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
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|---|---|---|---|---|---|---|---|
If someone is either not generous or not patient then someone is either not wise or wise.
Everyone who is both wise and brave is either not wise or not patient.
Everyone who is kind is either not humble or creative and vice versa.
Everyone who is strong or not creative is not rich and vice versa.
If paul is rich or kind then paul is not brave or not kind.
Everyone who is either not wise or not generous is either not humble or quiet.
Everyone who is quiet is kind.
If mary is not wise then susan is happy or not happy and vice versa.
If john is funny then paul is not creative and vice versa.
Everyone who is not happy is not patient or happy and vice versa.
Everyone who is either not strong or not tall is humble and vice versa.
If fred is not strong then someone is either tall or creative and vice versa.
If lucy is both not tall and not kind then john is not strong or curious and vice versa.
Everyone who is either old or not quiet is humble and vice versa.
Everyone who is both not wise and not quiet is not rich or not curious and vice versa.
Everyone who is not funny or not tall is both not kind and rich.
Someone is happy or rich.
Fred is not patient or old.
Mary is both strong and brave.
Lucy is both not kind and tall.
Paul is either generous or not tall.
Mary is both generous and not calm.
Someone is not old. | Paul is strong. | entailment | ((?[X]:((~generous(X)<~>~patient(X))))=>(?[X]:((~wise(X)<~>wise(X)))))&
(![X]:((wise(X)&brave(X))=>(~wise(X)<~>~patient(X))))&
(![X]:(kind(X)<=>(~humble(X)<~>creative(X))))&
(![X]:((strong(X)|~creative(X))<=>~rich(X)))&
(((rich(paul)|kind(paul)))=>((~brave(paul)|~kind(paul))))&
(![X]:((~wise(X)<~>~generous(X))=>(~humble(X)<~>quiet(X))))&
(![X]:(quiet(X)=>kind(X)))&
((~wise(mary))<=>((happy(susan)|~happy(susan))))&
((funny(john))<=>(~creative(paul)))&
(![X]:(~happy(X)<=>(~patient(X)|happy(X))))&
(![X]:((~strong(X)<~>~tall(X))<=>humble(X)))&
((~strong(fred))<=>(?[X]:((tall(X)<~>creative(X)))))&
(((~tall(lucy)&~kind(lucy)))<=>((~strong(john)|curious(john))))&
(![X]:((old(X)<~>~quiet(X))<=>humble(X)))&
(![X]:((~wise(X)&~quiet(X))<=>(~rich(X)|~curious(X))))&
(![X]:((~funny(X)|~tall(X))=>(~kind(X)&rich(X))))&
(?[X]:((happy(X)|rich(X))))&
((~patient(fred)|old(fred)))&
((strong(mary)&brave(mary)))&
((~kind(lucy)&tall(lucy)))&
((generous(paul)<~>~tall(paul)))&
((generous(mary)&~calm(mary)))&
(?[X]:(~old(X))) | strong(paul) | [
"p3",
"p5",
"p8",
"p10",
"p12",
"p14",
"p15",
"p19",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 8900648518592640314823325
% SZS output start Proof for 8900648518592640314823325
4. ! [X0] : ((~creative(X0) | strong(X0)) <=> ~rich(X0)) [input p3]
6. ! [X0] : ((~wise(X0) <~> ~generous(X0)) => (~humble(X0) <~> quiet(X0))) [input p5]
9. funny(john) <=> ~creative(paul) [input p8]
11. ! [X0] : ((~strong(X0) <~> ~tall(X0)) <=> humble(X0)) [input p10]
13. (~kind(lucy) & ~tall(lucy)) <=> (curious(john) | ~strong(john)) [input p12]
15. ! [X0] : ((~quiet(X0) & ~wise(X0)) <=> (~curious(X0) | ~rich(X0))) [input p14]
16. ! [X0] : ((~tall(X0) | ~funny(X0)) => (rich(X0) & ~kind(X0))) [input p15]
20. tall(lucy) & ~kind(lucy) [input p19]
21. generous(paul) <~> ~tall(paul) [input p20]
24. ~strong(paul) [input hypothesis]
32. ! [X0] : ((~humble(X0) <~> quiet(X0)) | (~wise(X0) <=> ~generous(X0))) [ennf transformation 6]
34. ! [X0] : ((rich(X0) & ~kind(X0)) | (tall(X0) & funny(X0))) [ennf transformation 16]
41. ! [X0] : (((~creative(X0) | strong(X0)) | rich(X0)) & (~rich(X0) | (creative(X0) & ~strong(X0)))) [nnf transformation 4]
42. ! [X0] : ((~creative(X0) | strong(X0) | rich(X0)) & (~rich(X0) | (creative(X0) & ~strong(X0)))) [flattening 41]
43. ! [X0] : (((~quiet(X0) | humble(X0)) & (quiet(X0) | ~humble(X0))) | ((~wise(X0) | generous(X0)) & (~generous(X0) | wise(X0)))) [nnf transformation 32]
46. (funny(john) | creative(paul)) & (~creative(paul) | ~funny(john)) [nnf transformation 9]
49. ! [X0] : ((((tall(X0) | strong(X0)) & (~tall(X0) | ~strong(X0))) | ~humble(X0)) & (humble(X0) | ((~strong(X0) | tall(X0)) & (~tall(X0) | strong(X0))))) [nnf transformation 11]
54. ((~kind(lucy) & ~tall(lucy)) | (~curious(john) & strong(john))) & ((curious(john) | ~strong(john)) | (kind(lucy) | tall(lucy))) [nnf transformation 13]
55. ((~kind(lucy) & ~tall(lucy)) | (~curious(john) & strong(john))) & (curious(john) | ~strong(john) | kind(lucy) | tall(lucy)) [flattening 54]
57. ! [X0] : (((~quiet(X0) & ~wise(X0)) | (curious(X0) & rich(X0))) & ((~curious(X0) | ~rich(X0)) | (quiet(X0) | wise(X0)))) [nnf transformation 15]
58. ! [X0] : (((~quiet(X0) & ~wise(X0)) | (curious(X0) & rich(X0))) & (~curious(X0) | ~rich(X0) | quiet(X0) | wise(X0))) [flattening 57]
61. (tall(paul) | ~generous(paul)) & (~tall(paul) | generous(paul)) [nnf transformation 21]
74. ~rich(X0) | ~strong(X0) [cnf transformation 42]
75. ~rich(X0) | creative(X0) [cnf transformation 42]
79. ~humble(X0) | quiet(X0) | ~generous(X0) | wise(X0) [cnf transformation 43]
87. ~creative(paul) | ~funny(john) [cnf transformation 46]
92. ~tall(X0) | humble(X0) | strong(X0) [cnf transformation 49]
101. ~tall(lucy) | strong(john) [cnf transformation 55]
110. ~wise(X0) | rich(X0) [cnf transformation 58]
112. ~quiet(X0) | rich(X0) [cnf transformation 58]
116. funny(X0) | rich(X0) [cnf transformation 34]
117. tall(X0) | rich(X0) [cnf transformation 34]
123. tall(lucy) [cnf transformation 20]
124. ~tall(paul) | generous(paul) [cnf transformation 61]
128. ~strong(paul) [cnf transformation 24]
143. 3 <=> rich(paul) [avatar definition]
144. rich(paul) <- (3) [avatar component clause 143]
145. ~rich(paul) <- (~3) [avatar component clause 143]
158. 6 <=> creative(paul) [avatar definition]
162. 7 <=> funny(john) [avatar definition]
163. ~funny(john) <- (~7) [avatar component clause 162]
166. ~7 | ~6 [avatar split clause 87,158,162]
200. 15 <=> strong(john) [avatar definition]
202. strong(john) <- (15) [avatar component clause 200]
205. 16 <=> tall(lucy) [avatar definition]
209. 15 | ~16 [avatar split clause 101,205,200]
212. 16 [avatar split clause 123,205]
215. 17 <=> generous(paul) [avatar definition]
216. generous(paul) <- (17) [avatar component clause 215]
219. 18 <=> tall(paul) [avatar definition]
220. ~tall(paul) <- (~18) [avatar component clause 219]
221. tall(paul) <- (18) [avatar component clause 219]
223. 17 | ~18 [avatar split clause 124,219,215]
227. rich(paul) <- (~18) [resolution 117,220]
228. 3 | 18 [avatar split clause 227,219,143]
229. creative(paul) <- (3) [resolution 144,75]
235. 6 | ~3 [avatar split clause 229,143,158]
244. rich(john) <- (~7) [resolution 163,116]
246. ~strong(john) <- (~7) [resolution 244,74]
247. $false <- (~7, 15) [subsumption resolution 246,202]
248. 7 | ~15 [avatar contradiction clause 247]
266. 21 <=> humble(paul) [avatar definition]
268. humble(paul) <- (21) [avatar component clause 266]
299. humble(paul) | strong(paul) <- (18) [resolution 92,221]
303. humble(paul) <- (18) [subsumption resolution 299,128]
304. 21 | ~18 [avatar split clause 303,219,266]
386. quiet(paul) | ~generous(paul) | wise(paul) <- (21) [resolution 79,268]
389. quiet(paul) | wise(paul) <- (17, 21) [subsumption resolution 386,216]
391. 32 <=> wise(paul) [avatar definition]
393. wise(paul) <- (32) [avatar component clause 391]
395. 33 <=> quiet(paul) [avatar definition]
397. quiet(paul) <- (33) [avatar component clause 395]
398. 32 | 33 | ~17 | ~21 [avatar split clause 389,266,215,395,391]
478. rich(paul) <- (32) [resolution 393,110]
479. $false <- (~3, 32) [subsumption resolution 478,145]
480. 3 | ~32 [avatar contradiction clause 479]
488. rich(paul) <- (33) [resolution 397,112]
491. $false <- (~3, 33) [subsumption resolution 488,145]
492. 3 | ~33 [avatar contradiction clause 491]
495. $false [avatar sat refutation 166,209,212,223,228,235,248,304,398,480,492]
% SZS output end Proof for 8900648518592640314823325
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not generous and wise then john is not creative and vice versa.
If someone is either not old or not rich then lucy is not kind or not creative and vice versa.
Everyone who is either not curious or humble is strong.
Everyone who is not strong or not calm is not strong or wise.
Everyone who is both old and patient is strong or creative and vice versa.
If lucy is not strong then mary is kind or not curious.
Everyone who is not kind is strong.
Everyone who is not quiet or not kind is either funny or calm and vice versa.
If lucy is not brave or not quiet then someone is either not curious or calm and vice versa.
Everyone who is both not wise and not rich is both old and not creative.
Everyone who is not generous or wise is old and vice versa.
Everyone who is funny is either not creative or kind.
Everyone who is both generous and funny is either generous or curious and vice versa.
Everyone who is humble or not patient is generous or not brave and vice versa.
Everyone who is either not curious or not brave is either wise or not patient.
If someone is either not wise or old then someone is tall or curious.
Someone is either funny or not creative.
Someone is not brave.
Fred is rich.
John is either wise or not kind.
Someone is either not patient or not calm.
Fred is not curious or brave.
Someone is both not old and generous.
Paul is either generous or not kind. | Lucy is creative. | neutral | ((?[X]:((~generous(X)&wise(X))))<=>(~creative(john)))&
((?[X]:((~old(X)<~>~rich(X))))<=>((~kind(lucy)|~creative(lucy))))&
(![X]:((~curious(X)<~>humble(X))=>strong(X)))&
(![X]:((~strong(X)|~calm(X))=>(~strong(X)|wise(X))))&
(![X]:((old(X)&patient(X))<=>(strong(X)|creative(X))))&
((~strong(lucy))=>((kind(mary)|~curious(mary))))&
(![X]:(~kind(X)=>strong(X)))&
(![X]:((~quiet(X)|~kind(X))<=>(funny(X)<~>calm(X))))&
(((~brave(lucy)|~quiet(lucy)))<=>(?[X]:((~curious(X)<~>calm(X)))))&
(![X]:((~wise(X)&~rich(X))=>(old(X)&~creative(X))))&
(![X]:((~generous(X)|wise(X))<=>old(X)))&
(![X]:(funny(X)=>(~creative(X)<~>kind(X))))&
(![X]:((generous(X)&funny(X))<=>(generous(X)<~>curious(X))))&
(![X]:((humble(X)|~patient(X))<=>(generous(X)|~brave(X))))&
(![X]:((~curious(X)<~>~brave(X))=>(wise(X)<~>~patient(X))))&
((?[X]:((~wise(X)<~>old(X))))=>(?[X]:((tall(X)|curious(X)))))&
(?[X]:((funny(X)<~>~creative(X))))&
(?[X]:(~brave(X)))&
(rich(fred))&
((wise(john)<~>~kind(john)))&
(?[X]:((~patient(X)<~>~calm(X))))&
((~curious(fred)|brave(fred)))&
(?[X]:((~old(X)&generous(X))))&
((generous(paul)<~>~kind(paul))) | creative(lucy) | [] | null | 0 |
Everyone who is either calm or strong is calm or funny and vice versa.
If someone is either not rich or not strong then alice is both not funny and not rich.
If someone is either patient or not tall then fred is strong or funny.
Everyone who is not wise is happy and vice versa.
Everyone who is both not old and tall is either calm or not old and vice versa.
Everyone who is both not curious and calm is not strong and vice versa.
Everyone who is old is both not wise and calm.
Everyone who is either not quiet or happy is either not humble or funny.
If mary is either not kind or strong then someone is humble.
Everyone who is either tall or not brave is both strong and generous.
If fred is kind then someone is both humble and not generous and vice versa.
If someone is not wise or not funny then someone is either quiet or not old.
Everyone who is both not humble and strong is either not quiet or not strong.
Everyone who is not kind is wise.
Everyone who is both kind and wise is both not old and happy and vice versa.
Everyone who is both not old and not rich is either not tall or brave and vice versa.
Lucy is either not creative or wise.
John is not tall or not happy.
Someone is rich.
Susan is either funny or not humble.
Someone is curious or quiet. | Alice is not tall. | contradiction | (![X]:((calm(X)<~>strong(X))<=>(calm(X)|funny(X))))&
((?[X]:((~rich(X)<~>~strong(X))))=>((~funny(alice)&~rich(alice))))&
((?[X]:((patient(X)<~>~tall(X))))=>((strong(fred)|funny(fred))))&
(![X]:(~wise(X)<=>happy(X)))&
(![X]:((~old(X)&tall(X))<=>(calm(X)<~>~old(X))))&
(![X]:((~curious(X)&calm(X))<=>~strong(X)))&
(![X]:(old(X)=>(~wise(X)&calm(X))))&
(![X]:((~quiet(X)<~>happy(X))=>(~humble(X)<~>funny(X))))&
(((~kind(mary)<~>strong(mary)))=>(?[X]:(humble(X))))&
(![X]:((tall(X)<~>~brave(X))=>(strong(X)&generous(X))))&
((kind(fred))<=>(?[X]:((humble(X)&~generous(X)))))&
((?[X]:((~wise(X)|~funny(X))))=>(?[X]:((quiet(X)<~>~old(X)))))&
(![X]:((~humble(X)&strong(X))=>(~quiet(X)<~>~strong(X))))&
(![X]:(~kind(X)=>wise(X)))&
(![X]:((kind(X)&wise(X))<=>(~old(X)&happy(X))))&
(![X]:((~old(X)&~rich(X))<=>(~tall(X)<~>brave(X))))&
((~creative(lucy)<~>wise(lucy)))&
((~tall(john)|~happy(john)))&
(?[X]:(rich(X)))&
((funny(susan)<~>~humble(susan)))&
(?[X]:((curious(X)|quiet(X)))) | ~tall(alice) | [
"p0",
"p1",
"p4",
"p6",
"p9",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 45810759798585349272034
% SZS output start Proof for 45810759798585349272034
1. ! [X0] : ((calm(X0) <~> strong(X0)) <=> (funny(X0) | calm(X0))) [input p0]
2. ? [X0] : (~rich(X0) <~> ~strong(X0)) => (~rich(alice) & ~funny(alice)) [input p1]
5. ! [X0] : ((tall(X0) & ~old(X0)) <=> (calm(X0) <~> ~old(X0))) [input p4]
7. ! [X0] : (old(X0) => (calm(X0) & ~wise(X0))) [input p6]
10. ! [X0] : ((tall(X0) <~> ~brave(X0)) => (generous(X0) & strong(X0))) [input p9]
16. ! [X0] : ((~rich(X0) & ~old(X0)) <=> (~tall(X0) <~> brave(X0))) [input p15]
22. ~tall(alice) [input hypothesis]
24. (~rich(alice) & ~funny(alice)) | ! [X0] : (~rich(X0) <=> ~strong(X0)) [ennf transformation 2]
27. ! [X0] : ((calm(X0) & ~wise(X0)) | ~old(X0)) [ennf transformation 7]
30. ! [X0] : ((generous(X0) & strong(X0)) | (tall(X0) <=> ~brave(X0))) [ennf transformation 10]
35. ! [X0] : ((((~strong(X0) | ~calm(X0)) & (strong(X0) | calm(X0))) | (~funny(X0) & ~calm(X0))) & ((funny(X0) | calm(X0)) | ((calm(X0) | ~strong(X0)) & (strong(X0) | ~calm(X0))))) [nnf transformation 1]
36. ! [X0] : ((((~strong(X0) | ~calm(X0)) & (strong(X0) | calm(X0))) | (~funny(X0) & ~calm(X0))) & (funny(X0) | calm(X0) | ((calm(X0) | ~strong(X0)) & (strong(X0) | ~calm(X0))))) [flattening 35]
37. (~rich(alice) & ~funny(alice)) | ! [X0] : ((~rich(X0) | strong(X0)) & (~strong(X0) | rich(X0))) [nnf transformation 24]
40. ! [X0] : (((tall(X0) & ~old(X0)) | ((calm(X0) | old(X0)) & (~old(X0) | ~calm(X0)))) & (((old(X0) | ~calm(X0)) & (~old(X0) | calm(X0))) | (~tall(X0) | old(X0)))) [nnf transformation 5]
41. ! [X0] : (((tall(X0) & ~old(X0)) | ((calm(X0) | old(X0)) & (~old(X0) | ~calm(X0)))) & (((old(X0) | ~calm(X0)) & (~old(X0) | calm(X0))) | ~tall(X0) | old(X0))) [flattening 40]
48. ! [X0] : ((generous(X0) & strong(X0)) | ((tall(X0) | brave(X0)) & (~brave(X0) | ~tall(X0)))) [nnf transformation 30]
60. ! [X0] : (((~rich(X0) & ~old(X0)) | ((~tall(X0) | ~brave(X0)) & (brave(X0) | tall(X0)))) & (((~brave(X0) | tall(X0)) & (brave(X0) | ~tall(X0))) | (rich(X0) | old(X0)))) [nnf transformation 16]
61. ! [X0] : (((~rich(X0) & ~old(X0)) | ((~tall(X0) | ~brave(X0)) & (brave(X0) | tall(X0)))) & (((~brave(X0) | tall(X0)) & (brave(X0) | ~tall(X0))) | rich(X0) | old(X0))) [flattening 60]
72. ~strong(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 36]
77. ~rich(alice) | ~rich(X0) | strong(X0) [cnf transformation 37]
84. ~old(X0) | ~old(X0) | ~calm(X0) [cnf transformation 41]
87. old(X0) | calm(X0) | tall(X0) [cnf transformation 41]
92. calm(X0) | ~old(X0) [cnf transformation 27]
100. brave(X0) | tall(X0) | strong(X0) [cnf transformation 48]
118. ~brave(X0) | tall(X0) | rich(X0) | old(X0) [cnf transformation 61]
130. ~tall(alice) [cnf transformation 22]
133. ~old(X0) | ~calm(X0) [duplicate literal removal 84]
135. ~strong(X0) | ~calm(X0) [duplicate literal removal 72]
138. 1 <=> ! [X0] : (~rich(X0) | strong(X0)) [avatar definition]
139. ~rich(X0) | strong(X0) <- (1) [avatar component clause 138]
141. 2 <=> rich(alice) [avatar definition]
143. ~rich(alice) <- (~2) [avatar component clause 141]
144. 1 | ~2 [avatar split clause 77,141,138]
170. ~old(X0) [subsumption resolution 92,133]
220. ~brave(X0) | tall(X0) | rich(X0) [subsumption resolution 118,170]
279. tall(X2) | calm(X2) [resolution 87,170]
281. calm(alice) [resolution 279,130]
298. tall(X0) | rich(X0) | tall(X0) | strong(X0) [resolution 220,100]
299. tall(X0) | rich(X0) | strong(X0) [duplicate literal removal 298]
302. rich(alice) | strong(alice) [resolution 299,130]
306. strong(alice) <- (~2) [subsumption resolution 302,143]
309. ~calm(alice) <- (~2) [resolution 306,135]
315. $false <- (~2) [subsumption resolution 281,309]
316. 2 [avatar contradiction clause 315]
317. strong(alice) <- (1) [subsumption resolution 302,139]
402. ~calm(alice) <- (1) [resolution 317,135]
403. $false <- (1) [subsumption resolution 402,281]
404. ~1 [avatar contradiction clause 403]
405. $false [avatar sat refutation 144,316,404]
% SZS output end Proof for 45810759798585349272034
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is creative or not strong is both funny and generous. Everyone who is either humble or not rich is both not humble and kind. Everyone who is either funny or rich is not funny. Everyone who is both curious and not curious is both patient and creative and vice versa. Everyone who is not curious is not brave and vice versa. If john is either strong or not funny then paul is brave. If alice is strong or funny then fred is either tall or not strong. Everyone who is both not funny and curious is either curious or not brave and vice versa. If someone is not creative or not generous then someone is calm and vice versa. Everyone who is either not brave or quiet is happy or not happy. If fred is either not creative or old then someone is old or not creative. Everyone who is not tall or calm is strong and vice versa. If fred is either not generous or brave then someone is both not patient and happy. If someone is either strong or happy then paul is not wise or not creative and vice versa. If someone is either curious or not humble then lucy is either not wise or not creative. If lucy is both happy and not wise then someone is happy or not rich and vice versa. Someone is curious or not brave. Someone is generous or not strong. Someone is not curious or patient. Mary is creative or old. Alice is not humble. Fred is both tall and not wise. Mary is not patient. Someone is not funny. | Paul is creative. | contradiction | (![X]:((creative(X)|~strong(X))=>(funny(X)&generous(X))))&
(![X]:((humble(X)<~>~rich(X))=>(~humble(X)&kind(X))))&
(![X]:((funny(X)<~>rich(X))=>~funny(X)))&
(![X]:((curious(X)&~curious(X))<=>(patient(X)&creative(X))))&
(![X]:(~curious(X)<=>~brave(X)))&
(((strong(john)<~>~funny(john)))=>(brave(paul)))&
(((strong(alice)|funny(alice)))=>((tall(fred)<~>~strong(fred))))&
(![X]:((~funny(X)&curious(X))<=>(curious(X)<~>~brave(X))))&
((?[X]:((~creative(X)|~generous(X))))<=>(?[X]:(calm(X))))&
(![X]:((~brave(X)<~>quiet(X))=>(happy(X)|~happy(X))))&
(((~creative(fred)<~>old(fred)))=>(?[X]:((old(X)|~creative(X)))))&
(![X]:((~tall(X)|calm(X))<=>strong(X)))&
(((~generous(fred)<~>brave(fred)))=>(?[X]:((~patient(X)&happy(X)))))&
((?[X]:((strong(X)<~>happy(X))))<=>((~wise(paul)|~creative(paul))))&
((?[X]:((curious(X)<~>~humble(X))))=>((~wise(lucy)<~>~creative(lucy))))&
(((happy(lucy)&~wise(lucy)))<=>(?[X]:((happy(X)|~rich(X)))))&
(?[X]:((curious(X)|~brave(X))))&
(?[X]:((generous(X)|~strong(X))))&
(?[X]:((~curious(X)|patient(X))))&
((creative(mary)|old(mary)))&
(~humble(alice))&
((tall(fred)&~wise(fred)))&
(~patient(mary))&
(?[X]:(~funny(X))) | creative(paul) | [
"p0",
"p4",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 1165539701031740083293979
% SZS output start Proof for 1165539701031740083293979
1. ! [X0] : ((~strong(X0) | creative(X0)) => (generous(X0) & funny(X0))) [input p0]
5. ! [X0] : (~curious(X0) <=> ~brave(X0)) [input p4]
8. ! [X0] : ((curious(X0) & ~funny(X0)) <=> (curious(X0) <~> ~brave(X0))) [input p7]
25. creative(paul) [input hypothesis]
28. ! [X0] : ((generous(X0) & funny(X0)) | (strong(X0) & ~creative(X0))) [ennf transformation 1]
42. ! [X0] : ((~curious(X0) | brave(X0)) & (~brave(X0) | curious(X0))) [nnf transformation 5]
45. ! [X0] : (((curious(X0) & ~funny(X0)) | ((curious(X0) | brave(X0)) & (~brave(X0) | ~curious(X0)))) & (((brave(X0) | ~curious(X0)) & (~brave(X0) | curious(X0))) | (~curious(X0) | funny(X0)))) [nnf transformation 8]
46. ! [X0] : (((curious(X0) & ~funny(X0)) | ((curious(X0) | brave(X0)) & (~brave(X0) | ~curious(X0)))) & (((brave(X0) | ~curious(X0)) & (~brave(X0) | curious(X0))) | ~curious(X0) | funny(X0))) [flattening 45]
80. ~creative(X0) | funny(X0) [cnf transformation 28]
92. ~brave(X0) | curious(X0) [cnf transformation 42]
93. ~curious(X0) | brave(X0) [cnf transformation 42]
102. ~funny(X0) | ~brave(X0) | ~curious(X0) [cnf transformation 46]
105. curious(X0) | curious(X0) | brave(X0) [cnf transformation 46]
144. creative(paul) [cnf transformation 25]
146. curious(X0) | brave(X0) [duplicate literal removal 105]
183. brave(X0) [subsumption resolution 146,93]
184. ~curious(X0) | ~funny(X0) [subsumption resolution 102,183]
241. 20 <=> creative(paul) [avatar definition]
243. creative(paul) <- (20) [avatar component clause 241]
329. 20 [avatar split clause 144,241]
330. funny(paul) <- (20) [resolution 80,243]
341. curious(X0) [resolution 92,183]
352. ~funny(X0) [resolution 184,341]
354. $false <- (20) [resolution 352,330]
359. ~20 [avatar contradiction clause 354]
360. $false [avatar sat refutation 329,359]
% SZS output end Proof for 1165539701031740083293979
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both wise and calm then alice is either creative or not happy and vice versa. Everyone who is both happy and quiet is not rich or not brave and vice versa. If someone is calm or curious then mary is either creative or humble. Everyone who is not humble or not wise is either humble or not quiet. If paul is both generous and tall then susan is both strong and not tall. If lucy is not funny then someone is both kind and not happy and vice versa. Everyone who is both not quiet and not humble is both tall and not calm and vice versa. If susan is both not generous and not rich then fred is not calm or kind. Everyone who is either not creative or creative is both brave and funny and vice versa. Everyone who is not brave or not strong is wise or not creative. Everyone who is either not quiet or not brave is wise and vice versa. Everyone who is not kind is either calm or not calm and vice versa. Everyone who is curious or strong is not funny or not kind and vice versa. Everyone who is both not generous and strong is both curious and wise and vice versa. If someone is both not creative and strong then fred is both old and not happy and vice versa. Everyone who is both not tall and happy is not kind and vice versa. Someone is not curious. Susan is both not calm and not kind. Someone is either not wise or curious. Fred is either not brave or humble. Someone is either creative or not generous. Lucy is either not brave or calm. Someone is not rich. | Susan is not quiet. | neutral | ((?[X]:((wise(X)&calm(X))))<=>((creative(alice)<~>~happy(alice))))&
(![X]:((happy(X)&quiet(X))<=>(~rich(X)|~brave(X))))&
((?[X]:((calm(X)|curious(X))))=>((creative(mary)<~>humble(mary))))&
(![X]:((~humble(X)|~wise(X))=>(humble(X)<~>~quiet(X))))&
(((generous(paul)&tall(paul)))=>((strong(susan)&~tall(susan))))&
((~funny(lucy))<=>(?[X]:((kind(X)&~happy(X)))))&
(![X]:((~quiet(X)&~humble(X))<=>(tall(X)&~calm(X))))&
(((~generous(susan)&~rich(susan)))=>((~calm(fred)|kind(fred))))&
(![X]:((~creative(X)<~>creative(X))<=>(brave(X)&funny(X))))&
(![X]:((~brave(X)|~strong(X))=>(wise(X)|~creative(X))))&
(![X]:((~quiet(X)<~>~brave(X))<=>wise(X)))&
(![X]:(~kind(X)<=>(calm(X)<~>~calm(X))))&
(![X]:((curious(X)|strong(X))<=>(~funny(X)|~kind(X))))&
(![X]:((~generous(X)&strong(X))<=>(curious(X)&wise(X))))&
((?[X]:((~creative(X)&strong(X))))<=>((old(fred)&~happy(fred))))&
(![X]:((~tall(X)&happy(X))<=>~kind(X)))&
(?[X]:(~curious(X)))&
((~calm(susan)&~kind(susan)))&
(?[X]:((~wise(X)<~>curious(X))))&
((~brave(fred)<~>humble(fred)))&
(?[X]:((creative(X)<~>~generous(X))))&
((~brave(lucy)<~>calm(lucy)))&
(?[X]:(~rich(X))) | ~quiet(susan) | [] | null | 0 |
If someone is either not wise or not old then someone is not humble or not curious and vice versa.
Everyone who is tall is either curious or rich and vice versa.
Everyone who is not funny is both not brave and funny.
Everyone who is both not kind and kind is patient.
If john is both old and not patient then lucy is either not happy or rich.
Everyone who is not brave or not quiet is not happy and vice versa.
If mary is not patient then paul is either rich or wise.
Everyone who is both not rich and wise is either not tall or not old.
If someone is both not calm and quiet then someone is not quiet or not kind.
Everyone who is either calm or not wise is not tall and vice versa.
Everyone who is not kind or not patient is either not patient or not old and vice versa.
If fred is either wise or not tall then paul is both old and not curious.
Everyone who is not funny or not curious is both not strong and not happy and vice versa.
If lucy is both tall and quiet then someone is both quiet and not humble.
Everyone who is happy is kind.
Everyone who is not kind or not old is both kind and old.
Someone is either happy or not happy.
Someone is either old or not quiet.
John is calm.
Someone is wise or not generous.
Mary is both not brave and rich. | Mary is rich. | entailment | ((?[X]:((~wise(X)<~>~old(X))))<=>(?[X]:((~humble(X)|~curious(X)))))&
(![X]:(tall(X)<=>(curious(X)<~>rich(X))))&
(![X]:(~funny(X)=>(~brave(X)&funny(X))))&
(![X]:((~kind(X)&kind(X))=>patient(X)))&
(((old(john)&~patient(john)))=>((~happy(lucy)<~>rich(lucy))))&
(![X]:((~brave(X)|~quiet(X))<=>~happy(X)))&
((~patient(mary))=>((rich(paul)<~>wise(paul))))&
(![X]:((~rich(X)&wise(X))=>(~tall(X)<~>~old(X))))&
((?[X]:((~calm(X)&quiet(X))))=>(?[X]:((~quiet(X)|~kind(X)))))&
(![X]:((calm(X)<~>~wise(X))<=>~tall(X)))&
(![X]:((~kind(X)|~patient(X))<=>(~patient(X)<~>~old(X))))&
(((wise(fred)<~>~tall(fred)))=>((old(paul)&~curious(paul))))&
(![X]:((~funny(X)|~curious(X))<=>(~strong(X)&~happy(X))))&
(((tall(lucy)&quiet(lucy)))=>(?[X]:((quiet(X)&~humble(X)))))&
(![X]:(happy(X)=>kind(X)))&
(![X]:((~kind(X)|~old(X))=>(kind(X)&old(X))))&
(?[X]:((happy(X)<~>~happy(X))))&
(?[X]:((old(X)<~>~quiet(X))))&
(calm(john))&
(?[X]:((wise(X)|~generous(X))))&
((~brave(mary)&rich(mary))) | rich(mary) | [
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 2266424012192869805413208
% SZS output start Proof for 2266424012192869805413208
21. rich(mary) & ~brave(mary) [input p20]
22. ~rich(mary) [input hypothesis]
123. rich(mary) [cnf transformation 21]
124. ~rich(mary) [cnf transformation 22]
248. $false [subsumption resolution 124,123]
% SZS output end Proof for 2266424012192869805413208
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not funny or strong is not brave.
If someone is either kind or not curious then someone is not curious or not generous.
If alice is not brave or not patient then someone is both generous and funny and vice versa.
Everyone who is either not tall or not rich is both not generous and not patient and vice versa.
If fred is either not funny or humble then someone is both not patient and quiet and vice versa.
If mary is not patient then paul is both not old and old.
Everyone who is both quiet and not humble is both not generous and old.
Everyone who is both creative and not brave is humble or not wise.
If someone is patient then someone is not brave or calm and vice versa.
Everyone who is strong or old is either strong or not curious and vice versa.
If john is not brave or creative then paul is old.
Everyone who is wise or patient is quiet or curious and vice versa.
If mary is either generous or calm then susan is quiet or calm and vice versa.
Everyone who is either tall or old is both kind and wise.
If someone is either quiet or funny then lucy is not strong and vice versa.
Everyone who is quiet is curious or rich and vice versa.
Susan is not calm.
Susan is creative.
Alice is either funny or not creative.
John is either quiet or not brave.
Someone is either old or not patient.
Lucy is both not funny and not wise.
Alice is either not rich or not brave.
Alice is either not brave or not strong. | Lucy is strong. | contradiction | (![X]:((~funny(X)<~>strong(X))=>~brave(X)))&
((?[X]:((kind(X)<~>~curious(X))))=>(?[X]:((~curious(X)|~generous(X)))))&
(((~brave(alice)|~patient(alice)))<=>(?[X]:((generous(X)&funny(X)))))&
(![X]:((~tall(X)<~>~rich(X))<=>(~generous(X)&~patient(X))))&
(((~funny(fred)<~>humble(fred)))<=>(?[X]:((~patient(X)&quiet(X)))))&
((~patient(mary))=>((~old(paul)&old(paul))))&
(![X]:((quiet(X)&~humble(X))=>(~generous(X)&old(X))))&
(![X]:((creative(X)&~brave(X))=>(humble(X)|~wise(X))))&
((?[X]:(patient(X)))<=>(?[X]:((~brave(X)|calm(X)))))&
(![X]:((strong(X)|old(X))<=>(strong(X)<~>~curious(X))))&
(((~brave(john)|creative(john)))=>(old(paul)))&
(![X]:((wise(X)|patient(X))<=>(quiet(X)|curious(X))))&
(((generous(mary)<~>calm(mary)))<=>((quiet(susan)|calm(susan))))&
(![X]:((tall(X)<~>old(X))=>(kind(X)&wise(X))))&
((?[X]:((quiet(X)<~>funny(X))))<=>(~strong(lucy)))&
(![X]:(quiet(X)<=>(curious(X)|rich(X))))&
(~calm(susan))&
(creative(susan))&
((funny(alice)<~>~creative(alice)))&
((quiet(john)<~>~brave(john)))&
(?[X]:((old(X)<~>~patient(X))))&
((~funny(lucy)&~wise(lucy)))&
((~rich(alice)<~>~brave(alice)))&
((~brave(alice)<~>~strong(alice))) | strong(lucy) | [
"p9",
"p14",
"p15",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 673769878929550379111977
% SZS output start Proof for 673769878929550379111977
10. ! [X0] : ((old(X0) | strong(X0)) <=> (strong(X0) <~> ~curious(X0))) [input p9]
15. ? [X0] : (quiet(X0) <~> funny(X0)) <=> ~strong(lucy) [input p14]
16. ! [X0] : (quiet(X0) <=> (rich(X0) | curious(X0))) [input p15]
22. ~wise(lucy) & ~funny(lucy) [input p21]
25. strong(lucy) [input hypothesis]
58. ! [X0] : (((old(X0) | strong(X0)) | ((strong(X0) | curious(X0)) & (~curious(X0) | ~strong(X0)))) & (((curious(X0) | ~strong(X0)) & (~curious(X0) | strong(X0))) | (~old(X0) & ~strong(X0)))) [nnf transformation 10]
59. ! [X0] : ((old(X0) | strong(X0) | ((strong(X0) | curious(X0)) & (~curious(X0) | ~strong(X0)))) & (((curious(X0) | ~strong(X0)) & (~curious(X0) | strong(X0))) | (~old(X0) & ~strong(X0)))) [flattening 58]
65. (? [X0] : ((~funny(X0) | ~quiet(X0)) & (funny(X0) | quiet(X0))) | strong(lucy)) & (~strong(lucy) | ! [X0] : ((quiet(X0) | ~funny(X0)) & (funny(X0) | ~quiet(X0)))) [nnf transformation 15]
66. (? [X0] : ((~funny(X0) | ~quiet(X0)) & (funny(X0) | quiet(X0))) | strong(lucy)) & (~strong(lucy) | ! [X1] : ((quiet(X1) | ~funny(X1)) & (funny(X1) | ~quiet(X1)))) [rectify 65]
67. ? [X0] : ((~funny(X0) | ~quiet(X0)) & (funny(X0) | quiet(X0))) => ((~funny(sK5) | ~quiet(sK5)) & (funny(sK5) | quiet(sK5))) [choice axiom]
68. (((~funny(sK5) | ~quiet(sK5)) & (funny(sK5) | quiet(sK5))) | strong(lucy)) & (~strong(lucy) | ! [X1] : ((quiet(X1) | ~funny(X1)) & (funny(X1) | ~quiet(X1)))) [skolemisation 66,67]
69. ! [X0] : ((quiet(X0) | (~rich(X0) & ~curious(X0))) & ((rich(X0) | curious(X0)) | ~quiet(X0))) [nnf transformation 16]
70. ! [X0] : ((quiet(X0) | (~rich(X0) & ~curious(X0))) & (rich(X0) | curious(X0) | ~quiet(X0))) [flattening 69]
109. curious(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 59]
129. ~strong(lucy) | funny(X1) | ~quiet(X1) [cnf transformation 68]
134. ~curious(X0) | quiet(X0) [cnf transformation 70]
144. ~funny(lucy) [cnf transformation 22]
150. strong(lucy) [cnf transformation 25]
151. ~strong(X0) | curious(X0) [duplicate literal removal 109]
285. 29 <=> strong(lucy) [avatar definition]
287. strong(lucy) <- (29) [avatar component clause 285]
303. 33 <=> ! [X1] : (funny(X1) | ~quiet(X1)) [avatar definition]
304. ~quiet(X1) | funny(X1) <- (33) [avatar component clause 303]
305. 33 | ~29 [avatar split clause 129,285,303]
345. 29 [avatar split clause 150,285]
346. curious(lucy) <- (29) [resolution 151,287]
347. quiet(lucy) <- (29) [resolution 346,134]
351. funny(lucy) <- (29, 33) [resolution 304,347]
353. $false <- (29, 33) [subsumption resolution 351,144]
354. ~29 | ~33 [avatar contradiction clause 353]
355. $false [avatar sat refutation 305,345,354]
% SZS output end Proof for 673769878929550379111977
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or not quiet is either generous or not creative and vice versa.
If someone is both brave and not old then lucy is either not calm or calm and vice versa.
If mary is not patient then alice is not calm.
If lucy is both not tall and calm then someone is quiet and vice versa.
If someone is not happy then someone is not wise or patient.
Everyone who is both not brave and not wise is either happy or not wise and vice versa.
If someone is not creative or quiet then someone is either not patient or not creative.
Everyone who is old is both not old and tall.
If someone is not happy then someone is not wise.
If someone is either calm or not generous then someone is not wise and vice versa.
Everyone who is funny or not patient is either tall or wise.
Everyone who is both old and not creative is curious or calm and vice versa.
If susan is either calm or old then mary is either not funny or not patient.
Everyone who is not brave or not patient is both calm and not patient.
If someone is both not tall and not strong then alice is either kind or not generous and vice versa.
Everyone who is both not patient and not quiet is either not funny or not strong.
Fred is both not humble and not funny.
John is not generous or not curious.
Susan is not creative.
Someone is either not strong or not quiet.
Lucy is both wise and humble. | Alice is not funny. | neutral | (![X]:((creative(X)|~quiet(X))<=>(generous(X)<~>~creative(X))))&
((?[X]:((brave(X)&~old(X))))<=>((~calm(lucy)<~>calm(lucy))))&
((~patient(mary))=>(~calm(alice)))&
(((~tall(lucy)&calm(lucy)))<=>(?[X]:(quiet(X))))&
((?[X]:(~happy(X)))=>(?[X]:((~wise(X)|patient(X)))))&
(![X]:((~brave(X)&~wise(X))<=>(happy(X)<~>~wise(X))))&
((?[X]:((~creative(X)|quiet(X))))=>(?[X]:((~patient(X)<~>~creative(X)))))&
(![X]:(old(X)=>(~old(X)&tall(X))))&
((?[X]:(~happy(X)))=>(?[X]:(~wise(X))))&
((?[X]:((calm(X)<~>~generous(X))))<=>(?[X]:(~wise(X))))&
(![X]:((funny(X)|~patient(X))=>(tall(X)<~>wise(X))))&
(![X]:((old(X)&~creative(X))<=>(curious(X)|calm(X))))&
(((calm(susan)<~>old(susan)))=>((~funny(mary)<~>~patient(mary))))&
(![X]:((~brave(X)|~patient(X))=>(calm(X)&~patient(X))))&
((?[X]:((~tall(X)&~strong(X))))<=>((kind(alice)<~>~generous(alice))))&
(![X]:((~patient(X)&~quiet(X))=>(~funny(X)<~>~strong(X))))&
((~humble(fred)&~funny(fred)))&
((~generous(john)|~curious(john)))&
(~creative(susan))&
(?[X]:((~strong(X)<~>~quiet(X))))&
((wise(lucy)&humble(lucy))) | ~funny(alice) | [] | null | 0 |
Everyone who is happy is both curious and creative and vice versa.
Everyone who is rich is not humble or not brave and vice versa.
Everyone who is either not wise or not calm is calm or wise.
If paul is either not creative or creative then someone is either brave or not quiet and vice versa.
Everyone who is both tall and kind is both kind and not strong.
If someone is creative or not brave then fred is both not calm and not humble.
Everyone who is strong or not tall is funny and vice versa.
Everyone who is brave is both wise and quiet and vice versa.
If paul is kind or patient then lucy is not brave.
Everyone who is either not calm or brave is both old and not patient.
If mary is both calm and not wise then fred is not patient or not rich and vice versa.
If mary is either not old or not tall then someone is not quiet or not funny.
Everyone who is either not happy or old is not curious and vice versa.
Everyone who is not curious is either old or not brave and vice versa.
If someone is both not brave and calm then lucy is both generous and humble.
Everyone who is both curious and brave is not quiet or not patient and vice versa.
Someone is not creative.
Someone is old or patient.
Someone is humble or wise.
Paul is rich or wise.
Someone is happy or wise.
Mary is either strong or not rich.
Lucy is either not happy or strong. | Fred is not calm. | entailment | (![X]:(happy(X)<=>(curious(X)&creative(X))))&
(![X]:(rich(X)<=>(~humble(X)|~brave(X))))&
(![X]:((~wise(X)<~>~calm(X))=>(calm(X)|wise(X))))&
(((~creative(paul)<~>creative(paul)))<=>(?[X]:((brave(X)<~>~quiet(X)))))&
(![X]:((tall(X)&kind(X))=>(kind(X)&~strong(X))))&
((?[X]:((creative(X)|~brave(X))))=>((~calm(fred)&~humble(fred))))&
(![X]:((strong(X)|~tall(X))<=>funny(X)))&
(![X]:(brave(X)<=>(wise(X)&quiet(X))))&
(((kind(paul)|patient(paul)))=>(~brave(lucy)))&
(![X]:((~calm(X)<~>brave(X))=>(old(X)&~patient(X))))&
(((calm(mary)&~wise(mary)))<=>((~patient(fred)|~rich(fred))))&
(((~old(mary)<~>~tall(mary)))=>(?[X]:((~quiet(X)|~funny(X)))))&
(![X]:((~happy(X)<~>old(X))<=>~curious(X)))&
(![X]:(~curious(X)<=>(old(X)<~>~brave(X))))&
((?[X]:((~brave(X)&calm(X))))=>((generous(lucy)&humble(lucy))))&
(![X]:((curious(X)&brave(X))<=>(~quiet(X)|~patient(X))))&
(?[X]:(~creative(X)))&
(?[X]:((old(X)|patient(X))))&
(?[X]:((humble(X)|wise(X))))&
((rich(paul)|wise(paul)))&
(?[X]:((happy(X)|wise(X))))&
((strong(mary)<~>~rich(mary)))&
((~happy(lucy)<~>strong(lucy))) | ~calm(fred) | [
"p0",
"p5",
"p7",
"p12",
"p13",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 3248582310923902595248629
% SZS output start Proof for 3248582310923902595248629
1. ! [X0] : (happy(X0) <=> (creative(X0) & curious(X0))) [input p0]
6. ? [X0] : (~brave(X0) | creative(X0)) => (~humble(fred) & ~calm(fred)) [input p5]
8. ! [X0] : (brave(X0) <=> (quiet(X0) & wise(X0))) [input p7]
13. ! [X0] : ((~happy(X0) <~> old(X0)) <=> ~curious(X0)) [input p12]
14. ! [X0] : (~curious(X0) <=> (old(X0) <~> ~brave(X0))) [input p13]
16. ! [X0] : ((brave(X0) & curious(X0)) <=> (~patient(X0) | ~quiet(X0))) [input p15]
18. ? [X0] : (patient(X0) | old(X0)) [input p17]
24. calm(fred) [input hypothesis]
31. (~humble(fred) & ~calm(fred)) | ! [X0] : (brave(X0) & ~creative(X0)) [ennf transformation 6]
37. ! [X0] : ((happy(X0) | (~creative(X0) | ~curious(X0))) & ((creative(X0) & curious(X0)) | ~happy(X0))) [nnf transformation 1]
38. ! [X0] : ((happy(X0) | ~creative(X0) | ~curious(X0)) & ((creative(X0) & curious(X0)) | ~happy(X0))) [flattening 37]
46. ! [X0] : ((brave(X0) | (~quiet(X0) | ~wise(X0))) & ((quiet(X0) & wise(X0)) | ~brave(X0))) [nnf transformation 8]
47. ! [X0] : ((brave(X0) | ~quiet(X0) | ~wise(X0)) & ((quiet(X0) & wise(X0)) | ~brave(X0))) [flattening 46]
54. ! [X0] : ((((~old(X0) | happy(X0)) & (old(X0) | ~happy(X0))) | curious(X0)) & (~curious(X0) | ((~happy(X0) | ~old(X0)) & (old(X0) | happy(X0))))) [nnf transformation 13]
55. ! [X0] : ((~curious(X0) | ((old(X0) | brave(X0)) & (~brave(X0) | ~old(X0)))) & (((brave(X0) | ~old(X0)) & (~brave(X0) | old(X0))) | curious(X0))) [nnf transformation 14]
56. ! [X0] : (((brave(X0) & curious(X0)) | (patient(X0) & quiet(X0))) & ((~patient(X0) | ~quiet(X0)) | (~brave(X0) | ~curious(X0)))) [nnf transformation 16]
57. ! [X0] : (((brave(X0) & curious(X0)) | (patient(X0) & quiet(X0))) & (~patient(X0) | ~quiet(X0) | ~brave(X0) | ~curious(X0))) [flattening 56]
60. ? [X0] : (patient(X0) | old(X0)) => (patient(sK3) | old(sK3)) [choice axiom]
61. patient(sK3) | old(sK3) [skolemisation 18,60]
68. ~happy(X0) | curious(X0) [cnf transformation 38]
87. ~calm(fred) | brave(X0) [cnf transformation 31]
93. ~brave(X0) | quiet(X0) [cnf transformation 47]
111. ~old(X0) | happy(X0) | curious(X0) [cnf transformation 54]
112. ~brave(X0) | old(X0) | curious(X0) [cnf transformation 55]
114. ~curious(X0) | ~brave(X0) | ~old(X0) [cnf transformation 55]
117. ~patient(X0) | ~quiet(X0) | ~brave(X0) | ~curious(X0) [cnf transformation 57]
120. brave(X0) | quiet(X0) [cnf transformation 57]
123. patient(sK3) | old(sK3) [cnf transformation 61]
131. calm(fred) [cnf transformation 24]
155. 4 <=> ! [X0] : brave(X0) [avatar definition]
156. brave(X0) <- (4) [avatar component clause 155]
167. 7 <=> calm(fred) [avatar definition]
170. 4 | ~7 [avatar split clause 87,167,155]
225. ~old(X0) | curious(X0) [subsumption resolution 111,68]
227. ~old(X0) | ~brave(X0) [subsumption resolution 114,225]
228. ~brave(X0) | curious(X0) [subsumption resolution 112,227]
237. quiet(X0) [subsumption resolution 120,93]
238. ~patient(X0) | ~brave(X0) | ~curious(X0) [subsumption resolution 117,237]
239. ~patient(X0) | ~brave(X0) [subsumption resolution 238,228]
241. 21 <=> old(sK3) [avatar definition]
243. old(sK3) <- (21) [avatar component clause 241]
245. 22 <=> patient(sK3) [avatar definition]
247. patient(sK3) <- (22) [avatar component clause 245]
248. 21 | 22 [avatar split clause 123,245,241]
296. 7 [avatar split clause 131,167]
320. ~brave(sK3) <- (21) [resolution 227,243]
321. $false <- (4, 21) [subsumption resolution 320,156]
322. ~4 | ~21 [avatar contradiction clause 321]
329. ~brave(sK3) <- (22) [resolution 239,247]
332. $false <- (4, 22) [subsumption resolution 329,156]
333. ~4 | ~22 [avatar contradiction clause 332]
334. $false [avatar sat refutation 170,248,296,322,333]
% SZS output end Proof for 3248582310923902595248629
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong is not generous or not rich.
Everyone who is not kind or humble is kind and vice versa.
If susan is happy or old then someone is not tall and vice versa.
Everyone who is not happy is both not creative and wise and vice versa.
If fred is either not funny or not calm then mary is not brave and vice versa.
Everyone who is tall or not funny is not curious and vice versa.
If someone is not humble then someone is not calm.
Everyone who is both not creative and not strong is happy or not creative.
Everyone who is kind or strong is either not quiet or not curious.
Everyone who is strong or curious is either tall or creative.
If alice is not strong then alice is not tall and vice versa.
If alice is not wise then fred is happy and vice versa.
If someone is funny then someone is not kind.
If alice is either not rich or not calm then someone is calm or not wise.
Everyone who is either tall or not old is both not creative and wise and vice versa.
Everyone who is either not rich or not creative is not brave.
Someone is not curious.
Someone is both not patient and wise.
Someone is either not rich or funny.
Someone is rich.
Someone is either happy or not strong.
