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 curious and not strong is either happy or not happy and vice versa.
If someone is not old then john is either not calm or not creative.
Everyone who is strong is either happy or creative.
If fred is not wise or not kind then john is not quiet or humble and vice versa.
Everyone who is either old or calm is either not tall or not funny.
If someone is either old or rich then someone is both not generous and kind and vice versa.
If alice is either not funny or brave then someone is rich and vice versa.
Everyone who is creative or not funny is either quiet or strong and vice versa.
Everyone who is not brave or tall is both not tall and curious and vice versa.
Everyone who is not brave is both not funny and curious and vice versa.
Everyone who is not curious is either not happy or curious and vice versa.
If someone is either rich or not humble then someone is either not quiet or humble.
Everyone who is both not happy and rich is calm.
If someone is not tall then lucy is both not funny and creative.
Everyone who is both kind and humble is both kind and brave.
Everyone who is either not patient or old is either not rich or tall and vice versa.
Alice is both not patient and brave.
Mary is either rich or not patient.
Someone is both brave and not wise.
Someone is either not rich or not funny.
Someone is not happy.
Lucy is not humble. | Fred is wise. | neutral | (![X]:((~curious(X)&~strong(X))<=>(happy(X)<~>~happy(X))))&
((?[X]:(~old(X)))=>((~calm(john)<~>~creative(john))))&
(![X]:(strong(X)=>(happy(X)<~>creative(X))))&
(((~wise(fred)|~kind(fred)))<=>((~quiet(john)|humble(john))))&
(![X]:((old(X)<~>calm(X))=>(~tall(X)<~>~funny(X))))&
((?[X]:((old(X)<~>rich(X))))<=>(?[X]:((~generous(X)&kind(X)))))&
(((~funny(alice)<~>brave(alice)))<=>(?[X]:(rich(X))))&
(![X]:((creative(X)|~funny(X))<=>(quiet(X)<~>strong(X))))&
(![X]:((~brave(X)|tall(X))<=>(~tall(X)&curious(X))))&
(![X]:(~brave(X)<=>(~funny(X)&curious(X))))&
(![X]:(~curious(X)<=>(~happy(X)<~>curious(X))))&
((?[X]:((rich(X)<~>~humble(X))))=>(?[X]:((~quiet(X)<~>humble(X)))))&
(![X]:((~happy(X)&rich(X))=>calm(X)))&
((?[X]:(~tall(X)))=>((~funny(lucy)&creative(lucy))))&
(![X]:((kind(X)&humble(X))=>(kind(X)&brave(X))))&
(![X]:((~patient(X)<~>old(X))<=>(~rich(X)<~>tall(X))))&
((~patient(alice)&brave(alice)))&
((rich(mary)<~>~patient(mary)))&
(?[X]:((brave(X)&~wise(X))))&
(?[X]:((~rich(X)<~>~funny(X))))&
(?[X]:(~happy(X)))&
(~humble(lucy)) | wise(fred) | [] | null | 0 |
Everyone who is either not old or strong is humble or wise and vice versa.
If susan is both old and not calm then alice is both not generous and not brave and vice versa.
If alice is either not quiet or creative then someone is not brave and vice versa.
If susan is not happy then someone is both not brave and not strong.
Everyone who is not funny or not rich is not curious or brave.
Everyone who is calm or not patient is strong.
Everyone who is both happy and not happy is funny and vice versa.
Everyone who is rich or curious is both not rich and not creative and vice versa.
If alice is both not creative and not patient then someone is not curious and vice versa.
If someone is not quiet then fred is strong.
Everyone who is either old or strong is happy.
Everyone who is either tall or not strong is generous and vice versa.
Everyone who is either not happy or patient is rich.
Everyone who is both kind and not old is either funny or curious.
If alice is calm or happy then someone is either not patient or patient and vice versa.
Everyone who is either kind or generous is not creative and vice versa.
Someone is not old.
Paul is humble or brave.
Paul is not quiet.
Someone is both strong and patient.
Susan is both tall and not patient.
Someone is rich or creative.
Lucy is not tall.
John is either not calm or not humble. | Alice is funny. | contradiction | (![X]:((~old(X)<~>strong(X))<=>(humble(X)|wise(X))))&
(((old(susan)&~calm(susan)))<=>((~generous(alice)&~brave(alice))))&
(((~quiet(alice)<~>creative(alice)))<=>(?[X]:(~brave(X))))&
((~happy(susan))=>(?[X]:((~brave(X)&~strong(X)))))&
(![X]:((~funny(X)|~rich(X))=>(~curious(X)|brave(X))))&
(![X]:((calm(X)|~patient(X))=>strong(X)))&
(![X]:((happy(X)&~happy(X))<=>funny(X)))&
(![X]:((rich(X)|curious(X))<=>(~rich(X)&~creative(X))))&
(((~creative(alice)&~patient(alice)))<=>(?[X]:(~curious(X))))&
((?[X]:(~quiet(X)))=>(strong(fred)))&
(![X]:((old(X)<~>strong(X))=>happy(X)))&
(![X]:((tall(X)<~>~strong(X))<=>generous(X)))&
(![X]:((~happy(X)<~>patient(X))=>rich(X)))&
(![X]:((kind(X)&~old(X))=>(funny(X)<~>curious(X))))&
(((calm(alice)|happy(alice)))<=>(?[X]:((~patient(X)<~>patient(X)))))&
(![X]:((kind(X)<~>generous(X))<=>~creative(X)))&
(?[X]:(~old(X)))&
((humble(paul)|brave(paul)))&
(~quiet(paul))&
(?[X]:((strong(X)&patient(X))))&
((tall(susan)&~patient(susan)))&
(?[X]:((rich(X)|creative(X))))&
(~tall(lucy))&
((~calm(john)<~>~humble(john))) | funny(alice) | [
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 2716354267574889350542445
% SZS output start Proof for 2716354267574889350542445
7. ! [X0] : ((~happy(X0) & happy(X0)) <=> funny(X0)) [input p6]
25. funny(alice) [input hypothesis]
45. ! [X0] : (((~happy(X0) & happy(X0)) | ~funny(X0)) & (funny(X0) | (happy(X0) | ~happy(X0)))) [nnf transformation 7]
46. ! [X0] : (((~happy(X0) & happy(X0)) | ~funny(X0)) & (funny(X0) | happy(X0) | ~happy(X0))) [flattening 45]
92. happy(X0) | ~funny(X0) [cnf transformation 46]
93. ~happy(X0) | ~funny(X0) [cnf transformation 46]
134. funny(alice) [cnf transformation 25]
192. ~funny(X0) [subsumption resolution 92,93]
254. $false [subsumption resolution 134,192]
% SZS output end Proof for 2716354267574889350542445
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either funny or quiet is both not strong and strong. Everyone who is not rich or not happy is happy. If someone is both funny and kind then someone is not quiet or happy and vice versa. If lucy is not curious or tall then john is humble or not wise. Everyone who is not old is both curious and not kind. If susan is creative then someone is wise and vice versa. If someone is humble or kind then lucy is both not humble and not wise. Everyone who is calm or humble is either not strong or generous. Everyone who is not quiet is both not happy and not wise and vice versa. Everyone who is tall is both not humble and not patient. Everyone who is either strong or calm is not kind or patient. If someone is both old and calm then someone is not funny. Everyone who is either rich or not curious is generous. Everyone who is both kind and not quiet is quiet or not old. Lucy is either not curious or not patient. Someone is wise or generous. Alice is not wise or not strong. Someone is either not kind or strong. Paul is calm. Paul is not wise or kind. Someone is either not patient or brave. Someone is either humble or generous. | Paul is not funny. | contradiction | (![X]:((funny(X)<~>quiet(X))=>(~strong(X)&strong(X))))&
(![X]:((~rich(X)|~happy(X))=>happy(X)))&
((?[X]:((funny(X)&kind(X))))<=>(?[X]:((~quiet(X)|happy(X)))))&
(((~curious(lucy)|tall(lucy)))=>((humble(john)|~wise(john))))&
(![X]:(~old(X)=>(curious(X)&~kind(X))))&
((creative(susan))<=>(?[X]:(wise(X))))&
((?[X]:((humble(X)|kind(X))))=>((~humble(lucy)&~wise(lucy))))&
(![X]:((calm(X)|humble(X))=>(~strong(X)<~>generous(X))))&
(![X]:(~quiet(X)<=>(~happy(X)&~wise(X))))&
(![X]:(tall(X)=>(~humble(X)&~patient(X))))&
(![X]:((strong(X)<~>calm(X))=>(~kind(X)|patient(X))))&
((?[X]:((old(X)&calm(X))))=>(?[X]:(~funny(X))))&
(![X]:((rich(X)<~>~curious(X))=>generous(X)))&
(![X]:((kind(X)&~quiet(X))=>(quiet(X)|~old(X))))&
((~curious(lucy)<~>~patient(lucy)))&
(?[X]:((wise(X)|generous(X))))&
((~wise(alice)|~strong(alice)))&
(?[X]:((~kind(X)<~>strong(X))))&
(calm(paul))&
((~wise(paul)|kind(paul)))&
(?[X]:((~patient(X)<~>brave(X))))&
(?[X]:((humble(X)<~>generous(X)))) | ~funny(paul) | [
"p0",
"p1",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 769644824527618415823741
% SZS output start Proof for 769644824527618415823741
1. ! [X0] : ((funny(X0) <~> quiet(X0)) => (strong(X0) & ~strong(X0))) [input p0]
2. ! [X0] : ((~happy(X0) | ~rich(X0)) => happy(X0)) [input p1]
9. ! [X0] : (~quiet(X0) <=> (~wise(X0) & ~happy(X0))) [input p8]
23. ~funny(paul) [input hypothesis]
28. ! [X0] : ((strong(X0) & ~strong(X0)) | (funny(X0) <=> quiet(X0))) [ennf transformation 1]
29. ! [X0] : (happy(X0) | (happy(X0) & rich(X0))) [ennf transformation 2]
41. ! [X0] : ((strong(X0) & ~strong(X0)) | ((funny(X0) | ~quiet(X0)) & (quiet(X0) | ~funny(X0)))) [nnf transformation 28]
52. ! [X0] : ((~quiet(X0) | (wise(X0) | happy(X0))) & ((~wise(X0) & ~happy(X0)) | quiet(X0))) [nnf transformation 9]
53. ! [X0] : ((~quiet(X0) | wise(X0) | happy(X0)) & ((~wise(X0) & ~happy(X0)) | quiet(X0))) [flattening 52]
72. ~strong(X0) | funny(X0) | ~quiet(X0) [cnf transformation 41]
74. strong(X0) | funny(X0) | ~quiet(X0) [cnf transformation 41]
76. happy(X0) | happy(X0) [cnf transformation 29]
95. ~happy(X0) | quiet(X0) [cnf transformation 53]
116. ~funny(paul) [cnf transformation 23]
118. happy(X0) [duplicate literal removal 76]
119. ~quiet(X0) | funny(X0) [subsumption resolution 72,74]
167. quiet(X0) [subsumption resolution 95,118]
244. funny(X0) [resolution 119,167]
245. $false [resolution 244,116]
% SZS output end Proof for 769644824527618415823741
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not calm then paul is not strong. Everyone who is either wise or not old is either creative or not creative and vice versa. Everyone who is either tall or not old is not strong or not old and vice versa. Everyone who is either rich or creative is not kind or patient and vice versa. Everyone who is both not strong and not happy is calm or not humble and vice versa. If someone is strong then someone is either curious or not brave and vice versa. If mary is strong then john is either brave or quiet and vice versa. Everyone who is not strong or generous is either wise or kind and vice versa. Everyone who is both generous and strong is not calm or not brave and vice versa. Everyone who is both not creative and wise is kind. Everyone who is quiet or not funny is not curious and vice versa. Everyone who is not patient or not happy is both not funny and not humble and vice versa. If someone is either old or not quiet then mary is both not creative and not old. Everyone who is both happy and not brave is both wise and brave. Everyone who is not calm or not wise is either generous or not brave. If fred is both happy and not kind then someone is both not quiet and generous and vice versa. Someone is both not creative and not humble. Fred is not creative. Mary is either generous or not curious. Paul is wise. Someone is brave or not strong. Someone is either patient or not funny. | John is calm. | entailment | ((~calm(lucy))=>(~strong(paul)))&
(![X]:((wise(X)<~>~old(X))<=>(creative(X)<~>~creative(X))))&
(![X]:((tall(X)<~>~old(X))<=>(~strong(X)|~old(X))))&
(![X]:((rich(X)<~>creative(X))<=>(~kind(X)|patient(X))))&
(![X]:((~strong(X)&~happy(X))<=>(calm(X)|~humble(X))))&
((?[X]:(strong(X)))<=>(?[X]:((curious(X)<~>~brave(X)))))&
((strong(mary))<=>((brave(john)<~>quiet(john))))&
(![X]:((~strong(X)|generous(X))<=>(wise(X)<~>kind(X))))&
(![X]:((generous(X)&strong(X))<=>(~calm(X)|~brave(X))))&
(![X]:((~creative(X)&wise(X))=>kind(X)))&
(![X]:((quiet(X)|~funny(X))<=>~curious(X)))&
(![X]:((~patient(X)|~happy(X))<=>(~funny(X)&~humble(X))))&
((?[X]:((old(X)<~>~quiet(X))))=>((~creative(mary)&~old(mary))))&
(![X]:((happy(X)&~brave(X))=>(wise(X)&brave(X))))&
(![X]:((~calm(X)|~wise(X))=>(generous(X)<~>~brave(X))))&
(((happy(fred)&~kind(fred)))<=>(?[X]:((~quiet(X)&generous(X)))))&
(?[X]:((~creative(X)&~humble(X))))&
(~creative(fred))&
((generous(mary)<~>~curious(mary)))&
(wise(paul))&
(?[X]:((brave(X)|~strong(X))))&
(?[X]:((patient(X)<~>~funny(X)))) | calm(john) | [
"p4",
"p5",
"p7",
"p8",
"p9",
"p10",
"p11",
"p13",
"p14",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 7586350584342913858140024
% SZS output start Proof for 7586350584342913858140024
5. ! [X0] : ((~happy(X0) & ~strong(X0)) <=> (~humble(X0) | calm(X0))) [input p4]
6. ? [X0] : strong(X0) <=> ? [X0] : (curious(X0) <~> ~brave(X0)) [input p5]
8. ! [X0] : ((generous(X0) | ~strong(X0)) <=> (wise(X0) <~> kind(X0))) [input p7]
9. ! [X0] : ((strong(X0) & generous(X0)) <=> (~brave(X0) | ~calm(X0))) [input p8]
10. ! [X0] : ((wise(X0) & ~creative(X0)) => kind(X0)) [input p9]
11. ! [X0] : ((~funny(X0) | quiet(X0)) <=> ~curious(X0)) [input p10]
12. ! [X0] : ((~happy(X0) | ~patient(X0)) <=> (~humble(X0) & ~funny(X0))) [input p11]
14. ! [X0] : ((~brave(X0) & happy(X0)) => (brave(X0) & wise(X0))) [input p13]
15. ! [X0] : ((~wise(X0) | ~calm(X0)) => (generous(X0) <~> ~brave(X0))) [input p14]
16. (~kind(fred) & happy(fred)) <=> ? [X0] : (generous(X0) & ~quiet(X0)) [input p15]
18. ~creative(fred) [input p17]
23. ~calm(john) [input hypothesis]
24. ? [X0] : strong(X0) <=> ? [X1] : (curious(X1) <~> ~brave(X1)) [rectify 6]
26. ! [X0] : (kind(X0) | (~wise(X0) | creative(X0))) [ennf transformation 10]
27. ! [X0] : (kind(X0) | ~wise(X0) | creative(X0)) [flattening 26]
29. ! [X0] : ((brave(X0) & wise(X0)) | (brave(X0) | ~happy(X0))) [ennf transformation 14]
30. ! [X0] : ((brave(X0) & wise(X0)) | brave(X0) | ~happy(X0)) [flattening 29]
31. ! [X0] : ((generous(X0) <~> ~brave(X0)) | (wise(X0) & calm(X0))) [ennf transformation 15]
37. ! [X0] : (((~happy(X0) & ~strong(X0)) | (humble(X0) & ~calm(X0))) & ((~humble(X0) | calm(X0)) | (happy(X0) | strong(X0)))) [nnf transformation 5]
38. ! [X0] : (((~happy(X0) & ~strong(X0)) | (humble(X0) & ~calm(X0))) & (~humble(X0) | calm(X0) | happy(X0) | strong(X0))) [flattening 37]
39. (? [X0] : strong(X0) | ! [X1] : ((curious(X1) | brave(X1)) & (~brave(X1) | ~curious(X1)))) & (? [X1] : ((brave(X1) | ~curious(X1)) & (~brave(X1) | curious(X1))) | ! [X0] : ~strong(X0)) [nnf transformation 24]
40. (? [X0] : strong(X0) | ! [X1] : ((curious(X1) | brave(X1)) & (~brave(X1) | ~curious(X1)))) & (? [X2] : ((brave(X2) | ~curious(X2)) & (~brave(X2) | curious(X2))) | ! [X3] : ~strong(X3)) [rectify 39]
41. ? [X0] : strong(X0) => strong(sK0) [choice axiom]
42. ? [X2] : ((brave(X2) | ~curious(X2)) & (~brave(X2) | curious(X2))) => ((brave(sK1) | ~curious(sK1)) & (~brave(sK1) | curious(sK1))) [choice axiom]
43. (strong(sK0) | ! [X1] : ((curious(X1) | brave(X1)) & (~brave(X1) | ~curious(X1)))) & (((brave(sK1) | ~curious(sK1)) & (~brave(sK1) | curious(sK1))) | ! [X3] : ~strong(X3)) [skolemisation 40,42,41]
45. ! [X0] : (((generous(X0) | ~strong(X0)) | ((wise(X0) | ~kind(X0)) & (kind(X0) | ~wise(X0)))) & (((~kind(X0) | ~wise(X0)) & (kind(X0) | wise(X0))) | (~generous(X0) & strong(X0)))) [nnf transformation 8]
46. ! [X0] : ((generous(X0) | ~strong(X0) | ((wise(X0) | ~kind(X0)) & (kind(X0) | ~wise(X0)))) & (((~kind(X0) | ~wise(X0)) & (kind(X0) | wise(X0))) | (~generous(X0) & strong(X0)))) [flattening 45]
47. ! [X0] : (((strong(X0) & generous(X0)) | (brave(X0) & calm(X0))) & ((~brave(X0) | ~calm(X0)) | (~strong(X0) | ~generous(X0)))) [nnf transformation 9]
48. ! [X0] : (((strong(X0) & generous(X0)) | (brave(X0) & calm(X0))) & (~brave(X0) | ~calm(X0) | ~strong(X0) | ~generous(X0))) [flattening 47]
49. ! [X0] : (((~funny(X0) | quiet(X0)) | curious(X0)) & (~curious(X0) | (funny(X0) & ~quiet(X0)))) [nnf transformation 11]
50. ! [X0] : ((~funny(X0) | quiet(X0) | curious(X0)) & (~curious(X0) | (funny(X0) & ~quiet(X0)))) [flattening 49]
51. ! [X0] : (((~happy(X0) | ~patient(X0)) | (humble(X0) | funny(X0))) & ((~humble(X0) & ~funny(X0)) | (happy(X0) & patient(X0)))) [nnf transformation 12]
52. ! [X0] : ((~happy(X0) | ~patient(X0) | humble(X0) | funny(X0)) & ((~humble(X0) & ~funny(X0)) | (happy(X0) & patient(X0)))) [flattening 51]
54. ! [X0] : (((brave(X0) | ~generous(X0)) & (~brave(X0) | generous(X0))) | (wise(X0) & calm(X0))) [nnf transformation 31]
55. ((~kind(fred) & happy(fred)) | ! [X0] : (~generous(X0) | quiet(X0))) & (? [X0] : (generous(X0) & ~quiet(X0)) | (kind(fred) | ~happy(fred))) [nnf transformation 16]
56. ((~kind(fred) & happy(fred)) | ! [X0] : (~generous(X0) | quiet(X0))) & (? [X0] : (generous(X0) & ~quiet(X0)) | kind(fred) | ~happy(fred)) [flattening 55]
57. ((~kind(fred) & happy(fred)) | ! [X0] : (~generous(X0) | quiet(X0))) & (? [X1] : (generous(X1) & ~quiet(X1)) | kind(fred) | ~happy(fred)) [rectify 56]
58. ? [X1] : (generous(X1) & ~quiet(X1)) => (generous(sK2) & ~quiet(sK2)) [choice axiom]
59. ((~kind(fred) & happy(fred)) | ! [X0] : (~generous(X0) | quiet(X0))) & ((generous(sK2) & ~quiet(sK2)) | kind(fred) | ~happy(fred)) [skolemisation 57,58]
91. ~strong(X0) | humble(X0) [cnf transformation 38]
92. ~happy(X0) | ~calm(X0) [cnf transformation 38]
94. ~brave(sK1) | curious(sK1) | ~strong(X3) [cnf transformation 43]
103. ~generous(X0) | wise(X0) | kind(X0) [cnf transformation 46]
109. generous(X0) | calm(X0) [cnf transformation 48]
110. generous(X0) | brave(X0) [cnf transformation 48]
111. strong(X0) | calm(X0) [cnf transformation 48]
112. brave(X0) | strong(X0) [cnf transformation 48]
113. ~wise(X0) | kind(X0) | creative(X0) [cnf transformation 27]
114. ~quiet(X0) | ~curious(X0) [cnf transformation 50]
115. ~curious(X0) | funny(X0) [cnf transformation 50]
118. ~funny(X0) | happy(X0) [cnf transformation 52]
120. ~humble(X0) | happy(X0) [cnf transformation 52]
127. brave(X0) | brave(X0) | ~happy(X0) [cnf transformation 30]
129. ~brave(X0) | generous(X0) | wise(X0) [cnf transformation 54]
135. ~kind(fred) | ~generous(X0) | quiet(X0) [cnf transformation 59]
138. ~creative(fred) [cnf transformation 18]
145. ~calm(john) [cnf transformation 23]
146. ~happy(X0) | brave(X0) [duplicate literal removal 127]
178. 6 <=> ! [X3] : ~strong(X3) [avatar definition]
179. ~strong(X3) <- (6) [avatar component clause 178]
181. 7 <=> curious(sK1) [avatar definition]
182. curious(sK1) <- (7) [avatar component clause 181]
185. 8 <=> brave(sK1) [avatar definition]
186. ~brave(sK1) <- (~8) [avatar component clause 185]
189. 6 | 7 | ~8 [avatar split clause 94,185,181,178]
226. generous(X0) | wise(X0) [subsumption resolution 129,110]
228. 16 <=> ! [X0] : (~generous(X0) | quiet(X0)) [avatar definition]
229. ~generous(X0) | quiet(X0) <- (16) [avatar component clause 228]
231. 17 <=> kind(fred) [avatar definition]
233. ~kind(fred) <- (~17) [avatar component clause 231]
234. 16 | ~17 [avatar split clause 135,231,228]
278. strong(sK1) <- (~8) [resolution 112,186]
280. humble(sK1) <- (~8) [resolution 278,91]
288. happy(sK1) <- (~8) [resolution 120,280]
295. brave(sK1) <- (~8) [resolution 288,146]
298. $false <- (~8) [subsumption resolution 295,186]
299. 8 [avatar contradiction clause 298]
305. funny(sK1) <- (7) [resolution 182,115]
306. happy(sK1) <- (7) [resolution 305,118]
310. ~calm(sK1) <- (7) [resolution 306,92]
365. wise(X0) | kind(X0) | wise(X0) [resolution 103,226]
368. kind(X0) | wise(X0) [duplicate literal removal 365]
488. 36 <=> generous(sK1) [avatar definition]
489. ~generous(sK1) <- (~36) [avatar component clause 488]
490. generous(sK1) <- (36) [avatar component clause 488]
504. quiet(sK1) <- (16, 36) [resolution 490,229]
520. ~curious(sK1) <- (16, 36) [resolution 504,114]
523. $false <- (7, 16, 36) [subsumption resolution 520,182]
524. ~7 | ~16 | ~36 [avatar contradiction clause 523]
530. calm(sK1) <- (~36) [resolution 489,109]
531. $false <- (7, ~36) [subsumption resolution 530,310]
532. ~7 | 36 [avatar contradiction clause 531]
537. calm(X0) <- (6) [resolution 179,111]
538. $false <- (6) [resolution 537,145]
539. ~6 [avatar contradiction clause 538]
543. wise(fred) <- (~17) [resolution 233,368]
651. kind(fred) | creative(fred) <- (~17) [resolution 543,113]
664. creative(fred) <- (~17) [subsumption resolution 651,233]
665. $false <- (~17) [subsumption resolution 664,138]
666. 17 [avatar contradiction clause 665]
667. $false [avatar sat refutation 189,234,299,524,532,539,666]
% SZS output end Proof for 7586350584342913858140024
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.042 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either kind or not old is either curious or not rich. If someone is both not rich and not kind then mary is not old and vice versa. Everyone who is both not old and not curious is either rich or not happy and vice versa. Everyone who is either patient or not old is patient and vice versa. If susan is not calm then someone is not old and vice versa. Everyone who is both not curious and rich is not quiet. If paul is funny or calm then mary is both not generous and tall and vice versa. If someone is either not creative or not humble then someone is not creative and vice versa. If john is kind then alice is happy or humble and vice versa. If john is quiet then susan is not quiet. Everyone who is both not creative and quiet is both not kind and wise and vice versa. If lucy is either not rich or not brave then someone is curious. Everyone who is either not happy or quiet is creative or not happy. If paul is both not quiet and old then someone is not wise or rich and vice versa. Everyone who is strong is both wise and curious. Everyone who is either not creative or not brave is quiet. Someone is either not humble or brave. Someone is not calm. Alice is kind. Someone is not kind. Someone is strong. Someone is not brave. Lucy is both not happy and calm. Paul is either quiet or not curious. | Susan is not generous. | neutral | (![X]:((kind(X)<~>~old(X))=>(curious(X)<~>~rich(X))))&
((?[X]:((~rich(X)&~kind(X))))<=>(~old(mary)))&
(![X]:((~old(X)&~curious(X))<=>(rich(X)<~>~happy(X))))&
(![X]:((patient(X)<~>~old(X))<=>patient(X)))&
((~calm(susan))<=>(?[X]:(~old(X))))&
(![X]:((~curious(X)&rich(X))=>~quiet(X)))&
(((funny(paul)|calm(paul)))<=>((~generous(mary)&tall(mary))))&
((?[X]:((~creative(X)<~>~humble(X))))<=>(?[X]:(~creative(X))))&
((kind(john))<=>((happy(alice)|humble(alice))))&
((quiet(john))=>(~quiet(susan)))&
(![X]:((~creative(X)&quiet(X))<=>(~kind(X)&wise(X))))&
(((~rich(lucy)<~>~brave(lucy)))=>(?[X]:(curious(X))))&
(![X]:((~happy(X)<~>quiet(X))=>(creative(X)|~happy(X))))&
(((~quiet(paul)&old(paul)))<=>(?[X]:((~wise(X)|rich(X)))))&
(![X]:(strong(X)=>(wise(X)&curious(X))))&
(![X]:((~creative(X)<~>~brave(X))=>quiet(X)))&
(?[X]:((~humble(X)<~>brave(X))))&
(?[X]:(~calm(X)))&
(kind(alice))&
(?[X]:(~kind(X)))&
(?[X]:(strong(X)))&
(?[X]:(~brave(X)))&
((~happy(lucy)&calm(lucy)))&
((quiet(paul)<~>~curious(paul))) | ~generous(susan) | [] | null | 0 |
If susan is not generous then someone is either happy or wise.
Everyone who is rich is tall.
Everyone who is not generous or not quiet is both kind and not tall and vice versa.
If someone is both tall and rich then susan is both creative and not kind and vice versa.
Everyone who is not happy or generous is happy and vice versa.
If someone is either not kind or curious then someone is not generous and vice versa.
If john is not brave then mary is either not old or not quiet.
Everyone who is either wise or happy is not patient and vice versa.
Everyone who is kind or old is calm.
Everyone who is wise or brave is not calm and vice versa.
Everyone who is rich or not funny is old and vice versa.
If mary is either calm or not happy then someone is both kind and not patient and vice versa.
Everyone who is not humble is both curious and not patient.
Everyone who is creative is either curious or not tall and vice versa.
Everyone who is both old and not old is quiet and vice versa.
Paul is creative or not strong.
Someone is either not generous or not wise.
Fred is kind or strong.
Paul is not rich or curious. | Mary is not rich. | entailment | ((~generous(susan))=>(?[X]:((happy(X)<~>wise(X)))))&
(![X]:(rich(X)=>tall(X)))&
(![X]:((~generous(X)|~quiet(X))<=>(kind(X)&~tall(X))))&
((?[X]:((tall(X)&rich(X))))<=>((creative(susan)&~kind(susan))))&
(![X]:((~happy(X)|generous(X))<=>happy(X)))&
((?[X]:((~kind(X)<~>curious(X))))<=>(?[X]:(~generous(X))))&
((~brave(john))=>((~old(mary)<~>~quiet(mary))))&
(![X]:((wise(X)<~>happy(X))<=>~patient(X)))&
(![X]:((kind(X)|old(X))=>calm(X)))&
(![X]:((wise(X)|brave(X))<=>~calm(X)))&
(![X]:((rich(X)|~funny(X))<=>old(X)))&
(((calm(mary)<~>~happy(mary)))<=>(?[X]:((kind(X)&~patient(X)))))&
(![X]:(~humble(X)=>(curious(X)&~patient(X))))&
(![X]:(creative(X)<=>(curious(X)<~>~tall(X))))&
(![X]:((old(X)&~old(X))<=>quiet(X)))&
((creative(paul)|~strong(paul)))&
(?[X]:((~generous(X)<~>~wise(X))))&
((kind(fred)|strong(fred)))&
((~rich(paul)|curious(paul))) | ~rich(mary) | [
"p1",
"p2",
"p3",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5111734770632124847941463
% SZS output start Proof for 5111734770632124847941463
2. ! [X0] : (rich(X0) => tall(X0)) [input p1]
3. ! [X0] : ((~quiet(X0) | ~generous(X0)) <=> (~tall(X0) & kind(X0))) [input p2]
4. ? [X0] : (rich(X0) & tall(X0)) <=> (~kind(susan) & creative(susan)) [input p3]
15. ! [X0] : ((~old(X0) & old(X0)) <=> quiet(X0)) [input p14]
20. rich(mary) [input hypothesis]
24. ! [X0] : (tall(X0) | ~rich(X0)) [ennf transformation 2]
30. ! [X0] : (((~quiet(X0) | ~generous(X0)) | (tall(X0) | ~kind(X0))) & ((~tall(X0) & kind(X0)) | (quiet(X0) & generous(X0)))) [nnf transformation 3]
31. ! [X0] : ((~quiet(X0) | ~generous(X0) | tall(X0) | ~kind(X0)) & ((~tall(X0) & kind(X0)) | (quiet(X0) & generous(X0)))) [flattening 30]
32. (? [X0] : (rich(X0) & tall(X0)) | (kind(susan) | ~creative(susan))) & ((~kind(susan) & creative(susan)) | ! [X0] : (~rich(X0) | ~tall(X0))) [nnf transformation 4]
33. (? [X0] : (rich(X0) & tall(X0)) | kind(susan) | ~creative(susan)) & ((~kind(susan) & creative(susan)) | ! [X0] : (~rich(X0) | ~tall(X0))) [flattening 32]
34. (? [X0] : (rich(X0) & tall(X0)) | kind(susan) | ~creative(susan)) & ((~kind(susan) & creative(susan)) | ! [X1] : (~rich(X1) | ~tall(X1))) [rectify 33]
35. ? [X0] : (rich(X0) & tall(X0)) => (rich(sK1) & tall(sK1)) [choice axiom]
36. ((rich(sK1) & tall(sK1)) | kind(susan) | ~creative(susan)) & ((~kind(susan) & creative(susan)) | ! [X1] : (~rich(X1) | ~tall(X1))) [skolemisation 34,35]
55. ! [X0] : (((~old(X0) & old(X0)) | ~quiet(X0)) & (quiet(X0) | (old(X0) | ~old(X0)))) [nnf transformation 15]
56. ! [X0] : (((~old(X0) & old(X0)) | ~quiet(X0)) & (quiet(X0) | old(X0) | ~old(X0))) [flattening 55]
62. ~rich(X0) | tall(X0) [cnf transformation 24]
64. kind(X0) | quiet(X0) [cnf transformation 31]
69. ~kind(susan) | ~rich(X1) | ~tall(X1) [cnf transformation 36]
104. old(X0) | ~quiet(X0) [cnf transformation 56]
105. ~old(X0) | ~quiet(X0) [cnf transformation 56]
111. rich(mary) [cnf transformation 20]
133. 5 <=> kind(susan) [avatar definition]
134. ~kind(susan) <- (~5) [avatar component clause 133]
146. ~kind(susan) | ~rich(X1) [subsumption resolution 69,62]
148. 8 <=> ! [X1] : ~rich(X1) [avatar definition]
149. ~rich(X1) <- (8) [avatar component clause 148]
150. 8 | ~5 [avatar split clause 146,133,148]
215. ~quiet(X0) [subsumption resolution 104,105]
258. $false <- (8) [resolution 149,111]
261. ~8 [avatar contradiction clause 258]
264. quiet(susan) <- (~5) [resolution 64,134]
267. $false <- (~5) [subsumption resolution 264,215]
268. 5 [avatar contradiction clause 267]
269. $false [avatar sat refutation 150,261,268]
% SZS output end Proof for 5111734770632124847941463
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 or not generous is either not calm or old and vice versa.
If alice is either curious or generous then someone is either calm or not quiet.
If someone is both funny and old then someone is both wise and happy.
If mary is kind or not tall then someone is both funny and not old and vice versa.
Everyone who is not kind is not patient or creative and vice versa.
Everyone who is creative is wise and vice versa.
If someone is not creative then fred is either calm or not generous.
If someone is not calm or tall then mary is not creative or quiet.
Everyone who is either not happy or calm is not creative and vice versa.
If john is generous or brave then someone is either not humble or happy.
Everyone who is both quiet and humble is not patient or curious.
Everyone who is both not strong and not quiet is generous and vice versa.
Everyone who is kind is not happy and vice versa.
If someone is not humble or not wise then paul is either funny or not rich and vice versa.
Everyone who is either wise or generous is both kind and tall.
Everyone who is kind or funny is not brave and vice versa.
Fred is patient or not strong.
Alice is not old.
Fred is not strong or humble.
Fred is rich.
Alice is either generous or rich.
Someone is not rich or happy.
Paul is both brave and patient.
Someone is calm. | Fred is calm. | contradiction | (![X]:((tall(X)|~generous(X))<=>(~calm(X)<~>old(X))))&
(((curious(alice)<~>generous(alice)))=>(?[X]:((calm(X)<~>~quiet(X)))))&
((?[X]:((funny(X)&old(X))))=>(?[X]:((wise(X)&happy(X)))))&
(((kind(mary)|~tall(mary)))<=>(?[X]:((funny(X)&~old(X)))))&
(![X]:(~kind(X)<=>(~patient(X)|creative(X))))&
(![X]:(creative(X)<=>wise(X)))&
((?[X]:(~creative(X)))=>((calm(fred)<~>~generous(fred))))&
((?[X]:((~calm(X)|tall(X))))=>((~creative(mary)|quiet(mary))))&
(![X]:((~happy(X)<~>calm(X))<=>~creative(X)))&
(((generous(john)|brave(john)))=>(?[X]:((~humble(X)<~>happy(X)))))&
(![X]:((quiet(X)&humble(X))=>(~patient(X)|curious(X))))&
(![X]:((~strong(X)&~quiet(X))<=>generous(X)))&
(![X]:(kind(X)<=>~happy(X)))&
((?[X]:((~humble(X)|~wise(X))))<=>((funny(paul)<~>~rich(paul))))&
(![X]:((wise(X)<~>generous(X))=>(kind(X)&tall(X))))&
(![X]:((kind(X)|funny(X))<=>~brave(X)))&
((patient(fred)|~strong(fred)))&
(~old(alice))&
((~strong(fred)|humble(fred)))&
(rich(fred))&
((generous(alice)<~>rich(alice)))&
(?[X]:((~rich(X)|happy(X))))&
((brave(paul)&patient(paul)))&
(?[X]:(calm(X))) | calm(fred) | [
"p4",
"p5",
"p6",
"p7",
"p8",
"p11",
"p12",
"p14",
"p15",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 923812028253049753886328
% SZS output start Proof for 923812028253049753886328
5. ! [X0] : (~kind(X0) <=> (creative(X0) | ~patient(X0))) [input p4]
6. ! [X0] : (creative(X0) <=> wise(X0)) [input p5]
7. ? [X0] : ~creative(X0) => (calm(fred) <~> ~generous(fred)) [input p6]
8. ? [X0] : (tall(X0) | ~calm(X0)) => (quiet(mary) | ~creative(mary)) [input p7]
9. ! [X0] : ((~happy(X0) <~> calm(X0)) <=> ~creative(X0)) [input p8]
12. ! [X0] : ((~quiet(X0) & ~strong(X0)) <=> generous(X0)) [input p11]
13. ! [X0] : (kind(X0) <=> ~happy(X0)) [input p12]
15. ! [X0] : ((wise(X0) <~> generous(X0)) => (tall(X0) & kind(X0))) [input p14]
16. ! [X0] : ((funny(X0) | kind(X0)) <=> ~brave(X0)) [input p15]
23. patient(paul) & brave(paul) [input p22]
25. calm(fred) [input hypothesis]
29. (calm(fred) <~> ~generous(fred)) | ! [X0] : creative(X0) [ennf transformation 7]
30. (quiet(mary) | ~creative(mary)) | ! [X0] : (~tall(X0) & calm(X0)) [ennf transformation 8]
31. quiet(mary) | ~creative(mary) | ! [X0] : (~tall(X0) & calm(X0)) [flattening 30]
35. ! [X0] : ((tall(X0) & kind(X0)) | (wise(X0) <=> generous(X0))) [ennf transformation 15]
49. ! [X0] : ((~kind(X0) | (~creative(X0) & patient(X0))) & ((creative(X0) | ~patient(X0)) | kind(X0))) [nnf transformation 5]
50. ! [X0] : ((~kind(X0) | (~creative(X0) & patient(X0))) & (creative(X0) | ~patient(X0) | kind(X0))) [flattening 49]
51. ! [X0] : ((creative(X0) | ~wise(X0)) & (wise(X0) | ~creative(X0))) [nnf transformation 6]
52. ((generous(fred) | ~calm(fred)) & (~generous(fred) | calm(fred))) | ! [X0] : creative(X0) [nnf transformation 29]
53. ! [X0] : ((((~calm(X0) | happy(X0)) & (calm(X0) | ~happy(X0))) | creative(X0)) & (~creative(X0) | ((~happy(X0) | ~calm(X0)) & (calm(X0) | happy(X0))))) [nnf transformation 9]
57. ! [X0] : (((~quiet(X0) & ~strong(X0)) | ~generous(X0)) & (generous(X0) | (quiet(X0) | strong(X0)))) [nnf transformation 12]
58. ! [X0] : (((~quiet(X0) & ~strong(X0)) | ~generous(X0)) & (generous(X0) | quiet(X0) | strong(X0))) [flattening 57]
59. ! [X0] : ((kind(X0) | happy(X0)) & (~happy(X0) | ~kind(X0))) [nnf transformation 13]
64. ! [X0] : ((tall(X0) & kind(X0)) | ((wise(X0) | ~generous(X0)) & (generous(X0) | ~wise(X0)))) [nnf transformation 35]
65. ! [X0] : (((funny(X0) | kind(X0)) | brave(X0)) & (~brave(X0) | (~funny(X0) & ~kind(X0)))) [nnf transformation 16]
66. ! [X0] : ((funny(X0) | kind(X0) | brave(X0)) & (~brave(X0) | (~funny(X0) & ~kind(X0)))) [flattening 65]
89. ~patient(X0) | creative(X0) | kind(X0) [cnf transformation 50]
91. ~creative(X0) | ~kind(X0) [cnf transformation 50]
92. ~creative(X0) | wise(X0) [cnf transformation 51]
93. ~wise(X0) | creative(X0) [cnf transformation 51]
95. generous(fred) | ~calm(fred) | creative(X0) [cnf transformation 52]
96. quiet(mary) | ~creative(mary) | calm(X0) [cnf transformation 31]
99. ~creative(X0) | ~happy(X0) | ~calm(X0) [cnf transformation 53]
101. ~calm(X0) | happy(X0) | creative(X0) [cnf transformation 53]
109. ~quiet(X0) | ~generous(X0) [cnf transformation 58]
110. ~kind(X0) | ~happy(X0) [cnf transformation 59]
111. kind(X0) | happy(X0) [cnf transformation 59]
118. ~wise(X0) | generous(X0) | kind(X0) [cnf transformation 64]
119. ~generous(X0) | wise(X0) | kind(X0) [cnf transformation 64]
122. ~brave(X0) | ~kind(X0) [cnf transformation 66]
132. brave(paul) [cnf transformation 23]
133. patient(paul) [cnf transformation 23]
135. calm(fred) [cnf transformation 25]
173. 9 <=> kind(mary) [avatar definition]
194. 13 <=> ! [X0] : creative(X0) [avatar definition]
195. creative(X0) <- (13) [avatar component clause 194]
197. 14 <=> calm(fred) [avatar definition]
198. calm(fred) <- (14) [avatar component clause 197]
201. 15 <=> generous(fred) [avatar definition]
203. generous(fred) <- (15) [avatar component clause 201]
204. 13 | ~14 | 15 [avatar split clause 95,201,197,194]
210. 17 <=> creative(mary) [avatar definition]
211. creative(mary) <- (17) [avatar component clause 210]
212. ~creative(mary) <- (~17) [avatar component clause 210]
214. 18 <=> quiet(mary) [avatar definition]
216. quiet(mary) <- (18) [avatar component clause 214]
219. 19 <=> ! [X0] : calm(X0) [avatar definition]
220. calm(X0) <- (19) [avatar component clause 219]
221. 19 | ~17 | 18 [avatar split clause 96,214,210,219]
299. 14 [avatar split clause 135,197]
301. $false <- (13, ~17) [resolution 212,195]
302. ~13 | 17 [avatar contradiction clause 301]
306. ~kind(paul) [resolution 122,132]
307. happy(paul) [resolution 306,111]
338. creative(paul) | kind(paul) [resolution 89,133]
340. creative(paul) [subsumption resolution 338,306]
344. ~happy(paul) | ~calm(paul) [resolution 99,340]
345. ~calm(paul) [subsumption resolution 344,307]
351. happy(fred) | creative(fred) <- (14) [resolution 101,198]
362. 43 <=> creative(fred) [avatar definition]
363. ~creative(fred) <- (~43) [avatar component clause 362]
364. creative(fred) <- (43) [avatar component clause 362]
366. 44 <=> happy(fred) [avatar definition]
367. ~happy(fred) <- (~44) [avatar component clause 366]
368. happy(fred) <- (44) [avatar component clause 366]
369. 43 | 44 | ~14 [avatar split clause 351,197,366,362]
380. ~happy(fred) | ~calm(fred) <- (43) [resolution 364,99]
383. ~kind(fred) <- (43) [resolution 364,91]
384. ~happy(fred) <- (14, 43) [subsumption resolution 380,198]
385. ~44 | ~14 | ~43 [avatar split clause 384,362,197,366]
386. wise(fred) | kind(fred) <- (15) [resolution 119,203]
392. 45 <=> generous(mary) [avatar definition]
407. wise(mary) <- (17) [resolution 211,92]
408. ~kind(mary) <- (17) [resolution 211,91]
410. ~generous(mary) <- (18) [resolution 216,109]
411. ~45 | ~18 [avatar split clause 410,214,392]
419. generous(mary) | kind(mary) <- (17) [resolution 407,118]
434. ~9 | ~17 [avatar split clause 408,210,173]
445. 9 | 45 | ~17 [avatar split clause 419,210,392,173]
460. $false <- (19) [resolution 220,345]
461. ~19 [avatar contradiction clause 460]
540. happy(fred) <- (43) [resolution 383,111]
541. $false <- (43, ~44) [subsumption resolution 540,367]
542. ~43 | 44 [avatar contradiction clause 541]
551. 55 <=> kind(fred) [avatar definition]
553. kind(fred) <- (55) [avatar component clause 551]
555. 56 <=> wise(fred) [avatar definition]
557. wise(fred) <- (56) [avatar component clause 555]
558. 55 | 56 | ~15 [avatar split clause 386,201,555,551]
563. ~happy(fred) <- (55) [resolution 553,110]
565. $false <- (44, 55) [subsumption resolution 563,368]
566. ~44 | ~55 [avatar contradiction clause 565]
571. creative(fred) <- (56) [resolution 557,93]
572. $false <- (~43, 56) [subsumption resolution 571,363]
573. 43 | ~56 [avatar contradiction clause 572]
574. $false [avatar sat refutation 204,221,299,302,369,385,411,434,445,461,542,558,566,573]
% SZS output end Proof for 923812028253049753886328
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both old and curious is not kind or not happy and vice versa.
If paul is either strong or calm then someone is both brave and generous.
If someone is both not humble and quiet then susan is kind and vice versa.
Everyone who is not calm or not kind is not brave.
Everyone who is both tall and not rich is either humble or not old and vice versa.
If alice is not humble then someone is not curious and vice versa.
Everyone who is either humble or rich is either wise or not kind and vice versa.
Everyone who is not wise or not quiet is both tall and generous.
If paul is both quiet and tall then someone is either not rich or not kind and vice versa.
If lucy is both not curious and not brave then someone is funny and vice versa.
Everyone who is both funny and not happy is both calm and strong and vice versa.
Everyone who is funny is both wise and not creative and vice versa.
Everyone who is wise is either generous or not old.
Everyone who is not quiet is not rich or curious.
Everyone who is both not creative and not tall is funny and vice versa.
Everyone who is strong is both not curious and not rich and vice versa.
Susan is either curious or tall.
Susan is not generous.
Someone is either not tall or quiet.
John is both not quiet and not kind.
Fred is either wise or happy.
Someone is rich or not wise.
Paul is brave.
Paul is either not curious or old. | Paul is not calm. | contradiction | (![X]:((old(X)&curious(X))<=>(~kind(X)|~happy(X))))&
(((strong(paul)<~>calm(paul)))=>(?[X]:((brave(X)&generous(X)))))&
((?[X]:((~humble(X)&quiet(X))))<=>(kind(susan)))&
(![X]:((~calm(X)|~kind(X))=>~brave(X)))&
(![X]:((tall(X)&~rich(X))<=>(humble(X)<~>~old(X))))&
((~humble(alice))<=>(?[X]:(~curious(X))))&
(![X]:((humble(X)<~>rich(X))<=>(wise(X)<~>~kind(X))))&
(![X]:((~wise(X)|~quiet(X))=>(tall(X)&generous(X))))&
(((quiet(paul)&tall(paul)))<=>(?[X]:((~rich(X)<~>~kind(X)))))&
(((~curious(lucy)&~brave(lucy)))<=>(?[X]:(funny(X))))&
(![X]:((funny(X)&~happy(X))<=>(calm(X)&strong(X))))&
(![X]:(funny(X)<=>(wise(X)&~creative(X))))&
(![X]:(wise(X)=>(generous(X)<~>~old(X))))&
(![X]:(~quiet(X)=>(~rich(X)|curious(X))))&
(![X]:((~creative(X)&~tall(X))<=>funny(X)))&
(![X]:(strong(X)<=>(~curious(X)&~rich(X))))&
((curious(susan)<~>tall(susan)))&
(~generous(susan))&
(?[X]:((~tall(X)<~>quiet(X))))&
((~quiet(john)&~kind(john)))&
((wise(fred)<~>happy(fred)))&
(?[X]:((rich(X)|~wise(X))))&
(brave(paul))&
((~curious(paul)<~>old(paul))) | ~calm(paul) | [
"p3",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 7534595112906370943505504
% SZS output start Proof for 7534595112906370943505504
4. ! [X0] : ((~kind(X0) | ~calm(X0)) => ~brave(X0)) [input p3]
23. brave(paul) [input p22]
25. ~calm(paul) [input hypothesis]
27. ! [X0] : (~brave(X0) | (kind(X0) & calm(X0))) [ennf transformation 4]
87. ~brave(X0) | calm(X0) [cnf transformation 27]
144. brave(paul) [cnf transformation 23]
147. ~calm(paul) [cnf transformation 25]
149. 1 <=> calm(paul) [avatar definition]
151. ~calm(paul) <- (~1) [avatar component clause 149]
287. ~1 [avatar split clause 147,149]
292. calm(paul) [resolution 87,144]
294. $false <- (~1) [subsumption resolution 292,151]
295. 1 [avatar contradiction clause 294]
296. $false [avatar sat refutation 287,295]
% SZS output end Proof for 7534595112906370943505504
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative is humble.
If paul is funny or generous then paul is not wise or not patient.
Everyone who is both not wise and creative is not wise and vice versa.
Everyone who is quiet is humble and vice versa.
Everyone who is not tall or curious is both not old and not kind and vice versa.
If paul is not strong then someone is creative and vice versa.
Everyone who is humble or not quiet is both not old and tall and vice versa.
If mary is not creative or curious then paul is tall or wise and vice versa.
Everyone who is either not funny or quiet is either quiet or not wise and vice versa.
Everyone who is not old or not strong is tall.
Everyone who is rich is not kind.
Everyone who is either curious or not creative is old and vice versa.
Everyone who is either not calm or not curious is strong or not kind.
If mary is not curious or not rich then john is not calm and vice versa.
If someone is either not rich or brave then alice is not calm and vice versa.
Everyone who is both creative and strong is either not patient or not old and vice versa.
Lucy is both strong and not calm.
Someone is either not patient or creative.
Someone is creative or calm.
Fred is tall.
Someone is generous or funny.
Lucy is rich.
Someone is both not patient and strong.
Someone is wise or funny. | Mary is funny. | entailment | (![X]:(~creative(X)=>humble(X)))&
(((funny(paul)|generous(paul)))=>((~wise(paul)|~patient(paul))))&
(![X]:((~wise(X)&creative(X))<=>~wise(X)))&
(![X]:(quiet(X)<=>humble(X)))&
(![X]:((~tall(X)|curious(X))<=>(~old(X)&~kind(X))))&
((~strong(paul))<=>(?[X]:(creative(X))))&
(![X]:((humble(X)|~quiet(X))<=>(~old(X)&tall(X))))&
(((~creative(mary)|curious(mary)))<=>((tall(paul)|wise(paul))))&
(![X]:((~funny(X)<~>quiet(X))<=>(quiet(X)<~>~wise(X))))&
(![X]:((~old(X)|~strong(X))=>tall(X)))&
(![X]:(rich(X)=>~kind(X)))&
(![X]:((curious(X)<~>~creative(X))<=>old(X)))&
(![X]:((~calm(X)<~>~curious(X))=>(strong(X)|~kind(X))))&
(((~curious(mary)|~rich(mary)))<=>(~calm(john)))&
((?[X]:((~rich(X)<~>brave(X))))<=>(~calm(alice)))&
(![X]:((creative(X)&strong(X))<=>(~patient(X)<~>~old(X))))&
((strong(lucy)&~calm(lucy)))&
(?[X]:((~patient(X)<~>creative(X))))&
(?[X]:((creative(X)|calm(X))))&
(tall(fred))&
(?[X]:((generous(X)|funny(X))))&
(rich(lucy))&
(?[X]:((~patient(X)&strong(X))))&
(?[X]:((wise(X)|funny(X)))) | funny(mary) | [
"p2",
"p4",
"p7",
"p8",
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 3853081659266664673467175
% SZS output start Proof for 3853081659266664673467175
3. ! [X0] : ((creative(X0) & ~wise(X0)) <=> ~wise(X0)) [input p2]
5. ! [X0] : ((curious(X0) | ~tall(X0)) <=> (~kind(X0) & ~old(X0))) [input p4]
8. (curious(mary) | ~creative(mary)) <=> (wise(paul) | tall(paul)) [input p7]
9. ! [X0] : ((~funny(X0) <~> quiet(X0)) <=> (quiet(X0) <~> ~wise(X0))) [input p8]
10. ! [X0] : ((~strong(X0) | ~old(X0)) => tall(X0)) [input p9]
12. ! [X0] : ((curious(X0) <~> ~creative(X0)) <=> old(X0)) [input p11]
25. ~funny(mary) [input hypothesis]
29. ! [X0] : (tall(X0) | (strong(X0) & old(X0))) [ennf transformation 10]
33. ! [X0] : (((creative(X0) & ~wise(X0)) | wise(X0)) & (~wise(X0) | (~creative(X0) | wise(X0)))) [nnf transformation 3]
34. ! [X0] : (((creative(X0) & ~wise(X0)) | wise(X0)) & (~wise(X0) | ~creative(X0) | wise(X0))) [flattening 33]
36. ! [X0] : (((curious(X0) | ~tall(X0)) | (kind(X0) | old(X0))) & ((~kind(X0) & ~old(X0)) | (~curious(X0) & tall(X0)))) [nnf transformation 5]
37. ! [X0] : ((curious(X0) | ~tall(X0) | kind(X0) | old(X0)) & ((~kind(X0) & ~old(X0)) | (~curious(X0) & tall(X0)))) [flattening 36]
44. ((curious(mary) | ~creative(mary)) | (~wise(paul) & ~tall(paul))) & ((wise(paul) | tall(paul)) | (~curious(mary) & creative(mary))) [nnf transformation 8]
45. (curious(mary) | ~creative(mary) | (~wise(paul) & ~tall(paul))) & (wise(paul) | tall(paul) | (~curious(mary) & creative(mary))) [flattening 44]
46. ! [X0] : ((((~quiet(X0) | funny(X0)) & (quiet(X0) | ~funny(X0))) | ((quiet(X0) | wise(X0)) & (~wise(X0) | ~quiet(X0)))) & (((wise(X0) | ~quiet(X0)) & (~wise(X0) | quiet(X0))) | ((~funny(X0) | ~quiet(X0)) & (quiet(X0) | funny(X0))))) [nnf transformation 9]
47. ! [X0] : ((((creative(X0) | ~curious(X0)) & (~creative(X0) | curious(X0))) | ~old(X0)) & (old(X0) | ((curious(X0) | creative(X0)) & (~creative(X0) | ~curious(X0))))) [nnf transformation 12]
73. wise(X0) | creative(X0) [cnf transformation 34]
76. ~old(X0) | tall(X0) [cnf transformation 37]
77. ~old(X0) | ~curious(X0) [cnf transformation 37]
90. curious(mary) | ~creative(mary) | ~tall(paul) [cnf transformation 45]
92. ~wise(X0) | quiet(X0) | quiet(X0) | funny(X0) [cnf transformation 46]
98. ~quiet(X0) | funny(X0) | ~wise(X0) | ~quiet(X0) [cnf transformation 46]
100. tall(X0) | old(X0) [cnf transformation 29]
103. old(X0) | ~creative(X0) | ~curious(X0) [cnf transformation 47]
133. ~funny(mary) [cnf transformation 25]
134. ~wise(X0) | quiet(X0) | funny(X0) [duplicate literal removal 92]
137. ~quiet(X0) | funny(X0) | ~wise(X0) [duplicate literal removal 98]
170. 8 <=> creative(mary) [avatar definition]
171. creative(mary) <- (8) [avatar component clause 170]
174. 9 <=> curious(mary) [avatar definition]
176. curious(mary) <- (9) [avatar component clause 174]
179. 10 <=> tall(paul) [avatar definition]
181. ~tall(paul) <- (~10) [avatar component clause 179]
182. ~10 | ~8 | 9 [avatar split clause 90,174,170,179]
186. ~wise(X0) | funny(X0) [subsumption resolution 134,137]
187. tall(X0) [subsumption resolution 100,76]
189. ~curious(X0) | ~creative(X0) [subsumption resolution 103,77]
263. funny(X0) | creative(X0) [resolution 186,73]
266. $false <- (~10) [subsumption resolution 181,187]
267. 10 [avatar contradiction clause 266]
277. creative(mary) [resolution 263,133]
281. 8 [avatar split clause 277,170]
282. ~creative(mary) <- (9) [resolution 176,189]
283. $false <- (8, 9) [subsumption resolution 282,171]
284. ~8 | ~9 [avatar contradiction clause 283]
285. $false [avatar sat refutation 182,267,281,284]
% SZS output end Proof for 3853081659266664673467175
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old is both not humble and brave and vice versa. Everyone who is kind is either creative or not patient and vice versa. If someone is both not curious and wise then lucy is happy and vice versa. If paul is either humble or not generous then alice is both not old and tall and vice versa. If someone is funny or not funny then someone is not creative. Everyone who is rich or not rich is not brave and vice versa. If someone is both kind and not old then someone is strong or not tall and vice versa. Everyone who is old or humble is both not generous and not brave. Everyone who is both not old and creative is both not patient and not strong and vice versa. If someone is both humble and strong then fred is happy or not kind and vice versa. If someone is both not brave and generous then someone is either not funny or quiet. If someone is calm or brave then someone is both not humble and not strong and vice versa. Everyone who is either generous or not humble is not strong or generous and vice versa. If someone is not funny or not humble then someone is either calm or not wise and vice versa. Everyone who is not wise or not curious is not curious and vice versa. Alice is calm. John is both strong and not quiet. Fred is either old or calm. Paul is humble. Fred is humble. Paul is both not old and strong. Alice is not tall or not brave. | Fred is not generous. | entailment | (![X]:(old(X)<=>(~humble(X)&brave(X))))&
(![X]:(kind(X)<=>(creative(X)<~>~patient(X))))&
((?[X]:((~curious(X)&wise(X))))<=>(happy(lucy)))&
(((humble(paul)<~>~generous(paul)))<=>((~old(alice)&tall(alice))))&
((?[X]:((funny(X)|~funny(X))))=>(?[X]:(~creative(X))))&
(![X]:((rich(X)|~rich(X))<=>~brave(X)))&
((?[X]:((kind(X)&~old(X))))<=>(?[X]:((strong(X)|~tall(X)))))&
(![X]:((old(X)|humble(X))=>(~generous(X)&~brave(X))))&
(![X]:((~old(X)&creative(X))<=>(~patient(X)&~strong(X))))&
((?[X]:((humble(X)&strong(X))))<=>((happy(fred)|~kind(fred))))&
((?[X]:((~brave(X)&generous(X))))=>(?[X]:((~funny(X)<~>quiet(X)))))&
((?[X]:((calm(X)|brave(X))))<=>(?[X]:((~humble(X)&~strong(X)))))&
(![X]:((generous(X)<~>~humble(X))<=>(~strong(X)|generous(X))))&
((?[X]:((~funny(X)|~humble(X))))<=>(?[X]:((calm(X)<~>~wise(X)))))&
(![X]:((~wise(X)|~curious(X))<=>~curious(X)))&
(calm(alice))&
((strong(john)&~quiet(john)))&
((old(fred)<~>calm(fred)))&
(humble(paul))&
(humble(fred))&
((~old(paul)&strong(paul)))&
((~tall(alice)|~brave(alice))) | ~generous(fred) | [
"p7",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 8901689538107436645158577
% SZS output start Proof for 8901689538107436645158577
8. ! [X0] : ((humble(X0) | old(X0)) => (~brave(X0) & ~generous(X0))) [input p7]
13. ! [X0] : ((generous(X0) <~> ~humble(X0)) <=> (generous(X0) | ~strong(X0))) [input p12]
23. generous(fred) [input hypothesis]
30. ! [X0] : ((~brave(X0) & ~generous(X0)) | (~humble(X0) & ~old(X0))) [ennf transformation 8]
67. ! [X0] : ((((humble(X0) | ~generous(X0)) & (~humble(X0) | generous(X0))) | (~generous(X0) & strong(X0))) & ((generous(X0) | ~strong(X0)) | ((generous(X0) | humble(X0)) & (~humble(X0) | ~generous(X0))))) [nnf transformation 13]
68. ! [X0] : ((((humble(X0) | ~generous(X0)) & (~humble(X0) | generous(X0))) | (~generous(X0) & strong(X0))) & (generous(X0) | ~strong(X0) | ((generous(X0) | humble(X0)) & (~humble(X0) | ~generous(X0))))) [flattening 67]
104. ~generous(X0) | ~humble(X0) [cnf transformation 30]
128. humble(X0) | ~generous(X0) | ~generous(X0) [cnf transformation 68]
148. generous(fred) [cnf transformation 23]
150. humble(X0) | ~generous(X0) [duplicate literal removal 128]
260. 24 <=> ! [X1] : ~generous(X1) [avatar definition]
261. ~generous(X1) <- (24) [avatar component clause 260]
295. ~generous(X0) [subsumption resolution 150,104]
296. 24 [avatar split clause 295,260]
348. $false <- (24) [resolution 261,148]
349. ~24 [avatar contradiction clause 348]
350. $false [avatar sat refutation 296,349]
% SZS output end Proof for 8901689538107436645158577
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both rich and not humble is both tall and not quiet.
If fred is both not creative and tall then someone is not funny.
If someone is not old then someone is wise.
Everyone who is brave is curious or not humble and vice versa.
If someone is calm then mary is both not strong and not curious.
Everyone who is either not happy or creative is strong or curious and vice versa.
If lucy is either brave or not kind then alice is both old and calm and vice versa.
If someone is both not funny and wise then mary is strong or not old and vice versa.
If alice is either not kind or humble then someone is not humble.
Everyone who is brave or not happy is not strong and vice versa.
If someone is both tall and creative then alice is either not curious or humble.
If lucy is either creative or generous then paul is both not patient and not creative.
Everyone who is either creative or not happy is humble.
Everyone who is both not patient and not brave is both tall and not brave.
Everyone who is both curious and not wise is both generous and tall and vice versa.
If mary is either tall or brave then susan is both not humble and not patient and vice versa.
Someone is both not generous and not old.
Someone is either not patient or not quiet.
Someone is not curious or old.
Someone is both not calm and not quiet.
Someone is curious.
Susan is both funny and creative.
Paul is both not curious and not creative.
Someone is not quiet. | Paul is not strong. | entailment | (![X]:((rich(X)&~humble(X))=>(tall(X)&~quiet(X))))&
(((~creative(fred)&tall(fred)))=>(?[X]:(~funny(X))))&
((?[X]:(~old(X)))=>(?[X]:(wise(X))))&
(![X]:(brave(X)<=>(curious(X)|~humble(X))))&
((?[X]:(calm(X)))=>((~strong(mary)&~curious(mary))))&
(![X]:((~happy(X)<~>creative(X))<=>(strong(X)|curious(X))))&
(((brave(lucy)<~>~kind(lucy)))<=>((old(alice)&calm(alice))))&
((?[X]:((~funny(X)&wise(X))))<=>((strong(mary)|~old(mary))))&
(((~kind(alice)<~>humble(alice)))=>(?[X]:(~humble(X))))&
(![X]:((brave(X)|~happy(X))<=>~strong(X)))&
((?[X]:((tall(X)&creative(X))))=>((~curious(alice)<~>humble(alice))))&
(((creative(lucy)<~>generous(lucy)))=>((~patient(paul)&~creative(paul))))&
(![X]:((creative(X)<~>~happy(X))=>humble(X)))&
(![X]:((~patient(X)&~brave(X))=>(tall(X)&~brave(X))))&
(![X]:((curious(X)&~wise(X))<=>(generous(X)&tall(X))))&
(((tall(mary)<~>brave(mary)))<=>((~humble(susan)&~patient(susan))))&
(?[X]:((~generous(X)&~old(X))))&
(?[X]:((~patient(X)<~>~quiet(X))))&
(?[X]:((~curious(X)|old(X))))&
(?[X]:((~calm(X)&~quiet(X))))&
(?[X]:(curious(X)))&
((funny(susan)&creative(susan)))&
((~curious(paul)&~creative(paul)))&
(?[X]:(~quiet(X))) | ~strong(paul) | [
"p5",
"p9",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 2370231756427330647885557
% SZS output start Proof for 2370231756427330647885557
6. ! [X0] : ((~happy(X0) <~> creative(X0)) <=> (curious(X0) | strong(X0))) [input p5]
10. ! [X0] : ((~happy(X0) | brave(X0)) <=> ~strong(X0)) [input p9]
23. ~creative(paul) & ~curious(paul) [input p22]
25. strong(paul) [input hypothesis]
45. ! [X0] : ((((~creative(X0) | happy(X0)) & (creative(X0) | ~happy(X0))) | (~curious(X0) & ~strong(X0))) & ((curious(X0) | strong(X0)) | ((~happy(X0) | ~creative(X0)) & (creative(X0) | happy(X0))))) [nnf transformation 6]
46. ! [X0] : ((((~creative(X0) | happy(X0)) & (creative(X0) | ~happy(X0))) | (~curious(X0) & ~strong(X0))) & (curious(X0) | strong(X0) | ((~happy(X0) | ~creative(X0)) & (creative(X0) | happy(X0))))) [flattening 45]
57. ! [X0] : (((~happy(X0) | brave(X0)) | strong(X0)) & (~strong(X0) | (happy(X0) & ~brave(X0)))) [nnf transformation 10]
58. ! [X0] : ((~happy(X0) | brave(X0) | strong(X0)) & (~strong(X0) | (happy(X0) & ~brave(X0)))) [flattening 57]
88. ~happy(X0) | creative(X0) | ~strong(X0) [cnf transformation 46]
106. ~strong(X0) | happy(X0) [cnf transformation 58]
139. ~creative(paul) [cnf transformation 23]
141. strong(paul) [cnf transformation 25]
250. 24 <=> creative(paul) [avatar definition]
252. ~creative(paul) <- (~24) [avatar component clause 250]
302. ~24 [avatar split clause 139,250]
307. happy(paul) [resolution 106,141]
311. creative(paul) | ~strong(paul) [resolution 307,88]
312. ~strong(paul) <- (~24) [subsumption resolution 311,252]
313. $false <- (~24) [subsumption resolution 312,141]
314. 24 [avatar contradiction clause 313]
315. $false [avatar sat refutation 302,314]
% SZS output end Proof for 2370231756427330647885557
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If susan is not wise or not happy then paul is not calm and vice versa.
Everyone who is both wise and not generous is both quiet and kind and vice versa.
Everyone who is generous is strong.
Everyone who is either rich or not generous is either not happy or not generous and vice versa.
Everyone who is not patient or not funny is not old or not creative.
