premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
values | proof_inputs
sequencelengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
|
|---|---|---|---|---|---|---|---|
Everyone who is old is both not generous and not calm.
Everyone who is not brave or not patient is not creative and vice versa.
Everyone who is generous is curious or patient and vice versa.
Everyone who is not old is both not curious and not rich.
Everyone who is not tall or tall is either not tall or generous.
Everyone who is both strong and not wise is both not creative and brave and vice versa.
If someone is humble then fred is happy or not kind.
If john is curious then someone is patient or not calm and vice versa.
If mary is curious then someone is both funny and generous.
Everyone who is old is either wise or not patient and vice versa.
If fred is strong or not calm then paul is not humble and vice versa.
If john is either not kind or not generous then alice is either not quiet or creative.
If someone is funny then someone is not quiet and vice versa.
Everyone who is either quiet or not creative is not rich and vice versa.
Everyone who is not tall is funny and vice versa.
Everyone who is not humble or humble is both not patient and not rich.
John is either not rich or not strong.
Paul is calm.
Someone is both not old and humble.
Someone is curious or not generous.
Fred is either not generous or rich. | John is quiet. | contradiction | (![X]:(old(X)=>(~generous(X)&~calm(X))))&
(![X]:((~brave(X)|~patient(X))<=>~creative(X)))&
(![X]:(generous(X)<=>(curious(X)|patient(X))))&
(![X]:(~old(X)=>(~curious(X)&~rich(X))))&
(![X]:((~tall(X)|tall(X))=>(~tall(X)<~>generous(X))))&
(![X]:((strong(X)&~wise(X))<=>(~creative(X)&brave(X))))&
((?[X]:(humble(X)))=>((happy(fred)|~kind(fred))))&
((curious(john))<=>(?[X]:((patient(X)|~calm(X)))))&
((curious(mary))=>(?[X]:((funny(X)&generous(X)))))&
(![X]:(old(X)<=>(wise(X)<~>~patient(X))))&
(((strong(fred)|~calm(fred)))<=>(~humble(paul)))&
(((~kind(john)<~>~generous(john)))=>((~quiet(alice)<~>creative(alice))))&
((?[X]:(funny(X)))<=>(?[X]:(~quiet(X))))&
(![X]:((quiet(X)<~>~creative(X))<=>~rich(X)))&
(![X]:(~tall(X)<=>funny(X)))&
(![X]:((~humble(X)|humble(X))=>(~patient(X)&~rich(X))))&
((~rich(john)<~>~strong(john)))&
(calm(paul))&
(?[X]:((~old(X)&humble(X))))&
(?[X]:((curious(X)|~generous(X))))&
((~generous(fred)<~>rich(fred))) | quiet(john) | [
"p1",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 706325680263252620769466
% SZS output start Proof for 706325680263252620769466
2. ! [X0] : ((~patient(X0) | ~brave(X0)) <=> ~creative(X0)) [input p1]
14. ! [X0] : ((quiet(X0) <~> ~creative(X0)) <=> ~rich(X0)) [input p13]
16. ! [X0] : ((humble(X0) | ~humble(X0)) => (~rich(X0) & ~patient(X0))) [input p15]
22. quiet(john) [input hypothesis]
30. ! [X0] : ((~rich(X0) & ~patient(X0)) | (~humble(X0) & humble(X0))) [ennf transformation 16]
31. ! [X0] : (((~patient(X0) | ~brave(X0)) | creative(X0)) & (~creative(X0) | (patient(X0) & brave(X0)))) [nnf transformation 2]
32. ! [X0] : ((~patient(X0) | ~brave(X0) | creative(X0)) & (~creative(X0) | (patient(X0) & brave(X0)))) [flattening 31]
53. ! [X0] : ((((creative(X0) | ~quiet(X0)) & (~creative(X0) | quiet(X0))) | rich(X0)) & (~rich(X0) | ((quiet(X0) | creative(X0)) & (~creative(X0) | ~quiet(X0))))) [nnf transformation 14]
64. ~creative(X0) | patient(X0) [cnf transformation 32]
100. ~quiet(X0) | creative(X0) | rich(X0) [cnf transformation 53]
103. ~patient(X0) | humble(X0) [cnf transformation 30]
104. ~humble(X0) | ~patient(X0) [cnf transformation 30]
105. ~rich(X0) | humble(X0) [cnf transformation 30]
106. ~humble(X0) | ~rich(X0) [cnf transformation 30]
115. quiet(john) [cnf transformation 22]
127. 3 <=> ! [X0] : ~patient(X0) [avatar definition]
128. ~patient(X0) <- (3) [avatar component clause 127]
204. ~rich(X0) [subsumption resolution 105,106]
205. ~patient(X0) [subsumption resolution 103,104]
206. 3 [avatar split clause 205,127]
248. 22 <=> creative(john) [avatar definition]
249. creative(john) <- (22) [avatar component clause 248]
275. creative(john) | rich(john) [resolution 100,115]
279. creative(john) [subsumption resolution 275,204]
280. 22 [avatar split clause 279,248]
282. patient(john) <- (22) [resolution 249,64]
284. $false <- (3, 22) [subsumption resolution 282,128]
285. ~3 | ~22 [avatar contradiction clause 284]
288. $false [avatar sat refutation 206,280,285]
% SZS output end Proof for 706325680263252620769466
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either humble or brave then someone is not patient and vice versa. If someone is not generous then someone is either not happy or not humble and vice versa. If lucy is rich then john is both calm and not wise. If someone is not humble or not happy then alice is creative. Everyone who is either tall or not humble is not happy or not tall. Everyone who is both not curious and not happy is happy or brave and vice versa. If someone is not generous then paul is both strong and quiet. If someone is both curious and happy then lucy is not quiet. Everyone who is both curious and tall is not quiet. Everyone who is rich or calm is not happy and vice versa. If mary is not rich or calm then lucy is not quiet. If someone is not humble or tall then someone is old or creative and vice versa. If someone is both wise and not wise then someone is wise or patient and vice versa. Everyone who is happy or kind is humble or quiet. If alice is not calm or funny then john is quiet or old. If mary is not brave then lucy is either curious or rich and vice versa. Someone is both not tall and generous. Susan is both humble and tall. John is curious. Mary is both kind and not tall. Someone is humble or not tall. | Alice is not happy. | entailment | ((?[X]:((humble(X)<~>brave(X))))<=>(?[X]:(~patient(X))))&
((?[X]:(~generous(X)))<=>(?[X]:((~happy(X)<~>~humble(X)))))&
((rich(lucy))=>((calm(john)&~wise(john))))&
((?[X]:((~humble(X)|~happy(X))))=>(creative(alice)))&
(![X]:((tall(X)<~>~humble(X))=>(~happy(X)|~tall(X))))&
(![X]:((~curious(X)&~happy(X))<=>(happy(X)|brave(X))))&
((?[X]:(~generous(X)))=>((strong(paul)&quiet(paul))))&
((?[X]:((curious(X)&happy(X))))=>(~quiet(lucy)))&
(![X]:((curious(X)&tall(X))=>~quiet(X)))&
(![X]:((rich(X)|calm(X))<=>~happy(X)))&
(((~rich(mary)|calm(mary)))=>(~quiet(lucy)))&
((?[X]:((~humble(X)|tall(X))))<=>(?[X]:((old(X)|creative(X)))))&
((?[X]:((wise(X)&~wise(X))))<=>(?[X]:((wise(X)|patient(X)))))&
(![X]:((happy(X)|kind(X))=>(humble(X)|quiet(X))))&
(((~calm(alice)|funny(alice)))=>((quiet(john)|old(john))))&
((~brave(mary))<=>((curious(lucy)<~>rich(lucy))))&
(?[X]:((~tall(X)&generous(X))))&
((humble(susan)&tall(susan)))&
(curious(john))&
((kind(mary)&~tall(mary)))&
(?[X]:((humble(X)|~tall(X)))) | ~happy(alice) | [
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 144949554501224663569552
% SZS output start Proof for 144949554501224663569552
6. ! [X0] : ((~happy(X0) & ~curious(X0)) <=> (brave(X0) | happy(X0))) [input p5]
22. happy(alice) [input hypothesis]
53. ! [X0] : (((~happy(X0) & ~curious(X0)) | (~brave(X0) & ~happy(X0))) & ((brave(X0) | happy(X0)) | (happy(X0) | curious(X0)))) [nnf transformation 6]
54. ! [X0] : (((~happy(X0) & ~curious(X0)) | (~brave(X0) & ~happy(X0))) & (brave(X0) | happy(X0) | happy(X0) | curious(X0))) [flattening 53]
89. ~happy(X0) | ~happy(X0) [cnf transformation 54]
123. happy(alice) [cnf transformation 22]
125. ~happy(X0) [duplicate literal removal 89]
301. $false [subsumption resolution 123,125]
% SZS output end Proof for 144949554501224663569552
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient or old then john is not funny or happy and vice versa.
Everyone who is both old and not kind is either rich or curious.
Everyone who is tall is not patient or not rich.
If someone is generous then someone is patient.
If someone is tall or not patient then lucy is tall or old.
Everyone who is either kind or wise is not strong or tall and vice versa.
Everyone who is patient or generous is not old or not tall.
If someone is either not tall or not wise then someone is both generous and not wise.
Everyone who is either not strong or not patient is either humble or not old.
Everyone who is both kind and rich is old or not brave and vice versa.
Everyone who is not patient or patient is both not patient and not calm and vice versa.
Everyone who is wise or not old is either not calm or not curious.
If susan is quiet then paul is either not patient or not kind and vice versa.
Everyone who is either strong or humble is calm.
Everyone who is calm is both patient and not wise.
Everyone who is both curious and not tall is tall.
Fred is not kind.
Someone is rich.
Susan is either not brave or happy.
John is either not brave or not patient.
Susan is either not brave or curious.
Someone is either kind or not strong. | Lucy is humble. | contradiction | ((?[X]:((patient(X)|old(X))))<=>((~funny(john)|happy(john))))&
(![X]:((old(X)&~kind(X))=>(rich(X)<~>curious(X))))&
(![X]:(tall(X)=>(~patient(X)|~rich(X))))&
((?[X]:(generous(X)))=>(?[X]:(patient(X))))&
((?[X]:((tall(X)|~patient(X))))=>((tall(lucy)|old(lucy))))&
(![X]:((kind(X)<~>wise(X))<=>(~strong(X)|tall(X))))&
(![X]:((patient(X)|generous(X))=>(~old(X)|~tall(X))))&
((?[X]:((~tall(X)<~>~wise(X))))=>(?[X]:((generous(X)&~wise(X)))))&
(![X]:((~strong(X)<~>~patient(X))=>(humble(X)<~>~old(X))))&
(![X]:((kind(X)&rich(X))<=>(old(X)|~brave(X))))&
(![X]:((~patient(X)|patient(X))<=>(~patient(X)&~calm(X))))&
(![X]:((wise(X)|~old(X))=>(~calm(X)<~>~curious(X))))&
((quiet(susan))<=>((~patient(paul)<~>~kind(paul))))&
(![X]:((strong(X)<~>humble(X))=>calm(X)))&
(![X]:(calm(X)=>(patient(X)&~wise(X))))&
(![X]:((curious(X)&~tall(X))=>tall(X)))&
(~kind(fred))&
(?[X]:(rich(X)))&
((~brave(susan)<~>happy(susan)))&
((~brave(john)<~>~patient(john)))&
((~brave(susan)<~>curious(susan)))&
(?[X]:((kind(X)<~>~strong(X)))) | humble(lucy) | [
"p3",
"p5",
"p7",
"p8",
"p9",
"p10",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 9025549023579717596885614
% SZS output start Proof for 9025549023579717596885614
4. ? [X0] : generous(X0) => ? [X0] : patient(X0) [input p3]
6. ! [X0] : ((kind(X0) <~> wise(X0)) <=> (tall(X0) | ~strong(X0))) [input p5]
8. ? [X0] : (~tall(X0) <~> ~wise(X0)) => ? [X0] : (~wise(X0) & generous(X0)) [input p7]
9. ! [X0] : ((~strong(X0) <~> ~patient(X0)) => (humble(X0) <~> ~old(X0))) [input p8]
10. ! [X0] : ((rich(X0) & kind(X0)) <=> (~brave(X0) | old(X0))) [input p9]
11. ! [X0] : ((patient(X0) | ~patient(X0)) <=> (~calm(X0) & ~patient(X0))) [input p10]
14. ! [X0] : ((strong(X0) <~> humble(X0)) => calm(X0)) [input p13]
23. humble(lucy) [input hypothesis]
24. ? [X0] : generous(X0) => ? [X1] : patient(X1) [rectify 4]
25. ? [X0] : (~tall(X0) <~> ~wise(X0)) => ? [X1] : (~wise(X1) & generous(X1)) [rectify 8]
30. ? [X1] : patient(X1) | ! [X0] : ~generous(X0) [ennf transformation 24]
35. ? [X1] : (~wise(X1) & generous(X1)) | ! [X0] : (~tall(X0) <=> ~wise(X0)) [ennf transformation 25]
36. ! [X0] : ((humble(X0) <~> ~old(X0)) | (~strong(X0) <=> ~patient(X0))) [ennf transformation 9]
38. ! [X0] : (calm(X0) | (strong(X0) <=> humble(X0))) [ennf transformation 14]
48. ? [X0] : patient(X0) | ! [X1] : ~generous(X1) [rectify 30]
49. ? [X0] : patient(X0) => patient(sK1) [choice axiom]
50. patient(sK1) | ! [X1] : ~generous(X1) [skolemisation 48,49]
51. ! [X0] : ((((~wise(X0) | ~kind(X0)) & (wise(X0) | kind(X0))) | (~tall(X0) & strong(X0))) & ((tall(X0) | ~strong(X0)) | ((kind(X0) | ~wise(X0)) & (wise(X0) | ~kind(X0))))) [nnf transformation 6]
52. ! [X0] : ((((~wise(X0) | ~kind(X0)) & (wise(X0) | kind(X0))) | (~tall(X0) & strong(X0))) & (tall(X0) | ~strong(X0) | ((kind(X0) | ~wise(X0)) & (wise(X0) | ~kind(X0))))) [flattening 51]
53. ? [X1] : (~wise(X1) & generous(X1)) | ! [X0] : ((~tall(X0) | wise(X0)) & (~wise(X0) | tall(X0))) [nnf transformation 35]
54. ? [X0] : (~wise(X0) & generous(X0)) | ! [X1] : ((~tall(X1) | wise(X1)) & (~wise(X1) | tall(X1))) [rectify 53]
55. ? [X0] : (~wise(X0) & generous(X0)) => (~wise(sK2) & generous(sK2)) [choice axiom]
56. (~wise(sK2) & generous(sK2)) | ! [X1] : ((~tall(X1) | wise(X1)) & (~wise(X1) | tall(X1))) [skolemisation 54,55]
57. ! [X0] : (((old(X0) | ~humble(X0)) & (~old(X0) | humble(X0))) | ((~strong(X0) | patient(X0)) & (~patient(X0) | strong(X0)))) [nnf transformation 36]
58. ! [X0] : (((rich(X0) & kind(X0)) | (brave(X0) & ~old(X0))) & ((~brave(X0) | old(X0)) | (~rich(X0) | ~kind(X0)))) [nnf transformation 10]
59. ! [X0] : (((rich(X0) & kind(X0)) | (brave(X0) & ~old(X0))) & (~brave(X0) | old(X0) | ~rich(X0) | ~kind(X0))) [flattening 58]
60. ! [X0] : (((patient(X0) | ~patient(X0)) | (calm(X0) | patient(X0))) & ((~calm(X0) & ~patient(X0)) | (~patient(X0) & patient(X0)))) [nnf transformation 11]
61. ! [X0] : ((patient(X0) | ~patient(X0) | calm(X0) | patient(X0)) & ((~calm(X0) & ~patient(X0)) | (~patient(X0) & patient(X0)))) [flattening 60]
64. ! [X0] : (calm(X0) | ((strong(X0) | ~humble(X0)) & (humble(X0) | ~strong(X0)))) [nnf transformation 38]
80. patient(sK1) | ~generous(X1) [cnf transformation 50]
83. ~strong(X0) | tall(X0) | wise(X0) | ~kind(X0) [cnf transformation 52]
88. ~wise(X0) | ~kind(X0) | ~tall(X0) [cnf transformation 52]
91. generous(sK2) | ~wise(X1) | tall(X1) [cnf transformation 56]
92. generous(sK2) | ~tall(X1) | wise(X1) [cnf transformation 56]
98. ~humble(X0) | old(X0) | ~strong(X0) | patient(X0) [cnf transformation 57]
100. ~old(X0) | kind(X0) [cnf transformation 59]
105. ~patient(X0) | ~patient(X0) [cnf transformation 61]
106. ~calm(X0) | patient(X0) [cnf transformation 61]
107. ~calm(X0) | ~patient(X0) [cnf transformation 61]
118. calm(X0) | strong(X0) | ~humble(X0) [cnf transformation 64]
132. humble(lucy) [cnf transformation 23]
134. ~patient(X0) [duplicate literal removal 105]
159. 6 <=> ! [X1] : ~patient(X1) [avatar definition]
160. ~patient(X1) <- (6) [avatar component clause 159]
163. 7 <=> ! [X1] : ~generous(X1) [avatar definition]
164. ~generous(X1) <- (7) [avatar component clause 163]
166. 8 <=> patient(sK1) [avatar definition]
168. patient(sK1) <- (8) [avatar component clause 166]
169. 7 | 8 [avatar split clause 80,166,163]
174. 10 <=> tall(lucy) [avatar definition]
175. ~tall(lucy) <- (~10) [avatar component clause 174]
176. tall(lucy) <- (10) [avatar component clause 174]
178. 11 <=> old(lucy) [avatar definition]
180. old(lucy) <- (11) [avatar component clause 178]
187. 13 <=> ! [X1] : (~tall(X1) | wise(X1)) [avatar definition]
188. ~tall(X1) | wise(X1) <- (13) [avatar component clause 187]
195. 15 <=> ! [X1] : (~wise(X1) | tall(X1)) [avatar definition]
196. ~wise(X1) | tall(X1) <- (15) [avatar component clause 195]
199. 16 <=> generous(sK2) [avatar definition]
201. generous(sK2) <- (16) [avatar component clause 199]
202. 13 | 16 [avatar split clause 92,199,187]
203. 15 | 16 [avatar split clause 91,199,195]
204. ~calm(X0) [subsumption resolution 106,107]
205. 6 [avatar split clause 134,159]
224. ~humble(X0) | strong(X0) [subsumption resolution 118,204]
268. wise(lucy) <- (10, 13) [resolution 188,176]
275. strong(lucy) [resolution 224,132]
294. ~kind(lucy) | ~tall(lucy) <- (10, 13) [resolution 88,268]
296. ~kind(lucy) <- (10, 13) [subsumption resolution 294,176]
313. tall(lucy) | wise(lucy) | ~kind(lucy) [resolution 83,275]
325. old(lucy) | ~strong(lucy) | patient(lucy) [resolution 98,132]
327. old(lucy) | patient(lucy) [subsumption resolution 325,275]
328. old(lucy) <- (6) [subsumption resolution 327,160]
329. 11 | ~6 [avatar split clause 328,159,178]
333. kind(lucy) <- (11) [resolution 180,100]
334. $false <- (10, 11, 13) [subsumption resolution 333,296]
335. ~10 | ~11 | ~13 [avatar contradiction clause 334]
336. tall(lucy) | wise(lucy) <- (11) [subsumption resolution 313,333]
337. wise(lucy) <- (11, 13) [subsumption resolution 336,188]
346. tall(lucy) <- (11, 13, 15) [resolution 337,196]
347. $false <- (~10, 11, 13, 15) [subsumption resolution 346,175]
348. 10 | ~11 | ~13 | ~15 [avatar contradiction clause 347]
349. $false <- (7, 16) [subsumption resolution 201,164]
350. ~7 | ~16 [avatar contradiction clause 349]
351. $false <- (6, 8) [subsumption resolution 168,160]
352. ~6 | ~8 [avatar contradiction clause 351]
353. $false [avatar sat refutation 169,202,203,205,329,335,348,350,352]
% SZS output end Proof for 9025549023579717596885614
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or quiet is calm or not old and vice versa. Everyone who is both wise and old is not calm or not creative and vice versa. Everyone who is patient or not calm is both curious and not funny and vice versa. If lucy is not humble then someone is rich or not strong and vice versa. If someone is either not curious or funny then someone is patient or quiet and vice versa. Everyone who is not wise or not funny is humble. Everyone who is both not curious and not brave is strong or funny. If paul is both rich and not old then mary is not rich or strong and vice versa. Everyone who is either brave or not creative is not rich. Everyone who is brave or not rich is not brave. Everyone who is not old is both not kind and kind. If someone is not wise or calm then paul is not patient. If mary is both not strong and not calm then someone is tall or brave. Everyone who is generous or kind is not funny. If someone is both not strong and not happy then john is both not wise and patient and vice versa. Everyone who is not curious or calm is old. Paul is either creative or humble. Lucy is not quiet or not humble. John is patient or quiet. Mary is both creative and not wise. Someone is not patient. Paul is either not funny or not old. John is either not curious or creative. | Lucy is calm. | entailment | (![X]:((~curious(X)<~>quiet(X))<=>(calm(X)|~old(X))))&
(![X]:((wise(X)&old(X))<=>(~calm(X)|~creative(X))))&
(![X]:((patient(X)|~calm(X))<=>(curious(X)&~funny(X))))&
((~humble(lucy))<=>(?[X]:((rich(X)|~strong(X)))))&
((?[X]:((~curious(X)<~>funny(X))))<=>(?[X]:((patient(X)|quiet(X)))))&
(![X]:((~wise(X)|~funny(X))=>humble(X)))&
(![X]:((~curious(X)&~brave(X))=>(strong(X)|funny(X))))&
(((rich(paul)&~old(paul)))<=>((~rich(mary)|strong(mary))))&
(![X]:((brave(X)<~>~creative(X))=>~rich(X)))&
(![X]:((brave(X)|~rich(X))=>~brave(X)))&
(![X]:(~old(X)=>(~kind(X)&kind(X))))&
((?[X]:((~wise(X)|calm(X))))=>(~patient(paul)))&
(((~strong(mary)&~calm(mary)))=>(?[X]:((tall(X)|brave(X)))))&
(![X]:((generous(X)|kind(X))=>~funny(X)))&
((?[X]:((~strong(X)&~happy(X))))<=>((~wise(john)&patient(john))))&
(![X]:((~curious(X)|calm(X))=>old(X)))&
((creative(paul)<~>humble(paul)))&
((~quiet(lucy)|~humble(lucy)))&
((patient(john)|quiet(john)))&
((creative(mary)&~wise(mary)))&
(?[X]:(~patient(X)))&
((~funny(paul)<~>~old(paul)))&
((~curious(john)<~>creative(john))) | calm(lucy) | [
"p2",
"p3",
"p5",
"p7",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 614268336983240898687731
% SZS output start Proof for 614268336983240898687731
3. ! [X0] : ((~calm(X0) | patient(X0)) <=> (~funny(X0) & curious(X0))) [input p2]
4. ~humble(lucy) <=> ? [X0] : (~strong(X0) | rich(X0)) [input p3]
6. ! [X0] : ((~funny(X0) | ~wise(X0)) => humble(X0)) [input p5]
8. (~old(paul) & rich(paul)) <=> (strong(mary) | ~rich(mary)) [input p7]
11. ! [X0] : (~old(X0) => (kind(X0) & ~kind(X0))) [input p10]
24. ~calm(lucy) [input hypothesis]
28. ! [X0] : (humble(X0) | (funny(X0) & wise(X0))) [ennf transformation 6]
33. ! [X0] : ((kind(X0) & ~kind(X0)) | old(X0)) [ennf transformation 11]
41. ! [X0] : (((~calm(X0) | patient(X0)) | (funny(X0) | ~curious(X0))) & ((~funny(X0) & curious(X0)) | (calm(X0) & ~patient(X0)))) [nnf transformation 3]
42. ! [X0] : ((~calm(X0) | patient(X0) | funny(X0) | ~curious(X0)) & ((~funny(X0) & curious(X0)) | (calm(X0) & ~patient(X0)))) [flattening 41]
43. (~humble(lucy) | ! [X0] : (strong(X0) & ~rich(X0))) & (? [X0] : (~strong(X0) | rich(X0)) | humble(lucy)) [nnf transformation 4]
44. (~humble(lucy) | ! [X0] : (strong(X0) & ~rich(X0))) & (? [X1] : (~strong(X1) | rich(X1)) | humble(lucy)) [rectify 43]
45. ? [X1] : (~strong(X1) | rich(X1)) => (~strong(sK0) | rich(sK0)) [choice axiom]
46. (~humble(lucy) | ! [X0] : (strong(X0) & ~rich(X0))) & ((~strong(sK0) | rich(sK0)) | humble(lucy)) [skolemisation 44,45]
52. ((~old(paul) & rich(paul)) | (~strong(mary) & rich(mary))) & ((strong(mary) | ~rich(mary)) | (old(paul) | ~rich(paul))) [nnf transformation 8]
53. ((~old(paul) & rich(paul)) | (~strong(mary) & rich(mary))) & (strong(mary) | ~rich(mary) | old(paul) | ~rich(paul)) [flattening 52]
79. ~funny(X0) | calm(X0) [cnf transformation 42]
83. ~humble(lucy) | strong(X0) [cnf transformation 46]
91. humble(X0) | funny(X0) [cnf transformation 28]
97. ~old(paul) | ~strong(mary) [cnf transformation 53]
102. ~kind(X0) | old(X0) [cnf transformation 33]
103. kind(X0) | old(X0) [cnf transformation 33]
124. ~calm(lucy) [cnf transformation 24]
127. 1 <=> ! [X0] : strong(X0) [avatar definition]
128. strong(X0) <- (1) [avatar component clause 127]
130. 2 <=> humble(lucy) [avatar definition]
132. ~humble(lucy) <- (~2) [avatar component clause 130]
133. 1 | ~2 [avatar split clause 83,130,127]
182. 14 <=> strong(mary) [avatar definition]
184. ~strong(mary) <- (~14) [avatar component clause 182]
186. 15 <=> old(paul) [avatar definition]
188. ~old(paul) <- (~15) [avatar component clause 186]
189. ~14 | ~15 [avatar split clause 97,186,182]
202. old(X0) [subsumption resolution 102,103]
283. funny(lucy) <- (~2) [resolution 91,132]
289. calm(lucy) <- (~2) [resolution 283,79]
291. $false <- (~2) [subsumption resolution 289,124]
292. 2 [avatar contradiction clause 291]
294. $false <- (1, ~14) [resolution 128,184]
297. ~1 | 14 [avatar contradiction clause 294]
301. $false <- (~15) [subsumption resolution 188,202]
302. 15 [avatar contradiction clause 301]
303. $false [avatar sat refutation 133,189,292,297,302]
% SZS output end Proof for 614268336983240898687731
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If susan is both not funny and generous then susan is not tall or wise.
If john is not calm then someone is both happy and tall.
Everyone who is both creative and tall is calm or not kind.
Everyone who is old is both generous and quiet and vice versa.
Everyone who is both not patient and wise is either old or not generous and vice versa.
If paul is not happy or not curious then lucy is either quiet or tall.
If alice is either not brave or humble then someone is not quiet and vice versa.
If someone is either not wise or not kind then fred is either not creative or not humble.
If someone is not old then someone is both wise and not brave and vice versa.
Everyone who is quiet is both patient and kind.
Everyone who is either not curious or creative is not funny.
If mary is wise then someone is tall or curious.
If fred is either not creative or strong then paul is either not brave or calm.
Everyone who is not strong or not brave is strong and vice versa.
Everyone who is both calm and old is not curious.
Everyone who is both not funny and not generous is either old or not creative.
Someone is both not tall and not humble.
Someone is either tall or not tall.
Someone is both creative and wise.
Someone is either rich or not rich.
Someone is either not kind or not generous.
Lucy is both strong and not generous.
Someone is not funny or tall.
Someone is calm or generous. | Lucy is not wise. | contradiction | (((~funny(susan)&generous(susan)))=>((~tall(susan)|wise(susan))))&
((~calm(john))=>(?[X]:((happy(X)&tall(X)))))&
(![X]:((creative(X)&tall(X))=>(calm(X)|~kind(X))))&
(![X]:(old(X)<=>(generous(X)&quiet(X))))&
(![X]:((~patient(X)&wise(X))<=>(old(X)<~>~generous(X))))&
(((~happy(paul)|~curious(paul)))=>((quiet(lucy)<~>tall(lucy))))&
(((~brave(alice)<~>humble(alice)))<=>(?[X]:(~quiet(X))))&
((?[X]:((~wise(X)<~>~kind(X))))=>((~creative(fred)<~>~humble(fred))))&
((?[X]:(~old(X)))<=>(?[X]:((wise(X)&~brave(X)))))&
(![X]:(quiet(X)=>(patient(X)&kind(X))))&
(![X]:((~curious(X)<~>creative(X))=>~funny(X)))&
((wise(mary))=>(?[X]:((tall(X)|curious(X)))))&
(((~creative(fred)<~>strong(fred)))=>((~brave(paul)<~>calm(paul))))&
(![X]:((~strong(X)|~brave(X))<=>strong(X)))&
(![X]:((calm(X)&old(X))=>~curious(X)))&
(![X]:((~funny(X)&~generous(X))=>(old(X)<~>~creative(X))))&
(?[X]:((~tall(X)&~humble(X))))&
(?[X]:((tall(X)<~>~tall(X))))&
(?[X]:((creative(X)&wise(X))))&
(?[X]:((rich(X)<~>~rich(X))))&
(?[X]:((~kind(X)<~>~generous(X))))&
((strong(lucy)&~generous(lucy)))&
(?[X]:((~funny(X)|tall(X))))&
(?[X]:((calm(X)|generous(X)))) | ~wise(lucy) | [
"p3",
"p4",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 3261491903350212435600584
% SZS output start Proof for 3261491903350212435600584
4. ! [X0] : (old(X0) <=> (quiet(X0) & generous(X0))) [input p3]
5. ! [X0] : ((wise(X0) & ~patient(X0)) <=> (old(X0) <~> ~generous(X0))) [input p4]
22. ~generous(lucy) & strong(lucy) [input p21]
25. ~wise(lucy) [input hypothesis]
46. ! [X0] : ((old(X0) | (~quiet(X0) | ~generous(X0))) & ((quiet(X0) & generous(X0)) | ~old(X0))) [nnf transformation 4]
47. ! [X0] : ((old(X0) | ~quiet(X0) | ~generous(X0)) & ((quiet(X0) & generous(X0)) | ~old(X0))) [flattening 46]
48. ! [X0] : (((wise(X0) & ~patient(X0)) | ((old(X0) | generous(X0)) & (~generous(X0) | ~old(X0)))) & (((generous(X0) | ~old(X0)) & (~generous(X0) | old(X0))) | (~wise(X0) | patient(X0)))) [nnf transformation 5]
49. ! [X0] : (((wise(X0) & ~patient(X0)) | ((old(X0) | generous(X0)) & (~generous(X0) | ~old(X0)))) & (((generous(X0) | ~old(X0)) & (~generous(X0) | old(X0))) | ~wise(X0) | patient(X0))) [flattening 48]
88. ~old(X0) | generous(X0) [cnf transformation 47]
96. wise(X0) | old(X0) | generous(X0) [cnf transformation 49]
136. ~generous(lucy) [cnf transformation 22]
139. ~wise(lucy) [cnf transformation 25]
168. wise(X0) | generous(X0) [subsumption resolution 96,88]
319. generous(lucy) [resolution 168,139]
321. $false [subsumption resolution 319,136]
% SZS output end Proof for 3261491903350212435600584
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is brave is creative or curious.
If someone is wise then someone is old and vice versa.
Everyone who is either brave or not humble is not rich.
Everyone who is either calm or kind is humble or not wise.
If someone is not rich or patient then susan is not happy or rich.
Everyone who is either humble or not wise is not quiet and vice versa.
If paul is not strong then someone is both not quiet and not calm and vice versa.
Everyone who is either funny or not strong is both humble and old.
If john is either not tall or not happy then someone is not creative and vice versa.
If paul is both not rich and not tall then someone is not funny and vice versa.
Everyone who is strong is not tall or not old.
If mary is either patient or not funny then someone is funny.
If alice is either generous or not brave then someone is both not tall and happy.
If someone is both not curious and not old then susan is both humble and not creative and vice versa.
If someone is not patient or rich then paul is either not rich or generous and vice versa.
If someone is both not happy and not kind then someone is both not wise and not old.
Susan is both not kind and generous.
Someone is both not funny and quiet.
Alice is both patient and not curious.
Lucy is not kind or brave.
Paul is not patient.
Lucy is either not humble or not tall.
Paul is patient or wise.
Someone is either happy or not humble. | Paul is tall. | contradiction | (![X]:(brave(X)=>(creative(X)|curious(X))))&
((?[X]:(wise(X)))<=>(?[X]:(old(X))))&
(![X]:((brave(X)<~>~humble(X))=>~rich(X)))&
(![X]:((calm(X)<~>kind(X))=>(humble(X)|~wise(X))))&
((?[X]:((~rich(X)|patient(X))))=>((~happy(susan)|rich(susan))))&
(![X]:((humble(X)<~>~wise(X))<=>~quiet(X)))&
((~strong(paul))<=>(?[X]:((~quiet(X)&~calm(X)))))&
(![X]:((funny(X)<~>~strong(X))=>(humble(X)&old(X))))&
(((~tall(john)<~>~happy(john)))<=>(?[X]:(~creative(X))))&
(((~rich(paul)&~tall(paul)))<=>(?[X]:(~funny(X))))&
(![X]:(strong(X)=>(~tall(X)|~old(X))))&
(((patient(mary)<~>~funny(mary)))=>(?[X]:(funny(X))))&
(((generous(alice)<~>~brave(alice)))=>(?[X]:((~tall(X)&happy(X)))))&
((?[X]:((~curious(X)&~old(X))))<=>((humble(susan)&~creative(susan))))&
((?[X]:((~patient(X)|rich(X))))<=>((~rich(paul)<~>generous(paul))))&
((?[X]:((~happy(X)&~kind(X))))=>(?[X]:((~wise(X)&~old(X)))))&
((~kind(susan)&generous(susan)))&
(?[X]:((~funny(X)&quiet(X))))&
((patient(alice)&~curious(alice)))&
((~kind(lucy)|brave(lucy)))&
(~patient(paul))&
((~humble(lucy)<~>~tall(lucy)))&
((patient(paul)|wise(paul)))&
(?[X]:((happy(X)<~>~humble(X)))) | tall(paul) | [
"p9",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 4459282369671791963226225
% SZS output start Proof for 4459282369671791963226225
10. (~tall(paul) & ~rich(paul)) <=> ? [X0] : ~funny(X0) [input p9]
18. ? [X0] : (quiet(X0) & ~funny(X0)) [input p17]
25. tall(paul) [input hypothesis]
58. ((~tall(paul) & ~rich(paul)) | ! [X0] : funny(X0)) & (? [X0] : ~funny(X0) | (tall(paul) | rich(paul))) [nnf transformation 10]
59. ((~tall(paul) & ~rich(paul)) | ! [X0] : funny(X0)) & (? [X0] : ~funny(X0) | tall(paul) | rich(paul)) [flattening 58]
60. ((~tall(paul) & ~rich(paul)) | ! [X0] : funny(X0)) & (? [X1] : ~funny(X1) | tall(paul) | rich(paul)) [rectify 59]
61. ? [X1] : ~funny(X1) => ~funny(sK4) [choice axiom]
62. ((~tall(paul) & ~rich(paul)) | ! [X0] : funny(X0)) & (~funny(sK4) | tall(paul) | rich(paul)) [skolemisation 60,61]
81. ? [X0] : (quiet(X0) & ~funny(X0)) => (quiet(sK10) & ~funny(sK10)) [choice axiom]
82. quiet(sK10) & ~funny(sK10) [skolemisation 18,81]
113. ~tall(paul) | funny(X0) [cnf transformation 62]
135. ~funny(sK10) [cnf transformation 82]
146. tall(paul) [cnf transformation 25]
217. 17 <=> ! [X0] : funny(X0) [avatar definition]
218. funny(X0) <- (17) [avatar component clause 217]
220. 18 <=> tall(paul) [avatar definition]
223. 17 | ~18 [avatar split clause 113,220,217]
358. 18 [avatar split clause 146,220]
361. $false <- (17) [resolution 218,135]
362. ~17 [avatar contradiction clause 361]
363. $false [avatar sat refutation 223,358,362]
% SZS output end Proof for 4459282369671791963226225
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious and not brave is old or not old and vice versa. Everyone who is both not wise and calm is both generous and patient. If someone is not patient or humble then someone is either kind or not kind. If mary is both not strong and not quiet then someone is both not curious and not old and vice versa. If someone is kind or not calm then mary is not tall. Everyone who is not happy or rich is quiet. Everyone who is not kind or not calm is strong. If someone is not humble or brave then someone is not brave and vice versa. If someone is both not brave and rich then someone is either not calm or not old and vice versa. If someone is humble then someone is both happy and not generous. If mary is both not strong and patient then someone is not funny. Everyone who is either quiet or not strong is patient or humble and vice versa. Everyone who is not tall or humble is quiet or happy. Everyone who is wise or not funny is strong or not creative. If fred is both not funny and not rich then someone is calm or not wise. Everyone who is not rich or not strong is not brave and vice versa. Someone is humble or happy. Someone is patient or not humble. Someone is curious or not calm. Someone is tall. Mary is either not old or not strong. Susan is not kind or creative. John is either not happy or generous. John is both kind and funny. | Mary is patient. | neutral | (![X]:((curious(X)&~brave(X))<=>(old(X)|~old(X))))&
(![X]:((~wise(X)&calm(X))=>(generous(X)&patient(X))))&
((?[X]:((~patient(X)|humble(X))))=>(?[X]:((kind(X)<~>~kind(X)))))&
(((~strong(mary)&~quiet(mary)))<=>(?[X]:((~curious(X)&~old(X)))))&
((?[X]:((kind(X)|~calm(X))))=>(~tall(mary)))&
(![X]:((~happy(X)|rich(X))=>quiet(X)))&
(![X]:((~kind(X)|~calm(X))=>strong(X)))&
((?[X]:((~humble(X)|brave(X))))<=>(?[X]:(~brave(X))))&
((?[X]:((~brave(X)&rich(X))))<=>(?[X]:((~calm(X)<~>~old(X)))))&
((?[X]:(humble(X)))=>(?[X]:((happy(X)&~generous(X)))))&
(((~strong(mary)&patient(mary)))=>(?[X]:(~funny(X))))&
(![X]:((quiet(X)<~>~strong(X))<=>(patient(X)|humble(X))))&
(![X]:((~tall(X)|humble(X))=>(quiet(X)|happy(X))))&
(![X]:((wise(X)|~funny(X))=>(strong(X)|~creative(X))))&
(((~funny(fred)&~rich(fred)))=>(?[X]:((calm(X)|~wise(X)))))&
(![X]:((~rich(X)|~strong(X))<=>~brave(X)))&
(?[X]:((humble(X)|happy(X))))&
(?[X]:((patient(X)|~humble(X))))&
(?[X]:((curious(X)|~calm(X))))&
(?[X]:(tall(X)))&
((~old(mary)<~>~strong(mary)))&
((~kind(susan)|creative(susan)))&
((~happy(john)<~>generous(john)))&
((kind(john)&funny(john))) | patient(mary) | [] | null | 0 |
If someone is both not brave and not calm then someone is either not brave or happy and vice versa.
Everyone who is not curious or not kind is both not rich and not funny.
If susan is happy then someone is not patient or patient and vice versa.
If fred is old or generous then someone is both quiet and not happy.
If someone is not funny or not happy then mary is not creative or not curious.
Everyone who is either not kind or not calm is wise or not wise and vice versa.
Everyone who is not happy is either curious or not creative.
If someone is humble or creative then someone is both rich and not old.
Everyone who is either not brave or not kind is either not rich or brave.
Everyone who is not tall is not creative and vice versa.
Everyone who is not calm is not patient or wise and vice versa.
If susan is generous or not creative then someone is either kind or not patient.
Everyone who is both not brave and not funny is either not brave or not curious.
Everyone who is tall is not kind or not quiet.
Everyone who is both not calm and happy is not tall or not rich.
Everyone who is either not strong or calm is not wise or not curious and vice versa.
Alice is either quiet or not rich.
Someone is not patient.
Fred is not brave.
Alice is not creative or humble.
Someone is both old and not happy.
Mary is either old or curious.
Someone is not funny or funny.
Susan is generous. | Mary is creative. | neutral | ((?[X]:((~brave(X)&~calm(X))))<=>(?[X]:((~brave(X)<~>happy(X)))))&
(![X]:((~curious(X)|~kind(X))=>(~rich(X)&~funny(X))))&
((happy(susan))<=>(?[X]:((~patient(X)|patient(X)))))&
(((old(fred)|generous(fred)))=>(?[X]:((quiet(X)&~happy(X)))))&
((?[X]:((~funny(X)|~happy(X))))=>((~creative(mary)|~curious(mary))))&
(![X]:((~kind(X)<~>~calm(X))<=>(wise(X)|~wise(X))))&
(![X]:(~happy(X)=>(curious(X)<~>~creative(X))))&
((?[X]:((humble(X)|creative(X))))=>(?[X]:((rich(X)&~old(X)))))&
(![X]:((~brave(X)<~>~kind(X))=>(~rich(X)<~>brave(X))))&
(![X]:(~tall(X)<=>~creative(X)))&
(![X]:(~calm(X)<=>(~patient(X)|wise(X))))&
(((generous(susan)|~creative(susan)))=>(?[X]:((kind(X)<~>~patient(X)))))&
(![X]:((~brave(X)&~funny(X))=>(~brave(X)<~>~curious(X))))&
(![X]:(tall(X)=>(~kind(X)|~quiet(X))))&
(![X]:((~calm(X)&happy(X))=>(~tall(X)|~rich(X))))&
(![X]:((~strong(X)<~>calm(X))<=>(~wise(X)|~curious(X))))&
((quiet(alice)<~>~rich(alice)))&
(?[X]:(~patient(X)))&
(~brave(fred))&
((~creative(alice)|humble(alice)))&
(?[X]:((old(X)&~happy(X))))&
((old(mary)<~>curious(mary)))&
(?[X]:((~funny(X)|funny(X))))&
(generous(susan)) | creative(mary) | [] | null | 0 |
Everyone who is both not curious and calm is both humble and patient and vice versa. If someone is not rich or brave then lucy is both old and wise. Everyone who is not humble is generous or tall. Everyone who is curious is both humble and rich and vice versa. If someone is both not patient and strong then john is strong and vice versa. If susan is calm or not kind then fred is both creative and not happy and vice versa. If fred is both not quiet and kind then someone is both wise and funny and vice versa. If someone is either not brave or not curious then someone is both rich and calm and vice versa. Everyone who is wise is both not humble and old and vice versa. If someone is generous then paul is not quiet or strong. If someone is kind or patient then lucy is either brave or not old. If someone is both not quiet and quiet then mary is creative and vice versa. If fred is not humble then fred is either creative or not strong. Everyone who is happy is either funny or kind. If someone is quiet then john is not brave and vice versa. Everyone who is not kind or strong is either kind or calm and vice versa. Someone is calm or not rich. Alice is calm or quiet. Lucy is happy. Fred is both patient and brave. Paul is not strong. Paul is brave or generous. Susan is not old or quiet. Mary is both not wise and not happy. | Mary is tall. | neutral | (![X]:((~curious(X)&calm(X))<=>(humble(X)&patient(X))))&
((?[X]:((~rich(X)|brave(X))))=>((old(lucy)&wise(lucy))))&
(![X]:(~humble(X)=>(generous(X)|tall(X))))&
(![X]:(curious(X)<=>(humble(X)&rich(X))))&
((?[X]:((~patient(X)&strong(X))))<=>(strong(john)))&
(((calm(susan)|~kind(susan)))<=>((creative(fred)&~happy(fred))))&
(((~quiet(fred)&kind(fred)))<=>(?[X]:((wise(X)&funny(X)))))&
((?[X]:((~brave(X)<~>~curious(X))))<=>(?[X]:((rich(X)&calm(X)))))&
(![X]:(wise(X)<=>(~humble(X)&old(X))))&
((?[X]:(generous(X)))=>((~quiet(paul)|strong(paul))))&
((?[X]:((kind(X)|patient(X))))=>((brave(lucy)<~>~old(lucy))))&
((?[X]:((~quiet(X)&quiet(X))))<=>(creative(mary)))&
((~humble(fred))=>((creative(fred)<~>~strong(fred))))&
(![X]:(happy(X)=>(funny(X)<~>kind(X))))&
((?[X]:(quiet(X)))<=>(~brave(john)))&
(![X]:((~kind(X)|strong(X))<=>(kind(X)<~>calm(X))))&
(?[X]:((calm(X)|~rich(X))))&
((calm(alice)|quiet(alice)))&
(happy(lucy))&
((patient(fred)&brave(fred)))&
(~strong(paul))&
((brave(paul)|generous(paul)))&
((~old(susan)|quiet(susan)))&
((~wise(mary)&~happy(mary))) | tall(mary) | [] | null | 0 |
If someone is quiet or not brave then someone is happy or not wise.
Everyone who is either strong or not creative is curious.
Everyone who is both not calm and not creative is not kind and vice versa.
If john is either not curious or not tall then alice is creative and vice versa.
Everyone who is not generous or not quiet is either not funny or not calm and vice versa.
If susan is kind then alice is not old.
Everyone who is funny is strong.
If someone is either not funny or not creative then someone is not humble and vice versa.
If susan is either curious or not wise then paul is creative and vice versa.
Everyone who is not tall is strong or not funny.
Everyone who is not humble or not funny is funny.
Everyone who is not wise or generous is both tall and generous and vice versa.
If lucy is old then mary is strong or brave.
If fred is both not old and curious then lucy is curious or not rich and vice versa.
Everyone who is curious is kind or creative and vice versa.
Everyone who is curious or funny is both curious and humble and vice versa.
Someone is not curious or not quiet.
Susan is either not strong or funny.
Fred is generous.
Someone is not happy or old.
Lucy is both not quiet and brave.
Susan is both tall and curious.
Someone is both quiet and not rich. | John is not funny. | contradiction | ((?[X]:((quiet(X)|~brave(X))))=>(?[X]:((happy(X)|~wise(X)))))&
(![X]:((strong(X)<~>~creative(X))=>curious(X)))&
(![X]:((~calm(X)&~creative(X))<=>~kind(X)))&
(((~curious(john)<~>~tall(john)))<=>(creative(alice)))&
(![X]:((~generous(X)|~quiet(X))<=>(~funny(X)<~>~calm(X))))&
((kind(susan))=>(~old(alice)))&
(![X]:(funny(X)=>strong(X)))&
((?[X]:((~funny(X)<~>~creative(X))))<=>(?[X]:(~humble(X))))&
(((curious(susan)<~>~wise(susan)))<=>(creative(paul)))&
(![X]:(~tall(X)=>(strong(X)|~funny(X))))&
(![X]:((~humble(X)|~funny(X))=>funny(X)))&
(![X]:((~wise(X)|generous(X))<=>(tall(X)&generous(X))))&
((old(lucy))=>((strong(mary)|brave(mary))))&
(((~old(fred)&curious(fred)))<=>((curious(lucy)|~rich(lucy))))&
(![X]:(curious(X)<=>(kind(X)|creative(X))))&
(![X]:((curious(X)|funny(X))<=>(curious(X)&humble(X))))&
(?[X]:((~curious(X)|~quiet(X))))&
((~strong(susan)<~>funny(susan)))&
(generous(fred))&
(?[X]:((~happy(X)|old(X))))&
((~quiet(lucy)&brave(lucy)))&
((tall(susan)&curious(susan)))&
(?[X]:((quiet(X)&~rich(X)))) | ~funny(john) | [
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 3572682362165343498935703
% SZS output start Proof for 3572682362165343498935703
11. ! [X0] : ((~funny(X0) | ~humble(X0)) => funny(X0)) [input p10]
24. ~funny(john) [input hypothesis]
36. ! [X0] : (funny(X0) | (funny(X0) & humble(X0))) [ennf transformation 11]
95. funny(X0) | funny(X0) [cnf transformation 36]
124. ~funny(john) [cnf transformation 24]
125. funny(X0) [duplicate literal removal 95]
239. $false [subsumption resolution 124,125]
% SZS output end Proof for 3572682362165343498935703
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is not wise then someone is wise. Everyone who is not brave is tall and vice versa. If mary is not old or patient then someone is both not patient and rich. If someone is happy or not generous then someone is either happy or strong. If mary is tall or generous then paul is not old and vice versa. If mary is happy then susan is both not brave and calm and vice versa. Everyone who is wise is funny and vice versa. If paul is both not tall and not strong then someone is not humble or curious and vice versa. Everyone who is kind or not creative is quiet. If someone is generous then someone is both strong and wise. If someone is not humble or patient then someone is both not generous and generous. Everyone who is not humble or not strong is not quiet. Everyone who is happy or not generous is both wise and not humble. Everyone who is patient is both patient and tall. If alice is not creative or kind then alice is either not patient or old and vice versa. If mary is not calm then lucy is both not generous and happy. Susan is both not brave and curious. Someone is either happy or humble. Someone is patient or old. Someone is either old or not old. Someone is not calm or kind. Someone is either not tall or not quiet. Alice is both quiet and wise. | Paul is not generous. | contradiction | ((~wise(lucy))=>(?[X]:(wise(X))))&
(![X]:(~brave(X)<=>tall(X)))&
(((~old(mary)|patient(mary)))=>(?[X]:((~patient(X)&rich(X)))))&
((?[X]:((happy(X)|~generous(X))))=>(?[X]:((happy(X)<~>strong(X)))))&
(((tall(mary)|generous(mary)))<=>(~old(paul)))&
((happy(mary))<=>((~brave(susan)&calm(susan))))&
(![X]:(wise(X)<=>funny(X)))&
(((~tall(paul)&~strong(paul)))<=>(?[X]:((~humble(X)|curious(X)))))&
(![X]:((kind(X)|~creative(X))=>quiet(X)))&
((?[X]:(generous(X)))=>(?[X]:((strong(X)&wise(X)))))&
((?[X]:((~humble(X)|patient(X))))=>(?[X]:((~generous(X)&generous(X)))))&
(![X]:((~humble(X)|~strong(X))=>~quiet(X)))&
(![X]:((happy(X)|~generous(X))=>(wise(X)&~humble(X))))&
(![X]:(patient(X)=>(patient(X)&tall(X))))&
(((~creative(alice)|kind(alice)))<=>((~patient(alice)<~>old(alice))))&
((~calm(mary))=>((~generous(lucy)&happy(lucy))))&
((~brave(susan)&curious(susan)))&
(?[X]:((happy(X)<~>humble(X))))&
(?[X]:((patient(X)|old(X))))&
(?[X]:((old(X)<~>~old(X))))&
(?[X]:((~calm(X)|kind(X))))&
(?[X]:((~tall(X)<~>~quiet(X))))&
((quiet(alice)&wise(alice))) | ~generous(paul) | [
"p10",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 649372480494221866616986
% SZS output start Proof for 649372480494221866616986
11. ? [X0] : (patient(X0) | ~humble(X0)) => ? [X0] : (generous(X0) & ~generous(X0)) [input p10]
13. ! [X0] : ((~generous(X0) | happy(X0)) => (~humble(X0) & wise(X0))) [input p12]
24. ~generous(paul) [input hypothesis]
27. ? [X0] : (patient(X0) | ~humble(X0)) => ? [X1] : (generous(X1) & ~generous(X1)) [rectify 11]
33. ! [X0] : ((~generous(X0) | happy(X0)) => ~humble(X0)) [pure predicate removal 13]
39. ? [X1] : (generous(X1) & ~generous(X1)) | ! [X0] : (~patient(X0) & humble(X0)) [ennf transformation 27]
41. ! [X0] : (~humble(X0) | (generous(X0) & ~happy(X0))) [ennf transformation 33]
63. ? [X0] : (generous(X0) & ~generous(X0)) | ! [X1] : (~patient(X1) & humble(X1)) [rectify 39]
64. ? [X0] : (generous(X0) & ~generous(X0)) => (generous(sK4) & ~generous(sK4)) [choice axiom]
65. (generous(sK4) & ~generous(sK4)) | ! [X1] : (~patient(X1) & humble(X1)) [skolemisation 63,64]
103. ~generous(sK4) | humble(X1) [cnf transformation 65]
105. generous(sK4) | humble(X1) [cnf transformation 65]
110. ~humble(X0) | generous(X0) [cnf transformation 41]
132. ~generous(paul) [cnf transformation 24]
148. 4 <=> ! [X1] : generous(X1) [avatar definition]
149. generous(X1) <- (4) [avatar component clause 148]
204. 16 <=> ! [X0] : humble(X0) [avatar definition]
205. humble(X0) <- (16) [avatar component clause 204]
234. 23 <=> generous(sK4) [avatar definition]
238. 16 | 23 [avatar split clause 105,234,204]
240. 16 | ~23 [avatar split clause 103,234,204]
336. generous(X0) <- (16) [resolution 110,205]
339. 4 | ~16 [avatar split clause 336,204,148]
340. $false <- (4) [resolution 149,132]
341. ~4 [avatar contradiction clause 340]
342. $false [avatar sat refutation 238,240,339,341]
% SZS output end Proof for 649372480494221866616986
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong or not strong is not old.
Everyone who is either not kind or old is either humble or not funny.
Everyone who is both not quiet and curious is either generous or not funny and vice versa.
If someone is wise then someone is funny and vice versa.
If someone is calm then someone is either not creative or not curious and vice versa.
Everyone who is not quiet is not generous.
If mary is old then someone is both not humble and generous.
Everyone who is not brave or not strong is both tall and curious.
Everyone who is either generous or old is both not brave and funny and vice versa.
Everyone who is humble or not humble is both not patient and tall.
Everyone who is not tall is curious.
If john is not funny then someone is both curious and rich.
Everyone who is not strong or not patient is either old or creative.
Everyone who is both old and brave is humble or not wise and vice versa.
If someone is both calm and not brave then someone is both not curious and funny.
Everyone who is not kind is brave.
Someone is both funny and kind.
Someone is either not old or not quiet.
Susan is not humble or funny.
John is funny or creative.
Alice is happy.
Susan is quiet.
Someone is both not funny and not rich.
Someone is both not generous and not rich. | Mary is creative. | entailment | (![X]:((strong(X)<~>~strong(X))=>~old(X)))&
(![X]:((~kind(X)<~>old(X))=>(humble(X)<~>~funny(X))))&
(![X]:((~quiet(X)&curious(X))<=>(generous(X)<~>~funny(X))))&
((?[X]:(wise(X)))<=>(?[X]:(funny(X))))&
((?[X]:(calm(X)))<=>(?[X]:((~creative(X)<~>~curious(X)))))&
(![X]:(~quiet(X)=>~generous(X)))&
((old(mary))=>(?[X]:((~humble(X)&generous(X)))))&
(![X]:((~brave(X)|~strong(X))=>(tall(X)&curious(X))))&
(![X]:((generous(X)<~>old(X))<=>(~brave(X)&funny(X))))&
(![X]:((humble(X)|~humble(X))=>(~patient(X)&tall(X))))&
(![X]:(~tall(X)=>curious(X)))&
((~funny(john))=>(?[X]:((curious(X)&rich(X)))))&
(![X]:((~strong(X)|~patient(X))=>(old(X)<~>creative(X))))&
(![X]:((old(X)&brave(X))<=>(humble(X)|~wise(X))))&
((?[X]:((calm(X)&~brave(X))))=>(?[X]:((~curious(X)&funny(X)))))&
(![X]:(~kind(X)=>brave(X)))&
(?[X]:((funny(X)&kind(X))))&
(?[X]:((~old(X)<~>~quiet(X))))&
((~humble(susan)|funny(susan)))&
((funny(john)|creative(john)))&
(happy(alice))&
(quiet(susan))&
(?[X]:((~funny(X)&~rich(X))))&
(?[X]:((~generous(X)&~rich(X)))) | creative(mary) | [
"p0",
"p9",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 7795303387097844473512242
% SZS output start Proof for 7795303387097844473512242
1. ! [X0] : ((strong(X0) <~> ~strong(X0)) => ~old(X0)) [input p0]
10. ! [X0] : ((~humble(X0) | humble(X0)) => (tall(X0) & ~patient(X0))) [input p9]
13. ! [X0] : ((~patient(X0) | ~strong(X0)) => (old(X0) <~> creative(X0))) [input p12]
25. ~creative(mary) [input hypothesis]
30. ! [X0] : ((~humble(X0) | humble(X0)) => ~patient(X0)) [pure predicate removal 10]
33. ! [X0] : (~old(X0) | (strong(X0) <=> ~strong(X0))) [ennf transformation 1]
38. ! [X0] : (~patient(X0) | (humble(X0) & ~humble(X0))) [ennf transformation 30]
40. ! [X0] : ((old(X0) <~> creative(X0)) | (patient(X0) & strong(X0))) [ennf transformation 13]
43. ! [X0] : (~old(X0) | ((strong(X0) | strong(X0)) & (~strong(X0) | ~strong(X0)))) [nnf transformation 33]
63. ! [X0] : (((~creative(X0) | ~old(X0)) & (creative(X0) | old(X0))) | (patient(X0) & strong(X0))) [nnf transformation 40]
78. ~old(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 43]
79. ~old(X0) | strong(X0) | strong(X0) [cnf transformation 43]
107. ~patient(X0) | ~humble(X0) [cnf transformation 38]
108. ~patient(X0) | humble(X0) [cnf transformation 38]
112. creative(X0) | old(X0) | patient(X0) [cnf transformation 63]
134. ~creative(mary) [cnf transformation 25]
135. ~old(X0) | ~strong(X0) [duplicate literal removal 78]
136. ~old(X0) | strong(X0) [duplicate literal removal 79]
137. ~old(X0) [subsumption resolution 135,136]
184. ~patient(X0) [subsumption resolution 107,108]
199. creative(X0) | patient(X0) [subsumption resolution 112,137]
200. creative(X0) [subsumption resolution 199,184]
217. $false [subsumption resolution 134,200]
% SZS output end Proof for 7795303387097844473512242
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind or rich then mary is not happy and vice versa. Everyone who is either not brave or not quiet is calm or happy and vice versa. If paul is both not calm and not old then someone is not wise and vice versa. Everyone who is both kind and rich is both not patient and not creative. If someone is both not funny and not curious then someone is both brave and not brave and vice versa. If someone is both strong and not happy then someone is humble and vice versa. If someone is quiet then susan is not patient or wise and vice versa. Everyone who is not funny is kind or not tall and vice versa. If lucy is both quiet and not calm then lucy is strong or wise and vice versa. Everyone who is calm is both not curious and not calm. Everyone who is not rich or quiet is either creative or curious. Everyone who is both not kind and not creative is both not humble and brave and vice versa. Everyone who is either brave or creative is not calm or old. Everyone who is either generous or not creative is not happy and vice versa. If someone is both generous and not generous then someone is not brave. If mary is brave or not rich then susan is both not happy and old and vice versa. Someone is creative. Fred is not strong. Paul is both old and not humble. Lucy is either wise or tall. Mary is both curious and not patient. Someone is brave or not old. Someone is patient or not patient. | Paul is rich. | neutral | ((?[X]:((kind(X)|rich(X))))<=>(~happy(mary)))&
(![X]:((~brave(X)<~>~quiet(X))<=>(calm(X)|happy(X))))&
(((~calm(paul)&~old(paul)))<=>(?[X]:(~wise(X))))&
(![X]:((kind(X)&rich(X))=>(~patient(X)&~creative(X))))&
((?[X]:((~funny(X)&~curious(X))))<=>(?[X]:((brave(X)&~brave(X)))))&
((?[X]:((strong(X)&~happy(X))))<=>(?[X]:(humble(X))))&
((?[X]:(quiet(X)))<=>((~patient(susan)|wise(susan))))&
(![X]:(~funny(X)<=>(kind(X)|~tall(X))))&
(((quiet(lucy)&~calm(lucy)))<=>((strong(lucy)|wise(lucy))))&
(![X]:(calm(X)=>(~curious(X)&~calm(X))))&
(![X]:((~rich(X)|quiet(X))=>(creative(X)<~>curious(X))))&
(![X]:((~kind(X)&~creative(X))<=>(~humble(X)&brave(X))))&
(![X]:((brave(X)<~>creative(X))=>(~calm(X)|old(X))))&
(![X]:((generous(X)<~>~creative(X))<=>~happy(X)))&
((?[X]:((generous(X)&~generous(X))))=>(?[X]:(~brave(X))))&
(((brave(mary)|~rich(mary)))<=>((~happy(susan)&old(susan))))&
(?[X]:(creative(X)))&
(~strong(fred))&
((old(paul)&~humble(paul)))&
((wise(lucy)<~>tall(lucy)))&
((curious(mary)&~patient(mary)))&
(?[X]:((brave(X)|~old(X))))&
(?[X]:((patient(X)|~patient(X)))) | rich(paul) | [] | null | 0 |
If someone is both curious and humble then paul is both tall and not happy. Everyone who is both not brave and old is either patient or wise. Everyone who is not calm is both strong and old. If lucy is either not creative or not rich then someone is both generous and wise. If alice is patient then someone is not happy and vice versa. Everyone who is not strong or kind is both not rich and not patient and vice versa. Everyone who is not rich or not wise is both generous and quiet and vice versa. Everyone who is happy is creative and vice versa. If someone is both brave and not funny then someone is either curious or not kind. If mary is not rich or not wise then someone is happy. If john is old or funny then susan is either not wise or calm and vice versa. Everyone who is both not kind and old is not happy. If someone is both not wise and funny then fred is not creative or not strong. If someone is humble then someone is not strong and vice versa. Everyone who is either patient or humble is old. Everyone who is both not happy and generous is not humble or calm. Susan is not creative or not funny. Paul is either rich or not wise. Paul is both brave and not kind. Alice is not rich or humble. Someone is curious or brave. Someone is wise or not strong. Someone is not creative or curious. Fred is both patient and brave. | John is not creative. | neutral | ((?[X]:((curious(X)&humble(X))))=>((tall(paul)&~happy(paul))))&
(![X]:((~brave(X)&old(X))=>(patient(X)<~>wise(X))))&
(![X]:(~calm(X)=>(strong(X)&old(X))))&
(((~creative(lucy)<~>~rich(lucy)))=>(?[X]:((generous(X)&wise(X)))))&
((patient(alice))<=>(?[X]:(~happy(X))))&
(![X]:((~strong(X)|kind(X))<=>(~rich(X)&~patient(X))))&
(![X]:((~rich(X)|~wise(X))<=>(generous(X)&quiet(X))))&
(![X]:(happy(X)<=>creative(X)))&
((?[X]:((brave(X)&~funny(X))))=>(?[X]:((curious(X)<~>~kind(X)))))&
(((~rich(mary)|~wise(mary)))=>(?[X]:(happy(X))))&
(((old(john)|funny(john)))<=>((~wise(susan)<~>calm(susan))))&
(![X]:((~kind(X)&old(X))=>~happy(X)))&
((?[X]:((~wise(X)&funny(X))))=>((~creative(fred)|~strong(fred))))&
((?[X]:(humble(X)))<=>(?[X]:(~strong(X))))&
(![X]:((patient(X)<~>humble(X))=>old(X)))&
(![X]:((~happy(X)&generous(X))=>(~humble(X)|calm(X))))&
((~creative(susan)|~funny(susan)))&
((rich(paul)<~>~wise(paul)))&
((brave(paul)&~kind(paul)))&
((~rich(alice)|humble(alice)))&
(?[X]:((curious(X)|brave(X))))&
(?[X]:((wise(X)|~strong(X))))&
(?[X]:((~creative(X)|curious(X))))&
((patient(fred)&brave(fred))) | ~creative(john) | [] | null | 0 |
Everyone who is not happy or not quiet is both curious and tall.