Someone is either not generous or strong. | Mary is not curious. | entailment | (![X]:(strong(X)=>(~generous(X)|~rich(X))))&
(![X]:((~kind(X)|humble(X))<=>kind(X)))&
(((happy(susan)|old(susan)))<=>(?[X]:(~tall(X))))&
(![X]:(~happy(X)<=>(~creative(X)&wise(X))))&
(((~funny(fred)<~>~calm(fred)))<=>(~brave(mary)))&
(![X]:((tall(X)|~funny(X))<=>~curious(X)))&
((?[X]:(~humble(X)))=>(?[X]:(~calm(X))))&
(![X]:((~creative(X)&~strong(X))=>(happy(X)|~creative(X))))&
(![X]:((kind(X)|strong(X))=>(~quiet(X)<~>~curious(X))))&
(![X]:((strong(X)|curious(X))=>(tall(X)<~>creative(X))))&
((~strong(alice))<=>(~tall(alice)))&
((~wise(alice))<=>(happy(fred)))&
((?[X]:(funny(X)))=>(?[X]:(~kind(X))))&
(((~rich(alice)<~>~calm(alice)))=>(?[X]:((calm(X)|~wise(X)))))&
(![X]:((tall(X)<~>~old(X))<=>(~creative(X)&wise(X))))&
(![X]:((~rich(X)<~>~creative(X))=>~brave(X)))&
(?[X]:(~curious(X)))&
(?[X]:((~patient(X)&wise(X))))&
(?[X]:((~rich(X)<~>funny(X))))&
(?[X]:(rich(X)))&
(?[X]:((happy(X)<~>~strong(X))))&
(?[X]:((~generous(X)<~>strong(X)))) | ~curious(mary) | [
"p1",
"p5",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 592430359869299431840881
% SZS output start Proof for 592430359869299431840881
2. ! [X0] : ((humble(X0) | ~kind(X0)) <=> kind(X0)) [input p1]
6. ! [X0] : ((~funny(X0) | tall(X0)) <=> ~curious(X0)) [input p5]
13. ? [X0] : funny(X0) => ? [X0] : ~kind(X0) [input p12]
23. curious(mary) [input hypothesis]
25. ? [X0] : funny(X0) => ? [X1] : ~kind(X1) [rectify 13]
34. ? [X1] : ~kind(X1) | ! [X0] : ~funny(X0) [ennf transformation 25]
37. ! [X0] : (((humble(X0) | ~kind(X0)) | ~kind(X0)) & (kind(X0) | (~humble(X0) & kind(X0)))) [nnf transformation 2]
38. ! [X0] : ((humble(X0) | ~kind(X0) | ~kind(X0)) & (kind(X0) | (~humble(X0) & kind(X0)))) [flattening 37]
47. ! [X0] : (((~funny(X0) | tall(X0)) | curious(X0)) & (~curious(X0) | (funny(X0) & ~tall(X0)))) [nnf transformation 6]
48. ! [X0] : ((~funny(X0) | tall(X0) | curious(X0)) & (~curious(X0) | (funny(X0) & ~tall(X0)))) [flattening 47]
56. ? [X0] : ~kind(X0) | ! [X1] : ~funny(X1) [rectify 34]
57. ? [X0] : ~kind(X0) => ~kind(sK2) [choice axiom]
58. ~kind(sK2) | ! [X1] : ~funny(X1) [skolemisation 56,57]
81. kind(X0) | kind(X0) [cnf transformation 38]
95. ~curious(X0) | funny(X0) [cnf transformation 48]
111. ~kind(sK2) | ~funny(X1) [cnf transformation 58]
131. curious(mary) [cnf transformation 23]
132. kind(X0) [duplicate literal removal 81]
199. ~funny(X1) [subsumption resolution 111,132]
242. funny(mary) [resolution 95,131]
243. $false [subsumption resolution 242,199]
% SZS output end Proof for 592430359869299431840881
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is funny is either not wise or calm and vice versa. If someone is kind or not strong then paul is happy or brave. If susan is either creative or tall then fred is not strong. If fred is quiet or not rich then susan is not happy or not old. Everyone who is rich or not wise is not brave. Everyone who is not strong or not generous is strong. If fred is either not old or kind then someone is strong and vice versa. Everyone who is not brave is both happy and not wise and vice versa. Everyone who is both not wise and rich is either generous or brave and vice versa. If susan is either strong or happy then paul is either patient or not tall and vice versa. Everyone who is brave is either tall or not brave and vice versa. Everyone who is either not humble or not old is both tall and old and vice versa. Everyone who is both patient and calm is humble or not happy. If someone is not creative then susan is not rich or happy. Everyone who is either patient or not wise is rich. If someone is both not curious and not kind then someone is patient and vice versa. Someone is not kind. Someone is both not wise and not creative. John is either tall or generous. Someone is quiet or not kind. Paul is either wise or funny. Lucy is both not creative and not generous. Alice is not funny. Someone is not humble. | Alice is not patient. | entailment | (![X]:(funny(X)<=>(~wise(X)<~>calm(X))))&
((?[X]:((kind(X)|~strong(X))))=>((happy(paul)|brave(paul))))&
(((creative(susan)<~>tall(susan)))=>(~strong(fred)))&
(((quiet(fred)|~rich(fred)))=>((~happy(susan)|~old(susan))))&
(![X]:((rich(X)|~wise(X))=>~brave(X)))&
(![X]:((~strong(X)|~generous(X))=>strong(X)))&
(((~old(fred)<~>kind(fred)))<=>(?[X]:(strong(X))))&
(![X]:(~brave(X)<=>(happy(X)&~wise(X))))&
(![X]:((~wise(X)&rich(X))<=>(generous(X)<~>brave(X))))&
(((strong(susan)<~>happy(susan)))<=>((patient(paul)<~>~tall(paul))))&
(![X]:(brave(X)<=>(tall(X)<~>~brave(X))))&
(![X]:((~humble(X)<~>~old(X))<=>(tall(X)&old(X))))&
(![X]:((patient(X)&calm(X))=>(humble(X)|~happy(X))))&
((?[X]:(~creative(X)))=>((~rich(susan)|happy(susan))))&
(![X]:((patient(X)<~>~wise(X))=>rich(X)))&
((?[X]:((~curious(X)&~kind(X))))<=>(?[X]:(patient(X))))&
(?[X]:(~kind(X)))&
(?[X]:((~wise(X)&~creative(X))))&
((tall(john)<~>generous(john)))&
(?[X]:((quiet(X)|~kind(X))))&
((wise(paul)<~>funny(paul)))&
((~creative(lucy)&~generous(lucy)))&
(~funny(alice))&
(?[X]:(~humble(X))) | ~patient(alice) | [
"p0",
"p4",
"p7",
"p10",
"p11",
"p12",
"p14",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 8441358291241670291434561
% SZS output start Proof for 8441358291241670291434561
1. ! [X0] : (funny(X0) <=> (~wise(X0) <~> calm(X0))) [input p0]
5. ! [X0] : ((~wise(X0) | rich(X0)) => ~brave(X0)) [input p4]
8. ! [X0] : (~brave(X0) <=> (~wise(X0) & happy(X0))) [input p7]
11. ! [X0] : (brave(X0) <=> (tall(X0) <~> ~brave(X0))) [input p10]
12. ! [X0] : ((~humble(X0) <~> ~old(X0)) <=> (old(X0) & tall(X0))) [input p11]
13. ! [X0] : ((calm(X0) & patient(X0)) => (~happy(X0) | humble(X0))) [input p12]
15. ! [X0] : ((patient(X0) <~> ~wise(X0)) => rich(X0)) [input p14]
23. ~funny(alice) [input p22]
25. patient(alice) [input hypothesis]
32. ! [X0] : (~brave(X0) | (wise(X0) & ~rich(X0))) [ennf transformation 5]
34. ! [X0] : ((~happy(X0) | humble(X0)) | (~calm(X0) | ~patient(X0))) [ennf transformation 13]
35. ! [X0] : (~happy(X0) | humble(X0) | ~calm(X0) | ~patient(X0)) [flattening 34]
38. ! [X0] : (rich(X0) | (patient(X0) <=> ~wise(X0))) [ennf transformation 15]
39. ! [X0] : ((funny(X0) | ((~wise(X0) | ~calm(X0)) & (calm(X0) | wise(X0)))) & (((~calm(X0) | wise(X0)) & (calm(X0) | ~wise(X0))) | ~funny(X0))) [nnf transformation 1]
45. ! [X0] : ((~brave(X0) | (wise(X0) | ~happy(X0))) & ((~wise(X0) & happy(X0)) | brave(X0))) [nnf transformation 8]
46. ! [X0] : ((~brave(X0) | wise(X0) | ~happy(X0)) & ((~wise(X0) & happy(X0)) | brave(X0))) [flattening 45]
50. ! [X0] : ((brave(X0) | ((tall(X0) | brave(X0)) & (~brave(X0) | ~tall(X0)))) & (((brave(X0) | ~tall(X0)) & (~brave(X0) | tall(X0))) | ~brave(X0))) [nnf transformation 11]
51. ! [X0] : ((((old(X0) | humble(X0)) & (~old(X0) | ~humble(X0))) | (~old(X0) | ~tall(X0))) & ((old(X0) & tall(X0)) | ((~humble(X0) | old(X0)) & (~old(X0) | humble(X0))))) [nnf transformation 12]
52. ! [X0] : ((((old(X0) | humble(X0)) & (~old(X0) | ~humble(X0))) | ~old(X0) | ~tall(X0)) & ((old(X0) & tall(X0)) | ((~humble(X0) | old(X0)) & (~old(X0) | humble(X0))))) [flattening 51]
53. ! [X0] : (rich(X0) | ((patient(X0) | wise(X0)) & (~wise(X0) | ~patient(X0)))) [nnf transformation 38]
71. calm(X0) | funny(X0) | wise(X0) [cnf transformation 39]
79. ~rich(X0) | ~brave(X0) [cnf transformation 32]
80. ~brave(X0) | wise(X0) [cnf transformation 32]
87. brave(X0) | happy(X0) [cnf transformation 46]
88. ~wise(X0) | brave(X0) [cnf transformation 46]
104. ~brave(X0) | tall(X0) | ~brave(X0) [cnf transformation 50]
107. brave(X0) | tall(X0) | brave(X0) [cnf transformation 50]
111. old(X0) | ~humble(X0) | old(X0) [cnf transformation 52]
112. ~old(X0) | ~humble(X0) | ~old(X0) | ~tall(X0) [cnf transformation 52]
114. ~happy(X0) | humble(X0) | ~calm(X0) | ~patient(X0) [cnf transformation 35]
116. ~patient(X0) | ~wise(X0) | rich(X0) [cnf transformation 53]
131. ~funny(alice) [cnf transformation 23]
133. patient(alice) [cnf transformation 25]
134. old(X0) | ~humble(X0) [duplicate literal removal 111]
135. ~old(X0) | ~humble(X0) | ~tall(X0) [duplicate literal removal 112]
136. ~brave(X0) | tall(X0) [duplicate literal removal 104]
137. tall(X0) | brave(X0) [duplicate literal removal 107]
229. tall(X0) [subsumption resolution 136,137]
230. ~humble(X0) | ~old(X0) [subsumption resolution 135,229]
231. ~humble(X0) [subsumption resolution 134,230]
232. ~patient(X0) | ~calm(X0) | ~happy(X0) [subsumption resolution 114,231]
295. happy(X0) | wise(X0) [resolution 87,80]
315. ~wise(alice) | rich(alice) [resolution 116,133]
318. 30 <=> rich(alice) [avatar definition]
320. rich(alice) <- (30) [avatar component clause 318]
322. 31 <=> wise(alice) [avatar definition]
323. wise(alice) <- (31) [avatar component clause 322]
324. ~wise(alice) <- (~31) [avatar component clause 322]
325. 30 | ~31 [avatar split clause 315,322,318]
338. ~calm(alice) | ~happy(alice) [resolution 232,133]
342. 34 <=> happy(alice) [avatar definition]
344. ~happy(alice) <- (~34) [avatar component clause 342]
346. 35 <=> calm(alice) [avatar definition]
348. ~calm(alice) <- (~35) [avatar component clause 346]
349. ~34 | ~35 [avatar split clause 338,346,342]
360. wise(alice) <- (~34) [resolution 344,295]
363. 31 | 34 [avatar split clause 360,342,322]
365. ~brave(alice) <- (30) [resolution 320,79]
367. brave(alice) <- (31) [resolution 323,88]
368. $false <- (30, 31) [subsumption resolution 367,365]
369. ~30 | ~31 [avatar contradiction clause 368]
375. funny(alice) | wise(alice) <- (~35) [resolution 348,71]
376. wise(alice) <- (~35) [subsumption resolution 375,131]
377. $false <- (~31, ~35) [subsumption resolution 376,324]
378. 31 | 35 [avatar contradiction clause 377]
379. $false [avatar sat refutation 325,349,363,369,378]
% SZS output end Proof for 8441358291241670291434561
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If mary is rich then someone is quiet and vice versa. If john is not patient or not old then someone is not rich. Everyone who is curious is either not humble or not creative. If someone is old then someone is both rich and not funny. Everyone who is kind is both quiet and creative and vice versa. Everyone who is both not old and wise is both calm and kind. Everyone who is not calm or brave is both not calm and not tall. Everyone who is calm is not funny and vice versa. Everyone who is both tall and quiet is brave or kind and vice versa. Everyone who is either wise or not funny is both not calm and brave. Everyone who is either rich or not rich is both creative and curious. If someone is not tall then someone is either not generous or not humble and vice versa. If alice is both generous and not humble then paul is not happy and vice versa. Everyone who is calm or not kind is happy and vice versa. If alice is both humble and not tall then someone is patient or not calm and vice versa. Everyone who is either calm or tall is both not patient and creative. Lucy is either not wise or curious. Someone is both strong and not generous. Someone is either not kind or wise. Paul is either strong or not brave. Someone is either old or funny. Someone is strong. Lucy is both curious and creative. | Paul is funny. | contradiction | ((rich(mary))<=>(?[X]:(quiet(X))))&
(((~patient(john)|~old(john)))=>(?[X]:(~rich(X))))&
(![X]:(curious(X)=>(~humble(X)<~>~creative(X))))&
((?[X]:(old(X)))=>(?[X]:((rich(X)&~funny(X)))))&
(![X]:(kind(X)<=>(quiet(X)&creative(X))))&
(![X]:((~old(X)&wise(X))=>(calm(X)&kind(X))))&
(![X]:((~calm(X)|brave(X))=>(~calm(X)&~tall(X))))&
(![X]:(calm(X)<=>~funny(X)))&
(![X]:((tall(X)&quiet(X))<=>(brave(X)|kind(X))))&
(![X]:((wise(X)<~>~funny(X))=>(~calm(X)&brave(X))))&
(![X]:((rich(X)<~>~rich(X))=>(creative(X)&curious(X))))&
((?[X]:(~tall(X)))<=>(?[X]:((~generous(X)<~>~humble(X)))))&
(((generous(alice)&~humble(alice)))<=>(~happy(paul)))&
(![X]:((calm(X)|~kind(X))<=>happy(X)))&
(((humble(alice)&~tall(alice)))<=>(?[X]:((patient(X)|~calm(X)))))&
(![X]:((calm(X)<~>tall(X))=>(~patient(X)&creative(X))))&
((~wise(lucy)<~>curious(lucy)))&
(?[X]:((strong(X)&~generous(X))))&
(?[X]:((~kind(X)<~>wise(X))))&
((strong(paul)<~>~brave(paul)))&
(?[X]:((old(X)<~>funny(X))))&
(?[X]:(strong(X)))&
((curious(lucy)&creative(lucy))) | funny(paul) | [
"p2",
"p7",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6695198712016284539239497
% SZS output start Proof for 6695198712016284539239497
3. ! [X0] : (curious(X0) => (~humble(X0) <~> ~creative(X0))) [input p2]
8. ! [X0] : (calm(X0) <=> ~funny(X0)) [input p7]
11. ! [X0] : ((rich(X0) <~> ~rich(X0)) => (curious(X0) & creative(X0))) [input p10]
15. (~tall(alice) & humble(alice)) <=> ? [X0] : (~calm(X0) | patient(X0)) [input p14]
24. funny(paul) [input hypothesis]
28. ! [X0] : ((~humble(X0) <~> ~creative(X0)) | ~curious(X0)) [ennf transformation 3]
34. ! [X0] : ((curious(X0) & creative(X0)) | (rich(X0) <=> ~rich(X0))) [ennf transformation 11]
42. ! [X0] : (((creative(X0) | humble(X0)) & (~creative(X0) | ~humble(X0))) | ~curious(X0)) [nnf transformation 28]
48. ! [X0] : ((calm(X0) | funny(X0)) & (~funny(X0) | ~calm(X0))) [nnf transformation 8]
52. ! [X0] : ((curious(X0) & creative(X0)) | ((rich(X0) | rich(X0)) & (~rich(X0) | ~rich(X0)))) [nnf transformation 34]
62. ((~tall(alice) & humble(alice)) | ! [X0] : (calm(X0) & ~patient(X0))) & (? [X0] : (~calm(X0) | patient(X0)) | (tall(alice) | ~humble(alice))) [nnf transformation 15]
63. ((~tall(alice) & humble(alice)) | ! [X0] : (calm(X0) & ~patient(X0))) & (? [X0] : (~calm(X0) | patient(X0)) | tall(alice) | ~humble(alice)) [flattening 62]
64. ((~tall(alice) & humble(alice)) | ! [X0] : (calm(X0) & ~patient(X0))) & (? [X1] : (~calm(X1) | patient(X1)) | tall(alice) | ~humble(alice)) [rectify 63]
65. ? [X1] : (~calm(X1) | patient(X1)) => (~calm(sK5) | patient(sK5)) [choice axiom]
66. ((~tall(alice) & humble(alice)) | ! [X0] : (calm(X0) & ~patient(X0))) & ((~calm(sK5) | patient(sK5)) | tall(alice) | ~humble(alice)) [skolemisation 64,65]
84. ~creative(X0) | ~humble(X0) | ~curious(X0) [cnf transformation 42]
97. ~calm(X0) | ~funny(X0) [cnf transformation 48]
108. creative(X0) | ~rich(X0) | ~rich(X0) [cnf transformation 52]
109. creative(X0) | rich(X0) | rich(X0) [cnf transformation 52]
110. curious(X0) | ~rich(X0) | ~rich(X0) [cnf transformation 52]
111. curious(X0) | rich(X0) | rich(X0) [cnf transformation 52]
124. humble(alice) | calm(X0) [cnf transformation 66]
144. funny(paul) [cnf transformation 24]
145. creative(X0) | ~rich(X0) [duplicate literal removal 108]
146. creative(X0) | rich(X0) [duplicate literal removal 109]
147. curious(X0) | ~rich(X0) [duplicate literal removal 110]
148. curious(X0) | rich(X0) [duplicate literal removal 111]
193. curious(X0) [subsumption resolution 147,148]
194. creative(X0) [subsumption resolution 145,146]
225. 17 <=> humble(alice) [avatar definition]
226. humble(alice) <- (17) [avatar component clause 225]
236. 19 <=> ! [X0] : calm(X0) [avatar definition]
237. calm(X0) <- (19) [avatar component clause 236]
247. 19 | 17 [avatar split clause 124,225,236]
302. ~humble(X1) | ~curious(X1) [resolution 84,194]
304. ~humble(X1) [subsumption resolution 302,193]
307. $false <- (17) [resolution 304,226]
308. ~17 [avatar contradiction clause 307]
312. ~funny(X1) <- (19) [resolution 237,97]
321. $false <- (19) [resolution 312,144]
324. ~19 [avatar contradiction clause 321]
325. $false [avatar sat refutation 247,308,324]
% SZS output end Proof for 6695198712016284539239497
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If paul is both not kind and not tall then someone is funny.
If someone is both not kind and not humble then lucy is old or wise.
If lucy is either happy or rich then someone is not quiet.
Everyone who is both not happy and not tall is either not generous or not rich and vice versa.
Everyone who is not rich or brave is rich and vice versa.
If paul is generous then someone is old.
Everyone who is not calm or not old is not kind.
If someone is both not curious and not old then someone is not kind and vice versa.
Everyone who is both tall and not strong is not calm and vice versa.
Everyone who is curious is either not humble or not tall.
Everyone who is not tall is either not kind or not curious.
Everyone who is generous is either not patient or curious.
If alice is both not happy and not kind then john is quiet or not creative.
Everyone who is not funny is creative or not tall.
Everyone who is not wise or not strong is both not creative and humble.
Everyone who is not calm is either rich or not strong and vice versa.
Alice is not kind or not wise.
Mary is not wise.
Lucy is both funny and wise. | Alice is patient. | neutral | (((~kind(paul)&~tall(paul)))=>(?[X]:(funny(X))))&
((?[X]:((~kind(X)&~humble(X))))=>((old(lucy)|wise(lucy))))&
(((happy(lucy)<~>rich(lucy)))=>(?[X]:(~quiet(X))))&
(![X]:((~happy(X)&~tall(X))<=>(~generous(X)<~>~rich(X))))&
(![X]:((~rich(X)|brave(X))<=>rich(X)))&
((generous(paul))=>(?[X]:(old(X))))&
(![X]:((~calm(X)|~old(X))=>~kind(X)))&
((?[X]:((~curious(X)&~old(X))))<=>(?[X]:(~kind(X))))&
(![X]:((tall(X)&~strong(X))<=>~calm(X)))&
(![X]:(curious(X)=>(~humble(X)<~>~tall(X))))&
(![X]:(~tall(X)=>(~kind(X)<~>~curious(X))))&
(![X]:(generous(X)=>(~patient(X)<~>curious(X))))&
(((~happy(alice)&~kind(alice)))=>((quiet(john)|~creative(john))))&
(![X]:(~funny(X)=>(creative(X)|~tall(X))))&
(![X]:((~wise(X)|~strong(X))=>(~creative(X)&humble(X))))&
(![X]:(~calm(X)<=>(rich(X)<~>~strong(X))))&
((~kind(alice)|~wise(alice)))&
(~wise(mary))&
((funny(lucy)&wise(lucy))) | patient(alice) | [] | null | 0 |
Everyone who is not curious is generous.
Everyone who is not curious is not funny or not creative and vice versa.
Everyone who is curious is either happy or not patient and vice versa.
If someone is kind or creative then lucy is both humble and not happy.
Everyone who is both creative and not creative is not generous or not quiet and vice versa.
Everyone who is both not curious and kind is both not happy and not strong.
If mary is both not old and brave then someone is happy and vice versa.
Everyone who is both old and not funny is either not curious or not old and vice versa.
If someone is either funny or not tall then someone is both not creative and kind.
Everyone who is not humble or not brave is not humble or humble.
If someone is both patient and not rich then someone is both wise and not old.
If lucy is humble or not calm then someone is either generous or strong.
If someone is not creative or not quiet then john is not generous.
Everyone who is not happy or creative is both calm and quiet.
Everyone who is curious is either creative or generous and vice versa.
Someone is wise.
John is not patient.
Lucy is either kind or not humble.
Someone is either calm or wise.
Lucy is rich.
Mary is either tall or not happy.
Susan is either strong or brave. | Lucy is not strong. | entailment | (![X]:(~curious(X)=>generous(X)))&
(![X]:(~curious(X)<=>(~funny(X)|~creative(X))))&
(![X]:(curious(X)<=>(happy(X)<~>~patient(X))))&
((?[X]:((kind(X)|creative(X))))=>((humble(lucy)&~happy(lucy))))&
(![X]:((creative(X)&~creative(X))<=>(~generous(X)|~quiet(X))))&
(![X]:((~curious(X)&kind(X))=>(~happy(X)&~strong(X))))&
(((~old(mary)&brave(mary)))<=>(?[X]:(happy(X))))&
(![X]:((old(X)&~funny(X))<=>(~curious(X)<~>~old(X))))&
((?[X]:((funny(X)<~>~tall(X))))=>(?[X]:((~creative(X)&kind(X)))))&
(![X]:((~humble(X)|~brave(X))=>(~humble(X)|humble(X))))&
((?[X]:((patient(X)&~rich(X))))=>(?[X]:((wise(X)&~old(X)))))&
(((humble(lucy)|~calm(lucy)))=>(?[X]:((generous(X)<~>strong(X)))))&
((?[X]:((~creative(X)|~quiet(X))))=>(~generous(john)))&
(![X]:((~happy(X)|creative(X))=>(calm(X)&quiet(X))))&
(![X]:(curious(X)<=>(creative(X)<~>generous(X))))&
(?[X]:(wise(X)))&
(~patient(john))&
((kind(lucy)<~>~humble(lucy)))&
(?[X]:((calm(X)<~>wise(X))))&
(rich(lucy))&
((tall(mary)<~>~happy(mary)))&
((strong(susan)<~>brave(susan))) | ~strong(lucy) | [
"p3",
"p4",
"p5",
"p12",
"p14",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 1225256415799918710986807
% SZS output start Proof for 1225256415799918710986807
4. ? [X0] : (creative(X0) | kind(X0)) => (~happy(lucy) & humble(lucy)) [input p3]
5. ! [X0] : ((~creative(X0) & creative(X0)) <=> (~quiet(X0) | ~generous(X0))) [input p4]
6. ! [X0] : ((kind(X0) & ~curious(X0)) => (~strong(X0) & ~happy(X0))) [input p5]
13. ? [X0] : (~quiet(X0) | ~creative(X0)) => ~generous(john) [input p12]
15. ! [X0] : (curious(X0) <=> (creative(X0) <~> generous(X0))) [input p14]
18. kind(lucy) <~> ~humble(lucy) [input p17]
23. strong(lucy) [input hypothesis]
29. (~happy(lucy) & humble(lucy)) | ! [X0] : (~creative(X0) & ~kind(X0)) [ennf transformation 4]
30. ! [X0] : ((~strong(X0) & ~happy(X0)) | (~kind(X0) | curious(X0))) [ennf transformation 6]
31. ! [X0] : ((~strong(X0) & ~happy(X0)) | ~kind(X0) | curious(X0)) [flattening 30]
36. ~generous(john) | ! [X0] : (quiet(X0) & creative(X0)) [ennf transformation 13]
41. ! [X0] : (((~creative(X0) & creative(X0)) | (quiet(X0) & generous(X0))) & ((~quiet(X0) | ~generous(X0)) | (creative(X0) | ~creative(X0)))) [nnf transformation 5]
42. ! [X0] : (((~creative(X0) & creative(X0)) | (quiet(X0) & generous(X0))) & (~quiet(X0) | ~generous(X0) | creative(X0) | ~creative(X0))) [flattening 41]
57. ! [X0] : ((curious(X0) | ((creative(X0) | ~generous(X0)) & (generous(X0) | ~creative(X0)))) & (((~generous(X0) | ~creative(X0)) & (generous(X0) | creative(X0))) | ~curious(X0))) [nnf transformation 15]
60. (humble(lucy) | ~kind(lucy)) & (~humble(lucy) | kind(lucy)) [nnf transformation 18]
75. humble(lucy) | ~creative(X0) [cnf transformation 29]
79. creative(X0) | generous(X0) [cnf transformation 42]
81. ~creative(X0) | generous(X0) [cnf transformation 42]
84. ~strong(X0) | ~kind(X0) | curious(X0) [cnf transformation 31]
104. ~generous(john) | creative(X0) [cnf transformation 36]
111. ~generous(X0) | ~creative(X0) | ~curious(X0) [cnf transformation 57]
116. ~humble(lucy) | kind(lucy) [cnf transformation 60]
124. strong(lucy) [cnf transformation 23]
129. 1 <=> ! [X0] : ~creative(X0) [avatar definition]
130. ~creative(X0) <- (1) [avatar component clause 129]
141. 4 <=> humble(lucy) [avatar definition]
144. 1 | 4 [avatar split clause 75,141,129]
147. generous(X0) [subsumption resolution 79,81]
197. creative(X0) [subsumption resolution 104,147]
199. ~creative(X0) | ~curious(X0) [subsumption resolution 111,147]
200. ~curious(X0) [subsumption resolution 199,197]
202. 15 <=> kind(lucy) [avatar definition]
206. 15 | ~4 [avatar split clause 116,141,202]
253. ~kind(lucy) | curious(lucy) [resolution 84,124]
259. ~kind(lucy) [subsumption resolution 253,200]
260. ~15 [avatar split clause 259,202]
261. $false <- (1) [subsumption resolution 130,197]
262. ~1 [avatar contradiction clause 261]
263. $false [avatar sat refutation 144,206,260,262]
% SZS output end Proof for 1225256415799918710986807
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave and not rich is either old or quiet.
If someone is generous or not brave then someone is creative and vice versa.
Everyone who is not patient is both not rich and calm.
If susan is not quiet or not rich then mary is both not rich and curious and vice versa.
Everyone who is both old and generous is both not funny and calm and vice versa.
Everyone who is both not funny and not calm is both not curious and not kind and vice versa.
If someone is brave or not curious then someone is both not humble and patient and vice versa.
If someone is both not strong and tall then someone is either not kind or quiet and vice versa.
Everyone who is either happy or generous is wise.
If lucy is either kind or curious then alice is not generous and vice versa.
If mary is both tall and kind then fred is generous or not happy.
If someone is generous then someone is both rich and funny.
Everyone who is both rich and not generous is brave.
If someone is quiet or brave then someone is either not strong or happy.
Everyone who is either old or humble is both old and not wise.
If john is both curious and patient then fred is not strong and vice versa.
Someone is not happy or not tall.
Lucy is both not rich and not patient.
Fred is both curious and generous.
Someone is generous.
Mary is quiet or not calm.
Someone is not generous. | Mary is not old. | neutral | (![X]:((brave(X)&~rich(X))=>(old(X)<~>quiet(X))))&
((?[X]:((generous(X)|~brave(X))))<=>(?[X]:(creative(X))))&
(![X]:(~patient(X)=>(~rich(X)&calm(X))))&
(((~quiet(susan)|~rich(susan)))<=>((~rich(mary)&curious(mary))))&
(![X]:((old(X)&generous(X))<=>(~funny(X)&calm(X))))&
(![X]:((~funny(X)&~calm(X))<=>(~curious(X)&~kind(X))))&
((?[X]:((brave(X)|~curious(X))))<=>(?[X]:((~humble(X)&patient(X)))))&
((?[X]:((~strong(X)&tall(X))))<=>(?[X]:((~kind(X)<~>quiet(X)))))&
(![X]:((happy(X)<~>generous(X))=>wise(X)))&
(((kind(lucy)<~>curious(lucy)))<=>(~generous(alice)))&
(((tall(mary)&kind(mary)))=>((generous(fred)|~happy(fred))))&
((?[X]:(generous(X)))=>(?[X]:((rich(X)&funny(X)))))&
(![X]:((rich(X)&~generous(X))=>brave(X)))&
((?[X]:((quiet(X)|brave(X))))=>(?[X]:((~strong(X)<~>happy(X)))))&
(![X]:((old(X)<~>humble(X))=>(old(X)&~wise(X))))&
(((curious(john)&patient(john)))<=>(~strong(fred)))&
(?[X]:((~happy(X)|~tall(X))))&
((~rich(lucy)&~patient(lucy)))&
((curious(fred)&generous(fred)))&
(?[X]:(generous(X)))&
((quiet(mary)|~calm(mary)))&
(?[X]:(~generous(X))) | ~old(mary) | [] | null | 0 |
Everyone who is both funny and not creative is either tall or generous. If paul is either brave or not generous then john is not creative and vice versa. Everyone who is either not brave or not funny is not humble and vice versa. Everyone who is either curious or creative is both not quiet and curious and vice versa. Everyone who is not curious is not old or brave and vice versa. If someone is either quiet or creative then lucy is both not quiet and not generous. Everyone who is both not strong and tall is both not curious and funny. Everyone who is either generous or calm is both not calm and happy and vice versa. Everyone who is both tall and quiet is not patient or rich and vice versa. Everyone who is not kind is quiet or wise and vice versa. Everyone who is both not brave and not wise is either old or not generous and vice versa. Everyone who is not curious is old or not kind. Everyone who is both not old and not happy is both not old and not rich and vice versa. Everyone who is either curious or not humble is not generous and vice versa. If mary is both not creative and curious then mary is not happy. Everyone who is both curious and not kind is not funny. Someone is both not generous and brave. Paul is not kind. Someone is not strong. Fred is not curious or wise. Someone is either brave or not happy. Fred is patient or happy. Someone is humble. Someone is curious. | Lucy is not strong. | neutral | (![X]:((funny(X)&~creative(X))=>(tall(X)<~>generous(X))))&
(((brave(paul)<~>~generous(paul)))<=>(~creative(john)))&
(![X]:((~brave(X)<~>~funny(X))<=>~humble(X)))&
(![X]:((curious(X)<~>creative(X))<=>(~quiet(X)&curious(X))))&
(![X]:(~curious(X)<=>(~old(X)|brave(X))))&
((?[X]:((quiet(X)<~>creative(X))))=>((~quiet(lucy)&~generous(lucy))))&
(![X]:((~strong(X)&tall(X))=>(~curious(X)&funny(X))))&
(![X]:((generous(X)<~>calm(X))<=>(~calm(X)&happy(X))))&
(![X]:((tall(X)&quiet(X))<=>(~patient(X)|rich(X))))&
(![X]:(~kind(X)<=>(quiet(X)|wise(X))))&
(![X]:((~brave(X)&~wise(X))<=>(old(X)<~>~generous(X))))&
(![X]:(~curious(X)=>(old(X)|~kind(X))))&
(![X]:((~old(X)&~happy(X))<=>(~old(X)&~rich(X))))&
(![X]:((curious(X)<~>~humble(X))<=>~generous(X)))&
(((~creative(mary)&curious(mary)))=>(~happy(mary)))&
(![X]:((curious(X)&~kind(X))=>~funny(X)))&
(?[X]:((~generous(X)&brave(X))))&
(~kind(paul))&
(?[X]:(~strong(X)))&
((~curious(fred)|wise(fred)))&
(?[X]:((brave(X)<~>~happy(X))))&
((patient(fred)|happy(fred)))&
(?[X]:(humble(X)))&
(?[X]:(curious(X))) | ~strong(lucy) | [] | null | 0 |
If lucy is patient then someone is not curious or strong and vice versa. Everyone who is either not calm or quiet is not rich or not wise and vice versa. Everyone who is old or not funny is not kind or funny and vice versa. Everyone who is either humble or not generous is both quiet and not tall. Everyone who is brave is funny. Everyone who is not humble or creative is either not wise or not strong. If lucy is not happy or not generous then someone is both not wise and not generous and vice versa. If john is not generous or not tall then mary is both humble and tall and vice versa. Everyone who is either not brave or humble is strong or not calm. If someone is calm then someone is either tall or not patient. Everyone who is kind is either not happy or strong and vice versa. If fred is not old or not rich then susan is both not curious and wise and vice versa. If someone is old then fred is both not wise and curious and vice versa. Everyone who is both not curious and brave is either rich or strong and vice versa. If john is either not generous or not old then someone is either wise or happy and vice versa. Everyone who is not brave is both humble and calm. Paul is both creative and not generous. Fred is both not kind and generous. Someone is tall or patient. Lucy is both funny and happy. Alice is not calm. Paul is not wise or not humble. Someone is either wise or creative. | Alice is not creative. | neutral | ((patient(lucy))<=>(?[X]:((~curious(X)|strong(X)))))&
(![X]:((~calm(X)<~>quiet(X))<=>(~rich(X)|~wise(X))))&
(![X]:((old(X)|~funny(X))<=>(~kind(X)|funny(X))))&
(![X]:((humble(X)<~>~generous(X))=>(quiet(X)&~tall(X))))&
(![X]:(brave(X)=>funny(X)))&
(![X]:((~humble(X)|creative(X))=>(~wise(X)<~>~strong(X))))&
(((~happy(lucy)|~generous(lucy)))<=>(?[X]:((~wise(X)&~generous(X)))))&
(((~generous(john)|~tall(john)))<=>((humble(mary)&tall(mary))))&
(![X]:((~brave(X)<~>humble(X))=>(strong(X)|~calm(X))))&
((?[X]:(calm(X)))=>(?[X]:((tall(X)<~>~patient(X)))))&
(![X]:(kind(X)<=>(~happy(X)<~>strong(X))))&
(((~old(fred)|~rich(fred)))<=>((~curious(susan)&wise(susan))))&
((?[X]:(old(X)))<=>((~wise(fred)&curious(fred))))&
(![X]:((~curious(X)&brave(X))<=>(rich(X)<~>strong(X))))&
(((~generous(john)<~>~old(john)))<=>(?[X]:((wise(X)<~>happy(X)))))&
(![X]:(~brave(X)=>(humble(X)&calm(X))))&
((creative(paul)&~generous(paul)))&
((~kind(fred)&generous(fred)))&
(?[X]:((tall(X)|patient(X))))&
((funny(lucy)&happy(lucy)))&
(~calm(alice))&
((~wise(paul)|~humble(paul)))&
(?[X]:((wise(X)<~>creative(X)))) | ~creative(alice) | [] | null | 0 |
Everyone who is not quiet or humble is not strong or not creative and vice versa.
Everyone who is quiet or rich is not curious or not brave.
If paul is funny then someone is not brave.
Everyone who is not rich is both not humble and not brave.
Everyone who is either not humble or not curious is not brave or not patient.
Everyone who is old or not curious is both not strong and not rich and vice versa.
Everyone who is strong or old is both not creative and not kind.
Everyone who is both not happy and happy is tall or patient.
Everyone who is either humble or old is either not strong or curious.
Everyone who is both rich and not patient is both not old and brave and vice versa.
Everyone who is rich is either not brave or brave.
If someone is both not happy and rich then paul is humble and vice versa.
If john is both not patient and not old then someone is both wise and not patient and vice versa.
If someone is quiet or not brave then someone is not strong.
Everyone who is kind or happy is both strong and quiet.
Everyone who is either curious or kind is either humble or not creative and vice versa.
Someone is generous or humble.
Someone is not kind or old.
Alice is both not funny and tall.
Fred is tall.
Mary is either calm or brave.
Someone is not curious. | Alice is calm. | neutral | (![X]:((~quiet(X)|humble(X))<=>(~strong(X)|~creative(X))))&
(![X]:((quiet(X)|rich(X))=>(~curious(X)|~brave(X))))&
((funny(paul))=>(?[X]:(~brave(X))))&
(![X]:(~rich(X)=>(~humble(X)&~brave(X))))&
(![X]:((~humble(X)<~>~curious(X))=>(~brave(X)|~patient(X))))&
(![X]:((old(X)|~curious(X))<=>(~strong(X)&~rich(X))))&
(![X]:((strong(X)|old(X))=>(~creative(X)&~kind(X))))&
(![X]:((~happy(X)&happy(X))=>(tall(X)|patient(X))))&
(![X]:((humble(X)<~>old(X))=>(~strong(X)<~>curious(X))))&
(![X]:((rich(X)&~patient(X))<=>(~old(X)&brave(X))))&
(![X]:(rich(X)=>(~brave(X)<~>brave(X))))&
((?[X]:((~happy(X)&rich(X))))<=>(humble(paul)))&
(((~patient(john)&~old(john)))<=>(?[X]:((wise(X)&~patient(X)))))&
((?[X]:((quiet(X)|~brave(X))))=>(?[X]:(~strong(X))))&
(![X]:((kind(X)|happy(X))=>(strong(X)&quiet(X))))&
(![X]:((curious(X)<~>kind(X))<=>(humble(X)<~>~creative(X))))&
(?[X]:((generous(X)|humble(X))))&
(?[X]:((~kind(X)|old(X))))&
((~funny(alice)&tall(alice)))&
(tall(fred))&
((calm(mary)<~>brave(mary)))&
(?[X]:(~curious(X))) | calm(alice) | [] | null | 0 |
Everyone who is both not happy and patient is humble or not brave.
Everyone who is not strong or generous is both not quiet and not patient and vice versa.
If someone is old then someone is both not calm and not quiet.
If alice is wise then john is not patient.
Everyone who is not calm or not rich is happy and vice versa.
Everyone who is quiet is not funny.
If john is kind or not patient then someone is not creative or not strong and vice versa.
If john is not strong or rich then someone is either not kind or old and vice versa.
Everyone who is both strong and not wise is both not happy and calm and vice versa.
Everyone who is not wise or not patient is either humble or not strong.
If john is both not kind and strong then john is both quiet and not brave.
Everyone who is not creative or not patient is both patient and not tall.
Everyone who is both quiet and not brave is not calm or not creative and vice versa.
Everyone who is both funny and not humble is both creative and patient.
Everyone who is both not curious and quiet is not brave and vice versa.
Everyone who is funny or not happy is either not funny or rich.
Someone is kind or rich.
John is either not humble or not curious.
Someone is either brave or not strong.
Paul is rich.
Someone is either not quiet or not tall. | Paul is happy. | neutral | (![X]:((~happy(X)&patient(X))=>(humble(X)|~brave(X))))&
(![X]:((~strong(X)|generous(X))<=>(~quiet(X)&~patient(X))))&
((?[X]:(old(X)))=>(?[X]:((~calm(X)&~quiet(X)))))&
((wise(alice))=>(~patient(john)))&
(![X]:((~calm(X)|~rich(X))<=>happy(X)))&
(![X]:(quiet(X)=>~funny(X)))&
(((kind(john)|~patient(john)))<=>(?[X]:((~creative(X)|~strong(X)))))&
(((~strong(john)|rich(john)))<=>(?[X]:((~kind(X)<~>old(X)))))&
(![X]:((strong(X)&~wise(X))<=>(~happy(X)&calm(X))))&
(![X]:((~wise(X)|~patient(X))=>(humble(X)<~>~strong(X))))&
(((~kind(john)&strong(john)))=>((quiet(john)&~brave(john))))&
(![X]:((~creative(X)|~patient(X))=>(patient(X)&~tall(X))))&
(![X]:((quiet(X)&~brave(X))<=>(~calm(X)|~creative(X))))&
(![X]:((funny(X)&~humble(X))=>(creative(X)&patient(X))))&
(![X]:((~curious(X)&quiet(X))<=>~brave(X)))&
(![X]:((funny(X)|~happy(X))=>(~funny(X)<~>rich(X))))&
(?[X]:((kind(X)|rich(X))))&
((~humble(john)<~>~curious(john)))&
(?[X]:((brave(X)<~>~strong(X))))&
(rich(paul))&
(?[X]:((~quiet(X)<~>~tall(X)))) | happy(paul) | [] | null | 0 |
Everyone who is not kind or not quiet is curious.
Everyone who is either funny or not generous is not patient and vice versa.
If someone is either patient or not happy then someone is not wise or not rich and vice versa.
If someone is creative then someone is not generous or not curious and vice versa.
Everyone who is not creative is calm or not kind and vice versa.
If someone is both strong and not strong then susan is both curious and quiet and vice versa.
Everyone who is not happy is both not calm and quiet.
If paul is not wise or strong then mary is not humble.
Everyone who is both funny and strong is both happy and not curious.
If lucy is both happy and generous then lucy is kind or not wise and vice versa.
If susan is both wise and not old then someone is not tall or generous.
Everyone who is either not rich or creative is quiet or strong and vice versa.
If alice is brave then someone is not generous.
If john is either not generous or not brave then someone is not quiet and vice versa.
Everyone who is kind or not creative is not creative.
If someone is both calm and rich then alice is humble.
John is both not strong and not creative.
Paul is both not calm and generous.
Lucy is generous.
John is humble or not generous.
Susan is either not curious or not strong.
Mary is both calm and funny.
Fred is not strong. | Susan is happy. | entailment | (![X]:((~kind(X)|~quiet(X))=>curious(X)))&
(![X]:((funny(X)<~>~generous(X))<=>~patient(X)))&
((?[X]:((patient(X)<~>~happy(X))))<=>(?[X]:((~wise(X)|~rich(X)))))&
((?[X]:(creative(X)))<=>(?[X]:((~generous(X)|~curious(X)))))&
(![X]:(~creative(X)<=>(calm(X)|~kind(X))))&
((?[X]:((strong(X)&~strong(X))))<=>((curious(susan)&quiet(susan))))&
(![X]:(~happy(X)=>(~calm(X)&quiet(X))))&
(((~wise(paul)|strong(paul)))=>(~humble(mary)))&
(![X]:((funny(X)&strong(X))=>(happy(X)&~curious(X))))&
(((happy(lucy)&generous(lucy)))<=>((kind(lucy)|~wise(lucy))))&
(((wise(susan)&~old(susan)))=>(?[X]:((~tall(X)|generous(X)))))&
(![X]:((~rich(X)<~>creative(X))<=>(quiet(X)|strong(X))))&
((brave(alice))=>(?[X]:(~generous(X))))&
(((~generous(john)<~>~brave(john)))<=>(?[X]:(~quiet(X))))&
(![X]:((kind(X)|~creative(X))=>~creative(X)))&
((?[X]:((calm(X)&rich(X))))=>(humble(alice)))&
((~strong(john)&~creative(john)))&
((~calm(paul)&generous(paul)))&
(generous(lucy))&
((humble(john)|~generous(john)))&
((~curious(susan)<~>~strong(susan)))&
((calm(mary)&funny(mary)))&
(~strong(fred)) | happy(susan) | [
"p3",
"p4",
"p5",
"p6",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 681205213628554996958760
% SZS output start Proof for 681205213628554996958760
4. ? [X0] : creative(X0) <=> ? [X0] : (~curious(X0) | ~generous(X0)) [input p3]
5. ! [X0] : (~creative(X0) <=> (~kind(X0) | calm(X0))) [input p4]
6. ? [X0] : (~strong(X0) & strong(X0)) <=> (quiet(susan) & curious(susan)) [input p5]
7. ! [X0] : (~happy(X0) => (quiet(X0) & ~calm(X0))) [input p6]
15. ! [X0] : ((~creative(X0) | kind(X0)) => ~creative(X0)) [input p14]
24. ~happy(susan) [input hypothesis]
26. ? [X0] : creative(X0) <=> ? [X1] : (~curious(X1) | ~generous(X1)) [rectify 4]
29. ! [X0] : ((quiet(X0) & ~calm(X0)) | happy(X0)) [ennf transformation 7]
34. ! [X0] : (~creative(X0) | (creative(X0) & ~kind(X0))) [ennf transformation 15]
42. (? [X0] : creative(X0) | ! [X1] : (curious(X1) & generous(X1))) & (? [X1] : (~curious(X1) | ~generous(X1)) | ! [X0] : ~creative(X0)) [nnf transformation 26]
43. (? [X0] : creative(X0) | ! [X1] : (curious(X1) & generous(X1))) & (? [X2] : (~curious(X2) | ~generous(X2)) | ! [X3] : ~creative(X3)) [rectify 42]
44. ? [X0] : creative(X0) => creative(sK2) [choice axiom]
45. ? [X2] : (~curious(X2) | ~generous(X2)) => (~curious(sK3) | ~generous(sK3)) [choice axiom]
46. (creative(sK2) | ! [X1] : (curious(X1) & generous(X1))) & ((~curious(sK3) | ~generous(sK3)) | ! [X3] : ~creative(X3)) [skolemisation 43,45,44]
47. ! [X0] : ((~creative(X0) | (kind(X0) & ~calm(X0))) & ((~kind(X0) | calm(X0)) | creative(X0))) [nnf transformation 5]
48. ! [X0] : ((~creative(X0) | (kind(X0) & ~calm(X0))) & (~kind(X0) | calm(X0) | creative(X0))) [flattening 47]
49. (? [X0] : (~strong(X0) & strong(X0)) | (~quiet(susan) | ~curious(susan))) & ((quiet(susan) & curious(susan)) | ! [X0] : (strong(X0) | ~strong(X0))) [nnf transformation 6]
50. (? [X0] : (~strong(X0) & strong(X0)) | ~quiet(susan) | ~curious(susan)) & ((quiet(susan) & curious(susan)) | ! [X0] : (strong(X0) | ~strong(X0))) [flattening 49]
51. (? [X0] : (~strong(X0) & strong(X0)) | ~quiet(susan) | ~curious(susan)) & ((quiet(susan) & curious(susan)) | ! [X1] : (strong(X1) | ~strong(X1))) [rectify 50]
52. ? [X0] : (~strong(X0) & strong(X0)) => (~strong(sK4) & strong(sK4)) [choice axiom]
53. ((~strong(sK4) & strong(sK4)) | ~quiet(susan) | ~curious(susan)) & ((quiet(susan) & curious(susan)) | ! [X1] : (strong(X1) | ~strong(X1))) [skolemisation 51,52]
79. creative(sK2) | curious(X1) [cnf transformation 46]
82. ~creative(X0) | kind(X0) [cnf transformation 48]
85. strong(sK4) | ~quiet(susan) | ~curious(susan) [cnf transformation 53]
86. ~strong(sK4) | ~quiet(susan) | ~curious(susan) [cnf transformation 53]
88. happy(X0) | quiet(X0) [cnf transformation 29]
109. ~creative(X0) | ~kind(X0) [cnf transformation 34]
123. ~happy(susan) [cnf transformation 24]
159. 9 <=> ! [X1] : curious(X1) [avatar definition]
160. curious(X1) <- (9) [avatar component clause 159]
162. 10 <=> creative(sK2) [avatar definition]
164. creative(sK2) <- (10) [avatar component clause 162]
165. 9 | 10 [avatar split clause 79,162,159]
171. 12 <=> ! [X3] : ~creative(X3) [avatar definition]
172. ~creative(X3) <- (12) [avatar component clause 171]
183. 15 <=> curious(susan) [avatar definition]
185. ~curious(susan) <- (~15) [avatar component clause 183]
187. 16 <=> quiet(susan) [avatar definition]
191. 17 <=> strong(sK4) [avatar definition]
194. ~15 | ~16 | ~17 [avatar split clause 86,191,187,183]
195. ~15 | ~16 | 17 [avatar split clause 85,191,187,183]
259. ~creative(X0) [subsumption resolution 109,82]
260. 12 [avatar split clause 259,171]
283. $false <- (10, 12) [subsumption resolution 164,172]
284. ~10 | ~12 [avatar contradiction clause 283]
291. quiet(susan) [resolution 88,123]
296. 16 [avatar split clause 291,187]
297. $false <- (9, ~15) [subsumption resolution 185,160]
298. ~9 | 15 [avatar contradiction clause 297]
299. $false [avatar sat refutation 165,194,195,260,284,296,298]
% SZS output end Proof for 681205213628554996958760
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not quiet then alice is either rich or not patient. Everyone who is creative or funny is either not brave or not humble and vice versa. If someone is both creative and happy then someone is either happy or not humble and vice versa. Everyone who is curious or tall is brave. Everyone who is creative or not funny is not creative and vice versa. If someone is not funny or not strong then someone is either not funny or creative. Everyone who is not generous or not curious is humble and vice versa. Everyone who is either calm or not happy is both humble and not kind. If john is either not old or not brave then someone is not happy or rich and vice versa. Everyone who is not wise or tall is either not generous or not strong and vice versa. If mary is both not curious and generous then someone is not creative and vice versa. Everyone who is either not curious or not funny is either not calm or humble. Everyone who is both wise and calm is not brave. Everyone who is patient is both generous and not humble. If fred is both tall and brave then someone is either wise or not strong and vice versa. If susan is either not calm or curious then someone is either not funny or not rich. Someone is kind. Someone is not happy. Someone is either rich or happy. Paul is not strong or curious. Someone is generous or humble. | John is not old. | entailment | ((?[X]:(~quiet(X)))=>((rich(alice)<~>~patient(alice))))&
(![X]:((creative(X)|funny(X))<=>(~brave(X)<~>~humble(X))))&
((?[X]:((creative(X)&happy(X))))<=>(?[X]:((happy(X)<~>~humble(X)))))&
(![X]:((curious(X)|tall(X))=>brave(X)))&
(![X]:((creative(X)|~funny(X))<=>~creative(X)))&
((?[X]:((~funny(X)|~strong(X))))=>(?[X]:((~funny(X)<~>creative(X)))))&
(![X]:((~generous(X)|~curious(X))<=>humble(X)))&
(![X]:((calm(X)<~>~happy(X))=>(humble(X)&~kind(X))))&
(((~old(john)<~>~brave(john)))<=>(?[X]:((~happy(X)|rich(X)))))&
(![X]:((~wise(X)|tall(X))<=>(~generous(X)<~>~strong(X))))&
(((~curious(mary)&generous(mary)))<=>(?[X]:(~creative(X))))&
(![X]:((~curious(X)<~>~funny(X))=>(~calm(X)<~>humble(X))))&
(![X]:((wise(X)&calm(X))=>~brave(X)))&
(![X]:(patient(X)=>(generous(X)&~humble(X))))&
(((tall(fred)&brave(fred)))<=>(?[X]:((wise(X)<~>~strong(X)))))&
(((~calm(susan)<~>curious(susan)))=>(?[X]:((~funny(X)<~>~rich(X)))))&
(?[X]:(kind(X)))&
(?[X]:(~happy(X)))&
(?[X]:((rich(X)<~>happy(X))))&
((~strong(paul)|curious(paul)))&
(?[X]:((generous(X)|humble(X)))) | ~old(john) | [
"p1",
"p3",
"p4",
"p6",
"p8",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 6408461995226193937336359
% SZS output start Proof for 6408461995226193937336359
2. ! [X0] : ((funny(X0) | creative(X0)) <=> (~brave(X0) <~> ~humble(X0))) [input p1]
4. ! [X0] : ((tall(X0) | curious(X0)) => brave(X0)) [input p3]
5. ! [X0] : ((~funny(X0) | creative(X0)) <=> ~creative(X0)) [input p4]
7. ! [X0] : ((~curious(X0) | ~generous(X0)) <=> humble(X0)) [input p6]
9. (~old(john) <~> ~brave(john)) <=> ? [X0] : (rich(X0) | ~happy(X0)) [input p8]
18. ? [X0] : ~happy(X0) [input p17]
22. old(john) [input hypothesis]
27. ! [X0] : (brave(X0) | (~tall(X0) & ~curious(X0))) [ennf transformation 4]
34. ! [X0] : (((funny(X0) | creative(X0)) | ((~brave(X0) | humble(X0)) & (~humble(X0) | brave(X0)))) & (((humble(X0) | brave(X0)) & (~humble(X0) | ~brave(X0))) | (~funny(X0) & ~creative(X0)))) [nnf transformation 2]
35. ! [X0] : ((funny(X0) | creative(X0) | ((~brave(X0) | humble(X0)) & (~humble(X0) | brave(X0)))) & (((humble(X0) | brave(X0)) & (~humble(X0) | ~brave(X0))) | (~funny(X0) & ~creative(X0)))) [flattening 34]
41. ! [X0] : (((~funny(X0) | creative(X0)) | creative(X0)) & (~creative(X0) | (funny(X0) & ~creative(X0)))) [nnf transformation 5]
42. ! [X0] : ((~funny(X0) | creative(X0) | creative(X0)) & (~creative(X0) | (funny(X0) & ~creative(X0)))) [flattening 41]
47. ! [X0] : (((~curious(X0) | ~generous(X0)) | ~humble(X0)) & (humble(X0) | (curious(X0) & generous(X0)))) [nnf transformation 7]
48. ! [X0] : ((~curious(X0) | ~generous(X0) | ~humble(X0)) & (humble(X0) | (curious(X0) & generous(X0)))) [flattening 47]
50. (((brave(john) | old(john)) & (~brave(john) | ~old(john))) | ! [X0] : (~rich(X0) & happy(X0))) & (? [X0] : (rich(X0) | ~happy(X0)) | ((~old(john) | brave(john)) & (~brave(john) | old(john)))) [nnf transformation 9]
51. (((brave(john) | old(john)) & (~brave(john) | ~old(john))) | ! [X0] : (~rich(X0) & happy(X0))) & (? [X1] : (rich(X1) | ~happy(X1)) | ((~old(john) | brave(john)) & (~brave(john) | old(john)))) [rectify 50]
52. ? [X1] : (rich(X1) | ~happy(X1)) => (rich(sK3) | ~happy(sK3)) [choice axiom]
53. (((brave(john) | old(john)) & (~brave(john) | ~old(john))) | ! [X0] : (~rich(X0) & happy(X0))) & ((rich(sK3) | ~happy(sK3)) | ((~old(john) | brave(john)) & (~brave(john) | old(john)))) [skolemisation 51,52]
72. ? [X0] : ~happy(X0) => ~happy(sK8) [choice axiom]
73. ~happy(sK8) [skolemisation 18,72]
83. ~humble(X0) | creative(X0) | funny(X0) | brave(X0) [cnf transformation 35]
91. ~curious(X0) | brave(X0) [cnf transformation 27]
93. ~creative(X0) | ~creative(X0) [cnf transformation 42]
95. ~funny(X0) | creative(X0) | creative(X0) [cnf transformation 42]
101. curious(X0) | humble(X0) [cnf transformation 48]
109. ~brave(john) | ~old(john) | happy(X0) [cnf transformation 53]
138. ~happy(sK8) [cnf transformation 73]
143. old(john) [cnf transformation 22]
144. ~creative(X0) [duplicate literal removal 93]
145. ~funny(X0) | creative(X0) [duplicate literal removal 95]
181. 9 <=> old(john) [avatar definition]
185. 10 <=> brave(john) [avatar definition]
186. ~brave(john) <- (~10) [avatar component clause 185]
190. 11 <=> ! [X0] : happy(X0) [avatar definition]
191. happy(X0) <- (11) [avatar component clause 190]
194. 11 | ~9 | ~10 [avatar split clause 109,185,181,190]
278. 9 [avatar split clause 143,181]
283. humble(X0) | brave(X0) [resolution 101,91]
384. creative(X0) | funny(X0) | brave(X0) | brave(X0) [resolution 83,283]
389. creative(X0) | funny(X0) | brave(X0) [duplicate literal removal 384]
390. brave(X0) | funny(X0) [subsumption resolution 389,144]
585. funny(john) <- (~10) [resolution 390,186]
639. creative(john) <- (~10) [resolution 585,145]
649. $false <- (~10) [subsumption resolution 639,144]
650. 10 [avatar contradiction clause 649]
660. $false <- (11) [resolution 191,138]
661. ~11 [avatar contradiction clause 660]
665. $false [avatar sat refutation 194,278,650,661]
% SZS output end Proof for 6408461995226193937336359
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either patient or not rich then someone is tall and vice versa.
Everyone who is tall is either curious or not funny.
Everyone who is creative or not generous is quiet or not patient.
If fred is both not funny and not tall then someone is both old and not brave.
If someone is either curious or old then alice is both old and humble and vice versa.
Everyone who is not wise or not kind is not quiet and vice versa.
If susan is not funny then someone is either generous or patient and vice versa.
If susan is not funny or not rich then susan is either not humble or not old and vice versa.
Everyone who is not generous or old is not brave.
Everyone who is not creative or not brave is not rich.
If someone is old or not rich then someone is not creative or not quiet.
Everyone who is both not generous and rich is both creative and funny and vice versa.
Everyone who is both happy and creative is kind or not generous.
Everyone who is either brave or not old is funny.
If john is both quiet and brave then paul is calm or kind and vice versa.
If someone is both not brave and strong then mary is creative.
John is either old or not creative.
Someone is generous.
John is not curious or not brave.
Someone is not kind or not rich.
Someone is not humble or not happy.
Mary is both quiet and not tall.
Someone is curious.
Someone is both strong and tall. | John is not creative. | neutral | ((?[X]:((patient(X)<~>~rich(X))))<=>(?[X]:(tall(X))))&
(![X]:(tall(X)=>(curious(X)<~>~funny(X))))&
(![X]:((creative(X)|~generous(X))=>(quiet(X)|~patient(X))))&
(((~funny(fred)&~tall(fred)))=>(?[X]:((old(X)&~brave(X)))))&
((?[X]:((curious(X)<~>old(X))))<=>((old(alice)&humble(alice))))&
(![X]:((~wise(X)|~kind(X))<=>~quiet(X)))&
((~funny(susan))<=>(?[X]:((generous(X)<~>patient(X)))))&
(((~funny(susan)|~rich(susan)))<=>((~humble(susan)<~>~old(susan))))&
(![X]:((~generous(X)|old(X))=>~brave(X)))&
(![X]:((~creative(X)|~brave(X))=>~rich(X)))&
((?[X]:((old(X)|~rich(X))))=>(?[X]:((~creative(X)|~quiet(X)))))&
(![X]:((~generous(X)&rich(X))<=>(creative(X)&funny(X))))&
(![X]:((happy(X)&creative(X))=>(kind(X)|~generous(X))))&
(![X]:((brave(X)<~>~old(X))=>funny(X)))&
(((quiet(john)&brave(john)))<=>((calm(paul)|kind(paul))))&
((?[X]:((~brave(X)&strong(X))))=>(creative(mary)))&
((old(john)<~>~creative(john)))&
(?[X]:(generous(X)))&
((~curious(john)|~brave(john)))&
(?[X]:((~kind(X)|~rich(X))))&
(?[X]:((~humble(X)|~happy(X))))&
((quiet(mary)&~tall(mary)))&
(?[X]:(curious(X)))&
(?[X]:((strong(X)&tall(X)))) | ~creative(john) | [] | null | 0 |
If paul is both patient and tall then someone is both not tall and calm and vice versa. Everyone who is either not patient or funny is either not kind or strong and vice versa. If john is either brave or funny then someone is both funny and not kind and vice versa. Everyone who is not old or not brave is creative. If fred is either calm or not brave then someone is wise and vice versa. Everyone who is not kind or wise is either not creative or rich and vice versa. If john is not happy then someone is strong or funny. Everyone who is both creative and quiet is either happy or wise and vice versa. Everyone who is either not old or wise is not brave or old and vice versa. Everyone who is not tall or not quiet is both strong and curious. If someone is not rich then someone is both not brave and patient and vice versa. If someone is generous or funny then lucy is both quiet and not brave and vice versa. If susan is either not strong or not rich then someone is rich. If lucy is both not tall and tall then mary is generous or not calm and vice versa. Everyone who is strong is not patient and vice versa. Everyone who is not calm or not rich is not brave and vice versa. Lucy is not generous. Alice is both quiet and not strong. Fred is not tall or not wise. Someone is funny. Someone is either tall or generous. Someone is either brave or not calm. Someone is happy or strong. Someone is both funny and not strong. | John is not creative. | contradiction | (((patient(paul)&tall(paul)))<=>(?[X]:((~tall(X)&calm(X)))))&
(![X]:((~patient(X)<~>funny(X))<=>(~kind(X)<~>strong(X))))&
(((brave(john)<~>funny(john)))<=>(?[X]:((funny(X)&~kind(X)))))&
(![X]:((~old(X)|~brave(X))=>creative(X)))&
(((calm(fred)<~>~brave(fred)))<=>(?[X]:(wise(X))))&
(![X]:((~kind(X)|wise(X))<=>(~creative(X)<~>rich(X))))&
((~happy(john))=>(?[X]:((strong(X)|funny(X)))))&
(![X]:((creative(X)&quiet(X))<=>(happy(X)<~>wise(X))))&
(![X]:((~old(X)<~>wise(X))<=>(~brave(X)|old(X))))&
(![X]:((~tall(X)|~quiet(X))=>(strong(X)&curious(X))))&
((?[X]:(~rich(X)))<=>(?[X]:((~brave(X)&patient(X)))))&
((?[X]:((generous(X)|funny(X))))<=>((quiet(lucy)&~brave(lucy))))&
(((~strong(susan)<~>~rich(susan)))=>(?[X]:(rich(X))))&
(((~tall(lucy)&tall(lucy)))<=>((generous(mary)|~calm(mary))))&
(![X]:(strong(X)<=>~patient(X)))&
(![X]:((~calm(X)|~rich(X))<=>~brave(X)))&
(~generous(lucy))&
((quiet(alice)&~strong(alice)))&
((~tall(fred)|~wise(fred)))&
(?[X]:(funny(X)))&
(?[X]:((tall(X)<~>generous(X))))&
(?[X]:((brave(X)<~>~calm(X))))&
(?[X]:((happy(X)|strong(X))))&
(?[X]:((funny(X)&~strong(X)))) | ~creative(john) | [
"p3",
"p5",
"p8",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 5161203910974856019777423
% SZS output start Proof for 5161203910974856019777423
4. ! [X0] : ((~brave(X0) | ~old(X0)) => creative(X0)) [input p3]
6. ! [X0] : ((wise(X0) | ~kind(X0)) <=> (~creative(X0) <~> rich(X0))) [input p5]
9. ! [X0] : ((~old(X0) <~> wise(X0)) <=> (old(X0) | ~brave(X0))) [input p8]
16. ! [X0] : ((~rich(X0) | ~calm(X0)) <=> ~brave(X0)) [input p15]
25. ~creative(john) [input hypothesis]
28. ! [X0] : (creative(X0) | (brave(X0) & old(X0))) [ennf transformation 4]
46. ! [X0] : (((wise(X0) | ~kind(X0)) | ((~creative(X0) | ~rich(X0)) & (rich(X0) | creative(X0)))) & (((~rich(X0) | creative(X0)) & (rich(X0) | ~creative(X0))) | (~wise(X0) & kind(X0)))) [nnf transformation 6]
47. ! [X0] : ((wise(X0) | ~kind(X0) | ((~creative(X0) | ~rich(X0)) & (rich(X0) | creative(X0)))) & (((~rich(X0) | creative(X0)) & (rich(X0) | ~creative(X0))) | (~wise(X0) & kind(X0)))) [flattening 46]
52. ! [X0] : ((((~wise(X0) | old(X0)) & (wise(X0) | ~old(X0))) | (~old(X0) & brave(X0))) & ((old(X0) | ~brave(X0)) | ((~old(X0) | ~wise(X0)) & (wise(X0) | old(X0))))) [nnf transformation 9]
53. ! [X0] : ((((~wise(X0) | old(X0)) & (wise(X0) | ~old(X0))) | (~old(X0) & brave(X0))) & (old(X0) | ~brave(X0) | ((~old(X0) | ~wise(X0)) & (wise(X0) | old(X0))))) [flattening 52]
70. ! [X0] : (((~rich(X0) | ~calm(X0)) | brave(X0)) & (~brave(X0) | (rich(X0) & calm(X0)))) [nnf transformation 16]
71. ! [X0] : ((~rich(X0) | ~calm(X0) | brave(X0)) & (~brave(X0) | (rich(X0) & calm(X0)))) [flattening 70]
102. creative(X0) | old(X0) [cnf transformation 28]
103. creative(X0) | brave(X0) [cnf transformation 28]
111. ~rich(X0) | creative(X0) | ~wise(X0) [cnf transformation 47]
124. wise(X0) | ~old(X0) | ~old(X0) [cnf transformation 53]
147. ~brave(X0) | rich(X0) [cnf transformation 71]
161. ~creative(john) [cnf transformation 25]
163. ~old(X0) | wise(X0) [duplicate literal removal 124]
191. 7 <=> brave(john) [avatar definition]
192. brave(john) <- (7) [avatar component clause 191]
364. old(john) [resolution 102,161]
365. brave(john) [resolution 103,161]
368. 7 [avatar split clause 365,191]
378. rich(john) <- (7) [resolution 147,192]
379. wise(john) [resolution 163,364]
407. creative(john) | ~wise(john) <- (7) [resolution 111,378]
408. ~wise(john) <- (7) [subsumption resolution 407,161]
409. $false <- (7) [subsumption resolution 408,379]
410. ~7 [avatar contradiction clause 409]
411. $false [avatar sat refutation 368,410]
% SZS output end Proof for 5161203910974856019777423
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich or not humble is tall and vice versa. Everyone who is kind or brave is both humble and not curious and vice versa. Everyone who is not tall or not funny is calm. If someone is either not curious or quiet then john is not tall or not patient and vice versa. Everyone who is rich is not kind and vice versa. If someone is both not funny and not quiet then someone is either wise or not tall. Everyone who is not funny is happy and vice versa. If someone is not brave then alice is not curious or funny and vice versa. Everyone who is funny is not creative. Everyone who is not humble is not generous and vice versa. If susan is both not calm and old then someone is either not curious or wise. If someone is both curious and rich then someone is either not creative or not happy and vice versa. If someone is both not brave and happy then lucy is either not brave or not old. Everyone who is rich is creative. Everyone who is calm is not rich. Alice is not quiet. Susan is both brave and creative. Mary is either wise or not old. Someone is wise. Someone is not humble or quiet. Someone is old or tall. Someone is kind or not rich. | Mary is kind. | entailment | (![X]:((~rich(X)|~humble(X))<=>tall(X)))&
(![X]:((kind(X)|brave(X))<=>(humble(X)&~curious(X))))&
(![X]:((~tall(X)|~funny(X))=>calm(X)))&
((?[X]:((~curious(X)<~>quiet(X))))<=>((~tall(john)|~patient(john))))&
(![X]:(rich(X)<=>~kind(X)))&
((?[X]:((~funny(X)&~quiet(X))))=>(?[X]:((wise(X)<~>~tall(X)))))&
(![X]:(~funny(X)<=>happy(X)))&
((?[X]:(~brave(X)))<=>((~curious(alice)|funny(alice))))&
(![X]:(funny(X)=>~creative(X)))&
(![X]:(~humble(X)<=>~generous(X)))&
(((~calm(susan)&old(susan)))=>(?[X]:((~curious(X)<~>wise(X)))))&
((?[X]:((curious(X)&rich(X))))<=>(?[X]:((~creative(X)<~>~happy(X)))))&
((?[X]:((~brave(X)&happy(X))))=>((~brave(lucy)<~>~old(lucy))))&
(![X]:(rich(X)=>creative(X)))&
(![X]:(calm(X)=>~rich(X)))&
(~quiet(alice))&
((brave(susan)&creative(susan)))&
((wise(mary)<~>~old(mary)))&
(?[X]:(wise(X)))&
(?[X]:((~humble(X)|quiet(X))))&
(?[X]:((old(X)|tall(X))))&
(?[X]:((kind(X)|~rich(X)))) | kind(mary) | [
"p2",
"p4",
"p8",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 1168477461174564800444232
% SZS output start Proof for 1168477461174564800444232
3. ! [X0] : ((~funny(X0) | ~tall(X0)) => calm(X0)) [input p2]
5. ! [X0] : (rich(X0) <=> ~kind(X0)) [input p4]
9. ! [X0] : (funny(X0) => ~creative(X0)) [input p8]
14. ! [X0] : (rich(X0) => creative(X0)) [input p13]
15. ! [X0] : (calm(X0) => ~rich(X0)) [input p14]
23. ~kind(mary) [input hypothesis]
26. ! [X0] : (calm(X0) | (funny(X0) & tall(X0))) [ennf transformation 3]
28. ! [X0] : (~creative(X0) | ~funny(X0)) [ennf transformation 9]
32. ! [X0] : (creative(X0) | ~rich(X0)) [ennf transformation 14]
33. ! [X0] : (~rich(X0) | ~calm(X0)) [ennf transformation 15]
43. ! [X0] : ((rich(X0) | kind(X0)) & (~kind(X0) | ~rich(X0))) [nnf transformation 5]
82. calm(X0) | funny(X0) [cnf transformation 26]
90. kind(X0) | rich(X0) [cnf transformation 43]
98. ~creative(X0) | ~funny(X0) [cnf transformation 28]
111. ~rich(X0) | creative(X0) [cnf transformation 32]
112. ~calm(X0) | ~rich(X0) [cnf transformation 33]
122. ~kind(mary) [cnf transformation 23]
278. rich(mary) [resolution 90,122]
288. creative(mary) [resolution 111,278]
290. ~rich(X0) | funny(X0) [resolution 112,82]
304. ~funny(mary) [resolution 288,98]
320. funny(mary) [resolution 290,278]
322. $false [subsumption resolution 320,304]
% SZS output end Proof for 1168477461174564800444232
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet or tall is both not strong and wise.