If someone is both not kind and not humble then someone is rich.
Everyone who is not rich or not quiet is both not tall and rich.
If someone is curious or not happy then someone is generous or not generous and vice versa.
Everyone who is not tall is not funny or not old and vice versa.
Everyone who is creative or rich is not quiet and vice versa.
If alice is not calm then mary is not kind or not curious.
Everyone who is not calm is either strong or not strong and vice versa.
If someone is not humble then someone is old.
Everyone who is not generous or strong is old or not funny and vice versa.
If paul is patient or not quiet then alice is either curious or not brave.
If someone is not calm or humble then someone is either kind or not happy and vice versa.
Alice is humble.
Someone is curious.
Mary is both kind and creative.
Someone is strong or not brave.
Mary is either not funny or not brave.
Someone is funny or humble.
Someone is creative.
Alice is creative. | Mary is not rich. | contradiction | (((~wise(susan)|~happy(susan)))<=>(~calm(paul)))&
(![X]:((wise(X)&~generous(X))<=>(quiet(X)&kind(X))))&
(![X]:(generous(X)=>strong(X)))&
(![X]:((rich(X)<~>~generous(X))<=>(~happy(X)<~>~generous(X))))&
(![X]:((~patient(X)|~funny(X))=>(~old(X)|~creative(X))))&
((?[X]:((~kind(X)&~humble(X))))=>(?[X]:(rich(X))))&
(![X]:((~rich(X)|~quiet(X))=>(~tall(X)&rich(X))))&
((?[X]:((curious(X)|~happy(X))))<=>(?[X]:((generous(X)|~generous(X)))))&
(![X]:(~tall(X)<=>(~funny(X)|~old(X))))&
(![X]:((creative(X)|rich(X))<=>~quiet(X)))&
((~calm(alice))=>((~kind(mary)|~curious(mary))))&
(![X]:(~calm(X)<=>(strong(X)<~>~strong(X))))&
((?[X]:(~humble(X)))=>(?[X]:(old(X))))&
(![X]:((~generous(X)|strong(X))<=>(old(X)|~funny(X))))&
(((patient(paul)|~quiet(paul)))=>((curious(alice)<~>~brave(alice))))&
((?[X]:((~calm(X)|humble(X))))<=>(?[X]:((kind(X)<~>~happy(X)))))&
(humble(alice))&
(?[X]:(curious(X)))&
((kind(mary)&creative(mary)))&
(?[X]:((strong(X)|~brave(X))))&
((~funny(mary)<~>~brave(mary)))&
(?[X]:((funny(X)|humble(X))))&
(?[X]:(creative(X)))&
(creative(alice)) | ~rich(mary) | [
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 854530218680265421493162
% SZS output start Proof for 854530218680265421493162
7. ! [X0] : ((~quiet(X0) | ~rich(X0)) => (rich(X0) & ~tall(X0))) [input p6]
25. ~rich(mary) [input hypothesis]
35. ! [X0] : ((rich(X0) & ~tall(X0)) | (quiet(X0) & rich(X0))) [ennf transformation 7]
99. rich(X0) | rich(X0) [cnf transformation 35]
139. ~rich(mary) [cnf transformation 25]
142. rich(X0) [duplicate literal removal 99]
275. $false [subsumption resolution 139,142]
% SZS output end Proof for 854530218680265421493162
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either wise or not tall is humble or strong and vice versa. Everyone who is patient is either brave or humble. Everyone who is brave or funny is funny or not rich and vice versa. Everyone who is either generous or quiet is tall and vice versa. If someone is either not brave or quiet then someone is both calm and not tall. If someone is not brave then lucy is either rich or not rich and vice versa. If john is either not happy or tall then mary is both funny and tall. Everyone who is either patient or not creative is happy or not strong. Everyone who is generous is both kind and curious and vice versa. Everyone who is either strong or generous is not funny or rich and vice versa. Everyone who is not creative is both not brave and strong. If someone is funny then someone is not curious or not brave. Everyone who is not patient or not old is not strong or not curious and vice versa. If someone is happy or rich then john is either not rich or not humble. Everyone who is both calm and not tall is humble or tall. Everyone who is either not old or curious is not rich or humble and vice versa. Paul is rich. John is either not strong or calm. John is either wise or kind. Fred is humble or not curious. Alice is not generous. Someone is quiet or tall. Mary is not strong. | John is not tall. | neutral | (![X]:((wise(X)<~>~tall(X))<=>(humble(X)|strong(X))))&
(![X]:(patient(X)=>(brave(X)<~>humble(X))))&
(![X]:((brave(X)|funny(X))<=>(funny(X)|~rich(X))))&
(![X]:((generous(X)<~>quiet(X))<=>tall(X)))&
((?[X]:((~brave(X)<~>quiet(X))))=>(?[X]:((calm(X)&~tall(X)))))&
((?[X]:(~brave(X)))<=>((rich(lucy)<~>~rich(lucy))))&
(((~happy(john)<~>tall(john)))=>((funny(mary)&tall(mary))))&
(![X]:((patient(X)<~>~creative(X))=>(happy(X)|~strong(X))))&
(![X]:(generous(X)<=>(kind(X)&curious(X))))&
(![X]:((strong(X)<~>generous(X))<=>(~funny(X)|rich(X))))&
(![X]:(~creative(X)=>(~brave(X)&strong(X))))&
((?[X]:(funny(X)))=>(?[X]:((~curious(X)|~brave(X)))))&
(![X]:((~patient(X)|~old(X))<=>(~strong(X)|~curious(X))))&
((?[X]:((happy(X)|rich(X))))=>((~rich(john)<~>~humble(john))))&
(![X]:((calm(X)&~tall(X))=>(humble(X)|tall(X))))&
(![X]:((~old(X)<~>curious(X))<=>(~rich(X)|humble(X))))&
(rich(paul))&
((~strong(john)<~>calm(john)))&
((wise(john)<~>kind(john)))&
((humble(fred)|~curious(fred)))&
(~generous(alice))&
(?[X]:((quiet(X)|tall(X))))&
(~strong(mary)) | ~tall(john) | [] | null | 0 |
Everyone who is brave is both not tall and quiet.
If john is either not patient or not quiet then lucy is either kind or not wise.
Everyone who is creative or not humble is either not kind or not rich and vice versa.
Everyone who is either funny or curious is calm or not humble and vice versa.
Everyone who is kind or not happy is either curious or not humble and vice versa.
Everyone who is not tall or not old is either not generous or strong and vice versa.
Everyone who is not patient or not humble is either not humble or not curious and vice versa.
Everyone who is not wise is not calm.
Everyone who is both not rich and patient is either kind or not patient.
If someone is either not kind or not happy then someone is creative.
If someone is not kind or not tall then paul is calm and vice versa.
If lucy is both brave and not strong then someone is either not humble or patient and vice versa.
Everyone who is either not tall or not humble is either not quiet or not humble and vice versa.
If fred is wise then fred is both not rich and happy and vice versa.
If lucy is both not funny and wise then someone is both not creative and not brave.
Everyone who is either not happy or creative is curious or not calm.
Paul is tall.
Mary is not strong.
Someone is not quiet.
Fred is either tall or not old.
Someone is both not curious and old.
Someone is both curious and not generous. | Paul is not strong. | neutral | (![X]:(brave(X)=>(~tall(X)&quiet(X))))&
(((~patient(john)<~>~quiet(john)))=>((kind(lucy)<~>~wise(lucy))))&
(![X]:((creative(X)|~humble(X))<=>(~kind(X)<~>~rich(X))))&
(![X]:((funny(X)<~>curious(X))<=>(calm(X)|~humble(X))))&
(![X]:((kind(X)|~happy(X))<=>(curious(X)<~>~humble(X))))&
(![X]:((~tall(X)|~old(X))<=>(~generous(X)<~>strong(X))))&
(![X]:((~patient(X)|~humble(X))<=>(~humble(X)<~>~curious(X))))&
(![X]:(~wise(X)=>~calm(X)))&
(![X]:((~rich(X)&patient(X))=>(kind(X)<~>~patient(X))))&
((?[X]:((~kind(X)<~>~happy(X))))=>(?[X]:(creative(X))))&
((?[X]:((~kind(X)|~tall(X))))<=>(calm(paul)))&
(((brave(lucy)&~strong(lucy)))<=>(?[X]:((~humble(X)<~>patient(X)))))&
(![X]:((~tall(X)<~>~humble(X))<=>(~quiet(X)<~>~humble(X))))&
((wise(fred))<=>((~rich(fred)&happy(fred))))&
(((~funny(lucy)&wise(lucy)))=>(?[X]:((~creative(X)&~brave(X)))))&
(![X]:((~happy(X)<~>creative(X))=>(curious(X)|~calm(X))))&
(tall(paul))&
(~strong(mary))&
(?[X]:(~quiet(X)))&
((tall(fred)<~>~old(fred)))&
(?[X]:((~curious(X)&old(X))))&
(?[X]:((curious(X)&~generous(X)))) | ~strong(paul) | [] | null | 0 |
If alice is brave then someone is tall or happy.
If fred is both generous and tall then fred is both not tall and strong.
Everyone who is either generous or not patient is tall and vice versa.
If someone is either calm or not tall then john is not brave and vice versa.
Everyone who is either not happy or not humble is either tall or curious and vice versa.
Everyone who is both not brave and not quiet is either not quiet or funny and vice versa.
Everyone who is both creative and curious is either not patient or not rich and vice versa.
Everyone who is both not brave and funny is both not happy and happy and vice versa.
If someone is both quiet and not old then someone is either kind or funny.
Everyone who is not generous is not quiet and vice versa.
Everyone who is not happy is either not old or generous.
Everyone who is not calm is calm.
If lucy is not calm then someone is not wise or tall and vice versa.
Everyone who is not funny is not quiet.
Everyone who is not patient is either old or not strong.
If someone is generous or happy then alice is generous.
Fred is both not creative and not generous.
John is either brave or not kind.
Someone is either not humble or not quiet.
Alice is either humble or not generous.
Mary is either not humble or not calm.
Someone is not old or not kind.
Someone is either strong or generous. | John is not funny. | contradiction | ((brave(alice))=>(?[X]:((tall(X)|happy(X)))))&
(((generous(fred)&tall(fred)))=>((~tall(fred)&strong(fred))))&
(![X]:((generous(X)<~>~patient(X))<=>tall(X)))&
((?[X]:((calm(X)<~>~tall(X))))<=>(~brave(john)))&
(![X]:((~happy(X)<~>~humble(X))<=>(tall(X)<~>curious(X))))&
(![X]:((~brave(X)&~quiet(X))<=>(~quiet(X)<~>funny(X))))&
(![X]:((creative(X)&curious(X))<=>(~patient(X)<~>~rich(X))))&
(![X]:((~brave(X)&funny(X))<=>(~happy(X)&happy(X))))&
((?[X]:((quiet(X)&~old(X))))=>(?[X]:((kind(X)<~>funny(X)))))&
(![X]:(~generous(X)<=>~quiet(X)))&
(![X]:(~happy(X)=>(~old(X)<~>generous(X))))&
(![X]:(~calm(X)=>calm(X)))&
((~calm(lucy))<=>(?[X]:((~wise(X)|tall(X)))))&
(![X]:(~funny(X)=>~quiet(X)))&
(![X]:(~patient(X)=>(old(X)<~>~strong(X))))&
((?[X]:((generous(X)|happy(X))))=>(generous(alice)))&
((~creative(fred)&~generous(fred)))&
((brave(john)<~>~kind(john)))&
(?[X]:((~humble(X)<~>~quiet(X))))&
((humble(alice)<~>~generous(alice)))&
((~humble(mary)<~>~calm(mary)))&
(?[X]:((~old(X)|~kind(X))))&
(?[X]:((strong(X)<~>generous(X)))) | ~funny(john) | [
"p3",
"p5",
"p11",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 5054610477213095890436479
% SZS output start Proof for 5054610477213095890436479
4. ? [X0] : (calm(X0) <~> ~tall(X0)) <=> ~brave(john) [input p3]
6. ! [X0] : ((~quiet(X0) & ~brave(X0)) <=> (~quiet(X0) <~> funny(X0))) [input p5]
12. ! [X0] : (~calm(X0) => calm(X0)) [input p11]
13. ~calm(lucy) <=> ? [X0] : (tall(X0) | ~wise(X0)) [input p12]
14. ! [X0] : (~funny(X0) => ~quiet(X0)) [input p13]
24. ~funny(john) [input hypothesis]
31. ! [X0] : (calm(X0) | calm(X0)) [ennf transformation 12]
32. ! [X0] : (~quiet(X0) | funny(X0)) [ennf transformation 14]
38. (? [X0] : ((tall(X0) | ~calm(X0)) & (~tall(X0) | calm(X0))) | brave(john)) & (~brave(john) | ! [X0] : ((calm(X0) | tall(X0)) & (~tall(X0) | ~calm(X0)))) [nnf transformation 4]
39. (? [X0] : ((tall(X0) | ~calm(X0)) & (~tall(X0) | calm(X0))) | brave(john)) & (~brave(john) | ! [X1] : ((calm(X1) | tall(X1)) & (~tall(X1) | ~calm(X1)))) [rectify 38]
40. ? [X0] : ((tall(X0) | ~calm(X0)) & (~tall(X0) | calm(X0))) => ((tall(sK1) | ~calm(sK1)) & (~tall(sK1) | calm(sK1))) [choice axiom]
41. (((tall(sK1) | ~calm(sK1)) & (~tall(sK1) | calm(sK1))) | brave(john)) & (~brave(john) | ! [X1] : ((calm(X1) | tall(X1)) & (~tall(X1) | ~calm(X1)))) [skolemisation 39,40]
43. ! [X0] : (((~quiet(X0) & ~brave(X0)) | ((~quiet(X0) | ~funny(X0)) & (funny(X0) | quiet(X0)))) & (((~funny(X0) | quiet(X0)) & (funny(X0) | ~quiet(X0))) | (quiet(X0) | brave(X0)))) [nnf transformation 6]
44. ! [X0] : (((~quiet(X0) & ~brave(X0)) | ((~quiet(X0) | ~funny(X0)) & (funny(X0) | quiet(X0)))) & (((~funny(X0) | quiet(X0)) & (funny(X0) | ~quiet(X0))) | quiet(X0) | brave(X0))) [flattening 43]
55. (~calm(lucy) | ! [X0] : (~tall(X0) & wise(X0))) & (? [X0] : (tall(X0) | ~wise(X0)) | calm(lucy)) [nnf transformation 13]
56. (~calm(lucy) | ! [X0] : (~tall(X0) & wise(X0))) & (? [X1] : (tall(X1) | ~wise(X1)) | calm(lucy)) [rectify 55]
57. ? [X1] : (tall(X1) | ~wise(X1)) => (tall(sK3) | ~wise(sK3)) [choice axiom]
58. (~calm(lucy) | ! [X0] : (~tall(X0) & wise(X0))) & ((tall(sK3) | ~wise(sK3)) | calm(lucy)) [skolemisation 56,57]
81. tall(sK1) | ~calm(sK1) | brave(john) [cnf transformation 41]
92. ~brave(X0) | funny(X0) | quiet(X0) [cnf transformation 44]
95. ~quiet(X0) | ~quiet(X0) | ~funny(X0) [cnf transformation 44]
112. calm(X0) | calm(X0) [cnf transformation 31]
115. ~calm(lucy) | ~tall(X0) [cnf transformation 58]
116. ~quiet(X0) | funny(X0) [cnf transformation 32]
134. ~funny(john) [cnf transformation 24]
135. calm(X0) [duplicate literal removal 112]
137. ~funny(X0) | ~quiet(X0) [duplicate literal removal 95]
167. 7 <=> brave(john) [avatar definition]
169. brave(john) <- (7) [avatar component clause 167]
171. 8 <=> calm(sK1) [avatar definition]
173. ~calm(sK1) <- (~8) [avatar component clause 171]
175. 9 <=> tall(sK1) [avatar definition]
177. tall(sK1) <- (9) [avatar component clause 175]
178. 7 | ~8 | 9 [avatar split clause 81,175,171,167]
202. ~tall(X0) [subsumption resolution 115,135]
204. ~quiet(X0) [subsumption resolution 116,137]
251. $false <- (~8) [subsumption resolution 173,135]
252. 8 [avatar contradiction clause 251]
253. $false <- (9) [subsumption resolution 177,202]
254. ~9 [avatar contradiction clause 253]
259. funny(john) | quiet(john) <- (7) [resolution 92,169]
260. quiet(john) <- (7) [subsumption resolution 259,134]
261. $false <- (7) [subsumption resolution 260,204]
262. ~7 [avatar contradiction clause 261]
263. $false [avatar sat refutation 178,252,254,262]
% SZS output end Proof for 5054610477213095890436479
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not quiet and not generous then someone is either not humble or not patient and vice versa. Everyone who is old or not old is both not calm and rich and vice versa. If someone is not wise then lucy is both calm and patient and vice versa. If mary is both not brave and rich then someone is either not patient or kind and vice versa. Everyone who is both quiet and not rich is either not creative or tall and vice versa. If someone is quiet or not kind then susan is not funny or not humble and vice versa. If someone is both not funny and quiet then someone is either not calm or not generous. Everyone who is curious or not creative is old and vice versa. Everyone who is both not generous and rich is both old and calm. If someone is either not wise or kind then paul is either wise or calm. Everyone who is not generous is not old and vice versa. If someone is both not wise and not rich then susan is either brave or tall. If someone is either not kind or not old then someone is not kind and vice versa. If someone is humble then lucy is both old and not generous. Everyone who is brave is happy. Everyone who is quiet is both not curious and not old and vice versa. John is both generous and rich. Someone is not wise or wise. Mary is either strong or quiet. Someone is funny or not quiet. Susan is either not generous or kind. John is either brave or kind. | Mary is not humble. | entailment | ((?[X]:((~quiet(X)&~generous(X))))<=>(?[X]:((~humble(X)<~>~patient(X)))))&
(![X]:((old(X)|~old(X))<=>(~calm(X)&rich(X))))&
((?[X]:(~wise(X)))<=>((calm(lucy)&patient(lucy))))&
(((~brave(mary)&rich(mary)))<=>(?[X]:((~patient(X)<~>kind(X)))))&
(![X]:((quiet(X)&~rich(X))<=>(~creative(X)<~>tall(X))))&
((?[X]:((quiet(X)|~kind(X))))<=>((~funny(susan)|~humble(susan))))&
((?[X]:((~funny(X)&quiet(X))))=>(?[X]:((~calm(X)<~>~generous(X)))))&
(![X]:((curious(X)|~creative(X))<=>old(X)))&
(![X]:((~generous(X)&rich(X))=>(old(X)&calm(X))))&
((?[X]:((~wise(X)<~>kind(X))))=>((wise(paul)<~>calm(paul))))&
(![X]:(~generous(X)<=>~old(X)))&
((?[X]:((~wise(X)&~rich(X))))=>((brave(susan)<~>tall(susan))))&
((?[X]:((~kind(X)<~>~old(X))))<=>(?[X]:(~kind(X))))&
((?[X]:(humble(X)))=>((old(lucy)&~generous(lucy))))&
(![X]:(brave(X)=>happy(X)))&
(![X]:(quiet(X)<=>(~curious(X)&~old(X))))&
((generous(john)&rich(john)))&
(?[X]:((~wise(X)|wise(X))))&
((strong(mary)<~>quiet(mary)))&
(?[X]:((funny(X)|~quiet(X))))&
((~generous(susan)<~>kind(susan)))&
((brave(john)<~>kind(john))) | ~humble(mary) | [
"p1",
"p8",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 2121204985622963044559365
% SZS output start Proof for 2121204985622963044559365
2. ! [X0] : ((~old(X0) | old(X0)) <=> (rich(X0) & ~calm(X0))) [input p1]
9. ! [X0] : ((rich(X0) & ~generous(X0)) => (calm(X0) & old(X0))) [input p8]
14. ? [X0] : humble(X0) => (~generous(lucy) & old(lucy)) [input p13]
23. humble(mary) [input hypothesis]
29. ! [X0] : ((calm(X0) & old(X0)) | (~rich(X0) | generous(X0))) [ennf transformation 9]
30. ! [X0] : ((calm(X0) & old(X0)) | ~rich(X0) | generous(X0)) [flattening 29]
33. (~generous(lucy) & old(lucy)) | ! [X0] : ~humble(X0) [ennf transformation 14]
39. ! [X0] : (((~old(X0) | old(X0)) | (~rich(X0) | calm(X0))) & ((rich(X0) & ~calm(X0)) | (old(X0) & ~old(X0)))) [nnf transformation 2]
40. ! [X0] : ((~old(X0) | old(X0) | ~rich(X0) | calm(X0)) & ((rich(X0) & ~calm(X0)) | (old(X0) & ~old(X0)))) [flattening 39]
87. ~calm(X0) | ~old(X0) [cnf transformation 40]
88. ~calm(X0) | old(X0) [cnf transformation 40]
89. rich(X0) | ~old(X0) [cnf transformation 40]
90. rich(X0) | old(X0) [cnf transformation 40]
117. calm(X0) | ~rich(X0) | generous(X0) [cnf transformation 30]
131. ~generous(lucy) | ~humble(X0) [cnf transformation 33]
145. humble(mary) [cnf transformation 23]
177. rich(X0) [subsumption resolution 89,90]
178. ~calm(X0) [subsumption resolution 87,88]
250. ~rich(X0) | generous(X0) [subsumption resolution 117,178]
251. generous(X0) [subsumption resolution 250,177]
279. ~humble(X0) [subsumption resolution 131,251]
312. $false [subsumption resolution 145,279]
% SZS output end Proof for 2121204985622963044559365
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is calm or quiet is both not patient and creative and vice versa.
Everyone who is not calm is not creative or not happy.
Everyone who is not happy or not curious is both calm and not rich.
Everyone who is both not curious and not old is either not calm or not funny and vice versa.
Everyone who is either tall or not tall is either not brave or not quiet and vice versa.
If someone is old or quiet then fred is rich or curious and vice versa.
Everyone who is curious is either rich or humble and vice versa.
Everyone who is both brave and tall is not tall or not curious.
Everyone who is humble is either old or not patient and vice versa.
Everyone who is not wise or not funny is either not humble or not brave and vice versa.
If john is either not humble or not generous then alice is tall.
If paul is both not generous and not funny then john is either creative or not brave.
Everyone who is either not wise or curious is either rich or not generous and vice versa.
Everyone who is either curious or not humble is not rich.
Alice is not quiet or not generous.
Susan is not patient.
Someone is rich or wise.
Alice is curious or not quiet.
John is either not quiet or not brave.
Someone is wise. | Susan is old. | neutral | (![X]:((calm(X)|quiet(X))<=>(~patient(X)&creative(X))))&
(![X]:(~calm(X)=>(~creative(X)|~happy(X))))&
(![X]:((~happy(X)|~curious(X))=>(calm(X)&~rich(X))))&
(![X]:((~curious(X)&~old(X))<=>(~calm(X)<~>~funny(X))))&
(![X]:((tall(X)<~>~tall(X))<=>(~brave(X)<~>~quiet(X))))&
((?[X]:((old(X)|quiet(X))))<=>((rich(fred)|curious(fred))))&
(![X]:(curious(X)<=>(rich(X)<~>humble(X))))&
(![X]:((brave(X)&tall(X))=>(~tall(X)|~curious(X))))&
(![X]:(humble(X)<=>(old(X)<~>~patient(X))))&
(![X]:((~wise(X)|~funny(X))<=>(~humble(X)<~>~brave(X))))&
(((~humble(john)<~>~generous(john)))=>(tall(alice)))&
(((~generous(paul)&~funny(paul)))=>((creative(john)<~>~brave(john))))&
(![X]:((~wise(X)<~>curious(X))<=>(rich(X)<~>~generous(X))))&
(![X]:((curious(X)<~>~humble(X))=>~rich(X)))&
((~quiet(alice)|~generous(alice)))&
(~patient(susan))&
(?[X]:((rich(X)|wise(X))))&
((curious(alice)|~quiet(alice)))&
((~quiet(john)<~>~brave(john)))&
(?[X]:(wise(X))) | old(susan) | [] | null | 0 |
If fred is rich or tall then someone is either humble or kind.
If someone is happy then alice is both not wise and not funny and vice versa.
If paul is not happy or not patient then john is not wise.
If susan is not kind or not tall then mary is brave and vice versa.
Everyone who is either not old or happy is not kind and vice versa.
If someone is either not wise or generous then someone is not patient.
Everyone who is tall is not rich and vice versa.
Everyone who is humble is not wise or not creative and vice versa.
Everyone who is both not wise and strong is either tall or happy and vice versa.
Everyone who is either not tall or rich is not brave or not creative.
Everyone who is either not old or not patient is both old and patient and vice versa.
Everyone who is happy is not patient and vice versa.
If paul is either generous or not happy then alice is both not patient and not brave.
If john is either not happy or curious then someone is quiet.
If someone is both calm and not creative then someone is both not patient and brave.
If someone is not patient then someone is quiet and vice versa.
John is not tall.
Fred is either not curious or kind.
Someone is both kind and not creative.
Someone is strong.
Lucy is either kind or quiet.
Someone is quiet.
Someone is either not calm or not old.
Someone is either wise or tall. | John is not humble. | contradiction | (((rich(fred)|tall(fred)))=>(?[X]:((humble(X)<~>kind(X)))))&
((?[X]:(happy(X)))<=>((~wise(alice)&~funny(alice))))&
(((~happy(paul)|~patient(paul)))=>(~wise(john)))&
(((~kind(susan)|~tall(susan)))<=>(brave(mary)))&
(![X]:((~old(X)<~>happy(X))<=>~kind(X)))&
((?[X]:((~wise(X)<~>generous(X))))=>(?[X]:(~patient(X))))&
(![X]:(tall(X)<=>~rich(X)))&
(![X]:(humble(X)<=>(~wise(X)|~creative(X))))&
(![X]:((~wise(X)&strong(X))<=>(tall(X)<~>happy(X))))&
(![X]:((~tall(X)<~>rich(X))=>(~brave(X)|~creative(X))))&
(![X]:((~old(X)<~>~patient(X))<=>(old(X)&patient(X))))&
(![X]:(happy(X)<=>~patient(X)))&
(((generous(paul)<~>~happy(paul)))=>((~patient(alice)&~brave(alice))))&
(((~happy(john)<~>curious(john)))=>(?[X]:(quiet(X))))&
((?[X]:((calm(X)&~creative(X))))=>(?[X]:((~patient(X)&brave(X)))))&
((?[X]:(~patient(X)))<=>(?[X]:(quiet(X))))&
(~tall(john))&
((~curious(fred)<~>kind(fred)))&
(?[X]:((kind(X)&~creative(X))))&
(?[X]:(strong(X)))&
((kind(lucy)<~>quiet(lucy)))&
(?[X]:(quiet(X)))&
(?[X]:((~calm(X)<~>~old(X))))&
(?[X]:((wise(X)<~>tall(X)))) | ~humble(john) | [
"p2",
"p7",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 504564909218920873393833
% SZS output start Proof for 504564909218920873393833
3. (~patient(paul) | ~happy(paul)) => ~wise(john) [input p2]
8. ! [X0] : (humble(X0) <=> (~creative(X0) | ~wise(X0))) [input p7]
11. ! [X0] : ((~old(X0) <~> ~patient(X0)) <=> (patient(X0) & old(X0))) [input p10]
25. ~humble(john) [input hypothesis]
30. ~wise(john) | (patient(paul) & happy(paul)) [ennf transformation 3]
53. ! [X0] : ((humble(X0) | (creative(X0) & wise(X0))) & ((~creative(X0) | ~wise(X0)) | ~humble(X0))) [nnf transformation 8]
54. ! [X0] : ((humble(X0) | (creative(X0) & wise(X0))) & (~creative(X0) | ~wise(X0) | ~humble(X0))) [flattening 53]
58. ! [X0] : ((((patient(X0) | old(X0)) & (~patient(X0) | ~old(X0))) | (~patient(X0) | ~old(X0))) & ((patient(X0) & old(X0)) | ((~old(X0) | patient(X0)) & (~patient(X0) | old(X0))))) [nnf transformation 11]
59. ! [X0] : ((((patient(X0) | old(X0)) & (~patient(X0) | ~old(X0))) | ~patient(X0) | ~old(X0)) & ((patient(X0) & old(X0)) | ((~old(X0) | patient(X0)) & (~patient(X0) | old(X0))))) [flattening 58]
95. ~wise(john) | patient(paul) [cnf transformation 30]
108. wise(X0) | humble(X0) [cnf transformation 54]
118. old(X0) | ~patient(X0) | old(X0) [cnf transformation 59]
121. patient(X0) | ~old(X0) | patient(X0) [cnf transformation 59]
122. ~patient(X0) | ~old(X0) | ~patient(X0) | ~old(X0) [cnf transformation 59]
149. ~humble(john) [cnf transformation 25]
150. old(X0) | ~patient(X0) [duplicate literal removal 118]
151. patient(X0) | ~old(X0) [duplicate literal removal 121]
152. ~patient(X0) | ~old(X0) [duplicate literal removal 122]
192. 9 <=> patient(paul) [avatar definition]
194. patient(paul) <- (9) [avatar component clause 192]
196. 10 <=> wise(john) [avatar definition]
198. ~wise(john) <- (~10) [avatar component clause 196]
199. 9 | ~10 [avatar split clause 95,196,192]
232. ~old(X0) [subsumption resolution 151,152]
233. ~patient(X0) [subsumption resolution 150,232]
304. humble(john) <- (~10) [resolution 108,198]
305. $false <- (~10) [subsumption resolution 304,149]
306. 10 [avatar contradiction clause 305]
307. $false <- (9) [subsumption resolution 194,233]
308. ~9 [avatar contradiction clause 307]
309. $false [avatar sat refutation 199,306,308]
% SZS output end Proof for 504564909218920873393833
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet or not quiet is old and vice versa.
If paul is both brave and funny then fred is either not creative or kind and vice versa.
If someone is either generous or tall then fred is either tall or humble and vice versa.
Everyone who is both calm and not generous is not funny or not generous and vice versa.
If someone is not curious or not funny then mary is either old or not calm and vice versa.
Everyone who is not funny is not quiet or kind.
If paul is both happy and not creative then someone is not old.
If someone is either old or not patient then alice is either not happy or not generous.
Everyone who is tall is not quiet and vice versa.
Everyone who is wise or not old is wise and vice versa.
If someone is happy or not kind then lucy is both brave and kind and vice versa.
Everyone who is humble or tall is tall and vice versa.
Everyone who is either not happy or calm is not quiet and vice versa.
Everyone who is either not wise or curious is both curious and not strong.
If someone is wise or old then someone is not happy or generous and vice versa.
Everyone who is either funny or humble is either not happy or not strong.
John is not kind.
Someone is rich or not generous.
Susan is both strong and brave.
Lucy is generous or not humble.
Paul is not tall or not brave.
Someone is not old or not strong.
Someone is calm or not strong. | Alice is tall. | neutral | (![X]:((quiet(X)|~quiet(X))<=>old(X)))&
(((brave(paul)&funny(paul)))<=>((~creative(fred)<~>kind(fred))))&
((?[X]:((generous(X)<~>tall(X))))<=>((tall(fred)<~>humble(fred))))&
(![X]:((calm(X)&~generous(X))<=>(~funny(X)|~generous(X))))&
((?[X]:((~curious(X)|~funny(X))))<=>((old(mary)<~>~calm(mary))))&
(![X]:(~funny(X)=>(~quiet(X)|kind(X))))&
(((happy(paul)&~creative(paul)))=>(?[X]:(~old(X))))&
((?[X]:((old(X)<~>~patient(X))))=>((~happy(alice)<~>~generous(alice))))&
(![X]:(tall(X)<=>~quiet(X)))&
(![X]:((wise(X)|~old(X))<=>wise(X)))&
((?[X]:((happy(X)|~kind(X))))<=>((brave(lucy)&kind(lucy))))&
(![X]:((humble(X)|tall(X))<=>tall(X)))&
(![X]:((~happy(X)<~>calm(X))<=>~quiet(X)))&
(![X]:((~wise(X)<~>curious(X))=>(curious(X)&~strong(X))))&
((?[X]:((wise(X)|old(X))))<=>(?[X]:((~happy(X)|generous(X)))))&
(![X]:((funny(X)<~>humble(X))=>(~happy(X)<~>~strong(X))))&
(~kind(john))&
(?[X]:((rich(X)|~generous(X))))&
((strong(susan)&brave(susan)))&
((generous(lucy)|~humble(lucy)))&
((~tall(paul)|~brave(paul)))&
(?[X]:((~old(X)|~strong(X))))&
(?[X]:((calm(X)|~strong(X)))) | tall(alice) | [] | null | 0 |
Everyone who is either happy or not tall is either not wise or not patient and vice versa.
If someone is both strong and not creative then someone is either not wise or not kind and vice versa.
If someone is both not creative and not generous then someone is kind or not funny and vice versa.
Everyone who is calm or funny is both old and funny.
If paul is not happy then someone is not old or not strong and vice versa.
Everyone who is not old is not humble and vice versa.
Everyone who is both not strong and strong is either not patient or generous.
If lucy is tall then someone is not happy.
If john is curious or strong then someone is either not kind or not humble and vice versa.
Everyone who is humble is both not wise and not brave.
If someone is either not humble or patient then lucy is either not strong or wise.
Everyone who is either not tall or not rich is either generous or not brave and vice versa.
Everyone who is not patient or not brave is not kind or tall and vice versa.
Everyone who is creative or not generous is either not funny or not calm.
If john is either not funny or generous then someone is either not creative or not wise and vice versa.
If lucy is either not calm or not rich then someone is both not humble and creative.
Someone is quiet.
Susan is not kind or not funny.
Someone is not generous.
Lucy is both curious and not strong.
Someone is either rich or not tall.
Susan is not quiet or happy.
John is not rich or generous.
Someone is not wise or funny. | Lucy is brave. | neutral | (![X]:((happy(X)<~>~tall(X))<=>(~wise(X)<~>~patient(X))))&
((?[X]:((strong(X)&~creative(X))))<=>(?[X]:((~wise(X)<~>~kind(X)))))&
((?[X]:((~creative(X)&~generous(X))))<=>(?[X]:((kind(X)|~funny(X)))))&
(![X]:((calm(X)|funny(X))=>(old(X)&funny(X))))&
((~happy(paul))<=>(?[X]:((~old(X)|~strong(X)))))&
(![X]:(~old(X)<=>~humble(X)))&
(![X]:((~strong(X)&strong(X))=>(~patient(X)<~>generous(X))))&
((tall(lucy))=>(?[X]:(~happy(X))))&
(((curious(john)|strong(john)))<=>(?[X]:((~kind(X)<~>~humble(X)))))&
(![X]:(humble(X)=>(~wise(X)&~brave(X))))&
((?[X]:((~humble(X)<~>patient(X))))=>((~strong(lucy)<~>wise(lucy))))&
(![X]:((~tall(X)<~>~rich(X))<=>(generous(X)<~>~brave(X))))&
(![X]:((~patient(X)|~brave(X))<=>(~kind(X)|tall(X))))&
(![X]:((creative(X)|~generous(X))=>(~funny(X)<~>~calm(X))))&
(((~funny(john)<~>generous(john)))<=>(?[X]:((~creative(X)<~>~wise(X)))))&
(((~calm(lucy)<~>~rich(lucy)))=>(?[X]:((~humble(X)&creative(X)))))&
(?[X]:(quiet(X)))&
((~kind(susan)|~funny(susan)))&
(?[X]:(~generous(X)))&
((curious(lucy)&~strong(lucy)))&
(?[X]:((rich(X)<~>~tall(X))))&
((~quiet(susan)|happy(susan)))&
((~rich(john)|generous(john)))&
(?[X]:((~wise(X)|funny(X)))) | brave(lucy) | [] | null | 0 |
If someone is either curious or strong then someone is both not old and not curious and vice versa.
Everyone who is not quiet is curious and vice versa.
If someone is either rich or brave then alice is either funny or wise and vice versa.
Everyone who is not strong is both wise and not kind.
Everyone who is either not quiet or not creative is either quiet or humble and vice versa.
If someone is not wise then someone is either not brave or creative.
Everyone who is rich is either wise or happy and vice versa.
Everyone who is not rich is not old and vice versa.
If someone is not generous then someone is either not generous or not strong and vice versa.
Everyone who is not wise is not generous and vice versa.
If lucy is both funny and not funny then alice is not kind or not tall.
If someone is both not quiet and generous then someone is both generous and not humble.
Everyone who is either funny or not humble is funny or humble.
Everyone who is happy or not curious is tall and vice versa.
If paul is both generous and wise then someone is not humble.
Everyone who is not generous or tall is both not funny and not strong.
John is curious or creative.
John is not patient or patient.
Lucy is wise or not kind.
Someone is not funny or old.
Mary is both funny and not creative.
Someone is quiet or calm.
Mary is both brave and generous. | Mary is not generous. | contradiction | ((?[X]:((curious(X)<~>strong(X))))<=>(?[X]:((~old(X)&~curious(X)))))&
(![X]:(~quiet(X)<=>curious(X)))&
((?[X]:((rich(X)<~>brave(X))))<=>((funny(alice)<~>wise(alice))))&
(![X]:(~strong(X)=>(wise(X)&~kind(X))))&
(![X]:((~quiet(X)<~>~creative(X))<=>(quiet(X)<~>humble(X))))&
((?[X]:(~wise(X)))=>(?[X]:((~brave(X)<~>creative(X)))))&
(![X]:(rich(X)<=>(wise(X)<~>happy(X))))&
(![X]:(~rich(X)<=>~old(X)))&
((?[X]:(~generous(X)))<=>(?[X]:((~generous(X)<~>~strong(X)))))&
(![X]:(~wise(X)<=>~generous(X)))&
(((funny(lucy)&~funny(lucy)))=>((~kind(alice)|~tall(alice))))&
((?[X]:((~quiet(X)&generous(X))))=>(?[X]:((generous(X)&~humble(X)))))&
(![X]:((funny(X)<~>~humble(X))=>(funny(X)|humble(X))))&
(![X]:((happy(X)|~curious(X))<=>tall(X)))&
(((generous(paul)&wise(paul)))=>(?[X]:(~humble(X))))&
(![X]:((~generous(X)|tall(X))=>(~funny(X)&~strong(X))))&
((curious(john)|creative(john)))&
((~patient(john)|patient(john)))&
((wise(lucy)|~kind(lucy)))&
(?[X]:((~funny(X)|old(X))))&
((funny(mary)&~creative(mary)))&
(?[X]:((quiet(X)|calm(X))))&
((brave(mary)&generous(mary))) | ~generous(mary) | [
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 8768753817331288311312106
% SZS output start Proof for 8768753817331288311312106
23. generous(mary) & brave(mary) [input p22]
24. ~generous(mary) [input hypothesis]
130. generous(mary) [cnf transformation 23]
131. ~generous(mary) [cnf transformation 24]
280. $false [subsumption resolution 131,130]
% SZS output end Proof for 8768753817331288311312106
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise and not creative is humble or generous and vice versa.
If someone is both not humble and not curious then paul is both not quiet and not brave.
Everyone who is either not wise or not old is strong and vice versa.
Everyone who is not curious or not old is wise and vice versa.
Everyone who is quiet is strong or not humble and vice versa.
If susan is either not brave or not tall then mary is not creative.
If someone is not happy or not funny then alice is not humble and vice versa.
If mary is both wise and curious then someone is brave.
If someone is brave then someone is not calm.
Everyone who is both not curious and not funny is not rich and vice versa.
Everyone who is either calm or humble is either not quiet or not brave.
Everyone who is both wise and humble is either wise or not brave and vice versa.
Everyone who is generous or strong is brave and vice versa.
Everyone who is old or rich is not generous or not curious and vice versa.
Everyone who is either kind or curious is both not old and not rich and vice versa.
Everyone who is patient is both creative and humble and vice versa.
Someone is both not funny and not creative.
Someone is both old and strong.
Mary is kind or not old.
Alice is wise or not calm.
Someone is both not kind and not calm.
Fred is not funny. | Susan is not brave. | contradiction | (![X]:((wise(X)&~creative(X))<=>(humble(X)|generous(X))))&
((?[X]:((~humble(X)&~curious(X))))=>((~quiet(paul)&~brave(paul))))&
(![X]:((~wise(X)<~>~old(X))<=>strong(X)))&
(![X]:((~curious(X)|~old(X))<=>wise(X)))&
(![X]:(quiet(X)<=>(strong(X)|~humble(X))))&
(((~brave(susan)<~>~tall(susan)))=>(~creative(mary)))&
((?[X]:((~happy(X)|~funny(X))))<=>(~humble(alice)))&
(((wise(mary)&curious(mary)))=>(?[X]:(brave(X))))&
((?[X]:(brave(X)))=>(?[X]:(~calm(X))))&
(![X]:((~curious(X)&~funny(X))<=>~rich(X)))&
(![X]:((calm(X)<~>humble(X))=>(~quiet(X)<~>~brave(X))))&
(![X]:((wise(X)&humble(X))<=>(wise(X)<~>~brave(X))))&
(![X]:((generous(X)|strong(X))<=>brave(X)))&
(![X]:((old(X)|rich(X))<=>(~generous(X)|~curious(X))))&
(![X]:((kind(X)<~>curious(X))<=>(~old(X)&~rich(X))))&
(![X]:(patient(X)<=>(creative(X)&humble(X))))&
(?[X]:((~funny(X)&~creative(X))))&
(?[X]:((old(X)&strong(X))))&
((kind(mary)|~old(mary)))&
((wise(alice)|~calm(alice)))&
(?[X]:((~kind(X)&~calm(X))))&
(~funny(fred)) | ~brave(susan) | [
"p0",
"p1",
"p2",
"p3",
"p4",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 8643406022734059462423227
% SZS output start Proof for 8643406022734059462423227
1. ! [X0] : ((~creative(X0) & wise(X0)) <=> (generous(X0) | humble(X0))) [input p0]
2. ? [X0] : (~curious(X0) & ~humble(X0)) => (~brave(paul) & ~quiet(paul)) [input p1]
3. ! [X0] : ((~wise(X0) <~> ~old(X0)) <=> strong(X0)) [input p2]
4. ! [X0] : ((~old(X0) | ~curious(X0)) <=> wise(X0)) [input p3]
5. ! [X0] : (quiet(X0) <=> (~humble(X0) | strong(X0))) [input p4]
12. ! [X0] : ((humble(X0) & wise(X0)) <=> (wise(X0) <~> ~brave(X0))) [input p11]
13. ! [X0] : ((strong(X0) | generous(X0)) <=> brave(X0)) [input p12]
23. ~brave(susan) [input hypothesis]
25. (~brave(paul) & ~quiet(paul)) | ! [X0] : (curious(X0) | humble(X0)) [ennf transformation 2]
31. ! [X0] : (((~creative(X0) & wise(X0)) | (~generous(X0) & ~humble(X0))) & ((generous(X0) | humble(X0)) | (creative(X0) | ~wise(X0)))) [nnf transformation 1]
32. ! [X0] : (((~creative(X0) & wise(X0)) | (~generous(X0) & ~humble(X0))) & (generous(X0) | humble(X0) | creative(X0) | ~wise(X0))) [flattening 31]
33. ! [X0] : ((((old(X0) | wise(X0)) & (~old(X0) | ~wise(X0))) | ~strong(X0)) & (strong(X0) | ((~wise(X0) | old(X0)) & (~old(X0) | wise(X0))))) [nnf transformation 3]
34. ! [X0] : (((~old(X0) | ~curious(X0)) | ~wise(X0)) & (wise(X0) | (old(X0) & curious(X0)))) [nnf transformation 4]
35. ! [X0] : ((~old(X0) | ~curious(X0) | ~wise(X0)) & (wise(X0) | (old(X0) & curious(X0)))) [flattening 34]
36. ! [X0] : ((quiet(X0) | (humble(X0) & ~strong(X0))) & ((~humble(X0) | strong(X0)) | ~quiet(X0))) [nnf transformation 5]
37. ! [X0] : ((quiet(X0) | (humble(X0) & ~strong(X0))) & (~humble(X0) | strong(X0) | ~quiet(X0))) [flattening 36]
51. ! [X0] : (((humble(X0) & wise(X0)) | ((wise(X0) | brave(X0)) & (~brave(X0) | ~wise(X0)))) & (((brave(X0) | ~wise(X0)) & (~brave(X0) | wise(X0))) | (~humble(X0) | ~wise(X0)))) [nnf transformation 12]
52. ! [X0] : (((humble(X0) & wise(X0)) | ((wise(X0) | brave(X0)) & (~brave(X0) | ~wise(X0)))) & (((brave(X0) | ~wise(X0)) & (~brave(X0) | wise(X0))) | ~humble(X0) | ~wise(X0))) [flattening 51]
53. ! [X0] : (((strong(X0) | generous(X0)) | ~brave(X0)) & (brave(X0) | (~strong(X0) & ~generous(X0)))) [nnf transformation 13]
54. ! [X0] : ((strong(X0) | generous(X0) | ~brave(X0)) & (brave(X0) | (~strong(X0) & ~generous(X0)))) [flattening 53]
66. ~humble(X0) | wise(X0) [cnf transformation 32]
70. ~quiet(paul) | curious(X0) | humble(X0) [cnf transformation 25]
71. ~brave(paul) | curious(X0) | humble(X0) [cnf transformation 25]
73. ~wise(X0) | strong(X0) | old(X0) [cnf transformation 33]
78. ~old(X0) | ~curious(X0) | ~wise(X0) [cnf transformation 35]
81. quiet(X0) | humble(X0) [cnf transformation 37]
97. brave(X0) | ~wise(X0) | ~humble(X0) | ~wise(X0) [cnf transformation 52]
101. humble(X0) | wise(X0) | brave(X0) [cnf transformation 52]
103. ~strong(X0) | brave(X0) [cnf transformation 54]
124. ~brave(susan) [cnf transformation 23]
125. brave(X0) | ~wise(X0) | ~humble(X0) [duplicate literal removal 97]
128. 1 <=> ! [X0] : (curious(X0) | humble(X0)) [avatar definition]
129. curious(X0) | humble(X0) <- (1) [avatar component clause 128]
131. 2 <=> brave(paul) [avatar definition]
133. ~brave(paul) <- (~2) [avatar component clause 131]
134. 1 | ~2 [avatar split clause 71,131,128]
136. 3 <=> quiet(paul) [avatar definition]
138. ~quiet(paul) <- (~3) [avatar component clause 136]
139. 1 | ~3 [avatar split clause 70,136,128]
145. 5 <=> brave(susan) [avatar definition]
147. ~brave(susan) <- (~5) [avatar component clause 145]
198. brave(X0) | wise(X0) [subsumption resolution 101,66]
199. ~humble(X0) | brave(X0) [subsumption resolution 125,66]
221. ~5 [avatar split clause 124,145]
226. humble(paul) <- (~3) [resolution 81,138]
232. wise(susan) <- (~5) [resolution 198,147]
233. brave(paul) <- (~3) [resolution 199,226]
234. $false <- (~2, ~3) [subsumption resolution 233,133]
235. 2 | 3 [avatar contradiction clause 234]
249. strong(susan) | old(susan) <- (~5) [resolution 73,232]
253. 21 <=> old(susan) [avatar definition]
255. old(susan) <- (21) [avatar component clause 253]
257. 22 <=> strong(susan) [avatar definition]
259. strong(susan) <- (22) [avatar component clause 257]
260. 21 | 22 | 5 [avatar split clause 249,145,257,253]
280. ~curious(susan) | ~wise(susan) <- (21) [resolution 78,255]
281. ~curious(susan) <- (~5, 21) [subsumption resolution 280,232]
307. humble(susan) <- (1, ~5, 21) [resolution 281,129]
613. brave(susan) <- (1, ~5, 21) [resolution 307,199]
616. $false <- (1, ~5, 21) [subsumption resolution 613,147]
617. ~1 | 5 | ~21 [avatar contradiction clause 616]
631. brave(susan) <- (22) [resolution 259,103]
633. $false <- (~5, 22) [subsumption resolution 631,147]
634. 5 | ~22 [avatar contradiction clause 633]
635. $false [avatar sat refutation 134,139,221,235,260,617,634]
% SZS output end Proof for 8643406022734059462423227
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both wise and funny is not tall and vice versa.
If john is both not humble and not funny then someone is both not wise and not brave and vice versa.
Everyone who is not brave or not curious is generous and vice versa.
If someone is creative then mary is both generous and not wise and vice versa.
Everyone who is both not kind and not funny is not rich or kind and vice versa.
Everyone who is not creative is either not humble or not patient.
If susan is either not patient or not brave then john is both not tall and not happy.
Everyone who is funny or calm is happy or creative.
Everyone who is both old and not strong is either strong or wise.
If alice is tall then fred is not quiet and vice versa.
If someone is either not funny or not creative then someone is calm or not strong and vice versa.
Everyone who is either old or tall is both brave and creative and vice versa.
Everyone who is both not funny and not calm is not kind or funny and vice versa.
Everyone who is either not rich or not curious is either not generous or not strong and vice versa.
If someone is either brave or patient then someone is either strong or humble and vice versa.
If paul is both funny and not rich then someone is not quiet or rich.
Someone is both not humble and generous.
Alice is not wise.
Someone is not quiet.
Someone is patient.
Someone is not wise or wise.
Someone is both brave and not humble.
Someone is either tall or happy. | John is not tall. | contradiction | (![X]:((wise(X)&funny(X))<=>~tall(X)))&
(((~humble(john)&~funny(john)))<=>(?[X]:((~wise(X)&~brave(X)))))&
(![X]:((~brave(X)|~curious(X))<=>generous(X)))&
((?[X]:(creative(X)))<=>((generous(mary)&~wise(mary))))&
(![X]:((~kind(X)&~funny(X))<=>(~rich(X)|kind(X))))&
(![X]:(~creative(X)=>(~humble(X)<~>~patient(X))))&
(((~patient(susan)<~>~brave(susan)))=>((~tall(john)&~happy(john))))&
(![X]:((funny(X)|calm(X))=>(happy(X)|creative(X))))&
(![X]:((old(X)&~strong(X))=>(strong(X)<~>wise(X))))&
((tall(alice))<=>(~quiet(fred)))&
((?[X]:((~funny(X)<~>~creative(X))))<=>(?[X]:((calm(X)|~strong(X)))))&
(![X]:((old(X)<~>tall(X))<=>(brave(X)&creative(X))))&
(![X]:((~funny(X)&~calm(X))<=>(~kind(X)|funny(X))))&
(![X]:((~rich(X)<~>~curious(X))<=>(~generous(X)<~>~strong(X))))&
((?[X]:((brave(X)<~>patient(X))))<=>(?[X]:((strong(X)<~>humble(X)))))&
(((funny(paul)&~rich(paul)))=>(?[X]:((~quiet(X)|rich(X)))))&
(?[X]:((~humble(X)&generous(X))))&
(~wise(alice))&
(?[X]:(~quiet(X)))&
(?[X]:(patient(X)))&
(?[X]:((~wise(X)|wise(X))))&
(?[X]:((brave(X)&~humble(X))))&
(?[X]:((tall(X)<~>happy(X)))) | ~tall(john) | [
"p0",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 2437027179126635709639855
% SZS output start Proof for 2437027179126635709639855
1. ! [X0] : ((funny(X0) & wise(X0)) <=> ~tall(X0)) [input p0]
13. ! [X0] : ((~calm(X0) & ~funny(X0)) <=> (funny(X0) | ~kind(X0))) [input p12]
24. ~tall(john) [input hypothesis]
35. ! [X0] : (((funny(X0) & wise(X0)) | tall(X0)) & (~tall(X0) | (~funny(X0) | ~wise(X0)))) [nnf transformation 1]
36. ! [X0] : (((funny(X0) & wise(X0)) | tall(X0)) & (~tall(X0) | ~funny(X0) | ~wise(X0))) [flattening 35]
62. ! [X0] : (((~calm(X0) & ~funny(X0)) | (~funny(X0) & kind(X0))) & ((funny(X0) | ~kind(X0)) | (calm(X0) | funny(X0)))) [nnf transformation 13]
63. ! [X0] : (((~calm(X0) & ~funny(X0)) | (~funny(X0) & kind(X0))) & (funny(X0) | ~kind(X0) | calm(X0) | funny(X0))) [flattening 62]
87. tall(X0) | funny(X0) [cnf transformation 36]
129. ~funny(X0) | ~funny(X0) [cnf transformation 63]
159. ~tall(john) [cnf transformation 24]
161. ~funny(X0) [duplicate literal removal 129]
222. 13 <=> tall(john) [avatar definition]
224. ~tall(john) <- (~13) [avatar component clause 222]
323. ~13 [avatar split clause 159,222]
332. funny(john) <- (~13) [resolution 87,224]
333. $false <- (~13) [subsumption resolution 332,161]
334. 13 [avatar contradiction clause 333]
335. $false [avatar sat refutation 323,334]
% SZS output end Proof for 2437027179126635709639855
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either calm or not calm is not generous and vice versa.
If someone is not funny or not curious then susan is either humble or strong.
Everyone who is either not patient or not calm is rich and vice versa.
Everyone who is both generous and funny is not quiet or not patient and vice versa.
Everyone who is not wise is old or tall and vice versa.
If someone is not generous then someone is calm and vice versa.
If susan is either not patient or humble then someone is either tall or old.
Everyone who is both not wise and strong is either rich or not calm.
If fred is not creative or not strong then someone is tall or not funny and vice versa.
Everyone who is both not strong and not funny is both not brave and not wise.
If someone is either strong or not kind then someone is both not rich and not humble.
Everyone who is not creative or not quiet is not creative or patient.
Everyone who is generous is both not tall and not kind.
Everyone who is both not old and not brave is not strong or not calm and vice versa.
If someone is either happy or old then fred is generous.
Everyone who is both creative and old is both quiet and humble.
Someone is either not creative or not rich.
Someone is either humble or generous.
Paul is creative or tall.
Someone is kind or creative.
Someone is not curious.
Alice is brave or creative.
Alice is wise.
Mary is not old. | Fred is not old. | entailment | (![X]:((calm(X)<~>~calm(X))<=>~generous(X)))&
((?[X]:((~funny(X)|~curious(X))))=>((humble(susan)<~>strong(susan))))&
(![X]:((~patient(X)<~>~calm(X))<=>rich(X)))&
(![X]:((generous(X)&funny(X))<=>(~quiet(X)|~patient(X))))&
(![X]:(~wise(X)<=>(old(X)|tall(X))))&
((?[X]:(~generous(X)))<=>(?[X]:(calm(X))))&
(((~patient(susan)<~>humble(susan)))=>(?[X]:((tall(X)<~>old(X)))))&
(![X]:((~wise(X)&strong(X))=>(rich(X)<~>~calm(X))))&
(((~creative(fred)|~strong(fred)))<=>(?[X]:((tall(X)|~funny(X)))))&
(![X]:((~strong(X)&~funny(X))=>(~brave(X)&~wise(X))))&
((?[X]:((strong(X)<~>~kind(X))))=>(?[X]:((~rich(X)&~humble(X)))))&
(![X]:((~creative(X)|~quiet(X))=>(~creative(X)|patient(X))))&
(![X]:(generous(X)=>(~tall(X)&~kind(X))))&
(![X]:((~old(X)&~brave(X))<=>(~strong(X)|~calm(X))))&
((?[X]:((happy(X)<~>old(X))))=>(generous(fred)))&
(![X]:((creative(X)&old(X))=>(quiet(X)&humble(X))))&
(?[X]:((~creative(X)<~>~rich(X))))&
(?[X]:((humble(X)<~>generous(X))))&
((creative(paul)|tall(paul)))&
(?[X]:((kind(X)|creative(X))))&
(?[X]:(~curious(X)))&
((brave(alice)|creative(alice)))&
(wise(alice))&
(~old(mary)) | ~old(fred) | [
"p0",
"p2",
"p3",
"p4",
"p7",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 6272814096068900328136132
% SZS output start Proof for 6272814096068900328136132
1. ! [X0] : ((calm(X0) <~> ~calm(X0)) <=> ~generous(X0)) [input p0]
3. ! [X0] : ((~patient(X0) <~> ~calm(X0)) <=> rich(X0)) [input p2]
4. ! [X0] : ((funny(X0) & generous(X0)) <=> (~patient(X0) | ~quiet(X0))) [input p3]
5. ! [X0] : (~wise(X0) <=> (tall(X0) | old(X0))) [input p4]
8. ! [X0] : ((strong(X0) & ~wise(X0)) => (rich(X0) <~> ~calm(X0))) [input p7]
14. ! [X0] : ((~brave(X0) & ~old(X0)) <=> (~calm(X0) | ~strong(X0))) [input p13]
25. old(fred) [input hypothesis]
30. ! [X0] : ((rich(X0) <~> ~calm(X0)) | (~strong(X0) | wise(X0))) [ennf transformation 8]
31. ! [X0] : ((rich(X0) <~> ~calm(X0)) | ~strong(X0) | wise(X0)) [flattening 30]
41. ! [X0] : ((((calm(X0) | ~calm(X0)) & (~calm(X0) | calm(X0))) | generous(X0)) & (~generous(X0) | ((calm(X0) | calm(X0)) & (~calm(X0) | ~calm(X0))))) [nnf transformation 1]
43. ! [X0] : ((((calm(X0) | patient(X0)) & (~calm(X0) | ~patient(X0))) | ~rich(X0)) & (rich(X0) | ((~patient(X0) | calm(X0)) & (~calm(X0) | patient(X0))))) [nnf transformation 3]
44. ! [X0] : (((funny(X0) & generous(X0)) | (patient(X0) & quiet(X0))) & ((~patient(X0) | ~quiet(X0)) | (~funny(X0) | ~generous(X0)))) [nnf transformation 4]
45. ! [X0] : (((funny(X0) & generous(X0)) | (patient(X0) & quiet(X0))) & (~patient(X0) | ~quiet(X0) | ~funny(X0) | ~generous(X0))) [flattening 44]
46. ! [X0] : ((~wise(X0) | (~tall(X0) & ~old(X0))) & ((tall(X0) | old(X0)) | wise(X0))) [nnf transformation 5]
47. ! [X0] : ((~wise(X0) | (~tall(X0) & ~old(X0))) & (tall(X0) | old(X0) | wise(X0))) [flattening 46]
56. ! [X0] : (((calm(X0) | ~rich(X0)) & (~calm(X0) | rich(X0))) | ~strong(X0) | wise(X0)) [nnf transformation 31]
66. ! [X0] : (((~brave(X0) & ~old(X0)) | (calm(X0) & strong(X0))) & ((~calm(X0) | ~strong(X0)) | (brave(X0) | old(X0)))) [nnf transformation 14]
67. ! [X0] : (((~brave(X0) & ~old(X0)) | (calm(X0) & strong(X0))) & (~calm(X0) | ~strong(X0) | brave(X0) | old(X0))) [flattening 66]
79. ~generous(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 41]
80. ~generous(X0) | calm(X0) | calm(X0) [cnf transformation 41]
89. ~rich(X0) | ~patient(X0) | ~calm(X0) [cnf transformation 43]
93. generous(X0) | patient(X0) [cnf transformation 45]
97. ~old(X0) | ~wise(X0) [cnf transformation 47]
105. ~strong(X0) | rich(X0) | ~calm(X0) | wise(X0) [cnf transformation 56]
122. ~old(X0) | strong(X0) [cnf transformation 67]
123. ~old(X0) | calm(X0) [cnf transformation 67]
140. old(fred) [cnf transformation 25]
141. ~generous(X0) | ~calm(X0) [duplicate literal removal 79]
142. ~generous(X0) | calm(X0) [duplicate literal removal 80]
143. ~generous(X0) [subsumption resolution 141,142]
162. patient(X0) [subsumption resolution 93,143]
182. 8 <=> strong(fred) [avatar definition]
183. strong(fred) <- (8) [avatar component clause 182]
258. ~wise(fred) [resolution 97,140]
259. strong(fred) [resolution 122,140]
260. 8 [avatar split clause 259,182]
261. calm(fred) [resolution 123,140]
302. rich(fred) | ~calm(fred) | wise(fred) <- (8) [resolution 105,183]
314. rich(fred) | wise(fred) <- (8) [subsumption resolution 302,261]
315. rich(fred) <- (8) [subsumption resolution 314,258]
321. ~patient(fred) | ~calm(fred) <- (8) [resolution 315,89]
322. ~calm(fred) <- (8) [subsumption resolution 321,162]
323. $false <- (8) [subsumption resolution 322,261]
324. ~8 [avatar contradiction clause 323]
325. $false [avatar sat refutation 260,324]
% SZS output end Proof for 6272814096068900328136132
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous and not funny then someone is not rich or strong and vice versa.
If mary is either humble or wise then someone is not rich or not tall and vice versa.
Everyone who is both creative and not wise is either not strong or generous and vice versa.
If paul is both not strong and brave then someone is happy or not humble.
Everyone who is either not brave or creative is either not rich or not patient.
Everyone who is not humble is either not funny or not curious and vice versa.
Everyone who is not happy is both generous and calm and vice versa.
If someone is brave then someone is kind or not quiet.
If someone is either kind or not rich then fred is not old and vice versa.
Everyone who is either rich or not brave is both happy and not old.
Everyone who is both not funny and curious is creative.
If someone is not calm or tall then someone is both not rich and not calm and vice versa.
If lucy is both tall and not funny then john is curious or not old and vice versa.
If paul is quiet or not generous then fred is humble and vice versa.
Everyone who is not humble is both not rich and happy.
If mary is both not kind and wise then mary is either strong or calm.
Alice is generous or not calm.
Someone is not funny or not kind.
Someone is not curious.
Mary is not old.
Someone is not tall or not creative.
Someone is calm or funny.
Alice is rich or not funny.
Alice is not patient or not happy. | Fred is not old. | neutral | ((?[X]:((generous(X)&~funny(X))))<=>(?[X]:((~rich(X)|strong(X)))))&
(((humble(mary)<~>wise(mary)))<=>(?[X]:((~rich(X)|~tall(X)))))&
(![X]:((creative(X)&~wise(X))<=>(~strong(X)<~>generous(X))))&
(((~strong(paul)&brave(paul)))=>(?[X]:((happy(X)|~humble(X)))))&
(![X]:((~brave(X)<~>creative(X))=>(~rich(X)<~>~patient(X))))&
(![X]:(~humble(X)<=>(~funny(X)<~>~curious(X))))&
(![X]:(~happy(X)<=>(generous(X)&calm(X))))&
((?[X]:(brave(X)))=>(?[X]:((kind(X)|~quiet(X)))))&
((?[X]:((kind(X)<~>~rich(X))))<=>(~old(fred)))&
(![X]:((rich(X)<~>~brave(X))=>(happy(X)&~old(X))))&
(![X]:((~funny(X)&curious(X))=>creative(X)))&
((?[X]:((~calm(X)|tall(X))))<=>(?[X]:((~rich(X)&~calm(X)))))&
(((tall(lucy)&~funny(lucy)))<=>((curious(john)|~old(john))))&
(((quiet(paul)|~generous(paul)))<=>(humble(fred)))&
(![X]:(~humble(X)=>(~rich(X)&happy(X))))&
(((~kind(mary)&wise(mary)))=>((strong(mary)<~>calm(mary))))&
((generous(alice)|~calm(alice)))&
(?[X]:((~funny(X)|~kind(X))))&
(?[X]:(~curious(X)))&
(~old(mary))&
(?[X]:((~tall(X)|~creative(X))))&
(?[X]:((calm(X)|funny(X))))&
((rich(alice)|~funny(alice)))&
((~patient(alice)|~happy(alice))) | ~old(fred) | [] | null | 0 |
Everyone who is not rich is creative or not brave.
Everyone who is not wise or not patient is either quiet or not curious and vice versa.
If alice is either patient or wise then paul is not patient and vice versa.
If someone is either quiet or not quiet then paul is both kind and tall.
Everyone who is not strong is not wise.
Everyone who is both funny and tall is either not old or not quiet and vice versa.
If someone is creative then someone is not creative or happy.
Everyone who is not generous or patient is rich and vice versa.
Everyone who is quiet or not strong is not quiet or old.
Everyone who is not strong or curious is both not strong and strong and vice versa.
Everyone who is both not funny and brave is either not generous or not curious and vice versa.
If someone is generous or humble then someone is not kind or tall and vice versa.
Everyone who is either creative or humble is generous or not strong.
Everyone who is not happy or patient is not old.
If susan is either rich or not patient then someone is not happy or tall and vice versa.
Everyone who is creative or not curious is both not calm and generous.
Fred is not funny or rich.
