premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
values | proof_inputs
sequencelengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
|
|---|---|---|---|---|---|---|---|
Everyone who is creative is not tall and vice versa.
Everyone who is either curious or creative is funny.
Everyone who is creative or tall is both not kind and quiet and vice versa.
Everyone who is not humble or not creative is either not creative or funny and vice versa.
Everyone who is not happy is patient or not creative and vice versa.
Everyone who is not humble is tall or happy.
Everyone who is not humble is both not rich and patient and vice versa.
If someone is both patient and not tall then john is both not quiet and not curious.
Everyone who is both kind and not old is either not generous or not creative.
Everyone who is both not tall and not strong is both generous and brave and vice versa.
If lucy is both not humble and not calm then someone is either curious or humble and vice versa.
Everyone who is both tall and not old is both not tall and not generous.
If paul is either patient or not kind then someone is rich and vice versa.
Everyone who is both not rich and strong is either not calm or not curious and vice versa.
If someone is either not old or not humble then fred is both wise and funny.
Someone is happy or not rich.
Alice is either not curious or curious.
Alice is not patient or not wise.
Susan is either not old or old.
Someone is brave. | Lucy is happy. | entailment | (![X]:(creative(X)<=>~tall(X)))&
(![X]:((curious(X)<~>creative(X))=>funny(X)))&
(![X]:((creative(X)|tall(X))<=>(~kind(X)&quiet(X))))&
(![X]:((~humble(X)|~creative(X))<=>(~creative(X)<~>funny(X))))&
(![X]:(~happy(X)<=>(patient(X)|~creative(X))))&
(![X]:(~humble(X)=>(tall(X)|happy(X))))&
(![X]:(~humble(X)<=>(~rich(X)&patient(X))))&
((?[X]:((patient(X)&~tall(X))))=>((~quiet(john)&~curious(john))))&
(![X]:((kind(X)&~old(X))=>(~generous(X)<~>~creative(X))))&
(![X]:((~tall(X)&~strong(X))<=>(generous(X)&brave(X))))&
(((~humble(lucy)&~calm(lucy)))<=>(?[X]:((curious(X)<~>humble(X)))))&
(![X]:((tall(X)&~old(X))=>(~tall(X)&~generous(X))))&
(((patient(paul)<~>~kind(paul)))<=>(?[X]:(rich(X))))&
(![X]:((~rich(X)&strong(X))<=>(~calm(X)<~>~curious(X))))&
((?[X]:((~old(X)<~>~humble(X))))=>((wise(fred)&funny(fred))))&
(?[X]:((happy(X)|~rich(X))))&
((~curious(alice)<~>curious(alice)))&
((~patient(alice)|~wise(alice)))&
((~old(susan)<~>old(susan)))&
(?[X]:(brave(X))) | happy(lucy) | [
"p0",
"p1",
"p2",
"p3",
"p4",
"p6",
"p7",
"p10",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6963043644051318508641644
% SZS output start Proof for 6963043644051318508641644
1. ! [X0] : (creative(X0) <=> ~tall(X0)) [input p0]
2. ! [X0] : ((curious(X0) <~> creative(X0)) => funny(X0)) [input p1]
3. ! [X0] : ((tall(X0) | creative(X0)) <=> (quiet(X0) & ~kind(X0))) [input p2]
4. ! [X0] : ((~creative(X0) | ~humble(X0)) <=> (~creative(X0) <~> funny(X0))) [input p3]
5. ! [X0] : (~happy(X0) <=> (~creative(X0) | patient(X0))) [input p4]
7. ! [X0] : (~humble(X0) <=> (patient(X0) & ~rich(X0))) [input p6]
8. ? [X0] : (~tall(X0) & patient(X0)) => (~curious(john) & ~quiet(john)) [input p7]
11. (~calm(lucy) & ~humble(lucy)) <=> ? [X0] : (curious(X0) <~> humble(X0)) [input p10]
12. ! [X0] : ((~old(X0) & tall(X0)) => (~generous(X0) & ~tall(X0))) [input p11]
15. ? [X0] : (~old(X0) <~> ~humble(X0)) => (funny(fred) & wise(fred)) [input p14]
21. ~happy(lucy) [input hypothesis]
22. ! [X0] : (funny(X0) | (curious(X0) <=> creative(X0))) [ennf transformation 2]
25. (~curious(john) & ~quiet(john)) | ! [X0] : (tall(X0) | ~patient(X0)) [ennf transformation 8]
28. ! [X0] : ((~generous(X0) & ~tall(X0)) | (old(X0) | ~tall(X0))) [ennf transformation 12]
29. ! [X0] : ((~generous(X0) & ~tall(X0)) | old(X0) | ~tall(X0)) [flattening 28]
30. (funny(fred) & wise(fred)) | ! [X0] : (~old(X0) <=> ~humble(X0)) [ennf transformation 15]
31. ! [X0] : ((creative(X0) | tall(X0)) & (~tall(X0) | ~creative(X0))) [nnf transformation 1]
32. ! [X0] : (funny(X0) | ((curious(X0) | ~creative(X0)) & (creative(X0) | ~curious(X0)))) [nnf transformation 22]
33. ! [X0] : (((tall(X0) | creative(X0)) | (~quiet(X0) | kind(X0))) & ((quiet(X0) & ~kind(X0)) | (~tall(X0) & ~creative(X0)))) [nnf transformation 3]
34. ! [X0] : ((tall(X0) | creative(X0) | ~quiet(X0) | kind(X0)) & ((quiet(X0) & ~kind(X0)) | (~tall(X0) & ~creative(X0)))) [flattening 33]
35. ! [X0] : (((~creative(X0) | ~humble(X0)) | ((~creative(X0) | ~funny(X0)) & (funny(X0) | creative(X0)))) & (((~funny(X0) | creative(X0)) & (funny(X0) | ~creative(X0))) | (creative(X0) & humble(X0)))) [nnf transformation 4]
36. ! [X0] : ((~creative(X0) | ~humble(X0) | ((~creative(X0) | ~funny(X0)) & (funny(X0) | creative(X0)))) & (((~funny(X0) | creative(X0)) & (funny(X0) | ~creative(X0))) | (creative(X0) & humble(X0)))) [flattening 35]
37. ! [X0] : ((~happy(X0) | (creative(X0) & ~patient(X0))) & ((~creative(X0) | patient(X0)) | happy(X0))) [nnf transformation 5]
38. ! [X0] : ((~happy(X0) | (creative(X0) & ~patient(X0))) & (~creative(X0) | patient(X0) | happy(X0))) [flattening 37]
39. ! [X0] : ((~humble(X0) | (~patient(X0) | rich(X0))) & ((patient(X0) & ~rich(X0)) | humble(X0))) [nnf transformation 7]
40. ! [X0] : ((~humble(X0) | ~patient(X0) | rich(X0)) & ((patient(X0) & ~rich(X0)) | humble(X0))) [flattening 39]
44. ((~calm(lucy) & ~humble(lucy)) | ! [X0] : ((curious(X0) | ~humble(X0)) & (humble(X0) | ~curious(X0)))) & (? [X0] : ((~humble(X0) | ~curious(X0)) & (humble(X0) | curious(X0))) | (calm(lucy) | humble(lucy))) [nnf transformation 11]
45. ((~calm(lucy) & ~humble(lucy)) | ! [X0] : ((curious(X0) | ~humble(X0)) & (humble(X0) | ~curious(X0)))) & (? [X0] : ((~humble(X0) | ~curious(X0)) & (humble(X0) | curious(X0))) | calm(lucy) | humble(lucy)) [flattening 44]
46. ((~calm(lucy) & ~humble(lucy)) | ! [X0] : ((curious(X0) | ~humble(X0)) & (humble(X0) | ~curious(X0)))) & (? [X1] : ((~humble(X1) | ~curious(X1)) & (humble(X1) | curious(X1))) | calm(lucy) | humble(lucy)) [rectify 45]
47. ? [X1] : ((~humble(X1) | ~curious(X1)) & (humble(X1) | curious(X1))) => ((~humble(sK0) | ~curious(sK0)) & (humble(sK0) | curious(sK0))) [choice axiom]
48. ((~calm(lucy) & ~humble(lucy)) | ! [X0] : ((curious(X0) | ~humble(X0)) & (humble(X0) | ~curious(X0)))) & (((~humble(sK0) | ~curious(sK0)) & (humble(sK0) | curious(sK0))) | calm(lucy) | humble(lucy)) [skolemisation 46,47]
55. (funny(fred) & wise(fred)) | ! [X0] : ((~old(X0) | humble(X0)) & (~humble(X0) | old(X0))) [nnf transformation 30]
62. ~tall(X0) | ~creative(X0) [cnf transformation 31]
63. tall(X0) | creative(X0) [cnf transformation 31]
64. ~curious(X0) | creative(X0) | funny(X0) [cnf transformation 32]
68. ~creative(X0) | quiet(X0) [cnf transformation 34]
69. ~tall(X0) | quiet(X0) [cnf transformation 34]
74. ~funny(X0) | creative(X0) | creative(X0) [cnf transformation 36]
76. ~creative(X0) | ~humble(X0) | ~creative(X0) | ~funny(X0) [cnf transformation 36]
77. ~creative(X0) | patient(X0) | happy(X0) [cnf transformation 38]
82. patient(X0) | humble(X0) [cnf transformation 40]
84. ~quiet(john) | tall(X0) | ~patient(X0) [cnf transformation 25]
95. ~humble(lucy) | curious(X0) | ~humble(X0) [cnf transformation 48]
98. ~tall(X0) | old(X0) | ~tall(X0) [cnf transformation 29]
112. funny(fred) | ~humble(X0) | old(X0) [cnf transformation 55]
113. funny(fred) | ~old(X0) | humble(X0) [cnf transformation 55]
121. ~happy(lucy) [cnf transformation 21]
122. ~tall(X0) | old(X0) [duplicate literal removal 98]
123. ~funny(X0) | creative(X0) [duplicate literal removal 74]
124. ~humble(X0) | ~creative(X0) | ~funny(X0) [duplicate literal removal 76]
126. 1 <=> ! [X0] : (tall(X0) | ~patient(X0)) [avatar definition]
127. ~patient(X0) | tall(X0) <- (1) [avatar component clause 126]
134. 3 <=> quiet(john) [avatar definition]
136. ~quiet(john) <- (~3) [avatar component clause 134]
137. 1 | ~3 [avatar split clause 84,134,126]
140. 4 <=> ! [X0] : (curious(X0) | ~humble(X0)) [avatar definition]
141. ~humble(X0) | curious(X0) <- (4) [avatar component clause 140]
152. 7 <=> humble(lucy) [avatar definition]
154. ~humble(lucy) <- (~7) [avatar component clause 152]
155. 4 | ~7 [avatar split clause 95,152,140]
187. 14 <=> ! [X0] : (~old(X0) | humble(X0)) [avatar definition]
188. ~old(X0) | humble(X0) <- (14) [avatar component clause 187]
190. 15 <=> funny(fred) [avatar definition]
192. funny(fred) <- (15) [avatar component clause 190]
193. 14 | 15 [avatar split clause 113,190,187]
195. 16 <=> ! [X0] : (~humble(X0) | old(X0)) [avatar definition]
196. ~humble(X0) | old(X0) <- (16) [avatar component clause 195]
197. 16 | 15 [avatar split clause 112,190,195]
223. quiet(X0) | creative(X0) [resolution 69,63]
224. quiet(X0) [subsumption resolution 223,68]
225. $false <- (~3) [resolution 224,136]
226. 3 [avatar contradiction clause 225]
230. old(X0) | creative(X0) [resolution 122,63]
232. humble(X0) | tall(X0) <- (1) [resolution 127,82]
329. humble(X0) | creative(X0) <- (14) [resolution 230,188]
331. tall(X1) | old(X1) <- (1, 16) [resolution 232,196]
332. tall(lucy) <- (1, ~7) [resolution 232,154]
334. old(X1) <- (1, 16) [subsumption resolution 331,122]
337. ~creative(lucy) <- (1, ~7) [resolution 332,62]
348. creative(lucy) <- (~7, 14) [resolution 329,154]
349. $false <- (1, ~7, 14) [subsumption resolution 348,337]
350. ~1 | 7 | ~14 [avatar contradiction clause 349]
351. creative(fred) <- (15) [resolution 192,123]
361. 27 <=> patient(fred) [avatar definition]
362. ~patient(fred) <- (~27) [avatar component clause 361]
363. patient(fred) <- (27) [avatar component clause 361]
366. tall(fred) <- (1, 27) [resolution 363,127]
373. 29 <=> humble(fred) [avatar definition]
374. humble(fred) <- (29) [avatar component clause 373]
382. ~creative(fred) <- (1, 27) [resolution 366,62]
383. $false <- (1, 15, 27) [subsumption resolution 382,351]
384. ~1 | ~15 | ~27 [avatar contradiction clause 383]
390. humble(fred) <- (~27) [resolution 362,82]
391. ~creative(fred) | ~funny(fred) <- (29) [resolution 374,124]
393. ~funny(fred) <- (15, 29) [subsumption resolution 391,351]
394. $false <- (15, 29) [subsumption resolution 393,192]
395. ~15 | ~29 [avatar contradiction clause 394]
397. 30 <=> tall(lucy) [avatar definition]
399. tall(lucy) <- (30) [avatar component clause 397]
413. 29 | 27 [avatar split clause 390,361,373]
414. humble(X0) <- (1, 14, 16) [subsumption resolution 188,334]
415. curious(X0) <- (1, 4, 14, 16) [subsumption resolution 141,414]
416. ~creative(X0) | ~funny(X0) <- (1, 14, 16) [resolution 414,124]
418. ~funny(X0) <- (1, 14, 16) [subsumption resolution 416,123]
420. creative(X1) | funny(X1) <- (1, 4, 14, 16) [resolution 415,64]
428. creative(X1) <- (1, 4, 14, 16) [subsumption resolution 420,418]
432. patient(X0) | happy(X0) <- (1, 4, 14, 16) [resolution 428,77]
450. happy(X1) | tall(X1) <- (1, 4, 14, 16) [resolution 432,127]
465. tall(lucy) <- (1, 4, 14, 16) [resolution 450,121]
468. 30 | ~1 | ~4 | ~14 | ~16 [avatar split clause 465,195,187,140,126,397]
471. ~creative(lucy) <- (30) [resolution 399,62]
472. $false <- (1, 4, 14, 16, 30) [subsumption resolution 471,428]
473. ~1 | ~4 | ~14 | ~16 | ~30 [avatar contradiction clause 472]
474. $false [avatar sat refutation 137,155,193,197,226,350,384,395,413,468,473]
% SZS output end Proof for 6963043644051318508641644
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is creative or not strong is either calm or rich and vice versa.
If mary is not quiet then someone is both generous and happy.
Everyone who is both creative and humble is either not kind or not tall.
If someone is not curious or creative then susan is both not creative and not quiet and vice versa.
If fred is both not strong and patient then alice is not calm or not strong.
If lucy is humble or not old then mary is both quiet and not calm and vice versa.
Everyone who is both not creative and old is quiet or not humble and vice versa.
Everyone who is kind or not wise is both wise and not strong and vice versa.
If someone is kind or not creative then someone is both not happy and strong and vice versa.
Everyone who is not tall is not strong or calm.
If someone is both patient and curious then john is patient.
Everyone who is both not strong and not funny is either not funny or brave.
Everyone who is not brave is either not old or humble.
Everyone who is either old or funny is either creative or wise.
If someone is not humble or not generous then someone is happy and vice versa.
If paul is funny then someone is not old or not strong.
Someone is either not strong or not wise.
Paul is not rich or not generous.
Someone is not patient or not quiet.
Someone is either not generous or not patient.
Paul is creative.
Someone is not calm.
Paul is not calm or generous. | Mary is quiet. | neutral | (![X]:((creative(X)|~strong(X))<=>(calm(X)<~>rich(X))))&
((~quiet(mary))=>(?[X]:((generous(X)&happy(X)))))&
(![X]:((creative(X)&humble(X))=>(~kind(X)<~>~tall(X))))&
((?[X]:((~curious(X)|creative(X))))<=>((~creative(susan)&~quiet(susan))))&
(((~strong(fred)&patient(fred)))=>((~calm(alice)|~strong(alice))))&
(((humble(lucy)|~old(lucy)))<=>((quiet(mary)&~calm(mary))))&
(![X]:((~creative(X)&old(X))<=>(quiet(X)|~humble(X))))&
(![X]:((kind(X)|~wise(X))<=>(wise(X)&~strong(X))))&
((?[X]:((kind(X)|~creative(X))))<=>(?[X]:((~happy(X)&strong(X)))))&
(![X]:(~tall(X)=>(~strong(X)|calm(X))))&
((?[X]:((patient(X)&curious(X))))=>(patient(john)))&
(![X]:((~strong(X)&~funny(X))=>(~funny(X)<~>brave(X))))&
(![X]:(~brave(X)=>(~old(X)<~>humble(X))))&
(![X]:((old(X)<~>funny(X))=>(creative(X)<~>wise(X))))&
((?[X]:((~humble(X)|~generous(X))))<=>(?[X]:(happy(X))))&
((funny(paul))=>(?[X]:((~old(X)|~strong(X)))))&
(?[X]:((~strong(X)<~>~wise(X))))&
((~rich(paul)|~generous(paul)))&
(?[X]:((~patient(X)|~quiet(X))))&
(?[X]:((~generous(X)<~>~patient(X))))&
(creative(paul))&
(?[X]:(~calm(X)))&
((~calm(paul)|generous(paul))) | quiet(mary) | [] | null | 0 |
If john is not happy or tall then paul is both not rich and wise and vice versa.
Everyone who is either strong or calm is either calm or old.
Everyone who is either not tall or happy is calm.
If paul is rich then alice is brave.
If john is both funny and not curious then someone is generous or patient and vice versa.
If someone is either rich or not wise then someone is creative.
If susan is either not patient or wise then someone is both creative and rich and vice versa.
If susan is funny then lucy is both old and happy and vice versa.
Everyone who is either not strong or not humble is strong and vice versa.
If someone is both generous and not funny then paul is both curious and not rich and vice versa.
If susan is not funny then susan is brave.
If fred is both patient and not happy then someone is either not quiet or not strong and vice versa.
Everyone who is either not strong or not quiet is calm or brave.
Everyone who is not wise or not generous is brave or generous.
Everyone who is both quiet and brave is not humble or not quiet and vice versa.
If alice is not funny then someone is both not happy and tall.
Someone is either not generous or not happy.
Someone is not brave or not calm.
Someone is both generous and not kind.
Someone is both not rich and old.
Mary is calm or not generous.
Mary is calm or tall.
Someone is kind or brave. | Mary is not brave. | contradiction | (((~happy(john)|tall(john)))<=>((~rich(paul)&wise(paul))))&
(![X]:((strong(X)<~>calm(X))=>(calm(X)<~>old(X))))&
(![X]:((~tall(X)<~>happy(X))=>calm(X)))&
((rich(paul))=>(brave(alice)))&
(((funny(john)&~curious(john)))<=>(?[X]:((generous(X)|patient(X)))))&
((?[X]:((rich(X)<~>~wise(X))))=>(?[X]:(creative(X))))&
(((~patient(susan)<~>wise(susan)))<=>(?[X]:((creative(X)&rich(X)))))&
((funny(susan))<=>((old(lucy)&happy(lucy))))&
(![X]:((~strong(X)<~>~humble(X))<=>strong(X)))&
((?[X]:((generous(X)&~funny(X))))<=>((curious(paul)&~rich(paul))))&
((~funny(susan))=>(brave(susan)))&
(((patient(fred)&~happy(fred)))<=>(?[X]:((~quiet(X)<~>~strong(X)))))&
(![X]:((~strong(X)<~>~quiet(X))=>(calm(X)|brave(X))))&
(![X]:((~wise(X)|~generous(X))=>(brave(X)|generous(X))))&
(![X]:((quiet(X)&brave(X))<=>(~humble(X)|~quiet(X))))&
((~funny(alice))=>(?[X]:((~happy(X)&tall(X)))))&
(?[X]:((~generous(X)<~>~happy(X))))&
(?[X]:((~brave(X)|~calm(X))))&
(?[X]:((generous(X)&~kind(X))))&
(?[X]:((~rich(X)&old(X))))&
((calm(mary)|~generous(mary)))&
((calm(mary)|tall(mary)))&
(?[X]:((kind(X)|brave(X)))) | ~brave(mary) | [
"p8",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3796021501560562909183083
% SZS output start Proof for 3796021501560562909183083
9. ! [X0] : ((~strong(X0) <~> ~humble(X0)) <=> strong(X0)) [input p8]
15. ! [X0] : ((brave(X0) & quiet(X0)) <=> (~quiet(X0) | ~humble(X0))) [input p14]
24. ~brave(mary) [input hypothesis]
55. ! [X0] : ((((humble(X0) | strong(X0)) & (~humble(X0) | ~strong(X0))) | ~strong(X0)) & (strong(X0) | ((~strong(X0) | humble(X0)) & (~humble(X0) | strong(X0))))) [nnf transformation 9]
67. ! [X0] : (((brave(X0) & quiet(X0)) | (quiet(X0) & humble(X0))) & ((~quiet(X0) | ~humble(X0)) | (~brave(X0) | ~quiet(X0)))) [nnf transformation 15]
68. ! [X0] : (((brave(X0) & quiet(X0)) | (quiet(X0) & humble(X0))) & (~quiet(X0) | ~humble(X0) | ~brave(X0) | ~quiet(X0))) [flattening 67]
110. strong(X0) | ~humble(X0) | strong(X0) [cnf transformation 55]
112. ~humble(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 55]
132. brave(X0) | humble(X0) [cnf transformation 68]
146. ~brave(mary) [cnf transformation 24]
150. strong(X0) | ~humble(X0) [duplicate literal removal 110]
151. ~humble(X0) | ~strong(X0) [duplicate literal removal 112]
259. ~humble(X0) [subsumption resolution 150,151]
312. brave(X0) [subsumption resolution 132,259]
352. $false [subsumption resolution 146,312]
% SZS output end Proof for 3796021501560562909183083
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not generous and not humble is strong or happy.
If someone is both not patient and not strong then alice is not humble or not patient and vice versa.
If susan is either generous or not quiet then someone is tall and vice versa.
Everyone who is both old and not rich is calm or not calm.
If lucy is not brave or not strong then mary is not generous and vice versa.
If lucy is not old or not rich then lucy is old or kind and vice versa.
If someone is not funny then someone is either not calm or strong and vice versa.
If someone is kind or not quiet then fred is not curious and vice versa.
Everyone who is funny or creative is calm.
If mary is both old and not funny then someone is not curious or not rich and vice versa.
Everyone who is tall is either strong or happy.
Everyone who is either funny or not quiet is either patient or happy and vice versa.
Everyone who is quiet is both not calm and not funny.
If someone is either kind or rich then john is both not old and rich.
Everyone who is brave or not tall is either funny or patient and vice versa.
If someone is both patient and creative then someone is either old or rich.
Someone is either not rich or not happy.
Paul is either not creative or creative.
John is quiet or patient.
Paul is not patient or not happy.
Fred is both curious and not brave.
John is calm or not wise.
Alice is brave.
Someone is either rich or not creative. | Fred is not calm. | entailment | (![X]:((~generous(X)&~humble(X))=>(strong(X)|happy(X))))&
((?[X]:((~patient(X)&~strong(X))))<=>((~humble(alice)|~patient(alice))))&
(((generous(susan)<~>~quiet(susan)))<=>(?[X]:(tall(X))))&
(![X]:((old(X)&~rich(X))=>(calm(X)|~calm(X))))&
(((~brave(lucy)|~strong(lucy)))<=>(~generous(mary)))&
(((~old(lucy)|~rich(lucy)))<=>((old(lucy)|kind(lucy))))&
((?[X]:(~funny(X)))<=>(?[X]:((~calm(X)<~>strong(X)))))&
((?[X]:((kind(X)|~quiet(X))))<=>(~curious(fred)))&
(![X]:((funny(X)|creative(X))=>calm(X)))&
(((old(mary)&~funny(mary)))<=>(?[X]:((~curious(X)|~rich(X)))))&
(![X]:(tall(X)=>(strong(X)<~>happy(X))))&
(![X]:((funny(X)<~>~quiet(X))<=>(patient(X)<~>happy(X))))&
(![X]:(quiet(X)=>(~calm(X)&~funny(X))))&
((?[X]:((kind(X)<~>rich(X))))=>((~old(john)&rich(john))))&
(![X]:((brave(X)|~tall(X))<=>(funny(X)<~>patient(X))))&
((?[X]:((patient(X)&creative(X))))=>(?[X]:((old(X)<~>rich(X)))))&
(?[X]:((~rich(X)<~>~happy(X))))&
((~creative(paul)<~>creative(paul)))&
((quiet(john)|patient(john)))&
((~patient(paul)|~happy(paul)))&
((curious(fred)&~brave(fred)))&
((calm(john)|~wise(john)))&
(brave(alice))&
(?[X]:((rich(X)<~>~creative(X)))) | ~calm(fred) | [
"p7",
"p12",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 4444919637816471795740368
% SZS output start Proof for 4444919637816471795740368
8. ? [X0] : (~quiet(X0) | kind(X0)) <=> ~curious(fred) [input p7]
13. ! [X0] : (quiet(X0) => (~funny(X0) & ~calm(X0))) [input p12]
21. ~brave(fred) & curious(fred) [input p20]
25. calm(fred) [input hypothesis]
35. ! [X0] : ((~funny(X0) & ~calm(X0)) | ~quiet(X0)) [ennf transformation 13]
56. (? [X0] : (~quiet(X0) | kind(X0)) | curious(fred)) & (~curious(fred) | ! [X0] : (quiet(X0) & ~kind(X0))) [nnf transformation 8]
57. (? [X0] : (~quiet(X0) | kind(X0)) | curious(fred)) & (~curious(fred) | ! [X1] : (quiet(X1) & ~kind(X1))) [rectify 56]
58. ? [X0] : (~quiet(X0) | kind(X0)) => (~quiet(sK4) | kind(sK4)) [choice axiom]
59. ((~quiet(sK4) | kind(sK4)) | curious(fred)) & (~curious(fred) | ! [X1] : (quiet(X1) & ~kind(X1))) [skolemisation 57,58]
104. ~curious(fred) | quiet(X1) [cnf transformation 59]
123. ~calm(X0) | ~quiet(X0) [cnf transformation 35]
143. curious(fred) [cnf transformation 21]
148. calm(fred) [cnf transformation 25]
251. 22 <=> curious(fred) [avatar definition]
264. 25 <=> ! [X1] : quiet(X1) [avatar definition]
265. quiet(X1) <- (25) [avatar component clause 264]
266. 25 | ~22 [avatar split clause 104,251,264]
357. 22 [avatar split clause 143,251]
374. ~quiet(fred) [resolution 123,148]
375. $false <- (25) [subsumption resolution 374,265]
376. ~25 [avatar contradiction clause 375]
377. $false [avatar sat refutation 266,357,376]
% SZS output end Proof for 4444919637816471795740368
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is tall is not patient.
If someone is not strong or not generous then someone is either not funny or not old and vice versa.
Everyone who is not wise or happy is not rich and vice versa.
Everyone who is both humble and brave is not tall.
Everyone who is not curious is both generous and not kind and vice versa.
Everyone who is not brave is both quiet and humble.
Everyone who is both not quiet and quiet is not humble or kind and vice versa.
If someone is not quiet or funny then someone is not creative or old and vice versa.
If susan is both humble and calm then someone is not curious or not strong.
Everyone who is either creative or quiet is both not patient and not generous.
Everyone who is either rich or not humble is old and vice versa.
Everyone who is either not happy or patient is both funny and not creative and vice versa.
Everyone who is either old or creative is either not calm or not tall.
Everyone who is rich is tall or old and vice versa.
If someone is tall or not rich then someone is either quiet or creative and vice versa.
Everyone who is kind or not generous is either strong or not quiet and vice versa.
Lucy is not patient.
John is not generous or generous.
Mary is tall or not strong.
Lucy is not calm or not humble.
Someone is generous or patient.
Alice is both generous and not rich.
Susan is not curious.
Lucy is humble or quiet. | Susan is funny. | neutral | (![X]:(tall(X)=>~patient(X)))&
((?[X]:((~strong(X)|~generous(X))))<=>(?[X]:((~funny(X)<~>~old(X)))))&
(![X]:((~wise(X)|happy(X))<=>~rich(X)))&
(![X]:((humble(X)&brave(X))=>~tall(X)))&
(![X]:(~curious(X)<=>(generous(X)&~kind(X))))&
(![X]:(~brave(X)=>(quiet(X)&humble(X))))&
(![X]:((~quiet(X)&quiet(X))<=>(~humble(X)|kind(X))))&
((?[X]:((~quiet(X)|funny(X))))<=>(?[X]:((~creative(X)|old(X)))))&
(((humble(susan)&calm(susan)))=>(?[X]:((~curious(X)|~strong(X)))))&
(![X]:((creative(X)<~>quiet(X))=>(~patient(X)&~generous(X))))&
(![X]:((rich(X)<~>~humble(X))<=>old(X)))&
(![X]:((~happy(X)<~>patient(X))<=>(funny(X)&~creative(X))))&
(![X]:((old(X)<~>creative(X))=>(~calm(X)<~>~tall(X))))&
(![X]:(rich(X)<=>(tall(X)|old(X))))&
((?[X]:((tall(X)|~rich(X))))<=>(?[X]:((quiet(X)<~>creative(X)))))&
(![X]:((kind(X)|~generous(X))<=>(strong(X)<~>~quiet(X))))&
(~patient(lucy))&
((~generous(john)|generous(john)))&
((tall(mary)|~strong(mary)))&
((~calm(lucy)|~humble(lucy)))&
(?[X]:((generous(X)|patient(X))))&
((generous(alice)&~rich(alice)))&
(~curious(susan))&
((humble(lucy)|quiet(lucy))) | funny(susan) | [] | null | 0 |
Everyone who is both brave and not creative is either curious or kind and vice versa.
Everyone who is wise or not curious is both not creative and not patient.
If someone is both not rich and not old then someone is either rich or curious.
Everyone who is both humble and creative is not quiet or kind and vice versa.
Everyone who is humble is wise.
Everyone who is both not happy and not funny is both not strong and happy.
Everyone who is not wise is not brave or happy and vice versa.
Everyone who is strong is either funny or curious.
If susan is not wise or not strong then fred is strong and vice versa.
Everyone who is not calm or funny is not funny and vice versa.
Everyone who is either not kind or not tall is either rich or not patient and vice versa.
Everyone who is both happy and not kind is either not strong or not old and vice versa.
If someone is both not patient and old then fred is both not curious and humble and vice versa.
If someone is both not strong and not funny then someone is brave and vice versa.
Everyone who is not funny or curious is not brave or tall and vice versa.
Someone is either kind or patient.
Susan is not patient or not creative.
Someone is either patient or not patient.
Alice is not quiet or not kind.
Susan is either not rich or not quiet. | Susan is funny. | contradiction | (![X]:((brave(X)&~creative(X))<=>(curious(X)<~>kind(X))))&
(![X]:((wise(X)|~curious(X))=>(~creative(X)&~patient(X))))&
((?[X]:((~rich(X)&~old(X))))=>(?[X]:((rich(X)<~>curious(X)))))&
(![X]:((humble(X)&creative(X))<=>(~quiet(X)|kind(X))))&
(![X]:(humble(X)=>wise(X)))&
(![X]:((~happy(X)&~funny(X))=>(~strong(X)&happy(X))))&
(![X]:(~wise(X)<=>(~brave(X)|happy(X))))&
(![X]:(strong(X)=>(funny(X)<~>curious(X))))&
(((~wise(susan)|~strong(susan)))<=>(strong(fred)))&
(![X]:((~calm(X)|funny(X))<=>~funny(X)))&
(![X]:((~kind(X)<~>~tall(X))<=>(rich(X)<~>~patient(X))))&
(![X]:((happy(X)&~kind(X))<=>(~strong(X)<~>~old(X))))&
((?[X]:((~patient(X)&old(X))))<=>((~curious(fred)&humble(fred))))&
((?[X]:((~strong(X)&~funny(X))))<=>(?[X]:(brave(X))))&
(![X]:((~funny(X)|curious(X))<=>(~brave(X)|tall(X))))&
(?[X]:((kind(X)<~>patient(X))))&
((~patient(susan)|~creative(susan)))&
(?[X]:((patient(X)<~>~patient(X))))&
((~quiet(alice)|~kind(alice)))&
((~rich(susan)<~>~quiet(susan))) | funny(susan) | [
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 6782370593544630778902494
% SZS output start Proof for 6782370593544630778902494
10. ! [X0] : ((funny(X0) | ~calm(X0)) <=> ~funny(X0)) [input p9]
21. funny(susan) [input hypothesis]
43. ! [X0] : (((funny(X0) | ~calm(X0)) | funny(X0)) & (~funny(X0) | (~funny(X0) & calm(X0)))) [nnf transformation 10]
44. ! [X0] : ((funny(X0) | ~calm(X0) | funny(X0)) & (~funny(X0) | (~funny(X0) & calm(X0)))) [flattening 43]
96. ~funny(X0) | ~funny(X0) [cnf transformation 44]
131. funny(susan) [cnf transformation 21]
132. ~funny(X0) [duplicate literal removal 96]
242. $false [subsumption resolution 131,132]
% SZS output end Proof for 6782370593544630778902494
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not brave or not calm is not patient and vice versa. Everyone who is kind is both wise and not funny and vice versa. Everyone who is not quiet or not wise is not strong. Everyone who is both not calm and not kind is kind and vice versa. Everyone who is either strong or not humble is patient or wise. If lucy is not patient then someone is not kind and vice versa. Everyone who is patient or generous is both not generous and not curious and vice versa. If john is rich or strong then someone is not humble or tall and vice versa. Everyone who is either creative or patient is not brave or not creative and vice versa. If fred is either not brave or brave then someone is either funny or not creative and vice versa. Everyone who is both curious and not tall is not wise. If lucy is brave or kind then someone is not old. If mary is both humble and not generous then someone is both not kind and not strong. Everyone who is either creative or funny is not calm or rich. Everyone who is both not rich and wise is either generous or not calm and vice versa. Someone is curious. John is both funny and brave. Mary is not brave or kind. Paul is not quiet. Someone is quiet or not kind. Susan is both not old and strong. Alice is not calm or not old. | Mary is not kind. | entailment | (![X]:((~brave(X)<~>~calm(X))<=>~patient(X)))&
(![X]:(kind(X)<=>(wise(X)&~funny(X))))&
(![X]:((~quiet(X)|~wise(X))=>~strong(X)))&
(![X]:((~calm(X)&~kind(X))<=>kind(X)))&
(![X]:((strong(X)<~>~humble(X))=>(patient(X)|wise(X))))&
((~patient(lucy))<=>(?[X]:(~kind(X))))&
(![X]:((patient(X)|generous(X))<=>(~generous(X)&~curious(X))))&
(((rich(john)|strong(john)))<=>(?[X]:((~humble(X)|tall(X)))))&
(![X]:((creative(X)<~>patient(X))<=>(~brave(X)|~creative(X))))&
(((~brave(fred)<~>brave(fred)))<=>(?[X]:((funny(X)<~>~creative(X)))))&
(![X]:((curious(X)&~tall(X))=>~wise(X)))&
(((brave(lucy)|kind(lucy)))=>(?[X]:(~old(X))))&
(((humble(mary)&~generous(mary)))=>(?[X]:((~kind(X)&~strong(X)))))&
(![X]:((creative(X)<~>funny(X))=>(~calm(X)|rich(X))))&
(![X]:((~rich(X)&wise(X))<=>(generous(X)<~>~calm(X))))&
(?[X]:(curious(X)))&
((funny(john)&brave(john)))&
((~brave(mary)|kind(mary)))&
(~quiet(paul))&
(?[X]:((quiet(X)|~kind(X))))&
((~old(susan)&strong(susan)))&
((~calm(alice)|~old(alice))) | ~kind(mary) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 4026277439007379669727366
% SZS output start Proof for 4026277439007379669727366
4. ! [X0] : ((~kind(X0) & ~calm(X0)) <=> kind(X0)) [input p3]
23. kind(mary) [input hypothesis]
39. ! [X0] : (((~kind(X0) & ~calm(X0)) | ~kind(X0)) & (kind(X0) | (kind(X0) | calm(X0)))) [nnf transformation 4]
40. ! [X0] : (((~kind(X0) & ~calm(X0)) | ~kind(X0)) & (kind(X0) | kind(X0) | calm(X0))) [flattening 39]
79. ~kind(X0) | ~kind(X0) [cnf transformation 40]
125. kind(mary) [cnf transformation 23]
135. ~kind(X0) [duplicate literal removal 79]
197. $false [subsumption resolution 125,135]
% SZS output end Proof for 4026277439007379669727366
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not kind and brave is not curious or not wise.
Everyone who is either not happy or not curious is generous and vice versa.
If paul is not creative then fred is not rich or rich and vice versa.
If someone is either not humble or not rich then someone is both creative and not curious and vice versa.
Everyone who is rich is both not wise and kind.
If susan is not tall then someone is rich or not calm.
If someone is brave or creative then someone is not tall and vice versa.
Everyone who is both not generous and creative is wise or not rich.
Everyone who is either not creative or not wise is either kind or not wise.
If alice is kind or not happy then someone is either not generous or not creative.
Everyone who is not funny is quiet.
Everyone who is not quiet or calm is both rich and not strong.
If paul is either old or not strong then someone is both not generous and not curious.
Everyone who is creative or kind is both not funny and not happy.
If someone is not happy or humble then someone is both brave and not calm.
If someone is funny or brave then lucy is not tall or not calm.
Mary is not kind.
Fred is not wise.
Mary is creative or not old.
Someone is funny.
Someone is not calm.
Someone is both rich and not creative.
Someone is both not strong and patient. | Paul is old. | neutral | (![X]:((~kind(X)&brave(X))=>(~curious(X)|~wise(X))))&
(![X]:((~happy(X)<~>~curious(X))<=>generous(X)))&
((~creative(paul))<=>((~rich(fred)|rich(fred))))&
((?[X]:((~humble(X)<~>~rich(X))))<=>(?[X]:((creative(X)&~curious(X)))))&
(![X]:(rich(X)=>(~wise(X)&kind(X))))&
((~tall(susan))=>(?[X]:((rich(X)|~calm(X)))))&
((?[X]:((brave(X)|creative(X))))<=>(?[X]:(~tall(X))))&
(![X]:((~generous(X)&creative(X))=>(wise(X)|~rich(X))))&
(![X]:((~creative(X)<~>~wise(X))=>(kind(X)<~>~wise(X))))&
(((kind(alice)|~happy(alice)))=>(?[X]:((~generous(X)<~>~creative(X)))))&
(![X]:(~funny(X)=>quiet(X)))&
(![X]:((~quiet(X)|calm(X))=>(rich(X)&~strong(X))))&
(((old(paul)<~>~strong(paul)))=>(?[X]:((~generous(X)&~curious(X)))))&
(![X]:((creative(X)|kind(X))=>(~funny(X)&~happy(X))))&
((?[X]:((~happy(X)|humble(X))))=>(?[X]:((brave(X)&~calm(X)))))&
((?[X]:((funny(X)|brave(X))))=>((~tall(lucy)|~calm(lucy))))&
(~kind(mary))&
(~wise(fred))&
((creative(mary)|~old(mary)))&
(?[X]:(funny(X)))&
(?[X]:(~calm(X)))&
(?[X]:((rich(X)&~creative(X))))&
(?[X]:((~strong(X)&patient(X)))) | old(paul) | [] | null | 0 |
Everyone who is not funny or not generous is old or creative and vice versa.
Everyone who is calm or rich is not generous.
Everyone who is patient is not creative or quiet.
If someone is kind then john is either brave or happy.
If john is rich or not generous then someone is not brave or not creative and vice versa.
Everyone who is either quiet or strong is curious or not old and vice versa.
Everyone who is both not brave and patient is both kind and not brave and vice versa.
Everyone who is not funny is either calm or not strong and vice versa.
If someone is not brave or not creative then alice is not old or happy and vice versa.
Everyone who is both brave and not curious is not tall.
Everyone who is either not funny or curious is not funny and vice versa.
If alice is both not calm and not kind then john is not kind and vice versa.
If susan is either not creative or not calm then john is both generous and not generous and vice versa.
If lucy is both not brave and not happy then someone is not wise or not funny and vice versa.
Everyone who is happy or curious is both not humble and not rich and vice versa.
Everyone who is either not strong or not curious is either not wise or not funny and vice versa.
Fred is both humble and not creative.
Someone is humble.
Alice is either not quiet or not rich.
Mary is strong or not happy.
Susan is not calm.
Someone is generous.
Paul is patient.
Lucy is either calm or strong. | Lucy is rich. | neutral | (![X]:((~funny(X)|~generous(X))<=>(old(X)|creative(X))))&
(![X]:((calm(X)|rich(X))=>~generous(X)))&
(![X]:(patient(X)=>(~creative(X)|quiet(X))))&
((?[X]:(kind(X)))=>((brave(john)<~>happy(john))))&
(((rich(john)|~generous(john)))<=>(?[X]:((~brave(X)|~creative(X)))))&
(![X]:((quiet(X)<~>strong(X))<=>(curious(X)|~old(X))))&
(![X]:((~brave(X)&patient(X))<=>(kind(X)&~brave(X))))&
(![X]:(~funny(X)<=>(calm(X)<~>~strong(X))))&
((?[X]:((~brave(X)|~creative(X))))<=>((~old(alice)|happy(alice))))&
(![X]:((brave(X)&~curious(X))=>~tall(X)))&
(![X]:((~funny(X)<~>curious(X))<=>~funny(X)))&
(((~calm(alice)&~kind(alice)))<=>(~kind(john)))&
(((~creative(susan)<~>~calm(susan)))<=>((generous(john)&~generous(john))))&
(((~brave(lucy)&~happy(lucy)))<=>(?[X]:((~wise(X)|~funny(X)))))&
(![X]:((happy(X)|curious(X))<=>(~humble(X)&~rich(X))))&
(![X]:((~strong(X)<~>~curious(X))<=>(~wise(X)<~>~funny(X))))&
((humble(fred)&~creative(fred)))&
(?[X]:(humble(X)))&
((~quiet(alice)<~>~rich(alice)))&
((strong(mary)|~happy(mary)))&
(~calm(susan))&
(?[X]:(generous(X)))&
(patient(paul))&
((calm(lucy)<~>strong(lucy))) | rich(lucy) | [] | null | 0 |
If someone is both strong and happy then fred is both not humble and rich.
If mary is rich or happy then fred is either not tall or happy and vice versa.
Everyone who is not rich or humble is not funny or not humble.
If someone is either quiet or not strong then someone is not generous.
Everyone who is not creative is either old or patient and vice versa.
If someone is either not strong or happy then paul is both funny and not brave.
Everyone who is both not humble and not calm is either rich or humble.
If someone is either not calm or not wise then someone is strong or wise and vice versa.
Everyone who is not calm or happy is not humble and vice versa.
Everyone who is either not funny or calm is both funny and not rich.
Everyone who is both brave and not quiet is both generous and not calm and vice versa.
If susan is not tall then someone is either not happy or not old and vice versa.
Everyone who is not calm or not old is not happy.
If someone is humble or old then someone is both happy and not calm and vice versa.
Everyone who is either old or not funny is either quiet or calm.
Everyone who is both quiet and curious is wise or kind and vice versa.
Someone is happy or strong.
John is either not wise or not happy.
Fred is funny.
John is either tall or not kind.
Someone is both curious and not brave. | Fred is rich. | entailment | ((?[X]:((strong(X)&happy(X))))=>((~humble(fred)&rich(fred))))&
(((rich(mary)|happy(mary)))<=>((~tall(fred)<~>happy(fred))))&
(![X]:((~rich(X)|humble(X))=>(~funny(X)|~humble(X))))&
((?[X]:((quiet(X)<~>~strong(X))))=>(?[X]:(~generous(X))))&
(![X]:(~creative(X)<=>(old(X)<~>patient(X))))&
((?[X]:((~strong(X)<~>happy(X))))=>((funny(paul)&~brave(paul))))&
(![X]:((~humble(X)&~calm(X))=>(rich(X)<~>humble(X))))&
((?[X]:((~calm(X)<~>~wise(X))))<=>(?[X]:((strong(X)|wise(X)))))&
(![X]:((~calm(X)|happy(X))<=>~humble(X)))&
(![X]:((~funny(X)<~>calm(X))=>(funny(X)&~rich(X))))&
(![X]:((brave(X)&~quiet(X))<=>(generous(X)&~calm(X))))&
((~tall(susan))<=>(?[X]:((~happy(X)<~>~old(X)))))&
(![X]:((~calm(X)|~old(X))=>~happy(X)))&
((?[X]:((humble(X)|old(X))))<=>(?[X]:((happy(X)&~calm(X)))))&
(![X]:((old(X)<~>~funny(X))=>(quiet(X)<~>calm(X))))&
(![X]:((quiet(X)&curious(X))<=>(wise(X)|kind(X))))&
(?[X]:((happy(X)|strong(X))))&
((~wise(john)<~>~happy(john)))&
(funny(fred))&
((tall(john)<~>~kind(john)))&
(?[X]:((curious(X)&~brave(X)))) | rich(fred) | [
"p6",
"p8",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 8090315510869007275478812
% SZS output start Proof for 8090315510869007275478812
7. ! [X0] : ((~calm(X0) & ~humble(X0)) => (rich(X0) <~> humble(X0))) [input p6]
9. ! [X0] : ((happy(X0) | ~calm(X0)) <=> ~humble(X0)) [input p8]
13. ! [X0] : ((~old(X0) | ~calm(X0)) => ~happy(X0)) [input p12]
14. ? [X0] : (old(X0) | humble(X0)) <=> ? [X0] : (~calm(X0) & happy(X0)) [input p13]
22. ~rich(fred) [input hypothesis]
25. ? [X0] : (old(X0) | humble(X0)) <=> ? [X1] : (~calm(X1) & happy(X1)) [rectify 14]
31. ! [X0] : ((rich(X0) <~> humble(X0)) | (calm(X0) | humble(X0))) [ennf transformation 7]
32. ! [X0] : ((rich(X0) <~> humble(X0)) | calm(X0) | humble(X0)) [flattening 31]
34. ! [X0] : (~happy(X0) | (old(X0) & calm(X0))) [ennf transformation 13]
43. ! [X0] : (((~humble(X0) | ~rich(X0)) & (humble(X0) | rich(X0))) | calm(X0) | humble(X0)) [nnf transformation 32]
49. ! [X0] : (((happy(X0) | ~calm(X0)) | humble(X0)) & (~humble(X0) | (~happy(X0) & calm(X0)))) [nnf transformation 9]
50. ! [X0] : ((happy(X0) | ~calm(X0) | humble(X0)) & (~humble(X0) | (~happy(X0) & calm(X0)))) [flattening 49]
58. (? [X0] : (old(X0) | humble(X0)) | ! [X1] : (calm(X1) | ~happy(X1))) & (? [X1] : (~calm(X1) & happy(X1)) | ! [X0] : (~old(X0) & ~humble(X0))) [nnf transformation 25]
59. (? [X0] : (old(X0) | humble(X0)) | ! [X1] : (calm(X1) | ~happy(X1))) & (? [X2] : (~calm(X2) & happy(X2)) | ! [X3] : (~old(X3) & ~humble(X3))) [rectify 58]
60. ? [X0] : (old(X0) | humble(X0)) => (old(sK4) | humble(sK4)) [choice axiom]
61. ? [X2] : (~calm(X2) & happy(X2)) => (~calm(sK5) & happy(sK5)) [choice axiom]
62. ((old(sK4) | humble(sK4)) | ! [X1] : (calm(X1) | ~happy(X1))) & ((~calm(sK5) & happy(sK5)) | ! [X3] : (~old(X3) & ~humble(X3))) [skolemisation 59,61,60]
88. humble(X0) | rich(X0) | calm(X0) | humble(X0) [cnf transformation 43]
98. ~calm(X0) | happy(X0) | humble(X0) [cnf transformation 50]
111. ~happy(X0) | calm(X0) [cnf transformation 34]
112. ~happy(X0) | old(X0) [cnf transformation 34]
113. happy(sK5) | ~humble(X3) [cnf transformation 62]
114. happy(sK5) | ~old(X3) [cnf transformation 62]
115. ~calm(sK5) | ~humble(X3) [cnf transformation 62]
116. ~calm(sK5) | ~old(X3) [cnf transformation 62]
135. ~rich(fred) [cnf transformation 22]
137. calm(X0) | rich(X0) | humble(X0) [duplicate literal removal 88]
143. 2 <=> rich(fred) [avatar definition]
144. ~rich(fred) <- (~2) [avatar component clause 143]
153. 4 <=> happy(fred) [avatar definition]
154. happy(fred) <- (4) [avatar component clause 153]
155. ~happy(fred) <- (~4) [avatar component clause 153]
236. 22 <=> ! [X0] : (~happy(X0) | old(X0)) [avatar definition]
237. ~happy(X0) | old(X0) <- (22) [avatar component clause 236]
257. 22 [avatar split clause 112,236]
259. 27 <=> ! [X3] : ~old(X3) [avatar definition]
260. ~old(X3) <- (27) [avatar component clause 259]
262. 28 <=> calm(sK5) [avatar definition]
264. ~calm(sK5) <- (~28) [avatar component clause 262]
265. 27 | ~28 [avatar split clause 116,262,259]
267. 29 <=> ! [X3] : ~humble(X3) [avatar definition]
268. ~humble(X3) <- (29) [avatar component clause 267]
269. 29 | ~28 [avatar split clause 115,262,267]
271. 30 <=> happy(sK5) [avatar definition]
273. happy(sK5) <- (30) [avatar component clause 271]
274. 27 | 30 [avatar split clause 114,271,259]
275. 29 | 30 [avatar split clause 113,271,267]
307. ~2 [avatar split clause 135,143]
308. ~happy(X0) <- (22, 27) [subsumption resolution 237,260]
310. $false <- (4, 22, 27) [subsumption resolution 154,308]
311. ~4 | ~22 | ~27 [avatar contradiction clause 310]
313. calm(sK5) <- (30) [resolution 111,273]
315. $false <- (~28, 30) [subsumption resolution 313,264]
316. 28 | ~30 [avatar contradiction clause 315]
379. rich(X2) | humble(X2) | happy(X2) | humble(X2) [resolution 137,98]
381. rich(X2) | humble(X2) | happy(X2) [duplicate literal removal 379]
384. rich(X2) | happy(X2) <- (29) [subsumption resolution 381,268]
416. happy(fred) <- (~2, 29) [resolution 384,144]
418. $false <- (~2, ~4, 29) [subsumption resolution 416,155]
419. 2 | 4 | ~29 [avatar contradiction clause 418]
422. $false [avatar sat refutation 257,265,269,274,275,307,311,316,419]
% SZS output end Proof for 8090315510869007275478812
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If fred is not creative then someone is either happy or not humble and vice versa.
If someone is both not happy and not tall then alice is humble and vice versa.
If mary is not rich then mary is not funny or not kind.
If lucy is strong or not rich then someone is creative and vice versa.
Everyone who is both not humble and not wise is either strong or not wise and vice versa.
If fred is either rich or not calm then someone is either not funny or not curious and vice versa.
If someone is happy then someone is quiet or old.
If fred is not old or not humble then susan is not rich.
Everyone who is creative is either wise or not old and vice versa.
Everyone who is both quiet and not patient is rich and vice versa.
Everyone who is either not calm or not humble is rich or curious and vice versa.
Everyone who is both not brave and patient is either not happy or quiet.
Everyone who is not rich or not calm is both not rich and creative.
If fred is happy or rich then fred is either generous or kind.
If john is not happy then susan is kind.
If paul is tall then paul is either humble or generous.
Paul is either not kind or kind.
Mary is both not tall and not happy.
Paul is not happy or not funny.
Fred is not kind or not old.
Fred is not creative.
Alice is not tall or funny.
Someone is both not brave and creative. | Lucy is rich. | contradiction | ((~creative(fred))<=>(?[X]:((happy(X)<~>~humble(X)))))&
((?[X]:((~happy(X)&~tall(X))))<=>(humble(alice)))&
((~rich(mary))=>((~funny(mary)|~kind(mary))))&
(((strong(lucy)|~rich(lucy)))<=>(?[X]:(creative(X))))&
(![X]:((~humble(X)&~wise(X))<=>(strong(X)<~>~wise(X))))&
(((rich(fred)<~>~calm(fred)))<=>(?[X]:((~funny(X)<~>~curious(X)))))&
((?[X]:(happy(X)))=>(?[X]:((quiet(X)|old(X)))))&
(((~old(fred)|~humble(fred)))=>(~rich(susan)))&
(![X]:(creative(X)<=>(wise(X)<~>~old(X))))&
(![X]:((quiet(X)&~patient(X))<=>rich(X)))&
(![X]:((~calm(X)<~>~humble(X))<=>(rich(X)|curious(X))))&
(![X]:((~brave(X)&patient(X))=>(~happy(X)<~>quiet(X))))&
(![X]:((~rich(X)|~calm(X))=>(~rich(X)&creative(X))))&
(((happy(fred)|rich(fred)))=>((generous(fred)<~>kind(fred))))&
((~happy(john))=>(kind(susan)))&
((tall(paul))=>((humble(paul)<~>generous(paul))))&
((~kind(paul)<~>kind(paul)))&
((~tall(mary)&~happy(mary)))&
((~happy(paul)|~funny(paul)))&
((~kind(fred)|~old(fred)))&
(~creative(fred))&
((~tall(alice)|funny(alice)))&
(?[X]:((~brave(X)&creative(X)))) | rich(lucy) | [
"p3",
"p4",
"p10",
"p12",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 6146540668736305940167664
% SZS output start Proof for 6146540668736305940167664
4. (~rich(lucy) | strong(lucy)) <=> ? [X0] : creative(X0) [input p3]
5. ! [X0] : ((~wise(X0) & ~humble(X0)) <=> (strong(X0) <~> ~wise(X0))) [input p4]
11. ! [X0] : ((~calm(X0) <~> ~humble(X0)) <=> (curious(X0) | rich(X0))) [input p10]
13. ! [X0] : ((~calm(X0) | ~rich(X0)) => (creative(X0) & ~rich(X0))) [input p12]
23. ? [X0] : (creative(X0) & ~brave(X0)) [input p22]
24. rich(lucy) [input hypothesis]
32. ! [X0] : ((creative(X0) & ~rich(X0)) | (calm(X0) & rich(X0))) [ennf transformation 13]
44. ((~rich(lucy) | strong(lucy)) | ! [X0] : ~creative(X0)) & (? [X0] : creative(X0) | (rich(lucy) & ~strong(lucy))) [nnf transformation 4]
45. (~rich(lucy) | strong(lucy) | ! [X0] : ~creative(X0)) & (? [X0] : creative(X0) | (rich(lucy) & ~strong(lucy))) [flattening 44]
46. (~rich(lucy) | strong(lucy) | ! [X0] : ~creative(X0)) & (? [X1] : creative(X1) | (rich(lucy) & ~strong(lucy))) [rectify 45]
47. ? [X1] : creative(X1) => creative(sK2) [choice axiom]
48. (~rich(lucy) | strong(lucy) | ! [X0] : ~creative(X0)) & (creative(sK2) | (rich(lucy) & ~strong(lucy))) [skolemisation 46,47]
49. ! [X0] : (((~wise(X0) & ~humble(X0)) | ((strong(X0) | wise(X0)) & (~wise(X0) | ~strong(X0)))) & (((wise(X0) | ~strong(X0)) & (~wise(X0) | strong(X0))) | (wise(X0) | humble(X0)))) [nnf transformation 5]
50. ! [X0] : (((~wise(X0) & ~humble(X0)) | ((strong(X0) | wise(X0)) & (~wise(X0) | ~strong(X0)))) & (((wise(X0) | ~strong(X0)) & (~wise(X0) | strong(X0))) | wise(X0) | humble(X0))) [flattening 49]
61. ! [X0] : ((((humble(X0) | calm(X0)) & (~humble(X0) | ~calm(X0))) | (~curious(X0) & ~rich(X0))) & ((curious(X0) | rich(X0)) | ((~calm(X0) | humble(X0)) & (~humble(X0) | calm(X0))))) [nnf transformation 11]
62. ! [X0] : ((((humble(X0) | calm(X0)) & (~humble(X0) | ~calm(X0))) | (~curious(X0) & ~rich(X0))) & (curious(X0) | rich(X0) | ((~calm(X0) | humble(X0)) & (~humble(X0) | calm(X0))))) [flattening 61]
67. ? [X0] : (creative(X0) & ~brave(X0)) => (creative(sK5) & ~brave(sK5)) [choice axiom]
68. creative(sK5) & ~brave(sK5) [skolemisation 23,67]
79. ~rich(lucy) | strong(lucy) | ~creative(X0) [cnf transformation 48]
81. wise(X0) | ~strong(X0) | wise(X0) | humble(X0) [cnf transformation 50]
84. ~wise(X0) | ~wise(X0) | ~strong(X0) [cnf transformation 50]
106. ~calm(X0) | ~humble(X0) | ~rich(X0) [cnf transformation 62]
113. ~rich(X0) | calm(X0) [cnf transformation 32]
132. creative(sK5) [cnf transformation 68]
133. rich(lucy) [cnf transformation 24]
134. wise(X0) | ~strong(X0) | humble(X0) [duplicate literal removal 81]
135. ~wise(X0) | ~strong(X0) [duplicate literal removal 84]
190. 13 <=> ! [X0] : ~creative(X0) [avatar definition]
191. ~creative(X0) <- (13) [avatar component clause 190]
193. 14 <=> strong(lucy) [avatar definition]
195. strong(lucy) <- (14) [avatar component clause 193]
197. 15 <=> rich(lucy) [avatar definition]
198. rich(lucy) <- (15) [avatar component clause 197]
200. 13 | 14 | ~15 [avatar split clause 79,197,193,190]
207. ~strong(X0) | humble(X0) [subsumption resolution 134,135]
323. 15 [avatar split clause 133,197]
324. $false <- (13) [resolution 191,132]
325. ~13 [avatar contradiction clause 324]
329. calm(lucy) <- (15) [resolution 113,198]
341. humble(lucy) <- (14) [resolution 207,195]
401. ~humble(lucy) | ~rich(lucy) <- (15) [resolution 106,329]
404. ~rich(lucy) <- (14, 15) [subsumption resolution 401,341]
405. $false <- (14, 15) [subsumption resolution 404,198]
406. ~14 | ~15 [avatar contradiction clause 405]
410. $false [avatar sat refutation 200,323,325,406]
% SZS output end Proof for 6146540668736305940167664
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is creative is both not generous and generous and vice versa. If susan is both not kind and not calm then someone is either kind or not rich. If someone is rich then someone is both not creative and not calm. Everyone who is either old or humble is either not happy or not old. Everyone who is both funny and wise is calm. If someone is calm then alice is not kind. If someone is not old or kind then someone is either not kind or kind. If paul is either brave or not tall then susan is both humble and not curious and vice versa. Everyone who is either quiet or not tall is old and vice versa. If john is both not creative and not kind then someone is not humble or generous. Everyone who is not kind is wise or not kind and vice versa. If someone is both not generous and not happy then lucy is creative and vice versa. Everyone who is not calm is tall or not funny. Everyone who is curious is either not quiet or wise. Everyone who is both generous and patient is both calm and not patient and vice versa. Everyone who is not calm is both not patient and rich. Fred is either not calm or patient. Someone is curious. Someone is not rich or not quiet. Alice is either creative or old. Susan is either kind or patient. Paul is not calm. Someone is strong or creative. Someone is either tall or happy. | Fred is not creative. | entailment | (![X]:(creative(X)<=>(~generous(X)&generous(X))))&
(((~kind(susan)&~calm(susan)))=>(?[X]:((kind(X)<~>~rich(X)))))&
((?[X]:(rich(X)))=>(?[X]:((~creative(X)&~calm(X)))))&
(![X]:((old(X)<~>humble(X))=>(~happy(X)<~>~old(X))))&
(![X]:((funny(X)&wise(X))=>calm(X)))&
((?[X]:(calm(X)))=>(~kind(alice)))&
((?[X]:((~old(X)|kind(X))))=>(?[X]:((~kind(X)<~>kind(X)))))&
(((brave(paul)<~>~tall(paul)))<=>((humble(susan)&~curious(susan))))&
(![X]:((quiet(X)<~>~tall(X))<=>old(X)))&
(((~creative(john)&~kind(john)))=>(?[X]:((~humble(X)|generous(X)))))&
(![X]:(~kind(X)<=>(wise(X)|~kind(X))))&
((?[X]:((~generous(X)&~happy(X))))<=>(creative(lucy)))&
(![X]:(~calm(X)=>(tall(X)|~funny(X))))&
(![X]:(curious(X)=>(~quiet(X)<~>wise(X))))&
(![X]:((generous(X)&patient(X))<=>(calm(X)&~patient(X))))&
(![X]:(~calm(X)=>(~patient(X)&rich(X))))&
((~calm(fred)<~>patient(fred)))&
(?[X]:(curious(X)))&
(?[X]:((~rich(X)|~quiet(X))))&
((creative(alice)<~>old(alice)))&
((kind(susan)<~>patient(susan)))&
(~calm(paul))&
(?[X]:((strong(X)|creative(X))))&
(?[X]:((tall(X)<~>happy(X)))) | ~creative(fred) | [
"p0",
"hypothesis"
] | % SZS status Unsatisfiable for 3442209343568801070833087
% SZS output start Proof for 3442209343568801070833087
1. ! [X0] : (creative(X0) <=> (generous(X0) & ~generous(X0))) [input p0]
25. creative(fred) [input hypothesis]
41. ! [X0] : ((creative(X0) | (~generous(X0) | generous(X0))) & ((generous(X0) & ~generous(X0)) | ~creative(X0))) [nnf transformation 1]
42. ! [X0] : ((creative(X0) | ~generous(X0) | generous(X0)) & ((generous(X0) & ~generous(X0)) | ~creative(X0))) [flattening 41]
78. ~generous(X0) | ~creative(X0) [cnf transformation 42]
79. generous(X0) | ~creative(X0) [cnf transformation 42]
130. creative(fred) [cnf transformation 25]
135. ~creative(X0) [subsumption resolution 78,79]
233. $false [subsumption resolution 130,135]
% SZS output end Proof for 3442209343568801070833087
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet is not wise or not humble. If someone is either patient or generous then lucy is not creative. If someone is either not kind or happy then someone is wise. If someone is both patient and kind then someone is not rich and vice versa. Everyone who is not calm or brave is both not humble and not calm and vice versa. If mary is strong or quiet then susan is either not creative or not brave. If someone is generous or happy then someone is happy. Everyone who is both not funny and calm is not humble. Everyone who is quiet is happy or not curious and vice versa. Everyone who is kind is not tall. Everyone who is both not old and kind is both not tall and not humble and vice versa. If john is either quiet or old then mary is both rich and calm and vice versa. If lucy is either not funny or creative then someone is curious and vice versa. Everyone who is either not calm or not quiet is not rich or brave and vice versa. Everyone who is quiet or creative is either not wise or kind and vice versa. If lucy is both humble and kind then paul is not patient. Someone is either curious or funny. Alice is either not curious or not brave. Someone is not patient or not tall. Lucy is either not kind or kind. Someone is both not calm and old. Someone is strong or not old. Someone is both not rich and curious. Susan is not happy. | Susan is brave. | neutral | (![X]:(~quiet(X)=>(~wise(X)|~humble(X))))&
((?[X]:((patient(X)<~>generous(X))))=>(~creative(lucy)))&
((?[X]:((~kind(X)<~>happy(X))))=>(?[X]:(wise(X))))&
((?[X]:((patient(X)&kind(X))))<=>(?[X]:(~rich(X))))&
(![X]:((~calm(X)|brave(X))<=>(~humble(X)&~calm(X))))&
(((strong(mary)|quiet(mary)))=>((~creative(susan)<~>~brave(susan))))&
((?[X]:((generous(X)|happy(X))))=>(?[X]:(happy(X))))&
(![X]:((~funny(X)&calm(X))=>~humble(X)))&
(![X]:(quiet(X)<=>(happy(X)|~curious(X))))&
(![X]:(kind(X)=>~tall(X)))&
(![X]:((~old(X)&kind(X))<=>(~tall(X)&~humble(X))))&
(((quiet(john)<~>old(john)))<=>((rich(mary)&calm(mary))))&
(((~funny(lucy)<~>creative(lucy)))<=>(?[X]:(curious(X))))&
(![X]:((~calm(X)<~>~quiet(X))<=>(~rich(X)|brave(X))))&
(![X]:((quiet(X)|creative(X))<=>(~wise(X)<~>kind(X))))&
(((humble(lucy)&kind(lucy)))=>(~patient(paul)))&
(?[X]:((curious(X)<~>funny(X))))&
((~curious(alice)<~>~brave(alice)))&
(?[X]:((~patient(X)|~tall(X))))&
((~kind(lucy)<~>kind(lucy)))&
(?[X]:((~calm(X)&old(X))))&
(?[X]:((strong(X)|~old(X))))&
(?[X]:((~rich(X)&curious(X))))&
(~happy(susan)) | brave(susan) | [] | null | 0 |
If fred is either not strong or calm then someone is brave.