Everyone who is kind or strong is either not tall or not quiet.
Everyone who is rich or not patient is either not generous or quiet and vice versa.
Everyone who is either tall or not creative is strong or patient and vice versa.
Everyone who is either not wise or not funny is kind and vice versa.
If someone is either happy or wise then someone is both wise and not rich and vice versa.
Everyone who is either not funny or old is both old and patient and vice versa.
If susan is rich or not patient then alice is both not calm and curious.
Everyone who is not funny or not patient is both creative and patient and vice versa.
Everyone who is both not rich and kind is humble.
Everyone who is not kind or not wise is not rich or not tall.
If paul is patient or funny then someone is rich and vice versa.
Everyone who is either not brave or brave is kind or not old and vice versa.
Everyone who is not calm is both not brave and not rich.
If alice is both not patient and quiet then someone is either generous or calm and vice versa.
Alice is not humble or patient.
Fred is both funny and wise.
Someone is either not humble or not strong.
Someone is either not quiet or not happy.
John is either not wise or not strong.
Fred is either quiet or not humble.
Someone is not kind. | Susan is not tall. | entailment | (![X]:((quiet(X)<~>tall(X))=>(~strong(X)&wise(X))))&
(![X]:((kind(X)|strong(X))=>(~tall(X)<~>~quiet(X))))&
(![X]:((rich(X)|~patient(X))<=>(~generous(X)<~>quiet(X))))&
(![X]:((tall(X)<~>~creative(X))<=>(strong(X)|patient(X))))&
(![X]:((~wise(X)<~>~funny(X))<=>kind(X)))&
((?[X]:((happy(X)<~>wise(X))))<=>(?[X]:((wise(X)&~rich(X)))))&
(![X]:((~funny(X)<~>old(X))<=>(old(X)&patient(X))))&
(((rich(susan)|~patient(susan)))=>((~calm(alice)&curious(alice))))&
(![X]:((~funny(X)|~patient(X))<=>(creative(X)&patient(X))))&
(![X]:((~rich(X)&kind(X))=>humble(X)))&
(![X]:((~kind(X)|~wise(X))=>(~rich(X)|~tall(X))))&
(((patient(paul)|funny(paul)))<=>(?[X]:(rich(X))))&
(![X]:((~brave(X)<~>brave(X))<=>(kind(X)|~old(X))))&
(![X]:(~calm(X)=>(~brave(X)&~rich(X))))&
(((~patient(alice)&quiet(alice)))<=>(?[X]:((generous(X)<~>calm(X)))))&
((~humble(alice)|patient(alice)))&
((funny(fred)&wise(fred)))&
(?[X]:((~humble(X)<~>~strong(X))))&
(?[X]:((~quiet(X)<~>~happy(X))))&
((~wise(john)<~>~strong(john)))&
((quiet(fred)<~>~humble(fred)))&
(?[X]:(~kind(X))) | ~tall(susan) | [
"p3",
"p6",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 784458031743992598336173
% SZS output start Proof for 784458031743992598336173
4. ! [X0] : ((tall(X0) <~> ~creative(X0)) <=> (patient(X0) | strong(X0))) [input p3]
7. ! [X0] : ((~funny(X0) <~> old(X0)) <=> (patient(X0) & old(X0))) [input p6]
9. ! [X0] : ((~patient(X0) | ~funny(X0)) <=> (patient(X0) & creative(X0))) [input p8]
23. tall(susan) [input hypothesis]
38. ! [X0] : ((((creative(X0) | ~tall(X0)) & (~creative(X0) | tall(X0))) | (~patient(X0) & ~strong(X0))) & ((patient(X0) | strong(X0)) | ((tall(X0) | creative(X0)) & (~creative(X0) | ~tall(X0))))) [nnf transformation 4]
39. ! [X0] : ((((creative(X0) | ~tall(X0)) & (~creative(X0) | tall(X0))) | (~patient(X0) & ~strong(X0))) & (patient(X0) | strong(X0) | ((tall(X0) | creative(X0)) & (~creative(X0) | ~tall(X0))))) [flattening 38]
46. ! [X0] : ((((~old(X0) | funny(X0)) & (old(X0) | ~funny(X0))) | (~patient(X0) | ~old(X0))) & ((patient(X0) & old(X0)) | ((~funny(X0) | ~old(X0)) & (old(X0) | funny(X0))))) [nnf transformation 7]
47. ! [X0] : ((((~old(X0) | funny(X0)) & (old(X0) | ~funny(X0))) | ~patient(X0) | ~old(X0)) & ((patient(X0) & old(X0)) | ((~funny(X0) | ~old(X0)) & (old(X0) | funny(X0))))) [flattening 46]
48. ! [X0] : (((~patient(X0) | ~funny(X0)) | (~patient(X0) | ~creative(X0))) & ((patient(X0) & creative(X0)) | (patient(X0) & funny(X0)))) [nnf transformation 9]
49. ! [X0] : ((~patient(X0) | ~funny(X0) | ~patient(X0) | ~creative(X0)) & ((patient(X0) & creative(X0)) | (patient(X0) & funny(X0)))) [flattening 48]
91. ~patient(X0) | ~tall(X0) | creative(X0) [cnf transformation 39]
102. old(X0) | old(X0) | funny(X0) [cnf transformation 47]
107. ~old(X0) | funny(X0) | ~patient(X0) | ~old(X0) [cnf transformation 47]
113. patient(X0) | patient(X0) [cnf transformation 49]
114. ~patient(X0) | ~funny(X0) | ~patient(X0) | ~creative(X0) [cnf transformation 49]
147. tall(susan) [cnf transformation 23]
150. patient(X0) [duplicate literal removal 113]
151. ~funny(X0) | ~patient(X0) | ~creative(X0) [duplicate literal removal 114]
152. old(X0) | funny(X0) [duplicate literal removal 102]
153. ~old(X0) | funny(X0) | ~patient(X0) [duplicate literal removal 107]
318. ~tall(X0) | creative(X0) [resolution 91,150]
319. creative(susan) [resolution 318,147]
377. funny(X1) | ~patient(X1) | funny(X1) [resolution 153,152]
378. funny(X1) | ~patient(X1) [duplicate literal removal 377]
380. funny(X1) [subsumption resolution 378,150]
381. ~patient(X0) | ~creative(X0) [resolution 380,151]
384. ~creative(X0) [subsumption resolution 381,150]
389. $false [resolution 384,319]
% SZS output end Proof for 784458031743992598336173
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not old or humble then someone is both curious and creative.
If susan is both not humble and not brave then someone is either not creative or kind and vice versa.
Everyone who is curious is either curious or tall and vice versa.
Everyone who is both creative and wise is creative or patient and vice versa.
If fred is both not funny and curious then lucy is not brave or not generous and vice versa.
If someone is either wise or not curious then susan is either creative or patient and vice versa.
Everyone who is not creative or not funny is both funny and curious.
If someone is either quiet or not brave then mary is humble.
If john is both old and not rich then someone is either not tall or not patient and vice versa.
Everyone who is both patient and rich is not rich or kind.
If someone is both not brave and not wise then someone is curious and vice versa.
If someone is not curious or not calm then someone is not generous or rich and vice versa.
If paul is either not curious or patient then lucy is not brave or kind.
Everyone who is both not patient and strong is humble or tall.
Everyone who is not tall or curious is wise and vice versa.
If alice is not generous or curious then lucy is old.
Susan is not old.
Someone is either curious or funny.
Lucy is not curious or not humble.
Mary is humble or brave.
Someone is quiet.
Fred is either patient or calm.
Someone is both patient and not generous. | John is not creative. | contradiction | ((?[X]:((~old(X)<~>humble(X))))=>(?[X]:((curious(X)&creative(X)))))&
(((~humble(susan)&~brave(susan)))<=>(?[X]:((~creative(X)<~>kind(X)))))&
(![X]:(curious(X)<=>(curious(X)<~>tall(X))))&
(![X]:((creative(X)&wise(X))<=>(creative(X)|patient(X))))&
(((~funny(fred)&curious(fred)))<=>((~brave(lucy)|~generous(lucy))))&
((?[X]:((wise(X)<~>~curious(X))))<=>((creative(susan)<~>patient(susan))))&
(![X]:((~creative(X)|~funny(X))=>(funny(X)&curious(X))))&
((?[X]:((quiet(X)<~>~brave(X))))=>(humble(mary)))&
(((old(john)&~rich(john)))<=>(?[X]:((~tall(X)<~>~patient(X)))))&
(![X]:((patient(X)&rich(X))=>(~rich(X)|kind(X))))&
((?[X]:((~brave(X)&~wise(X))))<=>(?[X]:(curious(X))))&
((?[X]:((~curious(X)|~calm(X))))<=>(?[X]:((~generous(X)|rich(X)))))&
(((~curious(paul)<~>patient(paul)))=>((~brave(lucy)|kind(lucy))))&
(![X]:((~patient(X)&strong(X))=>(humble(X)|tall(X))))&
(![X]:((~tall(X)|curious(X))<=>wise(X)))&
(((~generous(alice)|curious(alice)))=>(old(lucy)))&
(~old(susan))&
(?[X]:((curious(X)<~>funny(X))))&
((~curious(lucy)|~humble(lucy)))&
((humble(mary)|brave(mary)))&
(?[X]:(quiet(X)))&
((patient(fred)<~>calm(fred)))&
(?[X]:((patient(X)&~generous(X)))) | ~creative(john) | [
"p2",
"p6",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3223732154683424035547010
% SZS output start Proof for 3223732154683424035547010
3. ! [X0] : (curious(X0) <=> (curious(X0) <~> tall(X0))) [input p2]
7. ! [X0] : ((~funny(X0) | ~creative(X0)) => (curious(X0) & funny(X0))) [input p6]
11. ? [X0] : (~wise(X0) & ~brave(X0)) <=> ? [X0] : curious(X0) [input p10]
15. ! [X0] : ((curious(X0) | ~tall(X0)) <=> wise(X0)) [input p14]
24. ~creative(john) [input hypothesis]
26. ? [X0] : (~wise(X0) & ~brave(X0)) <=> ? [X1] : curious(X1) [rectify 11]
30. ! [X0] : ((curious(X0) & funny(X0)) | (funny(X0) & creative(X0))) [ennf transformation 7]
46. ! [X0] : ((curious(X0) | ((curious(X0) | ~tall(X0)) & (tall(X0) | ~curious(X0)))) & (((~tall(X0) | ~curious(X0)) & (tall(X0) | curious(X0))) | ~curious(X0))) [nnf transformation 3]
61. (? [X0] : (~wise(X0) & ~brave(X0)) | ! [X1] : ~curious(X1)) & (? [X1] : curious(X1) | ! [X0] : (wise(X0) | brave(X0))) [nnf transformation 26]
62. (? [X0] : (~wise(X0) & ~brave(X0)) | ! [X1] : ~curious(X1)) & (? [X2] : curious(X2) | ! [X3] : (wise(X3) | brave(X3))) [rectify 61]
63. ? [X0] : (~wise(X0) & ~brave(X0)) => (~wise(sK4) & ~brave(sK4)) [choice axiom]
64. ? [X2] : curious(X2) => curious(sK5) [choice axiom]
65. ((~wise(sK4) & ~brave(sK4)) | ! [X1] : ~curious(X1)) & (curious(sK5) | ! [X3] : (wise(X3) | brave(X3))) [skolemisation 62,64,63]
72. ! [X0] : (((curious(X0) | ~tall(X0)) | ~wise(X0)) & (wise(X0) | (~curious(X0) & tall(X0)))) [nnf transformation 15]
73. ! [X0] : ((curious(X0) | ~tall(X0) | ~wise(X0)) & (wise(X0) | (~curious(X0) & tall(X0)))) [flattening 72]
93. ~tall(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 46]
95. curious(X0) | curious(X0) | ~tall(X0) [cnf transformation 46]
116. creative(X0) | curious(X0) [cnf transformation 30]
129. ~wise(sK4) | ~curious(X1) [cnf transformation 65]
136. wise(X0) | tall(X0) [cnf transformation 73]
151. ~creative(john) [cnf transformation 24]
154. ~tall(X0) | ~curious(X0) [duplicate literal removal 93]
155. curious(X0) | ~tall(X0) [duplicate literal removal 95]
202. ~tall(X0) [subsumption resolution 154,155]
290. 28 <=> ! [X1] : ~curious(X1) [avatar definition]
291. ~curious(X1) <- (28) [avatar component clause 290]
293. 29 <=> wise(sK4) [avatar definition]
295. ~wise(sK4) <- (~29) [avatar component clause 293]
296. 28 | ~29 [avatar split clause 129,293,290]
356. wise(X0) [subsumption resolution 136,202]
396. $false <- (~29) [subsumption resolution 295,356]
397. 29 [avatar contradiction clause 396]
424. curious(john) [resolution 116,151]
427. $false <- (28) [subsumption resolution 424,291]
428. ~28 [avatar contradiction clause 427]
431. $false [avatar sat refutation 296,397,428]
% SZS output end Proof for 3223732154683424035547010
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not strong or not old is creative or tall.
If someone is not old or not rich then someone is either not funny or curious and vice versa.
Everyone who is both not kind and not brave is either not wise or generous and vice versa.
If lucy is both not generous and not tall then lucy is either calm or not generous and vice versa.
Everyone who is both kind and not patient is either not brave or patient and vice versa.
If john is either brave or not old then someone is both not quiet and not brave and vice versa.
Everyone who is calm is both not happy and not funny.
Everyone who is tall or curious is not humble or curious and vice versa.
Everyone who is wise or kind is both not brave and not calm.
If alice is both quiet and wise then mary is either not rich or not calm.
Everyone who is both not happy and curious is both rich and old.
If someone is both rich and not kind then someone is wise or generous.
If fred is either calm or not happy then alice is curious or not rich and vice versa.
Everyone who is either not happy or rich is creative.
Everyone who is not strong is humble.
If mary is either old or not brave then fred is kind or strong and vice versa.
Someone is both generous and rich.
Someone is not rich.
Someone is not creative.
John is not curious.
Someone is both not creative and not curious.
Someone is brave.
Someone is not tall.
Alice is both not quiet and rich. | Fred is strong. | neutral | (![X]:((~strong(X)|~old(X))=>(creative(X)|tall(X))))&
((?[X]:((~old(X)|~rich(X))))<=>(?[X]:((~funny(X)<~>curious(X)))))&
(![X]:((~kind(X)&~brave(X))<=>(~wise(X)<~>generous(X))))&
(((~generous(lucy)&~tall(lucy)))<=>((calm(lucy)<~>~generous(lucy))))&
(![X]:((kind(X)&~patient(X))<=>(~brave(X)<~>patient(X))))&
(((brave(john)<~>~old(john)))<=>(?[X]:((~quiet(X)&~brave(X)))))&
(![X]:(calm(X)=>(~happy(X)&~funny(X))))&
(![X]:((tall(X)|curious(X))<=>(~humble(X)|curious(X))))&
(![X]:((wise(X)|kind(X))=>(~brave(X)&~calm(X))))&
(((quiet(alice)&wise(alice)))=>((~rich(mary)<~>~calm(mary))))&
(![X]:((~happy(X)&curious(X))=>(rich(X)&old(X))))&
((?[X]:((rich(X)&~kind(X))))=>(?[X]:((wise(X)|generous(X)))))&
(((calm(fred)<~>~happy(fred)))<=>((curious(alice)|~rich(alice))))&
(![X]:((~happy(X)<~>rich(X))=>creative(X)))&
(![X]:(~strong(X)=>humble(X)))&
(((old(mary)<~>~brave(mary)))<=>((kind(fred)|strong(fred))))&
(?[X]:((generous(X)&rich(X))))&
(?[X]:(~rich(X)))&
(?[X]:(~creative(X)))&
(~curious(john))&
(?[X]:((~creative(X)&~curious(X))))&
(?[X]:(brave(X)))&
(?[X]:(~tall(X)))&
((~quiet(alice)&rich(alice))) | strong(fred) | [] | null | 0 |
If someone is funny then alice is not generous or generous and vice versa.
Everyone who is kind or strong is either humble or happy.
Everyone who is kind is both not strong and rich.
Everyone who is strong or not creative is not generous and vice versa.
Everyone who is either not strong or not tall is either creative or wise and vice versa.
Everyone who is curious or rich is not old or not curious and vice versa.
Everyone who is not generous or not quiet is happy or generous.
If john is not creative then someone is brave and vice versa.
If alice is both rich and not strong then lucy is creative.
Everyone who is curious is both brave and not curious and vice versa.
If paul is curious or generous then someone is not calm or creative.
If susan is not brave then lucy is either generous or not tall.
If someone is not patient then someone is either not happy or not strong and vice versa.
If lucy is strong or not quiet then mary is not kind or generous.
If someone is not wise or quiet then susan is not humble.
Someone is not tall.
Fred is tall.
Susan is either strong or not generous.
Susan is not old. | Mary is curious. | contradiction | ((?[X]:(funny(X)))<=>((~generous(alice)|generous(alice))))&
(![X]:((kind(X)|strong(X))=>(humble(X)<~>happy(X))))&
(![X]:(kind(X)=>(~strong(X)&rich(X))))&
(![X]:((strong(X)|~creative(X))<=>~generous(X)))&
(![X]:((~strong(X)<~>~tall(X))<=>(creative(X)<~>wise(X))))&
(![X]:((curious(X)|rich(X))<=>(~old(X)|~curious(X))))&
(![X]:((~generous(X)|~quiet(X))=>(happy(X)|generous(X))))&
((~creative(john))<=>(?[X]:(brave(X))))&
(((rich(alice)&~strong(alice)))=>(creative(lucy)))&
(![X]:(curious(X)<=>(brave(X)&~curious(X))))&
(((curious(paul)|generous(paul)))=>(?[X]:((~calm(X)|creative(X)))))&
((~brave(susan))=>((generous(lucy)<~>~tall(lucy))))&
((?[X]:(~patient(X)))<=>(?[X]:((~happy(X)<~>~strong(X)))))&
(((strong(lucy)|~quiet(lucy)))=>((~kind(mary)|generous(mary))))&
((?[X]:((~wise(X)|quiet(X))))=>(~humble(susan)))&
(?[X]:(~tall(X)))&
(tall(fred))&
((strong(susan)<~>~generous(susan)))&
(~old(susan)) | curious(mary) | [
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 26737843173428978440254
% SZS output start Proof for 26737843173428978440254
10. ! [X0] : (curious(X0) <=> (~curious(X0) & brave(X0))) [input p9]
20. curious(mary) [input hypothesis]
48. ! [X0] : ((curious(X0) | (curious(X0) | ~brave(X0))) & ((~curious(X0) & brave(X0)) | ~curious(X0))) [nnf transformation 10]
49. ! [X0] : ((curious(X0) | curious(X0) | ~brave(X0)) & ((~curious(X0) & brave(X0)) | ~curious(X0))) [flattening 48]
85. ~curious(X0) | ~curious(X0) [cnf transformation 49]
100. curious(mary) [cnf transformation 20]
101. ~curious(X0) [duplicate literal removal 85]
195. $false [subsumption resolution 100,101]
% SZS output end Proof for 26737843173428978440254
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient then mary is both not creative and not kind and vice versa.
Everyone who is humble is both creative and not old.
If someone is either happy or creative then someone is either not happy or not strong and vice versa.
If alice is brave or not kind then someone is not patient and vice versa.
Everyone who is not curious or strong is curious or funny.
Everyone who is not wise or not tall is generous or not tall.
If someone is quiet then someone is either not curious or not strong.
If someone is not happy or not wise then susan is not rich or not funny.
If someone is either wise or happy then susan is either not rich or not strong and vice versa.
Everyone who is either not old or not creative is not patient and vice versa.
Everyone who is not old or not wise is either curious or old.
Everyone who is tall or not quiet is either tall or rich and vice versa.
If alice is funny then someone is strong.
If lucy is both curious and tall then alice is either curious or generous.
Everyone who is either not quiet or not happy is either not humble or not rich.
Everyone who is either not strong or curious is funny and vice versa.
Someone is not funny.
Mary is strong or humble.
Someone is wise.
Paul is either not creative or strong.
Someone is not strong.
Susan is not funny or kind.
Someone is humble or quiet.
Someone is either not patient or funny. | Mary is not old. | neutral | ((patient(mary))<=>((~creative(mary)&~kind(mary))))&
(![X]:(humble(X)=>(creative(X)&~old(X))))&
((?[X]:((happy(X)<~>creative(X))))<=>(?[X]:((~happy(X)<~>~strong(X)))))&
(((brave(alice)|~kind(alice)))<=>(?[X]:(~patient(X))))&
(![X]:((~curious(X)|strong(X))=>(curious(X)|funny(X))))&
(![X]:((~wise(X)|~tall(X))=>(generous(X)|~tall(X))))&
((?[X]:(quiet(X)))=>(?[X]:((~curious(X)<~>~strong(X)))))&
((?[X]:((~happy(X)|~wise(X))))=>((~rich(susan)|~funny(susan))))&
((?[X]:((wise(X)<~>happy(X))))<=>((~rich(susan)<~>~strong(susan))))&
(![X]:((~old(X)<~>~creative(X))<=>~patient(X)))&
(![X]:((~old(X)|~wise(X))=>(curious(X)<~>old(X))))&
(![X]:((tall(X)|~quiet(X))<=>(tall(X)<~>rich(X))))&
((funny(alice))=>(?[X]:(strong(X))))&
(((curious(lucy)&tall(lucy)))=>((curious(alice)<~>generous(alice))))&
(![X]:((~quiet(X)<~>~happy(X))=>(~humble(X)<~>~rich(X))))&
(![X]:((~strong(X)<~>curious(X))<=>funny(X)))&
(?[X]:(~funny(X)))&
((strong(mary)|humble(mary)))&
(?[X]:(wise(X)))&
((~creative(paul)<~>strong(paul)))&
(?[X]:(~strong(X)))&
((~funny(susan)|kind(susan)))&
(?[X]:((humble(X)|quiet(X))))&
(?[X]:((~patient(X)<~>funny(X)))) | ~old(mary) | [] | null | 0 |
If alice is either not funny or not happy then someone is not rich and vice versa. If someone is both strong and kind then paul is wise. If fred is both not calm and strong then someone is either not curious or not calm and vice versa. If someone is both not humble and not strong then fred is strong. Everyone who is both humble and brave is not old or not generous and vice versa. If someone is generous or not old then someone is both not patient and happy. Everyone who is not rich or not calm is strong or curious and vice versa. Everyone who is both not kind and not curious is not tall. If john is either creative or brave then mary is both happy and creative and vice versa. Everyone who is either tall or rich is calm and vice versa. If someone is kind or brave then someone is either not calm or not patient and vice versa. If lucy is patient then someone is curious and vice versa. Everyone who is strong is not creative or old and vice versa. Everyone who is both not creative and humble is both old and not calm. Everyone who is not old is not old or not kind and vice versa. Everyone who is not creative or wise is calm or not generous. Someone is not humble. Fred is creative or not creative. Lucy is both wise and not brave. Someone is both not humble and strong. John is either not strong or generous. Fred is not kind or not curious. Paul is curious or not generous. Someone is not funny or not old. | Lucy is generous. | entailment | (((~funny(alice)<~>~happy(alice)))<=>(?[X]:(~rich(X))))&
((?[X]:((strong(X)&kind(X))))=>(wise(paul)))&
(((~calm(fred)&strong(fred)))<=>(?[X]:((~curious(X)<~>~calm(X)))))&
((?[X]:((~humble(X)&~strong(X))))=>(strong(fred)))&
(![X]:((humble(X)&brave(X))<=>(~old(X)|~generous(X))))&
((?[X]:((generous(X)|~old(X))))=>(?[X]:((~patient(X)&happy(X)))))&
(![X]:((~rich(X)|~calm(X))<=>(strong(X)|curious(X))))&
(![X]:((~kind(X)&~curious(X))=>~tall(X)))&
(((creative(john)<~>brave(john)))<=>((happy(mary)&creative(mary))))&
(![X]:((tall(X)<~>rich(X))<=>calm(X)))&
((?[X]:((kind(X)|brave(X))))<=>(?[X]:((~calm(X)<~>~patient(X)))))&
((patient(lucy))<=>(?[X]:(curious(X))))&
(![X]:(strong(X)<=>(~creative(X)|old(X))))&
(![X]:((~creative(X)&humble(X))=>(old(X)&~calm(X))))&
(![X]:(~old(X)<=>(~old(X)|~kind(X))))&
(![X]:((~creative(X)|wise(X))=>(calm(X)|~generous(X))))&
(?[X]:(~humble(X)))&
((creative(fred)|~creative(fred)))&
((wise(lucy)&~brave(lucy)))&
(?[X]:((~humble(X)&strong(X))))&
((~strong(john)<~>generous(john)))&
((~kind(fred)|~curious(fred)))&
((curious(paul)|~generous(paul)))&
(?[X]:((~funny(X)|~old(X)))) | generous(lucy) | [
"p4",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 74322673874276526280094
% SZS output start Proof for 74322673874276526280094
5. ! [X0] : ((brave(X0) & humble(X0)) <=> (~generous(X0) | ~old(X0))) [input p4]
19. ~brave(lucy) & wise(lucy) [input p18]
25. ~generous(lucy) [input hypothesis]
46. ! [X0] : (((brave(X0) & humble(X0)) | (generous(X0) & old(X0))) & ((~generous(X0) | ~old(X0)) | (~brave(X0) | ~humble(X0)))) [nnf transformation 5]
47. ! [X0] : (((brave(X0) & humble(X0)) | (generous(X0) & old(X0))) & (~generous(X0) | ~old(X0) | ~brave(X0) | ~humble(X0))) [flattening 46]
92. generous(X0) | brave(X0) [cnf transformation 47]
133. ~brave(lucy) [cnf transformation 19]
141. ~generous(lucy) [cnf transformation 25]
336. brave(lucy) [resolution 92,141]
339. $false [subsumption resolution 336,133]
% SZS output end Proof for 74322673874276526280094
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If mary is not wise then susan is not brave and vice versa. Everyone who is either not quiet or humble is both happy and kind and vice versa. If fred is both not calm and curious then alice is not kind and vice versa. Everyone who is tall is either calm or not humble. Everyone who is either not generous or curious is both not rich and not generous. Everyone who is either not kind or brave is both not patient and not happy and vice versa. Everyone who is not brave is both not kind and patient. Everyone who is curious or humble is not happy or funny and vice versa. If someone is not creative then someone is both not tall and not old. Everyone who is not funny is either not kind or not rich. If someone is not wise then fred is either tall or not quiet and vice versa. Everyone who is not humble is both not calm and not quiet. Everyone who is both happy and curious is not quiet or happy and vice versa. Everyone who is both not wise and not kind is not tall. Everyone who is wise is not old or not happy. John is rich or not tall. Someone is not curious or not strong. Fred is either humble or creative. | Fred is calm. | contradiction | ((~wise(mary))<=>(~brave(susan)))&
(![X]:((~quiet(X)<~>humble(X))<=>(happy(X)&kind(X))))&
(((~calm(fred)&curious(fred)))<=>(~kind(alice)))&
(![X]:(tall(X)=>(calm(X)<~>~humble(X))))&
(![X]:((~generous(X)<~>curious(X))=>(~rich(X)&~generous(X))))&
(![X]:((~kind(X)<~>brave(X))<=>(~patient(X)&~happy(X))))&
(![X]:(~brave(X)=>(~kind(X)&patient(X))))&
(![X]:((curious(X)|humble(X))<=>(~happy(X)|funny(X))))&
((?[X]:(~creative(X)))=>(?[X]:((~tall(X)&~old(X)))))&
(![X]:(~funny(X)=>(~kind(X)<~>~rich(X))))&
((?[X]:(~wise(X)))<=>((tall(fred)<~>~quiet(fred))))&
(![X]:(~humble(X)=>(~calm(X)&~quiet(X))))&
(![X]:((happy(X)&curious(X))<=>(~quiet(X)|happy(X))))&
(![X]:((~wise(X)&~kind(X))=>~tall(X)))&
(![X]:(wise(X)=>(~old(X)|~happy(X))))&
((rich(john)|~tall(john)))&
(?[X]:((~curious(X)|~strong(X))))&
((humble(fred)<~>creative(fred))) | calm(fred) | [
"p1",
"p2",
"p5",
"p6",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 2210512474068615456175362
% SZS output start Proof for 2210512474068615456175362
2. ! [X0] : ((~quiet(X0) <~> humble(X0)) <=> (kind(X0) & happy(X0))) [input p1]
3. (curious(fred) & ~calm(fred)) <=> ~kind(alice) [input p2]
6. ! [X0] : ((~kind(X0) <~> brave(X0)) <=> (~happy(X0) & ~patient(X0))) [input p5]
7. ! [X0] : (~brave(X0) => (patient(X0) & ~kind(X0))) [input p6]
12. ! [X0] : (~humble(X0) => (~quiet(X0) & ~calm(X0))) [input p11]
13. ! [X0] : ((curious(X0) & happy(X0)) <=> (happy(X0) | ~quiet(X0))) [input p12]
19. calm(fred) [input hypothesis]
26. ! [X0] : ((patient(X0) & ~kind(X0)) | brave(X0)) [ennf transformation 7]
29. ! [X0] : ((~quiet(X0) & ~calm(X0)) | humble(X0)) [ennf transformation 12]
33. ! [X0] : ((((~humble(X0) | quiet(X0)) & (humble(X0) | ~quiet(X0))) | (~kind(X0) | ~happy(X0))) & ((kind(X0) & happy(X0)) | ((~quiet(X0) | ~humble(X0)) & (humble(X0) | quiet(X0))))) [nnf transformation 2]
34. ! [X0] : ((((~humble(X0) | quiet(X0)) & (humble(X0) | ~quiet(X0))) | ~kind(X0) | ~happy(X0)) & ((kind(X0) & happy(X0)) | ((~quiet(X0) | ~humble(X0)) & (humble(X0) | quiet(X0))))) [flattening 33]
35. ((curious(fred) & ~calm(fred)) | kind(alice)) & (~kind(alice) | (~curious(fred) | calm(fred))) [nnf transformation 3]
36. ((curious(fred) & ~calm(fred)) | kind(alice)) & (~kind(alice) | ~curious(fred) | calm(fred)) [flattening 35]
39. ! [X0] : ((((~brave(X0) | kind(X0)) & (brave(X0) | ~kind(X0))) | (happy(X0) | patient(X0))) & ((~happy(X0) & ~patient(X0)) | ((~kind(X0) | ~brave(X0)) & (brave(X0) | kind(X0))))) [nnf transformation 6]
40. ! [X0] : ((((~brave(X0) | kind(X0)) & (brave(X0) | ~kind(X0))) | happy(X0) | patient(X0)) & ((~happy(X0) & ~patient(X0)) | ((~kind(X0) | ~brave(X0)) & (brave(X0) | kind(X0))))) [flattening 39]
51. ! [X0] : (((curious(X0) & happy(X0)) | (~happy(X0) & quiet(X0))) & ((happy(X0) | ~quiet(X0)) | (~curious(X0) | ~happy(X0)))) [nnf transformation 13]
52. ! [X0] : (((curious(X0) & happy(X0)) | (~happy(X0) & quiet(X0))) & (happy(X0) | ~quiet(X0) | ~curious(X0) | ~happy(X0))) [flattening 51]
56. happy(X0) | humble(X0) | quiet(X0) [cnf transformation 34]
57. ~humble(X0) | ~quiet(X0) | happy(X0) [cnf transformation 34]
63. ~calm(fred) | kind(alice) [cnf transformation 36]
74. ~kind(X0) | ~happy(X0) | ~brave(X0) [cnf transformation 40]
77. ~kind(X0) | brave(X0) [cnf transformation 26]
91. ~quiet(X0) | humble(X0) [cnf transformation 29]
93. happy(X0) | quiet(X0) [cnf transformation 52]
101. calm(fred) [cnf transformation 19]
114. 3 <=> kind(alice) [avatar definition]
116. kind(alice) <- (3) [avatar component clause 114]
123. 5 <=> calm(fred) [avatar definition]
126. 3 | ~5 [avatar split clause 63,123,114]
174. 5 [avatar split clause 101,123]
175. brave(alice) <- (3) [resolution 77,116]
194. ~happy(alice) | ~brave(alice) <- (3) [resolution 74,116]
196. ~happy(alice) <- (3) [subsumption resolution 194,175]
201. humble(alice) | quiet(alice) <- (3) [resolution 196,56]
202. quiet(alice) <- (3) [resolution 196,93]
203. humble(alice) <- (3) [subsumption resolution 201,91]
210. ~quiet(alice) | happy(alice) <- (3) [resolution 203,57]
211. happy(alice) <- (3) [subsumption resolution 210,202]
212. $false <- (3) [subsumption resolution 211,196]
213. ~3 [avatar contradiction clause 212]
214. $false [avatar sat refutation 126,174,213]
% SZS output end Proof for 2210512474068615456175362
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either rich or kind then alice is kind or not brave and vice versa.
If someone is not calm or creative then someone is curious or not patient and vice versa.
If someone is curious or humble then someone is either funny or strong and vice versa.
Everyone who is not curious is not rich or happy.
If alice is both not happy and not old then mary is not happy and vice versa.
Everyone who is either quiet or kind is not generous.
If someone is either rich or not rich then alice is generous or not curious.
If alice is generous or not funny then lucy is funny or not curious and vice versa.
Everyone who is either funny or humble is tall.
Everyone who is either kind or not happy is either rich or humble and vice versa.
Everyone who is not funny is wise or calm.
Everyone who is either not kind or not rich is either not generous or old.
Everyone who is either not funny or quiet is rich.
If john is either funny or not tall then mary is both brave and not old.
Everyone who is either calm or not happy is not generous and vice versa.
If paul is either not happy or not creative then someone is both funny and brave and vice versa.
Someone is wise.
Alice is not generous.
Someone is either not generous or not wise.
Someone is not rich or not patient.
Someone is either tall or humble.
Lucy is both not brave and not quiet.
Someone is not curious.
Susan is funny or creative. | Alice is not generous. | entailment | (((rich(alice)<~>kind(alice)))<=>((kind(alice)|~brave(alice))))&
((?[X]:((~calm(X)|creative(X))))<=>(?[X]:((curious(X)|~patient(X)))))&
((?[X]:((curious(X)|humble(X))))<=>(?[X]:((funny(X)<~>strong(X)))))&
(![X]:(~curious(X)=>(~rich(X)|happy(X))))&
(((~happy(alice)&~old(alice)))<=>(~happy(mary)))&
(![X]:((quiet(X)<~>kind(X))=>~generous(X)))&
((?[X]:((rich(X)<~>~rich(X))))=>((generous(alice)|~curious(alice))))&
(((generous(alice)|~funny(alice)))<=>((funny(lucy)|~curious(lucy))))&
(![X]:((funny(X)<~>humble(X))=>tall(X)))&
(![X]:((kind(X)<~>~happy(X))<=>(rich(X)<~>humble(X))))&
(![X]:(~funny(X)=>(wise(X)|calm(X))))&
(![X]:((~kind(X)<~>~rich(X))=>(~generous(X)<~>old(X))))&
(![X]:((~funny(X)<~>quiet(X))=>rich(X)))&
(((funny(john)<~>~tall(john)))=>((brave(mary)&~old(mary))))&
(![X]:((calm(X)<~>~happy(X))<=>~generous(X)))&
(((~happy(paul)<~>~creative(paul)))<=>(?[X]:((funny(X)&brave(X)))))&
(?[X]:(wise(X)))&
(~generous(alice))&
(?[X]:((~generous(X)<~>~wise(X))))&
(?[X]:((~rich(X)|~patient(X))))&
(?[X]:((tall(X)<~>humble(X))))&
((~brave(lucy)&~quiet(lucy)))&
(?[X]:(~curious(X)))&
((funny(susan)|creative(susan))) | ~generous(alice) | [
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 5786802779927411496890178
% SZS output start Proof for 5786802779927411496890178
18. ~generous(alice) [input p17]
25. generous(alice) [input hypothesis]
139. ~generous(alice) [cnf transformation 18]
149. generous(alice) [cnf transformation 25]
252. 23 <=> generous(alice) [avatar definition]
325. ~23 [avatar split clause 139,252]
364. 23 [avatar split clause 149,252]
365. $false [avatar sat refutation 325,364]
% SZS output end Proof for 5786802779927411496890178
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both wise and not kind then john is generous.
Everyone who is patient or strong is both humble and not kind and vice versa.
If someone is funny then someone is not strong and vice versa.
Everyone who is either not happy or happy is both not tall and strong and vice versa.
Everyone who is not quiet is either not kind or calm.
Everyone who is both curious and creative is not quiet or not rich.
If someone is quiet or wise then someone is both not tall and humble.
Everyone who is not creative is not wise or not humble and vice versa.
If paul is curious then fred is wise or old.
If john is humble or quiet then john is either not rich or not old.
Everyone who is generous or not happy is not calm and vice versa.
If someone is old or not quiet then someone is both happy and funny.
Everyone who is both not humble and funny is both not patient and funny.
Everyone who is not quiet or old is funny or creative and vice versa.
If mary is not curious then someone is both kind and not tall.
Someone is funny or not generous.
Someone is wise or not creative.
Lucy is rich.
Paul is not generous or curious. | Fred is not creative. | entailment | ((?[X]:((wise(X)&~kind(X))))=>(generous(john)))&
(![X]:((patient(X)|strong(X))<=>(humble(X)&~kind(X))))&
((?[X]:(funny(X)))<=>(?[X]:(~strong(X))))&
(![X]:((~happy(X)<~>happy(X))<=>(~tall(X)&strong(X))))&
(![X]:(~quiet(X)=>(~kind(X)<~>calm(X))))&
(![X]:((curious(X)&creative(X))=>(~quiet(X)|~rich(X))))&
((?[X]:((quiet(X)|wise(X))))=>(?[X]:((~tall(X)&humble(X)))))&
(![X]:(~creative(X)<=>(~wise(X)|~humble(X))))&
((curious(paul))=>((wise(fred)|old(fred))))&
(((humble(john)|quiet(john)))=>((~rich(john)<~>~old(john))))&
(![X]:((generous(X)|~happy(X))<=>~calm(X)))&
((?[X]:((old(X)|~quiet(X))))=>(?[X]:((happy(X)&funny(X)))))&
(![X]:((~humble(X)&funny(X))=>(~patient(X)&funny(X))))&
(![X]:((~quiet(X)|old(X))<=>(funny(X)|creative(X))))&
((~curious(mary))=>(?[X]:((kind(X)&~tall(X)))))&
(?[X]:((funny(X)|~generous(X))))&
(?[X]:((wise(X)|~creative(X))))&
(rich(lucy))&
((~generous(paul)|curious(paul))) | ~creative(fred) | [
"p2",
"p3",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 9220657483934816149517518
% SZS output start Proof for 9220657483934816149517518
3. ? [X0] : funny(X0) <=> ? [X0] : ~strong(X0) [input p2]
4. ! [X0] : ((~happy(X0) <~> happy(X0)) <=> (strong(X0) & ~tall(X0))) [input p3]
12. ? [X0] : (~quiet(X0) | old(X0)) => ? [X0] : (funny(X0) & happy(X0)) [input p11]
14. ! [X0] : ((old(X0) | ~quiet(X0)) <=> (creative(X0) | funny(X0))) [input p13]
20. creative(fred) [input hypothesis]
21. ? [X0] : funny(X0) <=> ? [X1] : ~strong(X1) [rectify 3]
23. ? [X0] : (~quiet(X0) | old(X0)) => ? [X1] : (funny(X1) & happy(X1)) [rectify 12]
32. ? [X1] : (funny(X1) & happy(X1)) | ! [X0] : (quiet(X0) & ~old(X0)) [ennf transformation 23]
38. (? [X0] : funny(X0) | ! [X1] : strong(X1)) & (? [X1] : ~strong(X1) | ! [X0] : ~funny(X0)) [nnf transformation 21]
39. (? [X0] : funny(X0) | ! [X1] : strong(X1)) & (? [X2] : ~strong(X2) | ! [X3] : ~funny(X3)) [rectify 38]
40. ? [X0] : funny(X0) => funny(sK0) [choice axiom]
41. ? [X2] : ~strong(X2) => ~strong(sK1) [choice axiom]
42. (funny(sK0) | ! [X1] : strong(X1)) & (~strong(sK1) | ! [X3] : ~funny(X3)) [skolemisation 39,41,40]
43. ! [X0] : ((((~happy(X0) | happy(X0)) & (happy(X0) | ~happy(X0))) | (~strong(X0) | tall(X0))) & ((strong(X0) & ~tall(X0)) | ((~happy(X0) | ~happy(X0)) & (happy(X0) | happy(X0))))) [nnf transformation 4]
44. ! [X0] : ((((~happy(X0) | happy(X0)) & (happy(X0) | ~happy(X0))) | ~strong(X0) | tall(X0)) & ((strong(X0) & ~tall(X0)) | ((~happy(X0) | ~happy(X0)) & (happy(X0) | happy(X0))))) [flattening 43]
54. ? [X0] : (funny(X0) & happy(X0)) | ! [X1] : (quiet(X1) & ~old(X1)) [rectify 32]
55. ? [X0] : (funny(X0) & happy(X0)) => (funny(sK3) & happy(sK3)) [choice axiom]
56. (funny(sK3) & happy(sK3)) | ! [X1] : (quiet(X1) & ~old(X1)) [skolemisation 54,55]
57. ! [X0] : (((old(X0) | ~quiet(X0)) | (~creative(X0) & ~funny(X0))) & ((creative(X0) | funny(X0)) | (~old(X0) & quiet(X0)))) [nnf transformation 14]
58. ! [X0] : ((old(X0) | ~quiet(X0) | (~creative(X0) & ~funny(X0))) & (creative(X0) | funny(X0) | (~old(X0) & quiet(X0)))) [flattening 57]
71. ~strong(sK1) | ~funny(X3) [cnf transformation 42]
75. strong(X0) | happy(X0) | happy(X0) [cnf transformation 44]
76. strong(X0) | ~happy(X0) | ~happy(X0) [cnf transformation 44]
99. funny(sK3) | ~old(X1) [cnf transformation 56]
100. funny(sK3) | quiet(X1) [cnf transformation 56]
106. ~creative(X0) | ~quiet(X0) | old(X0) [cnf transformation 58]
113. creative(fred) [cnf transformation 20]
116. strong(X0) | happy(X0) [duplicate literal removal 75]
117. ~happy(X0) | strong(X0) [duplicate literal removal 76]
127. 3 <=> ! [X1] : strong(X1) [avatar definition]
128. strong(X1) <- (3) [avatar component clause 127]
135. 5 <=> ! [X3] : ~funny(X3) [avatar definition]
136. ~funny(X3) <- (5) [avatar component clause 135]
138. 6 <=> strong(sK1) [avatar definition]
140. ~strong(sK1) <- (~6) [avatar component clause 138]
141. 5 | ~6 [avatar split clause 71,138,135]
142. strong(X0) [subsumption resolution 116,117]
143. 3 [avatar split clause 142,127]
191. 17 <=> ! [X1] : quiet(X1) [avatar definition]
192. quiet(X1) <- (17) [avatar component clause 191]
194. 18 <=> funny(sK3) [avatar definition]
196. funny(sK3) <- (18) [avatar component clause 194]
197. 17 | 18 [avatar split clause 100,194,191]
199. 19 <=> ! [X1] : ~old(X1) [avatar definition]
200. ~old(X1) <- (19) [avatar component clause 199]
201. 19 | 18 [avatar split clause 99,194,199]
233. $false <- (3, ~6) [resolution 140,128]
234. ~3 | 6 [avatar contradiction clause 233]
257. ~quiet(fred) | old(fred) [resolution 106,113]
259. old(fred) <- (17) [subsumption resolution 257,192]
260. $false <- (17, 19) [subsumption resolution 259,200]
261. ~17 | ~19 [avatar contradiction clause 260]
263. $false <- (5, 18) [subsumption resolution 196,136]
264. ~5 | ~18 [avatar contradiction clause 263]
265. $false [avatar sat refutation 141,143,197,201,234,261,264]
% SZS output end Proof for 9220657483934816149517518
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If susan is not patient or not calm then someone is either funny or not calm and vice versa.
If fred is both not creative and not tall then paul is kind and vice versa.
Everyone who is not creative or quiet is both not creative and quiet and vice versa.
Everyone who is brave or not wise is both not rich and creative and vice versa.
Everyone who is curious is either curious or humble and vice versa.
If alice is either not creative or curious then mary is quiet.
If someone is either not humble or not kind then lucy is both generous and not quiet and vice versa.
Everyone who is both calm and strong is both quiet and wise.
If lucy is both rich and not generous then paul is either creative or not tall and vice versa.
If someone is rich then paul is both not old and strong.
If someone is not creative or wise then fred is humble.
Everyone who is not kind or funny is either patient or tall and vice versa.
If alice is not patient then someone is brave.
Everyone who is either not funny or funny is either not kind or quiet and vice versa.
If lucy is both funny and tall then someone is either quiet or kind.
If fred is humble then john is both brave and happy and vice versa.
Someone is both calm and brave.
Someone is not funny.
Someone is both curious and patient.
Fred is not kind or quiet.
Someone is not kind or happy. | Alice is not kind. | entailment | (((~patient(susan)|~calm(susan)))<=>(?[X]:((funny(X)<~>~calm(X)))))&
(((~creative(fred)&~tall(fred)))<=>(kind(paul)))&
(![X]:((~creative(X)|quiet(X))<=>(~creative(X)&quiet(X))))&
(![X]:((brave(X)|~wise(X))<=>(~rich(X)&creative(X))))&
(![X]:(curious(X)<=>(curious(X)<~>humble(X))))&
(((~creative(alice)<~>curious(alice)))=>(quiet(mary)))&
((?[X]:((~humble(X)<~>~kind(X))))<=>((generous(lucy)&~quiet(lucy))))&
(![X]:((calm(X)&strong(X))=>(quiet(X)&wise(X))))&
(((rich(lucy)&~generous(lucy)))<=>((creative(paul)<~>~tall(paul))))&
((?[X]:(rich(X)))=>((~old(paul)&strong(paul))))&
((?[X]:((~creative(X)|wise(X))))=>(humble(fred)))&
(![X]:((~kind(X)|funny(X))<=>(patient(X)<~>tall(X))))&
((~patient(alice))=>(?[X]:(brave(X))))&
(![X]:((~funny(X)<~>funny(X))<=>(~kind(X)<~>quiet(X))))&
(((funny(lucy)&tall(lucy)))=>(?[X]:((quiet(X)<~>kind(X)))))&
((humble(fred))<=>((brave(john)&happy(john))))&
(?[X]:((calm(X)&brave(X))))&
(?[X]:(~funny(X)))&
(?[X]:((curious(X)&patient(X))))&
((~kind(fred)|quiet(fred)))&
(?[X]:((~kind(X)|happy(X)))) | ~kind(alice) | [
"p2",
"p4",
"p10",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 6600135787783766962559232
% SZS output start Proof for 6600135787783766962559232
3. ! [X0] : ((quiet(X0) | ~creative(X0)) <=> (quiet(X0) & ~creative(X0))) [input p2]
5. ! [X0] : (curious(X0) <=> (curious(X0) <~> humble(X0))) [input p4]
11. ? [X0] : (wise(X0) | ~creative(X0)) => humble(fred) [input p10]
14. ! [X0] : ((~funny(X0) <~> funny(X0)) <=> (~kind(X0) <~> quiet(X0))) [input p13]
22. kind(alice) [input hypothesis]
28. humble(fred) | ! [X0] : (~wise(X0) & creative(X0)) [ennf transformation 11]
39. ! [X0] : (((quiet(X0) | ~creative(X0)) | (~quiet(X0) | creative(X0))) & ((quiet(X0) & ~creative(X0)) | (~quiet(X0) & creative(X0)))) [nnf transformation 3]
40. ! [X0] : ((quiet(X0) | ~creative(X0) | ~quiet(X0) | creative(X0)) & ((quiet(X0) & ~creative(X0)) | (~quiet(X0) & creative(X0)))) [flattening 39]
43. ! [X0] : ((curious(X0) | ((curious(X0) | ~humble(X0)) & (humble(X0) | ~curious(X0)))) & (((~humble(X0) | ~curious(X0)) & (humble(X0) | curious(X0))) | ~curious(X0))) [nnf transformation 5]
56. ! [X0] : ((((~funny(X0) | funny(X0)) & (funny(X0) | ~funny(X0))) | ((~kind(X0) | ~quiet(X0)) & (quiet(X0) | kind(X0)))) & (((~quiet(X0) | kind(X0)) & (quiet(X0) | ~kind(X0))) | ((~funny(X0) | ~funny(X0)) & (funny(X0) | funny(X0))))) [nnf transformation 14]
80. ~quiet(X0) | ~creative(X0) [cnf transformation 40]
90. ~humble(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 43]
92. curious(X0) | curious(X0) | ~humble(X0) [cnf transformation 43]
110. humble(fred) | creative(X0) [cnf transformation 28]
119. quiet(X0) | ~kind(X0) | funny(X0) | funny(X0) [cnf transformation 56]
120. quiet(X0) | ~kind(X0) | ~funny(X0) | ~funny(X0) [cnf transformation 56]
139. kind(alice) [cnf transformation 22]
140. quiet(X0) | ~kind(X0) | funny(X0) [duplicate literal removal 119]
141. quiet(X0) | ~kind(X0) | ~funny(X0) [duplicate literal removal 120]
144. ~humble(X0) | ~curious(X0) [duplicate literal removal 90]
145. ~humble(X0) | curious(X0) [duplicate literal removal 92]
189. ~humble(X0) [subsumption resolution 144,145]
252. creative(X0) [subsumption resolution 110,189]
263. ~kind(X0) | quiet(X0) [subsumption resolution 140,141]
310. quiet(alice) [resolution 263,139]
313. ~creative(alice) [resolution 310,80]
314. $false [subsumption resolution 313,252]
% SZS output end Proof for 6600135787783766962559232
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong and old is either not wise or humble.
If someone is happy or patient then fred is either kind or not curious and vice versa.
Everyone who is either not quiet or patient is either funny or old.
Everyone who is not humble is either not funny or brave.
If someone is either not quiet or not creative then someone is creative or not rich.
Everyone who is both brave and not happy is either not humble or calm and vice versa.
Everyone who is tall or not curious is not tall or generous and vice versa.
Everyone who is not creative or not kind is both patient and not kind.
Everyone who is not calm is happy or rich and vice versa.
Everyone who is curious is both not strong and quiet and vice versa.
Everyone who is not humble or calm is either creative or happy and vice versa.
Everyone who is both calm and not humble is not rich and vice versa.
Everyone who is happy is not rich or not calm and vice versa.
If someone is both not funny and creative then someone is both not calm and not old.
Everyone who is both kind and old is both funny and not wise.
Mary is either kind or not kind.
Someone is both brave and not wise.
Alice is either happy or brave.
Someone is not curious or humble.
Mary is brave or not funny. | Fred is not calm. | entailment | (![X]:((~strong(X)&old(X))=>(~wise(X)<~>humble(X))))&
((?[X]:((happy(X)|patient(X))))<=>((kind(fred)<~>~curious(fred))))&
(![X]:((~quiet(X)<~>patient(X))=>(funny(X)<~>old(X))))&
(![X]:(~humble(X)=>(~funny(X)<~>brave(X))))&
((?[X]:((~quiet(X)<~>~creative(X))))=>(?[X]:((creative(X)|~rich(X)))))&
(![X]:((brave(X)&~happy(X))<=>(~humble(X)<~>calm(X))))&
(![X]:((tall(X)|~curious(X))<=>(~tall(X)|generous(X))))&
(![X]:((~creative(X)|~kind(X))=>(patient(X)&~kind(X))))&
(![X]:(~calm(X)<=>(happy(X)|rich(X))))&
(![X]:(curious(X)<=>(~strong(X)&quiet(X))))&
(![X]:((~humble(X)|calm(X))<=>(creative(X)<~>happy(X))))&
(![X]:((calm(X)&~humble(X))<=>~rich(X)))&
(![X]:(happy(X)<=>(~rich(X)|~calm(X))))&
((?[X]:((~funny(X)&creative(X))))=>(?[X]:((~calm(X)&~old(X)))))&
(![X]:((kind(X)&old(X))=>(funny(X)&~wise(X))))&
((kind(mary)<~>~kind(mary)))&
(?[X]:((brave(X)&~wise(X))))&
((happy(alice)<~>brave(alice)))&
(?[X]:((~curious(X)|humble(X))))&
((brave(mary)|~funny(mary))) | ~calm(fred) | [
"p8",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 162741499403607679696455
% SZS output start Proof for 162741499403607679696455
9. ! [X0] : (~calm(X0) <=> (rich(X0) | happy(X0))) [input p8]
12. ! [X0] : ((~humble(X0) & calm(X0)) <=> ~rich(X0)) [input p11]
13. ! [X0] : (happy(X0) <=> (~calm(X0) | ~rich(X0))) [input p12]
21. calm(fred) [input hypothesis]
48. ! [X0] : ((~calm(X0) | (~rich(X0) & ~happy(X0))) & ((rich(X0) | happy(X0)) | calm(X0))) [nnf transformation 9]
49. ! [X0] : ((~calm(X0) | (~rich(X0) & ~happy(X0))) & (rich(X0) | happy(X0) | calm(X0))) [flattening 48]
54. ! [X0] : (((~humble(X0) & calm(X0)) | rich(X0)) & (~rich(X0) | (humble(X0) | ~calm(X0)))) [nnf transformation 12]
55. ! [X0] : (((~humble(X0) & calm(X0)) | rich(X0)) & (~rich(X0) | humble(X0) | ~calm(X0))) [flattening 54]
56. ! [X0] : ((happy(X0) | (calm(X0) & rich(X0))) & ((~calm(X0) | ~rich(X0)) | ~happy(X0))) [nnf transformation 13]
57. ! [X0] : ((happy(X0) | (calm(X0) & rich(X0))) & (~calm(X0) | ~rich(X0) | ~happy(X0))) [flattening 56]
98. ~calm(X0) | ~happy(X0) [cnf transformation 49]
99. ~calm(X0) | ~rich(X0) [cnf transformation 49]
110. calm(X0) | rich(X0) [cnf transformation 55]
113. happy(X0) | rich(X0) [cnf transformation 57]
127. calm(fred) [cnf transformation 21]
223. ~rich(fred) [resolution 99,127]
226. rich(X1) | ~happy(X1) [resolution 110,98]
227. rich(X1) [subsumption resolution 226,113]
229. $false [resolution 227,223]
% SZS output end Proof for 162741499403607679696455
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or not happy is both patient and not funny and vice versa.
If fred is both happy and quiet then lucy is not patient or not wise and vice versa.
If john is both not humble and not calm then mary is both not rich and funny.
Everyone who is either strong or curious is not tall or not quiet and vice versa.
Everyone who is rich or not quiet is humble or calm and vice versa.
Everyone who is not quiet or patient is either not calm or not quiet and vice versa.
Everyone who is not brave is brave.
Everyone who is both humble and not calm is either calm or not brave.
Everyone who is either calm or not strong is either not curious or not calm and vice versa.
Everyone who is either not humble or not quiet is not rich and vice versa.
If someone is both happy and wise then someone is rich.
If john is old or not patient then someone is calm and vice versa.
Everyone who is not creative is strong.
Everyone who is either generous or happy is not brave and vice versa.
If someone is not old or wise then mary is not calm or not creative and vice versa.
If someone is both rich and curious then john is either tall or strong and vice versa.
Alice is not generous.
Someone is both happy and quiet.
Someone is generous or not strong.
Lucy is either humble or creative.
John is not strong.
Someone is not tall or not funny.
Lucy is not humble or tall.
Someone is humble or not brave. | John is not funny. | neutral | (![X]:((curious(X)<~>~happy(X))<=>(patient(X)&~funny(X))))&
(((happy(fred)&quiet(fred)))<=>((~patient(lucy)|~wise(lucy))))&
(((~humble(john)&~calm(john)))=>((~rich(mary)&funny(mary))))&
(![X]:((strong(X)<~>curious(X))<=>(~tall(X)|~quiet(X))))&
(![X]:((rich(X)|~quiet(X))<=>(humble(X)|calm(X))))&
(![X]:((~quiet(X)|patient(X))<=>(~calm(X)<~>~quiet(X))))&
(![X]:(~brave(X)=>brave(X)))&
(![X]:((humble(X)&~calm(X))=>(calm(X)<~>~brave(X))))&
(![X]:((calm(X)<~>~strong(X))<=>(~curious(X)<~>~calm(X))))&
(![X]:((~humble(X)<~>~quiet(X))<=>~rich(X)))&
((?[X]:((happy(X)&wise(X))))=>(?[X]:(rich(X))))&
(((old(john)|~patient(john)))<=>(?[X]:(calm(X))))&
(![X]:(~creative(X)=>strong(X)))&
(![X]:((generous(X)<~>happy(X))<=>~brave(X)))&
((?[X]:((~old(X)|wise(X))))<=>((~calm(mary)|~creative(mary))))&
((?[X]:((rich(X)&curious(X))))<=>((tall(john)<~>strong(john))))&
(~generous(alice))&
(?[X]:((happy(X)&quiet(X))))&
(?[X]:((generous(X)|~strong(X))))&
((humble(lucy)<~>creative(lucy)))&
(~strong(john))&
(?[X]:((~tall(X)|~funny(X))))&
((~humble(lucy)|tall(lucy)))&
(?[X]:((humble(X)|~brave(X)))) | ~funny(john) | [] | null | 0 |
If someone is either calm or not curious then lucy is either creative or not tall.
