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 both not old and not calm is either not tall or not happy and vice versa. Everyone who is not kind or not funny is either wise or not funny and vice versa. Everyone who is either happy or not calm is either not happy or not calm. Everyone who is not curious is not strong. If alice is quiet or not kind then susan is either not generous or not rich and vice versa. If someone is not brave then john is happy and vice versa. If john is not curious then someone is not tall and vice versa. Everyone who is old is both not old and not kind. Everyone who is either not kind or happy is not wise or not happy and vice versa. If susan is both brave and tall then someone is either not curious or not tall and vice versa. If alice is not calm or not kind then mary is brave. Everyone who is either generous or not creative is both not happy and happy. Everyone who is not strong or not curious is both humble and quiet. Everyone who is not kind is funny and vice versa. Everyone who is both not generous and not funny is not brave or not rich and vice versa. If someone is either not kind or not calm then alice is brave and vice versa. Someone is either kind or not quiet. Someone is both not calm and rich. Someone is either not old or tall. Susan is rich or not patient. John is generous or not rich. Someone is either curious or funny. Someone is either not old or brave. | Mary is not strong. | entailment | (![X]:((~old(X)&~calm(X))<=>(~tall(X)<~>~happy(X))))&
(![X]:((~kind(X)|~funny(X))<=>(wise(X)<~>~funny(X))))&
(![X]:((happy(X)<~>~calm(X))=>(~happy(X)<~>~calm(X))))&
(![X]:(~curious(X)=>~strong(X)))&
(((quiet(alice)|~kind(alice)))<=>((~generous(susan)<~>~rich(susan))))&
((?[X]:(~brave(X)))<=>(happy(john)))&
((~curious(john))<=>(?[X]:(~tall(X))))&
(![X]:(old(X)=>(~old(X)&~kind(X))))&
(![X]:((~kind(X)<~>happy(X))<=>(~wise(X)|~happy(X))))&
(((brave(susan)&tall(susan)))<=>(?[X]:((~curious(X)<~>~tall(X)))))&
(((~calm(alice)|~kind(alice)))=>(brave(mary)))&
(![X]:((generous(X)<~>~creative(X))=>(~happy(X)&happy(X))))&
(![X]:((~strong(X)|~curious(X))=>(humble(X)&quiet(X))))&
(![X]:(~kind(X)<=>funny(X)))&
(![X]:((~generous(X)&~funny(X))<=>(~brave(X)|~rich(X))))&
((?[X]:((~kind(X)<~>~calm(X))))<=>(brave(alice)))&
(?[X]:((kind(X)<~>~quiet(X))))&
(?[X]:((~calm(X)&rich(X))))&
(?[X]:((~old(X)<~>tall(X))))&
((rich(susan)|~patient(susan)))&
((generous(john)|~rich(john)))&
(?[X]:((curious(X)<~>funny(X))))&
(?[X]:((~old(X)<~>brave(X)))) | ~strong(mary) | [
"p0",
"p2",
"p3",
"p7",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 554624790938969559687973
% SZS output start Proof for 554624790938969559687973
1. ! [X0] : ((~calm(X0) & ~old(X0)) <=> (~tall(X0) <~> ~happy(X0))) [input p0]
3. ! [X0] : ((happy(X0) <~> ~calm(X0)) => (~happy(X0) <~> ~calm(X0))) [input p2]
4. ! [X0] : (~curious(X0) => ~strong(X0)) [input p3]
8. ! [X0] : (old(X0) => (~kind(X0) & ~old(X0))) [input p7]
10. (tall(susan) & brave(susan)) <=> ? [X0] : (~curious(X0) <~> ~tall(X0)) [input p9]
24. strong(mary) [input hypothesis]
27. ! [X0] : ((~happy(X0) <~> ~calm(X0)) | (happy(X0) <=> ~calm(X0))) [ennf transformation 3]
28. ! [X0] : (~strong(X0) | curious(X0)) [ennf transformation 4]
29. ! [X0] : ((~kind(X0) & ~old(X0)) | ~old(X0)) [ennf transformation 8]
33. ! [X0] : (((~calm(X0) & ~old(X0)) | ((~tall(X0) | happy(X0)) & (~happy(X0) | tall(X0)))) & (((happy(X0) | tall(X0)) & (~happy(X0) | ~tall(X0))) | (calm(X0) | old(X0)))) [nnf transformation 1]
34. ! [X0] : (((~calm(X0) & ~old(X0)) | ((~tall(X0) | happy(X0)) & (~happy(X0) | tall(X0)))) & (((happy(X0) | tall(X0)) & (~happy(X0) | ~tall(X0))) | calm(X0) | old(X0))) [flattening 33]
37. ! [X0] : (((calm(X0) | happy(X0)) & (~calm(X0) | ~happy(X0))) | ((happy(X0) | calm(X0)) & (~calm(X0) | ~happy(X0)))) [nnf transformation 27]
50. ((tall(susan) & brave(susan)) | ! [X0] : ((~curious(X0) | tall(X0)) & (~tall(X0) | curious(X0)))) & (? [X0] : ((tall(X0) | curious(X0)) & (~tall(X0) | ~curious(X0))) | (~tall(susan) | ~brave(susan))) [nnf transformation 10]
51. ((tall(susan) & brave(susan)) | ! [X0] : ((~curious(X0) | tall(X0)) & (~tall(X0) | curious(X0)))) & (? [X0] : ((tall(X0) | curious(X0)) & (~tall(X0) | ~curious(X0))) | ~tall(susan) | ~brave(susan)) [flattening 50]
52. ((tall(susan) & brave(susan)) | ! [X0] : ((~curious(X0) | tall(X0)) & (~tall(X0) | curious(X0)))) & (? [X1] : ((tall(X1) | curious(X1)) & (~tall(X1) | ~curious(X1))) | ~tall(susan) | ~brave(susan)) [rectify 51]
53. ? [X1] : ((tall(X1) | curious(X1)) & (~tall(X1) | ~curious(X1))) => ((tall(sK2) | curious(sK2)) & (~tall(sK2) | ~curious(sK2))) [choice axiom]
54. ((tall(susan) & brave(susan)) | ! [X0] : ((~curious(X0) | tall(X0)) & (~tall(X0) | curious(X0)))) & (((tall(sK2) | curious(sK2)) & (~tall(sK2) | ~curious(sK2))) | ~tall(susan) | ~brave(susan)) [skolemisation 52,53]
77. ~happy(X0) | ~tall(X0) | calm(X0) | old(X0) [cnf transformation 34]
82. ~tall(X0) | ~calm(X0) | happy(X0) [cnf transformation 34]
89. ~calm(X0) | ~happy(X0) | ~calm(X0) | ~happy(X0) [cnf transformation 37]
92. calm(X0) | happy(X0) | happy(X0) | calm(X0) [cnf transformation 37]
93. ~strong(X0) | curious(X0) [cnf transformation 28]
104. ~old(X0) | ~old(X0) [cnf transformation 29]
117. tall(susan) | ~curious(X0) | tall(X0) [cnf transformation 54]
148. strong(mary) [cnf transformation 24]
151. ~old(X0) [duplicate literal removal 104]
152. ~happy(X0) | ~calm(X0) [duplicate literal removal 89]
153. happy(X0) | calm(X0) [duplicate literal removal 92]
206. 11 <=> ! [X0] : (~curious(X0) | tall(X0)) [avatar definition]
207. ~curious(X0) | tall(X0) <- (11) [avatar component clause 206]
209. 12 <=> tall(susan) [avatar definition]
211. tall(susan) <- (12) [avatar component clause 209]
212. 11 | 12 [avatar split clause 117,209,206]
298. curious(mary) [resolution 93,148]
324. tall(mary) <- (11) [resolution 207,298]
353. ~calm(mary) | happy(mary) <- (11) [resolution 82,324]
356. happy(mary) <- (11) [subsumption resolution 353,153]
396. ~calm(mary) <- (11) [resolution 356,152]
405. ~tall(X0) | calm(X0) | old(X0) | calm(X0) [resolution 77,153]
414. ~tall(X0) | calm(X0) | old(X0) [duplicate literal removal 405]
415. ~tall(X0) | calm(X0) [subsumption resolution 414,151]
463. calm(mary) <- (11) [resolution 415,324]
468. $false <- (11) [subsumption resolution 463,396]
469. ~11 [avatar contradiction clause 468]
474. calm(susan) <- (12) [resolution 211,415]
475. ~calm(susan) | happy(susan) <- (12) [resolution 211,82]
496. happy(susan) <- (12) [subsumption resolution 475,474]
505. ~calm(susan) <- (12) [resolution 496,152]
506. $false <- (12) [subsumption resolution 505,474]
507. ~12 [avatar contradiction clause 506]
508. $false [avatar sat refutation 212,469,507]
% SZS output end Proof for 554624790938969559687973
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 fred is not brave or creative then fred is both not humble and old.
Everyone who is not creative or quiet is not wise and vice versa.
Everyone who is both patient and not old is not kind and vice versa.
Everyone who is not strong or happy is both funny and not wise and vice versa.
If someone is both not generous and not brave then alice is not brave and vice versa.
Everyone who is not curious is either tall or old and vice versa.
If someone is either not calm or happy then alice is not quiet or not humble and vice versa.
Everyone who is funny or not patient is rich or not generous and vice versa.
If someone is generous then someone is not humble or creative.
Everyone who is not generous or not happy is not wise.
Everyone who is quiet is old or patient.
If fred is happy then susan is either funny or creative and vice versa.
If lucy is wise or quiet then paul is not brave.
Everyone who is both happy and not curious is both not humble and not kind.
If someone is humble or not funny then alice is either patient or rich and vice versa.
Everyone who is tall or not kind is both old and wise.
John is either creative or wise.
Someone is not humble or not old.
John is either not kind or not calm.
Paul is either not quiet or not creative.
Fred is not generous or not strong.
Alice is not patient or not rich.
Alice is not wise.
Alice is happy or humble. | Alice is not quiet. | entailment | (((~brave(fred)|creative(fred)))=>((~humble(fred)&old(fred))))&
(![X]:((~creative(X)|quiet(X))<=>~wise(X)))&
(![X]:((patient(X)&~old(X))<=>~kind(X)))&
(![X]:((~strong(X)|happy(X))<=>(funny(X)&~wise(X))))&
((?[X]:((~generous(X)&~brave(X))))<=>(~brave(alice)))&
(![X]:(~curious(X)<=>(tall(X)<~>old(X))))&
((?[X]:((~calm(X)<~>happy(X))))<=>((~quiet(alice)|~humble(alice))))&
(![X]:((funny(X)|~patient(X))<=>(rich(X)|~generous(X))))&
((?[X]:(generous(X)))=>(?[X]:((~humble(X)|creative(X)))))&
(![X]:((~generous(X)|~happy(X))=>~wise(X)))&
(![X]:(quiet(X)=>(old(X)|patient(X))))&
((happy(fred))<=>((funny(susan)<~>creative(susan))))&
(((wise(lucy)|quiet(lucy)))=>(~brave(paul)))&
(![X]:((happy(X)&~curious(X))=>(~humble(X)&~kind(X))))&
((?[X]:((humble(X)|~funny(X))))<=>((patient(alice)<~>rich(alice))))&
(![X]:((tall(X)|~kind(X))=>(old(X)&wise(X))))&
((creative(john)<~>wise(john)))&
(?[X]:((~humble(X)|~old(X))))&
((~kind(john)<~>~calm(john)))&
((~quiet(paul)<~>~creative(paul)))&
((~generous(fred)|~strong(fred)))&
((~patient(alice)|~rich(alice)))&
(~wise(alice))&
((happy(alice)|humble(alice))) | ~quiet(alice) | [
"p1",
"p2",
"p3",
"p5",
"p6",
"p9",
"p10",
"p13",
"p15",
"p16",
"p18",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 112450170554068279351531
% SZS output start Proof for 112450170554068279351531
2. ! [X0] : ((quiet(X0) | ~creative(X0)) <=> ~wise(X0)) [input p1]
3. ! [X0] : ((~old(X0) & patient(X0)) <=> ~kind(X0)) [input p2]
4. ! [X0] : ((happy(X0) | ~strong(X0)) <=> (~wise(X0) & funny(X0))) [input p3]
6. ! [X0] : (~curious(X0) <=> (tall(X0) <~> old(X0))) [input p5]
7. ? [X0] : (~calm(X0) <~> happy(X0)) <=> (~humble(alice) | ~quiet(alice)) [input p6]
10. ! [X0] : ((~happy(X0) | ~generous(X0)) => ~wise(X0)) [input p9]
11. ! [X0] : (quiet(X0) => (patient(X0) | old(X0))) [input p10]
14. ! [X0] : ((~curious(X0) & happy(X0)) => (~kind(X0) & ~humble(X0))) [input p13]
16. ! [X0] : ((~kind(X0) | tall(X0)) => (wise(X0) & old(X0))) [input p15]
17. creative(john) <~> wise(john) [input p16]
19. ~kind(john) <~> ~calm(john) [input p18]
24. humble(alice) | happy(alice) [input p23]
25. quiet(alice) [input hypothesis]
27. ! [X0] : ((tall(X0) <~> old(X0)) => ~curious(X0)) [unused predicate definition removal 6]
29. ! [X0] : (~curious(X0) | (tall(X0) <=> old(X0))) [ennf transformation 27]
31. ! [X0] : (~wise(X0) | (happy(X0) & generous(X0))) [ennf transformation 10]
32. ! [X0] : ((patient(X0) | old(X0)) | ~quiet(X0)) [ennf transformation 11]
33. ! [X0] : (patient(X0) | old(X0) | ~quiet(X0)) [flattening 32]
35. ! [X0] : ((~kind(X0) & ~humble(X0)) | (curious(X0) | ~happy(X0))) [ennf transformation 14]
36. ! [X0] : ((~kind(X0) & ~humble(X0)) | curious(X0) | ~happy(X0)) [flattening 35]
37. ! [X0] : ((wise(X0) & old(X0)) | (kind(X0) & ~tall(X0))) [ennf transformation 16]
38. ! [X0] : (((quiet(X0) | ~creative(X0)) | wise(X0)) & (~wise(X0) | (~quiet(X0) & creative(X0)))) [nnf transformation 2]
39. ! [X0] : ((quiet(X0) | ~creative(X0) | wise(X0)) & (~wise(X0) | (~quiet(X0) & creative(X0)))) [flattening 38]
40. ! [X0] : (((~old(X0) & patient(X0)) | kind(X0)) & (~kind(X0) | (old(X0) | ~patient(X0)))) [nnf transformation 3]
41. ! [X0] : (((~old(X0) & patient(X0)) | kind(X0)) & (~kind(X0) | old(X0) | ~patient(X0))) [flattening 40]
42. ! [X0] : (((happy(X0) | ~strong(X0)) | (wise(X0) | ~funny(X0))) & ((~wise(X0) & funny(X0)) | (~happy(X0) & strong(X0)))) [nnf transformation 4]
43. ! [X0] : ((happy(X0) | ~strong(X0) | wise(X0) | ~funny(X0)) & ((~wise(X0) & funny(X0)) | (~happy(X0) & strong(X0)))) [flattening 42]
48. ! [X0] : (~curious(X0) | ((tall(X0) | ~old(X0)) & (old(X0) | ~tall(X0)))) [nnf transformation 29]
49. (? [X0] : ((~happy(X0) | calm(X0)) & (happy(X0) | ~calm(X0))) | (humble(alice) & quiet(alice))) & ((~humble(alice) | ~quiet(alice)) | ! [X0] : ((~calm(X0) | ~happy(X0)) & (happy(X0) | calm(X0)))) [nnf transformation 7]
50. (? [X0] : ((~happy(X0) | calm(X0)) & (happy(X0) | ~calm(X0))) | (humble(alice) & quiet(alice))) & (~humble(alice) | ~quiet(alice) | ! [X0] : ((~calm(X0) | ~happy(X0)) & (happy(X0) | calm(X0)))) [flattening 49]
51. (? [X0] : ((~happy(X0) | calm(X0)) & (happy(X0) | ~calm(X0))) | (humble(alice) & quiet(alice))) & (~humble(alice) | ~quiet(alice) | ! [X1] : ((~calm(X1) | ~happy(X1)) & (happy(X1) | calm(X1)))) [rectify 50]
52. ? [X0] : ((~happy(X0) | calm(X0)) & (happy(X0) | ~calm(X0))) => ((~happy(sK1) | calm(sK1)) & (happy(sK1) | ~calm(sK1))) [choice axiom]
53. (((~happy(sK1) | calm(sK1)) & (happy(sK1) | ~calm(sK1))) | (humble(alice) & quiet(alice))) & (~humble(alice) | ~quiet(alice) | ! [X1] : ((~calm(X1) | ~happy(X1)) & (happy(X1) | calm(X1)))) [skolemisation 51,52]
64. (~wise(john) | ~creative(john)) & (wise(john) | creative(john)) [nnf transformation 17]
67. (calm(john) | kind(john)) & (~calm(john) | ~kind(john)) [nnf transformation 19]
75. ~creative(X0) | quiet(X0) | wise(X0) [cnf transformation 39]
76. ~kind(X0) | old(X0) | ~patient(X0) [cnf transformation 41]
82. ~happy(X0) | ~wise(X0) [cnf transformation 43]
88. ~curious(X0) | tall(X0) | ~old(X0) [cnf transformation 48]
89. ~humble(alice) | ~quiet(alice) | happy(X1) | calm(X1) [cnf transformation 53]
101. ~wise(X0) | happy(X0) [cnf transformation 31]
102. ~quiet(X0) | old(X0) | patient(X0) [cnf transformation 33]
110. ~happy(X0) | curious(X0) | ~kind(X0) [cnf transformation 36]
119. wise(X0) | ~tall(X0) [cnf transformation 37]
120. wise(X0) | kind(X0) [cnf transformation 37]
121. wise(john) | creative(john) [cnf transformation 64]
124. ~calm(john) | ~kind(john) [cnf transformation 67]
131. humble(alice) | happy(alice) [cnf transformation 24]
132. quiet(alice) [cnf transformation 25]
172. 9 <=> humble(alice) [avatar definition]
185. 12 <=> quiet(alice) [avatar definition]
187. quiet(alice) <- (12) [avatar component clause 185]
196. 14 <=> ! [X1] : (happy(X1) | calm(X1)) [avatar definition]
197. calm(X1) | happy(X1) <- (14) [avatar component clause 196]
198. 14 | ~12 | ~9 [avatar split clause 89,172,185,196]
211. ~wise(X0) [subsumption resolution 101,82]
242. 24 <=> patient(alice) [avatar definition]
244. patient(alice) <- (24) [avatar component clause 242]
265. kind(X0) [subsumption resolution 120,211]
266. ~tall(X0) [subsumption resolution 119,211]
267. creative(john) [subsumption resolution 121,211]
277. ~calm(john) [subsumption resolution 124,265]
299. 35 <=> happy(alice) [avatar definition]
301. happy(alice) <- (35) [avatar component clause 299]
302. 35 | 9 [avatar split clause 131,172,299]
303. 12 [avatar split clause 132,185]
307. happy(john) <- (14) [resolution 197,277]
309. quiet(john) | wise(john) [resolution 75,267]
310. quiet(john) [subsumption resolution 309,211]
314. ~patient(X1) | old(X1) [resolution 76,265]
316. old(alice) | patient(alice) <- (12) [resolution 102,187]
318. old(john) | patient(john) [resolution 102,310]
321. old(john) [subsumption resolution 318,314]
329. 37 <=> curious(john) [avatar definition]
331. curious(john) <- (37) [avatar component clause 329]
334. curious(john) | ~kind(john) <- (14) [resolution 110,307]
335. curious(john) <- (14) [subsumption resolution 334,265]
336. 37 | ~14 [avatar split clause 335,196,329]
337. curious(alice) | ~kind(alice) <- (35) [resolution 301,110]
341. curious(alice) <- (35) [subsumption resolution 337,265]
344. tall(alice) | ~old(alice) <- (35) [resolution 341,88]
345. ~old(alice) <- (35) [subsumption resolution 344,266]
348. patient(alice) <- (12, 35) [subsumption resolution 316,345]
349. 24 | ~12 | ~35 [avatar split clause 348,299,185,242]
351. old(alice) <- (24) [resolution 244,314]
352. $false <- (24, 35) [subsumption resolution 351,345]
353. ~24 | ~35 [avatar contradiction clause 352]
379. tall(john) | ~old(john) <- (37) [resolution 331,88]
380. ~old(john) <- (37) [subsumption resolution 379,266]
381. $false <- (37) [subsumption resolution 380,321]
382. ~37 [avatar contradiction clause 381]
383. $false [avatar sat refutation 198,302,303,336,349,353,382]
% SZS output end Proof for 112450170554068279351531
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both rich and creative is both old and curious and vice versa.
Everyone who is not happy is not wise and vice versa.
Everyone who is either patient or humble is both not brave and not strong and vice versa.
Everyone who is wise or kind is either not kind or not curious and vice versa.
If someone is both not quiet and funny then someone is both not old and old and vice versa.
Everyone who is not strong is both quiet and not generous.
Everyone who is strong is humble.
If susan is both not funny and patient then someone is calm and vice versa.
If someone is both not humble and happy then someone is strong and vice versa.
Everyone who is both not quiet and humble is not patient and vice versa.
Everyone who is not quiet is both old and happy and vice versa.
If mary is both not wise and brave then someone is humble and vice versa.
Everyone who is tall is both patient and not generous.
Everyone who is both not generous and funny is curious and vice versa.
If mary is quiet then susan is either happy or not brave.
Everyone who is either kind or not generous is both quiet and calm and vice versa.
John is both not old and wise.
Paul is tall.
Paul is both not humble and not happy.
Someone is not humble.
Someone is either tall or not curious.
Someone is not funny or calm.
Alice is humble.
Someone is not wise or not quiet. | Paul is not quiet. | contradiction | (![X]:((rich(X)&creative(X))<=>(old(X)&curious(X))))&
(![X]:(~happy(X)<=>~wise(X)))&
(![X]:((patient(X)<~>humble(X))<=>(~brave(X)&~strong(X))))&
(![X]:((wise(X)|kind(X))<=>(~kind(X)<~>~curious(X))))&
((?[X]:((~quiet(X)&funny(X))))<=>(?[X]:((~old(X)&old(X)))))&
(![X]:(~strong(X)=>(quiet(X)&~generous(X))))&
(![X]:(strong(X)=>humble(X)))&
(((~funny(susan)&patient(susan)))<=>(?[X]:(calm(X))))&
((?[X]:((~humble(X)&happy(X))))<=>(?[X]:(strong(X))))&
(![X]:((~quiet(X)&humble(X))<=>~patient(X)))&
(![X]:(~quiet(X)<=>(old(X)&happy(X))))&
(((~wise(mary)&brave(mary)))<=>(?[X]:(humble(X))))&
(![X]:(tall(X)=>(patient(X)&~generous(X))))&
(![X]:((~generous(X)&funny(X))<=>curious(X)))&
((quiet(mary))=>((happy(susan)<~>~brave(susan))))&
(![X]:((kind(X)<~>~generous(X))<=>(quiet(X)&calm(X))))&
((~old(john)&wise(john)))&
(tall(paul))&
((~humble(paul)&~happy(paul)))&
(?[X]:(~humble(X)))&
(?[X]:((tall(X)<~>~curious(X))))&
(?[X]:((~funny(X)|calm(X))))&
(humble(alice))&
(?[X]:((~wise(X)|~quiet(X)))) | ~quiet(paul) | [
"p5",
"p6",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 201252492721395160461010
% SZS output start Proof for 201252492721395160461010
6. ! [X0] : (~strong(X0) => (~generous(X0) & quiet(X0))) [input p5]
7. ! [X0] : (strong(X0) => humble(X0)) [input p6]
19. ~happy(paul) & ~humble(paul) [input p18]
25. ~quiet(paul) [input hypothesis]
28. ! [X0] : ((~generous(X0) & quiet(X0)) | strong(X0)) [ennf transformation 6]
29. ! [X0] : (humble(X0) | ~strong(X0)) [ennf transformation 7]
99. quiet(X0) | strong(X0) [cnf transformation 28]
101. ~strong(X0) | humble(X0) [cnf transformation 29]
133. ~humble(paul) [cnf transformation 19]
141. ~quiet(paul) [cnf transformation 25]
257. strong(paul) [resolution 99,141]
264. humble(paul) [resolution 101,257]
266. $false [subsumption resolution 264,133]
% SZS output end Proof for 201252492721395160461010
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient and rich then someone is either creative or not tall and vice versa.
Everyone who is either funny or old is either kind or tall and vice versa.
Everyone who is both not rich and brave is either patient or creative and vice versa.
If paul is not strong or not generous then susan is not creative.
If alice is either tall or not humble then susan is patient and vice versa.
Everyone who is not creative is quiet.
If fred is not calm or not curious then john is not generous or patient.
Everyone who is not patient or not curious is not kind or not humble.
Everyone who is either not humble or not generous is both not creative and wise and vice versa.
Everyone who is not old or not strong is either creative or old.
Everyone who is not strong or not quiet is not humble and vice versa.
Everyone who is not generous or not happy is not old.
If someone is either not humble or quiet then paul is not generous.
Everyone who is quiet is either strong or not funny.
Everyone who is wise or rich is humble or funny.
Fred is funny.
John is both rich and quiet.
John is not strong or strong.
John is strong.
Someone is not happy or humble. | Susan is not rich. | neutral | ((?[X]:((~patient(X)&rich(X))))<=>(?[X]:((creative(X)<~>~tall(X)))))&
(![X]:((funny(X)<~>old(X))<=>(kind(X)<~>tall(X))))&
(![X]:((~rich(X)&brave(X))<=>(patient(X)<~>creative(X))))&
(((~strong(paul)|~generous(paul)))=>(~creative(susan)))&
(((tall(alice)<~>~humble(alice)))<=>(patient(susan)))&
(![X]:(~creative(X)=>quiet(X)))&
(((~calm(fred)|~curious(fred)))=>((~generous(john)|patient(john))))&
(![X]:((~patient(X)|~curious(X))=>(~kind(X)|~humble(X))))&
(![X]:((~humble(X)<~>~generous(X))<=>(~creative(X)&wise(X))))&
(![X]:((~old(X)|~strong(X))=>(creative(X)<~>old(X))))&
(![X]:((~strong(X)|~quiet(X))<=>~humble(X)))&
(![X]:((~generous(X)|~happy(X))=>~old(X)))&
((?[X]:((~humble(X)<~>quiet(X))))=>(~generous(paul)))&
(![X]:(quiet(X)=>(strong(X)<~>~funny(X))))&
(![X]:((wise(X)|rich(X))=>(humble(X)|funny(X))))&
(funny(fred))&
((rich(john)&quiet(john)))&
((~strong(john)|strong(john)))&
(strong(john))&
(?[X]:((~happy(X)|humble(X)))) | ~rich(susan) | [] | null | 0 |
If mary is not wise or patient then someone is either not quiet or not patient.
If someone is not curious or not kind then someone is both not kind and not brave and vice versa.
Everyone who is not strong or generous is calm or generous and vice versa.
If john is both not quiet and funny then someone is either not kind or not tall and vice versa.
If lucy is both not humble and not old then someone is wise and vice versa.
Everyone who is happy is either not strong or not funny and vice versa.
Everyone who is curious or not old is curious.
Everyone who is not happy or happy is strong.
If someone is not strong or not quiet then someone is both not funny and patient.
Everyone who is not tall or kind is curious and vice versa.
Everyone who is both brave and not quiet is both quiet and not rich and vice versa.
Everyone who is happy is not happy or not kind and vice versa.
If someone is both kind and generous then someone is both wise and not tall and vice versa.
Everyone who is not creative or not rich is wise or not happy.
Everyone who is either not funny or humble is patient.
If paul is either not tall or humble then someone is either happy or not humble.
Someone is either not tall or not creative.
Someone is both humble and creative.
Someone is not calm or strong.
Someone is either not funny or old.
Alice is brave or patient.
Susan is both generous and not wise.
Someone is either tall or creative. | Lucy is curious. | entailment | (((~wise(mary)|patient(mary)))=>(?[X]:((~quiet(X)<~>~patient(X)))))&
((?[X]:((~curious(X)|~kind(X))))<=>(?[X]:((~kind(X)&~brave(X)))))&
(![X]:((~strong(X)|generous(X))<=>(calm(X)|generous(X))))&
(((~quiet(john)&funny(john)))<=>(?[X]:((~kind(X)<~>~tall(X)))))&
(((~humble(lucy)&~old(lucy)))<=>(?[X]:(wise(X))))&
(![X]:(happy(X)<=>(~strong(X)<~>~funny(X))))&
(![X]:((curious(X)|~old(X))=>curious(X)))&
(![X]:((~happy(X)|happy(X))=>strong(X)))&
((?[X]:((~strong(X)|~quiet(X))))=>(?[X]:((~funny(X)&patient(X)))))&
(![X]:((~tall(X)|kind(X))<=>curious(X)))&
(![X]:((brave(X)&~quiet(X))<=>(quiet(X)&~rich(X))))&
(![X]:(happy(X)<=>(~happy(X)|~kind(X))))&
((?[X]:((kind(X)&generous(X))))<=>(?[X]:((wise(X)&~tall(X)))))&
(![X]:((~creative(X)|~rich(X))=>(wise(X)|~happy(X))))&
(![X]:((~funny(X)<~>humble(X))=>patient(X)))&
(((~tall(paul)<~>humble(paul)))=>(?[X]:((happy(X)<~>~humble(X)))))&
(?[X]:((~tall(X)<~>~creative(X))))&
(?[X]:((humble(X)&creative(X))))&
(?[X]:((~calm(X)|strong(X))))&
(?[X]:((~funny(X)<~>old(X))))&
((brave(alice)|patient(alice)))&
((generous(susan)&~wise(susan)))&
(?[X]:((tall(X)<~>creative(X)))) | curious(lucy) | [
"p3",
"p5",
"p7",
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 572158326222381618815843
% SZS output start Proof for 572158326222381618815843
4. (funny(john) & ~quiet(john)) <=> ? [X0] : (~kind(X0) <~> ~tall(X0)) [input p3]
6. ! [X0] : (happy(X0) <=> (~strong(X0) <~> ~funny(X0))) [input p5]
8. ! [X0] : ((happy(X0) | ~happy(X0)) => strong(X0)) [input p7]
10. ! [X0] : ((kind(X0) | ~tall(X0)) <=> curious(X0)) [input p9]
12. ! [X0] : (happy(X0) <=> (~kind(X0) | ~happy(X0))) [input p11]
24. ~curious(lucy) [input hypothesis]
30. ! [X0] : (strong(X0) | (~happy(X0) & happy(X0))) [ennf transformation 8]
46. ((funny(john) & ~quiet(john)) | ! [X0] : ((~kind(X0) | tall(X0)) & (~tall(X0) | kind(X0)))) & (? [X0] : ((tall(X0) | kind(X0)) & (~tall(X0) | ~kind(X0))) | (~funny(john) | quiet(john))) [nnf transformation 4]
47. ((funny(john) & ~quiet(john)) | ! [X0] : ((~kind(X0) | tall(X0)) & (~tall(X0) | kind(X0)))) & (? [X0] : ((tall(X0) | kind(X0)) & (~tall(X0) | ~kind(X0))) | ~funny(john) | quiet(john)) [flattening 46]
48. ((funny(john) & ~quiet(john)) | ! [X0] : ((~kind(X0) | tall(X0)) & (~tall(X0) | kind(X0)))) & (? [X1] : ((tall(X1) | kind(X1)) & (~tall(X1) | ~kind(X1))) | ~funny(john) | quiet(john)) [rectify 47]
49. ? [X1] : ((tall(X1) | kind(X1)) & (~tall(X1) | ~kind(X1))) => ((tall(sK3) | kind(sK3)) & (~tall(sK3) | ~kind(sK3))) [choice axiom]
50. ((funny(john) & ~quiet(john)) | ! [X0] : ((~kind(X0) | tall(X0)) & (~tall(X0) | kind(X0)))) & (((tall(sK3) | kind(sK3)) & (~tall(sK3) | ~kind(sK3))) | ~funny(john) | quiet(john)) [skolemisation 48,49]
56. ! [X0] : ((happy(X0) | ((~strong(X0) | funny(X0)) & (~funny(X0) | strong(X0)))) & (((funny(X0) | strong(X0)) & (~funny(X0) | ~strong(X0))) | ~happy(X0))) [nnf transformation 6]
60. ! [X0] : (((kind(X0) | ~tall(X0)) | ~curious(X0)) & (curious(X0) | (~kind(X0) & tall(X0)))) [nnf transformation 10]
61. ! [X0] : ((kind(X0) | ~tall(X0) | ~curious(X0)) & (curious(X0) | (~kind(X0) & tall(X0)))) [flattening 60]
64. ! [X0] : ((happy(X0) | (kind(X0) & happy(X0))) & ((~kind(X0) | ~happy(X0)) | ~happy(X0))) [nnf transformation 12]
65. ! [X0] : ((happy(X0) | (kind(X0) & happy(X0))) & (~kind(X0) | ~happy(X0) | ~happy(X0))) [flattening 64]
105. funny(john) | ~tall(X0) | kind(X0) [cnf transformation 50]
110. ~happy(X0) | ~strong(X0) | ~funny(X0) [cnf transformation 56]
116. strong(X0) | happy(X0) [cnf transformation 30]
117. ~happy(X0) | strong(X0) [cnf transformation 30]
122. tall(X0) | curious(X0) [cnf transformation 61]
129. ~kind(X0) | ~happy(X0) | ~happy(X0) [cnf transformation 65]
130. happy(X0) | happy(X0) [cnf transformation 65]
131. happy(X0) | kind(X0) [cnf transformation 65]
156. ~curious(lucy) [cnf transformation 24]
157. ~kind(X0) | ~happy(X0) [duplicate literal removal 129]
158. happy(X0) [duplicate literal removal 130]
202. 10 <=> ! [X3] : curious(X3) [avatar definition]
203. curious(X3) <- (10) [avatar component clause 202]
215. 13 <=> funny(john) [avatar definition]
217. funny(john) <- (13) [avatar component clause 215]
220. 14 <=> ! [X0] : (~tall(X0) | kind(X0)) [avatar definition]
221. ~tall(X0) | kind(X0) <- (14) [avatar component clause 220]
222. 14 | 13 [avatar split clause 105,215,220]
257. strong(X0) [subsumption resolution 116,117]
271. ~kind(X0) [subsumption resolution 157,158]
371. ~strong(X0) | ~funny(X0) | kind(X0) [resolution 110,131]
373. ~funny(X0) | kind(X0) [subsumption resolution 371,257]
374. ~funny(X0) [subsumption resolution 373,271]
377. $false <- (13) [resolution 374,217]
378. ~13 [avatar contradiction clause 377]
379. ~tall(X0) <- (14) [subsumption resolution 221,271]
380. curious(X0) <- (14) [resolution 379,122]
383. 10 | ~14 [avatar split clause 380,220,202]
384. $false <- (10) [resolution 203,156]
387. ~10 [avatar contradiction clause 384]
388. $false [avatar sat refutation 222,378,383,387]
% SZS output end Proof for 572158326222381618815843
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not strong or old is creative or wise and vice versa. Everyone who is funny is either patient or not tall and vice versa. Everyone who is either not patient or not generous is both humble and not brave. Everyone who is brave or strong is either strong or brave. If alice is wise or old then john is both strong and brave and vice versa. If someone is calm then paul is not quiet or not funny and vice versa. Everyone who is both happy and not strong is either strong or not curious and vice versa. Everyone who is not curious or not rich is both not creative and patient. Everyone who is either creative or old is not quiet or not old. If mary is either not quiet or old then mary is both rich and not calm and vice versa. If mary is old then susan is creative. If paul is both patient and quiet then someone is curious or strong. If fred is creative then someone is happy and vice versa. Everyone who is quiet is either not wise or not strong and vice versa. If mary is not funny or calm then someone is both quiet and not quiet. Everyone who is both not creative and happy is not patient. Someone is either not quiet or strong. Someone is either not kind or not quiet. John is funny or not rich. Someone is either not wise or calm. Susan is either generous or tall. Someone is not strong or not calm. Someone is both not brave and not curious. | Fred is not creative. | entailment | (![X]:((~strong(X)|old(X))<=>(creative(X)|wise(X))))&
(![X]:(funny(X)<=>(patient(X)<~>~tall(X))))&
(![X]:((~patient(X)<~>~generous(X))=>(humble(X)&~brave(X))))&
(![X]:((brave(X)|strong(X))=>(strong(X)<~>brave(X))))&
(((wise(alice)|old(alice)))<=>((strong(john)&brave(john))))&
((?[X]:(calm(X)))<=>((~quiet(paul)|~funny(paul))))&
(![X]:((happy(X)&~strong(X))<=>(strong(X)<~>~curious(X))))&
(![X]:((~curious(X)|~rich(X))=>(~creative(X)&patient(X))))&
(![X]:((creative(X)<~>old(X))=>(~quiet(X)|~old(X))))&
(((~quiet(mary)<~>old(mary)))<=>((rich(mary)&~calm(mary))))&
((old(mary))=>(creative(susan)))&
(((patient(paul)&quiet(paul)))=>(?[X]:((curious(X)|strong(X)))))&
((creative(fred))<=>(?[X]:(happy(X))))&
(![X]:(quiet(X)<=>(~wise(X)<~>~strong(X))))&
(((~funny(mary)|calm(mary)))=>(?[X]:((quiet(X)&~quiet(X)))))&
(![X]:((~creative(X)&happy(X))=>~patient(X)))&
(?[X]:((~quiet(X)<~>strong(X))))&
(?[X]:((~kind(X)<~>~quiet(X))))&
((funny(john)|~rich(john)))&
(?[X]:((~wise(X)<~>calm(X))))&
((generous(susan)<~>tall(susan)))&
(?[X]:((~strong(X)|~calm(X))))&
(?[X]:((~brave(X)&~curious(X)))) | ~creative(fred) | [
"p6",
"p7",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 9072528547448190139323176
% SZS output start Proof for 9072528547448190139323176
7. ! [X0] : ((~strong(X0) & happy(X0)) <=> (strong(X0) <~> ~curious(X0))) [input p6]
8. ! [X0] : ((~rich(X0) | ~curious(X0)) => (patient(X0) & ~creative(X0))) [input p7]
13. creative(fred) <=> ? [X0] : happy(X0) [input p12]
16. ! [X0] : ((happy(X0) & ~creative(X0)) => ~patient(X0)) [input p15]
24. creative(fred) [input hypothesis]
28. ! [X0] : ((patient(X0) & ~creative(X0)) | (rich(X0) & curious(X0))) [ennf transformation 8]
35. ! [X0] : (~patient(X0) | (~happy(X0) | creative(X0))) [ennf transformation 16]
36. ! [X0] : (~patient(X0) | ~happy(X0) | creative(X0)) [flattening 35]
49. ! [X0] : (((~strong(X0) & happy(X0)) | ((strong(X0) | curious(X0)) & (~curious(X0) | ~strong(X0)))) & (((curious(X0) | ~strong(X0)) & (~curious(X0) | strong(X0))) | (strong(X0) | ~happy(X0)))) [nnf transformation 7]
50. ! [X0] : (((~strong(X0) & happy(X0)) | ((strong(X0) | curious(X0)) & (~curious(X0) | ~strong(X0)))) & (((curious(X0) | ~strong(X0)) & (~curious(X0) | strong(X0))) | strong(X0) | ~happy(X0))) [flattening 49]
56. (creative(fred) | ! [X0] : ~happy(X0)) & (? [X0] : happy(X0) | ~creative(fred)) [nnf transformation 13]
57. (creative(fred) | ! [X0] : ~happy(X0)) & (? [X1] : happy(X1) | ~creative(fred)) [rectify 56]
58. ? [X1] : happy(X1) => happy(sK2) [choice axiom]
59. (creative(fred) | ! [X0] : ~happy(X0)) & (happy(sK2) | ~creative(fred)) [skolemisation 57,58]
99. ~curious(X0) | strong(X0) | strong(X0) | ~happy(X0) [cnf transformation 50]
103. ~strong(X0) | ~curious(X0) | ~strong(X0) [cnf transformation 50]
105. ~creative(X0) | curious(X0) [cnf transformation 28]
107. curious(X0) | patient(X0) [cnf transformation 28]
119. happy(sK2) | ~creative(fred) [cnf transformation 59]
129. ~happy(X0) | ~patient(X0) | creative(X0) [cnf transformation 36]
142. creative(fred) [cnf transformation 24]
144. ~curious(X0) | strong(X0) | ~happy(X0) [duplicate literal removal 99]
145. ~curious(X0) | ~strong(X0) [duplicate literal removal 103]
186. ~curious(X0) | ~happy(X0) [subsumption resolution 144,145]
231. 18 <=> creative(fred) [avatar definition]
236. 19 <=> happy(sK2) [avatar definition]
238. happy(sK2) <- (19) [avatar component clause 236]
239. ~18 | 19 [avatar split clause 119,236,231]
310. 18 [avatar split clause 142,231]
319. ~happy(X0) | patient(X0) [resolution 186,107]
354. patient(sK2) <- (19) [resolution 319,238]
458. ~patient(sK2) | creative(sK2) <- (19) [resolution 129,238]
460. creative(sK2) <- (19) [subsumption resolution 458,354]
464. curious(sK2) <- (19) [resolution 460,105]
545. ~happy(sK2) <- (19) [resolution 464,186]
547. $false <- (19) [subsumption resolution 545,238]
548. ~19 [avatar contradiction clause 547]
549. $false [avatar sat refutation 239,310,548]
% SZS output end Proof for 9072528547448190139323176
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both funny and generous is not creative and vice versa. Everyone who is patient is both kind and generous. Everyone who is not rich is both not calm and not funny. If someone is not calm or not creative then someone is funny or not creative. Everyone who is either not creative or wise is either old or brave and vice versa. Everyone who is not tall is quiet or not calm. Everyone who is not creative is happy and vice versa. If paul is either not strong or not happy then lucy is both creative and kind. Everyone who is not generous or tall is not old and vice versa. If someone is either not generous or not calm then john is not patient or not old. Everyone who is not humble is creative and vice versa. Everyone who is rich or quiet is both wise and not patient and vice versa. Everyone who is either rich or calm is creative and vice versa. Everyone who is both calm and curious is not wise or not curious. If mary is either generous or creative then someone is either not funny or not tall and vice versa. If lucy is not creative or kind then someone is both humble and not humble. Fred is kind or not patient. Fred is not creative. Someone is both old and not quiet. Susan is not calm or old. Alice is not rich or brave. Someone is both not old and not tall. John is either patient or not happy. Alice is both not old and not funny. | Lucy is rich. | entailment | (![X]:((funny(X)&generous(X))<=>~creative(X)))&
(![X]:(patient(X)=>(kind(X)&generous(X))))&
(![X]:(~rich(X)=>(~calm(X)&~funny(X))))&
((?[X]:((~calm(X)|~creative(X))))=>(?[X]:((funny(X)|~creative(X)))))&
(![X]:((~creative(X)<~>wise(X))<=>(old(X)<~>brave(X))))&
(![X]:(~tall(X)=>(quiet(X)|~calm(X))))&
(![X]:(~creative(X)<=>happy(X)))&
(((~strong(paul)<~>~happy(paul)))=>((creative(lucy)&kind(lucy))))&
(![X]:((~generous(X)|tall(X))<=>~old(X)))&
((?[X]:((~generous(X)<~>~calm(X))))=>((~patient(john)|~old(john))))&
(![X]:(~humble(X)<=>creative(X)))&
(![X]:((rich(X)|quiet(X))<=>(wise(X)&~patient(X))))&
(![X]:((rich(X)<~>calm(X))<=>creative(X)))&
(![X]:((calm(X)&curious(X))=>(~wise(X)|~curious(X))))&
(((generous(mary)<~>creative(mary)))<=>(?[X]:((~funny(X)<~>~tall(X)))))&
(((~creative(lucy)|kind(lucy)))=>(?[X]:((humble(X)&~humble(X)))))&
((kind(fred)|~patient(fred)))&
(~creative(fred))&
(?[X]:((old(X)&~quiet(X))))&
((~calm(susan)|old(susan)))&
((~rich(alice)|brave(alice)))&
(?[X]:((~old(X)&~tall(X))))&
((patient(john)<~>~happy(john)))&
((~old(alice)&~funny(alice))) | rich(lucy) | [
"p0",
"p2",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 140131061323154037569621
% SZS output start Proof for 140131061323154037569621
1. ! [X0] : ((generous(X0) & funny(X0)) <=> ~creative(X0)) [input p0]
3. ! [X0] : (~rich(X0) => (~funny(X0) & ~calm(X0))) [input p2]
13. ! [X0] : ((rich(X0) <~> calm(X0)) <=> creative(X0)) [input p12]
25. ~rich(lucy) [input hypothesis]
29. ! [X0] : ((~funny(X0) & ~calm(X0)) | rich(X0)) [ennf transformation 3]
37. ! [X0] : (((generous(X0) & funny(X0)) | creative(X0)) & (~creative(X0) | (~generous(X0) | ~funny(X0)))) [nnf transformation 1]
38. ! [X0] : (((generous(X0) & funny(X0)) | creative(X0)) & (~creative(X0) | ~generous(X0) | ~funny(X0))) [flattening 37]
51. ! [X0] : ((((~calm(X0) | ~rich(X0)) & (calm(X0) | rich(X0))) | ~creative(X0)) & (creative(X0) | ((rich(X0) | ~calm(X0)) & (calm(X0) | ~rich(X0))))) [nnf transformation 13]
64. creative(X0) | funny(X0) [cnf transformation 38]
68. ~calm(X0) | rich(X0) [cnf transformation 29]
69. ~funny(X0) | rich(X0) [cnf transformation 29]
101. calm(X0) | rich(X0) | ~creative(X0) [cnf transformation 51]
102. ~calm(X0) | ~rich(X0) | ~creative(X0) [cnf transformation 51]
127. ~rich(lucy) [cnf transformation 25]
178. ~calm(X0) | ~creative(X0) [subsumption resolution 102,68]
179. ~creative(X0) | rich(X0) [subsumption resolution 101,178]
258. rich(X1) | funny(X1) [resolution 179,64]
263. rich(X1) [subsumption resolution 258,69]
264. $false [resolution 263,127]
% SZS output end Proof for 140131061323154037569621
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not happy or not rich then alice is not happy and vice versa.
Everyone who is either kind or tall is not wise and vice versa.
Everyone who is patient or strong is humble or patient.
If someone is not funny then paul is tall or not funny.
Everyone who is brave is not brave or not kind.
If someone is both tall and quiet then mary is brave.
Everyone who is both funny and not strong is both generous and not humble.
Everyone who is calm is either not strong or humble and vice versa.
Everyone who is either generous or not rich is both old and kind and vice versa.
Everyone who is generous or kind is strong and vice versa.
Everyone who is not patient or humble is funny and vice versa.
If someone is both creative and old then someone is both old and creative.
Everyone who is generous or happy is either not tall or rich and vice versa.
Everyone who is either not generous or happy is creative.
Everyone who is either not wise or quiet is not rich or creative.
Everyone who is both not patient and creative is wise and vice versa.
Someone is both wise and not old.
Susan is both brave and rich.
Someone is either not strong or not generous.
Susan is both not humble and not curious.
Alice is either quiet or strong.
Someone is brave.
Paul is not creative or strong.
Someone is either wise or not funny. | Susan is generous. | contradiction | ((?[X]:((~happy(X)|~rich(X))))<=>(~happy(alice)))&
(![X]:((kind(X)<~>tall(X))<=>~wise(X)))&
(![X]:((patient(X)|strong(X))=>(humble(X)|patient(X))))&
((?[X]:(~funny(X)))=>((tall(paul)|~funny(paul))))&
(![X]:(brave(X)=>(~brave(X)|~kind(X))))&
((?[X]:((tall(X)&quiet(X))))=>(brave(mary)))&
(![X]:((funny(X)&~strong(X))=>(generous(X)&~humble(X))))&
(![X]:(calm(X)<=>(~strong(X)<~>humble(X))))&
(![X]:((generous(X)<~>~rich(X))<=>(old(X)&kind(X))))&
(![X]:((generous(X)|kind(X))<=>strong(X)))&
(![X]:((~patient(X)|humble(X))<=>funny(X)))&
((?[X]:((creative(X)&old(X))))=>(?[X]:((old(X)&creative(X)))))&
(![X]:((generous(X)|happy(X))<=>(~tall(X)<~>rich(X))))&
(![X]:((~generous(X)<~>happy(X))=>creative(X)))&
(![X]:((~wise(X)<~>quiet(X))=>(~rich(X)|creative(X))))&
(![X]:((~patient(X)&creative(X))<=>wise(X)))&
(?[X]:((wise(X)&~old(X))))&
((brave(susan)&rich(susan)))&
(?[X]:((~strong(X)<~>~generous(X))))&
((~humble(susan)&~curious(susan)))&
((quiet(alice)<~>strong(alice)))&
(?[X]:(brave(X)))&
((~creative(paul)|strong(paul)))&
(?[X]:((wise(X)<~>~funny(X)))) | generous(susan) | [
"p4",
"p8",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 4329162912376486312348571
% SZS output start Proof for 4329162912376486312348571
5. ! [X0] : (brave(X0) => (~kind(X0) | ~brave(X0))) [input p4]
9. ! [X0] : ((generous(X0) <~> ~rich(X0)) <=> (kind(X0) & old(X0))) [input p8]
18. rich(susan) & brave(susan) [input p17]
25. generous(susan) [input hypothesis]
32. ! [X0] : ((~kind(X0) | ~brave(X0)) | ~brave(X0)) [ennf transformation 5]
33. ! [X0] : (~kind(X0) | ~brave(X0) | ~brave(X0)) [flattening 32]
46. ! [X0] : ((((rich(X0) | ~generous(X0)) & (~rich(X0) | generous(X0))) | (~kind(X0) | ~old(X0))) & ((kind(X0) & old(X0)) | ((generous(X0) | rich(X0)) & (~rich(X0) | ~generous(X0))))) [nnf transformation 9]
47. ! [X0] : ((((rich(X0) | ~generous(X0)) & (~rich(X0) | generous(X0))) | ~kind(X0) | ~old(X0)) & ((kind(X0) & old(X0)) | ((generous(X0) | rich(X0)) & (~rich(X0) | ~generous(X0))))) [flattening 46]
82. ~kind(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 33]
88. ~generous(X0) | ~rich(X0) | kind(X0) [cnf transformation 47]
115. brave(susan) [cnf transformation 18]
116. rich(susan) [cnf transformation 18]
126. generous(susan) [cnf transformation 25]
127. ~brave(X0) | ~kind(X0) [duplicate literal removal 82]
219. ~kind(susan) [resolution 127,115]
302. ~rich(susan) | kind(susan) [resolution 88,126]
303. kind(susan) [subsumption resolution 302,116]
304. $false [subsumption resolution 303,219]
% SZS output end Proof for 4329162912376486312348571
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If mary is not brave then susan is funny or not calm and vice versa.
Everyone who is not happy or brave is either wise or not creative.
Everyone who is either not creative or strong is funny and vice versa.
If someone is not generous or not strong then someone is either not rich or humble.
Everyone who is not wise or not tall is both not curious and not creative.
Everyone who is both wise and not creative is both not patient and happy and vice versa.
If someone is either tall or not quiet then susan is creative and vice versa.
Everyone who is not patient or creative is not quiet and vice versa.
Everyone who is not kind or tall is quiet.
If someone is funny then someone is creative.
If lucy is both creative and not generous then someone is either rich or happy.
Everyone who is both not patient and not old is not kind or not happy and vice versa.
If john is patient or old then someone is both not tall and not rich and vice versa.
If paul is strong then john is either calm or funny and vice versa.
If paul is either calm or not old then someone is quiet.
Lucy is kind.
John is not old or not creative.
Mary is not creative.
Mary is patient.
Fred is patient or calm. | Mary is not generous. | neutral | ((~brave(mary))<=>((funny(susan)|~calm(susan))))&
(![X]:((~happy(X)|brave(X))=>(wise(X)<~>~creative(X))))&
(![X]:((~creative(X)<~>strong(X))<=>funny(X)))&
((?[X]:((~generous(X)|~strong(X))))=>(?[X]:((~rich(X)<~>humble(X)))))&
(![X]:((~wise(X)|~tall(X))=>(~curious(X)&~creative(X))))&
(![X]:((wise(X)&~creative(X))<=>(~patient(X)&happy(X))))&
((?[X]:((tall(X)<~>~quiet(X))))<=>(creative(susan)))&
(![X]:((~patient(X)|creative(X))<=>~quiet(X)))&
(![X]:((~kind(X)|tall(X))=>quiet(X)))&
((?[X]:(funny(X)))=>(?[X]:(creative(X))))&
(((creative(lucy)&~generous(lucy)))=>(?[X]:((rich(X)<~>happy(X)))))&
(![X]:((~patient(X)&~old(X))<=>(~kind(X)|~happy(X))))&
(((patient(john)|old(john)))<=>(?[X]:((~tall(X)&~rich(X)))))&
((strong(paul))<=>((calm(john)<~>funny(john))))&
(((calm(paul)<~>~old(paul)))=>(?[X]:(quiet(X))))&
(kind(lucy))&
((~old(john)|~creative(john)))&
(~creative(mary))&
(patient(mary))&
((patient(fred)|calm(fred))) | ~generous(mary) | [] | null | 0 |
If paul is not wise then someone is not calm or not humble.
If someone is either not creative or not happy then someone is either not tall or not calm and vice versa.
If someone is not strong or strong then someone is both happy and not tall and vice versa.
If someone is generous or not humble then john is both not creative and not quiet and vice versa.
If alice is either not old or not humble then lucy is funny or not quiet and vice versa.
Everyone who is both not patient and rich is curious or quiet and vice versa.
If someone is both not generous and not quiet then someone is tall or patient.
If someone is either old or not patient then alice is either rich or brave and vice versa.
Everyone who is both not kind and not calm is either funny or not wise.
Everyone who is strong or not creative is not creative.
If susan is either happy or not calm then someone is tall and vice versa.
If someone is either happy or creative then fred is either creative or not calm.
Everyone who is either not strong or not patient is either not tall or kind.
Everyone who is patient is both not patient and creative and vice versa.
Everyone who is creative is creative or not curious and vice versa.
If susan is funny or humble then susan is not humble and vice versa.
Susan is both not humble and not old.
Paul is not calm or not quiet.
Someone is both tall and calm.
John is not calm.
Mary is either funny or not kind.
Someone is not old. | Lucy is wise. | neutral | ((~wise(paul))=>(?[X]:((~calm(X)|~humble(X)))))&
((?[X]:((~creative(X)<~>~happy(X))))<=>(?[X]:((~tall(X)<~>~calm(X)))))&
((?[X]:((~strong(X)|strong(X))))<=>(?[X]:((happy(X)&~tall(X)))))&
((?[X]:((generous(X)|~humble(X))))<=>((~creative(john)&~quiet(john))))&
(((~old(alice)<~>~humble(alice)))<=>((funny(lucy)|~quiet(lucy))))&
(![X]:((~patient(X)&rich(X))<=>(curious(X)|quiet(X))))&
((?[X]:((~generous(X)&~quiet(X))))=>(?[X]:((tall(X)|patient(X)))))&
((?[X]:((old(X)<~>~patient(X))))<=>((rich(alice)<~>brave(alice))))&
(![X]:((~kind(X)&~calm(X))=>(funny(X)<~>~wise(X))))&
(![X]:((strong(X)|~creative(X))=>~creative(X)))&
(((happy(susan)<~>~calm(susan)))<=>(?[X]:(tall(X))))&
((?[X]:((happy(X)<~>creative(X))))=>((creative(fred)<~>~calm(fred))))&
(![X]:((~strong(X)<~>~patient(X))=>(~tall(X)<~>kind(X))))&
(![X]:(patient(X)<=>(~patient(X)&creative(X))))&
(![X]:(creative(X)<=>(creative(X)|~curious(X))))&
(((funny(susan)|humble(susan)))<=>(~humble(susan)))&
((~humble(susan)&~old(susan)))&
((~calm(paul)|~quiet(paul)))&
(?[X]:((tall(X)&calm(X))))&
(~calm(john))&
((funny(mary)<~>~kind(mary)))&
(?[X]:(~old(X))) | wise(lucy) | [] | null | 0 |
Everyone who is tall is not patient. Everyone who is brave is both tall and not funny and vice versa. 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. Someone is not tall or not generous. Someone is either strong or not quiet. 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. | John is not brave. | entailment | (![X]:(tall(X)=>~patient(X)))&
(![X]:(brave(X)<=>(tall(X)&~funny(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]:((~tall(X)|~generous(X))))&
(?[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))) | ~brave(john) | [
"p1",
"p4",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 5819129295878321081657658
% SZS output start Proof for 5819129295878321081657658
2. ! [X0] : (brave(X0) <=> (~funny(X0) & tall(X0))) [input p1]
5. ! [X0] : ((brave(X0) & humble(X0)) => ~tall(X0)) [input p4]
8. ! [X0] : ((quiet(X0) & ~quiet(X0)) <=> (kind(X0) | ~humble(X0))) [input p7]
25. brave(john) [input hypothesis]
31. ! [X0] : (~tall(X0) | (~brave(X0) | ~humble(X0))) [ennf transformation 5]
32. ! [X0] : (~tall(X0) | ~brave(X0) | ~humble(X0)) [flattening 31]
39. ! [X0] : ((brave(X0) | (funny(X0) | ~tall(X0))) & ((~funny(X0) & tall(X0)) | ~brave(X0))) [nnf transformation 2]
40. ! [X0] : ((brave(X0) | funny(X0) | ~tall(X0)) & ((~funny(X0) & tall(X0)) | ~brave(X0))) [flattening 39]
48. ! [X0] : (((quiet(X0) & ~quiet(X0)) | (~kind(X0) & humble(X0))) & ((kind(X0) | ~humble(X0)) | (~quiet(X0) | quiet(X0)))) [nnf transformation 8]
49. ! [X0] : (((quiet(X0) & ~quiet(X0)) | (~kind(X0) & humble(X0))) & (kind(X0) | ~humble(X0) | ~quiet(X0) | quiet(X0))) [flattening 48]
77. ~brave(X0) | tall(X0) [cnf transformation 40]
89. ~tall(X0) | ~brave(X0) | ~humble(X0) [cnf transformation 32]
95. ~quiet(X0) | humble(X0) [cnf transformation 49]
97. quiet(X0) | humble(X0) [cnf transformation 49]
141. brave(john) [cnf transformation 25]
176. ~humble(X0) | ~brave(X0) [subsumption resolution 89,77]
178. humble(X0) [subsumption resolution 95,97]
311. ~brave(X1) [resolution 176,178]
312. $false [resolution 311,141]
% SZS output end Proof for 5819129295878321081657658
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or not curious then alice is curious and vice versa.
