premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
values | proof_inputs
sequencelengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
|
|---|---|---|---|---|---|---|---|
Everyone who is both not humble and not curious is strong or not wise.
Everyone who is either happy or not humble is not funny and vice versa.
If someone is not funny or humble then alice is quiet.
If mary is not funny then mary is not humble.
Everyone who is not calm is strong or wise.
If john is both not wise and wise then alice is not happy.
Everyone who is either not rich or calm is quiet.
Everyone who is strong is not brave or not curious and vice versa.
If lucy is both curious and not humble then alice is not calm or not patient and vice versa.
Everyone who is either not generous or tall is either patient or kind and vice versa.
If someone is both not calm and not wise then someone is funny and vice versa.
Everyone who is not humble or generous is both not quiet and humble.
If someone is not brave then paul is both curious and not strong and vice versa.
Everyone who is not happy or creative is quiet or old and vice versa.
Everyone who is both rich and old is not creative or funny and vice versa.
John is both rich and not tall.
Someone is generous.
Someone is either old or not brave.
Fred is both curious and not old.
Fred is either not creative or kind.
Someone is both patient and not rich. | Mary is kind. | neutral | (![X]:((~humble(X)&~curious(X))=>(strong(X)|~wise(X))))&
(![X]:((happy(X)<~>~humble(X))<=>~funny(X)))&
((?[X]:((~funny(X)|humble(X))))=>(quiet(alice)))&
((~funny(mary))=>(~humble(mary)))&
(![X]:(~calm(X)=>(strong(X)|wise(X))))&
(((~wise(john)&wise(john)))=>(~happy(alice)))&
(![X]:((~rich(X)<~>calm(X))=>quiet(X)))&
(![X]:(strong(X)<=>(~brave(X)|~curious(X))))&
(((curious(lucy)&~humble(lucy)))<=>((~calm(alice)|~patient(alice))))&
(![X]:((~generous(X)<~>tall(X))<=>(patient(X)<~>kind(X))))&
((?[X]:((~calm(X)&~wise(X))))<=>(?[X]:(funny(X))))&
(![X]:((~humble(X)|generous(X))=>(~quiet(X)&humble(X))))&
((?[X]:(~brave(X)))<=>((curious(paul)&~strong(paul))))&
(![X]:((~happy(X)|creative(X))<=>(quiet(X)|old(X))))&
(![X]:((rich(X)&old(X))<=>(~creative(X)|funny(X))))&
((rich(john)&~tall(john)))&
(?[X]:(generous(X)))&
(?[X]:((old(X)<~>~brave(X))))&
((curious(fred)&~old(fred)))&
((~creative(fred)<~>kind(fred)))&
(?[X]:((patient(X)&~rich(X)))) | kind(mary) | [] | null | 0 |
If someone is both not strong and strong then someone is both calm and not brave and vice versa.
If mary is either not tall or not funny then mary is both happy and not humble.
Everyone who is calm or not tall is both rich and not old.
If someone is patient or generous then lucy is both generous and not funny.
If paul is both not calm and not patient then someone is either strong or curious and vice versa.
Everyone who is either not curious or not brave is either creative or not happy.
If fred is either not humble or not creative then lucy is both not generous and humble.
Everyone who is creative or not tall is not happy.
Everyone who is both not old and strong is either calm or brave and vice versa.
If someone is both brave and not calm then someone is either not wise or creative and vice versa.
Everyone who is both not strong and not curious is creative and vice versa.
If paul is both brave and not kind then someone is not old or not funny and vice versa.
Everyone who is generous or strong is both rich and kind.
If fred is brave or generous then mary is generous or calm.
Someone is not wise.
Someone is happy or not generous.
Someone is not brave or not rich.
Someone is either not quiet or not funny.
Someone is either not happy or not tall.
Someone is wise or humble. | Mary is tall. | entailment | ((?[X]:((~strong(X)&strong(X))))<=>(?[X]:((calm(X)&~brave(X)))))&
(((~tall(mary)<~>~funny(mary)))=>((happy(mary)&~humble(mary))))&
(![X]:((calm(X)|~tall(X))=>(rich(X)&~old(X))))&
((?[X]:((patient(X)|generous(X))))=>((generous(lucy)&~funny(lucy))))&
(((~calm(paul)&~patient(paul)))<=>(?[X]:((strong(X)<~>curious(X)))))&
(![X]:((~curious(X)<~>~brave(X))=>(creative(X)<~>~happy(X))))&
(((~humble(fred)<~>~creative(fred)))=>((~generous(lucy)&humble(lucy))))&
(![X]:((creative(X)|~tall(X))=>~happy(X)))&
(![X]:((~old(X)&strong(X))<=>(calm(X)<~>brave(X))))&
((?[X]:((brave(X)&~calm(X))))<=>(?[X]:((~wise(X)<~>creative(X)))))&
(![X]:((~strong(X)&~curious(X))<=>creative(X)))&
(((brave(paul)&~kind(paul)))<=>(?[X]:((~old(X)|~funny(X)))))&
(![X]:((generous(X)|strong(X))=>(rich(X)&kind(X))))&
(((brave(fred)|generous(fred)))=>((generous(mary)|calm(mary))))&
(?[X]:(~wise(X)))&
(?[X]:((happy(X)|~generous(X))))&
(?[X]:((~brave(X)|~rich(X))))&
(?[X]:((~quiet(X)<~>~funny(X))))&
(?[X]:((~happy(X)<~>~tall(X))))&
(?[X]:((wise(X)|humble(X)))) | tall(mary) | [
"p1",
"p2",
"p4",
"p5",
"p7",
"p8",
"p10",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 915064007908264410917016
% SZS output start Proof for 915064007908264410917016
2. (~tall(mary) <~> ~funny(mary)) => (~humble(mary) & happy(mary)) [input p1]
3. ! [X0] : ((~tall(X0) | calm(X0)) => (~old(X0) & rich(X0))) [input p2]
5. (~patient(paul) & ~calm(paul)) <=> ? [X0] : (strong(X0) <~> curious(X0)) [input p4]
6. ! [X0] : ((~curious(X0) <~> ~brave(X0)) => (creative(X0) <~> ~happy(X0))) [input p5]
8. ! [X0] : ((~tall(X0) | creative(X0)) => ~happy(X0)) [input p7]
9. ! [X0] : ((strong(X0) & ~old(X0)) <=> (calm(X0) <~> brave(X0))) [input p8]
11. ! [X0] : ((~curious(X0) & ~strong(X0)) <=> creative(X0)) [input p10]
12. (~kind(paul) & brave(paul)) <=> ? [X0] : (~funny(X0) | ~old(X0)) [input p11]
13. ! [X0] : ((strong(X0) | generous(X0)) => (kind(X0) & rich(X0))) [input p12]
21. ~tall(mary) [input hypothesis]
24. (~humble(mary) & happy(mary)) | (~tall(mary) <=> ~funny(mary)) [ennf transformation 2]
25. ! [X0] : ((~old(X0) & rich(X0)) | (tall(X0) & ~calm(X0))) [ennf transformation 3]
27. ! [X0] : ((creative(X0) <~> ~happy(X0)) | (~curious(X0) <=> ~brave(X0))) [ennf transformation 6]
29. ! [X0] : (~happy(X0) | (tall(X0) & ~creative(X0))) [ennf transformation 8]
30. ! [X0] : ((kind(X0) & rich(X0)) | (~strong(X0) & ~generous(X0))) [ennf transformation 13]
38. (~humble(mary) & happy(mary)) | ((~tall(mary) | funny(mary)) & (~funny(mary) | tall(mary))) [nnf transformation 24]
39. ((~patient(paul) & ~calm(paul)) | ! [X0] : ((strong(X0) | ~curious(X0)) & (curious(X0) | ~strong(X0)))) & (? [X0] : ((~curious(X0) | ~strong(X0)) & (curious(X0) | strong(X0))) | (patient(paul) | calm(paul))) [nnf transformation 5]
40. ((~patient(paul) & ~calm(paul)) | ! [X0] : ((strong(X0) | ~curious(X0)) & (curious(X0) | ~strong(X0)))) & (? [X0] : ((~curious(X0) | ~strong(X0)) & (curious(X0) | strong(X0))) | patient(paul) | calm(paul)) [flattening 39]
41. ((~patient(paul) & ~calm(paul)) | ! [X0] : ((strong(X0) | ~curious(X0)) & (curious(X0) | ~strong(X0)))) & (? [X1] : ((~curious(X1) | ~strong(X1)) & (curious(X1) | strong(X1))) | patient(paul) | calm(paul)) [rectify 40]
42. ? [X1] : ((~curious(X1) | ~strong(X1)) & (curious(X1) | strong(X1))) => ((~curious(sK2) | ~strong(sK2)) & (curious(sK2) | strong(sK2))) [choice axiom]
43. ((~patient(paul) & ~calm(paul)) | ! [X0] : ((strong(X0) | ~curious(X0)) & (curious(X0) | ~strong(X0)))) & (((~curious(sK2) | ~strong(sK2)) & (curious(sK2) | strong(sK2))) | patient(paul) | calm(paul)) [skolemisation 41,42]
44. ! [X0] : (((happy(X0) | ~creative(X0)) & (~happy(X0) | creative(X0))) | ((~curious(X0) | brave(X0)) & (~brave(X0) | curious(X0)))) [nnf transformation 27]
46. ! [X0] : (((strong(X0) & ~old(X0)) | ((calm(X0) | ~brave(X0)) & (brave(X0) | ~calm(X0)))) & (((~brave(X0) | ~calm(X0)) & (brave(X0) | calm(X0))) | (~strong(X0) | old(X0)))) [nnf transformation 9]