Everyone who is either strong or brave is creative.
If someone is tall then fred is not quiet or not generous.
Everyone who is not kind is either not brave or not humble.
If paul is both not humble and not funny then lucy is not creative and vice versa.
Everyone who is humble or not rich is either not brave or creative and vice versa.
Everyone who is happy is patient or kind and vice versa.
Everyone who is calm is either happy or wise and vice versa.
If mary is both not wise and not curious then someone is either strong or not quiet and vice versa.
If fred is either wise or tall then susan is both not happy and not brave and vice versa.
Everyone who is not generous or quiet is not generous or not brave and vice versa.
If someone is not calm then someone is calm or not generous and vice versa.
If someone is both brave and happy then john is tall or quiet and vice versa.
Everyone who is either not tall or creative is wise or not happy and vice versa.
If someone is either calm or funny then someone is either funny or not kind and vice versa.
If someone is rich then alice is old.
Paul is either not curious or not old.
Mary is both brave and happy.
Mary is not curious.
Someone is tall or not rich.
Someone is either not strong or generous.
Someone is patient.
Alice is not calm or patient. | Paul is not creative. | neutral | ((?[X]:((calm(X)<~>~curious(X))))=>((creative(lucy)<~>~tall(lucy))))&
(![X]:((strong(X)<~>brave(X))=>creative(X)))&
((?[X]:(tall(X)))=>((~quiet(fred)|~generous(fred))))&
(![X]:(~kind(X)=>(~brave(X)<~>~humble(X))))&
(((~humble(paul)&~funny(paul)))<=>(~creative(lucy)))&
(![X]:((humble(X)|~rich(X))<=>(~brave(X)<~>creative(X))))&
(![X]:(happy(X)<=>(patient(X)|kind(X))))&
(![X]:(calm(X)<=>(happy(X)<~>wise(X))))&
(((~wise(mary)&~curious(mary)))<=>(?[X]:((strong(X)<~>~quiet(X)))))&
(((wise(fred)<~>tall(fred)))<=>((~happy(susan)&~brave(susan))))&
(![X]:((~generous(X)|quiet(X))<=>(~generous(X)|~brave(X))))&
((?[X]:(~calm(X)))<=>(?[X]:((calm(X)|~generous(X)))))&
((?[X]:((brave(X)&happy(X))))<=>((tall(john)|quiet(john))))&
(![X]:((~tall(X)<~>creative(X))<=>(wise(X)|~happy(X))))&
((?[X]:((calm(X)<~>funny(X))))<=>(?[X]:((funny(X)<~>~kind(X)))))&
((?[X]:(rich(X)))=>(old(alice)))&
((~curious(paul)<~>~old(paul)))&
((brave(mary)&happy(mary)))&
(~curious(mary))&
(?[X]:((tall(X)|~rich(X))))&
(?[X]:((~strong(X)<~>generous(X))))&
(?[X]:(patient(X)))&
((~calm(alice)|patient(alice))) | ~creative(paul) | [] | null | 0 |
If paul is not old or happy then paul is calm or brave. Everyone who is either not happy or humble is either not funny or tall. If susan is either humble or happy then someone is strong. If someone is either not curious or kind then john is both not rich and not happy. If someone is not generous or not patient then someone is either not humble or not funny. Everyone who is generous or not curious is not calm. If someone is both funny and not calm then someone is either patient or not happy. Everyone who is both not kind and wise is brave or wise and vice versa. If someone is rich then someone is both not kind and not happy and vice versa. Everyone who is curious is happy. Everyone who is calm is either brave or calm and vice versa. If someone is old or not humble then someone is both not brave and not kind and vice versa. If alice is either not kind or not humble then fred is both not patient and not curious and vice versa. Everyone who is both not happy and old is tall. Everyone who is both quiet and happy is rich or not rich and vice versa. If someone is patient or not calm then someone is both quiet and not happy. Someone is not patient or wise. Paul is either not calm or strong. Paul is not tall or not happy. Alice is not generous. Alice is both not creative and happy. Lucy is not tall. Someone is either not brave or humble. | Susan is humble. | neutral | (((~old(paul)|happy(paul)))=>((calm(paul)|brave(paul))))&
(![X]:((~happy(X)<~>humble(X))=>(~funny(X)<~>tall(X))))&
(((humble(susan)<~>happy(susan)))=>(?[X]:(strong(X))))&
((?[X]:((~curious(X)<~>kind(X))))=>((~rich(john)&~happy(john))))&
((?[X]:((~generous(X)|~patient(X))))=>(?[X]:((~humble(X)<~>~funny(X)))))&
(![X]:((generous(X)|~curious(X))=>~calm(X)))&
((?[X]:((funny(X)&~calm(X))))=>(?[X]:((patient(X)<~>~happy(X)))))&
(![X]:((~kind(X)&wise(X))<=>(brave(X)|wise(X))))&
((?[X]:(rich(X)))<=>(?[X]:((~kind(X)&~happy(X)))))&
(![X]:(curious(X)=>happy(X)))&
(![X]:(calm(X)<=>(brave(X)<~>calm(X))))&
((?[X]:((old(X)|~humble(X))))<=>(?[X]:((~brave(X)&~kind(X)))))&
(((~kind(alice)<~>~humble(alice)))<=>((~patient(fred)&~curious(fred))))&
(![X]:((~happy(X)&old(X))=>tall(X)))&
(![X]:((quiet(X)&happy(X))<=>(rich(X)|~rich(X))))&
((?[X]:((patient(X)|~calm(X))))=>(?[X]:((quiet(X)&~happy(X)))))&
(?[X]:((~patient(X)|wise(X))))&
((~calm(paul)<~>strong(paul)))&
((~tall(paul)|~happy(paul)))&
(~generous(alice))&
((~creative(alice)&happy(alice)))&
(~tall(lucy))&
(?[X]:((~brave(X)<~>humble(X)))) | humble(susan) | [] | null | 0 |
Everyone who is either not patient or kind is strong and vice versa.
Everyone who is either wise or rich is patient and vice versa.
If someone is not wise or not curious then paul is calm.
Everyone who is not patient or old is not generous.
If mary is either not kind or not wise then someone is either not happy or tall and vice versa.
If fred is both not wise and not tall then someone is not funny.
If someone is quiet then someone is strong or happy.
If susan is both not funny and kind then fred is generous.
If someone is not brave then someone is not wise and vice versa.
If john is not creative or not kind then lucy is generous or not curious.
If mary is either not old or kind then fred is both not calm and not tall.
Everyone who is not patient is both not brave and humble and vice versa.
Everyone who is patient or wise is both patient and not brave.
Everyone who is both funny and not rich is not calm or not kind and vice versa.
If lucy is not humble then lucy is either strong or curious and vice versa.
If susan is both calm and generous then someone is either not creative or not humble and vice versa.
Susan is both not humble and not funny.
Paul is strong or calm.
Someone is not strong or generous.
Fred is not creative.
Paul is either not quiet or not strong.
Alice is both humble and not happy.
Lucy is old or humble.
Susan is both not happy and rich. | Susan is brave. | contradiction | (![X]:((~patient(X)<~>kind(X))<=>strong(X)))&
(![X]:((wise(X)<~>rich(X))<=>patient(X)))&
((?[X]:((~wise(X)|~curious(X))))=>(calm(paul)))&
(![X]:((~patient(X)|old(X))=>~generous(X)))&
(((~kind(mary)<~>~wise(mary)))<=>(?[X]:((~happy(X)<~>tall(X)))))&
(((~wise(fred)&~tall(fred)))=>(?[X]:(~funny(X))))&
((?[X]:(quiet(X)))=>(?[X]:((strong(X)|happy(X)))))&
(((~funny(susan)&kind(susan)))=>(generous(fred)))&
((?[X]:(~brave(X)))<=>(?[X]:(~wise(X))))&
(((~creative(john)|~kind(john)))=>((generous(lucy)|~curious(lucy))))&
(((~old(mary)<~>kind(mary)))=>((~calm(fred)&~tall(fred))))&
(![X]:(~patient(X)<=>(~brave(X)&humble(X))))&
(![X]:((patient(X)|wise(X))=>(patient(X)&~brave(X))))&
(![X]:((funny(X)&~rich(X))<=>(~calm(X)|~kind(X))))&
((~humble(lucy))<=>((strong(lucy)<~>curious(lucy))))&
(((calm(susan)&generous(susan)))<=>(?[X]:((~creative(X)<~>~humble(X)))))&
((~humble(susan)&~funny(susan)))&
((strong(paul)|calm(paul)))&
(?[X]:((~strong(X)|generous(X))))&
(~creative(fred))&
((~quiet(paul)<~>~strong(paul)))&
((humble(alice)&~happy(alice)))&
((old(lucy)|humble(lucy)))&
((~happy(susan)&rich(susan))) | brave(susan) | [
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 5138666408710046400967223
% SZS output start Proof for 5138666408710046400967223
12. ! [X0] : (~patient(X0) <=> (humble(X0) & ~brave(X0))) [input p11]
13. ! [X0] : ((wise(X0) | patient(X0)) => (~brave(X0) & patient(X0))) [input p12]
25. brave(susan) [input hypothesis]
38. ! [X0] : ((~brave(X0) & patient(X0)) | (~wise(X0) & ~patient(X0))) [ennf transformation 13]
56. ! [X0] : ((~patient(X0) | (~humble(X0) | brave(X0))) & ((humble(X0) & ~brave(X0)) | patient(X0))) [nnf transformation 12]
57. ! [X0] : ((~patient(X0) | ~humble(X0) | brave(X0)) & ((humble(X0) & ~brave(X0)) | patient(X0))) [flattening 56]
100. ~brave(X0) | patient(X0) [cnf transformation 57]
105. ~brave(X0) | ~patient(X0) [cnf transformation 38]
134. brave(susan) [cnf transformation 25]
258. ~brave(X0) [subsumption resolution 105,100]
325. $false [subsumption resolution 134,258]
% SZS output end Proof for 5138666408710046400967223
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If susan is not brave or rich then john is quiet and vice versa.
Everyone who is not kind or not humble is curious and vice versa.
If fred is patient or not tall then alice is not happy and vice versa.
Everyone who is not quiet or not generous is curious and vice versa.
Everyone who is not rich or curious is either wise or not creative.
Everyone who is either calm or not funny is not funny and vice versa.
If someone is either not tall or not patient then someone is either tall or not patient and vice versa.
If someone is both curious and not patient then someone is both not happy and not quiet.
Everyone who is either creative or not old is either old or strong.
If someone is rich or not generous then mary is wise.
If someone is not quiet or old then someone is creative.
If someone is not funny or not creative then paul is curious or not wise.
Everyone who is both not happy and kind is both not brave and not patient.
If john is not curious then someone is both not calm and not tall.
If someone is either creative or not kind then paul is either wise or not generous.
Everyone who is either not wise or wise is funny and vice versa.
Someone is patient.
Mary is either not funny or not curious.
Alice is not quiet or creative.
Mary is old.
Paul is not rich.
Someone is both quiet and not calm.
Alice is both not strong and not wise.
Someone is curious or not kind. | Alice is calm. | contradiction | (((~brave(susan)|rich(susan)))<=>(quiet(john)))&
(![X]:((~kind(X)|~humble(X))<=>curious(X)))&
(((patient(fred)|~tall(fred)))<=>(~happy(alice)))&
(![X]:((~quiet(X)|~generous(X))<=>curious(X)))&
(![X]:((~rich(X)|curious(X))=>(wise(X)<~>~creative(X))))&
(![X]:((calm(X)<~>~funny(X))<=>~funny(X)))&
((?[X]:((~tall(X)<~>~patient(X))))<=>(?[X]:((tall(X)<~>~patient(X)))))&
((?[X]:((curious(X)&~patient(X))))=>(?[X]:((~happy(X)&~quiet(X)))))&
(![X]:((creative(X)<~>~old(X))=>(old(X)<~>strong(X))))&
((?[X]:((rich(X)|~generous(X))))=>(wise(mary)))&
((?[X]:((~quiet(X)|old(X))))=>(?[X]:(creative(X))))&
((?[X]:((~funny(X)|~creative(X))))=>((curious(paul)|~wise(paul))))&
(![X]:((~happy(X)&kind(X))=>(~brave(X)&~patient(X))))&
((~curious(john))=>(?[X]:((~calm(X)&~tall(X)))))&
((?[X]:((creative(X)<~>~kind(X))))=>((wise(paul)<~>~generous(paul))))&
(![X]:((~wise(X)<~>wise(X))<=>funny(X)))&
(?[X]:(patient(X)))&
((~funny(mary)<~>~curious(mary)))&
((~quiet(alice)|creative(alice)))&
(old(mary))&
(~rich(paul))&
(?[X]:((quiet(X)&~calm(X))))&
((~strong(alice)&~wise(alice)))&
(?[X]:((curious(X)|~kind(X)))) | calm(alice) | [
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 2515713061788497948159037
% SZS output start Proof for 2515713061788497948159037
6. ! [X0] : ((calm(X0) <~> ~funny(X0)) <=> ~funny(X0)) [input p5]
25. calm(alice) [input hypothesis]
49. ! [X0] : ((((funny(X0) | ~calm(X0)) & (~funny(X0) | calm(X0))) | funny(X0)) & (~funny(X0) | ((calm(X0) | funny(X0)) & (~funny(X0) | ~calm(X0))))) [nnf transformation 6]
89. ~funny(X0) | ~funny(X0) | ~calm(X0) [cnf transformation 49]
92. funny(X0) | ~calm(X0) | funny(X0) [cnf transformation 49]
136. calm(alice) [cnf transformation 25]
141. ~funny(X0) | ~calm(X0) [duplicate literal removal 89]
142. funny(X0) | ~calm(X0) [duplicate literal removal 92]
173. ~calm(X0) [subsumption resolution 141,142]
308. $false [subsumption resolution 136,173]
% SZS output end Proof for 2515713061788497948159037
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If mary is both rich and not brave then mary is generous.
Everyone who is calm or happy is both not rich and not wise.
Everyone who is not humble is calm and vice versa.
If someone is patient then someone is creative.
If someone is both generous and not creative then lucy is not old.
Everyone who is not tall or brave is either brave or not humble.
Everyone who is not strong or calm is humble or funny.
If someone is not brave or brave then someone is quiet or generous.
Everyone who is both not brave and curious is rich or not funny.
If someone is either old or wise then susan is not curious or strong.
Everyone who is kind is both not happy and not humble and vice versa.
Everyone who is not tall is funny.
Everyone who is either not calm or not humble is not strong or brave and vice versa.
If someone is both wise and not generous then john is either not happy or creative and vice versa.
Everyone who is generous or creative is not funny or not creative.
Everyone who is both not curious and not quiet is not wise or old and vice versa.
Fred is kind or not rich.
Someone is not patient.
Paul is kind.
Fred is rich or not strong.
Paul is either rich or not happy.
Someone is either strong or patient.
Someone is both strong and quiet. | John is not tall. | neutral | (((rich(mary)&~brave(mary)))=>(generous(mary)))&
(![X]:((calm(X)|happy(X))=>(~rich(X)&~wise(X))))&
(![X]:(~humble(X)<=>calm(X)))&
((?[X]:(patient(X)))=>(?[X]:(creative(X))))&
((?[X]:((generous(X)&~creative(X))))=>(~old(lucy)))&
(![X]:((~tall(X)|brave(X))=>(brave(X)<~>~humble(X))))&
(![X]:((~strong(X)|calm(X))=>(humble(X)|funny(X))))&
((?[X]:((~brave(X)|brave(X))))=>(?[X]:((quiet(X)|generous(X)))))&
(![X]:((~brave(X)&curious(X))=>(rich(X)|~funny(X))))&
((?[X]:((old(X)<~>wise(X))))=>((~curious(susan)|strong(susan))))&
(![X]:(kind(X)<=>(~happy(X)&~humble(X))))&
(![X]:(~tall(X)=>funny(X)))&
(![X]:((~calm(X)<~>~humble(X))<=>(~strong(X)|brave(X))))&
((?[X]:((wise(X)&~generous(X))))<=>((~happy(john)<~>creative(john))))&
(![X]:((generous(X)|creative(X))=>(~funny(X)|~creative(X))))&
(![X]:((~curious(X)&~quiet(X))<=>(~wise(X)|old(X))))&
((kind(fred)|~rich(fred)))&
(?[X]:(~patient(X)))&
(kind(paul))&
((rich(fred)|~strong(fred)))&
((rich(paul)<~>~happy(paul)))&
(?[X]:((strong(X)<~>patient(X))))&
(?[X]:((strong(X)&quiet(X)))) | ~tall(john) | [] | null | 0 |
Everyone who is either kind or not brave is both not kind and kind and vice versa.
If someone is either calm or tall then someone is funny and vice versa.
Everyone who is not calm or quiet is both not wise and not generous.
If susan is not calm then someone is both not humble and not rich.
Everyone who is both not patient and not humble is not old or curious.
Everyone who is either patient or not strong is both not calm and brave and vice versa.
Everyone who is not strong is kind or not calm and vice versa.
If susan is old or not tall then someone is quiet.
If someone is both quiet and happy then fred is happy or generous and vice versa.
Everyone who is not wise or not rich is both not happy and not brave.
Everyone who is either not curious or not brave is curious or funny and vice versa.
Everyone who is not curious or not calm is not calm and vice versa.
Everyone who is either rich or curious is brave or not quiet and vice versa.
If someone is both brave and curious then susan is not humble or curious and vice versa.
Everyone who is generous is generous or not kind and vice versa.
If someone is both kind and quiet then someone is strong or not old.
Someone is not rich or not funny.
Lucy is either rich or happy.
Mary is not quiet.
Fred is either rich or curious.
Mary is both tall and not humble.
Someone is either not quiet or not creative. | Mary is not calm. | neutral | (![X]:((kind(X)<~>~brave(X))<=>(~kind(X)&kind(X))))&
((?[X]:((calm(X)<~>tall(X))))<=>(?[X]:(funny(X))))&
(![X]:((~calm(X)|quiet(X))=>(~wise(X)&~generous(X))))&
((~calm(susan))=>(?[X]:((~humble(X)&~rich(X)))))&
(![X]:((~patient(X)&~humble(X))=>(~old(X)|curious(X))))&
(![X]:((patient(X)<~>~strong(X))<=>(~calm(X)&brave(X))))&
(![X]:(~strong(X)<=>(kind(X)|~calm(X))))&
(((old(susan)|~tall(susan)))=>(?[X]:(quiet(X))))&
((?[X]:((quiet(X)&happy(X))))<=>((happy(fred)|generous(fred))))&
(![X]:((~wise(X)|~rich(X))=>(~happy(X)&~brave(X))))&
(![X]:((~curious(X)<~>~brave(X))<=>(curious(X)|funny(X))))&
(![X]:((~curious(X)|~calm(X))<=>~calm(X)))&
(![X]:((rich(X)<~>curious(X))<=>(brave(X)|~quiet(X))))&
((?[X]:((brave(X)&curious(X))))<=>((~humble(susan)|curious(susan))))&
(![X]:(generous(X)<=>(generous(X)|~kind(X))))&
((?[X]:((kind(X)&quiet(X))))=>(?[X]:((strong(X)|~old(X)))))&
(?[X]:((~rich(X)|~funny(X))))&
((rich(lucy)<~>happy(lucy)))&
(~quiet(mary))&
((rich(fred)<~>curious(fred)))&
((tall(mary)&~humble(mary)))&
(?[X]:((~quiet(X)<~>~creative(X)))) | ~calm(mary) | [] | null | 0 |
Everyone who is either quiet or calm is both funny and old. Everyone who is either kind or not tall is both calm and not creative and vice versa. Everyone who is either not wise or curious is both quiet and humble and vice versa. If someone is both not brave and not wise then susan is both not happy and not patient and vice versa. Everyone who is not creative or creative is quiet or wise and vice versa. If paul is both funny and tall then someone is either not funny or old and vice versa. Everyone who is not generous or calm is both not quiet and not calm and vice versa. If someone is kind then someone is not curious. If lucy is both calm and kind then susan is not calm or not generous. Everyone who is either not tall or not happy is not humble or not old. Everyone who is not happy is humble and vice versa. Everyone who is either not old or not kind is both not happy and curious. Everyone who is brave or not quiet is not patient or curious and vice versa. Everyone who is both not funny and curious is not happy and vice versa. Everyone who is either not calm or creative is not creative. If someone is not strong then someone is not creative or not strong. Alice is not humble or old. Someone is humble or tall. Alice is either humble or not patient. Alice is both not brave and happy. Someone is patient or quiet. Alice is quiet or not kind. Mary is either calm or not rich. | Mary is happy. | entailment | (![X]:((quiet(X)<~>calm(X))=>(funny(X)&old(X))))&
(![X]:((kind(X)<~>~tall(X))<=>(calm(X)&~creative(X))))&
(![X]:((~wise(X)<~>curious(X))<=>(quiet(X)&humble(X))))&
((?[X]:((~brave(X)&~wise(X))))<=>((~happy(susan)&~patient(susan))))&
(![X]:((~creative(X)|creative(X))<=>(quiet(X)|wise(X))))&
(((funny(paul)&tall(paul)))<=>(?[X]:((~funny(X)<~>old(X)))))&
(![X]:((~generous(X)|calm(X))<=>(~quiet(X)&~calm(X))))&
((?[X]:(kind(X)))=>(?[X]:(~curious(X))))&
(((calm(lucy)&kind(lucy)))=>((~calm(susan)|~generous(susan))))&
(![X]:((~tall(X)<~>~happy(X))=>(~humble(X)|~old(X))))&
(![X]:(~happy(X)<=>humble(X)))&
(![X]:((~old(X)<~>~kind(X))=>(~happy(X)&curious(X))))&
(![X]:((brave(X)|~quiet(X))<=>(~patient(X)|curious(X))))&
(![X]:((~funny(X)&curious(X))<=>~happy(X)))&
(![X]:((~calm(X)<~>creative(X))=>~creative(X)))&
((?[X]:(~strong(X)))=>(?[X]:((~creative(X)|~strong(X)))))&
((~humble(alice)|old(alice)))&
(?[X]:((humble(X)|tall(X))))&
((humble(alice)<~>~patient(alice)))&
((~brave(alice)&happy(alice)))&
(?[X]:((patient(X)|quiet(X))))&
((quiet(alice)|~kind(alice)))&
((calm(mary)<~>~rich(mary))) | happy(mary) | [
"p0",
"p2",
"p4",
"p6",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 8428626595353098488303724
% SZS output start Proof for 8428626595353098488303724
1. ! [X0] : ((quiet(X0) <~> calm(X0)) => (old(X0) & funny(X0))) [input p0]
3. ! [X0] : ((~wise(X0) <~> curious(X0)) <=> (humble(X0) & quiet(X0))) [input p2]
5. ! [X0] : ((creative(X0) | ~creative(X0)) <=> (wise(X0) | quiet(X0))) [input p4]
7. ! [X0] : ((calm(X0) | ~generous(X0)) <=> (~calm(X0) & ~quiet(X0))) [input p6]
14. ! [X0] : ((curious(X0) & ~funny(X0)) <=> ~happy(X0)) [input p13]
24. ~happy(mary) [input hypothesis]
27. ! [X0] : ((old(X0) & funny(X0)) | (quiet(X0) <=> calm(X0))) [ennf transformation 1]
36. ! [X0] : ((old(X0) & funny(X0)) | ((quiet(X0) | ~calm(X0)) & (calm(X0) | ~quiet(X0)))) [nnf transformation 27]
39. ! [X0] : ((((~curious(X0) | wise(X0)) & (curious(X0) | ~wise(X0))) | (~humble(X0) | ~quiet(X0))) & ((humble(X0) & quiet(X0)) | ((~wise(X0) | ~curious(X0)) & (curious(X0) | wise(X0))))) [nnf transformation 3]
40. ! [X0] : ((((~curious(X0) | wise(X0)) & (curious(X0) | ~wise(X0))) | ~humble(X0) | ~quiet(X0)) & ((humble(X0) & quiet(X0)) | ((~wise(X0) | ~curious(X0)) & (curious(X0) | wise(X0))))) [flattening 39]
46. ! [X0] : (((creative(X0) | ~creative(X0)) | (~wise(X0) & ~quiet(X0))) & ((wise(X0) | quiet(X0)) | (~creative(X0) & creative(X0)))) [nnf transformation 5]
47. ! [X0] : ((creative(X0) | ~creative(X0) | (~wise(X0) & ~quiet(X0))) & (wise(X0) | quiet(X0) | (~creative(X0) & creative(X0)))) [flattening 46]
53. ! [X0] : (((calm(X0) | ~generous(X0)) | (calm(X0) | quiet(X0))) & ((~calm(X0) & ~quiet(X0)) | (~calm(X0) & generous(X0)))) [nnf transformation 7]
54. ! [X0] : ((calm(X0) | ~generous(X0) | calm(X0) | quiet(X0)) & ((~calm(X0) & ~quiet(X0)) | (~calm(X0) & generous(X0)))) [flattening 53]
63. ! [X0] : (((curious(X0) & ~funny(X0)) | happy(X0)) & (~happy(X0) | (~curious(X0) | funny(X0)))) [nnf transformation 14]
64. ! [X0] : (((curious(X0) & ~funny(X0)) | happy(X0)) & (~happy(X0) | ~curious(X0) | funny(X0))) [flattening 63]
75. ~quiet(X0) | calm(X0) | funny(X0) [cnf transformation 36]
86. ~curious(X0) | ~wise(X0) | quiet(X0) [cnf transformation 40]
95. wise(X0) | quiet(X0) | creative(X0) [cnf transformation 47]
96. ~creative(X0) | quiet(X0) | wise(X0) [cnf transformation 47]
108. ~calm(X0) | ~calm(X0) [cnf transformation 54]
125. ~funny(X0) | happy(X0) [cnf transformation 64]
126. happy(X0) | curious(X0) [cnf transformation 64]
140. ~happy(mary) [cnf transformation 24]
142. ~calm(X0) [duplicate literal removal 108]
167. wise(X0) | quiet(X0) [subsumption resolution 95,96]
263. curious(mary) [resolution 126,140]
288. ~wise(mary) | quiet(mary) [resolution 86,263]
292. quiet(mary) [subsumption resolution 288,167]
303. calm(mary) | funny(mary) [resolution 292,75]
306. funny(mary) [subsumption resolution 303,142]
507. happy(mary) [resolution 306,125]
508. $false [subsumption resolution 507,140]
% SZS output end Proof for 8428626595353098488303724
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old is not tall or calm and vice versa.
If fred is either not generous or tall then someone is not creative.
Everyone who is either not kind or funny is not funny.
Everyone who is not patient or old is not brave or quiet and vice versa.
If someone is creative or generous then someone is either not strong or not creative and vice versa.
Everyone who is not happy or not curious is either generous or not old and vice versa.
Everyone who is old is not tall or not generous.
Everyone who is creative or not strong is either not curious or brave and vice versa.
If paul is not curious then john is both old and creative.
Everyone who is not strong is both not wise and tall and vice versa.
Everyone who is not kind is both not tall and not wise and vice versa.
Everyone who is either not happy or patient is not creative and vice versa.
If alice is not brave then john is either quiet or calm.
Everyone who is both happy and generous is wise or happy and vice versa.
Everyone who is both wise and curious is not patient or humble and vice versa.
Alice is either not patient or not wise.
Someone is either not old or rich.
Someone is creative.
Paul is not tall or curious.
Someone is humble or creative.
Susan is either kind or happy. | Susan is not generous. | entailment | (![X]:(~old(X)<=>(~tall(X)|calm(X))))&
(((~generous(fred)<~>tall(fred)))=>(?[X]:(~creative(X))))&
(![X]:((~kind(X)<~>funny(X))=>~funny(X)))&
(![X]:((~patient(X)|old(X))<=>(~brave(X)|quiet(X))))&
((?[X]:((creative(X)|generous(X))))<=>(?[X]:((~strong(X)<~>~creative(X)))))&
(![X]:((~happy(X)|~curious(X))<=>(generous(X)<~>~old(X))))&
(![X]:(old(X)=>(~tall(X)|~generous(X))))&
(![X]:((creative(X)|~strong(X))<=>(~curious(X)<~>brave(X))))&
((~curious(paul))=>((old(john)&creative(john))))&
(![X]:(~strong(X)<=>(~wise(X)&tall(X))))&
(![X]:(~kind(X)<=>(~tall(X)&~wise(X))))&
(![X]:((~happy(X)<~>patient(X))<=>~creative(X)))&
((~brave(alice))=>((quiet(john)<~>calm(john))))&
(![X]:((happy(X)&generous(X))<=>(wise(X)|happy(X))))&
(![X]:((wise(X)&curious(X))<=>(~patient(X)|humble(X))))&
((~patient(alice)<~>~wise(alice)))&
(?[X]:((~old(X)<~>rich(X))))&
(?[X]:(creative(X)))&
((~tall(paul)|curious(paul)))&
(?[X]:((humble(X)|creative(X))))&
((kind(susan)<~>happy(susan))) | ~generous(susan) | [
"p0",
"p3",
"p5",
"p6",
"p7",
"p9",
"p10",
"p11",
"p14",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 1669062834133796741305542
% SZS output start Proof for 1669062834133796741305542
1. ! [X0] : (~old(X0) <=> (calm(X0) | ~tall(X0))) [input p0]
4. ! [X0] : ((old(X0) | ~patient(X0)) <=> (quiet(X0) | ~brave(X0))) [input p3]
6. ! [X0] : ((~curious(X0) | ~happy(X0)) <=> (generous(X0) <~> ~old(X0))) [input p5]
7. ! [X0] : (old(X0) => (~generous(X0) | ~tall(X0))) [input p6]
8. ! [X0] : ((~strong(X0) | creative(X0)) <=> (~curious(X0) <~> brave(X0))) [input p7]
10. ! [X0] : (~strong(X0) <=> (tall(X0) & ~wise(X0))) [input p9]
11. ! [X0] : (~kind(X0) <=> (~wise(X0) & ~tall(X0))) [input p10]
12. ! [X0] : ((~happy(X0) <~> patient(X0)) <=> ~creative(X0)) [input p11]
15. ! [X0] : ((curious(X0) & wise(X0)) <=> (humble(X0) | ~patient(X0))) [input p14]
21. kind(susan) <~> happy(susan) [input p20]
22. generous(susan) [input hypothesis]
26. ! [X0] : ((~generous(X0) | ~tall(X0)) | ~old(X0)) [ennf transformation 7]
27. ! [X0] : (~generous(X0) | ~tall(X0) | ~old(X0)) [flattening 26]
30. ! [X0] : ((~old(X0) | (~calm(X0) & tall(X0))) & ((calm(X0) | ~tall(X0)) | old(X0))) [nnf transformation 1]
31. ! [X0] : ((~old(X0) | (~calm(X0) & tall(X0))) & (calm(X0) | ~tall(X0) | old(X0))) [flattening 30]
36. ! [X0] : (((old(X0) | ~patient(X0)) | (~quiet(X0) & brave(X0))) & ((quiet(X0) | ~brave(X0)) | (~old(X0) & patient(X0)))) [nnf transformation 4]
37. ! [X0] : ((old(X0) | ~patient(X0) | (~quiet(X0) & brave(X0))) & (quiet(X0) | ~brave(X0) | (~old(X0) & patient(X0)))) [flattening 36]
43. ! [X0] : (((~curious(X0) | ~happy(X0)) | ((generous(X0) | old(X0)) & (~old(X0) | ~generous(X0)))) & (((old(X0) | ~generous(X0)) & (~old(X0) | generous(X0))) | (curious(X0) & happy(X0)))) [nnf transformation 6]
44. ! [X0] : ((~curious(X0) | ~happy(X0) | ((generous(X0) | old(X0)) & (~old(X0) | ~generous(X0)))) & (((old(X0) | ~generous(X0)) & (~old(X0) | generous(X0))) | (curious(X0) & happy(X0)))) [flattening 43]
45. ! [X0] : (((~strong(X0) | creative(X0)) | ((~curious(X0) | ~brave(X0)) & (brave(X0) | curious(X0)))) & (((~brave(X0) | curious(X0)) & (brave(X0) | ~curious(X0))) | (strong(X0) & ~creative(X0)))) [nnf transformation 8]
46. ! [X0] : ((~strong(X0) | creative(X0) | ((~curious(X0) | ~brave(X0)) & (brave(X0) | curious(X0)))) & (((~brave(X0) | curious(X0)) & (brave(X0) | ~curious(X0))) | (strong(X0) & ~creative(X0)))) [flattening 45]
47. ! [X0] : ((~strong(X0) | (~tall(X0) | wise(X0))) & ((tall(X0) & ~wise(X0)) | strong(X0))) [nnf transformation 10]
48. ! [X0] : ((~strong(X0) | ~tall(X0) | wise(X0)) & ((tall(X0) & ~wise(X0)) | strong(X0))) [flattening 47]
49. ! [X0] : ((~kind(X0) | (wise(X0) | tall(X0))) & ((~wise(X0) & ~tall(X0)) | kind(X0))) [nnf transformation 11]
50. ! [X0] : ((~kind(X0) | wise(X0) | tall(X0)) & ((~wise(X0) & ~tall(X0)) | kind(X0))) [flattening 49]
51. ! [X0] : ((((~patient(X0) | happy(X0)) & (patient(X0) | ~happy(X0))) | creative(X0)) & (~creative(X0) | ((~happy(X0) | ~patient(X0)) & (patient(X0) | happy(X0))))) [nnf transformation 12]
55. ! [X0] : (((curious(X0) & wise(X0)) | (~humble(X0) & patient(X0))) & ((humble(X0) | ~patient(X0)) | (~curious(X0) | ~wise(X0)))) [nnf transformation 15]
56. ! [X0] : (((curious(X0) & wise(X0)) | (~humble(X0) & patient(X0))) & (humble(X0) | ~patient(X0) | ~curious(X0) | ~wise(X0))) [flattening 55]
65. (~happy(susan) | ~kind(susan)) & (happy(susan) | kind(susan)) [nnf transformation 21]
67. ~old(X0) | tall(X0) [cnf transformation 31]
75. ~patient(X0) | old(X0) | brave(X0) [cnf transformation 37]
85. ~generous(X0) | old(X0) | happy(X0) [cnf transformation 44]
86. ~generous(X0) | old(X0) | curious(X0) [cnf transformation 44]
89. ~generous(X0) | ~tall(X0) | ~old(X0) [cnf transformation 27]
95. ~curious(X0) | creative(X0) | ~strong(X0) | ~brave(X0) [cnf transformation 46]
99. strong(X0) | tall(X0) [cnf transformation 48]
101. ~tall(X0) | kind(X0) [cnf transformation 50]
102. ~wise(X0) | kind(X0) [cnf transformation 50]
105. ~happy(X0) | ~creative(X0) | ~patient(X0) [cnf transformation 51]
116. wise(X0) | patient(X0) [cnf transformation 56]
128. ~happy(susan) | ~kind(susan) [cnf transformation 65]
129. generous(susan) [cnf transformation 22]
179. ~generous(X0) | ~old(X0) [subsumption resolution 89,67]
242. 25 <=> kind(susan) [avatar definition]
244. ~kind(susan) <- (~25) [avatar component clause 242]
246. 26 <=> happy(susan) [avatar definition]
247. happy(susan) <- (26) [avatar component clause 246]
249. ~25 | ~26 [avatar split clause 128,246,242]
253. patient(X2) | kind(X2) [resolution 116,102]
261. ~old(susan) [resolution 179,129]
271. old(susan) | happy(susan) [resolution 85,129]
274. happy(susan) [subsumption resolution 271,261]
278. 26 [avatar split clause 274,246]
280. old(susan) | curious(susan) [resolution 86,129]
283. curious(susan) [subsumption resolution 280,261]
299. 29 <=> creative(susan) [avatar definition]
301. ~creative(susan) <- (~29) [avatar component clause 299]
303. 30 <=> brave(susan) [avatar definition]
322. 33 <=> strong(susan) [avatar definition]
323. ~strong(susan) <- (~33) [avatar component clause 322]
381. ~creative(susan) | ~patient(susan) <- (26) [resolution 105,247]
387. 41 <=> patient(susan) [avatar definition]
388. ~patient(susan) <- (~41) [avatar component clause 387]
389. patient(susan) <- (41) [avatar component clause 387]
401. ~41 | ~29 | ~26 [avatar split clause 381,246,299,387]
419. 44 <=> tall(susan) [avatar definition]
420. tall(susan) <- (44) [avatar component clause 419]
452. creative(susan) | ~strong(susan) | ~brave(susan) [resolution 95,283]
484. kind(susan) <- (~41) [resolution 388,253]
486. $false <- (~25, ~41) [subsumption resolution 484,244]
487. 25 | 41 [avatar contradiction clause 486]
491. ~strong(susan) | ~brave(susan) <- (~29) [subsumption resolution 452,301]
664. tall(susan) <- (~33) [resolution 323,99]
804. old(susan) | brave(susan) <- (41) [resolution 389,75]
827. kind(susan) <- (44) [resolution 420,101]
829. $false <- (~25, 44) [subsumption resolution 827,244]
830. 25 | ~44 [avatar contradiction clause 829]
831. 44 | 33 [avatar split clause 664,322,419]
832. brave(susan) <- (41) [subsumption resolution 804,261]
833. 30 | ~41 [avatar split clause 832,387,303]
834. ~30 | ~33 | 29 [avatar split clause 491,299,322,303]
835. $false [avatar sat refutation 249,278,401,487,830,831,833,834]
% SZS output end Proof for 1669062834133796741305542
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
If john is strong or not wise then john is either funny or not humble and vice versa.
Everyone who is not strong is both not kind and not brave and vice versa.
If fred is either old or not brave then someone is quiet and vice versa.
Everyone who is kind or calm is both patient and happy and vice versa.
If alice is happy or brave then someone is not kind and vice versa.
Everyone who is both not humble and not tall is not wise or funny and vice versa.
If someone is both creative and not creative then someone is either creative or not wise.
If someone is curious then someone is old.
Everyone who is not calm is strong or not wise and vice versa.
Everyone who is not happy is either patient or not creative.
Everyone who is not generous or not brave is both not happy and not quiet.
Everyone who is not brave or quiet is either not old or not tall and vice versa.
Everyone who is not kind or not generous is either wise or humble.
If someone is both curious and patient then someone is strong and vice versa.
If someone is not generous or not funny then lucy is not happy or not quiet.
Everyone who is both strong and not quiet is either tall or brave.
John is either not brave or patient.
Someone is not generous or not kind.
Susan is not generous or humble.
Someone is both funny and not humble.
Someone is not old.
Someone is not humble.
Someone is humble or calm. | Alice is brave. | entailment | (((strong(john)|~wise(john)))<=>((funny(john)<~>~humble(john))))&
(![X]:(~strong(X)<=>(~kind(X)&~brave(X))))&
(((old(fred)<~>~brave(fred)))<=>(?[X]:(quiet(X))))&
(![X]:((kind(X)|calm(X))<=>(patient(X)&happy(X))))&
(((happy(alice)|brave(alice)))<=>(?[X]:(~kind(X))))&
(![X]:((~humble(X)&~tall(X))<=>(~wise(X)|funny(X))))&
((?[X]:((creative(X)&~creative(X))))=>(?[X]:((creative(X)<~>~wise(X)))))&
((?[X]:(curious(X)))=>(?[X]:(old(X))))&
(![X]:(~calm(X)<=>(strong(X)|~wise(X))))&
(![X]:(~happy(X)=>(patient(X)<~>~creative(X))))&
(![X]:((~generous(X)|~brave(X))=>(~happy(X)&~quiet(X))))&
(![X]:((~brave(X)|quiet(X))<=>(~old(X)<~>~tall(X))))&
(![X]:((~kind(X)|~generous(X))=>(wise(X)<~>humble(X))))&
((?[X]:((curious(X)&patient(X))))<=>(?[X]:(strong(X))))&
((?[X]:((~generous(X)|~funny(X))))=>((~happy(lucy)|~quiet(lucy))))&
(![X]:((strong(X)&~quiet(X))=>(tall(X)<~>brave(X))))&
((~brave(john)<~>patient(john)))&
(?[X]:((~generous(X)|~kind(X))))&
((~generous(susan)|humble(susan)))&
(?[X]:((funny(X)&~humble(X))))&
(?[X]:(~old(X)))&
(?[X]:(~humble(X)))&
(?[X]:((humble(X)|calm(X)))) | brave(alice) | [
"p3",
"p4",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 7567619497309015350905570
% SZS output start Proof for 7567619497309015350905570
4. ! [X0] : ((calm(X0) | kind(X0)) <=> (happy(X0) & patient(X0))) [input p3]
5. (brave(alice) | happy(alice)) <=> ? [X0] : ~kind(X0) [input p4]
11. ! [X0] : ((~brave(X0) | ~generous(X0)) => (~quiet(X0) & ~happy(X0))) [input p10]
24. ~brave(alice) [input hypothesis]
31. ! [X0] : ((~quiet(X0) & ~happy(X0)) | (brave(X0) & generous(X0))) [ennf transformation 11]
45. ! [X0] : (((calm(X0) | kind(X0)) | (~happy(X0) | ~patient(X0))) & ((happy(X0) & patient(X0)) | (~calm(X0) & ~kind(X0)))) [nnf transformation 4]
46. ! [X0] : ((calm(X0) | kind(X0) | ~happy(X0) | ~patient(X0)) & ((happy(X0) & patient(X0)) | (~calm(X0) & ~kind(X0)))) [flattening 45]
47. ((brave(alice) | happy(alice)) | ! [X0] : kind(X0)) & (? [X0] : ~kind(X0) | (~brave(alice) & ~happy(alice))) [nnf transformation 5]
48. (brave(alice) | happy(alice) | ! [X0] : kind(X0)) & (? [X0] : ~kind(X0) | (~brave(alice) & ~happy(alice))) [flattening 47]
49. (brave(alice) | happy(alice) | ! [X0] : kind(X0)) & (? [X1] : ~kind(X1) | (~brave(alice) & ~happy(alice))) [rectify 48]
50. ? [X1] : ~kind(X1) => ~kind(sK1) [choice axiom]
51. (brave(alice) | happy(alice) | ! [X0] : kind(X0)) & (~kind(sK1) | (~brave(alice) & ~happy(alice))) [skolemisation 49,50]
99. ~kind(X0) | happy(X0) [cnf transformation 46]
104. brave(alice) | happy(alice) | kind(X0) [cnf transformation 51]
119. ~happy(X0) | brave(X0) [cnf transformation 31]
148. ~brave(alice) [cnf transformation 24]
191. 9 <=> ! [X0] : kind(X0) [avatar definition]
192. kind(X0) <- (9) [avatar component clause 191]
194. 10 <=> happy(alice) [avatar definition]
195. ~happy(alice) <- (~10) [avatar component clause 194]
196. happy(alice) <- (10) [avatar component clause 194]
198. 11 <=> brave(alice) [avatar definition]
199. ~brave(alice) <- (~11) [avatar component clause 198]
201. 9 | 10 | 11 [avatar split clause 104,198,194,191]
296. ~11 [avatar split clause 148,198]
302. brave(alice) <- (10) [resolution 119,196]
303. $false <- (10, ~11) [subsumption resolution 302,199]
304. ~10 | 11 [avatar contradiction clause 303]
305. happy(X0) <- (9) [resolution 192,99]
318. $false <- (9, ~10) [resolution 305,195]
319. ~9 | 10 [avatar contradiction clause 318]
322. $false [avatar sat refutation 201,296,304,319]
% SZS output end Proof for 7567619497309015350905570
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient or brave then someone is not generous or tall.
If someone is not tall then someone is either generous or curious and vice versa.
Everyone who is quiet or not wise is not calm and vice versa.
Everyone who is humble or wise is both not kind and patient.
Everyone who is either old or not curious is quiet or not quiet and vice versa.
Everyone who is not patient is both brave and not patient.
If someone is either quiet or not funny then someone is curious and vice versa.
Everyone who is old is both generous and not kind.
If someone is both not funny and funny then lucy is either tall or not quiet and vice versa.
Everyone who is either not old or curious is not humble.
If someone is not patient or strong then mary is not brave.
Everyone who is old or calm is either generous or not calm and vice versa.
Everyone who is both not rich and not happy is strong.
Everyone who is either not funny or strong is both funny and not kind and vice versa.
If paul is either strong or not old then someone is both humble and calm.
Everyone who is both humble and strong is both tall and not rich and vice versa.
Someone is curious.
Alice is either not calm or not wise.
Someone is either not quiet or patient.
Someone is wise or not rich.
Mary is generous.
Someone is not curious. | Alice is old. | contradiction | ((?[X]:((~patient(X)|brave(X))))=>(?[X]:((~generous(X)|tall(X)))))&
((?[X]:(~tall(X)))<=>(?[X]:((generous(X)<~>curious(X)))))&
(![X]:((quiet(X)|~wise(X))<=>~calm(X)))&
(![X]:((humble(X)|wise(X))=>(~kind(X)&patient(X))))&
(![X]:((old(X)<~>~curious(X))<=>(quiet(X)|~quiet(X))))&
(![X]:(~patient(X)=>(brave(X)&~patient(X))))&
((?[X]:((quiet(X)<~>~funny(X))))<=>(?[X]:(curious(X))))&
(![X]:(old(X)=>(generous(X)&~kind(X))))&
((?[X]:((~funny(X)&funny(X))))<=>((tall(lucy)<~>~quiet(lucy))))&
(![X]:((~old(X)<~>curious(X))=>~humble(X)))&
((?[X]:((~patient(X)|strong(X))))=>(~brave(mary)))&
(![X]:((old(X)|calm(X))<=>(generous(X)<~>~calm(X))))&
(![X]:((~rich(X)&~happy(X))=>strong(X)))&
(![X]:((~funny(X)<~>strong(X))<=>(funny(X)&~kind(X))))&
(((strong(paul)<~>~old(paul)))=>(?[X]:((humble(X)&calm(X)))))&
(![X]:((humble(X)&strong(X))<=>(tall(X)&~rich(X))))&
(?[X]:(curious(X)))&
((~calm(alice)<~>~wise(alice)))&
(?[X]:((~quiet(X)<~>patient(X))))&
(?[X]:((wise(X)|~rich(X))))&
(generous(mary))&
(?[X]:(~curious(X))) | old(alice) | [
"p2",
"p7",
"p11",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 6804441980947994542668404
% SZS output start Proof for 6804441980947994542668404
3. ! [X0] : ((~wise(X0) | quiet(X0)) <=> ~calm(X0)) [input p2]
8. ! [X0] : (old(X0) => (~kind(X0) & generous(X0))) [input p7]
12. ! [X0] : ((calm(X0) | old(X0)) <=> (generous(X0) <~> ~calm(X0))) [input p11]
18. ~calm(alice) <~> ~wise(alice) [input p17]
23. old(alice) [input hypothesis]
31. ! [X0] : ((~kind(X0) & generous(X0)) | ~old(X0)) [ennf transformation 8]
43. ! [X0] : (((~wise(X0) | quiet(X0)) | calm(X0)) & (~calm(X0) | (wise(X0) & ~quiet(X0)))) [nnf transformation 3]
44. ! [X0] : ((~wise(X0) | quiet(X0) | calm(X0)) & (~calm(X0) | (wise(X0) & ~quiet(X0)))) [flattening 43]
57. ! [X0] : (((calm(X0) | old(X0)) | ((generous(X0) | calm(X0)) & (~calm(X0) | ~generous(X0)))) & (((calm(X0) | ~generous(X0)) & (~calm(X0) | generous(X0))) | (~calm(X0) & ~old(X0)))) [nnf transformation 12]
58. ! [X0] : ((calm(X0) | old(X0) | ((generous(X0) | calm(X0)) & (~calm(X0) | ~generous(X0)))) & (((calm(X0) | ~generous(X0)) & (~calm(X0) | generous(X0))) | (~calm(X0) & ~old(X0)))) [flattening 57]
68. (wise(alice) | calm(alice)) & (~wise(alice) | ~calm(alice)) [nnf transformation 18]
83. ~calm(X0) | wise(X0) [cnf transformation 44]
101. ~old(X0) | generous(X0) [cnf transformation 31]
115. calm(X0) | ~generous(X0) | ~old(X0) [cnf transformation 58]
134. ~wise(alice) | ~calm(alice) [cnf transformation 68]
135. wise(alice) | calm(alice) [cnf transformation 68]
141. old(alice) [cnf transformation 23]
242. ~old(X0) | calm(X0) [subsumption resolution 115,101]
264. wise(alice) [subsumption resolution 135,83]
265. ~calm(alice) [subsumption resolution 134,264]
317. calm(alice) [resolution 242,141]
320. $false [subsumption resolution 317,265]
% SZS output end Proof for 6804441980947994542668404
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not tall then fred is both not quiet and not creative and vice versa.
Everyone who is either not wise or not brave is both not creative and quiet.
Everyone who is calm is humble or not creative and vice versa.
Everyone who is not generous is either not calm or wise and vice versa.
Everyone who is both patient and curious is either not humble or old.
If john is either not creative or brave then john is both happy and strong.
Everyone who is either humble or brave is patient or not strong and vice versa.
If lucy is either not old or happy then mary is either not quiet or not calm.
If mary is not strong or not humble then someone is not rich.
If someone is brave or not generous then susan is not generous or not calm and vice versa.
Everyone who is either patient or old is not quiet or brave and vice versa.
If susan is either not old or kind then someone is not curious.
Everyone who is not wise or not creative is rich or not rich.
Everyone who is both calm and humble is both brave and not creative and vice versa.
Everyone who is not curious or old is either strong or kind and vice versa.
Everyone who is both brave and not old is either curious or not generous.
Someone is either tall or old.
Someone is either generous or not rich.
Someone is rich.
Someone is not brave or not quiet.
Someone is both brave and happy.
Lucy is curious or brave.
Someone is either not tall or not quiet.
Paul is both not tall and wise. | Paul is wise. | entailment | ((?[X]:(~tall(X)))<=>((~quiet(fred)&~creative(fred))))&
(![X]:((~wise(X)<~>~brave(X))=>(~creative(X)&quiet(X))))&
(![X]:(calm(X)<=>(humble(X)|~creative(X))))&
(![X]:(~generous(X)<=>(~calm(X)<~>wise(X))))&
(![X]:((patient(X)&curious(X))=>(~humble(X)<~>old(X))))&
(((~creative(john)<~>brave(john)))=>((happy(john)&strong(john))))&
(![X]:((humble(X)<~>brave(X))<=>(patient(X)|~strong(X))))&
(((~old(lucy)<~>happy(lucy)))=>((~quiet(mary)<~>~calm(mary))))&
(((~strong(mary)|~humble(mary)))=>(?[X]:(~rich(X))))&
((?[X]:((brave(X)|~generous(X))))<=>((~generous(susan)|~calm(susan))))&
(![X]:((patient(X)<~>old(X))<=>(~quiet(X)|brave(X))))&
(((~old(susan)<~>kind(susan)))=>(?[X]:(~curious(X))))&
(![X]:((~wise(X)|~creative(X))=>(rich(X)|~rich(X))))&
(![X]:((calm(X)&humble(X))<=>(brave(X)&~creative(X))))&
(![X]:((~curious(X)|old(X))<=>(strong(X)<~>kind(X))))&
(![X]:((brave(X)&~old(X))=>(curious(X)<~>~generous(X))))&
(?[X]:((tall(X)<~>old(X))))&
(?[X]:((generous(X)<~>~rich(X))))&
(?[X]:(rich(X)))&
(?[X]:((~brave(X)|~quiet(X))))&
(?[X]:((brave(X)&happy(X))))&
((curious(lucy)|brave(lucy)))&
(?[X]:((~tall(X)<~>~quiet(X))))&
((~tall(paul)&wise(paul))) | wise(paul) | [
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 29504281467615340993268
% SZS output start Proof for 29504281467615340993268
24. wise(paul) & ~tall(paul) [input p23]
25. ~wise(paul) [input hypothesis]
153. wise(paul) [cnf transformation 24]
154. ~wise(paul) [cnf transformation 25]
317. $false [subsumption resolution 154,153]
% SZS output end Proof for 29504281467615340993268
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious and funny is not creative or not strong and vice versa.
Everyone who is not rich or not wise is humble or rich.
If someone is either not kind or not creative then someone is not patient or old and vice versa.
If mary is both creative and not funny then susan is not tall and vice versa.
Everyone who is either not happy or not kind is curious or funny.
Everyone who is both not old and calm is not creative or curious and vice versa.
Everyone who is either not brave or creative is both humble and brave.
Everyone who is not quiet is either not calm or old and vice versa.
If lucy is not creative then lucy is both not happy and old.
Everyone who is either not generous or not happy is not curious.
Everyone who is either not brave or wise is either quiet or happy and vice versa.
Everyone who is both not funny and not quiet is both curious and not generous and vice versa.
Everyone who is not strong is not rich or not strong and vice versa.
If someone is not happy or brave then someone is not curious.
Everyone who is both strong and not brave is both not strong and not tall.
If someone is not wise then someone is either not calm or not patient and vice versa.
Someone is not calm.
Lucy is both old and quiet.
John is both not quiet and patient.
Someone is generous.
Fred is both brave and not creative.
Someone is either happy or not brave.
Susan is either funny or not funny.
Fred is happy. | John is not funny. | contradiction | (![X]:((curious(X)&funny(X))<=>(~creative(X)|~strong(X))))&
(![X]:((~rich(X)|~wise(X))=>(humble(X)|rich(X))))&
((?[X]:((~kind(X)<~>~creative(X))))<=>(?[X]:((~patient(X)|old(X)))))&
(((creative(mary)&~funny(mary)))<=>(~tall(susan)))&
(![X]:((~happy(X)<~>~kind(X))=>(curious(X)|funny(X))))&
(![X]:((~old(X)&calm(X))<=>(~creative(X)|curious(X))))&
(![X]:((~brave(X)<~>creative(X))=>(humble(X)&brave(X))))&
(![X]:(~quiet(X)<=>(~calm(X)<~>old(X))))&
((~creative(lucy))=>((~happy(lucy)&old(lucy))))&
(![X]:((~generous(X)<~>~happy(X))=>~curious(X)))&
(![X]:((~brave(X)<~>wise(X))<=>(quiet(X)<~>happy(X))))&
(![X]:((~funny(X)&~quiet(X))<=>(curious(X)&~generous(X))))&
(![X]:(~strong(X)<=>(~rich(X)|~strong(X))))&
((?[X]:((~happy(X)|brave(X))))=>(?[X]:(~curious(X))))&
(![X]:((strong(X)&~brave(X))=>(~strong(X)&~tall(X))))&
((?[X]:(~wise(X)))<=>(?[X]:((~calm(X)<~>~patient(X)))))&
(?[X]:(~calm(X)))&
((old(lucy)&quiet(lucy)))&
((~quiet(john)&patient(john)))&
(?[X]:(generous(X)))&
((brave(fred)&~creative(fred)))&
(?[X]:((happy(X)<~>~brave(X))))&
((funny(susan)<~>~funny(susan)))&
(happy(fred)) | ~funny(john) | [
"p5",
"p7",
"p11",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 5407119669383994455232415
% SZS output start Proof for 5407119669383994455232415
6. ! [X0] : ((calm(X0) & ~old(X0)) <=> (curious(X0) | ~creative(X0))) [input p5]
8. ! [X0] : (~quiet(X0) <=> (~calm(X0) <~> old(X0))) [input p7]
12. ! [X0] : ((~quiet(X0) & ~funny(X0)) <=> (~generous(X0) & curious(X0))) [input p11]
19. patient(john) & ~quiet(john) [input p18]
25. ~funny(john) [input hypothesis]
49. ! [X0] : (((calm(X0) & ~old(X0)) | (~curious(X0) & creative(X0))) & ((curious(X0) | ~creative(X0)) | (~calm(X0) | old(X0)))) [nnf transformation 6]
50. ! [X0] : (((calm(X0) & ~old(X0)) | (~curious(X0) & creative(X0))) & (curious(X0) | ~creative(X0) | ~calm(X0) | old(X0))) [flattening 49]
52. ! [X0] : ((~quiet(X0) | ((~calm(X0) | ~old(X0)) & (old(X0) | calm(X0)))) & (((~old(X0) | calm(X0)) & (old(X0) | ~calm(X0))) | quiet(X0))) [nnf transformation 8]
55. ! [X0] : (((~quiet(X0) & ~funny(X0)) | (generous(X0) | ~curious(X0))) & ((~generous(X0) & curious(X0)) | (quiet(X0) | funny(X0)))) [nnf transformation 12]
56. ! [X0] : (((~quiet(X0) & ~funny(X0)) | generous(X0) | ~curious(X0)) & ((~generous(X0) & curious(X0)) | quiet(X0) | funny(X0))) [flattening 55]
93. ~old(X0) | ~curious(X0) [cnf transformation 50]
95. ~curious(X0) | calm(X0) [cnf transformation 50]
98. ~calm(X0) | old(X0) | quiet(X0) [cnf transformation 52]
114. quiet(X0) | curious(X0) | funny(X0) [cnf transformation 56]
132. ~quiet(john) [cnf transformation 19]
142. ~funny(john) [cnf transformation 25]
315. curious(john) | funny(john) [resolution 114,132]
323. curious(john) [subsumption resolution 315,142]
338. calm(john) [resolution 323,95]
366. old(john) | quiet(john) [resolution 338,98]
368. old(john) [subsumption resolution 366,132]
375. ~curious(john) [resolution 368,93]
377. $false [subsumption resolution 375,323]
% SZS output end Proof for 5407119669383994455232415
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.047 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not brave and not creative is not calm or not curious and vice versa.
If someone is either not creative or calm then lucy is either not kind or generous.
Everyone who is either humble or not generous is either not patient or generous.
Everyone who is wise or not wise is funny.
If someone is either not strong or not rich then someone is either not rich or quiet.
Everyone who is both not strong and not funny is humble or not creative and vice versa.
Everyone who is quiet is both funny and rich.
Everyone who is not creative or quiet is not rich.
Everyone who is either patient or not calm is either not wise or not quiet and vice versa.
If someone is both not calm and not strong then susan is strong.
Everyone who is either not creative or not humble is either calm or not tall and vice versa.
If someone is both not patient and not calm then lucy is either wise or strong and vice versa.
Everyone who is not old or not tall is rich and vice versa.
Everyone who is patient is either not happy or rich.
Everyone who is both humble and calm is both not kind and not rich and vice versa.
Everyone who is either not quiet or not generous is either creative or not kind.
Someone is not generous.
Someone is creative.
Someone is both not generous and not happy.
Someone is either not wise or quiet.
Someone is both not generous and old.
John is either funny or not funny.