Everyone who is either not old or not strong is old or quiet and vice versa.
If alice is both not generous and brave then mary is both creative and not calm and vice versa.
Everyone who is not tall is either not brave or not strong and vice versa.
If someone is wise or generous then someone is either creative or not funny and vice versa.
Everyone who is both tall and kind is either not old or old and vice versa.
Everyone who is funny is either not strong or kind.
If someone is calm or curious then someone is both not brave and not happy and vice versa.
Everyone who is both humble and tall is not curious.
Everyone who is rich or not strong is not wise and vice versa.
Everyone who is patient is funny or not rich.
If susan is both generous and not quiet then someone is kind.
Everyone who is rich or not curious is happy or not funny and vice versa.
Everyone who is both not humble and quiet is not brave and vice versa.
If paul is either strong or not funny then someone is not patient.
If someone is both tall and not kind then susan is not generous and vice versa.
Mary is kind or not calm.
Someone is not creative or brave.
Someone is either not old or happy.
Someone is generous.
Fred is rich.
Someone is not creative or not strong.
Paul is not curious or creative. | Paul is curious. | neutral | ((?[X]:((curious(X)<~>~curious(X))))<=>(curious(alice)))&
(![X]:((~old(X)<~>~strong(X))<=>(old(X)|quiet(X))))&
(((~generous(alice)&brave(alice)))<=>((creative(mary)&~calm(mary))))&
(![X]:(~tall(X)<=>(~brave(X)<~>~strong(X))))&
((?[X]:((wise(X)|generous(X))))<=>(?[X]:((creative(X)<~>~funny(X)))))&
(![X]:((tall(X)&kind(X))<=>(~old(X)<~>old(X))))&
(![X]:(funny(X)=>(~strong(X)<~>kind(X))))&
((?[X]:((calm(X)|curious(X))))<=>(?[X]:((~brave(X)&~happy(X)))))&
(![X]:((humble(X)&tall(X))=>~curious(X)))&
(![X]:((rich(X)|~strong(X))<=>~wise(X)))&
(![X]:(patient(X)=>(funny(X)|~rich(X))))&
(((generous(susan)&~quiet(susan)))=>(?[X]:(kind(X))))&
(![X]:((rich(X)|~curious(X))<=>(happy(X)|~funny(X))))&
(![X]:((~humble(X)&quiet(X))<=>~brave(X)))&
(((strong(paul)<~>~funny(paul)))=>(?[X]:(~patient(X))))&
((?[X]:((tall(X)&~kind(X))))<=>(~generous(susan)))&
((kind(mary)|~calm(mary)))&
(?[X]:((~creative(X)|brave(X))))&
(?[X]:((~old(X)<~>happy(X))))&
(?[X]:(generous(X)))&
(rich(fred))&
(?[X]:((~creative(X)|~strong(X))))&
((~curious(paul)|creative(paul))) | curious(paul) | [] | null | 0 |
If someone is not kind or old then someone is either not happy or happy and vice versa.
Everyone who is both generous and rich is not calm and vice versa.
If someone is both not generous and brave then someone is both not creative and not generous.
Everyone who is both not tall and not calm is not patient and vice versa.
Everyone who is either not wise or not generous is wise or not calm and vice versa.
Everyone who is patient or funny is calm.
Everyone who is humble or not humble is strong.
Everyone who is tall or not tall is not patient and vice versa.
If someone is not strong or not generous then someone is either patient or humble and vice versa.
Everyone who is either not rich or kind is funny and vice versa.
If someone is either not curious or strong then someone is quiet or not funny.
If someone is not calm or not curious then susan is either happy or curious and vice versa.
Everyone who is both generous and old is not quiet and vice versa.
Everyone who is either not rich or not generous is kind.
If paul is wise or generous then lucy is both quiet and not patient and vice versa.
Mary is old or not rich.
Someone is not generous or brave.
Lucy is either quiet or not curious. | Paul is not generous. | contradiction | ((?[X]:((~kind(X)|old(X))))<=>(?[X]:((~happy(X)<~>happy(X)))))&
(![X]:((generous(X)&rich(X))<=>~calm(X)))&
((?[X]:((~generous(X)&brave(X))))=>(?[X]:((~creative(X)&~generous(X)))))&
(![X]:((~tall(X)&~calm(X))<=>~patient(X)))&
(![X]:((~wise(X)<~>~generous(X))<=>(wise(X)|~calm(X))))&
(![X]:((patient(X)|funny(X))=>calm(X)))&
(![X]:((humble(X)|~humble(X))=>strong(X)))&
(![X]:((tall(X)|~tall(X))<=>~patient(X)))&
((?[X]:((~strong(X)|~generous(X))))<=>(?[X]:((patient(X)<~>humble(X)))))&
(![X]:((~rich(X)<~>kind(X))<=>funny(X)))&
((?[X]:((~curious(X)<~>strong(X))))=>(?[X]:((quiet(X)|~funny(X)))))&
((?[X]:((~calm(X)|~curious(X))))<=>((happy(susan)<~>curious(susan))))&
(![X]:((generous(X)&old(X))<=>~quiet(X)))&
(![X]:((~rich(X)<~>~generous(X))=>kind(X)))&
(((wise(paul)|generous(paul)))<=>((quiet(lucy)&~patient(lucy))))&
((old(mary)|~rich(mary)))&
(?[X]:((~generous(X)|brave(X))))&
((quiet(lucy)<~>~curious(lucy))) | ~generous(paul) | [
"p1",
"p3",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 5313821417525036214362158
% SZS output start Proof for 5313821417525036214362158
2. ! [X0] : ((rich(X0) & generous(X0)) <=> ~calm(X0)) [input p1]
4. ! [X0] : ((~calm(X0) & ~tall(X0)) <=> ~patient(X0)) [input p3]
8. ! [X0] : ((~tall(X0) | tall(X0)) <=> ~patient(X0)) [input p7]
19. ~generous(paul) [input hypothesis]
37. ! [X0] : (((rich(X0) & generous(X0)) | calm(X0)) & (~calm(X0) | (~rich(X0) | ~generous(X0)))) [nnf transformation 2]
38. ! [X0] : (((rich(X0) & generous(X0)) | calm(X0)) & (~calm(X0) | ~rich(X0) | ~generous(X0))) [flattening 37]
42. ! [X0] : (((~calm(X0) & ~tall(X0)) | patient(X0)) & (~patient(X0) | (calm(X0) | tall(X0)))) [nnf transformation 4]
43. ! [X0] : (((~calm(X0) & ~tall(X0)) | patient(X0)) & (~patient(X0) | calm(X0) | tall(X0))) [flattening 42]
46. ! [X0] : (((~tall(X0) | tall(X0)) | patient(X0)) & (~patient(X0) | (tall(X0) & ~tall(X0)))) [nnf transformation 8]
47. ! [X0] : ((~tall(X0) | tall(X0) | patient(X0)) & (~patient(X0) | (tall(X0) & ~tall(X0)))) [flattening 46]
77. calm(X0) | generous(X0) [cnf transformation 38]
82. ~calm(X0) | patient(X0) [cnf transformation 43]
93. ~patient(X0) | ~tall(X0) [cnf transformation 47]
94. ~patient(X0) | tall(X0) [cnf transformation 47]
126. ~generous(paul) [cnf transformation 19]
158. ~patient(X0) [subsumption resolution 93,94]
171. 9 <=> ! [X3] : generous(X3) [avatar definition]
172. generous(X3) <- (9) [avatar component clause 171]
229. 22 <=> generous(paul) [avatar definition]
230. ~generous(paul) <- (~22) [avatar component clause 229]
259. ~22 [avatar split clause 126,229]
264. $false <- (9, ~22) [resolution 230,172]
265. ~9 | 22 [avatar contradiction clause 264]
271. patient(X1) | generous(X1) [resolution 82,77]
273. generous(X1) [subsumption resolution 271,158]
274. 9 [avatar split clause 273,171]
275. $false [avatar sat refutation 259,265,274]
% SZS output end Proof for 5313821417525036214362158
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy or not curious is both patient and old and vice versa.
Everyone who is not generous or not quiet is not brave or happy and vice versa.
Everyone who is both funny and not quiet is not funny.
Everyone who is creative is either not brave or not creative and vice versa.
Everyone who is not calm is either curious or not quiet.
Everyone who is both calm and funny is both not strong and creative and vice versa.
If lucy is old then someone is funny and vice versa.
Everyone who is both not old and old is not wise and vice versa.
If susan is funny or not happy then john is both kind and not strong.
Everyone who is not brave or not kind is patient and vice versa.
If john is calm or old then someone is either not brave or not funny and vice versa.
If someone is both not patient and not kind then someone is not rich and vice versa.
Everyone who is both not old and strong is rich or creative.
If lucy is either not curious or not humble then paul is rich.
Everyone who is both not generous and happy is both rich and not kind and vice versa.
Everyone who is either tall or funny is kind or tall and vice versa.
Someone is both tall and happy.
Fred is creative or not tall.
Someone is not humble or not rich.
Someone is either humble or not tall.
Lucy is both curious and patient.
Lucy is not tall.
John is kind or not generous. | Fred is wise. | entailment | (![X]:((~happy(X)|~curious(X))<=>(patient(X)&old(X))))&
(![X]:((~generous(X)|~quiet(X))<=>(~brave(X)|happy(X))))&
(![X]:((funny(X)&~quiet(X))=>~funny(X)))&
(![X]:(creative(X)<=>(~brave(X)<~>~creative(X))))&
(![X]:(~calm(X)=>(curious(X)<~>~quiet(X))))&
(![X]:((calm(X)&funny(X))<=>(~strong(X)&creative(X))))&
((old(lucy))<=>(?[X]:(funny(X))))&
(![X]:((~old(X)&old(X))<=>~wise(X)))&
(((funny(susan)|~happy(susan)))=>((kind(john)&~strong(john))))&
(![X]:((~brave(X)|~kind(X))<=>patient(X)))&
(((calm(john)|old(john)))<=>(?[X]:((~brave(X)<~>~funny(X)))))&
((?[X]:((~patient(X)&~kind(X))))<=>(?[X]:(~rich(X))))&
(![X]:((~old(X)&strong(X))=>(rich(X)|creative(X))))&
(((~curious(lucy)<~>~humble(lucy)))=>(rich(paul)))&
(![X]:((~generous(X)&happy(X))<=>(rich(X)&~kind(X))))&
(![X]:((tall(X)<~>funny(X))<=>(kind(X)|tall(X))))&
(?[X]:((tall(X)&happy(X))))&
((creative(fred)|~tall(fred)))&
(?[X]:((~humble(X)|~rich(X))))&
(?[X]:((humble(X)<~>~tall(X))))&
((curious(lucy)&patient(lucy)))&
(~tall(lucy))&
((kind(john)|~generous(john))) | wise(fred) | [
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 184784500554522265408670
% SZS output start Proof for 184784500554522265408670
8. ! [X0] : ((old(X0) & ~old(X0)) <=> ~wise(X0)) [input p7]
24. ~wise(fred) [input hypothesis]
26. ! [X0] : (~wise(X0) => (old(X0) & ~old(X0))) [unused predicate definition removal 8]
30. ! [X0] : ((old(X0) & ~old(X0)) | wise(X0)) [ennf transformation 26]
93. ~old(X0) | wise(X0) [cnf transformation 30]
94. old(X0) | wise(X0) [cnf transformation 30]
134. ~wise(fred) [cnf transformation 24]
154. wise(X0) [subsumption resolution 93,94]
253. $false [subsumption resolution 134,154]
% SZS output end Proof for 184784500554522265408670
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble is both not strong and not creative and vice versa.
If alice is not wise then susan is brave or not old and vice versa.
Everyone who is both not strong and not rich is either not tall or funny and vice versa.
If susan is not calm then alice is either not calm or not funny and vice versa.
Everyone who is tall or brave is not wise and vice versa.
If someone is not calm then someone is not tall or not rich.
If alice is either wise or not brave then someone is both generous and not wise and vice versa.
If someone is calm then someone is calm or not funny and vice versa.
Everyone who is patient is tall or not old and vice versa.
Everyone who is generous is both rich and not quiet and vice versa.
Everyone who is not funny is either not old or patient and vice versa.
If someone is not tall then someone is not brave or not generous and vice versa.
Everyone who is either curious or not quiet is both not patient and not rich.
If fred is either generous or not patient then fred is not brave.
Everyone who is old is both creative and not funny and vice versa.
Everyone who is both not quiet and not curious is wise or not funny and vice versa.
Mary is either calm or patient.
Someone is brave.
John is either not funny or tall.
Susan is not curious.
Someone is tall. | Susan is not strong. | neutral | (![X]:(~humble(X)<=>(~strong(X)&~creative(X))))&
((~wise(alice))<=>((brave(susan)|~old(susan))))&
(![X]:((~strong(X)&~rich(X))<=>(~tall(X)<~>funny(X))))&
((~calm(susan))<=>((~calm(alice)<~>~funny(alice))))&
(![X]:((tall(X)|brave(X))<=>~wise(X)))&
((?[X]:(~calm(X)))=>(?[X]:((~tall(X)|~rich(X)))))&
(((wise(alice)<~>~brave(alice)))<=>(?[X]:((generous(X)&~wise(X)))))&
((?[X]:(calm(X)))<=>(?[X]:((calm(X)|~funny(X)))))&
(![X]:(patient(X)<=>(tall(X)|~old(X))))&
(![X]:(generous(X)<=>(rich(X)&~quiet(X))))&
(![X]:(~funny(X)<=>(~old(X)<~>patient(X))))&
((?[X]:(~tall(X)))<=>(?[X]:((~brave(X)|~generous(X)))))&
(![X]:((curious(X)<~>~quiet(X))=>(~patient(X)&~rich(X))))&
(((generous(fred)<~>~patient(fred)))=>(~brave(fred)))&
(![X]:(old(X)<=>(creative(X)&~funny(X))))&
(![X]:((~quiet(X)&~curious(X))<=>(wise(X)|~funny(X))))&
((calm(mary)<~>patient(mary)))&
(?[X]:(brave(X)))&
((~funny(john)<~>tall(john)))&
(~curious(susan))&
(?[X]:(tall(X))) | ~strong(susan) | [] | null | 0 |
If someone is funny or not funny then lucy is both brave and generous. Everyone who is wise is old. Everyone who is either patient or not wise is both brave and not creative. If someone is not quiet or creative then lucy is tall or wise. Everyone who is both not generous and happy is not happy and vice versa. If someone is not strong or not tall then fred is either not kind or curious. Everyone who is either not rich or funny is strong. If someone is old then fred is happy or not generous. Everyone who is tall is either not generous or not brave and vice versa. If lucy is not quiet then lucy is both not generous and not brave and vice versa. If alice is both not tall and not calm then fred is humble and vice versa. Everyone who is tall or not wise is either patient or not old and vice versa. Everyone who is either not tall or not wise is not calm or not creative and vice versa. Everyone who is not curious or humble is not funny or wise and vice versa. Everyone who is not kind or not rich is both not curious and not tall and vice versa. Everyone who is creative or not wise is both not patient and generous and vice versa. Paul is both old and generous. Someone is not funny or not tall. Susan is not patient or creative. Alice is not creative or not tall. Someone is humble or not creative. | Susan is not brave. | contradiction | ((?[X]:((funny(X)|~funny(X))))=>((brave(lucy)&generous(lucy))))&
(![X]:(wise(X)=>old(X)))&
(![X]:((patient(X)<~>~wise(X))=>(brave(X)&~creative(X))))&
((?[X]:((~quiet(X)|creative(X))))=>((tall(lucy)|wise(lucy))))&
(![X]:((~generous(X)&happy(X))<=>~happy(X)))&
((?[X]:((~strong(X)|~tall(X))))=>((~kind(fred)<~>curious(fred))))&
(![X]:((~rich(X)<~>funny(X))=>strong(X)))&
((?[X]:(old(X)))=>((happy(fred)|~generous(fred))))&
(![X]:(tall(X)<=>(~generous(X)<~>~brave(X))))&
((~quiet(lucy))<=>((~generous(lucy)&~brave(lucy))))&
(((~tall(alice)&~calm(alice)))<=>(humble(fred)))&
(![X]:((tall(X)|~wise(X))<=>(patient(X)<~>~old(X))))&
(![X]:((~tall(X)<~>~wise(X))<=>(~calm(X)|~creative(X))))&
(![X]:((~curious(X)|humble(X))<=>(~funny(X)|wise(X))))&
(![X]:((~kind(X)|~rich(X))<=>(~curious(X)&~tall(X))))&
(![X]:((creative(X)|~wise(X))<=>(~patient(X)&generous(X))))&
((old(paul)&generous(paul)))&
(?[X]:((~funny(X)|~tall(X))))&
((~patient(susan)|creative(susan)))&
((~creative(alice)|~tall(alice)))&
(?[X]:((humble(X)|~creative(X)))) | ~brave(susan) | [
"p1",
"p2",
"p4",
"p8",
"p11",
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 7753817043233354144215538
% SZS output start Proof for 7753817043233354144215538
2. ! [X0] : (wise(X0) => old(X0)) [input p1]
3. ! [X0] : ((patient(X0) <~> ~wise(X0)) => (~creative(X0) & brave(X0))) [input p2]
5. ! [X0] : ((happy(X0) & ~generous(X0)) <=> ~happy(X0)) [input p4]
9. ! [X0] : (tall(X0) <=> (~generous(X0) <~> ~brave(X0))) [input p8]
12. ! [X0] : ((~wise(X0) | tall(X0)) <=> (patient(X0) <~> ~old(X0))) [input p11]
16. ! [X0] : ((~wise(X0) | creative(X0)) <=> (generous(X0) & ~patient(X0))) [input p15]
19. creative(susan) | ~patient(susan) [input p18]
22. ~brave(susan) [input hypothesis]
26. ! [X0] : (old(X0) | ~wise(X0)) [ennf transformation 2]
27. ! [X0] : ((~creative(X0) & brave(X0)) | (patient(X0) <=> ~wise(X0))) [ennf transformation 3]
33. ! [X0] : ((~creative(X0) & brave(X0)) | ((patient(X0) | wise(X0)) & (~wise(X0) | ~patient(X0)))) [nnf transformation 27]
34. ! [X0] : (((happy(X0) & ~generous(X0)) | happy(X0)) & (~happy(X0) | (~happy(X0) | generous(X0)))) [nnf transformation 5]
35. ! [X0] : (((happy(X0) & ~generous(X0)) | happy(X0)) & (~happy(X0) | ~happy(X0) | generous(X0))) [flattening 34]
37. ! [X0] : ((tall(X0) | ((~generous(X0) | brave(X0)) & (~brave(X0) | generous(X0)))) & (((brave(X0) | generous(X0)) & (~brave(X0) | ~generous(X0))) | ~tall(X0))) [nnf transformation 9]
42. ! [X0] : (((~wise(X0) | tall(X0)) | ((patient(X0) | old(X0)) & (~old(X0) | ~patient(X0)))) & (((old(X0) | ~patient(X0)) & (~old(X0) | patient(X0))) | (wise(X0) & ~tall(X0)))) [nnf transformation 12]
43. ! [X0] : ((~wise(X0) | tall(X0) | ((patient(X0) | old(X0)) & (~old(X0) | ~patient(X0)))) & (((old(X0) | ~patient(X0)) & (~old(X0) | patient(X0))) | (wise(X0) & ~tall(X0)))) [flattening 42]
50. ! [X0] : (((~wise(X0) | creative(X0)) | (~generous(X0) | patient(X0))) & ((generous(X0) & ~patient(X0)) | (wise(X0) & ~creative(X0)))) [nnf transformation 16]
51. ! [X0] : ((~wise(X0) | creative(X0) | ~generous(X0) | patient(X0)) & ((generous(X0) & ~patient(X0)) | (wise(X0) & ~creative(X0)))) [flattening 50]
60. ~wise(X0) | old(X0) [cnf transformation 26]
62. patient(X0) | brave(X0) | wise(X0) [cnf transformation 33]
67. ~happy(X0) | ~happy(X0) | generous(X0) [cnf transformation 35]
69. happy(X0) | happy(X0) [cnf transformation 35]
76. tall(X0) | ~generous(X0) | brave(X0) [cnf transformation 37]
83. ~tall(X0) | patient(X0) | ~old(X0) [cnf transformation 43]
86. old(X0) | ~patient(X0) | wise(X0) [cnf transformation 43]
104. ~creative(X0) | ~patient(X0) [cnf transformation 51]
112. creative(susan) | ~patient(susan) [cnf transformation 19]
115. ~brave(susan) [cnf transformation 22]
116. ~happy(X0) | generous(X0) [duplicate literal removal 67]
117. happy(X0) [duplicate literal removal 69]
152. generous(X0) [subsumption resolution 116,117]
166. tall(X0) | brave(X0) [subsumption resolution 76,152]
191. ~patient(X0) | old(X0) [subsumption resolution 86,60]
202. ~patient(susan) [subsumption resolution 112,104]
230. brave(X1) | wise(X1) | old(X1) [resolution 62,191]
235. old(X1) | brave(X1) [subsumption resolution 230,60]
238. patient(X0) | ~old(X0) | brave(X0) [resolution 83,166]
239. patient(X0) | brave(X0) [subsumption resolution 238,235]
265. brave(susan) [resolution 239,202]
270. $false [subsumption resolution 265,115]
% SZS output end Proof for 7753817043233354144215538
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm or patient is both quiet and not calm.
If paul is both not rich and funny then john is both patient and kind and vice versa.
Everyone who is not quiet or not calm is humble and vice versa.
If someone is either brave or tall then paul is either not rich or not patient and vice versa.
If someone is funny then someone is either not happy or rich and vice versa.
Everyone who is not kind is creative or not patient and vice versa.
Everyone who is both brave and curious is both not quiet and generous and vice versa.
If paul is both happy and funny then mary is not funny and vice versa.
Everyone who is either not old or generous is both calm and generous and vice versa.
Everyone who is either not patient or funny is not humble.
If paul is both curious and not kind then someone is not brave.
If someone is not patient then someone is both not brave and not old and vice versa.
If someone is both funny and not brave then paul is both kind and humble.
Everyone who is not strong is either creative or not strong and vice versa.
Everyone who is both strong and old is tall.
Everyone who is strong or not kind is either not funny or not tall and vice versa.
Someone is not generous.
Susan is creative or not tall.
Someone is tall or not generous.
Fred is either funny or not quiet.
Mary is not wise or humble.
Mary is both strong and funny. | John is happy. | neutral | (![X]:((calm(X)|patient(X))=>(quiet(X)&~calm(X))))&
(((~rich(paul)&funny(paul)))<=>((patient(john)&kind(john))))&
(![X]:((~quiet(X)|~calm(X))<=>humble(X)))&
((?[X]:((brave(X)<~>tall(X))))<=>((~rich(paul)<~>~patient(paul))))&
((?[X]:(funny(X)))<=>(?[X]:((~happy(X)<~>rich(X)))))&
(![X]:(~kind(X)<=>(creative(X)|~patient(X))))&
(![X]:((brave(X)&curious(X))<=>(~quiet(X)&generous(X))))&
(((happy(paul)&funny(paul)))<=>(~funny(mary)))&
(![X]:((~old(X)<~>generous(X))<=>(calm(X)&generous(X))))&
(![X]:((~patient(X)<~>funny(X))=>~humble(X)))&
(((curious(paul)&~kind(paul)))=>(?[X]:(~brave(X))))&
((?[X]:(~patient(X)))<=>(?[X]:((~brave(X)&~old(X)))))&
((?[X]:((funny(X)&~brave(X))))=>((kind(paul)&humble(paul))))&
(![X]:(~strong(X)<=>(creative(X)<~>~strong(X))))&
(![X]:((strong(X)&old(X))=>tall(X)))&
(![X]:((strong(X)|~kind(X))<=>(~funny(X)<~>~tall(X))))&
(?[X]:(~generous(X)))&
((creative(susan)|~tall(susan)))&
(?[X]:((tall(X)|~generous(X))))&
((funny(fred)<~>~quiet(fred)))&
((~wise(mary)|humble(mary)))&
((strong(mary)&funny(mary))) | happy(john) | [] | null | 0 |
Everyone who is both tall and not funny is not strong or not quiet and vice versa.
Everyone who is funny or calm is not wise or brave.
Everyone who is either not creative or brave is both generous and not kind and vice versa.
Everyone who is not humble is both kind and curious and vice versa.
If john is both not funny and quiet then someone is both humble and not calm.
If someone is curious then someone is strong and vice versa.
If someone is either generous or creative then susan is brave and vice versa.
Everyone who is both creative and not brave is both calm and kind and vice versa.
Everyone who is patient is either quiet or creative and vice versa.
If someone is not funny then lucy is both not patient and humble.
Everyone who is both happy and calm is not strong or strong and vice versa.
If someone is both not strong and old then john is not kind.
If someone is both kind and not generous then paul is either humble or curious and vice versa.
If someone is both not kind and curious then mary is patient.
If someone is funny or not curious then someone is humble or not wise.
Everyone who is not quiet or wise is not generous and vice versa.
Someone is either patient or not happy.
Someone is both not quiet and not curious.
Paul is not kind.
Lucy is either kind or humble.
Alice is not rich or not wise.
Someone is not curious.
Someone is either not wise or not old. | Lucy is not kind. | entailment | (![X]:((tall(X)&~funny(X))<=>(~strong(X)|~quiet(X))))&
(![X]:((funny(X)|calm(X))=>(~wise(X)|brave(X))))&
(![X]:((~creative(X)<~>brave(X))<=>(generous(X)&~kind(X))))&
(![X]:(~humble(X)<=>(kind(X)&curious(X))))&
(((~funny(john)&quiet(john)))=>(?[X]:((humble(X)&~calm(X)))))&
((?[X]:(curious(X)))<=>(?[X]:(strong(X))))&
((?[X]:((generous(X)<~>creative(X))))<=>(brave(susan)))&
(![X]:((creative(X)&~brave(X))<=>(calm(X)&kind(X))))&
(![X]:(patient(X)<=>(quiet(X)<~>creative(X))))&
((?[X]:(~funny(X)))=>((~patient(lucy)&humble(lucy))))&
(![X]:((happy(X)&calm(X))<=>(~strong(X)|strong(X))))&
((?[X]:((~strong(X)&old(X))))=>(~kind(john)))&
((?[X]:((kind(X)&~generous(X))))<=>((humble(paul)<~>curious(paul))))&
((?[X]:((~kind(X)&curious(X))))=>(patient(mary)))&
((?[X]:((funny(X)|~curious(X))))=>(?[X]:((humble(X)|~wise(X)))))&
(![X]:((~quiet(X)|wise(X))<=>~generous(X)))&
(?[X]:((patient(X)<~>~happy(X))))&
(?[X]:((~quiet(X)&~curious(X))))&
(~kind(paul))&
((kind(lucy)<~>humble(lucy)))&
((~rich(alice)|~wise(alice)))&
(?[X]:(~curious(X)))&
(?[X]:((~wise(X)<~>~old(X)))) | ~kind(lucy) | [
"p0",
"p9",
"p17",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 1962956127827283770948917
% SZS output start Proof for 1962956127827283770948917
1. ! [X0] : ((~funny(X0) & tall(X0)) <=> (~quiet(X0) | ~strong(X0))) [input p0]
10. ? [X0] : ~funny(X0) => (humble(lucy) & ~patient(lucy)) [input p9]
18. ? [X0] : (~curious(X0) & ~quiet(X0)) [input p17]
20. kind(lucy) <~> humble(lucy) [input p19]
24. kind(lucy) [input hypothesis]
32. (humble(lucy) & ~patient(lucy)) | ! [X0] : funny(X0) [ennf transformation 10]
36. ! [X0] : (((~funny(X0) & tall(X0)) | (quiet(X0) & strong(X0))) & ((~quiet(X0) | ~strong(X0)) | (funny(X0) | ~tall(X0)))) [nnf transformation 1]
37. ! [X0] : (((~funny(X0) & tall(X0)) | (quiet(X0) & strong(X0))) & (~quiet(X0) | ~strong(X0) | funny(X0) | ~tall(X0))) [flattening 36]
70. ? [X0] : (~curious(X0) & ~quiet(X0)) => (~curious(sK7) & ~quiet(sK7)) [choice axiom]
71. ~curious(sK7) & ~quiet(sK7) [skolemisation 18,70]
72. (~humble(lucy) | ~kind(lucy)) & (humble(lucy) | kind(lucy)) [nnf transformation 20]
82. ~funny(X0) | quiet(X0) [cnf transformation 37]
111. humble(lucy) | funny(X0) [cnf transformation 32]
132. ~quiet(sK7) [cnf transformation 71]
136. ~humble(lucy) | ~kind(lucy) [cnf transformation 72]
140. kind(lucy) [cnf transformation 24]
198. 14 <=> ! [X0] : funny(X0) [avatar definition]
199. funny(X0) <- (14) [avatar component clause 198]
201. 15 <=> humble(lucy) [avatar definition]
204. 14 | 15 [avatar split clause 111,201,198]
274. 30 <=> kind(lucy) [avatar definition]
277. ~30 | ~15 [avatar split clause 136,201,274]
288. 30 [avatar split clause 140,274]
297. quiet(X0) <- (14) [resolution 82,199]
306. $false <- (14) [resolution 297,132]
309. ~14 [avatar contradiction clause 306]
310. $false [avatar sat refutation 204,277,288,309]
% SZS output end Proof for 1962956127827283770948917
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous or not happy then someone is either wise or rich and vice versa.
If someone is both not happy and not kind then someone is calm or curious.
If john is both not old and not quiet then someone is either not quiet or strong and vice versa.
Everyone who is both kind and curious is either patient or not tall and vice versa.
If paul is not humble then susan is either patient or happy and vice versa.
If paul is both not funny and calm then alice is wise or not tall and vice versa.
Everyone who is rich or not strong is both not humble and not creative and vice versa.
Everyone who is tall is both strong and old.
If someone is curious or funny then someone is not humble and vice versa.
Everyone who is generous or not funny is not funny.
Everyone who is not tall is happy and vice versa.
If paul is both not tall and kind then someone is not rich or not humble and vice versa.
Everyone who is tall is not old.
If someone is not quiet then someone is calm or not creative.
Everyone who is calm is not quiet or not wise and vice versa.
Someone is either not curious or generous.
Someone is both not strong and wise.
Fred is both brave and not kind.
John is humble.
Someone is not rich.
Someone is both not generous and funny.
Fred is either not quiet or not wise. | Alice is creative. | neutral | ((?[X]:((generous(X)<~>~happy(X))))<=>(?[X]:((wise(X)<~>rich(X)))))&
((?[X]:((~happy(X)&~kind(X))))=>(?[X]:((calm(X)|curious(X)))))&
(((~old(john)&~quiet(john)))<=>(?[X]:((~quiet(X)<~>strong(X)))))&
(![X]:((kind(X)&curious(X))<=>(patient(X)<~>~tall(X))))&
((~humble(paul))<=>((patient(susan)<~>happy(susan))))&
(((~funny(paul)&calm(paul)))<=>((wise(alice)|~tall(alice))))&
(![X]:((rich(X)|~strong(X))<=>(~humble(X)&~creative(X))))&
(![X]:(tall(X)=>(strong(X)&old(X))))&
((?[X]:((curious(X)|funny(X))))<=>(?[X]:(~humble(X))))&
(![X]:((generous(X)|~funny(X))=>~funny(X)))&
(![X]:(~tall(X)<=>happy(X)))&
(((~tall(paul)&kind(paul)))<=>(?[X]:((~rich(X)|~humble(X)))))&
(![X]:(tall(X)=>~old(X)))&
((?[X]:(~quiet(X)))=>(?[X]:((calm(X)|~creative(X)))))&
(![X]:(calm(X)<=>(~quiet(X)|~wise(X))))&
(?[X]:((~curious(X)<~>generous(X))))&
(?[X]:((~strong(X)&wise(X))))&
((brave(fred)&~kind(fred)))&
(humble(john))&
(?[X]:(~rich(X)))&
(?[X]:((~generous(X)&funny(X))))&
((~quiet(fred)<~>~wise(fred))) | creative(alice) | [] | null | 0 |
If fred is either generous or not humble then someone is both not wise and curious and vice versa. Everyone who is not creative or not rich is not happy or wise and vice versa. If someone is not old or not patient then someone is either tall or not happy and vice versa. Everyone who is both not generous and generous is not creative or not curious. If paul is not rich or quiet then someone is funny or not wise. Everyone who is not curious is not strong. Everyone who is tall or not calm is brave. If john is both not strong and not happy then someone is both kind and tall and vice versa. If someone is generous or old then someone is brave or not brave and vice versa. Everyone who is not creative or curious is either not curious or funny. If lucy is not happy or generous then someone is either not kind or rich. If john is either not funny or calm then paul is either wise or happy and vice versa. Everyone who is rich is both rich and calm and vice versa. If lucy is not kind then lucy is both wise and not calm and vice versa. Everyone who is both not happy and tall is not patient and vice versa. If paul is both strong and rich then john is not old. Lucy is kind or not old. Someone is happy or not curious. Someone is either tall or humble. Someone is not kind or wise. John is either curious or not calm. Someone is either not old or generous. Paul is both kind and not tall. Someone is brave. | John is not patient. | neutral | (((generous(fred)<~>~humble(fred)))<=>(?[X]:((~wise(X)&curious(X)))))&
(![X]:((~creative(X)|~rich(X))<=>(~happy(X)|wise(X))))&
((?[X]:((~old(X)|~patient(X))))<=>(?[X]:((tall(X)<~>~happy(X)))))&
(![X]:((~generous(X)&generous(X))=>(~creative(X)|~curious(X))))&
(((~rich(paul)|quiet(paul)))=>(?[X]:((funny(X)|~wise(X)))))&
(![X]:(~curious(X)=>~strong(X)))&
(![X]:((tall(X)|~calm(X))=>brave(X)))&
(((~strong(john)&~happy(john)))<=>(?[X]:((kind(X)&tall(X)))))&
((?[X]:((generous(X)|old(X))))<=>(?[X]:((brave(X)|~brave(X)))))&
(![X]:((~creative(X)|curious(X))=>(~curious(X)<~>funny(X))))&
(((~happy(lucy)|generous(lucy)))=>(?[X]:((~kind(X)<~>rich(X)))))&
(((~funny(john)<~>calm(john)))<=>((wise(paul)<~>happy(paul))))&
(![X]:(rich(X)<=>(rich(X)&calm(X))))&
((~kind(lucy))<=>((wise(lucy)&~calm(lucy))))&
(![X]:((~happy(X)&tall(X))<=>~patient(X)))&
(((strong(paul)&rich(paul)))=>(~old(john)))&
((kind(lucy)|~old(lucy)))&
(?[X]:((happy(X)|~curious(X))))&
(?[X]:((tall(X)<~>humble(X))))&
(?[X]:((~kind(X)|wise(X))))&
((curious(john)<~>~calm(john)))&
(?[X]:((~old(X)<~>generous(X))))&
((kind(paul)&~tall(paul)))&
(?[X]:(brave(X))) | ~patient(john) | [] | null | 0 |
If someone is not funny or not humble then someone is kind and vice versa. Everyone who is either not quiet or funny is both kind and not funny and vice versa. Everyone who is either funny or curious is brave or curious and vice versa. Everyone who is kind or generous is generous or wise. If alice is happy then fred is both kind and old and vice versa. If john is not brave then fred is either wise or not humble. Everyone who is calm or not creative is either not curious or humble. If fred is not tall or calm then paul is either not tall or generous and vice versa. If someone is calm or not creative then john is either not creative or not old. Everyone who is both tall and not brave is brave or funny and vice versa. If someone is patient then fred is both not wise and not calm. Everyone who is not creative or old is both old and wise. If someone is not wise then alice is either curious or not brave and vice versa. Everyone who is either kind or not old is brave. Everyone who is creative or not curious is either not kind or humble. Mary is either not calm or tall. Lucy is not happy or not quiet. Someone is generous. Someone is not humble. Someone is both not rich and not wise. Someone is both not happy and not kind. | Mary is not creative. | neutral | ((?[X]:((~funny(X)|~humble(X))))<=>(?[X]:(kind(X))))&
(![X]:((~quiet(X)<~>funny(X))<=>(kind(X)&~funny(X))))&
(![X]:((funny(X)<~>curious(X))<=>(brave(X)|curious(X))))&
(![X]:((kind(X)|generous(X))=>(generous(X)|wise(X))))&
((happy(alice))<=>((kind(fred)&old(fred))))&
((~brave(john))=>((wise(fred)<~>~humble(fred))))&
(![X]:((calm(X)|~creative(X))=>(~curious(X)<~>humble(X))))&
(((~tall(fred)|calm(fred)))<=>((~tall(paul)<~>generous(paul))))&
((?[X]:((calm(X)|~creative(X))))=>((~creative(john)<~>~old(john))))&
(![X]:((tall(X)&~brave(X))<=>(brave(X)|funny(X))))&
((?[X]:(patient(X)))=>((~wise(fred)&~calm(fred))))&
(![X]:((~creative(X)|old(X))=>(old(X)&wise(X))))&
((?[X]:(~wise(X)))<=>((curious(alice)<~>~brave(alice))))&
(![X]:((kind(X)<~>~old(X))=>brave(X)))&
(![X]:((creative(X)|~curious(X))=>(~kind(X)<~>humble(X))))&
((~calm(mary)<~>tall(mary)))&
((~happy(lucy)|~quiet(lucy)))&
(?[X]:(generous(X)))&
(?[X]:(~humble(X)))&
(?[X]:((~rich(X)&~wise(X))))&
(?[X]:((~happy(X)&~kind(X)))) | ~creative(mary) | [] | null | 0 |
Everyone who is old or not patient is both not old and patient.
Everyone who is not calm is not patient or not creative.
Everyone who is not wise or creative is not kind or strong.
Everyone who is not calm or not old is either happy or not kind and vice versa.
Everyone who is not curious is not humble or not rich and vice versa.
Everyone who is either creative or not rich is both patient and not old.
If paul is both not calm and not patient then john is either not funny or brave and vice versa.
Everyone who is either not brave or not rich is both not old and patient.
If john is both funny and not curious then someone is either not tall or curious.
If someone is generous or quiet then someone is both not kind and old and vice versa.
If someone is funny or not old then someone is either not rich or not old and vice versa.
If someone is both rich and humble then someone is both not old and not rich and vice versa.
Everyone who is brave or funny is calm or not tall and vice versa.
If susan is not curious or not patient then someone is quiet and vice versa.
Everyone who is both strong and kind is not tall and vice versa.
Someone is both funny and not kind.
Mary is either not curious or generous.
Someone is either strong or wise.
Someone is not generous or not quiet.
Someone is wise or not generous.
John is either not old or tall. | Mary is humble. | neutral | (![X]:((old(X)|~patient(X))=>(~old(X)&patient(X))))&
(![X]:(~calm(X)=>(~patient(X)|~creative(X))))&
(![X]:((~wise(X)|creative(X))=>(~kind(X)|strong(X))))&
(![X]:((~calm(X)|~old(X))<=>(happy(X)<~>~kind(X))))&
(![X]:(~curious(X)<=>(~humble(X)|~rich(X))))&
(![X]:((creative(X)<~>~rich(X))=>(patient(X)&~old(X))))&
(((~calm(paul)&~patient(paul)))<=>((~funny(john)<~>brave(john))))&
(![X]:((~brave(X)<~>~rich(X))=>(~old(X)&patient(X))))&
(((funny(john)&~curious(john)))=>(?[X]:((~tall(X)<~>curious(X)))))&
((?[X]:((generous(X)|quiet(X))))<=>(?[X]:((~kind(X)&old(X)))))&
((?[X]:((funny(X)|~old(X))))<=>(?[X]:((~rich(X)<~>~old(X)))))&
((?[X]:((rich(X)&humble(X))))<=>(?[X]:((~old(X)&~rich(X)))))&
(![X]:((brave(X)|funny(X))<=>(calm(X)|~tall(X))))&
(((~curious(susan)|~patient(susan)))<=>(?[X]:(quiet(X))))&
(![X]:((strong(X)&kind(X))<=>~tall(X)))&
(?[X]:((funny(X)&~kind(X))))&
((~curious(mary)<~>generous(mary)))&
(?[X]:((strong(X)<~>wise(X))))&
(?[X]:((~generous(X)|~quiet(X))))&
(?[X]:((wise(X)|~generous(X))))&
((~old(john)<~>tall(john))) | humble(mary) | [] | null | 0 |
If someone is patient or brave then lucy is either not creative or not kind and vice versa.
Everyone who is either not strong or not old is both not quiet and not patient.
Everyone who is both quiet and not tall is tall and vice versa.
Everyone who is not curious is patient.
Everyone who is creative is both strong and not curious.
Everyone who is not quiet or creative is kind or brave and vice versa.
If someone is both brave and rich then alice is not curious or not humble.
If someone is either calm or rich then john is not kind or curious and vice versa.
Everyone who is not tall or curious is not calm.
If john is curious or not funny then someone is both strong and funny.
Everyone who is not creative is funny.
If mary is both not happy and creative then susan is both strong and not happy and vice versa.
If mary is not old or not funny then mary is not creative or rich.
If lucy is either patient or creative then lucy is not tall or brave and vice versa.
Everyone who is rich or not kind is not happy or not funny and vice versa.
Everyone who is both not humble and not generous is not brave or kind and vice versa.
Alice is curious or not generous.
Alice is not brave or wise.
Fred is not brave.
Mary is tall or kind.
Someone is not tall.
Someone is either not patient or not funny.
Lucy is tall or not old.
Someone is either wise or not curious. | Fred is not calm. | entailment | ((?[X]:((patient(X)|brave(X))))<=>((~creative(lucy)<~>~kind(lucy))))&
(![X]:((~strong(X)<~>~old(X))=>(~quiet(X)&~patient(X))))&
(![X]:((quiet(X)&~tall(X))<=>tall(X)))&
(![X]:(~curious(X)=>patient(X)))&
(![X]:(creative(X)=>(strong(X)&~curious(X))))&
(![X]:((~quiet(X)|creative(X))<=>(kind(X)|brave(X))))&
((?[X]:((brave(X)&rich(X))))=>((~curious(alice)|~humble(alice))))&
((?[X]:((calm(X)<~>rich(X))))<=>((~kind(john)|curious(john))))&
(![X]:((~tall(X)|curious(X))=>~calm(X)))&
(((curious(john)|~funny(john)))=>(?[X]:((strong(X)&funny(X)))))&
(![X]:(~creative(X)=>funny(X)))&
(((~happy(mary)&creative(mary)))<=>((strong(susan)&~happy(susan))))&
(((~old(mary)|~funny(mary)))=>((~creative(mary)|rich(mary))))&
(((patient(lucy)<~>creative(lucy)))<=>((~tall(lucy)|brave(lucy))))&
(![X]:((rich(X)|~kind(X))<=>(~happy(X)|~funny(X))))&
(![X]:((~humble(X)&~generous(X))<=>(~brave(X)|kind(X))))&
((curious(alice)|~generous(alice)))&
((~brave(alice)|wise(alice)))&
(~brave(fred))&
((tall(mary)|kind(mary)))&
(?[X]:(~tall(X)))&
(?[X]:((~patient(X)<~>~funny(X))))&
((tall(lucy)|~old(lucy)))&
(?[X]:((wise(X)<~>~curious(X)))) | ~calm(fred) | [
"p2",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 5789032607407841147252602
% SZS output start Proof for 5789032607407841147252602
3. ! [X0] : ((~tall(X0) & quiet(X0)) <=> tall(X0)) [input p2]
9. ! [X0] : ((curious(X0) | ~tall(X0)) => ~calm(X0)) [input p8]
25. calm(fred) [input hypothesis]
31. ! [X0] : (~calm(X0) | (~curious(X0) & tall(X0))) [ennf transformation 9]
41. ! [X0] : (((~tall(X0) & quiet(X0)) | ~tall(X0)) & (tall(X0) | (tall(X0) | ~quiet(X0)))) [nnf transformation 3]
42. ! [X0] : (((~tall(X0) & quiet(X0)) | ~tall(X0)) & (tall(X0) | tall(X0) | ~quiet(X0))) [flattening 41]
80. ~tall(X0) | ~tall(X0) [cnf transformation 42]
95. ~calm(X0) | tall(X0) [cnf transformation 31]
133. calm(fred) [cnf transformation 25]
135. ~tall(X0) [duplicate literal removal 80]
206. ~calm(X0) [subsumption resolution 95,135]
309. $false [subsumption resolution 133,206]
% SZS output end Proof for 5789032607407841147252602
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 fred is not creative then lucy is not curious. If someone is patient then someone is not generous or not brave and vice versa. If john is strong or not patient then john is either rich or not wise and vice versa. Everyone who is both not kind and funny is both funny and not kind and vice versa. If someone is happy then someone is either not creative or not curious and vice versa. Everyone who is funny or not patient is both wise and not rich and vice versa. Everyone who is not rich is strong or not quiet and vice versa. If mary is not humble then susan is either wise or strong. If john is either quiet or not old then john is either kind or not curious and vice versa. If mary is either not tall or not rich then lucy is not creative. Everyone who is both tall and humble is not calm. Everyone who is curious or brave is not brave or not happy and vice versa. Everyone who is both quiet and not brave is either generous or not happy and vice versa. If someone is not generous then john is both creative and not funny and vice versa. Everyone who is generous or not creative is creative and vice versa. Everyone who is not creative is generous or not creative. Someone is either not rich or humble. Someone is not kind or tall. Mary is both not curious and not calm. Mary is not generous or wise. Someone is not quiet or wise. John is not humble or humble. | Mary is rich. | neutral | ((~creative(fred))=>(~curious(lucy)))&
((?[X]:(patient(X)))<=>(?[X]:((~generous(X)|~brave(X)))))&
(((strong(john)|~patient(john)))<=>((rich(john)<~>~wise(john))))&
(![X]:((~kind(X)&funny(X))<=>(funny(X)&~kind(X))))&
((?[X]:(happy(X)))<=>(?[X]:((~creative(X)<~>~curious(X)))))&
(![X]:((funny(X)|~patient(X))<=>(wise(X)&~rich(X))))&
(![X]:(~rich(X)<=>(strong(X)|~quiet(X))))&
((~humble(mary))=>((wise(susan)<~>strong(susan))))&
(((quiet(john)<~>~old(john)))<=>((kind(john)<~>~curious(john))))&
(((~tall(mary)<~>~rich(mary)))=>(~creative(lucy)))&
(![X]:((tall(X)&humble(X))=>~calm(X)))&
(![X]:((curious(X)|brave(X))<=>(~brave(X)|~happy(X))))&
(![X]:((quiet(X)&~brave(X))<=>(generous(X)<~>~happy(X))))&
((?[X]:(~generous(X)))<=>((creative(john)&~funny(john))))&
(![X]:((generous(X)|~creative(X))<=>creative(X)))&
(![X]:(~creative(X)=>(generous(X)|~creative(X))))&
(?[X]:((~rich(X)<~>humble(X))))&
(?[X]:((~kind(X)|tall(X))))&
((~curious(mary)&~calm(mary)))&
((~generous(mary)|wise(mary)))&
(?[X]:((~quiet(X)|wise(X))))&
((~humble(john)|humble(john))) | rich(mary) | [] | null | 0 |
Everyone who is not patient or not kind is either kind or not patient and vice versa.
If someone is not kind or quiet then lucy is either old or not generous.
Everyone who is both not creative and not generous is creative and vice versa.
If someone is not rich then someone is either curious or not calm.
Everyone who is patient is not quiet and vice versa.
If someone is either not kind or not tall then john is either not funny or not quiet and vice versa.
Everyone who is either patient or curious is both kind and humble and vice versa.
Everyone who is either not tall or curious is creative or brave.
If someone is either not humble or not calm then fred is strong and vice versa.
If lucy is tall or not creative then someone is both not calm and generous.
If someone is either funny or not happy then someone is both tall and happy.
Everyone who is either brave or not strong is wise and vice versa.
Everyone who is not wise is old and vice versa.
Everyone who is not funny or brave is both generous and tall and vice versa.
Someone is both generous and strong.
Susan is either old or not creative.
Someone is not strong or not creative.
Someone is not humble or not happy.
Lucy is humble.
Paul is either not wise or quiet. | Susan is not kind. | entailment | (![X]:((~patient(X)|~kind(X))<=>(kind(X)<~>~patient(X))))&
((?[X]:((~kind(X)|quiet(X))))=>((old(lucy)<~>~generous(lucy))))&
(![X]:((~creative(X)&~generous(X))<=>creative(X)))&
((?[X]:(~rich(X)))=>(?[X]:((curious(X)<~>~calm(X)))))&
(![X]:(patient(X)<=>~quiet(X)))&
((?[X]:((~kind(X)<~>~tall(X))))<=>((~funny(john)<~>~quiet(john))))&
(![X]:((patient(X)<~>curious(X))<=>(kind(X)&humble(X))))&
(![X]:((~tall(X)<~>curious(X))=>(creative(X)|brave(X))))&
((?[X]:((~humble(X)<~>~calm(X))))<=>(strong(fred)))&
(((tall(lucy)|~creative(lucy)))=>(?[X]:((~calm(X)&generous(X)))))&
((?[X]:((funny(X)<~>~happy(X))))=>(?[X]:((tall(X)&happy(X)))))&
(![X]:((brave(X)<~>~strong(X))<=>wise(X)))&
(![X]:(~wise(X)<=>old(X)))&
(![X]:((~funny(X)|brave(X))<=>(generous(X)&tall(X))))&
(?[X]:((generous(X)&strong(X))))&
((old(susan)<~>~creative(susan)))&
(?[X]:((~strong(X)|~creative(X))))&
(?[X]:((~humble(X)|~happy(X))))&
(humble(lucy))&
((~wise(paul)<~>quiet(paul))) | ~kind(susan) | [
"p0",
"hypothesis"
] | % SZS status Unsatisfiable for 1001245786546478393208407
% SZS output start Proof for 1001245786546478393208407
1. ! [X0] : ((~kind(X0) | ~patient(X0)) <=> (kind(X0) <~> ~patient(X0))) [input p0]
21. kind(susan) [input hypothesis]
30. ! [X0] : (((~kind(X0) | ~patient(X0)) | ((kind(X0) | patient(X0)) & (~patient(X0) | ~kind(X0)))) & (((patient(X0) | ~kind(X0)) & (~patient(X0) | kind(X0))) | (kind(X0) & patient(X0)))) [nnf transformation 1]
31. ! [X0] : ((~kind(X0) | ~patient(X0) | ((kind(X0) | patient(X0)) & (~patient(X0) | ~kind(X0)))) & (((patient(X0) | ~kind(X0)) & (~patient(X0) | kind(X0))) | (kind(X0) & patient(X0)))) [flattening 30]
67. patient(X0) | ~kind(X0) | patient(X0) [cnf transformation 31]
69. ~kind(X0) | ~patient(X0) | ~patient(X0) | ~kind(X0) [cnf transformation 31]
128. kind(susan) [cnf transformation 21]
132. patient(X0) | ~kind(X0) [duplicate literal removal 67]
133. ~kind(X0) | ~patient(X0) [duplicate literal removal 69]
134. ~kind(X0) [subsumption resolution 132,133]
232. $false [subsumption resolution 128,134]
% SZS output end Proof for 1001245786546478393208407
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not funny or quiet is not strong or not tall.
If someone is happy then someone is wise and vice versa.
If fred is rich or brave then someone is either kind or not calm and vice versa.
Everyone who is not funny or creative is both not quiet and kind.
Everyone who is either curious or happy is either not humble or creative.
If mary is funny or quiet then someone is both not kind and old and vice versa.
If someone is tall then alice is both brave and not patient and vice versa.
Everyone who is both tall and not wise is either brave or wise and vice versa.
If someone is not brave then mary is strong.
Everyone who is kind or rich is either wise or not quiet.
If someone is either curious or creative then susan is both quiet and brave.
Everyone who is not wise or wise is both generous and patient and vice versa.
Everyone who is either rich or funny is not patient.
Everyone who is both strong and curious is either kind or not tall.
Someone is humble or old.
Paul is either not kind or creative.
Alice is strong or not happy.
Mary is not strong or curious.
Someone is both not happy and patient.
Susan is either not happy or not patient.