Someone is both patient and kind. | Alice is not kind. | neutral | (![X]:(~rich(X)=>(creative(X)|~brave(X))))&
(![X]:((~wise(X)|~patient(X))<=>(quiet(X)<~>~curious(X))))&
(((patient(alice)<~>wise(alice)))<=>(~patient(paul)))&
((?[X]:((quiet(X)<~>~quiet(X))))=>((kind(paul)&tall(paul))))&
(![X]:(~strong(X)=>~wise(X)))&
(![X]:((funny(X)&tall(X))<=>(~old(X)<~>~quiet(X))))&
((?[X]:(creative(X)))=>(?[X]:((~creative(X)|happy(X)))))&
(![X]:((~generous(X)|patient(X))<=>rich(X)))&
(![X]:((quiet(X)|~strong(X))=>(~quiet(X)|old(X))))&
(![X]:((~strong(X)|curious(X))<=>(~strong(X)&strong(X))))&
(![X]:((~funny(X)&brave(X))<=>(~generous(X)<~>~curious(X))))&
((?[X]:((generous(X)|humble(X))))<=>(?[X]:((~kind(X)|tall(X)))))&
(![X]:((creative(X)<~>humble(X))=>(generous(X)|~strong(X))))&
(![X]:((~happy(X)|patient(X))=>~old(X)))&
(((rich(susan)<~>~patient(susan)))<=>(?[X]:((~happy(X)|tall(X)))))&
(![X]:((creative(X)|~curious(X))=>(~calm(X)&generous(X))))&
((~funny(fred)|rich(fred)))&
(?[X]:((patient(X)&kind(X)))) | ~kind(alice) | [] | null | 0 |
Everyone who is not happy is patient and vice versa. Everyone who is quiet or patient is both creative and not funny. Everyone who is both calm and not curious is either wise or not kind and vice versa. Everyone who is generous is both quiet and funny. Everyone who is not old or not funny is not creative or happy. Everyone who is both not patient and not wise is both creative and brave and vice versa. If someone is not strong or not old then someone is generous. Everyone who is not patient is both not curious and not wise. If paul is either not rich or not wise then someone is either wise or not brave. Everyone who is not patient or generous is not kind. Everyone who is both not old and humble is both not kind and curious and vice versa. If someone is either not brave or happy then someone is calm or not generous. Everyone who is not patient is humble and vice versa. If someone is both not tall and not wise then fred is both brave and not rich and vice versa. If someone is not creative then someone is both quiet and not creative and vice versa. Everyone who is either not brave or happy is not generous. Alice is kind or tall. Someone is not curious or not generous. Mary is either humble or curious. John is both not kind and creative. Someone is either funny or not creative. | Paul is not funny. | neutral | (![X]:(~happy(X)<=>patient(X)))&
(![X]:((quiet(X)|patient(X))=>(creative(X)&~funny(X))))&
(![X]:((calm(X)&~curious(X))<=>(wise(X)<~>~kind(X))))&
(![X]:(generous(X)=>(quiet(X)&funny(X))))&
(![X]:((~old(X)|~funny(X))=>(~creative(X)|happy(X))))&
(![X]:((~patient(X)&~wise(X))<=>(creative(X)&brave(X))))&
((?[X]:((~strong(X)|~old(X))))=>(?[X]:(generous(X))))&
(![X]:(~patient(X)=>(~curious(X)&~wise(X))))&
(((~rich(paul)<~>~wise(paul)))=>(?[X]:((wise(X)<~>~brave(X)))))&
(![X]:((~patient(X)|generous(X))=>~kind(X)))&
(![X]:((~old(X)&humble(X))<=>(~kind(X)&curious(X))))&
((?[X]:((~brave(X)<~>happy(X))))=>(?[X]:((calm(X)|~generous(X)))))&
(![X]:(~patient(X)<=>humble(X)))&
((?[X]:((~tall(X)&~wise(X))))<=>((brave(fred)&~rich(fred))))&
((?[X]:(~creative(X)))<=>(?[X]:((quiet(X)&~creative(X)))))&
(![X]:((~brave(X)<~>happy(X))=>~generous(X)))&
((kind(alice)|tall(alice)))&
(?[X]:((~curious(X)|~generous(X))))&
((humble(mary)<~>curious(mary)))&
((~kind(john)&creative(john)))&
(?[X]:((funny(X)<~>~creative(X)))) | ~funny(paul) | [] | null | 0 |
If alice is both strong and kind then alice is either calm or happy.
Everyone who is generous is generous or patient.
Everyone who is both not strong and not creative is quiet or happy and vice versa.
If someone is both tall and humble then susan is either not calm or not strong and vice versa.
If someone is either patient or not humble then someone is patient and vice versa.
If alice is both not calm and not humble then lucy is kind.
Everyone who is both happy and generous is either not curious or not brave and vice versa.
Everyone who is both calm and not strong is both not creative and not curious and vice versa.
Everyone who is either humble or not wise is not creative or kind and vice versa.
If someone is not calm or not rich then paul is not rich or strong.
If alice is tall then lucy is either quiet or not humble and vice versa.
If someone is both not funny and calm then paul is not rich or not calm and vice versa.
Everyone who is not tall or wise is both strong and calm.
Everyone who is either calm or not strong is both not wise and not calm.
If someone is old then someone is not wise or creative.
Everyone who is old is both not creative and patient.
Mary is old.
John is either calm or old.
Alice is either old or not creative.
Lucy is not calm or rich.
Fred is both not happy and not kind. | Mary is not humble. | entailment | (((strong(alice)&kind(alice)))=>((calm(alice)<~>happy(alice))))&
(![X]:(generous(X)=>(generous(X)|patient(X))))&
(![X]:((~strong(X)&~creative(X))<=>(quiet(X)|happy(X))))&
((?[X]:((tall(X)&humble(X))))<=>((~calm(susan)<~>~strong(susan))))&
((?[X]:((patient(X)<~>~humble(X))))<=>(?[X]:(patient(X))))&
(((~calm(alice)&~humble(alice)))=>(kind(lucy)))&
(![X]:((happy(X)&generous(X))<=>(~curious(X)<~>~brave(X))))&
(![X]:((calm(X)&~strong(X))<=>(~creative(X)&~curious(X))))&
(![X]:((humble(X)<~>~wise(X))<=>(~creative(X)|kind(X))))&
((?[X]:((~calm(X)|~rich(X))))=>((~rich(paul)|strong(paul))))&
((tall(alice))<=>((quiet(lucy)<~>~humble(lucy))))&
((?[X]:((~funny(X)&calm(X))))<=>((~rich(paul)|~calm(paul))))&
(![X]:((~tall(X)|wise(X))=>(strong(X)&calm(X))))&
(![X]:((calm(X)<~>~strong(X))=>(~wise(X)&~calm(X))))&
((?[X]:(old(X)))=>(?[X]:((~wise(X)|creative(X)))))&
(![X]:(old(X)=>(~creative(X)&patient(X))))&
(old(mary))&
((calm(john)<~>old(john)))&
((old(alice)<~>~creative(alice)))&
((~calm(lucy)|rich(lucy)))&
((~happy(fred)&~kind(fred))) | ~humble(mary) | [
"p8",
"p12",
"p13",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 8981162100035566344501167
% SZS output start Proof for 8981162100035566344501167
9. ! [X0] : ((humble(X0) <~> ~wise(X0)) <=> (kind(X0) | ~creative(X0))) [input p8]
13. ! [X0] : ((wise(X0) | ~tall(X0)) => (calm(X0) & strong(X0))) [input p12]
14. ! [X0] : ((calm(X0) <~> ~strong(X0)) => (~calm(X0) & ~wise(X0))) [input p13]
16. ! [X0] : (old(X0) => (patient(X0) & ~creative(X0))) [input p15]
17. old(mary) [input p16]
22. humble(mary) [input hypothesis]
33. ! [X0] : ((calm(X0) & strong(X0)) | (~wise(X0) & tall(X0))) [ennf transformation 13]
34. ! [X0] : ((~calm(X0) & ~wise(X0)) | (calm(X0) <=> ~strong(X0))) [ennf transformation 14]
36. ! [X0] : ((patient(X0) & ~creative(X0)) | ~old(X0)) [ennf transformation 16]
53. ! [X0] : ((((wise(X0) | ~humble(X0)) & (~wise(X0) | humble(X0))) | (~kind(X0) & creative(X0))) & ((kind(X0) | ~creative(X0)) | ((humble(X0) | wise(X0)) & (~wise(X0) | ~humble(X0))))) [nnf transformation 9]
54. ! [X0] : ((((wise(X0) | ~humble(X0)) & (~wise(X0) | humble(X0))) | (~kind(X0) & creative(X0))) & (kind(X0) | ~creative(X0) | ((humble(X0) | wise(X0)) & (~wise(X0) | ~humble(X0))))) [flattening 53]
61. ! [X0] : ((~calm(X0) & ~wise(X0)) | ((calm(X0) | strong(X0)) & (~strong(X0) | ~calm(X0)))) [nnf transformation 34]
100. ~humble(X0) | wise(X0) | creative(X0) [cnf transformation 54]
114. ~wise(X0) | strong(X0) [cnf transformation 33]
116. ~wise(X0) | calm(X0) [cnf transformation 33]
119. ~calm(X0) | ~strong(X0) | ~calm(X0) [cnf transformation 61]
122. ~old(X0) | ~creative(X0) [cnf transformation 36]
124. old(mary) [cnf transformation 17]
132. humble(mary) [cnf transformation 22]
133. ~calm(X0) | ~strong(X0) [duplicate literal removal 119]
301. ~creative(mary) [resolution 122,124]
353. wise(mary) | creative(mary) [resolution 100,132]
355. wise(mary) [subsumption resolution 353,301]
367. calm(mary) [resolution 355,116]
368. strong(mary) [resolution 355,114]
420. ~strong(mary) [resolution 367,133]
421. $false [subsumption resolution 420,368]
% SZS output end Proof for 8981162100035566344501167
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not quiet and kind is not generous and vice versa. Everyone who is not funny is happy. If alice is not wise then mary is either curious or not rich and vice versa. Everyone who is either not quiet or not curious is either not patient or not quiet and vice versa. If paul is quiet then someone is both curious and kind. Everyone who is either patient or creative is patient or not tall. If alice is not kind or not quiet then someone is both wise and old and vice versa. Everyone who is not happy is not strong. Everyone who is both humble and not strong is either not old or curious. Everyone who is tall is not rich or not creative. Everyone who is humble is either happy or curious and vice versa. If someone is both calm and not curious then lucy is either strong or not generous and vice versa. Everyone who is not strong or old is both not funny and not kind and vice versa. If alice is not calm or not curious then lucy is both rich and calm. If someone is happy or brave then someone is either not happy or happy and vice versa. Everyone who is both not kind and quiet is either generous or not humble and vice versa. Fred is curious. Someone is either happy or not calm. Fred is tall. Mary is brave. Someone is not tall. Someone is old. Lucy is rich or not strong. Someone is both quiet and not strong. | Fred is generous. | entailment | (![X]:((~quiet(X)&kind(X))<=>~generous(X)))&
(![X]:(~funny(X)=>happy(X)))&
((~wise(alice))<=>((curious(mary)<~>~rich(mary))))&
(![X]:((~quiet(X)<~>~curious(X))<=>(~patient(X)<~>~quiet(X))))&
((quiet(paul))=>(?[X]:((curious(X)&kind(X)))))&
(![X]:((patient(X)<~>creative(X))=>(patient(X)|~tall(X))))&
(((~kind(alice)|~quiet(alice)))<=>(?[X]:((wise(X)&old(X)))))&
(![X]:(~happy(X)=>~strong(X)))&
(![X]:((humble(X)&~strong(X))=>(~old(X)<~>curious(X))))&
(![X]:(tall(X)=>(~rich(X)|~creative(X))))&
(![X]:(humble(X)<=>(happy(X)<~>curious(X))))&
((?[X]:((calm(X)&~curious(X))))<=>((strong(lucy)<~>~generous(lucy))))&
(![X]:((~strong(X)|old(X))<=>(~funny(X)&~kind(X))))&
(((~calm(alice)|~curious(alice)))=>((rich(lucy)&calm(lucy))))&
((?[X]:((happy(X)|brave(X))))<=>(?[X]:((~happy(X)<~>happy(X)))))&
(![X]:((~kind(X)&quiet(X))<=>(generous(X)<~>~humble(X))))&
(curious(fred))&
(?[X]:((happy(X)<~>~calm(X))))&
(tall(fred))&
(brave(mary))&
(?[X]:(~tall(X)))&
(?[X]:(old(X)))&
((rich(lucy)|~strong(lucy)))&
(?[X]:((quiet(X)&~strong(X)))) | generous(fred) | [
"p0",
"p7",
"p10",
"p12",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 3590636091995080712747
% SZS output start Proof for 3590636091995080712747
1. ! [X0] : ((kind(X0) & ~quiet(X0)) <=> ~generous(X0)) [input p0]
8. ! [X0] : (~happy(X0) => ~strong(X0)) [input p7]
11. ! [X0] : (humble(X0) <=> (happy(X0) <~> curious(X0))) [input p10]
13. ! [X0] : ((old(X0) | ~strong(X0)) <=> (~kind(X0) & ~funny(X0))) [input p12]
16. ! [X0] : ((quiet(X0) & ~kind(X0)) <=> (generous(X0) <~> ~humble(X0))) [input p15]
17. curious(fred) [input p16]
25. ~generous(fred) [input hypothesis]
31. ! [X0] : (~strong(X0) | happy(X0)) [ennf transformation 8]
37. ! [X0] : (((kind(X0) & ~quiet(X0)) | generous(X0)) & (~generous(X0) | (~kind(X0) | quiet(X0)))) [nnf transformation 1]
38. ! [X0] : (((kind(X0) & ~quiet(X0)) | generous(X0)) & (~generous(X0) | ~kind(X0) | quiet(X0))) [flattening 37]
50. ! [X0] : ((humble(X0) | ((happy(X0) | ~curious(X0)) & (curious(X0) | ~happy(X0)))) & (((~curious(X0) | ~happy(X0)) & (curious(X0) | happy(X0))) | ~humble(X0))) [nnf transformation 11]
55. ! [X0] : (((old(X0) | ~strong(X0)) | (kind(X0) | funny(X0))) & ((~kind(X0) & ~funny(X0)) | (~old(X0) & strong(X0)))) [nnf transformation 13]
56. ! [X0] : ((old(X0) | ~strong(X0) | kind(X0) | funny(X0)) & ((~kind(X0) & ~funny(X0)) | (~old(X0) & strong(X0)))) [flattening 55]
62. ! [X0] : (((quiet(X0) & ~kind(X0)) | ((generous(X0) | humble(X0)) & (~humble(X0) | ~generous(X0)))) & (((humble(X0) | ~generous(X0)) & (~humble(X0) | generous(X0))) | (~quiet(X0) | kind(X0)))) [nnf transformation 16]
63. ! [X0] : (((quiet(X0) & ~kind(X0)) | ((generous(X0) | humble(X0)) & (~humble(X0) | ~generous(X0)))) & (((humble(X0) | ~generous(X0)) & (~humble(X0) | generous(X0))) | ~quiet(X0) | kind(X0))) [flattening 62]
74. ~quiet(X0) | generous(X0) [cnf transformation 38]
75. generous(X0) | kind(X0) [cnf transformation 38]
98. ~strong(X0) | happy(X0) [cnf transformation 31]
103. ~humble(X0) | ~happy(X0) | ~curious(X0) [cnf transformation 50]
114. ~kind(X0) | strong(X0) [cnf transformation 56]
132. quiet(X0) | generous(X0) | humble(X0) [cnf transformation 63]
133. curious(fred) [cnf transformation 17]
143. ~generous(fred) [cnf transformation 25]
268. humble(X0) | generous(X0) [subsumption resolution 132,74]
283. kind(fred) [resolution 75,143]
289. strong(fred) [resolution 114,283]
352. 33 <=> humble(fred) [avatar definition]
353. ~humble(fred) <- (~33) [avatar component clause 352]
354. humble(fred) <- (33) [avatar component clause 352]
356. 34 <=> happy(fred) [avatar definition]
360. ~happy(fred) | ~curious(fred) <- (33) [resolution 354,103]
362. ~happy(fred) <- (33) [subsumption resolution 360,133]
363. ~34 | ~33 [avatar split clause 362,352,356]
369. happy(fred) [resolution 289,98]
372. 34 [avatar split clause 369,356]
374. generous(fred) <- (~33) [resolution 353,268]
375. $false <- (~33) [subsumption resolution 374,143]
376. 33 [avatar contradiction clause 375]
377. $false [avatar sat refutation 363,372,376]
% SZS output end Proof for 3590636091995080712747
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not old and not strong then alice is both not kind and generous. If mary is creative or patient then someone is not quiet and vice versa. If someone is both not happy and humble then fred is not kind and vice versa. Everyone who is not curious or humble is both not strong and old. Everyone who is either strong or not old is not curious and vice versa. Everyone who is not kind or not creative is wise or not old. Everyone who is both tall and not funny is not old or happy. Everyone who is either not kind or kind is both strong and kind. If someone is both creative and not wise then someone is humble. Everyone who is either not quiet or not humble is not generous. If someone is not strong or generous then someone is either brave or not wise and vice versa. If john is either not patient or brave then someone is both not wise and creative. If john is kind or not wise then someone is not old or funny. If someone is both happy and not patient then someone is both not quiet and not creative. If someone is funny then someone is curious or happy. Everyone who is not funny is both creative and not funny. Someone is not humble or wise. Fred is not tall or not curious. Someone is not patient or not curious. Someone is not humble. Someone is kind or not humble. | Mary is old. | contradiction | ((?[X]:((~old(X)&~strong(X))))=>((~kind(alice)&generous(alice))))&
(((creative(mary)|patient(mary)))<=>(?[X]:(~quiet(X))))&
((?[X]:((~happy(X)&humble(X))))<=>(~kind(fred)))&
(![X]:((~curious(X)|humble(X))=>(~strong(X)&old(X))))&
(![X]:((strong(X)<~>~old(X))<=>~curious(X)))&
(![X]:((~kind(X)|~creative(X))=>(wise(X)|~old(X))))&
(![X]:((tall(X)&~funny(X))=>(~old(X)|happy(X))))&
(![X]:((~kind(X)<~>kind(X))=>(strong(X)&kind(X))))&
((?[X]:((creative(X)&~wise(X))))=>(?[X]:(humble(X))))&
(![X]:((~quiet(X)<~>~humble(X))=>~generous(X)))&
((?[X]:((~strong(X)|generous(X))))<=>(?[X]:((brave(X)<~>~wise(X)))))&
(((~patient(john)<~>brave(john)))=>(?[X]:((~wise(X)&creative(X)))))&
(((kind(john)|~wise(john)))=>(?[X]:((~old(X)|funny(X)))))&
((?[X]:((happy(X)&~patient(X))))=>(?[X]:((~quiet(X)&~creative(X)))))&
((?[X]:(funny(X)))=>(?[X]:((curious(X)|happy(X)))))&
(![X]:(~funny(X)=>(creative(X)&~funny(X))))&
(?[X]:((~humble(X)|wise(X))))&
((~tall(fred)|~curious(fred)))&
(?[X]:((~patient(X)|~curious(X))))&
(?[X]:(~humble(X)))&
(?[X]:((kind(X)|~humble(X)))) | old(mary) | [
"p3",
"p4",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 837880265160657210986603
% SZS output start Proof for 837880265160657210986603
4. ! [X0] : ((humble(X0) | ~curious(X0)) => (old(X0) & ~strong(X0))) [input p3]
5. ! [X0] : ((strong(X0) <~> ~old(X0)) <=> ~curious(X0)) [input p4]
8. ! [X0] : ((~kind(X0) <~> kind(X0)) => (kind(X0) & strong(X0))) [input p7]
22. old(mary) [input hypothesis]
30. ! [X0] : ((old(X0) & ~strong(X0)) | (~humble(X0) & curious(X0))) [ennf transformation 4]
33. ! [X0] : ((kind(X0) & strong(X0)) | (~kind(X0) <=> kind(X0))) [ennf transformation 8]
50. ! [X0] : ((((old(X0) | ~strong(X0)) & (~old(X0) | strong(X0))) | curious(X0)) & (~curious(X0) | ((strong(X0) | old(X0)) & (~old(X0) | ~strong(X0))))) [nnf transformation 5]
51. ! [X0] : ((kind(X0) & strong(X0)) | ((~kind(X0) | ~kind(X0)) & (kind(X0) | kind(X0)))) [nnf transformation 33]
88. ~strong(X0) | curious(X0) [cnf transformation 30]
90. curious(X0) | old(X0) [cnf transformation 30]
92. ~curious(X0) | ~old(X0) | ~strong(X0) [cnf transformation 50]
94. ~old(X0) | strong(X0) | curious(X0) [cnf transformation 50]
99. strong(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 51]
100. kind(X0) | kind(X0) | kind(X0) [cnf transformation 51]
126. old(mary) [cnf transformation 22]
128. strong(X0) | ~kind(X0) [duplicate literal removal 99]
129. kind(X0) [duplicate literal removal 100]
180. strong(X0) | curious(X0) [subsumption resolution 94,90]
181. curious(X0) [subsumption resolution 180,88]
184. ~strong(X0) | ~old(X0) [subsumption resolution 92,181]
185. strong(X0) [subsumption resolution 128,129]
287. ~old(X0) [resolution 184,185]
288. $false [resolution 287,126]
% SZS output end Proof for 837880265160657210986603
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either creative or not happy is quiet.
Everyone who is both not old and quiet is either not calm or not generous and vice versa.
Everyone who is patient or not wise is either not calm or not patient.
Everyone who is both tall and strong is not rich.
If mary is both patient and not generous then john is both creative and not old.
If john is not patient then someone is either not rich or not strong.
Everyone who is both not funny and quiet is quiet and vice versa.
If john is both funny and not funny then john is happy or not wise and vice versa.
If someone is either not happy or not old then someone is both patient and not generous and vice versa.
If paul is not funny or not kind then john is either not wise or strong.
Everyone who is not calm or not rich is both not tall and strong.
If john is not calm or not strong then alice is both wise and not rich.
If lucy is both not strong and not tall then someone is both not creative and not calm.
Everyone who is both not calm and not quiet is either not tall or rich and vice versa.
If fred is both old and kind then someone is generous.
Someone is quiet or humble.
Alice is not calm.
Someone is either not calm or not happy.
Someone is both kind and not creative.
Someone is either not calm or not old.
John is either not strong or wise.
Someone is patient. | John is not wise. | contradiction | (![X]:((creative(X)<~>~happy(X))=>quiet(X)))&
(![X]:((~old(X)&quiet(X))<=>(~calm(X)<~>~generous(X))))&
(![X]:((patient(X)|~wise(X))=>(~calm(X)<~>~patient(X))))&
(![X]:((tall(X)&strong(X))=>~rich(X)))&
(((patient(mary)&~generous(mary)))=>((creative(john)&~old(john))))&
((~patient(john))=>(?[X]:((~rich(X)<~>~strong(X)))))&
(![X]:((~funny(X)&quiet(X))<=>quiet(X)))&
(((funny(john)&~funny(john)))<=>((happy(john)|~wise(john))))&
((?[X]:((~happy(X)<~>~old(X))))<=>(?[X]:((patient(X)&~generous(X)))))&
(((~funny(paul)|~kind(paul)))=>((~wise(john)<~>strong(john))))&
(![X]:((~calm(X)|~rich(X))=>(~tall(X)&strong(X))))&
(((~calm(john)|~strong(john)))=>((wise(alice)&~rich(alice))))&
(((~strong(lucy)&~tall(lucy)))=>(?[X]:((~creative(X)&~calm(X)))))&
(![X]:((~calm(X)&~quiet(X))<=>(~tall(X)<~>rich(X))))&
(((old(fred)&kind(fred)))=>(?[X]:(generous(X))))&
(?[X]:((quiet(X)|humble(X))))&
(~calm(alice))&
(?[X]:((~calm(X)<~>~happy(X))))&
(?[X]:((kind(X)&~creative(X))))&
(?[X]:((~calm(X)<~>~old(X))))&
((~strong(john)<~>wise(john)))&
(?[X]:(patient(X))) | ~wise(john) | [
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 7094027206094701455736845
% SZS output start Proof for 7094027206094701455736845
8. (~funny(john) & funny(john)) <=> (~wise(john) | happy(john)) [input p7]
23. ~wise(john) [input hypothesis]
49. ((~funny(john) & funny(john)) | (wise(john) & ~happy(john))) & ((~wise(john) | happy(john)) | (funny(john) | ~funny(john))) [nnf transformation 8]
50. ((~funny(john) & funny(john)) | (wise(john) & ~happy(john))) & (~wise(john) | happy(john) | funny(john) | ~funny(john)) [flattening 49]
96. funny(john) | wise(john) [cnf transformation 50]
98. ~funny(john) | wise(john) [cnf transformation 50]
136. ~wise(john) [cnf transformation 23]
171. 8 <=> wise(john) [avatar definition]
175. 9 <=> funny(john) [avatar definition]
178. 8 | ~9 [avatar split clause 98,175,171]
184. 8 | 9 [avatar split clause 96,175,171]
308. ~8 [avatar split clause 136,171]
309. $false [avatar sat refutation 178,184,308]
% SZS output end Proof for 7094027206094701455736845
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If fred is either old or rich then someone is either creative or kind and vice versa.
If someone is humble then someone is both calm and funny and vice versa.
If someone is not kind or not creative then someone is both generous and happy.
If someone is either quiet or curious then john is curious.
If susan is either not humble or not wise then john is old or not brave.
Everyone who is both not curious and patient is curious or not wise and vice versa.
If fred is both not creative and brave then fred is humble or curious.
Everyone who is either old or wise is either happy or brave and vice versa.
Everyone who is both not funny and not curious is either not funny or strong and vice versa.
Everyone who is either not humble or happy is both creative and not wise and vice versa.
Everyone who is old or not generous is either brave or rich.
If john is both old and not humble then someone is not humble or quiet.
If someone is either not funny or happy then someone is not strong or creative.
Everyone who is happy or funny is patient.
Everyone who is both not calm and strong is patient or not tall.
If lucy is patient then lucy is curious.
Mary is brave or not calm.
Someone is both rich and not happy.
Susan is brave.
Susan is both not kind and not calm.
Someone is wise or not quiet.
Someone is not strong or curious.
Lucy is either quiet or not strong.
Someone is either not brave or curious. | Fred is not quiet. | entailment | (((old(fred)<~>rich(fred)))<=>(?[X]:((creative(X)<~>kind(X)))))&
((?[X]:(humble(X)))<=>(?[X]:((calm(X)&funny(X)))))&
((?[X]:((~kind(X)|~creative(X))))=>(?[X]:((generous(X)&happy(X)))))&
((?[X]:((quiet(X)<~>curious(X))))=>(curious(john)))&
(((~humble(susan)<~>~wise(susan)))=>((old(john)|~brave(john))))&
(![X]:((~curious(X)&patient(X))<=>(curious(X)|~wise(X))))&
(((~creative(fred)&brave(fred)))=>((humble(fred)|curious(fred))))&
(![X]:((old(X)<~>wise(X))<=>(happy(X)<~>brave(X))))&
(![X]:((~funny(X)&~curious(X))<=>(~funny(X)<~>strong(X))))&
(![X]:((~humble(X)<~>happy(X))<=>(creative(X)&~wise(X))))&
(![X]:((old(X)|~generous(X))=>(brave(X)<~>rich(X))))&
(((old(john)&~humble(john)))=>(?[X]:((~humble(X)|quiet(X)))))&
((?[X]:((~funny(X)<~>happy(X))))=>(?[X]:((~strong(X)|creative(X)))))&
(![X]:((happy(X)|funny(X))=>patient(X)))&
(![X]:((~calm(X)&strong(X))=>(patient(X)|~tall(X))))&
((patient(lucy))=>(curious(lucy)))&
((brave(mary)|~calm(mary)))&
(?[X]:((rich(X)&~happy(X))))&
(brave(susan))&
((~kind(susan)&~calm(susan)))&
(?[X]:((wise(X)|~quiet(X))))&
(?[X]:((~strong(X)|curious(X))))&
((quiet(lucy)<~>~strong(lucy)))&
(?[X]:((~brave(X)<~>curious(X)))) | ~quiet(fred) | [
"p3",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 3650157927078209575546249
% SZS output start Proof for 3650157927078209575546249
4. ? [X0] : (quiet(X0) <~> curious(X0)) => curious(john) [input p3]
6. ! [X0] : ((patient(X0) & ~curious(X0)) <=> (~wise(X0) | curious(X0))) [input p5]
25. quiet(fred) [input hypothesis]
33. curious(john) | ! [X0] : (quiet(X0) <=> curious(X0)) [ennf transformation 4]
56. curious(john) | ! [X0] : ((quiet(X0) | ~curious(X0)) & (curious(X0) | ~quiet(X0))) [nnf transformation 33]
58. ! [X0] : (((patient(X0) & ~curious(X0)) | (wise(X0) & ~curious(X0))) & ((~wise(X0) | curious(X0)) | (~patient(X0) | curious(X0)))) [nnf transformation 6]
59. ! [X0] : (((patient(X0) & ~curious(X0)) | (wise(X0) & ~curious(X0))) & (~wise(X0) | curious(X0) | ~patient(X0) | curious(X0))) [flattening 58]
95. curious(john) | curious(X0) | ~quiet(X0) [cnf transformation 56]
100. ~curious(X0) | ~curious(X0) [cnf transformation 59]
145. quiet(fred) [cnf transformation 25]
149. ~curious(X0) [duplicate literal removal 100]
217. 16 <=> curious(john) [avatar definition]
219. curious(john) <- (16) [avatar component clause 217]
222. 17 <=> ! [X0] : (curious(X0) | ~quiet(X0)) [avatar definition]
223. curious(X0) | ~quiet(X0) <- (17) [avatar component clause 222]
224. 17 | 16 [avatar split clause 95,217,222]
294. $false <- (16) [subsumption resolution 219,149]
295. ~16 [avatar contradiction clause 294]
296. ~quiet(X0) <- (17) [subsumption resolution 223,149]
297. $false <- (17) [resolution 296,145]
298. ~17 [avatar contradiction clause 297]
299. $false [avatar sat refutation 224,295,298]
% SZS output end Proof for 3650157927078209575546249
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 fred is either tall or humble then someone is either not calm or not strong.
If someone is both not humble and not strong then someone is either not humble or creative and vice versa.
If lucy is not quiet then mary is either not calm or not happy and vice versa.
Everyone who is not patient or strong is both creative and rich.
Everyone who is strong is both not funny and not rich.
If alice is humble or quiet then someone is creative and vice versa.
Everyone who is both not old and old is generous or curious.
If alice is either not rich or quiet then someone is both not quiet and humble and vice versa.
Everyone who is both calm and not patient is calm and vice versa.
Everyone who is not kind or generous is both wise and not curious.
Everyone who is not old or humble is not kind or happy and vice versa.
Everyone who is not humble is rich or not kind.
Everyone who is both not creative and not old is both strong and not generous and vice versa.
If mary is not old or not calm then someone is not quiet and vice versa.
If someone is not rich or not brave then someone is both curious and not kind.
Everyone who is either not creative or not curious is both calm and brave.
Paul is either kind or not humble.
Someone is both not wise and not generous.
Mary is tall.
Someone is not tall.
Someone is either not curious or not kind.
Lucy is not tall.
Alice is either rich or not tall.
Fred is both not strong and generous. | Alice is not tall. | contradiction | (((tall(fred)<~>humble(fred)))=>(?[X]:((~calm(X)<~>~strong(X)))))&
((?[X]:((~humble(X)&~strong(X))))<=>(?[X]:((~humble(X)<~>creative(X)))))&
((~quiet(lucy))<=>((~calm(mary)<~>~happy(mary))))&
(![X]:((~patient(X)|strong(X))=>(creative(X)&rich(X))))&
(![X]:(strong(X)=>(~funny(X)&~rich(X))))&
(((humble(alice)|quiet(alice)))<=>(?[X]:(creative(X))))&
(![X]:((~old(X)&old(X))=>(generous(X)|curious(X))))&
(((~rich(alice)<~>quiet(alice)))<=>(?[X]:((~quiet(X)&humble(X)))))&
(![X]:((calm(X)&~patient(X))<=>calm(X)))&
(![X]:((~kind(X)|generous(X))=>(wise(X)&~curious(X))))&
(![X]:((~old(X)|humble(X))<=>(~kind(X)|happy(X))))&
(![X]:(~humble(X)=>(rich(X)|~kind(X))))&
(![X]:((~creative(X)&~old(X))<=>(strong(X)&~generous(X))))&
(((~old(mary)|~calm(mary)))<=>(?[X]:(~quiet(X))))&
((?[X]:((~rich(X)|~brave(X))))=>(?[X]:((curious(X)&~kind(X)))))&
(![X]:((~creative(X)<~>~curious(X))=>(calm(X)&brave(X))))&
((kind(paul)<~>~humble(paul)))&
(?[X]:((~wise(X)&~generous(X))))&
(tall(mary))&
(?[X]:(~tall(X)))&
(?[X]:((~curious(X)<~>~kind(X))))&
(~tall(lucy))&
((rich(alice)<~>~tall(alice)))&
((~strong(fred)&generous(fred))) | ~tall(alice) | [
"p9",
"p14",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 6907938428632484283464581
% SZS output start Proof for 6907938428632484283464581
10. ! [X0] : ((generous(X0) | ~kind(X0)) => (~curious(X0) & wise(X0))) [input p9]
15. ? [X0] : (~brave(X0) | ~rich(X0)) => ? [X0] : (~kind(X0) & curious(X0)) [input p14]
23. rich(alice) <~> ~tall(alice) [input p22]
25. ~tall(alice) [input hypothesis]
27. ? [X0] : (~brave(X0) | ~rich(X0)) => ? [X1] : (~kind(X1) & curious(X1)) [rectify 15]
29. ? [X0] : ~rich(X0) => ? [X1] : (~kind(X1) & curious(X1)) [pure predicate removal 27]
36. ! [X0] : ((~curious(X0) & wise(X0)) | (~generous(X0) & kind(X0))) [ennf transformation 10]
39. ? [X1] : (~kind(X1) & curious(X1)) | ! [X0] : rich(X0) [ennf transformation 29]
70. ? [X0] : (~kind(X0) & curious(X0)) | ! [X1] : rich(X1) [rectify 39]
71. ? [X0] : (~kind(X0) & curious(X0)) => (~kind(sK6) & curious(sK6)) [choice axiom]
72. (~kind(sK6) & curious(sK6)) | ! [X1] : rich(X1) [skolemisation 70,71]
82. (tall(alice) | ~rich(alice)) & (~tall(alice) | rich(alice)) [nnf transformation 23]
117. ~curious(X0) | kind(X0) [cnf transformation 36]
131. curious(sK6) | rich(X1) [cnf transformation 72]
132. ~kind(sK6) | rich(X1) [cnf transformation 72]
145. tall(alice) | ~rich(alice) [cnf transformation 82]
148. ~tall(alice) [cnf transformation 25]
239. 20 <=> rich(alice) [avatar definition]
240. ~rich(alice) <- (~20) [avatar component clause 239]
272. 26 <=> ! [X1] : rich(X1) [avatar definition]
273. rich(X1) <- (26) [avatar component clause 272]
275. 27 <=> kind(sK6) [avatar definition]
277. ~kind(sK6) <- (~27) [avatar component clause 275]
278. 26 | ~27 [avatar split clause 132,275,272]
280. 28 <=> curious(sK6) [avatar definition]
282. curious(sK6) <- (28) [avatar component clause 280]
283. 26 | 28 [avatar split clause 131,280,272]
297. 31 <=> tall(alice) [avatar definition]
300. ~20 | 31 [avatar split clause 145,297,239]
302. ~31 [avatar split clause 148,297]
303. $false <- (~20, 26) [subsumption resolution 240,273]
304. 20 | ~26 [avatar contradiction clause 303]
310. kind(sK6) <- (28) [resolution 117,282]
311. $false <- (~27, 28) [subsumption resolution 310,277]
312. 27 | ~28 [avatar contradiction clause 311]
313. $false [avatar sat refutation 278,283,300,302,304,312]
% SZS output end Proof for 6907938428632484283464581
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient is old or not generous and vice versa. If alice is curious then someone is wise. Everyone who is not brave or not funny is both not generous and not strong. If someone is not wise or rich then someone is old or not brave and vice versa. Everyone who is either not happy or not tall is both curious and strong and vice versa. Everyone who is either not patient or strong is both kind and not funny and vice versa. If susan is both not tall and not old then someone is both wise and not rich. Everyone who is generous is not kind or not wise and vice versa. Everyone who is both wise and not creative is curious and vice versa. If someone is either not kind or creative then someone is either not patient or old. Everyone who is brave is not tall or generous and vice versa. Everyone who is generous or calm is either happy or tall. If someone is either not curious or rich then paul is creative or not curious and vice versa. Everyone who is either creative or old is not patient or quiet. If susan is curious or not generous then fred is both not patient and tall and vice versa. Someone is both not tall and not happy. Someone is both not brave and kind. John is not wise or not creative. Lucy is kind or not patient. Someone is not kind. Someone is either not quiet or not kind. Paul is either not calm or tall. | Susan is not tall. | neutral | (![X]:(patient(X)<=>(old(X)|~generous(X))))&
((curious(alice))=>(?[X]:(wise(X))))&
(![X]:((~brave(X)|~funny(X))=>(~generous(X)&~strong(X))))&
((?[X]:((~wise(X)|rich(X))))<=>(?[X]:((old(X)|~brave(X)))))&
(![X]:((~happy(X)<~>~tall(X))<=>(curious(X)&strong(X))))&
(![X]:((~patient(X)<~>strong(X))<=>(kind(X)&~funny(X))))&
(((~tall(susan)&~old(susan)))=>(?[X]:((wise(X)&~rich(X)))))&
(![X]:(generous(X)<=>(~kind(X)|~wise(X))))&
(![X]:((wise(X)&~creative(X))<=>curious(X)))&
((?[X]:((~kind(X)<~>creative(X))))=>(?[X]:((~patient(X)<~>old(X)))))&
(![X]:(brave(X)<=>(~tall(X)|generous(X))))&
(![X]:((generous(X)|calm(X))=>(happy(X)<~>tall(X))))&
((?[X]:((~curious(X)<~>rich(X))))<=>((creative(paul)|~curious(paul))))&
(![X]:((creative(X)<~>old(X))=>(~patient(X)|quiet(X))))&
(((curious(susan)|~generous(susan)))<=>((~patient(fred)&tall(fred))))&
(?[X]:((~tall(X)&~happy(X))))&
(?[X]:((~brave(X)&kind(X))))&
((~wise(john)|~creative(john)))&
((kind(lucy)|~patient(lucy)))&
(?[X]:(~kind(X)))&
(?[X]:((~quiet(X)<~>~kind(X))))&
((~calm(paul)<~>tall(paul))) | ~tall(susan) | [] | null | 0 |
If susan is curious then someone is both patient and calm.
If mary is either not generous or not curious then john is either not rich or rich and vice versa.
Everyone who is either curious or tall is either humble or not calm.
If susan is not quiet or not rich then someone is both patient and happy.
Everyone who is not strong or not quiet is either not brave or happy and vice versa.
If someone is either humble or calm then someone is not happy or not patient.
Everyone who is both calm and not wise is curious or not calm and vice versa.
Everyone who is either rich or quiet is either not funny or humble.
Everyone who is either not brave or not happy is both old and brave and vice versa.
If someone is either generous or not kind then someone is both not calm and humble and vice versa.
Everyone who is either patient or funny is not rich.
Everyone who is not brave or not patient is not funny and vice versa.
If alice is not creative then john is both not tall and quiet and vice versa.
Everyone who is both not funny and funny is quiet and vice versa.
Everyone who is quiet or not wise is not tall and vice versa.
If someone is quiet or not calm then lucy is not patient or not generous.
Someone is brave or not creative.
Someone is happy.
Lucy is not rich or not patient.
Alice is not old or creative.
Someone is both not quiet and patient.
Mary is old.
Someone is not generous or not curious.
John is either not creative or not funny. | Mary is rich. | contradiction | ((curious(susan))=>(?[X]:((patient(X)&calm(X)))))&
(((~generous(mary)<~>~curious(mary)))<=>((~rich(john)<~>rich(john))))&
(![X]:((curious(X)<~>tall(X))=>(humble(X)<~>~calm(X))))&
(((~quiet(susan)|~rich(susan)))=>(?[X]:((patient(X)&happy(X)))))&
(![X]:((~strong(X)|~quiet(X))<=>(~brave(X)<~>happy(X))))&
((?[X]:((humble(X)<~>calm(X))))=>(?[X]:((~happy(X)|~patient(X)))))&
(![X]:((calm(X)&~wise(X))<=>(curious(X)|~calm(X))))&
(![X]:((rich(X)<~>quiet(X))=>(~funny(X)<~>humble(X))))&
(![X]:((~brave(X)<~>~happy(X))<=>(old(X)&brave(X))))&
((?[X]:((generous(X)<~>~kind(X))))<=>(?[X]:((~calm(X)&humble(X)))))&
(![X]:((patient(X)<~>funny(X))=>~rich(X)))&
(![X]:((~brave(X)|~patient(X))<=>~funny(X)))&
((~creative(alice))<=>((~tall(john)&quiet(john))))&
(![X]:((~funny(X)&funny(X))<=>quiet(X)))&
(![X]:((quiet(X)|~wise(X))<=>~tall(X)))&
((?[X]:((quiet(X)|~calm(X))))=>((~patient(lucy)|~generous(lucy))))&
(?[X]:((brave(X)|~creative(X))))&
(?[X]:(happy(X)))&
((~rich(lucy)|~patient(lucy)))&
((~old(alice)|creative(alice)))&
(?[X]:((~quiet(X)&patient(X))))&
(old(mary))&
(?[X]:((~generous(X)|~curious(X))))&
((~creative(john)<~>~funny(john))) | rich(mary) | [
"p2",
"p4",
"p6",
"p7",
"p8",
"p11",
"p13",
"p14",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 7506549696759649889578824
% SZS output start Proof for 7506549696759649889578824
3. ! [X0] : ((curious(X0) <~> tall(X0)) => (humble(X0) <~> ~calm(X0))) [input p2]
5. ! [X0] : ((~quiet(X0) | ~strong(X0)) <=> (~brave(X0) <~> happy(X0))) [input p4]
7. ! [X0] : ((~wise(X0) & calm(X0)) <=> (~calm(X0) | curious(X0))) [input p6]
8. ! [X0] : ((rich(X0) <~> quiet(X0)) => (~funny(X0) <~> humble(X0))) [input p7]
9. ! [X0] : ((~brave(X0) <~> ~happy(X0)) <=> (brave(X0) & old(X0))) [input p8]
12. ! [X0] : ((~patient(X0) | ~brave(X0)) <=> ~funny(X0)) [input p11]
14. ! [X0] : ((funny(X0) & ~funny(X0)) <=> quiet(X0)) [input p13]
15. ! [X0] : ((~wise(X0) | quiet(X0)) <=> ~tall(X0)) [input p14]
22. old(mary) [input p21]
25. rich(mary) [input hypothesis]
29. ! [X0] : ((humble(X0) <~> ~calm(X0)) | (curious(X0) <=> tall(X0))) [ennf transformation 3]
32. ! [X0] : ((~funny(X0) <~> humble(X0)) | (rich(X0) <=> quiet(X0))) [ennf transformation 8]
39. ! [X0] : (((calm(X0) | ~humble(X0)) & (~calm(X0) | humble(X0))) | ((curious(X0) | ~tall(X0)) & (tall(X0) | ~curious(X0)))) [nnf transformation 29]
42. ! [X0] : (((~quiet(X0) | ~strong(X0)) | ((~brave(X0) | ~happy(X0)) & (happy(X0) | brave(X0)))) & (((~happy(X0) | brave(X0)) & (happy(X0) | ~brave(X0))) | (quiet(X0) & strong(X0)))) [nnf transformation 5]
43. ! [X0] : ((~quiet(X0) | ~strong(X0) | ((~brave(X0) | ~happy(X0)) & (happy(X0) | brave(X0)))) & (((~happy(X0) | brave(X0)) & (happy(X0) | ~brave(X0))) | (quiet(X0) & strong(X0)))) [flattening 42]
48. ! [X0] : (((~wise(X0) & calm(X0)) | (calm(X0) & ~curious(X0))) & ((~calm(X0) | curious(X0)) | (wise(X0) | ~calm(X0)))) [nnf transformation 7]
49. ! [X0] : (((~wise(X0) & calm(X0)) | (calm(X0) & ~curious(X0))) & (~calm(X0) | curious(X0) | wise(X0) | ~calm(X0))) [flattening 48]
50. ! [X0] : (((~humble(X0) | funny(X0)) & (humble(X0) | ~funny(X0))) | ((rich(X0) | ~quiet(X0)) & (quiet(X0) | ~rich(X0)))) [nnf transformation 32]
51. ! [X0] : ((((happy(X0) | brave(X0)) & (~happy(X0) | ~brave(X0))) | (~brave(X0) | ~old(X0))) & ((brave(X0) & old(X0)) | ((~brave(X0) | happy(X0)) & (~happy(X0) | brave(X0))))) [nnf transformation 9]
52. ! [X0] : ((((happy(X0) | brave(X0)) & (~happy(X0) | ~brave(X0))) | ~brave(X0) | ~old(X0)) & ((brave(X0) & old(X0)) | ((~brave(X0) | happy(X0)) & (~happy(X0) | brave(X0))))) [flattening 51]
59. ! [X0] : (((~patient(X0) | ~brave(X0)) | funny(X0)) & (~funny(X0) | (patient(X0) & brave(X0)))) [nnf transformation 12]
60. ! [X0] : ((~patient(X0) | ~brave(X0) | funny(X0)) & (~funny(X0) | (patient(X0) & brave(X0)))) [flattening 59]
63. ! [X0] : (((funny(X0) & ~funny(X0)) | ~quiet(X0)) & (quiet(X0) | (~funny(X0) | funny(X0)))) [nnf transformation 14]
64. ! [X0] : (((funny(X0) & ~funny(X0)) | ~quiet(X0)) & (quiet(X0) | ~funny(X0) | funny(X0))) [flattening 63]
65. ! [X0] : (((~wise(X0) | quiet(X0)) | tall(X0)) & (~tall(X0) | (wise(X0) & ~quiet(X0)))) [nnf transformation 15]
66. ! [X0] : ((~wise(X0) | quiet(X0) | tall(X0)) & (~tall(X0) | (wise(X0) & ~quiet(X0)))) [flattening 65]
86. ~calm(X0) | humble(X0) | tall(X0) | ~curious(X0) [cnf transformation 39]
87. ~tall(X0) | humble(X0) | curious(X0) | ~calm(X0) [cnf transformation 39]
95. ~brave(X0) | happy(X0) | quiet(X0) [cnf transformation 43]
102. ~calm(X0) | curious(X0) | wise(X0) | ~calm(X0) [cnf transformation 49]
104. calm(X0) | calm(X0) [cnf transformation 49]
105. ~wise(X0) | ~curious(X0) [cnf transformation 49]
109. ~humble(X0) | funny(X0) | quiet(X0) | ~rich(X0) [cnf transformation 50]
113. brave(X0) | ~happy(X0) | brave(X0) [cnf transformation 52]
115. ~happy(X0) | ~brave(X0) | ~brave(X0) | ~old(X0) [cnf transformation 52]
125. ~funny(X0) | brave(X0) [cnf transformation 60]
132. ~funny(X0) | ~quiet(X0) [cnf transformation 64]
133. ~quiet(X0) | funny(X0) [cnf transformation 64]
135. ~tall(X0) | wise(X0) [cnf transformation 66]
136. ~wise(X0) | quiet(X0) | tall(X0) [cnf transformation 66]
145. old(mary) [cnf transformation 22]
149. rich(mary) [cnf transformation 25]
150. ~happy(X0) | brave(X0) [duplicate literal removal 113]
151. ~old(X0) | ~brave(X0) | ~happy(X0) [duplicate literal removal 115]
152. ~calm(X0) | curious(X0) | wise(X0) [duplicate literal removal 102]
153. calm(X0) [duplicate literal removal 104]
181. 6 <=> curious(mary) [avatar definition]
183. curious(mary) <- (6) [avatar component clause 181]
224. wise(X0) | curious(X0) [subsumption resolution 152,153]
256. ~quiet(X0) [subsumption resolution 132,133]
257. ~wise(X0) | tall(X0) [subsumption resolution 136,256]
309. tall(X0) | curious(X0) [resolution 257,224]
329. 31 <=> funny(mary) [avatar definition]
331. funny(mary) <- (31) [avatar component clause 329]
354. ~brave(mary) | ~happy(mary) [resolution 151,145]
355. ~happy(mary) [subsumption resolution 354,150]
356. humble(X0) | tall(X0) | ~curious(X0) [resolution 86,153]
357. humble(X0) | tall(X0) [subsumption resolution 356,309]
358. humble(X0) | curious(X0) | ~calm(X0) | curious(X0) [resolution 87,309]
359. humble(X0) | curious(X0) | ~calm(X0) [duplicate literal removal 358]
360. humble(X0) | curious(X0) [subsumption resolution 359,153]
384. funny(X0) | quiet(X0) | ~rich(X0) | curious(X0) [resolution 109,360]
385. funny(X1) | quiet(X1) | ~rich(X1) | tall(X1) [resolution 109,357]
386. ~rich(X0) | funny(X0) | curious(X0) [subsumption resolution 384,256]
387. ~rich(X1) | funny(X1) | tall(X1) [subsumption resolution 385,256]
388. funny(mary) | tall(mary) [resolution 387,149]
391. 38 <=> tall(mary) [avatar definition]
393. tall(mary) <- (38) [avatar component clause 391]
394. 38 | 31 [avatar split clause 388,329,391]
401. wise(mary) <- (38) [resolution 393,135]
404. funny(mary) | curious(mary) [resolution 386,149]
415. brave(mary) <- (31) [resolution 331,125]
429. happy(mary) | quiet(mary) <- (31) [resolution 415,95]
431. quiet(mary) <- (31) [subsumption resolution 429,355]
432. $false <- (31) [subsumption resolution 431,256]
433. ~31 [avatar contradiction clause 432]
435. 6 | 31 [avatar split clause 404,329,181]
438. ~curious(mary) <- (38) [resolution 401,105]
439. $false <- (6, 38) [subsumption resolution 438,183]
440. ~6 | ~38 [avatar contradiction clause 439]
441. $false [avatar sat refutation 394,433,435,440]
% SZS output end Proof for 7506549696759649889578824
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
If john is happy or not curious then susan is not quiet and vice versa.
Everyone who is wise is old.
Everyone who is both not old and not rich is old or not strong and vice versa.
Everyone who is either rich or not humble is either not rich or funny.
Everyone who is either quiet or not patient is either not wise or creative.
Everyone who is happy is not wise and vice versa.
If someone is both not tall and not happy then susan is brave and vice versa.
If someone is patient or not curious then paul is generous.
If lucy is both quiet and not tall then paul is both kind and not old and vice versa.
Everyone who is either funny or not calm is not old or wise and vice versa.
Everyone who is either wise or rich is both not humble and patient.
Everyone who is either not brave or patient is either not quiet or not calm and vice versa.
If someone is either not calm or not tall then susan is either wise or not rich and vice versa.
Everyone who is not creative is not quiet.
If someone is both funny and not patient then lucy is either funny or not wise and vice versa.
Everyone who is strong is not quiet.
John is both not old and not brave.
Paul is both not calm and curious.
Someone is either calm or not happy.
Someone is either not curious or funny.
Mary is not rich or happy. | Lucy is not rich. | neutral | (((happy(john)|~curious(john)))<=>(~quiet(susan)))&
(![X]:(wise(X)=>old(X)))&
(![X]:((~old(X)&~rich(X))<=>(old(X)|~strong(X))))&
(![X]:((rich(X)<~>~humble(X))=>(~rich(X)<~>funny(X))))&
(![X]:((quiet(X)<~>~patient(X))=>(~wise(X)<~>creative(X))))&
(![X]:(happy(X)<=>~wise(X)))&
((?[X]:((~tall(X)&~happy(X))))<=>(brave(susan)))&
((?[X]:((patient(X)|~curious(X))))=>(generous(paul)))&
(((quiet(lucy)&~tall(lucy)))<=>((kind(paul)&~old(paul))))&
(![X]:((funny(X)<~>~calm(X))<=>(~old(X)|wise(X))))&
(![X]:((wise(X)<~>rich(X))=>(~humble(X)&patient(X))))&
(![X]:((~brave(X)<~>patient(X))<=>(~quiet(X)<~>~calm(X))))&
((?[X]:((~calm(X)<~>~tall(X))))<=>((wise(susan)<~>~rich(susan))))&
(![X]:(~creative(X)=>~quiet(X)))&
((?[X]:((funny(X)&~patient(X))))<=>((funny(lucy)<~>~wise(lucy))))&
(![X]:(strong(X)=>~quiet(X)))&
((~old(john)&~brave(john)))&
((~calm(paul)&curious(paul)))&
(?[X]:((calm(X)<~>~happy(X))))&
(?[X]:((~curious(X)<~>funny(X))))&
((~rich(mary)|happy(mary))) | ~rich(lucy) | [] | null | 0 |
If someone is either quiet or not wise then someone is either happy or not brave and vice versa.
Everyone who is not kind is generous.
Everyone who is either old or funny is not generous or tall.
If someone is either not tall or kind then someone is not curious and vice versa.
Everyone who is both strong and not brave is both not happy and not patient.
If john is either not rich or creative then someone is either kind or patient.
Everyone who is not kind or not generous is humble or not quiet and vice versa.
Everyone who is either generous or creative is either not creative or not strong and vice versa.
If someone is not kind then someone is either curious or calm and vice versa.
Everyone who is both happy and not curious is either kind or not calm.
Everyone who is either not kind or not humble is either not calm or not curious and vice versa.
If someone is not strong or not kind then susan is both funny and not humble and vice versa.
If mary is not wise then lucy is tall.
Everyone who is both creative and not quiet is either rich or not strong and vice versa.
John is wise or curious.
Someone is not funny.
Someone is both not happy and creative.
Alice is brave or not old.
Susan is not generous or tall. | John is not wise. | neutral | ((?[X]:((quiet(X)<~>~wise(X))))<=>(?[X]:((happy(X)<~>~brave(X)))))&
(![X]:(~kind(X)=>generous(X)))&
(![X]:((old(X)<~>funny(X))=>(~generous(X)|tall(X))))&
((?[X]:((~tall(X)<~>kind(X))))<=>(?[X]:(~curious(X))))&
(![X]:((strong(X)&~brave(X))=>(~happy(X)&~patient(X))))&
(((~rich(john)<~>creative(john)))=>(?[X]:((kind(X)<~>patient(X)))))&
(![X]:((~kind(X)|~generous(X))<=>(humble(X)|~quiet(X))))&
(![X]:((generous(X)<~>creative(X))<=>(~creative(X)<~>~strong(X))))&
((?[X]:(~kind(X)))<=>(?[X]:((curious(X)<~>calm(X)))))&
(![X]:((happy(X)&~curious(X))=>(kind(X)<~>~calm(X))))&
(![X]:((~kind(X)<~>~humble(X))<=>(~calm(X)<~>~curious(X))))&
((?[X]:((~strong(X)|~kind(X))))<=>((funny(susan)&~humble(susan))))&
((~wise(mary))=>(tall(lucy)))&
(![X]:((creative(X)&~quiet(X))<=>(rich(X)<~>~strong(X))))&
((wise(john)|curious(john)))&
(?[X]:(~funny(X)))&
(?[X]:((~happy(X)&creative(X))))&
((brave(alice)|~old(alice)))&
((~generous(susan)|tall(susan))) | ~wise(john) | [] | null | 0 |
If paul is creative then someone is either kind or not humble.
Everyone who is quiet is not curious.
If john is not creative then fred is both rich and not old.
If john is strong then alice is creative or not tall.
Everyone who is either not quiet or not wise is old and vice versa.
Everyone who is not strong is both quiet and rich.
Everyone who is not tall is not happy or creative.
Everyone who is either humble or not old is both not kind and humble and vice versa.
If someone is not creative then fred is strong.
If lucy is either patient or not brave then someone is generous or quiet.
If john is not brave then someone is not kind and vice versa.
Everyone who is both kind and not happy is not quiet.
Everyone who is not quiet is not patient and vice versa.
Everyone who is either not happy or not curious is both not brave and strong and vice versa.
Everyone who is both not kind and creative is either curious or not happy and vice versa.
Everyone who is not quiet or rich is either not kind or patient and vice versa.
Fred is both not rich and not funny.
Mary is either brave or not kind.
Alice is both quiet and happy.
Someone is both not humble and old.
Paul is creative or strong.
Mary is either not wise or wise.
Someone is humble or not patient. | Alice is not creative. | contradiction | ((creative(paul))=>(?[X]:((kind(X)<~>~humble(X)))))&
(![X]:(quiet(X)=>~curious(X)))&
((~creative(john))=>((rich(fred)&~old(fred))))&
((strong(john))=>((creative(alice)|~tall(alice))))&
(![X]:((~quiet(X)<~>~wise(X))<=>old(X)))&
(![X]:(~strong(X)=>(quiet(X)&rich(X))))&
(![X]:(~tall(X)=>(~happy(X)|creative(X))))&
(![X]:((humble(X)<~>~old(X))<=>(~kind(X)&humble(X))))&
((?[X]:(~creative(X)))=>(strong(fred)))&
(((patient(lucy)<~>~brave(lucy)))=>(?[X]:((generous(X)|quiet(X)))))&
((~brave(john))<=>(?[X]:(~kind(X))))&
(![X]:((kind(X)&~happy(X))=>~quiet(X)))&
(![X]:(~quiet(X)<=>~patient(X)))&
(![X]:((~happy(X)<~>~curious(X))<=>(~brave(X)&strong(X))))&
(![X]:((~kind(X)&creative(X))<=>(curious(X)<~>~happy(X))))&
(![X]:((~quiet(X)|rich(X))<=>(~kind(X)<~>patient(X))))&
((~rich(fred)&~funny(fred)))&
((brave(mary)<~>~kind(mary)))&
((quiet(alice)&happy(alice)))&
(?[X]:((~humble(X)&old(X))))&
((creative(paul)|strong(paul)))&
((~wise(mary)<~>wise(mary)))&
(?[X]:((humble(X)|~patient(X)))) | ~creative(alice) | [
"p3",
"p5",
"p6",
"p11",
"p12",
"p13",
"p14",
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 8068209555154707663356834
% SZS output start Proof for 8068209555154707663356834
4. strong(john) => (~tall(alice) | creative(alice)) [input p3]
6. ! [X0] : (~strong(X0) => (rich(X0) & quiet(X0))) [input p5]
7. ! [X0] : (~tall(X0) => (creative(X0) | ~happy(X0))) [input p6]
12. ! [X0] : ((~happy(X0) & kind(X0)) => ~quiet(X0)) [input p11]
13. ! [X0] : (~quiet(X0) <=> ~patient(X0)) [input p12]
14. ! [X0] : ((~happy(X0) <~> ~curious(X0)) <=> (strong(X0) & ~brave(X0))) [input p13]
15. ! [X0] : ((creative(X0) & ~kind(X0)) <=> (curious(X0) <~> ~happy(X0))) [input p14]
16. ! [X0] : ((rich(X0) | ~quiet(X0)) <=> (~kind(X0) <~> patient(X0))) [input p15]
19. happy(alice) & quiet(alice) [input p18]
24. ~creative(alice) [input hypothesis]
30. (~tall(alice) | creative(alice)) | ~strong(john) [ennf transformation 4]
31. ~tall(alice) | creative(alice) | ~strong(john) [flattening 30]
32. ! [X0] : ((rich(X0) & quiet(X0)) | strong(X0)) [ennf transformation 6]
33. ! [X0] : ((creative(X0) | ~happy(X0)) | tall(X0)) [ennf transformation 7]
34. ! [X0] : (creative(X0) | ~happy(X0) | tall(X0)) [flattening 33]
36. ! [X0] : (~quiet(X0) | (happy(X0) | ~kind(X0))) [ennf transformation 12]
37. ! [X0] : (~quiet(X0) | happy(X0) | ~kind(X0)) [flattening 36]
48. ! [X0] : ((~quiet(X0) | patient(X0)) & (~patient(X0) | quiet(X0))) [nnf transformation 13]
49. ! [X0] : ((((curious(X0) | happy(X0)) & (~curious(X0) | ~happy(X0))) | (~strong(X0) | brave(X0))) & ((strong(X0) & ~brave(X0)) | ((~happy(X0) | curious(X0)) & (~curious(X0) | happy(X0))))) [nnf transformation 14]
50. ! [X0] : ((((curious(X0) | happy(X0)) & (~curious(X0) | ~happy(X0))) | ~strong(X0) | brave(X0)) & ((strong(X0) & ~brave(X0)) | ((~happy(X0) | curious(X0)) & (~curious(X0) | happy(X0))))) [flattening 49]
51. ! [X0] : (((creative(X0) & ~kind(X0)) | ((curious(X0) | happy(X0)) & (~happy(X0) | ~curious(X0)))) & (((happy(X0) | ~curious(X0)) & (~happy(X0) | curious(X0))) | (~creative(X0) | kind(X0)))) [nnf transformation 15]
52. ! [X0] : (((creative(X0) & ~kind(X0)) | ((curious(X0) | happy(X0)) & (~happy(X0) | ~curious(X0)))) & (((happy(X0) | ~curious(X0)) & (~happy(X0) | curious(X0))) | ~creative(X0) | kind(X0))) [flattening 51]
53. ! [X0] : (((rich(X0) | ~quiet(X0)) | ((~kind(X0) | ~patient(X0)) & (patient(X0) | kind(X0)))) & (((~patient(X0) | kind(X0)) & (patient(X0) | ~kind(X0))) | (~rich(X0) & quiet(X0)))) [nnf transformation 16]
54. ! [X0] : ((rich(X0) | ~quiet(X0) | ((~kind(X0) | ~patient(X0)) & (patient(X0) | kind(X0)))) & (((~patient(X0) | kind(X0)) & (patient(X0) | ~kind(X0))) | (~rich(X0) & quiet(X0)))) [flattening 53]
66. ~tall(alice) | creative(alice) | ~strong(john) [cnf transformation 31]
71. strong(X0) | quiet(X0) [cnf transformation 32]
72. strong(X0) | rich(X0) [cnf transformation 32]
73. ~happy(X0) | creative(X0) | tall(X0) [cnf transformation 34]
83. ~quiet(X0) | happy(X0) | ~kind(X0) [cnf transformation 37]
85. ~quiet(X0) | patient(X0) [cnf transformation 48]
89. ~happy(X0) | strong(X0) | curious(X0) [cnf transformation 50]
94. ~happy(X0) | ~kind(X0) | ~curious(X0) [cnf transformation 52]
101. ~patient(X0) | kind(X0) | ~rich(X0) [cnf transformation 54]
108. happy(alice) [cnf transformation 19]
115. ~creative(alice) [cnf transformation 24]
147. 7 <=> strong(john) [avatar definition]
149. ~strong(john) <- (~7) [avatar component clause 147]
151. 8 <=> creative(alice) [avatar definition]
152. ~creative(alice) <- (~8) [avatar component clause 151]
155. 9 <=> tall(alice) [avatar definition]
158. ~7 | 8 | ~9 [avatar split clause 66,155,151,147]
207. ~8 [avatar split clause 115,151]
254. creative(alice) | tall(alice) [resolution 73,108]
255. tall(alice) <- (~8) [subsumption resolution 254,152]
258. 9 | 8 [avatar split clause 255,151,155]
259. rich(john) <- (~7) [resolution 149,72]
260. quiet(john) <- (~7) [resolution 149,71]
268. happy(john) | ~kind(john) <- (~7) [resolution 260,83]
270. patient(john) <- (~7) [resolution 260,85]
272. 26 <=> kind(john) [avatar definition]
273. kind(john) <- (26) [avatar component clause 272]
276. 27 <=> happy(john) [avatar definition]
278. happy(john) <- (27) [avatar component clause 276]
279. ~26 | 27 | 7 [avatar split clause 268,147,276,272]
311. kind(john) | ~rich(john) <- (~7) [resolution 101,270]
324. kind(john) <- (~7) [subsumption resolution 311,259]
325. 26 | 7 [avatar split clause 324,147,272]
341. ~kind(john) | ~curious(john) <- (27) [resolution 278,94]
342. strong(john) | curious(john) <- (27) [resolution 278,89]
344. ~curious(john) <- (26, 27) [subsumption resolution 341,273]
345. curious(john) <- (~7, 27) [subsumption resolution 342,149]
346. $false <- (~7, 26, 27) [subsumption resolution 345,344]
347. 7 | ~26 | ~27 [avatar contradiction clause 346]
348. $false [avatar sat refutation 158,207,258,279,325,347]
% SZS output end Proof for 8068209555154707663356834
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either strong or not happy then lucy is not humble or old and vice versa. Everyone who is either not curious or generous is either not brave or rich and vice versa. Everyone who is either not happy or curious is either not creative or not tall and vice versa. Everyone who is not wise or not brave is not brave or not generous and vice versa. Everyone who is not tall or patient is either not brave or not kind and vice versa. Everyone who is not funny or rich is strong or tall and vice versa. If paul is both not old and creative then susan is not humble or not rich. If someone is either happy or calm then lucy is not patient and vice versa. If mary is not creative then mary is either not happy or strong. If paul is funny or not humble then someone is both quiet and kind. If paul is both curious and happy then someone is both funny and not happy and vice versa. Everyone who is both quiet and not wise is both not old and brave. Everyone who is not wise is both tall and not generous and vice versa. Everyone who is either not curious or happy is kind or not kind and vice versa. Everyone who is both kind and not kind is both creative and wise and vice versa. If susan is either not kind or not funny then someone is not old or quiet. Someone is both not patient and not funny. Mary is either not kind or curious. Someone is funny. Fred is funny or old. John is both kind and not wise. John is either generous or calm. Someone is either not strong or wise. Lucy is either generous or patient. | Lucy is tall. | entailment | ((?[X]:((strong(X)<~>~happy(X))))<=>((~humble(lucy)|old(lucy))))&
(![X]:((~curious(X)<~>generous(X))<=>(~brave(X)<~>rich(X))))&
(![X]:((~happy(X)<~>curious(X))<=>(~creative(X)<~>~tall(X))))&
(![X]:((~wise(X)|~brave(X))<=>(~brave(X)|~generous(X))))&
(![X]:((~tall(X)|patient(X))<=>(~brave(X)<~>~kind(X))))&
(![X]:((~funny(X)|rich(X))<=>(strong(X)|tall(X))))&
(((~old(paul)&creative(paul)))=>((~humble(susan)|~rich(susan))))&
((?[X]:((happy(X)<~>calm(X))))<=>(~patient(lucy)))&
((~creative(mary))=>((~happy(mary)<~>strong(mary))))&
(((funny(paul)|~humble(paul)))=>(?[X]:((quiet(X)&kind(X)))))&
(((curious(paul)&happy(paul)))<=>(?[X]:((funny(X)&~happy(X)))))&
(![X]:((quiet(X)&~wise(X))=>(~old(X)&brave(X))))&
(![X]:(~wise(X)<=>(tall(X)&~generous(X))))&
(![X]:((~curious(X)<~>happy(X))<=>(kind(X)|~kind(X))))&
(![X]:((kind(X)&~kind(X))<=>(creative(X)&wise(X))))&
(((~kind(susan)<~>~funny(susan)))=>(?[X]:((~old(X)|quiet(X)))))&
(?[X]:((~patient(X)&~funny(X))))&
((~kind(mary)<~>curious(mary)))&
(?[X]:(funny(X)))&
((funny(fred)|old(fred)))&
((kind(john)&~wise(john)))&
((generous(john)<~>calm(john)))&
(?[X]:((~strong(X)<~>wise(X))))&
((generous(lucy)<~>patient(lucy))) | tall(lucy) | [
"p2",
"p12",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 554453767988915377419722
% SZS output start Proof for 554453767988915377419722
3. ! [X0] : ((~happy(X0) <~> curious(X0)) <=> (~creative(X0) <~> ~tall(X0))) [input p2]
13. ! [X0] : (~wise(X0) <=> (~generous(X0) & tall(X0))) [input p12]
14. ! [X0] : ((~curious(X0) <~> happy(X0)) <=> (~kind(X0) | kind(X0))) [input p13]
15. ! [X0] : ((~kind(X0) & kind(X0)) <=> (wise(X0) & creative(X0))) [input p14]
25. ~tall(lucy) [input hypothesis]
39. ! [X0] : ((((~curious(X0) | happy(X0)) & (curious(X0) | ~happy(X0))) | ((~creative(X0) | tall(X0)) & (~tall(X0) | creative(X0)))) & (((tall(X0) | creative(X0)) & (~tall(X0) | ~creative(X0))) | ((~happy(X0) | ~curious(X0)) & (curious(X0) | happy(X0))))) [nnf transformation 3]
58. ! [X0] : ((~wise(X0) | (generous(X0) | ~tall(X0))) & ((~generous(X0) & tall(X0)) | wise(X0))) [nnf transformation 13]
59. ! [X0] : ((~wise(X0) | generous(X0) | ~tall(X0)) & ((~generous(X0) & tall(X0)) | wise(X0))) [flattening 58]
60. ! [X0] : ((((~happy(X0) | curious(X0)) & (happy(X0) | ~curious(X0))) | (kind(X0) & ~kind(X0))) & ((~kind(X0) | kind(X0)) | ((~curious(X0) | ~happy(X0)) & (happy(X0) | curious(X0))))) [nnf transformation 14]
61. ! [X0] : ((((~happy(X0) | curious(X0)) & (happy(X0) | ~curious(X0))) | (kind(X0) & ~kind(X0))) & (~kind(X0) | kind(X0) | ((~curious(X0) | ~happy(X0)) & (happy(X0) | curious(X0))))) [flattening 60]
62. ! [X0] : (((~kind(X0) & kind(X0)) | (~wise(X0) | ~creative(X0))) & ((wise(X0) & creative(X0)) | (kind(X0) | ~kind(X0)))) [nnf transformation 15]
63. ! [X0] : (((~kind(X0) & kind(X0)) | ~wise(X0) | ~creative(X0)) & ((wise(X0) & creative(X0)) | kind(X0) | ~kind(X0))) [flattening 62]
93. tall(X0) | creative(X0) | curious(X0) | happy(X0) [cnf transformation 39]
94. ~curious(X0) | creative(X0) | ~happy(X0) | tall(X0) [cnf transformation 39]
130. wise(X0) | tall(X0) [cnf transformation 59]
135. happy(X0) | ~curious(X0) | ~kind(X0) [cnf transformation 61]
136. ~curious(X0) | happy(X0) | kind(X0) [cnf transformation 61]
137. ~happy(X0) | curious(X0) | ~kind(X0) [cnf transformation 61]
138. ~happy(X0) | curious(X0) | kind(X0) [cnf transformation 61]
141. kind(X0) | ~wise(X0) | ~creative(X0) [cnf transformation 63]
142. ~kind(X0) | ~wise(X0) | ~creative(X0) [cnf transformation 63]
159. ~tall(lucy) [cnf transformation 25]
284. ~happy(X0) | curious(X0) [subsumption resolution 137,138]
285. ~curious(X0) | happy(X0) [subsumption resolution 135,136]
286. ~wise(X0) | ~creative(X0) [subsumption resolution 141,142]
365. ~creative(X0) | tall(X0) [resolution 286,130]
501. 58 <=> happy(lucy) [avatar definition]
503. happy(lucy) <- (58) [avatar component clause 501]
513. 60 <=> curious(lucy) [avatar definition]
515. curious(lucy) <- (60) [avatar component clause 513]
612. creative(lucy) | curious(lucy) | happy(lucy) [resolution 93,159]
638. happy(lucy) <- (60) [resolution 515,285]
643. 58 | ~60 [avatar split clause 638,513,501]
648. creative(lucy) | curious(lucy) [subsumption resolution 612,284]
650. 72 <=> creative(lucy) [avatar definition]
651. ~creative(lucy) <- (~72) [avatar component clause 650]
652. creative(lucy) <- (72) [avatar component clause 650]
653. 60 | 72 [avatar split clause 648,650,513]
661. tall(lucy) <- (72) [resolution 652,365]
662. $false <- (72) [subsumption resolution 661,159]
663. ~72 [avatar contradiction clause 662]
727. creative(lucy) | ~happy(lucy) | tall(lucy) <- (60) [resolution 515,94]
731. ~happy(lucy) | tall(lucy) <- (60, ~72) [subsumption resolution 727,651]
732. tall(lucy) <- (58, 60, ~72) [subsumption resolution 731,503]
733. $false <- (58, 60, ~72) [subsumption resolution 732,159]
734. ~58 | ~60 | 72 [avatar contradiction clause 733]
739. $false [avatar sat refutation 643,653,663,734]
% SZS output end Proof for 554453767988915377419722
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.021 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not curious and not humble is either strong or curious and vice versa.