John is strong. | Susan is humble. | contradiction | (![X]:((~brave(X)&~creative(X))<=>(~calm(X)|~curious(X))))&
((?[X]:((~creative(X)<~>calm(X))))=>((~kind(lucy)<~>generous(lucy))))&
(![X]:((humble(X)<~>~generous(X))=>(~patient(X)<~>generous(X))))&
(![X]:((wise(X)|~wise(X))=>funny(X)))&
((?[X]:((~strong(X)<~>~rich(X))))=>(?[X]:((~rich(X)<~>quiet(X)))))&
(![X]:((~strong(X)&~funny(X))<=>(humble(X)|~creative(X))))&
(![X]:(quiet(X)=>(funny(X)&rich(X))))&
(![X]:((~creative(X)|quiet(X))=>~rich(X)))&
(![X]:((patient(X)<~>~calm(X))<=>(~wise(X)<~>~quiet(X))))&
((?[X]:((~calm(X)&~strong(X))))=>(strong(susan)))&
(![X]:((~creative(X)<~>~humble(X))<=>(calm(X)<~>~tall(X))))&
((?[X]:((~patient(X)&~calm(X))))<=>((wise(lucy)<~>strong(lucy))))&
(![X]:((~old(X)|~tall(X))<=>rich(X)))&
(![X]:(patient(X)=>(~happy(X)<~>rich(X))))&
(![X]:((humble(X)&calm(X))<=>(~kind(X)&~rich(X))))&
(![X]:((~quiet(X)<~>~generous(X))=>(creative(X)<~>~kind(X))))&
(?[X]:(~generous(X)))&
(?[X]:(creative(X)))&
(?[X]:((~generous(X)&~happy(X))))&
(?[X]:((~wise(X)<~>quiet(X))))&
(?[X]:((~generous(X)&old(X))))&
((funny(john)<~>~funny(john)))&
(strong(john)) | humble(susan) | [
"p3",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 7742415748644632501271054
% SZS output start Proof for 7742415748644632501271054
4. ! [X0] : ((~wise(X0) | wise(X0)) => funny(X0)) [input p3]
6. ! [X0] : ((~funny(X0) & ~strong(X0)) <=> (~creative(X0) | humble(X0))) [input p5]
24. humble(susan) [input hypothesis]
28. ! [X0] : (funny(X0) | (wise(X0) & ~wise(X0))) [ennf transformation 4]
43. ! [X0] : (((~funny(X0) & ~strong(X0)) | (creative(X0) & ~humble(X0))) & ((~creative(X0) | humble(X0)) | (funny(X0) | strong(X0)))) [nnf transformation 6]
44. ! [X0] : (((~funny(X0) & ~strong(X0)) | (creative(X0) & ~humble(X0))) & (~creative(X0) | humble(X0) | funny(X0) | strong(X0))) [flattening 43]
82. funny(X0) | ~wise(X0) [cnf transformation 28]
83. funny(X0) | wise(X0) [cnf transformation 28]
91. ~funny(X0) | ~humble(X0) [cnf transformation 44]
144. humble(susan) [cnf transformation 24]
169. funny(X0) [subsumption resolution 82,83]
189. ~humble(X0) [subsumption resolution 91,169]
234. $false [subsumption resolution 144,189]
% SZS output end Proof for 7742415748644632501271054
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or brave is both not curious and not rich and vice versa.
Everyone who is either not old or funny is not brave and vice versa.
Everyone who is not funny or old is both generous and creative.
If john is either calm or not strong then alice is funny.
Everyone who is not old is both not quiet and not generous and vice versa.
Everyone who is either wise or curious is not brave or not strong and vice versa.
Everyone who is generous is either kind or patient.
Everyone who is both not generous and not tall is wise or not old and vice versa.
Everyone who is curious is both humble and not rich.
If mary is old or not funny then susan is either not wise or happy and vice versa.
Everyone who is not kind or not strong is rich and vice versa.
If alice is not wise or calm then mary is both not calm and not funny and vice versa.
Everyone who is either not generous or wise is kind and vice versa.
If susan is both not humble and creative then fred is not humble or generous.
If paul is both quiet and rich then lucy is generous or rich.
Someone is quiet or funny.
Someone is strong or wise.
Lucy is both not strong and not humble.
Someone is humble. | Mary is kind. | neutral | (![X]:((~creative(X)<~>brave(X))<=>(~curious(X)&~rich(X))))&
(![X]:((~old(X)<~>funny(X))<=>~brave(X)))&
(![X]:((~funny(X)|old(X))=>(generous(X)&creative(X))))&
(((calm(john)<~>~strong(john)))=>(funny(alice)))&
(![X]:(~old(X)<=>(~quiet(X)&~generous(X))))&
(![X]:((wise(X)<~>curious(X))<=>(~brave(X)|~strong(X))))&
(![X]:(generous(X)=>(kind(X)<~>patient(X))))&
(![X]:((~generous(X)&~tall(X))<=>(wise(X)|~old(X))))&
(![X]:(curious(X)=>(humble(X)&~rich(X))))&
(((old(mary)|~funny(mary)))<=>((~wise(susan)<~>happy(susan))))&
(![X]:((~kind(X)|~strong(X))<=>rich(X)))&
(((~wise(alice)|calm(alice)))<=>((~calm(mary)&~funny(mary))))&
(![X]:((~generous(X)<~>wise(X))<=>kind(X)))&
(((~humble(susan)&creative(susan)))=>((~humble(fred)|generous(fred))))&
(((quiet(paul)&rich(paul)))=>((generous(lucy)|rich(lucy))))&
(?[X]:((quiet(X)|funny(X))))&
(?[X]:((strong(X)|wise(X))))&
((~strong(lucy)&~humble(lucy)))&
(?[X]:(humble(X))) | kind(mary) | [] | null | 0 |
If mary is either curious or not creative then someone is either wise or not funny and vice versa.
If someone is not rich then mary is both not rich and not strong and vice versa.
If mary is both not brave and not creative then someone is not rich.
If alice is either not old or not funny then fred is both generous and wise and vice versa.
If paul is either not patient or not generous then mary is both not humble and not rich and vice versa.
Everyone who is both rich and quiet is humble.
If someone is either brave or not funny then someone is both not rich and curious and vice versa.
Everyone who is either happy or curious is not kind or funny and vice versa.
Everyone who is both kind and creative is either not old or creative.
Everyone who is either not brave or patient is old or not calm and vice versa.
If someone is not rich then lucy is both kind and not generous and vice versa.
If mary is not old then paul is either not kind or not funny and vice versa.
Everyone who is wise or rich is generous.
If mary is happy or wise then someone is both calm and not humble.
Everyone who is not calm is not old and vice versa.
Everyone who is either not brave or kind is both kind and strong.
Fred is both creative and not patient.
Someone is not curious or creative.
Paul is both not quiet and funny.
Alice is brave or not old.
Someone is patient.
Someone is not strong or not funny.
Mary is both not wise and not quiet.
Someone is funny. | Fred is kind. | entailment | (((curious(mary)<~>~creative(mary)))<=>(?[X]:((wise(X)<~>~funny(X)))))&
((?[X]:(~rich(X)))<=>((~rich(mary)&~strong(mary))))&
(((~brave(mary)&~creative(mary)))=>(?[X]:(~rich(X))))&
(((~old(alice)<~>~funny(alice)))<=>((generous(fred)&wise(fred))))&
(((~patient(paul)<~>~generous(paul)))<=>((~humble(mary)&~rich(mary))))&
(![X]:((rich(X)&quiet(X))=>humble(X)))&
((?[X]:((brave(X)<~>~funny(X))))<=>(?[X]:((~rich(X)&curious(X)))))&
(![X]:((happy(X)<~>curious(X))<=>(~kind(X)|funny(X))))&
(![X]:((kind(X)&creative(X))=>(~old(X)<~>creative(X))))&
(![X]:((~brave(X)<~>patient(X))<=>(old(X)|~calm(X))))&
((?[X]:(~rich(X)))<=>((kind(lucy)&~generous(lucy))))&
((~old(mary))<=>((~kind(paul)<~>~funny(paul))))&
(![X]:((wise(X)|rich(X))=>generous(X)))&
(((happy(mary)|wise(mary)))=>(?[X]:((calm(X)&~humble(X)))))&
(![X]:(~calm(X)<=>~old(X)))&
(![X]:((~brave(X)<~>kind(X))=>(kind(X)&strong(X))))&
((creative(fred)&~patient(fred)))&
(?[X]:((~curious(X)|creative(X))))&
((~quiet(paul)&funny(paul)))&
((brave(alice)|~old(alice)))&
(?[X]:(patient(X)))&
(?[X]:((~strong(X)|~funny(X))))&
((~wise(mary)&~quiet(mary)))&
(?[X]:(funny(X))) | kind(fred) | [
"p9",
"p14",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 4817208560386211871978224
% SZS output start Proof for 4817208560386211871978224
10. ! [X0] : ((~brave(X0) <~> patient(X0)) <=> (~calm(X0) | old(X0))) [input p9]
15. ! [X0] : (~calm(X0) <=> ~old(X0)) [input p14]
16. ! [X0] : ((~brave(X0) <~> kind(X0)) => (strong(X0) & kind(X0))) [input p15]
17. ~patient(fred) & creative(fred) [input p16]
25. ~kind(fred) [input hypothesis]
36. ! [X0] : ((strong(X0) & kind(X0)) | (~brave(X0) <=> kind(X0))) [ennf transformation 16]
60. ! [X0] : ((((~patient(X0) | brave(X0)) & (patient(X0) | ~brave(X0))) | (calm(X0) & ~old(X0))) & ((~calm(X0) | old(X0)) | ((~brave(X0) | ~patient(X0)) & (patient(X0) | brave(X0))))) [nnf transformation 10]
61. ! [X0] : ((((~patient(X0) | brave(X0)) & (patient(X0) | ~brave(X0))) | (calm(X0) & ~old(X0))) & (~calm(X0) | old(X0) | ((~brave(X0) | ~patient(X0)) & (patient(X0) | brave(X0))))) [flattening 60]
70. ! [X0] : ((~calm(X0) | old(X0)) & (~old(X0) | calm(X0))) [nnf transformation 15]
71. ! [X0] : ((strong(X0) & kind(X0)) | ((~brave(X0) | ~kind(X0)) & (kind(X0) | brave(X0)))) [nnf transformation 36]
120. ~old(X0) | ~brave(X0) | patient(X0) [cnf transformation 61]
121. ~brave(X0) | patient(X0) | calm(X0) [cnf transformation 61]
138. ~calm(X0) | old(X0) [cnf transformation 70]
139. kind(X0) | kind(X0) | brave(X0) [cnf transformation 71]
144. ~patient(fred) [cnf transformation 17]
152. ~kind(fred) [cnf transformation 25]
153. kind(X0) | brave(X0) [duplicate literal removal 139]
372. brave(fred) [resolution 153,152]
437. patient(fred) | calm(fred) [resolution 121,372]
439. calm(fred) [subsumption resolution 437,144]
543. old(fred) [resolution 439,138]
578. ~brave(fred) | patient(fred) [resolution 543,120]
580. patient(fred) [subsumption resolution 578,372]
581. $false [subsumption resolution 580,144]
% SZS output end Proof for 4817208560386211871978224
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not old and not calm is either not tall or not happy and vice versa. Everyone who is not kind or not funny is either wise or not funny and vice versa. Everyone who is either happy or not calm is either not happy or not calm. Everyone who is not curious is not strong. If alice is quiet or not kind then susan is either not generous or not rich and vice versa. If someone is not brave then john is happy and vice versa. If john is not curious then someone is not tall and vice versa. Everyone who is old is both not old and not kind. Everyone who is either not kind or happy is not wise or not happy and vice versa. If susan is both brave and tall then someone is either not curious or not tall and vice versa. If alice is not calm or not kind then mary is brave. Everyone who is either generous or not creative is both not happy and happy. Everyone who is not strong or not curious is both humble and quiet. Everyone who is not kind is funny and vice versa. Everyone who is both not generous and not funny is not brave or not rich and vice versa. If someone is either not kind or not calm then alice is brave and vice versa. Someone is either kind or not quiet. Someone is both not calm and rich. Someone is either not old or tall. Susan is rich or not patient. John is generous or not rich. Someone is either curious or funny. Someone is either not old or brave. | John is humble. | entailment | (![X]:((~old(X)&~calm(X))<=>(~tall(X)<~>~happy(X))))&
(![X]:((~kind(X)|~funny(X))<=>(wise(X)<~>~funny(X))))&
(![X]:((happy(X)<~>~calm(X))=>(~happy(X)<~>~calm(X))))&
(![X]:(~curious(X)=>~strong(X)))&
(((quiet(alice)|~kind(alice)))<=>((~generous(susan)<~>~rich(susan))))&
((?[X]:(~brave(X)))<=>(happy(john)))&
((~curious(john))<=>(?[X]:(~tall(X))))&
(![X]:(old(X)=>(~old(X)&~kind(X))))&
(![X]:((~kind(X)<~>happy(X))<=>(~wise(X)|~happy(X))))&
(((brave(susan)&tall(susan)))<=>(?[X]:((~curious(X)<~>~tall(X)))))&
(((~calm(alice)|~kind(alice)))=>(brave(mary)))&
(![X]:((generous(X)<~>~creative(X))=>(~happy(X)&happy(X))))&
(![X]:((~strong(X)|~curious(X))=>(humble(X)&quiet(X))))&
(![X]:(~kind(X)<=>funny(X)))&
(![X]:((~generous(X)&~funny(X))<=>(~brave(X)|~rich(X))))&
((?[X]:((~kind(X)<~>~calm(X))))<=>(brave(alice)))&
(?[X]:((kind(X)<~>~quiet(X))))&
(?[X]:((~calm(X)&rich(X))))&
(?[X]:((~old(X)<~>tall(X))))&
((rich(susan)|~patient(susan)))&
((generous(john)|~rich(john)))&
(?[X]:((curious(X)<~>funny(X))))&
(?[X]:((~old(X)<~>brave(X)))) | humble(john) | [
"p3",
"p6",
"p7",
"p12",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 3738004102363340877160975
% SZS output start Proof for 3738004102363340877160975
4. ! [X0] : (~curious(X0) => ~strong(X0)) [input p3]
7. ~curious(john) <=> ? [X0] : ~tall(X0) [input p6]
8. ! [X0] : (old(X0) => (~kind(X0) & ~old(X0))) [input p7]
13. ! [X0] : ((~curious(X0) | ~strong(X0)) => (quiet(X0) & humble(X0))) [input p12]
19. ? [X0] : (~old(X0) <~> tall(X0)) [input p18]
24. ~humble(john) [input hypothesis]
27. ! [X0] : (~strong(X0) | curious(X0)) [ennf transformation 4]
28. ! [X0] : ((~kind(X0) & ~old(X0)) | ~old(X0)) [ennf transformation 8]
31. ! [X0] : ((quiet(X0) & humble(X0)) | (curious(X0) & strong(X0))) [ennf transformation 13]
43. (~curious(john) | ! [X0] : tall(X0)) & (? [X0] : ~tall(X0) | curious(john)) [nnf transformation 7]
44. (~curious(john) | ! [X0] : tall(X0)) & (? [X1] : ~tall(X1) | curious(john)) [rectify 43]
45. ? [X1] : ~tall(X1) => ~tall(sK1) [choice axiom]
46. (~curious(john) | ! [X0] : tall(X0)) & (~tall(sK1) | curious(john)) [skolemisation 44,45]
67. ? [X0] : ((~tall(X0) | old(X0)) & (tall(X0) | ~old(X0))) [nnf transformation 19]
68. ? [X0] : ((~tall(X0) | old(X0)) & (tall(X0) | ~old(X0))) => ((~tall(sK6) | old(sK6)) & (tall(sK6) | ~old(sK6))) [choice axiom]
69. (~tall(sK6) | old(sK6)) & (tall(sK6) | ~old(sK6)) [skolemisation 67,68]
92. ~strong(X0) | curious(X0) [cnf transformation 27]
102. ~curious(john) | tall(X0) [cnf transformation 46]
103. ~old(X0) | ~old(X0) [cnf transformation 28]
123. humble(X0) | strong(X0) [cnf transformation 31]
143. ~tall(sK6) | old(sK6) [cnf transformation 69]
149. ~humble(john) [cnf transformation 24]
152. ~old(X0) [duplicate literal removal 103]
193. 8 <=> ! [X0] : tall(X0) [avatar definition]
194. tall(X0) <- (8) [avatar component clause 193]
196. 9 <=> curious(john) [avatar definition]
199. 8 | ~9 [avatar split clause 102,196,193]
278. ~tall(sK6) [subsumption resolution 143,152]
300. strong(john) [resolution 123,149]
301. curious(john) [resolution 300,92]
304. 9 [avatar split clause 301,196]
307. $false <- (8) [resolution 194,278]
308. ~8 [avatar contradiction clause 307]
311. $false [avatar sat refutation 199,304,308]
% SZS output end Proof for 3738004102363340877160975
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both generous and quiet then someone is curious.
Everyone who is both not quiet and not humble is either funny or not humble.
Everyone who is both not kind and wise is both curious and strong and vice versa.
Everyone who is both humble and tall is both not generous and funny and vice versa.
If john is either old or not curious then someone is quiet and vice versa.
If someone is not calm or humble then someone is tall or happy.
Everyone who is both not strong and quiet is either not rich or not generous.
If john is not funny then someone is strong.
If alice is funny or not funny then mary is tall.
If mary is either not quiet or tall then someone is either humble or funny and vice versa.
If alice is not creative then someone is both not calm and rich and vice versa.
Everyone who is either curious or not strong is both not curious and kind.
Everyone who is not patient or calm is not kind or not funny.
If someone is curious then someone is either not strong or brave.
Everyone who is either not humble or not patient is both not calm and not quiet.
Everyone who is funny or not old is kind or rich and vice versa.
Mary is not patient.
Someone is both not quiet and not brave.
John is not curious or wise.
Someone is either not patient or not kind.
Someone is rich.
Someone is either tall or curious.
John is both calm and not strong.
Alice is both not brave and not strong. | Mary is brave. | neutral | ((?[X]:((generous(X)&quiet(X))))=>(?[X]:(curious(X))))&
(![X]:((~quiet(X)&~humble(X))=>(funny(X)<~>~humble(X))))&
(![X]:((~kind(X)&wise(X))<=>(curious(X)&strong(X))))&
(![X]:((humble(X)&tall(X))<=>(~generous(X)&funny(X))))&
(((old(john)<~>~curious(john)))<=>(?[X]:(quiet(X))))&
((?[X]:((~calm(X)|humble(X))))=>(?[X]:((tall(X)|happy(X)))))&
(![X]:((~strong(X)&quiet(X))=>(~rich(X)<~>~generous(X))))&
((~funny(john))=>(?[X]:(strong(X))))&
(((funny(alice)|~funny(alice)))=>(tall(mary)))&
(((~quiet(mary)<~>tall(mary)))<=>(?[X]:((humble(X)<~>funny(X)))))&
((~creative(alice))<=>(?[X]:((~calm(X)&rich(X)))))&
(![X]:((curious(X)<~>~strong(X))=>(~curious(X)&kind(X))))&
(![X]:((~patient(X)|calm(X))=>(~kind(X)|~funny(X))))&
((?[X]:(curious(X)))=>(?[X]:((~strong(X)<~>brave(X)))))&
(![X]:((~humble(X)<~>~patient(X))=>(~calm(X)&~quiet(X))))&
(![X]:((funny(X)|~old(X))<=>(kind(X)|rich(X))))&
(~patient(mary))&
(?[X]:((~quiet(X)&~brave(X))))&
((~curious(john)|wise(john)))&
(?[X]:((~patient(X)<~>~kind(X))))&
(?[X]:(rich(X)))&
(?[X]:((tall(X)<~>curious(X))))&
((calm(john)&~strong(john)))&
((~brave(alice)&~strong(alice))) | brave(mary) | [] | null | 0 |
If lucy is either not humble or funny then lucy is either not happy or humble.
If paul is both patient and generous then john is either not creative or quiet and vice versa.
Everyone who is happy or not strong is wise.
Everyone who is not wise is either patient or quiet and vice versa.
If john is both creative and tall then someone is not curious and vice versa.
Everyone who is curious is either calm or curious.
Everyone who is not wise is both not wise and not brave.
If alice is calm or strong then fred is not quiet or creative and vice versa.
Everyone who is not generous or creative is generous.
If someone is not creative or not quiet then someone is either not kind or not patient.
If someone is funny then someone is old.
If susan is both not strong and generous then john is not quiet or not wise.
If mary is both not old and funny then john is either not creative or old and vice versa.
If someone is either not creative or not tall then someone is either not calm or not humble and vice versa.
Everyone who is both tall and not generous is quiet or not calm and vice versa.
If susan is either calm or not happy then alice is either not curious or tall.
Someone is either not rich or not funny.
Mary is not wise.
Someone is not old.
Mary is either kind or not kind.
Mary is not tall.
Mary is not humble or patient.
Fred is not humble or not calm.
Susan is not tall or rich. | Paul is not calm. | contradiction | (((~humble(lucy)<~>funny(lucy)))=>((~happy(lucy)<~>humble(lucy))))&
(((patient(paul)&generous(paul)))<=>((~creative(john)<~>quiet(john))))&
(![X]:((happy(X)|~strong(X))=>wise(X)))&
(![X]:(~wise(X)<=>(patient(X)<~>quiet(X))))&
(((creative(john)&tall(john)))<=>(?[X]:(~curious(X))))&
(![X]:(curious(X)=>(calm(X)<~>curious(X))))&
(![X]:(~wise(X)=>(~wise(X)&~brave(X))))&
(((calm(alice)|strong(alice)))<=>((~quiet(fred)|creative(fred))))&
(![X]:((~generous(X)|creative(X))=>generous(X)))&
((?[X]:((~creative(X)|~quiet(X))))=>(?[X]:((~kind(X)<~>~patient(X)))))&
((?[X]:(funny(X)))=>(?[X]:(old(X))))&
(((~strong(susan)&generous(susan)))=>((~quiet(john)|~wise(john))))&
(((~old(mary)&funny(mary)))<=>((~creative(john)<~>old(john))))&
((?[X]:((~creative(X)<~>~tall(X))))<=>(?[X]:((~calm(X)<~>~humble(X)))))&
(![X]:((tall(X)&~generous(X))<=>(quiet(X)|~calm(X))))&
(((calm(susan)<~>~happy(susan)))=>((~curious(alice)<~>tall(alice))))&
(?[X]:((~rich(X)<~>~funny(X))))&
(~wise(mary))&
(?[X]:(~old(X)))&
((kind(mary)<~>~kind(mary)))&
(~tall(mary))&
((~humble(mary)|patient(mary)))&
((~humble(fred)|~calm(fred)))&
((~tall(susan)|rich(susan))) | ~calm(paul) | [
"p8",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 1873489105609887690288691
% SZS output start Proof for 1873489105609887690288691
9. ! [X0] : ((creative(X0) | ~generous(X0)) => generous(X0)) [input p8]
15. ! [X0] : ((~generous(X0) & tall(X0)) <=> (~calm(X0) | quiet(X0))) [input p14]
25. ~calm(paul) [input hypothesis]
34. ! [X0] : (generous(X0) | (~creative(X0) & generous(X0))) [ennf transformation 9]
66. ! [X0] : (((~generous(X0) & tall(X0)) | (calm(X0) & ~quiet(X0))) & ((~calm(X0) | quiet(X0)) | (generous(X0) | ~tall(X0)))) [nnf transformation 15]
67. ! [X0] : (((~generous(X0) & tall(X0)) | (calm(X0) & ~quiet(X0))) & (~calm(X0) | quiet(X0) | generous(X0) | ~tall(X0))) [flattening 66]
101. generous(X0) | generous(X0) [cnf transformation 34]
127. ~generous(X0) | calm(X0) [cnf transformation 67]
142. ~calm(paul) [cnf transformation 25]
143. generous(X0) [duplicate literal removal 101]
307. calm(X0) [subsumption resolution 127,143]
354. $false [subsumption resolution 142,307]
% SZS output end Proof for 1873489105609887690288691
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind is not strong and vice versa.
Everyone who is not funny or not old is tall or happy.
If lucy is both not tall and not humble then someone is either not strong or kind.
If someone is humble then someone is both calm and funny and vice versa.
If someone is not kind or not creative then someone is both generous and happy.
If someone is either quiet or curious then john is curious.
If susan is either not humble or not wise then john is old or not brave.
Everyone who is both not curious and patient is curious or not wise and vice versa.
If fred is both not creative and brave then fred is humble or curious.
Everyone who is either old or wise is either happy or brave and vice versa.
Everyone who is both not funny and not curious is either not funny or strong and vice versa.
Everyone who is either not humble or happy is both creative and not wise and vice versa.
Everyone who is old or not generous is either brave or rich.
If john is both old and not humble then someone is not humble or quiet.
If someone is either not funny or happy then someone is not strong or creative.
Everyone who is happy or funny is patient.
Someone is not funny or not tall.
Fred is strong or patient.
Someone is either quiet or funny.
Someone is either not humble or not old.
Someone is both kind and not rich.
Someone is not kind or not brave. | Lucy is tall. | neutral | (![X]:((~patient(X)<~>kind(X))<=>~strong(X)))&
(![X]:((~funny(X)|~old(X))=>(tall(X)|happy(X))))&
(((~tall(lucy)&~humble(lucy)))=>(?[X]:((~strong(X)<~>kind(X)))))&
((?[X]:(humble(X)))<=>(?[X]:((calm(X)&funny(X)))))&
((?[X]:((~kind(X)|~creative(X))))=>(?[X]:((generous(X)&happy(X)))))&
((?[X]:((quiet(X)<~>curious(X))))=>(curious(john)))&
(((~humble(susan)<~>~wise(susan)))=>((old(john)|~brave(john))))&
(![X]:((~curious(X)&patient(X))<=>(curious(X)|~wise(X))))&
(((~creative(fred)&brave(fred)))=>((humble(fred)|curious(fred))))&
(![X]:((old(X)<~>wise(X))<=>(happy(X)<~>brave(X))))&
(![X]:((~funny(X)&~curious(X))<=>(~funny(X)<~>strong(X))))&
(![X]:((~humble(X)<~>happy(X))<=>(creative(X)&~wise(X))))&
(![X]:((old(X)|~generous(X))=>(brave(X)<~>rich(X))))&
(((old(john)&~humble(john)))=>(?[X]:((~humble(X)|quiet(X)))))&
((?[X]:((~funny(X)<~>happy(X))))=>(?[X]:((~strong(X)|creative(X)))))&
(![X]:((happy(X)|funny(X))=>patient(X)))&
(?[X]:((~funny(X)|~tall(X))))&
((strong(fred)|patient(fred)))&
(?[X]:((quiet(X)<~>funny(X))))&
(?[X]:((~humble(X)<~>~old(X))))&
(?[X]:((kind(X)&~rich(X))))&
(?[X]:((~kind(X)|~brave(X)))) | tall(lucy) | [] | null | 0 |
Everyone who is both not creative and patient is curious and vice versa. If john is both not brave and not wise then someone is either humble or not strong. If someone is humble or not happy then someone is either patient or not old and vice versa. If fred is not strong or not generous then john is not tall or not kind and vice versa. If lucy is not rich then someone is not patient and vice versa. Everyone who is not curious or patient is not humble. If mary is both tall and happy then susan is either quiet or not strong. If someone is both not funny and not rich then someone is not kind or patient. If someone is funny then someone is not quiet. Everyone who is either not brave or rich is kind or calm and vice versa. Everyone who is both strong and not rich is both not tall and not strong and vice versa. Everyone who is both not wise and not rich is either not curious or not rich and vice versa. Everyone who is both not curious and not kind is either old or not kind. If someone is either not wise or not curious then john is both not patient and quiet and vice versa. If susan is rich or not quiet then alice is both not funny and quiet. Everyone who is either not generous or not rich is either tall or not happy and vice versa. Someone is both funny and not strong. Mary is either not strong or not kind. Fred is curious. Someone is quiet. Someone is either not quiet or rich. Mary is not kind or not tall. Someone is not tall or strong. Alice is both not tall and not happy. | Fred is humble. | contradiction | (![X]:((~creative(X)&patient(X))<=>curious(X)))&
(((~brave(john)&~wise(john)))=>(?[X]:((humble(X)<~>~strong(X)))))&
((?[X]:((humble(X)|~happy(X))))<=>(?[X]:((patient(X)<~>~old(X)))))&
(((~strong(fred)|~generous(fred)))<=>((~tall(john)|~kind(john))))&
((~rich(lucy))<=>(?[X]:(~patient(X))))&
(![X]:((~curious(X)|patient(X))=>~humble(X)))&
(((tall(mary)&happy(mary)))=>((quiet(susan)<~>~strong(susan))))&
((?[X]:((~funny(X)&~rich(X))))=>(?[X]:((~kind(X)|patient(X)))))&
((?[X]:(funny(X)))=>(?[X]:(~quiet(X))))&
(![X]:((~brave(X)<~>rich(X))<=>(kind(X)|calm(X))))&
(![X]:((strong(X)&~rich(X))<=>(~tall(X)&~strong(X))))&
(![X]:((~wise(X)&~rich(X))<=>(~curious(X)<~>~rich(X))))&
(![X]:((~curious(X)&~kind(X))=>(old(X)<~>~kind(X))))&
((?[X]:((~wise(X)<~>~curious(X))))<=>((~patient(john)&quiet(john))))&
(((rich(susan)|~quiet(susan)))=>((~funny(alice)&quiet(alice))))&
(![X]:((~generous(X)<~>~rich(X))<=>(tall(X)<~>~happy(X))))&
(?[X]:((funny(X)&~strong(X))))&
((~strong(mary)<~>~kind(mary)))&
(curious(fred))&
(?[X]:(quiet(X)))&
(?[X]:((~quiet(X)<~>rich(X))))&
((~kind(mary)|~tall(mary)))&
(?[X]:((~tall(X)|strong(X))))&
((~tall(alice)&~happy(alice))) | humble(fred) | [
"p0",
"p5",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 2640360939955115730730686
% SZS output start Proof for 2640360939955115730730686
1. ! [X0] : ((patient(X0) & ~creative(X0)) <=> curious(X0)) [input p0]
6. ! [X0] : ((patient(X0) | ~curious(X0)) => ~humble(X0)) [input p5]
19. curious(fred) [input p18]
25. humble(fred) [input hypothesis]
31. ! [X0] : (~humble(X0) | (~patient(X0) & curious(X0))) [ennf transformation 6]
39. ! [X0] : (((patient(X0) & ~creative(X0)) | ~curious(X0)) & (curious(X0) | (~patient(X0) | creative(X0)))) [nnf transformation 1]
40. ! [X0] : (((patient(X0) & ~creative(X0)) | ~curious(X0)) & (curious(X0) | ~patient(X0) | creative(X0))) [flattening 39]
87. ~curious(X0) | patient(X0) [cnf transformation 40]
103. ~humble(X0) | ~patient(X0) [cnf transformation 31]
148. curious(fred) [cnf transformation 19]
156. humble(fred) [cnf transformation 25]
356. patient(fred) [resolution 87,148]
358. ~patient(fred) [resolution 103,156]
359. $false [subsumption resolution 358,356]
% SZS output end Proof for 2640360939955115730730686
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both old and not quiet is not wise or not calm and vice versa.
If lucy is either not happy or not funny then fred is either not happy or not strong and vice versa.
Everyone who is not calm or patient is quiet.
Everyone who is both not old and not creative is not happy.
If someone is not creative or strong then paul is not curious or patient and vice versa.
Everyone who is both not wise and humble is either patient or strong.
Everyone who is either not creative or not happy is not patient.
Everyone who is either rich or not strong is not patient.
Everyone who is quiet is both old and happy and vice versa.
Everyone who is not quiet or old is both not brave and creative and vice versa.
If someone is either not patient or wise then someone is both tall and not rich.
Everyone who is both not tall and not humble is not wise and vice versa.
Everyone who is not happy or humble is happy or humble.
Everyone who is not strong is both strong and not generous.
Everyone who is not quiet or not rich is both not generous and not calm.
Lucy is funny or rich.
Fred is not brave or generous.
Someone is both tall and funny.
Someone is either not kind or happy.
Someone is generous.
Susan is either not kind or not brave.
Someone is tall. | Fred is curious. | neutral | (![X]:((old(X)&~quiet(X))<=>(~wise(X)|~calm(X))))&
(((~happy(lucy)<~>~funny(lucy)))<=>((~happy(fred)<~>~strong(fred))))&
(![X]:((~calm(X)|patient(X))=>quiet(X)))&
(![X]:((~old(X)&~creative(X))=>~happy(X)))&
((?[X]:((~creative(X)|strong(X))))<=>((~curious(paul)|patient(paul))))&
(![X]:((~wise(X)&humble(X))=>(patient(X)<~>strong(X))))&
(![X]:((~creative(X)<~>~happy(X))=>~patient(X)))&
(![X]:((rich(X)<~>~strong(X))=>~patient(X)))&
(![X]:(quiet(X)<=>(old(X)&happy(X))))&
(![X]:((~quiet(X)|old(X))<=>(~brave(X)&creative(X))))&
((?[X]:((~patient(X)<~>wise(X))))=>(?[X]:((tall(X)&~rich(X)))))&
(![X]:((~tall(X)&~humble(X))<=>~wise(X)))&
(![X]:((~happy(X)|humble(X))=>(happy(X)|humble(X))))&
(![X]:(~strong(X)=>(strong(X)&~generous(X))))&
(![X]:((~quiet(X)|~rich(X))=>(~generous(X)&~calm(X))))&
((funny(lucy)|rich(lucy)))&
((~brave(fred)|generous(fred)))&
(?[X]:((tall(X)&funny(X))))&
(?[X]:((~kind(X)<~>happy(X))))&
(?[X]:(generous(X)))&
((~kind(susan)<~>~brave(susan)))&
(?[X]:(tall(X))) | curious(fred) | [] | null | 0 |
If someone is patient or not humble then someone is not patient or not strong.
If alice is either curious or not kind then someone is both not brave and quiet.
If fred is old then someone is not happy and vice versa.
Everyone who is rich or humble is both calm and funny and vice versa.
Everyone who is generous is happy and vice versa.
Everyone who is both funny and curious is either patient or not tall.
Everyone who is both funny and not strong is kind or not brave and vice versa.
Everyone who is both not funny and not quiet is either humble or calm.
If fred is both brave and not rich then fred is not rich and vice versa.
If someone is rich then susan is either not creative or generous and vice versa.
Everyone who is both tall and not humble is either tall or not tall and vice versa.
Everyone who is either calm or not humble is not rich or not creative and vice versa.
If someone is not calm then susan is quiet or not humble and vice versa.
Everyone who is either not quiet or calm is not humble.
If someone is either not rich or not brave then alice is both not creative and not generous.
Everyone who is not strong or not quiet is not wise.
Someone is either not curious or happy.
Lucy is either not creative or generous.
Fred is brave or not rich.
Alice is wise or patient.
Fred is both not funny and not wise.
John is not wise or not patient.
Mary is rich.
Susan is either wise or not funny. | Alice is kind. | neutral | ((?[X]:((patient(X)|~humble(X))))=>(?[X]:((~patient(X)|~strong(X)))))&
(((curious(alice)<~>~kind(alice)))=>(?[X]:((~brave(X)&quiet(X)))))&
((old(fred))<=>(?[X]:(~happy(X))))&
(![X]:((rich(X)|humble(X))<=>(calm(X)&funny(X))))&
(![X]:(generous(X)<=>happy(X)))&
(![X]:((funny(X)&curious(X))=>(patient(X)<~>~tall(X))))&
(![X]:((funny(X)&~strong(X))<=>(kind(X)|~brave(X))))&
(![X]:((~funny(X)&~quiet(X))=>(humble(X)<~>calm(X))))&
(((brave(fred)&~rich(fred)))<=>(~rich(fred)))&
((?[X]:(rich(X)))<=>((~creative(susan)<~>generous(susan))))&
(![X]:((tall(X)&~humble(X))<=>(tall(X)<~>~tall(X))))&
(![X]:((calm(X)<~>~humble(X))<=>(~rich(X)|~creative(X))))&
((?[X]:(~calm(X)))<=>((quiet(susan)|~humble(susan))))&
(![X]:((~quiet(X)<~>calm(X))=>~humble(X)))&
((?[X]:((~rich(X)<~>~brave(X))))=>((~creative(alice)&~generous(alice))))&
(![X]:((~strong(X)|~quiet(X))=>~wise(X)))&
(?[X]:((~curious(X)<~>happy(X))))&
((~creative(lucy)<~>generous(lucy)))&
((brave(fred)|~rich(fred)))&
((wise(alice)|patient(alice)))&
((~funny(fred)&~wise(fred)))&
((~wise(john)|~patient(john)))&
(rich(mary))&
((wise(susan)<~>~funny(susan))) | kind(alice) | [] | null | 0 |
Everyone who is both quiet and not curious is generous or not curious.
If someone is not happy then someone is either funny or brave.
Everyone who is not humble or not calm is not happy or not funny.
Everyone who is creative or calm is strong.
Everyone who is not old is old or creative and vice versa.
If someone is not wise then mary is not brave.
Everyone who is either not funny or not curious is kind or brave and vice versa.
If john is not rich or not calm then someone is either not happy or not tall and vice versa.
If fred is both tall and happy then someone is not happy or strong.
Everyone who is both not curious and kind is not funny or not creative and vice versa.
If alice is both patient and brave then mary is curious.
If someone is not humble or funny then lucy is either happy or curious and vice versa.
Everyone who is not brave is not humble and vice versa.
Everyone who is both rich and generous is either generous or quiet and vice versa.
If paul is either brave or not quiet then alice is either rich or strong and vice versa.
If alice is either tall or not wise then paul is not generous or not humble.
Someone is patient or creative.
Alice is funny.
Someone is both not brave and creative.
Someone is not old or not strong.
Someone is both not brave and rich.
Paul is humble or patient.
Someone is happy.
Someone is either not humble or not curious. | Alice is kind. | contradiction | (![X]:((quiet(X)&~curious(X))=>(generous(X)|~curious(X))))&
((?[X]:(~happy(X)))=>(?[X]:((funny(X)<~>brave(X)))))&
(![X]:((~humble(X)|~calm(X))=>(~happy(X)|~funny(X))))&
(![X]:((creative(X)|calm(X))=>strong(X)))&
(![X]:(~old(X)<=>(old(X)|creative(X))))&
((?[X]:(~wise(X)))=>(~brave(mary)))&
(![X]:((~funny(X)<~>~curious(X))<=>(kind(X)|brave(X))))&
(((~rich(john)|~calm(john)))<=>(?[X]:((~happy(X)<~>~tall(X)))))&
(((tall(fred)&happy(fred)))=>(?[X]:((~happy(X)|strong(X)))))&
(![X]:((~curious(X)&kind(X))<=>(~funny(X)|~creative(X))))&
(((patient(alice)&brave(alice)))=>(curious(mary)))&
((?[X]:((~humble(X)|funny(X))))<=>((happy(lucy)<~>curious(lucy))))&
(![X]:(~brave(X)<=>~humble(X)))&
(![X]:((rich(X)&generous(X))<=>(generous(X)<~>quiet(X))))&
(((brave(paul)<~>~quiet(paul)))<=>((rich(alice)<~>strong(alice))))&
(((tall(alice)<~>~wise(alice)))=>((~generous(paul)|~humble(paul))))&
(?[X]:((patient(X)|creative(X))))&
(funny(alice))&
(?[X]:((~brave(X)&creative(X))))&
(?[X]:((~old(X)|~strong(X))))&
(?[X]:((~brave(X)&rich(X))))&
((humble(paul)|patient(paul)))&
(?[X]:(happy(X)))&
(?[X]:((~humble(X)<~>~curious(X)))) | kind(alice) | [
"p4",
"p6",
"p9",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 1708165808244715237628879
% SZS output start Proof for 1708165808244715237628879
5. ! [X0] : (~old(X0) <=> (creative(X0) | old(X0))) [input p4]
7. ! [X0] : ((~funny(X0) <~> ~curious(X0)) <=> (brave(X0) | kind(X0))) [input p6]
10. ! [X0] : ((kind(X0) & ~curious(X0)) <=> (~creative(X0) | ~funny(X0))) [input p9]
18. funny(alice) [input p17]
25. kind(alice) [input hypothesis]
44. ! [X0] : ((~old(X0) | (~creative(X0) & ~old(X0))) & ((creative(X0) | old(X0)) | old(X0))) [nnf transformation 5]
45. ! [X0] : ((~old(X0) | (~creative(X0) & ~old(X0))) & (creative(X0) | old(X0) | old(X0))) [flattening 44]
46. ! [X0] : ((((curious(X0) | funny(X0)) & (~curious(X0) | ~funny(X0))) | (~brave(X0) & ~kind(X0))) & ((brave(X0) | kind(X0)) | ((~funny(X0) | curious(X0)) & (~curious(X0) | funny(X0))))) [nnf transformation 7]
47. ! [X0] : ((((curious(X0) | funny(X0)) & (~curious(X0) | ~funny(X0))) | (~brave(X0) & ~kind(X0))) & (brave(X0) | kind(X0) | ((~funny(X0) | curious(X0)) & (~curious(X0) | funny(X0))))) [flattening 46]
55. ! [X0] : (((kind(X0) & ~curious(X0)) | (creative(X0) & funny(X0))) & ((~creative(X0) | ~funny(X0)) | (~kind(X0) | curious(X0)))) [nnf transformation 10]
56. ! [X0] : (((kind(X0) & ~curious(X0)) | (creative(X0) & funny(X0))) & (~creative(X0) | ~funny(X0) | ~kind(X0) | curious(X0))) [flattening 55]
86. creative(X0) | old(X0) | old(X0) [cnf transformation 45]
87. ~old(X0) | ~old(X0) [cnf transformation 45]
92. ~kind(X0) | ~funny(X0) | ~curious(X0) [cnf transformation 47]
94. curious(X0) | funny(X0) | ~kind(X0) [cnf transformation 47]
103. ~creative(X0) | ~funny(X0) | ~kind(X0) | curious(X0) [cnf transformation 56]
134. funny(alice) [cnf transformation 18]
144. kind(alice) [cnf transformation 25]
147. creative(X0) | old(X0) [duplicate literal removal 86]
148. ~old(X0) [duplicate literal removal 87]
162. creative(X0) [subsumption resolution 147,148]
216. ~funny(X0) | ~kind(X0) | curious(X0) [subsumption resolution 103,162]
217. ~kind(X0) | curious(X0) [subsumption resolution 216,94]
331. curious(alice) [resolution 217,144]
346. ~funny(alice) | ~curious(alice) [resolution 92,144]
348. ~curious(alice) [subsumption resolution 346,134]
349. $false [subsumption resolution 348,331]
% SZS output end Proof for 1708165808244715237628879
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Everyone who is not rich is both calm and kind and vice versa. If someone is strong or not wise then someone is rich or creative and vice versa. Everyone who is both not brave and not curious is either creative or not happy and vice versa. If someone is either generous or not tall then someone is not curious or curious and vice versa. If lucy is humble or funny then someone is both quiet and wise. If john is not old then someone is both not tall and not wise and vice versa. If someone is quiet or not curious then paul is not patient or not tall and vice versa. Everyone who is tall or generous is either funny or not funny and vice versa. If susan is generous or strong then lucy is either patient or old and vice versa. If someone is either happy or not happy then fred is old and vice versa. If someone is old or humble then someone is not wise or quiet. Everyone who is quiet or not happy is not rich or not wise. Everyone who is both rich and funny is either generous or not rich and vice versa. Everyone who is calm or not tall is not humble. Everyone who is not creative or funny is not kind. Everyone who is strong or not creative is either not generous or wise. Paul is happy or not strong. Mary is either funny or not old. Someone is both not quiet and kind. Someone is either rich or curious. Lucy is brave or calm. Someone is generous. Paul is both creative and patient. Someone is funny. | Fred is happy. | neutral | (![X]:(~rich(X)<=>(calm(X)&kind(X))))&
((?[X]:((strong(X)|~wise(X))))<=>(?[X]:((rich(X)|creative(X)))))&
(![X]:((~brave(X)&~curious(X))<=>(creative(X)<~>~happy(X))))&
((?[X]:((generous(X)<~>~tall(X))))<=>(?[X]:((~curious(X)|curious(X)))))&
(((humble(lucy)|funny(lucy)))=>(?[X]:((quiet(X)&wise(X)))))&
((~old(john))<=>(?[X]:((~tall(X)&~wise(X)))))&
((?[X]:((quiet(X)|~curious(X))))<=>((~patient(paul)|~tall(paul))))&
(![X]:((tall(X)|generous(X))<=>(funny(X)<~>~funny(X))))&
(((generous(susan)|strong(susan)))<=>((patient(lucy)<~>old(lucy))))&
((?[X]:((happy(X)<~>~happy(X))))<=>(old(fred)))&
((?[X]:((old(X)|humble(X))))=>(?[X]:((~wise(X)|quiet(X)))))&
(![X]:((quiet(X)|~happy(X))=>(~rich(X)|~wise(X))))&
(![X]:((rich(X)&funny(X))<=>(generous(X)<~>~rich(X))))&
(![X]:((calm(X)|~tall(X))=>~humble(X)))&
(![X]:((~creative(X)|funny(X))=>~kind(X)))&
(![X]:((strong(X)|~creative(X))=>(~generous(X)<~>wise(X))))&
((happy(paul)|~strong(paul)))&
((funny(mary)<~>~old(mary)))&
(?[X]:((~quiet(X)&kind(X))))&
(?[X]:((rich(X)<~>curious(X))))&
((brave(lucy)|calm(lucy)))&
(?[X]:(generous(X)))&
((creative(paul)&patient(paul)))&
(?[X]:(funny(X))) | happy(fred) | [] | null | 0 |
Everyone who is funny or rich is either funny or patient and vice versa. Everyone who is wise is quiet or not patient and vice versa. If someone is not old or not patient then someone is either humble or creative and vice versa. Everyone who is not curious or not rich is either not strong or brave and vice versa. If someone is not wise then someone is wise or tall and vice versa. If someone is not happy then john is tall or not strong and vice versa. If someone is not creative or not kind then someone is both funny and not tall. Everyone who is either not creative or not tall is both not curious and brave and vice versa. Everyone who is either not happy or rich is humble and vice versa. Everyone who is not tall is both not creative and not brave and vice versa. If alice is either humble or tall then john is both tall and not happy. Everyone who is not rich is both happy and not happy and vice versa. Everyone who is creative is either not wise or wise. Everyone who is either not humble or curious is both strong and not strong. If someone is not quiet or brave then someone is strong and vice versa. Someone is either not happy or not brave. Someone is either happy or brave. Someone is both not creative and strong. Someone is quiet. Lucy is humble. Paul is strong or not generous. Someone is both not brave and patient. Paul is not calm. | John is not quiet. | neutral | (![X]:((funny(X)|rich(X))<=>(funny(X)<~>patient(X))))&
(![X]:(wise(X)<=>(quiet(X)|~patient(X))))&
((?[X]:((~old(X)|~patient(X))))<=>(?[X]:((humble(X)<~>creative(X)))))&
(![X]:((~curious(X)|~rich(X))<=>(~strong(X)<~>brave(X))))&
((?[X]:(~wise(X)))<=>(?[X]:((wise(X)|tall(X)))))&
((?[X]:(~happy(X)))<=>((tall(john)|~strong(john))))&
((?[X]:((~creative(X)|~kind(X))))=>(?[X]:((funny(X)&~tall(X)))))&
(![X]:((~creative(X)<~>~tall(X))<=>(~curious(X)&brave(X))))&
(![X]:((~happy(X)<~>rich(X))<=>humble(X)))&
(![X]:(~tall(X)<=>(~creative(X)&~brave(X))))&
(((humble(alice)<~>tall(alice)))=>((tall(john)&~happy(john))))&
(![X]:(~rich(X)<=>(happy(X)&~happy(X))))&
(![X]:(creative(X)=>(~wise(X)<~>wise(X))))&
(![X]:((~humble(X)<~>curious(X))=>(strong(X)&~strong(X))))&
((?[X]:((~quiet(X)|brave(X))))<=>(?[X]:(strong(X))))&
(?[X]:((~happy(X)<~>~brave(X))))&
(?[X]:((happy(X)<~>brave(X))))&
(?[X]:((~creative(X)&strong(X))))&
(?[X]:(quiet(X)))&
(humble(lucy))&
((strong(paul)|~generous(paul)))&
(?[X]:((~brave(X)&patient(X))))&
(~calm(paul)) | ~quiet(john) | [] | null | 0 |
If john is both not brave and curious then someone is creative and vice versa. Everyone who is not wise or brave is brave or not old and vice versa. Everyone who is funny or not generous is both patient and old. Everyone who is either not funny or wise is brave and vice versa. Everyone who is wise or not kind is not patient and vice versa. Everyone who is creative is patient. If someone is not generous or rich then someone is not patient or not funny. Everyone who is either quiet or not happy is generous or not generous and vice versa. Everyone who is curious or not patient is both not happy and happy and vice versa. Everyone who is quiet is not wise or not curious. If someone is not creative or quiet then someone is both happy and calm and vice versa. Everyone who is not calm or not quiet is happy. If alice is either not creative or tall then someone is not calm or not funny. Everyone who is not kind or creative is either not tall or funny. Everyone who is either not curious or brave is either funny or generous. If someone is tall or kind then susan is humble. Someone is either not strong or not old. Susan is either strong or not wise. Mary is either not wise or old. Someone is either calm or not tall. Someone is both calm and rich. Someone is tall or old. | Mary is brave. | entailment | (((~brave(john)&curious(john)))<=>(?[X]:(creative(X))))&
(![X]:((~wise(X)|brave(X))<=>(brave(X)|~old(X))))&
(![X]:((funny(X)|~generous(X))=>(patient(X)&old(X))))&
(![X]:((~funny(X)<~>wise(X))<=>brave(X)))&
(![X]:((wise(X)|~kind(X))<=>~patient(X)))&
(![X]:(creative(X)=>patient(X)))&
((?[X]:((~generous(X)|rich(X))))=>(?[X]:((~patient(X)|~funny(X)))))&
(![X]:((quiet(X)<~>~happy(X))<=>(generous(X)|~generous(X))))&
(![X]:((curious(X)|~patient(X))<=>(~happy(X)&happy(X))))&
(![X]:(quiet(X)=>(~wise(X)|~curious(X))))&
((?[X]:((~creative(X)|quiet(X))))<=>(?[X]:((happy(X)&calm(X)))))&
(![X]:((~calm(X)|~quiet(X))=>happy(X)))&
(((~creative(alice)<~>tall(alice)))=>(?[X]:((~calm(X)|~funny(X)))))&
(![X]:((~kind(X)|creative(X))=>(~tall(X)<~>funny(X))))&
(![X]:((~curious(X)<~>brave(X))=>(funny(X)<~>generous(X))))&
((?[X]:((tall(X)|kind(X))))=>(humble(susan)))&
(?[X]:((~strong(X)<~>~old(X))))&
((strong(susan)<~>~wise(susan)))&
((~wise(mary)<~>old(mary)))&
(?[X]:((calm(X)<~>~tall(X))))&
(?[X]:((calm(X)&rich(X))))&
(?[X]:((tall(X)|old(X)))) | brave(mary) | [
"p2",
"p3",
"p4",
"p8",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 6757570965738975833399116
% SZS output start Proof for 6757570965738975833399116
3. ! [X0] : ((~generous(X0) | funny(X0)) => (old(X0) & patient(X0))) [input p2]
4. ! [X0] : ((~funny(X0) <~> wise(X0)) <=> brave(X0)) [input p3]
5. ! [X0] : ((~kind(X0) | wise(X0)) <=> ~patient(X0)) [input p4]
9. ! [X0] : ((~patient(X0) | curious(X0)) <=> (happy(X0) & ~happy(X0))) [input p8]
19. ~wise(mary) <~> old(mary) [input p18]
23. ~brave(mary) [input hypothesis]
27. ! [X0] : ((old(X0) & patient(X0)) | (generous(X0) & ~funny(X0))) [ennf transformation 3]
43. ! [X0] : ((((~wise(X0) | funny(X0)) & (wise(X0) | ~funny(X0))) | ~brave(X0)) & (brave(X0) | ((~funny(X0) | ~wise(X0)) & (wise(X0) | funny(X0))))) [nnf transformation 4]
44. ! [X0] : (((~kind(X0) | wise(X0)) | patient(X0)) & (~patient(X0) | (kind(X0) & ~wise(X0)))) [nnf transformation 5]
45. ! [X0] : ((~kind(X0) | wise(X0) | patient(X0)) & (~patient(X0) | (kind(X0) & ~wise(X0)))) [flattening 44]
51. ! [X0] : (((~patient(X0) | curious(X0)) | (~happy(X0) | happy(X0))) & ((happy(X0) & ~happy(X0)) | (patient(X0) & ~curious(X0)))) [nnf transformation 9]
52. ! [X0] : ((~patient(X0) | curious(X0) | ~happy(X0) | happy(X0)) & ((happy(X0) & ~happy(X0)) | (patient(X0) & ~curious(X0)))) [flattening 51]
67. (~old(mary) | wise(mary)) & (old(mary) | ~wise(mary)) [nnf transformation 19]
84. ~funny(X0) | old(X0) [cnf transformation 27]
86. funny(X0) | wise(X0) | brave(X0) [cnf transformation 43]
90. ~patient(X0) | ~wise(X0) [cnf transformation 45]
103. ~happy(X0) | patient(X0) [cnf transformation 52]
105. happy(X0) | patient(X0) [cnf transformation 52]
130. ~old(mary) | wise(mary) [cnf transformation 67]
136. ~brave(mary) [cnf transformation 23]
171. patient(X0) [subsumption resolution 103,105]
245. 23 <=> wise(mary) [avatar definition]
247. wise(mary) <- (23) [avatar component clause 245]
249. 24 <=> old(mary) [avatar definition]
251. ~old(mary) <- (~24) [avatar component clause 249]
252. 23 | ~24 [avatar split clause 130,249,245]
286. ~wise(X1) [resolution 90,171]
305. wise(X0) | brave(X0) | old(X0) [resolution 86,84]
308. old(X0) | brave(X0) [subsumption resolution 305,286]
312. brave(mary) <- (~24) [resolution 308,251]
315. $false <- (~24) [subsumption resolution 312,136]
316. 24 [avatar contradiction clause 315]
318. $false <- (23) [subsumption resolution 247,286]
319. ~23 [avatar contradiction clause 318]
320. $false [avatar sat refutation 252,316,319]
% SZS output end Proof for 6757570965738975833399116
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind and creative is either not old or not brave and vice versa. Everyone who is both not generous and humble is either not funny or brave. Everyone who is not brave is not rich or rich and vice versa. If someone is either not wise or not quiet then someone is either curious or not quiet. Everyone who is either strong or not old is both happy and creative and vice versa. If paul is tall or not calm then john is either humble or not creative. If someone is both not funny and not old then susan is quiet or creative. If paul is both funny and not rich then someone is not generous. If paul is either not funny or old then susan is not happy or not humble. If mary is not calm or generous then susan is both curious and not happy and vice versa. If someone is brave or rich then lucy is either creative or calm and vice versa. Everyone who is not wise or funny is both not rich and not funny. Everyone who is either calm or not wise is brave. Everyone who is tall is calm or not generous and vice versa. If susan is either patient or old then mary is both not patient and strong. Everyone who is both not humble and strong is either not tall or happy. Paul is not generous. Someone is not tall. Someone is tall. Someone is either happy or not brave. Someone is not generous or creative. Alice is either tall or not generous. Lucy is kind. | Alice is brave. | contradiction | (![X]:((kind(X)&creative(X))<=>(~old(X)<~>~brave(X))))&
(![X]:((~generous(X)&humble(X))=>(~funny(X)<~>brave(X))))&
(![X]:(~brave(X)<=>(~rich(X)|rich(X))))&
((?[X]:((~wise(X)<~>~quiet(X))))=>(?[X]:((curious(X)<~>~quiet(X)))))&
(![X]:((strong(X)<~>~old(X))<=>(happy(X)&creative(X))))&
(((tall(paul)|~calm(paul)))=>((humble(john)<~>~creative(john))))&
((?[X]:((~funny(X)&~old(X))))=>((quiet(susan)|creative(susan))))&
(((funny(paul)&~rich(paul)))=>(?[X]:(~generous(X))))&
(((~funny(paul)<~>old(paul)))=>((~happy(susan)|~humble(susan))))&
(((~calm(mary)|generous(mary)))<=>((curious(susan)&~happy(susan))))&
((?[X]:((brave(X)|rich(X))))<=>((creative(lucy)<~>calm(lucy))))&
(![X]:((~wise(X)|funny(X))=>(~rich(X)&~funny(X))))&
(![X]:((calm(X)<~>~wise(X))=>brave(X)))&
(![X]:(tall(X)<=>(calm(X)|~generous(X))))&
(((patient(susan)<~>old(susan)))=>((~patient(mary)&strong(mary))))&
(![X]:((~humble(X)&strong(X))=>(~tall(X)<~>happy(X))))&
(~generous(paul))&
(?[X]:(~tall(X)))&
(?[X]:(tall(X)))&
(?[X]:((happy(X)<~>~brave(X))))&
(?[X]:((~generous(X)|creative(X))))&
((tall(alice)<~>~generous(alice)))&
(kind(lucy)) | brave(alice) | [
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 4856647210649382896163893
% SZS output start Proof for 4856647210649382896163893
3. ! [X0] : (~brave(X0) <=> (rich(X0) | ~rich(X0))) [input p2]
24. brave(alice) [input hypothesis]
44. ! [X0] : ((~brave(X0) | (~rich(X0) & rich(X0))) & ((rich(X0) | ~rich(X0)) | brave(X0))) [nnf transformation 3]
45. ! [X0] : ((~brave(X0) | (~rich(X0) & rich(X0))) & (rich(X0) | ~rich(X0) | brave(X0))) [flattening 44]
86. ~brave(X0) | rich(X0) [cnf transformation 45]
87. ~brave(X0) | ~rich(X0) [cnf transformation 45]
141. brave(alice) [cnf transformation 24]
143. ~brave(X0) [subsumption resolution 86,87]
293. $false [subsumption resolution 141,143]
% SZS output end Proof for 4856647210649382896163893
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not patient or brave then someone is both happy and not happy. Everyone who is either curious or not tall is not brave and vice versa. Everyone who is tall is either not kind or kind. Everyone who is happy or not funny is not tall or not humble and vice versa. If someone is rich then someone is not funny. If paul is both curious and not quiet then someone is not wise or rich and vice versa. Everyone who is both not brave and tall is either not patient or strong and vice versa. If someone is both calm and not brave then someone is calm or brave and vice versa. Everyone who is either not patient or not rich is not wise or not strong. If someone is not happy then someone is not humble or brave and vice versa. Everyone who is not kind or kind is not brave and vice versa. If someone is not happy or funny then lucy is not happy. If someone is not strong then someone is not brave. Everyone who is humble or not rich is both not funny and brave and vice versa. Everyone who is not curious or tall is not brave. Someone is either not calm or quiet. Someone is old or not patient. John is both wise and rich. Susan is rich or not curious. Someone is both quiet and not calm. Someone is creative. | Susan is not wise. | neutral | ((?[X]:((~patient(X)|brave(X))))=>(?[X]:((happy(X)&~happy(X)))))&
(![X]:((curious(X)<~>~tall(X))<=>~brave(X)))&
(![X]:(tall(X)=>(~kind(X)<~>kind(X))))&
(![X]:((happy(X)|~funny(X))<=>(~tall(X)|~humble(X))))&
((?[X]:(rich(X)))=>(?[X]:(~funny(X))))&
(((curious(paul)&~quiet(paul)))<=>(?[X]:((~wise(X)|rich(X)))))&
(![X]:((~brave(X)&tall(X))<=>(~patient(X)<~>strong(X))))&
((?[X]:((calm(X)&~brave(X))))<=>(?[X]:((calm(X)|brave(X)))))&
(![X]:((~patient(X)<~>~rich(X))=>(~wise(X)|~strong(X))))&
((?[X]:(~happy(X)))<=>(?[X]:((~humble(X)|brave(X)))))&
(![X]:((~kind(X)|kind(X))<=>~brave(X)))&
((?[X]:((~happy(X)|funny(X))))=>(~happy(lucy)))&
((?[X]:(~strong(X)))=>(?[X]:(~brave(X))))&
(![X]:((humble(X)|~rich(X))<=>(~funny(X)&brave(X))))&
(![X]:((~curious(X)|tall(X))=>~brave(X)))&
(?[X]:((~calm(X)<~>quiet(X))))&
(?[X]:((old(X)|~patient(X))))&
((wise(john)&rich(john)))&
((rich(susan)|~curious(susan)))&
(?[X]:((quiet(X)&~calm(X))))&
(?[X]:(creative(X))) | ~wise(susan) | [] | null | 0 |
Everyone who is funny is both patient and kind and vice versa.
Everyone who is either curious or not generous is not happy or not funny and vice versa.
If fred is calm then john is wise and vice versa.
If susan is both not kind and old then someone is both patient and not wise and vice versa.
Everyone who is either curious or rich is either not quiet or wise and vice versa.
If mary is both not rich and brave then alice is not rich or rich.
Everyone who is old or not calm is either calm or creative and vice versa.
Everyone who is either creative or not strong is either not calm or not strong.
Everyone who is both not strong and humble is not old.
If susan is both brave and tall then someone is both old and patient.
Everyone who is not kind is not quiet or kind.
Everyone who is both calm and tall is humble.
Everyone who is either not funny or kind is either not brave or not tall and vice versa.
