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
listlengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
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|---|---|---|---|---|---|---|---|
Everyone who is generous is either happy or tall. Everyone who is brave or old is either not curious or creative and vice versa. Everyone who is not funny or not wise is both not rich and not wise and vice versa. If someone is either not rich or not old then mary is both funny and not creative and vice versa. If john is both not kind and wise then someone is either happy or not humble. Everyone who is not generous is both generous and patient and vice versa. If john is not calm or not funny then mary is patient and vice versa. If susan is both kind and not rich then someone is either wise or calm and vice versa. If someone is not humble then susan is not patient and vice versa. Everyone who is not curious is funny and vice versa. Everyone who is not generous or wise is not wise or not patient and vice versa. If someone is not creative then someone is both quiet and patient. Everyone who is both happy and calm is either humble or calm. If someone is either not funny or quiet then someone is creative or not wise. Everyone who is creative is not tall or not rich. Someone is both not happy and not kind. Fred is either not creative or not strong. Alice is either creative or not kind. Fred is either strong or not old. | Fred is brave. | contradiction | (![X]:(generous(X)=>(happy(X)<~>tall(X))))&
(![X]:((brave(X)|old(X))<=>(~curious(X)<~>creative(X))))&
(![X]:((~funny(X)|~wise(X))<=>(~rich(X)&~wise(X))))&
((?[X]:((~rich(X)<~>~old(X))))<=>((funny(mary)&~creative(mary))))&
(((~kind(john)&wise(john)))=>(?[X]:((happy(X)<~>~humble(X)))))&
(![X]:(~generous(X)<=>(generous(X)&patient(X))))&
(((~calm(john)|~funny(john)))<=>(patient(mary)))&
(((kind(susan)&~rich(susan)))<=>(?[X]:((wise(X)<~>calm(X)))))&
((?[X]:(~humble(X)))<=>(~patient(susan)))&
(![X]:(~curious(X)<=>funny(X)))&
(![X]:((~generous(X)|wise(X))<=>(~wise(X)|~patient(X))))&
((?[X]:(~creative(X)))=>(?[X]:((quiet(X)&patient(X)))))&
(![X]:((happy(X)&calm(X))=>(humble(X)<~>calm(X))))&
((?[X]:((~funny(X)<~>quiet(X))))=>(?[X]:((creative(X)|~wise(X)))))&
(![X]:(creative(X)=>(~tall(X)|~rich(X))))&
(?[X]:((~happy(X)&~kind(X))))&
((~creative(fred)<~>~strong(fred)))&
((creative(alice)<~>~kind(alice)))&
((strong(fred)<~>~old(fred))) | brave(fred) | [
"p1",
"p2",
"p5",
"p9",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 6056836937352616936292756
% SZS output start Proof for 6056836937352616936292756
2. ! [X0] : ((old(X0) | brave(X0)) <=> (~curious(X0) <~> creative(X0))) [input p1]
3. ! [X0] : ((~wise(X0) | ~funny(X0)) <=> (~wise(X0) & ~rich(X0))) [input p2]
6. ! [X0] : (~generous(X0) <=> (patient(X0) & generous(X0))) [input p5]
10. ! [X0] : (~curious(X0) <=> funny(X0)) [input p9]
11. ! [X0] : ((wise(X0) | ~generous(X0)) <=> (~patient(X0) | ~wise(X0))) [input p10]
12. ? [X0] : ~creative(X0) => ? [X0] : (patient(X0) & quiet(X0)) [input p11]
20. brave(fred) [input hypothesis]
21. ? [X0] : ~creative(X0) => ? [X1] : (patient(X1) & quiet(X1)) [rectify 12]
26. ? [X1] : (patient(X1) & quiet(X1)) | ! [X0] : creative(X0) [ennf transformation 21]
33. ! [X0] : (((old(X0) | brave(X0)) | ((~curious(X0) | ~creative(X0)) & (creative(X0) | curious(X0)))) & (((~creative(X0) | curious(X0)) & (creative(X0) | ~curious(X0))) | (~old(X0) & ~brave(X0)))) [nnf transformation 2]
34. ! [X0] : ((old(X0) | brave(X0) | ((~curious(X0) | ~creative(X0)) & (creative(X0) | curious(X0)))) & (((~creative(X0) | curious(X0)) & (creative(X0) | ~curious(X0))) | (~old(X0) & ~brave(X0)))) [flattening 33]
35. ! [X0] : (((~wise(X0) | ~funny(X0)) | (wise(X0) | rich(X0))) & ((~wise(X0) & ~rich(X0)) | (wise(X0) & funny(X0)))) [nnf transformation 3]
36. ! [X0] : ((~wise(X0) | ~funny(X0) | wise(X0) | rich(X0)) & ((~wise(X0) & ~rich(X0)) | (wise(X0) & funny(X0)))) [flattening 35]
45. ! [X0] : ((~generous(X0) | (~patient(X0) | ~generous(X0))) & ((patient(X0) & generous(X0)) | generous(X0))) [nnf transformation 6]
46. ! [X0] : ((~generous(X0) | ~patient(X0) | ~generous(X0)) & ((patient(X0) & generous(X0)) | generous(X0))) [flattening 45]
58. ! [X0] : ((~curious(X0) | ~funny(X0)) & (funny(X0) | curious(X0))) [nnf transformation 10]
59. ! [X0] : (((wise(X0) | ~generous(X0)) | (patient(X0) & wise(X0))) & ((~patient(X0) | ~wise(X0)) | (~wise(X0) & generous(X0)))) [nnf transformation 11]
60. ! [X0] : ((wise(X0) | ~generous(X0) | (patient(X0) & wise(X0))) & (~patient(X0) | ~wise(X0) | (~wise(X0) & generous(X0)))) [flattening 59]
61. ? [X0] : (patient(X0) & quiet(X0)) | ! [X1] : creative(X1) [rectify 26]
62. ? [X0] : (patient(X0) & quiet(X0)) => (patient(sK4) & quiet(sK4)) [choice axiom]
63. (patient(sK4) & quiet(sK4)) | ! [X1] : creative(X1) [skolemisation 61,62]
78. ~creative(X0) | curious(X0) | ~brave(X0) [cnf transformation 34]
84. ~wise(X0) | funny(X0) [cnf transformation 36]
95. generous(X0) | generous(X0) [cnf transformation 46]
110. ~funny(X0) | ~curious(X0) [cnf transformation 58]
112. ~patient(X0) | ~wise(X0) | ~wise(X0) [cnf transformation 60]
113. wise(X0) | ~generous(X0) | wise(X0) [cnf transformation 60]
116. patient(sK4) | creative(X1) [cnf transformation 63]
130. brave(fred) [cnf transformation 20]
132. ~patient(X0) | ~wise(X0) [duplicate literal removal 112]
133. wise(X0) | ~generous(X0) [duplicate literal removal 113]
134. generous(X0) [duplicate literal removal 95]
239. wise(X0) [subsumption resolution 133,134]
240. ~patient(X0) [subsumption resolution 132,239]
241. creative(X1) [subsumption resolution 116,240]
255. funny(X0) [resolution 84,239]
261. ~curious(X1) [resolution 110,255]
267. curious(X0) | ~brave(X0) [resolution 78,241]
268. ~brave(X0) [subsumption resolution 267,261]
271. $false [resolution 268,130]
% SZS output end Proof for 6056836937352616936292756
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise is either not brave or not happy.
Everyone who is not patient or humble is not humble.
If susan is both creative and not calm then someone is funny and vice versa.
Everyone who is rich is brave or not patient.
Everyone who is not humble or wise is both not curious and patient.
Everyone who is calm is either patient or wise and vice versa.
Everyone who is either humble or brave is both not funny and not calm.
Everyone who is not tall is both tall and not brave.
Everyone who is either kind or not generous is both not humble and quiet and vice versa.
If john is happy or not humble then someone is both creative and not rich.
Everyone who is not quiet or not kind is either kind or brave.
If fred is not patient then susan is not rich or not generous.
Everyone who is both patient and not patient is either kind or happy and vice versa.
Everyone who is tall is not happy or not kind.
Everyone who is creative is old.
Everyone who is not tall or kind is either not old or generous and vice versa.
Fred is both old and creative.
Someone is either not calm or not quiet.
Paul is both strong and not humble.
Lucy is either not patient or old. | Lucy is old. | entailment | (![X]:(wise(X)=>(~brave(X)<~>~happy(X))))&
(![X]:((~patient(X)|humble(X))=>~humble(X)))&
(((creative(susan)&~calm(susan)))<=>(?[X]:(funny(X))))&
(![X]:(rich(X)=>(brave(X)|~patient(X))))&
(![X]:((~humble(X)|wise(X))=>(~curious(X)&patient(X))))&
(![X]:(calm(X)<=>(patient(X)<~>wise(X))))&
(![X]:((humble(X)<~>brave(X))=>(~funny(X)&~calm(X))))&
(![X]:(~tall(X)=>(tall(X)&~brave(X))))&
(![X]:((kind(X)<~>~generous(X))<=>(~humble(X)&quiet(X))))&
(((happy(john)|~humble(john)))=>(?[X]:((creative(X)&~rich(X)))))&
(![X]:((~quiet(X)|~kind(X))=>(kind(X)<~>brave(X))))&
((~patient(fred))=>((~rich(susan)|~generous(susan))))&
(![X]:((patient(X)&~patient(X))<=>(kind(X)<~>happy(X))))&
(![X]:(tall(X)=>(~happy(X)|~kind(X))))&
(![X]:(creative(X)=>old(X)))&
(![X]:((~tall(X)|kind(X))<=>(~old(X)<~>generous(X))))&
((old(fred)&creative(fred)))&
(?[X]:((~calm(X)<~>~quiet(X))))&
((strong(paul)&~humble(paul)))&
((~patient(lucy)<~>old(lucy))) | old(lucy) | [
"p1",
"p4",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 9115035276234621620411638
% SZS output start Proof for 9115035276234621620411638
2. ! [X0] : ((humble(X0) | ~patient(X0)) => ~humble(X0)) [input p1]
5. ! [X0] : ((wise(X0) | ~humble(X0)) => (patient(X0) & ~curious(X0))) [input p4]
20. ~patient(lucy) <~> old(lucy) [input p19]
21. ~old(lucy) [input hypothesis]
23. ! [X0] : ((wise(X0) | ~humble(X0)) => patient(X0)) [pure predicate removal 5]
28. ! [X0] : (~humble(X0) | (~humble(X0) & patient(X0))) [ennf transformation 2]
29. ! [X0] : (patient(X0) | (~wise(X0) & humble(X0))) [ennf transformation 23]
57. (~old(lucy) | patient(lucy)) & (old(lucy) | ~patient(lucy)) [nnf transformation 20]
61. ~humble(X0) | ~humble(X0) [cnf transformation 28]
65. patient(X0) | humble(X0) [cnf transformation 29]
108. old(lucy) | ~patient(lucy) [cnf transformation 57]
110. ~old(lucy) [cnf transformation 21]
113. ~humble(X0) [duplicate literal removal 61]
132. patient(X0) [subsumption resolution 65,113]
158. old(lucy) [subsumption resolution 108,132]
159. $false [subsumption resolution 110,158]
% SZS output end Proof for 9115035276234621620411638
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 4989
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is kind or not rich then someone is either tall or quiet and vice versa. If someone is both not humble and curious then someone is both strong and not humble. Everyone who is either not generous or old is patient. Everyone who is both not kind and not calm is strong. Everyone who is either creative or brave is not funny or brave and vice versa. If someone is both humble and curious then someone is brave or creative and vice versa. Everyone who is either not curious or calm is either not generous or not kind. Everyone who is both brave and not patient is old or patient. Everyone who is not happy or patient is not wise or not brave and vice versa. If someone is quiet or funny then someone is both wise and tall and vice versa. Everyone who is either happy or not quiet is both not wise and curious. Everyone who is both not funny and not old is either brave or curious. Everyone who is wise is kind and vice versa. Everyone who is not strong is funny or not calm and vice versa. If someone is either not happy or not creative then someone is both old and happy and vice versa. If someone is not curious or calm then someone is humble and vice versa. Susan is not patient or not happy. Someone is both not kind and not funny. Mary is not generous or not funny. Lucy is both not quiet and not funny. Someone is not strong or not patient. Someone is not patient. Someone is both rich and not wise. | Mary is creative. | neutral | ((?[X]:((kind(X)|~rich(X))))<=>(?[X]:((tall(X)<~>quiet(X)))))&
((?[X]:((~humble(X)&curious(X))))=>(?[X]:((strong(X)&~humble(X)))))&
(![X]:((~generous(X)<~>old(X))=>patient(X)))&
(![X]:((~kind(X)&~calm(X))=>strong(X)))&
(![X]:((creative(X)<~>brave(X))<=>(~funny(X)|brave(X))))&
((?[X]:((humble(X)&curious(X))))<=>(?[X]:((brave(X)|creative(X)))))&
(![X]:((~curious(X)<~>calm(X))=>(~generous(X)<~>~kind(X))))&
(![X]:((brave(X)&~patient(X))=>(old(X)|patient(X))))&
(![X]:((~happy(X)|patient(X))<=>(~wise(X)|~brave(X))))&
((?[X]:((quiet(X)|funny(X))))<=>(?[X]:((wise(X)&tall(X)))))&
(![X]:((happy(X)<~>~quiet(X))=>(~wise(X)&curious(X))))&
(![X]:((~funny(X)&~old(X))=>(brave(X)<~>curious(X))))&
(![X]:(wise(X)<=>kind(X)))&
(![X]:(~strong(X)<=>(funny(X)|~calm(X))))&
((?[X]:((~happy(X)<~>~creative(X))))<=>(?[X]:((old(X)&happy(X)))))&
((?[X]:((~curious(X)|calm(X))))<=>(?[X]:(humble(X))))&
((~patient(susan)|~happy(susan)))&
(?[X]:((~kind(X)&~funny(X))))&
((~generous(mary)|~funny(mary)))&
((~quiet(lucy)&~funny(lucy)))&
(?[X]:((~strong(X)|~patient(X))))&
(?[X]:(~patient(X)))&
(?[X]:((rich(X)&~wise(X)))) | creative(mary) | [] | null | 0 |
Everyone who is tall is either strong or old and vice versa. Everyone who is both rich and old is either strong or humble and vice versa. Everyone who is strong or not creative is either not calm or generous and vice versa. Everyone who is both not generous and old is either not wise or quiet and vice versa. Everyone who is either funny or generous is either wise or not strong and vice versa. If someone is both not old and old then lucy is both not generous and not rich and vice versa. Everyone who is curious or not kind is not funny and vice versa. If someone is not happy then someone is not creative or not old. If paul is both creative and wise then john is calm and vice versa. If john is either not happy or not brave then someone is both strong and quiet and vice versa. If someone is either not wise or creative then mary is not quiet or kind. Everyone who is strong is both quiet and not curious. Everyone who is not patient is either not patient or wise. Everyone who is wise or not wise is both old and not funny. If john is not patient then someone is not kind or not happy and vice versa. If john is either not wise or not happy then someone is not rich or calm and vice versa. Mary is both patient and not happy. Someone is wise. Alice is not creative. Someone is either not curious or not tall. Someone is not strong. Alice is patient. Mary is not creative. | Mary is not tall. | contradiction | (![X]:(tall(X)<=>(strong(X)<~>old(X))))&
(![X]:((rich(X)&old(X))<=>(strong(X)<~>humble(X))))&
(![X]:((strong(X)|~creative(X))<=>(~calm(X)<~>generous(X))))&
(![X]:((~generous(X)&old(X))<=>(~wise(X)<~>quiet(X))))&
(![X]:((funny(X)<~>generous(X))<=>(wise(X)<~>~strong(X))))&
((?[X]:((~old(X)&old(X))))<=>((~generous(lucy)&~rich(lucy))))&
(![X]:((curious(X)|~kind(X))<=>~funny(X)))&
((?[X]:(~happy(X)))=>(?[X]:((~creative(X)|~old(X)))))&
(((creative(paul)&wise(paul)))<=>(calm(john)))&
(((~happy(john)<~>~brave(john)))<=>(?[X]:((strong(X)&quiet(X)))))&
((?[X]:((~wise(X)<~>creative(X))))=>((~quiet(mary)|kind(mary))))&
(![X]:(strong(X)=>(quiet(X)&~curious(X))))&
(![X]:(~patient(X)=>(~patient(X)<~>wise(X))))&
(![X]:((wise(X)|~wise(X))=>(old(X)&~funny(X))))&
((~patient(john))<=>(?[X]:((~kind(X)|~happy(X)))))&
(((~wise(john)<~>~happy(john)))<=>(?[X]:((~rich(X)|calm(X)))))&
((patient(mary)&~happy(mary)))&
(?[X]:(wise(X)))&
(~creative(alice))&
(?[X]:((~curious(X)<~>~tall(X))))&
(?[X]:(~strong(X)))&
(patient(alice))&
(~creative(mary)) | ~tall(mary) | [
"p0",
"p3",
"p4",
"p9",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 783795234037729898226996
% SZS output start Proof for 783795234037729898226996
1. ! [X0] : (tall(X0) <=> (strong(X0) <~> old(X0))) [input p0]
4. ! [X0] : ((old(X0) & ~generous(X0)) <=> (~wise(X0) <~> quiet(X0))) [input p3]
5. ! [X0] : ((funny(X0) <~> generous(X0)) <=> (wise(X0) <~> ~strong(X0))) [input p4]
10. (~happy(john) <~> ~brave(john)) <=> ? [X0] : (quiet(X0) & strong(X0)) [input p9]
12. ! [X0] : (strong(X0) => (~curious(X0) & quiet(X0))) [input p11]
14. ! [X0] : ((~wise(X0) | wise(X0)) => (~funny(X0) & old(X0))) [input p13]
24. ~tall(mary) [input hypothesis]
29. ! [X0] : ((~curious(X0) & quiet(X0)) | ~strong(X0)) [ennf transformation 12]
31. ! [X0] : ((~funny(X0) & old(X0)) | (wise(X0) & ~wise(X0))) [ennf transformation 14]
32. ! [X0] : ((tall(X0) | ((strong(X0) | ~old(X0)) & (old(X0) | ~strong(X0)))) & (((~old(X0) | ~strong(X0)) & (old(X0) | strong(X0))) | ~tall(X0))) [nnf transformation 1]
37. ! [X0] : (((old(X0) & ~generous(X0)) | ((~wise(X0) | ~quiet(X0)) & (quiet(X0) | wise(X0)))) & (((~quiet(X0) | wise(X0)) & (quiet(X0) | ~wise(X0))) | (~old(X0) | generous(X0)))) [nnf transformation 4]
38. ! [X0] : (((old(X0) & ~generous(X0)) | ((~wise(X0) | ~quiet(X0)) & (quiet(X0) | wise(X0)))) & (((~quiet(X0) | wise(X0)) & (quiet(X0) | ~wise(X0))) | ~old(X0) | generous(X0))) [flattening 37]
39. ! [X0] : ((((~generous(X0) | ~funny(X0)) & (generous(X0) | funny(X0))) | ((wise(X0) | strong(X0)) & (~strong(X0) | ~wise(X0)))) & (((strong(X0) | ~wise(X0)) & (~strong(X0) | wise(X0))) | ((funny(X0) | ~generous(X0)) & (generous(X0) | ~funny(X0))))) [nnf transformation 5]
52. (((brave(john) | happy(john)) & (~brave(john) | ~happy(john))) | ! [X0] : (~quiet(X0) | ~strong(X0))) & (? [X0] : (quiet(X0) & strong(X0)) | ((~happy(john) | brave(john)) & (~brave(john) | happy(john)))) [nnf transformation 10]
53. (((brave(john) | happy(john)) & (~brave(john) | ~happy(john))) | ! [X0] : (~quiet(X0) | ~strong(X0))) & (? [X1] : (quiet(X1) & strong(X1)) | ((~happy(john) | brave(john)) & (~brave(john) | happy(john)))) [rectify 52]
54. ? [X1] : (quiet(X1) & strong(X1)) => (quiet(sK2) & strong(sK2)) [choice axiom]
55. (((brave(john) | happy(john)) & (~brave(john) | ~happy(john))) | ! [X0] : (~quiet(X0) | ~strong(X0))) & ((quiet(sK2) & strong(sK2)) | ((~happy(john) | brave(john)) & (~brave(john) | happy(john)))) [skolemisation 53,54]
76. ~old(X0) | strong(X0) | tall(X0) [cnf transformation 32]
90. ~quiet(X0) | wise(X0) | ~old(X0) | generous(X0) [cnf transformation 38]
92. ~quiet(X0) | ~wise(X0) | ~generous(X0) [cnf transformation 38]
96. ~generous(X0) | wise(X0) | funny(X0) | ~strong(X0) [cnf transformation 39]
99. ~wise(X0) | funny(X0) | ~strong(X0) | generous(X0) [cnf transformation 39]
114. strong(sK2) | ~brave(john) | happy(john) [cnf transformation 55]
115. strong(sK2) | ~happy(john) | brave(john) [cnf transformation 55]
116. quiet(sK2) | ~brave(john) | happy(john) [cnf transformation 55]
117. quiet(sK2) | ~happy(john) | brave(john) [cnf transformation 55]
118. ~brave(john) | ~happy(john) | ~quiet(X0) | ~strong(X0) [cnf transformation 55]
119. brave(john) | happy(john) | ~quiet(X0) | ~strong(X0) [cnf transformation 55]
122. ~strong(X0) | quiet(X0) [cnf transformation 29]
126. old(X0) | ~wise(X0) [cnf transformation 31]
127. wise(X0) | old(X0) [cnf transformation 31]
128. ~funny(X0) | ~wise(X0) [cnf transformation 31]
129. ~funny(X0) | wise(X0) [cnf transformation 31]
148. ~tall(mary) [cnf transformation 24]
192. 10 <=> ! [X0] : (~quiet(X0) | ~strong(X0)) [avatar definition]
193. ~quiet(X0) | ~strong(X0) <- (10) [avatar component clause 192]
195. 11 <=> happy(john) [avatar definition]
199. 12 <=> brave(john) [avatar definition]
202. 10 | 11 | 12 [avatar split clause 119,199,195,192]
203. 10 | ~11 | ~12 [avatar split clause 118,199,195,192]
205. 13 <=> quiet(sK2) [avatar definition]
207. quiet(sK2) <- (13) [avatar component clause 205]
208. 12 | ~11 | 13 [avatar split clause 117,205,195,199]
209. 11 | ~12 | 13 [avatar split clause 116,205,199,195]
211. 14 <=> strong(sK2) [avatar definition]
213. strong(sK2) <- (14) [avatar component clause 211]
214. 12 | ~11 | 14 [avatar split clause 115,211,195,199]
215. 11 | ~12 | 14 [avatar split clause 114,211,199,195]
232. ~funny(X0) [subsumption resolution 128,129]
233. old(X0) [subsumption resolution 126,127]
286. ~strong(X0) <- (10) [subsumption resolution 193,122]
296. strong(X0) | tall(X0) [resolution 76,233]
297. tall(X0) <- (10) [subsumption resolution 296,286]
298. $false <- (10) [resolution 297,148]
302. ~10 [avatar contradiction clause 298]
347. ~wise(sK2) | ~generous(sK2) <- (13) [resolution 92,207]
351. 32 <=> generous(sK2) [avatar definition]
352. generous(sK2) <- (32) [avatar component clause 351]
353. ~generous(sK2) <- (~32) [avatar component clause 351]
355. 33 <=> wise(sK2) [avatar definition]
356. wise(sK2) <- (33) [avatar component clause 355]
357. ~wise(sK2) <- (~33) [avatar component clause 355]
358. ~32 | ~33 | ~13 [avatar split clause 347,205,355,351]
449. wise(sK2) | ~old(sK2) | generous(sK2) <- (13) [resolution 90,207]
454. wise(sK2) | generous(sK2) <- (13) [subsumption resolution 449,233]
458. 32 | 33 | ~13 [avatar split clause 454,205,355,351]
501. funny(sK2) | ~strong(sK2) | generous(sK2) <- (33) [resolution 99,356]
506. ~strong(sK2) | generous(sK2) <- (33) [subsumption resolution 501,232]
507. generous(sK2) <- (14, 33) [subsumption resolution 506,213]
508. $false <- (14, ~32, 33) [subsumption resolution 507,353]
509. ~14 | 32 | ~33 [avatar contradiction clause 508]
569. wise(sK2) | funny(sK2) | ~strong(sK2) <- (32) [resolution 352,96]
574. funny(sK2) | ~strong(sK2) <- (32, ~33) [subsumption resolution 569,357]
575. ~strong(sK2) <- (32, ~33) [subsumption resolution 574,232]
576. $false <- (14, 32, ~33) [subsumption resolution 575,213]
577. ~14 | ~32 | 33 [avatar contradiction clause 576]
589. $false [avatar sat refutation 202,203,208,209,214,215,302,358,458,509,577]
% SZS output end Proof for 783795234037729898226996
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm or not tall is creative or not curious and vice versa.
If someone is both not quiet and not funny then someone is not calm.
Everyone who is tall is either not curious or rich.
If someone is brave then someone is both tall and not funny and vice versa.
Everyone who is kind is both happy and kind.
Everyone who is either not old or tall is kind or not humble.
Everyone who is old is not patient or patient and vice versa.
If susan is patient then susan is both not happy and quiet.
If alice is not quiet or strong then alice is kind.
If susan is either curious or not old then someone is not patient or not quiet.
If someone is both brave and curious then alice is both not humble and not wise.
Everyone who is strong or not brave is tall or not tall.
If fred is not curious then someone is both generous and happy and vice versa.
Everyone who is not strong is both rich and kind and vice versa.
If paul is patient then fred is not brave and vice versa.
If someone is not wise or not curious then paul is not strong and vice versa.
Someone is happy.
John is either happy or not kind.
Someone is funny or quiet.
Susan is both not wise and kind.
John is either not strong or not rich.
Someone is generous.
Fred is not strong.
Someone is strong. | Fred is not kind. | contradiction | (![X]:((calm(X)|~tall(X))<=>(creative(X)|~curious(X))))&
((?[X]:((~quiet(X)&~funny(X))))=>(?[X]:(~calm(X))))&
(![X]:(tall(X)=>(~curious(X)<~>rich(X))))&
((?[X]:(brave(X)))<=>(?[X]:((tall(X)&~funny(X)))))&
(![X]:(kind(X)=>(happy(X)&kind(X))))&
(![X]:((~old(X)<~>tall(X))=>(kind(X)|~humble(X))))&
(![X]:(old(X)<=>(~patient(X)|patient(X))))&
((patient(susan))=>((~happy(susan)&quiet(susan))))&
(((~quiet(alice)|strong(alice)))=>(kind(alice)))&
(((curious(susan)<~>~old(susan)))=>(?[X]:((~patient(X)|~quiet(X)))))&
((?[X]:((brave(X)&curious(X))))=>((~humble(alice)&~wise(alice))))&
(![X]:((strong(X)|~brave(X))=>(tall(X)|~tall(X))))&
((~curious(fred))<=>(?[X]:((generous(X)&happy(X)))))&
(![X]:(~strong(X)<=>(rich(X)&kind(X))))&
((patient(paul))<=>(~brave(fred)))&
((?[X]:((~wise(X)|~curious(X))))<=>(~strong(paul)))&
(?[X]:(happy(X)))&
((happy(john)<~>~kind(john)))&
(?[X]:((funny(X)|quiet(X))))&
((~wise(susan)&kind(susan)))&
((~strong(john)<~>~rich(john)))&
(?[X]:(generous(X)))&
(~strong(fred))&
(?[X]:(strong(X))) | ~kind(fred) | [
"p13",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 4617738195550932043655712
% SZS output start Proof for 4617738195550932043655712
14. ! [X0] : (~strong(X0) <=> (kind(X0) & rich(X0))) [input p13]
23. ~strong(fred) [input p22]
25. ~kind(fred) [input hypothesis]
59. ! [X0] : ((~strong(X0) | (~kind(X0) | ~rich(X0))) & ((kind(X0) & rich(X0)) | strong(X0))) [nnf transformation 14]
60. ! [X0] : ((~strong(X0) | ~kind(X0) | ~rich(X0)) & ((kind(X0) & rich(X0)) | strong(X0))) [flattening 59]
104. strong(X0) | kind(X0) [cnf transformation 60]
120. ~strong(fred) [cnf transformation 23]
122. ~kind(fred) [cnf transformation 25]
288. kind(fred) [resolution 104,120]
290. $false [subsumption resolution 288,122]
% SZS output end Proof for 4617738195550932043655712
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 fred is both not calm and creative then alice is not patient and vice versa. If someone is both not strong and quiet then lucy is old and vice versa. Everyone who is both not wise and quiet is curious or not kind. If someone is both not strong and not happy then someone is not kind or not quiet. Everyone who is not tall is either funny or happy. Everyone who is humble or not strong is both not funny and patient. If someone is not curious then someone is funny and vice versa. Everyone who is both happy and not brave is not patient or brave. If someone is both generous and brave then someone is happy. If john is either not happy or brave then lucy is both not curious and not generous. Everyone who is both not happy and generous is calm or not old. If someone is both not rich and curious then susan is funny or not quiet. Everyone who is not creative or not happy is generous or not generous and vice versa. Everyone who is rich or strong is not wise. If fred is both not brave and not quiet then someone is both generous and happy and vice versa. If john is old or brave then alice is patient and vice versa. Someone is not quiet. Someone is not creative or kind. Someone is old or curious. Someone is not rich or generous. Someone is rich. Fred is not calm or not patient. Alice is not creative. Fred is both not funny and creative. | John is quiet. | neutral | (((~calm(fred)&creative(fred)))<=>(~patient(alice)))&
((?[X]:((~strong(X)&quiet(X))))<=>(old(lucy)))&
(![X]:((~wise(X)&quiet(X))=>(curious(X)|~kind(X))))&
((?[X]:((~strong(X)&~happy(X))))=>(?[X]:((~kind(X)|~quiet(X)))))&
(![X]:(~tall(X)=>(funny(X)<~>happy(X))))&
(![X]:((humble(X)|~strong(X))=>(~funny(X)&patient(X))))&
((?[X]:(~curious(X)))<=>(?[X]:(funny(X))))&
(![X]:((happy(X)&~brave(X))=>(~patient(X)|brave(X))))&
((?[X]:((generous(X)&brave(X))))=>(?[X]:(happy(X))))&
(((~happy(john)<~>brave(john)))=>((~curious(lucy)&~generous(lucy))))&
(![X]:((~happy(X)&generous(X))=>(calm(X)|~old(X))))&
((?[X]:((~rich(X)&curious(X))))=>((funny(susan)|~quiet(susan))))&
(![X]:((~creative(X)|~happy(X))<=>(generous(X)|~generous(X))))&
(![X]:((rich(X)|strong(X))=>~wise(X)))&
(((~brave(fred)&~quiet(fred)))<=>(?[X]:((generous(X)&happy(X)))))&
(((old(john)|brave(john)))<=>(patient(alice)))&
(?[X]:(~quiet(X)))&
(?[X]:((~creative(X)|kind(X))))&
(?[X]:((old(X)|curious(X))))&
(?[X]:((~rich(X)|generous(X))))&
(?[X]:(rich(X)))&
((~calm(fred)|~patient(fred)))&
(~creative(alice))&
((~funny(fred)&creative(fred))) | quiet(john) | [] | null | 0 |
If fred is either creative or wise then someone is kind.
Everyone who is strong is not creative or creative and vice versa.
Everyone who is not kind is both quiet and strong.
If susan is funny then alice is humble or curious.
If mary is old or humble then susan is both not humble and not creative and vice versa.
If john is both happy and patient then mary is either not patient or not tall.
If someone is either not curious or funny then alice is both not patient and creative.
If someone is not funny or generous then someone is both happy and not generous.
If someone is not generous or not brave then someone is not curious.
If john is either humble or strong then john is either curious or tall and vice versa.
If someone is not creative or not calm then someone is either wise or not quiet.
Everyone who is not quiet or rich is both happy and kind.
If fred is both not tall and tall then someone is both not happy and generous.
Everyone who is not brave is both not patient and not happy.
Everyone who is both not strong and quiet is not calm and vice versa.
If someone is brave then someone is both not tall and tall.
Someone is not generous.
Fred is not curious.
John is curious.
Someone is not generous or curious.
Mary is both tall and not humble.
Someone is either creative or strong. | Mary is not patient. | entailment | (((creative(fred)<~>wise(fred)))=>(?[X]:(kind(X))))&
(![X]:(strong(X)<=>(~creative(X)|creative(X))))&
(![X]:(~kind(X)=>(quiet(X)&strong(X))))&
((funny(susan))=>((humble(alice)|curious(alice))))&
(((old(mary)|humble(mary)))<=>((~humble(susan)&~creative(susan))))&
(((happy(john)&patient(john)))=>((~patient(mary)<~>~tall(mary))))&
((?[X]:((~curious(X)<~>funny(X))))=>((~patient(alice)&creative(alice))))&
((?[X]:((~funny(X)|generous(X))))=>(?[X]:((happy(X)&~generous(X)))))&
((?[X]:((~generous(X)|~brave(X))))=>(?[X]:(~curious(X))))&
(((humble(john)<~>strong(john)))<=>((curious(john)<~>tall(john))))&
((?[X]:((~creative(X)|~calm(X))))=>(?[X]:((wise(X)<~>~quiet(X)))))&
(![X]:((~quiet(X)|rich(X))=>(happy(X)&kind(X))))&
(((~tall(fred)&tall(fred)))=>(?[X]:((~happy(X)&generous(X)))))&
(![X]:(~brave(X)=>(~patient(X)&~happy(X))))&
(![X]:((~strong(X)&quiet(X))<=>~calm(X)))&
((?[X]:(brave(X)))=>(?[X]:((~tall(X)&tall(X)))))&
(?[X]:(~generous(X)))&
(~curious(fred))&
(curious(john))&
(?[X]:((~generous(X)|curious(X))))&
((tall(mary)&~humble(mary)))&
(?[X]:((creative(X)<~>strong(X)))) | ~patient(mary) | [
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 5835532576304947879436403
% SZS output start Proof for 5835532576304947879436403
14. ! [X0] : (~brave(X0) => (~happy(X0) & ~patient(X0))) [input p13]
16. ? [X0] : brave(X0) => ? [X0] : (tall(X0) & ~tall(X0)) [input p15]
23. patient(mary) [input hypothesis]
27. ? [X0] : brave(X0) => ? [X1] : (tall(X1) & ~tall(X1)) [rectify 16]
44. ! [X0] : ((~happy(X0) & ~patient(X0)) | brave(X0)) [ennf transformation 14]
47. ? [X1] : (tall(X1) & ~tall(X1)) | ! [X0] : ~brave(X0) [ennf transformation 27]
67. ? [X0] : (tall(X0) & ~tall(X0)) | ! [X1] : ~brave(X1) [rectify 47]
68. ? [X0] : (tall(X0) & ~tall(X0)) => (tall(sK4) & ~tall(sK4)) [choice axiom]
69. (tall(sK4) & ~tall(sK4)) | ! [X1] : ~brave(X1) [skolemisation 67,68]
113. ~patient(X0) | brave(X0) [cnf transformation 44]
116. ~tall(sK4) | ~brave(X1) [cnf transformation 69]
117. tall(sK4) | ~brave(X1) [cnf transformation 69]
126. patient(mary) [cnf transformation 23]
171. 10 <=> patient(mary) [avatar definition]
173. patient(mary) <- (10) [avatar component clause 171]
267. 30 <=> ! [X1] : ~brave(X1) [avatar definition]
268. ~brave(X1) <- (30) [avatar component clause 267]
270. 31 <=> tall(sK4) [avatar definition]
273. 30 | 31 [avatar split clause 117,270,267]
274. 30 | ~31 [avatar split clause 116,270,267]
288. 10 [avatar split clause 126,171]
293. brave(mary) <- (10) [resolution 113,173]
294. $false <- (10, 30) [subsumption resolution 293,268]
295. ~10 | ~30 [avatar contradiction clause 294]
296. $false [avatar sat refutation 273,274,288,295]
% SZS output end Proof for 5835532576304947879436403
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous or creative is either old or not curious.
If alice is both not brave and funny then someone is either not rich or brave and vice versa.
Everyone who is both old and not kind is quiet or wise.
Everyone who is humble or curious is both not calm and old and vice versa.
If fred is either happy or not patient then fred is either brave or not strong.
Everyone who is either old or not generous is either strong or old.
If mary is not strong or not quiet then john is not patient.
Everyone who is both not patient and patient is old or calm and vice versa.
If someone is generous then lucy is either happy or tall and vice versa.
Everyone who is either old or not happy is both quiet and not old.
Everyone who is either old or not old is both funny and not happy.
Everyone who is either curious or old is brave and vice versa.
Everyone who is either not quiet or not humble is not rich.
If john is both not quiet and brave then someone is either not wise or quiet and vice versa.
If someone is both not wise and not strong then fred is both not old and not kind.
Everyone who is quiet is both not curious and not patient.
Lucy is kind.
Fred is either wise or quiet.
Mary is not kind.
Paul is quiet or not humble.
Someone is both strong and not generous.
Susan is quiet or not patient.
Mary is patient or not brave. | Fred is not strong. | entailment | (![X]:((generous(X)|creative(X))=>(old(X)<~>~curious(X))))&
(((~brave(alice)&funny(alice)))<=>(?[X]:((~rich(X)<~>brave(X)))))&
(![X]:((old(X)&~kind(X))=>(quiet(X)|wise(X))))&
(![X]:((humble(X)|curious(X))<=>(~calm(X)&old(X))))&
(((happy(fred)<~>~patient(fred)))=>((brave(fred)<~>~strong(fred))))&
(![X]:((old(X)<~>~generous(X))=>(strong(X)<~>old(X))))&
(((~strong(mary)|~quiet(mary)))=>(~patient(john)))&
(![X]:((~patient(X)&patient(X))<=>(old(X)|calm(X))))&
((?[X]:(generous(X)))<=>((happy(lucy)<~>tall(lucy))))&
(![X]:((old(X)<~>~happy(X))=>(quiet(X)&~old(X))))&
(![X]:((old(X)<~>~old(X))=>(funny(X)&~happy(X))))&
(![X]:((curious(X)<~>old(X))<=>brave(X)))&
(![X]:((~quiet(X)<~>~humble(X))=>~rich(X)))&
(((~quiet(john)&brave(john)))<=>(?[X]:((~wise(X)<~>quiet(X)))))&
((?[X]:((~wise(X)&~strong(X))))=>((~old(fred)&~kind(fred))))&
(![X]:(quiet(X)=>(~curious(X)&~patient(X))))&
(kind(lucy))&
((wise(fred)<~>quiet(fred)))&
(~kind(mary))&
((quiet(paul)|~humble(paul)))&
(?[X]:((strong(X)&~generous(X))))&
((quiet(susan)|~patient(susan)))&
((patient(mary)|~brave(mary))) | ~strong(fred) | [
"p4",
"p7",
"p9",
"p10",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6784901556308390475171216
% SZS output start Proof for 6784901556308390475171216
5. (happy(fred) <~> ~patient(fred)) => (brave(fred) <~> ~strong(fred)) [input p4]
8. ! [X0] : ((patient(X0) & ~patient(X0)) <=> (calm(X0) | old(X0))) [input p7]
10. ! [X0] : ((old(X0) <~> ~happy(X0)) => (~old(X0) & quiet(X0))) [input p9]
11. ! [X0] : ((old(X0) <~> ~old(X0)) => (~happy(X0) & funny(X0))) [input p10]
12. ! [X0] : ((curious(X0) <~> old(X0)) <=> brave(X0)) [input p11]
16. ! [X0] : (quiet(X0) => (~patient(X0) & ~curious(X0))) [input p15]
24. strong(fred) [input hypothesis]
29. (brave(fred) <~> ~strong(fred)) | (happy(fred) <=> ~patient(fred)) [ennf transformation 5]
32. ! [X0] : ((~old(X0) & quiet(X0)) | (old(X0) <=> ~happy(X0))) [ennf transformation 10]
33. ! [X0] : ((~happy(X0) & funny(X0)) | (old(X0) <=> ~old(X0))) [ennf transformation 11]
36. ! [X0] : ((~patient(X0) & ~curious(X0)) | ~quiet(X0)) [ennf transformation 16]
45. ((strong(fred) | ~brave(fred)) & (~strong(fred) | brave(fred))) | ((happy(fred) | patient(fred)) & (~patient(fred) | ~happy(fred))) [nnf transformation 29]
47. ! [X0] : (((patient(X0) & ~patient(X0)) | (~calm(X0) & ~old(X0))) & ((calm(X0) | old(X0)) | (~patient(X0) | patient(X0)))) [nnf transformation 8]
48. ! [X0] : (((patient(X0) & ~patient(X0)) | (~calm(X0) & ~old(X0))) & (calm(X0) | old(X0) | ~patient(X0) | patient(X0))) [flattening 47]
53. ! [X0] : ((~old(X0) & quiet(X0)) | ((old(X0) | happy(X0)) & (~happy(X0) | ~old(X0)))) [nnf transformation 32]
54. ! [X0] : ((~happy(X0) & funny(X0)) | ((old(X0) | old(X0)) & (~old(X0) | ~old(X0)))) [nnf transformation 33]
55. ! [X0] : ((((~old(X0) | ~curious(X0)) & (old(X0) | curious(X0))) | ~brave(X0)) & (brave(X0) | ((curious(X0) | ~old(X0)) & (old(X0) | ~curious(X0))))) [nnf transformation 12]
80. ~strong(fred) | brave(fred) | happy(fred) | patient(fred) [cnf transformation 45]
90. ~patient(X0) | ~old(X0) [cnf transformation 48]
92. ~old(X0) | patient(X0) [cnf transformation 48]
99. quiet(X0) | old(X0) | happy(X0) [cnf transformation 53]
105. ~happy(X0) | old(X0) | old(X0) [cnf transformation 54]
108. old(X0) | curious(X0) | ~brave(X0) [cnf transformation 55]
120. ~quiet(X0) | ~curious(X0) [cnf transformation 36]
121. ~patient(X0) | ~quiet(X0) [cnf transformation 36]
131. strong(fred) [cnf transformation 24]
135. ~happy(X0) | old(X0) [duplicate literal removal 105]
168. 7 <=> patient(fred) [avatar definition]
170. patient(fred) <- (7) [avatar component clause 168]
172. 8 <=> happy(fred) [avatar definition]
174. happy(fred) <- (8) [avatar component clause 172]
176. 9 <=> brave(fred) [avatar definition]
177. brave(fred) <- (9) [avatar component clause 176]
180. 10 <=> strong(fred) [avatar definition]
185. 7 | 8 | 9 | ~10 [avatar split clause 80,180,176,172,168]
202. ~old(X0) [subsumption resolution 90,92]
222. happy(X0) | quiet(X0) [subsumption resolution 99,202]
223. ~happy(X0) [subsumption resolution 135,202]
225. ~brave(X0) | curious(X0) [subsumption resolution 108,202]
291. 10 [avatar split clause 131,180]
292. ~quiet(fred) <- (7) [resolution 121,170]
293. quiet(X0) [resolution 222,223]
295. ~curious(X0) [resolution 293,120]
302. $false <- (7) [subsumption resolution 292,293]
303. ~7 [avatar contradiction clause 302]
305. curious(fred) <- (9) [resolution 177,225]
306. $false <- (9) [subsumption resolution 305,295]
307. ~9 [avatar contradiction clause 306]
308. $false <- (8) [subsumption resolution 174,223]
309. ~8 [avatar contradiction clause 308]
310. $false [avatar sat refutation 185,291,303,307,309]
% SZS output end Proof for 6784901556308390475171216
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not funny or old then someone is not tall and vice versa. If fred is old then mary is either not happy or wise. If paul is tall or not quiet then lucy is either funny or not tall and vice versa. Everyone who is curious or calm is both tall and not quiet and vice versa. If susan is either wise or not happy then paul is not kind or kind and vice versa. If paul is brave then fred is either not generous or brave. If john is curious then someone is kind and vice versa. If lucy is calm or not strong then alice is either calm or humble and vice versa. If alice is not patient then someone is rich or humble and vice versa. Everyone who is both wise and not kind is either not rich or not generous. If someone is wise or creative then someone is not humble. Everyone who is either humble or creative is both creative and quiet and vice versa. If someone is not kind then someone is not patient or old. Everyone who is either happy or strong is humble or not calm and vice versa. Everyone who is not funny or tall is not patient. If john is either generous or rich then alice is both curious and not humble and vice versa. John is not wise. Someone is humble. Someone is either generous or not patient. Lucy is not wise or wise. Mary is either tall or humble. Mary is both rich and not old. Susan is brave. Susan is not rich. | Mary is not old. | entailment | ((?[X]:((~funny(X)|old(X))))<=>(?[X]:(~tall(X))))&
((old(fred))=>((~happy(mary)<~>wise(mary))))&
(((tall(paul)|~quiet(paul)))<=>((funny(lucy)<~>~tall(lucy))))&
(![X]:((curious(X)|calm(X))<=>(tall(X)&~quiet(X))))&
(((wise(susan)<~>~happy(susan)))<=>((~kind(paul)|kind(paul))))&
((brave(paul))=>((~generous(fred)<~>brave(fred))))&
((curious(john))<=>(?[X]:(kind(X))))&
(((calm(lucy)|~strong(lucy)))<=>((calm(alice)<~>humble(alice))))&
((~patient(alice))<=>(?[X]:((rich(X)|humble(X)))))&
(![X]:((wise(X)&~kind(X))=>(~rich(X)<~>~generous(X))))&
((?[X]:((wise(X)|creative(X))))=>(?[X]:(~humble(X))))&
(![X]:((humble(X)<~>creative(X))<=>(creative(X)&quiet(X))))&
((?[X]:(~kind(X)))=>(?[X]:((~patient(X)|old(X)))))&
(![X]:((happy(X)<~>strong(X))<=>(humble(X)|~calm(X))))&
(![X]:((~funny(X)|tall(X))=>~patient(X)))&
(((generous(john)<~>rich(john)))<=>((curious(alice)&~humble(alice))))&
(~wise(john))&
(?[X]:(humble(X)))&
(?[X]:((generous(X)<~>~patient(X))))&
((~wise(lucy)|wise(lucy)))&
((tall(mary)<~>humble(mary)))&
((rich(mary)&~old(mary)))&
(brave(susan))&
(~rich(susan)) | ~old(mary) | [
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 3902219765277270299760458
% SZS output start Proof for 3902219765277270299760458
22. ~old(mary) & rich(mary) [input p21]
25. old(mary) [input hypothesis]
146. ~old(mary) [cnf transformation 22]
149. old(mary) [cnf transformation 25]
360. $false [subsumption resolution 149,146]
% SZS output end Proof for 3902219765277270299760458
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not wise is not rich or humble.
Everyone who is not generous is both not tall and not quiet and vice versa.
Everyone who is not patient or not creative is not curious and vice versa.
Everyone who is humble or not brave is kind and vice versa.
If someone is strong then someone is both wise and not wise.
Everyone who is both not creative and funny is strong and vice versa.
If fred is calm then lucy is either not generous or generous.
Everyone who is both not strong and patient is both not patient and not quiet.
If someone is not tall or not funny then someone is not strong or brave and vice versa.
Everyone who is creative is either tall or humble and vice versa.
If someone is not happy then someone is quiet or not happy and vice versa.
Everyone who is either not happy or not funny is patient or not humble and vice versa.
If someone is creative then someone is not humble or creative.
If paul is not old then someone is either not calm or not happy.
Everyone who is both not kind and brave is both not quiet and old and vice versa.
If alice is either not generous or happy then lucy is both not generous and not humble.
Someone is either rich or curious.
Susan is both not strong and rich.
Alice is tall or not kind.
John is not rich.
Alice is both not funny and old.
Someone is not strong or wise. | Paul is patient. | contradiction | (![X]:(~wise(X)=>(~rich(X)|humble(X))))&
(![X]:(~generous(X)<=>(~tall(X)&~quiet(X))))&
(![X]:((~patient(X)|~creative(X))<=>~curious(X)))&
(![X]:((humble(X)|~brave(X))<=>kind(X)))&
((?[X]:(strong(X)))=>(?[X]:((wise(X)&~wise(X)))))&
(![X]:((~creative(X)&funny(X))<=>strong(X)))&
((calm(fred))=>((~generous(lucy)<~>generous(lucy))))&
(![X]:((~strong(X)&patient(X))=>(~patient(X)&~quiet(X))))&
((?[X]:((~tall(X)|~funny(X))))<=>(?[X]:((~strong(X)|brave(X)))))&
(![X]:(creative(X)<=>(tall(X)<~>humble(X))))&
((?[X]:(~happy(X)))<=>(?[X]:((quiet(X)|~happy(X)))))&
(![X]:((~happy(X)<~>~funny(X))<=>(patient(X)|~humble(X))))&
((?[X]:(creative(X)))=>(?[X]:((~humble(X)|creative(X)))))&
((~old(paul))=>(?[X]:((~calm(X)<~>~happy(X)))))&
(![X]:((~kind(X)&brave(X))<=>(~quiet(X)&old(X))))&
(((~generous(alice)<~>happy(alice)))=>((~generous(lucy)&~humble(lucy))))&
(?[X]:((rich(X)<~>curious(X))))&
((~strong(susan)&rich(susan)))&
((tall(alice)|~kind(alice)))&
(~rich(john))&
((~funny(alice)&old(alice)))&
(?[X]:((~strong(X)|wise(X)))) | patient(paul) | [
"p4",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 6392696044879882858992996
% SZS output start Proof for 6392696044879882858992996
5. ? [X0] : strong(X0) => ? [X0] : (~wise(X0) & wise(X0)) [input p4]
8. ! [X0] : ((patient(X0) & ~strong(X0)) => (~quiet(X0) & ~patient(X0))) [input p7]
23. patient(paul) [input hypothesis]
24. ? [X0] : strong(X0) => ? [X1] : (~wise(X1) & wise(X1)) [rectify 5]
30. ? [X1] : (~wise(X1) & wise(X1)) | ! [X0] : ~strong(X0) [ennf transformation 24]
32. ! [X0] : ((~quiet(X0) & ~patient(X0)) | (~patient(X0) | strong(X0))) [ennf transformation 8]
33. ! [X0] : ((~quiet(X0) & ~patient(X0)) | ~patient(X0) | strong(X0)) [flattening 32]
43. ? [X0] : (~wise(X0) & wise(X0)) | ! [X1] : ~strong(X1) [rectify 30]
44. ? [X0] : (~wise(X0) & wise(X0)) => (~wise(sK0) & wise(sK0)) [choice axiom]
45. (~wise(sK0) & wise(sK0)) | ! [X1] : ~strong(X1) [skolemisation 43,44]
86. wise(sK0) | ~strong(X1) [cnf transformation 45]
87. ~wise(sK0) | ~strong(X1) [cnf transformation 45]
93. ~patient(X0) | ~patient(X0) | strong(X0) [cnf transformation 33]
132. patient(paul) [cnf transformation 23]
133. ~patient(X0) | strong(X0) [duplicate literal removal 93]
135. 1 <=> ! [X1] : ~strong(X1) [avatar definition]
136. ~strong(X1) <- (1) [avatar component clause 135]
138. 2 <=> wise(sK0) [avatar definition]
141. 1 | ~2 [avatar split clause 87,138,135]
142. 1 | 2 [avatar split clause 86,138,135]
273. strong(paul) [resolution 133,132]
274. $false <- (1) [subsumption resolution 273,136]
275. ~1 [avatar contradiction clause 274]
276. $false [avatar sat refutation 141,142,275]
% SZS output end Proof for 6392696044879882858992996
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old is both funny and not kind and vice versa.
If someone is not curious then john is both quiet and not tall and vice versa.
If alice is both wise and not strong then fred is either wise or old.
If paul is both wise and patient then someone is patient.
If alice is both not calm and not patient then someone is humble.
Everyone who is not humble or rich is both not quiet and generous.
Everyone who is generous or not patient is not kind or creative.
Everyone who is both creative and generous is funny.
If someone is either not brave or brave then john is kind and vice versa.
If someone is not old then alice is quiet or patient and vice versa.
Everyone who is both not kind and wise is funny or curious.
If alice is not patient or not strong then alice is creative or curious and vice versa.
If someone is either not creative or humble then lucy is both not humble and kind.
Everyone who is quiet or not curious is both quiet and not curious and vice versa.
Everyone who is quiet is either creative or tall and vice versa.
If paul is brave or not rich then fred is not brave or old.
Someone is both humble and rich.
Someone is both creative and happy.
Someone is not old or humble.
Someone is both calm and old.
Susan is old.
Alice is curious.
Paul is patient or not curious. | John is not quiet. | neutral | (![X]:((rich(X)&old(X))<=>(funny(X)&~kind(X))))&
((?[X]:(~curious(X)))<=>((quiet(john)&~tall(john))))&
(((wise(alice)&~strong(alice)))=>((wise(fred)<~>old(fred))))&
(((wise(paul)&patient(paul)))=>(?[X]:(patient(X))))&
(((~calm(alice)&~patient(alice)))=>(?[X]:(humble(X))))&
(![X]:((~humble(X)|rich(X))=>(~quiet(X)&generous(X))))&
(![X]:((generous(X)|~patient(X))=>(~kind(X)|creative(X))))&
(![X]:((creative(X)&generous(X))=>funny(X)))&
((?[X]:((~brave(X)<~>brave(X))))<=>(kind(john)))&
((?[X]:(~old(X)))<=>((quiet(alice)|patient(alice))))&
(![X]:((~kind(X)&wise(X))=>(funny(X)|curious(X))))&
(((~patient(alice)|~strong(alice)))<=>((creative(alice)|curious(alice))))&
((?[X]:((~creative(X)<~>humble(X))))=>((~humble(lucy)&kind(lucy))))&
(![X]:((quiet(X)|~curious(X))<=>(quiet(X)&~curious(X))))&
(![X]:(quiet(X)<=>(creative(X)<~>tall(X))))&
(((brave(paul)|~rich(paul)))=>((~brave(fred)|old(fred))))&
(?[X]:((humble(X)&rich(X))))&
(?[X]:((creative(X)&happy(X))))&
(?[X]:((~old(X)|humble(X))))&
(?[X]:((calm(X)&old(X))))&
(old(susan))&
(curious(alice))&
((patient(paul)|~curious(paul))) | ~quiet(john) | [] | null | 0 |
Everyone who is either not curious or wise is not rich and vice versa. Everyone who is both old and not old is either funny or wise. If someone is not funny or happy then fred is funny and vice versa. If susan is kind or humble then someone is strong or not calm and vice versa. Everyone who is both wise and not curious is not kind. If someone is either not quiet or old then paul is not creative or not calm. Everyone who is both not patient and not curious is both not tall and not wise and vice versa. Everyone who is not generous or not quiet is brave or curious and vice versa. Everyone who is not humble is either not wise or tall. Everyone who is either old or tall is not wise. Everyone who is both not patient and tall is both rich and not rich and vice versa. If someone is not quiet or calm then someone is humble and vice versa. Everyone who is both not strong and not brave is happy and vice versa. If someone is both rich and not patient then someone is not brave or humble and vice versa. Everyone who is not brave or not strong is rich or tall and vice versa. If paul is either patient or not generous then someone is either not patient or not quiet. Someone is either not wise or wise. Someone is either calm or not rich. Lucy is either not humble or not curious. Someone is not patient. John is both strong and kind. Paul is either not happy or not wise. | Lucy is brave. | entailment | (![X]:((~curious(X)<~>wise(X))<=>~rich(X)))&
(![X]:((old(X)&~old(X))=>(funny(X)<~>wise(X))))&
((?[X]:((~funny(X)|happy(X))))<=>(funny(fred)))&
(((kind(susan)|humble(susan)))<=>(?[X]:((strong(X)|~calm(X)))))&
(![X]:((wise(X)&~curious(X))=>~kind(X)))&
((?[X]:((~quiet(X)<~>old(X))))=>((~creative(paul)|~calm(paul))))&
(![X]:((~patient(X)&~curious(X))<=>(~tall(X)&~wise(X))))&
(![X]:((~generous(X)|~quiet(X))<=>(brave(X)|curious(X))))&
(![X]:(~humble(X)=>(~wise(X)<~>tall(X))))&
(![X]:((old(X)<~>tall(X))=>~wise(X)))&
(![X]:((~patient(X)&tall(X))<=>(rich(X)&~rich(X))))&
((?[X]:((~quiet(X)|calm(X))))<=>(?[X]:(humble(X))))&
(![X]:((~strong(X)&~brave(X))<=>happy(X)))&
((?[X]:((rich(X)&~patient(X))))<=>(?[X]:((~brave(X)|humble(X)))))&
(![X]:((~brave(X)|~strong(X))<=>(rich(X)|tall(X))))&
(((patient(paul)<~>~generous(paul)))=>(?[X]:((~patient(X)<~>~quiet(X)))))&
(?[X]:((~wise(X)<~>wise(X))))&
(?[X]:((calm(X)<~>~rich(X))))&
((~humble(lucy)<~>~curious(lucy)))&
(?[X]:(~patient(X)))&
((strong(john)&kind(john)))&
((~happy(paul)<~>~wise(paul))) | brave(lucy) | [
"p0",
"p6",
"p10",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 3980627948693767262281677
% SZS output start Proof for 3980627948693767262281677
1. ! [X0] : ((~curious(X0) <~> wise(X0)) <=> ~rich(X0)) [input p0]
7. ! [X0] : ((~curious(X0) & ~patient(X0)) <=> (~wise(X0) & ~tall(X0))) [input p6]
11. ! [X0] : ((tall(X0) & ~patient(X0)) <=> (~rich(X0) & rich(X0))) [input p10]
14. ? [X0] : (~patient(X0) & rich(X0)) <=> ? [X0] : (humble(X0) | ~brave(X0)) [input p13]
23. ~brave(lucy) [input hypothesis]
25. ? [X0] : (~patient(X0) & rich(X0)) <=> ? [X1] : (humble(X1) | ~brave(X1)) [rectify 14]
34. ! [X0] : ((((~wise(X0) | curious(X0)) & (wise(X0) | ~curious(X0))) | rich(X0)) & (~rich(X0) | ((~curious(X0) | ~wise(X0)) & (wise(X0) | curious(X0))))) [nnf transformation 1]
45. ! [X0] : (((~curious(X0) & ~patient(X0)) | (wise(X0) | tall(X0))) & ((~wise(X0) & ~tall(X0)) | (curious(X0) | patient(X0)))) [nnf transformation 7]
46. ! [X0] : (((~curious(X0) & ~patient(X0)) | wise(X0) | tall(X0)) & ((~wise(X0) & ~tall(X0)) | curious(X0) | patient(X0))) [flattening 45]
51. ! [X0] : (((tall(X0) & ~patient(X0)) | (rich(X0) | ~rich(X0))) & ((~rich(X0) & rich(X0)) | (~tall(X0) | patient(X0)))) [nnf transformation 11]
52. ! [X0] : (((tall(X0) & ~patient(X0)) | rich(X0) | ~rich(X0)) & ((~rich(X0) & rich(X0)) | ~tall(X0) | patient(X0))) [flattening 51]
60. (? [X0] : (~patient(X0) & rich(X0)) | ! [X1] : (~humble(X1) & brave(X1))) & (? [X1] : (humble(X1) | ~brave(X1)) | ! [X0] : (patient(X0) | ~rich(X0))) [nnf transformation 25]
61. (? [X0] : (~patient(X0) & rich(X0)) | ! [X1] : (~humble(X1) & brave(X1))) & (? [X2] : (humble(X2) | ~brave(X2)) | ! [X3] : (patient(X3) | ~rich(X3))) [rectify 60]
62. ? [X0] : (~patient(X0) & rich(X0)) => (~patient(sK4) & rich(sK4)) [choice axiom]
63. ? [X2] : (humble(X2) | ~brave(X2)) => (humble(sK5) | ~brave(sK5)) [choice axiom]
64. ((~patient(sK4) & rich(sK4)) | ! [X1] : (~humble(X1) & brave(X1))) & ((humble(sK5) | ~brave(sK5)) | ! [X3] : (patient(X3) | ~rich(X3))) [skolemisation 61,63,62]
80. ~rich(X0) | wise(X0) | curious(X0) [cnf transformation 34]
81. ~rich(X0) | ~curious(X0) | ~wise(X0) [cnf transformation 34]
95. ~wise(X0) | curious(X0) | patient(X0) [cnf transformation 46]
97. ~curious(X0) | wise(X0) | tall(X0) [cnf transformation 46]
106. rich(X0) | ~tall(X0) | patient(X0) [cnf transformation 52]
107. ~rich(X0) | ~tall(X0) | patient(X0) [cnf transformation 52]
117. rich(sK4) | brave(X1) [cnf transformation 64]
119. ~patient(sK4) | brave(X1) [cnf transformation 64]
140. ~brave(lucy) [cnf transformation 23]
188. ~tall(X0) | patient(X0) [subsumption resolution 106,107]
214. 18 <=> patient(sK4) [avatar definition]
216. ~patient(sK4) <- (~18) [avatar component clause 214]
219. 19 <=> ! [X1] : brave(X1) [avatar definition]
220. brave(X1) <- (19) [avatar component clause 219]
221. 19 | ~18 [avatar split clause 119,214,219]
223. 20 <=> rich(sK4) [avatar definition]
225. rich(sK4) <- (20) [avatar component clause 223]
227. 19 | 20 [avatar split clause 117,223,219]
294. $false <- (19) [resolution 220,140]
295. ~19 [avatar contradiction clause 294]
305. wise(sK4) | curious(sK4) <- (20) [resolution 80,225]
307. 34 <=> curious(sK4) [avatar definition]
308. ~curious(sK4) <- (~34) [avatar component clause 307]
309. curious(sK4) <- (34) [avatar component clause 307]
311. 35 <=> wise(sK4) [avatar definition]
312. ~wise(sK4) <- (~35) [avatar component clause 311]
313. wise(sK4) <- (35) [avatar component clause 311]
314. 34 | 35 | ~20 [avatar split clause 305,223,311,307]
315. ~curious(sK4) | ~wise(sK4) <- (20) [resolution 81,225]
349. wise(sK4) | tall(sK4) <- (34) [resolution 97,309]
350. tall(sK4) <- (34, ~35) [subsumption resolution 349,312]
381. patient(sK4) <- (34, ~35) [resolution 350,188]
383. $false <- (~18, 34, ~35) [subsumption resolution 381,216]
384. 18 | ~34 | 35 [avatar contradiction clause 383]
385. ~35 | ~34 | ~20 [avatar split clause 315,223,307,311]
387. curious(sK4) | patient(sK4) <- (35) [resolution 313,95]
398. patient(sK4) <- (~34, 35) [subsumption resolution 387,308]
399. $false <- (~18, ~34, 35) [subsumption resolution 398,216]
400. 18 | 34 | ~35 [avatar contradiction clause 399]
401. $false [avatar sat refutation 221,227,295,314,384,385,400]
% SZS output end Proof for 3980627948693767262281677
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not tall or not creative is creative.
If mary is either strong or not quiet then lucy is either wise or curious and vice versa.
Everyone who is either wise or brave is not wise or not strong and vice versa.
If someone is either quiet or creative then john is either rich or not curious and vice versa.
Everyone who is not rich or brave is both calm and not calm.
If lucy is either not brave or not creative then someone is old or happy.
If lucy is both brave and not curious then someone is not happy and vice versa.
Everyone who is either not strong or patient is not rich and vice versa.
Everyone who is either not humble or not creative is either not generous or not happy and vice versa.
If paul is brave then someone is not strong.
Everyone who is either not brave or rich is not happy or happy.
Everyone who is kind or not brave is not creative and vice versa.
Everyone who is not kind or curious is not humble.
Everyone who is both not curious and funny is either not happy or brave and vice versa.
Everyone who is either curious or creative is either brave or kind.
If someone is either not happy or not calm then paul is both funny and kind and vice versa.
Someone is funny or happy.
Paul is either happy or not rich.
Someone is both not brave and generous.
Someone is happy.
Paul is kind. | John is not curious. | neutral | (![X]:((~tall(X)<~>~creative(X))=>creative(X)))&
(((strong(mary)<~>~quiet(mary)))<=>((wise(lucy)<~>curious(lucy))))&
(![X]:((wise(X)<~>brave(X))<=>(~wise(X)|~strong(X))))&
((?[X]:((quiet(X)<~>creative(X))))<=>((rich(john)<~>~curious(john))))&
(![X]:((~rich(X)|brave(X))=>(calm(X)&~calm(X))))&
(((~brave(lucy)<~>~creative(lucy)))=>(?[X]:((old(X)|happy(X)))))&
(((brave(lucy)&~curious(lucy)))<=>(?[X]:(~happy(X))))&
(![X]:((~strong(X)<~>patient(X))<=>~rich(X)))&
(![X]:((~humble(X)<~>~creative(X))<=>(~generous(X)<~>~happy(X))))&
((brave(paul))=>(?[X]:(~strong(X))))&
(![X]:((~brave(X)<~>rich(X))=>(~happy(X)|happy(X))))&
(![X]:((kind(X)|~brave(X))<=>~creative(X)))&
(![X]:((~kind(X)|curious(X))=>~humble(X)))&
(![X]:((~curious(X)&funny(X))<=>(~happy(X)<~>brave(X))))&
(![X]:((curious(X)<~>creative(X))=>(brave(X)<~>kind(X))))&
((?[X]:((~happy(X)<~>~calm(X))))<=>((funny(paul)&kind(paul))))&
(?[X]:((funny(X)|happy(X))))&
((happy(paul)<~>~rich(paul)))&
(?[X]:((~brave(X)&generous(X))))&
(?[X]:(happy(X)))&
(kind(paul)) | ~curious(john) | [] | null | 0 |
If paul is both generous and happy then someone is not funny or not wise and vice versa.