Everyone who is both not calm and generous is strong or tall.
If paul is not humble then susan is patient or not brave and vice versa.
If paul is either not rich or patient then fred is both happy and not rich.
If someone is tall then someone is not curious and vice versa.
If someone is wise or not happy then paul is either kind or tall and vice versa.
Everyone who is not generous is tall and vice versa.
If someone is either not brave or strong then someone is either not quiet or tall and vice versa.
If someone is both calm and not wise then alice is funny or calm and vice versa.
If paul is quiet then alice is both not curious and not calm.
If john is brave then john is either not funny or not kind and vice versa.
Everyone who is not quiet is not wise.
Everyone who is both not wise and strong is rich or humble and vice versa.
Everyone who is not generous is both not strong and not patient.
If fred is tall or funny then mary is strong.
Fred is kind or curious.
Lucy is either funny or not humble.
Lucy is either funny or not patient.
Alice is not wise or calm.
Mary is not generous or wise.
Someone is not curious or not patient.
Fred is not kind or strong. | Fred is not curious. | contradiction | (![X]:((~curious(X)&~humble(X))<=>(strong(X)<~>curious(X))))&
(![X]:((~calm(X)&generous(X))=>(strong(X)|tall(X))))&
((~humble(paul))<=>((patient(susan)|~brave(susan))))&
(((~rich(paul)<~>patient(paul)))=>((happy(fred)&~rich(fred))))&
((?[X]:(tall(X)))<=>(?[X]:(~curious(X))))&
((?[X]:((wise(X)|~happy(X))))<=>((kind(paul)<~>tall(paul))))&
(![X]:(~generous(X)<=>tall(X)))&
((?[X]:((~brave(X)<~>strong(X))))<=>(?[X]:((~quiet(X)<~>tall(X)))))&
((?[X]:((calm(X)&~wise(X))))<=>((funny(alice)|calm(alice))))&
((quiet(paul))=>((~curious(alice)&~calm(alice))))&
((brave(john))<=>((~funny(john)<~>~kind(john))))&
(![X]:(~quiet(X)=>~wise(X)))&
(![X]:((~wise(X)&strong(X))<=>(rich(X)|humble(X))))&
(![X]:(~generous(X)=>(~strong(X)&~patient(X))))&
(((tall(fred)|funny(fred)))=>(strong(mary)))&
((kind(fred)|curious(fred)))&
((funny(lucy)<~>~humble(lucy)))&
((funny(lucy)<~>~patient(lucy)))&
((~wise(alice)|calm(alice)))&
((~generous(mary)|wise(mary)))&
(?[X]:((~curious(X)|~patient(X))))&
((~kind(fred)|strong(fred))) | ~curious(fred) | [
"p0",
"p4",
"p6",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 2476122070185572766591972
% SZS output start Proof for 2476122070185572766591972
1. ! [X0] : ((~humble(X0) & ~curious(X0)) <=> (strong(X0) <~> curious(X0))) [input p0]
5. ? [X0] : tall(X0) <=> ? [X0] : ~curious(X0) [input p4]
7. ! [X0] : (~generous(X0) <=> tall(X0)) [input p6]
13. ! [X0] : ((strong(X0) & ~wise(X0)) <=> (humble(X0) | rich(X0))) [input p12]
14. ! [X0] : (~generous(X0) => (~patient(X0) & ~strong(X0))) [input p13]
23. ~curious(fred) [input hypothesis]
24. ? [X0] : tall(X0) <=> ? [X1] : ~curious(X1) [rectify 5]
31. ! [X0] : ((~patient(X0) & ~strong(X0)) | generous(X0)) [ennf transformation 14]
33. ! [X0] : (((~humble(X0) & ~curious(X0)) | ((strong(X0) | ~curious(X0)) & (curious(X0) | ~strong(X0)))) & (((~curious(X0) | ~strong(X0)) & (curious(X0) | strong(X0))) | (humble(X0) | curious(X0)))) [nnf transformation 1]
34. ! [X0] : (((~humble(X0) & ~curious(X0)) | ((strong(X0) | ~curious(X0)) & (curious(X0) | ~strong(X0)))) & (((~curious(X0) | ~strong(X0)) & (curious(X0) | strong(X0))) | humble(X0) | curious(X0))) [flattening 33]
38. (? [X0] : tall(X0) | ! [X1] : curious(X1)) & (? [X1] : ~curious(X1) | ! [X0] : ~tall(X0)) [nnf transformation 24]
39. (? [X0] : tall(X0) | ! [X1] : curious(X1)) & (? [X2] : ~curious(X2) | ! [X3] : ~tall(X3)) [rectify 38]
40. ? [X0] : tall(X0) => tall(sK0) [choice axiom]
41. ? [X2] : ~curious(X2) => ~curious(sK1) [choice axiom]
42. (tall(sK0) | ! [X1] : curious(X1)) & (~curious(sK1) | ! [X3] : ~tall(X3)) [skolemisation 39,41,40]
47. ! [X0] : ((~generous(X0) | ~tall(X0)) & (tall(X0) | generous(X0))) [nnf transformation 7]
59. ! [X0] : (((strong(X0) & ~wise(X0)) | (~humble(X0) & ~rich(X0))) & ((humble(X0) | rich(X0)) | (~strong(X0) | wise(X0)))) [nnf transformation 13]
60. ! [X0] : (((strong(X0) & ~wise(X0)) | (~humble(X0) & ~rich(X0))) & (humble(X0) | rich(X0) | ~strong(X0) | wise(X0))) [flattening 59]
65. curious(X0) | strong(X0) | humble(X0) | curious(X0) [cnf transformation 34]
68. ~curious(X0) | strong(X0) | ~curious(X0) [cnf transformation 34]
80. tall(sK0) | curious(X1) [cnf transformation 42]
88. ~tall(X0) | ~generous(X0) [cnf transformation 47]
113. strong(X0) | ~humble(X0) [cnf transformation 60]
114. ~strong(X0) | generous(X0) [cnf transformation 31]
127. ~curious(fred) [cnf transformation 23]
128. curious(X0) | strong(X0) | humble(X0) [duplicate literal removal 65]
129. ~curious(X0) | strong(X0) [duplicate literal removal 68]
130. strong(X0) | humble(X0) [subsumption resolution 128,129]
167. 8 <=> ! [X1] : curious(X1) [avatar definition]
168. curious(X1) <- (8) [avatar component clause 167]
170. 9 <=> tall(sK0) [avatar definition]
172. tall(sK0) <- (9) [avatar component clause 170]
173. 8 | 9 [avatar split clause 80,170,167]
296. strong(X0) [subsumption resolution 113,130]
298. generous(X0) [subsumption resolution 114,296]
304. 37 <=> curious(fred) [avatar definition]
305. ~curious(fred) <- (~37) [avatar component clause 304]
339. ~37 [avatar split clause 127,304]
348. ~generous(sK0) <- (9) [resolution 88,172]
352. $false <- (9) [subsumption resolution 348,298]
353. ~9 [avatar contradiction clause 352]
355. $false <- (8, ~37) [resolution 168,305]
356. ~8 | 37 [avatar contradiction clause 355]
358. $false [avatar sat refutation 173,339,353,356]
% SZS output end Proof for 2476122070185572766591972
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
If fred is either patient or not rich then someone is tall or not funny.
Everyone who is not old is not curious.
If alice is either calm or quiet then susan is not funny or not strong.
Everyone who is both not rich and quiet is both not funny and old and vice versa.
Everyone who is quiet is either happy or not quiet and vice versa.
If mary is not brave or not funny then lucy is either creative or wise.
Everyone who is brave or not kind is either happy or not tall and vice versa.
Everyone who is both not tall and not old is either not wise or not brave and vice versa.
Everyone who is not wise is either brave or not tall.
If someone is both brave and not funny then someone is not old or not funny.
Everyone who is both wise and not rich is both not strong and not generous and vice versa.
If someone is not happy or happy then alice is patient or rich and vice versa.
Everyone who is rich is brave or not rich and vice versa.
Everyone who is either not generous or wise is wise or not brave and vice versa.
Everyone who is tall or not tall is either not funny or kind.
Everyone who is old is either kind or not kind and vice versa.
Someone is not humble or funny.
Lucy is both not quiet and funny.
Fred is old.
Susan is wise or not old.
Susan is not creative or not generous. | Alice is not generous. | contradiction | (((patient(fred)<~>~rich(fred)))=>(?[X]:((tall(X)|~funny(X)))))&
(![X]:(~old(X)=>~curious(X)))&
(((calm(alice)<~>quiet(alice)))=>((~funny(susan)|~strong(susan))))&
(![X]:((~rich(X)&quiet(X))<=>(~funny(X)&old(X))))&
(![X]:(quiet(X)<=>(happy(X)<~>~quiet(X))))&
(((~brave(mary)|~funny(mary)))=>((creative(lucy)<~>wise(lucy))))&
(![X]:((brave(X)|~kind(X))<=>(happy(X)<~>~tall(X))))&
(![X]:((~tall(X)&~old(X))<=>(~wise(X)<~>~brave(X))))&
(![X]:(~wise(X)=>(brave(X)<~>~tall(X))))&
((?[X]:((brave(X)&~funny(X))))=>(?[X]:((~old(X)|~funny(X)))))&
(![X]:((wise(X)&~rich(X))<=>(~strong(X)&~generous(X))))&
((?[X]:((~happy(X)|happy(X))))<=>((patient(alice)|rich(alice))))&
(![X]:(rich(X)<=>(brave(X)|~rich(X))))&
(![X]:((~generous(X)<~>wise(X))<=>(wise(X)|~brave(X))))&
(![X]:((tall(X)|~tall(X))=>(~funny(X)<~>kind(X))))&
(![X]:(old(X)<=>(kind(X)<~>~kind(X))))&
(?[X]:((~humble(X)|funny(X))))&
((~quiet(lucy)&funny(lucy)))&
(old(fred))&
((wise(susan)|~old(susan)))&
((~creative(susan)|~generous(susan))) | ~generous(alice) | [
"p4",
"p6",
"p7",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 9177828239628049488400367
% SZS output start Proof for 9177828239628049488400367
5. ! [X0] : (quiet(X0) <=> (happy(X0) <~> ~quiet(X0))) [input p4]
7. ! [X0] : ((~kind(X0) | brave(X0)) <=> (happy(X0) <~> ~tall(X0))) [input p6]
8. ! [X0] : ((~old(X0) & ~tall(X0)) <=> (~wise(X0) <~> ~brave(X0))) [input p7]
13. ! [X0] : (rich(X0) <=> (~rich(X0) | brave(X0))) [input p12]
14. ! [X0] : ((~generous(X0) <~> wise(X0)) <=> (~brave(X0) | wise(X0))) [input p13]
22. ~generous(alice) [input hypothesis]
39. ! [X0] : ((quiet(X0) | ((happy(X0) | quiet(X0)) & (~quiet(X0) | ~happy(X0)))) & (((quiet(X0) | ~happy(X0)) & (~quiet(X0) | happy(X0))) | ~quiet(X0))) [nnf transformation 5]
41. ! [X0] : (((~kind(X0) | brave(X0)) | ((happy(X0) | tall(X0)) & (~tall(X0) | ~happy(X0)))) & (((tall(X0) | ~happy(X0)) & (~tall(X0) | happy(X0))) | (kind(X0) & ~brave(X0)))) [nnf transformation 7]
42. ! [X0] : ((~kind(X0) | brave(X0) | ((happy(X0) | tall(X0)) & (~tall(X0) | ~happy(X0)))) & (((tall(X0) | ~happy(X0)) & (~tall(X0) | happy(X0))) | (kind(X0) & ~brave(X0)))) [flattening 41]
43. ! [X0] : (((~old(X0) & ~tall(X0)) | ((~wise(X0) | brave(X0)) & (~brave(X0) | wise(X0)))) & (((brave(X0) | wise(X0)) & (~brave(X0) | ~wise(X0))) | (old(X0) | tall(X0)))) [nnf transformation 8]
44. ! [X0] : (((~old(X0) & ~tall(X0)) | ((~wise(X0) | brave(X0)) & (~brave(X0) | wise(X0)))) & (((brave(X0) | wise(X0)) & (~brave(X0) | ~wise(X0))) | old(X0) | tall(X0))) [flattening 43]
56. ! [X0] : ((rich(X0) | (rich(X0) & ~brave(X0))) & ((~rich(X0) | brave(X0)) | ~rich(X0))) [nnf transformation 13]
57. ! [X0] : ((rich(X0) | (rich(X0) & ~brave(X0))) & (~rich(X0) | brave(X0) | ~rich(X0))) [flattening 56]
58. ! [X0] : ((((~wise(X0) | generous(X0)) & (wise(X0) | ~generous(X0))) | (brave(X0) & ~wise(X0))) & ((~brave(X0) | wise(X0)) | ((~generous(X0) | ~wise(X0)) & (wise(X0) | generous(X0))))) [nnf transformation 14]
59. ! [X0] : ((((~wise(X0) | generous(X0)) & (wise(X0) | ~generous(X0))) | (brave(X0) & ~wise(X0))) & (~brave(X0) | wise(X0) | ((~generous(X0) | ~wise(X0)) & (wise(X0) | generous(X0))))) [flattening 58]
70. ~quiet(X0) | happy(X0) | ~quiet(X0) [cnf transformation 39]
73. quiet(X0) | happy(X0) | quiet(X0) [cnf transformation 39]
80. tall(X0) | ~happy(X0) | ~brave(X0) [cnf transformation 42]
86. ~tall(X0) | ~brave(X0) | wise(X0) [cnf transformation 44]
101. ~rich(X0) | brave(X0) | ~rich(X0) [cnf transformation 57]
103. rich(X0) | rich(X0) [cnf transformation 57]
108. ~wise(X0) | generous(X0) | ~wise(X0) [cnf transformation 59]
123. ~generous(alice) [cnf transformation 22]
127. ~wise(X0) | generous(X0) [duplicate literal removal 108]
128. ~rich(X0) | brave(X0) [duplicate literal removal 101]
129. rich(X0) [duplicate literal removal 103]
130. ~quiet(X0) | happy(X0) [duplicate literal removal 70]
131. happy(X0) | quiet(X0) [duplicate literal removal 73]
168. happy(X0) [subsumption resolution 130,131]
191. ~brave(X0) | tall(X0) [subsumption resolution 80,168]
192. ~brave(X0) | wise(X0) [subsumption resolution 86,191]
217. brave(X0) [subsumption resolution 128,129]
239. wise(X0) [resolution 192,217]
241. generous(X0) [resolution 239,127]
243. $false [resolution 241,123]
% SZS output end Proof for 9177828239628049488400367
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not old then mary is either not tall or happy and vice versa. If someone is either not humble or kind then someone is either not patient or tall. If someone is not humble then someone is either tall or humble and vice versa. If someone is either curious or rich then someone is creative or not funny 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. Everyone who is both calm and not curious is not funny and vice versa. If mary is not strong or strong then someone is creative. If someone is humble then susan is not curious and vice versa. John is generous. Someone is tall. Someone is either brave or not strong. Someone is not calm. | Alice is creative. | neutral | ((~old(alice))<=>((~tall(mary)<~>happy(mary))))&
((?[X]:((~humble(X)<~>kind(X))))=>(?[X]:((~patient(X)<~>tall(X)))))&
((?[X]:(~humble(X)))<=>(?[X]:((tall(X)<~>humble(X)))))&
((?[X]:((curious(X)<~>rich(X))))<=>(?[X]:((creative(X)|~funny(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))))&
(![X]:((calm(X)&~curious(X))<=>~funny(X)))&
(((~strong(mary)|strong(mary)))=>(?[X]:(creative(X))))&
((?[X]:(humble(X)))<=>(~curious(susan)))&
(generous(john))&
(?[X]:(tall(X)))&
(?[X]:((brave(X)<~>~strong(X))))&
(?[X]:(~calm(X))) | creative(alice) | [] | null | 0 |
If fred is both humble and not brave then mary is both kind and wise and vice versa. If someone is funny or not tall then someone is either strong or patient. Everyone who is either calm or wise is generous or not calm. Everyone who is both kind and humble is creative or calm. If susan is not tall or brave then mary is both not curious and calm. Everyone who is not kind or strong is both curious and not wise. Everyone who is not curious is not generous or not funny. If john is either old or not brave then alice is wise or tall. Everyone who is both not humble and curious is not old and vice versa. Everyone who is either humble or not old is creative and vice versa. Everyone who is either brave or not funny is brave and vice versa. Everyone who is not happy is either quiet or not rich. If john is either tall or strong then paul is brave or rich. Everyone who is either patient or not rich is either old or happy and vice versa. Everyone who is generous or not generous is not curious. If someone is rich then someone is either strong or patient and vice versa. Someone is quiet or not tall. Someone is either calm or wise. Paul is both not quiet and not patient. Someone is not quiet or wise. Lucy is either tall or not wise. Fred is either strong or not calm. | Paul is rich. | neutral | (((humble(fred)&~brave(fred)))<=>((kind(mary)&wise(mary))))&
((?[X]:((funny(X)|~tall(X))))=>(?[X]:((strong(X)<~>patient(X)))))&
(![X]:((calm(X)<~>wise(X))=>(generous(X)|~calm(X))))&
(![X]:((kind(X)&humble(X))=>(creative(X)|calm(X))))&
(((~tall(susan)|brave(susan)))=>((~curious(mary)&calm(mary))))&
(![X]:((~kind(X)|strong(X))=>(curious(X)&~wise(X))))&
(![X]:(~curious(X)=>(~generous(X)|~funny(X))))&
(((old(john)<~>~brave(john)))=>((wise(alice)|tall(alice))))&
(![X]:((~humble(X)&curious(X))<=>~old(X)))&
(![X]:((humble(X)<~>~old(X))<=>creative(X)))&
(![X]:((brave(X)<~>~funny(X))<=>brave(X)))&
(![X]:(~happy(X)=>(quiet(X)<~>~rich(X))))&
(((tall(john)<~>strong(john)))=>((brave(paul)|rich(paul))))&
(![X]:((patient(X)<~>~rich(X))<=>(old(X)<~>happy(X))))&
(![X]:((generous(X)|~generous(X))=>~curious(X)))&
((?[X]:(rich(X)))<=>(?[X]:((strong(X)<~>patient(X)))))&
(?[X]:((quiet(X)|~tall(X))))&
(?[X]:((calm(X)<~>wise(X))))&
((~quiet(paul)&~patient(paul)))&
(?[X]:((~quiet(X)|wise(X))))&
((tall(lucy)<~>~wise(lucy)))&
((strong(fred)<~>~calm(fred))) | rich(paul) | [] | null | 0 |
Everyone who is kind is not generous and vice versa. If paul is both old and quiet then someone is rich. Everyone who is both not tall and not kind is not funny. Everyone who is curious is wise or happy. Everyone who is either not strong or tall is not rich or not happy and vice versa. Everyone who is either calm or curious is both old and not curious and vice versa. If fred is rich or wise then mary is not generous. Everyone who is both not strong and not happy is funny or generous and vice versa. If someone is old then someone is both patient and rich and vice versa. If someone is either not strong or not generous then someone is both not creative and creative. If someone is not tall then fred is both patient and not quiet and vice versa. If someone is not wise or not tall then lucy is not curious or old and vice versa. Everyone who is either not funny or not quiet is both rich and not creative. Everyone who is both wise and curious is both strong and not kind and vice versa. Everyone who is either quiet or not kind is kind. If paul is creative then someone is both calm and creative. Someone is strong or not tall. John is either creative or rich. Susan is not funny or calm. Someone is both not tall and old. Someone is calm. Someone is either curious or not curious. Mary is not old. Someone is not tall. | Fred is patient. | entailment | (![X]:(kind(X)<=>~generous(X)))&
(((old(paul)&quiet(paul)))=>(?[X]:(rich(X))))&
(![X]:((~tall(X)&~kind(X))=>~funny(X)))&
(![X]:(curious(X)=>(wise(X)|happy(X))))&
(![X]:((~strong(X)<~>tall(X))<=>(~rich(X)|~happy(X))))&
(![X]:((calm(X)<~>curious(X))<=>(old(X)&~curious(X))))&
(((rich(fred)|wise(fred)))=>(~generous(mary)))&
(![X]:((~strong(X)&~happy(X))<=>(funny(X)|generous(X))))&
((?[X]:(old(X)))<=>(?[X]:((patient(X)&rich(X)))))&
((?[X]:((~strong(X)<~>~generous(X))))=>(?[X]:((~creative(X)&creative(X)))))&
((?[X]:(~tall(X)))<=>((patient(fred)&~quiet(fred))))&
((?[X]:((~wise(X)|~tall(X))))<=>((~curious(lucy)|old(lucy))))&
(![X]:((~funny(X)<~>~quiet(X))=>(rich(X)&~creative(X))))&
(![X]:((wise(X)&curious(X))<=>(strong(X)&~kind(X))))&
(![X]:((quiet(X)<~>~kind(X))=>kind(X)))&
((creative(paul))=>(?[X]:((calm(X)&creative(X)))))&
(?[X]:((strong(X)|~tall(X))))&
((creative(john)<~>rich(john)))&
((~funny(susan)|calm(susan)))&
(?[X]:((~tall(X)&old(X))))&
(?[X]:(calm(X)))&
(?[X]:((curious(X)<~>~curious(X))))&
(~old(mary))&
(?[X]:(~tall(X))) | patient(fred) | [
"p10",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 3607906389722035769265126
% SZS output start Proof for 3607906389722035769265126
11. ? [X0] : ~tall(X0) <=> (~quiet(fred) & patient(fred)) [input p10]
20. ? [X0] : (old(X0) & ~tall(X0)) [input p19]
25. ~patient(fred) [input hypothesis]
57. (? [X0] : ~tall(X0) | (quiet(fred) | ~patient(fred))) & ((~quiet(fred) & patient(fred)) | ! [X0] : tall(X0)) [nnf transformation 11]
58. (? [X0] : ~tall(X0) | quiet(fred) | ~patient(fred)) & ((~quiet(fred) & patient(fred)) | ! [X0] : tall(X0)) [flattening 57]
59. (? [X0] : ~tall(X0) | quiet(fred) | ~patient(fred)) & ((~quiet(fred) & patient(fred)) | ! [X1] : tall(X1)) [rectify 58]
60. ? [X0] : ~tall(X0) => ~tall(sK4) [choice axiom]
61. (~tall(sK4) | quiet(fred) | ~patient(fred)) & ((~quiet(fred) & patient(fred)) | ! [X1] : tall(X1)) [skolemisation 59,60]
76. ? [X0] : (old(X0) & ~tall(X0)) => (old(sK8) & ~tall(sK8)) [choice axiom]
77. old(sK8) & ~tall(sK8) [skolemisation 20,76]
116. patient(fred) | tall(X1) [cnf transformation 61]
139. ~tall(sK8) [cnf transformation 77]
146. ~patient(fred) [cnf transformation 25]
217. 15 <=> patient(fred) [avatar definition]
230. 18 <=> ! [X1] : tall(X1) [avatar definition]
231. tall(X1) <- (18) [avatar component clause 230]
233. 18 | 15 [avatar split clause 116,217,230]
299. ~15 [avatar split clause 146,217]
302. $false <- (18) [resolution 231,139]
305. ~18 [avatar contradiction clause 302]
306. $false [avatar sat refutation 233,299,305]
% SZS output end Proof for 3607906389722035769265126
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 lucy is not patient or patient then someone is strong or kind.
Everyone who is not wise or not quiet is either humble or not curious.
Everyone who is both not tall and humble is either not calm or kind and vice versa.
If someone is calm or not old then someone is either rich or not happy.
Everyone who is both not rich and brave is either not humble or calm and vice versa.
Everyone who is either not tall or humble is wise.
Everyone who is funny or strong is not quiet and vice versa.
If someone is not old or kind then someone is both wise and not brave and vice versa.
Everyone who is both rich and quiet is rich or quiet and vice versa.
Everyone who is either calm or not brave is either not old or kind.
If someone is either funny or not strong then someone is not strong and vice versa.
If someone is brave or humble then susan is rich and vice versa.
Everyone who is not funny is either wise or humble and vice versa.
If fred is either wise or curious then someone is either funny or not quiet.
If lucy is not tall then susan is either not wise or not tall.
If someone is either happy or patient then fred is funny and vice versa.
Someone is curious or not calm.
Alice is not wise.
Alice is either patient or not curious.
Someone is both not kind and not creative.
Mary is generous.
John is either not generous or funny.
Paul is not funny.
Alice is both patient and strong. | Susan is funny. | contradiction | (((~patient(lucy)|patient(lucy)))=>(?[X]:((strong(X)|kind(X)))))&
(![X]:((~wise(X)|~quiet(X))=>(humble(X)<~>~curious(X))))&
(![X]:((~tall(X)&humble(X))<=>(~calm(X)<~>kind(X))))&
((?[X]:((calm(X)|~old(X))))=>(?[X]:((rich(X)<~>~happy(X)))))&
(![X]:((~rich(X)&brave(X))<=>(~humble(X)<~>calm(X))))&
(![X]:((~tall(X)<~>humble(X))=>wise(X)))&
(![X]:((funny(X)|strong(X))<=>~quiet(X)))&
((?[X]:((~old(X)|kind(X))))<=>(?[X]:((wise(X)&~brave(X)))))&
(![X]:((rich(X)&quiet(X))<=>(rich(X)|quiet(X))))&
(![X]:((calm(X)<~>~brave(X))=>(~old(X)<~>kind(X))))&
((?[X]:((funny(X)<~>~strong(X))))<=>(?[X]:(~strong(X))))&
((?[X]:((brave(X)|humble(X))))<=>(rich(susan)))&
(![X]:(~funny(X)<=>(wise(X)<~>humble(X))))&
(((wise(fred)<~>curious(fred)))=>(?[X]:((funny(X)<~>~quiet(X)))))&
((~tall(lucy))=>((~wise(susan)<~>~tall(susan))))&
((?[X]:((happy(X)<~>patient(X))))<=>(funny(fred)))&
(?[X]:((curious(X)|~calm(X))))&
(~wise(alice))&
((patient(alice)<~>~curious(alice)))&
(?[X]:((~kind(X)&~creative(X))))&
(generous(mary))&
((~generous(john)<~>funny(john)))&
(~funny(paul))&
((patient(alice)&strong(alice))) | funny(susan) | [
"p1",
"p6",
"p8",
"p11",
"p17",
"p18",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 144035361142767802515358
% SZS output start Proof for 144035361142767802515358
2. ! [X0] : ((~quiet(X0) | ~wise(X0)) => (humble(X0) <~> ~curious(X0))) [input p1]
7. ! [X0] : ((strong(X0) | funny(X0)) <=> ~quiet(X0)) [input p6]
9. ! [X0] : ((quiet(X0) & rich(X0)) <=> (quiet(X0) | rich(X0))) [input p8]
12. ? [X0] : (humble(X0) | brave(X0)) <=> rich(susan) [input p11]
18. ~wise(alice) [input p17]
19. patient(alice) <~> ~curious(alice) [input p18]
24. strong(alice) & patient(alice) [input p23]
25. funny(susan) [input hypothesis]
31. ! [X0] : ((humble(X0) <~> ~curious(X0)) | (quiet(X0) & wise(X0))) [ennf transformation 2]
39. ! [X0] : (((curious(X0) | ~humble(X0)) & (~curious(X0) | humble(X0))) | (quiet(X0) & wise(X0))) [nnf transformation 31]
49. ! [X0] : (((strong(X0) | funny(X0)) | quiet(X0)) & (~quiet(X0) | (~strong(X0) & ~funny(X0)))) [nnf transformation 7]
50. ! [X0] : ((strong(X0) | funny(X0) | quiet(X0)) & (~quiet(X0) | (~strong(X0) & ~funny(X0)))) [flattening 49]
56. ! [X0] : (((quiet(X0) & rich(X0)) | (~quiet(X0) & ~rich(X0))) & ((quiet(X0) | rich(X0)) | (~quiet(X0) | ~rich(X0)))) [nnf transformation 9]
57. ! [X0] : (((quiet(X0) & rich(X0)) | (~quiet(X0) & ~rich(X0))) & (quiet(X0) | rich(X0) | ~quiet(X0) | ~rich(X0))) [flattening 56]
64. (? [X0] : (humble(X0) | brave(X0)) | ~rich(susan)) & (rich(susan) | ! [X0] : (~humble(X0) & ~brave(X0))) [nnf transformation 12]
65. (? [X0] : (humble(X0) | brave(X0)) | ~rich(susan)) & (rich(susan) | ! [X1] : (~humble(X1) & ~brave(X1))) [rectify 64]
66. ? [X0] : (humble(X0) | brave(X0)) => (humble(sK6) | brave(sK6)) [choice axiom]
67. ((humble(sK6) | brave(sK6)) | ~rich(susan)) & (rich(susan) | ! [X1] : (~humble(X1) & ~brave(X1))) [skolemisation 65,66]
79. (curious(alice) | ~patient(alice)) & (~curious(alice) | patient(alice)) [nnf transformation 19]
85. ~curious(X0) | humble(X0) | wise(X0) [cnf transformation 39]
107. ~funny(X0) | ~quiet(X0) [cnf transformation 50]
118. ~rich(X0) | quiet(X0) [cnf transformation 57]
129. rich(susan) | ~humble(X1) [cnf transformation 67]
146. ~wise(alice) [cnf transformation 18]
148. curious(alice) | ~patient(alice) [cnf transformation 79]
154. patient(alice) [cnf transformation 24]
156. funny(susan) [cnf transformation 25]
242. 20 <=> rich(susan) [avatar definition]
243. rich(susan) <- (20) [avatar component clause 242]
255. 23 <=> ! [X1] : ~humble(X1) [avatar definition]
256. ~humble(X1) <- (23) [avatar component clause 255]
257. 23 | 20 [avatar split clause 129,242,255]
332. 39 <=> patient(alice) [avatar definition]
336. 40 <=> curious(alice) [avatar definition]
338. curious(alice) <- (40) [avatar component clause 336]
339. ~39 | 40 [avatar split clause 148,336,332]
351. 39 [avatar split clause 154,332]
354. ~quiet(susan) [resolution 107,156]
356. quiet(susan) <- (20) [resolution 118,243]
357. $false <- (20) [subsumption resolution 356,354]
358. ~20 [avatar contradiction clause 357]
361. humble(alice) | wise(alice) <- (40) [resolution 85,338]
362. wise(alice) <- (23, 40) [subsumption resolution 361,256]
363. $false <- (23, 40) [subsumption resolution 362,146]
364. ~23 | ~40 [avatar contradiction clause 363]
365. $false [avatar sat refutation 257,339,351,358,364]
% SZS output end Proof for 144035361142767802515358
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either old or not quiet then paul is calm and vice versa.
Everyone who is not creative is tall.
Everyone who is generous is quiet.
If someone is not generous or not humble then john is not rich.
If lucy is either not curious or not humble then fred is not curious or not happy and vice versa.
If someone is rich or strong then alice is both generous and not patient and vice versa.
Everyone who is patient is not wise or not funny and vice versa.
If someone is not patient or generous then someone is not rich or not strong.
If someone is both strong and not patient then fred is either not wise or not strong and vice versa.
Everyone who is old or not strong is quiet or tall and vice versa.
Everyone who is both not creative and not funny is both curious and generous.
Everyone who is calm or patient is strong and vice versa.
If someone is not quiet then lucy is old and vice versa.
Everyone who is either not funny or quiet is either wise or not brave and vice versa.
If paul is tall then someone is tall.
Everyone who is either not happy or creative is not patient.
Someone is either creative or old.
Someone is either not rich or strong.
Someone is not tall.
Susan is either not generous or not creative.
Someone is humble.
Someone is either not generous or patient.
Paul is not generous or rich.
Someone is both humble and happy. | Alice is quiet. | entailment | ((?[X]:((old(X)<~>~quiet(X))))<=>(calm(paul)))&
(![X]:(~creative(X)=>tall(X)))&
(![X]:(generous(X)=>quiet(X)))&
((?[X]:((~generous(X)|~humble(X))))=>(~rich(john)))&
(((~curious(lucy)<~>~humble(lucy)))<=>((~curious(fred)|~happy(fred))))&
((?[X]:((rich(X)|strong(X))))<=>((generous(alice)&~patient(alice))))&
(![X]:(patient(X)<=>(~wise(X)|~funny(X))))&
((?[X]:((~patient(X)|generous(X))))=>(?[X]:((~rich(X)|~strong(X)))))&
((?[X]:((strong(X)&~patient(X))))<=>((~wise(fred)<~>~strong(fred))))&
(![X]:((old(X)|~strong(X))<=>(quiet(X)|tall(X))))&
(![X]:((~creative(X)&~funny(X))=>(curious(X)&generous(X))))&
(![X]:((calm(X)|patient(X))<=>strong(X)))&
((?[X]:(~quiet(X)))<=>(old(lucy)))&
(![X]:((~funny(X)<~>quiet(X))<=>(wise(X)<~>~brave(X))))&
((tall(paul))=>(?[X]:(tall(X))))&
(![X]:((~happy(X)<~>creative(X))=>~patient(X)))&
(?[X]:((creative(X)<~>old(X))))&
(?[X]:((~rich(X)<~>strong(X))))&
(?[X]:(~tall(X)))&
((~generous(susan)<~>~creative(susan)))&
(?[X]:(humble(X)))&
(?[X]:((~generous(X)<~>patient(X))))&
((~generous(paul)|rich(paul)))&
(?[X]:((humble(X)&happy(X)))) | quiet(alice) | [
"p2",
"p5",
"p6",
"p8",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 4786405951647764703833666
% SZS output start Proof for 4786405951647764703833666
3. ! [X0] : (generous(X0) => quiet(X0)) [input p2]
6. ? [X0] : (strong(X0) | rich(X0)) <=> (~patient(alice) & generous(alice)) [input p5]
7. ! [X0] : (patient(X0) <=> (~funny(X0) | ~wise(X0))) [input p6]
9. ? [X0] : (~patient(X0) & strong(X0)) <=> (~wise(fred) <~> ~strong(fred)) [input p8]
12. ! [X0] : ((patient(X0) | calm(X0)) <=> strong(X0)) [input p11]
25. ~quiet(alice) [input hypothesis]
28. ! [X0] : (quiet(X0) | ~generous(X0)) [ennf transformation 3]
41. (? [X0] : (strong(X0) | rich(X0)) | (patient(alice) | ~generous(alice))) & ((~patient(alice) & generous(alice)) | ! [X0] : (~strong(X0) & ~rich(X0))) [nnf transformation 6]
42. (? [X0] : (strong(X0) | rich(X0)) | patient(alice) | ~generous(alice)) & ((~patient(alice) & generous(alice)) | ! [X0] : (~strong(X0) & ~rich(X0))) [flattening 41]
43. (? [X0] : (strong(X0) | rich(X0)) | patient(alice) | ~generous(alice)) & ((~patient(alice) & generous(alice)) | ! [X1] : (~strong(X1) & ~rich(X1))) [rectify 42]
44. ? [X0] : (strong(X0) | rich(X0)) => (strong(sK1) | rich(sK1)) [choice axiom]
45. ((strong(sK1) | rich(sK1)) | patient(alice) | ~generous(alice)) & ((~patient(alice) & generous(alice)) | ! [X1] : (~strong(X1) & ~rich(X1))) [skolemisation 43,44]
46. ! [X0] : ((patient(X0) | (funny(X0) & wise(X0))) & ((~funny(X0) | ~wise(X0)) | ~patient(X0))) [nnf transformation 7]
47. ! [X0] : ((patient(X0) | (funny(X0) & wise(X0))) & (~funny(X0) | ~wise(X0) | ~patient(X0))) [flattening 46]
51. (? [X0] : (~patient(X0) & strong(X0)) | ((~wise(fred) | strong(fred)) & (~strong(fred) | wise(fred)))) & (((strong(fred) | wise(fred)) & (~strong(fred) | ~wise(fred))) | ! [X0] : (patient(X0) | ~strong(X0))) [nnf transformation 9]
52. (? [X0] : (~patient(X0) & strong(X0)) | ((~wise(fred) | strong(fred)) & (~strong(fred) | wise(fred)))) & (((strong(fred) | wise(fred)) & (~strong(fred) | ~wise(fred))) | ! [X1] : (patient(X1) | ~strong(X1))) [rectify 51]
53. ? [X0] : (~patient(X0) & strong(X0)) => (~patient(sK3) & strong(sK3)) [choice axiom]
54. ((~patient(sK3) & strong(sK3)) | ((~wise(fred) | strong(fred)) & (~strong(fred) | wise(fred)))) & (((strong(fred) | wise(fred)) & (~strong(fred) | ~wise(fred))) | ! [X1] : (patient(X1) | ~strong(X1))) [skolemisation 52,53]
57. ! [X0] : (((patient(X0) | calm(X0)) | ~strong(X0)) & (strong(X0) | (~patient(X0) & ~calm(X0)))) [nnf transformation 12]
58. ! [X0] : ((patient(X0) | calm(X0) | ~strong(X0)) & (strong(X0) | (~patient(X0) & ~calm(X0)))) [flattening 57]
88. ~generous(X0) | quiet(X0) [cnf transformation 28]
98. generous(alice) | ~strong(X1) [cnf transformation 45]
103. wise(X0) | patient(X0) [cnf transformation 47]
110. strong(sK3) | ~wise(fred) | strong(fred) [cnf transformation 54]
120. ~patient(X0) | strong(X0) [cnf transformation 58]
148. ~quiet(alice) [cnf transformation 25]
206. 13 <=> generous(alice) [avatar definition]
207. generous(alice) <- (13) [avatar component clause 206]
223. 17 <=> ! [X1] : ~strong(X1) [avatar definition]
224. ~strong(X1) <- (17) [avatar component clause 223]
230. 17 | 13 [avatar split clause 98,206,223]
249. 23 <=> strong(fred) [avatar definition]
251. strong(fred) <- (23) [avatar component clause 249]
253. 24 <=> wise(fred) [avatar definition]
255. ~wise(fred) <- (~24) [avatar component clause 253]
263. 26 <=> strong(sK3) [avatar definition]
265. strong(sK3) <- (26) [avatar component clause 263]
266. 23 | ~24 | 26 [avatar split clause 110,263,253,249]
346. quiet(alice) <- (13) [resolution 88,207]
348. $false <- (13) [subsumption resolution 346,148]
349. ~13 [avatar contradiction clause 348]
350. $false <- (17, 23) [resolution 224,251]
351. $false <- (17, 26) [resolution 224,265]
352. ~17 | ~26 [avatar contradiction clause 351]
353. ~17 | ~23 [avatar contradiction clause 350]
356. patient(fred) <- (~24) [resolution 103,255]
357. strong(fred) <- (~24) [resolution 120,356]
358. $false <- (17, ~24) [subsumption resolution 357,224]
359. ~17 | 24 [avatar contradiction clause 358]
360. $false [avatar sat refutation 230,266,349,352,353,359]
% SZS output end Proof for 4786405951647764703833666
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 alice is curious or generous then someone is humble or not wise and vice versa.
Everyone who is strong or not humble is both humble and calm.
If someone is both generous and funny then someone is either funny or quiet and vice versa.
Everyone who is both not funny and not quiet is calm and vice versa.
If lucy is not rich or strong then paul is either not creative or kind and vice versa.
If someone is either not tall or rich then someone is patient or kind and vice versa.
Everyone who is creative or not funny is both patient and not old and vice versa.
Everyone who is curious or funny is either rich or quiet.
If someone is either rich or not happy then john is not patient.
Everyone who is either brave or patient is both quiet and not old.
Everyone who is generous or not strong is either old or strong.
If someone is not curious or not quiet then fred is rich.
Everyone who is not brave or generous is either tall or curious and vice versa.
If fred is not brave or calm then someone is not funny.
Everyone who is funny is either brave or patient.
If susan is either tall or curious then someone is either strong or not funny and vice versa.
Mary is creative or not creative.
Someone is not quiet or wise.
Mary is generous.
Someone is either not humble or kind.
Alice is both tall and not old.
Alice is both not wise and not old. | Lucy is not calm. | contradiction | (((curious(alice)|generous(alice)))<=>(?[X]:((humble(X)|~wise(X)))))&
(![X]:((strong(X)|~humble(X))=>(humble(X)&calm(X))))&
((?[X]:((generous(X)&funny(X))))<=>(?[X]:((funny(X)<~>quiet(X)))))&
(![X]:((~funny(X)&~quiet(X))<=>calm(X)))&
(((~rich(lucy)|strong(lucy)))<=>((~creative(paul)<~>kind(paul))))&
((?[X]:((~tall(X)<~>rich(X))))<=>(?[X]:((patient(X)|kind(X)))))&
(![X]:((creative(X)|~funny(X))<=>(patient(X)&~old(X))))&
(![X]:((curious(X)|funny(X))=>(rich(X)<~>quiet(X))))&
((?[X]:((rich(X)<~>~happy(X))))=>(~patient(john)))&
(![X]:((brave(X)<~>patient(X))=>(quiet(X)&~old(X))))&
(![X]:((generous(X)|~strong(X))=>(old(X)<~>strong(X))))&
((?[X]:((~curious(X)|~quiet(X))))=>(rich(fred)))&
(![X]:((~brave(X)|generous(X))<=>(tall(X)<~>curious(X))))&
(((~brave(fred)|calm(fred)))=>(?[X]:(~funny(X))))&
(![X]:(funny(X)=>(brave(X)<~>patient(X))))&
(((tall(susan)<~>curious(susan)))<=>(?[X]:((strong(X)<~>~funny(X)))))&
((creative(mary)|~creative(mary)))&
(?[X]:((~quiet(X)|wise(X))))&
(generous(mary))&
(?[X]:((~humble(X)<~>kind(X))))&
((tall(alice)&~old(alice)))&
((~wise(alice)&~old(alice))) | ~calm(lucy) | [
"p1",
"p3",
"p6",
"p9",
"p10",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 815689215514766885917763
% SZS output start Proof for 815689215514766885917763
2. ! [X0] : ((~humble(X0) | strong(X0)) => (calm(X0) & humble(X0))) [input p1]
4. ! [X0] : ((~quiet(X0) & ~funny(X0)) <=> calm(X0)) [input p3]
7. ! [X0] : ((~funny(X0) | creative(X0)) <=> (~old(X0) & patient(X0))) [input p6]
10. ! [X0] : ((brave(X0) <~> patient(X0)) => (~old(X0) & quiet(X0))) [input p9]
11. ! [X0] : ((~strong(X0) | generous(X0)) => (old(X0) <~> strong(X0))) [input p10]
15. ! [X0] : (funny(X0) => (brave(X0) <~> patient(X0))) [input p14]
16. (tall(susan) <~> curious(susan)) <=> ? [X0] : (strong(X0) <~> ~funny(X0)) [input p15]
23. ~calm(lucy) [input hypothesis]
26. ! [X0] : ((calm(X0) & humble(X0)) | (humble(X0) & ~strong(X0))) [ennf transformation 2]
29. ! [X0] : ((~old(X0) & quiet(X0)) | (brave(X0) <=> patient(X0))) [ennf transformation 10]
30. ! [X0] : ((old(X0) <~> strong(X0)) | (strong(X0) & ~generous(X0))) [ennf transformation 11]
33. ! [X0] : ((brave(X0) <~> patient(X0)) | ~funny(X0)) [ennf transformation 15]
44. ! [X0] : (((~quiet(X0) & ~funny(X0)) | ~calm(X0)) & (calm(X0) | (quiet(X0) | funny(X0)))) [nnf transformation 4]
45. ! [X0] : (((~quiet(X0) & ~funny(X0)) | ~calm(X0)) & (calm(X0) | quiet(X0) | funny(X0))) [flattening 44]
53. ! [X0] : (((~funny(X0) | creative(X0)) | (old(X0) | ~patient(X0))) & ((~old(X0) & patient(X0)) | (funny(X0) & ~creative(X0)))) [nnf transformation 7]
54. ! [X0] : ((~funny(X0) | creative(X0) | old(X0) | ~patient(X0)) & ((~old(X0) & patient(X0)) | (funny(X0) & ~creative(X0)))) [flattening 53]
57. ! [X0] : ((~old(X0) & quiet(X0)) | ((brave(X0) | ~patient(X0)) & (patient(X0) | ~brave(X0)))) [nnf transformation 29]
58. ! [X0] : (((~strong(X0) | ~old(X0)) & (strong(X0) | old(X0))) | (strong(X0) & ~generous(X0))) [nnf transformation 30]
63. ! [X0] : (((~patient(X0) | ~brave(X0)) & (patient(X0) | brave(X0))) | ~funny(X0)) [nnf transformation 33]
64. (((~curious(susan) | ~tall(susan)) & (curious(susan) | tall(susan))) | ! [X0] : ((strong(X0) | funny(X0)) & (~funny(X0) | ~strong(X0)))) & (? [X0] : ((funny(X0) | ~strong(X0)) & (~funny(X0) | strong(X0))) | ((tall(susan) | ~curious(susan)) & (curious(susan) | ~tall(susan)))) [nnf transformation 16]
65. (((~curious(susan) | ~tall(susan)) & (curious(susan) | tall(susan))) | ! [X0] : ((strong(X0) | funny(X0)) & (~funny(X0) | ~strong(X0)))) & (? [X1] : ((funny(X1) | ~strong(X1)) & (~funny(X1) | strong(X1))) | ((tall(susan) | ~curious(susan)) & (curious(susan) | ~tall(susan)))) [rectify 64]
66. ? [X1] : ((funny(X1) | ~strong(X1)) & (~funny(X1) | strong(X1))) => ((funny(sK6) | ~strong(sK6)) & (~funny(sK6) | strong(sK6))) [choice axiom]
67. (((~curious(susan) | ~tall(susan)) & (curious(susan) | tall(susan))) | ! [X0] : ((strong(X0) | funny(X0)) & (~funny(X0) | ~strong(X0)))) & (((funny(sK6) | ~strong(sK6)) & (~funny(sK6) | strong(sK6))) | ((tall(susan) | ~curious(susan)) & (curious(susan) | ~tall(susan)))) [skolemisation 65,66]
79. ~strong(X0) | calm(X0) [cnf transformation 26]
88. ~funny(X0) | ~calm(X0) [cnf transformation 45]
103. patient(X0) | funny(X0) [cnf transformation 54]
105. ~old(X0) | funny(X0) [cnf transformation 54]
115. ~brave(X0) | patient(X0) | ~old(X0) [cnf transformation 57]
116. ~old(X0) | brave(X0) | ~patient(X0) [cnf transformation 57]
118. strong(X0) | old(X0) | strong(X0) [cnf transformation 58]
131. patient(X0) | brave(X0) | ~funny(X0) [cnf transformation 63]
132. ~brave(X0) | ~patient(X0) | ~funny(X0) [cnf transformation 63]
133. ~funny(sK6) | strong(sK6) | curious(susan) | ~tall(susan) [cnf transformation 67]
134. ~funny(sK6) | strong(sK6) | tall(susan) | ~curious(susan) [cnf transformation 67]
135. funny(sK6) | ~strong(sK6) | curious(susan) | ~tall(susan) [cnf transformation 67]
136. funny(sK6) | ~strong(sK6) | tall(susan) | ~curious(susan) [cnf transformation 67]
137. curious(susan) | tall(susan) | ~funny(X0) | ~strong(X0) [cnf transformation 67]
139. ~curious(susan) | ~tall(susan) | ~funny(X0) | ~strong(X0) [cnf transformation 67]
150. ~calm(lucy) [cnf transformation 23]
151. old(X0) | strong(X0) [duplicate literal removal 118]
223. 17 <=> strong(lucy) [avatar definition]
224. ~strong(lucy) <- (~17) [avatar component clause 223]
225. strong(lucy) <- (17) [avatar component clause 223]
304. brave(X0) | patient(X0) [subsumption resolution 131,103]
306. 35 <=> ! [X0] : (strong(X0) | funny(X0)) [avatar definition]
307. funny(X0) | strong(X0) <- (35) [avatar component clause 306]
309. 36 <=> tall(susan) [avatar definition]
313. 37 <=> curious(susan) [avatar definition]
318. 38 <=> ! [X0] : (~funny(X0) | ~strong(X0)) [avatar definition]
319. ~funny(X0) | ~strong(X0) <- (38) [avatar component clause 318]
320. 38 | ~36 | ~37 [avatar split clause 139,313,309,318]
322. 38 | 36 | 37 [avatar split clause 137,313,309,318]
324. 39 <=> strong(sK6) [avatar definition]
325. strong(sK6) <- (39) [avatar component clause 324]
328. 40 <=> funny(sK6) [avatar definition]
329. ~funny(sK6) <- (~40) [avatar component clause 328]
330. funny(sK6) <- (40) [avatar component clause 328]
331. ~37 | 36 | ~39 | 40 [avatar split clause 136,328,324,309,313]
332. ~36 | 37 | ~39 | 40 [avatar split clause 135,328,324,313,309]
333. ~37 | 36 | 39 | ~40 [avatar split clause 134,328,324,309,313]
334. ~36 | 37 | 39 | ~40 [avatar split clause 133,328,324,313,309]
350. strong(X0) | funny(X0) [resolution 151,105]
352. 35 [avatar split clause 350,306]
359. strong(sK6) <- (35, ~40) [resolution 307,329]
365. 39 | ~35 | 40 [avatar split clause 359,328,306,324]
366. calm(sK6) <- (39) [resolution 325,79]
429. patient(X0) | ~old(X0) | patient(X0) [resolution 115,304]
430. ~old(X0) | patient(X0) [duplicate literal removal 429]
431. brave(X0) | ~patient(X0) | strong(X0) [resolution 116,151]
432. brave(X0) | strong(X0) [subsumption resolution 431,304]
639. patient(X0) | strong(X0) [resolution 430,151]
644. strong(X2) | ~patient(X2) | ~funny(X2) [resolution 432,132]
647. ~patient(X2) | ~funny(X2) <- (38) [subsumption resolution 644,319]
701. calm(lucy) <- (17) [resolution 225,79]
702. $false <- (17) [subsumption resolution 701,150]
703. ~17 [avatar contradiction clause 702]
731. ~funny(X0) | strong(X0) <- (38) [resolution 647,639]
735. strong(X0) <- (35, 38) [subsumption resolution 731,307]
803. $false <- (~17, 35, 38) [resolution 735,224]
804. 17 | ~35 | ~38 [avatar contradiction clause 803]
832. ~calm(sK6) <- (40) [resolution 330,88]
833. $false <- (39, 40) [subsumption resolution 832,366]
834. ~39 | ~40 [avatar contradiction clause 833]
835. $false [avatar sat refutation 320,322,331,332,333,334,352,365,703,804,834]
% SZS output end Proof for 815689215514766885917763
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If someone is curious then mary is not brave.
Everyone who is not generous or brave is not calm or curious and vice versa.
If lucy is either old or brave then alice is humble and vice versa.
Everyone who is either not happy or not creative is not curious or not old.
Everyone who is both not calm and not wise is not humble or humble.
If susan is both not patient and not funny then mary is not creative or generous.
If someone is not rich or not brave then john is not funny.
Everyone who is both generous and not funny is not creative.
If susan is not wise or not creative then mary is calm.
If someone is either quiet or generous then someone is rich and vice versa.
Everyone who is calm or not happy is old and vice versa.
If mary is both not old and calm then someone is brave and vice versa.
Everyone who is either generous or not humble is not rich or not patient and vice versa.
If someone is both calm and old then paul is either not kind or generous and vice versa.
Everyone who is happy is generous or brave.
If someone is either kind or happy then someone is either not patient or not humble.
Someone is wise.
Alice is either kind or not happy.
Fred is not kind.
Mary is rich.
Susan is both tall and humble.
Someone is either not humble or tall.
Alice is not quiet.
Fred is tall. | Alice is old. | entailment | ((?[X]:(curious(X)))=>(~brave(mary)))&
(![X]:((~generous(X)|brave(X))<=>(~calm(X)|curious(X))))&
(((old(lucy)<~>brave(lucy)))<=>(humble(alice)))&
(![X]:((~happy(X)<~>~creative(X))=>(~curious(X)|~old(X))))&
(![X]:((~calm(X)&~wise(X))=>(~humble(X)|humble(X))))&
(((~patient(susan)&~funny(susan)))=>((~creative(mary)|generous(mary))))&
((?[X]:((~rich(X)|~brave(X))))=>(~funny(john)))&
(![X]:((generous(X)&~funny(X))=>~creative(X)))&
(((~wise(susan)|~creative(susan)))=>(calm(mary)))&
((?[X]:((quiet(X)<~>generous(X))))<=>(?[X]:(rich(X))))&
(![X]:((calm(X)|~happy(X))<=>old(X)))&
(((~old(mary)&calm(mary)))<=>(?[X]:(brave(X))))&
(![X]:((generous(X)<~>~humble(X))<=>(~rich(X)|~patient(X))))&
((?[X]:((calm(X)&old(X))))<=>((~kind(paul)<~>generous(paul))))&
(![X]:(happy(X)=>(generous(X)|brave(X))))&
((?[X]:((kind(X)<~>happy(X))))=>(?[X]:((~patient(X)<~>~humble(X)))))&
(?[X]:(wise(X)))&
((kind(alice)<~>~happy(alice)))&
(~kind(fred))&
(rich(mary))&
((tall(susan)&humble(susan)))&
(?[X]:((~humble(X)<~>tall(X))))&
(~quiet(alice))&
(tall(fred)) | old(alice) | [
"p1",
"p10",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 670944591580759715730952
% SZS output start Proof for 670944591580759715730952
2. ! [X0] : ((brave(X0) | ~generous(X0)) <=> (curious(X0) | ~calm(X0))) [input p1]
11. ! [X0] : ((~happy(X0) | calm(X0)) <=> old(X0)) [input p10]
12. (calm(mary) & ~old(mary)) <=> ? [X0] : brave(X0) [input p11]
15. ! [X0] : (happy(X0) => (brave(X0) | generous(X0))) [input p14]
25. ~old(alice) [input hypothesis]
40. ! [X0] : ((brave(X0) | generous(X0)) | ~happy(X0)) [ennf transformation 15]
41. ! [X0] : (brave(X0) | generous(X0) | ~happy(X0)) [flattening 40]
43. ! [X0] : (((brave(X0) | ~generous(X0)) | (~curious(X0) & calm(X0))) & ((curious(X0) | ~calm(X0)) | (~brave(X0) & generous(X0)))) [nnf transformation 2]
44. ! [X0] : ((brave(X0) | ~generous(X0) | (~curious(X0) & calm(X0))) & (curious(X0) | ~calm(X0) | (~brave(X0) & generous(X0)))) [flattening 43]
52. ! [X0] : (((~happy(X0) | calm(X0)) | ~old(X0)) & (old(X0) | (happy(X0) & ~calm(X0)))) [nnf transformation 11]
53. ! [X0] : ((~happy(X0) | calm(X0) | ~old(X0)) & (old(X0) | (happy(X0) & ~calm(X0)))) [flattening 52]
54. ((calm(mary) & ~old(mary)) | ! [X0] : ~brave(X0)) & (? [X0] : brave(X0) | (~calm(mary) | old(mary))) [nnf transformation 12]
55. ((calm(mary) & ~old(mary)) | ! [X0] : ~brave(X0)) & (? [X0] : brave(X0) | ~calm(mary) | old(mary)) [flattening 54]
56. ((calm(mary) & ~old(mary)) | ! [X0] : ~brave(X0)) & (? [X1] : brave(X1) | ~calm(mary) | old(mary)) [rectify 55]
57. ? [X1] : brave(X1) => brave(sK2) [choice axiom]
58. ((calm(mary) & ~old(mary)) | ! [X0] : ~brave(X0)) & (brave(sK2) | ~calm(mary) | old(mary)) [skolemisation 56,57]
76. ~generous(X0) | brave(X0) | calm(X0) [cnf transformation 44]
93. ~calm(X0) | old(X0) [cnf transformation 53]
94. happy(X0) | old(X0) [cnf transformation 53]
97. ~old(mary) | ~brave(X0) [cnf transformation 58]
98. calm(mary) | ~brave(X0) [cnf transformation 58]
111. ~happy(X0) | generous(X0) | brave(X0) [cnf transformation 41]
126. ~old(alice) [cnf transformation 25]
185. 14 <=> calm(mary) [avatar definition]
187. calm(mary) <- (14) [avatar component clause 185]
215. 21 <=> ! [X0] : ~brave(X0) [avatar definition]
216. ~brave(X0) <- (21) [avatar component clause 215]
217. 21 | 14 [avatar split clause 98,185,215]
219. 22 <=> old(mary) [avatar definition]
221. ~old(mary) <- (~22) [avatar component clause 219]
222. 21 | ~22 [avatar split clause 97,219,215]
273. 33 <=> happy(alice) [avatar definition]
274. ~happy(alice) <- (~33) [avatar component clause 273]
275. happy(alice) <- (33) [avatar component clause 273]
290. old(mary) <- (14) [resolution 93,187]
292. $false <- (14, ~22) [subsumption resolution 290,221]
293. ~14 | 22 [avatar contradiction clause 292]
294. old(alice) <- (~33) [resolution 94,274]
295. $false <- (~33) [subsumption resolution 294,126]
296. 33 [avatar contradiction clause 295]
377. generous(alice) | brave(alice) <- (33) [resolution 111,275]
379. generous(alice) <- (21, 33) [subsumption resolution 377,216]
421. brave(alice) | calm(alice) <- (21, 33) [resolution 379,76]
425. calm(alice) <- (21, 33) [subsumption resolution 421,216]
466. old(alice) <- (21, 33) [resolution 425,93]
467. $false <- (21, 33) [subsumption resolution 466,126]
468. ~21 | ~33 [avatar contradiction clause 467]
469. $false [avatar sat refutation 217,222,293,296,468]
% SZS output end Proof for 670944591580759715730952
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble or not happy then someone is not old.
Everyone who is both creative and not humble is both not brave and wise and vice versa.
Everyone who is both patient and not rich is both not old and old.
Everyone who is both not rich and not funny is both not calm and not wise and vice versa.
If mary is not creative then someone is both not kind and not quiet and vice versa.
Everyone who is both not kind and old is quiet and vice versa.
If fred is either old or generous then someone is happy or calm.
Everyone who is either creative or not curious is not creative or happy.
Everyone who is either humble or not quiet is not patient or not curious and vice versa.
Everyone who is both not happy and wise is both strong and rich and vice versa.
Everyone who is not old is kind or not generous and vice versa.
If someone is old then alice is both not brave and funny and vice versa.
Everyone who is both funny and calm is either tall or not tall and vice versa.
If someone is kind or not generous then someone is both not curious and curious and vice versa.
Someone is either not funny or not wise.
Susan is not wise or not patient.
Susan is rich or tall. | Fred is not funny. | contradiction | ((?[X]:((humble(X)|~happy(X))))=>(?[X]:(~old(X))))&
(![X]:((creative(X)&~humble(X))<=>(~brave(X)&wise(X))))&
(![X]:((patient(X)&~rich(X))=>(~old(X)&old(X))))&
(![X]:((~rich(X)&~funny(X))<=>(~calm(X)&~wise(X))))&
((~creative(mary))<=>(?[X]:((~kind(X)&~quiet(X)))))&
(![X]:((~kind(X)&old(X))<=>quiet(X)))&
(((old(fred)<~>generous(fred)))=>(?[X]:((happy(X)|calm(X)))))&
(![X]:((creative(X)<~>~curious(X))=>(~creative(X)|happy(X))))&
(![X]:((humble(X)<~>~quiet(X))<=>(~patient(X)|~curious(X))))&
(![X]:((~happy(X)&wise(X))<=>(strong(X)&rich(X))))&
(![X]:(~old(X)<=>(kind(X)|~generous(X))))&
((?[X]:(old(X)))<=>((~brave(alice)&funny(alice))))&
(![X]:((funny(X)&calm(X))<=>(tall(X)<~>~tall(X))))&
((?[X]:((kind(X)|~generous(X))))<=>(?[X]:((~curious(X)&curious(X)))))&
(?[X]:((~funny(X)<~>~wise(X))))&
((~wise(susan)|~patient(susan)))&
((rich(susan)|tall(susan))) | ~funny(fred) | [
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 6415594823566483688110403
% SZS output start Proof for 6415594823566483688110403
13. ! [X0] : ((calm(X0) & funny(X0)) <=> (tall(X0) <~> ~tall(X0))) [input p12]
18. ~funny(fred) [input hypothesis]
55. ! [X0] : (((calm(X0) & funny(X0)) | ((tall(X0) | tall(X0)) & (~tall(X0) | ~tall(X0)))) & (((tall(X0) | ~tall(X0)) & (~tall(X0) | tall(X0))) | (~calm(X0) | ~funny(X0)))) [nnf transformation 13]
56. ! [X0] : (((calm(X0) & funny(X0)) | ((tall(X0) | tall(X0)) & (~tall(X0) | ~tall(X0)))) & (((tall(X0) | ~tall(X0)) & (~tall(X0) | tall(X0))) | ~calm(X0) | ~funny(X0))) [flattening 55]
105. funny(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 56]
106. funny(X0) | tall(X0) | tall(X0) [cnf transformation 56]
118. ~funny(fred) [cnf transformation 18]
119. funny(X0) | ~tall(X0) [duplicate literal removal 105]
120. funny(X0) | tall(X0) [duplicate literal removal 106]
192. funny(X0) [subsumption resolution 119,120]
226. $false [subsumption resolution 118,192]
% SZS output end Proof for 6415594823566483688110403
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either wise or creative is either not old or creative. Everyone who is happy or not happy is both wise and not rich. Everyone who is not quiet is both wise and patient. Everyone who is either not generous or not funny is curious and vice versa. If someone is curious then fred is strong. Everyone who is curious or creative is not creative or funny. Everyone who is both strong and not tall is either creative or not happy. If someone is either tall or brave then someone is not rich or old and vice versa. If someone is old or curious then someone is not humble and vice versa. If someone is creative then susan is either funny or not strong and vice versa. If fred is both not funny and not happy then paul is funny and vice versa. Everyone who is either calm or curious is both not calm and generous and vice versa. If alice is not kind or not brave then someone is both happy and brave. Everyone who is both not funny and not brave is patient or kind. Everyone who is both not old and not calm is humble or brave and vice versa. Someone is not generous or not brave. Someone is wise or not calm. John is both not rich and not funny. Someone is not happy. John is both not rich and not humble. Alice is patient. Mary is not funny or happy. | Susan is not generous. | neutral | (![X]:((wise(X)<~>creative(X))=>(~old(X)<~>creative(X))))&
(![X]:((happy(X)|~happy(X))=>(wise(X)&~rich(X))))&
(![X]:(~quiet(X)=>(wise(X)&patient(X))))&
(![X]:((~generous(X)<~>~funny(X))<=>curious(X)))&
((?[X]:(curious(X)))=>(strong(fred)))&
(![X]:((curious(X)|creative(X))=>(~creative(X)|funny(X))))&
(![X]:((strong(X)&~tall(X))=>(creative(X)<~>~happy(X))))&
((?[X]:((tall(X)<~>brave(X))))<=>(?[X]:((~rich(X)|old(X)))))&
((?[X]:((old(X)|curious(X))))<=>(?[X]:(~humble(X))))&
((?[X]:(creative(X)))<=>((funny(susan)<~>~strong(susan))))&
(((~funny(fred)&~happy(fred)))<=>(funny(paul)))&
(![X]:((calm(X)<~>curious(X))<=>(~calm(X)&generous(X))))&
(((~kind(alice)|~brave(alice)))=>(?[X]:((happy(X)&brave(X)))))&
(![X]:((~funny(X)&~brave(X))=>(patient(X)|kind(X))))&
(![X]:((~old(X)&~calm(X))<=>(humble(X)|brave(X))))&
(?[X]:((~generous(X)|~brave(X))))&
(?[X]:((wise(X)|~calm(X))))&
((~rich(john)&~funny(john)))&
(?[X]:(~happy(X)))&
((~rich(john)&~humble(john)))&
(patient(alice))&
((~funny(mary)|happy(mary))) | ~generous(susan) | [] | null | 0 |
If someone is not old or calm then someone is not rich or rich and vice versa.