If john is either humble or not curious then alice is both not creative and not curious and vice versa.
Everyone who is not calm is both not curious and creative.
Everyone who is curious or brave is both tall and not strong and vice versa.
Paul is either not tall or tall.
Mary is not rich or not old.
Paul is both not kind and not humble.
Someone is both not happy and not creative.
John is either not patient or wise.
Someone is not quiet or not happy.
Someone is happy or rich. | Susan is old. | neutral | (![X]:(funny(X)<=>(patient(X)&kind(X))))&
(![X]:((curious(X)<~>~generous(X))<=>(~happy(X)|~funny(X))))&
((calm(fred))<=>(wise(john)))&
(((~kind(susan)&old(susan)))<=>(?[X]:((patient(X)&~wise(X)))))&
(![X]:((curious(X)<~>rich(X))<=>(~quiet(X)<~>wise(X))))&
(((~rich(mary)&brave(mary)))=>((~rich(alice)|rich(alice))))&
(![X]:((old(X)|~calm(X))<=>(calm(X)<~>creative(X))))&
(![X]:((creative(X)<~>~strong(X))=>(~calm(X)<~>~strong(X))))&
(![X]:((~strong(X)&humble(X))=>~old(X)))&
(((brave(susan)&tall(susan)))=>(?[X]:((old(X)&patient(X)))))&
(![X]:(~kind(X)=>(~quiet(X)|kind(X))))&
(![X]:((calm(X)&tall(X))=>humble(X)))&
(![X]:((~funny(X)<~>kind(X))<=>(~brave(X)<~>~tall(X))))&
(((humble(john)<~>~curious(john)))<=>((~creative(alice)&~curious(alice))))&
(![X]:(~calm(X)=>(~curious(X)&creative(X))))&
(![X]:((curious(X)|brave(X))<=>(tall(X)&~strong(X))))&
((~tall(paul)<~>tall(paul)))&
((~rich(mary)|~old(mary)))&
((~kind(paul)&~humble(paul)))&
(?[X]:((~happy(X)&~creative(X))))&
((~patient(john)<~>wise(john)))&
(?[X]:((~quiet(X)|~happy(X))))&
(?[X]:((happy(X)|rich(X)))) | old(susan) | [] | null | 0 |
If someone is old or not brave then someone is not patient and vice versa.
If fred is not strong then alice is not patient and vice versa.
Everyone who is brave is patient or not wise and vice versa.
If susan is not quiet then someone is rich or generous and vice versa.
Everyone who is both not calm and not creative is old.
Everyone who is both not old and not wise is not brave and vice versa.
Everyone who is curious is both creative and not wise.
Everyone who is both not creative and not generous is calm or kind and vice versa.
If john is either not strong or patient then someone is not old.
Everyone who is not happy is either brave or not creative.
If alice is both old and not old then fred is not creative or not strong and vice versa.
Everyone who is quiet or tall is not creative or happy.
Everyone who is brave is generous and vice versa.
Everyone who is not patient is either kind or calm.
If someone is not generous then someone is both humble and not old and vice versa.
If fred is patient or not kind then someone is either not wise or happy and vice versa.
Fred is both patient and not tall.
Susan is not curious or tall.
Someone is not funny.
Paul is quiet. | John is humble. | contradiction | ((?[X]:((old(X)|~brave(X))))<=>(?[X]:(~patient(X))))&
((~strong(fred))<=>(~patient(alice)))&
(![X]:(brave(X)<=>(patient(X)|~wise(X))))&
((~quiet(susan))<=>(?[X]:((rich(X)|generous(X)))))&
(![X]:((~calm(X)&~creative(X))=>old(X)))&
(![X]:((~old(X)&~wise(X))<=>~brave(X)))&
(![X]:(curious(X)=>(creative(X)&~wise(X))))&
(![X]:((~creative(X)&~generous(X))<=>(calm(X)|kind(X))))&
(((~strong(john)<~>patient(john)))=>(?[X]:(~old(X))))&
(![X]:(~happy(X)=>(brave(X)<~>~creative(X))))&
(((old(alice)&~old(alice)))<=>((~creative(fred)|~strong(fred))))&
(![X]:((quiet(X)|tall(X))=>(~creative(X)|happy(X))))&
(![X]:(brave(X)<=>generous(X)))&
(![X]:(~patient(X)=>(kind(X)<~>calm(X))))&
((?[X]:(~generous(X)))<=>(?[X]:((humble(X)&~old(X)))))&
(((patient(fred)|~kind(fred)))<=>(?[X]:((~wise(X)<~>happy(X)))))&
((patient(fred)&~tall(fred)))&
((~curious(susan)|tall(susan)))&
(?[X]:(~funny(X)))&
(quiet(paul)) | humble(john) | [
"p0",
"p2",
"p5",
"p7",
"p12",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 68708091297561968076347
% SZS output start Proof for 68708091297561968076347
1. ? [X0] : (~brave(X0) | old(X0)) <=> ? [X0] : ~patient(X0) [input p0]
3. ! [X0] : (brave(X0) <=> (~wise(X0) | patient(X0))) [input p2]
6. ! [X0] : ((~wise(X0) & ~old(X0)) <=> ~brave(X0)) [input p5]
8. ! [X0] : ((~generous(X0) & ~creative(X0)) <=> (kind(X0) | calm(X0))) [input p7]
13. ! [X0] : (brave(X0) <=> generous(X0)) [input p12]
14. ! [X0] : (~patient(X0) => (kind(X0) <~> calm(X0))) [input p13]
15. ? [X0] : ~generous(X0) <=> ? [X0] : (~old(X0) & humble(X0)) [input p14]
21. humble(john) [input hypothesis]
22. ? [X0] : (~brave(X0) | old(X0)) <=> ? [X1] : ~patient(X1) [rectify 1]
23. ? [X0] : ~generous(X0) <=> ? [X1] : (~old(X1) & humble(X1)) [rectify 15]
35. ! [X0] : ((kind(X0) <~> calm(X0)) | patient(X0)) [ennf transformation 14]
36. (? [X0] : (~brave(X0) | old(X0)) | ! [X1] : patient(X1)) & (? [X1] : ~patient(X1) | ! [X0] : (brave(X0) & ~old(X0))) [nnf transformation 22]
37. (? [X0] : (~brave(X0) | old(X0)) | ! [X1] : patient(X1)) & (? [X2] : ~patient(X2) | ! [X3] : (brave(X3) & ~old(X3))) [rectify 36]
38. ? [X0] : (~brave(X0) | old(X0)) => (~brave(sK0) | old(sK0)) [choice axiom]
39. ? [X2] : ~patient(X2) => ~patient(sK1) [choice axiom]
40. ((~brave(sK0) | old(sK0)) | ! [X1] : patient(X1)) & (~patient(sK1) | ! [X3] : (brave(X3) & ~old(X3))) [skolemisation 37,39,38]
42. ! [X0] : ((brave(X0) | (wise(X0) & ~patient(X0))) & ((~wise(X0) | patient(X0)) | ~brave(X0))) [nnf transformation 3]
43. ! [X0] : ((brave(X0) | (wise(X0) & ~patient(X0))) & (~wise(X0) | patient(X0) | ~brave(X0))) [flattening 42]
48. ! [X0] : (((~wise(X0) & ~old(X0)) | brave(X0)) & (~brave(X0) | (wise(X0) | old(X0)))) [nnf transformation 6]
49. ! [X0] : (((~wise(X0) & ~old(X0)) | brave(X0)) & (~brave(X0) | wise(X0) | old(X0))) [flattening 48]
50. ! [X0] : (((~generous(X0) & ~creative(X0)) | (~kind(X0) & ~calm(X0))) & ((kind(X0) | calm(X0)) | (generous(X0) | creative(X0)))) [nnf transformation 8]
51. ! [X0] : (((~generous(X0) & ~creative(X0)) | (~kind(X0) & ~calm(X0))) & (kind(X0) | calm(X0) | generous(X0) | creative(X0))) [flattening 50]
58. ! [X0] : ((brave(X0) | ~generous(X0)) & (generous(X0) | ~brave(X0))) [nnf transformation 13]
59. ! [X0] : (((~calm(X0) | ~kind(X0)) & (calm(X0) | kind(X0))) | patient(X0)) [nnf transformation 35]
60. (? [X0] : ~generous(X0) | ! [X1] : (old(X1) | ~humble(X1))) & (? [X1] : (~old(X1) & humble(X1)) | ! [X0] : generous(X0)) [nnf transformation 23]
61. (? [X0] : ~generous(X0) | ! [X1] : (old(X1) | ~humble(X1))) & (? [X2] : (~old(X2) & humble(X2)) | ! [X3] : generous(X3)) [rectify 60]
62. ? [X0] : ~generous(X0) => ~generous(sK4) [choice axiom]
63. ? [X2] : (~old(X2) & humble(X2)) => (~old(sK5) & humble(sK5)) [choice axiom]
64. (~generous(sK4) | ! [X1] : (old(X1) | ~humble(X1))) & ((~old(sK5) & humble(sK5)) | ! [X3] : generous(X3)) [skolemisation 61,63,62]
70. ~patient(sK1) | ~old(X3) [cnf transformation 40]
77. wise(X0) | brave(X0) [cnf transformation 43]
84. ~wise(X0) | brave(X0) [cnf transformation 49]
88. ~calm(X0) | ~generous(X0) [cnf transformation 51]
89. ~kind(X0) | ~generous(X0) [cnf transformation 51]
100. ~brave(X0) | generous(X0) [cnf transformation 58]
102. kind(X0) | calm(X0) | patient(X0) [cnf transformation 59]
106. ~generous(sK4) | old(X1) | ~humble(X1) [cnf transformation 64]
115. humble(john) [cnf transformation 21]
117. 1 <=> ! [X1] : patient(X1) [avatar definition]
118. patient(X1) <- (1) [avatar component clause 117]
129. 4 <=> ! [X3] : brave(X3) [avatar definition]
130. brave(X3) <- (4) [avatar component clause 129]
132. 5 <=> patient(sK1) [avatar definition]
134. ~patient(sK1) <- (~5) [avatar component clause 132]
137. 6 <=> ! [X3] : ~old(X3) [avatar definition]
138. ~old(X3) <- (6) [avatar component clause 137]
139. 6 | ~5 [avatar split clause 70,132,137]
171. brave(X0) [subsumption resolution 84,77]
172. 4 [avatar split clause 171,129]
201. 19 <=> ! [X1] : (old(X1) | ~humble(X1)) [avatar definition]
202. ~humble(X1) | old(X1) <- (19) [avatar component clause 201]
204. 20 <=> generous(sK4) [avatar definition]
206. ~generous(sK4) <- (~20) [avatar component clause 204]
207. 19 | ~20 [avatar split clause 106,204,201]
209. 21 <=> ! [X3] : generous(X3) [avatar definition]
210. generous(X3) <- (21) [avatar component clause 209]
250. $false <- (~20, 21) [subsumption resolution 206,210]
251. 20 | ~21 [avatar contradiction clause 250]
254. $false <- (1, ~5) [resolution 134,118]
255. ~1 | 5 [avatar contradiction clause 254]
261. generous(X0) <- (4) [resolution 100,130]
264. old(john) <- (19) [resolution 202,115]
289. calm(X0) | patient(X0) | ~generous(X0) [resolution 102,89]
291. calm(X0) | patient(X0) <- (21) [subsumption resolution 289,210]
302. patient(X0) | ~generous(X0) <- (21) [resolution 291,88]
304. patient(X0) <- (21) [subsumption resolution 302,210]
305. 1 | ~21 [avatar split clause 304,209,117]
308. $false <- (6, 19) [resolution 138,264]
313. ~6 | ~19 [avatar contradiction clause 308]
314. 21 | ~4 [avatar split clause 261,129,209]
315. $false [avatar sat refutation 139,172,207,251,255,305,313,314]
% SZS output end Proof for 68708091297561968076347
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old is not creative.
If fred is either not calm or not humble then someone is not patient or patient and vice versa.
Everyone who is not curious or humble is not funny or funny and vice versa.
If someone is both tall and not old then susan is either not happy or not brave.
Everyone who is not happy is either brave or patient and vice versa.
If someone is not calm or strong then someone is both not old and not brave and vice versa.
If john is both not wise and not happy then john is creative and vice versa.
Everyone who is not creative or kind is not happy and vice versa.
If john is not kind or not quiet then mary is both funny and not wise and vice versa.
If fred is strong then lucy is both not strong and happy.
If someone is calm then someone is not strong or not rich and vice versa.
Everyone who is not creative or tall is both patient and not wise.
If alice is not funny or not rich then paul is old or creative and vice versa.
Everyone who is tall is either not patient or wise.
If mary is rich or not funny then lucy is either not humble or creative and vice versa.
If mary is both strong and not patient then someone is not curious or not patient and vice versa.
Alice is both not kind and funny.
Someone is not brave.
Someone is either kind or brave.
Someone is not generous.
Someone is not kind or wise.
Someone is not quiet.
Someone is both brave and not kind.
Someone is either not creative or not patient. | Paul is not tall. | entailment | (![X]:(old(X)=>~creative(X)))&
(((~calm(fred)<~>~humble(fred)))<=>(?[X]:((~patient(X)|patient(X)))))&
(![X]:((~curious(X)|humble(X))<=>(~funny(X)|funny(X))))&
((?[X]:((tall(X)&~old(X))))=>((~happy(susan)<~>~brave(susan))))&
(![X]:(~happy(X)<=>(brave(X)<~>patient(X))))&
((?[X]:((~calm(X)|strong(X))))<=>(?[X]:((~old(X)&~brave(X)))))&
(((~wise(john)&~happy(john)))<=>(creative(john)))&
(![X]:((~creative(X)|kind(X))<=>~happy(X)))&
(((~kind(john)|~quiet(john)))<=>((funny(mary)&~wise(mary))))&
((strong(fred))=>((~strong(lucy)&happy(lucy))))&
((?[X]:(calm(X)))<=>(?[X]:((~strong(X)|~rich(X)))))&
(![X]:((~creative(X)|tall(X))=>(patient(X)&~wise(X))))&
(((~funny(alice)|~rich(alice)))<=>((old(paul)|creative(paul))))&
(![X]:(tall(X)=>(~patient(X)<~>wise(X))))&
(((rich(mary)|~funny(mary)))<=>((~humble(lucy)<~>creative(lucy))))&
(((strong(mary)&~patient(mary)))<=>(?[X]:((~curious(X)|~patient(X)))))&
((~kind(alice)&funny(alice)))&
(?[X]:(~brave(X)))&
(?[X]:((kind(X)<~>brave(X))))&
(?[X]:(~generous(X)))&
(?[X]:((~kind(X)|wise(X))))&
(?[X]:(~quiet(X)))&
(?[X]:((brave(X)&~kind(X))))&
(?[X]:((~creative(X)<~>~patient(X)))) | ~tall(paul) | [
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 2863323167726394853291106
% SZS output start Proof for 2863323167726394853291106
12. ! [X0] : ((tall(X0) | ~creative(X0)) => (~wise(X0) & patient(X0))) [input p11]
14. ! [X0] : (tall(X0) => (~patient(X0) <~> wise(X0))) [input p13]
25. tall(paul) [input hypothesis]
32. ! [X0] : ((~wise(X0) & patient(X0)) | (~tall(X0) & creative(X0))) [ennf transformation 12]
33. ! [X0] : ((~patient(X0) <~> wise(X0)) | ~tall(X0)) [ennf transformation 14]
60. ! [X0] : (((~wise(X0) | patient(X0)) & (wise(X0) | ~patient(X0))) | ~tall(X0)) [nnf transformation 33]
121. patient(X0) | ~tall(X0) [cnf transformation 32]
123. ~wise(X0) | ~tall(X0) [cnf transformation 32]
128. wise(X0) | ~patient(X0) | ~tall(X0) [cnf transformation 60]
152. tall(paul) [cnf transformation 25]
309. ~patient(X0) | ~tall(X0) [subsumption resolution 128,123]
310. ~tall(X0) [subsumption resolution 309,121]
382. $false [subsumption resolution 152,310]
% SZS output end Proof for 2863323167726394853291106
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not old or not kind then alice is calm or old. Everyone who is both kind and not creative is both generous and not brave. If john is tall or happy then someone is not rich or curious and vice versa. Everyone who is kind or humble is both humble and not old and vice versa. Everyone who is either not generous or funny is both not strong and not humble. Everyone who is not humble or calm is not quiet or not old. If lucy is not creative then someone is either wise or not patient and vice versa. Everyone who is either quiet or not generous is not brave. If susan is not tall then someone is either humble or creative. Everyone who is not kind is not rich and vice versa. If john is either not old or kind then mary is either tall or not generous. Everyone who is both patient and funny is either not curious or happy. Everyone who is either funny or not rich is both humble and not tall. Everyone who is rich or not generous is not tall or not strong. Everyone who is tall or patient is calm. If someone is not wise then someone is not rich and vice versa. Susan is both kind and happy. Paul is either not strong or not patient. Paul is generous or not patient. Someone is quiet. Someone is not generous or rich. Someone is not strong or strong. | Mary is not tall. | neutral | ((?[X]:((~old(X)<~>~kind(X))))=>((calm(alice)|old(alice))))&
(![X]:((kind(X)&~creative(X))=>(generous(X)&~brave(X))))&
(((tall(john)|happy(john)))<=>(?[X]:((~rich(X)|curious(X)))))&
(![X]:((kind(X)|humble(X))<=>(humble(X)&~old(X))))&
(![X]:((~generous(X)<~>funny(X))=>(~strong(X)&~humble(X))))&
(![X]:((~humble(X)|calm(X))=>(~quiet(X)|~old(X))))&
((~creative(lucy))<=>(?[X]:((wise(X)<~>~patient(X)))))&
(![X]:((quiet(X)<~>~generous(X))=>~brave(X)))&
((~tall(susan))=>(?[X]:((humble(X)<~>creative(X)))))&
(![X]:(~kind(X)<=>~rich(X)))&
(((~old(john)<~>kind(john)))=>((tall(mary)<~>~generous(mary))))&
(![X]:((patient(X)&funny(X))=>(~curious(X)<~>happy(X))))&
(![X]:((funny(X)<~>~rich(X))=>(humble(X)&~tall(X))))&
(![X]:((rich(X)|~generous(X))=>(~tall(X)|~strong(X))))&
(![X]:((tall(X)|patient(X))=>calm(X)))&
((?[X]:(~wise(X)))<=>(?[X]:(~rich(X))))&
((kind(susan)&happy(susan)))&
((~strong(paul)<~>~patient(paul)))&
((generous(paul)|~patient(paul)))&
(?[X]:(quiet(X)))&
(?[X]:((~generous(X)|rich(X))))&
(?[X]:((~strong(X)|strong(X)))) | ~tall(mary) | [] | null | 0 |
If paul is not funny then lucy is not funny and vice versa.
If john is not calm then mary is not patient or curious.
Everyone who is either not kind or not happy is calm and vice versa.
Everyone who is old is not calm or not kind.
Everyone who is brave is either brave or happy and vice versa.
Everyone who is patient is not patient or not wise.
Everyone who is funny is either curious or not patient.
If lucy is not happy or kind then susan is not happy and vice versa.
If fred is humble then someone is both not old and not tall.
Everyone who is both not calm and funny is both funny and brave and vice versa.
Everyone who is generous is both not generous and not calm.
Everyone who is either generous or not rich is both rich and strong.
Everyone who is either not old or generous is either not humble or not curious and vice versa.
If someone is both not quiet and not wise then john is both not happy and not humble.
Everyone who is either strong or tall is both not tall and patient and vice versa.
If someone is not patient then mary is both not happy and not rich.
Someone is not brave.
Lucy is not calm or happy.
Someone is either brave or generous.
Someone is either not kind or not strong.
Someone is both patient and not funny. | Fred is strong. | entailment | ((~funny(paul))<=>(~funny(lucy)))&
((~calm(john))=>((~patient(mary)|curious(mary))))&
(![X]:((~kind(X)<~>~happy(X))<=>calm(X)))&
(![X]:(old(X)=>(~calm(X)|~kind(X))))&
(![X]:(brave(X)<=>(brave(X)<~>happy(X))))&
(![X]:(patient(X)=>(~patient(X)|~wise(X))))&
(![X]:(funny(X)=>(curious(X)<~>~patient(X))))&
(((~happy(lucy)|kind(lucy)))<=>(~happy(susan)))&
((humble(fred))=>(?[X]:((~old(X)&~tall(X)))))&
(![X]:((~calm(X)&funny(X))<=>(funny(X)&brave(X))))&
(![X]:(generous(X)=>(~generous(X)&~calm(X))))&
(![X]:((generous(X)<~>~rich(X))=>(rich(X)&strong(X))))&
(![X]:((~old(X)<~>generous(X))<=>(~humble(X)<~>~curious(X))))&
((?[X]:((~quiet(X)&~wise(X))))=>((~happy(john)&~humble(john))))&
(![X]:((strong(X)<~>tall(X))<=>(~tall(X)&patient(X))))&
((?[X]:(~patient(X)))=>((~happy(mary)&~rich(mary))))&
(?[X]:(~brave(X)))&
((~calm(lucy)|happy(lucy)))&
(?[X]:((brave(X)<~>generous(X))))&
(?[X]:((~kind(X)<~>~strong(X))))&
(?[X]:((patient(X)&~funny(X)))) | strong(fred) | [
"p10",
"p11",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 5301261595830731000377795
% SZS output start Proof for 5301261595830731000377795
11. ! [X0] : (generous(X0) => (~calm(X0) & ~generous(X0))) [input p10]
12. ! [X0] : ((generous(X0) <~> ~rich(X0)) => (strong(X0) & rich(X0))) [input p11]
15. ! [X0] : ((strong(X0) <~> tall(X0)) <=> (patient(X0) & ~tall(X0))) [input p14]
16. ? [X0] : ~patient(X0) => (~rich(mary) & ~happy(mary)) [input p15]
22. ~strong(fred) [input hypothesis]
31. ! [X0] : ((~calm(X0) & ~generous(X0)) | ~generous(X0)) [ennf transformation 11]
32. ! [X0] : ((strong(X0) & rich(X0)) | (generous(X0) <=> ~rich(X0))) [ennf transformation 12]
33. (~rich(mary) & ~happy(mary)) | ! [X0] : patient(X0) [ennf transformation 16]
44. ! [X0] : ((strong(X0) & rich(X0)) | ((generous(X0) | rich(X0)) & (~rich(X0) | ~generous(X0)))) [nnf transformation 32]
46. ! [X0] : ((((~tall(X0) | ~strong(X0)) & (tall(X0) | strong(X0))) | (~patient(X0) | tall(X0))) & ((patient(X0) & ~tall(X0)) | ((strong(X0) | ~tall(X0)) & (tall(X0) | ~strong(X0))))) [nnf transformation 15]
47. ! [X0] : ((((~tall(X0) | ~strong(X0)) & (tall(X0) | strong(X0))) | ~patient(X0) | tall(X0)) & ((patient(X0) & ~tall(X0)) | ((strong(X0) | ~tall(X0)) & (tall(X0) | ~strong(X0))))) [flattening 46]
81. ~generous(X0) | ~generous(X0) [cnf transformation 31]
84. rich(X0) | generous(X0) | rich(X0) [cnf transformation 44]
96. ~tall(X0) | strong(X0) | ~tall(X0) [cnf transformation 47]
99. tall(X0) | strong(X0) | ~patient(X0) | tall(X0) [cnf transformation 47]
102. ~rich(mary) | patient(X0) [cnf transformation 33]
111. ~strong(fred) [cnf transformation 22]
112. ~tall(X0) | strong(X0) [duplicate literal removal 96]
113. ~patient(X0) | strong(X0) | tall(X0) [duplicate literal removal 99]
114. rich(X0) | generous(X0) [duplicate literal removal 84]
115. ~generous(X0) [duplicate literal removal 81]
157. rich(X0) [subsumption resolution 114,115]
162. patient(X0) [subsumption resolution 102,157]
195. strong(X0) | tall(X0) [resolution 113,162]
196. strong(X0) [subsumption resolution 195,112]
197. $false [resolution 196,111]
% SZS output end Proof for 5301261595830731000377795
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not wise or not calm is both patient and strong and vice versa. If someone is either not funny or not calm then john is not strong or humble and vice versa. If someone is not curious then someone is either humble or brave and vice versa. Everyone who is not brave is either not kind or not curious and vice versa. If susan is both not old and not strong then lucy is both not old and not patient and vice versa. Everyone who is either funny or rich is both not creative and not happy and vice versa. If someone is both not happy and not funny then fred is old. Everyone who is both humble and wise is curious or creative and vice versa. Everyone who is funny is not tall or not rich and vice versa. Everyone who is not wise or not patient is both generous and kind. If susan is either happy or not creative then someone is generous. If paul is creative then someone is patient or not wise. If someone is kind then someone is brave. If someone is brave then someone is either not strong or not kind. Everyone who is not patient or not wise is not generous. If paul is both not strong and not curious then john is not rich or rich and vice versa. Alice is either rich or patient. Someone is either calm or not generous. Paul is either not quiet or patient. Fred is not happy or kind. Someone is both funny and not rich. John is either creative or not happy. Someone is either not quiet or not brave. | Alice is creative. | contradiction | (![X]:((~wise(X)<~>~calm(X))<=>(patient(X)&strong(X))))&
((?[X]:((~funny(X)<~>~calm(X))))<=>((~strong(john)|humble(john))))&
((?[X]:(~curious(X)))<=>(?[X]:((humble(X)<~>brave(X)))))&
(![X]:(~brave(X)<=>(~kind(X)<~>~curious(X))))&
(((~old(susan)&~strong(susan)))<=>((~old(lucy)&~patient(lucy))))&
(![X]:((funny(X)<~>rich(X))<=>(~creative(X)&~happy(X))))&
((?[X]:((~happy(X)&~funny(X))))=>(old(fred)))&
(![X]:((humble(X)&wise(X))<=>(curious(X)|creative(X))))&
(![X]:(funny(X)<=>(~tall(X)|~rich(X))))&
(![X]:((~wise(X)|~patient(X))=>(generous(X)&kind(X))))&
(((happy(susan)<~>~creative(susan)))=>(?[X]:(generous(X))))&
((creative(paul))=>(?[X]:((patient(X)|~wise(X)))))&
((?[X]:(kind(X)))=>(?[X]:(brave(X))))&
((?[X]:(brave(X)))=>(?[X]:((~strong(X)<~>~kind(X)))))&
(![X]:((~patient(X)|~wise(X))=>~generous(X)))&
(((~strong(paul)&~curious(paul)))<=>((~rich(john)|rich(john))))&
((rich(alice)<~>patient(alice)))&
(?[X]:((calm(X)<~>~generous(X))))&
((~quiet(paul)<~>patient(paul)))&
((~happy(fred)|kind(fred)))&
(?[X]:((funny(X)&~rich(X))))&
((creative(john)<~>~happy(john)))&
(?[X]:((~quiet(X)<~>~brave(X)))) | creative(alice) | [
"p5",
"p8",
"p9",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 2982740341489524604478189
% SZS output start Proof for 2982740341489524604478189
6. ! [X0] : ((funny(X0) <~> rich(X0)) <=> (~happy(X0) & ~creative(X0))) [input p5]
9. ! [X0] : (funny(X0) <=> (~rich(X0) | ~tall(X0))) [input p8]
10. ! [X0] : ((~patient(X0) | ~wise(X0)) => (kind(X0) & generous(X0))) [input p9]
15. ! [X0] : ((~wise(X0) | ~patient(X0)) => ~generous(X0)) [input p14]
17. rich(alice) <~> patient(alice) [input p16]
24. creative(alice) [input hypothesis]
29. ! [X0] : ((kind(X0) & generous(X0)) | (patient(X0) & wise(X0))) [ennf transformation 10]
34. ! [X0] : (~generous(X0) | (wise(X0) & patient(X0))) [ennf transformation 15]
50. ! [X0] : ((((~rich(X0) | ~funny(X0)) & (rich(X0) | funny(X0))) | (happy(X0) | creative(X0))) & ((~happy(X0) & ~creative(X0)) | ((funny(X0) | ~rich(X0)) & (rich(X0) | ~funny(X0))))) [nnf transformation 6]
51. ! [X0] : ((((~rich(X0) | ~funny(X0)) & (rich(X0) | funny(X0))) | happy(X0) | creative(X0)) & ((~happy(X0) & ~creative(X0)) | ((funny(X0) | ~rich(X0)) & (rich(X0) | ~funny(X0))))) [flattening 50]
54. ! [X0] : ((funny(X0) | (rich(X0) & tall(X0))) & ((~rich(X0) | ~tall(X0)) | ~funny(X0))) [nnf transformation 9]
55. ! [X0] : ((funny(X0) | (rich(X0) & tall(X0))) & (~rich(X0) | ~tall(X0) | ~funny(X0))) [flattening 54]
70. (~patient(alice) | ~rich(alice)) & (patient(alice) | rich(alice)) [nnf transformation 17]
105. ~creative(X0) | rich(X0) | ~funny(X0) [cnf transformation 51]
119. rich(X0) | funny(X0) [cnf transformation 55]
121. generous(X0) | patient(X0) [cnf transformation 29]
130. ~generous(X0) | patient(X0) [cnf transformation 34]
138. ~patient(alice) | ~rich(alice) [cnf transformation 70]
150. creative(alice) [cnf transformation 24]
281. patient(X0) [subsumption resolution 130,121]
298. ~rich(alice) [subsumption resolution 138,281]
354. funny(alice) [resolution 119,298]
396. rich(alice) | ~funny(alice) [resolution 105,150]
398. ~funny(alice) [subsumption resolution 396,298]
399. $false [subsumption resolution 398,354]
% SZS output end Proof for 2982740341489524604478189
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not generous and patient is rich and vice versa.
Everyone who is not calm is both patient and curious and vice versa.
Everyone who is not curious is either not tall or humble and vice versa.
If paul is either wise or curious then someone is either funny or not happy.
Everyone who is not tall is generous or strong and vice versa.
Everyone who is not humble or not old is rich or quiet.
Everyone who is funny is strong and vice versa.
If susan is calm then someone is kind or strong.
Everyone who is humble is not rich and vice versa.
If someone is not kind or generous then someone is either not wise or generous.
Everyone who is generous or old is both quiet and not creative.
If someone is both not tall and tall then susan is either not patient or not wise.
Everyone who is not humble is both strong and not quiet and vice versa.
Everyone who is either wise or curious is both kind and not tall and vice versa.
Everyone who is both not generous and not old is both not tall and not brave.
If lucy is not humble then someone is not rich or quiet.
Someone is not tall or happy.
Susan is both not creative and brave.
Someone is both not wise and calm.
Someone is funny or not brave.
Someone is not funny.
Someone is not old or not creative.
Someone is either not quiet or not strong.
Someone is both not funny and calm. | Susan is not rich. | entailment | (![X]:((~generous(X)&patient(X))<=>rich(X)))&
(![X]:(~calm(X)<=>(patient(X)&curious(X))))&
(![X]:(~curious(X)<=>(~tall(X)<~>humble(X))))&
(((wise(paul)<~>curious(paul)))=>(?[X]:((funny(X)<~>~happy(X)))))&
(![X]:(~tall(X)<=>(generous(X)|strong(X))))&
(![X]:((~humble(X)|~old(X))=>(rich(X)|quiet(X))))&
(![X]:(funny(X)<=>strong(X)))&
((calm(susan))=>(?[X]:((kind(X)|strong(X)))))&
(![X]:(humble(X)<=>~rich(X)))&
((?[X]:((~kind(X)|generous(X))))=>(?[X]:((~wise(X)<~>generous(X)))))&
(![X]:((generous(X)|old(X))=>(quiet(X)&~creative(X))))&
((?[X]:((~tall(X)&tall(X))))=>((~patient(susan)<~>~wise(susan))))&
(![X]:(~humble(X)<=>(strong(X)&~quiet(X))))&
(![X]:((wise(X)<~>curious(X))<=>(kind(X)&~tall(X))))&
(![X]:((~generous(X)&~old(X))=>(~tall(X)&~brave(X))))&
((~humble(lucy))=>(?[X]:((~rich(X)|quiet(X)))))&
(?[X]:((~tall(X)|happy(X))))&
((~creative(susan)&brave(susan)))&
(?[X]:((~wise(X)&calm(X))))&
(?[X]:((funny(X)|~brave(X))))&
(?[X]:(~funny(X)))&
(?[X]:((~old(X)|~creative(X))))&
(?[X]:((~quiet(X)<~>~strong(X))))&
(?[X]:((~funny(X)&calm(X)))) | ~rich(susan) | [
"p0",
"p8",
"p10",
"p12",
"p14",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 1304030570916355976318794
% SZS output start Proof for 1304030570916355976318794
1. ! [X0] : ((patient(X0) & ~generous(X0)) <=> rich(X0)) [input p0]
9. ! [X0] : (humble(X0) <=> ~rich(X0)) [input p8]
11. ! [X0] : ((old(X0) | generous(X0)) => (~creative(X0) & quiet(X0))) [input p10]
13. ! [X0] : (~humble(X0) <=> (~quiet(X0) & strong(X0))) [input p12]
15. ! [X0] : ((~old(X0) & ~generous(X0)) => (~brave(X0) & ~tall(X0))) [input p14]
18. brave(susan) & ~creative(susan) [input p17]
25. rich(susan) [input hypothesis]
27. ! [X0] : ((old(X0) | generous(X0)) => quiet(X0)) [pure predicate removal 11]
28. brave(susan) [pure predicate removal 18]
35. ! [X0] : (quiet(X0) | (~old(X0) & ~generous(X0))) [ennf transformation 27]
37. ! [X0] : ((~brave(X0) & ~tall(X0)) | (old(X0) | generous(X0))) [ennf transformation 15]
38. ! [X0] : ((~brave(X0) & ~tall(X0)) | old(X0) | generous(X0)) [flattening 37]
40. ! [X0] : (((patient(X0) & ~generous(X0)) | ~rich(X0)) & (rich(X0) | (~patient(X0) | generous(X0)))) [nnf transformation 1]
41. ! [X0] : (((patient(X0) & ~generous(X0)) | ~rich(X0)) & (rich(X0) | ~patient(X0) | generous(X0))) [flattening 40]
53. ! [X0] : ((humble(X0) | rich(X0)) & (~rich(X0) | ~humble(X0))) [nnf transformation 9]
59. ! [X0] : ((~humble(X0) | (quiet(X0) | ~strong(X0))) & ((~quiet(X0) & strong(X0)) | humble(X0))) [nnf transformation 13]
60. ! [X0] : ((~humble(X0) | quiet(X0) | ~strong(X0)) & ((~quiet(X0) & strong(X0)) | humble(X0))) [flattening 59]
79. ~rich(X0) | ~generous(X0) [cnf transformation 41]
100. ~humble(X0) | ~rich(X0) [cnf transformation 53]
107. ~old(X0) | quiet(X0) [cnf transformation 35]
111. ~quiet(X0) | humble(X0) [cnf transformation 60]
120. ~brave(X0) | old(X0) | generous(X0) [cnf transformation 38]
123. brave(susan) [cnf transformation 28]
132. rich(susan) [cnf transformation 25]
226. ~generous(susan) [resolution 79,132]
378. old(susan) | generous(susan) [resolution 120,123]
379. old(susan) [subsumption resolution 378,226]
386. quiet(susan) [resolution 379,107]
417. humble(susan) [resolution 386,111]
510. ~rich(susan) [resolution 417,100]
521. $false [subsumption resolution 510,132]
% SZS output end Proof for 1304030570916355976318794
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both brave and not creative is either curious or kind and vice versa.
Everyone who is wise or not curious is both not creative and not patient.
If someone is both not rich and not old then someone is either rich or curious.
Everyone who is both humble and creative is not quiet or kind and vice versa.
Everyone who is humble is wise.
Everyone who is both not happy and not funny is both not strong and happy.
Everyone who is not wise is not brave or happy and vice versa.
Everyone who is strong is either funny or curious.
If susan is not wise or not strong then fred is strong and vice versa.
Everyone who is not calm or funny is not funny and vice versa.
Everyone who is either not kind or not tall is either rich or not patient and vice versa.
Everyone who is both happy and not kind is either not strong or not old and vice versa.
If someone is both not patient and old then fred is both not curious and humble and vice versa.
If someone is both not strong and not funny then someone is brave and vice versa.
Everyone who is not funny or curious is not brave or tall and vice versa.
Someone is either kind or patient.
Susan is not patient or not creative.
Someone is either patient or not patient.
Alice is not quiet or not kind.
Susan is either not rich or not quiet. | Susan is strong. | entailment | (![X]:((brave(X)&~creative(X))<=>(curious(X)<~>kind(X))))&
(![X]:((wise(X)|~curious(X))=>(~creative(X)&~patient(X))))&
((?[X]:((~rich(X)&~old(X))))=>(?[X]:((rich(X)<~>curious(X)))))&
(![X]:((humble(X)&creative(X))<=>(~quiet(X)|kind(X))))&
(![X]:(humble(X)=>wise(X)))&
(![X]:((~happy(X)&~funny(X))=>(~strong(X)&happy(X))))&
(![X]:(~wise(X)<=>(~brave(X)|happy(X))))&
(![X]:(strong(X)=>(funny(X)<~>curious(X))))&
(((~wise(susan)|~strong(susan)))<=>(strong(fred)))&
(![X]:((~calm(X)|funny(X))<=>~funny(X)))&
(![X]:((~kind(X)<~>~tall(X))<=>(rich(X)<~>~patient(X))))&
(![X]:((happy(X)&~kind(X))<=>(~strong(X)<~>~old(X))))&
((?[X]:((~patient(X)&old(X))))<=>((~curious(fred)&humble(fred))))&
((?[X]:((~strong(X)&~funny(X))))<=>(?[X]:(brave(X))))&
(![X]:((~funny(X)|curious(X))<=>(~brave(X)|tall(X))))&
(?[X]:((kind(X)<~>patient(X))))&
((~patient(susan)|~creative(susan)))&
(?[X]:((patient(X)<~>~patient(X))))&
((~quiet(alice)|~kind(alice)))&
((~rich(susan)<~>~quiet(susan))) | strong(susan) | [
"p0",
"p1",
"p3",
"p4",
"p5",
"p6",
"p9",
"p10",
"p11",
"p12",
"p14",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 5369095715030632775962191
% SZS output start Proof for 5369095715030632775962191
1. ! [X0] : ((~creative(X0) & brave(X0)) <=> (curious(X0) <~> kind(X0))) [input p0]
2. ! [X0] : ((~curious(X0) | wise(X0)) => (~patient(X0) & ~creative(X0))) [input p1]
4. ! [X0] : ((creative(X0) & humble(X0)) <=> (kind(X0) | ~quiet(X0))) [input p3]
5. ! [X0] : (humble(X0) => wise(X0)) [input p4]
6. ! [X0] : ((~funny(X0) & ~happy(X0)) => (happy(X0) & ~strong(X0))) [input p5]
7. ! [X0] : (~wise(X0) <=> (happy(X0) | ~brave(X0))) [input p6]
10. ! [X0] : ((funny(X0) | ~calm(X0)) <=> ~funny(X0)) [input p9]
11. ! [X0] : ((~kind(X0) <~> ~tall(X0)) <=> (rich(X0) <~> ~patient(X0))) [input p10]
12. ! [X0] : ((~kind(X0) & happy(X0)) <=> (~strong(X0) <~> ~old(X0))) [input p11]
13. ? [X0] : (old(X0) & ~patient(X0)) <=> (humble(fred) & ~curious(fred)) [input p12]
15. ! [X0] : ((curious(X0) | ~funny(X0)) <=> (tall(X0) | ~brave(X0))) [input p14]
20. ~rich(susan) <~> ~quiet(susan) [input p19]
21. ~strong(susan) [input hypothesis]
24. ! [X0] : ((~patient(X0) & ~creative(X0)) | (curious(X0) & ~wise(X0))) [ennf transformation 2]
26. ! [X0] : (wise(X0) | ~humble(X0)) [ennf transformation 5]
27. ! [X0] : ((happy(X0) & ~strong(X0)) | (funny(X0) | happy(X0))) [ennf transformation 6]
28. ! [X0] : ((happy(X0) & ~strong(X0)) | funny(X0) | happy(X0)) [flattening 27]
30. ! [X0] : (((~creative(X0) & brave(X0)) | ((curious(X0) | ~kind(X0)) & (kind(X0) | ~curious(X0)))) & (((~kind(X0) | ~curious(X0)) & (kind(X0) | curious(X0))) | (creative(X0) | ~brave(X0)))) [nnf transformation 1]
31. ! [X0] : (((~creative(X0) & brave(X0)) | ((curious(X0) | ~kind(X0)) & (kind(X0) | ~curious(X0)))) & (((~kind(X0) | ~curious(X0)) & (kind(X0) | curious(X0))) | creative(X0) | ~brave(X0))) [flattening 30]
36. ! [X0] : (((creative(X0) & humble(X0)) | (~kind(X0) & quiet(X0))) & ((kind(X0) | ~quiet(X0)) | (~creative(X0) | ~humble(X0)))) [nnf transformation 4]
37. ! [X0] : (((creative(X0) & humble(X0)) | (~kind(X0) & quiet(X0))) & (kind(X0) | ~quiet(X0) | ~creative(X0) | ~humble(X0))) [flattening 36]
38. ! [X0] : ((~wise(X0) | (~happy(X0) & brave(X0))) & ((happy(X0) | ~brave(X0)) | wise(X0))) [nnf transformation 7]
39. ! [X0] : ((~wise(X0) | (~happy(X0) & brave(X0))) & (happy(X0) | ~brave(X0) | wise(X0))) [flattening 38]
43. ! [X0] : (((funny(X0) | ~calm(X0)) | funny(X0)) & (~funny(X0) | (~funny(X0) & calm(X0)))) [nnf transformation 10]
44. ! [X0] : ((funny(X0) | ~calm(X0) | funny(X0)) & (~funny(X0) | (~funny(X0) & calm(X0)))) [flattening 43]
45. ! [X0] : ((((tall(X0) | kind(X0)) & (~tall(X0) | ~kind(X0))) | ((rich(X0) | patient(X0)) & (~patient(X0) | ~rich(X0)))) & (((patient(X0) | ~rich(X0)) & (~patient(X0) | rich(X0))) | ((~kind(X0) | tall(X0)) & (~tall(X0) | kind(X0))))) [nnf transformation 11]
46. ! [X0] : (((~kind(X0) & happy(X0)) | ((~strong(X0) | old(X0)) & (~old(X0) | strong(X0)))) & (((old(X0) | strong(X0)) & (~old(X0) | ~strong(X0))) | (kind(X0) | ~happy(X0)))) [nnf transformation 12]
47. ! [X0] : (((~kind(X0) & happy(X0)) | ((~strong(X0) | old(X0)) & (~old(X0) | strong(X0)))) & (((old(X0) | strong(X0)) & (~old(X0) | ~strong(X0))) | kind(X0) | ~happy(X0))) [flattening 46]
48. (? [X0] : (old(X0) & ~patient(X0)) | (~humble(fred) | curious(fred))) & ((humble(fred) & ~curious(fred)) | ! [X0] : (~old(X0) | patient(X0))) [nnf transformation 13]
49. (? [X0] : (old(X0) & ~patient(X0)) | ~humble(fred) | curious(fred)) & ((humble(fred) & ~curious(fred)) | ! [X0] : (~old(X0) | patient(X0))) [flattening 48]
50. (? [X0] : (old(X0) & ~patient(X0)) | ~humble(fred) | curious(fred)) & ((humble(fred) & ~curious(fred)) | ! [X1] : (~old(X1) | patient(X1))) [rectify 49]
51. ? [X0] : (old(X0) & ~patient(X0)) => (old(sK1) & ~patient(sK1)) [choice axiom]
52. ((old(sK1) & ~patient(sK1)) | ~humble(fred) | curious(fred)) & ((humble(fred) & ~curious(fred)) | ! [X1] : (~old(X1) | patient(X1))) [skolemisation 50,51]
58. ! [X0] : (((curious(X0) | ~funny(X0)) | (~tall(X0) & brave(X0))) & ((tall(X0) | ~brave(X0)) | (~curious(X0) & funny(X0)))) [nnf transformation 15]
59. ! [X0] : ((curious(X0) | ~funny(X0) | (~tall(X0) & brave(X0))) & (tall(X0) | ~brave(X0) | (~curious(X0) & funny(X0)))) [flattening 58]
66. (quiet(susan) | rich(susan)) & (~quiet(susan) | ~rich(susan)) [nnf transformation 20]
69. ~curious(X0) | kind(X0) | brave(X0) [cnf transformation 31]
76. ~patient(X0) | curious(X0) [cnf transformation 24]
80. quiet(X0) | humble(X0) [cnf transformation 37]
81. ~kind(X0) | humble(X0) [cnf transformation 37]
84. ~humble(X0) | wise(X0) [cnf transformation 26]
86. happy(X0) | funny(X0) | happy(X0) [cnf transformation 28]
89. ~happy(X0) | ~wise(X0) [cnf transformation 39]
96. ~funny(X0) | ~funny(X0) [cnf transformation 44]
98. ~tall(X0) | rich(X0) | ~patient(X0) | kind(X0) [cnf transformation 45]
107. ~happy(X0) | strong(X0) | kind(X0) | old(X0) [cnf transformation 47]
113. humble(fred) | ~old(X1) | patient(X1) [cnf transformation 52]
119. tall(X0) | ~brave(X0) | funny(X0) [cnf transformation 59]
129. ~quiet(susan) | ~rich(susan) [cnf transformation 66]
131. ~strong(susan) [cnf transformation 21]
132. ~funny(X0) [duplicate literal removal 96]
134. funny(X0) | happy(X0) [duplicate literal removal 86]
153. 5 <=> wise(susan) [avatar definition]
154. wise(susan) <- (5) [avatar component clause 153]
157. 6 <=> strong(susan) [avatar definition]
159. ~strong(susan) <- (~6) [avatar component clause 157]
168. 8 <=> humble(fred) [avatar definition]
169. humble(fred) <- (8) [avatar component clause 168]
182. 11 <=> ! [X1] : (~old(X1) | patient(X1)) [avatar definition]
183. ~old(X1) | patient(X1) <- (11) [avatar component clause 182]
184. 11 | 8 [avatar split clause 113,168,182]
203. ~brave(X0) | tall(X0) [subsumption resolution 119,132]
215. 18 <=> patient(susan) [avatar definition]
216. patient(susan) <- (18) [avatar component clause 215]
233. 22 <=> rich(susan) [avatar definition]
234. ~rich(susan) <- (~22) [avatar component clause 233]
237. 23 <=> quiet(susan) [avatar definition]
238. ~quiet(susan) <- (~23) [avatar component clause 237]
241. ~22 | ~23 [avatar split clause 129,237,233]
242. ~6 [avatar split clause 131,157]
247. humble(susan) <- (~23) [resolution 80,238]
256. wise(fred) <- (8) [resolution 84,169]
257. wise(susan) <- (~23) [resolution 84,247]
259. 5 | 23 [avatar split clause 257,237,153]
268. happy(X0) [resolution 134,132]
270. ~wise(X0) [resolution 268,89]
274. 24 <=> brave(susan) [avatar definition]
276. brave(susan) <- (24) [avatar component clause 274]
278. 25 <=> kind(susan) [avatar definition]
279. ~kind(susan) <- (~25) [avatar component clause 278]
280. kind(susan) <- (25) [avatar component clause 278]
288. $false <- (8) [resolution 270,256]
289. ~8 [avatar contradiction clause 288]
431. strong(X0) | kind(X0) | old(X0) [resolution 107,268]
432. kind(susan) | old(susan) <- (~6) [resolution 431,159]
443. 39 <=> old(susan) [avatar definition]
445. old(susan) <- (39) [avatar component clause 443]
446. 39 | 25 | 6 [avatar split clause 432,157,278,443]
471. 42 <=> curious(susan) [avatar definition]
472. curious(susan) <- (42) [avatar component clause 471]
483. 43 <=> humble(susan) [avatar definition]
484. humble(susan) <- (43) [avatar component clause 483]
495. patient(susan) <- (11, 39) [resolution 445,183]
498. 18 | ~11 | ~39 [avatar split clause 495,443,182,215]
500. curious(susan) <- (18) [resolution 216,76]
502. 42 | ~18 [avatar split clause 500,215,471]
510. kind(susan) | brave(susan) <- (42) [resolution 472,69]
511. brave(susan) <- (~25, 42) [subsumption resolution 510,279]
514. 24 | 25 | ~42 [avatar split clause 511,471,278,274]
517. tall(susan) <- (24) [resolution 276,203]
521. rich(susan) | ~patient(susan) | kind(susan) <- (24) [resolution 517,98]
522. ~patient(susan) | kind(susan) <- (~22, 24) [subsumption resolution 521,234]
526. 25 | ~18 | 22 | ~24 [avatar split clause 522,274,233,215,278]
533. $false <- (5) [subsumption resolution 154,270]
534. ~5 [avatar contradiction clause 533]
541. humble(susan) <- (25) [resolution 280,81]
542. 43 | ~25 [avatar split clause 541,278,483]
543. wise(susan) <- (43) [resolution 484,84]
544. $false <- (43) [subsumption resolution 543,270]
545. ~43 [avatar contradiction clause 544]
546. $false [avatar sat refutation 184,241,242,259,289,446,498,502,514,526,534,542,545]
% SZS output end Proof for 5369095715030632775962191
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not calm and not kind is both quiet and not creative and vice versa.
If someone is either quiet or tall then lucy is not rich and vice versa.
Everyone who is both creative and not tall is not quiet or not generous.
If susan is both happy and not tall then alice is rich and vice versa.
If someone is not creative or not wise then lucy is both not curious and patient.
If paul is either not funny or not kind then paul is rich or not creative.
Everyone who is tall or not happy is either curious or wise and vice versa.
Everyone who is both not creative and wise is strong and vice versa.
Everyone who is not funny or not happy is both not rich and not strong and vice versa.
Everyone who is not patient or not quiet is old or calm and vice versa.
Everyone who is happy is both funny and not old.
Everyone who is humble is either strong or not patient.
Everyone who is either not happy or brave is not old or funny and vice versa.
Everyone who is either brave or not old is wise or kind and vice versa.
Everyone who is either funny or creative is both rich and humble and vice versa.
If mary is not generous or not rich then someone is wise.
Susan is both happy and humble.
Alice is both tall and not old.
Someone is not old or not generous.
Fred is rich.
Alice is not generous or not kind.
Paul is curious.
Someone is not humble. | Paul is not creative. | neutral | (![X]:((~calm(X)&~kind(X))<=>(quiet(X)&~creative(X))))&
((?[X]:((quiet(X)<~>tall(X))))<=>(~rich(lucy)))&
(![X]:((creative(X)&~tall(X))=>(~quiet(X)|~generous(X))))&
(((happy(susan)&~tall(susan)))<=>(rich(alice)))&
((?[X]:((~creative(X)|~wise(X))))=>((~curious(lucy)&patient(lucy))))&
(((~funny(paul)<~>~kind(paul)))=>((rich(paul)|~creative(paul))))&
(![X]:((tall(X)|~happy(X))<=>(curious(X)<~>wise(X))))&
(![X]:((~creative(X)&wise(X))<=>strong(X)))&
(![X]:((~funny(X)|~happy(X))<=>(~rich(X)&~strong(X))))&
(![X]:((~patient(X)|~quiet(X))<=>(old(X)|calm(X))))&
(![X]:(happy(X)=>(funny(X)&~old(X))))&
(![X]:(humble(X)=>(strong(X)<~>~patient(X))))&
(![X]:((~happy(X)<~>brave(X))<=>(~old(X)|funny(X))))&
(![X]:((brave(X)<~>~old(X))<=>(wise(X)|kind(X))))&
(![X]:((funny(X)<~>creative(X))<=>(rich(X)&humble(X))))&
(((~generous(mary)|~rich(mary)))=>(?[X]:(wise(X))))&
((happy(susan)&humble(susan)))&
((tall(alice)&~old(alice)))&
(?[X]:((~old(X)|~generous(X))))&
(rich(fred))&
((~generous(alice)|~kind(alice)))&
(curious(paul))&
(?[X]:(~humble(X))) | ~creative(paul) | [] | null | 0 |
Everyone who is kind is either not humble or brave and vice versa.
If alice is either funny or calm then someone is not brave.
Everyone who is both not generous and not brave is either strong or kind.
Everyone who is both creative and brave is both not happy and not creative.
If mary is not wise then susan is either happy or funny and vice versa.
If someone is humble then paul is not wise.
Everyone who is not old or tall is not rich or humble.
If john is both not kind and not creative then susan is not calm and vice versa.
Everyone who is both tall and calm is either not generous or not calm and vice versa.
If susan is not rich then someone is either not funny or old and vice versa.
Everyone who is either wise or rich is creative and vice versa.
Everyone who is not tall is both quiet and not funny.
If paul is both not wise and not curious then john is either quiet or not brave.
Everyone who is not humble is rich or not calm.
If someone is both humble and calm then someone is not quiet.
Everyone who is both calm and rich is either calm or strong.
Someone is not rich.
Someone is both not quiet and patient.
Susan is not generous or not humble.
Paul is both rich and not kind.
Someone is both happy and not rich.
Susan is not wise or rich.
Paul is both not quiet and not patient.
Someone is both not rich and not old. | John is kind. | neutral | (![X]:(kind(X)<=>(~humble(X)<~>brave(X))))&
(((funny(alice)<~>calm(alice)))=>(?[X]:(~brave(X))))&
(![X]:((~generous(X)&~brave(X))=>(strong(X)<~>kind(X))))&
(![X]:((creative(X)&brave(X))=>(~happy(X)&~creative(X))))&
((~wise(mary))<=>((happy(susan)<~>funny(susan))))&
((?[X]:(humble(X)))=>(~wise(paul)))&
(![X]:((~old(X)|tall(X))=>(~rich(X)|humble(X))))&
(((~kind(john)&~creative(john)))<=>(~calm(susan)))&
(![X]:((tall(X)&calm(X))<=>(~generous(X)<~>~calm(X))))&
((~rich(susan))<=>(?[X]:((~funny(X)<~>old(X)))))&
(![X]:((wise(X)<~>rich(X))<=>creative(X)))&
(![X]:(~tall(X)=>(quiet(X)&~funny(X))))&
(((~wise(paul)&~curious(paul)))=>((quiet(john)<~>~brave(john))))&
(![X]:(~humble(X)=>(rich(X)|~calm(X))))&
((?[X]:((humble(X)&calm(X))))=>(?[X]:(~quiet(X))))&
(![X]:((calm(X)&rich(X))=>(calm(X)<~>strong(X))))&
(?[X]:(~rich(X)))&
(?[X]:((~quiet(X)&patient(X))))&
((~generous(susan)|~humble(susan)))&
((rich(paul)&~kind(paul)))&
(?[X]:((happy(X)&~rich(X))))&
((~wise(susan)|rich(susan)))&
((~quiet(paul)&~patient(paul)))&
(?[X]:((~rich(X)&~old(X)))) | kind(john) | [] | null | 0 |
If paul is old or not quiet then john is either not humble or patient and vice versa. If someone is both not generous and not funny then someone is not quiet. Everyone who is quiet or not curious is both not funny and generous and vice versa. If fred is both humble and not creative then someone is brave or not curious and vice versa. If fred is generous then john is funny and vice versa. Everyone who is not strong is creative or not generous and vice versa. If someone is either kind or not old then mary is both tall and not calm. Everyone who is both strong and not old is not happy or not generous and vice versa. Everyone who is calm is not quiet. Everyone who is both happy and not creative is not quiet or generous and vice versa. Everyone who is not calm is not funny or old and vice versa. Everyone who is both generous and not happy is not wise or not generous and vice versa. If someone is both quiet and rich then someone is either not kind or not humble and vice versa. If someone is either not happy or not wise then someone is rich or not quiet. Everyone who is both kind and strong is not quiet or not kind. Someone is strong. Someone is either not calm or not humble. Alice is both humble and not funny. Paul is either not funny or not curious. Someone is both old and not rich. | Mary is not rich. | neutral | (((old(paul)|~quiet(paul)))<=>((~humble(john)<~>patient(john))))&
((?[X]:((~generous(X)&~funny(X))))=>(?[X]:(~quiet(X))))&
(![X]:((quiet(X)|~curious(X))<=>(~funny(X)&generous(X))))&
(((humble(fred)&~creative(fred)))<=>(?[X]:((brave(X)|~curious(X)))))&
((generous(fred))<=>(funny(john)))&
(![X]:(~strong(X)<=>(creative(X)|~generous(X))))&
((?[X]:((kind(X)<~>~old(X))))=>((tall(mary)&~calm(mary))))&
(![X]:((strong(X)&~old(X))<=>(~happy(X)|~generous(X))))&
(![X]:(calm(X)=>~quiet(X)))&
(![X]:((happy(X)&~creative(X))<=>(~quiet(X)|generous(X))))&
(![X]:(~calm(X)<=>(~funny(X)|old(X))))&
(![X]:((generous(X)&~happy(X))<=>(~wise(X)|~generous(X))))&
((?[X]:((quiet(X)&rich(X))))<=>(?[X]:((~kind(X)<~>~humble(X)))))&
((?[X]:((~happy(X)<~>~wise(X))))=>(?[X]:((rich(X)|~quiet(X)))))&
(![X]:((kind(X)&strong(X))=>(~quiet(X)|~kind(X))))&
(?[X]:(strong(X)))&
(?[X]:((~calm(X)<~>~humble(X))))&
((humble(alice)&~funny(alice)))&
((~funny(paul)<~>~curious(paul)))&
(?[X]:((old(X)&~rich(X)))) | ~rich(mary) | [] | null | 0 |
If someone is not quiet or not patient then alice is not old or brave and vice versa. If someone is calm or not brave then someone is humble. Everyone who is curious or not funny is funny or wise. Everyone who is both calm and not rich is either not calm or not patient. Everyone who is either humble or not strong is brave or not patient. If someone is not old or funny then someone is both wise and creative and vice versa. If someone is not happy or not tall then fred is both kind and old and vice versa. If someone is not calm then someone is either not tall or not kind and vice versa. If someone is quiet then someone is patient. If someone is either not creative or not rich then someone is brave or humble and vice versa. Everyone who is not old or kind is both humble and not old and vice versa. Everyone who is both not calm and not happy is both not old and not strong and vice versa. If someone is curious then someone is both not curious and happy and vice versa. Everyone who is old is creative or brave and vice versa. Everyone who is not rich is both creative and brave and vice versa. If fred is both not rich and kind then john is not curious or humble. John is calm or generous. Someone is not strong. Fred is both patient and happy. Someone is humble or old. Paul is either not strong or not curious. Someone is humble or not strong. Someone is strong. Fred is either curious or not tall. | Paul is kind. | neutral | ((?[X]:((~quiet(X)|~patient(X))))<=>((~old(alice)|brave(alice))))&
((?[X]:((calm(X)|~brave(X))))=>(?[X]:(humble(X))))&
(![X]:((curious(X)|~funny(X))=>(funny(X)|wise(X))))&
(![X]:((calm(X)&~rich(X))=>(~calm(X)<~>~patient(X))))&
(![X]:((humble(X)<~>~strong(X))=>(brave(X)|~patient(X))))&
((?[X]:((~old(X)|funny(X))))<=>(?[X]:((wise(X)&creative(X)))))&
((?[X]:((~happy(X)|~tall(X))))<=>((kind(fred)&old(fred))))&
((?[X]:(~calm(X)))<=>(?[X]:((~tall(X)<~>~kind(X)))))&
((?[X]:(quiet(X)))=>(?[X]:(patient(X))))&
((?[X]:((~creative(X)<~>~rich(X))))<=>(?[X]:((brave(X)|humble(X)))))&
(![X]:((~old(X)|kind(X))<=>(humble(X)&~old(X))))&
(![X]:((~calm(X)&~happy(X))<=>(~old(X)&~strong(X))))&
((?[X]:(curious(X)))<=>(?[X]:((~curious(X)&happy(X)))))&
(![X]:(old(X)<=>(creative(X)|brave(X))))&
(![X]:(~rich(X)<=>(creative(X)&brave(X))))&
(((~rich(fred)&kind(fred)))=>((~curious(john)|humble(john))))&
((calm(john)|generous(john)))&
(?[X]:(~strong(X)))&
((patient(fred)&happy(fred)))&
(?[X]:((humble(X)|old(X))))&
((~strong(paul)<~>~curious(paul)))&
(?[X]:((humble(X)|~strong(X))))&
(?[X]:(strong(X)))&
((curious(fred)<~>~tall(fred))) | kind(paul) | [] | null | 0 |
If someone is either curious or rich then someone is not happy or not tall. Everyone who is not brave or patient is creative or wise and vice versa. Everyone who is both not calm and generous is not strong or strong and vice versa. If fred is either not happy or strong then paul is either not kind or not creative. Everyone who is either quiet or strong is not brave or not humble. Everyone who is not funny is not brave or not quiet. Everyone who is either not tall or not funny is either not curious or not calm. If someone is either not rich or calm then paul is either brave or not kind. Everyone who is wise or not kind is both humble and not curious. Everyone who is both generous and wise is either not humble or rich. Everyone who is funny or not rich is both not humble and calm. Everyone who is not funny is not curious and vice versa. Everyone who is not old is curious or not kind. If lucy is either tall or not tall then someone is tall or happy. Everyone who is wise or not kind is both funny and not tall. Everyone who is kind or patient is either not calm or creative and vice versa. Alice is either funny or not humble. Someone is both kind and not humble. Someone is either not strong or not curious. Someone is either old or quiet. Someone is funny or not tall. Lucy is strong. | Paul is not wise. | entailment | ((?[X]:((curious(X)<~>rich(X))))=>(?[X]:((~happy(X)|~tall(X)))))&
(![X]:((~brave(X)|patient(X))<=>(creative(X)|wise(X))))&
(![X]:((~calm(X)&generous(X))<=>(~strong(X)|strong(X))))&
(((~happy(fred)<~>strong(fred)))=>((~kind(paul)<~>~creative(paul))))&
(![X]:((quiet(X)<~>strong(X))=>(~brave(X)|~humble(X))))&
(![X]:(~funny(X)=>(~brave(X)|~quiet(X))))&
(![X]:((~tall(X)<~>~funny(X))=>(~curious(X)<~>~calm(X))))&
((?[X]:((~rich(X)<~>calm(X))))=>((brave(paul)<~>~kind(paul))))&
(![X]:((wise(X)|~kind(X))=>(humble(X)&~curious(X))))&
(![X]:((generous(X)&wise(X))=>(~humble(X)<~>rich(X))))&
(![X]:((funny(X)|~rich(X))=>(~humble(X)&calm(X))))&
(![X]:(~funny(X)<=>~curious(X)))&
(![X]:(~old(X)=>(curious(X)|~kind(X))))&
(((tall(lucy)<~>~tall(lucy)))=>(?[X]:((tall(X)|happy(X)))))&
(![X]:((wise(X)|~kind(X))=>(funny(X)&~tall(X))))&
(![X]:((kind(X)|patient(X))<=>(~calm(X)<~>creative(X))))&
((funny(alice)<~>~humble(alice)))&
(?[X]:((kind(X)&~humble(X))))&
(?[X]:((~strong(X)<~>~curious(X))))&
(?[X]:((old(X)<~>quiet(X))))&
(?[X]:((funny(X)|~tall(X))))&
(strong(lucy)) | ~wise(paul) | [
"p2",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 7817063788346533233162961
% SZS output start Proof for 7817063788346533233162961
3. ! [X0] : ((generous(X0) & ~calm(X0)) <=> (strong(X0) | ~strong(X0))) [input p2]
11. ! [X0] : ((~rich(X0) | funny(X0)) => (calm(X0) & ~humble(X0))) [input p10]
15. ! [X0] : ((~kind(X0) | wise(X0)) => (~tall(X0) & funny(X0))) [input p14]
23. wise(paul) [input hypothesis]
36. ! [X0] : ((calm(X0) & ~humble(X0)) | (rich(X0) & ~funny(X0))) [ennf transformation 11]
40. ! [X0] : ((~tall(X0) & funny(X0)) | (kind(X0) & ~wise(X0))) [ennf transformation 15]
47. ! [X0] : (((generous(X0) & ~calm(X0)) | (~strong(X0) & strong(X0))) & ((strong(X0) | ~strong(X0)) | (~generous(X0) | calm(X0)))) [nnf transformation 3]
48. ! [X0] : (((generous(X0) & ~calm(X0)) | (~strong(X0) & strong(X0))) & (strong(X0) | ~strong(X0) | ~generous(X0) | calm(X0))) [flattening 47]
78. ~calm(X0) | strong(X0) [cnf transformation 48]
79. ~calm(X0) | ~strong(X0) [cnf transformation 48]
105. calm(X0) | ~funny(X0) [cnf transformation 36]
112. funny(X0) | ~wise(X0) [cnf transformation 40]
132. wise(paul) [cnf transformation 23]
152. ~calm(X0) [subsumption resolution 78,79]
190. ~funny(X0) [subsumption resolution 105,152]
208. ~wise(X0) [subsumption resolution 112,190]
225. $false [subsumption resolution 132,208]
% SZS output end Proof for 7817063788346533233162961
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not brave is not rich or not tall.