If fred is funny then susan is not strong and vice versa.
Everyone who is either not happy or creative is either not tall or brave and vice versa.
If someone is not tall or curious then someone is not curious and vice versa.
If alice is both brave and not wise then someone is either not old or curious.
Everyone who is tall or not quiet is both quiet and not kind.
Everyone who is both strong and calm is either quiet or not wise.
If lucy is not kind then alice is either not patient or not curious and vice versa.
If someone is tall or funny then mary is either brave or kind.
Everyone who is strong is old.
If someone is both not creative and funny then fred is both not funny and not brave.
If someone is both not patient and not kind then alice is quiet and vice versa.
Everyone who is not curious or not brave is either happy or not funny and vice versa.
If someone is curious or creative then fred is not creative and vice versa.
If someone is either not wise or curious then lucy is rich or wise and vice versa.
If someone is either not brave or brave then alice is either generous or not happy.
Someone is both not happy and not old.
Someone is humble or not patient.
Alice is not kind or quiet.
Someone is funny or strong.
Susan is not humble. | Alice is brave. | neutral | (((generous(paul)&happy(paul)))<=>(?[X]:((~funny(X)|~wise(X)))))&
((funny(fred))<=>(~strong(susan)))&
(![X]:((~happy(X)<~>creative(X))<=>(~tall(X)<~>brave(X))))&
((?[X]:((~tall(X)|curious(X))))<=>(?[X]:(~curious(X))))&
(((brave(alice)&~wise(alice)))=>(?[X]:((~old(X)<~>curious(X)))))&
(![X]:((tall(X)|~quiet(X))=>(quiet(X)&~kind(X))))&
(![X]:((strong(X)&calm(X))=>(quiet(X)<~>~wise(X))))&
((~kind(lucy))<=>((~patient(alice)<~>~curious(alice))))&
((?[X]:((tall(X)|funny(X))))=>((brave(mary)<~>kind(mary))))&
(![X]:(strong(X)=>old(X)))&
((?[X]:((~creative(X)&funny(X))))=>((~funny(fred)&~brave(fred))))&
((?[X]:((~patient(X)&~kind(X))))<=>(quiet(alice)))&
(![X]:((~curious(X)|~brave(X))<=>(happy(X)<~>~funny(X))))&
((?[X]:((curious(X)|creative(X))))<=>(~creative(fred)))&
((?[X]:((~wise(X)<~>curious(X))))<=>((rich(lucy)|wise(lucy))))&
((?[X]:((~brave(X)<~>brave(X))))=>((generous(alice)<~>~happy(alice))))&
(?[X]:((~happy(X)&~old(X))))&
(?[X]:((humble(X)|~patient(X))))&
((~kind(alice)|quiet(alice)))&
(?[X]:((funny(X)|strong(X))))&
(~humble(susan)) | brave(alice) | [] | null | 0 |
Everyone who is not calm is either not curious or not humble and vice versa.
If mary is not rich then someone is curious or not humble.
Everyone who is both not rich and old is both wise and patient.
Everyone who is not happy or old is both not calm and curious and vice versa.
Everyone who is either humble or not generous is old.
If someone is both not calm and not quiet then someone is either not wise or not funny.
If someone is old or wise then someone is both not curious and not funny and vice versa.
Everyone who is not strong is not kind or old.
If alice is tall then john is not funny or curious and vice versa.
Everyone who is not brave or patient is either not calm or tall.
Everyone who is both not happy and not curious is not kind or not funny and vice versa.
If fred is not humble then mary is both kind and not old.
Everyone who is funny or not wise is not tall and vice versa.
If someone is not humble then someone is not old and vice versa.
Everyone who is either not calm or generous is both not patient and not creative.
If someone is either patient or not quiet then someone is either not strong or creative and vice versa.
Lucy is not curious.
John is not creative or humble.
Alice is both brave and not patient.
Someone is creative.
Someone is not calm or happy.
Alice is calm. | Fred is not creative. | neutral | (![X]:(~calm(X)<=>(~curious(X)<~>~humble(X))))&
((~rich(mary))=>(?[X]:((curious(X)|~humble(X)))))&
(![X]:((~rich(X)&old(X))=>(wise(X)&patient(X))))&
(![X]:((~happy(X)|old(X))<=>(~calm(X)&curious(X))))&
(![X]:((humble(X)<~>~generous(X))=>old(X)))&
((?[X]:((~calm(X)&~quiet(X))))=>(?[X]:((~wise(X)<~>~funny(X)))))&
((?[X]:((old(X)|wise(X))))<=>(?[X]:((~curious(X)&~funny(X)))))&
(![X]:(~strong(X)=>(~kind(X)|old(X))))&
((tall(alice))<=>((~funny(john)|curious(john))))&
(![X]:((~brave(X)|patient(X))=>(~calm(X)<~>tall(X))))&
(![X]:((~happy(X)&~curious(X))<=>(~kind(X)|~funny(X))))&
((~humble(fred))=>((kind(mary)&~old(mary))))&
(![X]:((funny(X)|~wise(X))<=>~tall(X)))&
((?[X]:(~humble(X)))<=>(?[X]:(~old(X))))&
(![X]:((~calm(X)<~>generous(X))=>(~patient(X)&~creative(X))))&
((?[X]:((patient(X)<~>~quiet(X))))<=>(?[X]:((~strong(X)<~>creative(X)))))&
(~curious(lucy))&
((~creative(john)|humble(john)))&
((brave(alice)&~patient(alice)))&
(?[X]:(creative(X)))&
(?[X]:((~calm(X)|happy(X))))&
(calm(alice)) | ~creative(fred) | [] | null | 0 |
Everyone who is generous or rich is both not wise and not calm. If someone is not happy or happy then mary is both tall and creative and vice versa. Everyone who is brave or not old is creative. If someone is creative or rich then mary is either old or quiet and vice versa. If someone is quiet or funny then someone is generous or tall and vice versa. If someone is both not kind and not brave then someone is both patient and brave and vice versa. If fred is not brave or not wise then fred is either brave or not humble. Everyone who is either wise or patient is happy or not happy. Everyone who is both not wise and humble is both humble and rich and vice versa. Everyone who is wise is rich. Everyone who is either tall or not strong is not creative. Everyone who is not generous or wise is patient or brave. If alice is not kind or not creative then lucy is either not old or rich and vice versa. If someone is patient then someone is calm. Everyone who is either happy or not rich is creative or not wise and vice versa. Everyone who is both not funny and brave is either not humble or curious. Someone is happy or not quiet. Mary is rich. Someone is both curious and not wise. John is both tall and quiet. Fred is either not rich or not tall. Someone is both tall and rich. Paul is both not rich and not quiet. Someone is not humble. | Alice is not creative. | neutral | (![X]:((generous(X)|rich(X))=>(~wise(X)&~calm(X))))&
((?[X]:((~happy(X)|happy(X))))<=>((tall(mary)&creative(mary))))&
(![X]:((brave(X)|~old(X))=>creative(X)))&
((?[X]:((creative(X)|rich(X))))<=>((old(mary)<~>quiet(mary))))&
((?[X]:((quiet(X)|funny(X))))<=>(?[X]:((generous(X)|tall(X)))))&
((?[X]:((~kind(X)&~brave(X))))<=>(?[X]:((patient(X)&brave(X)))))&
(((~brave(fred)|~wise(fred)))=>((brave(fred)<~>~humble(fred))))&
(![X]:((wise(X)<~>patient(X))=>(happy(X)|~happy(X))))&
(![X]:((~wise(X)&humble(X))<=>(humble(X)&rich(X))))&
(![X]:(wise(X)=>rich(X)))&
(![X]:((tall(X)<~>~strong(X))=>~creative(X)))&
(![X]:((~generous(X)|wise(X))=>(patient(X)|brave(X))))&
(((~kind(alice)|~creative(alice)))<=>((~old(lucy)<~>rich(lucy))))&
((?[X]:(patient(X)))=>(?[X]:(calm(X))))&
(![X]:((happy(X)<~>~rich(X))<=>(creative(X)|~wise(X))))&
(![X]:((~funny(X)&brave(X))=>(~humble(X)<~>curious(X))))&
(?[X]:((happy(X)|~quiet(X))))&
(rich(mary))&
(?[X]:((curious(X)&~wise(X))))&
((tall(john)&quiet(john)))&
((~rich(fred)<~>~tall(fred)))&
(?[X]:((tall(X)&rich(X))))&
((~rich(paul)&~quiet(paul)))&
(?[X]:(~humble(X))) | ~creative(alice) | [] | null | 0 |
If fred is quiet or patient then someone is not curious or wise and vice versa.
If mary is either curious or not creative then someone is either wise or not funny and vice versa.
If someone is not rich then mary is both not rich and not strong and vice versa.
If mary is both not brave and not creative then someone is not rich.
If alice is either not old or not funny then fred is both generous and wise and vice versa.
If paul is either not patient or not generous then mary is both not humble and not rich and vice versa.
Everyone who is both rich and quiet is humble.
If someone is either brave or not funny then someone is both not rich and curious and vice versa.
Everyone who is either happy or curious is not kind or funny and vice versa.
Everyone who is both kind and creative is either not old or creative.
Everyone who is either not brave or patient is old or not calm and vice versa.
If someone is not rich then lucy is both kind and not generous and vice versa.
If mary is not old then paul is either not kind or not funny and vice versa.
Everyone who is wise or rich is generous.
If mary is happy or wise then someone is both calm and not humble.
Everyone who is not calm is not old and vice versa.
Someone is either not brave or kind.
Fred is both not old and happy.
Fred is both creative and not patient.
Someone is not curious or creative.
Paul is both not quiet and funny.
Alice is brave or not old.
Someone is patient.
Someone is not strong or not funny. | Lucy is kind. | entailment | (((quiet(fred)|patient(fred)))<=>(?[X]:((~curious(X)|wise(X)))))&
(((curious(mary)<~>~creative(mary)))<=>(?[X]:((wise(X)<~>~funny(X)))))&
((?[X]:(~rich(X)))<=>((~rich(mary)&~strong(mary))))&
(((~brave(mary)&~creative(mary)))=>(?[X]:(~rich(X))))&
(((~old(alice)<~>~funny(alice)))<=>((generous(fred)&wise(fred))))&
(((~patient(paul)<~>~generous(paul)))<=>((~humble(mary)&~rich(mary))))&
(![X]:((rich(X)&quiet(X))=>humble(X)))&
((?[X]:((brave(X)<~>~funny(X))))<=>(?[X]:((~rich(X)&curious(X)))))&
(![X]:((happy(X)<~>curious(X))<=>(~kind(X)|funny(X))))&
(![X]:((kind(X)&creative(X))=>(~old(X)<~>creative(X))))&
(![X]:((~brave(X)<~>patient(X))<=>(old(X)|~calm(X))))&
((?[X]:(~rich(X)))<=>((kind(lucy)&~generous(lucy))))&
((~old(mary))<=>((~kind(paul)<~>~funny(paul))))&
(![X]:((wise(X)|rich(X))=>generous(X)))&
(((happy(mary)|wise(mary)))=>(?[X]:((calm(X)&~humble(X)))))&
(![X]:(~calm(X)<=>~old(X)))&
(?[X]:((~brave(X)<~>kind(X))))&
((~old(fred)&happy(fred)))&
((creative(fred)&~patient(fred)))&
(?[X]:((~curious(X)|creative(X))))&
((~quiet(paul)&funny(paul)))&
((brave(alice)|~old(alice)))&
(?[X]:(patient(X)))&
(?[X]:((~strong(X)|~funny(X)))) | kind(lucy) | [
"p5",
"p7",
"p10",
"p11",
"p13",
"p15",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 8098026306476688755261767
% SZS output start Proof for 8098026306476688755261767
6. (~patient(paul) <~> ~generous(paul)) <=> (~rich(mary) & ~humble(mary)) [input p5]
8. ? [X0] : (brave(X0) <~> ~funny(X0)) <=> ? [X0] : (curious(X0) & ~rich(X0)) [input p7]
11. ! [X0] : ((~brave(X0) <~> patient(X0)) <=> (~calm(X0) | old(X0))) [input p10]
12. ? [X0] : ~rich(X0) <=> (~generous(lucy) & kind(lucy)) [input p11]
14. ! [X0] : ((rich(X0) | wise(X0)) => generous(X0)) [input p13]
16. ! [X0] : (~calm(X0) <=> ~old(X0)) [input p15]
21. funny(paul) & ~quiet(paul) [input p20]
25. ~kind(lucy) [input hypothesis]
26. ? [X0] : (brave(X0) <~> ~funny(X0)) <=> ? [X1] : (curious(X1) & ~rich(X1)) [rectify 8]
33. ! [X0] : (generous(X0) | (~rich(X0) & ~wise(X0))) [ennf transformation 14]
53. (((generous(paul) | patient(paul)) & (~generous(paul) | ~patient(paul))) | (rich(mary) | humble(mary))) & ((~rich(mary) & ~humble(mary)) | ((~patient(paul) | generous(paul)) & (~generous(paul) | patient(paul)))) [nnf transformation 6]
54. (((generous(paul) | patient(paul)) & (~generous(paul) | ~patient(paul))) | rich(mary) | humble(mary)) & ((~rich(mary) & ~humble(mary)) | ((~patient(paul) | generous(paul)) & (~generous(paul) | patient(paul)))) [flattening 53]
55. (? [X0] : ((funny(X0) | ~brave(X0)) & (~funny(X0) | brave(X0))) | ! [X1] : (~curious(X1) | rich(X1))) & (? [X1] : (curious(X1) & ~rich(X1)) | ! [X0] : ((brave(X0) | funny(X0)) & (~funny(X0) | ~brave(X0)))) [nnf transformation 26]
56. (? [X0] : ((funny(X0) | ~brave(X0)) & (~funny(X0) | brave(X0))) | ! [X1] : (~curious(X1) | rich(X1))) & (? [X2] : (curious(X2) & ~rich(X2)) | ! [X3] : ((brave(X3) | funny(X3)) & (~funny(X3) | ~brave(X3)))) [rectify 55]
57. ? [X0] : ((funny(X0) | ~brave(X0)) & (~funny(X0) | brave(X0))) => ((funny(sK4) | ~brave(sK4)) & (~funny(sK4) | brave(sK4))) [choice axiom]
58. ? [X2] : (curious(X2) & ~rich(X2)) => (curious(sK5) & ~rich(sK5)) [choice axiom]
59. (((funny(sK4) | ~brave(sK4)) & (~funny(sK4) | brave(sK4))) | ! [X1] : (~curious(X1) | rich(X1))) & ((curious(sK5) & ~rich(sK5)) | ! [X3] : ((brave(X3) | funny(X3)) & (~funny(X3) | ~brave(X3)))) [skolemisation 56,58,57]
63. ! [X0] : ((((~patient(X0) | brave(X0)) & (patient(X0) | ~brave(X0))) | (calm(X0) & ~old(X0))) & ((~calm(X0) | old(X0)) | ((~brave(X0) | ~patient(X0)) & (patient(X0) | brave(X0))))) [nnf transformation 11]
64. ! [X0] : ((((~patient(X0) | brave(X0)) & (patient(X0) | ~brave(X0))) | (calm(X0) & ~old(X0))) & (~calm(X0) | old(X0) | ((~brave(X0) | ~patient(X0)) & (patient(X0) | brave(X0))))) [flattening 63]
65. (? [X0] : ~rich(X0) | (generous(lucy) | ~kind(lucy))) & ((~generous(lucy) & kind(lucy)) | ! [X0] : rich(X0)) [nnf transformation 12]
66. (? [X0] : ~rich(X0) | generous(lucy) | ~kind(lucy)) & ((~generous(lucy) & kind(lucy)) | ! [X0] : rich(X0)) [flattening 65]
67. (? [X0] : ~rich(X0) | generous(lucy) | ~kind(lucy)) & ((~generous(lucy) & kind(lucy)) | ! [X1] : rich(X1)) [rectify 66]
68. ? [X0] : ~rich(X0) => ~rich(sK6) [choice axiom]
69. (~rich(sK6) | generous(lucy) | ~kind(lucy)) & ((~generous(lucy) & kind(lucy)) | ! [X1] : rich(X1)) [skolemisation 67,68]
73. ! [X0] : ((~calm(X0) | old(X0)) & (~old(X0) | calm(X0))) [nnf transformation 16]
107. ~rich(mary) | ~generous(paul) | patient(paul) [cnf transformation 54]
112. ~rich(sK5) | ~funny(X3) | ~brave(X3) [cnf transformation 59]
130. ~old(X0) | brave(X0) | ~patient(X0) [cnf transformation 64]
131. ~patient(X0) | brave(X0) | calm(X0) [cnf transformation 64]
132. kind(lucy) | rich(X1) [cnf transformation 69]
140. ~rich(X0) | generous(X0) [cnf transformation 33]
146. ~calm(X0) | old(X0) [cnf transformation 73]
155. funny(paul) [cnf transformation 21]
159. ~kind(lucy) [cnf transformation 25]
218. 13 <=> rich(mary) [avatar definition]
219. ~rich(mary) <- (~13) [avatar component clause 218]
231. 16 <=> ! [X1] : rich(X1) [avatar definition]
232. rich(X1) <- (16) [avatar component clause 231]
271. 24 <=> patient(paul) [avatar definition]
273. patient(paul) <- (24) [avatar component clause 271]
275. 25 <=> generous(paul) [avatar definition]
276. ~generous(paul) <- (~25) [avatar component clause 275]
281. 24 | ~25 | ~13 [avatar split clause 107,218,275,271]
306. 31 <=> ! [X3] : (~funny(X3) | ~brave(X3)) [avatar definition]
307. ~brave(X3) | ~funny(X3) <- (31) [avatar component clause 306]
310. 32 <=> rich(sK5) [avatar definition]
312. ~rich(sK5) <- (~32) [avatar component clause 310]
314. 31 | ~32 [avatar split clause 112,310,306]
316. 33 <=> kind(lucy) [avatar definition]
329. 16 | 33 [avatar split clause 132,316,231]
331. 36 <=> funny(paul) [avatar definition]
333. funny(paul) <- (36) [avatar component clause 331]
386. 36 [avatar split clause 155,331]
401. ~33 [avatar split clause 159,316]
404. $false <- (16, ~32) [resolution 312,232]
405. ~16 | 32 [avatar contradiction clause 404]
406. generous(X0) <- (16) [resolution 140,232]
407. $false <- (16, ~25) [resolution 406,276]
408. ~16 | 25 [avatar contradiction clause 407]
411. $false <- (~13, 16) [subsumption resolution 219,232]
412. 13 | ~16 [avatar contradiction clause 411]
513. brave(paul) | calm(paul) <- (24) [resolution 131,273]
524. 67 <=> calm(paul) [avatar definition]
526. calm(paul) <- (67) [avatar component clause 524]
528. 68 <=> brave(paul) [avatar definition]
529. ~brave(paul) <- (~68) [avatar component clause 528]
530. brave(paul) <- (68) [avatar component clause 528]
531. 67 | 68 | ~24 [avatar split clause 513,271,528,524]
539. 70 <=> old(paul) [avatar definition]
541. old(paul) <- (70) [avatar component clause 539]
561. old(paul) <- (67) [resolution 526,146]
564. 70 | ~67 [avatar split clause 561,524,539]
566. ~funny(paul) <- (31, 68) [resolution 530,307]
567. $false <- (31, 36, 68) [subsumption resolution 566,333]
568. ~31 | ~36 | ~68 [avatar contradiction clause 567]
573. brave(paul) | ~patient(paul) <- (70) [resolution 541,130]
576. ~patient(paul) <- (~68, 70) [subsumption resolution 573,529]
577. $false <- (24, ~68, 70) [subsumption resolution 576,273]
578. ~24 | 68 | ~70 [avatar contradiction clause 577]
579. $false [avatar sat refutation 281,314,329,386,401,405,408,412,531,564,568,578]
% SZS output end Proof for 8098026306476688755261767
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is happy is not humble.
Everyone who is both quiet and humble is either not brave or not curious and vice versa.
Everyone who is both calm and brave is not happy and vice versa.
If someone is either quiet or wise then alice is both generous and strong.
If someone is either funny or humble then someone is both not tall and not quiet and vice versa.
Everyone who is old is wise and vice versa.
Everyone who is wise or not kind is not quiet.
If someone is tall then someone is both strong and brave and vice versa.
Everyone who is either old or not strong is both not kind and patient.
If susan is happy then someone is both quiet and generous and vice versa.
If someone is quiet then someone is strong.
Everyone who is calm is not quiet.
If someone is not old or humble then paul is wise and vice versa.
If someone is both humble and patient then paul is both not quiet and not happy and vice versa.
Everyone who is creative or not quiet is both brave and not strong and vice versa.
Everyone who is both calm and not brave is both not rich and not old.
Someone is humble.
Fred is not generous.
Someone is not humble.
Paul is either quiet or not tall. | Alice is kind. | entailment | (![X]:(happy(X)=>~humble(X)))&
(![X]:((quiet(X)&humble(X))<=>(~brave(X)<~>~curious(X))))&
(![X]:((calm(X)&brave(X))<=>~happy(X)))&
((?[X]:((quiet(X)<~>wise(X))))=>((generous(alice)&strong(alice))))&
((?[X]:((funny(X)<~>humble(X))))<=>(?[X]:((~tall(X)&~quiet(X)))))&
(![X]:(old(X)<=>wise(X)))&
(![X]:((wise(X)|~kind(X))=>~quiet(X)))&
((?[X]:(tall(X)))<=>(?[X]:((strong(X)&brave(X)))))&
(![X]:((old(X)<~>~strong(X))=>(~kind(X)&patient(X))))&
((happy(susan))<=>(?[X]:((quiet(X)&generous(X)))))&
((?[X]:(quiet(X)))=>(?[X]:(strong(X))))&
(![X]:(calm(X)=>~quiet(X)))&
((?[X]:((~old(X)|humble(X))))<=>(wise(paul)))&
((?[X]:((humble(X)&patient(X))))<=>((~quiet(paul)&~happy(paul))))&
(![X]:((creative(X)|~quiet(X))<=>(brave(X)&~strong(X))))&
(![X]:((calm(X)&~brave(X))=>(~rich(X)&~old(X))))&
(?[X]:(humble(X)))&
(~generous(fred))&
(?[X]:(~humble(X)))&
((quiet(paul)<~>~tall(paul))) | kind(alice) | [
"p3",
"p6",
"p12",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 2832204875425386187372622
% SZS output start Proof for 2832204875425386187372622
4. ? [X0] : (quiet(X0) <~> wise(X0)) => (strong(alice) & generous(alice)) [input p3]
7. ! [X0] : ((~kind(X0) | wise(X0)) => ~quiet(X0)) [input p6]
13. ? [X0] : (humble(X0) | ~old(X0)) <=> wise(paul) [input p12]
15. ! [X0] : ((~quiet(X0) | creative(X0)) <=> (~strong(X0) & brave(X0))) [input p14]
17. ? [X0] : humble(X0) [input p16]
21. ~kind(alice) [input hypothesis]
27. (strong(alice) & generous(alice)) | ! [X0] : (quiet(X0) <=> wise(X0)) [ennf transformation 4]
28. ! [X0] : (~quiet(X0) | (kind(X0) & ~wise(X0))) [ennf transformation 7]
38. (strong(alice) & generous(alice)) | ! [X0] : ((quiet(X0) | ~wise(X0)) & (wise(X0) | ~quiet(X0))) [nnf transformation 27]
58. (? [X0] : (humble(X0) | ~old(X0)) | ~wise(paul)) & (wise(paul) | ! [X0] : (~humble(X0) & old(X0))) [nnf transformation 13]
59. (? [X0] : (humble(X0) | ~old(X0)) | ~wise(paul)) & (wise(paul) | ! [X1] : (~humble(X1) & old(X1))) [rectify 58]
60. ? [X0] : (humble(X0) | ~old(X0)) => (humble(sK6) | ~old(sK6)) [choice axiom]
61. ((humble(sK6) | ~old(sK6)) | ~wise(paul)) & (wise(paul) | ! [X1] : (~humble(X1) & old(X1))) [skolemisation 59,60]
67. ! [X0] : (((~quiet(X0) | creative(X0)) | (strong(X0) | ~brave(X0))) & ((~strong(X0) & brave(X0)) | (quiet(X0) & ~creative(X0)))) [nnf transformation 15]
68. ! [X0] : ((~quiet(X0) | creative(X0) | strong(X0) | ~brave(X0)) & ((~strong(X0) & brave(X0)) | (quiet(X0) & ~creative(X0)))) [flattening 67]
69. ? [X0] : humble(X0) => humble(sK8) [choice axiom]
70. humble(sK8) [skolemisation 17,69]
87. strong(alice) | quiet(X0) | ~wise(X0) [cnf transformation 38]
96. ~wise(X0) | ~quiet(X0) [cnf transformation 28]
97. ~quiet(X0) | kind(X0) [cnf transformation 28]
111. wise(paul) | ~humble(X1) [cnf transformation 61]
120. ~strong(X0) | quiet(X0) [cnf transformation 68]
123. humble(sK8) [cnf transformation 70]
128. ~kind(alice) [cnf transformation 21]
130. 1 <=> ! [X0] : (quiet(X0) | ~wise(X0)) [avatar definition]
131. quiet(X0) | ~wise(X0) <- (1) [avatar component clause 130]
133. 2 <=> strong(alice) [avatar definition]
135. strong(alice) <- (2) [avatar component clause 133]
136. 1 | 2 [avatar split clause 87,133,130]
226. 23 <=> wise(paul) [avatar definition]
227. wise(paul) <- (23) [avatar component clause 226]
239. 26 <=> ! [X1] : ~humble(X1) [avatar definition]
240. ~humble(X1) <- (26) [avatar component clause 239]
241. 26 | 23 [avatar split clause 111,226,239]
284. quiet(alice) <- (2) [resolution 120,135]
290. kind(alice) <- (2) [resolution 284,97]
291. $false <- (2) [subsumption resolution 290,128]
292. ~2 [avatar contradiction clause 291]
295. ~wise(X0) <- (1) [subsumption resolution 131,96]
296. $false <- (1, 23) [resolution 295,227]
297. ~1 | ~23 [avatar contradiction clause 296]
298. $false <- (26) [resolution 240,123]
301. ~26 [avatar contradiction clause 298]
302. $false [avatar sat refutation 136,241,292,297,301]
% SZS output end Proof for 2832204875425386187372622
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is funny or brave is either tall or patient.
Everyone who is not wise or not strong is both funny and not strong and vice versa.
If someone is generous then paul is both patient and not strong.
Everyone who is both not happy and not humble is both not happy and rich and vice versa.
Everyone who is both happy and brave is either kind or not humble.
If lucy is not patient then paul is quiet.
If someone is either not tall or funny then fred is both not quiet and generous.
Everyone who is not quiet or not rich is either not old or calm and vice versa.
If someone is both quiet and not old then someone is quiet and vice versa.
Everyone who is kind is not funny and vice versa.
Everyone who is either not generous or humble is both not patient and old.
Everyone who is either not humble or kind is strong or humble and vice versa.
If alice is not quiet or not wise then someone is either not strong or old and vice versa.
Everyone who is not creative or not curious is not brave or not rich and vice versa.
Everyone who is patient is not wise.
If alice is either brave or not brave then john is not tall or humble and vice versa.
Someone is both not patient and strong.
Mary is strong.
Someone is tall or not rich.
Someone is not old.
Someone is not quiet. | Fred is funny. | contradiction | (![X]:((funny(X)|brave(X))=>(tall(X)<~>patient(X))))&
(![X]:((~wise(X)|~strong(X))<=>(funny(X)&~strong(X))))&
((?[X]:(generous(X)))=>((patient(paul)&~strong(paul))))&
(![X]:((~happy(X)&~humble(X))<=>(~happy(X)&rich(X))))&
(![X]:((happy(X)&brave(X))=>(kind(X)<~>~humble(X))))&
((~patient(lucy))=>(quiet(paul)))&
((?[X]:((~tall(X)<~>funny(X))))=>((~quiet(fred)&generous(fred))))&
(![X]:((~quiet(X)|~rich(X))<=>(~old(X)<~>calm(X))))&
((?[X]:((quiet(X)&~old(X))))<=>(?[X]:(quiet(X))))&
(![X]:(kind(X)<=>~funny(X)))&
(![X]:((~generous(X)<~>humble(X))=>(~patient(X)&old(X))))&
(![X]:((~humble(X)<~>kind(X))<=>(strong(X)|humble(X))))&
(((~quiet(alice)|~wise(alice)))<=>(?[X]:((~strong(X)<~>old(X)))))&
(![X]:((~creative(X)|~curious(X))<=>(~brave(X)|~rich(X))))&
(![X]:(patient(X)=>~wise(X)))&
(((brave(alice)<~>~brave(alice)))<=>((~tall(john)|humble(john))))&
(?[X]:((~patient(X)&strong(X))))&
(strong(mary))&
(?[X]:((tall(X)|~rich(X))))&
(?[X]:(~old(X)))&
(?[X]:(~quiet(X))) | funny(fred) | [
"p0",
"p1",
"p2",
"p6",
"p9",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8662355190158916791262240
% SZS output start Proof for 8662355190158916791262240
1. ! [X0] : ((brave(X0) | funny(X0)) => (tall(X0) <~> patient(X0))) [input p0]
2. ! [X0] : ((~strong(X0) | ~wise(X0)) <=> (~strong(X0) & funny(X0))) [input p1]
3. ? [X0] : generous(X0) => (~strong(paul) & patient(paul)) [input p2]
7. ? [X0] : (~tall(X0) <~> funny(X0)) => (generous(fred) & ~quiet(fred)) [input p6]
10. ! [X0] : (kind(X0) <=> ~funny(X0)) [input p9]
12. ! [X0] : ((~humble(X0) <~> kind(X0)) <=> (humble(X0) | strong(X0))) [input p11]
15. ! [X0] : (patient(X0) => ~wise(X0)) [input p14]
22. funny(fred) [input hypothesis]
24. ! [X0] : ((tall(X0) <~> patient(X0)) | (~brave(X0) & ~funny(X0))) [ennf transformation 1]
25. (~strong(paul) & patient(paul)) | ! [X0] : ~generous(X0) [ennf transformation 3]
29. (generous(fred) & ~quiet(fred)) | ! [X0] : (~tall(X0) <=> funny(X0)) [ennf transformation 7]
31. ! [X0] : (~wise(X0) | ~patient(X0)) [ennf transformation 15]
32. ! [X0] : (((~patient(X0) | ~tall(X0)) & (patient(X0) | tall(X0))) | (~brave(X0) & ~funny(X0))) [nnf transformation 24]
33. ! [X0] : (((~strong(X0) | ~wise(X0)) | (strong(X0) | ~funny(X0))) & ((~strong(X0) & funny(X0)) | (strong(X0) & wise(X0)))) [nnf transformation 2]
34. ! [X0] : ((~strong(X0) | ~wise(X0) | strong(X0) | ~funny(X0)) & ((~strong(X0) & funny(X0)) | (strong(X0) & wise(X0)))) [flattening 33]
38. (generous(fred) & ~quiet(fred)) | ! [X0] : ((~tall(X0) | ~funny(X0)) & (funny(X0) | tall(X0))) [nnf transformation 29]
46. ! [X0] : ((kind(X0) | funny(X0)) & (~funny(X0) | ~kind(X0))) [nnf transformation 10]
48. ! [X0] : ((((~kind(X0) | humble(X0)) & (kind(X0) | ~humble(X0))) | (~humble(X0) & ~strong(X0))) & ((humble(X0) | strong(X0)) | ((~humble(X0) | ~kind(X0)) & (kind(X0) | humble(X0))))) [nnf transformation 12]
49. ! [X0] : ((((~kind(X0) | humble(X0)) & (kind(X0) | ~humble(X0))) | (~humble(X0) & ~strong(X0))) & (humble(X0) | strong(X0) | ((~humble(X0) | ~kind(X0)) & (kind(X0) | humble(X0))))) [flattening 48]
67. ~funny(X0) | tall(X0) | patient(X0) [cnf transformation 32]
72. strong(X0) | funny(X0) [cnf transformation 34]
73. ~strong(X0) | wise(X0) [cnf transformation 34]
77. ~strong(paul) | ~generous(X0) [cnf transformation 25]
88. generous(fred) | ~tall(X0) | ~funny(X0) [cnf transformation 38]
98. ~kind(X0) | ~funny(X0) [cnf transformation 46]
104. humble(X0) | strong(X0) | kind(X0) | humble(X0) [cnf transformation 49]
107. kind(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 49]
120. ~wise(X0) | ~patient(X0) [cnf transformation 31]
133. funny(fred) [cnf transformation 22]
136. humble(X0) | strong(X0) | kind(X0) [duplicate literal removal 104]
137. ~humble(X0) | kind(X0) [duplicate literal removal 107]
139. 1 <=> ! [X0] : ~generous(X0) [avatar definition]
140. ~generous(X0) <- (1) [avatar component clause 139]
142. 2 <=> strong(paul) [avatar definition]
144. ~strong(paul) <- (~2) [avatar component clause 142]
145. 1 | ~2 [avatar split clause 77,142,139]
161. 6 <=> ! [X0] : (~tall(X0) | ~funny(X0)) [avatar definition]
162. ~tall(X0) | ~funny(X0) <- (6) [avatar component clause 161]
164. 7 <=> generous(fred) [avatar definition]
166. generous(fred) <- (7) [avatar component clause 164]
167. 6 | 7 [avatar split clause 88,164,161]
199. kind(X0) | strong(X0) [subsumption resolution 136,137]
260. strong(X0) | ~funny(X0) [resolution 199,98]
261. strong(X0) [subsumption resolution 260,72]
262. $false <- (~2) [resolution 261,144]
264. wise(X0) [resolution 261,73]
266. 2 [avatar contradiction clause 262]
270. $false <- (1, 7) [resolution 140,166]
271. ~1 | ~7 [avatar contradiction clause 270]
275. ~patient(X0) [resolution 264,120]
278. tall(fred) | patient(fred) [resolution 67,133]
280. tall(fred) [subsumption resolution 278,275]
286. ~funny(fred) <- (6) [resolution 280,162]
287. $false <- (6) [subsumption resolution 286,133]
288. ~6 [avatar contradiction clause 287]
289. $false [avatar sat refutation 145,167,266,271,288]
% SZS output end Proof for 8662355190158916791262240
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not old then john is brave or not happy and vice versa. Everyone who is brave is not brave. If mary is both humble and not calm then paul is happy. Everyone who is tall or not quiet is not calm or strong. If someone is both rich and not kind then susan is both not funny and not humble and vice versa. If someone is both brave and generous then someone is both not generous and not calm. Everyone who is not creative is calm and vice versa. If susan is brave or not strong then someone is both not quiet and rich and vice versa. If someone is either funny or not rich then someone is happy and vice versa. If someone is either not patient or not creative then someone is creative or tall and vice versa. If someone is brave then someone is generous. If someone is both humble and not funny then someone is not funny and vice versa. Everyone who is both generous and not funny is rich or not patient and vice versa. Everyone who is not curious or generous is both generous and calm. If someone is calm then lucy is either not curious or happy and vice versa. Everyone who is happy is both not kind and not funny. Mary is not brave. John is both wise and not brave. Someone is creative or not kind. Mary is either kind or patient. Mary is not kind. Mary is not curious. | Lucy is happy. | neutral | ((?[X]:(~old(X)))<=>((brave(john)|~happy(john))))&
(![X]:(brave(X)=>~brave(X)))&
(((humble(mary)&~calm(mary)))=>(happy(paul)))&
(![X]:((tall(X)|~quiet(X))=>(~calm(X)|strong(X))))&
((?[X]:((rich(X)&~kind(X))))<=>((~funny(susan)&~humble(susan))))&
((?[X]:((brave(X)&generous(X))))=>(?[X]:((~generous(X)&~calm(X)))))&
(![X]:(~creative(X)<=>calm(X)))&
(((brave(susan)|~strong(susan)))<=>(?[X]:((~quiet(X)&rich(X)))))&
((?[X]:((funny(X)<~>~rich(X))))<=>(?[X]:(happy(X))))&
((?[X]:((~patient(X)<~>~creative(X))))<=>(?[X]:((creative(X)|tall(X)))))&
((?[X]:(brave(X)))=>(?[X]:(generous(X))))&
((?[X]:((humble(X)&~funny(X))))<=>(?[X]:(~funny(X))))&
(![X]:((generous(X)&~funny(X))<=>(rich(X)|~patient(X))))&
(![X]:((~curious(X)|generous(X))=>(generous(X)&calm(X))))&
((?[X]:(calm(X)))<=>((~curious(lucy)<~>happy(lucy))))&
(![X]:(happy(X)=>(~kind(X)&~funny(X))))&
(~brave(mary))&
((wise(john)&~brave(john)))&
(?[X]:((creative(X)|~kind(X))))&
((kind(mary)<~>patient(mary)))&
(~kind(mary))&
(~curious(mary)) | happy(lucy) | [] | null | 0 |
Everyone who is both not strong and not old is either tall or funny and vice versa.
If mary is both not rich and kind then someone is not tall or not kind.
Everyone who is tall is either generous or wise.
Everyone who is either not humble or not rich is happy or funny and vice versa.
If someone is either old or not wise then paul is creative or wise.
Everyone who is generous is both not strong and creative.
Everyone who is old is both not rich and happy and vice versa.
If someone is not old then someone is both not quiet and not rich.
Everyone who is quiet is not funny and vice versa.
Everyone who is both tall and creative is old and vice versa.
Everyone who is wise is both not funny and kind.
Everyone who is either generous or not calm is not kind or tall.
If someone is either humble or creative then someone is tall.
Everyone who is not happy is either not rich or generous and vice versa.
Everyone who is either generous or calm is either wise or kind.
Someone is either not quiet or humble.
Someone is not funny.
Lucy is humble.
Someone is not quiet.
Fred is not rich.
Paul is not generous or not old. | Paul is not rich. | neutral | (![X]:((~strong(X)&~old(X))<=>(tall(X)<~>funny(X))))&
(((~rich(mary)&kind(mary)))=>(?[X]:((~tall(X)|~kind(X)))))&
(![X]:(tall(X)=>(generous(X)<~>wise(X))))&
(![X]:((~humble(X)<~>~rich(X))<=>(happy(X)|funny(X))))&
((?[X]:((old(X)<~>~wise(X))))=>((creative(paul)|wise(paul))))&
(![X]:(generous(X)=>(~strong(X)&creative(X))))&
(![X]:(old(X)<=>(~rich(X)&happy(X))))&
((?[X]:(~old(X)))=>(?[X]:((~quiet(X)&~rich(X)))))&
(![X]:(quiet(X)<=>~funny(X)))&
(![X]:((tall(X)&creative(X))<=>old(X)))&
(![X]:(wise(X)=>(~funny(X)&kind(X))))&
(![X]:((generous(X)<~>~calm(X))=>(~kind(X)|tall(X))))&
((?[X]:((humble(X)<~>creative(X))))=>(?[X]:(tall(X))))&
(![X]:(~happy(X)<=>(~rich(X)<~>generous(X))))&
(![X]:((generous(X)<~>calm(X))=>(wise(X)<~>kind(X))))&
(?[X]:((~quiet(X)<~>humble(X))))&
(?[X]:(~funny(X)))&
(humble(lucy))&
(?[X]:(~quiet(X)))&
(~rich(fred))&
((~generous(paul)|~old(paul))) | ~rich(paul) | [] | null | 0 |
Everyone who is either old or not rich is both happy and brave and vice versa. Everyone who is not funny or not calm is either patient or kind and vice versa. Everyone who is not brave is either brave or not happy. Everyone who is both not rich and not happy is wise. If someone is either not happy or brave then someone is happy or not wise and vice versa. If fred is calm or not kind then someone is patient and vice versa. Everyone who is either calm or generous is both old and tall and vice versa. Everyone who is rich or kind is both not old and curious and vice versa. Everyone who is either strong or not quiet is either rich or not brave and vice versa. Everyone who is not calm is humble. If someone is not old then someone is not funny. Everyone who is either old or not curious is patient or kind and vice versa. If paul is not tall or not brave then fred is curious and vice versa. Everyone who is both not patient and not brave is either not funny or not wise and vice versa. Everyone who is either not curious or wise is either not funny or patient. Everyone who is not strong is both patient and not curious. John is both not kind and not rich. John is both not patient and calm. Someone is not calm or old. Paul is not brave or curious. John is either quiet or not creative. Susan is both not quiet and not curious. Paul is not quiet or not generous. Susan is not kind or old. | Susan is happy. | contradiction | (![X]:((old(X)<~>~rich(X))<=>(happy(X)&brave(X))))&
(![X]:((~funny(X)|~calm(X))<=>(patient(X)<~>kind(X))))&
(![X]:(~brave(X)=>(brave(X)<~>~happy(X))))&
(![X]:((~rich(X)&~happy(X))=>wise(X)))&
((?[X]:((~happy(X)<~>brave(X))))<=>(?[X]:((happy(X)|~wise(X)))))&
(((calm(fred)|~kind(fred)))<=>(?[X]:(patient(X))))&
(![X]:((calm(X)<~>generous(X))<=>(old(X)&tall(X))))&
(![X]:((rich(X)|kind(X))<=>(~old(X)&curious(X))))&
(![X]:((strong(X)<~>~quiet(X))<=>(rich(X)<~>~brave(X))))&
(![X]:(~calm(X)=>humble(X)))&
((?[X]:(~old(X)))=>(?[X]:(~funny(X))))&
(![X]:((old(X)<~>~curious(X))<=>(patient(X)|kind(X))))&
(((~tall(paul)|~brave(paul)))<=>(curious(fred)))&
(![X]:((~patient(X)&~brave(X))<=>(~funny(X)<~>~wise(X))))&
(![X]:((~curious(X)<~>wise(X))=>(~funny(X)<~>patient(X))))&
(![X]:(~strong(X)=>(patient(X)&~curious(X))))&
((~kind(john)&~rich(john)))&
((~patient(john)&calm(john)))&
(?[X]:((~calm(X)|old(X))))&
((~brave(paul)|curious(paul)))&
((quiet(john)<~>~creative(john)))&
((~quiet(susan)&~curious(susan)))&
((~quiet(paul)|~generous(paul)))&
((~kind(susan)|old(susan))) | happy(susan) | [
"p0",
"p1",
"p2",
"p3",
"p7",
"p10",
"p11",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2788025434110040229276457
% SZS output start Proof for 2788025434110040229276457
1. ! [X0] : ((old(X0) <~> ~rich(X0)) <=> (brave(X0) & happy(X0))) [input p0]
2. ! [X0] : ((~calm(X0) | ~funny(X0)) <=> (patient(X0) <~> kind(X0))) [input p1]
3. ! [X0] : (~brave(X0) => (brave(X0) <~> ~happy(X0))) [input p2]
4. ! [X0] : ((~happy(X0) & ~rich(X0)) => wise(X0)) [input p3]
8. ! [X0] : ((kind(X0) | rich(X0)) <=> (curious(X0) & ~old(X0))) [input p7]
11. ? [X0] : ~old(X0) => ? [X0] : ~funny(X0) [input p10]
12. ! [X0] : ((old(X0) <~> ~curious(X0)) <=> (kind(X0) | patient(X0))) [input p11]
14. ! [X0] : ((~brave(X0) & ~patient(X0)) <=> (~funny(X0) <~> ~wise(X0))) [input p13]
15. ! [X0] : ((~curious(X0) <~> wise(X0)) => (~funny(X0) <~> patient(X0))) [input p14]
25. happy(susan) [input hypothesis]
27. ? [X0] : ~old(X0) => ? [X1] : ~funny(X1) [rectify 11]
29. ! [X0] : ((brave(X0) <~> ~happy(X0)) | brave(X0)) [ennf transformation 3]
30. ! [X0] : (wise(X0) | (happy(X0) | rich(X0))) [ennf transformation 4]
31. ! [X0] : (wise(X0) | happy(X0) | rich(X0)) [flattening 30]
32. ? [X1] : ~funny(X1) | ! [X0] : old(X0) [ennf transformation 27]
33. ! [X0] : ((~funny(X0) <~> patient(X0)) | (~curious(X0) <=> wise(X0))) [ennf transformation 15]
35. ! [X0] : ((((rich(X0) | ~old(X0)) & (~rich(X0) | old(X0))) | (~brave(X0) | ~happy(X0))) & ((brave(X0) & happy(X0)) | ((old(X0) | rich(X0)) & (~rich(X0) | ~old(X0))))) [nnf transformation 1]
36. ! [X0] : ((((rich(X0) | ~old(X0)) & (~rich(X0) | old(X0))) | ~brave(X0) | ~happy(X0)) & ((brave(X0) & happy(X0)) | ((old(X0) | rich(X0)) & (~rich(X0) | ~old(X0))))) [flattening 35]
37. ! [X0] : (((~calm(X0) | ~funny(X0)) | ((patient(X0) | ~kind(X0)) & (kind(X0) | ~patient(X0)))) & (((~kind(X0) | ~patient(X0)) & (kind(X0) | patient(X0))) | (calm(X0) & funny(X0)))) [nnf transformation 2]
38. ! [X0] : ((~calm(X0) | ~funny(X0) | ((patient(X0) | ~kind(X0)) & (kind(X0) | ~patient(X0)))) & (((~kind(X0) | ~patient(X0)) & (kind(X0) | patient(X0))) | (calm(X0) & funny(X0)))) [flattening 37]
39. ! [X0] : (((happy(X0) | ~brave(X0)) & (~happy(X0) | brave(X0))) | brave(X0)) [nnf transformation 29]
52. ! [X0] : (((kind(X0) | rich(X0)) | (~curious(X0) | old(X0))) & ((curious(X0) & ~old(X0)) | (~kind(X0) & ~rich(X0)))) [nnf transformation 8]
53. ! [X0] : ((kind(X0) | rich(X0) | ~curious(X0) | old(X0)) & ((curious(X0) & ~old(X0)) | (~kind(X0) & ~rich(X0)))) [flattening 52]
55. ? [X0] : ~funny(X0) | ! [X1] : old(X1) [rectify 32]
56. ? [X0] : ~funny(X0) => ~funny(sK3) [choice axiom]
57. ~funny(sK3) | ! [X1] : old(X1) [skolemisation 55,56]
58. ! [X0] : ((((curious(X0) | ~old(X0)) & (~curious(X0) | old(X0))) | (~kind(X0) & ~patient(X0))) & ((kind(X0) | patient(X0)) | ((old(X0) | curious(X0)) & (~curious(X0) | ~old(X0))))) [nnf transformation 12]
59. ! [X0] : ((((curious(X0) | ~old(X0)) & (~curious(X0) | old(X0))) | (~kind(X0) & ~patient(X0))) & (kind(X0) | patient(X0) | ((old(X0) | curious(X0)) & (~curious(X0) | ~old(X0))))) [flattening 58]
62. ! [X0] : (((~brave(X0) & ~patient(X0)) | ((~funny(X0) | wise(X0)) & (~wise(X0) | funny(X0)))) & (((wise(X0) | funny(X0)) & (~wise(X0) | ~funny(X0))) | (brave(X0) | patient(X0)))) [nnf transformation 14]
63. ! [X0] : (((~brave(X0) & ~patient(X0)) | ((~funny(X0) | wise(X0)) & (~wise(X0) | funny(X0)))) & (((wise(X0) | funny(X0)) & (~wise(X0) | ~funny(X0))) | brave(X0) | patient(X0))) [flattening 62]
64. ! [X0] : (((~patient(X0) | funny(X0)) & (patient(X0) | ~funny(X0))) | ((~curious(X0) | ~wise(X0)) & (wise(X0) | curious(X0)))) [nnf transformation 33]
71. brave(X0) | old(X0) | rich(X0) [cnf transformation 36]
72. ~brave(X0) | old(X0) | ~rich(X0) | ~happy(X0) [cnf transformation 36]
73. ~brave(X0) | ~old(X0) | rich(X0) | ~happy(X0) [cnf transformation 36]
74. kind(X0) | patient(X0) | funny(X0) [cnf transformation 38]
80. ~happy(X0) | brave(X0) | brave(X0) [cnf transformation 39]
82. wise(X0) | happy(X0) | rich(X0) [cnf transformation 31]
98. ~rich(X0) | ~old(X0) [cnf transformation 53]
99. ~kind(X0) | ~old(X0) [cnf transformation 53]
100. ~rich(X0) | curious(X0) [cnf transformation 53]
101. ~kind(X0) | curious(X0) [cnf transformation 53]
102. ~curious(X0) | rich(X0) | kind(X0) | old(X0) [cnf transformation 53]
111. ~funny(sK3) | old(X1) [cnf transformation 57]
114. ~curious(X0) | old(X0) | ~patient(X0) [cnf transformation 59]
115. ~curious(X0) | old(X0) | ~kind(X0) [cnf transformation 59]
123. ~wise(X0) | ~patient(X0) | funny(X0) [cnf transformation 63]
124. ~patient(X0) | ~funny(X0) | wise(X0) [cnf transformation 63]
125. ~wise(X0) | ~brave(X0) | funny(X0) [cnf transformation 63]
127. patient(X0) | ~funny(X0) | wise(X0) | curious(X0) [cnf transformation 64]
129. ~patient(X0) | funny(X0) | wise(X0) | curious(X0) [cnf transformation 64]
145. happy(susan) [cnf transformation 25]
146. ~happy(X0) | brave(X0) [duplicate literal removal 80]
197. 12 <=> ! [X1] : old(X1) [avatar definition]
198. old(X1) <- (12) [avatar component clause 197]
200. 13 <=> funny(sK3) [avatar definition]
202. ~funny(sK3) <- (~13) [avatar component clause 200]
203. 12 | ~13 [avatar split clause 111,200,197]
204. old(X0) | ~kind(X0) [subsumption resolution 115,101]
205. ~kind(X0) [subsumption resolution 204,99]
223. ~patient(X0) | wise(X0) | curious(X0) [subsumption resolution 129,124]
224. ~funny(X0) | wise(X0) | curious(X0) [subsumption resolution 127,223]
263. brave(susan) [resolution 146,145]
295. patient(X2) | funny(X2) [resolution 74,205]
371. ~patient(X0) | funny(X0) | happy(X0) | rich(X0) [resolution 123,82]
373. funny(X0) | happy(X0) | rich(X0) [subsumption resolution 371,295]
431. wise(X1) | curious(X1) | funny(X1) [resolution 223,295]
434. curious(X1) | wise(X1) [subsumption resolution 431,224]
448. old(susan) | ~rich(susan) | ~happy(susan) [resolution 72,263]
469. ~old(susan) | rich(susan) | ~happy(susan) [resolution 73,263]
589. wise(X1) | rich(X1) | kind(X1) | old(X1) [resolution 434,102]
594. wise(X1) | rich(X1) | old(X1) [subsumption resolution 589,205]
640. 54 <=> rich(sK3) [avatar definition]
641. ~rich(sK3) <- (~54) [avatar component clause 640]
642. rich(sK3) <- (54) [avatar component clause 640]
644. 55 <=> happy(sK3) [avatar definition]
646. happy(sK3) <- (55) [avatar component clause 644]
696. 63 <=> rich(susan) [avatar definition]
719. rich(susan) | ~happy(susan) <- (12) [subsumption resolution 469,198]
720. rich(susan) <- (12) [subsumption resolution 719,145]
721. 63 | ~12 [avatar split clause 720,197,696]
738. old(susan) | ~rich(susan) [subsumption resolution 448,145]
739. ~rich(susan) [subsumption resolution 738,98]
740. ~63 [avatar split clause 739,696]
746. happy(sK3) | rich(sK3) <- (~13) [resolution 202,373]
933. ~old(sK3) <- (54) [resolution 642,98]
943. 74 <=> brave(sK3) [avatar definition]
945. brave(sK3) <- (74) [avatar component clause 943]
948. 75 <=> old(sK3) [avatar definition]
949. old(sK3) <- (75) [avatar component clause 948]
950. ~old(sK3) <- (~75) [avatar component clause 948]
953. ~75 | ~54 [avatar split clause 933,640,948]
1014. 54 | 55 | 13 [avatar split clause 746,200,644,640]
1015. brave(sK3) <- (55) [resolution 646,146]
1016. 74 | ~55 [avatar split clause 1015,644,943]
1195. rich(X2) | old(X2) | ~brave(X2) | funny(X2) [resolution 594,125]
1200. funny(X2) | old(X2) | rich(X2) [subsumption resolution 1195,71]
1268. old(sK3) | rich(sK3) <- (~13) [resolution 1200,202]
1279. 83 <=> patient(sK3) [avatar definition]
1280. ~patient(sK3) <- (~83) [avatar component clause 1279]
1291. curious(sK3) <- (54) [resolution 642,100]
1298. old(sK3) | ~patient(sK3) <- (54) [resolution 1291,114]
1300. ~patient(sK3) <- (54, ~75) [subsumption resolution 1298,950]
1301. ~83 | ~54 | 75 [avatar split clause 1300,948,640,1279]
1305. funny(sK3) <- (~83) [resolution 1280,295]
1306. $false <- (~13, ~83) [subsumption resolution 1305,202]
1307. 13 | 83 [avatar contradiction clause 1306]
1311. 54 | 75 | 13 [avatar split clause 1268,200,948,640]
1315. ~old(sK3) | rich(sK3) | ~happy(sK3) <- (74) [resolution 945,73]
1317. rich(sK3) | ~happy(sK3) <- (74, 75) [subsumption resolution 1315,949]
1318. ~happy(sK3) <- (~54, 74, 75) [subsumption resolution 1317,641]
1319. $false <- (~54, 55, 74, 75) [subsumption resolution 1318,646]
1320. 54 | ~55 | ~74 | ~75 [avatar contradiction clause 1319]
1321. $false [avatar sat refutation 203,721,740,953,1014,1016,1301,1307,1311,1320]
% SZS output end Proof for 2788025434110040229276457
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5500
% Time elapsed: 0.043 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is creative or not happy is kind and vice versa.
If someone is not old or humble then someone is kind.
Everyone who is both not tall and not kind is either not kind or rich.
Everyone who is both not old and not generous is both quiet and rich.
If paul is not generous then lucy is kind.
If paul is both humble and not strong then someone is tall and vice versa.
Everyone who is both not kind and not curious is kind and vice versa.
If mary is funny or rich then john is either not strong or not quiet and vice versa.
If someone is both not brave and tall then paul is not strong and vice versa.
Everyone who is not rich is both not kind and not quiet and vice versa.
If alice is both not rich and not creative then fred is not strong and vice versa.
If lucy is not wise then lucy is both generous and funny.
Everyone who is not rich or not creative is funny and vice versa.
Everyone who is not rich is either not tall or not patient.
If mary is either strong or calm then paul is not humble.
If john is both not quiet and not rich then someone is either not wise or brave.
Someone is not wise or tall.
Someone is not brave.
Susan is not generous.
Alice is not kind or calm.
Someone is either kind or not tall. | Mary is not strong. | neutral | (![X]:((creative(X)|~happy(X))<=>kind(X)))&
((?[X]:((~old(X)|humble(X))))=>(?[X]:(kind(X))))&
(![X]:((~tall(X)&~kind(X))=>(~kind(X)<~>rich(X))))&
(![X]:((~old(X)&~generous(X))=>(quiet(X)&rich(X))))&
((~generous(paul))=>(kind(lucy)))&
(((humble(paul)&~strong(paul)))<=>(?[X]:(tall(X))))&
(![X]:((~kind(X)&~curious(X))<=>kind(X)))&
(((funny(mary)|rich(mary)))<=>((~strong(john)<~>~quiet(john))))&
((?[X]:((~brave(X)&tall(X))))<=>(~strong(paul)))&
(![X]:(~rich(X)<=>(~kind(X)&~quiet(X))))&
(((~rich(alice)&~creative(alice)))<=>(~strong(fred)))&
((~wise(lucy))=>((generous(lucy)&funny(lucy))))&
(![X]:((~rich(X)|~creative(X))<=>funny(X)))&
(![X]:(~rich(X)=>(~tall(X)<~>~patient(X))))&
(((strong(mary)<~>calm(mary)))=>(~humble(paul)))&
(((~quiet(john)&~rich(john)))=>(?[X]:((~wise(X)<~>brave(X)))))&
(?[X]:((~wise(X)|tall(X))))&
(?[X]:(~brave(X)))&
(~generous(susan))&
((~kind(alice)|calm(alice)))&
(?[X]:((kind(X)<~>~tall(X)))) | ~strong(mary) | [] | null | 0 |
Everyone who is happy is funny or humble and vice versa.
Everyone who is both not brave and quiet is not brave or wise.
If lucy is either quiet or brave then susan is strong and vice versa.
Everyone who is curious is both generous and curious.
If someone is both not quiet and not patient then lucy is old and vice versa.
If paul is rich or kind then someone is generous or brave and vice versa.
If someone is both quiet and not rich then paul is creative or not calm.
Everyone who is either generous or not strong is not tall and vice versa.
If someone is tall or brave then alice is generous or not curious and vice versa.
Everyone who is both not humble and not calm is not rich.
If paul is both not humble and rich then lucy is not generous or not brave and vice versa.
If mary is not curious then john is not old and vice versa.
Everyone who is either not wise or not humble is not strong or rich.
If someone is funny or not humble then fred is tall and vice versa.
Everyone who is both not kind and calm is both not funny and humble and vice versa.
Everyone who is creative or not curious is both not happy and not creative and vice versa.
Susan is either happy or kind.
Paul is both not generous and not funny.
Susan is both not happy and not tall.
Lucy is both patient and not wise.
Someone is either wise or kind.
Fred is not humble or generous.
Someone is either calm or not creative. | Fred is not rich. | neutral | (![X]:(happy(X)<=>(funny(X)|humble(X))))&
(![X]:((~brave(X)&quiet(X))=>(~brave(X)|wise(X))))&
(((quiet(lucy)<~>brave(lucy)))<=>(strong(susan)))&
(![X]:(curious(X)=>(generous(X)&curious(X))))&
((?[X]:((~quiet(X)&~patient(X))))<=>(old(lucy)))&
(((rich(paul)|kind(paul)))<=>(?[X]:((generous(X)|brave(X)))))&
((?[X]:((quiet(X)&~rich(X))))=>((creative(paul)|~calm(paul))))&
(![X]:((generous(X)<~>~strong(X))<=>~tall(X)))&
((?[X]:((tall(X)|brave(X))))<=>((generous(alice)|~curious(alice))))&
(![X]:((~humble(X)&~calm(X))=>~rich(X)))&
(((~humble(paul)&rich(paul)))<=>((~generous(lucy)|~brave(lucy))))&
((~curious(mary))<=>(~old(john)))&
(![X]:((~wise(X)<~>~humble(X))=>(~strong(X)|rich(X))))&
((?[X]:((funny(X)|~humble(X))))<=>(tall(fred)))&
(![X]:((~kind(X)&calm(X))<=>(~funny(X)&humble(X))))&
(![X]:((creative(X)|~curious(X))<=>(~happy(X)&~creative(X))))&
((happy(susan)<~>kind(susan)))&
((~generous(paul)&~funny(paul)))&
((~happy(susan)&~tall(susan)))&
((patient(lucy)&~wise(lucy)))&
(?[X]:((wise(X)<~>kind(X))))&
((~humble(fred)|generous(fred)))&
(?[X]:((calm(X)<~>~creative(X)))) | ~rich(fred) | [] | null | 0 |
If someone is not wise then someone is both not kind and not wise.
If susan is either not old or strong then alice is not generous.
If someone is creative or not creative then someone is not old or creative and vice versa.
If lucy is not happy then fred is either kind or curious and vice versa.
Everyone who is either not calm or happy is not funny or not brave and vice versa.
If someone is not rich or wise then alice is generous or humble.
If alice is either not wise or calm then alice is not strong.
If alice is curious or not patient then someone is either calm or kind.
Everyone who is both not kind and quiet is not happy and vice versa.
If john is both not strong and rich then someone is creative and vice versa.
If john is tall or humble then lucy is curious or rich and vice versa.
If fred is not curious or not wise then lucy is not old and vice versa.
Everyone who is either happy or not old is both kind and tall.
If lucy is kind or calm then someone is either brave or not brave and vice versa.
Everyone who is calm is both not calm and kind.
Everyone who is either old or not quiet is not humble and vice versa.
Someone is not strong or not quiet.
Someone is not strong or brave.
Paul is funny or rich.
Mary is either quiet or wise.
John is not happy or not curious.
Someone is generous.
Alice is not generous or not calm. | John is calm. | contradiction | ((?[X]:(~wise(X)))=>(?[X]:((~kind(X)&~wise(X)))))&
(((~old(susan)<~>strong(susan)))=>(~generous(alice)))&
((?[X]:((creative(X)|~creative(X))))<=>(?[X]:((~old(X)|creative(X)))))&
((~happy(lucy))<=>((kind(fred)<~>curious(fred))))&
(![X]:((~calm(X)<~>happy(X))<=>(~funny(X)|~brave(X))))&
((?[X]:((~rich(X)|wise(X))))=>((generous(alice)|humble(alice))))&
(((~wise(alice)<~>calm(alice)))=>(~strong(alice)))&
(((curious(alice)|~patient(alice)))=>(?[X]:((calm(X)<~>kind(X)))))&
(![X]:((~kind(X)&quiet(X))<=>~happy(X)))&
(((~strong(john)&rich(john)))<=>(?[X]:(creative(X))))&
(((tall(john)|humble(john)))<=>((curious(lucy)|rich(lucy))))&
(((~curious(fred)|~wise(fred)))<=>(~old(lucy)))&
(![X]:((happy(X)<~>~old(X))=>(kind(X)&tall(X))))&
(((kind(lucy)|calm(lucy)))<=>(?[X]:((brave(X)<~>~brave(X)))))&
(![X]:(calm(X)=>(~calm(X)&kind(X))))&
(![X]:((old(X)<~>~quiet(X))<=>~humble(X)))&
(?[X]:((~strong(X)|~quiet(X))))&
(?[X]:((~strong(X)|brave(X))))&
((funny(paul)|rich(paul)))&
((quiet(mary)<~>wise(mary)))&
((~happy(john)|~curious(john)))&
(?[X]:(generous(X)))&
((~generous(alice)|~calm(alice))) | calm(john) | [
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 768867040567258302133844
% SZS output start Proof for 768867040567258302133844
15. ! [X0] : (calm(X0) => (kind(X0) & ~calm(X0))) [input p14]
24. calm(john) [input hypothesis]
35. ! [X0] : ((kind(X0) & ~calm(X0)) | ~calm(X0)) [ennf transformation 15]
124. ~calm(X0) | ~calm(X0) [cnf transformation 35]
138. calm(john) [cnf transformation 24]
139. ~calm(X0) [duplicate literal removal 124]
350. $false [subsumption resolution 138,139]
% SZS output end Proof for 768867040567258302133844
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old and not generous is calm or creative and vice versa.
If susan is not brave then alice is not curious.
If someone is both not calm and happy then susan is either kind or wise and vice versa.
If someone is both not quiet and not calm then susan is both tall and not creative.
Everyone who is not patient is strong and vice versa.
Everyone who is either not kind or not strong is creative and vice versa.
Everyone who is both not quiet and not happy is creative or not rich.
If someone is either not humble or creative then fred is not calm or not humble and vice versa.
Everyone who is either calm or kind is both old and humble.
If someone is both kind and not calm then someone is not creative or generous and vice versa.
Everyone who is both kind and not kind is not tall.
Everyone who is calm is kind or wise and vice versa.
Everyone who is generous is both not rich and not old and vice versa.
Everyone who is not tall or tall is not rich and vice versa.
If paul is old then someone is both calm and patient.
If someone is either not wise or not generous then someone is not patient or not quiet and vice versa.
Someone is wise.
Someone is both curious and calm.
Someone is calm or not tall.
Someone is both creative and not brave.
Paul is either brave or wise.