Alice is not quiet. | Susan is not rich. | contradiction | (![X]:((~funny(X)<~>quiet(X))=>(~strong(X)|~tall(X))))&
((?[X]:(happy(X)))<=>(?[X]:(wise(X))))&
(((rich(fred)|brave(fred)))<=>(?[X]:((kind(X)<~>~calm(X)))))&
(![X]:((~funny(X)|creative(X))=>(~quiet(X)&kind(X))))&
(![X]:((curious(X)<~>happy(X))=>(~humble(X)<~>creative(X))))&
(((funny(mary)|quiet(mary)))<=>(?[X]:((~kind(X)&old(X)))))&
((?[X]:(tall(X)))<=>((brave(alice)&~patient(alice))))&
(![X]:((tall(X)&~wise(X))<=>(brave(X)<~>wise(X))))&
((?[X]:(~brave(X)))=>(strong(mary)))&
(![X]:((kind(X)|rich(X))=>(wise(X)<~>~quiet(X))))&
((?[X]:((curious(X)<~>creative(X))))=>((quiet(susan)&brave(susan))))&
(![X]:((~wise(X)|wise(X))<=>(generous(X)&patient(X))))&
(![X]:((rich(X)<~>funny(X))=>~patient(X)))&
(![X]:((strong(X)&curious(X))=>(kind(X)<~>~tall(X))))&
(?[X]:((humble(X)|old(X))))&
((~kind(paul)<~>creative(paul)))&
((strong(alice)|~happy(alice)))&
((~strong(mary)|curious(mary)))&
(?[X]:((~happy(X)&patient(X))))&
((~happy(susan)<~>~patient(susan)))&
(~quiet(alice)) | ~rich(susan) | [
"p3",
"p6",
"p7",
"p8",
"p9",
"p10",
"p11",
"p12",
"p13",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 5741602809582068596910975
% SZS output start Proof for 5741602809582068596910975
4. ! [X0] : ((creative(X0) | ~funny(X0)) => (kind(X0) & ~quiet(X0))) [input p3]
7. ? [X0] : tall(X0) <=> (~patient(alice) & brave(alice)) [input p6]
8. ! [X0] : ((~wise(X0) & tall(X0)) <=> (brave(X0) <~> wise(X0))) [input p7]
9. ? [X0] : ~brave(X0) => strong(mary) [input p8]
10. ! [X0] : ((rich(X0) | kind(X0)) => (wise(X0) <~> ~quiet(X0))) [input p9]
11. ? [X0] : (curious(X0) <~> creative(X0)) => (brave(susan) & quiet(susan)) [input p10]
12. ! [X0] : ((wise(X0) | ~wise(X0)) <=> (patient(X0) & generous(X0))) [input p11]
13. ! [X0] : ((rich(X0) <~> funny(X0)) => ~patient(X0)) [input p12]
14. ! [X0] : ((curious(X0) & strong(X0)) => (kind(X0) <~> ~tall(X0))) [input p13]
18. curious(mary) | ~strong(mary) [input p17]
22. ~rich(susan) [input hypothesis]
26. ! [X0] : ((kind(X0) & ~quiet(X0)) | (~creative(X0) & funny(X0))) [ennf transformation 4]
28. strong(mary) | ! [X0] : brave(X0) [ennf transformation 9]
29. ! [X0] : ((wise(X0) <~> ~quiet(X0)) | (~rich(X0) & ~kind(X0))) [ennf transformation 10]
30. (brave(susan) & quiet(susan)) | ! [X0] : (curious(X0) <=> creative(X0)) [ennf transformation 11]
31. ! [X0] : (~patient(X0) | (rich(X0) <=> funny(X0))) [ennf transformation 13]
32. ! [X0] : ((kind(X0) <~> ~tall(X0)) | (~curious(X0) | ~strong(X0))) [ennf transformation 14]
33. ! [X0] : ((kind(X0) <~> ~tall(X0)) | ~curious(X0) | ~strong(X0)) [flattening 32]
51. (? [X0] : tall(X0) | (patient(alice) | ~brave(alice))) & ((~patient(alice) & brave(alice)) | ! [X0] : ~tall(X0)) [nnf transformation 7]
52. (? [X0] : tall(X0) | patient(alice) | ~brave(alice)) & ((~patient(alice) & brave(alice)) | ! [X0] : ~tall(X0)) [flattening 51]
53. (? [X0] : tall(X0) | patient(alice) | ~brave(alice)) & ((~patient(alice) & brave(alice)) | ! [X1] : ~tall(X1)) [rectify 52]
54. ? [X0] : tall(X0) => tall(sK4) [choice axiom]
55. (tall(sK4) | patient(alice) | ~brave(alice)) & ((~patient(alice) & brave(alice)) | ! [X1] : ~tall(X1)) [skolemisation 53,54]
56. ! [X0] : (((~wise(X0) & tall(X0)) | ((brave(X0) | ~wise(X0)) & (wise(X0) | ~brave(X0)))) & (((~wise(X0) | ~brave(X0)) & (wise(X0) | brave(X0))) | (wise(X0) | ~tall(X0)))) [nnf transformation 8]
57. ! [X0] : (((~wise(X0) & tall(X0)) | ((brave(X0) | ~wise(X0)) & (wise(X0) | ~brave(X0)))) & (((~wise(X0) | ~brave(X0)) & (wise(X0) | brave(X0))) | wise(X0) | ~tall(X0))) [flattening 56]
58. ! [X0] : (((quiet(X0) | ~wise(X0)) & (~quiet(X0) | wise(X0))) | (~rich(X0) & ~kind(X0))) [nnf transformation 29]
59. (brave(susan) & quiet(susan)) | ! [X0] : ((curious(X0) | ~creative(X0)) & (creative(X0) | ~curious(X0))) [nnf transformation 30]
60. ! [X0] : (((wise(X0) | ~wise(X0)) | (~patient(X0) | ~generous(X0))) & ((patient(X0) & generous(X0)) | (~wise(X0) & wise(X0)))) [nnf transformation 12]
61. ! [X0] : ((wise(X0) | ~wise(X0) | ~patient(X0) | ~generous(X0)) & ((patient(X0) & generous(X0)) | (~wise(X0) & wise(X0)))) [flattening 60]
62. ! [X0] : (~patient(X0) | ((rich(X0) | ~funny(X0)) & (funny(X0) | ~rich(X0)))) [nnf transformation 31]
63. ! [X0] : (((tall(X0) | ~kind(X0)) & (~tall(X0) | kind(X0))) | ~curious(X0) | ~strong(X0)) [nnf transformation 33]
80. ~quiet(X0) | funny(X0) [cnf transformation 26]
82. kind(X0) | funny(X0) [cnf transformation 26]
83. ~creative(X0) | kind(X0) [cnf transformation 26]
94. ~patient(alice) | ~tall(X1) [cnf transformation 55]
98. ~brave(X0) | wise(X0) | tall(X0) [cnf transformation 57]
102. strong(mary) | brave(X0) [cnf transformation 28]
105. ~kind(X0) | ~wise(X0) | quiet(X0) [cnf transformation 58]
107. quiet(susan) | creative(X0) | ~curious(X0) [cnf transformation 59]
113. patient(X0) | wise(X0) [cnf transformation 61]
114. ~wise(X0) | patient(X0) [cnf transformation 61]
117. ~patient(X0) | rich(X0) | ~funny(X0) [cnf transformation 62]
119. ~curious(X0) | ~kind(X0) | tall(X0) | ~strong(X0) [cnf transformation 63]
124. curious(mary) | ~strong(mary) [cnf transformation 18]
130. ~rich(susan) [cnf transformation 22]
207. 17 <=> patient(alice) [avatar definition]
208. ~patient(alice) <- (~17) [avatar component clause 207]
216. 19 <=> ! [X1] : ~tall(X1) [avatar definition]
217. ~tall(X1) <- (19) [avatar component clause 216]
218. 19 | ~17 [avatar split clause 94,207,216]
222. 20 <=> ! [X0] : brave(X0) [avatar definition]
223. brave(X0) <- (20) [avatar component clause 222]
225. 21 <=> strong(mary) [avatar definition]
227. strong(mary) <- (21) [avatar component clause 225]
228. 20 | 21 [avatar split clause 102,225,222]
238. 24 <=> ! [X0] : (creative(X0) | ~curious(X0)) [avatar definition]
239. ~curious(X0) | creative(X0) <- (24) [avatar component clause 238]
242. 25 <=> quiet(susan) [avatar definition]
244. quiet(susan) <- (25) [avatar component clause 242]
246. 24 | 25 [avatar split clause 107,242,238]
247. patient(X0) [subsumption resolution 113,114]
249. ~funny(X0) | rich(X0) [subsumption resolution 117,247]
279. 32 <=> curious(mary) [avatar definition]
281. curious(mary) <- (32) [avatar component clause 279]
282. ~21 | 32 [avatar split clause 124,279,225]
284. $false <- (~17) [subsumption resolution 208,247]
285. 17 [avatar contradiction clause 284]
311. creative(mary) <- (24, 32) [resolution 281,239]
313. kind(mary) <- (24, 32) [resolution 311,83]
323. ~wise(X0) | quiet(X0) | funny(X0) [resolution 105,82]
338. ~kind(mary) | tall(mary) | ~strong(mary) <- (32) [resolution 119,281]
339. tall(mary) | ~strong(mary) <- (24, 32) [subsumption resolution 338,313]
340. ~strong(mary) <- (19, 24, 32) [subsumption resolution 339,217]
341. $false <- (19, 21, 24, 32) [subsumption resolution 340,227]
342. ~19 | ~21 | ~24 | ~32 [avatar contradiction clause 341]
395. ~wise(X0) | funny(X0) [subsumption resolution 323,80]
413. wise(X0) | tall(X0) <- (20) [resolution 223,98]
416. wise(X0) <- (19, 20) [subsumption resolution 413,217]
417. funny(susan) <- (25) [resolution 244,80]
457. rich(susan) <- (25) [resolution 417,249]
458. $false <- (25) [subsumption resolution 457,130]
459. ~25 [avatar contradiction clause 458]
474. funny(X0) <- (19, 20) [resolution 395,416]
476. rich(X0) <- (19, 20) [resolution 474,249]
515. $false <- (19, 20) [resolution 476,130]
521. ~19 | ~20 [avatar contradiction clause 515]
523. $false [avatar sat refutation 218,228,246,282,285,342,459,521]
% SZS output end Proof for 5741602809582068596910975
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both funny and not tall is not strong.
If lucy is kind then john is not creative or generous and vice versa.
If someone is not humble or not creative then someone is not old or not funny and vice versa.
If alice is either not humble or not tall then someone is brave and vice versa.
If someone is not calm then john is both not humble and not brave.
Everyone who is both not patient and not funny is creative or quiet and vice versa.
If someone is both wise and not patient then alice is not creative and vice versa.
If paul is either humble or rich then fred is both not quiet and not wise and vice versa.
Everyone who is not old or humble is funny or creative and vice versa.
If someone is either not generous or not patient then alice is not quiet or not old.
Everyone who is happy is not kind.
If mary is funny then someone is both old and creative and vice versa.
Everyone who is humble is tall or brave and vice versa.
Everyone who is either not creative or not kind is not calm or patient.
If someone is not generous or wise then paul is old and vice versa.
If someone is both not rich and not calm then someone is both not rich and happy.
Susan is both not patient and not humble.
Someone is brave or calm.
Someone is humble or not creative.
Susan is either old or not rich.
Someone is either not rich or not creative.
Someone is either not funny or generous.
Mary is either not strong or not tall.
Fred is wise or not strong. | John is brave. | neutral | (![X]:((funny(X)&~tall(X))=>~strong(X)))&
((kind(lucy))<=>((~creative(john)|generous(john))))&
((?[X]:((~humble(X)|~creative(X))))<=>(?[X]:((~old(X)|~funny(X)))))&
(((~humble(alice)<~>~tall(alice)))<=>(?[X]:(brave(X))))&
((?[X]:(~calm(X)))=>((~humble(john)&~brave(john))))&
(![X]:((~patient(X)&~funny(X))<=>(creative(X)|quiet(X))))&
((?[X]:((wise(X)&~patient(X))))<=>(~creative(alice)))&
(((humble(paul)<~>rich(paul)))<=>((~quiet(fred)&~wise(fred))))&
(![X]:((~old(X)|humble(X))<=>(funny(X)|creative(X))))&
((?[X]:((~generous(X)<~>~patient(X))))=>((~quiet(alice)|~old(alice))))&
(![X]:(happy(X)=>~kind(X)))&
((funny(mary))<=>(?[X]:((old(X)&creative(X)))))&
(![X]:(humble(X)<=>(tall(X)|brave(X))))&
(![X]:((~creative(X)<~>~kind(X))=>(~calm(X)|patient(X))))&
((?[X]:((~generous(X)|wise(X))))<=>(old(paul)))&
((?[X]:((~rich(X)&~calm(X))))=>(?[X]:((~rich(X)&happy(X)))))&
((~patient(susan)&~humble(susan)))&
(?[X]:((brave(X)|calm(X))))&
(?[X]:((humble(X)|~creative(X))))&
((old(susan)<~>~rich(susan)))&
(?[X]:((~rich(X)<~>~creative(X))))&
(?[X]:((~funny(X)<~>generous(X))))&
((~strong(mary)<~>~tall(mary)))&
((wise(fred)|~strong(fred))) | brave(john) | [] | null | 0 |
Everyone who is both humble and quiet is either quiet or calm and vice versa. If someone is either wise or brave then lucy is both not generous and not creative. If alice is either old or not strong then someone is not generous. If someone is not humble then someone is not creative or tall. Everyone who is both quiet and patient is not generous. Everyone who is either not strong or strong is both generous and creative. If someone is both funny and not quiet then someone is both generous and kind. If lucy is either not wise or calm then john is patient. If john is not wise then lucy is brave. Everyone who is generous or strong is brave and vice versa. Everyone who is not humble is both quiet and not humble. Everyone who is either quiet or wise is both rich and not wise and vice versa. If someone is both creative and rich then someone is both tall and not funny. Everyone who is not old is either not happy or generous. If someone is not creative then mary is funny or tall. If someone is both not patient and strong then susan is kind or not rich. Someone is not wise or not old. Someone is either not humble or quiet. Fred is wise. Someone is either not calm or not tall. Someone is either patient or kind. Someone is happy or not wise. Someone is not strong or humble. John is both creative and humble. | Alice is not patient. | entailment | (![X]:((humble(X)&quiet(X))<=>(quiet(X)<~>calm(X))))&
((?[X]:((wise(X)<~>brave(X))))=>((~generous(lucy)&~creative(lucy))))&
(((old(alice)<~>~strong(alice)))=>(?[X]:(~generous(X))))&
((?[X]:(~humble(X)))=>(?[X]:((~creative(X)|tall(X)))))&
(![X]:((quiet(X)&patient(X))=>~generous(X)))&
(![X]:((~strong(X)<~>strong(X))=>(generous(X)&creative(X))))&
((?[X]:((funny(X)&~quiet(X))))=>(?[X]:((generous(X)&kind(X)))))&
(((~wise(lucy)<~>calm(lucy)))=>(patient(john)))&
((~wise(john))=>(brave(lucy)))&
(![X]:((generous(X)|strong(X))<=>brave(X)))&
(![X]:(~humble(X)=>(quiet(X)&~humble(X))))&
(![X]:((quiet(X)<~>wise(X))<=>(rich(X)&~wise(X))))&
((?[X]:((creative(X)&rich(X))))=>(?[X]:((tall(X)&~funny(X)))))&
(![X]:(~old(X)=>(~happy(X)<~>generous(X))))&
((?[X]:(~creative(X)))=>((funny(mary)|tall(mary))))&
((?[X]:((~patient(X)&strong(X))))=>((kind(susan)|~rich(susan))))&
(?[X]:((~wise(X)|~old(X))))&
(?[X]:((~humble(X)<~>quiet(X))))&
(wise(fred))&
(?[X]:((~calm(X)<~>~tall(X))))&
(?[X]:((patient(X)<~>kind(X))))&
(?[X]:((happy(X)|~wise(X))))&
(?[X]:((~strong(X)|humble(X))))&
((creative(john)&humble(john))) | ~patient(alice) | [
"p1",
"p4",
"p5",
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 3511454056530067030484890
% SZS output start Proof for 3511454056530067030484890
2. ? [X0] : (wise(X0) <~> brave(X0)) => (~creative(lucy) & ~generous(lucy)) [input p1]
5. ! [X0] : ((patient(X0) & quiet(X0)) => ~generous(X0)) [input p4]
6. ! [X0] : ((~strong(X0) <~> strong(X0)) => (creative(X0) & generous(X0))) [input p5]
10. ! [X0] : ((strong(X0) | generous(X0)) <=> brave(X0)) [input p9]
12. ! [X0] : ((quiet(X0) <~> wise(X0)) <=> (~wise(X0) & rich(X0))) [input p11]
25. patient(alice) [input hypothesis]
29. (~creative(lucy) & ~generous(lucy)) | ! [X0] : (wise(X0) <=> brave(X0)) [ennf transformation 2]
32. ! [X0] : (~generous(X0) | (~patient(X0) | ~quiet(X0))) [ennf transformation 5]
33. ! [X0] : (~generous(X0) | ~patient(X0) | ~quiet(X0)) [flattening 32]
34. ! [X0] : ((creative(X0) & generous(X0)) | (~strong(X0) <=> strong(X0))) [ennf transformation 6]
47. (~creative(lucy) & ~generous(lucy)) | ! [X0] : ((wise(X0) | ~brave(X0)) & (brave(X0) | ~wise(X0))) [nnf transformation 29]
54. ! [X0] : ((creative(X0) & generous(X0)) | ((~strong(X0) | ~strong(X0)) & (strong(X0) | strong(X0)))) [nnf transformation 34]
59. ! [X0] : (((strong(X0) | generous(X0)) | ~brave(X0)) & (brave(X0) | (~strong(X0) & ~generous(X0)))) [nnf transformation 10]
60. ! [X0] : ((strong(X0) | generous(X0) | ~brave(X0)) & (brave(X0) | (~strong(X0) & ~generous(X0)))) [flattening 59]
61. ! [X0] : ((((~wise(X0) | ~quiet(X0)) & (wise(X0) | quiet(X0))) | (wise(X0) | ~rich(X0))) & ((~wise(X0) & rich(X0)) | ((quiet(X0) | ~wise(X0)) & (wise(X0) | ~quiet(X0))))) [nnf transformation 12]
62. ! [X0] : ((((~wise(X0) | ~quiet(X0)) & (wise(X0) | quiet(X0))) | wise(X0) | ~rich(X0)) & ((~wise(X0) & rich(X0)) | ((quiet(X0) | ~wise(X0)) & (wise(X0) | ~quiet(X0))))) [flattening 61]
89. ~generous(lucy) | wise(X0) | ~brave(X0) [cnf transformation 47]
95. ~patient(X0) | ~generous(X0) | ~quiet(X0) [cnf transformation 33]
96. generous(X0) | strong(X0) | strong(X0) [cnf transformation 54]
97. generous(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 54]
105. brave(X0) | ~generous(X0) [cnf transformation 60]
113. ~wise(X0) | quiet(X0) | ~wise(X0) [cnf transformation 62]
134. patient(alice) [cnf transformation 25]
135. ~wise(X0) | quiet(X0) [duplicate literal removal 113]
137. generous(X0) | strong(X0) [duplicate literal removal 96]
138. ~strong(X0) | generous(X0) [duplicate literal removal 97]
145. 1 <=> ! [X0] : (wise(X0) | ~brave(X0)) [avatar definition]
146. wise(X0) | ~brave(X0) <- (1) [avatar component clause 145]
157. 4 <=> generous(lucy) [avatar definition]
159. ~generous(lucy) <- (~4) [avatar component clause 157]
160. 1 | ~4 [avatar split clause 89,157,145]
189. generous(X0) [subsumption resolution 137,138]
221. brave(X0) [subsumption resolution 105,189]
303. $false <- (~4) [subsumption resolution 159,189]
304. 4 [avatar contradiction clause 303]
307. wise(X0) <- (1) [subsumption resolution 146,221]
315. quiet(X0) <- (1) [resolution 135,307]
328. ~generous(alice) | ~quiet(alice) [resolution 95,134]
330. ~quiet(alice) [subsumption resolution 328,189]
331. $false <- (1) [subsumption resolution 330,315]
332. ~1 [avatar contradiction clause 331]
336. $false [avatar sat refutation 160,304,332]
% SZS output end Proof for 3511454056530067030484890
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old or old is both brave and kind and vice versa. Everyone who is happy or not patient is not patient. Everyone who is both not quiet and not brave is not patient or funny. Everyone who is both not calm and creative is not humble or not creative and vice versa. Everyone who is either wise or not quiet is not patient. Everyone who is either not creative or not kind is rich or not patient and vice versa. If someone is not funny then someone is both wise and not humble. If someone is strong then alice is not rich. If someone is tall or not patient then someone is both not patient and creative and vice versa. Everyone who is not creative is both not funny and not quiet. If someone is not creative then someone is not tall or old. If alice is both strong and not old then someone is either not tall or tall and vice versa. Everyone who is quiet or not tall is calm. Everyone who is both wise and happy is both not happy and not old. Someone is either not rich or not strong. Paul is wise or strong. Mary is either old or creative. Someone is either old or not kind. | Alice is funny. | entailment | (![X]:((~old(X)<~>old(X))<=>(brave(X)&kind(X))))&
(![X]:((happy(X)|~patient(X))=>~patient(X)))&
(![X]:((~quiet(X)&~brave(X))=>(~patient(X)|funny(X))))&
(![X]:((~calm(X)&creative(X))<=>(~humble(X)|~creative(X))))&
(![X]:((wise(X)<~>~quiet(X))=>~patient(X)))&
(![X]:((~creative(X)<~>~kind(X))<=>(rich(X)|~patient(X))))&
((?[X]:(~funny(X)))=>(?[X]:((wise(X)&~humble(X)))))&
((?[X]:(strong(X)))=>(~rich(alice)))&
((?[X]:((tall(X)|~patient(X))))<=>(?[X]:((~patient(X)&creative(X)))))&
(![X]:(~creative(X)=>(~funny(X)&~quiet(X))))&
((?[X]:(~creative(X)))=>(?[X]:((~tall(X)|old(X)))))&
(((strong(alice)&~old(alice)))<=>(?[X]:((~tall(X)<~>tall(X)))))&
(![X]:((quiet(X)|~tall(X))=>calm(X)))&
(![X]:((wise(X)&happy(X))=>(~happy(X)&~old(X))))&
(?[X]:((~rich(X)<~>~strong(X))))&
((wise(paul)|strong(paul)))&
((old(mary)<~>creative(mary)))&
(?[X]:((old(X)<~>~kind(X)))) | funny(alice) | [
"p0",
"p3",
"p5",
"p6",
"p8",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 8552590718890994033560832
% SZS output start Proof for 8552590718890994033560832
1. ! [X0] : ((~old(X0) <~> old(X0)) <=> (kind(X0) & brave(X0))) [input p0]
4. ! [X0] : ((creative(X0) & ~calm(X0)) <=> (~creative(X0) | ~humble(X0))) [input p3]
6. ! [X0] : ((~creative(X0) <~> ~kind(X0)) <=> (~patient(X0) | rich(X0))) [input p5]
7. ? [X0] : ~funny(X0) => ? [X0] : (~humble(X0) & wise(X0)) [input p6]
9. ? [X0] : (~patient(X0) | tall(X0)) <=> ? [X0] : (creative(X0) & ~patient(X0)) [input p8]
13. ! [X0] : ((~tall(X0) | quiet(X0)) => calm(X0)) [input p12]
19. ~funny(alice) [input hypothesis]
20. ? [X0] : ~funny(X0) => ? [X1] : (~humble(X1) & wise(X1)) [rectify 7]
21. ? [X0] : (~patient(X0) | tall(X0)) <=> ? [X1] : (creative(X1) & ~patient(X1)) [rectify 9]
29. ? [X1] : (~humble(X1) & wise(X1)) | ! [X0] : funny(X0) [ennf transformation 20]
33. ! [X0] : (calm(X0) | (tall(X0) & ~quiet(X0))) [ennf transformation 13]
34. ! [X0] : ((((~old(X0) | old(X0)) & (old(X0) | ~old(X0))) | (~kind(X0) | ~brave(X0))) & ((kind(X0) & brave(X0)) | ((~old(X0) | ~old(X0)) & (old(X0) | old(X0))))) [nnf transformation 1]
35. ! [X0] : ((((~old(X0) | old(X0)) & (old(X0) | ~old(X0))) | ~kind(X0) | ~brave(X0)) & ((kind(X0) & brave(X0)) | ((~old(X0) | ~old(X0)) & (old(X0) | old(X0))))) [flattening 34]
36. ! [X0] : (((creative(X0) & ~calm(X0)) | (creative(X0) & humble(X0))) & ((~creative(X0) | ~humble(X0)) | (~creative(X0) | calm(X0)))) [nnf transformation 4]
37. ! [X0] : (((creative(X0) & ~calm(X0)) | (creative(X0) & humble(X0))) & (~creative(X0) | ~humble(X0) | ~creative(X0) | calm(X0))) [flattening 36]
39. ! [X0] : ((((kind(X0) | creative(X0)) & (~kind(X0) | ~creative(X0))) | (patient(X0) & ~rich(X0))) & ((~patient(X0) | rich(X0)) | ((~creative(X0) | kind(X0)) & (~kind(X0) | creative(X0))))) [nnf transformation 6]
40. ! [X0] : ((((kind(X0) | creative(X0)) & (~kind(X0) | ~creative(X0))) | (patient(X0) & ~rich(X0))) & (~patient(X0) | rich(X0) | ((~creative(X0) | kind(X0)) & (~kind(X0) | creative(X0))))) [flattening 39]
41. ? [X0] : (~humble(X0) & wise(X0)) | ! [X1] : funny(X1) [rectify 29]
42. ? [X0] : (~humble(X0) & wise(X0)) => (~humble(sK0) & wise(sK0)) [choice axiom]
43. (~humble(sK0) & wise(sK0)) | ! [X1] : funny(X1) [skolemisation 41,42]
44. (? [X0] : (~patient(X0) | tall(X0)) | ! [X1] : (~creative(X1) | patient(X1))) & (? [X1] : (creative(X1) & ~patient(X1)) | ! [X0] : (patient(X0) & ~tall(X0))) [nnf transformation 21]
45. (? [X0] : (~patient(X0) | tall(X0)) | ! [X1] : (~creative(X1) | patient(X1))) & (? [X2] : (creative(X2) & ~patient(X2)) | ! [X3] : (patient(X3) & ~tall(X3))) [rectify 44]
46. ? [X0] : (~patient(X0) | tall(X0)) => (~patient(sK1) | tall(sK1)) [choice axiom]
47. ? [X2] : (creative(X2) & ~patient(X2)) => (creative(sK2) & ~patient(sK2)) [choice axiom]
48. ((~patient(sK1) | tall(sK1)) | ! [X1] : (~creative(X1) | patient(X1))) & ((creative(sK2) & ~patient(sK2)) | ! [X3] : (patient(X3) & ~tall(X3))) [skolemisation 45,47,46]
66. kind(X0) | old(X0) | old(X0) [cnf transformation 35]
67. kind(X0) | ~old(X0) | ~old(X0) [cnf transformation 35]
73. ~calm(X0) | humble(X0) [cnf transformation 37]
76. creative(X0) | creative(X0) [cnf transformation 37]
82. ~kind(X0) | ~creative(X0) | patient(X0) [cnf transformation 40]
86. ~humble(sK0) | funny(X1) [cnf transformation 43]
88. ~patient(sK2) | ~tall(X3) [cnf transformation 48]
103. calm(X0) | tall(X0) [cnf transformation 33]
111. ~funny(alice) [cnf transformation 19]
117. creative(X0) [duplicate literal removal 76]
120. kind(X0) | old(X0) [duplicate literal removal 66]
121. kind(X0) | ~old(X0) [duplicate literal removal 67]
122. kind(X0) [subsumption resolution 120,121]
125. ~creative(X0) | patient(X0) [subsumption resolution 82,122]
126. patient(X0) [subsumption resolution 125,117]
130. 1 <=> ! [X1] : funny(X1) [avatar definition]
131. funny(X1) <- (1) [avatar component clause 130]
133. 2 <=> humble(sK0) [avatar definition]
135. ~humble(sK0) <- (~2) [avatar component clause 133]
136. 1 | ~2 [avatar split clause 86,133,130]
142. ~tall(X3) [subsumption resolution 88,126]
145. calm(X0) [subsumption resolution 103,142]
158. humble(X0) [resolution 73,145]
160. $false <- (~2) [resolution 158,135]
161. 2 [avatar contradiction clause 160]
162. $false <- (1) [resolution 131,111]
163. ~1 [avatar contradiction clause 162]
164. $false [avatar sat refutation 136,161,163]
% SZS output end Proof for 8552590718890994033560832
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is not brave then someone is humble and vice versa.
If someone is either wise or not strong then someone is calm or rich.
Everyone who is not rich is not rich or happy and vice versa.
Everyone who is not generous is either curious or not curious and vice versa.
Everyone who is either rich or not calm is not old or happy and vice versa.
Everyone who is humble or not happy is not humble.
If alice is not curious then someone is both creative and not old.
Everyone who is not happy or not tall is not wise or wise and vice versa.
Everyone who is either not funny or patient is either not calm or not rich.
If susan is either not happy or not brave then fred is either humble or not tall and vice versa.
Everyone who is either not rich or tall is both not brave and generous.
Everyone who is either humble or rich is humble and vice versa.
If someone is both not creative and rich then someone is both happy and rich.
Everyone who is strong or kind is not curious.
If someone is either patient or not wise then someone is not quiet and vice versa.
Everyone who is quiet is not calm or not humble.
Someone is both not generous and tall.
Someone is either generous or not humble.
Someone is both not brave and not strong.
Fred is tall or brave.
Someone is not patient.
Someone is tall or strong. | Lucy is not happy. | entailment | ((~brave(lucy))<=>(?[X]:(humble(X))))&
((?[X]:((wise(X)<~>~strong(X))))=>(?[X]:((calm(X)|rich(X)))))&
(![X]:(~rich(X)<=>(~rich(X)|happy(X))))&
(![X]:(~generous(X)<=>(curious(X)<~>~curious(X))))&
(![X]:((rich(X)<~>~calm(X))<=>(~old(X)|happy(X))))&
(![X]:((humble(X)|~happy(X))=>~humble(X)))&
((~curious(alice))=>(?[X]:((creative(X)&~old(X)))))&
(![X]:((~happy(X)|~tall(X))<=>(~wise(X)|wise(X))))&
(![X]:((~funny(X)<~>patient(X))=>(~calm(X)<~>~rich(X))))&
(((~happy(susan)<~>~brave(susan)))<=>((humble(fred)<~>~tall(fred))))&
(![X]:((~rich(X)<~>tall(X))=>(~brave(X)&generous(X))))&
(![X]:((humble(X)<~>rich(X))<=>humble(X)))&
((?[X]:((~creative(X)&rich(X))))=>(?[X]:((happy(X)&rich(X)))))&
(![X]:((strong(X)|kind(X))=>~curious(X)))&
((?[X]:((patient(X)<~>~wise(X))))<=>(?[X]:(~quiet(X))))&
(![X]:(quiet(X)=>(~calm(X)|~humble(X))))&
(?[X]:((~generous(X)&tall(X))))&
(?[X]:((generous(X)<~>~humble(X))))&
(?[X]:((~brave(X)&~strong(X))))&
((tall(fred)|brave(fred)))&
(?[X]:(~patient(X)))&
(?[X]:((tall(X)|strong(X)))) | ~happy(lucy) | [
"p3",
"p7",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 7281459696208024629835727
% SZS output start Proof for 7281459696208024629835727
4. ! [X0] : (~generous(X0) <=> (curious(X0) <~> ~curious(X0))) [input p3]
8. ! [X0] : ((~tall(X0) | ~happy(X0)) <=> (wise(X0) | ~wise(X0))) [input p7]
11. ! [X0] : ((~rich(X0) <~> tall(X0)) => (generous(X0) & ~brave(X0))) [input p10]
12. ! [X0] : ((humble(X0) <~> rich(X0)) <=> humble(X0)) [input p11]
23. happy(lucy) [input hypothesis]
34. ! [X0] : ((generous(X0) & ~brave(X0)) | (~rich(X0) <=> tall(X0))) [ennf transformation 11]
48. ! [X0] : ((~generous(X0) | ((curious(X0) | curious(X0)) & (~curious(X0) | ~curious(X0)))) & (((curious(X0) | ~curious(X0)) & (~curious(X0) | curious(X0))) | generous(X0))) [nnf transformation 4]
53. ! [X0] : (((~tall(X0) | ~happy(X0)) | (~wise(X0) & wise(X0))) & ((wise(X0) | ~wise(X0)) | (tall(X0) & happy(X0)))) [nnf transformation 8]
54. ! [X0] : ((~tall(X0) | ~happy(X0) | (~wise(X0) & wise(X0))) & (wise(X0) | ~wise(X0) | (tall(X0) & happy(X0)))) [flattening 53]
57. ! [X0] : ((generous(X0) & ~brave(X0)) | ((~rich(X0) | ~tall(X0)) & (tall(X0) | rich(X0)))) [nnf transformation 34]
58. ! [X0] : ((((~rich(X0) | ~humble(X0)) & (rich(X0) | humble(X0))) | ~humble(X0)) & (humble(X0) | ((humble(X0) | ~rich(X0)) & (rich(X0) | ~humble(X0))))) [nnf transformation 12]
84. ~generous(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 48]
85. ~generous(X0) | curious(X0) | curious(X0) [cnf transformation 48]
97. ~tall(X0) | ~happy(X0) | wise(X0) [cnf transformation 54]
98. ~tall(X0) | ~happy(X0) | ~wise(X0) [cnf transformation 54]
113. generous(X0) | tall(X0) | rich(X0) [cnf transformation 57]
116. humble(X0) | humble(X0) | ~rich(X0) [cnf transformation 58]
118. ~rich(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 58]
134. happy(lucy) [cnf transformation 23]
135. humble(X0) | ~rich(X0) [duplicate literal removal 116]
136. ~rich(X0) | ~humble(X0) [duplicate literal removal 118]
138. ~generous(X0) | ~curious(X0) [duplicate literal removal 84]
139. ~generous(X0) | curious(X0) [duplicate literal removal 85]
169. ~generous(X0) [subsumption resolution 138,139]
182. ~tall(X0) | ~happy(X0) [subsumption resolution 97,98]
208. tall(X0) | rich(X0) [subsumption resolution 113,169]
209. ~rich(X0) [subsumption resolution 135,136]
261. rich(X1) | ~happy(X1) [resolution 208,182]
262. ~happy(X1) [subsumption resolution 261,209]
265. $false [resolution 262,134]
% SZS output end Proof for 7281459696208024629835727
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy or not funny then someone is both not calm and wise.
Everyone who is not strong or not tall is brave and vice versa.
If susan is funny then lucy is both not strong and not calm and vice versa.
If john is either not calm or creative then someone is not creative or not happy and vice versa.
If paul is both patient and not tall then someone is either calm or funny.
If mary is either not tall or curious then someone is both wise and not kind.
Everyone who is either not curious or not calm is curious and vice versa.
If someone is happy or quiet then paul is quiet and vice versa.
If mary is not creative or not patient then mary is both calm and creative.
If someone is either not rich or calm then mary is not calm or wise and vice versa.
If someone is patient or not strong then lucy is either funny or old.
Everyone who is not brave is both not patient and not generous and vice versa.
Everyone who is rich is both kind and not calm.
Everyone who is either not funny or not creative is kind or not generous.
Everyone who is not generous or strong is not patient.
If someone is happy then someone is both quiet and kind.
Paul is both not patient and funny.
Mary is not strong.
Someone is not happy.
Someone is not old.
Someone is both happy and quiet.
Someone is either not calm or quiet.
Someone is not patient or wise. | Paul is not calm. | entailment | ((?[X]:((happy(X)<~>~funny(X))))=>(?[X]:((~calm(X)&wise(X)))))&
(![X]:((~strong(X)|~tall(X))<=>brave(X)))&
((funny(susan))<=>((~strong(lucy)&~calm(lucy))))&
(((~calm(john)<~>creative(john)))<=>(?[X]:((~creative(X)|~happy(X)))))&
(((patient(paul)&~tall(paul)))=>(?[X]:((calm(X)<~>funny(X)))))&
(((~tall(mary)<~>curious(mary)))=>(?[X]:((wise(X)&~kind(X)))))&
(![X]:((~curious(X)<~>~calm(X))<=>curious(X)))&
((?[X]:((happy(X)|quiet(X))))<=>(quiet(paul)))&
(((~creative(mary)|~patient(mary)))=>((calm(mary)&creative(mary))))&
((?[X]:((~rich(X)<~>calm(X))))<=>((~calm(mary)|wise(mary))))&
((?[X]:((patient(X)|~strong(X))))=>((funny(lucy)<~>old(lucy))))&
(![X]:(~brave(X)<=>(~patient(X)&~generous(X))))&
(![X]:(rich(X)=>(kind(X)&~calm(X))))&
(![X]:((~funny(X)<~>~creative(X))=>(kind(X)|~generous(X))))&
(![X]:((~generous(X)|strong(X))=>~patient(X)))&
((?[X]:(happy(X)))=>(?[X]:((quiet(X)&kind(X)))))&
((~patient(paul)&funny(paul)))&
(~strong(mary))&
(?[X]:(~happy(X)))&
(?[X]:(~old(X)))&
(?[X]:((happy(X)&quiet(X))))&
(?[X]:((~calm(X)<~>quiet(X))))&
(?[X]:((~patient(X)|wise(X)))) | ~calm(paul) | [
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 244494059056396436327732
% SZS output start Proof for 244494059056396436327732
7. ! [X0] : ((~curious(X0) <~> ~calm(X0)) <=> curious(X0)) [input p6]
24. calm(paul) [input hypothesis]
56. ! [X0] : ((((calm(X0) | curious(X0)) & (~calm(X0) | ~curious(X0))) | ~curious(X0)) & (curious(X0) | ((~curious(X0) | calm(X0)) & (~calm(X0) | curious(X0))))) [nnf transformation 7]
106. curious(X0) | ~calm(X0) | curious(X0) [cnf transformation 56]
108. ~calm(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 56]
148. calm(paul) [cnf transformation 24]
150. curious(X0) | ~calm(X0) [duplicate literal removal 106]
151. ~calm(X0) | ~curious(X0) [duplicate literal removal 108]
251. ~calm(X0) [subsumption resolution 150,151]
339. $false [subsumption resolution 148,251]
% SZS output end Proof for 244494059056396436327732
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is humble then paul is not calm or not wise.
Everyone who is not rich is both not happy and creative.
If someone is not kind then alice is both not creative and happy and vice versa.
Everyone who is generous is not rich or not old and vice versa.
Everyone who is happy or curious is generous or calm and vice versa.
If someone is not strong or rich then paul is not tall and vice versa.
Everyone who is happy is funny or rich.
If paul is both strong and not generous then susan is either happy or not wise.
Everyone who is not old or happy is wise or kind and vice versa.
If lucy is not creative or not rich then someone is generous and vice versa.
Everyone who is either calm or not rich is either generous or patient.
Everyone who is either not creative or strong is not creative and vice versa.
Everyone who is not patient is not funny or not quiet.
Everyone who is either not funny or not curious is either wise or funny.
If someone is wise or not happy then john is both happy and curious and vice versa.
Susan is not patient.
Fred is kind.
Someone is either not brave or rich.
John is quiet.
Alice is not strong. | John is not humble. | neutral | ((?[X]:(humble(X)))=>((~calm(paul)|~wise(paul))))&
(![X]:(~rich(X)=>(~happy(X)&creative(X))))&
((?[X]:(~kind(X)))<=>((~creative(alice)&happy(alice))))&
(![X]:(generous(X)<=>(~rich(X)|~old(X))))&
(![X]:((happy(X)|curious(X))<=>(generous(X)|calm(X))))&
((?[X]:((~strong(X)|rich(X))))<=>(~tall(paul)))&
(![X]:(happy(X)=>(funny(X)|rich(X))))&
(((strong(paul)&~generous(paul)))=>((happy(susan)<~>~wise(susan))))&
(![X]:((~old(X)|happy(X))<=>(wise(X)|kind(X))))&
(((~creative(lucy)|~rich(lucy)))<=>(?[X]:(generous(X))))&
(![X]:((calm(X)<~>~rich(X))=>(generous(X)<~>patient(X))))&
(![X]:((~creative(X)<~>strong(X))<=>~creative(X)))&
(![X]:(~patient(X)=>(~funny(X)|~quiet(X))))&
(![X]:((~funny(X)<~>~curious(X))=>(wise(X)<~>funny(X))))&
((?[X]:((wise(X)|~happy(X))))<=>((happy(john)&curious(john))))&
(~patient(susan))&
(kind(fred))&
(?[X]:((~brave(X)<~>rich(X))))&
(quiet(john))&
(~strong(alice)) | ~humble(john) | [] | null | 0 |
If paul is not quiet then someone is brave and vice versa.
Everyone who is wise is not curious and vice versa.
Everyone who is not happy or patient is not strong.
If john is either old or happy then john is either curious or happy and vice versa.
Everyone who is both not rich and old is curious or generous.
Everyone who is both not creative and creative is happy and vice versa.
If alice is humble then someone is both not wise and strong and vice versa.
Everyone who is not quiet is not calm.
Everyone who is both brave and curious is not tall or not rich and vice versa.
If paul is either not funny or not calm then someone is not quiet or not creative and vice versa.
Everyone who is either not strong or tall is both not kind and generous.
If someone is patient then mary is either humble or calm.
Everyone who is both not tall and patient is either not old or not brave and vice versa.
Everyone who is both not humble and brave is both not brave and not rich.
Everyone who is not generous is curious or not happy.
Paul is not old or not funny.
Paul is not funny or funny.
Susan is not wise.
Someone is humble or not brave.
Fred is not happy or not generous.
John is either rich or not generous.
Someone is both curious and not creative. | Fred is not calm. | neutral | ((~quiet(paul))<=>(?[X]:(brave(X))))&
(![X]:(wise(X)<=>~curious(X)))&
(![X]:((~happy(X)|patient(X))=>~strong(X)))&
(((old(john)<~>happy(john)))<=>((curious(john)<~>happy(john))))&
(![X]:((~rich(X)&old(X))=>(curious(X)|generous(X))))&
(![X]:((~creative(X)&creative(X))<=>happy(X)))&
((humble(alice))<=>(?[X]:((~wise(X)&strong(X)))))&
(![X]:(~quiet(X)=>~calm(X)))&
(![X]:((brave(X)&curious(X))<=>(~tall(X)|~rich(X))))&
(((~funny(paul)<~>~calm(paul)))<=>(?[X]:((~quiet(X)|~creative(X)))))&
(![X]:((~strong(X)<~>tall(X))=>(~kind(X)&generous(X))))&
((?[X]:(patient(X)))=>((humble(mary)<~>calm(mary))))&
(![X]:((~tall(X)&patient(X))<=>(~old(X)<~>~brave(X))))&
(![X]:((~humble(X)&brave(X))=>(~brave(X)&~rich(X))))&
(![X]:(~generous(X)=>(curious(X)|~happy(X))))&
((~old(paul)|~funny(paul)))&
((~funny(paul)|funny(paul)))&
(~wise(susan))&
(?[X]:((humble(X)|~brave(X))))&
((~happy(fred)|~generous(fred)))&
((rich(john)<~>~generous(john)))&
(?[X]:((curious(X)&~creative(X)))) | ~calm(fred) | [] | null | 0 |
If lucy is rich or not happy then john is either rich or not wise.
Everyone who is either not creative or not humble is old or not creative and vice versa.
If john is either not funny or not brave then someone is not brave or not humble.
If someone is not strong or not tall then someone is strong.
Everyone who is not old or not wise is not humble or strong and vice versa.
If paul is either not quiet or not tall then fred is wise and vice versa.
Everyone who is quiet is either not tall or curious and vice versa.
If alice is either curious or kind then someone is both not funny and not quiet.
If mary is both wise and patient then someone is not brave or not calm and vice versa.
Everyone who is not wise or creative is both tall and happy.
If someone is either not kind or not funny then someone is both brave and not old and vice versa.
Everyone who is both patient and tall is quiet or not patient and vice versa.
Everyone who is either funny or rich is not calm and vice versa.
If fred is either not wise or not happy then mary is happy or not funny.
Everyone who is not patient or not funny is not creative or old and vice versa.
If someone is not old then someone is not old or not rich.
Someone is not wise.
Mary is creative.
Paul is creative.
Someone is either not humble or wise.
Someone is patient.
Someone is patient or strong.
Mary is either not wise or calm. | Mary is not strong. | contradiction | (((rich(lucy)|~happy(lucy)))=>((rich(john)<~>~wise(john))))&
(![X]:((~creative(X)<~>~humble(X))<=>(old(X)|~creative(X))))&
(((~funny(john)<~>~brave(john)))=>(?[X]:((~brave(X)|~humble(X)))))&
((?[X]:((~strong(X)|~tall(X))))=>(?[X]:(strong(X))))&
(![X]:((~old(X)|~wise(X))<=>(~humble(X)|strong(X))))&
(((~quiet(paul)<~>~tall(paul)))<=>(wise(fred)))&
(![X]:(quiet(X)<=>(~tall(X)<~>curious(X))))&
(((curious(alice)<~>kind(alice)))=>(?[X]:((~funny(X)&~quiet(X)))))&
(((wise(mary)&patient(mary)))<=>(?[X]:((~brave(X)|~calm(X)))))&
(![X]:((~wise(X)|creative(X))=>(tall(X)&happy(X))))&
((?[X]:((~kind(X)<~>~funny(X))))<=>(?[X]:((brave(X)&~old(X)))))&
(![X]:((patient(X)&tall(X))<=>(quiet(X)|~patient(X))))&
(![X]:((funny(X)<~>rich(X))<=>~calm(X)))&
(((~wise(fred)<~>~happy(fred)))=>((happy(mary)|~funny(mary))))&
(![X]:((~patient(X)|~funny(X))<=>(~creative(X)|old(X))))&
((?[X]:(~old(X)))=>(?[X]:((~old(X)|~rich(X)))))&
(?[X]:(~wise(X)))&
(creative(mary))&
(creative(paul))&
(?[X]:((~humble(X)<~>wise(X))))&
(?[X]:(patient(X)))&
(?[X]:((patient(X)|strong(X))))&
((~wise(mary)<~>calm(mary))) | ~strong(mary) | [
"p1",
"p4",
"p8",
"p17",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 8528128806253639363297046
% SZS output start Proof for 8528128806253639363297046
2. ! [X0] : ((~creative(X0) <~> ~humble(X0)) <=> (~creative(X0) | old(X0))) [input p1]
5. ! [X0] : ((~wise(X0) | ~old(X0)) <=> (strong(X0) | ~humble(X0))) [input p4]
9. (patient(mary) & wise(mary)) <=> ? [X0] : (~calm(X0) | ~brave(X0)) [input p8]
18. creative(mary) [input p17]
23. ~wise(mary) <~> calm(mary) [input p22]
24. ~strong(mary) [input hypothesis]
37. ! [X0] : ((((humble(X0) | creative(X0)) & (~humble(X0) | ~creative(X0))) | (creative(X0) & ~old(X0))) & ((~creative(X0) | old(X0)) | ((~creative(X0) | humble(X0)) & (~humble(X0) | creative(X0))))) [nnf transformation 2]
38. ! [X0] : ((((humble(X0) | creative(X0)) & (~humble(X0) | ~creative(X0))) | (creative(X0) & ~old(X0))) & (~creative(X0) | old(X0) | ((~creative(X0) | humble(X0)) & (~humble(X0) | creative(X0))))) [flattening 37]
45. ! [X0] : (((~wise(X0) | ~old(X0)) | (~strong(X0) & humble(X0))) & ((strong(X0) | ~humble(X0)) | (wise(X0) & old(X0)))) [nnf transformation 5]
46. ! [X0] : ((~wise(X0) | ~old(X0) | (~strong(X0) & humble(X0))) & (strong(X0) | ~humble(X0) | (wise(X0) & old(X0)))) [flattening 45]
52. ((patient(mary) & wise(mary)) | ! [X0] : (calm(X0) & brave(X0))) & (? [X0] : (~calm(X0) | ~brave(X0)) | (~patient(mary) | ~wise(mary))) [nnf transformation 9]
53. ((patient(mary) & wise(mary)) | ! [X0] : (calm(X0) & brave(X0))) & (? [X0] : (~calm(X0) | ~brave(X0)) | ~patient(mary) | ~wise(mary)) [flattening 52]
54. ((patient(mary) & wise(mary)) | ! [X0] : (calm(X0) & brave(X0))) & (? [X1] : (~calm(X1) | ~brave(X1)) | ~patient(mary) | ~wise(mary)) [rectify 53]
55. ? [X1] : (~calm(X1) | ~brave(X1)) => (~calm(sK3) | ~brave(sK3)) [choice axiom]
56. ((patient(mary) & wise(mary)) | ! [X0] : (calm(X0) & brave(X0))) & ((~calm(sK3) | ~brave(sK3)) | ~patient(mary) | ~wise(mary)) [skolemisation 54,55]
80. (~calm(mary) | wise(mary)) & (calm(mary) | ~wise(mary)) [nnf transformation 23]
86. ~creative(X0) | old(X0) | ~creative(X0) | humble(X0) [cnf transformation 38]
87. ~old(X0) | ~creative(X0) | ~humble(X0) [cnf transformation 38]
90. humble(X0) | creative(X0) | creative(X0) [cnf transformation 38]
95. strong(X0) | ~humble(X0) | old(X0) [cnf transformation 46]
97. ~wise(X0) | ~old(X0) | humble(X0) [cnf transformation 46]
113. wise(mary) | calm(X0) [cnf transformation 56]
143. creative(mary) [cnf transformation 18]
150. ~calm(mary) | wise(mary) [cnf transformation 80]
151. ~strong(mary) [cnf transformation 24]
154. ~creative(X0) | old(X0) | humble(X0) [duplicate literal removal 86]
155. humble(X0) | creative(X0) [duplicate literal removal 90]
176. old(X0) | humble(X0) [subsumption resolution 154,155]
207. ~wise(X0) | humble(X0) [subsumption resolution 97,176]
208. strong(X0) | old(X0) [subsumption resolution 95,176]
246. 19 <=> ! [X0] : calm(X0) [avatar definition]
247. calm(X0) <- (19) [avatar component clause 246]
258. 22 <=> wise(mary) [avatar definition]
260. wise(mary) <- (22) [avatar component clause 258]
261. 19 | 22 [avatar split clause 113,258,246]
344. 40 <=> calm(mary) [avatar definition]
346. ~calm(mary) <- (~40) [avatar component clause 344]
347. 22 | ~40 [avatar split clause 150,344,258]
351. $false <- (19, ~40) [resolution 346,247]
352. ~19 | 40 [avatar contradiction clause 351]
370. humble(mary) <- (22) [resolution 207,260]
373. old(mary) [resolution 208,151]
388. ~creative(mary) | ~humble(mary) [resolution 87,373]
390. ~humble(mary) [subsumption resolution 388,143]
391. $false <- (22) [subsumption resolution 390,370]
392. ~22 [avatar contradiction clause 391]
393. $false [avatar sat refutation 261,347,352,392]
% SZS output end Proof for 8528128806253639363297046
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not curious or rich is calm and vice versa.
If someone is not creative then someone is either patient or not humble.
Everyone who is rich is both not rich and not creative.
If someone is both not rich and wise then someone is brave or happy.
If someone is generous or rich then someone is both not old and tall.
If someone is generous then lucy is both not generous and not funny.
Everyone who is either kind or curious is generous or strong and vice versa.
If someone is calm then someone is not calm or not humble and vice versa.
Everyone who is not patient is both curious and not quiet.
Everyone who is both not curious and not quiet is not tall.
Everyone who is both not quiet and kind is both strong and tall.
Everyone who is not happy or not old is either old or not calm.
Everyone who is either funny or tall is either quiet or generous and vice versa.
Everyone who is both calm and not brave is patient or not tall and vice versa.
Everyone who is humble or wise is generous and vice versa.
If someone is not quiet or not kind then someone is not happy.
Someone is quiet or funny.
Someone is not tall or not kind.
Paul is curious.
Alice is wise or old.
Alice is not strong or curious.
John is creative.
Someone is either not patient or not funny. | Lucy is not quiet. | neutral | (![X]:((~curious(X)<~>rich(X))<=>calm(X)))&
((?[X]:(~creative(X)))=>(?[X]:((patient(X)<~>~humble(X)))))&
(![X]:(rich(X)=>(~rich(X)&~creative(X))))&
((?[X]:((~rich(X)&wise(X))))=>(?[X]:((brave(X)|happy(X)))))&
((?[X]:((generous(X)|rich(X))))=>(?[X]:((~old(X)&tall(X)))))&
((?[X]:(generous(X)))=>((~generous(lucy)&~funny(lucy))))&
(![X]:((kind(X)<~>curious(X))<=>(generous(X)|strong(X))))&
((?[X]:(calm(X)))<=>(?[X]:((~calm(X)|~humble(X)))))&
(![X]:(~patient(X)=>(curious(X)&~quiet(X))))&
(![X]:((~curious(X)&~quiet(X))=>~tall(X)))&
(![X]:((~quiet(X)&kind(X))=>(strong(X)&tall(X))))&
(![X]:((~happy(X)|~old(X))=>(old(X)<~>~calm(X))))&
(![X]:((funny(X)<~>tall(X))<=>(quiet(X)<~>generous(X))))&
(![X]:((calm(X)&~brave(X))<=>(patient(X)|~tall(X))))&
(![X]:((humble(X)|wise(X))<=>generous(X)))&
((?[X]:((~quiet(X)|~kind(X))))=>(?[X]:(~happy(X))))&
(?[X]:((quiet(X)|funny(X))))&
(?[X]:((~tall(X)|~kind(X))))&
(curious(paul))&
((wise(alice)|old(alice)))&
((~strong(alice)|curious(alice)))&
(creative(john))&
(?[X]:((~patient(X)<~>~funny(X)))) | ~quiet(lucy) | [] | null | 0 |
Everyone who is not curious is not strong. If someone is not creative then someone is both not old and happy and vice versa. If paul is quiet then someone is both curious and not happy and vice versa. Everyone who is rich or old is not calm. Everyone who is not humble or humble is either happy or not creative. Everyone who is both generous and patient is creative and vice versa. If someone is either kind or not generous then someone is both not brave and creative and vice versa. If susan is both strong and rich then someone is not tall. If someone is either not funny or brave then someone is either not quiet or not brave. If someone is either patient or not humble then someone is both not happy and tall. Everyone who is both brave and not quiet is both not generous and not happy and vice versa. If someone is not tall or quiet then paul is not funny or quiet. Everyone who is both not generous and humble is not old or brave and vice versa. Everyone who is not kind or not old is either calm or not tall and vice versa. If mary is either strong or kind then susan is not curious. Everyone who is either not rich or not humble is both kind and not brave. Someone is not brave or not humble. Someone is not rich or not humble. | Paul is old. | entailment | (![X]:(~curious(X)=>~strong(X)))&
((?[X]:(~creative(X)))<=>(?[X]:((~old(X)&happy(X)))))&
((quiet(paul))<=>(?[X]:((curious(X)&~happy(X)))))&
(![X]:((rich(X)|old(X))=>~calm(X)))&
(![X]:((~humble(X)|humble(X))=>(happy(X)<~>~creative(X))))&
(![X]:((generous(X)&patient(X))<=>creative(X)))&
((?[X]:((kind(X)<~>~generous(X))))<=>(?[X]:((~brave(X)&creative(X)))))&
(((strong(susan)&rich(susan)))=>(?[X]:(~tall(X))))&
((?[X]:((~funny(X)<~>brave(X))))=>(?[X]:((~quiet(X)<~>~brave(X)))))&
((?[X]:((patient(X)<~>~humble(X))))=>(?[X]:((~happy(X)&tall(X)))))&
(![X]:((brave(X)&~quiet(X))<=>(~generous(X)&~happy(X))))&
((?[X]:((~tall(X)|quiet(X))))=>((~funny(paul)|quiet(paul))))&
(![X]:((~generous(X)&humble(X))<=>(~old(X)|brave(X))))&
(![X]:((~kind(X)|~old(X))<=>(calm(X)<~>~tall(X))))&
(((strong(mary)<~>kind(mary)))=>(~curious(susan)))&
(![X]:((~rich(X)<~>~humble(X))=>(kind(X)&~brave(X))))&
(?[X]:((~brave(X)|~humble(X))))&
(?[X]:((~rich(X)|~humble(X)))) | old(paul) | [
"p1",
"p4",
"p5",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 1575400241510041572618843
% SZS output start Proof for 1575400241510041572618843
2. ? [X0] : ~creative(X0) <=> ? [X0] : (happy(X0) & ~old(X0)) [input p1]
5. ! [X0] : ((humble(X0) | ~humble(X0)) => (happy(X0) <~> ~creative(X0))) [input p4]
6. ! [X0] : ((patient(X0) & generous(X0)) <=> creative(X0)) [input p5]
13. ! [X0] : ((humble(X0) & ~generous(X0)) <=> (brave(X0) | ~old(X0))) [input p12]
19. ~old(paul) [input hypothesis]
20. ? [X0] : ~creative(X0) <=> ? [X1] : (happy(X1) & ~old(X1)) [rectify 2]
26. ! [X0] : ((happy(X0) <~> ~creative(X0)) | (~humble(X0) & humble(X0))) [ennf transformation 5]
35. (? [X0] : ~creative(X0) | ! [X1] : (~happy(X1) | old(X1))) & (? [X1] : (happy(X1) & ~old(X1)) | ! [X0] : creative(X0)) [nnf transformation 20]
36. (? [X0] : ~creative(X0) | ! [X1] : (~happy(X1) | old(X1))) & (? [X2] : (happy(X2) & ~old(X2)) | ! [X3] : creative(X3)) [rectify 35]
37. ? [X0] : ~creative(X0) => ~creative(sK0) [choice axiom]
38. ? [X2] : (happy(X2) & ~old(X2)) => (happy(sK1) & ~old(sK1)) [choice axiom]
39. (~creative(sK0) | ! [X1] : (~happy(X1) | old(X1))) & ((happy(sK1) & ~old(sK1)) | ! [X3] : creative(X3)) [skolemisation 36,38,37]
44. ! [X0] : (((creative(X0) | ~happy(X0)) & (~creative(X0) | happy(X0))) | (~humble(X0) & humble(X0))) [nnf transformation 26]
45. ! [X0] : (((patient(X0) & generous(X0)) | ~creative(X0)) & (creative(X0) | (~patient(X0) | ~generous(X0)))) [nnf transformation 6]
46. ! [X0] : (((patient(X0) & generous(X0)) | ~creative(X0)) & (creative(X0) | ~patient(X0) | ~generous(X0))) [flattening 45]
64. ! [X0] : (((humble(X0) & ~generous(X0)) | (~brave(X0) & old(X0))) & ((brave(X0) | ~old(X0)) | (~humble(X0) | generous(X0)))) [nnf transformation 13]
65. ! [X0] : (((humble(X0) & ~generous(X0)) | (~brave(X0) & old(X0))) & (brave(X0) | ~old(X0) | ~humble(X0) | generous(X0))) [flattening 64]
75. ~old(sK1) | creative(X3) [cnf transformation 39]
76. happy(sK1) | creative(X3) [cnf transformation 39]
85. creative(X0) | ~happy(X0) | humble(X0) [cnf transformation 44]
86. creative(X0) | ~happy(X0) | ~humble(X0) [cnf transformation 44]
88. ~creative(X0) | generous(X0) [cnf transformation 46]
112. ~generous(X0) | old(X0) [cnf transformation 65]
130. ~old(paul) [cnf transformation 19]
140. 3 <=> ! [X3] : creative(X3) [avatar definition]
141. creative(X3) <- (3) [avatar component clause 140]
143. 4 <=> happy(sK1) [avatar definition]
145. happy(sK1) <- (4) [avatar component clause 143]
146. 3 | 4 [avatar split clause 76,143,140]
148. 5 <=> old(sK1) [avatar definition]
150. ~old(sK1) <- (~5) [avatar component clause 148]
151. 3 | ~5 [avatar split clause 75,148,140]
170. ~happy(X0) | creative(X0) [subsumption resolution 85,86]
293. generous(X0) <- (3) [resolution 88,141]
306. old(X0) <- (3) [resolution 112,293]
307. $false <- (3) [resolution 306,130]
308. ~3 [avatar contradiction clause 307]
316. creative(sK1) <- (4) [resolution 170,145]
318. generous(sK1) <- (4) [resolution 316,88]
323. old(sK1) <- (4) [resolution 318,112]
324. $false <- (4, ~5) [subsumption resolution 323,150]
325. ~4 | 5 [avatar contradiction clause 324]
326. $false [avatar sat refutation 146,151,308,325]
% SZS output end Proof for 1575400241510041572618843
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave or not generous is tall or rich.
If mary is not tall or creative then someone is both brave and wise.
If susan is both not funny and creative then john is either humble or not curious and vice versa.
If someone is either calm or humble then someone is either not wise or rich and vice versa.
If paul is not kind or calm then mary is either not strong or not generous.
Everyone who is not generous or wise is either creative or not strong.
Everyone who is either rich or curious is not rich and vice versa.
If someone is brave or funny then fred is not rich or funny.
Everyone who is both generous and not tall is either not humble or generous and vice versa.
Everyone who is either old or not generous is patient or rich.
If paul is either rich or not patient then someone is either funny or not quiet and vice versa.
If alice is strong then lucy is not creative or calm and vice versa.