47. ! [X0] : (((strong(X0) & ~old(X0)) | ((calm(X0) | ~brave(X0)) & (brave(X0) | ~calm(X0)))) & (((~brave(X0) | ~calm(X0)) & (brave(X0) | calm(X0))) | ~strong(X0) | old(X0))) [flattening 46]
53. ! [X0] : (((~curious(X0) & ~strong(X0)) | ~creative(X0)) & (creative(X0) | (curious(X0) | strong(X0)))) [nnf transformation 11]
54. ! [X0] : (((~curious(X0) & ~strong(X0)) | ~creative(X0)) & (creative(X0) | curious(X0) | strong(X0))) [flattening 53]
55. ((~kind(paul) & brave(paul)) | ! [X0] : (funny(X0) & old(X0))) & (? [X0] : (~funny(X0) | ~old(X0)) | (kind(paul) | ~brave(paul))) [nnf transformation 12]
56. ((~kind(paul) & brave(paul)) | ! [X0] : (funny(X0) & old(X0))) & (? [X0] : (~funny(X0) | ~old(X0)) | kind(paul) | ~brave(paul)) [flattening 55]
57. ((~kind(paul) & brave(paul)) | ! [X0] : (funny(X0) & old(X0))) & (? [X1] : (~funny(X1) | ~old(X1)) | kind(paul) | ~brave(paul)) [rectify 56]
58. ? [X1] : (~funny(X1) | ~old(X1)) => (~funny(sK5) | ~old(sK5)) [choice axiom]
59. ((~kind(paul) & brave(paul)) | ! [X0] : (funny(X0) & old(X0))) & ((~funny(sK5) | ~old(sK5)) | kind(paul) | ~brave(paul)) [skolemisation 57,58]
78. happy(mary) | ~funny(mary) | tall(mary) [cnf transformation 38]
84. ~old(X0) | ~calm(X0) [cnf transformation 25]
92. ~calm(paul) | curious(X0) | ~strong(X0) [cnf transformation 43]
93. ~calm(paul) | strong(X0) | ~curious(X0) [cnf transformation 43]
98. ~creative(X0) | happy(X0) | ~brave(X0) | curious(X0) [cnf transformation 44]
104. ~creative(X0) | ~happy(X0) [cnf transformation 29]
105. ~happy(X0) | tall(X0) [cnf transformation 29]
107. ~brave(X0) | ~calm(X0) | ~strong(X0) | old(X0) [cnf transformation 47]
111. ~brave(X0) | calm(X0) | strong(X0) [cnf transformation 47]
118. creative(X0) | curious(X0) | strong(X0) [cnf transformation 54]
123. brave(paul) | funny(X0) [cnf transformation 59]
125. ~kind(paul) | funny(X0) [cnf transformation 59]
129. ~strong(X0) | kind(X0) [cnf transformation 30]
140. ~tall(mary) [cnf transformation 21]
151. 3 <=> funny(mary) [avatar definition]
152. ~funny(mary) <- (~3) [avatar component clause 151]
155. 4 <=> tall(mary) [avatar definition]
157. ~tall(mary) <- (~4) [avatar component clause 155]
165. 6 <=> happy(mary) [avatar definition]
167. happy(mary) <- (6) [avatar component clause 165]
169. 4 | ~3 | 6 [avatar split clause 78,165,151,155]
189. 11 <=> ! [X0] : (strong(X0) | ~curious(X0)) [avatar definition]
190. ~curious(X0) | strong(X0) <- (11) [avatar component clause 189]
197. 13 <=> ! [X0] : (curious(X0) | ~strong(X0)) [avatar definition]
198. ~strong(X0) | curious(X0) <- (13) [avatar component clause 197]
201. 14 <=> calm(paul) [avatar definition]
202. calm(paul) <- (14) [avatar component clause 201]
203. ~calm(paul) <- (~14) [avatar component clause 201]
204. 11 | ~14 [avatar split clause 93,201,189]
205. 13 | ~14 [avatar split clause 92,201,197]
233. ~brave(X0) | ~calm(X0) | ~strong(X0) [subsumption resolution 107,84]
266. 27 <=> ! [X0] : funny(X0) [avatar definition]
267. funny(X0) <- (27) [avatar component clause 266]
269. 28 <=> kind(paul) [avatar definition]
271. ~kind(paul) <- (~28) [avatar component clause 269]
272. 27 | ~28 [avatar split clause 125,269,266]
278. 30 <=> brave(paul) [avatar definition]
280. brave(paul) <- (30) [avatar component clause 278]
281. 27 | 30 [avatar split clause 123,278,266]
349. ~4 [avatar split clause 140,155]
352. $false <- (~3, 27) [subsumption resolution 152,267]
353. 3 | ~27 [avatar contradiction clause 352]
358. tall(mary) <- (6) [resolution 105,167]
359. $false <- (~4, 6) [subsumption resolution 358,157]
360. 4 | ~6 [avatar contradiction clause 359]
368. calm(paul) | strong(paul) <- (30) [resolution 111,280]
370. strong(paul) <- (~14, 30) [subsumption resolution 368,203]
372. kind(paul) <- (~14, 30) [resolution 370,129]
374. $false <- (~14, ~28, 30) [subsumption resolution 372,271]
375. 14 | 28 | ~30 [avatar contradiction clause 374]
377. 45 <=> strong(paul) [avatar definition]
378. ~strong(paul) <- (~45) [avatar component clause 377]
394. curious(X2) | strong(X2) | ~happy(X2) [resolution 118,104]
397. ~happy(X2) | curious(X2) <- (13) [subsumption resolution 394,198]
399. ~calm(paul) | ~strong(paul) <- (30) [resolution 233,280]
401. ~strong(paul) <- (14, 30) [subsumption resolution 399,202]
402. ~45 | ~14 | ~30 [avatar split clause 401,278,201,377]
418. happy(X0) | ~brave(X0) | curious(X0) | curious(X0) | strong(X0) [resolution 98,118]
419. happy(X0) | ~brave(X0) | curious(X0) | strong(X0) [duplicate literal removal 418]
420. happy(X0) | ~brave(X0) | curious(X0) <- (13) [subsumption resolution 419,198]
421. ~brave(X0) | curious(X0) <- (13) [subsumption resolution 420,397]
516. curious(paul) <- (13, 30) [resolution 421,280]
519. strong(paul) <- (11, 13, 30) [resolution 516,190]
520. $false <- (11, 13, 30, ~45) [subsumption resolution 519,378]
521. ~11 | ~13 | ~30 | 45 [avatar contradiction clause 520]
522. $false [avatar sat refutation 169,204,205,272,281,349,353,360,375,402,521]
% SZS output end Proof for 915064007908264410917016
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is both not rich and quiet then someone is either not creative or not strong. Everyone who is curious is not kind. If someone is strong then john is either wise or not patient and vice versa. If fred is both not curious and rich then mary is either not patient or quiet. Everyone who is not quiet is either not humble or not strong and vice versa. Everyone who is both creative and rich is either not patient or creative and vice versa. Everyone who is both generous and patient is either not happy or not creative and vice versa. Everyone who is funny is strong or old. Everyone who is both not humble and funny is not humble or patient and vice versa. Everyone who is not strong or not curious is either generous or wise. If someone is both humble and kind then alice is both not patient and old and vice versa. Everyone who is either not creative or humble is both generous and old and vice versa. If susan is not quiet or generous then mary is either strong or brave. Everyone who is both tall and brave is funny and vice versa. Everyone who is funny or wise is quiet and vice versa. If alice is not curious or kind then susan is both not wise and quiet and vice versa. Lucy is quiet or happy. Someone is not curious. Someone is humble. John is quiet or rich. Someone is not rich or rich. Someone is patient or kind. Paul is both not kind and not rich. | John is strong. | neutral | (((~rich(lucy)&quiet(lucy)))=>(?[X]:((~creative(X)<~>~strong(X)))))&
(![X]:(curious(X)=>~kind(X)))&
((?[X]:(strong(X)))<=>((wise(john)<~>~patient(john))))&
(((~curious(fred)&rich(fred)))=>((~patient(mary)<~>quiet(mary))))&
(![X]:(~quiet(X)<=>(~humble(X)<~>~strong(X))))&
(![X]:((creative(X)&rich(X))<=>(~patient(X)<~>creative(X))))&
(![X]:((generous(X)&patient(X))<=>(~happy(X)<~>~creative(X))))&
(![X]:(funny(X)=>(strong(X)|old(X))))&
(![X]:((~humble(X)&funny(X))<=>(~humble(X)|patient(X))))&
(![X]:((~strong(X)|~curious(X))=>(generous(X)<~>wise(X))))&
((?[X]:((humble(X)&kind(X))))<=>((~patient(alice)&old(alice))))&
(![X]:((~creative(X)<~>humble(X))<=>(generous(X)&old(X))))&
(((~quiet(susan)|generous(susan)))=>((strong(mary)<~>brave(mary))))&
(![X]:((tall(X)&brave(X))<=>funny(X)))&
(![X]:((funny(X)|wise(X))<=>quiet(X)))&
(((~curious(alice)|kind(alice)))<=>((~wise(susan)&quiet(susan))))&
((quiet(lucy)|happy(lucy)))&
(?[X]:(~curious(X)))&
(?[X]:(humble(X)))&
((quiet(john)|rich(john)))&
(?[X]:((~rich(X)|rich(X))))&
(?[X]:((patient(X)|kind(X))))&
((~kind(paul)&~rich(paul))) | strong(john) | [] | null | 0 |
If someone is both quiet and not curious then fred is both calm and humble.
