ((?[X]:(~humble(X)))<=>(?[X]:((funny(X)<~>happy(X)))))&
(![X]:(~patient(X)<=>(old(X)&funny(X))))&
(![X]:((~generous(X)&strong(X))=>(rich(X)&wise(X))))&
((?[X]:(old(X)))<=>((curious(fred)&~quiet(fred))))&
(![X]:((generous(X)|~happy(X))=>(creative(X)&~generous(X))))&
(![X]:((funny(X)&rich(X))<=>(~wise(X)&~happy(X))))&
((?[X]:((~tall(X)|~calm(X))))=>(?[X]:((curious(X)<~>~creative(X)))))&
(![X]:(~generous(X)<=>(wise(X)<~>brave(X))))&
((?[X]:(~brave(X)))<=>(happy(susan)))&
((?[X]:((~curious(X)&~wise(X))))=>(creative(mary)))&
((?[X]:((old(X)|~creative(X))))=>(?[X]:((~strong(X)&~old(X)))))&
((?[X]:((happy(X)&humble(X))))<=>(?[X]:((~happy(X)&generous(X)))))&
(![X]:((~humble(X)<~>strong(X))<=>(~old(X)&~tall(X))))&
((?[X]:((happy(X)&~happy(X))))=>(?[X]:((humble(X)&curious(X)))))&
(![X]:((~tall(X)&~generous(X))<=>(~happy(X)&patient(X))))&
((?[X]:((~humble(X)&kind(X))))<=>(?[X]:((~tall(X)|creative(X)))))&
((~brave(mary)|~kind(mary)))&
(?[X]:((~rich(X)<~>tall(X))))&
((~wise(fred)<~>~generous(fred)))&
(?[X]:(wise(X)))&
(?[X]:((~humble(X)<~>~curious(X))))&
(?[X]:((rich(X)&~strong(X))))&
(?[X]:((calm(X)<~>brave(X)))) | humble(susan) | [
"p4",
"p7",
"p8",
"p11",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 3758523123959710974171037
% SZS output start Proof for 3758523123959710974171037
5. ! [X0] : ((~happy(X0) | generous(X0)) => (~generous(X0) & creative(X0))) [input p4]
8. ! [X0] : (~generous(X0) <=> (wise(X0) <~> brave(X0))) [input p7]
9. ? [X0] : ~brave(X0) <=> happy(susan) [input p8]
12. ? [X0] : (humble(X0) & happy(X0)) <=> ? [X0] : (generous(X0) & ~happy(X0)) [input p11]
19. ~wise(fred) <~> ~generous(fred) [input p18]
24. humble(susan) [input hypothesis]
28. ? [X0] : (humble(X0) & happy(X0)) <=> ? [X1] : (generous(X1) & ~happy(X1)) [rectify 12]
33. ! [X0] : ((~generous(X0) & creative(X0)) | (happy(X0) & ~generous(X0))) [ennf transformation 5]
56. ! [X0] : ((~generous(X0) | ((wise(X0) | ~brave(X0)) & (brave(X0) | ~wise(X0)))) & (((~brave(X0) | ~wise(X0)) & (brave(X0) | wise(X0))) | generous(X0))) [nnf transformation 8]
57. (? [X0] : ~brave(X0) | ~happy(susan)) & (happy(susan) | ! [X0] : brave(X0)) [nnf transformation 9]
58. (? [X0] : ~brave(X0) | ~happy(susan)) & (happy(susan) | ! [X1] : brave(X1)) [rectify 57]
59. ? [X0] : ~brave(X0) => ~brave(sK4) [choice axiom]
60. (~brave(sK4) | ~happy(susan)) & (happy(susan) | ! [X1] : brave(X1)) [skolemisation 58,59]
64. (? [X0] : (humble(X0) & happy(X0)) | ! [X1] : (~generous(X1) | happy(X1))) & (? [X1] : (generous(X1) & ~happy(X1)) | ! [X0] : (~humble(X0) | ~happy(X0))) [nnf transformation 28]
65. (? [X0] : (humble(X0) & happy(X0)) | ! [X1] : (~generous(X1) | happy(X1))) & (? [X2] : (generous(X2) & ~happy(X2)) | ! [X3] : (~humble(X3) | ~happy(X3))) [rectify 64]
66. ? [X0] : (humble(X0) & happy(X0)) => (humble(sK6) & happy(sK6)) [choice axiom]
67. ? [X2] : (generous(X2) & ~happy(X2)) => (generous(sK7) & ~happy(sK7)) [choice axiom]
68. ((humble(sK6) & happy(sK6)) | ! [X1] : (~generous(X1) | happy(X1))) & ((generous(sK7) & ~happy(sK7)) | ! [X3] : (~humble(X3) | ~happy(X3))) [skolemisation 65,67,66]
84. (generous(fred) | wise(fred)) & (~generous(fred) | ~wise(fred)) [nnf transformation 19]
109. ~generous(X0) | ~generous(X0) [cnf transformation 33]
120. ~brave(X0) | ~wise(X0) | generous(X0) [cnf transformation 56]
123. happy(susan) | brave(X1) [cnf transformation 60]
131. generous(sK7) | ~humble(X3) | ~happy(X3) [cnf transformation 68]
155. generous(fred) | wise(fred) [cnf transformation 84]
163. humble(susan) [cnf transformation 24]
164. ~generous(X0) [duplicate literal removal 109]
226. ~brave(X0) | ~wise(X0) [subsumption resolution 120,164]
229. 15 <=> happy(susan) [avatar definition]
230. happy(susan) <- (15) [avatar component clause 229]
238. 17 <=> ! [X1] : brave(X1) [avatar definition]
239. brave(X1) <- (17) [avatar component clause 238]
240. 17 | 15 [avatar split clause 123,229,238]
264. ~happy(X3) | ~humble(X3) [subsumption resolution 131,164]
313. wise(fred) [subsumption resolution 155,164]
348. ~humble(susan) <- (15) [resolution 264,230]
350. $false <- (15) [subsumption resolution 348,163]
351. ~15 [avatar contradiction clause 350]
354. ~wise(X0) <- (17) [resolution 239,226]
371. $false <- (17) [resolution 354,313]
378. ~17 [avatar contradiction clause 371]
379. $false [avatar sat refutation 240,351,378]
% SZS output end Proof for 3758523123959710974171037
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not kind and not brave is both curious and happy.
Everyone who is not wise is not tall or not funny and vice versa.
If someone is both quiet and not happy then someone is not old or not wise.
If lucy is not quiet or curious then someone is either not kind or calm and vice versa.
Everyone who is not tall is not rich or quiet and vice versa.
Everyone who is both wise and not brave is either wise or funny and vice versa.
Everyone who is not wise is both rich and tall and vice versa.
If paul is humble or happy then someone is either quiet or not rich and vice versa.
If john is kind or brave then someone is either not creative or not funny.
Everyone who is either not funny or not kind is either humble or brave and vice versa.
If someone is funny then fred is kind or not curious.
If someone is both not brave and not calm then someone is happy or not humble and vice versa.
Everyone who is both brave and quiet is either not generous or not brave.
If alice is kind then someone is both strong and creative.
If someone is not generous or not old then someone is humble or old and vice versa.
Everyone who is either not brave or happy is either tall or not generous and vice versa.
Fred is calm.
Paul is either quiet or calm.
Someone is both not strong and curious.
Someone is either not kind or generous.
Mary is both not quiet and not funny.
Someone is not calm or quiet.
John is either old or not humble. | Alice is not wise. | entailment | (![X]:((~kind(X)&~brave(X))=>(curious(X)&happy(X))))&
(![X]:(~wise(X)<=>(~tall(X)|~funny(X))))&
((?[X]:((quiet(X)&~happy(X))))=>(?[X]:((~old(X)|~wise(X)))))&
(((~quiet(lucy)|curious(lucy)))<=>(?[X]:((~kind(X)<~>calm(X)))))&
(![X]:(~tall(X)<=>(~rich(X)|quiet(X))))&
(![X]:((wise(X)&~brave(X))<=>(wise(X)<~>funny(X))))&
(![X]:(~wise(X)<=>(rich(X)&tall(X))))&
(((humble(paul)|happy(paul)))<=>(?[X]:((quiet(X)<~>~rich(X)))))&
(((kind(john)|brave(john)))=>(?[X]:((~creative(X)<~>~funny(X)))))&
(![X]:((~funny(X)<~>~kind(X))<=>(humble(X)<~>brave(X))))&
((?[X]:(funny(X)))=>((kind(fred)|~curious(fred))))&
((?[X]:((~brave(X)&~calm(X))))<=>(?[X]:((happy(X)|~humble(X)))))&
(![X]:((brave(X)&quiet(X))=>(~generous(X)<~>~brave(X))))&
((kind(alice))=>(?[X]:((strong(X)&creative(X)))))&
((?[X]:((~generous(X)|~old(X))))<=>(?[X]:((humble(X)|old(X)))))&
(![X]:((~brave(X)<~>happy(X))<=>(tall(X)<~>~generous(X))))&
(calm(fred))&
((quiet(paul)<~>calm(paul)))&
(?[X]:((~strong(X)&curious(X))))&
(?[X]:((~kind(X)<~>generous(X))))&
((~quiet(mary)&~funny(mary)))&
(?[X]:((~calm(X)|quiet(X))))&
((old(john)<~>~humble(john))) | ~wise(alice) | [
"p1",
"p4",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 3585527109444299837720230
% SZS output start Proof for 3585527109444299837720230
2. ! [X0] : (~wise(X0) <=> (~funny(X0) | ~tall(X0))) [input p1]
5. ! [X0] : (~tall(X0) <=> (quiet(X0) | ~rich(X0))) [input p4]
7. ! [X0] : (~wise(X0) <=> (tall(X0) & rich(X0))) [input p6]
24. wise(alice) [input hypothesis]
37. ! [X0] : ((~wise(X0) | (funny(X0) & tall(X0))) & ((~funny(X0) | ~tall(X0)) | wise(X0))) [nnf transformation 2]
38. ! [X0] : ((~wise(X0) | (funny(X0) & tall(X0))) & (~funny(X0) | ~tall(X0) | wise(X0))) [flattening 37]
47. ! [X0] : ((~tall(X0) | (~quiet(X0) & rich(X0))) & ((quiet(X0) | ~rich(X0)) | tall(X0))) [nnf transformation 5]
48. ! [X0] : ((~tall(X0) | (~quiet(X0) & rich(X0))) & (quiet(X0) | ~rich(X0) | tall(X0))) [flattening 47]
51. ! [X0] : ((~wise(X0) | (~tall(X0) | ~rich(X0))) & ((tall(X0) & rich(X0)) | wise(X0))) [nnf transformation 7]
52. ! [X0] : ((~wise(X0) | ~tall(X0) | ~rich(X0)) & ((tall(X0) & rich(X0)) | wise(X0))) [flattening 51]
88. ~wise(X0) | tall(X0) [cnf transformation 38]
98. ~tall(X0) | rich(X0) [cnf transformation 48]
107. tall(X0) | wise(X0) [cnf transformation 52]
108. ~wise(X0) | ~tall(X0) | ~rich(X0) [cnf transformation 52]
161. wise(alice) [cnf transformation 24]
206. ~rich(X0) | ~wise(X0) [subsumption resolution 108,88]
207. tall(X0) [subsumption resolution 107,88]
393. rich(X0) [resolution 98,207]
409. ~wise(X1) [resolution 206,393]
410. $false [resolution 409,161]
% SZS output end Proof for 3585527109444299837720230
% ------------------------------
% 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 tall or not brave is not old. Everyone who is both not brave and patient is not quiet and vice versa. Everyone who is both not tall and happy is both rich and tall. If someone is both not happy and old then someone is either humble or generous. If someone is curious or rich then someone is both rich and not generous and vice versa. If someone is either generous or wise then someone is curious. If someone is not curious then someone is not humble or old. If fred is both generous and not old then mary is brave or curious and vice versa. Everyone who is not old is either not happy or not wise and vice versa. If fred is both not calm and not old then someone is happy and vice versa. If john is either wise or happy then alice is old or strong. Everyone who is both not kind and not tall is not funny or brave. If mary is both kind and curious then alice is not wise or curious. Everyone who is either not patient or not brave is either not rich or not calm. If mary is both strong and creative then someone is both patient and not generous and vice versa. If fred is both creative and not quiet then someone is not old. Someone is not kind. Someone is humble or rich. Someone is not funny. Alice is not kind or tall. John is not funny or funny. Someone is humble or generous. Someone is wise or not quiet. Fred is brave or not calm. | Alice is tall. | neutral | (![X]:((~tall(X)|~brave(X))=>~old(X)))&
(![X]:((~brave(X)&patient(X))<=>~quiet(X)))&
(![X]:((~tall(X)&happy(X))=>(rich(X)&tall(X))))&
((?[X]:((~happy(X)&old(X))))=>(?[X]:((humble(X)<~>generous(X)))))&
((?[X]:((curious(X)|rich(X))))<=>(?[X]:((rich(X)&~generous(X)))))&
((?[X]:((generous(X)<~>wise(X))))=>(?[X]:(curious(X))))&
((?[X]:(~curious(X)))=>(?[X]:((~humble(X)|old(X)))))&
(((generous(fred)&~old(fred)))<=>((brave(mary)|curious(mary))))&
(![X]:(~old(X)<=>(~happy(X)<~>~wise(X))))&
(((~calm(fred)&~old(fred)))<=>(?[X]:(happy(X))))&
(((wise(john)<~>happy(john)))=>((old(alice)|strong(alice))))&
(![X]:((~kind(X)&~tall(X))=>(~funny(X)|brave(X))))&
(((kind(mary)&curious(mary)))=>((~wise(alice)|curious(alice))))&
(![X]:((~patient(X)<~>~brave(X))=>(~rich(X)<~>~calm(X))))&
(((strong(mary)&creative(mary)))<=>(?[X]:((patient(X)&~generous(X)))))&
(((creative(fred)&~quiet(fred)))=>(?[X]:(~old(X))))&
(?[X]:(~kind(X)))&
(?[X]:((humble(X)|rich(X))))&
(?[X]:(~funny(X)))&
((~kind(alice)|tall(alice)))&
((~funny(john)|funny(john)))&
(?[X]:((humble(X)|generous(X))))&
(?[X]:((wise(X)|~quiet(X))))&
((brave(fred)|~calm(fred))) | tall(alice) | [] | null | 0 |
Everyone who is both happy and wise is not quiet or quiet and vice versa. If someone is either humble or patient then paul is old. Everyone who is not strong or kind is both wise and happy and vice versa. Everyone who is not calm or not happy is wise or curious. Everyone who is both kind and not humble is not strong or not patient and vice versa. If someone is both old and humble then someone is either not humble or wise. If someone is both strong and funny then someone is either curious or old and vice versa. If susan is either not humble or generous then someone is not strong and vice versa. If lucy is either not strong or brave then lucy is either funny or rich. Everyone who is both patient and curious is generous and vice versa. Everyone who is calm is creative and vice versa. Everyone who is both not calm and not humble is both wise and not curious and vice versa. Everyone who is both not strong and old is both curious and not happy. Everyone who is not wise or not curious is not old and vice versa. Everyone who is generous or not strong is either curious or wise. If someone is calm or not generous then john is happy or brave. Someone is either not curious or old. Someone is either not patient or not generous. Mary is both happy and funny. Susan is not creative or tall. Someone is either generous or not patient. Susan is both funny and not tall. | Mary is not patient. | neutral | (![X]:((happy(X)&wise(X))<=>(~quiet(X)|quiet(X))))&
((?[X]:((humble(X)<~>patient(X))))=>(old(paul)))&
(![X]:((~strong(X)|kind(X))<=>(wise(X)&happy(X))))&
(![X]:((~calm(X)|~happy(X))=>(wise(X)|curious(X))))&
(![X]:((kind(X)&~humble(X))<=>(~strong(X)|~patient(X))))&
((?[X]:((old(X)&humble(X))))=>(?[X]:((~humble(X)<~>wise(X)))))&
((?[X]:((strong(X)&funny(X))))<=>(?[X]:((curious(X)<~>old(X)))))&
(((~humble(susan)<~>generous(susan)))<=>(?[X]:(~strong(X))))&
(((~strong(lucy)<~>brave(lucy)))=>((funny(lucy)<~>rich(lucy))))&
(![X]:((patient(X)&curious(X))<=>generous(X)))&
(![X]:(calm(X)<=>creative(X)))&
(![X]:((~calm(X)&~humble(X))<=>(wise(X)&~curious(X))))&
(![X]:((~strong(X)&old(X))=>(curious(X)&~happy(X))))&
(![X]:((~wise(X)|~curious(X))<=>~old(X)))&
(![X]:((generous(X)|~strong(X))=>(curious(X)<~>wise(X))))&
((?[X]:((calm(X)|~generous(X))))=>((happy(john)|brave(john))))&
(?[X]:((~curious(X)<~>old(X))))&
(?[X]:((~patient(X)<~>~generous(X))))&
((happy(mary)&funny(mary)))&
((~creative(susan)|tall(susan)))&
(?[X]:((generous(X)<~>~patient(X))))&
((funny(susan)&~tall(susan))) | ~patient(mary) | [] | null | 0 |
If lucy is not old or humble then someone is either patient or kind and vice versa.
Everyone who is both calm and not wise is either generous or not calm and vice versa.
If alice is both not humble and not creative then someone is either not patient or wise and vice versa.
Everyone who is both old and generous is not funny.
Everyone who is not brave or not happy is not brave.
If someone is not wise or brave then lucy is humble.
Everyone who is strong or generous is both not tall and calm.
Everyone who is not brave or not generous is either patient or not calm and vice versa.
Everyone who is both kind and tall is strong or not funny and vice versa.
Everyone who is both tall and not happy is either wise or not happy and vice versa.
Everyone who is strong is rich or not calm.
If mary is wise or not strong then someone is either not creative or not brave.
If someone is quiet then someone is not calm.
Everyone who is patient is not kind or not creative.
If someone is strong or rich then lucy is funny or not brave.
If fred is generous or funny then someone is both not rich and not tall and vice versa.
Someone is either patient or humble.
Someone is not happy.
Paul is both happy and brave.
Someone is not patient.
Someone is both generous and not brave.
Mary is not happy or not funny.
Someone is either strong or not tall. | Paul is tall. | contradiction | (((~old(lucy)|humble(lucy)))<=>(?[X]:((patient(X)<~>kind(X)))))&
(![X]:((calm(X)&~wise(X))<=>(generous(X)<~>~calm(X))))&
(((~humble(alice)&~creative(alice)))<=>(?[X]:((~patient(X)<~>wise(X)))))&
(![X]:((old(X)&generous(X))=>~funny(X)))&
(![X]:((~brave(X)|~happy(X))=>~brave(X)))&
((?[X]:((~wise(X)|brave(X))))=>(humble(lucy)))&
(![X]:((strong(X)|generous(X))=>(~tall(X)&calm(X))))&
(![X]:((~brave(X)|~generous(X))<=>(patient(X)<~>~calm(X))))&
(![X]:((kind(X)&tall(X))<=>(strong(X)|~funny(X))))&
(![X]:((tall(X)&~happy(X))<=>(wise(X)<~>~happy(X))))&
(![X]:(strong(X)=>(rich(X)|~calm(X))))&
(((wise(mary)|~strong(mary)))=>(?[X]:((~creative(X)<~>~brave(X)))))&
((?[X]:(quiet(X)))=>(?[X]:(~calm(X))))&
(![X]:(patient(X)=>(~kind(X)|~creative(X))))&
((?[X]:((strong(X)|rich(X))))=>((funny(lucy)|~brave(lucy))))&
(((generous(fred)|funny(fred)))<=>(?[X]:((~rich(X)&~tall(X)))))&
(?[X]:((patient(X)<~>humble(X))))&
(?[X]:(~happy(X)))&
((happy(paul)&brave(paul)))&
(?[X]:(~patient(X)))&
(?[X]:((generous(X)&~brave(X))))&
((~happy(mary)|~funny(mary)))&
(?[X]:((strong(X)<~>~tall(X)))) | tall(paul) | [
"p1",
"p6",
"p9",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 6185735258206277963709820
% SZS output start Proof for 6185735258206277963709820
2. ! [X0] : ((~wise(X0) & calm(X0)) <=> (generous(X0) <~> ~calm(X0))) [input p1]
7. ! [X0] : ((generous(X0) | strong(X0)) => (calm(X0) & ~tall(X0))) [input p6]
10. ! [X0] : ((~happy(X0) & tall(X0)) <=> (wise(X0) <~> ~happy(X0))) [input p9]
19. brave(paul) & happy(paul) [input p18]
24. tall(paul) [input hypothesis]
31. ! [X0] : ((calm(X0) & ~tall(X0)) | (~generous(X0) & ~strong(X0))) [ennf transformation 7]
44. ! [X0] : (((~wise(X0) & calm(X0)) | ((generous(X0) | calm(X0)) & (~calm(X0) | ~generous(X0)))) & (((calm(X0) | ~generous(X0)) & (~calm(X0) | generous(X0))) | (wise(X0) | ~calm(X0)))) [nnf transformation 2]
45. ! [X0] : (((~wise(X0) & calm(X0)) | ((generous(X0) | calm(X0)) & (~calm(X0) | ~generous(X0)))) & (((calm(X0) | ~generous(X0)) & (~calm(X0) | generous(X0))) | wise(X0) | ~calm(X0))) [flattening 44]
55. ! [X0] : (((~happy(X0) & tall(X0)) | ((wise(X0) | happy(X0)) & (~happy(X0) | ~wise(X0)))) & (((happy(X0) | ~wise(X0)) & (~happy(X0) | wise(X0))) | (happy(X0) | ~tall(X0)))) [nnf transformation 10]
56. ! [X0] : (((~happy(X0) & tall(X0)) | ((wise(X0) | happy(X0)) & (~happy(X0) | ~wise(X0)))) & (((happy(X0) | ~wise(X0)) & (~happy(X0) | wise(X0))) | happy(X0) | ~tall(X0))) [flattening 55]
83. ~calm(X0) | generous(X0) | wise(X0) | ~calm(X0) [cnf transformation 45]
86. calm(X0) | generous(X0) | calm(X0) [cnf transformation 45]
101. ~tall(X0) | ~generous(X0) [cnf transformation 31]
119. ~happy(X0) | ~happy(X0) | ~wise(X0) [cnf transformation 56]
137. happy(paul) [cnf transformation 19]
145. tall(paul) [cnf transformation 24]
147. ~happy(X0) | ~wise(X0) [duplicate literal removal 119]
148. ~calm(X0) | generous(X0) | wise(X0) [duplicate literal removal 83]
149. generous(X0) | calm(X0) [duplicate literal removal 86]
178. generous(X0) | wise(X0) [subsumption resolution 148,149]
298. ~generous(paul) [resolution 101,145]
304. ~wise(paul) [resolution 147,137]
306. wise(paul) [resolution 178,298]
307. $false [subsumption resolution 306,304]
% SZS output end Proof for 6185735258206277963709820
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not brave or strong is not calm and vice versa. Everyone who is both not creative and patient is curious and vice versa. If someone is both humble and generous then paul is not quiet or not kind and vice versa. Everyone who is wise or happy is both not generous and calm. If fred is both curious and kind then fred is both wise and kind. Everyone who is both not creative and old is both wise and old. Everyone who is tall is either not old or rich. If mary is humble or not curious then susan is brave and vice versa. Everyone who is strong is not curious or not tall. Everyone who is not happy is both quiet and calm. If alice is both not creative and not curious then someone is not calm and vice versa. If someone is either funny or not humble then someone is wise or not humble and vice versa. If alice is both not strong and tall then alice is not calm and vice versa. If someone is not strong then someone is either not kind or not quiet and vice versa. Everyone who is both quiet and not tall is both calm and not strong and vice versa. Everyone who is strong or not patient is happy. Someone is old or generous. Mary is both generous and patient. John is not humble. Someone is both not rich and old. Someone is either humble or not brave. Someone is either generous or patient. Alice is brave or not quiet. Paul is either strong or not patient. | Susan is not tall. | entailment | (![X]:((~brave(X)|strong(X))<=>~calm(X)))&
(![X]:((~creative(X)&patient(X))<=>curious(X)))&
((?[X]:((humble(X)&generous(X))))<=>((~quiet(paul)|~kind(paul))))&
(![X]:((wise(X)|happy(X))=>(~generous(X)&calm(X))))&
(((curious(fred)&kind(fred)))=>((wise(fred)&kind(fred))))&
(![X]:((~creative(X)&old(X))=>(wise(X)&old(X))))&
(![X]:(tall(X)=>(~old(X)<~>rich(X))))&
(((humble(mary)|~curious(mary)))<=>(brave(susan)))&
(![X]:(strong(X)=>(~curious(X)|~tall(X))))&
(![X]:(~happy(X)=>(quiet(X)&calm(X))))&
(((~creative(alice)&~curious(alice)))<=>(?[X]:(~calm(X))))&
((?[X]:((funny(X)<~>~humble(X))))<=>(?[X]:((wise(X)|~humble(X)))))&
(((~strong(alice)&tall(alice)))<=>(~calm(alice)))&
((?[X]:(~strong(X)))<=>(?[X]:((~kind(X)<~>~quiet(X)))))&
(![X]:((quiet(X)&~tall(X))<=>(calm(X)&~strong(X))))&
(![X]:((strong(X)|~patient(X))=>happy(X)))&
(?[X]:((old(X)|generous(X))))&
((generous(mary)&patient(mary)))&
(~humble(john))&
(?[X]:((~rich(X)&old(X))))&
(?[X]:((humble(X)<~>~brave(X))))&
(?[X]:((generous(X)<~>patient(X))))&
((brave(alice)|~quiet(alice)))&
((strong(paul)<~>~patient(paul))) | ~tall(susan) | [
"p0",
"p3",
"p9",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4720925980775631502141736
% SZS output start Proof for 4720925980775631502141736
1. ! [X0] : ((strong(X0) | ~brave(X0)) <=> ~calm(X0)) [input p0]
4. ! [X0] : ((happy(X0) | wise(X0)) => (calm(X0) & ~generous(X0))) [input p3]
10. ! [X0] : (~happy(X0) => (calm(X0) & quiet(X0))) [input p9]
15. ! [X0] : ((~tall(X0) & quiet(X0)) <=> (~strong(X0) & calm(X0))) [input p14]
25. tall(susan) [input hypothesis]
28. ! [X0] : ((calm(X0) & ~generous(X0)) | (~happy(X0) & ~wise(X0))) [ennf transformation 4]
36. ! [X0] : ((calm(X0) & quiet(X0)) | happy(X0)) [ennf transformation 10]
38. ! [X0] : (((strong(X0) | ~brave(X0)) | calm(X0)) & (~calm(X0) | (~strong(X0) & brave(X0)))) [nnf transformation 1]
39. ! [X0] : ((strong(X0) | ~brave(X0) | calm(X0)) & (~calm(X0) | (~strong(X0) & brave(X0)))) [flattening 38]
67. ! [X0] : (((~tall(X0) & quiet(X0)) | (strong(X0) | ~calm(X0))) & ((~strong(X0) & calm(X0)) | (tall(X0) | ~quiet(X0)))) [nnf transformation 15]
68. ! [X0] : (((~tall(X0) & quiet(X0)) | strong(X0) | ~calm(X0)) & ((~strong(X0) & calm(X0)) | tall(X0) | ~quiet(X0))) [flattening 67]
81. ~calm(X0) | ~strong(X0) [cnf transformation 39]
94. ~happy(X0) | calm(X0) [cnf transformation 28]
106. calm(X0) | happy(X0) [cnf transformation 36]
126. ~tall(X0) | strong(X0) | ~calm(X0) [cnf transformation 68]
142. tall(susan) [cnf transformation 25]
195. calm(X0) [subsumption resolution 106,94]
275. ~tall(X0) | strong(X0) [subsumption resolution 126,195]
330. ~strong(X0) [resolution 81,195]
342. strong(susan) [resolution 275,142]
343. $false [subsumption resolution 342,330]
% SZS output end Proof for 4720925980775631502141736
% ------------------------------
% 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 creative is creative or not tall and vice versa.
Everyone who is both happy and not patient is either not strong or generous and vice versa.
Everyone who is generous is not tall and vice versa.
If susan is not humble then someone is humble or funny.
Everyone who is either not calm or patient is not old and vice versa.
Everyone who is tall is not strong or not generous.
Everyone who is either humble or not quiet is both not rich and not generous.
If fred is calm then lucy is either rich or not strong.
If mary is strong then alice is curious or not brave and vice versa.
Everyone who is either not wise or not calm is either funny or not curious.
Everyone who is both not tall and not wise is not old or quiet and vice versa.
Everyone who is either generous or old is either humble or quiet and vice versa.
Everyone who is not tall is patient.
Everyone who is either not generous or not calm is both not creative and humble and vice versa.
Everyone who is not happy is both not old and not funny.
Fred is not brave.
John is kind or rich.
John is generous or wise.
Susan is funny or patient.
Someone is not old or not rich. | Alice is not wise. | entailment | (![X]:(~creative(X)<=>(creative(X)|~tall(X))))&
(![X]:((happy(X)&~patient(X))<=>(~strong(X)<~>generous(X))))&
(![X]:(generous(X)<=>~tall(X)))&
((~humble(susan))=>(?[X]:((humble(X)|funny(X)))))&
(![X]:((~calm(X)<~>patient(X))<=>~old(X)))&
(![X]:(tall(X)=>(~strong(X)|~generous(X))))&
(![X]:((humble(X)<~>~quiet(X))=>(~rich(X)&~generous(X))))&
((calm(fred))=>((rich(lucy)<~>~strong(lucy))))&
((strong(mary))<=>((curious(alice)|~brave(alice))))&
(![X]:((~wise(X)<~>~calm(X))=>(funny(X)<~>~curious(X))))&
(![X]:((~tall(X)&~wise(X))<=>(~old(X)|quiet(X))))&
(![X]:((generous(X)<~>old(X))<=>(humble(X)<~>quiet(X))))&
(![X]:(~tall(X)=>patient(X)))&
(![X]:((~generous(X)<~>~calm(X))<=>(~creative(X)&humble(X))))&
(![X]:(~happy(X)=>(~old(X)&~funny(X))))&
(~brave(fred))&
((kind(john)|rich(john)))&
((generous(john)|wise(john)))&
((funny(susan)|patient(susan)))&
(?[X]:((~old(X)|~rich(X)))) | ~wise(alice) | [
"p0",
"p2",
"p6",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 9203849101250017531591922
% SZS output start Proof for 9203849101250017531591922
1. ! [X0] : (~creative(X0) <=> (~tall(X0) | creative(X0))) [input p0]
3. ! [X0] : (generous(X0) <=> ~tall(X0)) [input p2]
7. ! [X0] : ((humble(X0) <~> ~quiet(X0)) => (~generous(X0) & ~rich(X0))) [input p6]
11. ! [X0] : ((~wise(X0) & ~tall(X0)) <=> (quiet(X0) | ~old(X0))) [input p10]
12. ! [X0] : ((generous(X0) <~> old(X0)) <=> (humble(X0) <~> quiet(X0))) [input p11]
21. wise(alice) [input hypothesis]
26. ! [X0] : ((~generous(X0) & ~rich(X0)) | (humble(X0) <=> ~quiet(X0))) [ennf transformation 7]
31. ! [X0] : ((~creative(X0) | (tall(X0) & ~creative(X0))) & ((~tall(X0) | creative(X0)) | creative(X0))) [nnf transformation 1]
32. ! [X0] : ((~creative(X0) | (tall(X0) & ~creative(X0))) & (~tall(X0) | creative(X0) | creative(X0))) [flattening 31]
35. ! [X0] : ((generous(X0) | tall(X0)) & (~tall(X0) | ~generous(X0))) [nnf transformation 3]
39. ! [X0] : ((~generous(X0) & ~rich(X0)) | ((humble(X0) | quiet(X0)) & (~quiet(X0) | ~humble(X0)))) [nnf transformation 26]
44. ! [X0] : (((~wise(X0) & ~tall(X0)) | (~quiet(X0) & old(X0))) & ((quiet(X0) | ~old(X0)) | (wise(X0) | tall(X0)))) [nnf transformation 11]
45. ! [X0] : (((~wise(X0) & ~tall(X0)) | (~quiet(X0) & old(X0))) & (quiet(X0) | ~old(X0) | wise(X0) | tall(X0))) [flattening 44]
46. ! [X0] : ((((~old(X0) | ~generous(X0)) & (old(X0) | generous(X0))) | ((humble(X0) | ~quiet(X0)) & (quiet(X0) | ~humble(X0)))) & (((~quiet(X0) | ~humble(X0)) & (quiet(X0) | humble(X0))) | ((generous(X0) | ~old(X0)) & (old(X0) | ~generous(X0))))) [nnf transformation 12]
51. ~tall(X0) | creative(X0) | creative(X0) [cnf transformation 32]
52. ~creative(X0) | ~creative(X0) [cnf transformation 32]
61. generous(X0) | tall(X0) [cnf transformation 35]
70. ~generous(X0) | ~quiet(X0) | ~humble(X0) [cnf transformation 39]
71. ~generous(X0) | humble(X0) | quiet(X0) [cnf transformation 39]
84. ~wise(X0) | old(X0) [cnf transformation 45]
92. ~old(X0) | ~generous(X0) | quiet(X0) | ~humble(X0) [cnf transformation 46]
93. ~old(X0) | ~generous(X0) | humble(X0) | ~quiet(X0) [cnf transformation 46]
107. wise(alice) [cnf transformation 21]
108. ~tall(X0) | creative(X0) [duplicate literal removal 51]
109. ~creative(X0) [duplicate literal removal 52]
110. ~tall(X0) [subsumption resolution 108,109]
111. generous(X0) [subsumption resolution 61,110]
125. quiet(X0) | humble(X0) [subsumption resolution 71,111]
126. ~quiet(X0) | ~humble(X0) [subsumption resolution 70,111]
157. ~old(X0) | humble(X0) | ~quiet(X0) [subsumption resolution 93,111]
158. ~quiet(X0) | ~old(X0) [subsumption resolution 157,126]
159. ~old(X0) | quiet(X0) | ~humble(X0) [subsumption resolution 92,111]
160. ~old(X0) | ~humble(X0) [subsumption resolution 159,126]
174. old(alice) [resolution 84,107]
179. ~old(X0) | humble(X0) [resolution 158,125]
180. ~old(X0) [subsumption resolution 179,160]
181. $false [resolution 180,174]
% SZS output end Proof for 9203849101250017531591922
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 4989
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not calm or brave is not wise.
If someone is creative or funny then someone is either not happy or happy.
If john is either old or not wise then lucy is either not generous or happy and vice versa.
If someone is humble or not tall then mary is not rich.
If someone is both not old and creative then someone is funny.
Everyone who is quiet is not brave or generous and vice versa.
Everyone who is both not funny and not kind is either funny or not funny and vice versa.
Everyone who is either wise or old is both kind and funny and vice versa.
If alice is not generous then john is brave or kind.
If alice is creative then someone is not calm or creative and vice versa.
Everyone who is both patient and old is not quiet.
Everyone who is not wise is creative.
If someone is either funny or curious then someone is both not generous and brave and vice versa.
Everyone who is brave is strong.
If susan is both funny and not happy then someone is funny and vice versa.
Mary is happy or tall.
Someone is not brave.
Someone is either not quiet or not strong.
Someone is either not rich or not brave. | Susan is not brave. | entailment | (![X]:((~calm(X)|brave(X))=>~wise(X)))&
((?[X]:((creative(X)|funny(X))))=>(?[X]:((~happy(X)<~>happy(X)))))&
(((old(john)<~>~wise(john)))<=>((~generous(lucy)<~>happy(lucy))))&
((?[X]:((humble(X)|~tall(X))))=>(~rich(mary)))&
((?[X]:((~old(X)&creative(X))))=>(?[X]:(funny(X))))&
(![X]:(quiet(X)<=>(~brave(X)|generous(X))))&
(![X]:((~funny(X)&~kind(X))<=>(funny(X)<~>~funny(X))))&
(![X]:((wise(X)<~>old(X))<=>(kind(X)&funny(X))))&
((~generous(alice))=>((brave(john)|kind(john))))&
((creative(alice))<=>(?[X]:((~calm(X)|creative(X)))))&
(![X]:((patient(X)&old(X))=>~quiet(X)))&
(![X]:(~wise(X)=>creative(X)))&
((?[X]:((funny(X)<~>curious(X))))<=>(?[X]:((~generous(X)&brave(X)))))&
(![X]:(brave(X)=>strong(X)))&
(((funny(susan)&~happy(susan)))<=>(?[X]:(funny(X))))&
((happy(mary)|tall(mary)))&
(?[X]:(~brave(X)))&
(?[X]:((~quiet(X)<~>~strong(X))))&
(?[X]:((~rich(X)<~>~brave(X)))) | ~brave(susan) | [
"p0",
"p4",
"p6",
"p7",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 4261376086414698201220104
% SZS output start Proof for 4261376086414698201220104
1. ! [X0] : ((brave(X0) | ~calm(X0)) => ~wise(X0)) [input p0]
5. ? [X0] : (creative(X0) & ~old(X0)) => ? [X0] : funny(X0) [input p4]
7. ! [X0] : ((~kind(X0) & ~funny(X0)) <=> (funny(X0) <~> ~funny(X0))) [input p6]
8. ! [X0] : ((wise(X0) <~> old(X0)) <=> (funny(X0) & kind(X0))) [input p7]
12. ! [X0] : (~wise(X0) => creative(X0)) [input p11]
20. brave(susan) [input hypothesis]
22. ? [X0] : (creative(X0) & ~old(X0)) => ? [X1] : funny(X1) [rectify 5]
28. ! [X0] : (~wise(X0) | (~brave(X0) & calm(X0))) [ennf transformation 1]
30. ? [X1] : funny(X1) | ! [X0] : (~creative(X0) | old(X0)) [ennf transformation 22]
33. ! [X0] : (creative(X0) | wise(X0)) [ennf transformation 12]
40. ? [X0] : funny(X0) | ! [X1] : (~creative(X1) | old(X1)) [rectify 30]
41. ? [X0] : funny(X0) => funny(sK1) [choice axiom]
42. funny(sK1) | ! [X1] : (~creative(X1) | old(X1)) [skolemisation 40,41]
45. ! [X0] : (((~kind(X0) & ~funny(X0)) | ((funny(X0) | funny(X0)) & (~funny(X0) | ~funny(X0)))) & (((funny(X0) | ~funny(X0)) & (~funny(X0) | funny(X0))) | (kind(X0) | funny(X0)))) [nnf transformation 7]
46. ! [X0] : (((~kind(X0) & ~funny(X0)) | ((funny(X0) | funny(X0)) & (~funny(X0) | ~funny(X0)))) & (((funny(X0) | ~funny(X0)) & (~funny(X0) | funny(X0))) | kind(X0) | funny(X0))) [flattening 45]
47. ! [X0] : ((((~old(X0) | ~wise(X0)) & (old(X0) | wise(X0))) | (~funny(X0) | ~kind(X0))) & ((funny(X0) & kind(X0)) | ((wise(X0) | ~old(X0)) & (old(X0) | ~wise(X0))))) [nnf transformation 8]
48. ! [X0] : ((((~old(X0) | ~wise(X0)) & (old(X0) | wise(X0))) | ~funny(X0) | ~kind(X0)) & ((funny(X0) & kind(X0)) | ((wise(X0) | ~old(X0)) & (old(X0) | ~wise(X0))))) [flattening 47]
72. ~wise(X0) | ~brave(X0) [cnf transformation 28]
85. funny(sK1) | ~creative(X1) | old(X1) [cnf transformation 42]
91. ~funny(X0) | ~funny(X0) | ~funny(X0) [cnf transformation 46]
97. funny(X0) | old(X0) | ~wise(X0) [cnf transformation 48]
98. funny(X0) | wise(X0) | ~old(X0) [cnf transformation 48]
105. creative(X0) | wise(X0) [cnf transformation 33]
121. brave(susan) [cnf transformation 20]
124. ~funny(X0) [duplicate literal removal 91]
153. 5 <=> ! [X1] : (~creative(X1) | old(X1)) [avatar definition]
154. ~creative(X1) | old(X1) <- (5) [avatar component clause 153]
156. 6 <=> funny(sK1) [avatar definition]
158. funny(sK1) <- (6) [avatar component clause 156]
159. 5 | 6 [avatar split clause 85,156,153]
161. ~old(X0) | wise(X0) [subsumption resolution 98,124]
162. ~wise(X0) | old(X0) [subsumption resolution 97,124]
259. $false <- (6) [subsumption resolution 158,124]
260. ~6 [avatar contradiction clause 259]
270. old(X0) | wise(X0) <- (5) [resolution 154,105]
278. old(X0) <- (5) [subsumption resolution 270,162]
281. wise(X0) <- (5) [resolution 278,161]
283. ~brave(X1) <- (5) [resolution 281,72]
285. $false <- (5) [resolution 283,121]
286. ~5 [avatar contradiction clause 285]
287. $false [avatar sat refutation 159,260,286]
% SZS output end Proof for 4261376086414698201220104
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not humble or kind is not rich and vice versa.
Everyone who is tall or not tall is either wise or curious.
Everyone who is brave or generous is both not generous and not kind and vice versa.
If someone is not humble or calm then john is happy or not brave.
Everyone who is both happy and generous is both quiet and kind and vice versa.
If someone is curious then susan is tall.
If lucy is both strong and curious then someone is both not tall and not old.
Everyone who is either wise or not happy is not funny and vice versa.
Everyone who is both not strong and not happy is not wise and vice versa.
If someone is not quiet or brave then someone is not curious.
If someone is either humble or old then mary is old.
Everyone who is both strong and rich is curious or funny.
If someone is patient then susan is not calm.
If mary is not happy then someone is not strong and vice versa.
If someone is both rich and kind then someone is either tall or brave and vice versa.
Everyone who is either strong or not curious is strong.
Someone is not brave or old.
Susan is either curious or kind.
Lucy is patient.
Someone is quiet.
Susan is either funny or not old.
Susan is either happy or not funny. | Susan is kind. | contradiction | (![X]:((~humble(X)<~>kind(X))<=>~rich(X)))&
(![X]:((tall(X)|~tall(X))=>(wise(X)<~>curious(X))))&
(![X]:((brave(X)|generous(X))<=>(~generous(X)&~kind(X))))&
((?[X]:((~humble(X)|calm(X))))=>((happy(john)|~brave(john))))&
(![X]:((happy(X)&generous(X))<=>(quiet(X)&kind(X))))&
((?[X]:(curious(X)))=>(tall(susan)))&
(((strong(lucy)&curious(lucy)))=>(?[X]:((~tall(X)&~old(X)))))&
(![X]:((wise(X)<~>~happy(X))<=>~funny(X)))&
(![X]:((~strong(X)&~happy(X))<=>~wise(X)))&
((?[X]:((~quiet(X)|brave(X))))=>(?[X]:(~curious(X))))&
((?[X]:((humble(X)<~>old(X))))=>(old(mary)))&
(![X]:((strong(X)&rich(X))=>(curious(X)|funny(X))))&
((?[X]:(patient(X)))=>(~calm(susan)))&
((~happy(mary))<=>(?[X]:(~strong(X))))&
((?[X]:((rich(X)&kind(X))))<=>(?[X]:((tall(X)<~>brave(X)))))&
(![X]:((strong(X)<~>~curious(X))=>strong(X)))&
(?[X]:((~brave(X)|old(X))))&
((curious(susan)<~>kind(susan)))&
(patient(lucy))&
(?[X]:(quiet(X)))&
((funny(susan)<~>~old(susan)))&
((happy(susan)<~>~funny(susan))) | kind(susan) | [
"p1",
"p7",
"p17",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 7264314732627415777970750
% SZS output start Proof for 7264314732627415777970750
2. ! [X0] : ((~tall(X0) | tall(X0)) => (wise(X0) <~> curious(X0))) [input p1]
8. ! [X0] : ((wise(X0) <~> ~happy(X0)) <=> ~funny(X0)) [input p7]
18. curious(susan) <~> kind(susan) [input p17]
22. happy(susan) <~> ~funny(susan) [input p21]
23. kind(susan) [input hypothesis]
29. ! [X0] : ((wise(X0) <~> curious(X0)) | (tall(X0) & ~tall(X0))) [ennf transformation 2]
41. ! [X0] : (((~curious(X0) | ~wise(X0)) & (curious(X0) | wise(X0))) | (tall(X0) & ~tall(X0))) [nnf transformation 29]
48. ! [X0] : ((((happy(X0) | ~wise(X0)) & (~happy(X0) | wise(X0))) | funny(X0)) & (~funny(X0) | ((wise(X0) | happy(X0)) & (~happy(X0) | ~wise(X0))))) [nnf transformation 8]
67. (~kind(susan) | ~curious(susan)) & (kind(susan) | curious(susan)) [nnf transformation 18]
71. (funny(susan) | ~happy(susan)) & (~funny(susan) | happy(susan)) [nnf transformation 22]
76. curious(X0) | wise(X0) | ~tall(X0) [cnf transformation 41]
77. curious(X0) | wise(X0) | tall(X0) [cnf transformation 41]
93. ~funny(X0) | ~happy(X0) | ~wise(X0) [cnf transformation 48]
96. ~wise(X0) | happy(X0) | funny(X0) [cnf transformation 48]
117. ~kind(susan) | ~curious(susan) [cnf transformation 67]
121. ~funny(susan) | happy(susan) [cnf transformation 71]
122. funny(susan) | ~happy(susan) [cnf transformation 71]
123. kind(susan) [cnf transformation 23]
128. curious(X0) | wise(X0) [subsumption resolution 76,77]
246. 28 <=> curious(susan) [avatar definition]
248. ~curious(susan) <- (~28) [avatar component clause 246]
250. 29 <=> kind(susan) [avatar definition]
253. ~28 | ~29 [avatar split clause 117,250,246]
256. 30 <=> funny(susan) [avatar definition]
257. funny(susan) <- (30) [avatar component clause 256]
266. 32 <=> happy(susan) [avatar definition]
267. happy(susan) <- (32) [avatar component clause 266]
269. ~32 | 30 [avatar split clause 122,256,266]
270. 32 | ~30 [avatar split clause 121,256,266]
271. 29 [avatar split clause 123,250]
278. wise(susan) <- (~28) [resolution 128,248]
325. happy(susan) | funny(susan) <- (~28) [resolution 96,278]
365. 30 | 32 | 28 [avatar split clause 325,246,266,256]
385. ~happy(susan) | ~wise(susan) <- (30) [resolution 257,93]
386. ~wise(susan) <- (30, 32) [subsumption resolution 385,267]
387. $false <- (~28, 30, 32) [subsumption resolution 386,278]
388. 28 | ~30 | ~32 [avatar contradiction clause 387]
389. $false [avatar sat refutation 253,269,270,271,365,388]
% SZS output end Proof for 7264314732627415777970750
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is either tall or not tall then someone is generous and vice versa.
Everyone who is both creative and brave is both generous and tall and vice versa.
If alice is not calm or not brave then paul is both creative and patient and vice versa.
Everyone who is not funny is generous.
If mary is either old or not curious then paul is either rich or not old.
If someone is tall or not patient then mary is strong and vice versa.
If someone is not generous then someone is either not curious or generous.
Everyone who is strong is both not humble and kind.
If someone is not quiet or generous then alice is not curious and vice versa.
Everyone who is not patient or patient is both not curious and happy and vice versa.
If someone is both quiet and not rich then susan is strong.
Everyone who is either kind or not brave is both not brave and kind and vice versa.
If someone is not humble or kind then lucy is both not funny and not calm and vice versa.
Someone is brave.
Paul is either strong or not curious.
Susan is either humble or old.
Paul is tall or not wise.
Susan is funny or not happy.