If someone is generous then fred is either quiet or not old and vice versa.
Everyone who is both funny and tall is old or not rich and vice versa.
If mary is both not happy and patient then someone is generous.
Everyone who is not funny or not tall is both creative and patient and vice versa.
If lucy is curious then someone is calm or generous and vice versa.
Everyone who is not curious or not funny is both not quiet and humble and vice versa.
If someone is wise then someone is not generous and vice versa.
If someone is either not wise or funny then someone is either humble or not curious.
Everyone who is humble is generous or brave and vice versa.
Everyone who is not quiet or rich is not patient or rich.
If susan is both happy and not tall then someone is either not curious or old and vice versa.
If someone is both not happy and wise then susan is either not creative or not old and vice versa.
If fred is both not generous and not rich then someone is either humble or not kind.
Everyone who is both humble and strong is brave or not wise and vice versa.
If someone is not creative then someone is both not curious and not generous and vice versa.
Lucy is not old.
Someone is not curious or not funny.
Someone is patient or humble.
John is kind.
Someone is generous or brave.
Alice is not calm or curious.
Someone is either quiet or not happy. | Fred is strong. | neutral | (![X]:((~happy(X)|~quiet(X))=>(curious(X)&tall(X))))&
((?[X]:(generous(X)))<=>((quiet(fred)<~>~old(fred))))&
(![X]:((funny(X)&tall(X))<=>(old(X)|~rich(X))))&
(((~happy(mary)&patient(mary)))=>(?[X]:(generous(X))))&
(![X]:((~funny(X)|~tall(X))<=>(creative(X)&patient(X))))&
((curious(lucy))<=>(?[X]:((calm(X)|generous(X)))))&
(![X]:((~curious(X)|~funny(X))<=>(~quiet(X)&humble(X))))&
((?[X]:(wise(X)))<=>(?[X]:(~generous(X))))&
((?[X]:((~wise(X)<~>funny(X))))=>(?[X]:((humble(X)<~>~curious(X)))))&
(![X]:(humble(X)<=>(generous(X)|brave(X))))&
(![X]:((~quiet(X)|rich(X))=>(~patient(X)|rich(X))))&
(((happy(susan)&~tall(susan)))<=>(?[X]:((~curious(X)<~>old(X)))))&
((?[X]:((~happy(X)&wise(X))))<=>((~creative(susan)<~>~old(susan))))&
(((~generous(fred)&~rich(fred)))=>(?[X]:((humble(X)<~>~kind(X)))))&
(![X]:((humble(X)&strong(X))<=>(brave(X)|~wise(X))))&
((?[X]:(~creative(X)))<=>(?[X]:((~curious(X)&~generous(X)))))&
(~old(lucy))&
(?[X]:((~curious(X)|~funny(X))))&
(?[X]:((patient(X)|humble(X))))&
(kind(john))&
(?[X]:((generous(X)|brave(X))))&
((~calm(alice)|curious(alice)))&
(?[X]:((quiet(X)<~>~happy(X)))) | strong(fred) | [] | null | 0 |
If someone is both not tall and not calm then someone is not brave or not curious.
Everyone who is not calm or rich is both quiet and patient.
Everyone who is both not wise and tall is either not wise or not calm and vice versa.
If susan is kind or not calm then someone is both wise and not generous.
Everyone who is not calm is creative and vice versa.
If paul is not creative then fred is calm and vice versa.
If someone is both not rich and humble then mary is not strong.
Everyone who is either not funny or not tall is both funny and not brave and vice versa.
Everyone who is either not old or not humble is not strong or not tall and vice versa.
If someone is either not patient or not old then someone is calm or not happy and vice versa.
If someone is both old and happy then alice is both not wise and not humble.
If someone is both not curious and brave then alice is not old or not humble.
Everyone who is not humble is generous or not tall.
Everyone who is both not generous and not humble is patient.
Someone is either patient or wise.
Someone is humble.
Someone is not calm or brave.
John is tall.
Paul is rich.
Someone is not wise or not brave. | John is curious. | neutral | ((?[X]:((~tall(X)&~calm(X))))=>(?[X]:((~brave(X)|~curious(X)))))&
(![X]:((~calm(X)|rich(X))=>(quiet(X)&patient(X))))&
(![X]:((~wise(X)&tall(X))<=>(~wise(X)<~>~calm(X))))&
(((kind(susan)|~calm(susan)))=>(?[X]:((wise(X)&~generous(X)))))&
(![X]:(~calm(X)<=>creative(X)))&
((~creative(paul))<=>(calm(fred)))&
((?[X]:((~rich(X)&humble(X))))=>(~strong(mary)))&
(![X]:((~funny(X)<~>~tall(X))<=>(funny(X)&~brave(X))))&
(![X]:((~old(X)<~>~humble(X))<=>(~strong(X)|~tall(X))))&
((?[X]:((~patient(X)<~>~old(X))))<=>(?[X]:((calm(X)|~happy(X)))))&
((?[X]:((old(X)&happy(X))))=>((~wise(alice)&~humble(alice))))&
((?[X]:((~curious(X)&brave(X))))=>((~old(alice)|~humble(alice))))&
(![X]:(~humble(X)=>(generous(X)|~tall(X))))&
(![X]:((~generous(X)&~humble(X))=>patient(X)))&
(?[X]:((patient(X)<~>wise(X))))&
(?[X]:(humble(X)))&
(?[X]:((~calm(X)|brave(X))))&
(tall(john))&
(rich(paul))&
(?[X]:((~wise(X)|~brave(X)))) | curious(john) | [] | null | 0 |
If lucy is either not old or wise then someone is either not humble or wise. If susan is either patient or brave then john is either wise or not curious and vice versa. Everyone who is not patient is both tall and patient. If fred is either not old or calm then john is creative and vice versa. If alice is either generous or not funny then someone is both old and creative and vice versa. Everyone who is both happy and not wise is not wise. If someone is tall then someone is rich and vice versa. Everyone who is patient or generous is either calm or not happy. If someone is old or not patient then paul is funny and vice versa. If mary is not funny then someone is either kind or patient. If someone is both not humble and rich then someone is both humble and creative and vice versa. If someone is both wise and not generous then lucy is not old or not creative. If john is not rich then someone is either not brave or patient. Everyone who is not old is either old or not tall. If someone is both tall and not rich then someone is either not creative or not calm and vice versa. If someone is funny then lucy is either funny or not old and vice versa. Someone is both not generous and patient. Paul is not tall. Someone is not strong or not old. Alice is not brave. John is either happy or not patient. Someone is both generous and not rich. Someone is both not brave and rich. Mary is wise or not happy. | John is calm. | entailment | (((~old(lucy)<~>wise(lucy)))=>(?[X]:((~humble(X)<~>wise(X)))))&
(((patient(susan)<~>brave(susan)))<=>((wise(john)<~>~curious(john))))&
(![X]:(~patient(X)=>(tall(X)&patient(X))))&
(((~old(fred)<~>calm(fred)))<=>(creative(john)))&
(((generous(alice)<~>~funny(alice)))<=>(?[X]:((old(X)&creative(X)))))&
(![X]:((happy(X)&~wise(X))=>~wise(X)))&
((?[X]:(tall(X)))<=>(?[X]:(rich(X))))&
(![X]:((patient(X)|generous(X))=>(calm(X)<~>~happy(X))))&
((?[X]:((old(X)|~patient(X))))<=>(funny(paul)))&
((~funny(mary))=>(?[X]:((kind(X)<~>patient(X)))))&
((?[X]:((~humble(X)&rich(X))))<=>(?[X]:((humble(X)&creative(X)))))&
((?[X]:((wise(X)&~generous(X))))=>((~old(lucy)|~creative(lucy))))&
((~rich(john))=>(?[X]:((~brave(X)<~>patient(X)))))&
(![X]:(~old(X)=>(old(X)<~>~tall(X))))&
((?[X]:((tall(X)&~rich(X))))<=>(?[X]:((~creative(X)<~>~calm(X)))))&
((?[X]:(funny(X)))<=>((funny(lucy)<~>~old(lucy))))&
(?[X]:((~generous(X)&patient(X))))&
(~tall(paul))&
(?[X]:((~strong(X)|~old(X))))&
(~brave(alice))&
((happy(john)<~>~patient(john)))&
(?[X]:((generous(X)&~rich(X))))&
(?[X]:((~brave(X)&rich(X))))&
((wise(mary)|~happy(mary))) | calm(john) | [
"p2",
"p7",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 7435801918507980270413321
% SZS output start Proof for 7435801918507980270413321
3. ! [X0] : (~patient(X0) => (patient(X0) & tall(X0))) [input p2]
8. ! [X0] : ((generous(X0) | patient(X0)) => (calm(X0) <~> ~happy(X0))) [input p7]
21. happy(john) <~> ~patient(john) [input p20]
25. ~calm(john) [input hypothesis]
31. ! [X0] : ((patient(X0) & tall(X0)) | patient(X0)) [ennf transformation 3]
34. ! [X0] : ((calm(X0) <~> ~happy(X0)) | (~generous(X0) & ~patient(X0))) [ennf transformation 8]
54. ! [X0] : (((happy(X0) | ~calm(X0)) & (~happy(X0) | calm(X0))) | (~generous(X0) & ~patient(X0))) [nnf transformation 34]
82. (patient(john) | ~happy(john)) & (~patient(john) | happy(john)) [nnf transformation 21]
100. patient(X0) | patient(X0) [cnf transformation 31]
114. ~happy(X0) | calm(X0) | ~patient(X0) [cnf transformation 54]
146. ~patient(john) | happy(john) [cnf transformation 82]
153. ~calm(john) [cnf transformation 25]
155. patient(X0) [duplicate literal removal 100]
258. ~happy(X0) | calm(X0) [subsumption resolution 114,155]
373. happy(john) [subsumption resolution 146,155]
391. calm(john) [resolution 258,373]
392. $false [subsumption resolution 391,153]
% SZS output end Proof for 7435801918507980270413321
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either brave or not brave is both not quiet and brave.
Everyone who is happy or rich is not happy.
Everyone who is not happy is not patient or not humble.
If someone is either not rich or calm then lucy is creative or not tall and vice versa.
Everyone who is generous or happy is not quiet and vice versa.
Everyone who is both not creative and calm is brave or not funny and vice versa.
If mary is both not strong and curious then fred is kind.
Everyone who is funny is both humble and patient.
Everyone who is not kind is funny.
Everyone who is kind is either not calm or brave and vice versa.
If someone is either quiet or kind then mary is either rich or not generous.
Everyone who is either curious or not funny is either creative or not calm and vice versa.
If someone is either not calm or not strong then someone is not happy and vice versa.
If someone is either not patient or not creative then lucy is not humble and vice versa.
Everyone who is either happy or strong is humble or old.
Everyone who is not kind or not old is either not kind or not wise.
Someone is not creative or happy.
Mary is both not strong and not quiet.
Someone is old or not brave.
Alice is either tall or not tall.
Mary is either tall or wise.
John is both humble and rich. | Mary is brave. | entailment | (![X]:((brave(X)<~>~brave(X))=>(~quiet(X)&brave(X))))&
(![X]:((happy(X)|rich(X))=>~happy(X)))&
(![X]:(~happy(X)=>(~patient(X)|~humble(X))))&
((?[X]:((~rich(X)<~>calm(X))))<=>((creative(lucy)|~tall(lucy))))&
(![X]:((generous(X)|happy(X))<=>~quiet(X)))&
(![X]:((~creative(X)&calm(X))<=>(brave(X)|~funny(X))))&
(((~strong(mary)&curious(mary)))=>(kind(fred)))&
(![X]:(funny(X)=>(humble(X)&patient(X))))&
(![X]:(~kind(X)=>funny(X)))&
(![X]:(kind(X)<=>(~calm(X)<~>brave(X))))&
((?[X]:((quiet(X)<~>kind(X))))=>((rich(mary)<~>~generous(mary))))&
(![X]:((curious(X)<~>~funny(X))<=>(creative(X)<~>~calm(X))))&
((?[X]:((~calm(X)<~>~strong(X))))<=>(?[X]:(~happy(X))))&
((?[X]:((~patient(X)<~>~creative(X))))<=>(~humble(lucy)))&
(![X]:((happy(X)<~>strong(X))=>(humble(X)|old(X))))&
(![X]:((~kind(X)|~old(X))=>(~kind(X)<~>~wise(X))))&
(?[X]:((~creative(X)|happy(X))))&
((~strong(mary)&~quiet(mary)))&
(?[X]:((old(X)|~brave(X))))&
((tall(alice)<~>~tall(alice)))&
((tall(mary)<~>wise(mary)))&
((humble(john)&rich(john))) | brave(mary) | [
"p0",
"hypothesis"
] | % SZS status Unsatisfiable for 5037558146507945891456935
% SZS output start Proof for 5037558146507945891456935
1. ! [X0] : ((brave(X0) <~> ~brave(X0)) => (brave(X0) & ~quiet(X0))) [input p0]
23. ~brave(mary) [input hypothesis]
28. ! [X0] : ((brave(X0) & ~quiet(X0)) | (brave(X0) <=> ~brave(X0))) [ennf transformation 1]
38. ! [X0] : ((brave(X0) & ~quiet(X0)) | ((brave(X0) | brave(X0)) & (~brave(X0) | ~brave(X0)))) [nnf transformation 28]
68. brave(X0) | brave(X0) | brave(X0) [cnf transformation 38]
125. ~brave(mary) [cnf transformation 23]
131. brave(X0) [duplicate literal removal 68]
216. $false [subsumption resolution 125,131]
% SZS output end Proof for 5037558146507945891456935
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet is not creative.
Everyone who is either not creative or kind is not happy or not patient and vice versa.
If mary is not quiet then someone is both not creative and creative and vice versa.
Everyone who is creative or not funny is both strong and wise.
If susan is tall or generous then someone is quiet.
Everyone who is both funny and not brave is patient.
If paul is either humble or not calm then someone is patient or not happy and vice versa.
Everyone who is strong or patient is both rich and funny and vice versa.
Everyone who is either not patient or tall is kind or not funny.
Everyone who is patient is both tall and not tall.
Everyone who is either not quiet or creative is both not happy and not quiet.
Everyone who is either not strong or not brave is not curious or tall.
Everyone who is not brave is either happy or not generous and vice versa.
Everyone who is not quiet is both not creative and not curious.
If someone is either not creative or humble then lucy is both not generous and not quiet.
If someone is rich then someone is both calm and not happy.
Someone is either quiet or strong.
Someone is curious.
Paul is rich or not wise.
Someone is creative or not kind.
Lucy is patient or not curious.
Someone is both not calm and rich.
Someone is rich or not creative.
Someone is either not curious or creative. | Mary is not strong. | neutral | (![X]:((~brave(X)<~>quiet(X))=>~creative(X)))&
(![X]:((~creative(X)<~>kind(X))<=>(~happy(X)|~patient(X))))&
((~quiet(mary))<=>(?[X]:((~creative(X)&creative(X)))))&
(![X]:((creative(X)|~funny(X))=>(strong(X)&wise(X))))&
(((tall(susan)|generous(susan)))=>(?[X]:(quiet(X))))&
(![X]:((funny(X)&~brave(X))=>patient(X)))&
(((humble(paul)<~>~calm(paul)))<=>(?[X]:((patient(X)|~happy(X)))))&
(![X]:((strong(X)|patient(X))<=>(rich(X)&funny(X))))&
(![X]:((~patient(X)<~>tall(X))=>(kind(X)|~funny(X))))&
(![X]:(patient(X)=>(tall(X)&~tall(X))))&
(![X]:((~quiet(X)<~>creative(X))=>(~happy(X)&~quiet(X))))&
(![X]:((~strong(X)<~>~brave(X))=>(~curious(X)|tall(X))))&
(![X]:(~brave(X)<=>(happy(X)<~>~generous(X))))&
(![X]:(~quiet(X)=>(~creative(X)&~curious(X))))&
((?[X]:((~creative(X)<~>humble(X))))=>((~generous(lucy)&~quiet(lucy))))&
((?[X]:(rich(X)))=>(?[X]:((calm(X)&~happy(X)))))&
(?[X]:((quiet(X)<~>strong(X))))&
(?[X]:(curious(X)))&
((rich(paul)|~wise(paul)))&
(?[X]:((creative(X)|~kind(X))))&
((patient(lucy)|~curious(lucy)))&
(?[X]:((~calm(X)&rich(X))))&
(?[X]:((rich(X)|~creative(X))))&
(?[X]:((~curious(X)<~>creative(X)))) | ~strong(mary) | [] | null | 0 |
If fred is both not generous and humble then john is happy or tall and vice versa.
Everyone who is kind or not happy is either not quiet or kind.
Everyone who is either funny or humble is not humble or not wise and vice versa.
Everyone who is not quiet is not generous or funny.
If mary is either generous or strong then someone is both not brave and not patient and vice versa.
Everyone who is either not brave or calm is either humble or not generous and vice versa.
Everyone who is both not happy and not humble is patient and vice versa.
If someone is either old or patient then paul is not generous and vice versa.
Everyone who is both not funny and brave is not curious or old and vice versa.
Everyone who is not humble is creative and vice versa.
Everyone who is creative is curious or humble.
If someone is happy or old then john is not creative.
Everyone who is either not happy or curious is either happy or not kind.
If someone is both not curious and not old then fred is either strong or not generous.
Everyone who is either not happy or not generous is happy or not rich.
Everyone who is both brave and not kind is not wise.
Someone is both funny and rich.
Fred is creative or happy.
Paul is not brave.
Lucy is old.
Someone is humble.
Someone is both not patient and strong.
Someone is not brave or not quiet.
Fred is either creative or strong. | Paul is not curious. | contradiction | (((~generous(fred)&humble(fred)))<=>((happy(john)|tall(john))))&
(![X]:((kind(X)|~happy(X))=>(~quiet(X)<~>kind(X))))&
(![X]:((funny(X)<~>humble(X))<=>(~humble(X)|~wise(X))))&
(![X]:(~quiet(X)=>(~generous(X)|funny(X))))&
(((generous(mary)<~>strong(mary)))<=>(?[X]:((~brave(X)&~patient(X)))))&
(![X]:((~brave(X)<~>calm(X))<=>(humble(X)<~>~generous(X))))&
(![X]:((~happy(X)&~humble(X))<=>patient(X)))&
((?[X]:((old(X)<~>patient(X))))<=>(~generous(paul)))&
(![X]:((~funny(X)&brave(X))<=>(~curious(X)|old(X))))&
(![X]:(~humble(X)<=>creative(X)))&
(![X]:(creative(X)=>(curious(X)|humble(X))))&
((?[X]:((happy(X)|old(X))))=>(~creative(john)))&
(![X]:((~happy(X)<~>curious(X))=>(happy(X)<~>~kind(X))))&
((?[X]:((~curious(X)&~old(X))))=>((strong(fred)<~>~generous(fred))))&
(![X]:((~happy(X)<~>~generous(X))=>(happy(X)|~rich(X))))&
(![X]:((brave(X)&~kind(X))=>~wise(X)))&
(?[X]:((funny(X)&rich(X))))&
((creative(fred)|happy(fred)))&
(~brave(paul))&
(old(lucy))&
(?[X]:(humble(X)))&
(?[X]:((~patient(X)&strong(X))))&
(?[X]:((~brave(X)|~quiet(X))))&
((creative(fred)<~>strong(fred))) | ~curious(paul) | [
"p8",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 6801363915594762119350321
% SZS output start Proof for 6801363915594762119350321
9. ! [X0] : ((brave(X0) & ~funny(X0)) <=> (old(X0) | ~curious(X0))) [input p8]
19. ~brave(paul) [input p18]
25. ~curious(paul) [input hypothesis]
54. ! [X0] : (((brave(X0) & ~funny(X0)) | (~old(X0) & curious(X0))) & ((old(X0) | ~curious(X0)) | (~brave(X0) | funny(X0)))) [nnf transformation 9]
55. ! [X0] : (((brave(X0) & ~funny(X0)) | (~old(X0) & curious(X0))) & (old(X0) | ~curious(X0) | ~brave(X0) | funny(X0))) [flattening 54]
109. curious(X0) | brave(X0) [cnf transformation 55]
128. ~brave(paul) [cnf transformation 19]
136. ~curious(paul) [cnf transformation 25]
257. brave(paul) [resolution 109,136]
258. $false [subsumption resolution 257,128]
% SZS output end Proof for 6801363915594762119350321
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not curious or funny is both old and not creative.
Everyone who is both old and patient is both not old and not strong.
Everyone who is not strong or not happy is both not happy and kind.
Everyone who is not kind or generous is calm and vice versa.
If john is both not quiet and tall then someone is tall or humble and vice versa.
Everyone who is curious or quiet is both funny and rich.
Everyone who is not patient is both not old and funny and vice versa.
Everyone who is not curious or calm is both not humble and kind and vice versa.
If john is humble then alice is either not rich or not quiet.
If john is both creative and funny then susan is either not quiet or brave and vice versa.
If mary is kind then paul is creative or curious and vice versa.
Everyone who is both not generous and not kind is both not happy and not creative.
If fred is both old and not humble then someone is either old or not tall and vice versa.
Everyone who is quiet is both humble and not creative and vice versa.
If paul is not creative or not strong then someone is strong and vice versa.
Everyone who is quiet is kind.
Someone is brave or strong.
Alice is wise.
Someone is not strong or not rich.
Someone is happy or not kind.
Mary is rich. | Paul is kind. | entailment | (![X]:((~curious(X)<~>funny(X))=>(old(X)&~creative(X))))&
(![X]:((old(X)&patient(X))=>(~old(X)&~strong(X))))&
(![X]:((~strong(X)|~happy(X))=>(~happy(X)&kind(X))))&
(![X]:((~kind(X)|generous(X))<=>calm(X)))&
(((~quiet(john)&tall(john)))<=>(?[X]:((tall(X)|humble(X)))))&
(![X]:((curious(X)|quiet(X))=>(funny(X)&rich(X))))&
(![X]:(~patient(X)<=>(~old(X)&funny(X))))&
(![X]:((~curious(X)|calm(X))<=>(~humble(X)&kind(X))))&
((humble(john))=>((~rich(alice)<~>~quiet(alice))))&
(((creative(john)&funny(john)))<=>((~quiet(susan)<~>brave(susan))))&
((kind(mary))<=>((creative(paul)|curious(paul))))&
(![X]:((~generous(X)&~kind(X))=>(~happy(X)&~creative(X))))&
(((old(fred)&~humble(fred)))<=>(?[X]:((old(X)<~>~tall(X)))))&
(![X]:(quiet(X)<=>(humble(X)&~creative(X))))&
(((~creative(paul)|~strong(paul)))<=>(?[X]:(strong(X))))&
(![X]:(quiet(X)=>kind(X)))&
(?[X]:((brave(X)|strong(X))))&
(wise(alice))&
(?[X]:((~strong(X)|~rich(X))))&
(?[X]:((happy(X)|~kind(X))))&
(rich(mary)) | kind(paul) | [
"p3",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 269918579429652326387541
% SZS output start Proof for 269918579429652326387541
4. ! [X0] : ((generous(X0) | ~kind(X0)) <=> calm(X0)) [input p3]
8. ! [X0] : ((calm(X0) | ~curious(X0)) <=> (kind(X0) & ~humble(X0))) [input p7]
22. ~kind(paul) [input hypothesis]
36. ! [X0] : (((generous(X0) | ~kind(X0)) | ~calm(X0)) & (calm(X0) | (~generous(X0) & kind(X0)))) [nnf transformation 4]
37. ! [X0] : ((generous(X0) | ~kind(X0) | ~calm(X0)) & (calm(X0) | (~generous(X0) & kind(X0)))) [flattening 36]
43. ! [X0] : (((calm(X0) | ~curious(X0)) | (~kind(X0) | humble(X0))) & ((kind(X0) & ~humble(X0)) | (~calm(X0) & curious(X0)))) [nnf transformation 8]
44. ! [X0] : ((calm(X0) | ~curious(X0) | ~kind(X0) | humble(X0)) & ((kind(X0) & ~humble(X0)) | (~calm(X0) & curious(X0)))) [flattening 43]
78. calm(X0) | kind(X0) [cnf transformation 37]
95. kind(X0) | ~calm(X0) [cnf transformation 44]
127. ~kind(paul) [cnf transformation 22]
158. kind(X0) [subsumption resolution 95,78]
252. $false [subsumption resolution 127,158]
% SZS output end Proof for 269918579429652326387541
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either calm or not funny is not curious and vice versa.
Everyone who is both generous and curious is funny and vice versa.
Everyone who is both not quiet and not happy is not old.
If someone is not strong or not tall then someone is curious or not quiet and vice versa.
If mary is curious then alice is not funny or not calm and vice versa.
Everyone who is not patient is not calm.
Everyone who is either rich or not strong is either patient or not wise.
If susan is both brave and not brave then alice is both not humble and not happy.
If susan is either curious or patient then alice is either not wise or generous.
Everyone who is either not patient or happy is either patient or not patient and vice versa.
If someone is both patient and generous then someone is both brave and not generous.
If someone is either not tall or curious then alice is either not curious or old and vice versa.
Everyone who is both not wise and not humble is creative or not kind and vice versa.
Everyone who is curious is not generous or not curious.
Everyone who is not rich or not brave is both funny and not happy.
If someone is both wise and quiet then fred is both not funny and not humble and vice versa.
Mary is either not generous or not patient.
Mary is both patient and not wise.
Someone is either calm or not strong.
Mary is either patient or not old.
Susan is either not patient or not old.
Alice is either not brave or strong.
Paul is humble.
Susan is both not funny and not humble. | Mary is not funny. | entailment | (![X]:((calm(X)<~>~funny(X))<=>~curious(X)))&
(![X]:((generous(X)&curious(X))<=>funny(X)))&
(![X]:((~quiet(X)&~happy(X))=>~old(X)))&
((?[X]:((~strong(X)|~tall(X))))<=>(?[X]:((curious(X)|~quiet(X)))))&
((curious(mary))<=>((~funny(alice)|~calm(alice))))&
(![X]:(~patient(X)=>~calm(X)))&
(![X]:((rich(X)<~>~strong(X))=>(patient(X)<~>~wise(X))))&
(((brave(susan)&~brave(susan)))=>((~humble(alice)&~happy(alice))))&
(((curious(susan)<~>patient(susan)))=>((~wise(alice)<~>generous(alice))))&
(![X]:((~patient(X)<~>happy(X))<=>(patient(X)<~>~patient(X))))&
((?[X]:((patient(X)&generous(X))))=>(?[X]:((brave(X)&~generous(X)))))&
((?[X]:((~tall(X)<~>curious(X))))<=>((~curious(alice)<~>old(alice))))&
(![X]:((~wise(X)&~humble(X))<=>(creative(X)|~kind(X))))&
(![X]:(curious(X)=>(~generous(X)|~curious(X))))&
(![X]:((~rich(X)|~brave(X))=>(funny(X)&~happy(X))))&
((?[X]:((wise(X)&quiet(X))))<=>((~funny(fred)&~humble(fred))))&
((~generous(mary)<~>~patient(mary)))&
((patient(mary)&~wise(mary)))&
(?[X]:((calm(X)<~>~strong(X))))&
((patient(mary)<~>~old(mary)))&
((~patient(susan)<~>~old(susan)))&
((~brave(alice)<~>strong(alice)))&
(humble(paul))&
((~funny(susan)&~humble(susan))) | ~funny(mary) | [
"p1",
"p16",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 4586974148701265616830575
% SZS output start Proof for 4586974148701265616830575
2. ! [X0] : ((curious(X0) & generous(X0)) <=> funny(X0)) [input p1]
17. ~generous(mary) <~> ~patient(mary) [input p16]
18. ~wise(mary) & patient(mary) [input p17]
25. funny(mary) [input hypothesis]
40. ! [X0] : (((curious(X0) & generous(X0)) | ~funny(X0)) & (funny(X0) | (~curious(X0) | ~generous(X0)))) [nnf transformation 2]
41. ! [X0] : (((curious(X0) & generous(X0)) | ~funny(X0)) & (funny(X0) | ~curious(X0) | ~generous(X0))) [flattening 40]
66. (patient(mary) | generous(mary)) & (~patient(mary) | ~generous(mary)) [nnf transformation 17]
78. ~funny(X0) | generous(X0) [cnf transformation 41]
131. ~patient(mary) | ~generous(mary) [cnf transformation 66]
133. patient(mary) [cnf transformation 18]
146. funny(mary) [cnf transformation 25]
290. 30 <=> generous(mary) [avatar definition]
291. ~generous(mary) <- (~30) [avatar component clause 290]
294. 31 <=> patient(mary) [avatar definition]
298. ~30 | ~31 [avatar split clause 131,294,290]
299. 31 [avatar split clause 133,294]
332. generous(mary) [resolution 78,146]
333. $false <- (~30) [subsumption resolution 332,291]
334. 30 [avatar contradiction clause 333]
335. $false [avatar sat refutation 298,299,334]
% SZS output end Proof for 4586974148701265616830575
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is patient or not curious is curious and vice versa.
Everyone who is not generous is both not wise and patient.
If someone is either quiet or not brave then john is either tall or not calm and vice versa.
Everyone who is both not humble and strong is not strong and vice versa.
Everyone who is both not brave and not quiet is quiet or not creative.
Everyone who is not wise or quiet is not creative and vice versa.
Everyone who is both quiet and old is not brave.
If someone is either quiet or not strong then mary is humble.
If fred is not humble then someone is either not curious or not funny and vice versa.
If someone is either old or creative then paul is happy and vice versa.
If john is not generous or not strong then someone is both brave and not creative and vice versa.
Everyone who is either not generous or generous is rich or generous and vice versa.
Everyone who is not calm is funny or not old.
Everyone who is brave is not curious and vice versa.
If someone is quiet or not strong then someone is either happy or not rich.
Everyone who is both not calm and tall is wise or not funny and vice versa.
Someone is both curious and happy.
Alice is both not calm and quiet.
Alice is either old or not strong.
Someone is not generous.
Alice is wise or not strong.
Someone is tall or humble.
Mary is either strong or not humble. | Alice is brave. | contradiction | (![X]:((patient(X)|~curious(X))<=>curious(X)))&
(![X]:(~generous(X)=>(~wise(X)&patient(X))))&
((?[X]:((quiet(X)<~>~brave(X))))<=>((tall(john)<~>~calm(john))))&
(![X]:((~humble(X)&strong(X))<=>~strong(X)))&
(![X]:((~brave(X)&~quiet(X))=>(quiet(X)|~creative(X))))&
(![X]:((~wise(X)|quiet(X))<=>~creative(X)))&
(![X]:((quiet(X)&old(X))=>~brave(X)))&
((?[X]:((quiet(X)<~>~strong(X))))=>(humble(mary)))&
((~humble(fred))<=>(?[X]:((~curious(X)<~>~funny(X)))))&
((?[X]:((old(X)<~>creative(X))))<=>(happy(paul)))&
(((~generous(john)|~strong(john)))<=>(?[X]:((brave(X)&~creative(X)))))&
(![X]:((~generous(X)<~>generous(X))<=>(rich(X)|generous(X))))&
(![X]:(~calm(X)=>(funny(X)|~old(X))))&
(![X]:(brave(X)<=>~curious(X)))&
((?[X]:((quiet(X)|~strong(X))))=>(?[X]:((happy(X)<~>~rich(X)))))&
(![X]:((~calm(X)&tall(X))<=>(wise(X)|~funny(X))))&
(?[X]:((curious(X)&happy(X))))&
((~calm(alice)&quiet(alice)))&
((old(alice)<~>~strong(alice)))&
(?[X]:(~generous(X)))&
((wise(alice)|~strong(alice)))&
(?[X]:((tall(X)|humble(X))))&
((strong(mary)<~>~humble(mary))) | brave(alice) | [
"p0",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 2413795401375040390288644
% SZS output start Proof for 2413795401375040390288644
1. ! [X0] : ((~curious(X0) | patient(X0)) <=> curious(X0)) [input p0]
14. ! [X0] : (brave(X0) <=> ~curious(X0)) [input p13]
24. brave(alice) [input hypothesis]
35. ! [X0] : (((~curious(X0) | patient(X0)) | ~curious(X0)) & (curious(X0) | (curious(X0) & ~patient(X0)))) [nnf transformation 1]
36. ! [X0] : ((~curious(X0) | patient(X0) | ~curious(X0)) & (curious(X0) | (curious(X0) & ~patient(X0)))) [flattening 35]
61. ! [X0] : ((brave(X0) | curious(X0)) & (~curious(X0) | ~brave(X0))) [nnf transformation 14]
77. curious(X0) | curious(X0) [cnf transformation 36]
119. ~curious(X0) | ~brave(X0) [cnf transformation 61]
141. brave(alice) [cnf transformation 24]
149. curious(X0) [duplicate literal removal 77]
225. ~brave(X0) [subsumption resolution 119,149]
242. $false [subsumption resolution 141,225]
% SZS output end Proof for 2413795401375040390288644
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm is both patient and humble.
Everyone who is both brave and old is either humble or not curious and vice versa.
Everyone who is either old or generous is not brave.
Everyone who is brave is either not curious or tall.
If someone is either not old or not rich then someone is either not brave or not curious.
If someone is either not humble or not strong then lucy is either curious or rich and vice versa.
If someone is not rich then paul is either not funny or not generous.
If someone is not generous or not happy then mary is both not kind and not happy.
Everyone who is either brave or not happy is either not generous or not strong.
Everyone who is both not old and not patient is not wise or quiet.
Everyone who is either humble or not funny is both not generous and rich and vice versa.
If someone is both quiet and generous then someone is either curious or not tall.
Everyone who is either not humble or not brave is funny.
Everyone who is both happy and tall is not tall or wise and vice versa.
If john is quiet or creative then paul is both quiet and not humble.
If lucy is wise then john is not curious and vice versa.
Fred is either not old or humble.
Lucy is both tall and not curious.
John is both not kind and happy.
Fred is either calm or not funny.
Someone is not happy or strong.
Lucy is either tall or not happy.
Someone is either funny or kind.
Paul is either tall or not quiet. | Mary is wise. | contradiction | (![X]:(~calm(X)=>(patient(X)&humble(X))))&
(![X]:((brave(X)&old(X))<=>(humble(X)<~>~curious(X))))&
(![X]:((old(X)<~>generous(X))=>~brave(X)))&
(![X]:(brave(X)=>(~curious(X)<~>tall(X))))&
((?[X]:((~old(X)<~>~rich(X))))=>(?[X]:((~brave(X)<~>~curious(X)))))&
((?[X]:((~humble(X)<~>~strong(X))))<=>((curious(lucy)<~>rich(lucy))))&
((?[X]:(~rich(X)))=>((~funny(paul)<~>~generous(paul))))&
((?[X]:((~generous(X)|~happy(X))))=>((~kind(mary)&~happy(mary))))&
(![X]:((brave(X)<~>~happy(X))=>(~generous(X)<~>~strong(X))))&
(![X]:((~old(X)&~patient(X))=>(~wise(X)|quiet(X))))&
(![X]:((humble(X)<~>~funny(X))<=>(~generous(X)&rich(X))))&
((?[X]:((quiet(X)&generous(X))))=>(?[X]:((curious(X)<~>~tall(X)))))&
(![X]:((~humble(X)<~>~brave(X))=>funny(X)))&
(![X]:((happy(X)&tall(X))<=>(~tall(X)|wise(X))))&
(((quiet(john)|creative(john)))=>((quiet(paul)&~humble(paul))))&
((wise(lucy))<=>(~curious(john)))&
((~old(fred)<~>humble(fred)))&
((tall(lucy)&~curious(lucy)))&
((~kind(john)&happy(john)))&
((calm(fred)<~>~funny(fred)))&
(?[X]:((~happy(X)|strong(X))))&
((tall(lucy)<~>~happy(lucy)))&
(?[X]:((funny(X)<~>kind(X))))&
((tall(paul)<~>~quiet(paul))) | wise(mary) | [
"p1",
"p3",
"p7",
"p10",
"p12",
"p13",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 5780740201988735466704773
% SZS output start Proof for 5780740201988735466704773
2. ! [X0] : ((old(X0) & brave(X0)) <=> (humble(X0) <~> ~curious(X0))) [input p1]
4. ! [X0] : (brave(X0) => (~curious(X0) <~> tall(X0))) [input p3]
8. ? [X0] : (~happy(X0) | ~generous(X0)) => (~happy(mary) & ~kind(mary)) [input p7]
11. ! [X0] : ((humble(X0) <~> ~funny(X0)) <=> (rich(X0) & ~generous(X0))) [input p10]
13. ! [X0] : ((~humble(X0) <~> ~brave(X0)) => funny(X0)) [input p12]
14. ! [X0] : ((tall(X0) & happy(X0)) <=> (wise(X0) | ~tall(X0))) [input p13]
18. ~curious(lucy) & tall(lucy) [input p17]
25. wise(mary) [input hypothesis]
33. ! [X0] : ((~curious(X0) <~> tall(X0)) | ~brave(X0)) [ennf transformation 4]
36. (~happy(mary) & ~kind(mary)) | ! [X0] : (happy(X0) & generous(X0)) [ennf transformation 8]
39. ! [X0] : (funny(X0) | (~humble(X0) <=> ~brave(X0))) [ennf transformation 13]
41. ! [X0] : (((old(X0) & brave(X0)) | ((humble(X0) | curious(X0)) & (~curious(X0) | ~humble(X0)))) & (((curious(X0) | ~humble(X0)) & (~curious(X0) | humble(X0))) | (~old(X0) | ~brave(X0)))) [nnf transformation 2]
42. ! [X0] : (((old(X0) & brave(X0)) | ((humble(X0) | curious(X0)) & (~curious(X0) | ~humble(X0)))) & (((curious(X0) | ~humble(X0)) & (~curious(X0) | humble(X0))) | ~old(X0) | ~brave(X0))) [flattening 41]
44. ! [X0] : (((~tall(X0) | curious(X0)) & (tall(X0) | ~curious(X0))) | ~brave(X0)) [nnf transformation 33]
55. ! [X0] : ((((funny(X0) | ~humble(X0)) & (~funny(X0) | humble(X0))) | (~rich(X0) | generous(X0))) & ((rich(X0) & ~generous(X0)) | ((humble(X0) | funny(X0)) & (~funny(X0) | ~humble(X0))))) [nnf transformation 11]
56. ! [X0] : ((((funny(X0) | ~humble(X0)) & (~funny(X0) | humble(X0))) | ~rich(X0) | generous(X0)) & ((rich(X0) & ~generous(X0)) | ((humble(X0) | funny(X0)) & (~funny(X0) | ~humble(X0))))) [flattening 55]
61. ! [X0] : (funny(X0) | ((~humble(X0) | brave(X0)) & (~brave(X0) | humble(X0)))) [nnf transformation 39]
62. ! [X0] : (((tall(X0) & happy(X0)) | (~wise(X0) & tall(X0))) & ((wise(X0) | ~tall(X0)) | (~tall(X0) | ~happy(X0)))) [nnf transformation 14]
63. ! [X0] : (((tall(X0) & happy(X0)) | (~wise(X0) & tall(X0))) & (wise(X0) | ~tall(X0) | ~tall(X0) | ~happy(X0))) [flattening 62]
78. curious(X0) | humble(X0) | brave(X0) [cnf transformation 42]
84. ~tall(X0) | curious(X0) | ~brave(X0) [cnf transformation 44]
101. ~happy(mary) | generous(X0) [cnf transformation 36]
107. ~funny(X0) | ~generous(X0) | ~humble(X0) [cnf transformation 56]
116. ~humble(X0) | funny(X0) | brave(X0) [cnf transformation 61]
119. ~wise(X0) | happy(X0) [cnf transformation 63]
120. tall(X0) | tall(X0) [cnf transformation 63]
129. ~curious(lucy) [cnf transformation 18]
141. wise(mary) [cnf transformation 25]
143. tall(X0) [duplicate literal removal 120]
167. 6 <=> curious(lucy) [avatar definition]
168. ~curious(lucy) <- (~6) [avatar component clause 167]
209. 15 <=> happy(mary) [avatar definition]
214. 16 <=> ! [X0] : generous(X0) [avatar definition]
215. generous(X0) <- (16) [avatar component clause 214]
216. 16 | ~15 [avatar split clause 101,209,214]
271. ~6 [avatar split clause 129,167]
309. happy(mary) [resolution 119,141]
312. 15 [avatar split clause 309,209]
349. humble(lucy) | brave(lucy) <- (~6) [resolution 78,168]
354. 38 <=> brave(lucy) [avatar definition]
355. ~brave(lucy) <- (~38) [avatar component clause 354]
356. brave(lucy) <- (38) [avatar component clause 354]
358. 39 <=> humble(lucy) [avatar definition]
360. humble(lucy) <- (39) [avatar component clause 358]
361. 38 | 39 | 6 [avatar split clause 349,167,358,354]
400. ~brave(X0) | curious(X0) [resolution 84,143]
413. funny(lucy) | brave(lucy) <- (39) [resolution 116,360]
417. funny(lucy) <- (~38, 39) [subsumption resolution 413,355]
464. ~generous(lucy) | ~humble(lucy) <- (~38, 39) [resolution 417,107]
465. ~humble(lucy) <- (16, ~38, 39) [subsumption resolution 464,215]
466. $false <- (16, ~38, 39) [subsumption resolution 465,360]
467. ~16 | 38 | ~39 [avatar contradiction clause 466]
477. curious(lucy) <- (38) [resolution 356,400]
480. $false <- (~6, 38) [subsumption resolution 477,168]
481. 6 | ~38 [avatar contradiction clause 480]
482. $false [avatar sat refutation 216,271,312,361,467,481]
% SZS output end Proof for 5780740201988735466704773
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not rich and patient is either kind or not old. Everyone who is both not quiet and not humble is not humble or not curious. If someone is both old and not quiet then paul is both not quiet and not generous. Everyone who is brave is both not old and wise. Everyone who is either happy or quiet is not wise and vice versa. If paul is both calm and not curious then someone is both not kind and not wise and vice versa. Everyone who is funny or not brave is either not brave or kind and vice versa. Everyone who is either not rich or humble is either strong or funny and vice versa. If alice is not wise or creative then alice is either kind or brave and vice versa. If someone is both patient and not calm then paul is creative or not strong. Everyone who is both curious and wise is kind or strong and vice versa. Everyone who is not calm or calm is not quiet and vice versa. If someone is both funny and not kind then someone is either not generous or tall and vice versa. If someone is funny then mary is not old and vice versa. Everyone who is not humble is not funny and vice versa. If someone is either not curious or quiet then someone is not strong. Alice is creative or not tall. Someone is both not curious and not humble. Someone is either not happy or not wise. Someone is either curious or tall. Someone is not old or not humble. Lucy is both wise and not brave. Someone is not strong. | Lucy is not quiet. | entailment | (![X]:((~rich(X)&patient(X))=>(kind(X)<~>~old(X))))&
(![X]:((~quiet(X)&~humble(X))=>(~humble(X)|~curious(X))))&
((?[X]:((old(X)&~quiet(X))))=>((~quiet(paul)&~generous(paul))))&
(![X]:(brave(X)=>(~old(X)&wise(X))))&
(![X]:((happy(X)<~>quiet(X))<=>~wise(X)))&
(((calm(paul)&~curious(paul)))<=>(?[X]:((~kind(X)&~wise(X)))))&
(![X]:((funny(X)|~brave(X))<=>(~brave(X)<~>kind(X))))&
(![X]:((~rich(X)<~>humble(X))<=>(strong(X)<~>funny(X))))&
(((~wise(alice)|creative(alice)))<=>((kind(alice)<~>brave(alice))))&
((?[X]:((patient(X)&~calm(X))))=>((creative(paul)|~strong(paul))))&
(![X]:((curious(X)&wise(X))<=>(kind(X)|strong(X))))&
(![X]:((~calm(X)|calm(X))<=>~quiet(X)))&
((?[X]:((funny(X)&~kind(X))))<=>(?[X]:((~generous(X)<~>tall(X)))))&
((?[X]:(funny(X)))<=>(~old(mary)))&
(![X]:(~humble(X)<=>~funny(X)))&
((?[X]:((~curious(X)<~>quiet(X))))=>(?[X]:(~strong(X))))&
((creative(alice)|~tall(alice)))&
(?[X]:((~curious(X)&~humble(X))))&
(?[X]:((~happy(X)<~>~wise(X))))&
(?[X]:((curious(X)<~>tall(X))))&
(?[X]:((~old(X)|~humble(X))))&
((wise(lucy)&~brave(lucy)))&
(?[X]:(~strong(X))) | ~quiet(lucy) | [
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 146119490018187412047362
% SZS output start Proof for 146119490018187412047362
12. ! [X0] : ((calm(X0) | ~calm(X0)) <=> ~quiet(X0)) [input p11]
24. quiet(lucy) [input hypothesis]
47. ! [X0] : (((calm(X0) | ~calm(X0)) | quiet(X0)) & (~quiet(X0) | (~calm(X0) & calm(X0)))) [nnf transformation 12]
48. ! [X0] : ((calm(X0) | ~calm(X0) | quiet(X0)) & (~quiet(X0) | (~calm(X0) & calm(X0)))) [flattening 47]
113. ~quiet(X0) | calm(X0) [cnf transformation 48]
114. ~quiet(X0) | ~calm(X0) [cnf transformation 48]
139. quiet(lucy) [cnf transformation 24]
202. ~quiet(X0) [subsumption resolution 113,114]
290. $false [subsumption resolution 139,202]
% SZS output end Proof for 146119490018187412047362
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is brave or generous is both strong and patient. Everyone who is both tall and not creative is either not strong or wise. Everyone who is brave is quiet and vice versa. Everyone who is humble is not wise. If paul is either tall or curious then paul is not strong and vice versa. If alice is either humble or not kind then alice is not patient. If someone is either curious or happy then mary is both not strong and kind. Everyone who is either funny or wise is not rich. Everyone who is tall is either wise or not funny and vice versa. Everyone who is both brave and kind is both not curious and wise. If someone is either rich or not wise then someone is wise and vice versa. If john is not creative or not generous then someone is either wise or old and vice versa. If someone is either kind or curious then lucy is either wise or not rich and vice versa. Everyone who is not happy or humble is both not strong and not wise and vice versa. Everyone who is either brave or creative is either not rich or rich and vice versa. Everyone who is humble is either not wise or not curious and vice versa. John is humble. Lucy is not calm or humble. Someone is both not rich and tall. Lucy is either creative or generous. John is either not funny or not strong. Mary is both rich and not calm. Someone is not happy. | Paul is not calm. | neutral | (![X]:((brave(X)|generous(X))=>(strong(X)&patient(X))))&
(![X]:((tall(X)&~creative(X))=>(~strong(X)<~>wise(X))))&
(![X]:(brave(X)<=>quiet(X)))&
(![X]:(humble(X)=>~wise(X)))&
(((tall(paul)<~>curious(paul)))<=>(~strong(paul)))&
(((humble(alice)<~>~kind(alice)))=>(~patient(alice)))&
((?[X]:((curious(X)<~>happy(X))))=>((~strong(mary)&kind(mary))))&
(![X]:((funny(X)<~>wise(X))=>~rich(X)))&
(![X]:(tall(X)<=>(wise(X)<~>~funny(X))))&
(![X]:((brave(X)&kind(X))=>(~curious(X)&wise(X))))&
((?[X]:((rich(X)<~>~wise(X))))<=>(?[X]:(wise(X))))&
(((~creative(john)|~generous(john)))<=>(?[X]:((wise(X)<~>old(X)))))&
((?[X]:((kind(X)<~>curious(X))))<=>((wise(lucy)<~>~rich(lucy))))&
(![X]:((~happy(X)|humble(X))<=>(~strong(X)&~wise(X))))&
(![X]:((brave(X)<~>creative(X))<=>(~rich(X)<~>rich(X))))&
(![X]:(humble(X)<=>(~wise(X)<~>~curious(X))))&
(humble(john))&
((~calm(lucy)|humble(lucy)))&
(?[X]:((~rich(X)&tall(X))))&
((creative(lucy)<~>generous(lucy)))&
((~funny(john)<~>~strong(john)))&
((rich(mary)&~calm(mary)))&
(?[X]:(~happy(X))) | ~calm(paul) | [] | null | 0 |
If mary is either patient or not strong then someone is both not happy and happy.
Everyone who is either not rich or creative is not tall and vice versa.
Everyone who is both not old and not creative is both not old and not curious and vice versa.
Everyone who is both calm and not patient is old or not curious and vice versa.
If someone is either generous or strong then someone is both old and not brave and vice versa.
Everyone who is either funny or not humble is strong or not calm.
If fred is not generous or not quiet then fred is either patient or not humble and vice versa.
Everyone who is both not quiet and not curious is not generous or tall and vice versa.
If john is curious then john is either not rich or creative and vice versa.
Everyone who is either brave or not happy is not rich.
If someone is brave or wise then mary is not creative or not humble and vice versa.
Everyone who is either not kind or calm is strong and vice versa.
If mary is not brave then someone is funny and vice versa.
Everyone who is both brave and not funny is either humble or kind.
If john is tall or brave then someone is not strong or not creative.
Everyone who is not generous is either not rich or not funny.
Susan is either curious or not creative.
Someone is not kind or creative.
Someone is old.
Lucy is either curious or not kind.
Someone is either not funny or funny.
Someone is not kind.
Mary is both not old and not happy. | John is generous. | neutral | (((patient(mary)<~>~strong(mary)))=>(?[X]:((~happy(X)&happy(X)))))&
(![X]:((~rich(X)<~>creative(X))<=>~tall(X)))&
(![X]:((~old(X)&~creative(X))<=>(~old(X)&~curious(X))))&
(![X]:((calm(X)&~patient(X))<=>(old(X)|~curious(X))))&
((?[X]:((generous(X)<~>strong(X))))<=>(?[X]:((old(X)&~brave(X)))))&
(![X]:((funny(X)<~>~humble(X))=>(strong(X)|~calm(X))))&
(((~generous(fred)|~quiet(fred)))<=>((patient(fred)<~>~humble(fred))))&
(![X]:((~quiet(X)&~curious(X))<=>(~generous(X)|tall(X))))&
((curious(john))<=>((~rich(john)<~>creative(john))))&
(![X]:((brave(X)<~>~happy(X))=>~rich(X)))&
((?[X]:((brave(X)|wise(X))))<=>((~creative(mary)|~humble(mary))))&
(![X]:((~kind(X)<~>calm(X))<=>strong(X)))&
((~brave(mary))<=>(?[X]:(funny(X))))&
(![X]:((brave(X)&~funny(X))=>(humble(X)<~>kind(X))))&
(((tall(john)|brave(john)))=>(?[X]:((~strong(X)|~creative(X)))))&
(![X]:(~generous(X)=>(~rich(X)<~>~funny(X))))&
((curious(susan)<~>~creative(susan)))&
(?[X]:((~kind(X)|creative(X))))&
(?[X]:(old(X)))&
((curious(lucy)<~>~kind(lucy)))&
(?[X]:((~funny(X)<~>funny(X))))&
(?[X]:(~kind(X)))&
((~old(mary)&~happy(mary))) | generous(john) | [] | null | 0 |
If alice is either happy or not funny then mary is either not creative or rich and vice versa.
If someone is both rich and happy then someone is either curious or calm.
If someone is not old or quiet then someone is not wise.
If lucy is generous or quiet then someone is both not wise and not happy and vice versa.
Everyone who is both brave and kind is brave or not funny.
Everyone who is not creative or not curious is either quiet or not creative.
If someone is kind or not brave then alice is not calm.
Everyone who is not humble is both brave and not wise.
Everyone who is not brave is either not strong or curious.
If someone is either not rich or not humble then someone is both not calm and not curious.
Everyone who is both not brave and not quiet is either not generous or quiet and vice versa.
If someone is either not generous or not happy then someone is not calm or not humble.
If john is either calm or brave then alice is not old or not curious.
Everyone who is funny is either wise or not happy.
If john is calm or rich then someone is both brave and not tall.
Everyone who is either not wise or strong is either funny or not brave.
Lucy is either not kind or not wise.
Alice is both calm and not wise.
Someone is both not generous and quiet.
Susan is either tall or wise.
John is either not kind or not tall.
Someone is not wise or not brave. | Mary is humble. | neutral | (((happy(alice)<~>~funny(alice)))<=>((~creative(mary)<~>rich(mary))))&
((?[X]:((rich(X)&happy(X))))=>(?[X]:((curious(X)<~>calm(X)))))&
((?[X]:((~old(X)|quiet(X))))=>(?[X]:(~wise(X))))&
(((generous(lucy)|quiet(lucy)))<=>(?[X]:((~wise(X)&~happy(X)))))&
(![X]:((brave(X)&kind(X))=>(brave(X)|~funny(X))))&
(![X]:((~creative(X)|~curious(X))=>(quiet(X)<~>~creative(X))))&
((?[X]:((kind(X)|~brave(X))))=>(~calm(alice)))&
(![X]:(~humble(X)=>(brave(X)&~wise(X))))&
(![X]:(~brave(X)=>(~strong(X)<~>curious(X))))&
((?[X]:((~rich(X)<~>~humble(X))))=>(?[X]:((~calm(X)&~curious(X)))))&
(![X]:((~brave(X)&~quiet(X))<=>(~generous(X)<~>quiet(X))))&
((?[X]:((~generous(X)<~>~happy(X))))=>(?[X]:((~calm(X)|~humble(X)))))&
(((calm(john)<~>brave(john)))=>((~old(alice)|~curious(alice))))&
(![X]:(funny(X)=>(wise(X)<~>~happy(X))))&
(((calm(john)|rich(john)))=>(?[X]:((brave(X)&~tall(X)))))&
(![X]:((~wise(X)<~>strong(X))=>(funny(X)<~>~brave(X))))&
((~kind(lucy)<~>~wise(lucy)))&
((calm(alice)&~wise(alice)))&
(?[X]:((~generous(X)&quiet(X))))&
((tall(susan)<~>wise(susan)))&
((~kind(john)<~>~tall(john)))&
(?[X]:((~wise(X)|~brave(X)))) | humble(mary) | [] | null | 0 |
If alice is calm or not wise then john is strong and vice versa.
Everyone who is both not kind and creative is calm or not creative.
Everyone who is not happy is either creative or calm and vice versa.
If fred is either strong or not curious then someone is old or not quiet and vice versa.
Everyone who is both not old and generous is not brave and vice versa.
Everyone who is either quiet or wise is either not wise or not funny.
Everyone who is kind or tall is not wise or funny and vice versa.
Everyone who is not tall is humble or not curious and vice versa.
Everyone who is old is happy or not quiet.
Everyone who is either not creative or rich is both happy and brave.
Everyone who is either not creative or rich is both not wise and quiet.
Everyone who is not old is kind and vice versa.
If susan is either calm or not wise then someone is either brave or creative and vice versa.
Everyone who is both rich and not funny is wise.
Everyone who is not brave is either not curious or brave and vice versa.
If paul is not quiet then paul is either not wise or calm and vice versa.
Fred is either calm or not wise.
Someone is either creative or not quiet.
John is either not patient or not brave.
Someone is both calm and not wise.
Paul is not happy or patient.
Someone is not brave.
Someone is either not tall or rich.
Someone is either not curious or brave. | Paul is patient. | neutral | (((calm(alice)|~wise(alice)))<=>(strong(john)))&
(![X]:((~kind(X)&creative(X))=>(calm(X)|~creative(X))))&
(![X]:(~happy(X)<=>(creative(X)<~>calm(X))))&
(((strong(fred)<~>~curious(fred)))<=>(?[X]:((old(X)|~quiet(X)))))&
(![X]:((~old(X)&generous(X))<=>~brave(X)))&
(![X]:((quiet(X)<~>wise(X))=>(~wise(X)<~>~funny(X))))&
(![X]:((kind(X)|tall(X))<=>(~wise(X)|funny(X))))&
(![X]:(~tall(X)<=>(humble(X)|~curious(X))))&
(![X]:(old(X)=>(happy(X)|~quiet(X))))&
(![X]:((~creative(X)<~>rich(X))=>(happy(X)&brave(X))))&
(![X]:((~creative(X)<~>rich(X))=>(~wise(X)&quiet(X))))&
(![X]:(~old(X)<=>kind(X)))&
(((calm(susan)<~>~wise(susan)))<=>(?[X]:((brave(X)<~>creative(X)))))&
(![X]:((rich(X)&~funny(X))=>wise(X)))&
(![X]:(~brave(X)<=>(~curious(X)<~>brave(X))))&
((~quiet(paul))<=>((~wise(paul)<~>calm(paul))))&
((calm(fred)<~>~wise(fred)))&
(?[X]:((creative(X)<~>~quiet(X))))&
((~patient(john)<~>~brave(john)))&
(?[X]:((calm(X)&~wise(X))))&
((~happy(paul)|patient(paul)))&
(?[X]:(~brave(X)))&
(?[X]:((~tall(X)<~>rich(X))))&
(?[X]:((~curious(X)<~>brave(X)))) | patient(paul) | [] | null | 0 |
If someone is not curious or quiet then alice is both brave and curious.
If someone is either not calm or not quiet then someone is not strong.
If lucy is not brave then alice is strong or tall and vice versa.
Everyone who is both brave and patient is either not strong or wise and vice versa.
Everyone who is both brave and not old is not rich or not old and vice versa.
Everyone who is both not curious and not strong is patient and vice versa.
Everyone who is generous or wise is both strong and not quiet.
Everyone who is tall is both rich and not humble and vice versa.
If someone is not funny or not tall then someone is either not creative or funny and vice versa.
If someone is calm or patient then lucy is strong or kind.
If someone is both creative and not curious then mary is either not calm or old.
Everyone who is either not brave or not tall is not old and vice versa.
If mary is not calm then john is either not patient or curious and vice versa.
Everyone who is not rich or old is not calm and vice versa.
If someone is calm or not brave then lucy is curious or wise.
John is either happy or quiet.
Mary is not tall or quiet.
Someone is not happy or not wise.
Someone is strong or rich.
Paul is both creative and kind.