Everyone who is not strong is either not old or not kind.
If susan is not tall then susan is humble or not generous and vice versa.
Everyone who is both old and not tall is not strong or not curious.
If fred is not patient or not creative then someone is not happy or humble.
Alice is not brave or not kind.
Someone is either not happy or not generous.
Someone is not generous or not rich.
Lucy is not tall.
Someone is not humble or not patient.
Someone is either not patient or not calm.
Someone is both not brave and not creative. | Paul is not old. | neutral | (![X]:((brave(X)|~generous(X))=>(tall(X)|rich(X))))&
(((~tall(mary)|creative(mary)))=>(?[X]:((brave(X)&wise(X)))))&
(((~funny(susan)&creative(susan)))<=>((humble(john)<~>~curious(john))))&
((?[X]:((calm(X)<~>humble(X))))<=>(?[X]:((~wise(X)<~>rich(X)))))&
(((~kind(paul)|calm(paul)))=>((~strong(mary)<~>~generous(mary))))&
(![X]:((~generous(X)|wise(X))=>(creative(X)<~>~strong(X))))&
(![X]:((rich(X)<~>curious(X))<=>~rich(X)))&
((?[X]:((brave(X)|funny(X))))=>((~rich(fred)|funny(fred))))&
(![X]:((generous(X)&~tall(X))<=>(~humble(X)<~>generous(X))))&
(![X]:((old(X)<~>~generous(X))=>(patient(X)|rich(X))))&
(((rich(paul)<~>~patient(paul)))<=>(?[X]:((funny(X)<~>~quiet(X)))))&
((strong(alice))<=>((~creative(lucy)|calm(lucy))))&
(![X]:(~strong(X)=>(~old(X)<~>~kind(X))))&
((~tall(susan))<=>((humble(susan)|~generous(susan))))&
(![X]:((old(X)&~tall(X))=>(~strong(X)|~curious(X))))&
(((~patient(fred)|~creative(fred)))=>(?[X]:((~happy(X)|humble(X)))))&
((~brave(alice)|~kind(alice)))&
(?[X]:((~happy(X)<~>~generous(X))))&
(?[X]:((~generous(X)|~rich(X))))&
(~tall(lucy))&
(?[X]:((~humble(X)|~patient(X))))&
(?[X]:((~patient(X)<~>~calm(X))))&
(?[X]:((~brave(X)&~creative(X)))) | ~old(paul) | [] | null | 0 |
If lucy is either curious or kind then someone is curious and vice versa. If someone is not curious then mary is not patient. Everyone who is either not humble or not brave is both happy and not creative and vice versa. If someone is either not brave or wise then susan is both not wise and kind and vice versa. Everyone who is not creative is not quiet or humble and vice versa. Everyone who is both not old and not calm is old and vice versa. Everyone who is either not quiet or wise is calm. If alice is tall then someone is not old or calm and vice versa. Everyone who is not curious or not generous is not creative or not wise and vice versa. If someone is not humble then someone is both not old and strong. Everyone who is not patient is brave or not calm. If someone is tall then lucy is either not brave or not strong. Everyone who is not brave is old or quiet and vice versa. If someone is both not happy and not humble then someone is not old and vice versa. If someone is humble then someone is both humble and not humble and vice versa. If someone is both not rich and not patient then mary is not happy and vice versa. Fred is both not generous and not brave. Alice is not funny. Alice is kind. Someone is both curious and not kind. Alice is either calm or not brave. Someone is either not happy or not patient. | Fred is patient. | entailment | (((curious(lucy)<~>kind(lucy)))<=>(?[X]:(curious(X))))&
((?[X]:(~curious(X)))=>(~patient(mary)))&
(![X]:((~humble(X)<~>~brave(X))<=>(happy(X)&~creative(X))))&
((?[X]:((~brave(X)<~>wise(X))))<=>((~wise(susan)&kind(susan))))&
(![X]:(~creative(X)<=>(~quiet(X)|humble(X))))&
(![X]:((~old(X)&~calm(X))<=>old(X)))&
(![X]:((~quiet(X)<~>wise(X))=>calm(X)))&
((tall(alice))<=>(?[X]:((~old(X)|calm(X)))))&
(![X]:((~curious(X)|~generous(X))<=>(~creative(X)|~wise(X))))&
((?[X]:(~humble(X)))=>(?[X]:((~old(X)&strong(X)))))&
(![X]:(~patient(X)=>(brave(X)|~calm(X))))&
((?[X]:(tall(X)))=>((~brave(lucy)<~>~strong(lucy))))&
(![X]:(~brave(X)<=>(old(X)|quiet(X))))&
((?[X]:((~happy(X)&~humble(X))))<=>(?[X]:(~old(X))))&
((?[X]:(humble(X)))<=>(?[X]:((humble(X)&~humble(X)))))&
((?[X]:((~rich(X)&~patient(X))))<=>(~happy(mary)))&
((~generous(fred)&~brave(fred)))&
(~funny(alice))&
(kind(alice))&
(?[X]:((curious(X)&~kind(X))))&
((calm(alice)<~>~brave(alice)))&
(?[X]:((~happy(X)<~>~patient(X)))) | patient(fred) | [
"p5",
"p10",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 8814674744955481867888989
% SZS output start Proof for 8814674744955481867888989
6. ! [X0] : ((~calm(X0) & ~old(X0)) <=> old(X0)) [input p5]
11. ! [X0] : (~patient(X0) => (~calm(X0) | brave(X0))) [input p10]
17. ~brave(fred) & ~generous(fred) [input p16]
23. ~patient(fred) [input hypothesis]
31. ! [X0] : ((~calm(X0) | brave(X0)) | patient(X0)) [ennf transformation 11]
32. ! [X0] : (~calm(X0) | brave(X0) | patient(X0)) [flattening 31]
47. ! [X0] : (((~calm(X0) & ~old(X0)) | ~old(X0)) & (old(X0) | (calm(X0) | old(X0)))) [nnf transformation 6]
48. ! [X0] : (((~calm(X0) & ~old(X0)) | ~old(X0)) & (old(X0) | calm(X0) | old(X0))) [flattening 47]
102. old(X0) | calm(X0) | old(X0) [cnf transformation 48]
103. ~old(X0) | ~old(X0) [cnf transformation 48]
116. ~calm(X0) | brave(X0) | patient(X0) [cnf transformation 32]
132. ~brave(fred) [cnf transformation 17]
140. ~patient(fred) [cnf transformation 23]
141. old(X0) | calm(X0) [duplicate literal removal 102]
142. ~old(X0) [duplicate literal removal 103]
198. calm(X0) [subsumption resolution 141,142]
208. brave(X0) | patient(X0) [subsumption resolution 116,198]
268. patient(fred) [resolution 208,132]
270. $false [subsumption resolution 268,140]
% SZS output end Proof for 8814674744955481867888989
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is humble or not old then john is both old and quiet and vice versa. Everyone who is both creative and not quiet is either happy or generous. Everyone who is both not quiet and not brave is both calm and generous. Everyone who is wise or patient is either not strong or happy and vice versa. If someone is creative or not kind then alice is both not tall and not quiet. Everyone who is humble is quiet or patient. If susan is both humble and not brave then susan is wise or patient. If someone is either creative or not brave then fred is not rich and vice versa. If paul is either not humble or funny then lucy is either patient or strong and vice versa. Everyone who is not curious or not kind is not strong or curious. Everyone who is both not tall and creative is both calm and not calm. Everyone who is either not wise or not quiet is both rich and generous. If someone is both brave and not calm then fred is not creative or rich and vice versa. If someone is humble or not tall then someone is generous and vice versa. Everyone who is generous or kind is not tall. Everyone who is both patient and not quiet is not patient and vice versa. Someone is either wise or not creative. Someone is both generous and brave. Someone is either not curious or not tall. Fred is not funny. Mary is brave or curious. Someone is creative or not happy. Someone is calm or not wise. Fred is both curious and old. | Paul is creative. | contradiction | ((?[X]:((humble(X)|~old(X))))<=>((old(john)&quiet(john))))&
(![X]:((creative(X)&~quiet(X))=>(happy(X)<~>generous(X))))&
(![X]:((~quiet(X)&~brave(X))=>(calm(X)&generous(X))))&
(![X]:((wise(X)|patient(X))<=>(~strong(X)<~>happy(X))))&
((?[X]:((creative(X)|~kind(X))))=>((~tall(alice)&~quiet(alice))))&
(![X]:(humble(X)=>(quiet(X)|patient(X))))&
(((humble(susan)&~brave(susan)))=>((wise(susan)|patient(susan))))&
((?[X]:((creative(X)<~>~brave(X))))<=>(~rich(fred)))&
(((~humble(paul)<~>funny(paul)))<=>((patient(lucy)<~>strong(lucy))))&
(![X]:((~curious(X)|~kind(X))=>(~strong(X)|curious(X))))&
(![X]:((~tall(X)&creative(X))=>(calm(X)&~calm(X))))&
(![X]:((~wise(X)<~>~quiet(X))=>(rich(X)&generous(X))))&
((?[X]:((brave(X)&~calm(X))))<=>((~creative(fred)|rich(fred))))&
((?[X]:((humble(X)|~tall(X))))<=>(?[X]:(generous(X))))&
(![X]:((generous(X)|kind(X))=>~tall(X)))&
(![X]:((patient(X)&~quiet(X))<=>~patient(X)))&
(?[X]:((wise(X)<~>~creative(X))))&
(?[X]:((generous(X)&brave(X))))&
(?[X]:((~curious(X)<~>~tall(X))))&
(~funny(fred))&
((brave(mary)|curious(mary)))&
(?[X]:((creative(X)|~happy(X))))&
(?[X]:((calm(X)|~wise(X))))&
((curious(fred)&old(fred))) | creative(paul) | [
"p4",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7652173246047974507524546
% SZS output start Proof for 7652173246047974507524546
5. ? [X0] : (~kind(X0) | creative(X0)) => (~quiet(alice) & ~tall(alice)) [input p4]
16. ! [X0] : ((~quiet(X0) & patient(X0)) <=> ~patient(X0)) [input p15]
25. creative(paul) [input hypothesis]
31. (~quiet(alice) & ~tall(alice)) | ! [X0] : (kind(X0) & ~creative(X0)) [ennf transformation 5]
66. ! [X0] : (((~quiet(X0) & patient(X0)) | patient(X0)) & (~patient(X0) | (quiet(X0) | ~patient(X0)))) [nnf transformation 16]
67. ! [X0] : (((~quiet(X0) & patient(X0)) | patient(X0)) & (~patient(X0) | quiet(X0) | ~patient(X0))) [flattening 66]
97. ~quiet(alice) | ~creative(X0) [cnf transformation 31]
131. ~patient(X0) | quiet(X0) | ~patient(X0) [cnf transformation 67]
132. patient(X0) | patient(X0) [cnf transformation 67]
146. creative(paul) [cnf transformation 25]
147. ~patient(X0) | quiet(X0) [duplicate literal removal 131]
148. patient(X0) [duplicate literal removal 132]
181. 8 <=> quiet(alice) [avatar definition]
183. ~quiet(alice) <- (~8) [avatar component clause 181]
186. 9 <=> ! [X0] : ~creative(X0) [avatar definition]
187. ~creative(X0) <- (9) [avatar component clause 186]
188. 9 | ~8 [avatar split clause 97,181,186]
300. quiet(X0) [subsumption resolution 147,148]
354. $false <- (~8) [subsumption resolution 183,300]
355. 8 [avatar contradiction clause 354]
360. $false <- (9) [resolution 187,146]
361. ~9 [avatar contradiction clause 360]
362. $false [avatar sat refutation 188,355,361]
% SZS output end Proof for 7652173246047974507524546
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is patient or strong is old or not generous.
Everyone who is both not happy and not wise is both happy and patient and vice versa.
If fred is patient then someone is not kind and vice versa.
Everyone who is not patient or wise is humble or creative and vice versa.
If lucy is not quiet then fred is not strong or kind.
Everyone who is both not kind and not patient is either not wise or not humble.
Everyone who is either not kind or not wise is either generous or not strong.
If fred is either kind or not patient then someone is either not patient or not old and vice versa.
If fred is not wise then susan is calm.
Everyone who is not tall or quiet is not strong or patient.
If mary is happy or not wise then someone is either calm or kind.
If someone is either happy or not creative then someone is not rich and vice versa.
If mary is either not patient or happy then someone is either generous or not strong and vice versa.
Everyone who is both not creative and not quiet is kind or creative and vice versa.
Everyone who is not happy is not happy or not patient and vice versa.
If someone is both happy and not rich then paul is not strong.
Someone is not strong or old.
Someone is both wise and not quiet.
Someone is either not strong or not quiet.
Someone is not quiet or tall.
Someone is either brave or creative. | Lucy is not strong. | neutral | (![X]:((patient(X)|strong(X))=>(old(X)|~generous(X))))&
(![X]:((~happy(X)&~wise(X))<=>(happy(X)&patient(X))))&
((patient(fred))<=>(?[X]:(~kind(X))))&
(![X]:((~patient(X)|wise(X))<=>(humble(X)|creative(X))))&
((~quiet(lucy))=>((~strong(fred)|kind(fred))))&
(![X]:((~kind(X)&~patient(X))=>(~wise(X)<~>~humble(X))))&
(![X]:((~kind(X)<~>~wise(X))=>(generous(X)<~>~strong(X))))&
(((kind(fred)<~>~patient(fred)))<=>(?[X]:((~patient(X)<~>~old(X)))))&
((~wise(fred))=>(calm(susan)))&
(![X]:((~tall(X)|quiet(X))=>(~strong(X)|patient(X))))&
(((happy(mary)|~wise(mary)))=>(?[X]:((calm(X)<~>kind(X)))))&
((?[X]:((happy(X)<~>~creative(X))))<=>(?[X]:(~rich(X))))&
(((~patient(mary)<~>happy(mary)))<=>(?[X]:((generous(X)<~>~strong(X)))))&
(![X]:((~creative(X)&~quiet(X))<=>(kind(X)|creative(X))))&
(![X]:(~happy(X)<=>(~happy(X)|~patient(X))))&
((?[X]:((happy(X)&~rich(X))))=>(~strong(paul)))&
(?[X]:((~strong(X)|old(X))))&
(?[X]:((wise(X)&~quiet(X))))&
(?[X]:((~strong(X)<~>~quiet(X))))&
(?[X]:((~quiet(X)|tall(X))))&
(?[X]:((brave(X)<~>creative(X)))) | ~strong(lucy) | [] | null | 0 |
If lucy is not rich or not funny then someone is both not curious and not rich and vice versa.
If someone is either not curious or not old then fred is tall.
Everyone who is either not patient or strong is not funny or not humble and vice versa.
If someone is not happy then someone is calm or rich.
If paul is both tall and not wise then someone is either not kind or not quiet.
If susan is curious then someone is wise.
If lucy is both not old and not calm then fred is both wise and curious.
If lucy is not calm then lucy is strong.
If someone is both wise and rich then fred is not creative or not quiet.
Everyone who is both creative and funny is both strong and not curious.
Everyone who is either not brave or not calm is not quiet or creative.
Everyone who is either not old or kind is strong or not brave.
If someone is both not patient and tall then fred is either brave or not curious.
Everyone who is not funny or old is either old or not creative and vice versa.
Everyone who is both not funny and not rich is not humble.
Everyone who is either not old or happy is either not quiet or not kind and vice versa.
Susan is both happy and not kind.
Someone is not creative or old.
Someone is either not rich or not happy.
Someone is both not old and strong.
Fred is not calm or happy.
Paul is not tall or not strong.
Susan is either not quiet or not happy. | Paul is curious. | neutral | (((~rich(lucy)|~funny(lucy)))<=>(?[X]:((~curious(X)&~rich(X)))))&
((?[X]:((~curious(X)<~>~old(X))))=>(tall(fred)))&
(![X]:((~patient(X)<~>strong(X))<=>(~funny(X)|~humble(X))))&
((?[X]:(~happy(X)))=>(?[X]:((calm(X)|rich(X)))))&
(((tall(paul)&~wise(paul)))=>(?[X]:((~kind(X)<~>~quiet(X)))))&
((curious(susan))=>(?[X]:(wise(X))))&
(((~old(lucy)&~calm(lucy)))=>((wise(fred)&curious(fred))))&
((~calm(lucy))=>(strong(lucy)))&
((?[X]:((wise(X)&rich(X))))=>((~creative(fred)|~quiet(fred))))&
(![X]:((creative(X)&funny(X))=>(strong(X)&~curious(X))))&
(![X]:((~brave(X)<~>~calm(X))=>(~quiet(X)|creative(X))))&
(![X]:((~old(X)<~>kind(X))=>(strong(X)|~brave(X))))&
((?[X]:((~patient(X)&tall(X))))=>((brave(fred)<~>~curious(fred))))&
(![X]:((~funny(X)|old(X))<=>(old(X)<~>~creative(X))))&
(![X]:((~funny(X)&~rich(X))=>~humble(X)))&
(![X]:((~old(X)<~>happy(X))<=>(~quiet(X)<~>~kind(X))))&
((happy(susan)&~kind(susan)))&
(?[X]:((~creative(X)|old(X))))&
(?[X]:((~rich(X)<~>~happy(X))))&
(?[X]:((~old(X)&strong(X))))&
((~calm(fred)|happy(fred)))&
((~tall(paul)|~strong(paul)))&
((~quiet(susan)<~>~happy(susan))) | curious(paul) | [] | null | 0 |
If someone is not kind then someone is both generous and not creative.
Everyone who is either not rich or not generous is either brave or old and vice versa.
Everyone who is either not kind or curious is either not funny or creative.
If fred is creative or not generous then someone is patient or not quiet and vice versa.
Everyone who is either creative or strong is either not humble or brave.
Everyone who is not strong is not old and vice versa.
Everyone who is both kind and quiet is curious and vice versa.
Everyone who is funny is either not generous or tall.
If someone is tall then someone is both not rich and not wise and vice versa.
Everyone who is not old is both strong and not happy and vice versa.
Everyone who is calm is not creative or old.
If susan is generous then fred is not strong and vice versa.
If someone is both happy and wise then someone is both calm and tall.
Everyone who is brave is either creative or curious and vice versa.
If someone is not brave then someone is either generous or not curious and vice versa.
Everyone who is not creative or tall is either calm or not happy.
Someone is either tall or funny.
Someone is not patient or not generous.
Someone is not patient.
Someone is strong or calm.
Someone is either kind or creative.
Someone is rich. | Susan is funny. | neutral | ((?[X]:(~kind(X)))=>(?[X]:((generous(X)&~creative(X)))))&
(![X]:((~rich(X)<~>~generous(X))<=>(brave(X)<~>old(X))))&
(![X]:((~kind(X)<~>curious(X))=>(~funny(X)<~>creative(X))))&
(((creative(fred)|~generous(fred)))<=>(?[X]:((patient(X)|~quiet(X)))))&
(![X]:((creative(X)<~>strong(X))=>(~humble(X)<~>brave(X))))&
(![X]:(~strong(X)<=>~old(X)))&
(![X]:((kind(X)&quiet(X))<=>curious(X)))&
(![X]:(funny(X)=>(~generous(X)<~>tall(X))))&
((?[X]:(tall(X)))<=>(?[X]:((~rich(X)&~wise(X)))))&
(![X]:(~old(X)<=>(strong(X)&~happy(X))))&
(![X]:(calm(X)=>(~creative(X)|old(X))))&
((generous(susan))<=>(~strong(fred)))&
((?[X]:((happy(X)&wise(X))))=>(?[X]:((calm(X)&tall(X)))))&
(![X]:(brave(X)<=>(creative(X)<~>curious(X))))&
((?[X]:(~brave(X)))<=>(?[X]:((generous(X)<~>~curious(X)))))&
(![X]:((~creative(X)|tall(X))=>(calm(X)<~>~happy(X))))&
(?[X]:((tall(X)<~>funny(X))))&
(?[X]:((~patient(X)|~generous(X))))&
(?[X]:(~patient(X)))&
(?[X]:((strong(X)|calm(X))))&
(?[X]:((kind(X)<~>creative(X))))&
(?[X]:(rich(X))) | funny(susan) | [] | null | 0 |
Everyone who is either not brave or funny is rich. Everyone who is both rich and generous is not old. If paul is not quiet then someone is both not rich and rich. Everyone who is both creative and generous is either not curious or not calm. If someone is either not kind or strong then mary is tall or humble and vice versa. If someone is both not creative and humble then mary is creative. Everyone who is both not generous and generous is not happy or not patient and vice versa. If paul is either happy or tall then someone is both not happy and curious. Everyone who is both not brave and creative is rich. Everyone who is both curious and not rich is humble or funny. Everyone who is strong or not creative is humble. Everyone who is not creative or generous is calm and vice versa. Everyone who is calm or creative is quiet and vice versa. Everyone who is either humble or happy is strong. Everyone who is quiet is both rich and not calm and vice versa. If mary is either kind or not quiet then fred is strong and vice versa. Paul is not generous or not calm. Someone is not humble or humble. Someone is both kind and not tall. Lucy is not curious or not brave. | Lucy is not patient. | contradiction | (![X]:((~brave(X)<~>funny(X))=>rich(X)))&
(![X]:((rich(X)&generous(X))=>~old(X)))&
((~quiet(paul))=>(?[X]:((~rich(X)&rich(X)))))&
(![X]:((creative(X)&generous(X))=>(~curious(X)<~>~calm(X))))&
((?[X]:((~kind(X)<~>strong(X))))<=>((tall(mary)|humble(mary))))&
((?[X]:((~creative(X)&humble(X))))=>(creative(mary)))&
(![X]:((~generous(X)&generous(X))<=>(~happy(X)|~patient(X))))&
(((happy(paul)<~>tall(paul)))=>(?[X]:((~happy(X)&curious(X)))))&
(![X]:((~brave(X)&creative(X))=>rich(X)))&
(![X]:((curious(X)&~rich(X))=>(humble(X)|funny(X))))&
(![X]:((strong(X)|~creative(X))=>humble(X)))&
(![X]:((~creative(X)|generous(X))<=>calm(X)))&
(![X]:((calm(X)|creative(X))<=>quiet(X)))&
(![X]:((humble(X)<~>happy(X))=>strong(X)))&
(![X]:(quiet(X)<=>(rich(X)&~calm(X))))&
(((kind(mary)<~>~quiet(mary)))<=>(strong(fred)))&
((~generous(paul)|~calm(paul)))&
(?[X]:((~humble(X)|humble(X))))&
(?[X]:((kind(X)&~tall(X))))&
((~curious(lucy)|~brave(lucy))) | ~patient(lucy) | [
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 5697508397092823120108098
% SZS output start Proof for 5697508397092823120108098
7. ! [X0] : ((generous(X0) & ~generous(X0)) <=> (~patient(X0) | ~happy(X0))) [input p6]
21. ~patient(lucy) [input hypothesis]
44. ! [X0] : (((generous(X0) & ~generous(X0)) | (patient(X0) & happy(X0))) & ((~patient(X0) | ~happy(X0)) | (~generous(X0) | generous(X0)))) [nnf transformation 7]
45. ! [X0] : (((generous(X0) & ~generous(X0)) | (patient(X0) & happy(X0))) & (~patient(X0) | ~happy(X0) | ~generous(X0) | generous(X0))) [flattening 44]
76. ~generous(X0) | patient(X0) [cnf transformation 45]
78. generous(X0) | patient(X0) [cnf transformation 45]
107. ~patient(lucy) [cnf transformation 21]
154. patient(X0) [subsumption resolution 76,78]
198. $false [subsumption resolution 107,154]
% SZS output end Proof for 5697508397092823120108098
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not wise or generous is either not wise or not creative and vice versa.
Everyone who is either not brave or happy is not calm and vice versa.
Everyone who is happy or not creative is not calm or not old and vice versa.
If someone is funny or not happy then someone is either not quiet or tall.
If someone is both humble and creative then susan is either patient or not generous.
Everyone who is both not happy and not quiet is both not strong and not kind.
Everyone who is both not quiet and not kind is generous or creative.
If someone is quiet or not patient then fred is either patient or wise and vice versa.
Everyone who is not old or creative is both old and not funny and vice versa.
If someone is either calm or not quiet then someone is wise and vice versa.
Everyone who is either not quiet or humble is kind and vice versa.
If someone is quiet then someone is either funny or not tall.
Everyone who is funny or not calm is either not humble or not funny.
Everyone who is either curious or brave is both funny and wise and vice versa.
If fred is either quiet or brave then someone is either not strong or not creative and vice versa.
Everyone who is either patient or not wise is both not old and not rich.
Susan is not humble or brave.
Paul is both calm and not quiet.
Susan is not funny or strong.
Someone is both not patient and creative.
Lucy is both calm and humble.
Alice is not wise or not brave.
Someone is either humble or wise. | Susan is not creative. | contradiction | (![X]:((~wise(X)|generous(X))<=>(~wise(X)<~>~creative(X))))&
(![X]:((~brave(X)<~>happy(X))<=>~calm(X)))&
(![X]:((happy(X)|~creative(X))<=>(~calm(X)|~old(X))))&
((?[X]:((funny(X)|~happy(X))))=>(?[X]:((~quiet(X)<~>tall(X)))))&
((?[X]:((humble(X)&creative(X))))=>((patient(susan)<~>~generous(susan))))&
(![X]:((~happy(X)&~quiet(X))=>(~strong(X)&~kind(X))))&
(![X]:((~quiet(X)&~kind(X))=>(generous(X)|creative(X))))&
((?[X]:((quiet(X)|~patient(X))))<=>((patient(fred)<~>wise(fred))))&
(![X]:((~old(X)|creative(X))<=>(old(X)&~funny(X))))&
((?[X]:((calm(X)<~>~quiet(X))))<=>(?[X]:(wise(X))))&
(![X]:((~quiet(X)<~>humble(X))<=>kind(X)))&
((?[X]:(quiet(X)))=>(?[X]:((funny(X)<~>~tall(X)))))&
(![X]:((funny(X)|~calm(X))=>(~humble(X)<~>~funny(X))))&
(![X]:((curious(X)<~>brave(X))<=>(funny(X)&wise(X))))&
(((quiet(fred)<~>brave(fred)))<=>(?[X]:((~strong(X)<~>~creative(X)))))&
(![X]:((patient(X)<~>~wise(X))=>(~old(X)&~rich(X))))&
((~humble(susan)|brave(susan)))&
((calm(paul)&~quiet(paul)))&
((~funny(susan)|strong(susan)))&
(?[X]:((~patient(X)&creative(X))))&
((calm(lucy)&humble(lucy)))&
((~wise(alice)|~brave(alice)))&
(?[X]:((humble(X)<~>wise(X)))) | ~creative(susan) | [
"p0",
"p2",
"p4",
"p8",
"p15",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 4055497716596871317623248
% SZS output start Proof for 4055497716596871317623248
1. ! [X0] : ((generous(X0) | ~wise(X0)) <=> (~wise(X0) <~> ~creative(X0))) [input p0]
3. ! [X0] : ((~creative(X0) | happy(X0)) <=> (~old(X0) | ~calm(X0))) [input p2]
5. ? [X0] : (creative(X0) & humble(X0)) => (patient(susan) <~> ~generous(susan)) [input p4]
9. ! [X0] : ((creative(X0) | ~old(X0)) <=> (~funny(X0) & old(X0))) [input p8]
16. ! [X0] : ((patient(X0) <~> ~wise(X0)) => (~rich(X0) & ~old(X0))) [input p15]
21. humble(lucy) & calm(lucy) [input p20]
24. ~creative(susan) [input hypothesis]
28. ! [X0] : ((patient(X0) <~> ~wise(X0)) => ~old(X0)) [pure predicate removal 16]
30. (patient(susan) <~> ~generous(susan)) | ! [X0] : (~creative(X0) | ~humble(X0)) [ennf transformation 5]
37. ! [X0] : (~old(X0) | (patient(X0) <=> ~wise(X0))) [ennf transformation 28]
38. ! [X0] : (((generous(X0) | ~wise(X0)) | ((~wise(X0) | creative(X0)) & (~creative(X0) | wise(X0)))) & (((creative(X0) | wise(X0)) & (~creative(X0) | ~wise(X0))) | (~generous(X0) & wise(X0)))) [nnf transformation 1]
39. ! [X0] : ((generous(X0) | ~wise(X0) | ((~wise(X0) | creative(X0)) & (~creative(X0) | wise(X0)))) & (((creative(X0) | wise(X0)) & (~creative(X0) | ~wise(X0))) | (~generous(X0) & wise(X0)))) [flattening 38]
41. ! [X0] : (((~creative(X0) | happy(X0)) | (old(X0) & calm(X0))) & ((~old(X0) | ~calm(X0)) | (creative(X0) & ~happy(X0)))) [nnf transformation 3]
42. ! [X0] : ((~creative(X0) | happy(X0) | (old(X0) & calm(X0))) & (~old(X0) | ~calm(X0) | (creative(X0) & ~happy(X0)))) [flattening 41]
47. ((generous(susan) | ~patient(susan)) & (~generous(susan) | patient(susan))) | ! [X0] : (~creative(X0) | ~humble(X0)) [nnf transformation 30]
52. ! [X0] : (((creative(X0) | ~old(X0)) | (funny(X0) | ~old(X0))) & ((~funny(X0) & old(X0)) | (~creative(X0) & old(X0)))) [nnf transformation 9]
53. ! [X0] : ((creative(X0) | ~old(X0) | funny(X0) | ~old(X0)) & ((~funny(X0) & old(X0)) | (~creative(X0) & old(X0)))) [flattening 52]
71. ! [X0] : (~old(X0) | ((patient(X0) | wise(X0)) & (~wise(X0) | ~patient(X0)))) [nnf transformation 37]
79. creative(X0) | wise(X0) | wise(X0) [cnf transformation 39]
82. generous(X0) | ~wise(X0) | ~wise(X0) | creative(X0) [cnf transformation 39]
88. ~old(X0) | ~calm(X0) | creative(X0) [cnf transformation 42]
95. ~generous(susan) | patient(susan) | ~creative(X0) | ~humble(X0) [cnf transformation 47]
106. old(X0) | old(X0) [cnf transformation 53]
139. ~old(X0) | ~wise(X0) | ~patient(X0) [cnf transformation 71]
147. calm(lucy) [cnf transformation 21]
148. humble(lucy) [cnf transformation 21]
152. ~creative(susan) [cnf transformation 24]
154. old(X0) [duplicate literal removal 106]
156. creative(X0) | wise(X0) [duplicate literal removal 79]
157. ~wise(X0) | generous(X0) | creative(X0) [duplicate literal removal 82]
177. 5 <=> ! [X0] : (~creative(X0) | ~humble(X0)) [avatar definition]
178. ~humble(X0) | ~creative(X0) <- (5) [avatar component clause 177]
180. 6 <=> patient(susan) [avatar definition]
181. patient(susan) <- (6) [avatar component clause 180]
184. 7 <=> generous(susan) [avatar definition]
188. 5 | 6 | ~7 [avatar split clause 95,184,180,177]
283. ~patient(X0) | ~wise(X0) [subsumption resolution 139,154]
324. wise(susan) [resolution 156,152]
367. ~calm(X0) | creative(X0) [resolution 88,154]
435. creative(lucy) [resolution 367,147]
535. generous(susan) | creative(susan) [resolution 157,324]
570. generous(susan) [subsumption resolution 535,152]
571. 7 [avatar split clause 570,184]
576. ~creative(lucy) <- (5) [resolution 178,148]
579. $false <- (5) [subsumption resolution 576,435]
580. ~5 [avatar contradiction clause 579]
581. ~wise(susan) <- (6) [resolution 181,283]
582. $false <- (6) [subsumption resolution 581,324]
583. ~6 [avatar contradiction clause 582]
584. $false [avatar sat refutation 188,571,580,583]
% SZS output end Proof for 4055497716596871317623248
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not generous and not strong is curious.
Everyone who is not quiet or quiet is not kind or creative.
If susan is both not strong and tall then someone is either not calm or quiet.
If someone is both not strong and not funny then paul is either tall or not wise and vice versa.
Everyone who is either strong or not kind is creative.
If mary is either strong or not kind then someone is curious.
Everyone who is both wise and patient is either kind or not strong and vice versa.
Everyone who is not creative is both not strong and quiet and vice versa.
Everyone who is either not tall or tall is tall or wise and vice versa.
Everyone who is either not quiet or not strong is generous or quiet.
If paul is not funny then someone is not happy.
Everyone who is tall is not old or tall and vice versa.
If someone is both quiet and funny then someone is both patient and funny.
Everyone who is both kind and not patient is not old.
If paul is not happy or brave then someone is either funny or brave and vice versa.
If someone is both not quiet and funny then paul is either curious or generous.
Someone is wise or not tall.
Someone is old or not old.
Someone is both not generous and wise.
Someone is both not kind and not old.
John is both funny and not tall.
John is brave.
Susan is generous.
Fred is both not funny and not patient. | Susan is not strong. | neutral | (![X]:((~generous(X)&~strong(X))=>curious(X)))&
(![X]:((~quiet(X)|quiet(X))=>(~kind(X)|creative(X))))&
(((~strong(susan)&tall(susan)))=>(?[X]:((~calm(X)<~>quiet(X)))))&
((?[X]:((~strong(X)&~funny(X))))<=>((tall(paul)<~>~wise(paul))))&
(![X]:((strong(X)<~>~kind(X))=>creative(X)))&
(((strong(mary)<~>~kind(mary)))=>(?[X]:(curious(X))))&
(![X]:((wise(X)&patient(X))<=>(kind(X)<~>~strong(X))))&
(![X]:(~creative(X)<=>(~strong(X)&quiet(X))))&
(![X]:((~tall(X)<~>tall(X))<=>(tall(X)|wise(X))))&
(![X]:((~quiet(X)<~>~strong(X))=>(generous(X)|quiet(X))))&
((~funny(paul))=>(?[X]:(~happy(X))))&
(![X]:(tall(X)<=>(~old(X)|tall(X))))&
((?[X]:((quiet(X)&funny(X))))=>(?[X]:((patient(X)&funny(X)))))&
(![X]:((kind(X)&~patient(X))=>~old(X)))&
(((~happy(paul)|brave(paul)))<=>(?[X]:((funny(X)<~>brave(X)))))&
((?[X]:((~quiet(X)&funny(X))))=>((curious(paul)<~>generous(paul))))&
(?[X]:((wise(X)|~tall(X))))&
(?[X]:((old(X)|~old(X))))&
(?[X]:((~generous(X)&wise(X))))&
(?[X]:((~kind(X)&~old(X))))&
((funny(john)&~tall(john)))&
(brave(john))&
(generous(susan))&
((~funny(fred)&~patient(fred))) | ~strong(susan) | [] | null | 0 |
Everyone who is both not kind and not wise is strong.
Everyone who is not calm or rich is both not tall and not rich and vice versa.
Everyone who is either old or funny is both brave and not quiet.
If mary is either creative or patient then someone is both rich and funny and vice versa.
Everyone who is rich is either rich or patient and vice versa.
If someone is tall or not humble then paul is either not rich or rich.
Everyone who is not calm is patient or not funny.
If mary is not patient then fred is curious and vice versa.
If someone is both patient and not tall then paul is not generous.
If someone is both not curious and not wise then lucy is curious or not rich and vice versa.
Everyone who is either not generous or curious is either wise or happy and vice versa.
Everyone who is both not old and not happy is either kind or not generous and vice versa.
Everyone who is both not kind and not quiet is both not generous and calm.
Everyone who is either funny or not humble is not tall or not generous.
Everyone who is not patient is both old and not tall and vice versa.
If someone is either not creative or wise then john is not creative and vice versa.
Someone is either creative or happy.
Fred is not old or not rich.
Someone is curious or wise.
Mary is not happy.
Mary is tall or not creative.
Paul is both old and not strong. | Mary is not quiet. | entailment | (![X]:((~kind(X)&~wise(X))=>strong(X)))&
(![X]:((~calm(X)|rich(X))<=>(~tall(X)&~rich(X))))&
(![X]:((old(X)<~>funny(X))=>(brave(X)&~quiet(X))))&
(((creative(mary)<~>patient(mary)))<=>(?[X]:((rich(X)&funny(X)))))&
(![X]:(rich(X)<=>(rich(X)<~>patient(X))))&
((?[X]:((tall(X)|~humble(X))))=>((~rich(paul)<~>rich(paul))))&
(![X]:(~calm(X)=>(patient(X)|~funny(X))))&
((~patient(mary))<=>(curious(fred)))&
((?[X]:((patient(X)&~tall(X))))=>(~generous(paul)))&
((?[X]:((~curious(X)&~wise(X))))<=>((curious(lucy)|~rich(lucy))))&
(![X]:((~generous(X)<~>curious(X))<=>(wise(X)<~>happy(X))))&
(![X]:((~old(X)&~happy(X))<=>(kind(X)<~>~generous(X))))&
(![X]:((~kind(X)&~quiet(X))=>(~generous(X)&calm(X))))&
(![X]:((funny(X)<~>~humble(X))=>(~tall(X)|~generous(X))))&
(![X]:(~patient(X)<=>(old(X)&~tall(X))))&
((?[X]:((~creative(X)<~>wise(X))))<=>(~creative(john)))&
(?[X]:((creative(X)<~>happy(X))))&
((~old(fred)|~rich(fred)))&
(?[X]:((curious(X)|wise(X))))&
(~happy(mary))&
((tall(mary)|~creative(mary)))&
((old(paul)&~strong(paul))) | ~quiet(mary) | [
"p1",
"p2",
"p4",
"p6",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4913206159947688018494976
% SZS output start Proof for 4913206159947688018494976
2. ! [X0] : ((rich(X0) | ~calm(X0)) <=> (~rich(X0) & ~tall(X0))) [input p1]
3. ! [X0] : ((old(X0) <~> funny(X0)) => (~quiet(X0) & brave(X0))) [input p2]
5. ! [X0] : (rich(X0) <=> (rich(X0) <~> patient(X0))) [input p4]
7. ! [X0] : (~calm(X0) => (~funny(X0) | patient(X0))) [input p6]
15. ! [X0] : (~patient(X0) <=> (~tall(X0) & old(X0))) [input p14]
23. quiet(mary) [input hypothesis]
24. ! [X0] : ((old(X0) <~> funny(X0)) => ~quiet(X0)) [pure predicate removal 3]
27. ! [X0] : (~quiet(X0) | (old(X0) <=> funny(X0))) [ennf transformation 24]
29. ! [X0] : ((~funny(X0) | patient(X0)) | calm(X0)) [ennf transformation 7]
30. ! [X0] : (~funny(X0) | patient(X0) | calm(X0)) [flattening 29]
36. ! [X0] : (((rich(X0) | ~calm(X0)) | (rich(X0) | tall(X0))) & ((~rich(X0) & ~tall(X0)) | (~rich(X0) & calm(X0)))) [nnf transformation 2]
37. ! [X0] : ((rich(X0) | ~calm(X0) | rich(X0) | tall(X0)) & ((~rich(X0) & ~tall(X0)) | (~rich(X0) & calm(X0)))) [flattening 36]
38. ! [X0] : (~quiet(X0) | ((old(X0) | ~funny(X0)) & (funny(X0) | ~old(X0)))) [nnf transformation 27]
43. ! [X0] : ((rich(X0) | ((rich(X0) | ~patient(X0)) & (patient(X0) | ~rich(X0)))) & (((~patient(X0) | ~rich(X0)) & (patient(X0) | rich(X0))) | ~rich(X0))) [nnf transformation 5]
55. ! [X0] : ((~patient(X0) | (tall(X0) | ~old(X0))) & ((~tall(X0) & old(X0)) | patient(X0))) [nnf transformation 15]
56. ! [X0] : ((~patient(X0) | tall(X0) | ~old(X0)) & ((~tall(X0) & old(X0)) | patient(X0))) [flattening 55]
70. ~rich(X0) | ~rich(X0) [cnf transformation 37]
71. rich(X0) | ~calm(X0) | rich(X0) | tall(X0) [cnf transformation 37]
72. ~quiet(X0) | funny(X0) | ~old(X0) [cnf transformation 38]
83. rich(X0) | rich(X0) | ~patient(X0) [cnf transformation 43]
88. ~funny(X0) | patient(X0) | calm(X0) [cnf transformation 30]
115. old(X0) | patient(X0) [cnf transformation 56]
116. ~tall(X0) | patient(X0) [cnf transformation 56]
130. quiet(mary) [cnf transformation 23]
132. rich(X0) | ~patient(X0) [duplicate literal removal 83]
133. ~rich(X0) [duplicate literal removal 70]
134. ~calm(X0) | rich(X0) | tall(X0) [duplicate literal removal 71]
153. ~patient(X0) [subsumption resolution 132,133]
154. ~funny(X0) | calm(X0) [subsumption resolution 88,153]
158. ~tall(X0) [subsumption resolution 116,153]
159. old(X0) [subsumption resolution 115,153]
213. funny(mary) | ~old(mary) [resolution 72,130]
214. funny(mary) [subsumption resolution 213,159]
215. calm(mary) [resolution 214,154]
225. rich(mary) | tall(mary) [resolution 134,215]
227. tall(mary) [subsumption resolution 225,133]
228. $false [subsumption resolution 227,158]
% SZS output end Proof for 4913206159947688018494976
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not tall then someone is both tall and curious and vice versa.
If someone is either funny or creative then alice is not rich and vice versa.
If lucy is old or not creative then mary is brave or not brave and vice versa.
If someone is either not brave or not funny then mary is both brave and not funny.
Everyone who is not rich is tall or brave.
Everyone who is both not generous and not funny is funny or calm.
Everyone who is either not generous or funny is either not calm or not happy.
If someone is not brave or strong then someone is not wise and vice versa.
Everyone who is not wise is both not generous and wise and vice versa.
If alice is either creative or strong then someone is either rich or humble and vice versa.
Everyone who is not calm or not happy is either old or strong and vice versa.
Everyone who is both not patient and wise is not patient and vice versa.
If someone is funny then mary is both not patient and generous and vice versa.
If someone is both not curious and not happy then susan is not patient and vice versa.
If lucy is not wise or patient then someone is not curious or not happy.
Someone is both generous and calm.
Someone is both funny and not patient.
Someone is generous or not old.
Alice is both calm and not quiet.
Paul is either not strong or not rich.
Mary is either humble or not brave.
Someone is either curious or not wise. | Lucy is wise. | entailment | ((?[X]:(~tall(X)))<=>(?[X]:((tall(X)&curious(X)))))&
((?[X]:((funny(X)<~>creative(X))))<=>(~rich(alice)))&
(((old(lucy)|~creative(lucy)))<=>((brave(mary)|~brave(mary))))&
((?[X]:((~brave(X)<~>~funny(X))))=>((brave(mary)&~funny(mary))))&
(![X]:(~rich(X)=>(tall(X)|brave(X))))&
(![X]:((~generous(X)&~funny(X))=>(funny(X)|calm(X))))&
(![X]:((~generous(X)<~>funny(X))=>(~calm(X)<~>~happy(X))))&
((?[X]:((~brave(X)|strong(X))))<=>(?[X]:(~wise(X))))&
(![X]:(~wise(X)<=>(~generous(X)&wise(X))))&
(((creative(alice)<~>strong(alice)))<=>(?[X]:((rich(X)<~>humble(X)))))&
(![X]:((~calm(X)|~happy(X))<=>(old(X)<~>strong(X))))&
(![X]:((~patient(X)&wise(X))<=>~patient(X)))&
((?[X]:(funny(X)))<=>((~patient(mary)&generous(mary))))&
((?[X]:((~curious(X)&~happy(X))))<=>(~patient(susan)))&
(((~wise(lucy)|patient(lucy)))=>(?[X]:((~curious(X)|~happy(X)))))&
(?[X]:((generous(X)&calm(X))))&
(?[X]:((funny(X)&~patient(X))))&
(?[X]:((generous(X)|~old(X))))&
((calm(alice)&~quiet(alice)))&
((~strong(paul)<~>~rich(paul)))&
((humble(mary)<~>~brave(mary)))&
(?[X]:((curious(X)<~>~wise(X)))) | wise(lucy) | [
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 1943118587989341943154598
% SZS output start Proof for 1943118587989341943154598
9. ! [X0] : (~wise(X0) <=> (wise(X0) & ~generous(X0))) [input p8]
23. ~wise(lucy) [input hypothesis]
52. ! [X0] : ((~wise(X0) | (~wise(X0) | generous(X0))) & ((wise(X0) & ~generous(X0)) | wise(X0))) [nnf transformation 9]
53. ! [X0] : ((~wise(X0) | ~wise(X0) | generous(X0)) & ((wise(X0) & ~generous(X0)) | wise(X0))) [flattening 52]
109. wise(X0) | wise(X0) [cnf transformation 53]
148. ~wise(lucy) [cnf transformation 23]
149. wise(X0) [duplicate literal removal 109]
225. 17 <=> ! [X1] : wise(X1) [avatar definition]
226. wise(X1) <- (17) [avatar component clause 225]
248. 17 [avatar split clause 149,225]
329. 40 <=> wise(lucy) [avatar definition]
330. ~wise(lucy) <- (~40) [avatar component clause 329]
368. ~40 [avatar split clause 148,329]
375. $false <- (17, ~40) [resolution 330,226]
376. ~17 | 40 [avatar contradiction clause 375]
377. $false [avatar sat refutation 248,368,376]
% SZS output end Proof for 1943118587989341943154598
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 someone is both wise and rich then mary is both humble and rich. If someone is happy then alice is not brave. Everyone who is not wise or not brave is brave and vice versa. If someone is either happy or not tall then someone is both happy and calm. Everyone who is both not creative and not wise is strong or not kind and vice versa. If paul is humble or brave then alice is humble or wise. Everyone who is both kind and not curious is either not rich or not creative and vice versa. If someone is either patient or not strong then someone is either curious or not tall and vice versa. Everyone who is not rich or not generous is both funny and not creative. If someone is not quiet or not brave then paul is happy or not generous and vice versa. If alice is either quiet or not generous then someone is not rich or not curious. If someone is kind or not tall then someone is either not patient or patient and vice versa. Everyone who is calm is either not rich or not quiet and vice versa. Everyone who is both funny and not rich is not rich or not happy. Everyone who is either not rich or not funny is either not tall or not humble and vice versa. Everyone who is both generous and not patient is both quiet and patient. John is funny. John is not patient. Someone is either not tall or not wise. Lucy is generous. Mary is both funny and old. | Alice is not brave. | contradiction | ((?[X]:((wise(X)&rich(X))))=>((humble(mary)&rich(mary))))&
((?[X]:(happy(X)))=>(~brave(alice)))&
(![X]:((~wise(X)|~brave(X))<=>brave(X)))&
((?[X]:((happy(X)<~>~tall(X))))=>(?[X]:((happy(X)&calm(X)))))&
(![X]:((~creative(X)&~wise(X))<=>(strong(X)|~kind(X))))&
(((humble(paul)|brave(paul)))=>((humble(alice)|wise(alice))))&
(![X]:((kind(X)&~curious(X))<=>(~rich(X)<~>~creative(X))))&
((?[X]:((patient(X)<~>~strong(X))))<=>(?[X]:((curious(X)<~>~tall(X)))))&
(![X]:((~rich(X)|~generous(X))=>(funny(X)&~creative(X))))&
((?[X]:((~quiet(X)|~brave(X))))<=>((happy(paul)|~generous(paul))))&
(((quiet(alice)<~>~generous(alice)))=>(?[X]:((~rich(X)|~curious(X)))))&
((?[X]:((kind(X)|~tall(X))))<=>(?[X]:((~patient(X)<~>patient(X)))))&
(![X]:(calm(X)<=>(~rich(X)<~>~quiet(X))))&
(![X]:((funny(X)&~rich(X))=>(~rich(X)|~happy(X))))&
(![X]:((~rich(X)<~>~funny(X))<=>(~tall(X)<~>~humble(X))))&
(![X]:((generous(X)&~patient(X))=>(quiet(X)&patient(X))))&
(funny(john))&
(~patient(john))&
(?[X]:((~tall(X)<~>~wise(X))))&
(generous(lucy))&
((funny(mary)&old(mary))) | ~brave(alice) | [
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 2706584981329657040475147
% SZS output start Proof for 2706584981329657040475147
3. ! [X0] : ((~brave(X0) | ~wise(X0)) <=> brave(X0)) [input p2]
22. ~brave(alice) [input hypothesis]
40. ! [X0] : (((~brave(X0) | ~wise(X0)) | ~brave(X0)) & (brave(X0) | (brave(X0) & wise(X0)))) [nnf transformation 3]
41. ! [X0] : ((~brave(X0) | ~wise(X0) | ~brave(X0)) & (brave(X0) | (brave(X0) & wise(X0)))) [flattening 40]
77. brave(X0) | brave(X0) [cnf transformation 41]
139. ~brave(alice) [cnf transformation 22]
143. brave(X0) [duplicate literal removal 77]
305. $false [subsumption resolution 139,143]
% SZS output end Proof for 2706584981329657040475147
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not rich and tall then someone is funny or creative and vice versa.
If someone is creative then someone is either happy or kind and vice versa.
If susan is either strong or not humble then mary is not funny or not generous.
Everyone who is both generous and not funny is both creative and not happy.
Everyone who is funny or rich is either not old or generous.
Everyone who is happy or not brave is not happy or not kind.
Everyone who is either humble or brave is either calm or not wise and vice versa.
If mary is not funny then someone is not rich or not strong and vice versa.
Everyone who is quiet or generous is both not wise and generous.
Everyone who is funny or not quiet is either wise or not old and vice versa.
If someone is generous or not tall then lucy is not quiet.
Everyone who is not brave is both not funny and not generous and vice versa.
Everyone who is creative is both not curious and curious and vice versa.
If someone is tall then fred is both old and not happy.
If someone is generous or funny then someone is either funny or not funny and vice versa.
If someone is either rich or curious then someone is not curious and vice versa.
Someone is either not curious or not humble.
Someone is not wise.
Susan is both not curious and not brave.
Someone is not strong.
Fred is not patient.
Someone is funny or curious.
Someone is not quiet or old. | Lucy is not generous. | entailment | ((?[X]:((~rich(X)&tall(X))))<=>(?[X]:((funny(X)|creative(X)))))&
((?[X]:(creative(X)))<=>(?[X]:((happy(X)<~>kind(X)))))&
(((strong(susan)<~>~humble(susan)))=>((~funny(mary)|~generous(mary))))&
(![X]:((generous(X)&~funny(X))=>(creative(X)&~happy(X))))&
(![X]:((funny(X)|rich(X))=>(~old(X)<~>generous(X))))&
(![X]:((happy(X)|~brave(X))=>(~happy(X)|~kind(X))))&
(![X]:((humble(X)<~>brave(X))<=>(calm(X)<~>~wise(X))))&
((~funny(mary))<=>(?[X]:((~rich(X)|~strong(X)))))&
(![X]:((quiet(X)|generous(X))=>(~wise(X)&generous(X))))&
(![X]:((funny(X)|~quiet(X))<=>(wise(X)<~>~old(X))))&
((?[X]:((generous(X)|~tall(X))))=>(~quiet(lucy)))&
(![X]:(~brave(X)<=>(~funny(X)&~generous(X))))&
(![X]:(creative(X)<=>(~curious(X)&curious(X))))&
((?[X]:(tall(X)))=>((old(fred)&~happy(fred))))&
((?[X]:((generous(X)|funny(X))))<=>(?[X]:((funny(X)<~>~funny(X)))))&
((?[X]:((rich(X)<~>curious(X))))<=>(?[X]:(~curious(X))))&
(?[X]:((~curious(X)<~>~humble(X))))&
(?[X]:(~wise(X)))&
((~curious(susan)&~brave(susan)))&
(?[X]:(~strong(X)))&
(~patient(fred))&
(?[X]:((funny(X)|curious(X))))&
(?[X]:((~quiet(X)|old(X)))) | ~generous(lucy) | [
"p3",
"p4",
"p8",
"p9",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 1383027613154645286747232
% SZS output start Proof for 1383027613154645286747232
4. ! [X0] : ((~funny(X0) & generous(X0)) => (~happy(X0) & creative(X0))) [input p3]
5. ! [X0] : ((rich(X0) | funny(X0)) => (~old(X0) <~> generous(X0))) [input p4]
9. ! [X0] : ((generous(X0) | quiet(X0)) => (generous(X0) & ~wise(X0))) [input p8]
10. ! [X0] : ((~quiet(X0) | funny(X0)) <=> (wise(X0) <~> ~old(X0))) [input p9]
13. ! [X0] : (creative(X0) <=> (curious(X0) & ~curious(X0))) [input p12]
24. generous(lucy) [input hypothesis]
32. ! [X0] : ((~happy(X0) & creative(X0)) | (funny(X0) | ~generous(X0))) [ennf transformation 4]
33. ! [X0] : ((~happy(X0) & creative(X0)) | funny(X0) | ~generous(X0)) [flattening 32]
34. ! [X0] : ((~old(X0) <~> generous(X0)) | (~rich(X0) & ~funny(X0))) [ennf transformation 5]
37. ! [X0] : ((generous(X0) & ~wise(X0)) | (~generous(X0) & ~quiet(X0))) [ennf transformation 9]
51. ! [X0] : (((~generous(X0) | old(X0)) & (generous(X0) | ~old(X0))) | (~rich(X0) & ~funny(X0))) [nnf transformation 34]
57. ! [X0] : (((~quiet(X0) | funny(X0)) | ((wise(X0) | old(X0)) & (~old(X0) | ~wise(X0)))) & (((old(X0) | ~wise(X0)) & (~old(X0) | wise(X0))) | (quiet(X0) & ~funny(X0)))) [nnf transformation 10]
58. ! [X0] : ((~quiet(X0) | funny(X0) | ((wise(X0) | old(X0)) & (~old(X0) | ~wise(X0)))) & (((old(X0) | ~wise(X0)) & (~old(X0) | wise(X0))) | (quiet(X0) & ~funny(X0)))) [flattening 57]
61. ! [X0] : ((creative(X0) | (~curious(X0) | curious(X0))) & ((curious(X0) & ~curious(X0)) | ~creative(X0))) [nnf transformation 13]
62. ! [X0] : ((creative(X0) | ~curious(X0) | curious(X0)) & ((curious(X0) & ~curious(X0)) | ~creative(X0))) [flattening 61]
95. ~generous(X0) | funny(X0) | creative(X0) [cnf transformation 33]
99. ~generous(X0) | old(X0) | ~funny(X0) [cnf transformation 51]
115. ~wise(X0) | ~generous(X0) [cnf transformation 37]
118. ~old(X0) | wise(X0) | ~funny(X0) [cnf transformation 58]
129. ~curious(X0) | ~creative(X0) [cnf transformation 62]
130. ~creative(X0) | curious(X0) [cnf transformation 62]
152. generous(lucy) [cnf transformation 24]
157. 1 <=> ! [X1] : ~creative(X1) [avatar definition]
158. ~creative(X1) <- (1) [avatar component clause 157]
257. ~creative(X0) [subsumption resolution 129,130]
258. 1 [avatar split clause 257,157]
352. funny(lucy) | creative(lucy) [resolution 95,152]
362. funny(lucy) <- (1) [subsumption resolution 352,158]
391. old(lucy) | ~funny(lucy) [resolution 99,152]
393. old(lucy) <- (1) [subsumption resolution 391,362]
402. wise(lucy) | ~funny(lucy) <- (1) [resolution 118,393]
404. wise(lucy) <- (1) [subsumption resolution 402,362]
459. ~generous(lucy) <- (1) [resolution 404,115]
470. $false <- (1) [subsumption resolution 459,152]
471. ~1 [avatar contradiction clause 470]
472. $false [avatar sat refutation 258,471]
% SZS output end Proof for 1383027613154645286747232
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
If someone is strong or not tall then john is both not quiet and not happy and vice versa.
Everyone who is not happy is not curious and vice versa.
Everyone who is not quiet or brave is both kind and not curious and vice versa.
If someone is either humble or strong then mary is either generous or not happy.
If mary is not strong or rich then lucy is not creative or kind and vice versa.
If john is not creative or not generous then someone is not strong.
Everyone who is both curious and not patient is patient and vice versa.
If john is generous then someone is both not patient and creative and vice versa.
Everyone who is either not curious or not humble is both not calm and humble and vice versa.
If mary is either not brave or kind then someone is not creative and vice versa.
If someone is either strong or patient then mary is both not humble and generous and vice versa.
Everyone who is creative or generous is both rich and not wise.
Everyone who is either not rich or not brave is both tall and kind.
If susan is not curious or kind then someone is not creative and vice versa.
Everyone who is both not strong and funny is both not old and curious and vice versa.
Everyone who is either not rich or patient is not quiet or not old and vice versa.
Paul is not calm.
John is creative.
Someone is either rich or tall.
Someone is either patient or quiet.