Fred is both generous and happy. | Paul is brave. | entailment | (((tall(lucy)<~>~tall(lucy)))<=>(?[X]:(generous(X))))&
(![X]:((creative(X)&brave(X))<=>(generous(X)&tall(X))))&
(((~calm(alice)|~brave(alice)))<=>((creative(paul)&patient(paul))))&
(![X]:(~funny(X)=>generous(X)))&
(((old(mary)<~>~curious(mary)))=>((rich(paul)<~>~old(paul))))&
((?[X]:((tall(X)|~patient(X))))<=>(strong(mary)))&
((?[X]:(~generous(X)))=>(?[X]:((~curious(X)<~>generous(X)))))&
(![X]:(strong(X)=>(~humble(X)&kind(X))))&
((?[X]:((~quiet(X)|generous(X))))<=>(~curious(alice)))&
(![X]:((~patient(X)|patient(X))<=>(~curious(X)&happy(X))))&
((?[X]:((quiet(X)&~rich(X))))=>(strong(susan)))&
(![X]:((kind(X)<~>~brave(X))<=>(~brave(X)&kind(X))))&
((?[X]:((~humble(X)|kind(X))))<=>((~funny(lucy)&~calm(lucy))))&
(?[X]:(brave(X)))&
((strong(paul)<~>~curious(paul)))&
((humble(susan)<~>old(susan)))&
((tall(paul)|~wise(paul)))&
((funny(susan)|~happy(susan)))&
((generous(fred)&happy(fred))) | brave(paul) | [
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 5920011240400221388295045
% SZS output start Proof for 5920011240400221388295045
12. ! [X0] : ((kind(X0) <~> ~brave(X0)) <=> (kind(X0) & ~brave(X0))) [input p11]
20. ~brave(paul) [input hypothesis]
51. ! [X0] : ((((brave(X0) | ~kind(X0)) & (~brave(X0) | kind(X0))) | (~kind(X0) | brave(X0))) & ((kind(X0) & ~brave(X0)) | ((kind(X0) | brave(X0)) & (~brave(X0) | ~kind(X0))))) [nnf transformation 12]
52. ! [X0] : ((((brave(X0) | ~kind(X0)) & (~brave(X0) | kind(X0))) | ~kind(X0) | brave(X0)) & ((kind(X0) & ~brave(X0)) | ((kind(X0) | brave(X0)) & (~brave(X0) | ~kind(X0))))) [flattening 51]
99. kind(X0) | kind(X0) | brave(X0) [cnf transformation 52]
101. brave(X0) | ~kind(X0) | ~kind(X0) | brave(X0) [cnf transformation 52]
115. ~brave(paul) [cnf transformation 20]
117. kind(X0) | brave(X0) [duplicate literal removal 99]
118. brave(X0) | ~kind(X0) [duplicate literal removal 101]
237. brave(X0) [subsumption resolution 117,118]
270. $false [subsumption resolution 115,237]
% SZS output end Proof for 5920011240400221388295045
% ------------------------------
% 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 mary is creative or kind then paul is either old or not humble. If someone is quiet then paul is not rich. Everyone who is both old and not generous is tall. Everyone who is not patient or not funny is not brave or not happy and vice versa. If paul is not old or funny then someone is not wise and vice versa. Everyone who is not funny or curious is patient and vice versa. If someone is either humble or not curious then someone is not kind and vice versa. If someone is both funny and not curious then susan is either not strong or not old and vice versa. If someone is brave or patient then someone is both funny and wise and vice versa. Everyone who is creative is rich. Everyone who is not strong is generous. If alice is not patient then paul is either not rich or not kind and vice versa. If someone is not wise then paul is patient or not funny and vice versa. If john is not rich or quiet then lucy is either not brave or not tall and vice versa. Everyone who is not patient or happy is calm or not quiet and vice versa. Everyone who is old or curious is strong and vice versa. Paul is either not curious or rich. Paul is wise or not wise. Someone is both not humble and not kind. Lucy is either calm or not funny. Fred is either tall or not old. Someone is both kind and not happy. Alice is not strong. | John is not humble. | neutral | (((creative(mary)|kind(mary)))=>((old(paul)<~>~humble(paul))))&
((?[X]:(quiet(X)))=>(~rich(paul)))&
(![X]:((old(X)&~generous(X))=>tall(X)))&
(![X]:((~patient(X)|~funny(X))<=>(~brave(X)|~happy(X))))&
(((~old(paul)|funny(paul)))<=>(?[X]:(~wise(X))))&
(![X]:((~funny(X)|curious(X))<=>patient(X)))&
((?[X]:((humble(X)<~>~curious(X))))<=>(?[X]:(~kind(X))))&
((?[X]:((funny(X)&~curious(X))))<=>((~strong(susan)<~>~old(susan))))&
((?[X]:((brave(X)|patient(X))))<=>(?[X]:((funny(X)&wise(X)))))&
(![X]:(creative(X)=>rich(X)))&
(![X]:(~strong(X)=>generous(X)))&
((~patient(alice))<=>((~rich(paul)<~>~kind(paul))))&
((?[X]:(~wise(X)))<=>((patient(paul)|~funny(paul))))&
(((~rich(john)|quiet(john)))<=>((~brave(lucy)<~>~tall(lucy))))&
(![X]:((~patient(X)|happy(X))<=>(calm(X)|~quiet(X))))&
(![X]:((old(X)|curious(X))<=>strong(X)))&
((~curious(paul)<~>rich(paul)))&
((wise(paul)|~wise(paul)))&
(?[X]:((~humble(X)&~kind(X))))&
((calm(lucy)<~>~funny(lucy)))&
((tall(fred)<~>~old(fred)))&
(?[X]:((kind(X)&~happy(X))))&
(~strong(alice)) | ~humble(john) | [] | null | 0 |
Everyone who is either quiet or patient is happy or curious. Everyone who is not rich or old is brave or not generous and vice versa. Everyone who is either not tall or not funny is either funny or humble. If someone is wise then alice is kind and vice versa. If paul is either not wise or not kind then someone is either not happy or not creative. Everyone who is either curious or not funny is wise and vice versa. If alice is not happy then someone is not happy or happy. Everyone who is happy or humble is not wise and vice versa. If lucy is not calm then susan is strong and vice versa. Everyone who is happy is rich or not humble and vice versa. Everyone who is either not brave or happy is calm. Everyone who is quiet or tall is both not kind and not patient and vice versa. Everyone who is not curious or patient is strong or not quiet. Everyone who is not humble or curious is either not calm or curious and vice versa. If lucy is either calm or not kind then someone is both not generous and humble. Everyone who is both not creative and strong is not brave and vice versa. Someone is rich. Someone is patient or happy. Someone is calm or not kind. Paul is creative or strong. Paul is either old or funny. Someone is both not calm and not rich. Alice is not strong. Someone is humble or not kind. | Susan is brave. | neutral | (![X]:((quiet(X)<~>patient(X))=>(happy(X)|curious(X))))&
(![X]:((~rich(X)|old(X))<=>(brave(X)|~generous(X))))&
(![X]:((~tall(X)<~>~funny(X))=>(funny(X)<~>humble(X))))&
((?[X]:(wise(X)))<=>(kind(alice)))&
(((~wise(paul)<~>~kind(paul)))=>(?[X]:((~happy(X)<~>~creative(X)))))&
(![X]:((curious(X)<~>~funny(X))<=>wise(X)))&
((~happy(alice))=>(?[X]:((~happy(X)|happy(X)))))&
(![X]:((happy(X)|humble(X))<=>~wise(X)))&
((~calm(lucy))<=>(strong(susan)))&
(![X]:(happy(X)<=>(rich(X)|~humble(X))))&
(![X]:((~brave(X)<~>happy(X))=>calm(X)))&
(![X]:((quiet(X)|tall(X))<=>(~kind(X)&~patient(X))))&
(![X]:((~curious(X)|patient(X))=>(strong(X)|~quiet(X))))&
(![X]:((~humble(X)|curious(X))<=>(~calm(X)<~>curious(X))))&
(((calm(lucy)<~>~kind(lucy)))=>(?[X]:((~generous(X)&humble(X)))))&
(![X]:((~creative(X)&strong(X))<=>~brave(X)))&
(?[X]:(rich(X)))&
(?[X]:((patient(X)|happy(X))))&
(?[X]:((calm(X)|~kind(X))))&
((creative(paul)|strong(paul)))&
((old(paul)<~>funny(paul)))&
(?[X]:((~calm(X)&~rich(X))))&
(~strong(alice))&
(?[X]:((humble(X)|~kind(X)))) | brave(susan) | [] | null | 0 |
If someone is not calm or not happy then someone is not old or wise. If john is not old or tall then someone is both not happy and humble. Everyone who is either tall or not curious is both not old and creative and vice versa. Everyone who is humble or not wise is not funny or brave and vice versa. If mary is both quiet and rich then someone is wise or not patient and vice versa. If john is not brave or humble then alice is not curious. Everyone who is not old or generous is humble. Everyone who is both not rich and old is both strong and not old. Everyone who is not tall or not generous is either not rich or creative and vice versa. Everyone who is not creative or not old is not calm and vice versa. If someone is not old or not brave then someone is both strong and tall. If someone is both happy and kind then mary is both quiet and not rich. If someone is both patient and not generous then paul is not kind and vice versa. Everyone who is both wise and tall is creative. Everyone who is both quiet and kind is either not generous or calm and vice versa. Everyone who is not happy or creative is both not tall and not old and vice versa. Someone is wise or not calm. Mary is either not happy or not rich. Someone is either tall or not happy. Susan is not happy or funny. Fred is not curious or humble. John is not quiet. Someone is creative or not funny. Fred is either happy or not humble. | John is not old. | neutral | ((?[X]:((~calm(X)|~happy(X))))=>(?[X]:((~old(X)|wise(X)))))&
(((~old(john)|tall(john)))=>(?[X]:((~happy(X)&humble(X)))))&
(![X]:((tall(X)<~>~curious(X))<=>(~old(X)&creative(X))))&
(![X]:((humble(X)|~wise(X))<=>(~funny(X)|brave(X))))&
(((quiet(mary)&rich(mary)))<=>(?[X]:((wise(X)|~patient(X)))))&
(((~brave(john)|humble(john)))=>(~curious(alice)))&
(![X]:((~old(X)|generous(X))=>humble(X)))&
(![X]:((~rich(X)&old(X))=>(strong(X)&~old(X))))&
(![X]:((~tall(X)|~generous(X))<=>(~rich(X)<~>creative(X))))&
(![X]:((~creative(X)|~old(X))<=>~calm(X)))&
((?[X]:((~old(X)|~brave(X))))=>(?[X]:((strong(X)&tall(X)))))&
((?[X]:((happy(X)&kind(X))))=>((quiet(mary)&~rich(mary))))&
((?[X]:((patient(X)&~generous(X))))<=>(~kind(paul)))&
(![X]:((wise(X)&tall(X))=>creative(X)))&
(![X]:((quiet(X)&kind(X))<=>(~generous(X)<~>calm(X))))&
(![X]:((~happy(X)|creative(X))<=>(~tall(X)&~old(X))))&
(?[X]:((wise(X)|~calm(X))))&
((~happy(mary)<~>~rich(mary)))&
(?[X]:((tall(X)<~>~happy(X))))&
((~happy(susan)|funny(susan)))&
((~curious(fred)|humble(fred)))&
(~quiet(john))&
(?[X]:((creative(X)|~funny(X))))&
((happy(fred)<~>~humble(fred))) | ~old(john) | [] | null | 0 |
If susan is strong then someone is either not strong or not brave.
If someone is both curious and kind then someone is either not rich or not strong.
Everyone who is both wise and brave is both old and tall and vice versa.
If someone is kind or generous then someone is both not generous and kind and vice versa.
If someone is tall then someone is either not patient or not strong.
Everyone who is not tall or calm is not patient and vice versa.
Everyone who is not rich is both wise and quiet and vice versa.
Everyone who is not brave or not kind is not kind.
If paul is tall then someone is not generous.
Everyone who is creative or not rich is either not brave or calm.
Everyone who is not strong or not tall is both not old and patient.
Everyone who is both not happy and quiet is either curious or calm.
Everyone who is both quiet and old is calm.
Everyone who is either not wise or strong is calm.
Everyone who is both generous and kind is creative or not generous.
If paul is not patient then john is happy.
Someone is creative or happy.
Someone is not funny or not strong.
Someone is old.
Someone is either not wise or not tall.
Fred is both strong and calm.
Someone is both happy and not brave.
Someone is not old or kind. | Paul is not patient. | neutral | ((strong(susan))=>(?[X]:((~strong(X)<~>~brave(X)))))&
((?[X]:((curious(X)&kind(X))))=>(?[X]:((~rich(X)<~>~strong(X)))))&
(![X]:((wise(X)&brave(X))<=>(old(X)&tall(X))))&
((?[X]:((kind(X)|generous(X))))<=>(?[X]:((~generous(X)&kind(X)))))&
((?[X]:(tall(X)))=>(?[X]:((~patient(X)<~>~strong(X)))))&
(![X]:((~tall(X)|calm(X))<=>~patient(X)))&
(![X]:(~rich(X)<=>(wise(X)&quiet(X))))&
(![X]:((~brave(X)|~kind(X))=>~kind(X)))&
((tall(paul))=>(?[X]:(~generous(X))))&
(![X]:((creative(X)|~rich(X))=>(~brave(X)<~>calm(X))))&
(![X]:((~strong(X)|~tall(X))=>(~old(X)&patient(X))))&
(![X]:((~happy(X)&quiet(X))=>(curious(X)<~>calm(X))))&
(![X]:((quiet(X)&old(X))=>calm(X)))&
(![X]:((~wise(X)<~>strong(X))=>calm(X)))&
(![X]:((generous(X)&kind(X))=>(creative(X)|~generous(X))))&
((~patient(paul))=>(happy(john)))&
(?[X]:((creative(X)|happy(X))))&
(?[X]:((~funny(X)|~strong(X))))&
(?[X]:(old(X)))&
(?[X]:((~wise(X)<~>~tall(X))))&
((strong(fred)&calm(fred)))&
(?[X]:((happy(X)&~brave(X))))&
(?[X]:((~old(X)|kind(X)))) | ~patient(paul) | [] | null | 0 |
If alice is tall or not old then lucy is both happy and not humble and vice versa. Everyone who is patient or curious is either kind or calm. Everyone who is both not wise and not brave is either not brave or not tall. If john is both humble and not patient then john is both patient and tall. If alice is not rich then someone is both not happy and not creative. If john is either humble or not rich then alice is humble or happy and vice versa. Everyone who is both not curious and generous is rich. Everyone who is patient or kind is patient or not brave. Everyone who is both old and tall is both old and not curious. If fred is creative or generous then alice is not happy. If someone is either humble or not brave then mary is both brave and patient. Everyone who is quiet is not happy. If paul is old then susan is rich or kind and vice versa. Everyone who is both not brave and not quiet is not brave or not generous. If someone is either generous or brave then lucy is either creative or not brave and vice versa. Everyone who is patient is both happy and funny and vice versa. Paul is tall or funny. Someone is both tall and not old. Susan is happy. Someone is either wise or not old. Lucy is both curious and not quiet. Someone is both not kind and not old. Someone is quiet. Mary is generous. | Fred is not patient. | neutral | (((tall(alice)|~old(alice)))<=>((happy(lucy)&~humble(lucy))))&
(![X]:((patient(X)|curious(X))=>(kind(X)<~>calm(X))))&
(![X]:((~wise(X)&~brave(X))=>(~brave(X)<~>~tall(X))))&
(((humble(john)&~patient(john)))=>((patient(john)&tall(john))))&
((~rich(alice))=>(?[X]:((~happy(X)&~creative(X)))))&
(((humble(john)<~>~rich(john)))<=>((humble(alice)|happy(alice))))&
(![X]:((~curious(X)&generous(X))=>rich(X)))&
(![X]:((patient(X)|kind(X))=>(patient(X)|~brave(X))))&
(![X]:((old(X)&tall(X))=>(old(X)&~curious(X))))&
(((creative(fred)|generous(fred)))=>(~happy(alice)))&
((?[X]:((humble(X)<~>~brave(X))))=>((brave(mary)&patient(mary))))&
(![X]:(quiet(X)=>~happy(X)))&
((old(paul))<=>((rich(susan)|kind(susan))))&
(![X]:((~brave(X)&~quiet(X))=>(~brave(X)|~generous(X))))&
((?[X]:((generous(X)<~>brave(X))))<=>((creative(lucy)<~>~brave(lucy))))&
(![X]:(patient(X)<=>(happy(X)&funny(X))))&
((tall(paul)|funny(paul)))&
(?[X]:((tall(X)&~old(X))))&
(happy(susan))&
(?[X]:((wise(X)<~>~old(X))))&
((curious(lucy)&~quiet(lucy)))&
(?[X]:((~kind(X)&~old(X))))&
(?[X]:(quiet(X)))&
(generous(mary)) | ~patient(fred) | [] | null | 0 |
If someone is not humble or not creative then alice is either not creative or not quiet and vice versa.
Everyone who is either not tall or brave is both not quiet and not rich.
If john is both old and not calm then someone is either kind or not curious and vice versa.
Everyone who is not funny or not curious is calm and vice versa.
Everyone who is both tall and humble is either calm or not tall and vice versa.
Everyone who is not brave or not humble is both curious and not strong and vice versa.
If lucy is not tall then paul is funny and vice versa.
If john is both not strong and patient then john is either not rich or patient.
If someone is either not happy or not calm then someone is not funny or not wise.
If susan is either not brave or not strong then mary is both not wise and wise and vice versa.
Everyone who is both generous and brave is either not brave or not calm and vice versa.
If someone is either patient or not curious then someone is both not tall and wise and vice versa.
Everyone who is not kind is either rich or not calm and vice versa.
Everyone who is not creative is both not curious and not old and vice versa.
If someone is quiet then john is not creative.
If john is patient then paul is not kind or not calm and vice versa.
Susan is both not calm and not rich.
Alice is both generous and patient.
Alice is not quiet or not calm.
Someone is either not old or generous.
Someone is not strong.
John is calm.
John is both quiet and patient.
Someone is old. | Alice is not tall. | contradiction | ((?[X]:((~humble(X)|~creative(X))))<=>((~creative(alice)<~>~quiet(alice))))&
(![X]:((~tall(X)<~>brave(X))=>(~quiet(X)&~rich(X))))&
(((old(john)&~calm(john)))<=>(?[X]:((kind(X)<~>~curious(X)))))&
(![X]:((~funny(X)|~curious(X))<=>calm(X)))&
(![X]:((tall(X)&humble(X))<=>(calm(X)<~>~tall(X))))&
(![X]:((~brave(X)|~humble(X))<=>(curious(X)&~strong(X))))&
((~tall(lucy))<=>(funny(paul)))&
(((~strong(john)&patient(john)))=>((~rich(john)<~>patient(john))))&
((?[X]:((~happy(X)<~>~calm(X))))=>(?[X]:((~funny(X)|~wise(X)))))&
(((~brave(susan)<~>~strong(susan)))<=>((~wise(mary)&wise(mary))))&
(![X]:((generous(X)&brave(X))<=>(~brave(X)<~>~calm(X))))&
((?[X]:((patient(X)<~>~curious(X))))<=>(?[X]:((~tall(X)&wise(X)))))&
(![X]:(~kind(X)<=>(rich(X)<~>~calm(X))))&
(![X]:(~creative(X)<=>(~curious(X)&~old(X))))&
((?[X]:(quiet(X)))=>(~creative(john)))&
((patient(john))<=>((~kind(paul)|~calm(paul))))&
((~calm(susan)&~rich(susan)))&
((generous(alice)&patient(alice)))&
((~quiet(alice)|~calm(alice)))&
(?[X]:((~old(X)<~>generous(X))))&
(?[X]:(~strong(X)))&
(calm(john))&
((quiet(john)&patient(john)))&
(?[X]:(old(X))) | ~tall(alice) | [
"p4",
"p10",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 8088164422747476670603059
% SZS output start Proof for 8088164422747476670603059
5. ! [X0] : ((humble(X0) & tall(X0)) <=> (calm(X0) <~> ~tall(X0))) [input p4]
11. ! [X0] : ((brave(X0) & generous(X0)) <=> (~brave(X0) <~> ~calm(X0))) [input p10]
18. patient(alice) & generous(alice) [input p17]
25. ~tall(alice) [input hypothesis]
45. ! [X0] : (((humble(X0) & tall(X0)) | ((calm(X0) | tall(X0)) & (~tall(X0) | ~calm(X0)))) & (((tall(X0) | ~calm(X0)) & (~tall(X0) | calm(X0))) | (~humble(X0) | ~tall(X0)))) [nnf transformation 5]
46. ! [X0] : (((humble(X0) & tall(X0)) | ((calm(X0) | tall(X0)) & (~tall(X0) | ~calm(X0)))) & (((tall(X0) | ~calm(X0)) & (~tall(X0) | calm(X0))) | ~humble(X0) | ~tall(X0))) [flattening 45]
57. ! [X0] : (((brave(X0) & generous(X0)) | ((~brave(X0) | calm(X0)) & (~calm(X0) | brave(X0)))) & (((calm(X0) | brave(X0)) & (~calm(X0) | ~brave(X0))) | (~brave(X0) | ~generous(X0)))) [nnf transformation 11]
58. ! [X0] : (((brave(X0) & generous(X0)) | ((~brave(X0) | calm(X0)) & (~calm(X0) | brave(X0)))) & (((calm(X0) | brave(X0)) & (~calm(X0) | ~brave(X0))) | ~brave(X0) | ~generous(X0))) [flattening 57]
98. tall(X0) | calm(X0) | tall(X0) [cnf transformation 46]
118. ~calm(X0) | ~brave(X0) | ~brave(X0) | ~generous(X0) [cnf transformation 58]
122. brave(X0) | ~calm(X0) | brave(X0) [cnf transformation 58]
143. generous(alice) [cnf transformation 18]
153. ~tall(alice) [cnf transformation 25]
154. ~calm(X0) | ~brave(X0) | ~generous(X0) [duplicate literal removal 118]
155. ~calm(X0) | brave(X0) [duplicate literal removal 122]
158. calm(X0) | tall(X0) [duplicate literal removal 98]
269. ~generous(X0) | ~calm(X0) [subsumption resolution 154,155]
321. 36 <=> calm(alice) [avatar definition]
323. ~calm(alice) <- (~36) [avatar component clause 321]
361. ~calm(alice) [resolution 269,143]
362. ~36 [avatar split clause 361,321]
363. tall(alice) <- (~36) [resolution 323,158]
364. $false <- (~36) [subsumption resolution 363,153]
365. 36 [avatar contradiction clause 364]
366. $false [avatar sat refutation 362,365]
% SZS output end Proof for 8088164422747476670603059
% ------------------------------
% 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 calm and kind is both humble and happy and vice versa.
If someone is both not tall and not quiet then paul is both not quiet and creative.
Everyone who is both not quiet and not funny is patient and vice versa.
Everyone who is both patient and not rich is both not happy and not creative and vice versa.
Everyone who is either not patient or not humble is tall and vice versa.
If paul is not wise then john is rich and vice versa.
If someone is not happy then someone is not creative and vice versa.
If someone is both happy and not curious then susan is either not curious or wise.
Everyone who is not happy is either not humble or rich.
If someone is either not calm or brave then paul is both rich and not calm.
If someone is tall or kind then paul is not happy and vice versa.
If john is curious or old then someone is wise or not rich.
If someone is either kind or not rich then someone is not happy or rich.
Everyone who is both not wise and brave is not kind and vice versa.
If someone is either patient or creative then someone is both funny and not funny.
Someone is either humble or not old.
Someone is not strong.
Alice is kind or creative.
Susan is patient.
Someone is both not curious and happy.
Someone is not humble.
Lucy is generous.
Someone is both happy and not calm. | Paul is happy. | contradiction | (![X]:((calm(X)&kind(X))<=>(humble(X)&happy(X))))&
((?[X]:((~tall(X)&~quiet(X))))=>((~quiet(paul)&creative(paul))))&
(![X]:((~quiet(X)&~funny(X))<=>patient(X)))&
(![X]:((patient(X)&~rich(X))<=>(~happy(X)&~creative(X))))&
(![X]:((~patient(X)<~>~humble(X))<=>tall(X)))&
((~wise(paul))<=>(rich(john)))&
((?[X]:(~happy(X)))<=>(?[X]:(~creative(X))))&
((?[X]:((happy(X)&~curious(X))))=>((~curious(susan)<~>wise(susan))))&
(![X]:(~happy(X)=>(~humble(X)<~>rich(X))))&
((?[X]:((~calm(X)<~>brave(X))))=>((rich(paul)&~calm(paul))))&
((?[X]:((tall(X)|kind(X))))<=>(~happy(paul)))&
(((curious(john)|old(john)))=>(?[X]:((wise(X)|~rich(X)))))&
((?[X]:((kind(X)<~>~rich(X))))=>(?[X]:((~happy(X)|rich(X)))))&
(![X]:((~wise(X)&brave(X))<=>~kind(X)))&
((?[X]:((patient(X)<~>creative(X))))=>(?[X]:((funny(X)&~funny(X)))))&
(?[X]:((humble(X)<~>~old(X))))&
(?[X]:(~strong(X)))&
((kind(alice)|creative(alice)))&
(patient(susan))&
(?[X]:((~curious(X)&happy(X))))&
(?[X]:(~humble(X)))&
(generous(lucy))&
(?[X]:((happy(X)&~calm(X)))) | happy(paul) | [
"p0",
"p1",
"p2",
"p4",
"p10",
"p14",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 5533424687574840757849748
% SZS output start Proof for 5533424687574840757849748
1. ! [X0] : ((kind(X0) & calm(X0)) <=> (happy(X0) & humble(X0))) [input p0]
2. ? [X0] : (~quiet(X0) & ~tall(X0)) => (creative(paul) & ~quiet(paul)) [input p1]
3. ! [X0] : ((~funny(X0) & ~quiet(X0)) <=> patient(X0)) [input p2]
5. ! [X0] : ((~patient(X0) <~> ~humble(X0)) <=> tall(X0)) [input p4]
11. ? [X0] : (kind(X0) | tall(X0)) <=> ~happy(paul) [input p10]
15. ? [X0] : (patient(X0) <~> creative(X0)) => ? [X0] : (~funny(X0) & funny(X0)) [input p14]
19. patient(susan) [input p18]
24. happy(paul) [input hypothesis]
27. ? [X0] : (patient(X0) <~> creative(X0)) => ? [X1] : (~funny(X1) & funny(X1)) [rectify 15]
30. (creative(paul) & ~quiet(paul)) | ! [X0] : (quiet(X0) | tall(X0)) [ennf transformation 2]
36. ? [X1] : (~funny(X1) & funny(X1)) | ! [X0] : (patient(X0) <=> creative(X0)) [ennf transformation 27]
37. ! [X0] : (((kind(X0) & calm(X0)) | (~happy(X0) | ~humble(X0))) & ((happy(X0) & humble(X0)) | (~kind(X0) | ~calm(X0)))) [nnf transformation 1]
38. ! [X0] : (((kind(X0) & calm(X0)) | ~happy(X0) | ~humble(X0)) & ((happy(X0) & humble(X0)) | ~kind(X0) | ~calm(X0))) [flattening 37]
39. ! [X0] : (((~funny(X0) & ~quiet(X0)) | ~patient(X0)) & (patient(X0) | (funny(X0) | quiet(X0)))) [nnf transformation 3]
40. ! [X0] : (((~funny(X0) & ~quiet(X0)) | ~patient(X0)) & (patient(X0) | funny(X0) | quiet(X0))) [flattening 39]
43. ! [X0] : ((((humble(X0) | patient(X0)) & (~humble(X0) | ~patient(X0))) | ~tall(X0)) & (tall(X0) | ((~patient(X0) | humble(X0)) & (~humble(X0) | patient(X0))))) [nnf transformation 5]
53. (? [X0] : (kind(X0) | tall(X0)) | happy(paul)) & (~happy(paul) | ! [X0] : (~kind(X0) & ~tall(X0))) [nnf transformation 11]
54. (? [X0] : (kind(X0) | tall(X0)) | happy(paul)) & (~happy(paul) | ! [X1] : (~kind(X1) & ~tall(X1))) [rectify 53]
55. ? [X0] : (kind(X0) | tall(X0)) => (kind(sK2) | tall(sK2)) [choice axiom]
56. ((kind(sK2) | tall(sK2)) | happy(paul)) & (~happy(paul) | ! [X1] : (~kind(X1) & ~tall(X1))) [skolemisation 54,55]
65. ? [X1] : (~funny(X1) & funny(X1)) | ! [X0] : ((patient(X0) | ~creative(X0)) & (creative(X0) | ~patient(X0))) [nnf transformation 36]
66. ? [X0] : (~funny(X0) & funny(X0)) | ! [X1] : ((patient(X1) | ~creative(X1)) & (creative(X1) | ~patient(X1))) [rectify 65]
67. ? [X0] : (~funny(X0) & funny(X0)) => (~funny(sK5) & funny(sK5)) [choice axiom]
68. (~funny(sK5) & funny(sK5)) | ! [X1] : ((patient(X1) | ~creative(X1)) & (creative(X1) | ~patient(X1))) [skolemisation 66,67]
81. ~happy(X0) | kind(X0) | ~humble(X0) [cnf transformation 38]
83. creative(paul) | quiet(X0) | tall(X0) [cnf transformation 30]
85. ~patient(X0) | ~quiet(X0) [cnf transformation 40]
92. ~patient(X0) | tall(X0) | humble(X0) [cnf transformation 43]
107. ~happy(paul) | ~tall(X1) [cnf transformation 56]
108. ~happy(paul) | ~kind(X1) [cnf transformation 56]
118. funny(sK5) | patient(X1) | ~creative(X1) [cnf transformation 68]
120. ~funny(sK5) | patient(X1) | ~creative(X1) [cnf transformation 68]
124. patient(susan) [cnf transformation 19]
130. happy(paul) [cnf transformation 24]
132. 1 <=> ! [X0] : (quiet(X0) | tall(X0)) [avatar definition]
133. quiet(X0) | tall(X0) <- (1) [avatar component clause 132]
135. 2 <=> creative(paul) [avatar definition]
137. creative(paul) <- (2) [avatar component clause 135]
138. 1 | 2 [avatar split clause 83,135,132]
202. 17 <=> happy(paul) [avatar definition]
204. happy(paul) <- (17) [avatar component clause 202]
215. 20 <=> ! [X1] : ~kind(X1) [avatar definition]
216. ~kind(X1) <- (20) [avatar component clause 215]
217. 20 | ~17 [avatar split clause 108,202,215]
219. 21 <=> ! [X1] : ~tall(X1) [avatar definition]
220. ~tall(X1) <- (21) [avatar component clause 219]
221. 21 | ~17 [avatar split clause 107,202,219]
257. 30 <=> ! [X1] : (patient(X1) | ~creative(X1)) [avatar definition]
258. ~creative(X1) | patient(X1) <- (30) [avatar component clause 257]
260. 31 <=> funny(sK5) [avatar definition]
263. 30 | ~31 [avatar split clause 120,260,257]
268. 30 | 31 [avatar split clause 118,260,257]
289. 17 [avatar split clause 130,202]
292. ~quiet(susan) [resolution 85,124]
315. kind(paul) | ~humble(paul) <- (17) [resolution 81,204]
343. quiet(X0) <- (1, 21) [subsumption resolution 133,220]
345. $false <- (1, 21) [resolution 343,292]
346. ~1 | ~21 [avatar contradiction clause 345]
348. patient(paul) <- (2, 30) [resolution 137,258]
373. tall(paul) | humble(paul) <- (2, 30) [resolution 92,348]
377. humble(paul) <- (2, 21, 30) [subsumption resolution 373,220]
382. ~humble(paul) <- (17, 20) [subsumption resolution 315,216]
383. $false <- (2, 17, 20, 21, 30) [subsumption resolution 382,377]
384. ~2 | ~17 | ~20 | ~21 | ~30 [avatar contradiction clause 383]
388. $false [avatar sat refutation 138,217,221,263,268,289,346,384]
% SZS output end Proof for 5533424687574840757849748
% ------------------------------
% 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 calm is both not brave and generous.
Everyone who is calm or kind is not creative or patient and vice versa.
Everyone who is generous is curious or not happy.
Everyone who is either kind or not happy is creative or tall.
If someone is generous or quiet then someone is not patient.
Everyone who is both not rich and brave is both not brave and not rich and vice versa.
Everyone who is not old is either not calm or patient.
If fred is quiet then someone is not funny or kind.
Everyone who is both calm and not creative is either not funny or wise and vice versa.
If someone is both humble and rich then fred is either not brave or curious and vice versa.
If someone is rich or creative then someone is not humble.
If susan is not strong or not patient then someone is not patient or not wise and vice versa.
Everyone who is both not creative and patient is either rich or not creative and vice versa.
If alice is both strong and patient then fred is either not quiet or generous.
Everyone who is old is both not humble and kind and vice versa.
Everyone who is either not quiet or not strong is quiet.
Susan is not brave.
Someone is either not brave or brave.
Fred is creative or tall.
Lucy is both not wise and generous.
Someone is not funny or kind.
Someone is either not kind or humble. | Susan is quiet. | neutral | (![X]:(calm(X)=>(~brave(X)&generous(X))))&
(![X]:((calm(X)|kind(X))<=>(~creative(X)|patient(X))))&
(![X]:(generous(X)=>(curious(X)|~happy(X))))&
(![X]:((kind(X)<~>~happy(X))=>(creative(X)|tall(X))))&
((?[X]:((generous(X)|quiet(X))))=>(?[X]:(~patient(X))))&
(![X]:((~rich(X)&brave(X))<=>(~brave(X)&~rich(X))))&
(![X]:(~old(X)=>(~calm(X)<~>patient(X))))&
((quiet(fred))=>(?[X]:((~funny(X)|kind(X)))))&
(![X]:((calm(X)&~creative(X))<=>(~funny(X)<~>wise(X))))&
((?[X]:((humble(X)&rich(X))))<=>((~brave(fred)<~>curious(fred))))&
((?[X]:((rich(X)|creative(X))))=>(?[X]:(~humble(X))))&
(((~strong(susan)|~patient(susan)))<=>(?[X]:((~patient(X)|~wise(X)))))&
(![X]:((~creative(X)&patient(X))<=>(rich(X)<~>~creative(X))))&
(((strong(alice)&patient(alice)))=>((~quiet(fred)<~>generous(fred))))&
(![X]:(old(X)<=>(~humble(X)&kind(X))))&
(![X]:((~quiet(X)<~>~strong(X))=>quiet(X)))&
(~brave(susan))&
(?[X]:((~brave(X)<~>brave(X))))&
((creative(fred)|tall(fred)))&
((~wise(lucy)&generous(lucy)))&
(?[X]:((~funny(X)|kind(X))))&
(?[X]:((~kind(X)<~>humble(X)))) | quiet(susan) | [] | null | 0 |
If alice is both not brave and kind then someone is generous.
If someone is wise or not calm then someone is both not curious and not strong.
Everyone who is both not calm and curious is either brave or not strong.
Everyone who is both not happy and not quiet is either not funny or rich.
Everyone who is both not tall and not brave is not old or humble and vice versa.
If paul is both not curious and not strong then someone is both happy and humble.
Everyone who is calm or brave is both not humble and creative and vice versa.
Everyone who is either not calm or not wise is either humble or not kind and vice versa.
Everyone who is not wise is either wise or creative and vice versa.
If lucy is either not old or not patient then lucy is both not wise and creative.
Everyone who is quiet or not generous is humble.
If john is calm then fred is not tall and vice versa.
Everyone who is both curious and calm is both generous and brave.
If someone is either not tall or tall then paul is not kind.
Everyone who is both patient and tall is either not patient or not kind and vice versa.
If lucy is either old or not old then someone is calm and vice versa.
Susan is kind.
Susan is quiet.
Susan is both not funny and patient.
John is both happy and calm.
Mary is either not strong or quiet.
Someone is strong.
Someone is not brave or not tall. | John is not quiet. | entailment | (((~brave(alice)&kind(alice)))=>(?[X]:(generous(X))))&
((?[X]:((wise(X)|~calm(X))))=>(?[X]:((~curious(X)&~strong(X)))))&
(![X]:((~calm(X)&curious(X))=>(brave(X)<~>~strong(X))))&
(![X]:((~happy(X)&~quiet(X))=>(~funny(X)<~>rich(X))))&
(![X]:((~tall(X)&~brave(X))<=>(~old(X)|humble(X))))&
(((~curious(paul)&~strong(paul)))=>(?[X]:((happy(X)&humble(X)))))&
(![X]:((calm(X)|brave(X))<=>(~humble(X)&creative(X))))&
(![X]:((~calm(X)<~>~wise(X))<=>(humble(X)<~>~kind(X))))&
(![X]:(~wise(X)<=>(wise(X)<~>creative(X))))&
(((~old(lucy)<~>~patient(lucy)))=>((~wise(lucy)&creative(lucy))))&
(![X]:((quiet(X)|~generous(X))=>humble(X)))&
((calm(john))<=>(~tall(fred)))&
(![X]:((curious(X)&calm(X))=>(generous(X)&brave(X))))&
((?[X]:((~tall(X)<~>tall(X))))=>(~kind(paul)))&
(![X]:((patient(X)&tall(X))<=>(~patient(X)<~>~kind(X))))&
(((old(lucy)<~>~old(lucy)))<=>(?[X]:(calm(X))))&
(kind(susan))&
(quiet(susan))&
((~funny(susan)&patient(susan)))&
((happy(john)&calm(john)))&
((~strong(mary)<~>quiet(mary)))&
(?[X]:(strong(X)))&
(?[X]:((~brave(X)|~tall(X)))) | ~quiet(john) | [
"p6",
"p10",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 6707745353099285084896709
% SZS output start Proof for 6707745353099285084896709
7. ! [X0] : ((brave(X0) | calm(X0)) <=> (creative(X0) & ~humble(X0))) [input p6]
11. ! [X0] : ((~generous(X0) | quiet(X0)) => humble(X0)) [input p10]
20. calm(john) & happy(john) [input p19]
24. quiet(john) [input hypothesis]
28. calm(john) [pure predicate removal 20]
30. ! [X0] : (quiet(X0) => humble(X0)) [pure predicate removal 11]
39. ! [X0] : (humble(X0) | ~quiet(X0)) [ennf transformation 30]
51. ! [X0] : (((brave(X0) | calm(X0)) | (~creative(X0) | humble(X0))) & ((creative(X0) & ~humble(X0)) | (~brave(X0) & ~calm(X0)))) [nnf transformation 7]
52. ! [X0] : ((brave(X0) | calm(X0) | ~creative(X0) | humble(X0)) & ((creative(X0) & ~humble(X0)) | (~brave(X0) & ~calm(X0)))) [flattening 51]
81. ~humble(X0) | ~calm(X0) [cnf transformation 52]
102. ~quiet(X0) | humble(X0) [cnf transformation 39]
121. calm(john) [cnf transformation 28]
126. quiet(john) [cnf transformation 24]
190. 12 <=> calm(john) [avatar definition]
192. calm(john) <- (12) [avatar component clause 190]
214. 12 [avatar split clause 121,190]
237. humble(john) [resolution 102,126]
242. ~calm(john) [resolution 237,81]
245. $false <- (12) [subsumption resolution 242,192]
246. ~12 [avatar contradiction clause 245]
247. $false [avatar sat refutation 214,246]
% SZS output end Proof for 6707745353099285084896709
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not wise or not humble is rich.
If paul is both patient and wise then someone is funny.
Everyone who is either humble or rich is not patient and vice versa.
Everyone who is both not patient and happy is either brave or not quiet and vice versa.
Everyone who is not generous is both not patient and rich.
If alice is humble then someone is humble.
Everyone who is strong or curious is happy or kind and vice versa.
If someone is either not strong or not creative then someone is both not tall and not funny.
Everyone who is funny is not strong.
If someone is both humble and not wise then someone is either not generous or rich and vice versa.
Everyone who is not brave or not strong is either not wise or quiet and vice versa.
If someone is wise then someone is humble and vice versa.
If paul is both not rich and not brave then susan is either happy or not brave.
If someone is patient then paul is calm and vice versa.
If someone is both not funny and strong then someone is not patient or not rich.
Everyone who is both not strong and happy is not creative.
Susan is either generous or humble.
Someone is both not humble and not creative.
Lucy is both not happy and generous.
Someone is both not calm and not tall.
Someone is either quiet or not creative.
Paul is not rich or not generous.
Someone is either not happy or kind. | Lucy is not curious. | neutral | (![X]:((~wise(X)|~humble(X))=>rich(X)))&
(((patient(paul)&wise(paul)))=>(?[X]:(funny(X))))&
(![X]:((humble(X)<~>rich(X))<=>~patient(X)))&
(![X]:((~patient(X)&happy(X))<=>(brave(X)<~>~quiet(X))))&
(![X]:(~generous(X)=>(~patient(X)&rich(X))))&
((humble(alice))=>(?[X]:(humble(X))))&
(![X]:((strong(X)|curious(X))<=>(happy(X)|kind(X))))&
((?[X]:((~strong(X)<~>~creative(X))))=>(?[X]:((~tall(X)&~funny(X)))))&
(![X]:(funny(X)=>~strong(X)))&
((?[X]:((humble(X)&~wise(X))))<=>(?[X]:((~generous(X)<~>rich(X)))))&
(![X]:((~brave(X)|~strong(X))<=>(~wise(X)<~>quiet(X))))&
((?[X]:(wise(X)))<=>(?[X]:(humble(X))))&
(((~rich(paul)&~brave(paul)))=>((happy(susan)<~>~brave(susan))))&
((?[X]:(patient(X)))<=>(calm(paul)))&
((?[X]:((~funny(X)&strong(X))))=>(?[X]:((~patient(X)|~rich(X)))))&
(![X]:((~strong(X)&happy(X))=>~creative(X)))&
((generous(susan)<~>humble(susan)))&
(?[X]:((~humble(X)&~creative(X))))&
((~happy(lucy)&generous(lucy)))&
(?[X]:((~calm(X)&~tall(X))))&
(?[X]:((quiet(X)<~>~creative(X))))&
((~rich(paul)|~generous(paul)))&
(?[X]:((~happy(X)<~>kind(X)))) | ~curious(lucy) | [] | null | 0 |
If someone is not calm or not strong then someone is both old and not kind.
Everyone who is not kind is either not creative or patient.
If paul is not patient or not funny then someone is both not curious and not quiet and vice versa.
Everyone who is either humble or not curious is either not tall or not wise.
Everyone who is tall is either patient or strong and vice versa.
Everyone who is both happy and not calm is strong or not patient.
If someone is either not strong or not humble then someone is strong and vice versa.
If someone is wise or kind then fred is not patient and vice versa.
If someone is not strong or happy then fred is either calm or not kind and vice versa.
Everyone who is either humble or not strong is not strong or not kind.
If someone is either quiet or patient then someone is not happy or strong and vice versa.
Everyone who is not rich or calm is both creative and not tall and vice versa.
Everyone who is either calm or tall is not old or funny and vice versa.
Everyone who is either not brave or not rich is both not quiet and patient and vice versa.
If john is not creative then lucy is not patient and vice versa.
Everyone who is calm or curious is creative and vice versa.
Someone is strong or not funny.
Someone is not rich or not old.
Someone is either not quiet or old.
Someone is both kind and not creative.
Someone is not funny.
Lucy is either strong or not generous.
Fred is either happy or not quiet.
Someone is both old and curious. | Fred is not old. | neutral | ((?[X]:((~calm(X)|~strong(X))))=>(?[X]:((old(X)&~kind(X)))))&
(![X]:(~kind(X)=>(~creative(X)<~>patient(X))))&
(((~patient(paul)|~funny(paul)))<=>(?[X]:((~curious(X)&~quiet(X)))))&
(![X]:((humble(X)<~>~curious(X))=>(~tall(X)<~>~wise(X))))&
(![X]:(tall(X)<=>(patient(X)<~>strong(X))))&
(![X]:((happy(X)&~calm(X))=>(strong(X)|~patient(X))))&
((?[X]:((~strong(X)<~>~humble(X))))<=>(?[X]:(strong(X))))&
((?[X]:((wise(X)|kind(X))))<=>(~patient(fred)))&
((?[X]:((~strong(X)|happy(X))))<=>((calm(fred)<~>~kind(fred))))&
(![X]:((humble(X)<~>~strong(X))=>(~strong(X)|~kind(X))))&
((?[X]:((quiet(X)<~>patient(X))))<=>(?[X]:((~happy(X)|strong(X)))))&
(![X]:((~rich(X)|calm(X))<=>(creative(X)&~tall(X))))&
(![X]:((calm(X)<~>tall(X))<=>(~old(X)|funny(X))))&
(![X]:((~brave(X)<~>~rich(X))<=>(~quiet(X)&patient(X))))&
((~creative(john))<=>(~patient(lucy)))&
(![X]:((calm(X)|curious(X))<=>creative(X)))&
(?[X]:((strong(X)|~funny(X))))&
(?[X]:((~rich(X)|~old(X))))&
(?[X]:((~quiet(X)<~>old(X))))&
(?[X]:((kind(X)&~creative(X))))&
(?[X]:(~funny(X)))&
((strong(lucy)<~>~generous(lucy)))&
((happy(fred)<~>~quiet(fred)))&
(?[X]:((old(X)&curious(X)))) | ~old(fred) | [] | null | 0 |
Everyone who is strong is happy or not old and vice versa.
Everyone who is both rich and not calm is both wise and tall.
Everyone who is not creative or humble is both wise and not calm.
If someone is either not funny or curious then someone is both not patient and generous and vice versa.
Everyone who is both not happy and not tall is humble and vice versa.
Everyone who is old is patient and vice versa.
If someone is either not brave or strong then someone is either patient or not kind.
If someone is quiet or humble then someone is either tall or not generous.
Everyone who is either calm or rich is quiet or brave.
Everyone who is both not generous and curious is either not old or brave.
Everyone who is either not patient or not generous is either wise or not strong and vice versa.
Everyone who is not strong or strong is both creative and not generous.
If someone is not curious or not funny then fred is both not tall and not curious.
If someone is old or rich then someone is both not humble and quiet and vice versa.
If someone is either not rich or generous then someone is happy and vice versa.
Everyone who is not old is humble or not tall and vice versa.
Mary is funny or strong.
Alice is tall.
Someone is both rich and creative.
Someone is not kind.
Lucy is both not curious and kind.
Alice is creative or not kind.
John is not old.
Someone is not tall or not curious. | Fred is not wise. | entailment | (![X]:(strong(X)<=>(happy(X)|~old(X))))&
(![X]:((rich(X)&~calm(X))=>(wise(X)&tall(X))))&
(![X]:((~creative(X)|humble(X))=>(wise(X)&~calm(X))))&
((?[X]:((~funny(X)<~>curious(X))))<=>(?[X]:((~patient(X)&generous(X)))))&
(![X]:((~happy(X)&~tall(X))<=>humble(X)))&
(![X]:(old(X)<=>patient(X)))&
((?[X]:((~brave(X)<~>strong(X))))=>(?[X]:((patient(X)<~>~kind(X)))))&
((?[X]:((quiet(X)|humble(X))))=>(?[X]:((tall(X)<~>~generous(X)))))&
(![X]:((calm(X)<~>rich(X))=>(quiet(X)|brave(X))))&
(![X]:((~generous(X)&curious(X))=>(~old(X)<~>brave(X))))&
(![X]:((~patient(X)<~>~generous(X))<=>(wise(X)<~>~strong(X))))&
(![X]:((~strong(X)|strong(X))=>(creative(X)&~generous(X))))&
((?[X]:((~curious(X)|~funny(X))))=>((~tall(fred)&~curious(fred))))&
((?[X]:((old(X)|rich(X))))<=>(?[X]:((~humble(X)&quiet(X)))))&
((?[X]:((~rich(X)<~>generous(X))))<=>(?[X]:(happy(X))))&
(![X]:(~old(X)<=>(humble(X)|~tall(X))))&
((funny(mary)|strong(mary)))&
(tall(alice))&
(?[X]:((rich(X)&creative(X))))&
(?[X]:(~kind(X)))&
((~curious(lucy)&kind(lucy)))&
((creative(alice)|~kind(alice)))&
(~old(john))&
(?[X]:((~tall(X)|~curious(X)))) | ~wise(fred) | [
"p0",
"p5",
"p10",
"p11",
"p12",
"p15",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 4630523851422947938669391
% SZS output start Proof for 4630523851422947938669391
1. ! [X0] : (strong(X0) <=> (~old(X0) | happy(X0))) [input p0]
6. ! [X0] : (old(X0) <=> patient(X0)) [input p5]
11. ! [X0] : ((~patient(X0) <~> ~generous(X0)) <=> (wise(X0) <~> ~strong(X0))) [input p10]
12. ! [X0] : ((strong(X0) | ~strong(X0)) => (~generous(X0) & creative(X0))) [input p11]
13. ? [X0] : (~funny(X0) | ~curious(X0)) => (~curious(fred) & ~tall(fred)) [input p12]
16. ! [X0] : (~old(X0) <=> (~tall(X0) | humble(X0))) [input p15]
21. kind(lucy) & ~curious(lucy) [input p20]
25. wise(fred) [input hypothesis]
34. ! [X0] : ((strong(X0) | ~strong(X0)) => ~generous(X0)) [pure predicate removal 12]
44. ! [X0] : (~generous(X0) | (~strong(X0) & strong(X0))) [ennf transformation 34]
45. (~curious(fred) & ~tall(fred)) | ! [X0] : (funny(X0) & curious(X0)) [ennf transformation 13]
46. ! [X0] : ((strong(X0) | (old(X0) & ~happy(X0))) & ((~old(X0) | happy(X0)) | ~strong(X0))) [nnf transformation 1]
47. ! [X0] : ((strong(X0) | (old(X0) & ~happy(X0))) & (~old(X0) | happy(X0) | ~strong(X0))) [flattening 46]
55. ! [X0] : ((old(X0) | ~patient(X0)) & (patient(X0) | ~old(X0))) [nnf transformation 6]
66. ! [X0] : ((((generous(X0) | patient(X0)) & (~generous(X0) | ~patient(X0))) | ((wise(X0) | strong(X0)) & (~strong(X0) | ~wise(X0)))) & (((strong(X0) | ~wise(X0)) & (~strong(X0) | wise(X0))) | ((~patient(X0) | generous(X0)) & (~generous(X0) | patient(X0))))) [nnf transformation 11]
77. ! [X0] : ((~old(X0) | (tall(X0) & ~humble(X0))) & ((~tall(X0) | humble(X0)) | old(X0))) [nnf transformation 16]
78. ! [X0] : ((~old(X0) | (tall(X0) & ~humble(X0))) & (~tall(X0) | humble(X0) | old(X0))) [flattening 77]
87. old(X0) | strong(X0) [cnf transformation 47]
101. ~old(X0) | patient(X0) [cnf transformation 55]
102. ~patient(X0) | old(X0) [cnf transformation 55]
121. ~wise(X0) | patient(X0) | ~strong(X0) | generous(X0) [cnf transformation 66]
123. ~generous(X0) | strong(X0) [cnf transformation 44]
124. ~generous(X0) | ~strong(X0) [cnf transformation 44]
125. ~tall(fred) | curious(X0) [cnf transformation 45]
140. ~old(X0) | tall(X0) [cnf transformation 78]
145. ~curious(lucy) [cnf transformation 21]
149. wise(fred) [cnf transformation 25]
217. ~generous(X0) [subsumption resolution 123,124]
227. 18 <=> ! [X0] : curious(X0) [avatar definition]
228. curious(X0) <- (18) [avatar component clause 227]
231. 19 <=> tall(fred) [avatar definition]
235. 18 | ~19 [avatar split clause 125,231,227]
308. patient(X0) | strong(X0) [resolution 101,87]
429. patient(fred) | ~strong(fred) | generous(fred) [resolution 121,149]
431. patient(fred) | ~strong(fred) [subsumption resolution 429,217]
432. patient(fred) [subsumption resolution 431,308]
435. old(fred) [resolution 432,102]
448. tall(fred) [resolution 435,140]
453. 19 [avatar split clause 448,231]
457. $false <- (18) [resolution 228,145]
462. ~18 [avatar contradiction clause 457]
467. $false [avatar sat refutation 235,453,462]
% SZS output end Proof for 4630523851422947938669391
% ------------------------------
% 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: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is strong or calm is both strong and brave.
Everyone who is wise is either not rich or not humble.
Everyone who is not strong or kind is not tall and vice versa.
Everyone who is both not quiet and generous is not wise and vice versa.
Everyone who is both not humble and curious is not patient or rich.
Everyone who is not strong is either not kind or old and vice versa.
If alice is old or quiet then someone is both not strong and not calm and vice versa.
Everyone who is either not humble or not calm is not humble or rich.
If paul is both not rich and patient then alice is not curious or not strong and vice versa.
If someone is either not old or not rich then susan is both not rich and quiet and vice versa.
If someone is wise or funny then john is either not calm or not happy.
If john is either not funny or not rich then fred is not strong or not patient.
If someone is not generous then paul is both not wise and not strong and vice versa.
If fred is either old or happy then someone is either patient or old.
If paul is humble then paul is not generous.
Everyone who is either not strong or not rich is either not patient or rich and vice versa.
Susan is either curious or not old.
Someone is both patient and creative.
Someone is not patient or not calm.
Mary is not funny.
Susan is not humble.
Fred is both not patient and wise.
Lucy is calm.
Lucy is either not happy or not quiet. | Lucy is not strong. | contradiction | (![X]:((strong(X)|calm(X))=>(strong(X)&brave(X))))&
(![X]:(wise(X)=>(~rich(X)<~>~humble(X))))&
(![X]:((~strong(X)|kind(X))<=>~tall(X)))&
(![X]:((~quiet(X)&generous(X))<=>~wise(X)))&
(![X]:((~humble(X)&curious(X))=>(~patient(X)|rich(X))))&
(![X]:(~strong(X)<=>(~kind(X)<~>old(X))))&
(((old(alice)|quiet(alice)))<=>(?[X]:((~strong(X)&~calm(X)))))&
(![X]:((~humble(X)<~>~calm(X))=>(~humble(X)|rich(X))))&
(((~rich(paul)&patient(paul)))<=>((~curious(alice)|~strong(alice))))&
((?[X]:((~old(X)<~>~rich(X))))<=>((~rich(susan)&quiet(susan))))&
((?[X]:((wise(X)|funny(X))))=>((~calm(john)<~>~happy(john))))&
(((~funny(john)<~>~rich(john)))=>((~strong(fred)|~patient(fred))))&
((?[X]:(~generous(X)))<=>((~wise(paul)&~strong(paul))))&
(((old(fred)<~>happy(fred)))=>(?[X]:((patient(X)<~>old(X)))))&
((humble(paul))=>(~generous(paul)))&
(![X]:((~strong(X)<~>~rich(X))<=>(~patient(X)<~>rich(X))))&
((curious(susan)<~>~old(susan)))&
(?[X]:((patient(X)&creative(X))))&
(?[X]:((~patient(X)|~calm(X))))&
(~funny(mary))&
(~humble(susan))&
((~patient(fred)&wise(fred)))&
(calm(lucy))&
((~happy(lucy)<~>~quiet(lucy))) | ~strong(lucy) | [
"p0",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 9136338845503959501440601
% SZS output start Proof for 9136338845503959501440601
1. ! [X0] : ((calm(X0) | strong(X0)) => (brave(X0) & strong(X0))) [input p0]
23. calm(lucy) [input p22]
25. ~strong(lucy) [input hypothesis]
27. ! [X0] : ((calm(X0) | strong(X0)) => strong(X0)) [pure predicate removal 1]
28. ! [X0] : (strong(X0) | (~calm(X0) & ~strong(X0))) [ennf transformation 27]
74. ~calm(X0) | strong(X0) [cnf transformation 28]
133. calm(lucy) [cnf transformation 23]
136. ~strong(lucy) [cnf transformation 25]
331. strong(lucy) [resolution 74,133]
333. $false [subsumption resolution 331,136]
% SZS output end Proof for 9136338845503959501440601
% ------------------------------
% 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 susan is not quiet or not happy then susan is kind and vice versa.