If john is old then someone is both wise and not rich and vice versa.
Everyone who is both not tall and quiet is kind and vice versa.
Everyone who is old is either patient or not tall.
Everyone who is calm or not generous is both not curious and not brave and vice versa.
If someone is both old and strong then paul is both patient and generous and vice versa.
If someone is calm then susan is both patient and brave and vice versa.
If someone is both tall and not patient then someone is not old or creative.
If someone is not kind then someone is either generous or calm.
If someone is either not funny or not happy then john is either funny or patient and vice versa.
Everyone who is both curious and funny is either happy or not creative and vice versa.
If someone is not strong or not patient then someone is both not rich and not strong and vice versa.
Everyone who is not humble is not generous or not brave.
Everyone who is either not funny or not creative is both kind and funny.
Everyone who is humble is both not strong and tall and vice versa.
Everyone who is not wise or not humble is generous.
Someone is both brave and not calm.
Someone is not calm or happy.
Someone is not old.
Someone is not happy.
Someone is not creative.
Someone is both brave and generous.
Someone is creative or not kind.
John is not old. | John is not strong. | neutral | ((?[X]:((~old(X)|calm(X))))<=>(?[X]:((~rich(X)|rich(X)))))&
((old(john))<=>(?[X]:((wise(X)&~rich(X)))))&
(![X]:((~tall(X)&quiet(X))<=>kind(X)))&
(![X]:(old(X)=>(patient(X)<~>~tall(X))))&
(![X]:((calm(X)|~generous(X))<=>(~curious(X)&~brave(X))))&
((?[X]:((old(X)&strong(X))))<=>((patient(paul)&generous(paul))))&
((?[X]:(calm(X)))<=>((patient(susan)&brave(susan))))&
((?[X]:((tall(X)&~patient(X))))=>(?[X]:((~old(X)|creative(X)))))&
((?[X]:(~kind(X)))=>(?[X]:((generous(X)<~>calm(X)))))&
((?[X]:((~funny(X)<~>~happy(X))))<=>((funny(john)<~>patient(john))))&
(![X]:((curious(X)&funny(X))<=>(happy(X)<~>~creative(X))))&
((?[X]:((~strong(X)|~patient(X))))<=>(?[X]:((~rich(X)&~strong(X)))))&
(![X]:(~humble(X)=>(~generous(X)|~brave(X))))&
(![X]:((~funny(X)<~>~creative(X))=>(kind(X)&funny(X))))&
(![X]:(humble(X)<=>(~strong(X)&tall(X))))&
(![X]:((~wise(X)|~humble(X))=>generous(X)))&
(?[X]:((brave(X)&~calm(X))))&
(?[X]:((~calm(X)|happy(X))))&
(?[X]:(~old(X)))&
(?[X]:(~happy(X)))&
(?[X]:(~creative(X)))&
(?[X]:((brave(X)&generous(X))))&
(?[X]:((creative(X)|~kind(X))))&
(~old(john)) | ~strong(john) | [] | null | 0 |
If susan is not tall or quiet then susan is either wise or kind.
Everyone who is either not rich or humble is quiet or tall and vice versa.
Everyone who is either happy or not old is not calm.
If fred is either not strong or not humble then fred is tall or not calm and vice versa.
Everyone who is either not brave or rich is not rich or not old and vice versa.
Everyone who is humble is both rich and not creative.
Everyone who is patient is either not curious or not creative and vice versa.
If someone is either curious or not brave then someone is either not happy or not strong.
Everyone who is not happy or not funny is both happy and kind and vice versa.
If alice is not quiet then someone is either not tall or not brave.
If fred is both not curious and patient then john is patient.
Everyone who is either funny or not happy is humble or kind.
If susan is either not curious or not brave then alice is either brave or creative and vice versa.
Everyone who is either brave or tall is either not brave or not quiet and vice versa.
If susan is both happy and not strong then susan is either humble or funny and vice versa.
Everyone who is generous is either brave or rich.
Someone is both patient and not generous.
Someone is both not rich and patient.
Mary is either not strong or not patient.
Someone is not funny or old.
Alice is either not curious or not humble.
Lucy is either brave or quiet.
Someone is either brave or not humble.
Fred is either funny or not rich. | Fred is tall. | entailment | (((~tall(susan)|quiet(susan)))=>((wise(susan)<~>kind(susan))))&
(![X]:((~rich(X)<~>humble(X))<=>(quiet(X)|tall(X))))&
(![X]:((happy(X)<~>~old(X))=>~calm(X)))&
(((~strong(fred)<~>~humble(fred)))<=>((tall(fred)|~calm(fred))))&
(![X]:((~brave(X)<~>rich(X))<=>(~rich(X)|~old(X))))&
(![X]:(humble(X)=>(rich(X)&~creative(X))))&
(![X]:(patient(X)<=>(~curious(X)<~>~creative(X))))&
((?[X]:((curious(X)<~>~brave(X))))=>(?[X]:((~happy(X)<~>~strong(X)))))&
(![X]:((~happy(X)|~funny(X))<=>(happy(X)&kind(X))))&
((~quiet(alice))=>(?[X]:((~tall(X)<~>~brave(X)))))&
(((~curious(fred)&patient(fred)))=>(patient(john)))&
(![X]:((funny(X)<~>~happy(X))=>(humble(X)|kind(X))))&
(((~curious(susan)<~>~brave(susan)))<=>((brave(alice)<~>creative(alice))))&
(![X]:((brave(X)<~>tall(X))<=>(~brave(X)<~>~quiet(X))))&
(((happy(susan)&~strong(susan)))<=>((humble(susan)<~>funny(susan))))&
(![X]:(generous(X)=>(brave(X)<~>rich(X))))&
(?[X]:((patient(X)&~generous(X))))&
(?[X]:((~rich(X)&patient(X))))&
((~strong(mary)<~>~patient(mary)))&
(?[X]:((~funny(X)|old(X))))&
((~curious(alice)<~>~humble(alice)))&
((brave(lucy)<~>quiet(lucy)))&
(?[X]:((brave(X)<~>~humble(X))))&
((funny(fred)<~>~rich(fred))) | tall(fred) | [
"p1",
"p5",
"p8",
"p11",
"p13",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 4017227198684292268217283
% SZS output start Proof for 4017227198684292268217283
2. ! [X0] : ((~rich(X0) <~> humble(X0)) <=> (tall(X0) | quiet(X0))) [input p1]
6. ! [X0] : (humble(X0) => (~creative(X0) & rich(X0))) [input p5]
9. ! [X0] : ((~funny(X0) | ~happy(X0)) <=> (kind(X0) & happy(X0))) [input p8]
12. ! [X0] : ((funny(X0) <~> ~happy(X0)) => (kind(X0) | humble(X0))) [input p11]
14. ! [X0] : ((brave(X0) <~> tall(X0)) <=> (~brave(X0) <~> ~quiet(X0))) [input p13]
24. funny(fred) <~> ~rich(fred) [input p23]
25. ~tall(fred) [input hypothesis]
31. ! [X0] : ((~creative(X0) & rich(X0)) | ~humble(X0)) [ennf transformation 6]
36. ! [X0] : ((kind(X0) | humble(X0)) | (funny(X0) <=> ~happy(X0))) [ennf transformation 12]
37. ! [X0] : (kind(X0) | humble(X0) | (funny(X0) <=> ~happy(X0))) [flattening 36]
39. ! [X0] : ((((~humble(X0) | rich(X0)) & (humble(X0) | ~rich(X0))) | (~tall(X0) & ~quiet(X0))) & ((tall(X0) | quiet(X0)) | ((~rich(X0) | ~humble(X0)) & (humble(X0) | rich(X0))))) [nnf transformation 2]
40. ! [X0] : ((((~humble(X0) | rich(X0)) & (humble(X0) | ~rich(X0))) | (~tall(X0) & ~quiet(X0))) & (tall(X0) | quiet(X0) | ((~rich(X0) | ~humble(X0)) & (humble(X0) | rich(X0))))) [flattening 39]
51. ! [X0] : (((~funny(X0) | ~happy(X0)) | (~kind(X0) | ~happy(X0))) & ((kind(X0) & happy(X0)) | (funny(X0) & happy(X0)))) [nnf transformation 9]
52. ! [X0] : ((~funny(X0) | ~happy(X0) | ~kind(X0) | ~happy(X0)) & ((kind(X0) & happy(X0)) | (funny(X0) & happy(X0)))) [flattening 51]
56. ! [X0] : (kind(X0) | humble(X0) | ((funny(X0) | happy(X0)) & (~happy(X0) | ~funny(X0)))) [nnf transformation 37]
58. ! [X0] : ((((~tall(X0) | ~brave(X0)) & (tall(X0) | brave(X0))) | ((~brave(X0) | quiet(X0)) & (~quiet(X0) | brave(X0)))) & (((quiet(X0) | brave(X0)) & (~quiet(X0) | ~brave(X0))) | ((brave(X0) | ~tall(X0)) & (tall(X0) | ~brave(X0))))) [nnf transformation 14]
73. (rich(fred) | ~funny(fred)) & (~rich(fred) | funny(fred)) [nnf transformation 24]
78. humble(X0) | quiet(X0) | tall(X0) | rich(X0) [cnf transformation 40]
79. ~humble(X0) | quiet(X0) | ~rich(X0) | tall(X0) [cnf transformation 40]
98. ~humble(X0) | rich(X0) [cnf transformation 31]
108. happy(X0) | happy(X0) [cnf transformation 52]
111. funny(X0) | kind(X0) [cnf transformation 52]
112. ~funny(X0) | ~happy(X0) | ~kind(X0) | ~happy(X0) [cnf transformation 52]
116. kind(X0) | humble(X0) | ~happy(X0) | ~funny(X0) [cnf transformation 56]
126. ~quiet(X0) | ~brave(X0) | tall(X0) | ~brave(X0) [cnf transformation 58]
130. tall(X0) | brave(X0) | ~quiet(X0) | brave(X0) [cnf transformation 58]
152. ~rich(fred) | funny(fred) [cnf transformation 73]
154. ~tall(fred) [cnf transformation 25]
155. ~quiet(X0) | ~brave(X0) | tall(X0) [duplicate literal removal 126]
157. ~quiet(X0) | brave(X0) | tall(X0) [duplicate literal removal 130]
159. happy(X0) [duplicate literal removal 108]
160. ~funny(X0) | ~happy(X0) | ~kind(X0) [duplicate literal removal 112]
192. 7 <=> humble(fred) [avatar definition]
193. ~humble(fred) <- (~7) [avatar component clause 192]
194. humble(fred) <- (7) [avatar component clause 192]
197. 8 <=> tall(fred) [avatar definition]
199. ~tall(fred) <- (~8) [avatar component clause 197]
251. kind(X0) | humble(X0) | ~funny(X0) [subsumption resolution 116,159]
252. humble(X0) | kind(X0) [subsumption resolution 251,111]
278. ~quiet(X0) | tall(X0) [subsumption resolution 155,157]
347. 36 <=> funny(fred) [avatar definition]
348. funny(fred) <- (36) [avatar component clause 347]
351. 37 <=> rich(fred) [avatar definition]
352. ~rich(fred) <- (~37) [avatar component clause 351]
353. rich(fred) <- (37) [avatar component clause 351]
355. 36 | ~37 [avatar split clause 152,351,347]
356. ~8 [avatar split clause 154,197]
365. kind(fred) <- (~7) [resolution 252,193]
447. quiet(X2) | tall(X2) | rich(X2) | rich(X2) [resolution 78,98]
453. quiet(X2) | tall(X2) | rich(X2) [duplicate literal removal 447]
456. rich(X2) | tall(X2) [subsumption resolution 453,278]
481. tall(fred) <- (~37) [resolution 456,352]
485. $false <- (~8, ~37) [subsumption resolution 481,199]
486. 8 | 37 [avatar contradiction clause 485]
487. ~happy(fred) | ~kind(fred) <- (36) [resolution 348,160]
488. ~kind(fred) <- (36) [subsumption resolution 487,159]
489. $false <- (~7, 36) [subsumption resolution 488,365]
490. 7 | ~36 [avatar contradiction clause 489]
491. quiet(fred) | ~rich(fred) | tall(fred) <- (7) [resolution 194,79]
495. quiet(fred) | tall(fred) <- (7, 37) [subsumption resolution 491,353]
496. quiet(fred) <- (7, ~8, 37) [subsumption resolution 495,199]
502. tall(fred) <- (7, ~8, 37) [resolution 496,278]
503. $false <- (7, ~8, 37) [subsumption resolution 502,199]
504. ~7 | 8 | ~37 [avatar contradiction clause 503]
505. $false [avatar sat refutation 355,356,486,490,504]
% SZS output end Proof for 4017227198684292268217283
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not brave or not generous is both not brave and not tall and vice versa.
Everyone who is not funny is either strong or not strong.
If someone is both happy and patient then someone is not kind or curious and vice versa.
Everyone who is not strong is not humble or not brave.
If someone is either not rich or old then alice is not rich or not old and vice versa.
Everyone who is both not patient and humble is both not patient and not curious and vice versa.
If fred is kind or quiet then someone is either curious or humble and vice versa.
Everyone who is strong or funny is quiet and vice versa.
If someone is not strong then someone is both calm and not calm and vice versa.
Everyone who is both not happy and quiet is either generous or not happy and vice versa.
If john is either strong or not humble then john is both brave and not wise.
Everyone who is not funny or not wise is both strong and not wise.
Everyone who is both not curious and tall is both brave and not wise and vice versa.
Everyone who is both not tall and tall is not wise or not calm and vice versa.
Everyone who is rich is not happy or not generous and vice versa.
Alice is not quiet or quiet.
John is curious.
Someone is either not funny or not happy.
Mary is either humble or strong.
Someone is either not happy or happy.
Someone is both not brave and rich. | Alice is not brave. | entailment | (![X]:((~brave(X)<~>~generous(X))<=>(~brave(X)&~tall(X))))&
(![X]:(~funny(X)=>(strong(X)<~>~strong(X))))&
((?[X]:((happy(X)&patient(X))))<=>(?[X]:((~kind(X)|curious(X)))))&
(![X]:(~strong(X)=>(~humble(X)|~brave(X))))&
((?[X]:((~rich(X)<~>old(X))))<=>((~rich(alice)|~old(alice))))&
(![X]:((~patient(X)&humble(X))<=>(~patient(X)&~curious(X))))&
(((kind(fred)|quiet(fred)))<=>(?[X]:((curious(X)<~>humble(X)))))&
(![X]:((strong(X)|funny(X))<=>quiet(X)))&
((?[X]:(~strong(X)))<=>(?[X]:((calm(X)&~calm(X)))))&
(![X]:((~happy(X)&quiet(X))<=>(generous(X)<~>~happy(X))))&
(((strong(john)<~>~humble(john)))=>((brave(john)&~wise(john))))&
(![X]:((~funny(X)|~wise(X))=>(strong(X)&~wise(X))))&
(![X]:((~curious(X)&tall(X))<=>(brave(X)&~wise(X))))&
(![X]:((~tall(X)&tall(X))<=>(~wise(X)|~calm(X))))&
(![X]:(rich(X)<=>(~happy(X)|~generous(X))))&
((~quiet(alice)|quiet(alice)))&
(curious(john))&
(?[X]:((~funny(X)<~>~happy(X))))&
((humble(mary)<~>strong(mary)))&
(?[X]:((~happy(X)<~>happy(X))))&
(?[X]:((~brave(X)&rich(X)))) | ~brave(alice) | [
"p0",
"p7",
"p8",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 5854725809474112682927864
% SZS output start Proof for 5854725809474112682927864
1. ! [X0] : ((~brave(X0) <~> ~generous(X0)) <=> (~tall(X0) & ~brave(X0))) [input p0]
8. ! [X0] : ((funny(X0) | strong(X0)) <=> quiet(X0)) [input p7]
9. ? [X0] : ~strong(X0) <=> ? [X0] : (~calm(X0) & calm(X0)) [input p8]
10. ! [X0] : ((quiet(X0) & ~happy(X0)) <=> (generous(X0) <~> ~happy(X0))) [input p9]
22. brave(alice) [input hypothesis]
24. ? [X0] : ~strong(X0) <=> ? [X1] : (~calm(X1) & calm(X1)) [rectify 9]
30. ! [X0] : ((((generous(X0) | brave(X0)) & (~generous(X0) | ~brave(X0))) | (tall(X0) | brave(X0))) & ((~tall(X0) & ~brave(X0)) | ((~brave(X0) | generous(X0)) & (~generous(X0) | brave(X0))))) [nnf transformation 1]
31. ! [X0] : ((((generous(X0) | brave(X0)) & (~generous(X0) | ~brave(X0))) | tall(X0) | brave(X0)) & ((~tall(X0) & ~brave(X0)) | ((~brave(X0) | generous(X0)) & (~generous(X0) | brave(X0))))) [flattening 30]
50. ! [X0] : (((funny(X0) | strong(X0)) | ~quiet(X0)) & (quiet(X0) | (~funny(X0) & ~strong(X0)))) [nnf transformation 8]
51. ! [X0] : ((funny(X0) | strong(X0) | ~quiet(X0)) & (quiet(X0) | (~funny(X0) & ~strong(X0)))) [flattening 50]
52. (? [X0] : ~strong(X0) | ! [X1] : (calm(X1) | ~calm(X1))) & (? [X1] : (~calm(X1) & calm(X1)) | ! [X0] : strong(X0)) [nnf transformation 24]
53. (? [X0] : ~strong(X0) | ! [X1] : (calm(X1) | ~calm(X1))) & (? [X2] : (~calm(X2) & calm(X2)) | ! [X3] : strong(X3)) [rectify 52]
54. ? [X0] : ~strong(X0) => ~strong(sK4) [choice axiom]
55. ? [X2] : (~calm(X2) & calm(X2)) => (~calm(sK5) & calm(sK5)) [choice axiom]
56. (~strong(sK4) | ! [X1] : (calm(X1) | ~calm(X1))) & ((~calm(sK5) & calm(sK5)) | ! [X3] : strong(X3)) [skolemisation 53,55,54]
57. ! [X0] : (((quiet(X0) & ~happy(X0)) | ((generous(X0) | happy(X0)) & (~happy(X0) | ~generous(X0)))) & (((happy(X0) | ~generous(X0)) & (~happy(X0) | generous(X0))) | (~quiet(X0) | happy(X0)))) [nnf transformation 10]
58. ! [X0] : (((quiet(X0) & ~happy(X0)) | ((generous(X0) | happy(X0)) & (~happy(X0) | ~generous(X0)))) & (((happy(X0) | ~generous(X0)) & (~happy(X0) | generous(X0))) | ~quiet(X0) | happy(X0))) [flattening 57]
76. ~brave(X0) | ~brave(X0) | generous(X0) [cnf transformation 31]
105. ~strong(X0) | quiet(X0) [cnf transformation 51]
108. calm(sK5) | strong(X3) [cnf transformation 56]
109. ~calm(sK5) | strong(X3) [cnf transformation 56]
112. happy(X0) | ~generous(X0) | ~quiet(X0) | happy(X0) [cnf transformation 58]
113. ~happy(X0) | ~happy(X0) | ~generous(X0) [cnf transformation 58]
147. brave(alice) [cnf transformation 22]
148. happy(X0) | ~generous(X0) | ~quiet(X0) [duplicate literal removal 112]
149. ~happy(X0) | ~generous(X0) [duplicate literal removal 113]
150. ~brave(X0) | generous(X0) [duplicate literal removal 76]
239. 20 <=> ! [X3] : strong(X3) [avatar definition]
240. strong(X3) <- (20) [avatar component clause 239]
242. 21 <=> calm(sK5) [avatar definition]
245. 20 | ~21 [avatar split clause 109,242,239]
246. 20 | 21 [avatar split clause 108,242,239]
247. ~quiet(X0) | ~generous(X0) [subsumption resolution 148,149]
294. quiet(X0) <- (20) [resolution 105,240]
309. generous(alice) [resolution 150,147]
316. ~generous(X0) <- (20) [resolution 247,294]
317. $false <- (20) [resolution 316,309]
318. ~20 [avatar contradiction clause 317]
319. $false [avatar sat refutation 245,246,318]
% SZS output end Proof for 5854725809474112682927864
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous or not brave is generous. Everyone who is either funny or wise is not patient and vice versa. If mary is not generous or brave then john is not old or not creative. If john is either not patient or quiet then someone is both not happy and not rich and vice versa. Everyone who is wise is either not funny or not wise. Everyone who is either calm or brave is wise. If paul is brave or wise then alice is both not kind and kind and vice versa. If john is either not generous or curious then someone is not happy and vice versa. If someone is curious or old then mary is creative or not funny and vice versa. If lucy is happy or not humble then someone is happy. Everyone who is both not kind and patient is not curious or not calm. Everyone who is not rich is both old and creative. Everyone who is calm is either brave or rich. If alice is not kind then someone is either not wise or old and vice versa. Everyone who is both calm and not calm is not kind or quiet and vice versa. Everyone who is either patient or not wise is not calm or not tall. Alice is either not strong or not creative. Alice is either not creative or not patient. Alice is either creative or calm. John is funny or not rich. Alice is both funny and humble. Susan is both funny and old. Susan is not brave or not generous. Someone is not rich or not creative. | John is not old. | contradiction | (![X]:((generous(X)<~>~brave(X))=>generous(X)))&
(![X]:((funny(X)<~>wise(X))<=>~patient(X)))&
(((~generous(mary)|brave(mary)))=>((~old(john)|~creative(john))))&
(((~patient(john)<~>quiet(john)))<=>(?[X]:((~happy(X)&~rich(X)))))&
(![X]:(wise(X)=>(~funny(X)<~>~wise(X))))&
(![X]:((calm(X)<~>brave(X))=>wise(X)))&
(((brave(paul)|wise(paul)))<=>((~kind(alice)&kind(alice))))&
(((~generous(john)<~>curious(john)))<=>(?[X]:(~happy(X))))&
((?[X]:((curious(X)|old(X))))<=>((creative(mary)|~funny(mary))))&
(((happy(lucy)|~humble(lucy)))=>(?[X]:(happy(X))))&
(![X]:((~kind(X)&patient(X))=>(~curious(X)|~calm(X))))&
(![X]:(~rich(X)=>(old(X)&creative(X))))&
(![X]:(calm(X)=>(brave(X)<~>rich(X))))&
((~kind(alice))<=>(?[X]:((~wise(X)<~>old(X)))))&
(![X]:((calm(X)&~calm(X))<=>(~kind(X)|quiet(X))))&
(![X]:((patient(X)<~>~wise(X))=>(~calm(X)|~tall(X))))&
((~strong(alice)<~>~creative(alice)))&
((~creative(alice)<~>~patient(alice)))&
((creative(alice)<~>calm(alice)))&
((funny(john)|~rich(john)))&
((funny(alice)&humble(alice)))&
((funny(susan)&old(susan)))&
((~brave(susan)|~generous(susan)))&
(?[X]:((~rich(X)|~creative(X)))) | ~old(john) | [
"p4",
"p11",
"p13",
"p14",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 6664713645480617877438146
% SZS output start Proof for 6664713645480617877438146
5. ! [X0] : (wise(X0) => (~funny(X0) <~> ~wise(X0))) [input p4]
12. ! [X0] : (~rich(X0) => (creative(X0) & old(X0))) [input p11]
14. ~kind(alice) <=> ? [X0] : (~wise(X0) <~> old(X0)) [input p13]
15. ! [X0] : ((~calm(X0) & calm(X0)) <=> (quiet(X0) | ~kind(X0))) [input p14]
20. ~rich(john) | funny(john) [input p19]
25. ~old(john) [input hypothesis]
32. ! [X0] : ((~funny(X0) <~> ~wise(X0)) | ~wise(X0)) [ennf transformation 5]
37. ! [X0] : ((creative(X0) & old(X0)) | rich(X0)) [ennf transformation 12]
45. ! [X0] : (((wise(X0) | funny(X0)) & (~wise(X0) | ~funny(X0))) | ~wise(X0)) [nnf transformation 32]
61. (~kind(alice) | ! [X0] : ((~wise(X0) | ~old(X0)) & (old(X0) | wise(X0)))) & (? [X0] : ((~old(X0) | wise(X0)) & (old(X0) | ~wise(X0))) | kind(alice)) [nnf transformation 14]
62. (~kind(alice) | ! [X0] : ((~wise(X0) | ~old(X0)) & (old(X0) | wise(X0)))) & (? [X1] : ((~old(X1) | wise(X1)) & (old(X1) | ~wise(X1))) | kind(alice)) [rectify 61]
63. ? [X1] : ((~old(X1) | wise(X1)) & (old(X1) | ~wise(X1))) => ((~old(sK4) | wise(sK4)) & (old(sK4) | ~wise(sK4))) [choice axiom]
64. (~kind(alice) | ! [X0] : ((~wise(X0) | ~old(X0)) & (old(X0) | wise(X0)))) & (((~old(sK4) | wise(sK4)) & (old(sK4) | ~wise(sK4))) | kind(alice)) [skolemisation 62,63]
65. ! [X0] : (((~calm(X0) & calm(X0)) | (~quiet(X0) & kind(X0))) & ((quiet(X0) | ~kind(X0)) | (calm(X0) | ~calm(X0)))) [nnf transformation 15]
66. ! [X0] : (((~calm(X0) & calm(X0)) | (~quiet(X0) & kind(X0))) & (quiet(X0) | ~kind(X0) | calm(X0) | ~calm(X0))) [flattening 65]
86. ~wise(X0) | ~funny(X0) | ~wise(X0) [cnf transformation 45]
105. rich(X0) | old(X0) [cnf transformation 37]
111. ~kind(alice) | old(X0) | wise(X0) [cnf transformation 64]
114. calm(X0) | kind(X0) [cnf transformation 66]
116. ~calm(X0) | kind(X0) [cnf transformation 66]
124. ~rich(john) | funny(john) [cnf transformation 20]
130. ~old(john) [cnf transformation 25]
131. ~wise(X0) | ~funny(X0) [duplicate literal removal 86]
138. 2 <=> old(john) [avatar definition]
140. ~old(john) <- (~2) [avatar component clause 138]
181. 11 <=> kind(alice) [avatar definition]
182. ~kind(alice) <- (~11) [avatar component clause 181]
251. 26 <=> ! [X0] : (old(X0) | wise(X0)) [avatar definition]
252. old(X0) | wise(X0) <- (26) [avatar component clause 251]
253. 26 | ~11 [avatar split clause 111,181,251]
265. kind(X0) [subsumption resolution 114,116]
289. 33 <=> funny(john) [avatar definition]
291. funny(john) <- (33) [avatar component clause 289]
293. 34 <=> rich(john) [avatar definition]
295. ~rich(john) <- (~34) [avatar component clause 293]
296. 33 | ~34 [avatar split clause 124,293,289]
315. ~2 [avatar split clause 130,138]
316. $false <- (~11) [subsumption resolution 182,265]
317. 11 [avatar contradiction clause 316]
319. old(john) <- (~34) [resolution 105,295]
321. $false <- (~2, ~34) [subsumption resolution 319,140]
322. 2 | 34 [avatar contradiction clause 321]
329. wise(john) <- (~2, 26) [resolution 252,140]
336. ~funny(john) <- (~2, 26) [resolution 329,131]
337. $false <- (~2, 26, 33) [subsumption resolution 336,291]
338. 2 | ~26 | ~33 [avatar contradiction clause 337]
339. $false [avatar sat refutation 253,296,315,317,322,338]
% SZS output end Proof for 6664713645480617877438146
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not wise or kind is both creative and calm and vice versa.
If someone is both wise and calm then someone is not calm.
If alice is both kind and not wise then alice is kind or not brave and vice versa.
Everyone who is not kind or kind is either calm or tall.
Everyone who is both creative and strong is quiet or patient and vice versa.
Everyone who is either quiet or humble is not rich or patient and vice versa.
Everyone who is both not tall and funny is not old or curious and vice versa.
Everyone who is either patient or not strong is both not calm and brave and vice versa.
Everyone who is not strong is kind or not calm and vice versa.
If susan is old or not tall then someone is quiet.
If someone is both quiet and happy then fred is happy or generous and vice versa.
Everyone who is not wise or not rich is both not happy and not brave.
Everyone who is either not curious or not brave is curious or funny and vice versa.
Everyone who is not curious or not calm is not calm and vice versa.
Everyone who is either rich or curious is brave or not quiet and vice versa.
Someone is humble or not brave.
Someone is not kind.
Susan is not funny or funny.
Someone is both not tall and not wise.
Susan is either not generous or rich.
Someone is either not calm or not quiet. | Fred is kind. | contradiction | (![X]:((~wise(X)<~>kind(X))<=>(creative(X)&calm(X))))&
((?[X]:((wise(X)&calm(X))))=>(?[X]:(~calm(X))))&
(((kind(alice)&~wise(alice)))<=>((kind(alice)|~brave(alice))))&
(![X]:((~kind(X)|kind(X))=>(calm(X)<~>tall(X))))&
(![X]:((creative(X)&strong(X))<=>(quiet(X)|patient(X))))&
(![X]:((quiet(X)<~>humble(X))<=>(~rich(X)|patient(X))))&
(![X]:((~tall(X)&funny(X))<=>(~old(X)|curious(X))))&
(![X]:((patient(X)<~>~strong(X))<=>(~calm(X)&brave(X))))&
(![X]:(~strong(X)<=>(kind(X)|~calm(X))))&
(((old(susan)|~tall(susan)))=>(?[X]:(quiet(X))))&
((?[X]:((quiet(X)&happy(X))))<=>((happy(fred)|generous(fred))))&
(![X]:((~wise(X)|~rich(X))=>(~happy(X)&~brave(X))))&
(![X]:((~curious(X)<~>~brave(X))<=>(curious(X)|funny(X))))&
(![X]:((~curious(X)|~calm(X))<=>~calm(X)))&
(![X]:((rich(X)<~>curious(X))<=>(brave(X)|~quiet(X))))&
(?[X]:((humble(X)|~brave(X))))&
(?[X]:(~kind(X)))&
((~funny(susan)|funny(susan)))&
(?[X]:((~tall(X)&~wise(X))))&
((~generous(susan)<~>rich(susan)))&
(?[X]:((~calm(X)<~>~quiet(X)))) | kind(fred) | [
"p0",
"p4",
"p7",
"p8",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 2300672049799273035784425
% SZS output start Proof for 2300672049799273035784425
1. ! [X0] : ((~wise(X0) <~> kind(X0)) <=> (calm(X0) & creative(X0))) [input p0]
5. ! [X0] : ((strong(X0) & creative(X0)) <=> (patient(X0) | quiet(X0))) [input p4]
8. ! [X0] : ((patient(X0) <~> ~strong(X0)) <=> (brave(X0) & ~calm(X0))) [input p7]
9. ! [X0] : (~strong(X0) <=> (~calm(X0) | kind(X0))) [input p8]
12. ! [X0] : ((~rich(X0) | ~wise(X0)) => (~brave(X0) & ~happy(X0))) [input p11]
22. kind(fred) [input hypothesis]
27. ! [X0] : ((~brave(X0) & ~happy(X0)) | (rich(X0) & wise(X0))) [ennf transformation 12]
28. ! [X0] : ((((~kind(X0) | wise(X0)) & (kind(X0) | ~wise(X0))) | (~calm(X0) | ~creative(X0))) & ((calm(X0) & creative(X0)) | ((~wise(X0) | ~kind(X0)) & (kind(X0) | wise(X0))))) [nnf transformation 1]
29. ! [X0] : ((((~kind(X0) | wise(X0)) & (kind(X0) | ~wise(X0))) | ~calm(X0) | ~creative(X0)) & ((calm(X0) & creative(X0)) | ((~wise(X0) | ~kind(X0)) & (kind(X0) | wise(X0))))) [flattening 28]
36. ! [X0] : (((strong(X0) & creative(X0)) | (~patient(X0) & ~quiet(X0))) & ((patient(X0) | quiet(X0)) | (~strong(X0) | ~creative(X0)))) [nnf transformation 5]
37. ! [X0] : (((strong(X0) & creative(X0)) | (~patient(X0) & ~quiet(X0))) & (patient(X0) | quiet(X0) | ~strong(X0) | ~creative(X0))) [flattening 36]
42. ! [X0] : ((((strong(X0) | ~patient(X0)) & (~strong(X0) | patient(X0))) | (~brave(X0) | calm(X0))) & ((brave(X0) & ~calm(X0)) | ((patient(X0) | strong(X0)) & (~strong(X0) | ~patient(X0))))) [nnf transformation 8]
43. ! [X0] : ((((strong(X0) | ~patient(X0)) & (~strong(X0) | patient(X0))) | ~brave(X0) | calm(X0)) & ((brave(X0) & ~calm(X0)) | ((patient(X0) | strong(X0)) & (~strong(X0) | ~patient(X0))))) [flattening 42]
44. ! [X0] : ((~strong(X0) | (calm(X0) & ~kind(X0))) & ((~calm(X0) | kind(X0)) | strong(X0))) [nnf transformation 9]
45. ! [X0] : ((~strong(X0) | (calm(X0) & ~kind(X0))) & (~calm(X0) | kind(X0) | strong(X0))) [flattening 44]
72. ~kind(X0) | ~wise(X0) | calm(X0) [cnf transformation 29]
89. ~patient(X0) | strong(X0) [cnf transformation 37]
102. ~calm(X0) | patient(X0) | strong(X0) [cnf transformation 43]
104. brave(X0) | patient(X0) | strong(X0) [cnf transformation 43]
108. ~strong(X0) | ~kind(X0) [cnf transformation 45]
109. ~strong(X0) | calm(X0) [cnf transformation 45]
119. ~brave(X0) | wise(X0) [cnf transformation 27]
145. kind(fred) [cnf transformation 22]
173. strong(X0) | brave(X0) [subsumption resolution 104,89]
175. ~calm(X0) | strong(X0) [subsumption resolution 102,89]
272. brave(X0) | calm(X0) [resolution 173,109]
315. ~wise(fred) | calm(fred) [resolution 72,145]
518. calm(X2) | wise(X2) [resolution 272,119]
615. calm(fred) [subsumption resolution 315,518]
618. strong(fred) [resolution 615,175]
647. ~kind(fred) [resolution 618,108]
658. $false [subsumption resolution 647,145]
% SZS output end Proof for 2300672049799273035784425
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old or curious is calm or not wise.
If someone is either strong or not kind then mary is either not happy or rich and vice versa.
If someone is creative or rich then paul is both not patient and not happy and vice versa.
If paul is quiet then lucy is not calm and vice versa.
If someone is not curious then lucy is either happy or wise and vice versa.
Everyone who is kind or not brave is not old or not wise.
If lucy is both not funny and old then alice is not creative or happy.
If alice is either not happy or not funny then someone is not quiet.
If someone is happy then someone is old.
If mary is not funny then someone is not wise or not rich.
Everyone who is not kind or strong is patient or not funny.
If susan is either not rich or patient then someone is both curious and generous and vice versa.
If alice is curious then someone is funny.
Everyone who is brave is either creative or curious and vice versa.
If paul is not calm then paul is brave and vice versa.
Everyone who is kind is rich.
Fred is both not rich and not wise.
Paul is not kind or not creative.
John is either not calm or strong.
Someone is either creative or quiet.
Fred is not humble or rich.
Someone is either funny or happy.
Susan is either not wise or patient.
Paul is both not rich and funny. | Alice is rich. | contradiction | (![X]:((old(X)|curious(X))=>(calm(X)|~wise(X))))&
((?[X]:((strong(X)<~>~kind(X))))<=>((~happy(mary)<~>rich(mary))))&
((?[X]:((creative(X)|rich(X))))<=>((~patient(paul)&~happy(paul))))&
((quiet(paul))<=>(~calm(lucy)))&
((?[X]:(~curious(X)))<=>((happy(lucy)<~>wise(lucy))))&
(![X]:((kind(X)|~brave(X))=>(~old(X)|~wise(X))))&
(((~funny(lucy)&old(lucy)))=>((~creative(alice)|happy(alice))))&
(((~happy(alice)<~>~funny(alice)))=>(?[X]:(~quiet(X))))&
((?[X]:(happy(X)))=>(?[X]:(old(X))))&
((~funny(mary))=>(?[X]:((~wise(X)|~rich(X)))))&
(![X]:((~kind(X)|strong(X))=>(patient(X)|~funny(X))))&
(((~rich(susan)<~>patient(susan)))<=>(?[X]:((curious(X)&generous(X)))))&
((curious(alice))=>(?[X]:(funny(X))))&
(![X]:(brave(X)<=>(creative(X)<~>curious(X))))&
((~calm(paul))<=>(brave(paul)))&
(![X]:(kind(X)=>rich(X)))&
((~rich(fred)&~wise(fred)))&
((~kind(paul)|~creative(paul)))&
((~calm(john)<~>strong(john)))&
(?[X]:((creative(X)<~>quiet(X))))&
((~humble(fred)|rich(fred)))&
(?[X]:((funny(X)<~>happy(X))))&
((~wise(susan)<~>patient(susan)))&
((~rich(paul)&funny(paul))) | rich(alice) | [
"p2",
"p10",
"p15",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 2759240943855599628132873
% SZS output start Proof for 2759240943855599628132873
3. ? [X0] : (rich(X0) | creative(X0)) <=> (~happy(paul) & ~patient(paul)) [input p2]
11. ! [X0] : ((strong(X0) | ~kind(X0)) => (~funny(X0) | patient(X0))) [input p10]
16. ! [X0] : (kind(X0) => rich(X0)) [input p15]
24. funny(paul) & ~rich(paul) [input p23]
25. rich(alice) [input hypothesis]
37. ! [X0] : ((~funny(X0) | patient(X0)) | (~strong(X0) & kind(X0))) [ennf transformation 11]
38. ! [X0] : (~funny(X0) | patient(X0) | (~strong(X0) & kind(X0))) [flattening 37]
40. ! [X0] : (rich(X0) | ~kind(X0)) [ennf transformation 16]
45. (? [X0] : (rich(X0) | creative(X0)) | (happy(paul) | patient(paul))) & ((~happy(paul) & ~patient(paul)) | ! [X0] : (~rich(X0) & ~creative(X0))) [nnf transformation 3]
46. (? [X0] : (rich(X0) | creative(X0)) | happy(paul) | patient(paul)) & ((~happy(paul) & ~patient(paul)) | ! [X0] : (~rich(X0) & ~creative(X0))) [flattening 45]
47. (? [X0] : (rich(X0) | creative(X0)) | happy(paul) | patient(paul)) & ((~happy(paul) & ~patient(paul)) | ! [X1] : (~rich(X1) & ~creative(X1))) [rectify 46]
48. ? [X0] : (rich(X0) | creative(X0)) => (rich(sK1) | creative(sK1)) [choice axiom]
49. ((rich(sK1) | creative(sK1)) | happy(paul) | patient(paul)) & ((~happy(paul) & ~patient(paul)) | ! [X1] : (~rich(X1) & ~creative(X1))) [skolemisation 47,48]
90. ~patient(paul) | ~rich(X1) [cnf transformation 49]
107. ~funny(X0) | patient(X0) | kind(X0) [cnf transformation 38]
122. ~kind(X0) | rich(X0) [cnf transformation 40]
134. ~rich(paul) [cnf transformation 24]
135. funny(paul) [cnf transformation 24]
136. rich(alice) [cnf transformation 25]
168. 7 <=> patient(paul) [avatar definition]
185. 11 <=> ! [X1] : ~rich(X1) [avatar definition]
186. ~rich(X1) <- (11) [avatar component clause 185]
192. 11 | ~7 [avatar split clause 90,168,185]
316. 39 <=> kind(paul) [avatar definition]
317. kind(paul) <- (39) [avatar component clause 316]
368. patient(paul) | kind(paul) [resolution 107,135]
381. 39 | 7 [avatar split clause 368,168,316]
384. $false <- (11) [resolution 186,136]
387. ~11 [avatar contradiction clause 384]
393. rich(paul) <- (39) [resolution 317,122]
403. $false <- (39) [subsumption resolution 393,134]
404. ~39 [avatar contradiction clause 403]
405. $false [avatar sat refutation 192,381,387,404]
% SZS output end Proof for 2759240943855599628132873
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If fred is not wise or quiet then mary is both not patient and not happy and vice versa.
If susan is both wise and not curious then mary is not strong or patient.
Everyone who is not calm or old is brave.
Everyone who is either old or not rich is rich and vice versa.
Everyone who is both not quiet and not patient is both quiet and not kind.
Everyone who is both not kind and not generous is not brave.
If lucy is happy then someone is creative.
Everyone who is either curious or not humble is creative.
Everyone who is creative or brave is both not happy and generous.
If mary is brave or not rich then fred is calm or not generous and vice versa.
Everyone who is both strong and creative is either funny or not happy.
If mary is both patient and calm then susan is calm or strong and vice versa.
Everyone who is happy or not quiet is either humble or strong and vice versa.
Everyone who is not quiet is brave.
If mary is not old then someone is either not quiet or strong and vice versa.
If someone is not patient then someone is either not tall or humble.
Someone is not generous or not creative.
Lucy is either rich or not quiet.
Someone is either tall or brave.
Paul is not wise.
Someone is not creative or humble.
Someone is both brave and not happy.
Lucy is humble or not patient. | Lucy is generous. | entailment | (((~wise(fred)|quiet(fred)))<=>((~patient(mary)&~happy(mary))))&
(((wise(susan)&~curious(susan)))=>((~strong(mary)|patient(mary))))&
(![X]:((~calm(X)|old(X))=>brave(X)))&
(![X]:((old(X)<~>~rich(X))<=>rich(X)))&
(![X]:((~quiet(X)&~patient(X))=>(quiet(X)&~kind(X))))&
(![X]:((~kind(X)&~generous(X))=>~brave(X)))&
((happy(lucy))=>(?[X]:(creative(X))))&
(![X]:((curious(X)<~>~humble(X))=>creative(X)))&
(![X]:((creative(X)|brave(X))=>(~happy(X)&generous(X))))&
(((brave(mary)|~rich(mary)))<=>((calm(fred)|~generous(fred))))&
(![X]:((strong(X)&creative(X))=>(funny(X)<~>~happy(X))))&
(((patient(mary)&calm(mary)))<=>((calm(susan)|strong(susan))))&
(![X]:((happy(X)|~quiet(X))<=>(humble(X)<~>strong(X))))&
(![X]:(~quiet(X)=>brave(X)))&
((~old(mary))<=>(?[X]:((~quiet(X)<~>strong(X)))))&
((?[X]:(~patient(X)))=>(?[X]:((~tall(X)<~>humble(X)))))&
(?[X]:((~generous(X)|~creative(X))))&
((rich(lucy)<~>~quiet(lucy)))&
(?[X]:((tall(X)<~>brave(X))))&
(~wise(paul))&
(?[X]:((~creative(X)|humble(X))))&
(?[X]:((brave(X)&~happy(X))))&
((humble(lucy)|~patient(lucy))) | generous(lucy) | [
"p2",
"p3",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 373779421544383576665029
% SZS output start Proof for 373779421544383576665029
3. ! [X0] : ((old(X0) | ~calm(X0)) => brave(X0)) [input p2]
4. ! [X0] : ((old(X0) <~> ~rich(X0)) <=> rich(X0)) [input p3]
9. ! [X0] : ((brave(X0) | creative(X0)) => (generous(X0) & ~happy(X0))) [input p8]
24. ~generous(lucy) [input hypothesis]
28. ! [X0] : (brave(X0) | (~old(X0) & calm(X0))) [ennf transformation 3]
35. ! [X0] : ((generous(X0) & ~happy(X0)) | (~brave(X0) & ~creative(X0))) [ennf transformation 9]
42. ! [X0] : ((((rich(X0) | ~old(X0)) & (~rich(X0) | old(X0))) | ~rich(X0)) & (rich(X0) | ((old(X0) | rich(X0)) & (~rich(X0) | ~old(X0))))) [nnf transformation 4]
78. ~old(X0) | brave(X0) [cnf transformation 28]
80. rich(X0) | old(X0) | rich(X0) [cnf transformation 42]
81. ~rich(X0) | old(X0) | ~rich(X0) [cnf transformation 42]
92. ~brave(X0) | generous(X0) [cnf transformation 35]
127. ~generous(lucy) [cnf transformation 24]
129. rich(X0) | old(X0) [duplicate literal removal 80]
130. ~rich(X0) | old(X0) [duplicate literal removal 81]
165. old(X0) [subsumption resolution 129,130]
268. brave(X0) [resolution 78,165]
275. generous(X0) [resolution 92,268]
285. $false [resolution 275,127]
% SZS output end Proof for 373779421544383576665029
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is old is not tall. Everyone who is not quiet is either curious or funny. If someone is both not rich and rich then john is either humble or not generous. If someone is either strong or not calm then someone is not tall or rich and vice versa. Everyone who is not wise or not creative is not humble or not strong. Everyone who is not generous or not humble is both old and calm. If fred is either not generous or kind then paul is calm. Everyone who is not patient or strong is brave. Everyone who is not calm is both not old and curious. Everyone who is not happy or funny is calm or old. Everyone who is not humble is old or not strong and vice versa. If john is creative then someone is both not funny and calm and vice versa. If someone is funny then someone is both creative and not quiet and vice versa. Everyone who is not rich is rich or not rich. Everyone who is not brave or not strong is either not rich or funny. Everyone who is tall or old is both humble and quiet and vice versa. Someone is both not rich and not kind. Lucy is not calm or rich. John is old or wise. Someone is brave or not funny. Susan is quiet. Someone is not tall or not rich. | Lucy is wise. | entailment | (![X]:(old(X)=>~tall(X)))&
(![X]:(~quiet(X)=>(curious(X)<~>funny(X))))&
((?[X]:((~rich(X)&rich(X))))=>((humble(john)<~>~generous(john))))&
((?[X]:((strong(X)<~>~calm(X))))<=>(?[X]:((~tall(X)|rich(X)))))&
(![X]:((~wise(X)|~creative(X))=>(~humble(X)|~strong(X))))&
(![X]:((~generous(X)|~humble(X))=>(old(X)&calm(X))))&
(((~generous(fred)<~>kind(fred)))=>(calm(paul)))&
(![X]:((~patient(X)|strong(X))=>brave(X)))&
(![X]:(~calm(X)=>(~old(X)&curious(X))))&
(![X]:((~happy(X)|funny(X))=>(calm(X)|old(X))))&
(![X]:(~humble(X)<=>(old(X)|~strong(X))))&
((creative(john))<=>(?[X]:((~funny(X)&calm(X)))))&
((?[X]:(funny(X)))<=>(?[X]:((creative(X)&~quiet(X)))))&
(![X]:(~rich(X)=>(rich(X)|~rich(X))))&
(![X]:((~brave(X)|~strong(X))=>(~rich(X)<~>funny(X))))&
(![X]:((tall(X)|old(X))<=>(humble(X)&quiet(X))))&
(?[X]:((~rich(X)&~kind(X))))&
((~calm(lucy)|rich(lucy)))&
((old(john)|wise(john)))&
(?[X]:((brave(X)|~funny(X))))&
(quiet(susan))&
(?[X]:((~tall(X)|~rich(X)))) | wise(lucy) | [
"p4",
"p5",
"p10",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6610946335427417049411316
% SZS output start Proof for 6610946335427417049411316
5. ! [X0] : ((~creative(X0) | ~wise(X0)) => (~strong(X0) | ~humble(X0))) [input p4]
6. ! [X0] : ((~humble(X0) | ~generous(X0)) => (calm(X0) & old(X0))) [input p5]
11. ! [X0] : (~humble(X0) <=> (~strong(X0) | old(X0))) [input p10]
16. ! [X0] : ((old(X0) | tall(X0)) <=> (quiet(X0) & humble(X0))) [input p15]
23. ~wise(lucy) [input hypothesis]
33. ! [X0] : ((~strong(X0) | ~humble(X0)) | (creative(X0) & wise(X0))) [ennf transformation 5]
34. ! [X0] : (~strong(X0) | ~humble(X0) | (creative(X0) & wise(X0))) [flattening 33]
35. ! [X0] : ((calm(X0) & old(X0)) | (humble(X0) & generous(X0))) [ennf transformation 6]
51. ! [X0] : ((~humble(X0) | (strong(X0) & ~old(X0))) & ((~strong(X0) | old(X0)) | humble(X0))) [nnf transformation 11]
52. ! [X0] : ((~humble(X0) | (strong(X0) & ~old(X0))) & (~strong(X0) | old(X0) | humble(X0))) [flattening 51]
63. ! [X0] : (((old(X0) | tall(X0)) | (~quiet(X0) | ~humble(X0))) & ((quiet(X0) & humble(X0)) | (~old(X0) & ~tall(X0)))) [nnf transformation 16]
64. ! [X0] : ((old(X0) | tall(X0) | ~quiet(X0) | ~humble(X0)) & ((quiet(X0) & humble(X0)) | (~old(X0) & ~tall(X0)))) [flattening 63]
80. ~strong(X0) | ~humble(X0) | wise(X0) [cnf transformation 34]
83. humble(X0) | old(X0) [cnf transformation 35]
92. ~humble(X0) | ~old(X0) [cnf transformation 52]
93. ~humble(X0) | strong(X0) [cnf transformation 52]
104. humble(X0) | ~old(X0) [cnf transformation 64]
114. ~wise(lucy) [cnf transformation 23]
205. ~old(X0) [subsumption resolution 104,92]
239. strong(X1) | old(X1) [resolution 93,83]
245. strong(X1) [subsumption resolution 239,205]
253. ~humble(X0) | wise(X0) [resolution 80,245]
255. wise(X0) | old(X0) [resolution 253,83]
257. wise(X0) [subsumption resolution 255,205]
260. $false [resolution 257,114]
% SZS output end Proof for 6610946335427417049411316
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
If mary is rich or tall then someone is either calm or rich and vice versa.
Everyone who is old is not strong or humble.
Everyone who is both not curious and quiet is not generous.
If susan is either not strong or not calm then paul is either not strong or not wise.
Everyone who is both not curious and happy is not curious or not kind and vice versa.
If someone is not quiet then fred is either not kind or not curious and vice versa.
If john is not humble or curious then someone is both not tall and not old and vice versa.
Everyone who is generous or not kind is not curious.
Everyone who is both happy and not wise is not wise or not creative.
Everyone who is both quiet and generous is patient.
Everyone who is both rich and not wise is kind or funny and vice versa.
If lucy is humble or not happy then fred is not patient or not happy.
If someone is either kind or not brave then someone is either strong or not old and vice versa.
Everyone who is calm is not brave or calm and vice versa.
If paul is calm or not generous then someone is calm or patient.
Everyone who is both not generous and not wise is not rich or quiet.
Mary is either not generous or old.
John is both not kind and not quiet.
Lucy is either not creative or happy.
Someone is not funny or rich.
Someone is tall or kind.
Someone is either not funny or not rich.
Someone is either creative or not brave.
Lucy is not wise or not humble. | Paul is strong. | neutral | (((rich(mary)|tall(mary)))<=>(?[X]:((calm(X)<~>rich(X)))))&
(![X]:(old(X)=>(~strong(X)|humble(X))))&
(![X]:((~curious(X)&quiet(X))=>~generous(X)))&
(((~strong(susan)<~>~calm(susan)))=>((~strong(paul)<~>~wise(paul))))&
(![X]:((~curious(X)&happy(X))<=>(~curious(X)|~kind(X))))&
((?[X]:(~quiet(X)))<=>((~kind(fred)<~>~curious(fred))))&
(((~humble(john)|curious(john)))<=>(?[X]:((~tall(X)&~old(X)))))&
(![X]:((generous(X)|~kind(X))=>~curious(X)))&
(![X]:((happy(X)&~wise(X))=>(~wise(X)|~creative(X))))&
(![X]:((quiet(X)&generous(X))=>patient(X)))&
(![X]:((rich(X)&~wise(X))<=>(kind(X)|funny(X))))&
(((humble(lucy)|~happy(lucy)))=>((~patient(fred)|~happy(fred))))&
((?[X]:((kind(X)<~>~brave(X))))<=>(?[X]:((strong(X)<~>~old(X)))))&
(![X]:(calm(X)<=>(~brave(X)|calm(X))))&
(((calm(paul)|~generous(paul)))=>(?[X]:((calm(X)|patient(X)))))&
(![X]:((~generous(X)&~wise(X))=>(~rich(X)|quiet(X))))&
((~generous(mary)<~>old(mary)))&
((~kind(john)&~quiet(john)))&
((~creative(lucy)<~>happy(lucy)))&
(?[X]:((~funny(X)|rich(X))))&
(?[X]:((tall(X)|kind(X))))&
(?[X]:((~funny(X)<~>~rich(X))))&
(?[X]:((creative(X)<~>~brave(X))))&
((~wise(lucy)|~humble(lucy))) | strong(paul) | [] | null | 0 |
If susan is either tall or not curious then susan is not happy or kind.
Everyone who is generous is tall and vice versa.
If fred is not brave then someone is either creative or not happy and vice versa.
If paul is both not strong and not old then someone is not tall or not brave and vice versa.
Everyone who is not rich is strong and vice versa.
If alice is both not creative and not wise then alice is not rich or humble and vice versa.
If someone is calm or happy then fred is either not wise or not generous.
Everyone who is both not wise and not kind is quiet and vice versa.
If fred is not wise or not humble then alice is either strong or patient.
Everyone who is both not patient and tall is both not curious and not calm.
If someone is not happy then paul is both rich and not happy.
If someone is either not brave or not strong then someone is rich or quiet.
Everyone who is both not quiet and strong is not brave or creative and vice versa.
Everyone who is brave or not quiet is not wise.
Everyone who is either happy or not brave is both not curious and quiet.
If someone is not brave then alice is both not happy and wise and vice versa.
Fred is rich or not generous.
Someone is generous.
Lucy is not curious or not tall.
Someone is either creative or not creative.
Someone is not kind or not generous. | Fred is rich. | entailment | (((tall(susan)<~>~curious(susan)))=>((~happy(susan)|kind(susan))))&
(![X]:(generous(X)<=>tall(X)))&
((~brave(fred))<=>(?[X]:((creative(X)<~>~happy(X)))))&
(((~strong(paul)&~old(paul)))<=>(?[X]:((~tall(X)|~brave(X)))))&
(![X]:(~rich(X)<=>strong(X)))&
(((~creative(alice)&~wise(alice)))<=>((~rich(alice)|humble(alice))))&
((?[X]:((calm(X)|happy(X))))=>((~wise(fred)<~>~generous(fred))))&
(![X]:((~wise(X)&~kind(X))<=>quiet(X)))&
(((~wise(fred)|~humble(fred)))=>((strong(alice)<~>patient(alice))))&
(![X]:((~patient(X)&tall(X))=>(~curious(X)&~calm(X))))&
((?[X]:(~happy(X)))=>((rich(paul)&~happy(paul))))&
((?[X]:((~brave(X)<~>~strong(X))))=>(?[X]:((rich(X)|quiet(X)))))&
(![X]:((~quiet(X)&strong(X))<=>(~brave(X)|creative(X))))&
(![X]:((brave(X)|~quiet(X))=>~wise(X)))&
(![X]:((happy(X)<~>~brave(X))=>(~curious(X)&quiet(X))))&
((?[X]:(~brave(X)))<=>((~happy(alice)&wise(alice))))&
((rich(fred)|~generous(fred)))&
(?[X]:(generous(X)))&
((~curious(lucy)|~tall(lucy)))&
(?[X]:((creative(X)<~>~creative(X))))&
(?[X]:((~kind(X)|~generous(X)))) | rich(fred) | [
"p2",
"p4",
"p5",
"p6",
"p7",
"p12",
"p13",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 804122789165208836344973
% SZS output start Proof for 804122789165208836344973
3. ~brave(fred) <=> ? [X0] : (creative(X0) <~> ~happy(X0)) [input p2]
5. ! [X0] : (~rich(X0) <=> strong(X0)) [input p4]
6. (~wise(alice) & ~creative(alice)) <=> (humble(alice) | ~rich(alice)) [input p5]
7. ? [X0] : (happy(X0) | calm(X0)) => (~wise(fred) <~> ~generous(fred)) [input p6]
8. ! [X0] : ((~kind(X0) & ~wise(X0)) <=> quiet(X0)) [input p7]
13. ! [X0] : ((strong(X0) & ~quiet(X0)) <=> (creative(X0) | ~brave(X0))) [input p12]
14. ! [X0] : ((~quiet(X0) | brave(X0)) => ~wise(X0)) [input p13]
16. ? [X0] : ~brave(X0) <=> (wise(alice) & ~happy(alice)) [input p15]
17. ~generous(fred) | rich(fred) [input p16]
22. ~rich(fred) [input hypothesis]
25. ? [X0] : happy(X0) => (~wise(fred) <~> ~generous(fred)) [pure predicate removal 7]
28. (~wise(fred) <~> ~generous(fred)) | ! [X0] : ~happy(X0) [ennf transformation 25]
34. ! [X0] : (~wise(X0) | (quiet(X0) & ~brave(X0))) [ennf transformation 14]
38. (~brave(fred) | ! [X0] : ((creative(X0) | happy(X0)) & (~happy(X0) | ~creative(X0)))) & (? [X0] : ((happy(X0) | ~creative(X0)) & (~happy(X0) | creative(X0))) | brave(fred)) [nnf transformation 3]
39. (~brave(fred) | ! [X0] : ((creative(X0) | happy(X0)) & (~happy(X0) | ~creative(X0)))) & (? [X1] : ((happy(X1) | ~creative(X1)) & (~happy(X1) | creative(X1))) | brave(fred)) [rectify 38]
40. ? [X1] : ((happy(X1) | ~creative(X1)) & (~happy(X1) | creative(X1))) => ((happy(sK0) | ~creative(sK0)) & (~happy(sK0) | creative(sK0))) [choice axiom]
41. (~brave(fred) | ! [X0] : ((creative(X0) | happy(X0)) & (~happy(X0) | ~creative(X0)))) & (((happy(sK0) | ~creative(sK0)) & (~happy(sK0) | creative(sK0))) | brave(fred)) [skolemisation 39,40]
47. ! [X0] : ((~rich(X0) | ~strong(X0)) & (strong(X0) | rich(X0))) [nnf transformation 5]
48. ((~wise(alice) & ~creative(alice)) | (~humble(alice) & rich(alice))) & ((humble(alice) | ~rich(alice)) | (wise(alice) | creative(alice))) [nnf transformation 6]
49. ((~wise(alice) & ~creative(alice)) | (~humble(alice) & rich(alice))) & (humble(alice) | ~rich(alice) | wise(alice) | creative(alice)) [flattening 48]
50. ((generous(fred) | wise(fred)) & (~generous(fred) | ~wise(fred))) | ! [X0] : ~happy(X0) [nnf transformation 28]
51. ! [X0] : (((~kind(X0) & ~wise(X0)) | ~quiet(X0)) & (quiet(X0) | (kind(X0) | wise(X0)))) [nnf transformation 8]
52. ! [X0] : (((~kind(X0) & ~wise(X0)) | ~quiet(X0)) & (quiet(X0) | kind(X0) | wise(X0))) [flattening 51]
58. ! [X0] : (((strong(X0) & ~quiet(X0)) | (~creative(X0) & brave(X0))) & ((creative(X0) | ~brave(X0)) | (~strong(X0) | quiet(X0)))) [nnf transformation 13]
59. ! [X0] : (((strong(X0) & ~quiet(X0)) | (~creative(X0) & brave(X0))) & (creative(X0) | ~brave(X0) | ~strong(X0) | quiet(X0))) [flattening 58]
61. (? [X0] : ~brave(X0) | (~wise(alice) | happy(alice))) & ((wise(alice) & ~happy(alice)) | ! [X0] : brave(X0)) [nnf transformation 16]
62. (? [X0] : ~brave(X0) | ~wise(alice) | happy(alice)) & ((wise(alice) & ~happy(alice)) | ! [X0] : brave(X0)) [flattening 61]
63. (? [X0] : ~brave(X0) | ~wise(alice) | happy(alice)) & ((wise(alice) & ~happy(alice)) | ! [X1] : brave(X1)) [rectify 62]
64. ? [X0] : ~brave(X0) => ~brave(sK3) [choice axiom]
65. (~brave(sK3) | ~wise(alice) | happy(alice)) & ((wise(alice) & ~happy(alice)) | ! [X1] : brave(X1)) [skolemisation 63,64]
80. ~brave(fred) | creative(X0) | happy(X0) [cnf transformation 41]
87. ~rich(X0) | ~strong(X0) [cnf transformation 47]
89. ~creative(alice) | rich(alice) [cnf transformation 49]
94. generous(fred) | wise(fred) | ~happy(X0) [cnf transformation 50]
96. ~quiet(X0) | ~wise(X0) [cnf transformation 52]
111. ~creative(X0) | strong(X0) [cnf transformation 59]
113. ~wise(X0) | quiet(X0) [cnf transformation 34]
119. wise(alice) | brave(X1) [cnf transformation 65]
121. ~generous(fred) | rich(fred) [cnf transformation 17]
127. ~rich(fred) [cnf transformation 22]
147. 5 <=> ! [X0] : (creative(X0) | happy(X0)) [avatar definition]
148. creative(X0) | happy(X0) <- (5) [avatar component clause 147]
150. 6 <=> brave(fred) [avatar definition]
152. ~brave(fred) <- (~6) [avatar component clause 150]
153. 5 | ~6 [avatar split clause 80,150,147]
169. 10 <=> ! [X0] : brave(X0) [avatar definition]
170. brave(X0) <- (10) [avatar component clause 169]
205. 18 <=> rich(alice) [avatar definition]
207. rich(alice) <- (18) [avatar component clause 205]
210. 19 <=> creative(alice) [avatar definition]
212. ~creative(alice) <- (~19) [avatar component clause 210]
214. 18 | ~19 [avatar split clause 89,210,205]
217. 20 <=> ! [X0] : ~happy(X0) [avatar definition]
218. ~happy(X0) <- (20) [avatar component clause 217]
220. 21 <=> wise(fred) [avatar definition]
222. wise(fred) <- (21) [avatar component clause 220]
224. 22 <=> generous(fred) [avatar definition]
227. 20 | 21 | 22 [avatar split clause 94,224,220,217]
274. ~wise(X0) [subsumption resolution 113,96]
276. brave(X1) [subsumption resolution 119,274]
277. 10 [avatar split clause 276,169]
284. 34 <=> rich(fred) [avatar definition]
287. 34 | ~22 [avatar split clause 121,224,284]
306. ~34 [avatar split clause 127,284]
307. $false <- (21) [subsumption resolution 222,274]
308. ~21 [avatar contradiction clause 307]
311. $false <- (~6, 10) [subsumption resolution 152,170]
312. 6 | ~10 [avatar contradiction clause 311]
334. happy(alice) <- (5, ~19) [resolution 148,212]
335. happy(X0) | strong(X0) <- (5) [resolution 148,111]
338. $false <- (5, ~19, 20) [subsumption resolution 334,218]
339. ~5 | 19 | ~20 [avatar contradiction clause 338]
340. strong(X0) <- (5, 20) [subsumption resolution 335,218]
342. ~strong(alice) <- (18) [resolution 207,87]
345. $false <- (5, 18, 20) [subsumption resolution 342,340]
346. ~5 | ~18 | ~20 [avatar contradiction clause 345]
349. $false [avatar sat refutation 153,214,227,277,287,306,308,312,339,346]
% SZS output end Proof for 804122789165208836344973
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not funny or kind is both not old and generous.
If paul is generous or not calm then someone is not quiet and vice versa.
Everyone who is funny is not brave or kind.
Everyone who is either old or not strong is either patient or brave and vice versa.
Everyone who is both not old and tall is rich.
Everyone who is both not rich and strong is tall and vice versa.
If john is either funny or not curious then paul is not kind or not calm.
If paul is strong then someone is old.
Everyone who is happy or not old is patient or not strong and vice versa.
Everyone who is both tall and not tall is rich or not strong and vice versa.
If paul is both not calm and not humble then mary is either brave or creative.
Everyone who is tall or rich is either not wise or brave.
Everyone who is both not humble and funny is either not quiet or not generous and vice versa.
Everyone who is not generous is funny or creative and vice versa.
If alice is either not wise or patient then mary is not quiet or happy and vice versa.
Someone is happy.
Someone is either not humble or not quiet.
John is curious or generous.