If alice is patient or old then fred is either happy or calm and vice versa.
If someone is strong or not funny then mary is funny or not tall and vice versa.
Everyone who is creative or not strong is both not creative and humble and vice versa.
If mary is both not tall and not quiet then someone is not strong or tall and vice versa.
If alice is either not happy or calm then someone is calm and vice versa.
Everyone who is calm is either not old or old and vice versa.
Everyone who is funny is humble and vice versa.
If john is both not humble and not happy then paul is kind or not humble.
If john is rich or not brave then fred is not wise or rich and vice versa.
Everyone who is both not creative and not quiet is either happy or brave and vice versa.
Everyone who is either not wise or not kind is both patient and wise and vice versa.
Everyone who is not wise or rich is both not rich and not quiet and vice versa.
If someone is rich or calm then someone is both wise and not kind and vice versa.
Everyone who is either calm or generous is kind and vice versa.
Someone is strong.
Someone is both not wise and not patient.
Mary is not funny.
Someone is generous or not patient.
Paul is patient or brave.
Fred is not creative or not patient.
Someone is not generous or not patient.
Someone is either not brave or not happy. | Mary is not humble. | entailment | (![X]:(~brave(X)=>(~rich(X)|~tall(X))))&
(((patient(alice)|old(alice)))<=>((happy(fred)<~>calm(fred))))&
((?[X]:((strong(X)|~funny(X))))<=>((funny(mary)|~tall(mary))))&
(![X]:((creative(X)|~strong(X))<=>(~creative(X)&humble(X))))&
(((~tall(mary)&~quiet(mary)))<=>(?[X]:((~strong(X)|tall(X)))))&
(((~happy(alice)<~>calm(alice)))<=>(?[X]:(calm(X))))&
(![X]:(calm(X)<=>(~old(X)<~>old(X))))&
(![X]:(funny(X)<=>humble(X)))&
(((~humble(john)&~happy(john)))=>((kind(paul)|~humble(paul))))&
(((rich(john)|~brave(john)))<=>((~wise(fred)|rich(fred))))&
(![X]:((~creative(X)&~quiet(X))<=>(happy(X)<~>brave(X))))&
(![X]:((~wise(X)<~>~kind(X))<=>(patient(X)&wise(X))))&
(![X]:((~wise(X)|rich(X))<=>(~rich(X)&~quiet(X))))&
((?[X]:((rich(X)|calm(X))))<=>(?[X]:((wise(X)&~kind(X)))))&
(![X]:((calm(X)<~>generous(X))<=>kind(X)))&
(?[X]:(strong(X)))&
(?[X]:((~wise(X)&~patient(X))))&
(~funny(mary))&
(?[X]:((generous(X)|~patient(X))))&
((patient(paul)|brave(paul)))&
((~creative(fred)|~patient(fred)))&
(?[X]:((~generous(X)|~patient(X))))&
(?[X]:((~brave(X)<~>~happy(X)))) | ~humble(mary) | [
"p7",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 369230142994379236427613
% SZS output start Proof for 369230142994379236427613
8. ! [X0] : (funny(X0) <=> humble(X0)) [input p7]
18. ~funny(mary) [input p17]
24. humble(mary) [input hypothesis]
49. ! [X0] : ((funny(X0) | ~humble(X0)) & (humble(X0) | ~funny(X0))) [nnf transformation 8]
105. ~humble(X0) | funny(X0) [cnf transformation 49]
140. ~funny(mary) [cnf transformation 18]
147. humble(mary) [cnf transformation 24]
192. 8 <=> funny(mary) [avatar definition]
194. ~funny(mary) <- (~8) [avatar component clause 192]
290. ~8 [avatar split clause 140,192]
335. funny(mary) [resolution 105,147]
337. $false <- (~8) [subsumption resolution 335,194]
338. 8 [avatar contradiction clause 337]
339. $false [avatar sat refutation 290,338]
% SZS output end Proof for 369230142994379236427613
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 john is not humble or old then paul is tall or rich and vice versa.
Everyone who is either not curious or wise is not generous.
If someone is either tall or curious then someone is wise or not curious.
Everyone who is not old or funny is both not brave and rich and vice versa.
Everyone who is generous or kind is old.
If someone is not patient or old then fred is either curious or brave and vice versa.
Everyone who is calm is both not brave and wise and vice versa.
Everyone who is curious or not rich is not patient.
Everyone who is either not curious or generous is either quiet or curious and vice versa.
If susan is not strong or humble then alice is both wise and not wise.
Everyone who is brave or not humble is both not generous and not happy.
Everyone who is patient is either not curious or happy.
Everyone who is both not strong and not humble is not patient or not funny and vice versa.
If lucy is not wise or tall then someone is either not kind or humble and vice versa.
If fred is kind then paul is not tall or funny and vice versa.
Lucy is brave or kind.
Someone is either not tall or creative.
Mary is brave.
Someone is not old or not patient.
Susan is old.
Someone is either strong or old.
Paul is both not rich and not funny. | Susan is rich. | entailment | (((~humble(john)|old(john)))<=>((tall(paul)|rich(paul))))&
(![X]:((~curious(X)<~>wise(X))=>~generous(X)))&
((?[X]:((tall(X)<~>curious(X))))=>(?[X]:((wise(X)|~curious(X)))))&
(![X]:((~old(X)|funny(X))<=>(~brave(X)&rich(X))))&
(![X]:((generous(X)|kind(X))=>old(X)))&
((?[X]:((~patient(X)|old(X))))<=>((curious(fred)<~>brave(fred))))&
(![X]:(calm(X)<=>(~brave(X)&wise(X))))&
(![X]:((curious(X)|~rich(X))=>~patient(X)))&
(![X]:((~curious(X)<~>generous(X))<=>(quiet(X)<~>curious(X))))&
(((~strong(susan)|humble(susan)))=>((wise(alice)&~wise(alice))))&
(![X]:((brave(X)|~humble(X))=>(~generous(X)&~happy(X))))&
(![X]:(patient(X)=>(~curious(X)<~>happy(X))))&
(![X]:((~strong(X)&~humble(X))<=>(~patient(X)|~funny(X))))&
(((~wise(lucy)|tall(lucy)))<=>(?[X]:((~kind(X)<~>humble(X)))))&
((kind(fred))<=>((~tall(paul)|funny(paul))))&
((brave(lucy)|kind(lucy)))&
(?[X]:((~tall(X)<~>creative(X))))&
(brave(mary))&
(?[X]:((~old(X)|~patient(X))))&
(old(susan))&
(?[X]:((strong(X)<~>old(X))))&
((~rich(paul)&~funny(paul))) | rich(susan) | [
"p7",
"p9",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 5678747341228110070388970
% SZS output start Proof for 5678747341228110070388970
8. ! [X0] : ((~rich(X0) | curious(X0)) => ~patient(X0)) [input p7]
10. (humble(susan) | ~strong(susan)) => (~wise(alice) & wise(alice)) [input p9]
13. ! [X0] : ((~humble(X0) & ~strong(X0)) <=> (~funny(X0) | ~patient(X0))) [input p12]
23. ~rich(susan) [input hypothesis]
28. ! [X0] : (~patient(X0) | (rich(X0) & ~curious(X0))) [ennf transformation 8]
29. (~wise(alice) & wise(alice)) | (~humble(susan) & strong(susan)) [ennf transformation 10]
47. ! [X0] : (((~humble(X0) & ~strong(X0)) | (funny(X0) & patient(X0))) & ((~funny(X0) | ~patient(X0)) | (humble(X0) | strong(X0)))) [nnf transformation 13]
48. ! [X0] : (((~humble(X0) & ~strong(X0)) | (funny(X0) & patient(X0))) & (~funny(X0) | ~patient(X0) | humble(X0) | strong(X0))) [flattening 47]
86. ~patient(X0) | rich(X0) [cnf transformation 28]
95. wise(alice) | strong(susan) [cnf transformation 29]
97. ~wise(alice) | strong(susan) [cnf transformation 29]
106. ~strong(X0) | patient(X0) [cnf transformation 48]
129. ~rich(susan) [cnf transformation 23]
205. 16 <=> wise(alice) [avatar definition]
210. 17 <=> strong(susan) [avatar definition]
212. strong(susan) <- (17) [avatar component clause 210]
213. 17 | ~16 [avatar split clause 97,205,210]
215. 17 | 16 [avatar split clause 95,205,210]
307. patient(susan) <- (17) [resolution 106,212]
311. rich(susan) <- (17) [resolution 307,86]
313. $false <- (17) [subsumption resolution 311,129]
314. ~17 [avatar contradiction clause 313]
315. $false [avatar sat refutation 213,215,314]
% SZS output end Proof for 5678747341228110070388970
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not patient and curious then lucy is kind or not calm.
Everyone who is not generous is curious.
Everyone who is both not curious and not tall is either not old or not strong.
Everyone who is not kind is both not quiet and not rich.
If paul is not quiet or patient then john is not creative or happy and vice versa.
Everyone who is not tall or wise is either not happy or humble.
If mary is not calm or not happy then someone is either not kind or strong.
Everyone who is either not curious or creative is both not creative and not strong.
Everyone who is not brave or not strong is both not humble and not tall.
If someone is both not quiet and not curious then susan is not quiet or not kind and vice versa.
If fred is not patient then john is old or not rich.
Everyone who is calm is not curious or curious and vice versa.
If paul is not humble or not patient then paul is either brave or not quiet.
If someone is happy then mary is humble or patient.
If someone is strong or quiet then alice is either quiet or kind and vice versa.
If someone is kind or curious then mary is either not wise or strong.
Someone is not wise or curious.
Susan is not funny or funny.
Susan is either generous or not strong.
Someone is both humble and not patient.
Mary is patient or not wise.
Someone is both not brave and kind. | Mary is not tall. | neutral | ((?[X]:((~patient(X)&curious(X))))=>((kind(lucy)|~calm(lucy))))&
(![X]:(~generous(X)=>curious(X)))&
(![X]:((~curious(X)&~tall(X))=>(~old(X)<~>~strong(X))))&
(![X]:(~kind(X)=>(~quiet(X)&~rich(X))))&
(((~quiet(paul)|patient(paul)))<=>((~creative(john)|happy(john))))&
(![X]:((~tall(X)|wise(X))=>(~happy(X)<~>humble(X))))&
(((~calm(mary)|~happy(mary)))=>(?[X]:((~kind(X)<~>strong(X)))))&
(![X]:((~curious(X)<~>creative(X))=>(~creative(X)&~strong(X))))&
(![X]:((~brave(X)|~strong(X))=>(~humble(X)&~tall(X))))&
((?[X]:((~quiet(X)&~curious(X))))<=>((~quiet(susan)|~kind(susan))))&
((~patient(fred))=>((old(john)|~rich(john))))&
(![X]:(calm(X)<=>(~curious(X)|curious(X))))&
(((~humble(paul)|~patient(paul)))=>((brave(paul)<~>~quiet(paul))))&
((?[X]:(happy(X)))=>((humble(mary)|patient(mary))))&
((?[X]:((strong(X)|quiet(X))))<=>((quiet(alice)<~>kind(alice))))&
((?[X]:((kind(X)|curious(X))))=>((~wise(mary)<~>strong(mary))))&
(?[X]:((~wise(X)|curious(X))))&
((~funny(susan)|funny(susan)))&
((generous(susan)<~>~strong(susan)))&
(?[X]:((humble(X)&~patient(X))))&
((patient(mary)|~wise(mary)))&
(?[X]:((~brave(X)&kind(X)))) | ~tall(mary) | [] | null | 0 |
If someone is old or not kind then someone is both not patient and not rich and vice versa.
Everyone who is strong or not old is both rich and not tall.
If someone is funny or not funny then someone is funny or rich and vice versa.
Everyone who is generous is both funny and happy.
Everyone who is both not funny and not humble is humble or not old and vice versa.
Everyone who is old is not brave and vice versa.
If someone is both curious and not creative then lucy is not curious or old.
If paul is not happy then susan is kind and vice versa.
If john is either not tall or patient then alice is brave.
Everyone who is wise is both funny and calm.
If someone is either not creative or curious then paul is either not patient or not rich.
Everyone who is humble or not funny is not rich or generous.
If someone is both calm and tall then someone is not humble and vice versa.
If someone is both patient and happy then john is not happy or not creative and vice versa.
Everyone who is not brave or happy is either not rich or humble and vice versa.
Everyone who is either not strong or tall is both tall and quiet and vice versa.
Paul is not creative or curious.
Someone is old.
Susan is not funny or not humble.
Someone is either not creative or calm.
Someone is either kind or generous.
Alice is either creative or rich.
Someone is funny or strong. | Lucy is humble. | contradiction | ((?[X]:((old(X)|~kind(X))))<=>(?[X]:((~patient(X)&~rich(X)))))&
(![X]:((strong(X)|~old(X))=>(rich(X)&~tall(X))))&
((?[X]:((funny(X)|~funny(X))))<=>(?[X]:((funny(X)|rich(X)))))&
(![X]:(generous(X)=>(funny(X)&happy(X))))&
(![X]:((~funny(X)&~humble(X))<=>(humble(X)|~old(X))))&
(![X]:(old(X)<=>~brave(X)))&
((?[X]:((curious(X)&~creative(X))))=>((~curious(lucy)|old(lucy))))&
((~happy(paul))<=>(kind(susan)))&
(((~tall(john)<~>patient(john)))=>(brave(alice)))&
(![X]:(wise(X)=>(funny(X)&calm(X))))&
((?[X]:((~creative(X)<~>curious(X))))=>((~patient(paul)<~>~rich(paul))))&
(![X]:((humble(X)|~funny(X))=>(~rich(X)|generous(X))))&
((?[X]:((calm(X)&tall(X))))<=>(?[X]:(~humble(X))))&
((?[X]:((patient(X)&happy(X))))<=>((~happy(john)|~creative(john))))&
(![X]:((~brave(X)|happy(X))<=>(~rich(X)<~>humble(X))))&
(![X]:((~strong(X)<~>tall(X))<=>(tall(X)&quiet(X))))&
((~creative(paul)|curious(paul)))&
(?[X]:(old(X)))&
((~funny(susan)|~humble(susan)))&
(?[X]:((~creative(X)<~>calm(X))))&
(?[X]:((kind(X)<~>generous(X))))&
((creative(alice)<~>rich(alice)))&
(?[X]:((funny(X)|strong(X)))) | humble(lucy) | [
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 164995041227837110125018
% SZS output start Proof for 164995041227837110125018
5. ! [X0] : ((~humble(X0) & ~funny(X0)) <=> (~old(X0) | humble(X0))) [input p4]
24. humble(lucy) [input hypothesis]
47. ! [X0] : (((~humble(X0) & ~funny(X0)) | (old(X0) & ~humble(X0))) & ((~old(X0) | humble(X0)) | (humble(X0) | funny(X0)))) [nnf transformation 5]
48. ! [X0] : (((~humble(X0) & ~funny(X0)) | (old(X0) & ~humble(X0))) & (~old(X0) | humble(X0) | humble(X0) | funny(X0))) [flattening 47]
96. ~humble(X0) | ~humble(X0) [cnf transformation 48]
141. humble(lucy) [cnf transformation 24]
145. ~humble(X0) [duplicate literal removal 96]
326. $false [subsumption resolution 141,145]
% SZS output end Proof for 164995041227837110125018
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not tall or not quiet is either patient or kind and vice versa.
If john is either old or funny then someone is both old and not quiet and vice versa.
Everyone who is both strong and wise is not patient or not old and vice versa.
If someone is patient or not curious then susan is not happy or not wise and vice versa.
Everyone who is both not patient and not generous is not generous.
If mary is both generous and strong then paul is both not quiet and creative.
Everyone who is both not wise and humble is funny.
Everyone who is not creative or not tall is kind.
Everyone who is either tall or not curious is either not tall or not brave.
Everyone who is kind or not curious is both not tall and calm.
Everyone who is happy is either tall or kind.
If someone is either not brave or quiet then someone is strong or quiet.
If someone is not tall then someone is both brave and generous.
If alice is quiet or not brave then susan is not strong and vice versa.
If fred is patient or curious then someone is quiet or not brave and vice versa.
Susan is either not funny or calm.
John is not curious or generous.
Someone is either not happy or brave.
Paul is both not brave and generous.
Susan is both not happy and quiet.
Someone is both kind and not humble.
Someone is either not calm or quiet. | Alice is tall. | contradiction | (![X]:((~tall(X)|~quiet(X))<=>(patient(X)<~>kind(X))))&
(((old(john)<~>funny(john)))<=>(?[X]:((old(X)&~quiet(X)))))&
(![X]:((strong(X)&wise(X))<=>(~patient(X)|~old(X))))&
((?[X]:((patient(X)|~curious(X))))<=>((~happy(susan)|~wise(susan))))&
(![X]:((~patient(X)&~generous(X))=>~generous(X)))&
(((generous(mary)&strong(mary)))=>((~quiet(paul)&creative(paul))))&
(![X]:((~wise(X)&humble(X))=>funny(X)))&
(![X]:((~creative(X)|~tall(X))=>kind(X)))&
(![X]:((tall(X)<~>~curious(X))=>(~tall(X)<~>~brave(X))))&
(![X]:((kind(X)|~curious(X))=>(~tall(X)&calm(X))))&
(![X]:(happy(X)=>(tall(X)<~>kind(X))))&
((?[X]:((~brave(X)<~>quiet(X))))=>(?[X]:((strong(X)|quiet(X)))))&
((?[X]:(~tall(X)))=>(?[X]:((brave(X)&generous(X)))))&
(((quiet(alice)|~brave(alice)))<=>(~strong(susan)))&
(((patient(fred)|curious(fred)))<=>(?[X]:((quiet(X)|~brave(X)))))&
((~funny(susan)<~>calm(susan)))&
((~curious(john)|generous(john)))&
(?[X]:((~happy(X)<~>brave(X))))&
((~brave(paul)&generous(paul)))&
((~happy(susan)&quiet(susan)))&
(?[X]:((kind(X)&~humble(X))))&
(?[X]:((~calm(X)<~>quiet(X)))) | tall(alice) | [
"p0",
"p2",
"p7",
"p8",
"p9",
"p13",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 2894032688256321028772812
% SZS output start Proof for 2894032688256321028772812
1. ! [X0] : ((~quiet(X0) | ~tall(X0)) <=> (patient(X0) <~> kind(X0))) [input p0]
3. ! [X0] : ((wise(X0) & strong(X0)) <=> (~old(X0) | ~patient(X0))) [input p2]
8. ! [X0] : ((~tall(X0) | ~creative(X0)) => kind(X0)) [input p7]
9. ! [X0] : ((tall(X0) <~> ~curious(X0)) => (~tall(X0) <~> ~brave(X0))) [input p8]
10. ! [X0] : ((~curious(X0) | kind(X0)) => (calm(X0) & ~tall(X0))) [input p9]
14. (~brave(alice) | quiet(alice)) <=> ~strong(susan) [input p13]
20. quiet(susan) & ~happy(susan) [input p19]
23. tall(alice) [input hypothesis]
28. ! [X0] : (~tall(X0) => kind(X0)) [pure predicate removal 8]
34. ! [X0] : (kind(X0) | tall(X0)) [ennf transformation 28]
35. ! [X0] : ((~tall(X0) <~> ~brave(X0)) | (tall(X0) <=> ~curious(X0))) [ennf transformation 9]
36. ! [X0] : ((calm(X0) & ~tall(X0)) | (curious(X0) & ~kind(X0))) [ennf transformation 10]
40. ! [X0] : (((~quiet(X0) | ~tall(X0)) | ((patient(X0) | ~kind(X0)) & (kind(X0) | ~patient(X0)))) & (((~kind(X0) | ~patient(X0)) & (kind(X0) | patient(X0))) | (quiet(X0) & tall(X0)))) [nnf transformation 1]
41. ! [X0] : ((~quiet(X0) | ~tall(X0) | ((patient(X0) | ~kind(X0)) & (kind(X0) | ~patient(X0)))) & (((~kind(X0) | ~patient(X0)) & (kind(X0) | patient(X0))) | (quiet(X0) & tall(X0)))) [flattening 40]
46. ! [X0] : (((wise(X0) & strong(X0)) | (old(X0) & patient(X0))) & ((~old(X0) | ~patient(X0)) | (~wise(X0) | ~strong(X0)))) [nnf transformation 3]
47. ! [X0] : (((wise(X0) & strong(X0)) | (old(X0) & patient(X0))) & (~old(X0) | ~patient(X0) | ~wise(X0) | ~strong(X0))) [flattening 46]
53. ! [X0] : (((brave(X0) | tall(X0)) & (~brave(X0) | ~tall(X0))) | ((tall(X0) | curious(X0)) & (~curious(X0) | ~tall(X0)))) [nnf transformation 35]
62. ((~brave(alice) | quiet(alice)) | strong(susan)) & (~strong(susan) | (brave(alice) & ~quiet(alice))) [nnf transformation 14]
63. (~brave(alice) | quiet(alice) | strong(susan)) & (~strong(susan) | (brave(alice) & ~quiet(alice))) [flattening 62]
80. ~kind(X0) | ~patient(X0) | tall(X0) [cnf transformation 41]
82. ~patient(X0) | ~tall(X0) | kind(X0) | ~quiet(X0) [cnf transformation 41]
91. strong(X0) | patient(X0) [cnf transformation 47]
101. kind(X0) | tall(X0) [cnf transformation 34]
102. ~brave(X0) | ~tall(X0) | ~curious(X0) | ~tall(X0) [cnf transformation 53]
106. ~kind(X0) | ~tall(X0) [cnf transformation 36]
107. ~tall(X0) | curious(X0) [cnf transformation 36]
117. ~strong(susan) | brave(alice) [cnf transformation 63]
131. quiet(susan) [cnf transformation 20]
135. tall(alice) [cnf transformation 23]
136. ~brave(X0) | ~tall(X0) | ~curious(X0) [duplicate literal removal 102]
232. 22 <=> strong(susan) [avatar definition]
233. ~strong(susan) <- (~22) [avatar component clause 232]
240. 24 <=> brave(alice) [avatar definition]
241. brave(alice) <- (24) [avatar component clause 240]
244. 24 | ~22 [avatar split clause 117,232,240]
312. patient(susan) <- (~22) [resolution 91,233]
318. curious(alice) [resolution 107,135]
330. ~patient(X2) | tall(X2) | tall(X2) [resolution 80,101]
331. ~patient(X2) | tall(X2) [duplicate literal removal 330]
352. ~tall(susan) | kind(susan) | ~quiet(susan) <- (~22) [resolution 82,312]
374. tall(susan) <- (~22) [resolution 331,312]
397. kind(susan) | ~quiet(susan) <- (~22) [subsumption resolution 352,374]
398. kind(susan) <- (~22) [subsumption resolution 397,131]
418. ~tall(susan) <- (~22) [resolution 398,106]
419. $false <- (~22) [subsumption resolution 418,374]
420. 22 [avatar contradiction clause 419]
421. ~tall(alice) | ~curious(alice) <- (24) [resolution 241,136]
422. ~curious(alice) <- (24) [subsumption resolution 421,135]
423. $false <- (24) [subsumption resolution 422,318]
424. ~24 [avatar contradiction clause 423]
425. $false [avatar sat refutation 244,420,424]
% SZS output end Proof for 2894032688256321028772812
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny and not calm is not rich. Everyone who is either calm or not quiet is not creative or funny and vice versa. If alice is either not quiet or not wise then john is both wise and curious. If someone is not old or not wise then someone is not kind and vice versa. Everyone who is either not humble or wise is not brave and vice versa. Everyone who is both not old and not happy is both not strong and curious and vice versa. Everyone who is not generous is either not curious or humble. Everyone who is happy or calm is both humble and not happy and vice versa. If someone is either quiet or not rich then susan is either wise or brave. If paul is tall then john is both not tall and not rich and vice versa. Everyone who is either not calm or strong is wise. If someone is both tall and not funny then someone is not brave or rich. Everyone who is patient or strong is rich and vice versa. Everyone who is creative or not strong is both not calm and strong and vice versa. If fred is both not rich and not humble then susan is both not funny and quiet and vice versa. Everyone who is strong is tall or not funny. Susan is patient or creative. Alice is both not kind and strong. Someone is both calm and tall. Fred is either not kind or not creative. John is either brave or generous. Alice is curious or tall. Someone is not happy. | John is not brave. | neutral | (![X]:((~funny(X)&~calm(X))=>~rich(X)))&
(![X]:((calm(X)<~>~quiet(X))<=>(~creative(X)|funny(X))))&
(((~quiet(alice)<~>~wise(alice)))=>((wise(john)&curious(john))))&
((?[X]:((~old(X)|~wise(X))))<=>(?[X]:(~kind(X))))&
(![X]:((~humble(X)<~>wise(X))<=>~brave(X)))&
(![X]:((~old(X)&~happy(X))<=>(~strong(X)&curious(X))))&
(![X]:(~generous(X)=>(~curious(X)<~>humble(X))))&
(![X]:((happy(X)|calm(X))<=>(humble(X)&~happy(X))))&
((?[X]:((quiet(X)<~>~rich(X))))=>((wise(susan)<~>brave(susan))))&
((tall(paul))<=>((~tall(john)&~rich(john))))&
(![X]:((~calm(X)<~>strong(X))=>wise(X)))&
((?[X]:((tall(X)&~funny(X))))=>(?[X]:((~brave(X)|rich(X)))))&
(![X]:((patient(X)|strong(X))<=>rich(X)))&
(![X]:((creative(X)|~strong(X))<=>(~calm(X)&strong(X))))&
(((~rich(fred)&~humble(fred)))<=>((~funny(susan)&quiet(susan))))&
(![X]:(strong(X)=>(tall(X)|~funny(X))))&
((patient(susan)|creative(susan)))&
((~kind(alice)&strong(alice)))&
(?[X]:((calm(X)&tall(X))))&
((~kind(fred)<~>~creative(fred)))&
((brave(john)<~>generous(john)))&
((curious(alice)|tall(alice)))&
(?[X]:(~happy(X))) | ~brave(john) | [] | null | 0 |
Everyone who is not curious is not kind 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. Everyone who is strong is brave and vice versa. If someone is both not happy and kind then someone is either not old or patient and vice versa. Paul is either strong or kind. Someone is not tall. Paul is funny or rich. Someone is kind. | Paul is quiet. | entailment | (![X]:(~curious(X)<=>~kind(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)<=>brave(X)))&
((?[X]:((~happy(X)&kind(X))))<=>(?[X]:((~old(X)<~>patient(X)))))&
((strong(paul)<~>kind(paul)))&
(?[X]:(~tall(X)))&
((funny(paul)|rich(paul)))&
(?[X]:(kind(X))) | quiet(paul) | [
"p4",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4306095518070951833361716
% SZS output start Proof for 4306095518070951833361716
5. ! [X0] : ((~wise(X0) <~> ~kind(X0)) <=> (brave(X0) & quiet(X0))) [input p4]
13. ! [X0] : ((~funny(X0) | ~quiet(X0)) <=> (wise(X0) & strong(X0))) [input p12]
16. strong(paul) <~> kind(paul) [input p15]
20. ~quiet(paul) [input hypothesis]
31. ! [X0] : ((((kind(X0) | wise(X0)) & (~kind(X0) | ~wise(X0))) | (~brave(X0) | ~quiet(X0))) & ((brave(X0) & quiet(X0)) | ((~wise(X0) | kind(X0)) & (~kind(X0) | wise(X0))))) [nnf transformation 5]
32. ! [X0] : ((((kind(X0) | wise(X0)) & (~kind(X0) | ~wise(X0))) | ~brave(X0) | ~quiet(X0)) & ((brave(X0) & quiet(X0)) | ((~wise(X0) | kind(X0)) & (~kind(X0) | wise(X0))))) [flattening 31]
50. ! [X0] : (((~funny(X0) | ~quiet(X0)) | (~wise(X0) | ~strong(X0))) & ((wise(X0) & strong(X0)) | (funny(X0) & quiet(X0)))) [nnf transformation 13]
51. ! [X0] : ((~funny(X0) | ~quiet(X0) | ~wise(X0) | ~strong(X0)) & ((wise(X0) & strong(X0)) | (funny(X0) & quiet(X0)))) [flattening 50]
58. (~kind(paul) | ~strong(paul)) & (kind(paul) | strong(paul)) [nnf transformation 16]
73. ~wise(X0) | quiet(X0) | kind(X0) [cnf transformation 32]
101. quiet(X0) | strong(X0) [cnf transformation 51]
103. quiet(X0) | wise(X0) [cnf transformation 51]
115. ~kind(paul) | ~strong(paul) [cnf transformation 58]
118. ~quiet(paul) [cnf transformation 20]
208. 20 <=> strong(paul) [avatar definition]
212. 21 <=> kind(paul) [avatar definition]
215. ~20 | ~21 [avatar split clause 115,212,208]
235. strong(paul) [resolution 101,118]
236. wise(paul) [resolution 103,118]
333. quiet(paul) | kind(paul) [resolution 73,236]
335. kind(paul) [subsumption resolution 333,118]
356. 20 [avatar split clause 235,208]
357. 21 [avatar split clause 335,212]
358. $false [avatar sat refutation 215,356,357]
% SZS output end Proof for 4306095518070951833361716
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 lucy is either not old or wise then susan is generous. Everyone who is either not creative or not curious is calm and vice versa. If someone is tall or not old then paul is both not happy and not patient. Everyone who is both funny and curious is either not happy or creative and vice versa. Everyone who is both kind and not happy is either rich or not creative and vice versa. If someone is not happy or not creative then alice is not old or creative. Everyone who is either generous or not brave is not humble and vice versa. If someone is either not creative or kind then fred is both not happy and strong. If someone is strong or creative then someone is humble and vice versa. Everyone who is both generous and wise is both creative and not old and vice versa. Everyone who is not happy is not generous and vice versa. Everyone who is not quiet is happy and vice versa. Everyone who is either not curious or creative is either humble or quiet and vice versa. Everyone who is both not curious and curious is not happy or funny. If paul is brave or rich then susan is both not generous and not funny and vice versa. Everyone who is either brave or not tall is both calm and curious. Someone is not curious or funny. Someone is either not wise or rich. Someone is curious or happy. Someone is brave or not happy. Someone is not happy. Someone is not wise or brave. Someone is not brave or tall. Someone is not kind. | Paul is not happy. | entailment | (((~old(lucy)<~>wise(lucy)))=>(generous(susan)))&
(![X]:((~creative(X)<~>~curious(X))<=>calm(X)))&
((?[X]:((tall(X)|~old(X))))=>((~happy(paul)&~patient(paul))))&
(![X]:((funny(X)&curious(X))<=>(~happy(X)<~>creative(X))))&
(![X]:((kind(X)&~happy(X))<=>(rich(X)<~>~creative(X))))&
((?[X]:((~happy(X)|~creative(X))))=>((~old(alice)|creative(alice))))&
(![X]:((generous(X)<~>~brave(X))<=>~humble(X)))&
((?[X]:((~creative(X)<~>kind(X))))=>((~happy(fred)&strong(fred))))&
((?[X]:((strong(X)|creative(X))))<=>(?[X]:(humble(X))))&
(![X]:((generous(X)&wise(X))<=>(creative(X)&~old(X))))&
(![X]:(~happy(X)<=>~generous(X)))&
(![X]:(~quiet(X)<=>happy(X)))&
(![X]:((~curious(X)<~>creative(X))<=>(humble(X)<~>quiet(X))))&
(![X]:((~curious(X)&curious(X))=>(~happy(X)|funny(X))))&
(((brave(paul)|rich(paul)))<=>((~generous(susan)&~funny(susan))))&
(![X]:((brave(X)<~>~tall(X))=>(calm(X)&curious(X))))&
(?[X]:((~curious(X)|funny(X))))&
(?[X]:((~wise(X)<~>rich(X))))&
(?[X]:((curious(X)|happy(X))))&
(?[X]:((brave(X)|~happy(X))))&
(?[X]:(~happy(X)))&
(?[X]:((~wise(X)|brave(X))))&
(?[X]:((~brave(X)|tall(X))))&
(?[X]:(~kind(X))) | ~happy(paul) | [
"p1",
"p2",
"p3",
"p6",
"p10",
"p11",
"p12",
"p15",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 3597430228050107919855610
% SZS output start Proof for 3597430228050107919855610
2. ! [X0] : ((~creative(X0) <~> ~curious(X0)) <=> calm(X0)) [input p1]
3. ? [X0] : (~old(X0) | tall(X0)) => (~patient(paul) & ~happy(paul)) [input p2]
4. ! [X0] : ((curious(X0) & funny(X0)) <=> (~happy(X0) <~> creative(X0))) [input p3]
7. ! [X0] : ((generous(X0) <~> ~brave(X0)) <=> ~humble(X0)) [input p6]
11. ! [X0] : (~happy(X0) <=> ~generous(X0)) [input p10]
12. ! [X0] : (~quiet(X0) <=> happy(X0)) [input p11]
13. ! [X0] : ((~curious(X0) <~> creative(X0)) <=> (humble(X0) <~> quiet(X0))) [input p12]
16. ! [X0] : ((brave(X0) <~> ~tall(X0)) => (curious(X0) & calm(X0))) [input p15]
23. ? [X0] : (tall(X0) | ~brave(X0)) [input p22]
25. happy(paul) [input hypothesis]
27. ! [X0] : (calm(X0) => (~creative(X0) <~> ~curious(X0))) [unused predicate definition removal 2]
28. ? [X0] : (~old(X0) | tall(X0)) => ~happy(paul) [pure predicate removal 3]
30. ! [X0] : ((~creative(X0) <~> ~curious(X0)) | ~calm(X0)) [ennf transformation 27]
31. ~happy(paul) | ! [X0] : (old(X0) & ~tall(X0)) [ennf transformation 28]
37. ! [X0] : ((curious(X0) & calm(X0)) | (brave(X0) <=> ~tall(X0))) [ennf transformation 16]
39. ! [X0] : (((curious(X0) | creative(X0)) & (~curious(X0) | ~creative(X0))) | ~calm(X0)) [nnf transformation 30]
40. ! [X0] : (((curious(X0) & funny(X0)) | ((~happy(X0) | ~creative(X0)) & (creative(X0) | happy(X0)))) & (((~creative(X0) | happy(X0)) & (creative(X0) | ~happy(X0))) | (~curious(X0) | ~funny(X0)))) [nnf transformation 4]
41. ! [X0] : (((curious(X0) & funny(X0)) | ((~happy(X0) | ~creative(X0)) & (creative(X0) | happy(X0)))) & (((~creative(X0) | happy(X0)) & (creative(X0) | ~happy(X0))) | ~curious(X0) | ~funny(X0))) [flattening 40]
44. ! [X0] : ((((brave(X0) | ~generous(X0)) & (~brave(X0) | generous(X0))) | humble(X0)) & (~humble(X0) | ((generous(X0) | brave(X0)) & (~brave(X0) | ~generous(X0))))) [nnf transformation 7]
53. ! [X0] : ((~happy(X0) | generous(X0)) & (~generous(X0) | happy(X0))) [nnf transformation 11]
54. ! [X0] : ((~quiet(X0) | ~happy(X0)) & (happy(X0) | quiet(X0))) [nnf transformation 12]
55. ! [X0] : ((((~creative(X0) | curious(X0)) & (creative(X0) | ~curious(X0))) | ((humble(X0) | ~quiet(X0)) & (quiet(X0) | ~humble(X0)))) & (((~quiet(X0) | ~humble(X0)) & (quiet(X0) | humble(X0))) | ((~curious(X0) | ~creative(X0)) & (creative(X0) | curious(X0))))) [nnf transformation 13]
58. ! [X0] : ((curious(X0) & calm(X0)) | ((brave(X0) | tall(X0)) & (~tall(X0) | ~brave(X0)))) [nnf transformation 37]
72. ? [X0] : (tall(X0) | ~brave(X0)) => (tall(sK8) | ~brave(sK8)) [choice axiom]
73. tall(sK8) | ~brave(sK8) [skolemisation 23,72]
78. ~calm(X0) | ~creative(X0) | ~curious(X0) [cnf transformation 39]
80. ~happy(paul) | ~tall(X0) [cnf transformation 31]
86. happy(X0) | creative(X0) | curious(X0) [cnf transformation 41]
97. ~humble(X0) | generous(X0) | brave(X0) [cnf transformation 44]
99. ~generous(X0) | brave(X0) | humble(X0) [cnf transformation 44]
111. ~generous(X0) | happy(X0) [cnf transformation 53]
112. ~happy(X0) | generous(X0) [cnf transformation 53]
113. quiet(X0) | happy(X0) [cnf transformation 54]
114. ~quiet(X0) | ~happy(X0) [cnf transformation 54]
119. ~humble(X0) | ~curious(X0) | quiet(X0) | creative(X0) [cnf transformation 55]
120. ~quiet(X0) | ~curious(X0) | humble(X0) | creative(X0) [cnf transformation 55]
130. brave(X0) | calm(X0) | tall(X0) [cnf transformation 58]
132. brave(X0) | curious(X0) | tall(X0) [cnf transformation 58]
140. tall(sK8) | ~brave(sK8) [cnf transformation 73]
142. happy(paul) [cnf transformation 25]
161. 5 <=> happy(paul) [avatar definition]
166. 6 <=> ! [X0] : ~tall(X0) [avatar definition]
167. ~tall(X0) <- (6) [avatar component clause 166]
168. 6 | ~5 [avatar split clause 80,161,166]
291. 34 <=> brave(sK8) [avatar definition]
293. ~brave(sK8) <- (~34) [avatar component clause 291]
295. 35 <=> tall(sK8) [avatar definition]
297. tall(sK8) <- (35) [avatar component clause 295]
298. ~34 | 35 [avatar split clause 140,295,291]
299. 5 [avatar split clause 142,161]
606. ~curious(X1) | humble(X1) | creative(X1) | happy(X1) [resolution 120,113]
608. humble(X1) | creative(X1) | happy(X1) [subsumption resolution 606,86]
685. $false <- (6, 35) [subsumption resolution 297,167]
686. ~6 | ~35 [avatar contradiction clause 685]
719. curious(sK8) | tall(sK8) <- (~34) [resolution 293,132]
720. calm(sK8) | tall(sK8) <- (~34) [resolution 293,130]
721. curious(sK8) <- (6, ~34) [subsumption resolution 719,167]
722. calm(sK8) <- (6, ~34) [subsumption resolution 720,167]
766. 74 <=> creative(sK8) [avatar definition]
768. ~creative(sK8) <- (~74) [avatar component clause 766]
770. 75 <=> quiet(sK8) [avatar definition]
772. quiet(sK8) <- (75) [avatar component clause 770]
774. 76 <=> humble(sK8) [avatar definition]
776. humble(sK8) <- (76) [avatar component clause 774]
779. ~creative(sK8) | ~curious(sK8) <- (6, ~34) [resolution 722,78]
846. creative(X2) | happy(X2) | generous(X2) | brave(X2) [resolution 608,97]
850. brave(X2) | generous(X2) | creative(X2) [subsumption resolution 846,112]
1207. generous(sK8) | creative(sK8) <- (~34) [resolution 850,293]
1209. generous(sK8) <- (~34, ~74) [subsumption resolution 1207,768]
1261. brave(sK8) | humble(sK8) <- (~34, ~74) [resolution 1209,99]
1264. humble(sK8) <- (~34, ~74) [subsumption resolution 1261,293]
1265. 76 | 34 | 74 [avatar split clause 1264,766,291,774]
1267. 98 <=> generous(sK8) [avatar definition]
1269. generous(sK8) <- (98) [avatar component clause 1267]
1271. 74 | 98 | 34 [avatar split clause 1207,291,1267,766]
1272. ~creative(sK8) <- (6, ~34) [subsumption resolution 779,721]
1273. ~74 | ~6 | 34 [avatar split clause 1272,291,166,766]
1278. ~happy(sK8) <- (75) [resolution 772,114]
1281. ~curious(sK8) | quiet(sK8) | creative(sK8) <- (76) [resolution 776,119]
1287. happy(sK8) <- (98) [resolution 1269,111]
1289. $false <- (75, 98) [subsumption resolution 1287,1278]
1290. ~75 | ~98 [avatar contradiction clause 1289]
1291. quiet(sK8) | creative(sK8) <- (6, ~34, 76) [subsumption resolution 1281,721]
1292. quiet(sK8) <- (6, ~34, ~74, 76) [subsumption resolution 1291,768]
1293. 75 | ~6 | 34 | 74 | ~76 [avatar split clause 1292,774,766,291,166,770]
1294. $false [avatar sat refutation 168,298,299,686,1265,1271,1273,1290,1293]
% SZS output end Proof for 3597430228050107919855610
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5628
% Time elapsed: 0.022 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not quiet or not humble is both not curious and humble.
Everyone who is wise or not kind is brave.
Everyone who is not calm is both generous and not wise and vice versa.
Everyone who is either old or calm is brave and vice versa.
Everyone who is either not quiet or generous is not curious or generous.
Everyone who is not humble or curious is both funny and calm and vice versa.
Everyone who is creative or not strong is both funny and generous.
Everyone who is not curious is not old and vice versa.
If john is not old then fred is either not humble or not happy.
If lucy is either generous or not funny then someone is quiet.
If lucy is rich then someone is both wise and not brave.
Everyone who is happy or not strong is either quiet or curious and vice versa.
If someone is creative then john is strong or generous and vice versa.
If fred is both curious and generous then someone is not quiet and vice versa.
Everyone who is both not wise and happy is either not kind or tall.
Everyone who is not wise or not happy is not curious or not rich and vice versa.
John is either happy or patient.
Someone is either not curious or not happy.
John is either not strong or creative.
Fred is humble or not calm.
Lucy is both happy and generous.
Someone is strong.
Someone is calm.
Lucy is both quiet and not wise. | Fred is humble. | entailment | (![X]:((~quiet(X)|~humble(X))=>(~curious(X)&humble(X))))&
(![X]:((wise(X)|~kind(X))=>brave(X)))&
(![X]:(~calm(X)<=>(generous(X)&~wise(X))))&
(![X]:((old(X)<~>calm(X))<=>brave(X)))&
(![X]:((~quiet(X)<~>generous(X))=>(~curious(X)|generous(X))))&
(![X]:((~humble(X)|curious(X))<=>(funny(X)&calm(X))))&
(![X]:((creative(X)|~strong(X))=>(funny(X)&generous(X))))&
(![X]:(~curious(X)<=>~old(X)))&
((~old(john))=>((~humble(fred)<~>~happy(fred))))&
(((generous(lucy)<~>~funny(lucy)))=>(?[X]:(quiet(X))))&
((rich(lucy))=>(?[X]:((wise(X)&~brave(X)))))&
(![X]:((happy(X)|~strong(X))<=>(quiet(X)<~>curious(X))))&
((?[X]:(creative(X)))<=>((strong(john)|generous(john))))&
(((curious(fred)&generous(fred)))<=>(?[X]:(~quiet(X))))&
(![X]:((~wise(X)&happy(X))=>(~kind(X)<~>tall(X))))&
(![X]:((~wise(X)|~happy(X))<=>(~curious(X)|~rich(X))))&
((happy(john)<~>patient(john)))&
(?[X]:((~curious(X)<~>~happy(X))))&
((~strong(john)<~>creative(john)))&
((humble(fred)|~calm(fred)))&
((happy(lucy)&generous(lucy)))&
(?[X]:(strong(X)))&
(?[X]:(calm(X)))&
((quiet(lucy)&~wise(lucy))) | humble(fred) | [
"p0",
"hypothesis"
] | % SZS status Unsatisfiable for 7478104020618561763741860
% SZS output start Proof for 7478104020618561763741860
1. ! [X0] : ((~humble(X0) | ~quiet(X0)) => (humble(X0) & ~curious(X0))) [input p0]
25. ~humble(fred) [input hypothesis]
26. ! [X0] : ((humble(X0) & ~curious(X0)) | (humble(X0) & quiet(X0))) [ennf transformation 1]
76. humble(X0) | humble(X0) [cnf transformation 26]
136. ~humble(fred) [cnf transformation 25]
138. humble(X0) [duplicate literal removal 76]
242. $false [subsumption resolution 136,138]
% SZS output end Proof for 7478104020618561763741860
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not humble is both not kind and funny and vice versa.
If alice is not humble then mary is strong or wise and vice versa.
Everyone who is both happy and not curious is both not generous and not rich and vice versa.
Everyone who is patient or humble is not funny and vice versa.
Everyone who is humble or curious is both happy and not patient and vice versa.
If alice is both happy and brave then susan is not wise or old and vice versa.
If paul is strong then someone is either not wise or quiet.
Everyone who is both quiet and kind is calm and vice versa.
If mary is either not creative or not calm then lucy is not quiet or not rich.
If someone is not brave or creative then someone is not curious and vice versa.
If paul is both not calm and calm then paul is not generous or patient and vice versa.
If lucy is not funny or wise then someone is either funny or tall.
If someone is not curious or not happy then susan is both not kind and not generous.
If someone is either old or not humble then alice is both not creative and brave and vice versa.
If lucy is both happy and not rich then someone is not happy or not kind and vice versa.
Everyone who is kind or not generous is either creative or not humble and vice versa.
Someone is either kind or not patient.
Someone is not creative or not curious.
Someone is either humble or not quiet.
Someone is not funny or not tall.
Lucy is tall.
Someone is strong.
Lucy is strong or funny.
Someone is either not old or not calm. | Paul is not funny. | neutral | (![X]:(~humble(X)<=>(~kind(X)&funny(X))))&
((~humble(alice))<=>((strong(mary)|wise(mary))))&
(![X]:((happy(X)&~curious(X))<=>(~generous(X)&~rich(X))))&
(![X]:((patient(X)|humble(X))<=>~funny(X)))&
(![X]:((humble(X)|curious(X))<=>(happy(X)&~patient(X))))&
(((happy(alice)&brave(alice)))<=>((~wise(susan)|old(susan))))&
((strong(paul))=>(?[X]:((~wise(X)<~>quiet(X)))))&
(![X]:((quiet(X)&kind(X))<=>calm(X)))&
(((~creative(mary)<~>~calm(mary)))=>((~quiet(lucy)|~rich(lucy))))&
((?[X]:((~brave(X)|creative(X))))<=>(?[X]:(~curious(X))))&
(((~calm(paul)&calm(paul)))<=>((~generous(paul)|patient(paul))))&
(((~funny(lucy)|wise(lucy)))=>(?[X]:((funny(X)<~>tall(X)))))&
((?[X]:((~curious(X)|~happy(X))))=>((~kind(susan)&~generous(susan))))&
((?[X]:((old(X)<~>~humble(X))))<=>((~creative(alice)&brave(alice))))&
(((happy(lucy)&~rich(lucy)))<=>(?[X]:((~happy(X)|~kind(X)))))&
(![X]:((kind(X)|~generous(X))<=>(creative(X)<~>~humble(X))))&
(?[X]:((kind(X)<~>~patient(X))))&
(?[X]:((~creative(X)|~curious(X))))&
(?[X]:((humble(X)<~>~quiet(X))))&
(?[X]:((~funny(X)|~tall(X))))&
(tall(lucy))&
(?[X]:(strong(X)))&
((strong(lucy)|funny(lucy)))&
(?[X]:((~old(X)<~>~calm(X)))) | ~funny(paul) | [] | null | 0 |
Everyone who is both creative and not patient is not generous or not rich and vice versa.
Everyone who is either not brave or not old is either not funny or not kind and vice versa.
If someone is either not generous or not happy then someone is either not calm or not strong and vice versa.
Everyone who is humble or not quiet is both patient and tall and vice versa.
Everyone who is creative or kind is both wise and strong.
If someone is both creative and not curious then someone is both funny and not humble.
If alice is either happy or quiet then someone is not strong or patient and vice versa.
Everyone who is not old is either not strong or not happy.
Everyone who is not old is either happy or humble.
Everyone who is not generous or not rich is quiet and vice versa.
Everyone who is quiet or not creative is either not creative or happy and vice versa.
If someone is not patient or not creative then someone is not rich or not kind.
Everyone who is quiet or not brave is either brave or patient and vice versa.
If lucy is either kind or not kind then someone is either quiet or funny.
Everyone who is either not happy or not strong is patient and vice versa.
Everyone who is happy or old is either calm or not curious and vice versa.
Someone is quiet or not creative.
Someone is creative or not brave.
Someone is both calm and not rich.
Paul is funny. | Lucy is brave. | entailment | (![X]:((creative(X)&~patient(X))<=>(~generous(X)|~rich(X))))&
(![X]:((~brave(X)<~>~old(X))<=>(~funny(X)<~>~kind(X))))&
((?[X]:((~generous(X)<~>~happy(X))))<=>(?[X]:((~calm(X)<~>~strong(X)))))&
(![X]:((humble(X)|~quiet(X))<=>(patient(X)&tall(X))))&
(![X]:((creative(X)|kind(X))=>(wise(X)&strong(X))))&
((?[X]:((creative(X)&~curious(X))))=>(?[X]:((funny(X)&~humble(X)))))&
(((happy(alice)<~>quiet(alice)))<=>(?[X]:((~strong(X)|patient(X)))))&
(![X]:(~old(X)=>(~strong(X)<~>~happy(X))))&
(![X]:(~old(X)=>(happy(X)<~>humble(X))))&
(![X]:((~generous(X)|~rich(X))<=>quiet(X)))&
(![X]:((quiet(X)|~creative(X))<=>(~creative(X)<~>happy(X))))&
((?[X]:((~patient(X)|~creative(X))))=>(?[X]:((~rich(X)|~kind(X)))))&
(![X]:((quiet(X)|~brave(X))<=>(brave(X)<~>patient(X))))&
(((kind(lucy)<~>~kind(lucy)))=>(?[X]:((quiet(X)<~>funny(X)))))&
(![X]:((~happy(X)<~>~strong(X))<=>patient(X)))&
(![X]:((happy(X)|old(X))<=>(calm(X)<~>~curious(X))))&
(?[X]:((quiet(X)|~creative(X))))&
(?[X]:((creative(X)|~brave(X))))&
(?[X]:((calm(X)&~rich(X))))&
(funny(paul)) | brave(lucy) | [
"p0",
"p3",
"p4",
"p6",
"p9",
"p10",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5652694847452483454245746
% SZS output start Proof for 5652694847452483454245746
1. ! [X0] : ((~patient(X0) & creative(X0)) <=> (~rich(X0) | ~generous(X0))) [input p0]
4. ! [X0] : ((~quiet(X0) | humble(X0)) <=> (tall(X0) & patient(X0))) [input p3]
5. ! [X0] : ((kind(X0) | creative(X0)) => (strong(X0) & wise(X0))) [input p4]
7. (happy(alice) <~> quiet(alice)) <=> ? [X0] : (patient(X0) | ~strong(X0)) [input p6]
10. ! [X0] : ((~rich(X0) | ~generous(X0)) <=> quiet(X0)) [input p9]
11. ! [X0] : ((~creative(X0) | quiet(X0)) <=> (~creative(X0) <~> happy(X0))) [input p10]
13. ! [X0] : ((~brave(X0) | quiet(X0)) <=> (brave(X0) <~> patient(X0))) [input p12]
15. ! [X0] : ((~happy(X0) <~> ~strong(X0)) <=> patient(X0)) [input p14]
21. ~brave(lucy) [input hypothesis]
25. ! [X0] : ((kind(X0) | creative(X0)) => strong(X0)) [pure predicate removal 5]
26. ! [X0] : (strong(X0) | (~kind(X0) & ~creative(X0))) [ennf transformation 25]
32. ! [X0] : (((~patient(X0) & creative(X0)) | (rich(X0) & generous(X0))) & ((~rich(X0) | ~generous(X0)) | (patient(X0) | ~creative(X0)))) [nnf transformation 1]
33. ! [X0] : (((~patient(X0) & creative(X0)) | (rich(X0) & generous(X0))) & (~rich(X0) | ~generous(X0) | patient(X0) | ~creative(X0))) [flattening 32]
40. ! [X0] : (((~quiet(X0) | humble(X0)) | (~tall(X0) | ~patient(X0))) & ((tall(X0) & patient(X0)) | (quiet(X0) & ~humble(X0)))) [nnf transformation 4]
41. ! [X0] : ((~quiet(X0) | humble(X0) | ~tall(X0) | ~patient(X0)) & ((tall(X0) & patient(X0)) | (quiet(X0) & ~humble(X0)))) [flattening 40]
45. (((~quiet(alice) | ~happy(alice)) & (quiet(alice) | happy(alice))) | ! [X0] : (~patient(X0) & strong(X0))) & (? [X0] : (patient(X0) | ~strong(X0)) | ((happy(alice) | ~quiet(alice)) & (quiet(alice) | ~happy(alice)))) [nnf transformation 7]
46. (((~quiet(alice) | ~happy(alice)) & (quiet(alice) | happy(alice))) | ! [X0] : (~patient(X0) & strong(X0))) & (? [X1] : (patient(X1) | ~strong(X1)) | ((happy(alice) | ~quiet(alice)) & (quiet(alice) | ~happy(alice)))) [rectify 45]
47. ? [X1] : (patient(X1) | ~strong(X1)) => (patient(sK3) | ~strong(sK3)) [choice axiom]
48. (((~quiet(alice) | ~happy(alice)) & (quiet(alice) | happy(alice))) | ! [X0] : (~patient(X0) & strong(X0))) & ((patient(sK3) | ~strong(sK3)) | ((happy(alice) | ~quiet(alice)) & (quiet(alice) | ~happy(alice)))) [skolemisation 46,47]
51. ! [X0] : (((~rich(X0) | ~generous(X0)) | ~quiet(X0)) & (quiet(X0) | (rich(X0) & generous(X0)))) [nnf transformation 10]
52. ! [X0] : ((~rich(X0) | ~generous(X0) | ~quiet(X0)) & (quiet(X0) | (rich(X0) & generous(X0)))) [flattening 51]
53. ! [X0] : (((~creative(X0) | quiet(X0)) | ((~creative(X0) | ~happy(X0)) & (happy(X0) | creative(X0)))) & (((~happy(X0) | creative(X0)) & (happy(X0) | ~creative(X0))) | (creative(X0) & ~quiet(X0)))) [nnf transformation 11]
54. ! [X0] : ((~creative(X0) | quiet(X0) | ((~creative(X0) | ~happy(X0)) & (happy(X0) | creative(X0)))) & (((~happy(X0) | creative(X0)) & (happy(X0) | ~creative(X0))) | (creative(X0) & ~quiet(X0)))) [flattening 53]
58. ! [X0] : (((~brave(X0) | quiet(X0)) | ((brave(X0) | ~patient(X0)) & (patient(X0) | ~brave(X0)))) & (((~patient(X0) | ~brave(X0)) & (patient(X0) | brave(X0))) | (brave(X0) & ~quiet(X0)))) [nnf transformation 13]
59. ! [X0] : ((~brave(X0) | quiet(X0) | ((brave(X0) | ~patient(X0)) & (patient(X0) | ~brave(X0)))) & (((~patient(X0) | ~brave(X0)) & (patient(X0) | brave(X0))) | (brave(X0) & ~quiet(X0)))) [flattening 58]
63. ! [X0] : ((((strong(X0) | happy(X0)) & (~strong(X0) | ~happy(X0))) | ~patient(X0)) & (patient(X0) | ((~happy(X0) | strong(X0)) & (~strong(X0) | happy(X0))))) [nnf transformation 15]
73. generous(X0) | creative(X0) [cnf transformation 33]
74. rich(X0) | creative(X0) [cnf transformation 33]
94. quiet(X0) | patient(X0) [cnf transformation 41]
98. ~creative(X0) | strong(X0) [cnf transformation 26]
105. quiet(alice) | happy(alice) | ~patient(X0) [cnf transformation 48]
107. ~quiet(alice) | ~happy(alice) | ~patient(X0) [cnf transformation 48]
114. ~quiet(X0) | ~generous(X0) | ~rich(X0) [cnf transformation 52]
115. ~quiet(X0) | ~creative(X0) | happy(X0) [cnf transformation 54]
118. ~happy(X0) | creative(X0) | creative(X0) [cnf transformation 54]
124. patient(X0) | brave(X0) | brave(X0) [cnf transformation 59]
135. ~strong(X0) | ~happy(X0) | ~patient(X0) [cnf transformation 63]
148. ~brave(lucy) [cnf transformation 21]
153. brave(X0) | patient(X0) [duplicate literal removal 124]
155. ~happy(X0) | creative(X0) [duplicate literal removal 118]
207. 12 <=> ! [X0] : ~patient(X0) [avatar definition]
208. ~patient(X0) <- (12) [avatar component clause 207]
210. 13 <=> happy(alice) [avatar definition]
211. happy(alice) <- (13) [avatar component clause 210]
212. ~happy(alice) <- (~13) [avatar component clause 210]
214. 14 <=> quiet(alice) [avatar definition]
215. quiet(alice) <- (14) [avatar component clause 214]
216. ~quiet(alice) <- (~14) [avatar component clause 214]
217. 12 | ~13 | ~14 [avatar split clause 107,214,210,207]
222. 12 | 13 | 14 [avatar split clause 105,214,210,207]
287. patient(alice) <- (~14) [resolution 94,216]
295. patient(lucy) [resolution 153,148]
300. creative(alice) <- (13) [resolution 155,211]
325. strong(alice) <- (13) [resolution 300,98]
459. ~happy(alice) | ~patient(alice) <- (13) [resolution 325,135]
462. ~patient(alice) <- (13) [subsumption resolution 459,211]
463. $false <- (13, ~14) [subsumption resolution 462,287]
464. ~13 | 14 [avatar contradiction clause 463]
467. ~creative(alice) | happy(alice) <- (14) [resolution 215,115]
468. ~generous(alice) | ~rich(alice) <- (14) [resolution 215,114]
478. ~creative(alice) <- (~13, 14) [subsumption resolution 467,212]
480. 49 <=> rich(alice) [avatar definition]
482. ~rich(alice) <- (~49) [avatar component clause 480]
484. 50 <=> generous(alice) [avatar definition]
486. ~generous(alice) <- (~50) [avatar component clause 484]
487. ~49 | ~50 | ~14 [avatar split clause 468,214,484,480]
500. creative(alice) <- (~50) [resolution 486,73]
501. $false <- (~13, 14, ~50) [subsumption resolution 500,478]
502. 13 | ~14 | 50 [avatar contradiction clause 501]
503. creative(alice) <- (~49) [resolution 482,74]
504. $false <- (~13, 14, ~49) [subsumption resolution 503,478]
505. 13 | ~14 | 49 [avatar contradiction clause 504]
506. $false <- (12) [resolution 208,295]
511. ~12 [avatar contradiction clause 506]
512. $false [avatar sat refutation 217,222,464,487,502,505,511]
% SZS output end Proof for 5652694847452483454245746
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not old is either not tall or kind and vice versa.