Someone is both not strong and patient. | Susan is not generous. | entailment | (![X]:((old(X)&~generous(X))<=>(calm(X)|creative(X))))&
((~brave(susan))=>(~curious(alice)))&
((?[X]:((~calm(X)&happy(X))))<=>((kind(susan)<~>wise(susan))))&
((?[X]:((~quiet(X)&~calm(X))))=>((tall(susan)&~creative(susan))))&
(![X]:(~patient(X)<=>strong(X)))&
(![X]:((~kind(X)<~>~strong(X))<=>creative(X)))&
(![X]:((~quiet(X)&~happy(X))=>(creative(X)|~rich(X))))&
((?[X]:((~humble(X)<~>creative(X))))<=>((~calm(fred)|~humble(fred))))&
(![X]:((calm(X)<~>kind(X))=>(old(X)&humble(X))))&
((?[X]:((kind(X)&~calm(X))))<=>(?[X]:((~creative(X)|generous(X)))))&
(![X]:((kind(X)&~kind(X))=>~tall(X)))&
(![X]:(calm(X)<=>(kind(X)|wise(X))))&
(![X]:(generous(X)<=>(~rich(X)&~old(X))))&
(![X]:((~tall(X)|tall(X))<=>~rich(X)))&
((old(paul))=>(?[X]:((calm(X)&patient(X)))))&
((?[X]:((~wise(X)<~>~generous(X))))<=>(?[X]:((~patient(X)|~quiet(X)))))&
(?[X]:(wise(X)))&
(?[X]:((curious(X)&calm(X))))&
(?[X]:((calm(X)|~tall(X))))&
(?[X]:((creative(X)&~brave(X))))&
((brave(paul)<~>wise(paul)))&
(?[X]:((~strong(X)&patient(X)))) | ~generous(susan) | [
"p0",
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 297002626052876788803444
% SZS output start Proof for 297002626052876788803444
1. ! [X0] : ((~generous(X0) & old(X0)) <=> (creative(X0) | calm(X0))) [input p0]
10. ? [X0] : (~calm(X0) & kind(X0)) <=> ? [X0] : (generous(X0) | ~creative(X0)) [input p9]
12. ! [X0] : (calm(X0) <=> (wise(X0) | kind(X0))) [input p11]
23. generous(susan) [input hypothesis]
24. ? [X0] : (~calm(X0) & kind(X0)) <=> ? [X1] : (generous(X1) | ~creative(X1)) [rectify 10]
34. ! [X0] : (((~generous(X0) & old(X0)) | (~creative(X0) & ~calm(X0))) & ((creative(X0) | calm(X0)) | (generous(X0) | ~old(X0)))) [nnf transformation 1]
35. ! [X0] : (((~generous(X0) & old(X0)) | (~creative(X0) & ~calm(X0))) & (creative(X0) | calm(X0) | generous(X0) | ~old(X0))) [flattening 34]
48. (? [X0] : (~calm(X0) & kind(X0)) | ! [X1] : (~generous(X1) & creative(X1))) & (? [X1] : (generous(X1) | ~creative(X1)) | ! [X0] : (calm(X0) | ~kind(X0))) [nnf transformation 24]
49. (? [X0] : (~calm(X0) & kind(X0)) | ! [X1] : (~generous(X1) & creative(X1))) & (? [X2] : (generous(X2) | ~creative(X2)) | ! [X3] : (calm(X3) | ~kind(X3))) [rectify 48]
50. ? [X0] : (~calm(X0) & kind(X0)) => (~calm(sK2) & kind(sK2)) [choice axiom]
51. ? [X2] : (generous(X2) | ~creative(X2)) => (generous(sK3) | ~creative(sK3)) [choice axiom]
52. ((~calm(sK2) & kind(sK2)) | ! [X1] : (~generous(X1) & creative(X1))) & ((generous(sK3) | ~creative(sK3)) | ! [X3] : (calm(X3) | ~kind(X3))) [skolemisation 49,51,50]
53. ! [X0] : ((calm(X0) | (~wise(X0) & ~kind(X0))) & ((wise(X0) | kind(X0)) | ~calm(X0))) [nnf transformation 12]
54. ! [X0] : ((calm(X0) | (~wise(X0) & ~kind(X0))) & (wise(X0) | kind(X0) | ~calm(X0))) [flattening 53]
81. ~creative(X0) | ~generous(X0) [cnf transformation 35]
109. kind(sK2) | creative(X1) [cnf transformation 52]
111. ~calm(sK2) | creative(X1) [cnf transformation 52]
115. calm(X0) | ~kind(X0) [cnf transformation 54]
141. generous(susan) [cnf transformation 23]
219. 17 <=> ! [X1] : ~generous(X1) [avatar definition]
220. ~generous(X1) <- (17) [avatar component clause 219]
222. 18 <=> calm(sK2) [avatar definition]
224. ~calm(sK2) <- (~18) [avatar component clause 222]
227. 19 <=> ! [X1] : creative(X1) [avatar definition]
228. creative(X1) <- (19) [avatar component clause 227]
229. 19 | ~18 [avatar split clause 111,222,227]
231. 20 <=> kind(sK2) [avatar definition]
233. kind(sK2) <- (20) [avatar component clause 231]
235. 19 | 20 [avatar split clause 109,231,227]
238. 21 <=> ! [X3] : (calm(X3) | ~kind(X3)) [avatar definition]
239. ~kind(X3) | calm(X3) <- (21) [avatar component clause 238]
245. 21 [avatar split clause 115,238]
316. $false <- (17) [resolution 220,141]
317. ~17 [avatar contradiction clause 316]
327. ~generous(X0) <- (19) [resolution 81,228]
328. 17 | ~19 [avatar split clause 327,227,219]
354. calm(sK2) <- (20, 21) [resolution 239,233]
355. $false <- (~18, 20, 21) [subsumption resolution 354,224]
356. 18 | ~20 | ~21 [avatar contradiction clause 355]
357. $false [avatar sat refutation 229,235,245,317,328,356]
% SZS output end Proof for 297002626052876788803444
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall or rich is either rich or patient. Everyone who is funny is not patient or wise. If someone is funny or not quiet then someone is generous and vice versa. If someone is either not wise or old then someone is not creative or not quiet and vice versa. If someone is both wise and not generous then lucy is funny or happy. If someone is both not brave and quiet then paul is happy and vice versa. Everyone who is curious or not quiet is strong or not funny and vice versa. Everyone who is not humble or generous is both tall and not generous. If fred is either funny or quiet then someone is either not strong or happy. If susan is either funny or kind then someone is both not brave and brave and vice versa. Everyone who is both not humble and rich is not happy and vice versa. If someone is not old then alice is both not kind and old and vice versa. Everyone who is wise is creative or happy. Everyone who is not patient is rich or tall and vice versa. If susan is not calm or humble then someone is both not patient and not creative. If lucy is not quiet then someone is not tall or not quiet and vice versa. Someone is not patient. Someone is not happy. Lucy is not old. Someone is not wise. Someone is wise or not tall. John is creative or not funny. Someone is not old or happy. | Lucy is not happy. | contradiction | (![X]:((tall(X)|rich(X))=>(rich(X)<~>patient(X))))&
(![X]:(funny(X)=>(~patient(X)|wise(X))))&
((?[X]:((funny(X)|~quiet(X))))<=>(?[X]:(generous(X))))&
((?[X]:((~wise(X)<~>old(X))))<=>(?[X]:((~creative(X)|~quiet(X)))))&
((?[X]:((wise(X)&~generous(X))))=>((funny(lucy)|happy(lucy))))&
((?[X]:((~brave(X)&quiet(X))))<=>(happy(paul)))&
(![X]:((curious(X)|~quiet(X))<=>(strong(X)|~funny(X))))&
(![X]:((~humble(X)|generous(X))=>(tall(X)&~generous(X))))&
(((funny(fred)<~>quiet(fred)))=>(?[X]:((~strong(X)<~>happy(X)))))&
(((funny(susan)<~>kind(susan)))<=>(?[X]:((~brave(X)&brave(X)))))&
(![X]:((~humble(X)&rich(X))<=>~happy(X)))&
((?[X]:(~old(X)))<=>((~kind(alice)&old(alice))))&
(![X]:(wise(X)=>(creative(X)|happy(X))))&
(![X]:(~patient(X)<=>(rich(X)|tall(X))))&
(((~calm(susan)|humble(susan)))=>(?[X]:((~patient(X)&~creative(X)))))&
((~quiet(lucy))<=>(?[X]:((~tall(X)|~quiet(X)))))&
(?[X]:(~patient(X)))&
(?[X]:(~happy(X)))&
(~old(lucy))&
(?[X]:(~wise(X)))&
(?[X]:((wise(X)|~tall(X))))&
((creative(john)|~funny(john)))&
(?[X]:((~old(X)|happy(X)))) | ~happy(lucy) | [
"p2",
"p4",
"p7",
"p15",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 8714201254910598386563528
% SZS output start Proof for 8714201254910598386563528
3. ? [X0] : (~quiet(X0) | funny(X0)) <=> ? [X0] : generous(X0) [input p2]
5. ? [X0] : (~generous(X0) & wise(X0)) => (happy(lucy) | funny(lucy)) [input p4]
8. ! [X0] : ((generous(X0) | ~humble(X0)) => (~generous(X0) & tall(X0))) [input p7]
16. ~quiet(lucy) <=> ? [X0] : (~quiet(X0) | ~tall(X0)) [input p15]
21. ? [X0] : (~tall(X0) | wise(X0)) [input p20]
24. ~happy(lucy) [input hypothesis]
25. ? [X0] : (~quiet(X0) | funny(X0)) <=> ? [X1] : generous(X1) [rectify 3]
31. (happy(lucy) | funny(lucy)) | ! [X0] : (generous(X0) | ~wise(X0)) [ennf transformation 5]
32. happy(lucy) | funny(lucy) | ! [X0] : (generous(X0) | ~wise(X0)) [flattening 31]
33. ! [X0] : ((~generous(X0) & tall(X0)) | (~generous(X0) & humble(X0))) [ennf transformation 8]
39. (? [X0] : (~quiet(X0) | funny(X0)) | ! [X1] : ~generous(X1)) & (? [X1] : generous(X1) | ! [X0] : (quiet(X0) & ~funny(X0))) [nnf transformation 25]
40. (? [X0] : (~quiet(X0) | funny(X0)) | ! [X1] : ~generous(X1)) & (? [X2] : generous(X2) | ! [X3] : (quiet(X3) & ~funny(X3))) [rectify 39]
41. ? [X0] : (~quiet(X0) | funny(X0)) => (~quiet(sK0) | funny(sK0)) [choice axiom]
42. ? [X2] : generous(X2) => generous(sK1) [choice axiom]
43. ((~quiet(sK0) | funny(sK0)) | ! [X1] : ~generous(X1)) & (generous(sK1) | ! [X3] : (quiet(X3) & ~funny(X3))) [skolemisation 40,42,41]
73. (~quiet(lucy) | ! [X0] : (quiet(X0) & tall(X0))) & (? [X0] : (~quiet(X0) | ~tall(X0)) | quiet(lucy)) [nnf transformation 16]
74. (~quiet(lucy) | ! [X0] : (quiet(X0) & tall(X0))) & (? [X1] : (~quiet(X1) | ~tall(X1)) | quiet(lucy)) [rectify 73]
75. ? [X1] : (~quiet(X1) | ~tall(X1)) => (~quiet(sK9) | ~tall(sK9)) [choice axiom]
76. (~quiet(lucy) | ! [X0] : (quiet(X0) & tall(X0))) & ((~quiet(sK9) | ~tall(sK9)) | quiet(lucy)) [skolemisation 74,75]
83. ? [X0] : (~tall(X0) | wise(X0)) => (~tall(sK13) | wise(sK13)) [choice axiom]
84. ~tall(sK13) | wise(sK13) [skolemisation 21,83]
92. generous(sK1) | ~funny(X3) [cnf transformation 43]
93. generous(sK1) | quiet(X3) [cnf transformation 43]
101. happy(lucy) | funny(lucy) | generous(X0) | ~wise(X0) [cnf transformation 32]
112. ~generous(X0) | ~generous(X0) [cnf transformation 33]
136. ~quiet(lucy) | tall(X0) [cnf transformation 76]
142. ~tall(sK13) | wise(sK13) [cnf transformation 84]
145. ~happy(lucy) [cnf transformation 24]
146. ~generous(X0) [duplicate literal removal 112]
149. 1 <=> ! [X1] : ~generous(X1) [avatar definition]
150. ~generous(X1) <- (1) [avatar component clause 149]
161. 4 <=> ! [X3] : quiet(X3) [avatar definition]
162. quiet(X3) <- (4) [avatar component clause 161]
164. 5 <=> generous(sK1) [avatar definition]
166. generous(sK1) <- (5) [avatar component clause 164]
167. 4 | 5 [avatar split clause 93,164,161]
169. 6 <=> ! [X3] : ~funny(X3) [avatar definition]
170. ~funny(X3) <- (6) [avatar component clause 169]
171. 6 | 5 [avatar split clause 92,164,169]
204. 14 <=> ! [X0] : (generous(X0) | ~wise(X0)) [avatar definition]
205. ~wise(X0) | generous(X0) <- (14) [avatar component clause 204]
207. 15 <=> funny(lucy) [avatar definition]
209. funny(lucy) <- (15) [avatar component clause 207]
211. 16 <=> happy(lucy) [avatar definition]
214. 14 | 15 | 16 [avatar split clause 101,211,207,204]
233. 1 [avatar split clause 146,149]
304. 35 <=> quiet(lucy) [avatar definition]
306. ~quiet(lucy) <- (~35) [avatar component clause 304]
309. 36 <=> ! [X0] : tall(X0) [avatar definition]
310. tall(X0) <- (36) [avatar component clause 309]
311. 36 | ~35 [avatar split clause 136,304,309]
322. 39 <=> wise(sK13) [avatar definition]
324. wise(sK13) <- (39) [avatar component clause 322]
326. 40 <=> tall(sK13) [avatar definition]
328. ~tall(sK13) <- (~40) [avatar component clause 326]
329. 39 | ~40 [avatar split clause 142,326,322]
348. ~16 [avatar split clause 145,211]
349. $false <- (1, 5) [resolution 166,150]
350. ~1 | ~5 [avatar contradiction clause 349]
353. $false <- (4, ~35) [resolution 306,162]
354. ~4 | 35 [avatar contradiction clause 353]
357. $false <- (36, ~40) [resolution 328,310]
358. ~36 | 40 [avatar contradiction clause 357]
364. generous(sK13) <- (14, 39) [resolution 205,324]
365. $false <- (1, 14, 39) [subsumption resolution 364,150]
366. ~1 | ~14 | ~39 [avatar contradiction clause 365]
367. $false <- (6, 15) [subsumption resolution 209,170]
368. ~6 | ~15 [avatar contradiction clause 367]
369. $false [avatar sat refutation 167,171,214,233,311,329,348,350,354,358,366,368]
% SZS output end Proof for 8714201254910598386563528
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 someone is either quiet or not calm then mary is both brave and generous.
Everyone who is quiet is not brave and vice versa.
If susan is not curious or strong then susan is wise.
If someone is not brave then john is both not quiet and not generous.
If lucy is humble then someone is not curious or not creative and vice versa.
If john is not curious then mary is either humble or not funny and vice versa.
If someone is both not funny and not tall then someone is both quiet and not old and vice versa.
If someone is strong then someone is creative.
If someone is either not generous or not humble then mary is either not creative or curious.
If alice is both not generous and creative then someone is not calm or not patient.
If mary is not calm or strong then someone is both generous and wise.
Everyone who is both not old and patient is either brave or not rich and vice versa.
Everyone who is not strong or happy is either not kind or not humble and vice versa.
If fred is either quiet or strong then paul is not old.
Everyone who is creative or not wise is either quiet or not rich and vice versa.
If someone is both happy and kind then susan is rich.
Someone is rich or not funny.
Someone is either happy or wise.
Mary is either patient or wise.
Alice is both not strong and not kind.
Someone is not kind.
Susan is both not happy and humble.
Someone is either generous or not brave.
John is not tall. | John is not brave. | contradiction | ((?[X]:((quiet(X)<~>~calm(X))))=>((brave(mary)&generous(mary))))&
(![X]:(quiet(X)<=>~brave(X)))&
(((~curious(susan)|strong(susan)))=>(wise(susan)))&
((?[X]:(~brave(X)))=>((~quiet(john)&~generous(john))))&
((humble(lucy))<=>(?[X]:((~curious(X)|~creative(X)))))&
((~curious(john))<=>((humble(mary)<~>~funny(mary))))&
((?[X]:((~funny(X)&~tall(X))))<=>(?[X]:((quiet(X)&~old(X)))))&
((?[X]:(strong(X)))=>(?[X]:(creative(X))))&
((?[X]:((~generous(X)<~>~humble(X))))=>((~creative(mary)<~>curious(mary))))&
(((~generous(alice)&creative(alice)))=>(?[X]:((~calm(X)|~patient(X)))))&
(((~calm(mary)|strong(mary)))=>(?[X]:((generous(X)&wise(X)))))&
(![X]:((~old(X)&patient(X))<=>(brave(X)<~>~rich(X))))&
(![X]:((~strong(X)|happy(X))<=>(~kind(X)<~>~humble(X))))&
(((quiet(fred)<~>strong(fred)))=>(~old(paul)))&
(![X]:((creative(X)|~wise(X))<=>(quiet(X)<~>~rich(X))))&
((?[X]:((happy(X)&kind(X))))=>(rich(susan)))&
(?[X]:((rich(X)|~funny(X))))&
(?[X]:((happy(X)<~>wise(X))))&
((patient(mary)<~>wise(mary)))&
((~strong(alice)&~kind(alice)))&
(?[X]:(~kind(X)))&
((~happy(susan)&humble(susan)))&
(?[X]:((generous(X)<~>~brave(X))))&
(~tall(john)) | ~brave(john) | [
"p1",
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 4036651446448614512761294
% SZS output start Proof for 4036651446448614512761294
2. ! [X0] : (quiet(X0) <=> ~brave(X0)) [input p1]
4. ? [X0] : ~brave(X0) => (~generous(john) & ~quiet(john)) [input p3]
25. ~brave(john) [input hypothesis]
30. (~generous(john) & ~quiet(john)) | ! [X0] : brave(X0) [ennf transformation 4]
39. ! [X0] : ((quiet(X0) | brave(X0)) & (~brave(X0) | ~quiet(X0))) [nnf transformation 2]
81. brave(X0) | quiet(X0) [cnf transformation 39]
84. ~quiet(john) | brave(X0) [cnf transformation 30]
141. ~brave(john) [cnf transformation 25]
175. 8 <=> ! [X0] : brave(X0) [avatar definition]
176. brave(X0) <- (8) [avatar component clause 175]
183. 10 <=> quiet(john) [avatar definition]
186. 8 | ~10 [avatar split clause 84,183,175]
375. quiet(john) [resolution 81,141]
380. 10 [avatar split clause 375,183]
381. $false <- (8) [resolution 176,141]
385. ~8 [avatar contradiction clause 381]
386. $false [avatar sat refutation 186,380,385]
% SZS output end Proof for 4036651446448614512761294
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not curious and not brave then susan is both happy and funny and vice versa.
If susan is either calm or not wise then someone is either happy or brave.
Everyone who is both not brave and quiet is both brave and not tall.
If someone is both not funny and quiet then john is either not creative or happy.
If someone is both not calm and calm then susan is strong.
Everyone who is either not creative or patient is kind and vice versa.
Everyone who is not rich is both not rich and not creative and vice versa.
If lucy is either not humble or not quiet then fred is both not funny and not rich and vice versa.
Everyone who is both not humble and not happy is not creative.
If john is both quiet and not rich then someone is not quiet and vice versa.
Everyone who is not tall is either brave or patient.
Everyone who is humble or wise is not patient.
Everyone who is both not patient and not kind is either not rich or funny.
If alice is both strong and not generous then someone is either not quiet or tall.
If fred is both happy and funny then someone is funny or not wise.
If lucy is wise or patient then john is both humble and happy.
Mary is both rich and not patient.
Susan is old.
Fred is not creative or not brave.
Lucy is rich or not tall.
Alice is both wise and not kind.
Paul is either not rich or not creative.
Paul is both happy and not brave.
Alice is old. | John is brave. | entailment | ((?[X]:((~curious(X)&~brave(X))))<=>((happy(susan)&funny(susan))))&
(((calm(susan)<~>~wise(susan)))=>(?[X]:((happy(X)<~>brave(X)))))&
(![X]:((~brave(X)&quiet(X))=>(brave(X)&~tall(X))))&
((?[X]:((~funny(X)&quiet(X))))=>((~creative(john)<~>happy(john))))&
((?[X]:((~calm(X)&calm(X))))=>(strong(susan)))&
(![X]:((~creative(X)<~>patient(X))<=>kind(X)))&
(![X]:(~rich(X)<=>(~rich(X)&~creative(X))))&
(((~humble(lucy)<~>~quiet(lucy)))<=>((~funny(fred)&~rich(fred))))&
(![X]:((~humble(X)&~happy(X))=>~creative(X)))&
(((quiet(john)&~rich(john)))<=>(?[X]:(~quiet(X))))&
(![X]:(~tall(X)=>(brave(X)<~>patient(X))))&
(![X]:((humble(X)|wise(X))=>~patient(X)))&
(![X]:((~patient(X)&~kind(X))=>(~rich(X)<~>funny(X))))&
(((strong(alice)&~generous(alice)))=>(?[X]:((~quiet(X)<~>tall(X)))))&
(((happy(fred)&funny(fred)))=>(?[X]:((funny(X)|~wise(X)))))&
(((wise(lucy)|patient(lucy)))=>((humble(john)&happy(john))))&
((rich(mary)&~patient(mary)))&
(old(susan))&
((~creative(fred)|~brave(fred)))&
((rich(lucy)|~tall(lucy)))&
((wise(alice)&~kind(alice)))&
((~rich(paul)<~>~creative(paul)))&
((happy(paul)&~brave(paul)))&
(old(alice)) | brave(john) | [
"p2",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 311489383355524517774140
% SZS output start Proof for 311489383355524517774140
3. ! [X0] : ((quiet(X0) & ~brave(X0)) => (~tall(X0) & brave(X0))) [input p2]
10. (~rich(john) & quiet(john)) <=> ? [X0] : ~quiet(X0) [input p9]
25. ~brave(john) [input hypothesis]
31. ! [X0] : ((~tall(X0) & brave(X0)) | (~quiet(X0) | brave(X0))) [ennf transformation 3]
32. ! [X0] : ((~tall(X0) & brave(X0)) | ~quiet(X0) | brave(X0)) [flattening 31]
57. ((~rich(john) & quiet(john)) | ! [X0] : quiet(X0)) & (? [X0] : ~quiet(X0) | (rich(john) | ~quiet(john))) [nnf transformation 10]
58. ((~rich(john) & quiet(john)) | ! [X0] : quiet(X0)) & (? [X0] : ~quiet(X0) | rich(john) | ~quiet(john)) [flattening 57]
59. ((~rich(john) & quiet(john)) | ! [X0] : quiet(X0)) & (? [X1] : ~quiet(X1) | rich(john) | ~quiet(john)) [rectify 58]
60. ? [X1] : ~quiet(X1) => ~quiet(sK2) [choice axiom]
61. ((~rich(john) & quiet(john)) | ! [X0] : quiet(X0)) & (~quiet(sK2) | rich(john) | ~quiet(john)) [skolemisation 59,60]
75. brave(X0) | ~quiet(X0) | brave(X0) [cnf transformation 32]
94. quiet(john) | quiet(X0) [cnf transformation 61]
117. ~brave(john) [cnf transformation 25]
118. ~quiet(X0) | brave(X0) [duplicate literal removal 75]
198. 17 <=> ! [X0] : quiet(X0) [avatar definition]
199. quiet(X0) <- (17) [avatar component clause 198]
206. 19 <=> quiet(john) [avatar definition]
207. ~quiet(john) <- (~19) [avatar component clause 206]
208. quiet(john) <- (19) [avatar component clause 206]
209. 17 | 19 [avatar split clause 94,206,198]
269. brave(john) <- (19) [resolution 118,208]
270. $false <- (19) [subsumption resolution 269,117]
271. ~19 [avatar contradiction clause 270]
273. $false <- (17, ~19) [resolution 207,199]
274. ~17 | 19 [avatar contradiction clause 273]
275. $false [avatar sat refutation 209,271,274]
% SZS output end Proof for 311489383355524517774140
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not curious or quiet is not kind and vice versa.
Everyone who is either kind or tall is either wise or not humble and vice versa.
If susan is not strong then someone is either tall or not rich and vice versa.
Everyone who is both not strong and not patient is patient and vice versa.
Everyone who is either not brave or old is not happy or not strong.
If someone is not humble or humble then someone is both not happy and not calm.
Everyone who is both strong and not creative is either quiet or patient and vice versa.
Everyone who is not rich or not happy is curious and vice versa.
Everyone who is not strong is not tall or strong.
Everyone who is not curious or happy is not humble or old.
Everyone who is not tall is both not rich and kind and vice versa.
Everyone who is not strong is either wise or strong.
If someone is either quiet or old then someone is not kind or not curious.
If mary is either wise or not kind then someone is tall and vice versa.
If paul is not humble then lucy is not wise.
Everyone who is rich or not tall is both not strong and not rich and vice versa.
Fred is not happy or not rich.
Someone is not quiet or not happy.
Susan is either not patient or generous.
Susan is not humble or not strong.
Someone is either brave or not calm.
Someone is funny. | Fred is quiet. | entailment | (![X]:((~curious(X)<~>quiet(X))<=>~kind(X)))&
(![X]:((kind(X)<~>tall(X))<=>(wise(X)<~>~humble(X))))&
((~strong(susan))<=>(?[X]:((tall(X)<~>~rich(X)))))&
(![X]:((~strong(X)&~patient(X))<=>patient(X)))&
(![X]:((~brave(X)<~>old(X))=>(~happy(X)|~strong(X))))&
((?[X]:((~humble(X)|humble(X))))=>(?[X]:((~happy(X)&~calm(X)))))&
(![X]:((strong(X)&~creative(X))<=>(quiet(X)<~>patient(X))))&
(![X]:((~rich(X)|~happy(X))<=>curious(X)))&
(![X]:(~strong(X)=>(~tall(X)|strong(X))))&
(![X]:((~curious(X)|happy(X))=>(~humble(X)|old(X))))&
(![X]:(~tall(X)<=>(~rich(X)&kind(X))))&
(![X]:(~strong(X)=>(wise(X)<~>strong(X))))&
((?[X]:((quiet(X)<~>old(X))))=>(?[X]:((~kind(X)|~curious(X)))))&
(((wise(mary)<~>~kind(mary)))<=>(?[X]:(tall(X))))&
((~humble(paul))=>(~wise(lucy)))&
(![X]:((rich(X)|~tall(X))<=>(~strong(X)&~rich(X))))&
((~happy(fred)|~rich(fred)))&
(?[X]:((~quiet(X)|~happy(X))))&
((~patient(susan)<~>generous(susan)))&
((~humble(susan)|~strong(susan)))&
(?[X]:((brave(X)<~>~calm(X))))&
(?[X]:(funny(X))) | quiet(fred) | [
"p0",
"p3",
"p7",
"p10",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 5298357223723940270951527
% SZS output start Proof for 5298357223723940270951527
1. ! [X0] : ((~curious(X0) <~> quiet(X0)) <=> ~kind(X0)) [input p0]
4. ! [X0] : ((~patient(X0) & ~strong(X0)) <=> patient(X0)) [input p3]
8. ! [X0] : ((~happy(X0) | ~rich(X0)) <=> curious(X0)) [input p7]
11. ! [X0] : (~tall(X0) <=> (kind(X0) & ~rich(X0))) [input p10]
16. ! [X0] : ((~tall(X0) | rich(X0)) <=> (~rich(X0) & ~strong(X0))) [input p15]
23. ~quiet(fred) [input hypothesis]
37. ! [X0] : ((((~quiet(X0) | curious(X0)) & (quiet(X0) | ~curious(X0))) | kind(X0)) & (~kind(X0) | ((~curious(X0) | ~quiet(X0)) & (quiet(X0) | curious(X0))))) [nnf transformation 1]
43. ! [X0] : (((~patient(X0) & ~strong(X0)) | ~patient(X0)) & (patient(X0) | (patient(X0) | strong(X0)))) [nnf transformation 4]
44. ! [X0] : (((~patient(X0) & ~strong(X0)) | ~patient(X0)) & (patient(X0) | patient(X0) | strong(X0))) [flattening 43]
51. ! [X0] : (((~happy(X0) | ~rich(X0)) | ~curious(X0)) & (curious(X0) | (happy(X0) & rich(X0)))) [nnf transformation 8]
52. ! [X0] : ((~happy(X0) | ~rich(X0) | ~curious(X0)) & (curious(X0) | (happy(X0) & rich(X0)))) [flattening 51]
53. ! [X0] : ((~tall(X0) | (~kind(X0) | rich(X0))) & ((kind(X0) & ~rich(X0)) | tall(X0))) [nnf transformation 11]
54. ! [X0] : ((~tall(X0) | ~kind(X0) | rich(X0)) & ((kind(X0) & ~rich(X0)) | tall(X0))) [flattening 53]
64. ! [X0] : (((~tall(X0) | rich(X0)) | (rich(X0) | strong(X0))) & ((~rich(X0) & ~strong(X0)) | (tall(X0) & ~rich(X0)))) [nnf transformation 16]
65. ! [X0] : ((~tall(X0) | rich(X0) | rich(X0) | strong(X0)) & ((~rich(X0) & ~strong(X0)) | (tall(X0) & ~rich(X0)))) [flattening 64]
74. ~curious(X0) | quiet(X0) | kind(X0) [cnf transformation 37]
88. patient(X0) | patient(X0) | strong(X0) [cnf transformation 44]
90. ~patient(X0) | ~patient(X0) [cnf transformation 44]
103. rich(X0) | curious(X0) [cnf transformation 52]
111. ~tall(X0) | ~kind(X0) | rich(X0) [cnf transformation 54]
122. ~strong(X0) | tall(X0) [cnf transformation 65]
123. ~rich(X0) | ~rich(X0) [cnf transformation 65]
133. ~quiet(fred) [cnf transformation 23]
134. ~rich(X0) [duplicate literal removal 123]
138. patient(X0) | strong(X0) [duplicate literal removal 88]
139. ~patient(X0) [duplicate literal removal 90]
162. strong(X0) [subsumption resolution 138,139]
230. tall(X0) [subsumption resolution 122,162]
258. curious(X0) [resolution 103,134]
263. kind(X0) | quiet(X0) [resolution 74,258]
274. ~kind(X1) | rich(X1) [resolution 111,230]
275. ~kind(X1) [subsumption resolution 274,134]
276. quiet(X0) [resolution 275,263]
278. $false [resolution 276,133]
% SZS output end Proof for 5298357223723940270951527
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative is old and vice versa. If paul is wise or not happy then mary is not curious or quiet and vice versa. If mary is either old or tall then alice is not rich. If mary is either curious or not wise then someone is happy or not happy and vice versa. Everyone who is both not patient and not tall is both calm and not quiet. Everyone who is both not calm and kind is not kind or brave and vice versa. Everyone who is either not humble or happy is either curious or brave. If john is tall or not patient then someone is not brave or kind and vice versa. If someone is both not kind and funny then john is both not funny and kind and vice versa. Everyone who is tall or not humble is both humble and not curious and vice versa. Everyone who is either kind or humble is not brave. Everyone who is not calm is both not wise and not creative. If someone is not funny or not quiet then lucy is not humble or patient and vice versa. Everyone who is either not old or calm is both humble and not happy. If someone is both not happy and not old then paul is either brave or not strong. If john is either not patient or generous then someone is both not tall and kind. John is rich. Someone is both not happy and curious. Susan is either humble or brave. Someone is not curious or tall. Mary is not generous. Alice is either wise or strong. | Paul is not generous. | neutral | (![X]:(creative(X)<=>old(X)))&
(((wise(paul)|~happy(paul)))<=>((~curious(mary)|quiet(mary))))&
(((old(mary)<~>tall(mary)))=>(~rich(alice)))&
(((curious(mary)<~>~wise(mary)))<=>(?[X]:((happy(X)|~happy(X)))))&
(![X]:((~patient(X)&~tall(X))=>(calm(X)&~quiet(X))))&
(![X]:((~calm(X)&kind(X))<=>(~kind(X)|brave(X))))&
(![X]:((~humble(X)<~>happy(X))=>(curious(X)<~>brave(X))))&
(((tall(john)|~patient(john)))<=>(?[X]:((~brave(X)|kind(X)))))&
((?[X]:((~kind(X)&funny(X))))<=>((~funny(john)&kind(john))))&
(![X]:((tall(X)|~humble(X))<=>(humble(X)&~curious(X))))&
(![X]:((kind(X)<~>humble(X))=>~brave(X)))&
(![X]:(~calm(X)=>(~wise(X)&~creative(X))))&
((?[X]:((~funny(X)|~quiet(X))))<=>((~humble(lucy)|patient(lucy))))&
(![X]:((~old(X)<~>calm(X))=>(humble(X)&~happy(X))))&
((?[X]:((~happy(X)&~old(X))))=>((brave(paul)<~>~strong(paul))))&
(((~patient(john)<~>generous(john)))=>(?[X]:((~tall(X)&kind(X)))))&
(rich(john))&
(?[X]:((~happy(X)&curious(X))))&
((humble(susan)<~>brave(susan)))&
(?[X]:((~curious(X)|tall(X))))&
(~generous(mary))&
((wise(alice)<~>strong(alice))) | ~generous(paul) | [] | null | 0 |
If someone is not brave then someone is tall and vice versa.
Everyone who is not calm is both not kind and patient and vice versa.
Everyone who is either generous or happy is patient or not happy and vice versa.
If mary is patient or not creative then lucy is wise and vice versa.
Everyone who is both brave and old is not old or funny and vice versa.
Everyone who is both creative and not creative is patient or strong and vice versa.
Everyone who is calm or happy is generous.
If someone is not strong then john is not calm or not quiet.
If paul is both not generous and wise then mary is both wise and old and vice versa.
Everyone who is patient is either strong or not generous and vice versa.
If someone is both not generous and not strong then someone is not kind.
If someone is either not wise or humble then someone is kind and vice versa.
Everyone who is either not brave or not creative is both rich and not creative and vice versa.
Everyone who is brave or not funny is either calm or not brave.
Alice is not humble or old.
Someone is rich.
Someone is both generous and old.
Someone is happy.
Lucy is either not happy or creative. | Lucy is not strong. | entailment | ((?[X]:(~brave(X)))<=>(?[X]:(tall(X))))&
(![X]:(~calm(X)<=>(~kind(X)&patient(X))))&
(![X]:((generous(X)<~>happy(X))<=>(patient(X)|~happy(X))))&
(((patient(mary)|~creative(mary)))<=>(wise(lucy)))&
(![X]:((brave(X)&old(X))<=>(~old(X)|funny(X))))&
(![X]:((creative(X)&~creative(X))<=>(patient(X)|strong(X))))&
(![X]:((calm(X)|happy(X))=>generous(X)))&
((?[X]:(~strong(X)))=>((~calm(john)|~quiet(john))))&
(((~generous(paul)&wise(paul)))<=>((wise(mary)&old(mary))))&
(![X]:(patient(X)<=>(strong(X)<~>~generous(X))))&
((?[X]:((~generous(X)&~strong(X))))=>(?[X]:(~kind(X))))&
((?[X]:((~wise(X)<~>humble(X))))<=>(?[X]:(kind(X))))&
(![X]:((~brave(X)<~>~creative(X))<=>(rich(X)&~creative(X))))&
(![X]:((brave(X)|~funny(X))=>(calm(X)<~>~brave(X))))&
((~humble(alice)|old(alice)))&
(?[X]:(rich(X)))&
(?[X]:((generous(X)&old(X))))&
(?[X]:(happy(X)))&
((~happy(lucy)<~>creative(lucy))) | ~strong(lucy) | [
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 2456155514892133470557005
% SZS output start Proof for 2456155514892133470557005
6. ! [X0] : ((~creative(X0) & creative(X0)) <=> (strong(X0) | patient(X0))) [input p5]
20. strong(lucy) [input hypothesis]
41. ! [X0] : (((~creative(X0) & creative(X0)) | (~strong(X0) & ~patient(X0))) & ((strong(X0) | patient(X0)) | (creative(X0) | ~creative(X0)))) [nnf transformation 6]
42. ! [X0] : (((~creative(X0) & creative(X0)) | (~strong(X0) & ~patient(X0))) & (strong(X0) | patient(X0) | creative(X0) | ~creative(X0))) [flattening 41]
85. creative(X0) | ~strong(X0) [cnf transformation 42]
87. ~creative(X0) | ~strong(X0) [cnf transformation 42]
120. strong(lucy) [cnf transformation 20]
161. ~strong(X0) [subsumption resolution 85,87]
213. $false [subsumption resolution 120,161]
% SZS output end Proof for 2456155514892133470557005
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.018 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both rich and happy then someone is not brave and vice versa. If someone is either creative or brave then lucy is both not quiet and tall and vice versa. If someone is calm or not tall then john is both brave and tall and vice versa. Everyone who is rich or not old is both not curious and not wise and vice versa. Everyone who is both not kind and not strong is either kind or not funny. Everyone who is not happy is brave. Everyone who is happy is not humble and vice versa. Everyone who is both not wise and generous is not calm. Everyone who is brave or rich is not patient or happy and vice versa. If someone is kind then paul is both not funny and not strong and vice versa. If lucy is calm or kind then someone is old or creative. Everyone who is strong or kind is not kind or not generous and vice versa. Everyone who is not wise is either not curious or not creative. Everyone who is both not curious and wise is not wise or not funny and vice versa. If someone is quiet or not kind then lucy is not generous or not wise and vice versa. Everyone who is either not strong or not patient is either not wise or not humble. Someone is either strong or calm. Mary is humble. Someone is both curious and not rich. Someone is both happy and curious. John is happy. Someone is not humble. Mary is creative or funny. | Mary is old. | entailment | ((?[X]:((rich(X)&happy(X))))<=>(?[X]:(~brave(X))))&
((?[X]:((creative(X)<~>brave(X))))<=>((~quiet(lucy)&tall(lucy))))&
((?[X]:((calm(X)|~tall(X))))<=>((brave(john)&tall(john))))&
(![X]:((rich(X)|~old(X))<=>(~curious(X)&~wise(X))))&
(![X]:((~kind(X)&~strong(X))=>(kind(X)<~>~funny(X))))&
(![X]:(~happy(X)=>brave(X)))&
(![X]:(happy(X)<=>~humble(X)))&
(![X]:((~wise(X)&generous(X))=>~calm(X)))&
(![X]:((brave(X)|rich(X))<=>(~patient(X)|happy(X))))&
((?[X]:(kind(X)))<=>((~funny(paul)&~strong(paul))))&
(((calm(lucy)|kind(lucy)))=>(?[X]:((old(X)|creative(X)))))&
(![X]:((strong(X)|kind(X))<=>(~kind(X)|~generous(X))))&
(![X]:(~wise(X)=>(~curious(X)<~>~creative(X))))&
(![X]:((~curious(X)&wise(X))<=>(~wise(X)|~funny(X))))&
((?[X]:((quiet(X)|~kind(X))))<=>((~generous(lucy)|~wise(lucy))))&
(![X]:((~strong(X)<~>~patient(X))=>(~wise(X)<~>~humble(X))))&
(?[X]:((strong(X)<~>calm(X))))&
(humble(mary))&
(?[X]:((curious(X)&~rich(X))))&
(?[X]:((happy(X)&curious(X))))&
(happy(john))&
(?[X]:(~humble(X)))&
((creative(mary)|funny(mary))) | old(mary) | [
"p3",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 3486727963325583183195145
% SZS output start Proof for 3486727963325583183195145
4. ! [X0] : ((~old(X0) | rich(X0)) <=> (~wise(X0) & ~curious(X0))) [input p3]
14. ! [X0] : ((wise(X0) & ~curious(X0)) <=> (~funny(X0) | ~wise(X0))) [input p13]
24. ~old(mary) [input hypothesis]
49. ! [X0] : (((~old(X0) | rich(X0)) | (wise(X0) | curious(X0))) & ((~wise(X0) & ~curious(X0)) | (old(X0) & ~rich(X0)))) [nnf transformation 4]
50. ! [X0] : ((~old(X0) | rich(X0) | wise(X0) | curious(X0)) & ((~wise(X0) & ~curious(X0)) | (old(X0) & ~rich(X0)))) [flattening 49]
65. ! [X0] : (((wise(X0) & ~curious(X0)) | (funny(X0) & wise(X0))) & ((~funny(X0) | ~wise(X0)) | (~wise(X0) | curious(X0)))) [nnf transformation 14]
66. ! [X0] : (((wise(X0) & ~curious(X0)) | (funny(X0) & wise(X0))) & (~funny(X0) | ~wise(X0) | ~wise(X0) | curious(X0))) [flattening 65]
99. ~wise(X0) | old(X0) [cnf transformation 50]
125. wise(X0) | wise(X0) [cnf transformation 66]
145. ~old(mary) [cnf transformation 24]
147. wise(X0) [duplicate literal removal 125]
315. old(X0) [resolution 99,147]
322. $false [resolution 315,145]
% SZS output end Proof for 3486727963325583183195145
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or not creative is not funny and vice versa. If someone is either happy or not rich then paul is either funny or not curious and vice versa. Everyone who is both strong and not brave is both not rich and humble. If lucy is both rich and calm then someone is either not tall or quiet. Everyone who is both calm and strong is rich. Everyone who is brave or not creative is old and vice versa. If susan is kind then someone is tall. If alice is patient or not funny then someone is not old and vice versa. Everyone who is not funny or not curious is not generous. Everyone who is not old or rich is both not brave and not tall and vice versa. If someone is either not funny or old then someone is either brave or not rich. If alice is either strong or brave then fred is not funny and vice versa. If paul is either not tall or not brave then fred is generous or happy and vice versa. Everyone who is not old is both wise and not creative and vice versa. Everyone who is not curious is not happy or funny. If susan is both not humble and tall then fred is not humble and vice versa. Someone is either kind or wise. Someone is both funny and not humble. Someone is not quiet or patient. Someone is either curious or funny. Someone is both brave and not rich. Someone is funny or not patient. Someone is not rich or creative. Fred is either happy or not wise. | Fred is not generous. | entailment | (![X]:((curious(X)|~creative(X))<=>~funny(X)))&
((?[X]:((happy(X)<~>~rich(X))))<=>((funny(paul)<~>~curious(paul))))&
(![X]:((strong(X)&~brave(X))=>(~rich(X)&humble(X))))&
(((rich(lucy)&calm(lucy)))=>(?[X]:((~tall(X)<~>quiet(X)))))&
(![X]:((calm(X)&strong(X))=>rich(X)))&
(![X]:((brave(X)|~creative(X))<=>old(X)))&
((kind(susan))=>(?[X]:(tall(X))))&
(((patient(alice)|~funny(alice)))<=>(?[X]:(~old(X))))&
(![X]:((~funny(X)|~curious(X))=>~generous(X)))&
(![X]:((~old(X)|rich(X))<=>(~brave(X)&~tall(X))))&
((?[X]:((~funny(X)<~>old(X))))=>(?[X]:((brave(X)<~>~rich(X)))))&
(((strong(alice)<~>brave(alice)))<=>(~funny(fred)))&
(((~tall(paul)<~>~brave(paul)))<=>((generous(fred)|happy(fred))))&
(![X]:(~old(X)<=>(wise(X)&~creative(X))))&
(![X]:(~curious(X)=>(~happy(X)|funny(X))))&
(((~humble(susan)&tall(susan)))<=>(~humble(fred)))&
(?[X]:((kind(X)<~>wise(X))))&
(?[X]:((funny(X)&~humble(X))))&
(?[X]:((~quiet(X)|patient(X))))&
(?[X]:((curious(X)<~>funny(X))))&
(?[X]:((brave(X)&~rich(X))))&
(?[X]:((funny(X)|~patient(X))))&
(?[X]:((~rich(X)|creative(X))))&
((happy(fred)<~>~wise(fred))) | ~generous(fred) | [
"p0",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 2284007851267492522622092
% SZS output start Proof for 2284007851267492522622092
1. ! [X0] : ((~creative(X0) | curious(X0)) <=> ~funny(X0)) [input p0]
9. ! [X0] : ((~curious(X0) | ~funny(X0)) => ~generous(X0)) [input p8]
25. generous(fred) [input hypothesis]
33. ! [X0] : (~generous(X0) | (curious(X0) & funny(X0))) [ennf transformation 9]
37. ! [X0] : (((~creative(X0) | curious(X0)) | funny(X0)) & (~funny(X0) | (creative(X0) & ~curious(X0)))) [nnf transformation 1]
38. ! [X0] : ((~creative(X0) | curious(X0) | funny(X0)) & (~funny(X0) | (creative(X0) & ~curious(X0)))) [flattening 37]
80. ~funny(X0) | ~curious(X0) [cnf transformation 38]
100. ~generous(X0) | funny(X0) [cnf transformation 33]
101. ~generous(X0) | curious(X0) [cnf transformation 33]
140. generous(fred) [cnf transformation 25]
223. 17 <=> funny(fred) [avatar definition]
225. funny(fred) <- (17) [avatar component clause 223]
252. 23 <=> generous(fred) [avatar definition]
253. generous(fred) <- (23) [avatar component clause 252]
321. 23 [avatar split clause 140,252]
326. ~curious(fred) <- (17) [resolution 80,225]
331. funny(fred) <- (23) [resolution 100,253]
332. curious(fred) <- (23) [resolution 101,253]
333. $false <- (17, 23) [subsumption resolution 332,326]
334. ~17 | ~23 [avatar contradiction clause 333]
335. 17 | ~23 [avatar split clause 331,252,223]
336. $false [avatar sat refutation 321,334,335]
% SZS output end Proof for 2284007851267492522622092
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not brave is not wise.
Everyone who is both creative and not old is not tall and vice versa.
Everyone who is not rich or brave is not calm or old.
Everyone who is both not strong and curious is not rich or humble and vice versa.
Everyone who is either kind or not curious is either brave or curious.
If fred is both tall and old then someone is either quiet or funny and vice versa.
Everyone who is either not tall or quiet is not strong or creative and vice versa.
Everyone who is both humble and not happy is calm or humble and vice versa.
If someone is curious or not wise then someone is both patient and not humble and vice versa.
If someone is both patient and happy then john is both not rich and calm and vice versa.
Everyone who is not rich is both humble and calm and vice versa.
If someone is not humble then someone is wise or tall.
If someone is not wise then lucy is happy and vice versa.
Everyone who is creative or tall is either not rich or not strong.
Everyone who is not funny or not rich is either not generous or rich and vice versa.
If fred is not patient then john is both strong and not funny.
Someone is not brave or patient.
Someone is funny or tall.
Paul is not strong.
Mary is either not rich or not old.
Someone is brave or calm.
John is not brave or not patient. | Mary is not strong. | entailment | (![X]:(~brave(X)=>~wise(X)))&
(![X]:((creative(X)&~old(X))<=>~tall(X)))&
(![X]:((~rich(X)|brave(X))=>(~calm(X)|old(X))))&
(![X]:((~strong(X)&curious(X))<=>(~rich(X)|humble(X))))&
(![X]:((kind(X)<~>~curious(X))=>(brave(X)<~>curious(X))))&
(((tall(fred)&old(fred)))<=>(?[X]:((quiet(X)<~>funny(X)))))&
(![X]:((~tall(X)<~>quiet(X))<=>(~strong(X)|creative(X))))&
(![X]:((humble(X)&~happy(X))<=>(calm(X)|humble(X))))&
((?[X]:((curious(X)|~wise(X))))<=>(?[X]:((patient(X)&~humble(X)))))&
((?[X]:((patient(X)&happy(X))))<=>((~rich(john)&calm(john))))&
(![X]:(~rich(X)<=>(humble(X)&calm(X))))&
((?[X]:(~humble(X)))=>(?[X]:((wise(X)|tall(X)))))&
((?[X]:(~wise(X)))<=>(happy(lucy)))&
(![X]:((creative(X)|tall(X))=>(~rich(X)<~>~strong(X))))&
(![X]:((~funny(X)|~rich(X))<=>(~generous(X)<~>rich(X))))&
((~patient(fred))=>((strong(john)&~funny(john))))&
(?[X]:((~brave(X)|patient(X))))&
(?[X]:((funny(X)|tall(X))))&
(~strong(paul))&
((~rich(mary)<~>~old(mary)))&
(?[X]:((brave(X)|calm(X))))&
((~brave(john)|~patient(john))) | ~strong(mary) | [
"p1",
"p3",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 7376705552709942716306382
% SZS output start Proof for 7376705552709942716306382
2. ! [X0] : ((~old(X0) & creative(X0)) <=> ~tall(X0)) [input p1]
4. ! [X0] : ((curious(X0) & ~strong(X0)) <=> (humble(X0) | ~rich(X0))) [input p3]
14. ! [X0] : ((tall(X0) | creative(X0)) => (~rich(X0) <~> ~strong(X0))) [input p13]
23. strong(mary) [input hypothesis]
31. ! [X0] : ((~rich(X0) <~> ~strong(X0)) | (~tall(X0) & ~creative(X0))) [ennf transformation 14]
33. ! [X0] : (((~old(X0) & creative(X0)) | tall(X0)) & (~tall(X0) | (old(X0) | ~creative(X0)))) [nnf transformation 2]
34. ! [X0] : (((~old(X0) & creative(X0)) | tall(X0)) & (~tall(X0) | old(X0) | ~creative(X0))) [flattening 33]
35. ! [X0] : (((curious(X0) & ~strong(X0)) | (~humble(X0) & rich(X0))) & ((humble(X0) | ~rich(X0)) | (~curious(X0) | strong(X0)))) [nnf transformation 4]
36. ! [X0] : (((curious(X0) & ~strong(X0)) | (~humble(X0) & rich(X0))) & (humble(X0) | ~rich(X0) | ~curious(X0) | strong(X0))) [flattening 35]
66. ! [X0] : (((strong(X0) | rich(X0)) & (~strong(X0) | ~rich(X0))) | (~tall(X0) & ~creative(X0))) [nnf transformation 31]
78. tall(X0) | creative(X0) [cnf transformation 34]
83. ~strong(X0) | rich(X0) [cnf transformation 36]
123. ~strong(X0) | ~rich(X0) | ~creative(X0) [cnf transformation 66]
124. ~strong(X0) | ~rich(X0) | ~tall(X0) [cnf transformation 66]
125. strong(X0) | rich(X0) | ~creative(X0) [cnf transformation 66]
142. strong(mary) [cnf transformation 23]
256. ~creative(X0) | rich(X0) [subsumption resolution 125,83]
257. ~strong(X0) | ~tall(X0) [subsumption resolution 124,83]
258. ~strong(X0) | ~creative(X0) [subsumption resolution 123,256]
373. ~tall(mary) [resolution 257,142]
374. ~creative(mary) [resolution 258,142]
387. creative(mary) [resolution 373,78]
388. $false [subsumption resolution 387,374]
% SZS output end Proof for 7376705552709942716306382
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is calm or not old is either not humble or strong.
Everyone who is not old or humble is quiet and vice versa.
Everyone who is funny or tall is both not tall and kind.
If someone is both not rich and not wise then alice is curious or not generous and vice versa.
Everyone who is both creative and patient is both patient and not curious.
Everyone who is both happy and creative is curious and vice versa.
If paul is funny or not brave then someone is both creative and not wise.
Everyone who is not funny is either not creative or humble and vice versa.
If susan is rich or not curious then someone is both not tall and not rich.
If mary is either not brave or humble then alice is old and vice versa.
If alice is either old or creative then someone is not quiet and vice versa.
Everyone who is not funny or patient is not calm and vice versa.
Everyone who is both not old and not creative is not tall and vice versa.
Everyone who is not rich is either old or humble.
Everyone who is creative or generous is either not brave or funny.
Someone is either rich or wise.
Someone is humble or not curious.
Lucy is either not generous or not rich.
Lucy is not generous or not tall.
Someone is calm or not curious.
Someone is kind.
Someone is either not quiet or not brave. | Mary is not creative. | entailment | (![X]:((calm(X)|~old(X))=>(~humble(X)<~>strong(X))))&
(![X]:((~old(X)|humble(X))<=>quiet(X)))&
(![X]:((funny(X)|tall(X))=>(~tall(X)&kind(X))))&
((?[X]:((~rich(X)&~wise(X))))<=>((curious(alice)|~generous(alice))))&
(![X]:((creative(X)&patient(X))=>(patient(X)&~curious(X))))&
(![X]:((happy(X)&creative(X))<=>curious(X)))&
(((funny(paul)|~brave(paul)))=>(?[X]:((creative(X)&~wise(X)))))&
(![X]:(~funny(X)<=>(~creative(X)<~>humble(X))))&
(((rich(susan)|~curious(susan)))=>(?[X]:((~tall(X)&~rich(X)))))&
(((~brave(mary)<~>humble(mary)))<=>(old(alice)))&
(((old(alice)<~>creative(alice)))<=>(?[X]:(~quiet(X))))&
(![X]:((~funny(X)|patient(X))<=>~calm(X)))&
(![X]:((~old(X)&~creative(X))<=>~tall(X)))&
(![X]:(~rich(X)=>(old(X)<~>humble(X))))&
(![X]:((creative(X)|generous(X))=>(~brave(X)<~>funny(X))))&
(?[X]:((rich(X)<~>wise(X))))&
(?[X]:((humble(X)|~curious(X))))&
((~generous(lucy)<~>~rich(lucy)))&
((~generous(lucy)|~tall(lucy)))&
(?[X]:((calm(X)|~curious(X))))&
(?[X]:(kind(X)))&
(?[X]:((~quiet(X)<~>~brave(X)))) | ~creative(mary) | [
"p2",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 1257255104561647997742564
% SZS output start Proof for 1257255104561647997742564
3. ! [X0] : ((tall(X0) | funny(X0)) => (kind(X0) & ~tall(X0))) [input p2]
13. ! [X0] : ((~creative(X0) & ~old(X0)) <=> ~tall(X0)) [input p12]
23. creative(mary) [input hypothesis]
24. ! [X0] : (~tall(X0) => (~creative(X0) & ~old(X0))) [unused predicate definition removal 13]
26. ! [X0] : ((tall(X0) | funny(X0)) => ~tall(X0)) [pure predicate removal 3]
28. ! [X0] : (~tall(X0) | (~tall(X0) & ~funny(X0))) [ennf transformation 26]
33. ! [X0] : ((~creative(X0) & ~old(X0)) | tall(X0)) [ennf transformation 24]
79. ~tall(X0) | ~tall(X0) [cnf transformation 28]
114. ~creative(X0) | tall(X0) [cnf transformation 33]
130. creative(mary) [cnf transformation 23]
131. ~tall(X0) [duplicate literal removal 79]
221. ~creative(X0) [subsumption resolution 114,131]
272. $false [subsumption resolution 130,221]
% SZS output end Proof for 1257255104561647997742564
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not quiet or kind is both not humble and not happy.
Everyone who is rich or creative is both generous and not quiet and vice versa.
If someone is either patient or creative then alice is both generous and not patient.
If paul is either not old or not tall then paul is both not wise and not calm and vice versa.
If someone is humble then someone is brave or not strong and vice versa.
If mary is strong then someone is either not tall or not funny and vice versa.
If john is either not humble or wise then paul is strong or not creative.
Everyone who is rich or not kind is rich or not wise.
Everyone who is either curious or not calm is both not brave and not patient and vice versa.
Everyone who is not happy or funny is kind.
Everyone who is both not strong and brave is not old or not calm and vice versa.
If someone is not kind or not patient then someone is not rich.
If someone is not tall or quiet then someone is either not rich or patient and vice versa.
Everyone who is rich or not rich is both curious and generous.
Everyone who is either not happy or not quiet is kind and vice versa.
Everyone who is quiet or not humble is not kind.
John is quiet.
Someone is either patient or not old.
Lucy is either not strong or patient.
Fred is not brave or patient.
Mary is not rich or not calm.
Someone is not patient or not kind.
Someone is not patient or not tall.
Someone is either rich or brave. | John is not generous. | contradiction | (![X]:((~quiet(X)<~>kind(X))=>(~humble(X)&~happy(X))))&
(![X]:((rich(X)|creative(X))<=>(generous(X)&~quiet(X))))&
((?[X]:((patient(X)<~>creative(X))))=>((generous(alice)&~patient(alice))))&
(((~old(paul)<~>~tall(paul)))<=>((~wise(paul)&~calm(paul))))&
((?[X]:(humble(X)))<=>(?[X]:((brave(X)|~strong(X)))))&
((strong(mary))<=>(?[X]:((~tall(X)<~>~funny(X)))))&
(((~humble(john)<~>wise(john)))=>((strong(paul)|~creative(paul))))&
(![X]:((rich(X)|~kind(X))=>(rich(X)|~wise(X))))&
(![X]:((curious(X)<~>~calm(X))<=>(~brave(X)&~patient(X))))&
(![X]:((~happy(X)|funny(X))=>kind(X)))&
(![X]:((~strong(X)&brave(X))<=>(~old(X)|~calm(X))))&
((?[X]:((~kind(X)|~patient(X))))=>(?[X]:(~rich(X))))&
((?[X]:((~tall(X)|quiet(X))))<=>(?[X]:((~rich(X)<~>patient(X)))))&
(![X]:((rich(X)|~rich(X))=>(curious(X)&generous(X))))&
(![X]:((~happy(X)<~>~quiet(X))<=>kind(X)))&
(![X]:((quiet(X)|~humble(X))=>~kind(X)))&
(quiet(john))&
(?[X]:((patient(X)<~>~old(X))))&
((~strong(lucy)<~>patient(lucy)))&
((~brave(fred)|patient(fred)))&
((~rich(mary)|~calm(mary)))&
(?[X]:((~patient(X)|~kind(X))))&
(?[X]:((~patient(X)|~tall(X))))&
(?[X]:((rich(X)<~>brave(X)))) | ~generous(john) | [
"p1",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 4878942763388742518306348
% SZS output start Proof for 4878942763388742518306348
2. ! [X0] : ((creative(X0) | rich(X0)) <=> (~quiet(X0) & generous(X0))) [input p1]
14. ! [X0] : ((~rich(X0) | rich(X0)) => (generous(X0) & curious(X0))) [input p13]
25. ~generous(john) [input hypothesis]
37. ! [X0] : ((generous(X0) & curious(X0)) | (rich(X0) & ~rich(X0))) [ennf transformation 14]
40. ! [X0] : (((creative(X0) | rich(X0)) | (quiet(X0) | ~generous(X0))) & ((~quiet(X0) & generous(X0)) | (~creative(X0) & ~rich(X0)))) [nnf transformation 2]
41. ! [X0] : ((creative(X0) | rich(X0) | quiet(X0) | ~generous(X0)) & ((~quiet(X0) & generous(X0)) | (~creative(X0) & ~rich(X0)))) [flattening 40]
83. generous(X0) | ~rich(X0) [cnf transformation 41]
133. generous(X0) | rich(X0) [cnf transformation 37]
151. ~generous(john) [cnf transformation 25]
302. generous(X0) [subsumption resolution 133,83]
371. $false [subsumption resolution 151,302]
% SZS output end Proof for 4878942763388742518306348
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise is both not wise and creative and vice versa.
If susan is kind then john is both tall and wise and vice versa.
Everyone who is wise is tall or wise.
Everyone who is not patient is generous or not curious and vice versa.
If lucy is either rich or not happy then someone is both creative and not old and vice versa.
Everyone who is patient is brave or not funny and vice versa.
Everyone who is either not brave or not patient is creative or not rich.
If someone is either happy or not creative then john is both patient and not rich and vice versa.
If someone is either not humble or not creative then someone is both strong and not strong.
Everyone who is not happy or not patient is both humble and creative.
If someone is brave then fred is either happy or kind and vice versa.
If someone is not generous or old then someone is rich or happy.
Everyone who is not kind or not strong is happy or not funny.
If someone is kind then paul is not quiet.
Alice is not funny or not patient.
Alice is both not generous and not quiet.
Susan is wise or not rich.
Alice is either not creative or not strong.
Mary is tall.
Alice is tall or not brave. | John is not brave. | contradiction | (![X]:(wise(X)<=>(~wise(X)&creative(X))))&
((kind(susan))<=>((tall(john)&wise(john))))&
(![X]:(wise(X)=>(tall(X)|wise(X))))&
(![X]:(~patient(X)<=>(generous(X)|~curious(X))))&
(((rich(lucy)<~>~happy(lucy)))<=>(?[X]:((creative(X)&~old(X)))))&
(![X]:(patient(X)<=>(brave(X)|~funny(X))))&
(![X]:((~brave(X)<~>~patient(X))=>(creative(X)|~rich(X))))&
((?[X]:((happy(X)<~>~creative(X))))<=>((patient(john)&~rich(john))))&
((?[X]:((~humble(X)<~>~creative(X))))=>(?[X]:((strong(X)&~strong(X)))))&
(![X]:((~happy(X)|~patient(X))=>(humble(X)&creative(X))))&
((?[X]:(brave(X)))<=>((happy(fred)<~>kind(fred))))&
((?[X]:((~generous(X)|old(X))))=>(?[X]:((rich(X)|happy(X)))))&
(![X]:((~kind(X)|~strong(X))=>(happy(X)|~funny(X))))&
((?[X]:(kind(X)))=>(~quiet(paul)))&
((~funny(alice)|~patient(alice)))&
((~generous(alice)&~quiet(alice)))&
((wise(susan)|~rich(susan)))&
((~creative(alice)<~>~strong(alice)))&
(tall(mary))&
((tall(alice)|~brave(alice))) | ~brave(john) | [
"p0",
"p6",
"p7",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 516318489813357873536825
% SZS output start Proof for 516318489813357873536825
1. ! [X0] : (wise(X0) <=> (creative(X0) & ~wise(X0))) [input p0]
7. ! [X0] : ((~brave(X0) <~> ~patient(X0)) => (~rich(X0) | creative(X0))) [input p6]
8. ? [X0] : (happy(X0) <~> ~creative(X0)) <=> (~rich(john) & patient(john)) [input p7]
10. ! [X0] : ((~patient(X0) | ~happy(X0)) => (creative(X0) & humble(X0))) [input p9]
21. ~brave(john) [input hypothesis]
28. ! [X0] : ((~rich(X0) | creative(X0)) | (~brave(X0) <=> ~patient(X0))) [ennf transformation 7]
29. ! [X0] : (~rich(X0) | creative(X0) | (~brave(X0) <=> ~patient(X0))) [flattening 28]
31. ! [X0] : ((creative(X0) & humble(X0)) | (patient(X0) & happy(X0))) [ennf transformation 10]
35. ! [X0] : ((wise(X0) | (~creative(X0) | wise(X0))) & ((creative(X0) & ~wise(X0)) | ~wise(X0))) [nnf transformation 1]
36. ! [X0] : ((wise(X0) | ~creative(X0) | wise(X0)) & ((creative(X0) & ~wise(X0)) | ~wise(X0))) [flattening 35]
47. ! [X0] : (~rich(X0) | creative(X0) | ((~brave(X0) | patient(X0)) & (~patient(X0) | brave(X0)))) [nnf transformation 29]
48. (? [X0] : ((creative(X0) | ~happy(X0)) & (~creative(X0) | happy(X0))) | (rich(john) | ~patient(john))) & ((~rich(john) & patient(john)) | ! [X0] : ((happy(X0) | creative(X0)) & (~creative(X0) | ~happy(X0)))) [nnf transformation 8]
49. (? [X0] : ((creative(X0) | ~happy(X0)) & (~creative(X0) | happy(X0))) | rich(john) | ~patient(john)) & ((~rich(john) & patient(john)) | ! [X0] : ((happy(X0) | creative(X0)) & (~creative(X0) | ~happy(X0)))) [flattening 48]
50. (? [X0] : ((creative(X0) | ~happy(X0)) & (~creative(X0) | happy(X0))) | rich(john) | ~patient(john)) & ((~rich(john) & patient(john)) | ! [X1] : ((happy(X1) | creative(X1)) & (~creative(X1) | ~happy(X1)))) [rectify 49]
51. ? [X0] : ((creative(X0) | ~happy(X0)) & (~creative(X0) | happy(X0))) => ((creative(sK1) | ~happy(sK1)) & (~creative(sK1) | happy(sK1))) [choice axiom]
52. (((creative(sK1) | ~happy(sK1)) & (~creative(sK1) | happy(sK1))) | rich(john) | ~patient(john)) & ((~rich(john) & patient(john)) | ! [X1] : ((happy(X1) | creative(X1)) & (~creative(X1) | ~happy(X1)))) [skolemisation 50,51]
65. ~wise(X0) | ~wise(X0) [cnf transformation 36]
67. wise(X0) | ~creative(X0) | wise(X0) [cnf transformation 36]
84. ~rich(X0) | creative(X0) | ~patient(X0) | brave(X0) [cnf transformation 47]
91. creative(sK1) | ~happy(sK1) | rich(john) | ~patient(john) [cnf transformation 52]
98. creative(X0) | happy(X0) [cnf transformation 31]
99. patient(X0) | creative(X0) [cnf transformation 31]
115. ~brave(john) [cnf transformation 21]
116. ~wise(X0) [duplicate literal removal 65]
117. ~creative(X0) | wise(X0) [duplicate literal removal 67]
145. 6 <=> patient(john) [avatar definition]
146. patient(john) <- (6) [avatar component clause 145]
147. ~patient(john) <- (~6) [avatar component clause 145]
149. 7 <=> rich(john) [avatar definition]
151. rich(john) <- (7) [avatar component clause 149]
153. 8 <=> happy(sK1) [avatar definition]
155. ~happy(sK1) <- (~8) [avatar component clause 153]
157. 9 <=> creative(sK1) [avatar definition]
159. creative(sK1) <- (9) [avatar component clause 157]
160. ~6 | 7 | ~8 | 9 [avatar split clause 91,157,153,149,145]
163. 10 <=> ! [X1] : (happy(X1) | creative(X1)) [avatar definition]
164. happy(X1) | creative(X1) <- (10) [avatar component clause 163]
186. 10 [avatar split clause 98,163]
253. creative(john) <- (~6) [resolution 99,147]
262. wise(john) <- (~6) [resolution 253,117]
263. $false <- (~6) [subsumption resolution 262,116]
264. 6 [avatar contradiction clause 263]
268. creative(sK1) <- (~8, 10) [resolution 164,155]
271. 9 | 8 | ~10 [avatar split clause 268,163,153,157]
273. wise(sK1) <- (9) [resolution 159,117]
274. $false <- (9) [subsumption resolution 273,116]
275. ~9 [avatar contradiction clause 274]
303. creative(john) | ~patient(john) | brave(john) <- (7) [resolution 84,151]
305. creative(john) | brave(john) <- (6, 7) [subsumption resolution 303,146]
306. creative(john) <- (6, 7) [subsumption resolution 305,115]
319. wise(john) <- (6, 7) [resolution 306,117]
320. $false <- (6, 7) [subsumption resolution 319,116]
321. ~6 | ~7 [avatar contradiction clause 320]
322. $false [avatar sat refutation 160,186,264,271,275,321]
% SZS output end Proof for 516318489813357873536825
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not creative or not strong is strong. If someone is humble then someone is humble or happy and vice versa. Everyone who is not curious is either calm or not calm and vice versa. If paul is either not quiet or quiet then paul is both not rich and humble. Everyone who is funny is curious and vice versa. Everyone who is not curious or not rich is either humble or not humble and vice versa. Everyone who is both old and wise is both old and rich and vice versa. Everyone who is tall is not calm or not tall and vice versa. If lucy is either wise or calm then someone is not rich or calm and vice versa. If someone is either not happy or not wise then someone is both creative and not creative and vice versa. Everyone who is not funny or creative is either brave or not patient. Everyone who is not old or not humble is either strong or patient and vice versa. If fred is not calm or tall then susan is patient or not strong. If someone is either not generous or old then fred is either not tall or not patient. Everyone who is both not rich and patient is curious. Someone is either calm or generous. Susan is both wise and tall. Someone is curious or not brave. John is not strong or wise. Someone is both not quiet and creative. John is either strong or funny. Someone is either brave or not kind. Fred is creative. | Fred is curious. | contradiction | (![X]:((~creative(X)|~strong(X))=>strong(X)))&
((?[X]:(humble(X)))<=>(?[X]:((humble(X)|happy(X)))))&
(![X]:(~curious(X)<=>(calm(X)<~>~calm(X))))&
(((~quiet(paul)<~>quiet(paul)))=>((~rich(paul)&humble(paul))))&
(![X]:(funny(X)<=>curious(X)))&
(![X]:((~curious(X)|~rich(X))<=>(humble(X)<~>~humble(X))))&
(![X]:((old(X)&wise(X))<=>(old(X)&rich(X))))&
(![X]:(tall(X)<=>(~calm(X)|~tall(X))))&
(((wise(lucy)<~>calm(lucy)))<=>(?[X]:((~rich(X)|calm(X)))))&
((?[X]:((~happy(X)<~>~wise(X))))<=>(?[X]:((creative(X)&~creative(X)))))&
(![X]:((~funny(X)|creative(X))=>(brave(X)<~>~patient(X))))&
(![X]:((~old(X)|~humble(X))<=>(strong(X)<~>patient(X))))&
(((~calm(fred)|tall(fred)))=>((patient(susan)|~strong(susan))))&
((?[X]:((~generous(X)<~>old(X))))=>((~tall(fred)<~>~patient(fred))))&
(![X]:((~rich(X)&patient(X))=>curious(X)))&
(?[X]:((calm(X)<~>generous(X))))&
((wise(susan)&tall(susan)))&
(?[X]:((curious(X)|~brave(X))))&
((~strong(john)|wise(john)))&
(?[X]:((~quiet(X)&creative(X))))&
((strong(john)<~>funny(john)))&
(?[X]:((brave(X)<~>~kind(X))))&
(creative(fred)) | curious(fred) | [
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 5978311887201116034720004
% SZS output start Proof for 5978311887201116034720004
3. ! [X0] : (~curious(X0) <=> (calm(X0) <~> ~calm(X0))) [input p2]
24. curious(fred) [input hypothesis]
40. ! [X0] : ((~curious(X0) | ((calm(X0) | calm(X0)) & (~calm(X0) | ~calm(X0)))) & (((calm(X0) | ~calm(X0)) & (~calm(X0) | calm(X0))) | curious(X0))) [nnf transformation 3]
80. ~curious(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 40]
81. ~curious(X0) | calm(X0) | calm(X0) [cnf transformation 40]
143. curious(fred) [cnf transformation 24]
152. ~curious(X0) | ~calm(X0) [duplicate literal removal 80]
153. ~curious(X0) | calm(X0) [duplicate literal removal 81]
176. ~curious(X0) [subsumption resolution 152,153]
260. $false [subsumption resolution 143,176]
% SZS output end Proof for 5978311887201116034720004
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient and not funny then fred is not creative and vice versa.