Everyone who is either not kind or rich is both patient and creative and vice versa.
Everyone who is both old and kind is happy or tall and vice versa.
Everyone who is not patient is tall.
If susan is kind then paul is either kind or not curious and vice versa.
Everyone who is either not generous or not brave is not humble or not brave and vice versa.
If someone is calm then someone is both old and happy and vice versa.
Everyone who is both kind and strong is not calm or old and vice versa.
Everyone who is funny or not curious is both not kind and strong.
If someone is either brave or not calm then someone is rich or strong.
If someone is both old and not wise then susan is either calm or not calm.
Everyone who is both creative and generous is either not patient or not calm and vice versa.
If susan is generous then someone is either not curious or not rich and vice versa.
If paul is not happy then fred is either not brave or tall and vice versa.
Everyone who is either happy or rich is strong or curious.
If fred is either generous or not brave then susan is both not quiet and not curious and vice versa.
Paul is not kind or not curious.
Someone is either not strong or wise.
Someone is not tall.
Fred is either not old or not funny.
Someone is both not funny and quiet.
Alice is curious or quiet.
Someone is funny.
Mary is not old or not rich. | Fred is brave. | neutral | (((~quiet(susan)|~happy(susan)))<=>(kind(susan)))&
(![X]:((~kind(X)<~>rich(X))<=>(patient(X)&creative(X))))&
(![X]:((old(X)&kind(X))<=>(happy(X)|tall(X))))&
(![X]:(~patient(X)=>tall(X)))&
((kind(susan))<=>((kind(paul)<~>~curious(paul))))&
(![X]:((~generous(X)<~>~brave(X))<=>(~humble(X)|~brave(X))))&
((?[X]:(calm(X)))<=>(?[X]:((old(X)&happy(X)))))&
(![X]:((kind(X)&strong(X))<=>(~calm(X)|old(X))))&
(![X]:((funny(X)|~curious(X))=>(~kind(X)&strong(X))))&
((?[X]:((brave(X)<~>~calm(X))))=>(?[X]:((rich(X)|strong(X)))))&
((?[X]:((old(X)&~wise(X))))=>((calm(susan)<~>~calm(susan))))&
(![X]:((creative(X)&generous(X))<=>(~patient(X)<~>~calm(X))))&
((generous(susan))<=>(?[X]:((~curious(X)<~>~rich(X)))))&
((~happy(paul))<=>((~brave(fred)<~>tall(fred))))&
(![X]:((happy(X)<~>rich(X))=>(strong(X)|curious(X))))&
(((generous(fred)<~>~brave(fred)))<=>((~quiet(susan)&~curious(susan))))&
((~kind(paul)|~curious(paul)))&
(?[X]:((~strong(X)<~>wise(X))))&
(?[X]:(~tall(X)))&
((~old(fred)<~>~funny(fred)))&
(?[X]:((~funny(X)&quiet(X))))&
((curious(alice)|quiet(alice)))&
(?[X]:(funny(X)))&
((~old(mary)|~rich(mary))) | brave(fred) | [] | null | 0 |
Everyone who is either quiet or not generous is patient or curious.
Everyone who is both not brave and generous is not rich and vice versa.
Everyone who is wise is both old and tall.
Everyone who is both quiet and not happy is either not creative or rich.
Everyone who is both generous and humble is either not wise or wise and vice versa.
If someone is both not brave and generous then fred is either not wise or not quiet and vice versa.
Everyone who is not curious or strong is both patient and not curious and vice versa.
Everyone who is not curious or not calm is both not quiet and not brave and vice versa.
If alice is not tall then lucy is not rich or not tall.
If someone is brave or not humble then john is patient.
Everyone who is not kind is not tall or happy.
If someone is either brave or calm then mary is both tall and not happy.
Everyone who is both not quiet and humble is tall or not humble and vice versa.
If mary is either not patient or not funny then someone is rich and vice versa.
If susan is generous then mary is either happy or kind and vice versa.
If someone is both not funny and not creative then paul is both brave and creative.
Someone is either tall or kind.
Alice is either quiet or not quiet.
Susan is not tall.
Someone is not wise or quiet.
Susan is either curious or patient.
Someone is either not old or not calm.
John is both not wise and not funny.
Someone is funny. | Susan is patient. | contradiction | (![X]:((quiet(X)<~>~generous(X))=>(patient(X)|curious(X))))&
(![X]:((~brave(X)&generous(X))<=>~rich(X)))&
(![X]:(wise(X)=>(old(X)&tall(X))))&
(![X]:((quiet(X)&~happy(X))=>(~creative(X)<~>rich(X))))&
(![X]:((generous(X)&humble(X))<=>(~wise(X)<~>wise(X))))&
((?[X]:((~brave(X)&generous(X))))<=>((~wise(fred)<~>~quiet(fred))))&
(![X]:((~curious(X)|strong(X))<=>(patient(X)&~curious(X))))&
(![X]:((~curious(X)|~calm(X))<=>(~quiet(X)&~brave(X))))&
((~tall(alice))=>((~rich(lucy)|~tall(lucy))))&
((?[X]:((brave(X)|~humble(X))))=>(patient(john)))&
(![X]:(~kind(X)=>(~tall(X)|happy(X))))&
((?[X]:((brave(X)<~>calm(X))))=>((tall(mary)&~happy(mary))))&
(![X]:((~quiet(X)&humble(X))<=>(tall(X)|~humble(X))))&
(((~patient(mary)<~>~funny(mary)))<=>(?[X]:(rich(X))))&
((generous(susan))<=>((happy(mary)<~>kind(mary))))&
((?[X]:((~funny(X)&~creative(X))))=>((brave(paul)&creative(paul))))&
(?[X]:((tall(X)<~>kind(X))))&
((quiet(alice)<~>~quiet(alice)))&
(~tall(susan))&
(?[X]:((~wise(X)|quiet(X))))&
((curious(susan)<~>patient(susan)))&
(?[X]:((~old(X)<~>~calm(X))))&
((~wise(john)&~funny(john)))&
(?[X]:(funny(X))) | patient(susan) | [
"p4",
"p7",
"p12",
"p18",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 2982901656034513869617439
% SZS output start Proof for 2982901656034513869617439
5. ! [X0] : ((humble(X0) & generous(X0)) <=> (~wise(X0) <~> wise(X0))) [input p4]
8. ! [X0] : ((~calm(X0) | ~curious(X0)) <=> (~brave(X0) & ~quiet(X0))) [input p7]
13. ! [X0] : ((humble(X0) & ~quiet(X0)) <=> (~humble(X0) | tall(X0))) [input p12]
19. ~tall(susan) [input p18]
21. curious(susan) <~> patient(susan) [input p20]
25. patient(susan) [input hypothesis]
42. ! [X0] : (((humble(X0) & generous(X0)) | ((~wise(X0) | ~wise(X0)) & (wise(X0) | wise(X0)))) & (((~wise(X0) | wise(X0)) & (wise(X0) | ~wise(X0))) | (~humble(X0) | ~generous(X0)))) [nnf transformation 5]
43. ! [X0] : (((humble(X0) & generous(X0)) | ((~wise(X0) | ~wise(X0)) & (wise(X0) | wise(X0)))) & (((~wise(X0) | wise(X0)) & (wise(X0) | ~wise(X0))) | ~humble(X0) | ~generous(X0))) [flattening 42]
50. ! [X0] : (((~calm(X0) | ~curious(X0)) | (brave(X0) | quiet(X0))) & ((~brave(X0) & ~quiet(X0)) | (calm(X0) & curious(X0)))) [nnf transformation 8]
51. ! [X0] : ((~calm(X0) | ~curious(X0) | brave(X0) | quiet(X0)) & ((~brave(X0) & ~quiet(X0)) | (calm(X0) & curious(X0)))) [flattening 50]
53. ! [X0] : (((humble(X0) & ~quiet(X0)) | (humble(X0) & ~tall(X0))) & ((~humble(X0) | tall(X0)) | (~humble(X0) | quiet(X0)))) [nnf transformation 13]
54. ! [X0] : (((humble(X0) & ~quiet(X0)) | (humble(X0) & ~tall(X0))) & (~humble(X0) | tall(X0) | ~humble(X0) | quiet(X0))) [flattening 53]
66. (~patient(susan) | ~curious(susan)) & (patient(susan) | curious(susan)) [nnf transformation 21]
85. humble(X0) | wise(X0) | wise(X0) [cnf transformation 43]
86. humble(X0) | ~wise(X0) | ~wise(X0) [cnf transformation 43]
98. ~quiet(X0) | curious(X0) [cnf transformation 51]
111. ~humble(X0) | tall(X0) | ~humble(X0) | quiet(X0) [cnf transformation 54]
130. ~tall(susan) [cnf transformation 19]
133. ~patient(susan) | ~curious(susan) [cnf transformation 66]
139. patient(susan) [cnf transformation 25]
140. ~humble(X0) | tall(X0) | quiet(X0) [duplicate literal removal 111]
144. humble(X0) | wise(X0) [duplicate literal removal 85]
145. ~wise(X0) | humble(X0) [duplicate literal removal 86]
146. humble(X0) [subsumption resolution 144,145]
203. tall(X0) | quiet(X0) [subsumption resolution 140,146]
264. 25 <=> curious(susan) [avatar definition]
266. ~curious(susan) <- (~25) [avatar component clause 264]
268. 26 <=> patient(susan) [avatar definition]
271. ~25 | ~26 [avatar split clause 133,268,264]
282. 26 [avatar split clause 139,268]
291. quiet(susan) [resolution 203,130]
297. curious(susan) [resolution 291,98]
298. $false <- (~25) [subsumption resolution 297,266]
299. 25 [avatar contradiction clause 298]
300. $false [avatar sat refutation 271,282,299]
% SZS output end Proof for 2982901656034513869617439
% ------------------------------
% 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 paul is both not creative and kind then susan is both happy and not tall.
Everyone who is not quiet or old is not patient or calm and vice versa.
If someone is not creative then paul is old and vice versa.
If susan is either generous or not quiet then lucy is not rich.
Everyone who is wise is creative or happy and vice versa.
Everyone who is funny is both not creative and generous and vice versa.
If paul is either tall or not creative then lucy is calm or not creative and vice versa.
Everyone who is not happy or not humble is rich and vice versa.
If someone is not strong or creative then mary is not rich and vice versa.
If someone is both calm and not humble then fred is either not humble or funny.
Everyone who is brave is either not patient or calm.
Everyone who is kind or not creative is not curious or kind and vice versa.
If lucy is both strong and old then someone is both quiet and strong.
Everyone who is old is both not humble and not funny.
If someone is not patient then fred is not happy.
Everyone who is old is happy or not kind and vice versa.
Someone is either not humble or not strong.
Mary is not kind or wise.
John is not happy.
Alice is curious or not curious.
Someone is either not old or kind.
Someone is generous.
Someone is either not generous or quiet. | Alice is calm. | neutral | (((~creative(paul)&kind(paul)))=>((happy(susan)&~tall(susan))))&
(![X]:((~quiet(X)|old(X))<=>(~patient(X)|calm(X))))&
((?[X]:(~creative(X)))<=>(old(paul)))&
(((generous(susan)<~>~quiet(susan)))=>(~rich(lucy)))&
(![X]:(wise(X)<=>(creative(X)|happy(X))))&
(![X]:(funny(X)<=>(~creative(X)&generous(X))))&
(((tall(paul)<~>~creative(paul)))<=>((calm(lucy)|~creative(lucy))))&
(![X]:((~happy(X)|~humble(X))<=>rich(X)))&
((?[X]:((~strong(X)|creative(X))))<=>(~rich(mary)))&
((?[X]:((calm(X)&~humble(X))))=>((~humble(fred)<~>funny(fred))))&
(![X]:(brave(X)=>(~patient(X)<~>calm(X))))&
(![X]:((kind(X)|~creative(X))<=>(~curious(X)|kind(X))))&
(((strong(lucy)&old(lucy)))=>(?[X]:((quiet(X)&strong(X)))))&
(![X]:(old(X)=>(~humble(X)&~funny(X))))&
((?[X]:(~patient(X)))=>(~happy(fred)))&
(![X]:(old(X)<=>(happy(X)|~kind(X))))&
(?[X]:((~humble(X)<~>~strong(X))))&
((~kind(mary)|wise(mary)))&
(~happy(john))&
((curious(alice)|~curious(alice)))&
(?[X]:((~old(X)<~>kind(X))))&
(?[X]:(generous(X)))&
(?[X]:((~generous(X)<~>quiet(X)))) | calm(alice) | [] | null | 0 |
Everyone who is not rich or old is rich.
Everyone who is either calm or wise is either quiet or not wise.
Everyone who is both not rich and happy is both old and happy.
Everyone who is strong is humble or funny and vice versa.
Everyone who is not brave is old.
If lucy is either kind or not strong then someone is happy or not creative.
Everyone who is both not happy and not tall is both not tall and funny and vice versa.
If alice is either creative or not humble then someone is both not tall and not brave and vice versa.
Everyone who is both not calm and not humble is happy and vice versa.
If someone is funny then paul is both not happy and not humble and vice versa.
If someone is generous then someone is either not strong or not calm.
If john is either not kind or tall then someone is not curious.
Everyone who is generous is either calm or wise and vice versa.
Everyone who is both not creative and not tall is not creative and vice versa.
If someone is funny then paul is not humble or quiet.
Everyone who is calm or curious is funny or not calm and vice versa.
Paul is both quiet and calm.
Paul is not generous or not wise.
Fred is both brave and generous.
Fred is both patient and funny.
Someone is humble or not funny.
Fred is either creative or not kind.
John is kind. | Fred is tall. | neutral | (![X]:((~rich(X)|old(X))=>rich(X)))&
(![X]:((calm(X)<~>wise(X))=>(quiet(X)<~>~wise(X))))&
(![X]:((~rich(X)&happy(X))=>(old(X)&happy(X))))&
(![X]:(strong(X)<=>(humble(X)|funny(X))))&
(![X]:(~brave(X)=>old(X)))&
(((kind(lucy)<~>~strong(lucy)))=>(?[X]:((happy(X)|~creative(X)))))&
(![X]:((~happy(X)&~tall(X))<=>(~tall(X)&funny(X))))&
(((creative(alice)<~>~humble(alice)))<=>(?[X]:((~tall(X)&~brave(X)))))&
(![X]:((~calm(X)&~humble(X))<=>happy(X)))&
((?[X]:(funny(X)))<=>((~happy(paul)&~humble(paul))))&
((?[X]:(generous(X)))=>(?[X]:((~strong(X)<~>~calm(X)))))&
(((~kind(john)<~>tall(john)))=>(?[X]:(~curious(X))))&
(![X]:(generous(X)<=>(calm(X)<~>wise(X))))&
(![X]:((~creative(X)&~tall(X))<=>~creative(X)))&
((?[X]:(funny(X)))=>((~humble(paul)|quiet(paul))))&
(![X]:((calm(X)|curious(X))<=>(funny(X)|~calm(X))))&
((quiet(paul)&calm(paul)))&
((~generous(paul)|~wise(paul)))&
((brave(fred)&generous(fred)))&
((patient(fred)&funny(fred)))&
(?[X]:((humble(X)|~funny(X))))&
((creative(fred)<~>~kind(fred)))&
(kind(john)) | tall(fred) | [] | null | 0 |
Everyone who is curious is either strong or happy and vice versa. Everyone who is old is calm or not wise and vice versa. Everyone who is happy or strong is not strong. Everyone who is both quiet and not brave is either tall or not brave and vice versa. If lucy is both old and not generous then paul is either calm or not tall. Everyone who is creative or wise is either calm or strong and vice versa. Everyone who is either not wise or not kind is both not strong and funny. Everyone who is both not patient and not happy is creative. Everyone who is brave or rich is not curious and vice versa. Everyone who is generous or brave is not quiet or wise. If someone is calm or not wise then someone is either happy or not funny. If paul is both not old and not quiet then mary is either calm or creative and vice versa. If someone is both not curious and old then paul is strong and vice versa. If susan is quiet then mary is patient and vice versa. If john is not old or not patient then mary is both strong and old and vice versa. Everyone who is both creative and not old is not kind or calm. Alice is both not generous and happy. Someone is both kind and not generous. Someone is both not tall and not humble. Mary is wise. Someone is old or rich. Paul is not tall. Paul is both not wise and not tall. | Mary is brave. | contradiction | (![X]:(curious(X)<=>(strong(X)<~>happy(X))))&
(![X]:(old(X)<=>(calm(X)|~wise(X))))&
(![X]:((happy(X)|strong(X))=>~strong(X)))&
(![X]:((quiet(X)&~brave(X))<=>(tall(X)<~>~brave(X))))&
(((old(lucy)&~generous(lucy)))=>((calm(paul)<~>~tall(paul))))&
(![X]:((creative(X)|wise(X))<=>(calm(X)<~>strong(X))))&
(![X]:((~wise(X)<~>~kind(X))=>(~strong(X)&funny(X))))&
(![X]:((~patient(X)&~happy(X))=>creative(X)))&
(![X]:((brave(X)|rich(X))<=>~curious(X)))&
(![X]:((generous(X)|brave(X))=>(~quiet(X)|wise(X))))&
((?[X]:((calm(X)|~wise(X))))=>(?[X]:((happy(X)<~>~funny(X)))))&
(((~old(paul)&~quiet(paul)))<=>((calm(mary)<~>creative(mary))))&
((?[X]:((~curious(X)&old(X))))<=>(strong(paul)))&
((quiet(susan))<=>(patient(mary)))&
(((~old(john)|~patient(john)))<=>((strong(mary)&old(mary))))&
(![X]:((creative(X)&~old(X))=>(~kind(X)|calm(X))))&
((~generous(alice)&happy(alice)))&
(?[X]:((kind(X)&~generous(X))))&
(?[X]:((~tall(X)&~humble(X))))&
(wise(mary))&
(?[X]:((old(X)|rich(X))))&
(~tall(paul))&
((~wise(paul)&~tall(paul))) | brave(mary) | [
"p1",
"p2",
"p5",
"p8",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 1986480806821878085725330
% SZS output start Proof for 1986480806821878085725330
2. ! [X0] : (old(X0) <=> (~wise(X0) | calm(X0))) [input p1]
3. ! [X0] : ((strong(X0) | happy(X0)) => ~strong(X0)) [input p2]
6. ! [X0] : ((wise(X0) | creative(X0)) <=> (calm(X0) <~> strong(X0))) [input p5]
9. ! [X0] : ((rich(X0) | brave(X0)) <=> ~curious(X0)) [input p8]
13. ? [X0] : (old(X0) & ~curious(X0)) <=> strong(paul) [input p12]
24. brave(mary) [input hypothesis]
27. ! [X0] : (~strong(X0) | (~strong(X0) & ~happy(X0))) [ennf transformation 3]
39. ! [X0] : ((old(X0) | (wise(X0) & ~calm(X0))) & ((~wise(X0) | calm(X0)) | ~old(X0))) [nnf transformation 2]
40. ! [X0] : ((old(X0) | (wise(X0) & ~calm(X0))) & (~wise(X0) | calm(X0) | ~old(X0))) [flattening 39]
44. ! [X0] : (((wise(X0) | creative(X0)) | ((calm(X0) | ~strong(X0)) & (strong(X0) | ~calm(X0)))) & (((~strong(X0) | ~calm(X0)) & (strong(X0) | calm(X0))) | (~wise(X0) & ~creative(X0)))) [nnf transformation 6]
45. ! [X0] : ((wise(X0) | creative(X0) | ((calm(X0) | ~strong(X0)) & (strong(X0) | ~calm(X0)))) & (((~strong(X0) | ~calm(X0)) & (strong(X0) | calm(X0))) | (~wise(X0) & ~creative(X0)))) [flattening 44]
47. ! [X0] : (((rich(X0) | brave(X0)) | curious(X0)) & (~curious(X0) | (~rich(X0) & ~brave(X0)))) [nnf transformation 9]
48. ! [X0] : ((rich(X0) | brave(X0) | curious(X0)) & (~curious(X0) | (~rich(X0) & ~brave(X0)))) [flattening 47]
55. (? [X0] : (old(X0) & ~curious(X0)) | ~strong(paul)) & (strong(paul) | ! [X0] : (~old(X0) | curious(X0))) [nnf transformation 13]
56. (? [X0] : (old(X0) & ~curious(X0)) | ~strong(paul)) & (strong(paul) | ! [X1] : (~old(X1) | curious(X1))) [rectify 55]
57. ? [X0] : (old(X0) & ~curious(X0)) => (old(sK1) & ~curious(sK1)) [choice axiom]
58. ((old(sK1) & ~curious(sK1)) | ~strong(paul)) & (strong(paul) | ! [X1] : (~old(X1) | curious(X1))) [skolemisation 56,57]
73. ~calm(X0) | old(X0) [cnf transformation 40]
74. wise(X0) | old(X0) [cnf transformation 40]
76. ~strong(X0) | ~strong(X0) [cnf transformation 27]
86. strong(X0) | calm(X0) | ~wise(X0) [cnf transformation 45]
96. ~brave(X0) | ~curious(X0) [cnf transformation 48]
111. strong(paul) | ~old(X1) | curious(X1) [cnf transformation 58]
132. brave(mary) [cnf transformation 24]
135. ~strong(X0) [duplicate literal removal 76]
156. ~wise(X0) | calm(X0) [subsumption resolution 86,135]
198. ~old(X1) | curious(X1) [subsumption resolution 111,135]
244. ~curious(mary) [resolution 96,132]
246. calm(X0) | old(X0) [resolution 156,74]
249. old(X0) [subsumption resolution 246,73]
253. curious(X0) [resolution 198,249]
257. $false [resolution 253,244]
% SZS output end Proof for 1986480806821878085725330
% ------------------------------
% 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 funny or not kind is both old and strong.
Everyone who is both kind and curious is happy.
Everyone who is not tall is creative and vice versa.
If someone is both generous and calm then mary is not wise or not strong.
If lucy is not kind then paul is not patient or old.
If someone is not happy then someone is either not quiet or not curious and vice versa.
Everyone who is both not wise and not patient is both not rich and wise and vice versa.
If paul is rich or not brave then someone is brave or humble and vice versa.
Everyone who is not funny or not quiet is quiet and vice versa.
Everyone who is both not humble and not curious is either humble or funny.
If mary is strong then someone is old or not strong and vice versa.
Everyone who is old or generous is not happy and vice versa.
If someone is not wise or not happy then lucy is old or not creative.
Everyone who is either not happy or not calm is not creative and vice versa.
Everyone who is not old is either not wise or wise.
Everyone who is curious or not rich is either tall or patient and vice versa.
Someone is not patient.
Fred is not quiet or calm.
Alice is not brave.
John is not funny.
Mary is not wise.
Alice is patient.
Susan is not calm.
Someone is both not humble and not wise. | Paul is not strong. | neutral | (![X]:((funny(X)|~kind(X))=>(old(X)&strong(X))))&
(![X]:((kind(X)&curious(X))=>happy(X)))&
(![X]:(~tall(X)<=>creative(X)))&
((?[X]:((generous(X)&calm(X))))=>((~wise(mary)|~strong(mary))))&
((~kind(lucy))=>((~patient(paul)|old(paul))))&
((?[X]:(~happy(X)))<=>(?[X]:((~quiet(X)<~>~curious(X)))))&
(![X]:((~wise(X)&~patient(X))<=>(~rich(X)&wise(X))))&
(((rich(paul)|~brave(paul)))<=>(?[X]:((brave(X)|humble(X)))))&
(![X]:((~funny(X)|~quiet(X))<=>quiet(X)))&
(![X]:((~humble(X)&~curious(X))=>(humble(X)<~>funny(X))))&
((strong(mary))<=>(?[X]:((old(X)|~strong(X)))))&
(![X]:((old(X)|generous(X))<=>~happy(X)))&
((?[X]:((~wise(X)|~happy(X))))=>((old(lucy)|~creative(lucy))))&
(![X]:((~happy(X)<~>~calm(X))<=>~creative(X)))&
(![X]:(~old(X)=>(~wise(X)<~>wise(X))))&
(![X]:((curious(X)|~rich(X))<=>(tall(X)<~>patient(X))))&
(?[X]:(~patient(X)))&
((~quiet(fred)|calm(fred)))&
(~brave(alice))&
(~funny(john))&
(~wise(mary))&
(patient(alice))&
(~calm(susan))&
(?[X]:((~humble(X)&~wise(X)))) | ~strong(paul) | [] | null | 0 |
Everyone who is both kind and not happy is either not happy or rich and vice versa. Everyone who is not quiet or not brave is calm or not wise. Everyone who is not tall or tall is brave and vice versa. If john is either quiet or not tall then someone is not old or happy and vice versa. If alice is creative then mary is curious and vice versa. Everyone who is quiet or generous is not curious. Everyone who is not kind is both not brave and funny. If someone is either humble or not tall then susan is both brave and patient and vice versa. If someone is wise or rich then someone is either old or not calm and vice versa. Everyone who is rich or funny is not quiet and vice versa. If someone is either not calm or not tall then mary is both not rich and tall and vice versa. If fred is both patient and calm then john is creative. Everyone who is not rich or rich is either patient or quiet. Everyone who is not tall is not quiet or not wise. If someone is both not old and generous then someone is either not generous or not strong. Everyone who is not funny or brave is either not creative or wise and vice versa. Lucy is either rich or not creative. John is not tall or not quiet. Mary is quiet. Lucy is either not old or strong. Mary is both not wise and tall. | Mary is strong. | neutral | (![X]:((kind(X)&~happy(X))<=>(~happy(X)<~>rich(X))))&
(![X]:((~quiet(X)|~brave(X))=>(calm(X)|~wise(X))))&
(![X]:((~tall(X)|tall(X))<=>brave(X)))&
(((quiet(john)<~>~tall(john)))<=>(?[X]:((~old(X)|happy(X)))))&
((creative(alice))<=>(curious(mary)))&
(![X]:((quiet(X)|generous(X))=>~curious(X)))&
(![X]:(~kind(X)=>(~brave(X)&funny(X))))&
((?[X]:((humble(X)<~>~tall(X))))<=>((brave(susan)&patient(susan))))&
((?[X]:((wise(X)|rich(X))))<=>(?[X]:((old(X)<~>~calm(X)))))&
(![X]:((rich(X)|funny(X))<=>~quiet(X)))&
((?[X]:((~calm(X)<~>~tall(X))))<=>((~rich(mary)&tall(mary))))&
(((patient(fred)&calm(fred)))=>(creative(john)))&
(![X]:((~rich(X)|rich(X))=>(patient(X)<~>quiet(X))))&
(![X]:(~tall(X)=>(~quiet(X)|~wise(X))))&
((?[X]:((~old(X)&generous(X))))=>(?[X]:((~generous(X)<~>~strong(X)))))&
(![X]:((~funny(X)|brave(X))<=>(~creative(X)<~>wise(X))))&
((rich(lucy)<~>~creative(lucy)))&
((~tall(john)|~quiet(john)))&
(quiet(mary))&
((~old(lucy)<~>strong(lucy)))&
((~wise(mary)&tall(mary))) | strong(mary) | [] | null | 0 |
If paul is either kind or not calm then mary is creative.
If someone is funny or humble then fred is either not brave or rich and vice versa.
Everyone who is either curious or not calm is both not wise and not humble.
Everyone who is either not curious or rich is either quiet or not tall.
Everyone who is either not old or strong is either strong or not wise and vice versa.
Everyone who is curious is either not generous or not calm and vice versa.
If john is either not generous or wise then someone is both creative and happy and vice versa.
If mary is both generous and not old then someone is either not wise or not calm and vice versa.
Everyone who is both patient and wise is brave or generous and vice versa.
Everyone who is brave or kind is old or brave.
If alice is either not curious or not patient then someone is generous.
Everyone who is either not creative or rich is either not happy or not wise and vice versa.
Everyone who is patient is not wise or not tall.
Everyone who is either not old or not tall is not rich.
Everyone who is either not tall or happy is humble or kind.
Everyone who is not rich or creative is rich or creative.
Fred is both not strong and kind.
Someone is both not kind and not humble.
John is both not kind and humble.
Alice is either calm or not strong.
Someone is both not tall and funny. | Alice is creative. | entailment | (((kind(paul)<~>~calm(paul)))=>(creative(mary)))&
((?[X]:((funny(X)|humble(X))))<=>((~brave(fred)<~>rich(fred))))&
(![X]:((curious(X)<~>~calm(X))=>(~wise(X)&~humble(X))))&
(![X]:((~curious(X)<~>rich(X))=>(quiet(X)<~>~tall(X))))&
(![X]:((~old(X)<~>strong(X))<=>(strong(X)<~>~wise(X))))&
(![X]:(curious(X)<=>(~generous(X)<~>~calm(X))))&
(((~generous(john)<~>wise(john)))<=>(?[X]:((creative(X)&happy(X)))))&
(((generous(mary)&~old(mary)))<=>(?[X]:((~wise(X)<~>~calm(X)))))&
(![X]:((patient(X)&wise(X))<=>(brave(X)|generous(X))))&
(![X]:((brave(X)|kind(X))=>(old(X)|brave(X))))&
(((~curious(alice)<~>~patient(alice)))=>(?[X]:(generous(X))))&
(![X]:((~creative(X)<~>rich(X))<=>(~happy(X)<~>~wise(X))))&
(![X]:(patient(X)=>(~wise(X)|~tall(X))))&
(![X]:((~old(X)<~>~tall(X))=>~rich(X)))&
(![X]:((~tall(X)<~>happy(X))=>(humble(X)|kind(X))))&
(![X]:((~rich(X)|creative(X))=>(rich(X)|creative(X))))&
((~strong(fred)&kind(fred)))&
(?[X]:((~kind(X)&~humble(X))))&
((~kind(john)&humble(john)))&
((calm(alice)<~>~strong(alice)))&
(?[X]:((~tall(X)&funny(X)))) | creative(alice) | [
"p2",
"p4",
"p5",
"p7",
"p8",
"p9",
"p11",
"p12",
"p13",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8181951848649198301422097
% SZS output start Proof for 8181951848649198301422097
3. ! [X0] : ((curious(X0) <~> ~calm(X0)) => (~humble(X0) & ~wise(X0))) [input p2]
5. ! [X0] : ((~old(X0) <~> strong(X0)) <=> (strong(X0) <~> ~wise(X0))) [input p4]
6. ! [X0] : (curious(X0) <=> (~generous(X0) <~> ~calm(X0))) [input p5]
8. (~old(mary) & generous(mary)) <=> ? [X0] : (~wise(X0) <~> ~calm(X0)) [input p7]
9. ! [X0] : ((wise(X0) & patient(X0)) <=> (generous(X0) | brave(X0))) [input p8]
10. ! [X0] : ((kind(X0) | brave(X0)) => (brave(X0) | old(X0))) [input p9]
12. ! [X0] : ((~creative(X0) <~> rich(X0)) <=> (~happy(X0) <~> ~wise(X0))) [input p11]
13. ! [X0] : (patient(X0) => (~tall(X0) | ~wise(X0))) [input p12]
14. ! [X0] : ((~old(X0) <~> ~tall(X0)) => ~rich(X0)) [input p13]
15. ! [X0] : ((~tall(X0) <~> happy(X0)) => (kind(X0) | humble(X0))) [input p14]
16. ! [X0] : ((creative(X0) | ~rich(X0)) => (creative(X0) | rich(X0))) [input p15]
22. ~creative(alice) [input hypothesis]
24. ! [X0] : ((~humble(X0) & ~wise(X0)) | (curious(X0) <=> ~calm(X0))) [ennf transformation 3]
26. ! [X0] : ((brave(X0) | old(X0)) | (~kind(X0) & ~brave(X0))) [ennf transformation 10]
27. ! [X0] : (brave(X0) | old(X0) | (~kind(X0) & ~brave(X0))) [flattening 26]
29. ! [X0] : ((~tall(X0) | ~wise(X0)) | ~patient(X0)) [ennf transformation 13]
30. ! [X0] : (~tall(X0) | ~wise(X0) | ~patient(X0)) [flattening 29]
31. ! [X0] : (~rich(X0) | (~old(X0) <=> ~tall(X0))) [ennf transformation 14]
32. ! [X0] : ((kind(X0) | humble(X0)) | (~tall(X0) <=> happy(X0))) [ennf transformation 15]
33. ! [X0] : (kind(X0) | humble(X0) | (~tall(X0) <=> happy(X0))) [flattening 32]
34. ! [X0] : ((creative(X0) | rich(X0)) | (~creative(X0) & rich(X0))) [ennf transformation 16]
35. ! [X0] : (creative(X0) | rich(X0) | (~creative(X0) & rich(X0))) [flattening 34]
41. ! [X0] : ((~humble(X0) & ~wise(X0)) | ((curious(X0) | calm(X0)) & (~calm(X0) | ~curious(X0)))) [nnf transformation 24]
43. ! [X0] : ((((~strong(X0) | old(X0)) & (strong(X0) | ~old(X0))) | ((strong(X0) | wise(X0)) & (~wise(X0) | ~strong(X0)))) & (((wise(X0) | ~strong(X0)) & (~wise(X0) | strong(X0))) | ((~old(X0) | ~strong(X0)) & (strong(X0) | old(X0))))) [nnf transformation 5]
44. ! [X0] : ((curious(X0) | ((~generous(X0) | calm(X0)) & (~calm(X0) | generous(X0)))) & (((calm(X0) | generous(X0)) & (~calm(X0) | ~generous(X0))) | ~curious(X0))) [nnf transformation 6]
49. ((~old(mary) & generous(mary)) | ! [X0] : ((~wise(X0) | calm(X0)) & (~calm(X0) | wise(X0)))) & (? [X0] : ((calm(X0) | wise(X0)) & (~calm(X0) | ~wise(X0))) | (old(mary) | ~generous(mary))) [nnf transformation 8]
50. ((~old(mary) & generous(mary)) | ! [X0] : ((~wise(X0) | calm(X0)) & (~calm(X0) | wise(X0)))) & (? [X0] : ((calm(X0) | wise(X0)) & (~calm(X0) | ~wise(X0))) | old(mary) | ~generous(mary)) [flattening 49]
51. ((~old(mary) & generous(mary)) | ! [X0] : ((~wise(X0) | calm(X0)) & (~calm(X0) | wise(X0)))) & (? [X1] : ((calm(X1) | wise(X1)) & (~calm(X1) | ~wise(X1))) | old(mary) | ~generous(mary)) [rectify 50]
52. ? [X1] : ((calm(X1) | wise(X1)) & (~calm(X1) | ~wise(X1))) => ((calm(sK2) | wise(sK2)) & (~calm(sK2) | ~wise(sK2))) [choice axiom]
53. ((~old(mary) & generous(mary)) | ! [X0] : ((~wise(X0) | calm(X0)) & (~calm(X0) | wise(X0)))) & (((calm(sK2) | wise(sK2)) & (~calm(sK2) | ~wise(sK2))) | old(mary) | ~generous(mary)) [skolemisation 51,52]
54. ! [X0] : (((wise(X0) & patient(X0)) | (~generous(X0) & ~brave(X0))) & ((generous(X0) | brave(X0)) | (~wise(X0) | ~patient(X0)))) [nnf transformation 9]
55. ! [X0] : (((wise(X0) & patient(X0)) | (~generous(X0) & ~brave(X0))) & (generous(X0) | brave(X0) | ~wise(X0) | ~patient(X0))) [flattening 54]
59. ! [X0] : ((((~rich(X0) | creative(X0)) & (rich(X0) | ~creative(X0))) | ((~happy(X0) | wise(X0)) & (~wise(X0) | happy(X0)))) & (((wise(X0) | happy(X0)) & (~wise(X0) | ~happy(X0))) | ((~creative(X0) | ~rich(X0)) & (rich(X0) | creative(X0))))) [nnf transformation 12]
60. ! [X0] : (~rich(X0) | ((~old(X0) | tall(X0)) & (~tall(X0) | old(X0)))) [nnf transformation 31]
61. ! [X0] : (kind(X0) | humble(X0) | ((~tall(X0) | ~happy(X0)) & (happy(X0) | tall(X0)))) [nnf transformation 33]
75. ~wise(X0) | ~calm(X0) | ~curious(X0) [cnf transformation 41]
76. ~wise(X0) | curious(X0) | calm(X0) [cnf transformation 41]
78. ~humble(X0) | curious(X0) | calm(X0) [cnf transformation 41]
83. ~wise(X0) | strong(X0) | strong(X0) | old(X0) [cnf transformation 43]
86. wise(X0) | ~strong(X0) | ~old(X0) | ~strong(X0) [cnf transformation 43]
88. strong(X0) | ~old(X0) | strong(X0) | wise(X0) [cnf transformation 43]
89. ~strong(X0) | old(X0) | ~wise(X0) | ~strong(X0) [cnf transformation 43]
92. ~curious(X0) | generous(X0) | calm(X0) [cnf transformation 44]
93. ~calm(X0) | curious(X0) | generous(X0) [cnf transformation 44]
103. generous(mary) | ~calm(X0) | wise(X0) [cnf transformation 53]
105. ~old(mary) | ~calm(X0) | wise(X0) [cnf transformation 53]
109. ~generous(X0) | patient(X0) [cnf transformation 55]
110. ~brave(X0) | wise(X0) [cnf transformation 55]
111. ~generous(X0) | wise(X0) [cnf transformation 55]
113. ~kind(X0) | old(X0) | brave(X0) [cnf transformation 27]
123. ~happy(X0) | creative(X0) | ~rich(X0) | wise(X0) [cnf transformation 59]
124. ~patient(X0) | ~wise(X0) | ~tall(X0) [cnf transformation 30]
125. ~tall(X0) | ~rich(X0) | old(X0) [cnf transformation 60]
126. ~old(X0) | ~rich(X0) | tall(X0) [cnf transformation 60]
127. happy(X0) | humble(X0) | kind(X0) | tall(X0) [cnf transformation 61]
129. creative(X0) | rich(X0) | rich(X0) [cnf transformation 35]
141. ~creative(alice) [cnf transformation 22]
142. rich(X0) | creative(X0) [duplicate literal removal 129]
143. ~wise(X0) | strong(X0) | old(X0) [duplicate literal removal 83]
144. wise(X0) | ~strong(X0) | ~old(X0) [duplicate literal removal 86]
145. ~old(X0) | strong(X0) | wise(X0) [duplicate literal removal 88]
146. ~strong(X0) | old(X0) | ~wise(X0) [duplicate literal removal 89]
189. ~old(X0) | wise(X0) [subsumption resolution 144,145]
190. ~wise(X0) | old(X0) [subsumption resolution 143,146]
220. 16 <=> old(mary) [avatar definition]
222. ~old(mary) <- (~16) [avatar component clause 220]
225. 17 <=> ! [X0] : (~calm(X0) | wise(X0)) [avatar definition]
226. ~calm(X0) | wise(X0) <- (17) [avatar component clause 225]
227. 17 | ~16 [avatar split clause 105,220,225]
229. 18 <=> generous(mary) [avatar definition]
231. generous(mary) <- (18) [avatar component clause 229]
233. 17 | 18 [avatar split clause 103,229,225]
245. 21 <=> patient(alice) [avatar definition]
247. patient(alice) <- (21) [avatar component clause 245]
249. 22 <=> curious(alice) [avatar definition]
250. curious(alice) <- (22) [avatar component clause 249]
251. ~curious(alice) <- (~22) [avatar component clause 249]
259. 24 <=> calm(alice) [avatar definition]
260. calm(alice) <- (24) [avatar component clause 259]
261. ~calm(alice) <- (~24) [avatar component clause 259]
297. wise(mary) <- (18) [resolution 231,111]
357. old(mary) <- (18) [resolution 297,190]
358. $false <- (~16, 18) [subsumption resolution 357,222]
359. 16 | ~18 [avatar contradiction clause 358]
503. humble(X0) | kind(X0) | tall(X0) | creative(X0) | ~rich(X0) | wise(X0) [resolution 127,123]
507. tall(X0) | kind(X0) | humble(X0) | creative(X0) | wise(X0) [subsumption resolution 503,142]
537. kind(X2) | humble(X2) | creative(X2) | wise(X2) | ~rich(X2) | old(X2) [resolution 507,125]
542. kind(X2) | humble(X2) | creative(X2) | ~rich(X2) | old(X2) [subsumption resolution 537,190]
543. old(X2) | humble(X2) | creative(X2) | kind(X2) [subsumption resolution 542,142]
622. wise(X2) | creative(X2) | kind(X2) | humble(X2) [resolution 543,189]
683. creative(X1) | kind(X1) | humble(X1) | curious(X1) | calm(X1) [resolution 622,76]
694. curious(X1) | kind(X1) | creative(X1) | calm(X1) [subsumption resolution 683,78]
823. kind(alice) | creative(alice) | calm(alice) <- (~22) [resolution 694,251]
829. kind(alice) | calm(alice) <- (~22) [subsumption resolution 823,141]
830. kind(alice) <- (~22, ~24) [subsumption resolution 829,261]
831. old(alice) | brave(alice) <- (~22, ~24) [resolution 830,113]
833. 66 <=> brave(alice) [avatar definition]
835. brave(alice) <- (66) [avatar component clause 833]
837. 67 <=> old(alice) [avatar definition]
839. old(alice) <- (67) [avatar component clause 837]
840. 66 | 67 | 22 | 24 [avatar split clause 831,259,249,837,833]
976. wise(alice) <- (66) [resolution 835,110]
982. ~wise(alice) | ~tall(alice) <- (21) [resolution 247,124]
987. generous(alice) | calm(alice) <- (22) [resolution 250,92]
989. generous(alice) <- (22, ~24) [subsumption resolution 987,261]
995. wise(alice) <- (22, ~24) [resolution 989,111]
1032. old(alice) <- (66) [resolution 976,190]
1041. 77 <=> rich(alice) [avatar definition]
1043. ~rich(alice) <- (~77) [avatar component clause 1041]
1045. 67 | ~66 [avatar split clause 1032,833,837]
1056. old(alice) <- (22, ~24) [resolution 995,190]
1061. 67 | ~22 | 24 [avatar split clause 1056,259,249,837]
1066. 78 <=> generous(alice) [avatar definition]
1068. generous(alice) <- (78) [avatar component clause 1066]
1070. 79 <=> wise(alice) [avatar definition]
1071. wise(alice) <- (79) [avatar component clause 1070]
1072. ~wise(alice) <- (~79) [avatar component clause 1070]
1075. 80 <=> tall(alice) [avatar definition]
1078. ~80 | ~79 | ~21 [avatar split clause 982,245,1070,1075]
1084. 24 | 78 | ~22 [avatar split clause 987,249,1066,259]
1092. wise(alice) <- (17, 24) [resolution 260,226]
1093. $false <- (17, 24, ~79) [subsumption resolution 1092,1072]
1094. ~17 | ~24 | 79 [avatar contradiction clause 1093]
1104. ~rich(alice) | tall(alice) <- (67) [resolution 839,126]
1105. wise(alice) <- (67) [resolution 839,189]
1109. 80 | ~77 | ~67 [avatar split clause 1104,837,1041,1075]
1112. 79 | ~67 [avatar split clause 1105,837,1070]
1114. ~calm(alice) | ~curious(alice) <- (79) [resolution 1071,75]
1115. curious(alice) | calm(alice) <- (79) [resolution 1071,76]
1118. old(alice) <- (79) [resolution 1071,190]
1121. calm(alice) <- (~22, 79) [subsumption resolution 1115,251]
1127. 24 | 22 | ~79 [avatar split clause 1121,1070,249,259]
1128. curious(alice) | generous(alice) <- (24) [resolution 260,93]
1136. patient(alice) <- (78) [resolution 1068,109]
1139. 21 | ~78 [avatar split clause 1136,1066,245]
1233. creative(alice) <- (~77) [resolution 1043,142]
1234. $false <- (~77) [subsumption resolution 1233,141]
1235. 77 [avatar contradiction clause 1234]
1236. 67 | ~79 [avatar split clause 1118,1070,837]
1241. 78 | 22 | ~24 [avatar split clause 1128,259,249,1066]
1242. ~curious(alice) <- (24, 79) [subsumption resolution 1114,260]
1243. ~22 | ~24 | ~79 [avatar split clause 1242,1070,259,249]
1244. $false [avatar sat refutation 227,233,359,840,1045,1061,1078,1084,1094,1109,1112,1127,1139,1235,1236,1241,1243]
% SZS output end Proof for 8181951848649198301422097
% ------------------------------
% 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: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both curious and not kind then lucy is not rich or brave. Everyone who is both not old and kind is not curious or curious and vice versa. If someone is either wise or rich then someone is either old or not rich and vice versa. If someone is both not wise and strong then someone is curious. If someone is either humble or curious then lucy is both generous and old and vice versa. If someone is happy or not calm then mary is not patient. If someone is tall or calm then fred is either not calm or old. If someone is either brave or curious then alice is not kind and vice versa. Everyone who is funny is both quiet and not calm. If alice is creative then paul is not creative or curious and vice versa. If john is curious then someone is both not humble and not strong. If fred is kind or funny then lucy is either not tall or rich and vice versa. If mary is quiet or old then alice is not rich or not happy. Everyone who is creative is not calm and vice versa. Everyone who is tall or not patient is not funny. Everyone who is not funny is curious. Susan is curious. Someone is either not creative or humble. Paul is creative. John is both tall and calm. Someone is not humble. Someone is either not quiet or not tall. Someone is not curious. Susan is humble or not strong. | Mary is curious. | entailment | ((?[X]:((curious(X)&~kind(X))))=>((~rich(lucy)|brave(lucy))))&
(![X]:((~old(X)&kind(X))<=>(~curious(X)|curious(X))))&
((?[X]:((wise(X)<~>rich(X))))<=>(?[X]:((old(X)<~>~rich(X)))))&
((?[X]:((~wise(X)&strong(X))))=>(?[X]:(curious(X))))&
((?[X]:((humble(X)<~>curious(X))))<=>((generous(lucy)&old(lucy))))&
((?[X]:((happy(X)|~calm(X))))=>(~patient(mary)))&
((?[X]:((tall(X)|calm(X))))=>((~calm(fred)<~>old(fred))))&
((?[X]:((brave(X)<~>curious(X))))<=>(~kind(alice)))&
(![X]:(funny(X)=>(quiet(X)&~calm(X))))&
((creative(alice))<=>((~creative(paul)|curious(paul))))&
((curious(john))=>(?[X]:((~humble(X)&~strong(X)))))&
(((kind(fred)|funny(fred)))<=>((~tall(lucy)<~>rich(lucy))))&
(((quiet(mary)|old(mary)))=>((~rich(alice)|~happy(alice))))&
(![X]:(creative(X)<=>~calm(X)))&
(![X]:((tall(X)|~patient(X))=>~funny(X)))&
(![X]:(~funny(X)=>curious(X)))&
(curious(susan))&
(?[X]:((~creative(X)<~>humble(X))))&
(creative(paul))&
((tall(john)&calm(john)))&
(?[X]:(~humble(X)))&
(?[X]:((~quiet(X)<~>~tall(X))))&
(?[X]:(~curious(X)))&
((humble(susan)|~strong(susan))) | curious(mary) | [
"p5",
"p13",
"p14",
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 8253758857763289930667498
% SZS output start Proof for 8253758857763289930667498
6. ? [X0] : (~calm(X0) | happy(X0)) => ~patient(mary) [input p5]
14. ! [X0] : (creative(X0) <=> ~calm(X0)) [input p13]
15. ! [X0] : ((~patient(X0) | tall(X0)) => ~funny(X0)) [input p14]
16. ! [X0] : (~funny(X0) => curious(X0)) [input p15]
19. creative(paul) [input p18]
25. ~curious(mary) [input hypothesis]
28. ? [X0] : ~calm(X0) => ~patient(mary) [pure predicate removal 6]
35. ~patient(mary) | ! [X0] : calm(X0) [ennf transformation 28]
39. ! [X0] : (~funny(X0) | (patient(X0) & ~tall(X0))) [ennf transformation 15]
40. ! [X0] : (curious(X0) | funny(X0)) [ennf transformation 16]
64. ! [X0] : ((creative(X0) | calm(X0)) & (~calm(X0) | ~creative(X0))) [nnf transformation 14]
95. ~patient(mary) | calm(X0) [cnf transformation 35]
116. ~creative(X0) | ~calm(X0) [cnf transformation 64]
119. ~funny(X0) | patient(X0) [cnf transformation 39]
120. funny(X0) | curious(X0) [cnf transformation 40]
124. creative(paul) [cnf transformation 19]
131. ~curious(mary) [cnf transformation 25]
178. 10 <=> ! [X0] : calm(X0) [avatar definition]
179. calm(X0) <- (10) [avatar component clause 178]
181. 11 <=> patient(mary) [avatar definition]
183. ~patient(mary) <- (~11) [avatar component clause 181]
184. 10 | ~11 [avatar split clause 95,181,178]
231. 22 <=> creative(paul) [avatar definition]
233. creative(paul) <- (22) [avatar component clause 231]
273. 22 [avatar split clause 124,231]
291. ~calm(paul) <- (22) [resolution 116,233]
296. patient(X0) | curious(X0) [resolution 120,119]
309. curious(mary) <- (~11) [resolution 296,183]
310. $false <- (~11) [subsumption resolution 309,131]
311. 11 [avatar contradiction clause 310]
313. $false <- (10, 22) [resolution 179,291]
314. ~10 | ~22 [avatar contradiction clause 313]
316. $false [avatar sat refutation 184,273,311,314]
% SZS output end Proof for 8253758857763289930667498
% ------------------------------
% 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 humble and not happy is both not happy and not strong and vice versa.
If alice is either quiet or curious then fred is both not funny and not kind.
Everyone who is both not happy and wise is either not humble or not tall.
If someone is both brave and not creative then lucy is not brave.
If alice is both not quiet and funny then lucy is either creative or not curious and vice versa.
Everyone who is both old and not tall is wise.
If fred is not funny then someone is not humble or not kind and vice versa.
Everyone who is happy or not happy is both old and not wise and vice versa.
Everyone who is either not calm or strong is either not creative or not old.
If mary is not funny then susan is either not rich or patient.
If susan is curious then fred is either tall or rich and vice versa.
If someone is not curious or strong then someone is strong or not quiet.
If john is patient then someone is rich.
If someone is either not calm or not kind then fred is kind and vice versa.
Everyone who is both not humble and not tall is not old or strong.
If susan is both wise and not rich then someone is generous.
Paul is not generous or creative.
Susan is either not calm or not generous.
Someone is curious.