Someone is both generous and rich. | Lucy is brave. | contradiction | ((?[X]:((~curious(X)|quiet(X))))=>((brave(alice)&curious(alice))))&
((?[X]:((~calm(X)<~>~quiet(X))))=>(?[X]:(~strong(X))))&
((~brave(lucy))<=>((strong(alice)|tall(alice))))&
(![X]:((brave(X)&patient(X))<=>(~strong(X)<~>wise(X))))&
(![X]:((brave(X)&~old(X))<=>(~rich(X)|~old(X))))&
(![X]:((~curious(X)&~strong(X))<=>patient(X)))&
(![X]:((generous(X)|wise(X))=>(strong(X)&~quiet(X))))&
(![X]:(tall(X)<=>(rich(X)&~humble(X))))&
((?[X]:((~funny(X)|~tall(X))))<=>(?[X]:((~creative(X)<~>funny(X)))))&
((?[X]:((calm(X)|patient(X))))=>((strong(lucy)|kind(lucy))))&
((?[X]:((creative(X)&~curious(X))))=>((~calm(mary)<~>old(mary))))&
(![X]:((~brave(X)<~>~tall(X))<=>~old(X)))&
((~calm(mary))<=>((~patient(john)<~>curious(john))))&
(![X]:((~rich(X)|old(X))<=>~calm(X)))&
((?[X]:((calm(X)|~brave(X))))=>((curious(lucy)|wise(lucy))))&
((happy(john)<~>quiet(john)))&
((~tall(mary)|quiet(mary)))&
(?[X]:((~happy(X)|~wise(X))))&
(?[X]:((strong(X)|rich(X))))&
((creative(paul)&kind(paul)))&
(?[X]:((generous(X)&rich(X)))) | brave(lucy) | [
"p0",
"p2",
"p3",
"p5",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 2960168446749259123311329
% SZS output start Proof for 2960168446749259123311329
1. ? [X0] : (quiet(X0) | ~curious(X0)) => (curious(alice) & brave(alice)) [input p0]
3. ~brave(lucy) <=> (tall(alice) | strong(alice)) [input p2]
4. ! [X0] : ((patient(X0) & brave(X0)) <=> (~strong(X0) <~> wise(X0))) [input p3]
6. ! [X0] : ((~strong(X0) & ~curious(X0)) <=> patient(X0)) [input p5]
7. ! [X0] : ((wise(X0) | generous(X0)) => (~quiet(X0) & strong(X0))) [input p6]
22. brave(lucy) [input hypothesis]
27. (curious(alice) & brave(alice)) | ! [X0] : (~quiet(X0) & curious(X0)) [ennf transformation 1]
29. ! [X0] : ((~quiet(X0) & strong(X0)) | (~wise(X0) & ~generous(X0))) [ennf transformation 7]
37. (~brave(lucy) | (~tall(alice) & ~strong(alice))) & ((tall(alice) | strong(alice)) | brave(lucy)) [nnf transformation 3]
38. (~brave(lucy) | (~tall(alice) & ~strong(alice))) & (tall(alice) | strong(alice) | brave(lucy)) [flattening 37]
39. ! [X0] : (((patient(X0) & brave(X0)) | ((~strong(X0) | ~wise(X0)) & (wise(X0) | strong(X0)))) & (((~wise(X0) | strong(X0)) & (wise(X0) | ~strong(X0))) | (~patient(X0) | ~brave(X0)))) [nnf transformation 4]
40. ! [X0] : (((patient(X0) & brave(X0)) | ((~strong(X0) | ~wise(X0)) & (wise(X0) | strong(X0)))) & (((~wise(X0) | strong(X0)) & (wise(X0) | ~strong(X0))) | ~patient(X0) | ~brave(X0))) [flattening 39]
43. ! [X0] : (((~strong(X0) & ~curious(X0)) | ~patient(X0)) & (patient(X0) | (strong(X0) | curious(X0)))) [nnf transformation 6]
44. ! [X0] : (((~strong(X0) & ~curious(X0)) | ~patient(X0)) & (patient(X0) | strong(X0) | curious(X0))) [flattening 43]
66. curious(alice) | curious(X0) [cnf transformation 27]
71. ~brave(lucy) | ~strong(alice) [cnf transformation 38]
77. wise(X0) | patient(X0) | strong(X0) [cnf transformation 40]
85. ~patient(X0) | ~curious(X0) [cnf transformation 44]
88. ~wise(X0) | strong(X0) [cnf transformation 29]
123. brave(lucy) [cnf transformation 22]
128. 2 <=> curious(alice) [avatar definition]
129. ~curious(alice) <- (~2) [avatar component clause 128]
130. curious(alice) <- (2) [avatar component clause 128]
133. 3 <=> ! [X0] : curious(X0) [avatar definition]
134. curious(X0) <- (3) [avatar component clause 133]
135. 3 | 2 [avatar split clause 66,128,133]
159. 9 <=> brave(lucy) [avatar definition]
164. 10 <=> strong(alice) [avatar definition]
166. ~strong(alice) <- (~10) [avatar component clause 164]
167. ~10 | ~9 [avatar split clause 71,159,164]
284. 9 [avatar split clause 123,159]
313. patient(X2) | strong(X2) | strong(X2) [resolution 77,88]
314. patient(X2) | strong(X2) [duplicate literal removal 313]
361. ~curious(X2) | strong(X2) [resolution 314,85]
363. strong(alice) <- (2) [resolution 361,130]
365. $false <- (2, ~10) [subsumption resolution 363,166]
366. ~2 | 10 [avatar contradiction clause 365]
367. $false <- (~2, 3) [subsumption resolution 129,134]
368. 2 | ~3 [avatar contradiction clause 367]
369. $false [avatar sat refutation 135,167,284,366,368]
% SZS output end Proof for 2960168446749259123311329
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not curious is quiet.
Everyone who is either curious or strong is not wise or not funny and vice versa.
If mary is either not funny or not calm then someone is not rich and vice versa.
If fred is either old or wise then paul is not calm and vice versa.
Everyone who is either not brave or tall is both wise and happy and vice versa.
Everyone who is either tall or not generous is not generous or not patient and vice versa.
Everyone who is strong is either not brave or humble.
If someone is generous then someone is creative or kind and vice versa.
Everyone who is not funny is creative or not creative and vice versa.
Everyone who is either not generous or kind is not generous or not kind and vice versa.
Everyone who is not wise or not generous is both not humble and not kind and vice versa.
If paul is both not curious and not funny then someone is strong.
Everyone who is creative or not wise is both not happy and tall and vice versa.
Everyone who is calm is not old or not wise and vice versa.
John is patient.
Mary is both not kind and not funny.
John is either creative or patient.
Someone is both old and not generous.
Someone is wise or not generous.
John is either curious or quiet. | Mary is rich. | neutral | (![X]:(~curious(X)=>quiet(X)))&
(![X]:((curious(X)<~>strong(X))<=>(~wise(X)|~funny(X))))&
(((~funny(mary)<~>~calm(mary)))<=>(?[X]:(~rich(X))))&
(((old(fred)<~>wise(fred)))<=>(~calm(paul)))&
(![X]:((~brave(X)<~>tall(X))<=>(wise(X)&happy(X))))&
(![X]:((tall(X)<~>~generous(X))<=>(~generous(X)|~patient(X))))&
(![X]:(strong(X)=>(~brave(X)<~>humble(X))))&
((?[X]:(generous(X)))<=>(?[X]:((creative(X)|kind(X)))))&
(![X]:(~funny(X)<=>(creative(X)|~creative(X))))&
(![X]:((~generous(X)<~>kind(X))<=>(~generous(X)|~kind(X))))&
(![X]:((~wise(X)|~generous(X))<=>(~humble(X)&~kind(X))))&
(((~curious(paul)&~funny(paul)))=>(?[X]:(strong(X))))&
(![X]:((creative(X)|~wise(X))<=>(~happy(X)&tall(X))))&
(![X]:(calm(X)<=>(~old(X)|~wise(X))))&
(patient(john))&
((~kind(mary)&~funny(mary)))&
((creative(john)<~>patient(john)))&
(?[X]:((old(X)&~generous(X))))&
(?[X]:((wise(X)|~generous(X))))&
((curious(john)<~>quiet(john))) | rich(mary) | [] | null | 0 |
Everyone who is either brave or not generous is not old or not quiet.
Everyone who is not old is both curious and tall.
If someone is both not happy and generous then lucy is not rich and vice versa.
If someone is not funny then alice is both not tall and strong and vice versa.
If someone is generous then susan is both not funny and calm and vice versa.
If mary is both not rich and old then susan is not calm or not tall.
If john is either not kind or creative then alice is not funny or wise.
Everyone who is either not happy or not tall is curious or strong and vice versa.
Everyone who is strong is curious or brave.
If lucy is both humble and not happy then susan is both not calm and not wise and vice versa.
If susan is either humble or not patient then alice is both funny and curious and vice versa.
If someone is humble or funny then someone is both generous and quiet and vice versa.
If fred is both wise and old then paul is either not humble or not rich.
If someone is not curious or not creative then someone is calm or not kind.
Everyone who is humble or generous is not creative or kind.
Everyone who is not calm or not tall is not quiet and vice versa.
Someone is either brave or not strong.
Susan is not rich.
Fred is either humble or not patient.
Someone is both not wise and not brave.
Mary is humble.
John is either calm or funny.
Paul is both happy and wise.
John is not strong or funny. | Alice is not quiet. | entailment | (![X]:((brave(X)<~>~generous(X))=>(~old(X)|~quiet(X))))&
(![X]:(~old(X)=>(curious(X)&tall(X))))&
((?[X]:((~happy(X)&generous(X))))<=>(~rich(lucy)))&
((?[X]:(~funny(X)))<=>((~tall(alice)&strong(alice))))&
((?[X]:(generous(X)))<=>((~funny(susan)&calm(susan))))&
(((~rich(mary)&old(mary)))=>((~calm(susan)|~tall(susan))))&
(((~kind(john)<~>creative(john)))=>((~funny(alice)|wise(alice))))&
(![X]:((~happy(X)<~>~tall(X))<=>(curious(X)|strong(X))))&
(![X]:(strong(X)=>(curious(X)|brave(X))))&
(((humble(lucy)&~happy(lucy)))<=>((~calm(susan)&~wise(susan))))&
(((humble(susan)<~>~patient(susan)))<=>((funny(alice)&curious(alice))))&
((?[X]:((humble(X)|funny(X))))<=>(?[X]:((generous(X)&quiet(X)))))&
(((wise(fred)&old(fred)))=>((~humble(paul)<~>~rich(paul))))&
((?[X]:((~curious(X)|~creative(X))))=>(?[X]:((calm(X)|~kind(X)))))&
(![X]:((humble(X)|generous(X))=>(~creative(X)|kind(X))))&
(![X]:((~calm(X)|~tall(X))<=>~quiet(X)))&
(?[X]:((brave(X)<~>~strong(X))))&
(~rich(susan))&
((humble(fred)<~>~patient(fred)))&
(?[X]:((~wise(X)&~brave(X))))&
(humble(mary))&
((calm(john)<~>funny(john)))&
((happy(paul)&wise(paul)))&
((~strong(john)|funny(john))) | ~quiet(alice) | [
"p3",
"p4",
"p11",
"p15",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 5294177482148123594151970
% SZS output start Proof for 5294177482148123594151970
4. ? [X0] : ~funny(X0) <=> (strong(alice) & ~tall(alice)) [input p3]
5. ? [X0] : generous(X0) <=> (calm(susan) & ~funny(susan)) [input p4]
12. ? [X0] : (funny(X0) | humble(X0)) <=> ? [X0] : (quiet(X0) & generous(X0)) [input p11]
16. ! [X0] : ((~tall(X0) | ~calm(X0)) <=> ~quiet(X0)) [input p15]
21. humble(mary) [input p20]
25. quiet(alice) [input hypothesis]
26. ? [X0] : (funny(X0) | humble(X0)) <=> ? [X1] : (quiet(X1) & generous(X1)) [rectify 12]
47. (? [X0] : ~funny(X0) | (~strong(alice) | tall(alice))) & ((strong(alice) & ~tall(alice)) | ! [X0] : funny(X0)) [nnf transformation 4]
48. (? [X0] : ~funny(X0) | ~strong(alice) | tall(alice)) & ((strong(alice) & ~tall(alice)) | ! [X0] : funny(X0)) [flattening 47]
49. (? [X0] : ~funny(X0) | ~strong(alice) | tall(alice)) & ((strong(alice) & ~tall(alice)) | ! [X1] : funny(X1)) [rectify 48]
50. ? [X0] : ~funny(X0) => ~funny(sK1) [choice axiom]
51. (~funny(sK1) | ~strong(alice) | tall(alice)) & ((strong(alice) & ~tall(alice)) | ! [X1] : funny(X1)) [skolemisation 49,50]
52. (? [X0] : generous(X0) | (~calm(susan) | funny(susan))) & ((calm(susan) & ~funny(susan)) | ! [X0] : ~generous(X0)) [nnf transformation 5]
53. (? [X0] : generous(X0) | ~calm(susan) | funny(susan)) & ((calm(susan) & ~funny(susan)) | ! [X0] : ~generous(X0)) [flattening 52]
54. (? [X0] : generous(X0) | ~calm(susan) | funny(susan)) & ((calm(susan) & ~funny(susan)) | ! [X1] : ~generous(X1)) [rectify 53]
55. ? [X0] : generous(X0) => generous(sK2) [choice axiom]
56. (generous(sK2) | ~calm(susan) | funny(susan)) & ((calm(susan) & ~funny(susan)) | ! [X1] : ~generous(X1)) [skolemisation 54,55]
64. (? [X0] : (funny(X0) | humble(X0)) | ! [X1] : (~quiet(X1) | ~generous(X1))) & (? [X1] : (quiet(X1) & generous(X1)) | ! [X0] : (~funny(X0) & ~humble(X0))) [nnf transformation 26]
65. (? [X0] : (funny(X0) | humble(X0)) | ! [X1] : (~quiet(X1) | ~generous(X1))) & (? [X2] : (quiet(X2) & generous(X2)) | ! [X3] : (~funny(X3) & ~humble(X3))) [rectify 64]
66. ? [X0] : (funny(X0) | humble(X0)) => (funny(sK3) | humble(sK3)) [choice axiom]
67. ? [X2] : (quiet(X2) & generous(X2)) => (quiet(sK4) & generous(sK4)) [choice axiom]
68. ((funny(sK3) | humble(sK3)) | ! [X1] : (~quiet(X1) | ~generous(X1))) & ((quiet(sK4) & generous(sK4)) | ! [X3] : (~funny(X3) & ~humble(X3))) [skolemisation 65,67,66]
73. ! [X0] : (((~tall(X0) | ~calm(X0)) | quiet(X0)) & (~quiet(X0) | (tall(X0) & calm(X0)))) [nnf transformation 16]
74. ! [X0] : ((~tall(X0) | ~calm(X0) | quiet(X0)) & (~quiet(X0) | (tall(X0) & calm(X0)))) [flattening 73]
89. ~tall(alice) | funny(X1) [cnf transformation 51]
92. ~funny(susan) | ~generous(X1) [cnf transformation 56]
115. generous(sK4) | ~humble(X3) [cnf transformation 68]
127. ~quiet(X0) | tall(X0) [cnf transformation 74]
136. humble(mary) [cnf transformation 21]
142. quiet(alice) [cnf transformation 25]
162. 5 <=> tall(alice) [avatar definition]
175. 8 <=> ! [X1] : funny(X1) [avatar definition]
176. funny(X1) <- (8) [avatar component clause 175]
178. 8 | ~5 [avatar split clause 89,162,175]
180. 9 <=> funny(susan) [avatar definition]
181. ~funny(susan) <- (~9) [avatar component clause 180]
193. 12 <=> ! [X1] : ~generous(X1) [avatar definition]
194. ~generous(X1) <- (12) [avatar component clause 193]
196. 12 | ~9 [avatar split clause 92,180,193]
283. 31 <=> ! [X3] : ~humble(X3) [avatar definition]
284. ~humble(X3) <- (31) [avatar component clause 283]
287. 32 <=> generous(sK4) [avatar definition]
289. generous(sK4) <- (32) [avatar component clause 287]
291. 31 | 32 [avatar split clause 115,287,283]
365. $false <- (31) [resolution 284,136]
366. ~31 [avatar contradiction clause 365]
371. tall(alice) [resolution 127,142]
375. 5 [avatar split clause 371,162]
382. $false <- (8, ~9) [subsumption resolution 181,176]
383. ~8 | 9 [avatar contradiction clause 382]
388. $false <- (12, 32) [resolution 194,289]
389. ~12 | ~32 [avatar contradiction clause 388]
392. $false [avatar sat refutation 178,196,291,366,375,383,389]
% SZS output end Proof for 5294177482148123594151970
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Everyone who is either not quiet or calm is both calm and not wise.
If susan is either not curious or not old then someone is both creative and not brave.
Everyone who is generous or funny is either not old or not quiet.
If fred is strong then someone is either not curious or not patient.
If paul is both strong and patient then someone is not kind or not humble and vice versa.
If someone is not quiet or quiet then paul is both not funny and old and vice versa.
If lucy is quiet then someone is not happy or creative.
If someone is not kind then fred is either not curious or creative and vice versa.
If someone is kind then mary is not kind and vice versa.
If paul is wise then someone is happy and vice versa.
If susan is both calm and not curious then fred is curious or not rich and vice versa.
If fred is strong or funny then someone is not funny.
Everyone who is funny or wise is either not kind or not creative.
Everyone who is both not strong and kind is not quiet.
If someone is not brave then mary is not patient or patient and vice versa.
Everyone who is wise is strong and vice versa.
Someone is calm or funny.
Someone is both calm and not creative.
Someone is both not patient and not old.
Someone is humble or not creative.
Paul is either not kind or not generous.
Someone is both generous and not brave.
John is either brave or not happy. | Susan is curious. | neutral | (![X]:((~quiet(X)<~>calm(X))=>(calm(X)&~wise(X))))&
(((~curious(susan)<~>~old(susan)))=>(?[X]:((creative(X)&~brave(X)))))&
(![X]:((generous(X)|funny(X))=>(~old(X)<~>~quiet(X))))&
((strong(fred))=>(?[X]:((~curious(X)<~>~patient(X)))))&
(((strong(paul)&patient(paul)))<=>(?[X]:((~kind(X)|~humble(X)))))&
((?[X]:((~quiet(X)|quiet(X))))<=>((~funny(paul)&old(paul))))&
((quiet(lucy))=>(?[X]:((~happy(X)|creative(X)))))&
((?[X]:(~kind(X)))<=>((~curious(fred)<~>creative(fred))))&
((?[X]:(kind(X)))<=>(~kind(mary)))&
((wise(paul))<=>(?[X]:(happy(X))))&
(((calm(susan)&~curious(susan)))<=>((curious(fred)|~rich(fred))))&
(((strong(fred)|funny(fred)))=>(?[X]:(~funny(X))))&
(![X]:((funny(X)|wise(X))=>(~kind(X)<~>~creative(X))))&
(![X]:((~strong(X)&kind(X))=>~quiet(X)))&
((?[X]:(~brave(X)))<=>((~patient(mary)|patient(mary))))&
(![X]:(wise(X)<=>strong(X)))&
(?[X]:((calm(X)|funny(X))))&
(?[X]:((calm(X)&~creative(X))))&
(?[X]:((~patient(X)&~old(X))))&
(?[X]:((humble(X)|~creative(X))))&
((~kind(paul)<~>~generous(paul)))&
(?[X]:((generous(X)&~brave(X))))&
((brave(john)<~>~happy(john))) | curious(susan) | [] | null | 0 |
If john is happy or old then someone is creative. Everyone who is not brave is curious or not brave. If someone is creative or brave then alice is both tall and not funny. Everyone who is both brave and old is either not humble or not happy and vice versa. Everyone who is not old is both tall and kind and vice versa. Everyone who is both not calm and creative is either kind or not old and vice versa. Everyone who is either wise or generous is patient. Everyone who is humble or calm is both calm and not quiet. If mary is tall then someone is not tall or not brave and vice versa. If someone is both calm and not old then paul is strong and vice versa. Everyone who is both calm and not old is not curious. If someone is wise then someone is both not calm and not brave and vice versa. Everyone who is generous or rich is calm and vice versa. Everyone who is both not calm and happy is not quiet or happy and vice versa. If lucy is either not quiet or old then john is either not creative or not old and vice versa. Everyone who is both not strong and kind is not patient. Someone is not generous or patient. Mary is both not rich and not quiet. Someone is creative or not tall. Someone is either happy or generous. Someone is both not funny and wise. Lucy is not funny or not kind. Someone is either not tall or patient. | Alice is creative. | contradiction | (((happy(john)|old(john)))=>(?[X]:(creative(X))))&
(![X]:(~brave(X)=>(curious(X)|~brave(X))))&
((?[X]:((creative(X)|brave(X))))=>((tall(alice)&~funny(alice))))&
(![X]:((brave(X)&old(X))<=>(~humble(X)<~>~happy(X))))&
(![X]:(~old(X)<=>(tall(X)&kind(X))))&
(![X]:((~calm(X)&creative(X))<=>(kind(X)<~>~old(X))))&
(![X]:((wise(X)<~>generous(X))=>patient(X)))&
(![X]:((humble(X)|calm(X))=>(calm(X)&~quiet(X))))&
((tall(mary))<=>(?[X]:((~tall(X)|~brave(X)))))&
((?[X]:((calm(X)&~old(X))))<=>(strong(paul)))&
(![X]:((calm(X)&~old(X))=>~curious(X)))&
((?[X]:(wise(X)))<=>(?[X]:((~calm(X)&~brave(X)))))&
(![X]:((generous(X)|rich(X))<=>calm(X)))&
(![X]:((~calm(X)&happy(X))<=>(~quiet(X)|happy(X))))&
(((~quiet(lucy)<~>old(lucy)))<=>((~creative(john)<~>~old(john))))&
(![X]:((~strong(X)&kind(X))=>~patient(X)))&
(?[X]:((~generous(X)|patient(X))))&
((~rich(mary)&~quiet(mary)))&
(?[X]:((creative(X)|~tall(X))))&
(?[X]:((happy(X)<~>generous(X))))&
(?[X]:((~funny(X)&wise(X))))&
((~funny(lucy)|~kind(lucy)))&
(?[X]:((~tall(X)<~>patient(X)))) | creative(alice) | [
"p2",
"p3",
"p4",
"p5",
"p7",
"p13",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 5607745295486424285979476
% SZS output start Proof for 5607745295486424285979476
3. ? [X0] : (brave(X0) | creative(X0)) => (~funny(alice) & tall(alice)) [input p2]
4. ! [X0] : ((old(X0) & brave(X0)) <=> (~humble(X0) <~> ~happy(X0))) [input p3]
5. ! [X0] : (~old(X0) <=> (kind(X0) & tall(X0))) [input p4]
6. ! [X0] : ((creative(X0) & ~calm(X0)) <=> (kind(X0) <~> ~old(X0))) [input p5]
8. ! [X0] : ((calm(X0) | humble(X0)) => (~quiet(X0) & calm(X0))) [input p7]
14. ! [X0] : ((happy(X0) & ~calm(X0)) <=> (happy(X0) | ~quiet(X0))) [input p13]
18. ~quiet(mary) & ~rich(mary) [input p17]
24. creative(alice) [input hypothesis]
27. ? [X0] : (brave(X0) | creative(X0)) => tall(alice) [pure predicate removal 3]
32. tall(alice) | ! [X0] : (~brave(X0) & ~creative(X0)) [ennf transformation 27]
34. ! [X0] : ((~quiet(X0) & calm(X0)) | (~calm(X0) & ~humble(X0))) [ennf transformation 8]
41. ! [X0] : (((old(X0) & brave(X0)) | ((~humble(X0) | happy(X0)) & (~happy(X0) | humble(X0)))) & (((happy(X0) | humble(X0)) & (~happy(X0) | ~humble(X0))) | (~old(X0) | ~brave(X0)))) [nnf transformation 4]
42. ! [X0] : (((old(X0) & brave(X0)) | ((~humble(X0) | happy(X0)) & (~happy(X0) | humble(X0)))) & (((happy(X0) | humble(X0)) & (~happy(X0) | ~humble(X0))) | ~old(X0) | ~brave(X0))) [flattening 41]
43. ! [X0] : ((~old(X0) | (~kind(X0) | ~tall(X0))) & ((kind(X0) & tall(X0)) | old(X0))) [nnf transformation 5]
44. ! [X0] : ((~old(X0) | ~kind(X0) | ~tall(X0)) & ((kind(X0) & tall(X0)) | old(X0))) [flattening 43]
45. ! [X0] : (((creative(X0) & ~calm(X0)) | ((kind(X0) | old(X0)) & (~old(X0) | ~kind(X0)))) & (((old(X0) | ~kind(X0)) & (~old(X0) | kind(X0))) | (~creative(X0) | calm(X0)))) [nnf transformation 6]
46. ! [X0] : (((creative(X0) & ~calm(X0)) | ((kind(X0) | old(X0)) & (~old(X0) | ~kind(X0)))) & (((old(X0) | ~kind(X0)) & (~old(X0) | kind(X0))) | ~creative(X0) | calm(X0))) [flattening 45]
63. ! [X0] : (((happy(X0) & ~calm(X0)) | (~happy(X0) & quiet(X0))) & ((happy(X0) | ~quiet(X0)) | (~happy(X0) | calm(X0)))) [nnf transformation 14]
64. ! [X0] : (((happy(X0) & ~calm(X0)) | (~happy(X0) & quiet(X0))) & (happy(X0) | ~quiet(X0) | ~happy(X0) | calm(X0))) [flattening 63]
82. tall(alice) | ~brave(X0) [cnf transformation 32]
85. ~happy(X0) | brave(X0) | humble(X0) [cnf transformation 42]
90. kind(X0) | old(X0) [cnf transformation 44]
91. ~kind(X0) | ~old(X0) | ~tall(X0) [cnf transformation 44]
92. ~old(X0) | kind(X0) | ~creative(X0) | calm(X0) [cnf transformation 46]
93. old(X0) | ~kind(X0) | ~creative(X0) | calm(X0) [cnf transformation 46]
100. ~humble(X0) | calm(X0) [cnf transformation 34]
103. ~quiet(X0) | ~calm(X0) [cnf transformation 34]
118. ~calm(X0) | quiet(X0) [cnf transformation 64]
120. quiet(X0) | happy(X0) [cnf transformation 64]
133. ~quiet(mary) [cnf transformation 18]
140. creative(alice) [cnf transformation 24]
156. 4 <=> ! [X0] : ~brave(X0) [avatar definition]
157. ~brave(X0) <- (4) [avatar component clause 156]
159. 5 <=> tall(alice) [avatar definition]
162. 4 | 5 [avatar split clause 82,159,156]
167. ~creative(X0) | old(X0) | calm(X0) [subsumption resolution 93,90]
168. ~creative(X0) | kind(X0) | calm(X0) [subsumption resolution 92,167]
229. ~calm(X0) [subsumption resolution 118,103]
299. happy(mary) [resolution 120,133]
304. brave(mary) | humble(mary) [resolution 85,299]
315. 34 <=> humble(mary) [avatar definition]
317. humble(mary) <- (34) [avatar component clause 315]
319. 35 <=> brave(mary) [avatar definition]
321. brave(mary) <- (35) [avatar component clause 319]
322. 34 | 35 [avatar split clause 304,319,315]
351. calm(mary) <- (34) [resolution 317,100]
352. $false <- (34) [subsumption resolution 351,229]
353. ~34 [avatar contradiction clause 352]
405. old(alice) | calm(alice) [resolution 167,140]
406. old(alice) [subsumption resolution 405,229]
407. kind(alice) | calm(alice) [resolution 168,140]
408. kind(alice) [subsumption resolution 407,229]
410. ~old(alice) | ~tall(alice) [resolution 408,91]
411. ~tall(alice) [subsumption resolution 410,406]
414. ~5 [avatar split clause 411,159]
417. $false <- (4, 35) [resolution 157,321]
418. ~4 | ~35 [avatar contradiction clause 417]
421. $false [avatar sat refutation 162,322,353,414,418]
% SZS output end Proof for 5607745295486424285979476
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not curious or not funny is both not tall and funny.
If someone is not wise or not kind then someone is not rich.
If someone is brave or curious then fred is either not happy or not brave.
If john is both patient and not funny then someone is not old or not tall and vice versa.
Everyone who is both not brave and happy is humble or not tall and vice versa.
If john is both brave and generous then susan is not funny.
Everyone who is both not humble and not strong is kind and vice versa.
If john is either tall or not funny then someone is old.
If someone is not old then fred is happy or patient.
Everyone who is not generous is patient or not old and vice versa.
Everyone who is either kind or not creative is not humble and vice versa.
Everyone who is either strong or happy is creative and vice versa.
If susan is patient then someone is both not curious and not rich and vice versa.
If someone is both not rich and old then someone is wise and vice versa.
If paul is patient or not generous then paul is not patient or not wise.
Everyone who is not generous or not quiet is either not wise or not kind.
Someone is not humble.
Someone is both quiet and creative.
Someone is both not strong and wise.
John is both not patient and curious.
Lucy is not generous or kind. | Lucy is brave. | neutral | (![X]:((~curious(X)<~>~funny(X))=>(~tall(X)&funny(X))))&
((?[X]:((~wise(X)|~kind(X))))=>(?[X]:(~rich(X))))&
((?[X]:((brave(X)|curious(X))))=>((~happy(fred)<~>~brave(fred))))&
(((patient(john)&~funny(john)))<=>(?[X]:((~old(X)|~tall(X)))))&
(![X]:((~brave(X)&happy(X))<=>(humble(X)|~tall(X))))&
(((brave(john)&generous(john)))=>(~funny(susan)))&
(![X]:((~humble(X)&~strong(X))<=>kind(X)))&
(((tall(john)<~>~funny(john)))=>(?[X]:(old(X))))&
((?[X]:(~old(X)))=>((happy(fred)|patient(fred))))&
(![X]:(~generous(X)<=>(patient(X)|~old(X))))&
(![X]:((kind(X)<~>~creative(X))<=>~humble(X)))&
(![X]:((strong(X)<~>happy(X))<=>creative(X)))&
((patient(susan))<=>(?[X]:((~curious(X)&~rich(X)))))&
((?[X]:((~rich(X)&old(X))))<=>(?[X]:(wise(X))))&
(((patient(paul)|~generous(paul)))=>((~patient(paul)|~wise(paul))))&
(![X]:((~generous(X)|~quiet(X))=>(~wise(X)<~>~kind(X))))&
(?[X]:(~humble(X)))&
(?[X]:((quiet(X)&creative(X))))&
(?[X]:((~strong(X)&wise(X))))&
((~patient(john)&curious(john)))&
((~generous(lucy)|kind(lucy))) | brave(lucy) | [] | null | 0 |
If paul is both quiet and not calm then someone is rich. If someone is either wise or not creative then someone is both creative and not wise. If someone is not quiet or not rich then someone is both calm and not kind and vice versa. If john is either creative or patient then fred is both not generous and not strong. If alice is not brave then susan is old or patient and vice versa. If john is funny then someone is either generous or funny. Everyone who is either not rich or not happy is not creative and vice versa. Everyone who is happy or patient is either patient or not rich and vice versa. If paul is happy then lucy is strong or not kind. If someone is not patient or not quiet then alice is both not kind and not creative. If paul is not happy then someone is humble or not creative and vice versa. Everyone who is both patient and not happy is funny and vice versa. If someone is either not calm or not kind then someone is not generous and vice versa. Everyone who is not quiet or not funny is either not happy or not quiet. If someone is either not creative or not kind then someone is quiet or patient and vice versa. Everyone who is both kind and rich is either brave or not brave. Mary is not creative or not kind. Paul is either curious or not brave. Someone is either not quiet or humble. John is both not generous and not old. Paul is generous. Susan is not quiet or funny. Mary is not happy. Lucy is not humble. | Alice is creative. | contradiction | (((quiet(paul)&~calm(paul)))=>(?[X]:(rich(X))))&
((?[X]:((wise(X)<~>~creative(X))))=>(?[X]:((creative(X)&~wise(X)))))&
((?[X]:((~quiet(X)|~rich(X))))<=>(?[X]:((calm(X)&~kind(X)))))&
(((creative(john)<~>patient(john)))=>((~generous(fred)&~strong(fred))))&
((~brave(alice))<=>((old(susan)|patient(susan))))&
((funny(john))=>(?[X]:((generous(X)<~>funny(X)))))&
(![X]:((~rich(X)<~>~happy(X))<=>~creative(X)))&
(![X]:((happy(X)|patient(X))<=>(patient(X)<~>~rich(X))))&
((happy(paul))=>((strong(lucy)|~kind(lucy))))&
((?[X]:((~patient(X)|~quiet(X))))=>((~kind(alice)&~creative(alice))))&
((~happy(paul))<=>(?[X]:((humble(X)|~creative(X)))))&
(![X]:((patient(X)&~happy(X))<=>funny(X)))&
((?[X]:((~calm(X)<~>~kind(X))))<=>(?[X]:(~generous(X))))&
(![X]:((~quiet(X)|~funny(X))=>(~happy(X)<~>~quiet(X))))&
((?[X]:((~creative(X)<~>~kind(X))))<=>(?[X]:((quiet(X)|patient(X)))))&
(![X]:((kind(X)&rich(X))=>(brave(X)<~>~brave(X))))&
((~creative(mary)|~kind(mary)))&
((curious(paul)<~>~brave(paul)))&
(?[X]:((~quiet(X)<~>humble(X))))&
((~generous(john)&~old(john)))&
(generous(paul))&
((~quiet(susan)|funny(susan)))&
(~happy(mary))&
(~humble(lucy)) | creative(alice) | [
"p6",
"p7",
"p9",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 7139810040774071877369928
% SZS output start Proof for 7139810040774071877369928
7. ! [X0] : ((~rich(X0) <~> ~happy(X0)) <=> ~creative(X0)) [input p6]
8. ! [X0] : ((patient(X0) | happy(X0)) <=> (patient(X0) <~> ~rich(X0))) [input p7]
10. ? [X0] : (~quiet(X0) | ~patient(X0)) => (~creative(alice) & ~kind(alice)) [input p9]
12. ! [X0] : ((~happy(X0) & patient(X0)) <=> funny(X0)) [input p11]
14. ! [X0] : ((~funny(X0) | ~quiet(X0)) => (~happy(X0) <~> ~quiet(X0))) [input p13]
25. creative(alice) [input hypothesis]
37. (~creative(alice) & ~kind(alice)) | ! [X0] : (quiet(X0) & patient(X0)) [ennf transformation 10]
38. ! [X0] : ((~happy(X0) <~> ~quiet(X0)) | (funny(X0) & quiet(X0))) [ennf transformation 14]
58. ! [X0] : ((((happy(X0) | rich(X0)) & (~happy(X0) | ~rich(X0))) | creative(X0)) & (~creative(X0) | ((~rich(X0) | happy(X0)) & (~happy(X0) | rich(X0))))) [nnf transformation 7]
59. ! [X0] : (((patient(X0) | happy(X0)) | ((patient(X0) | rich(X0)) & (~rich(X0) | ~patient(X0)))) & (((rich(X0) | ~patient(X0)) & (~rich(X0) | patient(X0))) | (~patient(X0) & ~happy(X0)))) [nnf transformation 8]
60. ! [X0] : ((patient(X0) | happy(X0) | ((patient(X0) | rich(X0)) & (~rich(X0) | ~patient(X0)))) & (((rich(X0) | ~patient(X0)) & (~rich(X0) | patient(X0))) | (~patient(X0) & ~happy(X0)))) [flattening 59]
65. ! [X0] : (((~happy(X0) & patient(X0)) | ~funny(X0)) & (funny(X0) | (happy(X0) | ~patient(X0)))) [nnf transformation 12]
66. ! [X0] : (((~happy(X0) & patient(X0)) | ~funny(X0)) & (funny(X0) | happy(X0) | ~patient(X0))) [flattening 65]
72. ! [X0] : (((quiet(X0) | happy(X0)) & (~quiet(X0) | ~happy(X0))) | (funny(X0) & quiet(X0))) [nnf transformation 38]
103. ~creative(X0) | ~rich(X0) | happy(X0) [cnf transformation 58]
109. rich(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 60]
115. ~creative(alice) | patient(X0) [cnf transformation 37]
116. ~creative(alice) | quiet(X0) [cnf transformation 37]
122. ~happy(X0) | ~funny(X0) [cnf transformation 66]
128. ~quiet(X0) | ~happy(X0) | funny(X0) [cnf transformation 72]
150. creative(alice) [cnf transformation 25]
152. ~patient(X0) | rich(X0) [duplicate literal removal 109]
198. 11 <=> ! [X3] : rich(X3) [avatar definition]
199. rich(X3) <- (11) [avatar component clause 198]
206. 13 <=> ! [X3] : quiet(X3) [avatar definition]
207. quiet(X3) <- (13) [avatar component clause 206]
278. 28 <=> creative(alice) [avatar definition]
279. creative(alice) <- (28) [avatar component clause 278]
281. 13 | ~28 [avatar split clause 116,278,206]
283. 29 <=> ! [X0] : patient(X0) [avatar definition]
284. patient(X0) <- (29) [avatar component clause 283]
285. 29 | ~28 [avatar split clause 115,278,283]
331. ~happy(X0) | ~quiet(X0) [subsumption resolution 128,122]
404. 28 [avatar split clause 150,278]
425. rich(X0) <- (29) [resolution 152,284]
434. 11 | ~29 [avatar split clause 425,283,198]
443. ~rich(alice) | happy(alice) <- (28) [resolution 103,279]
447. happy(alice) <- (11, 28) [subsumption resolution 443,199]
458. ~quiet(alice) <- (11, 28) [resolution 447,331]
460. $false <- (11, 13, 28) [subsumption resolution 458,207]
461. ~11 | ~13 | ~28 [avatar contradiction clause 460]
462. $false [avatar sat refutation 281,285,404,434,461]
% SZS output end Proof for 7139810040774071877369928
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If fred is either not rich or not strong then someone is not wise or calm and vice versa.
Everyone who is not strong or brave is either not generous or not old and vice versa.
If lucy is either quiet or not curious then someone is not brave and vice versa.
If alice is calm then someone is patient or old and vice versa.
If someone is both generous and old then someone is not rich or not happy and vice versa.
Everyone who is strong or not rich is either generous or creative.
Everyone who is patient or kind is not generous or not brave and vice versa.
Everyone who is curious is both creative and funny and vice versa.
Everyone who is either not funny or not wise is not curious and vice versa.
Everyone who is both quiet and not curious is either not humble or not curious and vice versa.
Everyone who is funny is not patient.
Everyone who is either not wise or tall is quiet or not happy.
If someone is not wise or not brave then someone is both kind and creative.
Everyone who is patient is creative or not wise.
Everyone who is either not creative or not calm is humble or funny and vice versa.
Someone is either wise or funny.
Paul is old or not funny.
Alice is not happy or old.
Susan is either not brave or creative.
Fred is not generous.
Someone is either wise or calm.
Someone is both not generous and happy. | Paul is not funny. | neutral | (((~rich(fred)<~>~strong(fred)))<=>(?[X]:((~wise(X)|calm(X)))))&
(![X]:((~strong(X)|brave(X))<=>(~generous(X)<~>~old(X))))&
(((quiet(lucy)<~>~curious(lucy)))<=>(?[X]:(~brave(X))))&
((calm(alice))<=>(?[X]:((patient(X)|old(X)))))&
((?[X]:((generous(X)&old(X))))<=>(?[X]:((~rich(X)|~happy(X)))))&
(![X]:((strong(X)|~rich(X))=>(generous(X)<~>creative(X))))&
(![X]:((patient(X)|kind(X))<=>(~generous(X)|~brave(X))))&
(![X]:(curious(X)<=>(creative(X)&funny(X))))&
(![X]:((~funny(X)<~>~wise(X))<=>~curious(X)))&
(![X]:((quiet(X)&~curious(X))<=>(~humble(X)<~>~curious(X))))&
(![X]:(funny(X)=>~patient(X)))&
(![X]:((~wise(X)<~>tall(X))=>(quiet(X)|~happy(X))))&
((?[X]:((~wise(X)|~brave(X))))=>(?[X]:((kind(X)&creative(X)))))&
(![X]:(patient(X)=>(creative(X)|~wise(X))))&
(![X]:((~creative(X)<~>~calm(X))<=>(humble(X)|funny(X))))&
(?[X]:((wise(X)<~>funny(X))))&
((old(paul)|~funny(paul)))&
((~happy(alice)|old(alice)))&
((~brave(susan)<~>creative(susan)))&
(~generous(fred))&
(?[X]:((wise(X)<~>calm(X))))&
(?[X]:((~generous(X)&happy(X)))) | ~funny(paul) | [] | null | 0 |
Everyone who is either not old or old is either happy or rich.
If paul is calm or tall then mary is calm.
If someone is not brave then susan is old and vice versa.
If mary is not strong or not creative then someone is not creative or funny and vice versa.
Everyone who is both strong and not calm is both not rich and kind.
Everyone who is strong is both generous and funny and vice versa.
If someone is either old or not generous then someone is quiet or not creative and vice versa.
If someone is both not wise and not funny then mary is not old or rich and vice versa.
Everyone who is rich or not happy is both not rich and generous and vice versa.
If someone is both not kind and happy then susan is calm or not brave.
Everyone who is not brave is either not calm or not old and vice versa.
Everyone who is either calm or not curious is both rich and humble and vice versa.
If someone is creative or kind then fred is both not tall and not quiet.
If someone is either not curious or not creative then someone is either not generous or not brave and vice versa.
If john is patient or humble then someone is both creative and not happy.
Someone is not patient.
Someone is both brave and curious.
Someone is not wise or not strong.
Someone is calm or funny.
Alice is brave or not quiet.
Someone is not funny or generous.
Someone is generous or not kind. | John is patient. | contradiction | (![X]:((~old(X)<~>old(X))=>(happy(X)<~>rich(X))))&
(((calm(paul)|tall(paul)))=>(calm(mary)))&
((?[X]:(~brave(X)))<=>(old(susan)))&
(((~strong(mary)|~creative(mary)))<=>(?[X]:((~creative(X)|funny(X)))))&
(![X]:((strong(X)&~calm(X))=>(~rich(X)&kind(X))))&
(![X]:(strong(X)<=>(generous(X)&funny(X))))&
((?[X]:((old(X)<~>~generous(X))))<=>(?[X]:((quiet(X)|~creative(X)))))&
((?[X]:((~wise(X)&~funny(X))))<=>((~old(mary)|rich(mary))))&
(![X]:((rich(X)|~happy(X))<=>(~rich(X)&generous(X))))&
((?[X]:((~kind(X)&happy(X))))=>((calm(susan)|~brave(susan))))&
(![X]:(~brave(X)<=>(~calm(X)<~>~old(X))))&
(![X]:((calm(X)<~>~curious(X))<=>(rich(X)&humble(X))))&
((?[X]:((creative(X)|kind(X))))=>((~tall(fred)&~quiet(fred))))&
((?[X]:((~curious(X)<~>~creative(X))))<=>(?[X]:((~generous(X)<~>~brave(X)))))&
(((patient(john)|humble(john)))=>(?[X]:((creative(X)&~happy(X)))))&
(?[X]:(~patient(X)))&
(?[X]:((brave(X)&curious(X))))&
(?[X]:((~wise(X)|~strong(X))))&
(?[X]:((calm(X)|funny(X))))&
((brave(alice)|~quiet(alice)))&
(?[X]:((~funny(X)|generous(X))))&
(?[X]:((generous(X)|~kind(X)))) | patient(john) | [
"p0",
"p8",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6691358821744031959105791
% SZS output start Proof for 6691358821744031959105791
1. ! [X0] : ((~old(X0) <~> old(X0)) => (happy(X0) <~> rich(X0))) [input p0]
9. ! [X0] : ((~happy(X0) | rich(X0)) <=> (generous(X0) & ~rich(X0))) [input p8]
15. (humble(john) | patient(john)) => ? [X0] : (~happy(X0) & creative(X0)) [input p14]
23. patient(john) [input hypothesis]
28. ! [X0] : ((happy(X0) <~> rich(X0)) | (~old(X0) <=> old(X0))) [ennf transformation 1]
35. ? [X0] : (~happy(X0) & creative(X0)) | (~humble(john) & ~patient(john)) [ennf transformation 15]
36. ! [X0] : (((~rich(X0) | ~happy(X0)) & (rich(X0) | happy(X0))) | ((~old(X0) | ~old(X0)) & (old(X0) | old(X0)))) [nnf transformation 28]
58. ! [X0] : (((~happy(X0) | rich(X0)) | (~generous(X0) | rich(X0))) & ((generous(X0) & ~rich(X0)) | (happy(X0) & ~rich(X0)))) [nnf transformation 9]
59. ! [X0] : ((~happy(X0) | rich(X0) | ~generous(X0) | rich(X0)) & ((generous(X0) & ~rich(X0)) | (happy(X0) & ~rich(X0)))) [flattening 58]
68. ? [X0] : (~happy(X0) & creative(X0)) => (~happy(sK7) & creative(sK7)) [choice axiom]
69. (~happy(sK7) & creative(sK7)) | (~humble(john) & ~patient(john)) [skolemisation 35,68]
82. rich(X0) | happy(X0) | old(X0) | old(X0) [cnf transformation 36]
83. rich(X0) | happy(X0) | ~old(X0) | ~old(X0) [cnf transformation 36]
110. ~rich(X0) | happy(X0) [cnf transformation 59]
137. ~happy(sK7) | ~patient(john) [cnf transformation 69]
147. patient(john) [cnf transformation 23]
150. rich(X0) | happy(X0) | old(X0) [duplicate literal removal 82]
151. rich(X0) | happy(X0) | ~old(X0) [duplicate literal removal 83]
155. rich(X0) | happy(X0) [subsumption resolution 150,151]
260. happy(X0) [subsumption resolution 110,155]
325. ~patient(john) [subsumption resolution 137,260]
371. $false [subsumption resolution 147,325]
% SZS output end Proof for 6691358821744031959105791
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or wise is either not funny or kind and vice versa.
Everyone who is both not calm and creative is both not happy and not patient and vice versa.
Everyone who is not tall or not calm is either not strong or curious and vice versa.
If alice is strong or happy then someone is not tall or not humble and vice versa.
If paul is both not creative and not generous then someone is quiet or not creative.
Everyone who is rich or patient is both humble and not humble.
If john is either not happy or not humble then paul is either brave or not quiet.
If someone is rich or not calm then someone is either not happy or patient.
Everyone who is both not brave and not strong is either not calm or not generous.
Everyone who is either not funny or quiet is humble or not creative and vice versa.
Everyone who is not funny or not calm is both kind and not strong.
Everyone who is either not brave or happy is either not brave or curious.
If someone is both rich and not humble then mary is both wise and not funny and vice versa.
Everyone who is creative or funny is both happy and not humble and vice versa.
If someone is both brave and humble then fred is not rich and vice versa.
Someone is either not tall or not calm.
Paul is old.
Someone is not brave or not humble.
Mary is quiet or old.
Mary is creative or rich.
Someone is humble.
Susan is old or tall.
Someone is either not calm or not tall. | Susan is not patient. | entailment | (![X]:((~curious(X)<~>wise(X))<=>(~funny(X)<~>kind(X))))&
(![X]:((~calm(X)&creative(X))<=>(~happy(X)&~patient(X))))&
(![X]:((~tall(X)|~calm(X))<=>(~strong(X)<~>curious(X))))&
(((strong(alice)|happy(alice)))<=>(?[X]:((~tall(X)|~humble(X)))))&
(((~creative(paul)&~generous(paul)))=>(?[X]:((quiet(X)|~creative(X)))))&
(![X]:((rich(X)|patient(X))=>(humble(X)&~humble(X))))&
(((~happy(john)<~>~humble(john)))=>((brave(paul)<~>~quiet(paul))))&
((?[X]:((rich(X)|~calm(X))))=>(?[X]:((~happy(X)<~>patient(X)))))&
(![X]:((~brave(X)&~strong(X))=>(~calm(X)<~>~generous(X))))&
(![X]:((~funny(X)<~>quiet(X))<=>(humble(X)|~creative(X))))&
(![X]:((~funny(X)|~calm(X))=>(kind(X)&~strong(X))))&
(![X]:((~brave(X)<~>happy(X))=>(~brave(X)<~>curious(X))))&
((?[X]:((rich(X)&~humble(X))))<=>((wise(mary)&~funny(mary))))&
(![X]:((creative(X)|funny(X))<=>(happy(X)&~humble(X))))&
((?[X]:((brave(X)&humble(X))))<=>(~rich(fred)))&
(?[X]:((~tall(X)<~>~calm(X))))&
(old(paul))&
(?[X]:((~brave(X)|~humble(X))))&
((quiet(mary)|old(mary)))&
((creative(mary)|rich(mary)))&
(?[X]:(humble(X)))&
((old(susan)|tall(susan)))&
(?[X]:((~calm(X)<~>~tall(X)))) | ~patient(susan) | [
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 5166038667309392592799251
% SZS output start Proof for 5166038667309392592799251
6. ! [X0] : ((patient(X0) | rich(X0)) => (~humble(X0) & humble(X0))) [input p5]
24. patient(susan) [input hypothesis]
31. ! [X0] : ((~humble(X0) & humble(X0)) | (~patient(X0) & ~rich(X0))) [ennf transformation 6]
104. humble(X0) | ~patient(X0) [cnf transformation 31]
106. ~humble(X0) | ~patient(X0) [cnf transformation 31]
150. patient(susan) [cnf transformation 24]
196. ~patient(X0) [subsumption resolution 104,106]
274. $false [subsumption resolution 150,196]
% SZS output end Proof for 5166038667309392592799251
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is not rich or not generous then someone is not brave and vice versa.
Everyone who is both not patient and strong is tall or not funny and vice versa.
If fred is funny or wise then someone is either patient or not generous and vice versa.
If someone is not quiet or brave then fred is curious or old and vice versa.
If paul is not patient then someone is brave.
Everyone who is both curious and rich is not brave.
If alice is wise then lucy is both not curious and kind and vice versa.
Everyone who is patient or not happy is either not calm or brave.
If someone is either not patient or quiet then fred is not humble or calm.
If someone is generous then someone is both tall and not curious and vice versa.
Everyone who is both wise and not tall is either strong or funny and vice versa.
If fred is strong or not tall then mary is both wise and funny.
If susan is kind then someone is either not quiet or strong.
If someone is not creative or brave then someone is both not tall and tall.
Everyone who is not brave or not curious is humble or not humble and vice versa.
If someone is not patient then someone is either curious or not strong.
Paul is both not rich and old.
Someone is not patient or quiet.
Someone is both not old and wise.
John is not wise or strong.
Someone is happy or strong.
Someone is either generous or strong.
Someone is either not rich or not generous. | Susan is brave. | contradiction | (((~rich(lucy)|~generous(lucy)))<=>(?[X]:(~brave(X))))&
(![X]:((~patient(X)&strong(X))<=>(tall(X)|~funny(X))))&
(((funny(fred)|wise(fred)))<=>(?[X]:((patient(X)<~>~generous(X)))))&
((?[X]:((~quiet(X)|brave(X))))<=>((curious(fred)|old(fred))))&
((~patient(paul))=>(?[X]:(brave(X))))&
(![X]:((curious(X)&rich(X))=>~brave(X)))&
((wise(alice))<=>((~curious(lucy)&kind(lucy))))&
(![X]:((patient(X)|~happy(X))=>(~calm(X)<~>brave(X))))&
((?[X]:((~patient(X)<~>quiet(X))))=>((~humble(fred)|calm(fred))))&
((?[X]:(generous(X)))<=>(?[X]:((tall(X)&~curious(X)))))&
(![X]:((wise(X)&~tall(X))<=>(strong(X)<~>funny(X))))&
(((strong(fred)|~tall(fred)))=>((wise(mary)&funny(mary))))&
((kind(susan))=>(?[X]:((~quiet(X)<~>strong(X)))))&
((?[X]:((~creative(X)|brave(X))))=>(?[X]:((~tall(X)&tall(X)))))&
(![X]:((~brave(X)|~curious(X))<=>(humble(X)|~humble(X))))&
((?[X]:(~patient(X)))=>(?[X]:((curious(X)<~>~strong(X)))))&
((~rich(paul)&old(paul)))&
(?[X]:((~patient(X)|quiet(X))))&
(?[X]:((~old(X)&wise(X))))&
((~wise(john)|strong(john)))&
(?[X]:((happy(X)|strong(X))))&
(?[X]:((generous(X)<~>strong(X))))&
(?[X]:((~rich(X)<~>~generous(X)))) | brave(susan) | [
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 5672026975055311723639762
% SZS output start Proof for 5672026975055311723639762
14. ? [X0] : (brave(X0) | ~creative(X0)) => ? [X0] : (tall(X0) & ~tall(X0)) [input p13]
24. brave(susan) [input hypothesis]
26. ? [X0] : (brave(X0) | ~creative(X0)) => ? [X1] : (tall(X1) & ~tall(X1)) [rectify 14]
28. ? [X0] : brave(X0) => ? [X1] : (tall(X1) & ~tall(X1)) [pure predicate removal 26]
39. ? [X1] : (tall(X1) & ~tall(X1)) | ! [X0] : ~brave(X0) [ennf transformation 28]
74. ? [X0] : (tall(X0) & ~tall(X0)) | ! [X1] : ~brave(X1) [rectify 39]
75. ? [X0] : (tall(X0) & ~tall(X0)) => (tall(sK7) & ~tall(sK7)) [choice axiom]
76. (tall(sK7) & ~tall(sK7)) | ! [X1] : ~brave(X1) [skolemisation 74,75]
135. ~tall(sK7) | ~brave(X1) [cnf transformation 76]
136. tall(sK7) | ~brave(X1) [cnf transformation 76]
153. brave(susan) [cnf transformation 24]
219. 15 <=> ! [X1] : ~brave(X1) [avatar definition]
220. ~brave(X1) <- (15) [avatar component clause 219]
325. 38 <=> tall(sK7) [avatar definition]
328. 15 | 38 [avatar split clause 136,325,219]
329. 15 | ~38 [avatar split clause 135,325,219]
374. $false <- (15) [resolution 220,153]
375. ~15 [avatar contradiction clause 374]
376. $false [avatar sat refutation 328,329,375]
% SZS output end Proof for 5672026975055311723639762
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If john is strong then john is either kind or not calm.
Everyone who is either not patient or not funny is either not funny or strong.
Everyone who is both not curious and not brave is either not strong or curious.
If mary is patient then paul is not generous or wise and vice versa.
Everyone who is both not kind and generous is both tall and not calm and vice versa.
If lucy is both not calm and not curious then alice is not old or humble and vice versa.
If fred is either not humble or calm then someone is either not funny or not generous.
Everyone who is quiet or not strong is both not rich and calm.
If fred is both not creative and generous then someone is either not rich or not generous and vice versa.
If lucy is both old and creative then someone is humble or rich.
Everyone who is not brave is not creative and vice versa.
If paul is not tall or not curious then fred is not creative and vice versa.
Everyone who is strong or calm is either not patient or wise and vice versa.
If someone is wise then someone is both happy and quiet and vice versa.
Everyone who is not creative is both brave and humble and vice versa.
Everyone who is either strong or not patient is not rich and vice versa.
Susan is rich.
Paul is kind.
Susan is calm or not curious.
Susan is not quiet or happy.
Someone is quiet.
Susan is both not happy and not patient.
John is not curious or not wise. | Lucy is not humble. | entailment | ((strong(john))=>((kind(john)<~>~calm(john))))&
(![X]:((~patient(X)<~>~funny(X))=>(~funny(X)<~>strong(X))))&
(![X]:((~curious(X)&~brave(X))=>(~strong(X)<~>curious(X))))&
((patient(mary))<=>((~generous(paul)|wise(paul))))&
(![X]:((~kind(X)&generous(X))<=>(tall(X)&~calm(X))))&
(((~calm(lucy)&~curious(lucy)))<=>((~old(alice)|humble(alice))))&
(((~humble(fred)<~>calm(fred)))=>(?[X]:((~funny(X)<~>~generous(X)))))&
(![X]:((quiet(X)|~strong(X))=>(~rich(X)&calm(X))))&
(((~creative(fred)&generous(fred)))<=>(?[X]:((~rich(X)<~>~generous(X)))))&
(((old(lucy)&creative(lucy)))=>(?[X]:((humble(X)|rich(X)))))&
(![X]:(~brave(X)<=>~creative(X)))&
(((~tall(paul)|~curious(paul)))<=>(~creative(fred)))&
(![X]:((strong(X)|calm(X))<=>(~patient(X)<~>wise(X))))&
((?[X]:(wise(X)))<=>(?[X]:((happy(X)&quiet(X)))))&
(![X]:(~creative(X)<=>(brave(X)&humble(X))))&
(![X]:((strong(X)<~>~patient(X))<=>~rich(X)))&
(rich(susan))&
(kind(paul))&
((calm(susan)|~curious(susan)))&
((~quiet(susan)|happy(susan)))&
(?[X]:(quiet(X)))&
((~happy(susan)&~patient(susan)))&
((~curious(john)|~wise(john))) | ~humble(lucy) | [
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2582812522120486472949957
% SZS output start Proof for 2582812522120486472949957
11. ! [X0] : (~brave(X0) <=> ~creative(X0)) [input p10]
15. ! [X0] : (~creative(X0) <=> (humble(X0) & brave(X0))) [input p14]
24. humble(lucy) [input hypothesis]
53. ! [X0] : ((~brave(X0) | creative(X0)) & (~creative(X0) | brave(X0))) [nnf transformation 11]
63. ! [X0] : ((~creative(X0) | (~humble(X0) | ~brave(X0))) & ((humble(X0) & brave(X0)) | creative(X0))) [nnf transformation 15]
64. ! [X0] : ((~creative(X0) | ~humble(X0) | ~brave(X0)) & ((humble(X0) & brave(X0)) | creative(X0))) [flattening 63]
103. ~creative(X0) | brave(X0) [cnf transformation 53]
104. ~brave(X0) | creative(X0) [cnf transformation 53]
117. brave(X0) | creative(X0) [cnf transformation 64]
119. ~creative(X0) | ~humble(X0) | ~brave(X0) [cnf transformation 64]
132. humble(lucy) [cnf transformation 24]
283. ~creative(X0) | ~humble(X0) [subsumption resolution 119,103]
284. creative(X0) [subsumption resolution 117,104]
327. ~humble(X1) [resolution 283,284]
329. $false [resolution 327,132]
% SZS output end Proof for 2582812522120486472949957
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If alice is quiet then fred is not humble.
Everyone who is either happy or not tall is not humble or not old and vice versa.
If susan is either strong or not calm then paul is both creative and curious and vice versa.
If susan is wise then someone is humble and vice versa.
Everyone who is not calm is not curious or not tall and vice versa.
Everyone who is curious or wise is either not humble or not quiet and vice versa.
If someone is either not quiet or humble then john is patient and vice versa.
If paul is either not funny or wise then someone is not curious and vice versa.
Everyone who is both not calm and generous is not strong and vice versa.
If fred is both not creative and not generous then someone is both not strong and not humble and vice versa.
Everyone who is not wise is tall or not creative and vice versa.
If someone is either not old or quiet then someone is either not kind or wise.
Everyone who is patient is both not patient and quiet and vice versa.
If paul is strong then someone is strong.
Everyone who is old or not quiet is both curious and not brave.
If paul is either wise or not old then fred is tall.
Mary is both not funny and old.
Lucy is brave or creative.
Someone is wise or funny.
Alice is both happy and wise.
Someone is either not strong or not generous.
Alice is not wise or generous. | Fred is quiet. | contradiction | ((quiet(alice))=>(~humble(fred)))&
(![X]:((happy(X)<~>~tall(X))<=>(~humble(X)|~old(X))))&
(((strong(susan)<~>~calm(susan)))<=>((creative(paul)&curious(paul))))&
((wise(susan))<=>(?[X]:(humble(X))))&
(![X]:(~calm(X)<=>(~curious(X)|~tall(X))))&
(![X]:((curious(X)|wise(X))<=>(~humble(X)<~>~quiet(X))))&
((?[X]:((~quiet(X)<~>humble(X))))<=>(patient(john)))&
(((~funny(paul)<~>wise(paul)))<=>(?[X]:(~curious(X))))&
(![X]:((~calm(X)&generous(X))<=>~strong(X)))&
(((~creative(fred)&~generous(fred)))<=>(?[X]:((~strong(X)&~humble(X)))))&
(![X]:(~wise(X)<=>(tall(X)|~creative(X))))&
((?[X]:((~old(X)<~>quiet(X))))=>(?[X]:((~kind(X)<~>wise(X)))))&
(![X]:(patient(X)<=>(~patient(X)&quiet(X))))&
((strong(paul))=>(?[X]:(strong(X))))&
(![X]:((old(X)|~quiet(X))=>(curious(X)&~brave(X))))&
(((wise(paul)<~>~old(paul)))=>(tall(fred)))&
((~funny(mary)&old(mary)))&
((brave(lucy)|creative(lucy)))&
(?[X]:((wise(X)|funny(X))))&
((happy(alice)&wise(alice)))&
(?[X]:((~strong(X)<~>~generous(X))))&
((~wise(alice)|generous(alice))) | quiet(fred) | [
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 1172445602225308507119607
% SZS output start Proof for 1172445602225308507119607
13. ! [X0] : (patient(X0) <=> (quiet(X0) & ~patient(X0))) [input p12]
23. quiet(fred) [input hypothesis]
63. ! [X0] : ((patient(X0) | (~quiet(X0) | patient(X0))) & ((quiet(X0) & ~patient(X0)) | ~patient(X0))) [nnf transformation 13]
64. ! [X0] : ((patient(X0) | ~quiet(X0) | patient(X0)) & ((quiet(X0) & ~patient(X0)) | ~patient(X0))) [flattening 63]
119. ~patient(X0) | ~patient(X0) [cnf transformation 64]
121. patient(X0) | ~quiet(X0) | patient(X0) [cnf transformation 64]
138. quiet(fred) [cnf transformation 23]
139. ~patient(X0) [duplicate literal removal 119]
140. ~quiet(X0) | patient(X0) [duplicate literal removal 121]
333. patient(fred) [resolution 140,138]
334. $false [subsumption resolution 333,139]
% SZS output end Proof for 1172445602225308507119607
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is rich is not brave or not funny.