Everyone who is either kind or brave is both patient and not strong.
If someone is both kind and rich then someone is both patient and tall.
Everyone who is either rich or funny is quiet and vice versa.
If lucy is both not old and not wise then susan is either happy or creative and vice versa.
If someone is either quiet or not humble then someone is not brave.
If john is either funny or not kind then mary is strong.
Everyone who is curious is both not humble and creative.
Everyone who is either patient or not generous is both curious and not tall.
Everyone who is either not tall or rich is kind or not tall.
If someone is both brave and not quiet then lucy is both quiet and curious.
If someone is either not rich or not humble then someone is not old or humble and vice versa.
If someone is either strong or not tall then someone is both rich and not kind and vice versa.
If john is either kind or not tall then fred is both not humble and old and vice versa.
If someone is patient then someone is not creative or wise.
Everyone who is either not creative or calm is either humble or funny.
Mary is wise.
Susan is not curious.
Lucy is either happy or not strong.
Someone is either kind or rich.
Lucy is both humble and patient.
Susan is patient or not generous.
Someone is not happy.
Fred is both not humble and patient. | Lucy is not generous. | entailment | ((?[X]:((~patient(X)&~funny(X))))<=>(~creative(fred)))&
(![X]:((kind(X)<~>brave(X))=>(patient(X)&~strong(X))))&
((?[X]:((kind(X)&rich(X))))=>(?[X]:((patient(X)&tall(X)))))&
(![X]:((rich(X)<~>funny(X))<=>quiet(X)))&
(((~old(lucy)&~wise(lucy)))<=>((happy(susan)<~>creative(susan))))&
((?[X]:((quiet(X)<~>~humble(X))))=>(?[X]:(~brave(X))))&
(((funny(john)<~>~kind(john)))=>(strong(mary)))&
(![X]:(curious(X)=>(~humble(X)&creative(X))))&
(![X]:((patient(X)<~>~generous(X))=>(curious(X)&~tall(X))))&
(![X]:((~tall(X)<~>rich(X))=>(kind(X)|~tall(X))))&
((?[X]:((brave(X)&~quiet(X))))=>((quiet(lucy)&curious(lucy))))&
((?[X]:((~rich(X)<~>~humble(X))))<=>(?[X]:((~old(X)|humble(X)))))&
((?[X]:((strong(X)<~>~tall(X))))<=>(?[X]:((rich(X)&~kind(X)))))&
(((kind(john)<~>~tall(john)))<=>((~humble(fred)&old(fred))))&
((?[X]:(patient(X)))=>(?[X]:((~creative(X)|wise(X)))))&
(![X]:((~creative(X)<~>calm(X))=>(humble(X)<~>funny(X))))&
(wise(mary))&
(~curious(susan))&
((happy(lucy)<~>~strong(lucy)))&
(?[X]:((kind(X)<~>rich(X))))&
((humble(lucy)&patient(lucy)))&
((patient(susan)|~generous(susan)))&
(?[X]:(~happy(X)))&
((~humble(fred)&patient(fred))) | ~generous(lucy) | [
"p7",
"p8",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 7648569320754763408132605
% SZS output start Proof for 7648569320754763408132605
8. ! [X0] : (curious(X0) => (creative(X0) & ~humble(X0))) [input p7]
9. ! [X0] : ((patient(X0) <~> ~generous(X0)) => (~tall(X0) & curious(X0))) [input p8]
21. patient(lucy) & humble(lucy) [input p20]
25. generous(lucy) [input hypothesis]
35. ! [X0] : ((creative(X0) & ~humble(X0)) | ~curious(X0)) [ennf transformation 8]
36. ! [X0] : ((~tall(X0) & curious(X0)) | (patient(X0) <=> ~generous(X0))) [ennf transformation 9]
58. ! [X0] : ((~tall(X0) & curious(X0)) | ((patient(X0) | generous(X0)) & (~generous(X0) | ~patient(X0)))) [nnf transformation 36]
105. ~curious(X0) | ~humble(X0) [cnf transformation 35]
107. ~generous(X0) | curious(X0) | ~patient(X0) [cnf transformation 58]
144. humble(lucy) [cnf transformation 21]
145. patient(lucy) [cnf transformation 21]
150. generous(lucy) [cnf transformation 25]
235. 19 <=> curious(lucy) [avatar definition]
237. curious(lucy) <- (19) [avatar component clause 235]
457. curious(lucy) | ~patient(lucy) [resolution 107,150]
458. curious(lucy) [subsumption resolution 457,145]
459. 19 [avatar split clause 458,235]
461. ~humble(lucy) <- (19) [resolution 237,105]
462. $false <- (19) [subsumption resolution 461,144]
463. ~19 [avatar contradiction clause 462]
464. $false [avatar sat refutation 459,463]
% SZS output end Proof for 7648569320754763408132605
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Everyone who is quiet is either patient or not patient.
Everyone who is kind or not rich is either happy or creative.
Everyone who is either creative or humble is not old.
If susan is not generous or curious then someone is either not happy or curious and vice versa.
Everyone who is generous or not curious is either not curious or not tall and vice versa.
Everyone who is funny is brave or patient and vice versa.
Everyone who is either not creative or not kind is tall and vice versa.
Everyone who is not kind is both not kind and not strong.
Everyone who is brave is tall or patient and vice versa.
If susan is either not funny or not humble then john is not humble and vice versa.
Everyone who is not funny is both funny and creative.
If john is old then someone is not quiet or brave.
If someone is not funny or creative then fred is either funny or rich.
Everyone who is strong is either humble or not creative and vice versa.
Everyone who is not old or old is not curious or brave and vice versa.
Everyone who is happy or funny is generous.
John is not strong.
Lucy is either not quiet or quiet.
Paul is not kind.
John is either brave or not calm.
Someone is both rich and kind.
Mary is either not patient or humble.
Mary is kind.
Someone is wise. | Susan is brave. | entailment | (![X]:(quiet(X)=>(patient(X)<~>~patient(X))))&
(![X]:((kind(X)|~rich(X))=>(happy(X)<~>creative(X))))&
(![X]:((creative(X)<~>humble(X))=>~old(X)))&
(((~generous(susan)|curious(susan)))<=>(?[X]:((~happy(X)<~>curious(X)))))&
(![X]:((generous(X)|~curious(X))<=>(~curious(X)<~>~tall(X))))&
(![X]:(funny(X)<=>(brave(X)|patient(X))))&
(![X]:((~creative(X)<~>~kind(X))<=>tall(X)))&
(![X]:(~kind(X)=>(~kind(X)&~strong(X))))&
(![X]:(brave(X)<=>(tall(X)|patient(X))))&
(((~funny(susan)<~>~humble(susan)))<=>(~humble(john)))&
(![X]:(~funny(X)=>(funny(X)&creative(X))))&
((old(john))=>(?[X]:((~quiet(X)|brave(X)))))&
((?[X]:((~funny(X)|creative(X))))=>((funny(fred)<~>rich(fred))))&
(![X]:(strong(X)<=>(humble(X)<~>~creative(X))))&
(![X]:((~old(X)|old(X))<=>(~curious(X)|brave(X))))&
(![X]:((happy(X)|funny(X))=>generous(X)))&
(~strong(john))&
((~quiet(lucy)<~>quiet(lucy)))&
(~kind(paul))&
((brave(john)<~>~calm(john)))&
(?[X]:((rich(X)&kind(X))))&
((~patient(mary)<~>humble(mary)))&
(kind(mary))&
(?[X]:(wise(X))) | brave(susan) | [
"p4",
"p8",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 448974509797520325227112
% SZS output start Proof for 448974509797520325227112
5. ! [X0] : ((~curious(X0) | generous(X0)) <=> (~curious(X0) <~> ~tall(X0))) [input p4]
9. ! [X0] : (brave(X0) <=> (patient(X0) | tall(X0))) [input p8]
15. ! [X0] : ((old(X0) | ~old(X0)) <=> (brave(X0) | ~curious(X0))) [input p14]
25. ~brave(susan) [input hypothesis]
45. ! [X0] : (((~curious(X0) | generous(X0)) | ((~curious(X0) | tall(X0)) & (~tall(X0) | curious(X0)))) & (((tall(X0) | curious(X0)) & (~tall(X0) | ~curious(X0))) | (curious(X0) & ~generous(X0)))) [nnf transformation 5]
46. ! [X0] : ((~curious(X0) | generous(X0) | ((~curious(X0) | tall(X0)) & (~tall(X0) | curious(X0)))) & (((tall(X0) | curious(X0)) & (~tall(X0) | ~curious(X0))) | (curious(X0) & ~generous(X0)))) [flattening 45]
50. ! [X0] : ((brave(X0) | (~patient(X0) & ~tall(X0))) & ((patient(X0) | tall(X0)) | ~brave(X0))) [nnf transformation 9]
51. ! [X0] : ((brave(X0) | (~patient(X0) & ~tall(X0))) & (patient(X0) | tall(X0) | ~brave(X0))) [flattening 50]
57. ! [X0] : (((old(X0) | ~old(X0)) | (~brave(X0) & curious(X0))) & ((brave(X0) | ~curious(X0)) | (~old(X0) & old(X0)))) [nnf transformation 15]
58. ! [X0] : ((old(X0) | ~old(X0) | (~brave(X0) & curious(X0))) & (brave(X0) | ~curious(X0) | (~old(X0) & old(X0)))) [flattening 57]
81. tall(X0) | curious(X0) | curious(X0) [cnf transformation 46]
94. ~tall(X0) | brave(X0) [cnf transformation 51]
109. brave(X0) | ~curious(X0) | old(X0) [cnf transformation 58]
110. brave(X0) | ~curious(X0) | ~old(X0) [cnf transformation 58]
126. ~brave(susan) [cnf transformation 25]
128. tall(X0) | curious(X0) [duplicate literal removal 81]
196. brave(X0) | ~curious(X0) [subsumption resolution 109,110]
222. curious(X0) | brave(X0) [resolution 128,94]
223. brave(X0) [subsumption resolution 222,196]
224. $false [resolution 223,126]
% SZS output end Proof for 448974509797520325227112
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not tall or not patient is patient or not old. Everyone who is not quiet or wise is calm. If someone is not calm or quiet then alice is both generous and humble. Everyone who is either curious or tall is either not wise or not quiet. If someone is either kind or not kind then alice is kind or not happy. If mary is either not brave or tall then alice is either wise or tall and vice versa. If susan is both old and calm then paul is either not kind or not quiet and vice versa. Everyone who is either not patient or not old is either not calm or not old. If someone is calm then someone is either not brave or not generous and vice versa. If alice is old then someone is either not calm or not happy and vice versa. Everyone who is either tall or old is not tall or kind and vice versa. If someone is either humble or not kind then someone is not patient or not tall and vice versa. Everyone who is not calm or not curious is both patient and wise. If susan is either not strong or not happy then someone is either not wise or not old. Everyone who is both not generous and creative is either not patient or humble and vice versa. Someone is both curious and not strong. Mary is either quiet or curious. Mary is either tall or brave. Someone is creative. Mary is either not rich or happy. John is not wise or not kind. | John is not humble. | neutral | (![X]:((~tall(X)<~>~patient(X))=>(patient(X)|~old(X))))&
(![X]:((~quiet(X)|wise(X))=>calm(X)))&
((?[X]:((~calm(X)|quiet(X))))=>((generous(alice)&humble(alice))))&
(![X]:((curious(X)<~>tall(X))=>(~wise(X)<~>~quiet(X))))&
((?[X]:((kind(X)<~>~kind(X))))=>((kind(alice)|~happy(alice))))&
(((~brave(mary)<~>tall(mary)))<=>((wise(alice)<~>tall(alice))))&
(((old(susan)&calm(susan)))<=>((~kind(paul)<~>~quiet(paul))))&
(![X]:((~patient(X)<~>~old(X))=>(~calm(X)<~>~old(X))))&
((?[X]:(calm(X)))<=>(?[X]:((~brave(X)<~>~generous(X)))))&
((old(alice))<=>(?[X]:((~calm(X)<~>~happy(X)))))&
(![X]:((tall(X)<~>old(X))<=>(~tall(X)|kind(X))))&
((?[X]:((humble(X)<~>~kind(X))))<=>(?[X]:((~patient(X)|~tall(X)))))&
(![X]:((~calm(X)|~curious(X))=>(patient(X)&wise(X))))&
(((~strong(susan)<~>~happy(susan)))=>(?[X]:((~wise(X)<~>~old(X)))))&
(![X]:((~generous(X)&creative(X))<=>(~patient(X)<~>humble(X))))&
(?[X]:((curious(X)&~strong(X))))&
((quiet(mary)<~>curious(mary)))&
((tall(mary)<~>brave(mary)))&
(?[X]:(creative(X)))&
((~rich(mary)<~>happy(mary)))&
((~wise(john)|~kind(john))) | ~humble(john) | [] | null | 0 |
Everyone who is both not generous and quiet is strong or not rich. Everyone who is not rich is either creative or strong and vice versa. Everyone who is either curious or not old is either not curious or rich and vice versa. Everyone who is kind or generous is both quiet and old. If lucy is not quiet then paul is not humble. If someone is quiet then mary is not wise or old and vice versa. Everyone who is funny or not curious is both not strong and not generous. If someone is calm or tall then someone is patient and vice versa. If fred is creative or not happy then someone is not brave and vice versa. If someone is not strong or patient then someone is not curious or humble. Everyone who is both rich and humble is both not happy and not creative and vice versa. Everyone who is not wise or happy is either not curious or not old and vice versa. If someone is not quiet or quiet then someone is both funny and not creative. If alice is both not old and rich then alice is old or not strong and vice versa. If someone is either not wise or not generous then someone is not happy and vice versa. Someone is not strong. Someone is either not kind or old. John is not patient. Someone is both quiet and not generous. Someone is both not happy and tall. Paul is not kind or humble. John is not tall or not funny. Fred is not old. | Mary is not wise. | neutral | (![X]:((~generous(X)&quiet(X))=>(strong(X)|~rich(X))))&
(![X]:(~rich(X)<=>(creative(X)<~>strong(X))))&
(![X]:((curious(X)<~>~old(X))<=>(~curious(X)<~>rich(X))))&
(![X]:((kind(X)|generous(X))=>(quiet(X)&old(X))))&
((~quiet(lucy))=>(~humble(paul)))&
((?[X]:(quiet(X)))<=>((~wise(mary)|old(mary))))&
(![X]:((funny(X)|~curious(X))=>(~strong(X)&~generous(X))))&
((?[X]:((calm(X)|tall(X))))<=>(?[X]:(patient(X))))&
(((creative(fred)|~happy(fred)))<=>(?[X]:(~brave(X))))&
((?[X]:((~strong(X)|patient(X))))=>(?[X]:((~curious(X)|humble(X)))))&
(![X]:((rich(X)&humble(X))<=>(~happy(X)&~creative(X))))&
(![X]:((~wise(X)|happy(X))<=>(~curious(X)<~>~old(X))))&
((?[X]:((~quiet(X)|quiet(X))))=>(?[X]:((funny(X)&~creative(X)))))&
(((~old(alice)&rich(alice)))<=>((old(alice)|~strong(alice))))&
((?[X]:((~wise(X)<~>~generous(X))))<=>(?[X]:(~happy(X))))&
(?[X]:(~strong(X)))&
(?[X]:((~kind(X)<~>old(X))))&
(~patient(john))&
(?[X]:((quiet(X)&~generous(X))))&
(?[X]:((~happy(X)&tall(X))))&
((~kind(paul)|humble(paul)))&
((~tall(john)|~funny(john)))&
(~old(fred)) | ~wise(mary) | [] | null | 0 |
If someone is not creative or tall then paul is both not brave and not wise and vice versa.
If someone is funny or not curious then susan is either strong or not generous and vice versa.
If someone is not tall then someone is not wise or quiet.
Everyone who is not happy is happy.
If someone is both quiet and not quiet then susan is both not curious and not generous.
If mary is either not wise or not calm then someone is generous.
Everyone who is both brave and not creative is kind and vice versa.
Everyone who is both not old and happy is not patient or not kind and vice versa.
If susan is curious then someone is either not tall or funny.
Everyone who is not rich or not happy is brave or generous.
If john is either curious or quiet then paul is creative or not strong.
If someone is both not tall and happy then someone is not generous and vice versa.
Everyone who is both not old and funny is not funny or rich and vice versa.
Everyone who is either strong or not old is both curious and not quiet.
Everyone who is both not patient and not creative is both not tall and not humble and vice versa.
If someone is not curious or not generous then someone is not strong and vice versa.
Someone is either tall or not calm.
Mary is not strong.
Someone is rich or not wise.
Someone is patient.
Mary is either creative or not patient.
John is not quiet.
Paul is calm.
Paul is not humble. | Paul is not rich. | contradiction | ((?[X]:((~creative(X)|tall(X))))<=>((~brave(paul)&~wise(paul))))&
((?[X]:((funny(X)|~curious(X))))<=>((strong(susan)<~>~generous(susan))))&
((?[X]:(~tall(X)))=>(?[X]:((~wise(X)|quiet(X)))))&
(![X]:(~happy(X)=>happy(X)))&
((?[X]:((quiet(X)&~quiet(X))))=>((~curious(susan)&~generous(susan))))&
(((~wise(mary)<~>~calm(mary)))=>(?[X]:(generous(X))))&
(![X]:((brave(X)&~creative(X))<=>kind(X)))&
(![X]:((~old(X)&happy(X))<=>(~patient(X)|~kind(X))))&
((curious(susan))=>(?[X]:((~tall(X)<~>funny(X)))))&
(![X]:((~rich(X)|~happy(X))=>(brave(X)|generous(X))))&
(((curious(john)<~>quiet(john)))=>((creative(paul)|~strong(paul))))&
((?[X]:((~tall(X)&happy(X))))<=>(?[X]:(~generous(X))))&
(![X]:((~old(X)&funny(X))<=>(~funny(X)|rich(X))))&
(![X]:((strong(X)<~>~old(X))=>(curious(X)&~quiet(X))))&
(![X]:((~patient(X)&~creative(X))<=>(~tall(X)&~humble(X))))&
((?[X]:((~curious(X)|~generous(X))))<=>(?[X]:(~strong(X))))&
(?[X]:((tall(X)<~>~calm(X))))&
(~strong(mary))&
(?[X]:((rich(X)|~wise(X))))&
(?[X]:(patient(X)))&
((creative(mary)<~>~patient(mary)))&
(~quiet(john))&
(calm(paul))&
(~humble(paul)) | ~rich(paul) | [
"p0",
"p6",
"p7",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 3755756024365857905302077
% SZS output start Proof for 3755756024365857905302077
1. ? [X0] : (tall(X0) | ~creative(X0)) <=> (~wise(paul) & ~brave(paul)) [input p0]
7. ! [X0] : ((~creative(X0) & brave(X0)) <=> kind(X0)) [input p6]
8. ! [X0] : ((happy(X0) & ~old(X0)) <=> (~kind(X0) | ~patient(X0))) [input p7]
13. ! [X0] : ((funny(X0) & ~old(X0)) <=> (rich(X0) | ~funny(X0))) [input p12]
25. ~rich(paul) [input hypothesis]
39. (? [X0] : (tall(X0) | ~creative(X0)) | (wise(paul) | brave(paul))) & ((~wise(paul) & ~brave(paul)) | ! [X0] : (~tall(X0) & creative(X0))) [nnf transformation 1]
40. (? [X0] : (tall(X0) | ~creative(X0)) | wise(paul) | brave(paul)) & ((~wise(paul) & ~brave(paul)) | ! [X0] : (~tall(X0) & creative(X0))) [flattening 39]
41. (? [X0] : (tall(X0) | ~creative(X0)) | wise(paul) | brave(paul)) & ((~wise(paul) & ~brave(paul)) | ! [X1] : (~tall(X1) & creative(X1))) [rectify 40]
42. ? [X0] : (tall(X0) | ~creative(X0)) => (tall(sK0) | ~creative(sK0)) [choice axiom]
43. ((tall(sK0) | ~creative(sK0)) | wise(paul) | brave(paul)) & ((~wise(paul) & ~brave(paul)) | ! [X1] : (~tall(X1) & creative(X1))) [skolemisation 41,42]
54. ! [X0] : (((~creative(X0) & brave(X0)) | ~kind(X0)) & (kind(X0) | (creative(X0) | ~brave(X0)))) [nnf transformation 7]
55. ! [X0] : (((~creative(X0) & brave(X0)) | ~kind(X0)) & (kind(X0) | creative(X0) | ~brave(X0))) [flattening 54]
56. ! [X0] : (((happy(X0) & ~old(X0)) | (kind(X0) & patient(X0))) & ((~kind(X0) | ~patient(X0)) | (~happy(X0) | old(X0)))) [nnf transformation 8]
57. ! [X0] : (((happy(X0) & ~old(X0)) | (kind(X0) & patient(X0))) & (~kind(X0) | ~patient(X0) | ~happy(X0) | old(X0))) [flattening 56]
67. ! [X0] : (((funny(X0) & ~old(X0)) | (~rich(X0) & funny(X0))) & ((rich(X0) | ~funny(X0)) | (~funny(X0) | old(X0)))) [nnf transformation 13]
68. ! [X0] : (((funny(X0) & ~old(X0)) | (~rich(X0) & funny(X0))) & (rich(X0) | ~funny(X0) | ~funny(X0) | old(X0))) [flattening 67]
85. ~brave(paul) | creative(X1) [cnf transformation 43]
103. ~kind(X0) | brave(X0) [cnf transformation 55]
104. ~kind(X0) | ~creative(X0) [cnf transformation 55]
107. ~old(X0) | kind(X0) [cnf transformation 57]
119. rich(X0) | ~funny(X0) | ~funny(X0) | old(X0) [cnf transformation 68]
122. funny(X0) | funny(X0) [cnf transformation 68]
145. ~rich(paul) [cnf transformation 25]
146. rich(X0) | ~funny(X0) | old(X0) [duplicate literal removal 119]
147. funny(X0) [duplicate literal removal 122]
150. 1 <=> brave(paul) [avatar definition]
171. 6 <=> ! [X1] : creative(X1) [avatar definition]
172. creative(X1) <- (6) [avatar component clause 171]
175. 6 | ~1 [avatar split clause 85,150,171]
254. 24 <=> creative(paul) [avatar definition]
255. ~creative(paul) <- (~24) [avatar component clause 254]
277. rich(X0) | old(X0) [subsumption resolution 146,147]
326. old(paul) [resolution 277,145]
329. kind(paul) [resolution 326,107]
336. ~creative(paul) [resolution 329,104]
337. brave(paul) [resolution 329,103]
338. ~24 [avatar split clause 336,254]
341. 1 [avatar split clause 337,150]
352. $false <- (6, ~24) [resolution 255,172]
353. ~6 | 24 [avatar contradiction clause 352]
354. $false [avatar sat refutation 175,338,341,353]
% SZS output end Proof for 3755756024365857905302077
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both generous and not kind is creative or brave. Everyone who is either not strong or not happy is not generous and vice versa. If john is not creative then someone is not old and vice versa. If susan is patient or not old then someone is both not calm and happy and vice versa. If susan is both not patient and not humble then lucy is both calm and not happy and vice versa. Everyone who is not calm is not tall and vice versa. If someone is old or creative then someone is both not humble and patient and vice versa. Everyone who is both rich and old is both quiet and humble. If someone is kind or not old then mary is not rich. Everyone who is both strong and patient is not rich or wise. Everyone who is either not kind or not generous is either wise or not funny. Everyone who is both not brave and curious is strong or brave and vice versa. If someone is patient or not calm then mary is either happy or humble and vice versa. If someone is both humble and not old then someone is both wise and not old and vice versa. If someone is happy then lucy is both not wise and curious and vice versa. Everyone who is both strong and not patient is not wise or not calm and vice versa. Lucy is either tall or not funny. Someone is either tall or not humble. Someone is not kind or strong. Someone is both not curious and quiet. Fred is not curious or brave. Mary is both not patient and not creative. Fred is not patient or humble. Someone is both wise and not rich. | Fred is not calm. | contradiction | (![X]:((generous(X)&~kind(X))=>(creative(X)|brave(X))))&
(![X]:((~strong(X)<~>~happy(X))<=>~generous(X)))&
((~creative(john))<=>(?[X]:(~old(X))))&
(((patient(susan)|~old(susan)))<=>(?[X]:((~calm(X)&happy(X)))))&
(((~patient(susan)&~humble(susan)))<=>((calm(lucy)&~happy(lucy))))&
(![X]:(~calm(X)<=>~tall(X)))&
((?[X]:((old(X)|creative(X))))<=>(?[X]:((~humble(X)&patient(X)))))&
(![X]:((rich(X)&old(X))=>(quiet(X)&humble(X))))&
((?[X]:((kind(X)|~old(X))))=>(~rich(mary)))&
(![X]:((strong(X)&patient(X))=>(~rich(X)|wise(X))))&
(![X]:((~kind(X)<~>~generous(X))=>(wise(X)<~>~funny(X))))&
(![X]:((~brave(X)&curious(X))<=>(strong(X)|brave(X))))&
((?[X]:((patient(X)|~calm(X))))<=>((happy(mary)<~>humble(mary))))&
((?[X]:((humble(X)&~old(X))))<=>(?[X]:((wise(X)&~old(X)))))&
((?[X]:(happy(X)))<=>((~wise(lucy)&curious(lucy))))&
(![X]:((strong(X)&~patient(X))<=>(~wise(X)|~calm(X))))&
((tall(lucy)<~>~funny(lucy)))&
(?[X]:((tall(X)<~>~humble(X))))&
(?[X]:((~kind(X)|strong(X))))&
(?[X]:((~curious(X)&quiet(X))))&
((~curious(fred)|brave(fred)))&
((~patient(mary)&~creative(mary)))&
((~patient(fred)|humble(fred)))&
(?[X]:((wise(X)&~rich(X)))) | ~calm(fred) | [
"p11",
"p15",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 4939478255277153806468893
% SZS output start Proof for 4939478255277153806468893
12. ! [X0] : ((curious(X0) & ~brave(X0)) <=> (brave(X0) | strong(X0))) [input p11]
16. ! [X0] : ((~patient(X0) & strong(X0)) <=> (~calm(X0) | ~wise(X0))) [input p15]
21. brave(fred) | ~curious(fred) [input p20]
25. ~calm(fred) [input hypothesis]
56. ! [X0] : (((curious(X0) & ~brave(X0)) | (~brave(X0) & ~strong(X0))) & ((brave(X0) | strong(X0)) | (~curious(X0) | brave(X0)))) [nnf transformation 12]
57. ! [X0] : (((curious(X0) & ~brave(X0)) | (~brave(X0) & ~strong(X0))) & (brave(X0) | strong(X0) | ~curious(X0) | brave(X0))) [flattening 56]
72. ! [X0] : (((~patient(X0) & strong(X0)) | (calm(X0) & wise(X0))) & ((~calm(X0) | ~wise(X0)) | (patient(X0) | ~strong(X0)))) [nnf transformation 16]
73. ! [X0] : (((~patient(X0) & strong(X0)) | (calm(X0) & wise(X0))) & (~calm(X0) | ~wise(X0) | patient(X0) | ~strong(X0))) [flattening 72]
113. ~brave(X0) | ~brave(X0) [cnf transformation 57]
114. ~strong(X0) | curious(X0) [cnf transformation 57]
131. calm(X0) | strong(X0) [cnf transformation 73]
140. brave(fred) | ~curious(fred) [cnf transformation 21]
145. ~calm(fred) [cnf transformation 25]
147. ~brave(X0) [duplicate literal removal 113]
333. ~curious(fred) [subsumption resolution 140,147]
347. strong(fred) [resolution 131,145]
350. curious(fred) [resolution 347,114]
351. $false [subsumption resolution 350,333]
% SZS output end Proof for 4939478255277153806468893
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.021 s
% ------------------------------
% ------------------------------
| 0 |
If someone is kind then alice is curious and vice versa. Everyone who is quiet is brave and vice versa. If paul is tall then paul is either not humble or not old. Everyone who is not quiet or not happy is quiet or not creative and vice versa. If someone is either not tall or not creative then someone is not creative. Everyone who is both not kind and not brave is either not brave or not strong and vice versa. Everyone who is not wise or not rich is curious and vice versa. Everyone who is either wise or not kind is both strong and wise and vice versa. If someone is both not generous and happy then someone is not patient or curious. Everyone who is both not creative and not generous is humble and vice versa. If fred is both not strong and not calm then lucy is not strong or tall. Everyone who is brave or curious is both generous and not rich and vice versa. Everyone who is not humble or not happy is either old or wise and vice versa. Everyone who is happy or brave is either not quiet or kind and vice versa. Everyone who is not curious is not generous and vice versa. Someone is not strong or not rich. Someone is curious or wise. Someone is both not old and wise. Someone is creative. Susan is either not tall or patient. John is brave or old. Someone is not curious or not calm. | John is not calm. | neutral | ((?[X]:(kind(X)))<=>(curious(alice)))&
(![X]:(quiet(X)<=>brave(X)))&
((tall(paul))=>((~humble(paul)<~>~old(paul))))&
(![X]:((~quiet(X)|~happy(X))<=>(quiet(X)|~creative(X))))&
((?[X]:((~tall(X)<~>~creative(X))))=>(?[X]:(~creative(X))))&
(![X]:((~kind(X)&~brave(X))<=>(~brave(X)<~>~strong(X))))&
(![X]:((~wise(X)|~rich(X))<=>curious(X)))&
(![X]:((wise(X)<~>~kind(X))<=>(strong(X)&wise(X))))&
((?[X]:((~generous(X)&happy(X))))=>(?[X]:((~patient(X)|curious(X)))))&
(![X]:((~creative(X)&~generous(X))<=>humble(X)))&
(((~strong(fred)&~calm(fred)))=>((~strong(lucy)|tall(lucy))))&
(![X]:((brave(X)|curious(X))<=>(generous(X)&~rich(X))))&
(![X]:((~humble(X)|~happy(X))<=>(old(X)<~>wise(X))))&
(![X]:((happy(X)|brave(X))<=>(~quiet(X)<~>kind(X))))&
(![X]:(~curious(X)<=>~generous(X)))&
(?[X]:((~strong(X)|~rich(X))))&
(?[X]:((curious(X)|wise(X))))&
(?[X]:((~old(X)&wise(X))))&
(?[X]:(creative(X)))&
((~tall(susan)<~>patient(susan)))&
((brave(john)|old(john)))&
(?[X]:((~curious(X)|~calm(X)))) | ~calm(john) | [] | null | 0 |
If lucy is calm then someone is either old or strong and vice versa.
Everyone who is either not old or not generous is both quiet and generous and vice versa.
Everyone who is calm is not creative and vice versa.
Everyone who is either generous or humble is both calm and not kind.
Everyone who is both not brave and curious is wise and vice versa.
If someone is both not creative and not generous then someone is wise or tall.
If fred is not old then someone is not wise.
If someone is quiet or calm then someone is patient or not happy.
If someone is either curious or not strong then someone is not funny or not curious and vice versa.
Everyone who is not strong or not tall is both not patient and not old and vice versa.
If someone is both curious and funny then paul is not kind.
If fred is both not creative and old then mary is both humble and not kind.
If susan is either humble or not happy then alice is both not tall and not happy.
Everyone who is both not old and not happy is not humble or tall and vice versa.
If alice is strong then alice is humble and vice versa.
Everyone who is both wise and creative is patient and vice versa.
Paul is either not humble or wise.
Lucy is happy or quiet.
Someone is not rich or not brave.
John is both humble and not strong.
Someone is either funny or rich.
Susan is not strong or not curious.
Lucy is both calm and quiet.
Alice is either creative or strong. | Susan is not patient. | entailment | ((calm(lucy))<=>(?[X]:((old(X)<~>strong(X)))))&
(![X]:((~old(X)<~>~generous(X))<=>(quiet(X)&generous(X))))&
(![X]:(calm(X)<=>~creative(X)))&
(![X]:((generous(X)<~>humble(X))=>(calm(X)&~kind(X))))&
(![X]:((~brave(X)&curious(X))<=>wise(X)))&
((?[X]:((~creative(X)&~generous(X))))=>(?[X]:((wise(X)|tall(X)))))&
((~old(fred))=>(?[X]:(~wise(X))))&
((?[X]:((quiet(X)|calm(X))))=>(?[X]:((patient(X)|~happy(X)))))&
((?[X]:((curious(X)<~>~strong(X))))<=>(?[X]:((~funny(X)|~curious(X)))))&
(![X]:((~strong(X)|~tall(X))<=>(~patient(X)&~old(X))))&
((?[X]:((curious(X)&funny(X))))=>(~kind(paul)))&
(((~creative(fred)&old(fred)))=>((humble(mary)&~kind(mary))))&
(((humble(susan)<~>~happy(susan)))=>((~tall(alice)&~happy(alice))))&
(![X]:((~old(X)&~happy(X))<=>(~humble(X)|tall(X))))&
((strong(alice))<=>(humble(alice)))&
(![X]:((wise(X)&creative(X))<=>patient(X)))&
((~humble(paul)<~>wise(paul)))&
((happy(lucy)|quiet(lucy)))&
(?[X]:((~rich(X)|~brave(X))))&
((humble(john)&~strong(john)))&
(?[X]:((funny(X)<~>rich(X))))&
((~strong(susan)|~curious(susan)))&
((calm(lucy)&quiet(lucy)))&
((creative(alice)<~>strong(alice))) | ~patient(susan) | [
"p4",
"p9",
"p15",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 6162565267684390861411373
% SZS output start Proof for 6162565267684390861411373
5. ! [X0] : ((curious(X0) & ~brave(X0)) <=> wise(X0)) [input p4]
10. ! [X0] : ((~tall(X0) | ~strong(X0)) <=> (~old(X0) & ~patient(X0))) [input p9]
16. ! [X0] : ((creative(X0) & wise(X0)) <=> patient(X0)) [input p15]
22. ~curious(susan) | ~strong(susan) [input p21]
25. patient(susan) [input hypothesis]
47. ! [X0] : (((curious(X0) & ~brave(X0)) | ~wise(X0)) & (wise(X0) | (~curious(X0) | brave(X0)))) [nnf transformation 5]
48. ! [X0] : (((curious(X0) & ~brave(X0)) | ~wise(X0)) & (wise(X0) | ~curious(X0) | brave(X0))) [flattening 47]
62. ! [X0] : (((~tall(X0) | ~strong(X0)) | (old(X0) | patient(X0))) & ((~old(X0) & ~patient(X0)) | (tall(X0) & strong(X0)))) [nnf transformation 10]
63. ! [X0] : ((~tall(X0) | ~strong(X0) | old(X0) | patient(X0)) & ((~old(X0) & ~patient(X0)) | (tall(X0) & strong(X0)))) [flattening 62]
68. ! [X0] : (((creative(X0) & wise(X0)) | ~patient(X0)) & (patient(X0) | (~creative(X0) | ~wise(X0)))) [nnf transformation 16]
69. ! [X0] : (((creative(X0) & wise(X0)) | ~patient(X0)) & (patient(X0) | ~creative(X0) | ~wise(X0))) [flattening 68]
93. ~wise(X0) | curious(X0) [cnf transformation 48]
104. ~patient(X0) | strong(X0) [cnf transformation 63]
122. ~patient(X0) | wise(X0) [cnf transformation 69]
132. ~curious(susan) | ~strong(susan) [cnf transformation 22]
137. patient(susan) [cnf transformation 25]
314. 39 <=> strong(susan) [avatar definition]
318. 40 <=> curious(susan) [avatar definition]
320. ~curious(susan) <- (~40) [avatar component clause 318]
321. ~39 | ~40 [avatar split clause 132,318,314]
334. strong(susan) [resolution 104,137]
335. 39 [avatar split clause 334,314]
337. wise(susan) [resolution 122,137]
339. curious(susan) [resolution 337,93]
341. $false <- (~40) [subsumption resolution 339,320]
342. 40 [avatar contradiction clause 341]
343. $false [avatar sat refutation 321,335,342]
% SZS output end Proof for 6162565267684390861411373
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble or not tall is either happy or not tall.
If alice is both kind and not tall then fred is both not patient and calm and vice versa.
If fred is not strong or quiet then paul is not generous.
Everyone who is either not strong or patient is either not wise or humble.
Everyone who is either generous or brave is funny and vice versa.
If mary is both not creative and not strong then someone is not generous and vice versa.
Everyone who is curious is not generous and vice versa.
Everyone who is both funny and tall is both quiet and wise.
If lucy is either not rich or not brave then fred is either not calm or happy and vice versa.
If alice is both not brave and funny then fred is patient.
Everyone who is patient is either quiet or brave.
If susan is both tall and calm then someone is not calm and vice versa.
If someone is both not patient and not old then someone is not tall or tall and vice versa.
Everyone who is both funny and rich is not happy.
Everyone who is wise is old or not funny.
Everyone who is not happy is not curious.
Paul is both brave and not calm.
Paul is not kind.
Someone is creative or brave.
Someone is both not calm and old.
Someone is either tall or quiet.
Susan is not wise.
Someone is tall or strong.
Paul is either creative or funny. | Paul is funny. | neutral | (![X]:((humble(X)|~tall(X))=>(happy(X)<~>~tall(X))))&
(((kind(alice)&~tall(alice)))<=>((~patient(fred)&calm(fred))))&
(((~strong(fred)|quiet(fred)))=>(~generous(paul)))&
(![X]:((~strong(X)<~>patient(X))=>(~wise(X)<~>humble(X))))&
(![X]:((generous(X)<~>brave(X))<=>funny(X)))&
(((~creative(mary)&~strong(mary)))<=>(?[X]:(~generous(X))))&
(![X]:(curious(X)<=>~generous(X)))&
(![X]:((funny(X)&tall(X))=>(quiet(X)&wise(X))))&
(((~rich(lucy)<~>~brave(lucy)))<=>((~calm(fred)<~>happy(fred))))&
(((~brave(alice)&funny(alice)))=>(patient(fred)))&
(![X]:(patient(X)=>(quiet(X)<~>brave(X))))&
(((tall(susan)&calm(susan)))<=>(?[X]:(~calm(X))))&
((?[X]:((~patient(X)&~old(X))))<=>(?[X]:((~tall(X)|tall(X)))))&
(![X]:((funny(X)&rich(X))=>~happy(X)))&
(![X]:(wise(X)=>(old(X)|~funny(X))))&
(![X]:(~happy(X)=>~curious(X)))&
((brave(paul)&~calm(paul)))&
(~kind(paul))&
(?[X]:((creative(X)|brave(X))))&
(?[X]:((~calm(X)&old(X))))&
(?[X]:((tall(X)<~>quiet(X))))&
(~wise(susan))&
(?[X]:((tall(X)|strong(X))))&
((creative(paul)<~>funny(paul))) | funny(paul) | [] | null | 0 |
If susan is not strong or rich then alice is either funny or not brave and vice versa.
Everyone who is curious is generous or curious and vice versa.
If someone is not quiet or calm then someone is tall or creative.
Everyone who is either quiet or tall is wise and vice versa.
If someone is either funny or not brave then mary is patient and vice versa.
If fred is not rich or not kind then susan is both old and not old.
If someone is either happy or not curious then someone is both not brave and brave.
If someone is not curious or creative then someone is not creative.
If someone is happy or not calm then susan is not quiet and vice versa.
Everyone who is both strong and rich is not calm or quiet and vice versa.
Everyone who is quiet or tall is not rich or not brave.
Everyone who is both calm and old is wise or curious and vice versa.
If someone is tall then john is both strong and not wise.
Everyone who is either strong or not generous is not wise and vice versa.
If someone is both not tall and not old then mary is rich or not generous and vice versa.
If alice is either strong or not funny then someone is either not humble or patient and vice versa.
Mary is not old or generous.
Paul is tall or not creative.
Someone is either not brave or strong.
Someone is patient.
Fred is both not strong and happy.
Someone is either not humble or not wise.
Lucy is both generous and tall. | Alice is not calm. | contradiction | (((~strong(susan)|rich(susan)))<=>((funny(alice)<~>~brave(alice))))&
(![X]:(curious(X)<=>(generous(X)|curious(X))))&
((?[X]:((~quiet(X)|calm(X))))=>(?[X]:((tall(X)|creative(X)))))&
(![X]:((quiet(X)<~>tall(X))<=>wise(X)))&
((?[X]:((funny(X)<~>~brave(X))))<=>(patient(mary)))&
(((~rich(fred)|~kind(fred)))=>((old(susan)&~old(susan))))&
((?[X]:((happy(X)<~>~curious(X))))=>(?[X]:((~brave(X)&brave(X)))))&
((?[X]:((~curious(X)|creative(X))))=>(?[X]:(~creative(X))))&
((?[X]:((happy(X)|~calm(X))))<=>(~quiet(susan)))&
(![X]:((strong(X)&rich(X))<=>(~calm(X)|quiet(X))))&
(![X]:((quiet(X)|tall(X))=>(~rich(X)|~brave(X))))&
(![X]:((calm(X)&old(X))<=>(wise(X)|curious(X))))&
((?[X]:(tall(X)))=>((strong(john)&~wise(john))))&
(![X]:((strong(X)<~>~generous(X))<=>~wise(X)))&
((?[X]:((~tall(X)&~old(X))))<=>((rich(mary)|~generous(mary))))&
(((strong(alice)<~>~funny(alice)))<=>(?[X]:((~humble(X)<~>patient(X)))))&
((~old(mary)|generous(mary)))&
((tall(paul)|~creative(paul)))&
(?[X]:((~brave(X)<~>strong(X))))&
(?[X]:(patient(X)))&
((~strong(fred)&happy(fred)))&
(?[X]:((~humble(X)<~>~wise(X))))&
((generous(lucy)&tall(lucy))) | ~calm(alice) | [
"p1",
"p9",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 6650692957806476262726016
% SZS output start Proof for 6650692957806476262726016
2. ! [X0] : (curious(X0) <=> (curious(X0) | generous(X0))) [input p1]
10. ! [X0] : ((rich(X0) & strong(X0)) <=> (quiet(X0) | ~calm(X0))) [input p9]
12. ! [X0] : ((old(X0) & calm(X0)) <=> (curious(X0) | wise(X0))) [input p11]
14. ! [X0] : ((strong(X0) <~> ~generous(X0)) <=> ~wise(X0)) [input p13]
24. ~calm(alice) [input hypothesis]
38. ! [X0] : ((curious(X0) | (~curious(X0) & ~generous(X0))) & ((curious(X0) | generous(X0)) | ~curious(X0))) [nnf transformation 2]
39. ! [X0] : ((curious(X0) | (~curious(X0) & ~generous(X0))) & (curious(X0) | generous(X0) | ~curious(X0))) [flattening 38]
59. ! [X0] : (((rich(X0) & strong(X0)) | (~quiet(X0) & calm(X0))) & ((quiet(X0) | ~calm(X0)) | (~rich(X0) | ~strong(X0)))) [nnf transformation 10]
60. ! [X0] : (((rich(X0) & strong(X0)) | (~quiet(X0) & calm(X0))) & (quiet(X0) | ~calm(X0) | ~rich(X0) | ~strong(X0))) [flattening 59]
61. ! [X0] : (((old(X0) & calm(X0)) | (~curious(X0) & ~wise(X0))) & ((curious(X0) | wise(X0)) | (~old(X0) | ~calm(X0)))) [nnf transformation 12]
62. ! [X0] : (((old(X0) & calm(X0)) | (~curious(X0) & ~wise(X0))) & (curious(X0) | wise(X0) | ~old(X0) | ~calm(X0))) [flattening 61]
63. ! [X0] : ((((generous(X0) | ~strong(X0)) & (~generous(X0) | strong(X0))) | wise(X0)) & (~wise(X0) | ((strong(X0) | generous(X0)) & (~generous(X0) | ~strong(X0))))) [nnf transformation 14]
88. ~generous(X0) | curious(X0) [cnf transformation 39]
112. calm(X0) | strong(X0) [cnf transformation 60]
119. ~wise(X0) | calm(X0) [cnf transformation 62]
120. ~curious(X0) | calm(X0) [cnf transformation 62]
128. ~strong(X0) | generous(X0) | wise(X0) [cnf transformation 63]
153. ~calm(alice) [cnf transformation 24]
313. 36 <=> strong(alice) [avatar definition]
314. strong(alice) <- (36) [avatar component clause 313]
374. strong(alice) [resolution 112,153]
378. 36 [avatar split clause 374,313]
416. generous(alice) | wise(alice) <- (36) [resolution 128,314]
420. 51 <=> wise(alice) [avatar definition]
422. wise(alice) <- (51) [avatar component clause 420]
424. 52 <=> generous(alice) [avatar definition]
426. generous(alice) <- (52) [avatar component clause 424]
427. 51 | 52 | ~36 [avatar split clause 416,313,424,420]
462. calm(alice) <- (51) [resolution 422,119]
475. $false <- (51) [subsumption resolution 462,153]
476. ~51 [avatar contradiction clause 475]
479. curious(alice) <- (52) [resolution 426,88]
483. calm(alice) <- (52) [resolution 479,120]
484. $false <- (52) [subsumption resolution 483,153]
485. ~52 [avatar contradiction clause 484]
486. $false [avatar sat refutation 378,427,476,485]
% SZS output end Proof for 6650692957806476262726016
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not happy or not strong is calm.
Everyone who is creative or tall is both patient and not rich.
If alice is either not tall or not brave then someone is not funny or funny.
If john is old or not generous then mary is both old and brave and vice versa.
Everyone who is strong or not strong is tall and vice versa.
If someone is both not curious and wise then someone is not brave and vice versa.
Everyone who is humble is not tall or not kind and vice versa.
If paul is not funny or not quiet then fred is patient or not humble.
If someone is either patient or humble then lucy is not tall or not curious and vice versa.
Everyone who is not calm is wise or not creative.
If someone is not quiet then mary is not generous and vice versa.
If lucy is brave then someone is either not creative or quiet and vice versa.
If lucy is either happy or not wise then someone is both wise and not generous.
Everyone who is both funny and not curious is both not old and calm.
Everyone who is either quiet or not brave is not old.
Paul is either not funny or not wise.
Someone is both not funny and happy.
Lucy is either humble or not wise.
Paul is either kind or not happy.
Someone is either not rich or not happy.
Alice is either not tall or not wise.
Someone is either wise or creative.
Fred is both not brave and wise. | Alice is wise. | contradiction | (![X]:((~happy(X)|~strong(X))=>calm(X)))&
(![X]:((creative(X)|tall(X))=>(patient(X)&~rich(X))))&
(((~tall(alice)<~>~brave(alice)))=>(?[X]:((~funny(X)|funny(X)))))&
(((old(john)|~generous(john)))<=>((old(mary)&brave(mary))))&
(![X]:((strong(X)|~strong(X))<=>tall(X)))&
((?[X]:((~curious(X)&wise(X))))<=>(?[X]:(~brave(X))))&
(![X]:(humble(X)<=>(~tall(X)|~kind(X))))&
(((~funny(paul)|~quiet(paul)))=>((patient(fred)|~humble(fred))))&
((?[X]:((patient(X)<~>humble(X))))<=>((~tall(lucy)|~curious(lucy))))&
(![X]:(~calm(X)=>(wise(X)|~creative(X))))&
((?[X]:(~quiet(X)))<=>(~generous(mary)))&
((brave(lucy))<=>(?[X]:((~creative(X)<~>quiet(X)))))&
(((happy(lucy)<~>~wise(lucy)))=>(?[X]:((wise(X)&~generous(X)))))&
(![X]:((funny(X)&~curious(X))=>(~old(X)&calm(X))))&
(![X]:((quiet(X)<~>~brave(X))=>~old(X)))&
((~funny(paul)<~>~wise(paul)))&
(?[X]:((~funny(X)&happy(X))))&
((humble(lucy)<~>~wise(lucy)))&
((kind(paul)<~>~happy(paul)))&
(?[X]:((~rich(X)<~>~happy(X))))&
((~tall(alice)<~>~wise(alice)))&
(?[X]:((wise(X)<~>creative(X))))&
((~brave(fred)&wise(fred))) | wise(alice) | [
"p4",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 2773341625901962841491653
% SZS output start Proof for 2773341625901962841491653
5. ! [X0] : ((~strong(X0) | strong(X0)) <=> tall(X0)) [input p4]
21. ~tall(alice) <~> ~wise(alice) [input p20]
24. wise(alice) [input hypothesis]
42. ! [X0] : (((~strong(X0) | strong(X0)) | ~tall(X0)) & (tall(X0) | (strong(X0) & ~strong(X0)))) [nnf transformation 5]
43. ! [X0] : ((~strong(X0) | strong(X0) | ~tall(X0)) & (tall(X0) | (strong(X0) & ~strong(X0)))) [flattening 42]
76. (wise(alice) | tall(alice)) & (~wise(alice) | ~tall(alice)) [nnf transformation 21]
91. tall(X0) | ~strong(X0) [cnf transformation 43]
92. tall(X0) | strong(X0) [cnf transformation 43]
131. ~wise(alice) | ~tall(alice) [cnf transformation 76]
137. wise(alice) [cnf transformation 24]
159. tall(X0) [subsumption resolution 91,92]
311. ~wise(alice) [subsumption resolution 131,159]
322. $false [subsumption resolution 137,311]
% SZS output end Proof for 2773341625901962841491653
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is wise or not old then fred is both quiet and not quiet and vice versa. Everyone who is either kind or generous is both not curious and not funny and vice versa. Everyone who is both not old and not quiet is either not old or not quiet and vice versa. Everyone who is generous is curious or old and vice versa. Everyone who is strong or not curious is either not kind or patient and vice versa. Everyone who is both funny and not patient is both old and not patient and vice versa. Everyone who is both quiet and not quiet is strong or calm and vice versa. If alice is happy then someone is both old and not quiet and vice versa. Everyone who is either rich or not curious is either not wise or not old and vice versa. Everyone who is either not patient or calm is either not tall or generous. Everyone who is both tall and not humble is both not patient and funny and vice versa. Everyone who is funny is not wise and vice versa. If fred is curious or brave then someone is either creative or not strong and vice versa. If mary is not wise or curious then fred is humble or not patient and vice versa. Everyone who is either funny or not brave is calm and vice versa. Fred is not kind or not curious. Someone is both generous and patient. Paul is humble. Someone is generous or not old. Mary is not brave. | Fred is not brave. | entailment | (((wise(paul)|~old(paul)))<=>((quiet(fred)&~quiet(fred))))&
(![X]:((kind(X)<~>generous(X))<=>(~curious(X)&~funny(X))))&
(![X]:((~old(X)&~quiet(X))<=>(~old(X)<~>~quiet(X))))&
(![X]:(generous(X)<=>(curious(X)|old(X))))&
(![X]:((strong(X)|~curious(X))<=>(~kind(X)<~>patient(X))))&
(![X]:((funny(X)&~patient(X))<=>(old(X)&~patient(X))))&
(![X]:((quiet(X)&~quiet(X))<=>(strong(X)|calm(X))))&
((happy(alice))<=>(?[X]:((old(X)&~quiet(X)))))&
(![X]:((rich(X)<~>~curious(X))<=>(~wise(X)<~>~old(X))))&
(![X]:((~patient(X)<~>calm(X))=>(~tall(X)<~>generous(X))))&
(![X]:((tall(X)&~humble(X))<=>(~patient(X)&funny(X))))&
(![X]:(funny(X)<=>~wise(X)))&
(((curious(fred)|brave(fred)))<=>(?[X]:((creative(X)<~>~strong(X)))))&
(((~wise(mary)|curious(mary)))<=>((humble(fred)|~patient(fred))))&
(![X]:((funny(X)<~>~brave(X))<=>calm(X)))&
((~kind(fred)|~curious(fred)))&
(?[X]:((generous(X)&patient(X))))&
(humble(paul))&
(?[X]:((generous(X)|~old(X))))&
(~brave(mary)) | ~brave(fred) | [
"p1",
"p2",
"p3",
"p4",
"p5",
"p6",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3939769759354263000890523
% SZS output start Proof for 3939769759354263000890523
2. ! [X0] : ((kind(X0) <~> generous(X0)) <=> (~funny(X0) & ~curious(X0))) [input p1]
3. ! [X0] : ((~quiet(X0) & ~old(X0)) <=> (~old(X0) <~> ~quiet(X0))) [input p2]
4. ! [X0] : (generous(X0) <=> (old(X0) | curious(X0))) [input p3]
5. ! [X0] : ((~curious(X0) | strong(X0)) <=> (~kind(X0) <~> patient(X0))) [input p4]
6. ! [X0] : ((~patient(X0) & funny(X0)) <=> (~patient(X0) & old(X0))) [input p5]
7. ! [X0] : ((~quiet(X0) & quiet(X0)) <=> (calm(X0) | strong(X0))) [input p6]
15. ! [X0] : ((funny(X0) <~> ~brave(X0)) <=> calm(X0)) [input p14]
16. ~curious(fred) | ~kind(fred) [input p15]
21. brave(fred) [input hypothesis]
25. ! [X0] : ((((~generous(X0) | ~kind(X0)) & (generous(X0) | kind(X0))) | (funny(X0) | curious(X0))) & ((~funny(X0) & ~curious(X0)) | ((kind(X0) | ~generous(X0)) & (generous(X0) | ~kind(X0))))) [nnf transformation 2]
26. ! [X0] : ((((~generous(X0) | ~kind(X0)) & (generous(X0) | kind(X0))) | funny(X0) | curious(X0)) & ((~funny(X0) & ~curious(X0)) | ((kind(X0) | ~generous(X0)) & (generous(X0) | ~kind(X0))))) [flattening 25]
27. ! [X0] : (((~quiet(X0) & ~old(X0)) | ((~old(X0) | quiet(X0)) & (~quiet(X0) | old(X0)))) & (((quiet(X0) | old(X0)) & (~quiet(X0) | ~old(X0))) | (quiet(X0) | old(X0)))) [nnf transformation 3]
28. ! [X0] : (((~quiet(X0) & ~old(X0)) | ((~old(X0) | quiet(X0)) & (~quiet(X0) | old(X0)))) & (((quiet(X0) | old(X0)) & (~quiet(X0) | ~old(X0))) | quiet(X0) | old(X0))) [flattening 27]
29. ! [X0] : ((generous(X0) | (~old(X0) & ~curious(X0))) & ((old(X0) | curious(X0)) | ~generous(X0))) [nnf transformation 4]
30. ! [X0] : ((generous(X0) | (~old(X0) & ~curious(X0))) & (old(X0) | curious(X0) | ~generous(X0))) [flattening 29]
31. ! [X0] : (((~curious(X0) | strong(X0)) | ((~kind(X0) | ~patient(X0)) & (patient(X0) | kind(X0)))) & (((~patient(X0) | kind(X0)) & (patient(X0) | ~kind(X0))) | (curious(X0) & ~strong(X0)))) [nnf transformation 5]
32. ! [X0] : ((~curious(X0) | strong(X0) | ((~kind(X0) | ~patient(X0)) & (patient(X0) | kind(X0)))) & (((~patient(X0) | kind(X0)) & (patient(X0) | ~kind(X0))) | (curious(X0) & ~strong(X0)))) [flattening 31]
33. ! [X0] : (((~patient(X0) & funny(X0)) | (patient(X0) | ~old(X0))) & ((~patient(X0) & old(X0)) | (patient(X0) | ~funny(X0)))) [nnf transformation 6]
34. ! [X0] : (((~patient(X0) & funny(X0)) | patient(X0) | ~old(X0)) & ((~patient(X0) & old(X0)) | patient(X0) | ~funny(X0))) [flattening 33]
35. ! [X0] : (((~quiet(X0) & quiet(X0)) | (~calm(X0) & ~strong(X0))) & ((calm(X0) | strong(X0)) | (quiet(X0) | ~quiet(X0)))) [nnf transformation 7]
36. ! [X0] : (((~quiet(X0) & quiet(X0)) | (~calm(X0) & ~strong(X0))) & (calm(X0) | strong(X0) | quiet(X0) | ~quiet(X0))) [flattening 35]
53. ! [X0] : ((((brave(X0) | ~funny(X0)) & (~brave(X0) | funny(X0))) | ~calm(X0)) & (calm(X0) | ((funny(X0) | brave(X0)) & (~brave(X0) | ~funny(X0))))) [nnf transformation 15]
64. ~curious(X0) | kind(X0) | ~generous(X0) [cnf transformation 26]
68. ~generous(X0) | ~kind(X0) | funny(X0) | curious(X0) [cnf transformation 26]
70. quiet(X0) | old(X0) | quiet(X0) | old(X0) [cnf transformation 28]
72. ~old(X0) | ~old(X0) | quiet(X0) [cnf transformation 28]
73. ~quiet(X0) | ~quiet(X0) | old(X0) [cnf transformation 28]
77. ~old(X0) | generous(X0) [cnf transformation 30]
81. ~patient(X0) | kind(X0) | curious(X0) [cnf transformation 32]
86. ~old(X0) | patient(X0) | funny(X0) [cnf transformation 34]
92. ~quiet(X0) | ~calm(X0) [cnf transformation 36]
124. calm(X0) | ~brave(X0) | ~funny(X0) [cnf transformation 53]
128. ~curious(fred) | ~kind(fred) [cnf transformation 16]
134. brave(fred) [cnf transformation 21]
135. quiet(X0) | old(X0) [duplicate literal removal 70]
136. ~old(X0) | quiet(X0) [duplicate literal removal 72]
137. ~quiet(X0) | old(X0) [duplicate literal removal 73]
154. quiet(X0) [subsumption resolution 135,136]
155. ~calm(X0) [subsumption resolution 92,154]
165. 5 <=> curious(fred) [avatar definition]
166. ~curious(fred) <- (~5) [avatar component clause 165]
167. curious(fred) <- (5) [avatar component clause 165]
169. 6 <=> brave(fred) [avatar definition]
171. brave(fred) <- (6) [avatar component clause 169]
202. ~brave(X0) | ~funny(X0) [subsumption resolution 124,155]
204. 12 <=> kind(fred) [avatar definition]
206. ~kind(fred) <- (~12) [avatar component clause 204]
207. ~12 | ~5 [avatar split clause 128,165,204]
208. 6 [avatar split clause 134,169]
212. old(X0) [resolution 137,154]
214. generous(X1) [resolution 212,77]
217. ~funny(fred) <- (6) [resolution 202,171]
259. patient(X0) | funny(X0) [resolution 86,212]
301. funny(X0) | kind(X0) | curious(X0) [resolution 259,81]
310. kind(fred) | ~generous(fred) <- (5) [resolution 167,64]
313. ~generous(fred) <- (5, ~12) [subsumption resolution 310,206]
314. $false <- (5, ~12) [subsumption resolution 313,214]
315. ~5 | 12 [avatar contradiction clause 314]
342. ~kind(X0) | funny(X0) | curious(X0) [resolution 68,214]
345. funny(X0) | curious(X0) [subsumption resolution 342,301]
358. curious(fred) <- (6) [resolution 345,217]
360. $false <- (~5, 6) [subsumption resolution 358,166]
361. 5 | ~6 [avatar contradiction clause 360]
362. $false [avatar sat refutation 207,208,315,361]
% SZS output end Proof for 3939769759354263000890523
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 someone is both wise and not quiet then someone is not patient or tall and vice versa. Everyone who is either not curious or not patient is either calm or not tall. If paul is tall or not creative then someone is both not wise and not kind. Everyone who is calm or patient is not happy and vice versa. Everyone who is not curious or not wise is not rich and vice versa. Everyone who is both tall and not kind is either strong or rich. Everyone who is either not patient or calm is either wise or not kind. If fred is either curious or not rich then paul is both patient and rich and vice versa. Everyone who is either not quiet or not wise is both not creative and not strong and vice versa. Everyone who is both humble and not generous is strong and vice versa. If someone is funny or not curious then paul is both happy and quiet. Everyone who is either not creative or creative is generous. If susan is both not strong and not calm then someone is not old or not humble. Everyone who is not kind or wise is not curious or not strong. Everyone who is strong is both not strong and not creative and vice versa. Everyone who is both not calm and not generous is calm or happy. Someone is both not tall and not brave. Susan is brave or not calm. Lucy is not strong. Someone is not happy. Someone is kind or not wise. Someone is not creative or creative. | Paul is not patient. | contradiction | ((?[X]:((wise(X)&~quiet(X))))<=>(?[X]:((~patient(X)|tall(X)))))&
(![X]:((~curious(X)<~>~patient(X))=>(calm(X)<~>~tall(X))))&
(((tall(paul)|~creative(paul)))=>(?[X]:((~wise(X)&~kind(X)))))&
(![X]:((calm(X)|patient(X))<=>~happy(X)))&
(![X]:((~curious(X)|~wise(X))<=>~rich(X)))&
(![X]:((tall(X)&~kind(X))=>(strong(X)<~>rich(X))))&
(![X]:((~patient(X)<~>calm(X))=>(wise(X)<~>~kind(X))))&
(((curious(fred)<~>~rich(fred)))<=>((patient(paul)&rich(paul))))&
(![X]:((~quiet(X)<~>~wise(X))<=>(~creative(X)&~strong(X))))&
(![X]:((humble(X)&~generous(X))<=>strong(X)))&
((?[X]:((funny(X)|~curious(X))))=>((happy(paul)&quiet(paul))))&
(![X]:((~creative(X)<~>creative(X))=>generous(X)))&
(((~strong(susan)&~calm(susan)))=>(?[X]:((~old(X)|~humble(X)))))&
(![X]:((~kind(X)|wise(X))=>(~curious(X)|~strong(X))))&
(![X]:(strong(X)<=>(~strong(X)&~creative(X))))&
(![X]:((~calm(X)&~generous(X))=>(calm(X)|happy(X))))&
(?[X]:((~tall(X)&~brave(X))))&
((brave(susan)|~calm(susan)))&
(~strong(lucy))&
(?[X]:(~happy(X)))&
(?[X]:((kind(X)|~wise(X))))&
(?[X]:((~creative(X)|creative(X)))) | ~patient(paul) | [
"p0",
"p8",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6312302548867095071641064
% SZS output start Proof for 6312302548867095071641064
1. ? [X0] : (~quiet(X0) & wise(X0)) <=> ? [X0] : (tall(X0) | ~patient(X0)) [input p0]
9. ! [X0] : ((~quiet(X0) <~> ~wise(X0)) <=> (~strong(X0) & ~creative(X0))) [input p8]
15. ! [X0] : (strong(X0) <=> (~creative(X0) & ~strong(X0))) [input p14]
23. ~patient(paul) [input hypothesis]
24. ? [X0] : (~quiet(X0) & wise(X0)) <=> ? [X1] : (tall(X1) | ~patient(X1)) [rectify 1]
38. (? [X0] : (~quiet(X0) & wise(X0)) | ! [X1] : (~tall(X1) & patient(X1))) & (? [X1] : (tall(X1) | ~patient(X1)) | ! [X0] : (quiet(X0) | ~wise(X0))) [nnf transformation 24]
39. (? [X0] : (~quiet(X0) & wise(X0)) | ! [X1] : (~tall(X1) & patient(X1))) & (? [X2] : (tall(X2) | ~patient(X2)) | ! [X3] : (quiet(X3) | ~wise(X3))) [rectify 38]
40. ? [X0] : (~quiet(X0) & wise(X0)) => (~quiet(sK0) & wise(sK0)) [choice axiom]
41. ? [X2] : (tall(X2) | ~patient(X2)) => (tall(sK1) | ~patient(sK1)) [choice axiom]
42. ((~quiet(sK0) & wise(sK0)) | ! [X1] : (~tall(X1) & patient(X1))) & ((tall(sK1) | ~patient(sK1)) | ! [X3] : (quiet(X3) | ~wise(X3))) [skolemisation 39,41,40]
54. ! [X0] : ((((wise(X0) | quiet(X0)) & (~wise(X0) | ~quiet(X0))) | (strong(X0) | creative(X0))) & ((~strong(X0) & ~creative(X0)) | ((~quiet(X0) | wise(X0)) & (~wise(X0) | quiet(X0))))) [nnf transformation 9]
55. ! [X0] : ((((wise(X0) | quiet(X0)) & (~wise(X0) | ~quiet(X0))) | strong(X0) | creative(X0)) & ((~strong(X0) & ~creative(X0)) | ((~quiet(X0) | wise(X0)) & (~wise(X0) | quiet(X0))))) [flattening 54]
59. ! [X0] : ((strong(X0) | (creative(X0) | strong(X0))) & ((~creative(X0) & ~strong(X0)) | ~strong(X0))) [nnf transformation 15]
60. ! [X0] : ((strong(X0) | creative(X0) | strong(X0)) & ((~creative(X0) & ~strong(X0)) | ~strong(X0))) [flattening 59]
70. wise(sK0) | patient(X1) [cnf transformation 42]
72. ~quiet(sK0) | patient(X1) [cnf transformation 42]
100. ~creative(X0) | ~wise(X0) | quiet(X0) [cnf transformation 55]
115. ~strong(X0) | ~strong(X0) [cnf transformation 60]
117. strong(X0) | creative(X0) | strong(X0) [cnf transformation 60]
126. ~patient(paul) [cnf transformation 23]
128. ~strong(X0) [duplicate literal removal 115]
129. strong(X0) | creative(X0) [duplicate literal removal 117]
136. 2 <=> quiet(sK0) [avatar definition]
141. 3 <=> ! [X1] : patient(X1) [avatar definition]
142. patient(X1) <- (3) [avatar component clause 141]
143. 3 | ~2 [avatar split clause 72,136,141]
145. 4 <=> wise(sK0) [avatar definition]
147. wise(sK0) <- (4) [avatar component clause 145]
149. 3 | 4 [avatar split clause 70,145,141]
151. 5 <=> ! [X3] : (quiet(X3) | ~wise(X3)) [avatar definition]
152. ~wise(X3) | quiet(X3) <- (5) [avatar component clause 151]
183. 12 <=> patient(paul) [avatar definition]
185. ~patient(paul) <- (~12) [avatar component clause 183]
239. ~12 [avatar split clause 126,183]
243. creative(X2) [resolution 129,128]
258. ~wise(X0) | quiet(X0) [resolution 100,243]
259. 5 [avatar split clause 258,151]
260. quiet(sK0) <- (4, 5) [resolution 152,147]
263. 2 | ~4 | ~5 [avatar split clause 260,151,145,136]
265. $false <- (3, ~12) [resolution 142,185]
266. ~3 | 12 [avatar contradiction clause 265]
268. $false [avatar sat refutation 143,149,239,259,263,266]
% SZS output end Proof for 6312302548867095071641064
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not brave or wise is both not creative and not quiet.