Mary is quiet. | Paul is generous. | neutral | (![X]:((~humble(X)&~happy(X))<=>(~happy(X)&~strong(X))))&
(((quiet(alice)<~>curious(alice)))=>((~funny(fred)&~kind(fred))))&
(![X]:((~happy(X)&wise(X))=>(~humble(X)<~>~tall(X))))&
((?[X]:((brave(X)&~creative(X))))=>(~brave(lucy)))&
(((~quiet(alice)&funny(alice)))<=>((creative(lucy)<~>~curious(lucy))))&
(![X]:((old(X)&~tall(X))=>wise(X)))&
((~funny(fred))<=>(?[X]:((~humble(X)|~kind(X)))))&
(![X]:((happy(X)|~happy(X))<=>(old(X)&~wise(X))))&
(![X]:((~calm(X)<~>strong(X))=>(~creative(X)<~>~old(X))))&
((~funny(mary))=>((~rich(susan)<~>patient(susan))))&
((curious(susan))<=>((tall(fred)<~>rich(fred))))&
((?[X]:((~curious(X)|strong(X))))=>(?[X]:((strong(X)|~quiet(X)))))&
((patient(john))=>(?[X]:(rich(X))))&
((?[X]:((~calm(X)<~>~kind(X))))<=>(kind(fred)))&
(![X]:((~humble(X)&~tall(X))=>(~old(X)|strong(X))))&
(((wise(susan)&~rich(susan)))=>(?[X]:(generous(X))))&
((~generous(paul)|creative(paul)))&
((~calm(susan)<~>~generous(susan)))&
(?[X]:(curious(X)))&
(quiet(mary)) | generous(paul) | [] | null | 0 |
If someone is not kind then someone is both rich and not happy. If someone is both generous and curious then someone is rich and vice versa. Everyone who is not kind or not wise is not old or not patient. Everyone who is both kind and humble is generous or happy and vice versa. Everyone who is both rich and funny is not old or wise and vice versa. Everyone who is either wise or not curious is both curious and not brave. Everyone who is both tall and funny is both not patient and not wise. Everyone who is either happy or curious is both brave and not humble and vice versa. Everyone who is old is funny or not kind. If someone is not wise or brave then someone is both not tall and curious. Everyone who is either curious or not curious is wise and vice versa. Everyone who is either creative or strong is quiet or not wise and vice versa. If mary is not humble or patient then lucy is funny or generous. If alice is quiet then someone is kind. If alice is either not kind or patient then mary is not tall. Everyone who is both old and quiet is either brave or rich and vice versa. Someone is both not brave and calm. Someone is not curious or not old. Someone is brave or creative. John is rich or not happy. Alice is not humble or not kind. Alice is either not brave or old. Alice is both creative and not happy. | Alice is not kind. | entailment | ((?[X]:(~kind(X)))=>(?[X]:((rich(X)&~happy(X)))))&
((?[X]:((generous(X)&curious(X))))<=>(?[X]:(rich(X))))&
(![X]:((~kind(X)|~wise(X))=>(~old(X)|~patient(X))))&
(![X]:((kind(X)&humble(X))<=>(generous(X)|happy(X))))&
(![X]:((rich(X)&funny(X))<=>(~old(X)|wise(X))))&
(![X]:((wise(X)<~>~curious(X))=>(curious(X)&~brave(X))))&
(![X]:((tall(X)&funny(X))=>(~patient(X)&~wise(X))))&
(![X]:((happy(X)<~>curious(X))<=>(brave(X)&~humble(X))))&
(![X]:(old(X)=>(funny(X)|~kind(X))))&
((?[X]:((~wise(X)|brave(X))))=>(?[X]:((~tall(X)&curious(X)))))&
(![X]:((curious(X)<~>~curious(X))<=>wise(X)))&
(![X]:((creative(X)<~>strong(X))<=>(quiet(X)|~wise(X))))&
(((~humble(mary)|patient(mary)))=>((funny(lucy)|generous(lucy))))&
((quiet(alice))=>(?[X]:(kind(X))))&
(((~kind(alice)<~>patient(alice)))=>(~tall(mary)))&
(![X]:((old(X)&quiet(X))<=>(brave(X)<~>rich(X))))&
(?[X]:((~brave(X)&calm(X))))&
(?[X]:((~curious(X)|~old(X))))&
(?[X]:((brave(X)|creative(X))))&
((rich(john)|~happy(john)))&
((~humble(alice)|~kind(alice)))&
((~brave(alice)<~>old(alice)))&
((creative(alice)&~happy(alice))) | ~kind(alice) | [
"p3",
"p4",
"p5",
"p7",
"p10",
"p15",
"p20",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 7276069756467175568218162
% SZS output start Proof for 7276069756467175568218162
4. ! [X0] : ((humble(X0) & kind(X0)) <=> (happy(X0) | generous(X0))) [input p3]
5. ! [X0] : ((funny(X0) & rich(X0)) <=> (wise(X0) | ~old(X0))) [input p4]
6. ! [X0] : ((wise(X0) <~> ~curious(X0)) => (~brave(X0) & curious(X0))) [input p5]
8. ! [X0] : ((happy(X0) <~> curious(X0)) <=> (~humble(X0) & brave(X0))) [input p7]
11. ! [X0] : ((curious(X0) <~> ~curious(X0)) <=> wise(X0)) [input p10]
16. ! [X0] : ((quiet(X0) & old(X0)) <=> (brave(X0) <~> rich(X0))) [input p15]
21. ~kind(alice) | ~humble(alice) [input p20]
22. ~brave(alice) <~> old(alice) [input p21]
24. kind(alice) [input hypothesis]
35. ! [X0] : ((~brave(X0) & curious(X0)) | (wise(X0) <=> ~curious(X0))) [ennf transformation 6]
50. ! [X0] : (((humble(X0) & kind(X0)) | (~happy(X0) & ~generous(X0))) & ((happy(X0) | generous(X0)) | (~humble(X0) | ~kind(X0)))) [nnf transformation 4]
51. ! [X0] : (((humble(X0) & kind(X0)) | (~happy(X0) & ~generous(X0))) & (happy(X0) | generous(X0) | ~humble(X0) | ~kind(X0))) [flattening 50]
52. ! [X0] : (((funny(X0) & rich(X0)) | (~wise(X0) & old(X0))) & ((wise(X0) | ~old(X0)) | (~funny(X0) | ~rich(X0)))) [nnf transformation 5]
53. ! [X0] : (((funny(X0) & rich(X0)) | (~wise(X0) & old(X0))) & (wise(X0) | ~old(X0) | ~funny(X0) | ~rich(X0))) [flattening 52]
54. ! [X0] : ((~brave(X0) & curious(X0)) | ((wise(X0) | curious(X0)) & (~curious(X0) | ~wise(X0)))) [nnf transformation 35]
55. ! [X0] : ((((~curious(X0) | ~happy(X0)) & (curious(X0) | happy(X0))) | (humble(X0) | ~brave(X0))) & ((~humble(X0) & brave(X0)) | ((happy(X0) | ~curious(X0)) & (curious(X0) | ~happy(X0))))) [nnf transformation 8]
56. ! [X0] : ((((~curious(X0) | ~happy(X0)) & (curious(X0) | happy(X0))) | humble(X0) | ~brave(X0)) & ((~humble(X0) & brave(X0)) | ((happy(X0) | ~curious(X0)) & (curious(X0) | ~happy(X0))))) [flattening 55]
60. ! [X0] : ((((curious(X0) | ~curious(X0)) & (~curious(X0) | curious(X0))) | ~wise(X0)) & (wise(X0) | ((curious(X0) | curious(X0)) & (~curious(X0) | ~curious(X0))))) [nnf transformation 11]
65. ! [X0] : (((quiet(X0) & old(X0)) | ((brave(X0) | ~rich(X0)) & (rich(X0) | ~brave(X0)))) & (((~rich(X0) | ~brave(X0)) & (rich(X0) | brave(X0))) | (~quiet(X0) | ~old(X0)))) [nnf transformation 16]
66. ! [X0] : (((quiet(X0) & old(X0)) | ((brave(X0) | ~rich(X0)) & (rich(X0) | ~brave(X0)))) & (((~rich(X0) | ~brave(X0)) & (rich(X0) | brave(X0))) | ~quiet(X0) | ~old(X0))) [flattening 65]
73. (~old(alice) | brave(alice)) & (old(alice) | ~brave(alice)) [nnf transformation 22]
83. ~happy(X0) | humble(X0) [cnf transformation 51]
85. old(X0) | rich(X0) [cnf transformation 53]
90. curious(X0) | wise(X0) | curious(X0) [cnf transformation 54]
91. ~brave(X0) | ~curious(X0) | ~wise(X0) [cnf transformation 54]
97. curious(X0) | happy(X0) | humble(X0) | ~brave(X0) [cnf transformation 56]
102. wise(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 60]
117. old(X0) | brave(X0) | ~rich(X0) [cnf transformation 66]
124. ~kind(alice) | ~humble(alice) [cnf transformation 21]
126. ~old(alice) | brave(alice) [cnf transformation 73]
129. kind(alice) [cnf transformation 24]
130. wise(X0) | ~curious(X0) [duplicate literal removal 102]
132. wise(X0) | curious(X0) [duplicate literal removal 90]
167. ~brave(X0) | humble(X0) | curious(X0) [subsumption resolution 97,83]
179. 11 <=> ! [X1] : wise(X1) [avatar definition]
180. wise(X1) <- (11) [avatar component clause 179]
182. wise(X0) [subsumption resolution 130,132]
183. 11 [avatar split clause 182,179]
206. brave(X0) | old(X0) [subsumption resolution 117,85]
236. 23 <=> humble(alice) [avatar definition]
238. ~humble(alice) <- (~23) [avatar component clause 236]
240. 24 <=> kind(alice) [avatar definition]
243. ~23 | ~24 [avatar split clause 124,240,236]
244. brave(alice) [subsumption resolution 126,206]
246. 24 [avatar split clause 129,240]
272. ~curious(alice) | ~wise(alice) [resolution 91,244]
275. ~curious(alice) <- (11) [subsumption resolution 272,180]
343. humble(alice) | curious(alice) [resolution 167,244]
345. curious(alice) <- (~23) [subsumption resolution 343,238]
346. $false <- (11, ~23) [subsumption resolution 345,275]
347. ~11 | 23 [avatar contradiction clause 346]
348. $false [avatar sat refutation 183,243,246,347]
% SZS output end Proof for 7276069756467175568218162
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both curious and not old then someone is wise and vice versa.
Everyone who is either not wise or not rich is not tall and vice versa.
If someone is either not creative or humble then someone is both not funny and patient and vice versa.
Everyone who is either not generous or not brave is not generous or happy and vice versa.
If someone is both old and generous then susan is wise and vice versa.
Everyone who is curious or not curious is either not happy or not old.
Everyone who is not old is both strong and not wise and vice versa.
If someone is both kind and not curious then someone is not curious or wise.
Everyone who is not creative or not happy is not happy or quiet and vice versa.
If someone is happy or not generous then paul is not strong and vice versa.
If someone is brave then alice is old or tall.
If alice is either funny or not quiet then someone is not quiet and vice versa.
Everyone who is both tall and old is funny.
If someone is either curious or old then someone is both not kind and tall.
Everyone who is both funny and not curious is not wise and vice versa.
Everyone who is tall or not calm is both not humble and creative and vice versa.
Someone is not brave or generous.
Someone is calm or brave.
Someone is either not calm or not generous.
Lucy is both patient and not wise.
Someone is brave or not patient.
Someone is both patient and not generous.
John is both not tall and happy.
Someone is not calm or not creative. | Alice is strong. | contradiction | ((?[X]:((curious(X)&~old(X))))<=>(?[X]:(wise(X))))&
(![X]:((~wise(X)<~>~rich(X))<=>~tall(X)))&
((?[X]:((~creative(X)<~>humble(X))))<=>(?[X]:((~funny(X)&patient(X)))))&
(![X]:((~generous(X)<~>~brave(X))<=>(~generous(X)|happy(X))))&
((?[X]:((old(X)&generous(X))))<=>(wise(susan)))&
(![X]:((curious(X)|~curious(X))=>(~happy(X)<~>~old(X))))&
(![X]:(~old(X)<=>(strong(X)&~wise(X))))&
((?[X]:((kind(X)&~curious(X))))=>(?[X]:((~curious(X)|wise(X)))))&
(![X]:((~creative(X)|~happy(X))<=>(~happy(X)|quiet(X))))&
((?[X]:((happy(X)|~generous(X))))<=>(~strong(paul)))&
((?[X]:(brave(X)))=>((old(alice)|tall(alice))))&
(((funny(alice)<~>~quiet(alice)))<=>(?[X]:(~quiet(X))))&
(![X]:((tall(X)&old(X))=>funny(X)))&
((?[X]:((curious(X)<~>old(X))))=>(?[X]:((~kind(X)&tall(X)))))&
(![X]:((funny(X)&~curious(X))<=>~wise(X)))&
(![X]:((tall(X)|~calm(X))<=>(~humble(X)&creative(X))))&
(?[X]:((~brave(X)|generous(X))))&
(?[X]:((calm(X)|brave(X))))&
(?[X]:((~calm(X)<~>~generous(X))))&
((patient(lucy)&~wise(lucy)))&
(?[X]:((brave(X)|~patient(X))))&
(?[X]:((patient(X)&~generous(X))))&
((~tall(john)&happy(john)))&
(?[X]:((~calm(X)|~creative(X)))) | strong(alice) | [
"p0",
"p3",
"p5",
"p6",
"p8",
"p10",
"p11",
"p14",
"p15",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 8474155542864813251589618
% SZS output start Proof for 8474155542864813251589618
1. ? [X0] : (~old(X0) & curious(X0)) <=> ? [X0] : wise(X0) [input p0]
4. ! [X0] : ((~generous(X0) <~> ~brave(X0)) <=> (happy(X0) | ~generous(X0))) [input p3]
6. ! [X0] : ((~curious(X0) | curious(X0)) => (~happy(X0) <~> ~old(X0))) [input p5]
7. ! [X0] : (~old(X0) <=> (~wise(X0) & strong(X0))) [input p6]
9. ! [X0] : ((~happy(X0) | ~creative(X0)) <=> (quiet(X0) | ~happy(X0))) [input p8]
11. ? [X0] : brave(X0) => (tall(alice) | old(alice)) [input p10]
12. (funny(alice) <~> ~quiet(alice)) <=> ? [X0] : ~quiet(X0) [input p11]
15. ! [X0] : ((~curious(X0) & funny(X0)) <=> ~wise(X0)) [input p14]
16. ! [X0] : ((~calm(X0) | tall(X0)) <=> (creative(X0) & ~humble(X0))) [input p15]
22. ? [X0] : (~generous(X0) & patient(X0)) [input p21]
25. strong(alice) [input hypothesis]
26. ? [X0] : (~old(X0) & curious(X0)) <=> ? [X1] : wise(X1) [rectify 1]
32. ! [X0] : ((~happy(X0) <~> ~old(X0)) | (curious(X0) & ~curious(X0))) [ennf transformation 6]
33. (tall(alice) | old(alice)) | ! [X0] : ~brave(X0) [ennf transformation 11]
34. tall(alice) | old(alice) | ! [X0] : ~brave(X0) [flattening 33]
38. (? [X0] : (~old(X0) & curious(X0)) | ! [X1] : ~wise(X1)) & (? [X1] : wise(X1) | ! [X0] : (old(X0) | ~curious(X0))) [nnf transformation 26]
39. (? [X0] : (~old(X0) & curious(X0)) | ! [X1] : ~wise(X1)) & (? [X2] : wise(X2) | ! [X3] : (old(X3) | ~curious(X3))) [rectify 38]
40. ? [X0] : (~old(X0) & curious(X0)) => (~old(sK0) & curious(sK0)) [choice axiom]
41. ? [X2] : wise(X2) => wise(sK1) [choice axiom]
42. ((~old(sK0) & curious(sK0)) | ! [X1] : ~wise(X1)) & (wise(sK1) | ! [X3] : (old(X3) | ~curious(X3))) [skolemisation 39,41,40]
49. ! [X0] : ((((brave(X0) | generous(X0)) & (~brave(X0) | ~generous(X0))) | (~happy(X0) & generous(X0))) & ((happy(X0) | ~generous(X0)) | ((~generous(X0) | brave(X0)) & (~brave(X0) | generous(X0))))) [nnf transformation 4]
50. ! [X0] : ((((brave(X0) | generous(X0)) & (~brave(X0) | ~generous(X0))) | (~happy(X0) & generous(X0))) & (happy(X0) | ~generous(X0) | ((~generous(X0) | brave(X0)) & (~brave(X0) | generous(X0))))) [flattening 49]
55. ! [X0] : (((old(X0) | happy(X0)) & (~old(X0) | ~happy(X0))) | (curious(X0) & ~curious(X0))) [nnf transformation 32]
56. ! [X0] : ((~old(X0) | (wise(X0) | ~strong(X0))) & ((~wise(X0) & strong(X0)) | old(X0))) [nnf transformation 7]
57. ! [X0] : ((~old(X0) | wise(X0) | ~strong(X0)) & ((~wise(X0) & strong(X0)) | old(X0))) [flattening 56]
58. ! [X0] : (((~happy(X0) | ~creative(X0)) | (~quiet(X0) & happy(X0))) & ((quiet(X0) | ~happy(X0)) | (happy(X0) & creative(X0)))) [nnf transformation 9]
59. ! [X0] : ((~happy(X0) | ~creative(X0) | (~quiet(X0) & happy(X0))) & (quiet(X0) | ~happy(X0) | (happy(X0) & creative(X0)))) [flattening 58]
64. (((quiet(alice) | ~funny(alice)) & (~quiet(alice) | funny(alice))) | ! [X0] : quiet(X0)) & (? [X0] : ~quiet(X0) | ((funny(alice) | quiet(alice)) & (~quiet(alice) | ~funny(alice)))) [nnf transformation 12]
65. (((quiet(alice) | ~funny(alice)) & (~quiet(alice) | funny(alice))) | ! [X0] : quiet(X0)) & (? [X1] : ~quiet(X1) | ((funny(alice) | quiet(alice)) & (~quiet(alice) | ~funny(alice)))) [rectify 64]
66. ? [X1] : ~quiet(X1) => ~quiet(sK6) [choice axiom]
67. (((quiet(alice) | ~funny(alice)) & (~quiet(alice) | funny(alice))) | ! [X0] : quiet(X0)) & (~quiet(sK6) | ((funny(alice) | quiet(alice)) & (~quiet(alice) | ~funny(alice)))) [skolemisation 65,66]
72. ! [X0] : (((~curious(X0) & funny(X0)) | wise(X0)) & (~wise(X0) | (curious(X0) | ~funny(X0)))) [nnf transformation 15]
73. ! [X0] : (((~curious(X0) & funny(X0)) | wise(X0)) & (~wise(X0) | curious(X0) | ~funny(X0))) [flattening 72]
74. ! [X0] : (((~calm(X0) | tall(X0)) | (~creative(X0) | humble(X0))) & ((creative(X0) & ~humble(X0)) | (calm(X0) & ~tall(X0)))) [nnf transformation 16]
75. ! [X0] : ((~calm(X0) | tall(X0) | ~creative(X0) | humble(X0)) & ((creative(X0) & ~humble(X0)) | (calm(X0) & ~tall(X0)))) [flattening 74]
85. ? [X0] : (~generous(X0) & patient(X0)) => (~generous(sK12) & patient(sK12)) [choice axiom]
86. ~generous(sK12) & patient(sK12) [skolemisation 22,85]
90. curious(sK0) | ~wise(X1) [cnf transformation 42]
91. ~old(sK0) | ~wise(X1) [cnf transformation 42]
106. brave(X0) | generous(X0) | generous(X0) [cnf transformation 50]
113. old(X0) | happy(X0) | ~curious(X0) [cnf transformation 55]
114. happy(X0) | old(X0) | curious(X0) [cnf transformation 55]
116. ~wise(X0) | old(X0) [cnf transformation 57]
117. ~strong(X0) | wise(X0) | ~old(X0) [cnf transformation 57]
121. ~quiet(X0) | ~creative(X0) | ~happy(X0) [cnf transformation 59]
125. tall(alice) | old(alice) | ~brave(X0) [cnf transformation 34]
129. quiet(alice) | ~funny(alice) | quiet(X0) [cnf transformation 67]
134. funny(X0) | wise(X0) [cnf transformation 73]
135. ~curious(X0) | wise(X0) [cnf transformation 73]
138. ~tall(X0) | creative(X0) [cnf transformation 75]
149. ~generous(sK12) [cnf transformation 86]
153. strong(alice) [cnf transformation 25]
155. brave(X0) | generous(X0) [duplicate literal removal 106]
157. 1 <=> ! [X1] : ~wise(X1) [avatar definition]
158. ~wise(X1) <- (1) [avatar component clause 157]
160. 2 <=> old(sK0) [avatar definition]
162. ~old(sK0) <- (~2) [avatar component clause 160]
163. 1 | ~2 [avatar split clause 91,160,157]
165. 3 <=> curious(sK0) [avatar definition]
167. curious(sK0) <- (3) [avatar component clause 165]
168. 1 | 3 [avatar split clause 90,165,157]
227. happy(X0) | old(X0) [subsumption resolution 113,114]
243. 20 <=> ! [X1] : generous(X1) [avatar definition]
244. generous(X1) <- (20) [avatar component clause 243]
251. 22 <=> ! [X0] : ~brave(X0) [avatar definition]
252. ~brave(X0) <- (22) [avatar component clause 251]
254. 23 <=> old(alice) [avatar definition]
258. 24 <=> tall(alice) [avatar definition]
260. tall(alice) <- (24) [avatar component clause 258]
261. 22 | 23 | 24 [avatar split clause 125,258,254,251]
263. 25 <=> ! [X0] : quiet(X0) [avatar definition]
264. quiet(X0) <- (25) [avatar component clause 263]
266. 26 <=> funny(alice) [avatar definition]
268. ~funny(alice) <- (~26) [avatar component clause 266]
270. 27 <=> quiet(alice) [avatar definition]
271. ~quiet(alice) <- (~27) [avatar component clause 270]
272. quiet(alice) <- (27) [avatar component clause 270]
273. 25 | ~26 | 27 [avatar split clause 129,270,266,263]
331. wise(alice) <- (~26) [resolution 134,268]
332. wise(sK0) <- (3) [resolution 135,167]
336. old(sK0) <- (3) [resolution 332,116]
337. $false <- (~2, 3) [subsumption resolution 336,162]
338. 2 | ~3 [avatar contradiction clause 337]
340. $false <- (1, ~26) [resolution 158,331]
343. ~1 | 26 [avatar contradiction clause 340]
345. $false <- (25, ~27) [resolution 264,271]
348. ~25 | 27 [avatar contradiction clause 345]
351. generous(X0) <- (22) [resolution 155,252]
352. 20 | ~22 [avatar split clause 351,251,243]
353. $false <- (20) [resolution 244,149]
358. ~20 [avatar contradiction clause 353]
387. creative(alice) <- (24) [resolution 260,138]
440. wise(alice) | ~old(alice) [resolution 117,153]
456. ~creative(alice) | ~happy(alice) <- (27) [resolution 121,272]
458. ~happy(alice) <- (24, 27) [subsumption resolution 456,387]
474. old(alice) <- (24, 27) [resolution 458,227]
479. 23 | ~24 | ~27 [avatar split clause 474,270,258,254]
482. ~old(alice) <- (1) [subsumption resolution 440,158]
483. ~23 | ~1 [avatar split clause 482,157,254]
484. $false [avatar sat refutation 163,168,261,273,338,343,348,352,358,479,483]
% SZS output end Proof for 8474155542864813251589618
% ------------------------------
% 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 quiet is either not wise or tall and vice versa.
Everyone who is happy or patient is both not creative and calm and vice versa.
If alice is both not rich and not happy then paul is both not humble and old.
If paul is tall then lucy is both not wise and generous and vice versa.
Everyone who is either tall or not old is either happy or not creative and vice versa.
If someone is either not patient or not generous then someone is not old or not quiet and vice versa.
If someone is not happy then alice is either not brave or rich.
Everyone who is generous is not wise or not generous and vice versa.
Everyone who is either humble or wise is either not rich or not quiet and vice versa.
Everyone who is both not curious and strong is not curious and vice versa.
If john is not strong then john is either not quiet or not humble and vice versa.
If mary is either not generous or kind then fred is not generous.
If lucy is both not quiet and not calm then mary is not funny.
Everyone who is wise or curious is either humble or not brave and vice versa.
Everyone who is kind or tall is calm or generous.
Everyone who is both old and curious is either strong or creative.
Someone is either rich or not patient.
Alice is not generous or not happy.
Paul is funny.
Susan is both funny and patient.
Someone is not funny.
Someone is not wise or quiet.
Someone is kind or patient.
Susan is either not calm or not strong. | Alice is not curious. | neutral | (![X]:(quiet(X)<=>(~wise(X)<~>tall(X))))&
(![X]:((happy(X)|patient(X))<=>(~creative(X)&calm(X))))&
(((~rich(alice)&~happy(alice)))=>((~humble(paul)&old(paul))))&
((tall(paul))<=>((~wise(lucy)&generous(lucy))))&
(![X]:((tall(X)<~>~old(X))<=>(happy(X)<~>~creative(X))))&
((?[X]:((~patient(X)<~>~generous(X))))<=>(?[X]:((~old(X)|~quiet(X)))))&
((?[X]:(~happy(X)))=>((~brave(alice)<~>rich(alice))))&
(![X]:(generous(X)<=>(~wise(X)|~generous(X))))&
(![X]:((humble(X)<~>wise(X))<=>(~rich(X)<~>~quiet(X))))&
(![X]:((~curious(X)&strong(X))<=>~curious(X)))&
((~strong(john))<=>((~quiet(john)<~>~humble(john))))&
(((~generous(mary)<~>kind(mary)))=>(~generous(fred)))&
(((~quiet(lucy)&~calm(lucy)))=>(~funny(mary)))&
(![X]:((wise(X)|curious(X))<=>(humble(X)<~>~brave(X))))&
(![X]:((kind(X)|tall(X))=>(calm(X)|generous(X))))&
(![X]:((old(X)&curious(X))=>(strong(X)<~>creative(X))))&
(?[X]:((rich(X)<~>~patient(X))))&
((~generous(alice)|~happy(alice)))&
(funny(paul))&
((funny(susan)&patient(susan)))&
(?[X]:(~funny(X)))&
(?[X]:((~wise(X)|quiet(X))))&
(?[X]:((kind(X)|patient(X))))&
((~calm(susan)<~>~strong(susan))) | ~curious(alice) | [] | null | 0 |
Everyone who is both not creative and strong is either not kind or not wise.
Everyone who is either happy or patient is not humble.
If someone is not humble or creative then someone is both not funny and not brave.
Everyone who is not funny or not creative is old or quiet.
Everyone who is both not calm and old is either calm or not patient and vice versa.
If someone is rich then someone is both humble and not old and vice versa.
Everyone who is either strong or not happy is not tall.
Everyone who is tall or not patient is either not patient or patient and vice versa.
If someone is both humble and not humble then mary is both not kind and creative and vice versa.
Everyone who is either not strong or not wise is either strong or not quiet and vice versa.
If someone is both creative and not rich then mary is not curious or not kind.
Everyone who is not humble is not creative or not funny.
Everyone who is both calm and not kind is either not happy or not patient and vice versa.
If someone is either not rich or brave then someone is both calm and wise and vice versa.
Everyone who is not happy is happy or not quiet.
Everyone who is both curious and kind is either not curious or creative and vice versa.
Paul is patient.
Alice is both patient and not brave.
Fred is either humble or brave.
Paul is both not humble and not calm.
Someone is humble.
Fred is both curious and not quiet.
Lucy is not old or quiet.
Susan is calm. | Fred is brave. | neutral | (![X]:((~creative(X)&strong(X))=>(~kind(X)<~>~wise(X))))&
(![X]:((happy(X)<~>patient(X))=>~humble(X)))&
((?[X]:((~humble(X)|creative(X))))=>(?[X]:((~funny(X)&~brave(X)))))&
(![X]:((~funny(X)|~creative(X))=>(old(X)|quiet(X))))&
(![X]:((~calm(X)&old(X))<=>(calm(X)<~>~patient(X))))&
((?[X]:(rich(X)))<=>(?[X]:((humble(X)&~old(X)))))&
(![X]:((strong(X)<~>~happy(X))=>~tall(X)))&
(![X]:((tall(X)|~patient(X))<=>(~patient(X)<~>patient(X))))&
((?[X]:((humble(X)&~humble(X))))<=>((~kind(mary)&creative(mary))))&
(![X]:((~strong(X)<~>~wise(X))<=>(strong(X)<~>~quiet(X))))&
((?[X]:((creative(X)&~rich(X))))=>((~curious(mary)|~kind(mary))))&
(![X]:(~humble(X)=>(~creative(X)|~funny(X))))&
(![X]:((calm(X)&~kind(X))<=>(~happy(X)<~>~patient(X))))&
((?[X]:((~rich(X)<~>brave(X))))<=>(?[X]:((calm(X)&wise(X)))))&
(![X]:(~happy(X)=>(happy(X)|~quiet(X))))&
(![X]:((curious(X)&kind(X))<=>(~curious(X)<~>creative(X))))&
(patient(paul))&
((patient(alice)&~brave(alice)))&
((humble(fred)<~>brave(fred)))&
((~humble(paul)&~calm(paul)))&
(?[X]:(humble(X)))&
((curious(fred)&~quiet(fred)))&
((~old(lucy)|quiet(lucy)))&
(calm(susan)) | brave(fred) | [] | null | 0 |
Everyone who is both not creative and quiet is not strong or not happy and vice versa. If fred is either rich or kind then someone is not patient or not funny and vice versa. If someone is both not rich and not happy then lucy is not tall or not humble. Everyone who is not brave is either not calm or brave. If susan is creative then paul is not tall or patient and vice versa. If someone is rich then someone is wise and vice versa. Everyone who is quiet or not creative is not calm or tall and vice versa. If fred is not kind or kind then someone is both not curious and not kind and vice versa. Everyone who is not calm or patient is not generous. If susan is old or not curious then mary is either not calm or happy and vice versa. If fred is either not humble or patient then paul is kind. Everyone who is not humble or rich is not generous. Everyone who is both not wise and brave is either not tall or happy. If lucy is quiet or tall then alice is happy or not tall and vice versa. If someone is both brave and creative then someone is either brave or not wise and vice versa. Everyone who is generous is not happy or wise and vice versa. Paul is either patient or humble. Someone is not calm or calm. Alice is quiet or not creative. Fred is humble. Alice is brave or not kind. Someone is not brave. Someone is both generous and not quiet. Someone is strong. | Mary is old. | neutral | (![X]:((~creative(X)&quiet(X))<=>(~strong(X)|~happy(X))))&
(((rich(fred)<~>kind(fred)))<=>(?[X]:((~patient(X)|~funny(X)))))&
((?[X]:((~rich(X)&~happy(X))))=>((~tall(lucy)|~humble(lucy))))&
(![X]:(~brave(X)=>(~calm(X)<~>brave(X))))&
((creative(susan))<=>((~tall(paul)|patient(paul))))&
((?[X]:(rich(X)))<=>(?[X]:(wise(X))))&
(![X]:((quiet(X)|~creative(X))<=>(~calm(X)|tall(X))))&
(((~kind(fred)|kind(fred)))<=>(?[X]:((~curious(X)&~kind(X)))))&
(![X]:((~calm(X)|patient(X))=>~generous(X)))&
(((old(susan)|~curious(susan)))<=>((~calm(mary)<~>happy(mary))))&
(((~humble(fred)<~>patient(fred)))=>(kind(paul)))&
(![X]:((~humble(X)|rich(X))=>~generous(X)))&
(![X]:((~wise(X)&brave(X))=>(~tall(X)<~>happy(X))))&
(((quiet(lucy)|tall(lucy)))<=>((happy(alice)|~tall(alice))))&
((?[X]:((brave(X)&creative(X))))<=>(?[X]:((brave(X)<~>~wise(X)))))&
(![X]:(generous(X)<=>(~happy(X)|wise(X))))&
((patient(paul)<~>humble(paul)))&
(?[X]:((~calm(X)|calm(X))))&
((quiet(alice)|~creative(alice)))&
(humble(fred))&
((brave(alice)|~kind(alice)))&
(?[X]:(~brave(X)))&
(?[X]:((generous(X)&~quiet(X))))&
(?[X]:(strong(X))) | old(mary) | [] | null | 0 |
If someone is both patient and not calm then someone is both tall and not tall. If someone is funny then alice is strong or not generous. Everyone who is not strong or kind is both calm and not old. Everyone who is not brave or not strong is old or wise. If someone is not curious or old then someone is not quiet. If someone is wise then paul is not patient or curious. Everyone who is strong or not tall is either rich or old. Everyone who is both generous and strong is both not rich and not brave. If alice is both happy and generous then alice is not quiet or not humble and vice versa. If someone is both generous and not rich then someone is curious and vice versa. If someone is both happy and wise then fred is both not funny and quiet and vice versa. Everyone who is curious is not calm. If someone is not quiet then susan is both not curious and not strong. Everyone who is both not kind and quiet is both creative and not rich. If lucy is not wise or wise then lucy is both patient and not rich and vice versa. If someone is both not brave and humble then susan is not curious or calm and vice versa. Alice is either humble or wise. Someone is not strong. Lucy is both not strong and not kind. Susan is both not humble and wise. Someone is quiet or not brave. Susan is patient or tall. Someone is humble or not strong. Someone is wise. | Paul is not rich. | neutral | ((?[X]:((patient(X)&~calm(X))))=>(?[X]:((tall(X)&~tall(X)))))&
((?[X]:(funny(X)))=>((strong(alice)|~generous(alice))))&
(![X]:((~strong(X)|kind(X))=>(calm(X)&~old(X))))&
(![X]:((~brave(X)|~strong(X))=>(old(X)|wise(X))))&
((?[X]:((~curious(X)|old(X))))=>(?[X]:(~quiet(X))))&
((?[X]:(wise(X)))=>((~patient(paul)|curious(paul))))&
(![X]:((strong(X)|~tall(X))=>(rich(X)<~>old(X))))&
(![X]:((generous(X)&strong(X))=>(~rich(X)&~brave(X))))&
(((happy(alice)&generous(alice)))<=>((~quiet(alice)|~humble(alice))))&
((?[X]:((generous(X)&~rich(X))))<=>(?[X]:(curious(X))))&
((?[X]:((happy(X)&wise(X))))<=>((~funny(fred)&quiet(fred))))&
(![X]:(curious(X)=>~calm(X)))&
((?[X]:(~quiet(X)))=>((~curious(susan)&~strong(susan))))&
(![X]:((~kind(X)&quiet(X))=>(creative(X)&~rich(X))))&
(((~wise(lucy)|wise(lucy)))<=>((patient(lucy)&~rich(lucy))))&
((?[X]:((~brave(X)&humble(X))))<=>((~curious(susan)|calm(susan))))&
((humble(alice)<~>wise(alice)))&
(?[X]:(~strong(X)))&
((~strong(lucy)&~kind(lucy)))&
((~humble(susan)&wise(susan)))&
(?[X]:((quiet(X)|~brave(X))))&
((patient(susan)|tall(susan)))&
(?[X]:((humble(X)|~strong(X))))&
(?[X]:(wise(X))) | ~rich(paul) | [] | null | 0 |
Everyone who is both quiet and kind is either not tall or brave and vice versa. If lucy is both not wise and not kind then someone is both creative and not strong. Everyone who is both not happy and not strong is not funny or not brave and vice versa. Everyone who is both humble and not patient is not kind and vice versa. If someone is wise or not humble then someone is quiet. If john is either brave or not rich then lucy is funny or happy. If john is both humble and not curious then someone is calm or not tall. If someone is patient or not quiet then someone is funny or not patient. If someone is both curious and not humble then someone is both calm and not old. Everyone who is funny or not humble is both not creative and strong. Everyone who is either not funny or patient is patient or quiet and vice versa. If someone is both not strong and not old then someone is brave or funny. Everyone who is either not strong or funny is both kind and brave. Everyone who is both quiet and not rich is both happy and tall. If someone is either not tall or not generous then someone is old and vice versa. If someone is not funny then fred is not kind or creative and vice versa. Someone is both old and not creative. Someone is both not wise and happy. Someone is either humble or not rich. Someone is either not brave or old. Fred is not humble or old. Someone is either not brave or happy. Someone is kind or brave. | Fred is not creative. | entailment | (![X]:((quiet(X)&kind(X))<=>(~tall(X)<~>brave(X))))&
(((~wise(lucy)&~kind(lucy)))=>(?[X]:((creative(X)&~strong(X)))))&
(![X]:((~happy(X)&~strong(X))<=>(~funny(X)|~brave(X))))&
(![X]:((humble(X)&~patient(X))<=>~kind(X)))&
((?[X]:((wise(X)|~humble(X))))=>(?[X]:(quiet(X))))&
(((brave(john)<~>~rich(john)))=>((funny(lucy)|happy(lucy))))&
(((humble(john)&~curious(john)))=>(?[X]:((calm(X)|~tall(X)))))&
((?[X]:((patient(X)|~quiet(X))))=>(?[X]:((funny(X)|~patient(X)))))&
((?[X]:((curious(X)&~humble(X))))=>(?[X]:((calm(X)&~old(X)))))&
(![X]:((funny(X)|~humble(X))=>(~creative(X)&strong(X))))&
(![X]:((~funny(X)<~>patient(X))<=>(patient(X)|quiet(X))))&
((?[X]:((~strong(X)&~old(X))))=>(?[X]:((brave(X)|funny(X)))))&
(![X]:((~strong(X)<~>funny(X))=>(kind(X)&brave(X))))&
(![X]:((quiet(X)&~rich(X))=>(happy(X)&tall(X))))&
((?[X]:((~tall(X)<~>~generous(X))))<=>(?[X]:(old(X))))&
((?[X]:(~funny(X)))<=>((~kind(fred)|creative(fred))))&
(?[X]:((old(X)&~creative(X))))&
(?[X]:((~wise(X)&happy(X))))&
(?[X]:((humble(X)<~>~rich(X))))&
(?[X]:((~brave(X)<~>old(X))))&
((~humble(fred)|old(fred)))&
(?[X]:((~brave(X)<~>happy(X))))&
(?[X]:((kind(X)|brave(X)))) | ~creative(fred) | [
"p2",
"p3",
"p9",
"p10",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 3586660946537670656468337
% SZS output start Proof for 3586660946537670656468337
3. ! [X0] : ((~strong(X0) & ~happy(X0)) <=> (~brave(X0) | ~funny(X0))) [input p2]
4. ! [X0] : ((~patient(X0) & humble(X0)) <=> ~kind(X0)) [input p3]
10. ! [X0] : ((~humble(X0) | funny(X0)) => (strong(X0) & ~creative(X0))) [input p9]
11. ! [X0] : ((~funny(X0) <~> patient(X0)) <=> (quiet(X0) | patient(X0))) [input p10]
13. ! [X0] : ((~strong(X0) <~> funny(X0)) => (brave(X0) & kind(X0))) [input p12]
24. creative(fred) [input hypothesis]
39. ! [X0] : ((strong(X0) & ~creative(X0)) | (humble(X0) & ~funny(X0))) [ennf transformation 10]
41. ! [X0] : ((brave(X0) & kind(X0)) | (~strong(X0) <=> funny(X0))) [ennf transformation 13]
48. ! [X0] : (((~strong(X0) & ~happy(X0)) | (brave(X0) & funny(X0))) & ((~brave(X0) | ~funny(X0)) | (strong(X0) | happy(X0)))) [nnf transformation 3]
49. ! [X0] : (((~strong(X0) & ~happy(X0)) | (brave(X0) & funny(X0))) & (~brave(X0) | ~funny(X0) | strong(X0) | happy(X0))) [flattening 48]
50. ! [X0] : (((~patient(X0) & humble(X0)) | kind(X0)) & (~kind(X0) | (patient(X0) | ~humble(X0)))) [nnf transformation 4]
51. ! [X0] : (((~patient(X0) & humble(X0)) | kind(X0)) & (~kind(X0) | patient(X0) | ~humble(X0))) [flattening 50]
59. ! [X0] : ((((~patient(X0) | funny(X0)) & (patient(X0) | ~funny(X0))) | (~quiet(X0) & ~patient(X0))) & ((quiet(X0) | patient(X0)) | ((~funny(X0) | ~patient(X0)) & (patient(X0) | funny(X0))))) [nnf transformation 11]
60. ! [X0] : ((((~patient(X0) | funny(X0)) & (patient(X0) | ~funny(X0))) | (~quiet(X0) & ~patient(X0))) & (quiet(X0) | patient(X0) | ((~funny(X0) | ~patient(X0)) & (patient(X0) | funny(X0))))) [flattening 59]
64. ! [X0] : ((brave(X0) & kind(X0)) | ((~strong(X0) | ~funny(X0)) & (funny(X0) | strong(X0)))) [nnf transformation 41]
101. ~strong(X0) | funny(X0) [cnf transformation 49]
103. ~humble(X0) | patient(X0) | ~kind(X0) [cnf transformation 51]
112. ~funny(X0) | ~creative(X0) [cnf transformation 39]
113. ~creative(X0) | humble(X0) [cnf transformation 39]
114. ~funny(X0) | strong(X0) [cnf transformation 39]
120. ~patient(X0) | funny(X0) | ~patient(X0) [cnf transformation 60]
123. kind(X0) | funny(X0) | strong(X0) [cnf transformation 64]
124. kind(X0) | ~strong(X0) | ~funny(X0) [cnf transformation 64]
148. creative(fred) [cnf transformation 24]
150. ~patient(X0) | funny(X0) [duplicate literal removal 120]
227. ~funny(X0) | kind(X0) [subsumption resolution 124,114]
228. kind(X0) | funny(X0) [subsumption resolution 123,101]
229. kind(X0) [subsumption resolution 228,227]
256. 24 <=> creative(fred) [avatar definition]
257. creative(fred) <- (24) [avatar component clause 256]
290. 31 <=> humble(fred) [avatar definition]
291. humble(fred) <- (31) [avatar component clause 290]
307. 24 [avatar split clause 148,256]
316. humble(fred) <- (24) [resolution 113,257]
319. 31 | ~24 [avatar split clause 316,256,290]
375. patient(fred) | ~kind(fred) <- (31) [resolution 103,291]
377. patient(fred) <- (31) [subsumption resolution 375,229]
378. funny(fred) <- (31) [resolution 377,150]
415. ~creative(fred) <- (31) [resolution 378,112]
416. $false <- (24, 31) [subsumption resolution 415,257]
417. ~24 | ~31 [avatar contradiction clause 416]
418. $false [avatar sat refutation 307,319,417]
% SZS output end Proof for 3586660946537670656468337
% ------------------------------
% 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 not humble or rich is generous.
Everyone who is not generous or not rich is brave.
If someone is both calm and rich then susan is either not rich or not wise and vice versa.
If paul is either generous or old then someone is wise and vice versa.
Everyone who is quiet or not calm is both not strong and not rich and vice versa.
Everyone who is either not patient or tall is not generous and vice versa.
Everyone who is kind or not old is either not rich or not happy.
Everyone who is either happy or not kind is both not kind and not humble.
Everyone who is either quiet or generous is both curious and not quiet and vice versa.
Everyone who is both quiet and creative is both patient and happy and vice versa.
Everyone who is not wise or patient is either generous or not patient.
Everyone who is both curious and strong is not kind and vice versa.
Everyone who is either not strong or kind is both curious and funny.
If john is not curious or not calm then someone is not old or not creative and vice versa.
Everyone who is wise or calm is not calm or old and vice versa.
Alice is old or not old.
Someone is both not tall and calm.
Alice is not kind.
Someone is either not curious or not brave.
Susan is either quiet or funny.