If alice is either brave or not generous then alice is both humble and not humble and vice versa.
Everyone who is calm is both not wise and humble.
Everyone who is both not funny and strong is wise or quiet and vice versa.
If paul is brave or not tall then someone is brave or happy.
Everyone who is not curious is patient and vice versa.
Everyone who is not generous is curious and vice versa.
Everyone who is not strong or old is both funny and not tall.
Everyone who is not creative or not brave is both tall and curious and vice versa.
Everyone who is both funny and not patient is either rich or not calm and vice versa.
If someone is not generous or funny then someone is funny and vice versa.
Everyone who is either not old or not calm is not strong or strong and vice versa.
Everyone who is both curious and tall is both not patient and creative.
Everyone who is either not quiet or generous is rich or creative and vice versa.
Everyone who is either not patient or not rich is both quiet and calm.
Everyone who is either not brave or not wise is either not funny or curious.
Paul is not generous or not wise.
Paul is either not curious or rich.
Someone is either not strong or not patient.
Someone is either rich or not happy.
Lucy is strong. | Lucy is not curious. | neutral | ((?[X]:((quiet(X)&~curious(X))))=>((calm(fred)&humble(fred))))&
(((brave(alice)<~>~generous(alice)))<=>((humble(alice)&~humble(alice))))&
(![X]:(calm(X)=>(~wise(X)&humble(X))))&
(![X]:((~funny(X)&strong(X))<=>(wise(X)|quiet(X))))&
(((brave(paul)|~tall(paul)))=>(?[X]:((brave(X)|happy(X)))))&
(![X]:(~curious(X)<=>patient(X)))&
(![X]:(~generous(X)<=>curious(X)))&
(![X]:((~strong(X)|old(X))=>(funny(X)&~tall(X))))&
(![X]:((~creative(X)|~brave(X))<=>(tall(X)&curious(X))))&
(![X]:((funny(X)&~patient(X))<=>(rich(X)<~>~calm(X))))&
((?[X]:((~generous(X)|funny(X))))<=>(?[X]:(funny(X))))&
(![X]:((~old(X)<~>~calm(X))<=>(~strong(X)|strong(X))))&
(![X]:((curious(X)&tall(X))=>(~patient(X)&creative(X))))&
(![X]:((~quiet(X)<~>generous(X))<=>(rich(X)|creative(X))))&
(![X]:((~patient(X)<~>~rich(X))=>(quiet(X)&calm(X))))&
(![X]:((~brave(X)<~>~wise(X))=>(~funny(X)<~>curious(X))))&
((~generous(paul)|~wise(paul)))&
((~curious(paul)<~>rich(paul)))&
(?[X]:((~strong(X)<~>~patient(X))))&
(?[X]:((rich(X)<~>~happy(X))))&
(strong(lucy)) | ~curious(lucy) | [] | null | 0 |
If someone is both not humble and not kind then fred is old and vice versa.
If alice is kind or not strong then paul is both old and not creative and vice versa.
If someone is wise then someone is both not kind and not quiet and vice versa.
If someone is not patient then alice is not generous and vice versa.
Everyone who is not patient or rich is both not rich and not old.
Everyone who is patient is either patient or kind.
Everyone who is either creative or wise is not tall.
Everyone who is both generous and strong is not quiet.
If john is both not funny and happy then fred is both not wise and not creative and vice versa.
Everyone who is not funny is calm or patient and vice versa.
If fred is either rich or not brave then alice is not patient.
Everyone who is not creative or not patient is both brave and quiet.
If someone is not generous then someone is kind or not brave and vice versa.
Everyone who is not rich is not happy or not generous.
Everyone who is either generous or not curious is not kind and vice versa.
If someone is either not patient or not generous then alice is funny.
Fred is not tall.
Someone is either not happy or rich.
Alice is tall or not funny.
Someone is both not old and not humble.
Someone is either creative or not wise.
Someone is curious or not old.
Someone is not creative or happy.
Someone is rich or not patient. | Alice is not funny. | neutral | ((?[X]:((~humble(X)&~kind(X))))<=>(old(fred)))&
(((kind(alice)|~strong(alice)))<=>((old(paul)&~creative(paul))))&
((?[X]:(wise(X)))<=>(?[X]:((~kind(X)&~quiet(X)))))&
((?[X]:(~patient(X)))<=>(~generous(alice)))&
(![X]:((~patient(X)|rich(X))=>(~rich(X)&~old(X))))&
(![X]:(patient(X)=>(patient(X)<~>kind(X))))&
(![X]:((creative(X)<~>wise(X))=>~tall(X)))&
(![X]:((generous(X)&strong(X))=>~quiet(X)))&
(((~funny(john)&happy(john)))<=>((~wise(fred)&~creative(fred))))&
(![X]:(~funny(X)<=>(calm(X)|patient(X))))&
(((rich(fred)<~>~brave(fred)))=>(~patient(alice)))&
(![X]:((~creative(X)|~patient(X))=>(brave(X)&quiet(X))))&
((?[X]:(~generous(X)))<=>(?[X]:((kind(X)|~brave(X)))))&
(![X]:(~rich(X)=>(~happy(X)|~generous(X))))&
(![X]:((generous(X)<~>~curious(X))<=>~kind(X)))&
((?[X]:((~patient(X)<~>~generous(X))))=>(funny(alice)))&
(~tall(fred))&
(?[X]:((~happy(X)<~>rich(X))))&
((tall(alice)|~funny(alice)))&
(?[X]:((~old(X)&~humble(X))))&
(?[X]:((creative(X)<~>~wise(X))))&
(?[X]:((curious(X)|~old(X))))&
(?[X]:((~creative(X)|happy(X))))&
(?[X]:((rich(X)|~patient(X)))) | ~funny(alice) | [] | null | 0 |
Everyone who is either not strong or not patient is not calm or not quiet and vice versa.
If paul is both strong and generous then someone is patient and vice versa.
Everyone who is creative is either not rich or tall and vice versa.
If someone is wise or calm then fred is old or not tall.
If someone is creative or not quiet then someone is both quiet and rich.
If paul is both curious and generous then someone is humble or funny.
If someone is curious or not patient then someone is both not tall and not wise.
If john is not curious or happy then susan is tall or curious and vice versa.
Everyone who is creative is both humble and not creative.
Everyone who is either creative or not generous is not funny.
Everyone who is not calm is either tall or not quiet and vice versa.
Everyone who is both kind and rich is not calm and vice versa.
If someone is either rich or calm then susan is not curious and vice versa.
If alice is not funny then paul is humble and vice versa.
Everyone who is either creative or rich is patient and vice versa.
Everyone who is both wise and not patient is both generous and not tall.
Paul is either creative or not rich.
Fred is not tall.
Fred is not kind or not rich.
Someone is either not brave or not humble.
Someone is not strong or not humble.
Susan is brave or not strong.