If someone is both not old and quiet then someone is either funny or not happy and vice versa.
Everyone who is either brave or not funny is either not patient or quiet and vice versa.
Everyone who is both happy and kind is not old or not humble and vice versa.
Everyone who is not kind or not creative is not strong or funny.
Everyone who is kind is not happy.
Everyone who is not wise is both kind and not tall and vice versa.
Everyone who is not kind is either calm or patient.
If lucy is not happy or quiet then lucy is both kind and generous and vice versa.
If someone is not kind or patient then fred is both funny and not generous.
Everyone who is either patient or humble is both not strong and curious.
Everyone who is either not funny or quiet is not humble.
Everyone who is both wise and humble is not strong or wise.
If john is both not creative and not rich then lucy is both not brave and happy.
Someone is either curious or not wise.
Someone is both strong and not generous.
Someone is not kind or not strong.
Someone is both not funny and wise.
Someone is tall or not tall.
Paul is either wise or not old.
Susan is both quiet and not creative. | John is not wise. | neutral | (![X]:((~brave(X)<~>wise(X))=>(~creative(X)&~quiet(X))))&
((?[X]:((~old(X)&quiet(X))))<=>(?[X]:((funny(X)<~>~happy(X)))))&
(![X]:((brave(X)<~>~funny(X))<=>(~patient(X)<~>quiet(X))))&
(![X]:((happy(X)&kind(X))<=>(~old(X)|~humble(X))))&
(![X]:((~kind(X)|~creative(X))=>(~strong(X)|funny(X))))&
(![X]:(kind(X)=>~happy(X)))&
(![X]:(~wise(X)<=>(kind(X)&~tall(X))))&
(![X]:(~kind(X)=>(calm(X)<~>patient(X))))&
(((~happy(lucy)|quiet(lucy)))<=>((kind(lucy)&generous(lucy))))&
((?[X]:((~kind(X)|patient(X))))=>((funny(fred)&~generous(fred))))&
(![X]:((patient(X)<~>humble(X))=>(~strong(X)&curious(X))))&
(![X]:((~funny(X)<~>quiet(X))=>~humble(X)))&
(![X]:((wise(X)&humble(X))=>(~strong(X)|wise(X))))&
(((~creative(john)&~rich(john)))=>((~brave(lucy)&happy(lucy))))&
(?[X]:((curious(X)<~>~wise(X))))&
(?[X]:((strong(X)&~generous(X))))&
(?[X]:((~kind(X)|~strong(X))))&
(?[X]:((~funny(X)&wise(X))))&
(?[X]:((tall(X)|~tall(X))))&
((wise(paul)<~>~old(paul)))&
((quiet(susan)&~creative(susan))) | ~wise(john) | [] | null | 0 |
Everyone who is either kind or funny is not strong and vice versa.
If someone is either not brave or curious then someone is calm.
If someone is both wise and quiet then someone is not kind or generous.
Everyone who is not tall is either quiet or not patient.
If paul is funny or quiet then lucy is either not rich or not strong and vice versa.
Everyone who is both not tall and funny is not old and vice versa.
Everyone who is generous is not generous or old and vice versa.
If paul is both calm and not calm then someone is kind or funny.
If someone is either patient or kind then lucy is either not wise or strong and vice versa.
If mary is not quiet or happy then someone is both creative and not rich.
Everyone who is both funny and kind is both brave and not tall and vice versa.
If paul is calm then someone is not rich or humble and vice versa.
If someone is both not brave and not calm then someone is happy or humble and vice versa.
Everyone who is both not kind and not funny is not quiet and vice versa.
Everyone who is not creative is both not happy and not calm.
Everyone who is tall or not calm is both not brave and humble.
John is either not humble or not happy.
Someone is not wise.
Someone is both not kind and not tall.
Susan is not tall or creative.
Someone is creative or wise. | Paul is not kind. | neutral | (![X]:((kind(X)<~>funny(X))<=>~strong(X)))&
((?[X]:((~brave(X)<~>curious(X))))=>(?[X]:(calm(X))))&
((?[X]:((wise(X)&quiet(X))))=>(?[X]:((~kind(X)|generous(X)))))&
(![X]:(~tall(X)=>(quiet(X)<~>~patient(X))))&
(((funny(paul)|quiet(paul)))<=>((~rich(lucy)<~>~strong(lucy))))&
(![X]:((~tall(X)&funny(X))<=>~old(X)))&
(![X]:(generous(X)<=>(~generous(X)|old(X))))&
(((calm(paul)&~calm(paul)))=>(?[X]:((kind(X)|funny(X)))))&
((?[X]:((patient(X)<~>kind(X))))<=>((~wise(lucy)<~>strong(lucy))))&
(((~quiet(mary)|happy(mary)))=>(?[X]:((creative(X)&~rich(X)))))&
(![X]:((funny(X)&kind(X))<=>(brave(X)&~tall(X))))&
((calm(paul))<=>(?[X]:((~rich(X)|humble(X)))))&
((?[X]:((~brave(X)&~calm(X))))<=>(?[X]:((happy(X)|humble(X)))))&
(![X]:((~kind(X)&~funny(X))<=>~quiet(X)))&
(![X]:(~creative(X)=>(~happy(X)&~calm(X))))&
(![X]:((tall(X)|~calm(X))=>(~brave(X)&humble(X))))&
((~humble(john)<~>~happy(john)))&
(?[X]:(~wise(X)))&
(?[X]:((~kind(X)&~tall(X))))&
((~tall(susan)|creative(susan)))&
(?[X]:((creative(X)|wise(X)))) | ~kind(paul) | [] | null | 0 |
If mary is wise or quiet then someone is either generous or kind.
If fred is either not brave or strong then john is not happy or curious.
Everyone who is both funny and not strong is not strong or happy and vice versa.
If paul is either tall or not patient then susan is both not funny and creative.
Everyone who is not rich or calm is both happy and humble.
If paul is both funny and not rich then someone is not creative and vice versa.
Everyone who is either not quiet or not calm is either rich or strong and vice versa.
Everyone who is not strong or not generous is not quiet and vice versa.
Everyone who is not patient or brave is happy or funny.
Everyone who is not rich or brave is either not calm or humble.
If someone is funny or not generous then susan is both brave and not wise.
If lucy is calm or not patient then someone is humble.
If someone is both rich and old then john is either not quiet or curious.
Everyone who is both quiet and not brave is either not rich or not happy and vice versa.
Everyone who is both not rich and strong is not rich or not brave and vice versa.
If someone is happy then paul is either not creative or happy.
Someone is creative or happy.
Someone is not quiet or generous.
Someone is not tall.
Susan is rich.
John is generous.
Fred is not patient.
Someone is either not strong or quiet.
Lucy is not strong or generous. | Fred is strong. | contradiction | (((wise(mary)|quiet(mary)))=>(?[X]:((generous(X)<~>kind(X)))))&
(((~brave(fred)<~>strong(fred)))=>((~happy(john)|curious(john))))&
(![X]:((funny(X)&~strong(X))<=>(~strong(X)|happy(X))))&
(((tall(paul)<~>~patient(paul)))=>((~funny(susan)&creative(susan))))&
(![X]:((~rich(X)|calm(X))=>(happy(X)&humble(X))))&
(((funny(paul)&~rich(paul)))<=>(?[X]:(~creative(X))))&
(![X]:((~quiet(X)<~>~calm(X))<=>(rich(X)<~>strong(X))))&
(![X]:((~strong(X)|~generous(X))<=>~quiet(X)))&
(![X]:((~patient(X)|brave(X))=>(happy(X)|funny(X))))&
(![X]:((~rich(X)|brave(X))=>(~calm(X)<~>humble(X))))&
((?[X]:((funny(X)|~generous(X))))=>((brave(susan)&~wise(susan))))&
(((calm(lucy)|~patient(lucy)))=>(?[X]:(humble(X))))&
((?[X]:((rich(X)&old(X))))=>((~quiet(john)<~>curious(john))))&
(![X]:((quiet(X)&~brave(X))<=>(~rich(X)<~>~happy(X))))&
(![X]:((~rich(X)&strong(X))<=>(~rich(X)|~brave(X))))&
((?[X]:(happy(X)))=>((~creative(paul)<~>happy(paul))))&
(?[X]:((creative(X)|happy(X))))&
(?[X]:((~quiet(X)|generous(X))))&
(?[X]:(~tall(X)))&
(rich(susan))&
(generous(john))&
(~patient(fred))&
(?[X]:((~strong(X)<~>quiet(X))))&
((~strong(lucy)|generous(lucy))) | strong(fred) | [
"p2",
"p4",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2097129170186113956884896
% SZS output start Proof for 2097129170186113956884896
3. ! [X0] : ((~strong(X0) & funny(X0)) <=> (happy(X0) | ~strong(X0))) [input p2]
5. ! [X0] : ((calm(X0) | ~rich(X0)) => (humble(X0) & happy(X0))) [input p4]
14. ! [X0] : ((~brave(X0) & quiet(X0)) <=> (~rich(X0) <~> ~happy(X0))) [input p13]
15. ! [X0] : ((strong(X0) & ~rich(X0)) <=> (~brave(X0) | ~rich(X0))) [input p14]
25. strong(fred) [input hypothesis]
32. ! [X0] : ((humble(X0) & happy(X0)) | (~calm(X0) & rich(X0))) [ennf transformation 5]
42. ! [X0] : (((~strong(X0) & funny(X0)) | (~happy(X0) & strong(X0))) & ((happy(X0) | ~strong(X0)) | (strong(X0) | ~funny(X0)))) [nnf transformation 3]
43. ! [X0] : (((~strong(X0) & funny(X0)) | (~happy(X0) & strong(X0))) & (happy(X0) | ~strong(X0) | strong(X0) | ~funny(X0))) [flattening 42]
56. ! [X0] : (((~brave(X0) & quiet(X0)) | ((~rich(X0) | happy(X0)) & (~happy(X0) | rich(X0)))) & (((happy(X0) | rich(X0)) & (~happy(X0) | ~rich(X0))) | (brave(X0) | ~quiet(X0)))) [nnf transformation 14]
57. ! [X0] : (((~brave(X0) & quiet(X0)) | ((~rich(X0) | happy(X0)) & (~happy(X0) | rich(X0)))) & (((happy(X0) | rich(X0)) & (~happy(X0) | ~rich(X0))) | brave(X0) | ~quiet(X0))) [flattening 56]
58. ! [X0] : (((strong(X0) & ~rich(X0)) | (brave(X0) & rich(X0))) & ((~brave(X0) | ~rich(X0)) | (~strong(X0) | rich(X0)))) [nnf transformation 15]
59. ! [X0] : (((strong(X0) & ~rich(X0)) | (brave(X0) & rich(X0))) & (~brave(X0) | ~rich(X0) | ~strong(X0) | rich(X0))) [flattening 58]
76. ~happy(X0) | ~strong(X0) [cnf transformation 43]
81. rich(X0) | happy(X0) [cnf transformation 32]
114. ~brave(X0) | ~rich(X0) | happy(X0) [cnf transformation 57]
117. ~rich(X0) | brave(X0) [cnf transformation 59]
131. strong(fred) [cnf transformation 25]
213. ~brave(X0) | happy(X0) [subsumption resolution 114,81]
265. brave(X0) | happy(X0) [resolution 117,81]
285. happy(X0) [subsumption resolution 265,213]
310. ~strong(X0) [resolution 285,76]
330. $false [resolution 310,131]
% SZS output end Proof for 2097129170186113956884896
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not tall or funny is both not strong and not generous.
If alice is not rich then john is either not wise or strong and vice versa.
Everyone who is strong is either old or not generous.
If alice is either creative or strong then paul is generous and vice versa.
Everyone who is both not calm and creative is both not brave and calm and vice versa.
Everyone who is either not generous or creative is either not kind or not strong and vice versa.
If someone is funny or brave then someone is not tall and vice versa.
Everyone who is funny or not tall is not rich and vice versa.
Everyone who is curious or not wise is generous or wise.
Everyone who is either humble or brave is both not funny and not calm.
Everyone who is not tall is both tall and not brave.
Everyone who is either kind or not generous is both not humble and quiet and vice versa.
If john is happy or not humble then someone is both creative and not rich.
Everyone who is not quiet or not kind is either kind or brave.
If fred is not patient then susan is not rich or not generous.
Lucy is not curious or not brave.
John is not quiet.
Lucy is humble or not calm.
Someone is not humble or not brave.
Mary is either not kind or old.
Someone is both not wise and curious. | Alice is creative. | contradiction | (![X]:((~tall(X)|funny(X))=>(~strong(X)&~generous(X))))&
((~rich(alice))<=>((~wise(john)<~>strong(john))))&
(![X]:(strong(X)=>(old(X)<~>~generous(X))))&
(((creative(alice)<~>strong(alice)))<=>(generous(paul)))&
(![X]:((~calm(X)&creative(X))<=>(~brave(X)&calm(X))))&
(![X]:((~generous(X)<~>creative(X))<=>(~kind(X)<~>~strong(X))))&
((?[X]:((funny(X)|brave(X))))<=>(?[X]:(~tall(X))))&
(![X]:((funny(X)|~tall(X))<=>~rich(X)))&
(![X]:((curious(X)|~wise(X))=>(generous(X)|wise(X))))&
(![X]:((humble(X)<~>brave(X))=>(~funny(X)&~calm(X))))&
(![X]:(~tall(X)=>(tall(X)&~brave(X))))&
(![X]:((kind(X)<~>~generous(X))<=>(~humble(X)&quiet(X))))&
(((happy(john)|~humble(john)))=>(?[X]:((creative(X)&~rich(X)))))&
(![X]:((~quiet(X)|~kind(X))=>(kind(X)<~>brave(X))))&
((~patient(fred))=>((~rich(susan)|~generous(susan))))&
((~curious(lucy)|~brave(lucy)))&
(~quiet(john))&
((humble(lucy)|~calm(lucy)))&
(?[X]:((~humble(X)|~brave(X))))&
((~kind(mary)<~>old(mary)))&
(?[X]:((~wise(X)&curious(X)))) | creative(alice) | [
"p4",
"p6",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 4157161528690505323521114
% SZS output start Proof for 4157161528690505323521114
5. ! [X0] : ((creative(X0) & ~calm(X0)) <=> (calm(X0) & ~brave(X0))) [input p4]
7. ? [X0] : (brave(X0) | funny(X0)) <=> ? [X0] : ~tall(X0) [input p6]
11. ! [X0] : (~tall(X0) => (~brave(X0) & tall(X0))) [input p10]
22. creative(alice) [input hypothesis]
23. ? [X0] : (brave(X0) | funny(X0)) <=> ? [X1] : ~tall(X1) [rectify 7]
31. ! [X0] : ((~brave(X0) & tall(X0)) | tall(X0)) [ennf transformation 11]
37. ! [X0] : (((creative(X0) & ~calm(X0)) | (~calm(X0) | brave(X0))) & ((calm(X0) & ~brave(X0)) | (~creative(X0) | calm(X0)))) [nnf transformation 5]
38. ! [X0] : (((creative(X0) & ~calm(X0)) | ~calm(X0) | brave(X0)) & ((calm(X0) & ~brave(X0)) | ~creative(X0) | calm(X0))) [flattening 37]
40. (? [X0] : (brave(X0) | funny(X0)) | ! [X1] : tall(X1)) & (? [X1] : ~tall(X1) | ! [X0] : (~brave(X0) & ~funny(X0))) [nnf transformation 23]
41. (? [X0] : (brave(X0) | funny(X0)) | ! [X1] : tall(X1)) & (? [X2] : ~tall(X2) | ! [X3] : (~brave(X3) & ~funny(X3))) [rectify 40]
42. ? [X0] : (brave(X0) | funny(X0)) => (brave(sK0) | funny(sK0)) [choice axiom]
43. ? [X2] : ~tall(X2) => ~tall(sK1) [choice axiom]
44. ((brave(sK0) | funny(sK0)) | ! [X1] : tall(X1)) & (~tall(sK1) | ! [X3] : (~brave(X3) & ~funny(X3))) [skolemisation 41,43,42]
73. calm(X0) | ~creative(X0) | calm(X0) [cnf transformation 38]
74. ~calm(X0) | ~calm(X0) | brave(X0) [cnf transformation 38]
85. ~tall(sK1) | ~brave(X3) [cnf transformation 44]
96. tall(X0) | tall(X0) [cnf transformation 31]
118. creative(alice) [cnf transformation 22]
120. tall(X0) [duplicate literal removal 96]
122. ~creative(X0) | calm(X0) [duplicate literal removal 73]
123. ~calm(X0) | brave(X0) [duplicate literal removal 74]
145. 5 <=> creative(alice) [avatar definition]
146. creative(alice) <- (5) [avatar component clause 145]
157. 7 <=> ! [X1] : tall(X1) [avatar definition]
158. tall(X1) <- (7) [avatar component clause 157]
169. 10 <=> ! [X3] : ~brave(X3) [avatar definition]
170. ~brave(X3) <- (10) [avatar component clause 169]
172. 11 <=> tall(sK1) [avatar definition]
174. ~tall(sK1) <- (~11) [avatar component clause 172]
175. 10 | ~11 [avatar split clause 85,172,169]
181. 7 [avatar split clause 120,157]
224. 5 [avatar split clause 118,145]
225. $false <- (7, ~11) [resolution 174,158]
226. ~7 | 11 [avatar contradiction clause 225]
234. calm(alice) <- (5) [resolution 122,146]
240. brave(alice) <- (5) [resolution 234,123]
241. $false <- (5, 10) [subsumption resolution 240,170]
242. ~5 | ~10 [avatar contradiction clause 241]
243. $false [avatar sat refutation 175,181,224,226,242]
% SZS output end Proof for 4157161528690505323521114
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient or not kind is not rich or not old.
Everyone who is not generous or happy is not generous or not happy.
Everyone who is quiet or not creative is either not quiet or funny.
Everyone who is generous is both funny and not curious and vice versa.
Everyone who is either not generous or not creative is both old and not rich.
Everyone who is not creative is curious.
Everyone who is either not funny or tall is both kind and rich and vice versa.
If john is rich or happy then susan is not kind.
If mary is either not curious or tall then someone is humble or not wise and vice versa.
If someone is not patient or kind then fred is either humble or not brave and vice versa.
Everyone who is either not creative or kind is old and vice versa.
If someone is tall then someone is not tall or quiet and vice versa.
If someone is creative then alice is wise and vice versa.
If fred is old or happy then lucy is either kind or quiet.
Everyone who is both brave and kind is not happy and vice versa.
If someone is wise then someone is both not wise and not kind and vice versa.
Someone is both brave and creative.
John is not happy.
Mary is both not wise and not kind.
Someone is either brave or not kind.
Alice is creative.
Lucy is not humble.
Susan is either tall or not rich.
John is rich. | Mary is not creative. | entailment | (![X]:((patient(X)<~>~kind(X))=>(~rich(X)|~old(X))))&
(![X]:((~generous(X)|happy(X))=>(~generous(X)|~happy(X))))&
(![X]:((quiet(X)|~creative(X))=>(~quiet(X)<~>funny(X))))&
(![X]:(generous(X)<=>(funny(X)&~curious(X))))&
(![X]:((~generous(X)<~>~creative(X))=>(old(X)&~rich(X))))&
(![X]:(~creative(X)=>curious(X)))&
(![X]:((~funny(X)<~>tall(X))<=>(kind(X)&rich(X))))&
(((rich(john)|happy(john)))=>(~kind(susan)))&
(((~curious(mary)<~>tall(mary)))<=>(?[X]:((humble(X)|~wise(X)))))&
((?[X]:((~patient(X)|kind(X))))<=>((humble(fred)<~>~brave(fred))))&
(![X]:((~creative(X)<~>kind(X))<=>old(X)))&
((?[X]:(tall(X)))<=>(?[X]:((~tall(X)|quiet(X)))))&
((?[X]:(creative(X)))<=>(wise(alice)))&
(((old(fred)|happy(fred)))=>((kind(lucy)<~>quiet(lucy))))&
(![X]:((brave(X)&kind(X))<=>~happy(X)))&
((?[X]:(wise(X)))<=>(?[X]:((~wise(X)&~kind(X)))))&
(?[X]:((brave(X)&creative(X))))&
(~happy(john))&
((~wise(mary)&~kind(mary)))&
(?[X]:((brave(X)<~>~kind(X))))&
(creative(alice))&
(~humble(lucy))&
((tall(susan)<~>~rich(susan)))&
(rich(john)) | ~creative(mary) | [
"p1",
"p4",
"p10",
"p14",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 3968392897149743612248832
% SZS output start Proof for 3968392897149743612248832
2. ! [X0] : ((happy(X0) | ~generous(X0)) => (~happy(X0) | ~generous(X0))) [input p1]
5. ! [X0] : ((~generous(X0) <~> ~creative(X0)) => (~rich(X0) & old(X0))) [input p4]
11. ! [X0] : ((~creative(X0) <~> kind(X0)) <=> old(X0)) [input p10]
15. ! [X0] : ((kind(X0) & brave(X0)) <=> ~happy(X0)) [input p14]
19. ~kind(mary) & ~wise(mary) [input p18]
25. creative(mary) [input hypothesis]
28. ! [X0] : (~happy(X0) => (kind(X0) & brave(X0))) [unused predicate definition removal 15]
31. ! [X0] : ((~happy(X0) | ~generous(X0)) | (~happy(X0) & generous(X0))) [ennf transformation 2]
32. ! [X0] : (~happy(X0) | ~generous(X0) | (~happy(X0) & generous(X0))) [flattening 31]
34. ! [X0] : ((~rich(X0) & old(X0)) | (~generous(X0) <=> ~creative(X0))) [ennf transformation 5]
38. ! [X0] : ((kind(X0) & brave(X0)) | happy(X0)) [ennf transformation 28]
43. ! [X0] : ((~rich(X0) & old(X0)) | ((~generous(X0) | creative(X0)) & (~creative(X0) | generous(X0)))) [nnf transformation 34]
54. ! [X0] : ((((~kind(X0) | creative(X0)) & (kind(X0) | ~creative(X0))) | ~old(X0)) & (old(X0) | ((~creative(X0) | ~kind(X0)) & (kind(X0) | creative(X0))))) [nnf transformation 11]
79. ~happy(X0) | ~generous(X0) | ~happy(X0) [cnf transformation 32]
87. ~creative(X0) | old(X0) | generous(X0) [cnf transformation 43]
114. ~creative(X0) | kind(X0) | ~old(X0) [cnf transformation 54]
126. happy(X0) | kind(X0) [cnf transformation 38]
134. ~kind(mary) [cnf transformation 19]
142. creative(mary) [cnf transformation 25]
144. ~happy(X0) | ~generous(X0) [duplicate literal removal 79]
324. ~generous(X0) | kind(X0) [resolution 144,126]
332. old(mary) | generous(mary) [resolution 87,142]
337. 38 <=> generous(mary) [avatar definition]
339. generous(mary) <- (38) [avatar component clause 337]
341. 39 <=> old(mary) [avatar definition]
343. old(mary) <- (39) [avatar component clause 341]
344. 38 | 39 [avatar split clause 332,341,337]
380. kind(mary) <- (38) [resolution 339,324]
383. $false <- (38) [subsumption resolution 380,134]
384. ~38 [avatar contradiction clause 383]
467. kind(mary) | ~old(mary) [resolution 114,142]
472. ~old(mary) [subsumption resolution 467,134]
473. $false <- (39) [subsumption resolution 472,343]
474. ~39 [avatar contradiction clause 473]
475. $false [avatar sat refutation 344,384,474]
% SZS output end Proof for 3968392897149743612248832
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
If paul is not kind then someone is both not kind and calm.
Everyone who is both patient and calm is not kind or happy.
Everyone who is either not rich or not strong is creative or quiet.
Everyone who is humble or creative is both wise and old and vice versa.
If someone is patient then susan is generous or creative.
Everyone who is both not calm and not wise is creative and vice versa.
If someone is funny or rich then someone is either rich or not curious.
If lucy is calm then paul is either not calm or not brave and vice versa.
Everyone who is not rich is tall.
If someone is either kind or rich then someone is not quiet or kind.
If someone is both strong and not calm then alice is funny.
If john is not patient or rich then susan is quiet or not curious and vice versa.
If someone is both not patient and not happy then someone is not kind or creative and vice versa.
If someone is not humble then paul is not old.
If someone is either not happy or humble then mary is not wise or brave.
Everyone who is both wise and not strong is either kind or calm.
Susan is old.
Susan is generous.
Someone is either not brave or happy.
Susan is happy or not rich.
Someone is not happy.
Someone is not generous or not wise.
Fred is both not calm and brave.
Paul is either old or calm. | John is creative. | contradiction | ((~kind(paul))=>(?[X]:((~kind(X)&calm(X)))))&
(![X]:((patient(X)&calm(X))=>(~kind(X)|happy(X))))&
(![X]:((~rich(X)<~>~strong(X))=>(creative(X)|quiet(X))))&
(![X]:((humble(X)|creative(X))<=>(wise(X)&old(X))))&
((?[X]:(patient(X)))=>((generous(susan)|creative(susan))))&
(![X]:((~calm(X)&~wise(X))<=>creative(X)))&
((?[X]:((funny(X)|rich(X))))=>(?[X]:((rich(X)<~>~curious(X)))))&
((calm(lucy))<=>((~calm(paul)<~>~brave(paul))))&
(![X]:(~rich(X)=>tall(X)))&
((?[X]:((kind(X)<~>rich(X))))=>(?[X]:((~quiet(X)|kind(X)))))&
((?[X]:((strong(X)&~calm(X))))=>(funny(alice)))&
(((~patient(john)|rich(john)))<=>((quiet(susan)|~curious(susan))))&
((?[X]:((~patient(X)&~happy(X))))<=>(?[X]:((~kind(X)|creative(X)))))&
((?[X]:(~humble(X)))=>(~old(paul)))&
((?[X]:((~happy(X)<~>humble(X))))=>((~wise(mary)|brave(mary))))&
(![X]:((wise(X)&~strong(X))=>(kind(X)<~>calm(X))))&
(old(susan))&
(generous(susan))&
(?[X]:((~brave(X)<~>happy(X))))&
((happy(susan)|~rich(susan)))&
(?[X]:(~happy(X)))&
(?[X]:((~generous(X)|~wise(X))))&
((~calm(fred)&brave(fred)))&
((old(paul)<~>calm(paul))) | creative(john) | [
"p3",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 9223353171855618009284473
% SZS output start Proof for 9223353171855618009284473
4. ! [X0] : ((creative(X0) | humble(X0)) <=> (old(X0) & wise(X0))) [input p3]
6. ! [X0] : ((~wise(X0) & ~calm(X0)) <=> creative(X0)) [input p5]
25. creative(john) [input hypothesis]
48. ! [X0] : (((creative(X0) | humble(X0)) | (~old(X0) | ~wise(X0))) & ((old(X0) & wise(X0)) | (~creative(X0) & ~humble(X0)))) [nnf transformation 4]
49. ! [X0] : ((creative(X0) | humble(X0) | ~old(X0) | ~wise(X0)) & ((old(X0) & wise(X0)) | (~creative(X0) & ~humble(X0)))) [flattening 48]
50. ! [X0] : (((~wise(X0) & ~calm(X0)) | ~creative(X0)) & (creative(X0) | (wise(X0) | calm(X0)))) [nnf transformation 6]
51. ! [X0] : (((~wise(X0) & ~calm(X0)) | ~creative(X0)) & (creative(X0) | wise(X0) | calm(X0))) [flattening 50]
84. wise(X0) | ~creative(X0) [cnf transformation 49]
91. ~wise(X0) | ~creative(X0) [cnf transformation 51]
128. creative(john) [cnf transformation 25]
155. ~creative(X0) [subsumption resolution 91,84]
313. $false [subsumption resolution 128,155]
% SZS output end Proof for 9223353171855618009284473
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not curious and tall is either not funny or not calm. If someone is both generous and not patient then someone is either creative or not old. Everyone who is not happy or tall is humble. If someone is generous or calm then alice is generous or curious and vice versa. Everyone who is not rich is not strong or rich. Everyone who is wise is not happy. If someone is not brave then lucy is not kind or curious. Everyone who is either old or funny is either creative or wise. If someone is not humble or not generous then someone is happy and vice versa. If paul is funny then someone is not old or not strong. If someone is either rich or not humble then paul is not rich and vice versa. If someone is not calm then someone is patient and vice versa. If mary is rich or strong then lucy is both not curious and quiet and vice versa. Everyone who is not wise is not humble. If someone is not funny or calm then susan is both happy and humble and vice versa. Everyone who is both funny and not wise is either not curious or funny and vice versa. Someone is happy or not patient. Lucy is not kind. Someone is either not humble or kind. John is not old. Someone is generous or creative. Mary is either not funny or not rich. | Paul is funny. | entailment | (![X]:((~curious(X)&tall(X))=>(~funny(X)<~>~calm(X))))&
((?[X]:((generous(X)&~patient(X))))=>(?[X]:((creative(X)<~>~old(X)))))&
(![X]:((~happy(X)|tall(X))=>humble(X)))&
((?[X]:((generous(X)|calm(X))))<=>((generous(alice)|curious(alice))))&
(![X]:(~rich(X)=>(~strong(X)|rich(X))))&
(![X]:(wise(X)=>~happy(X)))&
((?[X]:(~brave(X)))=>((~kind(lucy)|curious(lucy))))&
(![X]:((old(X)<~>funny(X))=>(creative(X)<~>wise(X))))&
((?[X]:((~humble(X)|~generous(X))))<=>(?[X]:(happy(X))))&
((funny(paul))=>(?[X]:((~old(X)|~strong(X)))))&
((?[X]:((rich(X)<~>~humble(X))))<=>(~rich(paul)))&
((?[X]:(~calm(X)))<=>(?[X]:(patient(X))))&
(((rich(mary)|strong(mary)))<=>((~curious(lucy)&quiet(lucy))))&
(![X]:(~wise(X)=>~humble(X)))&
((?[X]:((~funny(X)|calm(X))))<=>((happy(susan)&humble(susan))))&
(![X]:((funny(X)&~wise(X))<=>(~curious(X)<~>funny(X))))&
(?[X]:((happy(X)|~patient(X))))&
(~kind(lucy))&
(?[X]:((~humble(X)<~>kind(X))))&
(~old(john))&
(?[X]:((generous(X)|creative(X))))&
((~funny(mary)<~>~rich(mary))) | funny(paul) | [
"p5",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5083359010540700397209193
% SZS output start Proof for 5083359010540700397209193
6. ! [X0] : (wise(X0) => ~happy(X0)) [input p5]
14. ! [X0] : (~wise(X0) => ~humble(X0)) [input p13]
15. ? [X0] : (calm(X0) | ~funny(X0)) <=> (humble(susan) & happy(susan)) [input p14]
23. ~funny(paul) [input hypothesis]
34. ! [X0] : (~happy(X0) | ~wise(X0)) [ennf transformation 6]
37. ! [X0] : (~humble(X0) | wise(X0)) [ennf transformation 14]
66. (? [X0] : (calm(X0) | ~funny(X0)) | (~humble(susan) | ~happy(susan))) & ((humble(susan) & happy(susan)) | ! [X0] : (~calm(X0) & funny(X0))) [nnf transformation 15]
67. (? [X0] : (calm(X0) | ~funny(X0)) | ~humble(susan) | ~happy(susan)) & ((humble(susan) & happy(susan)) | ! [X0] : (~calm(X0) & funny(X0))) [flattening 66]
68. (? [X0] : (calm(X0) | ~funny(X0)) | ~humble(susan) | ~happy(susan)) & ((humble(susan) & happy(susan)) | ! [X1] : (~calm(X1) & funny(X1))) [rectify 67]
69. ? [X0] : (calm(X0) | ~funny(X0)) => (calm(sK8) | ~funny(sK8)) [choice axiom]
70. ((calm(sK8) | ~funny(sK8)) | ~humble(susan) | ~happy(susan)) & ((humble(susan) & happy(susan)) | ! [X1] : (~calm(X1) & funny(X1))) [skolemisation 68,69]
89. ~wise(X0) | ~happy(X0) [cnf transformation 34]
109. ~humble(X0) | wise(X0) [cnf transformation 37]
110. happy(susan) | funny(X1) [cnf transformation 70]
112. humble(susan) | funny(X1) [cnf transformation 70]
129. ~funny(paul) [cnf transformation 23]
197. 16 <=> funny(paul) [avatar definition]
199. ~funny(paul) <- (~16) [avatar component clause 197]
270. 32 <=> happy(susan) [avatar definition]
274. 33 <=> humble(susan) [avatar definition]
275. humble(susan) <- (33) [avatar component clause 274]
288. 36 <=> ! [X1] : funny(X1) [avatar definition]
289. funny(X1) <- (36) [avatar component clause 288]
290. 36 | 33 [avatar split clause 112,274,288]
292. 36 | 32 [avatar split clause 110,270,288]
328. ~16 [avatar split clause 129,197]
333. wise(susan) <- (33) [resolution 109,275]
338. ~happy(susan) <- (33) [resolution 333,89]
341. ~32 | ~33 [avatar split clause 338,274,270]
348. $false <- (~16, 36) [resolution 289,199]
353. 16 | ~36 [avatar contradiction clause 348]
354. $false [avatar sat refutation 290,292,328,341,353]
% SZS output end Proof for 5083359010540700397209193
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not strong or not humble then someone is not rich or not tall. Everyone who is both humble and tall is wise or not tall. Everyone who is either rich or not humble is wise or not old. If someone is not brave then paul is either rich or not funny. If someone is not rich then someone is either not old or funny and vice versa. If fred is old or not rich then someone is either not tall or wise. Everyone who is not quiet or kind is both not wise and patient. Everyone who is happy or strong is strong or not brave and vice versa. If someone is humble then someone is not wise or happy and vice versa. Everyone who is either brave or rich is generous and vice versa. Everyone who is not kind is both not humble and generous. If someone is patient or not quiet then someone is both creative and generous and vice versa. Everyone who is both rich and quiet is not humble or not calm and vice versa. Everyone who is either rich or not calm is calm or not strong. Everyone who is both not old and not creative is either not strong or humble and vice versa. Everyone who is not old or patient is not funny or not old. Susan is either not funny or calm. Alice is either not funny or not wise. Someone is not happy. John is calm or not calm. John is not kind or funny. Paul is wise. Someone is both not old and not wise. Someone is either not brave or kind. | Fred is not happy. | neutral | ((?[X]:((~strong(X)|~humble(X))))=>(?[X]:((~rich(X)|~tall(X)))))&
(![X]:((humble(X)&tall(X))=>(wise(X)|~tall(X))))&
(![X]:((rich(X)<~>~humble(X))=>(wise(X)|~old(X))))&
((?[X]:(~brave(X)))=>((rich(paul)<~>~funny(paul))))&
((?[X]:(~rich(X)))<=>(?[X]:((~old(X)<~>funny(X)))))&
(((old(fred)|~rich(fred)))=>(?[X]:((~tall(X)<~>wise(X)))))&
(![X]:((~quiet(X)|kind(X))=>(~wise(X)&patient(X))))&
(![X]:((happy(X)|strong(X))<=>(strong(X)|~brave(X))))&
((?[X]:(humble(X)))<=>(?[X]:((~wise(X)|happy(X)))))&
(![X]:((brave(X)<~>rich(X))<=>generous(X)))&
(![X]:(~kind(X)=>(~humble(X)&generous(X))))&
((?[X]:((patient(X)|~quiet(X))))<=>(?[X]:((creative(X)&generous(X)))))&
(![X]:((rich(X)&quiet(X))<=>(~humble(X)|~calm(X))))&
(![X]:((rich(X)<~>~calm(X))=>(calm(X)|~strong(X))))&
(![X]:((~old(X)&~creative(X))<=>(~strong(X)<~>humble(X))))&
(![X]:((~old(X)|patient(X))=>(~funny(X)|~old(X))))&
((~funny(susan)<~>calm(susan)))&
((~funny(alice)<~>~wise(alice)))&
(?[X]:(~happy(X)))&
((calm(john)|~calm(john)))&
((~kind(john)|funny(john)))&
(wise(paul))&
(?[X]:((~old(X)&~wise(X))))&
(?[X]:((~brave(X)<~>kind(X)))) | ~happy(fred) | [] | null | 0 |
Everyone who is not tall or not calm is rich.
Everyone who is calm is brave and vice versa.
If someone is both not rich and not brave then john is not calm or quiet.
If paul is not generous then paul is not calm and vice versa.
If john is curious then someone is rich.
If someone is strong or brave then mary is either not strong or not curious and vice versa.
If paul is quiet then someone is either not strong or not rich.
If someone is either curious or not old then paul is either brave or generous and vice versa.
If fred is not old or happy then mary is curious or strong and vice versa.
If someone is rich then john is both not funny and not curious.
Everyone who is either not curious or happy is brave or old and vice versa.
If fred is creative or strong then john is either not patient or brave.
Everyone who is kind or not humble is both quiet and not brave and vice versa.
If someone is either strong or not curious then someone is either not tall or not humble and vice versa.
Everyone who is generous is either old or not happy and vice versa.
Paul is humble.
Mary is brave or wise.
John is humble or happy.
Someone is not happy.
Someone is either not generous or not happy.
Mary is both strong and not tall. | Paul is happy. | contradiction | (![X]:((~tall(X)|~calm(X))=>rich(X)))&
(![X]:(calm(X)<=>brave(X)))&
((?[X]:((~rich(X)&~brave(X))))=>((~calm(john)|quiet(john))))&
((~generous(paul))<=>(~calm(paul)))&
((curious(john))=>(?[X]:(rich(X))))&
((?[X]:((strong(X)|brave(X))))<=>((~strong(mary)<~>~curious(mary))))&
((quiet(paul))=>(?[X]:((~strong(X)<~>~rich(X)))))&
((?[X]:((curious(X)<~>~old(X))))<=>((brave(paul)<~>generous(paul))))&
(((~old(fred)|happy(fred)))<=>((curious(mary)|strong(mary))))&
((?[X]:(rich(X)))=>((~funny(john)&~curious(john))))&
(![X]:((~curious(X)<~>happy(X))<=>(brave(X)|old(X))))&
(((creative(fred)|strong(fred)))=>((~patient(john)<~>brave(john))))&
(![X]:((kind(X)|~humble(X))<=>(quiet(X)&~brave(X))))&
((?[X]:((strong(X)<~>~curious(X))))<=>(?[X]:((~tall(X)<~>~humble(X)))))&
(![X]:(generous(X)<=>(old(X)<~>~happy(X))))&
(humble(paul))&
((brave(mary)|wise(mary)))&
((humble(john)|happy(john)))&
(?[X]:(~happy(X)))&
(?[X]:((~generous(X)<~>~happy(X))))&
((strong(mary)&~tall(mary))) | happy(paul) | [
"p1",
"p3",
"p7",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4053300407608595905664470
% SZS output start Proof for 4053300407608595905664470
2. ! [X0] : (calm(X0) <=> brave(X0)) [input p1]
4. ~generous(paul) <=> ~calm(paul) [input p3]
8. ? [X0] : (curious(X0) <~> ~old(X0)) <=> (brave(paul) <~> generous(paul)) [input p7]
11. ! [X0] : ((~curious(X0) <~> happy(X0)) <=> (old(X0) | brave(X0))) [input p10]
15. ! [X0] : (generous(X0) <=> (old(X0) <~> ~happy(X0))) [input p14]
22. happy(paul) [input hypothesis]
34. ! [X0] : ((calm(X0) | ~brave(X0)) & (brave(X0) | ~calm(X0))) [nnf transformation 2]
35. (~generous(paul) | calm(paul)) & (~calm(paul) | generous(paul)) [nnf transformation 4]
45. (? [X0] : ((old(X0) | ~curious(X0)) & (~old(X0) | curious(X0))) | ((brave(paul) | ~generous(paul)) & (generous(paul) | ~brave(paul)))) & (((~generous(paul) | ~brave(paul)) & (generous(paul) | brave(paul))) | ! [X0] : ((curious(X0) | old(X0)) & (~old(X0) | ~curious(X0)))) [nnf transformation 8]
46. (? [X0] : ((old(X0) | ~curious(X0)) & (~old(X0) | curious(X0))) | ((brave(paul) | ~generous(paul)) & (generous(paul) | ~brave(paul)))) & (((~generous(paul) | ~brave(paul)) & (generous(paul) | brave(paul))) | ! [X1] : ((curious(X1) | old(X1)) & (~old(X1) | ~curious(X1)))) [rectify 45]
47. ? [X0] : ((old(X0) | ~curious(X0)) & (~old(X0) | curious(X0))) => ((old(sK3) | ~curious(sK3)) & (~old(sK3) | curious(sK3))) [choice axiom]
48. (((old(sK3) | ~curious(sK3)) & (~old(sK3) | curious(sK3))) | ((brave(paul) | ~generous(paul)) & (generous(paul) | ~brave(paul)))) & (((~generous(paul) | ~brave(paul)) & (generous(paul) | brave(paul))) | ! [X1] : ((curious(X1) | old(X1)) & (~old(X1) | ~curious(X1)))) [skolemisation 46,47]
51. ! [X0] : ((((~happy(X0) | curious(X0)) & (happy(X0) | ~curious(X0))) | (~old(X0) & ~brave(X0))) & ((old(X0) | brave(X0)) | ((~curious(X0) | ~happy(X0)) & (happy(X0) | curious(X0))))) [nnf transformation 11]
52. ! [X0] : ((((~happy(X0) | curious(X0)) & (happy(X0) | ~curious(X0))) | (~old(X0) & ~brave(X0))) & (old(X0) | brave(X0) | ((~curious(X0) | ~happy(X0)) & (happy(X0) | curious(X0))))) [flattening 51]
61. ! [X0] : ((generous(X0) | ((old(X0) | happy(X0)) & (~happy(X0) | ~old(X0)))) & (((happy(X0) | ~old(X0)) & (~happy(X0) | old(X0))) | ~generous(X0))) [nnf transformation 15]
69. ~calm(X0) | brave(X0) [cnf transformation 34]
70. ~brave(X0) | calm(X0) [cnf transformation 34]
72. ~calm(paul) | generous(paul) [cnf transformation 35]
73. ~generous(paul) | calm(paul) [cnf transformation 35]
83. generous(paul) | brave(paul) | ~old(X1) | ~curious(X1) [cnf transformation 48]
84. generous(paul) | brave(paul) | curious(X1) | old(X1) [cnf transformation 48]
85. ~generous(paul) | ~brave(paul) | ~old(X1) | ~curious(X1) [cnf transformation 48]
97. ~happy(X0) | brave(X0) | ~curious(X0) | old(X0) [cnf transformation 52]
101. ~happy(X0) | curious(X0) | ~old(X0) [cnf transformation 52]
117. ~happy(X0) | old(X0) | ~generous(X0) [cnf transformation 61]
128. happy(paul) [cnf transformation 22]
142. 4 <=> calm(paul) [avatar definition]
143. ~calm(paul) <- (~4) [avatar component clause 142]
144. calm(paul) <- (4) [avatar component clause 142]
146. 5 <=> generous(paul) [avatar definition]
149. 4 | ~5 [avatar split clause 73,146,142]
150. 5 | ~4 [avatar split clause 72,142,146]
203. 17 <=> brave(paul) [avatar definition]
204. ~brave(paul) <- (~17) [avatar component clause 203]
205. brave(paul) <- (17) [avatar component clause 203]
219. 20 <=> ! [X1] : (curious(X1) | old(X1)) [avatar definition]
220. old(X1) | curious(X1) <- (20) [avatar component clause 219]
223. 21 <=> ! [X1] : (~old(X1) | ~curious(X1)) [avatar definition]
224. ~old(X1) | ~curious(X1) <- (21) [avatar component clause 223]
225. 21 | ~17 | ~5 [avatar split clause 85,146,203,223]
226. 20 | 17 | 5 [avatar split clause 84,146,203,219]
227. 21 | 17 | 5 [avatar split clause 83,146,203,223]
314. brave(paul) <- (4) [resolution 69,144]
315. $false <- (4, ~17) [subsumption resolution 314,204]
316. ~4 | 17 [avatar contradiction clause 315]
317. calm(paul) <- (17) [resolution 70,205]
318. $false <- (~4, 17) [subsumption resolution 317,143]
319. 4 | ~17 [avatar contradiction clause 318]
345. curious(paul) | ~old(paul) [resolution 101,128]
346. ~old(paul) <- (21) [subsumption resolution 345,224]
347. old(paul) | ~generous(paul) [resolution 117,128]
348. curious(paul) <- (20, 21) [resolution 346,220]
378. brave(paul) | ~curious(paul) | old(paul) [resolution 97,128]
388. ~generous(paul) <- (21) [subsumption resolution 347,346]
389. ~5 | ~21 [avatar split clause 388,223,146]
390. brave(paul) | old(paul) <- (20, 21) [subsumption resolution 378,348]
391. brave(paul) <- (20, 21) [subsumption resolution 390,346]
392. 17 | ~20 | ~21 [avatar split clause 391,223,219,203]
393. $false [avatar sat refutation 149,150,225,226,227,316,319,389,392]
% SZS output end Proof for 4053300407608595905664470
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm or not happy then someone is either not kind or funny and vice versa.
Everyone who is quiet is either not curious or not quiet and vice versa.
If fred is quiet then lucy is not curious or funny and vice versa.
If someone is either not kind or not old then someone is either funny or strong.
If lucy is both curious and not generous then fred is not strong and vice versa.
Everyone who is old is either not funny or not happy and vice versa.
Everyone who is both wise and strong is either brave or not creative.
If someone is humble then someone is either not generous or old and vice versa.
Everyone who is tall or calm is either not generous or generous and vice versa.
If susan is both not humble and funny then mary is funny or not kind and vice versa.
Everyone who is both not strong and tall is both not happy and not strong.
Everyone who is not wise or funny is wise or not old.
Everyone who is not strong is either not curious or calm.
Everyone who is either creative or not creative is curious or rich and vice versa.
If someone is humble then fred is quiet.
Fred is not kind or not generous.
Susan is either not kind or wise.
Alice is either old or not curious.
Fred is both old and tall.
Alice is not brave or not funny.
Paul is not funny or brave.
Someone is both rich and calm. | Fred is wise. | entailment | ((?[X]:((calm(X)<~>~happy(X))))<=>(?[X]:((~kind(X)<~>funny(X)))))&
(![X]:(quiet(X)<=>(~curious(X)<~>~quiet(X))))&
((quiet(fred))<=>((~curious(lucy)|funny(lucy))))&
((?[X]:((~kind(X)<~>~old(X))))=>(?[X]:((funny(X)<~>strong(X)))))&
(((curious(lucy)&~generous(lucy)))<=>(~strong(fred)))&
(![X]:(old(X)<=>(~funny(X)<~>~happy(X))))&
(![X]:((wise(X)&strong(X))=>(brave(X)<~>~creative(X))))&
((?[X]:(humble(X)))<=>(?[X]:((~generous(X)<~>old(X)))))&
(![X]:((tall(X)|calm(X))<=>(~generous(X)<~>generous(X))))&
(((~humble(susan)&funny(susan)))<=>((funny(mary)|~kind(mary))))&
(![X]:((~strong(X)&tall(X))=>(~happy(X)&~strong(X))))&
(![X]:((~wise(X)|funny(X))=>(wise(X)|~old(X))))&
(![X]:(~strong(X)=>(~curious(X)<~>calm(X))))&
(![X]:((creative(X)<~>~creative(X))<=>(curious(X)|rich(X))))&
((?[X]:(humble(X)))=>(quiet(fred)))&
((~kind(fred)|~generous(fred)))&
((~kind(susan)<~>wise(susan)))&
((old(alice)<~>~curious(alice)))&
((old(fred)&tall(fred)))&
((~brave(alice)|~funny(alice)))&
((~funny(paul)|brave(paul)))&
(?[X]:((rich(X)&calm(X)))) | wise(fred) | [
"p11",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 3802736134908790741410046
% SZS output start Proof for 3802736134908790741410046
12. ! [X0] : ((funny(X0) | ~wise(X0)) => (~old(X0) | wise(X0))) [input p11]
19. tall(fred) & old(fred) [input p18]
23. ~wise(fred) [input hypothesis]
32. ! [X0] : ((~old(X0) | wise(X0)) | (~funny(X0) & wise(X0))) [ennf transformation 12]
33. ! [X0] : (~old(X0) | wise(X0) | (~funny(X0) & wise(X0))) [flattening 32]
113. ~old(X0) | wise(X0) | wise(X0) [cnf transformation 33]
129. old(fred) [cnf transformation 19]
135. ~wise(fred) [cnf transformation 23]
138. ~old(X0) | wise(X0) [duplicate literal removal 113]
310. wise(fred) [resolution 138,129]
311. $false [subsumption resolution 310,135]
% SZS output end Proof for 3802736134908790741410046
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave or quiet is both not strong and not tall and vice versa.
Everyone who is either patient or curious is not old and vice versa.
Everyone who is creative or funny is either curious or happy.
If someone is not kind then john is tall and vice versa.
If someone is not strong or humble then john is not wise or not happy.
Everyone who is both not strong and humble is either strong or rich.
If someone is not humble then susan is both humble and not strong.
Everyone who is both rich and not quiet is curious.
Everyone who is both not funny and happy is either not happy or not kind and vice versa.
Everyone who is both generous and not humble is not generous.
Everyone who is not generous or not rich is both not wise and creative.
Everyone who is not humble or humble is calm and vice versa.
If someone is not happy then mary is not generous or generous.
Everyone who is not happy is creative.
Everyone who is either happy or calm is happy or not kind.
Everyone who is either not calm or calm is both quiet and not tall and vice versa.
Paul is either happy or curious.
Alice is patient or not happy.
Paul is not curious or kind.
Someone is either quiet or not brave.
Someone is both not curious and not strong.
Someone is not wise or not old. | Susan is wise. | neutral | (![X]:((brave(X)<~>quiet(X))<=>(~strong(X)&~tall(X))))&
(![X]:((patient(X)<~>curious(X))<=>~old(X)))&
(![X]:((creative(X)|funny(X))=>(curious(X)<~>happy(X))))&
((?[X]:(~kind(X)))<=>(tall(john)))&
((?[X]:((~strong(X)|humble(X))))=>((~wise(john)|~happy(john))))&
(![X]:((~strong(X)&humble(X))=>(strong(X)<~>rich(X))))&
((?[X]:(~humble(X)))=>((humble(susan)&~strong(susan))))&
(![X]:((rich(X)&~quiet(X))=>curious(X)))&
(![X]:((~funny(X)&happy(X))<=>(~happy(X)<~>~kind(X))))&
(![X]:((generous(X)&~humble(X))=>~generous(X)))&
(![X]:((~generous(X)|~rich(X))=>(~wise(X)&creative(X))))&
(![X]:((~humble(X)|humble(X))<=>calm(X)))&
((?[X]:(~happy(X)))=>((~generous(mary)|generous(mary))))&
(![X]:(~happy(X)=>creative(X)))&
(![X]:((happy(X)<~>calm(X))=>(happy(X)|~kind(X))))&
(![X]:((~calm(X)<~>calm(X))<=>(quiet(X)&~tall(X))))&
((happy(paul)<~>curious(paul)))&
((patient(alice)|~happy(alice)))&
((~curious(paul)|kind(paul)))&
(?[X]:((quiet(X)<~>~brave(X))))&
(?[X]:((~curious(X)&~strong(X))))&
(?[X]:((~wise(X)|~old(X)))) | wise(susan) | [] | null | 0 |
Everyone who is not patient is both happy and quiet and vice versa.
Everyone who is funny or not quiet is either creative or not generous and vice versa.
Everyone who is creative is both kind and patient.
If paul is either not calm or wise then someone is creative or wise and vice versa.
If alice is happy or not patient then someone is humble.
If susan is not creative or wise then someone is either brave or tall.
Everyone who is not calm or not funny is humble or not tall.
Everyone who is both not calm and strong is not patient and vice versa.
Everyone who is both not brave and kind is not strong and vice versa.
If someone is both patient and not generous then alice is patient.
Everyone who is not wise or not quiet is both patient and happy and vice versa.
Everyone who is either not creative or not rich is both not creative and not old and vice versa.
If someone is either not patient or curious then fred is not funny and vice versa.
If someone is not wise or old then someone is either kind or not calm.
Everyone who is not calm is brave or not happy and vice versa.
If someone is either not old or patient then susan is both creative and strong and vice versa.
Someone is both not kind and brave.
Someone is both not creative and not rich.
Susan is tall.
Someone is either not strong or patient.
Someone is calm or not humble.
Paul is either quiet or rich.
Someone is both not creative and not patient. | Paul is brave. | contradiction | (![X]:(~patient(X)<=>(happy(X)&quiet(X))))&
(![X]:((funny(X)|~quiet(X))<=>(creative(X)<~>~generous(X))))&
(![X]:(creative(X)=>(kind(X)&patient(X))))&
(((~calm(paul)<~>wise(paul)))<=>(?[X]:((creative(X)|wise(X)))))&
(((happy(alice)|~patient(alice)))=>(?[X]:(humble(X))))&
(((~creative(susan)|wise(susan)))=>(?[X]:((brave(X)<~>tall(X)))))&
(![X]:((~calm(X)|~funny(X))=>(humble(X)|~tall(X))))&
(![X]:((~calm(X)&strong(X))<=>~patient(X)))&
(![X]:((~brave(X)&kind(X))<=>~strong(X)))&
((?[X]:((patient(X)&~generous(X))))=>(patient(alice)))&
(![X]:((~wise(X)|~quiet(X))<=>(patient(X)&happy(X))))&
(![X]:((~creative(X)<~>~rich(X))<=>(~creative(X)&~old(X))))&
((?[X]:((~patient(X)<~>curious(X))))<=>(~funny(fred)))&
((?[X]:((~wise(X)|old(X))))=>(?[X]:((kind(X)<~>~calm(X)))))&
(![X]:(~calm(X)<=>(brave(X)|~happy(X))))&
((?[X]:((~old(X)<~>patient(X))))<=>((creative(susan)&strong(susan))))&
(?[X]:((~kind(X)&brave(X))))&
(?[X]:((~creative(X)&~rich(X))))&
(tall(susan))&
(?[X]:((~strong(X)<~>patient(X))))&
(?[X]:((calm(X)|~humble(X))))&
((quiet(paul)<~>rich(paul)))&
(?[X]:((~creative(X)&~patient(X)))) | brave(paul) | [
"p3",
"p7",
"p8",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5748151156794887138101686
% SZS output start Proof for 5748151156794887138101686
4. (~calm(paul) <~> wise(paul)) <=> ? [X0] : (wise(X0) | creative(X0)) [input p3]
8. ! [X0] : ((strong(X0) & ~calm(X0)) <=> ~patient(X0)) [input p7]
9. ! [X0] : ((kind(X0) & ~brave(X0)) <=> ~strong(X0)) [input p8]
11. ! [X0] : ((~quiet(X0) | ~wise(X0)) <=> (happy(X0) & patient(X0))) [input p10]
15. ! [X0] : (~calm(X0) <=> (~happy(X0) | brave(X0))) [input p14]
24. brave(paul) [input hypothesis]
37. (((~wise(paul) | calm(paul)) & (wise(paul) | ~calm(paul))) | ! [X0] : (~wise(X0) & ~creative(X0))) & (? [X0] : (wise(X0) | creative(X0)) | ((~calm(paul) | ~wise(paul)) & (wise(paul) | calm(paul)))) [nnf transformation 4]
38. (((~wise(paul) | calm(paul)) & (wise(paul) | ~calm(paul))) | ! [X0] : (~wise(X0) & ~creative(X0))) & (? [X1] : (wise(X1) | creative(X1)) | ((~calm(paul) | ~wise(paul)) & (wise(paul) | calm(paul)))) [rectify 37]
39. ? [X1] : (wise(X1) | creative(X1)) => (wise(sK0) | creative(sK0)) [choice axiom]
40. (((~wise(paul) | calm(paul)) & (wise(paul) | ~calm(paul))) | ! [X0] : (~wise(X0) & ~creative(X0))) & ((wise(sK0) | creative(sK0)) | ((~calm(paul) | ~wise(paul)) & (wise(paul) | calm(paul)))) [skolemisation 38,39]
46. ! [X0] : (((strong(X0) & ~calm(X0)) | patient(X0)) & (~patient(X0) | (~strong(X0) | calm(X0)))) [nnf transformation 8]
47. ! [X0] : (((strong(X0) & ~calm(X0)) | patient(X0)) & (~patient(X0) | ~strong(X0) | calm(X0))) [flattening 46]
48. ! [X0] : (((kind(X0) & ~brave(X0)) | strong(X0)) & (~strong(X0) | (~kind(X0) | brave(X0)))) [nnf transformation 9]
49. ! [X0] : (((kind(X0) & ~brave(X0)) | strong(X0)) & (~strong(X0) | ~kind(X0) | brave(X0))) [flattening 48]
50. ! [X0] : (((~quiet(X0) | ~wise(X0)) | (~happy(X0) | ~patient(X0))) & ((happy(X0) & patient(X0)) | (quiet(X0) & wise(X0)))) [nnf transformation 11]
51. ! [X0] : ((~quiet(X0) | ~wise(X0) | ~happy(X0) | ~patient(X0)) & ((happy(X0) & patient(X0)) | (quiet(X0) & wise(X0)))) [flattening 50]
62. ! [X0] : ((~calm(X0) | (happy(X0) & ~brave(X0))) & ((~happy(X0) | brave(X0)) | calm(X0))) [nnf transformation 15]
63. ! [X0] : ((~calm(X0) | (happy(X0) & ~brave(X0))) & (~happy(X0) | brave(X0) | calm(X0))) [flattening 62]
97. ~wise(paul) | calm(paul) | ~wise(X0) [cnf transformation 40]
106. ~strong(X0) | ~patient(X0) | calm(X0) [cnf transformation 47]
110. ~brave(X0) | strong(X0) [cnf transformation 49]
113. wise(X0) | patient(X0) [cnf transformation 51]
133. ~brave(X0) | ~calm(X0) [cnf transformation 63]
153. brave(paul) [cnf transformation 24]
157. 1 <=> ! [X0] : ~wise(X0) [avatar definition]
158. ~wise(X0) <- (1) [avatar component clause 157]
160. 2 <=> calm(paul) [avatar definition]
161. ~calm(paul) <- (~2) [avatar component clause 160]
164. 3 <=> wise(paul) [avatar definition]
165. wise(paul) <- (3) [avatar component clause 164]
166. ~wise(paul) <- (~3) [avatar component clause 164]
167. 1 | 2 | ~3 [avatar split clause 97,164,160,157]
313. strong(paul) [resolution 110,153]
314. patient(paul) <- (~3) [resolution 113,166]
319. ~calm(paul) [resolution 133,153]
380. ~patient(paul) | calm(paul) [resolution 106,313]
384. calm(paul) <- (~3) [subsumption resolution 380,314]
385. $false <- (~2, ~3) [subsumption resolution 384,161]
386. 2 | 3 [avatar contradiction clause 385]
394. $false <- (1, 3) [resolution 165,158]
395. ~1 | ~3 [avatar contradiction clause 394]
401. ~2 [avatar split clause 319,160]
402. $false [avatar sat refutation 167,386,395,401]
% SZS output end Proof for 5748151156794887138101686
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous or not rich is not happy and vice versa.
If someone is not tall or not funny then paul is either tall or not calm and vice versa.
Everyone who is either not tall or not strong is both not wise and not calm.
Everyone who is both wise and not old is curious or kind.
If susan is both old and not wise then mary is not old or not calm.
Everyone who is both generous and funny is both not quiet and not old.
If john is not tall then someone is not creative.
Everyone who is either rich or not brave is both tall and calm and vice versa.
Everyone who is either not happy or patient is either generous or not funny and vice versa.
If someone is either tall or calm then alice is either not tall or patient and vice versa.
If someone is either calm or wise then someone is both not calm and not creative and vice versa.
Everyone who is not curious or curious is not humble or not strong.
If someone is not patient then john is both creative and happy and vice versa.
If someone is both old and brave then someone is strong and vice versa.
Everyone who is not creative is either not old or not tall and vice versa.
If susan is not tall or not generous then susan is both generous and not calm.
Fred is old.
Someone is wise.