If mary is rich or quiet then someone is both curious and strong.
Everyone who is both not strong and rich is not rich or not creative.
Everyone who is brave is both not calm and humble and vice versa.
Everyone who is wise is both not funny and not tall and vice versa.
If someone is not kind or patient then john is both patient and not rich.
Everyone who is strong is either rich or not generous.
Everyone who is not old or not creative is both not generous and kind.
If lucy is either calm or not tall then someone is either not funny or not generous.
If someone is not tall or not kind then someone is either not strong or humble.
Everyone who is humble or curious is both brave and strong and vice versa.
If someone is both kind and not strong then fred is not old or humble and vice versa.
If someone is either not wise or strong then alice is both not kind and not calm and vice versa.
Everyone who is happy or not kind is either not generous or calm.
Everyone who is kind is both patient and not kind.
Everyone who is not strong or brave is not kind or not happy and vice versa.
Susan is happy.
Someone is both not kind and happy.
Lucy is not curious or happy.
Lucy is patient or strong.
Paul is not patient or old. | Fred is not humble. | entailment | (![X]:(~old(X)<=>(~tall(X)<~>kind(X))))&
(((rich(mary)|quiet(mary)))=>(?[X]:((curious(X)&strong(X)))))&
(![X]:((~strong(X)&rich(X))=>(~rich(X)|~creative(X))))&
(![X]:(brave(X)<=>(~calm(X)&humble(X))))&
(![X]:(wise(X)<=>(~funny(X)&~tall(X))))&
((?[X]:((~kind(X)|patient(X))))=>((patient(john)&~rich(john))))&
(![X]:(strong(X)=>(rich(X)<~>~generous(X))))&
(![X]:((~old(X)|~creative(X))=>(~generous(X)&kind(X))))&
(((calm(lucy)<~>~tall(lucy)))=>(?[X]:((~funny(X)<~>~generous(X)))))&
((?[X]:((~tall(X)|~kind(X))))=>(?[X]:((~strong(X)<~>humble(X)))))&
(![X]:((humble(X)|curious(X))<=>(brave(X)&strong(X))))&
((?[X]:((kind(X)&~strong(X))))<=>((~old(fred)|humble(fred))))&
((?[X]:((~wise(X)<~>strong(X))))<=>((~kind(alice)&~calm(alice))))&
(![X]:((happy(X)|~kind(X))=>(~generous(X)<~>calm(X))))&
(![X]:(kind(X)=>(patient(X)&~kind(X))))&
(![X]:((~strong(X)|brave(X))<=>(~kind(X)|~happy(X))))&
(happy(susan))&
(?[X]:((~kind(X)&happy(X))))&
((~curious(lucy)|happy(lucy)))&
((patient(lucy)|strong(lucy)))&
((~patient(paul)|old(paul))) | ~humble(fred) | [
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6582031779247518773690009
% SZS output start Proof for 6582031779247518773690009
12. ? [X0] : (~strong(X0) & kind(X0)) <=> (humble(fred) | ~old(fred)) [input p11]
15. ! [X0] : (kind(X0) => (~kind(X0) & patient(X0))) [input p14]
22. humble(fred) [input hypothesis]
34. ! [X0] : ((~kind(X0) & patient(X0)) | ~kind(X0)) [ennf transformation 15]
52. (? [X0] : (~strong(X0) & kind(X0)) | (~humble(fred) & old(fred))) & ((humble(fred) | ~old(fred)) | ! [X0] : (strong(X0) | ~kind(X0))) [nnf transformation 12]
53. (? [X0] : (~strong(X0) & kind(X0)) | (~humble(fred) & old(fred))) & (humble(fred) | ~old(fred) | ! [X0] : (strong(X0) | ~kind(X0))) [flattening 52]
54. (? [X0] : (~strong(X0) & kind(X0)) | (~humble(fred) & old(fred))) & (humble(fred) | ~old(fred) | ! [X1] : (strong(X1) | ~kind(X1))) [rectify 53]
55. ? [X0] : (~strong(X0) & kind(X0)) => (~strong(sK3) & kind(sK3)) [choice axiom]
56. ((~strong(sK3) & kind(sK3)) | (~humble(fred) & old(fred))) & (humble(fred) | ~old(fred) | ! [X1] : (strong(X1) | ~kind(X1))) [skolemisation 54,55]
105. kind(sK3) | ~humble(fred) [cnf transformation 56]
119. ~kind(X0) | ~kind(X0) [cnf transformation 34]
130. humble(fred) [cnf transformation 22]
131. ~kind(X0) [duplicate literal removal 119]
201. 15 <=> humble(fred) [avatar definition]
215. 18 <=> kind(sK3) [avatar definition]
217. kind(sK3) <- (18) [avatar component clause 215]
218. ~15 | 18 [avatar split clause 105,215,201]
280. 15 [avatar split clause 130,201]
281. $false <- (18) [subsumption resolution 217,131]
282. ~18 [avatar contradiction clause 281]
285. $false [avatar sat refutation 218,280,282]
% SZS output end Proof for 6582031779247518773690009
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not brave or rich is both generous and old.
Everyone who is both not strong and not happy is funny or generous and vice versa.
If someone is old then someone is both patient and rich and vice versa.
If someone is either not strong or not generous then someone is both not creative and creative.
If someone is not tall then fred is both patient and not quiet and vice versa.
If someone is not wise or not tall then lucy is not curious or old and vice versa.
Everyone who is either not funny or not quiet is both rich and not creative.
Everyone who is both wise and curious is both strong and not kind and vice versa.
Everyone who is either quiet or not kind is kind.
If paul is creative then someone is both calm and creative.
Everyone who is not strong or not tall is quiet or funny and vice versa.
If susan is either not creative or quiet then susan is not tall or old and vice versa.
If someone is creative then paul is both not tall and not kind.
Someone is patient or strong.
Paul is both not rich and funny.
Lucy is either not quiet or not kind.
Paul is strong or not happy.
Someone is both not old and not creative. | Fred is kind. | neutral | (![X]:((~brave(X)|rich(X))=>(generous(X)&old(X))))&
(![X]:((~strong(X)&~happy(X))<=>(funny(X)|generous(X))))&
((?[X]:(old(X)))<=>(?[X]:((patient(X)&rich(X)))))&
((?[X]:((~strong(X)<~>~generous(X))))=>(?[X]:((~creative(X)&creative(X)))))&
((?[X]:(~tall(X)))<=>((patient(fred)&~quiet(fred))))&
((?[X]:((~wise(X)|~tall(X))))<=>((~curious(lucy)|old(lucy))))&
(![X]:((~funny(X)<~>~quiet(X))=>(rich(X)&~creative(X))))&
(![X]:((wise(X)&curious(X))<=>(strong(X)&~kind(X))))&
(![X]:((quiet(X)<~>~kind(X))=>kind(X)))&
((creative(paul))=>(?[X]:((calm(X)&creative(X)))))&
(![X]:((~strong(X)|~tall(X))<=>(quiet(X)|funny(X))))&
(((~creative(susan)<~>quiet(susan)))<=>((~tall(susan)|old(susan))))&
((?[X]:(creative(X)))=>((~tall(paul)&~kind(paul))))&
(?[X]:((patient(X)|strong(X))))&
((~rich(paul)&funny(paul)))&
((~quiet(lucy)<~>~kind(lucy)))&
((strong(paul)|~happy(paul)))&
(?[X]:((~old(X)&~creative(X)))) | kind(fred) | [] | null | 0 |
If alice is old then alice is not tall or not generous and vice versa.
Everyone who is tall or not old is not creative and vice versa.
If fred is both not quiet and tall then john is wise or not old and vice versa.
Everyone who is both tall and not funny is not old or happy.
Everyone who is either not kind or kind is both strong and kind.
If someone is both creative and not wise then someone is humble.
Everyone who is either not quiet or not humble is not generous.
If someone is not strong or generous then someone is either brave or not wise and vice versa.
If john is either not patient or brave then someone is both not wise and creative.
If john is kind or not wise then someone is not old or funny.
If someone is both happy and not patient then someone is both not quiet and not creative.
If someone is funny then someone is curious or happy.
Everyone who is not funny is both creative and not funny.
Everyone who is not funny or not quiet is either curious or humble.
Everyone who is either tall or not strong is both curious and not quiet.
Everyone who is quiet is quiet or not quiet.
Susan is kind or not humble.
Alice is either not quiet or funny.
Someone is not brave.
Mary is tall or humble.
Someone is old or humble.
Someone is old. | Alice is not creative. | contradiction | ((old(alice))<=>((~tall(alice)|~generous(alice))))&
(![X]:((tall(X)|~old(X))<=>~creative(X)))&
(((~quiet(fred)&tall(fred)))<=>((wise(john)|~old(john))))&
(![X]:((tall(X)&~funny(X))=>(~old(X)|happy(X))))&
(![X]:((~kind(X)<~>kind(X))=>(strong(X)&kind(X))))&
((?[X]:((creative(X)&~wise(X))))=>(?[X]:(humble(X))))&
(![X]:((~quiet(X)<~>~humble(X))=>~generous(X)))&
((?[X]:((~strong(X)|generous(X))))<=>(?[X]:((brave(X)<~>~wise(X)))))&
(((~patient(john)<~>brave(john)))=>(?[X]:((~wise(X)&creative(X)))))&
(((kind(john)|~wise(john)))=>(?[X]:((~old(X)|funny(X)))))&
((?[X]:((happy(X)&~patient(X))))=>(?[X]:((~quiet(X)&~creative(X)))))&
((?[X]:(funny(X)))=>(?[X]:((curious(X)|happy(X)))))&
(![X]:(~funny(X)=>(creative(X)&~funny(X))))&
(![X]:((~funny(X)|~quiet(X))=>(curious(X)<~>humble(X))))&
(![X]:((tall(X)<~>~strong(X))=>(curious(X)&~quiet(X))))&
(![X]:(quiet(X)=>(quiet(X)|~quiet(X))))&
((kind(susan)|~humble(susan)))&
((~quiet(alice)<~>funny(alice)))&
(?[X]:(~brave(X)))&
((tall(mary)|humble(mary)))&
(?[X]:((old(X)|humble(X))))&
(?[X]:(old(X))) | ~creative(alice) | [
"p0",
"p1",
"p4",
"p12",
"p14",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 590183361524201887825202
% SZS output start Proof for 590183361524201887825202
1. old(alice) <=> (~generous(alice) | ~tall(alice)) [input p0]
2. ! [X0] : ((~old(X0) | tall(X0)) <=> ~creative(X0)) [input p1]
5. ! [X0] : ((~kind(X0) <~> kind(X0)) => (kind(X0) & strong(X0))) [input p4]
13. ! [X0] : (~funny(X0) => (~funny(X0) & creative(X0))) [input p12]
15. ! [X0] : ((tall(X0) <~> ~strong(X0)) => (~quiet(X0) & curious(X0))) [input p14]
18. ~quiet(alice) <~> funny(alice) [input p17]
23. ~creative(alice) [input hypothesis]
30. ! [X0] : ((kind(X0) & strong(X0)) | (~kind(X0) <=> kind(X0))) [ennf transformation 5]
37. ! [X0] : ((~funny(X0) & creative(X0)) | funny(X0)) [ennf transformation 13]
39. ! [X0] : ((~quiet(X0) & curious(X0)) | (tall(X0) <=> ~strong(X0))) [ennf transformation 15]
42. (old(alice) | (generous(alice) & tall(alice))) & ((~generous(alice) | ~tall(alice)) | ~old(alice)) [nnf transformation 1]
43. (old(alice) | (generous(alice) & tall(alice))) & (~generous(alice) | ~tall(alice) | ~old(alice)) [flattening 42]
44. ! [X0] : (((~old(X0) | tall(X0)) | creative(X0)) & (~creative(X0) | (old(X0) & ~tall(X0)))) [nnf transformation 2]
45. ! [X0] : ((~old(X0) | tall(X0) | creative(X0)) & (~creative(X0) | (old(X0) & ~tall(X0)))) [flattening 44]
48. ! [X0] : ((kind(X0) & strong(X0)) | ((~kind(X0) | ~kind(X0)) & (kind(X0) | kind(X0)))) [nnf transformation 30]
70. ! [X0] : ((~quiet(X0) & curious(X0)) | ((tall(X0) | strong(X0)) & (~strong(X0) | ~tall(X0)))) [nnf transformation 39]
71. (~funny(alice) | quiet(alice)) & (funny(alice) | ~quiet(alice)) [nnf transformation 18]
79. old(alice) | tall(alice) [cnf transformation 43]
83. ~old(X0) | tall(X0) | creative(X0) [cnf transformation 45]
91. strong(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 48]
92. kind(X0) | kind(X0) | kind(X0) [cnf transformation 48]
112. funny(X0) | creative(X0) [cnf transformation 37]
120. ~quiet(X0) | ~strong(X0) | ~tall(X0) [cnf transformation 70]
125. ~funny(alice) | quiet(alice) [cnf transformation 71]
130. ~creative(alice) [cnf transformation 23]
133. strong(X0) | ~kind(X0) [duplicate literal removal 91]
134. kind(X0) [duplicate literal removal 92]
141. 2 <=> old(alice) [avatar definition]
143. old(alice) <- (2) [avatar component clause 141]
146. 3 <=> tall(alice) [avatar definition]
149. 3 | 2 [avatar split clause 79,141,146]
172. strong(X0) [subsumption resolution 133,134]
264. ~quiet(X0) | ~tall(X0) [subsumption resolution 120,172]
267. 28 <=> quiet(alice) [avatar definition]
269. quiet(alice) <- (28) [avatar component clause 267]
271. 29 <=> funny(alice) [avatar definition]
273. ~funny(alice) <- (~29) [avatar component clause 271]
274. 28 | ~29 [avatar split clause 125,271,267]
295. creative(alice) <- (~29) [resolution 112,273]
302. $false <- (~29) [subsumption resolution 295,130]
303. 29 [avatar contradiction clause 302]
304. ~tall(alice) <- (28) [resolution 264,269]
306. tall(alice) | creative(alice) <- (2) [resolution 83,143]
340. tall(alice) <- (2) [subsumption resolution 306,130]
341. 3 | ~2 [avatar split clause 340,141,146]
342. ~3 | ~28 [avatar split clause 304,267,146]
343. $false [avatar sat refutation 149,274,303,341,342]
% SZS output end Proof for 590183361524201887825202
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not old and not calm then susan is both funny and not wise and vice versa.
Everyone who is brave or creative is either not generous or quiet.
If someone is both creative and rich then lucy is quiet or not funny.
If mary is either not wise or strong then susan is funny or not calm and vice versa.
If paul is calm then someone is either rich or humble.
If someone is not funny then lucy is not curious or funny and vice versa.
If lucy is not creative or brave then someone is either not tall or curious.
Everyone who is either not kind or quiet is both not patient and not tall.
If someone is either wise or happy then fred is not brave.
Everyone who is both calm and not wise is both not happy and old and vice versa.
If fred is either rich or happy then someone is not tall or calm and vice versa.
If mary is old or not brave then someone is not humble or not curious and vice versa.
Everyone who is not kind is both humble and not brave and vice versa.
If someone is tall then susan is both not patient and creative.
Everyone who is both not brave and not happy is both happy and patient.
Everyone who is not old or not calm is humble or not happy.
Someone is quiet.
Someone is old.
Lucy is both not brave and tall.
Paul is either kind or strong.
Someone is rich.
Susan is either tall or kind.
Someone is either not tall or not calm.
Alice is happy or tall. | Lucy is not happy. | contradiction | ((?[X]:((~old(X)&~calm(X))))<=>((funny(susan)&~wise(susan))))&
(![X]:((brave(X)|creative(X))=>(~generous(X)<~>quiet(X))))&
((?[X]:((creative(X)&rich(X))))=>((quiet(lucy)|~funny(lucy))))&
(((~wise(mary)<~>strong(mary)))<=>((funny(susan)|~calm(susan))))&
((calm(paul))=>(?[X]:((rich(X)<~>humble(X)))))&
((?[X]:(~funny(X)))<=>((~curious(lucy)|funny(lucy))))&
(((~creative(lucy)|brave(lucy)))=>(?[X]:((~tall(X)<~>curious(X)))))&
(![X]:((~kind(X)<~>quiet(X))=>(~patient(X)&~tall(X))))&
((?[X]:((wise(X)<~>happy(X))))=>(~brave(fred)))&
(![X]:((calm(X)&~wise(X))<=>(~happy(X)&old(X))))&
(((rich(fred)<~>happy(fred)))<=>(?[X]:((~tall(X)|calm(X)))))&
(((old(mary)|~brave(mary)))<=>(?[X]:((~humble(X)|~curious(X)))))&
(![X]:(~kind(X)<=>(humble(X)&~brave(X))))&
((?[X]:(tall(X)))=>((~patient(susan)&creative(susan))))&
(![X]:((~brave(X)&~happy(X))=>(happy(X)&patient(X))))&
(![X]:((~old(X)|~calm(X))=>(humble(X)|~happy(X))))&
(?[X]:(quiet(X)))&
(?[X]:(old(X)))&
((~brave(lucy)&tall(lucy)))&
((kind(paul)<~>strong(paul)))&
(?[X]:(rich(X)))&
((tall(susan)<~>kind(susan)))&
(?[X]:((~tall(X)<~>~calm(X))))&
((happy(alice)|tall(alice))) | ~happy(lucy) | [
"p14",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 670119340852679810989842
% SZS output start Proof for 670119340852679810989842
15. ! [X0] : ((~happy(X0) & ~brave(X0)) => (patient(X0) & happy(X0))) [input p14]
19. tall(lucy) & ~brave(lucy) [input p18]
25. ~happy(lucy) [input hypothesis]
34. ! [X0] : ((patient(X0) & happy(X0)) | (happy(X0) | brave(X0))) [ennf transformation 15]
35. ! [X0] : ((patient(X0) & happy(X0)) | happy(X0) | brave(X0)) [flattening 34]
132. happy(X0) | happy(X0) | brave(X0) [cnf transformation 35]
138. ~brave(lucy) [cnf transformation 19]
148. ~happy(lucy) [cnf transformation 25]
149. happy(X0) | brave(X0) [duplicate literal removal 132]
232. 18 <=> brave(lucy) [avatar definition]
234. ~brave(lucy) <- (~18) [avatar component clause 232]
330. ~18 [avatar split clause 138,232]
373. brave(lucy) [resolution 149,148]
375. $false <- (~18) [subsumption resolution 373,234]
376. 18 [avatar contradiction clause 375]
379. $false [avatar sat refutation 330,376]
% SZS output end Proof for 670119340852679810989842
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise or patient then john is either kind or not old and vice versa.
Everyone who is both patient and not humble is both not humble and not curious and vice versa.
If john is curious then someone is not creative or funny and vice versa.
Everyone who is either not tall or brave is not curious or not strong and vice versa.
Everyone who is either happy or rich is not patient or rich and vice versa.
If fred is both strong and wise then someone is not calm and vice versa.
Everyone who is both generous and not generous is not quiet and vice versa.
Everyone who is not patient is both funny and kind.
If someone is not brave then john is wise.
Everyone who is kind is both not rich and funny and vice versa.
If someone is kind or not wise then someone is calm and vice versa.
Everyone who is brave is not strong or humble.
Everyone who is either strong or not calm is either rich or funny.
Everyone who is not generous is not strong or creative.
Everyone who is both not kind and not wise is brave or not rich and vice versa.
If paul is either strong or old then paul is either not rich or humble and vice versa.
John is not kind.
Susan is not calm.
Mary is either not kind or happy.
Someone is not old.
Susan is not tall.
Mary is either quiet or not creative.
Someone is not wise or strong. | Paul is happy. | contradiction | (((wise(fred)<~>patient(fred)))<=>((kind(john)<~>~old(john))))&
(![X]:((patient(X)&~humble(X))<=>(~humble(X)&~curious(X))))&
((curious(john))<=>(?[X]:((~creative(X)|funny(X)))))&
(![X]:((~tall(X)<~>brave(X))<=>(~curious(X)|~strong(X))))&
(![X]:((happy(X)<~>rich(X))<=>(~patient(X)|rich(X))))&
(((strong(fred)&wise(fred)))<=>(?[X]:(~calm(X))))&
(![X]:((generous(X)&~generous(X))<=>~quiet(X)))&
(![X]:(~patient(X)=>(funny(X)&kind(X))))&
((?[X]:(~brave(X)))=>(wise(john)))&
(![X]:(kind(X)<=>(~rich(X)&funny(X))))&
((?[X]:((kind(X)|~wise(X))))<=>(?[X]:(calm(X))))&
(![X]:(brave(X)=>(~strong(X)|humble(X))))&
(![X]:((strong(X)<~>~calm(X))=>(rich(X)<~>funny(X))))&
(![X]:(~generous(X)=>(~strong(X)|creative(X))))&
(![X]:((~kind(X)&~wise(X))<=>(brave(X)|~rich(X))))&
(((strong(paul)<~>old(paul)))<=>((~rich(paul)<~>humble(paul))))&
(~kind(john))&
(~calm(susan))&
((~kind(mary)<~>happy(mary)))&
(?[X]:(~old(X)))&
(~tall(susan))&
((quiet(mary)<~>~creative(mary)))&
(?[X]:((~wise(X)|strong(X)))) | happy(paul) | [
"p4",
"p7",
"p9",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5791179371319053906230034
% SZS output start Proof for 5791179371319053906230034
5. ! [X0] : ((happy(X0) <~> rich(X0)) <=> (rich(X0) | ~patient(X0))) [input p4]
8. ! [X0] : (~patient(X0) => (kind(X0) & funny(X0))) [input p7]
10. ! [X0] : (kind(X0) <=> (funny(X0) & ~rich(X0))) [input p9]
15. ! [X0] : ((~wise(X0) & ~kind(X0)) <=> (~rich(X0) | brave(X0))) [input p14]
24. happy(paul) [input hypothesis]
26. ! [X0] : ((kind(X0) & funny(X0)) | patient(X0)) [ennf transformation 8]
42. ! [X0] : ((((~rich(X0) | ~happy(X0)) & (rich(X0) | happy(X0))) | (~rich(X0) & patient(X0))) & ((rich(X0) | ~patient(X0)) | ((happy(X0) | ~rich(X0)) & (rich(X0) | ~happy(X0))))) [nnf transformation 5]
43. ! [X0] : ((((~rich(X0) | ~happy(X0)) & (rich(X0) | happy(X0))) | (~rich(X0) & patient(X0))) & (rich(X0) | ~patient(X0) | ((happy(X0) | ~rich(X0)) & (rich(X0) | ~happy(X0))))) [flattening 42]
51. ! [X0] : ((kind(X0) | (~funny(X0) | rich(X0))) & ((funny(X0) & ~rich(X0)) | ~kind(X0))) [nnf transformation 10]
52. ! [X0] : ((kind(X0) | ~funny(X0) | rich(X0)) & ((funny(X0) & ~rich(X0)) | ~kind(X0))) [flattening 51]
59. ! [X0] : (((~wise(X0) & ~kind(X0)) | (rich(X0) & ~brave(X0))) & ((~rich(X0) | brave(X0)) | (wise(X0) | kind(X0)))) [nnf transformation 15]
60. ! [X0] : (((~wise(X0) & ~kind(X0)) | (rich(X0) & ~brave(X0))) & (~rich(X0) | brave(X0) | wise(X0) | kind(X0))) [flattening 59]
89. rich(X0) | ~patient(X0) | rich(X0) | ~happy(X0) [cnf transformation 43]
94. ~rich(X0) | ~happy(X0) | ~rich(X0) [cnf transformation 43]
102. kind(X0) | patient(X0) [cnf transformation 26]
104. ~rich(X0) | ~kind(X0) [cnf transformation 52]
118. ~kind(X0) | rich(X0) [cnf transformation 60]
138. happy(paul) [cnf transformation 24]
139. rich(X0) | ~patient(X0) | ~happy(X0) [duplicate literal removal 89]
140. ~rich(X0) | ~happy(X0) [duplicate literal removal 94]
186. ~happy(X0) | ~patient(X0) [subsumption resolution 139,140]
231. 20 <=> ! [X3] : ~kind(X3) [avatar definition]
232. ~kind(X3) <- (20) [avatar component clause 231]
234. ~kind(X0) [subsumption resolution 118,104]
235. 20 [avatar split clause 234,231]
292. patient(X0) <- (20) [resolution 102,232]
309. ~patient(paul) [resolution 186,138]
310. $false <- (20) [subsumption resolution 309,292]
311. ~20 [avatar contradiction clause 310]
312. $false [avatar sat refutation 235,311]
% SZS output end Proof for 5791179371319053906230034
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not patient is old or tall and vice versa. If mary is either strong or not humble then paul is happy. Everyone who is either wise or old is not generous or wise and vice versa. If alice is both kind and not humble then lucy is both not creative and brave. If alice is not patient or not calm then someone is not funny. If someone is not quiet or strong then fred is not rich or happy. If john is not curious or not patient then paul is either quiet or not happy and vice versa. Everyone who is not curious or not funny is old. If paul is not humble or not wise then alice is both funny and generous and vice versa. Everyone who is not generous is both not curious and funny and vice versa. Everyone who is old or curious is both rich and not strong. Everyone who is both not humble and not generous is either not patient or kind. Everyone who is both not curious and humble is quiet or not funny. If someone is either patient or not curious then someone is either not wise or wise. Everyone who is not quiet or not wise is both happy and generous and vice versa. Someone is brave or quiet. John is either not generous or not brave. Someone is either not wise or not brave. Someone is patient or humble. Someone is not curious or rich. Lucy is both happy and not quiet. | John is not funny. | contradiction | (![X]:(~patient(X)<=>(old(X)|tall(X))))&
(((strong(mary)<~>~humble(mary)))=>(happy(paul)))&
(![X]:((wise(X)<~>old(X))<=>(~generous(X)|wise(X))))&
(((kind(alice)&~humble(alice)))=>((~creative(lucy)&brave(lucy))))&
(((~patient(alice)|~calm(alice)))=>(?[X]:(~funny(X))))&
((?[X]:((~quiet(X)|strong(X))))=>((~rich(fred)|happy(fred))))&
(((~curious(john)|~patient(john)))<=>((quiet(paul)<~>~happy(paul))))&
(![X]:((~curious(X)|~funny(X))=>old(X)))&
(((~humble(paul)|~wise(paul)))<=>((funny(alice)&generous(alice))))&
(![X]:(~generous(X)<=>(~curious(X)&funny(X))))&
(![X]:((old(X)|curious(X))=>(rich(X)&~strong(X))))&
(![X]:((~humble(X)&~generous(X))=>(~patient(X)<~>kind(X))))&
(![X]:((~curious(X)&humble(X))=>(quiet(X)|~funny(X))))&
((?[X]:((patient(X)<~>~curious(X))))=>(?[X]:((~wise(X)<~>wise(X)))))&
(![X]:((~quiet(X)|~wise(X))<=>(happy(X)&generous(X))))&
(?[X]:((brave(X)|quiet(X))))&
((~generous(john)<~>~brave(john)))&
(?[X]:((~wise(X)<~>~brave(X))))&
(?[X]:((patient(X)|humble(X))))&
(?[X]:((~curious(X)|rich(X))))&
((happy(lucy)&~quiet(lucy))) | ~funny(john) | [
"p2",
"p7",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4171068845606485886324371
% SZS output start Proof for 4171068845606485886324371
3. ! [X0] : ((wise(X0) <~> old(X0)) <=> (wise(X0) | ~generous(X0))) [input p2]
8. ! [X0] : ((~funny(X0) | ~curious(X0)) => old(X0)) [input p7]
15. ! [X0] : ((~wise(X0) | ~quiet(X0)) <=> (generous(X0) & happy(X0))) [input p14]
22. ~funny(john) [input hypothesis]
32. ! [X0] : (old(X0) | (funny(X0) & curious(X0))) [ennf transformation 8]
42. ! [X0] : ((((~old(X0) | ~wise(X0)) & (old(X0) | wise(X0))) | (~wise(X0) & generous(X0))) & ((wise(X0) | ~generous(X0)) | ((wise(X0) | ~old(X0)) & (old(X0) | ~wise(X0))))) [nnf transformation 3]
43. ! [X0] : ((((~old(X0) | ~wise(X0)) & (old(X0) | wise(X0))) | (~wise(X0) & generous(X0))) & (wise(X0) | ~generous(X0) | ((wise(X0) | ~old(X0)) & (old(X0) | ~wise(X0))))) [flattening 42]
57. ! [X0] : (((~wise(X0) | ~quiet(X0)) | (~generous(X0) | ~happy(X0))) & ((generous(X0) & happy(X0)) | (wise(X0) & quiet(X0)))) [nnf transformation 15]
58. ! [X0] : ((~wise(X0) | ~quiet(X0) | ~generous(X0) | ~happy(X0)) & ((generous(X0) & happy(X0)) | (wise(X0) & quiet(X0)))) [flattening 57]
75. wise(X0) | ~generous(X0) | wise(X0) | ~old(X0) [cnf transformation 43]
79. ~old(X0) | ~wise(X0) | ~wise(X0) [cnf transformation 43]
91. funny(X0) | old(X0) [cnf transformation 32]
114. generous(X0) | wise(X0) [cnf transformation 58]
125. ~funny(john) [cnf transformation 22]
126. wise(X0) | ~generous(X0) | ~old(X0) [duplicate literal removal 75]
127. ~wise(X0) | ~old(X0) [duplicate literal removal 79]
142. ~generous(X0) | ~old(X0) [subsumption resolution 126,127]
259. old(john) [resolution 91,125]
284. ~old(X0) | wise(X0) [resolution 142,114]
289. ~old(X0) [subsumption resolution 284,127]
295. $false [subsumption resolution 259,289]
% SZS output end Proof for 4171068845606485886324371
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not curious is either quiet or not funny and vice versa.
If susan is both not happy and not humble then susan is either not quiet or not old.
Everyone who is both not happy and not rich is strong or not creative.
If lucy is not patient then lucy is patient.
Everyone who is not creative is both not creative and not brave.
If fred is both rich and not creative then lucy is not quiet and vice versa.
Everyone who is generous is either happy or humble and vice versa.
Everyone who is not tall is both happy and not quiet and vice versa.
Everyone who is either generous or not rich is not strong and vice versa.
If lucy is humble then someone is both not patient and strong and vice versa.
If someone is either not patient or not generous then susan is humble and vice versa.
Everyone who is both generous and kind is humble and vice versa.
If someone is either not strong or not wise then alice is not tall or rich.
If alice is both tall and not old then someone is both humble and not creative and vice versa.
Everyone who is rich is both not happy and not creative.
Everyone who is both not generous and rich is both strong and not funny.
Paul is either wise or not brave.
Someone is either happy or not brave.
Someone is both curious and not creative.
Someone is funny or not old.
Someone is creative or not funny.
Someone is wise or not generous.
John is either not patient or humble.
Someone is not generous. | Lucy is not patient. | contradiction | (![X]:(~curious(X)<=>(quiet(X)<~>~funny(X))))&
(((~happy(susan)&~humble(susan)))=>((~quiet(susan)<~>~old(susan))))&
(![X]:((~happy(X)&~rich(X))=>(strong(X)|~creative(X))))&
((~patient(lucy))=>(patient(lucy)))&
(![X]:(~creative(X)=>(~creative(X)&~brave(X))))&
(((rich(fred)&~creative(fred)))<=>(~quiet(lucy)))&
(![X]:(generous(X)<=>(happy(X)<~>humble(X))))&
(![X]:(~tall(X)<=>(happy(X)&~quiet(X))))&
(![X]:((generous(X)<~>~rich(X))<=>~strong(X)))&
((humble(lucy))<=>(?[X]:((~patient(X)&strong(X)))))&
((?[X]:((~patient(X)<~>~generous(X))))<=>(humble(susan)))&
(![X]:((generous(X)&kind(X))<=>humble(X)))&
((?[X]:((~strong(X)<~>~wise(X))))=>((~tall(alice)|rich(alice))))&
(((tall(alice)&~old(alice)))<=>(?[X]:((humble(X)&~creative(X)))))&
(![X]:(rich(X)=>(~happy(X)&~creative(X))))&
(![X]:((~generous(X)&rich(X))=>(strong(X)&~funny(X))))&
((wise(paul)<~>~brave(paul)))&
(?[X]:((happy(X)<~>~brave(X))))&
(?[X]:((curious(X)&~creative(X))))&
(?[X]:((funny(X)|~old(X))))&
(?[X]:((creative(X)|~funny(X))))&
(?[X]:((wise(X)|~generous(X))))&
((~patient(john)<~>humble(john)))&
(?[X]:(~generous(X))) | ~patient(lucy) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 6698657315827339919195550
% SZS output start Proof for 6698657315827339919195550
4. ~patient(lucy) => patient(lucy) [input p3]
25. ~patient(lucy) [input hypothesis]
32. patient(lucy) | patient(lucy) [ennf transformation 4]
83. patient(lucy) | patient(lucy) [cnf transformation 32]
132. ~patient(lucy) [cnf transformation 25]
133. patient(lucy) [duplicate literal removal 83]
295. $false [subsumption resolution 132,133]
% SZS output end Proof for 6698657315827339919195550
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 lucy is not old or old then john is tall and vice versa. Everyone who is both not old and not patient is either quiet or not old. If someone is not funny or old then someone is either curious or rich. If alice is both old and rich then lucy is not rich and vice versa. Everyone who is both not patient and not rich is either creative or humble and vice versa. Everyone who is funny or generous is both not strong and not kind. If paul is either not old or not rich then paul is not creative and vice versa. Everyone who is not old is both rich and patient and vice versa. Everyone who is not calm is happy and vice versa. Everyone who is both not patient and not happy is both not funny and quiet and vice versa. Everyone who is calm is both not old and not kind and vice versa. If john is both not kind and creative then lucy is both brave and creative and vice versa. If lucy is not wise then paul is quiet. Everyone who is old is either not old or quiet. Everyone who is happy or calm is both creative and not wise. If someone is not rich then john is both not kind and not quiet and vice versa. Susan is not calm. Someone is either curious or not funny. Someone is either not creative or humble. Fred is both curious and not strong. Someone is either brave or generous. Someone is both old and not curious. John is both quiet and generous. | Paul is calm. | contradiction | (((~old(lucy)|old(lucy)))<=>(tall(john)))&
(![X]:((~old(X)&~patient(X))=>(quiet(X)<~>~old(X))))&
((?[X]:((~funny(X)|old(X))))=>(?[X]:((curious(X)<~>rich(X)))))&
(((old(alice)&rich(alice)))<=>(~rich(lucy)))&
(![X]:((~patient(X)&~rich(X))<=>(creative(X)<~>humble(X))))&
(![X]:((funny(X)|generous(X))=>(~strong(X)&~kind(X))))&
(((~old(paul)<~>~rich(paul)))<=>(~creative(paul)))&
(![X]:(~old(X)<=>(rich(X)&patient(X))))&
(![X]:(~calm(X)<=>happy(X)))&
(![X]:((~patient(X)&~happy(X))<=>(~funny(X)&quiet(X))))&
(![X]:(calm(X)<=>(~old(X)&~kind(X))))&
(((~kind(john)&creative(john)))<=>((brave(lucy)&creative(lucy))))&
((~wise(lucy))=>(quiet(paul)))&
(![X]:(old(X)=>(~old(X)<~>quiet(X))))&
(![X]:((happy(X)|calm(X))=>(creative(X)&~wise(X))))&
((?[X]:(~rich(X)))<=>((~kind(john)&~quiet(john))))&
(~calm(susan))&
(?[X]:((curious(X)<~>~funny(X))))&
(?[X]:((~creative(X)<~>humble(X))))&
((curious(fred)&~strong(fred)))&
(?[X]:((brave(X)<~>generous(X))))&
(?[X]:((old(X)&~curious(X))))&
((quiet(john)&generous(john))) | calm(paul) | [
"p6",
"p8",
"p10",
"p14",
"p15",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 8723203013846129198666351
% SZS output start Proof for 8723203013846129198666351
7. (~old(paul) <~> ~rich(paul)) <=> ~creative(paul) [input p6]
9. ! [X0] : (~calm(X0) <=> happy(X0)) [input p8]
11. ! [X0] : (calm(X0) <=> (~kind(X0) & ~old(X0))) [input p10]
15. ! [X0] : ((calm(X0) | happy(X0)) => (~wise(X0) & creative(X0))) [input p14]
16. ? [X0] : ~rich(X0) <=> (~quiet(john) & ~kind(john)) [input p15]
23. generous(john) & quiet(john) [input p22]
24. calm(paul) [input hypothesis]
34. ! [X0] : ((~wise(X0) & creative(X0)) | (~calm(X0) & ~happy(X0))) [ennf transformation 15]
46. (((rich(paul) | old(paul)) & (~rich(paul) | ~old(paul))) | creative(paul)) & (~creative(paul) | ((~old(paul) | rich(paul)) & (~rich(paul) | old(paul)))) [nnf transformation 7]
49. ! [X0] : ((~calm(X0) | ~happy(X0)) & (happy(X0) | calm(X0))) [nnf transformation 9]
52. ! [X0] : ((calm(X0) | (kind(X0) | old(X0))) & ((~kind(X0) & ~old(X0)) | ~calm(X0))) [nnf transformation 11]
53. ! [X0] : ((calm(X0) | kind(X0) | old(X0)) & ((~kind(X0) & ~old(X0)) | ~calm(X0))) [flattening 52]
57. (? [X0] : ~rich(X0) | (quiet(john) | kind(john))) & ((~quiet(john) & ~kind(john)) | ! [X0] : rich(X0)) [nnf transformation 16]
58. (? [X0] : ~rich(X0) | quiet(john) | kind(john)) & ((~quiet(john) & ~kind(john)) | ! [X0] : rich(X0)) [flattening 57]
59. (? [X0] : ~rich(X0) | quiet(john) | kind(john)) & ((~quiet(john) & ~kind(john)) | ! [X1] : rich(X1)) [rectify 58]
60. ? [X0] : ~rich(X0) => ~rich(sK1) [choice axiom]
61. (~rich(sK1) | quiet(john) | kind(john)) & ((~quiet(john) & ~kind(john)) | ! [X1] : rich(X1)) [skolemisation 59,60]
93. ~creative(paul) | ~rich(paul) | old(paul) [cnf transformation 46]
100. happy(X0) | calm(X0) [cnf transformation 49]
106. ~calm(X0) | ~old(X0) [cnf transformation 53]
116. ~happy(X0) | creative(X0) [cnf transformation 34]
117. creative(X0) | ~calm(X0) [cnf transformation 34]
121. ~quiet(john) | rich(X1) [cnf transformation 61]
133. quiet(john) [cnf transformation 23]
135. calm(paul) [cnf transformation 24]
182. 10 <=> creative(paul) [avatar definition]
183. ~creative(paul) <- (~10) [avatar component clause 182]
186. 11 <=> old(paul) [avatar definition]
190. 12 <=> rich(paul) [avatar definition]
191. ~rich(paul) <- (~12) [avatar component clause 190]
196. 11 | ~12 | ~10 [avatar split clause 93,182,190,186]
227. 19 <=> quiet(john) [avatar definition]
236. 21 <=> ! [X1] : rich(X1) [avatar definition]
237. rich(X1) <- (21) [avatar component clause 236]
238. 21 | ~19 [avatar split clause 121,227,236]
270. 19 [avatar split clause 133,227]
271. $false <- (~12, 21) [subsumption resolution 191,237]
272. 12 | ~21 [avatar contradiction clause 271]
276. ~old(paul) [resolution 106,135]
278. creative(X0) | calm(X0) [resolution 116,100]
279. creative(X0) [subsumption resolution 278,117]
280. $false <- (~10) [resolution 279,183]
285. 10 [avatar contradiction clause 280]
286. ~11 [avatar split clause 276,186]
287. $false [avatar sat refutation 196,238,270,272,285,286]
% SZS output end Proof for 8723203013846129198666351
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise or kind is both kind and not brave and vice versa.
Everyone who is not kind or kind is either calm or tall.
Everyone who is both creative and strong is quiet or patient and vice versa.
Everyone who is either quiet or humble is not rich or patient and vice versa.
Everyone who is both not tall and funny is not old or curious and vice versa.
Everyone who is either patient or not strong is both not calm and brave and vice versa.
Everyone who is not strong is kind or not calm and vice versa.
If susan is old or not tall then someone is quiet.
If someone is both quiet and happy then fred is happy or generous and vice versa.
Everyone who is not wise or not rich is both not happy and not brave.
Everyone who is either not curious or not brave is curious or funny and vice versa.
Everyone who is not curious or not calm is not calm and vice versa.
Everyone who is either rich or curious is brave or not quiet and vice versa.
Everyone who is generous is generous or not kind and vice versa.
If someone is both kind and quiet then someone is strong or not old.
John is both brave and not creative.
Someone is not rich or not funny.
Lucy is either rich or happy.
Mary is not quiet.
Fred is either rich or curious.
Mary is both tall and not humble.
Someone is either not quiet or not creative. | Lucy is strong. | neutral | (![X]:((~wise(X)<~>kind(X))<=>(kind(X)&~brave(X))))&
(![X]:((~kind(X)|kind(X))=>(calm(X)<~>tall(X))))&
(![X]:((creative(X)&strong(X))<=>(quiet(X)|patient(X))))&
(![X]:((quiet(X)<~>humble(X))<=>(~rich(X)|patient(X))))&
(![X]:((~tall(X)&funny(X))<=>(~old(X)|curious(X))))&
(![X]:((patient(X)<~>~strong(X))<=>(~calm(X)&brave(X))))&
(![X]:(~strong(X)<=>(kind(X)|~calm(X))))&
(((old(susan)|~tall(susan)))=>(?[X]:(quiet(X))))&
((?[X]:((quiet(X)&happy(X))))<=>((happy(fred)|generous(fred))))&
(![X]:((~wise(X)|~rich(X))=>(~happy(X)&~brave(X))))&
(![X]:((~curious(X)<~>~brave(X))<=>(curious(X)|funny(X))))&
(![X]:((~curious(X)|~calm(X))<=>~calm(X)))&
(![X]:((rich(X)<~>curious(X))<=>(brave(X)|~quiet(X))))&
(![X]:(generous(X)<=>(generous(X)|~kind(X))))&
((?[X]:((kind(X)&quiet(X))))=>(?[X]:((strong(X)|~old(X)))))&
((brave(john)&~creative(john)))&
(?[X]:((~rich(X)|~funny(X))))&
((rich(lucy)<~>happy(lucy)))&
(~quiet(mary))&
((rich(fred)<~>curious(fred)))&
((tall(mary)&~humble(mary)))&
(?[X]:((~quiet(X)<~>~creative(X)))) | strong(lucy) | [] | null | 0 |
Everyone who is not wise or not generous is both patient and not tall.
Everyone who is either not wise or wise is either not kind or old and vice versa.
If someone is both not generous and calm then someone is both strong and happy and vice versa.
If alice is not generous then alice is either not kind or wise and vice versa.
If lucy is either tall or not kind then someone is not rich and vice versa.
Everyone who is rich is calm and vice versa.
Everyone who is both rich and not happy is not wise.
Everyone who is both creative and funny is not kind.
Everyone who is either not calm or not rich is not patient or not wise and vice versa.
If mary is either not rich or curious then susan is not tall or not humble and vice versa.
If someone is happy then susan is quiet or not patient.
If someone is calm or generous then mary is both not quiet and tall.
If someone is either creative or not funny then someone is not creative or wise and vice versa.
Everyone who is happy or wise is brave or curious.
If paul is not brave then lucy is both not old and not funny and vice versa.
Everyone who is either not happy or not rich is not patient.
Susan is either wise or generous.
Someone is rich.
Susan is either curious or not tall.
Paul is both not curious and not generous.
Alice is happy or not kind.
Someone is both not tall and not strong.
Someone is not calm or not funny. | Paul is not patient. | contradiction | (![X]:((~wise(X)|~generous(X))=>(patient(X)&~tall(X))))&
(![X]:((~wise(X)<~>wise(X))<=>(~kind(X)<~>old(X))))&
((?[X]:((~generous(X)&calm(X))))<=>(?[X]:((strong(X)&happy(X)))))&
((~generous(alice))<=>((~kind(alice)<~>wise(alice))))&
(((tall(lucy)<~>~kind(lucy)))<=>(?[X]:(~rich(X))))&
(![X]:(rich(X)<=>calm(X)))&
(![X]:((rich(X)&~happy(X))=>~wise(X)))&
(![X]:((creative(X)&funny(X))=>~kind(X)))&
(![X]:((~calm(X)<~>~rich(X))<=>(~patient(X)|~wise(X))))&
(((~rich(mary)<~>curious(mary)))<=>((~tall(susan)|~humble(susan))))&
((?[X]:(happy(X)))=>((quiet(susan)|~patient(susan))))&
((?[X]:((calm(X)|generous(X))))=>((~quiet(mary)&tall(mary))))&
((?[X]:((creative(X)<~>~funny(X))))<=>(?[X]:((~creative(X)|wise(X)))))&
(![X]:((happy(X)|wise(X))=>(brave(X)|curious(X))))&
((~brave(paul))<=>((~old(lucy)&~funny(lucy))))&
(![X]:((~happy(X)<~>~rich(X))=>~patient(X)))&
((wise(susan)<~>generous(susan)))&
(?[X]:(rich(X)))&
((curious(susan)<~>~tall(susan)))&
((~curious(paul)&~generous(paul)))&
((happy(alice)|~kind(alice)))&
(?[X]:((~tall(X)&~strong(X))))&
(?[X]:((~calm(X)|~funny(X)))) | ~patient(paul) | [
"p5",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 5967515001010099565904858
% SZS output start Proof for 5967515001010099565904858
6. ! [X0] : (rich(X0) <=> calm(X0)) [input p5]
9. ! [X0] : ((~calm(X0) <~> ~rich(X0)) <=> (~wise(X0) | ~patient(X0))) [input p8]
24. ~patient(paul) [input hypothesis]
49. ! [X0] : ((rich(X0) | ~calm(X0)) & (calm(X0) | ~rich(X0))) [nnf transformation 6]
50. ! [X0] : ((((rich(X0) | calm(X0)) & (~rich(X0) | ~calm(X0))) | (wise(X0) & patient(X0))) & ((~wise(X0) | ~patient(X0)) | ((~calm(X0) | rich(X0)) & (~rich(X0) | calm(X0))))) [nnf transformation 9]
51. ! [X0] : ((((rich(X0) | calm(X0)) & (~rich(X0) | ~calm(X0))) | (wise(X0) & patient(X0))) & (~wise(X0) | ~patient(X0) | ((~calm(X0) | rich(X0)) & (~rich(X0) | calm(X0))))) [flattening 50]
94. calm(X0) | ~rich(X0) [cnf transformation 49]
95. rich(X0) | ~calm(X0) [cnf transformation 49]
100. ~rich(X0) | ~calm(X0) | patient(X0) [cnf transformation 51]
102. rich(X0) | calm(X0) | patient(X0) [cnf transformation 51]
139. ~patient(paul) [cnf transformation 24]
208. calm(X0) | patient(X0) [subsumption resolution 102,94]
211. ~calm(X0) | patient(X0) [subsumption resolution 100,95]
212. patient(X0) [subsumption resolution 211,208]
318. $false [subsumption resolution 139,212]
% SZS output end Proof for 5967515001010099565904858
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not funny and not brave then someone is wise.
If susan is either patient or curious then someone is both not quiet and not curious and vice versa.
If someone is not funny or not old then someone is either not creative or generous and vice versa.
Everyone who is creative is not generous and vice versa.
If someone is both patient and not happy then alice is both strong and not humble.
Everyone who is both generous and not curious is funny and vice versa.
If someone is either patient or tall then john is either not kind or not generous and vice versa.
Everyone who is either not wise or curious is humble or generous and vice versa.
If susan is wise or not strong then mary is not humble or not wise and vice versa.
If someone is rich then fred is happy or not creative and vice versa.
Everyone who is not strong is either not wise or not calm.
Everyone who is either rich or not creative is not patient and vice versa.
Everyone who is both not calm and wise is wise and vice versa.
Everyone who is both old and not strong is not curious.
Everyone who is either not rich or happy is calm or strong.
If mary is both funny and not humble then alice is rich or not calm.
Someone is not wise or curious.
Someone is not wise.
Someone is either not creative or not strong.
Alice is old or rich.
Paul is both not calm and old.
Someone is either wise or generous.
Someone is both happy and rich. | Mary is quiet. | neutral | ((?[X]:((~funny(X)&~brave(X))))=>(?[X]:(wise(X))))&
(((patient(susan)<~>curious(susan)))<=>(?[X]:((~quiet(X)&~curious(X)))))&
((?[X]:((~funny(X)|~old(X))))<=>(?[X]:((~creative(X)<~>generous(X)))))&
(![X]:(creative(X)<=>~generous(X)))&
((?[X]:((patient(X)&~happy(X))))=>((strong(alice)&~humble(alice))))&
(![X]:((generous(X)&~curious(X))<=>funny(X)))&
((?[X]:((patient(X)<~>tall(X))))<=>((~kind(john)<~>~generous(john))))&
(![X]:((~wise(X)<~>curious(X))<=>(humble(X)|generous(X))))&
(((wise(susan)|~strong(susan)))<=>((~humble(mary)|~wise(mary))))&
((?[X]:(rich(X)))<=>((happy(fred)|~creative(fred))))&
(![X]:(~strong(X)=>(~wise(X)<~>~calm(X))))&
(![X]:((rich(X)<~>~creative(X))<=>~patient(X)))&
(![X]:((~calm(X)&wise(X))<=>wise(X)))&
(![X]:((old(X)&~strong(X))=>~curious(X)))&
(![X]:((~rich(X)<~>happy(X))=>(calm(X)|strong(X))))&
(((funny(mary)&~humble(mary)))=>((rich(alice)|~calm(alice))))&
(?[X]:((~wise(X)|curious(X))))&
(?[X]:(~wise(X)))&
(?[X]:((~creative(X)<~>~strong(X))))&
((old(alice)|rich(alice)))&
((~calm(paul)&old(paul)))&
(?[X]:((wise(X)<~>generous(X))))&
(?[X]:((happy(X)&rich(X)))) | quiet(mary) | [] | null | 0 |
Everyone who is both not rich and kind is either not rich or funny and vice versa.
If someone is not tall then someone is not strong and vice versa.
If someone is happy then someone is both quiet and not patient and vice versa.
If someone is not curious then alice is either not creative or funny and vice versa.
If susan is either not happy or kind then susan is either not tall or not old and vice versa.
Everyone who is either old or not generous is calm or happy.
If someone is not happy or tall then someone is either patient or not kind.
If fred is not happy then fred is either brave or not quiet and vice versa.
Everyone who is strong is both strong and not quiet and vice versa.
If susan is old or patient then alice is both not curious and curious.
If paul is both not quiet and not rich then someone is creative or not tall.
Everyone who is funny is both not calm and humble and vice versa.
Everyone who is both happy and brave is funny or old and vice versa.
Everyone who is both not kind and kind is wise or quiet and vice versa.
If someone is both not strong and creative then someone is either old or quiet.
Susan is not wise.
Someone is not brave.
Someone is humble.
Lucy is either creative or tall.
Paul is not generous or not calm.
Fred is either tall or patient.
Someone is not rich or happy. | Susan is not funny. | entailment | (![X]:((~rich(X)&kind(X))<=>(~rich(X)<~>funny(X))))&
((?[X]:(~tall(X)))<=>(?[X]:(~strong(X))))&
((?[X]:(happy(X)))<=>(?[X]:((quiet(X)&~patient(X)))))&
((?[X]:(~curious(X)))<=>((~creative(alice)<~>funny(alice))))&
(((~happy(susan)<~>kind(susan)))<=>((~tall(susan)<~>~old(susan))))&
(![X]:((old(X)<~>~generous(X))=>(calm(X)|happy(X))))&
((?[X]:((~happy(X)|tall(X))))=>(?[X]:((patient(X)<~>~kind(X)))))&
((~happy(fred))<=>((brave(fred)<~>~quiet(fred))))&
(![X]:(strong(X)<=>(strong(X)&~quiet(X))))&
(((old(susan)|patient(susan)))=>((~curious(alice)&curious(alice))))&
(((~quiet(paul)&~rich(paul)))=>(?[X]:((creative(X)|~tall(X)))))&
(![X]:(funny(X)<=>(~calm(X)&humble(X))))&
(![X]:((happy(X)&brave(X))<=>(funny(X)|old(X))))&
(![X]:((~kind(X)&kind(X))<=>(wise(X)|quiet(X))))&
((?[X]:((~strong(X)&creative(X))))=>(?[X]:((old(X)<~>quiet(X)))))&
(~wise(susan))&
(?[X]:(~brave(X)))&
(?[X]:(humble(X)))&
((creative(lucy)<~>tall(lucy)))&
((~generous(paul)|~calm(paul)))&
((tall(fred)<~>patient(fred)))&
(?[X]:((~rich(X)|happy(X)))) | ~funny(susan) | [
"p2",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 9153532642125529260889119
% SZS output start Proof for 9153532642125529260889119
3. ? [X0] : happy(X0) <=> ? [X0] : (~patient(X0) & quiet(X0)) [input p2]
13. ! [X0] : ((brave(X0) & happy(X0)) <=> (old(X0) | funny(X0))) [input p12]
14. ! [X0] : ((kind(X0) & ~kind(X0)) <=> (quiet(X0) | wise(X0))) [input p13]
23. funny(susan) [input hypothesis]
25. ? [X0] : happy(X0) <=> ? [X1] : (~patient(X1) & quiet(X1)) [rectify 3]
42. (? [X0] : happy(X0) | ! [X1] : (patient(X1) | ~quiet(X1))) & (? [X1] : (~patient(X1) & quiet(X1)) | ! [X0] : ~happy(X0)) [nnf transformation 25]
43. (? [X0] : happy(X0) | ! [X1] : (patient(X1) | ~quiet(X1))) & (? [X2] : (~patient(X2) & quiet(X2)) | ! [X3] : ~happy(X3)) [rectify 42]
44. ? [X0] : happy(X0) => happy(sK2) [choice axiom]
45. ? [X2] : (~patient(X2) & quiet(X2)) => (~patient(sK3) & quiet(sK3)) [choice axiom]
46. (happy(sK2) | ! [X1] : (patient(X1) | ~quiet(X1))) & ((~patient(sK3) & quiet(sK3)) | ! [X3] : ~happy(X3)) [skolemisation 43,45,44]
64. ! [X0] : (((brave(X0) & happy(X0)) | (~old(X0) & ~funny(X0))) & ((old(X0) | funny(X0)) | (~brave(X0) | ~happy(X0)))) [nnf transformation 13]
65. ! [X0] : (((brave(X0) & happy(X0)) | (~old(X0) & ~funny(X0))) & (old(X0) | funny(X0) | ~brave(X0) | ~happy(X0))) [flattening 64]
66. ! [X0] : (((kind(X0) & ~kind(X0)) | (~quiet(X0) & ~wise(X0))) & ((quiet(X0) | wise(X0)) | (~kind(X0) | kind(X0)))) [nnf transformation 14]
67. ! [X0] : (((kind(X0) & ~kind(X0)) | (~quiet(X0) & ~wise(X0))) & (quiet(X0) | wise(X0) | ~kind(X0) | kind(X0))) [flattening 66]
88. quiet(sK3) | ~happy(X3) [cnf transformation 46]
125. ~funny(X0) | happy(X0) [cnf transformation 65]
131. ~kind(X0) | ~quiet(X0) [cnf transformation 67]
133. kind(X0) | ~quiet(X0) [cnf transformation 67]
145. funny(susan) [cnf transformation 23]
174. 7 <=> ! [X3] : ~happy(X3) [avatar definition]
175. ~happy(X3) <- (7) [avatar component clause 174]
182. 9 <=> quiet(sK3) [avatar definition]
184. quiet(sK3) <- (9) [avatar component clause 182]
185. 7 | 9 [avatar split clause 88,182,174]
292. ~quiet(X0) [subsumption resolution 131,133]
342. happy(susan) [resolution 125,145]
345. $false <- (7) [subsumption resolution 342,175]
346. ~7 [avatar contradiction clause 345]
349. $false <- (9) [subsumption resolution 184,292]
350. ~9 [avatar contradiction clause 349]
351. $false [avatar sat refutation 185,346,350]
% SZS output end Proof for 9153532642125529260889119
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
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