Someone is either not wise or not kind. | Paul is strong. | entailment | (![X]:((~strong(X)<~>~patient(X))<=>(~calm(X)|~quiet(X))))&
(((strong(paul)&generous(paul)))<=>(?[X]:(patient(X))))&
(![X]:(creative(X)<=>(~rich(X)<~>tall(X))))&
((?[X]:((wise(X)|calm(X))))=>((old(fred)|~tall(fred))))&
((?[X]:((creative(X)|~quiet(X))))=>(?[X]:((quiet(X)&rich(X)))))&
(((curious(paul)&generous(paul)))=>(?[X]:((humble(X)|funny(X)))))&
((?[X]:((curious(X)|~patient(X))))=>(?[X]:((~tall(X)&~wise(X)))))&
(((~curious(john)|happy(john)))<=>((tall(susan)|curious(susan))))&
(![X]:(creative(X)=>(humble(X)&~creative(X))))&
(![X]:((creative(X)<~>~generous(X))=>~funny(X)))&
(![X]:(~calm(X)<=>(tall(X)<~>~quiet(X))))&
(![X]:((kind(X)&rich(X))<=>~calm(X)))&
((?[X]:((rich(X)<~>calm(X))))<=>(~curious(susan)))&
((~funny(alice))<=>(humble(paul)))&
(![X]:((creative(X)<~>rich(X))<=>patient(X)))&
(![X]:((wise(X)&~patient(X))=>(generous(X)&~tall(X))))&
((creative(paul)<~>~rich(paul)))&
(~tall(fred))&
((~kind(fred)|~rich(fred)))&
(?[X]:((~brave(X)<~>~humble(X))))&
(?[X]:((~strong(X)|~humble(X))))&
((brave(susan)|~strong(susan)))&
(?[X]:((~wise(X)<~>~kind(X)))) | strong(paul) | [
"p1",
"p2",
"p8",
"p14",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 2876456247250556942273982
% SZS output start Proof for 2876456247250556942273982
2. (generous(paul) & strong(paul)) <=> ? [X0] : patient(X0) [input p1]
3. ! [X0] : (creative(X0) <=> (~rich(X0) <~> tall(X0))) [input p2]
9. ! [X0] : (creative(X0) => (~creative(X0) & humble(X0))) [input p8]
15. ! [X0] : ((creative(X0) <~> rich(X0)) <=> patient(X0)) [input p14]
18. ~tall(fred) [input p17]
24. ~strong(paul) [input hypothesis]
32. ! [X0] : ((~creative(X0) & humble(X0)) | ~creative(X0)) [ennf transformation 9]
38. ((generous(paul) & strong(paul)) | ! [X0] : ~patient(X0)) & (? [X0] : patient(X0) | (~generous(paul) | ~strong(paul))) [nnf transformation 2]
39. ((generous(paul) & strong(paul)) | ! [X0] : ~patient(X0)) & (? [X0] : patient(X0) | ~generous(paul) | ~strong(paul)) [flattening 38]
40. ((generous(paul) & strong(paul)) | ! [X0] : ~patient(X0)) & (? [X1] : patient(X1) | ~generous(paul) | ~strong(paul)) [rectify 39]
41. ? [X1] : patient(X1) => patient(sK0) [choice axiom]
42. ((generous(paul) & strong(paul)) | ! [X0] : ~patient(X0)) & (patient(sK0) | ~generous(paul) | ~strong(paul)) [skolemisation 40,41]
43. ! [X0] : ((creative(X0) | ((~rich(X0) | ~tall(X0)) & (tall(X0) | rich(X0)))) & (((~tall(X0) | rich(X0)) & (tall(X0) | ~rich(X0))) | ~creative(X0))) [nnf transformation 3]
63. ! [X0] : ((((~rich(X0) | ~creative(X0)) & (rich(X0) | creative(X0))) | ~patient(X0)) & (patient(X0) | ((creative(X0) | ~rich(X0)) & (rich(X0) | ~creative(X0))))) [nnf transformation 15]
80. strong(paul) | ~patient(X0) [cnf transformation 42]
84. tall(X0) | creative(X0) | rich(X0) [cnf transformation 43]
100. ~creative(X0) | ~creative(X0) [cnf transformation 32]
117. ~rich(X0) | creative(X0) | patient(X0) [cnf transformation 63]
124. ~tall(fred) [cnf transformation 18]
132. ~strong(paul) [cnf transformation 24]
133. ~creative(X0) [duplicate literal removal 100]
135. 1 <=> ! [X0] : ~patient(X0) [avatar definition]
136. ~patient(X0) <- (1) [avatar component clause 135]
143. 3 <=> strong(paul) [avatar definition]
146. 1 | 3 [avatar split clause 80,143,135]
161. 7 <=> ! [X1] : ~creative(X1) [avatar definition]
162. ~creative(X1) <- (7) [avatar component clause 161]
221. 7 [avatar split clause 133,161]
266. 29 <=> rich(fred) [avatar definition]
267. rich(fred) <- (29) [avatar component clause 266]
308. ~3 [avatar split clause 132,143]
316. creative(fred) | rich(fred) [resolution 84,124]
320. rich(fred) <- (7) [subsumption resolution 316,162]
325. 29 | ~7 [avatar split clause 320,161,266]
403. creative(fred) | patient(fred) <- (29) [resolution 117,267]
407. patient(fred) <- (7, 29) [subsumption resolution 403,162]
408. $false <- (1, 7, 29) [subsumption resolution 407,136]
409. ~1 | ~7 | ~29 [avatar contradiction clause 408]
419. $false [avatar sat refutation 146,221,308,325,409]
% SZS output end Proof for 2876456247250556942273982
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is kind is not wise or tall.
If someone is both not funny and not patient then someone is brave.
Everyone who is either curious or kind is not curious.
Everyone who is creative or old is not calm and vice versa.
Everyone who is not creative is not tall or funny and vice versa.
Everyone who is either not humble or not kind is not patient.
If someone is not happy then mary is not happy or not wise.
If someone is both curious and not rich then susan is either funny or not kind.
If someone is not curious or not creative then someone is both not wise and calm and vice versa.
Everyone who is either curious or not wise is both not calm and rich.
Everyone who is brave is not creative and vice versa.
If someone is either not curious or generous then mary is either kind or creative and vice versa.
Everyone who is not creative or not calm is not generous or not rich and vice versa.
Everyone who is happy is both curious and funny.
Everyone who is both not creative and not old is both calm and humble and vice versa.
Someone is old.
Someone is either not happy or humble.
Someone is not wise or not strong.
Someone is both not rich and not happy.
Paul is not tall or not old.
Someone is not wise or tall.
Alice is not strong or old.
Someone is old or not wise. | Paul is not creative. | neutral | (![X]:(kind(X)=>(~wise(X)|tall(X))))&
((?[X]:((~funny(X)&~patient(X))))=>(?[X]:(brave(X))))&
(![X]:((curious(X)<~>kind(X))=>~curious(X)))&
(![X]:((creative(X)|old(X))<=>~calm(X)))&
(![X]:(~creative(X)<=>(~tall(X)|funny(X))))&
(![X]:((~humble(X)<~>~kind(X))=>~patient(X)))&
((?[X]:(~happy(X)))=>((~happy(mary)|~wise(mary))))&
((?[X]:((curious(X)&~rich(X))))=>((funny(susan)<~>~kind(susan))))&
((?[X]:((~curious(X)|~creative(X))))<=>(?[X]:((~wise(X)&calm(X)))))&
(![X]:((curious(X)<~>~wise(X))=>(~calm(X)&rich(X))))&
(![X]:(brave(X)<=>~creative(X)))&
((?[X]:((~curious(X)<~>generous(X))))<=>((kind(mary)<~>creative(mary))))&
(![X]:((~creative(X)|~calm(X))<=>(~generous(X)|~rich(X))))&
(![X]:(happy(X)=>(curious(X)&funny(X))))&
(![X]:((~creative(X)&~old(X))<=>(calm(X)&humble(X))))&
(?[X]:(old(X)))&
(?[X]:((~happy(X)<~>humble(X))))&
(?[X]:((~wise(X)|~strong(X))))&
(?[X]:((~rich(X)&~happy(X))))&
((~tall(paul)|~old(paul)))&
(?[X]:((~wise(X)|tall(X))))&
((~strong(alice)|old(alice)))&
(?[X]:((old(X)|~wise(X)))) | ~creative(paul) | [] | null | 0 |
If someone is both curious and not happy then someone is tall or brave and vice versa.
If someone is both quiet and generous then paul is calm or not kind and vice versa.
If alice is not patient or not kind then lucy is not strong.
If mary is rich or old then someone is creative or not humble.
Everyone who is both calm and kind is quiet.
If fred is brave then someone is both strong and not creative and vice versa.