Susan is brave or rich. | Alice is tall. | contradiction | (![X]:((~humble(X)|rich(X))=>generous(X)))&
(![X]:((~generous(X)|~rich(X))=>brave(X)))&
((?[X]:((calm(X)&rich(X))))<=>((~rich(susan)<~>~wise(susan))))&
(((generous(paul)<~>old(paul)))<=>(?[X]:(wise(X))))&
(![X]:((quiet(X)|~calm(X))<=>(~strong(X)&~rich(X))))&
(![X]:((~patient(X)<~>tall(X))<=>~generous(X)))&
(![X]:((kind(X)|~old(X))=>(~rich(X)<~>~happy(X))))&
(![X]:((happy(X)<~>~kind(X))=>(~kind(X)&~humble(X))))&
(![X]:((quiet(X)<~>generous(X))<=>(curious(X)&~quiet(X))))&
(![X]:((quiet(X)&creative(X))<=>(patient(X)&happy(X))))&
(![X]:((~wise(X)|patient(X))=>(generous(X)<~>~patient(X))))&
(![X]:((curious(X)&strong(X))<=>~kind(X)))&
(![X]:((~strong(X)<~>kind(X))=>(curious(X)&funny(X))))&
(((~curious(john)|~calm(john)))<=>(?[X]:((~old(X)|~creative(X)))))&
(![X]:((wise(X)|calm(X))<=>(~calm(X)|old(X))))&
((old(alice)|~old(alice)))&
(?[X]:((~tall(X)&calm(X))))&
(~kind(alice))&
(?[X]:((~curious(X)<~>~brave(X))))&
((quiet(susan)<~>funny(susan)))&
((brave(susan)|rich(susan))) | tall(alice) | [
"p0",
"p3",
"p4",
"p5",
"p6",
"p7",
"p8",
"p10",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 2360457787022893977535288
% SZS output start Proof for 2360457787022893977535288
1. ! [X0] : ((rich(X0) | ~humble(X0)) => generous(X0)) [input p0]
4. (generous(paul) <~> old(paul)) <=> ? [X0] : wise(X0) [input p3]
5. ! [X0] : ((~calm(X0) | quiet(X0)) <=> (~rich(X0) & ~strong(X0))) [input p4]
6. ! [X0] : ((~patient(X0) <~> tall(X0)) <=> ~generous(X0)) [input p5]
7. ! [X0] : ((~old(X0) | kind(X0)) => (~rich(X0) <~> ~happy(X0))) [input p6]
8. ! [X0] : ((happy(X0) <~> ~kind(X0)) => (~humble(X0) & ~kind(X0))) [input p7]
9. ! [X0] : ((quiet(X0) <~> generous(X0)) <=> (~quiet(X0) & curious(X0))) [input p8]
11. ! [X0] : ((patient(X0) | ~wise(X0)) => (generous(X0) <~> ~patient(X0))) [input p10]
12. ! [X0] : ((strong(X0) & curious(X0)) <=> ~kind(X0)) [input p11]
14. (~calm(john) | ~curious(john)) <=> ? [X0] : (~creative(X0) | ~old(X0)) [input p13]
22. tall(alice) [input hypothesis]
23. ! [X0] : (generous(X0) | (~rich(X0) & humble(X0))) [ennf transformation 1]
25. ! [X0] : ((~rich(X0) <~> ~happy(X0)) | (old(X0) & ~kind(X0))) [ennf transformation 7]
26. ! [X0] : ((~humble(X0) & ~kind(X0)) | (happy(X0) <=> ~kind(X0))) [ennf transformation 8]
27. ! [X0] : ((generous(X0) <~> ~patient(X0)) | (~patient(X0) & wise(X0))) [ennf transformation 11]
33. (((~old(paul) | ~generous(paul)) & (old(paul) | generous(paul))) | ! [X0] : ~wise(X0)) & (? [X0] : wise(X0) | ((generous(paul) | ~old(paul)) & (old(paul) | ~generous(paul)))) [nnf transformation 4]
34. (((~old(paul) | ~generous(paul)) & (old(paul) | generous(paul))) | ! [X0] : ~wise(X0)) & (? [X1] : wise(X1) | ((generous(paul) | ~old(paul)) & (old(paul) | ~generous(paul)))) [rectify 33]
35. ? [X1] : wise(X1) => wise(sK1) [choice axiom]
36. (((~old(paul) | ~generous(paul)) & (old(paul) | generous(paul))) | ! [X0] : ~wise(X0)) & (wise(sK1) | ((generous(paul) | ~old(paul)) & (old(paul) | ~generous(paul)))) [skolemisation 34,35]
37. ! [X0] : (((~calm(X0) | quiet(X0)) | (rich(X0) | strong(X0))) & ((~rich(X0) & ~strong(X0)) | (calm(X0) & ~quiet(X0)))) [nnf transformation 5]
38. ! [X0] : ((~calm(X0) | quiet(X0) | rich(X0) | strong(X0)) & ((~rich(X0) & ~strong(X0)) | (calm(X0) & ~quiet(X0)))) [flattening 37]
39. ! [X0] : ((((~tall(X0) | patient(X0)) & (tall(X0) | ~patient(X0))) | generous(X0)) & (~generous(X0) | ((~patient(X0) | ~tall(X0)) & (tall(X0) | patient(X0))))) [nnf transformation 6]
40. ! [X0] : (((happy(X0) | rich(X0)) & (~happy(X0) | ~rich(X0))) | (old(X0) & ~kind(X0))) [nnf transformation 25]
41. ! [X0] : ((~humble(X0) & ~kind(X0)) | ((happy(X0) | kind(X0)) & (~kind(X0) | ~happy(X0)))) [nnf transformation 26]
42. ! [X0] : ((((~generous(X0) | ~quiet(X0)) & (generous(X0) | quiet(X0))) | (quiet(X0) | ~curious(X0))) & ((~quiet(X0) & curious(X0)) | ((quiet(X0) | ~generous(X0)) & (generous(X0) | ~quiet(X0))))) [nnf transformation 9]
43. ! [X0] : ((((~generous(X0) | ~quiet(X0)) & (generous(X0) | quiet(X0))) | quiet(X0) | ~curious(X0)) & ((~quiet(X0) & curious(X0)) | ((quiet(X0) | ~generous(X0)) & (generous(X0) | ~quiet(X0))))) [flattening 42]
46. ! [X0] : (((patient(X0) | ~generous(X0)) & (~patient(X0) | generous(X0))) | (~patient(X0) & wise(X0))) [nnf transformation 27]
47. ! [X0] : (((strong(X0) & curious(X0)) | kind(X0)) & (~kind(X0) | (~strong(X0) | ~curious(X0)))) [nnf transformation 12]
48. ! [X0] : (((strong(X0) & curious(X0)) | kind(X0)) & (~kind(X0) | ~strong(X0) | ~curious(X0))) [flattening 47]
50. ((~calm(john) | ~curious(john)) | ! [X0] : (creative(X0) & old(X0))) & (? [X0] : (~creative(X0) | ~old(X0)) | (calm(john) & curious(john))) [nnf transformation 14]
51. (~calm(john) | ~curious(john) | ! [X0] : (creative(X0) & old(X0))) & (? [X0] : (~creative(X0) | ~old(X0)) | (calm(john) & curious(john))) [flattening 50]
52. (~calm(john) | ~curious(john) | ! [X0] : (creative(X0) & old(X0))) & (? [X1] : (~creative(X1) | ~old(X1)) | (calm(john) & curious(john))) [rectify 51]
53. ? [X1] : (~creative(X1) | ~old(X1)) => (~creative(sK2) | ~old(sK2)) [choice axiom]
54. (~calm(john) | ~curious(john) | ! [X0] : (creative(X0) & old(X0))) & ((~creative(sK2) | ~old(sK2)) | (calm(john) & curious(john))) [skolemisation 52,53]
63. generous(X0) | humble(X0) [cnf transformation 23]
64. ~rich(X0) | generous(X0) [cnf transformation 23]
76. ~old(paul) | ~generous(paul) | ~wise(X0) [cnf transformation 36]
77. ~strong(X0) | ~quiet(X0) [cnf transformation 38]
78. ~strong(X0) | calm(X0) [cnf transformation 38]
79. ~quiet(X0) | ~rich(X0) [cnf transformation 38]
80. ~rich(X0) | calm(X0) [cnf transformation 38]
83. ~tall(X0) | ~patient(X0) | ~generous(X0) [cnf transformation 39]
85. ~tall(X0) | patient(X0) | generous(X0) [cnf transformation 39]
88. ~kind(X0) | rich(X0) | happy(X0) [cnf transformation 40]
90. ~kind(X0) | ~kind(X0) | ~happy(X0) [cnf transformation 41]
92. ~happy(X0) | ~kind(X0) | ~humble(X0) [cnf transformation 41]
95. ~generous(X0) | quiet(X0) | curious(X0) [cnf transformation 43]
96. ~quiet(X0) | generous(X0) | ~quiet(X0) [cnf transformation 43]
98. generous(X0) | quiet(X0) | quiet(X0) | ~curious(X0) [cnf transformation 43]
105. ~patient(X0) | generous(X0) | ~patient(X0) [cnf transformation 46]
106. ~generous(X0) | patient(X0) | wise(X0) [cnf transformation 46]
109. curious(X0) | kind(X0) [cnf transformation 48]
110. kind(X0) | strong(X0) [cnf transformation 48]
117. ~calm(john) | ~curious(john) | old(X0) [cnf transformation 54]
132. tall(alice) [cnf transformation 22]
135. ~patient(X0) | generous(X0) [duplicate literal removal 105]
136. ~quiet(X0) | generous(X0) [duplicate literal removal 96]
137. ~curious(X0) | quiet(X0) | generous(X0) [duplicate literal removal 98]
138. ~happy(X0) | ~kind(X0) [duplicate literal removal 90]
165. 6 <=> ! [X0] : ~wise(X0) [avatar definition]
166. ~wise(X0) <- (6) [avatar component clause 165]
168. 7 <=> generous(paul) [avatar definition]
170. ~generous(paul) <- (~7) [avatar component clause 168]
172. 8 <=> old(paul) [avatar definition]
174. ~old(paul) <- (~8) [avatar component clause 172]
175. 6 | ~7 | ~8 [avatar split clause 76,172,168,165]
188. 11 <=> curious(john) [avatar definition]
190. ~curious(john) <- (~11) [avatar component clause 188]
192. 12 <=> calm(john) [avatar definition]
194. ~calm(john) <- (~12) [avatar component clause 192]
197. 13 <=> ! [X0] : old(X0) [avatar definition]
198. old(X0) <- (13) [avatar component clause 197]
199. 13 | ~11 | ~12 [avatar split clause 117,192,188,197]
259. $false <- (~8, 13) [resolution 198,174]
262. 8 | ~13 [avatar contradiction clause 259]
311. ~patient(alice) | ~generous(alice) [resolution 83,132]
312. ~patient(alice) [subsumption resolution 311,135]
314. patient(alice) | generous(alice) [resolution 85,132]
315. generous(alice) [subsumption resolution 314,312]
318. happy(X0) | rich(X0) | strong(X0) [resolution 88,110]
391. patient(alice) | wise(alice) [resolution 106,315]
393. wise(alice) [subsumption resolution 391,312]
399. 35 <=> kind(john) [avatar definition]
400. kind(john) <- (35) [avatar component clause 399]
401. ~kind(john) <- (~35) [avatar component clause 399]
403. 36 <=> strong(john) [avatar definition]
404. strong(john) <- (36) [avatar component clause 403]
416. strong(john) <- (~35) [resolution 401,110]
417. 36 | 35 [avatar split clause 416,399,403]
440. rich(john) | happy(john) <- (35) [resolution 400,88]
442. 43 <=> happy(john) [avatar definition]
444. happy(john) <- (43) [avatar component clause 442]
446. 44 <=> rich(john) [avatar definition]
448. rich(john) <- (44) [avatar component clause 446]
449. 43 | 44 | ~35 [avatar split clause 440,399,446,442]
454. quiet(X0) | generous(X0) | kind(X0) [resolution 137,109]
458. kind(X0) | generous(X0) [subsumption resolution 454,136]
499. generous(X1) | rich(X1) | happy(X1) [resolution 458,88]
500. happy(X1) | generous(X1) [subsumption resolution 499,64]
519. ~kind(john) <- (43) [resolution 444,138]
535. ~35 | ~43 [avatar split clause 519,442,399]
545. calm(john) <- (36) [resolution 404,78]
547. $false <- (~12, 36) [subsumption resolution 545,194]
548. 12 | ~36 [avatar contradiction clause 547]
557. rich(X5) | strong(X5) | ~kind(X5) [resolution 318,138]
559. strong(X5) | rich(X5) [subsumption resolution 557,110]
576. calm(john) <- (44) [resolution 448,80]
580. 12 | ~44 [avatar split clause 576,446,192]
626. generous(X2) | ~kind(X2) | ~humble(X2) [resolution 500,92]
632. generous(X2) | ~kind(X2) [subsumption resolution 626,63]
633. generous(X2) [subsumption resolution 632,458]
637. rich(X2) | ~quiet(X2) [resolution 559,77]
641. ~quiet(X2) [subsumption resolution 637,79]
727. quiet(X1) | curious(X1) [resolution 633,95]
729. $false <- (~7) [resolution 633,170]
730. 7 [avatar contradiction clause 729]
731. curious(X1) [subsumption resolution 727,641]
735. $false <- (6) [resolution 166,393]
738. ~6 [avatar contradiction clause 735]
744. $false <- (~11) [subsumption resolution 190,731]
745. 11 [avatar contradiction clause 744]
746. $false [avatar sat refutation 175,199,262,417,449,535,548,580,730,738,745]
% SZS output end Proof for 2360457787022893977535288
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is either creative or rich then someone is not patient and vice versa. If someone is strong or tall then paul is either not curious or not old. If someone is not patient then someone is not creative or curious and vice versa. Everyone who is either not humble or kind is not funny. If someone is either creative or kind then mary is either not tall or not humble and vice versa. Everyone who is not curious or not quiet is not generous and vice versa. Everyone who is either not wise or rich is not rich or not happy and vice versa. If susan is either not calm or quiet then someone is not kind and vice versa. If paul is either strong or not strong then alice is curious or old. If fred is either tall or humble then someone is both kind and not brave. If fred is either humble or creative then someone is rich and vice versa. If lucy is brave or humble then someone is either calm or not strong and vice versa. If lucy is not tall or not rich then someone is not wise and vice versa. Everyone who is humble is either not tall or not rich and vice versa. Everyone who is not kind or curious is either rich or not kind. Everyone who is not patient or not quiet is not rich or not funny and vice versa. Someone is not generous or tall. John is either curious or wise. Lucy is not quiet. Someone is either old or happy. Mary is both brave and rich. Alice is patient or not calm. Paul is either not funny or old. Someone is not patient. | Mary is not brave. | contradiction | (((creative(lucy)<~>rich(lucy)))<=>(?[X]:(~patient(X))))&
((?[X]:((strong(X)|tall(X))))=>((~curious(paul)<~>~old(paul))))&
((?[X]:(~patient(X)))<=>(?[X]:((~creative(X)|curious(X)))))&
(![X]:((~humble(X)<~>kind(X))=>~funny(X)))&
((?[X]:((creative(X)<~>kind(X))))<=>((~tall(mary)<~>~humble(mary))))&
(![X]:((~curious(X)|~quiet(X))<=>~generous(X)))&
(![X]:((~wise(X)<~>rich(X))<=>(~rich(X)|~happy(X))))&
(((~calm(susan)<~>quiet(susan)))<=>(?[X]:(~kind(X))))&
(((strong(paul)<~>~strong(paul)))=>((curious(alice)|old(alice))))&
(((tall(fred)<~>humble(fred)))=>(?[X]:((kind(X)&~brave(X)))))&
(((humble(fred)<~>creative(fred)))<=>(?[X]:(rich(X))))&
(((brave(lucy)|humble(lucy)))<=>(?[X]:((calm(X)<~>~strong(X)))))&
(((~tall(lucy)|~rich(lucy)))<=>(?[X]:(~wise(X))))&
(![X]:(humble(X)<=>(~tall(X)<~>~rich(X))))&
(![X]:((~kind(X)|curious(X))=>(rich(X)<~>~kind(X))))&
(![X]:((~patient(X)|~quiet(X))<=>(~rich(X)|~funny(X))))&
(?[X]:((~generous(X)|tall(X))))&
((curious(john)<~>wise(john)))&
(~quiet(lucy))&
(?[X]:((old(X)<~>happy(X))))&
((brave(mary)&rich(mary)))&
((patient(alice)|~calm(alice)))&
((~funny(paul)<~>old(paul)))&
(?[X]:(~patient(X))) | ~brave(mary) | [
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 2820154881928318613556603
% SZS output start Proof for 2820154881928318613556603
21. rich(mary) & brave(mary) [input p20]
25. ~brave(mary) [input hypothesis]
157. brave(mary) [cnf transformation 21]
163. ~brave(mary) [cnf transformation 25]
412. $false [subsumption resolution 163,157]
% SZS output end Proof for 2820154881928318613556603
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not creative or kind then someone is not rich. If someone is tall then paul is happy. Everyone who is both tall and not old is either patient or calm and vice versa. If someone is both creative and rich then someone is either not funny or rich and vice versa. Everyone who is both not strong and happy is both not calm and not brave and vice versa. If someone is both kind and not generous then fred is either patient or curious and vice versa. Everyone who is either brave or patient is both patient and strong and vice versa. If someone is humble then someone is not creative. Everyone who is both brave and tall is either not calm or curious and vice versa. Everyone who is either not patient or wise is not calm. Everyone who is either not brave or calm is both not generous and generous. If lucy is both not brave and not tall then john is rich. If susan is calm then someone is both creative and not old and vice versa. Everyone who is both not brave and not curious is both quiet and not tall. If someone is either wise or curious then paul is both not generous and not calm and vice versa. If john is both strong and not curious then paul is both not funny and creative and vice versa. Someone is both not calm and brave. Someone is either not tall or humble. Someone is patient. Someone is either not rich or not strong. Someone is either not happy or not tall. | Paul is not wise. | entailment | ((?[X]:((~creative(X)<~>kind(X))))=>(?[X]:(~rich(X))))&
((?[X]:(tall(X)))=>(happy(paul)))&
(![X]:((tall(X)&~old(X))<=>(patient(X)<~>calm(X))))&
((?[X]:((creative(X)&rich(X))))<=>(?[X]:((~funny(X)<~>rich(X)))))&
(![X]:((~strong(X)&happy(X))<=>(~calm(X)&~brave(X))))&
((?[X]:((kind(X)&~generous(X))))<=>((patient(fred)<~>curious(fred))))&
(![X]:((brave(X)<~>patient(X))<=>(patient(X)&strong(X))))&
((?[X]:(humble(X)))=>(?[X]:(~creative(X))))&
(![X]:((brave(X)&tall(X))<=>(~calm(X)<~>curious(X))))&
(![X]:((~patient(X)<~>wise(X))=>~calm(X)))&
(![X]:((~brave(X)<~>calm(X))=>(~generous(X)&generous(X))))&
(((~brave(lucy)&~tall(lucy)))=>(rich(john)))&
((calm(susan))<=>(?[X]:((creative(X)&~old(X)))))&
(![X]:((~brave(X)&~curious(X))=>(quiet(X)&~tall(X))))&
((?[X]:((wise(X)<~>curious(X))))<=>((~generous(paul)&~calm(paul))))&
(((strong(john)&~curious(john)))<=>((~funny(paul)&creative(paul))))&
(?[X]:((~calm(X)&brave(X))))&
(?[X]:((~tall(X)<~>humble(X))))&
(?[X]:(patient(X)))&
(?[X]:((~rich(X)<~>~strong(X))))&
(?[X]:((~happy(X)<~>~tall(X)))) | ~wise(paul) | [
"p1",
"p2",
"p4",
"p6",
"p8",
"p10",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 866109711270866814044116
% SZS output start Proof for 866109711270866814044116
2. ? [X0] : tall(X0) => happy(paul) [input p1]
3. ! [X0] : ((~old(X0) & tall(X0)) <=> (patient(X0) <~> calm(X0))) [input p2]
5. ! [X0] : ((happy(X0) & ~strong(X0)) <=> (~brave(X0) & ~calm(X0))) [input p4]
7. ! [X0] : ((brave(X0) <~> patient(X0)) <=> (strong(X0) & patient(X0))) [input p6]
9. ! [X0] : ((tall(X0) & brave(X0)) <=> (~calm(X0) <~> curious(X0))) [input p8]
11. ! [X0] : ((~brave(X0) <~> calm(X0)) => (generous(X0) & ~generous(X0))) [input p10]
15. ? [X0] : (wise(X0) <~> curious(X0)) <=> (~calm(paul) & ~generous(paul)) [input p14]
17. ? [X0] : (brave(X0) & ~calm(X0)) [input p16]
22. wise(paul) [input hypothesis]
28. happy(paul) | ! [X0] : ~tall(X0) [ennf transformation 2]
31. ! [X0] : ((generous(X0) & ~generous(X0)) | (~brave(X0) <=> calm(X0))) [ennf transformation 11]
40. ! [X0] : (((~old(X0) & tall(X0)) | ((patient(X0) | ~calm(X0)) & (calm(X0) | ~patient(X0)))) & (((~calm(X0) | ~patient(X0)) & (calm(X0) | patient(X0))) | (old(X0) | ~tall(X0)))) [nnf transformation 3]
41. ! [X0] : (((~old(X0) & tall(X0)) | ((patient(X0) | ~calm(X0)) & (calm(X0) | ~patient(X0)))) & (((~calm(X0) | ~patient(X0)) & (calm(X0) | patient(X0))) | old(X0) | ~tall(X0))) [flattening 40]
47. ! [X0] : (((happy(X0) & ~strong(X0)) | (brave(X0) | calm(X0))) & ((~brave(X0) & ~calm(X0)) | (~happy(X0) | strong(X0)))) [nnf transformation 5]
48. ! [X0] : (((happy(X0) & ~strong(X0)) | brave(X0) | calm(X0)) & ((~brave(X0) & ~calm(X0)) | ~happy(X0) | strong(X0))) [flattening 47]
53. ! [X0] : ((((~patient(X0) | ~brave(X0)) & (patient(X0) | brave(X0))) | (~strong(X0) | ~patient(X0))) & ((strong(X0) & patient(X0)) | ((brave(X0) | ~patient(X0)) & (patient(X0) | ~brave(X0))))) [nnf transformation 7]
54. ! [X0] : ((((~patient(X0) | ~brave(X0)) & (patient(X0) | brave(X0))) | ~strong(X0) | ~patient(X0)) & ((strong(X0) & patient(X0)) | ((brave(X0) | ~patient(X0)) & (patient(X0) | ~brave(X0))))) [flattening 53]
58. ! [X0] : (((tall(X0) & brave(X0)) | ((~calm(X0) | ~curious(X0)) & (curious(X0) | calm(X0)))) & (((~curious(X0) | calm(X0)) & (curious(X0) | ~calm(X0))) | (~tall(X0) | ~brave(X0)))) [nnf transformation 9]
59. ! [X0] : (((tall(X0) & brave(X0)) | ((~calm(X0) | ~curious(X0)) & (curious(X0) | calm(X0)))) & (((~curious(X0) | calm(X0)) & (curious(X0) | ~calm(X0))) | ~tall(X0) | ~brave(X0))) [flattening 58]
61. ! [X0] : ((generous(X0) & ~generous(X0)) | ((~brave(X0) | ~calm(X0)) & (calm(X0) | brave(X0)))) [nnf transformation 31]
66. (? [X0] : ((~curious(X0) | ~wise(X0)) & (curious(X0) | wise(X0))) | (calm(paul) | generous(paul))) & ((~calm(paul) & ~generous(paul)) | ! [X0] : ((wise(X0) | ~curious(X0)) & (curious(X0) | ~wise(X0)))) [nnf transformation 15]
67. (? [X0] : ((~curious(X0) | ~wise(X0)) & (curious(X0) | wise(X0))) | calm(paul) | generous(paul)) & ((~calm(paul) & ~generous(paul)) | ! [X0] : ((wise(X0) | ~curious(X0)) & (curious(X0) | ~wise(X0)))) [flattening 66]
68. (? [X0] : ((~curious(X0) | ~wise(X0)) & (curious(X0) | wise(X0))) | calm(paul) | generous(paul)) & ((~calm(paul) & ~generous(paul)) | ! [X1] : ((wise(X1) | ~curious(X1)) & (curious(X1) | ~wise(X1)))) [rectify 67]
69. ? [X0] : ((~curious(X0) | ~wise(X0)) & (curious(X0) | wise(X0))) => ((~curious(sK6) | ~wise(sK6)) & (curious(sK6) | wise(sK6))) [choice axiom]
70. (((~curious(sK6) | ~wise(sK6)) & (curious(sK6) | wise(sK6))) | calm(paul) | generous(paul)) & ((~calm(paul) & ~generous(paul)) | ! [X1] : ((wise(X1) | ~curious(X1)) & (curious(X1) | ~wise(X1)))) [skolemisation 68,69]
73. ? [X0] : (brave(X0) & ~calm(X0)) => (brave(sK7) & ~calm(sK7)) [choice axiom]
74. brave(sK7) & ~calm(sK7) [skolemisation 17,73]
88. happy(paul) | ~tall(X0) [cnf transformation 28]
91. ~patient(X0) | calm(X0) | tall(X0) [cnf transformation 41]
101. ~calm(X0) | ~happy(X0) | strong(X0) [cnf transformation 48]
102. ~brave(X0) | ~happy(X0) | strong(X0) [cnf transformation 48]
111. patient(X0) | patient(X0) | ~brave(X0) [cnf transformation 54]
116. ~patient(X0) | ~brave(X0) | ~strong(X0) | ~patient(X0) [cnf transformation 54]
121. ~curious(X0) | ~calm(X0) | brave(X0) [cnf transformation 59]
126. ~generous(X0) | calm(X0) | brave(X0) [cnf transformation 61]
127. ~generous(X0) | ~brave(X0) | ~calm(X0) [cnf transformation 61]
128. generous(X0) | calm(X0) | brave(X0) [cnf transformation 61]
129. ~brave(X0) | generous(X0) | ~calm(X0) [cnf transformation 61]
137. ~calm(paul) | curious(X1) | ~wise(X1) [cnf transformation 70]
145. ~calm(sK7) [cnf transformation 74]
146. brave(sK7) [cnf transformation 74]
154. wise(paul) [cnf transformation 22]
155. ~brave(X0) | patient(X0) [duplicate literal removal 111]
156. ~brave(X0) | ~patient(X0) | ~strong(X0) [duplicate literal removal 116]
170. 4 <=> ! [X0] : ~tall(X0) [avatar definition]
171. ~tall(X0) <- (4) [avatar component clause 170]
173. 5 <=> happy(paul) [avatar definition]
175. happy(paul) <- (5) [avatar component clause 173]
176. 4 | 5 [avatar split clause 88,173,170]
241. ~brave(X0) | ~calm(X0) [subsumption resolution 127,129]
242. brave(X0) | calm(X0) [subsumption resolution 126,128]
279. 28 <=> calm(paul) [avatar definition]
281. calm(paul) <- (28) [avatar component clause 279]
297. 32 <=> ! [X1] : (curious(X1) | ~wise(X1)) [avatar definition]
298. ~wise(X1) | curious(X1) <- (32) [avatar component clause 297]
299. 32 | ~28 [avatar split clause 137,279,297]
352. patient(sK7) [resolution 155,146]
357. calm(X1) | patient(X1) [resolution 242,155]
360. calm(sK7) | tall(sK7) [resolution 91,352]
363. tall(sK7) [subsumption resolution 360,145]
364. $false <- (4) [subsumption resolution 363,171]
365. ~4 [avatar contradiction clause 364]
398. ~happy(X0) | strong(X0) | calm(X0) [resolution 102,242]
417. ~happy(X0) | strong(X0) [subsumption resolution 398,101]
443. 51 <=> strong(paul) [avatar definition]
445. strong(paul) <- (51) [avatar component clause 443]
447. 52 <=> brave(paul) [avatar definition]
449. brave(paul) <- (52) [avatar component clause 447]
542. ~patient(X1) | ~strong(X1) | calm(X1) [resolution 156,242]
547. ~strong(X1) | calm(X1) [subsumption resolution 542,357]
630. 64 <=> curious(paul) [avatar definition]
632. curious(paul) <- (64) [avatar component clause 630]
635. strong(paul) <- (5) [resolution 417,175]
639. calm(paul) <- (51) [resolution 445,547]
643. 28 | ~51 [avatar split clause 639,443,279]
662. ~calm(paul) <- (52) [resolution 449,241]
674. $false <- (28, 52) [subsumption resolution 662,281]
675. ~28 | ~52 [avatar contradiction clause 674]
676. curious(paul) <- (32) [resolution 298,154]
678. 64 | ~32 [avatar split clause 676,297,630]
755. ~calm(paul) | brave(paul) <- (64) [resolution 632,121]
759. brave(paul) <- (64) [subsumption resolution 755,242]
760. 52 | ~64 [avatar split clause 759,630,447]
764. 51 | ~5 [avatar split clause 635,173,443]
765. $false [avatar sat refutation 176,299,365,643,675,678,760,764]
% SZS output end Proof for 866109711270866814044116
% ------------------------------
% 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: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not creative and curious is not humble. Everyone who is either not creative or generous is either not patient or old. Everyone who is either not generous or quiet is not patient and vice versa. Everyone who is both not tall and not happy is either quiet or humble and vice versa. Everyone who is curious is either old or not patient and vice versa. Everyone who is funny is not funny or not creative and vice versa. If alice is either not curious or humble then lucy is either creative or not wise. If someone is either not brave or not curious then mary is curious or calm and vice versa. Everyone who is both happy and not happy is calm or quiet and vice versa. If someone is rich or patient then someone is kind. Everyone who is tall is creative or rich. If someone is not creative or tall then someone is funny or happy and vice versa. Everyone who is either not old or not brave is both not calm and not tall. Everyone who is either calm or creative is generous or rich and vice versa. Fred is either not patient or not strong. Someone is both funny and not generous. Someone is either humble or not patient. | Fred is strong. | entailment | (![X]:((~creative(X)&curious(X))=>~humble(X)))&
(![X]:((~creative(X)<~>generous(X))=>(~patient(X)<~>old(X))))&
(![X]:((~generous(X)<~>quiet(X))<=>~patient(X)))&
(![X]:((~tall(X)&~happy(X))<=>(quiet(X)<~>humble(X))))&
(![X]:(curious(X)<=>(old(X)<~>~patient(X))))&
(![X]:(funny(X)<=>(~funny(X)|~creative(X))))&
(((~curious(alice)<~>humble(alice)))=>((creative(lucy)<~>~wise(lucy))))&
((?[X]:((~brave(X)<~>~curious(X))))<=>((curious(mary)|calm(mary))))&
(![X]:((happy(X)&~happy(X))<=>(calm(X)|quiet(X))))&
((?[X]:((rich(X)|patient(X))))=>(?[X]:(kind(X))))&
(![X]:(tall(X)=>(creative(X)|rich(X))))&
((?[X]:((~creative(X)|tall(X))))<=>(?[X]:((funny(X)|happy(X)))))&
(![X]:((~old(X)<~>~brave(X))=>(~calm(X)&~tall(X))))&
(![X]:((calm(X)<~>creative(X))<=>(generous(X)|rich(X))))&
((~patient(fred)<~>~strong(fred)))&
(?[X]:((funny(X)&~generous(X))))&
(?[X]:((humble(X)<~>~patient(X)))) | strong(fred) | [
"p2",
"p5",
"p8",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 247127391256251191573142
% SZS output start Proof for 247127391256251191573142
3. ! [X0] : ((~generous(X0) <~> quiet(X0)) <=> ~patient(X0)) [input p2]
6. ! [X0] : (funny(X0) <=> (~creative(X0) | ~funny(X0))) [input p5]
9. ! [X0] : ((~happy(X0) & happy(X0)) <=> (quiet(X0) | calm(X0))) [input p8]
14. ! [X0] : ((calm(X0) <~> creative(X0)) <=> (rich(X0) | generous(X0))) [input p13]
15. ~patient(fred) <~> ~strong(fred) [input p14]
18. ~strong(fred) [input hypothesis]
30. ! [X0] : ((((~quiet(X0) | generous(X0)) & (quiet(X0) | ~generous(X0))) | patient(X0)) & (~patient(X0) | ((~generous(X0) | ~quiet(X0)) & (quiet(X0) | generous(X0))))) [nnf transformation 3]
34. ! [X0] : ((funny(X0) | (creative(X0) & funny(X0))) & ((~creative(X0) | ~funny(X0)) | ~funny(X0))) [nnf transformation 6]
35. ! [X0] : ((funny(X0) | (creative(X0) & funny(X0))) & (~creative(X0) | ~funny(X0) | ~funny(X0))) [flattening 34]
42. ! [X0] : (((~happy(X0) & happy(X0)) | (~quiet(X0) & ~calm(X0))) & ((quiet(X0) | calm(X0)) | (happy(X0) | ~happy(X0)))) [nnf transformation 9]
43. ! [X0] : (((~happy(X0) & happy(X0)) | (~quiet(X0) & ~calm(X0))) & (quiet(X0) | calm(X0) | happy(X0) | ~happy(X0))) [flattening 42]
50. ! [X0] : ((((~creative(X0) | ~calm(X0)) & (creative(X0) | calm(X0))) | (~rich(X0) & ~generous(X0))) & ((rich(X0) | generous(X0)) | ((calm(X0) | ~creative(X0)) & (creative(X0) | ~calm(X0))))) [nnf transformation 14]
51. ! [X0] : ((((~creative(X0) | ~calm(X0)) & (creative(X0) | calm(X0))) | (~rich(X0) & ~generous(X0))) & (rich(X0) | generous(X0) | ((calm(X0) | ~creative(X0)) & (creative(X0) | ~calm(X0))))) [flattening 50]
52. (strong(fred) | patient(fred)) & (~strong(fred) | ~patient(fred)) [nnf transformation 15]
63. ~patient(X0) | quiet(X0) | generous(X0) [cnf transformation 30]
77. ~creative(X0) | ~funny(X0) | ~funny(X0) [cnf transformation 35]
78. funny(X0) | funny(X0) [cnf transformation 35]
91. happy(X0) | ~calm(X0) [cnf transformation 43]
92. happy(X0) | ~quiet(X0) [cnf transformation 43]
93. ~calm(X0) | ~happy(X0) [cnf transformation 43]
94. ~happy(X0) | ~quiet(X0) [cnf transformation 43]
106. creative(X0) | calm(X0) | ~generous(X0) [cnf transformation 51]
111. strong(fred) | patient(fred) [cnf transformation 52]
116. ~strong(fred) [cnf transformation 18]
117. ~creative(X0) | ~funny(X0) [duplicate literal removal 77]
118. funny(X0) [duplicate literal removal 78]
119. ~creative(X0) [subsumption resolution 117,118]
164. ~quiet(X0) [subsumption resolution 92,94]
165. ~calm(X0) [subsumption resolution 91,93]
169. calm(X0) | ~generous(X0) [subsumption resolution 106,119]
170. ~generous(X0) [subsumption resolution 169,165]
172. 10 <=> patient(fred) [avatar definition]
174. patient(fred) <- (10) [avatar component clause 172]
176. 11 <=> strong(fred) [avatar definition]
179. 10 | 11 [avatar split clause 111,176,172]
191. ~11 [avatar split clause 116,176]
194. quiet(fred) | generous(fred) <- (10) [resolution 63,174]
195. generous(fred) <- (10) [subsumption resolution 194,164]
196. $false <- (10) [subsumption resolution 195,170]
197. ~10 [avatar contradiction clause 196]
198. $false [avatar sat refutation 179,191,197]
% SZS output end Proof for 247127391256251191573142
% ------------------------------
% 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 either not rich or brave and vice versa. If john is not rich or not calm then someone is happy or curious and vice versa. Everyone who is not calm is not tall. Everyone who is either creative or not patient is strong. If someone is either quiet or tall then fred is not brave or not happy and vice versa. Everyone who is not generous is not happy or strong. Everyone who is both humble and not patient is not tall and vice versa. Everyone who is not old is not rich and vice versa. If someone is both strong and not calm then someone is strong and vice versa. If susan is both not kind and not calm then someone is kind or funny and vice versa. Everyone who is either not quiet or quiet is strong. Everyone who is generous is old or not rich and vice versa. If lucy is either quiet or kind then fred is not quiet or not brave and vice versa. Everyone who is old is both humble and not happy and vice versa. Everyone who is not calm or humble is both strong and not happy and vice versa. If someone is either not old or not calm then paul is not strong or brave. Someone is either strong or not funny. Someone is both not calm and humble. Someone is not funny. Someone is both not humble and not kind. Paul is either not strong or rich. Someone is wise. Someone is both calm and creative. | Lucy is not strong. | contradiction | (![X]:(~funny(X)<=>(~rich(X)<~>brave(X))))&
(((~rich(john)|~calm(john)))<=>(?[X]:((happy(X)|curious(X)))))&
(![X]:(~calm(X)=>~tall(X)))&
(![X]:((creative(X)<~>~patient(X))=>strong(X)))&
((?[X]:((quiet(X)<~>tall(X))))<=>((~brave(fred)|~happy(fred))))&
(![X]:(~generous(X)=>(~happy(X)|strong(X))))&
(![X]:((humble(X)&~patient(X))<=>~tall(X)))&
(![X]:(~old(X)<=>~rich(X)))&
((?[X]:((strong(X)&~calm(X))))<=>(?[X]:(strong(X))))&
(((~kind(susan)&~calm(susan)))<=>(?[X]:((kind(X)|funny(X)))))&
(![X]:((~quiet(X)<~>quiet(X))=>strong(X)))&
(![X]:(generous(X)<=>(old(X)|~rich(X))))&
(((quiet(lucy)<~>kind(lucy)))<=>((~quiet(fred)|~brave(fred))))&
(![X]:(old(X)<=>(humble(X)&~happy(X))))&
(![X]:((~calm(X)|humble(X))<=>(strong(X)&~happy(X))))&
((?[X]:((~old(X)<~>~calm(X))))=>((~strong(paul)|brave(paul))))&
(?[X]:((strong(X)<~>~funny(X))))&
(?[X]:((~calm(X)&humble(X))))&
(?[X]:(~funny(X)))&
(?[X]:((~humble(X)&~kind(X))))&
((~strong(paul)<~>rich(paul)))&
(?[X]:(wise(X)))&
(?[X]:((calm(X)&creative(X)))) | ~strong(lucy) | [
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 8223437123519645963638074
% SZS output start Proof for 8223437123519645963638074
11. ! [X0] : ((~quiet(X0) <~> quiet(X0)) => strong(X0)) [input p10]
24. ~strong(lucy) [input hypothesis]
32. ! [X0] : (strong(X0) | (~quiet(X0) <=> quiet(X0))) [ennf transformation 11]
62. ! [X0] : (strong(X0) | ((~quiet(X0) | ~quiet(X0)) & (quiet(X0) | quiet(X0)))) [nnf transformation 32]
113. strong(X0) | quiet(X0) | quiet(X0) [cnf transformation 62]
114. strong(X0) | ~quiet(X0) | ~quiet(X0) [cnf transformation 62]
143. ~strong(lucy) [cnf transformation 24]
144. strong(X0) | quiet(X0) [duplicate literal removal 113]
145. strong(X0) | ~quiet(X0) [duplicate literal removal 114]
248. strong(X0) [subsumption resolution 144,145]
284. $false [subsumption resolution 143,248]
% SZS output end Proof for 8223437123519645963638074
% ------------------------------
% 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 quiet or not humble then someone is tall or not rich and vice versa.
If someone is not wise then someone is not humble.
Everyone who is not kind or not humble is not old and vice versa.
If someone is both not wise and brave then lucy is not brave or generous.
Everyone who is not kind is not wise and vice versa.
Everyone who is humble is not old or tall.
If john is brave or not generous then susan is old or funny and vice versa.
Everyone who is either not patient or rich is not happy or quiet.
Everyone who is either kind or not kind is both curious and quiet.
If john is either generous or not tall then someone is not strong.
If someone is kind or brave then alice is old or quiet and vice versa.
Everyone who is either curious or not humble is wise and vice versa.
Everyone who is either not tall or rich is both not old and not generous and vice versa.
Everyone who is both rich and wise is both tall and not generous and vice versa.
Everyone who is either not generous or not happy is tall.
Everyone who is either not calm or old is quiet or funny.
Fred is not curious or humble.
Paul is not patient or patient.
Someone is creative.
Alice is not calm or strong.
Someone is quiet or patient.
Lucy is calm.
Someone is either not funny or tall. | Fred is generous. | entailment | ((?[X]:((quiet(X)|~humble(X))))<=>(?[X]:((tall(X)|~rich(X)))))&
((?[X]:(~wise(X)))=>(?[X]:(~humble(X))))&
(![X]:((~kind(X)|~humble(X))<=>~old(X)))&
((?[X]:((~wise(X)&brave(X))))=>((~brave(lucy)|generous(lucy))))&
(![X]:(~kind(X)<=>~wise(X)))&
(![X]:(humble(X)=>(~old(X)|tall(X))))&
(((brave(john)|~generous(john)))<=>((old(susan)|funny(susan))))&
(![X]:((~patient(X)<~>rich(X))=>(~happy(X)|quiet(X))))&
(![X]:((kind(X)<~>~kind(X))=>(curious(X)&quiet(X))))&
(((generous(john)<~>~tall(john)))=>(?[X]:(~strong(X))))&
((?[X]:((kind(X)|brave(X))))<=>((old(alice)|quiet(alice))))&
(![X]:((curious(X)<~>~humble(X))<=>wise(X)))&
(![X]:((~tall(X)<~>rich(X))<=>(~old(X)&~generous(X))))&
(![X]:((rich(X)&wise(X))<=>(tall(X)&~generous(X))))&
(![X]:((~generous(X)<~>~happy(X))=>tall(X)))&
(![X]:((~calm(X)<~>old(X))=>(quiet(X)|funny(X))))&
((~curious(fred)|humble(fred)))&
((~patient(paul)|patient(paul)))&
(?[X]:(creative(X)))&
((~calm(alice)|strong(alice)))&
(?[X]:((quiet(X)|patient(X))))&
(calm(lucy))&
(?[X]:((~funny(X)<~>tall(X)))) | generous(fred) | [
"p2",
"p4",
"p5",
"p8",
"p11",
"p12",
"p13",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 2609505143635117507833256
% SZS output start Proof for 2609505143635117507833256
3. ! [X0] : ((~humble(X0) | ~kind(X0)) <=> ~old(X0)) [input p2]
5. ! [X0] : (~kind(X0) <=> ~wise(X0)) [input p4]
6. ! [X0] : (humble(X0) => (tall(X0) | ~old(X0))) [input p5]
9. ! [X0] : ((kind(X0) <~> ~kind(X0)) => (quiet(X0) & curious(X0))) [input p8]
12. ! [X0] : ((curious(X0) <~> ~humble(X0)) <=> wise(X0)) [input p11]
13. ! [X0] : ((~tall(X0) <~> rich(X0)) <=> (~generous(X0) & ~old(X0))) [input p12]
14. ! [X0] : ((wise(X0) & rich(X0)) <=> (~generous(X0) & tall(X0))) [input p13]
17. humble(fred) | ~curious(fred) [input p16]
24. ~generous(fred) [input hypothesis]
31. ! [X0] : ((tall(X0) | ~old(X0)) | ~humble(X0)) [ennf transformation 6]
32. ! [X0] : (tall(X0) | ~old(X0) | ~humble(X0)) [flattening 31]
35. ! [X0] : ((quiet(X0) & curious(X0)) | (kind(X0) <=> ~kind(X0))) [ennf transformation 9]
48. ! [X0] : (((~humble(X0) | ~kind(X0)) | old(X0)) & (~old(X0) | (humble(X0) & kind(X0)))) [nnf transformation 3]
49. ! [X0] : ((~humble(X0) | ~kind(X0) | old(X0)) & (~old(X0) | (humble(X0) & kind(X0)))) [flattening 48]
50. ! [X0] : ((~kind(X0) | wise(X0)) & (~wise(X0) | kind(X0))) [nnf transformation 5]
54. ! [X0] : ((quiet(X0) & curious(X0)) | ((kind(X0) | kind(X0)) & (~kind(X0) | ~kind(X0)))) [nnf transformation 35]
63. ! [X0] : ((((humble(X0) | ~curious(X0)) & (~humble(X0) | curious(X0))) | ~wise(X0)) & (wise(X0) | ((curious(X0) | humble(X0)) & (~humble(X0) | ~curious(X0))))) [nnf transformation 12]
64. ! [X0] : ((((~rich(X0) | tall(X0)) & (rich(X0) | ~tall(X0))) | (generous(X0) | old(X0))) & ((~generous(X0) & ~old(X0)) | ((~tall(X0) | ~rich(X0)) & (rich(X0) | tall(X0))))) [nnf transformation 13]
65. ! [X0] : ((((~rich(X0) | tall(X0)) & (rich(X0) | ~tall(X0))) | generous(X0) | old(X0)) & ((~generous(X0) & ~old(X0)) | ((~tall(X0) | ~rich(X0)) & (rich(X0) | tall(X0))))) [flattening 64]
66. ! [X0] : (((wise(X0) & rich(X0)) | (generous(X0) | ~tall(X0))) & ((~generous(X0) & tall(X0)) | (~wise(X0) | ~rich(X0)))) [nnf transformation 14]
67. ! [X0] : (((wise(X0) & rich(X0)) | generous(X0) | ~tall(X0)) & ((~generous(X0) & tall(X0)) | ~wise(X0) | ~rich(X0))) [flattening 66]
81. ~old(X0) | humble(X0) [cnf transformation 49]
82. ~kind(X0) | ~humble(X0) | old(X0) [cnf transformation 49]
84. ~wise(X0) | kind(X0) [cnf transformation 50]
86. tall(X0) | ~old(X0) | ~humble(X0) [cnf transformation 32]
93. curious(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 54]
94. curious(X0) | kind(X0) | kind(X0) [cnf transformation 54]
103. wise(X0) | ~humble(X0) | ~curious(X0) [cnf transformation 63]
108. ~old(X0) | ~tall(X0) | ~rich(X0) [cnf transformation 65]
115. ~tall(X0) | generous(X0) | rich(X0) [cnf transformation 67]
121. humble(fred) | ~curious(fred) [cnf transformation 17]
128. ~generous(fred) [cnf transformation 24]
129. curious(X0) | ~kind(X0) [duplicate literal removal 93]
130. curious(X0) | kind(X0) [duplicate literal removal 94]
185. ~old(X0) | tall(X0) [subsumption resolution 86,81]
207. curious(X0) [subsumption resolution 129,130]
234. ~humble(X0) | wise(X0) [subsumption resolution 103,207]
236. ~old(X0) | ~rich(X0) [subsumption resolution 108,185]
237. humble(fred) [subsumption resolution 121,207]
261. wise(fred) [resolution 234,237]
263. kind(fred) [resolution 261,84]
272. ~humble(fred) | old(fred) [resolution 263,82]
274. old(fred) [subsumption resolution 272,237]
278. 27 <=> rich(fred) [avatar definition]
282. 28 <=> tall(fred) [avatar definition]
284. tall(fred) <- (28) [avatar component clause 282]
288. ~rich(fred) [resolution 274,236]
289. tall(fred) [resolution 274,185]
292. 28 [avatar split clause 289,282]
295. generous(fred) | rich(fred) <- (28) [resolution 284,115]
296. rich(fred) <- (28) [subsumption resolution 295,128]
299. 27 | ~28 [avatar split clause 296,282,278]
300. ~27 [avatar split clause 288,278]
301. $false [avatar sat refutation 292,299,300]
% SZS output end Proof for 2609505143635117507833256
% ------------------------------
% 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 happy is old or patient and vice versa.
Everyone who is old or not quiet is generous and vice versa.
Everyone who is either not strong or creative is not quiet or calm.
If someone is either not strong or not happy then alice is both not tall and strong.
If someone is quiet or not kind then someone is either not happy or rich and vice versa.
Everyone who is not generous or patient is kind or funny.
If someone is both happy and not funny then fred is either not creative or curious and vice versa.
Everyone who is either not happy or not kind is patient or rich and vice versa.
If alice is quiet then alice is either not old or not rich.
Everyone who is either not wise or not funny is not kind or humble and vice versa.
Everyone who is both calm and not patient is brave.
Everyone who is both wise and curious is either not wise or patient.
Everyone who is both not happy and quiet is either not brave or not generous and vice versa.
If lucy is not wise then someone is not creative or not generous and vice versa.
Everyone who is patient is not rich and vice versa.
Everyone who is either not strong or tall is strong or not kind.
Lucy is generous or quiet.
Paul is either patient or not strong.
Someone is generous or patient.
Someone is both not brave and humble.
Fred is not quiet or brave.
Mary is kind or rich.
Susan is both wise and not brave.
Someone is both not rich and not old. | Susan is generous. | entailment | (![X]:(~happy(X)<=>(old(X)|patient(X))))&
(![X]:((old(X)|~quiet(X))<=>generous(X)))&
(![X]:((~strong(X)<~>creative(X))=>(~quiet(X)|calm(X))))&
((?[X]:((~strong(X)<~>~happy(X))))=>((~tall(alice)&strong(alice))))&
((?[X]:((quiet(X)|~kind(X))))<=>(?[X]:((~happy(X)<~>rich(X)))))&
(![X]:((~generous(X)|patient(X))=>(kind(X)|funny(X))))&
((?[X]:((happy(X)&~funny(X))))<=>((~creative(fred)<~>curious(fred))))&
(![X]:((~happy(X)<~>~kind(X))<=>(patient(X)|rich(X))))&
((quiet(alice))=>((~old(alice)<~>~rich(alice))))&
(![X]:((~wise(X)<~>~funny(X))<=>(~kind(X)|humble(X))))&
(![X]:((calm(X)&~patient(X))=>brave(X)))&
(![X]:((wise(X)&curious(X))=>(~wise(X)<~>patient(X))))&
(![X]:((~happy(X)&quiet(X))<=>(~brave(X)<~>~generous(X))))&
((~wise(lucy))<=>(?[X]:((~creative(X)|~generous(X)))))&
(![X]:(patient(X)<=>~rich(X)))&
(![X]:((~strong(X)<~>tall(X))=>(strong(X)|~kind(X))))&
((generous(lucy)|quiet(lucy)))&
((patient(paul)<~>~strong(paul)))&
(?[X]:((generous(X)|patient(X))))&
(?[X]:((~brave(X)&humble(X))))&
((~quiet(fred)|brave(fred)))&
((kind(mary)|rich(mary)))&
((wise(susan)&~brave(susan)))&
(?[X]:((~rich(X)&~old(X)))) | generous(susan) | [
"p0",
"p1",
"p5",
"p7",
"p9",
"p12",
"p14",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 7754564221929333977519468
% SZS output start Proof for 7754564221929333977519468
1. ! [X0] : (~happy(X0) <=> (patient(X0) | old(X0))) [input p0]
2. ! [X0] : ((~quiet(X0) | old(X0)) <=> generous(X0)) [input p1]
6. ! [X0] : ((patient(X0) | ~generous(X0)) => (funny(X0) | kind(X0))) [input p5]
8. ! [X0] : ((~happy(X0) <~> ~kind(X0)) <=> (rich(X0) | patient(X0))) [input p7]
10. ! [X0] : ((~wise(X0) <~> ~funny(X0)) <=> (humble(X0) | ~kind(X0))) [input p9]
13. ! [X0] : ((quiet(X0) & ~happy(X0)) <=> (~brave(X0) <~> ~generous(X0))) [input p12]
15. ! [X0] : (patient(X0) <=> ~rich(X0)) [input p14]
23. ~brave(susan) & wise(susan) [input p22]
25. ~generous(susan) [input hypothesis]
30. ! [X0] : ((funny(X0) | kind(X0)) | (~patient(X0) & generous(X0))) [ennf transformation 6]
31. ! [X0] : (funny(X0) | kind(X0) | (~patient(X0) & generous(X0))) [flattening 30]
39. ! [X0] : ((~happy(X0) | (~patient(X0) & ~old(X0))) & ((patient(X0) | old(X0)) | happy(X0))) [nnf transformation 1]
40. ! [X0] : ((~happy(X0) | (~patient(X0) & ~old(X0))) & (patient(X0) | old(X0) | happy(X0))) [flattening 39]
41. ! [X0] : (((~quiet(X0) | old(X0)) | ~generous(X0)) & (generous(X0) | (quiet(X0) & ~old(X0)))) [nnf transformation 2]
42. ! [X0] : ((~quiet(X0) | old(X0) | ~generous(X0)) & (generous(X0) | (quiet(X0) & ~old(X0)))) [flattening 41]
54. ! [X0] : ((((kind(X0) | happy(X0)) & (~kind(X0) | ~happy(X0))) | (~rich(X0) & ~patient(X0))) & ((rich(X0) | patient(X0)) | ((~happy(X0) | kind(X0)) & (~kind(X0) | happy(X0))))) [nnf transformation 8]
55. ! [X0] : ((((kind(X0) | happy(X0)) & (~kind(X0) | ~happy(X0))) | (~rich(X0) & ~patient(X0))) & (rich(X0) | patient(X0) | ((~happy(X0) | kind(X0)) & (~kind(X0) | happy(X0))))) [flattening 54]
57. ! [X0] : ((((funny(X0) | wise(X0)) & (~funny(X0) | ~wise(X0))) | (~humble(X0) & kind(X0))) & ((humble(X0) | ~kind(X0)) | ((~wise(X0) | funny(X0)) & (~funny(X0) | wise(X0))))) [nnf transformation 10]
58. ! [X0] : ((((funny(X0) | wise(X0)) & (~funny(X0) | ~wise(X0))) | (~humble(X0) & kind(X0))) & (humble(X0) | ~kind(X0) | ((~wise(X0) | funny(X0)) & (~funny(X0) | wise(X0))))) [flattening 57]
60. ! [X0] : (((quiet(X0) & ~happy(X0)) | ((~brave(X0) | generous(X0)) & (~generous(X0) | brave(X0)))) & (((generous(X0) | brave(X0)) & (~generous(X0) | ~brave(X0))) | (~quiet(X0) | happy(X0)))) [nnf transformation 13]
61. ! [X0] : (((quiet(X0) & ~happy(X0)) | ((~brave(X0) | generous(X0)) & (~generous(X0) | brave(X0)))) & (((generous(X0) | brave(X0)) & (~generous(X0) | ~brave(X0))) | ~quiet(X0) | happy(X0))) [flattening 60]
66. ! [X0] : ((patient(X0) | rich(X0)) & (~rich(X0) | ~patient(X0))) [nnf transformation 15]
77. ~patient(X0) | ~happy(X0) [cnf transformation 40]
79. generous(X0) | quiet(X0) [cnf transformation 42]
93. funny(X0) | kind(X0) | generous(X0) [cnf transformation 31]
104. ~rich(X0) | ~happy(X0) | ~kind(X0) [cnf transformation 55]
111. ~wise(X0) | ~funny(X0) | kind(X0) [cnf transformation 58]
119. generous(X0) | brave(X0) | ~quiet(X0) | happy(X0) [cnf transformation 61]
122. quiet(X0) | ~generous(X0) | brave(X0) [cnf transformation 61]
128. rich(X0) | patient(X0) [cnf transformation 66]
139. wise(susan) [cnf transformation 23]
140. ~brave(susan) [cnf transformation 23]
143. ~generous(susan) [cnf transformation 25]
239. brave(X0) | quiet(X0) [subsumption resolution 122,79]
240. brave(X0) | generous(X0) | happy(X0) [subsumption resolution 119,239]
340. ~happy(X0) | ~kind(X0) | patient(X0) [resolution 104,128]
341. ~kind(X0) | ~happy(X0) [subsumption resolution 340,77]
354. ~funny(susan) | kind(susan) [resolution 111,139]
356. 40 <=> kind(susan) [avatar definition]
358. kind(susan) <- (40) [avatar component clause 356]
360. 41 <=> funny(susan) [avatar definition]
362. ~funny(susan) <- (~41) [avatar component clause 360]
363. 40 | ~41 [avatar split clause 354,360,356]
364. kind(susan) | generous(susan) <- (~41) [resolution 362,93]
365. kind(susan) <- (~41) [subsumption resolution 364,143]
366. 40 | 41 [avatar split clause 365,360,356]
506. generous(susan) | happy(susan) [resolution 240,140]
514. happy(susan) [subsumption resolution 506,143]
586. ~happy(susan) <- (40) [resolution 341,358]
589. $false <- (40) [subsumption resolution 586,514]
590. ~40 [avatar contradiction clause 589]
593. $false [avatar sat refutation 363,366,590]
% SZS output end Proof for 7754564221929333977519468
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
If someone is quiet or not tall then someone is either tall or brave.
If mary is not tall or humble then alice is not wise or not kind.
If someone is calm then lucy is not kind or not generous and vice versa.
If someone is both not tall and curious then fred is old or humble.
If someone is both tall and not humble then fred is not generous.
If paul is wise or generous then paul is both not old and not funny and vice versa.
Everyone who is either generous or wise is funny or not generous and vice versa.
Everyone who is not strong is either not old or not calm and vice versa.
Everyone who is either not patient or patient is generous.
Everyone who is not calm or not happy is creative or humble.
Everyone who is happy is either calm or not patient and vice versa.
Everyone who is either not generous or not old is funny or quiet.
If someone is not happy then mary is not quiet or not old and vice versa.
Everyone who is not curious is both not tall and not patient and vice versa.
Everyone who is both not happy and funny is not curious.
Everyone who is either not brave or not kind is either wise or funny.
Someone is not happy.
Someone is not funny or not generous.
John is old.
Someone is both not patient and not tall.
Alice is either patient or not humble. | Mary is not tall. | neutral | ((?[X]:((quiet(X)|~tall(X))))=>(?[X]:((tall(X)<~>brave(X)))))&
(((~tall(mary)|humble(mary)))=>((~wise(alice)|~kind(alice))))&
((?[X]:(calm(X)))<=>((~kind(lucy)|~generous(lucy))))&
((?[X]:((~tall(X)&curious(X))))=>((old(fred)|humble(fred))))&
((?[X]:((tall(X)&~humble(X))))=>(~generous(fred)))&
(((wise(paul)|generous(paul)))<=>((~old(paul)&~funny(paul))))&
(![X]:((generous(X)<~>wise(X))<=>(funny(X)|~generous(X))))&
(![X]:(~strong(X)<=>(~old(X)<~>~calm(X))))&
(![X]:((~patient(X)<~>patient(X))=>generous(X)))&
(![X]:((~calm(X)|~happy(X))=>(creative(X)|humble(X))))&
(![X]:(happy(X)<=>(calm(X)<~>~patient(X))))&
(![X]:((~generous(X)<~>~old(X))=>(funny(X)|quiet(X))))&
((?[X]:(~happy(X)))<=>((~quiet(mary)|~old(mary))))&
(![X]:(~curious(X)<=>(~tall(X)&~patient(X))))&
(![X]:((~happy(X)&funny(X))=>~curious(X)))&
(![X]:((~brave(X)<~>~kind(X))=>(wise(X)<~>funny(X))))&
(?[X]:(~happy(X)))&
(?[X]:((~funny(X)|~generous(X))))&
(old(john))&
(?[X]:((~patient(X)&~tall(X))))&
((patient(alice)<~>~humble(alice))) | ~tall(mary) | [] | null | 0 |
Everyone who is both strong and patient is creative and vice versa.
If alice is strong or rich then someone is either not kind or not rich.
Everyone who is both funny and not creative is either not creative or happy.
If someone is not creative then someone is either not rich or creative.
Everyone who is both humble and not creative is both not creative and not generous and vice versa.
If susan is both not generous and not humble then paul is old or not calm and vice versa.
Everyone who is either not creative or wise is both not funny and tall.
If susan is either quiet or rich then someone is both happy and strong.
Everyone who is not rich is either patient or kind and vice versa.
Everyone who is patient or funny is both not patient and not generous.
If mary is both patient and not tall then lucy is not rich or not curious.
If john is calm or not curious then fred is not happy or not wise.
Everyone who is either brave or patient is generous.
If someone is not rich then paul is either not tall or not humble and vice versa.
Everyone who is both not generous and not quiet is either creative or old and vice versa.
Everyone who is wise or not quiet is both tall and patient.
Someone is both not old and tall.
Someone is not tall or generous.
Paul is both strong and not old.
Someone is not funny or calm.
Someone is both not rich and brave.
Someone is curious or not calm.
Susan is both not curious and not wise.