Someone is either not calm or patient. | Paul is not wise. | neutral | ((?[X]:((strong(X)|~tall(X))))<=>((~quiet(john)&~happy(john))))&
(![X]:(~happy(X)<=>~curious(X)))&
(![X]:((~quiet(X)|brave(X))<=>(kind(X)&~curious(X))))&
((?[X]:((humble(X)<~>strong(X))))=>((generous(mary)<~>~happy(mary))))&
(((~strong(mary)|rich(mary)))<=>((~creative(lucy)|kind(lucy))))&
(((~creative(john)|~generous(john)))=>(?[X]:(~strong(X))))&
(![X]:((curious(X)&~patient(X))<=>patient(X)))&
((generous(john))<=>(?[X]:((~patient(X)&creative(X)))))&
(![X]:((~curious(X)<~>~humble(X))<=>(~calm(X)&humble(X))))&
(((~brave(mary)<~>kind(mary)))<=>(?[X]:(~creative(X))))&
((?[X]:((strong(X)<~>patient(X))))<=>((~humble(mary)&generous(mary))))&
(![X]:((creative(X)|generous(X))=>(rich(X)&~wise(X))))&
(![X]:((~rich(X)<~>~brave(X))=>(tall(X)&kind(X))))&
(((~curious(susan)|kind(susan)))<=>(?[X]:(~creative(X))))&
(![X]:((~strong(X)&funny(X))<=>(~old(X)&curious(X))))&
(![X]:((~rich(X)<~>patient(X))<=>(~quiet(X)|~old(X))))&
(~calm(paul))&
(creative(john))&
(?[X]:((rich(X)<~>tall(X))))&
(?[X]:((patient(X)<~>quiet(X))))&
(?[X]:((~calm(X)<~>patient(X)))) | ~wise(paul) | [] | null | 0 |
Everyone who is either not patient or not kind is either tall or happy and vice versa. Everyone who is happy or not creative is either calm or not happy and vice versa. Everyone who is both rich and creative is both not old and calm and vice versa. If paul is not calm or patient then someone is happy and vice versa. Everyone who is either not funny or not creative is both not rich and not patient and vice versa. If mary is not tall or not curious then fred is both not brave and not creative. Everyone who is calm or curious is either not funny or not brave and vice versa. If someone is not curious then fred is rich or not funny and vice versa. If fred is tall or wise then someone is either not kind or kind and vice versa. If susan is curious or not brave then fred is either creative or not generous. If susan is both tall and not brave then someone is funny. Everyone who is both not generous and not quiet is not brave or not generous. Everyone who is not generous or rich is not funny. If mary is both not funny and not generous then someone is both not curious and not wise. If someone is either not wise or not curious then someone is rich and vice versa. If someone is not calm then someone is not calm or funny and vice versa. Susan is not patient. Fred is funny or brave. Susan is not wise. Someone is both not calm and strong. Someone is not generous or not quiet. Someone is not happy. Someone is strong or not patient. Lucy is either quiet or not curious. | Susan is strong. | neutral | (![X]:((~patient(X)<~>~kind(X))<=>(tall(X)<~>happy(X))))&
(![X]:((happy(X)|~creative(X))<=>(calm(X)<~>~happy(X))))&
(![X]:((rich(X)&creative(X))<=>(~old(X)&calm(X))))&
(((~calm(paul)|patient(paul)))<=>(?[X]:(happy(X))))&
(![X]:((~funny(X)<~>~creative(X))<=>(~rich(X)&~patient(X))))&
(((~tall(mary)|~curious(mary)))=>((~brave(fred)&~creative(fred))))&
(![X]:((calm(X)|curious(X))<=>(~funny(X)<~>~brave(X))))&
((?[X]:(~curious(X)))<=>((rich(fred)|~funny(fred))))&
(((tall(fred)|wise(fred)))<=>(?[X]:((~kind(X)<~>kind(X)))))&
(((curious(susan)|~brave(susan)))=>((creative(fred)<~>~generous(fred))))&
(((tall(susan)&~brave(susan)))=>(?[X]:(funny(X))))&
(![X]:((~generous(X)&~quiet(X))=>(~brave(X)|~generous(X))))&
(![X]:((~generous(X)|rich(X))=>~funny(X)))&
(((~funny(mary)&~generous(mary)))=>(?[X]:((~curious(X)&~wise(X)))))&
((?[X]:((~wise(X)<~>~curious(X))))<=>(?[X]:(rich(X))))&
((?[X]:(~calm(X)))<=>(?[X]:((~calm(X)|funny(X)))))&
(~patient(susan))&
((funny(fred)|brave(fred)))&
(~wise(susan))&
(?[X]:((~calm(X)&strong(X))))&
(?[X]:((~generous(X)|~quiet(X))))&
(?[X]:(~happy(X)))&
(?[X]:((strong(X)|~patient(X))))&
((quiet(lucy)<~>~curious(lucy))) | strong(susan) | [] | null | 0 |
Everyone who is tall is both rich and calm and vice versa.
If someone is not humble or wise then someone is not generous and vice versa.
Everyone who is not quiet is both tall and not generous.
If fred is both not patient and not brave then fred is both not generous and not humble and vice versa.
Everyone who is either not old or patient is not happy and vice versa.
If mary is creative then someone is either tall or not strong and vice versa.
If someone is kind then someone is either wise or rich.
If someone is generous then someone is wise or humble and vice versa.
Everyone who is both happy and not rich is either old or not happy and vice versa.
Everyone who is quiet is creative and vice versa.
If fred is happy or not quiet then someone is either strong or patient and vice versa.
Everyone who is funny is either not curious or happy and vice versa.
Everyone who is calm is both strong and generous 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.
Someone is old or not quiet.
Lucy is not rich.
Someone is either not old or not strong.
Someone is tall or brave.
Someone is both funny and not kind.
Someone is funny or not patient.
Someone is old or not old.
Someone is not creative or not rich. | Lucy is not curious. | entailment | (![X]:(tall(X)<=>(rich(X)&calm(X))))&
((?[X]:((~humble(X)|wise(X))))<=>(?[X]:(~generous(X))))&
(![X]:(~quiet(X)=>(tall(X)&~generous(X))))&
(((~patient(fred)&~brave(fred)))<=>((~generous(fred)&~humble(fred))))&
(![X]:((~old(X)<~>patient(X))<=>~happy(X)))&
((creative(mary))<=>(?[X]:((tall(X)<~>~strong(X)))))&
((?[X]:(kind(X)))=>(?[X]:((wise(X)<~>rich(X)))))&
((?[X]:(generous(X)))<=>(?[X]:((wise(X)|humble(X)))))&
(![X]:((happy(X)&~rich(X))<=>(old(X)<~>~happy(X))))&
(![X]:(quiet(X)<=>creative(X)))&
(((happy(fred)|~quiet(fred)))<=>(?[X]:((strong(X)<~>patient(X)))))&
(![X]:(funny(X)<=>(~curious(X)<~>happy(X))))&
(![X]:(calm(X)<=>(strong(X)&generous(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]:((old(X)|~quiet(X))))&
(~rich(lucy))&
(?[X]:((~old(X)<~>~strong(X))))&
(?[X]:((tall(X)|brave(X))))&
(?[X]:((funny(X)&~kind(X))))&
(?[X]:((funny(X)|~patient(X))))&
(?[X]:((old(X)|~old(X))))&
(?[X]:((~creative(X)|~rich(X)))) | ~curious(lucy) | [
"p8",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 4729235587490299953608826
% SZS output start Proof for 4729235587490299953608826
9. ! [X0] : ((~rich(X0) & happy(X0)) <=> (old(X0) <~> ~happy(X0))) [input p8]
16. ! [X0] : ((~kind(X0) | old(X0)) => (~curious(X0) & old(X0))) [input p15]
18. ~rich(lucy) [input p17]
25. curious(lucy) [input hypothesis]
33. ! [X0] : ((~curious(X0) & old(X0)) | (kind(X0) & ~old(X0))) [ennf transformation 16]
57. ! [X0] : (((~rich(X0) & happy(X0)) | ((old(X0) | happy(X0)) & (~happy(X0) | ~old(X0)))) & (((happy(X0) | ~old(X0)) & (~happy(X0) | old(X0))) | (rich(X0) | ~happy(X0)))) [nnf transformation 9]
58. ! [X0] : (((~rich(X0) & happy(X0)) | ((old(X0) | happy(X0)) & (~happy(X0) | ~old(X0)))) & (((happy(X0) | ~old(X0)) & (~happy(X0) | old(X0))) | rich(X0) | ~happy(X0))) [flattening 57]
110. ~happy(X0) | old(X0) | rich(X0) | ~happy(X0) [cnf transformation 58]
113. happy(X0) | old(X0) | happy(X0) [cnf transformation 58]
136. ~curious(X0) | ~old(X0) [cnf transformation 33]
139. ~rich(lucy) [cnf transformation 18]
148. curious(lucy) [cnf transformation 25]
149. ~happy(X0) | old(X0) | rich(X0) [duplicate literal removal 110]
150. happy(X0) | old(X0) [duplicate literal removal 113]
251. old(X0) | rich(X0) [subsumption resolution 149,150]
368. ~old(lucy) [resolution 136,148]
376. rich(lucy) [resolution 251,368]
377. $false [subsumption resolution 376,139]
% SZS output end Proof for 4729235587490299953608826
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not old or not tall then someone is strong or not strong and vice versa.
If someone is both not patient and not quiet then someone is either not generous or not tall.
Everyone who is old is generous or funny and vice versa.
If someone is both not wise and strong then someone is either not brave or not wise.
If someone is either brave or not calm then someone is not wise or not patient and vice versa.
Everyone who is either brave or not brave is either generous or funny and vice versa.
If someone is both generous and creative then susan is both generous and rich and vice versa.
Everyone who is not wise is both kind and not calm.
If someone is strong then someone is not brave or patient and vice versa.
Everyone who is either wise or patient is either not kind or not patient and vice versa.
If alice is not strong then someone is both not tall and not kind and vice versa.
Everyone who is strong or kind is not funny or wise and vice versa.
Everyone who is both not calm and old is both not rich and not old and vice versa.
Everyone who is not patient or not creative is not old and vice versa.
If john is not quiet then alice is not creative or old and vice versa.
Everyone who is generous or not old is both not generous and not rich.
Someone is wise.
Fred is not rich or not strong.
Someone is not humble.
Lucy is happy or generous.
Alice is not tall or not funny.
Someone is not wise or kind. | Alice is generous. | contradiction | ((?[X]:((~old(X)|~tall(X))))<=>(?[X]:((strong(X)|~strong(X)))))&
((?[X]:((~patient(X)&~quiet(X))))=>(?[X]:((~generous(X)<~>~tall(X)))))&
(![X]:(old(X)<=>(generous(X)|funny(X))))&
((?[X]:((~wise(X)&strong(X))))=>(?[X]:((~brave(X)<~>~wise(X)))))&
((?[X]:((brave(X)<~>~calm(X))))<=>(?[X]:((~wise(X)|~patient(X)))))&
(![X]:((brave(X)<~>~brave(X))<=>(generous(X)<~>funny(X))))&
((?[X]:((generous(X)&creative(X))))<=>((generous(susan)&rich(susan))))&
(![X]:(~wise(X)=>(kind(X)&~calm(X))))&
((?[X]:(strong(X)))<=>(?[X]:((~brave(X)|patient(X)))))&
(![X]:((wise(X)<~>patient(X))<=>(~kind(X)<~>~patient(X))))&
((~strong(alice))<=>(?[X]:((~tall(X)&~kind(X)))))&
(![X]:((strong(X)|kind(X))<=>(~funny(X)|wise(X))))&
(![X]:((~calm(X)&old(X))<=>(~rich(X)&~old(X))))&
(![X]:((~patient(X)|~creative(X))<=>~old(X)))&
((~quiet(john))<=>((~creative(alice)|old(alice))))&
(![X]:((generous(X)|~old(X))=>(~generous(X)&~rich(X))))&
(?[X]:(wise(X)))&
((~rich(fred)|~strong(fred)))&
(?[X]:(~humble(X)))&
((happy(lucy)|generous(lucy)))&
((~tall(alice)|~funny(alice)))&
(?[X]:((~wise(X)|kind(X)))) | generous(alice) | [
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1982589989147811059796369
% SZS output start Proof for 1982589989147811059796369
16. ! [X0] : ((~old(X0) | generous(X0)) => (~rich(X0) & ~generous(X0))) [input p15]
23. generous(alice) [input hypothesis]
34. ! [X0] : ((~rich(X0) & ~generous(X0)) | (old(X0) & ~generous(X0))) [ennf transformation 16]
142. ~generous(X0) | ~generous(X0) [cnf transformation 34]
150. generous(alice) [cnf transformation 23]
151. ~generous(X0) [duplicate literal removal 142]
327. $false [subsumption resolution 150,151]
% SZS output end Proof for 1982589989147811059796369
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall is funny or not patient and vice versa.
Everyone who is both not brave and not kind is both not curious and patient and vice versa.
If someone is not generous then susan is old and vice versa.
Everyone who is not funny is not generous or kind.
If someone is either quiet or old then someone is either generous or old and vice versa.
Everyone who is either patient or rich is strong or not calm.
Everyone who is not strong or not happy is both not generous and happy.
If someone is not generous or not tall then john is not funny and vice versa.
Everyone who is both not kind and creative is either not old or kind.
Everyone who is either humble or old is both rich and not happy and vice versa.
Everyone who is both brave and strong is either curious or funny.
Everyone who is not curious is creative or wise and vice versa.
Everyone who is either rich or not rich is either not calm or not creative and vice versa.
If someone is both generous and not creative then someone is either happy or not strong.
If someone is either not tall or happy then susan is either not strong or not creative and vice versa.
Everyone who is either not generous or funny is not happy or rich and vice versa.
Lucy is both not strong and not old.
Someone is quiet.
Someone is creative.
Paul is quiet or not generous.
Someone is both not calm and not strong.
Lucy is strong or tall.
Someone is not generous or strong. | Susan is not humble. | contradiction | (![X]:(tall(X)<=>(funny(X)|~patient(X))))&
(![X]:((~brave(X)&~kind(X))<=>(~curious(X)&patient(X))))&
((?[X]:(~generous(X)))<=>(old(susan)))&
(![X]:(~funny(X)=>(~generous(X)|kind(X))))&
((?[X]:((quiet(X)<~>old(X))))<=>(?[X]:((generous(X)<~>old(X)))))&
(![X]:((patient(X)<~>rich(X))=>(strong(X)|~calm(X))))&
(![X]:((~strong(X)|~happy(X))=>(~generous(X)&happy(X))))&
((?[X]:((~generous(X)|~tall(X))))<=>(~funny(john)))&
(![X]:((~kind(X)&creative(X))=>(~old(X)<~>kind(X))))&
(![X]:((humble(X)<~>old(X))<=>(rich(X)&~happy(X))))&
(![X]:((brave(X)&strong(X))=>(curious(X)<~>funny(X))))&
(![X]:(~curious(X)<=>(creative(X)|wise(X))))&
(![X]:((rich(X)<~>~rich(X))<=>(~calm(X)<~>~creative(X))))&
((?[X]:((generous(X)&~creative(X))))=>(?[X]:((happy(X)<~>~strong(X)))))&
((?[X]:((~tall(X)<~>happy(X))))<=>((~strong(susan)<~>~creative(susan))))&
(![X]:((~generous(X)<~>funny(X))<=>(~happy(X)|rich(X))))&
((~strong(lucy)&~old(lucy)))&
(?[X]:(quiet(X)))&
(?[X]:(creative(X)))&
((quiet(paul)|~generous(paul)))&
(?[X]:((~calm(X)&~strong(X))))&
((strong(lucy)|tall(lucy)))&
(?[X]:((~generous(X)|strong(X)))) | ~humble(susan) | [
"p2",
"p6",
"p9",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 714617225346375897877761
% SZS output start Proof for 714617225346375897877761
3. ? [X0] : ~generous(X0) <=> old(susan) [input p2]
7. ! [X0] : ((~happy(X0) | ~strong(X0)) => (happy(X0) & ~generous(X0))) [input p6]
10. ! [X0] : ((humble(X0) <~> old(X0)) <=> (~happy(X0) & rich(X0))) [input p9]
17. ~old(lucy) & ~strong(lucy) [input p16]
24. ~humble(susan) [input hypothesis]
31. ! [X0] : ((happy(X0) & ~generous(X0)) | (happy(X0) & strong(X0))) [ennf transformation 7]
41. (? [X0] : ~generous(X0) | ~old(susan)) & (old(susan) | ! [X0] : generous(X0)) [nnf transformation 3]
42. (? [X0] : ~generous(X0) | ~old(susan)) & (old(susan) | ! [X1] : generous(X1)) [rectify 41]
43. ? [X0] : ~generous(X0) => ~generous(sK0) [choice axiom]
44. (~generous(sK0) | ~old(susan)) & (old(susan) | ! [X1] : generous(X1)) [skolemisation 42,43]
56. ! [X0] : ((((~old(X0) | ~humble(X0)) & (old(X0) | humble(X0))) | (happy(X0) | ~rich(X0))) & ((~happy(X0) & rich(X0)) | ((humble(X0) | ~old(X0)) & (old(X0) | ~humble(X0))))) [nnf transformation 10]
57. ! [X0] : ((((~old(X0) | ~humble(X0)) & (old(X0) | humble(X0))) | happy(X0) | ~rich(X0)) & ((~happy(X0) & rich(X0)) | ((humble(X0) | ~old(X0)) & (old(X0) | ~humble(X0))))) [flattening 56]
87. old(susan) | generous(X1) [cnf transformation 44]
100. ~generous(X0) | strong(X0) [cnf transformation 31]
103. happy(X0) | happy(X0) [cnf transformation 31]
112. ~happy(X0) | humble(X0) | ~old(X0) [cnf transformation 57]
144. ~strong(lucy) [cnf transformation 17]
153. ~humble(susan) [cnf transformation 24]
159. happy(X0) [duplicate literal removal 103]
161. 1 <=> old(susan) [avatar definition]
162. old(susan) <- (1) [avatar component clause 161]
170. 3 <=> ! [X1] : generous(X1) [avatar definition]
171. generous(X1) <- (3) [avatar component clause 170]
172. 3 | 1 [avatar split clause 87,161,170]
227. ~old(X0) | humble(X0) [subsumption resolution 112,159]
280. humble(susan) <- (1) [resolution 227,162]
281. $false <- (1) [subsumption resolution 280,153]
282. ~1 [avatar contradiction clause 281]
283. strong(X0) <- (3) [resolution 171,100]
287. $false <- (3) [resolution 283,144]
292. ~3 [avatar contradiction clause 287]
293. $false [avatar sat refutation 172,282,292]
% SZS output end Proof for 714617225346375897877761
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not patient or wise is both funny and tall. If someone is happy then mary is not generous or funny. If someone is funny then mary is either brave or not curious. Everyone who is not old is not patient. If someone is both not quiet and quiet then mary is happy. If someone is either not brave or not curious then fred is both not funny and strong and vice versa. If someone is old or not old then someone is both rich and happy. If someone is not strong or tall then john is rich or humble and vice versa. If someone is creative then someone is either not tall or happy and vice versa. Everyone who is not wise is not strong. Everyone who is not strong is both not humble and patient and vice versa. If someone is strong or not quiet then someone is both not patient and not calm. If someone is either not tall or happy then john is not wise. If fred is not creative then susan is both not happy and happy. Everyone who is not strong or brave is either not curious or quiet. Everyone who is both not rich and brave is both generous and not kind. Someone is rich or patient. John is not old or curious. Fred is both not curious and happy. Someone is not tall or not strong. Someone is both not calm and kind. Someone is not curious. Paul is strong. | Paul is not funny. | contradiction | (![X]:((~patient(X)|wise(X))=>(funny(X)&tall(X))))&
((?[X]:(happy(X)))=>((~generous(mary)|funny(mary))))&
((?[X]:(funny(X)))=>((brave(mary)<~>~curious(mary))))&
(![X]:(~old(X)=>~patient(X)))&
((?[X]:((~quiet(X)&quiet(X))))=>(happy(mary)))&
((?[X]:((~brave(X)<~>~curious(X))))<=>((~funny(fred)&strong(fred))))&
((?[X]:((old(X)|~old(X))))=>(?[X]:((rich(X)&happy(X)))))&
((?[X]:((~strong(X)|tall(X))))<=>((rich(john)|humble(john))))&
((?[X]:(creative(X)))<=>(?[X]:((~tall(X)<~>happy(X)))))&
(![X]:(~wise(X)=>~strong(X)))&
(![X]:(~strong(X)<=>(~humble(X)&patient(X))))&
((?[X]:((strong(X)|~quiet(X))))=>(?[X]:((~patient(X)&~calm(X)))))&
((?[X]:((~tall(X)<~>happy(X))))=>(~wise(john)))&
((~creative(fred))=>((~happy(susan)&happy(susan))))&
(![X]:((~strong(X)|brave(X))=>(~curious(X)<~>quiet(X))))&
(![X]:((~rich(X)&brave(X))=>(generous(X)&~kind(X))))&
(?[X]:((rich(X)|patient(X))))&
((~old(john)|curious(john)))&
((~curious(fred)&happy(fred)))&
(?[X]:((~tall(X)|~strong(X))))&
(?[X]:((~calm(X)&kind(X))))&
(?[X]:(~curious(X)))&
(strong(paul)) | ~funny(paul) | [
"p0",
"p9",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 3614878315904673063933099
% SZS output start Proof for 3614878315904673063933099
1. ! [X0] : ((wise(X0) | ~patient(X0)) => (tall(X0) & funny(X0))) [input p0]
10. ! [X0] : (~wise(X0) => ~strong(X0)) [input p9]
23. strong(paul) [input p22]
24. ~funny(paul) [input hypothesis]
30. ! [X0] : ((tall(X0) & funny(X0)) | (~wise(X0) & patient(X0))) [ennf transformation 1]
37. ! [X0] : (~strong(X0) | wise(X0)) [ennf transformation 10]
79. ~wise(X0) | funny(X0) [cnf transformation 30]
105. ~strong(X0) | wise(X0) [cnf transformation 37]
128. strong(paul) [cnf transformation 23]
129. ~funny(paul) [cnf transformation 24]
325. wise(paul) [resolution 105,128]
328. funny(paul) [resolution 325,79]
329. $false [subsumption resolution 328,129]
% SZS output end Proof for 3614878315904673063933099
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If alice is both strong and not patient then someone is not funny.
If susan is not curious then alice is not funny or not quiet and vice versa.
If paul is not strong then someone is either not creative or not strong and vice versa.
Everyone who is not creative or not funny is brave and vice versa.
If fred is brave then someone is funny and vice versa.
Everyone who is both not calm and patient is either not curious or not calm and vice versa.
Everyone who is both old and not curious is rich.
If susan is both rich and not quiet then alice is either not patient or not happy and vice versa.
If fred is not funny then someone is creative or not old and vice versa.
Everyone who is both tall and not humble is either brave or curious and vice versa.
If john is either rich or not tall then mary is either generous or creative.
If paul is rich then someone is both not tall and wise and vice versa.
Everyone who is either not curious or generous is either funny or not curious.
Everyone who is either old or not generous is old or kind and vice versa.
Everyone who is old is not funny.
Everyone who is either tall or not brave is funny and vice versa.
Mary is either tall or humble.
Someone is both patient and curious.
Paul is not generous or not curious.
Susan is either not old or quiet.
Someone is either humble or brave.
Paul is not creative or not tall.
Susan is not curious.
Fred is humble or strong. | Fred is not generous. | entailment | (((strong(alice)&~patient(alice)))=>(?[X]:(~funny(X))))&
((~curious(susan))<=>((~funny(alice)|~quiet(alice))))&
((~strong(paul))<=>(?[X]:((~creative(X)<~>~strong(X)))))&
(![X]:((~creative(X)|~funny(X))<=>brave(X)))&
((brave(fred))<=>(?[X]:(funny(X))))&
(![X]:((~calm(X)&patient(X))<=>(~curious(X)<~>~calm(X))))&
(![X]:((old(X)&~curious(X))=>rich(X)))&
(((rich(susan)&~quiet(susan)))<=>((~patient(alice)<~>~happy(alice))))&
((~funny(fred))<=>(?[X]:((creative(X)|~old(X)))))&
(![X]:((tall(X)&~humble(X))<=>(brave(X)<~>curious(X))))&
(((rich(john)<~>~tall(john)))=>((generous(mary)<~>creative(mary))))&
((rich(paul))<=>(?[X]:((~tall(X)&wise(X)))))&
(![X]:((~curious(X)<~>generous(X))=>(funny(X)<~>~curious(X))))&
(![X]:((old(X)<~>~generous(X))<=>(old(X)|kind(X))))&
(![X]:(old(X)=>~funny(X)))&
(![X]:((tall(X)<~>~brave(X))<=>funny(X)))&
((tall(mary)<~>humble(mary)))&
(?[X]:((patient(X)&curious(X))))&
((~generous(paul)|~curious(paul)))&
((~old(susan)<~>quiet(susan)))&
(?[X]:((humble(X)<~>brave(X))))&
((~creative(paul)|~tall(paul)))&
(~curious(susan))&
((humble(fred)|strong(fred))) | ~generous(fred) | [
"p3",
"p4",
"p8",
"p9",
"p12",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 39357060612730937571269
% SZS output start Proof for 39357060612730937571269
4. ! [X0] : ((~funny(X0) | ~creative(X0)) <=> brave(X0)) [input p3]
5. brave(fred) <=> ? [X0] : funny(X0) [input p4]
9. ~funny(fred) <=> ? [X0] : (~old(X0) | creative(X0)) [input p8]
10. ! [X0] : ((~humble(X0) & tall(X0)) <=> (brave(X0) <~> curious(X0))) [input p9]
13. ! [X0] : ((~curious(X0) <~> generous(X0)) => (funny(X0) <~> ~curious(X0))) [input p12]
15. ! [X0] : (old(X0) => ~funny(X0)) [input p14]
16. ! [X0] : ((tall(X0) <~> ~brave(X0)) <=> funny(X0)) [input p15]
25. generous(fred) [input hypothesis]
31. ! [X0] : ((funny(X0) <~> ~curious(X0)) | (~curious(X0) <=> generous(X0))) [ennf transformation 13]
32. ! [X0] : (~funny(X0) | ~old(X0)) [ennf transformation 15]
41. ! [X0] : (((~funny(X0) | ~creative(X0)) | ~brave(X0)) & (brave(X0) | (funny(X0) & creative(X0)))) [nnf transformation 4]
42. ! [X0] : ((~funny(X0) | ~creative(X0) | ~brave(X0)) & (brave(X0) | (funny(X0) & creative(X0)))) [flattening 41]
43. (brave(fred) | ! [X0] : ~funny(X0)) & (? [X0] : funny(X0) | ~brave(fred)) [nnf transformation 5]
44. (brave(fred) | ! [X0] : ~funny(X0)) & (? [X1] : funny(X1) | ~brave(fred)) [rectify 43]
45. ? [X1] : funny(X1) => funny(sK2) [choice axiom]
46. (brave(fred) | ! [X0] : ~funny(X0)) & (funny(sK2) | ~brave(fred)) [skolemisation 44,45]
51. (~funny(fred) | ! [X0] : (old(X0) & ~creative(X0))) & (? [X0] : (~old(X0) | creative(X0)) | funny(fred)) [nnf transformation 9]
52. (~funny(fred) | ! [X0] : (old(X0) & ~creative(X0))) & (? [X1] : (~old(X1) | creative(X1)) | funny(fred)) [rectify 51]
53. ? [X1] : (~old(X1) | creative(X1)) => (~old(sK3) | creative(sK3)) [choice axiom]
54. (~funny(fred) | ! [X0] : (old(X0) & ~creative(X0))) & ((~old(sK3) | creative(sK3)) | funny(fred)) [skolemisation 52,53]
55. ! [X0] : (((~humble(X0) & tall(X0)) | ((brave(X0) | ~curious(X0)) & (curious(X0) | ~brave(X0)))) & (((~curious(X0) | ~brave(X0)) & (curious(X0) | brave(X0))) | (humble(X0) | ~tall(X0)))) [nnf transformation 10]
56. ! [X0] : (((~humble(X0) & tall(X0)) | ((brave(X0) | ~curious(X0)) & (curious(X0) | ~brave(X0)))) & (((~curious(X0) | ~brave(X0)) & (curious(X0) | brave(X0))) | humble(X0) | ~tall(X0))) [flattening 55]
62. ! [X0] : (((curious(X0) | ~funny(X0)) & (~curious(X0) | funny(X0))) | ((~curious(X0) | ~generous(X0)) & (generous(X0) | curious(X0)))) [nnf transformation 31]
65. ! [X0] : ((((brave(X0) | ~tall(X0)) & (~brave(X0) | tall(X0))) | ~funny(X0)) & (funny(X0) | ((tall(X0) | brave(X0)) & (~brave(X0) | ~tall(X0))))) [nnf transformation 16]
81. brave(X0) | creative(X0) [cnf transformation 42]
82. brave(X0) | funny(X0) [cnf transformation 42]
84. funny(sK2) | ~brave(fred) [cnf transformation 46]
100. ~funny(fred) | ~creative(X0) [cnf transformation 54]
101. ~funny(fred) | old(X0) [cnf transformation 54]
104. ~brave(X0) | curious(X0) | tall(X0) [cnf transformation 56]
116. ~curious(X0) | funny(X0) | ~curious(X0) | ~generous(X0) [cnf transformation 62]
125. ~old(X0) | ~funny(X0) [cnf transformation 32]
126. funny(X0) | ~brave(X0) | ~tall(X0) [cnf transformation 65]
129. brave(X0) | ~tall(X0) | ~funny(X0) [cnf transformation 65]
142. generous(fred) [cnf transformation 25]
145. ~generous(X0) | funny(X0) | ~curious(X0) [duplicate literal removal 116]
200. 12 <=> ! [X0] : ~funny(X0) [avatar definition]
201. ~funny(X0) <- (12) [avatar component clause 200]
203. 13 <=> brave(fred) [avatar definition]
204. ~brave(fred) <- (~13) [avatar component clause 203]
208. 14 <=> funny(sK2) [avatar definition]
210. funny(sK2) <- (14) [avatar component clause 208]
211. ~13 | 14 [avatar split clause 84,208,203]
232. 18 <=> ! [X0] : old(X0) [avatar definition]
233. old(X0) <- (18) [avatar component clause 232]
235. 19 <=> funny(fred) [avatar definition]
238. 18 | ~19 [avatar split clause 101,235,232]
240. 20 <=> ! [X0] : ~creative(X0) [avatar definition]
241. ~creative(X0) <- (20) [avatar component clause 240]
242. 20 | ~19 [avatar split clause 100,235,240]
291. ~tall(X0) | brave(X0) [subsumption resolution 129,82]
292. ~tall(X0) | funny(X0) [subsumption resolution 126,291]
380. curious(X0) | tall(X0) | funny(X0) [resolution 104,82]
385. curious(X0) | funny(X0) [subsumption resolution 380,292]
439. funny(fred) | ~curious(fred) [resolution 145,142]
444. funny(fred) [subsumption resolution 439,385]
445. 19 [avatar split clause 444,235]
452. $false <- (12, 14) [resolution 201,210]
453. ~12 | ~14 [avatar contradiction clause 452]
457. creative(fred) <- (~13) [resolution 204,81]
458. $false <- (~13, 20) [subsumption resolution 457,241]
459. 13 | ~20 [avatar contradiction clause 458]
472. ~funny(X2) <- (18) [resolution 233,125]
475. 12 | ~18 [avatar split clause 472,232,200]
476. $false [avatar sat refutation 211,238,242,445,453,459,475]
% SZS output end Proof for 39357060612730937571269
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If susan is either not patient or not brave then paul is both not happy and humble. Everyone who is both wise and not tall is not humble or calm and vice versa. If someone is both not old and kind then someone is both not rich and not calm. If someone is strong or not calm then someone is not tall and vice versa. Everyone who is both rich and not calm is either not tall or not creative. Everyone who is generous is not brave. If someone is strong then susan is both not curious and patient and vice versa. If someone is creative or not generous then someone is both kind and not humble. Everyone who is not calm or strong is not creative and vice versa. Everyone who is not funny is old or not brave and vice versa. If fred is old or generous then mary is not tall and vice versa. If someone is either generous or old then someone is humble or not tall. Everyone who is both tall and not curious is kind and vice versa. If mary is generous or not calm then fred is both not wise and kind and vice versa. Everyone who is either wise or not creative is both not wise and strong and vice versa. Someone is either not tall or tall. Someone is not curious. Someone is both old and not curious. Alice is both kind and happy. Someone is humble. Someone is not curious or not creative. Someone is either not happy or creative. | Mary is funny. | contradiction | (((~patient(susan)<~>~brave(susan)))=>((~happy(paul)&humble(paul))))&
(![X]:((wise(X)&~tall(X))<=>(~humble(X)|calm(X))))&
((?[X]:((~old(X)&kind(X))))=>(?[X]:((~rich(X)&~calm(X)))))&
((?[X]:((strong(X)|~calm(X))))<=>(?[X]:(~tall(X))))&
(![X]:((rich(X)&~calm(X))=>(~tall(X)<~>~creative(X))))&
(![X]:(generous(X)=>~brave(X)))&
((?[X]:(strong(X)))<=>((~curious(susan)&patient(susan))))&
((?[X]:((creative(X)|~generous(X))))=>(?[X]:((kind(X)&~humble(X)))))&
(![X]:((~calm(X)|strong(X))<=>~creative(X)))&
(![X]:(~funny(X)<=>(old(X)|~brave(X))))&
(((old(fred)|generous(fred)))<=>(~tall(mary)))&
((?[X]:((generous(X)<~>old(X))))=>(?[X]:((humble(X)|~tall(X)))))&
(![X]:((tall(X)&~curious(X))<=>kind(X)))&
(((generous(mary)|~calm(mary)))<=>((~wise(fred)&kind(fred))))&
(![X]:((wise(X)<~>~creative(X))<=>(~wise(X)&strong(X))))&
(?[X]:((~tall(X)<~>tall(X))))&
(?[X]:(~curious(X)))&
(?[X]:((old(X)&~curious(X))))&
((kind(alice)&happy(alice)))&
(?[X]:(humble(X)))&
(?[X]:((~curious(X)|~creative(X))))&
(?[X]:((~happy(X)<~>creative(X)))) | funny(mary) | [
"p1",
"p5",
"p7",
"p9",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 4240217830473100754469775
% SZS output start Proof for 4240217830473100754469775
2. ! [X0] : ((~tall(X0) & wise(X0)) <=> (calm(X0) | ~humble(X0))) [input p1]
6. ! [X0] : (generous(X0) => ~brave(X0)) [input p5]
8. ? [X0] : (~generous(X0) | creative(X0)) => ? [X0] : (~humble(X0) & kind(X0)) [input p7]
10. ! [X0] : (~funny(X0) <=> (~brave(X0) | old(X0))) [input p9]
13. ! [X0] : ((~curious(X0) & tall(X0)) <=> kind(X0)) [input p12]
23. funny(mary) [input hypothesis]
26. ? [X0] : (~generous(X0) | creative(X0)) => ? [X1] : (~humble(X1) & kind(X1)) [rectify 8]
28. ! [X0] : ((~brave(X0) | old(X0)) => ~funny(X0)) [unused predicate definition removal 10]
33. ! [X0] : (~brave(X0) | ~generous(X0)) [ennf transformation 6]
34. ? [X1] : (~humble(X1) & kind(X1)) | ! [X0] : (generous(X0) & ~creative(X0)) [ennf transformation 26]
35. ! [X0] : (~funny(X0) | (brave(X0) & ~old(X0))) [ennf transformation 28]
38. ! [X0] : (((~tall(X0) & wise(X0)) | (~calm(X0) & humble(X0))) & ((calm(X0) | ~humble(X0)) | (tall(X0) | ~wise(X0)))) [nnf transformation 2]
39. ! [X0] : (((~tall(X0) & wise(X0)) | (~calm(X0) & humble(X0))) & (calm(X0) | ~humble(X0) | tall(X0) | ~wise(X0))) [flattening 38]
53. ? [X0] : (~humble(X0) & kind(X0)) | ! [X1] : (generous(X1) & ~creative(X1)) [rectify 34]
54. ? [X0] : (~humble(X0) & kind(X0)) => (~humble(sK4) & kind(sK4)) [choice axiom]
55. (~humble(sK4) & kind(sK4)) | ! [X1] : (generous(X1) & ~creative(X1)) [skolemisation 53,54]
64. ! [X0] : (((~curious(X0) & tall(X0)) | ~kind(X0)) & (kind(X0) | (curious(X0) | ~tall(X0)))) [nnf transformation 13]
65. ! [X0] : (((~curious(X0) & tall(X0)) | ~kind(X0)) & (kind(X0) | curious(X0) | ~tall(X0))) [flattening 64]
91. ~tall(X0) | humble(X0) [cnf transformation 39]
97. ~generous(X0) | ~brave(X0) [cnf transformation 33]
102. kind(sK4) | generous(X1) [cnf transformation 55]
104. ~humble(sK4) | generous(X1) [cnf transformation 55]
109. ~funny(X0) | brave(X0) [cnf transformation 35]
116. ~kind(X0) | tall(X0) [cnf transformation 65]
140. funny(mary) [cnf transformation 23]
207. 15 <=> ! [X1] : generous(X1) [avatar definition]
208. generous(X1) <- (15) [avatar component clause 207]
210. 16 <=> humble(sK4) [avatar definition]
213. 15 | ~16 [avatar split clause 104,210,207]
219. 18 <=> kind(sK4) [avatar definition]
221. kind(sK4) <- (18) [avatar component clause 219]
222. 15 | 18 [avatar split clause 102,219,207]
285. brave(mary) [resolution 109,140]
287. tall(sK4) <- (18) [resolution 116,221]
290. humble(sK4) <- (18) [resolution 287,91]
293. 16 | ~18 [avatar split clause 290,219,210]
294. ~brave(X0) <- (15) [resolution 208,97]
297. $false <- (15) [resolution 294,285]
298. ~15 [avatar contradiction clause 297]
299. $false [avatar sat refutation 213,222,293,298]
% SZS output end Proof for 4240217830473100754469775
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not brave and old then mary is both old and strong and vice versa. Everyone who is not wise or not old is curious and vice versa. Everyone who is either calm or humble is both not generous and kind and vice versa. If someone is either brave or patient then someone is both not curious and not tall and vice versa. Everyone who is either not tall or not generous is humble and vice versa. If paul is patient then someone is both not tall and not generous and vice versa. Everyone who is both not tall and creative is humble or not wise and vice versa. Everyone who is not wise or kind is patient and vice versa. If mary is both tall and not rich then lucy is either creative or funny. If alice is both not brave and kind then someone is old. Everyone who is either not humble or not calm is quiet or not generous and vice versa. If john is both not tall and not calm then susan is not happy. Everyone who is not tall or not quiet is generous and vice versa. Everyone who is either not happy or generous is either happy or not strong. If fred is strong or not patient then fred is curious and vice versa. Someone is either strong or patient. Someone is either brave or creative. Someone is tall. Someone is not rich or calm. John is both not quiet and wise. Paul is either happy or humble. | Paul is generous. | entailment | ((?[X]:((~brave(X)&old(X))))<=>((old(mary)&strong(mary))))&
(![X]:((~wise(X)|~old(X))<=>curious(X)))&
(![X]:((calm(X)<~>humble(X))<=>(~generous(X)&kind(X))))&
((?[X]:((brave(X)<~>patient(X))))<=>(?[X]:((~curious(X)&~tall(X)))))&
(![X]:((~tall(X)<~>~generous(X))<=>humble(X)))&
((patient(paul))<=>(?[X]:((~tall(X)&~generous(X)))))&
(![X]:((~tall(X)&creative(X))<=>(humble(X)|~wise(X))))&
(![X]:((~wise(X)|kind(X))<=>patient(X)))&
(((tall(mary)&~rich(mary)))=>((creative(lucy)<~>funny(lucy))))&
(((~brave(alice)&kind(alice)))=>(?[X]:(old(X))))&
(![X]:((~humble(X)<~>~calm(X))<=>(quiet(X)|~generous(X))))&
(((~tall(john)&~calm(john)))=>(~happy(susan)))&
(![X]:((~tall(X)|~quiet(X))<=>generous(X)))&
(![X]:((~happy(X)<~>generous(X))=>(happy(X)<~>~strong(X))))&
(((strong(fred)|~patient(fred)))<=>(curious(fred)))&
(?[X]:((strong(X)<~>patient(X))))&
(?[X]:((brave(X)<~>creative(X))))&
(?[X]:(tall(X)))&
(?[X]:((~rich(X)|calm(X))))&
((~quiet(john)&wise(john)))&
((happy(paul)<~>humble(paul))) | generous(paul) | [
"p4",
"p6",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 7769524052846449674681692
% SZS output start Proof for 7769524052846449674681692
5. ! [X0] : ((~tall(X0) <~> ~generous(X0)) <=> humble(X0)) [input p4]
7. ! [X0] : ((creative(X0) & ~tall(X0)) <=> (~wise(X0) | humble(X0))) [input p6]
13. ! [X0] : ((~quiet(X0) | ~tall(X0)) <=> generous(X0)) [input p12]
22. ~generous(paul) [input hypothesis]
45. ! [X0] : ((((generous(X0) | tall(X0)) & (~generous(X0) | ~tall(X0))) | ~humble(X0)) & (humble(X0) | ((~tall(X0) | generous(X0)) & (~generous(X0) | tall(X0))))) [nnf transformation 5]
50. ! [X0] : (((creative(X0) & ~tall(X0)) | (wise(X0) & ~humble(X0))) & ((~wise(X0) | humble(X0)) | (~creative(X0) | tall(X0)))) [nnf transformation 7]
51. ! [X0] : (((creative(X0) & ~tall(X0)) | (wise(X0) & ~humble(X0))) & (~wise(X0) | humble(X0) | ~creative(X0) | tall(X0))) [flattening 50]
59. ! [X0] : (((~quiet(X0) | ~tall(X0)) | ~generous(X0)) & (generous(X0) | (quiet(X0) & tall(X0)))) [nnf transformation 13]
60. ! [X0] : ((~quiet(X0) | ~tall(X0) | ~generous(X0)) & (generous(X0) | (quiet(X0) & tall(X0)))) [flattening 59]
95. ~tall(X0) | humble(X0) | generous(X0) [cnf transformation 45]
102. ~tall(X0) | ~humble(X0) [cnf transformation 51]
119. generous(X0) | tall(X0) [cnf transformation 60]
139. ~generous(paul) [cnf transformation 22]
197. 13 <=> ! [X0] : (generous(X0) | tall(X0)) [avatar definition]
198. tall(X0) | generous(X0) <- (13) [avatar component clause 197]
258. 13 [avatar split clause 119,197]
333. generous(X1) | ~humble(X1) <- (13) [resolution 198,102]
397. humble(X0) | generous(X0) | generous(X0) <- (13) [resolution 95,198]
401. humble(X0) | generous(X0) <- (13) [duplicate literal removal 397]
402. generous(X0) <- (13) [subsumption resolution 401,333]
410. $false <- (13) [resolution 402,139]
414. ~13 [avatar contradiction clause 410]
415. $false [avatar sat refutation 258,414]
% SZS output end Proof for 7769524052846449674681692
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If alice is not generous or curious then paul is kind. If lucy is not wise then someone is not quiet and vice versa. Everyone who is not generous or wise is either curious or happy. Everyone who is not rich or not funny is wise. Everyone who is both not curious and patient is not calm and vice versa. If paul is either not humble or old then someone is either tall or not humble and vice versa. If alice is either not quiet or not creative then lucy is both not funny and not calm and vice versa. If someone is either not creative or not happy then someone is brave or kind. If lucy is not calm then someone is not brave and vice versa. Everyone who is old is either generous or wise and vice versa. If lucy is strong then someone is either not kind or not rich and vice versa. Everyone who is either not curious or rich is not creative or not brave and vice versa. Everyone who is not kind or not patient is both rich and funny. Everyone who is brave or not patient is both not funny and old. If someone is both tall and not kind then alice is not creative and vice versa. Everyone who is either not funny or not happy is either rich or not generous and vice versa. Alice is either not kind or calm. Someone is either not curious or not generous. Paul is not tall. Susan is not old or not wise. Paul is not strong. Fred is happy. Paul is either kind or not rich. Fred is not brave. | Paul is not tall. | entailment | (((~generous(alice)|curious(alice)))=>(kind(paul)))&
((~wise(lucy))<=>(?[X]:(~quiet(X))))&
(![X]:((~generous(X)|wise(X))=>(curious(X)<~>happy(X))))&
(![X]:((~rich(X)|~funny(X))=>wise(X)))&
(![X]:((~curious(X)&patient(X))<=>~calm(X)))&
(((~humble(paul)<~>old(paul)))<=>(?[X]:((tall(X)<~>~humble(X)))))&
(((~quiet(alice)<~>~creative(alice)))<=>((~funny(lucy)&~calm(lucy))))&
((?[X]:((~creative(X)<~>~happy(X))))=>(?[X]:((brave(X)|kind(X)))))&
((~calm(lucy))<=>(?[X]:(~brave(X))))&
(![X]:(old(X)<=>(generous(X)<~>wise(X))))&
((strong(lucy))<=>(?[X]:((~kind(X)<~>~rich(X)))))&
(![X]:((~curious(X)<~>rich(X))<=>(~creative(X)|~brave(X))))&
(![X]:((~kind(X)|~patient(X))=>(rich(X)&funny(X))))&
(![X]:((brave(X)|~patient(X))=>(~funny(X)&old(X))))&
((?[X]:((tall(X)&~kind(X))))<=>(~creative(alice)))&
(![X]:((~funny(X)<~>~happy(X))<=>(rich(X)<~>~generous(X))))&
((~kind(alice)<~>calm(alice)))&
(?[X]:((~curious(X)<~>~generous(X))))&
(~tall(paul))&
((~old(susan)|~wise(susan)))&
(~strong(paul))&
(happy(fred))&
((kind(paul)<~>~rich(paul)))&
(~brave(fred)) | ~tall(paul) | [
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 6662878683926688452621449
% SZS output start Proof for 6662878683926688452621449
19. ~tall(paul) [input p18]
25. tall(paul) [input hypothesis]
139. ~tall(paul) [cnf transformation 19]
146. tall(paul) [cnf transformation 25]
320. $false [subsumption resolution 146,139]
% SZS output end Proof for 6662878683926688452621449
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not funny or not old then someone is both humble and kind. Everyone who is both not wise and not generous is not kind or curious and vice versa. Everyone who is not curious or not rich is not quiet and vice versa. If someone is both kind and humble then someone is happy or calm. If john is not kind or happy then lucy is either old or brave and vice versa. Everyone who is wise or not kind is either humble or strong and vice versa. If someone is not calm then someone is creative and vice versa. Everyone who is not patient is both not curious and not happy and vice versa. If john is tall then fred is both calm and quiet. Everyone who is both not strong and not patient is both kind and not patient and vice versa. Everyone who is not humble or strong is either not generous or generous. Everyone who is both not quiet and kind is both not quiet and not creative. Everyone who is both not kind and not brave is tall or not curious and vice versa. Everyone who is generous or curious is not quiet. Everyone who is not old or calm is calm. Everyone who is not wise is either curious or kind. Lucy is calm. Mary is either not tall or not funny. Fred is not brave. | John is not creative. | neutral | ((?[X]:((~funny(X)|~old(X))))=>(?[X]:((humble(X)&kind(X)))))&
(![X]:((~wise(X)&~generous(X))<=>(~kind(X)|curious(X))))&
(![X]:((~curious(X)|~rich(X))<=>~quiet(X)))&
((?[X]:((kind(X)&humble(X))))=>(?[X]:((happy(X)|calm(X)))))&
(((~kind(john)|happy(john)))<=>((old(lucy)<~>brave(lucy))))&
(![X]:((wise(X)|~kind(X))<=>(humble(X)<~>strong(X))))&
((?[X]:(~calm(X)))<=>(?[X]:(creative(X))))&
(![X]:(~patient(X)<=>(~curious(X)&~happy(X))))&
((tall(john))=>((calm(fred)&quiet(fred))))&
(![X]:((~strong(X)&~patient(X))<=>(kind(X)&~patient(X))))&
(![X]:((~humble(X)|strong(X))=>(~generous(X)<~>generous(X))))&
(![X]:((~quiet(X)&kind(X))=>(~quiet(X)&~creative(X))))&
(![X]:((~kind(X)&~brave(X))<=>(tall(X)|~curious(X))))&
(![X]:((generous(X)|curious(X))=>~quiet(X)))&
(![X]:((~old(X)|calm(X))=>calm(X)))&
(![X]:(~wise(X)=>(curious(X)<~>kind(X))))&
(calm(lucy))&
((~tall(mary)<~>~funny(mary)))&
(~brave(fred)) | ~creative(john) | [] | null | 0 |
Everyone who is either not calm or creative is strong.
If someone is not calm then mary is both old and generous.
Everyone who is both rich and not curious is tall.
If someone is not curious or not strong then susan is either not tall or quiet.
If someone is either kind or not humble then john is either brave or not generous and vice versa.
If someone is funny or not old then someone is not quiet or not creative.
Everyone who is strong or quiet is either not humble or funny.
Everyone who is either old or strong is not old or not funny and vice versa.
If someone is either not happy or calm then lucy is not curious or generous and vice versa.
Everyone who is both humble and kind is both not old and happy and vice versa.
Everyone who is humble is patient and vice versa.
Everyone who is either quiet or not brave is either not strong or generous and vice versa.
If someone is not kind then someone is not brave.
If mary is quiet then john is both calm and not kind and vice versa.
Everyone who is either generous or funny is not generous or tall and vice versa.
If paul is tall then someone is either tall or calm and vice versa.
Someone is patient or not kind.
Someone is tall.
Lucy is both not brave and not funny.
Someone is both generous and not brave.
Someone is either not patient or curious.
Someone is humble or not calm.
Alice is both funny and not calm.
Someone is not happy or funny. | Lucy is patient. | contradiction | (![X]:((~calm(X)<~>creative(X))=>strong(X)))&
((?[X]:(~calm(X)))=>((old(mary)&generous(mary))))&
(![X]:((rich(X)&~curious(X))=>tall(X)))&
((?[X]:((~curious(X)|~strong(X))))=>((~tall(susan)<~>quiet(susan))))&
((?[X]:((kind(X)<~>~humble(X))))<=>((brave(john)<~>~generous(john))))&
((?[X]:((funny(X)|~old(X))))=>(?[X]:((~quiet(X)|~creative(X)))))&
(![X]:((strong(X)|quiet(X))=>(~humble(X)<~>funny(X))))&
(![X]:((old(X)<~>strong(X))<=>(~old(X)|~funny(X))))&
((?[X]:((~happy(X)<~>calm(X))))<=>((~curious(lucy)|generous(lucy))))&
(![X]:((humble(X)&kind(X))<=>(~old(X)&happy(X))))&
(![X]:(humble(X)<=>patient(X)))&
(![X]:((quiet(X)<~>~brave(X))<=>(~strong(X)<~>generous(X))))&
((?[X]:(~kind(X)))=>(?[X]:(~brave(X))))&
((quiet(mary))<=>((calm(john)&~kind(john))))&
(![X]:((generous(X)<~>funny(X))<=>(~generous(X)|tall(X))))&
((tall(paul))<=>(?[X]:((tall(X)<~>calm(X)))))&
(?[X]:((patient(X)|~kind(X))))&
(?[X]:(tall(X)))&
((~brave(lucy)&~funny(lucy)))&
(?[X]:((generous(X)&~brave(X))))&
(?[X]:((~patient(X)<~>curious(X))))&
(?[X]:((humble(X)|~calm(X))))&
((funny(alice)&~calm(alice)))&
(?[X]:((~happy(X)|funny(X)))) | patient(lucy) | [
"p6",
"p7",
"p10",
"p11",
"p14",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 7327383482700420836777321
% SZS output start Proof for 7327383482700420836777321
7. ! [X0] : ((quiet(X0) | strong(X0)) => (~humble(X0) <~> funny(X0))) [input p6]
8. ! [X0] : ((old(X0) <~> strong(X0)) <=> (~funny(X0) | ~old(X0))) [input p7]
11. ! [X0] : (humble(X0) <=> patient(X0)) [input p10]
12. ! [X0] : ((quiet(X0) <~> ~brave(X0)) <=> (~strong(X0) <~> generous(X0))) [input p11]
15. ! [X0] : ((generous(X0) <~> funny(X0)) <=> (tall(X0) | ~generous(X0))) [input p14]
19. ~funny(lucy) & ~brave(lucy) [input p18]
25. patient(lucy) [input hypothesis]
33. ! [X0] : ((~humble(X0) <~> funny(X0)) | (~quiet(X0) & ~strong(X0))) [ennf transformation 7]
44. ! [X0] : (((~funny(X0) | humble(X0)) & (funny(X0) | ~humble(X0))) | (~quiet(X0) & ~strong(X0))) [nnf transformation 33]
45. ! [X0] : ((((~strong(X0) | ~old(X0)) & (strong(X0) | old(X0))) | (funny(X0) & old(X0))) & ((~funny(X0) | ~old(X0)) | ((old(X0) | ~strong(X0)) & (strong(X0) | ~old(X0))))) [nnf transformation 8]
46. ! [X0] : ((((~strong(X0) | ~old(X0)) & (strong(X0) | old(X0))) | (funny(X0) & old(X0))) & (~funny(X0) | ~old(X0) | ((old(X0) | ~strong(X0)) & (strong(X0) | ~old(X0))))) [flattening 45]
54. ! [X0] : ((humble(X0) | ~patient(X0)) & (patient(X0) | ~humble(X0))) [nnf transformation 11]
55. ! [X0] : ((((brave(X0) | ~quiet(X0)) & (~brave(X0) | quiet(X0))) | ((~strong(X0) | ~generous(X0)) & (generous(X0) | strong(X0)))) & (((~generous(X0) | strong(X0)) & (generous(X0) | ~strong(X0))) | ((quiet(X0) | brave(X0)) & (~brave(X0) | ~quiet(X0))))) [nnf transformation 12]
61. ! [X0] : ((((~funny(X0) | ~generous(X0)) & (funny(X0) | generous(X0))) | (~tall(X0) & generous(X0))) & ((tall(X0) | ~generous(X0)) | ((generous(X0) | ~funny(X0)) & (funny(X0) | ~generous(X0))))) [nnf transformation 15]
62. ! [X0] : ((((~funny(X0) | ~generous(X0)) & (funny(X0) | generous(X0))) | (~tall(X0) & generous(X0))) & (tall(X0) | ~generous(X0) | ((generous(X0) | ~funny(X0)) & (funny(X0) | ~generous(X0))))) [flattening 61]
98. ~humble(X0) | funny(X0) | ~strong(X0) [cnf transformation 44]
99. ~humble(X0) | funny(X0) | ~quiet(X0) [cnf transformation 44]
102. ~funny(X0) | ~old(X0) | strong(X0) | ~old(X0) [cnf transformation 46]
104. strong(X0) | old(X0) | old(X0) [cnf transformation 46]
119. ~patient(X0) | humble(X0) [cnf transformation 54]
123. ~generous(X0) | strong(X0) | quiet(X0) | brave(X0) [cnf transformation 55]
134. funny(X0) | generous(X0) | generous(X0) [cnf transformation 62]
144. ~brave(lucy) [cnf transformation 19]
145. ~funny(lucy) [cnf transformation 19]
154. patient(lucy) [cnf transformation 25]
156. funny(X0) | generous(X0) [duplicate literal removal 134]
157. ~funny(X0) | ~old(X0) | strong(X0) [duplicate literal removal 102]
158. old(X0) | strong(X0) [duplicate literal removal 104]
236. ~funny(X0) | strong(X0) [subsumption resolution 157,158]
348. humble(lucy) [resolution 119,154]
355. generous(X0) | strong(X0) [resolution 236,156]
363. funny(lucy) | ~strong(lucy) [resolution 98,348]
364. ~strong(lucy) [subsumption resolution 363,145]
365. funny(lucy) | ~quiet(lucy) [resolution 99,348]
366. ~quiet(lucy) [subsumption resolution 365,145]
490. strong(X0) | quiet(X0) | brave(X0) | strong(X0) [resolution 123,355]
495. brave(X0) | quiet(X0) | strong(X0) [duplicate literal removal 490]
606. quiet(lucy) | strong(lucy) [resolution 495,144]
612. strong(lucy) [subsumption resolution 606,366]
613. $false [subsumption resolution 612,364]
% SZS output end Proof for 7327383482700420836777321
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind or generous is both rich and brave.
Everyone who is not quiet is funny or strong.
Everyone who is not patient is not old and vice versa.
If someone is funny then mary is not quiet.
Everyone who is either happy or patient is either not wise or kind and vice versa.
Everyone who is funny or not curious is not wise.
If someone is both patient and brave then lucy is not brave or not curious and vice versa.
If someone is not old then fred is either wise or rich and vice versa.
If someone is either not tall or not happy then someone is both not humble and brave and vice versa.
Everyone who is not old or not strong is either not tall or wise and vice versa.
If fred is not kind or not happy then john is both not wise and not strong.
If mary is humble or not creative then paul is not tall.
Everyone who is both quiet and not humble is tall or not curious and vice versa.
Everyone who is either not patient or humble is not generous or not brave and vice versa.
If someone is not kind then someone is curious or humble.
If someone is either funny or not generous then someone is both not curious and not brave and vice versa.
Someone is not old.
Paul is either not kind or not calm.
Someone is both tall and brave.
Fred is either old or not rich.
Someone is not wise.
Lucy is not generous or rich.
Someone is humble.