If paul is humble or patient then someone is calm or not happy.
Everyone who is either not happy or not generous is humble and vice versa.
If someone is both not old and old then someone is creative and vice versa.
Everyone who is rich is not tall.
If alice is either not wise or strong then susan is not wise and vice versa.
Everyone who is either not kind or happy is both brave and not old and vice versa.
Everyone who is not quiet or not calm is not curious.
Everyone who is both happy and not wise is calm and vice versa.
If someone is both not calm and not funny then someone is either not kind or not creative and vice versa.
If someone is wise then mary is tall and vice versa.
Lucy is humble or patient.
Someone is either brave or not tall.
Someone is either not kind or not curious.
Someone is not old or not quiet.
Someone is either happy or quiet.
Someone is either generous or not rich.
Paul is quiet or calm.
Someone is either not kind or strong. | Susan is wise. | contradiction | ((?[X]:((curious(X)&~happy(X))))<=>(?[X]:((tall(X)|brave(X)))))&
((?[X]:((quiet(X)&generous(X))))<=>((calm(paul)|~kind(paul))))&
(((~patient(alice)|~kind(alice)))=>(~strong(lucy)))&
(((rich(mary)|old(mary)))=>(?[X]:((creative(X)|~humble(X)))))&
(![X]:((calm(X)&kind(X))=>quiet(X)))&
((brave(fred))<=>(?[X]:((strong(X)&~creative(X)))))&
(((humble(paul)|patient(paul)))=>(?[X]:((calm(X)|~happy(X)))))&
(![X]:((~happy(X)<~>~generous(X))<=>humble(X)))&
((?[X]:((~old(X)&old(X))))<=>(?[X]:(creative(X))))&
(![X]:(rich(X)=>~tall(X)))&
(((~wise(alice)<~>strong(alice)))<=>(~wise(susan)))&
(![X]:((~kind(X)<~>happy(X))<=>(brave(X)&~old(X))))&
(![X]:((~quiet(X)|~calm(X))=>~curious(X)))&
(![X]:((happy(X)&~wise(X))<=>calm(X)))&
((?[X]:((~calm(X)&~funny(X))))<=>(?[X]:((~kind(X)<~>~creative(X)))))&
((?[X]:(wise(X)))<=>(tall(mary)))&
((humble(lucy)|patient(lucy)))&
(?[X]:((brave(X)<~>~tall(X))))&
(?[X]:((~kind(X)<~>~curious(X))))&
(?[X]:((~old(X)|~quiet(X))))&
(?[X]:((happy(X)<~>quiet(X))))&
(?[X]:((generous(X)<~>~rich(X))))&
((quiet(paul)|calm(paul)))&
(?[X]:((~kind(X)<~>strong(X)))) | wise(susan) | [
"p0",
"p12",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6184532631673993064811625
% SZS output start Proof for 6184532631673993064811625
1. ? [X0] : (~happy(X0) & curious(X0)) <=> ? [X0] : (brave(X0) | tall(X0)) [input p0]
13. ! [X0] : ((~calm(X0) | ~quiet(X0)) => ~curious(X0)) [input p12]
14. ! [X0] : ((~wise(X0) & happy(X0)) <=> calm(X0)) [input p13]
16. ? [X0] : wise(X0) <=> tall(mary) [input p15]
25. wise(susan) [input hypothesis]
26. ? [X0] : (~happy(X0) & curious(X0)) <=> ? [X1] : (brave(X1) | tall(X1)) [rectify 1]
35. ! [X0] : (~curious(X0) | (calm(X0) & quiet(X0))) [ennf transformation 13]
36. (? [X0] : (~happy(X0) & curious(X0)) | ! [X1] : (~brave(X1) & ~tall(X1))) & (? [X1] : (brave(X1) | tall(X1)) | ! [X0] : (happy(X0) | ~curious(X0))) [nnf transformation 26]
37. (? [X0] : (~happy(X0) & curious(X0)) | ! [X1] : (~brave(X1) & ~tall(X1))) & (? [X2] : (brave(X2) | tall(X2)) | ! [X3] : (happy(X3) | ~curious(X3))) [rectify 36]
38. ? [X0] : (~happy(X0) & curious(X0)) => (~happy(sK0) & curious(sK0)) [choice axiom]
39. ? [X2] : (brave(X2) | tall(X2)) => (brave(sK1) | tall(sK1)) [choice axiom]
40. ((~happy(sK0) & curious(sK0)) | ! [X1] : (~brave(X1) & ~tall(X1))) & ((brave(sK1) | tall(sK1)) | ! [X3] : (happy(X3) | ~curious(X3))) [skolemisation 37,39,38]
63. ! [X0] : (((~wise(X0) & happy(X0)) | ~calm(X0)) & (calm(X0) | (wise(X0) | ~happy(X0)))) [nnf transformation 14]
64. ! [X0] : (((~wise(X0) & happy(X0)) | ~calm(X0)) & (calm(X0) | wise(X0) | ~happy(X0))) [flattening 63]
70. (? [X0] : wise(X0) | ~tall(mary)) & (tall(mary) | ! [X0] : ~wise(X0)) [nnf transformation 16]
71. (? [X0] : wise(X0) | ~tall(mary)) & (tall(mary) | ! [X1] : ~wise(X1)) [rectify 70]
72. ? [X0] : wise(X0) => wise(sK10) [choice axiom]
73. (wise(sK10) | ~tall(mary)) & (tall(mary) | ! [X1] : ~wise(X1)) [skolemisation 71,72]
92. curious(sK0) | ~tall(X1) [cnf transformation 40]
94. ~happy(sK0) | ~tall(X1) [cnf transformation 40]
130. ~curious(X0) | calm(X0) [cnf transformation 35]
132. ~calm(X0) | happy(X0) [cnf transformation 64]
140. tall(mary) | ~wise(X1) [cnf transformation 73]
155. wise(susan) [cnf transformation 25]
160. 2 <=> happy(sK0) [avatar definition]
165. 3 <=> ! [X1] : ~tall(X1) [avatar definition]
166. ~tall(X1) <- (3) [avatar component clause 165]
167. 3 | ~2 [avatar split clause 94,160,165]
169. 4 <=> curious(sK0) [avatar definition]
171. curious(sK0) <- (4) [avatar component clause 169]
173. 3 | 4 [avatar split clause 92,169,165]
288. 30 <=> wise(susan) [avatar definition]
290. wise(susan) <- (30) [avatar component clause 288]
335. 40 <=> tall(mary) [avatar definition]
336. tall(mary) <- (40) [avatar component clause 335]
344. 42 <=> ! [X1] : ~wise(X1) [avatar definition]
345. ~wise(X1) <- (42) [avatar component clause 344]
346. 42 | 40 [avatar split clause 140,335,344]
420. 30 [avatar split clause 155,288]
423. calm(sK0) <- (4) [resolution 130,171]
425. happy(sK0) <- (4) [resolution 423,132]
428. 2 | ~4 [avatar split clause 425,169,160]
429. $false <- (3, 40) [resolution 166,336]
430. ~3 | ~40 [avatar contradiction clause 429]
431. $false <- (30, 42) [resolution 345,290]
436. ~30 | ~42 [avatar contradiction clause 431]
437. $false [avatar sat refutation 167,173,346,420,428,430,436]
% SZS output end Proof for 6184532631673993064811625
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not funny or not brave is either calm or not funny and vice versa.
If someone is kind then someone is both funny and patient and vice versa.
If someone is funny or happy then alice is tall or wise and vice versa.
If paul is either not tall or patient then mary is both not kind and wise and vice versa.
Everyone who is not brave is both not kind and not creative.
Everyone who is generous is both not happy and not generous.
If john is either funny or not patient then someone is humble or not rich.
If someone is both generous and humble then paul is funny and vice versa.
If someone is both not happy and not generous then paul is both not creative and not generous and vice versa.
Everyone who is both not brave and generous is both not brave and creative and vice versa.
If john is creative then someone is both not calm and not curious.
If someone is humble then alice is not humble or generous and vice versa.
If paul is either not creative or curious then alice is both not old and not brave.
Everyone who is kind is both not humble and not funny.
Everyone who is generous is strong or wise and vice versa.
Everyone who is calm or happy is either creative or not funny.
Susan is rich.
Someone is both not generous and not happy.
Someone is either generous or not brave.
John is humble or not generous.