Someone is both calm and happy. | John is funny. | contradiction | (![X]:((strong(X)&patient(X))<=>creative(X)))&
(((strong(alice)|rich(alice)))=>(?[X]:((~kind(X)<~>~rich(X)))))&
(![X]:((funny(X)&~creative(X))=>(~creative(X)<~>happy(X))))&
((?[X]:(~creative(X)))=>(?[X]:((~rich(X)<~>creative(X)))))&
(![X]:((humble(X)&~creative(X))<=>(~creative(X)&~generous(X))))&
(((~generous(susan)&~humble(susan)))<=>((old(paul)|~calm(paul))))&
(![X]:((~creative(X)<~>wise(X))=>(~funny(X)&tall(X))))&
(((quiet(susan)<~>rich(susan)))=>(?[X]:((happy(X)&strong(X)))))&
(![X]:(~rich(X)<=>(patient(X)<~>kind(X))))&
(![X]:((patient(X)|funny(X))=>(~patient(X)&~generous(X))))&
(((patient(mary)&~tall(mary)))=>((~rich(lucy)|~curious(lucy))))&
(((calm(john)|~curious(john)))=>((~happy(fred)|~wise(fred))))&
(![X]:((brave(X)<~>patient(X))=>generous(X)))&
((?[X]:(~rich(X)))<=>((~tall(paul)<~>~humble(paul))))&
(![X]:((~generous(X)&~quiet(X))<=>(creative(X)<~>old(X))))&
(![X]:((wise(X)|~quiet(X))=>(tall(X)&patient(X))))&
(?[X]:((~old(X)&tall(X))))&
(?[X]:((~tall(X)|generous(X))))&
((strong(paul)&~old(paul)))&
(?[X]:((~funny(X)|calm(X))))&
(?[X]:((~rich(X)&brave(X))))&
(?[X]:((curious(X)|~calm(X))))&
((~curious(susan)&~wise(susan)))&
(?[X]:((calm(X)&happy(X)))) | funny(john) | [
"p0",
"p6",
"p9",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4015878365199441459749522
% SZS output start Proof for 4015878365199441459749522
1. ! [X0] : ((patient(X0) & strong(X0)) <=> creative(X0)) [input p0]
7. ! [X0] : ((~creative(X0) <~> wise(X0)) => (tall(X0) & ~funny(X0))) [input p6]
10. ! [X0] : ((funny(X0) | patient(X0)) => (~generous(X0) & ~patient(X0))) [input p9]
16. ! [X0] : ((~quiet(X0) | wise(X0)) => (patient(X0) & tall(X0))) [input p15]
25. funny(john) [input hypothesis]
31. ! [X0] : ((tall(X0) & ~funny(X0)) | (~creative(X0) <=> wise(X0))) [ennf transformation 7]
33. ! [X0] : ((~generous(X0) & ~patient(X0)) | (~funny(X0) & ~patient(X0))) [ennf transformation 10]
39. ! [X0] : ((patient(X0) & tall(X0)) | (quiet(X0) & ~wise(X0))) [ennf transformation 16]
40. ! [X0] : (((patient(X0) & strong(X0)) | ~creative(X0)) & (creative(X0) | (~patient(X0) | ~strong(X0)))) [nnf transformation 1]
41. ! [X0] : (((patient(X0) & strong(X0)) | ~creative(X0)) & (creative(X0) | ~patient(X0) | ~strong(X0))) [flattening 40]
54. ! [X0] : ((tall(X0) & ~funny(X0)) | ((~creative(X0) | ~wise(X0)) & (wise(X0) | creative(X0)))) [nnf transformation 31]
80. ~creative(X0) | patient(X0) [cnf transformation 41]
98. ~funny(X0) | wise(X0) | creative(X0) [cnf transformation 54]
110. ~patient(X0) | ~patient(X0) [cnf transformation 33]
131. patient(X0) | ~wise(X0) [cnf transformation 39]
146. funny(john) [cnf transformation 25]
147. ~patient(X0) [duplicate literal removal 110]
262. ~wise(X0) [subsumption resolution 131,147]
322. wise(john) | creative(john) [resolution 98,146]
323. creative(john) [subsumption resolution 322,262]
324. patient(john) [resolution 323,80]
326. $false [subsumption resolution 324,147]
% SZS output end Proof for 4015878365199441459749522
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not creative or not tall then alice is either not curious or not wise. Everyone who is calm or generous is humble or not old and vice versa. Everyone who is not calm is not humble or strong and vice versa. If someone is humble then someone is either not kind or generous. If someone is either funny or curious then john is not brave or not wise and vice versa. If someone is both not rich and not kind then someone is both old and not strong and vice versa. If someone is brave or happy then lucy is creative or funny. If someone is rich or not kind then someone is both not humble and not strong. If john is not quiet or kind then someone is not kind or brave. Everyone who is not brave is not curious and vice versa. If alice is not funny then someone is both brave and quiet. Everyone who is not calm is old or happy. Everyone who is brave or not curious is wise and vice versa. Everyone who is not patient or patient is not tall or not rich and vice versa. Everyone who is humble is funny. Everyone who is either brave or kind is both tall and not funny. Someone is both not calm and humble. Fred is either rich or generous. Someone is either wise or strong. Someone is both brave and not old. Fred is both curious and not creative. Alice is not kind. John is both not humble and funny. Susan is both not happy and not brave. | Fred is not creative. | entailment | ((?[X]:((~creative(X)|~tall(X))))=>((~curious(alice)<~>~wise(alice))))&
(![X]:((calm(X)|generous(X))<=>(humble(X)|~old(X))))&
(![X]:(~calm(X)<=>(~humble(X)|strong(X))))&
((?[X]:(humble(X)))=>(?[X]:((~kind(X)<~>generous(X)))))&
((?[X]:((funny(X)<~>curious(X))))<=>((~brave(john)|~wise(john))))&
((?[X]:((~rich(X)&~kind(X))))<=>(?[X]:((old(X)&~strong(X)))))&
((?[X]:((brave(X)|happy(X))))=>((creative(lucy)|funny(lucy))))&
((?[X]:((rich(X)|~kind(X))))=>(?[X]:((~humble(X)&~strong(X)))))&
(((~quiet(john)|kind(john)))=>(?[X]:((~kind(X)|brave(X)))))&
(![X]:(~brave(X)<=>~curious(X)))&
((~funny(alice))=>(?[X]:((brave(X)&quiet(X)))))&
(![X]:(~calm(X)=>(old(X)|happy(X))))&
(![X]:((brave(X)|~curious(X))<=>wise(X)))&
(![X]:((~patient(X)|patient(X))<=>(~tall(X)|~rich(X))))&
(![X]:(humble(X)=>funny(X)))&
(![X]:((brave(X)<~>kind(X))=>(tall(X)&~funny(X))))&
(?[X]:((~calm(X)&humble(X))))&
((rich(fred)<~>generous(fred)))&
(?[X]:((wise(X)<~>strong(X))))&
(?[X]:((brave(X)&~old(X))))&
((curious(fred)&~creative(fred)))&
(~kind(alice))&
((~humble(john)&funny(john)))&
((~happy(susan)&~brave(susan))) | ~creative(fred) | [
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 9117525741448562867703571
% SZS output start Proof for 9117525741448562867703571
21. ~creative(fred) & curious(fred) [input p20]
25. creative(fred) [input hypothesis]
137. ~creative(fred) [cnf transformation 21]
143. creative(fred) [cnf transformation 25]
306. $false [subsumption resolution 143,137]
% SZS output end Proof for 9117525741448562867703571
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either quiet or not wise is both not generous and strong and vice versa.
If someone is both not creative and brave then someone is kind or calm.
If someone is not creative then someone is not happy or not patient and vice versa.
If fred is both kind and not brave then someone is not old.
Everyone who is brave or not strong is both not strong and not patient and vice versa.
If susan is not creative then mary is either kind or not brave and vice versa.
If paul is quiet then someone is rich and vice versa.
If fred is not wise or not humble then someone is either old or funny.
If fred is not wise then paul is generous or not humble and vice versa.
If someone is not wise or old then someone is both not curious and tall.
Everyone who is both curious and kind is not calm or not brave and vice versa.
Everyone who is either curious or not quiet is both old and not creative and vice versa.
If susan is not strong then fred is both not happy and curious.
If fred is both not patient and not funny then someone is either not patient or funny.
Someone is either calm or not wise.
Someone is not rich or not curious.
Mary is either not funny or not generous.
Susan is wise.
Lucy is humble or rich. | Fred is rich. | neutral | (![X]:((quiet(X)<~>~wise(X))<=>(~generous(X)&strong(X))))&
((?[X]:((~creative(X)&brave(X))))=>(?[X]:((kind(X)|calm(X)))))&
((?[X]:(~creative(X)))<=>(?[X]:((~happy(X)|~patient(X)))))&
(((kind(fred)&~brave(fred)))=>(?[X]:(~old(X))))&
(![X]:((brave(X)|~strong(X))<=>(~strong(X)&~patient(X))))&
((~creative(susan))<=>((kind(mary)<~>~brave(mary))))&
((quiet(paul))<=>(?[X]:(rich(X))))&
(((~wise(fred)|~humble(fred)))=>(?[X]:((old(X)<~>funny(X)))))&
((~wise(fred))<=>((generous(paul)|~humble(paul))))&
((?[X]:((~wise(X)|old(X))))=>(?[X]:((~curious(X)&tall(X)))))&
(![X]:((curious(X)&kind(X))<=>(~calm(X)|~brave(X))))&
(![X]:((curious(X)<~>~quiet(X))<=>(old(X)&~creative(X))))&
((~strong(susan))=>((~happy(fred)&curious(fred))))&
(((~patient(fred)&~funny(fred)))=>(?[X]:((~patient(X)<~>funny(X)))))&
(?[X]:((calm(X)<~>~wise(X))))&
(?[X]:((~rich(X)|~curious(X))))&
((~funny(mary)<~>~generous(mary)))&
(wise(susan))&
((humble(lucy)|rich(lucy))) | rich(fred) | [] | null | 0 |
If someone is generous then mary is not tall or not quiet and vice versa.
Everyone who is either curious or not funny is both strong and not patient and vice versa.
If someone is not rich or not quiet then alice is both calm and not old.
If someone is rich or strong then mary is not strong or not tall.
Everyone who is either not funny or humble is both not old and curious.
Everyone who is funny or kind is both tall and quiet.
If someone is both funny and strong then paul is not funny.
If someone is either calm or not strong then mary is either not patient or humble.
Everyone who is generous or happy is both not quiet and funny and vice versa.
If someone is either not tall or not happy then someone is either not humble or humble and vice versa.
If alice is not humble or calm then someone is tall and vice versa.
Everyone who is either not funny or happy is rich and vice versa.
If someone is both not patient and humble then alice is not rich or not calm.
Everyone who is curious is curious or not wise.
Everyone who is either not humble or curious is both generous and happy and vice versa.
If alice is not quiet or kind then john is either tall or happy and vice versa.
Someone is not kind or tall.
Fred is tall or old.
Someone is brave.
Someone is both not rich and not generous.
Someone is humble.
Paul is both creative and tall.
Someone is not old or kind. | Alice is not quiet. | contradiction | ((?[X]:(generous(X)))<=>((~tall(mary)|~quiet(mary))))&
(![X]:((curious(X)<~>~funny(X))<=>(strong(X)&~patient(X))))&
((?[X]:((~rich(X)|~quiet(X))))=>((calm(alice)&~old(alice))))&
((?[X]:((rich(X)|strong(X))))=>((~strong(mary)|~tall(mary))))&
(![X]:((~funny(X)<~>humble(X))=>(~old(X)&curious(X))))&
(![X]:((funny(X)|kind(X))=>(tall(X)&quiet(X))))&
((?[X]:((funny(X)&strong(X))))=>(~funny(paul)))&
((?[X]:((calm(X)<~>~strong(X))))=>((~patient(mary)<~>humble(mary))))&
(![X]:((generous(X)|happy(X))<=>(~quiet(X)&funny(X))))&
((?[X]:((~tall(X)<~>~happy(X))))<=>(?[X]:((~humble(X)<~>humble(X)))))&
(((~humble(alice)|calm(alice)))<=>(?[X]:(tall(X))))&
(![X]:((~funny(X)<~>happy(X))<=>rich(X)))&
((?[X]:((~patient(X)&humble(X))))=>((~rich(alice)|~calm(alice))))&
(![X]:(curious(X)=>(curious(X)|~wise(X))))&
(![X]:((~humble(X)<~>curious(X))<=>(generous(X)&happy(X))))&
(((~quiet(alice)|kind(alice)))<=>((tall(john)<~>happy(john))))&
(?[X]:((~kind(X)|tall(X))))&
((tall(fred)|old(fred)))&
(?[X]:(brave(X)))&
(?[X]:((~rich(X)&~generous(X))))&
(?[X]:(humble(X)))&
((creative(paul)&tall(paul)))&
(?[X]:((~old(X)|kind(X)))) | ~quiet(alice) | [
"p0",
"p1",
"p2",
"p4",
"p5",
"p8",
"p11",
"p12",
"p14",
"p19",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 3412224653587095512226359
% SZS output start Proof for 3412224653587095512226359
1. ? [X0] : generous(X0) <=> (~quiet(mary) | ~tall(mary)) [input p0]
2. ! [X0] : ((curious(X0) <~> ~funny(X0)) <=> (~patient(X0) & strong(X0))) [input p1]
3. ? [X0] : (~quiet(X0) | ~rich(X0)) => (~old(alice) & calm(alice)) [input p2]
5. ! [X0] : ((~funny(X0) <~> humble(X0)) => (curious(X0) & ~old(X0))) [input p4]
6. ! [X0] : ((kind(X0) | funny(X0)) => (quiet(X0) & tall(X0))) [input p5]
9. ! [X0] : ((happy(X0) | generous(X0)) <=> (funny(X0) & ~quiet(X0))) [input p8]
12. ! [X0] : ((~funny(X0) <~> happy(X0)) <=> rich(X0)) [input p11]
13. ? [X0] : (humble(X0) & ~patient(X0)) => (~calm(alice) | ~rich(alice)) [input p12]
15. ! [X0] : ((~humble(X0) <~> curious(X0)) <=> (happy(X0) & generous(X0))) [input p14]
20. ? [X0] : (~generous(X0) & ~rich(X0)) [input p19]
21. ? [X0] : humble(X0) [input p20]
24. ~quiet(alice) [input hypothesis]
29. (~old(alice) & calm(alice)) | ! [X0] : (quiet(X0) & rich(X0)) [ennf transformation 3]
32. ! [X0] : ((curious(X0) & ~old(X0)) | (~funny(X0) <=> humble(X0))) [ennf transformation 5]
33. ! [X0] : ((quiet(X0) & tall(X0)) | (~kind(X0) & ~funny(X0))) [ennf transformation 6]
36. (~calm(alice) | ~rich(alice)) | ! [X0] : (~humble(X0) | patient(X0)) [ennf transformation 13]
37. ~calm(alice) | ~rich(alice) | ! [X0] : (~humble(X0) | patient(X0)) [flattening 36]
38. (? [X0] : generous(X0) | (quiet(mary) & tall(mary))) & ((~quiet(mary) | ~tall(mary)) | ! [X0] : ~generous(X0)) [nnf transformation 1]
39. (? [X0] : generous(X0) | (quiet(mary) & tall(mary))) & (~quiet(mary) | ~tall(mary) | ! [X0] : ~generous(X0)) [flattening 38]
40. (? [X0] : generous(X0) | (quiet(mary) & tall(mary))) & (~quiet(mary) | ~tall(mary) | ! [X1] : ~generous(X1)) [rectify 39]
41. ? [X0] : generous(X0) => generous(sK0) [choice axiom]
42. (generous(sK0) | (quiet(mary) & tall(mary))) & (~quiet(mary) | ~tall(mary) | ! [X1] : ~generous(X1)) [skolemisation 40,41]
43. ! [X0] : ((((funny(X0) | ~curious(X0)) & (~funny(X0) | curious(X0))) | (patient(X0) | ~strong(X0))) & ((~patient(X0) & strong(X0)) | ((curious(X0) | funny(X0)) & (~funny(X0) | ~curious(X0))))) [nnf transformation 2]
44. ! [X0] : ((((funny(X0) | ~curious(X0)) & (~funny(X0) | curious(X0))) | patient(X0) | ~strong(X0)) & ((~patient(X0) & strong(X0)) | ((curious(X0) | funny(X0)) & (~funny(X0) | ~curious(X0))))) [flattening 43]
45. ! [X0] : ((curious(X0) & ~old(X0)) | ((~funny(X0) | ~humble(X0)) & (humble(X0) | funny(X0)))) [nnf transformation 32]
47. ! [X0] : (((happy(X0) | generous(X0)) | (~funny(X0) | quiet(X0))) & ((funny(X0) & ~quiet(X0)) | (~happy(X0) & ~generous(X0)))) [nnf transformation 9]
48. ! [X0] : ((happy(X0) | generous(X0) | ~funny(X0) | quiet(X0)) & ((funny(X0) & ~quiet(X0)) | (~happy(X0) & ~generous(X0)))) [flattening 47]
59. ! [X0] : ((((~happy(X0) | funny(X0)) & (happy(X0) | ~funny(X0))) | ~rich(X0)) & (rich(X0) | ((~funny(X0) | ~happy(X0)) & (happy(X0) | funny(X0))))) [nnf transformation 12]
60. ! [X0] : ((((~curious(X0) | humble(X0)) & (curious(X0) | ~humble(X0))) | (~happy(X0) | ~generous(X0))) & ((happy(X0) & generous(X0)) | ((~humble(X0) | ~curious(X0)) & (curious(X0) | humble(X0))))) [nnf transformation 15]
61. ! [X0] : ((((~curious(X0) | humble(X0)) & (curious(X0) | ~humble(X0))) | ~happy(X0) | ~generous(X0)) & ((happy(X0) & generous(X0)) | ((~humble(X0) | ~curious(X0)) & (curious(X0) | humble(X0))))) [flattening 60]
66. ? [X0] : (~generous(X0) & ~rich(X0)) => (~generous(sK5) & ~rich(sK5)) [choice axiom]
67. ~generous(sK5) & ~rich(sK5) [skolemisation 20,66]
68. ? [X0] : humble(X0) => humble(sK6) [choice axiom]
69. humble(sK6) [skolemisation 21,68]
72. ~quiet(mary) | ~tall(mary) | ~generous(X1) [cnf transformation 42]
73. generous(sK0) | tall(mary) [cnf transformation 42]
74. generous(sK0) | quiet(mary) [cnf transformation 42]
78. ~patient(X0) | curious(X0) | funny(X0) [cnf transformation 44]
81. calm(alice) | rich(X0) [cnf transformation 29]
89. humble(X0) | curious(X0) | funny(X0) [cnf transformation 45]
90. ~humble(X0) | ~funny(X0) | curious(X0) [cnf transformation 45]
93. ~funny(X0) | quiet(X0) [cnf transformation 33]
100. ~quiet(X0) | ~generous(X0) [cnf transformation 48]
102. ~generous(X0) | funny(X0) [cnf transformation 48]
103. ~happy(X0) | funny(X0) [cnf transformation 48]
116. rich(X0) | happy(X0) | funny(X0) [cnf transformation 59]
117. rich(X0) | ~funny(X0) | ~happy(X0) [cnf transformation 59]
120. ~calm(alice) | ~rich(alice) | ~humble(X0) | patient(X0) [cnf transformation 37]
122. ~humble(X0) | generous(X0) | ~curious(X0) [cnf transformation 61]
135. ~rich(sK5) [cnf transformation 67]
137. humble(sK6) [cnf transformation 69]
140. ~quiet(alice) [cnf transformation 24]
146. 1 <=> quiet(mary) [avatar definition]
150. 2 <=> generous(sK0) [avatar definition]
152. generous(sK0) <- (2) [avatar component clause 150]
153. 1 | 2 [avatar split clause 74,150,146]
155. 3 <=> tall(mary) [avatar definition]
158. 3 | 2 [avatar split clause 73,150,155]
160. 4 <=> ! [X1] : ~generous(X1) [avatar definition]
161. ~generous(X1) <- (4) [avatar component clause 160]
162. 4 | ~3 | ~1 [avatar split clause 72,146,155,160]
172. 7 <=> ! [X0] : rich(X0) [avatar definition]
173. rich(X0) <- (7) [avatar component clause 172]
176. 8 <=> calm(alice) [avatar definition]
180. 7 | 8 [avatar split clause 81,176,172]
251. ~happy(X0) | rich(X0) [subsumption resolution 117,103]
252. rich(X0) | funny(X0) [subsumption resolution 116,251]
254. 25 <=> ! [X0] : (~humble(X0) | patient(X0)) [avatar definition]
255. ~humble(X0) | patient(X0) <- (25) [avatar component clause 254]
257. 26 <=> rich(alice) [avatar definition]
259. ~rich(alice) <- (~26) [avatar component clause 257]
260. 25 | ~26 | ~8 [avatar split clause 120,176,257,254]
270. 29 <=> quiet(alice) [avatar definition]
272. ~quiet(alice) <- (~29) [avatar component clause 270]
301. ~29 [avatar split clause 140,270]
304. $false <- (7) [resolution 173,135]
305. ~7 [avatar contradiction clause 304]
312. funny(sK0) <- (2) [resolution 102,152]
317. quiet(sK0) <- (2) [resolution 312,93]
320. funny(alice) <- (~26) [resolution 252,259]
366. quiet(alice) <- (~26) [resolution 320,93]
377. $false <- (~26, ~29) [subsumption resolution 366,272]
378. 26 | 29 [avatar contradiction clause 377]
379. ~generous(sK0) <- (2) [resolution 317,100]
380. $false <- (2) [subsumption resolution 379,152]
381. ~2 [avatar contradiction clause 380]
407. 46 <=> curious(sK6) [avatar definition]
409. curious(sK6) <- (46) [avatar component clause 407]
425. curious(X1) | funny(X1) | patient(X1) <- (25) [resolution 89,255]
427. curious(X1) | funny(X1) <- (25) [subsumption resolution 425,78]
428. ~funny(sK6) | curious(sK6) [resolution 90,137]
434. curious(sK6) <- (25) [subsumption resolution 428,427]
435. 46 | ~25 [avatar split clause 434,254,407]
477. generous(sK6) | ~curious(sK6) [resolution 122,137]
482. ~curious(sK6) <- (4) [subsumption resolution 477,161]
483. $false <- (4, 46) [subsumption resolution 482,409]
484. ~4 | ~46 [avatar contradiction clause 483]
488. $false [avatar sat refutation 153,158,162,180,260,301,305,378,381,435,484]
% SZS output end Proof for 3412224653587095512226359
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either old or funny is either strong or rich.
Everyone who is quiet is curious or kind.
Everyone who is both not kind and brave is not quiet or patient and vice versa.
Everyone who is not old is not wise and vice versa.
If fred is both not patient and wise then lucy is not happy or generous.
If someone is either creative or not calm then john is rich or calm and vice versa.
Everyone who is generous is not curious or not humble and vice versa.
If lucy is both brave and not patient then someone is brave.
If susan is either not creative or curious then susan is either not tall or generous and vice versa.
If john is generous then someone is either not wise or humble and vice versa.
Everyone who is not strong is not old.
If fred is both not tall and calm then someone is both creative and not quiet.
Everyone who is not quiet is not tall.
Everyone who is quiet is brave or not quiet.
If lucy is tall then someone is either kind or not brave and vice versa.
Everyone who is either creative or not patient is either not generous or not strong and vice versa.
Fred is kind.
Someone is rich or tall.
Mary is tall.
Lucy is both not humble and not kind.
Someone is both funny and strong.
Lucy is generous or not creative.
Someone is not funny or brave. | Lucy is not quiet. | contradiction | (![X]:((old(X)<~>funny(X))=>(strong(X)<~>rich(X))))&
(![X]:(quiet(X)=>(curious(X)|kind(X))))&
(![X]:((~kind(X)&brave(X))<=>(~quiet(X)|patient(X))))&
(![X]:(~old(X)<=>~wise(X)))&
(((~patient(fred)&wise(fred)))=>((~happy(lucy)|generous(lucy))))&
((?[X]:((creative(X)<~>~calm(X))))<=>((rich(john)|calm(john))))&
(![X]:(generous(X)<=>(~curious(X)|~humble(X))))&
(((brave(lucy)&~patient(lucy)))=>(?[X]:(brave(X))))&
(((~creative(susan)<~>curious(susan)))<=>((~tall(susan)<~>generous(susan))))&
((generous(john))<=>(?[X]:((~wise(X)<~>humble(X)))))&
(![X]:(~strong(X)=>~old(X)))&
(((~tall(fred)&calm(fred)))=>(?[X]:((creative(X)&~quiet(X)))))&
(![X]:(~quiet(X)=>~tall(X)))&
(![X]:(quiet(X)=>(brave(X)|~quiet(X))))&
((tall(lucy))<=>(?[X]:((kind(X)<~>~brave(X)))))&
(![X]:((creative(X)<~>~patient(X))<=>(~generous(X)<~>~strong(X))))&
(kind(fred))&
(?[X]:((rich(X)|tall(X))))&
(tall(mary))&
((~humble(lucy)&~kind(lucy)))&
(?[X]:((funny(X)&strong(X))))&
((generous(lucy)|~creative(lucy)))&
(?[X]:((~funny(X)|brave(X)))) | ~quiet(lucy) | [
"p2",
"p12",
"p13",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 710019899353675931787852
% SZS output start Proof for 710019899353675931787852
3. ! [X0] : ((brave(X0) & ~kind(X0)) <=> (patient(X0) | ~quiet(X0))) [input p2]
13. ! [X0] : (~quiet(X0) => ~tall(X0)) [input p12]
14. ! [X0] : (quiet(X0) => (~quiet(X0) | brave(X0))) [input p13]
15. tall(lucy) <=> ? [X0] : (kind(X0) <~> ~brave(X0)) [input p14]
17. kind(fred) [input p16]
24. ~quiet(lucy) [input hypothesis]
34. ! [X0] : (~tall(X0) | quiet(X0)) [ennf transformation 13]
35. ! [X0] : ((~quiet(X0) | brave(X0)) | ~quiet(X0)) [ennf transformation 14]
36. ! [X0] : (~quiet(X0) | brave(X0) | ~quiet(X0)) [flattening 35]
38. ! [X0] : (((brave(X0) & ~kind(X0)) | (~patient(X0) & quiet(X0))) & ((patient(X0) | ~quiet(X0)) | (~brave(X0) | kind(X0)))) [nnf transformation 3]
39. ! [X0] : (((brave(X0) & ~kind(X0)) | (~patient(X0) & quiet(X0))) & (patient(X0) | ~quiet(X0) | ~brave(X0) | kind(X0))) [flattening 38]
57. (tall(lucy) | ! [X0] : ((kind(X0) | brave(X0)) & (~brave(X0) | ~kind(X0)))) & (? [X0] : ((brave(X0) | ~kind(X0)) & (~brave(X0) | kind(X0))) | ~tall(lucy)) [nnf transformation 15]
58. (tall(lucy) | ! [X0] : ((kind(X0) | brave(X0)) & (~brave(X0) | ~kind(X0)))) & (? [X1] : ((brave(X1) | ~kind(X1)) & (~brave(X1) | kind(X1))) | ~tall(lucy)) [rectify 57]
59. ? [X1] : ((brave(X1) | ~kind(X1)) & (~brave(X1) | kind(X1))) => ((brave(sK4) | ~kind(sK4)) & (~brave(sK4) | kind(sK4))) [choice axiom]
60. (tall(lucy) | ! [X0] : ((kind(X0) | brave(X0)) & (~brave(X0) | ~kind(X0)))) & (((brave(sK4) | ~kind(sK4)) & (~brave(sK4) | kind(sK4))) | ~tall(lucy)) [skolemisation 58,59]
76. brave(X0) | quiet(X0) [cnf transformation 39]
105. ~tall(X0) | quiet(X0) [cnf transformation 34]
106. ~quiet(X0) | brave(X0) | ~quiet(X0) [cnf transformation 36]
109. tall(lucy) | ~brave(X0) | ~kind(X0) [cnf transformation 60]
119. kind(fred) [cnf transformation 17]
128. ~quiet(lucy) [cnf transformation 24]
129. ~quiet(X0) | brave(X0) [duplicate literal removal 106]
237. brave(X0) [subsumption resolution 129,76]
238. tall(lucy) | ~kind(X0) [subsumption resolution 109,237]
240. 23 <=> ! [X0] : ~kind(X0) [avatar definition]
241. ~kind(X0) <- (23) [avatar component clause 240]
243. 24 <=> tall(lucy) [avatar definition]
245. tall(lucy) <- (24) [avatar component clause 243]
246. 23 | 24 [avatar split clause 238,243,240]
273. $false <- (23) [resolution 241,119]
274. ~23 [avatar contradiction clause 273]
284. quiet(lucy) <- (24) [resolution 105,245]
285. $false <- (24) [subsumption resolution 284,128]
286. ~24 [avatar contradiction clause 285]
287. $false [avatar sat refutation 246,274,286]
% SZS output end Proof for 710019899353675931787852
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not kind is creative or old.
Everyone who is both not wise and not calm is both tall and patient and vice versa.
Everyone who is not generous or not quiet is both calm and not curious and vice versa.
Everyone who is humble or not generous is not humble or not curious and vice versa.
If someone is curious then fred is not creative or calm and vice versa.
If fred is curious then fred is not funny or not wise and vice versa.
If someone is not rich then someone is both not curious and old.
If fred is either quiet or not creative then fred is either not generous or old.
If lucy is either happy or funny then lucy is either strong or old and vice versa.
If mary is both funny and not creative then someone is either not generous or rich.
If alice is not funny then lucy is creative or not happy and vice versa.
Everyone who is not kind or tall is both not strong and not wise.
Everyone who is both generous and not brave is happy or not calm.
If someone is strong or not happy then someone is not old.
If alice is both creative and happy then lucy is either not tall or patient.
John is both not wise and not calm.
Lucy is humble.
Someone is not generous.
Someone is both not creative and tall.
Susan is brave.
Alice is both rich and not wise. | Fred is not creative. | contradiction | (![X]:(~kind(X)=>(creative(X)|old(X))))&
(![X]:((~wise(X)&~calm(X))<=>(tall(X)&patient(X))))&
(![X]:((~generous(X)|~quiet(X))<=>(calm(X)&~curious(X))))&
(![X]:((humble(X)|~generous(X))<=>(~humble(X)|~curious(X))))&
((?[X]:(curious(X)))<=>((~creative(fred)|calm(fred))))&
((curious(fred))<=>((~funny(fred)|~wise(fred))))&
((?[X]:(~rich(X)))=>(?[X]:((~curious(X)&old(X)))))&
(((quiet(fred)<~>~creative(fred)))=>((~generous(fred)<~>old(fred))))&
(((happy(lucy)<~>funny(lucy)))<=>((strong(lucy)<~>old(lucy))))&
(((funny(mary)&~creative(mary)))=>(?[X]:((~generous(X)<~>rich(X)))))&
((~funny(alice))<=>((creative(lucy)|~happy(lucy))))&
(![X]:((~kind(X)|tall(X))=>(~strong(X)&~wise(X))))&
(![X]:((generous(X)&~brave(X))=>(happy(X)|~calm(X))))&
((?[X]:((strong(X)|~happy(X))))=>(?[X]:(~old(X))))&
(((creative(alice)&happy(alice)))=>((~tall(lucy)<~>patient(lucy))))&
((~wise(john)&~calm(john)))&
(humble(lucy))&
(?[X]:(~generous(X)))&
(?[X]:((~creative(X)&tall(X))))&
(brave(susan))&
((rich(alice)&~wise(alice))) | ~creative(fred) | [
"p2",
"p3",
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 5398361229733936604336097
% SZS output start Proof for 5398361229733936604336097
3. ! [X0] : ((~quiet(X0) | ~generous(X0)) <=> (~curious(X0) & calm(X0))) [input p2]
4. ! [X0] : ((~generous(X0) | humble(X0)) <=> (~curious(X0) | ~humble(X0))) [input p3]
5. ? [X0] : curious(X0) <=> (calm(fred) | ~creative(fred)) [input p4]
22. ~creative(fred) [input hypothesis]
39. ! [X0] : (((~quiet(X0) | ~generous(X0)) | (curious(X0) | ~calm(X0))) & ((~curious(X0) & calm(X0)) | (quiet(X0) & generous(X0)))) [nnf transformation 3]
40. ! [X0] : ((~quiet(X0) | ~generous(X0) | curious(X0) | ~calm(X0)) & ((~curious(X0) & calm(X0)) | (quiet(X0) & generous(X0)))) [flattening 39]
41. ! [X0] : (((~generous(X0) | humble(X0)) | (curious(X0) & humble(X0))) & ((~curious(X0) | ~humble(X0)) | (generous(X0) & ~humble(X0)))) [nnf transformation 4]
42. ! [X0] : ((~generous(X0) | humble(X0) | (curious(X0) & humble(X0))) & (~curious(X0) | ~humble(X0) | (generous(X0) & ~humble(X0)))) [flattening 41]
43. (? [X0] : curious(X0) | (~calm(fred) & creative(fred))) & ((calm(fred) | ~creative(fred)) | ! [X0] : ~curious(X0)) [nnf transformation 5]
44. (? [X0] : curious(X0) | (~calm(fred) & creative(fred))) & (calm(fred) | ~creative(fred) | ! [X0] : ~curious(X0)) [flattening 43]
45. (? [X0] : curious(X0) | (~calm(fred) & creative(fred))) & (calm(fred) | ~creative(fred) | ! [X1] : ~curious(X1)) [rectify 44]
46. ? [X0] : curious(X0) => curious(sK0) [choice axiom]
47. (curious(sK0) | (~calm(fred) & creative(fred))) & (calm(fred) | ~creative(fred) | ! [X1] : ~curious(X1)) [skolemisation 45,46]
74. ~curious(X0) | generous(X0) [cnf transformation 40]
77. ~curious(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 42]
79. ~generous(X0) | humble(X0) | humble(X0) [cnf transformation 42]
82. curious(sK0) | creative(fred) [cnf transformation 47]
120. ~creative(fred) [cnf transformation 22]
121. ~humble(X0) | ~curious(X0) [duplicate literal removal 77]
122. ~generous(X0) | humble(X0) [duplicate literal removal 79]
128. 2 <=> curious(sK0) [avatar definition]
130. curious(sK0) <- (2) [avatar component clause 128]
133. 3 <=> creative(fred) [avatar definition]
136. 3 | 2 [avatar split clause 82,128,133]
268. ~3 [avatar split clause 120,133]
272. generous(sK0) <- (2) [resolution 74,130]
280. humble(sK0) <- (2) [resolution 122,272]
286. ~curious(sK0) <- (2) [resolution 280,121]
287. $false <- (2) [subsumption resolution 286,130]
288. ~2 [avatar contradiction clause 287]
289. $false [avatar sat refutation 136,268,288]
% SZS output end Proof for 5398361229733936604336097
% ------------------------------
% 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 |
If someone is curious then someone is humble or not strong.
If someone is both patient and not creative then someone is not old and vice versa.
Everyone who is both not humble and not quiet is not funny or not brave and vice versa.
Everyone who is both not wise and not humble is wise.
Everyone who is happy or not old is both not happy and not funny and vice versa.
If someone is both rich and not patient then paul is not tall and vice versa.
Everyone who is either generous or not quiet is both patient and not quiet and vice versa.
If lucy is old or tall then someone is either humble or not humble and vice versa.
If someone is either not kind or not wise then paul is not strong and vice versa.
Everyone who is either not brave or not old is both not funny and not old and vice versa.
Everyone who is not creative or not brave is either not calm or calm and vice versa.
Everyone who is brave or creative is both not calm and old.
If someone is either not calm or tall then susan is either not wise or humble and vice versa.
If someone is either not funny or not curious then fred is not funny or generous and vice versa.
If paul is quiet or curious then someone is not creative or not generous and vice versa.
If paul is strong or not creative then someone is strong or not funny.
John is either creative or not patient.
John is not kind.
Someone is either not curious or not humble.
Someone is not happy.
Someone is either not old or not strong.
Someone is happy or kind. | John is rich. | neutral | ((?[X]:(curious(X)))=>(?[X]:((humble(X)|~strong(X)))))&
((?[X]:((patient(X)&~creative(X))))<=>(?[X]:(~old(X))))&
(![X]:((~humble(X)&~quiet(X))<=>(~funny(X)|~brave(X))))&
(![X]:((~wise(X)&~humble(X))=>wise(X)))&
(![X]:((happy(X)|~old(X))<=>(~happy(X)&~funny(X))))&
((?[X]:((rich(X)&~patient(X))))<=>(~tall(paul)))&
(![X]:((generous(X)<~>~quiet(X))<=>(patient(X)&~quiet(X))))&
(((old(lucy)|tall(lucy)))<=>(?[X]:((humble(X)<~>~humble(X)))))&
((?[X]:((~kind(X)<~>~wise(X))))<=>(~strong(paul)))&
(![X]:((~brave(X)<~>~old(X))<=>(~funny(X)&~old(X))))&
(![X]:((~creative(X)|~brave(X))<=>(~calm(X)<~>calm(X))))&
(![X]:((brave(X)|creative(X))=>(~calm(X)&old(X))))&
((?[X]:((~calm(X)<~>tall(X))))<=>((~wise(susan)<~>humble(susan))))&
((?[X]:((~funny(X)<~>~curious(X))))<=>((~funny(fred)|generous(fred))))&
(((quiet(paul)|curious(paul)))<=>(?[X]:((~creative(X)|~generous(X)))))&
(((strong(paul)|~creative(paul)))=>(?[X]:((strong(X)|~funny(X)))))&
((creative(john)<~>~patient(john)))&
(~kind(john))&
(?[X]:((~curious(X)<~>~humble(X))))&
(?[X]:(~happy(X)))&
(?[X]:((~old(X)<~>~strong(X))))&
(?[X]:((happy(X)|kind(X)))) | rich(john) | [] | null | 0 |
Everyone who is not calm or not brave is both not strong and strong and vice versa. Everyone who is creative is not strong and vice versa. If someone is either humble or not calm then lucy is both not creative and not rich. If someone is not old or not happy then susan is not calm or happy. Everyone who is brave is not creative. Everyone who is either not brave or not tall is humble. Everyone who is quiet is not happy or not creative and vice versa. Everyone who is both happy and brave is not tall or quiet and vice versa. Everyone who is brave is calm or humble. Everyone who is either funny or not calm is humble or curious. Everyone who is not calm or not tall is rich and vice versa. If someone is not wise or happy then alice is both brave and wise and vice versa. If someone is either wise or patient then someone is not patient or not kind. If someone is generous or not generous then john is quiet. If john is not strong then someone is either quiet or humble and vice versa. Paul is either humble or generous. John is either curious or rich. Someone is not humble or tall. Someone is funny. Someone is strong. Susan is both humble and calm. Someone is not old or not curious. | Lucy is not tall. | contradiction | (![X]:((~calm(X)|~brave(X))<=>(~strong(X)&strong(X))))&
(![X]:(creative(X)<=>~strong(X)))&
((?[X]:((humble(X)<~>~calm(X))))=>((~creative(lucy)&~rich(lucy))))&
((?[X]:((~old(X)|~happy(X))))=>((~calm(susan)|happy(susan))))&
(![X]:(brave(X)=>~creative(X)))&
(![X]:((~brave(X)<~>~tall(X))=>humble(X)))&
(![X]:(quiet(X)<=>(~happy(X)|~creative(X))))&
(![X]:((happy(X)&brave(X))<=>(~tall(X)|quiet(X))))&
(![X]:(brave(X)=>(calm(X)|humble(X))))&
(![X]:((funny(X)<~>~calm(X))=>(humble(X)|curious(X))))&
(![X]:((~calm(X)|~tall(X))<=>rich(X)))&
((?[X]:((~wise(X)|happy(X))))<=>((brave(alice)&wise(alice))))&
((?[X]:((wise(X)<~>patient(X))))=>(?[X]:((~patient(X)|~kind(X)))))&
((?[X]:((generous(X)|~generous(X))))=>(quiet(john)))&
((~strong(john))<=>(?[X]:((quiet(X)<~>humble(X)))))&
((humble(paul)<~>generous(paul)))&
((curious(john)<~>rich(john)))&
(?[X]:((~humble(X)|tall(X))))&
(?[X]:(funny(X)))&
(?[X]:(strong(X)))&
((humble(susan)&calm(susan)))&
(?[X]:((~old(X)|~curious(X)))) | ~tall(lucy) | [
"p0",
"p1",
"p2",
"p4",
"p6",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 7405808642022735605195849
% SZS output start Proof for 7405808642022735605195849
1. ! [X0] : ((~brave(X0) | ~calm(X0)) <=> (strong(X0) & ~strong(X0))) [input p0]
2. ! [X0] : (creative(X0) <=> ~strong(X0)) [input p1]
3. ? [X0] : (humble(X0) <~> ~calm(X0)) => (~rich(lucy) & ~creative(lucy)) [input p2]
5. ! [X0] : (brave(X0) => ~creative(X0)) [input p4]
7. ! [X0] : (quiet(X0) <=> (~creative(X0) | ~happy(X0))) [input p6]
11. ! [X0] : ((~tall(X0) | ~calm(X0)) <=> rich(X0)) [input p10]
15. ~strong(john) <=> ? [X0] : (quiet(X0) <~> humble(X0)) [input p14]
23. ~tall(lucy) [input hypothesis]
26. (~rich(lucy) & ~creative(lucy)) | ! [X0] : (humble(X0) <=> ~calm(X0)) [ennf transformation 3]
29. ! [X0] : (~creative(X0) | ~brave(X0)) [ennf transformation 5]
36. ! [X0] : (((~brave(X0) | ~calm(X0)) | (~strong(X0) | strong(X0))) & ((strong(X0) & ~strong(X0)) | (brave(X0) & calm(X0)))) [nnf transformation 1]
37. ! [X0] : ((~brave(X0) | ~calm(X0) | ~strong(X0) | strong(X0)) & ((strong(X0) & ~strong(X0)) | (brave(X0) & calm(X0)))) [flattening 36]
38. ! [X0] : ((creative(X0) | strong(X0)) & (~strong(X0) | ~creative(X0))) [nnf transformation 2]
39. (~rich(lucy) & ~creative(lucy)) | ! [X0] : ((humble(X0) | calm(X0)) & (~calm(X0) | ~humble(X0))) [nnf transformation 26]
41. ! [X0] : ((quiet(X0) | (creative(X0) & happy(X0))) & ((~creative(X0) | ~happy(X0)) | ~quiet(X0))) [nnf transformation 7]
42. ! [X0] : ((quiet(X0) | (creative(X0) & happy(X0))) & (~creative(X0) | ~happy(X0) | ~quiet(X0))) [flattening 41]
46. ! [X0] : (((~tall(X0) | ~calm(X0)) | ~rich(X0)) & (rich(X0) | (tall(X0) & calm(X0)))) [nnf transformation 11]
47. ! [X0] : ((~tall(X0) | ~calm(X0) | ~rich(X0)) & (rich(X0) | (tall(X0) & calm(X0)))) [flattening 46]
53. (~strong(john) | ! [X0] : ((quiet(X0) | ~humble(X0)) & (humble(X0) | ~quiet(X0)))) & (? [X0] : ((~humble(X0) | ~quiet(X0)) & (humble(X0) | quiet(X0))) | strong(john)) [nnf transformation 15]
54. (~strong(john) | ! [X0] : ((quiet(X0) | ~humble(X0)) & (humble(X0) | ~quiet(X0)))) & (? [X1] : ((~humble(X1) | ~quiet(X1)) & (humble(X1) | quiet(X1))) | strong(john)) [rectify 53]
55. ? [X1] : ((~humble(X1) | ~quiet(X1)) & (humble(X1) | quiet(X1))) => ((~humble(sK1) | ~quiet(sK1)) & (humble(sK1) | quiet(sK1))) [choice axiom]
56. (~strong(john) | ! [X0] : ((quiet(X0) | ~humble(X0)) & (humble(X0) | ~quiet(X0)))) & (((~humble(sK1) | ~quiet(sK1)) & (humble(sK1) | quiet(sK1))) | strong(john)) [skolemisation 54,55]
67. ~strong(X0) | calm(X0) [cnf transformation 37]
68. ~strong(X0) | brave(X0) [cnf transformation 37]
69. strong(X0) | calm(X0) [cnf transformation 37]
70. strong(X0) | brave(X0) [cnf transformation 37]
73. creative(X0) | strong(X0) [cnf transformation 38]
76. ~rich(lucy) | ~calm(X0) | ~humble(X0) [cnf transformation 39]
80. ~creative(X0) | ~brave(X0) [cnf transformation 29]
85. quiet(X0) | creative(X0) [cnf transformation 42]
95. tall(X0) | rich(X0) [cnf transformation 47]
106. ~strong(john) | humble(X0) | ~quiet(X0) [cnf transformation 56]
118. ~tall(lucy) [cnf transformation 23]
119. brave(X0) [subsumption resolution 68,70]
120. calm(X0) [subsumption resolution 67,69]
121. ~rich(lucy) | ~humble(X0) [subsumption resolution 76,120]
123. 1 <=> ! [X0] : ~humble(X0) [avatar definition]
124. ~humble(X0) <- (1) [avatar component clause 123]
126. 2 <=> rich(lucy) [avatar definition]
129. 1 | ~2 [avatar split clause 121,126,123]
150. ~creative(X0) [subsumption resolution 80,119]
152. quiet(X0) [subsumption resolution 85,150]
179. ~strong(john) | humble(X0) [subsumption resolution 106,152]
181. 12 <=> ! [X0] : humble(X0) [avatar definition]
182. humble(X0) <- (12) [avatar component clause 181]
184. 13 <=> strong(john) [avatar definition]
186. ~strong(john) <- (~13) [avatar component clause 184]
187. 12 | ~13 [avatar split clause 179,184,181]
227. strong(X1) [resolution 73,150]
229. $false <- (~13) [resolution 227,186]
230. 13 [avatar contradiction clause 229]
233. rich(lucy) [resolution 95,118]
236. 2 [avatar split clause 233,126]
237. $false <- (1, 12) [subsumption resolution 124,182]
238. ~1 | ~12 [avatar contradiction clause 237]
239. $false [avatar sat refutation 129,187,230,236,238]
% SZS output end Proof for 7405808642022735605195849
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either quiet or not generous is both not humble and not creative. If someone is both wise and creative then someone is happy or not generous and vice versa. Everyone who is rich or wise is not creative or happy and vice versa. Everyone who is either not patient or not brave is creative or not tall. Everyone who is funny is not quiet or rich and vice versa. If lucy is wise then someone is both wise and not patient. Everyone who is happy or not calm is both not strong and humble and vice versa. Everyone who is tall or not brave is either rich or not curious and vice versa. Everyone who is rich or tall is either not curious or happy and vice versa. Everyone who is either calm or not humble is rich or brave and vice versa. Everyone who is not curious is either not tall or humble. Everyone who is both not brave and not old is either not calm or not wise and vice versa. If someone is both not generous and not strong then alice is either strong or patient and vice versa. If lucy is either old or humble then someone is both old and not kind and vice versa. Everyone who is not wise or creative is curious or not kind and vice versa. Alice is not wise or not old. Someone is both not kind and quiet. Susan is patient. Someone is both happy and curious. Susan is not old or not brave. Someone is either not generous or not curious. Mary is old or not patient. Someone is either not patient or tall. | Susan is curious. | neutral | (![X]:((quiet(X)<~>~generous(X))=>(~humble(X)&~creative(X))))&
((?[X]:((wise(X)&creative(X))))<=>(?[X]:((happy(X)|~generous(X)))))&
(![X]:((rich(X)|wise(X))<=>(~creative(X)|happy(X))))&
(![X]:((~patient(X)<~>~brave(X))=>(creative(X)|~tall(X))))&
(![X]:(funny(X)<=>(~quiet(X)|rich(X))))&
((wise(lucy))=>(?[X]:((wise(X)&~patient(X)))))&
(![X]:((happy(X)|~calm(X))<=>(~strong(X)&humble(X))))&
(![X]:((tall(X)|~brave(X))<=>(rich(X)<~>~curious(X))))&
(![X]:((rich(X)|tall(X))<=>(~curious(X)<~>happy(X))))&
(![X]:((calm(X)<~>~humble(X))<=>(rich(X)|brave(X))))&
(![X]:(~curious(X)=>(~tall(X)<~>humble(X))))&
(![X]:((~brave(X)&~old(X))<=>(~calm(X)<~>~wise(X))))&
((?[X]:((~generous(X)&~strong(X))))<=>((strong(alice)<~>patient(alice))))&
(((old(lucy)<~>humble(lucy)))<=>(?[X]:((old(X)&~kind(X)))))&
(![X]:((~wise(X)|creative(X))<=>(curious(X)|~kind(X))))&
((~wise(alice)|~old(alice)))&
(?[X]:((~kind(X)&quiet(X))))&
(patient(susan))&
(?[X]:((happy(X)&curious(X))))&
((~old(susan)|~brave(susan)))&
(?[X]:((~generous(X)<~>~curious(X))))&
((old(mary)|~patient(mary)))&
(?[X]:((~patient(X)<~>tall(X)))) | curious(susan) | [] | null | 0 |
Everyone who is either creative or brave is not curious and vice versa. If mary is both not creative and not curious then lucy is either old or not generous. Everyone who is not kind or not patient is not humble or wise. If lucy is either not calm or not kind then fred is either kind or curious and vice versa. Everyone who is not patient or brave is either calm or not happy and vice versa. If someone is either tall or happy then alice is patient or not happy and vice versa. Everyone who is either not rich or not old is either not humble or funny. Everyone who is not happy or not creative is kind or humble. If mary is either not strong or rich then someone is either funny or not brave. Everyone who is creative or not quiet is both not patient and not tall and vice versa. If susan is either rich or not funny then fred is either old or rich. Everyone who is both not tall and not funny is both patient and not old. Everyone who is either rich or not humble is not kind or rich. Everyone who is not quiet is either not strong or not creative. Everyone who is either strong or rich is rich or patient and vice versa. If someone is both kind and not wise then someone is tall or not humble. Someone is either brave or old. Alice is either not happy or calm. Someone is old or not wise. Fred is kind. Mary is not patient. Alice is not creative. Someone is not wise or not humble. | Fred is kind. | entailment | (![X]:((creative(X)<~>brave(X))<=>~curious(X)))&
(((~creative(mary)&~curious(mary)))=>((old(lucy)<~>~generous(lucy))))&
(![X]:((~kind(X)|~patient(X))=>(~humble(X)|wise(X))))&
(((~calm(lucy)<~>~kind(lucy)))<=>((kind(fred)<~>curious(fred))))&
(![X]:((~patient(X)|brave(X))<=>(calm(X)<~>~happy(X))))&
((?[X]:((tall(X)<~>happy(X))))<=>((patient(alice)|~happy(alice))))&
(![X]:((~rich(X)<~>~old(X))=>(~humble(X)<~>funny(X))))&
(![X]:((~happy(X)|~creative(X))=>(kind(X)|humble(X))))&
(((~strong(mary)<~>rich(mary)))=>(?[X]:((funny(X)<~>~brave(X)))))&
(![X]:((creative(X)|~quiet(X))<=>(~patient(X)&~tall(X))))&
(((rich(susan)<~>~funny(susan)))=>((old(fred)<~>rich(fred))))&
(![X]:((~tall(X)&~funny(X))=>(patient(X)&~old(X))))&
(![X]:((rich(X)<~>~humble(X))=>(~kind(X)|rich(X))))&
(![X]:(~quiet(X)=>(~strong(X)<~>~creative(X))))&
(![X]:((strong(X)<~>rich(X))<=>(rich(X)|patient(X))))&
((?[X]:((kind(X)&~wise(X))))=>(?[X]:((tall(X)|~humble(X)))))&
(?[X]:((brave(X)<~>old(X))))&
((~happy(alice)<~>calm(alice)))&
(?[X]:((old(X)|~wise(X))))&
(kind(fred))&
(~patient(mary))&
(~creative(alice))&
(?[X]:((~wise(X)|~humble(X)))) | kind(fred) | [
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 7236384203824749513683357
% SZS output start Proof for 7236384203824749513683357
20. kind(fred) [input p19]
24. ~kind(fred) [input hypothesis]
138. kind(fred) [cnf transformation 20]
142. ~kind(fred) [cnf transformation 24]
169. 6 <=> kind(fred) [avatar definition]
294. 6 [avatar split clause 138,169]
304. ~6 [avatar split clause 142,169]
305. $false [avatar sat refutation 294,304]
% SZS output end Proof for 7236384203824749513683357
% ------------------------------
% 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 rich is both not creative and happy.