Lucy is both calm and not tall. | Lucy is curious. | neutral | (![X]:((kind(X)|generous(X))=>(rich(X)&brave(X))))&
(![X]:(~quiet(X)=>(funny(X)|strong(X))))&
(![X]:(~patient(X)<=>~old(X)))&
((?[X]:(funny(X)))=>(~quiet(mary)))&
(![X]:((happy(X)<~>patient(X))<=>(~wise(X)<~>kind(X))))&
(![X]:((funny(X)|~curious(X))=>~wise(X)))&
((?[X]:((patient(X)&brave(X))))<=>((~brave(lucy)|~curious(lucy))))&
((?[X]:(~old(X)))<=>((wise(fred)<~>rich(fred))))&
((?[X]:((~tall(X)<~>~happy(X))))<=>(?[X]:((~humble(X)&brave(X)))))&
(![X]:((~old(X)|~strong(X))<=>(~tall(X)<~>wise(X))))&
(((~kind(fred)|~happy(fred)))=>((~wise(john)&~strong(john))))&
(((humble(mary)|~creative(mary)))=>(~tall(paul)))&
(![X]:((quiet(X)&~humble(X))<=>(tall(X)|~curious(X))))&
(![X]:((~patient(X)<~>humble(X))<=>(~generous(X)|~brave(X))))&
((?[X]:(~kind(X)))=>(?[X]:((curious(X)|humble(X)))))&
((?[X]:((funny(X)<~>~generous(X))))<=>(?[X]:((~curious(X)&~brave(X)))))&
(?[X]:(~old(X)))&
((~kind(paul)<~>~calm(paul)))&
(?[X]:((tall(X)&brave(X))))&
((old(fred)<~>~rich(fred)))&
(?[X]:(~wise(X)))&
((~generous(lucy)|rich(lucy)))&
(?[X]:(humble(X)))&
((calm(lucy)&~tall(lucy))) | curious(lucy) | [] | null | 0 |
If someone is both not kind and strong then someone is not generous or rich.
If someone is both not strong and not wise then alice is calm.
If john is either strong or happy then someone is funny.
If paul is both not old and not creative then fred is not strong and vice versa.
Everyone who is tall is not curious.
Everyone who is not quiet is kind or happy.
If someone is both rich and brave then someone is either happy or not patient.
Everyone who is both quiet and kind is either not happy or not tall.
Everyone who is tall or not happy is either not old or not patient.
Everyone who is either creative or not rich is old.
Everyone who is not funny or not curious is either not brave or tall and vice versa.
Everyone who is either creative or not strong is not humble or not wise and vice versa.
Everyone who is either calm or wise is rich and vice versa.
If someone is either not tall or not rich then someone is curious and vice versa.
If alice is both brave and patient then someone is both brave and not tall and vice versa.
If paul is brave then paul is either strong or not rich.
Someone is both tall and wise.
Lucy is not curious or calm.
Alice is not wise or curious.
Mary is either not rich or happy.
Someone is curious or not patient.
Mary is brave.
John is not curious.
Paul is generous. | Mary is brave. | entailment | ((?[X]:((~kind(X)&strong(X))))=>(?[X]:((~generous(X)|rich(X)))))&
((?[X]:((~strong(X)&~wise(X))))=>(calm(alice)))&
(((strong(john)<~>happy(john)))=>(?[X]:(funny(X))))&
(((~old(paul)&~creative(paul)))<=>(~strong(fred)))&
(![X]:(tall(X)=>~curious(X)))&
(![X]:(~quiet(X)=>(kind(X)|happy(X))))&
((?[X]:((rich(X)&brave(X))))=>(?[X]:((happy(X)<~>~patient(X)))))&
(![X]:((quiet(X)&kind(X))=>(~happy(X)<~>~tall(X))))&
(![X]:((tall(X)|~happy(X))=>(~old(X)<~>~patient(X))))&
(![X]:((creative(X)<~>~rich(X))=>old(X)))&
(![X]:((~funny(X)|~curious(X))<=>(~brave(X)<~>tall(X))))&
(![X]:((creative(X)<~>~strong(X))<=>(~humble(X)|~wise(X))))&
(![X]:((calm(X)<~>wise(X))<=>rich(X)))&
((?[X]:((~tall(X)<~>~rich(X))))<=>(?[X]:(curious(X))))&
(((brave(alice)&patient(alice)))<=>(?[X]:((brave(X)&~tall(X)))))&
((brave(paul))=>((strong(paul)<~>~rich(paul))))&
(?[X]:((tall(X)&wise(X))))&
((~curious(lucy)|calm(lucy)))&
((~wise(alice)|curious(alice)))&
((~rich(mary)<~>happy(mary)))&
(?[X]:((curious(X)|~patient(X))))&
(brave(mary))&
(~curious(john))&
(generous(paul)) | brave(mary) | [
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 4184815874730301815406079
% SZS output start Proof for 4184815874730301815406079
22. brave(mary) [input p21]
25. ~brave(mary) [input hypothesis]
129. brave(mary) [cnf transformation 22]
132. ~brave(mary) [cnf transformation 25]
296. $false [subsumption resolution 132,129]
% SZS output end Proof for 4184815874730301815406079
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both rich and humble is either rich or not curious and vice versa.
Everyone who is either happy or calm is not creative and vice versa.
Everyone who is tall or not kind is either not patient or creative.
Everyone who is rich is both funny and not kind and vice versa.
Everyone who is not kind is either quiet or not rich and vice versa.
If susan is either not kind or not generous then susan is both not creative and quiet and vice versa.
If paul is either old or not funny then someone is kind.
If paul is both strong and happy then john is creative or curious.
Everyone who is either humble or not curious is not happy or not tall and vice versa.
Everyone who is happy or funny is either not funny or not rich.
Everyone who is both strong and quiet is both not calm and not humble.
If someone is not funny then paul is both not humble and humble and vice versa.
Everyone who is both not happy and wise is funny.
Everyone who is happy or not strong is both quiet and happy and vice versa.
Everyone who is old is both not patient and strong and vice versa.
If someone is not rich then someone is quiet or not old and vice versa.
Someone is either not strong or calm.
Fred is either funny or not generous.
Someone is creative.
Someone is tall or creative.
Someone is quiet or not wise.
Someone is not curious or not brave.
Fred is humble. | Fred is not strong. | entailment | (![X]:((rich(X)&humble(X))<=>(rich(X)<~>~curious(X))))&
(![X]:((happy(X)<~>calm(X))<=>~creative(X)))&
(![X]:((tall(X)|~kind(X))=>(~patient(X)<~>creative(X))))&
(![X]:(rich(X)<=>(funny(X)&~kind(X))))&
(![X]:(~kind(X)<=>(quiet(X)<~>~rich(X))))&
(((~kind(susan)<~>~generous(susan)))<=>((~creative(susan)&quiet(susan))))&
(((old(paul)<~>~funny(paul)))=>(?[X]:(kind(X))))&
(((strong(paul)&happy(paul)))=>((creative(john)|curious(john))))&
(![X]:((humble(X)<~>~curious(X))<=>(~happy(X)|~tall(X))))&
(![X]:((happy(X)|funny(X))=>(~funny(X)<~>~rich(X))))&
(![X]:((strong(X)&quiet(X))=>(~calm(X)&~humble(X))))&
((?[X]:(~funny(X)))<=>((~humble(paul)&humble(paul))))&
(![X]:((~happy(X)&wise(X))=>funny(X)))&
(![X]:((happy(X)|~strong(X))<=>(quiet(X)&happy(X))))&
(![X]:(old(X)<=>(~patient(X)&strong(X))))&
((?[X]:(~rich(X)))<=>(?[X]:((quiet(X)|~old(X)))))&
(?[X]:((~strong(X)<~>calm(X))))&
((funny(fred)<~>~generous(fred)))&
(?[X]:(creative(X)))&
(?[X]:((tall(X)|creative(X))))&
(?[X]:((quiet(X)|~wise(X))))&
(?[X]:((~curious(X)|~brave(X))))&
(humble(fred)) | ~strong(fred) | [
"p3",
"p4",
"p9",
"p10",
"p11",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 1450003476093839574675139
% SZS output start Proof for 1450003476093839574675139
4. ! [X0] : (rich(X0) <=> (~kind(X0) & funny(X0))) [input p3]
5. ! [X0] : (~kind(X0) <=> (quiet(X0) <~> ~rich(X0))) [input p4]
10. ! [X0] : ((funny(X0) | happy(X0)) => (~funny(X0) <~> ~rich(X0))) [input p9]
11. ! [X0] : ((quiet(X0) & strong(X0)) => (~humble(X0) & ~calm(X0))) [input p10]
12. ? [X0] : ~funny(X0) <=> (humble(paul) & ~humble(paul)) [input p11]
23. humble(fred) [input p22]
24. strong(fred) [input hypothesis]
33. ! [X0] : ((~funny(X0) <~> ~rich(X0)) | (~funny(X0) & ~happy(X0))) [ennf transformation 10]
34. ! [X0] : ((~humble(X0) & ~calm(X0)) | (~quiet(X0) | ~strong(X0))) [ennf transformation 11]
35. ! [X0] : ((~humble(X0) & ~calm(X0)) | ~quiet(X0) | ~strong(X0)) [flattening 34]
40. ! [X0] : ((rich(X0) | (kind(X0) | ~funny(X0))) & ((~kind(X0) & funny(X0)) | ~rich(X0))) [nnf transformation 4]
41. ! [X0] : ((rich(X0) | kind(X0) | ~funny(X0)) & ((~kind(X0) & funny(X0)) | ~rich(X0))) [flattening 40]
42. ! [X0] : ((~kind(X0) | ((quiet(X0) | rich(X0)) & (~rich(X0) | ~quiet(X0)))) & (((rich(X0) | ~quiet(X0)) & (~rich(X0) | quiet(X0))) | kind(X0))) [nnf transformation 5]
50. ! [X0] : (((rich(X0) | funny(X0)) & (~rich(X0) | ~funny(X0))) | (~funny(X0) & ~happy(X0))) [nnf transformation 33]
51. (? [X0] : ~funny(X0) | (~humble(paul) | humble(paul))) & ((humble(paul) & ~humble(paul)) | ! [X0] : funny(X0)) [nnf transformation 12]
52. (? [X0] : ~funny(X0) | ~humble(paul) | humble(paul)) & ((humble(paul) & ~humble(paul)) | ! [X0] : funny(X0)) [flattening 51]
53. (? [X0] : ~funny(X0) | ~humble(paul) | humble(paul)) & ((humble(paul) & ~humble(paul)) | ! [X1] : funny(X1)) [rectify 52]
54. ? [X0] : ~funny(X0) => ~funny(sK1) [choice axiom]
55. (~funny(sK1) | ~humble(paul) | humble(paul)) & ((humble(paul) & ~humble(paul)) | ! [X1] : funny(X1)) [skolemisation 53,54]
87. ~rich(X0) | funny(X0) [cnf transformation 41]
88. ~kind(X0) | ~rich(X0) [cnf transformation 41]
89. ~funny(X0) | kind(X0) | rich(X0) [cnf transformation 41]
93. ~kind(X0) | quiet(X0) | rich(X0) [cnf transformation 42]
110. ~rich(X0) | ~funny(X0) | ~funny(X0) [cnf transformation 50]
114. ~strong(X0) | ~quiet(X0) | ~humble(X0) [cnf transformation 35]
115. ~humble(paul) | funny(X1) [cnf transformation 55]
116. humble(paul) | funny(X1) [cnf transformation 55]
135. humble(fred) [cnf transformation 23]
136. strong(fred) [cnf transformation 24]
137. ~rich(X0) | ~funny(X0) [duplicate literal removal 110]
141. ~kind(X0) | quiet(X0) [subsumption resolution 93,88]
200. ~rich(X0) [subsumption resolution 137,87]
202. 12 <=> ! [X1] : funny(X1) [avatar definition]
203. funny(X1) <- (12) [avatar component clause 202]
205. 13 <=> humble(paul) [avatar definition]
208. 12 | 13 [avatar split clause 116,205,202]
209. 12 | ~13 [avatar split clause 115,205,202]
335. kind(X0) | rich(X0) <- (12) [resolution 89,203]
336. kind(X0) <- (12) [subsumption resolution 335,200]
352. quiet(X0) <- (12) [resolution 336,141]
364. ~quiet(fred) | ~humble(fred) [resolution 114,136]
368. ~humble(fred) <- (12) [subsumption resolution 364,352]
369. $false <- (12) [subsumption resolution 368,135]
370. ~12 [avatar contradiction clause 369]
375. $false [avatar sat refutation 208,209,370]
% SZS output end Proof for 1450003476093839574675139
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.021 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not kind or not strong then someone is curious or happy.
If fred is either not curious or tall then someone is both funny and not humble and vice versa.
Everyone who is humble is generous.
Everyone who is either quiet or not patient is calm or not creative and vice versa.
If paul is not happy then fred is either kind or not creative and vice versa.
Everyone who is funny or not wise is not curious or tall.
If someone is either patient or kind then someone is funny.
Everyone who is creative or not old is patient or kind and vice versa.
Everyone who is either kind or humble is funny or not kind.
Everyone who is both strong and brave is wise.
Everyone who is both not rich and not generous is humble and vice versa.
If someone is wise then someone is both wise and calm.
If mary is not quiet or wise then paul is not strong and vice versa.
Everyone who is curious or not humble is not quiet or humble.
If paul is not rich then paul is both not strong and brave and vice versa.
Everyone who is brave is not rich and vice versa.
Someone is calm or not creative.
John is not curious or not kind.
Alice is not rich.
Susan is either not curious or creative.
Someone is patient or rich.
Mary is not happy. | Mary is not patient. | neutral | ((?[X]:((~kind(X)<~>~strong(X))))=>(?[X]:((curious(X)|happy(X)))))&
(((~curious(fred)<~>tall(fred)))<=>(?[X]:((funny(X)&~humble(X)))))&
(![X]:(humble(X)=>generous(X)))&
(![X]:((quiet(X)<~>~patient(X))<=>(calm(X)|~creative(X))))&
((~happy(paul))<=>((kind(fred)<~>~creative(fred))))&
(![X]:((funny(X)|~wise(X))=>(~curious(X)|tall(X))))&
((?[X]:((patient(X)<~>kind(X))))=>(?[X]:(funny(X))))&
(![X]:((creative(X)|~old(X))<=>(patient(X)|kind(X))))&
(![X]:((kind(X)<~>humble(X))=>(funny(X)|~kind(X))))&
(![X]:((strong(X)&brave(X))=>wise(X)))&
(![X]:((~rich(X)&~generous(X))<=>humble(X)))&
((?[X]:(wise(X)))=>(?[X]:((wise(X)&calm(X)))))&
(((~quiet(mary)|wise(mary)))<=>(~strong(paul)))&
(![X]:((curious(X)|~humble(X))=>(~quiet(X)|humble(X))))&
((~rich(paul))<=>((~strong(paul)&brave(paul))))&
(![X]:(brave(X)<=>~rich(X)))&
(?[X]:((calm(X)|~creative(X))))&
((~curious(john)|~kind(john)))&
(~rich(alice))&
((~curious(susan)<~>creative(susan)))&
(?[X]:((patient(X)|rich(X))))&
(~happy(mary)) | ~patient(mary) | [] | null | 0 |
Everyone who is not kind is rich or not calm and vice versa.
Everyone who is both curious and quiet is not tall and vice versa.
Everyone who is either happy or old is happy or quiet and vice versa.
Everyone who is either wise or creative is both not patient and not happy.
Everyone who is both not curious and not strong is not old and vice versa.
If someone is patient then someone is either funny or not brave and vice versa.
Everyone who is not patient or rich is either calm or old.
Everyone who is patient is either old or calm and vice versa.
If alice is both happy and not rich then someone is both rich and funny and vice versa.
If someone is rich or patient then someone is humble.
If mary is happy or not wise then fred is not curious or old and vice versa.
If mary is either not rich or not patient then susan is curious or quiet and vice versa.
If john is not tall then john is not wise or not tall and vice versa.
Everyone who is both funny and not calm is either not funny or not quiet.
Everyone who is both not quiet and wise is either not curious or not creative and vice versa.
If someone is both funny and not creative then someone is either curious or not tall.
Someone is both happy and wise.
Someone is either not funny or curious.
Fred is curious.
Someone is not curious.
Someone is old or tall.
Someone is both wise and patient.
Someone is either not quiet or not creative.
Mary is strong. | Mary is not kind. | entailment | (![X]:(~kind(X)<=>(rich(X)|~calm(X))))&
(![X]:((curious(X)&quiet(X))<=>~tall(X)))&
(![X]:((happy(X)<~>old(X))<=>(happy(X)|quiet(X))))&
(![X]:((wise(X)<~>creative(X))=>(~patient(X)&~happy(X))))&
(![X]:((~curious(X)&~strong(X))<=>~old(X)))&
((?[X]:(patient(X)))<=>(?[X]:((funny(X)<~>~brave(X)))))&
(![X]:((~patient(X)|rich(X))=>(calm(X)<~>old(X))))&
(![X]:(patient(X)<=>(old(X)<~>calm(X))))&
(((happy(alice)&~rich(alice)))<=>(?[X]:((rich(X)&funny(X)))))&
((?[X]:((rich(X)|patient(X))))=>(?[X]:(humble(X))))&
(((happy(mary)|~wise(mary)))<=>((~curious(fred)|old(fred))))&
(((~rich(mary)<~>~patient(mary)))<=>((curious(susan)|quiet(susan))))&
((~tall(john))<=>((~wise(john)|~tall(john))))&
(![X]:((funny(X)&~calm(X))=>(~funny(X)<~>~quiet(X))))&
(![X]:((~quiet(X)&wise(X))<=>(~curious(X)<~>~creative(X))))&
((?[X]:((funny(X)&~creative(X))))=>(?[X]:((curious(X)<~>~tall(X)))))&
(?[X]:((happy(X)&wise(X))))&
(?[X]:((~funny(X)<~>curious(X))))&
(curious(fred))&
(?[X]:(~curious(X)))&
(?[X]:((old(X)|tall(X))))&
(?[X]:((wise(X)&patient(X))))&
(?[X]:((~quiet(X)<~>~creative(X))))&
(strong(mary)) | ~kind(mary) | [
"p0",
"p4",
"p6",
"p7",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 5889910052449298820413294
% SZS output start Proof for 5889910052449298820413294
1. ! [X0] : (~kind(X0) <=> (~calm(X0) | rich(X0))) [input p0]
5. ! [X0] : ((~strong(X0) & ~curious(X0)) <=> ~old(X0)) [input p4]
7. ! [X0] : ((rich(X0) | ~patient(X0)) => (calm(X0) <~> old(X0))) [input p6]
8. ! [X0] : (patient(X0) <=> (old(X0) <~> calm(X0))) [input p7]
24. strong(mary) [input p23]
25. kind(mary) [input hypothesis]
29. ! [X0] : ((~calm(X0) | rich(X0)) => ~kind(X0)) [unused predicate definition removal 1]
31. ! [X0] : (~kind(X0) | (calm(X0) & ~rich(X0))) [ennf transformation 29]
33. ! [X0] : ((calm(X0) <~> old(X0)) | (~rich(X0) & patient(X0))) [ennf transformation 7]
42. ! [X0] : (((~strong(X0) & ~curious(X0)) | old(X0)) & (~old(X0) | (strong(X0) | curious(X0)))) [nnf transformation 5]
43. ! [X0] : (((~strong(X0) & ~curious(X0)) | old(X0)) & (~old(X0) | strong(X0) | curious(X0))) [flattening 42]
49. ! [X0] : (((~old(X0) | ~calm(X0)) & (old(X0) | calm(X0))) | (~rich(X0) & patient(X0))) [nnf transformation 33]
50. ! [X0] : ((patient(X0) | ((old(X0) | ~calm(X0)) & (calm(X0) | ~old(X0)))) & (((~calm(X0) | ~old(X0)) & (calm(X0) | old(X0))) | ~patient(X0))) [nnf transformation 8]
84. ~kind(X0) | calm(X0) [cnf transformation 31]
100. ~strong(X0) | old(X0) [cnf transformation 43]
105. old(X0) | calm(X0) | patient(X0) [cnf transformation 49]
107. ~old(X0) | ~calm(X0) | patient(X0) [cnf transformation 49]
110. ~calm(X0) | ~old(X0) | ~patient(X0) [cnf transformation 50]
111. patient(X0) | calm(X0) | ~old(X0) [cnf transformation 50]
112. patient(X0) | old(X0) | ~calm(X0) [cnf transformation 50]
151. strong(mary) [cnf transformation 24]
152. kind(mary) [cnf transformation 25]
182. patient(X0) | old(X0) [subsumption resolution 112,105]
183. patient(X0) | ~old(X0) [subsumption resolution 111,107]
184. patient(X0) [subsumption resolution 183,182]
185. ~old(X0) | ~calm(X0) [subsumption resolution 110,184]
300. calm(mary) [resolution 84,152]
306. old(mary) [resolution 100,151]
316. ~calm(mary) [resolution 185,306]
317. $false [subsumption resolution 316,300]
% SZS output end Proof for 5889910052449298820413294
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous is curious.
Everyone who is either quiet or kind is not wise and vice versa.
If paul is not curious or funny then someone is not quiet and vice versa.
Everyone who is happy is both creative and not strong and vice versa.
Everyone who is quiet is creative or not generous.
If paul is not kind then fred is both curious and not happy.
If someone is quiet or not generous then someone is both not old and not tall and vice versa.
Everyone who is curious or strong is both not wise and not humble and vice versa.
If someone is both not generous and not humble then susan is not generous.
If paul is creative or wise then lucy is rich or happy and vice versa.
Everyone who is both calm and not quiet is not rich or not wise.
Everyone who is patient or wise is quiet and vice versa.
Everyone who is both tall and generous is not tall or not creative and vice versa.
Everyone who is brave or not wise is happy or not humble and vice versa.
If john is either kind or not humble then someone is not curious and vice versa.
Everyone who is both not curious and happy is quiet or curious.
Someone is both not quiet and not calm.
Fred is either not kind or brave.
John is both not rich and not strong. | John is not generous. | contradiction | (![X]:(generous(X)=>curious(X)))&
(![X]:((quiet(X)<~>kind(X))<=>~wise(X)))&
(((~curious(paul)|funny(paul)))<=>(?[X]:(~quiet(X))))&
(![X]:(happy(X)<=>(creative(X)&~strong(X))))&
(![X]:(quiet(X)=>(creative(X)|~generous(X))))&
((~kind(paul))=>((curious(fred)&~happy(fred))))&
((?[X]:((quiet(X)|~generous(X))))<=>(?[X]:((~old(X)&~tall(X)))))&
(![X]:((curious(X)|strong(X))<=>(~wise(X)&~humble(X))))&
((?[X]:((~generous(X)&~humble(X))))=>(~generous(susan)))&
(((creative(paul)|wise(paul)))<=>((rich(lucy)|happy(lucy))))&
(![X]:((calm(X)&~quiet(X))=>(~rich(X)|~wise(X))))&
(![X]:((patient(X)|wise(X))<=>quiet(X)))&
(![X]:((tall(X)&generous(X))<=>(~tall(X)|~creative(X))))&
(![X]:((brave(X)|~wise(X))<=>(happy(X)|~humble(X))))&
(((kind(john)<~>~humble(john)))<=>(?[X]:(~curious(X))))&
(![X]:((~curious(X)&happy(X))=>(quiet(X)|curious(X))))&
(?[X]:((~quiet(X)&~calm(X))))&
((~kind(fred)<~>brave(fred)))&
((~rich(john)&~strong(john))) | ~generous(john) | [
"p6",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 5724308007762847131295108
% SZS output start Proof for 5724308007762847131295108
7. ? [X0] : (~generous(X0) | quiet(X0)) <=> ? [X0] : (~tall(X0) & ~old(X0)) [input p6]
13. ! [X0] : ((generous(X0) & tall(X0)) <=> (~creative(X0) | ~tall(X0))) [input p12]
20. ~generous(john) [input hypothesis]
21. ? [X0] : (~generous(X0) | quiet(X0)) <=> ? [X1] : (~tall(X1) & ~old(X1)) [rectify 7]
39. (? [X0] : (~generous(X0) | quiet(X0)) | ! [X1] : (tall(X1) | old(X1))) & (? [X1] : (~tall(X1) & ~old(X1)) | ! [X0] : (generous(X0) & ~quiet(X0))) [nnf transformation 21]
40. (? [X0] : (~generous(X0) | quiet(X0)) | ! [X1] : (tall(X1) | old(X1))) & (? [X2] : (~tall(X2) & ~old(X2)) | ! [X3] : (generous(X3) & ~quiet(X3))) [rectify 39]
41. ? [X0] : (~generous(X0) | quiet(X0)) => (~generous(sK1) | quiet(sK1)) [choice axiom]
42. ? [X2] : (~tall(X2) & ~old(X2)) => (~tall(sK2) & ~old(sK2)) [choice axiom]
43. ((~generous(sK1) | quiet(sK1)) | ! [X1] : (tall(X1) | old(X1))) & ((~tall(sK2) & ~old(sK2)) | ! [X3] : (generous(X3) & ~quiet(X3))) [skolemisation 40,42,41]
50. ! [X0] : (((generous(X0) & tall(X0)) | (creative(X0) & tall(X0))) & ((~creative(X0) | ~tall(X0)) | (~generous(X0) | ~tall(X0)))) [nnf transformation 13]
51. ! [X0] : (((generous(X0) & tall(X0)) | (creative(X0) & tall(X0))) & (~creative(X0) | ~tall(X0) | ~generous(X0) | ~tall(X0))) [flattening 50]
78. ~tall(sK2) | generous(X3) [cnf transformation 43]
94. tall(X0) | tall(X0) [cnf transformation 51]
112. ~generous(john) [cnf transformation 20]
115. tall(X0) [duplicate literal removal 94]
161. 11 <=> ! [X3] : generous(X3) [avatar definition]
162. generous(X3) <- (11) [avatar component clause 161]
164. 12 <=> tall(sK2) [avatar definition]
166. ~tall(sK2) <- (~12) [avatar component clause 164]
167. 11 | ~12 [avatar split clause 78,164,161]
236. $false <- (~12) [subsumption resolution 166,115]
237. 12 [avatar contradiction clause 236]
238. $false <- (11) [resolution 162,112]
241. ~11 [avatar contradiction clause 238]
242. $false [avatar sat refutation 167,237,241]
% SZS output end Proof for 5724308007762847131295108
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is funny or not calm is brave and vice versa.
If fred is not calm or not tall then someone is curious or calm and vice versa.
If susan is either not creative or patient then paul is both not patient and not brave and vice versa.
Everyone who is either quiet or generous is not quiet.
Everyone who is happy is either funny or not wise.
If someone is not rich or not patient then paul is not brave.
Everyone who is either not happy or not creative is tall or patient and vice versa.
If someone is both creative and tall then mary is strong or old.
Everyone who is not patient or humble is either brave or not generous and vice versa.
Everyone who is not kind or brave is not rich or happy and vice versa.
Everyone who is not rich is both not curious and happy and vice versa.
If someone is either happy or curious then someone is both happy and not wise and vice versa.
Everyone who is not tall or happy is both humble and not generous.
Everyone who is either curious or brave is not tall or not wise and vice versa.
If lucy is either not old or calm then susan is tall.
Everyone who is either not patient or not humble is either not rich or funny.
John is not patient or not curious.
Susan is both not brave and not generous.
Someone is either not strong or not tall.
Someone is both not old and wise.
Someone is either not brave or brave.
Someone is not calm or not funny.
Paul is either not tall or not rich. | Paul is not generous. | entailment | (![X]:((funny(X)|~calm(X))<=>brave(X)))&
(((~calm(fred)|~tall(fred)))<=>(?[X]:((curious(X)|calm(X)))))&
(((~creative(susan)<~>patient(susan)))<=>((~patient(paul)&~brave(paul))))&
(![X]:((quiet(X)<~>generous(X))=>~quiet(X)))&
(![X]:(happy(X)=>(funny(X)<~>~wise(X))))&
((?[X]:((~rich(X)|~patient(X))))=>(~brave(paul)))&
(![X]:((~happy(X)<~>~creative(X))<=>(tall(X)|patient(X))))&
((?[X]:((creative(X)&tall(X))))=>((strong(mary)|old(mary))))&
(![X]:((~patient(X)|humble(X))<=>(brave(X)<~>~generous(X))))&
(![X]:((~kind(X)|brave(X))<=>(~rich(X)|happy(X))))&
(![X]:(~rich(X)<=>(~curious(X)&happy(X))))&
((?[X]:((happy(X)<~>curious(X))))<=>(?[X]:((happy(X)&~wise(X)))))&
(![X]:((~tall(X)|happy(X))=>(humble(X)&~generous(X))))&
(![X]:((curious(X)<~>brave(X))<=>(~tall(X)|~wise(X))))&
(((~old(lucy)<~>calm(lucy)))=>(tall(susan)))&
(![X]:((~patient(X)<~>~humble(X))=>(~rich(X)<~>funny(X))))&
((~patient(john)|~curious(john)))&
((~brave(susan)&~generous(susan)))&
(?[X]:((~strong(X)<~>~tall(X))))&
(?[X]:((~old(X)&wise(X))))&
(?[X]:((~brave(X)<~>brave(X))))&
(?[X]:((~calm(X)|~funny(X))))&
((~tall(paul)<~>~rich(paul))) | ~generous(paul) | [
"p10",
"p12",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 3724715872438133235938880
% SZS output start Proof for 3724715872438133235938880
11. ! [X0] : (~rich(X0) <=> (happy(X0) & ~curious(X0))) [input p10]
13. ! [X0] : ((happy(X0) | ~tall(X0)) => (~generous(X0) & humble(X0))) [input p12]
23. ~tall(paul) <~> ~rich(paul) [input p22]
24. generous(paul) [input hypothesis]
31. ! [X0] : ((~generous(X0) & humble(X0)) | (~happy(X0) & tall(X0))) [ennf transformation 13]
51. ! [X0] : ((~rich(X0) | (~happy(X0) | curious(X0))) & ((happy(X0) & ~curious(X0)) | rich(X0))) [nnf transformation 11]
52. ! [X0] : ((~rich(X0) | ~happy(X0) | curious(X0)) & ((happy(X0) & ~curious(X0)) | rich(X0))) [flattening 51]
72. (rich(paul) | tall(paul)) & (~rich(paul) | ~tall(paul)) [nnf transformation 23]
110. rich(X0) | happy(X0) [cnf transformation 52]
120. ~generous(X0) | tall(X0) [cnf transformation 31]
121. ~happy(X0) | ~generous(X0) [cnf transformation 31]
144. ~rich(paul) | ~tall(paul) [cnf transformation 72]
146. generous(paul) [cnf transformation 24]
290. 32 <=> tall(paul) [avatar definition]
294. 33 <=> rich(paul) [avatar definition]
295. ~rich(paul) <- (~33) [avatar component clause 294]
298. ~32 | ~33 [avatar split clause 144,294,290]
302. happy(paul) <- (~33) [resolution 110,295]
304. tall(paul) [resolution 120,146]
305. ~generous(paul) <- (~33) [resolution 121,302]
306. $false <- (~33) [subsumption resolution 305,146]
307. 33 [avatar contradiction clause 306]
308. 32 [avatar split clause 304,290]
309. $false [avatar sat refutation 298,307,308]
% SZS output end Proof for 3724715872438133235938880
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If susan is not rich then susan is humble or not calm. Everyone who is not calm is either quiet or humble and vice versa. If fred is not creative or not generous then someone is not calm or not tall. Everyone who is funny is not kind or patient and vice versa. If someone is either brave or funny then someone is both not generous and brave. Everyone who is not generous or wise is either not humble or not quiet. Everyone who is both wise and not wise is both not rich and not tall and vice versa. If someone is not creative or not brave then susan is both not calm and not creative and vice versa. Everyone who is either generous or not humble is brave or not old and vice versa. Everyone who is funny or not generous is both patient and old. Everyone who is either not funny or wise is brave and vice versa. Everyone who is wise or not kind is not patient and vice versa. Everyone who is creative is patient. If someone is not generous or rich then someone is not patient or not funny. Everyone who is either quiet or not happy is generous or not generous and vice versa. John is either quiet or strong. Paul is curious or happy. Someone is either quiet or curious. John is either patient or not quiet. Lucy is not curious. Alice is either not creative or tall. Someone is not calm or not funny. | Fred is patient. | contradiction | ((~rich(susan))=>((humble(susan)|~calm(susan))))&
(![X]:(~calm(X)<=>(quiet(X)<~>humble(X))))&
(((~creative(fred)|~generous(fred)))=>(?[X]:((~calm(X)|~tall(X)))))&
(![X]:(funny(X)<=>(~kind(X)|patient(X))))&
((?[X]:((brave(X)<~>funny(X))))=>(?[X]:((~generous(X)&brave(X)))))&
(![X]:((~generous(X)|wise(X))=>(~humble(X)<~>~quiet(X))))&
(![X]:((wise(X)&~wise(X))<=>(~rich(X)&~tall(X))))&
((?[X]:((~creative(X)|~brave(X))))<=>((~calm(susan)&~creative(susan))))&
(![X]:((generous(X)<~>~humble(X))<=>(brave(X)|~old(X))))&
(![X]:((funny(X)|~generous(X))=>(patient(X)&old(X))))&
(![X]:((~funny(X)<~>wise(X))<=>brave(X)))&
(![X]:((wise(X)|~kind(X))<=>~patient(X)))&
(![X]:(creative(X)=>patient(X)))&
((?[X]:((~generous(X)|rich(X))))=>(?[X]:((~patient(X)|~funny(X)))))&
(![X]:((quiet(X)<~>~happy(X))<=>(generous(X)|~generous(X))))&
((quiet(john)<~>strong(john)))&
((curious(paul)|happy(paul)))&
(?[X]:((quiet(X)<~>curious(X))))&
((patient(john)<~>~quiet(john)))&
(~curious(lucy))&
((~creative(alice)<~>tall(alice)))&
(?[X]:((~calm(X)|~funny(X)))) | patient(fred) | [
"p3",
"p4",
"p9",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 114979278284973708145461
% SZS output start Proof for 114979278284973708145461
4. ! [X0] : (funny(X0) <=> (patient(X0) | ~kind(X0))) [input p3]
5. ? [X0] : (brave(X0) <~> funny(X0)) => ? [X0] : (brave(X0) & ~generous(X0)) [input p4]
10. ! [X0] : ((~generous(X0) | funny(X0)) => (old(X0) & patient(X0))) [input p9]
11. ! [X0] : ((~funny(X0) <~> wise(X0)) <=> brave(X0)) [input p10]
12. ! [X0] : ((~kind(X0) | wise(X0)) <=> ~patient(X0)) [input p11]
23. patient(fred) [input hypothesis]
24. ? [X0] : (brave(X0) <~> funny(X0)) => ? [X1] : (brave(X1) & ~generous(X1)) [rectify 5]
29. ? [X1] : (brave(X1) & ~generous(X1)) | ! [X0] : (brave(X0) <=> funny(X0)) [ennf transformation 24]
31. ! [X0] : ((old(X0) & patient(X0)) | (generous(X0) & ~funny(X0))) [ennf transformation 10]
37. ! [X0] : ((funny(X0) | (~patient(X0) & kind(X0))) & ((patient(X0) | ~kind(X0)) | ~funny(X0))) [nnf transformation 4]
38. ! [X0] : ((funny(X0) | (~patient(X0) & kind(X0))) & (patient(X0) | ~kind(X0) | ~funny(X0))) [flattening 37]
39. ? [X1] : (brave(X1) & ~generous(X1)) | ! [X0] : ((brave(X0) | ~funny(X0)) & (funny(X0) | ~brave(X0))) [nnf transformation 29]
40. ? [X0] : (brave(X0) & ~generous(X0)) | ! [X1] : ((brave(X1) | ~funny(X1)) & (funny(X1) | ~brave(X1))) [rectify 39]
41. ? [X0] : (brave(X0) & ~generous(X0)) => (brave(sK1) & ~generous(sK1)) [choice axiom]
42. (brave(sK1) & ~generous(sK1)) | ! [X1] : ((brave(X1) | ~funny(X1)) & (funny(X1) | ~brave(X1))) [skolemisation 40,41]
53. ! [X0] : ((((~wise(X0) | funny(X0)) & (wise(X0) | ~funny(X0))) | ~brave(X0)) & (brave(X0) | ((~funny(X0) | ~wise(X0)) & (wise(X0) | funny(X0))))) [nnf transformation 11]
54. ! [X0] : (((~kind(X0) | wise(X0)) | patient(X0)) & (~patient(X0) | (kind(X0) & ~wise(X0)))) [nnf transformation 12]
55. ! [X0] : ((~kind(X0) | wise(X0) | patient(X0)) & (~patient(X0) | (kind(X0) & ~wise(X0)))) [flattening 54]
77. kind(X0) | funny(X0) [cnf transformation 38]
78. ~patient(X0) | funny(X0) [cnf transformation 38]
82. brave(sK1) | brave(X1) | ~funny(X1) [cnf transformation 42]
102. ~funny(X0) | patient(X0) [cnf transformation 31]
108. ~brave(X0) | ~funny(X0) | wise(X0) [cnf transformation 53]
109. ~wise(X0) | funny(X0) | ~brave(X0) [cnf transformation 53]
110. ~wise(X0) | ~patient(X0) [cnf transformation 55]
112. ~kind(X0) | wise(X0) | patient(X0) [cnf transformation 55]
133. patient(fred) [cnf transformation 23]
166. 8 <=> ! [X1] : (brave(X1) | ~funny(X1)) [avatar definition]
167. ~funny(X1) | brave(X1) <- (8) [avatar component clause 166]
169. 9 <=> brave(sK1) [avatar definition]
171. brave(sK1) <- (9) [avatar component clause 169]
172. 8 | 9 [avatar split clause 82,169,166]
174. 10 <=> ! [X1] : (funny(X1) | ~brave(X1)) [avatar definition]
175. ~brave(X1) | funny(X1) <- (10) [avatar component clause 174]
277. funny(fred) [resolution 78,133]
343. brave(fred) <- (8) [resolution 167,277]
345. funny(sK1) <- (9, 10) [resolution 175,171]
348. patient(sK1) <- (9, 10) [resolution 345,102]
417. ~funny(sK1) | wise(sK1) <- (9) [resolution 108,171]
418. ~funny(fred) | wise(fred) <- (8) [resolution 108,343]
420. wise(sK1) <- (9, 10) [subsumption resolution 417,345]
421. wise(fred) <- (8) [subsumption resolution 418,277]
430. wise(X0) | patient(X0) | funny(X0) [resolution 112,77]
434. wise(X0) | funny(X0) [subsumption resolution 430,78]
444. ~patient(sK1) <- (9, 10) [resolution 420,110]
445. $false <- (9, 10) [subsumption resolution 444,348]
446. ~9 | ~10 [avatar contradiction clause 445]
499. ~patient(fred) <- (8) [resolution 421,110]
501. $false <- (8) [subsumption resolution 499,133]
502. ~8 [avatar contradiction clause 501]
536. funny(X0) | funny(X0) | ~brave(X0) [resolution 434,109]
542. funny(X0) | ~brave(X0) [duplicate literal removal 536]
543. 10 [avatar split clause 542,174]
544. $false [avatar sat refutation 172,446,502,543]
% SZS output end Proof for 114979278284973708145461
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not happy and tall then someone is not tall or not patient and vice versa. If susan is not quiet or funny then lucy is both not tall and not calm and vice versa. If someone is strong or patient then paul is creative or not patient and vice versa. If someone is either not calm or creative then alice is either brave or humble and vice versa. If someone is either generous or not wise then someone is either generous or funny. If paul is either calm or not old then john is calm and vice versa. Everyone who is brave is wise or happy. Everyone who is not quiet is either rich or not humble. Everyone who is old is not wise or not tall and vice versa. Everyone who is strong or quiet is tall and vice versa. Everyone who is either old or not funny is both not humble and not patient and vice versa. If someone is not calm then someone is both old and strong and vice versa. Everyone who is both brave and wise is not generous. Everyone who is either not kind or kind is not quiet or humble and vice versa. Everyone who is not rich or brave is not patient. Everyone who is creative or humble is either not curious or kind. John is both not happy and wise. Someone is both kind and wise. Lucy is either curious or not curious. Someone is either not rich or not happy. John is not humble. Paul is calm. Lucy is not old or not wise. Paul is not old. | Paul is not wise. | contradiction | ((?[X]:((~happy(X)&tall(X))))<=>(?[X]:((~tall(X)|~patient(X)))))&
(((~quiet(susan)|funny(susan)))<=>((~tall(lucy)&~calm(lucy))))&
((?[X]:((strong(X)|patient(X))))<=>((creative(paul)|~patient(paul))))&
((?[X]:((~calm(X)<~>creative(X))))<=>((brave(alice)<~>humble(alice))))&
((?[X]:((generous(X)<~>~wise(X))))=>(?[X]:((generous(X)<~>funny(X)))))&
(((calm(paul)<~>~old(paul)))<=>(calm(john)))&
(![X]:(brave(X)=>(wise(X)|happy(X))))&
(![X]:(~quiet(X)=>(rich(X)<~>~humble(X))))&
(![X]:(old(X)<=>(~wise(X)|~tall(X))))&
(![X]:((strong(X)|quiet(X))<=>tall(X)))&
(![X]:((old(X)<~>~funny(X))<=>(~humble(X)&~patient(X))))&
((?[X]:(~calm(X)))<=>(?[X]:((old(X)&strong(X)))))&
(![X]:((brave(X)&wise(X))=>~generous(X)))&
(![X]:((~kind(X)<~>kind(X))<=>(~quiet(X)|humble(X))))&
(![X]:((~rich(X)|brave(X))=>~patient(X)))&
(![X]:((creative(X)|humble(X))=>(~curious(X)<~>kind(X))))&
((~happy(john)&wise(john)))&
(?[X]:((kind(X)&wise(X))))&
((curious(lucy)<~>~curious(lucy)))&
(?[X]:((~rich(X)<~>~happy(X))))&
(~humble(john))&
(calm(paul))&
((~old(lucy)|~wise(lucy)))&
(~old(paul)) | ~wise(paul) | [
"p8",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 8848470460842805437978865
% SZS output start Proof for 8848470460842805437978865
9. ! [X0] : (old(X0) <=> (~tall(X0) | ~wise(X0))) [input p8]
24. ~old(paul) [input p23]
25. ~wise(paul) [input hypothesis]
59. ! [X0] : ((old(X0) | (tall(X0) & wise(X0))) & ((~tall(X0) | ~wise(X0)) | ~old(X0))) [nnf transformation 9]
60. ! [X0] : ((old(X0) | (tall(X0) & wise(X0))) & (~tall(X0) | ~wise(X0) | ~old(X0))) [flattening 59]
113. old(X0) | wise(X0) [cnf transformation 60]
151. ~old(paul) [cnf transformation 24]
152. ~wise(paul) [cnf transformation 25]
289. 30 <=> old(paul) [avatar definition]
290. ~old(paul) <- (~30) [avatar component clause 289]
338. ~30 [avatar split clause 151,289]
347. wise(paul) <- (~30) [resolution 113,290]
348. $false <- (~30) [subsumption resolution 347,152]
349. 30 [avatar contradiction clause 348]
350. $false [avatar sat refutation 338,349]
% SZS output end Proof for 8848470460842805437978865
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not curious or not rich is strong.
Everyone who is not generous or not patient is either not quiet or quiet and vice versa.
Everyone who is both kind and not calm is not kind or brave.
If alice is both not creative and not happy then someone is either not strong or not rich.
If someone is rich or not generous then paul is both wise and not old and vice versa.
Everyone who is not quiet or creative is either not brave or not wise and vice versa.
Everyone who is both not patient and quiet is not strong and vice versa.
Everyone who is not kind is either happy or not happy and vice versa.
Everyone who is not wise or generous is tall and vice versa.
If someone is calm then lucy is not humble and vice versa.
If john is either not rich or not creative then susan is both generous and tall.
If someone is not tall or not old then fred is funny and vice versa.
If mary is both quiet and not quiet then someone is either generous or not brave.
If paul is not strong or humble then someone is both not humble and not patient and vice versa.
If susan is patient or funny then susan is both not patient and strong and vice versa.
Everyone who is both brave and generous is not brave.
Fred is not calm or kind.
Mary is creative.
Someone is both not generous and creative.
Mary is either happy or kind.
Someone is both not old and not generous.
Paul is either not humble or brave.
Alice is either not humble or not brave. | Alice is not strong. | neutral | (![X]:((~curious(X)|~rich(X))=>strong(X)))&
(![X]:((~generous(X)|~patient(X))<=>(~quiet(X)<~>quiet(X))))&
(![X]:((kind(X)&~calm(X))=>(~kind(X)|brave(X))))&
(((~creative(alice)&~happy(alice)))=>(?[X]:((~strong(X)<~>~rich(X)))))&
((?[X]:((rich(X)|~generous(X))))<=>((wise(paul)&~old(paul))))&
(![X]:((~quiet(X)|creative(X))<=>(~brave(X)<~>~wise(X))))&
(![X]:((~patient(X)&quiet(X))<=>~strong(X)))&
(![X]:(~kind(X)<=>(happy(X)<~>~happy(X))))&
(![X]:((~wise(X)|generous(X))<=>tall(X)))&
((?[X]:(calm(X)))<=>(~humble(lucy)))&
(((~rich(john)<~>~creative(john)))=>((generous(susan)&tall(susan))))&
((?[X]:((~tall(X)|~old(X))))<=>(funny(fred)))&
(((quiet(mary)&~quiet(mary)))=>(?[X]:((generous(X)<~>~brave(X)))))&
(((~strong(paul)|humble(paul)))<=>(?[X]:((~humble(X)&~patient(X)))))&
(((patient(susan)|funny(susan)))<=>((~patient(susan)&strong(susan))))&
(![X]:((brave(X)&generous(X))=>~brave(X)))&
((~calm(fred)|kind(fred)))&
(creative(mary))&
(?[X]:((~generous(X)&creative(X))))&
((happy(mary)<~>kind(mary)))&
(?[X]:((~old(X)&~generous(X))))&
((~humble(paul)<~>brave(paul)))&
((~humble(alice)<~>~brave(alice))) | ~strong(alice) | [] | null | 0 |
Everyone who is both not generous and wise is either not curious or not calm and vice versa.
Everyone who is both not tall and not happy is not patient and vice versa.
If someone is either kind or generous then someone is not humble.
Everyone who is both not wise and rich is funny or humble and vice versa.
Everyone who is either quiet or humble is both not tall and not old and vice versa.
If someone is not tall or not calm then susan is old.
If someone is not humble then alice is both kind and brave and vice versa.
If lucy is not funny or not brave then lucy is either funny or not curious and vice versa.
Everyone who is both curious and brave is both not patient and old and vice versa.
If someone is either curious or funny then mary is both not funny and not old.
Everyone who is not funny or not brave is not wise.
Everyone who is both not happy and brave is either not calm or strong and vice versa.
Everyone who is both not generous and not wise is either not kind or not generous.
Everyone who is both not tall and generous is brave or not brave and vice versa.
If paul is not wise or not calm then fred is either not wise or not brave and vice versa.
Everyone who is both kind and quiet is rich and vice versa.
John is both humble and not wise.
Someone is both strong and not quiet.
Lucy is not funny.
Fred is not patient or not old.
Someone is either quiet or wise.
Someone is both brave and curious.
Lucy is brave.
Someone is happy or not happy. | Alice is kind. | entailment | (![X]:((~generous(X)&wise(X))<=>(~curious(X)<~>~calm(X))))&
(![X]:((~tall(X)&~happy(X))<=>~patient(X)))&
((?[X]:((kind(X)<~>generous(X))))=>(?[X]:(~humble(X))))&
(![X]:((~wise(X)&rich(X))<=>(funny(X)|humble(X))))&
(![X]:((quiet(X)<~>humble(X))<=>(~tall(X)&~old(X))))&
((?[X]:((~tall(X)|~calm(X))))=>(old(susan)))&
((?[X]:(~humble(X)))<=>((kind(alice)&brave(alice))))&
(((~funny(lucy)|~brave(lucy)))<=>((funny(lucy)<~>~curious(lucy))))&
(![X]:((curious(X)&brave(X))<=>(~patient(X)&old(X))))&
((?[X]:((curious(X)<~>funny(X))))=>((~funny(mary)&~old(mary))))&
(![X]:((~funny(X)|~brave(X))=>~wise(X)))&
(![X]:((~happy(X)&brave(X))<=>(~calm(X)<~>strong(X))))&
(![X]:((~generous(X)&~wise(X))=>(~kind(X)<~>~generous(X))))&
(![X]:((~tall(X)&generous(X))<=>(brave(X)|~brave(X))))&
(((~wise(paul)|~calm(paul)))<=>((~wise(fred)<~>~brave(fred))))&
(![X]:((kind(X)&quiet(X))<=>rich(X)))&
((humble(john)&~wise(john)))&
(?[X]:((strong(X)&~quiet(X))))&
(~funny(lucy))&
((~patient(fred)|~old(fred)))&
(?[X]:((quiet(X)<~>wise(X))))&
(?[X]:((brave(X)&curious(X))))&
(brave(lucy))&
(?[X]:((happy(X)|~happy(X)))) | kind(alice) | [
"p2",
"p6",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 3082505354303817630109568
% SZS output start Proof for 3082505354303817630109568
3. ? [X0] : (kind(X0) <~> generous(X0)) => ? [X0] : ~humble(X0) [input p2]
7. ? [X0] : ~humble(X0) <=> (brave(alice) & kind(alice)) [input p6]
14. ! [X0] : ((generous(X0) & ~tall(X0)) <=> (~brave(X0) | brave(X0))) [input p13]
25. ~kind(alice) [input hypothesis]
26. ? [X0] : (kind(X0) <~> generous(X0)) => ? [X1] : ~humble(X1) [rectify 3]
27. ? [X1] : ~humble(X1) | ! [X0] : (kind(X0) <=> generous(X0)) [ennf transformation 26]
37. ? [X1] : ~humble(X1) | ! [X0] : ((kind(X0) | ~generous(X0)) & (generous(X0) | ~kind(X0))) [nnf transformation 27]
38. ? [X0] : ~humble(X0) | ! [X1] : ((kind(X1) | ~generous(X1)) & (generous(X1) | ~kind(X1))) [rectify 37]
39. ? [X0] : ~humble(X0) => ~humble(sK0) [choice axiom]
40. ~humble(sK0) | ! [X1] : ((kind(X1) | ~generous(X1)) & (generous(X1) | ~kind(X1))) [skolemisation 38,39]
45. (? [X0] : ~humble(X0) | (~brave(alice) | ~kind(alice))) & ((brave(alice) & kind(alice)) | ! [X0] : humble(X0)) [nnf transformation 7]
46. (? [X0] : ~humble(X0) | ~brave(alice) | ~kind(alice)) & ((brave(alice) & kind(alice)) | ! [X0] : humble(X0)) [flattening 45]
47. (? [X0] : ~humble(X0) | ~brave(alice) | ~kind(alice)) & ((brave(alice) & kind(alice)) | ! [X1] : humble(X1)) [rectify 46]
48. ? [X0] : ~humble(X0) => ~humble(sK1) [choice axiom]
49. (~humble(sK1) | ~brave(alice) | ~kind(alice)) & ((brave(alice) & kind(alice)) | ! [X1] : humble(X1)) [skolemisation 47,48]
58. ! [X0] : (((generous(X0) & ~tall(X0)) | (brave(X0) & ~brave(X0))) & ((~brave(X0) | brave(X0)) | (~generous(X0) | tall(X0)))) [nnf transformation 14]
59. ! [X0] : (((generous(X0) & ~tall(X0)) | (brave(X0) & ~brave(X0))) & (~brave(X0) | brave(X0) | ~generous(X0) | tall(X0))) [flattening 58]
83. ~humble(sK0) | kind(X1) | ~generous(X1) [cnf transformation 40]
97. kind(alice) | humble(X1) [cnf transformation 49]
127. generous(X0) | ~brave(X0) [cnf transformation 59]
128. generous(X0) | brave(X0) [cnf transformation 59]
150. ~kind(alice) [cnf transformation 25]
155. 1 <=> ! [X1] : (kind(X1) | ~generous(X1)) [avatar definition]
156. kind(X1) | ~generous(X1) <- (1) [avatar component clause 155]
158. 2 <=> humble(sK0) [avatar definition]
160. ~humble(sK0) <- (~2) [avatar component clause 158]
161. 1 | ~2 [avatar split clause 83,158,155]
179. 7 <=> kind(alice) [avatar definition]
181. ~kind(alice) <- (~7) [avatar component clause 179]
192. 10 <=> ! [X1] : humble(X1) [avatar definition]
193. humble(X1) <- (10) [avatar component clause 192]
195. 10 | 7 [avatar split clause 97,179,192]
232. generous(X0) [subsumption resolution 127,128]
259. ~7 [avatar split clause 150,179]
260. $false <- (~2, 10) [subsumption resolution 160,193]
261. 2 | ~10 [avatar contradiction clause 260]
262. kind(X1) <- (1) [subsumption resolution 156,232]
263. $false <- (1, ~7) [resolution 262,181]
264. ~1 | 7 [avatar contradiction clause 263]
265. $false [avatar sat refutation 161,195,259,261,264]
% SZS output end Proof for 3082505354303817630109568
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not rich or humble is patient or wise.
If alice is tall or not patient then someone is both quiet and patient and vice versa.
Everyone who is not calm is both not patient and curious and vice versa.
If lucy is both not wise and wise then someone is wise or not quiet and vice versa.
Everyone who is both not humble and not tall is both calm and not funny and vice versa.
Everyone who is either curious or not quiet is either not old or calm and vice versa.
If someone is not strong or not creative then someone is humble and vice versa.
If fred is both calm and old then someone is not old or not humble.
Everyone who is either not humble or patient is not wise.
Everyone who is either not rich or not tall is tall or calm and vice versa.
Everyone who is both not happy and not wise is not calm and vice versa.
If someone is not patient then susan is both rich and not tall and vice versa.
Everyone who is tall is either not rich or quiet.
If someone is either wise or curious then someone is not funny or not curious.
Everyone who is not brave or not curious is not kind and vice versa.
If someone is curious then someone is either not creative or tall.
Someone is curious or tall.
Someone is not wise.
Someone is brave or not kind.
Someone is either not funny or curious.