If mary is either not wise or not humble then someone is either not rich or not strong and vice versa.
Everyone who is old or not rich is curious.
If mary is both kind and not humble then someone is wise.
Everyone who is happy is either not generous or not curious and vice versa.
If paul is not rich then someone is both not strong and wise.
Everyone who is both not patient and happy is strong or not tall and vice versa.
Everyone who is generous or creative is not creative or old and vice versa.
If paul is either not curious or calm then mary is both tall and not curious.
Everyone who is either creative or curious is both not strong and happy and vice versa.
Everyone who is either happy or not brave is either tall or curious and vice versa.
If paul is both not wise and old then someone is old or patient and vice versa.
Everyone who is humble is either strong or not humble and vice versa.
Everyone who is old is either not calm or not generous.
If someone is either old or not brave then someone is both not funny and funny and vice versa.
If mary is either not kind or curious then someone is tall or not happy and vice versa.
Someone is both creative and tall.
John is not quiet.
Alice is either not generous or not calm.
Someone is either brave or old.
Someone is either funny or quiet.
Fred is both curious and funny.
Someone is either not happy or not generous. | Alice is not patient. | entailment | (((~strong(fred)<~>calm(fred)))=>(?[X]:(brave(X))))&
(((~wise(mary)<~>~humble(mary)))<=>(?[X]:((~rich(X)<~>~strong(X)))))&
(![X]:((old(X)|~rich(X))=>curious(X)))&
(((kind(mary)&~humble(mary)))=>(?[X]:(wise(X))))&
(![X]:(happy(X)<=>(~generous(X)<~>~curious(X))))&
((~rich(paul))=>(?[X]:((~strong(X)&wise(X)))))&
(![X]:((~patient(X)&happy(X))<=>(strong(X)|~tall(X))))&
(![X]:((generous(X)|creative(X))<=>(~creative(X)|old(X))))&
(((~curious(paul)<~>calm(paul)))=>((tall(mary)&~curious(mary))))&
(![X]:((creative(X)<~>curious(X))<=>(~strong(X)&happy(X))))&
(![X]:((happy(X)<~>~brave(X))<=>(tall(X)<~>curious(X))))&
(((~wise(paul)&old(paul)))<=>(?[X]:((old(X)|patient(X)))))&
(![X]:(humble(X)<=>(strong(X)<~>~humble(X))))&
(![X]:(old(X)=>(~calm(X)<~>~generous(X))))&
((?[X]:((old(X)<~>~brave(X))))<=>(?[X]:((~funny(X)&funny(X)))))&
(((~kind(mary)<~>curious(mary)))<=>(?[X]:((tall(X)|~happy(X)))))&
(?[X]:((creative(X)&tall(X))))&
(~quiet(john))&
((~generous(alice)<~>~calm(alice)))&
(?[X]:((brave(X)<~>old(X))))&
(?[X]:((funny(X)<~>quiet(X))))&
((curious(fred)&funny(fred)))&
(?[X]:((~happy(X)<~>~generous(X)))) | ~patient(alice) | [
"p6",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 7433797902530716521921068
% SZS output start Proof for 7433797902530716521921068
7. ! [X0] : ((happy(X0) & ~patient(X0)) <=> (~tall(X0) | strong(X0))) [input p6]
13. ! [X0] : (humble(X0) <=> (strong(X0) <~> ~humble(X0))) [input p12]
24. patient(alice) [input hypothesis]
45. ! [X0] : (((happy(X0) & ~patient(X0)) | (tall(X0) & ~strong(X0))) & ((~tall(X0) | strong(X0)) | (~happy(X0) | patient(X0)))) [nnf transformation 7]
46. ! [X0] : (((happy(X0) & ~patient(X0)) | (tall(X0) & ~strong(X0))) & (~tall(X0) | strong(X0) | ~happy(X0) | patient(X0))) [flattening 45]
58. ! [X0] : ((humble(X0) | ((strong(X0) | humble(X0)) & (~humble(X0) | ~strong(X0)))) & (((humble(X0) | ~strong(X0)) & (~humble(X0) | strong(X0))) | ~humble(X0))) [nnf transformation 13]
101. ~patient(X0) | ~strong(X0) [cnf transformation 46]
132. ~humble(X0) | strong(X0) | ~humble(X0) [cnf transformation 58]
135. humble(X0) | strong(X0) | humble(X0) [cnf transformation 58]
163. patient(alice) [cnf transformation 24]
164. ~humble(X0) | strong(X0) [duplicate literal removal 132]
165. humble(X0) | strong(X0) [duplicate literal removal 135]
286. strong(X0) [subsumption resolution 164,165]
371. ~strong(alice) [resolution 101,163]
372. $false [subsumption resolution 371,286]
% SZS output end Proof for 7433797902530716521921068
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.022 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not rich or old is funny and vice versa. Everyone who is either not calm or not rich is either not generous or strong. Everyone who is either not calm or not strong is both not humble and not strong. If someone is both curious and brave then someone is not calm and vice versa. If someone is either happy or not kind then someone is not creative and vice versa. Everyone who is either not creative or happy is humble or old. If someone is creative or strong then someone is not curious. Everyone who is not kind or humble is not quiet and vice versa. If john is not creative then fred is both not happy and calm and vice versa. Everyone who is not strong or brave is either not patient or not happy and vice versa. Everyone who is both not calm and wise is both patient and not patient. If john is both quiet and patient then lucy is either not tall or not patient and vice versa. Everyone who is kind or quiet is humble and vice versa. If paul is both not wise and not creative then someone is both not old and happy. If someone is either not funny or not generous then fred is tall and vice versa. If someone is either not humble or curious then someone is either not creative or kind. Someone is either kind or wise. Someone is not curious. Mary is both happy and not humble. Someone is either not rich or not kind. Susan is kind. Someone is not patient or funny. Susan is not rich. Someone is both humble and not tall. | Paul is quiet. | contradiction | (![X]:((~rich(X)|old(X))<=>funny(X)))&
(![X]:((~calm(X)<~>~rich(X))=>(~generous(X)<~>strong(X))))&
(![X]:((~calm(X)<~>~strong(X))=>(~humble(X)&~strong(X))))&
((?[X]:((curious(X)&brave(X))))<=>(?[X]:(~calm(X))))&
((?[X]:((happy(X)<~>~kind(X))))<=>(?[X]:(~creative(X))))&
(![X]:((~creative(X)<~>happy(X))=>(humble(X)|old(X))))&
((?[X]:((creative(X)|strong(X))))=>(?[X]:(~curious(X))))&
(![X]:((~kind(X)|humble(X))<=>~quiet(X)))&
((~creative(john))<=>((~happy(fred)&calm(fred))))&
(![X]:((~strong(X)|brave(X))<=>(~patient(X)<~>~happy(X))))&
(![X]:((~calm(X)&wise(X))=>(patient(X)&~patient(X))))&
(((quiet(john)&patient(john)))<=>((~tall(lucy)<~>~patient(lucy))))&
(![X]:((kind(X)|quiet(X))<=>humble(X)))&
(((~wise(paul)&~creative(paul)))=>(?[X]:((~old(X)&happy(X)))))&
((?[X]:((~funny(X)<~>~generous(X))))<=>(tall(fred)))&
((?[X]:((~humble(X)<~>curious(X))))=>(?[X]:((~creative(X)<~>kind(X)))))&
(?[X]:((kind(X)<~>wise(X))))&
(?[X]:(~curious(X)))&
((happy(mary)&~humble(mary)))&
(?[X]:((~rich(X)<~>~kind(X))))&
(kind(susan))&
(?[X]:((~patient(X)|funny(X))))&
(~rich(susan))&
(?[X]:((humble(X)&~tall(X)))) | quiet(paul) | [
"p7",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 427669342800728123380592
% SZS output start Proof for 427669342800728123380592
8. ! [X0] : ((humble(X0) | ~kind(X0)) <=> ~quiet(X0)) [input p7]
13. ! [X0] : ((quiet(X0) | kind(X0)) <=> humble(X0)) [input p12]
25. quiet(paul) [input hypothesis]
58. ! [X0] : (((humble(X0) | ~kind(X0)) | quiet(X0)) & (~quiet(X0) | (~humble(X0) & kind(X0)))) [nnf transformation 8]
59. ! [X0] : ((humble(X0) | ~kind(X0) | quiet(X0)) & (~quiet(X0) | (~humble(X0) & kind(X0)))) [flattening 58]
66. ! [X0] : (((quiet(X0) | kind(X0)) | ~humble(X0)) & (humble(X0) | (~quiet(X0) & ~kind(X0)))) [nnf transformation 13]
67. ! [X0] : ((quiet(X0) | kind(X0) | ~humble(X0)) & (humble(X0) | (~quiet(X0) & ~kind(X0)))) [flattening 66]
113. ~quiet(X0) | ~humble(X0) [cnf transformation 59]
133. humble(X0) | ~quiet(X0) [cnf transformation 67]
157. quiet(paul) [cnf transformation 25]
256. ~quiet(X0) [subsumption resolution 133,113]
344. $false [subsumption resolution 157,256]
% SZS output end Proof for 427669342800728123380592
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous and not humble is either generous or rich. Everyone who is both generous and quiet is not brave. Everyone who is both kind and not humble is both not brave and not calm and vice versa. Everyone who is not generous or not funny is both calm and not wise. If someone is both not tall and not strong then someone is either not brave or not rich. If someone is both wise and happy then someone is humble and vice versa. If someone is funny then someone is calm or not tall. Everyone who is either quiet or not rich is not wise. If someone is not patient or strong then lucy is either quiet or calm and vice versa. Everyone who is either funny or not kind is not brave or strong. Everyone who is either wise or not brave is either creative or strong and vice versa. If someone is both not funny and not curious then john is curious and vice versa. Everyone who is both brave and not patient is both not happy and wise. Everyone who is either strong or not patient is not rich. If someone is not tall then alice is not wise. If someone is both not kind and curious then alice is not humble and vice versa. Alice is not rich. Mary is not funny. Paul is either not humble or brave. Lucy is not old. Fred is both brave and rich. Someone is both strong and generous. Someone is both rich and funny. Paul is both not curious and not tall. | Lucy is not calm. | neutral | (![X]:((generous(X)&~humble(X))=>(generous(X)<~>rich(X))))&
(![X]:((generous(X)&quiet(X))=>~brave(X)))&
(![X]:((kind(X)&~humble(X))<=>(~brave(X)&~calm(X))))&
(![X]:((~generous(X)|~funny(X))=>(calm(X)&~wise(X))))&
((?[X]:((~tall(X)&~strong(X))))=>(?[X]:((~brave(X)<~>~rich(X)))))&
((?[X]:((wise(X)&happy(X))))<=>(?[X]:(humble(X))))&
((?[X]:(funny(X)))=>(?[X]:((calm(X)|~tall(X)))))&
(![X]:((quiet(X)<~>~rich(X))=>~wise(X)))&
((?[X]:((~patient(X)|strong(X))))<=>((quiet(lucy)<~>calm(lucy))))&
(![X]:((funny(X)<~>~kind(X))=>(~brave(X)|strong(X))))&
(![X]:((wise(X)<~>~brave(X))<=>(creative(X)<~>strong(X))))&
((?[X]:((~funny(X)&~curious(X))))<=>(curious(john)))&
(![X]:((brave(X)&~patient(X))=>(~happy(X)&wise(X))))&
(![X]:((strong(X)<~>~patient(X))=>~rich(X)))&
((?[X]:(~tall(X)))=>(~wise(alice)))&
((?[X]:((~kind(X)&curious(X))))<=>(~humble(alice)))&
(~rich(alice))&
(~funny(mary))&
((~humble(paul)<~>brave(paul)))&
(~old(lucy))&
((brave(fred)&rich(fred)))&
(?[X]:((strong(X)&generous(X))))&
(?[X]:((rich(X)&funny(X))))&
((~curious(paul)&~tall(paul))) | ~calm(lucy) | [] | null | 0 |
If someone is both not calm and not wise then lucy is not quiet. Everyone who is both quiet and not happy is not calm and vice versa. Everyone who is not humble is not curious or calm and vice versa. Everyone who is not funny is both funny and not old. Everyone who is both not curious and not generous is either old or not rich and vice versa. If someone is either not humble or brave then someone is both curious and not creative and vice versa. Everyone who is not brave is either humble or not old. Everyone who is quiet or patient is either wise or not curious. If paul is not funny then alice is either not happy or happy. Everyone who is either humble or not wise is not rich or not humble and vice versa. If paul is not calm then paul is both not funny and not kind. If lucy is not funny or funny then fred is either wise or patient. Everyone who is either not creative or rich is either wise or kind and vice versa. Everyone who is brave is both quiet and rich and vice versa. Everyone who is either not patient or curious is both not kind and funny and vice versa. Everyone who is either quiet or curious is both not strong and not kind and vice versa. Someone is not quiet or not funny. Paul is either not calm or not old. Someone is quiet or wise. Someone is not happy. Lucy is rich. Someone is both strong and calm. Fred is calm. Someone is not patient. | Lucy is funny. | entailment | ((?[X]:((~calm(X)&~wise(X))))=>(~quiet(lucy)))&
(![X]:((quiet(X)&~happy(X))<=>~calm(X)))&
(![X]:(~humble(X)<=>(~curious(X)|calm(X))))&
(![X]:(~funny(X)=>(funny(X)&~old(X))))&
(![X]:((~curious(X)&~generous(X))<=>(old(X)<~>~rich(X))))&
((?[X]:((~humble(X)<~>brave(X))))<=>(?[X]:((curious(X)&~creative(X)))))&
(![X]:(~brave(X)=>(humble(X)<~>~old(X))))&
(![X]:((quiet(X)|patient(X))=>(wise(X)<~>~curious(X))))&
((~funny(paul))=>((~happy(alice)<~>happy(alice))))&
(![X]:((humble(X)<~>~wise(X))<=>(~rich(X)|~humble(X))))&
((~calm(paul))=>((~funny(paul)&~kind(paul))))&
(((~funny(lucy)|funny(lucy)))=>((wise(fred)<~>patient(fred))))&
(![X]:((~creative(X)<~>rich(X))<=>(wise(X)<~>kind(X))))&
(![X]:(brave(X)<=>(quiet(X)&rich(X))))&
(![X]:((~patient(X)<~>curious(X))<=>(~kind(X)&funny(X))))&
(![X]:((quiet(X)<~>curious(X))<=>(~strong(X)&~kind(X))))&
(?[X]:((~quiet(X)|~funny(X))))&
((~calm(paul)<~>~old(paul)))&
(?[X]:((quiet(X)|wise(X))))&
(?[X]:(~happy(X)))&
(rich(lucy))&
(?[X]:((strong(X)&calm(X))))&
(calm(fred))&
(?[X]:(~patient(X))) | funny(lucy) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 437034725621272951272693
% SZS output start Proof for 437034725621272951272693
4. ! [X0] : (~funny(X0) => (~old(X0) & funny(X0))) [input p3]
25. ~funny(lucy) [input hypothesis]
28. ! [X0] : ((~old(X0) & funny(X0)) | funny(X0)) [ennf transformation 4]
76. funny(X0) | funny(X0) [cnf transformation 28]
143. ~funny(lucy) [cnf transformation 25]
146. funny(X0) [duplicate literal removal 76]
232. $false [subsumption resolution 143,146]
% SZS output end Proof for 437034725621272951272693
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is kind or humble is not kind or wise.
Everyone who is not wise or humble is not wise or tall and vice versa.
Everyone who is not kind is happy or old and vice versa.
If mary is not calm or rich then someone is either not kind or not calm.
If alice is either curious or not old then someone is either not rich or not strong.
Everyone who is curious or wise is either calm or humble.
If someone is both not quiet and not rich then alice is both patient and old and vice versa.
Everyone who is not old or creative is both not calm and not tall and vice versa.
Everyone who is either not rich or brave is both not brave and not happy and vice versa.
If john is not creative or humble then mary is not calm.
Everyone who is both rich and humble is both not kind and funny and vice versa.
If someone is either strong or tall then john is tall or kind.
Everyone who is both not creative and not calm is both happy and not quiet and vice versa.
If someone is not old or happy then lucy is either not creative or not wise and vice versa.
Everyone who is either funny or tall is strong.
Everyone who is either not curious or quiet is brave or generous.
Fred is either curious or not rich.
Someone is either humble or not tall.
Someone is brave.
Alice is not calm or curious.
Alice is happy.
Lucy is wise.
Someone is funny.
Fred is happy. | Lucy is not creative. | entailment | (![X]:((kind(X)|humble(X))=>(~kind(X)|wise(X))))&
(![X]:((~wise(X)|humble(X))<=>(~wise(X)|tall(X))))&
(![X]:(~kind(X)<=>(happy(X)|old(X))))&
(((~calm(mary)|rich(mary)))=>(?[X]:((~kind(X)<~>~calm(X)))))&
(((curious(alice)<~>~old(alice)))=>(?[X]:((~rich(X)<~>~strong(X)))))&
(![X]:((curious(X)|wise(X))=>(calm(X)<~>humble(X))))&
((?[X]:((~quiet(X)&~rich(X))))<=>((patient(alice)&old(alice))))&
(![X]:((~old(X)|creative(X))<=>(~calm(X)&~tall(X))))&
(![X]:((~rich(X)<~>brave(X))<=>(~brave(X)&~happy(X))))&
(((~creative(john)|humble(john)))=>(~calm(mary)))&
(![X]:((rich(X)&humble(X))<=>(~kind(X)&funny(X))))&
((?[X]:((strong(X)<~>tall(X))))=>((tall(john)|kind(john))))&
(![X]:((~creative(X)&~calm(X))<=>(happy(X)&~quiet(X))))&
((?[X]:((~old(X)|happy(X))))<=>((~creative(lucy)<~>~wise(lucy))))&
(![X]:((funny(X)<~>tall(X))=>strong(X)))&
(![X]:((~curious(X)<~>quiet(X))=>(brave(X)|generous(X))))&
((curious(fred)<~>~rich(fred)))&
(?[X]:((humble(X)<~>~tall(X))))&
(?[X]:(brave(X)))&
((~calm(alice)|curious(alice)))&
(happy(alice))&
(wise(lucy))&
(?[X]:(funny(X)))&
(happy(fred)) | ~creative(lucy) | [
"p13",
"p20",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 4922332763464874394330719
% SZS output start Proof for 4922332763464874394330719
14. ? [X0] : (happy(X0) | ~old(X0)) <=> (~creative(lucy) <~> ~wise(lucy)) [input p13]
21. happy(alice) [input p20]
22. wise(lucy) [input p21]
25. creative(lucy) [input hypothesis]
61. (? [X0] : (happy(X0) | ~old(X0)) | ((~creative(lucy) | wise(lucy)) & (~wise(lucy) | creative(lucy)))) & (((wise(lucy) | creative(lucy)) & (~wise(lucy) | ~creative(lucy))) | ! [X0] : (~happy(X0) & old(X0))) [nnf transformation 14]
62. (? [X0] : (happy(X0) | ~old(X0)) | ((~creative(lucy) | wise(lucy)) & (~wise(lucy) | creative(lucy)))) & (((wise(lucy) | creative(lucy)) & (~wise(lucy) | ~creative(lucy))) | ! [X1] : (~happy(X1) & old(X1))) [rectify 61]
63. ? [X0] : (happy(X0) | ~old(X0)) => (happy(sK3) | ~old(sK3)) [choice axiom]
64. ((happy(sK3) | ~old(sK3)) | ((~creative(lucy) | wise(lucy)) & (~wise(lucy) | creative(lucy)))) & (((wise(lucy) | creative(lucy)) & (~wise(lucy) | ~creative(lucy))) | ! [X1] : (~happy(X1) & old(X1))) [skolemisation 62,63]
123. ~wise(lucy) | ~creative(lucy) | ~happy(X1) [cnf transformation 64]
136. happy(alice) [cnf transformation 21]
137. wise(lucy) [cnf transformation 22]
140. creative(lucy) [cnf transformation 25]
230. 19 <=> wise(lucy) [avatar definition]
234. 20 <=> creative(lucy) [avatar definition]
248. 23 <=> ! [X1] : ~happy(X1) [avatar definition]
249. ~happy(X1) <- (23) [avatar component clause 248]
255. 23 | ~20 | ~19 [avatar split clause 123,230,234,248]
282. 19 [avatar split clause 137,230]
283. 20 [avatar split clause 140,234]
284. $false <- (23) [resolution 249,136]
287. ~23 [avatar contradiction clause 284]
288. $false [avatar sat refutation 255,282,283,287]
% SZS output end Proof for 4922332763464874394330719
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave is either not happy or calm.
Everyone who is brave is curious and vice versa.
If john is not wise or not creative then john is brave and vice versa.
Everyone who is both not tall and tall is both curious and strong and vice versa.
Everyone who is both humble and not calm is either funny or not humble.
Everyone who is tall is both not humble and not quiet and vice versa.
Everyone who is not brave or strong is old and vice versa.
If someone is both curious and funny then lucy is not happy or not creative and vice versa.
Everyone who is not calm is both patient and tall.
If someone is either curious or creative then someone is old and vice versa.
Everyone who is either not brave or curious is both creative and not tall.
Everyone who is not curious is not brave or strong.
If someone is either creative or generous then someone is either not humble or not happy.
If susan is rich then paul is happy or not humble.
If someone is not kind then lucy is tall or patient.
If paul is both brave and patient then someone is both funny and quiet and vice versa.
Lucy is brave or not humble.
Lucy is generous or not quiet.
John is strong.
Someone is not tall.
Someone is strong or not calm.
Someone is not creative or kind.
Someone is not strong. | John is brave. | contradiction | (![X]:((~humble(X)<~>brave(X))=>(~happy(X)<~>calm(X))))&
(![X]:(brave(X)<=>curious(X)))&
(((~wise(john)|~creative(john)))<=>(brave(john)))&
(![X]:((~tall(X)&tall(X))<=>(curious(X)&strong(X))))&
(![X]:((humble(X)&~calm(X))=>(funny(X)<~>~humble(X))))&
(![X]:(tall(X)<=>(~humble(X)&~quiet(X))))&
(![X]:((~brave(X)|strong(X))<=>old(X)))&
((?[X]:((curious(X)&funny(X))))<=>((~happy(lucy)|~creative(lucy))))&
(![X]:(~calm(X)=>(patient(X)&tall(X))))&
((?[X]:((curious(X)<~>creative(X))))<=>(?[X]:(old(X))))&
(![X]:((~brave(X)<~>curious(X))=>(creative(X)&~tall(X))))&
(![X]:(~curious(X)=>(~brave(X)|strong(X))))&
((?[X]:((creative(X)<~>generous(X))))=>(?[X]:((~humble(X)<~>~happy(X)))))&
((rich(susan))=>((happy(paul)|~humble(paul))))&
((?[X]:(~kind(X)))=>((tall(lucy)|patient(lucy))))&
(((brave(paul)&patient(paul)))<=>(?[X]:((funny(X)&quiet(X)))))&
((brave(lucy)|~humble(lucy)))&
((generous(lucy)|~quiet(lucy)))&
(strong(john))&
(?[X]:(~tall(X)))&
(?[X]:((strong(X)|~calm(X))))&
(?[X]:((~creative(X)|kind(X))))&
(?[X]:(~strong(X))) | brave(john) | [
"p1",
"p3",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 6091087025760853128519510
% SZS output start Proof for 6091087025760853128519510
2. ! [X0] : (brave(X0) <=> curious(X0)) [input p1]
4. ! [X0] : ((tall(X0) & ~tall(X0)) <=> (strong(X0) & curious(X0))) [input p3]
19. strong(john) [input p18]
24. brave(john) [input hypothesis]
39. ! [X0] : ((brave(X0) | ~curious(X0)) & (curious(X0) | ~brave(X0))) [nnf transformation 2]
42. ! [X0] : (((tall(X0) & ~tall(X0)) | (~strong(X0) | ~curious(X0))) & ((strong(X0) & curious(X0)) | (~tall(X0) | tall(X0)))) [nnf transformation 4]
43. ! [X0] : (((tall(X0) & ~tall(X0)) | ~strong(X0) | ~curious(X0)) & ((strong(X0) & curious(X0)) | ~tall(X0) | tall(X0))) [flattening 42]
79. ~brave(X0) | curious(X0) [cnf transformation 39]
86. ~tall(X0) | ~strong(X0) | ~curious(X0) [cnf transformation 43]
87. tall(X0) | ~strong(X0) | ~curious(X0) [cnf transformation 43]
122. strong(john) [cnf transformation 19]
126. brave(john) [cnf transformation 24]
129. 1 <=> brave(john) [avatar definition]
130. brave(john) <- (1) [avatar component clause 129]
143. ~strong(X0) | ~curious(X0) [subsumption resolution 86,87]
266. 1 [avatar split clause 126,129]
267. curious(john) <- (1) [resolution 79,130]
280. ~curious(john) [resolution 143,122]
281. $false <- (1) [subsumption resolution 280,267]
282. ~1 [avatar contradiction clause 281]
283. $false [avatar sat refutation 266,282]
% SZS output end Proof for 6091087025760853128519510
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not calm then someone is brave.
Everyone who is either not quiet or generous is both brave and not strong.
If someone is not happy then someone is either funny or brave.
Everyone who is not humble or not calm is not happy or not funny.
Everyone who is creative or calm is strong.
Everyone who is not old is old or creative and vice versa.
If someone is not wise then mary is not brave.
Everyone who is either not funny or not curious is kind or brave and vice versa.
If john is not rich or not calm then someone is either not happy or not tall and vice versa.
If fred is both tall and happy then someone is not happy or strong.
Everyone who is both not curious and kind is not funny or not creative and vice versa.
If alice is both patient and brave then mary is curious.
If someone is not humble or funny then lucy is either happy or curious and vice versa.
Everyone who is not brave is not humble and vice versa.
Everyone who is both rich and generous is either generous or quiet and vice versa.
If paul is either brave or not quiet then alice is either rich or strong and vice versa.
Lucy is happy or not creative.
Someone is either not calm or not generous.
Alice is funny.
Someone is both not brave and creative.
Someone is not old or not strong.
Someone is both not brave and rich.
Paul is humble or patient. | Paul is generous. | entailment | ((?[X]:(~calm(X)))=>(?[X]:(brave(X))))&
(![X]:((~quiet(X)<~>generous(X))=>(brave(X)&~strong(X))))&
((?[X]:(~happy(X)))=>(?[X]:((funny(X)<~>brave(X)))))&
(![X]:((~humble(X)|~calm(X))=>(~happy(X)|~funny(X))))&
(![X]:((creative(X)|calm(X))=>strong(X)))&
(![X]:(~old(X)<=>(old(X)|creative(X))))&
((?[X]:(~wise(X)))=>(~brave(mary)))&
(![X]:((~funny(X)<~>~curious(X))<=>(kind(X)|brave(X))))&
(((~rich(john)|~calm(john)))<=>(?[X]:((~happy(X)<~>~tall(X)))))&
(((tall(fred)&happy(fred)))=>(?[X]:((~happy(X)|strong(X)))))&
(![X]:((~curious(X)&kind(X))<=>(~funny(X)|~creative(X))))&
(((patient(alice)&brave(alice)))=>(curious(mary)))&
((?[X]:((~humble(X)|funny(X))))<=>((happy(lucy)<~>curious(lucy))))&
(![X]:(~brave(X)<=>~humble(X)))&
(![X]:((rich(X)&generous(X))<=>(generous(X)<~>quiet(X))))&
(((brave(paul)<~>~quiet(paul)))<=>((rich(alice)<~>strong(alice))))&
((happy(lucy)|~creative(lucy)))&
(?[X]:((~calm(X)<~>~generous(X))))&
(funny(alice))&
(?[X]:((~brave(X)&creative(X))))&
(?[X]:((~old(X)|~strong(X))))&
(?[X]:((~brave(X)&rich(X))))&
((humble(paul)|patient(paul))) | generous(paul) | [
"p1",
"p4",
"p5",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 7503996403492957532589887
% SZS output start Proof for 7503996403492957532589887
2. ! [X0] : ((~quiet(X0) <~> generous(X0)) => (~strong(X0) & brave(X0))) [input p1]
5. ! [X0] : ((calm(X0) | creative(X0)) => strong(X0)) [input p4]
6. ! [X0] : (~old(X0) <=> (creative(X0) | old(X0))) [input p5]
15. ! [X0] : ((generous(X0) & rich(X0)) <=> (generous(X0) <~> quiet(X0))) [input p14]
24. ~generous(paul) [input hypothesis]
29. ! [X0] : ((~strong(X0) & brave(X0)) | (~quiet(X0) <=> generous(X0))) [ennf transformation 2]
33. ! [X0] : (strong(X0) | (~calm(X0) & ~creative(X0))) [ennf transformation 5]
41. ! [X0] : ((~strong(X0) & brave(X0)) | ((~quiet(X0) | ~generous(X0)) & (generous(X0) | quiet(X0)))) [nnf transformation 29]
46. ! [X0] : ((~old(X0) | (~creative(X0) & ~old(X0))) & ((creative(X0) | old(X0)) | old(X0))) [nnf transformation 6]
47. ! [X0] : ((~old(X0) | (~creative(X0) & ~old(X0))) & (creative(X0) | old(X0) | old(X0))) [flattening 46]
64. ! [X0] : (((generous(X0) & rich(X0)) | ((generous(X0) | ~quiet(X0)) & (quiet(X0) | ~generous(X0)))) & (((~quiet(X0) | ~generous(X0)) & (quiet(X0) | generous(X0))) | (~generous(X0) | ~rich(X0)))) [nnf transformation 15]
65. ! [X0] : (((generous(X0) & rich(X0)) | ((generous(X0) | ~quiet(X0)) & (quiet(X0) | ~generous(X0)))) & (((~quiet(X0) | ~generous(X0)) & (quiet(X0) | generous(X0))) | ~generous(X0) | ~rich(X0))) [flattening 64]
79. ~strong(X0) | generous(X0) | quiet(X0) [cnf transformation 41]
85. ~creative(X0) | strong(X0) [cnf transformation 33]
87. creative(X0) | old(X0) | old(X0) [cnf transformation 47]
88. ~old(X0) | ~old(X0) [cnf transformation 47]
122. generous(X0) | generous(X0) | ~quiet(X0) [cnf transformation 65]
141. ~generous(paul) [cnf transformation 24]
143. ~quiet(X0) | generous(X0) [duplicate literal removal 122]
144. creative(X0) | old(X0) [duplicate literal removal 87]
145. ~old(X0) [duplicate literal removal 88]
167. creative(X0) [subsumption resolution 144,145]
306. strong(X0) [resolution 85,167]
341. generous(X0) | quiet(X0) [resolution 79,306]
342. generous(X0) [subsumption resolution 341,143]
345. $false [resolution 342,141]
% SZS output end Proof for 7503996403492957532589887
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either wise or humble is curious.
If someone is not quiet or not generous then someone is either tall or patient.
Everyone who is both quiet and not strong is both brave and happy.
Everyone who is not kind or funny is either not strong or not rich and vice versa.
If john is both happy and not strong then someone is either not strong or not generous and vice versa.
Everyone who is not strong or wise is not calm or humble.
If alice is not humble then someone is either brave or humble and vice versa.
If mary is generous or patient then someone is either not strong or calm.
Everyone who is both not curious and not quiet is either calm or not calm and vice versa.
Everyone who is strong or wise is both not quiet and not generous and vice versa.
If someone is either not quiet or not generous then susan is both quiet and humble.
If susan is both not kind and not creative then fred is not generous or creative.
If someone is both not quiet and not tall then mary is both rich and not humble and vice versa.
If susan is both not happy and not humble then someone is both not humble and not calm and vice versa.
If someone is both patient and happy then someone is both not tall and quiet.
Fred is humble or happy.
Susan is rich or not creative.
Susan is both happy and brave.
Lucy is either not quiet or not wise.
Alice is both not quiet and rich. | John is not rich. | neutral | (![X]:((wise(X)<~>humble(X))=>curious(X)))&
((?[X]:((~quiet(X)|~generous(X))))=>(?[X]:((tall(X)<~>patient(X)))))&
(![X]:((quiet(X)&~strong(X))=>(brave(X)&happy(X))))&
(![X]:((~kind(X)|funny(X))<=>(~strong(X)<~>~rich(X))))&
(((happy(john)&~strong(john)))<=>(?[X]:((~strong(X)<~>~generous(X)))))&
(![X]:((~strong(X)|wise(X))=>(~calm(X)|humble(X))))&
((~humble(alice))<=>(?[X]:((brave(X)<~>humble(X)))))&
(((generous(mary)|patient(mary)))=>(?[X]:((~strong(X)<~>calm(X)))))&
(![X]:((~curious(X)&~quiet(X))<=>(calm(X)<~>~calm(X))))&
(![X]:((strong(X)|wise(X))<=>(~quiet(X)&~generous(X))))&
((?[X]:((~quiet(X)<~>~generous(X))))=>((quiet(susan)&humble(susan))))&
(((~kind(susan)&~creative(susan)))=>((~generous(fred)|creative(fred))))&
((?[X]:((~quiet(X)&~tall(X))))<=>((rich(mary)&~humble(mary))))&
(((~happy(susan)&~humble(susan)))<=>(?[X]:((~humble(X)&~calm(X)))))&
((?[X]:((patient(X)&happy(X))))=>(?[X]:((~tall(X)&quiet(X)))))&
((humble(fred)|happy(fred)))&
((rich(susan)|~creative(susan)))&
((happy(susan)&brave(susan)))&
((~quiet(lucy)<~>~wise(lucy)))&
((~quiet(alice)&rich(alice))) | ~rich(john) | [] | null | 0 |
Everyone who is funny is both not tall and not rich and vice versa. If someone is both tall and quiet then someone is both not old and not quiet. Everyone who is either curious or not curious is not old or kind and vice versa. Everyone who is not brave or curious is not curious and vice versa. If someone is curious or humble then john is creative. If someone is either not kind or not happy then alice is both funny and not humble and vice versa. Everyone who is both generous and not generous is generous. Everyone who is both brave and not patient is either wise or not quiet. Everyone who is either tall or patient is both not quiet and not creative. Everyone who is either not funny or not kind is curious or not patient and vice versa. If someone is either creative or brave then someone is wise or kind. Everyone who is both creative and strong is patient or old and vice versa. If someone is quiet or not strong then fred is both quiet and not strong and vice versa. Everyone who is funny or creative is not tall or not rich and vice versa. Everyone who is curious or not funny is calm or generous. If alice is both not calm and kind then someone is either tall or not strong and vice versa. Someone is either not creative or kind. Paul is not strong. Someone is funny or not patient. Someone is both calm and rich. Someone is either not generous or not creative. Someone is both tall and rich. | John is not generous. | neutral | (![X]:(funny(X)<=>(~tall(X)&~rich(X))))&
((?[X]:((tall(X)&quiet(X))))=>(?[X]:((~old(X)&~quiet(X)))))&
(![X]:((curious(X)<~>~curious(X))<=>(~old(X)|kind(X))))&
(![X]:((~brave(X)|curious(X))<=>~curious(X)))&
((?[X]:((curious(X)|humble(X))))=>(creative(john)))&
((?[X]:((~kind(X)<~>~happy(X))))<=>((funny(alice)&~humble(alice))))&
(![X]:((generous(X)&~generous(X))=>generous(X)))&
(![X]:((brave(X)&~patient(X))=>(wise(X)<~>~quiet(X))))&
(![X]:((tall(X)<~>patient(X))=>(~quiet(X)&~creative(X))))&
(![X]:((~funny(X)<~>~kind(X))<=>(curious(X)|~patient(X))))&
((?[X]:((creative(X)<~>brave(X))))=>(?[X]:((wise(X)|kind(X)))))&
(![X]:((creative(X)&strong(X))<=>(patient(X)|old(X))))&
((?[X]:((quiet(X)|~strong(X))))<=>((quiet(fred)&~strong(fred))))&
(![X]:((funny(X)|creative(X))<=>(~tall(X)|~rich(X))))&
(![X]:((curious(X)|~funny(X))=>(calm(X)|generous(X))))&
(((~calm(alice)&kind(alice)))<=>(?[X]:((tall(X)<~>~strong(X)))))&
(?[X]:((~creative(X)<~>kind(X))))&
(~strong(paul))&
(?[X]:((funny(X)|~patient(X))))&
(?[X]:((calm(X)&rich(X))))&
(?[X]:((~generous(X)<~>~creative(X))))&
(?[X]:((tall(X)&rich(X)))) | ~generous(john) | [] | null | 0 |
Everyone who is both quiet and tall is both not funny and not generous.
If someone is tall then someone is both not humble and wise and vice versa.
Everyone who is either funny or not patient is quiet or creative.
Everyone who is not quiet is not tall and vice versa.
If someone is both quiet and not curious then someone is both creative and curious.
Everyone who is both not funny and creative is not curious and vice versa.
If someone is both not strong and not old then paul is either happy or not strong and vice versa.
Everyone who is both generous and strong is patient and vice versa.
If alice is not happy then someone is either happy or strong.
If someone is both not quiet and not tall then john is either patient or funny and vice versa.
Everyone who is either curious or not funny is both patient and not brave and vice versa.
If someone is not quiet then mary is strong and vice versa.
Everyone who is both funny and tall is calm or happy.
Everyone who is kind or old is both not humble and rich and vice versa.
If john is either old or not strong then paul is either patient or not happy.
Everyone who is both not creative and not strong is both not happy and old.
Alice is wise.
Someone is not brave or strong.
John is either not creative or not happy.
Lucy is both not humble and not tall.
Paul is quiet or not wise.
Mary is both not old and quiet. | John is generous. | entailment | (![X]:((quiet(X)&tall(X))=>(~funny(X)&~generous(X))))&
((?[X]:(tall(X)))<=>(?[X]:((~humble(X)&wise(X)))))&
(![X]:((funny(X)<~>~patient(X))=>(quiet(X)|creative(X))))&
(![X]:(~quiet(X)<=>~tall(X)))&
((?[X]:((quiet(X)&~curious(X))))=>(?[X]:((creative(X)&curious(X)))))&
(![X]:((~funny(X)&creative(X))<=>~curious(X)))&
((?[X]:((~strong(X)&~old(X))))<=>((happy(paul)<~>~strong(paul))))&
(![X]:((generous(X)&strong(X))<=>patient(X)))&
((~happy(alice))=>(?[X]:((happy(X)<~>strong(X)))))&
((?[X]:((~quiet(X)&~tall(X))))<=>((patient(john)<~>funny(john))))&
(![X]:((curious(X)<~>~funny(X))<=>(patient(X)&~brave(X))))&
((?[X]:(~quiet(X)))<=>(strong(mary)))&
(![X]:((funny(X)&tall(X))=>(calm(X)|happy(X))))&
(![X]:((kind(X)|old(X))<=>(~humble(X)&rich(X))))&
(((old(john)<~>~strong(john)))=>((patient(paul)<~>~happy(paul))))&
(![X]:((~creative(X)&~strong(X))=>(~happy(X)&old(X))))&
(wise(alice))&
(?[X]:((~brave(X)|strong(X))))&
((~creative(john)<~>~happy(john)))&
((~humble(lucy)&~tall(lucy)))&
((quiet(paul)|~wise(paul)))&
((~old(mary)&quiet(mary))) | generous(john) | [
"p3",
"p5",
"p7",
"p9",
"p10",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 4303124322926332472276615
% SZS output start Proof for 4303124322926332472276615
4. ! [X0] : (~quiet(X0) <=> ~tall(X0)) [input p3]
6. ! [X0] : ((creative(X0) & ~funny(X0)) <=> ~curious(X0)) [input p5]
8. ! [X0] : ((strong(X0) & generous(X0)) <=> patient(X0)) [input p7]
10. ? [X0] : (~tall(X0) & ~quiet(X0)) <=> (patient(john) <~> funny(john)) [input p9]
11. ! [X0] : ((curious(X0) <~> ~funny(X0)) <=> (~brave(X0) & patient(X0))) [input p10]
20. ~tall(lucy) & ~humble(lucy) [input p19]
23. ~generous(john) [input hypothesis]
42. ! [X0] : ((~quiet(X0) | tall(X0)) & (~tall(X0) | quiet(X0))) [nnf transformation 4]
46. ! [X0] : (((creative(X0) & ~funny(X0)) | curious(X0)) & (~curious(X0) | (~creative(X0) | funny(X0)))) [nnf transformation 6]
47. ! [X0] : (((creative(X0) & ~funny(X0)) | curious(X0)) & (~curious(X0) | ~creative(X0) | funny(X0))) [flattening 46]
52. ! [X0] : (((strong(X0) & generous(X0)) | ~patient(X0)) & (patient(X0) | (~strong(X0) | ~generous(X0)))) [nnf transformation 8]
53. ! [X0] : (((strong(X0) & generous(X0)) | ~patient(X0)) & (patient(X0) | ~strong(X0) | ~generous(X0))) [flattening 52]
57. (? [X0] : (~tall(X0) & ~quiet(X0)) | ((patient(john) | ~funny(john)) & (funny(john) | ~patient(john)))) & (((~funny(john) | ~patient(john)) & (funny(john) | patient(john))) | ! [X0] : (tall(X0) | quiet(X0))) [nnf transformation 10]
58. (? [X0] : (~tall(X0) & ~quiet(X0)) | ((patient(john) | ~funny(john)) & (funny(john) | ~patient(john)))) & (((~funny(john) | ~patient(john)) & (funny(john) | patient(john))) | ! [X1] : (tall(X1) | quiet(X1))) [rectify 57]
59. ? [X0] : (~tall(X0) & ~quiet(X0)) => (~tall(sK5) & ~quiet(sK5)) [choice axiom]
60. ((~tall(sK5) & ~quiet(sK5)) | ((patient(john) | ~funny(john)) & (funny(john) | ~patient(john)))) & (((~funny(john) | ~patient(john)) & (funny(john) | patient(john))) | ! [X1] : (tall(X1) | quiet(X1))) [skolemisation 58,59]
61. ! [X0] : ((((funny(X0) | ~curious(X0)) & (~funny(X0) | curious(X0))) | (brave(X0) | ~patient(X0))) & ((~brave(X0) & patient(X0)) | ((curious(X0) | funny(X0)) & (~funny(X0) | ~curious(X0))))) [nnf transformation 11]
62. ! [X0] : ((((funny(X0) | ~curious(X0)) & (~funny(X0) | curious(X0))) | brave(X0) | ~patient(X0)) & ((~brave(X0) & patient(X0)) | ((curious(X0) | funny(X0)) & (~funny(X0) | ~curious(X0))))) [flattening 61]
80. ~tall(X0) | quiet(X0) [cnf transformation 42]
81. ~quiet(X0) | tall(X0) [cnf transformation 42]
85. ~funny(X0) | curious(X0) [cnf transformation 47]
94. ~patient(X0) | generous(X0) [cnf transformation 53]
98. funny(john) | patient(john) | tall(X1) | quiet(X1) [cnf transformation 60]
104. patient(X0) | ~funny(X0) | ~curious(X0) [cnf transformation 62]
105. patient(X0) | curious(X0) | funny(X0) [cnf transformation 62]
128. ~tall(lucy) [cnf transformation 20]
132. ~generous(john) [cnf transformation 23]
207. 17 <=> funny(john) [avatar definition]
208. funny(john) <- (17) [avatar component clause 207]
211. 18 <=> patient(john) [avatar definition]
212. ~patient(john) <- (~18) [avatar component clause 211]
213. patient(john) <- (18) [avatar component clause 211]
228. 21 <=> ! [X1] : quiet(X1) [avatar definition]
229. quiet(X1) <- (21) [avatar component clause 228]
231. funny(john) | patient(john) | quiet(X1) [subsumption resolution 98,80]
232. 21 | 18 | 17 [avatar split clause 231,207,211,228]
235. curious(X0) | patient(X0) [subsumption resolution 105,85]
236. ~funny(X0) | patient(X0) [subsumption resolution 104,235]
309. patient(john) <- (17) [resolution 236,208]
310. $false <- (17, ~18) [subsumption resolution 309,212]
311. ~17 | 18 [avatar contradiction clause 310]
313. generous(john) <- (18) [resolution 213,94]
315. $false <- (18) [subsumption resolution 313,132]
316. ~18 [avatar contradiction clause 315]
318. tall(X1) <- (21) [resolution 229,81]
324. $false <- (21) [resolution 318,128]
327. ~21 [avatar contradiction clause 324]
328. $false [avatar sat refutation 232,311,316,327]
% SZS output end Proof for 4303124322926332472276615
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is rich is both creative and old and vice versa.
If someone is both happy and not funny then someone is not creative and vice versa.
Everyone who is either not quiet or calm is not creative.
Everyone who is quiet is both curious and not generous.
Everyone who is strong or rich is old or not calm.
Everyone who is rich or tall is generous.
If mary is both not wise and funny then alice is not humble and vice versa.
If susan is either curious or not creative then paul is not humble or brave and vice versa.
If someone is either not patient or patient then john is not curious or brave.
Everyone who is strong or quiet is either not wise or not strong and vice versa.
Everyone who is both not old and not wise is both not strong and not quiet and vice versa.
Everyone who is both happy and brave is both not creative and not wise.
Everyone who is both funny and not quiet is either not quiet or not curious.
If john is both not wise and strong then fred is tall and vice versa.
If paul is not generous or not humble then someone is not patient.
If alice is either funny or not wise then someone is both not strong and humble and vice versa.
Susan is not tall.
Paul is tall or strong.
Paul is kind or not patient.
Someone is either not rich or calm.
Susan is quiet or calm.
Someone is either kind or not strong. | Mary is funny. | neutral | (![X]:(rich(X)<=>(creative(X)&old(X))))&
((?[X]:((happy(X)&~funny(X))))<=>(?[X]:(~creative(X))))&
(![X]:((~quiet(X)<~>calm(X))=>~creative(X)))&
(![X]:(quiet(X)=>(curious(X)&~generous(X))))&
(![X]:((strong(X)|rich(X))=>(old(X)|~calm(X))))&
(![X]:((rich(X)|tall(X))=>generous(X)))&
(((~wise(mary)&funny(mary)))<=>(~humble(alice)))&
(((curious(susan)<~>~creative(susan)))<=>((~humble(paul)|brave(paul))))&
((?[X]:((~patient(X)<~>patient(X))))=>((~curious(john)|brave(john))))&
(![X]:((strong(X)|quiet(X))<=>(~wise(X)<~>~strong(X))))&
(![X]:((~old(X)&~wise(X))<=>(~strong(X)&~quiet(X))))&
(![X]:((happy(X)&brave(X))=>(~creative(X)&~wise(X))))&
(![X]:((funny(X)&~quiet(X))=>(~quiet(X)<~>~curious(X))))&
(((~wise(john)&strong(john)))<=>(tall(fred)))&
(((~generous(paul)|~humble(paul)))=>(?[X]:(~patient(X))))&
(((funny(alice)<~>~wise(alice)))<=>(?[X]:((~strong(X)&humble(X)))))&
(~tall(susan))&
((tall(paul)|strong(paul)))&
((kind(paul)|~patient(paul)))&
(?[X]:((~rich(X)<~>calm(X))))&
((quiet(susan)|calm(susan)))&
(?[X]:((kind(X)<~>~strong(X)))) | funny(mary) | [] | null | 0 |
If lucy is either not funny or not curious then fred is either not brave or generous and vice versa.
Everyone who is both not generous and curious is both not patient and humble and vice versa.
If fred is either not tall or brave then someone is both funny and brave and vice versa.
Everyone who is not happy or creative is not patient and vice versa.
Everyone who is either brave or not curious is quiet.
Everyone who is both not wise and strong is not happy or curious.
Everyone who is both not happy and not quiet is either humble or funny and vice versa.
Everyone who is both brave and not kind is not funny or quiet and vice versa.
Everyone who is patient is both not wise and wise and vice versa.
If fred is curious then john is humble and vice versa.
If someone is patient or funny then someone is not funny.
If someone is tall then lucy is both curious and not rich.
If susan is quiet or old then fred is either not kind or not happy and vice versa.
If john is brave then john is either not rich or tall.
If someone is calm or funny then john is both not brave and not generous.
Everyone who is both quiet and kind is both not brave and humble and vice versa.
Someone is not tall.
Alice is not wise or brave.
Someone is not quiet or not generous.
Someone is rich.
Someone is rich or not happy.
John is not curious or not strong. | Susan is kind. | contradiction | (((~funny(lucy)<~>~curious(lucy)))<=>((~brave(fred)<~>generous(fred))))&
(![X]:((~generous(X)&curious(X))<=>(~patient(X)&humble(X))))&
(((~tall(fred)<~>brave(fred)))<=>(?[X]:((funny(X)&brave(X)))))&
(![X]:((~happy(X)|creative(X))<=>~patient(X)))&
(![X]:((brave(X)<~>~curious(X))=>quiet(X)))&
(![X]:((~wise(X)&strong(X))=>(~happy(X)|curious(X))))&
(![X]:((~happy(X)&~quiet(X))<=>(humble(X)<~>funny(X))))&
(![X]:((brave(X)&~kind(X))<=>(~funny(X)|quiet(X))))&
(![X]:(patient(X)<=>(~wise(X)&wise(X))))&
((curious(fred))<=>(humble(john)))&
((?[X]:((patient(X)|funny(X))))=>(?[X]:(~funny(X))))&
((?[X]:(tall(X)))=>((curious(lucy)&~rich(lucy))))&
(((quiet(susan)|old(susan)))<=>((~kind(fred)<~>~happy(fred))))&
((brave(john))=>((~rich(john)<~>tall(john))))&
((?[X]:((calm(X)|funny(X))))=>((~brave(john)&~generous(john))))&
(![X]:((quiet(X)&kind(X))<=>(~brave(X)&humble(X))))&
(?[X]:(~tall(X)))&
((~wise(alice)|brave(alice)))&
(?[X]:((~quiet(X)|~generous(X))))&
(?[X]:(rich(X)))&
(?[X]:((rich(X)|~happy(X))))&
((~curious(john)|~strong(john))) | kind(susan) | [
"p1",
"p4",
"p7",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3548283085527595319245201
% SZS output start Proof for 3548283085527595319245201
2. ! [X0] : ((curious(X0) & ~generous(X0)) <=> (humble(X0) & ~patient(X0))) [input p1]
5. ! [X0] : ((brave(X0) <~> ~curious(X0)) => quiet(X0)) [input p4]
8. ! [X0] : ((~kind(X0) & brave(X0)) <=> (quiet(X0) | ~funny(X0))) [input p7]
15. ? [X0] : (funny(X0) | calm(X0)) => (~generous(john) & ~brave(john)) [input p14]
16. ! [X0] : ((kind(X0) & quiet(X0)) <=> (humble(X0) & ~brave(X0))) [input p15]
23. kind(susan) [input hypothesis]
25. ? [X0] : funny(X0) => (~generous(john) & ~brave(john)) [pure predicate removal 15]
28. ! [X0] : (quiet(X0) | (brave(X0) <=> ~curious(X0))) [ennf transformation 5]
32. (~generous(john) & ~brave(john)) | ! [X0] : ~funny(X0) [ennf transformation 25]
34. ! [X0] : (((curious(X0) & ~generous(X0)) | (~humble(X0) | patient(X0))) & ((humble(X0) & ~patient(X0)) | (~curious(X0) | generous(X0)))) [nnf transformation 2]
35. ! [X0] : (((curious(X0) & ~generous(X0)) | ~humble(X0) | patient(X0)) & ((humble(X0) & ~patient(X0)) | ~curious(X0) | generous(X0))) [flattening 34]
42. ! [X0] : (quiet(X0) | ((brave(X0) | curious(X0)) & (~curious(X0) | ~brave(X0)))) [nnf transformation 28]
45. ! [X0] : (((~kind(X0) & brave(X0)) | (~quiet(X0) & funny(X0))) & ((quiet(X0) | ~funny(X0)) | (kind(X0) | ~brave(X0)))) [nnf transformation 8]
46. ! [X0] : (((~kind(X0) & brave(X0)) | (~quiet(X0) & funny(X0))) & (quiet(X0) | ~funny(X0) | kind(X0) | ~brave(X0))) [flattening 45]
56. ! [X0] : (((kind(X0) & quiet(X0)) | (~humble(X0) | brave(X0))) & ((humble(X0) & ~brave(X0)) | (~kind(X0) | ~quiet(X0)))) [nnf transformation 16]
57. ! [X0] : (((kind(X0) & quiet(X0)) | ~humble(X0) | brave(X0)) & ((humble(X0) & ~brave(X0)) | ~kind(X0) | ~quiet(X0))) [flattening 56]
75. ~curious(X0) | humble(X0) | generous(X0) [cnf transformation 35]
88. quiet(X0) | brave(X0) | curious(X0) [cnf transformation 42]
97. ~quiet(X0) | brave(X0) [cnf transformation 46]
98. ~kind(X0) | funny(X0) [cnf transformation 46]
117. ~brave(john) | ~funny(X0) [cnf transformation 32]
118. ~generous(john) | ~funny(X0) [cnf transformation 32]
121. quiet(X0) | ~humble(X0) | brave(X0) [cnf transformation 57]
128. kind(susan) [cnf transformation 23]
176. 9 <=> humble(john) [avatar definition]
177. humble(john) <- (9) [avatar component clause 176]
178. ~humble(john) <- (~9) [avatar component clause 176]
186. 11 <=> ! [X1] : ~funny(X1) [avatar definition]
187. ~funny(X1) <- (11) [avatar component clause 186]
225. 19 <=> brave(john) [avatar definition]
227. ~brave(john) <- (~19) [avatar component clause 225]
239. 22 <=> generous(john) [avatar definition]
241. ~generous(john) <- (~22) [avatar component clause 239]
242. 11 | ~22 [avatar split clause 118,239,186]
243. 11 | ~19 [avatar split clause 117,225,186]
244. ~humble(X0) | brave(X0) [subsumption resolution 121,97]
273. funny(susan) [resolution 98,128]
291. brave(X0) | curious(X0) | brave(X0) [resolution 88,97]
292. brave(X0) | curious(X0) [duplicate literal removal 291]
422. curious(john) <- (~19) [resolution 292,227]
428. humble(john) | generous(john) <- (~19) [resolution 422,75]
429. generous(john) <- (~9, ~19) [subsumption resolution 428,178]
430. $false <- (~9, ~19, ~22) [subsumption resolution 429,241]
431. 9 | 19 | 22 [avatar contradiction clause 430]
432. $false <- (11) [resolution 187,273]
435. ~11 [avatar contradiction clause 432]
445. brave(john) <- (9) [resolution 177,244]
461. $false <- (9, ~19) [subsumption resolution 445,227]
462. ~9 | 19 [avatar contradiction clause 461]
463. $false [avatar sat refutation 242,243,431,435,462]
% SZS output end Proof for 3548283085527595319245201
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If john is not wise or curious then someone is either humble or not old and vice versa.