Lucy is both not tall and humble. | Susan is not happy. | neutral | (![X]:((~funny(X)|~brave(X))<=>(calm(X)<~>~funny(X))))&
((?[X]:(kind(X)))<=>(?[X]:((funny(X)&patient(X)))))&
((?[X]:((funny(X)|happy(X))))<=>((tall(alice)|wise(alice))))&
(((~tall(paul)<~>patient(paul)))<=>((~kind(mary)&wise(mary))))&
(![X]:(~brave(X)=>(~kind(X)&~creative(X))))&
(![X]:(generous(X)=>(~happy(X)&~generous(X))))&
(((funny(john)<~>~patient(john)))=>(?[X]:((humble(X)|~rich(X)))))&
((?[X]:((generous(X)&humble(X))))<=>(funny(paul)))&
((?[X]:((~happy(X)&~generous(X))))<=>((~creative(paul)&~generous(paul))))&
(![X]:((~brave(X)&generous(X))<=>(~brave(X)&creative(X))))&
((creative(john))=>(?[X]:((~calm(X)&~curious(X)))))&
((?[X]:(humble(X)))<=>((~humble(alice)|generous(alice))))&
(((~creative(paul)<~>curious(paul)))=>((~old(alice)&~brave(alice))))&
(![X]:(kind(X)=>(~humble(X)&~funny(X))))&
(![X]:(generous(X)<=>(strong(X)|wise(X))))&
(![X]:((calm(X)|happy(X))=>(creative(X)<~>~funny(X))))&
(rich(susan))&
(?[X]:((~generous(X)&~happy(X))))&
(?[X]:((generous(X)<~>~brave(X))))&
((humble(john)|~generous(john)))&
((~tall(lucy)&humble(lucy))) | ~happy(susan) | [] | null | 0 |
Everyone who is either strong or happy is both patient and curious.
Everyone who is either generous or not strong is not strong and vice versa.
Everyone who is both brave and funny is either not kind or not happy.
If someone is not happy or not brave then mary is both not patient and funny and vice versa.
If john is both kind and rich then alice is creative or not tall and vice versa.
Everyone who is humble is either kind or rich and vice versa.
Everyone who is both patient and not calm is either brave or creative and vice versa.
Everyone who is either not strong or humble is either tall or not wise and vice versa.
If fred is happy or calm then someone is both not brave and not patient and vice versa.
If lucy is either creative or happy then susan is not old and vice versa.
Everyone who is either curious or not old is either curious or not strong and vice versa.
If john is either not strong or not wise then someone is quiet or brave.
Everyone who is either generous or tall is old.
Everyone who is either not wise or not old is not humble and vice versa.
Everyone who is either not brave or not creative is not strong and vice versa.
Alice is strong or not calm.
Fred is calm.
Alice is both not humble and creative.
Paul is either happy or curious.
Paul is either not generous or wise.
Someone is strong.
Someone is humble. | Paul is not old. | contradiction | (![X]:((strong(X)<~>happy(X))=>(patient(X)&curious(X))))&
(![X]:((generous(X)<~>~strong(X))<=>~strong(X)))&
(![X]:((brave(X)&funny(X))=>(~kind(X)<~>~happy(X))))&
((?[X]:((~happy(X)|~brave(X))))<=>((~patient(mary)&funny(mary))))&
(((kind(john)&rich(john)))<=>((creative(alice)|~tall(alice))))&
(![X]:(humble(X)<=>(kind(X)<~>rich(X))))&
(![X]:((patient(X)&~calm(X))<=>(brave(X)<~>creative(X))))&
(![X]:((~strong(X)<~>humble(X))<=>(tall(X)<~>~wise(X))))&
(((happy(fred)|calm(fred)))<=>(?[X]:((~brave(X)&~patient(X)))))&
(((creative(lucy)<~>happy(lucy)))<=>(~old(susan)))&
(![X]:((curious(X)<~>~old(X))<=>(curious(X)<~>~strong(X))))&
(((~strong(john)<~>~wise(john)))=>(?[X]:((quiet(X)|brave(X)))))&
(![X]:((generous(X)<~>tall(X))=>old(X)))&
(![X]:((~wise(X)<~>~old(X))<=>~humble(X)))&
(![X]:((~brave(X)<~>~creative(X))<=>~strong(X)))&
((strong(alice)|~calm(alice)))&
(calm(fred))&
((~humble(alice)&creative(alice)))&
((happy(paul)<~>curious(paul)))&
((~generous(paul)<~>wise(paul)))&
(?[X]:(strong(X)))&
(?[X]:(humble(X))) | ~old(paul) | [
"p1",
"p7",
"p10",
"p12",
"p13",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 2932134146681439979163170
% SZS output start Proof for 2932134146681439979163170
2. ! [X0] : ((generous(X0) <~> ~strong(X0)) <=> ~strong(X0)) [input p1]
8. ! [X0] : ((~strong(X0) <~> humble(X0)) <=> (tall(X0) <~> ~wise(X0))) [input p7]
11. ! [X0] : ((curious(X0) <~> ~old(X0)) <=> (curious(X0) <~> ~strong(X0))) [input p10]
13. ! [X0] : ((generous(X0) <~> tall(X0)) => old(X0)) [input p12]
14. ! [X0] : ((~wise(X0) <~> ~old(X0)) <=> ~humble(X0)) [input p13]
20. ~generous(paul) <~> wise(paul) [input p19]
23. ~old(paul) [input hypothesis]
28. ! [X0] : (old(X0) | (generous(X0) <=> tall(X0))) [ennf transformation 13]
30. ! [X0] : ((((strong(X0) | ~generous(X0)) & (~strong(X0) | generous(X0))) | strong(X0)) & (~strong(X0) | ((generous(X0) | strong(X0)) & (~strong(X0) | ~generous(X0))))) [nnf transformation 2]
42. ! [X0] : ((((~humble(X0) | strong(X0)) & (humble(X0) | ~strong(X0))) | ((tall(X0) | wise(X0)) & (~wise(X0) | ~tall(X0)))) & (((wise(X0) | ~tall(X0)) & (~wise(X0) | tall(X0))) | ((~strong(X0) | ~humble(X0)) & (humble(X0) | strong(X0))))) [nnf transformation 8]
49. ! [X0] : ((((old(X0) | ~curious(X0)) & (~old(X0) | curious(X0))) | ((curious(X0) | strong(X0)) & (~strong(X0) | ~curious(X0)))) & (((strong(X0) | ~curious(X0)) & (~strong(X0) | curious(X0))) | ((curious(X0) | old(X0)) & (~old(X0) | ~curious(X0))))) [nnf transformation 11]
50. ! [X0] : (old(X0) | ((generous(X0) | ~tall(X0)) & (tall(X0) | ~generous(X0)))) [nnf transformation 28]
51. ! [X0] : ((((old(X0) | wise(X0)) & (~old(X0) | ~wise(X0))) | humble(X0)) & (~humble(X0) | ((~wise(X0) | old(X0)) & (~old(X0) | wise(X0))))) [nnf transformation 14]
54. (~wise(paul) | generous(paul)) & (wise(paul) | ~generous(paul)) [nnf transformation 20]
63. ~strong(X0) | ~strong(X0) | ~generous(X0) [cnf transformation 30]
66. strong(X0) | ~generous(X0) | strong(X0) [cnf transformation 30]
96. ~humble(X0) | strong(X0) | tall(X0) | wise(X0) [cnf transformation 42]
107. ~strong(X0) | curious(X0) | curious(X0) | old(X0) [cnf transformation 49]
112. old(X0) | ~curious(X0) | ~strong(X0) | ~curious(X0) [cnf transformation 49]
115. old(X0) | generous(X0) | ~tall(X0) [cnf transformation 50]
119. old(X0) | wise(X0) | humble(X0) [cnf transformation 51]
131. ~wise(paul) | generous(paul) [cnf transformation 54]
134. ~old(paul) [cnf transformation 23]
135. ~strong(X0) | curious(X0) | old(X0) [duplicate literal removal 107]
138. ~curious(X0) | old(X0) | ~strong(X0) [duplicate literal removal 112]
139. ~strong(X0) | ~generous(X0) [duplicate literal removal 63]
140. ~generous(X0) | strong(X0) [duplicate literal removal 66]
141. ~generous(X0) [subsumption resolution 139,140]
231. ~strong(X0) | old(X0) [subsumption resolution 135,138]
232. ~tall(X0) | old(X0) [subsumption resolution 115,141]
254. ~wise(paul) [subsumption resolution 131,141]
285. 28 <=> strong(paul) [avatar definition]
287. strong(paul) <- (28) [avatar component clause 285]
393. wise(paul) | humble(paul) [resolution 119,134]
399. humble(paul) [subsumption resolution 393,254]
523. 62 <=> tall(paul) [avatar definition]
524. tall(paul) <- (62) [avatar component clause 523]
538. strong(paul) | tall(paul) | wise(paul) [resolution 96,399]
544. strong(paul) | tall(paul) [subsumption resolution 538,254]
545. 62 | 28 [avatar split clause 544,285,523]
549. old(paul) <- (28) [resolution 287,231]
552. $false <- (28) [subsumption resolution 549,134]
553. ~28 [avatar contradiction clause 552]
632. old(paul) <- (62) [resolution 524,232]
633. $false <- (62) [subsumption resolution 632,134]
634. ~62 [avatar contradiction clause 633]
635. $false [avatar sat refutation 545,553,634]
% SZS output end Proof for 2932134146681439979163170
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not brave and not creative is either not old or not humble.