Everyone who is not humble or rich is brave or not calm and vice versa.
If someone is both brave and not creative then someone is not patient.
Everyone who is both not kind and humble is generous or not strong and vice versa.
If susan is both not kind and calm then someone is either wise or not happy and vice versa.
If someone is not generous or not rich then paul is not funny and vice versa.
Everyone who is not quiet or not patient is either kind or not happy and vice versa.
If susan is both not calm and strong then alice is both not calm and not brave and vice versa.
Everyone who is not rich is curious or not rich.
If susan is not generous then someone is either happy or wise.
Everyone who is rich is tall.
Everyone who is not generous or not quiet is both kind and not tall and vice versa.
If someone is both tall and rich then susan is both creative and not kind and vice versa.
Everyone who is not happy or generous is happy and vice versa.
If someone is either not kind or curious then someone is not generous and vice versa.
If john is not brave then mary is either not old or not quiet.
Paul is patient.
Someone is creative.
Someone is either not old or humble.
Someone is either old or quiet. | Susan is happy. | entailment | (![X]:(rich(X)=>(~creative(X)&happy(X))))&
(![X]:((~humble(X)|rich(X))<=>(brave(X)|~calm(X))))&
((?[X]:((brave(X)&~creative(X))))=>(?[X]:(~patient(X))))&
(![X]:((~kind(X)&humble(X))<=>(generous(X)|~strong(X))))&
(((~kind(susan)&calm(susan)))<=>(?[X]:((wise(X)<~>~happy(X)))))&
((?[X]:((~generous(X)|~rich(X))))<=>(~funny(paul)))&
(![X]:((~quiet(X)|~patient(X))<=>(kind(X)<~>~happy(X))))&
(((~calm(susan)&strong(susan)))<=>((~calm(alice)&~brave(alice))))&
(![X]:(~rich(X)=>(curious(X)|~rich(X))))&
((~generous(susan))=>(?[X]:((happy(X)<~>wise(X)))))&
(![X]:(rich(X)=>tall(X)))&
(![X]:((~generous(X)|~quiet(X))<=>(kind(X)&~tall(X))))&
((?[X]:((tall(X)&rich(X))))<=>((creative(susan)&~kind(susan))))&
(![X]:((~happy(X)|generous(X))<=>happy(X)))&
((?[X]:((~kind(X)<~>curious(X))))<=>(?[X]:(~generous(X))))&
((~brave(john))=>((~old(mary)<~>~quiet(mary))))&
(patient(paul))&
(?[X]:(creative(X)))&
(?[X]:((~old(X)<~>humble(X))))&
(?[X]:((old(X)<~>quiet(X)))) | happy(susan) | [
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 7825563659859307538376760
% SZS output start Proof for 7825563659859307538376760
14. ! [X0] : ((generous(X0) | ~happy(X0)) <=> happy(X0)) [input p13]
21. ~happy(susan) [input hypothesis]
61. ! [X0] : (((generous(X0) | ~happy(X0)) | ~happy(X0)) & (happy(X0) | (~generous(X0) & happy(X0)))) [nnf transformation 14]
62. ! [X0] : ((generous(X0) | ~happy(X0) | ~happy(X0)) & (happy(X0) | (~generous(X0) & happy(X0)))) [flattening 61]
121. happy(X0) | happy(X0) [cnf transformation 62]
136. ~happy(susan) [cnf transformation 21]
137. happy(X0) [duplicate literal removal 121]
303. $false [subsumption resolution 136,137]
% SZS output end Proof for 7825563659859307538376760
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not quiet or calm is both patient and kind.
Everyone who is not wise or not kind is either not brave or old.
If someone is brave then someone is not rich or not kind and vice versa.
Everyone who is both not patient and not quiet is not humble.
If someone is both brave and calm then someone is not quiet or old.
If paul is both not generous and funny then mary is either not calm or curious.
Everyone who is kind or not wise is both strong and rich.
If someone is both strong and not calm then someone is strong or calm.
Everyone who is strong or not creative is not brave.
If someone is either kind or not old then susan is both funny and calm.
If someone is both not creative and generous then someone is both wise and not kind and vice versa.
Everyone who is quiet or not funny is both generous and not old and vice versa.
If john is rich then mary is either not brave or not wise.
If alice is not calm or funny then susan is happy or creative.
If paul is either not old or not wise then someone is both funny and not strong and vice versa.
Everyone who is either quiet or not generous is not wise and vice versa.
Someone is both curious and not patient.
John is either not rich or rich.
Someone is funny or not brave.
Someone is either quiet or not happy.
Someone is either not kind or not strong.
Susan is not happy or not funny.
Alice is both funny and wise.
Mary is both not tall and happy. | Susan is creative. | entailment | (![X]:((~quiet(X)<~>calm(X))=>(patient(X)&kind(X))))&
(![X]:((~wise(X)|~kind(X))=>(~brave(X)<~>old(X))))&
((?[X]:(brave(X)))<=>(?[X]:((~rich(X)|~kind(X)))))&
(![X]:((~patient(X)&~quiet(X))=>~humble(X)))&
((?[X]:((brave(X)&calm(X))))=>(?[X]:((~quiet(X)|old(X)))))&
(((~generous(paul)&funny(paul)))=>((~calm(mary)<~>curious(mary))))&
(![X]:((kind(X)|~wise(X))=>(strong(X)&rich(X))))&
((?[X]:((strong(X)&~calm(X))))=>(?[X]:((strong(X)|calm(X)))))&
(![X]:((strong(X)|~creative(X))=>~brave(X)))&
((?[X]:((kind(X)<~>~old(X))))=>((funny(susan)&calm(susan))))&
((?[X]:((~creative(X)&generous(X))))<=>(?[X]:((wise(X)&~kind(X)))))&
(![X]:((quiet(X)|~funny(X))<=>(generous(X)&~old(X))))&
((rich(john))=>((~brave(mary)<~>~wise(mary))))&
(((~calm(alice)|funny(alice)))=>((happy(susan)|creative(susan))))&
(((~old(paul)<~>~wise(paul)))<=>(?[X]:((funny(X)&~strong(X)))))&
(![X]:((quiet(X)<~>~generous(X))<=>~wise(X)))&
(?[X]:((curious(X)&~patient(X))))&
((~rich(john)<~>rich(john)))&
(?[X]:((funny(X)|~brave(X))))&
(?[X]:((quiet(X)<~>~happy(X))))&
(?[X]:((~kind(X)<~>~strong(X))))&
((~happy(susan)|~funny(susan)))&
((funny(alice)&wise(alice)))&
((~tall(mary)&happy(mary))) | creative(susan) | [
"p1",
"p6",
"p8",
"p9",
"p13",
"p20",
"p21",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 7750307858978747683189025
% SZS output start Proof for 7750307858978747683189025
2. ! [X0] : ((~kind(X0) | ~wise(X0)) => (~brave(X0) <~> old(X0))) [input p1]
7. ! [X0] : ((~wise(X0) | kind(X0)) => (rich(X0) & strong(X0))) [input p6]
9. ! [X0] : ((~creative(X0) | strong(X0)) => ~brave(X0)) [input p8]
10. ? [X0] : (kind(X0) <~> ~old(X0)) => (calm(susan) & funny(susan)) [input p9]
14. (funny(alice) | ~calm(alice)) => (creative(susan) | happy(susan)) [input p13]
21. ? [X0] : (~kind(X0) <~> ~strong(X0)) [input p20]
22. ~funny(susan) | ~happy(susan) [input p21]
23. wise(alice) & funny(alice) [input p22]
25. ~creative(susan) [input hypothesis]
33. ! [X0] : ((~brave(X0) <~> old(X0)) | (kind(X0) & wise(X0))) [ennf transformation 2]
37. ! [X0] : ((rich(X0) & strong(X0)) | (wise(X0) & ~kind(X0))) [ennf transformation 7]
39. ! [X0] : (~brave(X0) | (creative(X0) & ~strong(X0))) [ennf transformation 9]
40. (calm(susan) & funny(susan)) | ! [X0] : (kind(X0) <=> ~old(X0)) [ennf transformation 10]
42. (creative(susan) | happy(susan)) | (~funny(alice) & calm(alice)) [ennf transformation 14]
43. creative(susan) | happy(susan) | (~funny(alice) & calm(alice)) [flattening 42]
45. ! [X0] : (((~old(X0) | brave(X0)) & (old(X0) | ~brave(X0))) | (kind(X0) & wise(X0))) [nnf transformation 33]
58. (calm(susan) & funny(susan)) | ! [X0] : ((kind(X0) | old(X0)) & (~old(X0) | ~kind(X0))) [nnf transformation 40]
80. ? [X0] : ((strong(X0) | kind(X0)) & (~strong(X0) | ~kind(X0))) [nnf transformation 21]
81. ? [X0] : ((strong(X0) | kind(X0)) & (~strong(X0) | ~kind(X0))) => ((strong(sK10) | kind(sK10)) & (~strong(sK10) | ~kind(sK10))) [choice axiom]
82. (strong(sK10) | kind(sK10)) & (~strong(sK10) | ~kind(sK10)) [skolemisation 80,81]
90. ~old(X0) | brave(X0) | kind(X0) [cnf transformation 45]
97. ~kind(X0) | strong(X0) [cnf transformation 37]
102. ~strong(X0) | ~brave(X0) [cnf transformation 39]
105. funny(susan) | kind(X0) | old(X0) [cnf transformation 58]
120. creative(susan) | happy(susan) | ~funny(alice) [cnf transformation 43]
138. ~strong(sK10) | ~kind(sK10) [cnf transformation 82]
139. strong(sK10) | kind(sK10) [cnf transformation 82]
140. ~funny(susan) | ~happy(susan) [cnf transformation 22]
141. funny(alice) [cnf transformation 23]
144. ~creative(susan) [cnf transformation 25]
212. 17 <=> ! [X0] : (kind(X0) | old(X0)) [avatar definition]
213. old(X0) | kind(X0) <- (17) [avatar component clause 212]
224. 20 <=> funny(susan) [avatar definition]
227. 17 | 20 [avatar split clause 105,224,212]
270. 30 <=> funny(alice) [avatar definition]
274. 31 <=> happy(susan) [avatar definition]
278. 32 <=> creative(susan) [avatar definition]
281. ~30 | 31 | 32 [avatar split clause 120,278,274,270]
333. strong(sK10) [subsumption resolution 139,97]
334. ~kind(sK10) [subsumption resolution 138,333]
335. ~31 | ~20 [avatar split clause 140,224,274]
336. 30 [avatar split clause 141,270]
337. ~32 [avatar split clause 144,278]
340. ~brave(sK10) [resolution 102,333]
437. brave(X0) | kind(X0) | kind(X0) <- (17) [resolution 90,213]
438. brave(X0) | kind(X0) <- (17) [duplicate literal removal 437]
514. kind(sK10) <- (17) [resolution 438,340]
518. $false <- (17) [subsumption resolution 514,334]
519. ~17 [avatar contradiction clause 518]
520. $false [avatar sat refutation 227,281,335,336,337,519]
% SZS output end Proof for 7750307858978747683189025
% ------------------------------
% 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 lucy is not tall or curious then fred is both wise and patient and vice versa.
If alice is not funny then someone is both not happy and funny.
Everyone who is not funny is not tall.
If susan is not funny or tall then paul is not humble or strong and vice versa.
Everyone who is either not humble or not funny is not tall and vice versa.
Everyone who is not kind is either not strong or wise.
If someone is wise or funny then someone is creative or kind.
If alice is not patient then alice is both not strong and creative.
If fred is both not wise and not brave then someone is either happy or not curious and vice versa.
Everyone who is either not strong or not brave is not tall.
If fred is either generous or not creative then someone is both humble and not kind.
Everyone who is not curious or not rich is old or not funny.
Everyone who is either not quiet or quiet is both not calm and tall.
If mary is calm then someone is either strong or humble and vice versa.
Everyone who is not wise is both not wise and not humble.
If john is both curious and not creative then someone is either creative or not kind.
Someone is either wise or not wise.
Fred is either not tall or not calm.
John is either creative or not curious.
Someone is not creative or curious.
Someone is not tall or patient.
Mary is either not strong or generous. | Lucy is not strong. | contradiction | (((~tall(lucy)|curious(lucy)))<=>((wise(fred)&patient(fred))))&
((~funny(alice))=>(?[X]:((~happy(X)&funny(X)))))&
(![X]:(~funny(X)=>~tall(X)))&
(((~funny(susan)|tall(susan)))<=>((~humble(paul)|strong(paul))))&
(![X]:((~humble(X)<~>~funny(X))<=>~tall(X)))&
(![X]:(~kind(X)=>(~strong(X)<~>wise(X))))&
((?[X]:((wise(X)|funny(X))))=>(?[X]:((creative(X)|kind(X)))))&
((~patient(alice))=>((~strong(alice)&creative(alice))))&
(((~wise(fred)&~brave(fred)))<=>(?[X]:((happy(X)<~>~curious(X)))))&
(![X]:((~strong(X)<~>~brave(X))=>~tall(X)))&
(((generous(fred)<~>~creative(fred)))=>(?[X]:((humble(X)&~kind(X)))))&
(![X]:((~curious(X)|~rich(X))=>(old(X)|~funny(X))))&
(![X]:((~quiet(X)<~>quiet(X))=>(~calm(X)&tall(X))))&
((calm(mary))<=>(?[X]:((strong(X)<~>humble(X)))))&
(![X]:(~wise(X)=>(~wise(X)&~humble(X))))&
(((curious(john)&~creative(john)))=>(?[X]:((creative(X)<~>~kind(X)))))&
(?[X]:((wise(X)<~>~wise(X))))&
((~tall(fred)<~>~calm(fred)))&
((creative(john)<~>~curious(john)))&
(?[X]:((~creative(X)|curious(X))))&
(?[X]:((~tall(X)|patient(X))))&
((~strong(mary)<~>generous(mary))) | ~strong(lucy) | [
"p2",
"p4",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 8312331820010104709490474
% SZS output start Proof for 8312331820010104709490474
3. ! [X0] : (~funny(X0) => ~tall(X0)) [input p2]
5. ! [X0] : ((~humble(X0) <~> ~funny(X0)) <=> ~tall(X0)) [input p4]
13. ! [X0] : ((~quiet(X0) <~> quiet(X0)) => (tall(X0) & ~calm(X0))) [input p12]
14. calm(mary) <=> ? [X0] : (strong(X0) <~> humble(X0)) [input p13]
23. ~strong(lucy) [input hypothesis]
27. ! [X0] : (~tall(X0) | funny(X0)) [ennf transformation 3]
33. ! [X0] : ((tall(X0) & ~calm(X0)) | (~quiet(X0) <=> quiet(X0))) [ennf transformation 13]
43. ! [X0] : ((((funny(X0) | humble(X0)) & (~funny(X0) | ~humble(X0))) | tall(X0)) & (~tall(X0) | ((~humble(X0) | funny(X0)) & (~funny(X0) | humble(X0))))) [nnf transformation 5]
57. ! [X0] : ((tall(X0) & ~calm(X0)) | ((~quiet(X0) | ~quiet(X0)) & (quiet(X0) | quiet(X0)))) [nnf transformation 33]
58. (calm(mary) | ! [X0] : ((strong(X0) | ~humble(X0)) & (humble(X0) | ~strong(X0)))) & (? [X0] : ((~humble(X0) | ~strong(X0)) & (humble(X0) | strong(X0))) | ~calm(mary)) [nnf transformation 14]
59. (calm(mary) | ! [X0] : ((strong(X0) | ~humble(X0)) & (humble(X0) | ~strong(X0)))) & (? [X1] : ((~humble(X1) | ~strong(X1)) & (humble(X1) | strong(X1))) | ~calm(mary)) [rectify 58]
60. ? [X1] : ((~humble(X1) | ~strong(X1)) & (humble(X1) | strong(X1))) => ((~humble(sK4) | ~strong(sK4)) & (humble(sK4) | strong(sK4))) [choice axiom]
61. (calm(mary) | ! [X0] : ((strong(X0) | ~humble(X0)) & (humble(X0) | ~strong(X0)))) & (((~humble(sK4) | ~strong(sK4)) & (humble(sK4) | strong(sK4))) | ~calm(mary)) [skolemisation 59,60]
82. ~tall(X0) | funny(X0) [cnf transformation 27]
87. ~tall(X0) | ~funny(X0) | humble(X0) [cnf transformation 43]
90. funny(X0) | humble(X0) | tall(X0) [cnf transformation 43]
109. ~calm(X0) | quiet(X0) | quiet(X0) [cnf transformation 57]
110. ~calm(X0) | ~quiet(X0) | ~quiet(X0) [cnf transformation 57]
111. tall(X0) | quiet(X0) | quiet(X0) [cnf transformation 57]
112. tall(X0) | ~quiet(X0) | ~quiet(X0) [cnf transformation 57]
116. calm(mary) | strong(X0) | ~humble(X0) [cnf transformation 61]
131. ~strong(lucy) [cnf transformation 23]
132. ~calm(X0) | quiet(X0) [duplicate literal removal 109]
133. ~calm(X0) | ~quiet(X0) [duplicate literal removal 110]
134. tall(X0) | quiet(X0) [duplicate literal removal 111]
135. ~quiet(X0) | tall(X0) [duplicate literal removal 112]
191. humble(X0) | funny(X0) [subsumption resolution 90,82]
192. ~tall(X0) | humble(X0) [subsumption resolution 87,191]
267. tall(X0) [subsumption resolution 134,135]
268. ~calm(X0) [subsumption resolution 132,133]
269. ~humble(X0) | strong(X0) [subsumption resolution 116,268]
316. humble(X0) [resolution 192,267]
327. strong(X0) [resolution 269,316]
329. $false [resolution 327,131]
% SZS output end Proof for 8312331820010104709490474
% ------------------------------
% 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 kind is either not generous or not wise.
Everyone who is both curious and not creative is both not rich and old and vice versa.
Everyone who is either rich or not kind is old or not wise and vice versa.
Everyone who is both not patient and not wise is funny and vice versa.
Everyone who is not curious or funny is both not calm and wise.
Everyone who is old or not strong is tall.
Everyone who is either not old or not quiet is not curious.
If alice is wise or quiet then someone is either tall or curious.
Everyone who is not kind is both strong and calm.
Everyone who is not creative is not brave and vice versa.
Everyone who is both not quiet and not patient is patient or not calm.
Everyone who is humble or quiet is either old or not happy.
Everyone who is not funny is both rich and not wise.
Everyone who is not funny is funny or patient and vice versa.
Everyone who is not tall or happy is rich or strong.
John is not funny.
Someone is either not strong or not tall.
Someone is not tall or not brave.
Lucy is both happy and humble.
John is not calm or not old.
Susan is not curious or not strong. | John is patient. | entailment | (![X]:(kind(X)=>(~generous(X)<~>~wise(X))))&
(![X]:((curious(X)&~creative(X))<=>(~rich(X)&old(X))))&
(![X]:((rich(X)<~>~kind(X))<=>(old(X)|~wise(X))))&
(![X]:((~patient(X)&~wise(X))<=>funny(X)))&
(![X]:((~curious(X)|funny(X))=>(~calm(X)&wise(X))))&
(![X]:((old(X)|~strong(X))=>tall(X)))&
(![X]:((~old(X)<~>~quiet(X))=>~curious(X)))&
(((wise(alice)|quiet(alice)))=>(?[X]:((tall(X)<~>curious(X)))))&
(![X]:(~kind(X)=>(strong(X)&calm(X))))&
(![X]:(~creative(X)<=>~brave(X)))&
(![X]:((~quiet(X)&~patient(X))=>(patient(X)|~calm(X))))&
(![X]:((humble(X)|quiet(X))=>(old(X)<~>~happy(X))))&
(![X]:(~funny(X)=>(rich(X)&~wise(X))))&
(![X]:(~funny(X)<=>(funny(X)|patient(X))))&
(![X]:((~tall(X)|happy(X))=>(rich(X)|strong(X))))&
(~funny(john))&
(?[X]:((~strong(X)<~>~tall(X))))&
(?[X]:((~tall(X)|~brave(X))))&
((happy(lucy)&humble(lucy)))&
((~calm(john)|~old(john)))&
((~curious(susan)|~strong(susan))) | patient(john) | [
"p3",
"p4",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 2557399408771670913847234
% SZS output start Proof for 2557399408771670913847234
4. ! [X0] : ((~wise(X0) & ~patient(X0)) <=> funny(X0)) [input p3]
5. ! [X0] : ((funny(X0) | ~curious(X0)) => (wise(X0) & ~calm(X0))) [input p4]
14. ! [X0] : (~funny(X0) <=> (patient(X0) | funny(X0))) [input p13]
22. ~patient(john) [input hypothesis]
24. ! [X0] : ((wise(X0) & ~calm(X0)) | (~funny(X0) & curious(X0))) [ennf transformation 5]
40. ! [X0] : (((~wise(X0) & ~patient(X0)) | ~funny(X0)) & (funny(X0) | (wise(X0) | patient(X0)))) [nnf transformation 4]
41. ! [X0] : (((~wise(X0) & ~patient(X0)) | ~funny(X0)) & (funny(X0) | wise(X0) | patient(X0))) [flattening 40]
48. ! [X0] : ((~funny(X0) | (~patient(X0) & ~funny(X0))) & ((patient(X0) | funny(X0)) | funny(X0))) [nnf transformation 14]
49. ! [X0] : ((~funny(X0) | (~patient(X0) & ~funny(X0))) & (patient(X0) | funny(X0) | funny(X0))) [flattening 48]
69. ~wise(X0) | ~funny(X0) [cnf transformation 41]
73. wise(X0) | ~funny(X0) [cnf transformation 24]
93. patient(X0) | funny(X0) | funny(X0) [cnf transformation 49]
106. ~patient(john) [cnf transformation 22]
107. patient(X0) | funny(X0) [duplicate literal removal 93]
110. ~funny(X0) [subsumption resolution 73,69]
133. patient(X0) [subsumption resolution 107,110]
170. $false [subsumption resolution 106,133]
% SZS output end Proof for 2557399408771670913847234
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 4989
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not wise or not rich then alice is either not rich or brave and vice versa.
If john is either strong or not curious then someone is tall.
Everyone who is both not kind and not creative is wise or kind and vice versa.
Everyone who is either not wise or not quiet is not curious.
If someone is not strong then someone is not kind or curious and vice versa.
Everyone who is both not quiet and funny is both strong and not generous and vice versa.
If paul is rich then lucy is either not strong or not quiet.
Everyone who is either wise or not generous is either calm or not curious.
Everyone who is rich or creative is strong.
Everyone who is not generous or calm is both calm and funny and vice versa.
If paul is either not rich or not kind then someone is either generous or not tall and vice versa.
Everyone who is both calm and patient is either not calm or not kind.
Everyone who is quiet is not humble.
Everyone who is both not funny and not strong is either not old or not creative and vice versa.
If mary is both strong and brave then mary is both not strong and tall and vice versa.
Everyone who is both not strong and not tall is not rich or not curious and vice versa.
Someone is either patient or not rich.
Someone is either not happy or not curious.
Someone is old.
Mary is not generous or creative.
Someone is both old and not humble.
Someone is both happy and strong.
Someone is either strong or not wise.
Mary is both not kind and generous. | Mary is not old. | contradiction | ((?[X]:((~wise(X)<~>~rich(X))))<=>((~rich(alice)<~>brave(alice))))&
(((strong(john)<~>~curious(john)))=>(?[X]:(tall(X))))&
(![X]:((~kind(X)&~creative(X))<=>(wise(X)|kind(X))))&
(![X]:((~wise(X)<~>~quiet(X))=>~curious(X)))&
((?[X]:(~strong(X)))<=>(?[X]:((~kind(X)|curious(X)))))&
(![X]:((~quiet(X)&funny(X))<=>(strong(X)&~generous(X))))&
((rich(paul))=>((~strong(lucy)<~>~quiet(lucy))))&
(![X]:((wise(X)<~>~generous(X))=>(calm(X)<~>~curious(X))))&
(![X]:((rich(X)|creative(X))=>strong(X)))&
(![X]:((~generous(X)|calm(X))<=>(calm(X)&funny(X))))&
(((~rich(paul)<~>~kind(paul)))<=>(?[X]:((generous(X)<~>~tall(X)))))&
(![X]:((calm(X)&patient(X))=>(~calm(X)<~>~kind(X))))&
(![X]:(quiet(X)=>~humble(X)))&
(![X]:((~funny(X)&~strong(X))<=>(~old(X)<~>~creative(X))))&
(((strong(mary)&brave(mary)))<=>((~strong(mary)&tall(mary))))&
(![X]:((~strong(X)&~tall(X))<=>(~rich(X)|~curious(X))))&
(?[X]:((patient(X)<~>~rich(X))))&
(?[X]:((~happy(X)<~>~curious(X))))&
(?[X]:(old(X)))&
((~generous(mary)|creative(mary)))&
(?[X]:((old(X)&~humble(X))))&
(?[X]:((happy(X)&strong(X))))&
(?[X]:((strong(X)<~>~wise(X))))&
((~kind(mary)&generous(mary))) | ~old(mary) | [
"p8",
"p13",
"p19",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 363324029773646151512527
% SZS output start Proof for 363324029773646151512527
9. ! [X0] : ((creative(X0) | rich(X0)) => strong(X0)) [input p8]
14. ! [X0] : ((~strong(X0) & ~funny(X0)) <=> (~old(X0) <~> ~creative(X0))) [input p13]
20. creative(mary) | ~generous(mary) [input p19]
24. generous(mary) & ~kind(mary) [input p23]
25. ~old(mary) [input hypothesis]
33. ! [X0] : (strong(X0) | (~creative(X0) & ~rich(X0))) [ennf transformation 9]
62. ! [X0] : (((~strong(X0) & ~funny(X0)) | ((~old(X0) | creative(X0)) & (~creative(X0) | old(X0)))) & (((creative(X0) | old(X0)) & (~creative(X0) | ~old(X0))) | (strong(X0) | funny(X0)))) [nnf transformation 14]
63. ! [X0] : (((~strong(X0) & ~funny(X0)) | ((~old(X0) | creative(X0)) & (~creative(X0) | old(X0)))) & (((creative(X0) | old(X0)) & (~creative(X0) | ~old(X0))) | strong(X0) | funny(X0))) [flattening 62]
114. ~creative(X0) | strong(X0) [cnf transformation 33]
134. ~strong(X0) | ~creative(X0) | old(X0) [cnf transformation 63]
150. creative(mary) | ~generous(mary) [cnf transformation 20]
157. generous(mary) [cnf transformation 24]
158. ~old(mary) [cnf transformation 25]
255. ~creative(X0) | old(X0) [subsumption resolution 134,114]
294. 26 <=> generous(mary) [avatar definition]
298. 27 <=> creative(mary) [avatar definition]
300. creative(mary) <- (27) [avatar component clause 298]
301. ~26 | 27 [avatar split clause 150,298,294]
312. 26 [avatar split clause 157,294]
336. old(mary) <- (27) [resolution 255,300]
338. $false <- (27) [subsumption resolution 336,158]
339. ~27 [avatar contradiction clause 338]
340. $false [avatar sat refutation 301,312,339]
% SZS output end Proof for 363324029773646151512527
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not creative or not brave then lucy is both not calm and not happy and vice versa. Everyone who is either not curious or not old is not creative or not curious and vice versa. Everyone who is both not old and not humble is both creative and patient. If john is not wise then mary is either not quiet or calm. Everyone who is not wise is not rich and vice versa. Everyone who is not creative is kind or quiet and vice versa. Everyone who is both not happy and funny is either tall or brave and vice versa. Everyone who is either old or not kind is creative. Everyone who is both not quiet and not brave is both not quiet and curious and vice versa. If paul is tall then fred is either old or creative. Everyone who is not brave or curious is both strong and not kind. Everyone who is humble or not generous is both not curious and happy. If someone is not rich or patient then mary is brave. Everyone who is either quiet or wise is not quiet and vice versa. If fred is both not curious and not calm then someone is either not humble or not tall. Everyone who is happy is either not generous or not rich. Someone is wise. Someone is either creative or humble. Someone is both generous and not funny. Mary is not brave or tall. Someone is rich or not happy. John is either not kind or patient. | Mary is funny. | neutral | ((?[X]:((~creative(X)<~>~brave(X))))<=>((~calm(lucy)&~happy(lucy))))&
(![X]:((~curious(X)<~>~old(X))<=>(~creative(X)|~curious(X))))&
(![X]:((~old(X)&~humble(X))=>(creative(X)&patient(X))))&
((~wise(john))=>((~quiet(mary)<~>calm(mary))))&
(![X]:(~wise(X)<=>~rich(X)))&
(![X]:(~creative(X)<=>(kind(X)|quiet(X))))&
(![X]:((~happy(X)&funny(X))<=>(tall(X)<~>brave(X))))&
(![X]:((old(X)<~>~kind(X))=>creative(X)))&
(![X]:((~quiet(X)&~brave(X))<=>(~quiet(X)&curious(X))))&
((tall(paul))=>((old(fred)<~>creative(fred))))&
(![X]:((~brave(X)|curious(X))=>(strong(X)&~kind(X))))&
(![X]:((humble(X)|~generous(X))=>(~curious(X)&happy(X))))&
((?[X]:((~rich(X)|patient(X))))=>(brave(mary)))&
(![X]:((quiet(X)<~>wise(X))<=>~quiet(X)))&
(((~curious(fred)&~calm(fred)))=>(?[X]:((~humble(X)<~>~tall(X)))))&
(![X]:(happy(X)=>(~generous(X)<~>~rich(X))))&
(?[X]:(wise(X)))&
(?[X]:((creative(X)<~>humble(X))))&
(?[X]:((generous(X)&~funny(X))))&
((~brave(mary)|tall(mary)))&
(?[X]:((rich(X)|~happy(X))))&
((~kind(john)<~>patient(john))) | funny(mary) | [] | null | 0 |
If someone is patient or old then john is not funny or happy and vice versa.
Everyone who is both old and not kind is either rich or curious.
Everyone who is tall is not patient or not rich.
If someone is generous then someone is patient.
If someone is tall or not patient then lucy is tall or old.
Everyone who is either kind or wise is not strong or tall and vice versa.
Everyone who is patient or generous is not old or not tall.
If someone is either not tall or not wise then someone is both generous and not wise.
Everyone who is either not strong or not patient is either humble or not old.
Everyone who is both kind and rich is old or not brave and vice versa.
Everyone who is not patient or patient is both not patient and not calm and vice versa.
Everyone who is wise or not old is either not calm or not curious.
If susan is quiet then paul is either not patient or not kind and vice versa.
Everyone who is either strong or humble is calm.
Everyone who is calm is both patient and not wise.
Everyone who is both curious and not tall is tall.
Fred is not kind.
Someone is rich.
Susan is either not brave or happy.
John is either not brave or not patient.
Susan is either not brave or curious.
Someone is either kind or not strong. | Paul is not humble. | entailment | ((?[X]:((patient(X)|old(X))))<=>((~funny(john)|happy(john))))&
(![X]:((old(X)&~kind(X))=>(rich(X)<~>curious(X))))&
(![X]:(tall(X)=>(~patient(X)|~rich(X))))&
((?[X]:(generous(X)))=>(?[X]:(patient(X))))&
((?[X]:((tall(X)|~patient(X))))=>((tall(lucy)|old(lucy))))&
(![X]:((kind(X)<~>wise(X))<=>(~strong(X)|tall(X))))&
(![X]:((patient(X)|generous(X))=>(~old(X)|~tall(X))))&
((?[X]:((~tall(X)<~>~wise(X))))=>(?[X]:((generous(X)&~wise(X)))))&
(![X]:((~strong(X)<~>~patient(X))=>(humble(X)<~>~old(X))))&
(![X]:((kind(X)&rich(X))<=>(old(X)|~brave(X))))&
(![X]:((~patient(X)|patient(X))<=>(~patient(X)&~calm(X))))&
(![X]:((wise(X)|~old(X))=>(~calm(X)<~>~curious(X))))&
((quiet(susan))<=>((~patient(paul)<~>~kind(paul))))&
(![X]:((strong(X)<~>humble(X))=>calm(X)))&
(![X]:(calm(X)=>(patient(X)&~wise(X))))&
(![X]:((curious(X)&~tall(X))=>tall(X)))&
(~kind(fred))&
(?[X]:(rich(X)))&
((~brave(susan)<~>happy(susan)))&
((~brave(john)<~>~patient(john)))&
((~brave(susan)<~>curious(susan)))&
(?[X]:((kind(X)<~>~strong(X)))) | ~humble(paul) | [
"p3",
"p5",
"p7",
"p8",
"p9",
"p10",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 7174256869705566356440760
% SZS output start Proof for 7174256869705566356440760
4. ? [X0] : generous(X0) => ? [X0] : patient(X0) [input p3]
6. ! [X0] : ((kind(X0) <~> wise(X0)) <=> (tall(X0) | ~strong(X0))) [input p5]
8. ? [X0] : (~tall(X0) <~> ~wise(X0)) => ? [X0] : (~wise(X0) & generous(X0)) [input p7]
9. ! [X0] : ((~strong(X0) <~> ~patient(X0)) => (humble(X0) <~> ~old(X0))) [input p8]
10. ! [X0] : ((rich(X0) & kind(X0)) <=> (~brave(X0) | old(X0))) [input p9]
11. ! [X0] : ((patient(X0) | ~patient(X0)) <=> (~calm(X0) & ~patient(X0))) [input p10]
14. ! [X0] : ((strong(X0) <~> humble(X0)) => calm(X0)) [input p13]
23. humble(paul) [input hypothesis]
24. ? [X0] : generous(X0) => ? [X1] : patient(X1) [rectify 4]
25. ? [X0] : (~tall(X0) <~> ~wise(X0)) => ? [X1] : (~wise(X1) & generous(X1)) [rectify 8]
30. ? [X1] : patient(X1) | ! [X0] : ~generous(X0) [ennf transformation 24]
35. ? [X1] : (~wise(X1) & generous(X1)) | ! [X0] : (~tall(X0) <=> ~wise(X0)) [ennf transformation 25]
36. ! [X0] : ((humble(X0) <~> ~old(X0)) | (~strong(X0) <=> ~patient(X0))) [ennf transformation 9]
38. ! [X0] : (calm(X0) | (strong(X0) <=> humble(X0))) [ennf transformation 14]
48. ? [X0] : patient(X0) | ! [X1] : ~generous(X1) [rectify 30]
49. ? [X0] : patient(X0) => patient(sK1) [choice axiom]
50. patient(sK1) | ! [X1] : ~generous(X1) [skolemisation 48,49]
51. ! [X0] : ((((~wise(X0) | ~kind(X0)) & (wise(X0) | kind(X0))) | (~tall(X0) & strong(X0))) & ((tall(X0) | ~strong(X0)) | ((kind(X0) | ~wise(X0)) & (wise(X0) | ~kind(X0))))) [nnf transformation 6]
52. ! [X0] : ((((~wise(X0) | ~kind(X0)) & (wise(X0) | kind(X0))) | (~tall(X0) & strong(X0))) & (tall(X0) | ~strong(X0) | ((kind(X0) | ~wise(X0)) & (wise(X0) | ~kind(X0))))) [flattening 51]
53. ? [X1] : (~wise(X1) & generous(X1)) | ! [X0] : ((~tall(X0) | wise(X0)) & (~wise(X0) | tall(X0))) [nnf transformation 35]
54. ? [X0] : (~wise(X0) & generous(X0)) | ! [X1] : ((~tall(X1) | wise(X1)) & (~wise(X1) | tall(X1))) [rectify 53]
55. ? [X0] : (~wise(X0) & generous(X0)) => (~wise(sK2) & generous(sK2)) [choice axiom]
56. (~wise(sK2) & generous(sK2)) | ! [X1] : ((~tall(X1) | wise(X1)) & (~wise(X1) | tall(X1))) [skolemisation 54,55]
57. ! [X0] : (((old(X0) | ~humble(X0)) & (~old(X0) | humble(X0))) | ((~strong(X0) | patient(X0)) & (~patient(X0) | strong(X0)))) [nnf transformation 36]
58. ! [X0] : (((rich(X0) & kind(X0)) | (brave(X0) & ~old(X0))) & ((~brave(X0) | old(X0)) | (~rich(X0) | ~kind(X0)))) [nnf transformation 10]
59. ! [X0] : (((rich(X0) & kind(X0)) | (brave(X0) & ~old(X0))) & (~brave(X0) | old(X0) | ~rich(X0) | ~kind(X0))) [flattening 58]
60. ! [X0] : (((patient(X0) | ~patient(X0)) | (calm(X0) | patient(X0))) & ((~calm(X0) & ~patient(X0)) | (~patient(X0) & patient(X0)))) [nnf transformation 11]
61. ! [X0] : ((patient(X0) | ~patient(X0) | calm(X0) | patient(X0)) & ((~calm(X0) & ~patient(X0)) | (~patient(X0) & patient(X0)))) [flattening 60]
64. ! [X0] : (calm(X0) | ((strong(X0) | ~humble(X0)) & (humble(X0) | ~strong(X0)))) [nnf transformation 38]
80. patient(sK1) | ~generous(X1) [cnf transformation 50]
83. ~strong(X0) | tall(X0) | wise(X0) | ~kind(X0) [cnf transformation 52]
88. ~wise(X0) | ~kind(X0) | ~tall(X0) [cnf transformation 52]
91. generous(sK2) | ~wise(X1) | tall(X1) [cnf transformation 56]
92. generous(sK2) | ~tall(X1) | wise(X1) [cnf transformation 56]
98. ~humble(X0) | old(X0) | ~strong(X0) | patient(X0) [cnf transformation 57]
100. ~old(X0) | kind(X0) [cnf transformation 59]
105. ~patient(X0) | ~patient(X0) [cnf transformation 61]
106. ~calm(X0) | patient(X0) [cnf transformation 61]
107. ~calm(X0) | ~patient(X0) [cnf transformation 61]
118. calm(X0) | strong(X0) | ~humble(X0) [cnf transformation 64]
132. humble(paul) [cnf transformation 23]
134. ~patient(X0) [duplicate literal removal 105]
159. 6 <=> ! [X1] : ~patient(X1) [avatar definition]
160. ~patient(X1) <- (6) [avatar component clause 159]
163. 7 <=> ! [X1] : ~generous(X1) [avatar definition]
164. ~generous(X1) <- (7) [avatar component clause 163]
166. 8 <=> patient(sK1) [avatar definition]
168. patient(sK1) <- (8) [avatar component clause 166]
169. 7 | 8 [avatar split clause 80,166,163]
187. 13 <=> ! [X1] : (~tall(X1) | wise(X1)) [avatar definition]
188. ~tall(X1) | wise(X1) <- (13) [avatar component clause 187]
195. 15 <=> ! [X1] : (~wise(X1) | tall(X1)) [avatar definition]
196. ~wise(X1) | tall(X1) <- (15) [avatar component clause 195]
199. 16 <=> generous(sK2) [avatar definition]
201. generous(sK2) <- (16) [avatar component clause 199]
202. 13 | 16 [avatar split clause 92,199,187]
203. 15 | 16 [avatar split clause 91,199,195]
204. ~calm(X0) [subsumption resolution 106,107]
205. 6 [avatar split clause 134,159]
209. 17 <=> kind(paul) [avatar definition]
210. ~kind(paul) <- (~17) [avatar component clause 209]
211. kind(paul) <- (17) [avatar component clause 209]
213. 18 <=> patient(paul) [avatar definition]
214. patient(paul) <- (18) [avatar component clause 213]
215. ~patient(paul) <- (~18) [avatar component clause 213]
224. ~humble(X0) | strong(X0) [subsumption resolution 118,204]
275. strong(paul) [resolution 224,132]
321. tall(paul) | wise(paul) | ~kind(paul) [resolution 83,275]
333. old(paul) | ~strong(paul) | patient(paul) [resolution 98,132]
335. old(paul) | patient(paul) [subsumption resolution 333,275]
336. old(paul) <- (~18) [subsumption resolution 335,215]
340. kind(paul) <- (~18) [resolution 336,100]
352. $false <- (~17, ~18) [subsumption resolution 340,210]
353. 17 | 18 [avatar contradiction clause 352]
354. wise(paul) | ~kind(paul) <- (13) [subsumption resolution 321,188]
356. 31 <=> wise(paul) [avatar definition]
358. wise(paul) <- (31) [avatar component clause 356]
359. ~17 | 31 | ~13 [avatar split clause 354,187,356,209]
361. $false <- (6, 18) [subsumption resolution 214,160]
362. ~6 | ~18 [avatar contradiction clause 361]
363. tall(paul) | wise(paul) <- (17) [subsumption resolution 321,211]
364. tall(paul) <- (15, 17) [subsumption resolution 363,196]
368. $false <- (7, 16) [subsumption resolution 201,164]
369. ~7 | ~16 [avatar contradiction clause 368]
370. $false <- (6, 8) [subsumption resolution 168,160]
371. ~6 | ~8 [avatar contradiction clause 370]
399. ~kind(paul) | ~tall(paul) <- (31) [resolution 358,88]
403. ~tall(paul) <- (17, 31) [subsumption resolution 399,211]
404. $false <- (15, 17, 31) [subsumption resolution 403,364]
405. ~15 | ~17 | ~31 [avatar contradiction clause 404]
407. $false [avatar sat refutation 169,202,203,205,353,359,362,369,371,405]
% SZS output end Proof for 7174256869705566356440760
% ------------------------------
% 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 creative is not strong.
If lucy is strong then fred is both not strong and patient and vice versa.
If someone is both not brave and rich then alice is both not kind and wise and vice versa.
If mary is both brave and strong then susan is humble and vice versa.
Everyone who is both funny and curious is both not kind and not humble.
Everyone who is not humble is either not funny or not patient.
Everyone who is brave is not wise and vice versa.
Everyone who is tall is both not strong and not rich and vice versa.
Everyone who is both not old and patient is not strong or calm.
If someone is both curious and not humble then someone is both kind and happy and vice versa.
Everyone who is both curious and humble is both not wise and kind.
If john is both not kind and not calm then someone is either calm or strong.
Everyone who is both not creative and not quiet is generous or not calm and vice versa.
If susan is both brave and not creative then someone is quiet and vice versa.
If someone is wise or not happy then john is not wise.
If alice is not rich or tall then john is not creative.
John is brave or rich.
John is generous.
Someone is calm.
Paul is both happy and not quiet.
Mary is happy.
Someone is either not wise or not creative.
John is both not funny and not creative.
Someone is generous. | Fred is brave. | neutral | (![X]:(creative(X)=>~strong(X)))&
((strong(lucy))<=>((~strong(fred)&patient(fred))))&
((?[X]:((~brave(X)&rich(X))))<=>((~kind(alice)&wise(alice))))&
(((brave(mary)&strong(mary)))<=>(humble(susan)))&
(![X]:((funny(X)&curious(X))=>(~kind(X)&~humble(X))))&
(![X]:(~humble(X)=>(~funny(X)<~>~patient(X))))&
(![X]:(brave(X)<=>~wise(X)))&
(![X]:(tall(X)<=>(~strong(X)&~rich(X))))&
(![X]:((~old(X)&patient(X))=>(~strong(X)|calm(X))))&
((?[X]:((curious(X)&~humble(X))))<=>(?[X]:((kind(X)&happy(X)))))&
(![X]:((curious(X)&humble(X))=>(~wise(X)&kind(X))))&
(((~kind(john)&~calm(john)))=>(?[X]:((calm(X)<~>strong(X)))))&
(![X]:((~creative(X)&~quiet(X))<=>(generous(X)|~calm(X))))&
(((brave(susan)&~creative(susan)))<=>(?[X]:(quiet(X))))&
((?[X]:((wise(X)|~happy(X))))=>(~wise(john)))&
(((~rich(alice)|tall(alice)))=>(~creative(john)))&
((brave(john)|rich(john)))&
(generous(john))&
(?[X]:(calm(X)))&
((happy(paul)&~quiet(paul)))&
(happy(mary))&
(?[X]:((~wise(X)<~>~creative(X))))&
((~funny(john)&~creative(john)))&
(?[X]:(generous(X))) | brave(fred) | [] | null | 0 |
Everyone who is calm or old is both wise and not quiet and vice versa. Everyone who is quiet or not brave is not happy or wise and vice versa. If paul is tall or old then susan is both generous and not old and vice versa. If susan is rich or not funny then alice is happy or not generous and vice versa. Everyone who is not humble or not calm is both not wise and brave and vice versa. Everyone who is either brave or not patient is not calm. Everyone who is not rich or kind is either not tall or kind and vice versa. Everyone who is not quiet is either not humble or happy and vice versa. If lucy is either creative or not wise then alice is not funny or strong and vice versa. If john is both patient and tall then someone is both not patient and tall. Everyone who is strong or kind is happy and vice versa. Everyone who is funny is both tall and brave. Everyone who is either not calm or strong is not strong. Everyone who is happy or not creative is both brave and not generous. If john is both not strong and strong then someone is brave or generous. Everyone who is not funny is both not kind and patient and vice versa. Someone is creative. Someone is tall. Someone is quiet. Someone is not calm or rich. | Susan is brave. | entailment | (![X]:((calm(X)|old(X))<=>(wise(X)&~quiet(X))))&
(![X]:((quiet(X)|~brave(X))<=>(~happy(X)|wise(X))))&
(((tall(paul)|old(paul)))<=>((generous(susan)&~old(susan))))&
(((rich(susan)|~funny(susan)))<=>((happy(alice)|~generous(alice))))&
(![X]:((~humble(X)|~calm(X))<=>(~wise(X)&brave(X))))&
(![X]:((brave(X)<~>~patient(X))=>~calm(X)))&
(![X]:((~rich(X)|kind(X))<=>(~tall(X)<~>kind(X))))&
(![X]:(~quiet(X)<=>(~humble(X)<~>happy(X))))&
(((creative(lucy)<~>~wise(lucy)))<=>((~funny(alice)|strong(alice))))&
(((patient(john)&tall(john)))=>(?[X]:((~patient(X)&tall(X)))))&
(![X]:((strong(X)|kind(X))<=>happy(X)))&
(![X]:(funny(X)=>(tall(X)&brave(X))))&
(![X]:((~calm(X)<~>strong(X))=>~strong(X)))&
(![X]:((happy(X)|~creative(X))=>(brave(X)&~generous(X))))&
(((~strong(john)&strong(john)))=>(?[X]:((brave(X)|generous(X)))))&
(![X]:(~funny(X)<=>(~kind(X)&patient(X))))&
(?[X]:(creative(X)))&
(?[X]:(tall(X)))&
(?[X]:(quiet(X)))&
(?[X]:((~calm(X)|rich(X)))) | brave(susan) | [
"p0",
"p1",
"p4",
"p7",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 6165111927084763508188938
% SZS output start Proof for 6165111927084763508188938
1. ! [X0] : ((old(X0) | calm(X0)) <=> (~quiet(X0) & wise(X0))) [input p0]
2. ! [X0] : ((~brave(X0) | quiet(X0)) <=> (wise(X0) | ~happy(X0))) [input p1]
5. ! [X0] : ((~calm(X0) | ~humble(X0)) <=> (brave(X0) & ~wise(X0))) [input p4]
8. ! [X0] : (~quiet(X0) <=> (~humble(X0) <~> happy(X0))) [input p7]
14. ! [X0] : ((~creative(X0) | happy(X0)) => (~generous(X0) & brave(X0))) [input p13]
21. ~brave(susan) [input hypothesis]
27. ! [X0] : ((~generous(X0) & brave(X0)) | (creative(X0) & ~happy(X0))) [ennf transformation 14]
30. ! [X0] : (((old(X0) | calm(X0)) | (quiet(X0) | ~wise(X0))) & ((~quiet(X0) & wise(X0)) | (~old(X0) & ~calm(X0)))) [nnf transformation 1]
31. ! [X0] : ((old(X0) | calm(X0) | quiet(X0) | ~wise(X0)) & ((~quiet(X0) & wise(X0)) | (~old(X0) & ~calm(X0)))) [flattening 30]
32. ! [X0] : (((~brave(X0) | quiet(X0)) | (~wise(X0) & happy(X0))) & ((wise(X0) | ~happy(X0)) | (brave(X0) & ~quiet(X0)))) [nnf transformation 2]
33. ! [X0] : ((~brave(X0) | quiet(X0) | (~wise(X0) & happy(X0))) & (wise(X0) | ~happy(X0) | (brave(X0) & ~quiet(X0)))) [flattening 32]
38. ! [X0] : (((~calm(X0) | ~humble(X0)) | (~brave(X0) | wise(X0))) & ((brave(X0) & ~wise(X0)) | (calm(X0) & humble(X0)))) [nnf transformation 5]
39. ! [X0] : ((~calm(X0) | ~humble(X0) | ~brave(X0) | wise(X0)) & ((brave(X0) & ~wise(X0)) | (calm(X0) & humble(X0)))) [flattening 38]
43. ! [X0] : ((~quiet(X0) | ((~humble(X0) | ~happy(X0)) & (happy(X0) | humble(X0)))) & (((~happy(X0) | humble(X0)) & (happy(X0) | ~humble(X0))) | quiet(X0))) [nnf transformation 8]
65. ~quiet(X0) | ~calm(X0) [cnf transformation 31]
70. ~brave(X0) | quiet(X0) | happy(X0) [cnf transformation 33]
83. humble(X0) | brave(X0) [cnf transformation 39]
84. brave(X0) | calm(X0) [cnf transformation 39]
94. ~humble(X0) | happy(X0) | quiet(X0) [cnf transformation 43]
113. ~happy(X0) | brave(X0) [cnf transformation 27]
125. ~brave(susan) [cnf transformation 21]
222. calm(susan) [resolution 84,125]
254. happy(X0) | quiet(X0) | brave(X0) [resolution 94,83]
257. happy(X0) | quiet(X0) [subsumption resolution 254,70]
261. brave(X3) | quiet(X3) [resolution 257,113]
283. 26 <=> quiet(susan) [avatar definition]
284. quiet(susan) <- (26) [avatar component clause 283]
332. quiet(susan) [resolution 261,125]
341. 26 [avatar split clause 332,283]
364. ~calm(susan) <- (26) [resolution 284,65]
366. $false <- (26) [subsumption resolution 364,222]
367. ~26 [avatar contradiction clause 366]
368. $false [avatar sat refutation 341,367]
% SZS output end Proof for 6165111927084763508188938
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If fred is patient or humble then someone is either not brave or not curious.
If someone is both calm and not rich then someone is both generous and not old and vice versa.
Everyone who is both not creative and strong is not curious and vice versa.
If lucy is either not old or calm then someone is both not curious and creative.
If someone is not tall or not calm then someone is strong and vice versa.
Everyone who is not happy or not quiet is not generous or not calm and vice versa.
Everyone who is not humble is not wise and vice versa.
Everyone who is either creative or not kind is either curious or wise.
If someone is either not rich or not wise then lucy is patient or not humble and vice versa.
If mary is brave then john is both not kind and not brave.
Everyone who is both not tall and not brave is not creative or rich and vice versa.
Everyone who is not wise is not patient and vice versa.
Everyone who is not old is both not funny and patient.
Everyone who is calm or funny is patient.
Everyone who is both wise and not kind is rich and vice versa.
Everyone who is both funny and not wise is tall or brave and vice versa.
Mary is both not tall and patient.
Paul is either not quiet or humble.
Paul is either not tall or not rich.
Someone is generous or not brave.
Someone is either kind or not quiet.
Someone is calm.
Someone is not wise.