Someone is not brave. | John is kind. | neutral | (![X]:((~funny(X)<~>kind(X))=>(~old(X)&generous(X))))&
(((generous(paul)|~calm(paul)))<=>(?[X]:(~quiet(X))))&
(![X]:(funny(X)=>(~brave(X)|kind(X))))&
(![X]:((old(X)<~>~strong(X))<=>(patient(X)<~>brave(X))))&
(![X]:((~old(X)&tall(X))=>rich(X)))&
(![X]:((~rich(X)&strong(X))<=>tall(X)))&
(((funny(john)<~>~curious(john)))=>((~kind(paul)|~calm(paul))))&
((strong(paul))=>(?[X]:(old(X))))&
(![X]:((happy(X)|~old(X))<=>(patient(X)|~strong(X))))&
(![X]:((tall(X)&~tall(X))<=>(rich(X)|~strong(X))))&
(((~calm(paul)&~humble(paul)))=>((brave(mary)<~>creative(mary))))&
(![X]:((tall(X)|rich(X))=>(~wise(X)<~>brave(X))))&
(![X]:((~humble(X)&funny(X))<=>(~quiet(X)<~>~generous(X))))&
(![X]:(~generous(X)<=>(funny(X)|creative(X))))&
(((~wise(alice)<~>patient(alice)))<=>((~quiet(mary)|happy(mary))))&
(?[X]:(happy(X)))&
(?[X]:((~humble(X)<~>~quiet(X))))&
((curious(john)|generous(john)))&
(?[X]:(~brave(X))) | kind(john) | [] | null | 0 |
If someone is old or not strong then lucy is either creative or strong and vice versa.
If fred is calm or not calm then mary is not curious or generous and vice versa.
If paul is not patient then someone is brave or rich and vice versa.
Everyone who is either not brave or rich is either happy or not happy and vice versa.
If someone is either not strong or not rich then someone is not kind and vice versa.
Everyone who is rich is either brave or curious.
If fred is either not patient or not brave then someone is not kind or happy and vice versa.
Everyone who is not wise is both not creative and wise and vice versa.
Everyone who is not humble or not brave is not rich and vice versa.
Everyone who is old is both not rich and rich and vice versa.
Everyone who is both not quiet and not brave is both not old and calm and vice versa.
If lucy is not humble then susan is both brave and not quiet and vice versa.
If susan is both not old and rich then mary is either not wise or not generous.
Everyone who is either not creative or wise is creative and vice versa.
If someone is not funny or patient then lucy is old or tall.
Everyone who is both quiet and rich is humble or rich.
Paul is patient.
Someone is either funny or rich.
Alice is not rich or not patient.
Someone is brave or not generous.
Fred is both tall and funny. | Paul is rich. | contradiction | ((?[X]:((old(X)|~strong(X))))<=>((creative(lucy)<~>strong(lucy))))&
(((calm(fred)|~calm(fred)))<=>((~curious(mary)|generous(mary))))&
((~patient(paul))<=>(?[X]:((brave(X)|rich(X)))))&
(![X]:((~brave(X)<~>rich(X))<=>(happy(X)<~>~happy(X))))&
((?[X]:((~strong(X)<~>~rich(X))))<=>(?[X]:(~kind(X))))&
(![X]:(rich(X)=>(brave(X)<~>curious(X))))&
(((~patient(fred)<~>~brave(fred)))<=>(?[X]:((~kind(X)|happy(X)))))&
(![X]:(~wise(X)<=>(~creative(X)&wise(X))))&
(![X]:((~humble(X)|~brave(X))<=>~rich(X)))&
(![X]:(old(X)<=>(~rich(X)&rich(X))))&
(![X]:((~quiet(X)&~brave(X))<=>(~old(X)&calm(X))))&
((~humble(lucy))<=>((brave(susan)&~quiet(susan))))&
(((~old(susan)&rich(susan)))=>((~wise(mary)<~>~generous(mary))))&
(![X]:((~creative(X)<~>wise(X))<=>creative(X)))&
((?[X]:((~funny(X)|patient(X))))=>((old(lucy)|tall(lucy))))&
(![X]:((quiet(X)&rich(X))=>(humble(X)|rich(X))))&
(patient(paul))&
(?[X]:((funny(X)<~>rich(X))))&
((~rich(alice)|~patient(alice)))&
(?[X]:((brave(X)|~generous(X))))&
((tall(fred)&funny(fred))) | rich(paul) | [
"p2",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 2635458715907865439524219
% SZS output start Proof for 2635458715907865439524219
3. ~patient(paul) <=> ? [X0] : (rich(X0) | brave(X0)) [input p2]
17. patient(paul) [input p16]
22. rich(paul) [input hypothesis]
37. (~patient(paul) | ! [X0] : (~rich(X0) & ~brave(X0))) & (? [X0] : (rich(X0) | brave(X0)) | patient(paul)) [nnf transformation 3]
38. (~patient(paul) | ! [X0] : (~rich(X0) & ~brave(X0))) & (? [X1] : (rich(X1) | brave(X1)) | patient(paul)) [rectify 37]
39. ? [X1] : (rich(X1) | brave(X1)) => (rich(sK1) | brave(sK1)) [choice axiom]
40. (~patient(paul) | ! [X0] : (~rich(X0) & ~brave(X0))) & ((rich(sK1) | brave(sK1)) | patient(paul)) [skolemisation 38,39]
81. ~patient(paul) | ~rich(X0) [cnf transformation 40]
125. patient(paul) [cnf transformation 17]
131. rich(paul) [cnf transformation 22]
183. 10 <=> ! [X0] : ~rich(X0) [avatar definition]
184. ~rich(X0) <- (10) [avatar component clause 183]
186. 11 <=> patient(paul) [avatar definition]
189. 10 | ~11 [avatar split clause 81,186,183]
283. 11 [avatar split clause 125,186]
312. $false <- (10) [resolution 184,131]
313. ~10 [avatar contradiction clause 312]
314. $false [avatar sat refutation 189,283,313]
% SZS output end Proof for 2635458715907865439524219
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy is quiet. If someone is calm then paul is both strong and tall. Everyone who is either curious or patient is not funny and vice versa. If john is either not brave or not calm then someone is both quiet and not happy and vice versa. Everyone who is both tall and generous is either humble or not creative and vice versa. If someone is calm or not old then someone is either brave or patient. Everyone who is happy or generous is not quiet or wise and vice versa. Everyone who is both strong and funny is not funny and vice versa. Everyone who is patient is funny or not funny and vice versa. If someone is wise or not generous then john is either not happy or not calm. Everyone who is not rich is not kind or not humble and vice versa. If someone is both happy and not old then paul is happy or not patient. Everyone who is not calm or not creative is not quiet and vice versa. If john is not rich then lucy is kind. Everyone who is not calm is happy or not calm and vice versa. Someone is funny. Someone is either generous or not funny. Someone is not strong. Someone is either not tall or not patient. Mary is not quiet. Someone is curious or rich. Someone is humble or not quiet. | Paul is funny. | entailment | (![X]:(happy(X)=>quiet(X)))&
((?[X]:(calm(X)))=>((strong(paul)&tall(paul))))&
(![X]:((curious(X)<~>patient(X))<=>~funny(X)))&
(((~brave(john)<~>~calm(john)))<=>(?[X]:((quiet(X)&~happy(X)))))&
(![X]:((tall(X)&generous(X))<=>(humble(X)<~>~creative(X))))&
((?[X]:((calm(X)|~old(X))))=>(?[X]:((brave(X)<~>patient(X)))))&
(![X]:((happy(X)|generous(X))<=>(~quiet(X)|wise(X))))&
(![X]:((strong(X)&funny(X))<=>~funny(X)))&
(![X]:(patient(X)<=>(funny(X)|~funny(X))))&
((?[X]:((wise(X)|~generous(X))))=>((~happy(john)<~>~calm(john))))&
(![X]:(~rich(X)<=>(~kind(X)|~humble(X))))&
((?[X]:((happy(X)&~old(X))))=>((happy(paul)|~patient(paul))))&
(![X]:((~calm(X)|~creative(X))<=>~quiet(X)))&
((~rich(john))=>(kind(lucy)))&
(![X]:(~calm(X)<=>(happy(X)|~calm(X))))&
(?[X]:(funny(X)))&
(?[X]:((generous(X)<~>~funny(X))))&
(?[X]:(~strong(X)))&
(?[X]:((~tall(X)<~>~patient(X))))&
(~quiet(mary))&
(?[X]:((curious(X)|rich(X))))&
(?[X]:((humble(X)|~quiet(X)))) | funny(paul) | [
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 664979437278649986781575
% SZS output start Proof for 664979437278649986781575
8. ! [X0] : ((funny(X0) & strong(X0)) <=> ~funny(X0)) [input p7]
23. ~funny(paul) [input hypothesis]
48. ! [X0] : (((funny(X0) & strong(X0)) | funny(X0)) & (~funny(X0) | (~funny(X0) | ~strong(X0)))) [nnf transformation 8]
49. ! [X0] : (((funny(X0) & strong(X0)) | funny(X0)) & (~funny(X0) | ~funny(X0) | ~strong(X0))) [flattening 48]
98. funny(X0) | funny(X0) [cnf transformation 49]
122. ~funny(paul) [cnf transformation 23]
124. funny(X0) [duplicate literal removal 98]
211. $false [subsumption resolution 122,124]
% SZS output end Proof for 664979437278649986781575
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not generous and wise is either not curious or not calm and vice versa.
If someone is not happy or not kind then someone is either tall or kind.
Everyone who is strong is both not kind and old and vice versa.
Everyone who is creative or not strong is not calm or not happy.
If someone is either not kind or patient then susan is both not happy and wise.
Everyone who is old is both not strong and strong.
Everyone who is happy is either not humble or not happy.
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.
Lucy is not funny.
Fred is not patient or not old.
Someone is either quiet or wise.
Lucy is brave.
Someone is happy or not happy. | Fred is generous. | entailment | (![X]:((~generous(X)&wise(X))<=>(~curious(X)<~>~calm(X))))&
((?[X]:((~happy(X)|~kind(X))))=>(?[X]:((tall(X)<~>kind(X)))))&
(![X]:(strong(X)<=>(~kind(X)&old(X))))&
(![X]:((creative(X)|~strong(X))=>(~calm(X)|~happy(X))))&
((?[X]:((~kind(X)<~>patient(X))))=>((~happy(susan)&wise(susan))))&
(![X]:(old(X)=>(~strong(X)&strong(X))))&
(![X]:(happy(X)=>(~humble(X)<~>~happy(X))))&
(((~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)))&
(~funny(lucy))&
((~patient(fred)|~old(fred)))&
(?[X]:((quiet(X)<~>wise(X))))&
(brave(lucy))&
(?[X]:((happy(X)|~happy(X)))) | generous(fred) | [
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 226500388130301297678349
% SZS output start Proof for 226500388130301297678349
14. ! [X0] : ((generous(X0) & ~tall(X0)) <=> (~brave(X0) | brave(X0))) [input p13]
23. ~generous(fred) [input hypothesis]
54. ! [X0] : (((generous(X0) & ~tall(X0)) | (brave(X0) & ~brave(X0))) & ((~brave(X0) | brave(X0)) | (~generous(X0) | tall(X0)))) [nnf transformation 14]
55. ! [X0] : (((generous(X0) & ~tall(X0)) | (brave(X0) & ~brave(X0))) & (~brave(X0) | brave(X0) | ~generous(X0) | tall(X0))) [flattening 54]
112. generous(X0) | ~brave(X0) [cnf transformation 55]
113. generous(X0) | brave(X0) [cnf transformation 55]
128. ~generous(fred) [cnf transformation 23]
202. generous(X0) [subsumption resolution 112,113]
241. $false [subsumption resolution 128,202]
% SZS output end Proof for 226500388130301297678349
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both calm and curious then someone is curious or humble and vice versa.
If someone is tall or creative then john is wise or rich.
Everyone who is either not kind or old is not creative.
Everyone who is both not wise and not strong is either kind or not brave and vice versa.
If lucy is not strong then fred is wise or tall and vice versa.
If someone is funny then someone is both strong and brave and vice versa.
Everyone who is both patient and not calm is not happy or brave and vice versa.
If susan is both not creative and kind then someone is either not humble or brave.
Everyone who is not old is not funny or not happy and vice versa.
If susan is either not strong or humble then someone is happy and vice versa.
If someone is not generous or tall then someone is both humble and not rich.
If someone is both not generous and rich then someone is not old.
Everyone who is not rich or not humble is creative or not calm.
If fred is curious then someone is strong or not strong and vice versa.
If susan is not humble then john is either not strong or calm.
Everyone who is not strong or curious is either wise or generous.
John is either not calm or generous.
Lucy is curious.
Paul is either generous or curious.
Someone is either not strong or humble.
Paul is either not curious or not calm.
Susan is either strong or not humble.
John is strong or generous.
Fred is both creative and patient. | John is rich. | neutral | ((?[X]:((calm(X)&curious(X))))<=>(?[X]:((curious(X)|humble(X)))))&
((?[X]:((tall(X)|creative(X))))=>((wise(john)|rich(john))))&
(![X]:((~kind(X)<~>old(X))=>~creative(X)))&
(![X]:((~wise(X)&~strong(X))<=>(kind(X)<~>~brave(X))))&
((~strong(lucy))<=>((wise(fred)|tall(fred))))&
((?[X]:(funny(X)))<=>(?[X]:((strong(X)&brave(X)))))&
(![X]:((patient(X)&~calm(X))<=>(~happy(X)|brave(X))))&
(((~creative(susan)&kind(susan)))=>(?[X]:((~humble(X)<~>brave(X)))))&
(![X]:(~old(X)<=>(~funny(X)|~happy(X))))&
(((~strong(susan)<~>humble(susan)))<=>(?[X]:(happy(X))))&
((?[X]:((~generous(X)|tall(X))))=>(?[X]:((humble(X)&~rich(X)))))&
((?[X]:((~generous(X)&rich(X))))=>(?[X]:(~old(X))))&
(![X]:((~rich(X)|~humble(X))=>(creative(X)|~calm(X))))&
((curious(fred))<=>(?[X]:((strong(X)|~strong(X)))))&
((~humble(susan))=>((~strong(john)<~>calm(john))))&
(![X]:((~strong(X)|curious(X))=>(wise(X)<~>generous(X))))&
((~calm(john)<~>generous(john)))&
(curious(lucy))&
((generous(paul)<~>curious(paul)))&
(?[X]:((~strong(X)<~>humble(X))))&
((~curious(paul)<~>~calm(paul)))&
((strong(susan)<~>~humble(susan)))&
((strong(john)|generous(john)))&
((creative(fred)&patient(fred))) | rich(john) | [] | null | 0 |
Everyone who is either wise or not patient is both not rich and generous and vice versa.
If someone is either happy or strong then mary is both not humble and not strong.
Everyone who is humble is either patient or not brave and vice versa.
Everyone who is not curious or not patient is not tall or brave.
If someone is either not brave or not creative then someone is humble or not rich and vice versa.
Everyone who is curious or funny is both generous and not rich.
Everyone who is either not tall or not wise is old or patient and vice versa.
Everyone who is both not brave and kind is both not generous and happy.
Everyone who is not tall is both not happy and not generous.
If someone is happy then mary is both tall and not creative and vice versa.
Everyone who is not funny or strong is humble.
If someone is both tall and happy then someone is both not curious and not kind.
If fred is either not brave or not curious then alice is either creative or patient.
Everyone who is both not calm and not brave is not curious or strong.
If mary is not happy then someone is not happy and vice versa.
If someone is old then lucy is both not happy and not wise and vice versa.
Mary is either brave or old.
Fred is both not funny and tall.
Fred is both not happy and humble.
Someone is not old.
Alice is not tall.
Someone is quiet.
Someone is not rich or old.
Someone is either not kind or kind. | Mary is not humble. | contradiction | (![X]:((wise(X)<~>~patient(X))<=>(~rich(X)&generous(X))))&
((?[X]:((happy(X)<~>strong(X))))=>((~humble(mary)&~strong(mary))))&
(![X]:(humble(X)<=>(patient(X)<~>~brave(X))))&
(![X]:((~curious(X)|~patient(X))=>(~tall(X)|brave(X))))&
((?[X]:((~brave(X)<~>~creative(X))))<=>(?[X]:((humble(X)|~rich(X)))))&
(![X]:((curious(X)|funny(X))=>(generous(X)&~rich(X))))&
(![X]:((~tall(X)<~>~wise(X))<=>(old(X)|patient(X))))&
(![X]:((~brave(X)&kind(X))=>(~generous(X)&happy(X))))&
(![X]:(~tall(X)=>(~happy(X)&~generous(X))))&
((?[X]:(happy(X)))<=>((tall(mary)&~creative(mary))))&
(![X]:((~funny(X)|strong(X))=>humble(X)))&
((?[X]:((tall(X)&happy(X))))=>(?[X]:((~curious(X)&~kind(X)))))&
(((~brave(fred)<~>~curious(fred)))=>((creative(alice)<~>patient(alice))))&
(![X]:((~calm(X)&~brave(X))=>(~curious(X)|strong(X))))&
((~happy(mary))<=>(?[X]:(~happy(X))))&
((?[X]:(old(X)))<=>((~happy(lucy)&~wise(lucy))))&
((brave(mary)<~>old(mary)))&
((~funny(fred)&tall(fred)))&
((~happy(fred)&humble(fred)))&
(?[X]:(~old(X)))&
(~tall(alice))&
(?[X]:(quiet(X)))&
(?[X]:((~rich(X)|old(X))))&
(?[X]:((~kind(X)<~>kind(X)))) | ~humble(mary) | [
"p0",
"p2",
"p3",
"p5",
"p6",
"p8",
"p10",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 1398917150174394510845025
% SZS output start Proof for 1398917150174394510845025
1. ! [X0] : ((wise(X0) <~> ~patient(X0)) <=> (generous(X0) & ~rich(X0))) [input p0]
3. ! [X0] : (humble(X0) <=> (patient(X0) <~> ~brave(X0))) [input p2]
4. ! [X0] : ((~patient(X0) | ~curious(X0)) => (brave(X0) | ~tall(X0))) [input p3]
6. ! [X0] : ((funny(X0) | curious(X0)) => (~rich(X0) & generous(X0))) [input p5]
7. ! [X0] : ((~tall(X0) <~> ~wise(X0)) <=> (patient(X0) | old(X0))) [input p6]
9. ! [X0] : (~tall(X0) => (~generous(X0) & ~happy(X0))) [input p8]
11. ! [X0] : ((strong(X0) | ~funny(X0)) => humble(X0)) [input p10]
17. brave(mary) <~> old(mary) [input p16]
25. ~humble(mary) [input hypothesis]
31. ! [X0] : ((brave(X0) | ~tall(X0)) | (patient(X0) & curious(X0))) [ennf transformation 4]
32. ! [X0] : (brave(X0) | ~tall(X0) | (patient(X0) & curious(X0))) [flattening 31]
33. ! [X0] : ((~rich(X0) & generous(X0)) | (~funny(X0) & ~curious(X0))) [ennf transformation 6]
36. ! [X0] : ((~generous(X0) & ~happy(X0)) | tall(X0)) [ennf transformation 9]
37. ! [X0] : (humble(X0) | (~strong(X0) & funny(X0))) [ennf transformation 11]
40. ! [X0] : ((((patient(X0) | ~wise(X0)) & (~patient(X0) | wise(X0))) | (~generous(X0) | rich(X0))) & ((generous(X0) & ~rich(X0)) | ((wise(X0) | patient(X0)) & (~patient(X0) | ~wise(X0))))) [nnf transformation 1]
41. ! [X0] : ((((patient(X0) | ~wise(X0)) & (~patient(X0) | wise(X0))) | ~generous(X0) | rich(X0)) & ((generous(X0) & ~rich(X0)) | ((wise(X0) | patient(X0)) & (~patient(X0) | ~wise(X0))))) [flattening 40]
43. ! [X0] : ((humble(X0) | ((patient(X0) | brave(X0)) & (~brave(X0) | ~patient(X0)))) & (((brave(X0) | ~patient(X0)) & (~brave(X0) | patient(X0))) | ~humble(X0))) [nnf transformation 3]
49. ! [X0] : ((((wise(X0) | tall(X0)) & (~wise(X0) | ~tall(X0))) | (~patient(X0) & ~old(X0))) & ((patient(X0) | old(X0)) | ((~tall(X0) | wise(X0)) & (~wise(X0) | tall(X0))))) [nnf transformation 7]
50. ! [X0] : ((((wise(X0) | tall(X0)) & (~wise(X0) | ~tall(X0))) | (~patient(X0) & ~old(X0))) & (patient(X0) | old(X0) | ((~tall(X0) | wise(X0)) & (~wise(X0) | tall(X0))))) [flattening 49]
69. (~old(mary) | ~brave(mary)) & (old(mary) | brave(mary)) [nnf transformation 17]
80. generous(X0) | wise(X0) | patient(X0) [cnf transformation 41]
81. ~generous(X0) | wise(X0) | ~patient(X0) | rich(X0) [cnf transformation 41]
82. ~generous(X0) | ~wise(X0) | patient(X0) | rich(X0) [cnf transformation 41]
89. ~brave(X0) | humble(X0) | ~patient(X0) [cnf transformation 43]
92. ~tall(X0) | brave(X0) | patient(X0) [cnf transformation 32]
100. ~funny(X0) | generous(X0) [cnf transformation 33]
102. ~funny(X0) | ~rich(X0) [cnf transformation 33]
104. ~tall(X0) | old(X0) | patient(X0) | wise(X0) [cnf transformation 50]
106. ~tall(X0) | ~wise(X0) | ~patient(X0) [cnf transformation 50]
108. ~patient(X0) | tall(X0) | wise(X0) [cnf transformation 50]
112. ~generous(X0) | tall(X0) [cnf transformation 36]
116. funny(X0) | humble(X0) [cnf transformation 37]
130. ~old(mary) | ~brave(mary) [cnf transformation 69]
140. ~humble(mary) [cnf transformation 25]
154. 4 <=> humble(mary) [avatar definition]
156. ~humble(mary) <- (~4) [avatar component clause 154]
194. 13 <=> tall(mary) [avatar definition]
195. tall(mary) <- (13) [avatar component clause 194]
275. 30 <=> brave(mary) [avatar definition]
276. brave(mary) <- (30) [avatar component clause 275]
279. 31 <=> old(mary) [avatar definition]
281. ~old(mary) <- (~31) [avatar component clause 279]
282. ~30 | ~31 [avatar split clause 130,279,275]
293. ~4 [avatar split clause 140,154]
296. ~rich(X0) | humble(X0) [resolution 116,102]
297. humble(X1) | generous(X1) [resolution 116,100]
298. generous(mary) <- (~4) [resolution 297,156]
299. tall(mary) <- (~4) [resolution 298,112]
300. wise(X0) | patient(X0) | tall(X0) [resolution 80,112]
301. tall(X0) | wise(X0) [subsumption resolution 300,108]
319. humble(mary) | ~patient(mary) <- (30) [resolution 89,276]
322. ~patient(mary) <- (~4, 30) [subsumption resolution 319,156]
358. brave(mary) | patient(mary) <- (13) [resolution 92,195]
372. ~wise(mary) | ~patient(mary) <- (13) [resolution 106,195]
382. wise(mary) | ~patient(mary) | rich(mary) <- (~4) [resolution 81,298]
394. ~wise(mary) | patient(mary) | rich(mary) <- (~4) [resolution 82,298]
397. ~wise(mary) | rich(mary) <- (~4, 30) [subsumption resolution 394,322]
399. 41 <=> rich(mary) [avatar definition]
400. ~rich(mary) <- (~41) [avatar component clause 399]
401. rich(mary) <- (41) [avatar component clause 399]
403. 42 <=> wise(mary) [avatar definition]
406. 41 | ~42 | 4 | ~30 [avatar split clause 397,275,154,403,399]
425. old(X0) | patient(X0) | wise(X0) | wise(X0) [resolution 104,301]
429. old(X0) | patient(X0) | wise(X0) [duplicate literal removal 425]
474. patient(mary) | wise(mary) <- (~31) [resolution 429,281]
487. wise(mary) <- (~4, 30, ~31) [subsumption resolution 474,322]
490. 42 | 4 | ~30 | 31 [avatar split clause 487,279,275,154,403]
492. humble(mary) <- (41) [resolution 401,296]
494. $false <- (~4, 41) [subsumption resolution 492,156]
495. 4 | ~41 [avatar contradiction clause 494]
498. 53 <=> patient(mary) [avatar definition]
504. 53 | 30 | ~13 [avatar split clause 358,194,275,498]
510. ~53 | ~42 | ~13 [avatar split clause 372,194,403,498]
511. wise(mary) | ~patient(mary) <- (~4, ~41) [subsumption resolution 382,400]
512. ~53 | 42 | 4 | 41 [avatar split clause 511,399,154,403,498]
515. 13 | 4 [avatar split clause 299,154,194]
516. $false [avatar sat refutation 282,293,406,490,495,504,510,512,515]
% SZS output end Proof for 1398917150174394510845025
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both calm and tall is both generous and patient.
If someone is not humble or calm then someone is either not funny or rich.
Everyone who is both brave and patient is both not wise and not humble.
Everyone who is wise is both old and happy.
Everyone who is either not wise or wise is either not generous or not patient.
If someone is either happy or not calm then paul is either not curious or not tall and vice versa.
If someone is either happy or not kind then someone is both not patient and rich.
If someone is either kind or not kind then someone is not brave or not happy and vice versa.
If lucy is either brave or not quiet then someone is both quiet and old and vice versa.
If alice is generous then john is both not quiet and not curious.
If someone is not brave or creative then someone is humble or not tall and vice versa.
Everyone who is both not old and calm is not curious.
Everyone who is not happy is curious and vice versa.
Everyone who is either quiet or curious is either not kind or strong and vice versa.
Everyone who is kind is calm or not quiet and vice versa.
If susan is not rich or funny then someone is both not strong and not calm.
Fred is quiet or generous.
Someone is not kind or quiet.
Susan is either old or tall.
Someone is not rich.
Someone is both creative and not wise.
Someone is either not tall or not calm.
Someone is both quiet and old.
Paul is strong. | Paul is not wise. | entailment | (![X]:((calm(X)&tall(X))=>(generous(X)&patient(X))))&
((?[X]:((~humble(X)|calm(X))))=>(?[X]:((~funny(X)<~>rich(X)))))&
(![X]:((brave(X)&patient(X))=>(~wise(X)&~humble(X))))&
(![X]:(wise(X)=>(old(X)&happy(X))))&
(![X]:((~wise(X)<~>wise(X))=>(~generous(X)<~>~patient(X))))&
((?[X]:((happy(X)<~>~calm(X))))<=>((~curious(paul)<~>~tall(paul))))&
((?[X]:((happy(X)<~>~kind(X))))=>(?[X]:((~patient(X)&rich(X)))))&
((?[X]:((kind(X)<~>~kind(X))))<=>(?[X]:((~brave(X)|~happy(X)))))&
(((brave(lucy)<~>~quiet(lucy)))<=>(?[X]:((quiet(X)&old(X)))))&
((generous(alice))=>((~quiet(john)&~curious(john))))&
((?[X]:((~brave(X)|creative(X))))<=>(?[X]:((humble(X)|~tall(X)))))&
(![X]:((~old(X)&calm(X))=>~curious(X)))&
(![X]:(~happy(X)<=>curious(X)))&
(![X]:((quiet(X)<~>curious(X))<=>(~kind(X)<~>strong(X))))&
(![X]:(kind(X)<=>(calm(X)|~quiet(X))))&
(((~rich(susan)|funny(susan)))=>(?[X]:((~strong(X)&~calm(X)))))&
((quiet(fred)|generous(fred)))&
(?[X]:((~kind(X)|quiet(X))))&
((old(susan)<~>tall(susan)))&
(?[X]:(~rich(X)))&
(?[X]:((creative(X)&~wise(X))))&
(?[X]:((~tall(X)<~>~calm(X))))&
(?[X]:((quiet(X)&old(X))))&
(strong(paul)) | ~wise(paul) | [
"p0",
"p3",
"p4",
"p5",
"p12",
"p13",
"p14",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 1941861765473275508248774
% SZS output start Proof for 1941861765473275508248774
1. ! [X0] : ((tall(X0) & calm(X0)) => (patient(X0) & generous(X0))) [input p0]
4. ! [X0] : (wise(X0) => (happy(X0) & old(X0))) [input p3]
5. ! [X0] : ((~wise(X0) <~> wise(X0)) => (~generous(X0) <~> ~patient(X0))) [input p4]
6. ? [X0] : (happy(X0) <~> ~calm(X0)) <=> (~curious(paul) <~> ~tall(paul)) [input p5]
13. ! [X0] : (~happy(X0) <=> curious(X0)) [input p12]
14. ! [X0] : ((quiet(X0) <~> curious(X0)) <=> (~kind(X0) <~> strong(X0))) [input p13]
15. ! [X0] : (kind(X0) <=> (~quiet(X0) | calm(X0))) [input p14]
24. strong(paul) [input p23]
25. wise(paul) [input hypothesis]
30. ! [X0] : ((patient(X0) & generous(X0)) | (~tall(X0) | ~calm(X0))) [ennf transformation 1]
31. ! [X0] : ((patient(X0) & generous(X0)) | ~tall(X0) | ~calm(X0)) [flattening 30]
35. ! [X0] : ((happy(X0) & old(X0)) | ~wise(X0)) [ennf transformation 4]
36. ! [X0] : ((~generous(X0) <~> ~patient(X0)) | (~wise(X0) <=> wise(X0))) [ennf transformation 5]
46. ! [X0] : (((patient(X0) | generous(X0)) & (~patient(X0) | ~generous(X0))) | ((~wise(X0) | ~wise(X0)) & (wise(X0) | wise(X0)))) [nnf transformation 36]
47. (? [X0] : ((calm(X0) | ~happy(X0)) & (~calm(X0) | happy(X0))) | ((~curious(paul) | tall(paul)) & (~tall(paul) | curious(paul)))) & (((tall(paul) | curious(paul)) & (~tall(paul) | ~curious(paul))) | ! [X0] : ((happy(X0) | calm(X0)) & (~calm(X0) | ~happy(X0)))) [nnf transformation 6]
48. (? [X0] : ((calm(X0) | ~happy(X0)) & (~calm(X0) | happy(X0))) | ((~curious(paul) | tall(paul)) & (~tall(paul) | curious(paul)))) & (((tall(paul) | curious(paul)) & (~tall(paul) | ~curious(paul))) | ! [X1] : ((happy(X1) | calm(X1)) & (~calm(X1) | ~happy(X1)))) [rectify 47]
49. ? [X0] : ((calm(X0) | ~happy(X0)) & (~calm(X0) | happy(X0))) => ((calm(sK1) | ~happy(sK1)) & (~calm(sK1) | happy(sK1))) [choice axiom]
50. (((calm(sK1) | ~happy(sK1)) & (~calm(sK1) | happy(sK1))) | ((~curious(paul) | tall(paul)) & (~tall(paul) | curious(paul)))) & (((tall(paul) | curious(paul)) & (~tall(paul) | ~curious(paul))) | ! [X1] : ((happy(X1) | calm(X1)) & (~calm(X1) | ~happy(X1)))) [skolemisation 48,49]
69. ! [X0] : ((~happy(X0) | ~curious(X0)) & (curious(X0) | happy(X0))) [nnf transformation 13]
70. ! [X0] : ((((~curious(X0) | ~quiet(X0)) & (curious(X0) | quiet(X0))) | ((~kind(X0) | ~strong(X0)) & (strong(X0) | kind(X0)))) & (((~strong(X0) | kind(X0)) & (strong(X0) | ~kind(X0))) | ((quiet(X0) | ~curious(X0)) & (curious(X0) | ~quiet(X0))))) [nnf transformation 14]
71. ! [X0] : ((kind(X0) | (quiet(X0) & ~calm(X0))) & ((~quiet(X0) | calm(X0)) | ~kind(X0))) [nnf transformation 15]
72. ! [X0] : ((kind(X0) | (quiet(X0) & ~calm(X0))) & (~quiet(X0) | calm(X0) | ~kind(X0))) [flattening 71]
87. ~tall(X0) | generous(X0) | ~calm(X0) [cnf transformation 31]
88. ~tall(X0) | patient(X0) | ~calm(X0) [cnf transformation 31]
96. ~wise(X0) | happy(X0) [cnf transformation 35]
97. ~patient(X0) | ~generous(X0) | wise(X0) | wise(X0) [cnf transformation 46]
98. ~patient(X0) | ~generous(X0) | ~wise(X0) | ~wise(X0) [cnf transformation 46]
103. tall(paul) | curious(paul) | ~calm(X1) | ~happy(X1) [cnf transformation 50]
133. ~curious(X0) | ~happy(X0) [cnf transformation 69]
136. ~strong(X0) | kind(X0) | curious(X0) | ~quiet(X0) [cnf transformation 70]
139. ~strong(X0) | quiet(X0) | ~kind(X0) | curious(X0) [cnf transformation 70]
142. ~quiet(X0) | calm(X0) | ~kind(X0) [cnf transformation 72]
144. quiet(X0) | kind(X0) [cnf transformation 72]
160. strong(paul) [cnf transformation 24]
161. wise(paul) [cnf transformation 25]
164. ~patient(X0) | ~generous(X0) | wise(X0) [duplicate literal removal 97]
165. ~wise(X0) | ~generous(X0) | ~patient(X0) [duplicate literal removal 98]
187. ~patient(X0) | ~generous(X0) [subsumption resolution 164,165]
189. 5 <=> tall(paul) [avatar definition]
191. tall(paul) <- (5) [avatar component clause 189]
193. 6 <=> curious(paul) [avatar definition]
194. curious(paul) <- (6) [avatar component clause 193]
195. ~curious(paul) <- (~6) [avatar component clause 193]
213. 10 <=> ! [X1] : (~calm(X1) | ~happy(X1)) [avatar definition]
214. ~happy(X1) | ~calm(X1) <- (10) [avatar component clause 213]
215. 10 | 6 | 5 [avatar split clause 103,189,193,213]
374. happy(paul) [resolution 96,161]
386. generous(paul) | ~calm(paul) <- (5) [resolution 87,191]
389. 45 <=> calm(paul) [avatar definition]
390. calm(paul) <- (45) [avatar component clause 389]
391. ~calm(paul) <- (~45) [avatar component clause 389]
393. 46 <=> generous(paul) [avatar definition]
395. generous(paul) <- (46) [avatar component clause 393]
396. ~45 | 46 | ~5 [avatar split clause 386,189,393,389]
405. 48 <=> patient(paul) [avatar definition]
406. patient(paul) <- (48) [avatar component clause 405]
469. kind(paul) | curious(paul) | ~quiet(paul) [resolution 136,160]
470. kind(paul) | ~quiet(paul) <- (~6) [subsumption resolution 469,195]
471. kind(paul) <- (~6) [subsumption resolution 470,144]
480. quiet(paul) | ~kind(paul) | curious(paul) [resolution 139,160]
483. quiet(paul) | curious(paul) <- (~6) [subsumption resolution 480,471]
484. quiet(paul) <- (~6) [subsumption resolution 483,195]
486. calm(paul) | ~kind(paul) <- (~6) [resolution 484,142]
487. ~kind(paul) <- (~6, ~45) [subsumption resolution 486,391]
488. $false <- (~6, ~45) [subsumption resolution 487,471]
489. 6 | 45 [avatar contradiction clause 488]
503. ~happy(paul) <- (6) [resolution 194,133]
504. $false <- (6) [subsumption resolution 503,374]
505. ~6 [avatar contradiction clause 504]
513. ~calm(paul) <- (10) [resolution 214,374]
516. $false <- (10, 45) [subsumption resolution 513,390]
517. ~10 | ~45 [avatar contradiction clause 516]
518. patient(paul) | ~calm(paul) <- (5) [resolution 191,88]
520. patient(paul) <- (5, 45) [subsumption resolution 518,390]
521. 48 | ~5 | ~45 [avatar split clause 520,389,189,405]
528. ~generous(paul) <- (48) [resolution 406,187]
529. $false <- (46, 48) [subsumption resolution 528,395]
530. ~46 | ~48 [avatar contradiction clause 529]
531. $false [avatar sat refutation 215,396,489,505,517,521,530]
% SZS output end Proof for 1941861765473275508248774
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not patient and happy is not tall and vice versa. If someone is tall or rich then susan is not old or not curious. Everyone who is not calm or not brave is both happy and not wise and vice versa. Everyone who is either happy or not creative is either not calm or not curious and vice versa. If fred is not funny or not kind then someone is funny. Everyone who is not kind or not quiet is both not humble and happy and vice versa. Everyone who is both happy and not kind is not old. If someone is either not rich or creative then alice is creative and vice versa. Everyone who is creative or curious is not kind or not creative. Everyone who is not brave is not curious or not humble and vice versa. If someone is either happy or not rich then someone is either not humble or not rich and vice versa. If john is both funny and tall then susan is either not humble or funny. Everyone who is not calm or not curious is kind. If someone is both not quiet and patient then fred is patient and vice versa. If john is both quiet and old then susan is not humble and vice versa. Everyone who is not generous is not brave and vice versa. Lucy is either not kind or not rich. Someone is generous. Someone is not old. Someone is not wise. Someone is both tall and strong. | Susan is not strong. | neutral | (![X]:((~patient(X)&happy(X))<=>~tall(X)))&
((?[X]:((tall(X)|rich(X))))=>((~old(susan)|~curious(susan))))&
(![X]:((~calm(X)|~brave(X))<=>(happy(X)&~wise(X))))&
(![X]:((happy(X)<~>~creative(X))<=>(~calm(X)<~>~curious(X))))&
(((~funny(fred)|~kind(fred)))=>(?[X]:(funny(X))))&
(![X]:((~kind(X)|~quiet(X))<=>(~humble(X)&happy(X))))&
(![X]:((happy(X)&~kind(X))=>~old(X)))&
((?[X]:((~rich(X)<~>creative(X))))<=>(creative(alice)))&
(![X]:((creative(X)|curious(X))=>(~kind(X)|~creative(X))))&
(![X]:(~brave(X)<=>(~curious(X)|~humble(X))))&
((?[X]:((happy(X)<~>~rich(X))))<=>(?[X]:((~humble(X)<~>~rich(X)))))&
(((funny(john)&tall(john)))=>((~humble(susan)<~>funny(susan))))&
(![X]:((~calm(X)|~curious(X))=>kind(X)))&
((?[X]:((~quiet(X)&patient(X))))<=>(patient(fred)))&
(((quiet(john)&old(john)))<=>(~humble(susan)))&
(![X]:(~generous(X)<=>~brave(X)))&
((~kind(lucy)<~>~rich(lucy)))&
(?[X]:(generous(X)))&
(?[X]:(~old(X)))&
(?[X]:(~wise(X)))&
(?[X]:((tall(X)&strong(X)))) | ~strong(susan) | [] | null | 0 |
Everyone who is happy is not strong and vice versa.
Everyone who is either not tall or strong is either quiet or not brave and vice versa.
If someone is quiet or brave then someone is both strong and funny.
If susan is both not patient and old then someone is both calm and humble and vice versa.
Everyone who is both rich and not funny is happy and vice versa.
Everyone who is either not old or strong is brave.
Everyone who is either not kind or calm is both creative and tall.
Everyone who is generous or not creative is not happy or kind.
If john is calm or old then someone is both not generous and strong and vice versa.
Everyone who is either calm or not patient is not calm or not tall.
If someone is not curious then someone is both funny and happy and vice versa.
If someone is wise then paul is not generous and vice versa.
Everyone who is both not happy and not old is patient or not curious.
Everyone who is happy or not strong is humble or not rich and vice versa.
If fred is either not brave or not tall then lucy is humble.
If fred is not quiet or not patient then susan is both quiet and funny and vice versa.
Someone is either quiet or not happy.
Alice is not wise or kind.
Alice is either rich or not patient.
Someone is either quiet or not wise.
Someone is either tall or not patient.
Someone is not tall.
Mary is both not wise and curious. | Lucy is rich. | entailment | (![X]:(happy(X)<=>~strong(X)))&
(![X]:((~tall(X)<~>strong(X))<=>(quiet(X)<~>~brave(X))))&
((?[X]:((quiet(X)|brave(X))))=>(?[X]:((strong(X)&funny(X)))))&
(((~patient(susan)&old(susan)))<=>(?[X]:((calm(X)&humble(X)))))&
(![X]:((rich(X)&~funny(X))<=>happy(X)))&
(![X]:((~old(X)<~>strong(X))=>brave(X)))&
(![X]:((~kind(X)<~>calm(X))=>(creative(X)&tall(X))))&
(![X]:((generous(X)|~creative(X))=>(~happy(X)|kind(X))))&
(((calm(john)|old(john)))<=>(?[X]:((~generous(X)&strong(X)))))&
(![X]:((calm(X)<~>~patient(X))=>(~calm(X)|~tall(X))))&
((?[X]:(~curious(X)))<=>(?[X]:((funny(X)&happy(X)))))&
((?[X]:(wise(X)))<=>(~generous(paul)))&
(![X]:((~happy(X)&~old(X))=>(patient(X)|~curious(X))))&
(![X]:((happy(X)|~strong(X))<=>(humble(X)|~rich(X))))&
(((~brave(fred)<~>~tall(fred)))=>(humble(lucy)))&
(((~quiet(fred)|~patient(fred)))<=>((quiet(susan)&funny(susan))))&
(?[X]:((quiet(X)<~>~happy(X))))&
((~wise(alice)|kind(alice)))&
((rich(alice)<~>~patient(alice)))&
(?[X]:((quiet(X)<~>~wise(X))))&
(?[X]:((tall(X)<~>~patient(X))))&
(?[X]:(~tall(X)))&
((~wise(mary)&curious(mary))) | rich(lucy) | [
"p0",
"p4",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 1741262077470194475880819
% SZS output start Proof for 1741262077470194475880819
1. ! [X0] : (happy(X0) <=> ~strong(X0)) [input p0]
5. ! [X0] : ((~funny(X0) & rich(X0)) <=> happy(X0)) [input p4]
14. ! [X0] : ((~strong(X0) | happy(X0)) <=> (~rich(X0) | humble(X0))) [input p13]
24. ~rich(lucy) [input hypothesis]
39. ! [X0] : ((happy(X0) | strong(X0)) & (~strong(X0) | ~happy(X0))) [nnf transformation 1]
49. ! [X0] : (((~funny(X0) & rich(X0)) | ~happy(X0)) & (happy(X0) | (funny(X0) | ~rich(X0)))) [nnf transformation 5]
50. ! [X0] : (((~funny(X0) & rich(X0)) | ~happy(X0)) & (happy(X0) | funny(X0) | ~rich(X0))) [flattening 49]
68. ! [X0] : (((~strong(X0) | happy(X0)) | (rich(X0) & ~humble(X0))) & ((~rich(X0) | humble(X0)) | (strong(X0) & ~happy(X0)))) [nnf transformation 14]
69. ! [X0] : ((~strong(X0) | happy(X0) | (rich(X0) & ~humble(X0))) & (~rich(X0) | humble(X0) | (strong(X0) & ~happy(X0)))) [flattening 68]
86. happy(X0) | strong(X0) [cnf transformation 39]
104. rich(X0) | ~happy(X0) [cnf transformation 50]
127. ~strong(X0) | happy(X0) | rich(X0) [cnf transformation 69]
147. ~rich(lucy) [cnf transformation 24]
240. happy(X0) | rich(X0) [subsumption resolution 127,86]
241. rich(X0) [subsumption resolution 240,104]
320. $false [subsumption resolution 147,241]
% SZS output end Proof for 1741262077470194475880819
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not patient or wise then someone is both not calm and old and vice versa.
If someone is either calm or kind then susan is both happy and brave and vice versa.
Everyone who is patient is either tall or funny.
If lucy is both not rich and generous then paul is not happy and vice versa.
If someone is both not tall and not humble then fred is both brave and not happy.
If mary is both curious and patient then someone is happy or quiet and vice versa.
Everyone who is strong or rich is not patient and vice versa.
If alice is not calm then alice is not curious.
Everyone who is kind or happy is not wise or not strong and vice versa.
If susan is either funny or calm then someone is happy or not patient and vice versa.
Everyone who is not quiet is either tall or not wise and vice versa.
If someone is either creative or not quiet then fred is humble or not wise.
Everyone who is either tall or not curious is not creative or not kind.
Everyone who is kind is either not happy or calm.
Everyone who is happy or not quiet is rich or not wise.
If lucy is not patient then someone is both patient and not calm.
Someone is not brave or not creative.
Someone is not funny or humble.
Someone is not brave.
Susan is rich or not funny.
Susan is both rich and not wise.
Fred is funny or patient.
Alice is both not quiet and happy.
John is both strong and not quiet. | Mary is not curious. | contradiction | ((?[X]:((~patient(X)<~>wise(X))))<=>(?[X]:((~calm(X)&old(X)))))&
((?[X]:((calm(X)<~>kind(X))))<=>((happy(susan)&brave(susan))))&
(![X]:(patient(X)=>(tall(X)<~>funny(X))))&
(((~rich(lucy)&generous(lucy)))<=>(~happy(paul)))&
((?[X]:((~tall(X)&~humble(X))))=>((brave(fred)&~happy(fred))))&
(((curious(mary)&patient(mary)))<=>(?[X]:((happy(X)|quiet(X)))))&
(![X]:((strong(X)|rich(X))<=>~patient(X)))&
((~calm(alice))=>(~curious(alice)))&
(![X]:((kind(X)|happy(X))<=>(~wise(X)|~strong(X))))&
(((funny(susan)<~>calm(susan)))<=>(?[X]:((happy(X)|~patient(X)))))&
(![X]:(~quiet(X)<=>(tall(X)<~>~wise(X))))&
((?[X]:((creative(X)<~>~quiet(X))))=>((humble(fred)|~wise(fred))))&
(![X]:((tall(X)<~>~curious(X))=>(~creative(X)|~kind(X))))&
(![X]:(kind(X)=>(~happy(X)<~>calm(X))))&
(![X]:((happy(X)|~quiet(X))=>(rich(X)|~wise(X))))&
((~patient(lucy))=>(?[X]:((patient(X)&~calm(X)))))&
(?[X]:((~brave(X)|~creative(X))))&
(?[X]:((~funny(X)|humble(X))))&
(?[X]:(~brave(X)))&
((rich(susan)|~funny(susan)))&
((rich(susan)&~wise(susan)))&
((funny(fred)|patient(fred)))&
((~quiet(alice)&happy(alice)))&
((strong(john)&~quiet(john))) | ~curious(mary) | [
"p5",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 3700973781540201600223070
% SZS output start Proof for 3700973781540201600223070
6. (patient(mary) & curious(mary)) <=> ? [X0] : (quiet(X0) | happy(X0)) [input p5]
23. happy(alice) & ~quiet(alice) [input p22]
25. ~curious(mary) [input hypothesis]
51. ((patient(mary) & curious(mary)) | ! [X0] : (~quiet(X0) & ~happy(X0))) & (? [X0] : (quiet(X0) | happy(X0)) | (~patient(mary) | ~curious(mary))) [nnf transformation 6]
52. ((patient(mary) & curious(mary)) | ! [X0] : (~quiet(X0) & ~happy(X0))) & (? [X0] : (quiet(X0) | happy(X0)) | ~patient(mary) | ~curious(mary)) [flattening 51]
53. ((patient(mary) & curious(mary)) | ! [X0] : (~quiet(X0) & ~happy(X0))) & (? [X1] : (quiet(X1) | happy(X1)) | ~patient(mary) | ~curious(mary)) [rectify 52]
54. ? [X1] : (quiet(X1) | happy(X1)) => (quiet(sK3) | happy(sK3)) [choice axiom]
55. ((patient(mary) & curious(mary)) | ! [X0] : (~quiet(X0) & ~happy(X0))) & ((quiet(sK3) | happy(sK3)) | ~patient(mary) | ~curious(mary)) [skolemisation 53,54]
88. curious(mary) | ~happy(X0) [cnf transformation 55]
122. happy(alice) [cnf transformation 23]
125. ~curious(mary) [cnf transformation 25]
209. 19 <=> ! [X0] : ~happy(X0) [avatar definition]
210. ~happy(X0) <- (19) [avatar component clause 209]
213. 20 <=> curious(mary) [avatar definition]
217. 19 | 20 [avatar split clause 88,213,209]
290. ~20 [avatar split clause 125,213]
297. $false <- (19) [resolution 210,122]
298. ~19 [avatar contradiction clause 297]
299. $false [avatar sat refutation 217,290,298]
% SZS output end Proof for 3700973781540201600223070
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong or curious is not patient and vice versa.
If john is generous or not creative then paul is both not kind and not calm.
If mary is both strong and not brave then alice is either not humble or rich and vice versa.
Everyone who is not generous is either patient or not generous and vice versa.
Everyone who is not quiet is not patient.
If someone is brave then susan is both not strong and not funny and vice versa.
If lucy is rich then someone is either not tall or not old.
Everyone who is both not old and not strong is strong or not strong and vice versa.
If someone is calm then alice is strong or humble and vice versa.
If paul is either happy or not brave then john is both not funny and not old.
Everyone who is both brave and not patient is either not humble or strong and vice versa.
If someone is either not strong or kind then fred is either tall or not old.
Everyone who is either not quiet or quiet is calm and vice versa.
If someone is not generous then paul is humble and vice versa.
If susan is either rich or strong then lucy is either not happy or not creative and vice versa.
Everyone who is kind or not brave is patient or not old.
Susan is not tall.
Paul is either not funny or wise.
Mary is either kind or happy.
Mary is either not patient or not wise.
Someone is either rich or curious.
Lucy is both humble and happy.
Someone is funny.
Susan is either not tall or patient. | Susan is not wise. | neutral | (![X]:((~strong(X)<~>curious(X))<=>~patient(X)))&
(((generous(john)|~creative(john)))=>((~kind(paul)&~calm(paul))))&
(((strong(mary)&~brave(mary)))<=>((~humble(alice)<~>rich(alice))))&
(![X]:(~generous(X)<=>(patient(X)<~>~generous(X))))&
(![X]:(~quiet(X)=>~patient(X)))&
((?[X]:(brave(X)))<=>((~strong(susan)&~funny(susan))))&
((rich(lucy))=>(?[X]:((~tall(X)<~>~old(X)))))&
(![X]:((~old(X)&~strong(X))<=>(strong(X)|~strong(X))))&
((?[X]:(calm(X)))<=>((strong(alice)|humble(alice))))&
(((happy(paul)<~>~brave(paul)))=>((~funny(john)&~old(john))))&
(![X]:((brave(X)&~patient(X))<=>(~humble(X)<~>strong(X))))&
((?[X]:((~strong(X)<~>kind(X))))=>((tall(fred)<~>~old(fred))))&
(![X]:((~quiet(X)<~>quiet(X))<=>calm(X)))&
((?[X]:(~generous(X)))<=>(humble(paul)))&
(((rich(susan)<~>strong(susan)))<=>((~happy(lucy)<~>~creative(lucy))))&
(![X]:((kind(X)|~brave(X))=>(patient(X)|~old(X))))&
(~tall(susan))&
((~funny(paul)<~>wise(paul)))&
((kind(mary)<~>happy(mary)))&
((~patient(mary)<~>~wise(mary)))&
(?[X]:((rich(X)<~>curious(X))))&
((humble(lucy)&happy(lucy)))&
(?[X]:(funny(X)))&
((~tall(susan)<~>patient(susan))) | ~wise(susan) | [] | null | 0 |
Everyone who is both not patient and funny is both funny and not humble. If mary is not tall or not quiet then susan is not old and vice versa. If someone is either not quiet or not generous then mary is either wise or kind. If paul is not humble then someone is both not brave and not patient. If someone is both brave and not kind then someone is both calm and wise and vice versa. Everyone who is both not quiet and not creative is either wise or quiet. Everyone who is both not generous and not quiet is old or not humble. If john is not strong or not humble then fred is not strong. Everyone who is both not rich and not kind is humble or not brave. Everyone who is either funny or not funny is not strong or quiet. Everyone who is funny or not humble is either rich or not rich. Everyone who is brave or old is both not creative and not curious and vice versa. Everyone who is not curious or not tall is not curious or not happy and vice versa. If lucy is brave then alice is both strong and not rich. If alice is either not brave or quiet then lucy is either not curious or not brave. If someone is both not patient and patient then someone is not quiet or humble and vice versa. Alice is curious or creative. Someone is either not curious or not humble. Someone is not old or not brave. Alice is both not calm and not wise. Someone is not patient or not brave. John is either humble or not wise. Mary is funny or happy. Someone is either not calm or not happy. | Alice is not quiet. | contradiction | (![X]:((~patient(X)&funny(X))=>(funny(X)&~humble(X))))&
(((~tall(mary)|~quiet(mary)))<=>(~old(susan)))&
((?[X]:((~quiet(X)<~>~generous(X))))=>((wise(mary)<~>kind(mary))))&
((~humble(paul))=>(?[X]:((~brave(X)&~patient(X)))))&
((?[X]:((brave(X)&~kind(X))))<=>(?[X]:((calm(X)&wise(X)))))&
(![X]:((~quiet(X)&~creative(X))=>(wise(X)<~>quiet(X))))&
(![X]:((~generous(X)&~quiet(X))=>(old(X)|~humble(X))))&
(((~strong(john)|~humble(john)))=>(~strong(fred)))&
(![X]:((~rich(X)&~kind(X))=>(humble(X)|~brave(X))))&
(![X]:((funny(X)<~>~funny(X))=>(~strong(X)|quiet(X))))&
(![X]:((funny(X)|~humble(X))=>(rich(X)<~>~rich(X))))&
(![X]:((brave(X)|old(X))<=>(~creative(X)&~curious(X))))&
(![X]:((~curious(X)|~tall(X))<=>(~curious(X)|~happy(X))))&
((brave(lucy))=>((strong(alice)&~rich(alice))))&
(((~brave(alice)<~>quiet(alice)))=>((~curious(lucy)<~>~brave(lucy))))&
((?[X]:((~patient(X)&patient(X))))<=>(?[X]:((~quiet(X)|humble(X)))))&
((curious(alice)|creative(alice)))&
(?[X]:((~curious(X)<~>~humble(X))))&
(?[X]:((~old(X)|~brave(X))))&
((~calm(alice)&~wise(alice)))&
(?[X]:((~patient(X)|~brave(X))))&
((humble(john)<~>~wise(john)))&
((funny(mary)|happy(mary)))&
(?[X]:((~calm(X)<~>~happy(X)))) | ~quiet(alice) | [
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 367412039558392316145104
% SZS output start Proof for 367412039558392316145104
16. ? [X0] : (patient(X0) & ~patient(X0)) <=> ? [X0] : (humble(X0) | ~quiet(X0)) [input p15]
25. ~quiet(alice) [input hypothesis]
27. ? [X0] : (patient(X0) & ~patient(X0)) <=> ? [X1] : (humble(X1) | ~quiet(X1)) [rectify 16]
62. (? [X0] : (patient(X0) & ~patient(X0)) | ! [X1] : (~humble(X1) & quiet(X1))) & (? [X1] : (humble(X1) | ~quiet(X1)) | ! [X0] : (~patient(X0) | patient(X0))) [nnf transformation 27]
63. (? [X0] : (patient(X0) & ~patient(X0)) | ! [X1] : (~humble(X1) & quiet(X1))) & (? [X2] : (humble(X2) | ~quiet(X2)) | ! [X3] : (~patient(X3) | patient(X3))) [rectify 62]
64. ? [X0] : (patient(X0) & ~patient(X0)) => (patient(sK3) & ~patient(sK3)) [choice axiom]
65. ? [X2] : (humble(X2) | ~quiet(X2)) => (humble(sK4) | ~quiet(sK4)) [choice axiom]
66. ((patient(sK3) & ~patient(sK3)) | ! [X1] : (~humble(X1) & quiet(X1))) & ((humble(sK4) | ~quiet(sK4)) | ! [X3] : (~patient(X3) | patient(X3))) [skolemisation 63,65,64]
121. ~patient(sK3) | quiet(X1) [cnf transformation 66]
123. patient(sK3) | quiet(X1) [cnf transformation 66]
137. ~quiet(alice) [cnf transformation 25]
244. 23 <=> quiet(alice) [avatar definition]
246. ~quiet(alice) <- (~23) [avatar component clause 244]
261. 27 <=> patient(sK3) [avatar definition]
266. 28 <=> ! [X1] : quiet(X1) [avatar definition]
267. quiet(X1) <- (28) [avatar component clause 266]
268. 28 | 27 [avatar split clause 123,261,266]
270. 28 | ~27 [avatar split clause 121,261,266]
333. ~23 [avatar split clause 137,244]
334. $false <- (~23, 28) [subsumption resolution 246,267]
335. 23 | ~28 [avatar contradiction clause 334]
336. $false [avatar sat refutation 268,270,333,335]
% SZS output end Proof for 367412039558392316145104
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 fred is either patient or not old then paul is both not generous and old and vice versa.
Everyone who is both patient and not rich is not brave.
Everyone who is both not tall and not strong is not old and vice versa.
If someone is both calm and tall then fred is both not strong and not curious and vice versa.
Everyone who is either strong or not happy is either not funny or not wise.
If someone is both not happy and calm then someone is calm or not humble.
Everyone who is both curious and not calm is both quiet and not funny and vice versa.
If someone is tall or quiet then someone is either calm or tall and vice versa.
Everyone who is either old or strong is not old or not kind.
If someone is not brave or not strong then someone is either not patient or not generous.
Everyone who is not calm or tall is either not humble or not brave.
If someone is either humble or not calm then someone is both not kind and tall and vice versa.
Everyone who is both calm and quiet is generous or wise.
Everyone who is either tall or not curious is both not kind and curious and vice versa.
Everyone who is both tall and not rich is both creative and curious.
Everyone who is kind is brave and vice versa.
Mary is tall or not patient.
Someone is either curious or humble.
Alice is quiet.
Susan is not old.
Someone is both kind and not wise.
Someone is not quiet or strong.
Someone is not happy or not calm. | Alice is not patient. | neutral | (((patient(fred)<~>~old(fred)))<=>((~generous(paul)&old(paul))))&
(![X]:((patient(X)&~rich(X))=>~brave(X)))&
(![X]:((~tall(X)&~strong(X))<=>~old(X)))&
((?[X]:((calm(X)&tall(X))))<=>((~strong(fred)&~curious(fred))))&
(![X]:((strong(X)<~>~happy(X))=>(~funny(X)<~>~wise(X))))&
((?[X]:((~happy(X)&calm(X))))=>(?[X]:((calm(X)|~humble(X)))))&
(![X]:((curious(X)&~calm(X))<=>(quiet(X)&~funny(X))))&
((?[X]:((tall(X)|quiet(X))))<=>(?[X]:((calm(X)<~>tall(X)))))&
(![X]:((old(X)<~>strong(X))=>(~old(X)|~kind(X))))&
((?[X]:((~brave(X)|~strong(X))))=>(?[X]:((~patient(X)<~>~generous(X)))))&
(![X]:((~calm(X)|tall(X))=>(~humble(X)<~>~brave(X))))&
((?[X]:((humble(X)<~>~calm(X))))<=>(?[X]:((~kind(X)&tall(X)))))&
(![X]:((calm(X)&quiet(X))=>(generous(X)|wise(X))))&
(![X]:((tall(X)<~>~curious(X))<=>(~kind(X)&curious(X))))&
(![X]:((tall(X)&~rich(X))=>(creative(X)&curious(X))))&
(![X]:(kind(X)<=>brave(X)))&
((tall(mary)|~patient(mary)))&
(?[X]:((curious(X)<~>humble(X))))&
(quiet(alice))&
(~old(susan))&
(?[X]:((kind(X)&~wise(X))))&
(?[X]:((~quiet(X)|strong(X))))&
(?[X]:((~happy(X)|~calm(X)))) | ~patient(alice) | [] | null | 0 |
If john is both not brave and tall then paul is either kind or not quiet and vice versa.
Everyone who is not happy is both not strong and quiet and vice versa.
Everyone who is both generous and not quiet is not old and vice versa.
If lucy is not creative then paul is creative or strong.
If paul is quiet or strong then someone is not old or not wise.
Everyone who is generous or not wise is not curious or not strong.
Everyone who is not creative is either rich or not wise.
Everyone who is both funny and happy is either not funny or not tall.
If paul is either not humble or rich then alice is both not generous and not creative.
Everyone who is both not tall and generous is either not happy or wise and vice versa.
Everyone who is either creative or not humble is both not strong and curious.
Everyone who is both patient and strong is not humble or patient.
If alice is both not tall and not wise then john is either not brave or not patient and vice versa.
If susan is not funny then someone is either not calm or brave.
If lucy is both creative and not humble then fred is not humble and vice versa.
Everyone who is either not brave or not calm is not strong.
Someone is not patient or not calm.
John is humble.
Someone is both not calm and quiet.
Paul is not old.
Paul is kind.
Someone is quiet.
Someone is either not humble or humble.
Susan is not rich. | Alice is generous. | neutral | (((~brave(john)&tall(john)))<=>((kind(paul)<~>~quiet(paul))))&
(![X]:(~happy(X)<=>(~strong(X)&quiet(X))))&
(![X]:((generous(X)&~quiet(X))<=>~old(X)))&
((~creative(lucy))=>((creative(paul)|strong(paul))))&
(((quiet(paul)|strong(paul)))=>(?[X]:((~old(X)|~wise(X)))))&
(![X]:((generous(X)|~wise(X))=>(~curious(X)|~strong(X))))&
(![X]:(~creative(X)=>(rich(X)<~>~wise(X))))&
(![X]:((funny(X)&happy(X))=>(~funny(X)<~>~tall(X))))&
(((~humble(paul)<~>rich(paul)))=>((~generous(alice)&~creative(alice))))&
(![X]:((~tall(X)&generous(X))<=>(~happy(X)<~>wise(X))))&
(![X]:((creative(X)<~>~humble(X))=>(~strong(X)&curious(X))))&
(![X]:((patient(X)&strong(X))=>(~humble(X)|patient(X))))&
(((~tall(alice)&~wise(alice)))<=>((~brave(john)<~>~patient(john))))&
((~funny(susan))=>(?[X]:((~calm(X)<~>brave(X)))))&
(((creative(lucy)&~humble(lucy)))<=>(~humble(fred)))&
(![X]:((~brave(X)<~>~calm(X))=>~strong(X)))&
(?[X]:((~patient(X)|~calm(X))))&
(humble(john))&
(?[X]:((~calm(X)&quiet(X))))&
(~old(paul))&
(kind(paul))&
(?[X]:(quiet(X)))&
(?[X]:((~humble(X)<~>humble(X))))&
(~rich(susan)) | generous(alice) | [] | null | 0 |
Everyone who is strong is strong or not patient.
If someone is happy then someone is not happy and vice versa.
Everyone who is not patient is both humble and funny and vice versa.
Everyone who is wise is either not tall or happy and vice versa.
If someone is not strong or not calm then fred is either not quiet or funny and vice versa.
Everyone who is both not quiet and patient is either not rich or humble and vice versa.
Everyone who is both kind and funny is either not calm or kind.
If someone is calm or kind then susan is either funny or generous and vice versa.
Everyone who is either not funny or quiet is not quiet and vice versa.
Everyone who is not tall is either not patient or not rich.
Everyone who is not humble or funny is both not tall and not happy and vice versa.
Everyone who is happy or wise is both generous and not tall and vice versa.
If someone is either not curious or calm then someone is both not strong and funny and vice versa.
If someone is both not generous and not happy then lucy is not tall.
Everyone who is either quiet or strong is old.
Everyone who is either not rich or not calm is both not old and kind and vice versa.
Someone is wise.
Someone is not humble or brave.
Someone is both creative and not quiet.
Fred is either not curious or not strong.
Someone is either happy or not creative.
Fred is either strong or rich.