If paul is both wise and not brave then mary is calm and vice versa.
If paul is not happy then someone is not wise or not patient.
Everyone who is both not humble and not old is both not patient and not quiet and vice versa.
If paul is either old or not wise then someone is not patient.
Everyone who is both not calm and not curious is not rich and vice versa.
Everyone who is creative or not wise is either patient or strong and vice versa.
If someone is either rich or happy then someone is generous or not patient.
Everyone who is either not old or not curious is either generous or patient and vice versa.
Everyone who is not rich is not calm and vice versa.
Everyone who is not wise is not funny and vice versa.
If fred is brave or not humble then someone is not curious or not rich and vice versa.
Everyone who is not brave is humble.
Everyone who is either not humble or old is quiet.
If someone is either old or not kind then someone is humble or old and vice versa.
Everyone who is strong or not humble is not brave or wise and vice versa.
Someone is either not kind or not creative.
Susan is both not strong and not old.
Someone is both creative and tall.
Someone is either humble or tall.
Someone is either calm or brave.
Paul is both happy and not old.
Someone is either not humble or rich.
Susan is not funny. | Susan is not creative. | neutral | (![X]:((~brave(X)&~creative(X))=>(~old(X)<~>~humble(X))))&
(((wise(paul)&~brave(paul)))<=>(calm(mary)))&
((~happy(paul))=>(?[X]:((~wise(X)|~patient(X)))))&
(![X]:((~humble(X)&~old(X))<=>(~patient(X)&~quiet(X))))&
(((old(paul)<~>~wise(paul)))=>(?[X]:(~patient(X))))&
(![X]:((~calm(X)&~curious(X))<=>~rich(X)))&
(![X]:((creative(X)|~wise(X))<=>(patient(X)<~>strong(X))))&
((?[X]:((rich(X)<~>happy(X))))=>(?[X]:((generous(X)|~patient(X)))))&
(![X]:((~old(X)<~>~curious(X))<=>(generous(X)<~>patient(X))))&
(![X]:(~rich(X)<=>~calm(X)))&
(![X]:(~wise(X)<=>~funny(X)))&
(((brave(fred)|~humble(fred)))<=>(?[X]:((~curious(X)|~rich(X)))))&
(![X]:(~brave(X)=>humble(X)))&
(![X]:((~humble(X)<~>old(X))=>quiet(X)))&
((?[X]:((old(X)<~>~kind(X))))<=>(?[X]:((humble(X)|old(X)))))&
(![X]:((strong(X)|~humble(X))<=>(~brave(X)|wise(X))))&
(?[X]:((~kind(X)<~>~creative(X))))&
((~strong(susan)&~old(susan)))&
(?[X]:((creative(X)&tall(X))))&
(?[X]:((humble(X)<~>tall(X))))&
(?[X]:((calm(X)<~>brave(X))))&
((happy(paul)&~old(paul)))&
(?[X]:((~humble(X)<~>rich(X))))&
(~funny(susan)) | ~creative(susan) | [] | null | 0 |
Everyone who is not quiet or not tall is both not quiet and old and vice versa.
Everyone who is not brave or not humble is not funny.
Everyone who is not generous is not old or wise.
Everyone who is tall is curious or not patient.
Everyone who is both quiet and tall is both wise and calm and vice versa.
Everyone who is both not wise and not kind is not calm.
If someone is both patient and happy then paul is either curious or not rich and vice versa.
If someone is wise or not tall then mary is either not humble or not funny and vice versa.
If mary is not kind or curious then john is either happy or not quiet.
Everyone who is curious or not rich is not generous or old.
Everyone who is both not calm and not old is either humble or strong.
Everyone who is not happy or not kind is not humble or tall and vice versa.
If someone is both not patient and not rich then someone is either calm or wise.
Everyone who is brave or strong is happy or generous and vice versa.
If someone is either not rich or not humble then someone is not calm.
If someone is tall or strong then someone is not tall.
John is humble.
Someone is old or not kind.
Someone is not patient.
Someone is not wise or patient.
Someone is patient or not tall.
John is both not old and generous.
Someone is humble or curious. | Paul is curious. | neutral | (![X]:((~quiet(X)|~tall(X))<=>(~quiet(X)&old(X))))&
(![X]:((~brave(X)|~humble(X))=>~funny(X)))&
(![X]:(~generous(X)=>(~old(X)|wise(X))))&
(![X]:(tall(X)=>(curious(X)|~patient(X))))&
(![X]:((quiet(X)&tall(X))<=>(wise(X)&calm(X))))&
(![X]:((~wise(X)&~kind(X))=>~calm(X)))&
((?[X]:((patient(X)&happy(X))))<=>((curious(paul)<~>~rich(paul))))&
((?[X]:((wise(X)|~tall(X))))<=>((~humble(mary)<~>~funny(mary))))&
(((~kind(mary)|curious(mary)))=>((happy(john)<~>~quiet(john))))&
(![X]:((curious(X)|~rich(X))=>(~generous(X)|old(X))))&
(![X]:((~calm(X)&~old(X))=>(humble(X)<~>strong(X))))&
(![X]:((~happy(X)|~kind(X))<=>(~humble(X)|tall(X))))&
((?[X]:((~patient(X)&~rich(X))))=>(?[X]:((calm(X)<~>wise(X)))))&
(![X]:((brave(X)|strong(X))<=>(happy(X)|generous(X))))&
((?[X]:((~rich(X)<~>~humble(X))))=>(?[X]:(~calm(X))))&
((?[X]:((tall(X)|strong(X))))=>(?[X]:(~tall(X))))&
(humble(john))&
(?[X]:((old(X)|~kind(X))))&
(?[X]:(~patient(X)))&
(?[X]:((~wise(X)|patient(X))))&
(?[X]:((patient(X)|~tall(X))))&
((~old(john)&generous(john)))&
(?[X]:((humble(X)|curious(X)))) | curious(paul) | [] | null | 0 |
Everyone who is both wise and not patient is not kind or not brave and vice versa.
If someone is both generous and creative then fred is either not old or not funny.
Everyone who is patient is either strong or generous.
Everyone who is both curious and patient is both wise and patient and vice versa.
Everyone who is brave is either old or not generous.
If someone is brave then susan is both generous and not wise and vice versa.
Everyone who is not patient or creative is both not tall and not wise and vice versa.
If someone is either brave or calm then someone is either not happy or not rich.
If someone is humble or not wise then someone is not patient.
If susan is both strong and not generous then someone is brave.
If someone is brave or kind then someone is not humble or not curious.
If fred is either not kind or wise then susan is both patient and not humble.
Everyone who is both not old and wise is both not happy and not curious and vice versa.
Everyone who is either not rich or not patient is either not quiet or not curious.
If someone is tall then someone is old and vice versa.
Everyone who is both not calm and not humble is either curious or not wise and vice versa.
Someone is kind or creative.
Someone is both not funny and happy.
Someone is not happy.
Mary is both brave and tall.
Someone is not patient.
Someone is generous.
Mary is either not rich or not calm.