If someone is creative or not curious then mary is not generous and vice versa.
If someone is both generous and not humble then someone is not happy.
Everyone who is not creative is not calm or not tall.
Everyone who is either wise or generous is not wise or not calm and vice versa.
Everyone who is not wise or creative is both not happy and not rich.
Everyone who is either generous or not curious is not calm.
If fred is either not rich or old then paul is either not calm or not kind.
Everyone who is humble is curious or tall and vice versa.
Everyone who is strong is not curious and vice versa.
If john is both not funny and funny then someone is generous.
Everyone who is not wise or funny is not brave or humble and vice versa.
Everyone who is both curious and not patient is either not funny or not rich.
Everyone who is both creative and kind is not patient and vice versa.
If fred is not humble then someone is either not kind or not rich and vice versa.
If mary is either curious or humble then someone is not generous or not happy and vice versa.
Paul is both curious and not generous.
Someone is wise.
Lucy is both rich and generous.
Susan is generous.
Paul is patient or not wise.
Someone is either curious or not generous.
Mary is wise or not quiet.
Susan is both brave and wise. | Susan is not funny. | neutral | (((~wise(john)|curious(john)))<=>(?[X]:((humble(X)<~>~old(X)))))&
((?[X]:((creative(X)|~curious(X))))<=>(~generous(mary)))&
((?[X]:((generous(X)&~humble(X))))=>(?[X]:(~happy(X))))&
(![X]:(~creative(X)=>(~calm(X)|~tall(X))))&
(![X]:((wise(X)<~>generous(X))<=>(~wise(X)|~calm(X))))&
(![X]:((~wise(X)|creative(X))=>(~happy(X)&~rich(X))))&
(![X]:((generous(X)<~>~curious(X))=>~calm(X)))&
(((~rich(fred)<~>old(fred)))=>((~calm(paul)<~>~kind(paul))))&
(![X]:(humble(X)<=>(curious(X)|tall(X))))&
(![X]:(strong(X)<=>~curious(X)))&
(((~funny(john)&funny(john)))=>(?[X]:(generous(X))))&
(![X]:((~wise(X)|funny(X))<=>(~brave(X)|humble(X))))&
(![X]:((curious(X)&~patient(X))=>(~funny(X)<~>~rich(X))))&
(![X]:((creative(X)&kind(X))<=>~patient(X)))&
((~humble(fred))<=>(?[X]:((~kind(X)<~>~rich(X)))))&
(((curious(mary)<~>humble(mary)))<=>(?[X]:((~generous(X)|~happy(X)))))&
((curious(paul)&~generous(paul)))&
(?[X]:(wise(X)))&
((rich(lucy)&generous(lucy)))&
(generous(susan))&
((patient(paul)|~wise(paul)))&
(?[X]:((curious(X)<~>~generous(X))))&
((wise(mary)|~quiet(mary)))&
((brave(susan)&wise(susan))) | ~funny(susan) | [] | null | 0 |
Everyone who is calm or not quiet is kind or rich and vice versa. Everyone who is either funny or not patient is old or not creative. If lucy is not kind then someone is generous or not funny and vice versa. If susan is both not curious and humble then mary is either not curious or happy. Everyone who is wise or not generous is both brave and not wise and vice versa. Everyone who is either rich or not strong is both not generous and not wise and vice versa. Everyone who is both funny and kind is not calm and vice versa. Everyone who is strong is either calm or generous and vice versa. If someone is curious then john is patient. If alice is not happy or not tall then paul is tall or strong and vice versa. Everyone who is not quiet or patient is not rich. Everyone who is rich or not rich is not funny and vice versa. Everyone who is quiet is both humble and generous and vice versa. If lucy is not happy then fred is either not creative or rich and vice versa. Everyone who is creative is kind or patient and vice versa. Everyone who is both wise and generous is both rich and not happy. Susan is either rich or kind. Fred is either rich or curious. Mary is not kind or patient. Fred is not happy or not wise. Susan is calm or not creative. Alice is either not funny or not old. | Fred is humble. | entailment | (![X]:((calm(X)|~quiet(X))<=>(kind(X)|rich(X))))&
(![X]:((funny(X)<~>~patient(X))=>(old(X)|~creative(X))))&
((~kind(lucy))<=>(?[X]:((generous(X)|~funny(X)))))&
(((~curious(susan)&humble(susan)))=>((~curious(mary)<~>happy(mary))))&
(![X]:((wise(X)|~generous(X))<=>(brave(X)&~wise(X))))&
(![X]:((rich(X)<~>~strong(X))<=>(~generous(X)&~wise(X))))&
(![X]:((funny(X)&kind(X))<=>~calm(X)))&
(![X]:(strong(X)<=>(calm(X)<~>generous(X))))&
((?[X]:(curious(X)))=>(patient(john)))&
(((~happy(alice)|~tall(alice)))<=>((tall(paul)|strong(paul))))&
(![X]:((~quiet(X)|patient(X))=>~rich(X)))&
(![X]:((rich(X)|~rich(X))<=>~funny(X)))&
(![X]:(quiet(X)<=>(humble(X)&generous(X))))&
((~happy(lucy))<=>((~creative(fred)<~>rich(fred))))&
(![X]:(creative(X)<=>(kind(X)|patient(X))))&
(![X]:((wise(X)&generous(X))=>(rich(X)&~happy(X))))&
((rich(susan)<~>kind(susan)))&
((rich(fred)<~>curious(fred)))&
((~kind(mary)|patient(mary)))&
((~happy(fred)|~wise(fred)))&
((calm(susan)|~creative(susan)))&
((~funny(alice)<~>~old(alice))) | humble(fred) | [
"p4",
"p5",
"p6",
"p7",
"p10",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 958521895955483359214082
% SZS output start Proof for 958521895955483359214082
5. ! [X0] : ((~generous(X0) | wise(X0)) <=> (~wise(X0) & brave(X0))) [input p4]
6. ! [X0] : ((rich(X0) <~> ~strong(X0)) <=> (~wise(X0) & ~generous(X0))) [input p5]
7. ! [X0] : ((kind(X0) & funny(X0)) <=> ~calm(X0)) [input p6]
8. ! [X0] : (strong(X0) <=> (calm(X0) <~> generous(X0))) [input p7]
11. ! [X0] : ((patient(X0) | ~quiet(X0)) => ~rich(X0)) [input p10]
12. ! [X0] : ((~rich(X0) | rich(X0)) <=> ~funny(X0)) [input p11]
13. ! [X0] : (quiet(X0) <=> (generous(X0) & humble(X0))) [input p12]
23. ~humble(fred) [input hypothesis]
29. ! [X0] : (~rich(X0) | (~patient(X0) & quiet(X0))) [ennf transformation 11]
40. ! [X0] : (((~generous(X0) | wise(X0)) | (wise(X0) | ~brave(X0))) & ((~wise(X0) & brave(X0)) | (generous(X0) & ~wise(X0)))) [nnf transformation 5]
41. ! [X0] : ((~generous(X0) | wise(X0) | wise(X0) | ~brave(X0)) & ((~wise(X0) & brave(X0)) | (generous(X0) & ~wise(X0)))) [flattening 40]
42. ! [X0] : ((((strong(X0) | ~rich(X0)) & (~strong(X0) | rich(X0))) | (wise(X0) | generous(X0))) & ((~wise(X0) & ~generous(X0)) | ((rich(X0) | strong(X0)) & (~strong(X0) | ~rich(X0))))) [nnf transformation 6]
43. ! [X0] : ((((strong(X0) | ~rich(X0)) & (~strong(X0) | rich(X0))) | wise(X0) | generous(X0)) & ((~wise(X0) & ~generous(X0)) | ((rich(X0) | strong(X0)) & (~strong(X0) | ~rich(X0))))) [flattening 42]
44. ! [X0] : (((kind(X0) & funny(X0)) | calm(X0)) & (~calm(X0) | (~kind(X0) | ~funny(X0)))) [nnf transformation 7]
45. ! [X0] : (((kind(X0) & funny(X0)) | calm(X0)) & (~calm(X0) | ~kind(X0) | ~funny(X0))) [flattening 44]
46. ! [X0] : ((strong(X0) | ((calm(X0) | ~generous(X0)) & (generous(X0) | ~calm(X0)))) & (((~generous(X0) | ~calm(X0)) & (generous(X0) | calm(X0))) | ~strong(X0))) [nnf transformation 8]
49. ! [X0] : (((~rich(X0) | rich(X0)) | funny(X0)) & (~funny(X0) | (rich(X0) & ~rich(X0)))) [nnf transformation 12]
50. ! [X0] : ((~rich(X0) | rich(X0) | funny(X0)) & (~funny(X0) | (rich(X0) & ~rich(X0)))) [flattening 49]
51. ! [X0] : ((quiet(X0) | (~generous(X0) | ~humble(X0))) & ((generous(X0) & humble(X0)) | ~quiet(X0))) [nnf transformation 13]
52. ! [X0] : ((quiet(X0) | ~generous(X0) | ~humble(X0)) & ((generous(X0) & humble(X0)) | ~quiet(X0))) [flattening 51]
72. ~wise(X0) | ~wise(X0) [cnf transformation 41]
76. ~generous(X0) | rich(X0) | strong(X0) [cnf transformation 43]
79. ~strong(X0) | rich(X0) | wise(X0) | generous(X0) [cnf transformation 43]
82. funny(X0) | calm(X0) [cnf transformation 45]
85. ~strong(X0) | ~calm(X0) | ~generous(X0) [cnf transformation 46]
86. ~calm(X0) | generous(X0) | strong(X0) [cnf transformation 46]
93. ~rich(X0) | quiet(X0) [cnf transformation 29]
95. ~funny(X0) | ~rich(X0) [cnf transformation 50]
96. ~funny(X0) | rich(X0) [cnf transformation 50]
98. ~quiet(X0) | humble(X0) [cnf transformation 52]
119. ~humble(fred) [cnf transformation 23]
120. ~wise(X0) [duplicate literal removal 72]
162. ~strong(X0) | rich(X0) | generous(X0) [subsumption resolution 79,120]
191. ~funny(X0) [subsumption resolution 95,96]
193. 16 <=> rich(fred) [avatar definition]
194. rich(fred) <- (16) [avatar component clause 193]
195. ~rich(fred) <- (~16) [avatar component clause 193]
243. calm(X0) [resolution 82,191]
247. quiet(fred) <- (16) [resolution 93,194]
250. humble(fred) <- (16) [resolution 98,247]
252. $false <- (16) [subsumption resolution 250,119]
253. ~16 [avatar contradiction clause 252]
312. strong(X0) | generous(X0) [resolution 86,243]
458. generous(X0) | rich(X0) | generous(X0) [resolution 312,162]
464. generous(X0) | rich(X0) [duplicate literal removal 458]
467. rich(X1) | rich(X1) | strong(X1) [resolution 464,76]
468. strong(X1) | rich(X1) [duplicate literal removal 467]
479. rich(X1) | ~calm(X1) | ~generous(X1) [resolution 468,85]
485. rich(X1) | ~generous(X1) [subsumption resolution 479,243]
486. rich(X1) [subsumption resolution 485,464]
491. $false <- (~16) [resolution 486,195]
492. 16 [avatar contradiction clause 491]
494. $false [avatar sat refutation 253,492]
% SZS output end Proof for 958521895955483359214082
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind or humble is either not funny or not kind and vice versa.
If mary is kind then someone is strong.
If fred is not humble then lucy is humble and vice versa.
If someone is not happy or not quiet then someone is both happy and not funny and vice versa.
If someone is creative or rich then someone is not rich or kind and vice versa.
Everyone who is either not strong or not humble is both curious and not quiet and vice versa.
Everyone who is not happy is either rich or humble.
If susan is not brave or not rich then someone is not happy and vice versa.
If someone is not generous then fred is both wise and strong.
Everyone who is wise is both not happy and tall and vice versa.
Everyone who is strong is both not tall and creative.
Everyone who is curious or not generous is not patient or not kind.
Everyone who is both not happy and generous is not strong.
If someone is not curious then mary is tall or not brave and vice versa.
If someone is both not patient and quiet then someone is either not generous or not curious and vice versa.
Everyone who is not strong is both not quiet and not tall.
Someone is humble or not brave.
Paul is not calm or curious.
Someone is funny or patient.
Someone is either not funny or not patient.
Someone is creative or not rich.
Susan is not calm or not kind.
Someone is either not brave or humble. | Mary is not wise. | entailment | (![X]:((kind(X)|humble(X))<=>(~funny(X)<~>~kind(X))))&
((kind(mary))=>(?[X]:(strong(X))))&
((~humble(fred))<=>(humble(lucy)))&
((?[X]:((~happy(X)|~quiet(X))))<=>(?[X]:((happy(X)&~funny(X)))))&
((?[X]:((creative(X)|rich(X))))<=>(?[X]:((~rich(X)|kind(X)))))&
(![X]:((~strong(X)<~>~humble(X))<=>(curious(X)&~quiet(X))))&
(![X]:(~happy(X)=>(rich(X)<~>humble(X))))&
(((~brave(susan)|~rich(susan)))<=>(?[X]:(~happy(X))))&
((?[X]:(~generous(X)))=>((wise(fred)&strong(fred))))&
(![X]:(wise(X)<=>(~happy(X)&tall(X))))&
(![X]:(strong(X)=>(~tall(X)&creative(X))))&
(![X]:((curious(X)|~generous(X))=>(~patient(X)|~kind(X))))&
(![X]:((~happy(X)&generous(X))=>~strong(X)))&
((?[X]:(~curious(X)))<=>((tall(mary)|~brave(mary))))&
((?[X]:((~patient(X)&quiet(X))))<=>(?[X]:((~generous(X)<~>~curious(X)))))&
(![X]:(~strong(X)=>(~quiet(X)&~tall(X))))&
(?[X]:((humble(X)|~brave(X))))&
((~calm(paul)|curious(paul)))&
(?[X]:((funny(X)|patient(X))))&
(?[X]:((~funny(X)<~>~patient(X))))&
(?[X]:((creative(X)|~rich(X))))&
((~calm(susan)|~kind(susan)))&
(?[X]:((~brave(X)<~>humble(X)))) | ~wise(mary) | [
"p9",
"p10",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2862777497792260359821827
% SZS output start Proof for 2862777497792260359821827
10. ! [X0] : (wise(X0) <=> (tall(X0) & ~happy(X0))) [input p9]
11. ! [X0] : (strong(X0) => (creative(X0) & ~tall(X0))) [input p10]
16. ! [X0] : (~strong(X0) => (~tall(X0) & ~quiet(X0))) [input p15]
24. wise(mary) [input hypothesis]
28. ! [X0] : (wise(X0) => (tall(X0) & ~happy(X0))) [unused predicate definition removal 10]
34. ! [X0] : ((tall(X0) & ~happy(X0)) | ~wise(X0)) [ennf transformation 28]
35. ! [X0] : ((creative(X0) & ~tall(X0)) | ~strong(X0)) [ennf transformation 11]
40. ! [X0] : ((~tall(X0) & ~quiet(X0)) | strong(X0)) [ennf transformation 16]
118. ~wise(X0) | tall(X0) [cnf transformation 34]
119. ~tall(X0) | ~strong(X0) [cnf transformation 35]
134. ~tall(X0) | strong(X0) [cnf transformation 40]
142. wise(mary) [cnf transformation 24]
303. ~tall(X0) [subsumption resolution 134,119]
359. tall(mary) [resolution 118,142]
360. $false [subsumption resolution 359,303]
% SZS output end Proof for 2862777497792260359821827
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous then someone is tall or not curious. Everyone who is both not wise and not patient is both not tall and not wise. Everyone who is either not curious or not generous is not old and vice versa. Everyone who is both humble and strong is both not creative and not quiet. If paul is either not happy or tall then fred is either patient or generous and vice versa. Everyone who is either rich or not wise is not rich and vice versa. If mary is not kind then someone is both strong and curious and vice versa. If someone is both not strong and creative then lucy is not strong or not funny. If fred is either not patient or not quiet then someone is either not kind or patient. If someone is either humble or not happy then someone is not quiet. Everyone who is both not calm and not tall is either quiet or not wise. If someone is creative then john is both not creative and quiet. Everyone who is quiet or patient is patient or not kind. Everyone who is curious is both not tall and tall. Everyone who is patient is not tall and vice versa. If mary is not brave then fred is not calm. Paul is calm. Susan is either not rich or wise. Someone is not kind or old. Fred is not happy. Alice is not funny. Someone is both not curious and not kind. Someone is not humble. | Fred is curious. | contradiction | ((?[X]:(~generous(X)))=>(?[X]:((tall(X)|~curious(X)))))&
(![X]:((~wise(X)&~patient(X))=>(~tall(X)&~wise(X))))&
(![X]:((~curious(X)<~>~generous(X))<=>~old(X)))&
(![X]:((humble(X)&strong(X))=>(~creative(X)&~quiet(X))))&
(((~happy(paul)<~>tall(paul)))<=>((patient(fred)<~>generous(fred))))&
(![X]:((rich(X)<~>~wise(X))<=>~rich(X)))&
((~kind(mary))<=>(?[X]:((strong(X)&curious(X)))))&
((?[X]:((~strong(X)&creative(X))))=>((~strong(lucy)|~funny(lucy))))&
(((~patient(fred)<~>~quiet(fred)))=>(?[X]:((~kind(X)<~>patient(X)))))&
((?[X]:((humble(X)<~>~happy(X))))=>(?[X]:(~quiet(X))))&
(![X]:((~calm(X)&~tall(X))=>(quiet(X)<~>~wise(X))))&
((?[X]:(creative(X)))=>((~creative(john)&quiet(john))))&
(![X]:((quiet(X)|patient(X))=>(patient(X)|~kind(X))))&
(![X]:(curious(X)=>(~tall(X)&tall(X))))&
(![X]:(patient(X)<=>~tall(X)))&
((~brave(mary))=>(~calm(fred)))&
(calm(paul))&
((~rich(susan)<~>wise(susan)))&
(?[X]:((~kind(X)|old(X))))&
(~happy(fred))&
(~funny(alice))&
(?[X]:((~curious(X)&~kind(X))))&
(?[X]:(~humble(X))) | curious(fred) | [
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 1437346488903575179259900
% SZS output start Proof for 1437346488903575179259900
14. ! [X0] : (curious(X0) => (tall(X0) & ~tall(X0))) [input p13]
24. curious(fred) [input hypothesis]
45. ! [X0] : ((tall(X0) & ~tall(X0)) | ~curious(X0)) [ennf transformation 14]
100. ~tall(X0) | ~curious(X0) [cnf transformation 45]
101. tall(X0) | ~curious(X0) [cnf transformation 45]
111. curious(fred) [cnf transformation 24]
197. ~curious(X0) [subsumption resolution 100,101]
208. $false [subsumption resolution 111,197]
% SZS output end Proof for 1437346488903575179259900
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not rich or patient is both not generous and wise and vice versa. Everyone who is both not funny and not kind is not calm and vice versa. Everyone who is either brave or not kind is not tall or humble. If mary is not old then someone is not quiet and vice versa. Everyone who is calm is not generous or not curious and vice versa. Everyone who is not happy is not brave or humble and vice versa. Everyone who is not creative or funny is both tall and old. Everyone who is either not funny or not tall is not calm and vice versa. If someone is not happy then someone is rich or generous and vice versa. Everyone who is quiet or not happy is not curious and vice versa. Everyone who is either not humble or not curious is both tall and happy. If someone is not calm then someone is both funny and not creative. Everyone who is not funny is creative and vice versa. If mary is not happy or brave then someone is not strong or funny and vice versa. Everyone who is either not patient or not calm is both not old and funny. Everyone who is not patient is not kind. Someone is both calm and not tall. Mary is either patient or strong. Someone is not old. Someone is either not curious or generous. Someone is calm or not kind. Someone is not brave or not calm. Someone is not patient or not generous. Someone is generous or old. | Mary is happy. | neutral | (![X]:((~rich(X)|patient(X))<=>(~generous(X)&wise(X))))&
(![X]:((~funny(X)&~kind(X))<=>~calm(X)))&
(![X]:((brave(X)<~>~kind(X))=>(~tall(X)|humble(X))))&
((~old(mary))<=>(?[X]:(~quiet(X))))&
(![X]:(calm(X)<=>(~generous(X)|~curious(X))))&
(![X]:(~happy(X)<=>(~brave(X)|humble(X))))&
(![X]:((~creative(X)|funny(X))=>(tall(X)&old(X))))&
(![X]:((~funny(X)<~>~tall(X))<=>~calm(X)))&
((?[X]:(~happy(X)))<=>(?[X]:((rich(X)|generous(X)))))&
(![X]:((quiet(X)|~happy(X))<=>~curious(X)))&
(![X]:((~humble(X)<~>~curious(X))=>(tall(X)&happy(X))))&
((?[X]:(~calm(X)))=>(?[X]:((funny(X)&~creative(X)))))&
(![X]:(~funny(X)<=>creative(X)))&
(((~happy(mary)|brave(mary)))<=>(?[X]:((~strong(X)|funny(X)))))&
(![X]:((~patient(X)<~>~calm(X))=>(~old(X)&funny(X))))&
(![X]:(~patient(X)=>~kind(X)))&
(?[X]:((calm(X)&~tall(X))))&
((patient(mary)<~>strong(mary)))&
(?[X]:(~old(X)))&
(?[X]:((~curious(X)<~>generous(X))))&
(?[X]:((calm(X)|~kind(X))))&
(?[X]:((~brave(X)|~calm(X))))&
(?[X]:((~patient(X)|~generous(X))))&
(?[X]:((generous(X)|old(X)))) | happy(mary) | [] | null | 0 |
Everyone who is creative or funny is either not brave or not humble and vice versa.
If someone is both creative and happy then someone is either happy or not humble and vice versa.
Everyone who is curious or tall is brave.
Everyone who is creative or not funny is not creative and vice versa.
If someone is not funny or not strong then someone is either not funny or creative.
Everyone who is not generous or not curious is humble and vice versa.
Everyone who is either calm or not happy is both humble and not kind.
If john is either not old or not brave then someone is not happy or rich and vice versa.
Everyone who is not wise or tall is either not generous or not strong and vice versa.
If mary is both not curious and generous then someone is not creative and vice versa.
Everyone who is either not curious or not funny is either not calm or humble.
Everyone who is both wise and calm is not brave.
Everyone who is patient is both generous and not humble.
If fred is both tall and brave then someone is either wise or not strong and vice versa.
If susan is either not calm or curious then someone is either not funny or not rich.
Everyone who is both patient and happy is not calm and vice versa.
Someone is not happy.
Someone is either rich or happy.
Paul is not strong or curious.
Someone is generous or humble.
John is tall. | Fred is old. | neutral | (![X]:((creative(X)|funny(X))<=>(~brave(X)<~>~humble(X))))&
((?[X]:((creative(X)&happy(X))))<=>(?[X]:((happy(X)<~>~humble(X)))))&
(![X]:((curious(X)|tall(X))=>brave(X)))&
(![X]:((creative(X)|~funny(X))<=>~creative(X)))&
((?[X]:((~funny(X)|~strong(X))))=>(?[X]:((~funny(X)<~>creative(X)))))&
(![X]:((~generous(X)|~curious(X))<=>humble(X)))&
(![X]:((calm(X)<~>~happy(X))=>(humble(X)&~kind(X))))&
(((~old(john)<~>~brave(john)))<=>(?[X]:((~happy(X)|rich(X)))))&
(![X]:((~wise(X)|tall(X))<=>(~generous(X)<~>~strong(X))))&
(((~curious(mary)&generous(mary)))<=>(?[X]:(~creative(X))))&
(![X]:((~curious(X)<~>~funny(X))=>(~calm(X)<~>humble(X))))&
(![X]:((wise(X)&calm(X))=>~brave(X)))&
(![X]:(patient(X)=>(generous(X)&~humble(X))))&
(((tall(fred)&brave(fred)))<=>(?[X]:((wise(X)<~>~strong(X)))))&
(((~calm(susan)<~>curious(susan)))=>(?[X]:((~funny(X)<~>~rich(X)))))&
(![X]:((patient(X)&happy(X))<=>~calm(X)))&
(?[X]:(~happy(X)))&
(?[X]:((rich(X)<~>happy(X))))&
((~strong(paul)|curious(paul)))&
(?[X]:((generous(X)|humble(X))))&
(tall(john)) | old(fred) | [] | null | 0 |
If someone is either not rich or calm then someone is strong and vice versa.
If someone is brave or not strong then someone is rich or not calm and vice versa.
Everyone who is either calm or quiet is kind.
If lucy is either not calm or curious then john is both not curious and not wise.
Everyone who is not curious is happy or old and vice versa.
If john is not old or not wise then susan is both happy and humble.
Everyone who is either patient or humble is wise or not funny and vice versa.
Everyone who is creative or patient is both kind and not kind.
Everyone who is either not funny or quiet is not creative or patient and vice versa.
Everyone who is wise is both wise and generous.
If john is funny or old then someone is both old and not humble and vice versa.
If someone is both not curious and not creative then lucy is not happy.
If someone is wise or not quiet then someone is not strong and vice versa.
Everyone who is not brave or not tall is both humble and not creative.
Everyone who is both not brave and not rich is not happy and vice versa.
If someone is either quiet or brave then someone is tall or not creative.
Alice is not old.
Someone is either not humble or old.
Paul is either humble or not humble.
Alice is either not quiet or humble.
Someone is both rich and not patient.
Fred is either not generous or humble.
Someone is kind.
Paul is both not humble and not creative. | Paul is not wise. | entailment | ((?[X]:((~rich(X)<~>calm(X))))<=>(?[X]:(strong(X))))&
((?[X]:((brave(X)|~strong(X))))<=>(?[X]:((rich(X)|~calm(X)))))&
(![X]:((calm(X)<~>quiet(X))=>kind(X)))&
(((~calm(lucy)<~>curious(lucy)))=>((~curious(john)&~wise(john))))&
(![X]:(~curious(X)<=>(happy(X)|old(X))))&
(((~old(john)|~wise(john)))=>((happy(susan)&humble(susan))))&
(![X]:((patient(X)<~>humble(X))<=>(wise(X)|~funny(X))))&
(![X]:((creative(X)|patient(X))=>(kind(X)&~kind(X))))&
(![X]:((~funny(X)<~>quiet(X))<=>(~creative(X)|patient(X))))&
(![X]:(wise(X)=>(wise(X)&generous(X))))&
(((funny(john)|old(john)))<=>(?[X]:((old(X)&~humble(X)))))&
((?[X]:((~curious(X)&~creative(X))))=>(~happy(lucy)))&
((?[X]:((wise(X)|~quiet(X))))<=>(?[X]:(~strong(X))))&
(![X]:((~brave(X)|~tall(X))=>(humble(X)&~creative(X))))&
(![X]:((~brave(X)&~rich(X))<=>~happy(X)))&
((?[X]:((quiet(X)<~>brave(X))))=>(?[X]:((tall(X)|~creative(X)))))&
(~old(alice))&
(?[X]:((~humble(X)<~>old(X))))&
((humble(paul)<~>~humble(paul)))&
((~quiet(alice)<~>humble(alice)))&
(?[X]:((rich(X)&~patient(X))))&
((~generous(fred)<~>humble(fred)))&
(?[X]:(kind(X)))&
((~humble(paul)&~creative(paul))) | ~wise(paul) | [
"p6",
"p7",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 5615338767053627512104711
% SZS output start Proof for 5615338767053627512104711
7. ! [X0] : ((patient(X0) <~> humble(X0)) <=> (~funny(X0) | wise(X0))) [input p6]
8. ! [X0] : ((patient(X0) | creative(X0)) => (~kind(X0) & kind(X0))) [input p7]
24. ~creative(paul) & ~humble(paul) [input p23]
25. wise(paul) [input hypothesis]
35. ! [X0] : ((~kind(X0) & kind(X0)) | (~patient(X0) & ~creative(X0))) [ennf transformation 8]
53. ! [X0] : ((((~humble(X0) | ~patient(X0)) & (humble(X0) | patient(X0))) | (funny(X0) & ~wise(X0))) & ((~funny(X0) | wise(X0)) | ((patient(X0) | ~humble(X0)) & (humble(X0) | ~patient(X0))))) [nnf transformation 7]
54. ! [X0] : ((((~humble(X0) | ~patient(X0)) & (humble(X0) | patient(X0))) | (funny(X0) & ~wise(X0))) & (~funny(X0) | wise(X0) | ((patient(X0) | ~humble(X0)) & (humble(X0) | ~patient(X0))))) [flattening 53]
102. ~wise(X0) | patient(X0) | humble(X0) [cnf transformation 54]
107. kind(X0) | ~patient(X0) [cnf transformation 35]
109. ~patient(X0) | ~kind(X0) [cnf transformation 35]
144. ~humble(paul) [cnf transformation 24]
146. wise(paul) [cnf transformation 25]
240. ~patient(X0) [subsumption resolution 107,109]
345. patient(paul) | humble(paul) [resolution 102,146]
346. humble(paul) [subsumption resolution 345,240]
347. $false [subsumption resolution 346,144]
% SZS output end Proof for 5615338767053627512104711
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not rich or happy then fred is either not happy or curious and vice versa.
Everyone who is both creative and happy is both generous and calm.
Everyone who is either not creative or not rich is either not funny or not rich and vice versa.
If someone is either happy or humble then paul is not happy or not rich.
Everyone who is either creative or not creative is both not strong and not wise and vice versa.
Everyone who is either rich or not strong is not patient.
If lucy is generous or funny then someone is not strong.
If someone is both not happy and tall then alice is both tall and quiet.
If susan is either not patient or not wise then someone is not tall and vice versa.
If susan is calm then john is quiet.
If fred is both not strong and not happy then susan is not old or not kind and vice versa.
If someone is humble or brave then someone is either creative or not calm.
Everyone who is either not humble or not wise is not patient or quiet.
If someone is either rich or happy then mary is both not quiet and old.
Everyone who is not happy is not kind and vice versa.
Everyone who is not kind or not calm is not wise and vice versa.
Susan is tall.
John is not old.
Mary is not creative.
Someone is funny.
Someone is calm or curious.
Susan is quiet.
Fred is not brave or not humble. | Lucy is strong. | contradiction | ((?[X]:((~rich(X)<~>happy(X))))<=>((~happy(fred)<~>curious(fred))))&
(![X]:((creative(X)&happy(X))=>(generous(X)&calm(X))))&
(![X]:((~creative(X)<~>~rich(X))<=>(~funny(X)<~>~rich(X))))&
((?[X]:((happy(X)<~>humble(X))))=>((~happy(paul)|~rich(paul))))&
(![X]:((creative(X)<~>~creative(X))<=>(~strong(X)&~wise(X))))&
(![X]:((rich(X)<~>~strong(X))=>~patient(X)))&
(((generous(lucy)|funny(lucy)))=>(?[X]:(~strong(X))))&
((?[X]:((~happy(X)&tall(X))))=>((tall(alice)&quiet(alice))))&
(((~patient(susan)<~>~wise(susan)))<=>(?[X]:(~tall(X))))&
((calm(susan))=>(quiet(john)))&
(((~strong(fred)&~happy(fred)))<=>((~old(susan)|~kind(susan))))&
((?[X]:((humble(X)|brave(X))))=>(?[X]:((creative(X)<~>~calm(X)))))&
(![X]:((~humble(X)<~>~wise(X))=>(~patient(X)|quiet(X))))&
((?[X]:((rich(X)<~>happy(X))))=>((~quiet(mary)&old(mary))))&
(![X]:(~happy(X)<=>~kind(X)))&
(![X]:((~kind(X)|~calm(X))<=>~wise(X)))&
(tall(susan))&
(~old(john))&
(~creative(mary))&
(?[X]:(funny(X)))&
(?[X]:((calm(X)|curious(X))))&
(quiet(susan))&
((~brave(fred)|~humble(fred))) | strong(lucy) | [
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 401697831089022552071822
% SZS output start Proof for 401697831089022552071822
5. ! [X0] : ((creative(X0) <~> ~creative(X0)) <=> (~wise(X0) & ~strong(X0))) [input p4]
24. strong(lucy) [input hypothesis]
46. ! [X0] : ((((creative(X0) | ~creative(X0)) & (~creative(X0) | creative(X0))) | (wise(X0) | strong(X0))) & ((~wise(X0) & ~strong(X0)) | ((creative(X0) | creative(X0)) & (~creative(X0) | ~creative(X0))))) [nnf transformation 5]
47. ! [X0] : ((((creative(X0) | ~creative(X0)) & (~creative(X0) | creative(X0))) | wise(X0) | strong(X0)) & ((~wise(X0) & ~strong(X0)) | ((creative(X0) | creative(X0)) & (~creative(X0) | ~creative(X0))))) [flattening 46]
90. ~strong(X0) | ~creative(X0) | ~creative(X0) [cnf transformation 47]
91. ~strong(X0) | creative(X0) | creative(X0) [cnf transformation 47]
131. strong(lucy) [cnf transformation 24]
132. ~strong(X0) | ~creative(X0) [duplicate literal removal 90]
133. ~strong(X0) | creative(X0) [duplicate literal removal 91]
189. ~strong(X0) [subsumption resolution 132,133]
282. $false [subsumption resolution 131,189]
% SZS output end Proof for 401697831089022552071822
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not creative and not strong then lucy is either quiet or not quiet.
Everyone who is both not curious and not wise is not tall and vice versa.
If someone is either humble or kind then someone is both funny and not curious and vice versa.
Everyone who is either funny or rich is curious or not happy.
Everyone who is both strong and not tall is not happy or quiet and vice versa.
Everyone who is not brave is both funny and strong and vice versa.
If someone is either not patient or curious then lucy is funny.
Everyone who is not quiet or creative is happy or not creative and vice versa.
Everyone who is both wise and tall is either not patient or not calm and vice versa.
Everyone who is curious or funny is calm and vice versa.
Everyone who is both not rich and curious is not rich.
If mary is both quiet and calm then someone is both brave and wise and vice versa.
Everyone who is both not humble and brave is not patient or humble and vice versa.
If john is not kind or calm then someone is not curious.
If john is both not humble and humble then john is either not humble or not kind and vice versa.
Everyone who is quiet or curious is not rich or not brave.
Someone is either not wise or not generous.
Someone is both not old and not tall.
Someone is not creative.
Someone is both not happy and patient.
Someone is not quiet.
Someone is either not calm or curious.
Someone is not quiet or not wise.
Fred is patient. | Fred is tall. | neutral | ((?[X]:((~creative(X)&~strong(X))))=>((quiet(lucy)<~>~quiet(lucy))))&
(![X]:((~curious(X)&~wise(X))<=>~tall(X)))&
((?[X]:((humble(X)<~>kind(X))))<=>(?[X]:((funny(X)&~curious(X)))))&
(![X]:((funny(X)<~>rich(X))=>(curious(X)|~happy(X))))&
(![X]:((strong(X)&~tall(X))<=>(~happy(X)|quiet(X))))&
(![X]:(~brave(X)<=>(funny(X)&strong(X))))&
((?[X]:((~patient(X)<~>curious(X))))=>(funny(lucy)))&
(![X]:((~quiet(X)|creative(X))<=>(happy(X)|~creative(X))))&
(![X]:((wise(X)&tall(X))<=>(~patient(X)<~>~calm(X))))&
(![X]:((curious(X)|funny(X))<=>calm(X)))&
(![X]:((~rich(X)&curious(X))=>~rich(X)))&
(((quiet(mary)&calm(mary)))<=>(?[X]:((brave(X)&wise(X)))))&
(![X]:((~humble(X)&brave(X))<=>(~patient(X)|humble(X))))&
(((~kind(john)|calm(john)))=>(?[X]:(~curious(X))))&
(((~humble(john)&humble(john)))<=>((~humble(john)<~>~kind(john))))&
(![X]:((quiet(X)|curious(X))=>(~rich(X)|~brave(X))))&
(?[X]:((~wise(X)<~>~generous(X))))&
(?[X]:((~old(X)&~tall(X))))&
(?[X]:(~creative(X)))&
(?[X]:((~happy(X)&patient(X))))&
(?[X]:(~quiet(X)))&
(?[X]:((~calm(X)<~>curious(X))))&
(?[X]:((~quiet(X)|~wise(X))))&
(patient(fred)) | tall(fred) | [] | null | 0 |
Everyone who is both not creative and curious is not strong.
Everyone who is both not calm and happy is strong and vice versa.
Everyone who is either creative or not quiet is both old and not patient and vice versa.
Everyone who is either not patient or not creative is not rich or not kind and vice versa.
If lucy is not calm then someone is both not patient and old and vice versa.
If someone is both funny and curious then susan is calm or not tall and vice versa.
If mary is either not old or generous then someone is not wise.
Everyone who is either not rich or rich is both not wise and curious and vice versa.
If paul is not old then lucy is calm or generous and vice versa.
If someone is either not calm or not strong then someone is either not calm or not kind.
Everyone who is both generous and not wise is not calm.
If someone is either not old or not rich then someone is generous.
Everyone who is not humble or calm is wise or not kind.
If someone is humble then someone is strong or kind and vice versa.
Everyone who is creative is both wise and not strong.
Everyone who is either curious or humble is both creative and patient and vice versa.
Someone is either old or not curious.
Lucy is either not kind or not patient.
Someone is either kind or not rich.
Mary is wise or not kind.
Paul is creative or not wise.
Alice is curious.
Someone is both old and not patient. | Mary is not calm. | neutral | (![X]:((~creative(X)&curious(X))=>~strong(X)))&
(![X]:((~calm(X)&happy(X))<=>strong(X)))&
(![X]:((creative(X)<~>~quiet(X))<=>(old(X)&~patient(X))))&
(![X]:((~patient(X)<~>~creative(X))<=>(~rich(X)|~kind(X))))&
((~calm(lucy))<=>(?[X]:((~patient(X)&old(X)))))&
((?[X]:((funny(X)&curious(X))))<=>((calm(susan)|~tall(susan))))&
(((~old(mary)<~>generous(mary)))=>(?[X]:(~wise(X))))&
(![X]:((~rich(X)<~>rich(X))<=>(~wise(X)&curious(X))))&
((~old(paul))<=>((calm(lucy)|generous(lucy))))&
((?[X]:((~calm(X)<~>~strong(X))))=>(?[X]:((~calm(X)<~>~kind(X)))))&
(![X]:((generous(X)&~wise(X))=>~calm(X)))&
((?[X]:((~old(X)<~>~rich(X))))=>(?[X]:(generous(X))))&
(![X]:((~humble(X)|calm(X))=>(wise(X)|~kind(X))))&
((?[X]:(humble(X)))<=>(?[X]:((strong(X)|kind(X)))))&
(![X]:(creative(X)=>(wise(X)&~strong(X))))&
(![X]:((curious(X)<~>humble(X))<=>(creative(X)&patient(X))))&
(?[X]:((old(X)<~>~curious(X))))&
((~kind(lucy)<~>~patient(lucy)))&
(?[X]:((kind(X)<~>~rich(X))))&
((wise(mary)|~kind(mary)))&
((creative(paul)|~wise(paul)))&
(curious(alice))&
(?[X]:((old(X)&~patient(X)))) | ~calm(mary) | [] | null | 0 |
If someone is not funny then susan is not funny or not quiet.
If someone is not rich then susan is brave or calm.
Everyone who is both not generous and tall is either not tall or not patient.
Everyone who is either not kind or old is not brave.
Everyone who is both not patient and brave is either tall or not wise.
Everyone who is both not creative and curious is not humble or not funny and vice versa.
Everyone who is either not patient or creative is either not patient or not brave.
Everyone who is both not creative and creative is not creative or not rich.
Everyone who is quiet is not patient or old.
If someone is not generous then mary is quiet.
Everyone who is both wise and not tall is not patient or not calm and vice versa.
If someone is patient or not patient then paul is both not strong and kind and vice versa.
Everyone who is patient or not quiet is curious or wise.
Everyone who is either tall or generous is both not quiet and brave.
If someone is rich or calm then paul is both not calm and wise and vice versa.
If someone is humble or generous then susan is either brave or not creative.
Susan is generous or old.
Susan is both humble and not curious.
Someone is funny or humble.
Mary is not funny or not quiet.
Someone is rich.
Someone is curious or calm.
Someone is both kind and wise.
Someone is not strong. | Susan is not brave. | entailment | ((?[X]:(~funny(X)))=>((~funny(susan)|~quiet(susan))))&
((?[X]:(~rich(X)))=>((brave(susan)|calm(susan))))&
(![X]:((~generous(X)&tall(X))=>(~tall(X)<~>~patient(X))))&
(![X]:((~kind(X)<~>old(X))=>~brave(X)))&
(![X]:((~patient(X)&brave(X))=>(tall(X)<~>~wise(X))))&
(![X]:((~creative(X)&curious(X))<=>(~humble(X)|~funny(X))))&
(![X]:((~patient(X)<~>creative(X))=>(~patient(X)<~>~brave(X))))&
(![X]:((~creative(X)&creative(X))=>(~creative(X)|~rich(X))))&
(![X]:(quiet(X)=>(~patient(X)|old(X))))&
((?[X]:(~generous(X)))=>(quiet(mary)))&
(![X]:((wise(X)&~tall(X))<=>(~patient(X)|~calm(X))))&
((?[X]:((patient(X)|~patient(X))))<=>((~strong(paul)&kind(paul))))&
(![X]:((patient(X)|~quiet(X))=>(curious(X)|wise(X))))&
(![X]:((tall(X)<~>generous(X))=>(~quiet(X)&brave(X))))&
((?[X]:((rich(X)|calm(X))))<=>((~calm(paul)&wise(paul))))&
((?[X]:((humble(X)|generous(X))))=>((brave(susan)<~>~creative(susan))))&
((generous(susan)|old(susan)))&
((humble(susan)&~curious(susan)))&
(?[X]:((funny(X)|humble(X))))&
((~funny(mary)|~quiet(mary)))&
(?[X]:(rich(X)))&
(?[X]:((curious(X)|calm(X))))&
(?[X]:((kind(X)&wise(X))))&
(?[X]:(~strong(X))) | ~brave(susan) | [
"p4",
"p6",
"p10",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 5862135484704486790444566
% SZS output start Proof for 5862135484704486790444566
5. ! [X0] : ((brave(X0) & ~patient(X0)) => (tall(X0) <~> ~wise(X0))) [input p4]
7. ! [X0] : ((~patient(X0) <~> creative(X0)) => (~patient(X0) <~> ~brave(X0))) [input p6]
11. ! [X0] : ((~tall(X0) & wise(X0)) <=> (~calm(X0) | ~patient(X0))) [input p10]
16. ? [X0] : (generous(X0) | humble(X0)) => (brave(susan) <~> ~creative(susan)) [input p15]
18. ~curious(susan) & humble(susan) [input p17]
25. brave(susan) [input hypothesis]
33. ! [X0] : ((tall(X0) <~> ~wise(X0)) | (~brave(X0) | patient(X0))) [ennf transformation 5]
34. ! [X0] : ((tall(X0) <~> ~wise(X0)) | ~brave(X0) | patient(X0)) [flattening 33]
35. ! [X0] : ((~patient(X0) <~> ~brave(X0)) | (~patient(X0) <=> creative(X0))) [ennf transformation 7]
44. (brave(susan) <~> ~creative(susan)) | ! [X0] : (~generous(X0) & ~humble(X0)) [ennf transformation 16]
47. ! [X0] : (((wise(X0) | ~tall(X0)) & (~wise(X0) | tall(X0))) | ~brave(X0) | patient(X0)) [nnf transformation 34]
50. ! [X0] : (((brave(X0) | patient(X0)) & (~brave(X0) | ~patient(X0))) | ((~patient(X0) | ~creative(X0)) & (creative(X0) | patient(X0)))) [nnf transformation 35]
51. ! [X0] : (((~tall(X0) & wise(X0)) | (calm(X0) & patient(X0))) & ((~calm(X0) | ~patient(X0)) | (tall(X0) | ~wise(X0)))) [nnf transformation 11]
52. ! [X0] : (((~tall(X0) & wise(X0)) | (calm(X0) & patient(X0))) & (~calm(X0) | ~patient(X0) | tall(X0) | ~wise(X0))) [flattening 51]
64. ((creative(susan) | ~brave(susan)) & (~creative(susan) | brave(susan))) | ! [X0] : (~generous(X0) & ~humble(X0)) [nnf transformation 44]
81. ~wise(X0) | tall(X0) | ~brave(X0) | patient(X0) [cnf transformation 47]
89. ~brave(X0) | ~patient(X0) | ~patient(X0) | ~creative(X0) [cnf transformation 50]
96. wise(X0) | patient(X0) [cnf transformation 52]
98. ~tall(X0) | patient(X0) [cnf transformation 52]
118. creative(susan) | ~brave(susan) | ~humble(X0) [cnf transformation 64]
121. humble(susan) [cnf transformation 18]
130. brave(susan) [cnf transformation 25]
132. ~creative(X0) | ~patient(X0) | ~brave(X0) [duplicate literal removal 89]
151. 5 <=> brave(susan) [avatar definition]
153. brave(susan) <- (5) [avatar component clause 151]
218. 20 <=> creative(susan) [avatar definition]
220. creative(susan) <- (20) [avatar component clause 218]
223. 21 <=> ! [X0] : ~humble(X0) [avatar definition]
224. ~humble(X0) <- (21) [avatar component clause 223]
225. 21 | ~5 | 20 [avatar split clause 118,218,151,223]
260. 5 [avatar split clause 130,151]
269. $false <- (21) [resolution 224,121]
270. ~21 [avatar contradiction clause 269]
279. ~patient(susan) | ~brave(susan) <- (20) [resolution 132,220]
280. ~patient(susan) <- (5, 20) [subsumption resolution 279,153]
285. tall(X1) | ~brave(X1) | patient(X1) | patient(X1) [resolution 81,96]
289. tall(X1) | ~brave(X1) | patient(X1) [duplicate literal removal 285]
291. ~brave(X1) | patient(X1) [subsumption resolution 289,98]
292. patient(susan) <- (5) [resolution 291,153]
293. $false <- (5, 20) [subsumption resolution 292,280]
294. ~5 | ~20 [avatar contradiction clause 293]
295. $false [avatar sat refutation 225,260,270,294]
% SZS output end Proof for 5862135484704486790444566
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet or not humble then alice is either rich or strong and vice versa. Everyone who is kind or not brave is generous. If lucy is both not creative and tall then someone is both calm and not old and vice versa. Everyone who is either tall or not funny is humble and vice versa. If someone is both not rich and humble then mary is not brave or not humble and vice versa. Everyone who is generous or tall is either not generous or brave and vice versa. Everyone who is either old or rich is both wise and not brave and vice versa. Everyone who is not calm or not happy is both not patient and not kind. Everyone who is rich or not curious is rich. Everyone who is either quiet or not tall is either not creative or not calm. If someone is humble or not humble then someone is either humble or not calm. Everyone who is both not quiet and brave is either creative or curious and vice versa. Everyone who is either not rich or not happy is either not strong or not quiet and vice versa. If someone is generous or not creative then someone is brave or not calm and vice versa. If john is either not quiet or humble then someone is either rich or creative and vice versa. Everyone who is both generous and not tall is quiet or not kind. Mary is both curious and kind. Lucy is not happy or happy. Alice is not generous. Alice is both not curious and rich. John is either not kind or curious. Someone is rich or not old. Someone is both generous and not rich. | Mary is not patient. | neutral | ((?[X]:((quiet(X)<~>~humble(X))))<=>((rich(alice)<~>strong(alice))))&
(![X]:((kind(X)|~brave(X))=>generous(X)))&
(((~creative(lucy)&tall(lucy)))<=>(?[X]:((calm(X)&~old(X)))))&
(![X]:((tall(X)<~>~funny(X))<=>humble(X)))&
((?[X]:((~rich(X)&humble(X))))<=>((~brave(mary)|~humble(mary))))&
(![X]:((generous(X)|tall(X))<=>(~generous(X)<~>brave(X))))&
(![X]:((old(X)<~>rich(X))<=>(wise(X)&~brave(X))))&
(![X]:((~calm(X)|~happy(X))=>(~patient(X)&~kind(X))))&
(![X]:((rich(X)|~curious(X))=>rich(X)))&
(![X]:((quiet(X)<~>~tall(X))=>(~creative(X)<~>~calm(X))))&
((?[X]:((humble(X)|~humble(X))))=>(?[X]:((humble(X)<~>~calm(X)))))&
(![X]:((~quiet(X)&brave(X))<=>(creative(X)<~>curious(X))))&
(![X]:((~rich(X)<~>~happy(X))<=>(~strong(X)<~>~quiet(X))))&
((?[X]:((generous(X)|~creative(X))))<=>(?[X]:((brave(X)|~calm(X)))))&
(((~quiet(john)<~>humble(john)))<=>(?[X]:((rich(X)<~>creative(X)))))&
(![X]:((generous(X)&~tall(X))=>(quiet(X)|~kind(X))))&
((curious(mary)&kind(mary)))&
((~happy(lucy)|happy(lucy)))&
(~generous(alice))&
((~curious(alice)&rich(alice)))&
((~kind(john)<~>curious(john)))&
(?[X]:((rich(X)|~old(X))))&
(?[X]:((generous(X)&~rich(X)))) | ~patient(mary) | [] | null | 0 |
If someone is both creative and happy then susan is not generous.
Everyone who is not brave or humble is humble.
If paul is funny then fred is both brave and not patient and vice versa.
Everyone who is either not old or not humble is both not curious and rich and vice versa.
Everyone who is both not tall and generous is not patient or not humble.
If paul is not old or not curious then mary is not happy and vice versa.
Everyone who is both not humble and quiet is both not strong and not kind and vice versa.
Everyone who is happy is either not quiet or not patient and vice versa.
Everyone who is not rich or creative is creative or rich.
Everyone who is curious or rich is not rich or not calm and vice versa.
Everyone who is both happy and not curious is wise or kind and vice versa.
If susan is not brave then fred is either curious or not humble.
Everyone who is either not kind or curious is either calm or not creative and vice versa.
If john is either not funny or not rich then lucy is not wise or patient and vice versa.
Everyone who is not happy or kind is old or not patient and vice versa.
If alice is calm then someone is either creative or not humble and vice versa.
Someone is either not happy or not kind.
Someone is both not calm and old.
Alice is either not creative or not patient.
John is strong or curious. | Paul is old. | neutral | ((?[X]:((creative(X)&happy(X))))=>(~generous(susan)))&
(![X]:((~brave(X)|humble(X))=>humble(X)))&
((funny(paul))<=>((brave(fred)&~patient(fred))))&
(![X]:((~old(X)<~>~humble(X))<=>(~curious(X)&rich(X))))&
(![X]:((~tall(X)&generous(X))=>(~patient(X)|~humble(X))))&
(((~old(paul)|~curious(paul)))<=>(~happy(mary)))&
(![X]:((~humble(X)&quiet(X))<=>(~strong(X)&~kind(X))))&
(![X]:(happy(X)<=>(~quiet(X)<~>~patient(X))))&
(![X]:((~rich(X)|creative(X))=>(creative(X)|rich(X))))&
(![X]:((curious(X)|rich(X))<=>(~rich(X)|~calm(X))))&
(![X]:((happy(X)&~curious(X))<=>(wise(X)|kind(X))))&
((~brave(susan))=>((curious(fred)<~>~humble(fred))))&
(![X]:((~kind(X)<~>curious(X))<=>(calm(X)<~>~creative(X))))&
(((~funny(john)<~>~rich(john)))<=>((~wise(lucy)|patient(lucy))))&
(![X]:((~happy(X)|kind(X))<=>(old(X)|~patient(X))))&
((calm(alice))<=>(?[X]:((creative(X)<~>~humble(X)))))&
(?[X]:((~happy(X)<~>~kind(X))))&
(?[X]:((~calm(X)&old(X))))&
((~creative(alice)<~>~patient(alice)))&
((strong(john)|curious(john))) | old(paul) | [] | null | 0 |
Everyone who is curious is either curious or not kind.
If mary is either not quiet or strong then someone is both patient and not rich.
Everyone who is either not rich or generous is either not patient or strong and vice versa.
If mary is both happy and generous then susan is both old and curious and vice versa.
Everyone who is either not happy or calm is either generous or not creative and vice versa.
Everyone who is both not funny and not humble is humble or curious.
If fred is both not humble and wise then fred is both not brave and not calm.
If someone is both rich and calm then alice is both not old and wise and vice versa.
If someone is creative or wise then fred is either not brave or quiet and vice versa.
If someone is both not brave and not calm then someone is both funny and creative.
Everyone who is quiet or not creative is happy.
Everyone who is both generous and calm is either calm or happy and vice versa.
If someone is not brave then susan is happy or not funny.
Everyone who is both not generous and not happy is quiet and vice versa.
If susan is both not strong and not funny then someone is kind or not generous and vice versa.
If someone is both not curious and not patient then alice is both calm and kind and vice versa.
Paul is not humble.
Susan is both wise and strong.
Alice is either not brave or wise.
Someone is either brave or not kind.
Paul is generous.
Someone is both funny and old.