Alice is not happy. | Fred is curious. | entailment | (![X]:(strong(X)=>(strong(X)|~patient(X))))&
((?[X]:(happy(X)))<=>(?[X]:(~happy(X))))&
(![X]:(~patient(X)<=>(humble(X)&funny(X))))&
(![X]:(wise(X)<=>(~tall(X)<~>happy(X))))&
((?[X]:((~strong(X)|~calm(X))))<=>((~quiet(fred)<~>funny(fred))))&
(![X]:((~quiet(X)&patient(X))<=>(~rich(X)<~>humble(X))))&
(![X]:((kind(X)&funny(X))=>(~calm(X)<~>kind(X))))&
((?[X]:((calm(X)|kind(X))))<=>((funny(susan)<~>generous(susan))))&
(![X]:((~funny(X)<~>quiet(X))<=>~quiet(X)))&
(![X]:(~tall(X)=>(~patient(X)<~>~rich(X))))&
(![X]:((~humble(X)|funny(X))<=>(~tall(X)&~happy(X))))&
(![X]:((happy(X)|wise(X))<=>(generous(X)&~tall(X))))&
((?[X]:((~curious(X)<~>calm(X))))<=>(?[X]:((~strong(X)&funny(X)))))&
((?[X]:((~generous(X)&~happy(X))))=>(~tall(lucy)))&
(![X]:((quiet(X)<~>strong(X))=>old(X)))&
(![X]:((~rich(X)<~>~calm(X))<=>(~old(X)&kind(X))))&
(?[X]:(wise(X)))&
(?[X]:((~humble(X)|brave(X))))&
(?[X]:((creative(X)&~quiet(X))))&
((~curious(fred)<~>~strong(fred)))&
(?[X]:((happy(X)<~>~creative(X))))&
((strong(fred)<~>rich(fred)))&
(~happy(alice)) | curious(fred) | [
"p2",
"p3",
"p4",
"p5",
"p8",
"p9",
"p10",
"p11",
"p12",
"p14",
"p15",
"p16",
"p19",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 8185873538161921569409111
% SZS output start Proof for 8185873538161921569409111
3. ! [X0] : (~patient(X0) <=> (funny(X0) & humble(X0))) [input p2]
4. ! [X0] : (wise(X0) <=> (~tall(X0) <~> happy(X0))) [input p3]
5. ? [X0] : (~calm(X0) | ~strong(X0)) <=> (~quiet(fred) <~> funny(fred)) [input p4]
6. ! [X0] : ((patient(X0) & ~quiet(X0)) <=> (~rich(X0) <~> humble(X0))) [input p5]
9. ! [X0] : ((~funny(X0) <~> quiet(X0)) <=> ~quiet(X0)) [input p8]
10. ! [X0] : (~tall(X0) => (~patient(X0) <~> ~rich(X0))) [input p9]
11. ! [X0] : ((funny(X0) | ~humble(X0)) <=> (~happy(X0) & ~tall(X0))) [input p10]
12. ! [X0] : ((wise(X0) | happy(X0)) <=> (~tall(X0) & generous(X0))) [input p11]
13. ? [X0] : (~curious(X0) <~> calm(X0)) <=> ? [X0] : (funny(X0) & ~strong(X0)) [input p12]
15. ! [X0] : ((quiet(X0) <~> strong(X0)) => old(X0)) [input p14]
16. ! [X0] : ((~rich(X0) <~> ~calm(X0)) <=> (kind(X0) & ~old(X0))) [input p15]
17. ? [X0] : wise(X0) [input p16]
20. ~curious(fred) <~> ~strong(fred) [input p19]
22. strong(fred) <~> rich(fred) [input p21]
24. ~curious(fred) [input hypothesis]
26. ? [X0] : (~curious(X0) <~> calm(X0)) <=> ? [X1] : (funny(X1) & ~strong(X1)) [rectify 13]
32. ! [X0] : ((~patient(X0) <~> ~rich(X0)) | tall(X0)) [ennf transformation 10]
34. ! [X0] : (old(X0) | (quiet(X0) <=> strong(X0))) [ennf transformation 15]
40. ! [X0] : ((~patient(X0) | (~funny(X0) | ~humble(X0))) & ((funny(X0) & humble(X0)) | patient(X0))) [nnf transformation 3]
41. ! [X0] : ((~patient(X0) | ~funny(X0) | ~humble(X0)) & ((funny(X0) & humble(X0)) | patient(X0))) [flattening 40]
42. ! [X0] : ((wise(X0) | ((~tall(X0) | ~happy(X0)) & (happy(X0) | tall(X0)))) & (((~happy(X0) | tall(X0)) & (happy(X0) | ~tall(X0))) | ~wise(X0))) [nnf transformation 4]
43. (? [X0] : (~calm(X0) | ~strong(X0)) | ((~quiet(fred) | ~funny(fred)) & (funny(fred) | quiet(fred)))) & (((~funny(fred) | quiet(fred)) & (funny(fred) | ~quiet(fred))) | ! [X0] : (calm(X0) & strong(X0))) [nnf transformation 5]
44. (? [X0] : (~calm(X0) | ~strong(X0)) | ((~quiet(fred) | ~funny(fred)) & (funny(fred) | quiet(fred)))) & (((~funny(fred) | quiet(fred)) & (funny(fred) | ~quiet(fred))) | ! [X1] : (calm(X1) & strong(X1))) [rectify 43]
45. ? [X0] : (~calm(X0) | ~strong(X0)) => (~calm(sK2) | ~strong(sK2)) [choice axiom]
46. ((~calm(sK2) | ~strong(sK2)) | ((~quiet(fred) | ~funny(fred)) & (funny(fred) | quiet(fred)))) & (((~funny(fred) | quiet(fred)) & (funny(fred) | ~quiet(fred))) | ! [X1] : (calm(X1) & strong(X1))) [skolemisation 44,45]
47. ! [X0] : (((patient(X0) & ~quiet(X0)) | ((~rich(X0) | ~humble(X0)) & (humble(X0) | rich(X0)))) & (((~humble(X0) | rich(X0)) & (humble(X0) | ~rich(X0))) | (~patient(X0) | quiet(X0)))) [nnf transformation 6]
48. ! [X0] : (((patient(X0) & ~quiet(X0)) | ((~rich(X0) | ~humble(X0)) & (humble(X0) | rich(X0)))) & (((~humble(X0) | rich(X0)) & (humble(X0) | ~rich(X0))) | ~patient(X0) | quiet(X0))) [flattening 47]
54. ! [X0] : ((((~quiet(X0) | funny(X0)) & (quiet(X0) | ~funny(X0))) | quiet(X0)) & (~quiet(X0) | ((~funny(X0) | ~quiet(X0)) & (quiet(X0) | funny(X0))))) [nnf transformation 9]
55. ! [X0] : (((rich(X0) | patient(X0)) & (~rich(X0) | ~patient(X0))) | tall(X0)) [nnf transformation 32]
56. ! [X0] : (((funny(X0) | ~humble(X0)) | (happy(X0) | tall(X0))) & ((~happy(X0) & ~tall(X0)) | (~funny(X0) & humble(X0)))) [nnf transformation 11]
57. ! [X0] : ((funny(X0) | ~humble(X0) | happy(X0) | tall(X0)) & ((~happy(X0) & ~tall(X0)) | (~funny(X0) & humble(X0)))) [flattening 56]
58. ! [X0] : (((wise(X0) | happy(X0)) | (tall(X0) | ~generous(X0))) & ((~tall(X0) & generous(X0)) | (~wise(X0) & ~happy(X0)))) [nnf transformation 12]
59. ! [X0] : ((wise(X0) | happy(X0) | tall(X0) | ~generous(X0)) & ((~tall(X0) & generous(X0)) | (~wise(X0) & ~happy(X0)))) [flattening 58]
60. (? [X0] : ((~calm(X0) | curious(X0)) & (calm(X0) | ~curious(X0))) | ! [X1] : (~funny(X1) | strong(X1))) & (? [X1] : (funny(X1) & ~strong(X1)) | ! [X0] : ((~curious(X0) | ~calm(X0)) & (calm(X0) | curious(X0)))) [nnf transformation 26]
61. (? [X0] : ((~calm(X0) | curious(X0)) & (calm(X0) | ~curious(X0))) | ! [X1] : (~funny(X1) | strong(X1))) & (? [X2] : (funny(X2) & ~strong(X2)) | ! [X3] : ((~curious(X3) | ~calm(X3)) & (calm(X3) | curious(X3)))) [rectify 60]
62. ? [X0] : ((~calm(X0) | curious(X0)) & (calm(X0) | ~curious(X0))) => ((~calm(sK4) | curious(sK4)) & (calm(sK4) | ~curious(sK4))) [choice axiom]
63. ? [X2] : (funny(X2) & ~strong(X2)) => (funny(sK5) & ~strong(sK5)) [choice axiom]
64. (((~calm(sK4) | curious(sK4)) & (calm(sK4) | ~curious(sK4))) | ! [X1] : (~funny(X1) | strong(X1))) & ((funny(sK5) & ~strong(sK5)) | ! [X3] : ((~curious(X3) | ~calm(X3)) & (calm(X3) | curious(X3)))) [skolemisation 61,63,62]
65. ! [X0] : (old(X0) | ((quiet(X0) | ~strong(X0)) & (strong(X0) | ~quiet(X0)))) [nnf transformation 34]
66. ! [X0] : ((((calm(X0) | rich(X0)) & (~calm(X0) | ~rich(X0))) | (~kind(X0) | old(X0))) & ((kind(X0) & ~old(X0)) | ((~rich(X0) | calm(X0)) & (~calm(X0) | rich(X0))))) [nnf transformation 16]
67. ! [X0] : ((((calm(X0) | rich(X0)) & (~calm(X0) | ~rich(X0))) | ~kind(X0) | old(X0)) & ((kind(X0) & ~old(X0)) | ((~rich(X0) | calm(X0)) & (~calm(X0) | rich(X0))))) [flattening 66]
68. ? [X0] : wise(X0) => wise(sK6) [choice axiom]
69. wise(sK6) [skolemisation 17,68]
72. (strong(fred) | curious(fred)) & (~strong(fred) | ~curious(fred)) [nnf transformation 20]
76. (~rich(fred) | ~strong(fred)) & (rich(fred) | strong(fred)) [nnf transformation 22]
80. humble(X0) | patient(X0) [cnf transformation 41]
83. ~tall(X0) | happy(X0) | ~wise(X0) [cnf transformation 42]
84. ~wise(X0) | tall(X0) | ~happy(X0) [cnf transformation 42]
87. funny(fred) | ~quiet(fred) | strong(X1) [cnf transformation 46]
88. funny(fred) | ~quiet(fred) | calm(X1) [cnf transformation 46]
95. ~quiet(X0) | humble(X0) | rich(X0) [cnf transformation 48]
98. patient(X0) | ~rich(X0) | ~humble(X0) [cnf transformation 48]
108. ~quiet(X0) | ~funny(X0) | ~quiet(X0) [cnf transformation 54]
109. quiet(X0) | ~funny(X0) | quiet(X0) [cnf transformation 54]
111. ~rich(X0) | ~patient(X0) | tall(X0) [cnf transformation 55]
112. rich(X0) | patient(X0) | tall(X0) [cnf transformation 55]
113. ~tall(X0) | humble(X0) [cnf transformation 57]
117. funny(X0) | ~humble(X0) | happy(X0) | tall(X0) [cnf transformation 57]
120. ~tall(X0) | ~happy(X0) [cnf transformation 59]
125. funny(sK5) | calm(X3) | curious(X3) [cnf transformation 64]
131. ~strong(X0) | quiet(X0) | old(X0) [cnf transformation 65]
132. ~old(X0) | ~calm(X0) | rich(X0) [cnf transformation 67]
138. wise(sK6) [cnf transformation 69]
142. strong(fred) | curious(fred) [cnf transformation 72]
146. ~rich(fred) | ~strong(fred) [cnf transformation 76]
148. ~curious(fred) [cnf transformation 24]
149. ~quiet(X0) | ~funny(X0) [duplicate literal removal 108]
150. ~funny(X0) | quiet(X0) [duplicate literal removal 109]
169. 5 <=> funny(fred) [avatar definition]
170. funny(fred) <- (5) [avatar component clause 169]
173. 6 <=> quiet(fred) [avatar definition]
175. ~quiet(fred) <- (~6) [avatar component clause 173]
187. 9 <=> ! [X1] : calm(X1) [avatar definition]
188. calm(X1) <- (9) [avatar component clause 187]
191. 10 <=> ! [X1] : strong(X1) [avatar definition]
192. strong(X1) <- (10) [avatar component clause 191]
194. 9 | ~6 | 5 [avatar split clause 88,169,173,187]
195. 10 | ~6 | 5 [avatar split clause 87,169,173,191]
196. ~rich(X0) | patient(X0) [subsumption resolution 98,80]
226. ~funny(X0) [subsumption resolution 149,150]
227. tall(X0) | patient(X0) [subsumption resolution 112,196]
228. ~rich(X0) | tall(X0) [subsumption resolution 111,227]
229. ~humble(X0) | happy(X0) | tall(X0) [subsumption resolution 117,226]
231. curious(X3) | calm(X3) [subsumption resolution 125,226]
242. 19 <=> curious(fred) [avatar definition]
243. ~curious(fred) <- (~19) [avatar component clause 242]
246. 20 <=> strong(fred) [avatar definition]
248. strong(fred) <- (20) [avatar component clause 246]
249. 19 | 20 [avatar split clause 142,246,242]
262. 23 <=> rich(fred) [avatar definition]
264. ~rich(fred) <- (~23) [avatar component clause 262]
265. ~20 | ~23 [avatar split clause 146,262,246]
267. ~19 [avatar split clause 148,242]
277. calm(fred) <- (~19) [resolution 231,243]
281. tall(sK6) | ~happy(sK6) [resolution 84,138]
282. ~happy(sK6) [subsumption resolution 281,120]
308. quiet(fred) | old(fred) <- (20) [resolution 131,248]
309. old(fred) <- (~6, 20) [subsumption resolution 308,175]
310. ~calm(fred) | rich(fred) <- (~6, 20) [resolution 132,309]
311. rich(fred) <- (~6, ~19, 20) [subsumption resolution 310,277]
312. $false <- (~6, ~19, 20, ~23) [subsumption resolution 311,264]
313. 6 | 19 | ~20 | 23 [avatar contradiction clause 312]
324. old(X0) | quiet(X0) <- (10) [resolution 192,131]
408. quiet(X1) | ~calm(X1) | rich(X1) <- (10) [resolution 324,132]
409. rich(X1) | quiet(X1) <- (9, 10) [subsumption resolution 408,188]
419. quiet(X3) | tall(X3) <- (9, 10) [resolution 409,228]
436. tall(X1) | humble(X1) | rich(X1) <- (9, 10) [resolution 419,95]
439. rich(X1) | humble(X1) <- (9, 10) [subsumption resolution 436,113]
468. humble(X3) | tall(X3) <- (9, 10) [resolution 439,228]
472. humble(X3) <- (9, 10) [subsumption resolution 468,113]
475. tall(X1) | happy(X1) <- (9, 10) [resolution 472,229]
478. happy(X1) | happy(X1) | ~wise(X1) <- (9, 10) [resolution 475,83]
482. ~wise(X1) | happy(X1) <- (9, 10) [duplicate literal removal 478]
489. happy(sK6) <- (9, 10) [resolution 482,138]
491. $false <- (9, 10) [subsumption resolution 489,282]
492. ~9 | ~10 [avatar contradiction clause 491]
495. $false <- (5) [subsumption resolution 170,226]
496. ~5 [avatar contradiction clause 495]
497. $false [avatar sat refutation 194,195,249,265,267,313,492,496]
% SZS output end Proof for 8185873538161921569409111
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not strong or not wise is both funny and patient. Everyone who is both funny and not creative is not wise or not old and vice versa. If mary is creative then someone is not brave and vice versa. Everyone who is tall is both not happy and happy and vice versa. Everyone who is quiet is either not creative or patient. Everyone who is not old is either not strong or not happy. Everyone who is not old is either happy or humble. Everyone who is not generous or not rich is quiet and vice versa. Everyone who is quiet or not creative is either not creative or happy and vice versa. If someone is not patient or not creative then someone is not rich or not kind. Everyone who is quiet or not brave is either brave or patient and vice versa. If lucy is either kind or not kind then someone is either quiet or funny. Everyone who is either not happy or not strong is patient and vice versa. Everyone who is happy or old is either calm or not curious and vice versa. Everyone who is kind is not old or rich and vice versa. Lucy is either creative or calm. Paul is funny. Mary is both funny and patient. Susan is strong. Someone is both kind and not brave. Someone is either strong or not kind. Lucy is curious. | Susan is not generous. | contradiction | (![X]:((~strong(X)|~wise(X))=>(funny(X)&patient(X))))&
(![X]:((funny(X)&~creative(X))<=>(~wise(X)|~old(X))))&
((creative(mary))<=>(?[X]:(~brave(X))))&
(![X]:(tall(X)<=>(~happy(X)&happy(X))))&
(![X]:(quiet(X)=>(~creative(X)<~>patient(X))))&
(![X]:(~old(X)=>(~strong(X)<~>~happy(X))))&
(![X]:(~old(X)=>(happy(X)<~>humble(X))))&
(![X]:((~generous(X)|~rich(X))<=>quiet(X)))&
(![X]:((quiet(X)|~creative(X))<=>(~creative(X)<~>happy(X))))&
((?[X]:((~patient(X)|~creative(X))))=>(?[X]:((~rich(X)|~kind(X)))))&
(![X]:((quiet(X)|~brave(X))<=>(brave(X)<~>patient(X))))&
(((kind(lucy)<~>~kind(lucy)))=>(?[X]:((quiet(X)<~>funny(X)))))&
(![X]:((~happy(X)<~>~strong(X))<=>patient(X)))&
(![X]:((happy(X)|old(X))<=>(calm(X)<~>~curious(X))))&
(![X]:(kind(X)<=>(~old(X)|rich(X))))&
((creative(lucy)<~>calm(lucy)))&
(funny(paul))&
((funny(mary)&patient(mary)))&
(strong(susan))&
(?[X]:((kind(X)&~brave(X))))&
(?[X]:((strong(X)<~>~kind(X))))&
(curious(lucy)) | ~generous(susan) | [
"p0",
"p4",
"p7",
"p8",
"p12",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 7717449803728375457760729
% SZS output start Proof for 7717449803728375457760729
1. ! [X0] : ((~wise(X0) | ~strong(X0)) => (patient(X0) & funny(X0))) [input p0]
5. ! [X0] : (quiet(X0) => (~creative(X0) <~> patient(X0))) [input p4]
8. ! [X0] : ((~rich(X0) | ~generous(X0)) <=> quiet(X0)) [input p7]
9. ! [X0] : ((~creative(X0) | quiet(X0)) <=> (~creative(X0) <~> happy(X0))) [input p8]
13. ! [X0] : ((~happy(X0) <~> ~strong(X0)) <=> patient(X0)) [input p12]
19. strong(susan) [input p18]
23. ~generous(susan) [input hypothesis]
25. ! [X0] : ((patient(X0) & funny(X0)) | (wise(X0) & strong(X0))) [ennf transformation 1]
26. ! [X0] : ((~creative(X0) <~> patient(X0)) | ~quiet(X0)) [ennf transformation 5]
37. ! [X0] : (((~patient(X0) | creative(X0)) & (patient(X0) | ~creative(X0))) | ~quiet(X0)) [nnf transformation 26]
40. ! [X0] : (((~rich(X0) | ~generous(X0)) | ~quiet(X0)) & (quiet(X0) | (rich(X0) & generous(X0)))) [nnf transformation 8]
41. ! [X0] : ((~rich(X0) | ~generous(X0) | ~quiet(X0)) & (quiet(X0) | (rich(X0) & generous(X0)))) [flattening 40]
42. ! [X0] : (((~creative(X0) | quiet(X0)) | ((~creative(X0) | ~happy(X0)) & (happy(X0) | creative(X0)))) & (((~happy(X0) | creative(X0)) & (happy(X0) | ~creative(X0))) | (creative(X0) & ~quiet(X0)))) [nnf transformation 9]
43. ! [X0] : ((~creative(X0) | quiet(X0) | ((~creative(X0) | ~happy(X0)) & (happy(X0) | creative(X0)))) & (((~happy(X0) | creative(X0)) & (happy(X0) | ~creative(X0))) | (creative(X0) & ~quiet(X0)))) [flattening 42]
52. ! [X0] : ((((strong(X0) | happy(X0)) & (~strong(X0) | ~happy(X0))) | ~patient(X0)) & (patient(X0) | ((~happy(X0) | strong(X0)) & (~strong(X0) | happy(X0))))) [nnf transformation 13]
65. patient(X0) | strong(X0) [cnf transformation 25]
74. ~quiet(X0) | ~creative(X0) | patient(X0) [cnf transformation 37]
75. ~quiet(X0) | creative(X0) | ~patient(X0) [cnf transformation 37]
80. generous(X0) | quiet(X0) [cnf transformation 41]
83. ~quiet(X0) | ~creative(X0) | happy(X0) [cnf transformation 43]
86. ~happy(X0) | creative(X0) | creative(X0) [cnf transformation 43]
101. patient(X0) | ~strong(X0) | happy(X0) [cnf transformation 52]
103. ~happy(X0) | ~strong(X0) | ~patient(X0) [cnf transformation 52]
104. strong(X0) | happy(X0) | ~patient(X0) [cnf transformation 52]
119. strong(susan) [cnf transformation 19]
125. ~generous(susan) [cnf transformation 23]
132. ~happy(X0) | creative(X0) [duplicate literal removal 86]
179. happy(X0) | strong(X0) [subsumption resolution 104,65]
180. happy(X0) | patient(X0) [subsumption resolution 101,179]
207. quiet(susan) [resolution 80,125]
214. patient(X0) | creative(X0) [resolution 180,132]
218. ~creative(susan) | patient(susan) [resolution 74,207]
220. patient(susan) [subsumption resolution 218,214]
222. creative(susan) | ~patient(susan) [resolution 75,207]
224. creative(susan) [subsumption resolution 222,220]
246. ~creative(susan) | happy(susan) [resolution 83,207]
250. happy(susan) [subsumption resolution 246,224]
272. ~strong(susan) | ~patient(susan) [resolution 250,103]
275. ~patient(susan) [subsumption resolution 272,119]
276. $false [subsumption resolution 275,220]
% SZS output end Proof for 7717449803728375457760729
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative is both creative and happy and vice versa.
If someone is quiet or wise then susan is both not brave and not wise.
If someone is both not old and strong then someone is both not calm and brave and vice versa.
Everyone who is strong or not quiet is not happy or not rich.
If someone is generous then mary is either not happy or rich and vice versa.
If john is not brave or not happy then someone is patient or not tall and vice versa.
Everyone who is kind or generous is both rich and not calm.
Everyone who is funny is either calm or not rich.
Everyone who is either not strong or not generous is tall or not strong.
If paul is either funny or creative then someone is funny or not curious.
If paul is both creative and not humble then someone is strong or not quiet.
Everyone who is either quiet or creative is not generous.
If mary is not creative then someone is not brave.
Everyone who is old or not old is kind.
Everyone who is generous is both not patient and not curious and vice versa.
Someone is rich.
Paul is either not funny or not curious.
Someone is either wise or not tall.
Fred is either not brave or not quiet.
Someone is strong.
John is both not tall and patient. | Fred is not happy. | entailment | (![X]:(~creative(X)<=>(creative(X)&happy(X))))&
((?[X]:((quiet(X)|wise(X))))=>((~brave(susan)&~wise(susan))))&
((?[X]:((~old(X)&strong(X))))<=>(?[X]:((~calm(X)&brave(X)))))&
(![X]:((strong(X)|~quiet(X))=>(~happy(X)|~rich(X))))&
((?[X]:(generous(X)))<=>((~happy(mary)<~>rich(mary))))&
(((~brave(john)|~happy(john)))<=>(?[X]:((patient(X)|~tall(X)))))&
(![X]:((kind(X)|generous(X))=>(rich(X)&~calm(X))))&
(![X]:(funny(X)=>(calm(X)<~>~rich(X))))&
(![X]:((~strong(X)<~>~generous(X))=>(tall(X)|~strong(X))))&
(((funny(paul)<~>creative(paul)))=>(?[X]:((funny(X)|~curious(X)))))&
(((creative(paul)&~humble(paul)))=>(?[X]:((strong(X)|~quiet(X)))))&
(![X]:((quiet(X)<~>creative(X))=>~generous(X)))&
((~creative(mary))=>(?[X]:(~brave(X))))&
(![X]:((old(X)|~old(X))=>kind(X)))&
(![X]:(generous(X)<=>(~patient(X)&~curious(X))))&
(?[X]:(rich(X)))&
((~funny(paul)<~>~curious(paul)))&
(?[X]:((wise(X)<~>~tall(X))))&
((~brave(fred)<~>~quiet(fred)))&
(?[X]:(strong(X)))&
((~tall(john)&patient(john))) | ~happy(fred) | [
"p0",
"hypothesis"
] | % SZS status Unsatisfiable for 867237408227529625180635
% SZS output start Proof for 867237408227529625180635
1. ! [X0] : (~creative(X0) <=> (happy(X0) & creative(X0))) [input p0]
22. happy(fred) [input hypothesis]
36. ! [X0] : ((~creative(X0) | (~happy(X0) | ~creative(X0))) & ((happy(X0) & creative(X0)) | creative(X0))) [nnf transformation 1]
37. ! [X0] : ((~creative(X0) | ~happy(X0) | ~creative(X0)) & ((happy(X0) & creative(X0)) | creative(X0))) [flattening 36]
71. creative(X0) | creative(X0) [cnf transformation 37]
73. ~creative(X0) | ~happy(X0) | ~creative(X0) [cnf transformation 37]
120. happy(fred) [cnf transformation 22]
122. creative(X0) [duplicate literal removal 71]
123. ~happy(X0) | ~creative(X0) [duplicate literal removal 73]
265. ~creative(fred) [resolution 123,120]
267. $false [subsumption resolution 265,122]
% SZS output end Proof for 867237408227529625180635
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich then john is both happy and strong.
If someone is not kind then someone is tall and vice versa.
If someone is strong or humble then someone is quiet and vice versa.
Everyone who is both not quiet and not generous is old or generous.
Everyone who is tall or calm is both not patient and not kind and vice versa.
If john is both not quiet and not rich then susan is not curious or not strong.
Everyone who is not strong or wise is not tall.
Everyone who is either not old or rich is not quiet or funny and vice versa.
Everyone who is patient is wise or patient and vice versa.
If someone is both quiet and not generous then fred is not funny or not quiet.
If susan is either generous or not brave then someone is both not creative and happy and vice versa.
Everyone who is either old or not quiet is not strong.
Everyone who is both not tall and patient is creative or strong and vice versa.
If someone is either creative or not happy then someone is either not patient or strong and vice versa.
Everyone who is both humble and happy is both curious and creative and vice versa.
If someone is not old or tall then fred is both not funny and funny and vice versa.
Mary is not calm.
Susan is either not calm or not funny.
Lucy is not creative.
Lucy is wise.
Paul is both not wise and old.
Someone is both not generous and humble.
Someone is rich.
Paul is quiet. | Lucy is old. | entailment | ((?[X]:(rich(X)))=>((happy(john)&strong(john))))&
((?[X]:(~kind(X)))<=>(?[X]:(tall(X))))&
((?[X]:((strong(X)|humble(X))))<=>(?[X]:(quiet(X))))&
(![X]:((~quiet(X)&~generous(X))=>(old(X)|generous(X))))&
(![X]:((tall(X)|calm(X))<=>(~patient(X)&~kind(X))))&
(((~quiet(john)&~rich(john)))=>((~curious(susan)|~strong(susan))))&
(![X]:((~strong(X)|wise(X))=>~tall(X)))&
(![X]:((~old(X)<~>rich(X))<=>(~quiet(X)|funny(X))))&
(![X]:(patient(X)<=>(wise(X)|patient(X))))&
((?[X]:((quiet(X)&~generous(X))))=>((~funny(fred)|~quiet(fred))))&
(((generous(susan)<~>~brave(susan)))<=>(?[X]:((~creative(X)&happy(X)))))&
(![X]:((old(X)<~>~quiet(X))=>~strong(X)))&
(![X]:((~tall(X)&patient(X))<=>(creative(X)|strong(X))))&
((?[X]:((creative(X)<~>~happy(X))))<=>(?[X]:((~patient(X)<~>strong(X)))))&
(![X]:((humble(X)&happy(X))<=>(curious(X)&creative(X))))&
((?[X]:((~old(X)|tall(X))))<=>((~funny(fred)&funny(fred))))&
(~calm(mary))&
((~calm(susan)<~>~funny(susan)))&
(~creative(lucy))&
(wise(lucy))&
((~wise(paul)&old(paul)))&
(?[X]:((~generous(X)&humble(X))))&
(?[X]:(rich(X)))&
(quiet(paul)) | old(lucy) | [
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 437569526060153145277077
% SZS output start Proof for 437569526060153145277077
16. ? [X0] : (tall(X0) | ~old(X0)) <=> (funny(fred) & ~funny(fred)) [input p15]
25. ~old(lucy) [input hypothesis]
68. (? [X0] : (tall(X0) | ~old(X0)) | (~funny(fred) | funny(fred))) & ((funny(fred) & ~funny(fred)) | ! [X0] : (~tall(X0) & old(X0))) [nnf transformation 16]
69. (? [X0] : (tall(X0) | ~old(X0)) | ~funny(fred) | funny(fred)) & ((funny(fred) & ~funny(fred)) | ! [X0] : (~tall(X0) & old(X0))) [flattening 68]
70. (? [X0] : (tall(X0) | ~old(X0)) | ~funny(fred) | funny(fred)) & ((funny(fred) & ~funny(fred)) | ! [X1] : (~tall(X1) & old(X1))) [rectify 69]
71. ? [X0] : (tall(X0) | ~old(X0)) => (tall(sK7) | ~old(sK7)) [choice axiom]
72. ((tall(sK7) | ~old(sK7)) | ~funny(fred) | funny(fred)) & ((funny(fred) & ~funny(fred)) | ! [X1] : (~tall(X1) & old(X1))) [skolemisation 70,71]
129. ~funny(fred) | old(X1) [cnf transformation 72]
131. funny(fred) | old(X1) [cnf transformation 72]
145. ~old(lucy) [cnf transformation 25]
221. 19 <=> funny(fred) [avatar definition]
294. 33 <=> ! [X1] : old(X1) [avatar definition]
295. old(X1) <- (33) [avatar component clause 294]
296. 33 | 19 [avatar split clause 131,221,294]
298. 33 | ~19 [avatar split clause 129,221,294]
309. $false <- (33) [resolution 295,145]
310. ~33 [avatar contradiction clause 309]
311. $false [avatar sat refutation 296,298,310]
% SZS output end Proof for 437569526060153145277077
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not wise and kind is not funny. If someone is either wise or humble then someone is not kind or not happy and vice versa. If mary is both not wise and funny then alice is either not happy or old and vice versa. Everyone who is not quiet is either not creative or not kind. Everyone who is both not happy and brave is wise or brave. Everyone who is brave is not calm or patient and vice versa. Everyone who is not humble is both not quiet and old. Everyone who is generous or curious is not curious. If someone is funny then someone is old or strong. Everyone who is either rich or creative is either not quiet or calm and vice versa. Everyone who is both not tall and not humble is not kind or humble. If someone is both not rich and curious then someone is tall and vice versa. If someone is either not brave or not humble then alice is both not wise and not happy. Everyone who is either curious or calm is wise or tall. If someone is both humble and happy then someone is either not old or creative. If john is kind or not kind then fred is not humble or happy. Someone is both kind and old. Lucy is tall or not creative. John is either wise or quiet. Someone is either not curious or not kind. Fred is either not curious or rich. Someone is wise or creative. | Fred is humble. | neutral | (![X]:((~wise(X)&kind(X))=>~funny(X)))&
((?[X]:((wise(X)<~>humble(X))))<=>(?[X]:((~kind(X)|~happy(X)))))&
(((~wise(mary)&funny(mary)))<=>((~happy(alice)<~>old(alice))))&
(![X]:(~quiet(X)=>(~creative(X)<~>~kind(X))))&
(![X]:((~happy(X)&brave(X))=>(wise(X)|brave(X))))&
(![X]:(brave(X)<=>(~calm(X)|patient(X))))&
(![X]:(~humble(X)=>(~quiet(X)&old(X))))&
(![X]:((generous(X)|curious(X))=>~curious(X)))&
((?[X]:(funny(X)))=>(?[X]:((old(X)|strong(X)))))&
(![X]:((rich(X)<~>creative(X))<=>(~quiet(X)<~>calm(X))))&
(![X]:((~tall(X)&~humble(X))=>(~kind(X)|humble(X))))&
((?[X]:((~rich(X)&curious(X))))<=>(?[X]:(tall(X))))&
((?[X]:((~brave(X)<~>~humble(X))))=>((~wise(alice)&~happy(alice))))&
(![X]:((curious(X)<~>calm(X))=>(wise(X)|tall(X))))&
((?[X]:((humble(X)&happy(X))))=>(?[X]:((~old(X)<~>creative(X)))))&
(((kind(john)|~kind(john)))=>((~humble(fred)|happy(fred))))&
(?[X]:((kind(X)&old(X))))&
((tall(lucy)|~creative(lucy)))&
((wise(john)<~>quiet(john)))&
(?[X]:((~curious(X)<~>~kind(X))))&
((~curious(fred)<~>rich(fred)))&
(?[X]:((wise(X)|creative(X)))) | humble(fred) | [] | null | 0 |
If fred is either happy or humble then someone is brave.
Everyone who is strong is creative and vice versa.
Everyone who is rich is both generous and creative and vice versa.
If someone is not curious then alice is both not tall and not calm and vice versa.
If fred is both strong and rich then someone is funny.
Everyone who is both not brave and generous is either not funny or not happy and vice versa.
Everyone who is either not wise or not tall is either quiet or not brave and vice versa.
Everyone who is not brave or not kind is creative or not quiet.
Everyone who is either not brave or kind is not curious.
If fred is tall or strong then john is both brave and not rich and vice versa.
Everyone who is either not calm or not funny is quiet or not creative and vice versa.
Everyone who is not funny is both creative and not rich and vice versa.
Everyone who is not tall is not humble and vice versa.
Everyone who is not curious or strong is both not wise and not brave and vice versa.
Everyone who is either patient or not kind is both strong and calm.
Everyone who is wise is either not generous or creative.
Susan is not happy.
Someone is both patient and calm.
Someone is both kind and old.
Someone is curious or not tall.
John is either not quiet or not wise.
John is either not calm or old.
Someone is not brave or not creative.
Lucy is not happy. | John is not rich. | neutral | (((happy(fred)<~>humble(fred)))=>(?[X]:(brave(X))))&
(![X]:(strong(X)<=>creative(X)))&
(![X]:(rich(X)<=>(generous(X)&creative(X))))&
((?[X]:(~curious(X)))<=>((~tall(alice)&~calm(alice))))&
(((strong(fred)&rich(fred)))=>(?[X]:(funny(X))))&
(![X]:((~brave(X)&generous(X))<=>(~funny(X)<~>~happy(X))))&
(![X]:((~wise(X)<~>~tall(X))<=>(quiet(X)<~>~brave(X))))&
(![X]:((~brave(X)|~kind(X))=>(creative(X)|~quiet(X))))&
(![X]:((~brave(X)<~>kind(X))=>~curious(X)))&
(((tall(fred)|strong(fred)))<=>((brave(john)&~rich(john))))&
(![X]:((~calm(X)<~>~funny(X))<=>(quiet(X)|~creative(X))))&
(![X]:(~funny(X)<=>(creative(X)&~rich(X))))&
(![X]:(~tall(X)<=>~humble(X)))&
(![X]:((~curious(X)|strong(X))<=>(~wise(X)&~brave(X))))&
(![X]:((patient(X)<~>~kind(X))=>(strong(X)&calm(X))))&
(![X]:(wise(X)=>(~generous(X)<~>creative(X))))&
(~happy(susan))&
(?[X]:((patient(X)&calm(X))))&
(?[X]:((kind(X)&old(X))))&
(?[X]:((curious(X)|~tall(X))))&
((~quiet(john)<~>~wise(john)))&
((~calm(john)<~>old(john)))&
(?[X]:((~brave(X)|~creative(X))))&
(~happy(lucy)) | ~rich(john) | [] | null | 0 |
Everyone who is not generous or not creative is either not quiet or not humble.
If alice is either not strong or creative then someone is either calm or brave and vice versa.
If alice is both not strong and not old then fred is either not generous or happy and vice versa.
Everyone who is not kind is not tall or curious.
Everyone who is both creative and generous is not happy.
Everyone who is either humble or wise is not funny and vice versa.
Everyone who is either not rich or generous is either not tall or funny and vice versa.
Everyone who is not kind is not humble or not generous and vice versa.
Everyone who is either old or funny is old or not strong and vice versa.
Everyone who is both quiet and not happy is not strong or not rich and vice versa.
If mary is both curious and not generous then alice is brave and vice versa.
If someone is not kind then someone is both not old and not funny.
Everyone who is not wise or not curious is both not generous and not calm and vice versa.
If lucy is creative then susan is not calm or not strong.
Everyone who is either quiet or wise is happy or not quiet and vice versa.
Everyone who is either not kind or curious is patient and vice versa.
Someone is not kind.
Lucy is either curious or not funny.
Alice is either happy or quiet.
Susan is not old or old.
Someone is curious or not rich.
Mary is both not calm and not kind.
Someone is both not strong and not brave.
Susan is both calm and generous. | Alice is creative. | neutral | (![X]:((~generous(X)|~creative(X))=>(~quiet(X)<~>~humble(X))))&
(((~strong(alice)<~>creative(alice)))<=>(?[X]:((calm(X)<~>brave(X)))))&
(((~strong(alice)&~old(alice)))<=>((~generous(fred)<~>happy(fred))))&
(![X]:(~kind(X)=>(~tall(X)|curious(X))))&
(![X]:((creative(X)&generous(X))=>~happy(X)))&
(![X]:((humble(X)<~>wise(X))<=>~funny(X)))&
(![X]:((~rich(X)<~>generous(X))<=>(~tall(X)<~>funny(X))))&
(![X]:(~kind(X)<=>(~humble(X)|~generous(X))))&
(![X]:((old(X)<~>funny(X))<=>(old(X)|~strong(X))))&
(![X]:((quiet(X)&~happy(X))<=>(~strong(X)|~rich(X))))&
(((curious(mary)&~generous(mary)))<=>(brave(alice)))&
((?[X]:(~kind(X)))=>(?[X]:((~old(X)&~funny(X)))))&
(![X]:((~wise(X)|~curious(X))<=>(~generous(X)&~calm(X))))&
((creative(lucy))=>((~calm(susan)|~strong(susan))))&
(![X]:((quiet(X)<~>wise(X))<=>(happy(X)|~quiet(X))))&
(![X]:((~kind(X)<~>curious(X))<=>patient(X)))&
(?[X]:(~kind(X)))&
((curious(lucy)<~>~funny(lucy)))&
((happy(alice)<~>quiet(alice)))&
((~old(susan)|old(susan)))&
(?[X]:((curious(X)|~rich(X))))&
((~calm(mary)&~kind(mary)))&
(?[X]:((~strong(X)&~brave(X))))&
((calm(susan)&generous(susan))) | creative(alice) | [] | null | 0 |
If someone is not happy or not funny then paul is calm and vice versa. If someone is not patient or calm then mary is not old. Everyone who is calm is not tall. Everyone who is patient or not quiet is both not funny and not patient. Everyone who is not generous or not kind is both curious and not humble and vice versa. Everyone who is not quiet is both not creative and not calm. Everyone who is funny is not strong or not old. If paul is patient or brave then someone is not brave or wise. Everyone who is both not strong and not happy is not tall and vice versa. Everyone who is both not funny and not brave is both kind and patient. If mary is not strong or not quiet then someone is not brave and vice versa. Everyone who is not creative is not curious. If someone is either not generous or not happy then someone is curious or creative and vice versa. If someone is patient then someone is both not rich and not generous. Everyone who is not generous or calm is either calm or not generous. If susan is either happy or calm then fred is kind. Alice is either rich or calm. Someone is both quiet and not tall. Mary is both kind and wise. Susan is either creative or old. Lucy is both rich and not quiet. Someone is either wise or tall. Paul is either not brave or patient. Someone is both happy and tall. | Fred is kind. | neutral | ((?[X]:((~happy(X)|~funny(X))))<=>(calm(paul)))&
((?[X]:((~patient(X)|calm(X))))=>(~old(mary)))&
(![X]:(calm(X)=>~tall(X)))&
(![X]:((patient(X)|~quiet(X))=>(~funny(X)&~patient(X))))&
(![X]:((~generous(X)|~kind(X))<=>(curious(X)&~humble(X))))&
(![X]:(~quiet(X)=>(~creative(X)&~calm(X))))&
(![X]:(funny(X)=>(~strong(X)|~old(X))))&
(((patient(paul)|brave(paul)))=>(?[X]:((~brave(X)|wise(X)))))&
(![X]:((~strong(X)&~happy(X))<=>~tall(X)))&
(![X]:((~funny(X)&~brave(X))=>(kind(X)&patient(X))))&
(((~strong(mary)|~quiet(mary)))<=>(?[X]:(~brave(X))))&
(![X]:(~creative(X)=>~curious(X)))&
((?[X]:((~generous(X)<~>~happy(X))))<=>(?[X]:((curious(X)|creative(X)))))&
((?[X]:(patient(X)))=>(?[X]:((~rich(X)&~generous(X)))))&
(![X]:((~generous(X)|calm(X))=>(calm(X)<~>~generous(X))))&
(((happy(susan)<~>calm(susan)))=>(kind(fred)))&
((rich(alice)<~>calm(alice)))&
(?[X]:((quiet(X)&~tall(X))))&
((kind(mary)&wise(mary)))&
((creative(susan)<~>old(susan)))&
((rich(lucy)&~quiet(lucy)))&
(?[X]:((wise(X)<~>tall(X))))&
((~brave(paul)<~>patient(paul)))&
(?[X]:((happy(X)&tall(X)))) | kind(fred) | [] | null | 0 |
If paul is both not brave and not quiet then john is either curious or not old and vice versa. If someone is humble then susan is both calm and strong and vice versa. If paul is quiet or not old then mary is old and vice versa. If someone is either not brave or calm then mary is either not happy or brave and vice versa. Everyone who is not brave is kind and vice versa. If john is humble or not patient then someone is either not generous or not curious and vice versa. If lucy is not funny or wise then lucy is either not wise or tall. If someone is happy then someone is not strong. Everyone who is rich or not tall is both curious and not creative and vice versa. Everyone who is not humble or not strong is strong and vice versa. If someone is happy or kind then someone is either not curious or funny and vice versa. Everyone who is generous is either happy or not tall and vice versa. Everyone who is not old or curious is brave and vice versa. Everyone who is both not wise and creative is not tall or not funny and vice versa. Everyone who is either not curious or wise is not wise and vice versa. Someone is creative. Susan is either tall or calm. Lucy is both not brave and kind. Paul is either brave or not tall. Fred is old or calm. Susan is not kind or strong. Susan is old or not curious. | Fred is wise. | neutral | (((~brave(paul)&~quiet(paul)))<=>((curious(john)<~>~old(john))))&
((?[X]:(humble(X)))<=>((calm(susan)&strong(susan))))&
(((quiet(paul)|~old(paul)))<=>(old(mary)))&
((?[X]:((~brave(X)<~>calm(X))))<=>((~happy(mary)<~>brave(mary))))&
(![X]:(~brave(X)<=>kind(X)))&
(((humble(john)|~patient(john)))<=>(?[X]:((~generous(X)<~>~curious(X)))))&
(((~funny(lucy)|wise(lucy)))=>((~wise(lucy)<~>tall(lucy))))&
((?[X]:(happy(X)))=>(?[X]:(~strong(X))))&
(![X]:((rich(X)|~tall(X))<=>(curious(X)&~creative(X))))&
(![X]:((~humble(X)|~strong(X))<=>strong(X)))&
((?[X]:((happy(X)|kind(X))))<=>(?[X]:((~curious(X)<~>funny(X)))))&
(![X]:(generous(X)<=>(happy(X)<~>~tall(X))))&
(![X]:((~old(X)|curious(X))<=>brave(X)))&
(![X]:((~wise(X)&creative(X))<=>(~tall(X)|~funny(X))))&
(![X]:((~curious(X)<~>wise(X))<=>~wise(X)))&
(?[X]:(creative(X)))&
((tall(susan)<~>calm(susan)))&
((~brave(lucy)&kind(lucy)))&
((brave(paul)<~>~tall(paul)))&
((old(fred)|calm(fred)))&
((~kind(susan)|strong(susan)))&
((old(susan)|~curious(susan))) | wise(fred) | [] | null | 0 |
Everyone who is brave is not patient or happy. Everyone who is not strong is humble or wise and vice versa. Everyone who is tall is either kind or not rich and vice versa. If mary is not strong or wise then someone is both not quiet and not patient. Everyone who is happy is both not kind and tall and vice versa. If someone is not humble or funny then alice is not funny or patient and vice versa. If john is either not rich or not funny then alice is both brave and not old and vice versa. Everyone who is generous or funny is not rich or creative and vice versa. Everyone who is patient is brave. If someone is patient then someone is humble or not brave. If someone is patient or curious then someone is funny or not kind and vice versa. Everyone who is both not rich and rich is both funny and wise and vice versa. If paul is not creative or not patient then someone is curious or patient. If someone is tall then paul is patient or happy. If someone is not calm then john is either not humble or not brave. If someone is not calm or not brave then someone is both curious and old and vice versa. Paul is not curious or not funny. Someone is not humble or not tall. Susan is both not old and not wise. Susan is calm. Someone is not creative or wise. Fred is either not funny or not old. Alice is both not strong and kind. Lucy is either wise or not creative. | Alice is happy. | contradiction | (![X]:(brave(X)=>(~patient(X)|happy(X))))&
(![X]:(~strong(X)<=>(humble(X)|wise(X))))&
(![X]:(tall(X)<=>(kind(X)<~>~rich(X))))&
(((~strong(mary)|wise(mary)))=>(?[X]:((~quiet(X)&~patient(X)))))&
(![X]:(happy(X)<=>(~kind(X)&tall(X))))&
((?[X]:((~humble(X)|funny(X))))<=>((~funny(alice)|patient(alice))))&
(((~rich(john)<~>~funny(john)))<=>((brave(alice)&~old(alice))))&
(![X]:((generous(X)|funny(X))<=>(~rich(X)|creative(X))))&
(![X]:(patient(X)=>brave(X)))&
((?[X]:(patient(X)))=>(?[X]:((humble(X)|~brave(X)))))&
((?[X]:((patient(X)|curious(X))))<=>(?[X]:((funny(X)|~kind(X)))))&
(![X]:((~rich(X)&rich(X))<=>(funny(X)&wise(X))))&
(((~creative(paul)|~patient(paul)))=>(?[X]:((curious(X)|patient(X)))))&
((?[X]:(tall(X)))=>((patient(paul)|happy(paul))))&
((?[X]:(~calm(X)))=>((~humble(john)<~>~brave(john))))&
((?[X]:((~calm(X)|~brave(X))))<=>(?[X]:((curious(X)&old(X)))))&
((~curious(paul)|~funny(paul)))&
(?[X]:((~humble(X)|~tall(X))))&
((~old(susan)&~wise(susan)))&
(calm(susan))&
(?[X]:((~creative(X)|wise(X))))&
((~funny(fred)<~>~old(fred)))&
((~strong(alice)&kind(alice)))&
((wise(lucy)<~>~creative(lucy))) | happy(alice) | [
"p4",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 388794208479012245894433
% SZS output start Proof for 388794208479012245894433
5. ! [X0] : (happy(X0) <=> (tall(X0) & ~kind(X0))) [input p4]
23. kind(alice) & ~strong(alice) [input p22]
25. happy(alice) [input hypothesis]
29. ! [X0] : (happy(X0) => (tall(X0) & ~kind(X0))) [unused predicate definition removal 5]
34. ! [X0] : ((tall(X0) & ~kind(X0)) | ~happy(X0)) [ennf transformation 29]
89. ~kind(X0) | ~happy(X0) [cnf transformation 34]
134. kind(alice) [cnf transformation 23]
137. happy(alice) [cnf transformation 25]
367. ~happy(alice) [resolution 89,134]
368. $false [subsumption resolution 367,137]
% SZS output end Proof for 388794208479012245894433
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is kind is generous. If fred is either not humble or not kind then susan is either kind or wise. If someone is either calm or rich then someone is both not brave and quiet. Everyone who is both not quiet and wise is not happy. Everyone who is both humble and not funny is both strong and funny. If lucy is both rich and not brave then someone is kind and vice versa. Everyone who is both not rich and not wise is either happy or rich and vice versa. If someone is both patient and funny then someone is brave or humble and vice versa. Everyone who is both curious and not brave is not rich or brave and vice versa. Everyone who is not patient or old is either patient or not wise. Everyone who is both not funny and creative is not wise or not happy and vice versa. If someone is patient then lucy is either kind or tall and vice versa. Everyone who is patient is humble and vice versa. If someone is generous then alice is not old or strong and vice versa. If someone is not creative or quiet then someone is both not rich and humble and vice versa. Alice is either not strong or humble. Someone is humble or kind. Someone is both not curious and old. Fred is either not kind or not calm. | Susan is humble. | contradiction | (![X]:(kind(X)=>generous(X)))&
(((~humble(fred)<~>~kind(fred)))=>((kind(susan)<~>wise(susan))))&
((?[X]:((calm(X)<~>rich(X))))=>(?[X]:((~brave(X)&quiet(X)))))&
(![X]:((~quiet(X)&wise(X))=>~happy(X)))&
(![X]:((humble(X)&~funny(X))=>(strong(X)&funny(X))))&
(((rich(lucy)&~brave(lucy)))<=>(?[X]:(kind(X))))&
(![X]:((~rich(X)&~wise(X))<=>(happy(X)<~>rich(X))))&
((?[X]:((patient(X)&funny(X))))<=>(?[X]:((brave(X)|humble(X)))))&
(![X]:((curious(X)&~brave(X))<=>(~rich(X)|brave(X))))&
(![X]:((~patient(X)|old(X))=>(patient(X)<~>~wise(X))))&
(![X]:((~funny(X)&creative(X))<=>(~wise(X)|~happy(X))))&
((?[X]:(patient(X)))<=>((kind(lucy)<~>tall(lucy))))&
(![X]:(patient(X)<=>humble(X)))&
((?[X]:(generous(X)))<=>((~old(alice)|strong(alice))))&
((?[X]:((~creative(X)|quiet(X))))<=>(?[X]:((~rich(X)&humble(X)))))&
((~strong(alice)<~>humble(alice)))&
(?[X]:((humble(X)|kind(X))))&
(?[X]:((~curious(X)&old(X))))&
((~kind(fred)<~>~calm(fred))) | humble(susan) | [
"p3",
"p4",
"p6",
"p7",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2068947139836743541166607
% SZS output start Proof for 2068947139836743541166607
4. ! [X0] : ((wise(X0) & ~quiet(X0)) => ~happy(X0)) [input p3]
5. ! [X0] : ((~funny(X0) & humble(X0)) => (funny(X0) & strong(X0))) [input p4]
7. ! [X0] : ((~wise(X0) & ~rich(X0)) <=> (happy(X0) <~> rich(X0))) [input p6]
8. ? [X0] : (funny(X0) & patient(X0)) <=> ? [X0] : (humble(X0) | brave(X0)) [input p7]
11. ! [X0] : ((creative(X0) & ~funny(X0)) <=> (~happy(X0) | ~wise(X0))) [input p10]
15. ? [X0] : (quiet(X0) | ~creative(X0)) <=> ? [X0] : (humble(X0) & ~rich(X0)) [input p14]
20. humble(susan) [input hypothesis]
22. ? [X0] : (funny(X0) & patient(X0)) <=> ? [X1] : (humble(X1) | brave(X1)) [rectify 8]
23. ? [X0] : (quiet(X0) | ~creative(X0)) <=> ? [X1] : (humble(X1) & ~rich(X1)) [rectify 15]
27. ! [X0] : (~happy(X0) | (~wise(X0) | quiet(X0))) [ennf transformation 4]
28. ! [X0] : (~happy(X0) | ~wise(X0) | quiet(X0)) [flattening 27]
29. ! [X0] : ((funny(X0) & strong(X0)) | (funny(X0) | ~humble(X0))) [ennf transformation 5]
30. ! [X0] : ((funny(X0) & strong(X0)) | funny(X0) | ~humble(X0)) [flattening 29]
42. ! [X0] : (((~wise(X0) & ~rich(X0)) | ((happy(X0) | ~rich(X0)) & (rich(X0) | ~happy(X0)))) & (((~rich(X0) | ~happy(X0)) & (rich(X0) | happy(X0))) | (wise(X0) | rich(X0)))) [nnf transformation 7]
43. ! [X0] : (((~wise(X0) & ~rich(X0)) | ((happy(X0) | ~rich(X0)) & (rich(X0) | ~happy(X0)))) & (((~rich(X0) | ~happy(X0)) & (rich(X0) | happy(X0))) | wise(X0) | rich(X0))) [flattening 42]
44. (? [X0] : (funny(X0) & patient(X0)) | ! [X1] : (~humble(X1) & ~brave(X1))) & (? [X1] : (humble(X1) | brave(X1)) | ! [X0] : (~funny(X0) | ~patient(X0))) [nnf transformation 22]
45. (? [X0] : (funny(X0) & patient(X0)) | ! [X1] : (~humble(X1) & ~brave(X1))) & (? [X2] : (humble(X2) | brave(X2)) | ! [X3] : (~funny(X3) | ~patient(X3))) [rectify 44]
46. ? [X0] : (funny(X0) & patient(X0)) => (funny(sK2) & patient(sK2)) [choice axiom]
47. ? [X2] : (humble(X2) | brave(X2)) => (humble(sK3) | brave(sK3)) [choice axiom]
48. ((funny(sK2) & patient(sK2)) | ! [X1] : (~humble(X1) & ~brave(X1))) & ((humble(sK3) | brave(sK3)) | ! [X3] : (~funny(X3) | ~patient(X3))) [skolemisation 45,47,46]
52. ! [X0] : (((creative(X0) & ~funny(X0)) | (happy(X0) & wise(X0))) & ((~happy(X0) | ~wise(X0)) | (~creative(X0) | funny(X0)))) [nnf transformation 11]
53. ! [X0] : (((creative(X0) & ~funny(X0)) | (happy(X0) & wise(X0))) & (~happy(X0) | ~wise(X0) | ~creative(X0) | funny(X0))) [flattening 52]
64. (? [X0] : (quiet(X0) | ~creative(X0)) | ! [X1] : (~humble(X1) | rich(X1))) & (? [X1] : (humble(X1) & ~rich(X1)) | ! [X0] : (~quiet(X0) & creative(X0))) [nnf transformation 23]
65. (? [X0] : (quiet(X0) | ~creative(X0)) | ! [X1] : (~humble(X1) | rich(X1))) & (? [X2] : (humble(X2) & ~rich(X2)) | ! [X3] : (~quiet(X3) & creative(X3))) [rectify 64]
66. ? [X0] : (quiet(X0) | ~creative(X0)) => (quiet(sK6) | ~creative(sK6)) [choice axiom]
67. ? [X2] : (humble(X2) & ~rich(X2)) => (humble(sK7) & ~rich(sK7)) [choice axiom]
68. ((quiet(sK6) | ~creative(sK6)) | ! [X1] : (~humble(X1) | rich(X1))) & ((humble(sK7) & ~rich(sK7)) | ! [X3] : (~quiet(X3) & creative(X3))) [skolemisation 65,67,66]
84. ~happy(X0) | ~wise(X0) | quiet(X0) [cnf transformation 28]
86. funny(X0) | funny(X0) | ~humble(X0) [cnf transformation 30]
94. ~happy(X0) | rich(X0) | ~wise(X0) [cnf transformation 43]
100. funny(sK2) | ~humble(X1) [cnf transformation 48]
111. ~funny(X0) | wise(X0) [cnf transformation 53]
112. ~funny(X0) | happy(X0) [cnf transformation 53]
125. ~rich(sK7) | ~quiet(X3) [cnf transformation 68]
127. humble(sK7) | ~quiet(X3) [cnf transformation 68]
136. humble(susan) [cnf transformation 20]
142. ~humble(X0) | funny(X0) [duplicate literal removal 86]
201. 13 <=> ! [X1] : ~humble(X1) [avatar definition]
202. ~humble(X1) <- (13) [avatar component clause 201]
204. 14 <=> funny(sK2) [avatar definition]
206. funny(sK2) <- (14) [avatar component clause 204]
207. 13 | 14 [avatar split clause 100,204,201]
281. 31 <=> ! [X3] : ~quiet(X3) [avatar definition]
282. ~quiet(X3) <- (31) [avatar component clause 281]
284. 32 <=> humble(sK7) [avatar definition]
286. humble(sK7) <- (32) [avatar component clause 284]
287. 31 | 32 [avatar split clause 127,284,281]
293. 34 <=> rich(sK7) [avatar definition]
295. ~rich(sK7) <- (~34) [avatar component clause 293]
296. 31 | ~34 [avatar split clause 125,293,281]
319. $false <- (13) [resolution 202,136]
320. ~13 [avatar contradiction clause 319]
322. wise(sK2) <- (14) [resolution 111,206]
323. happy(sK2) <- (14) [resolution 112,206]
340. funny(sK7) <- (32) [resolution 142,286]
363. ~wise(sK2) | quiet(sK2) <- (14) [resolution 84,323]
366. quiet(sK2) <- (14) [subsumption resolution 363,322]
384. happy(sK7) <- (32) [resolution 340,112]
385. wise(sK7) <- (32) [resolution 340,111]
439. rich(sK7) | ~wise(sK7) <- (32) [resolution 384,94]
441. ~wise(sK7) <- (32, ~34) [subsumption resolution 439,295]
442. $false <- (32, ~34) [subsumption resolution 441,385]
443. ~32 | 34 [avatar contradiction clause 442]
447. $false <- (14, 31) [resolution 282,366]
448. ~14 | ~31 [avatar contradiction clause 447]
451. $false [avatar sat refutation 207,287,296,320,443,448]
% SZS output end Proof for 2068947139836743541166607
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not funny and happy is old or not generous.
If john is either not calm or not happy then someone is not kind and vice versa.
If someone is either tall or generous then someone is not brave and vice versa.
If someone is not wise then alice is both not creative and quiet and vice versa.
Everyone who is wise is both tall and funny.
If mary is patient then paul is calm or humble.
Everyone who is wise is either not old or calm.
If john is both creative and calm then mary is not calm or wise.
Everyone who is curious is either not calm or brave and vice versa.
Everyone who is both patient and not funny is either calm or kind.
Everyone who is not funny or funny is both quiet and not brave.
If someone is tall then lucy is either not tall or patient.
If john is both not curious and not happy then someone is not calm or strong and vice versa.
Everyone who is either not tall or patient is old.
Everyone who is kind is curious or rich and vice versa.
If someone is both not calm and funny then susan is either not strong or not funny and vice versa.
Paul is either brave or not kind.
Someone is both not humble and calm.
Alice is either not happy or quiet.
Lucy is not generous or wise.
Mary is either old or not old.
Someone is both happy and quiet.