Someone is tall or wise.
Susan is either old or kind.
Fred is curious.
Alice is either humble or not rich.
Someone is generous. | Susan is not wise. | neutral | (![X]:((generous(X)|~rich(X))<=>~happy(X)))&
((?[X]:((~tall(X)|~funny(X))))<=>((tall(paul)<~>~calm(paul))))&
(![X]:((~tall(X)<~>~strong(X))=>(~wise(X)&~calm(X))))&
(![X]:((wise(X)&~old(X))=>(curious(X)|kind(X))))&
(((old(susan)&~wise(susan)))=>((~old(mary)|~calm(mary))))&
(![X]:((generous(X)&funny(X))=>(~quiet(X)&~old(X))))&
((~tall(john))=>(?[X]:(~creative(X))))&
(![X]:((rich(X)<~>~brave(X))<=>(tall(X)&calm(X))))&
(![X]:((~happy(X)<~>patient(X))<=>(generous(X)<~>~funny(X))))&
((?[X]:((tall(X)<~>calm(X))))<=>((~tall(alice)<~>patient(alice))))&
((?[X]:((calm(X)<~>wise(X))))<=>(?[X]:((~calm(X)&~creative(X)))))&
(![X]:((~curious(X)|curious(X))=>(~humble(X)|~strong(X))))&
((?[X]:(~patient(X)))<=>((creative(john)&happy(john))))&
((?[X]:((old(X)&brave(X))))<=>(?[X]:(strong(X))))&
(![X]:(~creative(X)<=>(~old(X)<~>~tall(X))))&
(((~tall(susan)|~generous(susan)))=>((generous(susan)&~calm(susan))))&
(old(fred))&
(?[X]:(wise(X)))&
(?[X]:((tall(X)|wise(X))))&
((old(susan)<~>kind(susan)))&
(curious(fred))&
((humble(alice)<~>~rich(alice)))&
(?[X]:(generous(X))) | ~wise(susan) | [] | null | 0 |
If someone is both not funny and calm then susan is either tall or not creative and vice versa.
Everyone who is either rich or quiet is either not old or not happy.
Everyone who is happy is tall and vice versa.
If susan is both not humble and curious then someone is not brave or quiet and vice versa.
Everyone who is old is not calm.
Everyone who is not calm is either not funny or not creative.
If paul is kind or not generous then someone is both happy and rich.
Everyone who is not patient is creative or happy and vice versa.
Everyone who is both not calm and brave is either creative or not humble and vice versa.
If someone is both kind and not creative then someone is patient and vice versa.
Everyone who is both not patient and humble is both strong and not patient.
Everyone who is both not patient and funny is not calm or not generous.
If someone is either humble or not kind then someone is tall or not happy.
Everyone who is curious is both wise and not creative and vice versa.
Everyone who is both not generous and tall is both not strong and not old and vice versa.
Everyone who is calm is both not quiet and patient and vice versa.
Mary is either wise or funny.
Someone is not funny or not humble.
Someone is rich or not old.
Lucy is not kind or not happy.
Someone is not humble.
Someone is funny.
Alice is both tall and rich.
Fred is both patient and rich. | Mary is not tall. | neutral | ((?[X]:((~funny(X)&calm(X))))<=>((tall(susan)<~>~creative(susan))))&
(![X]:((rich(X)<~>quiet(X))=>(~old(X)<~>~happy(X))))&
(![X]:(happy(X)<=>tall(X)))&
(((~humble(susan)&curious(susan)))<=>(?[X]:((~brave(X)|quiet(X)))))&
(![X]:(old(X)=>~calm(X)))&
(![X]:(~calm(X)=>(~funny(X)<~>~creative(X))))&
(((kind(paul)|~generous(paul)))=>(?[X]:((happy(X)&rich(X)))))&
(![X]:(~patient(X)<=>(creative(X)|happy(X))))&
(![X]:((~calm(X)&brave(X))<=>(creative(X)<~>~humble(X))))&
((?[X]:((kind(X)&~creative(X))))<=>(?[X]:(patient(X))))&
(![X]:((~patient(X)&humble(X))=>(strong(X)&~patient(X))))&
(![X]:((~patient(X)&funny(X))=>(~calm(X)|~generous(X))))&
((?[X]:((humble(X)<~>~kind(X))))=>(?[X]:((tall(X)|~happy(X)))))&
(![X]:(curious(X)<=>(wise(X)&~creative(X))))&
(![X]:((~generous(X)&tall(X))<=>(~strong(X)&~old(X))))&
(![X]:(calm(X)<=>(~quiet(X)&patient(X))))&
((wise(mary)<~>funny(mary)))&
(?[X]:((~funny(X)|~humble(X))))&
(?[X]:((rich(X)|~old(X))))&
((~kind(lucy)|~happy(lucy)))&
(?[X]:(~humble(X)))&
(?[X]:(funny(X)))&
((tall(alice)&rich(alice)))&
((patient(fred)&rich(fred))) | ~tall(mary) | [] | null | 0 |
Everyone who is funny is either not wise or calm and vice versa.
If someone is funny or not tall then susan is not wise.
Everyone who is not patient or calm is either wise or humble and vice versa.
If lucy is not wise then susan is brave or creative.
Everyone who is both not wise and not brave is quiet or not rich and vice versa.
If someone is tall then someone is both not wise and generous and vice versa.
If someone is either not wise or not humble then someone is wise.
If someone is not wise then someone is not rich or humble and vice versa.
Everyone who is patient is either brave or not patient and vice versa.
If paul is funny then fred is strong and vice versa.
Everyone who is either not humble or not rich is not strong or not humble and vice versa.
Everyone who is rich or not old is both tall and old.
Everyone who is both patient and calm is humble or not happy.
If someone is not creative then susan is not rich or happy.
Everyone who is either patient or not wise is rich.
If someone is both not curious and not kind then someone is patient and vice versa.
Someone is not kind.
Someone is both not wise and not creative.
John is either tall or generous.
Someone is quiet or not kind.
Paul is either wise or funny.
Lucy is both not creative and not generous.
Alice is not funny.
Someone is not humble. | Alice is not brave. | contradiction | (![X]:(funny(X)<=>(~wise(X)<~>calm(X))))&
((?[X]:((funny(X)|~tall(X))))=>(~wise(susan)))&
(![X]:((~patient(X)|calm(X))<=>(wise(X)<~>humble(X))))&
((~wise(lucy))=>((brave(susan)|creative(susan))))&
(![X]:((~wise(X)&~brave(X))<=>(quiet(X)|~rich(X))))&
((?[X]:(tall(X)))<=>(?[X]:((~wise(X)&generous(X)))))&
((?[X]:((~wise(X)<~>~humble(X))))=>(?[X]:(wise(X))))&
((?[X]:(~wise(X)))<=>(?[X]:((~rich(X)|humble(X)))))&
(![X]:(patient(X)<=>(brave(X)<~>~patient(X))))&
((funny(paul))<=>(strong(fred)))&
(![X]:((~humble(X)<~>~rich(X))<=>(~strong(X)|~humble(X))))&
(![X]:((rich(X)|~old(X))=>(tall(X)&old(X))))&
(![X]:((patient(X)&calm(X))=>(humble(X)|~happy(X))))&
((?[X]:(~creative(X)))=>((~rich(susan)|happy(susan))))&
(![X]:((patient(X)<~>~wise(X))=>rich(X)))&
((?[X]:((~curious(X)&~kind(X))))<=>(?[X]:(patient(X))))&
(?[X]:(~kind(X)))&
(?[X]:((~wise(X)&~creative(X))))&
((tall(john)<~>generous(john)))&
(?[X]:((quiet(X)|~kind(X))))&
((wise(paul)<~>funny(paul)))&
((~creative(lucy)&~generous(lucy)))&
(~funny(alice))&
(?[X]:(~humble(X))) | ~brave(alice) | [
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 66223436984415744425830
% SZS output start Proof for 66223436984415744425830
9. ! [X0] : (patient(X0) <=> (brave(X0) <~> ~patient(X0))) [input p8]
25. ~brave(alice) [input hypothesis]
60. ! [X0] : ((patient(X0) | ((brave(X0) | patient(X0)) & (~patient(X0) | ~brave(X0)))) & (((patient(X0) | ~brave(X0)) & (~patient(X0) | brave(X0))) | ~patient(X0))) [nnf transformation 9]
106. ~patient(X0) | brave(X0) | ~patient(X0) [cnf transformation 60]
109. patient(X0) | brave(X0) | patient(X0) [cnf transformation 60]
138. ~brave(alice) [cnf transformation 25]
141. ~patient(X0) | brave(X0) [duplicate literal removal 106]
142. patient(X0) | brave(X0) [duplicate literal removal 109]
225. brave(X0) [subsumption resolution 141,142]
296. $false [subsumption resolution 138,225]
% SZS output end Proof for 66223436984415744425830
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either generous or not creative then someone is brave.
Everyone who is not tall is patient or not creative and vice versa.
Everyone who is not funny or not calm is not kind or patient.
If someone is both quiet and rich then someone is not wise or humble and vice versa.
If someone is not curious then someone is kind or funny and vice versa.
If someone is either not old or wise then fred is not patient or not rich and vice versa.
Everyone who is either not generous or not strong is both not kind and kind and vice versa.
Everyone who is not calm or curious is both humble and creative.
Everyone who is both wise and not rich is either not old or not calm and vice versa.
If someone is calm then mary is both funny and tall.
Everyone who is either not generous or not funny is not patient or brave.
Everyone who is not old or wise is both strong and not old.
Everyone who is not tall or not brave is not patient or not curious and vice versa.
Everyone who is funny is not happy.
Everyone who is both not wise and not calm is not strong.
Everyone who is happy or not wise is tall.
John is old or funny.
John is not funny or not brave.
Mary is either not wise or generous.
Someone is either not rich or funny.
Someone is either wise or humble.
John is humble or not curious.
Lucy is happy or not tall. | Mary is old. | neutral | ((?[X]:((generous(X)<~>~creative(X))))=>(?[X]:(brave(X))))&
(![X]:(~tall(X)<=>(patient(X)|~creative(X))))&
(![X]:((~funny(X)|~calm(X))=>(~kind(X)|patient(X))))&
((?[X]:((quiet(X)&rich(X))))<=>(?[X]:((~wise(X)|humble(X)))))&
((?[X]:(~curious(X)))<=>(?[X]:((kind(X)|funny(X)))))&
((?[X]:((~old(X)<~>wise(X))))<=>((~patient(fred)|~rich(fred))))&
(![X]:((~generous(X)<~>~strong(X))<=>(~kind(X)&kind(X))))&
(![X]:((~calm(X)|curious(X))=>(humble(X)&creative(X))))&
(![X]:((wise(X)&~rich(X))<=>(~old(X)<~>~calm(X))))&
((?[X]:(calm(X)))=>((funny(mary)&tall(mary))))&
(![X]:((~generous(X)<~>~funny(X))=>(~patient(X)|brave(X))))&
(![X]:((~old(X)|wise(X))=>(strong(X)&~old(X))))&
(![X]:((~tall(X)|~brave(X))<=>(~patient(X)|~curious(X))))&
(![X]:(funny(X)=>~happy(X)))&
(![X]:((~wise(X)&~calm(X))=>~strong(X)))&
(![X]:((happy(X)|~wise(X))=>tall(X)))&
((old(john)|funny(john)))&
((~funny(john)|~brave(john)))&
((~wise(mary)<~>generous(mary)))&
(?[X]:((~rich(X)<~>funny(X))))&
(?[X]:((wise(X)<~>humble(X))))&
((humble(john)|~curious(john)))&
((happy(lucy)|~tall(lucy))) | old(mary) | [] | null | 0 |
If susan is either rich or not rich then lucy is both humble and not calm and vice versa. If fred is both not tall and not rich then someone is both not funny and quiet. If someone is either not brave or brave then someone is both not happy and not curious and vice versa. If someone is not generous or not curious then someone is not creative. Everyone who is not generous or creative is happy or not humble. Everyone who is either wise or not rich is not tall or quiet and vice versa. If someone is strong then lucy is not kind. Everyone who is not kind is both old and not wise and vice versa. Everyone who is curious or not patient is either creative or not brave. Everyone who is not wise is not tall or humble. Everyone who is not tall or not curious is creative. Everyone who is tall or kind is not rich. Everyone who is both not happy and not humble is not funny or curious and vice versa. Everyone who is not calm is humble and vice versa. If someone is either not generous or not strong then fred is not funny. Everyone who is either humble or not rich is either not calm or tall. Mary is both funny and tall. Someone is not generous or not curious. Someone is both not old and not wise. Fred is both patient and not quiet. Someone is both calm and not old. | Fred is not tall. | contradiction | (((rich(susan)<~>~rich(susan)))<=>((humble(lucy)&~calm(lucy))))&
(((~tall(fred)&~rich(fred)))=>(?[X]:((~funny(X)&quiet(X)))))&
((?[X]:((~brave(X)<~>brave(X))))<=>(?[X]:((~happy(X)&~curious(X)))))&
((?[X]:((~generous(X)|~curious(X))))=>(?[X]:(~creative(X))))&
(![X]:((~generous(X)|creative(X))=>(happy(X)|~humble(X))))&
(![X]:((wise(X)<~>~rich(X))<=>(~tall(X)|quiet(X))))&
((?[X]:(strong(X)))=>(~kind(lucy)))&
(![X]:(~kind(X)<=>(old(X)&~wise(X))))&
(![X]:((curious(X)|~patient(X))=>(creative(X)<~>~brave(X))))&
(![X]:(~wise(X)=>(~tall(X)|humble(X))))&
(![X]:((~tall(X)|~curious(X))=>creative(X)))&
(![X]:((tall(X)|kind(X))=>~rich(X)))&
(![X]:((~happy(X)&~humble(X))<=>(~funny(X)|curious(X))))&
(![X]:(~calm(X)<=>humble(X)))&
((?[X]:((~generous(X)<~>~strong(X))))=>(~funny(fred)))&
(![X]:((humble(X)<~>~rich(X))=>(~calm(X)<~>tall(X))))&
((funny(mary)&tall(mary)))&
(?[X]:((~generous(X)|~curious(X))))&
(?[X]:((~old(X)&~wise(X))))&
((patient(fred)&~quiet(fred)))&
(?[X]:((calm(X)&~old(X)))) | ~tall(fred) | [
"p1",
"p5",
"p7",
"p9",
"p11",
"p12",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3954671712735708088578738
% SZS output start Proof for 3954671712735708088578738
2. (~rich(fred) & ~tall(fred)) => ? [X0] : (quiet(X0) & ~funny(X0)) [input p1]
6. ! [X0] : ((wise(X0) <~> ~rich(X0)) <=> (quiet(X0) | ~tall(X0))) [input p5]
8. ! [X0] : (~kind(X0) <=> (~wise(X0) & old(X0))) [input p7]
10. ! [X0] : (~wise(X0) => (humble(X0) | ~tall(X0))) [input p9]
12. ! [X0] : ((kind(X0) | tall(X0)) => ~rich(X0)) [input p11]
13. ! [X0] : ((~humble(X0) & ~happy(X0)) <=> (curious(X0) | ~funny(X0))) [input p12]
14. ! [X0] : (~calm(X0) <=> humble(X0)) [input p13]
16. ! [X0] : ((humble(X0) <~> ~rich(X0)) => (~calm(X0) <~> tall(X0))) [input p15]
22. ~tall(fred) [input hypothesis]
25. ! [X0] : (~kind(X0) => (~wise(X0) & old(X0))) [unused predicate definition removal 8]
28. ? [X0] : (quiet(X0) & ~funny(X0)) | (rich(fred) | tall(fred)) [ennf transformation 2]
29. ? [X0] : (quiet(X0) & ~funny(X0)) | rich(fred) | tall(fred) [flattening 28]
34. ! [X0] : ((~wise(X0) & old(X0)) | kind(X0)) [ennf transformation 25]
36. ! [X0] : ((humble(X0) | ~tall(X0)) | wise(X0)) [ennf transformation 10]
37. ! [X0] : (humble(X0) | ~tall(X0) | wise(X0)) [flattening 36]
39. ! [X0] : (~rich(X0) | (~kind(X0) & ~tall(X0))) [ennf transformation 12]
41. ! [X0] : ((~calm(X0) <~> tall(X0)) | (humble(X0) <=> ~rich(X0))) [ennf transformation 16]
44. ? [X0] : (quiet(X0) & ~funny(X0)) => (quiet(sK0) & ~funny(sK0)) [choice axiom]
45. (quiet(sK0) & ~funny(sK0)) | rich(fred) | tall(fred) [skolemisation 29,44]
54. ! [X0] : ((((rich(X0) | ~wise(X0)) & (~rich(X0) | wise(X0))) | (~quiet(X0) & tall(X0))) & ((quiet(X0) | ~tall(X0)) | ((wise(X0) | rich(X0)) & (~rich(X0) | ~wise(X0))))) [nnf transformation 6]
55. ! [X0] : ((((rich(X0) | ~wise(X0)) & (~rich(X0) | wise(X0))) | (~quiet(X0) & tall(X0))) & (quiet(X0) | ~tall(X0) | ((wise(X0) | rich(X0)) & (~rich(X0) | ~wise(X0))))) [flattening 54]
57. ! [X0] : (((~humble(X0) & ~happy(X0)) | (~curious(X0) & funny(X0))) & ((curious(X0) | ~funny(X0)) | (humble(X0) | happy(X0)))) [nnf transformation 13]
58. ! [X0] : (((~humble(X0) & ~happy(X0)) | (~curious(X0) & funny(X0))) & (curious(X0) | ~funny(X0) | humble(X0) | happy(X0))) [flattening 57]
59. ! [X0] : ((~calm(X0) | ~humble(X0)) & (humble(X0) | calm(X0))) [nnf transformation 14]
61. ! [X0] : (((~tall(X0) | calm(X0)) & (tall(X0) | ~calm(X0))) | ((humble(X0) | rich(X0)) & (~rich(X0) | ~humble(X0)))) [nnf transformation 41]
74. ~funny(sK0) | rich(fred) | tall(fred) [cnf transformation 45]
75. quiet(sK0) | rich(fred) | tall(fred) [cnf transformation 45]
88. ~rich(X0) | wise(X0) | tall(X0) [cnf transformation 55]
89. ~quiet(X0) | wise(X0) | ~rich(X0) [cnf transformation 55]
91. ~wise(X0) | rich(X0) | ~quiet(X0) [cnf transformation 55]
94. ~wise(X0) | kind(X0) [cnf transformation 34]
97. ~tall(X0) | humble(X0) | wise(X0) [cnf transformation 37]
101. ~kind(X0) | ~rich(X0) [cnf transformation 39]
105. ~humble(X0) | funny(X0) [cnf transformation 58]
107. calm(X0) | humble(X0) [cnf transformation 59]
108. ~calm(X0) | ~humble(X0) [cnf transformation 59]
112. tall(X0) | ~calm(X0) | humble(X0) | rich(X0) [cnf transformation 61]
123. ~tall(fred) [cnf transformation 22]
149. 4 <=> tall(fred) [avatar definition]
150. ~tall(fred) <- (~4) [avatar component clause 149]
153. 5 <=> rich(fred) [avatar definition]
155. rich(fred) <- (5) [avatar component clause 153]
157. 6 <=> quiet(sK0) [avatar definition]
159. quiet(sK0) <- (6) [avatar component clause 157]
160. 4 | 5 | 6 [avatar split clause 75,157,153,149]
162. 7 <=> funny(sK0) [avatar definition]
164. ~funny(sK0) <- (~7) [avatar component clause 162]
165. 4 | 5 | ~7 [avatar split clause 74,162,153,149]
216. ~calm(X0) | tall(X0) | rich(X0) [subsumption resolution 112,108]
226. ~4 [avatar split clause 123,149]
254. wise(fred) | tall(fred) <- (5) [resolution 88,155]
255. wise(fred) <- (~4, 5) [subsumption resolution 254,150]
256. kind(fred) <- (~4, 5) [resolution 255,94]
257. ~rich(fred) <- (~4, 5) [resolution 256,101]
258. $false <- (~4, 5) [subsumption resolution 257,155]
259. 4 | ~5 [avatar contradiction clause 258]
260. wise(sK0) | ~rich(sK0) <- (6) [resolution 159,89]
262. 24 <=> rich(sK0) [avatar definition]
263. rich(sK0) <- (24) [avatar component clause 262]
264. ~rich(sK0) <- (~24) [avatar component clause 262]
266. 25 <=> wise(sK0) [avatar definition]
268. wise(sK0) <- (25) [avatar component clause 266]
269. ~24 | 25 | ~6 [avatar split clause 260,157,266,262]
290. tall(X0) | rich(X0) | humble(X0) [resolution 216,107]
325. rich(X1) | humble(X1) | humble(X1) | wise(X1) [resolution 290,97]
327. wise(X1) | humble(X1) | rich(X1) [duplicate literal removal 325]
347. humble(X1) | rich(X1) | rich(X1) | ~quiet(X1) [resolution 327,91]
351. ~quiet(X1) | rich(X1) | humble(X1) [duplicate literal removal 347]
369. rich(sK0) | humble(sK0) <- (6) [resolution 351,159]
370. humble(sK0) <- (6, ~24) [subsumption resolution 369,264]
373. funny(sK0) <- (6, ~24) [resolution 370,105]
374. $false <- (6, ~7, ~24) [subsumption resolution 373,164]
375. ~6 | 7 | 24 [avatar contradiction clause 374]
385. kind(sK0) <- (25) [resolution 268,94]
386. ~rich(sK0) <- (25) [resolution 385,101]
387. $false <- (24, 25) [subsumption resolution 386,263]
388. ~24 | ~25 [avatar contradiction clause 387]
389. $false [avatar sat refutation 160,165,226,259,269,375,388]
% SZS output end Proof for 3954671712735708088578738
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.021 s
% ------------------------------
% ------------------------------
| 0 |
If fred is not quiet or humble then susan is patient or happy. Everyone who is not quiet or not happy is creative and vice versa. Everyone who is either humble or funny is not wise or not humble and vice versa. If someone is not happy then someone is both not strong and not old and vice versa. Everyone who is not old is either funny or not creative. Everyone who is either tall or not wise is both wise and creative. If someone is either not funny or not patient then someone is both not wise and not creative and vice versa. Everyone who is quiet is both patient and not kind and vice versa. If someone is either not curious or not creative then mary is curious and vice versa. If someone is wise then mary is either kind or strong. Everyone who is curious is either strong or brave. If someone is not kind then someone is both not generous and generous and vice versa. Everyone who is not curious is not strong. If someone is wise then mary is happy or not funny. If fred is generous or wise then alice is either not happy or not funny and vice versa. Everyone who is not brave is not creative and vice versa. Susan is not funny. Someone is quiet or old. Someone is creative or rich. Someone is not humble or generous. Someone is not quiet. | Susan is patient. | contradiction | (((~quiet(fred)|humble(fred)))=>((patient(susan)|happy(susan))))&
(![X]:((~quiet(X)|~happy(X))<=>creative(X)))&
(![X]:((humble(X)<~>funny(X))<=>(~wise(X)|~humble(X))))&
((?[X]:(~happy(X)))<=>(?[X]:((~strong(X)&~old(X)))))&
(![X]:(~old(X)=>(funny(X)<~>~creative(X))))&
(![X]:((tall(X)<~>~wise(X))=>(wise(X)&creative(X))))&
((?[X]:((~funny(X)<~>~patient(X))))<=>(?[X]:((~wise(X)&~creative(X)))))&
(![X]:(quiet(X)<=>(patient(X)&~kind(X))))&
((?[X]:((~curious(X)<~>~creative(X))))<=>(curious(mary)))&
((?[X]:(wise(X)))=>((kind(mary)<~>strong(mary))))&
(![X]:(curious(X)=>(strong(X)<~>brave(X))))&
((?[X]:(~kind(X)))<=>(?[X]:((~generous(X)&generous(X)))))&
(![X]:(~curious(X)=>~strong(X)))&
((?[X]:(wise(X)))=>((happy(mary)|~funny(mary))))&
(((generous(fred)|wise(fred)))<=>((~happy(alice)<~>~funny(alice))))&
(![X]:(~brave(X)<=>~creative(X)))&
(~funny(susan))&
(?[X]:((quiet(X)|old(X))))&
(?[X]:((creative(X)|rich(X))))&
(?[X]:((~humble(X)|generous(X))))&
(?[X]:(~quiet(X))) | patient(susan) | [
"p1",
"p6",
"p7",
"p11",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 9091258598058590218423008
% SZS output start Proof for 9091258598058590218423008
2. ! [X0] : ((~happy(X0) | ~quiet(X0)) <=> creative(X0)) [input p1]
7. ? [X0] : (~funny(X0) <~> ~patient(X0)) <=> ? [X0] : (~creative(X0) & ~wise(X0)) [input p6]
8. ! [X0] : (quiet(X0) <=> (~kind(X0) & patient(X0))) [input p7]
12. ? [X0] : ~kind(X0) <=> ? [X0] : (generous(X0) & ~generous(X0)) [input p11]
17. ~funny(susan) [input p16]
22. patient(susan) [input hypothesis]
24. ? [X0] : (~funny(X0) <~> ~patient(X0)) <=> ? [X1] : (~creative(X1) & ~wise(X1)) [rectify 7]
25. ? [X0] : ~kind(X0) <=> ? [X1] : (generous(X1) & ~generous(X1)) [rectify 12]
36. ! [X0] : (((~happy(X0) | ~quiet(X0)) | ~creative(X0)) & (creative(X0) | (happy(X0) & quiet(X0)))) [nnf transformation 2]
37. ! [X0] : ((~happy(X0) | ~quiet(X0) | ~creative(X0)) & (creative(X0) | (happy(X0) & quiet(X0)))) [flattening 36]
47. (? [X0] : ((patient(X0) | funny(X0)) & (~patient(X0) | ~funny(X0))) | ! [X1] : (creative(X1) | wise(X1))) & (? [X1] : (~creative(X1) & ~wise(X1)) | ! [X0] : ((~funny(X0) | patient(X0)) & (~patient(X0) | funny(X0)))) [nnf transformation 24]
48. (? [X0] : ((patient(X0) | funny(X0)) & (~patient(X0) | ~funny(X0))) | ! [X1] : (creative(X1) | wise(X1))) & (? [X2] : (~creative(X2) & ~wise(X2)) | ! [X3] : ((~funny(X3) | patient(X3)) & (~patient(X3) | funny(X3)))) [rectify 47]
49. ? [X0] : ((patient(X0) | funny(X0)) & (~patient(X0) | ~funny(X0))) => ((patient(sK2) | funny(sK2)) & (~patient(sK2) | ~funny(sK2))) [choice axiom]
50. ? [X2] : (~creative(X2) & ~wise(X2)) => (~creative(sK3) & ~wise(sK3)) [choice axiom]
51. (((patient(sK2) | funny(sK2)) & (~patient(sK2) | ~funny(sK2))) | ! [X1] : (creative(X1) | wise(X1))) & ((~creative(sK3) & ~wise(sK3)) | ! [X3] : ((~funny(X3) | patient(X3)) & (~patient(X3) | funny(X3)))) [skolemisation 48,50,49]
52. ! [X0] : ((quiet(X0) | (kind(X0) | ~patient(X0))) & ((~kind(X0) & patient(X0)) | ~quiet(X0))) [nnf transformation 8]
53. ! [X0] : ((quiet(X0) | kind(X0) | ~patient(X0)) & ((~kind(X0) & patient(X0)) | ~quiet(X0))) [flattening 52]
60. (? [X0] : ~kind(X0) | ! [X1] : (~generous(X1) | generous(X1))) & (? [X1] : (generous(X1) & ~generous(X1)) | ! [X0] : kind(X0)) [nnf transformation 25]
61. (? [X0] : ~kind(X0) | ! [X1] : (~generous(X1) | generous(X1))) & (? [X2] : (generous(X2) & ~generous(X2)) | ! [X3] : kind(X3)) [rectify 60]
62. ? [X0] : ~kind(X0) => ~kind(sK5) [choice axiom]
63. ? [X2] : (generous(X2) & ~generous(X2)) => (generous(sK6) & ~generous(sK6)) [choice axiom]
64. (~kind(sK5) | ! [X1] : (~generous(X1) | generous(X1))) & ((generous(sK6) & ~generous(sK6)) | ! [X3] : kind(X3)) [skolemisation 61,63,62]
76. creative(X0) | quiet(X0) [cnf transformation 37]
96. ~creative(sK3) | ~patient(X3) | funny(X3) [cnf transformation 51]
101. ~kind(X0) | ~quiet(X0) [cnf transformation 53]
111. ~generous(sK6) | kind(X3) [cnf transformation 64]
112. generous(sK6) | kind(X3) [cnf transformation 64]
124. ~funny(susan) [cnf transformation 17]
128. patient(susan) [cnf transformation 22]
137. 2 <=> patient(susan) [avatar definition]
139. patient(susan) <- (2) [avatar component clause 137]
189. 14 <=> creative(sK3) [avatar definition]
191. ~creative(sK3) <- (~14) [avatar component clause 189]
194. 15 <=> ! [X3] : (~patient(X3) | funny(X3)) [avatar definition]
195. ~patient(X3) | funny(X3) <- (15) [avatar component clause 194]
196. 15 | ~14 [avatar split clause 96,189,194]
239. 25 <=> ! [X3] : kind(X3) [avatar definition]
240. kind(X3) <- (25) [avatar component clause 239]
242. 26 <=> generous(sK6) [avatar definition]
245. 25 | 26 [avatar split clause 112,242,239]
246. 25 | ~26 [avatar split clause 111,242,239]
296. 2 [avatar split clause 128,137]
302. quiet(sK3) <- (~14) [resolution 76,191]
309. ~quiet(X0) <- (25) [resolution 101,240]
314. $false <- (~14, 25) [resolution 309,302]
317. 14 | ~25 [avatar contradiction clause 314]
330. funny(susan) <- (2, 15) [resolution 195,139]
332. $false <- (2, 15) [subsumption resolution 330,124]
333. ~2 | ~15 [avatar contradiction clause 332]
334. $false [avatar sat refutation 196,245,246,296,317,333]
% SZS output end Proof for 9091258598058590218423008
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not wise or not kind is both old and not tall and vice versa. If fred is both wise and kind then fred is both quiet and old and vice versa. Everyone who is both not generous and happy is both not patient and strong and vice versa. If someone is either not tall or tall then someone is patient or not generous and vice versa. If lucy is both old and not strong then john is both not brave and not tall and vice versa. Everyone who is both not humble and not patient is both calm and not quiet. Everyone who is humble is both creative and not strong. Everyone who is old is both quiet and brave and vice versa. If john is not generous then someone is quiet and vice versa. If susan is not generous or funny then susan is not curious or not creative and vice versa. Everyone who is not old or not curious is humble and vice versa. If paul is not wise then someone is happy and vice versa. Everyone who is old is strong or not calm. Everyone who is not strong is either not calm or tall. If lucy is not humble or brave then alice is not humble or not funny. Everyone who is not wise or generous is both not kind and not happy. John is both rich and not humble. Someone is not rich or not funny. Alice is not curious. Someone is both funny and wise. Someone is not quiet. Mary is happy or not quiet. Someone is old. | Susan is not happy. | entailment | (![X]:((~wise(X)<~>~kind(X))<=>(old(X)&~tall(X))))&
(((wise(fred)&kind(fred)))<=>((quiet(fred)&old(fred))))&
(![X]:((~generous(X)&happy(X))<=>(~patient(X)&strong(X))))&
((?[X]:((~tall(X)<~>tall(X))))<=>(?[X]:((patient(X)|~generous(X)))))&
(((old(lucy)&~strong(lucy)))<=>((~brave(john)&~tall(john))))&
(![X]:((~humble(X)&~patient(X))=>(calm(X)&~quiet(X))))&
(![X]:(humble(X)=>(creative(X)&~strong(X))))&
(![X]:(old(X)<=>(quiet(X)&brave(X))))&
((~generous(john))<=>(?[X]:(quiet(X))))&
(((~generous(susan)|funny(susan)))<=>((~curious(susan)|~creative(susan))))&
(![X]:((~old(X)|~curious(X))<=>humble(X)))&
((~wise(paul))<=>(?[X]:(happy(X))))&
(![X]:(old(X)=>(strong(X)|~calm(X))))&
(![X]:(~strong(X)=>(~calm(X)<~>tall(X))))&
(((~humble(lucy)|brave(lucy)))=>((~humble(alice)|~funny(alice))))&
(![X]:((~wise(X)|generous(X))=>(~kind(X)&~happy(X))))&
((rich(john)&~humble(john)))&
(?[X]:((~rich(X)|~funny(X))))&
(~curious(alice))&
(?[X]:((funny(X)&wise(X))))&
(?[X]:(~quiet(X)))&
((happy(mary)|~quiet(mary)))&
(?[X]:(old(X))) | ~happy(susan) | [
"p2",
"p5",
"p6",
"p7",
"p10",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 958769926306314495545228
% SZS output start Proof for 958769926306314495545228
3. ! [X0] : ((happy(X0) & ~generous(X0)) <=> (strong(X0) & ~patient(X0))) [input p2]
6. ! [X0] : ((~patient(X0) & ~humble(X0)) => (~quiet(X0) & calm(X0))) [input p5]
7. ! [X0] : (humble(X0) => (~strong(X0) & creative(X0))) [input p6]
8. ! [X0] : (old(X0) <=> (brave(X0) & quiet(X0))) [input p7]
11. ! [X0] : ((~curious(X0) | ~old(X0)) <=> humble(X0)) [input p10]
16. ! [X0] : ((generous(X0) | ~wise(X0)) => (~happy(X0) & ~kind(X0))) [input p15]
24. happy(susan) [input hypothesis]
26. ! [X0] : ((~quiet(X0) & calm(X0)) | (patient(X0) | humble(X0))) [ennf transformation 6]
27. ! [X0] : ((~quiet(X0) & calm(X0)) | patient(X0) | humble(X0)) [flattening 26]
28. ! [X0] : ((~strong(X0) & creative(X0)) | ~humble(X0)) [ennf transformation 7]
34. ! [X0] : ((~happy(X0) & ~kind(X0)) | (~generous(X0) & wise(X0))) [ennf transformation 16]
39. ! [X0] : (((happy(X0) & ~generous(X0)) | (~strong(X0) | patient(X0))) & ((strong(X0) & ~patient(X0)) | (~happy(X0) | generous(X0)))) [nnf transformation 3]
40. ! [X0] : (((happy(X0) & ~generous(X0)) | ~strong(X0) | patient(X0)) & ((strong(X0) & ~patient(X0)) | ~happy(X0) | generous(X0))) [flattening 39]
48. ! [X0] : ((old(X0) | (~brave(X0) | ~quiet(X0))) & ((brave(X0) & quiet(X0)) | ~old(X0))) [nnf transformation 8]
49. ! [X0] : ((old(X0) | ~brave(X0) | ~quiet(X0)) & ((brave(X0) & quiet(X0)) | ~old(X0))) [flattening 48]
56. ! [X0] : (((~curious(X0) | ~old(X0)) | ~humble(X0)) & (humble(X0) | (curious(X0) & old(X0)))) [nnf transformation 11]
57. ! [X0] : ((~curious(X0) | ~old(X0) | ~humble(X0)) & (humble(X0) | (curious(X0) & old(X0)))) [flattening 56]
81. ~patient(X0) | ~happy(X0) | generous(X0) [cnf transformation 40]
82. ~happy(X0) | strong(X0) | generous(X0) [cnf transformation 40]
96. ~quiet(X0) | patient(X0) | humble(X0) [cnf transformation 27]
98. ~humble(X0) | ~strong(X0) [cnf transformation 28]
99. ~old(X0) | quiet(X0) [cnf transformation 49]
108. humble(X0) | old(X0) [cnf transformation 57]
121. ~happy(X0) | ~generous(X0) [cnf transformation 34]
131. happy(susan) [cnf transformation 24]
209. 17 <=> generous(susan) [avatar definition]
211. ~generous(susan) <- (~17) [avatar component clause 209]
281. ~strong(X0) | old(X0) [resolution 108,98]
293. ~generous(susan) [resolution 121,131]
312. 34 <=> old(susan) [avatar definition]
314. old(susan) <- (34) [avatar component clause 312]
331. strong(susan) | generous(susan) [resolution 82,131]
333. strong(susan) <- (~17) [subsumption resolution 331,211]
335. old(susan) <- (~17) [resolution 333,281]
336. 34 | 17 [avatar split clause 335,209,312]
338. 37 <=> strong(susan) [avatar definition]
340. strong(susan) <- (37) [avatar component clause 338]
341. 17 | 37 [avatar split clause 331,338,209]
342. ~17 [avatar split clause 293,209]
351. quiet(susan) <- (34) [resolution 314,99]
459. patient(susan) | humble(susan) <- (34) [resolution 351,96]
461. 49 <=> humble(susan) [avatar definition]
463. humble(susan) <- (49) [avatar component clause 461]
465. 50 <=> patient(susan) [avatar definition]
467. patient(susan) <- (50) [avatar component clause 465]
468. 49 | 50 | ~34 [avatar split clause 459,312,465,461]
489. ~strong(susan) <- (49) [resolution 463,98]
491. $false <- (37, 49) [subsumption resolution 489,340]
492. ~37 | ~49 [avatar contradiction clause 491]
497. ~happy(susan) | generous(susan) <- (50) [resolution 467,81]
498. generous(susan) <- (50) [subsumption resolution 497,131]
499. $false <- (~17, 50) [subsumption resolution 498,211]
500. 17 | ~50 [avatar contradiction clause 499]
501. $false [avatar sat refutation 336,341,342,468,492,500]
% SZS output end Proof for 958769926306314495545228
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 john is either curious or wise then someone is creative or tall and vice versa. Everyone who is both not happy and not tall is both not funny and quiet. If someone is both not strong and humble then someone is either not tall or not quiet and vice versa. If someone is not humble or not wise then someone is curious or not quiet and vice versa. If someone is either not strong or tall then mary is humble or not happy and vice versa. If someone is either not quiet or not curious then someone is either strong or quiet and vice versa. Everyone who is curious or not old is wise or calm and vice versa. Everyone who is both strong and tall is either not patient or quiet and vice versa. If fred is humble then lucy is not wise and vice versa. If john is either not generous or not rich then susan is not rich and vice versa. Everyone who is either humble or happy is either not wise or happy and vice versa. Everyone who is either curious or generous is patient or quiet. If mary is either not patient or rich then someone is generous and vice versa. Everyone who is humble or creative is tall and vice versa. If fred is not wise or kind then someone is rich or patient. Everyone who is humble is both not quiet and not patient. John is not quiet or happy. Someone is not patient. Someone is either creative or rich. Lucy is calm or not generous. Paul is not patient or not creative. John is either not generous or calm. Fred is humble or not quiet. | Susan is wise. | entailment | (((curious(john)<~>wise(john)))<=>(?[X]:((creative(X)|tall(X)))))&
(![X]:((~happy(X)&~tall(X))=>(~funny(X)&quiet(X))))&
((?[X]:((~strong(X)&humble(X))))<=>(?[X]:((~tall(X)<~>~quiet(X)))))&
((?[X]:((~humble(X)|~wise(X))))<=>(?[X]:((curious(X)|~quiet(X)))))&
((?[X]:((~strong(X)<~>tall(X))))<=>((humble(mary)|~happy(mary))))&
((?[X]:((~quiet(X)<~>~curious(X))))<=>(?[X]:((strong(X)<~>quiet(X)))))&
(![X]:((curious(X)|~old(X))<=>(wise(X)|calm(X))))&
(![X]:((strong(X)&tall(X))<=>(~patient(X)<~>quiet(X))))&
((humble(fred))<=>(~wise(lucy)))&
(((~generous(john)<~>~rich(john)))<=>(~rich(susan)))&
(![X]:((humble(X)<~>happy(X))<=>(~wise(X)<~>happy(X))))&
(![X]:((curious(X)<~>generous(X))=>(patient(X)|quiet(X))))&
(((~patient(mary)<~>rich(mary)))<=>(?[X]:(generous(X))))&
(![X]:((humble(X)|creative(X))<=>tall(X)))&
(((~wise(fred)|kind(fred)))=>(?[X]:((rich(X)|patient(X)))))&
(![X]:(humble(X)=>(~quiet(X)&~patient(X))))&
((~quiet(john)|happy(john)))&
(?[X]:(~patient(X)))&
(?[X]:((creative(X)<~>rich(X))))&
((calm(lucy)|~generous(lucy)))&
((~patient(paul)|~creative(paul)))&
((~generous(john)<~>calm(john)))&
((humble(fred)|~quiet(fred))) | wise(susan) | [
"p2",
"p7",
"p10",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1625592854470248235401894
% SZS output start Proof for 1625592854470248235401894
3. ? [X0] : (humble(X0) & ~strong(X0)) <=> ? [X0] : (~tall(X0) <~> ~quiet(X0)) [input p2]
8. ! [X0] : ((tall(X0) & strong(X0)) <=> (~patient(X0) <~> quiet(X0))) [input p7]
11. ! [X0] : ((humble(X0) <~> happy(X0)) <=> (~wise(X0) <~> happy(X0))) [input p10]
14. ! [X0] : ((creative(X0) | humble(X0)) <=> tall(X0)) [input p13]
16. ! [X0] : (humble(X0) => (~patient(X0) & ~quiet(X0))) [input p15]
24. ~wise(susan) [input hypothesis]
25. ? [X0] : (humble(X0) & ~strong(X0)) <=> ? [X1] : (~tall(X1) <~> ~quiet(X1)) [rectify 3]
35. ! [X0] : ((~patient(X0) & ~quiet(X0)) | ~humble(X0)) [ennf transformation 16]
40. (? [X0] : (humble(X0) & ~strong(X0)) | ! [X1] : ((~tall(X1) | quiet(X1)) & (~quiet(X1) | tall(X1)))) & (? [X1] : ((quiet(X1) | tall(X1)) & (~quiet(X1) | ~tall(X1))) | ! [X0] : (~humble(X0) | strong(X0))) [nnf transformation 25]
41. (? [X0] : (humble(X0) & ~strong(X0)) | ! [X1] : ((~tall(X1) | quiet(X1)) & (~quiet(X1) | tall(X1)))) & (? [X2] : ((quiet(X2) | tall(X2)) & (~quiet(X2) | ~tall(X2))) | ! [X3] : (~humble(X3) | strong(X3))) [rectify 40]
42. ? [X0] : (humble(X0) & ~strong(X0)) => (humble(sK1) & ~strong(sK1)) [choice axiom]
43. ? [X2] : ((quiet(X2) | tall(X2)) & (~quiet(X2) | ~tall(X2))) => ((quiet(sK2) | tall(sK2)) & (~quiet(sK2) | ~tall(sK2))) [choice axiom]
44. ((humble(sK1) & ~strong(sK1)) | ! [X1] : ((~tall(X1) | quiet(X1)) & (~quiet(X1) | tall(X1)))) & (((quiet(sK2) | tall(sK2)) & (~quiet(sK2) | ~tall(sK2))) | ! [X3] : (~humble(X3) | strong(X3))) [skolemisation 41,43,42]
62. ! [X0] : (((tall(X0) & strong(X0)) | ((~patient(X0) | ~quiet(X0)) & (quiet(X0) | patient(X0)))) & (((~quiet(X0) | patient(X0)) & (quiet(X0) | ~patient(X0))) | (~tall(X0) | ~strong(X0)))) [nnf transformation 8]
63. ! [X0] : (((tall(X0) & strong(X0)) | ((~patient(X0) | ~quiet(X0)) & (quiet(X0) | patient(X0)))) & (((~quiet(X0) | patient(X0)) & (quiet(X0) | ~patient(X0))) | ~tall(X0) | ~strong(X0))) [flattening 62]
66. ! [X0] : ((((~happy(X0) | ~humble(X0)) & (happy(X0) | humble(X0))) | ((~wise(X0) | ~happy(X0)) & (happy(X0) | wise(X0)))) & (((~happy(X0) | wise(X0)) & (happy(X0) | ~wise(X0))) | ((humble(X0) | ~happy(X0)) & (happy(X0) | ~humble(X0))))) [nnf transformation 11]
72. ! [X0] : (((creative(X0) | humble(X0)) | ~tall(X0)) & (tall(X0) | (~creative(X0) & ~humble(X0)))) [nnf transformation 14]
73. ! [X0] : ((creative(X0) | humble(X0) | ~tall(X0)) & (tall(X0) | (~creative(X0) & ~humble(X0)))) [flattening 72]
92. ~strong(sK1) | ~tall(X1) | quiet(X1) [cnf transformation 44]
94. humble(sK1) | ~tall(X1) | quiet(X1) [cnf transformation 44]
119. patient(X0) | quiet(X0) | strong(X0) [cnf transformation 63]
132. ~happy(X0) | wise(X0) | humble(X0) | ~happy(X0) [cnf transformation 66]
133. happy(X0) | humble(X0) | happy(X0) | wise(X0) [cnf transformation 66]
143. ~humble(X0) | tall(X0) [cnf transformation 73]
147. ~humble(X0) | ~quiet(X0) [cnf transformation 35]
148. ~patient(X0) | ~humble(X0) [cnf transformation 35]
158. ~wise(susan) [cnf transformation 24]
160. ~happy(X0) | wise(X0) | humble(X0) [duplicate literal removal 132]
161. humble(X0) | happy(X0) | wise(X0) [duplicate literal removal 133]
192. 7 <=> ! [X1] : (~tall(X1) | quiet(X1)) [avatar definition]
193. ~tall(X1) | quiet(X1) <- (7) [avatar component clause 192]
195. 8 <=> humble(sK1) [avatar definition]
197. humble(sK1) <- (8) [avatar component clause 195]
198. 7 | 8 [avatar split clause 94,195,192]
204. 10 <=> strong(sK1) [avatar definition]
206. ~strong(sK1) <- (~10) [avatar component clause 204]
207. 7 | ~10 [avatar split clause 92,204,192]
210. 11 <=> ! [X3] : (~humble(X3) | strong(X3)) [avatar definition]
211. ~humble(X3) | strong(X3) <- (11) [avatar component clause 210]
239. 18 <=> ! [X3] : wise(X3) [avatar definition]
240. wise(X3) <- (18) [avatar component clause 239]
344. humble(X0) | wise(X0) [subsumption resolution 160,161]
428. strong(sK1) <- (8, 11) [resolution 211,197]
429. $false <- (8, ~10, 11) [subsumption resolution 428,206]
430. ~8 | 10 | ~11 [avatar contradiction clause 429]
431. ~quiet(X0) | wise(X0) [resolution 344,147]
432. tall(X1) | wise(X1) [resolution 344,143]
486. quiet(X0) | strong(X0) | ~humble(X0) [resolution 119,148]
496. strong(X0) | ~humble(X0) [subsumption resolution 486,147]
497. 11 [avatar split clause 496,210]
649. wise(X1) | quiet(X1) <- (7) [resolution 432,193]
653. wise(X1) <- (7) [subsumption resolution 649,431]
654. 18 | ~7 [avatar split clause 653,192,239]
655. $false <- (18) [resolution 240,158]
658. ~18 [avatar contradiction clause 655]
659. $false [avatar sat refutation 198,207,430,497,654,658]
% SZS output end Proof for 1625592854470248235401894
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is tall or not strong is not brave. Everyone who is both old and tall is both not calm and not strong. Everyone who is both not patient and creative is either not happy or kind and vice versa. Everyone who is both not tall and not strong is both creative and quiet and vice versa. Everyone who is rich or not brave is both not generous and tall and vice versa. If alice is not creative or not brave then someone is creative or generous and vice versa. Everyone who is both not rich and not humble is not brave or kind and vice versa. Everyone who is both not patient and happy is not patient and vice versa. Everyone who is humble or not patient is both creative and not wise. Everyone who is either creative or old is old. If mary is curious or not old then someone is either brave or not kind. Everyone who is not happy or brave is not calm. Everyone who is either not happy or generous is either old or curious and vice versa. If someone is not calm or wise then alice is either generous or strong and vice versa. Everyone who is either funny or not quiet is both wise and not kind and vice versa. Everyone who is either not patient or not quiet is both not brave and kind and vice versa. Fred is either brave or not patient. Paul is quiet. Fred is generous or not old. Paul is generous. Someone is both not tall and happy. Paul is both not creative and generous. Someone is tall. | Alice is not generous. | entailment | (![X]:((tall(X)|~strong(X))=>~brave(X)))&
(![X]:((old(X)&tall(X))=>(~calm(X)&~strong(X))))&
(![X]:((~patient(X)&creative(X))<=>(~happy(X)<~>kind(X))))&
(![X]:((~tall(X)&~strong(X))<=>(creative(X)&quiet(X))))&
(![X]:((rich(X)|~brave(X))<=>(~generous(X)&tall(X))))&
(((~creative(alice)|~brave(alice)))<=>(?[X]:((creative(X)|generous(X)))))&
(![X]:((~rich(X)&~humble(X))<=>(~brave(X)|kind(X))))&
(![X]:((~patient(X)&happy(X))<=>~patient(X)))&
(![X]:((humble(X)|~patient(X))=>(creative(X)&~wise(X))))&
(![X]:((creative(X)<~>old(X))=>old(X)))&
(((curious(mary)|~old(mary)))=>(?[X]:((brave(X)<~>~kind(X)))))&
(![X]:((~happy(X)|brave(X))=>~calm(X)))&
(![X]:((~happy(X)<~>generous(X))<=>(old(X)<~>curious(X))))&
((?[X]:((~calm(X)|wise(X))))<=>((generous(alice)<~>strong(alice))))&
(![X]:((funny(X)<~>~quiet(X))<=>(wise(X)&~kind(X))))&
(![X]:((~patient(X)<~>~quiet(X))<=>(~brave(X)&kind(X))))&
((brave(fred)<~>~patient(fred)))&
(quiet(paul))&
((generous(fred)|~old(fred)))&
(generous(paul))&
(?[X]:((~tall(X)&happy(X))))&
((~creative(paul)&generous(paul)))&
(?[X]:(tall(X))) | ~generous(alice) | [
"p0",
"p4",
"p11",
"p13",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 90490397639296785145842
% SZS output start Proof for 90490397639296785145842
1. ! [X0] : ((~strong(X0) | tall(X0)) => ~brave(X0)) [input p0]
5. ! [X0] : ((~brave(X0) | rich(X0)) <=> (tall(X0) & ~generous(X0))) [input p4]
12. ! [X0] : ((brave(X0) | ~happy(X0)) => ~calm(X0)) [input p11]
14. ? [X0] : (wise(X0) | ~calm(X0)) <=> (generous(alice) <~> strong(alice)) [input p13]
20. generous(paul) [input p19]
24. generous(alice) [input hypothesis]
25. ! [X0] : (~brave(X0) | (strong(X0) & ~tall(X0))) [ennf transformation 1]
31. ! [X0] : (~calm(X0) | (~brave(X0) & happy(X0))) [ennf transformation 12]
36. ! [X0] : (((~brave(X0) | rich(X0)) | (~tall(X0) | generous(X0))) & ((tall(X0) & ~generous(X0)) | (brave(X0) & ~rich(X0)))) [nnf transformation 5]
37. ! [X0] : ((~brave(X0) | rich(X0) | ~tall(X0) | generous(X0)) & ((tall(X0) & ~generous(X0)) | (brave(X0) & ~rich(X0)))) [flattening 36]
52. (? [X0] : (wise(X0) | ~calm(X0)) | ((generous(alice) | ~strong(alice)) & (strong(alice) | ~generous(alice)))) & (((~strong(alice) | ~generous(alice)) & (strong(alice) | generous(alice))) | ! [X0] : (~wise(X0) & calm(X0))) [nnf transformation 14]
53. (? [X0] : (wise(X0) | ~calm(X0)) | ((generous(alice) | ~strong(alice)) & (strong(alice) | ~generous(alice)))) & (((~strong(alice) | ~generous(alice)) & (strong(alice) | generous(alice))) | ! [X1] : (~wise(X1) & calm(X1))) [rectify 52]
54. ? [X0] : (wise(X0) | ~calm(X0)) => (wise(sK2) | ~calm(sK2)) [choice axiom]
55. ((wise(sK2) | ~calm(sK2)) | ((generous(alice) | ~strong(alice)) & (strong(alice) | ~generous(alice)))) & (((~strong(alice) | ~generous(alice)) & (strong(alice) | generous(alice))) | ! [X1] : (~wise(X1) & calm(X1))) [skolemisation 53,54]
66. ~brave(X0) | strong(X0) [cnf transformation 25]
80. ~generous(X0) | brave(X0) [cnf transformation 37]
107. ~calm(X0) | ~brave(X0) [cnf transformation 31]
118. ~strong(alice) | ~generous(alice) | calm(X1) [cnf transformation 55]
138. generous(paul) [cnf transformation 20]
144. generous(alice) [cnf transformation 24]
154. 3 <=> brave(alice) [avatar definition]
155. brave(alice) <- (3) [avatar component clause 154]
193. 11 <=> strong(alice) [avatar definition]
197. 12 <=> generous(alice) [avatar definition]
199. generous(alice) <- (12) [avatar component clause 197]
215. 16 <=> ! [X1] : calm(X1) [avatar definition]
216. calm(X1) <- (16) [avatar component clause 215]
217. 16 | ~12 | ~11 [avatar split clause 118,193,197,215]
239. 12 [avatar split clause 144,197]
242. brave(paul) [resolution 80,138]
243. brave(alice) <- (12) [resolution 80,199]
246. 3 | ~12 [avatar split clause 243,197,154]
247. strong(alice) <- (3) [resolution 155,66]
251. 11 | ~3 [avatar split clause 247,154,193]
263. ~brave(X0) <- (16) [resolution 107,216]
268. $false <- (16) [resolution 263,242]
269. ~16 [avatar contradiction clause 268]
271. $false [avatar sat refutation 217,239,246,251,269]
% SZS output end Proof for 90490397639296785145842
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not curious or curious then mary is both humble and wise and vice versa.
If susan is not calm or not tall then john is either not rich or quiet.
Everyone who is both generous and not happy is both not quiet and not kind.
If someone is not funny then someone is both not funny and not wise and vice versa.
If someone is not rich then someone is not humble.
Everyone who is not patient or not calm is not calm.
If someone is both quiet and not kind then lucy is patient or strong.
Everyone who is both happy and tall is not brave and vice versa.
If alice is either brave or not quiet then someone is not rich.
If paul is not patient then someone is both kind and not humble.
If someone is generous then someone is both not humble and not old and vice versa.
Everyone who is not curious or not strong is both not calm and not wise.
Everyone who is patient or strong is generous.
Everyone who is not generous is either not funny or not humble.
If susan is quiet then someone is both strong and not old and vice versa.
Everyone who is not old or quiet is either brave or not strong and vice versa.
Alice is patient.
Someone is not humble or not calm.
Someone is either rich or not kind.
Someone is not funny.
Someone is old or not happy.
Susan is either not calm or happy.
Lucy is not generous.
Mary is both humble and strong. | Lucy is not wise. | entailment | ((?[X]:((~curious(X)|curious(X))))<=>((humble(mary)&wise(mary))))&
(((~calm(susan)|~tall(susan)))=>((~rich(john)<~>quiet(john))))&
(![X]:((generous(X)&~happy(X))=>(~quiet(X)&~kind(X))))&
((?[X]:(~funny(X)))<=>(?[X]:((~funny(X)&~wise(X)))))&
((?[X]:(~rich(X)))=>(?[X]:(~humble(X))))&
(![X]:((~patient(X)|~calm(X))=>~calm(X)))&
((?[X]:((quiet(X)&~kind(X))))=>((patient(lucy)|strong(lucy))))&
(![X]:((happy(X)&tall(X))<=>~brave(X)))&
(((brave(alice)<~>~quiet(alice)))=>(?[X]:(~rich(X))))&
((~patient(paul))=>(?[X]:((kind(X)&~humble(X)))))&
((?[X]:(generous(X)))<=>(?[X]:((~humble(X)&~old(X)))))&
(![X]:((~curious(X)|~strong(X))=>(~calm(X)&~wise(X))))&
(![X]:((patient(X)|strong(X))=>generous(X)))&
(![X]:(~generous(X)=>(~funny(X)<~>~humble(X))))&
((quiet(susan))<=>(?[X]:((strong(X)&~old(X)))))&
(![X]:((~old(X)|quiet(X))<=>(brave(X)<~>~strong(X))))&
(patient(alice))&
(?[X]:((~humble(X)|~calm(X))))&
(?[X]:((rich(X)<~>~kind(X))))&
(?[X]:(~funny(X)))&
(?[X]:((old(X)|~happy(X))))&
((~calm(susan)<~>happy(susan)))&
(~generous(lucy))&
((humble(mary)&strong(mary))) | ~wise(lucy) | [
"p11",
"p12",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 4202588835569695636805222
% SZS output start Proof for 4202588835569695636805222
12. ! [X0] : ((~strong(X0) | ~curious(X0)) => (~wise(X0) & ~calm(X0))) [input p11]
13. ! [X0] : ((strong(X0) | patient(X0)) => generous(X0)) [input p12]
23. ~generous(lucy) [input p22]
25. wise(lucy) [input hypothesis]
38. ! [X0] : ((~wise(X0) & ~calm(X0)) | (strong(X0) & curious(X0))) [ennf transformation 12]
39. ! [X0] : (generous(X0) | (~strong(X0) & ~patient(X0))) [ennf transformation 13]
115. ~wise(X0) | strong(X0) [cnf transformation 38]
117. ~strong(X0) | generous(X0) [cnf transformation 39]
137. ~generous(lucy) [cnf transformation 23]
140. wise(lucy) [cnf transformation 25]
216. 18 <=> strong(lucy) [avatar definition]
218. strong(lucy) <- (18) [avatar component clause 216]
324. strong(lucy) [resolution 115,140]
326. 18 [avatar split clause 324,216]
330. generous(lucy) <- (18) [resolution 117,218]
331. $false <- (18) [subsumption resolution 330,137]
332. ~18 [avatar contradiction clause 331]
333. $false [avatar sat refutation 326,332]
% SZS output end Proof for 4202588835569695636805222
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave then someone is either not humble or generous and vice versa.
Everyone who is generous is either rich or not old and vice versa.
If susan is not curious then alice is either patient or creative and vice versa.
Everyone who is either not curious or not kind is both not humble and not happy.
Everyone who is not brave or strong is either funny or not happy.
Everyone who is both not happy and not creative is both not brave and quiet and vice versa.
If someone is both brave and happy then someone is not brave.
Everyone who is not strong is rich or humble and vice versa.
If susan is not curious or not patient then fred is humble and vice versa.
Everyone who is both humble and kind is both not old and happy and vice versa.
Everyone who is humble is patient and vice versa.
Everyone who is either quiet or not brave is either not strong or generous and vice versa.
If someone is not kind then someone is not brave.
If mary is quiet then john is both calm and not kind and vice versa.
Everyone who is either generous or funny is not generous or tall and vice versa.
If paul is tall then someone is either tall or calm and vice versa.
Someone is patient or not kind.
Someone is tall.
Lucy is both not brave and not funny.
Someone is both generous and not brave.
Someone is either not patient or curious.
Someone is humble or not calm.
Alice is both funny and not calm.
Someone is not happy or funny. | Lucy is funny. | contradiction | ((?[X]:(brave(X)))<=>(?[X]:((~humble(X)<~>generous(X)))))&
(![X]:(generous(X)<=>(rich(X)<~>~old(X))))&
((~curious(susan))<=>((patient(alice)<~>creative(alice))))&
(![X]:((~curious(X)<~>~kind(X))=>(~humble(X)&~happy(X))))&
(![X]:((~brave(X)|strong(X))=>(funny(X)<~>~happy(X))))&
(![X]:((~happy(X)&~creative(X))<=>(~brave(X)&quiet(X))))&
((?[X]:((brave(X)&happy(X))))=>(?[X]:(~brave(X))))&
(![X]:(~strong(X)<=>(rich(X)|humble(X))))&
(((~curious(susan)|~patient(susan)))<=>(humble(fred)))&
(![X]:((humble(X)&kind(X))<=>(~old(X)&happy(X))))&
(![X]:(humble(X)<=>patient(X)))&
(![X]:((quiet(X)<~>~brave(X))<=>(~strong(X)<~>generous(X))))&
((?[X]:(~kind(X)))=>(?[X]:(~brave(X))))&
((quiet(mary))<=>((calm(john)&~kind(john))))&
(![X]:((generous(X)<~>funny(X))<=>(~generous(X)|tall(X))))&
((tall(paul))<=>(?[X]:((tall(X)<~>calm(X)))))&
(?[X]:((patient(X)|~kind(X))))&
(?[X]:(tall(X)))&
((~brave(lucy)&~funny(lucy)))&
(?[X]:((generous(X)&~brave(X))))&
(?[X]:((~patient(X)<~>curious(X))))&
(?[X]:((humble(X)|~calm(X))))&
((funny(alice)&~calm(alice)))&
(?[X]:((~happy(X)|funny(X)))) | funny(lucy) | [
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 6071067507508637176529152
% SZS output start Proof for 6071067507508637176529152
19. ~funny(lucy) & ~brave(lucy) [input p18]
25. funny(lucy) [input hypothesis]
141. ~funny(lucy) [cnf transformation 19]
150. funny(lucy) [cnf transformation 25]
296. $false [subsumption resolution 150,141]
% SZS output end Proof for 6071067507508637176529152
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either happy or not quiet then john is both not kind and happy and vice versa.
Everyone who is either brave or curious is either calm or curious and vice versa.
Everyone who is not humble or creative is both not quiet and rich and vice versa.
If paul is both tall and not humble then alice is strong or not kind.
If paul is either not tall or not generous then mary is both not creative and old and vice versa.
Everyone who is both not tall and brave is patient or not calm and vice versa.
Everyone who is strong is not wise and vice versa.
If paul is both not curious and not old then fred is either not kind or not quiet and vice versa.
Everyone who is both not old and not funny is not brave or rich.
If mary is both humble and strong then susan is not old and vice versa.
If alice is not old then someone is both happy and not wise.
Everyone who is not strong or brave is old.
Everyone who is creative or kind is either not creative or brave and vice versa.
If someone is calm or not calm then someone is both not wise and not tall and vice versa.
If someone is either not generous or not strong then someone is both rich and not creative.
Everyone who is kind is rich and vice versa.
Mary is humble or calm.
Someone is not patient.
Susan is happy.
Someone is creative.
Paul is generous or not happy.
Susan is both old and not rich.