Everyone who is strong or curious is not funny.
Everyone who is creative or calm is not patient.
If mary is both funny and not happy then someone is not generous or tall.
If someone is not humble then alice is either not tall or funny and vice versa.
Everyone who is both not strong and rich is both happy and not creative and vice versa.
Everyone who is either quiet or strong is humble.
Everyone who is old is both not happy and not patient.
If lucy is happy or not quiet then john is either not happy or not rich and vice versa.
If someone is both not funny and not old then someone is patient and vice versa.
Everyone who is both patient and not calm is quiet or not kind and vice versa.
Everyone who is either strong or not strong is curious and vice versa.
If someone is not tall or humble then lucy is humble.
Everyone who is either brave or not humble is both kind and not old.
Everyone who is happy is both not funny and not brave and vice versa.
If alice is both not curious and not funny then someone is either brave or not old.
Alice is both not tall and rich.
Someone is either not happy or kind.
Paul is quiet or tall.
Someone is either humble or not brave.
Someone is quiet or generous.
Someone is both not calm and happy.
Someone is not happy. | John is not kind. | neutral | (![X]:(rich(X)=>(~brave(X)|~funny(X))))&
(![X]:((strong(X)|curious(X))=>~funny(X)))&
(![X]:((creative(X)|calm(X))=>~patient(X)))&
(((funny(mary)&~happy(mary)))=>(?[X]:((~generous(X)|tall(X)))))&
((?[X]:(~humble(X)))<=>((~tall(alice)<~>funny(alice))))&
(![X]:((~strong(X)&rich(X))<=>(happy(X)&~creative(X))))&
(![X]:((quiet(X)<~>strong(X))=>humble(X)))&
(![X]:(old(X)=>(~happy(X)&~patient(X))))&
(((happy(lucy)|~quiet(lucy)))<=>((~happy(john)<~>~rich(john))))&
((?[X]:((~funny(X)&~old(X))))<=>(?[X]:(patient(X))))&
(![X]:((patient(X)&~calm(X))<=>(quiet(X)|~kind(X))))&
(![X]:((strong(X)<~>~strong(X))<=>curious(X)))&
((?[X]:((~tall(X)|humble(X))))=>(humble(lucy)))&
(![X]:((brave(X)<~>~humble(X))=>(kind(X)&~old(X))))&
(![X]:(happy(X)<=>(~funny(X)&~brave(X))))&
(((~curious(alice)&~funny(alice)))=>(?[X]:((brave(X)<~>~old(X)))))&
((~tall(alice)&rich(alice)))&
(?[X]:((~happy(X)<~>kind(X))))&
((quiet(paul)|tall(paul)))&
(?[X]:((humble(X)<~>~brave(X))))&
(?[X]:((quiet(X)|generous(X))))&
(?[X]:((~calm(X)&happy(X))))&
(?[X]:(~happy(X))) | ~kind(john) | [] | null | 0 |
If someone is both old and quiet then someone is humble and vice versa. Everyone who is either calm or funny is either wise or not kind and vice versa. Everyone who is quiet or not wise is not happy or old. If mary is either humble or not old then paul is either old or not calm and vice versa. Everyone who is not happy is not rich or not quiet and vice versa. Everyone who is both not old and not generous is not wise and vice versa. Everyone who is not wise or humble is both not strong and rich and vice versa. Everyone who is not happy or creative is both not creative and not brave. Everyone who is both quiet and not tall is both not funny and not creative and vice versa. If someone is not quiet then someone is both not patient and strong and vice versa. If someone is not rich then fred is not strong. Everyone who is either not calm or not quiet is either not funny or patient and vice versa. If fred is brave or generous then someone is not kind. If someone is both not humble and strong then paul is wise or kind. Lucy is not wise or not quiet. Someone is either happy or patient. Someone is not humble or generous. Fred is either not quiet or calm. Someone is both not old and quiet. | Fred is old. | neutral | ((?[X]:((old(X)&quiet(X))))<=>(?[X]:(humble(X))))&
(![X]:((calm(X)<~>funny(X))<=>(wise(X)<~>~kind(X))))&
(![X]:((quiet(X)|~wise(X))=>(~happy(X)|old(X))))&
(((humble(mary)<~>~old(mary)))<=>((old(paul)<~>~calm(paul))))&
(![X]:(~happy(X)<=>(~rich(X)|~quiet(X))))&
(![X]:((~old(X)&~generous(X))<=>~wise(X)))&
(![X]:((~wise(X)|humble(X))<=>(~strong(X)&rich(X))))&
(![X]:((~happy(X)|creative(X))=>(~creative(X)&~brave(X))))&
(![X]:((quiet(X)&~tall(X))<=>(~funny(X)&~creative(X))))&
((?[X]:(~quiet(X)))<=>(?[X]:((~patient(X)&strong(X)))))&
((?[X]:(~rich(X)))=>(~strong(fred)))&
(![X]:((~calm(X)<~>~quiet(X))<=>(~funny(X)<~>patient(X))))&
(((brave(fred)|generous(fred)))=>(?[X]:(~kind(X))))&
((?[X]:((~humble(X)&strong(X))))=>((wise(paul)|kind(paul))))&
((~wise(lucy)|~quiet(lucy)))&
(?[X]:((happy(X)<~>patient(X))))&
(?[X]:((~humble(X)|generous(X))))&
((~quiet(fred)<~>calm(fred)))&
(?[X]:((~old(X)&quiet(X)))) | old(fred) | [] | null | 0 |
Everyone who is both not calm and humble is both not wise and quiet and vice versa.
If someone is not wise or not old then fred is either creative or not brave and vice versa.
If alice is not calm or not happy then john is patient.
Everyone who is not generous is quiet or not kind and vice versa.
If someone is happy then someone is either kind or funny and vice versa.
Everyone who is not curious is either not curious or funny and vice versa.
Everyone who is not happy is curious and vice versa.
If fred is patient or quiet then someone is both not generous and tall.
Everyone who is not curious or not funny is either not old or not quiet.
If someone is either calm or not brave then someone is both not calm and not brave and vice versa.
Everyone who is both quiet and not kind is both not creative and kind.
If someone is not tall then someone is both not strong and kind.
If lucy is calm or not quiet then alice is both calm and curious and vice versa.
Everyone who is not kind or strong is either not humble or patient and vice versa.
If someone is not rich then alice is calm.
Everyone who is either quiet or not calm is not humble or wise.
Lucy is not happy or not tall.
Someone is quiet.
Someone is not old or not generous.
Someone is either not wise or curious.
Lucy is rich or kind.
Someone is strong.
Someone is either old or not curious.
Lucy is not kind or tall. | Lucy is not curious. | neutral | (![X]:((~calm(X)&humble(X))<=>(~wise(X)&quiet(X))))&
((?[X]:((~wise(X)|~old(X))))<=>((creative(fred)<~>~brave(fred))))&
(((~calm(alice)|~happy(alice)))=>(patient(john)))&
(![X]:(~generous(X)<=>(quiet(X)|~kind(X))))&
((?[X]:(happy(X)))<=>(?[X]:((kind(X)<~>funny(X)))))&
(![X]:(~curious(X)<=>(~curious(X)<~>funny(X))))&
(![X]:(~happy(X)<=>curious(X)))&
(((patient(fred)|quiet(fred)))=>(?[X]:((~generous(X)&tall(X)))))&
(![X]:((~curious(X)|~funny(X))=>(~old(X)<~>~quiet(X))))&
((?[X]:((calm(X)<~>~brave(X))))<=>(?[X]:((~calm(X)&~brave(X)))))&
(![X]:((quiet(X)&~kind(X))=>(~creative(X)&kind(X))))&
((?[X]:(~tall(X)))=>(?[X]:((~strong(X)&kind(X)))))&
(((calm(lucy)|~quiet(lucy)))<=>((calm(alice)&curious(alice))))&
(![X]:((~kind(X)|strong(X))<=>(~humble(X)<~>patient(X))))&
((?[X]:(~rich(X)))=>(calm(alice)))&
(![X]:((quiet(X)<~>~calm(X))=>(~humble(X)|wise(X))))&
((~happy(lucy)|~tall(lucy)))&
(?[X]:(quiet(X)))&
(?[X]:((~old(X)|~generous(X))))&
(?[X]:((~wise(X)<~>curious(X))))&
((rich(lucy)|kind(lucy)))&
(?[X]:(strong(X)))&
(?[X]:((old(X)<~>~curious(X))))&
((~kind(lucy)|tall(lucy))) | ~curious(lucy) | [] | null | 0 |
Everyone who is both not humble and not tall is not humble or not wise.
If alice is not rich then someone is not rich or generous and vice versa.
Everyone who is strong is calm or not creative.
If lucy is both not brave and funny then someone is not kind.
If someone is either not kind or wise then john is either not tall or strong and vice versa.
If someone is not quiet or not calm then fred is not funny.
If alice is both wise and not curious then someone is both not old and happy.
Everyone who is old is generous.
Everyone who is both not generous and not strong is both not kind and happy.
If someone is kind or not calm then alice is not brave and vice versa.
If paul is calm then someone is both old and not humble.
If alice is quiet or calm then susan is not kind or curious and vice versa.
If someone is both humble and not wise then someone is both not rich and wise.
Everyone who is both not strong and happy is either kind or not kind and vice versa.
If someone is brave or curious then fred is either not generous or not patient and vice versa.
If someone is not funny then lucy is both not curious and funny.
Someone is brave or creative.
Someone is both not patient and brave.
Someone is not quiet.
Susan is happy or not funny.
Someone is either creative or not creative.
Someone is both wise and funny.
Someone is both not strong and not kind. | Lucy is strong. | contradiction | (![X]:((~humble(X)&~tall(X))=>(~humble(X)|~wise(X))))&
((~rich(alice))<=>(?[X]:((~rich(X)|generous(X)))))&
(![X]:(strong(X)=>(calm(X)|~creative(X))))&
(((~brave(lucy)&funny(lucy)))=>(?[X]:(~kind(X))))&
((?[X]:((~kind(X)<~>wise(X))))<=>((~tall(john)<~>strong(john))))&
((?[X]:((~quiet(X)|~calm(X))))=>(~funny(fred)))&
(((wise(alice)&~curious(alice)))=>(?[X]:((~old(X)&happy(X)))))&
(![X]:(old(X)=>generous(X)))&
(![X]:((~generous(X)&~strong(X))=>(~kind(X)&happy(X))))&
((?[X]:((kind(X)|~calm(X))))<=>(~brave(alice)))&
((calm(paul))=>(?[X]:((old(X)&~humble(X)))))&
(((quiet(alice)|calm(alice)))<=>((~kind(susan)|curious(susan))))&
((?[X]:((humble(X)&~wise(X))))=>(?[X]:((~rich(X)&wise(X)))))&
(![X]:((~strong(X)&happy(X))<=>(kind(X)<~>~kind(X))))&
((?[X]:((brave(X)|curious(X))))<=>((~generous(fred)<~>~patient(fred))))&
((?[X]:(~funny(X)))=>((~curious(lucy)&funny(lucy))))&
(?[X]:((brave(X)|creative(X))))&
(?[X]:((~patient(X)&brave(X))))&
(?[X]:(~quiet(X)))&
((happy(susan)|~funny(susan)))&
(?[X]:((creative(X)<~>~creative(X))))&
(?[X]:((wise(X)&funny(X))))&
(?[X]:((~strong(X)&~kind(X)))) | strong(lucy) | [
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 4460119354365306426116891
% SZS output start Proof for 4460119354365306426116891
14. ! [X0] : ((happy(X0) & ~strong(X0)) <=> (kind(X0) <~> ~kind(X0))) [input p13]
24. strong(lucy) [input hypothesis]
64. ! [X0] : (((happy(X0) & ~strong(X0)) | ((kind(X0) | kind(X0)) & (~kind(X0) | ~kind(X0)))) & (((kind(X0) | ~kind(X0)) & (~kind(X0) | kind(X0))) | (~happy(X0) | strong(X0)))) [nnf transformation 14]
65. ! [X0] : (((happy(X0) & ~strong(X0)) | ((kind(X0) | kind(X0)) & (~kind(X0) | ~kind(X0)))) & (((kind(X0) | ~kind(X0)) & (~kind(X0) | kind(X0))) | ~happy(X0) | strong(X0))) [flattening 64]
117. ~strong(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 65]
118. ~strong(X0) | kind(X0) | kind(X0) [cnf transformation 65]
140. strong(lucy) [cnf transformation 24]
141. ~strong(X0) | ~kind(X0) [duplicate literal removal 117]
142. ~strong(X0) | kind(X0) [duplicate literal removal 118]
305. ~strong(X0) [subsumption resolution 141,142]
352. $false [subsumption resolution 140,305]
% SZS output end Proof for 4460119354365306426116891
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall and creative is old or quiet and vice versa. If alice is old then fred is not tall or not rich. If mary is calm then someone is not calm or rich and vice versa. Everyone who is not humble is not patient or not creative and vice versa. Everyone who is not patient is either creative or not calm. If someone is not funny or rich then john is not calm or creative. Everyone who is strong is not brave or not rich and vice versa. If paul is both calm and patient then someone is patient. If someone is either not kind or not brave then someone is both quiet and creative. Everyone who is either wise or not quiet is not rich or not patient. Everyone who is not tall is not funny and vice versa. If mary is either rich or generous then someone is not old or tall and vice versa. If someone is either patient or not creative then alice is not calm or creative and vice versa. If john is either not rich or patient then fred is not patient. If someone is not funny or not old then alice is both not wise and creative. If someone is either curious or quiet then someone is either not generous or funny. Someone is not calm. Someone is either not happy or not quiet. Mary is not quiet. Paul is generous or not patient. Mary is quiet or old. Someone is either not calm or quiet. Someone is creative or not old. | Paul is quiet. | neutral | (![X]:((tall(X)&creative(X))<=>(old(X)|quiet(X))))&
((old(alice))=>((~tall(fred)|~rich(fred))))&
((calm(mary))<=>(?[X]:((~calm(X)|rich(X)))))&
(![X]:(~humble(X)<=>(~patient(X)|~creative(X))))&
(![X]:(~patient(X)=>(creative(X)<~>~calm(X))))&
((?[X]:((~funny(X)|rich(X))))=>((~calm(john)|creative(john))))&
(![X]:(strong(X)<=>(~brave(X)|~rich(X))))&
(((calm(paul)&patient(paul)))=>(?[X]:(patient(X))))&
((?[X]:((~kind(X)<~>~brave(X))))=>(?[X]:((quiet(X)&creative(X)))))&
(![X]:((wise(X)<~>~quiet(X))=>(~rich(X)|~patient(X))))&
(![X]:(~tall(X)<=>~funny(X)))&
(((rich(mary)<~>generous(mary)))<=>(?[X]:((~old(X)|tall(X)))))&
((?[X]:((patient(X)<~>~creative(X))))<=>((~calm(alice)|creative(alice))))&
(((~rich(john)<~>patient(john)))=>(~patient(fred)))&
((?[X]:((~funny(X)|~old(X))))=>((~wise(alice)&creative(alice))))&
((?[X]:((curious(X)<~>quiet(X))))=>(?[X]:((~generous(X)<~>funny(X)))))&
(?[X]:(~calm(X)))&
(?[X]:((~happy(X)<~>~quiet(X))))&
(~quiet(mary))&
((generous(paul)|~patient(paul)))&
((quiet(mary)|old(mary)))&
(?[X]:((~calm(X)<~>quiet(X))))&
(?[X]:((creative(X)|~old(X)))) | quiet(paul) | [] | null | 0 |
Everyone who is not quiet or not calm is either not rich or brave and vice versa.
Everyone who is both not tall and wise is not wise.
Everyone who is kind or not rich is quiet and vice versa.
If someone is quiet or not rich then someone is not rich.
Everyone who is not generous is not quiet or not patient.
If mary is either not creative or kind then paul is not rich or curious.
Everyone who is either not quiet or wise is wise and vice versa.
Everyone who is not wise or not funny is not calm and vice versa.
Everyone who is either not happy or wise is both creative and wise and vice versa.
If someone is either not quiet or patient then someone is either not quiet or not generous and vice versa.
Everyone who is not old or old is quiet or wise and vice versa.
Everyone who is either brave or patient is brave and vice versa.
Everyone who is not kind is both not tall and not happy.
Everyone who is not tall or kind is rich or curious and vice versa.
If susan is both not patient and not rich then fred is kind and vice versa.
If paul is not rich then someone is either not quiet or not wise and vice versa.
Someone is happy.
Someone is calm or rich.
John is not patient.
Someone is tall.
Someone is not rich or not creative.
Someone is both not curious and not calm.
Someone is not calm. | Susan is not quiet. | contradiction | (![X]:((~quiet(X)|~calm(X))<=>(~rich(X)<~>brave(X))))&
(![X]:((~tall(X)&wise(X))=>~wise(X)))&
(![X]:((kind(X)|~rich(X))<=>quiet(X)))&
((?[X]:((quiet(X)|~rich(X))))=>(?[X]:(~rich(X))))&
(![X]:(~generous(X)=>(~quiet(X)|~patient(X))))&
(((~creative(mary)<~>kind(mary)))=>((~rich(paul)|curious(paul))))&
(![X]:((~quiet(X)<~>wise(X))<=>wise(X)))&
(![X]:((~wise(X)|~funny(X))<=>~calm(X)))&
(![X]:((~happy(X)<~>wise(X))<=>(creative(X)&wise(X))))&
((?[X]:((~quiet(X)<~>patient(X))))<=>(?[X]:((~quiet(X)<~>~generous(X)))))&
(![X]:((~old(X)|old(X))<=>(quiet(X)|wise(X))))&
(![X]:((brave(X)<~>patient(X))<=>brave(X)))&
(![X]:(~kind(X)=>(~tall(X)&~happy(X))))&
(![X]:((~tall(X)|kind(X))<=>(rich(X)|curious(X))))&
(((~patient(susan)&~rich(susan)))<=>(kind(fred)))&
((~rich(paul))<=>(?[X]:((~quiet(X)<~>~wise(X)))))&
(?[X]:(happy(X)))&
(?[X]:((calm(X)|rich(X))))&
(~patient(john))&
(?[X]:(tall(X)))&
(?[X]:((~rich(X)|~creative(X))))&
(?[X]:((~curious(X)&~calm(X))))&
(?[X]:(~calm(X))) | ~quiet(susan) | [
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 7526474388600596866765239
% SZS output start Proof for 7526474388600596866765239
7. ! [X0] : ((~quiet(X0) <~> wise(X0)) <=> wise(X0)) [input p6]
24. ~quiet(susan) [input hypothesis]
43. ! [X0] : ((((~wise(X0) | quiet(X0)) & (wise(X0) | ~quiet(X0))) | ~wise(X0)) & (wise(X0) | ((~quiet(X0) | ~wise(X0)) & (wise(X0) | quiet(X0))))) [nnf transformation 7]
91. wise(X0) | wise(X0) | quiet(X0) [cnf transformation 43]
94. ~wise(X0) | quiet(X0) | ~wise(X0) [cnf transformation 43]
141. ~quiet(susan) [cnf transformation 24]
146. wise(X0) | quiet(X0) [duplicate literal removal 91]
147. ~wise(X0) | quiet(X0) [duplicate literal removal 94]
179. quiet(X0) [subsumption resolution 146,147]
246. $false [subsumption resolution 141,179]
% SZS output end Proof for 7526474388600596866765239
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If paul is either strong or not patient then someone is both happy and funny and vice versa. If someone is rich then john is not strong and vice versa. If someone is both not old and calm then fred is either strong or happy and vice versa. Everyone who is both not kind and generous is either not kind or patient. Everyone who is strong or curious is either strong or brave and vice versa. Everyone who is both not generous and calm is tall or rich and vice versa. If paul is calm then alice is both not creative and creative. Everyone who is tall is not strong or old. Everyone who is either not patient or not old is humble and vice versa. If someone is kind then someone is not generous and vice versa. Everyone who is not funny is either not patient or not tall. Everyone who is either not patient or funny is not happy and vice versa. If fred is tall or not tall then someone is kind. If someone is either not patient or not wise then someone is either not calm or not old and vice versa. If john is tall then someone is old or brave. Everyone who is not strong or not brave is not humble and vice versa. Lucy is both wise and happy. Someone is not old. Fred is both not brave and not old. Mary is both patient and curious. John is both not happy and not brave. Someone is either not brave or not humble. Lucy is not rich or not generous. | Fred is not humble. | entailment | (((strong(paul)<~>~patient(paul)))<=>(?[X]:((happy(X)&funny(X)))))&
((?[X]:(rich(X)))<=>(~strong(john)))&
((?[X]:((~old(X)&calm(X))))<=>((strong(fred)<~>happy(fred))))&
(![X]:((~kind(X)&generous(X))=>(~kind(X)<~>patient(X))))&
(![X]:((strong(X)|curious(X))<=>(strong(X)<~>brave(X))))&
(![X]:((~generous(X)&calm(X))<=>(tall(X)|rich(X))))&
((calm(paul))=>((~creative(alice)&creative(alice))))&
(![X]:(tall(X)=>(~strong(X)|old(X))))&
(![X]:((~patient(X)<~>~old(X))<=>humble(X)))&
((?[X]:(kind(X)))<=>(?[X]:(~generous(X))))&
(![X]:(~funny(X)=>(~patient(X)<~>~tall(X))))&
(![X]:((~patient(X)<~>funny(X))<=>~happy(X)))&
(((tall(fred)|~tall(fred)))=>(?[X]:(kind(X))))&
((?[X]:((~patient(X)<~>~wise(X))))<=>(?[X]:((~calm(X)<~>~old(X)))))&
((tall(john))=>(?[X]:((old(X)|brave(X)))))&
(![X]:((~strong(X)|~brave(X))<=>~humble(X)))&
((wise(lucy)&happy(lucy)))&
(?[X]:(~old(X)))&
((~brave(fred)&~old(fred)))&
((patient(mary)&curious(mary)))&
((~happy(john)&~brave(john)))&
(?[X]:((~brave(X)<~>~humble(X))))&
((~rich(lucy)|~generous(lucy))) | ~humble(fred) | [
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 2475155474695371637639316
% SZS output start Proof for 2475155474695371637639316
16. ! [X0] : ((~brave(X0) | ~strong(X0)) <=> ~humble(X0)) [input p15]
19. ~old(fred) & ~brave(fred) [input p18]
24. humble(fred) [input hypothesis]
69. ! [X0] : (((~brave(X0) | ~strong(X0)) | humble(X0)) & (~humble(X0) | (brave(X0) & strong(X0)))) [nnf transformation 16]
70. ! [X0] : ((~brave(X0) | ~strong(X0) | humble(X0)) & (~humble(X0) | (brave(X0) & strong(X0)))) [flattening 69]
130. ~humble(X0) | brave(X0) [cnf transformation 70]
135. ~brave(fred) [cnf transformation 19]
144. humble(fred) [cnf transformation 24]
304. brave(fred) [resolution 130,144]
305. $false [subsumption resolution 304,135]
% SZS output end Proof for 2475155474695371637639316
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy or not humble then someone is either not creative or happy.
Everyone who is strong or not rich is either not wise or not old.
Everyone who is not creative is not creative or not patient.
If john is both not brave and not old then susan is strong and vice versa.
Everyone who is not kind or not happy is both not tall and not curious.
If john is either wise or not patient then mary is strong and vice versa.
Everyone who is either wise or not old is patient or curious and vice versa.
Everyone who is both kind and quiet is both wise and not patient and vice versa.
If lucy is either calm or not generous then fred is both wise and quiet.
If susan is both not calm and not generous then susan is old or brave.
If someone is either patient or quiet then someone is not rich or brave.
Everyone who is not old or curious is calm or rich.
If someone is not tall or generous then someone is not strong and vice versa.
If lucy is wise then fred is humble or not old.
If mary is either not kind or wise then someone is not creative or wise and vice versa.
Everyone who is both not old and not curious is either not strong or not kind and vice versa.
Lucy is both not curious and humble.
Alice is not old or not funny.
Someone is calm or rich.
Someone is not strong or calm.
Fred is not generous or not brave.
Mary is wise or not wise.
Someone is not creative or not generous.
Someone is both quiet and happy. | John is not curious. | entailment | ((?[X]:((happy(X)|~humble(X))))=>(?[X]:((~creative(X)<~>happy(X)))))&
(![X]:((strong(X)|~rich(X))=>(~wise(X)<~>~old(X))))&
(![X]:(~creative(X)=>(~creative(X)|~patient(X))))&
(((~brave(john)&~old(john)))<=>(strong(susan)))&
(![X]:((~kind(X)|~happy(X))=>(~tall(X)&~curious(X))))&
(((wise(john)<~>~patient(john)))<=>(strong(mary)))&
(![X]:((wise(X)<~>~old(X))<=>(patient(X)|curious(X))))&
(![X]:((kind(X)&quiet(X))<=>(wise(X)&~patient(X))))&
(((calm(lucy)<~>~generous(lucy)))=>((wise(fred)&quiet(fred))))&
(((~calm(susan)&~generous(susan)))=>((old(susan)|brave(susan))))&
((?[X]:((patient(X)<~>quiet(X))))=>(?[X]:((~rich(X)|brave(X)))))&
(![X]:((~old(X)|curious(X))=>(calm(X)|rich(X))))&
((?[X]:((~tall(X)|generous(X))))<=>(?[X]:(~strong(X))))&
((wise(lucy))=>((humble(fred)|~old(fred))))&
(((~kind(mary)<~>wise(mary)))<=>(?[X]:((~creative(X)|wise(X)))))&
(![X]:((~old(X)&~curious(X))<=>(~strong(X)<~>~kind(X))))&
((~curious(lucy)&humble(lucy)))&
((~old(alice)|~funny(alice)))&
(?[X]:((calm(X)|rich(X))))&
(?[X]:((~strong(X)|calm(X))))&
((~generous(fred)|~brave(fred)))&
((wise(mary)|~wise(mary)))&
(?[X]:((~creative(X)|~generous(X))))&
(?[X]:((quiet(X)&happy(X)))) | ~curious(john) | [
"p1",
"p4",
"p6",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 5764807694767937244373835
% SZS output start Proof for 5764807694767937244373835
2. ! [X0] : ((~rich(X0) | strong(X0)) => (~wise(X0) <~> ~old(X0))) [input p1]
5. ! [X0] : ((~happy(X0) | ~kind(X0)) => (~curious(X0) & ~tall(X0))) [input p4]
7. ! [X0] : ((wise(X0) <~> ~old(X0)) <=> (curious(X0) | patient(X0))) [input p6]
16. ! [X0] : ((~curious(X0) & ~old(X0)) <=> (~strong(X0) <~> ~kind(X0))) [input p15]
25. curious(john) [input hypothesis]
34. ! [X0] : ((~wise(X0) <~> ~old(X0)) | (rich(X0) & ~strong(X0))) [ennf transformation 2]
37. ! [X0] : ((~curious(X0) & ~tall(X0)) | (happy(X0) & kind(X0))) [ennf transformation 5]
48. ! [X0] : (((old(X0) | wise(X0)) & (~old(X0) | ~wise(X0))) | (rich(X0) & ~strong(X0))) [nnf transformation 34]
52. ! [X0] : ((((old(X0) | ~wise(X0)) & (~old(X0) | wise(X0))) | (~curious(X0) & ~patient(X0))) & ((curious(X0) | patient(X0)) | ((wise(X0) | old(X0)) & (~old(X0) | ~wise(X0))))) [nnf transformation 7]
53. ! [X0] : ((((old(X0) | ~wise(X0)) & (~old(X0) | wise(X0))) | (~curious(X0) & ~patient(X0))) & (curious(X0) | patient(X0) | ((wise(X0) | old(X0)) & (~old(X0) | ~wise(X0))))) [flattening 52]
70. ! [X0] : (((~curious(X0) & ~old(X0)) | ((~strong(X0) | kind(X0)) & (~kind(X0) | strong(X0)))) & (((kind(X0) | strong(X0)) & (~kind(X0) | ~strong(X0))) | (curious(X0) | old(X0)))) [nnf transformation 16]
71. ! [X0] : (((~curious(X0) & ~old(X0)) | ((~strong(X0) | kind(X0)) & (~kind(X0) | strong(X0)))) & (((kind(X0) | strong(X0)) & (~kind(X0) | ~strong(X0))) | curious(X0) | old(X0))) [flattening 70]
82. ~old(X0) | ~wise(X0) | ~strong(X0) [cnf transformation 48]
84. ~strong(X0) | wise(X0) | old(X0) [cnf transformation 48]
92. ~curious(X0) | kind(X0) [cnf transformation 37]
101. ~curious(X0) | wise(X0) | ~old(X0) [cnf transformation 53]
103. ~curious(X0) | ~wise(X0) | old(X0) [cnf transformation 53]
130. ~curious(X0) | ~kind(X0) | strong(X0) [cnf transformation 71]
140. curious(john) [cnf transformation 25]
159. 5 <=> old(john) [avatar definition]
160. old(john) <- (5) [avatar component clause 159]
161. ~old(john) <- (~5) [avatar component clause 159]
174. 8 <=> wise(john) [avatar definition]
175. wise(john) <- (8) [avatar component clause 174]
176. ~wise(john) <- (~8) [avatar component clause 174]
290. ~curious(X0) | strong(X0) [subsumption resolution 130,92]
330. strong(john) [resolution 290,140]
333. wise(john) | old(john) [resolution 84,330]
340. old(john) <- (~8) [subsumption resolution 333,176]
343. 5 | 8 [avatar split clause 340,174,159]
345. ~wise(john) | ~strong(john) <- (5) [resolution 160,82]
351. wise(john) | ~old(john) [resolution 101,140]
355. wise(john) <- (5) [subsumption resolution 351,160]
356. 8 | ~5 [avatar split clause 355,159,174]
357. ~wise(john) <- (5) [subsumption resolution 345,330]
358. ~8 | ~5 [avatar split clause 357,159,174]
370. ~wise(john) | old(john) [resolution 103,140]
371. old(john) <- (8) [subsumption resolution 370,175]
372. $false <- (~5, 8) [subsumption resolution 371,161]
373. 5 | ~8 [avatar contradiction clause 372]
374. $false [avatar sat refutation 343,356,358,373]
% SZS output end Proof for 5764807694767937244373835
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not brave is either not quiet or quiet.
Everyone who is either patient or not funny is funny and vice versa.
If someone is either rich or not quiet then paul is not humble.
If someone is either strong or curious then someone is not funny or not wise.
Everyone who is either funny or wise is patient.
Everyone who is either humble or not generous is not creative and vice versa.
Everyone who is either humble or not tall is either brave or not rich and vice versa.
Everyone who is either quiet or not old is strong.
If someone is not happy or not curious then fred is both wise and not wise.
Everyone who is both not old and wise is happy.
If someone is not kind or not curious then lucy is generous or not patient and vice versa.
If someone is either not kind or not quiet then someone is both calm and not patient and vice versa.
Everyone who is patient is either calm or not creative.
If susan is both not calm and not strong then someone is not humble and vice versa.
If john is both not happy and not brave then john is both calm and not kind and vice versa.
Everyone who is both quiet and funny is not calm and vice versa.
Lucy is both not quiet and creative.
Someone is strong or old.
Someone is rich.
Someone is not generous or tall.
Someone is either not happy or not strong.
John is either generous or not kind.
Lucy is curious or not rich. | Susan is not strong. | entailment | (![X]:(~brave(X)=>(~quiet(X)<~>quiet(X))))&
(![X]:((patient(X)<~>~funny(X))<=>funny(X)))&
((?[X]:((rich(X)<~>~quiet(X))))=>(~humble(paul)))&
((?[X]:((strong(X)<~>curious(X))))=>(?[X]:((~funny(X)|~wise(X)))))&
(![X]:((funny(X)<~>wise(X))=>patient(X)))&
(![X]:((humble(X)<~>~generous(X))<=>~creative(X)))&
(![X]:((humble(X)<~>~tall(X))<=>(brave(X)<~>~rich(X))))&
(![X]:((quiet(X)<~>~old(X))=>strong(X)))&
((?[X]:((~happy(X)|~curious(X))))=>((wise(fred)&~wise(fred))))&
(![X]:((~old(X)&wise(X))=>happy(X)))&
((?[X]:((~kind(X)|~curious(X))))<=>((generous(lucy)|~patient(lucy))))&
((?[X]:((~kind(X)<~>~quiet(X))))<=>(?[X]:((calm(X)&~patient(X)))))&
(![X]:(patient(X)=>(calm(X)<~>~creative(X))))&
(((~calm(susan)&~strong(susan)))<=>(?[X]:(~humble(X))))&
(((~happy(john)&~brave(john)))<=>((calm(john)&~kind(john))))&
(![X]:((quiet(X)&funny(X))<=>~calm(X)))&
((~quiet(lucy)&creative(lucy)))&
(?[X]:((strong(X)|old(X))))&
(?[X]:(rich(X)))&
(?[X]:((~generous(X)|tall(X))))&
(?[X]:((~happy(X)<~>~strong(X))))&
((generous(john)<~>~kind(john)))&
((curious(lucy)|~rich(lucy))) | ~strong(susan) | [
"p1",
"p5",
"p10",
"p11",
"p13",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 5064230198217951511246941
% SZS output start Proof for 5064230198217951511246941
2. ! [X0] : ((patient(X0) <~> ~funny(X0)) <=> funny(X0)) [input p1]
6. ! [X0] : ((humble(X0) <~> ~generous(X0)) <=> ~creative(X0)) [input p5]
11. ? [X0] : (~curious(X0) | ~kind(X0)) <=> (~patient(lucy) | generous(lucy)) [input p10]
12. ? [X0] : (~kind(X0) <~> ~quiet(X0)) <=> ? [X0] : (~patient(X0) & calm(X0)) [input p11]
14. (~strong(susan) & ~calm(susan)) <=> ? [X0] : ~humble(X0) [input p13]
17. creative(lucy) & ~quiet(lucy) [input p16]
24. strong(susan) [input hypothesis]
26. ? [X0] : (~kind(X0) <~> ~quiet(X0)) <=> ? [X1] : (~patient(X1) & calm(X1)) [rectify 12]
37. ! [X0] : ((((funny(X0) | ~patient(X0)) & (~funny(X0) | patient(X0))) | ~funny(X0)) & (funny(X0) | ((patient(X0) | funny(X0)) & (~funny(X0) | ~patient(X0))))) [nnf transformation 2]
44. ! [X0] : ((((generous(X0) | ~humble(X0)) & (~generous(X0) | humble(X0))) | creative(X0)) & (~creative(X0) | ((humble(X0) | generous(X0)) & (~generous(X0) | ~humble(X0))))) [nnf transformation 6]
47. (? [X0] : (~curious(X0) | ~kind(X0)) | (patient(lucy) & ~generous(lucy))) & ((~patient(lucy) | generous(lucy)) | ! [X0] : (curious(X0) & kind(X0))) [nnf transformation 11]
48. (? [X0] : (~curious(X0) | ~kind(X0)) | (patient(lucy) & ~generous(lucy))) & (~patient(lucy) | generous(lucy) | ! [X0] : (curious(X0) & kind(X0))) [flattening 47]
49. (? [X0] : (~curious(X0) | ~kind(X0)) | (patient(lucy) & ~generous(lucy))) & (~patient(lucy) | generous(lucy) | ! [X1] : (curious(X1) & kind(X1))) [rectify 48]
50. ? [X0] : (~curious(X0) | ~kind(X0)) => (~curious(sK1) | ~kind(sK1)) [choice axiom]
51. ((~curious(sK1) | ~kind(sK1)) | (patient(lucy) & ~generous(lucy))) & (~patient(lucy) | generous(lucy) | ! [X1] : (curious(X1) & kind(X1))) [skolemisation 49,50]
52. (? [X0] : ((quiet(X0) | kind(X0)) & (~quiet(X0) | ~kind(X0))) | ! [X1] : (patient(X1) | ~calm(X1))) & (? [X1] : (~patient(X1) & calm(X1)) | ! [X0] : ((~kind(X0) | quiet(X0)) & (~quiet(X0) | kind(X0)))) [nnf transformation 26]
53. (? [X0] : ((quiet(X0) | kind(X0)) & (~quiet(X0) | ~kind(X0))) | ! [X1] : (patient(X1) | ~calm(X1))) & (? [X2] : (~patient(X2) & calm(X2)) | ! [X3] : ((~kind(X3) | quiet(X3)) & (~quiet(X3) | kind(X3)))) [rectify 52]
54. ? [X0] : ((quiet(X0) | kind(X0)) & (~quiet(X0) | ~kind(X0))) => ((quiet(sK2) | kind(sK2)) & (~quiet(sK2) | ~kind(sK2))) [choice axiom]
55. ? [X2] : (~patient(X2) & calm(X2)) => (~patient(sK3) & calm(sK3)) [choice axiom]
56. (((quiet(sK2) | kind(sK2)) & (~quiet(sK2) | ~kind(sK2))) | ! [X1] : (patient(X1) | ~calm(X1))) & ((~patient(sK3) & calm(sK3)) | ! [X3] : ((~kind(X3) | quiet(X3)) & (~quiet(X3) | kind(X3)))) [skolemisation 53,55,54]
58. ((~strong(susan) & ~calm(susan)) | ! [X0] : humble(X0)) & (? [X0] : ~humble(X0) | (strong(susan) | calm(susan))) [nnf transformation 14]
59. ((~strong(susan) & ~calm(susan)) | ! [X0] : humble(X0)) & (? [X0] : ~humble(X0) | strong(susan) | calm(susan)) [flattening 58]
60. ((~strong(susan) & ~calm(susan)) | ! [X0] : humble(X0)) & (? [X1] : ~humble(X1) | strong(susan) | calm(susan)) [rectify 59]
61. ? [X1] : ~humble(X1) => ~humble(sK4) [choice axiom]
62. ((~strong(susan) & ~calm(susan)) | ! [X0] : humble(X0)) & (~humble(sK4) | strong(susan) | calm(susan)) [skolemisation 60,61]
80. funny(X0) | patient(X0) | funny(X0) [cnf transformation 37]
81. ~funny(X0) | patient(X0) | ~funny(X0) [cnf transformation 37]
89. ~creative(X0) | ~generous(X0) | ~humble(X0) [cnf transformation 44]
108. ~patient(lucy) | generous(lucy) | kind(X1) [cnf transformation 51]
115. ~patient(sK3) | ~kind(X3) | quiet(X3) [cnf transformation 56]
122. ~strong(susan) | humble(X0) [cnf transformation 62]
130. ~quiet(lucy) [cnf transformation 17]
131. creative(lucy) [cnf transformation 17]
140. strong(susan) [cnf transformation 24]
141. funny(X0) | patient(X0) [duplicate literal removal 80]
142. ~funny(X0) | patient(X0) [duplicate literal removal 81]
143. patient(X0) [subsumption resolution 141,142]
187. 11 <=> generous(lucy) [avatar definition]
201. generous(lucy) | kind(X1) [subsumption resolution 108,143]
203. 14 <=> ! [X1] : kind(X1) [avatar definition]
204. kind(X1) <- (14) [avatar component clause 203]
205. 14 | 11 [avatar split clause 201,187,203]
206. ~kind(X3) | quiet(X3) [subsumption resolution 115,143]
211. 15 <=> ! [X0] : humble(X0) [avatar definition]
212. humble(X0) <- (15) [avatar component clause 211]
214. 16 <=> strong(susan) [avatar definition]
217. 15 | ~16 [avatar split clause 122,214,211]
291. 16 [avatar split clause 140,214]
316. ~generous(lucy) | ~humble(lucy) [resolution 89,131]
320. ~generous(lucy) <- (15) [subsumption resolution 316,212]
321. ~11 | ~15 [avatar split clause 320,211,187]
323. quiet(X0) <- (14) [resolution 204,206]
325. $false <- (14) [resolution 323,130]
329. ~14 [avatar contradiction clause 325]
330. $false [avatar sat refutation 205,217,291,321,329]
% SZS output end Proof for 5064230198217951511246941
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious and kind is happy and vice versa.
If lucy is both brave and humble then someone is patient or wise.
Everyone who is rich is either creative or not calm and vice versa.
If someone is either curious or creative then susan is either calm or creative.
If mary is generous then someone is not brave or not patient and vice versa.
Everyone who is either not wise or not happy is kind or patient and vice versa.
Everyone who is either not tall or not calm is not rich.
Everyone who is both rich and not patient is tall or curious.
Everyone who is not creative is both not quiet and happy.
If someone is brave or strong then someone is either not tall or happy and vice versa.
Everyone who is not wise or not kind is happy.
If fred is either not calm or tall then lucy is not brave or kind.
Everyone who is not curious or generous is curious and vice versa.
Everyone who is either not happy or not calm is not tall and vice versa.
Everyone who is either tall or not quiet is either wise or not funny and vice versa.
Susan is not happy.
Fred is not patient.
Mary is brave or curious.
Someone is patient.
Susan is calm or not rich. | Lucy is brave. | contradiction | (![X]:((~curious(X)&kind(X))<=>happy(X)))&
(((brave(lucy)&humble(lucy)))=>(?[X]:((patient(X)|wise(X)))))&
(![X]:(rich(X)<=>(creative(X)<~>~calm(X))))&
((?[X]:((curious(X)<~>creative(X))))=>((calm(susan)<~>creative(susan))))&
((generous(mary))<=>(?[X]:((~brave(X)|~patient(X)))))&
(![X]:((~wise(X)<~>~happy(X))<=>(kind(X)|patient(X))))&
(![X]:((~tall(X)<~>~calm(X))=>~rich(X)))&
(![X]:((rich(X)&~patient(X))=>(tall(X)|curious(X))))&
(![X]:(~creative(X)=>(~quiet(X)&happy(X))))&
((?[X]:((brave(X)|strong(X))))<=>(?[X]:((~tall(X)<~>happy(X)))))&
(![X]:((~wise(X)|~kind(X))=>happy(X)))&
(((~calm(fred)<~>tall(fred)))=>((~brave(lucy)|kind(lucy))))&
(![X]:((~curious(X)|generous(X))<=>curious(X)))&
(![X]:((~happy(X)<~>~calm(X))<=>~tall(X)))&
(![X]:((tall(X)<~>~quiet(X))<=>(wise(X)<~>~funny(X))))&
(~happy(susan))&
(~patient(fred))&
((brave(mary)|curious(mary)))&
(?[X]:(patient(X)))&
((calm(susan)|~rich(susan))) | brave(lucy) | [
"p0",
"p2",
"p6",
"p8",
"p9",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 4113147115785298862493341
% SZS output start Proof for 4113147115785298862493341
1. ! [X0] : ((kind(X0) & ~curious(X0)) <=> happy(X0)) [input p0]
3. ! [X0] : (rich(X0) <=> (creative(X0) <~> ~calm(X0))) [input p2]
7. ! [X0] : ((~tall(X0) <~> ~calm(X0)) => ~rich(X0)) [input p6]
9. ! [X0] : (~creative(X0) => (happy(X0) & ~quiet(X0))) [input p8]
10. ? [X0] : (strong(X0) | brave(X0)) <=> ? [X0] : (~tall(X0) <~> happy(X0)) [input p9]
13. ! [X0] : ((generous(X0) | ~curious(X0)) <=> curious(X0)) [input p12]
14. ! [X0] : ((~happy(X0) <~> ~calm(X0)) <=> ~tall(X0)) [input p13]
21. brave(lucy) [input hypothesis]
22. ? [X0] : (strong(X0) | brave(X0)) <=> ? [X1] : (~tall(X1) <~> happy(X1)) [rectify 10]
23. ! [X0] : ((creative(X0) <~> ~calm(X0)) => rich(X0)) [unused predicate definition removal 3]
25. ! [X0] : (rich(X0) | (creative(X0) <=> ~calm(X0))) [ennf transformation 23]
27. ! [X0] : (~rich(X0) | (~tall(X0) <=> ~calm(X0))) [ennf transformation 7]
30. ! [X0] : ((happy(X0) & ~quiet(X0)) | creative(X0)) [ennf transformation 9]
34. ! [X0] : (((kind(X0) & ~curious(X0)) | ~happy(X0)) & (happy(X0) | (~kind(X0) | curious(X0)))) [nnf transformation 1]
35. ! [X0] : (((kind(X0) & ~curious(X0)) | ~happy(X0)) & (happy(X0) | ~kind(X0) | curious(X0))) [flattening 34]
36. ! [X0] : (rich(X0) | ((creative(X0) | calm(X0)) & (~calm(X0) | ~creative(X0)))) [nnf transformation 25]
44. ! [X0] : (~rich(X0) | ((~tall(X0) | calm(X0)) & (~calm(X0) | tall(X0)))) [nnf transformation 27]
45. (? [X0] : (strong(X0) | brave(X0)) | ! [X1] : ((~tall(X1) | ~happy(X1)) & (happy(X1) | tall(X1)))) & (? [X1] : ((~happy(X1) | tall(X1)) & (happy(X1) | ~tall(X1))) | ! [X0] : (~strong(X0) & ~brave(X0))) [nnf transformation 22]
46. (? [X0] : (strong(X0) | brave(X0)) | ! [X1] : ((~tall(X1) | ~happy(X1)) & (happy(X1) | tall(X1)))) & (? [X2] : ((~happy(X2) | tall(X2)) & (happy(X2) | ~tall(X2))) | ! [X3] : (~strong(X3) & ~brave(X3))) [rectify 45]
47. ? [X0] : (strong(X0) | brave(X0)) => (strong(sK1) | brave(sK1)) [choice axiom]
48. ? [X2] : ((~happy(X2) | tall(X2)) & (happy(X2) | ~tall(X2))) => ((~happy(sK2) | tall(sK2)) & (happy(sK2) | ~tall(sK2))) [choice axiom]
49. ((strong(sK1) | brave(sK1)) | ! [X1] : ((~tall(X1) | ~happy(X1)) & (happy(X1) | tall(X1)))) & (((~happy(sK2) | tall(sK2)) & (happy(sK2) | ~tall(sK2))) | ! [X3] : (~strong(X3) & ~brave(X3))) [skolemisation 46,48,47]
51. ! [X0] : (((generous(X0) | ~curious(X0)) | ~curious(X0)) & (curious(X0) | (~generous(X0) & curious(X0)))) [nnf transformation 13]
52. ! [X0] : ((generous(X0) | ~curious(X0) | ~curious(X0)) & (curious(X0) | (~generous(X0) & curious(X0)))) [flattening 51]
53. ! [X0] : ((((calm(X0) | happy(X0)) & (~calm(X0) | ~happy(X0))) | tall(X0)) & (~tall(X0) | ((~happy(X0) | calm(X0)) & (~calm(X0) | happy(X0))))) [nnf transformation 14]
58. ~happy(X0) | ~curious(X0) [cnf transformation 35]
60. ~calm(X0) | rich(X0) | ~creative(X0) [cnf transformation 36]
75. ~calm(X0) | ~rich(X0) | tall(X0) [cnf transformation 44]
79. creative(X0) | happy(X0) [cnf transformation 30]
80. happy(sK2) | ~tall(sK2) | ~brave(X3) [cnf transformation 49]
90. curious(X0) | curious(X0) [cnf transformation 52]
96. tall(X0) | happy(X0) | calm(X0) [cnf transformation 53]
110. brave(lucy) [cnf transformation 21]
111. curious(X0) [duplicate literal removal 90]
174. 15 <=> tall(sK2) [avatar definition]
175. ~tall(sK2) <- (~15) [avatar component clause 174]
178. 16 <=> happy(sK2) [avatar definition]
179. happy(sK2) <- (16) [avatar component clause 178]
180. ~happy(sK2) <- (~16) [avatar component clause 178]
183. 17 <=> ! [X3] : ~brave(X3) [avatar definition]
184. ~brave(X3) <- (17) [avatar component clause 183]
187. 17 | ~15 | 16 [avatar split clause 80,178,174,183]
242. ~curious(sK2) <- (16) [resolution 179,58]
243. $false <- (16) [subsumption resolution 242,111]
244. ~16 [avatar contradiction clause 243]
246. 19 <=> calm(sK2) [avatar definition]
248. calm(sK2) <- (19) [avatar component clause 246]
250. 20 <=> rich(sK2) [avatar definition]
252. ~rich(sK2) <- (~20) [avatar component clause 250]
256. $false <- (17) [resolution 184,110]
259. ~17 [avatar contradiction clause 256]
263. happy(sK2) | calm(sK2) <- (~15) [resolution 175,96]
264. calm(sK2) <- (~15, ~16) [subsumption resolution 263,180]
267. 19 | 15 | 16 [avatar split clause 264,178,174,246]
269. ~rich(sK2) | tall(sK2) <- (19) [resolution 248,75]
270. rich(sK2) | ~creative(sK2) <- (19) [resolution 248,60]
271. ~creative(sK2) <- (19, ~20) [subsumption resolution 270,252]
272. happy(sK2) <- (19, ~20) [resolution 271,79]
273. $false <- (~16, 19, ~20) [subsumption resolution 272,180]
274. 16 | ~19 | 20 [avatar contradiction clause 273]
280. ~rich(sK2) <- (~15, 19) [subsumption resolution 269,175]
281. ~20 | 15 | ~19 [avatar split clause 280,246,174,250]
282. $false [avatar sat refutation 187,244,259,267,274,281]
% SZS output end Proof for 4113147115785298862493341
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 alice is funny then someone is not kind and vice versa. Everyone who is not kind is both old and not calm and vice versa. Everyone who is not strong is either not funny or happy. Everyone who is both creative and happy is both kind and brave and vice versa. If someone is either not quiet or old then someone is both not old and curious. If lucy is both tall and not calm then someone is not brave. If susan is both not old and patient then someone is either not generous or patient and vice versa. If susan is either not strong or not kind then someone is not old or not patient. Everyone who is not quiet or strong is both not strong and wise and vice versa. Everyone who is either not humble or calm is either not happy or generous. Everyone who is both brave and not creative is old and vice versa. Everyone who is curious or calm is not rich and vice versa. If mary is either patient or humble then mary is not kind or not rich. If someone is either curious or generous then someone is either strong or not calm. If someone is both old and tall then lucy is generous and vice versa. Everyone who is both not creative and not old is not strong. Someone is not curious or not funny. Susan is not quiet or not humble. Someone is not rich. Someone is both not kind and not quiet. Susan is tall or not happy. Susan is both not creative and not wise. | Mary is old. | neutral | ((funny(alice))<=>(?[X]:(~kind(X))))&
(![X]:(~kind(X)<=>(old(X)&~calm(X))))&
(![X]:(~strong(X)=>(~funny(X)<~>happy(X))))&
(![X]:((creative(X)&happy(X))<=>(kind(X)&brave(X))))&
((?[X]:((~quiet(X)<~>old(X))))=>(?[X]:((~old(X)&curious(X)))))&
(((tall(lucy)&~calm(lucy)))=>(?[X]:(~brave(X))))&
(((~old(susan)&patient(susan)))<=>(?[X]:((~generous(X)<~>patient(X)))))&
(((~strong(susan)<~>~kind(susan)))=>(?[X]:((~old(X)|~patient(X)))))&
(![X]:((~quiet(X)|strong(X))<=>(~strong(X)&wise(X))))&
(![X]:((~humble(X)<~>calm(X))=>(~happy(X)<~>generous(X))))&
(![X]:((brave(X)&~creative(X))<=>old(X)))&
(![X]:((curious(X)|calm(X))<=>~rich(X)))&
(((patient(mary)<~>humble(mary)))=>((~kind(mary)|~rich(mary))))&
((?[X]:((curious(X)<~>generous(X))))=>(?[X]:((strong(X)<~>~calm(X)))))&
((?[X]:((old(X)&tall(X))))<=>(generous(lucy)))&
(![X]:((~creative(X)&~old(X))=>~strong(X)))&
(?[X]:((~curious(X)|~funny(X))))&
((~quiet(susan)|~humble(susan)))&
(?[X]:(~rich(X)))&
(?[X]:((~kind(X)&~quiet(X))))&
((tall(susan)|~happy(susan)))&
((~creative(susan)&~wise(susan))) | old(mary) | [] | null | 0 |
Everyone who is brave or not curious is old. Everyone who is either not rich or not strong is both not tall and tall. Everyone who is not humble or not rich is rich or not happy. If mary is both curious and wise then someone is quiet or not funny and vice versa. Everyone who is not patient or not funny is either patient or happy. If alice is not humble or not patient then someone is not strong or not patient. Everyone who is either calm or creative is not curious or rich and vice versa. Everyone who is either calm or not rich is not humble and vice versa. If someone is curious or not old then someone is both humble and kind. Everyone who is not calm is not old and vice versa. Everyone who is either not curious or not humble is not wise or wise. Everyone who is either not happy or not wise is either strong or not patient and vice versa. If someone is humble or old then alice is both not kind and humble. If fred is strong then someone is both not wise and creative. If someone is both patient and not brave then john is both old and not strong. Everyone who is both creative and brave is both strong and wise and vice versa. Lucy is both not wise and not old. Lucy is patient or curious. Someone is not wise. Someone is not strong or tall. Someone is kind or not humble. Someone is either not kind or wise. | Alice is not quiet. | entailment | (![X]:((brave(X)|~curious(X))=>old(X)))&
(![X]:((~rich(X)<~>~strong(X))=>(~tall(X)&tall(X))))&
(![X]:((~humble(X)|~rich(X))=>(rich(X)|~happy(X))))&
(((curious(mary)&wise(mary)))<=>(?[X]:((quiet(X)|~funny(X)))))&
(![X]:((~patient(X)|~funny(X))=>(patient(X)<~>happy(X))))&
(((~humble(alice)|~patient(alice)))=>(?[X]:((~strong(X)|~patient(X)))))&
(![X]:((calm(X)<~>creative(X))<=>(~curious(X)|rich(X))))&
(![X]:((calm(X)<~>~rich(X))<=>~humble(X)))&
((?[X]:((curious(X)|~old(X))))=>(?[X]:((humble(X)&kind(X)))))&
(![X]:(~calm(X)<=>~old(X)))&
(![X]:((~curious(X)<~>~humble(X))=>(~wise(X)|wise(X))))&
(![X]:((~happy(X)<~>~wise(X))<=>(strong(X)<~>~patient(X))))&
((?[X]:((humble(X)|old(X))))=>((~kind(alice)&humble(alice))))&
((strong(fred))=>(?[X]:((~wise(X)&creative(X)))))&
((?[X]:((patient(X)&~brave(X))))=>((old(john)&~strong(john))))&
(![X]:((creative(X)&brave(X))<=>(strong(X)&wise(X))))&
((~wise(lucy)&~old(lucy)))&
((patient(lucy)|curious(lucy)))&
(?[X]:(~wise(X)))&
(?[X]:((~strong(X)|tall(X))))&
(?[X]:((kind(X)|~humble(X))))&
(?[X]:((~kind(X)<~>wise(X)))) | ~quiet(alice) | [
"p0",
"p1",
"p2",
"p3",
"p4",
"p6",
"p9",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 561098933446412348549002
% SZS output start Proof for 561098933446412348549002
1. ! [X0] : ((~curious(X0) | brave(X0)) => old(X0)) [input p0]
2. ! [X0] : ((~rich(X0) <~> ~strong(X0)) => (tall(X0) & ~tall(X0))) [input p1]
3. ! [X0] : ((~rich(X0) | ~humble(X0)) => (~happy(X0) | rich(X0))) [input p2]
4. (wise(mary) & curious(mary)) <=> ? [X0] : (~funny(X0) | quiet(X0)) [input p3]
5. ! [X0] : ((~funny(X0) | ~patient(X0)) => (patient(X0) <~> happy(X0))) [input p4]
7. ! [X0] : ((calm(X0) <~> creative(X0)) <=> (rich(X0) | ~curious(X0))) [input p6]
10. ! [X0] : (~calm(X0) <=> ~old(X0)) [input p9]
12. ! [X0] : ((~happy(X0) <~> ~wise(X0)) <=> (strong(X0) <~> ~patient(X0))) [input p11]
16. ! [X0] : ((brave(X0) & creative(X0)) <=> (wise(X0) & strong(X0))) [input p15]
23. quiet(alice) [input hypothesis]
25. ! [X0] : (old(X0) | (curious(X0) & ~brave(X0))) [ennf transformation 1]
26. ! [X0] : ((tall(X0) & ~tall(X0)) | (~rich(X0) <=> ~strong(X0))) [ennf transformation 2]
27. ! [X0] : ((~happy(X0) | rich(X0)) | (rich(X0) & humble(X0))) [ennf transformation 3]
28. ! [X0] : (~happy(X0) | rich(X0) | (rich(X0) & humble(X0))) [flattening 27]
29. ! [X0] : ((patient(X0) <~> happy(X0)) | (funny(X0) & patient(X0))) [ennf transformation 5]
37. ! [X0] : ((tall(X0) & ~tall(X0)) | ((~rich(X0) | strong(X0)) & (~strong(X0) | rich(X0)))) [nnf transformation 26]
38. ((wise(mary) & curious(mary)) | ! [X0] : (funny(X0) & ~quiet(X0))) & (? [X0] : (~funny(X0) | quiet(X0)) | (~wise(mary) | ~curious(mary))) [nnf transformation 4]
39. ((wise(mary) & curious(mary)) | ! [X0] : (funny(X0) & ~quiet(X0))) & (? [X0] : (~funny(X0) | quiet(X0)) | ~wise(mary) | ~curious(mary)) [flattening 38]
40. ((wise(mary) & curious(mary)) | ! [X0] : (funny(X0) & ~quiet(X0))) & (? [X1] : (~funny(X1) | quiet(X1)) | ~wise(mary) | ~curious(mary)) [rectify 39]
41. ? [X1] : (~funny(X1) | quiet(X1)) => (~funny(sK0) | quiet(sK0)) [choice axiom]
42. ((wise(mary) & curious(mary)) | ! [X0] : (funny(X0) & ~quiet(X0))) & ((~funny(sK0) | quiet(sK0)) | ~wise(mary) | ~curious(mary)) [skolemisation 40,41]
43. ! [X0] : (((~happy(X0) | ~patient(X0)) & (happy(X0) | patient(X0))) | (funny(X0) & patient(X0))) [nnf transformation 29]
46. ! [X0] : ((((~creative(X0) | ~calm(X0)) & (creative(X0) | calm(X0))) | (~rich(X0) & curious(X0))) & ((rich(X0) | ~curious(X0)) | ((calm(X0) | ~creative(X0)) & (creative(X0) | ~calm(X0))))) [nnf transformation 7]
47. ! [X0] : ((((~creative(X0) | ~calm(X0)) & (creative(X0) | calm(X0))) | (~rich(X0) & curious(X0))) & (rich(X0) | ~curious(X0) | ((calm(X0) | ~creative(X0)) & (creative(X0) | ~calm(X0))))) [flattening 46]
52. ! [X0] : ((~calm(X0) | old(X0)) & (~old(X0) | calm(X0))) [nnf transformation 10]
54. ! [X0] : ((((wise(X0) | happy(X0)) & (~wise(X0) | ~happy(X0))) | ((strong(X0) | patient(X0)) & (~patient(X0) | ~strong(X0)))) & (((patient(X0) | ~strong(X0)) & (~patient(X0) | strong(X0))) | ((~happy(X0) | wise(X0)) & (~wise(X0) | happy(X0))))) [nnf transformation 12]
57. ! [X0] : (((brave(X0) & creative(X0)) | (~wise(X0) | ~strong(X0))) & ((wise(X0) & strong(X0)) | (~brave(X0) | ~creative(X0)))) [nnf transformation 16]
58. ! [X0] : (((brave(X0) & creative(X0)) | ~wise(X0) | ~strong(X0)) & ((wise(X0) & strong(X0)) | ~brave(X0) | ~creative(X0))) [flattening 57]
68. ~brave(X0) | old(X0) [cnf transformation 25]
70. ~tall(X0) | ~strong(X0) | rich(X0) [cnf transformation 37]
71. ~tall(X0) | ~rich(X0) | strong(X0) [cnf transformation 37]
72. ~strong(X0) | tall(X0) | rich(X0) [cnf transformation 37]
73. ~rich(X0) | tall(X0) | strong(X0) [cnf transformation 37]
75. ~happy(X0) | rich(X0) | rich(X0) [cnf transformation 28]
79. wise(mary) | ~quiet(X0) [cnf transformation 42]
81. happy(X0) | patient(X0) | patient(X0) [cnf transformation 43]
92. ~creative(X0) | ~calm(X0) | ~rich(X0) [cnf transformation 47]
101. ~old(X0) | calm(X0) [cnf transformation 52]
105. ~patient(X0) | strong(X0) | ~wise(X0) | happy(X0) [cnf transformation 54]
110. ~wise(X0) | ~happy(X0) | strong(X0) | patient(X0) [cnf transformation 54]
123. ~wise(X0) | creative(X0) | ~strong(X0) [cnf transformation 58]
124. ~wise(X0) | brave(X0) | ~strong(X0) [cnf transformation 58]
133. quiet(alice) [cnf transformation 23]
134. patient(X0) | happy(X0) [duplicate literal removal 81]
135. ~happy(X0) | rich(X0) [duplicate literal removal 75]
136. ~rich(X0) | strong(X0) [subsumption resolution 71,73]
137. ~strong(X0) | rich(X0) [subsumption resolution 70,72]
142. 2 <=> wise(mary) [avatar definition]
144. wise(mary) <- (2) [avatar component clause 142]
147. 3 <=> ! [X0] : ~quiet(X0) [avatar definition]
148. ~quiet(X0) <- (3) [avatar component clause 147]
149. 3 | 2 [avatar split clause 79,142,147]
202. ~wise(X0) | strong(X0) | patient(X0) [subsumption resolution 110,134]
204. ~wise(X0) | strong(X0) | happy(X0) [subsumption resolution 105,202]
431. creative(mary) | ~strong(mary) <- (2) [resolution 123,144]
433. 50 <=> strong(mary) [avatar definition]
434. strong(mary) <- (50) [avatar component clause 433]
435. ~strong(mary) <- (~50) [avatar component clause 433]
437. 51 <=> creative(mary) [avatar definition]
439. creative(mary) <- (51) [avatar component clause 437]
440. ~50 | 51 | ~2 [avatar split clause 431,142,437,433]
460. strong(mary) | happy(mary) <- (2) [resolution 204,144]
461. happy(mary) <- (2, ~50) [subsumption resolution 460,435]
480. rich(mary) <- (2, ~50) [resolution 461,135]
543. strong(mary) <- (2, ~50) [resolution 480,136]
549. 62 <=> calm(mary) [avatar definition]
550. ~calm(mary) <- (~62) [avatar component clause 549]
555. $false <- (2, ~50) [subsumption resolution 543,435]
556. ~2 | 50 [avatar contradiction clause 555]
559. $false <- (3) [resolution 148,133]
560. ~3 [avatar contradiction clause 559]
563. brave(mary) | ~strong(mary) <- (2) [resolution 144,124]
565. brave(mary) <- (2, 50) [subsumption resolution 563,434]
569. rich(mary) <- (50) [resolution 434,137]
571. 63 <=> rich(mary) [avatar definition]
573. rich(mary) <- (63) [avatar component clause 571]
579. 63 | ~50 [avatar split clause 569,433,571]
583. ~calm(mary) | ~rich(mary) <- (51) [resolution 439,92]
585. ~calm(mary) <- (51, 63) [subsumption resolution 583,573]
586. ~62 | ~51 | ~63 [avatar split clause 585,571,437,549]
587. old(mary) <- (2, 50) [resolution 565,68]
594. calm(mary) <- (2, 50) [resolution 587,101]
595. $false <- (2, 50, ~62) [subsumption resolution 594,550]
596. ~2 | ~50 | 62 [avatar contradiction clause 595]
597. $false [avatar sat refutation 149,440,556,560,579,586,596]
% SZS output end Proof for 561098933446412348549002
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not wise or not brave is old and vice versa.