Alice is not strong. | Susan is rich. | entailment | (![X]:((~rich(X)|humble(X))=>(patient(X)|wise(X))))&
(((tall(alice)|~patient(alice)))<=>(?[X]:((quiet(X)&patient(X)))))&
(![X]:(~calm(X)<=>(~patient(X)&curious(X))))&
(((~wise(lucy)&wise(lucy)))<=>(?[X]:((wise(X)|~quiet(X)))))&
(![X]:((~humble(X)&~tall(X))<=>(calm(X)&~funny(X))))&
(![X]:((curious(X)<~>~quiet(X))<=>(~old(X)<~>calm(X))))&
((?[X]:((~strong(X)|~creative(X))))<=>(?[X]:(humble(X))))&
(((calm(fred)&old(fred)))=>(?[X]:((~old(X)|~humble(X)))))&
(![X]:((~humble(X)<~>patient(X))=>~wise(X)))&
(![X]:((~rich(X)<~>~tall(X))<=>(tall(X)|calm(X))))&
(![X]:((~happy(X)&~wise(X))<=>~calm(X)))&
((?[X]:(~patient(X)))<=>((rich(susan)&~tall(susan))))&
(![X]:(tall(X)=>(~rich(X)<~>quiet(X))))&
((?[X]:((wise(X)<~>curious(X))))=>(?[X]:((~funny(X)|~curious(X)))))&
(![X]:((~brave(X)|~curious(X))<=>~kind(X)))&
((?[X]:(curious(X)))=>(?[X]:((~creative(X)<~>tall(X)))))&
(?[X]:((curious(X)|tall(X))))&
(?[X]:(~wise(X)))&
(?[X]:((brave(X)|~kind(X))))&
(?[X]:((~funny(X)<~>curious(X))))&
(~strong(alice)) | rich(susan) | [
"p1",
"p3",
"p9",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 3361806631053852612167622
% SZS output start Proof for 3361806631053852612167622
2. (~patient(alice) | tall(alice)) <=> ? [X0] : (patient(X0) & quiet(X0)) [input p1]
4. (wise(lucy) & ~wise(lucy)) <=> ? [X0] : (~quiet(X0) | wise(X0)) [input p3]
10. ! [X0] : ((~rich(X0) <~> ~tall(X0)) <=> (calm(X0) | tall(X0))) [input p9]
12. ? [X0] : ~patient(X0) <=> (~tall(susan) & rich(susan)) [input p11]
13. ! [X0] : (tall(X0) => (~rich(X0) <~> quiet(X0))) [input p12]
22. ~rich(susan) [input hypothesis]
32. ! [X0] : ((~rich(X0) <~> quiet(X0)) | ~tall(X0)) [ennf transformation 13]
37. ((~patient(alice) | tall(alice)) | ! [X0] : (~patient(X0) | ~quiet(X0))) & (? [X0] : (patient(X0) & quiet(X0)) | (patient(alice) & ~tall(alice))) [nnf transformation 2]
38. (~patient(alice) | tall(alice) | ! [X0] : (~patient(X0) | ~quiet(X0))) & (? [X0] : (patient(X0) & quiet(X0)) | (patient(alice) & ~tall(alice))) [flattening 37]
39. (~patient(alice) | tall(alice) | ! [X0] : (~patient(X0) | ~quiet(X0))) & (? [X1] : (patient(X1) & quiet(X1)) | (patient(alice) & ~tall(alice))) [rectify 38]
40. ? [X1] : (patient(X1) & quiet(X1)) => (patient(sK0) & quiet(sK0)) [choice axiom]
41. (~patient(alice) | tall(alice) | ! [X0] : (~patient(X0) | ~quiet(X0))) & ((patient(sK0) & quiet(sK0)) | (patient(alice) & ~tall(alice))) [skolemisation 39,40]
44. ((wise(lucy) & ~wise(lucy)) | ! [X0] : (quiet(X0) & ~wise(X0))) & (? [X0] : (~quiet(X0) | wise(X0)) | (~wise(lucy) | wise(lucy))) [nnf transformation 4]
45. ((wise(lucy) & ~wise(lucy)) | ! [X0] : (quiet(X0) & ~wise(X0))) & (? [X0] : (~quiet(X0) | wise(X0)) | ~wise(lucy) | wise(lucy)) [flattening 44]
46. ((wise(lucy) & ~wise(lucy)) | ! [X0] : (quiet(X0) & ~wise(X0))) & (? [X1] : (~quiet(X1) | wise(X1)) | ~wise(lucy) | wise(lucy)) [rectify 45]
47. ? [X1] : (~quiet(X1) | wise(X1)) => (~quiet(sK1) | wise(sK1)) [choice axiom]
48. ((wise(lucy) & ~wise(lucy)) | ! [X0] : (quiet(X0) & ~wise(X0))) & ((~quiet(sK1) | wise(sK1)) | ~wise(lucy) | wise(lucy)) [skolemisation 46,47]
60. ! [X0] : ((((tall(X0) | rich(X0)) & (~tall(X0) | ~rich(X0))) | (~calm(X0) & ~tall(X0))) & ((calm(X0) | tall(X0)) | ((~rich(X0) | tall(X0)) & (~tall(X0) | rich(X0))))) [nnf transformation 10]
61. ! [X0] : ((((tall(X0) | rich(X0)) & (~tall(X0) | ~rich(X0))) | (~calm(X0) & ~tall(X0))) & (calm(X0) | tall(X0) | ((~rich(X0) | tall(X0)) & (~tall(X0) | rich(X0))))) [flattening 60]
64. (? [X0] : ~patient(X0) | (tall(susan) | ~rich(susan))) & ((~tall(susan) & rich(susan)) | ! [X0] : patient(X0)) [nnf transformation 12]
65. (? [X0] : ~patient(X0) | tall(susan) | ~rich(susan)) & ((~tall(susan) & rich(susan)) | ! [X0] : patient(X0)) [flattening 64]
66. (? [X0] : ~patient(X0) | tall(susan) | ~rich(susan)) & ((~tall(susan) & rich(susan)) | ! [X1] : patient(X1)) [rectify 65]
67. ? [X0] : ~patient(X0) => ~patient(sK5) [choice axiom]
68. (~patient(sK5) | tall(susan) | ~rich(susan)) & ((~tall(susan) & rich(susan)) | ! [X1] : patient(X1)) [skolemisation 66,67]
69. ! [X0] : (((~quiet(X0) | rich(X0)) & (quiet(X0) | ~rich(X0))) | ~tall(X0)) [nnf transformation 32]
93. ~patient(alice) | tall(alice) | ~patient(X0) | ~quiet(X0) [cnf transformation 41]
99. ~wise(lucy) | quiet(X0) [cnf transformation 48]
101. wise(lucy) | quiet(X0) [cnf transformation 48]
122. ~tall(X0) | ~rich(X0) | ~tall(X0) [cnf transformation 61]
129. rich(susan) | patient(X1) [cnf transformation 68]
133. ~quiet(X0) | rich(X0) | ~tall(X0) [cnf transformation 69]
145. ~rich(susan) [cnf transformation 22]
147. ~tall(X0) | ~rich(X0) [duplicate literal removal 122]
149. 1 <=> ! [X0] : (~patient(X0) | ~quiet(X0)) [avatar definition]
150. ~patient(X0) | ~quiet(X0) <- (1) [avatar component clause 149]
152. 2 <=> tall(alice) [avatar definition]
154. tall(alice) <- (2) [avatar component clause 152]
156. 3 <=> patient(alice) [avatar definition]
158. ~patient(alice) <- (~3) [avatar component clause 156]
159. 1 | 2 | ~3 [avatar split clause 93,156,152,149]
173. 6 <=> ! [X0] : quiet(X0) [avatar definition]
174. quiet(X0) <- (6) [avatar component clause 173]
176. 7 <=> wise(lucy) [avatar definition]
179. 6 | 7 [avatar split clause 101,176,173]
184. 6 | ~7 [avatar split clause 99,176,173]
234. 19 <=> rich(susan) [avatar definition]
243. 21 <=> ! [X1] : patient(X1) [avatar definition]
244. patient(X1) <- (21) [avatar component clause 243]
250. 21 | 19 [avatar split clause 129,234,243]
251. ~quiet(X0) | ~tall(X0) [subsumption resolution 133,147]
309. ~19 [avatar split clause 145,234]
310. $false <- (~3, 21) [subsumption resolution 158,244]
311. 3 | ~21 [avatar contradiction clause 310]
315. ~tall(X0) <- (6) [resolution 251,174]
316. $false <- (2, 6) [resolution 315,154]
317. ~2 | ~6 [avatar contradiction clause 316]
318. ~quiet(X0) <- (1, 21) [subsumption resolution 150,244]
319. $false <- (1, 6, 21) [subsumption resolution 318,174]
320. ~1 | ~6 | ~21 [avatar contradiction clause 319]
321. $false [avatar sat refutation 159,179,184,250,309,311,317,320]
% SZS output end Proof for 3361806631053852612167622
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not funny is not curious or not quiet and vice versa.
Everyone who is strong or not curious is both not strong and not tall.
Everyone who is old is both funny and not creative.
Everyone who is not rich or funny is not happy.
Everyone who is curious or not happy is not brave or humble and vice versa.
If susan is both not happy and tall then someone is either not humble or not patient and vice versa.
If paul is either not calm or kind then john is quiet and vice versa.
Everyone who is both not tall and not old is not generous or not old and vice versa.
If someone is not old or not generous then alice is wise and vice versa.
Everyone who is both funny and curious is either generous or not old.
Everyone who is both not funny and not humble is both not kind and old.
Everyone who is not kind is funny and vice versa.
Everyone who is both not quiet and funny is not kind or generous.
If someone is not wise or not brave then susan is not funny or curious.
If someone is old then someone is both wise and generous and vice versa.
If paul is both funny and tall then someone is not curious and vice versa.
Someone is both calm and not happy.
Someone is not humble.
Alice is either kind or calm.
Lucy is either quiet or not happy.
Someone is either not humble or patient.
John is not humble.
Someone is patient or brave.
Mary is both rich and not strong. | Mary is not strong. | entailment | (![X]:(~funny(X)<=>(~curious(X)|~quiet(X))))&
(![X]:((strong(X)|~curious(X))=>(~strong(X)&~tall(X))))&
(![X]:(old(X)=>(funny(X)&~creative(X))))&
(![X]:((~rich(X)|funny(X))=>~happy(X)))&
(![X]:((curious(X)|~happy(X))<=>(~brave(X)|humble(X))))&
(((~happy(susan)&tall(susan)))<=>(?[X]:((~humble(X)<~>~patient(X)))))&
(((~calm(paul)<~>kind(paul)))<=>(quiet(john)))&
(![X]:((~tall(X)&~old(X))<=>(~generous(X)|~old(X))))&
((?[X]:((~old(X)|~generous(X))))<=>(wise(alice)))&
(![X]:((funny(X)&curious(X))=>(generous(X)<~>~old(X))))&
(![X]:((~funny(X)&~humble(X))=>(~kind(X)&old(X))))&
(![X]:(~kind(X)<=>funny(X)))&
(![X]:((~quiet(X)&funny(X))=>(~kind(X)|generous(X))))&
((?[X]:((~wise(X)|~brave(X))))=>((~funny(susan)|curious(susan))))&
((?[X]:(old(X)))<=>(?[X]:((wise(X)&generous(X)))))&
(((funny(paul)&tall(paul)))<=>(?[X]:(~curious(X))))&
(?[X]:((calm(X)&~happy(X))))&
(?[X]:(~humble(X)))&
((kind(alice)<~>calm(alice)))&
((quiet(lucy)<~>~happy(lucy)))&
(?[X]:((~humble(X)<~>patient(X))))&
(~humble(john))&
(?[X]:((patient(X)|brave(X))))&
((rich(mary)&~strong(mary))) | ~strong(mary) | [
"p1",
"hypothesis"
] | % SZS status Unsatisfiable for 5334816733421440066479943
% SZS output start Proof for 5334816733421440066479943
2. ! [X0] : ((~curious(X0) | strong(X0)) => (~tall(X0) & ~strong(X0))) [input p1]
25. strong(mary) [input hypothesis]
30. ! [X0] : ((~tall(X0) & ~strong(X0)) | (curious(X0) & ~strong(X0))) [ennf transformation 2]
83. ~strong(X0) | ~strong(X0) [cnf transformation 30]
138. strong(mary) [cnf transformation 25]
139. ~strong(X0) [duplicate literal removal 83]
282. $false [subsumption resolution 138,139]
% SZS output end Proof for 5334816733421440066479943
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall and not generous is happy or wise.
If someone is either not old or wise then lucy is happy or humble and vice versa.
Everyone who is either not tall or not patient is both kind and happy and vice versa.
If john is not curious then someone is not old or not calm and vice versa.
If fred is not quiet then someone is not strong or funny and vice versa.
Everyone who is both not strong and happy is not creative and vice versa.
Everyone who is either not generous or not old is not generous or funny.
If someone is kind then someone is both not humble and rich and vice versa.
Everyone who is not kind is either not happy or not calm and vice versa.
Everyone who is not funny or funny is not wise or not quiet and vice versa.
If someone is calm then fred is happy.
Everyone who is not creative is quiet or patient.
If someone is either not rich or not curious then someone is rich.
If someone is either not curious or old then john is not kind or not patient and vice versa.
Everyone who is both not happy and not patient is not kind and vice versa.
If fred is tall or wise then someone is both not rich and generous and vice versa.
Fred is either not wise or kind.
Paul is not tall.
Fred is creative or old.
Mary is calm or not funny.
Someone is both not curious and funny.
Someone is not kind or not old.
Paul is old.
Mary is both not humble and not creative. | Fred is not strong. | neutral | (![X]:((~tall(X)&~generous(X))=>(happy(X)|wise(X))))&
((?[X]:((~old(X)<~>wise(X))))<=>((happy(lucy)|humble(lucy))))&
(![X]:((~tall(X)<~>~patient(X))<=>(kind(X)&happy(X))))&
((~curious(john))<=>(?[X]:((~old(X)|~calm(X)))))&
((~quiet(fred))<=>(?[X]:((~strong(X)|funny(X)))))&
(![X]:((~strong(X)&happy(X))<=>~creative(X)))&
(![X]:((~generous(X)<~>~old(X))=>(~generous(X)|funny(X))))&
((?[X]:(kind(X)))<=>(?[X]:((~humble(X)&rich(X)))))&
(![X]:(~kind(X)<=>(~happy(X)<~>~calm(X))))&
(![X]:((~funny(X)|funny(X))<=>(~wise(X)|~quiet(X))))&
((?[X]:(calm(X)))=>(happy(fred)))&
(![X]:(~creative(X)=>(quiet(X)|patient(X))))&
((?[X]:((~rich(X)<~>~curious(X))))=>(?[X]:(rich(X))))&
((?[X]:((~curious(X)<~>old(X))))<=>((~kind(john)|~patient(john))))&
(![X]:((~happy(X)&~patient(X))<=>~kind(X)))&
(((tall(fred)|wise(fred)))<=>(?[X]:((~rich(X)&generous(X)))))&
((~wise(fred)<~>kind(fred)))&
(~tall(paul))&
((creative(fred)|old(fred)))&
((calm(mary)|~funny(mary)))&
(?[X]:((~curious(X)&funny(X))))&
(?[X]:((~kind(X)|~old(X))))&
(old(paul))&
((~humble(mary)&~creative(mary))) | ~strong(fred) | [] | null | 0 |
If fred is either not calm or happy then fred is not old or wise and vice versa.
Everyone who is both happy and not generous is either creative or not tall and vice versa.
Everyone who is generous is both quiet and curious and vice versa.
If someone is either funny or not tall then mary is not humble or not kind.
If lucy is either calm or not kind then alice is not curious or brave.
Everyone who is both generous and tall is not curious and vice versa.
Everyone who is both humble and calm is both tall and not strong and vice versa.
Everyone who is funny is both not kind and not curious and vice versa.
If someone is not tall then susan is not wise or brave.
If fred is both generous and not curious then alice is generous or not kind.
If fred is not rich then someone is not old and vice versa.
Everyone who is either not creative or happy is both not rich and curious and vice versa.
If paul is quiet or not calm then john is generous and vice versa.
Everyone who is humble or not curious is either not patient or not rich and vice versa.
Everyone who is either quiet or not happy is both curious and not brave and vice versa.
Everyone who is not brave is old.
Someone is either not brave or not humble.
Someone is creative.
Mary is kind.
Mary is not calm or old.
Someone is both not strong and not kind.
Someone is either not creative or not tall.
Someone is wise or not strong.
Lucy is either calm or not curious. | Susan is generous. | neutral | (((~calm(fred)<~>happy(fred)))<=>((~old(fred)|wise(fred))))&
(![X]:((happy(X)&~generous(X))<=>(creative(X)<~>~tall(X))))&
(![X]:(generous(X)<=>(quiet(X)&curious(X))))&
((?[X]:((funny(X)<~>~tall(X))))=>((~humble(mary)|~kind(mary))))&
(((calm(lucy)<~>~kind(lucy)))=>((~curious(alice)|brave(alice))))&
(![X]:((generous(X)&tall(X))<=>~curious(X)))&
(![X]:((humble(X)&calm(X))<=>(tall(X)&~strong(X))))&
(![X]:(funny(X)<=>(~kind(X)&~curious(X))))&
((?[X]:(~tall(X)))=>((~wise(susan)|brave(susan))))&
(((generous(fred)&~curious(fred)))=>((generous(alice)|~kind(alice))))&
((~rich(fred))<=>(?[X]:(~old(X))))&
(![X]:((~creative(X)<~>happy(X))<=>(~rich(X)&curious(X))))&
(((quiet(paul)|~calm(paul)))<=>(generous(john)))&
(![X]:((humble(X)|~curious(X))<=>(~patient(X)<~>~rich(X))))&
(![X]:((quiet(X)<~>~happy(X))<=>(curious(X)&~brave(X))))&
(![X]:(~brave(X)=>old(X)))&
(?[X]:((~brave(X)<~>~humble(X))))&
(?[X]:(creative(X)))&
(kind(mary))&
((~calm(mary)|old(mary)))&
(?[X]:((~strong(X)&~kind(X))))&
(?[X]:((~creative(X)<~>~tall(X))))&
(?[X]:((wise(X)|~strong(X))))&
((calm(lucy)<~>~curious(lucy))) | generous(susan) | [] | null | 0 |
Everyone who is either happy or not strong is not strong and vice versa.
Everyone who is wise or brave is not funny or brave and vice versa.
If john is not happy or not kind then someone is either not tall or humble.
If alice is not brave or tall then someone is calm.
Everyone who is creative is not brave.
Everyone who is either strong or tall is funny or not old and vice versa.
Everyone who is both not rich and rich is not quiet or brave.
Everyone who is both not curious and not funny is generous or curious and vice versa.
If someone is either not calm or not wise then mary is either not old or not brave.
Everyone who is either not patient or generous is both not wise and patient and vice versa.
Everyone who is humble is both not humble and rich and vice versa.
If someone is both creative and brave then fred is either rich or brave.
If john is both quiet and humble then alice is both not old and old and vice versa.
Everyone who is both not happy and old is not patient or not quiet.
If susan is both not happy and calm then someone is either not tall or not quiet and vice versa.
If someone is either rich or not humble then someone is generous and vice versa.
Lucy is either brave or curious.
Alice is not humble.
Paul is both not tall and not patient.
Susan is old or wise.
Susan is either tall or creative.
Susan is either funny or not strong.
Paul is either rich or not creative. | Mary is old. | neutral | (![X]:((happy(X)<~>~strong(X))<=>~strong(X)))&
(![X]:((wise(X)|brave(X))<=>(~funny(X)|brave(X))))&
(((~happy(john)|~kind(john)))=>(?[X]:((~tall(X)<~>humble(X)))))&
(((~brave(alice)|tall(alice)))=>(?[X]:(calm(X))))&
(![X]:(creative(X)=>~brave(X)))&
(![X]:((strong(X)<~>tall(X))<=>(funny(X)|~old(X))))&
(![X]:((~rich(X)&rich(X))=>(~quiet(X)|brave(X))))&
(![X]:((~curious(X)&~funny(X))<=>(generous(X)|curious(X))))&
((?[X]:((~calm(X)<~>~wise(X))))=>((~old(mary)<~>~brave(mary))))&
(![X]:((~patient(X)<~>generous(X))<=>(~wise(X)&patient(X))))&
(![X]:(humble(X)<=>(~humble(X)&rich(X))))&
((?[X]:((creative(X)&brave(X))))=>((rich(fred)<~>brave(fred))))&
(((quiet(john)&humble(john)))<=>((~old(alice)&old(alice))))&
(![X]:((~happy(X)&old(X))=>(~patient(X)|~quiet(X))))&
(((~happy(susan)&calm(susan)))<=>(?[X]:((~tall(X)<~>~quiet(X)))))&
((?[X]:((rich(X)<~>~humble(X))))<=>(?[X]:(generous(X))))&
((brave(lucy)<~>curious(lucy)))&
(~humble(alice))&
((~tall(paul)&~patient(paul)))&
((old(susan)|wise(susan)))&
((tall(susan)<~>creative(susan)))&
((funny(susan)<~>~strong(susan)))&
((rich(paul)<~>~creative(paul))) | old(mary) | [] | null | 0 |
Everyone who is both not calm and not generous is both humble and not strong.
If lucy is not patient or not kind then susan is not curious.
If susan is both not generous and not rich then someone is not quiet and vice versa.
If someone is tall or generous then someone is either not old or brave.
If someone is brave then john is both humble and rich and vice versa.
Everyone who is either not curious or creative is either happy or not calm and vice versa.
If alice is both not wise and patient then alice is both humble and not quiet.
Everyone who is either happy or not patient is both not happy and kind.
Everyone who is both patient and not kind is not wise.
Everyone who is funny or not strong is calm or not creative.
If susan is not tall then someone is not old or not funny.
If mary is not calm then someone is either calm or not tall and vice versa.
If someone is either not calm or not kind then alice is both humble and not patient.
If someone is generous then mary is both not wise and not generous and vice versa.
If someone is either funny or not old then john is wise and vice versa.
If someone is not funny or tall then someone is both rich and not quiet and vice versa.
Alice is not old.
Alice is both wise and calm.
Someone is not strong.
Lucy is not calm or tall.
Susan is not old.
Alice is both humble and not strong.
Mary is not happy.
Someone is wise or creative. | Mary is generous. | contradiction | (![X]:((~calm(X)&~generous(X))=>(humble(X)&~strong(X))))&
(((~patient(lucy)|~kind(lucy)))=>(~curious(susan)))&
(((~generous(susan)&~rich(susan)))<=>(?[X]:(~quiet(X))))&
((?[X]:((tall(X)|generous(X))))=>(?[X]:((~old(X)<~>brave(X)))))&
((?[X]:(brave(X)))<=>((humble(john)&rich(john))))&
(![X]:((~curious(X)<~>creative(X))<=>(happy(X)<~>~calm(X))))&
(((~wise(alice)&patient(alice)))=>((humble(alice)&~quiet(alice))))&
(![X]:((happy(X)<~>~patient(X))=>(~happy(X)&kind(X))))&
(![X]:((patient(X)&~kind(X))=>~wise(X)))&
(![X]:((funny(X)|~strong(X))=>(calm(X)|~creative(X))))&
((~tall(susan))=>(?[X]:((~old(X)|~funny(X)))))&
((~calm(mary))<=>(?[X]:((calm(X)<~>~tall(X)))))&
((?[X]:((~calm(X)<~>~kind(X))))=>((humble(alice)&~patient(alice))))&
((?[X]:(generous(X)))<=>((~wise(mary)&~generous(mary))))&
((?[X]:((funny(X)<~>~old(X))))<=>(wise(john)))&
((?[X]:((~funny(X)|tall(X))))<=>(?[X]:((rich(X)&~quiet(X)))))&
(~old(alice))&
((wise(alice)&calm(alice)))&
(?[X]:(~strong(X)))&
((~calm(lucy)|tall(lucy)))&
(~old(susan))&
((humble(alice)&~strong(alice)))&
(~happy(mary))&
(?[X]:((wise(X)|creative(X)))) | generous(mary) | [
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 139258655035928038450254
% SZS output start Proof for 139258655035928038450254
14. ? [X0] : generous(X0) <=> (~generous(mary) & ~wise(mary)) [input p13]
25. generous(mary) [input hypothesis]
64. (? [X0] : generous(X0) | (generous(mary) | wise(mary))) & ((~generous(mary) & ~wise(mary)) | ! [X0] : ~generous(X0)) [nnf transformation 14]
65. (? [X0] : generous(X0) | generous(mary) | wise(mary)) & ((~generous(mary) & ~wise(mary)) | ! [X0] : ~generous(X0)) [flattening 64]
66. (? [X0] : generous(X0) | generous(mary) | wise(mary)) & ((~generous(mary) & ~wise(mary)) | ! [X1] : ~generous(X1)) [rectify 65]
67. ? [X0] : generous(X0) => generous(sK5) [choice axiom]
68. (generous(sK5) | generous(mary) | wise(mary)) & ((~generous(mary) & ~wise(mary)) | ! [X1] : ~generous(X1)) [skolemisation 66,67]
123. ~generous(mary) | ~generous(X1) [cnf transformation 68]
144. generous(mary) [cnf transformation 25]
179. 8 <=> ! [X1] : ~generous(X1) [avatar definition]
180. ~generous(X1) <- (8) [avatar component clause 179]
282. 31 <=> generous(mary) [avatar definition]
284. generous(mary) <- (31) [avatar component clause 282]
290. 8 | ~31 [avatar split clause 123,282,179]
361. 31 [avatar split clause 144,282]
368. $false <- (8, 31) [resolution 284,180]
369. ~8 | ~31 [avatar contradiction clause 368]
370. $false [avatar sat refutation 290,361,369]
% SZS output end Proof for 139258655035928038450254
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 lucy is curious or old then someone is quiet or not calm. If someone is either kind or strong then someone is generous and vice versa. If paul is either patient or not creative then someone is both not rich and funny and vice versa. If someone is patient then someone is either not funny or funny. If someone is generous then mary is brave or not rich and vice versa. If someone is both not brave and humble then someone is not strong or not humble. Everyone who is either patient or creative is both old and quiet. Everyone who is both not happy and generous is not calm and vice versa. Everyone who is not strong is kind or old and vice versa. Everyone who is kind or old is quiet and vice versa. Everyone who is both not humble and funny is either not generous or creative and vice versa. Everyone who is funny or generous is not quiet. If someone is either tall or kind then fred is calm. Everyone who is wise or not patient is not generous. If fred is both quiet and not quiet then mary is happy and vice versa. Everyone who is both rich and not wise is either not calm or not old and vice versa. John is not curious or old. Someone is either not quiet or tall. Paul is creative or humble. Fred is both generous and rich. Alice is both not funny and not strong. Mary is either humble or wise. Lucy is both rich and old. Someone is tall or quiet. | Fred is quiet. | contradiction | (((curious(lucy)|old(lucy)))=>(?[X]:((quiet(X)|~calm(X)))))&
((?[X]:((kind(X)<~>strong(X))))<=>(?[X]:(generous(X))))&
(((patient(paul)<~>~creative(paul)))<=>(?[X]:((~rich(X)&funny(X)))))&
((?[X]:(patient(X)))=>(?[X]:((~funny(X)<~>funny(X)))))&
((?[X]:(generous(X)))<=>((brave(mary)|~rich(mary))))&
((?[X]:((~brave(X)&humble(X))))=>(?[X]:((~strong(X)|~humble(X)))))&
(![X]:((patient(X)<~>creative(X))=>(old(X)&quiet(X))))&
(![X]:((~happy(X)&generous(X))<=>~calm(X)))&
(![X]:(~strong(X)<=>(kind(X)|old(X))))&
(![X]:((kind(X)|old(X))<=>quiet(X)))&
(![X]:((~humble(X)&funny(X))<=>(~generous(X)<~>creative(X))))&
(![X]:((funny(X)|generous(X))=>~quiet(X)))&
((?[X]:((tall(X)<~>kind(X))))=>(calm(fred)))&
(![X]:((wise(X)|~patient(X))=>~generous(X)))&
(((quiet(fred)&~quiet(fred)))<=>(happy(mary)))&
(![X]:((rich(X)&~wise(X))<=>(~calm(X)<~>~old(X))))&
((~curious(john)|old(john)))&
(?[X]:((~quiet(X)<~>tall(X))))&
((creative(paul)|humble(paul)))&
((generous(fred)&rich(fred)))&
((~funny(alice)&~strong(alice)))&
((humble(mary)<~>wise(mary)))&
((rich(lucy)&old(lucy)))&
(?[X]:((tall(X)|quiet(X)))) | quiet(fred) | [
"p11",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 8925076285623617853902679
% SZS output start Proof for 8925076285623617853902679
12. ! [X0] : ((generous(X0) | funny(X0)) => ~quiet(X0)) [input p11]
20. rich(fred) & generous(fred) [input p19]
25. quiet(fred) [input hypothesis]
35. ! [X0] : (~quiet(X0) | (~generous(X0) & ~funny(X0))) [ennf transformation 12]
118. ~generous(X0) | ~quiet(X0) [cnf transformation 35]
135. generous(fred) [cnf transformation 20]
144. quiet(fred) [cnf transformation 25]
252. 25 <=> quiet(fred) [avatar definition]
253. quiet(fred) <- (25) [avatar component clause 252]
292. 25 [avatar split clause 144,252]
299. ~quiet(fred) [resolution 118,135]
302. $false <- (25) [subsumption resolution 299,253]
303. ~25 [avatar contradiction clause 302]
304. $false [avatar sat refutation 292,303]
% SZS output end Proof for 8925076285623617853902679
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 john is patient then lucy is not quiet.
Everyone who is both brave and rich is calm or not patient.
Everyone who is both calm and curious is either not patient or rich.
Everyone who is both humble and not tall is quiet and vice versa.
If someone is not strong then someone is both quiet and not rich and vice versa.
Everyone who is old is not wise or patient.
If someone is both not happy and curious then someone is happy or not wise.
If mary is both rich and not old then susan is quiet or not patient.
Everyone who is either not patient or not funny is old.
Everyone who is both happy and funny is either generous or creative and vice versa.
If someone is either not strong or wise then someone is rich or not rich.
Everyone who is kind is both generous and not happy.
If someone is both quiet and brave then someone is not calm and vice versa.
Everyone who is either not kind or tall is calm.
Everyone who is not wise is either rich or not strong and vice versa.
Fred is both not kind and not funny.
Someone is either not old or happy.
Lucy is wise.
John is rich or not brave.
Mary is either patient or not rich.
Someone is both generous and not quiet.
Mary is funny or happy.
Someone is not generous. | Fred is not creative. | neutral | ((patient(john))=>(~quiet(lucy)))&
(![X]:((brave(X)&rich(X))=>(calm(X)|~patient(X))))&
(![X]:((calm(X)&curious(X))=>(~patient(X)<~>rich(X))))&
(![X]:((humble(X)&~tall(X))<=>quiet(X)))&
((?[X]:(~strong(X)))<=>(?[X]:((quiet(X)&~rich(X)))))&
(![X]:(old(X)=>(~wise(X)|patient(X))))&
((?[X]:((~happy(X)&curious(X))))=>(?[X]:((happy(X)|~wise(X)))))&
(((rich(mary)&~old(mary)))=>((quiet(susan)|~patient(susan))))&
(![X]:((~patient(X)<~>~funny(X))=>old(X)))&
(![X]:((happy(X)&funny(X))<=>(generous(X)<~>creative(X))))&
((?[X]:((~strong(X)<~>wise(X))))=>(?[X]:((rich(X)|~rich(X)))))&
(![X]:(kind(X)=>(generous(X)&~happy(X))))&
((?[X]:((quiet(X)&brave(X))))<=>(?[X]:(~calm(X))))&
(![X]:((~kind(X)<~>tall(X))=>calm(X)))&
(![X]:(~wise(X)<=>(rich(X)<~>~strong(X))))&
((~kind(fred)&~funny(fred)))&
(?[X]:((~old(X)<~>happy(X))))&
(wise(lucy))&
((rich(john)|~brave(john)))&
((patient(mary)<~>~rich(mary)))&
(?[X]:((generous(X)&~quiet(X))))&
((funny(mary)|happy(mary)))&
(?[X]:(~generous(X))) | ~creative(fred) | [] | null | 0 |
Everyone who is not curious is not wise or not old.
If someone is either brave or not funny then lucy is rich.
If someone is generous or creative then someone is both not tall and not kind and vice versa.
Everyone who is both not old and old is generous.
Everyone who is generous is not wise and vice versa.
Everyone who is old is not tall or not humble.
If john is both not kind and wise then someone is not rich.
Everyone who is not happy or not brave is not rich.
Everyone who is either humble or not generous is either not generous or not old.
If paul is either old or curious then susan is both quiet and not old.
Everyone who is not tall or not creative is both humble and wise.
Everyone who is tall is humble or wise and vice versa.
Everyone who is either creative or tall is humble.
Everyone who is either humble or curious is not rich or not tall.
Everyone who is old or not funny is funny or generous.
Everyone who is funny or brave is rich and vice versa.
Alice is not quiet or not happy.
Susan is not strong or not generous.
Someone is curious.
Someone is not old or curious. | Susan is wise. | entailment | (![X]:(~curious(X)=>(~wise(X)|~old(X))))&
((?[X]:((brave(X)<~>~funny(X))))=>(rich(lucy)))&
((?[X]:((generous(X)|creative(X))))<=>(?[X]:((~tall(X)&~kind(X)))))&
(![X]:((~old(X)&old(X))=>generous(X)))&
(![X]:(generous(X)<=>~wise(X)))&
(![X]:(old(X)=>(~tall(X)|~humble(X))))&
(((~kind(john)&wise(john)))=>(?[X]:(~rich(X))))&
(![X]:((~happy(X)|~brave(X))=>~rich(X)))&
(![X]:((humble(X)<~>~generous(X))=>(~generous(X)<~>~old(X))))&
(((old(paul)<~>curious(paul)))=>((quiet(susan)&~old(susan))))&
(![X]:((~tall(X)|~creative(X))=>(humble(X)&wise(X))))&
(![X]:(tall(X)<=>(humble(X)|wise(X))))&
(![X]:((creative(X)<~>tall(X))=>humble(X)))&
(![X]:((humble(X)<~>curious(X))=>(~rich(X)|~tall(X))))&
(![X]:((old(X)|~funny(X))=>(funny(X)|generous(X))))&
(![X]:((funny(X)|brave(X))<=>rich(X)))&
((~quiet(alice)|~happy(alice)))&
((~strong(susan)|~generous(susan)))&
(?[X]:(curious(X)))&
(?[X]:((~old(X)|curious(X)))) | wise(susan) | [
"p2",
"p4",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 5597847520363459833823419
% SZS output start Proof for 5597847520363459833823419
3. ? [X0] : (creative(X0) | generous(X0)) <=> ? [X0] : (~kind(X0) & ~tall(X0)) [input p2]
5. ! [X0] : (generous(X0) <=> ~wise(X0)) [input p4]
11. ! [X0] : ((~creative(X0) | ~tall(X0)) => (wise(X0) & humble(X0))) [input p10]
12. ! [X0] : (tall(X0) <=> (wise(X0) | humble(X0))) [input p11]
21. ~wise(susan) [input hypothesis]
22. ? [X0] : (creative(X0) | generous(X0)) <=> ? [X1] : (~kind(X1) & ~tall(X1)) [rectify 3]
36. ! [X0] : ((wise(X0) & humble(X0)) | (creative(X0) & tall(X0))) [ennf transformation 11]
43. (? [X0] : (creative(X0) | generous(X0)) | ! [X1] : (kind(X1) | tall(X1))) & (? [X1] : (~kind(X1) & ~tall(X1)) | ! [X0] : (~creative(X0) & ~generous(X0))) [nnf transformation 22]
44. (? [X0] : (creative(X0) | generous(X0)) | ! [X1] : (kind(X1) | tall(X1))) & (? [X2] : (~kind(X2) & ~tall(X2)) | ! [X3] : (~creative(X3) & ~generous(X3))) [rectify 43]
45. ? [X0] : (creative(X0) | generous(X0)) => (creative(sK0) | generous(sK0)) [choice axiom]
46. ? [X2] : (~kind(X2) & ~tall(X2)) => (~kind(sK1) & ~tall(sK1)) [choice axiom]
47. ((creative(sK0) | generous(sK0)) | ! [X1] : (kind(X1) | tall(X1))) & ((~kind(sK1) & ~tall(sK1)) | ! [X3] : (~creative(X3) & ~generous(X3))) [skolemisation 44,46,45]
48. ! [X0] : ((generous(X0) | wise(X0)) & (~wise(X0) | ~generous(X0))) [nnf transformation 5]
53. ! [X0] : ((tall(X0) | (~wise(X0) & ~humble(X0))) & ((wise(X0) | humble(X0)) | ~tall(X0))) [nnf transformation 12]
54. ! [X0] : ((tall(X0) | (~wise(X0) & ~humble(X0))) & (wise(X0) | humble(X0) | ~tall(X0))) [flattening 53]
66. ~tall(sK1) | ~generous(X3) [cnf transformation 47]
73. generous(X0) | wise(X0) [cnf transformation 48]
88. wise(X0) | tall(X0) [cnf transformation 36]
92. tall(X0) | ~wise(X0) [cnf transformation 54]
105. ~wise(susan) [cnf transformation 21]
142. 9 <=> ! [X3] : ~generous(X3) [avatar definition]
143. ~generous(X3) <- (9) [avatar component clause 142]
146. 10 <=> tall(sK1) [avatar definition]
148. ~tall(sK1) <- (~10) [avatar component clause 146]
150. 9 | ~10 [avatar split clause 66,146,142]
184. tall(X0) [subsumption resolution 92,88]
206. $false <- (~10) [subsumption resolution 148,184]
207. 10 [avatar contradiction clause 206]
209. wise(X1) <- (9) [resolution 73,143]
210. $false <- (9) [resolution 209,105]
211. ~9 [avatar contradiction clause 210]
212. $false [avatar sat refutation 150,207,211]
% SZS output end Proof for 5597847520363459833823419
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 fred is not wise or not old then susan is either funny or patient and vice versa.
If someone is not humble then someone is not calm or not kind and vice versa.
Everyone who is brave or not rich is either not rich or not quiet and vice versa.
Everyone who is strong is not creative or humble.
If someone is both not rich and not old then someone is either happy or not old.
Everyone who is not old is wise and vice versa.
Everyone who is both not patient and not curious is curious.
Everyone who is creative or not wise is both happy and not generous.
Everyone who is brave or not quiet is either not patient or rich and vice versa.
If someone is either not strong or not quiet then someone is curious or not patient and vice versa.
If someone is either kind or not funny then fred is not brave.
If someone is either not kind or old then someone is curious or calm.
If mary is not rich then someone is not rich or not humble and vice versa.
Everyone who is tall is both generous and not calm.
Everyone who is either not creative or wise is strong or not humble.
Everyone who is quiet is not strong.
Someone is not calm or not strong.
Mary is not quiet or not generous.
Someone is either not calm or patient.
Someone is not calm.
Susan is either not quiet or not strong.
Someone is both brave and not generous.
Paul is either humble or not creative.
Someone is quiet. | Susan is not old. | neutral | (((~wise(fred)|~old(fred)))<=>((funny(susan)<~>patient(susan))))&
((?[X]:(~humble(X)))<=>(?[X]:((~calm(X)|~kind(X)))))&
(![X]:((brave(X)|~rich(X))<=>(~rich(X)<~>~quiet(X))))&
(![X]:(strong(X)=>(~creative(X)|humble(X))))&
((?[X]:((~rich(X)&~old(X))))=>(?[X]:((happy(X)<~>~old(X)))))&
(![X]:(~old(X)<=>wise(X)))&
(![X]:((~patient(X)&~curious(X))=>curious(X)))&
(![X]:((creative(X)|~wise(X))=>(happy(X)&~generous(X))))&
(![X]:((brave(X)|~quiet(X))<=>(~patient(X)<~>rich(X))))&
((?[X]:((~strong(X)<~>~quiet(X))))<=>(?[X]:((curious(X)|~patient(X)))))&
((?[X]:((kind(X)<~>~funny(X))))=>(~brave(fred)))&
((?[X]:((~kind(X)<~>old(X))))=>(?[X]:((curious(X)|calm(X)))))&
((~rich(mary))<=>(?[X]:((~rich(X)|~humble(X)))))&
(![X]:(tall(X)=>(generous(X)&~calm(X))))&
(![X]:((~creative(X)<~>wise(X))=>(strong(X)|~humble(X))))&
(![X]:(quiet(X)=>~strong(X)))&
(?[X]:((~calm(X)|~strong(X))))&
((~quiet(mary)|~generous(mary)))&
(?[X]:((~calm(X)<~>patient(X))))&
(?[X]:(~calm(X)))&
((~quiet(susan)<~>~strong(susan)))&
(?[X]:((brave(X)&~generous(X))))&
((humble(paul)<~>~creative(paul)))&
(?[X]:(quiet(X))) | ~old(susan) | [] | null | 0 |
Everyone who is quiet is generous or not strong and vice versa.
If someone is calm or rich then someone is happy and vice versa.
Everyone who is not old is both not happy and patient and vice versa.
If someone is generous then someone is both not kind and not curious.
Everyone who is not humble or creative is funny.
Everyone who is not patient or wise is either not happy or quiet.
If someone is either kind or humble then lucy is both not old and funny.
Everyone who is not wise is either not curious or kind.
If lucy is not strong or humble then paul is brave or not calm and vice versa.
If alice is not brave or not calm then someone is both wise and happy.
Everyone who is either kind or not happy is not strong or calm and vice versa.
Everyone who is not happy or not creative is either not brave or brave and vice versa.
If someone is kind then someone is not funny.
Everyone who is either old or wise is either funny or creative.
Everyone who is not brave or creative is both happy and rich.
Everyone who is both wise and not strong is quiet and vice versa.
Fred is not creative.
Lucy is either not curious or funny.
Someone is patient or calm.
Someone is either not kind or not strong.
Mary is either not rich or not wise.
Someone is not humble or quiet.
Alice is not kind.
Mary is both not quiet and old. | Paul is humble. | neutral | (![X]:(quiet(X)<=>(generous(X)|~strong(X))))&
((?[X]:((calm(X)|rich(X))))<=>(?[X]:(happy(X))))&
(![X]:(~old(X)<=>(~happy(X)&patient(X))))&
((?[X]:(generous(X)))=>(?[X]:((~kind(X)&~curious(X)))))&
(![X]:((~humble(X)|creative(X))=>funny(X)))&
(![X]:((~patient(X)|wise(X))=>(~happy(X)<~>quiet(X))))&
((?[X]:((kind(X)<~>humble(X))))=>((~old(lucy)&funny(lucy))))&
(![X]:(~wise(X)=>(~curious(X)<~>kind(X))))&
(((~strong(lucy)|humble(lucy)))<=>((brave(paul)|~calm(paul))))&
(((~brave(alice)|~calm(alice)))=>(?[X]:((wise(X)&happy(X)))))&
(![X]:((kind(X)<~>~happy(X))<=>(~strong(X)|calm(X))))&
(![X]:((~happy(X)|~creative(X))<=>(~brave(X)<~>brave(X))))&
((?[X]:(kind(X)))=>(?[X]:(~funny(X))))&
(![X]:((old(X)<~>wise(X))=>(funny(X)<~>creative(X))))&
(![X]:((~brave(X)|creative(X))=>(happy(X)&rich(X))))&
(![X]:((wise(X)&~strong(X))<=>quiet(X)))&
(~creative(fred))&
((~curious(lucy)<~>funny(lucy)))&
(?[X]:((patient(X)|calm(X))))&
(?[X]:((~kind(X)<~>~strong(X))))&
((~rich(mary)<~>~wise(mary)))&
(?[X]:((~humble(X)|quiet(X))))&
(~kind(alice))&
((~quiet(mary)&old(mary))) | humble(paul) | [] | null | 0 |
Everyone who is either rich or not funny is not funny or old and vice versa. Everyone who is not curious or funny is both not brave and quiet and vice versa. Everyone who is either funny or not brave is either not rich or generous and vice versa. If mary is not brave then lucy is wise or not calm. Everyone who is both old and not curious is both old and strong and vice versa. If alice is not calm or humble then someone is either not brave or not strong. Everyone who is quiet is both not humble and curious. Everyone who is brave is either not rich or not old. If someone is both not rich and not generous then someone is both not curious and patient and vice versa. Everyone who is both not funny and happy is not brave. If paul is either curious or wise then someone is either not patient or not strong. If someone is not wise or kind then someone is not calm or tall. Everyone who is calm is either not strong or not calm and vice versa. Everyone who is not wise or not creative is both calm and not rich and vice versa. Everyone who is not humble is strong and vice versa. If john is both not strong and humble then someone is not quiet. Someone is curious or not happy. Someone is either strong or not quiet. Fred is curious or happy. Fred is not happy or not humble. Fred is both brave and tall. Someone is creative or not funny. Someone is not old or curious. Paul is either kind or not happy. | John is not old. | contradiction | (![X]:((rich(X)<~>~funny(X))<=>(~funny(X)|old(X))))&
(![X]:((~curious(X)|funny(X))<=>(~brave(X)&quiet(X))))&
(![X]:((funny(X)<~>~brave(X))<=>(~rich(X)<~>generous(X))))&
((~brave(mary))=>((wise(lucy)|~calm(lucy))))&
(![X]:((old(X)&~curious(X))<=>(old(X)&strong(X))))&
(((~calm(alice)|humble(alice)))=>(?[X]:((~brave(X)<~>~strong(X)))))&
(![X]:(quiet(X)=>(~humble(X)&curious(X))))&
(![X]:(brave(X)=>(~rich(X)<~>~old(X))))&
((?[X]:((~rich(X)&~generous(X))))<=>(?[X]:((~curious(X)&patient(X)))))&
(![X]:((~funny(X)&happy(X))=>~brave(X)))&
(((curious(paul)<~>wise(paul)))=>(?[X]:((~patient(X)<~>~strong(X)))))&
((?[X]:((~wise(X)|kind(X))))=>(?[X]:((~calm(X)|tall(X)))))&
(![X]:(calm(X)<=>(~strong(X)<~>~calm(X))))&
(![X]:((~wise(X)|~creative(X))<=>(calm(X)&~rich(X))))&
(![X]:(~humble(X)<=>strong(X)))&
(((~strong(john)&humble(john)))=>(?[X]:(~quiet(X))))&
(?[X]:((curious(X)|~happy(X))))&
(?[X]:((strong(X)<~>~quiet(X))))&
((curious(fred)|happy(fred)))&
((~happy(fred)|~humble(fred)))&
((brave(fred)&tall(fred)))&
(?[X]:((creative(X)|~funny(X))))&
(?[X]:((~old(X)|curious(X))))&
((kind(paul)<~>~happy(paul))) | ~old(john) | [
"p0",
"p1",
"p2",
"p6",
"p7",
"p8",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4434832262710251340286366
% SZS output start Proof for 4434832262710251340286366
1. ! [X0] : ((rich(X0) <~> ~funny(X0)) <=> (old(X0) | ~funny(X0))) [input p0]
2. ! [X0] : ((funny(X0) | ~curious(X0)) <=> (quiet(X0) & ~brave(X0))) [input p1]
3. ! [X0] : ((funny(X0) <~> ~brave(X0)) <=> (~rich(X0) <~> generous(X0))) [input p2]
7. ! [X0] : (quiet(X0) => (curious(X0) & ~humble(X0))) [input p6]
8. ! [X0] : (brave(X0) => (~rich(X0) <~> ~old(X0))) [input p7]
9. ? [X0] : (~generous(X0) & ~rich(X0)) <=> ? [X0] : (patient(X0) & ~curious(X0)) [input p8]
13. ! [X0] : (calm(X0) <=> (~strong(X0) <~> ~calm(X0))) [input p12]
15. ! [X0] : (~humble(X0) <=> strong(X0)) [input p14]
25. ~old(john) [input hypothesis]
26. ? [X0] : (~generous(X0) & ~rich(X0)) <=> ? [X1] : (patient(X1) & ~curious(X1)) [rectify 9]
28. ! [X0] : (~humble(X0) => strong(X0)) [unused predicate definition removal 15]
34. ! [X0] : ((curious(X0) & ~humble(X0)) | ~quiet(X0)) [ennf transformation 7]
35. ! [X0] : ((~rich(X0) <~> ~old(X0)) | ~brave(X0)) [ennf transformation 8]
39. ! [X0] : (strong(X0) | humble(X0)) [ennf transformation 28]
42. ! [X0] : ((((funny(X0) | ~rich(X0)) & (~funny(X0) | rich(X0))) | (~old(X0) & funny(X0))) & ((old(X0) | ~funny(X0)) | ((rich(X0) | funny(X0)) & (~funny(X0) | ~rich(X0))))) [nnf transformation 1]
43. ! [X0] : ((((funny(X0) | ~rich(X0)) & (~funny(X0) | rich(X0))) | (~old(X0) & funny(X0))) & (old(X0) | ~funny(X0) | ((rich(X0) | funny(X0)) & (~funny(X0) | ~rich(X0))))) [flattening 42]
44. ! [X0] : (((funny(X0) | ~curious(X0)) | (~quiet(X0) | brave(X0))) & ((quiet(X0) & ~brave(X0)) | (~funny(X0) & curious(X0)))) [nnf transformation 2]
45. ! [X0] : ((funny(X0) | ~curious(X0) | ~quiet(X0) | brave(X0)) & ((quiet(X0) & ~brave(X0)) | (~funny(X0) & curious(X0)))) [flattening 44]
46. ! [X0] : ((((brave(X0) | ~funny(X0)) & (~brave(X0) | funny(X0))) | ((~rich(X0) | ~generous(X0)) & (generous(X0) | rich(X0)))) & (((~generous(X0) | rich(X0)) & (generous(X0) | ~rich(X0))) | ((funny(X0) | brave(X0)) & (~brave(X0) | ~funny(X0))))) [nnf transformation 3]
52. ! [X0] : (((old(X0) | rich(X0)) & (~old(X0) | ~rich(X0))) | ~brave(X0)) [nnf transformation 35]
53. (? [X0] : (~generous(X0) & ~rich(X0)) | ! [X1] : (~patient(X1) | curious(X1))) & (? [X1] : (patient(X1) & ~curious(X1)) | ! [X0] : (generous(X0) | rich(X0))) [nnf transformation 26]
54. (? [X0] : (~generous(X0) & ~rich(X0)) | ! [X1] : (~patient(X1) | curious(X1))) & (? [X2] : (patient(X2) & ~curious(X2)) | ! [X3] : (generous(X3) | rich(X3))) [rectify 53]
55. ? [X0] : (~generous(X0) & ~rich(X0)) => (~generous(sK1) & ~rich(sK1)) [choice axiom]
56. ? [X2] : (patient(X2) & ~curious(X2)) => (patient(sK2) & ~curious(sK2)) [choice axiom]
57. ((~generous(sK1) & ~rich(sK1)) | ! [X1] : (~patient(X1) | curious(X1))) & ((patient(sK2) & ~curious(sK2)) | ! [X3] : (generous(X3) | rich(X3))) [skolemisation 54,56,55]
61. ! [X0] : ((calm(X0) | ((~strong(X0) | calm(X0)) & (~calm(X0) | strong(X0)))) & (((calm(X0) | strong(X0)) & (~calm(X0) | ~strong(X0))) | ~calm(X0))) [nnf transformation 13]
76. old(X0) | ~funny(X0) | ~funny(X0) | ~rich(X0) [cnf transformation 43]
80. funny(X0) | ~rich(X0) | funny(X0) [cnf transformation 43]
84. quiet(X0) | curious(X0) [cnf transformation 45]
85. ~funny(X0) | quiet(X0) [cnf transformation 45]
90. ~generous(X0) | rich(X0) | funny(X0) | brave(X0) [cnf transformation 46]
94. brave(X0) | ~funny(X0) | ~rich(X0) | ~generous(X0) [cnf transformation 46]
104. ~humble(X0) | ~quiet(X0) [cnf transformation 34]
105. curious(X0) | ~quiet(X0) [cnf transformation 34]
107. old(X0) | rich(X0) | ~brave(X0) [cnf transformation 52]
108. ~curious(sK2) | generous(X3) | rich(X3) [cnf transformation 57]
117. ~calm(X0) | ~strong(X0) | ~calm(X0) [cnf transformation 61]
120. calm(X0) | ~strong(X0) | calm(X0) [cnf transformation 61]
126. strong(X0) | humble(X0) [cnf transformation 39]
138. ~old(john) [cnf transformation 25]
139. ~calm(X0) | ~strong(X0) [duplicate literal removal 117]
140. ~strong(X0) | calm(X0) [duplicate literal removal 120]
141. old(X0) | ~funny(X0) | ~rich(X0) [duplicate literal removal 76]
142. ~rich(X0) | funny(X0) [duplicate literal removal 80]
143. ~rich(X0) | old(X0) [subsumption resolution 141,142]
144. ~generous(X0) | ~rich(X0) | brave(X0) [subsumption resolution 94,142]
147. ~generous(X0) | funny(X0) | brave(X0) [subsumption resolution 90,144]
181. curious(X0) [subsumption resolution 105,84]
182. ~brave(X0) | old(X0) [subsumption resolution 107,143]
185. 8 <=> ! [X3] : (generous(X3) | rich(X3)) [avatar definition]
186. generous(X3) | rich(X3) <- (8) [avatar component clause 185]
192. generous(X3) | rich(X3) [subsumption resolution 108,181]
193. 8 [avatar split clause 192,185]
211. ~strong(X0) [subsumption resolution 139,140]
212. humble(X0) [subsumption resolution 126,211]
244. ~quiet(X0) [resolution 104,212]
261. funny(X0) | brave(X0) | rich(X0) <- (8) [resolution 147,186]
262. brave(X0) | funny(X0) <- (8) [subsumption resolution 261,142]
265. old(X2) | funny(X2) <- (8) [resolution 262,182]
269. funny(john) <- (8) [resolution 265,138]
276. quiet(john) <- (8) [resolution 269,85]
277. $false <- (8) [subsumption resolution 276,244]
278. ~8 [avatar contradiction clause 277]
279. $false [avatar sat refutation 193,278]
% SZS output end Proof for 4434832262710251340286366
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is kind or not patient is both not brave and not rich and vice versa.
Everyone who is both rich and not strong is old and vice versa.
Everyone who is both not brave and funny is kind or curious and vice versa.
If someone is brave then mary is both old and patient.
Everyone who is not happy is either funny or not brave and vice versa.
Everyone who is both not creative and not curious is not patient or not old.
Everyone who is strong is not strong or patient and vice versa.
Everyone who is kind or happy is quiet and vice versa.
Everyone who is not funny is wise and vice versa.
Everyone who is kind or rich is patient or quiet.
If someone is both old and generous then someone is not generous.
Everyone who is not rich is quiet or strong.
Everyone who is creative or humble is kind or happy and vice versa.
If someone is both not wise and curious then mary is both strong and creative and vice versa.
If lucy is either quiet or kind then paul is both not creative and not wise.
If alice is not quiet or quiet then paul is either brave or not calm and vice versa.
Alice is strong.
Someone is either not tall or not creative.
Susan is either not kind or not rich.
Lucy is both rich and not creative.
Someone is either creative or not wise.
Someone is quiet or brave. | Lucy is strong. | entailment | (![X]:((kind(X)|~patient(X))<=>(~brave(X)&~rich(X))))&
(![X]:((rich(X)&~strong(X))<=>old(X)))&
(![X]:((~brave(X)&funny(X))<=>(kind(X)|curious(X))))&
((?[X]:(brave(X)))=>((old(mary)&patient(mary))))&
(![X]:(~happy(X)<=>(funny(X)<~>~brave(X))))&
(![X]:((~creative(X)&~curious(X))=>(~patient(X)|~old(X))))&
(![X]:(strong(X)<=>(~strong(X)|patient(X))))&
(![X]:((kind(X)|happy(X))<=>quiet(X)))&
(![X]:(~funny(X)<=>wise(X)))&
(![X]:((kind(X)|rich(X))=>(patient(X)|quiet(X))))&
((?[X]:((old(X)&generous(X))))=>(?[X]:(~generous(X))))&
(![X]:(~rich(X)=>(quiet(X)|strong(X))))&
(![X]:((creative(X)|humble(X))<=>(kind(X)|happy(X))))&
((?[X]:((~wise(X)&curious(X))))<=>((strong(mary)&creative(mary))))&
(((quiet(lucy)<~>kind(lucy)))=>((~creative(paul)&~wise(paul))))&
(((~quiet(alice)|quiet(alice)))<=>((brave(paul)<~>~calm(paul))))&
(strong(alice))&
(?[X]:((~tall(X)<~>~creative(X))))&
((~kind(susan)<~>~rich(susan)))&
((rich(lucy)&~creative(lucy)))&
(?[X]:((creative(X)<~>~wise(X))))&
(?[X]:((quiet(X)|brave(X)))) | strong(lucy) | [
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 6588381111020487866889595
% SZS output start Proof for 6588381111020487866889595
7. ! [X0] : (strong(X0) <=> (patient(X0) | ~strong(X0))) [input p6]
23. ~strong(lucy) [input hypothesis]
41. ! [X0] : ((strong(X0) | (~patient(X0) & strong(X0))) & ((patient(X0) | ~strong(X0)) | ~strong(X0))) [nnf transformation 7]
42. ! [X0] : ((strong(X0) | (~patient(X0) & strong(X0))) & (patient(X0) | ~strong(X0) | ~strong(X0))) [flattening 41]
86. strong(X0) | strong(X0) [cnf transformation 42]
124. ~strong(lucy) [cnf transformation 23]
126. strong(X0) [duplicate literal removal 86]
233. $false [subsumption resolution 124,126]
% SZS output end Proof for 6588381111020487866889595
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich and happy is quiet or calm. If someone is not patient or not tall then alice is not funny and vice versa. If someone is not tall or humble then lucy is not happy or not strong and vice versa. If someone is either not wise or not brave then someone is rich or happy and vice versa. Everyone who is not old or patient is curious or not strong. If susan is not generous then someone is patient or rich. If susan is either humble or creative then someone is both not tall and kind and vice versa. Everyone who is not tall is kind or happy. Everyone who is not strong is not quiet and vice versa. Everyone who is wise is either not patient or old. Everyone who is not rich or not kind is not humble or calm. Everyone who is both patient and old is both not calm and kind. If someone is humble then someone is both humble and rich and vice versa. Everyone who is not humble is not strong. Everyone who is not humble or not tall is not brave or not happy. If someone is strong or not funny then someone is patient. Someone is old or generous. John is both not strong and old. Someone is either patient or not rich. Fred is either not rich or strong. Someone is either funny or not strong. John is not curious. Someone is both creative and quiet. Lucy is quiet or creative. | Lucy is creative. | neutral | (![X]:((~rich(X)&happy(X))=>(quiet(X)|calm(X))))&
((?[X]:((~patient(X)|~tall(X))))<=>(~funny(alice)))&
((?[X]:((~tall(X)|humble(X))))<=>((~happy(lucy)|~strong(lucy))))&
((?[X]:((~wise(X)<~>~brave(X))))<=>(?[X]:((rich(X)|happy(X)))))&
(![X]:((~old(X)|patient(X))=>(curious(X)|~strong(X))))&
((~generous(susan))=>(?[X]:((patient(X)|rich(X)))))&
(((humble(susan)<~>creative(susan)))<=>(?[X]:((~tall(X)&kind(X)))))&
(![X]:(~tall(X)=>(kind(X)|happy(X))))&
(![X]:(~strong(X)<=>~quiet(X)))&
(![X]:(wise(X)=>(~patient(X)<~>old(X))))&
(![X]:((~rich(X)|~kind(X))=>(~humble(X)|calm(X))))&
(![X]:((patient(X)&old(X))=>(~calm(X)&kind(X))))&
((?[X]:(humble(X)))<=>(?[X]:((humble(X)&rich(X)))))&
(![X]:(~humble(X)=>~strong(X)))&
(![X]:((~humble(X)|~tall(X))=>(~brave(X)|~happy(X))))&
((?[X]:((strong(X)|~funny(X))))=>(?[X]:(patient(X))))&
(?[X]:((old(X)|generous(X))))&
((~strong(john)&old(john)))&
(?[X]:((patient(X)<~>~rich(X))))&
((~rich(fred)<~>strong(fred)))&
(?[X]:((funny(X)<~>~strong(X))))&
(~curious(john))&
(?[X]:((creative(X)&quiet(X))))&
((quiet(lucy)|creative(lucy))) | creative(lucy) | [] | null | 0 |
If someone is curious then someone is humble or not strong.
If someone is both patient and not creative then someone is not old and vice versa.
Everyone who is both not humble and not quiet is not funny or not brave and vice versa.
Everyone who is both not wise and not humble is wise.
Everyone who is happy or not old is both not happy and not funny and vice versa.
If someone is both rich and not patient then paul is not tall and vice versa.
Everyone who is either generous or not quiet is both patient and not quiet and vice versa.
If lucy is old or tall then someone is either humble or not humble and vice versa.
If someone is either not kind or not wise then paul is not strong and vice versa.
Everyone who is either not brave or not old is both not funny and not old and vice versa.
Everyone who is not creative or not brave is either not calm or calm and vice versa.
Everyone who is brave or creative is both not calm and old.
If someone is either not calm or tall then susan is either not wise or humble and vice versa.
If someone is either not funny or not curious then fred is not funny or generous and vice versa.