Someone is either funny or not tall. | Fred is not rich. | entailment | ((?[X]:((happy(X)<~>~quiet(X))))<=>((~kind(john)&happy(john))))&
(![X]:((brave(X)<~>curious(X))<=>(calm(X)<~>curious(X))))&
(![X]:((~humble(X)|creative(X))<=>(~quiet(X)&rich(X))))&
(((tall(paul)&~humble(paul)))=>((strong(alice)|~kind(alice))))&
(((~tall(paul)<~>~generous(paul)))<=>((~creative(mary)&old(mary))))&
(![X]:((~tall(X)&brave(X))<=>(patient(X)|~calm(X))))&
(![X]:(strong(X)<=>~wise(X)))&
(((~curious(paul)&~old(paul)))<=>((~kind(fred)<~>~quiet(fred))))&
(![X]:((~old(X)&~funny(X))=>(~brave(X)|rich(X))))&
(((humble(mary)&strong(mary)))<=>(~old(susan)))&
((~old(alice))=>(?[X]:((happy(X)&~wise(X)))))&
(![X]:((~strong(X)|brave(X))=>old(X)))&
(![X]:((creative(X)|kind(X))<=>(~creative(X)<~>brave(X))))&
((?[X]:((calm(X)|~calm(X))))<=>(?[X]:((~wise(X)&~tall(X)))))&
((?[X]:((~generous(X)<~>~strong(X))))=>(?[X]:((rich(X)&~creative(X)))))&
(![X]:(kind(X)<=>rich(X)))&
((humble(mary)|calm(mary)))&
(?[X]:(~patient(X)))&
(happy(susan))&
(?[X]:(creative(X)))&
((generous(paul)|~happy(paul)))&
((old(susan)&~rich(susan)))&
(?[X]:((funny(X)<~>~tall(X)))) | ~rich(fred) | [
"p1",
"p2",
"p5",
"p7",
"p11",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4017676901660940533380510
% SZS output start Proof for 4017676901660940533380510
2. ! [X0] : ((brave(X0) <~> curious(X0)) <=> (calm(X0) <~> curious(X0))) [input p1]
3. ! [X0] : ((creative(X0) | ~humble(X0)) <=> (rich(X0) & ~quiet(X0))) [input p2]
6. ! [X0] : ((brave(X0) & ~tall(X0)) <=> (~calm(X0) | patient(X0))) [input p5]
8. (~old(paul) & ~curious(paul)) <=> (~kind(fred) <~> ~quiet(fred)) [input p7]
12. ! [X0] : ((brave(X0) | ~strong(X0)) => old(X0)) [input p11]
13. ! [X0] : ((kind(X0) | creative(X0)) <=> (~creative(X0) <~> brave(X0))) [input p12]
16. ! [X0] : (kind(X0) <=> rich(X0)) [input p15]
24. rich(fred) [input hypothesis]
32. ! [X0] : (old(X0) | (~brave(X0) & strong(X0))) [ennf transformation 12]
39. ! [X0] : ((((~curious(X0) | ~brave(X0)) & (curious(X0) | brave(X0))) | ((calm(X0) | ~curious(X0)) & (curious(X0) | ~calm(X0)))) & (((~curious(X0) | ~calm(X0)) & (curious(X0) | calm(X0))) | ((brave(X0) | ~curious(X0)) & (curious(X0) | ~brave(X0))))) [nnf transformation 2]
40. ! [X0] : (((creative(X0) | ~humble(X0)) | (~rich(X0) | quiet(X0))) & ((rich(X0) & ~quiet(X0)) | (~creative(X0) & humble(X0)))) [nnf transformation 3]
41. ! [X0] : ((creative(X0) | ~humble(X0) | ~rich(X0) | quiet(X0)) & ((rich(X0) & ~quiet(X0)) | (~creative(X0) & humble(X0)))) [flattening 40]
44. ! [X0] : (((brave(X0) & ~tall(X0)) | (calm(X0) & ~patient(X0))) & ((~calm(X0) | patient(X0)) | (~brave(X0) | tall(X0)))) [nnf transformation 6]
45. ! [X0] : (((brave(X0) & ~tall(X0)) | (calm(X0) & ~patient(X0))) & (~calm(X0) | patient(X0) | ~brave(X0) | tall(X0))) [flattening 44]
47. ((~old(paul) & ~curious(paul)) | ((~kind(fred) | quiet(fred)) & (~quiet(fred) | kind(fred)))) & (((quiet(fred) | kind(fred)) & (~quiet(fred) | ~kind(fred))) | (old(paul) | curious(paul))) [nnf transformation 8]
48. ((~old(paul) & ~curious(paul)) | ((~kind(fred) | quiet(fred)) & (~quiet(fred) | kind(fred)))) & (((quiet(fred) | kind(fred)) & (~quiet(fred) | ~kind(fred))) | old(paul) | curious(paul)) [flattening 47]
53. ! [X0] : (((kind(X0) | creative(X0)) | ((~creative(X0) | ~brave(X0)) & (brave(X0) | creative(X0)))) & (((~brave(X0) | creative(X0)) & (brave(X0) | ~creative(X0))) | (~kind(X0) & ~creative(X0)))) [nnf transformation 13]
54. ! [X0] : ((kind(X0) | creative(X0) | ((~creative(X0) | ~brave(X0)) & (brave(X0) | creative(X0)))) & (((~brave(X0) | creative(X0)) & (brave(X0) | ~creative(X0))) | (~kind(X0) & ~creative(X0)))) [flattening 53]
64. ! [X0] : ((kind(X0) | ~rich(X0)) & (rich(X0) | ~kind(X0))) [nnf transformation 16]
78. curious(X0) | calm(X0) | curious(X0) | ~brave(X0) [cnf transformation 39]
81. ~curious(X0) | ~calm(X0) | brave(X0) | ~curious(X0) [cnf transformation 39]
82. curious(X0) | brave(X0) | curious(X0) | ~calm(X0) [cnf transformation 39]
85. ~curious(X0) | ~brave(X0) | calm(X0) | ~curious(X0) [cnf transformation 39]
87. ~creative(X0) | ~quiet(X0) [cnf transformation 41]
102. brave(X0) | calm(X0) [cnf transformation 45]
110. ~old(paul) | ~kind(fred) | quiet(fred) [cnf transformation 48]
118. ~brave(X0) | old(X0) [cnf transformation 32]
122. ~brave(X0) | creative(X0) | ~kind(X0) [cnf transformation 54]
135. ~rich(X0) | kind(X0) [cnf transformation 64]
145. rich(fred) [cnf transformation 24]
148. curious(X0) | calm(X0) | ~brave(X0) [duplicate literal removal 78]
149. ~curious(X0) | ~calm(X0) | brave(X0) [duplicate literal removal 81]
150. ~calm(X0) | brave(X0) | curious(X0) [duplicate literal removal 82]
151. ~curious(X0) | ~brave(X0) | calm(X0) [duplicate literal removal 85]
180. ~calm(X0) | brave(X0) [subsumption resolution 149,150]
181. ~brave(X0) | calm(X0) [subsumption resolution 148,151]
217. calm(X0) [subsumption resolution 102,181]
220. 14 <=> quiet(fred) [avatar definition]
222. quiet(fred) <- (14) [avatar component clause 220]
224. 15 <=> kind(fred) [avatar definition]
225. kind(fred) <- (15) [avatar component clause 224]
228. 16 <=> old(paul) [avatar definition]
230. ~old(paul) <- (~16) [avatar component clause 228]
231. 14 | ~15 | ~16 [avatar split clause 110,228,224,220]
319. kind(fred) [resolution 135,145]
323. 15 [avatar split clause 319,224]
328. brave(X0) [resolution 180,217]
333. old(X1) [resolution 328,118]
346. ~kind(X0) | creative(X0) [resolution 122,328]
353. $false <- (~16) [resolution 333,230]
354. 16 [avatar contradiction clause 353]
388. creative(fred) <- (15) [resolution 346,225]
396. ~quiet(fred) <- (15) [resolution 388,87]
397. $false <- (14, 15) [subsumption resolution 396,222]
398. ~14 | ~15 [avatar contradiction clause 397]
399. $false [avatar sat refutation 231,323,354,398]
% SZS output end Proof for 4017676901660940533380510
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If someone is wise or not generous then alice is kind or not quiet and vice versa.
Everyone who is not funny is humble and vice versa.
If someone is old or not funny then someone is not old and vice versa.
If someone is both not kind and wise then someone is either brave or not rich.
Everyone who is not quiet is both not brave and curious.
If susan is both not curious and calm then someone is both not patient and not rich and vice versa.
If someone is both creative and curious then someone is patient or not funny and vice versa.
If someone is humble or not quiet then someone is both rich and old and vice versa.
If susan is either not funny or not generous then fred is both not calm and not happy.
Everyone who is creative or not strong is not creative.
Everyone who is creative is tall.
Everyone who is both patient and not kind is kind or not generous and vice versa.
Everyone who is both not kind and not creative is either curious or not humble and vice versa.
Everyone who is both brave and not rich is either curious or not wise and vice versa.
Everyone who is both wise and not rich is both not happy and not kind.
Susan is not creative or brave.
Someone is not old or not tall.
Someone is not happy or not brave.
John is either happy or not patient. | Fred is not tall. | neutral | ((?[X]:((wise(X)|~generous(X))))<=>((kind(alice)|~quiet(alice))))&
(![X]:(~funny(X)<=>humble(X)))&
((?[X]:((old(X)|~funny(X))))<=>(?[X]:(~old(X))))&
((?[X]:((~kind(X)&wise(X))))=>(?[X]:((brave(X)<~>~rich(X)))))&
(![X]:(~quiet(X)=>(~brave(X)&curious(X))))&
(((~curious(susan)&calm(susan)))<=>(?[X]:((~patient(X)&~rich(X)))))&
((?[X]:((creative(X)&curious(X))))<=>(?[X]:((patient(X)|~funny(X)))))&
((?[X]:((humble(X)|~quiet(X))))<=>(?[X]:((rich(X)&old(X)))))&
(((~funny(susan)<~>~generous(susan)))=>((~calm(fred)&~happy(fred))))&
(![X]:((creative(X)|~strong(X))=>~creative(X)))&
(![X]:(creative(X)=>tall(X)))&
(![X]:((patient(X)&~kind(X))<=>(kind(X)|~generous(X))))&
(![X]:((~kind(X)&~creative(X))<=>(curious(X)<~>~humble(X))))&
(![X]:((brave(X)&~rich(X))<=>(curious(X)<~>~wise(X))))&
(![X]:((wise(X)&~rich(X))=>(~happy(X)&~kind(X))))&
((~creative(susan)|brave(susan)))&
(?[X]:((~old(X)|~tall(X))))&
(?[X]:((~happy(X)|~brave(X))))&
((happy(john)<~>~patient(john))) | ~tall(fred) | [] | null | 0 |
If someone is not kind or generous then mary is old or not wise and vice versa. Everyone who is both humble and curious is not funny or patient. If paul is not tall then someone is creative. If fred is both generous and not curious then fred is both strong and patient and vice versa. If john is both curious and not humble then paul is wise. Everyone who is both not strong and not creative is either wise or not generous. Everyone who is not quiet is strong. If susan is both not brave and not quiet then someone is creative or wise. Everyone who is either not patient or humble is both curious and not old and vice versa. If john is both quiet and creative then mary is happy or not rich and vice versa. Everyone who is both not funny and happy is either rich or not tall. Everyone who is both not rich and not creative is not humble. Everyone who is both brave and not happy is both not kind and rich and vice versa. If someone is both not creative and not quiet then john is both rich and not patient. Everyone who is both not humble and quiet is either not happy or not old and vice versa. Everyone who is old is either not wise or kind and vice versa. John is not quiet. Someone is either not creative or generous. Mary is either not happy or quiet. Mary is either strong or not kind. Someone is not rich or not kind. Someone is not quiet. Paul is either quiet or brave. Someone is both creative and not brave. | Susan is not brave. | neutral | ((?[X]:((~kind(X)|generous(X))))<=>((old(mary)|~wise(mary))))&
(![X]:((humble(X)&curious(X))=>(~funny(X)|patient(X))))&
((~tall(paul))=>(?[X]:(creative(X))))&
(((generous(fred)&~curious(fred)))<=>((strong(fred)&patient(fred))))&
(((curious(john)&~humble(john)))=>(wise(paul)))&
(![X]:((~strong(X)&~creative(X))=>(wise(X)<~>~generous(X))))&
(![X]:(~quiet(X)=>strong(X)))&
(((~brave(susan)&~quiet(susan)))=>(?[X]:((creative(X)|wise(X)))))&
(![X]:((~patient(X)<~>humble(X))<=>(curious(X)&~old(X))))&
(((quiet(john)&creative(john)))<=>((happy(mary)|~rich(mary))))&
(![X]:((~funny(X)&happy(X))=>(rich(X)<~>~tall(X))))&
(![X]:((~rich(X)&~creative(X))=>~humble(X)))&
(![X]:((brave(X)&~happy(X))<=>(~kind(X)&rich(X))))&
((?[X]:((~creative(X)&~quiet(X))))=>((rich(john)&~patient(john))))&
(![X]:((~humble(X)&quiet(X))<=>(~happy(X)<~>~old(X))))&
(![X]:(old(X)<=>(~wise(X)<~>kind(X))))&
(~quiet(john))&
(?[X]:((~creative(X)<~>generous(X))))&
((~happy(mary)<~>quiet(mary)))&
((strong(mary)<~>~kind(mary)))&
(?[X]:((~rich(X)|~kind(X))))&
(?[X]:(~quiet(X)))&
((quiet(paul)<~>brave(paul)))&
(?[X]:((creative(X)&~brave(X)))) | ~brave(susan) | [] | null | 0 |
If fred is either not creative or not happy then fred is not happy or not brave and vice versa.
Everyone who is either curious or brave is not generous.
Everyone who is patient is both happy and not brave.
Everyone who is not wise or not generous is both curious and not patient.
Everyone who is both humble and not quiet is not humble and vice versa.
If someone is not kind or not patient then susan is either not wise or not humble and vice versa.
Everyone who is kind or rich is both curious and humble.
If someone is happy then someone is calm or not kind and vice versa.
If mary is wise then paul is either not brave or not generous and vice versa.
If someone is not calm then lucy is not generous or curious.
If alice is strong then alice is both calm and not tall.
If paul is not strong or not kind then someone is wise.
If someone is tall then fred is both tall and quiet.
Everyone who is both quiet and brave is patient.
Everyone who is both not creative and not quiet is not funny.
Everyone who is either not funny or wise is strong or patient.
Someone is either funny or creative.
Someone is not creative or humble.
Susan is funny.
Someone is not wise.
Someone is not creative.
Someone is both not curious and not old.
Someone is either happy or not curious. | Susan is not generous. | entailment | (((~creative(fred)<~>~happy(fred)))<=>((~happy(fred)|~brave(fred))))&
(![X]:((curious(X)<~>brave(X))=>~generous(X)))&
(![X]:(patient(X)=>(happy(X)&~brave(X))))&
(![X]:((~wise(X)|~generous(X))=>(curious(X)&~patient(X))))&
(![X]:((humble(X)&~quiet(X))<=>~humble(X)))&
((?[X]:((~kind(X)|~patient(X))))<=>((~wise(susan)<~>~humble(susan))))&
(![X]:((kind(X)|rich(X))=>(curious(X)&humble(X))))&
((?[X]:(happy(X)))<=>(?[X]:((calm(X)|~kind(X)))))&
((wise(mary))<=>((~brave(paul)<~>~generous(paul))))&
((?[X]:(~calm(X)))=>((~generous(lucy)|curious(lucy))))&
((strong(alice))=>((calm(alice)&~tall(alice))))&
(((~strong(paul)|~kind(paul)))=>(?[X]:(wise(X))))&
((?[X]:(tall(X)))=>((tall(fred)&quiet(fred))))&
(![X]:((quiet(X)&brave(X))=>patient(X)))&
(![X]:((~creative(X)&~quiet(X))=>~funny(X)))&
(![X]:((~funny(X)<~>wise(X))=>(strong(X)|patient(X))))&
(?[X]:((funny(X)<~>creative(X))))&
(?[X]:((~creative(X)|humble(X))))&
(funny(susan))&
(?[X]:(~wise(X)))&
(?[X]:(~creative(X)))&
(?[X]:((~curious(X)&~old(X))))&
(?[X]:((happy(X)<~>~curious(X)))) | ~generous(susan) | [
"p1",
"p2",
"p3",
"p4",
"p5",
"p6",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 6535182697421168180213416
% SZS output start Proof for 6535182697421168180213416
2. ! [X0] : ((curious(X0) <~> brave(X0)) => ~generous(X0)) [input p1]
3. ! [X0] : (patient(X0) => (~brave(X0) & happy(X0))) [input p2]
4. ! [X0] : ((~generous(X0) | ~wise(X0)) => (~patient(X0) & curious(X0))) [input p3]
5. ! [X0] : ((~quiet(X0) & humble(X0)) <=> ~humble(X0)) [input p4]
6. ? [X0] : (~patient(X0) | ~kind(X0)) <=> (~wise(susan) <~> ~humble(susan)) [input p5]
7. ! [X0] : ((rich(X0) | kind(X0)) => (humble(X0) & curious(X0))) [input p6]
14. ! [X0] : ((brave(X0) & quiet(X0)) => patient(X0)) [input p13]
24. generous(susan) [input hypothesis]
27. ! [X0] : (kind(X0) => (humble(X0) & curious(X0))) [pure predicate removal 7]
28. ! [X0] : (~generous(X0) | (curious(X0) <=> brave(X0))) [ennf transformation 2]
29. ! [X0] : ((~brave(X0) & happy(X0)) | ~patient(X0)) [ennf transformation 3]
30. ! [X0] : ((~patient(X0) & curious(X0)) | (generous(X0) & wise(X0))) [ennf transformation 4]
31. ! [X0] : ((humble(X0) & curious(X0)) | ~kind(X0)) [ennf transformation 27]
37. ! [X0] : (patient(X0) | (~brave(X0) | ~quiet(X0))) [ennf transformation 14]
38. ! [X0] : (patient(X0) | ~brave(X0) | ~quiet(X0)) [flattening 37]
45. ! [X0] : (~generous(X0) | ((curious(X0) | ~brave(X0)) & (brave(X0) | ~curious(X0)))) [nnf transformation 28]
46. ! [X0] : (((~quiet(X0) & humble(X0)) | humble(X0)) & (~humble(X0) | (quiet(X0) | ~humble(X0)))) [nnf transformation 5]
47. ! [X0] : (((~quiet(X0) & humble(X0)) | humble(X0)) & (~humble(X0) | quiet(X0) | ~humble(X0))) [flattening 46]
48. (? [X0] : (~patient(X0) | ~kind(X0)) | ((~wise(susan) | humble(susan)) & (~humble(susan) | wise(susan)))) & (((humble(susan) | wise(susan)) & (~humble(susan) | ~wise(susan))) | ! [X0] : (patient(X0) & kind(X0))) [nnf transformation 6]
49. (? [X0] : (~patient(X0) | ~kind(X0)) | ((~wise(susan) | humble(susan)) & (~humble(susan) | wise(susan)))) & (((humble(susan) | wise(susan)) & (~humble(susan) | ~wise(susan))) | ! [X1] : (patient(X1) & kind(X1))) [rectify 48]
50. ? [X0] : (~patient(X0) | ~kind(X0)) => (~patient(sK0) | ~kind(sK0)) [choice axiom]
51. ((~patient(sK0) | ~kind(sK0)) | ((~wise(susan) | humble(susan)) & (~humble(susan) | wise(susan)))) & (((humble(susan) | wise(susan)) & (~humble(susan) | ~wise(susan))) | ! [X1] : (patient(X1) & kind(X1))) [skolemisation 49,50]
81. ~generous(X0) | brave(X0) | ~curious(X0) [cnf transformation 45]
84. ~patient(X0) | ~brave(X0) [cnf transformation 29]
85. wise(X0) | curious(X0) [cnf transformation 30]
88. ~patient(X0) | generous(X0) [cnf transformation 30]
89. ~humble(X0) | quiet(X0) | ~humble(X0) [cnf transformation 47]
90. humble(X0) | humble(X0) [cnf transformation 47]
92. ~humble(susan) | ~wise(susan) | kind(X1) [cnf transformation 51]
93. ~humble(susan) | ~wise(susan) | patient(X1) [cnf transformation 51]
98. ~kind(X0) | curious(X0) [cnf transformation 31]
114. patient(X0) | ~brave(X0) | ~quiet(X0) [cnf transformation 38]
127. generous(susan) [cnf transformation 24]
128. ~humble(X0) | quiet(X0) [duplicate literal removal 89]
129. humble(X0) [duplicate literal removal 90]
148. quiet(X0) [subsumption resolution 128,129]
151. 4 <=> wise(susan) [avatar definition]
152. ~wise(susan) <- (~4) [avatar component clause 151]
163. ~wise(susan) | patient(X1) [subsumption resolution 93,129]
165. 7 <=> ! [X1] : patient(X1) [avatar definition]
166. patient(X1) <- (7) [avatar component clause 165]
167. 7 | ~4 [avatar split clause 163,151,165]
168. ~wise(susan) | kind(X1) [subsumption resolution 92,129]
170. 8 <=> ! [X1] : kind(X1) [avatar definition]
171. kind(X1) <- (8) [avatar component clause 170]
172. 8 | ~4 [avatar split clause 168,151,170]
255. patient(X0) | ~brave(X0) [subsumption resolution 114,148]
256. ~brave(X0) [subsumption resolution 255,84]
279. curious(susan) <- (~4) [resolution 85,152]
283. brave(susan) | ~curious(susan) [resolution 81,127]
285. ~curious(susan) [subsumption resolution 283,256]
286. $false <- (~4) [subsumption resolution 285,279]
287. 4 [avatar contradiction clause 286]
289. generous(X0) <- (7) [resolution 166,88]
295. curious(X0) <- (8) [resolution 171,98]
304. brave(X1) | ~curious(X1) <- (7) [resolution 289,81]
306. ~curious(X1) <- (7) [subsumption resolution 304,256]
307. $false <- (7, 8) [subsumption resolution 306,295]
308. ~7 | ~8 [avatar contradiction clause 307]
309. $false [avatar sat refutation 167,172,287,308]
% SZS output end Proof for 6535182697421168180213416
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not rich or not humble is tall and vice versa. If alice is both quiet and calm then someone is kind. If someone is both not funny and kind then john is both tall and not humble. Everyone who is both not generous and curious is either not tall or not funny and vice versa. Everyone who is brave is not creative or not tall and vice versa. If fred is humble then susan is both not patient and happy and vice versa. Everyone who is not brave or not wise is not strong. Everyone who is either not patient or humble is either not strong or calm. If susan is both not creative and not kind then fred is either strong or not generous and vice versa. If someone is either quiet or not creative then mary is either kind or generous and vice versa. Everyone who is not wise is brave or not funny. Everyone who is not wise is curious or tall and vice versa. Everyone who is not happy or strong is either not brave or not old and vice versa. Everyone who is rich is creative. Everyone who is calm is not rich. If someone is either happy or not funny then someone is both tall and not brave and vice versa. Alice is not quiet. Susan is both brave and creative. Mary is either wise or not old. Someone is wise. Someone is not humble or quiet. Someone is old or tall. Someone is kind or not rich. John is curious. | Fred is not brave. | contradiction | (![X]:((~rich(X)|~humble(X))<=>tall(X)))&
(((quiet(alice)&calm(alice)))=>(?[X]:(kind(X))))&
((?[X]:((~funny(X)&kind(X))))=>((tall(john)&~humble(john))))&
(![X]:((~generous(X)&curious(X))<=>(~tall(X)<~>~funny(X))))&
(![X]:(brave(X)<=>(~creative(X)|~tall(X))))&
((humble(fred))<=>((~patient(susan)&happy(susan))))&
(![X]:((~brave(X)|~wise(X))=>~strong(X)))&
(![X]:((~patient(X)<~>humble(X))=>(~strong(X)<~>calm(X))))&
(((~creative(susan)&~kind(susan)))<=>((strong(fred)<~>~generous(fred))))&
((?[X]:((quiet(X)<~>~creative(X))))<=>((kind(mary)<~>generous(mary))))&
(![X]:(~wise(X)=>(brave(X)|~funny(X))))&
(![X]:(~wise(X)<=>(curious(X)|tall(X))))&
(![X]:((~happy(X)|strong(X))<=>(~brave(X)<~>~old(X))))&
(![X]:(rich(X)=>creative(X)))&
(![X]:(calm(X)=>~rich(X)))&
((?[X]:((happy(X)<~>~funny(X))))<=>(?[X]:((tall(X)&~brave(X)))))&
(~quiet(alice))&
((brave(susan)&creative(susan)))&
((wise(mary)<~>~old(mary)))&
(?[X]:(wise(X)))&
(?[X]:((~humble(X)|quiet(X))))&
(?[X]:((old(X)|tall(X))))&
(?[X]:((kind(X)|~rich(X))))&
(curious(john)) | ~brave(fred) | [
"p3",
"p4",
"p6",
"p8",
"p10",
"p11",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 2341228891722338697190311
% SZS output start Proof for 2341228891722338697190311
4. ! [X0] : ((curious(X0) & ~generous(X0)) <=> (~tall(X0) <~> ~funny(X0))) [input p3]
5. ! [X0] : (brave(X0) <=> (~tall(X0) | ~creative(X0))) [input p4]
7. ! [X0] : ((~wise(X0) | ~brave(X0)) => ~strong(X0)) [input p6]
9. (~kind(susan) & ~creative(susan)) <=> (strong(fred) <~> ~generous(fred)) [input p8]
11. ! [X0] : (~wise(X0) => (~funny(X0) | brave(X0))) [input p10]
12. ! [X0] : (~wise(X0) <=> (tall(X0) | curious(X0))) [input p11]
18. creative(susan) & brave(susan) [input p17]
25. ~brave(fred) [input hypothesis]
30. ! [X0] : (~strong(X0) | (wise(X0) & brave(X0))) [ennf transformation 7]
32. ! [X0] : ((~funny(X0) | brave(X0)) | wise(X0)) [ennf transformation 11]
33. ! [X0] : (~funny(X0) | brave(X0) | wise(X0)) [flattening 32]
40. ! [X0] : (((curious(X0) & ~generous(X0)) | ((~tall(X0) | funny(X0)) & (~funny(X0) | tall(X0)))) & (((funny(X0) | tall(X0)) & (~funny(X0) | ~tall(X0))) | (~curious(X0) | generous(X0)))) [nnf transformation 4]
41. ! [X0] : (((curious(X0) & ~generous(X0)) | ((~tall(X0) | funny(X0)) & (~funny(X0) | tall(X0)))) & (((funny(X0) | tall(X0)) & (~funny(X0) | ~tall(X0))) | ~curious(X0) | generous(X0))) [flattening 40]
42. ! [X0] : ((brave(X0) | (tall(X0) & creative(X0))) & ((~tall(X0) | ~creative(X0)) | ~brave(X0))) [nnf transformation 5]
43. ! [X0] : ((brave(X0) | (tall(X0) & creative(X0))) & (~tall(X0) | ~creative(X0) | ~brave(X0))) [flattening 42]
47. ((~kind(susan) & ~creative(susan)) | ((strong(fred) | generous(fred)) & (~generous(fred) | ~strong(fred)))) & (((generous(fred) | ~strong(fred)) & (~generous(fred) | strong(fred))) | (kind(susan) | creative(susan))) [nnf transformation 9]
48. ((~kind(susan) & ~creative(susan)) | ((strong(fred) | generous(fred)) & (~generous(fred) | ~strong(fred)))) & (((generous(fred) | ~strong(fred)) & (~generous(fred) | strong(fred))) | kind(susan) | creative(susan)) [flattening 47]
53. ! [X0] : ((~wise(X0) | (~tall(X0) & ~curious(X0))) & ((tall(X0) | curious(X0)) | wise(X0))) [nnf transformation 12]
54. ! [X0] : ((~wise(X0) | (~tall(X0) & ~curious(X0))) & (tall(X0) | curious(X0) | wise(X0))) [flattening 53]
80. ~generous(X0) | ~tall(X0) | funny(X0) [cnf transformation 41]
85. brave(X0) | tall(X0) [cnf transformation 43]
89. ~strong(X0) | brave(X0) [cnf transformation 30]
98. ~creative(susan) | strong(fred) | generous(fred) [cnf transformation 48]
109. ~funny(X0) | brave(X0) | wise(X0) [cnf transformation 33]
112. ~wise(X0) | ~tall(X0) [cnf transformation 54]
129. creative(susan) [cnf transformation 18]
137. ~brave(fred) [cnf transformation 25]
180. 10 <=> generous(fred) [avatar definition]
182. generous(fred) <- (10) [avatar component clause 180]
184. 11 <=> strong(fred) [avatar definition]
186. strong(fred) <- (11) [avatar component clause 184]
194. 13 <=> creative(susan) [avatar definition]
197. 10 | 11 | ~13 [avatar split clause 98,194,184,180]
267. 13 [avatar split clause 129,194]
306. tall(fred) [resolution 85,137]
350. ~tall(fred) | funny(fred) <- (10) [resolution 80,182]
352. funny(fred) <- (10) [subsumption resolution 350,306]
411. brave(fred) | wise(fred) <- (10) [resolution 109,352]
422. wise(fred) <- (10) [subsumption resolution 411,137]
625. ~tall(fred) <- (10) [resolution 422,112]
627. $false <- (10) [subsumption resolution 625,306]
628. ~10 [avatar contradiction clause 627]
641. brave(fred) <- (11) [resolution 186,89]
652. $false <- (11) [subsumption resolution 641,137]
653. ~11 [avatar contradiction clause 652]
654. $false [avatar sat refutation 197,267,628,653]
% SZS output end Proof for 2341228891722338697190311
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is tall or not old is both calm and brave.
Everyone who is happy or not kind is not rich and vice versa.
Everyone who is both happy and not old is not calm and vice versa.
Everyone who is happy is both not creative and brave and vice versa.
If john is either not kind or calm then someone is rich and vice versa.
Everyone who is creative or not calm is funny or brave and vice versa.
Everyone who is not happy is either not calm or not humble.
Everyone who is brave or quiet is not quiet or curious and vice versa.
If fred is not wise then someone is both humble and not brave.
If someone is not creative or strong then mary is either kind or tall.
If someone is brave then paul is not patient and vice versa.
If someone is funny or not quiet then someone is kind or brave.
Everyone who is not funny is both not funny and calm.
If mary is not brave or not patient then mary is either kind or not creative and vice versa.
John is not rich.
Susan is either funny or quiet.
Fred is either not strong or calm. | Paul is creative. | neutral | (![X]:((tall(X)|~old(X))=>(calm(X)&brave(X))))&
(![X]:((happy(X)|~kind(X))<=>~rich(X)))&
(![X]:((happy(X)&~old(X))<=>~calm(X)))&
(![X]:(happy(X)<=>(~creative(X)&brave(X))))&
(((~kind(john)<~>calm(john)))<=>(?[X]:(rich(X))))&
(![X]:((creative(X)|~calm(X))<=>(funny(X)|brave(X))))&
(![X]:(~happy(X)=>(~calm(X)<~>~humble(X))))&
(![X]:((brave(X)|quiet(X))<=>(~quiet(X)|curious(X))))&
((~wise(fred))=>(?[X]:((humble(X)&~brave(X)))))&
((?[X]:((~creative(X)|strong(X))))=>((kind(mary)<~>tall(mary))))&
((?[X]:(brave(X)))<=>(~patient(paul)))&
((?[X]:((funny(X)|~quiet(X))))=>(?[X]:((kind(X)|brave(X)))))&
(![X]:(~funny(X)=>(~funny(X)&calm(X))))&
(((~brave(mary)|~patient(mary)))<=>((kind(mary)<~>~creative(mary))))&
(~rich(john))&
((funny(susan)<~>quiet(susan)))&
((~strong(fred)<~>calm(fred))) | creative(paul) | [] | null | 0 |
If mary is both not patient and not brave then someone is both creative and not brave. If someone is both creative and generous then alice is not patient or tall and vice versa. Everyone who is not old is both not curious and not brave. Everyone who is not humble or strong is either old or kind. If mary is tall then someone is humble or not brave. If someone is either tall or quiet then john is not rich. Everyone who is either kind or patient is strong or not calm. Everyone who is tall is patient. If susan is calm then john is either not funny or not creative. If john is funny then mary is old or wise and vice versa. Everyone who is not kind or calm is not wise or wise. Everyone who is either kind or not patient is both not wise and calm. If someone is both tall and old then someone is not quiet and vice versa. If someone is either not tall or humble then someone is not calm or happy and vice versa. Everyone who is funny or curious is either not strong or old. Everyone who is either strong or not happy is either not humble or not old. Someone is wise. Someone is both strong and patient. Mary is both humble and quiet. John is both happy and kind. Someone is both funny and brave. Mary is generous or not brave. Someone is not humble. | Alice is tall. | neutral | (((~patient(mary)&~brave(mary)))=>(?[X]:((creative(X)&~brave(X)))))&
((?[X]:((creative(X)&generous(X))))<=>((~patient(alice)|tall(alice))))&
(![X]:(~old(X)=>(~curious(X)&~brave(X))))&
(![X]:((~humble(X)|strong(X))=>(old(X)<~>kind(X))))&
((tall(mary))=>(?[X]:((humble(X)|~brave(X)))))&
((?[X]:((tall(X)<~>quiet(X))))=>(~rich(john)))&
(![X]:((kind(X)<~>patient(X))=>(strong(X)|~calm(X))))&
(![X]:(tall(X)=>patient(X)))&
((calm(susan))=>((~funny(john)<~>~creative(john))))&
((funny(john))<=>((old(mary)|wise(mary))))&
(![X]:((~kind(X)|calm(X))=>(~wise(X)|wise(X))))&
(![X]:((kind(X)<~>~patient(X))=>(~wise(X)&calm(X))))&
((?[X]:((tall(X)&old(X))))<=>(?[X]:(~quiet(X))))&
((?[X]:((~tall(X)<~>humble(X))))<=>(?[X]:((~calm(X)|happy(X)))))&
(![X]:((funny(X)|curious(X))=>(~strong(X)<~>old(X))))&
(![X]:((strong(X)<~>~happy(X))=>(~humble(X)<~>~old(X))))&
(?[X]:(wise(X)))&
(?[X]:((strong(X)&patient(X))))&
((humble(mary)&quiet(mary)))&
((happy(john)&kind(john)))&
(?[X]:((funny(X)&brave(X))))&
((generous(mary)|~brave(mary)))&
(?[X]:(~humble(X))) | tall(alice) | [] | null | 0 |
If someone is both curious and generous then someone is either not humble or wise and vice versa.
Everyone who is either not creative or not tall is creative and vice versa.
If someone is humble or not generous then someone is both strong and not wise and vice versa.
Everyone who is generous is calm or not old and vice versa.
Everyone who is both not wise and not curious is quiet and vice versa.
Everyone who is both rich and happy is wise or old.
Everyone who is either not tall or not old is either not wise or humble.
If someone is either not rich or rich then someone is not happy or not old and vice versa.
If someone is not humble or not funny then someone is brave or not strong.
If susan is either not funny or quiet then alice is either strong or rich and vice versa.
Everyone who is calm or not creative is both not generous and creative and vice versa.
If mary is not curious then someone is either old or brave.
If someone is both old and rich then alice is not brave or quiet.
Everyone who is not creative is not quiet and vice versa.
Everyone who is both not patient and generous is either not happy or not curious.
Everyone who is either not tall or curious is either patient or kind and vice versa.
John is either creative or happy.
Someone is not generous or not curious.
John is calm or not brave.
Lucy is wise or happy.
Someone is both creative and strong. | Mary is not funny. | neutral | ((?[X]:((curious(X)&generous(X))))<=>(?[X]:((~humble(X)<~>wise(X)))))&
(![X]:((~creative(X)<~>~tall(X))<=>creative(X)))&
((?[X]:((humble(X)|~generous(X))))<=>(?[X]:((strong(X)&~wise(X)))))&
(![X]:(generous(X)<=>(calm(X)|~old(X))))&
(![X]:((~wise(X)&~curious(X))<=>quiet(X)))&
(![X]:((rich(X)&happy(X))=>(wise(X)|old(X))))&
(![X]:((~tall(X)<~>~old(X))=>(~wise(X)<~>humble(X))))&
((?[X]:((~rich(X)<~>rich(X))))<=>(?[X]:((~happy(X)|~old(X)))))&
((?[X]:((~humble(X)|~funny(X))))=>(?[X]:((brave(X)|~strong(X)))))&
(((~funny(susan)<~>quiet(susan)))<=>((strong(alice)<~>rich(alice))))&
(![X]:((calm(X)|~creative(X))<=>(~generous(X)&creative(X))))&
((~curious(mary))=>(?[X]:((old(X)<~>brave(X)))))&
((?[X]:((old(X)&rich(X))))=>((~brave(alice)|quiet(alice))))&
(![X]:(~creative(X)<=>~quiet(X)))&
(![X]:((~patient(X)&generous(X))=>(~happy(X)<~>~curious(X))))&
(![X]:((~tall(X)<~>curious(X))<=>(patient(X)<~>kind(X))))&
((creative(john)<~>happy(john)))&
(?[X]:((~generous(X)|~curious(X))))&
((calm(john)|~brave(john)))&
((wise(lucy)|happy(lucy)))&
(?[X]:((creative(X)&strong(X)))) | ~funny(mary) | [] | null | 0 |
Everyone who is brave or creative is not kind and vice versa.
Everyone who is both not brave and funny is either quiet or patient and vice versa.
Everyone who is either not wise or not quiet is not generous or not curious.
Everyone who is not tall is curious and vice versa.
If fred is either tall or kind then someone is either not calm or kind.
Everyone who is either not creative or creative is brave or funny and vice versa.
Everyone who is either not strong or not quiet is both not tall and rich.
Everyone who is not generous is not creative or not happy and vice versa.
Everyone who is not humble or not rich is either not brave or not generous and vice versa.
Everyone who is either not wise or not kind is not old or funny and vice versa.
If someone is not kind then someone is both not creative and generous and vice versa.
Everyone who is either quiet or not brave is either not strong or not quiet and vice versa.
Everyone who is rich or not kind is either not rich or kind.
If lucy is either not curious or not quiet then someone is either strong or happy.
Everyone who is rich or not happy is both tall and old.
Someone is kind or happy.
Someone is not creative or strong.
Lucy is creative or funny.
Susan is wise or not brave.
John is both happy and calm. | Susan is not humble. | contradiction | (![X]:((brave(X)|creative(X))<=>~kind(X)))&
(![X]:((~brave(X)&funny(X))<=>(quiet(X)<~>patient(X))))&
(![X]:((~wise(X)<~>~quiet(X))=>(~generous(X)|~curious(X))))&
(![X]:(~tall(X)<=>curious(X)))&
(((tall(fred)<~>kind(fred)))=>(?[X]:((~calm(X)<~>kind(X)))))&
(![X]:((~creative(X)<~>creative(X))<=>(brave(X)|funny(X))))&
(![X]:((~strong(X)<~>~quiet(X))=>(~tall(X)&rich(X))))&
(![X]:(~generous(X)<=>(~creative(X)|~happy(X))))&
(![X]:((~humble(X)|~rich(X))<=>(~brave(X)<~>~generous(X))))&
(![X]:((~wise(X)<~>~kind(X))<=>(~old(X)|funny(X))))&
((?[X]:(~kind(X)))<=>(?[X]:((~creative(X)&generous(X)))))&
(![X]:((quiet(X)<~>~brave(X))<=>(~strong(X)<~>~quiet(X))))&
(![X]:((rich(X)|~kind(X))=>(~rich(X)<~>kind(X))))&
(((~curious(lucy)<~>~quiet(lucy)))=>(?[X]:((strong(X)<~>happy(X)))))&
(![X]:((rich(X)|~happy(X))=>(tall(X)&old(X))))&
(?[X]:((kind(X)|happy(X))))&
(?[X]:((~creative(X)|strong(X))))&
((creative(lucy)|funny(lucy)))&
((wise(susan)|~brave(susan)))&
((happy(john)&calm(john))) | ~humble(susan) | [
"p0",
"p7",
"p8",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 8611281510507736394200760
% SZS output start Proof for 8611281510507736394200760
1. ! [X0] : ((creative(X0) | brave(X0)) <=> ~kind(X0)) [input p0]
8. ! [X0] : (~generous(X0) <=> (~happy(X0) | ~creative(X0))) [input p7]
9. ! [X0] : ((~rich(X0) | ~humble(X0)) <=> (~brave(X0) <~> ~generous(X0))) [input p8]
11. ? [X0] : ~kind(X0) <=> ? [X0] : (generous(X0) & ~creative(X0)) [input p10]
21. ~humble(susan) [input hypothesis]
22. ? [X0] : ~kind(X0) <=> ? [X1] : (generous(X1) & ~creative(X1)) [rectify 11]
30. ! [X0] : (((creative(X0) | brave(X0)) | kind(X0)) & (~kind(X0) | (~creative(X0) & ~brave(X0)))) [nnf transformation 1]
31. ! [X0] : ((creative(X0) | brave(X0) | kind(X0)) & (~kind(X0) | (~creative(X0) & ~brave(X0)))) [flattening 30]
42. ! [X0] : ((~generous(X0) | (happy(X0) & creative(X0))) & ((~happy(X0) | ~creative(X0)) | generous(X0))) [nnf transformation 8]
43. ! [X0] : ((~generous(X0) | (happy(X0) & creative(X0))) & (~happy(X0) | ~creative(X0) | generous(X0))) [flattening 42]
44. ! [X0] : (((~rich(X0) | ~humble(X0)) | ((~brave(X0) | generous(X0)) & (~generous(X0) | brave(X0)))) & (((generous(X0) | brave(X0)) & (~generous(X0) | ~brave(X0))) | (rich(X0) & humble(X0)))) [nnf transformation 9]
45. ! [X0] : ((~rich(X0) | ~humble(X0) | ((~brave(X0) | generous(X0)) & (~generous(X0) | brave(X0)))) & (((generous(X0) | brave(X0)) & (~generous(X0) | ~brave(X0))) | (rich(X0) & humble(X0)))) [flattening 44]
48. (? [X0] : ~kind(X0) | ! [X1] : (~generous(X1) | creative(X1))) & (? [X1] : (generous(X1) & ~creative(X1)) | ! [X0] : kind(X0)) [nnf transformation 22]
49. (? [X0] : ~kind(X0) | ! [X1] : (~generous(X1) | creative(X1))) & (? [X2] : (generous(X2) & ~creative(X2)) | ! [X3] : kind(X3)) [rectify 48]
50. ? [X0] : ~kind(X0) => ~kind(sK1) [choice axiom]
51. ? [X2] : (generous(X2) & ~creative(X2)) => (generous(sK2) & ~creative(sK2)) [choice axiom]
52. (~kind(sK1) | ! [X1] : (~generous(X1) | creative(X1))) & ((generous(sK2) & ~creative(sK2)) | ! [X3] : kind(X3)) [skolemisation 49,51,50]
62. ~kind(X0) | ~brave(X0) [cnf transformation 31]
63. ~kind(X0) | ~creative(X0) [cnf transformation 31]
90. ~generous(X0) | creative(X0) [cnf transformation 43]
94. humble(X0) | brave(X0) | generous(X0) [cnf transformation 45]
104. ~creative(sK2) | kind(X3) [cnf transformation 52]
105. generous(sK2) | kind(X3) [cnf transformation 52]
133. ~humble(susan) [cnf transformation 21]
164. 5 <=> ! [X3] : kind(X3) [avatar definition]
165. kind(X3) <- (5) [avatar component clause 164]
167. 6 <=> generous(sK2) [avatar definition]
169. generous(sK2) <- (6) [avatar component clause 167]
170. 5 | 6 [avatar split clause 105,167,164]
172. 7 <=> creative(sK2) [avatar definition]
175. 5 | ~7 [avatar split clause 104,172,164]
230. 19 <=> brave(susan) [avatar definition]
231. brave(susan) <- (19) [avatar component clause 230]
232. ~brave(susan) <- (~19) [avatar component clause 230]
240. creative(sK2) <- (6) [resolution 90,169]
243. 7 | ~6 [avatar split clause 240,167,172]
247. ~creative(X0) <- (5) [resolution 165,63]
248. ~brave(X1) <- (5) [resolution 165,62]
295. brave(susan) | generous(susan) [resolution 94,133]
296. generous(susan) <- (~19) [subsumption resolution 295,232]
300. creative(susan) <- (~19) [resolution 296,90]
301. $false <- (5, ~19) [subsumption resolution 300,247]
302. ~5 | 19 [avatar contradiction clause 301]
304. $false <- (5, 19) [subsumption resolution 231,248]
305. ~5 | ~19 [avatar contradiction clause 304]
306. $false [avatar sat refutation 170,175,243,302,305]
% SZS output end Proof for 8611281510507736394200760
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 john is strong or not wise then john is either funny or not humble and vice versa.
Everyone who is not strong is both not kind and not brave and vice versa.
If fred is either old or not brave then someone is quiet and vice versa.
Everyone who is kind or calm is both patient and happy and vice versa.
If alice is happy or brave then someone is not kind and vice versa.
Everyone who is both not humble and not tall is not wise or funny and vice versa.
If someone is both creative and not creative then someone is either creative or not wise.
If someone is curious then someone is old.
Everyone who is not calm is strong or not wise and vice versa.
Everyone who is not happy is either patient or not creative.
Everyone who is not generous or not brave is both not happy and not quiet.
Everyone who is not brave or quiet is either not old or not tall and vice versa.
Everyone who is not kind or not generous is either wise or humble.
If someone is both curious and patient then someone is strong and vice versa.
If someone is not generous or not funny then lucy is not happy or not quiet.
Everyone who is both strong and not quiet is either tall or brave.
John is either not brave or patient.
Someone is not generous or not kind.
Susan is not generous or humble.
Someone is both funny and not humble.
Someone is not old.
Someone is not humble.
Someone is humble or calm. | John is not patient. | contradiction | (((strong(john)|~wise(john)))<=>((funny(john)<~>~humble(john))))&
(![X]:(~strong(X)<=>(~kind(X)&~brave(X))))&
(((old(fred)<~>~brave(fred)))<=>(?[X]:(quiet(X))))&
(![X]:((kind(X)|calm(X))<=>(patient(X)&happy(X))))&
(((happy(alice)|brave(alice)))<=>(?[X]:(~kind(X))))&
(![X]:((~humble(X)&~tall(X))<=>(~wise(X)|funny(X))))&
((?[X]:((creative(X)&~creative(X))))=>(?[X]:((creative(X)<~>~wise(X)))))&
((?[X]:(curious(X)))=>(?[X]:(old(X))))&
(![X]:(~calm(X)<=>(strong(X)|~wise(X))))&
(![X]:(~happy(X)=>(patient(X)<~>~creative(X))))&
(![X]:((~generous(X)|~brave(X))=>(~happy(X)&~quiet(X))))&
(![X]:((~brave(X)|quiet(X))<=>(~old(X)<~>~tall(X))))&
(![X]:((~kind(X)|~generous(X))=>(wise(X)<~>humble(X))))&
((?[X]:((curious(X)&patient(X))))<=>(?[X]:(strong(X))))&
((?[X]:((~generous(X)|~funny(X))))=>((~happy(lucy)|~quiet(lucy))))&
(![X]:((strong(X)&~quiet(X))=>(tall(X)<~>brave(X))))&
((~brave(john)<~>patient(john)))&
(?[X]:((~generous(X)|~kind(X))))&
((~generous(susan)|humble(susan)))&
(?[X]:((funny(X)&~humble(X))))&
(?[X]:(~old(X)))&
(?[X]:(~humble(X)))&
(?[X]:((humble(X)|calm(X)))) | ~patient(john) | [
"p1",
"p3",
"p5",
"p8",
"p12",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 7258043660153746925573872
% SZS output start Proof for 7258043660153746925573872
2. ! [X0] : (~strong(X0) <=> (~brave(X0) & ~kind(X0))) [input p1]
4. ! [X0] : ((calm(X0) | kind(X0)) <=> (happy(X0) & patient(X0))) [input p3]
6. ! [X0] : ((~tall(X0) & ~humble(X0)) <=> (funny(X0) | ~wise(X0))) [input p5]
9. ! [X0] : (~calm(X0) <=> (~wise(X0) | strong(X0))) [input p8]
13. ! [X0] : ((~generous(X0) | ~kind(X0)) => (wise(X0) <~> humble(X0))) [input p12]
17. ~brave(john) <~> patient(john) [input p16]
24. ~patient(john) [input hypothesis]
32. ! [X0] : ((wise(X0) <~> humble(X0)) | (generous(X0) & kind(X0))) [ennf transformation 13]
39. ! [X0] : ((~strong(X0) | (brave(X0) | kind(X0))) & ((~brave(X0) & ~kind(X0)) | strong(X0))) [nnf transformation 2]
40. ! [X0] : ((~strong(X0) | brave(X0) | kind(X0)) & ((~brave(X0) & ~kind(X0)) | strong(X0))) [flattening 39]
45. ! [X0] : (((calm(X0) | kind(X0)) | (~happy(X0) | ~patient(X0))) & ((happy(X0) & patient(X0)) | (~calm(X0) & ~kind(X0)))) [nnf transformation 4]
46. ! [X0] : ((calm(X0) | kind(X0) | ~happy(X0) | ~patient(X0)) & ((happy(X0) & patient(X0)) | (~calm(X0) & ~kind(X0)))) [flattening 45]
52. ! [X0] : (((~tall(X0) & ~humble(X0)) | (~funny(X0) & wise(X0))) & ((funny(X0) | ~wise(X0)) | (tall(X0) | humble(X0)))) [nnf transformation 6]
53. ! [X0] : (((~tall(X0) & ~humble(X0)) | (~funny(X0) & wise(X0))) & (funny(X0) | ~wise(X0) | tall(X0) | humble(X0))) [flattening 52]
61. ! [X0] : ((~calm(X0) | (wise(X0) & ~strong(X0))) & ((~wise(X0) | strong(X0)) | calm(X0))) [nnf transformation 9]
62. ! [X0] : ((~calm(X0) | (wise(X0) & ~strong(X0))) & (~wise(X0) | strong(X0) | calm(X0))) [flattening 61]
66. ! [X0] : (((~humble(X0) | ~wise(X0)) & (humble(X0) | wise(X0))) | (generous(X0) & kind(X0))) [nnf transformation 32]
73. (~patient(john) | brave(john)) & (patient(john) | ~brave(john)) [nnf transformation 17]
92. ~strong(X0) | brave(X0) | kind(X0) [cnf transformation 40]
97. ~kind(X0) | patient(X0) [cnf transformation 46]
98. ~calm(X0) | patient(X0) [cnf transformation 46]
106. ~humble(X0) | wise(X0) [cnf transformation 53]
113. ~wise(X0) | strong(X0) | calm(X0) [cnf transformation 62]
128. humble(X0) | wise(X0) | kind(X0) [cnf transformation 66]
139. patient(john) | ~brave(john) [cnf transformation 73]
148. ~patient(john) [cnf transformation 24]
158. 3 <=> strong(john) [avatar definition]
159. ~strong(john) <- (~3) [avatar component clause 158]
160. strong(john) <- (3) [avatar component clause 158]
162. 4 <=> wise(john) [avatar definition]
163. wise(john) <- (4) [avatar component clause 162]
219. kind(X0) | wise(X0) [subsumption resolution 128,106]
260. 24 <=> brave(john) [avatar definition]
261. ~brave(john) <- (~24) [avatar component clause 260]
264. 25 <=> patient(john) [avatar definition]
266. ~patient(john) <- (~25) [avatar component clause 264]
268. ~24 | 25 [avatar split clause 139,264,260]
296. ~25 [avatar split clause 148,264]
318. patient(X1) | wise(X1) [resolution 219,97]
531. wise(john) <- (~25) [resolution 318,266]
536. 4 | 25 [avatar split clause 531,264,162]
542. strong(john) | calm(john) <- (4) [resolution 163,113]
543. calm(john) <- (~3, 4) [subsumption resolution 542,159]
559. patient(john) <- (~3, 4) [resolution 543,98]
560. $false <- (~3, 4, ~25) [subsumption resolution 559,266]
561. 3 | ~4 | 25 [avatar contradiction clause 560]
568. brave(john) | kind(john) <- (3) [resolution 160,92]
569. kind(john) <- (3, ~24) [subsumption resolution 568,261]
578. patient(john) <- (3, ~24) [resolution 569,97]
580. $false <- (3, ~24, ~25) [subsumption resolution 578,266]
581. ~3 | 24 | 25 [avatar contradiction clause 580]
582. $false [avatar sat refutation 268,296,536,561,581]
% SZS output end Proof for 7258043660153746925573872
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not kind or not curious is generous and vice versa.
Everyone who is not kind is not quiet or not humble and vice versa.
Everyone who is both generous and happy is both kind and not kind and vice versa.
Everyone who is happy or tall is both wise and curious and vice versa.
Everyone who is not creative or wise is either humble or wise and vice versa.
If mary is either calm or curious then someone is strong.
If mary is either not patient or wise then someone is not kind.
If someone is strong then alice is both not old and strong.
If someone is both quiet and not tall then john is either funny or rich and vice versa.
If alice is not creative or patient then fred is not strong and vice versa.
Everyone who is rich or not calm is rich or curious.
Everyone who is both patient and not creative is either rich or not funny.
Everyone who is either not creative or not quiet is happy and vice versa.
If alice is either not patient or wise then paul is not creative.
If paul is quiet or strong then mary is either not old or not funny.
If paul is either not happy or not rich then someone is rich or not patient and vice versa.
Paul is not rich.
Someone is strong.
Alice is tall or not patient.
Someone is either funny or not happy.
Someone is either not old or calm.
Lucy is either not strong or not calm.
Someone is both not old and not creative.
Mary is quiet. | Alice is kind. | contradiction | (![X]:((~kind(X)<~>~curious(X))<=>generous(X)))&
(![X]:(~kind(X)<=>(~quiet(X)|~humble(X))))&
(![X]:((generous(X)&happy(X))<=>(kind(X)&~kind(X))))&
(![X]:((happy(X)|tall(X))<=>(wise(X)&curious(X))))&
(![X]:((~creative(X)|wise(X))<=>(humble(X)<~>wise(X))))&
(((calm(mary)<~>curious(mary)))=>(?[X]:(strong(X))))&
(((~patient(mary)<~>wise(mary)))=>(?[X]:(~kind(X))))&
((?[X]:(strong(X)))=>((~old(alice)&strong(alice))))&
((?[X]:((quiet(X)&~tall(X))))<=>((funny(john)<~>rich(john))))&
(((~creative(alice)|patient(alice)))<=>(~strong(fred)))&
(![X]:((rich(X)|~calm(X))=>(rich(X)|curious(X))))&
(![X]:((patient(X)&~creative(X))=>(rich(X)<~>~funny(X))))&
(![X]:((~creative(X)<~>~quiet(X))<=>happy(X)))&
(((~patient(alice)<~>wise(alice)))=>(~creative(paul)))&
(((quiet(paul)|strong(paul)))=>((~old(mary)<~>~funny(mary))))&
(((~happy(paul)<~>~rich(paul)))<=>(?[X]:((rich(X)|~patient(X)))))&
(~rich(paul))&
(?[X]:(strong(X)))&
((tall(alice)|~patient(alice)))&
(?[X]:((funny(X)<~>~happy(X))))&
(?[X]:((~old(X)<~>calm(X))))&
((~strong(lucy)<~>~calm(lucy)))&
(?[X]:((~old(X)&~creative(X))))&
(quiet(mary)) | kind(alice) | [
"p0",
"p1",
"p2",
"p3",
"p4",
"p15",
"p16",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 4272641683763792378873447
% SZS output start Proof for 4272641683763792378873447
1. ! [X0] : ((~kind(X0) <~> ~curious(X0)) <=> generous(X0)) [input p0]
2. ! [X0] : (~kind(X0) <=> (~humble(X0) | ~quiet(X0))) [input p1]
3. ! [X0] : ((happy(X0) & generous(X0)) <=> (~kind(X0) & kind(X0))) [input p2]
4. ! [X0] : ((tall(X0) | happy(X0)) <=> (curious(X0) & wise(X0))) [input p3]
5. ! [X0] : ((wise(X0) | ~creative(X0)) <=> (humble(X0) <~> wise(X0))) [input p4]
16. (~happy(paul) <~> ~rich(paul)) <=> ? [X0] : (~patient(X0) | rich(X0)) [input p15]
17. ~rich(paul) [input p16]
19. ~patient(alice) | tall(alice) [input p18]
25. kind(alice) [input hypothesis]
35. ! [X0] : ((((curious(X0) | kind(X0)) & (~curious(X0) | ~kind(X0))) | ~generous(X0)) & (generous(X0) | ((~kind(X0) | curious(X0)) & (~curious(X0) | kind(X0))))) [nnf transformation 1]
36. ! [X0] : ((~kind(X0) | (humble(X0) & quiet(X0))) & ((~humble(X0) | ~quiet(X0)) | kind(X0))) [nnf transformation 2]
37. ! [X0] : ((~kind(X0) | (humble(X0) & quiet(X0))) & (~humble(X0) | ~quiet(X0) | kind(X0))) [flattening 36]
38. ! [X0] : (((happy(X0) & generous(X0)) | (kind(X0) | ~kind(X0))) & ((~kind(X0) & kind(X0)) | (~happy(X0) | ~generous(X0)))) [nnf transformation 3]
39. ! [X0] : (((happy(X0) & generous(X0)) | kind(X0) | ~kind(X0)) & ((~kind(X0) & kind(X0)) | ~happy(X0) | ~generous(X0))) [flattening 38]
40. ! [X0] : (((tall(X0) | happy(X0)) | (~curious(X0) | ~wise(X0))) & ((curious(X0) & wise(X0)) | (~tall(X0) & ~happy(X0)))) [nnf transformation 4]
41. ! [X0] : ((tall(X0) | happy(X0) | ~curious(X0) | ~wise(X0)) & ((curious(X0) & wise(X0)) | (~tall(X0) & ~happy(X0)))) [flattening 40]
42. ! [X0] : (((wise(X0) | ~creative(X0)) | ((humble(X0) | ~wise(X0)) & (wise(X0) | ~humble(X0)))) & (((~wise(X0) | ~humble(X0)) & (wise(X0) | humble(X0))) | (~wise(X0) & creative(X0)))) [nnf transformation 5]
43. ! [X0] : ((wise(X0) | ~creative(X0) | ((humble(X0) | ~wise(X0)) & (wise(X0) | ~humble(X0)))) & (((~wise(X0) | ~humble(X0)) & (wise(X0) | humble(X0))) | (~wise(X0) & creative(X0)))) [flattening 42]
60. (((rich(paul) | happy(paul)) & (~rich(paul) | ~happy(paul))) | ! [X0] : (patient(X0) & ~rich(X0))) & (? [X0] : (~patient(X0) | rich(X0)) | ((~happy(paul) | rich(paul)) & (~rich(paul) | happy(paul)))) [nnf transformation 16]
61. (((rich(paul) | happy(paul)) & (~rich(paul) | ~happy(paul))) | ! [X0] : (patient(X0) & ~rich(X0))) & (? [X1] : (~patient(X1) | rich(X1)) | ((~happy(paul) | rich(paul)) & (~rich(paul) | happy(paul)))) [rectify 60]
62. ? [X1] : (~patient(X1) | rich(X1)) => (~patient(sK3) | rich(sK3)) [choice axiom]
63. (((rich(paul) | happy(paul)) & (~rich(paul) | ~happy(paul))) | ! [X0] : (patient(X0) & ~rich(X0))) & ((~patient(sK3) | rich(sK3)) | ((~happy(paul) | rich(paul)) & (~rich(paul) | happy(paul)))) [skolemisation 61,62]
75. ~curious(X0) | generous(X0) | kind(X0) [cnf transformation 35]
81. ~kind(X0) | humble(X0) [cnf transformation 37]
82. kind(X0) | ~happy(X0) | ~generous(X0) [cnf transformation 39]
83. ~kind(X0) | ~happy(X0) | ~generous(X0) [cnf transformation 39]
86. ~happy(X0) | wise(X0) [cnf transformation 41]
87. ~tall(X0) | wise(X0) [cnf transformation 41]
88. ~happy(X0) | curious(X0) [cnf transformation 41]
94. ~wise(X0) | ~humble(X0) | ~wise(X0) [cnf transformation 43]
131. rich(paul) | happy(paul) | patient(X0) [cnf transformation 63]
132. ~rich(paul) [cnf transformation 17]
134. ~patient(alice) | tall(alice) [cnf transformation 19]
144. kind(alice) [cnf transformation 25]
145. ~wise(X0) | ~humble(X0) [duplicate literal removal 94]
147. ~happy(X0) | ~generous(X0) [subsumption resolution 82,83]
223. 17 <=> patient(alice) [avatar definition]
224. ~patient(alice) <- (~17) [avatar component clause 223]
230. 18 <=> wise(alice) [avatar definition]
231. wise(alice) <- (18) [avatar component clause 230]
260. 24 <=> ! [X0] : patient(X0) [avatar definition]
261. patient(X0) <- (24) [avatar component clause 260]
263. 25 <=> happy(paul) [avatar definition]
265. happy(paul) <- (25) [avatar component clause 263]
267. 26 <=> rich(paul) [avatar definition]
270. 24 | 25 | 26 [avatar split clause 131,267,263,260]
287. ~26 [avatar split clause 132,267]
289. 30 <=> tall(alice) [avatar definition]
291. tall(alice) <- (30) [avatar component clause 289]
292. 30 | ~17 [avatar split clause 134,223,289]
326. humble(alice) [resolution 81,144]
327. wise(paul) <- (25) [resolution 86,265]
328. curious(paul) <- (25) [resolution 88,265]
329. ~humble(paul) <- (25) [resolution 145,327]
330. ~generous(paul) <- (25) [resolution 147,265]
331. generous(paul) | kind(paul) <- (25) [resolution 75,328]
332. kind(paul) <- (25) [subsumption resolution 331,330]
348. humble(paul) <- (25) [resolution 332,81]
350. $false <- (25) [subsumption resolution 348,329]
351. ~25 [avatar contradiction clause 350]
354. $false <- (~17, 24) [resolution 261,224]
357. 17 | ~24 [avatar contradiction clause 354]
361. wise(alice) <- (30) [resolution 291,87]
364. 18 | ~30 [avatar split clause 361,289,230]
366. ~humble(alice) <- (18) [resolution 231,145]
367. $false <- (18) [subsumption resolution 366,326]
368. ~18 [avatar contradiction clause 367]
369. $false [avatar sat refutation 270,287,292,351,357,364,368]
% SZS output end Proof for 4272641683763792378873447
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not creative is curious or not kind and vice versa.
If someone is quiet or not strong then susan is patient or not quiet and vice versa.
Everyone who is both not patient and not quiet is both not old and patient and vice versa.
Everyone who is both creative and strong is humble and vice versa.
If someone is either tall or not strong then alice is patient or not creative and vice versa.
Everyone who is not rich or brave is strong and vice versa.
If john is either not strong or not happy then lucy is not humble or not strong and vice versa.
Everyone who is not tall or generous is patient and vice versa.
If paul is either creative or not wise then mary is calm.
Everyone who is quiet or strong is both not happy and old.
Everyone who is rich or old is not funny.
If someone is either patient or not happy then someone is both strong and not creative.
If someone is either not old or old then paul is not creative or kind.
Everyone who is quiet or creative is humble or curious.
Everyone who is not humble is either rich or strong.
If someone is not patient then someone is not kind or not strong and vice versa.
Mary is both calm and not quiet.
Paul is either kind or not brave.
Alice is kind.
Mary is funny or not generous.
Someone is either not rich or not calm.
John is both happy and not curious.
Someone is not strong or happy. | John is not happy. | contradiction | (![X]:(~creative(X)<=>(curious(X)|~kind(X))))&
((?[X]:((quiet(X)|~strong(X))))<=>((patient(susan)|~quiet(susan))))&
(![X]:((~patient(X)&~quiet(X))<=>(~old(X)&patient(X))))&
(![X]:((creative(X)&strong(X))<=>humble(X)))&
((?[X]:((tall(X)<~>~strong(X))))<=>((patient(alice)|~creative(alice))))&
(![X]:((~rich(X)|brave(X))<=>strong(X)))&
(((~strong(john)<~>~happy(john)))<=>((~humble(lucy)|~strong(lucy))))&
(![X]:((~tall(X)|generous(X))<=>patient(X)))&
(((creative(paul)<~>~wise(paul)))=>(calm(mary)))&
(![X]:((quiet(X)|strong(X))=>(~happy(X)&old(X))))&
(![X]:((rich(X)|old(X))=>~funny(X)))&
((?[X]:((patient(X)<~>~happy(X))))=>(?[X]:((strong(X)&~creative(X)))))&
((?[X]:((~old(X)<~>old(X))))=>((~creative(paul)|kind(paul))))&
(![X]:((quiet(X)|creative(X))=>(humble(X)|curious(X))))&
(![X]:(~humble(X)=>(rich(X)<~>strong(X))))&
((?[X]:(~patient(X)))<=>(?[X]:((~kind(X)|~strong(X)))))&
((calm(mary)&~quiet(mary)))&
((kind(paul)<~>~brave(paul)))&
(kind(alice))&
((funny(mary)|~generous(mary)))&
(?[X]:((~rich(X)<~>~calm(X))))&
((happy(john)&~curious(john)))&
(?[X]:((~strong(X)|happy(X)))) | ~happy(john) | [
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 2080074291140907623295776
% SZS output start Proof for 2080074291140907623295776
22. ~curious(john) & happy(john) [input p21]
24. ~happy(john) [input hypothesis]
137. happy(john) [cnf transformation 22]
140. ~happy(john) [cnf transformation 24]
208. 15 <=> happy(john) [avatar definition]
307. 15 [avatar split clause 137,208]
309. ~15 [avatar split clause 140,208]
310. $false [avatar sat refutation 307,309]
% SZS output end Proof for 2080074291140907623295776
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not funny or not generous is not brave or curious and vice versa.
Everyone who is not brave or quiet is both humble and generous.
If someone is either not strong or not humble then someone is tall and vice versa.
Everyone who is not brave is either not calm or strong.
Everyone who is patient is both humble and not generous.
Everyone who is not old or not patient is not creative and vice versa.
If someone is both not calm and not funny then alice is either tall or not creative.
Everyone who is either strong or not creative is both happy and quiet.
If someone is both rich and quiet then lucy is not brave or happy and vice versa.
Everyone who is either not old or funny is not wise and vice versa.
Everyone who is both wise and kind is both not curious and not calm and vice versa.
Everyone who is curious or not brave is either not happy or funny and vice versa.
If alice is either wise or not calm then fred is curious or funny.
If john is both kind and not humble then lucy is generous.
If someone is either not rich or funny then mary is both strong and not rich.
Everyone who is kind or not creative is both tall and not funny.
Lucy is strong or not creative.
Someone is strong.
John is wise or funny.
Someone is either not humble or funny.
Alice is both patient and not tall. | Alice is not funny. | neutral | (![X]:((~funny(X)|~generous(X))<=>(~brave(X)|curious(X))))&
(![X]:((~brave(X)|quiet(X))=>(humble(X)&generous(X))))&
((?[X]:((~strong(X)<~>~humble(X))))<=>(?[X]:(tall(X))))&
(![X]:(~brave(X)=>(~calm(X)<~>strong(X))))&
(![X]:(patient(X)=>(humble(X)&~generous(X))))&
(![X]:((~old(X)|~patient(X))<=>~creative(X)))&
((?[X]:((~calm(X)&~funny(X))))=>((tall(alice)<~>~creative(alice))))&
(![X]:((strong(X)<~>~creative(X))=>(happy(X)&quiet(X))))&
((?[X]:((rich(X)&quiet(X))))<=>((~brave(lucy)|happy(lucy))))&
(![X]:((~old(X)<~>funny(X))<=>~wise(X)))&
(![X]:((wise(X)&kind(X))<=>(~curious(X)&~calm(X))))&
(![X]:((curious(X)|~brave(X))<=>(~happy(X)<~>funny(X))))&
(((wise(alice)<~>~calm(alice)))=>((curious(fred)|funny(fred))))&
(((kind(john)&~humble(john)))=>(generous(lucy)))&
((?[X]:((~rich(X)<~>funny(X))))=>((strong(mary)&~rich(mary))))&
(![X]:((kind(X)|~creative(X))=>(tall(X)&~funny(X))))&
((strong(lucy)|~creative(lucy)))&
(?[X]:(strong(X)))&
((wise(john)|funny(john)))&
(?[X]:((~humble(X)<~>funny(X))))&
((patient(alice)&~tall(alice))) | ~funny(alice) | [] | null | 0 |
If someone is funny then someone is calm or not old.