Everyone who is both not humble and not funny is either old or quiet.
If john is either not generous or not quiet then someone is either wise or patient.
Everyone who is generous is either old or generous and vice versa.
If someone is both old and not patient then someone is either patient or not quiet and vice versa.
If someone is patient then paul is old or kind and vice versa.
Everyone who is both patient and not calm is not wise or calm.
Everyone who is both not kind and not brave is not old or not kind and vice versa.
Everyone who is quiet or not strong is strong or funny.
Everyone who is not generous or humble is generous.
Everyone who is both not generous and humble is either happy or not wise and vice versa.
Everyone who is not rich or curious is both not quiet and not wise and vice versa.
If alice is quiet then someone is quiet.
Lucy is not tall or calm.
Someone is not kind or not strong.
John is not curious.
Alice is funny or creative. | John is not humble. | neutral | (![X]:((~wise(X)<~>~brave(X))<=>old(X)))&
(![X]:((~humble(X)&~funny(X))=>(old(X)<~>quiet(X))))&
(((~generous(john)<~>~quiet(john)))=>(?[X]:((wise(X)<~>patient(X)))))&
(![X]:(generous(X)<=>(old(X)<~>generous(X))))&
((?[X]:((old(X)&~patient(X))))<=>(?[X]:((patient(X)<~>~quiet(X)))))&
((?[X]:(patient(X)))<=>((old(paul)|kind(paul))))&
(![X]:((patient(X)&~calm(X))=>(~wise(X)|calm(X))))&
(![X]:((~kind(X)&~brave(X))<=>(~old(X)|~kind(X))))&
(![X]:((quiet(X)|~strong(X))=>(strong(X)|funny(X))))&
(![X]:((~generous(X)|humble(X))=>generous(X)))&
(![X]:((~generous(X)&humble(X))<=>(happy(X)<~>~wise(X))))&
(![X]:((~rich(X)|curious(X))<=>(~quiet(X)&~wise(X))))&
((quiet(alice))=>(?[X]:(quiet(X))))&
((~tall(lucy)|calm(lucy)))&
(?[X]:((~kind(X)|~strong(X))))&
(~curious(john))&
((funny(alice)|creative(alice))) | ~humble(john) | [] | null | 0 |
If someone is not curious then paul is not patient or happy and vice versa.
If someone is either not strong or not wise then john is both not patient and funny.
Everyone who is both calm and creative is strong and vice versa.
Everyone who is not calm or patient is not kind and vice versa.
Everyone who is both not rich and not funny is not tall.
If john is either not funny or calm then paul is calm or creative and vice versa.
Everyone who is humble or not funny is both not calm and curious.
If alice is not happy then fred is both not generous and not happy.
If susan is not brave then someone is either rich or not strong and vice versa.
If someone is creative then paul is either not quiet or not funny.
Everyone who is not old is strong or not patient and vice versa.
If someone is generous then someone is either calm or rich.
If mary is both humble and funny then someone is both humble and quiet and vice versa.
Everyone who is either wise or not strong is humble or wise and vice versa.
If john is either not strong or creative then someone is both not strong and quiet and vice versa.
Everyone who is kind is not brave and vice versa.
Lucy is either not wise or creative.
Alice is either patient or rich.
Paul is kind or happy.
Alice is either patient or strong.
Alice is either not strong or not funny.
Someone is both not kind and not generous.
Someone is creative or quiet. | Alice is kind. | contradiction | ((?[X]:(~curious(X)))<=>((~patient(paul)|happy(paul))))&
((?[X]:((~strong(X)<~>~wise(X))))=>((~patient(john)&funny(john))))&
(![X]:((calm(X)&creative(X))<=>strong(X)))&
(![X]:((~calm(X)|patient(X))<=>~kind(X)))&
(![X]:((~rich(X)&~funny(X))=>~tall(X)))&
(((~funny(john)<~>calm(john)))<=>((calm(paul)|creative(paul))))&
(![X]:((humble(X)|~funny(X))=>(~calm(X)&curious(X))))&
((~happy(alice))=>((~generous(fred)&~happy(fred))))&
((~brave(susan))<=>(?[X]:((rich(X)<~>~strong(X)))))&
((?[X]:(creative(X)))=>((~quiet(paul)<~>~funny(paul))))&
(![X]:(~old(X)<=>(strong(X)|~patient(X))))&
((?[X]:(generous(X)))=>(?[X]:((calm(X)<~>rich(X)))))&
(((humble(mary)&funny(mary)))<=>(?[X]:((humble(X)&quiet(X)))))&
(![X]:((wise(X)<~>~strong(X))<=>(humble(X)|wise(X))))&
(((~strong(john)<~>creative(john)))<=>(?[X]:((~strong(X)&quiet(X)))))&
(![X]:(kind(X)<=>~brave(X)))&
((~wise(lucy)<~>creative(lucy)))&
((patient(alice)<~>rich(alice)))&
((kind(paul)|happy(paul)))&
((patient(alice)<~>strong(alice)))&
((~strong(alice)<~>~funny(alice)))&
(?[X]:((~kind(X)&~generous(X))))&
(?[X]:((creative(X)|quiet(X)))) | kind(alice) | [
"p2",
"p3",
"p6",
"p19",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 87027631467734232529858
% SZS output start Proof for 87027631467734232529858
3. ! [X0] : ((creative(X0) & calm(X0)) <=> strong(X0)) [input p2]
4. ! [X0] : ((patient(X0) | ~calm(X0)) <=> ~kind(X0)) [input p3]
7. ! [X0] : ((~funny(X0) | humble(X0)) => (curious(X0) & ~calm(X0))) [input p6]
20. patient(alice) <~> strong(alice) [input p19]
21. ~strong(alice) <~> ~funny(alice) [input p20]
24. kind(alice) [input hypothesis]
31. ! [X0] : ((curious(X0) & ~calm(X0)) | (funny(X0) & ~humble(X0))) [ennf transformation 7]
40. ! [X0] : (((creative(X0) & calm(X0)) | ~strong(X0)) & (strong(X0) | (~creative(X0) | ~calm(X0)))) [nnf transformation 3]
41. ! [X0] : (((creative(X0) & calm(X0)) | ~strong(X0)) & (strong(X0) | ~creative(X0) | ~calm(X0))) [flattening 40]
42. ! [X0] : (((patient(X0) | ~calm(X0)) | kind(X0)) & (~kind(X0) | (~patient(X0) & calm(X0)))) [nnf transformation 4]
43. ! [X0] : ((patient(X0) | ~calm(X0) | kind(X0)) & (~kind(X0) | (~patient(X0) & calm(X0)))) [flattening 42]
65. (~strong(alice) | ~patient(alice)) & (strong(alice) | patient(alice)) [nnf transformation 20]
66. (funny(alice) | strong(alice)) & (~funny(alice) | ~strong(alice)) [nnf transformation 21]
79. ~strong(X0) | calm(X0) [cnf transformation 41]
82. ~kind(X0) | ~patient(X0) [cnf transformation 43]
91. ~calm(X0) | funny(X0) [cnf transformation 31]
124. strong(alice) | patient(alice) [cnf transformation 65]
126. ~funny(alice) | ~strong(alice) [cnf transformation 66]
130. kind(alice) [cnf transformation 24]
294. 34 <=> patient(alice) [avatar definition]
309. 37 <=> strong(alice) [avatar definition]
310. strong(alice) <- (37) [avatar component clause 309]
313. 34 | 37 [avatar split clause 124,309,294]
315. 38 <=> funny(alice) [avatar definition]
316. ~funny(alice) <- (~38) [avatar component clause 315]
319. ~37 | ~38 [avatar split clause 126,315,309]
331. calm(alice) <- (37) [resolution 79,310]
338. ~patient(alice) [resolution 82,130]
340. funny(alice) <- (37) [resolution 91,331]
342. $false <- (37, ~38) [subsumption resolution 340,316]
343. ~37 | 38 [avatar contradiction clause 342]
347. ~34 [avatar split clause 338,294]
348. $false [avatar sat refutation 313,319,343,347]
% SZS output end Proof for 87027631467734232529858
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either calm or not calm then susan is humble or not generous and vice versa.
Everyone who is either not quiet or not humble is either not curious or old and vice versa.
Everyone who is brave is both quiet and humble and vice versa.
If someone is calm or funny then someone is either funny or generous and vice versa.
Everyone who is not wise or creative is wise or not happy and vice versa.
Everyone who is not brave or not tall is both happy and calm and vice versa.
If someone is not strong or humble then susan is not curious or not quiet and vice versa.
If alice is either not kind or quiet then fred is both not old and not tall and vice versa.
Everyone who is tall or not funny is either not rich or not old and vice versa.
If someone is not old then someone is patient and vice versa.
Everyone who is generous or old is rich or creative and vice versa.
Everyone who is both not generous and not quiet is both quiet and not humble and vice versa.
Everyone who is not happy or tall is either not quiet or not humble.
Everyone who is not wise or not curious is not humble and vice versa.
Everyone who is not strong or not generous is either generous or funny and vice versa.
If someone is either curious or old then someone is both not kind and funny.
Susan is either generous or not humble.
Someone is both humble and wise.
Someone is strong or not creative.
Someone is not kind or brave.
Someone is both rich and creative. | Alice is not curious. | neutral | (((calm(john)<~>~calm(john)))<=>((humble(susan)|~generous(susan))))&
(![X]:((~quiet(X)<~>~humble(X))<=>(~curious(X)<~>old(X))))&
(![X]:(brave(X)<=>(quiet(X)&humble(X))))&
((?[X]:((calm(X)|funny(X))))<=>(?[X]:((funny(X)<~>generous(X)))))&
(![X]:((~wise(X)|creative(X))<=>(wise(X)|~happy(X))))&
(![X]:((~brave(X)|~tall(X))<=>(happy(X)&calm(X))))&
((?[X]:((~strong(X)|humble(X))))<=>((~curious(susan)|~quiet(susan))))&
(((~kind(alice)<~>quiet(alice)))<=>((~old(fred)&~tall(fred))))&
(![X]:((tall(X)|~funny(X))<=>(~rich(X)<~>~old(X))))&
((?[X]:(~old(X)))<=>(?[X]:(patient(X))))&
(![X]:((generous(X)|old(X))<=>(rich(X)|creative(X))))&
(![X]:((~generous(X)&~quiet(X))<=>(quiet(X)&~humble(X))))&
(![X]:((~happy(X)|tall(X))=>(~quiet(X)<~>~humble(X))))&
(![X]:((~wise(X)|~curious(X))<=>~humble(X)))&
(![X]:((~strong(X)|~generous(X))<=>(generous(X)<~>funny(X))))&
((?[X]:((curious(X)<~>old(X))))=>(?[X]:((~kind(X)&funny(X)))))&
((generous(susan)<~>~humble(susan)))&
(?[X]:((humble(X)&wise(X))))&
(?[X]:((strong(X)|~creative(X))))&
(?[X]:((~kind(X)|brave(X))))&
(?[X]:((rich(X)&creative(X)))) | ~curious(alice) | [] | null | 0 |
If someone is either happy or not curious then mary is either rich or not strong.
Everyone who is either happy or generous is both not happy and strong.
If someone is either not strong or brave then someone is curious or not old and vice versa.
If paul is either not strong or wise then paul is rich or not calm and vice versa.
If john is either not rich or not curious then someone is either not wise or not happy and vice versa.
Everyone who is brave is both funny and not strong and vice versa.
Everyone who is either brave or not quiet is not curious or old and vice versa.
If susan is not old or tall then alice is either not old or not creative and vice versa.
If mary is either happy or rich then fred is not creative or strong and vice versa.
If susan is not wise or calm then someone is not kind or not rich.
Everyone who is both generous and not tall is not curious and vice versa.
If someone is humble or not creative then someone is both old and not old.
Everyone who is old is both kind and strong.
Everyone who is not generous or not creative is both not generous and brave.
If someone is quiet then alice is either not humble or wise.
Everyone who is either funny or rich is strong and vice versa.
John is not quiet.
Someone is either not rich or not creative.
Someone is not curious.
Someone is either generous or tall.
Fred is both not humble and not funny.
Someone is not patient or happy. | Fred is creative. | entailment | ((?[X]:((happy(X)<~>~curious(X))))=>((rich(mary)<~>~strong(mary))))&
(![X]:((happy(X)<~>generous(X))=>(~happy(X)&strong(X))))&
((?[X]:((~strong(X)<~>brave(X))))<=>(?[X]:((curious(X)|~old(X)))))&
(((~strong(paul)<~>wise(paul)))<=>((rich(paul)|~calm(paul))))&
(((~rich(john)<~>~curious(john)))<=>(?[X]:((~wise(X)<~>~happy(X)))))&
(![X]:(brave(X)<=>(funny(X)&~strong(X))))&
(![X]:((brave(X)<~>~quiet(X))<=>(~curious(X)|old(X))))&
(((~old(susan)|tall(susan)))<=>((~old(alice)<~>~creative(alice))))&
(((happy(mary)<~>rich(mary)))<=>((~creative(fred)|strong(fred))))&
(((~wise(susan)|calm(susan)))=>(?[X]:((~kind(X)|~rich(X)))))&
(![X]:((generous(X)&~tall(X))<=>~curious(X)))&
((?[X]:((humble(X)|~creative(X))))=>(?[X]:((old(X)&~old(X)))))&
(![X]:(old(X)=>(kind(X)&strong(X))))&
(![X]:((~generous(X)|~creative(X))=>(~generous(X)&brave(X))))&
((?[X]:(quiet(X)))=>((~humble(alice)<~>wise(alice))))&
(![X]:((funny(X)<~>rich(X))<=>strong(X)))&
(~quiet(john))&
(?[X]:((~rich(X)<~>~creative(X))))&
(?[X]:(~curious(X)))&
(?[X]:((generous(X)<~>tall(X))))&
((~humble(fred)&~funny(fred)))&
(?[X]:((~patient(X)|happy(X)))) | creative(fred) | [
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 3284275315264503149958137
% SZS output start Proof for 3284275315264503149958137
12. ? [X0] : (~creative(X0) | humble(X0)) => ? [X0] : (~old(X0) & old(X0)) [input p11]
23. ~creative(fred) [input hypothesis]
25. ? [X0] : (~creative(X0) | humble(X0)) => ? [X1] : (~old(X1) & old(X1)) [rectify 12]
30. ? [X1] : (~old(X1) & old(X1)) | ! [X0] : (creative(X0) & ~humble(X0)) [ennf transformation 25]
59. ? [X0] : (~old(X0) & old(X0)) | ! [X1] : (creative(X1) & ~humble(X1)) [rectify 30]
60. ? [X0] : (~old(X0) & old(X0)) => (~old(sK4) & old(sK4)) [choice axiom]
61. (~old(sK4) & old(sK4)) | ! [X1] : (creative(X1) & ~humble(X1)) [skolemisation 59,60]
127. old(sK4) | creative(X1) [cnf transformation 61]
129. ~old(sK4) | creative(X1) [cnf transformation 61]
150. ~creative(fred) [cnf transformation 23]
289. 29 <=> creative(fred) [avatar definition]
290. ~creative(fred) <- (~29) [avatar component clause 289]
316. 34 <=> ! [X1] : creative(X1) [avatar definition]
317. creative(X1) <- (34) [avatar component clause 316]
319. 35 <=> old(sK4) [avatar definition]
322. 34 | ~35 [avatar split clause 129,319,316]
327. 34 | 35 [avatar split clause 127,319,316]
362. ~29 [avatar split clause 150,289]
363. $false <- (~29, 34) [subsumption resolution 290,317]
364. 29 | ~34 [avatar contradiction clause 363]
365. $false [avatar sat refutation 322,327,362,364]
% SZS output end Proof for 3284275315264503149958137
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not wise and kind is either not funny or old and vice versa.
Everyone who is wise or funny is old or not generous.
Everyone who is both not kind and not rich is not humble.
If someone is both not funny and patient then someone is either not patient or calm and vice versa.
Everyone who is either happy or not wise is old and vice versa.
Everyone who is not old is both not strong and funny.
Everyone who is both not tall and not generous is either not tall or curious.
Everyone who is both not funny and not old is both brave and patient.
Everyone who is creative is both not rich and not tall and vice versa.
If susan is either wise or not generous then someone is either not brave or rich and vice versa.
If alice is both not calm and not curious then someone is either happy or strong and vice versa.
Everyone who is tall or not tall is both kind and humble.
If someone is generous then john is both brave and curious.
Everyone who is both old and not rich is either humble or not brave.
If someone is not patient then lucy is calm and vice versa.
Everyone who is both humble and not kind is rich or creative and vice versa.
Someone is not happy or not curious.
Paul is either not humble or not happy.
Someone is both patient and not old.
Alice is both not creative and curious.
Someone is either not curious or not funny.
John is not happy or not wise.
Someone is both not generous and strong.
Lucy is either not wise or quiet. | John is not funny. | contradiction | (![X]:((~wise(X)&kind(X))<=>(~funny(X)<~>old(X))))&
(![X]:((wise(X)|funny(X))=>(old(X)|~generous(X))))&
(![X]:((~kind(X)&~rich(X))=>~humble(X)))&
((?[X]:((~funny(X)&patient(X))))<=>(?[X]:((~patient(X)<~>calm(X)))))&
(![X]:((happy(X)<~>~wise(X))<=>old(X)))&
(![X]:(~old(X)=>(~strong(X)&funny(X))))&
(![X]:((~tall(X)&~generous(X))=>(~tall(X)<~>curious(X))))&
(![X]:((~funny(X)&~old(X))=>(brave(X)&patient(X))))&
(![X]:(creative(X)<=>(~rich(X)&~tall(X))))&
(((wise(susan)<~>~generous(susan)))<=>(?[X]:((~brave(X)<~>rich(X)))))&
(((~calm(alice)&~curious(alice)))<=>(?[X]:((happy(X)<~>strong(X)))))&
(![X]:((tall(X)|~tall(X))=>(kind(X)&humble(X))))&
((?[X]:(generous(X)))=>((brave(john)&curious(john))))&
(![X]:((old(X)&~rich(X))=>(humble(X)<~>~brave(X))))&
((?[X]:(~patient(X)))<=>(calm(lucy)))&
(![X]:((humble(X)&~kind(X))<=>(rich(X)|creative(X))))&
(?[X]:((~happy(X)|~curious(X))))&
((~humble(paul)<~>~happy(paul)))&
(?[X]:((patient(X)&~old(X))))&
((~creative(alice)&curious(alice)))&
(?[X]:((~curious(X)<~>~funny(X))))&
((~happy(john)|~wise(john)))&
(?[X]:((~generous(X)&strong(X))))&
((~wise(lucy)<~>quiet(lucy))) | ~funny(john) | [
"p0",
"p4",
"p5",
"p11",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 3270301595797836174886750
% SZS output start Proof for 3270301595797836174886750
1. ! [X0] : ((kind(X0) & ~wise(X0)) <=> (~funny(X0) <~> old(X0))) [input p0]
5. ! [X0] : ((happy(X0) <~> ~wise(X0)) <=> old(X0)) [input p4]
6. ! [X0] : (~old(X0) => (funny(X0) & ~strong(X0))) [input p5]
12. ! [X0] : ((~tall(X0) | tall(X0)) => (humble(X0) & kind(X0))) [input p11]
22. ~wise(john) | ~happy(john) [input p21]
25. ~funny(john) [input hypothesis]
31. ! [X0] : ((funny(X0) & ~strong(X0)) | old(X0)) [ennf transformation 6]
36. ! [X0] : ((humble(X0) & kind(X0)) | (tall(X0) & ~tall(X0))) [ennf transformation 12]
40. ! [X0] : (((kind(X0) & ~wise(X0)) | ((~funny(X0) | ~old(X0)) & (old(X0) | funny(X0)))) & (((~old(X0) | funny(X0)) & (old(X0) | ~funny(X0))) | (~kind(X0) | wise(X0)))) [nnf transformation 1]
41. ! [X0] : (((kind(X0) & ~wise(X0)) | ((~funny(X0) | ~old(X0)) & (old(X0) | funny(X0)))) & (((~old(X0) | funny(X0)) & (old(X0) | ~funny(X0))) | ~kind(X0) | wise(X0))) [flattening 40]
47. ! [X0] : ((((wise(X0) | ~happy(X0)) & (~wise(X0) | happy(X0))) | ~old(X0)) & (old(X0) | ((happy(X0) | wise(X0)) & (~wise(X0) | ~happy(X0))))) [nnf transformation 5]
79. ~old(X0) | funny(X0) | ~kind(X0) | wise(X0) [cnf transformation 41]
95. ~old(X0) | happy(X0) | ~wise(X0) [cnf transformation 47]
98. old(X0) | funny(X0) [cnf transformation 31]
120. kind(X0) | ~tall(X0) [cnf transformation 36]
121. tall(X0) | kind(X0) [cnf transformation 36]
144. ~wise(john) | ~happy(john) [cnf transformation 22]
149. ~funny(john) [cnf transformation 25]
241. kind(X0) [subsumption resolution 120,121]
293. 30 <=> happy(john) [avatar definition]
295. ~happy(john) <- (~30) [avatar component clause 293]
297. 31 <=> wise(john) [avatar definition]
300. ~30 | ~31 [avatar split clause 144,297,293]
349. 38 <=> old(john) [avatar definition]
350. ~old(john) <- (~38) [avatar component clause 349]
351. old(john) <- (38) [avatar component clause 349]
372. funny(john) <- (~38) [resolution 350,98]
373. $false <- (~38) [subsumption resolution 372,149]
374. 38 [avatar contradiction clause 373]
376. happy(john) | ~wise(john) <- (38) [resolution 351,95]
396. funny(X1) | ~kind(X1) | wise(X1) | funny(X1) [resolution 79,98]
399. funny(X1) | ~kind(X1) | wise(X1) [duplicate literal removal 396]
401. funny(X1) | wise(X1) [subsumption resolution 399,241]
414. wise(john) [resolution 401,149]
421. 31 [avatar split clause 414,297]
422. ~wise(john) <- (~30, 38) [subsumption resolution 376,295]
423. ~31 | 30 | ~38 [avatar split clause 422,349,293,297]
424. $false [avatar sat refutation 300,374,421,423]
% SZS output end Proof for 3270301595797836174886750
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny or tall is strong and vice versa.
Everyone who is either funny or not old is generous.
If lucy is both rich and funny then john is not tall and vice versa.
If someone is both not strong and kind then someone is happy and vice versa.
If john is both happy and not old then someone is either brave or not tall.
Everyone who is not humble is generous or kind.
If mary is creative then someone is humble or patient and vice versa.
Everyone who is not patient is both strong and patient and vice versa.
If someone is either strong or not happy then someone is either not curious or not rich.
Everyone who is not quiet or not funny is both not humble and not happy and vice versa.
Everyone who is not creative is either old or kind.
If someone is both strong and kind then someone is both not rich and kind.
If someone is either not happy or patient then susan is either not strong or not old.
Everyone who is both not generous and not happy is generous or curious and vice versa.
Everyone who is both humble and happy is not quiet or brave and vice versa.
Alice is not kind or not generous.
Susan is wise.
Someone is not tall or strong.
John is either not rich or not brave.
Someone is either calm or not kind.
Someone is rich. | John is not strong. | entailment | (![X]:((~funny(X)|tall(X))<=>strong(X)))&
(![X]:((funny(X)<~>~old(X))=>generous(X)))&
(((rich(lucy)&funny(lucy)))<=>(~tall(john)))&
((?[X]:((~strong(X)&kind(X))))<=>(?[X]:(happy(X))))&
(((happy(john)&~old(john)))=>(?[X]:((brave(X)<~>~tall(X)))))&
(![X]:(~humble(X)=>(generous(X)|kind(X))))&
((creative(mary))<=>(?[X]:((humble(X)|patient(X)))))&
(![X]:(~patient(X)<=>(strong(X)&patient(X))))&
((?[X]:((strong(X)<~>~happy(X))))=>(?[X]:((~curious(X)<~>~rich(X)))))&
(![X]:((~quiet(X)|~funny(X))<=>(~humble(X)&~happy(X))))&
(![X]:(~creative(X)=>(old(X)<~>kind(X))))&
((?[X]:((strong(X)&kind(X))))=>(?[X]:((~rich(X)&kind(X)))))&
((?[X]:((~happy(X)<~>patient(X))))=>((~strong(susan)<~>~old(susan))))&
(![X]:((~generous(X)&~happy(X))<=>(generous(X)|curious(X))))&
(![X]:((humble(X)&happy(X))<=>(~quiet(X)|brave(X))))&
((~kind(alice)|~generous(alice)))&
(wise(susan))&
(?[X]:((~tall(X)|strong(X))))&
((~rich(john)<~>~brave(john)))&
(?[X]:((calm(X)<~>~kind(X))))&
(?[X]:(rich(X))) | ~strong(john) | [
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 1618533226139365012487594
% SZS output start Proof for 1618533226139365012487594
8. ! [X0] : (~patient(X0) <=> (patient(X0) & strong(X0))) [input p7]
22. strong(john) [input hypothesis]
53. ! [X0] : ((~patient(X0) | (~patient(X0) | ~strong(X0))) & ((patient(X0) & strong(X0)) | patient(X0))) [nnf transformation 8]
54. ! [X0] : ((~patient(X0) | ~patient(X0) | ~strong(X0)) & ((patient(X0) & strong(X0)) | patient(X0))) [flattening 53]
96. patient(X0) | patient(X0) [cnf transformation 54]
97. ~patient(X0) | ~patient(X0) | ~strong(X0) [cnf transformation 54]
132. strong(john) [cnf transformation 22]
135. patient(X0) [duplicate literal removal 96]
136. ~patient(X0) | ~strong(X0) [duplicate literal removal 97]
287. ~strong(X0) [resolution 136,135]
288. $false [resolution 287,132]
% SZS output end Proof for 1618533226139365012487594
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either funny or patient then someone is either calm or not humble.
If someone is not quiet then someone is both quiet and happy and vice versa.
Everyone who is either not brave or calm is either not funny or humble and vice versa.
Everyone who is both not brave and funny is not humble.
Everyone who is not strong or not quiet is both quiet and not old.
Everyone who is both not quiet and not strong is either not patient or not kind.
If alice is either not wise or kind then john is patient or calm.
If someone is both not patient and not kind then someone is either not old or tall and vice versa.
Everyone who is not tall is not brave.
Everyone who is either not humble or not funny is not tall.
Everyone who is either patient or not curious is either not tall or wise and vice versa.
Everyone who is both tall and curious is both happy and not kind and vice versa.
If lucy is strong or kind then someone is kind or not humble.
Everyone who is old is either quiet or not rich.
Everyone who is not strong is either curious or not tall.
If fred is not brave then someone is rich and vice versa.
Alice is wise.
Someone is not funny or happy.
Susan is both not happy and not funny.
Someone is either not creative or kind.
Alice is either funny or not kind.
Alice is both funny and not rich. | Alice is not wise. | contradiction | ((?[X]:((funny(X)<~>patient(X))))=>(?[X]:((calm(X)<~>~humble(X)))))&
((?[X]:(~quiet(X)))<=>(?[X]:((quiet(X)&happy(X)))))&
(![X]:((~brave(X)<~>calm(X))<=>(~funny(X)<~>humble(X))))&
(![X]:((~brave(X)&funny(X))=>~humble(X)))&
(![X]:((~strong(X)|~quiet(X))=>(quiet(X)&~old(X))))&
(![X]:((~quiet(X)&~strong(X))=>(~patient(X)<~>~kind(X))))&
(((~wise(alice)<~>kind(alice)))=>((patient(john)|calm(john))))&
((?[X]:((~patient(X)&~kind(X))))<=>(?[X]:((~old(X)<~>tall(X)))))&
(![X]:(~tall(X)=>~brave(X)))&
(![X]:((~humble(X)<~>~funny(X))=>~tall(X)))&
(![X]:((patient(X)<~>~curious(X))<=>(~tall(X)<~>wise(X))))&
(![X]:((tall(X)&curious(X))<=>(happy(X)&~kind(X))))&
(((strong(lucy)|kind(lucy)))=>(?[X]:((kind(X)|~humble(X)))))&
(![X]:(old(X)=>(quiet(X)<~>~rich(X))))&
(![X]:(~strong(X)=>(curious(X)<~>~tall(X))))&
((~brave(fred))<=>(?[X]:(rich(X))))&
(wise(alice))&
(?[X]:((~funny(X)|happy(X))))&
((~happy(susan)&~funny(susan)))&
(?[X]:((~creative(X)<~>kind(X))))&
((funny(alice)<~>~kind(alice)))&
((funny(alice)&~rich(alice))) | ~wise(alice) | [
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 4232103139396862082551174
% SZS output start Proof for 4232103139396862082551174
17. wise(alice) [input p16]
23. ~wise(alice) [input hypothesis]
128. wise(alice) [cnf transformation 17]
138. ~wise(alice) [cnf transformation 23]
185. 11 <=> wise(alice) [avatar definition]
261. 11 [avatar split clause 128,185]
288. ~11 [avatar split clause 138,185]
289. $false [avatar sat refutation 261,288]
% SZS output end Proof for 4232103139396862082551174
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient or happy is not curious or brave and vice versa.
If fred is not wise or happy then lucy is both strong and wise and vice versa.
If someone is tall then susan is not patient and vice versa.
If mary is humble or kind then paul is not rich or strong.
Everyone who is either humble or not kind is not strong or creative and vice versa.
Everyone who is both not rich and happy is not tall.
Everyone who is both not humble and not old is old and vice versa.
Everyone who is not old or brave is either generous or not creative and vice versa.
Everyone who is both generous and not brave is either funny or kind and vice versa.
Everyone who is either curious or rich is strong.
Everyone who is not funny or funny is curious or not humble.
Everyone who is kind is both not humble and funny.
If someone is both quiet and curious then someone is either happy or brave and vice versa.
Everyone who is rich or not strong is strong or not humble.
If someone is brave or curious then paul is either not curious or not generous.
Everyone who is either humble or not funny is not wise.
Alice is calm.
Someone is happy.
Fred is not quiet.
Mary is either funny or curious.
Someone is both wise and rich.
Someone is humble.
Lucy is both not patient and happy.
Someone is tall. | Paul is not funny. | entailment | (![X]:((~patient(X)<~>happy(X))<=>(~curious(X)|brave(X))))&
(((~wise(fred)|happy(fred)))<=>((strong(lucy)&wise(lucy))))&
((?[X]:(tall(X)))<=>(~patient(susan)))&
(((humble(mary)|kind(mary)))=>((~rich(paul)|strong(paul))))&
(![X]:((humble(X)<~>~kind(X))<=>(~strong(X)|creative(X))))&
(![X]:((~rich(X)&happy(X))=>~tall(X)))&
(![X]:((~humble(X)&~old(X))<=>old(X)))&
(![X]:((~old(X)|brave(X))<=>(generous(X)<~>~creative(X))))&
(![X]:((generous(X)&~brave(X))<=>(funny(X)<~>kind(X))))&
(![X]:((curious(X)<~>rich(X))=>strong(X)))&
(![X]:((~funny(X)|funny(X))=>(curious(X)|~humble(X))))&
(![X]:(kind(X)=>(~humble(X)&funny(X))))&
((?[X]:((quiet(X)&curious(X))))<=>(?[X]:((happy(X)<~>brave(X)))))&
(![X]:((rich(X)|~strong(X))=>(strong(X)|~humble(X))))&
((?[X]:((brave(X)|curious(X))))=>((~curious(paul)<~>~generous(paul))))&
(![X]:((humble(X)<~>~funny(X))=>~wise(X)))&
(calm(alice))&
(?[X]:(happy(X)))&
(~quiet(fred))&
((funny(mary)<~>curious(mary)))&
(?[X]:((wise(X)&rich(X))))&
(?[X]:(humble(X)))&
((~patient(lucy)&happy(lucy)))&
(?[X]:(tall(X))) | ~funny(paul) | [
"p6",
"p8",
"p10",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8997621142333351397872398
% SZS output start Proof for 8997621142333351397872398
7. ! [X0] : ((~old(X0) & ~humble(X0)) <=> old(X0)) [input p6]
9. ! [X0] : ((~brave(X0) & generous(X0)) <=> (funny(X0) <~> kind(X0))) [input p8]
11. ! [X0] : ((funny(X0) | ~funny(X0)) => (~humble(X0) | curious(X0))) [input p10]
12. ! [X0] : (kind(X0) => (funny(X0) & ~humble(X0))) [input p11]
15. ? [X0] : (curious(X0) | brave(X0)) => (~curious(paul) <~> ~generous(paul)) [input p14]
25. funny(paul) [input hypothesis]
33. ! [X0] : ((~humble(X0) | curious(X0)) | (~funny(X0) & funny(X0))) [ennf transformation 11]
34. ! [X0] : (~humble(X0) | curious(X0) | (~funny(X0) & funny(X0))) [flattening 33]
35. ! [X0] : ((funny(X0) & ~humble(X0)) | ~kind(X0)) [ennf transformation 12]
38. (~curious(paul) <~> ~generous(paul)) | ! [X0] : (~curious(X0) & ~brave(X0)) [ennf transformation 15]
50. ! [X0] : (((~old(X0) & ~humble(X0)) | ~old(X0)) & (old(X0) | (old(X0) | humble(X0)))) [nnf transformation 7]
51. ! [X0] : (((~old(X0) & ~humble(X0)) | ~old(X0)) & (old(X0) | old(X0) | humble(X0))) [flattening 50]
54. ! [X0] : (((~brave(X0) & generous(X0)) | ((funny(X0) | ~kind(X0)) & (kind(X0) | ~funny(X0)))) & (((~kind(X0) | ~funny(X0)) & (kind(X0) | funny(X0))) | (brave(X0) | ~generous(X0)))) [nnf transformation 9]
55. ! [X0] : (((~brave(X0) & generous(X0)) | ((funny(X0) | ~kind(X0)) & (kind(X0) | ~funny(X0)))) & (((~kind(X0) | ~funny(X0)) & (kind(X0) | funny(X0))) | brave(X0) | ~generous(X0))) [flattening 54]
62. ((generous(paul) | curious(paul)) & (~generous(paul) | ~curious(paul))) | ! [X0] : (~curious(X0) & ~brave(X0)) [nnf transformation 38]
95. old(X0) | old(X0) | humble(X0) [cnf transformation 51]
97. ~old(X0) | ~old(X0) [cnf transformation 51]
106. ~funny(X0) | kind(X0) | generous(X0) [cnf transformation 55]
112. ~humble(X0) | curious(X0) | funny(X0) [cnf transformation 34]
113. ~humble(X0) | curious(X0) | ~funny(X0) [cnf transformation 34]
114. ~humble(X0) | ~kind(X0) [cnf transformation 35]
125. ~generous(paul) | ~curious(paul) | ~curious(X0) [cnf transformation 62]
140. funny(paul) [cnf transformation 25]
142. old(X0) | humble(X0) [duplicate literal removal 95]
143. ~old(X0) [duplicate literal removal 97]
196. humble(X0) [subsumption resolution 142,143]
199. ~funny(X0) | curious(X0) [subsumption resolution 113,196]
200. curious(X0) | funny(X0) [subsumption resolution 112,196]
201. curious(X0) [subsumption resolution 200,199]
202. ~kind(X0) [subsumption resolution 114,196]
231. ~generous(paul) | ~curious(X0) [subsumption resolution 125,201]
232. ~generous(paul) [subsumption resolution 231,201]
277. kind(paul) | generous(paul) [resolution 106,140]
278. generous(paul) [subsumption resolution 277,202]
279. $false [subsumption resolution 278,232]
% SZS output end Proof for 8997621142333351397872398
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not generous then someone is either wise or not tall.
Everyone who is creative or not strong is not funny or kind and vice versa.
If paul is creative or rich then lucy is either calm or not funny.
Everyone who is humble or patient is not wise or not quiet.
If someone is both wise and not humble then someone is both not happy and not patient and vice versa.
Everyone who is both not curious and calm is not humble or not tall.
Everyone who is generous is old.
Everyone who is either not curious or kind is both old and not quiet and vice versa.
If susan is both not curious and humble then paul is funny.
If lucy is not generous then mary is generous and vice versa.
Everyone who is both curious and not patient is both not tall and tall and vice versa.
Everyone who is both not curious and patient is generous.
Everyone who is both not humble and old is either curious or not tall and vice versa.
Everyone who is not kind is patient or humble.
Everyone who is either patient or creative is both not kind and old and vice versa.
If susan is both not calm and not brave then someone is both kind and not humble and vice versa.
Someone is either generous or kind.
Someone is not creative or kind.
Mary is both not tall and funny.
Someone is either not quiet or calm.
Someone is not strong or not humble.
Paul is both patient and not kind.
Lucy is either wise or quiet.
Paul is not quiet. | Mary is creative. | neutral | ((?[X]:(~generous(X)))=>(?[X]:((wise(X)<~>~tall(X)))))&
(![X]:((creative(X)|~strong(X))<=>(~funny(X)|kind(X))))&
(((creative(paul)|rich(paul)))=>((calm(lucy)<~>~funny(lucy))))&
(![X]:((humble(X)|patient(X))=>(~wise(X)|~quiet(X))))&
((?[X]:((wise(X)&~humble(X))))<=>(?[X]:((~happy(X)&~patient(X)))))&
(![X]:((~curious(X)&calm(X))=>(~humble(X)|~tall(X))))&
(![X]:(generous(X)=>old(X)))&
(![X]:((~curious(X)<~>kind(X))<=>(old(X)&~quiet(X))))&
(((~curious(susan)&humble(susan)))=>(funny(paul)))&
((~generous(lucy))<=>(generous(mary)))&
(![X]:((curious(X)&~patient(X))<=>(~tall(X)&tall(X))))&
(![X]:((~curious(X)&patient(X))=>generous(X)))&
(![X]:((~humble(X)&old(X))<=>(curious(X)<~>~tall(X))))&
(![X]:(~kind(X)=>(patient(X)|humble(X))))&
(![X]:((patient(X)<~>creative(X))<=>(~kind(X)&old(X))))&
(((~calm(susan)&~brave(susan)))<=>(?[X]:((kind(X)&~humble(X)))))&
(?[X]:((generous(X)<~>kind(X))))&
(?[X]:((~creative(X)|kind(X))))&
((~tall(mary)&funny(mary)))&
(?[X]:((~quiet(X)<~>calm(X))))&
(?[X]:((~strong(X)|~humble(X))))&
((patient(paul)&~kind(paul)))&
((wise(lucy)<~>quiet(lucy)))&
(~quiet(paul)) | creative(mary) | [] | null | 0 |
If paul is both patient and not calm then someone is tall or generous and vice versa. Everyone who is either wise or not funny is both not happy and funny and vice versa. If someone is both not funny and brave then someone is both not patient and happy. Everyone who is not strong is funny or tall and vice versa. If paul is happy or not brave then lucy is tall and vice versa. Everyone who is both curious and humble is either curious or not generous and vice versa. Everyone who is quiet or rich is not wise or patient and vice versa. If paul is strong or not old then someone is either not creative or not brave. Everyone who is both old and happy is both not wise and curious and vice versa. Everyone who is both not curious and humble is either tall or humble. Everyone who is humble or not brave is both patient and quiet. If fred is both not funny and kind then mary is not creative and vice versa. Everyone who is either curious or tall is not patient. Everyone who is either not old or not generous is either not old or not humble. If someone is both not funny and not old then paul is either brave or patient. If someone is both old and not creative then someone is not old and vice versa. Susan is both not quiet and not strong. Mary is both quiet and wise. Alice is both not tall and not curious. Someone is both happy and funny. John is either not creative or quiet. Paul is creative. Someone is both not curious and happy. Lucy is kind. | Alice is not humble. | neutral | (((patient(paul)&~calm(paul)))<=>(?[X]:((tall(X)|generous(X)))))&
(![X]:((wise(X)<~>~funny(X))<=>(~happy(X)&funny(X))))&
((?[X]:((~funny(X)&brave(X))))=>(?[X]:((~patient(X)&happy(X)))))&
(![X]:(~strong(X)<=>(funny(X)|tall(X))))&
(((happy(paul)|~brave(paul)))<=>(tall(lucy)))&
(![X]:((curious(X)&humble(X))<=>(curious(X)<~>~generous(X))))&
(![X]:((quiet(X)|rich(X))<=>(~wise(X)|patient(X))))&
(((strong(paul)|~old(paul)))=>(?[X]:((~creative(X)<~>~brave(X)))))&
(![X]:((old(X)&happy(X))<=>(~wise(X)&curious(X))))&
(![X]:((~curious(X)&humble(X))=>(tall(X)<~>humble(X))))&
(![X]:((humble(X)|~brave(X))=>(patient(X)&quiet(X))))&
(((~funny(fred)&kind(fred)))<=>(~creative(mary)))&
(![X]:((curious(X)<~>tall(X))=>~patient(X)))&
(![X]:((~old(X)<~>~generous(X))=>(~old(X)<~>~humble(X))))&
((?[X]:((~funny(X)&~old(X))))=>((brave(paul)<~>patient(paul))))&
((?[X]:((old(X)&~creative(X))))<=>(?[X]:(~old(X))))&
((~quiet(susan)&~strong(susan)))&
((quiet(mary)&wise(mary)))&
((~tall(alice)&~curious(alice)))&
(?[X]:((happy(X)&funny(X))))&
((~creative(john)<~>quiet(john)))&
(creative(paul))&
(?[X]:((~curious(X)&happy(X))))&
(kind(lucy)) | ~humble(alice) | [] | null | 0 |
Everyone who is either not rich or humble is creative or wise.
Everyone who is both not calm and happy is not strong.
If lucy is not calm then someone is not calm.
If susan is either not quiet or patient then paul is both not quiet and strong and vice versa.
Everyone who is either curious or not rich is both not old and not rich and vice versa.
If someone is either not rich or not humble then fred is either humble or kind and vice versa.
If mary is not generous or not brave then someone is either not wise or not old and vice versa.
If fred is humble then someone is either not humble or not tall.
If someone is both not quiet and tall then someone is quiet and vice versa.
Everyone who is not creative is not tall or creative and vice versa.
Everyone who is not quiet or not old is both not quiet and calm.
Everyone who is both calm and not generous is both kind and not rich and vice versa.
Everyone who is either generous or patient is both old and not old.
Everyone who is curious or not funny is not brave or strong.
If lucy is rich or generous then someone is either not old or not humble and vice versa.
Everyone who is not humble or kind is either not curious or brave and vice versa.
Alice is kind.
Someone is not humble.
Mary is either kind or humble.
Alice is either humble or kind.
Susan is either generous or not quiet.
Someone is not quiet.
Someone is both humble and rich.
Mary is either kind or not tall. | Susan is not quiet. | entailment | (![X]:((~rich(X)<~>humble(X))=>(creative(X)|wise(X))))&
(![X]:((~calm(X)&happy(X))=>~strong(X)))&
((~calm(lucy))=>(?[X]:(~calm(X))))&
(((~quiet(susan)<~>patient(susan)))<=>((~quiet(paul)&strong(paul))))&
(![X]:((curious(X)<~>~rich(X))<=>(~old(X)&~rich(X))))&
((?[X]:((~rich(X)<~>~humble(X))))<=>((humble(fred)<~>kind(fred))))&
(((~generous(mary)|~brave(mary)))<=>(?[X]:((~wise(X)<~>~old(X)))))&
((humble(fred))=>(?[X]:((~humble(X)<~>~tall(X)))))&
((?[X]:((~quiet(X)&tall(X))))<=>(?[X]:(quiet(X))))&
(![X]:(~creative(X)<=>(~tall(X)|creative(X))))&
(![X]:((~quiet(X)|~old(X))=>(~quiet(X)&calm(X))))&
(![X]:((calm(X)&~generous(X))<=>(kind(X)&~rich(X))))&
(![X]:((generous(X)<~>patient(X))=>(old(X)&~old(X))))&
(![X]:((curious(X)|~funny(X))=>(~brave(X)|strong(X))))&
(((rich(lucy)|generous(lucy)))<=>(?[X]:((~old(X)<~>~humble(X)))))&
(![X]:((~humble(X)|kind(X))<=>(~curious(X)<~>brave(X))))&
(kind(alice))&
(?[X]:(~humble(X)))&
((kind(mary)<~>humble(mary)))&
((humble(alice)<~>kind(alice)))&
((generous(susan)<~>~quiet(susan)))&
(?[X]:(~quiet(X)))&
(?[X]:((humble(X)&rich(X))))&
((kind(mary)<~>~tall(mary))) | ~quiet(susan) | [
"p8",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 8393430341909689991888497
% SZS output start Proof for 8393430341909689991888497
9. ? [X0] : (tall(X0) & ~quiet(X0)) <=> ? [X0] : quiet(X0) [input p8]
10. ! [X0] : (~creative(X0) <=> (creative(X0) | ~tall(X0))) [input p9]
25. quiet(susan) [input hypothesis]
26. ? [X0] : (tall(X0) & ~quiet(X0)) <=> ? [X1] : quiet(X1) [rectify 9]
56. (? [X0] : (tall(X0) & ~quiet(X0)) | ! [X1] : ~quiet(X1)) & (? [X1] : quiet(X1) | ! [X0] : (~tall(X0) | quiet(X0))) [nnf transformation 26]
57. (? [X0] : (tall(X0) & ~quiet(X0)) | ! [X1] : ~quiet(X1)) & (? [X2] : quiet(X2) | ! [X3] : (~tall(X3) | quiet(X3))) [rectify 56]
58. ? [X0] : (tall(X0) & ~quiet(X0)) => (tall(sK4) & ~quiet(sK4)) [choice axiom]
59. ? [X2] : quiet(X2) => quiet(sK5) [choice axiom]
60. ((tall(sK4) & ~quiet(sK4)) | ! [X1] : ~quiet(X1)) & (quiet(sK5) | ! [X3] : (~tall(X3) | quiet(X3))) [skolemisation 57,59,58]
61. ! [X0] : ((~creative(X0) | (~creative(X0) & tall(X0))) & ((creative(X0) | ~tall(X0)) | creative(X0))) [nnf transformation 10]
62. ! [X0] : ((~creative(X0) | (~creative(X0) & tall(X0))) & (creative(X0) | ~tall(X0) | creative(X0))) [flattening 61]
116. tall(sK4) | ~quiet(X1) [cnf transformation 60]
117. creative(X0) | ~tall(X0) | creative(X0) [cnf transformation 62]
119. ~creative(X0) | ~creative(X0) [cnf transformation 62]
158. quiet(susan) [cnf transformation 25]
159. creative(X0) | ~tall(X0) [duplicate literal removal 117]
160. ~creative(X0) [duplicate literal removal 119]
181. 5 <=> quiet(susan) [avatar definition]
183. quiet(susan) <- (5) [avatar component clause 181]
263. 21 <=> ! [X1] : ~quiet(X1) [avatar definition]
264. ~quiet(X1) <- (21) [avatar component clause 263]
266. 22 <=> tall(sK4) [avatar definition]
268. tall(sK4) <- (22) [avatar component clause 266]
269. 21 | 22 [avatar split clause 116,266,263]
283. ~tall(X0) [subsumption resolution 159,160]
333. 5 [avatar split clause 158,181]
334. $false <- (5, 21) [subsumption resolution 183,264]
335. ~5 | ~21 [avatar contradiction clause 334]
336. $false <- (22) [subsumption resolution 268,283]
337. ~22 [avatar contradiction clause 336]
338. $false [avatar sat refutation 269,333,335,337]
% SZS output end Proof for 8393430341909689991888497
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not generous or kind then someone is not happy.
If lucy is not strong or not humble then someone is patient or happy.
Everyone who is both brave and creative is not humble and vice versa.
Everyone who is not funny is funny or calm and vice versa.
Everyone who is not funny is creative or rich and vice versa.
If someone is both curious and wise then mary is either happy or strong and vice versa.
If paul is calm or wise then someone is not funny and vice versa.
Everyone who is either not patient or wise is both not old and kind.
Everyone who is both not funny and not creative is happy and vice versa.
If alice is either happy or not wise then someone is both not creative and quiet and vice versa.
Everyone who is both not patient and happy is either not calm or creative and vice versa.
If someone is not kind then someone is tall and vice versa.
Everyone who is both creative and not happy is either generous or patient and vice versa.
Everyone who is either not curious or funny is either generous or not quiet and vice versa.
If john is either not happy or happy then susan is either not happy or generous and vice versa.
If someone is creative or curious then paul is not strong or not happy.
Someone is not kind.
Someone is both patient and not quiet.
Fred is not strong or not patient.
Fred is either not brave or not kind.
Someone is not wise.
Susan is both not strong and humble. | Fred is not quiet. | entailment | ((?[X]:((~generous(X)<~>kind(X))))=>(?[X]:(~happy(X))))&
(((~strong(lucy)|~humble(lucy)))=>(?[X]:((patient(X)|happy(X)))))&
(![X]:((brave(X)&creative(X))<=>~humble(X)))&
(![X]:(~funny(X)<=>(funny(X)|calm(X))))&
(![X]:(~funny(X)<=>(creative(X)|rich(X))))&
((?[X]:((curious(X)&wise(X))))<=>((happy(mary)<~>strong(mary))))&
(((calm(paul)|wise(paul)))<=>(?[X]:(~funny(X))))&
(![X]:((~patient(X)<~>wise(X))=>(~old(X)&kind(X))))&
(![X]:((~funny(X)&~creative(X))<=>happy(X)))&
(((happy(alice)<~>~wise(alice)))<=>(?[X]:((~creative(X)&quiet(X)))))&
(![X]:((~patient(X)&happy(X))<=>(~calm(X)<~>creative(X))))&
((?[X]:(~kind(X)))<=>(?[X]:(tall(X))))&
(![X]:((creative(X)&~happy(X))<=>(generous(X)<~>patient(X))))&
(![X]:((~curious(X)<~>funny(X))<=>(generous(X)<~>~quiet(X))))&
(((~happy(john)<~>happy(john)))<=>((~happy(susan)<~>generous(susan))))&
((?[X]:((creative(X)|curious(X))))=>((~strong(paul)|~happy(paul))))&
(?[X]:(~kind(X)))&
(?[X]:((patient(X)&~quiet(X))))&
((~strong(fred)|~patient(fred)))&
((~brave(fred)<~>~kind(fred)))&
(?[X]:(~wise(X)))&
((~strong(susan)&humble(susan))) | ~quiet(fred) | [
"p0",
"p3",
"p7",
"p8",
"p9",
"p10",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 2111931039520306260425192
% SZS output start Proof for 2111931039520306260425192
1. ? [X0] : (~generous(X0) <~> kind(X0)) => ? [X0] : ~happy(X0) [input p0]
4. ! [X0] : (~funny(X0) <=> (calm(X0) | funny(X0))) [input p3]
8. ! [X0] : ((~patient(X0) <~> wise(X0)) => (kind(X0) & ~old(X0))) [input p7]
9. ! [X0] : ((~creative(X0) & ~funny(X0)) <=> happy(X0)) [input p8]
10. (happy(alice) <~> ~wise(alice)) <=> ? [X0] : (quiet(X0) & ~creative(X0)) [input p9]
11. ! [X0] : ((happy(X0) & ~patient(X0)) <=> (~calm(X0) <~> creative(X0))) [input p10]
13. ! [X0] : ((~happy(X0) & creative(X0)) <=> (generous(X0) <~> patient(X0))) [input p12]
23. quiet(fred) [input hypothesis]
24. ? [X0] : (~generous(X0) <~> kind(X0)) => ? [X1] : ~happy(X1) [rectify 1]
27. ! [X0] : ((~patient(X0) <~> wise(X0)) => kind(X0)) [pure predicate removal 8]
28. ? [X1] : ~happy(X1) | ! [X0] : (~generous(X0) <=> kind(X0)) [ennf transformation 24]
32. ! [X0] : (kind(X0) | (~patient(X0) <=> wise(X0))) [ennf transformation 27]
35. ? [X1] : ~happy(X1) | ! [X0] : ((~generous(X0) | ~kind(X0)) & (kind(X0) | generous(X0))) [nnf transformation 28]
36. ? [X0] : ~happy(X0) | ! [X1] : ((~generous(X1) | ~kind(X1)) & (kind(X1) | generous(X1))) [rectify 35]
37. ? [X0] : ~happy(X0) => ~happy(sK0) [choice axiom]
38. ~happy(sK0) | ! [X1] : ((~generous(X1) | ~kind(X1)) & (kind(X1) | generous(X1))) [skolemisation 36,37]
41. ! [X0] : ((~funny(X0) | (~calm(X0) & ~funny(X0))) & ((calm(X0) | funny(X0)) | funny(X0))) [nnf transformation 4]
42. ! [X0] : ((~funny(X0) | (~calm(X0) & ~funny(X0))) & (calm(X0) | funny(X0) | funny(X0))) [flattening 41]
54. ! [X0] : (kind(X0) | ((~patient(X0) | ~wise(X0)) & (wise(X0) | patient(X0)))) [nnf transformation 32]
55. ! [X0] : (((~creative(X0) & ~funny(X0)) | ~happy(X0)) & (happy(X0) | (creative(X0) | funny(X0)))) [nnf transformation 9]
56. ! [X0] : (((~creative(X0) & ~funny(X0)) | ~happy(X0)) & (happy(X0) | creative(X0) | funny(X0))) [flattening 55]
57. (((wise(alice) | ~happy(alice)) & (~wise(alice) | happy(alice))) | ! [X0] : (~quiet(X0) | creative(X0))) & (? [X0] : (quiet(X0) & ~creative(X0)) | ((happy(alice) | wise(alice)) & (~wise(alice) | ~happy(alice)))) [nnf transformation 10]
58. (((wise(alice) | ~happy(alice)) & (~wise(alice) | happy(alice))) | ! [X0] : (~quiet(X0) | creative(X0))) & (? [X1] : (quiet(X1) & ~creative(X1)) | ((happy(alice) | wise(alice)) & (~wise(alice) | ~happy(alice)))) [rectify 57]
59. ? [X1] : (quiet(X1) & ~creative(X1)) => (quiet(sK4) & ~creative(sK4)) [choice axiom]
60. (((wise(alice) | ~happy(alice)) & (~wise(alice) | happy(alice))) | ! [X0] : (~quiet(X0) | creative(X0))) & ((quiet(sK4) & ~creative(sK4)) | ((happy(alice) | wise(alice)) & (~wise(alice) | ~happy(alice)))) [skolemisation 58,59]
61. ! [X0] : (((happy(X0) & ~patient(X0)) | ((~calm(X0) | ~creative(X0)) & (creative(X0) | calm(X0)))) & (((~creative(X0) | calm(X0)) & (creative(X0) | ~calm(X0))) | (~happy(X0) | patient(X0)))) [nnf transformation 11]
62. ! [X0] : (((happy(X0) & ~patient(X0)) | ((~calm(X0) | ~creative(X0)) & (creative(X0) | calm(X0)))) & (((~creative(X0) | calm(X0)) & (creative(X0) | ~calm(X0))) | ~happy(X0) | patient(X0))) [flattening 61]
68. ! [X0] : (((~happy(X0) & creative(X0)) | ((generous(X0) | ~patient(X0)) & (patient(X0) | ~generous(X0)))) & (((~patient(X0) | ~generous(X0)) & (patient(X0) | generous(X0))) | (happy(X0) | ~creative(X0)))) [nnf transformation 13]
69. ! [X0] : (((~happy(X0) & creative(X0)) | ((generous(X0) | ~patient(X0)) & (patient(X0) | ~generous(X0)))) & (((~patient(X0) | ~generous(X0)) & (patient(X0) | generous(X0))) | happy(X0) | ~creative(X0))) [flattening 68]
80. ~happy(sK0) | ~generous(X1) | ~kind(X1) [cnf transformation 38]
84. calm(X0) | funny(X0) | funny(X0) [cnf transformation 42]
85. ~funny(X0) | ~funny(X0) [cnf transformation 42]
100. ~wise(X0) | ~patient(X0) | kind(X0) [cnf transformation 54]
101. happy(X0) | creative(X0) | funny(X0) [cnf transformation 56]
103. ~creative(X0) | ~happy(X0) [cnf transformation 56]
109. wise(alice) | ~happy(alice) | ~quiet(X0) | creative(X0) [cnf transformation 60]
110. creative(X0) | ~calm(X0) | ~happy(X0) | patient(X0) [cnf transformation 62]
115. happy(X0) | ~calm(X0) | ~creative(X0) [cnf transformation 62]
123. ~happy(X0) | generous(X0) | ~patient(X0) [cnf transformation 69]
151. quiet(fred) [cnf transformation 23]
156. calm(X0) | funny(X0) [duplicate literal removal 84]
157. ~funny(X0) [duplicate literal removal 85]
159. 1 <=> ! [X1] : (~generous(X1) | ~kind(X1)) [avatar definition]
160. ~kind(X1) | ~generous(X1) <- (1) [avatar component clause 159]
162. 2 <=> happy(sK0) [avatar definition]
164. ~happy(sK0) <- (~2) [avatar component clause 162]
165. 1 | ~2 [avatar split clause 80,162,159]
188. calm(X0) [subsumption resolution 156,157]
215. creative(X0) | happy(X0) [subsumption resolution 101,157]
217. 13 <=> ! [X0] : (~quiet(X0) | creative(X0)) [avatar definition]
218. ~quiet(X0) | creative(X0) <- (13) [avatar component clause 217]
220. 14 <=> happy(alice) [avatar definition]
221. happy(alice) <- (14) [avatar component clause 220]
222. ~happy(alice) <- (~14) [avatar component clause 220]
224. 15 <=> wise(alice) [avatar definition]
226. wise(alice) <- (15) [avatar component clause 224]
227. 13 | ~14 | 15 [avatar split clause 109,224,220,217]
241. happy(X0) | ~creative(X0) [subsumption resolution 115,188]
242. ~creative(X0) [subsumption resolution 241,103]
243. ~calm(X0) | ~happy(X0) | patient(X0) [subsumption resolution 110,242]
244. ~happy(X0) | patient(X0) [subsumption resolution 243,188]
261. ~happy(X0) | generous(X0) [subsumption resolution 123,244]
315. ~quiet(X0) <- (13) [subsumption resolution 218,242]
320. $false <- (13) [resolution 315,151]
321. ~13 [avatar contradiction clause 320]
324. happy(X1) [resolution 215,242]
325. $false <- (~2) [resolution 324,164]
328. 2 [avatar contradiction clause 325]
333. patient(alice) <- (14) [resolution 244,221]
335. generous(alice) <- (14) [resolution 261,221]
351. ~patient(alice) | kind(alice) <- (15) [resolution 100,226]
355. kind(alice) <- (14, 15) [subsumption resolution 351,333]
362. ~generous(alice) <- (1, 14, 15) [resolution 355,160]
363. $false <- (1, 14, 15) [subsumption resolution 362,335]
364. ~1 | ~14 | ~15 [avatar contradiction clause 363]
365. $false <- (~14) [subsumption resolution 222,324]
366. 14 [avatar contradiction clause 365]
367. $false [avatar sat refutation 165,227,321,328,364,366]
% SZS output end Proof for 2111931039520306260425192
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm then someone is not humble.