If paul is quiet or curious then someone is not creative or not generous and vice versa.
If paul is strong or not creative then someone is strong or not funny.
John is either creative or not patient.
John is not kind.
Someone is either not curious or not humble.
Someone is not happy.
Someone is either not old or not strong.
Someone is happy or kind. | Lucy is not rich. | neutral | ((?[X]:(curious(X)))=>(?[X]:((humble(X)|~strong(X)))))&
((?[X]:((patient(X)&~creative(X))))<=>(?[X]:(~old(X))))&
(![X]:((~humble(X)&~quiet(X))<=>(~funny(X)|~brave(X))))&
(![X]:((~wise(X)&~humble(X))=>wise(X)))&
(![X]:((happy(X)|~old(X))<=>(~happy(X)&~funny(X))))&
((?[X]:((rich(X)&~patient(X))))<=>(~tall(paul)))&
(![X]:((generous(X)<~>~quiet(X))<=>(patient(X)&~quiet(X))))&
(((old(lucy)|tall(lucy)))<=>(?[X]:((humble(X)<~>~humble(X)))))&
((?[X]:((~kind(X)<~>~wise(X))))<=>(~strong(paul)))&
(![X]:((~brave(X)<~>~old(X))<=>(~funny(X)&~old(X))))&
(![X]:((~creative(X)|~brave(X))<=>(~calm(X)<~>calm(X))))&
(![X]:((brave(X)|creative(X))=>(~calm(X)&old(X))))&
((?[X]:((~calm(X)<~>tall(X))))<=>((~wise(susan)<~>humble(susan))))&
((?[X]:((~funny(X)<~>~curious(X))))<=>((~funny(fred)|generous(fred))))&
(((quiet(paul)|curious(paul)))<=>(?[X]:((~creative(X)|~generous(X)))))&
(((strong(paul)|~creative(paul)))=>(?[X]:((strong(X)|~funny(X)))))&
((creative(john)<~>~patient(john)))&
(~kind(john))&
(?[X]:((~curious(X)<~>~humble(X))))&
(?[X]:(~happy(X)))&
(?[X]:((~old(X)<~>~strong(X))))&
(?[X]:((happy(X)|kind(X)))) | ~rich(lucy) | [] | null | 0 |
If someone is either strong or generous then paul is wise and vice versa.
Everyone who is tall or old is old and vice versa.
If mary is both not generous and not patient then paul is wise or generous.
Everyone who is funny is either tall or strong and vice versa.
Everyone who is not calm is not patient or happy.
If john is not calm or quiet then someone is either old or not old.
Everyone who is patient is both brave and quiet and vice versa.
Everyone who is quiet is funny or rich and vice versa.
Everyone who is both not kind and old is either patient or not brave and vice versa.
If someone is both not brave and not patient then lucy is both patient and kind and vice versa.
Everyone who is not wise or not kind is not patient and vice versa.
If someone is not humble or not strong then someone is both brave and not old and vice versa.
If someone is either not generous or calm then paul is curious or old and vice versa.
If someone is humble then someone is either creative or patient and vice versa.
Everyone who is either kind or creative is rich or not curious and vice versa.
Everyone who is not quiet is not happy.
Susan is either not tall or not calm.
Someone is either patient or old.
Someone is not humble.
Someone is not tall or humble.
Someone is not strong or not old.
John is not old. | Paul is not humble. | neutral | ((?[X]:((strong(X)<~>generous(X))))<=>(wise(paul)))&
(![X]:((tall(X)|old(X))<=>old(X)))&
(((~generous(mary)&~patient(mary)))=>((wise(paul)|generous(paul))))&
(![X]:(funny(X)<=>(tall(X)<~>strong(X))))&
(![X]:(~calm(X)=>(~patient(X)|happy(X))))&
(((~calm(john)|quiet(john)))=>(?[X]:((old(X)<~>~old(X)))))&
(![X]:(patient(X)<=>(brave(X)&quiet(X))))&
(![X]:(quiet(X)<=>(funny(X)|rich(X))))&
(![X]:((~kind(X)&old(X))<=>(patient(X)<~>~brave(X))))&
((?[X]:((~brave(X)&~patient(X))))<=>((patient(lucy)&kind(lucy))))&
(![X]:((~wise(X)|~kind(X))<=>~patient(X)))&
((?[X]:((~humble(X)|~strong(X))))<=>(?[X]:((brave(X)&~old(X)))))&
((?[X]:((~generous(X)<~>calm(X))))<=>((curious(paul)|old(paul))))&
((?[X]:(humble(X)))<=>(?[X]:((creative(X)<~>patient(X)))))&
(![X]:((kind(X)<~>creative(X))<=>(rich(X)|~curious(X))))&
(![X]:(~quiet(X)=>~happy(X)))&
((~tall(susan)<~>~calm(susan)))&
(?[X]:((patient(X)<~>old(X))))&
(?[X]:(~humble(X)))&
(?[X]:((~tall(X)|humble(X))))&
(?[X]:((~strong(X)|~old(X))))&
(~old(john)) | ~humble(paul) | [] | null | 0 |
Everyone who is either not calm or quiet is both old and not brave.
If someone is humble then lucy is creative or tall and vice versa.
If someone is either humble or not funny then someone is rich or not brave.
Everyone who is both not old and generous is both not generous and wise.
Everyone who is both not calm and humble is either not happy or not funny.
Everyone who is not curious is not humble.
Everyone who is calm or rich is either not rich or not brave.
Everyone who is either not happy or not calm is either kind or calm.
Everyone who is both not creative and humble is both quiet and humble and vice versa.
If someone is either wise or not quiet then alice is both creative and humble and vice versa.
If paul is either generous or not generous then someone is both tall and creative.
If someone is not kind or not rich then mary is both not rich and patient.
Everyone who is both not strong and quiet is not generous or calm and vice versa.
If someone is both not funny and happy then john is both not happy and tall and vice versa.
If someone is both funny and creative then someone is not humble.
Everyone who is both kind and brave is not calm and vice versa.
Someone is not funny or not patient.
Paul is both not tall and happy.
Alice is either not wise or curious.
Lucy is both creative and not strong.
Someone is kind.
John is not humble.
Someone is not rich.
John is either wise or not kind. | John is not wise. | entailment | (![X]:((~calm(X)<~>quiet(X))=>(old(X)&~brave(X))))&
((?[X]:(humble(X)))<=>((creative(lucy)|tall(lucy))))&
((?[X]:((humble(X)<~>~funny(X))))=>(?[X]:((rich(X)|~brave(X)))))&
(![X]:((~old(X)&generous(X))=>(~generous(X)&wise(X))))&
(![X]:((~calm(X)&humble(X))=>(~happy(X)<~>~funny(X))))&
(![X]:(~curious(X)=>~humble(X)))&
(![X]:((calm(X)|rich(X))=>(~rich(X)<~>~brave(X))))&
(![X]:((~happy(X)<~>~calm(X))=>(kind(X)<~>calm(X))))&
(![X]:((~creative(X)&humble(X))<=>(quiet(X)&humble(X))))&
((?[X]:((wise(X)<~>~quiet(X))))<=>((creative(alice)&humble(alice))))&
(((generous(paul)<~>~generous(paul)))=>(?[X]:((tall(X)&creative(X)))))&
((?[X]:((~kind(X)|~rich(X))))=>((~rich(mary)&patient(mary))))&
(![X]:((~strong(X)&quiet(X))<=>(~generous(X)|calm(X))))&
((?[X]:((~funny(X)&happy(X))))<=>((~happy(john)&tall(john))))&
((?[X]:((funny(X)&creative(X))))=>(?[X]:(~humble(X))))&
(![X]:((kind(X)&brave(X))<=>~calm(X)))&
(?[X]:((~funny(X)|~patient(X))))&
((~tall(paul)&happy(paul)))&
((~wise(alice)<~>curious(alice)))&
((creative(lucy)&~strong(lucy)))&
(?[X]:(kind(X)))&
(~humble(john))&
(?[X]:(~rich(X)))&
((wise(john)<~>~kind(john))) | ~wise(john) | [
"p0",
"p8",
"p9",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8466395393075341090215571
% SZS output start Proof for 8466395393075341090215571
1. ! [X0] : ((~calm(X0) <~> quiet(X0)) => (~brave(X0) & old(X0))) [input p0]
9. ! [X0] : ((humble(X0) & ~creative(X0)) <=> (humble(X0) & quiet(X0))) [input p8]
10. ? [X0] : (wise(X0) <~> ~quiet(X0)) <=> (humble(alice) & creative(alice)) [input p9]
13. ! [X0] : ((quiet(X0) & ~strong(X0)) <=> (calm(X0) | ~generous(X0))) [input p12]
16. ! [X0] : ((brave(X0) & kind(X0)) <=> ~calm(X0)) [input p15]
25. wise(john) [input hypothesis]
28. ! [X0] : ((~calm(X0) <~> quiet(X0)) => ~brave(X0)) [pure predicate removal 1]
30. ! [X0] : (~brave(X0) | (~calm(X0) <=> quiet(X0))) [ennf transformation 28]
40. ! [X0] : (~brave(X0) | ((~calm(X0) | ~quiet(X0)) & (quiet(X0) | calm(X0)))) [nnf transformation 30]
53. ! [X0] : (((humble(X0) & ~creative(X0)) | (~humble(X0) | ~quiet(X0))) & ((humble(X0) & quiet(X0)) | (~humble(X0) | creative(X0)))) [nnf transformation 9]
54. ! [X0] : (((humble(X0) & ~creative(X0)) | ~humble(X0) | ~quiet(X0)) & ((humble(X0) & quiet(X0)) | ~humble(X0) | creative(X0))) [flattening 53]
55. (? [X0] : ((quiet(X0) | ~wise(X0)) & (~quiet(X0) | wise(X0))) | (~humble(alice) | ~creative(alice))) & ((humble(alice) & creative(alice)) | ! [X0] : ((wise(X0) | quiet(X0)) & (~quiet(X0) | ~wise(X0)))) [nnf transformation 10]
56. (? [X0] : ((quiet(X0) | ~wise(X0)) & (~quiet(X0) | wise(X0))) | ~humble(alice) | ~creative(alice)) & ((humble(alice) & creative(alice)) | ! [X0] : ((wise(X0) | quiet(X0)) & (~quiet(X0) | ~wise(X0)))) [flattening 55]
57. (? [X0] : ((quiet(X0) | ~wise(X0)) & (~quiet(X0) | wise(X0))) | ~humble(alice) | ~creative(alice)) & ((humble(alice) & creative(alice)) | ! [X1] : ((wise(X1) | quiet(X1)) & (~quiet(X1) | ~wise(X1)))) [rectify 56]
58. ? [X0] : ((quiet(X0) | ~wise(X0)) & (~quiet(X0) | wise(X0))) => ((quiet(sK2) | ~wise(sK2)) & (~quiet(sK2) | wise(sK2))) [choice axiom]
59. (((quiet(sK2) | ~wise(sK2)) & (~quiet(sK2) | wise(sK2))) | ~humble(alice) | ~creative(alice)) & ((humble(alice) & creative(alice)) | ! [X1] : ((wise(X1) | quiet(X1)) & (~quiet(X1) | ~wise(X1)))) [skolemisation 57,58]
63. ! [X0] : (((quiet(X0) & ~strong(X0)) | (~calm(X0) & generous(X0))) & ((calm(X0) | ~generous(X0)) | (~quiet(X0) | strong(X0)))) [nnf transformation 13]
64. ! [X0] : (((quiet(X0) & ~strong(X0)) | (~calm(X0) & generous(X0))) & (calm(X0) | ~generous(X0) | ~quiet(X0) | strong(X0))) [flattening 63]
73. ! [X0] : (((brave(X0) & kind(X0)) | calm(X0)) & (~calm(X0) | (~brave(X0) | ~kind(X0)))) [nnf transformation 16]
74. ! [X0] : (((brave(X0) & kind(X0)) | calm(X0)) & (~calm(X0) | ~brave(X0) | ~kind(X0))) [flattening 73]
83. ~brave(X0) | quiet(X0) | calm(X0) [cnf transformation 40]
103. ~creative(X0) | ~humble(X0) | ~quiet(X0) [cnf transformation 54]
105. creative(alice) | ~quiet(X1) | ~wise(X1) [cnf transformation 59]
107. humble(alice) | ~quiet(X1) | ~wise(X1) [cnf transformation 59]
123. ~calm(X0) | quiet(X0) [cnf transformation 64]
131. brave(X0) | calm(X0) [cnf transformation 74]
144. wise(john) [cnf transformation 25]
187. 9 <=> creative(alice) [avatar definition]
188. creative(alice) <- (9) [avatar component clause 187]
191. 10 <=> humble(alice) [avatar definition]
192. humble(alice) <- (10) [avatar component clause 191]
209. 14 <=> ! [X1] : (~quiet(X1) | ~wise(X1)) [avatar definition]
210. ~wise(X1) | ~quiet(X1) <- (14) [avatar component clause 209]
211. 14 | 10 [avatar split clause 107,191,209]
213. 14 | 9 [avatar split clause 105,187,209]
300. 33 <=> wise(john) [avatar definition]
301. wise(john) <- (33) [avatar component clause 300]
309. 33 [avatar split clause 144,300]
314. ~quiet(john) <- (14, 33) [resolution 210,301]
316. quiet(X0) | calm(X0) | calm(X0) [resolution 83,131]
317. quiet(X0) | calm(X0) [duplicate literal removal 316]
318. quiet(X0) [subsumption resolution 317,123]
319. $false <- (14, 33) [resolution 318,314]
320. ~14 | ~33 [avatar contradiction clause 319]
347. ~humble(alice) | ~quiet(alice) <- (9) [resolution 103,188]
350. ~quiet(alice) <- (9, 10) [subsumption resolution 347,192]
351. $false <- (9, 10) [subsumption resolution 350,318]
352. ~9 | ~10 [avatar contradiction clause 351]
353. $false [avatar sat refutation 211,213,309,320,352]
% SZS output end Proof for 8466395393075341090215571
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
If paul is not rich then lucy is either creative or calm and vice versa. Everyone who is both not curious and not humble is not strong or not patient and vice versa. If someone is both not happy and old then john is humble or happy. If mary is kind or creative then someone is not calm or not curious. If someone is either not kind or not curious then someone is not tall and vice versa. Everyone who is not humble is not quiet or not kind and vice versa. Everyone who is strong or curious is either patient or not rich. Everyone who is either happy or strong is both calm and not funny. Everyone who is either not patient or not humble is either not happy or generous and vice versa. Everyone who is wise is both not humble and humble. If someone is strong or not calm then someone is either not funny or not wise and vice versa. Everyone who is either curious or not generous is humble or brave and vice versa. Everyone who is both not happy and kind is brave or not tall and vice versa. Everyone who is not humble is both kind and calm. Everyone who is either kind or not tall is not patient and vice versa. Everyone who is not humble is either not funny or not brave. Someone is old or not creative. Mary is both calm and not old. John is not wise. John is either kind or happy. | Mary is creative. | neutral | ((~rich(paul))<=>((creative(lucy)<~>calm(lucy))))&
(![X]:((~curious(X)&~humble(X))<=>(~strong(X)|~patient(X))))&
((?[X]:((~happy(X)&old(X))))=>((humble(john)|happy(john))))&
(((kind(mary)|creative(mary)))=>(?[X]:((~calm(X)|~curious(X)))))&
((?[X]:((~kind(X)<~>~curious(X))))<=>(?[X]:(~tall(X))))&
(![X]:(~humble(X)<=>(~quiet(X)|~kind(X))))&
(![X]:((strong(X)|curious(X))=>(patient(X)<~>~rich(X))))&
(![X]:((happy(X)<~>strong(X))=>(calm(X)&~funny(X))))&
(![X]:((~patient(X)<~>~humble(X))<=>(~happy(X)<~>generous(X))))&
(![X]:(wise(X)=>(~humble(X)&humble(X))))&
((?[X]:((strong(X)|~calm(X))))<=>(?[X]:((~funny(X)<~>~wise(X)))))&
(![X]:((curious(X)<~>~generous(X))<=>(humble(X)|brave(X))))&
(![X]:((~happy(X)&kind(X))<=>(brave(X)|~tall(X))))&
(![X]:(~humble(X)=>(kind(X)&calm(X))))&
(![X]:((kind(X)<~>~tall(X))<=>~patient(X)))&
(![X]:(~humble(X)=>(~funny(X)<~>~brave(X))))&
(?[X]:((old(X)|~creative(X))))&
((calm(mary)&~old(mary)))&
(~wise(john))&
((kind(john)<~>happy(john))) | creative(mary) | [] | null | 0 |
Everyone who is funny is quiet. Everyone who is generous or not funny is not quiet or not kind and vice versa. Everyone who is patient or not wise is tall or not wise and vice versa. Everyone who is either kind or generous is either not old or tall and vice versa. Everyone who is not wise is either not patient or strong. If susan is old then someone is either funny or not brave and vice versa. Everyone who is not curious is both generous and not happy and vice versa. Everyone who is tall is happy or not tall. If someone is both not patient and not kind then someone is both calm and old and vice versa. If mary is both not creative and wise then someone is not old or not creative and vice versa. Everyone who is not strong or quiet is patient and vice versa. If john is not rich then someone is old. Everyone who is not tall or not rich is tall and vice versa. Everyone who is not quiet or strong is either not curious or not old. If susan is not tall then alice is calm. Everyone who is either not brave or wise is both kind and not tall. Someone is quiet. Someone is either not wise or curious. Someone is either generous or old. Someone is either not creative or wise. Someone is either not old or not humble. John is generous. | Alice is not wise. | neutral | (![X]:(funny(X)=>quiet(X)))&
(![X]:((generous(X)|~funny(X))<=>(~quiet(X)|~kind(X))))&
(![X]:((patient(X)|~wise(X))<=>(tall(X)|~wise(X))))&
(![X]:((kind(X)<~>generous(X))<=>(~old(X)<~>tall(X))))&
(![X]:(~wise(X)=>(~patient(X)<~>strong(X))))&
((old(susan))<=>(?[X]:((funny(X)<~>~brave(X)))))&
(![X]:(~curious(X)<=>(generous(X)&~happy(X))))&
(![X]:(tall(X)=>(happy(X)|~tall(X))))&
((?[X]:((~patient(X)&~kind(X))))<=>(?[X]:((calm(X)&old(X)))))&
(((~creative(mary)&wise(mary)))<=>(?[X]:((~old(X)|~creative(X)))))&
(![X]:((~strong(X)|quiet(X))<=>patient(X)))&
((~rich(john))=>(?[X]:(old(X))))&
(![X]:((~tall(X)|~rich(X))<=>tall(X)))&
(![X]:((~quiet(X)|strong(X))=>(~curious(X)<~>~old(X))))&
((~tall(susan))=>(calm(alice)))&
(![X]:((~brave(X)<~>wise(X))=>(kind(X)&~tall(X))))&
(?[X]:(quiet(X)))&
(?[X]:((~wise(X)<~>curious(X))))&
(?[X]:((generous(X)<~>old(X))))&
(?[X]:((~creative(X)<~>wise(X))))&
(?[X]:((~old(X)<~>~humble(X))))&
(generous(john)) | ~wise(alice) | [] | null | 0 |
Everyone who is funny or not calm is both not quiet and humble. If someone is either not strong or not creative then fred is either creative or not old. Everyone who is both not curious and old is kind and vice versa. Everyone who is quiet or calm is not curious and vice versa. Everyone who is not humble is calm. Everyone who is both patient and funny is curious or rich. Everyone who is not rich or patient is both happy and not quiet and vice versa. If lucy is either not tall or patient then susan is brave and vice versa. Everyone who is patient is old or calm and vice versa. If someone is either quiet or brave then john is either tall or quiet. If someone is not wise then john is not funny or not wise and vice versa. If mary is not humble then someone is not creative or quiet and vice versa. If fred is either not creative or not brave then someone is curious or rich and vice versa. Everyone who is either happy or brave is not rich. Everyone who is generous or patient is either not quiet or kind. If someone is calm or happy then lucy is either quiet or not quiet. Someone is not old or not brave. Someone is patient or old. Someone is not kind or not happy. Paul is generous or not creative. Lucy is not strong or strong. Someone is either funny or not brave. Someone is both not rich and calm. | Mary is not creative. | neutral | (![X]:((funny(X)|~calm(X))=>(~quiet(X)&humble(X))))&
((?[X]:((~strong(X)<~>~creative(X))))=>((creative(fred)<~>~old(fred))))&
(![X]:((~curious(X)&old(X))<=>kind(X)))&
(![X]:((quiet(X)|calm(X))<=>~curious(X)))&
(![X]:(~humble(X)=>calm(X)))&
(![X]:((patient(X)&funny(X))=>(curious(X)|rich(X))))&
(![X]:((~rich(X)|patient(X))<=>(happy(X)&~quiet(X))))&
(((~tall(lucy)<~>patient(lucy)))<=>(brave(susan)))&
(![X]:(patient(X)<=>(old(X)|calm(X))))&
((?[X]:((quiet(X)<~>brave(X))))=>((tall(john)<~>quiet(john))))&
((?[X]:(~wise(X)))<=>((~funny(john)|~wise(john))))&
((~humble(mary))<=>(?[X]:((~creative(X)|quiet(X)))))&
(((~creative(fred)<~>~brave(fred)))<=>(?[X]:((curious(X)|rich(X)))))&
(![X]:((happy(X)<~>brave(X))=>~rich(X)))&
(![X]:((generous(X)|patient(X))=>(~quiet(X)<~>kind(X))))&
((?[X]:((calm(X)|happy(X))))=>((quiet(lucy)<~>~quiet(lucy))))&
(?[X]:((~old(X)|~brave(X))))&
(?[X]:((patient(X)|old(X))))&
(?[X]:((~kind(X)|~happy(X))))&
((generous(paul)|~creative(paul)))&
((~strong(lucy)|strong(lucy)))&
(?[X]:((funny(X)<~>~brave(X))))&
(?[X]:((~rich(X)&calm(X)))) | ~creative(mary) | [] | null | 0 |
If mary is either not curious or strong then someone is both calm and not kind and vice versa.
If someone is either tall or strong then someone is humble and vice versa.
Everyone who is not quiet or kind is happy or calm.
Everyone who is both not old and happy is both not curious and not creative and vice versa.
Everyone who is kind or tall is either wise or happy.
Everyone who is not humble or funny is either not strong or not calm.
Everyone who is wise is not humble or kind and vice versa.
If mary is both not humble and patient then alice is generous or not patient and vice versa.
Everyone who is both generous and rich is not generous.
If someone is not generous then someone is either wise or not strong and vice versa.
If fred is either not calm or wise then lucy is not strong.
Everyone who is both old and patient is either not tall or patient and vice versa.
If someone is not calm or not happy then john is both curious and not patient.
Everyone who is both not brave and not old is old.
Everyone who is old or not rich is both not tall and rich.
Everyone who is both not generous and not humble is not tall or tall and vice versa.
Someone is either happy or not happy.
Alice is both patient and not old.
John is either old or not old.
Someone is both not kind and quiet.
Mary is not humble.
Someone is not patient or tall. | Mary is not patient. | entailment | (((~curious(mary)<~>strong(mary)))<=>(?[X]:((calm(X)&~kind(X)))))&
((?[X]:((tall(X)<~>strong(X))))<=>(?[X]:(humble(X))))&
(![X]:((~quiet(X)|kind(X))=>(happy(X)|calm(X))))&
(![X]:((~old(X)&happy(X))<=>(~curious(X)&~creative(X))))&
(![X]:((kind(X)|tall(X))=>(wise(X)<~>happy(X))))&
(![X]:((~humble(X)|funny(X))=>(~strong(X)<~>~calm(X))))&
(![X]:(wise(X)<=>(~humble(X)|kind(X))))&
(((~humble(mary)&patient(mary)))<=>((generous(alice)|~patient(alice))))&
(![X]:((generous(X)&rich(X))=>~generous(X)))&
((?[X]:(~generous(X)))<=>(?[X]:((wise(X)<~>~strong(X)))))&
(((~calm(fred)<~>wise(fred)))=>(~strong(lucy)))&
(![X]:((old(X)&patient(X))<=>(~tall(X)<~>patient(X))))&
((?[X]:((~calm(X)|~happy(X))))=>((curious(john)&~patient(john))))&
(![X]:((~brave(X)&~old(X))=>old(X)))&
(![X]:((old(X)|~rich(X))=>(~tall(X)&rich(X))))&
(![X]:((~generous(X)&~humble(X))<=>(~tall(X)|tall(X))))&
(?[X]:((happy(X)<~>~happy(X))))&
((patient(alice)&~old(alice)))&
((old(john)<~>~old(john)))&
(?[X]:((~kind(X)&quiet(X))))&
(~humble(mary))&
(?[X]:((~patient(X)|tall(X)))) | ~patient(mary) | [
"p7",
"p15",
"p17",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 6966118470833318112400873
% SZS output start Proof for 6966118470833318112400873
8. (patient(mary) & ~humble(mary)) <=> (~patient(alice) | generous(alice)) [input p7]
16. ! [X0] : ((~humble(X0) & ~generous(X0)) <=> (tall(X0) | ~tall(X0))) [input p15]
18. ~old(alice) & patient(alice) [input p17]
21. ~humble(mary) [input p20]
23. patient(mary) [input hypothesis]
54. ((patient(mary) & ~humble(mary)) | (patient(alice) & ~generous(alice))) & ((~patient(alice) | generous(alice)) | (~patient(mary) | humble(mary))) [nnf transformation 8]
55. ((patient(mary) & ~humble(mary)) | (patient(alice) & ~generous(alice))) & (~patient(alice) | generous(alice) | ~patient(mary) | humble(mary)) [flattening 54]
64. ! [X0] : (((~humble(X0) & ~generous(X0)) | (~tall(X0) & tall(X0))) & ((tall(X0) | ~tall(X0)) | (humble(X0) | generous(X0)))) [nnf transformation 16]
65. ! [X0] : (((~humble(X0) & ~generous(X0)) | (~tall(X0) & tall(X0))) & (tall(X0) | ~tall(X0) | humble(X0) | generous(X0))) [flattening 64]
98. ~patient(alice) | generous(alice) | ~patient(mary) | humble(mary) [cnf transformation 55]
125. ~generous(X0) | tall(X0) [cnf transformation 65]
126. ~generous(X0) | ~tall(X0) [cnf transformation 65]
131. patient(alice) [cnf transformation 18]
136. ~humble(mary) [cnf transformation 21]
138. patient(mary) [cnf transformation 23]
194. 12 <=> patient(alice) [avatar definition]
198. 13 <=> patient(mary) [avatar definition]
203. 14 <=> generous(alice) [avatar definition]
204. generous(alice) <- (14) [avatar component clause 203]
208. 15 <=> humble(mary) [avatar definition]
213. 15 | ~13 | 14 | ~12 [avatar split clause 98,194,203,198,208]
275. ~generous(X0) [subsumption resolution 125,126]
276. 12 [avatar split clause 131,194]
277. ~15 [avatar split clause 136,208]
279. 13 [avatar split clause 138,198]
280. $false <- (14) [subsumption resolution 204,275]
281. ~14 [avatar contradiction clause 280]
282. $false [avatar sat refutation 213,276,277,279,281]
% SZS output end Proof for 6966118470833318112400873
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either humble or strong is calm and vice versa.
Everyone who is both not quiet and quiet is not happy.
Everyone who is curious is both calm and not rich.
If someone is rich or not funny then john is patient or not quiet and vice versa.
If someone is creative or not tall then someone is kind.
Everyone who is both strong and funny is strong or brave.
If mary is both not quiet and curious then alice is either not kind or wise.
Everyone who is either not wise or not curious is curious.
Everyone who is not old is patient or humble.
Everyone who is both not humble and not old is not quiet or not curious and vice versa.
Everyone who is rich is either not strong or not patient.
Everyone who is creative is not rich and vice versa.
If someone is either generous or humble then someone is both not strong and not quiet.
Everyone who is not calm or not kind is not funny and vice versa.
Everyone who is happy is wise.
If someone is not kind or not patient then someone is either not generous or not brave and vice versa.
Lucy is either generous or not happy.
Someone is both strong and quiet.
Someone is both creative and funny.
Susan is either brave or not happy.
Alice is not generous.
Alice is not calm.
Lucy is either humble or not rich.
Someone is quiet. | Lucy is not rich. | entailment | (![X]:((humble(X)<~>strong(X))<=>calm(X)))&
(![X]:((~quiet(X)&quiet(X))=>~happy(X)))&
(![X]:(curious(X)=>(calm(X)&~rich(X))))&
((?[X]:((rich(X)|~funny(X))))<=>((patient(john)|~quiet(john))))&
((?[X]:((creative(X)|~tall(X))))=>(?[X]:(kind(X))))&
(![X]:((strong(X)&funny(X))=>(strong(X)|brave(X))))&
(((~quiet(mary)&curious(mary)))=>((~kind(alice)<~>wise(alice))))&
(![X]:((~wise(X)<~>~curious(X))=>curious(X)))&
(![X]:(~old(X)=>(patient(X)|humble(X))))&
(![X]:((~humble(X)&~old(X))<=>(~quiet(X)|~curious(X))))&
(![X]:(rich(X)=>(~strong(X)<~>~patient(X))))&
(![X]:(creative(X)<=>~rich(X)))&
((?[X]:((generous(X)<~>humble(X))))=>(?[X]:((~strong(X)&~quiet(X)))))&
(![X]:((~calm(X)|~kind(X))<=>~funny(X)))&
(![X]:(happy(X)=>wise(X)))&
((?[X]:((~kind(X)|~patient(X))))<=>(?[X]:((~generous(X)<~>~brave(X)))))&
((generous(lucy)<~>~happy(lucy)))&
(?[X]:((strong(X)&quiet(X))))&
(?[X]:((creative(X)&funny(X))))&
((brave(susan)<~>~happy(susan)))&
(~generous(alice))&
(~calm(alice))&
((humble(lucy)<~>~rich(lucy)))&
(?[X]:(quiet(X))) | ~rich(lucy) | [
"p2",
"p9",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 3585821176085400144930615
% SZS output start Proof for 3585821176085400144930615
3. ! [X0] : (curious(X0) => (~rich(X0) & calm(X0))) [input p2]
10. ! [X0] : ((~old(X0) & ~humble(X0)) <=> (~curious(X0) | ~quiet(X0))) [input p9]
23. humble(lucy) <~> ~rich(lucy) [input p22]
25. rich(lucy) [input hypothesis]
32. ! [X0] : ((~rich(X0) & calm(X0)) | ~curious(X0)) [ennf transformation 3]
55. ! [X0] : (((~old(X0) & ~humble(X0)) | (curious(X0) & quiet(X0))) & ((~curious(X0) | ~quiet(X0)) | (old(X0) | humble(X0)))) [nnf transformation 10]
56. ! [X0] : (((~old(X0) & ~humble(X0)) | (curious(X0) & quiet(X0))) & (~curious(X0) | ~quiet(X0) | old(X0) | humble(X0))) [flattening 55]
76. (rich(lucy) | ~humble(lucy)) & (~rich(lucy) | humble(lucy)) [nnf transformation 23]
85. ~rich(X0) | ~curious(X0) [cnf transformation 32]
99. ~humble(X0) | curious(X0) [cnf transformation 56]
130. ~rich(lucy) | humble(lucy) [cnf transformation 76]
133. rich(lucy) [cnf transformation 25]
260. 29 <=> humble(lucy) [avatar definition]
261. humble(lucy) <- (29) [avatar component clause 260]
264. 30 <=> rich(lucy) [avatar definition]
266. rich(lucy) <- (30) [avatar component clause 264]
268. 29 | ~30 [avatar split clause 130,264,260]
269. 30 [avatar split clause 133,264]
272. ~curious(lucy) <- (30) [resolution 85,266]
274. curious(lucy) <- (29) [resolution 99,261]
275. $false <- (29, 30) [subsumption resolution 274,272]
276. ~29 | ~30 [avatar contradiction clause 275]
277. $false [avatar sat refutation 268,269,276]
% SZS output end Proof for 3585821176085400144930615
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old and not old is either not patient or curious and vice versa. Everyone who is either creative or happy is not tall and vice versa. If someone is quiet or brave then someone is both creative and not happy and vice versa. Everyone who is either not quiet or not curious is not funny or patient. Everyone who is both rich and not creative is both strong and not humble. If fred is either not calm or rich then someone is both strong and calm. If someone is either generous or funny then john is both generous and patient and vice versa. Everyone who is not humble is both strong and curious and vice versa. Everyone who is rich or not strong is not kind. Everyone who is rich is old and vice versa. If fred is both funny and not calm then someone is kind or not quiet and vice versa. Everyone who is not quiet or happy is both patient and generous and vice versa. If someone is happy then mary is either kind or not patient and vice versa. If someone is not humble or not patient then someone is not kind or happy. Everyone who is both not brave and humble is not happy or old and vice versa. Everyone who is either not calm or kind is both not wise and not funny. Someone is either brave or creative. Someone is either not wise or old. Fred is old. Someone is happy or not strong. Someone is old or not curious. Susan is either brave or not rich. Someone is tall or not humble. | Fred is kind. | contradiction | (![X]:((old(X)&~old(X))<=>(~patient(X)<~>curious(X))))&
(![X]:((creative(X)<~>happy(X))<=>~tall(X)))&
((?[X]:((quiet(X)|brave(X))))<=>(?[X]:((creative(X)&~happy(X)))))&
(![X]:((~quiet(X)<~>~curious(X))=>(~funny(X)|patient(X))))&
(![X]:((rich(X)&~creative(X))=>(strong(X)&~humble(X))))&
(((~calm(fred)<~>rich(fred)))=>(?[X]:((strong(X)&calm(X)))))&
((?[X]:((generous(X)<~>funny(X))))<=>((generous(john)&patient(john))))&
(![X]:(~humble(X)<=>(strong(X)&curious(X))))&
(![X]:((rich(X)|~strong(X))=>~kind(X)))&
(![X]:(rich(X)<=>old(X)))&
(((funny(fred)&~calm(fred)))<=>(?[X]:((kind(X)|~quiet(X)))))&
(![X]:((~quiet(X)|happy(X))<=>(patient(X)&generous(X))))&
((?[X]:(happy(X)))<=>((kind(mary)<~>~patient(mary))))&
((?[X]:((~humble(X)|~patient(X))))=>(?[X]:((~kind(X)|happy(X)))))&
(![X]:((~brave(X)&humble(X))<=>(~happy(X)|old(X))))&
(![X]:((~calm(X)<~>kind(X))=>(~wise(X)&~funny(X))))&
(?[X]:((brave(X)<~>creative(X))))&
(?[X]:((~wise(X)<~>old(X))))&
(old(fred))&
(?[X]:((happy(X)|~strong(X))))&
(?[X]:((old(X)|~curious(X))))&
((brave(susan)<~>~rich(susan)))&
(?[X]:((tall(X)|~humble(X)))) | kind(fred) | [
"p8",
"p9",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 2746652496809562530629996
% SZS output start Proof for 2746652496809562530629996
9. ! [X0] : ((~strong(X0) | rich(X0)) => ~kind(X0)) [input p8]
10. ! [X0] : (rich(X0) <=> old(X0)) [input p9]
19. old(fred) [input p18]
24. kind(fred) [input hypothesis]
34. ! [X0] : (~kind(X0) | (strong(X0) & ~rich(X0))) [ennf transformation 9]
56. ! [X0] : ((rich(X0) | ~old(X0)) & (old(X0) | ~rich(X0))) [nnf transformation 10]
117. ~kind(X0) | ~rich(X0) [cnf transformation 34]
120. ~old(X0) | rich(X0) [cnf transformation 56]
150. old(fred) [cnf transformation 19]
156. kind(fred) [cnf transformation 24]
191. 8 <=> rich(fred) [avatar definition]
193. ~rich(fred) <- (~8) [avatar component clause 191]
359. ~rich(fred) [resolution 117,156]
362. ~8 [avatar split clause 359,191]
364. rich(fred) [resolution 120,150]
365. $false <- (~8) [subsumption resolution 364,193]
366. 8 [avatar contradiction clause 365]
367. $false [avatar sat refutation 362,366]
% SZS output end Proof for 2746652496809562530629996
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either kind or not calm is both not rich and not tall.
Everyone who is either rich or not generous is not calm or patient and vice versa.
If someone is either old or generous then someone is funny.
Everyone who is both tall and not rich is patient or not old.
Everyone who is either quiet or generous is both wise and funny and vice versa.
If paul is not rich then someone is both not funny and quiet and vice versa.
If susan is either not brave or not tall then susan is brave or quiet.
Everyone who is rich is both not patient and curious and vice versa.
If someone is calm or not curious then someone is quiet.
Everyone who is not tall or not curious is both calm and kind.
If someone is not funny then someone is not tall or not kind.
Everyone who is generous is both not creative and not rich and vice versa.
If lucy is either rich or funny then someone is not calm or curious.
If paul is strong or humble then someone is both tall and strong.
Everyone who is either patient or brave is not generous.
If someone is both funny and not brave then someone is happy.
Someone is not curious or kind.
Fred is either curious or rich.
Someone is funny.
Someone is both wise and old.
Someone is either not rich or brave.
Paul is either not calm or creative.
Someone is both not quiet and rich.
Lucy is not happy. | Fred is rich. | contradiction | (![X]:((kind(X)<~>~calm(X))=>(~rich(X)&~tall(X))))&
(![X]:((rich(X)<~>~generous(X))<=>(~calm(X)|patient(X))))&
((?[X]:((old(X)<~>generous(X))))=>(?[X]:(funny(X))))&
(![X]:((tall(X)&~rich(X))=>(patient(X)|~old(X))))&
(![X]:((quiet(X)<~>generous(X))<=>(wise(X)&funny(X))))&
((~rich(paul))<=>(?[X]:((~funny(X)&quiet(X)))))&
(((~brave(susan)<~>~tall(susan)))=>((brave(susan)|quiet(susan))))&
(![X]:(rich(X)<=>(~patient(X)&curious(X))))&
((?[X]:((calm(X)|~curious(X))))=>(?[X]:(quiet(X))))&
(![X]:((~tall(X)|~curious(X))=>(calm(X)&kind(X))))&
((?[X]:(~funny(X)))=>(?[X]:((~tall(X)|~kind(X)))))&
(![X]:(generous(X)<=>(~creative(X)&~rich(X))))&
(((rich(lucy)<~>funny(lucy)))=>(?[X]:((~calm(X)|curious(X)))))&
(((strong(paul)|humble(paul)))=>(?[X]:((tall(X)&strong(X)))))&
(![X]:((patient(X)<~>brave(X))=>~generous(X)))&
((?[X]:((funny(X)&~brave(X))))=>(?[X]:(happy(X))))&
(?[X]:((~curious(X)|kind(X))))&
((curious(fred)<~>rich(fred)))&
(?[X]:(funny(X)))&
(?[X]:((wise(X)&old(X))))&
(?[X]:((~rich(X)<~>brave(X))))&
((~calm(paul)<~>creative(paul)))&
(?[X]:((~quiet(X)&rich(X))))&
(~happy(lucy)) | rich(fred) | [
"p7",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 5160165292309177793875699
% SZS output start Proof for 5160165292309177793875699
8. ! [X0] : (rich(X0) <=> (curious(X0) & ~patient(X0))) [input p7]
18. curious(fred) <~> rich(fred) [input p17]
25. rich(fred) [input hypothesis]
58. ! [X0] : ((rich(X0) | (~curious(X0) | patient(X0))) & ((curious(X0) & ~patient(X0)) | ~rich(X0))) [nnf transformation 8]
59. ! [X0] : ((rich(X0) | ~curious(X0) | patient(X0)) & ((curious(X0) & ~patient(X0)) | ~rich(X0))) [flattening 58]
79. (~rich(fred) | ~curious(fred)) & (rich(fred) | curious(fred)) [nnf transformation 18]
115. curious(X0) | ~rich(X0) [cnf transformation 59]
136. ~rich(fred) | ~curious(fred) [cnf transformation 79]
147. rich(fred) [cnf transformation 25]
255. ~rich(fred) [subsumption resolution 136,115]
277. $false [subsumption resolution 147,255]
% SZS output end Proof for 5160165292309177793875699
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either calm or not quiet and vice versa. Everyone who is old or calm is both kind and old. If mary is brave then someone is either not curious or not funny. If someone is both brave and not patient then someone is kind. Everyone who is not quiet or creative is wise or not curious and vice versa. If mary is either happy or quiet then john is both not curious and old and vice versa. Everyone who is both not kind and not wise is either curious or generous. If alice is not creative or not old then someone is either not wise or not strong. Everyone who is either not generous or not patient is not quiet. Everyone who is either not old or not patient is both not patient and patient. Everyone who is creative is not rich or wise and vice versa. If fred is either not wise or funny then someone is both not quiet and creative and vice versa. If lucy is both not curious and not patient then fred is either not brave or not strong. If someone is kind then someone is not generous or humble. If someone is not wise then someone is both creative and not humble and vice versa. If someone is either curious or creative then fred is not calm. Mary is both funny and curious. Someone is both not wise and not brave. Someone is not humble or quiet. Susan is not old or curious. Alice is both not tall and brave. Fred is not funny or not calm. Lucy is not brave. | Susan is old. | neutral | (![X]:(~strong(X)<=>(calm(X)<~>~quiet(X))))&
(![X]:((old(X)|calm(X))=>(kind(X)&old(X))))&
((brave(mary))=>(?[X]:((~curious(X)<~>~funny(X)))))&
((?[X]:((brave(X)&~patient(X))))=>(?[X]:(kind(X))))&
(![X]:((~quiet(X)|creative(X))<=>(wise(X)|~curious(X))))&
(((happy(mary)<~>quiet(mary)))<=>((~curious(john)&old(john))))&
(![X]:((~kind(X)&~wise(X))=>(curious(X)<~>generous(X))))&
(((~creative(alice)|~old(alice)))=>(?[X]:((~wise(X)<~>~strong(X)))))&
(![X]:((~generous(X)<~>~patient(X))=>~quiet(X)))&
(![X]:((~old(X)<~>~patient(X))=>(~patient(X)&patient(X))))&
(![X]:(creative(X)<=>(~rich(X)|wise(X))))&
(((~wise(fred)<~>funny(fred)))<=>(?[X]:((~quiet(X)&creative(X)))))&
(((~curious(lucy)&~patient(lucy)))=>((~brave(fred)<~>~strong(fred))))&
((?[X]:(kind(X)))=>(?[X]:((~generous(X)|humble(X)))))&
((?[X]:(~wise(X)))<=>(?[X]:((creative(X)&~humble(X)))))&
((?[X]:((curious(X)<~>creative(X))))=>(~calm(fred)))&
((funny(mary)&curious(mary)))&
(?[X]:((~wise(X)&~brave(X))))&
(?[X]:((~humble(X)|quiet(X))))&
((~old(susan)|curious(susan)))&
((~tall(alice)&brave(alice)))&
((~funny(fred)|~calm(fred)))&
(~brave(lucy)) | old(susan) | [] | null | 0 |
Everyone who is both old and not rich is either not quiet or not old and vice versa.
If lucy is either kind or not curious then mary is not tall or not quiet and vice versa.
Everyone who is either curious or not funny is both strong and not patient and vice versa.
If someone is not rich or not quiet then alice is both calm and not old.
If someone is rich or strong then mary is not strong or not tall.
Everyone who is either not funny or humble is both not old and curious.
Everyone who is funny or kind is both tall and quiet.
If someone is both funny and strong then paul is not funny.
If someone is either calm or not strong then mary is either not patient or humble.
Everyone who is generous or happy is both not quiet and funny and vice versa.
If someone is either not tall or not happy then someone is either not humble or humble and vice versa.
If alice is not humble or calm then someone is tall and vice versa.
Everyone who is either not funny or happy is rich and vice versa.
If someone is both not patient and humble then alice is not rich or not calm.
Everyone who is curious is curious or not wise.
Someone is not kind or tall.
Fred is tall or old.
Someone is brave. | Mary is funny. | contradiction | (![X]:((old(X)&~rich(X))<=>(~quiet(X)<~>~old(X))))&
(((kind(lucy)<~>~curious(lucy)))<=>((~tall(mary)|~quiet(mary))))&
(![X]:((curious(X)<~>~funny(X))<=>(strong(X)&~patient(X))))&
((?[X]:((~rich(X)|~quiet(X))))=>((calm(alice)&~old(alice))))&
((?[X]:((rich(X)|strong(X))))=>((~strong(mary)|~tall(mary))))&
(![X]:((~funny(X)<~>humble(X))=>(~old(X)&curious(X))))&
(![X]:((funny(X)|kind(X))=>(tall(X)&quiet(X))))&
((?[X]:((funny(X)&strong(X))))=>(~funny(paul)))&
((?[X]:((calm(X)<~>~strong(X))))=>((~patient(mary)<~>humble(mary))))&
(![X]:((generous(X)|happy(X))<=>(~quiet(X)&funny(X))))&
((?[X]:((~tall(X)<~>~happy(X))))<=>(?[X]:((~humble(X)<~>humble(X)))))&
(((~humble(alice)|calm(alice)))<=>(?[X]:(tall(X))))&
(![X]:((~funny(X)<~>happy(X))<=>rich(X)))&
((?[X]:((~patient(X)&humble(X))))=>((~rich(alice)|~calm(alice))))&
(![X]:(curious(X)=>(curious(X)|~wise(X))))&
(?[X]:((~kind(X)|tall(X))))&
((tall(fred)|old(fred)))&
(?[X]:(brave(X))) | funny(mary) | [
"p0",
"p6",
"p9",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 2266283776987322125925312
% SZS output start Proof for 2266283776987322125925312
1. ! [X0] : ((~rich(X0) & old(X0)) <=> (~quiet(X0) <~> ~old(X0))) [input p0]
7. ! [X0] : ((kind(X0) | funny(X0)) => (quiet(X0) & tall(X0))) [input p6]
10. ! [X0] : ((happy(X0) | generous(X0)) <=> (funny(X0) & ~quiet(X0))) [input p9]
13. ! [X0] : ((~funny(X0) <~> happy(X0)) <=> rich(X0)) [input p12]
19. funny(mary) [input hypothesis]
27. ! [X0] : ((quiet(X0) & tall(X0)) | (~kind(X0) & ~funny(X0))) [ennf transformation 7]
32. ! [X0] : (((~rich(X0) & old(X0)) | ((~quiet(X0) | old(X0)) & (~old(X0) | quiet(X0)))) & (((old(X0) | quiet(X0)) & (~old(X0) | ~quiet(X0))) | (rich(X0) | ~old(X0)))) [nnf transformation 1]
33. ! [X0] : (((~rich(X0) & old(X0)) | ((~quiet(X0) | old(X0)) & (~old(X0) | quiet(X0)))) & (((old(X0) | quiet(X0)) & (~old(X0) | ~quiet(X0))) | rich(X0) | ~old(X0))) [flattening 32]
40. ! [X0] : (((happy(X0) | generous(X0)) | (~funny(X0) | quiet(X0))) & ((funny(X0) & ~quiet(X0)) | (~happy(X0) & ~generous(X0)))) [nnf transformation 10]
41. ! [X0] : ((happy(X0) | generous(X0) | ~funny(X0) | quiet(X0)) & ((funny(X0) & ~quiet(X0)) | (~happy(X0) & ~generous(X0)))) [flattening 40]
52. ! [X0] : ((((~happy(X0) | funny(X0)) & (happy(X0) | ~funny(X0))) | ~rich(X0)) & (rich(X0) | ((~funny(X0) | ~happy(X0)) & (happy(X0) | funny(X0))))) [nnf transformation 13]
55. ~old(X0) | ~quiet(X0) | rich(X0) | ~old(X0) [cnf transformation 33]
58. old(X0) | ~quiet(X0) | old(X0) [cnf transformation 33]
85. ~funny(X0) | quiet(X0) [cnf transformation 27]
93. ~happy(X0) | ~quiet(X0) [cnf transformation 41]
95. ~happy(X0) | funny(X0) [cnf transformation 41]
108. rich(X0) | happy(X0) | funny(X0) [cnf transformation 52]
109. rich(X0) | ~funny(X0) | ~happy(X0) [cnf transformation 52]
110. ~funny(X0) | happy(X0) | ~rich(X0) [cnf transformation 52]
115. funny(mary) [cnf transformation 19]
120. ~old(X0) | ~quiet(X0) | rich(X0) [duplicate literal removal 55]
121. ~quiet(X0) | old(X0) [duplicate literal removal 58]
122. ~quiet(X0) | rich(X0) [subsumption resolution 120,121]
124. 1 <=> quiet(mary) [avatar definition]
126. quiet(mary) <- (1) [avatar component clause 124]
154. 7 <=> ! [X0] : rich(X0) [avatar definition]
155. rich(X0) <- (7) [avatar component clause 154]
233. ~happy(X0) | rich(X0) [subsumption resolution 109,95]
234. funny(X0) | rich(X0) [subsumption resolution 108,233]
264. quiet(mary) [resolution 85,115]
271. rich(X0) | quiet(X0) [resolution 234,85]
316. happy(mary) | ~rich(mary) [resolution 110,115]
327. 31 <=> rich(mary) [avatar definition]
329. ~rich(mary) <- (~31) [avatar component clause 327]
331. 32 <=> happy(mary) [avatar definition]
333. happy(mary) <- (32) [avatar component clause 331]
334. ~31 | 32 [avatar split clause 316,331,327]
339. rich(X0) [subsumption resolution 271,122]
340. 7 [avatar split clause 339,154]
342. 1 [avatar split clause 264,124]
353. $false <- (7, ~31) [resolution 329,155]
354. ~7 | 31 [avatar contradiction clause 353]
357. ~quiet(mary) <- (32) [resolution 333,93]
358. $false <- (1, 32) [subsumption resolution 357,126]
359. ~1 | ~32 [avatar contradiction clause 358]
360. $false [avatar sat refutation 334,340,342,354,359]
% SZS output end Proof for 2266283776987322125925312
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not generous and not creative is curious or not creative.
If someone is not calm then someone is either not wise or not rich.
If someone is brave then someone is both happy and not happy and vice versa.
Everyone who is not funny or not creative is either not strong or rich.
Everyone who is both brave and generous is funny and vice versa.
Everyone who is either not calm or not brave is either creative or not creative and vice versa.
Everyone who is not tall is not creative and vice versa.
Everyone who is brave is either creative or not patient and vice versa.
Everyone who is quiet is both not quiet and not patient.
Everyone who is both quiet and not calm is not generous or calm.
Everyone who is not old is either rich or old.
If paul is both not curious and not funny then someone is not creative or not quiet and vice versa.
Everyone who is either not generous or not patient is either not generous or humble.
Everyone who is not tall is both generous and patient.
Everyone who is both not old and not funny is not happy or generous.
Everyone who is either old or calm is both old and not rich.
Someone is not wise or curious.
Alice is humble.
Paul is either not patient or wise.
Paul is either tall or not rich.
Someone is either old or not humble.
Someone is either not calm or not brave.
Fred is not tall.
Lucy is either not creative or humble. | Lucy is brave. | contradiction | (![X]:((~generous(X)&~creative(X))=>(curious(X)|~creative(X))))&
((?[X]:(~calm(X)))=>(?[X]:((~wise(X)<~>~rich(X)))))&
((?[X]:(brave(X)))<=>(?[X]:((happy(X)&~happy(X)))))&
(![X]:((~funny(X)|~creative(X))=>(~strong(X)<~>rich(X))))&
(![X]:((brave(X)&generous(X))<=>funny(X)))&
(![X]:((~calm(X)<~>~brave(X))<=>(creative(X)<~>~creative(X))))&
(![X]:(~tall(X)<=>~creative(X)))&
(![X]:(brave(X)<=>(creative(X)<~>~patient(X))))&
(![X]:(quiet(X)=>(~quiet(X)&~patient(X))))&
(![X]:((quiet(X)&~calm(X))=>(~generous(X)|calm(X))))&
(![X]:(~old(X)=>(rich(X)<~>old(X))))&
(((~curious(paul)&~funny(paul)))<=>(?[X]:((~creative(X)|~quiet(X)))))&
(![X]:((~generous(X)<~>~patient(X))=>(~generous(X)<~>humble(X))))&
(![X]:(~tall(X)=>(generous(X)&patient(X))))&
(![X]:((~old(X)&~funny(X))=>(~happy(X)|generous(X))))&
(![X]:((old(X)<~>calm(X))=>(old(X)&~rich(X))))&
(?[X]:((~wise(X)|curious(X))))&
(humble(alice))&
((~patient(paul)<~>wise(paul)))&
((tall(paul)<~>~rich(paul)))&
(?[X]:((old(X)<~>~humble(X))))&
(?[X]:((~calm(X)<~>~brave(X))))&
(~tall(fred))&
((~creative(lucy)<~>humble(lucy))) | brave(lucy) | [
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 533581634829823669280948
% SZS output start Proof for 533581634829823669280948
3. ? [X0] : brave(X0) <=> ? [X0] : (~happy(X0) & happy(X0)) [input p2]
25. brave(lucy) [input hypothesis]
27. ? [X0] : brave(X0) <=> ? [X1] : (~happy(X1) & happy(X1)) [rectify 3]
45. (? [X0] : brave(X0) | ! [X1] : (happy(X1) | ~happy(X1))) & (? [X1] : (~happy(X1) & happy(X1)) | ! [X0] : ~brave(X0)) [nnf transformation 27]
46. (? [X0] : brave(X0) | ! [X1] : (happy(X1) | ~happy(X1))) & (? [X2] : (~happy(X2) & happy(X2)) | ! [X3] : ~brave(X3)) [rectify 45]
47. ? [X0] : brave(X0) => brave(sK1) [choice axiom]
48. ? [X2] : (~happy(X2) & happy(X2)) => (~happy(sK2) & happy(sK2)) [choice axiom]
49. (brave(sK1) | ! [X1] : (happy(X1) | ~happy(X1))) & ((~happy(sK2) & happy(sK2)) | ! [X3] : ~brave(X3)) [skolemisation 46,48,47]
78. happy(sK2) | ~brave(X3) [cnf transformation 49]
79. ~happy(sK2) | ~brave(X3) [cnf transformation 49]
136. brave(lucy) [cnf transformation 25]
161. 4 <=> ! [X3] : ~brave(X3) [avatar definition]
162. ~brave(X3) <- (4) [avatar component clause 161]
164. 5 <=> happy(sK2) [avatar definition]
167. 4 | ~5 [avatar split clause 79,164,161]
168. 4 | 5 [avatar split clause 78,164,161]
224. $false <- (4) [resolution 162,136]
225. ~4 [avatar contradiction clause 224]
226. $false [avatar sat refutation 167,168,225]
% SZS output end Proof for 533581634829823669280948
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is rich is either humble or not patient.
If john is both brave and humble then someone is wise or tall.
If someone is either not brave or humble then someone is either not creative or tall and vice versa.
Everyone who is not wise or not quiet is not humble and vice versa.
Everyone who is both rich and curious is either not creative or not curious.
Everyone who is both generous and kind is not kind.
If someone is both not wise and generous then someone is not funny or not calm.
Everyone who is either brave or quiet is both not calm and funny.
Everyone who is both brave and not calm is either patient or funny.
If someone is funny or wise then susan is both not brave and generous.
If alice is either not old or quiet then someone is either rich or not generous and vice versa.
If susan is curious or not tall then someone is quiet or curious and vice versa.
Everyone who is not calm or brave is either brave or not funny.
Everyone who is not happy is both not tall and calm and vice versa.
Everyone who is both not happy and not rich is wise.
Everyone who is either not old or not funny is both funny and wise.
Paul is rich.
Susan is not generous.
Someone is not humble or not old.
Someone is both not wise and not kind.
John is not rich.
Fred is tall or brave.
Someone is both creative and not calm.
Someone is not brave or kind. | Paul is not tall. | neutral | (![X]:(rich(X)=>(humble(X)<~>~patient(X))))&
(((brave(john)&humble(john)))=>(?[X]:((wise(X)|tall(X)))))&
((?[X]:((~brave(X)<~>humble(X))))<=>(?[X]:((~creative(X)<~>tall(X)))))&
(![X]:((~wise(X)|~quiet(X))<=>~humble(X)))&
(![X]:((rich(X)&curious(X))=>(~creative(X)<~>~curious(X))))&
(![X]:((generous(X)&kind(X))=>~kind(X)))&
((?[X]:((~wise(X)&generous(X))))=>(?[X]:((~funny(X)|~calm(X)))))&
(![X]:((brave(X)<~>quiet(X))=>(~calm(X)&funny(X))))&
(![X]:((brave(X)&~calm(X))=>(patient(X)<~>funny(X))))&
((?[X]:((funny(X)|wise(X))))=>((~brave(susan)&generous(susan))))&
(((~old(alice)<~>quiet(alice)))<=>(?[X]:((rich(X)<~>~generous(X)))))&
(((curious(susan)|~tall(susan)))<=>(?[X]:((quiet(X)|curious(X)))))&
(![X]:((~calm(X)|brave(X))=>(brave(X)<~>~funny(X))))&
(![X]:(~happy(X)<=>(~tall(X)&calm(X))))&
(![X]:((~happy(X)&~rich(X))=>wise(X)))&
(![X]:((~old(X)<~>~funny(X))=>(funny(X)&wise(X))))&
(rich(paul))&
(~generous(susan))&
(?[X]:((~humble(X)|~old(X))))&
(?[X]:((~wise(X)&~kind(X))))&
(~rich(john))&
((tall(fred)|brave(fred)))&
(?[X]:((creative(X)&~calm(X))))&
(?[X]:((~brave(X)|kind(X)))) | ~tall(paul) | [] | null | 0 |
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