Fred is either not creative or not brave. | Alice is not calm. | entailment | (![X]:(curious(X)=>(curious(X)<~>~kind(X))))&
(((~quiet(mary)<~>strong(mary)))=>(?[X]:((patient(X)&~rich(X)))))&
(![X]:((~rich(X)<~>generous(X))<=>(~patient(X)<~>strong(X))))&
(((happy(mary)&generous(mary)))<=>((old(susan)&curious(susan))))&
(![X]:((~happy(X)<~>calm(X))<=>(generous(X)<~>~creative(X))))&
(![X]:((~funny(X)&~humble(X))=>(humble(X)|curious(X))))&
(((~humble(fred)&wise(fred)))=>((~brave(fred)&~calm(fred))))&
((?[X]:((rich(X)&calm(X))))<=>((~old(alice)&wise(alice))))&
((?[X]:((creative(X)|wise(X))))<=>((~brave(fred)<~>quiet(fred))))&
((?[X]:((~brave(X)&~calm(X))))=>(?[X]:((funny(X)&creative(X)))))&
(![X]:((quiet(X)|~creative(X))=>happy(X)))&
(![X]:((generous(X)&calm(X))<=>(calm(X)<~>happy(X))))&
((?[X]:(~brave(X)))=>((happy(susan)|~funny(susan))))&
(![X]:((~generous(X)&~happy(X))<=>quiet(X)))&
(((~strong(susan)&~funny(susan)))<=>(?[X]:((kind(X)|~generous(X)))))&
((?[X]:((~curious(X)&~patient(X))))<=>((calm(alice)&kind(alice))))&
(~humble(paul))&
((wise(susan)&strong(susan)))&
((~brave(alice)<~>wise(alice)))&
(?[X]:((brave(X)<~>~kind(X))))&
(generous(paul))&
(?[X]:((funny(X)&old(X))))&
((~creative(fred)<~>~brave(fred))) | ~calm(alice) | [
"p4",
"p10",
"p11",
"p14",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 3827686464900959789734814
% SZS output start Proof for 3827686464900959789734814
5. ! [X0] : ((~happy(X0) <~> calm(X0)) <=> (generous(X0) <~> ~creative(X0))) [input p4]
11. ! [X0] : ((~creative(X0) | quiet(X0)) => happy(X0)) [input p10]
12. ! [X0] : ((calm(X0) & generous(X0)) <=> (calm(X0) <~> happy(X0))) [input p11]
15. (~funny(susan) & ~strong(susan)) <=> ? [X0] : (~generous(X0) | kind(X0)) [input p14]
18. strong(susan) & wise(susan) [input p17]
24. calm(alice) [input hypothesis]
33. ! [X0] : (happy(X0) | (creative(X0) & ~quiet(X0))) [ennf transformation 11]
43. ! [X0] : ((((~calm(X0) | happy(X0)) & (calm(X0) | ~happy(X0))) | ((generous(X0) | creative(X0)) & (~creative(X0) | ~generous(X0)))) & (((creative(X0) | ~generous(X0)) & (~creative(X0) | generous(X0))) | ((~happy(X0) | ~calm(X0)) & (calm(X0) | happy(X0))))) [nnf transformation 5]
56. ! [X0] : (((calm(X0) & generous(X0)) | ((calm(X0) | ~happy(X0)) & (happy(X0) | ~calm(X0)))) & (((~happy(X0) | ~calm(X0)) & (happy(X0) | calm(X0))) | (~calm(X0) | ~generous(X0)))) [nnf transformation 12]
57. ! [X0] : (((calm(X0) & generous(X0)) | ((calm(X0) | ~happy(X0)) & (happy(X0) | ~calm(X0)))) & (((~happy(X0) | ~calm(X0)) & (happy(X0) | calm(X0))) | ~calm(X0) | ~generous(X0))) [flattening 56]
60. ((~funny(susan) & ~strong(susan)) | ! [X0] : (generous(X0) & ~kind(X0))) & (? [X0] : (~generous(X0) | kind(X0)) | (funny(susan) | strong(susan))) [nnf transformation 15]
61. ((~funny(susan) & ~strong(susan)) | ! [X0] : (generous(X0) & ~kind(X0))) & (? [X0] : (~generous(X0) | kind(X0)) | funny(susan) | strong(susan)) [flattening 60]
62. ((~funny(susan) & ~strong(susan)) | ! [X0] : (generous(X0) & ~kind(X0))) & (? [X1] : (~generous(X1) | kind(X1)) | funny(susan) | strong(susan)) [rectify 61]
63. ? [X1] : (~generous(X1) | kind(X1)) => (~generous(sK4) | kind(sK4)) [choice axiom]
64. ((~funny(susan) & ~strong(susan)) | ! [X0] : (generous(X0) & ~kind(X0))) & ((~generous(sK4) | kind(sK4)) | funny(susan) | strong(susan)) [skolemisation 62,63]
101. ~creative(X0) | happy(X0) | ~calm(X0) | ~generous(X0) [cnf transformation 43]
119. creative(X0) | happy(X0) [cnf transformation 33]
121. ~happy(X0) | ~calm(X0) | ~calm(X0) | ~generous(X0) [cnf transformation 57]
125. calm(X0) | calm(X0) | ~happy(X0) [cnf transformation 57]
132. ~strong(susan) | generous(X0) [cnf transformation 64]
141. strong(susan) [cnf transformation 18]
151. calm(alice) [cnf transformation 24]
152. ~happy(X0) | ~calm(X0) | ~generous(X0) [duplicate literal removal 121]
153. ~happy(X0) | calm(X0) [duplicate literal removal 125]
274. ~happy(X0) | ~generous(X0) [subsumption resolution 152,153]
290. 29 <=> ! [X0] : generous(X0) [avatar definition]
291. generous(X0) <- (29) [avatar component clause 290]
298. 31 <=> strong(susan) [avatar definition]
301. 29 | ~31 [avatar split clause 132,298,290]
313. 34 <=> calm(alice) [avatar definition]
314. calm(alice) <- (34) [avatar component clause 313]
335. 31 [avatar split clause 141,298]
358. 34 [avatar split clause 151,313]
509. happy(X0) | ~calm(X0) | ~generous(X0) | happy(X0) [resolution 101,119]
510. happy(X0) | ~calm(X0) | ~generous(X0) [duplicate literal removal 509]
523. ~calm(X0) | happy(X0) <- (29) [subsumption resolution 510,291]
538. happy(alice) <- (29, 34) [resolution 523,314]
541. ~generous(alice) <- (29, 34) [resolution 538,274]
543. $false <- (29, 34) [subsumption resolution 541,291]
544. ~29 | ~34 [avatar contradiction clause 543]
545. $false [avatar sat refutation 301,335,358,544]
% SZS output end Proof for 3827686464900959789734814
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not patient or humble then paul is both not tall and wise and vice versa.
Everyone who is generous or not happy is not generous or not rich and vice versa.
Everyone who is either funny or creative is kind or funny and vice versa.
Everyone who is not quiet is calm and vice versa.
If lucy is either not curious or not patient then someone is both wise and not funny and vice versa.
Everyone who is either not old or tall is both generous and old.
Everyone who is curious or generous is not creative or not tall and vice versa.
Everyone who is both not tall and humble is strong and vice versa.
If fred is both funny and not kind then someone is not humble or calm and vice versa.
If susan is either rich or wise then someone is calm or wise and vice versa.
Everyone who is patient is either generous or not tall and vice versa.
Everyone who is not tall or not rich is calm.
If mary is both humble and not patient then susan is not kind and vice versa.
If someone is either not funny or strong then mary is either tall or not calm and vice versa.
Everyone who is either wise or not calm is not tall or wise.
Everyone who is not rich or kind is not calm.
Fred is both not humble and quiet.
Someone is not old or kind.
Alice is either rich or not creative.
Someone is both not humble and not wise.
Someone is both rich and quiet.
Lucy is either not humble or humble.
Someone is either creative or not wise. | Paul is not old. | contradiction | ((?[X]:((~patient(X)|humble(X))))<=>((~tall(paul)&wise(paul))))&
(![X]:((generous(X)|~happy(X))<=>(~generous(X)|~rich(X))))&
(![X]:((funny(X)<~>creative(X))<=>(kind(X)|funny(X))))&
(![X]:(~quiet(X)<=>calm(X)))&
(((~curious(lucy)<~>~patient(lucy)))<=>(?[X]:((wise(X)&~funny(X)))))&
(![X]:((~old(X)<~>tall(X))=>(generous(X)&old(X))))&
(![X]:((curious(X)|generous(X))<=>(~creative(X)|~tall(X))))&
(![X]:((~tall(X)&humble(X))<=>strong(X)))&
(((funny(fred)&~kind(fred)))<=>(?[X]:((~humble(X)|calm(X)))))&
(((rich(susan)<~>wise(susan)))<=>(?[X]:((calm(X)|wise(X)))))&
(![X]:(patient(X)<=>(generous(X)<~>~tall(X))))&
(![X]:((~tall(X)|~rich(X))=>calm(X)))&
(((humble(mary)&~patient(mary)))<=>(~kind(susan)))&
((?[X]:((~funny(X)<~>strong(X))))<=>((tall(mary)<~>~calm(mary))))&
(![X]:((wise(X)<~>~calm(X))=>(~tall(X)|wise(X))))&
(![X]:((~rich(X)|kind(X))=>~calm(X)))&
((~humble(fred)&quiet(fred)))&
(?[X]:((~old(X)|kind(X))))&
((rich(alice)<~>~creative(alice)))&
(?[X]:((~humble(X)&~wise(X))))&
(?[X]:((rich(X)&quiet(X))))&
((~humble(lucy)<~>humble(lucy)))&
(?[X]:((creative(X)<~>~wise(X)))) | ~old(paul) | [
"p0",
"p1",
"p3",
"p5",
"p10",
"p11",
"p15",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 1932316179829525476737546
% SZS output start Proof for 1932316179829525476737546
1. ? [X0] : (humble(X0) | ~patient(X0)) <=> (wise(paul) & ~tall(paul)) [input p0]
2. ! [X0] : ((~happy(X0) | generous(X0)) <=> (~rich(X0) | ~generous(X0))) [input p1]
4. ! [X0] : (~quiet(X0) <=> calm(X0)) [input p3]
6. ! [X0] : ((~old(X0) <~> tall(X0)) => (old(X0) & generous(X0))) [input p5]
11. ! [X0] : (patient(X0) <=> (generous(X0) <~> ~tall(X0))) [input p10]
12. ! [X0] : ((~rich(X0) | ~tall(X0)) => calm(X0)) [input p11]
16. ! [X0] : ((kind(X0) | ~rich(X0)) => ~calm(X0)) [input p15]
21. ? [X0] : (quiet(X0) & rich(X0)) [input p20]
24. ~old(paul) [input hypothesis]
25. ! [X0] : (calm(X0) => ~quiet(X0)) [unused predicate definition removal 4]
26. ! [X0] : (~quiet(X0) | ~calm(X0)) [ennf transformation 25]
27. ! [X0] : ((old(X0) & generous(X0)) | (~old(X0) <=> tall(X0))) [ennf transformation 6]
28. ! [X0] : (calm(X0) | (rich(X0) & tall(X0))) [ennf transformation 12]
31. ! [X0] : (~calm(X0) | (~kind(X0) & rich(X0))) [ennf transformation 16]
32. (? [X0] : (humble(X0) | ~patient(X0)) | (~wise(paul) | tall(paul))) & ((wise(paul) & ~tall(paul)) | ! [X0] : (~humble(X0) & patient(X0))) [nnf transformation 1]
33. (? [X0] : (humble(X0) | ~patient(X0)) | ~wise(paul) | tall(paul)) & ((wise(paul) & ~tall(paul)) | ! [X0] : (~humble(X0) & patient(X0))) [flattening 32]
34. (? [X0] : (humble(X0) | ~patient(X0)) | ~wise(paul) | tall(paul)) & ((wise(paul) & ~tall(paul)) | ! [X1] : (~humble(X1) & patient(X1))) [rectify 33]
35. ? [X0] : (humble(X0) | ~patient(X0)) => (humble(sK0) | ~patient(sK0)) [choice axiom]
36. ((humble(sK0) | ~patient(sK0)) | ~wise(paul) | tall(paul)) & ((wise(paul) & ~tall(paul)) | ! [X1] : (~humble(X1) & patient(X1))) [skolemisation 34,35]
37. ! [X0] : (((~happy(X0) | generous(X0)) | (rich(X0) & generous(X0))) & ((~rich(X0) | ~generous(X0)) | (happy(X0) & ~generous(X0)))) [nnf transformation 2]
38. ! [X0] : ((~happy(X0) | generous(X0) | (rich(X0) & generous(X0))) & (~rich(X0) | ~generous(X0) | (happy(X0) & ~generous(X0)))) [flattening 37]
45. ! [X0] : ((old(X0) & generous(X0)) | ((~old(X0) | ~tall(X0)) & (tall(X0) | old(X0)))) [nnf transformation 27]
59. ! [X0] : ((patient(X0) | ((generous(X0) | tall(X0)) & (~tall(X0) | ~generous(X0)))) & (((tall(X0) | ~generous(X0)) & (~tall(X0) | generous(X0))) | ~patient(X0))) [nnf transformation 11]
72. ? [X0] : (quiet(X0) & rich(X0)) => (quiet(sK7) & rich(sK7)) [choice axiom]
73. quiet(sK7) & rich(sK7) [skolemisation 21,72]
78. ~tall(paul) | patient(X1) [cnf transformation 36]
83. ~rich(X0) | ~generous(X0) | ~generous(X0) [cnf transformation 38]
93. ~calm(X0) | ~quiet(X0) [cnf transformation 26]
102. old(X0) | tall(X0) | old(X0) [cnf transformation 45]
122. ~tall(X0) | generous(X0) | ~patient(X0) [cnf transformation 59]
126. calm(X0) | tall(X0) [cnf transformation 28]
127. calm(X0) | rich(X0) [cnf transformation 28]
141. ~calm(X0) | rich(X0) [cnf transformation 31]
151. quiet(sK7) [cnf transformation 73]
156. ~old(paul) [cnf transformation 24]
158. old(X0) | tall(X0) [duplicate literal removal 102]
161. ~rich(X0) | ~generous(X0) [duplicate literal removal 83]
164. 1 <=> tall(paul) [avatar definition]
185. 6 <=> ! [X1] : patient(X1) [avatar definition]
186. patient(X1) <- (6) [avatar component clause 185]
189. 6 | ~1 [avatar split clause 78,164,185]
316. rich(X0) [subsumption resolution 141,127]
355. ~quiet(X0) | tall(X0) [resolution 126,93]
361. tall(paul) [resolution 158,156]
365. 1 [avatar split clause 361,164]
367. ~generous(X0) [resolution 161,316]
379. tall(sK7) [resolution 355,151]
420. generous(sK7) | ~patient(sK7) [resolution 122,379]
433. ~patient(sK7) [subsumption resolution 420,367]
434. $false <- (6) [subsumption resolution 433,186]
435. ~6 [avatar contradiction clause 434]
436. $false [avatar sat refutation 189,365,435]
% SZS output end Proof for 1932316179829525476737546
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not curious and not humble is either strong or curious and vice versa.
Everyone who is both not calm and generous is strong or tall.
If paul is not humble then susan is patient or not brave and vice versa.
If paul is either not rich or patient then fred is both happy and not rich.
If someone is tall then someone is not curious and vice versa.
If someone is wise or not happy then paul is either kind or tall and vice versa.
Everyone who is not generous is tall and vice versa.
If someone is either not brave or strong then someone is either not quiet or tall and vice versa.
If someone is both calm and not wise then alice is funny or calm and vice versa.
If paul is quiet then alice is both not curious and not calm.
If john is brave then john is either not funny or not kind and vice versa.
Everyone who is not quiet is not wise.
Everyone who is both not wise and strong is rich or humble and vice versa.
Everyone who is not generous is both not strong and not patient.
If fred is tall or funny then mary is strong.
Fred is kind or curious.
Lucy is either funny or not humble.
Lucy is either funny or not patient.
Alice is not wise or calm.
Mary is not generous or wise.
Someone is not curious or not patient.
Fred is not kind or strong. | Lucy is not curious. | contradiction | (![X]:((~curious(X)&~humble(X))<=>(strong(X)<~>curious(X))))&
(![X]:((~calm(X)&generous(X))=>(strong(X)|tall(X))))&
((~humble(paul))<=>((patient(susan)|~brave(susan))))&
(((~rich(paul)<~>patient(paul)))=>((happy(fred)&~rich(fred))))&
((?[X]:(tall(X)))<=>(?[X]:(~curious(X))))&
((?[X]:((wise(X)|~happy(X))))<=>((kind(paul)<~>tall(paul))))&
(![X]:(~generous(X)<=>tall(X)))&
((?[X]:((~brave(X)<~>strong(X))))<=>(?[X]:((~quiet(X)<~>tall(X)))))&
((?[X]:((calm(X)&~wise(X))))<=>((funny(alice)|calm(alice))))&
((quiet(paul))=>((~curious(alice)&~calm(alice))))&
((brave(john))<=>((~funny(john)<~>~kind(john))))&
(![X]:(~quiet(X)=>~wise(X)))&
(![X]:((~wise(X)&strong(X))<=>(rich(X)|humble(X))))&
(![X]:(~generous(X)=>(~strong(X)&~patient(X))))&
(((tall(fred)|funny(fred)))=>(strong(mary)))&
((kind(fred)|curious(fred)))&
((funny(lucy)<~>~humble(lucy)))&
((funny(lucy)<~>~patient(lucy)))&
((~wise(alice)|calm(alice)))&
((~generous(mary)|wise(mary)))&
(?[X]:((~curious(X)|~patient(X))))&
((~kind(fred)|strong(fred))) | ~curious(lucy) | [
"p0",
"p4",
"p6",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 6567822707638905332535134
% SZS output start Proof for 6567822707638905332535134
1. ! [X0] : ((~humble(X0) & ~curious(X0)) <=> (strong(X0) <~> curious(X0))) [input p0]
5. ? [X0] : tall(X0) <=> ? [X0] : ~curious(X0) [input p4]
7. ! [X0] : (~generous(X0) <=> tall(X0)) [input p6]
13. ! [X0] : ((strong(X0) & ~wise(X0)) <=> (humble(X0) | rich(X0))) [input p12]
14. ! [X0] : (~generous(X0) => (~patient(X0) & ~strong(X0))) [input p13]
23. ~curious(lucy) [input hypothesis]
24. ? [X0] : tall(X0) <=> ? [X1] : ~curious(X1) [rectify 5]
31. ! [X0] : ((~patient(X0) & ~strong(X0)) | generous(X0)) [ennf transformation 14]
33. ! [X0] : (((~humble(X0) & ~curious(X0)) | ((strong(X0) | ~curious(X0)) & (curious(X0) | ~strong(X0)))) & (((~curious(X0) | ~strong(X0)) & (curious(X0) | strong(X0))) | (humble(X0) | curious(X0)))) [nnf transformation 1]
34. ! [X0] : (((~humble(X0) & ~curious(X0)) | ((strong(X0) | ~curious(X0)) & (curious(X0) | ~strong(X0)))) & (((~curious(X0) | ~strong(X0)) & (curious(X0) | strong(X0))) | humble(X0) | curious(X0))) [flattening 33]
38. (? [X0] : tall(X0) | ! [X1] : curious(X1)) & (? [X1] : ~curious(X1) | ! [X0] : ~tall(X0)) [nnf transformation 24]
39. (? [X0] : tall(X0) | ! [X1] : curious(X1)) & (? [X2] : ~curious(X2) | ! [X3] : ~tall(X3)) [rectify 38]
40. ? [X0] : tall(X0) => tall(sK0) [choice axiom]
41. ? [X2] : ~curious(X2) => ~curious(sK1) [choice axiom]
42. (tall(sK0) | ! [X1] : curious(X1)) & (~curious(sK1) | ! [X3] : ~tall(X3)) [skolemisation 39,41,40]
47. ! [X0] : ((~generous(X0) | ~tall(X0)) & (tall(X0) | generous(X0))) [nnf transformation 7]
59. ! [X0] : (((strong(X0) & ~wise(X0)) | (~humble(X0) & ~rich(X0))) & ((humble(X0) | rich(X0)) | (~strong(X0) | wise(X0)))) [nnf transformation 13]
60. ! [X0] : (((strong(X0) & ~wise(X0)) | (~humble(X0) & ~rich(X0))) & (humble(X0) | rich(X0) | ~strong(X0) | wise(X0))) [flattening 59]
65. curious(X0) | strong(X0) | humble(X0) | curious(X0) [cnf transformation 34]
68. ~curious(X0) | strong(X0) | ~curious(X0) [cnf transformation 34]
80. tall(sK0) | curious(X1) [cnf transformation 42]
88. ~tall(X0) | ~generous(X0) [cnf transformation 47]
113. strong(X0) | ~humble(X0) [cnf transformation 60]
114. ~strong(X0) | generous(X0) [cnf transformation 31]
127. ~curious(lucy) [cnf transformation 23]
128. curious(X0) | strong(X0) | humble(X0) [duplicate literal removal 65]
129. ~curious(X0) | strong(X0) [duplicate literal removal 68]
130. strong(X0) | humble(X0) [subsumption resolution 128,129]
167. 8 <=> ! [X1] : curious(X1) [avatar definition]
168. curious(X1) <- (8) [avatar component clause 167]
170. 9 <=> tall(sK0) [avatar definition]
172. tall(sK0) <- (9) [avatar component clause 170]
173. 8 | 9 [avatar split clause 80,170,167]
296. strong(X0) [subsumption resolution 113,130]
298. generous(X0) [subsumption resolution 114,296]
341. $false <- (8) [resolution 168,127]
342. ~8 [avatar contradiction clause 341]
344. ~generous(sK0) <- (9) [resolution 88,172]
347. $false <- (9) [subsumption resolution 344,298]
348. ~9 [avatar contradiction clause 347]
351. $false [avatar sat refutation 173,342,348]
% SZS output end Proof for 6567822707638905332535134
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is old is not happy or not rich and vice versa. Everyone who is calm is either rich or not curious and vice versa. Everyone who is either kind or not curious is either not rich or not curious. If mary is either happy or humble then someone is not tall. If someone is generous then alice is both not generous and not wise. If john is patient or wise then someone is not quiet or not generous and vice versa. If fred is either not patient or not creative then someone is old. Everyone who is both not patient and not creative is both not wise and brave and vice versa. Everyone who is not rich or not wise is either wise or generous and vice versa. If paul is both rich and not strong then alice is both not strong and quiet. Everyone who is not old or not brave is happy or rich and vice versa. Everyone who is old or brave is not happy. Everyone who is both not patient and not funny is either strong or not quiet. Everyone who is not tall or wise is not creative. If mary is either quiet or not humble then someone is both not humble and strong and vice versa. If susan is not tall then someone is strong or not patient and vice versa. Someone is both humble and old. Someone is wise or not brave. Fred is not strong or wise. Fred is both wise and not humble. Mary is either not funny or not tall. Someone is both not curious and not happy. | Susan is wise. | entailment | (![X]:(old(X)<=>(~happy(X)|~rich(X))))&
(![X]:(calm(X)<=>(rich(X)<~>~curious(X))))&
(![X]:((kind(X)<~>~curious(X))=>(~rich(X)<~>~curious(X))))&
(((happy(mary)<~>humble(mary)))=>(?[X]:(~tall(X))))&
((?[X]:(generous(X)))=>((~generous(alice)&~wise(alice))))&
(((patient(john)|wise(john)))<=>(?[X]:((~quiet(X)|~generous(X)))))&
(((~patient(fred)<~>~creative(fred)))=>(?[X]:(old(X))))&
(![X]:((~patient(X)&~creative(X))<=>(~wise(X)&brave(X))))&
(![X]:((~rich(X)|~wise(X))<=>(wise(X)<~>generous(X))))&
(((rich(paul)&~strong(paul)))=>((~strong(alice)&quiet(alice))))&
(![X]:((~old(X)|~brave(X))<=>(happy(X)|rich(X))))&
(![X]:((old(X)|brave(X))=>~happy(X)))&
(![X]:((~patient(X)&~funny(X))=>(strong(X)<~>~quiet(X))))&
(![X]:((~tall(X)|wise(X))=>~creative(X)))&
(((quiet(mary)<~>~humble(mary)))<=>(?[X]:((~humble(X)&strong(X)))))&
((~tall(susan))<=>(?[X]:((strong(X)|~patient(X)))))&
(?[X]:((humble(X)&old(X))))&
(?[X]:((wise(X)|~brave(X))))&
((~strong(fred)|wise(fred)))&
((wise(fred)&~humble(fred)))&
((~funny(mary)<~>~tall(mary)))&
(?[X]:((~curious(X)&~happy(X)))) | wise(susan) | [
"p4",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 5391442077935156223397517
% SZS output start Proof for 5391442077935156223397517
5. ? [X0] : generous(X0) => (~wise(alice) & ~generous(alice)) [input p4]
9. ! [X0] : ((~wise(X0) | ~rich(X0)) <=> (wise(X0) <~> generous(X0))) [input p8]
23. ~wise(susan) [input hypothesis]
26. (~wise(alice) & ~generous(alice)) | ! [X0] : ~generous(X0) [ennf transformation 5]
50. ! [X0] : (((~wise(X0) | ~rich(X0)) | ((wise(X0) | ~generous(X0)) & (generous(X0) | ~wise(X0)))) & (((~generous(X0) | ~wise(X0)) & (generous(X0) | wise(X0))) | (wise(X0) & rich(X0)))) [nnf transformation 9]
51. ! [X0] : ((~wise(X0) | ~rich(X0) | ((wise(X0) | ~generous(X0)) & (generous(X0) | ~wise(X0)))) & (((~generous(X0) | ~wise(X0)) & (generous(X0) | wise(X0))) | (wise(X0) & rich(X0)))) [flattening 50]
79. ~generous(alice) | ~generous(X0) [cnf transformation 26]
80. ~wise(alice) | ~generous(X0) [cnf transformation 26]
92. generous(X0) | wise(X0) | wise(X0) [cnf transformation 51]
128. ~wise(susan) [cnf transformation 23]
129. wise(X0) | generous(X0) [duplicate literal removal 92]
148. 4 <=> ! [X0] : ~generous(X0) [avatar definition]
149. ~generous(X0) <- (4) [avatar component clause 148]
151. 5 <=> wise(alice) [avatar definition]
153. ~wise(alice) <- (~5) [avatar component clause 151]
154. 4 | ~5 [avatar split clause 80,151,148]
156. 6 <=> generous(alice) [avatar definition]
158. ~generous(alice) <- (~6) [avatar component clause 156]
159. 4 | ~6 [avatar split clause 79,156,148]
292. generous(susan) [resolution 129,128]
293. generous(alice) <- (~5) [resolution 129,153]
294. $false <- (~5, ~6) [subsumption resolution 293,158]
295. 5 | 6 [avatar contradiction clause 294]
296. $false <- (4) [resolution 292,149]
297. ~4 [avatar contradiction clause 296]
298. $false [avatar sat refutation 154,159,295,297]
% SZS output end Proof for 5391442077935156223397517
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny or funny is both creative and not quiet. If someone is both calm and humble then someone is not happy and vice versa. If someone is either not calm or not patient then paul is wise. Everyone who is either not old or creative is both curious and generous. Everyone who is wise or not calm is both not creative and calm and vice versa. If someone is not generous then susan is humble or happy. If someone is not funny or not generous then someone is both brave and patient and vice versa. Everyone who is not happy is calm. Everyone who is either creative or not old is not kind and vice versa. If someone is either patient or not kind then someone is either strong or not strong and vice versa. Everyone who is either quiet or not tall is both calm and not curious and vice versa. If someone is either calm or not calm then fred is not creative or not quiet and vice versa. If paul is not rich then paul is tall or not curious and vice versa. If someone is kind or generous then alice is either brave or not tall. If someone is not old then lucy is not patient or patient. Everyone who is not kind is either creative or not wise and vice versa. Someone is happy or not brave. Alice is either not wise or rich. Someone is not tall or brave. Someone is humble or kind. Mary is both brave and rich. Someone is creative or not creative. Someone is either not kind or not curious. Lucy is rich or not humble. | Lucy is old. | contradiction | (![X]:((~funny(X)|funny(X))=>(creative(X)&~quiet(X))))&
((?[X]:((calm(X)&humble(X))))<=>(?[X]:(~happy(X))))&
((?[X]:((~calm(X)<~>~patient(X))))=>(wise(paul)))&
(![X]:((~old(X)<~>creative(X))=>(curious(X)&generous(X))))&
(![X]:((wise(X)|~calm(X))<=>(~creative(X)&calm(X))))&
((?[X]:(~generous(X)))=>((humble(susan)|happy(susan))))&
((?[X]:((~funny(X)|~generous(X))))<=>(?[X]:((brave(X)&patient(X)))))&
(![X]:(~happy(X)=>calm(X)))&
(![X]:((creative(X)<~>~old(X))<=>~kind(X)))&
((?[X]:((patient(X)<~>~kind(X))))<=>(?[X]:((strong(X)<~>~strong(X)))))&
(![X]:((quiet(X)<~>~tall(X))<=>(calm(X)&~curious(X))))&
((?[X]:((calm(X)<~>~calm(X))))<=>((~creative(fred)|~quiet(fred))))&
((~rich(paul))<=>((tall(paul)|~curious(paul))))&
((?[X]:((kind(X)|generous(X))))=>((brave(alice)<~>~tall(alice))))&
((?[X]:(~old(X)))=>((~patient(lucy)|patient(lucy))))&
(![X]:(~kind(X)<=>(creative(X)<~>~wise(X))))&
(?[X]:((happy(X)|~brave(X))))&
((~wise(alice)<~>rich(alice)))&
(?[X]:((~tall(X)|brave(X))))&
(?[X]:((humble(X)|kind(X))))&
((brave(mary)&rich(mary)))&
(?[X]:((creative(X)|~creative(X))))&
(?[X]:((~kind(X)<~>~curious(X))))&
((rich(lucy)|~humble(lucy))) | old(lucy) | [
"p0",
"p4",
"p8",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8326219265438680459817088
% SZS output start Proof for 8326219265438680459817088
1. ! [X0] : ((funny(X0) | ~funny(X0)) => (~quiet(X0) & creative(X0))) [input p0]
5. ! [X0] : ((~calm(X0) | wise(X0)) <=> (calm(X0) & ~creative(X0))) [input p4]
9. ! [X0] : ((creative(X0) <~> ~old(X0)) <=> ~kind(X0)) [input p8]
16. ! [X0] : (~kind(X0) <=> (creative(X0) <~> ~wise(X0))) [input p15]
25. old(lucy) [input hypothesis]
29. ! [X0] : ((~quiet(X0) & creative(X0)) | (~funny(X0) & funny(X0))) [ennf transformation 1]
45. ! [X0] : (((~calm(X0) | wise(X0)) | (~calm(X0) | creative(X0))) & ((calm(X0) & ~creative(X0)) | (calm(X0) & ~wise(X0)))) [nnf transformation 5]
46. ! [X0] : ((~calm(X0) | wise(X0) | ~calm(X0) | creative(X0)) & ((calm(X0) & ~creative(X0)) | (calm(X0) & ~wise(X0)))) [flattening 45]
52. ! [X0] : ((((old(X0) | ~creative(X0)) & (~old(X0) | creative(X0))) | kind(X0)) & (~kind(X0) | ((creative(X0) | old(X0)) & (~old(X0) | ~creative(X0))))) [nnf transformation 9]
68. ! [X0] : ((~kind(X0) | ((creative(X0) | wise(X0)) & (~wise(X0) | ~creative(X0)))) & (((wise(X0) | ~creative(X0)) & (~wise(X0) | creative(X0))) | kind(X0))) [nnf transformation 16]
81. creative(X0) | funny(X0) [cnf transformation 29]
82. ~funny(X0) | creative(X0) [cnf transformation 29]
94. ~creative(X0) | ~wise(X0) [cnf transformation 46]
106. ~kind(X0) | ~old(X0) | ~creative(X0) [cnf transformation 52]
139. wise(X0) | ~creative(X0) | kind(X0) [cnf transformation 68]
153. old(lucy) [cnf transformation 25]
163. creative(X0) [subsumption resolution 81,82]
199. ~wise(X0) [subsumption resolution 94,163]
240. ~kind(X0) | ~old(X0) [subsumption resolution 106,163]
294. ~creative(X0) | kind(X0) [subsumption resolution 139,199]
295. kind(X0) [subsumption resolution 294,163]
341. ~old(X1) [resolution 240,295]
342. $false [resolution 341,153]
% SZS output end Proof for 8326219265438680459817088
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not creative then someone is both not rich and quiet.
If mary is not strong or rich then alice is either humble or wise and vice versa.
Everyone who is tall or not tall is both calm and not patient.
If john is both rich and brave then someone is either not happy or happy and vice versa.
If someone is either not generous or humble then lucy is not rich and vice versa.
Everyone who is not wise is either not strong or humble and vice versa.
Everyone who is not brave or not curious is not brave.
If someone is funny then susan is both curious and rich and vice versa.
Everyone who is both not patient and not funny is both calm and not humble and vice versa.
If someone is both not strong and strong then someone is both tall and patient.
Everyone who is both not happy and kind is either old or curious.
Everyone who is not wise or not tall is not generous and vice versa.
Everyone who is not patient or calm is old or not kind.
Everyone who is both not old and not generous is either quiet or not strong.
If susan is strong then susan is calm.
If john is kind then paul is either not humble or not kind and vice versa.
Someone is either funny or not generous.
Someone is not rich.
Paul is not old or strong.
Fred is quiet.
Paul is old.
Alice is both not wise and curious.
Someone is not brave.
Someone is either tall or kind. | John is not patient. | entailment | ((?[X]:(~creative(X)))=>(?[X]:((~rich(X)&quiet(X)))))&
(((~strong(mary)|rich(mary)))<=>((humble(alice)<~>wise(alice))))&
(![X]:((tall(X)|~tall(X))=>(calm(X)&~patient(X))))&
(((rich(john)&brave(john)))<=>(?[X]:((~happy(X)<~>happy(X)))))&
((?[X]:((~generous(X)<~>humble(X))))<=>(~rich(lucy)))&
(![X]:(~wise(X)<=>(~strong(X)<~>humble(X))))&
(![X]:((~brave(X)|~curious(X))=>~brave(X)))&
((?[X]:(funny(X)))<=>((curious(susan)&rich(susan))))&
(![X]:((~patient(X)&~funny(X))<=>(calm(X)&~humble(X))))&
((?[X]:((~strong(X)&strong(X))))=>(?[X]:((tall(X)&patient(X)))))&
(![X]:((~happy(X)&kind(X))=>(old(X)<~>curious(X))))&
(![X]:((~wise(X)|~tall(X))<=>~generous(X)))&
(![X]:((~patient(X)|calm(X))=>(old(X)|~kind(X))))&
(![X]:((~old(X)&~generous(X))=>(quiet(X)<~>~strong(X))))&
((strong(susan))=>(calm(susan)))&
((kind(john))<=>((~humble(paul)<~>~kind(paul))))&
(?[X]:((funny(X)<~>~generous(X))))&
(?[X]:(~rich(X)))&
((~old(paul)|strong(paul)))&
(quiet(fred))&
(old(paul))&
((~wise(alice)&curious(alice)))&
(?[X]:(~brave(X)))&
(?[X]:((tall(X)<~>kind(X)))) | ~patient(john) | [
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 667345026250500044352300
% SZS output start Proof for 667345026250500044352300
3. ! [X0] : ((~tall(X0) | tall(X0)) => (~patient(X0) & calm(X0))) [input p2]
25. patient(john) [input hypothesis]
29. ! [X0] : ((~patient(X0) & calm(X0)) | (tall(X0) & ~tall(X0))) [ennf transformation 3]
84. ~patient(X0) | ~tall(X0) [cnf transformation 29]
85. ~patient(X0) | tall(X0) [cnf transformation 29]
136. patient(john) [cnf transformation 25]
163. ~patient(X0) [subsumption resolution 84,85]
273. $false [subsumption resolution 136,163]
% SZS output end Proof for 667345026250500044352300
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong then susan is not curious or old and vice versa.
If fred is both not wise and kind then fred is either quiet or funny.
If susan is both creative and not creative then someone is not old.
If mary is both not brave and not strong then paul is either not old or generous.
If someone is not generous or kind then paul is either not brave or not generous and vice versa.
Everyone who is either not old or quiet is either creative or quiet.
Everyone who is not strong or not brave is not wise and vice versa.
Everyone who is both not happy and wise is old and vice versa.
Everyone who is quiet or strong is both not wise and not strong.
If someone is either generous or not rich then fred is not funny or not creative and vice versa.
Everyone who is not kind is both not curious and not old and vice versa.
Everyone who is both not tall and patient is happy or not calm and vice versa.
Everyone who is not brave is either generous or curious and vice versa.
If lucy is rich or kind then someone is brave or not wise and vice versa.
Everyone who is not wise is both not funny and not generous.
Everyone who is calm is both funny and rich.
Alice is creative or not patient.
Paul is patient.
Someone is not generous.
Alice is both patient and not humble.
Someone is either not tall or not happy.
Someone is not old or not kind.
Someone is either not generous or tall. | Paul is not brave. | contradiction | ((?[X]:(~strong(X)))<=>((~curious(susan)|old(susan))))&
(((~wise(fred)&kind(fred)))=>((quiet(fred)<~>funny(fred))))&
(((creative(susan)&~creative(susan)))=>(?[X]:(~old(X))))&
(((~brave(mary)&~strong(mary)))=>((~old(paul)<~>generous(paul))))&
((?[X]:((~generous(X)|kind(X))))<=>((~brave(paul)<~>~generous(paul))))&
(![X]:((~old(X)<~>quiet(X))=>(creative(X)<~>quiet(X))))&
(![X]:((~strong(X)|~brave(X))<=>~wise(X)))&
(![X]:((~happy(X)&wise(X))<=>old(X)))&
(![X]:((quiet(X)|strong(X))=>(~wise(X)&~strong(X))))&
((?[X]:((generous(X)<~>~rich(X))))<=>((~funny(fred)|~creative(fred))))&
(![X]:(~kind(X)<=>(~curious(X)&~old(X))))&
(![X]:((~tall(X)&patient(X))<=>(happy(X)|~calm(X))))&
(![X]:(~brave(X)<=>(generous(X)<~>curious(X))))&
(((rich(lucy)|kind(lucy)))<=>(?[X]:((brave(X)|~wise(X)))))&
(![X]:(~wise(X)=>(~funny(X)&~generous(X))))&
(![X]:(calm(X)=>(funny(X)&rich(X))))&
((creative(alice)|~patient(alice)))&
(patient(paul))&
(?[X]:(~generous(X)))&
((patient(alice)&~humble(alice)))&
(?[X]:((~tall(X)<~>~happy(X))))&
(?[X]:((~old(X)|~kind(X))))&
(?[X]:((~generous(X)<~>tall(X)))) | ~brave(paul) | [
"p4",
"p6",
"p8",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4783897432639255027651243
% SZS output start Proof for 4783897432639255027651243
5. ? [X0] : (kind(X0) | ~generous(X0)) <=> (~brave(paul) <~> ~generous(paul)) [input p4]
7. ! [X0] : ((~brave(X0) | ~strong(X0)) <=> ~wise(X0)) [input p6]
9. ! [X0] : ((strong(X0) | quiet(X0)) => (~strong(X0) & ~wise(X0))) [input p8]
15. ! [X0] : (~wise(X0) => (~generous(X0) & ~funny(X0))) [input p14]
24. ~brave(paul) [input hypothesis]
33. ! [X0] : ((~strong(X0) & ~wise(X0)) | (~strong(X0) & ~quiet(X0))) [ennf transformation 9]
34. ! [X0] : ((~generous(X0) & ~funny(X0)) | wise(X0)) [ennf transformation 15]
45. (? [X0] : (kind(X0) | ~generous(X0)) | ((~brave(paul) | generous(paul)) & (~generous(paul) | brave(paul)))) & (((generous(paul) | brave(paul)) & (~generous(paul) | ~brave(paul))) | ! [X0] : (~kind(X0) & generous(X0))) [nnf transformation 5]
46. (? [X0] : (kind(X0) | ~generous(X0)) | ((~brave(paul) | generous(paul)) & (~generous(paul) | brave(paul)))) & (((generous(paul) | brave(paul)) & (~generous(paul) | ~brave(paul))) | ! [X1] : (~kind(X1) & generous(X1))) [rectify 45]
47. ? [X0] : (kind(X0) | ~generous(X0)) => (kind(sK2) | ~generous(sK2)) [choice axiom]
48. ((kind(sK2) | ~generous(sK2)) | ((~brave(paul) | generous(paul)) & (~generous(paul) | brave(paul)))) & (((generous(paul) | brave(paul)) & (~generous(paul) | ~brave(paul))) | ! [X1] : (~kind(X1) & generous(X1))) [skolemisation 46,47]
50. ! [X0] : (((~brave(X0) | ~strong(X0)) | wise(X0)) & (~wise(X0) | (brave(X0) & strong(X0)))) [nnf transformation 7]
51. ! [X0] : ((~brave(X0) | ~strong(X0) | wise(X0)) & (~wise(X0) | (brave(X0) & strong(X0)))) [flattening 50]
89. generous(paul) | brave(paul) | generous(X1) [cnf transformation 48]
97. ~wise(X0) | strong(X0) [cnf transformation 51]
106. ~strong(X0) | ~strong(X0) [cnf transformation 33]
130. ~generous(X0) | wise(X0) [cnf transformation 34]
142. ~brave(paul) [cnf transformation 24]
143. ~strong(X0) [duplicate literal removal 106]
195. 12 <=> generous(paul) [avatar definition]
196. generous(paul) <- (12) [avatar component clause 195]
197. ~generous(paul) <- (~12) [avatar component clause 195]
201. 13 <=> brave(paul) [avatar definition]
219. 17 <=> ! [X1] : generous(X1) [avatar definition]
220. generous(X1) <- (17) [avatar component clause 219]
221. 17 | 13 | 12 [avatar split clause 89,195,201,219]
294. ~13 [avatar split clause 142,201]
298. wise(paul) <- (12) [resolution 130,196]
300. strong(paul) <- (12) [resolution 298,97]
303. $false <- (12) [subsumption resolution 300,143]
304. ~12 [avatar contradiction clause 303]
305. $false <- (~12, 17) [subsumption resolution 197,220]
306. 12 | ~17 [avatar contradiction clause 305]
307. $false [avatar sat refutation 221,294,304,306]
% SZS output end Proof for 4783897432639255027651243
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall is both not tall and not creative and vice versa. If someone is not kind or not happy then john is both calm and happy and vice versa. If someone is not strong or curious then someone is either not tall or curious and vice versa. If alice is both not kind and not rich then someone is either not wise or tall. If fred is both not curious and not quiet then someone is strong or not rich. Everyone who is both not brave and creative is both kind and not wise. If alice is not happy then someone is not calm and vice versa. Everyone who is both not happy and brave is both happy and kind. Everyone who is both not calm and strong is generous and vice versa. Everyone who is funny is either not curious or happy and vice versa. Everyone who is not patient is both humble and not funny. If lucy is happy then someone is funny or patient. Everyone who is old or not kind is both old and not curious. Everyone who is not calm or strong is either not wise or old and vice versa. Mary is either strong or not calm. John is tall or old. Paul is either generous or humble. Paul is not quiet. Someone is not patient or not humble. Fred is either not humble or not rich. | Paul is wise. | neutral | (![X]:(tall(X)<=>(~tall(X)&~creative(X))))&
((?[X]:((~kind(X)|~happy(X))))<=>((calm(john)&happy(john))))&
((?[X]:((~strong(X)|curious(X))))<=>(?[X]:((~tall(X)<~>curious(X)))))&
(((~kind(alice)&~rich(alice)))=>(?[X]:((~wise(X)<~>tall(X)))))&
(((~curious(fred)&~quiet(fred)))=>(?[X]:((strong(X)|~rich(X)))))&
(![X]:((~brave(X)&creative(X))=>(kind(X)&~wise(X))))&
((~happy(alice))<=>(?[X]:(~calm(X))))&
(![X]:((~happy(X)&brave(X))=>(happy(X)&kind(X))))&
(![X]:((~calm(X)&strong(X))<=>generous(X)))&
(![X]:(funny(X)<=>(~curious(X)<~>happy(X))))&
(![X]:(~patient(X)=>(humble(X)&~funny(X))))&
((happy(lucy))=>(?[X]:((funny(X)|patient(X)))))&
(![X]:((old(X)|~kind(X))=>(old(X)&~curious(X))))&
(![X]:((~calm(X)|strong(X))<=>(~wise(X)<~>old(X))))&
((strong(mary)<~>~calm(mary)))&
((tall(john)|old(john)))&
((generous(paul)<~>humble(paul)))&
(~quiet(paul))&
(?[X]:((~patient(X)|~humble(X))))&
((~humble(fred)<~>~rich(fred))) | wise(paul) | [] | null | 0 |
Everyone who is not humble or strong is old and vice versa.
Everyone who is calm or rich is quiet or happy and vice versa.
Everyone who is either patient or not humble is either patient or not tall.
Everyone who is funny is both not funny and wise.
Everyone who is quiet or old is not patient.
Everyone who is both not curious and creative is happy or not wise and vice versa.
Everyone who is both not quiet and not old is not generous or happy.
Everyone who is not calm is both brave and calm.
Everyone who is both happy and kind is both old and not brave and vice versa.
Everyone who is not generous or tall is not old.
Everyone who is either not old or wise is not kind.
Everyone who is generous or curious is quiet.
Everyone who is humble or brave is either not generous or humble and vice versa.
Everyone who is both not strong and creative is either not patient or not old and vice versa.
If mary is both funny and not wise then someone is both rich and not funny and vice versa.
Everyone who is both not humble and not generous is either generous or happy and vice versa.
John is not brave.
Someone is not humble.
John is calm or not tall. | John is humble. | contradiction | (![X]:((~humble(X)|strong(X))<=>old(X)))&
(![X]:((calm(X)|rich(X))<=>(quiet(X)|happy(X))))&
(![X]:((patient(X)<~>~humble(X))=>(patient(X)<~>~tall(X))))&
(![X]:(funny(X)=>(~funny(X)&wise(X))))&
(![X]:((quiet(X)|old(X))=>~patient(X)))&
(![X]:((~curious(X)&creative(X))<=>(happy(X)|~wise(X))))&
(![X]:((~quiet(X)&~old(X))=>(~generous(X)|happy(X))))&
(![X]:(~calm(X)=>(brave(X)&calm(X))))&
(![X]:((happy(X)&kind(X))<=>(old(X)&~brave(X))))&
(![X]:((~generous(X)|tall(X))=>~old(X)))&
(![X]:((~old(X)<~>wise(X))=>~kind(X)))&
(![X]:((generous(X)|curious(X))=>quiet(X)))&
(![X]:((humble(X)|brave(X))<=>(~generous(X)<~>humble(X))))&
(![X]:((~strong(X)&creative(X))<=>(~patient(X)<~>~old(X))))&
(((funny(mary)&~wise(mary)))<=>(?[X]:((rich(X)&~funny(X)))))&
(![X]:((~humble(X)&~generous(X))<=>(generous(X)<~>happy(X))))&
(~brave(john))&
(?[X]:(~humble(X)))&
((calm(john)|~tall(john))) | humble(john) | [
"p0",
"p4",
"p5",
"p9",
"p11",
"p12",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 322076399441748749896221
% SZS output start Proof for 322076399441748749896221
1. ! [X0] : ((strong(X0) | ~humble(X0)) <=> old(X0)) [input p0]
5. ! [X0] : ((old(X0) | quiet(X0)) => ~patient(X0)) [input p4]
6. ! [X0] : ((creative(X0) & ~curious(X0)) <=> (~wise(X0) | happy(X0))) [input p5]
10. ! [X0] : ((tall(X0) | ~generous(X0)) => ~old(X0)) [input p9]
12. ! [X0] : ((curious(X0) | generous(X0)) => quiet(X0)) [input p11]
13. ! [X0] : ((brave(X0) | humble(X0)) <=> (~generous(X0) <~> humble(X0))) [input p12]
14. ! [X0] : ((creative(X0) & ~strong(X0)) <=> (~patient(X0) <~> ~old(X0))) [input p13]
16. ! [X0] : ((~generous(X0) & ~humble(X0)) <=> (generous(X0) <~> happy(X0))) [input p15]
20. humble(john) [input hypothesis]
23. ! [X0] : (~patient(X0) | (~old(X0) & ~quiet(X0))) [ennf transformation 5]
27. ! [X0] : (~old(X0) | (~tall(X0) & generous(X0))) [ennf transformation 10]
29. ! [X0] : (quiet(X0) | (~curious(X0) & ~generous(X0))) [ennf transformation 12]
30. ! [X0] : (((strong(X0) | ~humble(X0)) | ~old(X0)) & (old(X0) | (~strong(X0) & humble(X0)))) [nnf transformation 1]
31. ! [X0] : ((strong(X0) | ~humble(X0) | ~old(X0)) & (old(X0) | (~strong(X0) & humble(X0)))) [flattening 30]
35. ! [X0] : (((creative(X0) & ~curious(X0)) | (wise(X0) & ~happy(X0))) & ((~wise(X0) | happy(X0)) | (~creative(X0) | curious(X0)))) [nnf transformation 6]
36. ! [X0] : (((creative(X0) & ~curious(X0)) | (wise(X0) & ~happy(X0))) & (~wise(X0) | happy(X0) | ~creative(X0) | curious(X0))) [flattening 35]
40. ! [X0] : (((brave(X0) | humble(X0)) | ((~generous(X0) | ~humble(X0)) & (humble(X0) | generous(X0)))) & (((~humble(X0) | generous(X0)) & (humble(X0) | ~generous(X0))) | (~brave(X0) & ~humble(X0)))) [nnf transformation 13]
41. ! [X0] : ((brave(X0) | humble(X0) | ((~generous(X0) | ~humble(X0)) & (humble(X0) | generous(X0)))) & (((~humble(X0) | generous(X0)) & (humble(X0) | ~generous(X0))) | (~brave(X0) & ~humble(X0)))) [flattening 40]
42. ! [X0] : (((creative(X0) & ~strong(X0)) | ((~patient(X0) | old(X0)) & (~old(X0) | patient(X0)))) & (((old(X0) | patient(X0)) & (~old(X0) | ~patient(X0))) | (~creative(X0) | strong(X0)))) [nnf transformation 14]
43. ! [X0] : (((creative(X0) & ~strong(X0)) | ((~patient(X0) | old(X0)) & (~old(X0) | patient(X0)))) & (((old(X0) | patient(X0)) & (~old(X0) | ~patient(X0))) | ~creative(X0) | strong(X0))) [flattening 42]
49. ! [X0] : (((~generous(X0) & ~humble(X0)) | ((generous(X0) | ~happy(X0)) & (happy(X0) | ~generous(X0)))) & (((~happy(X0) | ~generous(X0)) & (happy(X0) | generous(X0))) | (generous(X0) | humble(X0)))) [nnf transformation 16]
50. ! [X0] : (((~generous(X0) & ~humble(X0)) | ((generous(X0) | ~happy(X0)) & (happy(X0) | ~generous(X0)))) & (((~happy(X0) | ~generous(X0)) & (happy(X0) | generous(X0))) | generous(X0) | humble(X0))) [flattening 49]
53. old(X0) | humble(X0) [cnf transformation 31]
54. ~strong(X0) | old(X0) [cnf transformation 31]
55. ~old(X0) | ~humble(X0) | strong(X0) [cnf transformation 31]
66. ~patient(X0) | ~quiet(X0) [cnf transformation 23]
67. ~patient(X0) | ~old(X0) [cnf transformation 23]
71. ~happy(X0) | creative(X0) [cnf transformation 36]
80. ~old(X0) | generous(X0) [cnf transformation 27]
84. ~generous(X0) | quiet(X0) [cnf transformation 29]
88. ~humble(X0) | generous(X0) | ~humble(X0) [cnf transformation 41]
93. old(X0) | patient(X0) | ~creative(X0) | strong(X0) [cnf transformation 43]
94. ~strong(X0) | ~old(X0) | patient(X0) [cnf transformation 43]
102. happy(X0) | generous(X0) | generous(X0) | humble(X0) [cnf transformation 50]
106. ~generous(X0) | happy(X0) | ~generous(X0) [cnf transformation 50]
111. humble(john) [cnf transformation 20]
112. happy(X0) | generous(X0) | humble(X0) [duplicate literal removal 102]
113. ~generous(X0) | happy(X0) [duplicate literal removal 106]
114. ~humble(X0) | generous(X0) [duplicate literal removal 88]
122. ~strong(X0) | ~old(X0) [subsumption resolution 94,67]
123. ~strong(X0) [subsumption resolution 122,54]
124. ~creative(X0) | patient(X0) | old(X0) [subsumption resolution 93,123]
137. happy(X0) | generous(X0) [subsumption resolution 112,114]
138. happy(X0) [subsumption resolution 137,113]
139. creative(X0) [resolution 71,138]
140. generous(X0) | humble(X0) [resolution 80,53]
141. generous(X0) [subsumption resolution 140,114]
142. quiet(X0) [resolution 84,141]
158. patient(X1) | old(X1) [resolution 124,139]
164. old(X3) | ~quiet(X3) [resolution 158,66]
166. old(X3) [subsumption resolution 164,142]
170. ~humble(X2) | strong(X2) [resolution 166,55]
173. ~humble(X2) [subsumption resolution 170,123]
180. $false [resolution 173,111]
% SZS output end Proof for 322076399441748749896221
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not old or not happy then fred is calm and vice versa.
Everyone who is wise is not brave.
If susan is not kind then someone is brave.
Everyone who is brave is either kind or not curious and vice versa.
If paul is not creative then someone is both not patient and calm and vice versa.
Everyone who is both quiet and funny is curious or calm and vice versa.
Everyone who is not funny or calm is not quiet and vice versa.
Everyone who is old is humble.
Everyone who is funny is both not happy and tall and vice versa.
Everyone who is brave is not funny.
If lucy is brave then lucy is tall or patient and vice versa.
If mary is not wise then someone is both patient and not kind.
Everyone who is either curious or brave is either funny or tall.
Everyone who is not tall or not humble is calm or brave.
If mary is quiet or not rich then lucy is not rich and vice versa.
Someone is both not creative and not curious.
Lucy is both brave and generous.
Someone is not patient.
Mary is not tall or patient.
Someone is not creative.
Someone is wise or old. | Fred is old. | entailment | ((?[X]:((~old(X)<~>~happy(X))))<=>(calm(fred)))&
(![X]:(wise(X)=>~brave(X)))&
((~kind(susan))=>(?[X]:(brave(X))))&
(![X]:(brave(X)<=>(kind(X)<~>~curious(X))))&
((~creative(paul))<=>(?[X]:((~patient(X)&calm(X)))))&
(![X]:((quiet(X)&funny(X))<=>(curious(X)|calm(X))))&
(![X]:((~funny(X)|calm(X))<=>~quiet(X)))&
(![X]:(old(X)=>humble(X)))&
(![X]:(funny(X)<=>(~happy(X)&tall(X))))&
(![X]:(brave(X)=>~funny(X)))&
((brave(lucy))<=>((tall(lucy)|patient(lucy))))&
((~wise(mary))=>(?[X]:((patient(X)&~kind(X)))))&
(![X]:((curious(X)<~>brave(X))=>(funny(X)<~>tall(X))))&
(![X]:((~tall(X)|~humble(X))=>(calm(X)|brave(X))))&
(((quiet(mary)|~rich(mary)))<=>(~rich(lucy)))&
(?[X]:((~creative(X)&~curious(X))))&
((brave(lucy)&generous(lucy)))&
(?[X]:(~patient(X)))&
((~tall(mary)|patient(mary)))&
(?[X]:(~creative(X)))&
(?[X]:((wise(X)|old(X)))) | old(fred) | [
"p0",
"p5",
"p6",
"p8",
"p9",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 5605400372166620552814367
% SZS output start Proof for 5605400372166620552814367
1. ? [X0] : (~old(X0) <~> ~happy(X0)) <=> calm(fred) [input p0]
6. ! [X0] : ((funny(X0) & quiet(X0)) <=> (calm(X0) | curious(X0))) [input p5]
7. ! [X0] : ((calm(X0) | ~funny(X0)) <=> ~quiet(X0)) [input p6]
9. ! [X0] : (funny(X0) <=> (tall(X0) & ~happy(X0))) [input p8]
10. ! [X0] : (brave(X0) => ~funny(X0)) [input p9]
13. ! [X0] : ((curious(X0) <~> brave(X0)) => (funny(X0) <~> tall(X0))) [input p12]
14. ! [X0] : ((~humble(X0) | ~tall(X0)) => (brave(X0) | calm(X0))) [input p13]
22. ~old(fred) [input hypothesis]
25. ! [X0] : (~tall(X0) => (brave(X0) | calm(X0))) [pure predicate removal 14]
28. ! [X0] : (~funny(X0) | ~brave(X0)) [ennf transformation 10]
30. ! [X0] : ((funny(X0) <~> tall(X0)) | (curious(X0) <=> brave(X0))) [ennf transformation 13]
31. ! [X0] : ((brave(X0) | calm(X0)) | tall(X0)) [ennf transformation 25]
32. ! [X0] : (brave(X0) | calm(X0) | tall(X0)) [flattening 31]
33. (? [X0] : ((happy(X0) | old(X0)) & (~happy(X0) | ~old(X0))) | ~calm(fred)) & (calm(fred) | ! [X0] : ((~old(X0) | happy(X0)) & (~happy(X0) | old(X0)))) [nnf transformation 1]
34. (? [X0] : ((happy(X0) | old(X0)) & (~happy(X0) | ~old(X0))) | ~calm(fred)) & (calm(fred) | ! [X1] : ((~old(X1) | happy(X1)) & (~happy(X1) | old(X1)))) [rectify 33]
35. ? [X0] : ((happy(X0) | old(X0)) & (~happy(X0) | ~old(X0))) => ((happy(sK0) | old(sK0)) & (~happy(sK0) | ~old(sK0))) [choice axiom]
36. (((happy(sK0) | old(sK0)) & (~happy(sK0) | ~old(sK0))) | ~calm(fred)) & (calm(fred) | ! [X1] : ((~old(X1) | happy(X1)) & (~happy(X1) | old(X1)))) [skolemisation 34,35]
44. ! [X0] : (((funny(X0) & quiet(X0)) | (~calm(X0) & ~curious(X0))) & ((calm(X0) | curious(X0)) | (~funny(X0) | ~quiet(X0)))) [nnf transformation 6]
45. ! [X0] : (((funny(X0) & quiet(X0)) | (~calm(X0) & ~curious(X0))) & (calm(X0) | curious(X0) | ~funny(X0) | ~quiet(X0))) [flattening 44]
46. ! [X0] : (((calm(X0) | ~funny(X0)) | quiet(X0)) & (~quiet(X0) | (~calm(X0) & funny(X0)))) [nnf transformation 7]
47. ! [X0] : ((calm(X0) | ~funny(X0) | quiet(X0)) & (~quiet(X0) | (~calm(X0) & funny(X0)))) [flattening 46]
48. ! [X0] : ((funny(X0) | (~tall(X0) | happy(X0))) & ((tall(X0) & ~happy(X0)) | ~funny(X0))) [nnf transformation 9]
49. ! [X0] : ((funny(X0) | ~tall(X0) | happy(X0)) & ((tall(X0) & ~happy(X0)) | ~funny(X0))) [flattening 48]
54. ! [X0] : (((~tall(X0) | ~funny(X0)) & (tall(X0) | funny(X0))) | ((curious(X0) | ~brave(X0)) & (brave(X0) | ~curious(X0)))) [nnf transformation 30]
65. calm(fred) | ~happy(X1) | old(X1) [cnf transformation 36]
78. ~funny(X0) | curious(X0) | calm(X0) | ~quiet(X0) [cnf transformation 45]
80. ~calm(X0) | quiet(X0) [cnf transformation 45]
81. ~curious(X0) | funny(X0) [cnf transformation 45]
84. ~quiet(X0) | ~calm(X0) [cnf transformation 47]
85. calm(X0) | ~funny(X0) | quiet(X0) [cnf transformation 47]
87. ~funny(X0) | tall(X0) [cnf transformation 49]
88. ~tall(X0) | funny(X0) | happy(X0) [cnf transformation 49]
89. ~funny(X0) | ~brave(X0) [cnf transformation 28]
96. tall(X0) | funny(X0) | curious(X0) | ~brave(X0) [cnf transformation 54]
97. ~tall(X0) | ~funny(X0) | brave(X0) | ~curious(X0) [cnf transformation 54]
99. brave(X0) | calm(X0) | tall(X0) [cnf transformation 32]
110. ~old(fred) [cnf transformation 22]
112. 1 <=> calm(fred) [avatar definition]
113. calm(fred) <- (1) [avatar component clause 112]
130. 5 <=> ! [X1] : (~happy(X1) | old(X1)) [avatar definition]
131. ~happy(X1) | old(X1) <- (5) [avatar component clause 130]
132. 5 | 1 [avatar split clause 65,112,130]
160. ~funny(X0) | quiet(X0) [subsumption resolution 85,80]
161. ~calm(X0) [subsumption resolution 84,80]
191. ~tall(X0) | ~funny(X0) | ~curious(X0) [subsumption resolution 97,89]
192. ~funny(X0) | ~curious(X0) [subsumption resolution 191,87]
193. ~curious(X0) [subsumption resolution 192,81]
194. tall(X0) | funny(X0) | ~brave(X0) [subsumption resolution 96,193]
195. ~brave(X0) | tall(X0) [subsumption resolution 194,87]
196. brave(X0) | tall(X0) [subsumption resolution 99,161]
197. tall(X0) [subsumption resolution 196,195]
235. funny(X0) | happy(X0) [resolution 88,197]
237. happy(X0) | curious(X0) | calm(X0) | ~quiet(X0) [resolution 235,78]
238. happy(X1) | quiet(X1) [resolution 235,160]
242. happy(X0) | calm(X0) | ~quiet(X0) [subsumption resolution 237,193]
243. happy(X0) | ~quiet(X0) [subsumption resolution 242,161]
244. happy(X1) [subsumption resolution 238,243]
250. old(X0) <- (5) [resolution 244,131]
252. $false <- (5) [resolution 250,110]
254. ~5 [avatar contradiction clause 252]
255. $false <- (1) [subsumption resolution 113,161]
256. ~1 [avatar contradiction clause 255]
257. $false [avatar sat refutation 132,254,256]
% SZS output end Proof for 5605400372166620552814367
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If susan is both not old and wise then someone is either not generous or not humble.