Everyone who is either not curious or generous is not happy and vice versa.
Everyone who is either not funny or not humble is either not kind or kind and vice versa.
Everyone who is not funny is either not humble or not creative and vice versa.
If someone is both not happy and strong then alice is both generous and not strong.
Everyone who is curious or not generous is both not creative and not strong.
Everyone who is wise or strong is creative and vice versa.
Everyone who is both happy and not calm is not curious and vice versa.
Everyone who is both not calm and calm is both wise and not happy and vice versa.
Everyone who is not tall is both not kind and quiet.
If someone is either not happy or funny then someone is patient and vice versa.
Everyone who is not quiet is both brave and not generous and vice versa.
Everyone who is either not rich or strong is either funny or rich and vice versa.
Everyone who is kind or humble is not strong or funny and vice versa.
If paul is not curious or not humble then john is either not creative or not generous and vice versa.
If someone is happy then alice is rich or happy.
Someone is both quiet and rich.
Susan is either humble or not curious.
Someone is quiet.
Alice is either curious or not rich.
Someone is not brave.
Alice is not humble or not kind. | Alice is humble. | contradiction | ((?[X]:((~curious(X)|calm(X))))=>(?[X]:(~humble(X))))&
(![X]:((~curious(X)<~>generous(X))<=>~happy(X)))&
(![X]:((~funny(X)<~>~humble(X))<=>(~kind(X)<~>kind(X))))&
(![X]:(~funny(X)<=>(~humble(X)<~>~creative(X))))&
((?[X]:((~happy(X)&strong(X))))=>((generous(alice)&~strong(alice))))&
(![X]:((curious(X)|~generous(X))=>(~creative(X)&~strong(X))))&
(![X]:((wise(X)|strong(X))<=>creative(X)))&
(![X]:((happy(X)&~calm(X))<=>~curious(X)))&
(![X]:((~calm(X)&calm(X))<=>(wise(X)&~happy(X))))&
(![X]:(~tall(X)=>(~kind(X)&quiet(X))))&
((?[X]:((~happy(X)<~>funny(X))))<=>(?[X]:(patient(X))))&
(![X]:(~quiet(X)<=>(brave(X)&~generous(X))))&
(![X]:((~rich(X)<~>strong(X))<=>(funny(X)<~>rich(X))))&
(![X]:((kind(X)|humble(X))<=>(~strong(X)|funny(X))))&
(((~curious(paul)|~humble(paul)))<=>((~creative(john)<~>~generous(john))))&
((?[X]:(happy(X)))=>((rich(alice)|happy(alice))))&
(?[X]:((quiet(X)&rich(X))))&
((humble(susan)<~>~curious(susan)))&
(?[X]:(quiet(X)))&
((curious(alice)<~>~rich(alice)))&
(?[X]:(~brave(X)))&
((~humble(alice)|~kind(alice))) | humble(alice) | [
"p2",
"p3",
"p6",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 4980327873632614513976605
% SZS output start Proof for 4980327873632614513976605
3. ! [X0] : ((~funny(X0) <~> ~humble(X0)) <=> (~kind(X0) <~> kind(X0))) [input p2]
4. ! [X0] : (~funny(X0) <=> (~humble(X0) <~> ~creative(X0))) [input p3]
7. ! [X0] : ((strong(X0) | wise(X0)) <=> creative(X0)) [input p6]
13. ! [X0] : ((~rich(X0) <~> strong(X0)) <=> (funny(X0) <~> rich(X0))) [input p12]
23. humble(alice) [input hypothesis]
42. ! [X0] : ((((humble(X0) | funny(X0)) & (~humble(X0) | ~funny(X0))) | ((~kind(X0) | ~kind(X0)) & (kind(X0) | kind(X0)))) & (((~kind(X0) | kind(X0)) & (kind(X0) | ~kind(X0))) | ((~funny(X0) | humble(X0)) & (~humble(X0) | funny(X0))))) [nnf transformation 3]
43. ! [X0] : ((~funny(X0) | ((~humble(X0) | creative(X0)) & (~creative(X0) | humble(X0)))) & (((creative(X0) | humble(X0)) & (~creative(X0) | ~humble(X0))) | funny(X0))) [nnf transformation 4]
44. ! [X0] : (((strong(X0) | wise(X0)) | ~creative(X0)) & (creative(X0) | (~strong(X0) & ~wise(X0)))) [nnf transformation 7]
45. ! [X0] : ((strong(X0) | wise(X0) | ~creative(X0)) & (creative(X0) | (~strong(X0) & ~wise(X0)))) [flattening 44]
55. ! [X0] : ((((~strong(X0) | rich(X0)) & (strong(X0) | ~rich(X0))) | ((funny(X0) | ~rich(X0)) & (rich(X0) | ~funny(X0)))) & (((~rich(X0) | ~funny(X0)) & (rich(X0) | funny(X0))) | ((~rich(X0) | ~strong(X0)) & (strong(X0) | rich(X0))))) [nnf transformation 13]
74. ~humble(X0) | ~funny(X0) | kind(X0) | kind(X0) [cnf transformation 42]
75. ~humble(X0) | ~funny(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 42]
76. humble(X0) | funny(X0) | kind(X0) | kind(X0) [cnf transformation 42]
77. humble(X0) | funny(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 42]
78. ~creative(X0) | ~humble(X0) | funny(X0) [cnf transformation 43]
80. ~funny(X0) | ~creative(X0) | humble(X0) [cnf transformation 43]
89. creative(X0) | ~strong(X0) [cnf transformation 45]
102. rich(X0) | funny(X0) | strong(X0) | rich(X0) [cnf transformation 55]
107. strong(X0) | ~rich(X0) | funny(X0) | ~rich(X0) [cnf transformation 55]
127. humble(alice) [cnf transformation 23]
128. rich(X0) | funny(X0) | strong(X0) [duplicate literal removal 102]
130. strong(X0) | ~rich(X0) | funny(X0) [duplicate literal removal 107]
132. ~humble(X0) | ~funny(X0) | kind(X0) [duplicate literal removal 74]
133. ~humble(X0) | ~funny(X0) | ~kind(X0) [duplicate literal removal 75]
134. humble(X0) | funny(X0) | kind(X0) [duplicate literal removal 76]
135. humble(X0) | funny(X0) | ~kind(X0) [duplicate literal removal 77]
148. funny(X0) | humble(X0) [subsumption resolution 134,135]
149. ~funny(X0) | ~humble(X0) [subsumption resolution 132,133]
150. ~funny(X0) | ~creative(X0) [subsumption resolution 80,149]
151. ~creative(X0) | funny(X0) [subsumption resolution 78,148]
152. ~creative(X0) [subsumption resolution 151,150]
166. ~strong(X0) [subsumption resolution 89,152]
193. ~rich(X0) | funny(X0) [subsumption resolution 130,166]
194. rich(X0) | funny(X0) [subsumption resolution 128,166]
195. funny(X0) [subsumption resolution 194,193]
244. 22 <=> humble(alice) [avatar definition]
245. humble(alice) <- (22) [avatar component clause 244]
252. 22 [avatar split clause 127,244]
264. ~humble(X1) [resolution 149,195]
265. $false <- (22) [resolution 264,245]
266. ~22 [avatar contradiction clause 265]
267. $false [avatar sat refutation 252,266]
% SZS output end Proof for 4980327873632614513976605
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 susan is both not brave and old then fred is both not old and not patient and vice versa. If someone is not rich or kind then susan is either funny or brave and vice versa. If susan is not curious then someone is happy. If susan is calm or rich then paul is both not quiet and not curious. If alice is not creative then alice is either not rich or kind. Everyone who is either creative or not brave is not patient or curious and vice versa. Everyone who is both creative and not old is both not kind and not generous and vice versa. Everyone who is not generous or patient is wise and vice versa. Everyone who is both not quiet and calm is both not generous and not humble and vice versa. If fred is not strong or generous then fred is both not old and not funny and vice versa. Everyone who is both creative and not curious is not quiet or funny and vice versa. If john is not patient then someone is either quiet or humble and vice versa. Everyone who is not curious is curious or not old. Everyone who is either kind or curious is both not calm and kind. If someone is old or patient then alice is wise or calm and vice versa. Everyone who is not kind or quiet is both not creative and not kind. Someone is both not wise and not calm. Someone is either happy or curious. John is quiet. Alice is not funny. Fred is either strong or brave. | Susan is kind. | contradiction | (((~brave(susan)&old(susan)))<=>((~old(fred)&~patient(fred))))&
((?[X]:((~rich(X)|kind(X))))<=>((funny(susan)<~>brave(susan))))&
((~curious(susan))=>(?[X]:(happy(X))))&
(((calm(susan)|rich(susan)))=>((~quiet(paul)&~curious(paul))))&
((~creative(alice))=>((~rich(alice)<~>kind(alice))))&
(![X]:((creative(X)<~>~brave(X))<=>(~patient(X)|curious(X))))&
(![X]:((creative(X)&~old(X))<=>(~kind(X)&~generous(X))))&
(![X]:((~generous(X)|patient(X))<=>wise(X)))&
(![X]:((~quiet(X)&calm(X))<=>(~generous(X)&~humble(X))))&
(((~strong(fred)|generous(fred)))<=>((~old(fred)&~funny(fred))))&
(![X]:((creative(X)&~curious(X))<=>(~quiet(X)|funny(X))))&
((~patient(john))<=>(?[X]:((quiet(X)<~>humble(X)))))&
(![X]:(~curious(X)=>(curious(X)|~old(X))))&
(![X]:((kind(X)<~>curious(X))=>(~calm(X)&kind(X))))&
((?[X]:((old(X)|patient(X))))<=>((wise(alice)|calm(alice))))&
(![X]:((~kind(X)|quiet(X))=>(~creative(X)&~kind(X))))&
(?[X]:((~wise(X)&~calm(X))))&
(?[X]:((happy(X)<~>curious(X))))&
(quiet(john))&
(~funny(alice))&
((strong(fred)<~>brave(fred))) | kind(susan) | [
"p1",
"p5",
"p6",
"p10",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 5168219749947477525725888
% SZS output start Proof for 5168219749947477525725888
2. ? [X0] : (kind(X0) | ~rich(X0)) <=> (funny(susan) <~> brave(susan)) [input p1]
6. ! [X0] : ((creative(X0) <~> ~brave(X0)) <=> (curious(X0) | ~patient(X0))) [input p5]
7. ! [X0] : ((~old(X0) & creative(X0)) <=> (~generous(X0) & ~kind(X0))) [input p6]
11. ! [X0] : ((~curious(X0) & creative(X0)) <=> (funny(X0) | ~quiet(X0))) [input p10]
13. ! [X0] : (~curious(X0) => (~old(X0) | curious(X0))) [input p12]
16. ! [X0] : ((quiet(X0) | ~kind(X0)) => (~kind(X0) & ~creative(X0))) [input p15]
22. kind(susan) [input hypothesis]
26. ! [X0] : ((~old(X0) | curious(X0)) | curious(X0)) [ennf transformation 13]
27. ! [X0] : (~old(X0) | curious(X0) | curious(X0)) [flattening 26]
29. ! [X0] : ((~kind(X0) & ~creative(X0)) | (~quiet(X0) & kind(X0))) [ennf transformation 16]
32. (? [X0] : (kind(X0) | ~rich(X0)) | ((funny(susan) | ~brave(susan)) & (brave(susan) | ~funny(susan)))) & (((~brave(susan) | ~funny(susan)) & (brave(susan) | funny(susan))) | ! [X0] : (~kind(X0) & rich(X0))) [nnf transformation 2]
33. (? [X0] : (kind(X0) | ~rich(X0)) | ((funny(susan) | ~brave(susan)) & (brave(susan) | ~funny(susan)))) & (((~brave(susan) | ~funny(susan)) & (brave(susan) | funny(susan))) | ! [X1] : (~kind(X1) & rich(X1))) [rectify 32]
34. ? [X0] : (kind(X0) | ~rich(X0)) => (kind(sK0) | ~rich(sK0)) [choice axiom]
35. ((kind(sK0) | ~rich(sK0)) | ((funny(susan) | ~brave(susan)) & (brave(susan) | ~funny(susan)))) & (((~brave(susan) | ~funny(susan)) & (brave(susan) | funny(susan))) | ! [X1] : (~kind(X1) & rich(X1))) [skolemisation 33,34]
39. ! [X0] : ((((brave(X0) | ~creative(X0)) & (~brave(X0) | creative(X0))) | (~curious(X0) & patient(X0))) & ((curious(X0) | ~patient(X0)) | ((creative(X0) | brave(X0)) & (~brave(X0) | ~creative(X0))))) [nnf transformation 6]
40. ! [X0] : ((((brave(X0) | ~creative(X0)) & (~brave(X0) | creative(X0))) | (~curious(X0) & patient(X0))) & (curious(X0) | ~patient(X0) | ((creative(X0) | brave(X0)) & (~brave(X0) | ~creative(X0))))) [flattening 39]
41. ! [X0] : (((~old(X0) & creative(X0)) | (generous(X0) | kind(X0))) & ((~generous(X0) & ~kind(X0)) | (old(X0) | ~creative(X0)))) [nnf transformation 7]
42. ! [X0] : (((~old(X0) & creative(X0)) | generous(X0) | kind(X0)) & ((~generous(X0) & ~kind(X0)) | old(X0) | ~creative(X0))) [flattening 41]
49. ! [X0] : (((~curious(X0) & creative(X0)) | (~funny(X0) & quiet(X0))) & ((funny(X0) | ~quiet(X0)) | (curious(X0) | ~creative(X0)))) [nnf transformation 11]
50. ! [X0] : (((~curious(X0) & creative(X0)) | (~funny(X0) & quiet(X0))) & (funny(X0) | ~quiet(X0) | curious(X0) | ~creative(X0))) [flattening 49]
72. brave(susan) | funny(susan) | ~kind(X1) [cnf transformation 35]
84. ~creative(X0) | ~patient(X0) | ~brave(X0) | curious(X0) [cnf transformation 40]
86. ~brave(X0) | creative(X0) | patient(X0) [cnf transformation 40]
90. ~creative(X0) | old(X0) | ~kind(X0) [cnf transformation 42]
107. creative(X0) | quiet(X0) [cnf transformation 50]
108. ~funny(X0) | creative(X0) [cnf transformation 50]
109. ~curious(X0) | quiet(X0) [cnf transformation 50]
115. ~old(X0) | curious(X0) | curious(X0) [cnf transformation 27]
124. ~creative(X0) | kind(X0) [cnf transformation 29]
125. ~creative(X0) | ~quiet(X0) [cnf transformation 29]
127. ~quiet(X0) | ~kind(X0) [cnf transformation 29]
136. kind(susan) [cnf transformation 22]
138. ~old(X0) | curious(X0) [duplicate literal removal 115]
148. 3 <=> old(susan) [avatar definition]
149. ~old(susan) <- (~3) [avatar component clause 148]
150. old(susan) <- (3) [avatar component clause 148]
153. 4 <=> brave(susan) [avatar definition]
154. brave(susan) <- (4) [avatar component clause 153]
160. 5 <=> funny(susan) [avatar definition]
162. funny(susan) <- (5) [avatar component clause 160]
174. 8 <=> ! [X1] : ~kind(X1) [avatar definition]
175. ~kind(X1) <- (8) [avatar component clause 174]
181. 8 | 5 | 4 [avatar split clause 72,153,160,174]
184. 10 <=> curious(susan) [avatar definition]
185. ~curious(susan) <- (~10) [avatar component clause 184]
186. curious(susan) <- (10) [avatar component clause 184]
311. quiet(susan) <- (10) [resolution 109,186]
313. quiet(X0) | kind(X0) [resolution 124,107]
318. ~kind(susan) <- (10) [resolution 127,311]
319. $false <- (10) [subsumption resolution 318,136]
320. ~10 [avatar contradiction clause 319]
327. creative(susan) | patient(susan) <- (4) [resolution 86,154]
329. 36 <=> patient(susan) [avatar definition]
331. patient(susan) <- (36) [avatar component clause 329]
333. 37 <=> creative(susan) [avatar definition]
335. creative(susan) <- (37) [avatar component clause 333]
336. 36 | 37 | ~4 [avatar split clause 327,153,333,329]
358. old(X0) | ~kind(X0) | quiet(X0) [resolution 90,107]
360. quiet(X0) | old(X0) [subsumption resolution 358,313]
401. ~patient(X0) | ~brave(X0) | curious(X0) | quiet(X0) [resolution 84,107]
402. ~patient(X0) | ~brave(X0) | quiet(X0) [subsumption resolution 401,109]
523. $false <- (8) [resolution 175,136]
524. ~8 [avatar contradiction clause 523]
541. ~brave(susan) | quiet(susan) <- (36) [resolution 402,331]
544. quiet(susan) <- (4, 36) [subsumption resolution 541,154]
548. ~kind(susan) <- (4, 36) [resolution 544,127]
558. $false <- (4, 36) [subsumption resolution 548,136]
559. ~4 | ~36 [avatar contradiction clause 558]
566. ~quiet(susan) <- (37) [resolution 335,125]
581. curious(susan) <- (3) [resolution 150,138]
582. $false <- (3, ~10) [subsumption resolution 581,185]
583. ~3 | 10 [avatar contradiction clause 582]
588. creative(susan) <- (5) [resolution 162,108]
593. old(susan) <- (37) [resolution 566,360]
595. $false <- (~3, 37) [subsumption resolution 593,149]
596. 3 | ~37 [avatar contradiction clause 595]
600. 37 | ~5 [avatar split clause 588,160,333]
601. $false [avatar sat refutation 181,320,336,524,559,583,596,600]
% SZS output end Proof for 5168219749947477525725888
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
If alice is both generous and funny then someone is both not patient and curious and vice versa.
Everyone who is funny is either old or strong.
Everyone who is not tall is not happy or not tall.
If someone is both generous and brave then lucy is both not kind and funny and vice versa.
Everyone who is not wise or humble is both patient and not tall.
Everyone who is both wise and funny is either humble or not happy and vice versa.
If alice is both not funny and kind then fred is humble and vice versa.
Everyone who is both calm and not creative is not wise or not quiet.
Everyone who is both calm and not calm is either not funny or creative and vice versa.
Everyone who is rich is both wise and calm and vice versa.
If someone is not wise or not old then someone is happy or old and vice versa.
If someone is both old and not old then someone is not wise and vice versa.
If paul is not wise or humble then someone is both humble and brave.
Everyone who is both rich and strong is not kind or kind and vice versa.
Everyone who is not patient or not happy is kind or not brave and vice versa.
If lucy is not rich or generous then someone is old or not wise and vice versa.
Lucy is brave.
Someone is funny or rich.
Someone is either generous or not calm.
Someone is both brave and creative.
Susan is funny.
Fred is generous or brave. | Susan is old. | contradiction | (((generous(alice)&funny(alice)))<=>(?[X]:((~patient(X)&curious(X)))))&
(![X]:(funny(X)=>(old(X)<~>strong(X))))&
(![X]:(~tall(X)=>(~happy(X)|~tall(X))))&
((?[X]:((generous(X)&brave(X))))<=>((~kind(lucy)&funny(lucy))))&
(![X]:((~wise(X)|humble(X))=>(patient(X)&~tall(X))))&
(![X]:((wise(X)&funny(X))<=>(humble(X)<~>~happy(X))))&
(((~funny(alice)&kind(alice)))<=>(humble(fred)))&
(![X]:((calm(X)&~creative(X))=>(~wise(X)|~quiet(X))))&
(![X]:((calm(X)&~calm(X))<=>(~funny(X)<~>creative(X))))&
(![X]:(rich(X)<=>(wise(X)&calm(X))))&
((?[X]:((~wise(X)|~old(X))))<=>(?[X]:((happy(X)|old(X)))))&
((?[X]:((old(X)&~old(X))))<=>(?[X]:(~wise(X))))&
(((~wise(paul)|humble(paul)))=>(?[X]:((humble(X)&brave(X)))))&
(![X]:((rich(X)&strong(X))<=>(~kind(X)|kind(X))))&
(![X]:((~patient(X)|~happy(X))<=>(kind(X)|~brave(X))))&
(((~rich(lucy)|generous(lucy)))<=>(?[X]:((old(X)|~wise(X)))))&
(brave(lucy))&
(?[X]:((funny(X)|rich(X))))&
(?[X]:((generous(X)<~>~calm(X))))&
(?[X]:((brave(X)&creative(X))))&
(funny(susan))&
((generous(fred)|brave(fred))) | old(susan) | [
"p1",
"p13",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 802272246876435394758067
% SZS output start Proof for 802272246876435394758067
2. ! [X0] : (funny(X0) => (old(X0) <~> strong(X0))) [input p1]
14. ! [X0] : ((strong(X0) & rich(X0)) <=> (kind(X0) | ~kind(X0))) [input p13]
21. funny(susan) [input p20]
23. old(susan) [input hypothesis]
27. ! [X0] : ((old(X0) <~> strong(X0)) | ~funny(X0)) [ennf transformation 2]
37. ! [X0] : (((~strong(X0) | ~old(X0)) & (strong(X0) | old(X0))) | ~funny(X0)) [nnf transformation 27]
63. ! [X0] : (((strong(X0) & rich(X0)) | (~kind(X0) & kind(X0))) & ((kind(X0) | ~kind(X0)) | (~strong(X0) | ~rich(X0)))) [nnf transformation 14]
64. ! [X0] : (((strong(X0) & rich(X0)) | (~kind(X0) & kind(X0))) & (kind(X0) | ~kind(X0) | ~strong(X0) | ~rich(X0))) [flattening 63]
84. ~strong(X0) | ~old(X0) | ~funny(X0) [cnf transformation 37]
126. strong(X0) | kind(X0) [cnf transformation 64]
127. ~kind(X0) | strong(X0) [cnf transformation 64]
142. funny(susan) [cnf transformation 21]
144. old(susan) [cnf transformation 23]
262. strong(X0) [subsumption resolution 126,127]
317. ~old(X0) | ~funny(X0) [resolution 84,262]
318. ~funny(susan) [resolution 317,144]
320. $false [subsumption resolution 318,142]
% SZS output end Proof for 802272246876435394758067
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not strong or not creative then john is both not creative and wise and vice versa.
Everyone who is kind or not humble is both not quiet and calm and vice versa.
If someone is both brave and calm then mary is patient or not generous and vice versa.
Everyone who is not old or not humble is not tall or happy and vice versa.
Everyone who is both curious and quiet is not brave.
Everyone who is not old is both not tall and not happy.
If someone is brave or not creative then susan is both brave and not kind and vice versa.
Everyone who is not calm or not humble is not tall and vice versa.
Everyone who is not funny or kind is either not patient or humble and vice versa.
If someone is either not patient or not creative then someone is humble and vice versa.
Everyone who is either not curious or curious is rich and vice versa.
Everyone who is either happy or not creative is both not brave and funny and vice versa.
If alice is not wise or calm then john is both not kind and old.
Everyone who is not patient is both not creative and not old.
Everyone who is both brave and not humble is not tall.
Everyone who is happy or curious is either not calm or old.
John is either not happy or not calm.
Alice is not tall.
Mary is either tall or generous.
Someone is either not rich or creative.
Someone is either tall or funny.
Someone is both not strong and not patient.
Mary is both brave and not calm.
Someone is either not generous or humble. | Susan is curious. | neutral | ((?[X]:((~strong(X)|~creative(X))))<=>((~creative(john)&wise(john))))&
(![X]:((kind(X)|~humble(X))<=>(~quiet(X)&calm(X))))&
((?[X]:((brave(X)&calm(X))))<=>((patient(mary)|~generous(mary))))&
(![X]:((~old(X)|~humble(X))<=>(~tall(X)|happy(X))))&
(![X]:((curious(X)&quiet(X))=>~brave(X)))&
(![X]:(~old(X)=>(~tall(X)&~happy(X))))&
((?[X]:((brave(X)|~creative(X))))<=>((brave(susan)&~kind(susan))))&
(![X]:((~calm(X)|~humble(X))<=>~tall(X)))&
(![X]:((~funny(X)|kind(X))<=>(~patient(X)<~>humble(X))))&
((?[X]:((~patient(X)<~>~creative(X))))<=>(?[X]:(humble(X))))&
(![X]:((~curious(X)<~>curious(X))<=>rich(X)))&
(![X]:((happy(X)<~>~creative(X))<=>(~brave(X)&funny(X))))&
(((~wise(alice)|calm(alice)))=>((~kind(john)&old(john))))&
(![X]:(~patient(X)=>(~creative(X)&~old(X))))&
(![X]:((brave(X)&~humble(X))=>~tall(X)))&
(![X]:((happy(X)|curious(X))=>(~calm(X)<~>old(X))))&
((~happy(john)<~>~calm(john)))&
(~tall(alice))&
((tall(mary)<~>generous(mary)))&
(?[X]:((~rich(X)<~>creative(X))))&
(?[X]:((tall(X)<~>funny(X))))&
(?[X]:((~strong(X)&~patient(X))))&
((brave(mary)&~calm(mary)))&
(?[X]:((~generous(X)<~>humble(X)))) | curious(susan) | [] | null | 0 |
Everyone who is both tall and not strong is both calm and not rich and vice versa.
Everyone who is tall is both quiet and kind and vice versa.
If lucy is either quiet or rich then someone is either not creative or humble and vice versa.
If someone is either kind or not generous then lucy is humble.
If someone is not creative then someone is both strong and not happy and vice versa.
Everyone who is not happy or not quiet is generous or not calm.
Everyone who is not generous is creative.
Everyone who is quiet or not kind is generous and vice versa.
If someone is either not generous or happy then someone is either calm or not calm and vice versa.
If lucy is either generous or not old then paul is not tall.
If fred is either creative or not rich then someone is not strong and vice versa.
Everyone who is curious is either not strong or not calm and vice versa.
If someone is either not kind or not generous then someone is not tall or not brave and vice versa.
Everyone who is old is either not creative or not calm.
Everyone who is both not creative and not wise is both calm and not tall and vice versa.
If john is either not generous or generous then someone is either not old or not calm.
Susan is either not creative or quiet.
Paul is brave.
Someone is either not curious or quiet.
Someone is either not creative or brave.
Fred is both not kind and quiet.
Susan is either wise or creative.
John is both not funny and happy. | Fred is creative. | neutral | (![X]:((tall(X)&~strong(X))<=>(calm(X)&~rich(X))))&
(![X]:(tall(X)<=>(quiet(X)&kind(X))))&
(((quiet(lucy)<~>rich(lucy)))<=>(?[X]:((~creative(X)<~>humble(X)))))&
((?[X]:((kind(X)<~>~generous(X))))=>(humble(lucy)))&
((?[X]:(~creative(X)))<=>(?[X]:((strong(X)&~happy(X)))))&
(![X]:((~happy(X)|~quiet(X))=>(generous(X)|~calm(X))))&
(![X]:(~generous(X)=>creative(X)))&
(![X]:((quiet(X)|~kind(X))<=>generous(X)))&
((?[X]:((~generous(X)<~>happy(X))))<=>(?[X]:((calm(X)<~>~calm(X)))))&
(((generous(lucy)<~>~old(lucy)))=>(~tall(paul)))&
(((creative(fred)<~>~rich(fred)))<=>(?[X]:(~strong(X))))&
(![X]:(curious(X)<=>(~strong(X)<~>~calm(X))))&
((?[X]:((~kind(X)<~>~generous(X))))<=>(?[X]:((~tall(X)|~brave(X)))))&
(![X]:(old(X)=>(~creative(X)<~>~calm(X))))&
(![X]:((~creative(X)&~wise(X))<=>(calm(X)&~tall(X))))&
(((~generous(john)<~>generous(john)))=>(?[X]:((~old(X)<~>~calm(X)))))&
((~creative(susan)<~>quiet(susan)))&
(brave(paul))&
(?[X]:((~curious(X)<~>quiet(X))))&
(?[X]:((~creative(X)<~>brave(X))))&
((~kind(fred)&quiet(fred)))&
((wise(susan)<~>creative(susan)))&
((~funny(john)&happy(john))) | creative(fred) | [] | null | 0 |
Everyone who is not curious is not kind and vice versa.
Everyone who is not calm is not happy or strong and vice versa.
Everyone who is either strong or not wise is happy and vice versa.
Everyone who is curious is calm.
Everyone who is either curious or not brave is strong and vice versa.
Everyone who is either not wise or not kind is both quiet and brave and vice versa.
Everyone who is both curious and not creative is not funny or calm and vice versa.
If fred is rich then someone is both not strong and kind.
Everyone who is not brave or quiet is quiet and vice versa.
If mary is not wise then someone is either not old or brave.
Everyone who is not calm or not old is either not generous or calm and vice versa.
If fred is calm or not kind then alice is old and vice versa.
If someone is either generous or curious then someone is brave.
Everyone who is not quiet or not funny is both strong and wise and vice versa.
Someone is not strong.
Someone is brave or not old.
Someone is tall.
Susan is either not old or not happy. | Susan is not tall. | neutral | (![X]:(~curious(X)<=>~kind(X)))&
(![X]:(~calm(X)<=>(~happy(X)|strong(X))))&
(![X]:((strong(X)<~>~wise(X))<=>happy(X)))&
(![X]:(curious(X)=>calm(X)))&
(![X]:((curious(X)<~>~brave(X))<=>strong(X)))&
(![X]:((~wise(X)<~>~kind(X))<=>(quiet(X)&brave(X))))&
(![X]:((curious(X)&~creative(X))<=>(~funny(X)|calm(X))))&
((rich(fred))=>(?[X]:((~strong(X)&kind(X)))))&
(![X]:((~brave(X)|quiet(X))<=>quiet(X)))&
((~wise(mary))=>(?[X]:((~old(X)<~>brave(X)))))&
(![X]:((~calm(X)|~old(X))<=>(~generous(X)<~>calm(X))))&
(((calm(fred)|~kind(fred)))<=>(old(alice)))&
((?[X]:((generous(X)<~>curious(X))))=>(?[X]:(brave(X))))&
(![X]:((~quiet(X)|~funny(X))<=>(strong(X)&wise(X))))&
(?[X]:(~strong(X)))&
(?[X]:((brave(X)|~old(X))))&
(?[X]:(tall(X)))&
((~old(susan)<~>~happy(susan))) | ~tall(susan) | [] | null | 0 |
Everyone who is not old is both not funny and funny and vice versa.
If susan is not quiet then lucy is not brave and vice versa.
If someone is either wise or curious then alice is either not wise or kind and vice versa.
If lucy is wise then someone is both not happy and not tall.
Everyone who is happy is patient.
Everyone who is curious is both not patient and patient and vice versa.
Everyone who is both not old and old is not tall or not calm.
Everyone who is both not brave and not generous is either kind or humble and vice versa.
Everyone who is not generous or funny is both kind and not humble and vice versa.
Everyone who is both old and generous is old.
If someone is both humble and funny then someone is not generous.
Everyone who is either quiet or creative is not rich or brave and vice versa.
Everyone who is not calm is tall.
If someone is kind then susan is either quiet or rich and vice versa.
Everyone who is not creative or generous is either not old or not patient and vice versa.
Everyone who is rich is not wise or not happy and vice versa.
Someone is strong.
Fred is not old or not rich.
Someone is both not wise and tall.
Someone is not old or rich.
Susan is old or not old.
Someone is either not brave or not patient. | Alice is not patient. | neutral | (![X]:(~old(X)<=>(~funny(X)&funny(X))))&
((~quiet(susan))<=>(~brave(lucy)))&
((?[X]:((wise(X)<~>curious(X))))<=>((~wise(alice)<~>kind(alice))))&
((wise(lucy))=>(?[X]:((~happy(X)&~tall(X)))))&
(![X]:(happy(X)=>patient(X)))&
(![X]:(curious(X)<=>(~patient(X)&patient(X))))&
(![X]:((~old(X)&old(X))=>(~tall(X)|~calm(X))))&
(![X]:((~brave(X)&~generous(X))<=>(kind(X)<~>humble(X))))&
(![X]:((~generous(X)|funny(X))<=>(kind(X)&~humble(X))))&
(![X]:((old(X)&generous(X))=>old(X)))&
((?[X]:((humble(X)&funny(X))))=>(?[X]:(~generous(X))))&
(![X]:((quiet(X)<~>creative(X))<=>(~rich(X)|brave(X))))&
(![X]:(~calm(X)=>tall(X)))&
((?[X]:(kind(X)))<=>((quiet(susan)<~>rich(susan))))&
(![X]:((~creative(X)|generous(X))<=>(~old(X)<~>~patient(X))))&
(![X]:(rich(X)<=>(~wise(X)|~happy(X))))&
(?[X]:(strong(X)))&
((~old(fred)|~rich(fred)))&
(?[X]:((~wise(X)&tall(X))))&
(?[X]:((~old(X)|rich(X))))&
((old(susan)|~old(susan)))&
(?[X]:((~brave(X)<~>~patient(X)))) | ~patient(alice) | [] | null | 0 |
If someone is quiet or creative then mary is not creative or not generous and vice versa.
Everyone who is either not strong or creative is wise.
Everyone who is not calm is both not funny and calm and vice versa.
If alice is wise or patient then someone is wise or not quiet.
If someone is not quiet then mary is both not wise and kind.
If someone is either happy or not rich then someone is old or not kind and vice versa.
Everyone who is either rich or not wise is not generous or happy and vice versa.
Everyone who is either old or not quiet is either not quiet or not kind.
If john is both not curious and not generous then susan is not calm.
Everyone who is both kind and funny is rich.
Everyone who is rich is quiet or not funny.
If susan is tall then someone is either brave or generous and vice versa.
Everyone who is not funny is either strong or not humble.
Everyone who is not wise or kind is both not strong and tall and vice versa.
If someone is both strong and rich then mary is not rich or kind and vice versa.
Everyone who is old is not calm or curious.
Someone is not brave.
Someone is either humble or strong.
Someone is humble or tall.
Someone is wise.
Lucy is tall or calm.
Someone is either not happy or generous. | Susan is not humble. | neutral | ((?[X]:((quiet(X)|creative(X))))<=>((~creative(mary)|~generous(mary))))&
(![X]:((~strong(X)<~>creative(X))=>wise(X)))&
(![X]:(~calm(X)<=>(~funny(X)&calm(X))))&
(((wise(alice)|patient(alice)))=>(?[X]:((wise(X)|~quiet(X)))))&
((?[X]:(~quiet(X)))=>((~wise(mary)&kind(mary))))&
((?[X]:((happy(X)<~>~rich(X))))<=>(?[X]:((old(X)|~kind(X)))))&
(![X]:((rich(X)<~>~wise(X))<=>(~generous(X)|happy(X))))&
(![X]:((old(X)<~>~quiet(X))=>(~quiet(X)<~>~kind(X))))&
(((~curious(john)&~generous(john)))=>(~calm(susan)))&
(![X]:((kind(X)&funny(X))=>rich(X)))&
(![X]:(rich(X)=>(quiet(X)|~funny(X))))&
((tall(susan))<=>(?[X]:((brave(X)<~>generous(X)))))&
(![X]:(~funny(X)=>(strong(X)<~>~humble(X))))&
(![X]:((~wise(X)|kind(X))<=>(~strong(X)&tall(X))))&
((?[X]:((strong(X)&rich(X))))<=>((~rich(mary)|kind(mary))))&
(![X]:(old(X)=>(~calm(X)|curious(X))))&
(?[X]:(~brave(X)))&
(?[X]:((humble(X)<~>strong(X))))&
(?[X]:((humble(X)|tall(X))))&
(?[X]:(wise(X)))&
((tall(lucy)|calm(lucy)))&
(?[X]:((~happy(X)<~>generous(X)))) | ~humble(susan) | [] | null | 0 |
If someone is both not creative and not curious then alice is quiet or not creative.
If someone is either not quiet or calm then someone is either rich or not calm.
If john is not happy then fred is patient or wise.
If susan is rich or strong then lucy is either not quiet or calm and vice versa.
If fred is either not creative or happy then alice is both curious and not calm and vice versa.
Everyone who is old or not generous is not old and vice versa.
If someone is either not old or not generous then someone is both not funny and rich and vice versa.
If someone is both calm and brave then lucy is both not curious and strong and vice versa.
If someone is both curious and not brave then fred is not strong or not curious.
Everyone who is both humble and not happy is not strong.
If someone is both creative and not generous then lucy is brave or funny and vice versa.
If someone is either funny or not quiet then someone is both not generous and not old.
If someone is both not curious and rich then mary is either kind or generous.
If someone is not tall then someone is either brave or not old.
Everyone who is tall is both calm and patient and vice versa.
If someone is either patient or wise then paul is not funny and vice versa.
Someone is either not brave or not strong.
Someone is not old or not patient.
Mary is both funny and quiet.
Susan is patient.
Someone is kind or old.
Alice is either not generous or kind.
Someone is both not quiet and not brave. | Mary is funny. | entailment | ((?[X]:((~creative(X)&~curious(X))))=>((quiet(alice)|~creative(alice))))&
((?[X]:((~quiet(X)<~>calm(X))))=>(?[X]:((rich(X)<~>~calm(X)))))&
((~happy(john))=>((patient(fred)|wise(fred))))&
(((rich(susan)|strong(susan)))<=>((~quiet(lucy)<~>calm(lucy))))&
(((~creative(fred)<~>happy(fred)))<=>((curious(alice)&~calm(alice))))&
(![X]:((old(X)|~generous(X))<=>~old(X)))&
((?[X]:((~old(X)<~>~generous(X))))<=>(?[X]:((~funny(X)&rich(X)))))&
((?[X]:((calm(X)&brave(X))))<=>((~curious(lucy)&strong(lucy))))&
((?[X]:((curious(X)&~brave(X))))=>((~strong(fred)|~curious(fred))))&
(![X]:((humble(X)&~happy(X))=>~strong(X)))&
((?[X]:((creative(X)&~generous(X))))<=>((brave(lucy)|funny(lucy))))&
((?[X]:((funny(X)<~>~quiet(X))))=>(?[X]:((~generous(X)&~old(X)))))&
((?[X]:((~curious(X)&rich(X))))=>((kind(mary)<~>generous(mary))))&
((?[X]:(~tall(X)))=>(?[X]:((brave(X)<~>~old(X)))))&
(![X]:(tall(X)<=>(calm(X)&patient(X))))&
((?[X]:((patient(X)<~>wise(X))))<=>(~funny(paul)))&
(?[X]:((~brave(X)<~>~strong(X))))&
(?[X]:((~old(X)|~patient(X))))&
((funny(mary)&quiet(mary)))&
(patient(susan))&
(?[X]:((kind(X)|old(X))))&
((~generous(alice)<~>kind(alice)))&
(?[X]:((~quiet(X)&~brave(X)))) | funny(mary) | [
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 7031000698201036579821496
% SZS output start Proof for 7031000698201036579821496
19. quiet(mary) & funny(mary) [input p18]
24. ~funny(mary) [input hypothesis]
144. funny(mary) [cnf transformation 19]
152. ~funny(mary) [cnf transformation 24]
387. $false [subsumption resolution 152,144]
% SZS output end Proof for 7031000698201036579821496
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.022 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not tall or wise is both calm and not funny.
Everyone who is either not tall or not wise is either not curious or humble.
Everyone who is both quiet and old is either patient or creative.
If alice is not humble or not quiet then someone is creative or brave.
If someone is both brave and patient then fred is both creative and tall and vice versa.
Everyone who is happy is rich or calm.
Everyone who is both not brave and not creative is both funny and not quiet.
Everyone who is either funny or humble is not brave or funny and vice versa.
If someone is kind then mary is tall.
Everyone who is both tall and not funny is both not curious and not generous and vice versa.
Everyone who is wise or not tall is humble or not kind and vice versa.
Everyone who is rich or old is both not funny and patient and vice versa.
Everyone who is wise or generous is not happy and vice versa.
Everyone who is both not funny and calm is calm or not kind and vice versa.
Everyone who is either not generous or funny is strong and vice versa.
Everyone who is both not happy and curious is not generous and vice versa.
Someone is both old and not creative.
Someone is either not happy or brave.
John is not strong or not wise.
Susan is both not wise and not kind.
Someone is not creative or not humble.
Someone is curious or wise.
Lucy is rich.
Mary is either not brave or brave. | Fred is calm. | contradiction | (![X]:((~tall(X)<~>wise(X))=>(calm(X)&~funny(X))))&
(![X]:((~tall(X)<~>~wise(X))=>(~curious(X)<~>humble(X))))&
(![X]:((quiet(X)&old(X))=>(patient(X)<~>creative(X))))&
(((~humble(alice)|~quiet(alice)))=>(?[X]:((creative(X)|brave(X)))))&
((?[X]:((brave(X)&patient(X))))<=>((creative(fred)&tall(fred))))&
(![X]:(happy(X)=>(rich(X)|calm(X))))&
(![X]:((~brave(X)&~creative(X))=>(funny(X)&~quiet(X))))&
(![X]:((funny(X)<~>humble(X))<=>(~brave(X)|funny(X))))&
((?[X]:(kind(X)))=>(tall(mary)))&
(![X]:((tall(X)&~funny(X))<=>(~curious(X)&~generous(X))))&
(![X]:((wise(X)|~tall(X))<=>(humble(X)|~kind(X))))&
(![X]:((rich(X)|old(X))<=>(~funny(X)&patient(X))))&
(![X]:((wise(X)|generous(X))<=>~happy(X)))&
(![X]:((~funny(X)&calm(X))<=>(calm(X)|~kind(X))))&
(![X]:((~generous(X)<~>funny(X))<=>strong(X)))&
(![X]:((~happy(X)&curious(X))<=>~generous(X)))&
(?[X]:((old(X)&~creative(X))))&
(?[X]:((~happy(X)<~>brave(X))))&
((~strong(john)|~wise(john)))&
((~wise(susan)&~kind(susan)))&
(?[X]:((~creative(X)|~humble(X))))&
(?[X]:((curious(X)|wise(X))))&
(rich(lucy))&
((~brave(mary)<~>brave(mary))) | calm(fred) | [
"p4",
"p6",
"p7",
"p9",
"p11",
"p13",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 8273665733858981414891828
% SZS output start Proof for 8273665733858981414891828
5. ? [X0] : (patient(X0) & brave(X0)) <=> (tall(fred) & creative(fred)) [input p4]
7. ! [X0] : ((~creative(X0) & ~brave(X0)) => (~quiet(X0) & funny(X0))) [input p6]
8. ! [X0] : ((funny(X0) <~> humble(X0)) <=> (funny(X0) | ~brave(X0))) [input p7]
10. ! [X0] : ((~funny(X0) & tall(X0)) <=> (~generous(X0) & ~curious(X0))) [input p9]
12. ! [X0] : ((old(X0) | rich(X0)) <=> (patient(X0) & ~funny(X0))) [input p11]
14. ! [X0] : ((calm(X0) & ~funny(X0)) <=> (~kind(X0) | calm(X0))) [input p13]
16. ! [X0] : ((curious(X0) & ~happy(X0)) <=> ~generous(X0)) [input p15]
17. ? [X0] : (~creative(X0) & old(X0)) [input p16]
25. calm(fred) [input hypothesis]
34. ! [X0] : ((~quiet(X0) & funny(X0)) | (creative(X0) | brave(X0))) [ennf transformation 7]
35. ! [X0] : ((~quiet(X0) & funny(X0)) | creative(X0) | brave(X0)) [flattening 34]
43. (? [X0] : (patient(X0) & brave(X0)) | (~tall(fred) | ~creative(fred))) & ((tall(fred) & creative(fred)) | ! [X0] : (~patient(X0) | ~brave(X0))) [nnf transformation 5]
44. (? [X0] : (patient(X0) & brave(X0)) | ~tall(fred) | ~creative(fred)) & ((tall(fred) & creative(fred)) | ! [X0] : (~patient(X0) | ~brave(X0))) [flattening 43]
45. (? [X0] : (patient(X0) & brave(X0)) | ~tall(fred) | ~creative(fred)) & ((tall(fred) & creative(fred)) | ! [X1] : (~patient(X1) | ~brave(X1))) [rectify 44]
46. ? [X0] : (patient(X0) & brave(X0)) => (patient(sK1) & brave(sK1)) [choice axiom]
47. ((patient(sK1) & brave(sK1)) | ~tall(fred) | ~creative(fred)) & ((tall(fred) & creative(fred)) | ! [X1] : (~patient(X1) | ~brave(X1))) [skolemisation 45,46]
48. ! [X0] : ((((~humble(X0) | ~funny(X0)) & (humble(X0) | funny(X0))) | (~funny(X0) & brave(X0))) & ((funny(X0) | ~brave(X0)) | ((funny(X0) | ~humble(X0)) & (humble(X0) | ~funny(X0))))) [nnf transformation 8]
49. ! [X0] : ((((~humble(X0) | ~funny(X0)) & (humble(X0) | funny(X0))) | (~funny(X0) & brave(X0))) & (funny(X0) | ~brave(X0) | ((funny(X0) | ~humble(X0)) & (humble(X0) | ~funny(X0))))) [flattening 48]
50. ! [X0] : (((~funny(X0) & tall(X0)) | (generous(X0) | curious(X0))) & ((~generous(X0) & ~curious(X0)) | (funny(X0) | ~tall(X0)))) [nnf transformation 10]
51. ! [X0] : (((~funny(X0) & tall(X0)) | generous(X0) | curious(X0)) & ((~generous(X0) & ~curious(X0)) | funny(X0) | ~tall(X0))) [flattening 50]
54. ! [X0] : (((old(X0) | rich(X0)) | (~patient(X0) | funny(X0))) & ((patient(X0) & ~funny(X0)) | (~old(X0) & ~rich(X0)))) [nnf transformation 12]
55. ! [X0] : ((old(X0) | rich(X0) | ~patient(X0) | funny(X0)) & ((patient(X0) & ~funny(X0)) | (~old(X0) & ~rich(X0)))) [flattening 54]
58. ! [X0] : (((calm(X0) & ~funny(X0)) | (kind(X0) & ~calm(X0))) & ((~kind(X0) | calm(X0)) | (~calm(X0) | funny(X0)))) [nnf transformation 14]
59. ! [X0] : (((calm(X0) & ~funny(X0)) | (kind(X0) & ~calm(X0))) & (~kind(X0) | calm(X0) | ~calm(X0) | funny(X0))) [flattening 58]
61. ! [X0] : (((curious(X0) & ~happy(X0)) | generous(X0)) & (~generous(X0) | (~curious(X0) | happy(X0)))) [nnf transformation 16]
62. ! [X0] : (((curious(X0) & ~happy(X0)) | generous(X0)) & (~generous(X0) | ~curious(X0) | happy(X0))) [flattening 61]
63. ? [X0] : (~creative(X0) & old(X0)) => (~creative(sK2) & old(sK2)) [choice axiom]
64. ~creative(sK2) & old(sK2) [skolemisation 17,63]
86. tall(fred) | ~patient(X1) | ~brave(X1) [cnf transformation 47]
90. brave(X0) | creative(X0) | funny(X0) [cnf transformation 35]
93. funny(X0) | ~brave(X0) | funny(X0) | ~humble(X0) [cnf transformation 49]
94. brave(X0) | funny(X0) | humble(X0) [cnf transformation 49]
97. ~humble(X0) | ~funny(X0) | ~funny(X0) [cnf transformation 49]
99. ~curious(X0) | funny(X0) | ~tall(X0) [cnf transformation 51]
100. ~generous(X0) | funny(X0) | ~tall(X0) [cnf transformation 51]
108. ~old(X0) | ~funny(X0) [cnf transformation 55]
110. ~old(X0) | patient(X0) [cnf transformation 55]
116. ~funny(X0) | ~calm(X0) [cnf transformation 59]
124. generous(X0) | curious(X0) [cnf transformation 62]
125. old(sK2) [cnf transformation 64]
126. ~creative(sK2) [cnf transformation 64]
137. calm(fred) [cnf transformation 25]
138. funny(X0) | ~brave(X0) | ~humble(X0) [duplicate literal removal 93]
139. ~humble(X0) | ~funny(X0) [duplicate literal removal 97]
163. 6 <=> tall(fred) [avatar definition]
164. tall(fred) <- (6) [avatar component clause 163]
177. 9 <=> ! [X1] : (~patient(X1) | ~brave(X1)) [avatar definition]
178. ~brave(X1) | ~patient(X1) <- (9) [avatar component clause 177]
179. 9 | 6 [avatar split clause 86,163,177]
181. ~brave(X0) | ~humble(X0) [subsumption resolution 138,139]
221. ~funny(sK2) [resolution 108,125]
223. patient(sK2) [resolution 110,125]
230. creative(X0) | funny(X0) | ~humble(X0) [resolution 90,181]
240. ~humble(X0) | creative(X0) [subsumption resolution 230,139]
272. funny(X0) | ~tall(X0) | curious(X0) [resolution 100,124]
273. ~tall(X0) | funny(X0) [subsumption resolution 272,99]
280. funny(fred) <- (6) [resolution 273,164]
286. ~calm(fred) <- (6) [resolution 280,116]
290. $false <- (6) [subsumption resolution 286,137]
291. ~6 [avatar contradiction clause 290]
293. ~patient(X0) | funny(X0) | humble(X0) <- (9) [resolution 178,94]
321. funny(sK2) | humble(sK2) <- (9) [resolution 293,223]
323. humble(sK2) <- (9) [subsumption resolution 321,221]
346. creative(sK2) <- (9) [resolution 323,240]
364. $false <- (9) [subsumption resolution 346,126]
365. ~9 [avatar contradiction clause 364]
366. $false [avatar sat refutation 179,291,365]
% SZS output end Proof for 8273665733858981414891828
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either creative or not tall then fred is not humble or not generous and vice versa. If someone is old then paul is rich and vice versa. Everyone who is either not wise or not patient is both humble and not rich and vice versa. Everyone who is either not rich or not patient is not calm and vice versa. Everyone who is not quiet is either not quiet or not patient. Everyone who is both not wise and kind is either rich or funny and vice versa. Everyone who is tall or quiet is not rich and vice versa. Everyone who is either funny or tall is either kind or not rich. Everyone who is tall or not wise is either not funny or not happy. Everyone who is either strong or not strong is happy or not wise and vice versa. If lucy is not rich or not calm then someone is either old or not strong. If fred is old then someone is not old or happy and vice versa. If lucy is not old then fred is either not kind or not creative. If someone is not quiet then someone is calm and vice versa. If paul is both curious and not funny then someone is humble and vice versa. If alice is either wise or not creative then paul is not creative or creative. John is either patient or creative. Paul is both strong and not generous. Someone is not funny or not rich. Someone is both funny and not patient. John is not wise. | Paul is not patient. | contradiction | ((?[X]:((creative(X)<~>~tall(X))))<=>((~humble(fred)|~generous(fred))))&
((?[X]:(old(X)))<=>(rich(paul)))&
(![X]:((~wise(X)<~>~patient(X))<=>(humble(X)&~rich(X))))&
(![X]:((~rich(X)<~>~patient(X))<=>~calm(X)))&
(![X]:(~quiet(X)=>(~quiet(X)<~>~patient(X))))&
(![X]:((~wise(X)&kind(X))<=>(rich(X)<~>funny(X))))&
(![X]:((tall(X)|quiet(X))<=>~rich(X)))&
(![X]:((funny(X)<~>tall(X))=>(kind(X)<~>~rich(X))))&
(![X]:((tall(X)|~wise(X))=>(~funny(X)<~>~happy(X))))&
(![X]:((strong(X)<~>~strong(X))<=>(happy(X)|~wise(X))))&
(((~rich(lucy)|~calm(lucy)))=>(?[X]:((old(X)<~>~strong(X)))))&
((old(fred))<=>(?[X]:((~old(X)|happy(X)))))&
((~old(lucy))=>((~kind(fred)<~>~creative(fred))))&
((?[X]:(~quiet(X)))<=>(?[X]:(calm(X))))&
(((curious(paul)&~funny(paul)))<=>(?[X]:(humble(X))))&
(((wise(alice)<~>~creative(alice)))=>((~creative(paul)|creative(paul))))&
((patient(john)<~>creative(john)))&
((strong(paul)&~generous(paul)))&
(?[X]:((~funny(X)|~rich(X))))&
(?[X]:((funny(X)&~patient(X))))&
(~wise(john)) | ~patient(paul) | [
"p1",
"p4",
"p6",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 3617232603491319048879443
% SZS output start Proof for 3617232603491319048879443
2. ? [X0] : old(X0) <=> rich(paul) [input p1]
5. ! [X0] : (~quiet(X0) => (~quiet(X0) <~> ~patient(X0))) [input p4]
7. ! [X0] : ((quiet(X0) | tall(X0)) <=> ~rich(X0)) [input p6]
12. old(fred) <=> ? [X0] : (happy(X0) | ~old(X0)) [input p11]
22. ~patient(paul) [input hypothesis]
24. ! [X0] : ((~quiet(X0) <~> ~patient(X0)) | quiet(X0)) [ennf transformation 5]
36. (? [X0] : old(X0) | ~rich(paul)) & (rich(paul) | ! [X0] : ~old(X0)) [nnf transformation 2]
37. (? [X0] : old(X0) | ~rich(paul)) & (rich(paul) | ! [X1] : ~old(X1)) [rectify 36]
38. ? [X0] : old(X0) => old(sK1) [choice axiom]
39. (old(sK1) | ~rich(paul)) & (rich(paul) | ! [X1] : ~old(X1)) [skolemisation 37,38]
43. ! [X0] : (((patient(X0) | quiet(X0)) & (~patient(X0) | ~quiet(X0))) | quiet(X0)) [nnf transformation 24]
46. ! [X0] : (((quiet(X0) | tall(X0)) | rich(X0)) & (~rich(X0) | (~quiet(X0) & ~tall(X0)))) [nnf transformation 7]
47. ! [X0] : ((quiet(X0) | tall(X0) | rich(X0)) & (~rich(X0) | (~quiet(X0) & ~tall(X0)))) [flattening 46]
55. (old(fred) | ! [X0] : (~happy(X0) & old(X0))) & (? [X0] : (happy(X0) | ~old(X0)) | ~old(fred)) [nnf transformation 12]
56. (old(fred) | ! [X0] : (~happy(X0) & old(X0))) & (? [X1] : (happy(X1) | ~old(X1)) | ~old(fred)) [rectify 55]
57. ? [X1] : (happy(X1) | ~old(X1)) => (happy(sK3) | ~old(sK3)) [choice axiom]
58. (old(fred) | ! [X0] : (~happy(X0) & old(X0))) & ((happy(sK3) | ~old(sK3)) | ~old(fred)) [skolemisation 56,57]
82. rich(paul) | ~old(X1) [cnf transformation 39]
95. patient(X0) | quiet(X0) | quiet(X0) [cnf transformation 43]
103. ~quiet(X0) | ~rich(X0) [cnf transformation 47]
124. old(fred) | old(X0) [cnf transformation 58]
143. ~patient(paul) [cnf transformation 22]
146. quiet(X0) | patient(X0) [duplicate literal removal 95]
176. 7 <=> rich(paul) [avatar definition]
177. rich(paul) <- (7) [avatar component clause 176]
185. 9 <=> ! [X1] : ~old(X1) [avatar definition]
186. ~old(X1) <- (9) [avatar component clause 185]
187. 9 | 7 [avatar split clause 82,176,185]
216. 15 <=> old(fred) [avatar definition]
218. old(fred) <- (15) [avatar component clause 216]
221. 16 <=> ! [X0] : old(X0) [avatar definition]
222. old(X0) <- (16) [avatar component clause 221]
223. 16 | 15 [avatar split clause 124,216,221]
307. $false <- (9, 15) [resolution 186,218]
310. ~9 | ~15 [avatar contradiction clause 307]
312. $false <- (9, 16) [subsumption resolution 222,186]
313. ~9 | ~16 [avatar contradiction clause 312]
327. ~rich(X0) | patient(X0) [resolution 146,103]
329. patient(paul) <- (7) [resolution 327,177]
330. $false <- (7) [subsumption resolution 329,143]
331. ~7 [avatar contradiction clause 330]
332. $false [avatar sat refutation 187,223,310,313,331]
% SZS output end Proof for 3617232603491319048879443
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not happy or funny is either calm or brave.
If someone is either not rich or curious then someone is both humble and happy and vice versa.
If lucy is both kind and brave then someone is both not old and kind.
Everyone who is not generous or not wise is either funny or not humble.
Everyone who is happy is curious.
Everyone who is either not rich or not tall is happy or not creative and vice versa.
If susan is both tall and not funny then someone is not generous.
If susan is not old then fred is not wise or not old and vice versa.
Everyone who is either humble or rich is not quiet and vice versa.
If someone is both not rich and brave then someone is old or rich.
Everyone who is not calm or patient is strong or not happy.
Everyone who is either wise or kind is either patient or brave.
If someone is not funny then paul is not tall and vice versa.
Everyone who is calm is creative.
If someone is not tall or not curious then someone is strong and vice versa.
If someone is strong or quiet then someone is generous or old.
Lucy is funny or humble.
John is not wise or not rich.
Someone is both humble and brave.
Lucy is both tall and not calm.
Fred is not calm.
Someone is either not quiet or curious.
John is strong.
Mary is creative. | Lucy is kind. | neutral | (![X]:((~happy(X)<~>funny(X))=>(calm(X)<~>brave(X))))&
((?[X]:((~rich(X)<~>curious(X))))<=>(?[X]:((humble(X)&happy(X)))))&
(((kind(lucy)&brave(lucy)))=>(?[X]:((~old(X)&kind(X)))))&
(![X]:((~generous(X)|~wise(X))=>(funny(X)<~>~humble(X))))&
(![X]:(happy(X)=>curious(X)))&
(![X]:((~rich(X)<~>~tall(X))<=>(happy(X)|~creative(X))))&
(((tall(susan)&~funny(susan)))=>(?[X]:(~generous(X))))&
((~old(susan))<=>((~wise(fred)|~old(fred))))&
(![X]:((humble(X)<~>rich(X))<=>~quiet(X)))&
((?[X]:((~rich(X)&brave(X))))=>(?[X]:((old(X)|rich(X)))))&
(![X]:((~calm(X)|patient(X))=>(strong(X)|~happy(X))))&
(![X]:((wise(X)<~>kind(X))=>(patient(X)<~>brave(X))))&
((?[X]:(~funny(X)))<=>(~tall(paul)))&
(![X]:(calm(X)=>creative(X)))&
((?[X]:((~tall(X)|~curious(X))))<=>(?[X]:(strong(X))))&
((?[X]:((strong(X)|quiet(X))))=>(?[X]:((generous(X)|old(X)))))&
((funny(lucy)|humble(lucy)))&
((~wise(john)|~rich(john)))&
(?[X]:((humble(X)&brave(X))))&
((tall(lucy)&~calm(lucy)))&
(~calm(fred))&
(?[X]:((~quiet(X)<~>curious(X))))&
(strong(john))&
(creative(mary)) | kind(lucy) | [] | null | 0 |
If alice is not funny then fred is both not curious and creative.
If john is either tall or quiet then someone is either not calm or not curious.
If fred is either not brave or tall then paul is calm.
Everyone who is not kind or not rich is either calm or wise.
Everyone who is either not generous or rich is both quiet and old.
If susan is both not kind and not calm then susan is either old or not happy.
Everyone who is both not funny and rich is both not happy and patient and vice versa.
If someone is both brave and tall then someone is quiet or not calm.
Everyone who is not rich or patient is both old and not happy and vice versa.
If someone is both quiet and strong then someone is not brave or old and vice versa.
If someone is not strong then alice is both happy and not brave.
Everyone who is both humble and funny is old.
Everyone who is either quiet or rich is happy and vice versa.
Everyone who is not happy or not wise is not strong or not quiet and vice versa.
Someone is not patient or creative.
Lucy is not brave or not old.
Lucy is not humble or happy.