Paul is not old. | Paul is not humble. | contradiction | (((patient(fred)|humble(fred)))=>(?[X]:((~brave(X)<~>~curious(X)))))&
((?[X]:((calm(X)&~rich(X))))<=>(?[X]:((generous(X)&~old(X)))))&
(![X]:((~creative(X)&strong(X))<=>~curious(X)))&
(((~old(lucy)<~>calm(lucy)))=>(?[X]:((~curious(X)&creative(X)))))&
((?[X]:((~tall(X)|~calm(X))))<=>(?[X]:(strong(X))))&
(![X]:((~happy(X)|~quiet(X))<=>(~generous(X)|~calm(X))))&
(![X]:(~humble(X)<=>~wise(X)))&
(![X]:((creative(X)<~>~kind(X))=>(curious(X)<~>wise(X))))&
((?[X]:((~rich(X)<~>~wise(X))))<=>((patient(lucy)|~humble(lucy))))&
((brave(mary))=>((~kind(john)&~brave(john))))&
(![X]:((~tall(X)&~brave(X))<=>(~creative(X)|rich(X))))&
(![X]:(~wise(X)<=>~patient(X)))&
(![X]:(~old(X)=>(~funny(X)&patient(X))))&
(![X]:((calm(X)|funny(X))=>patient(X)))&
(![X]:((wise(X)&~kind(X))<=>rich(X)))&
(![X]:((funny(X)&~wise(X))<=>(tall(X)|brave(X))))&
((~tall(mary)&patient(mary)))&
((~quiet(paul)<~>humble(paul)))&
((~tall(paul)<~>~rich(paul)))&
(?[X]:((generous(X)|~brave(X))))&
(?[X]:((kind(X)<~>~quiet(X))))&
(?[X]:(calm(X)))&
(?[X]:(~wise(X)))&
(~old(paul)) | ~humble(paul) | [
"p6",
"p11",
"p12",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 9042680741218096391741640
% SZS output start Proof for 9042680741218096391741640
7. ! [X0] : (~humble(X0) <=> ~wise(X0)) [input p6]
12. ! [X0] : (~wise(X0) <=> ~patient(X0)) [input p11]
13. ! [X0] : (~old(X0) => (patient(X0) & ~funny(X0))) [input p12]
24. ~old(paul) [input p23]
25. ~humble(paul) [input hypothesis]
32. ! [X0] : ((patient(X0) & ~funny(X0)) | old(X0)) [ennf transformation 13]
54. ! [X0] : ((~humble(X0) | wise(X0)) & (~wise(X0) | humble(X0))) [nnf transformation 7]
63. ! [X0] : ((~wise(X0) | patient(X0)) & (~patient(X0) | wise(X0))) [nnf transformation 12]
101. ~wise(X0) | humble(X0) [cnf transformation 54]
120. ~patient(X0) | wise(X0) [cnf transformation 63]
123. old(X0) | patient(X0) [cnf transformation 32]
145. ~old(paul) [cnf transformation 24]
146. ~humble(paul) [cnf transformation 25]
287. 31 <=> humble(paul) [avatar definition]
289. ~humble(paul) <- (~31) [avatar component clause 287]
320. ~31 [avatar split clause 146,287]
330. patient(paul) [resolution 123,145]
334. wise(paul) [resolution 330,120]
337. humble(paul) [resolution 334,101]
338. $false <- (~31) [subsumption resolution 337,289]
339. 31 [avatar contradiction clause 338]
340. $false [avatar sat refutation 320,339]
% SZS output end Proof for 9042680741218096391741640
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If someone is quiet then paul is generous and vice versa.
If lucy is both not brave and not quiet then someone is rich and vice versa.
Everyone who is both not patient and wise is wise or not old and vice versa.
Everyone who is both not brave and funny is either not happy or kind.
Everyone who is either not quiet or not curious is not creative or wise and vice versa.
Everyone who is either not tall or funny is strong or humble and vice versa.
Everyone who is not quiet or funny is wise or not generous.
If lucy is generous then susan is not curious.
If someone is both not kind and curious then someone is kind or humble and vice versa.
Everyone who is humble is tall or curious.
Everyone who is either not old or not quiet is brave or not curious and vice versa.
Everyone who is not kind is either not generous or not brave and vice versa.
Everyone who is either funny or curious is not funny and vice versa.
Everyone who is curious is not humble and vice versa.
If someone is tall or not curious then alice is both quiet and not humble and vice versa.
Everyone who is both not calm and happy is either calm or not humble.
Mary is not creative.
Susan is not strong.
Someone is both not funny and not brave.
John is both wise and not happy.
Someone is funny.
Someone is either not kind or kind.
Someone is either generous or creative. | Lucy is curious. | entailment | ((?[X]:(quiet(X)))<=>(generous(paul)))&
(((~brave(lucy)&~quiet(lucy)))<=>(?[X]:(rich(X))))&
(![X]:((~patient(X)&wise(X))<=>(wise(X)|~old(X))))&
(![X]:((~brave(X)&funny(X))=>(~happy(X)<~>kind(X))))&
(![X]:((~quiet(X)<~>~curious(X))<=>(~creative(X)|wise(X))))&
(![X]:((~tall(X)<~>funny(X))<=>(strong(X)|humble(X))))&
(![X]:((~quiet(X)|funny(X))=>(wise(X)|~generous(X))))&
((generous(lucy))=>(~curious(susan)))&
((?[X]:((~kind(X)&curious(X))))<=>(?[X]:((kind(X)|humble(X)))))&
(![X]:(humble(X)=>(tall(X)|curious(X))))&
(![X]:((~old(X)<~>~quiet(X))<=>(brave(X)|~curious(X))))&
(![X]:(~kind(X)<=>(~generous(X)<~>~brave(X))))&
(![X]:((funny(X)<~>curious(X))<=>~funny(X)))&
(![X]:(curious(X)<=>~humble(X)))&
((?[X]:((tall(X)|~curious(X))))<=>((quiet(alice)&~humble(alice))))&
(![X]:((~calm(X)&happy(X))=>(calm(X)<~>~humble(X))))&
(~creative(mary))&
(~strong(susan))&
(?[X]:((~funny(X)&~brave(X))))&
((wise(john)&~happy(john)))&
(?[X]:(funny(X)))&
(?[X]:((~kind(X)<~>kind(X))))&
(?[X]:((generous(X)<~>creative(X)))) | curious(lucy) | [
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 6557621086273808452660214
% SZS output start Proof for 6557621086273808452660214
13. ! [X0] : ((funny(X0) <~> curious(X0)) <=> ~funny(X0)) [input p12]
24. ~curious(lucy) [input hypothesis]
59. ! [X0] : ((((~curious(X0) | ~funny(X0)) & (curious(X0) | funny(X0))) | funny(X0)) & (~funny(X0) | ((funny(X0) | ~curious(X0)) & (curious(X0) | ~funny(X0))))) [nnf transformation 13]
120. ~funny(X0) | curious(X0) | ~funny(X0) [cnf transformation 59]
122. curious(X0) | funny(X0) | funny(X0) [cnf transformation 59]
144. ~curious(lucy) [cnf transformation 24]
146. ~funny(X0) | curious(X0) [duplicate literal removal 120]
147. curious(X0) | funny(X0) [duplicate literal removal 122]
218. curious(X0) [subsumption resolution 146,147]
250. $false [subsumption resolution 144,218]
% SZS output end Proof for 6557621086273808452660214
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not happy and not old then lucy is either not old or not kind and vice versa.
If someone is not calm or not funny then mary is old or not humble and vice versa.
Everyone who is either patient or not happy is both not calm and not patient and vice versa.
Everyone who is both humble and not creative is strong and vice versa.
If susan is not kind or not brave then someone is both tall and not brave.
Everyone who is either patient or not tall is patient or creative and vice versa.
If someone is both not funny and not strong then paul is not rich or calm.
Everyone who is either calm or wise is not humble.
Everyone who is patient is not creative or not tall and vice versa.
If someone is both not curious and not brave then john is both not humble and not brave and vice versa.
Everyone who is both funny and wise is either not brave or strong.
If susan is both happy and not calm then paul is either old or quiet and vice versa.
If mary is brave then fred is strong or not humble and vice versa.
If someone is either old or not calm then john is not brave and vice versa.
Everyone who is either not kind or happy is creative.
If susan is either not brave or not tall then someone is both patient and not rich and vice versa.
Lucy is both not funny and not old.
Someone is either not rich or generous.
Alice is either strong or patient.
Someone is either not wise or funny.
Someone is funny.
John is calm or not happy.
John is either not calm or curious. | Alice is brave. | neutral | ((?[X]:((~happy(X)&~old(X))))<=>((~old(lucy)<~>~kind(lucy))))&
((?[X]:((~calm(X)|~funny(X))))<=>((old(mary)|~humble(mary))))&
(![X]:((patient(X)<~>~happy(X))<=>(~calm(X)&~patient(X))))&
(![X]:((humble(X)&~creative(X))<=>strong(X)))&
(((~kind(susan)|~brave(susan)))=>(?[X]:((tall(X)&~brave(X)))))&
(![X]:((patient(X)<~>~tall(X))<=>(patient(X)|creative(X))))&
((?[X]:((~funny(X)&~strong(X))))=>((~rich(paul)|calm(paul))))&
(![X]:((calm(X)<~>wise(X))=>~humble(X)))&
(![X]:(patient(X)<=>(~creative(X)|~tall(X))))&
((?[X]:((~curious(X)&~brave(X))))<=>((~humble(john)&~brave(john))))&
(![X]:((funny(X)&wise(X))=>(~brave(X)<~>strong(X))))&
(((happy(susan)&~calm(susan)))<=>((old(paul)<~>quiet(paul))))&
((brave(mary))<=>((strong(fred)|~humble(fred))))&
((?[X]:((old(X)<~>~calm(X))))<=>(~brave(john)))&
(![X]:((~kind(X)<~>happy(X))=>creative(X)))&
(((~brave(susan)<~>~tall(susan)))<=>(?[X]:((patient(X)&~rich(X)))))&
((~funny(lucy)&~old(lucy)))&
(?[X]:((~rich(X)<~>generous(X))))&
((strong(alice)<~>patient(alice)))&
(?[X]:((~wise(X)<~>funny(X))))&
(?[X]:(funny(X)))&
((calm(john)|~happy(john)))&
((~calm(john)<~>curious(john))) | brave(alice) | [] | null | 0 |
Everyone who is both not curious and not old is not old or not creative and vice versa.
If someone is both not curious and not humble then paul is both not happy and calm.
Everyone who is wise or not creative is generous or not tall.
Everyone who is either quiet or not creative is either happy or tall and vice versa.
If someone is both funny and not humble then someone is both funny and curious.
Everyone who is not wise is not creative or calm.
If someone is kind then someone is both not strong and kind and vice versa.
If john is either strong or not patient then mary is kind.
If someone is both tall and not happy then john is not rich or not strong.
If paul is either not tall or not kind then someone is old and vice versa.
Everyone who is brave is strong or not humble and vice versa.
If mary is not brave then mary is not calm.
If mary is both not creative and not tall then someone is not creative or tall and vice versa.
Everyone who is not tall or not patient is wise and vice versa.
If susan is both not old and quiet then paul is not curious.
Everyone who is either not tall or not quiet is funny or brave and vice versa.
Someone is not kind or brave.
John is both not generous and not calm.
Lucy is either rich or humble.
Susan is either not quiet or not creative.
Someone is strong or wise.
Susan is both not calm and not old.
John is patient.
Someone is either not creative or not humble. | Susan is old. | contradiction | (![X]:((~curious(X)&~old(X))<=>(~old(X)|~creative(X))))&
((?[X]:((~curious(X)&~humble(X))))=>((~happy(paul)&calm(paul))))&
(![X]:((wise(X)|~creative(X))=>(generous(X)|~tall(X))))&
(![X]:((quiet(X)<~>~creative(X))<=>(happy(X)<~>tall(X))))&
((?[X]:((funny(X)&~humble(X))))=>(?[X]:((funny(X)&curious(X)))))&
(![X]:(~wise(X)=>(~creative(X)|calm(X))))&
((?[X]:(kind(X)))<=>(?[X]:((~strong(X)&kind(X)))))&
(((strong(john)<~>~patient(john)))=>(kind(mary)))&
((?[X]:((tall(X)&~happy(X))))=>((~rich(john)|~strong(john))))&
(((~tall(paul)<~>~kind(paul)))<=>(?[X]:(old(X))))&
(![X]:(brave(X)<=>(strong(X)|~humble(X))))&
((~brave(mary))=>(~calm(mary)))&
(((~creative(mary)&~tall(mary)))<=>(?[X]:((~creative(X)|tall(X)))))&
(![X]:((~tall(X)|~patient(X))<=>wise(X)))&
(((~old(susan)&quiet(susan)))=>(~curious(paul)))&
(![X]:((~tall(X)<~>~quiet(X))<=>(funny(X)|brave(X))))&
(?[X]:((~kind(X)|brave(X))))&
((~generous(john)&~calm(john)))&
((rich(lucy)<~>humble(lucy)))&
((~quiet(susan)<~>~creative(susan)))&
(?[X]:((strong(X)|wise(X))))&
((~calm(susan)&~old(susan)))&
(patient(john))&
(?[X]:((~creative(X)<~>~humble(X)))) | old(susan) | [
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 3248303695559188254164325
% SZS output start Proof for 3248303695559188254164325
22. ~old(susan) & ~calm(susan) [input p21]
25. old(susan) [input hypothesis]
134. ~old(susan) [cnf transformation 22]
138. old(susan) [cnf transformation 25]
264. 29 <=> old(susan) [avatar definition]
310. ~29 [avatar split clause 134,264]
322. 29 [avatar split clause 138,264]
323. $false [avatar sat refutation 310,322]
% SZS output end Proof for 3248303695559188254164325
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either rich or not patient then lucy is not generous or not creative and vice versa.
Everyone who is either not curious or creative is both not old and curious.
Everyone who is curious or not kind is wise and vice versa.
Everyone who is calm is kind or not calm and vice versa.
If mary is curious then alice is funny or not curious.
Everyone who is not patient is not tall or patient and vice versa.
Everyone who is wise or not funny is tall or not quiet.
If someone is both strong and not wise then someone is kind or tall and vice versa.
If someone is not curious then someone is both not rich and creative.
Everyone who is not brave or calm is either not creative or strong.
Everyone who is either not rich or not kind is kind and vice versa.
Everyone who is both rich and not brave is not old or tall and vice versa.
If someone is not tall or not wise then someone is not brave or creative.
If mary is either not kind or not brave then susan is both not funny and not kind.
If someone is tall or not kind then someone is both curious and tall.
Everyone who is both not calm and rich is either not curious or funny.
Paul is strong.
Mary is both not patient and not funny.
Lucy is humble or quiet.
Mary is not strong.
Alice is either humble or curious.
Alice is wise. | Lucy is strong. | neutral | ((?[X]:((rich(X)<~>~patient(X))))<=>((~generous(lucy)|~creative(lucy))))&
(![X]:((~curious(X)<~>creative(X))=>(~old(X)&curious(X))))&
(![X]:((curious(X)|~kind(X))<=>wise(X)))&
(![X]:(calm(X)<=>(kind(X)|~calm(X))))&
((curious(mary))=>((funny(alice)|~curious(alice))))&
(![X]:(~patient(X)<=>(~tall(X)|patient(X))))&
(![X]:((wise(X)|~funny(X))=>(tall(X)|~quiet(X))))&
((?[X]:((strong(X)&~wise(X))))<=>(?[X]:((kind(X)|tall(X)))))&
((?[X]:(~curious(X)))=>(?[X]:((~rich(X)&creative(X)))))&
(![X]:((~brave(X)|calm(X))=>(~creative(X)<~>strong(X))))&
(![X]:((~rich(X)<~>~kind(X))<=>kind(X)))&
(![X]:((rich(X)&~brave(X))<=>(~old(X)|tall(X))))&
((?[X]:((~tall(X)|~wise(X))))=>(?[X]:((~brave(X)|creative(X)))))&
(((~kind(mary)<~>~brave(mary)))=>((~funny(susan)&~kind(susan))))&
((?[X]:((tall(X)|~kind(X))))=>(?[X]:((curious(X)&tall(X)))))&
(![X]:((~calm(X)&rich(X))=>(~curious(X)<~>funny(X))))&
(strong(paul))&
((~patient(mary)&~funny(mary)))&
((humble(lucy)|quiet(lucy)))&
(~strong(mary))&
((humble(alice)<~>curious(alice)))&
(wise(alice)) | strong(lucy) | [] | null | 0 |
Everyone who is either not tall or not funny is both not brave and not kind.
Everyone who is not humble is happy or not calm and vice versa.
If someone is not brave or rich then susan is not kind.
If mary is either not generous or not happy then someone is kind or not strong and vice versa.
Everyone who is not creative or not happy is not quiet or not wise and vice versa.
Everyone who is not happy is not generous.
If someone is both quiet and not happy then alice is not happy.
If someone is either not funny or not happy then alice is either strong or not wise and vice versa.
If someone is not rich or calm then mary is either not quiet or funny and vice versa.
If someone is kind or calm then susan is humble and vice versa.
Everyone who is not kind is not calm.
Everyone who is patient is not generous or quiet.
If someone is either not rich or quiet then someone is either not brave or not old and vice versa.
If susan is wise or not curious then john is calm.
Everyone who is not kind or funny is either not quiet or not wise and vice versa.
Everyone who is both not wise and curious is not happy or quiet.
Susan is quiet or kind.
Susan is either rich or not wise.
Fred is either tall or brave.
Someone is rich.
Someone is either wise or not happy.
Lucy is not calm.
Lucy is not wise.
Lucy is tall. | John is not humble. | entailment | (![X]:((~tall(X)<~>~funny(X))=>(~brave(X)&~kind(X))))&
(![X]:(~humble(X)<=>(happy(X)|~calm(X))))&
((?[X]:((~brave(X)|rich(X))))=>(~kind(susan)))&
(((~generous(mary)<~>~happy(mary)))<=>(?[X]:((kind(X)|~strong(X)))))&
(![X]:((~creative(X)|~happy(X))<=>(~quiet(X)|~wise(X))))&
(![X]:(~happy(X)=>~generous(X)))&
((?[X]:((quiet(X)&~happy(X))))=>(~happy(alice)))&
((?[X]:((~funny(X)<~>~happy(X))))<=>((strong(alice)<~>~wise(alice))))&
((?[X]:((~rich(X)|calm(X))))<=>((~quiet(mary)<~>funny(mary))))&
((?[X]:((kind(X)|calm(X))))<=>(humble(susan)))&
(![X]:(~kind(X)=>~calm(X)))&
(![X]:(patient(X)=>(~generous(X)|quiet(X))))&
((?[X]:((~rich(X)<~>quiet(X))))<=>(?[X]:((~brave(X)<~>~old(X)))))&
(((wise(susan)|~curious(susan)))=>(calm(john)))&
(![X]:((~kind(X)|funny(X))<=>(~quiet(X)<~>~wise(X))))&
(![X]:((~wise(X)&curious(X))=>(~happy(X)|quiet(X))))&
((quiet(susan)|kind(susan)))&
((rich(susan)<~>~wise(susan)))&
((tall(fred)<~>brave(fred)))&
(?[X]:(rich(X)))&
(?[X]:((wise(X)<~>~happy(X))))&
(~calm(lucy))&
(~wise(lucy))&
(tall(lucy)) | ~humble(john) | [
"p1",
"p2",
"p9",
"p10",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 1000337361964693303133475
% SZS output start Proof for 1000337361964693303133475
2. ! [X0] : (~humble(X0) <=> (~calm(X0) | happy(X0))) [input p1]
3. ? [X0] : (rich(X0) | ~brave(X0)) => ~kind(susan) [input p2]
10. ? [X0] : (calm(X0) | kind(X0)) <=> humble(susan) [input p9]
11. ! [X0] : (~kind(X0) => ~calm(X0)) [input p10]
20. ? [X0] : rich(X0) [input p19]
25. humble(john) [input hypothesis]
29. ~kind(susan) | ! [X0] : (~rich(X0) & brave(X0)) [ennf transformation 3]
32. ! [X0] : (~calm(X0) | kind(X0)) [ennf transformation 11]
37. ! [X0] : ((~humble(X0) | (calm(X0) & ~happy(X0))) & ((~calm(X0) | happy(X0)) | humble(X0))) [nnf transformation 2]
38. ! [X0] : ((~humble(X0) | (calm(X0) & ~happy(X0))) & (~calm(X0) | happy(X0) | humble(X0))) [flattening 37]
53. (? [X0] : (calm(X0) | kind(X0)) | ~humble(susan)) & (humble(susan) | ! [X0] : (~calm(X0) & ~kind(X0))) [nnf transformation 10]
54. (? [X0] : (calm(X0) | kind(X0)) | ~humble(susan)) & (humble(susan) | ! [X1] : (~calm(X1) & ~kind(X1))) [rectify 53]
55. ? [X0] : (calm(X0) | kind(X0)) => (calm(sK3) | kind(sK3)) [choice axiom]
56. ((calm(sK3) | kind(sK3)) | ~humble(susan)) & (humble(susan) | ! [X1] : (~calm(X1) & ~kind(X1))) [skolemisation 54,55]
66. ? [X0] : rich(X0) => rich(sK6) [choice axiom]
67. rich(sK6) [skolemisation 20,66]
77. ~humble(X0) | calm(X0) [cnf transformation 38]
79. ~kind(susan) | ~rich(X0) [cnf transformation 29]
106. humble(susan) | ~kind(X1) [cnf transformation 56]
109. ~calm(X0) | kind(X0) [cnf transformation 32]
132. rich(sK6) [cnf transformation 67]
138. humble(john) [cnf transformation 25]
140. 1 <=> ! [X0] : ~rich(X0) [avatar definition]
141. ~rich(X0) <- (1) [avatar component clause 140]
143. 2 <=> kind(susan) [avatar definition]
146. 1 | ~2 [avatar split clause 79,143,140]
164. 7 <=> ! [X0] : ~kind(X0) [avatar definition]
165. ~kind(X0) <- (7) [avatar component clause 164]
246. 24 <=> humble(susan) [avatar definition]
247. humble(susan) <- (24) [avatar component clause 246]
259. 7 | 24 [avatar split clause 106,246,164]
301. 36 <=> calm(john) [avatar definition]
303. calm(john) <- (36) [avatar component clause 301]
342. calm(john) [resolution 77,138]
345. 36 [avatar split clause 342,301]
348. calm(susan) <- (24) [resolution 247,77]
350. kind(john) <- (36) [resolution 109,303]
351. kind(susan) <- (24) [resolution 109,348]
354. $false <- (7, 36) [subsumption resolution 350,165]
355. ~7 | ~36 [avatar contradiction clause 354]
358. 2 | ~24 [avatar split clause 351,246,143]
360. $false <- (1) [resolution 141,132]
361. ~1 [avatar contradiction clause 360]
362. $false [avatar sat refutation 146,259,345,355,358,361]
% SZS output end Proof for 1000337361964693303133475
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If mary is either not curious or not patient then john is both not happy and not calm.
If someone is both creative and quiet then someone is not generous and vice versa.
Everyone who is both not creative and not curious is not wise or kind and vice versa.
If mary is either not funny or not curious then someone is either not strong or not humble.
If someone is not humble or not funny then someone is both not happy and not rich and vice versa.
If someone is both humble and old then someone is not rich or generous.
Everyone who is kind is not old or not curious and vice versa.
Everyone who is both not quiet and wise is not generous.
If someone is creative then mary is both not calm and kind and vice versa.
If lucy is both not wise and not funny then someone is either not funny or not creative and vice versa.
If fred is brave then someone is not wise.
Everyone who is not curious is not generous and vice versa.
If someone is rich or old then lucy is tall.
Everyone who is not tall or tall is not calm.
Everyone who is wise is not patient.
Everyone who is either old or humble is patient or happy.
Someone is not creative.
Fred is quiet.
Someone is both old and not rich.
Someone is not wise.
Paul is both not funny and patient.
Alice is both old and not humble.
Someone is both curious and old. | Mary is generous. | contradiction | (((~curious(mary)<~>~patient(mary)))=>((~happy(john)&~calm(john))))&
((?[X]:((creative(X)&quiet(X))))<=>(?[X]:(~generous(X))))&
(![X]:((~creative(X)&~curious(X))<=>(~wise(X)|kind(X))))&
(((~funny(mary)<~>~curious(mary)))=>(?[X]:((~strong(X)<~>~humble(X)))))&
((?[X]:((~humble(X)|~funny(X))))<=>(?[X]:((~happy(X)&~rich(X)))))&
((?[X]:((humble(X)&old(X))))=>(?[X]:((~rich(X)|generous(X)))))&
(![X]:(kind(X)<=>(~old(X)|~curious(X))))&
(![X]:((~quiet(X)&wise(X))=>~generous(X)))&
((?[X]:(creative(X)))<=>((~calm(mary)&kind(mary))))&
(((~wise(lucy)&~funny(lucy)))<=>(?[X]:((~funny(X)<~>~creative(X)))))&
((brave(fred))=>(?[X]:(~wise(X))))&
(![X]:(~curious(X)<=>~generous(X)))&
((?[X]:((rich(X)|old(X))))=>(tall(lucy)))&
(![X]:((~tall(X)|tall(X))=>~calm(X)))&
(![X]:(wise(X)=>~patient(X)))&
(![X]:((old(X)<~>humble(X))=>(patient(X)|happy(X))))&
(?[X]:(~creative(X)))&
(quiet(fred))&
(?[X]:((old(X)&~rich(X))))&
(?[X]:(~wise(X)))&
((~funny(paul)&patient(paul)))&
((old(alice)&~humble(alice)))&
(?[X]:((curious(X)&old(X)))) | generous(mary) | [
"p1",
"p2",
"p8",
"p11",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 3869508061253905979398132
% SZS output start Proof for 3869508061253905979398132
2. ? [X0] : (quiet(X0) & creative(X0)) <=> ? [X0] : ~generous(X0) [input p1]
3. ! [X0] : ((~curious(X0) & ~creative(X0)) <=> (kind(X0) | ~wise(X0))) [input p2]
9. ? [X0] : creative(X0) <=> (kind(mary) & ~calm(mary)) [input p8]
12. ! [X0] : (~curious(X0) <=> ~generous(X0)) [input p11]
20. ? [X0] : ~wise(X0) [input p19]
24. generous(mary) [input hypothesis]
25. ? [X0] : (quiet(X0) & creative(X0)) <=> ? [X1] : ~generous(X1) [rectify 2]
40. (? [X0] : (quiet(X0) & creative(X0)) | ! [X1] : generous(X1)) & (? [X1] : ~generous(X1) | ! [X0] : (~quiet(X0) | ~creative(X0))) [nnf transformation 25]
41. (? [X0] : (quiet(X0) & creative(X0)) | ! [X1] : generous(X1)) & (? [X2] : ~generous(X2) | ! [X3] : (~quiet(X3) | ~creative(X3))) [rectify 40]
42. ? [X0] : (quiet(X0) & creative(X0)) => (quiet(sK0) & creative(sK0)) [choice axiom]
43. ? [X2] : ~generous(X2) => ~generous(sK1) [choice axiom]
44. ((quiet(sK0) & creative(sK0)) | ! [X1] : generous(X1)) & (~generous(sK1) | ! [X3] : (~quiet(X3) | ~creative(X3))) [skolemisation 41,43,42]
45. ! [X0] : (((~curious(X0) & ~creative(X0)) | (~kind(X0) & wise(X0))) & ((kind(X0) | ~wise(X0)) | (curious(X0) | creative(X0)))) [nnf transformation 3]
46. ! [X0] : (((~curious(X0) & ~creative(X0)) | (~kind(X0) & wise(X0))) & (kind(X0) | ~wise(X0) | curious(X0) | creative(X0))) [flattening 45]
60. (? [X0] : creative(X0) | (~kind(mary) | calm(mary))) & ((kind(mary) & ~calm(mary)) | ! [X0] : ~creative(X0)) [nnf transformation 9]
61. (? [X0] : creative(X0) | ~kind(mary) | calm(mary)) & ((kind(mary) & ~calm(mary)) | ! [X0] : ~creative(X0)) [flattening 60]
62. (? [X0] : creative(X0) | ~kind(mary) | calm(mary)) & ((kind(mary) & ~calm(mary)) | ! [X1] : ~creative(X1)) [rectify 61]
63. ? [X0] : creative(X0) => creative(sK6) [choice axiom]
64. (creative(sK6) | ~kind(mary) | calm(mary)) & ((kind(mary) & ~calm(mary)) | ! [X1] : ~creative(X1)) [skolemisation 62,63]
70. ! [X0] : ((~curious(X0) | generous(X0)) & (~generous(X0) | curious(X0))) [nnf transformation 12]
76. ? [X0] : ~wise(X0) => ~wise(sK10) [choice axiom]
77. ~wise(sK10) [skolemisation 20,76]
85. creative(sK0) | generous(X1) [cnf transformation 44]
90. ~curious(X0) | wise(X0) [cnf transformation 46]
91. ~kind(X0) | ~curious(X0) [cnf transformation 46]
107. kind(mary) | ~creative(X1) [cnf transformation 64]
115. ~generous(X0) | curious(X0) [cnf transformation 70]
128. ~wise(sK10) [cnf transformation 77]
135. generous(mary) [cnf transformation 24]
141. 2 <=> curious(mary) [avatar definition]
157. 5 <=> ! [X1] : generous(X1) [avatar definition]
158. generous(X1) <- (5) [avatar component clause 157]
165. 7 <=> creative(sK0) [avatar definition]
167. creative(sK0) <- (7) [avatar component clause 165]
168. 5 | 7 [avatar split clause 85,165,157]
240. 24 <=> kind(mary) [avatar definition]
241. kind(mary) <- (24) [avatar component clause 240]
249. 26 <=> ! [X1] : ~creative(X1) [avatar definition]
250. ~creative(X1) <- (26) [avatar component clause 249]
251. 26 | 24 [avatar split clause 107,240,249]
300. ~curious(mary) <- (24) [resolution 91,241]
303. curious(mary) [resolution 115,135]
306. 2 [avatar split clause 303,141]
307. ~2 | ~24 [avatar split clause 300,240,141]
310. $false <- (7, 26) [resolution 250,167]
313. ~7 | ~26 [avatar contradiction clause 310]
314. curious(X0) <- (5) [resolution 158,115]
319. wise(X1) <- (5) [resolution 314,90]
321. $false <- (5) [resolution 319,128]
322. ~5 [avatar contradiction clause 321]
323. $false [avatar sat refutation 168,251,306,307,313,322]
% SZS output end Proof for 3869508061253905979398132
% ------------------------------
% 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 someone is either funny or not humble then alice is not calm. Everyone who is both not quiet and not tall is either not calm or not kind and vice versa. Everyone who is both tall and not brave is either not happy or kind and vice versa. Everyone who is both not brave and happy is not tall or patient and vice versa. If someone is kind or not wise then paul is not humble. If susan is either humble or wise then susan is brave. Everyone who is both strong and calm is either quiet or calm and vice versa. Everyone who is either not old or humble is old. Everyone who is both tall and not rich is both creative and not creative. Everyone who is generous or not rich is either not rich or wise. If fred is either not generous or strong then alice is calm and vice versa. Everyone who is not creative or not tall is either funny or not kind and vice versa. If mary is humble or kind then paul is not quiet or not strong and vice versa. If someone is both happy and not patient then someone is either generous or not generous and vice versa. If paul is both happy and not creative then someone is not wise. Everyone who is not happy is tall and vice versa. Someone is wise. Someone is both kind and generous. John is both not funny and old. Someone is not patient or not kind. Alice is either patient or not tall. Someone is curious or humble. | Alice is not happy. | contradiction | ((?[X]:((funny(X)<~>~humble(X))))=>(~calm(alice)))&
(![X]:((~quiet(X)&~tall(X))<=>(~calm(X)<~>~kind(X))))&
(![X]:((tall(X)&~brave(X))<=>(~happy(X)<~>kind(X))))&
(![X]:((~brave(X)&happy(X))<=>(~tall(X)|patient(X))))&
((?[X]:((kind(X)|~wise(X))))=>(~humble(paul)))&
(((humble(susan)<~>wise(susan)))=>(brave(susan)))&
(![X]:((strong(X)&calm(X))<=>(quiet(X)<~>calm(X))))&
(![X]:((~old(X)<~>humble(X))=>old(X)))&
(![X]:((tall(X)&~rich(X))=>(creative(X)&~creative(X))))&
(![X]:((generous(X)|~rich(X))=>(~rich(X)<~>wise(X))))&
(((~generous(fred)<~>strong(fred)))<=>(calm(alice)))&
(![X]:((~creative(X)|~tall(X))<=>(funny(X)<~>~kind(X))))&
(((humble(mary)|kind(mary)))<=>((~quiet(paul)|~strong(paul))))&
((?[X]:((happy(X)&~patient(X))))<=>(?[X]:((generous(X)<~>~generous(X)))))&
(((happy(paul)&~creative(paul)))=>(?[X]:(~wise(X))))&
(![X]:(~happy(X)<=>tall(X)))&
(?[X]:(wise(X)))&
(?[X]:((kind(X)&generous(X))))&
((~funny(john)&old(john)))&
(?[X]:((~patient(X)|~kind(X))))&
((patient(alice)<~>~tall(alice)))&
(?[X]:((curious(X)|humble(X)))) | ~happy(alice) | [
"p3",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 173699384380999126224338
% SZS output start Proof for 173699384380999126224338
4. ! [X0] : ((happy(X0) & ~brave(X0)) <=> (patient(X0) | ~tall(X0))) [input p3]
21. patient(alice) <~> ~tall(alice) [input p20]
23. ~happy(alice) [input hypothesis]
40. ! [X0] : (((happy(X0) & ~brave(X0)) | (~patient(X0) & tall(X0))) & ((patient(X0) | ~tall(X0)) | (~happy(X0) | brave(X0)))) [nnf transformation 4]
41. ! [X0] : (((happy(X0) & ~brave(X0)) | (~patient(X0) & tall(X0))) & (patient(X0) | ~tall(X0) | ~happy(X0) | brave(X0))) [flattening 40]
66. (tall(alice) | ~patient(alice)) & (~tall(alice) | patient(alice)) [nnf transformation 21]
84. happy(X0) | tall(X0) [cnf transformation 41]
85. ~patient(X0) | happy(X0) [cnf transformation 41]
133. ~tall(alice) | patient(alice) [cnf transformation 66]
135. ~happy(alice) [cnf transformation 23]
255. 25 <=> patient(alice) [avatar definition]
256. patient(alice) <- (25) [avatar component clause 255]
259. 26 <=> tall(alice) [avatar definition]
263. 25 | ~26 [avatar split clause 133,259,255]
270. tall(alice) [resolution 84,135]
273. 26 [avatar split clause 270,259]
275. happy(alice) <- (25) [resolution 85,256]
276. $false <- (25) [subsumption resolution 275,135]
277. ~25 [avatar contradiction clause 276]
278. $false [avatar sat refutation 263,273,277]
% SZS output end Proof for 173699384380999126224338
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not humble and not generous is humble and vice versa.
Everyone who is humble or curious is not generous or not strong and vice versa.
Everyone who is either wise or not curious is not calm or strong.
Everyone who is either not curious or tall is both not humble and humble and vice versa.
Everyone who is funny is either old or not funny and vice versa.
If someone is tall or patient then fred is either rich or funny.
Everyone who is generous is happy or not tall.
Everyone who is happy is not calm or generous.
If someone is not patient then someone is not rich or not brave.
Everyone who is not funny or not old is patient.
Everyone who is both not curious and not funny is both not patient and tall.
Everyone who is both brave and not humble is not patient.
If someone is not strong then someone is both not generous and humble and vice versa.
Everyone who is both creative and kind is old and vice versa.
If mary is either not tall or not wise then someone is funny or not funny and vice versa.
Someone is either not quiet or brave.
Lucy is either kind or patient.
Mary is either kind or quiet.
Someone is rich or not strong.
Someone is rich or wise.
Fred is creative.
Someone is either creative or calm. | Fred is calm. | neutral | (![X]:((~humble(X)&~generous(X))<=>humble(X)))&
(![X]:((humble(X)|curious(X))<=>(~generous(X)|~strong(X))))&
(![X]:((wise(X)<~>~curious(X))=>(~calm(X)|strong(X))))&
(![X]:((~curious(X)<~>tall(X))<=>(~humble(X)&humble(X))))&
(![X]:(funny(X)<=>(old(X)<~>~funny(X))))&
((?[X]:((tall(X)|patient(X))))=>((rich(fred)<~>funny(fred))))&
(![X]:(generous(X)=>(happy(X)|~tall(X))))&
(![X]:(happy(X)=>(~calm(X)|generous(X))))&
((?[X]:(~patient(X)))=>(?[X]:((~rich(X)|~brave(X)))))&
(![X]:((~funny(X)|~old(X))=>patient(X)))&
(![X]:((~curious(X)&~funny(X))=>(~patient(X)&tall(X))))&
(![X]:((brave(X)&~humble(X))=>~patient(X)))&
((?[X]:(~strong(X)))<=>(?[X]:((~generous(X)&humble(X)))))&
(![X]:((creative(X)&kind(X))<=>old(X)))&
(((~tall(mary)<~>~wise(mary)))<=>(?[X]:((funny(X)|~funny(X)))))&
(?[X]:((~quiet(X)<~>brave(X))))&
((kind(lucy)<~>patient(lucy)))&
((kind(mary)<~>quiet(mary)))&
(?[X]:((rich(X)|~strong(X))))&
(?[X]:((rich(X)|wise(X))))&
(creative(fred))&
(?[X]:((creative(X)<~>calm(X)))) | calm(fred) | [] | null | 0 |
If paul is either rich or tall then mary is both curious and kind and vice versa.
If someone is not curious then lucy is creative.
Everyone who is both funny and rich is both strong and generous and vice versa.
Everyone who is both tall and not wise is calm or wise and vice versa.
If fred is either not old or not rich then lucy is both wise and brave.
Everyone who is both not kind and wise is either humble or not strong.
Everyone who is not creative is either not creative or curious and vice versa.
If someone is strong then someone is either not old or not patient and vice versa.
Everyone who is either quiet or not quiet is creative or not creative and vice versa.
If someone is not patient then someone is old or rich.
If someone is not happy then someone is either not kind or funny.
Everyone who is both not kind and not rich is not patient or patient and vice versa.
Everyone who is both not humble and kind is either not curious or strong and vice versa.
If someone is either wise or not strong then lucy is not tall.
If susan is both not tall and strong then someone is both not calm and not strong and vice versa.
Someone is both tall and not old.
Someone is not humble.
Paul is both not kind and not patient.
Susan is either strong or kind.
Mary is quiet.
Fred is not funny. | Susan is not strong. | contradiction | (((rich(paul)<~>tall(paul)))<=>((curious(mary)&kind(mary))))&
((?[X]:(~curious(X)))=>(creative(lucy)))&
(![X]:((funny(X)&rich(X))<=>(strong(X)&generous(X))))&
(![X]:((tall(X)&~wise(X))<=>(calm(X)|wise(X))))&
(((~old(fred)<~>~rich(fred)))=>((wise(lucy)&brave(lucy))))&
(![X]:((~kind(X)&wise(X))=>(humble(X)<~>~strong(X))))&
(![X]:(~creative(X)<=>(~creative(X)<~>curious(X))))&
((?[X]:(strong(X)))<=>(?[X]:((~old(X)<~>~patient(X)))))&
(![X]:((quiet(X)<~>~quiet(X))<=>(creative(X)|~creative(X))))&
((?[X]:(~patient(X)))=>(?[X]:((old(X)|rich(X)))))&
((?[X]:(~happy(X)))=>(?[X]:((~kind(X)<~>funny(X)))))&
(![X]:((~kind(X)&~rich(X))<=>(~patient(X)|patient(X))))&
(![X]:((~humble(X)&kind(X))<=>(~curious(X)<~>strong(X))))&
((?[X]:((wise(X)<~>~strong(X))))=>(~tall(lucy)))&
(((~tall(susan)&strong(susan)))<=>(?[X]:((~calm(X)&~strong(X)))))&
(?[X]:((tall(X)&~old(X))))&
(?[X]:(~humble(X)))&
((~kind(paul)&~patient(paul)))&
((strong(susan)<~>kind(susan)))&
(quiet(mary))&
(~funny(fred)) | ~strong(susan) | [
"p6",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 1278121186494287106495268
% SZS output start Proof for 1278121186494287106495268
7. ! [X0] : (~creative(X0) <=> (~creative(X0) <~> curious(X0))) [input p6]
12. ! [X0] : ((~rich(X0) & ~kind(X0)) <=> (patient(X0) | ~patient(X0))) [input p11]
13. ! [X0] : ((kind(X0) & ~humble(X0)) <=> (~curious(X0) <~> strong(X0))) [input p12]
22. ~strong(susan) [input hypothesis]
42. ! [X0] : ((~creative(X0) | ((~creative(X0) | ~curious(X0)) & (curious(X0) | creative(X0)))) & (((~curious(X0) | creative(X0)) & (curious(X0) | ~creative(X0))) | creative(X0))) [nnf transformation 7]
53. ! [X0] : (((~rich(X0) & ~kind(X0)) | (~patient(X0) & patient(X0))) & ((patient(X0) | ~patient(X0)) | (rich(X0) | kind(X0)))) [nnf transformation 12]
54. ! [X0] : (((~rich(X0) & ~kind(X0)) | (~patient(X0) & patient(X0))) & (patient(X0) | ~patient(X0) | rich(X0) | kind(X0))) [flattening 53]
55. ! [X0] : (((kind(X0) & ~humble(X0)) | ((~curious(X0) | ~strong(X0)) & (strong(X0) | curious(X0)))) & (((~strong(X0) | curious(X0)) & (strong(X0) | ~curious(X0))) | (~kind(X0) | humble(X0)))) [nnf transformation 13]
56. ! [X0] : (((kind(X0) & ~humble(X0)) | ((~curious(X0) | ~strong(X0)) & (strong(X0) | curious(X0)))) & (((~strong(X0) | curious(X0)) & (strong(X0) | ~curious(X0))) | ~kind(X0) | humble(X0))) [flattening 55]
89. ~curious(X0) | creative(X0) | creative(X0) [cnf transformation 42]
91. ~creative(X0) | ~creative(X0) | ~curious(X0) [cnf transformation 42]
104. ~kind(X0) | patient(X0) [cnf transformation 54]
105. ~kind(X0) | ~patient(X0) [cnf transformation 54]
112. kind(X0) | strong(X0) | curious(X0) [cnf transformation 56]
129. ~strong(susan) [cnf transformation 22]
132. ~curious(X0) | creative(X0) [duplicate literal removal 89]
133. ~creative(X0) | ~curious(X0) [duplicate literal removal 91]
179. ~curious(X0) [subsumption resolution 132,133]
218. ~kind(X0) [subsumption resolution 104,105]
219. strong(X0) | curious(X0) [subsumption resolution 112,218]
220. strong(X0) [subsumption resolution 219,179]
223. $false [subsumption resolution 129,220]
% SZS output end Proof for 1278121186494287106495268
% ------------------------------
% 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: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is patient is both not old and kind and vice versa.
Everyone who is not wise or wise is both patient and not happy.
If someone is either quiet or happy then alice is either not curious or rich and vice versa.
If someone is either not wise or curious then someone is curious or not creative.
If someone is both not quiet and not calm then someone is both not humble and calm and vice versa.
Everyone who is not generous or not creative is either funny or calm and vice versa.
If someone is either generous or funny then mary is both not generous and not wise.
If someone is both not creative and not funny then someone is both rich and kind.
Everyone who is curious or kind is both strong and patient and vice versa.
Everyone who is either strong or generous is both not strong and curious.
If someone is tall or not humble then someone is funny and vice versa.
Everyone who is not curious is both not wise and kind.
If susan is patient then someone is old or funny.
If someone is patient then someone is generous.
If someone is both not generous and not patient then lucy is either humble or not creative.
If someone is both not old and brave then someone is either quiet or not generous and vice versa.
Someone is creative or not old.
Alice is either generous or not tall.
John is wise.
Someone is quiet.
Fred is either not curious or strong.
John is either rich or patient.
Someone is generous.
Alice is not rich. | Alice is not generous. | contradiction | (![X]:(patient(X)<=>(~old(X)&kind(X))))&
(![X]:((~wise(X)|wise(X))=>(patient(X)&~happy(X))))&
((?[X]:((quiet(X)<~>happy(X))))<=>((~curious(alice)<~>rich(alice))))&
((?[X]:((~wise(X)<~>curious(X))))=>(?[X]:((curious(X)|~creative(X)))))&
((?[X]:((~quiet(X)&~calm(X))))<=>(?[X]:((~humble(X)&calm(X)))))&
(![X]:((~generous(X)|~creative(X))<=>(funny(X)<~>calm(X))))&
((?[X]:((generous(X)<~>funny(X))))=>((~generous(mary)&~wise(mary))))&
((?[X]:((~creative(X)&~funny(X))))=>(?[X]:((rich(X)&kind(X)))))&
(![X]:((curious(X)|kind(X))<=>(strong(X)&patient(X))))&
(![X]:((strong(X)<~>generous(X))=>(~strong(X)&curious(X))))&
((?[X]:((tall(X)|~humble(X))))<=>(?[X]:(funny(X))))&
(![X]:(~curious(X)=>(~wise(X)&kind(X))))&
((patient(susan))=>(?[X]:((old(X)|funny(X)))))&
((?[X]:(patient(X)))=>(?[X]:(generous(X))))&
((?[X]:((~generous(X)&~patient(X))))=>((humble(lucy)<~>~creative(lucy))))&
((?[X]:((~old(X)&brave(X))))<=>(?[X]:((quiet(X)<~>~generous(X)))))&
(?[X]:((creative(X)|~old(X))))&
((generous(alice)<~>~tall(alice)))&
(wise(john))&
(?[X]:(quiet(X)))&
((~curious(fred)<~>strong(fred)))&
((rich(john)<~>patient(john)))&
(?[X]:(generous(X)))&
(~rich(alice)) | ~generous(alice) | [
"p0",
"p1",
"p8",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 6207522409565280398739973
% SZS output start Proof for 6207522409565280398739973
1. ! [X0] : (patient(X0) <=> (kind(X0) & ~old(X0))) [input p0]
2. ! [X0] : ((wise(X0) | ~wise(X0)) => (~happy(X0) & patient(X0))) [input p1]
9. ! [X0] : ((kind(X0) | curious(X0)) <=> (patient(X0) & strong(X0))) [input p8]
10. ! [X0] : ((strong(X0) <~> generous(X0)) => (curious(X0) & ~strong(X0))) [input p9]
25. ~generous(alice) [input hypothesis]
32. ! [X0] : ((~happy(X0) & patient(X0)) | (~wise(X0) & wise(X0))) [ennf transformation 2]
36. ! [X0] : ((curious(X0) & ~strong(X0)) | (strong(X0) <=> generous(X0))) [ennf transformation 10]
41. ! [X0] : ((patient(X0) | (~kind(X0) | old(X0))) & ((kind(X0) & ~old(X0)) | ~patient(X0))) [nnf transformation 1]
42. ! [X0] : ((patient(X0) | ~kind(X0) | old(X0)) & ((kind(X0) & ~old(X0)) | ~patient(X0))) [flattening 41]
62. ! [X0] : (((kind(X0) | curious(X0)) | (~patient(X0) | ~strong(X0))) & ((patient(X0) & strong(X0)) | (~kind(X0) & ~curious(X0)))) [nnf transformation 9]
63. ! [X0] : ((kind(X0) | curious(X0) | ~patient(X0) | ~strong(X0)) & ((patient(X0) & strong(X0)) | (~kind(X0) & ~curious(X0)))) [flattening 62]
64. ! [X0] : ((curious(X0) & ~strong(X0)) | ((strong(X0) | ~generous(X0)) & (generous(X0) | ~strong(X0)))) [nnf transformation 36]
91. ~patient(X0) | kind(X0) [cnf transformation 42]
93. patient(X0) | wise(X0) [cnf transformation 32]
94. ~wise(X0) | patient(X0) [cnf transformation 32]
124. ~kind(X0) | strong(X0) [cnf transformation 63]
128. ~strong(X0) | generous(X0) | ~strong(X0) [cnf transformation 64]
158. ~generous(alice) [cnf transformation 25]
159. ~strong(X0) | generous(X0) [duplicate literal removal 128]
161. patient(X0) [subsumption resolution 93,94]
335. 39 <=> generous(alice) [avatar definition]
337. ~generous(alice) <- (~39) [avatar component clause 335]
355. ~39 [avatar split clause 158,335]
359. kind(X0) [resolution 91,161]
361. strong(X0) [resolution 124,359]
369. generous(X0) [resolution 159,361]
377. $false <- (~39) [resolution 369,337]
378. 39 [avatar contradiction clause 377]
381. $false [avatar sat refutation 355,378]
% SZS output end Proof for 6207522409565280398739973
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If john is both not brave and rich then someone is patient or not strong and vice versa. If alice is either not quiet or generous then alice is either not old or calm and vice versa. Everyone who is not generous is either kind or rich and vice versa. If susan is not brave then alice is wise or rich. Everyone who is both tall and not brave is both not happy and not humble. Everyone who is not tall is not brave or old and vice versa. Everyone who is either calm or curious is strong. Everyone who is either not strong or not funny is either tall or not kind and vice versa. If john is tall then someone is both curious and not creative. If someone is patient or not curious then lucy is kind. If mary is both not patient and humble then mary is both not kind and generous and vice versa. Everyone who is either old or quiet is either not humble or patient and vice versa. If someone is either not curious or not strong then someone is both strong and generous and vice versa. Everyone who is happy is humble or kind and vice versa. If lucy is not old or not curious then someone is not calm or happy. Everyone who is both not strong and rich is both happy and rich. Mary is creative or not brave. Lucy is either not old or kind. Someone is not curious. Someone is either rich or calm. Alice is not strong. Fred is both strong and happy. Someone is not wise. | Fred is strong. | entailment | (((~brave(john)&rich(john)))<=>(?[X]:((patient(X)|~strong(X)))))&
(((~quiet(alice)<~>generous(alice)))<=>((~old(alice)<~>calm(alice))))&
(![X]:(~generous(X)<=>(kind(X)<~>rich(X))))&
((~brave(susan))=>((wise(alice)|rich(alice))))&
(![X]:((tall(X)&~brave(X))=>(~happy(X)&~humble(X))))&
(![X]:(~tall(X)<=>(~brave(X)|old(X))))&
(![X]:((calm(X)<~>curious(X))=>strong(X)))&
(![X]:((~strong(X)<~>~funny(X))<=>(tall(X)<~>~kind(X))))&
((tall(john))=>(?[X]:((curious(X)&~creative(X)))))&
((?[X]:((patient(X)|~curious(X))))=>(kind(lucy)))&
(((~patient(mary)&humble(mary)))<=>((~kind(mary)&generous(mary))))&
(![X]:((old(X)<~>quiet(X))<=>(~humble(X)<~>patient(X))))&
((?[X]:((~curious(X)<~>~strong(X))))<=>(?[X]:((strong(X)&generous(X)))))&
(![X]:(happy(X)<=>(humble(X)|kind(X))))&
(((~old(lucy)|~curious(lucy)))=>(?[X]:((~calm(X)|happy(X)))))&
(![X]:((~strong(X)&rich(X))=>(happy(X)&rich(X))))&
((creative(mary)|~brave(mary)))&
((~old(lucy)<~>kind(lucy)))&
(?[X]:(~curious(X)))&
(?[X]:((rich(X)<~>calm(X))))&
(~strong(alice))&
((strong(fred)&happy(fred)))&
(?[X]:(~wise(X))) | strong(fred) | [
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 2445523650684969879895955
% SZS output start Proof for 2445523650684969879895955
22. happy(fred) & strong(fred) [input p21]
24. ~strong(fred) [input hypothesis]
138. strong(fred) [cnf transformation 22]
141. ~strong(fred) [cnf transformation 24]
319. $false [subsumption resolution 141,138]
% SZS output end Proof for 2445523650684969879895955
% ------------------------------
% 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 |
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