Lucy is not generous. | Paul is rich. | contradiction | (![X]:((~funny(X)&happy(X))=>(old(X)|~generous(X))))&
(((~calm(john)<~>~happy(john)))<=>(?[X]:(~kind(X))))&
((?[X]:((tall(X)<~>generous(X))))<=>(?[X]:(~brave(X))))&
((?[X]:(~wise(X)))<=>((~creative(alice)&quiet(alice))))&
(![X]:(wise(X)=>(tall(X)&funny(X))))&
((patient(mary))=>((calm(paul)|humble(paul))))&
(![X]:(wise(X)=>(~old(X)<~>calm(X))))&
(((creative(john)&calm(john)))=>((~calm(mary)|wise(mary))))&
(![X]:(curious(X)<=>(~calm(X)<~>brave(X))))&
(![X]:((patient(X)&~funny(X))=>(calm(X)<~>kind(X))))&
(![X]:((~funny(X)|funny(X))=>(quiet(X)&~brave(X))))&
((?[X]:(tall(X)))=>((~tall(lucy)<~>patient(lucy))))&
(((~curious(john)&~happy(john)))<=>(?[X]:((~calm(X)|strong(X)))))&
(![X]:((~tall(X)<~>patient(X))=>old(X)))&
(![X]:(kind(X)<=>(curious(X)|rich(X))))&
((?[X]:((~calm(X)&funny(X))))<=>((~strong(susan)<~>~funny(susan))))&
((brave(paul)<~>~kind(paul)))&
(?[X]:((~humble(X)&calm(X))))&
((~happy(alice)<~>quiet(alice)))&
((~generous(lucy)|wise(lucy)))&
((old(mary)<~>~old(mary)))&
(?[X]:((happy(X)&quiet(X))))&
(~generous(lucy)) | rich(paul) | [
"p10",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 649524101078985619754615
% SZS output start Proof for 649524101078985619754615
11. ! [X0] : ((funny(X0) | ~funny(X0)) => (~brave(X0) & quiet(X0))) [input p10]
15. ! [X0] : (kind(X0) <=> (rich(X0) | curious(X0))) [input p14]
17. brave(paul) <~> ~kind(paul) [input p16]
24. rich(paul) [input hypothesis]
36. ! [X0] : ((~brave(X0) & quiet(X0)) | (~funny(X0) & funny(X0))) [ennf transformation 11]
63. ! [X0] : ((kind(X0) | (~rich(X0) & ~curious(X0))) & ((rich(X0) | curious(X0)) | ~kind(X0))) [nnf transformation 15]
64. ! [X0] : ((kind(X0) | (~rich(X0) & ~curious(X0))) & (rich(X0) | curious(X0) | ~kind(X0))) [flattening 63]
69. (kind(paul) | ~brave(paul)) & (~kind(paul) | brave(paul)) [nnf transformation 17]
102. ~brave(X0) | funny(X0) [cnf transformation 36]
103. ~brave(X0) | ~funny(X0) [cnf transformation 36]
115. ~rich(X0) | kind(X0) [cnf transformation 64]
122. ~kind(paul) | brave(paul) [cnf transformation 69]
134. rich(paul) [cnf transformation 24]
223. ~brave(X0) [subsumption resolution 102,103]
286. ~kind(paul) [subsumption resolution 122,223]
302. kind(paul) [resolution 115,134]
303. $false [subsumption resolution 302,286]
% SZS output end Proof for 649524101078985619754615
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not rich and tall is creative and vice versa. If mary is either funny or not strong then someone is calm and vice versa. Everyone who is not humble is either rich or happy and vice versa. Everyone who is either strong or happy is funny and vice versa. If mary is either creative or generous then someone is not brave. Everyone who is not old or not kind is either not tall or old and vice versa. If lucy is not patient or not wise then lucy is both not generous and not tall and vice versa. Everyone who is funny or not curious is funny. Everyone who is both kind and not strong is either generous or not quiet and vice versa. If someone is both not calm and not kind then susan is not kind and vice versa. Everyone who is either not wise or not strong is either tall or not patient and vice versa. If someone is not happy then someone is either not rich or not strong and vice versa. If susan is rich then someone is either generous or not kind and vice versa. Everyone who is generous is not happy or not creative. If susan is humble or not tall then susan is not happy and vice versa. Lucy is old or not rich. Someone is either not rich or rich. Fred is calm. John is either funny or curious. Someone is both calm and not tall. Lucy is generous or happy. Alice is not old. Someone is both not brave and creative. | Mary is creative. | neutral | (![X]:((~rich(X)&tall(X))<=>creative(X)))&
(((funny(mary)<~>~strong(mary)))<=>(?[X]:(calm(X))))&
(![X]:(~humble(X)<=>(rich(X)<~>happy(X))))&
(![X]:((strong(X)<~>happy(X))<=>funny(X)))&
(((creative(mary)<~>generous(mary)))=>(?[X]:(~brave(X))))&
(![X]:((~old(X)|~kind(X))<=>(~tall(X)<~>old(X))))&
(((~patient(lucy)|~wise(lucy)))<=>((~generous(lucy)&~tall(lucy))))&
(![X]:((funny(X)|~curious(X))=>funny(X)))&
(![X]:((kind(X)&~strong(X))<=>(generous(X)<~>~quiet(X))))&
((?[X]:((~calm(X)&~kind(X))))<=>(~kind(susan)))&
(![X]:((~wise(X)<~>~strong(X))<=>(tall(X)<~>~patient(X))))&
((?[X]:(~happy(X)))<=>(?[X]:((~rich(X)<~>~strong(X)))))&
((rich(susan))<=>(?[X]:((generous(X)<~>~kind(X)))))&
(![X]:(generous(X)=>(~happy(X)|~creative(X))))&
(((humble(susan)|~tall(susan)))<=>(~happy(susan)))&
((old(lucy)|~rich(lucy)))&
(?[X]:((~rich(X)<~>rich(X))))&
(calm(fred))&
((funny(john)<~>curious(john)))&
(?[X]:((calm(X)&~tall(X))))&
((generous(lucy)|happy(lucy)))&
(~old(alice))&
(?[X]:((~brave(X)&creative(X)))) | creative(mary) | [] | 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 kind. | 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))) | kind(susan) | [] | null | 0 |
If someone is either curious or not happy then alice is either not happy or not calm and vice versa. If mary is creative then paul is tall. Everyone who is both not calm and brave is brave or not brave. If susan is either not rich or not quiet then someone is not generous or curious and vice versa. Everyone who is either not humble or not creative is either not brave or not wise. If fred is not happy then alice is happy or not quiet. If fred is strong or tall then someone is not calm or kind and vice versa. Everyone who is either patient or not calm is either not funny or not old. Everyone who is tall is either not creative or strong. Everyone who is either not rich or not happy is not funny or calm. Everyone who is both not curious and brave is wise or tall. If john is not generous or not brave then alice is rich. If someone is creative or not humble then someone is funny or wise and vice versa. Everyone who is kind is not happy or not curious. Everyone who is not patient or not happy is rich or kind and vice versa. Everyone who is creative or not happy is both strong and not generous. Someone is both not happy and not old. Fred is not funny or humble. Paul is either happy or not funny. Paul is not wise. Fred is not kind. Someone is not old. Someone is either not creative or strong. Fred is not funny. | John is generous. | neutral | ((?[X]:((curious(X)<~>~happy(X))))<=>((~happy(alice)<~>~calm(alice))))&
((creative(mary))=>(tall(paul)))&
(![X]:((~calm(X)&brave(X))=>(brave(X)|~brave(X))))&
(((~rich(susan)<~>~quiet(susan)))<=>(?[X]:((~generous(X)|curious(X)))))&
(![X]:((~humble(X)<~>~creative(X))=>(~brave(X)<~>~wise(X))))&
((~happy(fred))=>((happy(alice)|~quiet(alice))))&
(((strong(fred)|tall(fred)))<=>(?[X]:((~calm(X)|kind(X)))))&
(![X]:((patient(X)<~>~calm(X))=>(~funny(X)<~>~old(X))))&
(![X]:(tall(X)=>(~creative(X)<~>strong(X))))&
(![X]:((~rich(X)<~>~happy(X))=>(~funny(X)|calm(X))))&
(![X]:((~curious(X)&brave(X))=>(wise(X)|tall(X))))&
(((~generous(john)|~brave(john)))=>(rich(alice)))&
((?[X]:((creative(X)|~humble(X))))<=>(?[X]:((funny(X)|wise(X)))))&
(![X]:(kind(X)=>(~happy(X)|~curious(X))))&
(![X]:((~patient(X)|~happy(X))<=>(rich(X)|kind(X))))&
(![X]:((creative(X)|~happy(X))=>(strong(X)&~generous(X))))&
(?[X]:((~happy(X)&~old(X))))&
((~funny(fred)|humble(fred)))&
((happy(paul)<~>~funny(paul)))&
(~wise(paul))&
(~kind(fred))&
(?[X]:(~old(X)))&
(?[X]:((~creative(X)<~>strong(X))))&
(~funny(fred)) | generous(john) | [] | null | 0 |
Everyone who is both not brave and not humble is quiet or not tall and vice versa. Everyone who is either not brave or patient is both old and kind and vice versa. Everyone who is not curious is not quiet. Everyone who is not brave or not humble is either patient or not humble and vice versa. Everyone who is happy or not calm is either not wise or not old and vice versa. Everyone who is not wise or humble is happy. Everyone who is strong or not generous is calm. Everyone who is both not funny and not tall is not brave or not rich. If someone is not creative or not curious then someone is both not calm and kind and vice versa. Everyone who is patient or not kind is funny or not calm. Everyone who is wise is funny or rich and vice versa. If susan is both kind and rich then paul is both not patient and not quiet. Everyone who is old or strong is tall and vice versa. If someone is not wise or not strong then someone is either not old or happy and vice versa. Everyone who is not funny or not quiet is both not old and not brave and vice versa. If mary is either not patient or curious then john is either old or not kind. Alice is either old or rich. Someone is not old or not curious. John is not rich or curious. | Alice is not curious. | contradiction | (![X]:((~brave(X)&~humble(X))<=>(quiet(X)|~tall(X))))&
(![X]:((~brave(X)<~>patient(X))<=>(old(X)&kind(X))))&
(![X]:(~curious(X)=>~quiet(X)))&
(![X]:((~brave(X)|~humble(X))<=>(patient(X)<~>~humble(X))))&
(![X]:((happy(X)|~calm(X))<=>(~wise(X)<~>~old(X))))&
(![X]:((~wise(X)|humble(X))=>happy(X)))&
(![X]:((strong(X)|~generous(X))=>calm(X)))&
(![X]:((~funny(X)&~tall(X))=>(~brave(X)|~rich(X))))&
((?[X]:((~creative(X)|~curious(X))))<=>(?[X]:((~calm(X)&kind(X)))))&
(![X]:((patient(X)|~kind(X))=>(funny(X)|~calm(X))))&
(![X]:(wise(X)<=>(funny(X)|rich(X))))&
(((kind(susan)&rich(susan)))=>((~patient(paul)&~quiet(paul))))&
(![X]:((old(X)|strong(X))<=>tall(X)))&
((?[X]:((~wise(X)|~strong(X))))<=>(?[X]:((~old(X)<~>happy(X)))))&
(![X]:((~funny(X)|~quiet(X))<=>(~old(X)&~brave(X))))&
(((~patient(mary)<~>curious(mary)))=>((old(john)<~>~kind(john))))&
((old(alice)<~>rich(alice)))&
(?[X]:((~old(X)|~curious(X))))&
((~rich(john)|curious(john))) | ~curious(alice) | [
"p0",
"p1",
"p3",
"p4",
"p5",
"p6",
"p8",
"p10",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6329033282012275961931168
% SZS output start Proof for 6329033282012275961931168
1. ! [X0] : ((~humble(X0) & ~brave(X0)) <=> (~tall(X0) | quiet(X0))) [input p0]
2. ! [X0] : ((~brave(X0) <~> patient(X0)) <=> (kind(X0) & old(X0))) [input p1]
4. ! [X0] : ((~humble(X0) | ~brave(X0)) <=> (patient(X0) <~> ~humble(X0))) [input p3]
5. ! [X0] : ((~calm(X0) | happy(X0)) <=> (~wise(X0) <~> ~old(X0))) [input p4]
6. ! [X0] : ((humble(X0) | ~wise(X0)) => happy(X0)) [input p5]
7. ! [X0] : ((~generous(X0) | strong(X0)) => calm(X0)) [input p6]
9. ? [X0] : (~curious(X0) | ~creative(X0)) <=> ? [X0] : (kind(X0) & ~calm(X0)) [input p8]
11. ! [X0] : (wise(X0) <=> (rich(X0) | funny(X0))) [input p10]
14. ? [X0] : (~strong(X0) | ~wise(X0)) <=> ? [X0] : (~old(X0) <~> happy(X0)) [input p13]
15. ! [X0] : ((~quiet(X0) | ~funny(X0)) <=> (~brave(X0) & ~old(X0))) [input p14]
20. ~curious(alice) [input hypothesis]
21. ? [X0] : (~curious(X0) | ~creative(X0)) <=> ? [X1] : (kind(X1) & ~calm(X1)) [rectify 9]
22. ? [X0] : (~strong(X0) | ~wise(X0)) <=> ? [X1] : (~old(X1) <~> happy(X1)) [rectify 14]
23. ! [X0] : (strong(X0) => calm(X0)) [pure predicate removal 7]
25. ! [X0] : (happy(X0) | (~humble(X0) & wise(X0))) [ennf transformation 6]
26. ! [X0] : (calm(X0) | ~strong(X0)) [ennf transformation 23]
34. ! [X0] : (((~humble(X0) & ~brave(X0)) | (tall(X0) & ~quiet(X0))) & ((~tall(X0) | quiet(X0)) | (humble(X0) | brave(X0)))) [nnf transformation 1]
35. ! [X0] : (((~humble(X0) & ~brave(X0)) | (tall(X0) & ~quiet(X0))) & (~tall(X0) | quiet(X0) | humble(X0) | brave(X0))) [flattening 34]
36. ! [X0] : ((((~patient(X0) | brave(X0)) & (patient(X0) | ~brave(X0))) | (~kind(X0) | ~old(X0))) & ((kind(X0) & old(X0)) | ((~brave(X0) | ~patient(X0)) & (patient(X0) | brave(X0))))) [nnf transformation 2]
37. ! [X0] : ((((~patient(X0) | brave(X0)) & (patient(X0) | ~brave(X0))) | ~kind(X0) | ~old(X0)) & ((kind(X0) & old(X0)) | ((~brave(X0) | ~patient(X0)) & (patient(X0) | brave(X0))))) [flattening 36]
38. ! [X0] : (((~humble(X0) | ~brave(X0)) | ((patient(X0) | humble(X0)) & (~humble(X0) | ~patient(X0)))) & (((humble(X0) | ~patient(X0)) & (~humble(X0) | patient(X0))) | (humble(X0) & brave(X0)))) [nnf transformation 4]
39. ! [X0] : ((~humble(X0) | ~brave(X0) | ((patient(X0) | humble(X0)) & (~humble(X0) | ~patient(X0)))) & (((humble(X0) | ~patient(X0)) & (~humble(X0) | patient(X0))) | (humble(X0) & brave(X0)))) [flattening 38]
40. ! [X0] : (((~calm(X0) | happy(X0)) | ((~wise(X0) | old(X0)) & (~old(X0) | wise(X0)))) & (((old(X0) | wise(X0)) & (~old(X0) | ~wise(X0))) | (calm(X0) & ~happy(X0)))) [nnf transformation 5]
41. ! [X0] : ((~calm(X0) | happy(X0) | ((~wise(X0) | old(X0)) & (~old(X0) | wise(X0)))) & (((old(X0) | wise(X0)) & (~old(X0) | ~wise(X0))) | (calm(X0) & ~happy(X0)))) [flattening 40]
42. (? [X0] : (~curious(X0) | ~creative(X0)) | ! [X1] : (~kind(X1) | calm(X1))) & (? [X1] : (kind(X1) & ~calm(X1)) | ! [X0] : (curious(X0) & creative(X0))) [nnf transformation 21]
43. (? [X0] : (~curious(X0) | ~creative(X0)) | ! [X1] : (~kind(X1) | calm(X1))) & (? [X2] : (kind(X2) & ~calm(X2)) | ! [X3] : (curious(X3) & creative(X3))) [rectify 42]
44. ? [X0] : (~curious(X0) | ~creative(X0)) => (~curious(sK0) | ~creative(sK0)) [choice axiom]
45. ? [X2] : (kind(X2) & ~calm(X2)) => (kind(sK1) & ~calm(sK1)) [choice axiom]
46. ((~curious(sK0) | ~creative(sK0)) | ! [X1] : (~kind(X1) | calm(X1))) & ((kind(sK1) & ~calm(sK1)) | ! [X3] : (curious(X3) & creative(X3))) [skolemisation 43,45,44]
47. ! [X0] : ((wise(X0) | (~rich(X0) & ~funny(X0))) & ((rich(X0) | funny(X0)) | ~wise(X0))) [nnf transformation 11]
48. ! [X0] : ((wise(X0) | (~rich(X0) & ~funny(X0))) & (rich(X0) | funny(X0) | ~wise(X0))) [flattening 47]
51. (? [X0] : (~strong(X0) | ~wise(X0)) | ! [X1] : ((~old(X1) | ~happy(X1)) & (happy(X1) | old(X1)))) & (? [X1] : ((~happy(X1) | old(X1)) & (happy(X1) | ~old(X1))) | ! [X0] : (strong(X0) & wise(X0))) [nnf transformation 22]
52. (? [X0] : (~strong(X0) | ~wise(X0)) | ! [X1] : ((~old(X1) | ~happy(X1)) & (happy(X1) | old(X1)))) & (? [X2] : ((~happy(X2) | old(X2)) & (happy(X2) | ~old(X2))) | ! [X3] : (strong(X3) & wise(X3))) [rectify 51]
53. ? [X0] : (~strong(X0) | ~wise(X0)) => (~strong(sK2) | ~wise(sK2)) [choice axiom]
54. ? [X2] : ((~happy(X2) | old(X2)) & (happy(X2) | ~old(X2))) => ((~happy(sK3) | old(sK3)) & (happy(sK3) | ~old(sK3))) [choice axiom]
55. ((~strong(sK2) | ~wise(sK2)) | ! [X1] : ((~old(X1) | ~happy(X1)) & (happy(X1) | old(X1)))) & (((~happy(sK3) | old(sK3)) & (happy(sK3) | ~old(sK3))) | ! [X3] : (strong(X3) & wise(X3))) [skolemisation 52,54,53]
56. ! [X0] : (((~quiet(X0) | ~funny(X0)) | (brave(X0) | old(X0))) & ((~brave(X0) & ~old(X0)) | (quiet(X0) & funny(X0)))) [nnf transformation 15]
57. ! [X0] : ((~quiet(X0) | ~funny(X0) | brave(X0) | old(X0)) & ((~brave(X0) & ~old(X0)) | (quiet(X0) & funny(X0)))) [flattening 56]
63. ~quiet(X0) | ~brave(X0) [cnf transformation 35]
67. old(X0) | patient(X0) | brave(X0) [cnf transformation 37]
77. humble(X0) | ~patient(X0) | humble(X0) [cnf transformation 39]
80. ~wise(X0) | ~old(X0) | ~happy(X0) [cnf transformation 41]
87. ~humble(X0) | happy(X0) [cnf transformation 25]
88. ~strong(X0) | calm(X0) [cnf transformation 26]
91. ~calm(sK1) | curious(X3) [cnf transformation 46]
98. ~funny(X0) | wise(X0) [cnf transformation 48]
106. happy(sK3) | ~old(sK3) | strong(X3) [cnf transformation 55]
108. ~happy(sK3) | old(sK3) | strong(X3) [cnf transformation 55]
111. ~old(X0) | funny(X0) [cnf transformation 57]
114. ~brave(X0) | quiet(X0) [cnf transformation 57]
124. ~curious(alice) [cnf transformation 20]
125. ~patient(X0) | humble(X0) [duplicate literal removal 77]
140. 4 <=> ! [X3] : curious(X3) [avatar definition]
141. curious(X3) <- (4) [avatar component clause 140]
152. 7 <=> calm(sK1) [avatar definition]
154. ~calm(sK1) <- (~7) [avatar component clause 152]
155. 4 | ~7 [avatar split clause 91,152,140]
192. 16 <=> ! [X3] : strong(X3) [avatar definition]
193. strong(X3) <- (16) [avatar component clause 192]
195. 17 <=> old(sK3) [avatar definition]
196. ~old(sK3) <- (~17) [avatar component clause 195]
197. old(sK3) <- (17) [avatar component clause 195]
199. 18 <=> happy(sK3) [avatar definition]
201. ~happy(sK3) <- (~18) [avatar component clause 199]
202. 16 | 17 | ~18 [avatar split clause 108,199,195,192]
207. 16 | ~17 | 18 [avatar split clause 106,199,195,192]
210. ~brave(X0) [subsumption resolution 114,63]
275. patient(sK3) | brave(sK3) <- (~17) [resolution 67,196]
282. patient(sK3) <- (~17) [subsumption resolution 275,210]
292. humble(sK3) <- (~17) [resolution 282,125]
315. happy(sK3) <- (~17) [resolution 292,87]
317. $false <- (~17, ~18) [subsumption resolution 315,201]
318. 17 | 18 [avatar contradiction clause 317]
320. funny(sK3) <- (17) [resolution 197,111]
330. wise(sK3) <- (17) [resolution 320,98]
356. ~old(sK3) | ~happy(sK3) <- (17) [resolution 330,80]
358. ~happy(sK3) <- (17) [subsumption resolution 356,197]
361. ~18 | ~17 [avatar split clause 358,195,199]
363. calm(X1) <- (16) [resolution 193,88]
375. $false <- (~7, 16) [resolution 363,154]
378. 7 | ~16 [avatar contradiction clause 375]
380. $false <- (4) [resolution 141,124]
383. ~4 [avatar contradiction clause 380]
384. $false [avatar sat refutation 155,202,207,318,361,378,383]
% SZS output end Proof for 6329033282012275961931168
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong then someone is not rich or not old. Everyone who is happy or not calm is not funny and vice versa. Everyone who is either old or not humble is strong or curious and vice versa. If someone is not calm then alice is both not humble and not tall and vice versa. Everyone who is not old or not strong is kind. Everyone who is humble is both not kind and tall and vice versa. If someone is quiet or wise then someone is not quiet and vice versa. If someone is both happy and not tall then lucy is calm. If someone is either funny or not humble then someone is creative or tall. Everyone who is humble or curious is both patient and wise and vice versa. Everyone who is either generous or not wise is either strong or funny and vice versa. Everyone who is either not brave or not tall is not brave. If john is either humble or quiet then susan is rich or not old. Everyone who is not brave or not humble is tall or happy. Everyone who is brave is either brave or not rich. If john is generous then lucy is not quiet. Someone is quiet or not quiet. John is not tall or rich. Someone is both rich and not humble. Someone is curious or not funny. Susan is rich or not brave. Someone is either not wise or not creative. Someone is either not strong or generous. Someone is not patient or not old. | Alice is tall. | neutral | ((?[X]:(~strong(X)))=>(?[X]:((~rich(X)|~old(X)))))&
(![X]:((happy(X)|~calm(X))<=>~funny(X)))&
(![X]:((old(X)<~>~humble(X))<=>(strong(X)|curious(X))))&
((?[X]:(~calm(X)))<=>((~humble(alice)&~tall(alice))))&
(![X]:((~old(X)|~strong(X))=>kind(X)))&
(![X]:(humble(X)<=>(~kind(X)&tall(X))))&
((?[X]:((quiet(X)|wise(X))))<=>(?[X]:(~quiet(X))))&
((?[X]:((happy(X)&~tall(X))))=>(calm(lucy)))&
((?[X]:((funny(X)<~>~humble(X))))=>(?[X]:((creative(X)|tall(X)))))&
(![X]:((humble(X)|curious(X))<=>(patient(X)&wise(X))))&
(![X]:((generous(X)<~>~wise(X))<=>(strong(X)<~>funny(X))))&
(![X]:((~brave(X)<~>~tall(X))=>~brave(X)))&
(((humble(john)<~>quiet(john)))=>((rich(susan)|~old(susan))))&
(![X]:((~brave(X)|~humble(X))=>(tall(X)|happy(X))))&
(![X]:(brave(X)=>(brave(X)<~>~rich(X))))&
((generous(john))=>(~quiet(lucy)))&
(?[X]:((quiet(X)|~quiet(X))))&
((~tall(john)|rich(john)))&
(?[X]:((rich(X)&~humble(X))))&
(?[X]:((curious(X)|~funny(X))))&
((rich(susan)|~brave(susan)))&
(?[X]:((~wise(X)<~>~creative(X))))&
(?[X]:((~strong(X)<~>generous(X))))&
(?[X]:((~patient(X)|~old(X)))) | tall(alice) | [] | null | 0 |
Everyone who is calm or curious is both not kind and calm and vice versa.
If fred is both not wise and wise then someone is either not humble or not calm and vice versa.
Everyone who is happy is either funny or not patient and vice versa.
Everyone who is not calm is both kind and patient.
Everyone who is both wise and not generous is tall and vice versa.
Everyone who is either not funny or not patient is either old or not rich and vice versa.
If someone is both not creative and quiet then someone is both funny and not rich.
Everyone who is not creative is either not wise or quiet and vice versa.
If paul is kind or funny then susan is either funny or not quiet and vice versa.
If someone is either not old or not brave then alice is not wise or not humble and vice versa.
Everyone who is not kind or rich is both humble and not humble.
Everyone who is either not generous or not happy is either calm or not calm.
Everyone who is quiet is either rich or old.
If john is both rich and not tall then someone is humble.
Everyone who is not brave is not quiet or not curious and vice versa.
If someone is either not happy or not old then someone is not brave.
John is not happy or not rich.
Someone is either not humble or not old.
Mary is not calm.
Someone is either old or wise.
Lucy is both not funny and not strong.
Someone is quiet. | Mary is not happy. | neutral | (![X]:((calm(X)|curious(X))<=>(~kind(X)&calm(X))))&
(((~wise(fred)&wise(fred)))<=>(?[X]:((~humble(X)<~>~calm(X)))))&
(![X]:(happy(X)<=>(funny(X)<~>~patient(X))))&
(![X]:(~calm(X)=>(kind(X)&patient(X))))&
(![X]:((wise(X)&~generous(X))<=>tall(X)))&
(![X]:((~funny(X)<~>~patient(X))<=>(old(X)<~>~rich(X))))&
((?[X]:((~creative(X)&quiet(X))))=>(?[X]:((funny(X)&~rich(X)))))&
(![X]:(~creative(X)<=>(~wise(X)<~>quiet(X))))&
(((kind(paul)|funny(paul)))<=>((funny(susan)<~>~quiet(susan))))&
((?[X]:((~old(X)<~>~brave(X))))<=>((~wise(alice)|~humble(alice))))&
(![X]:((~kind(X)|rich(X))=>(humble(X)&~humble(X))))&
(![X]:((~generous(X)<~>~happy(X))=>(calm(X)<~>~calm(X))))&
(![X]:(quiet(X)=>(rich(X)<~>old(X))))&
(((rich(john)&~tall(john)))=>(?[X]:(humble(X))))&
(![X]:(~brave(X)<=>(~quiet(X)|~curious(X))))&
((?[X]:((~happy(X)<~>~old(X))))=>(?[X]:(~brave(X))))&
((~happy(john)|~rich(john)))&
(?[X]:((~humble(X)<~>~old(X))))&
(~calm(mary))&
(?[X]:((old(X)<~>wise(X))))&
((~funny(lucy)&~strong(lucy)))&
(?[X]:(quiet(X))) | ~happy(mary) | [] | null | 0 |
Everyone who is both not strong and not curious is either creative or rich.
Everyone who is both not generous and not strong is happy.
Everyone who is not generous is not curious.
If someone is not creative or happy then john is not funny and vice versa.
Everyone who is patient or wise is either patient or tall and vice versa.
Everyone who is either happy or tall is old and vice versa.
Everyone who is not kind or wise is creative and vice versa.
If mary is either strong or rich then someone is either not curious or creative.
If mary is rich then someone is generous or patient and vice versa.
Everyone who is humble is either not rich or not brave.
Everyone who is either not funny or tall is either not wise or humble and vice versa.
Everyone who is humble or strong is both not patient and patient.
If mary is creative then someone is either quiet or kind and vice versa.
If someone is either kind or quiet then someone is not wise and vice versa.
Everyone who is either tall or not rich is happy or creative and vice versa.
Paul is tall.
Mary is funny or happy.
Someone is not old.
Someone is either not kind or strong.
Someone is both generous and old.
Someone is not humble.
Someone is not old or not kind. | Paul is wise. | entailment | (![X]:((~strong(X)&~curious(X))=>(creative(X)<~>rich(X))))&
(![X]:((~generous(X)&~strong(X))=>happy(X)))&
(![X]:(~generous(X)=>~curious(X)))&
((?[X]:((~creative(X)|happy(X))))<=>(~funny(john)))&
(![X]:((patient(X)|wise(X))<=>(patient(X)<~>tall(X))))&
(![X]:((happy(X)<~>tall(X))<=>old(X)))&
(![X]:((~kind(X)|wise(X))<=>creative(X)))&
(((strong(mary)<~>rich(mary)))=>(?[X]:((~curious(X)<~>creative(X)))))&
((rich(mary))<=>(?[X]:((generous(X)|patient(X)))))&
(![X]:(humble(X)=>(~rich(X)<~>~brave(X))))&
(![X]:((~funny(X)<~>tall(X))<=>(~wise(X)<~>humble(X))))&
(![X]:((humble(X)|strong(X))=>(~patient(X)&patient(X))))&
((creative(mary))<=>(?[X]:((quiet(X)<~>kind(X)))))&
((?[X]:((kind(X)<~>quiet(X))))<=>(?[X]:(~wise(X))))&
(![X]:((tall(X)<~>~rich(X))<=>(happy(X)|creative(X))))&
(tall(paul))&
((funny(mary)|happy(mary)))&
(?[X]:(~old(X)))&
(?[X]:((~kind(X)<~>strong(X))))&
(?[X]:((generous(X)&old(X))))&
(?[X]:(~humble(X)))&
(?[X]:((~old(X)|~kind(X)))) | wise(paul) | [
"p4",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7893126792874391469957395
% SZS output start Proof for 7893126792874391469957395
5. ! [X0] : ((wise(X0) | patient(X0)) <=> (patient(X0) <~> tall(X0))) [input p4]
16. tall(paul) [input p15]
23. ~wise(paul) [input hypothesis]
38. ! [X0] : (((wise(X0) | patient(X0)) | ((patient(X0) | ~tall(X0)) & (tall(X0) | ~patient(X0)))) & (((~tall(X0) | ~patient(X0)) & (tall(X0) | patient(X0))) | (~wise(X0) & ~patient(X0)))) [nnf transformation 5]
39. ! [X0] : ((wise(X0) | patient(X0) | ((patient(X0) | ~tall(X0)) & (tall(X0) | ~patient(X0)))) & (((~tall(X0) | ~patient(X0)) & (tall(X0) | patient(X0))) | (~wise(X0) & ~patient(X0)))) [flattening 38]
83. ~tall(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 39]
86. wise(X0) | patient(X0) | patient(X0) | ~tall(X0) [cnf transformation 39]
129. tall(paul) [cnf transformation 16]
138. ~wise(paul) [cnf transformation 23]
139. ~tall(X0) | ~patient(X0) [duplicate literal removal 83]
140. ~tall(X0) | patient(X0) | wise(X0) [duplicate literal removal 86]
266. ~patient(paul) [resolution 139,129]
377. patient(paul) | wise(paul) [resolution 140,129]
403. patient(paul) [subsumption resolution 377,138]
408. $false [subsumption resolution 266,403]
% SZS output end Proof for 7893126792874391469957395
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave is both not rich and not generous.
Everyone who is both tall and not tall is humble or quiet and vice versa.
Everyone who is strong is not generous or humble and vice versa.
Everyone who is happy is both not tall and patient.
If someone is not rich then mary is not tall or not brave.
Everyone who is not curious is tall or not calm and vice versa.
If someone is curious or kind then someone is both brave and not tall and vice versa.
Everyone who is not calm or not kind is quiet or generous and vice versa.
If susan is not old then someone is either strong or not brave.
Everyone who is either curious or not tall is quiet and vice versa.
If mary is either old or not brave then fred is either not happy or calm and vice versa.
Everyone who is either not calm or patient is humble and vice versa.
Everyone who is generous is not rich and vice versa.
If someone is both not creative and curious then mary is not rich.
If someone is either not wise or funny then john is not old and vice versa.
Everyone who is both not strong and not wise is both generous and not brave and vice versa.
Someone is generous.
Someone is not strong.
Lucy is not patient. | Susan is not generous. | contradiction | (![X]:(brave(X)=>(~rich(X)&~generous(X))))&
(![X]:((tall(X)&~tall(X))<=>(humble(X)|quiet(X))))&
(![X]:(strong(X)<=>(~generous(X)|humble(X))))&
(![X]:(happy(X)=>(~tall(X)&patient(X))))&
((?[X]:(~rich(X)))=>((~tall(mary)|~brave(mary))))&
(![X]:(~curious(X)<=>(tall(X)|~calm(X))))&
((?[X]:((curious(X)|kind(X))))<=>(?[X]:((brave(X)&~tall(X)))))&
(![X]:((~calm(X)|~kind(X))<=>(quiet(X)|generous(X))))&
((~old(susan))=>(?[X]:((strong(X)<~>~brave(X)))))&
(![X]:((curious(X)<~>~tall(X))<=>quiet(X)))&
(((old(mary)<~>~brave(mary)))<=>((~happy(fred)<~>calm(fred))))&
(![X]:((~calm(X)<~>patient(X))<=>humble(X)))&
(![X]:(generous(X)<=>~rich(X)))&
((?[X]:((~creative(X)&curious(X))))=>(~rich(mary)))&
((?[X]:((~wise(X)<~>funny(X))))<=>(~old(john)))&
(![X]:((~strong(X)&~wise(X))<=>(generous(X)&~brave(X))))&
(?[X]:(generous(X)))&
(?[X]:(~strong(X)))&
(~patient(lucy)) | ~generous(susan) | [
"p0",
"p1",
"p6",
"p7",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 4308939220001191546264690
% SZS output start Proof for 4308939220001191546264690
1. ! [X0] : (brave(X0) => (~generous(X0) & ~rich(X0))) [input p0]
2. ! [X0] : ((~tall(X0) & tall(X0)) <=> (quiet(X0) | humble(X0))) [input p1]
7. ? [X0] : (kind(X0) | curious(X0)) <=> ? [X0] : (~tall(X0) & brave(X0)) [input p6]
8. ! [X0] : ((~kind(X0) | ~calm(X0)) <=> (generous(X0) | quiet(X0))) [input p7]
13. ! [X0] : (generous(X0) <=> ~rich(X0)) [input p12]
20. ~generous(susan) [input hypothesis]
21. ? [X0] : (kind(X0) | curious(X0)) <=> ? [X1] : (~tall(X1) & brave(X1)) [rectify 7]
23. ! [X0] : ((~generous(X0) & ~rich(X0)) | ~brave(X0)) [ennf transformation 1]
28. ! [X0] : (((~tall(X0) & tall(X0)) | (~quiet(X0) & ~humble(X0))) & ((quiet(X0) | humble(X0)) | (tall(X0) | ~tall(X0)))) [nnf transformation 2]
29. ! [X0] : (((~tall(X0) & tall(X0)) | (~quiet(X0) & ~humble(X0))) & (quiet(X0) | humble(X0) | tall(X0) | ~tall(X0))) [flattening 28]
34. (? [X0] : (kind(X0) | curious(X0)) | ! [X1] : (tall(X1) | ~brave(X1))) & (? [X1] : (~tall(X1) & brave(X1)) | ! [X0] : (~kind(X0) & ~curious(X0))) [nnf transformation 21]
35. (? [X0] : (kind(X0) | curious(X0)) | ! [X1] : (tall(X1) | ~brave(X1))) & (? [X2] : (~tall(X2) & brave(X2)) | ! [X3] : (~kind(X3) & ~curious(X3))) [rectify 34]
36. ? [X0] : (kind(X0) | curious(X0)) => (kind(sK0) | curious(sK0)) [choice axiom]
37. ? [X2] : (~tall(X2) & brave(X2)) => (~tall(sK1) & brave(sK1)) [choice axiom]
38. ((kind(sK0) | curious(sK0)) | ! [X1] : (tall(X1) | ~brave(X1))) & ((~tall(sK1) & brave(sK1)) | ! [X3] : (~kind(X3) & ~curious(X3))) [skolemisation 35,37,36]
39. ! [X0] : (((~kind(X0) | ~calm(X0)) | (~generous(X0) & ~quiet(X0))) & ((generous(X0) | quiet(X0)) | (kind(X0) & calm(X0)))) [nnf transformation 8]
40. ! [X0] : ((~kind(X0) | ~calm(X0) | (~generous(X0) & ~quiet(X0))) & (generous(X0) | quiet(X0) | (kind(X0) & calm(X0)))) [flattening 39]
47. ! [X0] : ((generous(X0) | rich(X0)) & (~rich(X0) | ~generous(X0))) [nnf transformation 13]
58. ~rich(X0) | ~brave(X0) [cnf transformation 23]
59. ~generous(X0) | ~brave(X0) [cnf transformation 23]
62. tall(X0) | ~quiet(X0) [cnf transformation 29]
64. ~quiet(X0) | ~tall(X0) [cnf transformation 29]
75. brave(sK1) | ~kind(X3) [cnf transformation 38]
80. generous(X0) | quiet(X0) | kind(X0) [cnf transformation 40]
102. generous(X0) | rich(X0) [cnf transformation 47]
114. ~generous(susan) [cnf transformation 20]
115. ~quiet(X0) [subsumption resolution 62,64]
143. 7 <=> ! [X3] : ~kind(X3) [avatar definition]
144. ~kind(X3) <- (7) [avatar component clause 143]
155. 10 <=> brave(sK1) [avatar definition]
157. brave(sK1) <- (10) [avatar component clause 155]
158. 7 | 10 [avatar split clause 75,155,143]
160. kind(X0) | generous(X0) [subsumption resolution 80,115]
232. rich(X1) | ~brave(X1) [resolution 102,59]
233. ~brave(X1) [subsumption resolution 232,58]
236. generous(X0) <- (7) [resolution 160,144]
237. $false <- (7) [resolution 236,114]
240. ~7 [avatar contradiction clause 237]
241. $false <- (10) [subsumption resolution 157,233]
242. ~10 [avatar contradiction clause 241]
243. $false [avatar sat refutation 158,240,242]
% SZS output end Proof for 4308939220001191546264690
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
If john is happy then fred is both calm and not wise and vice versa. Everyone who is either brave or not old is wise or not tall. Everyone who is happy is either rich or not funny and vice versa. If alice is both old and kind then someone is either calm or not brave. Everyone who is not happy is either humble or not humble. Everyone who is not strong or humble is both patient and happy and vice versa. If lucy is either funny or old then someone is not old or not wise. Everyone who is not strong or humble is either calm or not creative. If fred is brave then someone is brave. If susan is brave then paul is either not calm or happy. Everyone who is both calm and creative is wise or generous and vice versa. If someone is funny or brave then someone is not kind. If someone is both old and not generous then someone is either quiet or not strong. Everyone who is not quiet or kind is both brave and not old. If susan is tall then paul is either brave or patient and vice versa. If alice is both not rich and tall then lucy is either wise or curious. Fred is either not funny or not wise. Mary is not kind. Someone is either not calm or calm. Someone is not strong or not old. Alice is both humble and patient. Lucy is both not strong and not old. Someone is both generous and happy. | Lucy is not old. | entailment | ((happy(john))<=>((calm(fred)&~wise(fred))))&
(![X]:((brave(X)<~>~old(X))=>(wise(X)|~tall(X))))&
(![X]:(happy(X)<=>(rich(X)<~>~funny(X))))&
(((old(alice)&kind(alice)))=>(?[X]:((calm(X)<~>~brave(X)))))&
(![X]:(~happy(X)=>(humble(X)<~>~humble(X))))&
(![X]:((~strong(X)|humble(X))<=>(patient(X)&happy(X))))&
(((funny(lucy)<~>old(lucy)))=>(?[X]:((~old(X)|~wise(X)))))&
(![X]:((~strong(X)|humble(X))=>(calm(X)<~>~creative(X))))&
((brave(fred))=>(?[X]:(brave(X))))&
((brave(susan))=>((~calm(paul)<~>happy(paul))))&
(![X]:((calm(X)&creative(X))<=>(wise(X)|generous(X))))&
((?[X]:((funny(X)|brave(X))))=>(?[X]:(~kind(X))))&
((?[X]:((old(X)&~generous(X))))=>(?[X]:((quiet(X)<~>~strong(X)))))&
(![X]:((~quiet(X)|kind(X))=>(brave(X)&~old(X))))&
((tall(susan))<=>((brave(paul)<~>patient(paul))))&
(((~rich(alice)&tall(alice)))=>((wise(lucy)<~>curious(lucy))))&
((~funny(fred)<~>~wise(fred)))&
(~kind(mary))&
(?[X]:((~calm(X)<~>calm(X))))&
(?[X]:((~strong(X)|~old(X))))&
((humble(alice)&patient(alice)))&
((~strong(lucy)&~old(lucy)))&
(?[X]:((generous(X)&happy(X)))) | ~old(lucy) | [
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 2609306437072505516311230
% SZS output start Proof for 2609306437072505516311230
22. ~old(lucy) & ~strong(lucy) [input p21]
24. old(lucy) [input hypothesis]
120. ~old(lucy) [cnf transformation 22]
123. old(lucy) [cnf transformation 24]
140. 4 <=> old(lucy) [avatar definition]
242. ~4 [avatar split clause 120,140]
243. 4 [avatar split clause 123,140]
244. $false [avatar sat refutation 242,243]
% SZS output end Proof for 2609306437072505516311230
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not funny or not calm then paul is either not kind or funny. If fred is not brave then paul is not generous or tall. Everyone who is kind is both rich and not creative. Everyone who is generous or not rich is either patient or not happy and vice versa. If someone is both not brave and humble then someone is either not kind or not strong and vice versa. Everyone who is not calm or not kind is both strong and not curious and vice versa. If someone is either calm or not old then someone is either not happy or creative. Everyone who is not calm or wise is not wise and vice versa. If someone is either funny or not old then someone is not rich or not curious. If someone is both not kind and not creative then lucy is not brave and vice versa. Everyone who is not curious is both not rich and happy. If lucy is either brave or not humble then someone is kind or calm and vice versa. Everyone who is both not brave and not rich is not kind or not curious. If paul is curious or not creative then paul is both not kind and not brave and vice versa. If someone is both curious and tall then paul is both wise and not calm and vice versa. Everyone who is kind is either strong or not kind. Susan is not funny or quiet. Susan is brave or wise. Lucy is tall or not happy. Someone is both not creative and old. Someone is both not tall and strong. Mary is both not wise and humble. Someone is not happy or not creative. Fred is brave or rich. | Susan is not patient. | contradiction | ((?[X]:((~funny(X)|~calm(X))))=>((~kind(paul)<~>funny(paul))))&
((~brave(fred))=>((~generous(paul)|tall(paul))))&
(![X]:(kind(X)=>(rich(X)&~creative(X))))&
(![X]:((generous(X)|~rich(X))<=>(patient(X)<~>~happy(X))))&
((?[X]:((~brave(X)&humble(X))))<=>(?[X]:((~kind(X)<~>~strong(X)))))&
(![X]:((~calm(X)|~kind(X))<=>(strong(X)&~curious(X))))&
((?[X]:((calm(X)<~>~old(X))))=>(?[X]:((~happy(X)<~>creative(X)))))&
(![X]:((~calm(X)|wise(X))<=>~wise(X)))&
((?[X]:((funny(X)<~>~old(X))))=>(?[X]:((~rich(X)|~curious(X)))))&
((?[X]:((~kind(X)&~creative(X))))<=>(~brave(lucy)))&
(![X]:(~curious(X)=>(~rich(X)&happy(X))))&
(((brave(lucy)<~>~humble(lucy)))<=>(?[X]:((kind(X)|calm(X)))))&
(![X]:((~brave(X)&~rich(X))=>(~kind(X)|~curious(X))))&
(((curious(paul)|~creative(paul)))<=>((~kind(paul)&~brave(paul))))&
((?[X]:((curious(X)&tall(X))))<=>((wise(paul)&~calm(paul))))&
(![X]:(kind(X)=>(strong(X)<~>~kind(X))))&
((~funny(susan)|quiet(susan)))&
((brave(susan)|wise(susan)))&
((tall(lucy)|~happy(lucy)))&
(?[X]:((~creative(X)&old(X))))&
(?[X]:((~tall(X)&strong(X))))&
((~wise(mary)&humble(mary)))&
(?[X]:((~happy(X)|~creative(X))))&
((brave(fred)|rich(fred))) | ~patient(susan) | [
"p2",
"p3",
"p5",
"p7",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 6740596766383853019899792
% SZS output start Proof for 6740596766383853019899792
3. ! [X0] : (kind(X0) => (~creative(X0) & rich(X0))) [input p2]
4. ! [X0] : ((~rich(X0) | generous(X0)) <=> (patient(X0) <~> ~happy(X0))) [input p3]
6. ! [X0] : ((~kind(X0) | ~calm(X0)) <=> (~curious(X0) & strong(X0))) [input p5]
8. ! [X0] : ((wise(X0) | ~calm(X0)) <=> ~wise(X0)) [input p7]
11. ! [X0] : (~curious(X0) => (happy(X0) & ~rich(X0))) [input p10]
12. (brave(lucy) <~> ~humble(lucy)) <=> ? [X0] : (calm(X0) | kind(X0)) [input p11]
25. ~patient(susan) [input hypothesis]
33. ! [X0] : ((~creative(X0) & rich(X0)) | ~kind(X0)) [ennf transformation 3]
36. ! [X0] : ((happy(X0) & ~rich(X0)) | curious(X0)) [ennf transformation 11]
41. ! [X0] : (((~rich(X0) | generous(X0)) | ((patient(X0) | happy(X0)) & (~happy(X0) | ~patient(X0)))) & (((happy(X0) | ~patient(X0)) & (~happy(X0) | patient(X0))) | (rich(X0) & ~generous(X0)))) [nnf transformation 4]
42. ! [X0] : ((~rich(X0) | generous(X0) | ((patient(X0) | happy(X0)) & (~happy(X0) | ~patient(X0)))) & (((happy(X0) | ~patient(X0)) & (~happy(X0) | patient(X0))) | (rich(X0) & ~generous(X0)))) [flattening 41]
48. ! [X0] : (((~kind(X0) | ~calm(X0)) | (curious(X0) | ~strong(X0))) & ((~curious(X0) & strong(X0)) | (kind(X0) & calm(X0)))) [nnf transformation 6]
49. ! [X0] : ((~kind(X0) | ~calm(X0) | curious(X0) | ~strong(X0)) & ((~curious(X0) & strong(X0)) | (kind(X0) & calm(X0)))) [flattening 48]
54. ! [X0] : (((wise(X0) | ~calm(X0)) | wise(X0)) & (~wise(X0) | (~wise(X0) & calm(X0)))) [nnf transformation 8]
55. ! [X0] : ((wise(X0) | ~calm(X0) | wise(X0)) & (~wise(X0) | (~wise(X0) & calm(X0)))) [flattening 54]
64. (((humble(lucy) | ~brave(lucy)) & (~humble(lucy) | brave(lucy))) | ! [X0] : (~calm(X0) & ~kind(X0))) & (? [X0] : (calm(X0) | kind(X0)) | ((brave(lucy) | humble(lucy)) & (~humble(lucy) | ~brave(lucy)))) [nnf transformation 12]
65. (((humble(lucy) | ~brave(lucy)) & (~humble(lucy) | brave(lucy))) | ! [X0] : (~calm(X0) & ~kind(X0))) & (? [X1] : (calm(X1) | kind(X1)) | ((brave(lucy) | humble(lucy)) & (~humble(lucy) | ~brave(lucy)))) [rectify 64]
66. ? [X1] : (calm(X1) | kind(X1)) => (calm(sK5) | kind(sK5)) [choice axiom]
67. (((humble(lucy) | ~brave(lucy)) & (~humble(lucy) | brave(lucy))) | ! [X0] : (~calm(X0) & ~kind(X0))) & ((calm(sK5) | kind(sK5)) | ((brave(lucy) | humble(lucy)) & (~humble(lucy) | ~brave(lucy)))) [skolemisation 65,66]
87. ~kind(X0) | rich(X0) [cnf transformation 33]
90. ~happy(X0) | patient(X0) | rich(X0) [cnf transformation 42]
103. ~curious(X0) | calm(X0) [cnf transformation 49]
104. ~curious(X0) | kind(X0) [cnf transformation 49]
111. ~wise(X0) | ~wise(X0) [cnf transformation 55]
112. wise(X0) | ~calm(X0) | wise(X0) [cnf transformation 55]
118. ~rich(X0) | curious(X0) [cnf transformation 36]
119. curious(X0) | happy(X0) [cnf transformation 36]
120. calm(sK5) | kind(sK5) | ~humble(lucy) | ~brave(lucy) [cnf transformation 67]
121. calm(sK5) | kind(sK5) | brave(lucy) | humble(lucy) [cnf transformation 67]
122. ~humble(lucy) | brave(lucy) | ~kind(X0) [cnf transformation 67]
124. humble(lucy) | ~brave(lucy) | ~kind(X0) [cnf transformation 67]
148. ~patient(susan) [cnf transformation 25]
150. ~wise(X0) [duplicate literal removal 111]
151. ~calm(X0) | wise(X0) [duplicate literal removal 112]
249. 23 <=> brave(lucy) [avatar definition]
270. 28 <=> humble(lucy) [avatar definition]
275. 29 <=> ! [X0] : ~kind(X0) [avatar definition]
276. ~kind(X0) <- (29) [avatar component clause 275]
277. 29 | ~23 | 28 [avatar split clause 124,270,249,275]
279. 29 | 23 | ~28 [avatar split clause 122,270,249,275]
281. 30 <=> kind(sK5) [avatar definition]
283. kind(sK5) <- (30) [avatar component clause 281]
285. 31 <=> calm(sK5) [avatar definition]
286. ~calm(sK5) <- (~31) [avatar component clause 285]
287. calm(sK5) <- (31) [avatar component clause 285]
288. 28 | 23 | 30 | 31 [avatar split clause 121,285,281,249,270]
289. ~23 | ~28 | 30 | 31 [avatar split clause 120,285,281,270,249]
357. happy(X0) | kind(X0) [resolution 119,104]
359. happy(X0) <- (29) [subsumption resolution 357,276]
382. patient(X0) | rich(X0) <- (29) [resolution 90,359]
409. rich(susan) <- (29) [resolution 382,148]
417. curious(susan) <- (29) [resolution 409,118]
419. kind(susan) <- (29) [resolution 417,104]
421. $false <- (29) [subsumption resolution 419,276]
422. ~29 [avatar contradiction clause 421]
428. wise(sK5) <- (31) [resolution 287,151]
429. $false <- (31) [subsumption resolution 428,150]
430. ~31 [avatar contradiction clause 429]
431. rich(sK5) <- (30) [resolution 283,87]
462. curious(sK5) <- (30) [resolution 431,118]
485. calm(sK5) <- (30) [resolution 462,103]
486. $false <- (30, ~31) [subsumption resolution 485,286]
487. ~30 | 31 [avatar contradiction clause 486]
488. $false [avatar sat refutation 277,279,288,289,422,430,487]
% SZS output end Proof for 6740596766383853019899792
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not wise or not quiet is either humble or not wise and vice versa.
If someone is funny or creative then john is old or wise.
Everyone who is patient or not humble is not generous or curious and vice versa.
If mary is both not rich and funny then alice is not kind or kind and vice versa.
Everyone who is not old is both brave and wise.
Everyone who is either quiet or not old is old or not tall.
Everyone who is both creative and not patient is not tall or not strong and vice versa.
Everyone who is either brave or not old is humble and vice versa.
If someone is either not curious or not old then someone is both tall and wise and vice versa.
If someone is not generous or calm then fred is either not quiet or tall and vice versa.
Everyone who is both humble and happy is not old or strong and vice versa.
If someone is both not patient and brave then paul is tall or wise and vice versa.
Everyone who is either curious or not funny is both not wise and calm and vice versa.
If alice is both humble and patient then someone is both happy and calm.
If someone is not tall then mary is both not quiet and patient and vice versa.
Everyone who is both brave and curious is both quiet and creative and vice versa.
Someone is either not kind or not generous.
Someone is not tall or creative.
Someone is both not happy and not quiet.
Someone is patient.
Someone is either not creative or calm.
Someone is brave or rich.
Fred is not happy or not humble.
Someone is not happy or not rich. | Fred is generous. | entailment | (![X]:((~wise(X)<~>~quiet(X))<=>(humble(X)<~>~wise(X))))&
((?[X]:((funny(X)|creative(X))))=>((old(john)|wise(john))))&
(![X]:((patient(X)|~humble(X))<=>(~generous(X)|curious(X))))&
(((~rich(mary)&funny(mary)))<=>((~kind(alice)|kind(alice))))&
(![X]:(~old(X)=>(brave(X)&wise(X))))&
(![X]:((quiet(X)<~>~old(X))=>(old(X)|~tall(X))))&
(![X]:((creative(X)&~patient(X))<=>(~tall(X)|~strong(X))))&
(![X]:((brave(X)<~>~old(X))<=>humble(X)))&
((?[X]:((~curious(X)<~>~old(X))))<=>(?[X]:((tall(X)&wise(X)))))&
((?[X]:((~generous(X)|calm(X))))<=>((~quiet(fred)<~>tall(fred))))&
(![X]:((humble(X)&happy(X))<=>(~old(X)|strong(X))))&
((?[X]:((~patient(X)&brave(X))))<=>((tall(paul)|wise(paul))))&
(![X]:((curious(X)<~>~funny(X))<=>(~wise(X)&calm(X))))&
(((humble(alice)&patient(alice)))=>(?[X]:((happy(X)&calm(X)))))&
((?[X]:(~tall(X)))<=>((~quiet(mary)&patient(mary))))&
(![X]:((brave(X)&curious(X))<=>(quiet(X)&creative(X))))&
(?[X]:((~kind(X)<~>~generous(X))))&
(?[X]:((~tall(X)|creative(X))))&
(?[X]:((~happy(X)&~quiet(X))))&
(?[X]:(patient(X)))&
(?[X]:((~creative(X)<~>calm(X))))&
(?[X]:((brave(X)|rich(X))))&
((~happy(fred)|~humble(fred)))&
(?[X]:((~happy(X)|~rich(X)))) | generous(fred) | [
"p0",
"p2",
"p4",
"p6",
"p7",
"p9",
"p10",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3433343022301592629407415
% SZS output start Proof for 3433343022301592629407415
1. ! [X0] : ((~wise(X0) <~> ~quiet(X0)) <=> (humble(X0) <~> ~wise(X0))) [input p0]
3. ! [X0] : ((~humble(X0) | patient(X0)) <=> (curious(X0) | ~generous(X0))) [input p2]
5. ! [X0] : (~old(X0) => (wise(X0) & brave(X0))) [input p4]
7. ! [X0] : ((~patient(X0) & creative(X0)) <=> (~strong(X0) | ~tall(X0))) [input p6]
8. ! [X0] : ((brave(X0) <~> ~old(X0)) <=> humble(X0)) [input p7]
10. ? [X0] : (calm(X0) | ~generous(X0)) <=> (~quiet(fred) <~> tall(fred)) [input p9]
11. ! [X0] : ((happy(X0) & humble(X0)) <=> (strong(X0) | ~old(X0))) [input p10]
16. ! [X0] : ((curious(X0) & brave(X0)) <=> (creative(X0) & quiet(X0))) [input p15]
25. ~generous(fred) [input hypothesis]
29. ! [X0] : ((wise(X0) & brave(X0)) | old(X0)) [ennf transformation 5]
34. ! [X0] : ((((quiet(X0) | wise(X0)) & (~quiet(X0) | ~wise(X0))) | ((humble(X0) | wise(X0)) & (~wise(X0) | ~humble(X0)))) & (((wise(X0) | ~humble(X0)) & (~wise(X0) | humble(X0))) | ((~wise(X0) | quiet(X0)) & (~quiet(X0) | wise(X0))))) [nnf transformation 1]
35. ! [X0] : (((~humble(X0) | patient(X0)) | (~curious(X0) & generous(X0))) & ((curious(X0) | ~generous(X0)) | (humble(X0) & ~patient(X0)))) [nnf transformation 3]
36. ! [X0] : ((~humble(X0) | patient(X0) | (~curious(X0) & generous(X0))) & (curious(X0) | ~generous(X0) | (humble(X0) & ~patient(X0)))) [flattening 35]
40. ! [X0] : (((~patient(X0) & creative(X0)) | (strong(X0) & tall(X0))) & ((~strong(X0) | ~tall(X0)) | (patient(X0) | ~creative(X0)))) [nnf transformation 7]
41. ! [X0] : (((~patient(X0) & creative(X0)) | (strong(X0) & tall(X0))) & (~strong(X0) | ~tall(X0) | patient(X0) | ~creative(X0))) [flattening 40]
42. ! [X0] : ((((old(X0) | ~brave(X0)) & (~old(X0) | brave(X0))) | ~humble(X0)) & (humble(X0) | ((brave(X0) | old(X0)) & (~old(X0) | ~brave(X0))))) [nnf transformation 8]
48. (? [X0] : (calm(X0) | ~generous(X0)) | ((~quiet(fred) | ~tall(fred)) & (tall(fred) | quiet(fred)))) & (((~tall(fred) | quiet(fred)) & (tall(fred) | ~quiet(fred))) | ! [X0] : (~calm(X0) & generous(X0))) [nnf transformation 10]
49. (? [X0] : (calm(X0) | ~generous(X0)) | ((~quiet(fred) | ~tall(fred)) & (tall(fred) | quiet(fred)))) & (((~tall(fred) | quiet(fred)) & (tall(fred) | ~quiet(fred))) | ! [X1] : (~calm(X1) & generous(X1))) [rectify 48]
50. ? [X0] : (calm(X0) | ~generous(X0)) => (calm(sK2) | ~generous(sK2)) [choice axiom]
51. ((calm(sK2) | ~generous(sK2)) | ((~quiet(fred) | ~tall(fred)) & (tall(fred) | quiet(fred)))) & (((~tall(fred) | quiet(fred)) & (tall(fred) | ~quiet(fred))) | ! [X1] : (~calm(X1) & generous(X1))) [skolemisation 49,50]
52. ! [X0] : (((happy(X0) & humble(X0)) | (~strong(X0) & old(X0))) & ((strong(X0) | ~old(X0)) | (~happy(X0) | ~humble(X0)))) [nnf transformation 11]
53. ! [X0] : (((happy(X0) & humble(X0)) | (~strong(X0) & old(X0))) & (strong(X0) | ~old(X0) | ~happy(X0) | ~humble(X0))) [flattening 52]
68. ! [X0] : (((curious(X0) & brave(X0)) | (~creative(X0) | ~quiet(X0))) & ((creative(X0) & quiet(X0)) | (~curious(X0) | ~brave(X0)))) [nnf transformation 16]
69. ! [X0] : (((curious(X0) & brave(X0)) | ~creative(X0) | ~quiet(X0)) & ((creative(X0) & quiet(X0)) | ~curious(X0) | ~brave(X0))) [flattening 68]
87. ~wise(X0) | humble(X0) | ~wise(X0) | quiet(X0) [cnf transformation 34]
88. wise(X0) | ~humble(X0) | ~quiet(X0) | wise(X0) [cnf transformation 34]
90. ~quiet(X0) | ~wise(X0) | ~wise(X0) | ~humble(X0) [cnf transformation 34]
93. quiet(X0) | wise(X0) | humble(X0) | wise(X0) [cnf transformation 34]
98. ~humble(X0) | patient(X0) | generous(X0) [cnf transformation 36]
105. brave(X0) | old(X0) [cnf transformation 29]
111. strong(X0) | creative(X0) [cnf transformation 41]
112. ~patient(X0) | tall(X0) [cnf transformation 41]
114. ~brave(X0) | ~old(X0) | humble(X0) [cnf transformation 42]
116. ~old(X0) | brave(X0) | ~humble(X0) [cnf transformation 42]
117. old(X0) | ~brave(X0) | ~humble(X0) [cnf transformation 42]
126. ~tall(fred) | quiet(fred) | generous(X1) [cnf transformation 51]
131. humble(X0) | old(X0) [cnf transformation 53]
132. ~strong(X0) | humble(X0) [cnf transformation 53]
153. ~creative(X0) | brave(X0) | ~quiet(X0) [cnf transformation 69]
166. ~generous(fred) [cnf transformation 25]
168. ~wise(X0) | humble(X0) | quiet(X0) [duplicate literal removal 87]
169. wise(X0) | ~humble(X0) | ~quiet(X0) [duplicate literal removal 88]
170. ~humble(X0) | ~wise(X0) | ~quiet(X0) [duplicate literal removal 90]
171. humble(X0) | wise(X0) | quiet(X0) [duplicate literal removal 93]
172. ~humble(X0) | ~quiet(X0) [subsumption resolution 169,170]
173. humble(X0) | quiet(X0) [subsumption resolution 168,171]
206. ~humble(X0) | old(X0) [subsumption resolution 117,105]
207. ~humble(X0) | brave(X0) [subsumption resolution 116,105]
240. 15 <=> tall(fred) [avatar definition]
242. ~tall(fred) <- (~15) [avatar component clause 240]
244. 16 <=> quiet(fred) [avatar definition]
245. quiet(fred) <- (16) [avatar component clause 244]
246. ~quiet(fred) <- (~16) [avatar component clause 244]
262. 20 <=> ! [X1] : generous(X1) [avatar definition]
263. generous(X1) <- (20) [avatar component clause 262]
264. 20 | 16 | ~15 [avatar split clause 126,240,244,262]
267. old(X0) [subsumption resolution 131,206]
384. creative(X0) | humble(X0) [resolution 132,111]
408. generous(X0) | patient(X0) | quiet(X0) [resolution 98,173]
513. brave(X0) | ~quiet(X0) | humble(X0) [resolution 153,384]
518. brave(X0) | humble(X0) [subsumption resolution 513,173]
519. brave(X0) [subsumption resolution 518,207]
522. ~old(X2) | humble(X2) [resolution 519,114]
525. humble(X2) [subsumption resolution 522,267]
587. ~quiet(X4) [resolution 525,172]
616. patient(fred) | quiet(fred) [resolution 408,166]
619. patient(fred) <- (~16) [subsumption resolution 616,246]
623. tall(fred) <- (~16) [resolution 619,112]
624. $false <- (~15, ~16) [subsumption resolution 623,242]
625. 15 | 16 [avatar contradiction clause 624]
627. $false <- (16) [subsumption resolution 245,587]
628. ~16 [avatar contradiction clause 627]
635. $false <- (20) [resolution 263,166]
640. ~20 [avatar contradiction clause 635]
641. $false [avatar sat refutation 264,625,628,640]
% SZS output end Proof for 3433343022301592629407415
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not kind is not strong or patient and vice versa.
If paul is kind or not curious then someone is either curious or not rich.
Everyone who is both calm and not funny is either creative or not wise.
If someone is either not brave or not patient then someone is calm or happy.
Everyone who is either not wise or not patient is humble or patient.
Everyone who is patient or not strong is not curious and vice versa.
If someone is either calm or not happy then someone is not tall.
If susan is either generous or brave then someone is either not generous or brave and vice versa.
If someone is either calm or kind then lucy is both humble and not rich.
Everyone who is both brave and quiet is both not generous and not brave and vice versa.
Everyone who is strong or funny is both rich and not brave.
Everyone who is either funny or curious is both not happy and creative and vice versa.
Everyone who is calm or brave is both not wise and not calm.
If susan is both wise and tall then someone is both brave and not tall.
If someone is calm or patient then paul is either not generous or not rich and vice versa.
Everyone who is not brave or not quiet is kind or not tall and vice versa.
Someone is kind.
Someone is either not happy or not curious.
Fred is either not happy or wise.
Someone is tall or not calm.
Alice is both not kind and happy.
Someone is generous or not creative. | Alice is not curious. | entailment | (![X]:(~kind(X)<=>(~strong(X)|patient(X))))&
(((kind(paul)|~curious(paul)))=>(?[X]:((curious(X)<~>~rich(X)))))&
(![X]:((calm(X)&~funny(X))=>(creative(X)<~>~wise(X))))&
((?[X]:((~brave(X)<~>~patient(X))))=>(?[X]:((calm(X)|happy(X)))))&
(![X]:((~wise(X)<~>~patient(X))=>(humble(X)|patient(X))))&
(![X]:((patient(X)|~strong(X))<=>~curious(X)))&
((?[X]:((calm(X)<~>~happy(X))))=>(?[X]:(~tall(X))))&
(((generous(susan)<~>brave(susan)))<=>(?[X]:((~generous(X)<~>brave(X)))))&
((?[X]:((calm(X)<~>kind(X))))=>((humble(lucy)&~rich(lucy))))&
(![X]:((brave(X)&quiet(X))<=>(~generous(X)&~brave(X))))&
(![X]:((strong(X)|funny(X))=>(rich(X)&~brave(X))))&
(![X]:((funny(X)<~>curious(X))<=>(~happy(X)&creative(X))))&
(![X]:((calm(X)|brave(X))=>(~wise(X)&~calm(X))))&
(((wise(susan)&tall(susan)))=>(?[X]:((brave(X)&~tall(X)))))&
((?[X]:((calm(X)|patient(X))))<=>((~generous(paul)<~>~rich(paul))))&
(![X]:((~brave(X)|~quiet(X))<=>(kind(X)|~tall(X))))&
(?[X]:(kind(X)))&
(?[X]:((~happy(X)<~>~curious(X))))&
((~happy(fred)<~>wise(fred)))&
(?[X]:((tall(X)|~calm(X))))&
((~kind(alice)&happy(alice)))&
(?[X]:((generous(X)|~creative(X)))) | ~curious(alice) | [
"p0",
"p5",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 577311490806591820383437
% SZS output start Proof for 577311490806591820383437
1. ! [X0] : (~kind(X0) <=> (patient(X0) | ~strong(X0))) [input p0]
6. ! [X0] : ((~strong(X0) | patient(X0)) <=> ~curious(X0)) [input p5]
21. happy(alice) & ~kind(alice) [input p20]
23. curious(alice) [input hypothesis]
38. ! [X0] : ((~kind(X0) | (~patient(X0) & strong(X0))) & ((patient(X0) | ~strong(X0)) | kind(X0))) [nnf transformation 1]
39. ! [X0] : ((~kind(X0) | (~patient(X0) & strong(X0))) & (patient(X0) | ~strong(X0) | kind(X0))) [flattening 38]
48. ! [X0] : (((~strong(X0) | patient(X0)) | curious(X0)) & (~curious(X0) | (strong(X0) & ~patient(X0)))) [nnf transformation 6]
49. ! [X0] : ((~strong(X0) | patient(X0) | curious(X0)) & (~curious(X0) | (strong(X0) & ~patient(X0)))) [flattening 48]
81. ~strong(X0) | patient(X0) | kind(X0) [cnf transformation 39]
92. ~curious(X0) | ~patient(X0) [cnf transformation 49]
93. ~curious(X0) | strong(X0) [cnf transformation 49]
143. ~kind(alice) [cnf transformation 21]
146. curious(alice) [cnf transformation 23]
313. ~patient(alice) [resolution 92,146]
314. strong(alice) [resolution 93,146]
338. patient(alice) | kind(alice) [resolution 81,314]
339. kind(alice) [subsumption resolution 338,313]
340. $false [subsumption resolution 339,143]
% SZS output end Proof for 577311490806591820383437
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
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| 0 |
If mary is not happy or rich then alice is either creative or not curious and vice versa. Everyone who is calm or not kind is both not rich and not strong and vice versa. Everyone who is quiet or not tall is either not calm or patient and vice versa. Everyone who is not humble is either not old or curious. If someone is both wise and patient then lucy is not curious or humble. Everyone who is not funny or not generous is either funny or curious and vice versa. Everyone who is both old and curious is either brave or funny and vice versa. If paul is not kind or funny then susan is both rich and not calm and vice versa. If john is not wise or kind then someone is happy and vice versa. If mary is not rich then alice is both not patient and not tall and vice versa. Everyone who is not generous or not happy is not generous or humble. Everyone who is both wise and rich is either not quiet or not tall. Everyone who is not brave is both brave and not rich. If lucy is not brave or not happy then paul is both not kind and not wise and vice versa. Everyone who is not funny is either not tall or kind and vice versa. If someone is patient then paul is both not wise and not funny. Alice is both not humble and kind. Susan is not creative. Lucy is not rich. Lucy is humble. Someone is either not curious or creative. Alice is either not creative or rich. Someone is brave. Lucy is patient. | Susan is not rich. | neutral | (((~happy(mary)|rich(mary)))<=>((creative(alice)<~>~curious(alice))))&
(![X]:((calm(X)|~kind(X))<=>(~rich(X)&~strong(X))))&
(![X]:((quiet(X)|~tall(X))<=>(~calm(X)<~>patient(X))))&
(![X]:(~humble(X)=>(~old(X)<~>curious(X))))&
((?[X]:((wise(X)&patient(X))))=>((~curious(lucy)|humble(lucy))))&
(![X]:((~funny(X)|~generous(X))<=>(funny(X)<~>curious(X))))&
(![X]:((old(X)&curious(X))<=>(brave(X)<~>funny(X))))&
(((~kind(paul)|funny(paul)))<=>((rich(susan)&~calm(susan))))&
(((~wise(john)|kind(john)))<=>(?[X]:(happy(X))))&
((~rich(mary))<=>((~patient(alice)&~tall(alice))))&
(![X]:((~generous(X)|~happy(X))=>(~generous(X)|humble(X))))&
(![X]:((wise(X)&rich(X))=>(~quiet(X)<~>~tall(X))))&
(![X]:(~brave(X)=>(brave(X)&~rich(X))))&
(((~brave(lucy)|~happy(lucy)))<=>((~kind(paul)&~wise(paul))))&
(![X]:(~funny(X)<=>(~tall(X)<~>kind(X))))&
((?[X]:(patient(X)))=>((~wise(paul)&~funny(paul))))&
((~humble(alice)&kind(alice)))&
(~creative(susan))&
(~rich(lucy))&
(humble(lucy))&
(?[X]:((~curious(X)<~>creative(X))))&
((~creative(alice)<~>rich(alice)))&
(?[X]:(brave(X)))&
(patient(lucy)) | ~rich(susan) | [] | null | 0 |
If someone is tall then mary is either not curious or humble.
Everyone who is both not tall and kind is wise.
If someone is both quiet and funny then mary is either not wise or not strong.
If someone is kind or not old then mary is either creative or brave and vice versa.
Everyone who is not kind is both creative and not creative.
Everyone who is creative or tall is both happy and not generous.
Everyone who is not wise or not patient is happy or not humble and vice versa.
Everyone who is either not tall or not happy is not wise or not patient.
Everyone who is brave is either curious or patient.
Everyone who is either not strong or old is both patient and generous.
If fred is either not strong or tall then susan is curious.
Everyone who is either curious or brave is both not curious and generous and vice versa.
Everyone who is quiet is either brave or not patient.
Everyone who is not wise is not happy and vice versa.
If someone is not humble or not kind then alice is happy or old and vice versa.
Everyone who is not humble or patient is not curious or not creative.
Someone is not brave.
Someone is either old or brave.
Someone is either not calm or rich.
Fred is curious or tall.
Mary is either not happy or humble. | Fred is patient. | contradiction | ((?[X]:(tall(X)))=>((~curious(mary)<~>humble(mary))))&
(![X]:((~tall(X)&kind(X))=>wise(X)))&
((?[X]:((quiet(X)&funny(X))))=>((~wise(mary)<~>~strong(mary))))&
((?[X]:((kind(X)|~old(X))))<=>((creative(mary)<~>brave(mary))))&
(![X]:(~kind(X)=>(creative(X)&~creative(X))))&
(![X]:((creative(X)|tall(X))=>(happy(X)&~generous(X))))&
(![X]:((~wise(X)|~patient(X))<=>(happy(X)|~humble(X))))&
(![X]:((~tall(X)<~>~happy(X))=>(~wise(X)|~patient(X))))&
(![X]:(brave(X)=>(curious(X)<~>patient(X))))&
(![X]:((~strong(X)<~>old(X))=>(patient(X)&generous(X))))&
(((~strong(fred)<~>tall(fred)))=>(curious(susan)))&
(![X]:((curious(X)<~>brave(X))<=>(~curious(X)&generous(X))))&
(![X]:(quiet(X)=>(brave(X)<~>~patient(X))))&
(![X]:(~wise(X)<=>~happy(X)))&
((?[X]:((~humble(X)|~kind(X))))<=>((happy(alice)|old(alice))))&
(![X]:((~humble(X)|patient(X))=>(~curious(X)|~creative(X))))&
(?[X]:(~brave(X)))&
(?[X]:((old(X)<~>brave(X))))&
(?[X]:((~calm(X)<~>rich(X))))&
((curious(fred)|tall(fred)))&
((~happy(mary)<~>humble(mary))) | patient(fred) | [
"p1",
"p4",
"p5",
"p6",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 6355826508863027910472194
% SZS output start Proof for 6355826508863027910472194
2. ! [X0] : ((kind(X0) & ~tall(X0)) => wise(X0)) [input p1]
5. ! [X0] : (~kind(X0) => (~creative(X0) & creative(X0))) [input p4]
6. ! [X0] : ((tall(X0) | creative(X0)) => (~generous(X0) & happy(X0))) [input p5]
7. ! [X0] : ((~patient(X0) | ~wise(X0)) <=> (~humble(X0) | happy(X0))) [input p6]
14. ! [X0] : (~wise(X0) <=> ~happy(X0)) [input p13]
22. patient(fred) [input hypothesis]
26. ! [X0] : (wise(X0) | (~kind(X0) | tall(X0))) [ennf transformation 2]
27. ! [X0] : (wise(X0) | ~kind(X0) | tall(X0)) [flattening 26]
28. ! [X0] : ((~creative(X0) & creative(X0)) | kind(X0)) [ennf transformation 5]
29. ! [X0] : ((~generous(X0) & happy(X0)) | (~tall(X0) & ~creative(X0))) [ennf transformation 6]
42. ! [X0] : (((~patient(X0) | ~wise(X0)) | (humble(X0) & ~happy(X0))) & ((~humble(X0) | happy(X0)) | (patient(X0) & wise(X0)))) [nnf transformation 7]
43. ! [X0] : ((~patient(X0) | ~wise(X0) | (humble(X0) & ~happy(X0))) & (~humble(X0) | happy(X0) | (patient(X0) & wise(X0)))) [flattening 42]
50. ! [X0] : ((~wise(X0) | happy(X0)) & (~happy(X0) | wise(X0))) [nnf transformation 14]
67. ~kind(X0) | wise(X0) | tall(X0) [cnf transformation 27]
74. creative(X0) | kind(X0) [cnf transformation 28]
75. ~creative(X0) | kind(X0) [cnf transformation 28]
77. ~tall(X0) | happy(X0) [cnf transformation 29]
82. ~patient(X0) | ~wise(X0) | ~happy(X0) [cnf transformation 43]
100. ~happy(X0) | wise(X0) [cnf transformation 50]
101. ~wise(X0) | happy(X0) [cnf transformation 50]
116. patient(fred) [cnf transformation 22]
160. kind(X0) [subsumption resolution 74,75]
229. wise(X0) | tall(X0) [resolution 67,160]
230. tall(X0) | happy(X0) [resolution 229,101]
231. happy(X0) [subsumption resolution 230,77]
233. wise(X0) [resolution 231,100]
239. ~wise(fred) | ~happy(fred) [resolution 82,116]
243. ~happy(fred) [subsumption resolution 239,233]
244. $false [subsumption resolution 243,231]
% SZS output end Proof for 6355826508863027910472194
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
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