Everyone who is tall or creative is either not tall or kind.
Everyone who is both curious and not old is either curious or not wise and vice versa.
If someone is wise then mary is not quiet and vice versa.
Everyone who is not creative is calm or not old.
If someone is both not old and not strong then someone is rich or not happy.
If someone is quiet then susan is either wise or generous and vice versa.
If someone is not curious then someone is old and vice versa.
If susan is not kind then someone is not happy or not strong and vice versa.
Everyone who is generous or rich is not patient and vice versa.
Everyone who is both patient and not tall is tall or not funny and vice versa.
If paul is either generous or not strong then someone is either humble or not creative.
Everyone who is both curious and tall is both not strong and not generous and vice versa.
Everyone who is both not funny and strong is humble and vice versa.
Everyone who is either kind or calm is curious or not generous.
If someone is both not strong and patient then alice is patient.
Someone is patient.
Someone is either rich or not patient.
Susan is both not strong and brave.
Someone is either patient or wise.
Someone is both not creative and generous.
John is either not generous or rich.
Paul is both funny and kind.
Someone is both strong and not funny. | Paul is tall. | contradiction | (((~old(susan)&wise(susan)))=>(?[X]:((~generous(X)<~>~humble(X)))))&
(![X]:((tall(X)|creative(X))=>(~tall(X)<~>kind(X))))&
(![X]:((curious(X)&~old(X))<=>(curious(X)<~>~wise(X))))&
((?[X]:(wise(X)))<=>(~quiet(mary)))&
(![X]:(~creative(X)=>(calm(X)|~old(X))))&
((?[X]:((~old(X)&~strong(X))))=>(?[X]:((rich(X)|~happy(X)))))&
((?[X]:(quiet(X)))<=>((wise(susan)<~>generous(susan))))&
((?[X]:(~curious(X)))<=>(?[X]:(old(X))))&
((~kind(susan))<=>(?[X]:((~happy(X)|~strong(X)))))&
(![X]:((generous(X)|rich(X))<=>~patient(X)))&
(![X]:((patient(X)&~tall(X))<=>(tall(X)|~funny(X))))&
(((generous(paul)<~>~strong(paul)))=>(?[X]:((humble(X)<~>~creative(X)))))&
(![X]:((curious(X)&tall(X))<=>(~strong(X)&~generous(X))))&
(![X]:((~funny(X)&strong(X))<=>humble(X)))&
(![X]:((kind(X)<~>calm(X))=>(curious(X)|~generous(X))))&
((?[X]:((~strong(X)&patient(X))))=>(patient(alice)))&
(?[X]:(patient(X)))&
(?[X]:((rich(X)<~>~patient(X))))&
((~strong(susan)&brave(susan)))&
(?[X]:((patient(X)<~>wise(X))))&
(?[X]:((~creative(X)&generous(X))))&
((~generous(john)<~>rich(john)))&
((funny(paul)&kind(paul)))&
(?[X]:((strong(X)&~funny(X)))) | tall(paul) | [
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 6227914986726667369240492
% SZS output start Proof for 6227914986726667369240492
11. ! [X0] : ((~tall(X0) & patient(X0)) <=> (~funny(X0) | tall(X0))) [input p10]
25. tall(paul) [input hypothesis]
67. ! [X0] : (((~tall(X0) & patient(X0)) | (funny(X0) & ~tall(X0))) & ((~funny(X0) | tall(X0)) | (tall(X0) | ~patient(X0)))) [nnf transformation 11]
68. ! [X0] : (((~tall(X0) & patient(X0)) | (funny(X0) & ~tall(X0))) & (~funny(X0) | tall(X0) | tall(X0) | ~patient(X0))) [flattening 67]
121. ~tall(X0) | ~tall(X0) [cnf transformation 68]
151. tall(paul) [cnf transformation 25]
153. ~tall(X0) [duplicate literal removal 121]
305. $false [subsumption resolution 151,153]
% SZS output end Proof for 6227914986726667369240492
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is not tall then fred is both creative and not strong and vice versa. If mary is funny then someone is either not creative or not curious and vice versa. Everyone who is either kind or old is not humble. If someone is both not quiet and not funny then someone is both brave and calm and vice versa. If someone is not strong then someone is not creative or strong and vice versa. If someone is strong then alice is either not quiet or not old and vice versa. If someone is either not kind or not happy then alice is both not tall and wise. Everyone who is wise or not wise is rich. If alice is either not patient or not strong then paul is both not patient and not quiet. Everyone who is not wise is either not creative or not curious and vice versa. If alice is either generous or not creative then paul is either not old or funny. If someone is funny then fred is both patient and not funny and vice versa. If mary is not rich or not quiet then someone is either not wise or not strong and vice versa. Everyone who is both not creative and not rich is either not old or kind and vice versa. Everyone who is either not strong or quiet is not quiet or patient. Everyone who is both not kind and humble is either wise or patient and vice versa. Someone is not old. Someone is either creative or quiet. Fred is both calm and happy. Someone is not patient or old. Mary is not tall. Someone is not creative. Lucy is either not tall or not happy. Someone is not tall. | Lucy is rich. | entailment | ((~tall(paul))<=>((creative(fred)&~strong(fred))))&
((funny(mary))<=>(?[X]:((~creative(X)<~>~curious(X)))))&
(![X]:((kind(X)<~>old(X))=>~humble(X)))&
((?[X]:((~quiet(X)&~funny(X))))<=>(?[X]:((brave(X)&calm(X)))))&
((?[X]:(~strong(X)))<=>(?[X]:((~creative(X)|strong(X)))))&
((?[X]:(strong(X)))<=>((~quiet(alice)<~>~old(alice))))&
((?[X]:((~kind(X)<~>~happy(X))))=>((~tall(alice)&wise(alice))))&
(![X]:((wise(X)|~wise(X))=>rich(X)))&
(((~patient(alice)<~>~strong(alice)))=>((~patient(paul)&~quiet(paul))))&
(![X]:(~wise(X)<=>(~creative(X)<~>~curious(X))))&
(((generous(alice)<~>~creative(alice)))=>((~old(paul)<~>funny(paul))))&
((?[X]:(funny(X)))<=>((patient(fred)&~funny(fred))))&
(((~rich(mary)|~quiet(mary)))<=>(?[X]:((~wise(X)<~>~strong(X)))))&
(![X]:((~creative(X)&~rich(X))<=>(~old(X)<~>kind(X))))&
(![X]:((~strong(X)<~>quiet(X))=>(~quiet(X)|patient(X))))&
(![X]:((~kind(X)&humble(X))<=>(wise(X)<~>patient(X))))&
(?[X]:(~old(X)))&
(?[X]:((creative(X)<~>quiet(X))))&
((calm(fred)&happy(fred)))&
(?[X]:((~patient(X)|old(X))))&
(~tall(mary))&
(?[X]:(~creative(X)))&
((~tall(lucy)<~>~happy(lucy)))&
(?[X]:(~tall(X))) | rich(lucy) | [
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 2338109805459328151297079
% SZS output start Proof for 2338109805459328151297079
8. ! [X0] : ((~wise(X0) | wise(X0)) => rich(X0)) [input p7]
25. ~rich(lucy) [input hypothesis]
30. ! [X0] : (rich(X0) | (wise(X0) & ~wise(X0))) [ennf transformation 8]
111. rich(X0) | ~wise(X0) [cnf transformation 30]
112. rich(X0) | wise(X0) [cnf transformation 30]
159. ~rich(lucy) [cnf transformation 25]
282. rich(X0) [subsumption resolution 111,112]
396. $false [subsumption resolution 159,282]
% SZS output end Proof for 2338109805459328151297079
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich or curious is calm.
Everyone who is not happy or tall is either not strong or rich and vice versa.
If paul is both wise and not creative then alice is either not tall or not brave and vice versa.
Everyone who is not old is generous or not tall and vice versa.
Everyone who is both not wise and not happy is brave and vice versa.
Everyone who is not humble or not happy is not generous or rich and vice versa.
If fred is not rich or not happy then someone is either quiet or patient and vice versa.
Everyone who is either kind or old is tall or not curious.
If someone is both not curious and not calm then someone is either wise or funny.
Everyone who is not brave is not wise.
Everyone who is both quiet and not brave is either not brave or not tall.
Everyone who is funny or not brave is tall and vice versa.
Everyone who is either old or humble is not brave and vice versa.
If someone is not patient or humble then someone is calm or strong and vice versa.
If someone is either tall or patient then fred is not patient and vice versa.
If lucy is either not funny or not quiet then alice is either quiet or tall.
Someone is not wise or brave.
Someone is either not calm or not strong.
Alice is not quiet or not rich.
Lucy is either not quiet or not kind.
Someone is not brave.
Paul is both quiet and kind.
Someone is not curious.
Susan is either not quiet or funny. | Lucy is not curious. | neutral | (![X]:((rich(X)<~>curious(X))=>calm(X)))&
(![X]:((~happy(X)|tall(X))<=>(~strong(X)<~>rich(X))))&
(((wise(paul)&~creative(paul)))<=>((~tall(alice)<~>~brave(alice))))&
(![X]:(~old(X)<=>(generous(X)|~tall(X))))&
(![X]:((~wise(X)&~happy(X))<=>brave(X)))&
(![X]:((~humble(X)|~happy(X))<=>(~generous(X)|rich(X))))&
(((~rich(fred)|~happy(fred)))<=>(?[X]:((quiet(X)<~>patient(X)))))&
(![X]:((kind(X)<~>old(X))=>(tall(X)|~curious(X))))&
((?[X]:((~curious(X)&~calm(X))))=>(?[X]:((wise(X)<~>funny(X)))))&
(![X]:(~brave(X)=>~wise(X)))&
(![X]:((quiet(X)&~brave(X))=>(~brave(X)<~>~tall(X))))&
(![X]:((funny(X)|~brave(X))<=>tall(X)))&
(![X]:((old(X)<~>humble(X))<=>~brave(X)))&
((?[X]:((~patient(X)|humble(X))))<=>(?[X]:((calm(X)|strong(X)))))&
((?[X]:((tall(X)<~>patient(X))))<=>(~patient(fred)))&
(((~funny(lucy)<~>~quiet(lucy)))=>((quiet(alice)<~>tall(alice))))&
(?[X]:((~wise(X)|brave(X))))&
(?[X]:((~calm(X)<~>~strong(X))))&
((~quiet(alice)|~rich(alice)))&
((~quiet(lucy)<~>~kind(lucy)))&
(?[X]:(~brave(X)))&
((quiet(paul)&kind(paul)))&
(?[X]:(~curious(X)))&
((~quiet(susan)<~>funny(susan))) | ~curious(lucy) | [] | null | 0 |
If susan is not tall then someone is either happy or not brave.
If susan is either old or not funny then someone is old or generous.
Everyone who is either quiet or not calm is happy.
Everyone who is strong or not wise is either quiet or not strong and vice versa.
If paul is either not tall or not strong then mary is both not wise and not funny.
Everyone who is not humble or not creative is quiet and vice versa.
Everyone who is both curious and not happy is either not quiet or brave.
If someone is either brave or strong then alice is both not old and old and vice versa.
Everyone who is not old is creative and vice versa.
Everyone who is not patient or not calm is not humble or curious and vice versa.
Everyone who is not strong is both wise and kind.
If someone is either not funny or creative then paul is not curious.
Everyone who is not quiet or curious is not old or not funny and vice versa.
Everyone who is brave or calm is both calm and not funny and vice versa.
Everyone who is both not curious and not calm is both calm and not old.
If someone is funny or calm then someone is both quiet and not happy.
Susan is happy.
Mary is not funny.
Lucy is both kind and patient.
Someone is quiet or not strong.
Someone is rich.
Fred is tall. | Fred is strong. | contradiction | ((~tall(susan))=>(?[X]:((happy(X)<~>~brave(X)))))&
(((old(susan)<~>~funny(susan)))=>(?[X]:((old(X)|generous(X)))))&
(![X]:((quiet(X)<~>~calm(X))=>happy(X)))&
(![X]:((strong(X)|~wise(X))<=>(quiet(X)<~>~strong(X))))&
(((~tall(paul)<~>~strong(paul)))=>((~wise(mary)&~funny(mary))))&
(![X]:((~humble(X)|~creative(X))<=>quiet(X)))&
(![X]:((curious(X)&~happy(X))=>(~quiet(X)<~>brave(X))))&
((?[X]:((brave(X)<~>strong(X))))<=>((~old(alice)&old(alice))))&
(![X]:(~old(X)<=>creative(X)))&
(![X]:((~patient(X)|~calm(X))<=>(~humble(X)|curious(X))))&
(![X]:(~strong(X)=>(wise(X)&kind(X))))&
((?[X]:((~funny(X)<~>creative(X))))=>(~curious(paul)))&
(![X]:((~quiet(X)|curious(X))<=>(~old(X)|~funny(X))))&
(![X]:((brave(X)|calm(X))<=>(calm(X)&~funny(X))))&
(![X]:((~curious(X)&~calm(X))=>(calm(X)&~old(X))))&
((?[X]:((funny(X)|calm(X))))=>(?[X]:((quiet(X)&~happy(X)))))&
(happy(susan))&
(~funny(mary))&
((kind(lucy)&patient(lucy)))&
(?[X]:((quiet(X)|~strong(X))))&
(?[X]:(rich(X)))&
(tall(fred)) | strong(fred) | [
"p2",
"p3",
"p6",
"p7",
"p10",
"p13",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7177709730260071324443030
% SZS output start Proof for 7177709730260071324443030
3. ! [X0] : ((quiet(X0) <~> ~calm(X0)) => happy(X0)) [input p2]
4. ! [X0] : ((~wise(X0) | strong(X0)) <=> (quiet(X0) <~> ~strong(X0))) [input p3]
7. ! [X0] : ((~happy(X0) & curious(X0)) => (~quiet(X0) <~> brave(X0))) [input p6]
8. ? [X0] : (brave(X0) <~> strong(X0)) <=> (old(alice) & ~old(alice)) [input p7]
11. ! [X0] : (~strong(X0) => (kind(X0) & wise(X0))) [input p10]
14. ! [X0] : ((calm(X0) | brave(X0)) <=> (~funny(X0) & calm(X0))) [input p13]
15. ! [X0] : ((~calm(X0) & ~curious(X0)) => (~old(X0) & calm(X0))) [input p14]
16. ? [X0] : (calm(X0) | funny(X0)) => ? [X0] : (~happy(X0) & quiet(X0)) [input p15]
23. strong(fred) [input hypothesis]
24. ? [X0] : (calm(X0) | funny(X0)) => ? [X1] : (~happy(X1) & quiet(X1)) [rectify 16]
26. ! [X0] : (~strong(X0) => wise(X0)) [pure predicate removal 11]
30. ! [X0] : (happy(X0) | (quiet(X0) <=> ~calm(X0))) [ennf transformation 3]
32. ! [X0] : ((~quiet(X0) <~> brave(X0)) | (happy(X0) | ~curious(X0))) [ennf transformation 7]
33. ! [X0] : ((~quiet(X0) <~> brave(X0)) | happy(X0) | ~curious(X0)) [flattening 32]
34. ! [X0] : (wise(X0) | strong(X0)) [ennf transformation 26]
36. ! [X0] : ((~old(X0) & calm(X0)) | (calm(X0) | curious(X0))) [ennf transformation 15]
37. ! [X0] : ((~old(X0) & calm(X0)) | calm(X0) | curious(X0)) [flattening 36]
38. ? [X1] : (~happy(X1) & quiet(X1)) | ! [X0] : (~calm(X0) & ~funny(X0)) [ennf transformation 24]
42. ! [X0] : (happy(X0) | ((quiet(X0) | calm(X0)) & (~calm(X0) | ~quiet(X0)))) [nnf transformation 30]
43. ! [X0] : (((~wise(X0) | strong(X0)) | ((quiet(X0) | strong(X0)) & (~strong(X0) | ~quiet(X0)))) & (((strong(X0) | ~quiet(X0)) & (~strong(X0) | quiet(X0))) | (wise(X0) & ~strong(X0)))) [nnf transformation 4]
44. ! [X0] : ((~wise(X0) | strong(X0) | ((quiet(X0) | strong(X0)) & (~strong(X0) | ~quiet(X0)))) & (((strong(X0) | ~quiet(X0)) & (~strong(X0) | quiet(X0))) | (wise(X0) & ~strong(X0)))) [flattening 43]
48. ! [X0] : (((~brave(X0) | quiet(X0)) & (brave(X0) | ~quiet(X0))) | happy(X0) | ~curious(X0)) [nnf transformation 33]
49. (? [X0] : ((~strong(X0) | ~brave(X0)) & (strong(X0) | brave(X0))) | (~old(alice) | old(alice))) & ((old(alice) & ~old(alice)) | ! [X0] : ((brave(X0) | ~strong(X0)) & (strong(X0) | ~brave(X0)))) [nnf transformation 8]
50. (? [X0] : ((~strong(X0) | ~brave(X0)) & (strong(X0) | brave(X0))) | ~old(alice) | old(alice)) & ((old(alice) & ~old(alice)) | ! [X0] : ((brave(X0) | ~strong(X0)) & (strong(X0) | ~brave(X0)))) [flattening 49]
51. (? [X0] : ((~strong(X0) | ~brave(X0)) & (strong(X0) | brave(X0))) | ~old(alice) | old(alice)) & ((old(alice) & ~old(alice)) | ! [X1] : ((brave(X1) | ~strong(X1)) & (strong(X1) | ~brave(X1)))) [rectify 50]
52. ? [X0] : ((~strong(X0) | ~brave(X0)) & (strong(X0) | brave(X0))) => ((~strong(sK1) | ~brave(sK1)) & (strong(sK1) | brave(sK1))) [choice axiom]
53. (((~strong(sK1) | ~brave(sK1)) & (strong(sK1) | brave(sK1))) | ~old(alice) | old(alice)) & ((old(alice) & ~old(alice)) | ! [X1] : ((brave(X1) | ~strong(X1)) & (strong(X1) | ~brave(X1)))) [skolemisation 51,52]
60. ! [X0] : (((calm(X0) | brave(X0)) | (funny(X0) | ~calm(X0))) & ((~funny(X0) & calm(X0)) | (~calm(X0) & ~brave(X0)))) [nnf transformation 14]
61. ! [X0] : ((calm(X0) | brave(X0) | funny(X0) | ~calm(X0)) & ((~funny(X0) & calm(X0)) | (~calm(X0) & ~brave(X0)))) [flattening 60]
62. ? [X0] : (~happy(X0) & quiet(X0)) | ! [X1] : (~calm(X1) & ~funny(X1)) [rectify 38]
63. ? [X0] : (~happy(X0) & quiet(X0)) => (~happy(sK2) & quiet(sK2)) [choice axiom]
64. (~happy(sK2) & quiet(sK2)) | ! [X1] : (~calm(X1) & ~funny(X1)) [skolemisation 62,63]
69. ~calm(X0) | happy(X0) | ~quiet(X0) [cnf transformation 42]
71. ~strong(X0) | quiet(X0) | ~strong(X0) [cnf transformation 44]
76. ~wise(X0) | strong(X0) | quiet(X0) | strong(X0) [cnf transformation 44]
84. ~curious(X0) | ~quiet(X0) | happy(X0) | brave(X0) [cnf transformation 48]
87. ~old(alice) | brave(X1) | ~strong(X1) [cnf transformation 53]
89. old(alice) | brave(X1) | ~strong(X1) [cnf transformation 53]
98. wise(X0) | strong(X0) [cnf transformation 34]
105. ~brave(X0) | calm(X0) [cnf transformation 61]
110. calm(X0) | calm(X0) | curious(X0) [cnf transformation 37]
115. ~happy(sK2) | ~calm(X1) [cnf transformation 64]
121. strong(fred) [cnf transformation 23]
122. curious(X0) | calm(X0) [duplicate literal removal 110]
123. ~strong(X0) | quiet(X0) [duplicate literal removal 71]
124. ~wise(X0) | strong(X0) | quiet(X0) [duplicate literal removal 76]
160. 8 <=> ! [X1] : (brave(X1) | ~strong(X1)) [avatar definition]
161. ~strong(X1) | brave(X1) <- (8) [avatar component clause 160]
163. 9 <=> old(alice) [avatar definition]
166. 8 | 9 [avatar split clause 89,163,160]
171. 8 | ~9 [avatar split clause 87,163,160]
186. 14 <=> ! [X1] : ~calm(X1) [avatar definition]
187. ~calm(X1) <- (14) [avatar component clause 186]
189. 15 <=> happy(sK2) [avatar definition]
191. ~happy(sK2) <- (~15) [avatar component clause 189]
192. 14 | ~15 [avatar split clause 115,189,186]
213. brave(fred) <- (8) [resolution 161,121]
215. calm(fred) <- (8) [resolution 213,105]
310. $false <- (8, 14) [resolution 187,215]
311. ~8 | ~14 [avatar contradiction clause 310]
356. strong(X0) | quiet(X0) | strong(X0) [resolution 124,98]
358. strong(X0) | quiet(X0) [duplicate literal removal 356]
359. quiet(X0) [subsumption resolution 358,123]
360. ~quiet(X0) | happy(X0) | brave(X0) | calm(X0) [resolution 84,122]
363. happy(X0) | brave(X0) | calm(X0) [subsumption resolution 360,359]
364. calm(X0) | happy(X0) [subsumption resolution 363,105]
398. happy(X0) | happy(X0) | ~quiet(X0) [resolution 364,69]
401. happy(X0) | ~quiet(X0) [duplicate literal removal 398]
402. happy(X0) [subsumption resolution 401,359]
415. $false <- (~15) [resolution 402,191]
416. 15 [avatar contradiction clause 415]
418. $false [avatar sat refutation 166,171,192,311,416]
% SZS output end Proof for 7177709730260071324443030
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not rich and happy is either not generous or not calm. If someone is not happy then alice is both wise and not old. Everyone who is happy is generous. If someone is not wise or not kind then john is calm and vice versa. Everyone who is not tall is both not creative and wise and vice versa. If paul is old or not generous then someone is old and vice versa. Everyone who is both not rich and not curious is not brave and vice versa. Everyone who is either old or not creative is generous or creative and vice versa. Everyone who is both humble and funny is quiet and vice versa. If someone is either not funny or not humble then mary is not brave or brave. If someone is either not brave or old then lucy is not patient or not creative. If john is brave or not calm then someone is either generous or happy. If someone is either not rich or creative then alice is both not strong and tall and vice versa. If someone is both creative and not tall then someone is either not strong or strong. If someone is tall or not tall then lucy is quiet. Everyone who is not calm is both not quiet and not curious. Someone is either generous or not strong. Lucy is not creative or not quiet. Someone is not happy. Someone is not brave. Paul is calm or not calm. Someone is not wise or not generous. Fred is not tall. Someone is patient or happy. | Lucy is rich. | entailment | (![X]:((~rich(X)&happy(X))=>(~generous(X)<~>~calm(X))))&
((?[X]:(~happy(X)))=>((wise(alice)&~old(alice))))&
(![X]:(happy(X)=>generous(X)))&
((?[X]:((~wise(X)|~kind(X))))<=>(calm(john)))&
(![X]:(~tall(X)<=>(~creative(X)&wise(X))))&
(((old(paul)|~generous(paul)))<=>(?[X]:(old(X))))&
(![X]:((~rich(X)&~curious(X))<=>~brave(X)))&
(![X]:((old(X)<~>~creative(X))<=>(generous(X)|creative(X))))&
(![X]:((humble(X)&funny(X))<=>quiet(X)))&
((?[X]:((~funny(X)<~>~humble(X))))=>((~brave(mary)|brave(mary))))&
((?[X]:((~brave(X)<~>old(X))))=>((~patient(lucy)|~creative(lucy))))&
(((brave(john)|~calm(john)))=>(?[X]:((generous(X)<~>happy(X)))))&
((?[X]:((~rich(X)<~>creative(X))))<=>((~strong(alice)&tall(alice))))&
((?[X]:((creative(X)&~tall(X))))=>(?[X]:((~strong(X)<~>strong(X)))))&
((?[X]:((tall(X)|~tall(X))))=>(quiet(lucy)))&
(![X]:(~calm(X)=>(~quiet(X)&~curious(X))))&
(?[X]:((generous(X)<~>~strong(X))))&
((~creative(lucy)|~quiet(lucy)))&
(?[X]:(~happy(X)))&
(?[X]:(~brave(X)))&
((calm(paul)|~calm(paul)))&
(?[X]:((~wise(X)|~generous(X))))&
(~tall(fred))&
(?[X]:((patient(X)|happy(X)))) | rich(lucy) | [
"p1",
"p4",
"p7",
"p12",
"p14",
"p17",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 1127519220295370212682428
% SZS output start Proof for 1127519220295370212682428
2. ? [X0] : ~happy(X0) => (~old(alice) & wise(alice)) [input p1]
5. ! [X0] : (~tall(X0) <=> (wise(X0) & ~creative(X0))) [input p4]
8. ! [X0] : ((old(X0) <~> ~creative(X0)) <=> (creative(X0) | generous(X0))) [input p7]
13. ? [X0] : (~rich(X0) <~> creative(X0)) <=> (tall(alice) & ~strong(alice)) [input p12]
15. ? [X0] : (~tall(X0) | tall(X0)) => quiet(lucy) [input p14]
18. ~quiet(lucy) | ~creative(lucy) [input p17]
19. ? [X0] : ~happy(X0) [input p18]
25. ~rich(lucy) [input hypothesis]
29. (~old(alice) & wise(alice)) | ! [X0] : happy(X0) [ennf transformation 2]
37. quiet(lucy) | ! [X0] : (tall(X0) & ~tall(X0)) [ennf transformation 15]
44. ! [X0] : ((~tall(X0) | (~wise(X0) | creative(X0))) & ((wise(X0) & ~creative(X0)) | tall(X0))) [nnf transformation 5]
45. ! [X0] : ((~tall(X0) | ~wise(X0) | creative(X0)) & ((wise(X0) & ~creative(X0)) | tall(X0))) [flattening 44]
53. ! [X0] : ((((creative(X0) | ~old(X0)) & (~creative(X0) | old(X0))) | (~creative(X0) & ~generous(X0))) & ((creative(X0) | generous(X0)) | ((old(X0) | creative(X0)) & (~creative(X0) | ~old(X0))))) [nnf transformation 8]
54. ! [X0] : ((((creative(X0) | ~old(X0)) & (~creative(X0) | old(X0))) | (~creative(X0) & ~generous(X0))) & (creative(X0) | generous(X0) | ((old(X0) | creative(X0)) & (~creative(X0) | ~old(X0))))) [flattening 53]
62. (? [X0] : ((~creative(X0) | rich(X0)) & (creative(X0) | ~rich(X0))) | (~tall(alice) | strong(alice))) & ((tall(alice) & ~strong(alice)) | ! [X0] : ((~rich(X0) | ~creative(X0)) & (creative(X0) | rich(X0)))) [nnf transformation 13]
63. (? [X0] : ((~creative(X0) | rich(X0)) & (creative(X0) | ~rich(X0))) | ~tall(alice) | strong(alice)) & ((tall(alice) & ~strong(alice)) | ! [X0] : ((~rich(X0) | ~creative(X0)) & (creative(X0) | rich(X0)))) [flattening 62]
64. (? [X0] : ((~creative(X0) | rich(X0)) & (creative(X0) | ~rich(X0))) | ~tall(alice) | strong(alice)) & ((tall(alice) & ~strong(alice)) | ! [X1] : ((~rich(X1) | ~creative(X1)) & (creative(X1) | rich(X1)))) [rectify 63]
65. ? [X0] : ((~creative(X0) | rich(X0)) & (creative(X0) | ~rich(X0))) => ((~creative(sK3) | rich(sK3)) & (creative(sK3) | ~rich(sK3))) [choice axiom]
66. (((~creative(sK3) | rich(sK3)) & (creative(sK3) | ~rich(sK3))) | ~tall(alice) | strong(alice)) & ((tall(alice) & ~strong(alice)) | ! [X1] : ((~rich(X1) | ~creative(X1)) & (creative(X1) | rich(X1)))) [skolemisation 64,65]
74. ? [X0] : ~happy(X0) => ~happy(sK6) [choice axiom]
75. ~happy(sK6) [skolemisation 19,74]
84. wise(alice) | happy(X0) [cnf transformation 29]
85. ~old(alice) | happy(X0) [cnf transformation 29]
92. ~tall(X0) | ~wise(X0) | creative(X0) [cnf transformation 45]
102. ~creative(X0) | old(X0) | ~creative(X0) [cnf transformation 54]
118. tall(alice) | creative(X1) | rich(X1) [cnf transformation 66]
124. quiet(lucy) | ~tall(X0) [cnf transformation 37]
125. quiet(lucy) | tall(X0) [cnf transformation 37]
130. ~quiet(lucy) | ~creative(lucy) [cnf transformation 18]
131. ~happy(sK6) [cnf transformation 75]
137. ~rich(lucy) [cnf transformation 25]
139. ~creative(X0) | old(X0) [duplicate literal removal 102]
141. 1 <=> ! [X0] : happy(X0) [avatar definition]
142. happy(X0) <- (1) [avatar component clause 141]
144. 2 <=> old(alice) [avatar definition]
147. 1 | ~2 [avatar split clause 85,144,141]
149. 3 <=> wise(alice) [avatar definition]
151. wise(alice) <- (3) [avatar component clause 149]
152. 1 | 3 [avatar split clause 84,149,141]
201. 15 <=> creative(lucy) [avatar definition]
203. ~creative(lucy) <- (~15) [avatar component clause 201]
234. 21 <=> tall(alice) [avatar definition]
235. tall(alice) <- (21) [avatar component clause 234]
252. 25 <=> ! [X1] : (creative(X1) | rich(X1)) [avatar definition]
253. creative(X1) | rich(X1) <- (25) [avatar component clause 252]
254. 25 | 21 [avatar split clause 118,234,252]
258. 26 <=> ! [X0] : tall(X0) [avatar definition]
259. tall(X0) <- (26) [avatar component clause 258]
261. 27 <=> quiet(lucy) [avatar definition]
264. 26 | 27 [avatar split clause 125,261,258]
266. 28 <=> ! [X0] : ~tall(X0) [avatar definition]
267. ~tall(X0) <- (28) [avatar component clause 266]
268. 28 | 27 [avatar split clause 124,261,266]
279. ~15 | ~27 [avatar split clause 130,261,201]
310. ~wise(alice) | creative(alice) <- (21) [resolution 92,235]
312. creative(alice) <- (3, 21) [subsumption resolution 310,151]
313. old(alice) <- (3, 21) [resolution 312,139]
317. 2 | ~3 | ~21 [avatar split clause 313,234,149,144]
318. $false <- (1) [resolution 142,131]
320. ~1 [avatar contradiction clause 318]
323. rich(lucy) <- (~15, 25) [resolution 253,203]
328. $false <- (~15, 25) [subsumption resolution 323,137]
329. 15 | ~25 [avatar contradiction clause 328]
333. $false <- (26, 28) [subsumption resolution 259,267]
334. ~26 | ~28 [avatar contradiction clause 333]
335. $false [avatar sat refutation 147,152,254,264,268,279,317,320,329,334]
% SZS output end Proof for 1127519220295370212682428
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not patient and creative is either not patient or calm.
Everyone who is not tall or humble is either not patient or not generous and vice versa.
Everyone who is both not quiet and not strong is either wise or not patient and vice versa.
Everyone who is not curious or not wise is both humble and old and vice versa.
Everyone who is brave or not humble is either quiet or happy.
Everyone who is either not brave or tall is both kind and brave.
If someone is either tall or kind then someone is not patient and vice versa.
Everyone who is both patient and happy is happy or wise and vice versa.
If alice is tall or not rich then someone is either not brave or not wise and vice versa.
If paul is both brave and tall then someone is both happy and not curious and vice versa.
If susan is not old then fred is not wise or not old.
Everyone who is either humble or rich is not quiet and vice versa.
If someone is both not rich and brave then someone is old or rich.
Everyone who is not calm or patient is strong or not happy.
Everyone who is either wise or kind is either patient or brave.
If someone is not funny then paul is not tall and vice versa.
Lucy is either funny or not quiet.
Someone is not tall or not curious.
Someone is strong.
Paul is not kind.
Someone is curious or creative.
Susan is strong.
Alice is both strong and not quiet.
Someone is both strong and patient. | Alice is not humble. | contradiction | (![X]:((~patient(X)&creative(X))=>(~patient(X)<~>calm(X))))&
(![X]:((~tall(X)|humble(X))<=>(~patient(X)<~>~generous(X))))&
(![X]:((~quiet(X)&~strong(X))<=>(wise(X)<~>~patient(X))))&
(![X]:((~curious(X)|~wise(X))<=>(humble(X)&old(X))))&
(![X]:((brave(X)|~humble(X))=>(quiet(X)<~>happy(X))))&
(![X]:((~brave(X)<~>tall(X))=>(kind(X)&brave(X))))&
((?[X]:((tall(X)<~>kind(X))))<=>(?[X]:(~patient(X))))&
(![X]:((patient(X)&happy(X))<=>(happy(X)|wise(X))))&
(((tall(alice)|~rich(alice)))<=>(?[X]:((~brave(X)<~>~wise(X)))))&
(((brave(paul)&tall(paul)))<=>(?[X]:((happy(X)&~curious(X)))))&
((~old(susan))=>((~wise(fred)|~old(fred))))&
(![X]:((humble(X)<~>rich(X))<=>~quiet(X)))&
((?[X]:((~rich(X)&brave(X))))=>(?[X]:((old(X)|rich(X)))))&
(![X]:((~calm(X)|patient(X))=>(strong(X)|~happy(X))))&
(![X]:((wise(X)<~>kind(X))=>(patient(X)<~>brave(X))))&
((?[X]:(~funny(X)))<=>(~tall(paul)))&
((funny(lucy)<~>~quiet(lucy)))&
(?[X]:((~tall(X)|~curious(X))))&
(?[X]:(strong(X)))&
(~kind(paul))&
(?[X]:((curious(X)|creative(X))))&
(strong(susan))&
((strong(alice)&~quiet(alice)))&
(?[X]:((strong(X)&patient(X)))) | ~humble(alice) | [
"p2",
"p3",
"p7",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 801317506030789470734535
% SZS output start Proof for 801317506030789470734535
3. ! [X0] : ((~strong(X0) & ~quiet(X0)) <=> (wise(X0) <~> ~patient(X0))) [input p2]
4. ! [X0] : ((~wise(X0) | ~curious(X0)) <=> (old(X0) & humble(X0))) [input p3]
8. ! [X0] : ((happy(X0) & patient(X0)) <=> (wise(X0) | happy(X0))) [input p7]
14. ! [X0] : ((patient(X0) | ~calm(X0)) => (~happy(X0) | strong(X0))) [input p13]
25. ~humble(alice) [input hypothesis]
35. ! [X0] : ((~happy(X0) | strong(X0)) | (~patient(X0) & calm(X0))) [ennf transformation 14]
36. ! [X0] : (~happy(X0) | strong(X0) | (~patient(X0) & calm(X0))) [flattening 35]
41. ! [X0] : (((~strong(X0) & ~quiet(X0)) | ((wise(X0) | patient(X0)) & (~patient(X0) | ~wise(X0)))) & (((patient(X0) | ~wise(X0)) & (~patient(X0) | wise(X0))) | (strong(X0) | quiet(X0)))) [nnf transformation 3]
42. ! [X0] : (((~strong(X0) & ~quiet(X0)) | ((wise(X0) | patient(X0)) & (~patient(X0) | ~wise(X0)))) & (((patient(X0) | ~wise(X0)) & (~patient(X0) | wise(X0))) | strong(X0) | quiet(X0))) [flattening 41]
43. ! [X0] : (((~wise(X0) | ~curious(X0)) | (~old(X0) | ~humble(X0))) & ((old(X0) & humble(X0)) | (wise(X0) & curious(X0)))) [nnf transformation 4]
44. ! [X0] : ((~wise(X0) | ~curious(X0) | ~old(X0) | ~humble(X0)) & ((old(X0) & humble(X0)) | (wise(X0) & curious(X0)))) [flattening 43]
52. ! [X0] : (((happy(X0) & patient(X0)) | (~wise(X0) & ~happy(X0))) & ((wise(X0) | happy(X0)) | (~happy(X0) | ~patient(X0)))) [nnf transformation 8]
53. ! [X0] : (((happy(X0) & patient(X0)) | (~wise(X0) & ~happy(X0))) & (wise(X0) | happy(X0) | ~happy(X0) | ~patient(X0))) [flattening 52]
94. ~wise(X0) | ~patient(X0) | ~strong(X0) [cnf transformation 42]
97. wise(X0) | humble(X0) [cnf transformation 44]
114. ~happy(X0) | patient(X0) [cnf transformation 53]
115. ~wise(X0) | patient(X0) [cnf transformation 53]
117. ~wise(X0) | happy(X0) [cnf transformation 53]
135. ~happy(X0) | strong(X0) | ~patient(X0) [cnf transformation 36]
153. ~humble(alice) [cnf transformation 25]
257. ~happy(X0) | strong(X0) [subsumption resolution 135,114]
301. humble(X0) | patient(X0) [resolution 115,97]
303. happy(X0) | humble(X0) [resolution 117,97]
319. humble(X0) | strong(X0) [resolution 303,257]
347. ~patient(X1) | ~strong(X1) | humble(X1) [resolution 94,97]
350. ~strong(X1) | humble(X1) [subsumption resolution 347,301]
351. humble(X1) [subsumption resolution 350,319]
357. $false [resolution 351,153]
% SZS output end Proof for 801317506030789470734535
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet then fred is either creative or generous. Everyone who is not kind or not old is wise and vice versa. Everyone who is kind is funny or not rich. If paul is not funny or calm then paul is not generous or humble and vice versa. Everyone who is both happy and not curious is not happy or curious. Everyone who is not curious is both not generous and not humble. If someone is either patient or funny then someone is either brave or wise and vice versa. Everyone who is not creative is not patient. If someone is not old then someone is both not brave and not tall. Everyone who is both calm and not old is either brave or not tall. Everyone who is both not generous and not rich is either not creative or rich and vice versa. Everyone who is both not quiet and kind is creative or not generous. If someone is old or not tall then alice is both patient and calm and vice versa. Everyone who is either tall or calm is not tall or not rich and vice versa. Everyone who is humble or not funny is either not tall or not kind and vice versa. If someone is both creative and generous then someone is either calm or rich and vice versa. Fred is either not wise or wise. Someone is both curious and rich. Someone is not funny. Paul is brave. Paul is either kind or not funny. Fred is either happy or creative. John is either funny or tall. Alice is funny. | Fred is not wise. | neutral | ((?[X]:(quiet(X)))=>((creative(fred)<~>generous(fred))))&
(![X]:((~kind(X)|~old(X))<=>wise(X)))&
(![X]:(kind(X)=>(funny(X)|~rich(X))))&
(((~funny(paul)|calm(paul)))<=>((~generous(paul)|humble(paul))))&
(![X]:((happy(X)&~curious(X))=>(~happy(X)|curious(X))))&
(![X]:(~curious(X)=>(~generous(X)&~humble(X))))&
((?[X]:((patient(X)<~>funny(X))))<=>(?[X]:((brave(X)<~>wise(X)))))&
(![X]:(~creative(X)=>~patient(X)))&
((?[X]:(~old(X)))=>(?[X]:((~brave(X)&~tall(X)))))&
(![X]:((calm(X)&~old(X))=>(brave(X)<~>~tall(X))))&
(![X]:((~generous(X)&~rich(X))<=>(~creative(X)<~>rich(X))))&
(![X]:((~quiet(X)&kind(X))=>(creative(X)|~generous(X))))&
((?[X]:((old(X)|~tall(X))))<=>((patient(alice)&calm(alice))))&
(![X]:((tall(X)<~>calm(X))<=>(~tall(X)|~rich(X))))&
(![X]:((humble(X)|~funny(X))<=>(~tall(X)<~>~kind(X))))&
((?[X]:((creative(X)&generous(X))))<=>(?[X]:((calm(X)<~>rich(X)))))&
((~wise(fred)<~>wise(fred)))&
(?[X]:((curious(X)&rich(X))))&
(?[X]:(~funny(X)))&
(brave(paul))&
((kind(paul)<~>~funny(paul)))&
((happy(fred)<~>creative(fred)))&
((funny(john)<~>tall(john)))&
(funny(alice)) | ~wise(fred) | [] | null | 0 |
If susan is not quiet or funny then someone is either not generous or not calm and vice versa.
Everyone who is wise or generous is both not rich and not tall.
If someone is both quiet and not generous then mary is either not quiet or brave and vice versa.
Everyone who is both calm and patient is either wise or not tall and vice versa.
Everyone who is not brave is not calm and vice versa.
If fred is either not strong or not generous then someone is not tall or old.
Everyone who is either rich or happy is both not quiet and not brave and vice versa.
Everyone who is both not wise and not old is not humble or kind.
Everyone who is either rich or not creative is either creative or tall.
If john is both not old and not quiet then alice is both not funny and calm and vice versa.
Everyone who is not wise is curious or not quiet.
Everyone who is both curious and not calm is wise.
If someone is either not rich or kind then someone is both not rich and wise and vice versa.
If someone is both calm and brave then someone is both quiet and not patient.
Everyone who is humble or quiet is quiet or not creative.
If someone is both calm and not generous then susan is not generous and vice versa.
Susan is not old.
Someone is both not tall and not strong.
Mary is kind or humble.
Someone is not brave or not patient.
Someone is either not quiet or not patient.
Someone is calm.
Someone is brave.
Someone is either not calm or not strong. | Susan is funny. | neutral | (((~quiet(susan)|funny(susan)))<=>(?[X]:((~generous(X)<~>~calm(X)))))&
(![X]:((wise(X)|generous(X))=>(~rich(X)&~tall(X))))&
((?[X]:((quiet(X)&~generous(X))))<=>((~quiet(mary)<~>brave(mary))))&
(![X]:((calm(X)&patient(X))<=>(wise(X)<~>~tall(X))))&
(![X]:(~brave(X)<=>~calm(X)))&
(((~strong(fred)<~>~generous(fred)))=>(?[X]:((~tall(X)|old(X)))))&
(![X]:((rich(X)<~>happy(X))<=>(~quiet(X)&~brave(X))))&
(![X]:((~wise(X)&~old(X))=>(~humble(X)|kind(X))))&
(![X]:((rich(X)<~>~creative(X))=>(creative(X)<~>tall(X))))&
(((~old(john)&~quiet(john)))<=>((~funny(alice)&calm(alice))))&
(![X]:(~wise(X)=>(curious(X)|~quiet(X))))&
(![X]:((curious(X)&~calm(X))=>wise(X)))&
((?[X]:((~rich(X)<~>kind(X))))<=>(?[X]:((~rich(X)&wise(X)))))&
((?[X]:((calm(X)&brave(X))))=>(?[X]:((quiet(X)&~patient(X)))))&
(![X]:((humble(X)|quiet(X))=>(quiet(X)|~creative(X))))&
((?[X]:((calm(X)&~generous(X))))<=>(~generous(susan)))&
(~old(susan))&
(?[X]:((~tall(X)&~strong(X))))&
((kind(mary)|humble(mary)))&
(?[X]:((~brave(X)|~patient(X))))&
(?[X]:((~quiet(X)<~>~patient(X))))&
(?[X]:(calm(X)))&
(?[X]:(brave(X)))&
(?[X]:((~calm(X)<~>~strong(X)))) | funny(susan) | [] | null | 0 |
Everyone who is both brave and not patient is either quiet or not curious.
Everyone who is both not rich and funny is not happy or brave and vice versa.
Everyone who is either brave or not happy is humble or generous and vice versa.
Everyone who is both old and funny is happy.
If paul is strong then someone is both not calm and not quiet and vice versa.
If fred is either kind or calm then mary is both not brave and not happy and vice versa.
Everyone who is either not old or curious is generous or not kind.
If paul is not patient then lucy is both not happy and patient.
Everyone who is either generous or not creative is creative and vice versa.
If fred is both funny and not tall then mary is wise.
If alice is both old and generous then someone is quiet.
Everyone who is both not curious and creative is brave and vice versa.
If paul is both humble and not curious then someone is tall or happy and vice versa.
Everyone who is both funny and not brave is both not creative and old and vice versa.
Everyone who is not brave or not humble is either not old or not quiet and vice versa.
If someone is not quiet then alice is calm.
Someone is not calm or not strong.
Someone is not humble.
John is calm.
Fred is either generous or not quiet. | Mary is not quiet. | neutral | (![X]:((brave(X)&~patient(X))=>(quiet(X)<~>~curious(X))))&
(![X]:((~rich(X)&funny(X))<=>(~happy(X)|brave(X))))&
(![X]:((brave(X)<~>~happy(X))<=>(humble(X)|generous(X))))&
(![X]:((old(X)&funny(X))=>happy(X)))&
((strong(paul))<=>(?[X]:((~calm(X)&~quiet(X)))))&
(((kind(fred)<~>calm(fred)))<=>((~brave(mary)&~happy(mary))))&
(![X]:((~old(X)<~>curious(X))=>(generous(X)|~kind(X))))&
((~patient(paul))=>((~happy(lucy)&patient(lucy))))&
(![X]:((generous(X)<~>~creative(X))<=>creative(X)))&
(((funny(fred)&~tall(fred)))=>(wise(mary)))&
(((old(alice)&generous(alice)))=>(?[X]:(quiet(X))))&
(![X]:((~curious(X)&creative(X))<=>brave(X)))&
(((humble(paul)&~curious(paul)))<=>(?[X]:((tall(X)|happy(X)))))&
(![X]:((funny(X)&~brave(X))<=>(~creative(X)&old(X))))&
(![X]:((~brave(X)|~humble(X))<=>(~old(X)<~>~quiet(X))))&
((?[X]:(~quiet(X)))=>(calm(alice)))&
(?[X]:((~calm(X)|~strong(X))))&
(?[X]:(~humble(X)))&
(calm(john))&
((generous(fred)<~>~quiet(fred))) | ~quiet(mary) | [] | null | 0 |
If someone is not tall then lucy is both happy and not kind.
Everyone who is patient is not kind or wise and vice versa.
Everyone who is not brave is curious or kind.
Everyone who is both humble and not humble is both not quiet and not creative.
Everyone who is either not calm or brave is quiet and vice versa.
Everyone who is funny or not brave is both not happy and not calm.
Everyone who is not old or not tall is not creative.
Everyone who is not wise is both not tall and not brave.
Everyone who is rich is either old or wise and vice versa.
Everyone who is both not funny and patient is not rich.
Everyone who is not wise or not creative is not tall or calm.
If someone is not happy then someone is either not creative or calm and vice versa.
If mary is either strong or calm then mary is strong.
Everyone who is not creative or wise is not quiet or not creative and vice versa.
If someone is quiet then paul is happy or not quiet.
Everyone who is either not creative or not quiet is either calm or old.
Someone is not kind.
Someone is not creative.
Susan is either not wise or not funny.
John is wise.
Someone is patient.
Alice is not old or funny.
Someone is both old and funny.
Someone is not rich or not generous. | Lucy is not funny. | entailment | ((?[X]:(~tall(X)))=>((happy(lucy)&~kind(lucy))))&
(![X]:(patient(X)<=>(~kind(X)|wise(X))))&
(![X]:(~brave(X)=>(curious(X)|kind(X))))&
(![X]:((humble(X)&~humble(X))=>(~quiet(X)&~creative(X))))&
(![X]:((~calm(X)<~>brave(X))<=>quiet(X)))&
(![X]:((funny(X)|~brave(X))=>(~happy(X)&~calm(X))))&
(![X]:((~old(X)|~tall(X))=>~creative(X)))&
(![X]:(~wise(X)=>(~tall(X)&~brave(X))))&
(![X]:(rich(X)<=>(old(X)<~>wise(X))))&
(![X]:((~funny(X)&patient(X))=>~rich(X)))&
(![X]:((~wise(X)|~creative(X))=>(~tall(X)|calm(X))))&
((?[X]:(~happy(X)))<=>(?[X]:((~creative(X)<~>calm(X)))))&
(((strong(mary)<~>calm(mary)))=>(strong(mary)))&
(![X]:((~creative(X)|wise(X))<=>(~quiet(X)|~creative(X))))&
((?[X]:(quiet(X)))=>((happy(paul)|~quiet(paul))))&
(![X]:((~creative(X)<~>~quiet(X))=>(calm(X)<~>old(X))))&
(?[X]:(~kind(X)))&
(?[X]:(~creative(X)))&
((~wise(susan)<~>~funny(susan)))&
(wise(john))&
(?[X]:(patient(X)))&
((~old(alice)|funny(alice)))&
(?[X]:((old(X)&funny(X))))&
(?[X]:((~rich(X)|~generous(X)))) | ~funny(lucy) | [
"p0",
"p4",
"p5",
"p7",
"p10",
"p11",
"p13",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 4312202552145636809662659
% SZS output start Proof for 4312202552145636809662659
1. ? [X0] : ~tall(X0) => (~kind(lucy) & happy(lucy)) [input p0]
5. ! [X0] : ((~calm(X0) <~> brave(X0)) <=> quiet(X0)) [input p4]
6. ! [X0] : ((~brave(X0) | funny(X0)) => (~calm(X0) & ~happy(X0))) [input p5]
8. ! [X0] : (~wise(X0) => (~brave(X0) & ~tall(X0))) [input p7]
11. ! [X0] : ((~creative(X0) | ~wise(X0)) => (calm(X0) | ~tall(X0))) [input p10]
12. ? [X0] : ~happy(X0) <=> ? [X0] : (~creative(X0) <~> calm(X0)) [input p11]
14. ! [X0] : ((wise(X0) | ~creative(X0)) <=> (~creative(X0) | ~quiet(X0))) [input p13]
23. ? [X0] : (funny(X0) & old(X0)) [input p22]
25. funny(lucy) [input hypothesis]
26. ? [X0] : ~happy(X0) <=> ? [X1] : (~creative(X1) <~> calm(X1)) [rectify 12]
30. (~kind(lucy) & happy(lucy)) | ! [X0] : tall(X0) [ennf transformation 1]
33. ! [X0] : ((~calm(X0) & ~happy(X0)) | (brave(X0) & ~funny(X0))) [ennf transformation 6]
35. ! [X0] : ((~brave(X0) & ~tall(X0)) | wise(X0)) [ennf transformation 8]
39. ! [X0] : ((calm(X0) | ~tall(X0)) | (creative(X0) & wise(X0))) [ennf transformation 11]
40. ! [X0] : (calm(X0) | ~tall(X0) | (creative(X0) & wise(X0))) [flattening 39]
47. ! [X0] : ((((~brave(X0) | calm(X0)) & (brave(X0) | ~calm(X0))) | ~quiet(X0)) & (quiet(X0) | ((~calm(X0) | ~brave(X0)) & (brave(X0) | calm(X0))))) [nnf transformation 5]
49. (? [X0] : ~happy(X0) | ! [X1] : ((~creative(X1) | ~calm(X1)) & (calm(X1) | creative(X1)))) & (? [X1] : ((~calm(X1) | creative(X1)) & (calm(X1) | ~creative(X1))) | ! [X0] : happy(X0)) [nnf transformation 26]
50. (? [X0] : ~happy(X0) | ! [X1] : ((~creative(X1) | ~calm(X1)) & (calm(X1) | creative(X1)))) & (? [X2] : ((~calm(X2) | creative(X2)) & (calm(X2) | ~creative(X2))) | ! [X3] : happy(X3)) [rectify 49]
51. ? [X0] : ~happy(X0) => ~happy(sK0) [choice axiom]
52. ? [X2] : ((~calm(X2) | creative(X2)) & (calm(X2) | ~creative(X2))) => ((~calm(sK1) | creative(sK1)) & (calm(sK1) | ~creative(sK1))) [choice axiom]
53. (~happy(sK0) | ! [X1] : ((~creative(X1) | ~calm(X1)) & (calm(X1) | creative(X1)))) & (((~calm(sK1) | creative(sK1)) & (calm(sK1) | ~creative(sK1))) | ! [X3] : happy(X3)) [skolemisation 50,52,51]
55. ! [X0] : (((wise(X0) | ~creative(X0)) | (creative(X0) & quiet(X0))) & ((~creative(X0) | ~quiet(X0)) | (~wise(X0) & creative(X0)))) [nnf transformation 14]
56. ! [X0] : ((wise(X0) | ~creative(X0) | (creative(X0) & quiet(X0))) & (~creative(X0) | ~quiet(X0) | (~wise(X0) & creative(X0)))) [flattening 55]
65. ? [X0] : (funny(X0) & old(X0)) => (funny(sK5) & old(sK5)) [choice axiom]
66. funny(sK5) & old(sK5) [skolemisation 23,65]
67. happy(lucy) | tall(X0) [cnf transformation 30]
74. calm(X0) | brave(X0) | quiet(X0) [cnf transformation 47]
75. ~calm(X0) | quiet(X0) | ~brave(X0) [cnf transformation 47]
76. ~calm(X0) | brave(X0) | ~quiet(X0) [cnf transformation 47]
78. ~funny(X0) | ~happy(X0) [cnf transformation 33]
81. ~calm(X0) | brave(X0) [cnf transformation 33]
84. ~tall(X0) | wise(X0) [cnf transformation 35]
90. ~tall(X0) | calm(X0) | creative(X0) [cnf transformation 40]
91. calm(sK1) | ~creative(sK1) | happy(X3) [cnf transformation 53]
92. ~calm(sK1) | creative(sK1) | happy(X3) [cnf transformation 53]
98. ~creative(X0) | ~quiet(X0) | ~wise(X0) [cnf transformation 56]
114. funny(sK5) [cnf transformation 66]
115. funny(lucy) [cnf transformation 25]
118. 1 <=> ! [X0] : tall(X0) [avatar definition]
119. tall(X0) <- (1) [avatar component clause 118]
126. 3 <=> happy(lucy) [avatar definition]
129. 1 | 3 [avatar split clause 67,126,118]
139. 6 <=> ! [X1] : (calm(X1) | creative(X1)) [avatar definition]
140. calm(X1) | creative(X1) <- (6) [avatar component clause 139]
143. 7 <=> ! [X3] : happy(X3) [avatar definition]
144. happy(X3) <- (7) [avatar component clause 143]
146. 8 <=> creative(sK1) [avatar definition]
148. creative(sK1) <- (8) [avatar component clause 146]
150. 9 <=> calm(sK1) [avatar definition]
151. calm(sK1) <- (9) [avatar component clause 150]
152. ~calm(sK1) <- (~9) [avatar component clause 150]
153. 7 | 8 | ~9 [avatar split clause 92,150,146,143]
154. 7 | ~8 | 9 [avatar split clause 91,150,146,143]
199. ~happy(sK5) [resolution 78,114]
200. ~happy(lucy) [resolution 78,115]
203. ~3 [avatar split clause 200,126]
206. wise(X0) <- (1) [resolution 84,119]
213. brave(X0) | quiet(X0) | brave(X0) [resolution 74,81]
218. quiet(X0) | brave(X0) [duplicate literal removal 213]
256. calm(X0) | creative(X0) <- (1) [resolution 90,119]
257. 6 | ~1 [avatar split clause 256,118,139]
263. creative(sK1) <- (6, ~9) [resolution 140,152]
269. 8 | ~6 | 9 [avatar split clause 263,150,139,146]
273. $false <- (7) [resolution 144,199]
274. ~7 [avatar contradiction clause 273]
279. brave(sK1) | ~quiet(sK1) <- (9) [resolution 151,76]
280. quiet(sK1) | ~brave(sK1) <- (9) [resolution 151,75]
282. brave(sK1) <- (9) [subsumption resolution 279,218]
283. quiet(sK1) <- (9) [subsumption resolution 280,282]
284. ~quiet(sK1) | ~wise(sK1) <- (8) [resolution 98,148]
285. ~wise(sK1) <- (8, 9) [subsumption resolution 284,283]
286. $false <- (1, 8, 9) [subsumption resolution 285,206]
287. ~1 | ~8 | ~9 [avatar contradiction clause 286]
288. $false [avatar sat refutation 129,153,154,203,257,269,274,287]
% SZS output end Proof for 4312202552145636809662659
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not tall and not old then john is both quiet and wise.
If mary is not rich or not quiet then susan is either not humble or happy.
If someone is both curious and not strong then someone is kind.
Everyone who is not generous or patient is both wise and not wise and vice versa.
If someone is quiet or rich then someone is either curious or not rich and vice versa.
If someone is either not patient or not tall then someone is either not rich or creative and vice versa.
Everyone who is either not brave or strong is not quiet or patient and vice versa.
Everyone who is not tall is either not patient or calm.
If someone is both old and humble then susan is not wise or not old and vice versa.
If someone is both old and not old then someone is either not humble or kind and vice versa.
If someone is both not brave and not funny then susan is not brave or strong and vice versa.
Everyone who is either happy or not brave is humble or not happy and vice versa.
If john is both not rich and not happy then someone is not wise and vice versa.
If lucy is both not happy and old then someone is happy or not creative.
Everyone who is not patient is both happy and creative.
Everyone who is creative or old is not humble.
Susan is either wise or not creative.
Someone is quiet or not brave.