Someone is either not wise or curious. | Lucy is patient. | contradiction | ((~funny(alice))=>((~curious(fred)&creative(fred))))&
(((tall(john)<~>quiet(john)))=>(?[X]:((~calm(X)<~>~curious(X)))))&
(((~brave(fred)<~>tall(fred)))=>(calm(paul)))&
(![X]:((~kind(X)|~rich(X))=>(calm(X)<~>wise(X))))&
(![X]:((~generous(X)<~>rich(X))=>(quiet(X)&old(X))))&
(((~kind(susan)&~calm(susan)))=>((old(susan)<~>~happy(susan))))&
(![X]:((~funny(X)&rich(X))<=>(~happy(X)&patient(X))))&
((?[X]:((brave(X)&tall(X))))=>(?[X]:((quiet(X)|~calm(X)))))&
(![X]:((~rich(X)|patient(X))<=>(old(X)&~happy(X))))&
((?[X]:((quiet(X)&strong(X))))<=>(?[X]:((~brave(X)|old(X)))))&
((?[X]:(~strong(X)))=>((happy(alice)&~brave(alice))))&
(![X]:((humble(X)&funny(X))=>old(X)))&
(![X]:((quiet(X)<~>rich(X))<=>happy(X)))&
(![X]:((~happy(X)|~wise(X))<=>(~strong(X)|~quiet(X))))&
(?[X]:((~patient(X)|creative(X))))&
((~brave(lucy)|~old(lucy)))&
((~humble(lucy)|happy(lucy)))&
(?[X]:((~wise(X)<~>curious(X)))) | patient(lucy) | [
"p8",
"p9",
"p12",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3877911741709214655289919
% SZS output start Proof for 3877911741709214655289919
9. ! [X0] : ((patient(X0) | ~rich(X0)) <=> (~happy(X0) & old(X0))) [input p8]
10. ? [X0] : (strong(X0) & quiet(X0)) <=> ? [X0] : (old(X0) | ~brave(X0)) [input p9]
13. ! [X0] : ((quiet(X0) <~> rich(X0)) <=> happy(X0)) [input p12]
14. ! [X0] : ((~wise(X0) | ~happy(X0)) <=> (~quiet(X0) | ~strong(X0))) [input p13]
16. ~old(lucy) | ~brave(lucy) [input p15]
19. patient(lucy) [input hypothesis]
21. ? [X0] : (strong(X0) & quiet(X0)) <=> ? [X1] : (old(X1) | ~brave(X1)) [rectify 10]
46. ! [X0] : (((patient(X0) | ~rich(X0)) | (happy(X0) | ~old(X0))) & ((~happy(X0) & old(X0)) | (~patient(X0) & rich(X0)))) [nnf transformation 9]
47. ! [X0] : ((patient(X0) | ~rich(X0) | happy(X0) | ~old(X0)) & ((~happy(X0) & old(X0)) | (~patient(X0) & rich(X0)))) [flattening 46]
48. (? [X0] : (strong(X0) & quiet(X0)) | ! [X1] : (~old(X1) & brave(X1))) & (? [X1] : (old(X1) | ~brave(X1)) | ! [X0] : (~strong(X0) | ~quiet(X0))) [nnf transformation 21]
49. (? [X0] : (strong(X0) & quiet(X0)) | ! [X1] : (~old(X1) & brave(X1))) & (? [X2] : (old(X2) | ~brave(X2)) | ! [X3] : (~strong(X3) | ~quiet(X3))) [rectify 48]
50. ? [X0] : (strong(X0) & quiet(X0)) => (strong(sK2) & quiet(sK2)) [choice axiom]
51. ? [X2] : (old(X2) | ~brave(X2)) => (old(sK3) | ~brave(sK3)) [choice axiom]
52. ((strong(sK2) & quiet(sK2)) | ! [X1] : (~old(X1) & brave(X1))) & ((old(sK3) | ~brave(sK3)) | ! [X3] : (~strong(X3) | ~quiet(X3))) [skolemisation 49,51,50]
53. ! [X0] : ((((~rich(X0) | ~quiet(X0)) & (rich(X0) | quiet(X0))) | ~happy(X0)) & (happy(X0) | ((quiet(X0) | ~rich(X0)) & (rich(X0) | ~quiet(X0))))) [nnf transformation 13]
54. ! [X0] : (((~wise(X0) | ~happy(X0)) | (quiet(X0) & strong(X0))) & ((~quiet(X0) | ~strong(X0)) | (wise(X0) & happy(X0)))) [nnf transformation 14]
55. ! [X0] : ((~wise(X0) | ~happy(X0) | (quiet(X0) & strong(X0))) & (~quiet(X0) | ~strong(X0) | (wise(X0) & happy(X0)))) [flattening 54]
78. ~patient(X0) | old(X0) [cnf transformation 47]
79. ~happy(X0) | rich(X0) [cnf transformation 47]
83. quiet(sK2) | brave(X1) [cnf transformation 52]
85. strong(sK2) | brave(X1) [cnf transformation 52]
92. ~rich(X0) | ~quiet(X0) | ~happy(X0) [cnf transformation 53]
93. ~quiet(X0) | ~strong(X0) | happy(X0) [cnf transformation 55]
97. ~old(lucy) | ~brave(lucy) [cnf transformation 16]
100. patient(lucy) [cnf transformation 19]
160. 14 <=> strong(sK2) [avatar definition]
162. strong(sK2) <- (14) [avatar component clause 160]
165. 15 <=> ! [X1] : brave(X1) [avatar definition]
166. brave(X1) <- (15) [avatar component clause 165]
167. 15 | 14 [avatar split clause 85,160,165]
169. 16 <=> quiet(sK2) [avatar definition]
171. quiet(sK2) <- (16) [avatar component clause 169]
173. 15 | 16 [avatar split clause 83,169,165]
175. 17 <=> ! [X3] : (~strong(X3) | ~quiet(X3)) [avatar definition]
176. ~strong(X3) | ~quiet(X3) <- (17) [avatar component clause 175]
199. ~quiet(X0) | ~happy(X0) [subsumption resolution 92,79]
202. ~quiet(X0) | ~strong(X0) [subsumption resolution 93,199]
203. 17 [avatar split clause 202,175]
205. 23 <=> brave(lucy) [avatar definition]
207. ~brave(lucy) <- (~23) [avatar component clause 205]
209. 24 <=> old(lucy) [avatar definition]
211. ~old(lucy) <- (~24) [avatar component clause 209]
212. ~23 | ~24 [avatar split clause 97,209,205]
228. old(lucy) [resolution 78,100]
229. $false <- (~24) [subsumption resolution 228,211]
230. 24 [avatar contradiction clause 229]
235. $false <- (15, ~23) [subsumption resolution 207,166]
236. ~15 | 23 [avatar contradiction clause 235]
241. ~quiet(sK2) <- (14, 17) [resolution 176,162]
242. $false <- (14, 16, 17) [subsumption resolution 241,171]
243. ~14 | ~16 | ~17 [avatar contradiction clause 242]
244. $false [avatar sat refutation 167,173,203,212,230,236,243]
% SZS output end Proof for 3877911741709214655289919
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.016 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not humble is brave. If someone is both humble and brave then fred is both not kind and wise and vice versa. If susan is not humble or patient then someone is not generous and vice versa. Everyone who is both not funny and not happy is not creative and vice versa. If alice is both quiet and not kind then mary is either not humble or calm. Everyone who is both not rich and not generous is both brave and not wise and vice versa. Everyone who is not funny or patient is kind. Everyone who is both not quiet and not funny is either not funny or not happy. If someone is calm then someone is not old or patient. If fred is either humble or happy then someone is either not wise or quiet. Everyone who is either brave or not patient is not patient or not brave. If someone is either old or not funny then paul is either old or brave. If someone is not creative then someone is both not strong and happy and vice versa. Everyone who is generous or not generous is either kind or not old and vice versa. Everyone who is tall is either tall or not happy. Everyone who is generous or not wise is both not funny and not old and vice versa. Someone is either wise or not old. Someone is not funny or not tall. Lucy is either brave or not happy. Susan is not generous. Someone is both wise and happy. Mary is either quiet or brave. | Alice is not wise. | contradiction | (![X]:(~humble(X)=>brave(X)))&
((?[X]:((humble(X)&brave(X))))<=>((~kind(fred)&wise(fred))))&
(((~humble(susan)|patient(susan)))<=>(?[X]:(~generous(X))))&
(![X]:((~funny(X)&~happy(X))<=>~creative(X)))&
(((quiet(alice)&~kind(alice)))=>((~humble(mary)<~>calm(mary))))&
(![X]:((~rich(X)&~generous(X))<=>(brave(X)&~wise(X))))&
(![X]:((~funny(X)|patient(X))=>kind(X)))&
(![X]:((~quiet(X)&~funny(X))=>(~funny(X)<~>~happy(X))))&
((?[X]:(calm(X)))=>(?[X]:((~old(X)|patient(X)))))&
(((humble(fred)<~>happy(fred)))=>(?[X]:((~wise(X)<~>quiet(X)))))&
(![X]:((brave(X)<~>~patient(X))=>(~patient(X)|~brave(X))))&
((?[X]:((old(X)<~>~funny(X))))=>((old(paul)<~>brave(paul))))&
((?[X]:(~creative(X)))<=>(?[X]:((~strong(X)&happy(X)))))&
(![X]:((generous(X)|~generous(X))<=>(kind(X)<~>~old(X))))&
(![X]:(tall(X)=>(tall(X)<~>~happy(X))))&
(![X]:((generous(X)|~wise(X))<=>(~funny(X)&~old(X))))&
(?[X]:((wise(X)<~>~old(X))))&
(?[X]:((~funny(X)|~tall(X))))&
((brave(lucy)<~>~happy(lucy)))&
(~generous(susan))&
(?[X]:((wise(X)&happy(X))))&
((quiet(mary)<~>brave(mary))) | ~wise(alice) | [
"p6",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6281680662521296510325512
% SZS output start Proof for 6281680662521296510325512
7. ! [X0] : ((patient(X0) | ~funny(X0)) => kind(X0)) [input p6]
14. ! [X0] : ((~generous(X0) | generous(X0)) <=> (kind(X0) <~> ~old(X0))) [input p13]
16. ! [X0] : ((~wise(X0) | generous(X0)) <=> (~old(X0) & ~funny(X0))) [input p15]
23. ~wise(alice) [input hypothesis]
29. ! [X0] : (kind(X0) | (~patient(X0) & funny(X0))) [ennf transformation 7]
67. ! [X0] : (((~generous(X0) | generous(X0)) | ((kind(X0) | old(X0)) & (~old(X0) | ~kind(X0)))) & (((old(X0) | ~kind(X0)) & (~old(X0) | kind(X0))) | (generous(X0) & ~generous(X0)))) [nnf transformation 14]
68. ! [X0] : ((~generous(X0) | generous(X0) | ((kind(X0) | old(X0)) & (~old(X0) | ~kind(X0)))) & (((old(X0) | ~kind(X0)) & (~old(X0) | kind(X0))) | (generous(X0) & ~generous(X0)))) [flattening 67]
70. ! [X0] : (((~wise(X0) | generous(X0)) | (old(X0) | funny(X0))) & ((~old(X0) & ~funny(X0)) | (wise(X0) & ~generous(X0)))) [nnf transformation 16]
71. ! [X0] : ((~wise(X0) | generous(X0) | old(X0) | funny(X0)) & ((~old(X0) & ~funny(X0)) | (wise(X0) & ~generous(X0)))) [flattening 70]
98. funny(X0) | kind(X0) [cnf transformation 29]
118. old(X0) | ~kind(X0) | ~generous(X0) [cnf transformation 68]
119. ~kind(X0) | old(X0) | generous(X0) [cnf transformation 68]
125. ~funny(X0) | wise(X0) [cnf transformation 71]
127. ~old(X0) | wise(X0) [cnf transformation 71]
139. ~wise(alice) [cnf transformation 23]
189. 11 <=> kind(alice) [avatar definition]
191. kind(alice) <- (11) [avatar component clause 189]
273. ~kind(X0) | old(X0) [subsumption resolution 118,119]
323. wise(X0) | kind(X0) [resolution 125,98]
405. kind(alice) [resolution 323,139]
409. 11 [avatar split clause 405,189]
412. old(alice) <- (11) [resolution 191,273]
418. 47 <=> old(alice) [avatar definition]
420. old(alice) <- (47) [avatar component clause 418]
422. 47 | ~11 [avatar split clause 412,189,418]
425. wise(alice) <- (47) [resolution 420,127]
427. $false <- (47) [subsumption resolution 425,139]
428. ~47 [avatar contradiction clause 427]
430. $false [avatar sat refutation 409,422,428]
% SZS output end Proof for 6281680662521296510325512
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If susan is not wise then fred is not funny.
Everyone who is patient or not rich is both generous and not patient and vice versa.
If john is either not old or curious then someone is either not curious or wise and vice versa.
Everyone who is not brave is either not generous or generous and vice versa.
Everyone who is either old or tall is either quiet or not brave.
Everyone who is not funny is both not humble and brave.
Everyone who is both quiet and not funny is either not quiet or creative.
Everyone who is either not humble or quiet is both not rich and happy and vice versa.
If someone is not patient then someone is either generous or patient and vice versa.
If paul is not brave then someone is both not kind and curious.
Everyone who is not kind is either not humble or brave and vice versa.
If someone is not generous or strong then someone is either not generous or not brave.
Everyone who is either not calm or not generous is both not creative and not kind.
Everyone who is not strong or strong is generous and vice versa.
Everyone who is both not strong and generous is not brave or not humble and vice versa.
Someone is not brave.
Someone is not brave or not curious.
John is either not wise or calm.
Lucy is kind or rich.
Fred is either patient or creative.
Someone is patient or not tall. | Paul is not strong. | entailment | ((~wise(susan))=>(~funny(fred)))&
(![X]:((patient(X)|~rich(X))<=>(generous(X)&~patient(X))))&
(((~old(john)<~>curious(john)))<=>(?[X]:((~curious(X)<~>wise(X)))))&
(![X]:(~brave(X)<=>(~generous(X)<~>generous(X))))&
(![X]:((old(X)<~>tall(X))=>(quiet(X)<~>~brave(X))))&
(![X]:(~funny(X)=>(~humble(X)&brave(X))))&
(![X]:((quiet(X)&~funny(X))=>(~quiet(X)<~>creative(X))))&
(![X]:((~humble(X)<~>quiet(X))<=>(~rich(X)&happy(X))))&
((?[X]:(~patient(X)))<=>(?[X]:((generous(X)<~>patient(X)))))&
((~brave(paul))=>(?[X]:((~kind(X)&curious(X)))))&
(![X]:(~kind(X)<=>(~humble(X)<~>brave(X))))&
((?[X]:((~generous(X)|strong(X))))=>(?[X]:((~generous(X)<~>~brave(X)))))&
(![X]:((~calm(X)<~>~generous(X))=>(~creative(X)&~kind(X))))&
(![X]:((~strong(X)|strong(X))<=>generous(X)))&
(![X]:((~strong(X)&generous(X))<=>(~brave(X)|~humble(X))))&
(?[X]:(~brave(X)))&
(?[X]:((~brave(X)|~curious(X))))&
((~wise(john)<~>calm(john)))&
((kind(lucy)|rich(lucy)))&
((patient(fred)<~>creative(fred)))&
(?[X]:((patient(X)|~tall(X)))) | ~strong(paul) | [
"p3",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6029189692344817949964109
% SZS output start Proof for 6029189692344817949964109
4. ! [X0] : (~brave(X0) <=> (~generous(X0) <~> generous(X0))) [input p3]
15. ! [X0] : ((generous(X0) & ~strong(X0)) <=> (~humble(X0) | ~brave(X0))) [input p14]
22. strong(paul) [input hypothesis]
39. ! [X0] : ((~brave(X0) | ((~generous(X0) | ~generous(X0)) & (generous(X0) | generous(X0)))) & (((~generous(X0) | generous(X0)) & (generous(X0) | ~generous(X0))) | brave(X0))) [nnf transformation 4]
59. ! [X0] : (((generous(X0) & ~strong(X0)) | (humble(X0) & brave(X0))) & ((~humble(X0) | ~brave(X0)) | (~generous(X0) | strong(X0)))) [nnf transformation 15]
60. ! [X0] : (((generous(X0) & ~strong(X0)) | (humble(X0) & brave(X0))) & (~humble(X0) | ~brave(X0) | ~generous(X0) | strong(X0))) [flattening 59]
85. ~brave(X0) | generous(X0) | generous(X0) [cnf transformation 39]
86. ~brave(X0) | ~generous(X0) | ~generous(X0) [cnf transformation 39]
123. ~strong(X0) | brave(X0) [cnf transformation 60]
135. strong(paul) [cnf transformation 22]
137. ~brave(X0) | generous(X0) [duplicate literal removal 85]
138. ~brave(X0) | ~generous(X0) [duplicate literal removal 86]
180. ~brave(X0) [subsumption resolution 137,138]
192. 9 <=> ! [X1] : ~strong(X1) [avatar definition]
193. ~strong(X1) <- (9) [avatar component clause 192]
208. ~strong(X0) [subsumption resolution 123,180]
209. 9 [avatar split clause 208,192]
233. $false <- (9) [resolution 193,135]
234. ~9 [avatar contradiction clause 233]
235. $false [avatar sat refutation 209,234]
% SZS output end Proof for 6029189692344817949964109
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not wise or kind is both tall and wise.
If mary is either not rich or not quiet then someone is not creative or tall and vice versa.
If someone is not generous then susan is both kind and humble.
If lucy is strong or not patient then susan is not rich and vice versa.
If mary is both brave and not calm then someone is both rich and not rich.
Everyone who is not creative or strong is both not generous and rich.
Everyone who is not rich is old or not creative.
If someone is both not happy and wise then someone is not happy.
Everyone who is not tall or not rich is not curious or not strong and vice versa.
If susan is curious or not wise then fred is not old or not wise and vice versa.
Everyone who is not quiet is generous and vice versa.
If someone is not calm or not humble then fred is either not old or wise.
Everyone who is either not creative or calm is either tall or not patient.
Everyone who is both brave and funny is either not humble or not generous and vice versa.
If someone is not kind then lucy is not old.
John is either not quiet or not strong.
Paul is both not happy and not kind.
Someone is either not humble or not brave.
Someone is not creative.
Paul is both not calm and rich.
Lucy is either not strong or funny.
Someone is either brave or not curious.
Someone is both generous and not calm. | Susan is not strong. | entailment | (![X]:((~wise(X)|kind(X))=>(tall(X)&wise(X))))&
(((~rich(mary)<~>~quiet(mary)))<=>(?[X]:((~creative(X)|tall(X)))))&
((?[X]:(~generous(X)))=>((kind(susan)&humble(susan))))&
(((strong(lucy)|~patient(lucy)))<=>(~rich(susan)))&
(((brave(mary)&~calm(mary)))=>(?[X]:((rich(X)&~rich(X)))))&
(![X]:((~creative(X)|strong(X))=>(~generous(X)&rich(X))))&
(![X]:(~rich(X)=>(old(X)|~creative(X))))&
((?[X]:((~happy(X)&wise(X))))=>(?[X]:(~happy(X))))&
(![X]:((~tall(X)|~rich(X))<=>(~curious(X)|~strong(X))))&
(((curious(susan)|~wise(susan)))<=>((~old(fred)|~wise(fred))))&
(![X]:(~quiet(X)<=>generous(X)))&
((?[X]:((~calm(X)|~humble(X))))=>((~old(fred)<~>wise(fred))))&
(![X]:((~creative(X)<~>calm(X))=>(tall(X)<~>~patient(X))))&
(![X]:((brave(X)&funny(X))<=>(~humble(X)<~>~generous(X))))&
((?[X]:(~kind(X)))=>(~old(lucy)))&
((~quiet(john)<~>~strong(john)))&
((~happy(paul)&~kind(paul)))&
(?[X]:((~humble(X)<~>~brave(X))))&
(?[X]:(~creative(X)))&
((~calm(paul)&rich(paul)))&
((~strong(lucy)<~>funny(lucy)))&
(?[X]:((brave(X)<~>~curious(X))))&
(?[X]:((generous(X)&~calm(X)))) | ~strong(susan) | [
"p0",
"p2",
"p5",
"p8",
"p9",
"p11",
"p18",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 4847565152061988190523713
% SZS output start Proof for 4847565152061988190523713
1. ! [X0] : ((kind(X0) | ~wise(X0)) => (wise(X0) & tall(X0))) [input p0]
3. ? [X0] : ~generous(X0) => (humble(susan) & kind(susan)) [input p2]
6. ! [X0] : ((strong(X0) | ~creative(X0)) => (rich(X0) & ~generous(X0))) [input p5]
9. ! [X0] : ((~rich(X0) | ~tall(X0)) <=> (~strong(X0) | ~curious(X0))) [input p8]
10. (~wise(susan) | curious(susan)) <=> (~wise(fred) | ~old(fred)) [input p9]
12. ? [X0] : (~humble(X0) | ~calm(X0)) => (~old(fred) <~> wise(fred)) [input p11]
19. ? [X0] : ~creative(X0) [input p18]
20. rich(paul) & ~calm(paul) [input p19]
24. strong(susan) [input hypothesis]
26. ! [X0] : ((wise(X0) & tall(X0)) | (~kind(X0) & wise(X0))) [ennf transformation 1]
27. (humble(susan) & kind(susan)) | ! [X0] : generous(X0) [ennf transformation 3]
30. ! [X0] : ((rich(X0) & ~generous(X0)) | (~strong(X0) & creative(X0))) [ennf transformation 6]
34. (~old(fred) <~> wise(fred)) | ! [X0] : (humble(X0) & calm(X0)) [ennf transformation 12]
48. ! [X0] : (((~rich(X0) | ~tall(X0)) | (strong(X0) & curious(X0))) & ((~strong(X0) | ~curious(X0)) | (rich(X0) & tall(X0)))) [nnf transformation 9]
49. ! [X0] : ((~rich(X0) | ~tall(X0) | (strong(X0) & curious(X0))) & (~strong(X0) | ~curious(X0) | (rich(X0) & tall(X0)))) [flattening 48]
50. ((~wise(susan) | curious(susan)) | (wise(fred) & old(fred))) & ((~wise(fred) | ~old(fred)) | (wise(susan) & ~curious(susan))) [nnf transformation 10]
51. (~wise(susan) | curious(susan) | (wise(fred) & old(fred))) & (~wise(fred) | ~old(fred) | (wise(susan) & ~curious(susan))) [flattening 50]
53. ((~wise(fred) | old(fred)) & (wise(fred) | ~old(fred))) | ! [X0] : (humble(X0) & calm(X0)) [nnf transformation 34]
61. ? [X0] : ~creative(X0) => ~creative(sK4) [choice axiom]
62. ~creative(sK4) [skolemisation 19,61]
70. ~kind(X0) | tall(X0) [cnf transformation 26]
71. wise(X0) | wise(X0) [cnf transformation 26]
79. kind(susan) | generous(X0) [cnf transformation 27]
86. ~generous(X0) | creative(X0) [cnf transformation 30]
89. ~strong(X0) | rich(X0) [cnf transformation 30]
94. ~rich(X0) | ~tall(X0) | curious(X0) [cnf transformation 49]
96. ~wise(fred) | ~old(fred) | ~curious(susan) [cnf transformation 51]
104. ~wise(fred) | old(fred) | calm(X0) [cnf transformation 53]
123. ~creative(sK4) [cnf transformation 62]
124. ~calm(paul) [cnf transformation 20]
132. strong(susan) [cnf transformation 24]
133. wise(X0) [duplicate literal removal 71]
147. 4 <=> ! [X0] : creative(X0) [avatar definition]
148. creative(X0) <- (4) [avatar component clause 147]
163. 7 <=> ! [X0] : generous(X0) [avatar definition]
164. generous(X0) <- (7) [avatar component clause 163]
171. 9 <=> kind(susan) [avatar definition]
173. kind(susan) <- (9) [avatar component clause 171]
174. 7 | 9 [avatar split clause 79,171,163]
176. 10 <=> rich(susan) [avatar definition]
178. rich(susan) <- (10) [avatar component clause 176]
216. 18 <=> old(fred) [avatar definition]
220. 19 <=> curious(susan) [avatar definition]
224. ~old(fred) | ~curious(susan) [subsumption resolution 96,133]
225. ~19 | ~18 [avatar split clause 224,216,220]
231. old(fred) | calm(X0) [subsumption resolution 104,133]
233. 21 <=> ! [X0] : calm(X0) [avatar definition]
234. calm(X0) <- (21) [avatar component clause 233]
235. 21 | 18 [avatar split clause 231,216,233]
281. creative(X0) <- (7) [resolution 86,164]
282. 4 | ~7 [avatar split clause 281,163,147]
283. $false <- (4) [resolution 148,123]
286. ~4 [avatar contradiction clause 283]
288. tall(susan) <- (9) [resolution 173,70]
292. rich(susan) [resolution 89,132]
295. 10 [avatar split clause 292,176]
302. ~tall(susan) | curious(susan) <- (10) [resolution 94,178]
316. curious(susan) <- (9, 10) [subsumption resolution 302,288]
351. 19 | ~9 | ~10 [avatar split clause 316,176,171,220]
354. $false <- (21) [resolution 234,124]
357. ~21 [avatar contradiction clause 354]
358. $false [avatar sat refutation 174,225,235,282,286,295,351,357]
% SZS output end Proof for 4847565152061988190523713
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If mary is not calm then lucy is not patient or not kind. If someone is either not old or rich then john is tall or not rich and vice versa. If alice is either not strong or happy then fred is both rich and creative and vice versa. If someone is both not quiet and not rich then john is strong or not funny and vice versa. If paul is funny or not generous then paul is calm or brave and vice versa. Everyone who is calm or kind is not funny. Everyone who is not generous or not rich is both not patient and strong and vice versa. If susan is either patient or quiet then susan is both kind and patient and vice versa. Everyone who is old or happy is not funny. Everyone who is either generous or not tall is either not tall or tall. Everyone who is strong or not strong is creative or humble. Everyone who is both kind and not tall is both not creative and generous. Everyone who is both not brave and quiet is either calm or brave and vice versa. Everyone who is both not brave and not patient is either quiet or wise. Everyone who is either patient or funny is either patient or tall. Everyone who is not rich is both not kind and not tall and vice versa. Paul is not curious or not generous. Fred is not humble or brave. Lucy is either wise or not patient. Mary is not quiet. Fred is both not curious and patient. Paul is not rich or not creative. Alice is either kind or creative. Someone is either not old or funny. | Fred is not patient. | contradiction | ((~calm(mary))=>((~patient(lucy)|~kind(lucy))))&
((?[X]:((~old(X)<~>rich(X))))<=>((tall(john)|~rich(john))))&
(((~strong(alice)<~>happy(alice)))<=>((rich(fred)&creative(fred))))&
((?[X]:((~quiet(X)&~rich(X))))<=>((strong(john)|~funny(john))))&
(((funny(paul)|~generous(paul)))<=>((calm(paul)|brave(paul))))&
(![X]:((calm(X)|kind(X))=>~funny(X)))&
(![X]:((~generous(X)|~rich(X))<=>(~patient(X)&strong(X))))&
(((patient(susan)<~>quiet(susan)))<=>((kind(susan)&patient(susan))))&
(![X]:((old(X)|happy(X))=>~funny(X)))&
(![X]:((generous(X)<~>~tall(X))=>(~tall(X)<~>tall(X))))&
(![X]:((strong(X)|~strong(X))=>(creative(X)|humble(X))))&
(![X]:((kind(X)&~tall(X))=>(~creative(X)&generous(X))))&
(![X]:((~brave(X)&quiet(X))<=>(calm(X)<~>brave(X))))&
(![X]:((~brave(X)&~patient(X))=>(quiet(X)<~>wise(X))))&
(![X]:((patient(X)<~>funny(X))=>(patient(X)<~>tall(X))))&
(![X]:(~rich(X)<=>(~kind(X)&~tall(X))))&
((~curious(paul)|~generous(paul)))&
((~humble(fred)|brave(fred)))&
((wise(lucy)<~>~patient(lucy)))&
(~quiet(mary))&
((~curious(fred)&patient(fred)))&
((~rich(paul)|~creative(paul)))&
((kind(alice)<~>creative(alice)))&
(?[X]:((~old(X)<~>funny(X)))) | ~patient(fred) | [
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 2200212701554951274218693
% SZS output start Proof for 2200212701554951274218693
21. patient(fred) & ~curious(fred) [input p20]
25. ~patient(fred) [input hypothesis]
26. patient(fred) [pure predicate removal 21]
134. patient(fred) [cnf transformation 26]
140. ~patient(fred) [cnf transformation 25]
312. $false [subsumption resolution 140,134]
% SZS output end Proof for 2200212701554951274218693
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 mary is not quiet then fred is quiet. If mary is funny or not humble then susan is both not calm and generous and vice versa. Everyone who is both patient and not happy is not generous or patient. If john is either not generous or not curious then someone is either rich or brave. Everyone who is humble is rich or not calm. Everyone who is both not happy and creative is either not curious or quiet and vice versa. If someone is either curious or patient then someone is either quiet or not strong. Everyone who is either not strong or not funny is both old and not generous. If someone is not rich then someone is either strong or not rich. Everyone who is not rich is calm and vice versa. If someone is not tall or old then john is not humble or old and vice versa. Everyone who is either wise or curious is either quiet or not wise and vice versa. If alice is both calm and old then someone is not brave or humble. Everyone who is not funny or wise is not curious. If someone is either curious or creative then susan is both not calm and patient and vice versa. If paul is old or funny then someone is either rich or not generous. Someone is not happy or wise. Susan is both rich and strong. Alice is either strong or not strong. Mary is funny. Someone is not old or patient. Alice is either tall or curious. Susan is not rich or humble. Someone is either not wise or strong. | Susan is calm. | contradiction | ((~quiet(mary))=>(quiet(fred)))&
(((funny(mary)|~humble(mary)))<=>((~calm(susan)&generous(susan))))&
(![X]:((patient(X)&~happy(X))=>(~generous(X)|patient(X))))&
(((~generous(john)<~>~curious(john)))=>(?[X]:((rich(X)<~>brave(X)))))&
(![X]:(humble(X)=>(rich(X)|~calm(X))))&
(![X]:((~happy(X)&creative(X))<=>(~curious(X)<~>quiet(X))))&
((?[X]:((curious(X)<~>patient(X))))=>(?[X]:((quiet(X)<~>~strong(X)))))&
(![X]:((~strong(X)<~>~funny(X))=>(old(X)&~generous(X))))&
((?[X]:(~rich(X)))=>(?[X]:((strong(X)<~>~rich(X)))))&
(![X]:(~rich(X)<=>calm(X)))&
((?[X]:((~tall(X)|old(X))))<=>((~humble(john)|old(john))))&
(![X]:((wise(X)<~>curious(X))<=>(quiet(X)<~>~wise(X))))&
(((calm(alice)&old(alice)))=>(?[X]:((~brave(X)|humble(X)))))&
(![X]:((~funny(X)|wise(X))=>~curious(X)))&
((?[X]:((curious(X)<~>creative(X))))<=>((~calm(susan)&patient(susan))))&
(((old(paul)|funny(paul)))=>(?[X]:((rich(X)<~>~generous(X)))))&
(?[X]:((~happy(X)|wise(X))))&
((rich(susan)&strong(susan)))&
((strong(alice)<~>~strong(alice)))&
(funny(mary))&
(?[X]:((~old(X)|patient(X))))&
((tall(alice)<~>curious(alice)))&
((~rich(susan)|humble(susan)))&
(?[X]:((~wise(X)<~>strong(X)))) | calm(susan) | [
"p1",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 615822541846378228964722
% SZS output start Proof for 615822541846378228964722
2. (~humble(mary) | funny(mary)) <=> (generous(susan) & ~calm(susan)) [input p1]
20. funny(mary) [input p19]
25. calm(susan) [input hypothesis]
41. ((~humble(mary) | funny(mary)) | (~generous(susan) | calm(susan))) & ((generous(susan) & ~calm(susan)) | (humble(mary) & ~funny(mary))) [nnf transformation 2]
42. (~humble(mary) | funny(mary) | ~generous(susan) | calm(susan)) & ((generous(susan) & ~calm(susan)) | (humble(mary) & ~funny(mary))) [flattening 41]
84. ~calm(susan) | ~funny(mary) [cnf transformation 42]
143. funny(mary) [cnf transformation 20]
150. calm(susan) [cnf transformation 25]
165. 3 <=> calm(susan) [avatar definition]
173. 5 <=> funny(mary) [avatar definition]
184. ~5 | ~3 [avatar split clause 84,165,173]
334. 5 [avatar split clause 143,173]
365. 3 [avatar split clause 150,165]
366. $false [avatar sat refutation 184,334,365]
% SZS output end Proof for 615822541846378228964722
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If john is both patient and generous then someone is not quiet and vice versa. Everyone who is either quiet or creative is both not tall and strong. If someone is calm then fred is calm or generous and vice versa. If someone is either not tall or patient then alice is generous or humble and vice versa. If someone is not rich or not strong then fred is both wise and not funny. Everyone who is either strong or not old is not calm. If lucy is creative or not brave then mary is not strong or not creative and vice versa. If someone is both not creative and not quiet then someone is curious or not tall. Everyone who is both not kind and not old is rich or not old and vice versa. If someone is not happy then someone is both funny and strong and vice versa. Everyone who is both rich and not old is either not funny or brave. Everyone who is either kind or not kind is either brave or creative and vice versa. If someone is quiet or not rich then john is either happy or not strong and vice versa. Everyone who is not kind is both not wise and not kind. Everyone who is both old and not brave is curious and vice versa. If someone is not happy or not calm then john is not rich or not curious and vice versa. Someone is old or not creative. Susan is strong. Fred is either not generous or creative. John is both generous and not funny. Paul is happy. Someone is creative or not brave. Susan is either funny or rich. Lucy is either funny or patient. | John is generous. | entailment | (((patient(john)&generous(john)))<=>(?[X]:(~quiet(X))))&
(![X]:((quiet(X)<~>creative(X))=>(~tall(X)&strong(X))))&
((?[X]:(calm(X)))<=>((calm(fred)|generous(fred))))&
((?[X]:((~tall(X)<~>patient(X))))<=>((generous(alice)|humble(alice))))&
((?[X]:((~rich(X)|~strong(X))))=>((wise(fred)&~funny(fred))))&
(![X]:((strong(X)<~>~old(X))=>~calm(X)))&
(((creative(lucy)|~brave(lucy)))<=>((~strong(mary)|~creative(mary))))&
((?[X]:((~creative(X)&~quiet(X))))=>(?[X]:((curious(X)|~tall(X)))))&
(![X]:((~kind(X)&~old(X))<=>(rich(X)|~old(X))))&
((?[X]:(~happy(X)))<=>(?[X]:((funny(X)&strong(X)))))&
(![X]:((rich(X)&~old(X))=>(~funny(X)<~>brave(X))))&
(![X]:((kind(X)<~>~kind(X))<=>(brave(X)<~>creative(X))))&
((?[X]:((quiet(X)|~rich(X))))<=>((happy(john)<~>~strong(john))))&
(![X]:(~kind(X)=>(~wise(X)&~kind(X))))&
(![X]:((old(X)&~brave(X))<=>curious(X)))&
((?[X]:((~happy(X)|~calm(X))))<=>((~rich(john)|~curious(john))))&
(?[X]:((old(X)|~creative(X))))&
(strong(susan))&
((~generous(fred)<~>creative(fred)))&
((generous(john)&~funny(john)))&
(happy(paul))&
(?[X]:((creative(X)|~brave(X))))&
((funny(susan)<~>rich(susan)))&
((funny(lucy)<~>patient(lucy))) | generous(john) | [
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 471364456704330050017529
% SZS output start Proof for 471364456704330050017529
20. ~funny(john) & generous(john) [input p19]
25. ~generous(john) [input hypothesis]
148. generous(john) [cnf transformation 20]
156. ~generous(john) [cnf transformation 25]
165. 2 <=> generous(john) [avatar definition]
363. 2 [avatar split clause 148,165]
385. ~2 [avatar split clause 156,165]
386. $false [avatar sat refutation 363,385]
% SZS output end Proof for 471364456704330050017529
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient or not wise is both wise and calm and vice versa. Everyone who is humble is both calm and wise and vice versa. Everyone who is both not tall and not strong is either not wise or not strong and vice versa. Everyone who is both old and creative is either strong or not wise and vice versa. If paul is not brave then alice is brave and vice versa. If mary is creative or not calm then lucy is tall or not strong and vice versa. Everyone who is either creative or not funny is brave and vice versa. If lucy is both not kind and not humble then fred is both not generous and not curious. Everyone who is either patient or tall is strong or not tall and vice versa. Everyone who is not quiet is not wise or not calm. Everyone who is either not wise or tall is both not rich and not quiet. If mary is calm or not curious then mary is not old. If fred is both not quiet and not patient then someone is both tall and not happy. Everyone who is not calm or humble is either not curious or not tall and vice versa. Someone is either brave or calm. Paul is brave. Someone is generous or wise. Someone is either kind or not rich. Someone is kind or not wise. Someone is not patient or funny. | Fred is happy. | neutral | (![X]:((~patient(X)<~>~wise(X))<=>(wise(X)&calm(X))))&
(![X]:(humble(X)<=>(calm(X)&wise(X))))&
(![X]:((~tall(X)&~strong(X))<=>(~wise(X)<~>~strong(X))))&
(![X]:((old(X)&creative(X))<=>(strong(X)<~>~wise(X))))&
((~brave(paul))<=>(brave(alice)))&
(((creative(mary)|~calm(mary)))<=>((tall(lucy)|~strong(lucy))))&
(![X]:((creative(X)<~>~funny(X))<=>brave(X)))&
(((~kind(lucy)&~humble(lucy)))=>((~generous(fred)&~curious(fred))))&
(![X]:((patient(X)<~>tall(X))<=>(strong(X)|~tall(X))))&
(![X]:(~quiet(X)=>(~wise(X)|~calm(X))))&
(![X]:((~wise(X)<~>tall(X))=>(~rich(X)&~quiet(X))))&
(((calm(mary)|~curious(mary)))=>(~old(mary)))&
(((~quiet(fred)&~patient(fred)))=>(?[X]:((tall(X)&~happy(X)))))&
(![X]:((~calm(X)|humble(X))<=>(~curious(X)<~>~tall(X))))&
(?[X]:((brave(X)<~>calm(X))))&
(brave(paul))&
(?[X]:((generous(X)|wise(X))))&
(?[X]:((kind(X)<~>~rich(X))))&
(?[X]:((kind(X)|~wise(X))))&
(?[X]:((~patient(X)|funny(X)))) | happy(fred) | [] | null | 0 |
Everyone who is strong or kind is both not humble and not funny and vice versa.
If someone is either not humble or old then someone is both kind and not generous and vice versa.
If someone is both tall and brave then someone is generous or not wise and vice versa.
If fred is not creative or strong then alice is both kind and not tall.
Everyone who is not kind is not humble and vice versa.
Everyone who is humble is strong or not calm.
Everyone who is either tall or generous is not humble or not kind and vice versa.
If lucy is either not patient or not generous then someone is both generous and calm.
Everyone who is not tall or not wise is both tall and not curious.
If fred is rich or not curious then someone is funny or not rich and vice versa.
Everyone who is both not strong and not generous is not calm or brave.
Everyone who is calm or not wise is either not happy or not tall and vice versa.
If paul is tall then someone is tall or brave.
Everyone who is both not generous and not happy is not funny.
If alice is either not creative or rich then lucy is either calm or strong.
Someone is happy.
John is not happy.
Someone is old or not brave.
Lucy is either happy or not funny.
Someone is wise.
Someone is curious. | Alice is not old. | contradiction | (![X]:((strong(X)|kind(X))<=>(~humble(X)&~funny(X))))&
((?[X]:((~humble(X)<~>old(X))))<=>(?[X]:((kind(X)&~generous(X)))))&
((?[X]:((tall(X)&brave(X))))<=>(?[X]:((generous(X)|~wise(X)))))&
(((~creative(fred)|strong(fred)))=>((kind(alice)&~tall(alice))))&
(![X]:(~kind(X)<=>~humble(X)))&
(![X]:(humble(X)=>(strong(X)|~calm(X))))&
(![X]:((tall(X)<~>generous(X))<=>(~humble(X)|~kind(X))))&
(((~patient(lucy)<~>~generous(lucy)))=>(?[X]:((generous(X)&calm(X)))))&
(![X]:((~tall(X)|~wise(X))=>(tall(X)&~curious(X))))&
(((rich(fred)|~curious(fred)))<=>(?[X]:((funny(X)|~rich(X)))))&
(![X]:((~strong(X)&~generous(X))=>(~calm(X)|brave(X))))&
(![X]:((calm(X)|~wise(X))<=>(~happy(X)<~>~tall(X))))&
((tall(paul))=>(?[X]:((tall(X)|brave(X)))))&
(![X]:((~generous(X)&~happy(X))=>~funny(X)))&
(((~creative(alice)<~>rich(alice)))=>((calm(lucy)<~>strong(lucy))))&
(?[X]:(happy(X)))&
(~happy(john))&
(?[X]:((old(X)|~brave(X))))&
((happy(lucy)<~>~funny(lucy)))&
(?[X]:(wise(X)))&
(?[X]:(curious(X))) | ~old(alice) | [
"p0",
"p1",
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 5308545299363722129468738
% SZS output start Proof for 5308545299363722129468738
1. ! [X0] : ((kind(X0) | strong(X0)) <=> (~funny(X0) & ~humble(X0))) [input p0]
2. ? [X0] : (~humble(X0) <~> old(X0)) <=> ? [X0] : (~generous(X0) & kind(X0)) [input p1]
5. ! [X0] : (~kind(X0) <=> ~humble(X0)) [input p4]
22. ~old(alice) [input hypothesis]
23. ? [X0] : (~humble(X0) <~> old(X0)) <=> ? [X1] : (~generous(X1) & kind(X1)) [rectify 2]
36. ! [X0] : (((kind(X0) | strong(X0)) | (funny(X0) | humble(X0))) & ((~funny(X0) & ~humble(X0)) | (~kind(X0) & ~strong(X0)))) [nnf transformation 1]
37. ! [X0] : ((kind(X0) | strong(X0) | funny(X0) | humble(X0)) & ((~funny(X0) & ~humble(X0)) | (~kind(X0) & ~strong(X0)))) [flattening 36]
38. (? [X0] : ((~old(X0) | humble(X0)) & (old(X0) | ~humble(X0))) | ! [X1] : (generous(X1) | ~kind(X1))) & (? [X1] : (~generous(X1) & kind(X1)) | ! [X0] : ((~humble(X0) | ~old(X0)) & (old(X0) | humble(X0)))) [nnf transformation 23]
39. (? [X0] : ((~old(X0) | humble(X0)) & (old(X0) | ~humble(X0))) | ! [X1] : (generous(X1) | ~kind(X1))) & (? [X2] : (~generous(X2) & kind(X2)) | ! [X3] : ((~humble(X3) | ~old(X3)) & (old(X3) | humble(X3)))) [rectify 38]
40. ? [X0] : ((~old(X0) | humble(X0)) & (old(X0) | ~humble(X0))) => ((~old(sK0) | humble(sK0)) & (old(sK0) | ~humble(sK0))) [choice axiom]
41. ? [X2] : (~generous(X2) & kind(X2)) => (~generous(sK1) & kind(sK1)) [choice axiom]
42. (((~old(sK0) | humble(sK0)) & (old(sK0) | ~humble(sK0))) | ! [X1] : (generous(X1) | ~kind(X1))) & ((~generous(sK1) & kind(sK1)) | ! [X3] : ((~humble(X3) | ~old(X3)) & (old(X3) | humble(X3)))) [skolemisation 39,41,40]
48. ! [X0] : ((~kind(X0) | humble(X0)) & (~humble(X0) | kind(X0))) [nnf transformation 5]
74. ~humble(X0) | ~kind(X0) [cnf transformation 37]
78. kind(sK1) | old(X3) | humble(X3) [cnf transformation 42]
93. ~humble(X0) | kind(X0) [cnf transformation 48]
94. ~kind(X0) | humble(X0) [cnf transformation 48]
134. ~old(alice) [cnf transformation 22]
158. 6 <=> ! [X3] : (old(X3) | humble(X3)) [avatar definition]
159. old(X3) | humble(X3) <- (6) [avatar component clause 158]
162. 7 <=> kind(sK1) [avatar definition]
164. kind(sK1) <- (7) [avatar component clause 162]
166. 6 | 7 [avatar split clause 78,162,158]
217. ~kind(X0) [subsumption resolution 94,74]
218. ~humble(X0) [subsumption resolution 93,217]
312. $false <- (7) [subsumption resolution 164,217]
313. ~7 [avatar contradiction clause 312]
314. old(X3) <- (6) [subsumption resolution 159,218]
317. $false <- (6) [resolution 314,134]
318. ~6 [avatar contradiction clause 317]
319. $false [avatar sat refutation 166,313,318]
% SZS output end Proof for 5308545299363722129468738
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not calm or funny then someone is either kind or not funny and vice versa.
If lucy is both humble and not rich then someone is humble or not humble and vice versa.
Everyone who is both not brave and not wise is not patient and vice versa.
If someone is both not strong and not brave then someone is quiet.
Everyone who is both not tall and not patient is not generous or not patient and vice versa.
If john is either tall or not wise then someone is both rich and not wise.
If someone is not curious or kind then someone is both patient and not funny and vice versa.
If susan is not generous then susan is old.
If someone is either not quiet or tall then susan is both not kind and humble.
Everyone who is old or wise is either quiet or not wise and vice versa.
Everyone who is not funny is either patient or quiet.
Everyone who is both not funny and curious is quiet.
If someone is patient then someone is either not tall or not creative and vice versa.
If someone is both not happy and not tall then fred is both not generous and calm and vice versa.
Everyone who is both happy and not funny is both brave and patient and vice versa.
If someone is not happy or kind then susan is funny or not curious.
Someone is both not quiet and not happy.
Alice is happy.
Mary is both generous and not funny.
Someone is wise or not wise.
Someone is strong or not curious.
Mary is either not quiet or not tall.
Someone is not funny.
Someone is either old or not funny. | Fred is generous. | contradiction | (((~calm(john)|funny(john)))<=>(?[X]:((kind(X)<~>~funny(X)))))&
(((humble(lucy)&~rich(lucy)))<=>(?[X]:((humble(X)|~humble(X)))))&
(![X]:((~brave(X)&~wise(X))<=>~patient(X)))&
((?[X]:((~strong(X)&~brave(X))))=>(?[X]:(quiet(X))))&
(![X]:((~tall(X)&~patient(X))<=>(~generous(X)|~patient(X))))&
(((tall(john)<~>~wise(john)))=>(?[X]:((rich(X)&~wise(X)))))&
((?[X]:((~curious(X)|kind(X))))<=>(?[X]:((patient(X)&~funny(X)))))&
((~generous(susan))=>(old(susan)))&
((?[X]:((~quiet(X)<~>tall(X))))=>((~kind(susan)&humble(susan))))&
(![X]:((old(X)|wise(X))<=>(quiet(X)<~>~wise(X))))&
(![X]:(~funny(X)=>(patient(X)<~>quiet(X))))&
(![X]:((~funny(X)&curious(X))=>quiet(X)))&
((?[X]:(patient(X)))<=>(?[X]:((~tall(X)<~>~creative(X)))))&
((?[X]:((~happy(X)&~tall(X))))<=>((~generous(fred)&calm(fred))))&
(![X]:((happy(X)&~funny(X))<=>(brave(X)&patient(X))))&
((?[X]:((~happy(X)|kind(X))))=>((funny(susan)|~curious(susan))))&
(?[X]:((~quiet(X)&~happy(X))))&
(happy(alice))&
((generous(mary)&~funny(mary)))&
(?[X]:((wise(X)|~wise(X))))&
(?[X]:((strong(X)|~curious(X))))&
((~quiet(mary)<~>~tall(mary)))&
(?[X]:(~funny(X)))&
(?[X]:((old(X)<~>~funny(X)))) | generous(fred) | [
"p2",
"p4",
"p9",
"p13",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 610732946073701221545957
% SZS output start Proof for 610732946073701221545957
3. ! [X0] : ((~wise(X0) & ~brave(X0)) <=> ~patient(X0)) [input p2]
5. ! [X0] : ((~patient(X0) & ~tall(X0)) <=> (~patient(X0) | ~generous(X0))) [input p4]
10. ! [X0] : ((wise(X0) | old(X0)) <=> (quiet(X0) <~> ~wise(X0))) [input p9]
14. ? [X0] : (~tall(X0) & ~happy(X0)) <=> (calm(fred) & ~generous(fred)) [input p13]
15. ! [X0] : ((~funny(X0) & happy(X0)) <=> (patient(X0) & brave(X0))) [input p14]
17. ? [X0] : (~happy(X0) & ~quiet(X0)) [input p16]
25. generous(fred) [input hypothesis]
49. ! [X0] : (((~wise(X0) & ~brave(X0)) | patient(X0)) & (~patient(X0) | (wise(X0) | brave(X0)))) [nnf transformation 3]
50. ! [X0] : (((~wise(X0) & ~brave(X0)) | patient(X0)) & (~patient(X0) | wise(X0) | brave(X0))) [flattening 49]
51. ! [X0] : (((~patient(X0) & ~tall(X0)) | (patient(X0) & generous(X0))) & ((~patient(X0) | ~generous(X0)) | (patient(X0) | tall(X0)))) [nnf transformation 5]
52. ! [X0] : (((~patient(X0) & ~tall(X0)) | (patient(X0) & generous(X0))) & (~patient(X0) | ~generous(X0) | patient(X0) | tall(X0))) [flattening 51]
62. ! [X0] : (((wise(X0) | old(X0)) | ((quiet(X0) | wise(X0)) & (~wise(X0) | ~quiet(X0)))) & (((wise(X0) | ~quiet(X0)) & (~wise(X0) | quiet(X0))) | (~wise(X0) & ~old(X0)))) [nnf transformation 10]
63. ! [X0] : ((wise(X0) | old(X0) | ((quiet(X0) | wise(X0)) & (~wise(X0) | ~quiet(X0)))) & (((wise(X0) | ~quiet(X0)) & (~wise(X0) | quiet(X0))) | (~wise(X0) & ~old(X0)))) [flattening 62]
70. (? [X0] : (~tall(X0) & ~happy(X0)) | (~calm(fred) | generous(fred))) & ((calm(fred) & ~generous(fred)) | ! [X0] : (tall(X0) | happy(X0))) [nnf transformation 14]
71. (? [X0] : (~tall(X0) & ~happy(X0)) | ~calm(fred) | generous(fred)) & ((calm(fred) & ~generous(fred)) | ! [X0] : (tall(X0) | happy(X0))) [flattening 70]
72. (? [X0] : (~tall(X0) & ~happy(X0)) | ~calm(fred) | generous(fred)) & ((calm(fred) & ~generous(fred)) | ! [X1] : (tall(X1) | happy(X1))) [rectify 71]
73. ? [X0] : (~tall(X0) & ~happy(X0)) => (~tall(sK7) & ~happy(sK7)) [choice axiom]
74. ((~tall(sK7) & ~happy(sK7)) | ~calm(fred) | generous(fred)) & ((calm(fred) & ~generous(fred)) | ! [X1] : (tall(X1) | happy(X1))) [skolemisation 72,73]
75. ! [X0] : (((~funny(X0) & happy(X0)) | (~patient(X0) | ~brave(X0))) & ((patient(X0) & brave(X0)) | (funny(X0) | ~happy(X0)))) [nnf transformation 15]
76. ! [X0] : (((~funny(X0) & happy(X0)) | ~patient(X0) | ~brave(X0)) & ((patient(X0) & brave(X0)) | funny(X0) | ~happy(X0))) [flattening 75]
77. ? [X0] : (~happy(X0) & ~quiet(X0)) => (~happy(sK8) & ~quiet(sK8)) [choice axiom]
78. ~happy(sK8) & ~quiet(sK8) [skolemisation 17,77]
98. ~patient(X0) | wise(X0) | brave(X0) [cnf transformation 50]
99. ~brave(X0) | patient(X0) [cnf transformation 50]
103. ~tall(X0) | patient(X0) [cnf transformation 52]
121. ~wise(X0) | quiet(X0) | ~wise(X0) [cnf transformation 63]
133. ~generous(fred) | tall(X1) | happy(X1) [cnf transformation 74]
139. happy(X0) | ~patient(X0) | ~brave(X0) [cnf transformation 76]
143. ~quiet(sK8) [cnf transformation 78]
144. ~happy(sK8) [cnf transformation 78]
154. generous(fred) [cnf transformation 25]
155. ~wise(X0) | quiet(X0) [duplicate literal removal 121]
306. 34 <=> generous(fred) [avatar definition]
324. 38 <=> ! [X1] : (tall(X1) | happy(X1)) [avatar definition]
325. happy(X1) | tall(X1) <- (38) [avatar component clause 324]
327. 38 | ~34 [avatar split clause 133,306,324]
329. ~brave(X0) | happy(X0) [subsumption resolution 139,99]
363. 34 [avatar split clause 154,306]
397. tall(sK8) <- (38) [resolution 325,144]
399. patient(sK8) <- (38) [resolution 397,103]
482. wise(sK8) | brave(sK8) <- (38) [resolution 399,98]
485. 54 <=> brave(sK8) [avatar definition]
487. brave(sK8) <- (54) [avatar component clause 485]
489. 55 <=> wise(sK8) [avatar definition]
491. wise(sK8) <- (55) [avatar component clause 489]
492. 54 | 55 | ~38 [avatar split clause 482,324,489,485]
530. happy(sK8) <- (54) [resolution 487,329]
533. $false <- (54) [subsumption resolution 530,144]
534. ~54 [avatar contradiction clause 533]
537. quiet(sK8) <- (55) [resolution 491,155]
539. $false <- (55) [subsumption resolution 537,143]
540. ~55 [avatar contradiction clause 539]
541. $false [avatar sat refutation 327,363,492,534,540]
% SZS output end Proof for 610732946073701221545957
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative is not rich and vice versa. If fred is not humble or not generous then john is humble and vice versa. Everyone who is either patient or humble is either not brave or not funny. If someone is both brave and happy then someone is either patient or not strong. If someone is both not patient and old then someone is not generous or not happy and vice versa. If someone is both kind and not patient then paul is humble. Everyone who is both calm and patient is patient and vice versa. Everyone who is not strong or not wise is both not strong and creative. If someone is either not curious or not quiet then mary is either patient or kind and vice versa. Everyone who is both not generous and old is both not old and old. Everyone who is not kind is not tall or curious and vice versa. Everyone who is strong is not brave and vice versa. Everyone who is strong is not calm or not rich and vice versa. If someone is both not funny and humble then someone is not strong or not tall and vice versa. If someone is either not humble or not patient then someone is old. Everyone who is not brave is not calm and vice versa. Alice is brave or not happy. Lucy is curious. Lucy is not kind or old. Someone is not strong. Fred is either not calm or tall. Someone is creative. | John is humble. | neutral | (![X]:(~creative(X)<=>~rich(X)))&
(((~humble(fred)|~generous(fred)))<=>(humble(john)))&
(![X]:((patient(X)<~>humble(X))=>(~brave(X)<~>~funny(X))))&
((?[X]:((brave(X)&happy(X))))=>(?[X]:((patient(X)<~>~strong(X)))))&
((?[X]:((~patient(X)&old(X))))<=>(?[X]:((~generous(X)|~happy(X)))))&
((?[X]:((kind(X)&~patient(X))))=>(humble(paul)))&
(![X]:((calm(X)&patient(X))<=>patient(X)))&
(![X]:((~strong(X)|~wise(X))=>(~strong(X)&creative(X))))&
((?[X]:((~curious(X)<~>~quiet(X))))<=>((patient(mary)<~>kind(mary))))&
(![X]:((~generous(X)&old(X))=>(~old(X)&old(X))))&
(![X]:(~kind(X)<=>(~tall(X)|curious(X))))&
(![X]:(strong(X)<=>~brave(X)))&
(![X]:(strong(X)<=>(~calm(X)|~rich(X))))&
((?[X]:((~funny(X)&humble(X))))<=>(?[X]:((~strong(X)|~tall(X)))))&
((?[X]:((~humble(X)<~>~patient(X))))=>(?[X]:(old(X))))&
(![X]:(~brave(X)<=>~calm(X)))&
((brave(alice)|~happy(alice)))&
(curious(lucy))&
((~kind(lucy)|old(lucy)))&
(?[X]:(~strong(X)))&
((~calm(fred)<~>tall(fred)))&
(?[X]:(creative(X))) | humble(john) | [] | null | 0 |
Everyone who is both curious and not creative is not funny and vice versa.
Everyone who is not funny is not rich and vice versa.
If someone is wise or quiet then someone is either patient or not strong.
Everyone who is either tall or not strong is not creative and vice versa.
If someone is both not humble and generous then fred is both not happy and patient.
If john is both not creative and wise then someone is either not quiet or calm and vice versa.
Everyone who is either generous or tall is either not patient or brave.
If lucy is either not funny or not tall then someone is calm and vice versa.
Everyone who is both patient and kind is either generous or not humble.
If fred is either not curious or curious then someone is both patient and not tall and vice versa.
Everyone who is not tall is either happy or not curious and vice versa.
Everyone who is either not rich or strong is both wise and happy and vice versa.
If mary is humble or not curious then someone is not generous.
If someone is both humble and not kind then someone is not old or not brave and vice versa.
Everyone who is not generous is strong or not quiet.
If john is curious or not tall then someone is not wise and vice versa.
Someone is patient or happy.
Alice is both creative and brave.
Lucy is both creative and kind.
Someone is wise or patient.
Fred is both not rich and wise.
Someone is creative.
Mary is calm.
Fred is either creative or calm. | Fred is calm. | entailment | (![X]:((curious(X)&~creative(X))<=>~funny(X)))&
(![X]:(~funny(X)<=>~rich(X)))&
((?[X]:((wise(X)|quiet(X))))=>(?[X]:((patient(X)<~>~strong(X)))))&
(![X]:((tall(X)<~>~strong(X))<=>~creative(X)))&
((?[X]:((~humble(X)&generous(X))))=>((~happy(fred)&patient(fred))))&
(((~creative(john)&wise(john)))<=>(?[X]:((~quiet(X)<~>calm(X)))))&
(![X]:((generous(X)<~>tall(X))=>(~patient(X)<~>brave(X))))&
(((~funny(lucy)<~>~tall(lucy)))<=>(?[X]:(calm(X))))&
(![X]:((patient(X)&kind(X))=>(generous(X)<~>~humble(X))))&
(((~curious(fred)<~>curious(fred)))<=>(?[X]:((patient(X)&~tall(X)))))&
(![X]:(~tall(X)<=>(happy(X)<~>~curious(X))))&
(![X]:((~rich(X)<~>strong(X))<=>(wise(X)&happy(X))))&
(((humble(mary)|~curious(mary)))=>(?[X]:(~generous(X))))&
((?[X]:((humble(X)&~kind(X))))<=>(?[X]:((~old(X)|~brave(X)))))&
(![X]:(~generous(X)=>(strong(X)|~quiet(X))))&
(((curious(john)|~tall(john)))<=>(?[X]:(~wise(X))))&
(?[X]:((patient(X)|happy(X))))&
((creative(alice)&brave(alice)))&
((creative(lucy)&kind(lucy)))&
(?[X]:((wise(X)|patient(X))))&
((~rich(fred)&wise(fred)))&
(?[X]:(creative(X)))&
(calm(mary))&
((creative(fred)<~>calm(fred))) | calm(fred) | [
"p0",
"p1",
"p20",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 6251413497564149252860387
% SZS output start Proof for 6251413497564149252860387
1. ! [X0] : ((~creative(X0) & curious(X0)) <=> ~funny(X0)) [input p0]
2. ! [X0] : (~funny(X0) <=> ~rich(X0)) [input p1]
21. wise(fred) & ~rich(fred) [input p20]
24. creative(fred) <~> calm(fred) [input p23]
25. ~calm(fred) [input hypothesis]
36. ! [X0] : (((~creative(X0) & curious(X0)) | funny(X0)) & (~funny(X0) | (creative(X0) | ~curious(X0)))) [nnf transformation 1]
37. ! [X0] : (((~creative(X0) & curious(X0)) | funny(X0)) & (~funny(X0) | creative(X0) | ~curious(X0))) [flattening 36]
38. ! [X0] : ((~funny(X0) | rich(X0)) & (~rich(X0) | funny(X0))) [nnf transformation 2]
80. (~calm(fred) | ~creative(fred)) & (calm(fred) | creative(fred)) [nnf transformation 24]
83. ~creative(X0) | funny(X0) [cnf transformation 37]
85. ~funny(X0) | rich(X0) [cnf transformation 38]
145. ~rich(fred) [cnf transformation 21]
149. calm(fred) | creative(fred) [cnf transformation 80]
151. ~calm(fred) [cnf transformation 25]
331. 39 <=> creative(fred) [avatar definition]
332. creative(fred) <- (39) [avatar component clause 331]
335. 40 <=> calm(fred) [avatar definition]
339. 39 | 40 [avatar split clause 149,335,331]
340. ~40 [avatar split clause 151,335]
346. funny(fred) <- (39) [resolution 83,332]
351. rich(fred) <- (39) [resolution 85,346]
354. $false <- (39) [subsumption resolution 351,145]
355. ~39 [avatar contradiction clause 354]
356. $false [avatar sat refutation 339,340,355]
% SZS output end Proof for 6251413497564149252860387
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich then someone is not wise or not funny and vice versa.
Everyone who is not quiet is not humble and vice versa.
If mary is both not funny and strong then someone is either calm or not strong and vice versa.
Everyone who is happy or curious is not funny or happy.
If someone is old then susan is both generous and not generous.
Everyone who is not quiet is both not rich and humble and vice versa.
If someone is old then mary is either not old or not kind.
Everyone who is either not curious or not creative is both not strong and old.
If paul is curious or funny then mary is not curious or not strong.
Everyone who is wise or brave is both strong and funny.
Everyone who is both not generous and not patient is not humble and vice versa.
Everyone who is not calm is happy.