If someone is brave then susan is either patient or happy.
Everyone who is creative is either not strong or not tall and vice versa.
If paul is not generous then paul is either brave or not generous and vice versa.
Everyone who is not curious or brave is either not tall or quiet and vice versa.
Everyone who is not rich is not old.
Everyone who is quiet is not happy.
If fred is patient then someone is generous.
Everyone who is both kind and not brave is either creative or not generous and vice versa.
If someone is not old then lucy is quiet and vice versa.
Everyone who is quiet is creative.
Everyone who is curious is either not patient or not quiet.
If someone is calm or not generous then john is not kind and vice versa.
Everyone who is either not brave or calm is either not creative or wise and vice versa.
If someone is either funny or old then someone is brave or rich.
Everyone who is generous or not brave is both not calm and not funny.
Lucy is both humble and not old.
Susan is not generous.
Someone is either not brave or tall.
Mary is either funny or patient.
Susan is tall.
Alice is not strong or generous.
John is creative.
Alice is not strong or not calm. | Lucy is happy. | contradiction | ((?[X]:(funny(X)))=>(?[X]:((calm(X)|~old(X)))))&
((?[X]:(brave(X)))=>((patient(susan)<~>happy(susan))))&
(![X]:(creative(X)<=>(~strong(X)<~>~tall(X))))&
((~generous(paul))<=>((brave(paul)<~>~generous(paul))))&
(![X]:((~curious(X)|brave(X))<=>(~tall(X)<~>quiet(X))))&
(![X]:(~rich(X)=>~old(X)))&
(![X]:(quiet(X)=>~happy(X)))&
((patient(fred))=>(?[X]:(generous(X))))&
(![X]:((kind(X)&~brave(X))<=>(creative(X)<~>~generous(X))))&
((?[X]:(~old(X)))<=>(quiet(lucy)))&
(![X]:(quiet(X)=>creative(X)))&
(![X]:(curious(X)=>(~patient(X)<~>~quiet(X))))&
((?[X]:((calm(X)|~generous(X))))<=>(~kind(john)))&
(![X]:((~brave(X)<~>calm(X))<=>(~creative(X)<~>wise(X))))&
((?[X]:((funny(X)<~>old(X))))=>(?[X]:((brave(X)|rich(X)))))&
(![X]:((generous(X)|~brave(X))=>(~calm(X)&~funny(X))))&
((humble(lucy)&~old(lucy)))&
(~generous(susan))&
(?[X]:((~brave(X)<~>tall(X))))&
((funny(mary)<~>patient(mary)))&
(tall(susan))&
((~strong(alice)|generous(alice)))&
(creative(john))&
((~strong(alice)|~calm(alice))) | happy(lucy) | [
"p6",
"p9",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 6138084994580921826970261
% SZS output start Proof for 6138084994580921826970261
7. ! [X0] : (quiet(X0) => ~happy(X0)) [input p6]
10. ? [X0] : ~old(X0) <=> quiet(lucy) [input p9]
17. ~old(lucy) & humble(lucy) [input p16]
25. happy(lucy) [input hypothesis]
28. ~old(lucy) [pure predicate removal 17]
33. ! [X0] : (~happy(X0) | ~quiet(X0)) [ennf transformation 7]
50. (? [X0] : ~old(X0) | ~quiet(lucy)) & (quiet(lucy) | ! [X0] : old(X0)) [nnf transformation 10]
51. (? [X0] : ~old(X0) | ~quiet(lucy)) & (quiet(lucy) | ! [X1] : old(X1)) [rectify 50]
52. ? [X0] : ~old(X0) => ~old(sK2) [choice axiom]
53. (~old(sK2) | ~quiet(lucy)) & (quiet(lucy) | ! [X1] : old(X1)) [skolemisation 51,52]
81. ~quiet(X0) | ~happy(X0) [cnf transformation 33]
89. quiet(lucy) | old(X1) [cnf transformation 53]
109. ~old(lucy) [cnf transformation 28]
119. happy(lucy) [cnf transformation 25]
167. 11 <=> quiet(lucy) [avatar definition]
168. quiet(lucy) <- (11) [avatar component clause 167]
176. 13 <=> ! [X1] : old(X1) [avatar definition]
177. old(X1) <- (13) [avatar component clause 176]
178. 13 | 11 [avatar split clause 89,167,176]
234. ~happy(lucy) <- (11) [resolution 81,168]
235. $false <- (11) [subsumption resolution 234,119]
236. ~11 [avatar contradiction clause 235]
237. $false <- (13) [resolution 177,109]
242. ~13 [avatar contradiction clause 237]
243. $false [avatar sat refutation 178,236,242]
% SZS output end Proof for 6138084994580921826970261
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not old and not calm is either not tall or not happy and vice versa. Everyone who is not kind or not funny is either wise or not funny and vice versa. Everyone who is either happy or not calm is either not happy or not rich. If fred is both not brave and quiet then john is either not rich or not kind and vice versa. Everyone who is rich is happy. Everyone who is both not generous and quiet is either not quiet or not old and vice versa. Everyone who is not patient or rich is calm or not creative and vice versa. Everyone who is quiet or tall is both generous and funny. Everyone who is either not calm or not generous is not happy or happy and vice versa. If someone is not wise or not patient then alice is both not old and brave and vice versa. If someone is either quiet or not tall then susan is both not strong and not generous and vice versa. Everyone who is both not humble and brave is not calm. If susan is either kind or funny then lucy is not humble. Everyone who is humble or not strong is wise or creative and vice versa. If fred is either funny or not generous then mary is both rich and not creative. If fred is quiet then someone is either generous or rich. Someone is patient. John is generous or not rich. Someone is either curious or funny. Someone is either not old or brave. Someone is not creative. Alice is either brave or rich. Someone is not strong. Alice is either tall or kind. | Susan is rich. | contradiction | (![X]:((~old(X)&~calm(X))<=>(~tall(X)<~>~happy(X))))&
(![X]:((~kind(X)|~funny(X))<=>(wise(X)<~>~funny(X))))&
(![X]:((happy(X)<~>~calm(X))=>(~happy(X)<~>~rich(X))))&
(((~brave(fred)&quiet(fred)))<=>((~rich(john)<~>~kind(john))))&
(![X]:(rich(X)=>happy(X)))&
(![X]:((~generous(X)&quiet(X))<=>(~quiet(X)<~>~old(X))))&
(![X]:((~patient(X)|rich(X))<=>(calm(X)|~creative(X))))&
(![X]:((quiet(X)|tall(X))=>(generous(X)&funny(X))))&
(![X]:((~calm(X)<~>~generous(X))<=>(~happy(X)|happy(X))))&
((?[X]:((~wise(X)|~patient(X))))<=>((~old(alice)&brave(alice))))&
((?[X]:((quiet(X)<~>~tall(X))))<=>((~strong(susan)&~generous(susan))))&
(![X]:((~humble(X)&brave(X))=>~calm(X)))&
(((kind(susan)<~>funny(susan)))=>(~humble(lucy)))&
(![X]:((humble(X)|~strong(X))<=>(wise(X)|creative(X))))&
(((funny(fred)<~>~generous(fred)))=>((rich(mary)&~creative(mary))))&
((quiet(fred))=>(?[X]:((generous(X)<~>rich(X)))))&
(?[X]:(patient(X)))&
((generous(john)|~rich(john)))&
(?[X]:((curious(X)<~>funny(X))))&
(?[X]:((~old(X)<~>brave(X))))&
(?[X]:(~creative(X)))&
((brave(alice)<~>rich(alice)))&
(?[X]:(~strong(X)))&
((tall(alice)<~>kind(alice))) | rich(susan) | [
"p0",
"p2",
"p4",
"p5",
"p7",
"p8",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 5296283955863059663283239
% SZS output start Proof for 5296283955863059663283239
1. ! [X0] : ((~calm(X0) & ~old(X0)) <=> (~tall(X0) <~> ~happy(X0))) [input p0]
3. ! [X0] : ((happy(X0) <~> ~calm(X0)) => (~happy(X0) <~> ~rich(X0))) [input p2]
5. ! [X0] : (rich(X0) => happy(X0)) [input p4]
6. ! [X0] : ((quiet(X0) & ~generous(X0)) <=> (~quiet(X0) <~> ~old(X0))) [input p5]
8. ! [X0] : ((tall(X0) | quiet(X0)) => (funny(X0) & generous(X0))) [input p7]
9. ! [X0] : ((~calm(X0) <~> ~generous(X0)) <=> (happy(X0) | ~happy(X0))) [input p8]
11. ? [X0] : (quiet(X0) <~> ~tall(X0)) <=> (~generous(susan) & ~strong(susan)) [input p10]
25. rich(susan) [input hypothesis]
26. ! [X0] : ((~happy(X0) <~> ~rich(X0)) | (happy(X0) <=> ~calm(X0))) [ennf transformation 3]
27. ! [X0] : (happy(X0) | ~rich(X0)) [ennf transformation 5]
28. ! [X0] : ((funny(X0) & generous(X0)) | (~tall(X0) & ~quiet(X0))) [ennf transformation 8]
34. ! [X0] : (((~calm(X0) & ~old(X0)) | ((~tall(X0) | happy(X0)) & (~happy(X0) | tall(X0)))) & (((happy(X0) | tall(X0)) & (~happy(X0) | ~tall(X0))) | (calm(X0) | old(X0)))) [nnf transformation 1]
35. ! [X0] : (((~calm(X0) & ~old(X0)) | ((~tall(X0) | happy(X0)) & (~happy(X0) | tall(X0)))) & (((happy(X0) | tall(X0)) & (~happy(X0) | ~tall(X0))) | calm(X0) | old(X0))) [flattening 34]
38. ! [X0] : (((rich(X0) | happy(X0)) & (~rich(X0) | ~happy(X0))) | ((happy(X0) | calm(X0)) & (~calm(X0) | ~happy(X0)))) [nnf transformation 26]
41. ! [X0] : (((quiet(X0) & ~generous(X0)) | ((~quiet(X0) | old(X0)) & (~old(X0) | quiet(X0)))) & (((old(X0) | quiet(X0)) & (~old(X0) | ~quiet(X0))) | (~quiet(X0) | generous(X0)))) [nnf transformation 6]
42. ! [X0] : (((quiet(X0) & ~generous(X0)) | ((~quiet(X0) | old(X0)) & (~old(X0) | quiet(X0)))) & (((old(X0) | quiet(X0)) & (~old(X0) | ~quiet(X0))) | ~quiet(X0) | generous(X0))) [flattening 41]
45. ! [X0] : ((((generous(X0) | calm(X0)) & (~generous(X0) | ~calm(X0))) | (~happy(X0) & happy(X0))) & ((happy(X0) | ~happy(X0)) | ((~calm(X0) | generous(X0)) & (~generous(X0) | calm(X0))))) [nnf transformation 9]
46. ! [X0] : ((((generous(X0) | calm(X0)) & (~generous(X0) | ~calm(X0))) | (~happy(X0) & happy(X0))) & (happy(X0) | ~happy(X0) | ((~calm(X0) | generous(X0)) & (~generous(X0) | calm(X0))))) [flattening 45]
52. (? [X0] : ((tall(X0) | ~quiet(X0)) & (~tall(X0) | quiet(X0))) | (generous(susan) | strong(susan))) & ((~generous(susan) & ~strong(susan)) | ! [X0] : ((quiet(X0) | tall(X0)) & (~tall(X0) | ~quiet(X0)))) [nnf transformation 11]
53. (? [X0] : ((tall(X0) | ~quiet(X0)) & (~tall(X0) | quiet(X0))) | generous(susan) | strong(susan)) & ((~generous(susan) & ~strong(susan)) | ! [X0] : ((quiet(X0) | tall(X0)) & (~tall(X0) | ~quiet(X0)))) [flattening 52]
54. (? [X0] : ((tall(X0) | ~quiet(X0)) & (~tall(X0) | quiet(X0))) | generous(susan) | strong(susan)) & ((~generous(susan) & ~strong(susan)) | ! [X1] : ((quiet(X1) | tall(X1)) & (~tall(X1) | ~quiet(X1)))) [rectify 53]
55. ? [X0] : ((tall(X0) | ~quiet(X0)) & (~tall(X0) | quiet(X0))) => ((tall(sK1) | ~quiet(sK1)) & (~tall(sK1) | quiet(sK1))) [choice axiom]
56. (((tall(sK1) | ~quiet(sK1)) & (~tall(sK1) | quiet(sK1))) | generous(susan) | strong(susan)) & ((~generous(susan) & ~strong(susan)) | ! [X1] : ((quiet(X1) | tall(X1)) & (~tall(X1) | ~quiet(X1)))) [skolemisation 54,55]
78. ~happy(X0) | ~tall(X0) | calm(X0) | old(X0) [cnf transformation 35]
80. ~happy(X0) | ~old(X0) | tall(X0) [cnf transformation 35]
90. ~rich(X0) | ~happy(X0) | ~calm(X0) | ~happy(X0) [cnf transformation 38]
93. rich(X0) | happy(X0) | happy(X0) | calm(X0) [cnf transformation 38]
100. ~rich(X0) | happy(X0) [cnf transformation 27]
104. ~generous(X0) | ~quiet(X0) | old(X0) [cnf transformation 42]
105. quiet(X0) | ~old(X0) | quiet(X0) [cnf transformation 42]
111. ~quiet(X0) | generous(X0) [cnf transformation 28]
112. ~tall(X0) | generous(X0) [cnf transformation 28]
117. ~generous(X0) | ~calm(X0) | happy(X0) [cnf transformation 46]
118. ~generous(X0) | ~calm(X0) | ~happy(X0) [cnf transformation 46]
119. generous(X0) | calm(X0) | happy(X0) [cnf transformation 46]
120. ~happy(X0) | calm(X0) | generous(X0) [cnf transformation 46]
128. ~generous(susan) | ~tall(X1) | ~quiet(X1) [cnf transformation 56]
129. ~generous(susan) | quiet(X1) | tall(X1) [cnf transformation 56]
157. rich(susan) [cnf transformation 25]
159. ~old(X0) | quiet(X0) [duplicate literal removal 105]
160. ~rich(X0) | ~happy(X0) | ~calm(X0) [duplicate literal removal 90]
161. rich(X0) | happy(X0) | calm(X0) [duplicate literal removal 93]
187. generous(X0) | calm(X0) [subsumption resolution 119,120]
188. ~generous(X0) | ~calm(X0) [subsumption resolution 117,118]
221. 12 <=> generous(susan) [avatar definition]
222. ~generous(susan) <- (~12) [avatar component clause 221]
235. 15 <=> ! [X1] : (quiet(X1) | tall(X1)) [avatar definition]
236. quiet(X1) | tall(X1) <- (15) [avatar component clause 235]
237. 15 | ~12 [avatar split clause 129,221,235]
239. 16 <=> ! [X1] : (~tall(X1) | ~quiet(X1)) [avatar definition]
240. ~quiet(X1) | ~tall(X1) <- (16) [avatar component clause 239]
241. 16 | ~12 [avatar split clause 128,221,239]
329. happy(susan) [resolution 100,157]
338. 34 <=> tall(susan) [avatar definition]
339. ~tall(susan) <- (~34) [avatar component clause 338]
340. tall(susan) <- (34) [avatar component clause 338]
342. 35 <=> old(susan) [avatar definition]
343. old(susan) <- (35) [avatar component clause 342]
351. 36 <=> calm(susan) [avatar definition]
353. ~calm(susan) <- (~36) [avatar component clause 351]
359. tall(X1) | generous(X1) <- (15) [resolution 236,111]
363. generous(X1) <- (15) [subsumption resolution 359,112]
394. ~calm(X0) <- (15) [resolution 363,188]
409. ~quiet(X0) | old(X0) <- (15) [resolution 104,363]
471. ~happy(susan) | ~calm(susan) [resolution 160,157]
476. happy(X1) | calm(X1) | happy(X1) [resolution 161,100]
481. happy(X1) | calm(X1) [duplicate literal removal 476]
482. happy(X1) <- (15) [subsumption resolution 481,394]
485. ~old(X2) | tall(X2) <- (15) [resolution 482,80]
490. ~tall(susan) | calm(susan) | old(susan) [resolution 78,329]
508. old(X0) | tall(X0) <- (15) [resolution 409,236]
510. tall(X0) <- (15) [subsumption resolution 508,485]
518. $false <- (15, ~34) [resolution 510,339]
523. ~15 | 34 [avatar contradiction clause 518]
529. quiet(susan) <- (35) [resolution 343,159]
534. ~tall(susan) <- (16, 35) [resolution 529,240]
537. $false <- (15, 16, 35) [subsumption resolution 534,510]
538. ~15 | ~16 | ~35 [avatar contradiction clause 537]
541. ~calm(susan) [subsumption resolution 471,329]
581. calm(susan) | old(susan) <- (34) [subsumption resolution 490,340]
582. 35 | 36 | ~34 [avatar split clause 581,338,351,342]
583. ~36 [avatar split clause 541,351]
587. calm(susan) <- (~12) [resolution 222,187]
588. $false <- (~12, ~36) [subsumption resolution 587,353]
589. 12 | 36 [avatar contradiction clause 588]
590. $false [avatar sat refutation 237,241,523,538,582,583,589]
% SZS output end Proof for 5296283955863059663283239
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich then paul is calm and vice versa.
Everyone who is not strong or not quiet is not happy or not generous and vice versa.
If mary is creative or old then susan is both old and not strong.
Everyone who is both not tall and humble is either not funny or old.
If someone is not calm then susan is both not humble and not funny and vice versa.
Everyone who is quiet is not rich and vice versa.
If someone is either strong or not tall then someone is brave and vice versa.
Everyone who is not patient is quiet or not generous and vice versa.
If someone is either strong or not kind then someone is brave and vice versa.
If someone is both not calm and not patient then lucy is curious.
Everyone who is old or not curious is either not calm or not creative and vice versa.
Everyone who is not rich or kind is curious.
Everyone who is not old is not happy and vice versa.
If someone is not brave then someone is not generous or brave and vice versa.
If lucy is brave then someone is not patient and vice versa.
Everyone who is happy or not humble is not patient or not happy.
Someone is either not happy or not humble.
Someone is not quiet or not calm.
Someone is not creative or generous.
Someone is humble.
Someone is either creative or not happy.
Someone is not rich or not happy.
Mary is either brave or not happy. | Lucy is not strong. | neutral | ((?[X]:(rich(X)))<=>(calm(paul)))&
(![X]:((~strong(X)|~quiet(X))<=>(~happy(X)|~generous(X))))&
(((creative(mary)|old(mary)))=>((old(susan)&~strong(susan))))&
(![X]:((~tall(X)&humble(X))=>(~funny(X)<~>old(X))))&
((?[X]:(~calm(X)))<=>((~humble(susan)&~funny(susan))))&
(![X]:(quiet(X)<=>~rich(X)))&
((?[X]:((strong(X)<~>~tall(X))))<=>(?[X]:(brave(X))))&
(![X]:(~patient(X)<=>(quiet(X)|~generous(X))))&
((?[X]:((strong(X)<~>~kind(X))))<=>(?[X]:(brave(X))))&
((?[X]:((~calm(X)&~patient(X))))=>(curious(lucy)))&
(![X]:((old(X)|~curious(X))<=>(~calm(X)<~>~creative(X))))&
(![X]:((~rich(X)|kind(X))=>curious(X)))&
(![X]:(~old(X)<=>~happy(X)))&
((?[X]:(~brave(X)))<=>(?[X]:((~generous(X)|brave(X)))))&
((brave(lucy))<=>(?[X]:(~patient(X))))&
(![X]:((happy(X)|~humble(X))=>(~patient(X)|~happy(X))))&
(?[X]:((~happy(X)<~>~humble(X))))&
(?[X]:((~quiet(X)|~calm(X))))&
(?[X]:((~creative(X)|generous(X))))&
(?[X]:(humble(X)))&
(?[X]:((creative(X)<~>~happy(X))))&
(?[X]:((~rich(X)|~happy(X))))&
((brave(mary)<~>~happy(mary))) | ~strong(lucy) | [] | null | 0 |
Everyone who is not happy or rich is either not brave or strong. Everyone who is both not creative and brave is strong or not curious. Everyone who is not tall or not creative is not funny or patient and vice versa. Everyone who is not humble or strong is not old or not strong. Everyone who is brave is both humble and not wise and vice versa. If someone is creative then someone is either rich or not quiet. If lucy is either not tall or generous then susan is not calm or not funny and vice versa. If someone is not calm or wise then susan is both not creative and not rich and vice versa. If lucy is not happy then paul is funny. If alice is not creative or not happy then paul is either not patient or rich. If john is not tall or generous then lucy is either not rich or kind and vice versa. If someone is strong then alice is calm or not tall. Everyone who is rich or not creative is not humble or not patient. Everyone who is not happy is not brave. If someone is happy or strong then lucy is not rich and vice versa. If mary is both not humble and not generous then someone is both tall and not kind and vice versa. John is rich or not rich. Someone is either not old or not humble. Someone is patient or creative. Fred is not patient. Susan is funny or tall. Someone is not happy. Fred is either generous or kind. | Fred is not brave. | neutral | (![X]:((~happy(X)|rich(X))=>(~brave(X)<~>strong(X))))&
(![X]:((~creative(X)&brave(X))=>(strong(X)|~curious(X))))&
(![X]:((~tall(X)|~creative(X))<=>(~funny(X)|patient(X))))&
(![X]:((~humble(X)|strong(X))=>(~old(X)|~strong(X))))&
(![X]:(brave(X)<=>(humble(X)&~wise(X))))&
((?[X]:(creative(X)))=>(?[X]:((rich(X)<~>~quiet(X)))))&
(((~tall(lucy)<~>generous(lucy)))<=>((~calm(susan)|~funny(susan))))&
((?[X]:((~calm(X)|wise(X))))<=>((~creative(susan)&~rich(susan))))&
((~happy(lucy))=>(funny(paul)))&
(((~creative(alice)|~happy(alice)))=>((~patient(paul)<~>rich(paul))))&
(((~tall(john)|generous(john)))<=>((~rich(lucy)<~>kind(lucy))))&
((?[X]:(strong(X)))=>((calm(alice)|~tall(alice))))&
(![X]:((rich(X)|~creative(X))=>(~humble(X)|~patient(X))))&
(![X]:(~happy(X)=>~brave(X)))&
((?[X]:((happy(X)|strong(X))))<=>(~rich(lucy)))&
(((~humble(mary)&~generous(mary)))<=>(?[X]:((tall(X)&~kind(X)))))&
((rich(john)|~rich(john)))&
(?[X]:((~old(X)<~>~humble(X))))&
(?[X]:((patient(X)|creative(X))))&
(~patient(fred))&
((funny(susan)|tall(susan)))&
(?[X]:(~happy(X)))&
((generous(fred)<~>kind(fred))) | ~brave(fred) | [] | null | 0 |
Everyone who is brave or not curious is both brave and old and vice versa.
Everyone who is happy is funny or kind.
If lucy is not funny then mary is either not quiet or not creative and vice versa.
Everyone who is both happy and calm is not creative or not humble and vice versa.
If someone is not happy then mary is not calm and vice versa.
If alice is not creative or not brave then lucy is not kind.
If someone is either brave or strong then alice is happy.
If someone is not funny then someone is either not patient or not brave.
If susan is either not quiet or strong then john is not quiet or not kind.
Everyone who is not brave or calm is both not calm and not quiet.
Everyone who is funny is not calm.
Everyone who is either not humble or not happy is either brave or wise.
Everyone who is patient is both brave and not wise.
If fred is both creative and not wise then someone is not creative and vice versa.
If someone is patient or strong then mary is not funny or kind and vice versa.
Everyone who is tall is both not creative and funny and vice versa.
Someone is quiet.
Paul is wise.
Lucy is not curious.
Someone is not rich or not strong. | Paul is patient. | contradiction | (![X]:((brave(X)|~curious(X))<=>(brave(X)&old(X))))&
(![X]:(happy(X)=>(funny(X)|kind(X))))&
((~funny(lucy))<=>((~quiet(mary)<~>~creative(mary))))&
(![X]:((happy(X)&calm(X))<=>(~creative(X)|~humble(X))))&
((?[X]:(~happy(X)))<=>(~calm(mary)))&
(((~creative(alice)|~brave(alice)))=>(~kind(lucy)))&
((?[X]:((brave(X)<~>strong(X))))=>(happy(alice)))&
((?[X]:(~funny(X)))=>(?[X]:((~patient(X)<~>~brave(X)))))&
(((~quiet(susan)<~>strong(susan)))=>((~quiet(john)|~kind(john))))&
(![X]:((~brave(X)|calm(X))=>(~calm(X)&~quiet(X))))&
(![X]:(funny(X)=>~calm(X)))&
(![X]:((~humble(X)<~>~happy(X))=>(brave(X)<~>wise(X))))&
(![X]:(patient(X)=>(brave(X)&~wise(X))))&
(((creative(fred)&~wise(fred)))<=>(?[X]:(~creative(X))))&
((?[X]:((patient(X)|strong(X))))<=>((~funny(mary)|kind(mary))))&
(![X]:(tall(X)<=>(~creative(X)&funny(X))))&
(?[X]:(quiet(X)))&
(wise(paul))&
(~curious(lucy))&
(?[X]:((~rich(X)|~strong(X)))) | patient(paul) | [
"p12",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 7063013509858196337976953
% SZS output start Proof for 7063013509858196337976953
13. ! [X0] : (patient(X0) => (~wise(X0) & brave(X0))) [input p12]
18. wise(paul) [input p17]
21. patient(paul) [input hypothesis]
34. ! [X0] : ((~wise(X0) & brave(X0)) | ~patient(X0)) [ennf transformation 13]
98. ~wise(X0) | ~patient(X0) [cnf transformation 34]
107. wise(paul) [cnf transformation 18]
109. patient(paul) [cnf transformation 21]
269. ~patient(paul) [resolution 98,107]
271. $false [subsumption resolution 269,109]
% SZS output end Proof for 7063013509858196337976953
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If someone is patient then lucy is either creative or not quiet and vice versa.
Everyone who is curious is not strong or not tall and vice versa.
If fred is strong or patient then someone is either old or brave.
If john is happy then lucy is either not patient or humble and vice versa.
Everyone who is either happy or not old is not patient or not creative.
If fred is not tall or rich then someone is either generous or not patient and vice versa.
Everyone who is both not rich and kind is not happy.
If alice is quiet or generous then someone is not generous or not rich and vice versa.
Everyone who is both not brave and curious is kind and vice versa.
Everyone who is both not curious and patient is either funny or rich.
Everyone who is both happy and not patient is either happy or kind.
Everyone who is not patient or not humble is patient and vice versa.
Everyone who is wise or not strong is not patient and vice versa.
Everyone who is happy or not wise is tall and vice versa.
Everyone who is either not brave or not creative is both rich and not calm and vice versa.
Everyone who is both quiet and rich is not calm or kind.
Susan is both not creative and not rich.
Someone is either not brave or humble.
Mary is tall.
Mary is either not brave or rich.
Someone is both quiet and rich.
Someone is quiet or not creative.
John is not brave. | Alice is not kind. | entailment | ((?[X]:(patient(X)))<=>((creative(lucy)<~>~quiet(lucy))))&
(![X]:(curious(X)<=>(~strong(X)|~tall(X))))&
(((strong(fred)|patient(fred)))=>(?[X]:((old(X)<~>brave(X)))))&
((happy(john))<=>((~patient(lucy)<~>humble(lucy))))&
(![X]:((happy(X)<~>~old(X))=>(~patient(X)|~creative(X))))&
(((~tall(fred)|rich(fred)))<=>(?[X]:((generous(X)<~>~patient(X)))))&
(![X]:((~rich(X)&kind(X))=>~happy(X)))&
(((quiet(alice)|generous(alice)))<=>(?[X]:((~generous(X)|~rich(X)))))&
(![X]:((~brave(X)&curious(X))<=>kind(X)))&
(![X]:((~curious(X)&patient(X))=>(funny(X)<~>rich(X))))&
(![X]:((happy(X)&~patient(X))=>(happy(X)<~>kind(X))))&
(![X]:((~patient(X)|~humble(X))<=>patient(X)))&
(![X]:((wise(X)|~strong(X))<=>~patient(X)))&
(![X]:((happy(X)|~wise(X))<=>tall(X)))&
(![X]:((~brave(X)<~>~creative(X))<=>(rich(X)&~calm(X))))&
(![X]:((quiet(X)&rich(X))=>(~calm(X)|kind(X))))&
((~creative(susan)&~rich(susan)))&
(?[X]:((~brave(X)<~>humble(X))))&
(tall(mary))&
((~brave(mary)<~>rich(mary)))&
(?[X]:((quiet(X)&rich(X))))&
(?[X]:((quiet(X)|~creative(X))))&
(~brave(john)) | ~kind(alice) | [
"p1",
"p8",
"p11",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 151613506505516555670628
% SZS output start Proof for 151613506505516555670628
2. ! [X0] : (curious(X0) <=> (~tall(X0) | ~strong(X0))) [input p1]
9. ! [X0] : ((curious(X0) & ~brave(X0)) <=> kind(X0)) [input p8]
12. ! [X0] : ((~humble(X0) | ~patient(X0)) <=> patient(X0)) [input p11]
13. ! [X0] : ((~strong(X0) | wise(X0)) <=> ~patient(X0)) [input p12]
14. ! [X0] : ((~wise(X0) | happy(X0)) <=> tall(X0)) [input p13]
24. kind(alice) [input hypothesis]
40. ! [X0] : ((curious(X0) | (tall(X0) & strong(X0))) & ((~tall(X0) | ~strong(X0)) | ~curious(X0))) [nnf transformation 2]
41. ! [X0] : ((curious(X0) | (tall(X0) & strong(X0))) & (~tall(X0) | ~strong(X0) | ~curious(X0))) [flattening 40]
57. ! [X0] : (((curious(X0) & ~brave(X0)) | ~kind(X0)) & (kind(X0) | (~curious(X0) | brave(X0)))) [nnf transformation 9]
58. ! [X0] : (((curious(X0) & ~brave(X0)) | ~kind(X0)) & (kind(X0) | ~curious(X0) | brave(X0))) [flattening 57]
61. ! [X0] : (((~humble(X0) | ~patient(X0)) | ~patient(X0)) & (patient(X0) | (humble(X0) & patient(X0)))) [nnf transformation 12]
62. ! [X0] : ((~humble(X0) | ~patient(X0) | ~patient(X0)) & (patient(X0) | (humble(X0) & patient(X0)))) [flattening 61]
63. ! [X0] : (((~strong(X0) | wise(X0)) | patient(X0)) & (~patient(X0) | (strong(X0) & ~wise(X0)))) [nnf transformation 13]
64. ! [X0] : ((~strong(X0) | wise(X0) | patient(X0)) & (~patient(X0) | (strong(X0) & ~wise(X0)))) [flattening 63]
65. ! [X0] : (((~wise(X0) | happy(X0)) | ~tall(X0)) & (tall(X0) | (wise(X0) & ~happy(X0)))) [nnf transformation 14]
66. ! [X0] : ((~wise(X0) | happy(X0) | ~tall(X0)) & (tall(X0) | (wise(X0) & ~happy(X0)))) [flattening 65]
81. ~tall(X0) | ~strong(X0) | ~curious(X0) [cnf transformation 41]
107. ~kind(X0) | curious(X0) [cnf transformation 58]
112. patient(X0) | patient(X0) [cnf transformation 62]
115. ~patient(X0) | ~wise(X0) [cnf transformation 64]
116. ~patient(X0) | strong(X0) [cnf transformation 64]
119. tall(X0) | wise(X0) [cnf transformation 66]
139. kind(alice) [cnf transformation 24]
140. patient(X0) [duplicate literal removal 112]
252. strong(X0) [subsumption resolution 116,140]
253. ~wise(X0) [subsumption resolution 115,140]
254. tall(X0) [subsumption resolution 119,253]
296. curious(alice) [resolution 107,139]
301. ~strong(X1) | ~curious(X1) [resolution 81,254]
302. ~curious(X1) [subsumption resolution 301,252]
313. $false [resolution 302,296]
% SZS output end Proof for 151613506505516555670628
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not funny then someone is either not funny or patient and vice versa.
Everyone who is not patient or not generous is either calm or not happy.
Everyone who is not tall or not happy is both not calm and old.
If someone is both tall and not strong then john is both wise and not humble and vice versa.
If someone is brave then paul is both quiet and rich.
Everyone who is either happy or rich is not calm or not creative and vice versa.
If someone is kind then fred is rich and vice versa.
If someone is creative or brave then someone is both wise and kind and vice versa.
If alice is not generous or not tall then paul is not quiet and vice versa.
Everyone who is both calm and not curious is kind or patient and vice versa.
Everyone who is either not funny or not generous is either not curious or tall.
Everyone who is humble is not tall.
If paul is humble or not brave then alice is generous.
Everyone who is calm is both not creative and not strong.
If someone is not quiet or generous then alice is old.
Someone is either not tall or creative.
Mary is not old or not rich.
Someone is both not calm and tall.
Lucy is kind or humble.
Someone is not brave or not old.
Someone is humble or brave.
Someone is both curious and generous. | John is wise. | entailment | ((?[X]:(~funny(X)))<=>(?[X]:((~funny(X)<~>patient(X)))))&
(![X]:((~patient(X)|~generous(X))=>(calm(X)<~>~happy(X))))&
(![X]:((~tall(X)|~happy(X))=>(~calm(X)&old(X))))&
((?[X]:((tall(X)&~strong(X))))<=>((wise(john)&~humble(john))))&
((?[X]:(brave(X)))=>((quiet(paul)&rich(paul))))&
(![X]:((happy(X)<~>rich(X))<=>(~calm(X)|~creative(X))))&
((?[X]:(kind(X)))<=>(rich(fred)))&
((?[X]:((creative(X)|brave(X))))<=>(?[X]:((wise(X)&kind(X)))))&
(((~generous(alice)|~tall(alice)))<=>(~quiet(paul)))&
(![X]:((calm(X)&~curious(X))<=>(kind(X)|patient(X))))&
(![X]:((~funny(X)<~>~generous(X))=>(~curious(X)<~>tall(X))))&
(![X]:(humble(X)=>~tall(X)))&
(((humble(paul)|~brave(paul)))=>(generous(alice)))&
(![X]:(calm(X)=>(~creative(X)&~strong(X))))&
((?[X]:((~quiet(X)|generous(X))))=>(old(alice)))&
(?[X]:((~tall(X)<~>creative(X))))&
((~old(mary)|~rich(mary)))&
(?[X]:((~calm(X)&tall(X))))&
((kind(lucy)|humble(lucy)))&
(?[X]:((~brave(X)|~old(X))))&
(?[X]:((humble(X)|brave(X))))&
(?[X]:((curious(X)&generous(X)))) | wise(john) | [
"p1",
"p2",
"p3",
"p5",
"p6",
"p9",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 1859358287638561407598458
% SZS output start Proof for 1859358287638561407598458
2. ! [X0] : ((~generous(X0) | ~patient(X0)) => (calm(X0) <~> ~happy(X0))) [input p1]
3. ! [X0] : ((~happy(X0) | ~tall(X0)) => (old(X0) & ~calm(X0))) [input p2]
4. ? [X0] : (~strong(X0) & tall(X0)) <=> (~humble(john) & wise(john)) [input p3]
6. ! [X0] : ((happy(X0) <~> rich(X0)) <=> (~creative(X0) | ~calm(X0))) [input p5]
7. ? [X0] : kind(X0) <=> rich(fred) [input p6]
10. ! [X0] : ((~curious(X0) & calm(X0)) <=> (patient(X0) | kind(X0))) [input p9]
14. ! [X0] : (calm(X0) => (~strong(X0) & ~creative(X0))) [input p13]
23. ~wise(john) [input hypothesis]
26. ! [X0] : ((calm(X0) <~> ~happy(X0)) | (generous(X0) & patient(X0))) [ennf transformation 2]
27. ! [X0] : ((old(X0) & ~calm(X0)) | (happy(X0) & tall(X0))) [ennf transformation 3]
32. ! [X0] : ((~strong(X0) & ~creative(X0)) | ~calm(X0)) [ennf transformation 14]
39. ! [X0] : (((happy(X0) | ~calm(X0)) & (~happy(X0) | calm(X0))) | (generous(X0) & patient(X0))) [nnf transformation 26]
40. (? [X0] : (~strong(X0) & tall(X0)) | (humble(john) | ~wise(john))) & ((~humble(john) & wise(john)) | ! [X0] : (strong(X0) | ~tall(X0))) [nnf transformation 4]
41. (? [X0] : (~strong(X0) & tall(X0)) | humble(john) | ~wise(john)) & ((~humble(john) & wise(john)) | ! [X0] : (strong(X0) | ~tall(X0))) [flattening 40]
42. (? [X0] : (~strong(X0) & tall(X0)) | humble(john) | ~wise(john)) & ((~humble(john) & wise(john)) | ! [X1] : (strong(X1) | ~tall(X1))) [rectify 41]
43. ? [X0] : (~strong(X0) & tall(X0)) => (~strong(sK2) & tall(sK2)) [choice axiom]
44. ((~strong(sK2) & tall(sK2)) | humble(john) | ~wise(john)) & ((~humble(john) & wise(john)) | ! [X1] : (strong(X1) | ~tall(X1))) [skolemisation 42,43]
45. ! [X0] : ((((~rich(X0) | ~happy(X0)) & (rich(X0) | happy(X0))) | (creative(X0) & calm(X0))) & ((~creative(X0) | ~calm(X0)) | ((happy(X0) | ~rich(X0)) & (rich(X0) | ~happy(X0))))) [nnf transformation 6]
46. ! [X0] : ((((~rich(X0) | ~happy(X0)) & (rich(X0) | happy(X0))) | (creative(X0) & calm(X0))) & (~creative(X0) | ~calm(X0) | ((happy(X0) | ~rich(X0)) & (rich(X0) | ~happy(X0))))) [flattening 45]
47. (? [X0] : kind(X0) | ~rich(fred)) & (rich(fred) | ! [X0] : ~kind(X0)) [nnf transformation 7]
48. (? [X0] : kind(X0) | ~rich(fred)) & (rich(fred) | ! [X1] : ~kind(X1)) [rectify 47]
49. ? [X0] : kind(X0) => kind(sK3) [choice axiom]
50. (kind(sK3) | ~rich(fred)) & (rich(fred) | ! [X1] : ~kind(X1)) [skolemisation 48,49]
58. ! [X0] : (((~curious(X0) & calm(X0)) | (~patient(X0) & ~kind(X0))) & ((patient(X0) | kind(X0)) | (curious(X0) | ~calm(X0)))) [nnf transformation 10]
59. ! [X0] : (((~curious(X0) & calm(X0)) | (~patient(X0) & ~kind(X0))) & (patient(X0) | kind(X0) | curious(X0) | ~calm(X0))) [flattening 58]
76. ~happy(X0) | calm(X0) | patient(X0) [cnf transformation 39]
80. ~calm(X0) | tall(X0) [cnf transformation 27]
81. ~calm(X0) | happy(X0) [cnf transformation 27]
84. wise(john) | strong(X1) | ~tall(X1) [cnf transformation 44]
92. rich(X0) | happy(X0) | calm(X0) [cnf transformation 46]
97. kind(sK3) | ~rich(fred) [cnf transformation 50]
107. ~kind(X0) | calm(X0) [cnf transformation 59]
108. ~patient(X0) | calm(X0) [cnf transformation 59]
119. ~strong(X0) | ~calm(X0) [cnf transformation 32]
132. ~wise(john) [cnf transformation 23]
159. 7 <=> wise(john) [avatar definition]
177. 11 <=> ! [X1] : (strong(X1) | ~tall(X1)) [avatar definition]
178. ~tall(X1) | strong(X1) <- (11) [avatar component clause 177]
180. 11 | 7 [avatar split clause 84,159,177]
194. rich(X0) | happy(X0) [subsumption resolution 92,81]
197. 15 <=> rich(fred) [avatar definition]
199. ~rich(fred) <- (~15) [avatar component clause 197]
201. 16 <=> kind(sK3) [avatar definition]
203. kind(sK3) <- (16) [avatar component clause 201]
204. ~15 | 16 [avatar split clause 97,201,197]
315. ~7 [avatar split clause 132,159]
316. calm(sK3) <- (16) [resolution 107,203]
319. tall(sK3) <- (16) [resolution 316,80]
335. strong(sK3) <- (11, 16) [resolution 319,178]
353. 41 <=> calm(fred) [avatar definition]
355. calm(fred) <- (41) [avatar component clause 353]
357. 42 <=> happy(fred) [avatar definition]
358. happy(fred) <- (42) [avatar component clause 357]
363. ~calm(sK3) <- (11, 16) [resolution 335,119]
364. $false <- (11, 16) [subsumption resolution 363,316]
365. ~11 | ~16 [avatar contradiction clause 364]
366. happy(fred) <- (~15) [resolution 199,194]
369. 42 | 15 [avatar split clause 366,197,357]
374. calm(fred) | patient(fred) <- (42) [resolution 358,76]
380. calm(fred) <- (42) [subsumption resolution 374,108]
381. 41 | ~42 [avatar split clause 380,357,353]
387. tall(fred) <- (41) [resolution 355,80]
473. strong(fred) <- (11, 41) [resolution 387,178]
504. ~calm(fred) <- (11, 41) [resolution 473,119]
505. $false <- (11, 41) [subsumption resolution 504,355]
506. ~11 | ~41 [avatar contradiction clause 505]
507. $false [avatar sat refutation 180,204,315,365,369,381,506]
% SZS output end Proof for 1859358287638561407598458
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 is both happy and patient.
Everyone who is both old and happy is tall.
Everyone who is either not kind or quiet is either not kind or generous.
Everyone who is either not wise or not quiet is kind and vice versa.
Everyone who is kind or not generous is both not strong and wise.
Everyone who is creative or quiet is either strong or not generous.
Everyone who is not kind or not happy is both not curious and not happy and vice versa.
If mary is happy or patient then someone is either brave or not brave and vice versa.
Everyone who is both patient and quiet is both not calm and happy and vice versa.
If someone is not old then someone is generous or kind and vice versa.
If paul is strong or not patient then fred is both not creative and not strong.
If alice is not brave or wise then someone is not tall and vice versa.
Everyone who is not quiet or not rich is not brave.
Lucy is either not wise or not patient.
Mary is humble or not tall.
Someone is either not brave or brave.
Someone is humble.
Lucy is not humble.
Alice is either rich or quiet.
John is not tall or not kind.
Lucy is both not curious and not creative. | Mary is not calm. | contradiction | (![X]:(~strong(X)=>(happy(X)&patient(X))))&
(![X]:((old(X)&happy(X))=>tall(X)))&
(![X]:((~kind(X)<~>quiet(X))=>(~kind(X)<~>generous(X))))&
(![X]:((~wise(X)<~>~quiet(X))<=>kind(X)))&
(![X]:((kind(X)|~generous(X))=>(~strong(X)&wise(X))))&
(![X]:((creative(X)|quiet(X))=>(strong(X)<~>~generous(X))))&
(![X]:((~kind(X)|~happy(X))<=>(~curious(X)&~happy(X))))&
(((happy(mary)|patient(mary)))<=>(?[X]:((brave(X)<~>~brave(X)))))&
(![X]:((patient(X)&quiet(X))<=>(~calm(X)&happy(X))))&
((?[X]:(~old(X)))<=>(?[X]:((generous(X)|kind(X)))))&
(((strong(paul)|~patient(paul)))=>((~creative(fred)&~strong(fred))))&
(((~brave(alice)|wise(alice)))<=>(?[X]:(~tall(X))))&
(![X]:((~quiet(X)|~rich(X))=>~brave(X)))&
((~wise(lucy)<~>~patient(lucy)))&
((humble(mary)|~tall(mary)))&
(?[X]:((~brave(X)<~>brave(X))))&
(?[X]:(humble(X)))&
(~humble(lucy))&
((rich(alice)<~>quiet(alice)))&
((~tall(john)|~kind(john)))&
((~curious(lucy)&~creative(lucy))) | ~calm(mary) | [
"p0",
"p2",
"p3",
"p4",
"p5",
"p6",
"p7",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 7375071962523841886171918
% SZS output start Proof for 7375071962523841886171918
1. ! [X0] : (~strong(X0) => (patient(X0) & happy(X0))) [input p0]
3. ! [X0] : ((~kind(X0) <~> quiet(X0)) => (~kind(X0) <~> generous(X0))) [input p2]
4. ! [X0] : ((~wise(X0) <~> ~quiet(X0)) <=> kind(X0)) [input p3]
5. ! [X0] : ((~generous(X0) | kind(X0)) => (wise(X0) & ~strong(X0))) [input p4]
6. ! [X0] : ((quiet(X0) | creative(X0)) => (strong(X0) <~> ~generous(X0))) [input p5]
7. ! [X0] : ((~happy(X0) | ~kind(X0)) <=> (~happy(X0) & ~curious(X0))) [input p6]
8. (patient(mary) | happy(mary)) <=> ? [X0] : (brave(X0) <~> ~brave(X0)) [input p7]
9. ! [X0] : ((quiet(X0) & patient(X0)) <=> (happy(X0) & ~calm(X0))) [input p8]
22. ~calm(mary) [input hypothesis]
26. ! [X0] : (quiet(X0) => (strong(X0) <~> ~generous(X0))) [pure predicate removal 6]
27. ! [X0] : ((patient(X0) & happy(X0)) | strong(X0)) [ennf transformation 1]
30. ! [X0] : ((~kind(X0) <~> generous(X0)) | (~kind(X0) <=> quiet(X0))) [ennf transformation 3]
31. ! [X0] : ((wise(X0) & ~strong(X0)) | (generous(X0) & ~kind(X0))) [ennf transformation 5]
32. ! [X0] : ((strong(X0) <~> ~generous(X0)) | ~quiet(X0)) [ennf transformation 26]
35. ! [X0] : (((~generous(X0) | kind(X0)) & (generous(X0) | ~kind(X0))) | ((~kind(X0) | ~quiet(X0)) & (quiet(X0) | kind(X0)))) [nnf transformation 30]
36. ! [X0] : ((((quiet(X0) | wise(X0)) & (~quiet(X0) | ~wise(X0))) | ~kind(X0)) & (kind(X0) | ((~wise(X0) | quiet(X0)) & (~quiet(X0) | wise(X0))))) [nnf transformation 4]
37. ! [X0] : (((generous(X0) | ~strong(X0)) & (~generous(X0) | strong(X0))) | ~quiet(X0)) [nnf transformation 32]
38. ! [X0] : (((~happy(X0) | ~kind(X0)) | (happy(X0) | curious(X0))) & ((~happy(X0) & ~curious(X0)) | (happy(X0) & kind(X0)))) [nnf transformation 7]
39. ! [X0] : ((~happy(X0) | ~kind(X0) | happy(X0) | curious(X0)) & ((~happy(X0) & ~curious(X0)) | (happy(X0) & kind(X0)))) [flattening 38]
40. ((patient(mary) | happy(mary)) | ! [X0] : ((brave(X0) | brave(X0)) & (~brave(X0) | ~brave(X0)))) & (? [X0] : ((brave(X0) | ~brave(X0)) & (~brave(X0) | brave(X0))) | (~patient(mary) & ~happy(mary))) [nnf transformation 8]
41. (patient(mary) | happy(mary) | ! [X0] : ((brave(X0) | brave(X0)) & (~brave(X0) | ~brave(X0)))) & (? [X0] : ((brave(X0) | ~brave(X0)) & (~brave(X0) | brave(X0))) | (~patient(mary) & ~happy(mary))) [flattening 40]
42. (patient(mary) | happy(mary) | ! [X0] : ((brave(X0) | brave(X0)) & (~brave(X0) | ~brave(X0)))) & (? [X1] : ((brave(X1) | ~brave(X1)) & (~brave(X1) | brave(X1))) | (~patient(mary) & ~happy(mary))) [rectify 41]
43. ? [X1] : ((brave(X1) | ~brave(X1)) & (~brave(X1) | brave(X1))) => ((brave(sK0) | ~brave(sK0)) & (~brave(sK0) | brave(sK0))) [choice axiom]
44. (patient(mary) | happy(mary) | ! [X0] : ((brave(X0) | brave(X0)) & (~brave(X0) | ~brave(X0)))) & (((brave(sK0) | ~brave(sK0)) & (~brave(sK0) | brave(sK0))) | (~patient(mary) & ~happy(mary))) [skolemisation 42,43]
45. ! [X0] : (((quiet(X0) & patient(X0)) | (~happy(X0) | calm(X0))) & ((happy(X0) & ~calm(X0)) | (~quiet(X0) | ~patient(X0)))) [nnf transformation 9]
46. ! [X0] : (((quiet(X0) & patient(X0)) | ~happy(X0) | calm(X0)) & ((happy(X0) & ~calm(X0)) | ~quiet(X0) | ~patient(X0))) [flattening 45]
64. happy(X0) | strong(X0) [cnf transformation 27]
68. generous(X0) | ~kind(X0) | ~kind(X0) | ~quiet(X0) [cnf transformation 35]
69. ~generous(X0) | kind(X0) | quiet(X0) | kind(X0) [cnf transformation 35]
72. ~wise(X0) | kind(X0) | quiet(X0) [cnf transformation 36]
75. ~kind(X0) | ~strong(X0) [cnf transformation 31]
78. wise(X0) | generous(X0) [cnf transformation 31]
79. ~generous(X0) | strong(X0) | ~quiet(X0) [cnf transformation 37]
83. ~happy(X0) | kind(X0) [cnf transformation 39]
90. patient(mary) | happy(mary) | ~brave(X0) | ~brave(X0) [cnf transformation 44]
91. patient(mary) | happy(mary) | brave(X0) | brave(X0) [cnf transformation 44]
93. ~quiet(X0) | happy(X0) | ~patient(X0) [cnf transformation 46]
95. ~happy(X0) | quiet(X0) | calm(X0) [cnf transformation 46]
117. ~calm(mary) [cnf transformation 22]
118. patient(mary) | happy(mary) | ~brave(X0) [duplicate literal removal 90]
119. patient(mary) | happy(mary) | brave(X0) [duplicate literal removal 91]
120. ~quiet(X0) | ~kind(X0) | generous(X0) [duplicate literal removal 68]
121. ~generous(X0) | kind(X0) | quiet(X0) [duplicate literal removal 69]
123. 1 <=> ! [X0] : brave(X0) [avatar definition]
124. brave(X0) <- (1) [avatar component clause 123]
126. 2 <=> happy(mary) [avatar definition]
127. ~happy(mary) <- (~2) [avatar component clause 126]
128. happy(mary) <- (2) [avatar component clause 126]
130. 3 <=> patient(mary) [avatar definition]
132. patient(mary) <- (3) [avatar component clause 130]
133. 1 | 2 | 3 [avatar split clause 119,130,126,123]
135. 4 <=> ! [X0] : ~brave(X0) [avatar definition]
136. ~brave(X0) <- (4) [avatar component clause 135]
137. 4 | 2 | 3 [avatar split clause 118,130,126,135]
249. kind(X1) | quiet(X1) | generous(X1) [resolution 72,78]
260. quiet(X1) | kind(X1) [subsumption resolution 249,121]
289. strong(mary) <- (~2) [resolution 127,64]
294. happy(X0) | ~patient(X0) | kind(X0) [resolution 93,260]
300. calm(X0) | quiet(X0) | strong(X0) [resolution 95,64]
317. ~patient(X0) | kind(X0) [subsumption resolution 294,83]
341. quiet(mary) | strong(mary) [resolution 300,117]
349. kind(mary) <- (3) [resolution 317,132]
352. ~strong(mary) <- (3) [resolution 349,75]
353. $false <- (~2, 3) [subsumption resolution 352,289]
354. 2 | ~3 [avatar contradiction clause 353]
355. $false <- (1, 4) [subsumption resolution 124,136]
356. ~1 | ~4 [avatar contradiction clause 355]
358. 33 <=> strong(mary) [avatar definition]
359. ~strong(mary) <- (~33) [avatar component clause 358]
362. 34 <=> quiet(mary) [avatar definition]
364. quiet(mary) <- (34) [avatar component clause 362]
365. 33 | 34 [avatar split clause 341,362,358]
372. kind(mary) <- (2) [resolution 128,83]
399. ~strong(mary) <- (2) [resolution 372,75]
400. ~33 | ~2 [avatar split clause 399,126,358]
401. ~kind(mary) | generous(mary) <- (34) [resolution 364,120]
404. generous(mary) <- (2, 34) [subsumption resolution 401,372]
409. strong(mary) | ~quiet(mary) <- (2, 34) [resolution 404,79]
410. ~quiet(mary) <- (2, ~33, 34) [subsumption resolution 409,359]
411. $false <- (2, ~33, 34) [subsumption resolution 410,364]
412. ~2 | 33 | ~34 [avatar contradiction clause 411]
413. $false [avatar sat refutation 133,137,354,356,365,400,412]
% SZS output end Proof for 7375071962523841886171918
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both kind and happy then susan is either not humble or happy.
If lucy is not funny then someone is humble.
If someone is either not curious or not strong then fred is strong or not wise.
If lucy is both patient and creative then someone is both not rich and strong.
Everyone who is either not curious or generous is happy.
Everyone who is not curious is tall or generous and vice versa.
If mary is not tall or rich then paul is not generous or happy and vice versa.
Everyone who is not curious is either patient or generous.
Everyone who is calm or not patient is both tall and brave and vice versa.
Everyone who is patient or brave is patient or not brave.
If someone is not old or not kind then lucy is both not humble and funny.
If fred is both not humble and happy then someone is not humble or not patient.
Everyone who is wise or not old is either not patient or tall.
If someone is brave or patient then someone is kind.
Everyone who is strong is both wise and not curious.
If susan is not curious then someone is humble.
Someone is calm.
Someone is curious or not happy.
Someone is either not tall or calm.
Fred is curious.
Someone is not curious or patient.
Someone is both tall and not rich.
Someone is both strong and funny.
Alice is not quiet. | Fred is generous. | contradiction | ((?[X]:((kind(X)&happy(X))))=>((~humble(susan)<~>happy(susan))))&
((~funny(lucy))=>(?[X]:(humble(X))))&
((?[X]:((~curious(X)<~>~strong(X))))=>((strong(fred)|~wise(fred))))&
(((patient(lucy)&creative(lucy)))=>(?[X]:((~rich(X)&strong(X)))))&
(![X]:((~curious(X)<~>generous(X))=>happy(X)))&
(![X]:(~curious(X)<=>(tall(X)|generous(X))))&
(((~tall(mary)|rich(mary)))<=>((~generous(paul)|happy(paul))))&
(![X]:(~curious(X)=>(patient(X)<~>generous(X))))&
(![X]:((calm(X)|~patient(X))<=>(tall(X)&brave(X))))&
(![X]:((patient(X)|brave(X))=>(patient(X)|~brave(X))))&
((?[X]:((~old(X)|~kind(X))))=>((~humble(lucy)&funny(lucy))))&
(((~humble(fred)&happy(fred)))=>(?[X]:((~humble(X)|~patient(X)))))&
(![X]:((wise(X)|~old(X))=>(~patient(X)<~>tall(X))))&
((?[X]:((brave(X)|patient(X))))=>(?[X]:(kind(X))))&
(![X]:(strong(X)=>(wise(X)&~curious(X))))&
((~curious(susan))=>(?[X]:(humble(X))))&
(?[X]:(calm(X)))&
(?[X]:((curious(X)|~happy(X))))&
(?[X]:((~tall(X)<~>calm(X))))&
(curious(fred))&
(?[X]:((~curious(X)|patient(X))))&
(?[X]:((tall(X)&~rich(X))))&
(?[X]:((strong(X)&funny(X))))&
(~quiet(alice)) | generous(fred) | [
"p5",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 5077720932806805171790005
% SZS output start Proof for 5077720932806805171790005
6. ! [X0] : (~curious(X0) <=> (generous(X0) | tall(X0))) [input p5]
20. curious(fred) [input p19]
25. generous(fred) [input hypothesis]
51. ! [X0] : ((~curious(X0) | (~generous(X0) & ~tall(X0))) & ((generous(X0) | tall(X0)) | curious(X0))) [nnf transformation 6]
52. ! [X0] : ((~curious(X0) | (~generous(X0) & ~tall(X0))) & (generous(X0) | tall(X0) | curious(X0))) [flattening 51]
87. ~generous(X0) | ~curious(X0) [cnf transformation 52]
114. curious(fred) [cnf transformation 20]
119. generous(fred) [cnf transformation 25]
224. ~curious(fred) [resolution 87,119]
225. $false [subsumption resolution 224,114]
% SZS output end Proof for 5077720932806805171790005
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not happy or not funny then paul is not quiet or not generous and vice versa. Everyone who is quiet is calm or not kind and vice versa. If someone is both kind and not curious then john is wise and vice versa. Everyone who is calm is tall or not brave. If fred is both tall and not happy then john is creative and vice versa. If john is humble then alice is both not funny and not wise and vice versa. Everyone who is tall or brave is both not quiet and not kind. If susan is generous or not wise then someone is both not wise and happy and vice versa. If someone is both strong and generous then paul is not happy. Everyone who is either not wise or not generous is not funny or quiet. Everyone who is not wise is not rich or not tall. If mary is both not old and not humble then lucy is curious. Everyone who is either not old or wise is not strong or humble and vice versa. Everyone who is not patient is both strong and not curious. If someone is not creative then lucy is both strong and not rich and vice versa. Everyone who is either strong or not creative is calm. Someone is either quiet or funny. Mary is either not funny or strong. Someone is wise. Someone is generous or not funny. Mary is not quiet. Alice is either wise or not calm. Mary is not happy. | Paul is not rich. | neutral | ((?[X]:((~happy(X)<~>~funny(X))))<=>((~quiet(paul)|~generous(paul))))&
(![X]:(quiet(X)<=>(calm(X)|~kind(X))))&
((?[X]:((kind(X)&~curious(X))))<=>(wise(john)))&
(![X]:(calm(X)=>(tall(X)|~brave(X))))&
(((tall(fred)&~happy(fred)))<=>(creative(john)))&
((humble(john))<=>((~funny(alice)&~wise(alice))))&
(![X]:((tall(X)|brave(X))=>(~quiet(X)&~kind(X))))&
(((generous(susan)|~wise(susan)))<=>(?[X]:((~wise(X)&happy(X)))))&
((?[X]:((strong(X)&generous(X))))=>(~happy(paul)))&
(![X]:((~wise(X)<~>~generous(X))=>(~funny(X)|quiet(X))))&
(![X]:(~wise(X)=>(~rich(X)|~tall(X))))&
(((~old(mary)&~humble(mary)))=>(curious(lucy)))&
(![X]:((~old(X)<~>wise(X))<=>(~strong(X)|humble(X))))&
(![X]:(~patient(X)=>(strong(X)&~curious(X))))&
((?[X]:(~creative(X)))<=>((strong(lucy)&~rich(lucy))))&
(![X]:((strong(X)<~>~creative(X))=>calm(X)))&
(?[X]:((quiet(X)<~>funny(X))))&
((~funny(mary)<~>strong(mary)))&
(?[X]:(wise(X)))&
(?[X]:((generous(X)|~funny(X))))&
(~quiet(mary))&
((wise(alice)<~>~calm(alice)))&
(~happy(mary)) | ~rich(paul) | [] | null | 0 |
Everyone who is either calm or rich is both old and not calm. Everyone who is not calm is funny. Everyone who is both creative and not rich is either not brave or curious. Everyone who is either creative or funny is both patient and old. Everyone who is either funny or not kind is both generous and not kind. If paul is both generous and not humble then lucy is both not old and wise and vice versa. If fred is both not tall and not happy then lucy is both rich and not happy and vice versa. Everyone who is both not funny and not tall is either not quiet or not curious. If someone is both not tall and humble then someone is not wise or kind and vice versa. If john is rich or not tall then mary is either patient or not strong. If someone is both curious and rich then someone is wise and vice versa. If susan is either old or curious then mary is not wise or not rich and vice versa. If lucy is quiet then someone is not patient. Everyone who is not brave is either not strong or not curious. Everyone who is both wise and brave is humble. If someone is both strong and not brave then alice is strong and vice versa. Susan is both brave and quiet. Mary is curious or quiet. Lucy is brave. Someone is not humble or kind. Someone is not kind. Someone is either patient or not funny. John is calm or not brave. Fred is both curious and not strong. | Paul is patient. | neutral | (![X]:((calm(X)<~>rich(X))=>(old(X)&~calm(X))))&
(![X]:(~calm(X)=>funny(X)))&
(![X]:((creative(X)&~rich(X))=>(~brave(X)<~>curious(X))))&
(![X]:((creative(X)<~>funny(X))=>(patient(X)&old(X))))&
(![X]:((funny(X)<~>~kind(X))=>(generous(X)&~kind(X))))&
(((generous(paul)&~humble(paul)))<=>((~old(lucy)&wise(lucy))))&
(((~tall(fred)&~happy(fred)))<=>((rich(lucy)&~happy(lucy))))&
(![X]:((~funny(X)&~tall(X))=>(~quiet(X)<~>~curious(X))))&
((?[X]:((~tall(X)&humble(X))))<=>(?[X]:((~wise(X)|kind(X)))))&
(((rich(john)|~tall(john)))=>((patient(mary)<~>~strong(mary))))&
((?[X]:((curious(X)&rich(X))))<=>(?[X]:(wise(X))))&
(((old(susan)<~>curious(susan)))<=>((~wise(mary)|~rich(mary))))&
((quiet(lucy))=>(?[X]:(~patient(X))))&
(![X]:(~brave(X)=>(~strong(X)<~>~curious(X))))&
(![X]:((wise(X)&brave(X))=>humble(X)))&
((?[X]:((strong(X)&~brave(X))))<=>(strong(alice)))&
((brave(susan)&quiet(susan)))&
((curious(mary)|quiet(mary)))&
(brave(lucy))&
(?[X]:((~humble(X)|kind(X))))&
(?[X]:(~kind(X)))&
(?[X]:((patient(X)<~>~funny(X))))&
((calm(john)|~brave(john)))&
((curious(fred)&~strong(fred))) | patient(paul) | [] | null | 0 |
Everyone who is either quiet or kind is either not calm or happy. Everyone who is not kind or kind is either calm or not brave and vice versa. Everyone who is either old or creative is not kind or funny and vice versa. Everyone who is both not generous and happy is either wise or not happy. Everyone who is not funny or not quiet is both not patient and not generous. If someone is both tall and funny then someone is both not funny and not quiet. If someone is not creative or creative then alice is either not kind or quiet and vice versa. If susan is either quiet or not happy then alice is both patient and generous. If john is either funny or happy then paul is both not old and not patient and vice versa. If paul is not brave or rich then someone is not quiet and vice versa. Everyone who is brave or not generous is old or not brave and vice versa. Everyone who is patient is kind and vice versa. If someone is either rich or happy then fred is both not calm and not kind and vice versa. Everyone who is both not wise and not generous is either funny or not brave. If someone is either not calm or funny then john is both not creative and not rich and vice versa. If someone is generous or rich then susan is either happy or wise. Susan is both not strong and generous. Lucy is either generous or not brave. Alice is both not strong and not wise. Mary is not curious. Fred is not happy or calm. Lucy is either not calm or calm. Someone is quiet or not quiet. | Fred is not calm. | neutral | (![X]:((quiet(X)<~>kind(X))=>(~calm(X)<~>happy(X))))&
(![X]:((~kind(X)|kind(X))<=>(calm(X)<~>~brave(X))))&
(![X]:((old(X)<~>creative(X))<=>(~kind(X)|funny(X))))&
(![X]:((~generous(X)&happy(X))=>(wise(X)<~>~happy(X))))&
(![X]:((~funny(X)|~quiet(X))=>(~patient(X)&~generous(X))))&
((?[X]:((tall(X)&funny(X))))=>(?[X]:((~funny(X)&~quiet(X)))))&
((?[X]:((~creative(X)|creative(X))))<=>((~kind(alice)<~>quiet(alice))))&
(((quiet(susan)<~>~happy(susan)))=>((patient(alice)&generous(alice))))&
(((funny(john)<~>happy(john)))<=>((~old(paul)&~patient(paul))))&
(((~brave(paul)|rich(paul)))<=>(?[X]:(~quiet(X))))&
(![X]:((brave(X)|~generous(X))<=>(old(X)|~brave(X))))&
(![X]:(patient(X)<=>kind(X)))&
((?[X]:((rich(X)<~>happy(X))))<=>((~calm(fred)&~kind(fred))))&
(![X]:((~wise(X)&~generous(X))=>(funny(X)<~>~brave(X))))&
((?[X]:((~calm(X)<~>funny(X))))<=>((~creative(john)&~rich(john))))&
((?[X]:((generous(X)|rich(X))))=>((happy(susan)<~>wise(susan))))&
((~strong(susan)&generous(susan)))&
((generous(lucy)<~>~brave(lucy)))&
((~strong(alice)&~wise(alice)))&
(~curious(mary))&
((~happy(fred)|calm(fred)))&
((~calm(lucy)<~>calm(lucy)))&
(?[X]:((quiet(X)|~quiet(X)))) | ~calm(fred) | [] | null | 0 |
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