Someone is either quiet or not quiet. | Susan is not kind. | contradiction | ((?[X]:((~tall(X)&~old(X))))=>((quiet(john)&wise(john))))&
(((~rich(mary)|~quiet(mary)))=>((~humble(susan)<~>happy(susan))))&
((?[X]:((curious(X)&~strong(X))))=>(?[X]:(kind(X))))&
(![X]:((~generous(X)|patient(X))<=>(wise(X)&~wise(X))))&
((?[X]:((quiet(X)|rich(X))))<=>(?[X]:((curious(X)<~>~rich(X)))))&
((?[X]:((~patient(X)<~>~tall(X))))<=>(?[X]:((~rich(X)<~>creative(X)))))&
(![X]:((~brave(X)<~>strong(X))<=>(~quiet(X)|patient(X))))&
(![X]:(~tall(X)=>(~patient(X)<~>calm(X))))&
((?[X]:((old(X)&humble(X))))<=>((~wise(susan)|~old(susan))))&
((?[X]:((old(X)&~old(X))))<=>(?[X]:((~humble(X)<~>kind(X)))))&
((?[X]:((~brave(X)&~funny(X))))<=>((~brave(susan)|strong(susan))))&
(![X]:((happy(X)<~>~brave(X))<=>(humble(X)|~happy(X))))&
(((~rich(john)&~happy(john)))<=>(?[X]:(~wise(X))))&
(((~happy(lucy)&old(lucy)))=>(?[X]:((happy(X)|~creative(X)))))&
(![X]:(~patient(X)=>(happy(X)&creative(X))))&
(![X]:((creative(X)|old(X))=>~humble(X)))&
((wise(susan)<~>~creative(susan)))&
(?[X]:((quiet(X)|~brave(X))))&
(?[X]:((quiet(X)<~>~quiet(X)))) | ~kind(susan) | [
"p3",
"p9",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 341909351291560787429039
% SZS output start Proof for 341909351291560787429039
4. ! [X0] : ((patient(X0) | ~generous(X0)) <=> (~wise(X0) & wise(X0))) [input p3]
10. ? [X0] : (~old(X0) & old(X0)) <=> ? [X0] : (~humble(X0) <~> kind(X0)) [input p9]
15. ! [X0] : (~patient(X0) => (creative(X0) & happy(X0))) [input p14]
16. ! [X0] : ((old(X0) | creative(X0)) => ~humble(X0)) [input p15]
20. ~kind(susan) [input hypothesis]
24. ? [X0] : (~old(X0) & old(X0)) <=> ? [X1] : (~humble(X1) <~> kind(X1)) [rectify 10]
31. ! [X0] : ((creative(X0) & happy(X0)) | patient(X0)) [ennf transformation 15]
32. ! [X0] : (~humble(X0) | (~old(X0) & ~creative(X0))) [ennf transformation 16]
37. ! [X0] : (((patient(X0) | ~generous(X0)) | (wise(X0) | ~wise(X0))) & ((~wise(X0) & wise(X0)) | (~patient(X0) & generous(X0)))) [nnf transformation 4]
38. ! [X0] : ((patient(X0) | ~generous(X0) | wise(X0) | ~wise(X0)) & ((~wise(X0) & wise(X0)) | (~patient(X0) & generous(X0)))) [flattening 37]
57. (? [X0] : (~old(X0) & old(X0)) | ! [X1] : ((~humble(X1) | ~kind(X1)) & (kind(X1) | humble(X1)))) & (? [X1] : ((~kind(X1) | humble(X1)) & (kind(X1) | ~humble(X1))) | ! [X0] : (old(X0) | ~old(X0))) [nnf transformation 24]
58. (? [X0] : (~old(X0) & old(X0)) | ! [X1] : ((~humble(X1) | ~kind(X1)) & (kind(X1) | humble(X1)))) & (? [X2] : ((~kind(X2) | humble(X2)) & (kind(X2) | ~humble(X2))) | ! [X3] : (old(X3) | ~old(X3))) [rectify 57]
59. ? [X0] : (~old(X0) & old(X0)) => (~old(sK6) & old(sK6)) [choice axiom]
60. ? [X2] : ((~kind(X2) | humble(X2)) & (kind(X2) | ~humble(X2))) => ((~kind(sK7) | humble(sK7)) & (kind(sK7) | ~humble(sK7))) [choice axiom]
61. ((~old(sK6) & old(sK6)) | ! [X1] : ((~humble(X1) | ~kind(X1)) & (kind(X1) | humble(X1)))) & (((~kind(sK7) | humble(sK7)) & (kind(sK7) | ~humble(sK7))) | ! [X3] : (old(X3) | ~old(X3))) [skolemisation 58,60,59]
90. wise(X0) | ~patient(X0) [cnf transformation 38]
92. ~wise(X0) | ~patient(X0) [cnf transformation 38]
123. old(sK6) | kind(X1) | humble(X1) [cnf transformation 61]
125. ~old(sK6) | kind(X1) | humble(X1) [cnf transformation 61]
143. creative(X0) | patient(X0) [cnf transformation 31]
144. ~humble(X0) | ~creative(X0) [cnf transformation 32]
151. ~kind(susan) [cnf transformation 20]
195. ~patient(X0) [subsumption resolution 90,92]
291. 30 <=> old(sK6) [avatar definition]
296. 31 <=> ! [X1] : (kind(X1) | humble(X1)) [avatar definition]
297. kind(X1) | humble(X1) <- (31) [avatar component clause 296]
298. 31 | ~30 [avatar split clause 125,291,296]
300. 31 | 30 [avatar split clause 123,291,296]
361. creative(X0) [subsumption resolution 143,195]
364. ~humble(X0) [subsumption resolution 144,361]
378. kind(X1) <- (31) [subsumption resolution 297,364]
393. $false <- (31) [resolution 378,151]
394. ~31 [avatar contradiction clause 393]
395. $false [avatar sat refutation 298,300,394]
% SZS output end Proof for 341909351291560787429039
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If fred is not old then paul is either calm or not tall. Everyone who is not creative or not old is either funny or not old and vice versa. Everyone who is both not curious and not funny is both creative and not quiet. If john is either not tall or rich then alice is not rich and vice versa. Everyone who is old is not tall. Everyone who is wise or quiet is not rich. Everyone who is either kind or generous is both tall and curious. If someone is either creative or quiet then someone is both old and tall and vice versa. If someone is not humble or wise then someone is both calm and quiet and vice versa. If susan is funny then alice is humble. If someone is both not quiet and not patient then someone is not wise. If someone is kind or not old then susan is both patient and not quiet. Everyone who is kind or not funny is both funny and tall. Everyone who is not strong or happy is both not calm and not rich and vice versa. Everyone who is either not wise or not brave is not curious. Someone is either not humble or strong. Someone is not wise. Someone is brave or not brave. Mary is not curious or tall. Someone is not quiet or not curious. Someone is not happy. Someone is not strong or brave. | Paul is calm. | neutral | ((~old(fred))=>((calm(paul)<~>~tall(paul))))&
(![X]:((~creative(X)|~old(X))<=>(funny(X)<~>~old(X))))&
(![X]:((~curious(X)&~funny(X))=>(creative(X)&~quiet(X))))&
(((~tall(john)<~>rich(john)))<=>(~rich(alice)))&
(![X]:(old(X)=>~tall(X)))&
(![X]:((wise(X)|quiet(X))=>~rich(X)))&
(![X]:((kind(X)<~>generous(X))=>(tall(X)&curious(X))))&
((?[X]:((creative(X)<~>quiet(X))))<=>(?[X]:((old(X)&tall(X)))))&
((?[X]:((~humble(X)|wise(X))))<=>(?[X]:((calm(X)&quiet(X)))))&
((funny(susan))=>(humble(alice)))&
((?[X]:((~quiet(X)&~patient(X))))=>(?[X]:(~wise(X))))&
((?[X]:((kind(X)|~old(X))))=>((patient(susan)&~quiet(susan))))&
(![X]:((kind(X)|~funny(X))=>(funny(X)&tall(X))))&
(![X]:((~strong(X)|happy(X))<=>(~calm(X)&~rich(X))))&
(![X]:((~wise(X)<~>~brave(X))=>~curious(X)))&
(?[X]:((~humble(X)<~>strong(X))))&
(?[X]:(~wise(X)))&
(?[X]:((brave(X)|~brave(X))))&
((~curious(mary)|tall(mary)))&
(?[X]:((~quiet(X)|~curious(X))))&
(?[X]:(~happy(X)))&
(?[X]:((~strong(X)|brave(X)))) | calm(paul) | [] | null | 0 |
Everyone who is both not brave and not humble is quiet or not tall and vice versa. Everyone who is either not brave or patient is both old and kind and vice versa. Everyone who is not curious is not quiet. Everyone who is not brave or not humble is either patient or not humble and vice versa. Everyone who is happy or not calm is either not wise or not old and vice versa. Everyone who is not wise or humble is happy. Everyone who is strong or not generous is calm. Everyone who is both not funny and not tall is not brave or not rich. If someone is not creative or not curious then someone is both not calm and kind and vice versa. Everyone who is patient or not kind is funny or not calm. Everyone who is wise is funny or rich and vice versa. If susan is both kind and rich then paul is both not patient and not quiet. Everyone who is old or strong is tall and vice versa. If someone is not wise or not strong then someone is either not old or happy and vice versa. Everyone who is not funny or not quiet is both not old and not brave and vice versa. If mary is either not patient or curious then john is either old or not kind. Alice is either old or rich. Someone is not old or not curious. John is not rich or curious. | Paul is patient. | neutral | (![X]:((~brave(X)&~humble(X))<=>(quiet(X)|~tall(X))))&
(![X]:((~brave(X)<~>patient(X))<=>(old(X)&kind(X))))&
(![X]:(~curious(X)=>~quiet(X)))&
(![X]:((~brave(X)|~humble(X))<=>(patient(X)<~>~humble(X))))&
(![X]:((happy(X)|~calm(X))<=>(~wise(X)<~>~old(X))))&
(![X]:((~wise(X)|humble(X))=>happy(X)))&
(![X]:((strong(X)|~generous(X))=>calm(X)))&
(![X]:((~funny(X)&~tall(X))=>(~brave(X)|~rich(X))))&
((?[X]:((~creative(X)|~curious(X))))<=>(?[X]:((~calm(X)&kind(X)))))&
(![X]:((patient(X)|~kind(X))=>(funny(X)|~calm(X))))&
(![X]:(wise(X)<=>(funny(X)|rich(X))))&
(((kind(susan)&rich(susan)))=>((~patient(paul)&~quiet(paul))))&
(![X]:((old(X)|strong(X))<=>tall(X)))&
((?[X]:((~wise(X)|~strong(X))))<=>(?[X]:((~old(X)<~>happy(X)))))&
(![X]:((~funny(X)|~quiet(X))<=>(~old(X)&~brave(X))))&
(((~patient(mary)<~>curious(mary)))=>((old(john)<~>~kind(john))))&
((old(alice)<~>rich(alice)))&
(?[X]:((~old(X)|~curious(X))))&
((~rich(john)|curious(john))) | patient(paul) | [] | null | 0 |
If lucy is either not happy or not strong then fred is either not funny or tall and vice versa.
Everyone who is tall or not quiet is both not calm and not funny and vice versa.
If john is curious or not wise then mary is either calm or happy.
Everyone who is either curious or creative is not funny or curious and vice versa.
If alice is not creative or not humble then someone is both happy and not old and vice versa.
If someone is either generous or not generous then someone is either calm or rich and vice versa.
Everyone who is both not creative and not wise is either curious or not tall.
Everyone who is both not curious and not generous is calm and vice versa.
Everyone who is curious or rich is either kind or brave.
Everyone who is both not kind and not generous is creative or rich and vice versa.
If someone is generous or not old then someone is not old and vice versa.
If john is not creative then lucy is either not generous or calm.
If mary is not strong or not wise then someone is either not creative or happy.
Everyone who is creative or old is either not creative or not calm.
If someone is either not creative or tall then paul is both creative and old.
Someone is not curious or quiet.
Someone is not kind.
Susan is either not generous or not wise.
Someone is funny or wise.
Susan is patient. | Susan is calm. | contradiction | (((~happy(lucy)<~>~strong(lucy)))<=>((~funny(fred)<~>tall(fred))))&
(![X]:((tall(X)|~quiet(X))<=>(~calm(X)&~funny(X))))&
(((curious(john)|~wise(john)))=>((calm(mary)<~>happy(mary))))&
(![X]:((curious(X)<~>creative(X))<=>(~funny(X)|curious(X))))&
(((~creative(alice)|~humble(alice)))<=>(?[X]:((happy(X)&~old(X)))))&
((?[X]:((generous(X)<~>~generous(X))))<=>(?[X]:((calm(X)<~>rich(X)))))&
(![X]:((~creative(X)&~wise(X))=>(curious(X)<~>~tall(X))))&
(![X]:((~curious(X)&~generous(X))<=>calm(X)))&
(![X]:((curious(X)|rich(X))=>(kind(X)<~>brave(X))))&
(![X]:((~kind(X)&~generous(X))<=>(creative(X)|rich(X))))&
((?[X]:((generous(X)|~old(X))))<=>(?[X]:(~old(X))))&
((~creative(john))=>((~generous(lucy)<~>calm(lucy))))&
(((~strong(mary)|~wise(mary)))=>(?[X]:((~creative(X)<~>happy(X)))))&
(![X]:((creative(X)|old(X))=>(~creative(X)<~>~calm(X))))&
((?[X]:((~creative(X)<~>tall(X))))=>((creative(paul)&old(paul))))&
(?[X]:((~curious(X)|quiet(X))))&
(?[X]:(~kind(X)))&
((~generous(susan)<~>~wise(susan)))&
(?[X]:((funny(X)|wise(X))))&
(patient(susan)) | calm(susan) | [
"p1",
"p3",
"p7",
"p9",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 1145472029635118316543855
% SZS output start Proof for 1145472029635118316543855
2. ! [X0] : ((~quiet(X0) | tall(X0)) <=> (~funny(X0) & ~calm(X0))) [input p1]
4. ! [X0] : ((curious(X0) <~> creative(X0)) <=> (curious(X0) | ~funny(X0))) [input p3]
8. ! [X0] : ((~generous(X0) & ~curious(X0)) <=> calm(X0)) [input p7]
10. ! [X0] : ((~generous(X0) & ~kind(X0)) <=> (rich(X0) | creative(X0))) [input p9]
14. ! [X0] : ((old(X0) | creative(X0)) => (~creative(X0) <~> ~calm(X0))) [input p13]
15. ? [X0] : (~creative(X0) <~> tall(X0)) => (old(paul) & creative(paul)) [input p14]
21. calm(susan) [input hypothesis]
31. ! [X0] : ((~creative(X0) <~> ~calm(X0)) | (~old(X0) & ~creative(X0))) [ennf transformation 14]
32. (old(paul) & creative(paul)) | ! [X0] : (~creative(X0) <=> tall(X0)) [ennf transformation 15]
34. ! [X0] : (((~quiet(X0) | tall(X0)) | (funny(X0) | calm(X0))) & ((~funny(X0) & ~calm(X0)) | (quiet(X0) & ~tall(X0)))) [nnf transformation 2]
35. ! [X0] : ((~quiet(X0) | tall(X0) | funny(X0) | calm(X0)) & ((~funny(X0) & ~calm(X0)) | (quiet(X0) & ~tall(X0)))) [flattening 34]
37. ! [X0] : ((((~creative(X0) | ~curious(X0)) & (creative(X0) | curious(X0))) | (~curious(X0) & funny(X0))) & ((curious(X0) | ~funny(X0)) | ((curious(X0) | ~creative(X0)) & (creative(X0) | ~curious(X0))))) [nnf transformation 4]
38. ! [X0] : ((((~creative(X0) | ~curious(X0)) & (creative(X0) | curious(X0))) | (~curious(X0) & funny(X0))) & (curious(X0) | ~funny(X0) | ((curious(X0) | ~creative(X0)) & (creative(X0) | ~curious(X0))))) [flattening 37]
50. ! [X0] : (((~generous(X0) & ~curious(X0)) | ~calm(X0)) & (calm(X0) | (generous(X0) | curious(X0)))) [nnf transformation 8]
51. ! [X0] : (((~generous(X0) & ~curious(X0)) | ~calm(X0)) & (calm(X0) | generous(X0) | curious(X0))) [flattening 50]
53. ! [X0] : (((~generous(X0) & ~kind(X0)) | (~rich(X0) & ~creative(X0))) & ((rich(X0) | creative(X0)) | (generous(X0) | kind(X0)))) [nnf transformation 10]
54. ! [X0] : (((~generous(X0) & ~kind(X0)) | (~rich(X0) & ~creative(X0))) & (rich(X0) | creative(X0) | generous(X0) | kind(X0))) [flattening 53]
64. ! [X0] : (((calm(X0) | creative(X0)) & (~calm(X0) | ~creative(X0))) | (~old(X0) & ~creative(X0))) [nnf transformation 31]
65. (old(paul) & creative(paul)) | ! [X0] : ((~creative(X0) | ~tall(X0)) & (tall(X0) | creative(X0))) [nnf transformation 32]
81. ~calm(X0) | ~tall(X0) [cnf transformation 35]
95. ~creative(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 38]
111. generous(X0) | calm(X0) | curious(X0) [cnf transformation 51]
121. ~generous(X0) | ~creative(X0) [cnf transformation 54]
132. ~calm(X0) | ~creative(X0) | ~creative(X0) [cnf transformation 64]
136. creative(paul) | tall(X0) | creative(X0) [cnf transformation 65]
145. calm(susan) [cnf transformation 21]
146. ~creative(X0) | ~calm(X0) [duplicate literal removal 132]
152. ~creative(X0) | ~curious(X0) [duplicate literal removal 95]
304. 31 <=> ! [X0] : (tall(X0) | creative(X0)) [avatar definition]
305. creative(X0) | tall(X0) <- (31) [avatar component clause 304]
308. 32 <=> creative(paul) [avatar definition]
310. creative(paul) <- (32) [avatar component clause 308]
312. 31 | 32 [avatar split clause 136,308,304]
341. ~tall(susan) [resolution 81,145]
396. calm(X0) | curious(X0) | ~creative(X0) [resolution 111,121]
400. curious(X0) | ~creative(X0) [subsumption resolution 396,146]
401. ~creative(X0) [subsumption resolution 400,152]
440. $false <- (32) [resolution 401,310]
443. ~32 [avatar contradiction clause 440]
446. tall(X0) <- (31) [subsumption resolution 305,401]
454. $false <- (31) [resolution 446,341]
457. ~31 [avatar contradiction clause 454]
460. $false [avatar sat refutation 312,443,457]
% SZS output end Proof for 1145472029635118316543855
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not calm then someone is both brave and creative and vice versa.
Everyone who is curious or not wise is kind.
Everyone who is either not tall or strong is either not rich or not brave and vice versa.
If someone is not tall or not generous then susan is tall and vice versa.
If alice is not brave then someone is either not funny or not calm.
Everyone who is either not quiet or not humble is not generous or calm and vice versa.
Everyone who is wise or generous is both old and calm.
Everyone who is happy or wise is both brave and not curious and vice versa.
If fred is brave then someone is not brave and vice versa.
Everyone who is either kind or old is not humble or not quiet.
If susan is both generous and creative then someone is not creative.
Everyone who is old is not wise and vice versa.
Everyone who is either kind or not funny is either not quiet or funny.
Everyone who is both not happy and wise is both calm and strong and vice versa.
If someone is not brave then john is not funny and vice versa.
Everyone who is both happy and rich is strong and vice versa.
Someone is funny or tall.
Lucy is either rich or patient.
Lucy is not brave.
Someone is both not curious and quiet.
Someone is brave.
Someone is quiet or not generous.
Someone is not humble. | John is calm. | neutral | ((?[X]:(~calm(X)))<=>(?[X]:((brave(X)&creative(X)))))&
(![X]:((curious(X)|~wise(X))=>kind(X)))&
(![X]:((~tall(X)<~>strong(X))<=>(~rich(X)<~>~brave(X))))&
((?[X]:((~tall(X)|~generous(X))))<=>(tall(susan)))&
((~brave(alice))=>(?[X]:((~funny(X)<~>~calm(X)))))&
(![X]:((~quiet(X)<~>~humble(X))<=>(~generous(X)|calm(X))))&
(![X]:((wise(X)|generous(X))=>(old(X)&calm(X))))&
(![X]:((happy(X)|wise(X))<=>(brave(X)&~curious(X))))&
((brave(fred))<=>(?[X]:(~brave(X))))&
(![X]:((kind(X)<~>old(X))=>(~humble(X)|~quiet(X))))&
(((generous(susan)&creative(susan)))=>(?[X]:(~creative(X))))&
(![X]:(old(X)<=>~wise(X)))&
(![X]:((kind(X)<~>~funny(X))=>(~quiet(X)<~>funny(X))))&
(![X]:((~happy(X)&wise(X))<=>(calm(X)&strong(X))))&
((?[X]:(~brave(X)))<=>(~funny(john)))&
(![X]:((happy(X)&rich(X))<=>strong(X)))&
(?[X]:((funny(X)|tall(X))))&
((rich(lucy)<~>patient(lucy)))&
(~brave(lucy))&
(?[X]:((~curious(X)&quiet(X))))&
(?[X]:(brave(X)))&
(?[X]:((quiet(X)|~generous(X))))&
(?[X]:(~humble(X))) | calm(john) | [] | null | 0 |
If john is tall then paul is either not happy or not strong and vice versa.
If someone is curious or not humble then someone is not strong or wise and vice versa.
Everyone who is either old or not funny is strong.
If alice is both not wise and happy then alice is curious.
If lucy is either not rich or wise then someone is not wise.
Everyone who is both not brave and not happy is either not brave or patient and vice versa.
Everyone who is both strong and not humble is not happy or old.
Everyone who is either not curious or not happy is wise or quiet.
If someone is either quiet or patient then mary is either not tall or wise and vice versa.
If alice is both quiet and happy then someone is not happy or not patient and vice versa.
Everyone who is funny is curious or old and vice versa.
Everyone who is either not happy or quiet is either happy or not humble.
If someone is both happy and creative then someone is not strong or brave and vice versa.
Everyone who is not brave or not old is either not quiet or not generous and vice versa.
Everyone who is strong is strong or not rich and vice versa.
If paul is tall or not rich then someone is both not funny and kind.
Someone is both not funny and wise.
Someone is funny.
Someone is not brave or funny.
Someone is calm or old.
Fred is either not kind or quiet.
Someone is curious or not old.
Mary is not strong.
Someone is not patient or not quiet. | Mary is wise. | neutral | ((tall(john))<=>((~happy(paul)<~>~strong(paul))))&
((?[X]:((curious(X)|~humble(X))))<=>(?[X]:((~strong(X)|wise(X)))))&
(![X]:((old(X)<~>~funny(X))=>strong(X)))&
(((~wise(alice)&happy(alice)))=>(curious(alice)))&
(((~rich(lucy)<~>wise(lucy)))=>(?[X]:(~wise(X))))&
(![X]:((~brave(X)&~happy(X))<=>(~brave(X)<~>patient(X))))&
(![X]:((strong(X)&~humble(X))=>(~happy(X)|old(X))))&
(![X]:((~curious(X)<~>~happy(X))=>(wise(X)|quiet(X))))&
((?[X]:((quiet(X)<~>patient(X))))<=>((~tall(mary)<~>wise(mary))))&
(((quiet(alice)&happy(alice)))<=>(?[X]:((~happy(X)|~patient(X)))))&
(![X]:(funny(X)<=>(curious(X)|old(X))))&
(![X]:((~happy(X)<~>quiet(X))=>(happy(X)<~>~humble(X))))&
((?[X]:((happy(X)&creative(X))))<=>(?[X]:((~strong(X)|brave(X)))))&
(![X]:((~brave(X)|~old(X))<=>(~quiet(X)<~>~generous(X))))&
(![X]:(strong(X)<=>(strong(X)|~rich(X))))&
(((tall(paul)|~rich(paul)))=>(?[X]:((~funny(X)&kind(X)))))&
(?[X]:((~funny(X)&wise(X))))&
(?[X]:(funny(X)))&
(?[X]:((~brave(X)|funny(X))))&
(?[X]:((calm(X)|old(X))))&
((~kind(fred)<~>quiet(fred)))&
(?[X]:((curious(X)|~old(X))))&
(~strong(mary))&
(?[X]:((~patient(X)|~quiet(X)))) | wise(mary) | [] | null | 0 |
If someone is not rich or not curious then someone is both curious and kind. Everyone who is quiet or not happy is rich and vice versa. If john is both not funny and not creative then someone is not curious or generous. If someone is quiet or not rich then someone is both not curious and not patient and vice versa. Everyone who is either not patient or not old is wise or not happy and vice versa. Everyone who is calm or quiet is both not kind and happy. If someone is both funny and humble then paul is not funny and vice versa. Everyone who is either not calm or funny is kind and vice versa. If susan is calm or old then alice is either not quiet or not creative and vice versa. Everyone who is quiet or not generous is calm or humble and vice versa. Everyone who is calm is both tall and not humble. If john is either tall or kind then someone is either not old or not calm and vice versa. Everyone who is happy is calm and vice versa. Everyone who is not patient or not calm is both not humble and old and vice versa. Everyone who is patient is not quiet. Someone is not wise or rich. Paul is both brave and not creative. John is not wise or brave. Someone is not old. Someone is either wise or happy. Mary is either not rich or old. Someone is happy. | Paul is old. | entailment | ((?[X]:((~rich(X)|~curious(X))))=>(?[X]:((curious(X)&kind(X)))))&
(![X]:((quiet(X)|~happy(X))<=>rich(X)))&
(((~funny(john)&~creative(john)))=>(?[X]:((~curious(X)|generous(X)))))&
((?[X]:((quiet(X)|~rich(X))))<=>(?[X]:((~curious(X)&~patient(X)))))&
(![X]:((~patient(X)<~>~old(X))<=>(wise(X)|~happy(X))))&
(![X]:((calm(X)|quiet(X))=>(~kind(X)&happy(X))))&
((?[X]:((funny(X)&humble(X))))<=>(~funny(paul)))&
(![X]:((~calm(X)<~>funny(X))<=>kind(X)))&
(((calm(susan)|old(susan)))<=>((~quiet(alice)<~>~creative(alice))))&
(![X]:((quiet(X)|~generous(X))<=>(calm(X)|humble(X))))&
(![X]:(calm(X)=>(tall(X)&~humble(X))))&
(((tall(john)<~>kind(john)))<=>(?[X]:((~old(X)<~>~calm(X)))))&
(![X]:(happy(X)<=>calm(X)))&
(![X]:((~patient(X)|~calm(X))<=>(~humble(X)&old(X))))&
(![X]:(patient(X)=>~quiet(X)))&
(?[X]:((~wise(X)|rich(X))))&
((brave(paul)&~creative(paul)))&
((~wise(john)|brave(john)))&
(?[X]:(~old(X)))&
(?[X]:((wise(X)<~>happy(X))))&
((~rich(mary)<~>old(mary)))&
(?[X]:(happy(X))) | old(paul) | [
"p5",
"p6",
"p7",
"p10",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 6028806040673875254925235
% SZS output start Proof for 6028806040673875254925235
6. ! [X0] : ((quiet(X0) | calm(X0)) => (happy(X0) & ~kind(X0))) [input p5]
7. ? [X0] : (humble(X0) & funny(X0)) <=> ~funny(paul) [input p6]
8. ! [X0] : ((~calm(X0) <~> funny(X0)) <=> kind(X0)) [input p7]
11. ! [X0] : (calm(X0) => (~humble(X0) & tall(X0))) [input p10]
14. ! [X0] : ((~calm(X0) | ~patient(X0)) <=> (old(X0) & ~humble(X0))) [input p13]
23. ~old(paul) [input hypothesis]
31. ! [X0] : ((happy(X0) & ~kind(X0)) | (~quiet(X0) & ~calm(X0))) [ennf transformation 6]
32. ! [X0] : ((~humble(X0) & tall(X0)) | ~calm(X0)) [ennf transformation 11]
48. (? [X0] : (humble(X0) & funny(X0)) | funny(paul)) & (~funny(paul) | ! [X0] : (~humble(X0) | ~funny(X0))) [nnf transformation 7]
49. (? [X0] : (humble(X0) & funny(X0)) | funny(paul)) & (~funny(paul) | ! [X1] : (~humble(X1) | ~funny(X1))) [rectify 48]
50. ? [X0] : (humble(X0) & funny(X0)) => (humble(sK4) & funny(sK4)) [choice axiom]
51. ((humble(sK4) & funny(sK4)) | funny(paul)) & (~funny(paul) | ! [X1] : (~humble(X1) | ~funny(X1))) [skolemisation 49,50]
52. ! [X0] : ((((~funny(X0) | calm(X0)) & (funny(X0) | ~calm(X0))) | ~kind(X0)) & (kind(X0) | ((~calm(X0) | ~funny(X0)) & (funny(X0) | calm(X0))))) [nnf transformation 8]
62. ! [X0] : (((~calm(X0) | ~patient(X0)) | (~old(X0) | humble(X0))) & ((old(X0) & ~humble(X0)) | (calm(X0) & patient(X0)))) [nnf transformation 14]
63. ! [X0] : ((~calm(X0) | ~patient(X0) | ~old(X0) | humble(X0)) & ((old(X0) & ~humble(X0)) | (calm(X0) & patient(X0)))) [flattening 62]
93. ~calm(X0) | ~kind(X0) [cnf transformation 31]
99. humble(sK4) | funny(paul) [cnf transformation 51]
101. kind(X0) | ~calm(X0) | ~funny(X0) [cnf transformation 52]
103. ~funny(X0) | calm(X0) | ~kind(X0) [cnf transformation 52]
115. ~humble(X0) | ~calm(X0) [cnf transformation 32]
127. ~humble(X0) | calm(X0) [cnf transformation 63]
129. calm(X0) | old(X0) [cnf transformation 63]
140. ~old(paul) [cnf transformation 23]
204. 15 <=> funny(paul) [avatar definition]
206. funny(paul) <- (15) [avatar component clause 204]
208. 16 <=> humble(sK4) [avatar definition]
210. humble(sK4) <- (16) [avatar component clause 208]
211. 15 | 16 [avatar split clause 99,208,204]
221. ~funny(X0) | ~kind(X0) [subsumption resolution 103,93]
222. ~calm(X0) | ~funny(X0) [subsumption resolution 101,221]
276. ~humble(X0) [subsumption resolution 127,115]
312. $false <- (16) [subsumption resolution 210,276]
313. ~16 [avatar contradiction clause 312]
347. ~funny(X0) | old(X0) [resolution 222,129]
510. old(paul) <- (15) [resolution 347,206]
512. $false <- (15) [subsumption resolution 510,140]
513. ~15 [avatar contradiction clause 512]
514. $false [avatar sat refutation 211,313,513]
% SZS output end Proof for 6028806040673875254925235
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both old and not rich is either rich or not old and vice versa.
If someone is patient then alice is either not creative or not funny.
If someone is both not rich and not creative then paul is both happy and not brave.
If someone is not calm then john is not rich and vice versa.
If susan is both kind and not patient then someone is not patient and vice versa.
If lucy is both not brave and brave then someone is both old and tall and vice versa.
Everyone who is not brave or strong is not creative or not generous and vice versa.
Everyone who is either humble or curious is both humble and wise and vice versa.
Everyone who is either old or brave is both not tall and calm and vice versa.
Everyone who is either not brave or strong is both calm and creative and vice versa.
If john is either not happy or not creative then someone is generous or not rich.
If someone is strong or rich then someone is not curious.
If someone is either humble or old then someone is either not quiet or not rich.
Everyone who is not happy is either not creative or not curious and vice versa.
Everyone who is not strong or generous is quiet and vice versa.
If paul is either quiet or generous then lucy is both creative and happy and vice versa.
Someone is not creative.
Mary is not tall.
Mary is calm or not humble.
Someone is both not happy and not wise.
Lucy is both not patient and not tall.
Someone is brave or tall.
Someone is not happy or creative.
Fred is either kind or tall. | Fred is calm. | entailment | (![X]:((old(X)&~rich(X))<=>(rich(X)<~>~old(X))))&
((?[X]:(patient(X)))=>((~creative(alice)<~>~funny(alice))))&
((?[X]:((~rich(X)&~creative(X))))=>((happy(paul)&~brave(paul))))&
((?[X]:(~calm(X)))<=>(~rich(john)))&
(((kind(susan)&~patient(susan)))<=>(?[X]:(~patient(X))))&
(((~brave(lucy)&brave(lucy)))<=>(?[X]:((old(X)&tall(X)))))&
(![X]:((~brave(X)|strong(X))<=>(~creative(X)|~generous(X))))&
(![X]:((humble(X)<~>curious(X))<=>(humble(X)&wise(X))))&
(![X]:((old(X)<~>brave(X))<=>(~tall(X)&calm(X))))&
(![X]:((~brave(X)<~>strong(X))<=>(calm(X)&creative(X))))&
(((~happy(john)<~>~creative(john)))=>(?[X]:((generous(X)|~rich(X)))))&
((?[X]:((strong(X)|rich(X))))=>(?[X]:(~curious(X))))&
((?[X]:((humble(X)<~>old(X))))=>(?[X]:((~quiet(X)<~>~rich(X)))))&
(![X]:(~happy(X)<=>(~creative(X)<~>~curious(X))))&
(![X]:((~strong(X)|generous(X))<=>quiet(X)))&
(((quiet(paul)<~>generous(paul)))<=>((creative(lucy)&happy(lucy))))&
(?[X]:(~creative(X)))&
(~tall(mary))&
((calm(mary)|~humble(mary)))&
(?[X]:((~happy(X)&~wise(X))))&
((~patient(lucy)&~tall(lucy)))&
(?[X]:((brave(X)|tall(X))))&
(?[X]:((~happy(X)|creative(X))))&
((kind(fred)<~>tall(fred))) | calm(fred) | [
"p0",
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 340384373304586456422419
% SZS output start Proof for 340384373304586456422419
1. ! [X0] : ((~rich(X0) & old(X0)) <=> (rich(X0) <~> ~old(X0))) [input p0]
4. ? [X0] : ~calm(X0) <=> ~rich(john) [input p3]
25. ~calm(fred) [input hypothesis]
33. ! [X0] : (((~rich(X0) & old(X0)) | ((rich(X0) | old(X0)) & (~old(X0) | ~rich(X0)))) & (((old(X0) | ~rich(X0)) & (~old(X0) | rich(X0))) | (rich(X0) | ~old(X0)))) [nnf transformation 1]
34. ! [X0] : (((~rich(X0) & old(X0)) | ((rich(X0) | old(X0)) & (~old(X0) | ~rich(X0)))) & (((old(X0) | ~rich(X0)) & (~old(X0) | rich(X0))) | rich(X0) | ~old(X0))) [flattening 33]
36. (? [X0] : ~calm(X0) | rich(john)) & (~rich(john) | ! [X0] : calm(X0)) [nnf transformation 4]
37. (? [X0] : ~calm(X0) | rich(john)) & (~rich(john) | ! [X1] : calm(X1)) [rectify 36]
38. ? [X0] : ~calm(X0) => ~calm(sK0) [choice axiom]
39. (~calm(sK0) | rich(john)) & (~rich(john) | ! [X1] : calm(X1)) [skolemisation 37,38]
82. ~old(X0) | rich(X0) | rich(X0) | ~old(X0) [cnf transformation 34]
85. old(X0) | rich(X0) | old(X0) [cnf transformation 34]
92. ~rich(john) | calm(X1) [cnf transformation 39]
155. ~calm(fred) [cnf transformation 25]
158. ~old(X0) | rich(X0) [duplicate literal removal 82]
159. old(X0) | rich(X0) [duplicate literal removal 85]
161. rich(X0) [subsumption resolution 158,159]
175. calm(X1) [subsumption resolution 92,161]
291. $false [subsumption resolution 155,175]
% SZS output end Proof for 340384373304586456422419
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not humble and happy is not brave.
If john is patient or not generous then someone is not curious or not humble and vice versa.
Everyone who is both curious and funny is funny.
Everyone who is humble is both brave and strong.
Everyone who is curious or not humble is tall and vice versa.
If someone is not curious then someone is both wise and not generous and vice versa.
If someone is curious then someone is either old or not calm and vice versa.
If someone is both tall and creative then paul is not strong or brave and vice versa.
If someone is either funny or calm then someone is both creative and quiet.
If someone is either brave or strong then someone is not tall or not wise.
Everyone who is wise is not humble.
Everyone who is humble or wise is either not funny or not strong and vice versa.
If someone is not rich then someone is both not rich and old and vice versa.
Everyone who is quiet or funny is either not creative or brave and vice versa.
Everyone who is both not tall and not humble is not happy or not brave and vice versa.
Everyone who is quiet is tall and vice versa.
Susan is either brave or kind.
Someone is either tall or kind.
Alice is not funny.
Someone is patient.
Susan is both humble and tall.
John is not happy or not calm. | Paul is not happy. | contradiction | (![X]:((~humble(X)&happy(X))=>~brave(X)))&
(((patient(john)|~generous(john)))<=>(?[X]:((~curious(X)|~humble(X)))))&
(![X]:((curious(X)&funny(X))=>funny(X)))&
(![X]:(humble(X)=>(brave(X)&strong(X))))&
(![X]:((curious(X)|~humble(X))<=>tall(X)))&
((?[X]:(~curious(X)))<=>(?[X]:((wise(X)&~generous(X)))))&
((?[X]:(curious(X)))<=>(?[X]:((old(X)<~>~calm(X)))))&
((?[X]:((tall(X)&creative(X))))<=>((~strong(paul)|brave(paul))))&
((?[X]:((funny(X)<~>calm(X))))=>(?[X]:((creative(X)&quiet(X)))))&
((?[X]:((brave(X)<~>strong(X))))=>(?[X]:((~tall(X)|~wise(X)))))&
(![X]:(wise(X)=>~humble(X)))&
(![X]:((humble(X)|wise(X))<=>(~funny(X)<~>~strong(X))))&
((?[X]:(~rich(X)))<=>(?[X]:((~rich(X)&old(X)))))&
(![X]:((quiet(X)|funny(X))<=>(~creative(X)<~>brave(X))))&
(![X]:((~tall(X)&~humble(X))<=>(~happy(X)|~brave(X))))&
(![X]:(quiet(X)<=>tall(X)))&
((brave(susan)<~>kind(susan)))&
(?[X]:((tall(X)<~>kind(X))))&
(~funny(alice))&
(?[X]:(patient(X)))&
((humble(susan)&tall(susan)))&
((~happy(john)|~calm(john))) | ~happy(paul) | [
"p4",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6929469910763232307593123
% SZS output start Proof for 6929469910763232307593123
5. ! [X0] : ((~humble(X0) | curious(X0)) <=> tall(X0)) [input p4]
15. ! [X0] : ((~humble(X0) & ~tall(X0)) <=> (~brave(X0) | ~happy(X0))) [input p14]
23. ~happy(paul) [input hypothesis]
42. ! [X0] : (((~humble(X0) | curious(X0)) | ~tall(X0)) & (tall(X0) | (humble(X0) & ~curious(X0)))) [nnf transformation 5]
43. ! [X0] : ((~humble(X0) | curious(X0) | ~tall(X0)) & (tall(X0) | (humble(X0) & ~curious(X0)))) [flattening 42]
76. ! [X0] : (((~humble(X0) & ~tall(X0)) | (brave(X0) & happy(X0))) & ((~brave(X0) | ~happy(X0)) | (humble(X0) | tall(X0)))) [nnf transformation 15]
77. ! [X0] : (((~humble(X0) & ~tall(X0)) | (brave(X0) & happy(X0))) & (~brave(X0) | ~happy(X0) | humble(X0) | tall(X0))) [flattening 76]
94. tall(X0) | humble(X0) [cnf transformation 43]
131. ~tall(X0) | happy(X0) [cnf transformation 77]
133. ~humble(X0) | happy(X0) [cnf transformation 77]
146. ~happy(paul) [cnf transformation 23]
337. happy(X0) | humble(X0) [resolution 131,94]
342. happy(X0) [subsumption resolution 337,133]
343. $false [resolution 342,146]
% SZS output end Proof for 6929469910763232307593123
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise and not kind is creative and vice versa.
If susan is not creative then someone is brave.
Everyone who is both quiet and not quiet is quiet and vice versa.
Everyone who is not patient is either not tall or not funny.
If someone is both strong and not strong then lucy is both rich and patient.
If someone is patient or not funny then someone is both not kind and quiet.
If paul is not brave then mary is not humble and vice versa.
Everyone who is not rich or not funny is not strong and vice versa.
If alice is not calm then alice is creative or not tall.
Everyone who is not kind or brave is not humble or not funny and vice versa.
If someone is not quiet then susan is not calm or not old and vice versa.
If lucy is not calm then someone is creative and vice versa.
If someone is happy then lucy is not tall and vice versa.
If someone is either calm or not funny then fred is either not brave or wise and vice versa.
If someone is both old and not wise then someone is patient or humble.
If someone is quiet then lucy is not quiet or not calm.
John is not rich or tall.
Mary is rich or humble.
Alice is not curious.
Someone is both generous and not humble.
Someone is not creative or patient.
Susan is generous.
Susan is brave.
Someone is either not kind or creative. | Lucy is tall. | contradiction | (![X]:((~wise(X)&~kind(X))<=>creative(X)))&
((~creative(susan))=>(?[X]:(brave(X))))&
(![X]:((quiet(X)&~quiet(X))<=>quiet(X)))&
(![X]:(~patient(X)=>(~tall(X)<~>~funny(X))))&
((?[X]:((strong(X)&~strong(X))))=>((rich(lucy)&patient(lucy))))&
((?[X]:((patient(X)|~funny(X))))=>(?[X]:((~kind(X)&quiet(X)))))&
((~brave(paul))<=>(~humble(mary)))&
(![X]:((~rich(X)|~funny(X))<=>~strong(X)))&
((~calm(alice))=>((creative(alice)|~tall(alice))))&
(![X]:((~kind(X)|brave(X))<=>(~humble(X)|~funny(X))))&
((?[X]:(~quiet(X)))<=>((~calm(susan)|~old(susan))))&
((~calm(lucy))<=>(?[X]:(creative(X))))&
((?[X]:(happy(X)))<=>(~tall(lucy)))&
((?[X]:((calm(X)<~>~funny(X))))<=>((~brave(fred)<~>wise(fred))))&
((?[X]:((old(X)&~wise(X))))=>(?[X]:((patient(X)|humble(X)))))&
((?[X]:(quiet(X)))=>((~quiet(lucy)|~calm(lucy))))&
((~rich(john)|tall(john)))&
((rich(mary)|humble(mary)))&
(~curious(alice))&
(?[X]:((generous(X)&~humble(X))))&
(?[X]:((~creative(X)|patient(X))))&
(generous(susan))&
(brave(susan))&
(?[X]:((~kind(X)<~>creative(X)))) | tall(lucy) | [
"p2",
"p3",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 9031364414209107606310658
% SZS output start Proof for 9031364414209107606310658
3. ! [X0] : ((~quiet(X0) & quiet(X0)) <=> quiet(X0)) [input p2]
4. ! [X0] : (~patient(X0) => (~tall(X0) <~> ~funny(X0))) [input p3]
6. ? [X0] : (~funny(X0) | patient(X0)) => ? [X0] : (quiet(X0) & ~kind(X0)) [input p5]
25. tall(lucy) [input hypothesis]
26. ? [X0] : (~funny(X0) | patient(X0)) => ? [X1] : (quiet(X1) & ~kind(X1)) [rectify 6]
32. ! [X0] : ((~tall(X0) <~> ~funny(X0)) | patient(X0)) [ennf transformation 4]
34. ? [X1] : (quiet(X1) & ~kind(X1)) | ! [X0] : (funny(X0) & ~patient(X0)) [ennf transformation 26]
44. ! [X0] : (((~quiet(X0) & quiet(X0)) | ~quiet(X0)) & (quiet(X0) | (quiet(X0) | ~quiet(X0)))) [nnf transformation 3]
45. ! [X0] : (((~quiet(X0) & quiet(X0)) | ~quiet(X0)) & (quiet(X0) | quiet(X0) | ~quiet(X0))) [flattening 44]
46. ! [X0] : (((funny(X0) | tall(X0)) & (~funny(X0) | ~tall(X0))) | patient(X0)) [nnf transformation 32]
47. ? [X0] : (quiet(X0) & ~kind(X0)) | ! [X1] : (funny(X1) & ~patient(X1)) [rectify 34]
48. ? [X0] : (quiet(X0) & ~kind(X0)) => (quiet(sK1) & ~kind(sK1)) [choice axiom]
49. (quiet(sK1) & ~kind(sK1)) | ! [X1] : (funny(X1) & ~patient(X1)) [skolemisation 47,48]
88. ~quiet(X0) | ~quiet(X0) [cnf transformation 45]
89. ~funny(X0) | ~tall(X0) | patient(X0) [cnf transformation 46]
95. quiet(sK1) | ~patient(X1) [cnf transformation 49]
96. quiet(sK1) | funny(X1) [cnf transformation 49]
131. tall(lucy) [cnf transformation 25]
133. ~quiet(X0) [duplicate literal removal 88]
143. funny(X1) [subsumption resolution 96,133]
144. ~patient(X1) [subsumption resolution 95,133]
195. 13 <=> tall(lucy) [avatar definition]
197. tall(lucy) <- (13) [avatar component clause 195]
256. 13 [avatar split clause 131,195]
264. ~tall(X0) | patient(X0) [resolution 89,143]
265. ~tall(X0) [subsumption resolution 264,144]
266. $false <- (13) [resolution 265,197]
267. ~13 [avatar contradiction clause 266]
268. $false [avatar sat refutation 256,267]
% SZS output end Proof for 9031364414209107606310658
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.022 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not calm and generous then susan is strong or humble.
If fred is not funny then mary is old or not funny and vice versa.
If alice is either not old or not kind then someone is either not happy or generous.
If someone is strong or not rich then someone is tall.
If lucy is both not kind and rich then someone is either kind or funny.
If mary is not calm then alice is both not calm and strong.
Everyone who is either strong or tall is both tall and strong.
Everyone who is not brave or kind is not kind and vice versa.
Everyone who is curious or creative is both brave and happy and vice versa.
If someone is not calm then lucy is either creative or not brave.
If someone is not strong then alice is not brave and vice versa.
If someone is both rich and calm then someone is not brave and vice versa.
If someone is both not brave and not wise then susan is not strong or not rich.
Everyone who is either rich or not strong is both not generous and not kind and vice versa.
Everyone who is calm or not curious is not humble.
Everyone who is funny is both kind and not wise and vice versa.
Fred is not tall.
Someone is either happy or not quiet.
Someone is not creative.
Someone is not curious or not humble.
Someone is not generous.
Alice is both not patient and not tall.
Lucy is either quiet or not funny. | Alice is patient. | contradiction | ((?[X]:((~calm(X)&generous(X))))=>((strong(susan)|humble(susan))))&
((~funny(fred))<=>((old(mary)|~funny(mary))))&
(((~old(alice)<~>~kind(alice)))=>(?[X]:((~happy(X)<~>generous(X)))))&
((?[X]:((strong(X)|~rich(X))))=>(?[X]:(tall(X))))&
(((~kind(lucy)&rich(lucy)))=>(?[X]:((kind(X)<~>funny(X)))))&
((~calm(mary))=>((~calm(alice)&strong(alice))))&
(![X]:((strong(X)<~>tall(X))=>(tall(X)&strong(X))))&
(![X]:((~brave(X)|kind(X))<=>~kind(X)))&
(![X]:((curious(X)|creative(X))<=>(brave(X)&happy(X))))&
((?[X]:(~calm(X)))=>((creative(lucy)<~>~brave(lucy))))&
((?[X]:(~strong(X)))<=>(~brave(alice)))&
((?[X]:((rich(X)&calm(X))))<=>(?[X]:(~brave(X))))&
((?[X]:((~brave(X)&~wise(X))))=>((~strong(susan)|~rich(susan))))&
(![X]:((rich(X)<~>~strong(X))<=>(~generous(X)&~kind(X))))&
(![X]:((calm(X)|~curious(X))=>~humble(X)))&
(![X]:(funny(X)<=>(kind(X)&~wise(X))))&
(~tall(fred))&
(?[X]:((happy(X)<~>~quiet(X))))&
(?[X]:(~creative(X)))&
(?[X]:((~curious(X)|~humble(X))))&
(?[X]:(~generous(X)))&
((~patient(alice)&~tall(alice)))&
((quiet(lucy)<~>~funny(lucy))) | patient(alice) | [
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 3035380048310894459932088
% SZS output start Proof for 3035380048310894459932088
22. ~tall(alice) & ~patient(alice) [input p21]
24. patient(alice) [input hypothesis]
130. ~patient(alice) [cnf transformation 22]
134. patient(alice) [cnf transformation 24]
299. $false [subsumption resolution 134,130]
% SZS output end Proof for 3035380048310894459932088
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong is generous and vice versa. If lucy is old or creative then someone is both not creative and quiet and vice versa. If alice is both old and brave then john is either tall or humble. If fred is not patient or not strong then lucy is not patient and vice versa. Everyone who is both not rich and not calm is both creative and patient and vice versa. If someone is kind or old then someone is quiet or strong. If lucy is not tall then someone is both quiet and old and vice versa. Everyone who is both wise and humble is generous and vice versa. Everyone who is either quiet or tall is both rich and kind and vice versa. If someone is both not kind and rich then john is both tall and strong and vice versa. Everyone who is not curious is either not curious or not generous and vice versa. Everyone who is tall or not quiet is brave. If someone is not calm or not patient then susan is generous or not old and vice versa. Everyone who is quiet is patient or not kind and vice versa. If someone is either calm or humble then someone is either happy or quiet and vice versa. If mary is both not generous and quiet then someone is either not creative or kind. Someone is either kind or not rich. Mary is generous. Mary is both generous and not creative. John is not creative. Someone is not creative. Susan is strong or funny. | Mary is humble. | entailment | (![X]:(~strong(X)<=>generous(X)))&
(((old(lucy)|creative(lucy)))<=>(?[X]:((~creative(X)&quiet(X)))))&
(((old(alice)&brave(alice)))=>((tall(john)<~>humble(john))))&
(((~patient(fred)|~strong(fred)))<=>(~patient(lucy)))&
(![X]:((~rich(X)&~calm(X))<=>(creative(X)&patient(X))))&
((?[X]:((kind(X)|old(X))))=>(?[X]:((quiet(X)|strong(X)))))&
((~tall(lucy))<=>(?[X]:((quiet(X)&old(X)))))&
(![X]:((wise(X)&humble(X))<=>generous(X)))&
(![X]:((quiet(X)<~>tall(X))<=>(rich(X)&kind(X))))&
((?[X]:((~kind(X)&rich(X))))<=>((tall(john)&strong(john))))&
(![X]:(~curious(X)<=>(~curious(X)<~>~generous(X))))&
(![X]:((tall(X)|~quiet(X))=>brave(X)))&
((?[X]:((~calm(X)|~patient(X))))<=>((generous(susan)|~old(susan))))&
(![X]:(quiet(X)<=>(patient(X)|~kind(X))))&
((?[X]:((calm(X)<~>humble(X))))<=>(?[X]:((happy(X)<~>quiet(X)))))&
(((~generous(mary)&quiet(mary)))=>(?[X]:((~creative(X)<~>kind(X)))))&
(?[X]:((kind(X)<~>~rich(X))))&
(generous(mary))&
((generous(mary)&~creative(mary)))&
(~creative(john))&
(?[X]:(~creative(X)))&
((strong(susan)|funny(susan))) | humble(mary) | [
"p0",
"p7",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 3678154794297518468802991
% SZS output start Proof for 3678154794297518468802991
1. ! [X0] : (~strong(X0) <=> generous(X0)) [input p0]
8. ! [X0] : ((humble(X0) & wise(X0)) <=> generous(X0)) [input p7]
11. ! [X0] : (~curious(X0) <=> (~curious(X0) <~> ~generous(X0))) [input p10]
23. ~humble(mary) [input hypothesis]
33. ! [X0] : ((~strong(X0) | ~generous(X0)) & (generous(X0) | strong(X0))) [nnf transformation 1]
51. ! [X0] : (((humble(X0) & wise(X0)) | ~generous(X0)) & (generous(X0) | (~humble(X0) | ~wise(X0)))) [nnf transformation 8]
52. ! [X0] : (((humble(X0) & wise(X0)) | ~generous(X0)) & (generous(X0) | ~humble(X0) | ~wise(X0))) [flattening 51]
60. ! [X0] : ((~curious(X0) | ((~curious(X0) | generous(X0)) & (~generous(X0) | curious(X0)))) & (((generous(X0) | curious(X0)) & (~generous(X0) | ~curious(X0))) | curious(X0))) [nnf transformation 11]
81. generous(X0) | strong(X0) [cnf transformation 33]
82. ~generous(X0) | ~strong(X0) [cnf transformation 33]
104. ~generous(X0) | humble(X0) [cnf transformation 52]
116. generous(X0) | curious(X0) | curious(X0) [cnf transformation 60]
118. ~curious(X0) | ~curious(X0) | generous(X0) [cnf transformation 60]
145. ~humble(mary) [cnf transformation 23]
146. generous(X0) | curious(X0) [duplicate literal removal 116]
147. ~curious(X0) | generous(X0) [duplicate literal removal 118]
258. generous(X0) [subsumption resolution 146,147]
321. ~strong(X1) [resolution 82,258]
327. humble(X0) | strong(X0) [resolution 104,81]
329. humble(X0) [subsumption resolution 327,321]
332. $false [resolution 329,145]
% SZS output end Proof for 3678154794297518468802991
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is calm or kind is both quiet and not patient.
If john is not happy then someone is tall or not tall.
Everyone who is not happy is humble or not strong and vice versa.
If susan is either creative or curious then lucy is not calm and vice versa.
If someone is creative then someone is strong or tall and vice versa.
If mary is either not creative or generous then john is both not wise and not generous.
If someone is not wise then alice is both not generous and not tall and vice versa.
If someone is calm then someone is patient or not patient and vice versa.
Everyone who is either humble or patient is not rich or strong.
If someone is either not tall or not rich then someone is humble.
Everyone who is either old or not tall is both not tall and wise and vice versa.
Everyone who is both curious and not calm is either generous or quiet and vice versa.
Everyone who is either humble or not tall is either brave or not brave and vice versa.
If someone is humble then alice is both not wise and not kind.
Everyone who is not funny is not brave and vice versa.
Everyone who is quiet is kind.
Someone is happy or strong.
Paul is either not quiet or patient.
Someone is either not funny or generous.
John is not old.
Someone is either not creative or not calm.
John is patient.
Someone is tall or not funny. | Mary is calm. | neutral | (![X]:((calm(X)|kind(X))=>(quiet(X)&~patient(X))))&
((~happy(john))=>(?[X]:((tall(X)|~tall(X)))))&
(![X]:(~happy(X)<=>(humble(X)|~strong(X))))&
(((creative(susan)<~>curious(susan)))<=>(~calm(lucy)))&
((?[X]:(creative(X)))<=>(?[X]:((strong(X)|tall(X)))))&
(((~creative(mary)<~>generous(mary)))=>((~wise(john)&~generous(john))))&
((?[X]:(~wise(X)))<=>((~generous(alice)&~tall(alice))))&
((?[X]:(calm(X)))<=>(?[X]:((patient(X)|~patient(X)))))&
(![X]:((humble(X)<~>patient(X))=>(~rich(X)|strong(X))))&
((?[X]:((~tall(X)<~>~rich(X))))=>(?[X]:(humble(X))))&
(![X]:((old(X)<~>~tall(X))<=>(~tall(X)&wise(X))))&
(![X]:((curious(X)&~calm(X))<=>(generous(X)<~>quiet(X))))&
(![X]:((humble(X)<~>~tall(X))<=>(brave(X)<~>~brave(X))))&
((?[X]:(humble(X)))=>((~wise(alice)&~kind(alice))))&
(![X]:(~funny(X)<=>~brave(X)))&
(![X]:(quiet(X)=>kind(X)))&
(?[X]:((happy(X)|strong(X))))&
((~quiet(paul)<~>patient(paul)))&
(?[X]:((~funny(X)<~>generous(X))))&
(~old(john))&
(?[X]:((~creative(X)<~>~calm(X))))&
(patient(john))&
(?[X]:((tall(X)|~funny(X)))) | calm(mary) | [] | null | 0 |
Everyone who is either kind or not tall is both not humble and not curious and vice versa.
Everyone who is either generous or not tall is both not patient and brave.
If fred is not curious or funny then lucy is not generous or patient and vice versa.
If lucy is not rich then fred is strong or funny.
Everyone who is calm is both kind and not wise.
Everyone who is generous is either not creative or wise and vice versa.
If fred is not kind then someone is not happy or strong and vice versa.
If paul is not tall then someone is patient and vice versa.
Everyone who is wise is strong and vice versa.
If susan is generous then someone is both kind and calm and vice versa.
If lucy is either not humble or humble then someone is not old and vice versa.
Everyone who is not funny is either old or not creative.
Everyone who is not calm is either funny or generous and vice versa.
If someone is either kind or creative then susan is both brave and not quiet and vice versa.
If john is not quiet then mary is generous or not humble and vice versa.
Everyone who is both not wise and patient is either rich or not quiet and vice versa.
Fred is not strong.
Paul is either not rich or not quiet.
Lucy is either brave or not strong.
Someone is not strong or quiet.
Mary is either funny or not old.
Paul is both creative and tall.
Alice is tall or not creative.
John is not tall or calm. | Lucy is humble. | neutral | (![X]:((kind(X)<~>~tall(X))<=>(~humble(X)&~curious(X))))&
(![X]:((generous(X)<~>~tall(X))=>(~patient(X)&brave(X))))&
(((~curious(fred)|funny(fred)))<=>((~generous(lucy)|patient(lucy))))&
((~rich(lucy))=>((strong(fred)|funny(fred))))&
(![X]:(calm(X)=>(kind(X)&~wise(X))))&
(![X]:(generous(X)<=>(~creative(X)<~>wise(X))))&
((~kind(fred))<=>(?[X]:((~happy(X)|strong(X)))))&
((~tall(paul))<=>(?[X]:(patient(X))))&
(![X]:(wise(X)<=>strong(X)))&
((generous(susan))<=>(?[X]:((kind(X)&calm(X)))))&
(((~humble(lucy)<~>humble(lucy)))<=>(?[X]:(~old(X))))&
(![X]:(~funny(X)=>(old(X)<~>~creative(X))))&
(![X]:(~calm(X)<=>(funny(X)<~>generous(X))))&
((?[X]:((kind(X)<~>creative(X))))<=>((brave(susan)&~quiet(susan))))&
((~quiet(john))<=>((generous(mary)|~humble(mary))))&
(![X]:((~wise(X)&patient(X))<=>(rich(X)<~>~quiet(X))))&
(~strong(fred))&
((~rich(paul)<~>~quiet(paul)))&
((brave(lucy)<~>~strong(lucy)))&
(?[X]:((~strong(X)|quiet(X))))&
((funny(mary)<~>~old(mary)))&
((creative(paul)&tall(paul)))&
((tall(alice)|~creative(alice)))&
((~tall(john)|calm(john))) | humble(lucy) | [] | null | 0 |
If mary is either not patient or humble then someone is either not humble or rich and vice versa.
Everyone who is not kind or quiet is either not kind or tall.
Everyone who is not calm is quiet.
Everyone who is kind is not old.
Everyone who is not funny is not rich or not tall.