Everyone who is tall or rich is humble.
If someone is both not kind and not funny then mary is either kind or not tall.
If paul is kind or tall then paul is either tall or not wise and vice versa.
If someone is either humble or not generous then someone is either calm or not quiet.
Someone is both not calm and not kind.
Paul is both patient and not kind.
Someone is not happy or not kind.
Paul is strong.
Someone is curious or not quiet.
Someone is both strong and happy. | Susan is generous. | contradiction | ((?[X]:(~rich(X)))<=>(?[X]:((~wise(X)|~funny(X)))))&
(![X]:(~quiet(X)<=>~humble(X)))&
(((~funny(mary)&strong(mary)))<=>(?[X]:((calm(X)<~>~strong(X)))))&
(![X]:((happy(X)|curious(X))=>(~funny(X)|happy(X))))&
((?[X]:(old(X)))=>((generous(susan)&~generous(susan))))&
(![X]:(~quiet(X)<=>(~rich(X)&humble(X))))&
((?[X]:(old(X)))=>((~old(mary)<~>~kind(mary))))&
(![X]:((~curious(X)<~>~creative(X))=>(~strong(X)&old(X))))&
(((curious(paul)|funny(paul)))=>((~curious(mary)|~strong(mary))))&
(![X]:((wise(X)|brave(X))=>(strong(X)&funny(X))))&
(![X]:((~generous(X)&~patient(X))<=>~humble(X)))&
(![X]:(~calm(X)=>happy(X)))&
(![X]:((tall(X)|rich(X))=>humble(X)))&
((?[X]:((~kind(X)&~funny(X))))=>((kind(mary)<~>~tall(mary))))&
(((kind(paul)|tall(paul)))<=>((tall(paul)<~>~wise(paul))))&
((?[X]:((humble(X)<~>~generous(X))))=>(?[X]:((calm(X)<~>~quiet(X)))))&
(?[X]:((~calm(X)&~kind(X))))&
((patient(paul)&~kind(paul)))&
(?[X]:((~happy(X)|~kind(X))))&
(strong(paul))&
(?[X]:((curious(X)|~quiet(X))))&
(?[X]:((strong(X)&happy(X)))) | generous(susan) | [
"p0",
"p1",
"p2",
"p5",
"p9",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8855979590613082249426877
% SZS output start Proof for 8855979590613082249426877
1. ? [X0] : ~rich(X0) <=> ? [X0] : (~funny(X0) | ~wise(X0)) [input p0]
2. ! [X0] : (~quiet(X0) <=> ~humble(X0)) [input p1]
3. (strong(mary) & ~funny(mary)) <=> ? [X0] : (calm(X0) <~> ~strong(X0)) [input p2]
6. ! [X0] : (~quiet(X0) <=> (humble(X0) & ~rich(X0))) [input p5]
10. ! [X0] : ((brave(X0) | wise(X0)) => (funny(X0) & strong(X0))) [input p9]
16. ? [X0] : (humble(X0) <~> ~generous(X0)) => ? [X0] : (calm(X0) <~> ~quiet(X0)) [input p15]
23. generous(susan) [input hypothesis]
24. ? [X0] : ~rich(X0) <=> ? [X1] : (~funny(X1) | ~wise(X1)) [rectify 1]
25. ? [X0] : (humble(X0) <~> ~generous(X0)) => ? [X1] : (calm(X1) <~> ~quiet(X1)) [rectify 16]
26. ! [X0] : (wise(X0) => (funny(X0) & strong(X0))) [pure predicate removal 10]
34. ! [X0] : ((funny(X0) & strong(X0)) | ~wise(X0)) [ennf transformation 26]
38. ? [X1] : (calm(X1) <~> ~quiet(X1)) | ! [X0] : (humble(X0) <=> ~generous(X0)) [ennf transformation 25]
39. (? [X0] : ~rich(X0) | ! [X1] : (funny(X1) & wise(X1))) & (? [X1] : (~funny(X1) | ~wise(X1)) | ! [X0] : rich(X0)) [nnf transformation 24]
40. (? [X0] : ~rich(X0) | ! [X1] : (funny(X1) & wise(X1))) & (? [X2] : (~funny(X2) | ~wise(X2)) | ! [X3] : rich(X3)) [rectify 39]
41. ? [X0] : ~rich(X0) => ~rich(sK0) [choice axiom]
42. ? [X2] : (~funny(X2) | ~wise(X2)) => (~funny(sK1) | ~wise(sK1)) [choice axiom]
43. (~rich(sK0) | ! [X1] : (funny(X1) & wise(X1))) & ((~funny(sK1) | ~wise(sK1)) | ! [X3] : rich(X3)) [skolemisation 40,42,41]
44. ! [X0] : ((~quiet(X0) | humble(X0)) & (~humble(X0) | quiet(X0))) [nnf transformation 2]
45. ((strong(mary) & ~funny(mary)) | ! [X0] : ((calm(X0) | strong(X0)) & (~strong(X0) | ~calm(X0)))) & (? [X0] : ((strong(X0) | ~calm(X0)) & (~strong(X0) | calm(X0))) | (~strong(mary) | funny(mary))) [nnf transformation 3]
46. ((strong(mary) & ~funny(mary)) | ! [X0] : ((calm(X0) | strong(X0)) & (~strong(X0) | ~calm(X0)))) & (? [X0] : ((strong(X0) | ~calm(X0)) & (~strong(X0) | calm(X0))) | ~strong(mary) | funny(mary)) [flattening 45]
47. ((strong(mary) & ~funny(mary)) | ! [X0] : ((calm(X0) | strong(X0)) & (~strong(X0) | ~calm(X0)))) & (? [X1] : ((strong(X1) | ~calm(X1)) & (~strong(X1) | calm(X1))) | ~strong(mary) | funny(mary)) [rectify 46]
48. ? [X1] : ((strong(X1) | ~calm(X1)) & (~strong(X1) | calm(X1))) => ((strong(sK2) | ~calm(sK2)) & (~strong(sK2) | calm(sK2))) [choice axiom]
49. ((strong(mary) & ~funny(mary)) | ! [X0] : ((calm(X0) | strong(X0)) & (~strong(X0) | ~calm(X0)))) & (((strong(sK2) | ~calm(sK2)) & (~strong(sK2) | calm(sK2))) | ~strong(mary) | funny(mary)) [skolemisation 47,48]
50. ! [X0] : ((~quiet(X0) | (~humble(X0) | rich(X0))) & ((humble(X0) & ~rich(X0)) | quiet(X0))) [nnf transformation 6]
51. ! [X0] : ((~quiet(X0) | ~humble(X0) | rich(X0)) & ((humble(X0) & ~rich(X0)) | quiet(X0))) [flattening 50]
59. ? [X1] : ((quiet(X1) | ~calm(X1)) & (~quiet(X1) | calm(X1))) | ! [X0] : ((humble(X0) | generous(X0)) & (~generous(X0) | ~humble(X0))) [nnf transformation 38]
60. ? [X0] : ((quiet(X0) | ~calm(X0)) & (~quiet(X0) | calm(X0))) | ! [X1] : ((humble(X1) | generous(X1)) & (~generous(X1) | ~humble(X1))) [rectify 59]
61. ? [X0] : ((quiet(X0) | ~calm(X0)) & (~quiet(X0) | calm(X0))) => ((quiet(sK3) | ~calm(sK3)) & (~quiet(sK3) | calm(sK3))) [choice axiom]
62. ((quiet(sK3) | ~calm(sK3)) & (~quiet(sK3) | calm(sK3))) | ! [X1] : ((humble(X1) | generous(X1)) & (~generous(X1) | ~humble(X1))) [skolemisation 60,61]
72. ~rich(sK0) | wise(X1) [cnf transformation 43]
73. ~rich(sK0) | funny(X1) [cnf transformation 43]
74. ~humble(X0) | quiet(X0) [cnf transformation 44]
75. ~quiet(X0) | humble(X0) [cnf transformation 44]
78. ~funny(mary) | ~strong(X0) | ~calm(X0) [cnf transformation 49]
87. humble(X0) | quiet(X0) [cnf transformation 51]
88. ~quiet(X0) | ~humble(X0) | rich(X0) [cnf transformation 51]
97. ~wise(X0) | strong(X0) [cnf transformation 34]
113. ~quiet(sK3) | calm(sK3) | ~generous(X1) | ~humble(X1) [cnf transformation 62]
126. generous(susan) [cnf transformation 23]
130. 1 <=> ! [X1] : funny(X1) [avatar definition]
131. funny(X1) <- (1) [avatar component clause 130]
133. 2 <=> rich(sK0) [avatar definition]
135. ~rich(sK0) <- (~2) [avatar component clause 133]
136. 1 | ~2 [avatar split clause 73,133,130]
138. 3 <=> ! [X1] : wise(X1) [avatar definition]
139. wise(X1) <- (3) [avatar component clause 138]
140. 3 | ~2 [avatar split clause 72,133,138]
142. 4 <=> ! [X3] : rich(X3) [avatar definition]
143. rich(X3) <- (4) [avatar component clause 142]
162. 9 <=> ! [X0] : (~strong(X0) | ~calm(X0)) [avatar definition]
163. ~calm(X0) | ~strong(X0) <- (9) [avatar component clause 162]
166. 10 <=> funny(mary) [avatar definition]
168. ~funny(mary) <- (~10) [avatar component clause 166]
170. 9 | ~10 [avatar split clause 78,166,162]
185. 14 <=> generous(susan) [avatar definition]
186. generous(susan) <- (14) [avatar component clause 185]
190. ~humble(X0) | rich(X0) [subsumption resolution 88,74]
191. humble(X0) [subsumption resolution 87,75]
244. 25 <=> ! [X1] : ~generous(X1) [avatar definition]
245. ~generous(X1) <- (25) [avatar component clause 244]
247. 26 <=> calm(sK3) [avatar definition]
248. calm(sK3) <- (26) [avatar component clause 247]
251. 27 <=> quiet(sK3) [avatar definition]
252. ~quiet(sK3) <- (~27) [avatar component clause 251]
255. ~quiet(sK3) | calm(sK3) | ~generous(X1) [subsumption resolution 113,191]
256. 25 | 26 | ~27 [avatar split clause 255,251,247,244]
276. 14 [avatar split clause 126,185]
277. quiet(X0) [resolution 74,191]
278. $false <- (~27) [resolution 277,252]
282. 27 [avatar contradiction clause 278]
283. $false <- (14, 25) [resolution 245,186]
284. ~14 | ~25 [avatar contradiction clause 283]
289. rich(X0) [resolution 190,191]
290. 4 [avatar split clause 289,142]
291. $false <- (~2, 4) [resolution 143,135]
293. 2 | ~4 [avatar contradiction clause 291]
294. $false <- (1, ~10) [resolution 131,168]
295. ~1 | 10 [avatar contradiction clause 294]
298. strong(X1) <- (3) [resolution 139,97]
302. ~strong(sK3) <- (9, 26) [resolution 163,248]
305. $false <- (3, 9, 26) [subsumption resolution 302,298]
306. ~3 | ~9 | ~26 [avatar contradiction clause 305]
309. $false [avatar sat refutation 136,140,170,256,276,282,284,290,293,295,306]
% SZS output end Proof for 8855979590613082249426877
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not calm and funny then someone is either strong or tall. If alice is not funny or not quiet then mary is either tall or strong. If someone is brave then paul is either rich or strong and vice versa. If someone is either funny or not quiet then john is either not humble or not generous. Everyone who is not wise or strong is both calm and generous. Everyone who is either not calm or quiet is both old and not humble. Everyone who is either not kind or tall is either old or not wise. Everyone who is not strong or patient is either not old or kind. Everyone who is not funny or not tall is both tall and not brave and vice versa. If paul is brave or patient then someone is either strong or not happy and vice versa. Everyone who is both tall and kind is either wise or old and vice versa. If someone is old then someone is both not calm and not tall and vice versa. If someone is both creative and not funny then paul is both generous and funny. Everyone who is both calm and not kind is either not humble or not funny and vice versa. Everyone who is both not humble and happy is not old or generous and vice versa. If paul is both not quiet and happy then alice is not rich and vice versa. Paul is either not funny or happy. Someone is both curious and not quiet. Alice is not funny or not creative. Someone is not kind or patient. | Paul is not funny. | contradiction | ((?[X]:((~calm(X)&funny(X))))=>(?[X]:((strong(X)<~>tall(X)))))&
(((~funny(alice)|~quiet(alice)))=>((tall(mary)<~>strong(mary))))&
((?[X]:(brave(X)))<=>((rich(paul)<~>strong(paul))))&
((?[X]:((funny(X)<~>~quiet(X))))=>((~humble(john)<~>~generous(john))))&
(![X]:((~wise(X)|strong(X))=>(calm(X)&generous(X))))&
(![X]:((~calm(X)<~>quiet(X))=>(old(X)&~humble(X))))&
(![X]:((~kind(X)<~>tall(X))=>(old(X)<~>~wise(X))))&
(![X]:((~strong(X)|patient(X))=>(~old(X)<~>kind(X))))&
(![X]:((~funny(X)|~tall(X))<=>(tall(X)&~brave(X))))&
(((brave(paul)|patient(paul)))<=>(?[X]:((strong(X)<~>~happy(X)))))&
(![X]:((tall(X)&kind(X))<=>(wise(X)<~>old(X))))&
((?[X]:(old(X)))<=>(?[X]:((~calm(X)&~tall(X)))))&
((?[X]:((creative(X)&~funny(X))))=>((generous(paul)&funny(paul))))&
(![X]:((calm(X)&~kind(X))<=>(~humble(X)<~>~funny(X))))&
(![X]:((~humble(X)&happy(X))<=>(~old(X)|generous(X))))&
(((~quiet(paul)&happy(paul)))<=>(~rich(alice)))&
((~funny(paul)<~>happy(paul)))&
(?[X]:((curious(X)&~quiet(X))))&
((~funny(alice)|~creative(alice)))&
(?[X]:((~kind(X)|patient(X)))) | ~funny(paul) | [
"p8",
"p11",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 607107280488577085674076
% SZS output start Proof for 607107280488577085674076
9. ! [X0] : ((~tall(X0) | ~funny(X0)) <=> (~brave(X0) & tall(X0))) [input p8]
12. ? [X0] : old(X0) <=> ? [X0] : (~tall(X0) & ~calm(X0)) [input p11]
15. ! [X0] : ((happy(X0) & ~humble(X0)) <=> (generous(X0) | ~old(X0))) [input p14]
17. ~funny(paul) <~> happy(paul) [input p16]
21. ~funny(paul) [input hypothesis]
23. ? [X0] : old(X0) <=> ? [X1] : (~tall(X1) & ~calm(X1)) [rectify 12]
47. ! [X0] : (((~tall(X0) | ~funny(X0)) | (brave(X0) | ~tall(X0))) & ((~brave(X0) & tall(X0)) | (tall(X0) & funny(X0)))) [nnf transformation 9]
48. ! [X0] : ((~tall(X0) | ~funny(X0) | brave(X0) | ~tall(X0)) & ((~brave(X0) & tall(X0)) | (tall(X0) & funny(X0)))) [flattening 47]
56. (? [X0] : old(X0) | ! [X1] : (tall(X1) | calm(X1))) & (? [X1] : (~tall(X1) & ~calm(X1)) | ! [X0] : ~old(X0)) [nnf transformation 23]
57. (? [X0] : old(X0) | ! [X1] : (tall(X1) | calm(X1))) & (? [X2] : (~tall(X2) & ~calm(X2)) | ! [X3] : ~old(X3)) [rectify 56]
58. ? [X0] : old(X0) => old(sK3) [choice axiom]
59. ? [X2] : (~tall(X2) & ~calm(X2)) => (~tall(sK4) & ~calm(sK4)) [choice axiom]
60. (old(sK3) | ! [X1] : (tall(X1) | calm(X1))) & ((~tall(sK4) & ~calm(sK4)) | ! [X3] : ~old(X3)) [skolemisation 57,59,58]
63. ! [X0] : (((happy(X0) & ~humble(X0)) | (~generous(X0) & old(X0))) & ((generous(X0) | ~old(X0)) | (~happy(X0) | humble(X0)))) [nnf transformation 15]
64. ! [X0] : (((happy(X0) & ~humble(X0)) | (~generous(X0) & old(X0))) & (generous(X0) | ~old(X0) | ~happy(X0) | humble(X0))) [flattening 63]
67. (~happy(paul) | funny(paul)) & (happy(paul) | ~funny(paul)) [nnf transformation 17]
103. tall(X0) | tall(X0) [cnf transformation 48]
120. ~tall(sK4) | ~old(X3) [cnf transformation 60]
131. happy(X0) | old(X0) [cnf transformation 64]
137. ~happy(paul) | funny(paul) [cnf transformation 67]
140. ~funny(paul) [cnf transformation 21]
141. tall(X0) [duplicate literal removal 103]
243. ~old(X3) [subsumption resolution 120,141]
244. happy(X0) [subsumption resolution 131,243]
257. funny(paul) [subsumption resolution 137,244]
267. $false [subsumption resolution 140,257]
% SZS output end Proof for 607107280488577085674076
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not calm or quiet is both old and not brave.
If someone is both strong and not humble then paul is both kind and not humble and vice versa.
If someone is either creative or not tall then someone is either humble or rich and vice versa.
Everyone who is both not patient and not quiet is not strong or not kind.
If mary is either wise or not generous then mary is either quiet or not happy.
Everyone who is creative is both strong and wise and vice versa.
Everyone who is not generous is kind.
Everyone who is both calm and not brave is both not wise and funny and vice versa.
Everyone who is either kind or calm is not patient or humble.
Everyone who is either brave or not humble is not creative.
If paul is both not quiet and quiet then someone is not humble and vice versa.
If mary is patient then fred is not quiet or not calm.
If someone is creative then someone is not rich and vice versa.
Everyone who is not rich or old is not happy or curious and vice versa.
If fred is not kind or not calm then fred is either rich or not calm.
Everyone who is not calm or not kind is not kind and vice versa.
John is not generous or rich.
Someone is either not humble or curious.
Someone is either not old or not patient.
Someone is both not patient and strong.
Someone is funny.
Someone is both patient and brave.
Someone is humble. | John is rich. | neutral | (![X]:((~calm(X)<~>quiet(X))=>(old(X)&~brave(X))))&
((?[X]:((strong(X)&~humble(X))))<=>((kind(paul)&~humble(paul))))&
((?[X]:((creative(X)<~>~tall(X))))<=>(?[X]:((humble(X)<~>rich(X)))))&
(![X]:((~patient(X)&~quiet(X))=>(~strong(X)|~kind(X))))&
(((wise(mary)<~>~generous(mary)))=>((quiet(mary)<~>~happy(mary))))&
(![X]:(creative(X)<=>(strong(X)&wise(X))))&
(![X]:(~generous(X)=>kind(X)))&
(![X]:((calm(X)&~brave(X))<=>(~wise(X)&funny(X))))&
(![X]:((kind(X)<~>calm(X))=>(~patient(X)|humble(X))))&
(![X]:((brave(X)<~>~humble(X))=>~creative(X)))&
(((~quiet(paul)&quiet(paul)))<=>(?[X]:(~humble(X))))&
((patient(mary))=>((~quiet(fred)|~calm(fred))))&
((?[X]:(creative(X)))<=>(?[X]:(~rich(X))))&
(![X]:((~rich(X)|old(X))<=>(~happy(X)|curious(X))))&
(((~kind(fred)|~calm(fred)))=>((rich(fred)<~>~calm(fred))))&
(![X]:((~calm(X)|~kind(X))<=>~kind(X)))&
((~generous(john)|rich(john)))&
(?[X]:((~humble(X)<~>curious(X))))&
(?[X]:((~old(X)<~>~patient(X))))&
(?[X]:((~patient(X)&strong(X))))&
(?[X]:(funny(X)))&
(?[X]:((patient(X)&brave(X))))&
(?[X]:(humble(X))) | rich(john) | [] | null | 0 |
Everyone who is either not wise or calm is both not brave and not funny.
Everyone who is both calm and not calm is creative or not happy.
Everyone who is old is not patient.
Everyone who is either not tall or tall is not kind.
Everyone who is not strong is generous.
If someone is either quiet or kind then someone is wise and vice versa.
If someone is rich then fred is both quiet and not tall and vice versa.
Everyone who is either not tall or not creative is both not calm and strong.
Everyone who is both not patient and brave is not strong.
Everyone who is rich is brave or rich and vice versa.
If paul is both tall and not humble then alice is rich and vice versa.
Everyone who is not tall or not funny is both happy and not happy.
If someone is tall then lucy is not generous or not patient and vice versa.
If someone is not kind then someone is quiet or generous.
If fred is brave or not kind then mary is humble.
If someone is either not strong or strong then someone is not tall or strong and vice versa.
Paul is either not happy or tall.
Paul is not kind.
Someone is either wise or not generous.
Alice is not strong or calm.
Alice is either quiet or not wise.
Paul is not calm.
Lucy is both not curious and not old. | Fred is not kind. | entailment | (![X]:((~wise(X)<~>calm(X))=>(~brave(X)&~funny(X))))&
(![X]:((calm(X)&~calm(X))=>(creative(X)|~happy(X))))&
(![X]:(old(X)=>~patient(X)))&
(![X]:((~tall(X)<~>tall(X))=>~kind(X)))&
(![X]:(~strong(X)=>generous(X)))&
((?[X]:((quiet(X)<~>kind(X))))<=>(?[X]:(wise(X))))&
((?[X]:(rich(X)))<=>((quiet(fred)&~tall(fred))))&
(![X]:((~tall(X)<~>~creative(X))=>(~calm(X)&strong(X))))&
(![X]:((~patient(X)&brave(X))=>~strong(X)))&
(![X]:(rich(X)<=>(brave(X)|rich(X))))&
(((tall(paul)&~humble(paul)))<=>(rich(alice)))&
(![X]:((~tall(X)|~funny(X))=>(happy(X)&~happy(X))))&
((?[X]:(tall(X)))<=>((~generous(lucy)|~patient(lucy))))&
((?[X]:(~kind(X)))=>(?[X]:((quiet(X)|generous(X)))))&
(((brave(fred)|~kind(fred)))=>(humble(mary)))&
((?[X]:((~strong(X)<~>strong(X))))<=>(?[X]:((~tall(X)|strong(X)))))&
((~happy(paul)<~>tall(paul)))&
(~kind(paul))&
(?[X]:((wise(X)<~>~generous(X))))&
((~strong(alice)|calm(alice)))&
((quiet(alice)<~>~wise(alice)))&
(~calm(paul))&
((~curious(lucy)&~old(lucy))) | ~kind(fred) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 5840770648657699779226222
% SZS output start Proof for 5840770648657699779226222
4. ! [X0] : ((~tall(X0) <~> tall(X0)) => ~kind(X0)) [input p3]
24. kind(fred) [input hypothesis]
34. ! [X0] : (~kind(X0) | (~tall(X0) <=> tall(X0))) [ennf transformation 4]
43. ! [X0] : (~kind(X0) | ((~tall(X0) | ~tall(X0)) & (tall(X0) | tall(X0)))) [nnf transformation 34]
82. ~kind(X0) | tall(X0) | tall(X0) [cnf transformation 43]
83. ~kind(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 43]
128. kind(fred) [cnf transformation 24]
131. ~kind(X0) | tall(X0) [duplicate literal removal 82]
132. ~kind(X0) | ~tall(X0) [duplicate literal removal 83]
133. ~kind(X0) [subsumption resolution 131,132]
252. $false [subsumption resolution 128,133]
% SZS output end Proof for 5840770648657699779226222
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy is both humble and funny.
If someone is not wise then someone is either curious or not old.
Everyone who is either not wise or not rich is either strong or happy and vice versa.
If someone is both creative and not funny then paul is either wise or not quiet.
Everyone who is either not curious or not old is not quiet and vice versa.
Everyone who is humble is either brave or generous and vice versa.
Everyone who is not curious or not old is either wise or kind and vice versa.
Everyone who is brave or not wise is wise.
Everyone who is funny is both not quiet and not strong.
Everyone who is rich is both not curious and not wise and vice versa.
If someone is not calm or not humble then alice is both not calm and not generous and vice versa.
Everyone who is either not old or strong is both quiet and tall.
Everyone who is tall is both rich and creative and vice versa.
Everyone who is either rich or kind is either not patient or not curious and vice versa.
Everyone who is not rich or not tall is not wise or not happy and vice versa.
If fred is either not humble or wise then alice is not curious and vice versa.
Paul is not brave or not generous.
Someone is both patient and not kind.
Someone is not creative or not funny.
Susan is either not tall or humble.
Paul is not calm or not happy.
Someone is not quiet or funny. | Fred is not kind. | entailment | (![X]:(happy(X)=>(humble(X)&funny(X))))&
((?[X]:(~wise(X)))=>(?[X]:((curious(X)<~>~old(X)))))&
(![X]:((~wise(X)<~>~rich(X))<=>(strong(X)<~>happy(X))))&
((?[X]:((creative(X)&~funny(X))))=>((wise(paul)<~>~quiet(paul))))&
(![X]:((~curious(X)<~>~old(X))<=>~quiet(X)))&
(![X]:(humble(X)<=>(brave(X)<~>generous(X))))&
(![X]:((~curious(X)|~old(X))<=>(wise(X)<~>kind(X))))&
(![X]:((brave(X)|~wise(X))=>wise(X)))&
(![X]:(funny(X)=>(~quiet(X)&~strong(X))))&
(![X]:(rich(X)<=>(~curious(X)&~wise(X))))&
((?[X]:((~calm(X)|~humble(X))))<=>((~calm(alice)&~generous(alice))))&
(![X]:((~old(X)<~>strong(X))=>(quiet(X)&tall(X))))&
(![X]:(tall(X)<=>(rich(X)&creative(X))))&
(![X]:((rich(X)<~>kind(X))<=>(~patient(X)<~>~curious(X))))&
(![X]:((~rich(X)|~tall(X))<=>(~wise(X)|~happy(X))))&
(((~humble(fred)<~>wise(fred)))<=>(~curious(alice)))&
((~brave(paul)|~generous(paul)))&
(?[X]:((patient(X)&~kind(X))))&
(?[X]:((~creative(X)|~funny(X))))&
((~tall(susan)<~>humble(susan)))&
((~calm(paul)|~happy(paul)))&
(?[X]:((~quiet(X)|funny(X)))) | ~kind(fred) | [
"p2",
"p6",
"p7",
"p9",
"p11",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5716288887780609008867280
% SZS output start Proof for 5716288887780609008867280
3. ! [X0] : ((~wise(X0) <~> ~rich(X0)) <=> (strong(X0) <~> happy(X0))) [input p2]
7. ! [X0] : ((~old(X0) | ~curious(X0)) <=> (wise(X0) <~> kind(X0))) [input p6]
8. ! [X0] : ((~wise(X0) | brave(X0)) => wise(X0)) [input p7]
10. ! [X0] : (rich(X0) <=> (~wise(X0) & ~curious(X0))) [input p9]
12. ! [X0] : ((~old(X0) <~> strong(X0)) => (tall(X0) & quiet(X0))) [input p11]
13. ! [X0] : (tall(X0) <=> (creative(X0) & rich(X0))) [input p12]
15. ! [X0] : ((~tall(X0) | ~rich(X0)) <=> (~happy(X0) | ~wise(X0))) [input p14]
23. kind(fred) [input hypothesis]
28. ! [X0] : (wise(X0) | (wise(X0) & ~brave(X0))) [ennf transformation 8]
30. ! [X0] : ((tall(X0) & quiet(X0)) | (~old(X0) <=> strong(X0))) [ennf transformation 12]
35. ! [X0] : ((((rich(X0) | wise(X0)) & (~rich(X0) | ~wise(X0))) | ((strong(X0) | ~happy(X0)) & (happy(X0) | ~strong(X0)))) & (((~happy(X0) | ~strong(X0)) & (happy(X0) | strong(X0))) | ((~wise(X0) | rich(X0)) & (~rich(X0) | wise(X0))))) [nnf transformation 3]
39. ! [X0] : (((~old(X0) | ~curious(X0)) | ((wise(X0) | ~kind(X0)) & (kind(X0) | ~wise(X0)))) & (((~kind(X0) | ~wise(X0)) & (kind(X0) | wise(X0))) | (old(X0) & curious(X0)))) [nnf transformation 7]
40. ! [X0] : ((~old(X0) | ~curious(X0) | ((wise(X0) | ~kind(X0)) & (kind(X0) | ~wise(X0)))) & (((~kind(X0) | ~wise(X0)) & (kind(X0) | wise(X0))) | (old(X0) & curious(X0)))) [flattening 39]
41. ! [X0] : ((rich(X0) | (wise(X0) | curious(X0))) & ((~wise(X0) & ~curious(X0)) | ~rich(X0))) [nnf transformation 10]
42. ! [X0] : ((rich(X0) | wise(X0) | curious(X0)) & ((~wise(X0) & ~curious(X0)) | ~rich(X0))) [flattening 41]
48. ! [X0] : ((tall(X0) & quiet(X0)) | ((~old(X0) | ~strong(X0)) & (strong(X0) | old(X0)))) [nnf transformation 30]
49. ! [X0] : ((tall(X0) | (~creative(X0) | ~rich(X0))) & ((creative(X0) & rich(X0)) | ~tall(X0))) [nnf transformation 13]
50. ! [X0] : ((tall(X0) | ~creative(X0) | ~rich(X0)) & ((creative(X0) & rich(X0)) | ~tall(X0))) [flattening 49]
52. ! [X0] : (((~tall(X0) | ~rich(X0)) | (happy(X0) & wise(X0))) & ((~happy(X0) | ~wise(X0)) | (tall(X0) & rich(X0)))) [nnf transformation 15]
53. ! [X0] : ((~tall(X0) | ~rich(X0) | (happy(X0) & wise(X0))) & (~happy(X0) | ~wise(X0) | (tall(X0) & rich(X0)))) [flattening 52]
67. ~wise(X0) | strong(X0) | happy(X0) | rich(X0) [cnf transformation 35]
86. ~kind(X0) | ~wise(X0) | curious(X0) [cnf transformation 40]
87. ~kind(X0) | ~wise(X0) | old(X0) [cnf transformation 40]
91. wise(X0) | wise(X0) [cnf transformation 28]
94. ~rich(X0) | ~curious(X0) [cnf transformation 42]
95. ~rich(X0) | ~wise(X0) [cnf transformation 42]
105. ~strong(X0) | ~old(X0) | tall(X0) [cnf transformation 48]
106. ~tall(X0) | rich(X0) [cnf transformation 50]
118. ~happy(X0) | ~wise(X0) | tall(X0) [cnf transformation 53]
119. ~tall(X0) | ~rich(X0) | wise(X0) [cnf transformation 53]
133. kind(fred) [cnf transformation 23]
134. wise(X0) [duplicate literal removal 91]
136. 1 <=> ! [X1] : wise(X1) [avatar definition]
137. wise(X1) <- (1) [avatar component clause 136]
161. 1 [avatar split clause 134,136]
194. ~tall(X0) | ~rich(X0) [subsumption resolution 119,95]
195. ~tall(X0) [subsumption resolution 194,106]
196. ~wise(X0) | ~happy(X0) [subsumption resolution 118,195]
246. ~happy(X0) <- (1) [resolution 196,137]
282. ~wise(fred) | curious(fred) [resolution 86,133]
286. curious(fred) <- (1) [subsumption resolution 282,137]
287. ~wise(fred) | old(fred) [resolution 87,133]
291. old(fred) <- (1) [subsumption resolution 287,137]
351. strong(X0) | happy(X0) | rich(X0) <- (1) [resolution 67,137]
352. strong(X0) | rich(X0) <- (1) [subsumption resolution 351,246]
353. rich(X0) | ~old(X0) | tall(X0) <- (1) [resolution 352,105]
356. ~old(X0) | rich(X0) <- (1) [subsumption resolution 353,195]
363. rich(fred) <- (1) [resolution 356,291]
392. ~curious(fred) <- (1) [resolution 363,94]
395. $false <- (1) [subsumption resolution 392,286]
396. ~1 [avatar contradiction clause 395]
397. $false [avatar sat refutation 161,396]
% SZS output end Proof for 5716288887780609008867280
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not old and rich is not old or creative.
If someone is both generous and quiet then someone is either calm or wise.
If someone is generous then alice is either generous or not calm.
If john is not funny then paul is both not old and creative.
If someone is either not funny or patient then paul is not funny.
If someone is creative or not curious then paul is not creative or not tall.
Everyone who is not tall is quiet or not calm.
If someone is not strong or humble then someone is happy or patient.
If someone is both not humble and not funny then paul is either not quiet or not patient and vice versa.
If someone is humble or not kind then mary is either not strong or patient and vice versa.
If mary is either not happy or wise then someone is both not humble and happy.
Everyone who is either humble or kind is either not generous or quiet and vice versa.
If susan is not humble or happy then someone is both rich and not quiet.
Everyone who is not tall is both humble and funny and vice versa.
Everyone who is either kind or generous is not old.
Everyone who is not tall is either kind or not humble and vice versa.
Someone is humble.
Someone is either wise or kind.
John is either not quiet or not tall.
Someone is old or calm.
Someone is either not brave or curious.
Paul is creative.
Susan is either not kind or not strong.
Someone is not tall or generous. | Paul is creative. | entailment | (![X]:((~old(X)&rich(X))=>(~old(X)|creative(X))))&
((?[X]:((generous(X)&quiet(X))))=>(?[X]:((calm(X)<~>wise(X)))))&
((?[X]:(generous(X)))=>((generous(alice)<~>~calm(alice))))&
((~funny(john))=>((~old(paul)&creative(paul))))&
((?[X]:((~funny(X)<~>patient(X))))=>(~funny(paul)))&
((?[X]:((creative(X)|~curious(X))))=>((~creative(paul)|~tall(paul))))&
(![X]:(~tall(X)=>(quiet(X)|~calm(X))))&
((?[X]:((~strong(X)|humble(X))))=>(?[X]:((happy(X)|patient(X)))))&
((?[X]:((~humble(X)&~funny(X))))<=>((~quiet(paul)<~>~patient(paul))))&
((?[X]:((humble(X)|~kind(X))))<=>((~strong(mary)<~>patient(mary))))&
(((~happy(mary)<~>wise(mary)))=>(?[X]:((~humble(X)&happy(X)))))&
(![X]:((humble(X)<~>kind(X))<=>(~generous(X)<~>quiet(X))))&
(((~humble(susan)|happy(susan)))=>(?[X]:((rich(X)&~quiet(X)))))&
(![X]:(~tall(X)<=>(humble(X)&funny(X))))&
(![X]:((kind(X)<~>generous(X))=>~old(X)))&
(![X]:(~tall(X)<=>(kind(X)<~>~humble(X))))&
(?[X]:(humble(X)))&
(?[X]:((wise(X)<~>kind(X))))&
((~quiet(john)<~>~tall(john)))&
(?[X]:((old(X)|calm(X))))&
(?[X]:((~brave(X)<~>curious(X))))&
(creative(paul))&
((~kind(susan)<~>~strong(susan)))&
(?[X]:((~tall(X)|generous(X)))) | creative(paul) | [
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 6384485380730457592694144
% SZS output start Proof for 6384485380730457592694144
22. creative(paul) [input p21]
25. ~creative(paul) [input hypothesis]
142. creative(paul) [cnf transformation 22]
146. ~creative(paul) [cnf transformation 25]
178. 8 <=> creative(paul) [avatar definition]
358. 8 [avatar split clause 142,178]
378. ~8 [avatar split clause 146,178]
379. $false [avatar sat refutation 358,378]
% SZS output end Proof for 6384485380730457592694144
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not funny and not calm is happy and vice versa. If someone is kind then alice is not happy. Everyone who is either not strong or not patient is both funny and not strong. Everyone who is either humble or old is creative or rich and vice versa. Everyone who is happy is rich or not creative and vice versa. Everyone who is not old is either not strong or rich. If paul is funny or not strong then alice is both happy and patient. If alice is either not kind or not wise then susan is either calm or not humble. If someone is either not rich or not funny then alice is not quiet and vice versa. Everyone who is funny is both wise and not rich and vice versa. If someone is humble or strong then someone is both funny and kind. Everyone who is either humble or calm is either not curious or creative. Everyone who is old is creative. If someone is both humble and creative then someone is both generous and not curious. If someone is both not funny and humble then susan is not strong or creative and vice versa. Everyone who is both not old and kind is creative or not strong and vice versa. John is wise. Someone is both wise and calm. Someone is strong or quiet. Someone is either creative or not calm. Someone is both tall and not funny. John is either patient or not brave. Someone is not happy. Someone is wise or curious. | Paul is funny. | contradiction | (![X]:((~funny(X)&~calm(X))<=>happy(X)))&
((?[X]:(kind(X)))=>(~happy(alice)))&
(![X]:((~strong(X)<~>~patient(X))=>(funny(X)&~strong(X))))&
(![X]:((humble(X)<~>old(X))<=>(creative(X)|rich(X))))&
(![X]:(happy(X)<=>(rich(X)|~creative(X))))&
(![X]:(~old(X)=>(~strong(X)<~>rich(X))))&
(((funny(paul)|~strong(paul)))=>((happy(alice)&patient(alice))))&
(((~kind(alice)<~>~wise(alice)))=>((calm(susan)<~>~humble(susan))))&
((?[X]:((~rich(X)<~>~funny(X))))<=>(~quiet(alice)))&
(![X]:(funny(X)<=>(wise(X)&~rich(X))))&
((?[X]:((humble(X)|strong(X))))=>(?[X]:((funny(X)&kind(X)))))&
(![X]:((humble(X)<~>calm(X))=>(~curious(X)<~>creative(X))))&
(![X]:(old(X)=>creative(X)))&
((?[X]:((humble(X)&creative(X))))=>(?[X]:((generous(X)&~curious(X)))))&
((?[X]:((~funny(X)&humble(X))))<=>((~strong(susan)|creative(susan))))&
(![X]:((~old(X)&kind(X))<=>(creative(X)|~strong(X))))&
(wise(john))&
(?[X]:((wise(X)&calm(X))))&
(?[X]:((strong(X)|quiet(X))))&
(?[X]:((creative(X)<~>~calm(X))))&
(?[X]:((tall(X)&~funny(X))))&
((patient(john)<~>~brave(john)))&
(?[X]:(~happy(X)))&
(?[X]:((wise(X)|curious(X)))) | funny(paul) | [
"p1",
"p6",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6194257989178742160392517
% SZS output start Proof for 6194257989178742160392517
2. ? [X0] : kind(X0) => ~happy(alice) [input p1]
7. (~strong(paul) | funny(paul)) => (patient(alice) & happy(alice)) [input p6]
11. ? [X0] : (strong(X0) | humble(X0)) => ? [X0] : (kind(X0) & funny(X0)) [input p10]
15. ? [X0] : (humble(X0) & ~funny(X0)) <=> (creative(susan) | ~strong(susan)) [input p14]
25. funny(paul) [input hypothesis]
26. ? [X0] : (strong(X0) | humble(X0)) => ? [X1] : (kind(X1) & funny(X1)) [rectify 11]
30. ~happy(alice) | ! [X0] : ~kind(X0) [ennf transformation 2]
33. (patient(alice) & happy(alice)) | (strong(paul) & ~funny(paul)) [ennf transformation 7]
35. ? [X1] : (kind(X1) & funny(X1)) | ! [X0] : (~strong(X0) & ~humble(X0)) [ennf transformation 26]
54. ? [X0] : (kind(X0) & funny(X0)) | ! [X1] : (~strong(X1) & ~humble(X1)) [rectify 35]
55. ? [X0] : (kind(X0) & funny(X0)) => (kind(sK1) & funny(sK1)) [choice axiom]
56. (kind(sK1) & funny(sK1)) | ! [X1] : (~strong(X1) & ~humble(X1)) [skolemisation 54,55]
61. (? [X0] : (humble(X0) & ~funny(X0)) | (~creative(susan) & strong(susan))) & ((creative(susan) | ~strong(susan)) | ! [X0] : (~humble(X0) | funny(X0))) [nnf transformation 15]
62. (? [X0] : (humble(X0) & ~funny(X0)) | (~creative(susan) & strong(susan))) & (creative(susan) | ~strong(susan) | ! [X0] : (~humble(X0) | funny(X0))) [flattening 61]
63. (? [X0] : (humble(X0) & ~funny(X0)) | (~creative(susan) & strong(susan))) & (creative(susan) | ~strong(susan) | ! [X1] : (~humble(X1) | funny(X1))) [rectify 62]
64. ? [X0] : (humble(X0) & ~funny(X0)) => (humble(sK3) & ~funny(sK3)) [choice axiom]
65. ((humble(sK3) & ~funny(sK3)) | (~creative(susan) & strong(susan))) & (creative(susan) | ~strong(susan) | ! [X1] : (~humble(X1) | funny(X1))) [skolemisation 63,64]
85. ~happy(alice) | ~kind(X0) [cnf transformation 30]
101. happy(alice) | ~funny(paul) [cnf transformation 33]
118. kind(sK1) | ~humble(X1) [cnf transformation 56]
119. kind(sK1) | ~strong(X1) [cnf transformation 56]
129. humble(sK3) | strong(susan) [cnf transformation 65]
147. funny(paul) [cnf transformation 25]
150. 1 <=> ! [X0] : ~kind(X0) [avatar definition]
151. ~kind(X0) <- (1) [avatar component clause 150]
153. 2 <=> happy(alice) [avatar definition]
156. 1 | ~2 [avatar split clause 85,153,150]
167. 5 <=> funny(paul) [avatar definition]
172. ~5 | 2 [avatar split clause 101,153,167]
216. 15 <=> ! [X1] : ~strong(X1) [avatar definition]
217. ~strong(X1) <- (15) [avatar component clause 216]
219. 16 <=> kind(sK1) [avatar definition]
221. kind(sK1) <- (16) [avatar component clause 219]
222. 15 | 16 [avatar split clause 119,219,216]
224. 17 <=> ! [X1] : ~humble(X1) [avatar definition]
225. ~humble(X1) <- (17) [avatar component clause 224]
226. 17 | 16 [avatar split clause 118,219,224]
246. 22 <=> humble(sK3) [avatar definition]
248. humble(sK3) <- (22) [avatar component clause 246]
251. 23 <=> strong(susan) [avatar definition]
253. strong(susan) <- (23) [avatar component clause 251]
254. 23 | 22 [avatar split clause 129,246,251]
305. 5 [avatar split clause 147,167]
306. $false <- (17, 22) [resolution 248,225]
307. ~17 | ~22 [avatar contradiction clause 306]
308. $false <- (1, 16) [subsumption resolution 221,151]
309. ~1 | ~16 [avatar contradiction clause 308]
310. $false <- (15, 23) [subsumption resolution 253,217]
311. ~15 | ~23 [avatar contradiction clause 310]
312. $false [avatar sat refutation 156,172,222,226,254,305,307,309,311]
% SZS output end Proof for 6194257989178742160392517
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not humble or not brave then fred is brave and vice versa.
If someone is patient or not generous then fred is happy and vice versa.
Everyone who is not patient is either not strong or funny.
Everyone who is both not kind and tall is not calm or rich.
If someone is not humble then someone is kind or not tall.
Everyone who is brave is either not generous or humble and vice versa.
Everyone who is either not calm or not curious is generous or not strong and vice versa.
Everyone who is either quiet or curious is both curious and happy and vice versa.
Everyone who is creative or not wise is brave.
Everyone who is not strong or not generous is strong and vice versa.
If someone is both not wise and not generous then susan is either not rich or not kind and vice versa.
Everyone who is patient is not generous or not wise.
If someone is both generous and not funny then someone is curious and vice versa.
If someone is both not old and curious then fred is either not kind or quiet.
If paul is both not generous and not humble then john is funny.
Everyone who is either not humble or not wise is either not old or generous and vice versa.
Alice is strong or curious.
Susan is not happy or happy.
Someone is not patient or not generous.
Lucy is not curious or not calm.
Someone is both not calm and creative.
Susan is not kind or curious. | Paul is not calm. | entailment | ((?[X]:((~humble(X)<~>~brave(X))))<=>(brave(fred)))&
((?[X]:((patient(X)|~generous(X))))<=>(happy(fred)))&
(![X]:(~patient(X)=>(~strong(X)<~>funny(X))))&
(![X]:((~kind(X)&tall(X))=>(~calm(X)|rich(X))))&
((?[X]:(~humble(X)))=>(?[X]:((kind(X)|~tall(X)))))&
(![X]:(brave(X)<=>(~generous(X)<~>humble(X))))&
(![X]:((~calm(X)<~>~curious(X))<=>(generous(X)|~strong(X))))&
(![X]:((quiet(X)<~>curious(X))<=>(curious(X)&happy(X))))&
(![X]:((creative(X)|~wise(X))=>brave(X)))&
(![X]:((~strong(X)|~generous(X))<=>strong(X)))&
((?[X]:((~wise(X)&~generous(X))))<=>((~rich(susan)<~>~kind(susan))))&
(![X]:(patient(X)=>(~generous(X)|~wise(X))))&
((?[X]:((generous(X)&~funny(X))))<=>(?[X]:(curious(X))))&
((?[X]:((~old(X)&curious(X))))=>((~kind(fred)<~>quiet(fred))))&
(((~generous(paul)&~humble(paul)))=>(funny(john)))&
(![X]:((~humble(X)<~>~wise(X))<=>(~old(X)<~>generous(X))))&
((strong(alice)|curious(alice)))&
((~happy(susan)|happy(susan)))&
(?[X]:((~patient(X)|~generous(X))))&
((~curious(lucy)|~calm(lucy)))&
(?[X]:((~calm(X)&creative(X))))&
((~kind(susan)|curious(susan))) | ~calm(paul) | [
"p6",
"p9",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 8961433977348758982649333
% SZS output start Proof for 8961433977348758982649333
7. ! [X0] : ((~calm(X0) <~> ~curious(X0)) <=> (~strong(X0) | generous(X0))) [input p6]
10. ! [X0] : ((~generous(X0) | ~strong(X0)) <=> strong(X0)) [input p9]
13. ? [X0] : (~funny(X0) & generous(X0)) <=> ? [X0] : curious(X0) [input p12]
23. calm(paul) [input hypothesis]
25. ? [X0] : (~funny(X0) & generous(X0)) <=> ? [X1] : curious(X1) [rectify 13]
45. ! [X0] : ((((curious(X0) | calm(X0)) & (~curious(X0) | ~calm(X0))) | (strong(X0) & ~generous(X0))) & ((~strong(X0) | generous(X0)) | ((~calm(X0) | curious(X0)) & (~curious(X0) | calm(X0))))) [nnf transformation 7]
46. ! [X0] : ((((curious(X0) | calm(X0)) & (~curious(X0) | ~calm(X0))) | (strong(X0) & ~generous(X0))) & (~strong(X0) | generous(X0) | ((~calm(X0) | curious(X0)) & (~curious(X0) | calm(X0))))) [flattening 45]
49. ! [X0] : (((~generous(X0) | ~strong(X0)) | ~strong(X0)) & (strong(X0) | (generous(X0) & strong(X0)))) [nnf transformation 10]
50. ! [X0] : ((~generous(X0) | ~strong(X0) | ~strong(X0)) & (strong(X0) | (generous(X0) & strong(X0)))) [flattening 49]
55. (? [X0] : (~funny(X0) & generous(X0)) | ! [X1] : ~curious(X1)) & (? [X1] : curious(X1) | ! [X0] : (funny(X0) | ~generous(X0))) [nnf transformation 25]
56. (? [X0] : (~funny(X0) & generous(X0)) | ! [X1] : ~curious(X1)) & (? [X2] : curious(X2) | ! [X3] : (funny(X3) | ~generous(X3))) [rectify 55]
57. ? [X0] : (~funny(X0) & generous(X0)) => (~funny(sK3) & generous(sK3)) [choice axiom]
58. ? [X2] : curious(X2) => curious(sK4) [choice axiom]
59. ((~funny(sK3) & generous(sK3)) | ! [X1] : ~curious(X1)) & (curious(sK4) | ! [X3] : (funny(X3) | ~generous(X3))) [skolemisation 56,58,57]
80. ~calm(X0) | generous(X0) | ~strong(X0) | curious(X0) [cnf transformation 46]
93. strong(X0) | strong(X0) [cnf transformation 50]
95. ~generous(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 50]
104. generous(sK3) | ~curious(X1) [cnf transformation 59]
124. calm(paul) [cnf transformation 23]
125. strong(X0) [duplicate literal removal 93]
126. ~strong(X0) | ~generous(X0) [duplicate literal removal 95]
198. 16 <=> ! [X1] : ~curious(X1) [avatar definition]
199. ~curious(X1) <- (16) [avatar component clause 198]
206. 18 <=> generous(sK3) [avatar definition]
208. generous(sK3) <- (18) [avatar component clause 206]
209. 16 | 18 [avatar split clause 104,206,198]
270. ~generous(X1) [resolution 126,125]
334. generous(paul) | ~strong(paul) | curious(paul) [resolution 80,124]
335. ~strong(paul) | curious(paul) [subsumption resolution 334,270]
336. curious(paul) [subsumption resolution 335,125]
337. $false <- (16) [subsumption resolution 336,199]
338. ~16 [avatar contradiction clause 337]
339. $false <- (18) [subsumption resolution 208,270]
340. ~18 [avatar contradiction clause 339]
341. $false [avatar sat refutation 209,338,340]
% SZS output end Proof for 8961433977348758982649333
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient is both not calm and curious.
If someone is either not curious or strong then susan is either quiet or not curious.
Everyone who is not brave is either not funny or not patient and vice versa.
Everyone who is both not humble and not brave is not patient and vice versa.
If someone is not brave then someone is either brave or not creative.
Everyone who is brave is both not humble and not curious.
If lucy is either not curious or not brave then john is not quiet or not creative.
If someone is both not wise and not rich then someone is either not tall or not happy.
Everyone who is not wise or calm is strong or not curious.
If susan is both humble and kind then lucy is not rich or patient.
If mary is funny or old then someone is both not calm and not patient.
Everyone who is both not creative and not patient is not happy or strong and vice versa.
Everyone who is either not tall or rich is either patient or old and vice versa.
Everyone who is happy or not generous is not creative and vice versa.
If mary is creative then someone is either rich or not humble and vice versa.
Someone is generous or not quiet.
Alice is both tall and not brave.
Someone is kind.
Susan is not tall.
John is old. | Alice is not old. | contradiction | (![X]:((generous(X)|patient(X))=>(~calm(X)&curious(X))))&
((?[X]:((~curious(X)<~>strong(X))))=>((quiet(susan)<~>~curious(susan))))&
(![X]:(~brave(X)<=>(~funny(X)<~>~patient(X))))&
(![X]:((~humble(X)&~brave(X))<=>~patient(X)))&
((?[X]:(~brave(X)))=>(?[X]:((brave(X)<~>~creative(X)))))&
(![X]:(brave(X)=>(~humble(X)&~curious(X))))&
(((~curious(lucy)<~>~brave(lucy)))=>((~quiet(john)|~creative(john))))&
((?[X]:((~wise(X)&~rich(X))))=>(?[X]:((~tall(X)<~>~happy(X)))))&
(![X]:((~wise(X)|calm(X))=>(strong(X)|~curious(X))))&
(((humble(susan)&kind(susan)))=>((~rich(lucy)|patient(lucy))))&
(((funny(mary)|old(mary)))=>(?[X]:((~calm(X)&~patient(X)))))&
(![X]:((~creative(X)&~patient(X))<=>(~happy(X)|strong(X))))&
(![X]:((~tall(X)<~>rich(X))<=>(patient(X)<~>old(X))))&
(![X]:((happy(X)|~generous(X))<=>~creative(X)))&
((creative(mary))<=>(?[X]:((rich(X)<~>~humble(X)))))&
(?[X]:((generous(X)|~quiet(X))))&
((tall(alice)&~brave(alice)))&
(?[X]:(kind(X)))&
(~tall(susan))&
(old(john)) | ~old(alice) | [
"p3",
"p11",
"p12",
"p13",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 920744389410945031512452
% SZS output start Proof for 920744389410945031512452
4. ! [X0] : ((~brave(X0) & ~humble(X0)) <=> ~patient(X0)) [input p3]
12. ! [X0] : ((~patient(X0) & ~creative(X0)) <=> (strong(X0) | ~happy(X0))) [input p11]
13. ! [X0] : ((~tall(X0) <~> rich(X0)) <=> (patient(X0) <~> old(X0))) [input p12]
14. ! [X0] : ((~generous(X0) | happy(X0)) <=> ~creative(X0)) [input p13]
15. creative(mary) <=> ? [X0] : (rich(X0) <~> ~humble(X0)) [input p14]
17. ~brave(alice) & tall(alice) [input p16]
21. ~old(alice) [input hypothesis]
40. ! [X0] : (((~brave(X0) & ~humble(X0)) | patient(X0)) & (~patient(X0) | (brave(X0) | humble(X0)))) [nnf transformation 4]
41. ! [X0] : (((~brave(X0) & ~humble(X0)) | patient(X0)) & (~patient(X0) | brave(X0) | humble(X0))) [flattening 40]
49. ! [X0] : (((~patient(X0) & ~creative(X0)) | (~strong(X0) & happy(X0))) & ((strong(X0) | ~happy(X0)) | (patient(X0) | creative(X0)))) [nnf transformation 12]
50. ! [X0] : (((~patient(X0) & ~creative(X0)) | (~strong(X0) & happy(X0))) & (strong(X0) | ~happy(X0) | patient(X0) | creative(X0))) [flattening 49]
51. ! [X0] : ((((~rich(X0) | tall(X0)) & (rich(X0) | ~tall(X0))) | ((patient(X0) | ~old(X0)) & (old(X0) | ~patient(X0)))) & (((~old(X0) | ~patient(X0)) & (old(X0) | patient(X0))) | ((~tall(X0) | ~rich(X0)) & (rich(X0) | tall(X0))))) [nnf transformation 13]
52. ! [X0] : (((~generous(X0) | happy(X0)) | creative(X0)) & (~creative(X0) | (generous(X0) & ~happy(X0)))) [nnf transformation 14]
53. ! [X0] : ((~generous(X0) | happy(X0) | creative(X0)) & (~creative(X0) | (generous(X0) & ~happy(X0)))) [flattening 52]
54. (creative(mary) | ! [X0] : ((rich(X0) | humble(X0)) & (~humble(X0) | ~rich(X0)))) & (? [X0] : ((humble(X0) | ~rich(X0)) & (~humble(X0) | rich(X0))) | ~creative(mary)) [nnf transformation 15]
55. (creative(mary) | ! [X0] : ((rich(X0) | humble(X0)) & (~humble(X0) | ~rich(X0)))) & (? [X1] : ((humble(X1) | ~rich(X1)) & (~humble(X1) | rich(X1))) | ~creative(mary)) [rectify 54]
56. ? [X1] : ((humble(X1) | ~rich(X1)) & (~humble(X1) | rich(X1))) => ((humble(sK2) | ~rich(sK2)) & (~humble(sK2) | rich(sK2))) [choice axiom]
57. (creative(mary) | ! [X0] : ((rich(X0) | humble(X0)) & (~humble(X0) | ~rich(X0)))) & (((humble(sK2) | ~rich(sK2)) & (~humble(sK2) | rich(sK2))) | ~creative(mary)) [skolemisation 55,56]
72. ~patient(X0) | brave(X0) | humble(X0) [cnf transformation 41]
73. ~humble(X0) | patient(X0) [cnf transformation 41]
85. ~creative(X0) | happy(X0) [cnf transformation 50]
90. ~tall(X0) | patient(X0) | old(X0) | ~rich(X0) [cnf transformation 51]
93. ~tall(X0) | rich(X0) | old(X0) | ~patient(X0) [cnf transformation 51]
97. ~creative(X0) | ~happy(X0) [cnf transformation 53]
102. creative(mary) | ~humble(X0) | ~rich(X0) [cnf transformation 57]
103. creative(mary) | rich(X0) | humble(X0) [cnf transformation 57]
105. tall(alice) [cnf transformation 17]
106. ~brave(alice) [cnf transformation 17]
110. ~old(alice) [cnf transformation 21]
194. ~creative(X0) [subsumption resolution 97,85]
195. rich(X0) | humble(X0) [subsumption resolution 103,194]
196. ~rich(X0) | ~humble(X0) [subsumption resolution 102,194]
218. patient(alice) | old(alice) | ~rich(alice) [resolution 90,105]
219. patient(alice) | ~rich(alice) [subsumption resolution 218,110]
221. 21 <=> rich(alice) [avatar definition]
222. rich(alice) <- (21) [avatar component clause 221]
223. ~rich(alice) <- (~21) [avatar component clause 221]
225. 22 <=> patient(alice) [avatar definition]
227. patient(alice) <- (22) [avatar component clause 225]
228. ~21 | 22 [avatar split clause 219,225,221]
229. humble(alice) <- (~21) [resolution 223,195]
249. patient(alice) <- (~21) [resolution 229,73]
250. 22 | 21 [avatar split clause 249,221,225]
251. rich(alice) | old(alice) | ~patient(alice) [resolution 93,105]
256. rich(alice) | ~patient(alice) [subsumption resolution 251,110]
257. rich(alice) <- (22) [subsumption resolution 256,227]
258. 21 | ~22 [avatar split clause 257,225,221]
259. ~humble(alice) <- (21) [resolution 222,196]
265. brave(alice) | humble(alice) <- (22) [resolution 227,72]
268. humble(alice) <- (22) [subsumption resolution 265,106]
269. $false <- (21, 22) [subsumption resolution 268,259]
270. ~21 | ~22 [avatar contradiction clause 269]
271. $false [avatar sat refutation 228,250,258,270]
% SZS output end Proof for 920744389410945031512452
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either wise or not curious then someone is strong and vice versa.
If someone is either not old or brave then mary is either not quiet or brave.
Everyone who is not strong is either old or strong and vice versa.
Everyone who is not happy is either humble or rich and vice versa.
If lucy is not brave or rich then alice is either not old or tall.
If someone is both not brave and not humble then alice is not generous and vice versa.
If someone is both not creative and rich then john is not humble or not tall.
Everyone who is not strong is not brave and vice versa.
Everyone who is generous or not kind is brave or not brave.
If lucy is not old then someone is both strong and not tall and vice versa.
Everyone who is both brave and strong is either not funny or not curious.
If alice is both not old and not rich then lucy is curious and vice versa.
Everyone who is both not happy and not creative is either not tall or brave.
If someone is both creative and not generous then fred is both rich and strong.
Everyone who is either brave or not funny is strong.
If alice is either happy or funny then alice is either not quiet or not wise and vice versa.
Alice is not funny or old.
Someone is either wise or not humble.
Someone is either not happy or not patient.
John is both not strong and curious.
Someone is either not strong or not rich.
Someone is not funny.
Paul is both not rich and old.
Someone is both not rich and brave. | John is brave. | contradiction | ((?[X]:((wise(X)<~>~curious(X))))<=>(?[X]:(strong(X))))&
((?[X]:((~old(X)<~>brave(X))))=>((~quiet(mary)<~>brave(mary))))&
(![X]:(~strong(X)<=>(old(X)<~>strong(X))))&
(![X]:(~happy(X)<=>(humble(X)<~>rich(X))))&
(((~brave(lucy)|rich(lucy)))=>((~old(alice)<~>tall(alice))))&
((?[X]:((~brave(X)&~humble(X))))<=>(~generous(alice)))&
((?[X]:((~creative(X)&rich(X))))=>((~humble(john)|~tall(john))))&
(![X]:(~strong(X)<=>~brave(X)))&
(![X]:((generous(X)|~kind(X))=>(brave(X)|~brave(X))))&
((~old(lucy))<=>(?[X]:((strong(X)&~tall(X)))))&
(![X]:((brave(X)&strong(X))=>(~funny(X)<~>~curious(X))))&
(((~old(alice)&~rich(alice)))<=>(curious(lucy)))&
(![X]:((~happy(X)&~creative(X))=>(~tall(X)<~>brave(X))))&
((?[X]:((creative(X)&~generous(X))))=>((rich(fred)&strong(fred))))&
(![X]:((brave(X)<~>~funny(X))=>strong(X)))&
(((happy(alice)<~>funny(alice)))<=>((~quiet(alice)<~>~wise(alice))))&
((~funny(alice)|old(alice)))&
(?[X]:((wise(X)<~>~humble(X))))&
(?[X]:((~happy(X)<~>~patient(X))))&
((~strong(john)&curious(john)))&
(?[X]:((~strong(X)<~>~rich(X))))&
(?[X]:(~funny(X)))&
((~rich(paul)&old(paul)))&
(?[X]:((~rich(X)&brave(X)))) | brave(john) | [
"p7",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 5282106904930703901369465
% SZS output start Proof for 5282106904930703901369465
8. ! [X0] : (~strong(X0) <=> ~brave(X0)) [input p7]
20. curious(john) & ~strong(john) [input p19]
25. brave(john) [input hypothesis]
53. ! [X0] : ((~strong(X0) | brave(X0)) & (~brave(X0) | strong(X0))) [nnf transformation 8]
101. ~brave(X0) | strong(X0) [cnf transformation 53]
131. ~strong(john) [cnf transformation 20]
140. brave(john) [cnf transformation 25]
316. strong(john) [resolution 101,140]
317. $false [subsumption resolution 316,131]
% SZS output end Proof for 5282106904930703901369465
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
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