Everyone who is not rich or not happy is not calm or brave.
Everyone who is creative is funny or kind.
Everyone who is both not funny and tall is quiet or brave and vice versa.
Everyone who is both patient and kind is either not happy or not quiet.
Everyone who is creative or rich is not rich.
Everyone who is generous is both calm and not creative.
If someone is either not funny or not humble then susan is not patient.
Everyone who is either not funny or not old is calm or not kind.
If someone is not creative then john is both strong and not tall and vice versa.
Everyone who is patient or not calm is both not wise and old.
If john is funny or curious then lucy is either generous or tall.
Someone is either humble or curious.
John is calm.
Fred is wise or rich.
Someone is not tall or not quiet.
Susan is both curious and not rich. | Fred is calm. | entailment | (((~patient(mary)<~>humble(mary)))<=>(?[X]:((~humble(X)<~>rich(X)))))&
(![X]:((~kind(X)|quiet(X))=>(~kind(X)<~>tall(X))))&
(![X]:(~calm(X)=>quiet(X)))&
(![X]:(kind(X)=>~old(X)))&
(![X]:(~funny(X)=>(~rich(X)|~tall(X))))&
(![X]:((~rich(X)|~happy(X))=>(~calm(X)|brave(X))))&
(![X]:(creative(X)=>(funny(X)|kind(X))))&
(![X]:((~funny(X)&tall(X))<=>(quiet(X)|brave(X))))&
(![X]:((patient(X)&kind(X))=>(~happy(X)<~>~quiet(X))))&
(![X]:((creative(X)|rich(X))=>~rich(X)))&
(![X]:(generous(X)=>(calm(X)&~creative(X))))&
((?[X]:((~funny(X)<~>~humble(X))))=>(~patient(susan)))&
(![X]:((~funny(X)<~>~old(X))=>(calm(X)|~kind(X))))&
((?[X]:(~creative(X)))<=>((strong(john)&~tall(john))))&
(![X]:((patient(X)|~calm(X))=>(~wise(X)&old(X))))&
(((funny(john)|curious(john)))=>((generous(lucy)<~>tall(lucy))))&
(?[X]:((humble(X)<~>curious(X))))&
(calm(john))&
((wise(fred)|rich(fred)))&
(?[X]:((~tall(X)|~quiet(X))))&
((curious(susan)&~rich(susan))) | calm(fred) | [
"p9",
"p14",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 6179614632080574953454897
% SZS output start Proof for 6179614632080574953454897
10. ! [X0] : ((rich(X0) | creative(X0)) => ~rich(X0)) [input p9]
15. ! [X0] : ((~calm(X0) | patient(X0)) => (old(X0) & ~wise(X0))) [input p14]
19. rich(fred) | wise(fred) [input p18]
22. ~calm(fred) [input hypothesis]
34. ! [X0] : (~rich(X0) | (~rich(X0) & ~creative(X0))) [ennf transformation 10]
39. ! [X0] : ((old(X0) & ~wise(X0)) | (calm(X0) & ~patient(X0))) [ennf transformation 15]
88. ~rich(X0) | ~rich(X0) [cnf transformation 34]
99. ~wise(X0) | calm(X0) [cnf transformation 39]
109. rich(fred) | wise(fred) [cnf transformation 19]
113. ~calm(fred) [cnf transformation 22]
114. ~rich(X0) [duplicate literal removal 88]
207. wise(fred) [subsumption resolution 109,114]
212. calm(fred) [resolution 99,207]
213. $false [subsumption resolution 212,113]
% SZS output end Proof for 6179614632080574953454897
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not calm or tall then someone is either rich or not old. If fred is both not creative and not patient then someone is not funny and vice versa. If john is brave or humble then someone is generous or kind. If someone is either creative or not patient then someone is both not humble and patient and vice versa. If alice is both not rich and quiet then someone is not tall. Everyone who is both not patient and not creative is rich or not kind. Everyone who is either creative or tall is either not tall or rich. Everyone who is creative is both not rich and old. If someone is either not curious or humble then someone is either brave or wise. Everyone who is either wise or not rich is strong. If john is either not funny or kind then someone is both not wise and strong. If john is either not wise or not generous then someone is both not brave and not curious and vice versa. Everyone who is humble or old is both not humble and not quiet and vice versa. Everyone who is either not rich or quiet is both not funny and not tall. If lucy is both not generous and tall then someone is both calm and not humble and vice versa. Everyone who is not brave is not happy or not creative. John is either not curious or calm. Someone is humble or tall. Paul is funny or old. Someone is brave or not generous. Someone is both quiet and not humble. Someone is rich or not strong. Alice is not creative. Someone is strong or not brave. | Fred is not humble. | entailment | ((?[X]:((~calm(X)|tall(X))))=>(?[X]:((rich(X)<~>~old(X)))))&
(((~creative(fred)&~patient(fred)))<=>(?[X]:(~funny(X))))&
(((brave(john)|humble(john)))=>(?[X]:((generous(X)|kind(X)))))&
((?[X]:((creative(X)<~>~patient(X))))<=>(?[X]:((~humble(X)&patient(X)))))&
(((~rich(alice)&quiet(alice)))=>(?[X]:(~tall(X))))&
(![X]:((~patient(X)&~creative(X))=>(rich(X)|~kind(X))))&
(![X]:((creative(X)<~>tall(X))=>(~tall(X)<~>rich(X))))&
(![X]:(creative(X)=>(~rich(X)&old(X))))&
((?[X]:((~curious(X)<~>humble(X))))=>(?[X]:((brave(X)<~>wise(X)))))&
(![X]:((wise(X)<~>~rich(X))=>strong(X)))&
(((~funny(john)<~>kind(john)))=>(?[X]:((~wise(X)&strong(X)))))&
(((~wise(john)<~>~generous(john)))<=>(?[X]:((~brave(X)&~curious(X)))))&
(![X]:((humble(X)|old(X))<=>(~humble(X)&~quiet(X))))&
(![X]:((~rich(X)<~>quiet(X))=>(~funny(X)&~tall(X))))&
(((~generous(lucy)&tall(lucy)))<=>(?[X]:((calm(X)&~humble(X)))))&
(![X]:(~brave(X)=>(~happy(X)|~creative(X))))&
((~curious(john)<~>calm(john)))&
(?[X]:((humble(X)|tall(X))))&
((funny(paul)|old(paul)))&
(?[X]:((brave(X)|~generous(X))))&
(?[X]:((quiet(X)&~humble(X))))&
(?[X]:((rich(X)|~strong(X))))&
(~creative(alice))&
(?[X]:((strong(X)|~brave(X)))) | ~humble(fred) | [
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 714782346409923199961516
% SZS output start Proof for 714782346409923199961516
13. ! [X0] : ((old(X0) | humble(X0)) <=> (~quiet(X0) & ~humble(X0))) [input p12]
25. humble(fred) [input hypothesis]
73. ! [X0] : (((old(X0) | humble(X0)) | (quiet(X0) | humble(X0))) & ((~quiet(X0) & ~humble(X0)) | (~old(X0) & ~humble(X0)))) [nnf transformation 13]
74. ! [X0] : ((old(X0) | humble(X0) | quiet(X0) | humble(X0)) & ((~quiet(X0) & ~humble(X0)) | (~old(X0) & ~humble(X0)))) [flattening 73]
131. ~humble(X0) | ~humble(X0) [cnf transformation 74]
154. humble(fred) [cnf transformation 25]
155. ~humble(X0) [duplicate literal removal 131]
387. $false [subsumption resolution 154,155]
% SZS output end Proof for 714782346409923199961516
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old or calm then someone is not old.
Everyone who is not curious is either not generous or not creative.
Everyone who is not rich is either not strong or funny and vice versa.
If someone is funny or brave then mary is both creative and strong and vice versa.
Everyone who is either not brave or not old is wise and vice versa.
If susan is either not rich or wise then john is either not happy or not kind and vice versa.
If fred is wise or not kind then lucy is not wise or wise and vice versa.
Everyone who is either not patient or not generous is either brave or funny and vice versa.
If someone is either not happy or kind then lucy is calm.
Everyone who is not tall is not creative or not wise and vice versa.
Everyone who is not old or not generous is not funny or kind.
Everyone who is both humble and not tall is either brave or creative.
Everyone who is creative is kind and vice versa.
If lucy is both creative and calm then someone is both funny and not brave and vice versa.
If lucy is creative or not tall then someone is not quiet.
Everyone who is not kind is both not funny and not calm.
John is both not quiet and tall.
Alice is not curious or not creative.
John is funny.
Susan is not strong.
Paul is both calm and not rich.
Lucy is either not calm or not happy.
Someone is both not brave and strong.
Someone is not wise. | John is kind. | entailment | ((?[X]:((old(X)<~>calm(X))))=>(?[X]:(~old(X))))&
(![X]:(~curious(X)=>(~generous(X)<~>~creative(X))))&
(![X]:(~rich(X)<=>(~strong(X)<~>funny(X))))&
((?[X]:((funny(X)|brave(X))))<=>((creative(mary)&strong(mary))))&
(![X]:((~brave(X)<~>~old(X))<=>wise(X)))&
(((~rich(susan)<~>wise(susan)))<=>((~happy(john)<~>~kind(john))))&
(((wise(fred)|~kind(fred)))<=>((~wise(lucy)|wise(lucy))))&
(![X]:((~patient(X)<~>~generous(X))<=>(brave(X)<~>funny(X))))&
((?[X]:((~happy(X)<~>kind(X))))=>(calm(lucy)))&
(![X]:(~tall(X)<=>(~creative(X)|~wise(X))))&
(![X]:((~old(X)|~generous(X))=>(~funny(X)|kind(X))))&
(![X]:((humble(X)&~tall(X))=>(brave(X)<~>creative(X))))&
(![X]:(creative(X)<=>kind(X)))&
(((creative(lucy)&calm(lucy)))<=>(?[X]:((funny(X)&~brave(X)))))&
(((creative(lucy)|~tall(lucy)))=>(?[X]:(~quiet(X))))&
(![X]:(~kind(X)=>(~funny(X)&~calm(X))))&
((~quiet(john)&tall(john)))&
((~curious(alice)|~creative(alice)))&
(funny(john))&
(~strong(susan))&
((calm(paul)&~rich(paul)))&
((~calm(lucy)<~>~happy(lucy)))&
(?[X]:((~brave(X)&strong(X))))&
(?[X]:(~wise(X))) | kind(john) | [
"p9",
"p12",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 8788984013630788368201887
% SZS output start Proof for 8788984013630788368201887
10. ! [X0] : (~tall(X0) <=> (~wise(X0) | ~creative(X0))) [input p9]
13. ! [X0] : (creative(X0) <=> kind(X0)) [input p12]
17. tall(john) & ~quiet(john) [input p16]
25. ~kind(john) [input hypothesis]
27. ! [X0] : ((~wise(X0) | ~creative(X0)) => ~tall(X0)) [unused predicate definition removal 10]
28. tall(john) [pure predicate removal 17]
34. ! [X0] : (~tall(X0) | (wise(X0) & creative(X0))) [ennf transformation 27]
55. ! [X0] : ((creative(X0) | ~kind(X0)) & (kind(X0) | ~creative(X0))) [nnf transformation 13]
105. ~tall(X0) | creative(X0) [cnf transformation 34]
109. ~creative(X0) | kind(X0) [cnf transformation 55]
117. tall(john) [cnf transformation 28]
128. ~kind(john) [cnf transformation 25]
169. 10 <=> kind(john) [avatar definition]
170. ~kind(john) <- (~10) [avatar component clause 169]
252. ~10 [avatar split clause 128,169]
253. creative(john) [resolution 105,117]
256. kind(john) [resolution 109,253]
257. $false <- (~10) [subsumption resolution 256,170]
258. 10 [avatar contradiction clause 257]
259. $false [avatar sat refutation 252,258]
% SZS output end Proof for 8788984013630788368201887
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not kind is either humble or old.
If someone is either not kind or patient then someone is either brave or not generous and vice versa.
Everyone who is both kind and not quiet is old or happy and vice versa.
Everyone who is curious is both not old and not curious.
If someone is both not funny and not happy then susan is not happy or kind and vice versa.
Everyone who is not brave is either not strong or not humble and vice versa.
If susan is both not curious and calm then someone is both not patient and not rich and vice versa.
If someone is humble or not quiet then someone is both rich and old and vice versa.
If susan is either not funny or not generous then fred is both not calm and not happy.
Everyone who is creative or not strong is not creative.
Everyone who is creative is tall.
Everyone who is both not kind and not creative is either curious or not humble and vice versa.
Everyone who is both brave and not rich is either curious or not wise and vice versa.
Mary is not strong.
Someone is either not generous or funny.
Paul is tall.
Paul is both generous and not wise.
Alice is not curious or tall.
Someone is not wise. | Fred is not calm. | neutral | (![X]:(~kind(X)=>(humble(X)<~>old(X))))&
((?[X]:((~kind(X)<~>patient(X))))<=>(?[X]:((brave(X)<~>~generous(X)))))&
(![X]:((kind(X)&~quiet(X))<=>(old(X)|happy(X))))&
(![X]:(curious(X)=>(~old(X)&~curious(X))))&
((?[X]:((~funny(X)&~happy(X))))<=>((~happy(susan)|kind(susan))))&
(![X]:(~brave(X)<=>(~strong(X)<~>~humble(X))))&
(((~curious(susan)&calm(susan)))<=>(?[X]:((~patient(X)&~rich(X)))))&
((?[X]:((humble(X)|~quiet(X))))<=>(?[X]:((rich(X)&old(X)))))&
(((~funny(susan)<~>~generous(susan)))=>((~calm(fred)&~happy(fred))))&
(![X]:((creative(X)|~strong(X))=>~creative(X)))&
(![X]:(creative(X)=>tall(X)))&
(![X]:((~kind(X)&~creative(X))<=>(curious(X)<~>~humble(X))))&
(![X]:((brave(X)&~rich(X))<=>(curious(X)<~>~wise(X))))&
(~strong(mary))&
(?[X]:((~generous(X)<~>funny(X))))&
(tall(paul))&
((generous(paul)&~wise(paul)))&
((~curious(alice)|tall(alice)))&
(?[X]:(~wise(X))) | ~calm(fred) | [] | null | 0 |
Everyone who is not curious is both not old and not quiet. Everyone who is both kind and not wise is both not humble and rich. If someone is not creative then someone is both not happy and humble and vice versa. Everyone who is not tall is either not old or not brave and vice versa. If someone is either calm or not kind then mary is either not calm or not old and vice versa. Everyone who is patient or tall is funny or calm and vice versa. Everyone who is either not old or not creative is wise or generous. Everyone who is both old and not strong is funny and vice versa. If john is either not strong or creative then mary is both not old and not strong. If someone is wise or not funny then someone is both not humble and creative and vice versa. Everyone who is happy or not humble is both brave and humble. If someone is either not kind or not creative then someone is not generous and vice versa. If someone is either rich or calm then someone is not curious and vice versa. If someone is tall or brave then susan is not calm or not creative and vice versa. If fred is not patient or humble then someone is not tall. Lucy is not happy. Lucy is brave or not calm. Lucy is both not creative and funny. Fred is happy. Lucy is brave or not tall. Mary is either calm or humble. Someone is not brave. | Fred is kind. | contradiction | (![X]:(~curious(X)=>(~old(X)&~quiet(X))))&
(![X]:((kind(X)&~wise(X))=>(~humble(X)&rich(X))))&
((?[X]:(~creative(X)))<=>(?[X]:((~happy(X)&humble(X)))))&
(![X]:(~tall(X)<=>(~old(X)<~>~brave(X))))&
((?[X]:((calm(X)<~>~kind(X))))<=>((~calm(mary)<~>~old(mary))))&
(![X]:((patient(X)|tall(X))<=>(funny(X)|calm(X))))&
(![X]:((~old(X)<~>~creative(X))=>(wise(X)|generous(X))))&
(![X]:((old(X)&~strong(X))<=>funny(X)))&
(((~strong(john)<~>creative(john)))=>((~old(mary)&~strong(mary))))&
((?[X]:((wise(X)|~funny(X))))<=>(?[X]:((~humble(X)&creative(X)))))&
(![X]:((happy(X)|~humble(X))=>(brave(X)&humble(X))))&
((?[X]:((~kind(X)<~>~creative(X))))<=>(?[X]:(~generous(X))))&
((?[X]:((rich(X)<~>calm(X))))<=>(?[X]:(~curious(X))))&
((?[X]:((tall(X)|brave(X))))<=>((~calm(susan)|~creative(susan))))&
(((~patient(fred)|humble(fred)))=>(?[X]:(~tall(X))))&
(~happy(lucy))&
((brave(lucy)|~calm(lucy)))&
((~creative(lucy)&funny(lucy)))&
(happy(fred))&
((brave(lucy)|~tall(lucy)))&
((calm(mary)<~>humble(mary)))&
(?[X]:(~brave(X))) | kind(fred) | [
"p1",
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 373571433468524299952935
% SZS output start Proof for 373571433468524299952935
2. ! [X0] : ((~wise(X0) & kind(X0)) => (rich(X0) & ~humble(X0))) [input p1]
10. ? [X0] : (~funny(X0) | wise(X0)) <=> ? [X0] : (creative(X0) & ~humble(X0)) [input p9]
11. ! [X0] : ((~humble(X0) | happy(X0)) => (humble(X0) & brave(X0))) [input p10]
23. kind(fred) [input hypothesis]
25. ? [X0] : (~funny(X0) | wise(X0)) <=> ? [X1] : (creative(X1) & ~humble(X1)) [rectify 10]
30. ! [X0] : ((rich(X0) & ~humble(X0)) | (wise(X0) | ~kind(X0))) [ennf transformation 2]
31. ! [X0] : ((rich(X0) & ~humble(X0)) | wise(X0) | ~kind(X0)) [flattening 30]
35. ! [X0] : ((humble(X0) & brave(X0)) | (humble(X0) & ~happy(X0))) [ennf transformation 11]
53. (? [X0] : (~funny(X0) | wise(X0)) | ! [X1] : (~creative(X1) | humble(X1))) & (? [X1] : (creative(X1) & ~humble(X1)) | ! [X0] : (funny(X0) & ~wise(X0))) [nnf transformation 25]
54. (? [X0] : (~funny(X0) | wise(X0)) | ! [X1] : (~creative(X1) | humble(X1))) & (? [X2] : (creative(X2) & ~humble(X2)) | ! [X3] : (funny(X3) & ~wise(X3))) [rectify 53]
55. ? [X0] : (~funny(X0) | wise(X0)) => (~funny(sK3) | wise(sK3)) [choice axiom]
56. ? [X2] : (creative(X2) & ~humble(X2)) => (creative(sK4) & ~humble(sK4)) [choice axiom]
57. ((~funny(sK3) | wise(sK3)) | ! [X1] : (~creative(X1) | humble(X1))) & ((creative(sK4) & ~humble(sK4)) | ! [X3] : (funny(X3) & ~wise(X3))) [skolemisation 54,56,55]
79. ~humble(X0) | wise(X0) | ~kind(X0) [cnf transformation 31]
109. ~humble(sK4) | ~wise(X3) [cnf transformation 57]
117. humble(X0) | humble(X0) [cnf transformation 35]
141. kind(fred) [cnf transformation 23]
142. humble(X0) [duplicate literal removal 117]
231. 20 <=> ! [X3] : ~wise(X3) [avatar definition]
232. ~wise(X3) <- (20) [avatar component clause 231]
235. 21 <=> humble(sK4) [avatar definition]
237. ~humble(sK4) <- (~21) [avatar component clause 235]
239. 20 | ~21 [avatar split clause 109,235,231]
333. $false <- (~21) [subsumption resolution 237,142]
334. 21 [avatar contradiction clause 333]
371. wise(X0) | ~kind(X0) [resolution 79,142]
372. ~kind(X0) <- (20) [subsumption resolution 371,232]
393. $false <- (20) [resolution 372,141]
400. ~20 [avatar contradiction clause 393]
402. $false [avatar sat refutation 239,334,400]
% SZS output end Proof for 373571433468524299952935
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not patient or old is funny and vice versa.
If lucy is wise then paul is rich and vice versa.
If john is not funny or not wise then fred is both brave and strong.
If lucy is rich or happy then someone is either kind or calm.
Everyone who is not strong or not patient is both strong and calm.
If fred is either tall or happy then someone is either not strong or not calm and vice versa.
Everyone who is humble or not wise is both not generous and funny.
If paul is not quiet or not kind then someone is either tall or wise and vice versa.
Everyone who is either not rich or not generous is both not generous and not kind.
Everyone who is either strong or kind is both not strong and not kind and vice versa.
If john is both not quiet and not rich then someone is tall and vice versa.
If paul is not rich then someone is not patient.
Everyone who is patient is not patient or not quiet.
Everyone who is either not generous or quiet is not curious or not tall and vice versa.
If alice is either not funny or happy then someone is both not kind and old.
Everyone who is either not old or not strong is either humble or not funny and vice versa.
Paul is both not brave and kind.
Susan is not creative or curious.
Someone is not creative or kind.
Alice is either not curious or not kind.
Lucy is not calm.
Someone is both not humble and not calm.
Someone is both not curious and not happy. | Alice is not kind. | contradiction | (![X]:((~patient(X)<~>old(X))<=>funny(X)))&
((wise(lucy))<=>(rich(paul)))&
(((~funny(john)|~wise(john)))=>((brave(fred)&strong(fred))))&
(((rich(lucy)|happy(lucy)))=>(?[X]:((kind(X)<~>calm(X)))))&
(![X]:((~strong(X)|~patient(X))=>(strong(X)&calm(X))))&
(((tall(fred)<~>happy(fred)))<=>(?[X]:((~strong(X)<~>~calm(X)))))&
(![X]:((humble(X)|~wise(X))=>(~generous(X)&funny(X))))&
(((~quiet(paul)|~kind(paul)))<=>(?[X]:((tall(X)<~>wise(X)))))&
(![X]:((~rich(X)<~>~generous(X))=>(~generous(X)&~kind(X))))&
(![X]:((strong(X)<~>kind(X))<=>(~strong(X)&~kind(X))))&
(((~quiet(john)&~rich(john)))<=>(?[X]:(tall(X))))&
((~rich(paul))=>(?[X]:(~patient(X))))&
(![X]:(patient(X)=>(~patient(X)|~quiet(X))))&
(![X]:((~generous(X)<~>quiet(X))<=>(~curious(X)|~tall(X))))&
(((~funny(alice)<~>happy(alice)))=>(?[X]:((~kind(X)&old(X)))))&
(![X]:((~old(X)<~>~strong(X))<=>(humble(X)<~>~funny(X))))&
((~brave(paul)&kind(paul)))&
((~creative(susan)|curious(susan)))&
(?[X]:((~creative(X)|kind(X))))&
((~curious(alice)<~>~kind(alice)))&
(~calm(lucy))&
(?[X]:((~humble(X)&~calm(X))))&
(?[X]:((~curious(X)&~happy(X)))) | ~kind(alice) | [
"p4",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 1577437492987016925347782
% SZS output start Proof for 1577437492987016925347782
5. ! [X0] : ((~patient(X0) | ~strong(X0)) => (calm(X0) & strong(X0))) [input p4]
10. ! [X0] : ((strong(X0) <~> kind(X0)) <=> (~kind(X0) & ~strong(X0))) [input p9]
24. ~kind(alice) [input hypothesis]
29. ! [X0] : ((calm(X0) & strong(X0)) | (patient(X0) & strong(X0))) [ennf transformation 5]
51. ! [X0] : ((((~kind(X0) | ~strong(X0)) & (kind(X0) | strong(X0))) | (kind(X0) | strong(X0))) & ((~kind(X0) & ~strong(X0)) | ((strong(X0) | ~kind(X0)) & (kind(X0) | ~strong(X0))))) [nnf transformation 10]
52. ! [X0] : ((((~kind(X0) | ~strong(X0)) & (kind(X0) | strong(X0))) | kind(X0) | strong(X0)) & ((~kind(X0) & ~strong(X0)) | ((strong(X0) | ~kind(X0)) & (kind(X0) | ~strong(X0))))) [flattening 51]
85. strong(X0) | strong(X0) [cnf transformation 29]
111. ~strong(X0) | kind(X0) | ~strong(X0) [cnf transformation 52]
149. ~kind(alice) [cnf transformation 24]
151. ~strong(X0) | kind(X0) [duplicate literal removal 111]
155. strong(X0) [duplicate literal removal 85]
257. kind(X0) [subsumption resolution 151,155]
305. $false [subsumption resolution 149,257]
% SZS output end Proof for 1577437492987016925347782
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.046 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either funny or rich is not happy or not old and vice versa. Everyone who is not curious is both brave and not funny and vice versa. If fred is brave then someone is kind or not patient. Everyone who is not wise or kind is not strong and vice versa. Everyone who is not kind or wise is not kind. If someone is either not calm or funny then alice is not old or calm and vice versa. If someone is not strong or not calm then fred is both not funny and strong and vice versa. If paul is strong then alice is both curious and calm and vice versa. Everyone who is both not creative and not happy is either curious or not tall. Everyone who is not strong or calm is not quiet. If john is old then someone is not funny. If susan is not curious or calm then fred is either brave or not wise. Everyone who is humble is either calm or not tall. If someone is patient or not old then alice is not brave or generous and vice versa. If someone is both not humble and strong then alice is not happy or not patient. Everyone who is generous or funny is patient or not rich and vice versa. Lucy is not brave. Alice is old. Someone is either calm or curious. Someone is strong or not wise. Paul is curious. Susan is not creative or not patient. Someone is either creative or not creative. Someone is both not tall and curious. | Fred is not kind. | entailment | (![X]:((funny(X)<~>rich(X))<=>(~happy(X)|~old(X))))&
(![X]:(~curious(X)<=>(brave(X)&~funny(X))))&
((brave(fred))=>(?[X]:((kind(X)|~patient(X)))))&
(![X]:((~wise(X)|kind(X))<=>~strong(X)))&
(![X]:((~kind(X)|wise(X))=>~kind(X)))&
((?[X]:((~calm(X)<~>funny(X))))<=>((~old(alice)|calm(alice))))&
((?[X]:((~strong(X)|~calm(X))))<=>((~funny(fred)&strong(fred))))&
((strong(paul))<=>((curious(alice)&calm(alice))))&
(![X]:((~creative(X)&~happy(X))=>(curious(X)<~>~tall(X))))&
(![X]:((~strong(X)|calm(X))=>~quiet(X)))&
((old(john))=>(?[X]:(~funny(X))))&
(((~curious(susan)|calm(susan)))=>((brave(fred)<~>~wise(fred))))&
(![X]:(humble(X)=>(calm(X)<~>~tall(X))))&
((?[X]:((patient(X)|~old(X))))<=>((~brave(alice)|generous(alice))))&
((?[X]:((~humble(X)&strong(X))))=>((~happy(alice)|~patient(alice))))&
(![X]:((generous(X)|funny(X))<=>(patient(X)|~rich(X))))&
(~brave(lucy))&
(old(alice))&
(?[X]:((calm(X)<~>curious(X))))&
(?[X]:((strong(X)|~wise(X))))&
(curious(paul))&
((~creative(susan)|~patient(susan)))&
(?[X]:((creative(X)<~>~creative(X))))&
(?[X]:((~tall(X)&curious(X)))) | ~kind(fred) | [
"p3",
"p4",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 3155559906124503843884363
% SZS output start Proof for 3155559906124503843884363
4. ! [X0] : ((kind(X0) | ~wise(X0)) <=> ~strong(X0)) [input p3]
5. ! [X0] : ((wise(X0) | ~kind(X0)) => ~kind(X0)) [input p4]
7. ? [X0] : (~calm(X0) | ~strong(X0)) <=> (strong(fred) & ~funny(fred)) [input p6]
25. kind(fred) [input hypothesis]
28. ! [X0] : (~kind(X0) | (~wise(X0) & kind(X0))) [ennf transformation 5]
42. ! [X0] : (((kind(X0) | ~wise(X0)) | strong(X0)) & (~strong(X0) | (~kind(X0) & wise(X0)))) [nnf transformation 4]
43. ! [X0] : ((kind(X0) | ~wise(X0) | strong(X0)) & (~strong(X0) | (~kind(X0) & wise(X0)))) [flattening 42]
49. (? [X0] : (~calm(X0) | ~strong(X0)) | (~strong(fred) | funny(fred))) & ((strong(fred) & ~funny(fred)) | ! [X0] : (calm(X0) & strong(X0))) [nnf transformation 7]
50. (? [X0] : (~calm(X0) | ~strong(X0)) | ~strong(fred) | funny(fred)) & ((strong(fred) & ~funny(fred)) | ! [X0] : (calm(X0) & strong(X0))) [flattening 49]
51. (? [X0] : (~calm(X0) | ~strong(X0)) | ~strong(fred) | funny(fred)) & ((strong(fred) & ~funny(fred)) | ! [X1] : (calm(X1) & strong(X1))) [rectify 50]
52. ? [X0] : (~calm(X0) | ~strong(X0)) => (~calm(sK2) | ~strong(sK2)) [choice axiom]
53. ((~calm(sK2) | ~strong(sK2)) | ~strong(fred) | funny(fred)) & ((strong(fred) & ~funny(fred)) | ! [X1] : (calm(X1) & strong(X1))) [skolemisation 51,52]
88. ~strong(X0) | wise(X0) [cnf transformation 43]
89. ~strong(X0) | ~kind(X0) [cnf transformation 43]
92. ~wise(X0) | ~kind(X0) [cnf transformation 28]
101. strong(fred) | strong(X1) [cnf transformation 53]
136. kind(fred) [cnf transformation 25]
183. 11 <=> strong(fred) [avatar definition]
184. strong(fred) <- (11) [avatar component clause 183]
200. 15 <=> ! [X1] : strong(X1) [avatar definition]
201. strong(X1) <- (15) [avatar component clause 200]
202. 15 | 11 [avatar split clause 101,183,200]
230. 21 <=> wise(fred) [avatar definition]
231. ~wise(fred) <- (~21) [avatar component clause 230]
232. wise(fred) <- (21) [avatar component clause 230]
314. wise(fred) <- (11) [resolution 88,184]
315. $false <- (11, ~21) [subsumption resolution 314,231]
316. ~11 | 21 [avatar contradiction clause 315]
328. ~kind(X0) <- (15) [resolution 89,201]
331. ~kind(fred) <- (21) [resolution 92,232]
333. $false <- (15) [resolution 328,136]
334. ~15 [avatar contradiction clause 333]
335. $false <- (21) [subsumption resolution 331,136]
336. ~21 [avatar contradiction clause 335]
337. $false [avatar sat refutation 202,316,334,336]
% SZS output end Proof for 3155559906124503843884363
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not rich and not generous is either quiet or not tall and vice versa.
If someone is both not funny and curious then someone is both quiet and not humble and vice versa.
If fred is either strong or not creative then someone is patient or creative.
If susan is both not brave and wise then someone is calm.
Everyone who is both wise and generous is both not quiet and curious and vice versa.
If fred is not quiet or not kind then someone is both happy and creative and vice versa.
If susan is both strong and not patient then someone is either curious or quiet.
Everyone who is creative is funny.
Everyone who is not brave is either brave or not happy and vice versa.
Everyone who is not old is either generous or not patient.
If lucy is both patient and not happy then paul is either quiet or not humble.
Everyone who is rich is patient and vice versa.
Everyone who is both not wise and not generous is both happy and generous.
If someone is strong or not quiet then someone is curious or not tall.
If paul is either brave or not calm then mary is not kind or not humble and vice versa.
Everyone who is both not rich and brave is both brave and not calm and vice versa.
Susan is both not curious and old.
Someone is curious.
Fred is either not calm or not rich.
Someone is generous.
Someone is both quiet and not happy.
Someone is either curious or humble. | Lucy is generous. | neutral | (![X]:((~rich(X)&~generous(X))<=>(quiet(X)<~>~tall(X))))&
((?[X]:((~funny(X)&curious(X))))<=>(?[X]:((quiet(X)&~humble(X)))))&
(((strong(fred)<~>~creative(fred)))=>(?[X]:((patient(X)|creative(X)))))&
(((~brave(susan)&wise(susan)))=>(?[X]:(calm(X))))&
(![X]:((wise(X)&generous(X))<=>(~quiet(X)&curious(X))))&
(((~quiet(fred)|~kind(fred)))<=>(?[X]:((happy(X)&creative(X)))))&
(((strong(susan)&~patient(susan)))=>(?[X]:((curious(X)<~>quiet(X)))))&
(![X]:(creative(X)=>funny(X)))&
(![X]:(~brave(X)<=>(brave(X)<~>~happy(X))))&
(![X]:(~old(X)=>(generous(X)<~>~patient(X))))&
(((patient(lucy)&~happy(lucy)))=>((quiet(paul)<~>~humble(paul))))&
(![X]:(rich(X)<=>patient(X)))&
(![X]:((~wise(X)&~generous(X))=>(happy(X)&generous(X))))&
((?[X]:((strong(X)|~quiet(X))))=>(?[X]:((curious(X)|~tall(X)))))&
(((brave(paul)<~>~calm(paul)))<=>((~kind(mary)|~humble(mary))))&
(![X]:((~rich(X)&brave(X))<=>(brave(X)&~calm(X))))&
((~curious(susan)&old(susan)))&
(?[X]:(curious(X)))&
((~calm(fred)<~>~rich(fred)))&
(?[X]:(generous(X)))&
(?[X]:((quiet(X)&~happy(X))))&
(?[X]:((curious(X)<~>humble(X)))) | generous(lucy) | [] | null | 0 |
If someone is either rich or not old then someone is both generous and not creative. If someone is both happy and creative then someone is humble and vice versa. Everyone who is not happy is both not creative and not happy and vice versa. If someone is either not humble or not kind then paul is either not kind or humble and vice versa. Everyone who is both calm and not kind is either not funny or calm and vice versa. If paul is either happy or not patient then john is either not quiet or not patient and vice versa. If someone is not patient or not calm then fred is both not rich and old and vice versa. Everyone who is not patient is both not curious and not old. If someone is not tall then someone is either not rich or not quiet and vice versa. Everyone who is not funny is patient or not generous. Everyone who is either humble or generous is both not humble and wise and vice versa. Everyone who is patient is either wise or quiet and vice versa. Everyone who is not rich or not quiet is not tall or not funny. Everyone who is both not funny and not happy is patient or not tall and vice versa. Everyone who is brave is not humble and vice versa. If alice is funny or not calm then paul is either old or kind. Someone is either not creative or not quiet. Lucy is not calm. Someone is rich or not tall. Someone is not brave. Paul is both not happy and wise. Mary is both not calm and creative. Someone is either not patient or patient. Alice is both rich and funny. | Mary is curious. | contradiction | ((?[X]:((rich(X)<~>~old(X))))=>(?[X]:((generous(X)&~creative(X)))))&
((?[X]:((happy(X)&creative(X))))<=>(?[X]:(humble(X))))&
(![X]:(~happy(X)<=>(~creative(X)&~happy(X))))&
((?[X]:((~humble(X)<~>~kind(X))))<=>((~kind(paul)<~>humble(paul))))&
(![X]:((calm(X)&~kind(X))<=>(~funny(X)<~>calm(X))))&
(((happy(paul)<~>~patient(paul)))<=>((~quiet(john)<~>~patient(john))))&
((?[X]:((~patient(X)|~calm(X))))<=>((~rich(fred)&old(fred))))&
(![X]:(~patient(X)=>(~curious(X)&~old(X))))&
((?[X]:(~tall(X)))<=>(?[X]:((~rich(X)<~>~quiet(X)))))&
(![X]:(~funny(X)=>(patient(X)|~generous(X))))&
(![X]:((humble(X)<~>generous(X))<=>(~humble(X)&wise(X))))&
(![X]:(patient(X)<=>(wise(X)<~>quiet(X))))&
(![X]:((~rich(X)|~quiet(X))=>(~tall(X)|~funny(X))))&
(![X]:((~funny(X)&~happy(X))<=>(patient(X)|~tall(X))))&
(![X]:(brave(X)<=>~humble(X)))&
(((funny(alice)|~calm(alice)))=>((old(paul)<~>kind(paul))))&
(?[X]:((~creative(X)<~>~quiet(X))))&
(~calm(lucy))&
(?[X]:((rich(X)|~tall(X))))&
(?[X]:(~brave(X)))&
((~happy(paul)&wise(paul)))&
((~calm(mary)&creative(mary)))&
(?[X]:((~patient(X)<~>patient(X))))&
((rich(alice)&funny(alice))) | curious(mary) | [
"p2",
"p7",
"p13",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 2732197631689103675476201
% SZS output start Proof for 2732197631689103675476201
3. ! [X0] : (~happy(X0) <=> (~happy(X0) & ~creative(X0))) [input p2]
8. ! [X0] : (~patient(X0) => (~old(X0) & ~curious(X0))) [input p7]
14. ! [X0] : ((~happy(X0) & ~funny(X0)) <=> (~tall(X0) | patient(X0))) [input p13]
22. creative(mary) & ~calm(mary) [input p21]
25. curious(mary) [input hypothesis]
31. ! [X0] : ((~old(X0) & ~curious(X0)) | patient(X0)) [ennf transformation 8]
47. ! [X0] : ((~happy(X0) | (happy(X0) | creative(X0))) & ((~happy(X0) & ~creative(X0)) | happy(X0))) [nnf transformation 3]
48. ! [X0] : ((~happy(X0) | happy(X0) | creative(X0)) & ((~happy(X0) & ~creative(X0)) | happy(X0))) [flattening 47]
69. ! [X0] : (((~happy(X0) & ~funny(X0)) | (tall(X0) & ~patient(X0))) & ((~tall(X0) | patient(X0)) | (happy(X0) | funny(X0)))) [nnf transformation 14]
70. ! [X0] : (((~happy(X0) & ~funny(X0)) | (tall(X0) & ~patient(X0))) & (~tall(X0) | patient(X0) | happy(X0) | funny(X0))) [flattening 69]
89. ~creative(X0) | happy(X0) [cnf transformation 48]
119. ~curious(X0) | patient(X0) [cnf transformation 31]
141. ~patient(X0) | ~happy(X0) [cnf transformation 70]
156. creative(mary) [cnf transformation 22]
161. curious(mary) [cnf transformation 25]
365. happy(mary) [resolution 89,156]
368. patient(mary) [resolution 119,161]
375. ~happy(mary) [resolution 141,368]
377. $false [subsumption resolution 375,365]
% SZS output end Proof for 2732197631689103675476201
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall is either quiet or kind. Everyone who is both generous and quiet is not creative or not happy. Everyone who is not wise or humble is both tall and not humble and vice versa. Everyone who is kind is either not rich or not tall and vice versa. Everyone who is either patient or not quiet is both not wise and happy. If someone is patient or humble then mary is either not curious or calm. If fred is not old then someone is either creative or patient and vice versa. Everyone who is not tall is both not strong and not wise. Everyone who is not happy or not patient is both not humble and funny and vice versa. Everyone who is not generous or kind is not rich and vice versa. If someone is either patient or not wise then john is not creative. If paul is brave or wise then someone is kind and vice versa. Everyone who is either tall or old is both not brave and happy. Everyone who is both wise and not quiet is humble or not brave. If someone is not kind then someone is both not tall and curious and vice versa. Everyone who is not kind or not tall is either strong or not calm and vice versa. Someone is funny or not generous. Lucy is patient or not old. Fred is happy or funny. Someone is not brave or old. John is either not calm or not brave. John is kind or not rich. | Mary is not old. | neutral | (![X]:(tall(X)=>(quiet(X)<~>kind(X))))&
(![X]:((generous(X)&quiet(X))=>(~creative(X)|~happy(X))))&
(![X]:((~wise(X)|humble(X))<=>(tall(X)&~humble(X))))&
(![X]:(kind(X)<=>(~rich(X)<~>~tall(X))))&
(![X]:((patient(X)<~>~quiet(X))=>(~wise(X)&happy(X))))&
((?[X]:((patient(X)|humble(X))))=>((~curious(mary)<~>calm(mary))))&
((~old(fred))<=>(?[X]:((creative(X)<~>patient(X)))))&
(![X]:(~tall(X)=>(~strong(X)&~wise(X))))&
(![X]:((~happy(X)|~patient(X))<=>(~humble(X)&funny(X))))&
(![X]:((~generous(X)|kind(X))<=>~rich(X)))&
((?[X]:((patient(X)<~>~wise(X))))=>(~creative(john)))&
(((brave(paul)|wise(paul)))<=>(?[X]:(kind(X))))&
(![X]:((tall(X)<~>old(X))=>(~brave(X)&happy(X))))&
(![X]:((wise(X)&~quiet(X))=>(humble(X)|~brave(X))))&
((?[X]:(~kind(X)))<=>(?[X]:((~tall(X)&curious(X)))))&
(![X]:((~kind(X)|~tall(X))<=>(strong(X)<~>~calm(X))))&
(?[X]:((funny(X)|~generous(X))))&
((patient(lucy)|~old(lucy)))&
((happy(fred)|funny(fred)))&
(?[X]:((~brave(X)|old(X))))&
((~calm(john)<~>~brave(john)))&
((kind(john)|~rich(john))) | ~old(mary) | [] | null | 0 |
Everyone who is either not old or not creative is either humble or generous and vice versa.
If someone is creative or calm then someone is not old or rich and vice versa.
Everyone who is either creative or generous is both not strong and creative.
If fred is not kind or funny then mary is not quiet.
Everyone who is not wise is rich or not patient and vice versa.
If paul is kind or brave then someone is not patient.
Everyone who is both not wise and not brave is not tall.
If someone is both generous and not rich then fred is not wise.
Everyone who is not curious or not patient is both brave and not rich.
If susan is both not humble and generous then alice is either not old or not tall.
Everyone who is not patient or not rich is generous and vice versa.
If someone is funny then someone is calm.
Everyone who is both rich and old is generous or not brave and vice versa.
If someone is not creative then lucy is not generous or not creative and vice versa.
If someone is not tall then lucy is either brave or not calm and vice versa.
If susan is not patient then john is both not quiet and humble and vice versa.
Someone is both rich and happy.
Someone is both not calm and funny.
Someone is not tall or patient.
Someone is calm or not rich.
Alice is kind.
Someone is either not generous or brave.
Someone is either not generous or not patient. | Lucy is not patient. | contradiction | (![X]:((~old(X)<~>~creative(X))<=>(humble(X)<~>generous(X))))&
((?[X]:((creative(X)|calm(X))))<=>(?[X]:((~old(X)|rich(X)))))&
(![X]:((creative(X)<~>generous(X))=>(~strong(X)&creative(X))))&
(((~kind(fred)|funny(fred)))=>(~quiet(mary)))&
(![X]:(~wise(X)<=>(rich(X)|~patient(X))))&
(((kind(paul)|brave(paul)))=>(?[X]:(~patient(X))))&
(![X]:((~wise(X)&~brave(X))=>~tall(X)))&
((?[X]:((generous(X)&~rich(X))))=>(~wise(fred)))&
(![X]:((~curious(X)|~patient(X))=>(brave(X)&~rich(X))))&
(((~humble(susan)&generous(susan)))=>((~old(alice)<~>~tall(alice))))&
(![X]:((~patient(X)|~rich(X))<=>generous(X)))&
((?[X]:(funny(X)))=>(?[X]:(calm(X))))&
(![X]:((rich(X)&old(X))<=>(generous(X)|~brave(X))))&
((?[X]:(~creative(X)))<=>((~generous(lucy)|~creative(lucy))))&
((?[X]:(~tall(X)))<=>((brave(lucy)<~>~calm(lucy))))&
((~patient(susan))<=>((~quiet(john)&humble(john))))&
(?[X]:((rich(X)&happy(X))))&
(?[X]:((~calm(X)&funny(X))))&
(?[X]:((~tall(X)|patient(X))))&
(?[X]:((calm(X)|~rich(X))))&
(kind(alice))&
(?[X]:((~generous(X)<~>brave(X))))&
(?[X]:((~generous(X)<~>~patient(X)))) | ~patient(lucy) | [
"p8",
"p10",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 3546311908501406539649979
% SZS output start Proof for 3546311908501406539649979
9. ! [X0] : ((~patient(X0) | ~curious(X0)) => (~rich(X0) & brave(X0))) [input p8]
11. ! [X0] : ((~rich(X0) | ~patient(X0)) <=> generous(X0)) [input p10]
13. ! [X0] : ((old(X0) & rich(X0)) <=> (~brave(X0) | generous(X0))) [input p12]
24. ~patient(lucy) [input hypothesis]
28. ! [X0] : (~patient(X0) => (~rich(X0) & brave(X0))) [pure predicate removal 9]
36. ! [X0] : ((~rich(X0) & brave(X0)) | patient(X0)) [ennf transformation 28]
52. ! [X0] : (((~rich(X0) | ~patient(X0)) | ~generous(X0)) & (generous(X0) | (rich(X0) & patient(X0)))) [nnf transformation 11]
53. ! [X0] : ((~rich(X0) | ~patient(X0) | ~generous(X0)) & (generous(X0) | (rich(X0) & patient(X0)))) [flattening 52]
57. ! [X0] : (((old(X0) & rich(X0)) | (brave(X0) & ~generous(X0))) & ((~brave(X0) | generous(X0)) | (~old(X0) | ~rich(X0)))) [nnf transformation 13]
58. ! [X0] : (((old(X0) & rich(X0)) | (brave(X0) & ~generous(X0))) & (~brave(X0) | generous(X0) | ~old(X0) | ~rich(X0))) [flattening 57]
108. ~rich(X0) | patient(X0) [cnf transformation 36]
111. patient(X0) | generous(X0) [cnf transformation 53]
113. ~rich(X0) | ~patient(X0) | ~generous(X0) [cnf transformation 53]
116. rich(X0) | ~generous(X0) [cnf transformation 58]
140. ~patient(lucy) [cnf transformation 24]
228. ~rich(X0) | ~generous(X0) [subsumption resolution 113,108]
237. ~generous(X0) [subsumption resolution 116,228]
310. generous(lucy) [resolution 111,140]
313. $false [subsumption resolution 310,237]
% SZS output end Proof for 3546311908501406539649979
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If mary is strong or not brave then mary is both not rich and quiet.
If someone is both tall and not generous then someone is either not strong or creative.
Everyone who is either not happy or calm is not creative.
If alice is both not happy and not funny then lucy is not strong or quiet and vice versa.
Everyone who is not curious or quiet is calm.
Everyone who is both brave and generous is not calm or quiet.
Everyone who is both not brave and happy is quiet and vice versa.
If someone is either curious or not wise then someone is not old or not tall.
If someone is either wise or strong then someone is not humble.
If alice is both not humble and brave then someone is both not happy and calm.
Everyone who is patient is either not quiet or strong and vice versa.
Everyone who is funny or wise is happy.
Everyone who is both patient and rich is not funny and vice versa.
If lucy is not humble or happy then susan is either not wise or happy and vice versa.
If someone is not brave or brave then lucy is either not quiet or curious.
Everyone who is either old or wise is both not creative and not funny and vice versa.
Someone is not patient or brave.
Alice is wise or not quiet.
Someone is not creative.
Susan is funny or not rich.
Lucy is not creative or not funny.
Paul is not kind.
Someone is kind.
John is either curious or not brave. | Alice is funny. | neutral | (((strong(mary)|~brave(mary)))=>((~rich(mary)&quiet(mary))))&
((?[X]:((tall(X)&~generous(X))))=>(?[X]:((~strong(X)<~>creative(X)))))&
(![X]:((~happy(X)<~>calm(X))=>~creative(X)))&
(((~happy(alice)&~funny(alice)))<=>((~strong(lucy)|quiet(lucy))))&
(![X]:((~curious(X)|quiet(X))=>calm(X)))&
(![X]:((brave(X)&generous(X))=>(~calm(X)|quiet(X))))&
(![X]:((~brave(X)&happy(X))<=>quiet(X)))&
((?[X]:((curious(X)<~>~wise(X))))=>(?[X]:((~old(X)|~tall(X)))))&
((?[X]:((wise(X)<~>strong(X))))=>(?[X]:(~humble(X))))&
(((~humble(alice)&brave(alice)))=>(?[X]:((~happy(X)&calm(X)))))&
(![X]:(patient(X)<=>(~quiet(X)<~>strong(X))))&
(![X]:((funny(X)|wise(X))=>happy(X)))&
(![X]:((patient(X)&rich(X))<=>~funny(X)))&
(((~humble(lucy)|happy(lucy)))<=>((~wise(susan)<~>happy(susan))))&
((?[X]:((~brave(X)|brave(X))))=>((~quiet(lucy)<~>curious(lucy))))&
(![X]:((old(X)<~>wise(X))<=>(~creative(X)&~funny(X))))&
(?[X]:((~patient(X)|brave(X))))&
((wise(alice)|~quiet(alice)))&
(?[X]:(~creative(X)))&
((funny(susan)|~rich(susan)))&
((~creative(lucy)|~funny(lucy)))&
(~kind(paul))&
(?[X]:(kind(X)))&
((curious(john)<~>~brave(john))) | funny(alice) | [] | null | 0 |
Everyone who is creative is either rich or creative and vice versa.
Everyone who is not wise or strong is both patient and not creative and vice versa.
If someone is either not tall or not old then susan is strong and vice versa.
If someone is strong or patient then mary is both generous and not calm.
If alice is tall or creative then fred is not kind or not humble and vice versa.
Everyone who is not creative or quiet is both tall and not strong.
If john is not happy or not kind then john is not quiet and vice versa.
If someone is not curious then lucy is happy.
Everyone who is not kind or not rich is either kind or not humble.
If john is both not happy and strong then someone is happy or kind.
Everyone who is not brave is tall or not funny and vice versa.
Everyone who is generous is not kind or quiet and vice versa.
Everyone who is both not generous and creative is both patient and tall.
If someone is curious then fred is funny and vice versa.
Everyone who is not rich is both not humble and not curious and vice versa.
Mary is both tall and quiet.
Lucy is tall or happy.
Someone is generous.
Someone is not happy.
Someone is wise.
Mary is not strong. | Fred is not humble. | entailment | (![X]:(creative(X)<=>(rich(X)<~>creative(X))))&
(![X]:((~wise(X)|strong(X))<=>(patient(X)&~creative(X))))&
((?[X]:((~tall(X)<~>~old(X))))<=>(strong(susan)))&
((?[X]:((strong(X)|patient(X))))=>((generous(mary)&~calm(mary))))&
(((tall(alice)|creative(alice)))<=>((~kind(fred)|~humble(fred))))&
(![X]:((~creative(X)|quiet(X))=>(tall(X)&~strong(X))))&
(((~happy(john)|~kind(john)))<=>(~quiet(john)))&
((?[X]:(~curious(X)))=>(happy(lucy)))&
(![X]:((~kind(X)|~rich(X))=>(kind(X)<~>~humble(X))))&
(((~happy(john)&strong(john)))=>(?[X]:((happy(X)|kind(X)))))&
(![X]:(~brave(X)<=>(tall(X)|~funny(X))))&
(![X]:(generous(X)<=>(~kind(X)|quiet(X))))&
(![X]:((~generous(X)&creative(X))=>(patient(X)&tall(X))))&
((?[X]:(curious(X)))<=>(funny(fred)))&
(![X]:(~rich(X)<=>(~humble(X)&~curious(X))))&
((tall(mary)&quiet(mary)))&
((tall(lucy)|happy(lucy)))&
(?[X]:(generous(X)))&
(?[X]:(~happy(X)))&
(?[X]:(wise(X)))&
(~strong(mary)) | ~humble(fred) | [
"p0",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 647575779670411227441476
% SZS output start Proof for 647575779670411227441476
1. ! [X0] : (creative(X0) <=> (rich(X0) <~> creative(X0))) [input p0]
15. ! [X0] : (~rich(X0) <=> (~curious(X0) & ~humble(X0))) [input p14]
22. humble(fred) [input hypothesis]
35. ! [X0] : ((creative(X0) | ((rich(X0) | ~creative(X0)) & (creative(X0) | ~rich(X0)))) & (((~creative(X0) | ~rich(X0)) & (creative(X0) | rich(X0))) | ~creative(X0))) [nnf transformation 1]
53. ! [X0] : ((~rich(X0) | (curious(X0) | humble(X0))) & ((~curious(X0) & ~humble(X0)) | rich(X0))) [nnf transformation 15]
54. ! [X0] : ((~rich(X0) | curious(X0) | humble(X0)) & ((~curious(X0) & ~humble(X0)) | rich(X0))) [flattening 53]
62. ~creative(X0) | ~rich(X0) | ~creative(X0) [cnf transformation 35]
63. creative(X0) | creative(X0) | ~rich(X0) [cnf transformation 35]
98. ~humble(X0) | rich(X0) [cnf transformation 54]
108. humble(fred) [cnf transformation 22]
110. ~creative(X0) | ~rich(X0) [duplicate literal removal 62]
111. creative(X0) | ~rich(X0) [duplicate literal removal 63]
112. ~rich(X0) [subsumption resolution 110,111]
223. ~humble(X0) [subsumption resolution 98,112]
229. $false [subsumption resolution 108,223]
% SZS output end Proof for 647575779670411227441476
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either creative or not patient then someone is patient or not generous.
Everyone who is not funny is not calm and vice versa.
Everyone who is either not kind or not creative is old or calm.
If mary is both not brave and quiet then someone is either old or not happy.
Everyone who is not brave is not kind or strong.
If someone is either generous or not tall then someone is curious or not patient.
Everyone who is funny or not calm is both not brave and curious and vice versa.
If susan is rich then someone is old or kind.
If fred is both not old and rich then someone is both not kind and wise and vice versa.
If someone is not curious then someone is creative or rich and vice versa.
Everyone who is not rich or not curious is tall.
If susan is either wise or generous then lucy is either not funny or tall and vice versa.
Everyone who is not patient or not humble is either creative or tall and vice versa.
Everyone who is both humble and strong is both humble and not patient and vice versa.
Everyone who is either humble or quiet is both not funny and not kind.
Everyone who is tall or rich is both not patient and not happy.
John is either kind or not kind.
Someone is not funny.
Someone is either funny or happy.
Paul is either not happy or not generous.
Someone is both not creative and not patient. | Paul is not generous. | contradiction | ((?[X]:((creative(X)<~>~patient(X))))=>(?[X]:((patient(X)|~generous(X)))))&
(![X]:(~funny(X)<=>~calm(X)))&
(![X]:((~kind(X)<~>~creative(X))=>(old(X)|calm(X))))&
(((~brave(mary)&quiet(mary)))=>(?[X]:((old(X)<~>~happy(X)))))&
(![X]:(~brave(X)=>(~kind(X)|strong(X))))&
((?[X]:((generous(X)<~>~tall(X))))=>(?[X]:((curious(X)|~patient(X)))))&
(![X]:((funny(X)|~calm(X))<=>(~brave(X)&curious(X))))&
((rich(susan))=>(?[X]:((old(X)|kind(X)))))&
(((~old(fred)&rich(fred)))<=>(?[X]:((~kind(X)&wise(X)))))&
((?[X]:(~curious(X)))<=>(?[X]:((creative(X)|rich(X)))))&
(![X]:((~rich(X)|~curious(X))=>tall(X)))&
(((wise(susan)<~>generous(susan)))<=>((~funny(lucy)<~>tall(lucy))))&
(![X]:((~patient(X)|~humble(X))<=>(creative(X)<~>tall(X))))&
(![X]:((humble(X)&strong(X))<=>(humble(X)&~patient(X))))&
(![X]:((humble(X)<~>quiet(X))=>(~funny(X)&~kind(X))))&
(![X]:((tall(X)|rich(X))=>(~patient(X)&~happy(X))))&
((kind(john)<~>~kind(john)))&
(?[X]:(~funny(X)))&
(?[X]:((funny(X)<~>happy(X))))&
((~happy(paul)<~>~generous(paul)))&
(?[X]:((~creative(X)&~patient(X)))) | ~generous(paul) | [
"p10",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 4241382071190943389976028
% SZS output start Proof for 4241382071190943389976028
11. ! [X0] : ((~curious(X0) | ~rich(X0)) => tall(X0)) [input p10]
16. ! [X0] : ((rich(X0) | tall(X0)) => (~happy(X0) & ~patient(X0))) [input p15]
20. ~happy(paul) <~> ~generous(paul) [input p19]
22. ~generous(paul) [input hypothesis]
35. ! [X0] : (tall(X0) | (curious(X0) & rich(X0))) [ennf transformation 11]
37. ! [X0] : ((~happy(X0) & ~patient(X0)) | (~rich(X0) & ~tall(X0))) [ennf transformation 16]
77. (generous(paul) | happy(paul)) & (~generous(paul) | ~happy(paul)) [nnf transformation 20]
104. rich(X0) | tall(X0) [cnf transformation 35]
130. ~tall(X0) | ~happy(X0) [cnf transformation 37]
131. ~rich(X0) | ~happy(X0) [cnf transformation 37]
138. generous(paul) | happy(paul) [cnf transformation 77]
141. ~generous(paul) [cnf transformation 22]
287. 33 <=> happy(paul) [avatar definition]
289. happy(paul) <- (33) [avatar component clause 287]
291. 34 <=> generous(paul) [avatar definition]
294. 33 | 34 [avatar split clause 138,291,287]
296. ~34 [avatar split clause 141,291]
314. ~happy(X0) | tall(X0) [resolution 131,104]
320. ~happy(X0) [subsumption resolution 314,130]
334. $false <- (33) [resolution 320,289]
335. ~33 [avatar contradiction clause 334]
336. $false [avatar sat refutation 294,296,335]
% SZS output end Proof for 4241382071190943389976028
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy then fred is both not rich and brave. If alice is either not patient or not old then someone is not tall. Everyone who is not rich or old is both kind and tall and vice versa. Everyone who is not wise or generous is wise. If someone is either patient or not tall then someone is both curious and not happy and vice versa. Everyone who is not old or wise is either wise or curious. If paul is creative or calm then paul is either not quiet or tall and vice versa. If lucy is not brave or wise then fred is quiet. If alice is either not rich or wise then someone is both not old and funny. If someone is both tall and patient then paul is not brave or rich. Everyone who is both happy and not strong is both not creative and not wise and vice versa. If alice is not old or tall then someone is not brave or not quiet. Everyone who is kind or not humble is brave or not curious and vice versa. Everyone who is not funny is tall or rich and vice versa. Everyone who is not kind or not generous is creative or not happy and vice versa. Everyone who is not creative is brave or happy. Someone is both not kind and strong. Someone is strong or calm. Someone is either humble or not rich. Someone is kind or not strong. Someone is either not wise or quiet. Someone is not creative or not humble. Someone is not funny. Susan is brave or not calm. | Alice is not patient. | entailment | ((?[X]:(~happy(X)))=>((~rich(fred)&brave(fred))))&
(((~patient(alice)<~>~old(alice)))=>(?[X]:(~tall(X))))&
(![X]:((~rich(X)|old(X))<=>(kind(X)&tall(X))))&
(![X]:((~wise(X)|generous(X))=>wise(X)))&
((?[X]:((patient(X)<~>~tall(X))))<=>(?[X]:((curious(X)&~happy(X)))))&
(![X]:((~old(X)|wise(X))=>(wise(X)<~>curious(X))))&
(((creative(paul)|calm(paul)))<=>((~quiet(paul)<~>tall(paul))))&
(((~brave(lucy)|wise(lucy)))=>(quiet(fred)))&
(((~rich(alice)<~>wise(alice)))=>(?[X]:((~old(X)&funny(X)))))&
((?[X]:((tall(X)&patient(X))))=>((~brave(paul)|rich(paul))))&
(![X]:((happy(X)&~strong(X))<=>(~creative(X)&~wise(X))))&
(((~old(alice)|tall(alice)))=>(?[X]:((~brave(X)|~quiet(X)))))&
(![X]:((kind(X)|~humble(X))<=>(brave(X)|~curious(X))))&
(![X]:(~funny(X)<=>(tall(X)|rich(X))))&
(![X]:((~kind(X)|~generous(X))<=>(creative(X)|~happy(X))))&
(![X]:(~creative(X)=>(brave(X)|happy(X))))&
(?[X]:((~kind(X)&strong(X))))&
(?[X]:((strong(X)|calm(X))))&
(?[X]:((humble(X)<~>~rich(X))))&
(?[X]:((kind(X)|~strong(X))))&
(?[X]:((~wise(X)<~>quiet(X))))&
(?[X]:((~creative(X)|~humble(X))))&
(?[X]:(~funny(X)))&
((brave(susan)|~calm(susan))) | ~patient(alice) | [
"p2",
"p3",
"p4",
"p5",
"p8",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 5208328156459358423379855
% SZS output start Proof for 5208328156459358423379855
3. ! [X0] : ((old(X0) | ~rich(X0)) <=> (tall(X0) & kind(X0))) [input p2]
4. ! [X0] : ((generous(X0) | ~wise(X0)) => wise(X0)) [input p3]
5. ? [X0] : (patient(X0) <~> ~tall(X0)) <=> ? [X0] : (~happy(X0) & curious(X0)) [input p4]
6. ! [X0] : ((wise(X0) | ~old(X0)) => (wise(X0) <~> curious(X0))) [input p5]
9. (~rich(alice) <~> wise(alice)) => ? [X0] : (funny(X0) & ~old(X0)) [input p8]
14. ! [X0] : (~funny(X0) <=> (rich(X0) | tall(X0))) [input p13]
25. patient(alice) [input hypothesis]
26. ? [X0] : (patient(X0) <~> ~tall(X0)) <=> ? [X1] : (~happy(X1) & curious(X1)) [rectify 5]
29. ! [X0] : (wise(X0) | (~generous(X0) & wise(X0))) [ennf transformation 4]
30. ! [X0] : ((wise(X0) <~> curious(X0)) | (~wise(X0) & old(X0))) [ennf transformation 6]
32. ? [X0] : (funny(X0) & ~old(X0)) | (~rich(alice) <=> wise(alice)) [ennf transformation 9]
41. ! [X0] : (((old(X0) | ~rich(X0)) | (~tall(X0) | ~kind(X0))) & ((tall(X0) & kind(X0)) | (~old(X0) & rich(X0)))) [nnf transformation 3]
42. ! [X0] : ((old(X0) | ~rich(X0) | ~tall(X0) | ~kind(X0)) & ((tall(X0) & kind(X0)) | (~old(X0) & rich(X0)))) [flattening 41]
43. (? [X0] : ((tall(X0) | ~patient(X0)) & (~tall(X0) | patient(X0))) | ! [X1] : (happy(X1) | ~curious(X1))) & (? [X1] : (~happy(X1) & curious(X1)) | ! [X0] : ((patient(X0) | tall(X0)) & (~tall(X0) | ~patient(X0)))) [nnf transformation 26]
44. (? [X0] : ((tall(X0) | ~patient(X0)) & (~tall(X0) | patient(X0))) | ! [X1] : (happy(X1) | ~curious(X1))) & (? [X2] : (~happy(X2) & curious(X2)) | ! [X3] : ((patient(X3) | tall(X3)) & (~tall(X3) | ~patient(X3)))) [rectify 43]
45. ? [X0] : ((tall(X0) | ~patient(X0)) & (~tall(X0) | patient(X0))) => ((tall(sK1) | ~patient(sK1)) & (~tall(sK1) | patient(sK1))) [choice axiom]
46. ? [X2] : (~happy(X2) & curious(X2)) => (~happy(sK2) & curious(sK2)) [choice axiom]
47. (((tall(sK1) | ~patient(sK1)) & (~tall(sK1) | patient(sK1))) | ! [X1] : (happy(X1) | ~curious(X1))) & ((~happy(sK2) & curious(sK2)) | ! [X3] : ((patient(X3) | tall(X3)) & (~tall(X3) | ~patient(X3)))) [skolemisation 44,46,45]
48. ! [X0] : (((~curious(X0) | ~wise(X0)) & (curious(X0) | wise(X0))) | (~wise(X0) & old(X0))) [nnf transformation 30]
51. ? [X0] : (funny(X0) & ~old(X0)) | ((~rich(alice) | ~wise(alice)) & (wise(alice) | rich(alice))) [nnf transformation 32]
52. ? [X0] : (funny(X0) & ~old(X0)) => (funny(sK3) & ~old(sK3)) [choice axiom]
53. (funny(sK3) & ~old(sK3)) | ((~rich(alice) | ~wise(alice)) & (wise(alice) | rich(alice))) [skolemisation 51,52]
60. ! [X0] : ((~funny(X0) | (~rich(X0) & ~tall(X0))) & ((rich(X0) | tall(X0)) | funny(X0))) [nnf transformation 14]
61. ! [X0] : ((~funny(X0) | (~rich(X0) & ~tall(X0))) & (rich(X0) | tall(X0) | funny(X0))) [flattening 60]
86. tall(X0) | rich(X0) [cnf transformation 42]
89. wise(X0) | wise(X0) [cnf transformation 29]
91. curious(sK2) | ~tall(X3) | ~patient(X3) [cnf transformation 47]
100. ~curious(X0) | ~wise(X0) | ~wise(X0) [cnf transformation 48]
112. funny(sK3) | ~rich(alice) | ~wise(alice) [cnf transformation 53]
125. ~funny(X0) | ~tall(X0) [cnf transformation 61]
126. ~funny(X0) | ~rich(X0) [cnf transformation 61]
143. patient(alice) [cnf transformation 25]
144. ~curious(X0) | ~wise(X0) [duplicate literal removal 100]
145. wise(X0) [duplicate literal removal 89]
164. 5 <=> patient(alice) [avatar definition]
165. patient(alice) <- (5) [avatar component clause 164]
195. 12 <=> ! [X3] : (~tall(X3) | ~patient(X3)) [avatar definition]
196. ~tall(X3) | ~patient(X3) <- (12) [avatar component clause 195]
199. 13 <=> curious(sK2) [avatar definition]
201. curious(sK2) <- (13) [avatar component clause 199]
203. 12 | 13 [avatar split clause 91,199,195]
204. ~curious(X0) [subsumption resolution 144,145]
228. funny(sK3) | ~rich(alice) [subsumption resolution 112,145]
230. 18 <=> rich(alice) [avatar definition]
232. ~rich(alice) <- (~18) [avatar component clause 230]
234. 19 <=> funny(sK3) [avatar definition]
236. funny(sK3) <- (19) [avatar component clause 234]
237. ~18 | 19 [avatar split clause 228,234,230]
316. 5 [avatar split clause 143,164]
327. ~patient(X1) | rich(X1) <- (12) [resolution 196,86]
328. rich(alice) <- (5, 12) [resolution 327,165]
331. $false <- (5, 12, ~18) [subsumption resolution 328,232]
332. ~5 | ~12 | 18 [avatar contradiction clause 331]
333. $false <- (13) [subsumption resolution 201,204]
334. ~13 [avatar contradiction clause 333]
335. ~rich(sK3) <- (19) [resolution 236,126]
336. ~tall(sK3) <- (19) [resolution 236,125]
341. rich(sK3) <- (19) [resolution 336,86]
342. $false <- (19) [subsumption resolution 341,335]
343. ~19 [avatar contradiction clause 342]
344. $false [avatar sat refutation 203,237,316,332,334,343]
% SZS output end Proof for 5208328156459358423379855
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not brave or calm is generous or not calm.
If mary is both not funny and generous then john is both tall and not quiet.
Everyone who is either not patient or not tall is either not rich or not generous and vice versa.
If susan is either calm or not quiet then someone is not generous and vice versa.
If fred is both not creative and patient then someone is not rich or generous.
If john is either not calm or not rich then someone is not creative.
If someone is either not humble or humble then paul is either not humble or strong.
If susan is either curious or not strong then mary is calm or not generous.
If alice is either not brave or not patient then someone is not brave or old.
If lucy is either curious or not calm then susan is either quiet or funny.
Everyone who is both humble and rich is rich or happy.
Everyone who is not humble or happy is both not rich and humble.
Everyone who is either rich or not curious is quiet and vice versa.
If someone is either curious or kind then someone is not creative or old and vice versa.
If someone is not tall then someone is both not happy and not wise and vice versa.
Everyone who is both generous and curious is both not humble and not calm.
Mary is either not calm or funny.
Someone is both not wise and humble.
Mary is both happy and quiet.
Someone is strong.
Alice is old.
Someone is happy or humble.
Someone is both not funny and not rich.
Paul is either brave or not curious. | Lucy is not humble. | contradiction | (![X]:((~brave(X)|calm(X))=>(generous(X)|~calm(X))))&
(((~funny(mary)&generous(mary)))=>((tall(john)&~quiet(john))))&
(![X]:((~patient(X)<~>~tall(X))<=>(~rich(X)<~>~generous(X))))&
(((calm(susan)<~>~quiet(susan)))<=>(?[X]:(~generous(X))))&
(((~creative(fred)&patient(fred)))=>(?[X]:((~rich(X)|generous(X)))))&
(((~calm(john)<~>~rich(john)))=>(?[X]:(~creative(X))))&
((?[X]:((~humble(X)<~>humble(X))))=>((~humble(paul)<~>strong(paul))))&
(((curious(susan)<~>~strong(susan)))=>((calm(mary)|~generous(mary))))&
(((~brave(alice)<~>~patient(alice)))=>(?[X]:((~brave(X)|old(X)))))&
(((curious(lucy)<~>~calm(lucy)))=>((quiet(susan)<~>funny(susan))))&
(![X]:((humble(X)&rich(X))=>(rich(X)|happy(X))))&
(![X]:((~humble(X)|happy(X))=>(~rich(X)&humble(X))))&
(![X]:((rich(X)<~>~curious(X))<=>quiet(X)))&
((?[X]:((curious(X)<~>kind(X))))<=>(?[X]:((~creative(X)|old(X)))))&
((?[X]:(~tall(X)))<=>(?[X]:((~happy(X)&~wise(X)))))&
(![X]:((generous(X)&curious(X))=>(~humble(X)&~calm(X))))&
((~calm(mary)<~>funny(mary)))&
(?[X]:((~wise(X)&humble(X))))&
((happy(mary)&quiet(mary)))&
(?[X]:(strong(X)))&
(old(alice))&
(?[X]:((happy(X)|humble(X))))&
(?[X]:((~funny(X)&~rich(X))))&
((brave(paul)<~>~curious(paul))) | ~humble(lucy) | [
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 2655868403103391545691500
% SZS output start Proof for 2655868403103391545691500
12. ! [X0] : ((happy(X0) | ~humble(X0)) => (humble(X0) & ~rich(X0))) [input p11]
25. ~humble(lucy) [input hypothesis]
42. ! [X0] : ((humble(X0) & ~rich(X0)) | (~happy(X0) & humble(X0))) [ennf transformation 12]
116. humble(X0) | humble(X0) [cnf transformation 42]
146. ~humble(lucy) [cnf transformation 25]
147. humble(X0) [duplicate literal removal 116]
234. 19 <=> ! [X0] : humble(X0) [avatar definition]
235. humble(X0) <- (19) [avatar component clause 234]
287. 19 [avatar split clause 147,234]
363. $false <- (19) [resolution 235,146]
364. ~19 [avatar contradiction clause 363]
365. $false [avatar sat refutation 287,364]
% SZS output end Proof for 2655868403103391545691500
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not rich then someone is both not creative and brave and vice versa. Everyone who is kind is either not quiet or kind and vice versa. If someone is not calm then mary is not humble or rich. Everyone who is humble or not funny is both funny and not strong. If paul is either calm or rich then lucy is both wise and not tall and vice versa. If someone is generous then someone is not humble and vice versa. If mary is either not wise or humble then susan is both not old and not brave and vice versa. If lucy is not strong or not calm then fred is old or generous. Everyone who is either wise or not old is creative or brave and vice versa. Everyone who is quiet is both not strong and not tall. If mary is either humble or not calm then mary is quiet and vice versa. Everyone who is curious is both strong and not patient. Everyone who is either not old or not wise is either curious or creative. Everyone who is tall or brave is not tall and vice versa. If someone is humble then someone is either creative or quiet. Everyone who is both funny and patient is both not generous and not tall and vice versa. Fred is both not creative and funny. Lucy is either not patient or not funny. Someone is not generous. Someone is either humble or tall. Paul is brave or not happy. Susan is both not calm and not patient. | Fred is old. | neutral | ((?[X]:(~rich(X)))<=>(?[X]:((~creative(X)&brave(X)))))&
(![X]:(kind(X)<=>(~quiet(X)<~>kind(X))))&
((?[X]:(~calm(X)))=>((~humble(mary)|rich(mary))))&
(![X]:((humble(X)|~funny(X))=>(funny(X)&~strong(X))))&
(((calm(paul)<~>rich(paul)))<=>((wise(lucy)&~tall(lucy))))&
((?[X]:(generous(X)))<=>(?[X]:(~humble(X))))&
(((~wise(mary)<~>humble(mary)))<=>((~old(susan)&~brave(susan))))&
(((~strong(lucy)|~calm(lucy)))=>((old(fred)|generous(fred))))&
(![X]:((wise(X)<~>~old(X))<=>(creative(X)|brave(X))))&
(![X]:(quiet(X)=>(~strong(X)&~tall(X))))&
(((humble(mary)<~>~calm(mary)))<=>(quiet(mary)))&
(![X]:(curious(X)=>(strong(X)&~patient(X))))&
(![X]:((~old(X)<~>~wise(X))=>(curious(X)<~>creative(X))))&
(![X]:((tall(X)|brave(X))<=>~tall(X)))&
((?[X]:(humble(X)))=>(?[X]:((creative(X)<~>quiet(X)))))&
(![X]:((funny(X)&patient(X))<=>(~generous(X)&~tall(X))))&
((~creative(fred)&funny(fred)))&
((~patient(lucy)<~>~funny(lucy)))&
(?[X]:(~generous(X)))&
(?[X]:((humble(X)<~>tall(X))))&
((brave(paul)|~happy(paul)))&
((~calm(susan)&~patient(susan))) | old(fred) | [] | null | 0 |
If lucy is both calm and not kind then someone is not humble or not old and vice versa. If mary is either not brave or not tall then mary is either generous or not calm and vice versa. Everyone who is either not patient or not quiet is either not quiet or quiet and vice versa. If someone is both not brave and creative then someone is not kind and vice versa. If someone is not quiet or humble then someone is either not rich or not creative. If susan is old or not humble then someone is both calm and not rich. If someone is not tall or not rich then mary is funny or creative and vice versa. Everyone who is funny or old is not kind or not strong and vice versa. If lucy is humble then someone is strong and vice versa. Everyone who is both not humble and not kind is not curious or not tall and vice versa. Everyone who is either not humble or not curious is either not old or not strong and vice versa. Everyone who is creative or generous is either not patient or calm. If someone is either not humble or not wise then alice is kind and vice versa. Everyone who is funny or patient is either happy or not strong. Everyone who is both not happy and humble is rich. If alice is old or humble then someone is calm or tall and vice versa. Fred is both not funny and not patient. Someone is either not brave or not calm. Someone is brave or creative. Someone is either not happy or strong. Susan is both not patient and not humble. Someone is either brave or not strong. | Lucy is rich. | neutral | (((calm(lucy)&~kind(lucy)))<=>(?[X]:((~humble(X)|~old(X)))))&
(((~brave(mary)<~>~tall(mary)))<=>((generous(mary)<~>~calm(mary))))&
(![X]:((~patient(X)<~>~quiet(X))<=>(~quiet(X)<~>quiet(X))))&
((?[X]:((~brave(X)&creative(X))))<=>(?[X]:(~kind(X))))&
((?[X]:((~quiet(X)|humble(X))))=>(?[X]:((~rich(X)<~>~creative(X)))))&
(((old(susan)|~humble(susan)))=>(?[X]:((calm(X)&~rich(X)))))&
((?[X]:((~tall(X)|~rich(X))))<=>((funny(mary)|creative(mary))))&
(![X]:((funny(X)|old(X))<=>(~kind(X)|~strong(X))))&
((humble(lucy))<=>(?[X]:(strong(X))))&
(![X]:((~humble(X)&~kind(X))<=>(~curious(X)|~tall(X))))&
(![X]:((~humble(X)<~>~curious(X))<=>(~old(X)<~>~strong(X))))&
(![X]:((creative(X)|generous(X))=>(~patient(X)<~>calm(X))))&
((?[X]:((~humble(X)<~>~wise(X))))<=>(kind(alice)))&
(![X]:((funny(X)|patient(X))=>(happy(X)<~>~strong(X))))&
(![X]:((~happy(X)&humble(X))=>rich(X)))&
(((old(alice)|humble(alice)))<=>(?[X]:((calm(X)|tall(X)))))&
((~funny(fred)&~patient(fred)))&
(?[X]:((~brave(X)<~>~calm(X))))&
(?[X]:((brave(X)|creative(X))))&
(?[X]:((~happy(X)<~>strong(X))))&
((~patient(susan)&~humble(susan)))&
(?[X]:((brave(X)<~>~strong(X)))) | rich(lucy) | [] | null | 0 |
If someone is either old or not quiet then paul is both not tall and not curious.
If someone is both strong and curious then lucy is quiet or not brave and vice versa.
Everyone who is not rich is both not quiet and curious.
Everyone who is either generous or not quiet is either wise or not kind.
If someone is both not humble and calm then someone is both not funny and not generous and vice versa.
Everyone who is both not patient and creative is both funny and wise and vice versa.
Everyone who is old or not strong is kind or not patient and vice versa.
If someone is wise then susan is either not happy or not old and vice versa.
Everyone who is either not old or not kind is not calm or not kind.
If someone is strong then susan is both creative and kind.
Everyone who is not calm or happy is not patient or quiet.
If someone is both not strong and old then someone is either not rich or funny.
If someone is both not old and not tall then john is either rich or not wise and vice versa.
If someone is both strong and not happy then someone is tall or strong and vice versa.
Everyone who is both curious and brave is both funny and not creative.
If someone is either not rich or old then someone is not creative or creative.
Susan is humble.
Susan is not brave.
John is creative.
Someone is not creative.
Lucy is not curious.
Alice is creative.
Mary is not rich.
Susan is either not generous or quiet. | Mary is curious. | entailment | ((?[X]:((old(X)<~>~quiet(X))))=>((~tall(paul)&~curious(paul))))&
((?[X]:((strong(X)&curious(X))))<=>((quiet(lucy)|~brave(lucy))))&
(![X]:(~rich(X)=>(~quiet(X)&curious(X))))&
(![X]:((generous(X)<~>~quiet(X))=>(wise(X)<~>~kind(X))))&
((?[X]:((~humble(X)&calm(X))))<=>(?[X]:((~funny(X)&~generous(X)))))&
(![X]:((~patient(X)&creative(X))<=>(funny(X)&wise(X))))&
(![X]:((old(X)|~strong(X))<=>(kind(X)|~patient(X))))&
((?[X]:(wise(X)))<=>((~happy(susan)<~>~old(susan))))&
(![X]:((~old(X)<~>~kind(X))=>(~calm(X)|~kind(X))))&
((?[X]:(strong(X)))=>((creative(susan)&kind(susan))))&
(![X]:((~calm(X)|happy(X))=>(~patient(X)|quiet(X))))&
((?[X]:((~strong(X)&old(X))))=>(?[X]:((~rich(X)<~>funny(X)))))&
((?[X]:((~old(X)&~tall(X))))<=>((rich(john)<~>~wise(john))))&
((?[X]:((strong(X)&~happy(X))))<=>(?[X]:((tall(X)|strong(X)))))&
(![X]:((curious(X)&brave(X))=>(funny(X)&~creative(X))))&
((?[X]:((~rich(X)<~>old(X))))=>(?[X]:((~creative(X)|creative(X)))))&
(humble(susan))&
(~brave(susan))&
(creative(john))&
(?[X]:(~creative(X)))&
(~curious(lucy))&
(creative(alice))&
(~rich(mary))&
((~generous(susan)<~>quiet(susan))) | curious(mary) | [
"p2",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 1499342402939194809965093
% SZS output start Proof for 1499342402939194809965093
3. ! [X0] : (~rich(X0) => (curious(X0) & ~quiet(X0))) [input p2]
23. ~rich(mary) [input p22]
25. ~curious(mary) [input hypothesis]
31. ! [X0] : ((curious(X0) & ~quiet(X0)) | rich(X0)) [ennf transformation 3]
93. rich(X0) | curious(X0) [cnf transformation 31]
143. ~rich(mary) [cnf transformation 23]
146. ~curious(mary) [cnf transformation 25]
325. curious(mary) [resolution 93,143]
328. $false [subsumption resolution 325,146]
% SZS output end Proof for 1499342402939194809965093
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong is strong.
If someone is funny then someone is either tall or calm.
If someone is not calm or not tall then someone is either not patient or not tall.
If someone is either quiet or not curious then susan is both calm and not generous and vice versa.
Everyone who is kind or quiet is wise or rich and vice versa.
If someone is either brave or not generous then mary is not calm or kind and vice versa.
Everyone who is both not wise and patient is both not creative and not calm.
If lucy is not brave or generous then someone is brave or calm.
Everyone who is either not wise or quiet is not rich.
Everyone who is not calm is happy.
If mary is generous or calm then someone is humble and vice versa.
Everyone who is both not tall and not strong is either strong or rich and vice versa.
If someone is both not quiet and wise then fred is happy or old and vice versa.
If someone is both not rich and calm then someone is old or not quiet and vice versa.
If lucy is patient or not patient then someone is either creative or quiet and vice versa.
If john is not strong or not wise then someone is both not generous and not old and vice versa.
Someone is either not curious or not patient.
Susan is both not old and quiet.
Someone is not calm.
Susan is either not old or not strong.
Someone is both brave and strong.
Lucy is both not happy and curious.
Someone is not wise.
Someone is both not funny and not brave. | Mary is quiet. | entailment | (![X]:(~strong(X)=>strong(X)))&
((?[X]:(funny(X)))=>(?[X]:((tall(X)<~>calm(X)))))&
((?[X]:((~calm(X)|~tall(X))))=>(?[X]:((~patient(X)<~>~tall(X)))))&
((?[X]:((quiet(X)<~>~curious(X))))<=>((calm(susan)&~generous(susan))))&
(![X]:((kind(X)|quiet(X))<=>(wise(X)|rich(X))))&
((?[X]:((brave(X)<~>~generous(X))))<=>((~calm(mary)|kind(mary))))&
(![X]:((~wise(X)&patient(X))=>(~creative(X)&~calm(X))))&
(((~brave(lucy)|generous(lucy)))=>(?[X]:((brave(X)|calm(X)))))&
(![X]:((~wise(X)<~>quiet(X))=>~rich(X)))&
(![X]:(~calm(X)=>happy(X)))&
(((generous(mary)|calm(mary)))<=>(?[X]:(humble(X))))&
(![X]:((~tall(X)&~strong(X))<=>(strong(X)<~>rich(X))))&
((?[X]:((~quiet(X)&wise(X))))<=>((happy(fred)|old(fred))))&
((?[X]:((~rich(X)&calm(X))))<=>(?[X]:((old(X)|~quiet(X)))))&
(((patient(lucy)|~patient(lucy)))<=>(?[X]:((creative(X)<~>quiet(X)))))&
(((~strong(john)|~wise(john)))<=>(?[X]:((~generous(X)&~old(X)))))&
(?[X]:((~curious(X)<~>~patient(X))))&
((~old(susan)&quiet(susan)))&
(?[X]:(~calm(X)))&
((~old(susan)<~>~strong(susan)))&
(?[X]:((brave(X)&strong(X))))&
((~happy(lucy)&curious(lucy)))&
(?[X]:(~wise(X)))&
(?[X]:((~funny(X)&~brave(X)))) | quiet(mary) | [
"p0",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 2247312445744200055539468
% SZS output start Proof for 2247312445744200055539468
1. ! [X0] : (~strong(X0) => strong(X0)) [input p0]
12. ! [X0] : ((~strong(X0) & ~tall(X0)) <=> (strong(X0) <~> rich(X0))) [input p11]
14. ? [X0] : (calm(X0) & ~rich(X0)) <=> ? [X0] : (~quiet(X0) | old(X0)) [input p13]
25. ~quiet(mary) [input hypothesis]
28. ? [X0] : (calm(X0) & ~rich(X0)) <=> ? [X1] : (~quiet(X1) | old(X1)) [rectify 14]
31. ! [X0] : (strong(X0) | strong(X0)) [ennf transformation 1]
62. ! [X0] : (((~strong(X0) & ~tall(X0)) | ((strong(X0) | ~rich(X0)) & (rich(X0) | ~strong(X0)))) & (((~rich(X0) | ~strong(X0)) & (rich(X0) | strong(X0))) | (strong(X0) | tall(X0)))) [nnf transformation 12]
63. ! [X0] : (((~strong(X0) & ~tall(X0)) | ((strong(X0) | ~rich(X0)) & (rich(X0) | ~strong(X0)))) & (((~rich(X0) | ~strong(X0)) & (rich(X0) | strong(X0))) | strong(X0) | tall(X0))) [flattening 62]
69. (? [X0] : (calm(X0) & ~rich(X0)) | ! [X1] : (quiet(X1) & ~old(X1))) & (? [X1] : (~quiet(X1) | old(X1)) | ! [X0] : (~calm(X0) | rich(X0))) [nnf transformation 28]
70. (? [X0] : (calm(X0) & ~rich(X0)) | ! [X1] : (quiet(X1) & ~old(X1))) & (? [X2] : (~quiet(X2) | old(X2)) | ! [X3] : (~calm(X3) | rich(X3))) [rectify 69]
71. ? [X0] : (calm(X0) & ~rich(X0)) => (calm(sK6) & ~rich(sK6)) [choice axiom]
72. ? [X2] : (~quiet(X2) | old(X2)) => (~quiet(sK7) | old(sK7)) [choice axiom]
73. ((calm(sK6) & ~rich(sK6)) | ! [X1] : (quiet(X1) & ~old(X1))) & ((~quiet(sK7) | old(sK7)) | ! [X3] : (~calm(X3) | rich(X3))) [skolemisation 70,72,71]
96. strong(X0) | strong(X0) [cnf transformation 31]
131. ~strong(X0) | rich(X0) | ~strong(X0) [cnf transformation 63]
140. ~rich(sK6) | quiet(X1) [cnf transformation 73]
167. ~quiet(mary) [cnf transformation 25]
169. ~strong(X0) | rich(X0) [duplicate literal removal 131]
170. strong(X0) [duplicate literal removal 96]
277. rich(X0) [subsumption resolution 169,170]
303. 29 <=> ! [X1] : quiet(X1) [avatar definition]
304. quiet(X1) <- (29) [avatar component clause 303]
314. quiet(X1) [subsumption resolution 140,277]
315. 29 [avatar split clause 314,303]
369. $false <- (29) [resolution 304,167]
370. ~29 [avatar contradiction clause 369]
371. $false [avatar sat refutation 315,370]
% SZS output end Proof for 2247312445744200055539468
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not patient or not creative is curious or funny. Everyone who is both happy and calm is both not brave and not tall. Everyone who is strong is both calm and generous. Everyone who is both calm and tall is not generous. Everyone who is not brave is both not funny and not calm. If someone is both not generous and humble then john is both quiet and generous and vice versa. Everyone who is both happy and funny is not brave and vice versa. Everyone who is both wise and not wise is both not brave and not calm and vice versa. If paul is either wise or curious then someone is not humble or not kind. If someone is either not happy or not humble then someone is either not humble or not curious and vice versa. Everyone who is not curious or not tall is kind and vice versa. If lucy is both not happy and funny then alice is not kind and vice versa. Everyone who is not strong is calm. Everyone who is both rich and strong is either kind or not quiet. Everyone who is either kind or happy is not wise. Alice is not happy. Someone is not kind. Someone is either not calm or strong. Someone is not creative. Someone is old or humble. Lucy is either curious or not funny. Someone is both strong and patient. | Lucy is creative. | neutral | (![X]:((~patient(X)|~creative(X))=>(curious(X)|funny(X))))&
(![X]:((happy(X)&calm(X))=>(~brave(X)&~tall(X))))&
(![X]:(strong(X)=>(calm(X)&generous(X))))&
(![X]:((calm(X)&tall(X))=>~generous(X)))&
(![X]:(~brave(X)=>(~funny(X)&~calm(X))))&
((?[X]:((~generous(X)&humble(X))))<=>((quiet(john)&generous(john))))&
(![X]:((happy(X)&funny(X))<=>~brave(X)))&
(![X]:((wise(X)&~wise(X))<=>(~brave(X)&~calm(X))))&
(((wise(paul)<~>curious(paul)))=>(?[X]:((~humble(X)|~kind(X)))))&
((?[X]:((~happy(X)<~>~humble(X))))<=>(?[X]:((~humble(X)<~>~curious(X)))))&
(![X]:((~curious(X)|~tall(X))<=>kind(X)))&
(((~happy(lucy)&funny(lucy)))<=>(~kind(alice)))&
(![X]:(~strong(X)=>calm(X)))&
(![X]:((rich(X)&strong(X))=>(kind(X)<~>~quiet(X))))&
(![X]:((kind(X)<~>happy(X))=>~wise(X)))&
(~happy(alice))&
(?[X]:(~kind(X)))&
(?[X]:((~calm(X)<~>strong(X))))&
(?[X]:(~creative(X)))&
(?[X]:((old(X)|humble(X))))&
((curious(lucy)<~>~funny(lucy)))&
(?[X]:((strong(X)&patient(X)))) | creative(lucy) | [] | null | 0 |
Everyone who is both tall and old is either not happy or not kind and vice versa.
Everyone who is not rich is either strong or generous.
Everyone who is kind or curious is not creative and vice versa.
If lucy is both rich and not patient then someone is not humble.
If lucy is funny or old then someone is either not strong or not curious.
Everyone who is old is curious or not calm and vice versa.
If someone is not humble then someone is wise and vice versa.
Everyone who is either creative or curious is both wise and generous.
Everyone who is both quiet and creative is not old or not humble.
If paul is both not calm and not humble then susan is not humble.
Everyone who is not humble or strong is not wise or tall.
If someone is not funny or happy then someone is not rich and vice versa.
Everyone who is curious is both brave and strong and vice versa.
If someone is rich then susan is rich and vice versa.
If mary is either generous or not happy then alice is not creative or not rich and vice versa.
Everyone who is either funny or not creative is not creative and vice versa.
Someone is both not funny and wise.
Paul is not creative or strong.
Someone is either quiet or brave.
Someone is either not brave or not tall.
Lucy is both not generous and not calm.
Someone is curious or funny.
Someone is not rich or curious. | Lucy is kind. | entailment | (![X]:((tall(X)&old(X))<=>(~happy(X)<~>~kind(X))))&
(![X]:(~rich(X)=>(strong(X)<~>generous(X))))&
(![X]:((kind(X)|curious(X))<=>~creative(X)))&
(((rich(lucy)&~patient(lucy)))=>(?[X]:(~humble(X))))&
(((funny(lucy)|old(lucy)))=>(?[X]:((~strong(X)<~>~curious(X)))))&
(![X]:(old(X)<=>(curious(X)|~calm(X))))&
((?[X]:(~humble(X)))<=>(?[X]:(wise(X))))&
(![X]:((creative(X)<~>curious(X))=>(wise(X)&generous(X))))&
(![X]:((quiet(X)&creative(X))=>(~old(X)|~humble(X))))&
(((~calm(paul)&~humble(paul)))=>(~humble(susan)))&
(![X]:((~humble(X)|strong(X))=>(~wise(X)|tall(X))))&
((?[X]:((~funny(X)|happy(X))))<=>(?[X]:(~rich(X))))&
(![X]:(curious(X)<=>(brave(X)&strong(X))))&
((?[X]:(rich(X)))<=>(rich(susan)))&
(((generous(mary)<~>~happy(mary)))<=>((~creative(alice)|~rich(alice))))&
(![X]:((funny(X)<~>~creative(X))<=>~creative(X)))&
(?[X]:((~funny(X)&wise(X))))&
((~creative(paul)|strong(paul)))&
(?[X]:((quiet(X)<~>brave(X))))&
(?[X]:((~brave(X)<~>~tall(X))))&
((~generous(lucy)&~calm(lucy)))&
(?[X]:((curious(X)|funny(X))))&
(?[X]:((~rich(X)|curious(X)))) | kind(lucy) | [
"p2",
"p7",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 7918402853190177735136796
% SZS output start Proof for 7918402853190177735136796
3. ! [X0] : ((curious(X0) | kind(X0)) <=> ~creative(X0)) [input p2]
8. ! [X0] : ((creative(X0) <~> curious(X0)) => (generous(X0) & wise(X0))) [input p7]
21. ~calm(lucy) & ~generous(lucy) [input p20]
24. ~kind(lucy) [input hypothesis]
30. ! [X0] : ((generous(X0) & wise(X0)) | (creative(X0) <=> curious(X0))) [ennf transformation 8]
40. ! [X0] : (((curious(X0) | kind(X0)) | creative(X0)) & (~creative(X0) | (~curious(X0) & ~kind(X0)))) [nnf transformation 3]
41. ! [X0] : ((curious(X0) | kind(X0) | creative(X0)) & (~creative(X0) | (~curious(X0) & ~kind(X0)))) [flattening 40]
52. ! [X0] : ((generous(X0) & wise(X0)) | ((creative(X0) | ~curious(X0)) & (curious(X0) | ~creative(X0)))) [nnf transformation 30]
88. ~creative(X0) | ~curious(X0) [cnf transformation 41]
89. creative(X0) | kind(X0) | curious(X0) [cnf transformation 41]
101. generous(X0) | curious(X0) | ~creative(X0) [cnf transformation 52]
102. generous(X0) | creative(X0) | ~curious(X0) [cnf transformation 52]
132. ~generous(lucy) [cnf transformation 21]
136. ~kind(lucy) [cnf transformation 24]
175. ~curious(X0) | generous(X0) [subsumption resolution 102,88]
176. ~creative(X0) | generous(X0) [subsumption resolution 101,175]
356. kind(X1) | curious(X1) | generous(X1) [resolution 89,176]
361. generous(X1) | kind(X1) [subsumption resolution 356,175]
512. kind(lucy) [resolution 361,132]
515. $false [subsumption resolution 512,136]
% SZS output end Proof for 7918402853190177735136796
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If susan is either not tall or quiet then someone is creative or quiet and vice versa. Everyone who is not happy is both curious and rich and vice versa. If someone is patient then someone is both happy and strong. Everyone who is either not humble or not creative is both generous and wise. If susan is not rich then someone is either not patient or not tall and vice versa. If mary is not tall then fred is either generous or patient and vice versa. Everyone who is either not quiet or not creative is either not funny or happy and vice versa. Everyone who is both brave and not curious is either not humble or creative and vice versa. If paul is not rich then paul is brave or not wise and vice versa. Everyone who is not old or happy is both strong and happy. Everyone who is not brave or curious is both not brave and not wise and vice versa. If susan is either humble or wise then someone is either not kind or old and vice versa. Everyone who is both rich and calm is both funny and rich. If someone is either not rich or not quiet then someone is not funny and vice versa. If susan is both rich and not rich then mary is either not kind or not happy and vice versa. Lucy is not rich or not patient. Someone is both patient and calm. Someone is not rich or not calm. Someone is both quiet and not creative. Someone is quiet or not patient. | Paul is not wise. | neutral | (((~tall(susan)<~>quiet(susan)))<=>(?[X]:((creative(X)|quiet(X)))))&
(![X]:(~happy(X)<=>(curious(X)&rich(X))))&
((?[X]:(patient(X)))=>(?[X]:((happy(X)&strong(X)))))&
(![X]:((~humble(X)<~>~creative(X))=>(generous(X)&wise(X))))&
((~rich(susan))<=>(?[X]:((~patient(X)<~>~tall(X)))))&
((~tall(mary))<=>((generous(fred)<~>patient(fred))))&
(![X]:((~quiet(X)<~>~creative(X))<=>(~funny(X)<~>happy(X))))&
(![X]:((brave(X)&~curious(X))<=>(~humble(X)<~>creative(X))))&
((~rich(paul))<=>((brave(paul)|~wise(paul))))&
(![X]:((~old(X)|happy(X))=>(strong(X)&happy(X))))&
(![X]:((~brave(X)|curious(X))<=>(~brave(X)&~wise(X))))&
(((humble(susan)<~>wise(susan)))<=>(?[X]:((~kind(X)<~>old(X)))))&
(![X]:((rich(X)&calm(X))=>(funny(X)&rich(X))))&
((?[X]:((~rich(X)<~>~quiet(X))))<=>(?[X]:(~funny(X))))&
(((rich(susan)&~rich(susan)))<=>((~kind(mary)<~>~happy(mary))))&
((~rich(lucy)|~patient(lucy)))&
(?[X]:((patient(X)&calm(X))))&
(?[X]:((~rich(X)|~calm(X))))&
(?[X]:((quiet(X)&~creative(X))))&
(?[X]:((quiet(X)|~patient(X)))) | ~wise(paul) | [] | null | 0 |
If someone is tall then john is kind or brave and vice versa. Everyone who is both not funny and humble is not generous or not brave. Everyone who is generous is not old. Everyone who is both humble and funny is not rich or strong and vice versa. Everyone who is strong is creative or not brave. Everyone who is brave or not old is not kind and vice versa. Everyone who is both rich and funny is both strong and calm and vice versa. Everyone who is not creative is not happy. Everyone who is strong or humble is either quiet or creative. If alice is not funny then lucy is not old. If mary is not wise or not tall then paul is both quiet and not brave and vice versa. Everyone who is brave or not generous is not funny. Everyone who is not generous is either not happy or rich. If someone is both curious and not kind then someone is old or not happy. Everyone who is both not kind and not humble is calm and vice versa. Someone is strong or wise. Someone is curious or calm. Someone is calm or not funny. Someone is either old or not curious. Someone is either not tall or not calm. Susan is both not rich and not creative. John is happy or funny. Alice is funny. | Susan is not calm. | entailment | ((?[X]:(tall(X)))<=>((kind(john)|brave(john))))&
(![X]:((~funny(X)&humble(X))=>(~generous(X)|~brave(X))))&
(![X]:(generous(X)=>~old(X)))&
(![X]:((humble(X)&funny(X))<=>(~rich(X)|strong(X))))&
(![X]:(strong(X)=>(creative(X)|~brave(X))))&
(![X]:((brave(X)|~old(X))<=>~kind(X)))&
(![X]:((rich(X)&funny(X))<=>(strong(X)&calm(X))))&
(![X]:(~creative(X)=>~happy(X)))&
(![X]:((strong(X)|humble(X))=>(quiet(X)<~>creative(X))))&
((~funny(alice))=>(~old(lucy)))&
(((~wise(mary)|~tall(mary)))<=>((quiet(paul)&~brave(paul))))&
(![X]:((brave(X)|~generous(X))=>~funny(X)))&
(![X]:(~generous(X)=>(~happy(X)<~>rich(X))))&
((?[X]:((curious(X)&~kind(X))))=>(?[X]:((old(X)|~happy(X)))))&
(![X]:((~kind(X)&~humble(X))<=>calm(X)))&
(?[X]:((strong(X)|wise(X))))&
(?[X]:((curious(X)|calm(X))))&
(?[X]:((calm(X)|~funny(X))))&
(?[X]:((old(X)<~>~curious(X))))&
(?[X]:((~tall(X)<~>~calm(X))))&
((~rich(susan)&~creative(susan)))&
((happy(john)|funny(john)))&
(funny(alice)) | ~calm(susan) | [
"p3",
"p14",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 732704321090386495709830
% SZS output start Proof for 732704321090386495709830
4. ! [X0] : ((funny(X0) & humble(X0)) <=> (strong(X0) | ~rich(X0))) [input p3]
15. ! [X0] : ((~humble(X0) & ~kind(X0)) <=> calm(X0)) [input p14]
21. ~creative(susan) & ~rich(susan) [input p20]
24. calm(susan) [input hypothesis]
42. ! [X0] : (((funny(X0) & humble(X0)) | (~strong(X0) & rich(X0))) & ((strong(X0) | ~rich(X0)) | (~funny(X0) | ~humble(X0)))) [nnf transformation 4]
43. ! [X0] : (((funny(X0) & humble(X0)) | (~strong(X0) & rich(X0))) & (strong(X0) | ~rich(X0) | ~funny(X0) | ~humble(X0))) [flattening 42]
55. ! [X0] : (((~humble(X0) & ~kind(X0)) | ~calm(X0)) & (calm(X0) | (humble(X0) | kind(X0)))) [nnf transformation 15]
56. ! [X0] : (((~humble(X0) & ~kind(X0)) | ~calm(X0)) & (calm(X0) | humble(X0) | kind(X0))) [flattening 55]
75. rich(X0) | humble(X0) [cnf transformation 43]
105. ~calm(X0) | ~humble(X0) [cnf transformation 56]
113. ~rich(susan) [cnf transformation 21]
117. calm(susan) [cnf transformation 24]
235. humble(susan) [resolution 75,113]
249. ~humble(susan) [resolution 105,117]
250. $false [subsumption resolution 249,235]
% SZS output end Proof for 732704321090386495709830
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 susan is not rich then someone is either quiet or happy.
If mary is either not kind or funny then mary is not rich or not happy.
If someone is both not quiet and old then someone is either not strong or not curious.
Everyone who is brave is both not generous and not patient and vice versa.
Everyone who is not strong or rich is either curious or funny.
Everyone who is both creative and rich is both not wise and not creative.
Everyone who is not kind is either not rich or happy and vice versa.
Everyone who is either calm or not wise is both not patient and funny and vice versa.
Everyone who is either not quiet or not strong is either not happy or patient and vice versa.
Everyone who is both tall and not strong is not patient and vice versa.
If someone is not patient or strong then someone is humble.
If john is either brave or wise then mary is either old or happy.
Everyone who is strong is quiet and vice versa.
Everyone who is either not funny or creative is not calm and vice versa.
If fred is either not happy or brave then someone is brave and vice versa.
Everyone who is both not curious and patient is either not brave or patient and vice versa.
Someone is quiet or not brave.
Someone is curious or not funny.
Someone is either not strong or not rich.
Someone is either brave or not quiet.
Someone is not kind or not calm.
John is tall or not curious.
John is wise or old.
Mary is not happy. | Mary is not strong. | neutral | ((~rich(susan))=>(?[X]:((quiet(X)<~>happy(X)))))&
(((~kind(mary)<~>funny(mary)))=>((~rich(mary)|~happy(mary))))&
((?[X]:((~quiet(X)&old(X))))=>(?[X]:((~strong(X)<~>~curious(X)))))&
(![X]:(brave(X)<=>(~generous(X)&~patient(X))))&
(![X]:((~strong(X)|rich(X))=>(curious(X)<~>funny(X))))&
(![X]:((creative(X)&rich(X))=>(~wise(X)&~creative(X))))&
(![X]:(~kind(X)<=>(~rich(X)<~>happy(X))))&
(![X]:((calm(X)<~>~wise(X))<=>(~patient(X)&funny(X))))&
(![X]:((~quiet(X)<~>~strong(X))<=>(~happy(X)<~>patient(X))))&
(![X]:((tall(X)&~strong(X))<=>~patient(X)))&
((?[X]:((~patient(X)|strong(X))))=>(?[X]:(humble(X))))&
(((brave(john)<~>wise(john)))=>((old(mary)<~>happy(mary))))&
(![X]:(strong(X)<=>quiet(X)))&
(![X]:((~funny(X)<~>creative(X))<=>~calm(X)))&
(((~happy(fred)<~>brave(fred)))<=>(?[X]:(brave(X))))&
(![X]:((~curious(X)&patient(X))<=>(~brave(X)<~>patient(X))))&
(?[X]:((quiet(X)|~brave(X))))&
(?[X]:((curious(X)|~funny(X))))&
(?[X]:((~strong(X)<~>~rich(X))))&
(?[X]:((brave(X)<~>~quiet(X))))&
(?[X]:((~kind(X)|~calm(X))))&
((tall(john)|~curious(john)))&
((wise(john)|old(john)))&
(~happy(mary)) | ~strong(mary) | [] | null | 0 |
If mary is kind then mary is humble and vice versa. If lucy is both not happy and not wise then someone is not strong or not happy and vice versa. If paul is tall then someone is both old and not old and vice versa. If someone is humble or not humble then alice is either not brave or patient and vice versa. If susan is calm or not curious then john is both not wise and happy. If someone is not kind then someone is not strong. If someone is generous or not patient then someone is not happy or curious. If alice is either not calm or not wise then someone is both tall and not humble and vice versa. If someone is both tall and strong then paul is not tall or not kind and vice versa. Everyone who is generous or not brave is both not tall and not old and vice versa. Everyone who is not humble is both not strong and not calm and vice versa. Everyone who is both brave and not strong is both not old and not calm. If susan is both calm and wise then someone is not curious. Everyone who is either not wise or funny is calm or not curious. If john is rich then paul is not wise or not tall and vice versa. Everyone who is curious or not tall is both old and not wise. Someone is strong or not funny. Mary is both curious and not patient. Mary is not calm. Someone is either brave or not patient. Paul is either quiet or not curious. Someone is not tall. Susan is either humble or not happy. | John is not generous. | entailment | ((kind(mary))<=>(humble(mary)))&
(((~happy(lucy)&~wise(lucy)))<=>(?[X]:((~strong(X)|~happy(X)))))&
((tall(paul))<=>(?[X]:((old(X)&~old(X)))))&
((?[X]:((humble(X)|~humble(X))))<=>((~brave(alice)<~>patient(alice))))&
(((calm(susan)|~curious(susan)))=>((~wise(john)&happy(john))))&
((?[X]:(~kind(X)))=>(?[X]:(~strong(X))))&
((?[X]:((generous(X)|~patient(X))))=>(?[X]:((~happy(X)|curious(X)))))&
(((~calm(alice)<~>~wise(alice)))<=>(?[X]:((tall(X)&~humble(X)))))&
((?[X]:((tall(X)&strong(X))))<=>((~tall(paul)|~kind(paul))))&
(![X]:((generous(X)|~brave(X))<=>(~tall(X)&~old(X))))&
(![X]:(~humble(X)<=>(~strong(X)&~calm(X))))&
(![X]:((brave(X)&~strong(X))=>(~old(X)&~calm(X))))&
(((calm(susan)&wise(susan)))=>(?[X]:(~curious(X))))&
(![X]:((~wise(X)<~>funny(X))=>(calm(X)|~curious(X))))&
((rich(john))<=>((~wise(paul)|~tall(paul))))&
(![X]:((curious(X)|~tall(X))=>(old(X)&~wise(X))))&
(?[X]:((strong(X)|~funny(X))))&
((curious(mary)&~patient(mary)))&
(~calm(mary))&
(?[X]:((brave(X)<~>~patient(X))))&
((quiet(paul)<~>~curious(paul)))&
(?[X]:(~tall(X)))&
((humble(susan)<~>~happy(susan))) | ~generous(john) | [
"p9",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 5433087136422213766444880
% SZS output start Proof for 5433087136422213766444880
10. ! [X0] : ((~brave(X0) | generous(X0)) <=> (~old(X0) & ~tall(X0))) [input p9]
16. ! [X0] : ((~tall(X0) | curious(X0)) => (~wise(X0) & old(X0))) [input p15]
24. generous(john) [input hypothesis]
36. ! [X0] : ((~wise(X0) & old(X0)) | (tall(X0) & ~curious(X0))) [ennf transformation 16]
66. ! [X0] : (((~brave(X0) | generous(X0)) | (old(X0) | tall(X0))) & ((~old(X0) & ~tall(X0)) | (brave(X0) & ~generous(X0)))) [nnf transformation 10]
67. ! [X0] : ((~brave(X0) | generous(X0) | old(X0) | tall(X0)) & ((~old(X0) & ~tall(X0)) | (brave(X0) & ~generous(X0)))) [flattening 66]
118. ~generous(X0) | ~tall(X0) [cnf transformation 67]
120. ~generous(X0) | ~old(X0) [cnf transformation 67]
135. old(X0) | tall(X0) [cnf transformation 36]
149. generous(john) [cnf transformation 24]
364. ~tall(john) [resolution 118,149]
366. ~old(john) [resolution 120,149]
371. tall(john) [resolution 135,366]
373. $false [subsumption resolution 371,364]
% SZS output end Proof for 5433087136422213766444880
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not rich then someone is either strong or not funny and vice versa.
Everyone who is not brave or curious is either humble or happy and vice versa.
Everyone who is both not calm and old is patient.
If someone is not brave or not kind then susan is old or not patient and vice versa.
If john is both calm and not strong then someone is calm or not calm.
Everyone who is both not wise and kind is curious or not old.
If someone is either kind or curious then john is both not tall and calm.
Everyone who is not rich or not quiet is creative or not wise.
Everyone who is either curious or not humble is both generous and happy and vice versa.
Everyone who is not patient or patient is both calm and not generous.
If someone is strong or not kind then someone is not humble or strong and vice versa.
Everyone who is both not old and funny is both not creative and humble and vice versa.
Everyone who is both not curious and wise is either not humble or not brave.
Everyone who is either not humble or not curious is wise.
Everyone who is old or happy is not old.
Everyone who is not humble is old or not old.
Someone is either generous or not rich.
John is both kind and happy.
Someone is both wise and curious.
Someone is either strong or patient.
Someone is either not wise or patient.
Someone is happy or creative.
Someone is both not generous and not tall.
Susan is not generous or not old. | John is not generous. | entailment | ((~rich(mary))<=>(?[X]:((strong(X)<~>~funny(X)))))&
(![X]:((~brave(X)|curious(X))<=>(humble(X)<~>happy(X))))&
(![X]:((~calm(X)&old(X))=>patient(X)))&
((?[X]:((~brave(X)|~kind(X))))<=>((old(susan)|~patient(susan))))&
(((calm(john)&~strong(john)))=>(?[X]:((calm(X)|~calm(X)))))&
(![X]:((~wise(X)&kind(X))=>(curious(X)|~old(X))))&
((?[X]:((kind(X)<~>curious(X))))=>((~tall(john)&calm(john))))&
(![X]:((~rich(X)|~quiet(X))=>(creative(X)|~wise(X))))&
(![X]:((curious(X)<~>~humble(X))<=>(generous(X)&happy(X))))&
(![X]:((~patient(X)|patient(X))=>(calm(X)&~generous(X))))&
((?[X]:((strong(X)|~kind(X))))<=>(?[X]:((~humble(X)|strong(X)))))&
(![X]:((~old(X)&funny(X))<=>(~creative(X)&humble(X))))&
(![X]:((~curious(X)&wise(X))=>(~humble(X)<~>~brave(X))))&
(![X]:((~humble(X)<~>~curious(X))=>wise(X)))&
(![X]:((old(X)|happy(X))=>~old(X)))&
(![X]:(~humble(X)=>(old(X)|~old(X))))&
(?[X]:((generous(X)<~>~rich(X))))&
((kind(john)&happy(john)))&
(?[X]:((wise(X)&curious(X))))&
(?[X]:((strong(X)<~>patient(X))))&
(?[X]:((~wise(X)<~>patient(X))))&
(?[X]:((happy(X)|creative(X))))&
(?[X]:((~generous(X)&~tall(X))))&
((~generous(susan)|~old(susan))) | ~generous(john) | [
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 55355500356990373823603
% SZS output start Proof for 55355500356990373823603
10. ! [X0] : ((patient(X0) | ~patient(X0)) => (~generous(X0) & calm(X0))) [input p9]
25. generous(john) [input hypothesis]
39. ! [X0] : ((~generous(X0) & calm(X0)) | (~patient(X0) & patient(X0))) [ennf transformation 10]
114. ~generous(X0) | patient(X0) [cnf transformation 39]
115. ~generous(X0) | ~patient(X0) [cnf transformation 39]
144. generous(john) [cnf transformation 25]
210. ~generous(X0) [subsumption resolution 114,115]
268. $false [subsumption resolution 144,210]
% SZS output end Proof for 55355500356990373823603
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall or not rich is either funny or not generous. Everyone who is not curious or creative is creative. If paul is patient then someone is either happy or not curious. If someone is not creative or not kind then someone is not tall. If someone is both old and not calm then someone is not strong and vice versa. If susan is old then lucy is either rich or happy. Everyone who is not tall or patient is not calm. Everyone who is not rich or not calm is either wise or not rich. If alice is not humble or not quiet then lucy is tall or not humble and vice versa. Everyone who is not calm or generous is not funny or not calm and vice versa. Everyone who is either strong or not happy is either patient or not brave. If alice is both humble and not brave then susan is either not wise or curious. If someone is either not patient or curious then alice is kind and vice versa. If someone is funny or not wise then susan is either creative or brave. If lucy is not calm or not creative then lucy is either brave or wise. Everyone who is both not strong and not old is either not calm or not creative and vice versa. Susan is not brave. Fred is funny or patient. Someone is patient or not funny. Someone is either curious or not curious. Someone is either not patient or not old. Paul is not rich or creative. Someone is generous or not curious. Someone is not brave or not funny. | Fred is not calm. | entailment | (![X]:((tall(X)|~rich(X))=>(funny(X)<~>~generous(X))))&
(![X]:((~curious(X)|creative(X))=>creative(X)))&
((patient(paul))=>(?[X]:((happy(X)<~>~curious(X)))))&
((?[X]:((~creative(X)|~kind(X))))=>(?[X]:(~tall(X))))&
((?[X]:((old(X)&~calm(X))))<=>(?[X]:(~strong(X))))&
((old(susan))=>((rich(lucy)<~>happy(lucy))))&
(![X]:((~tall(X)|patient(X))=>~calm(X)))&
(![X]:((~rich(X)|~calm(X))=>(wise(X)<~>~rich(X))))&
(((~humble(alice)|~quiet(alice)))<=>((tall(lucy)|~humble(lucy))))&
(![X]:((~calm(X)|generous(X))<=>(~funny(X)|~calm(X))))&
(![X]:((strong(X)<~>~happy(X))=>(patient(X)<~>~brave(X))))&
(((humble(alice)&~brave(alice)))=>((~wise(susan)<~>curious(susan))))&
((?[X]:((~patient(X)<~>curious(X))))<=>(kind(alice)))&
((?[X]:((funny(X)|~wise(X))))=>((creative(susan)<~>brave(susan))))&
(((~calm(lucy)|~creative(lucy)))=>((brave(lucy)<~>wise(lucy))))&
(![X]:((~strong(X)&~old(X))<=>(~calm(X)<~>~creative(X))))&
(~brave(susan))&
((funny(fred)|patient(fred)))&
(?[X]:((patient(X)|~funny(X))))&
(?[X]:((curious(X)<~>~curious(X))))&
(?[X]:((~patient(X)<~>~old(X))))&
((~rich(paul)|creative(paul)))&
(?[X]:((generous(X)|~curious(X))))&
(?[X]:((~brave(X)|~funny(X)))) | ~calm(fred) | [
"p0",
"p6",
"p9",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 4126342943607700319609785
% SZS output start Proof for 4126342943607700319609785
1. ! [X0] : ((~rich(X0) | tall(X0)) => (funny(X0) <~> ~generous(X0))) [input p0]
7. ! [X0] : ((patient(X0) | ~tall(X0)) => ~calm(X0)) [input p6]
10. ! [X0] : ((generous(X0) | ~calm(X0)) <=> (~calm(X0) | ~funny(X0))) [input p9]
18. patient(fred) | funny(fred) [input p17]
25. calm(fred) [input hypothesis]
28. ! [X0] : ((funny(X0) <~> ~generous(X0)) | (rich(X0) & ~tall(X0))) [ennf transformation 1]
33. ! [X0] : (~calm(X0) | (~patient(X0) & tall(X0))) [ennf transformation 7]
40. ! [X0] : (((generous(X0) | ~funny(X0)) & (~generous(X0) | funny(X0))) | (rich(X0) & ~tall(X0))) [nnf transformation 28]
56. ! [X0] : (((generous(X0) | ~calm(X0)) | (calm(X0) & funny(X0))) & ((~calm(X0) | ~funny(X0)) | (~generous(X0) & calm(X0)))) [nnf transformation 10]
57. ! [X0] : ((generous(X0) | ~calm(X0) | (calm(X0) & funny(X0))) & (~calm(X0) | ~funny(X0) | (~generous(X0) & calm(X0)))) [flattening 56]
82. ~funny(X0) | generous(X0) | ~tall(X0) [cnf transformation 40]
95. ~calm(X0) | tall(X0) [cnf transformation 33]
96. ~calm(X0) | ~patient(X0) [cnf transformation 33]
106. ~calm(X0) | ~funny(X0) | ~generous(X0) [cnf transformation 57]
134. patient(fred) | funny(fred) [cnf transformation 18]
143. calm(fred) [cnf transformation 25]
302. 35 <=> funny(fred) [avatar definition]
304. funny(fred) <- (35) [avatar component clause 302]
306. 36 <=> patient(fred) [avatar definition]
309. 35 | 36 [avatar split clause 134,306,302]
358. tall(fred) [resolution 95,143]
359. ~patient(fred) [resolution 96,143]
360. ~36 [avatar split clause 359,306]
361. generous(fred) | ~tall(fred) <- (35) [resolution 82,304]
362. generous(fred) <- (35) [subsumption resolution 361,358]
366. ~funny(fred) | ~generous(fred) [resolution 106,143]
367. ~generous(fred) <- (35) [subsumption resolution 366,304]
368. $false <- (35) [subsumption resolution 367,362]
369. ~35 [avatar contradiction clause 368]
370. $false [avatar sat refutation 309,360,369]
% SZS output end Proof for 4126342943607700319609785
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
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