Susan is either generous or happy. | Susan is not patient. | entailment | (![X]:((wise(X)&~patient(X))<=>(~kind(X)|~brave(X))))&
((?[X]:((generous(X)&creative(X))))=>((~old(fred)<~>~funny(fred))))&
(![X]:(patient(X)=>(strong(X)<~>generous(X))))&
(![X]:((curious(X)&patient(X))<=>(wise(X)&patient(X))))&
(![X]:(brave(X)=>(old(X)<~>~generous(X))))&
((?[X]:(brave(X)))<=>((generous(susan)&~wise(susan))))&
(![X]:((~patient(X)|creative(X))<=>(~tall(X)&~wise(X))))&
((?[X]:((brave(X)<~>calm(X))))=>(?[X]:((~happy(X)<~>~rich(X)))))&
((?[X]:((humble(X)|~wise(X))))=>(?[X]:(~patient(X))))&
(((strong(susan)&~generous(susan)))=>(?[X]:(brave(X))))&
((?[X]:((brave(X)|kind(X))))=>(?[X]:((~humble(X)|~curious(X)))))&
(((~kind(fred)<~>wise(fred)))=>((patient(susan)&~humble(susan))))&
(![X]:((~old(X)&wise(X))<=>(~happy(X)&~curious(X))))&
(![X]:((~rich(X)<~>~patient(X))=>(~quiet(X)<~>~curious(X))))&
((?[X]:(tall(X)))<=>(?[X]:(old(X))))&
(![X]:((~calm(X)&~humble(X))<=>(curious(X)<~>~wise(X))))&
(?[X]:((kind(X)|creative(X))))&
(?[X]:((~funny(X)&happy(X))))&
(?[X]:(~happy(X)))&
((brave(mary)&tall(mary)))&
(?[X]:(~patient(X)))&
(?[X]:(generous(X)))&
((~rich(mary)<~>~calm(mary)))&
((generous(susan)<~>happy(susan))) | ~patient(susan) | [
"p0",
"p3",
"p4",
"p5",
"p12",
"p19",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 3450333193935861830558493
% SZS output start Proof for 3450333193935861830558493
1. ! [X0] : ((~patient(X0) & wise(X0)) <=> (~brave(X0) | ~kind(X0))) [input p0]
4. ! [X0] : ((patient(X0) & curious(X0)) <=> (patient(X0) & wise(X0))) [input p3]
5. ! [X0] : (brave(X0) => (old(X0) <~> ~generous(X0))) [input p4]
6. ? [X0] : brave(X0) <=> (~wise(susan) & generous(susan)) [input p5]
13. ! [X0] : ((wise(X0) & ~old(X0)) <=> (~curious(X0) & ~happy(X0))) [input p12]
20. tall(mary) & brave(mary) [input p19]
24. generous(susan) <~> happy(susan) [input p23]
25. patient(susan) [input hypothesis]
32. ! [X0] : ((old(X0) <~> ~generous(X0)) | ~brave(X0)) [ennf transformation 5]
40. ! [X0] : (((~patient(X0) & wise(X0)) | (brave(X0) & kind(X0))) & ((~brave(X0) | ~kind(X0)) | (patient(X0) | ~wise(X0)))) [nnf transformation 1]
41. ! [X0] : (((~patient(X0) & wise(X0)) | (brave(X0) & kind(X0))) & (~brave(X0) | ~kind(X0) | patient(X0) | ~wise(X0))) [flattening 40]
44. ! [X0] : (((patient(X0) & curious(X0)) | (~patient(X0) | ~wise(X0))) & ((patient(X0) & wise(X0)) | (~patient(X0) | ~curious(X0)))) [nnf transformation 4]
45. ! [X0] : (((patient(X0) & curious(X0)) | ~patient(X0) | ~wise(X0)) & ((patient(X0) & wise(X0)) | ~patient(X0) | ~curious(X0))) [flattening 44]
46. ! [X0] : (((generous(X0) | ~old(X0)) & (~generous(X0) | old(X0))) | ~brave(X0)) [nnf transformation 32]
47. (? [X0] : brave(X0) | (wise(susan) | ~generous(susan))) & ((~wise(susan) & generous(susan)) | ! [X0] : ~brave(X0)) [nnf transformation 6]
48. (? [X0] : brave(X0) | wise(susan) | ~generous(susan)) & ((~wise(susan) & generous(susan)) | ! [X0] : ~brave(X0)) [flattening 47]
49. (? [X0] : brave(X0) | wise(susan) | ~generous(susan)) & ((~wise(susan) & generous(susan)) | ! [X1] : ~brave(X1)) [rectify 48]
50. ? [X0] : brave(X0) => brave(sK0) [choice axiom]
51. (brave(sK0) | wise(susan) | ~generous(susan)) & ((~wise(susan) & generous(susan)) | ! [X1] : ~brave(X1)) [skolemisation 49,50]
67. ! [X0] : (((wise(X0) & ~old(X0)) | (curious(X0) | happy(X0))) & ((~curious(X0) & ~happy(X0)) | (~wise(X0) | old(X0)))) [nnf transformation 13]
68. ! [X0] : (((wise(X0) & ~old(X0)) | curious(X0) | happy(X0)) & ((~curious(X0) & ~happy(X0)) | ~wise(X0) | old(X0))) [flattening 67]
88. (~happy(susan) | ~generous(susan)) & (happy(susan) | generous(susan)) [nnf transformation 24]
93. ~patient(X0) | brave(X0) [cnf transformation 41]
98. ~curious(X0) | ~patient(X0) | wise(X0) [cnf transformation 45]
102. ~generous(X0) | old(X0) | ~brave(X0) [cnf transformation 46]
104. generous(susan) | ~brave(X1) [cnf transformation 51]
105. ~wise(susan) | ~brave(X1) [cnf transformation 51]
127. ~old(X0) | curious(X0) | happy(X0) [cnf transformation 68]
145. brave(mary) [cnf transformation 20]
152. ~happy(susan) | ~generous(susan) [cnf transformation 88]
153. patient(susan) [cnf transformation 25]
168. 4 <=> generous(susan) [avatar definition]
169. generous(susan) <- (4) [avatar component clause 168]
172. 5 <=> wise(susan) [avatar definition]
173. ~wise(susan) <- (~5) [avatar component clause 172]
181. 7 <=> ! [X1] : ~brave(X1) [avatar definition]
182. ~brave(X1) <- (7) [avatar component clause 181]
183. 7 | ~5 [avatar split clause 105,172,181]
184. 7 | 4 [avatar split clause 104,168,181]
251. 23 <=> patient(susan) [avatar definition]
253. patient(susan) <- (23) [avatar component clause 251]
291. 32 <=> happy(susan) [avatar definition]
293. ~happy(susan) <- (~32) [avatar component clause 291]
294. ~4 | ~32 [avatar split clause 152,291,168]
296. 23 [avatar split clause 153,251]
304. brave(susan) <- (23) [resolution 93,253]
380. old(susan) | ~brave(susan) <- (4) [resolution 102,169]
390. old(susan) <- (4, 23) [subsumption resolution 380,304]
425. curious(susan) | happy(susan) <- (4, 23) [resolution 127,390]
435. curious(susan) <- (4, 23, ~32) [subsumption resolution 425,293]
475. $false <- (7) [resolution 182,145]
478. ~7 [avatar contradiction clause 475]
560. ~patient(susan) | wise(susan) <- (4, 23, ~32) [resolution 435,98]
567. wise(susan) <- (4, 23, ~32) [subsumption resolution 560,253]
568. $false <- (4, ~5, 23, ~32) [subsumption resolution 567,173]
569. ~4 | 5 | ~23 | 32 [avatar contradiction clause 568]
570. $false [avatar sat refutation 183,184,294,296,478,569]
% SZS output end Proof for 3450333193935861830558493
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both wise and not calm is quiet. Everyone who is not patient or not generous is happy or humble. If someone is brave or humble then mary is not generous. Everyone who is funny is not quiet and vice versa. If lucy is generous then someone is either not old or tall and vice versa. If paul is kind or strong then lucy is either not creative or funny and vice versa. If john is either not funny or strong then someone is either wise or happy and vice versa. Everyone who is both not funny and patient is both quiet and not strong. Everyone who is not quiet or not curious is both not strong and tall. Everyone who is not funny is both not strong and wise and vice versa. If paul is both wise and not humble then someone is either not tall or curious and vice versa. Everyone who is either brave or tall is not funny. If someone is curious then mary is not happy. Everyone who is quiet is either not funny or not creative and vice versa. If someone is both old and kind then someone is humble and vice versa. Everyone who is calm is both not old and not funny and vice versa. Mary is both not curious and kind. Fred is both not quiet and not kind. Someone is not patient or strong. Someone is generous or not happy. Someone is either humble or not patient. Mary is not happy or not wise. Susan is either not humble or not kind. | Mary is generous. | contradiction | (![X]:((wise(X)&~calm(X))=>quiet(X)))&
(![X]:((~patient(X)|~generous(X))=>(happy(X)|humble(X))))&
((?[X]:((brave(X)|humble(X))))=>(~generous(mary)))&
(![X]:(funny(X)<=>~quiet(X)))&
((generous(lucy))<=>(?[X]:((~old(X)<~>tall(X)))))&
(((kind(paul)|strong(paul)))<=>((~creative(lucy)<~>funny(lucy))))&
(((~funny(john)<~>strong(john)))<=>(?[X]:((wise(X)<~>happy(X)))))&
(![X]:((~funny(X)&patient(X))=>(quiet(X)&~strong(X))))&
(![X]:((~quiet(X)|~curious(X))=>(~strong(X)&tall(X))))&
(![X]:(~funny(X)<=>(~strong(X)&wise(X))))&
(((wise(paul)&~humble(paul)))<=>(?[X]:((~tall(X)<~>curious(X)))))&
(![X]:((brave(X)<~>tall(X))=>~funny(X)))&
((?[X]:(curious(X)))=>(~happy(mary)))&
(![X]:(quiet(X)<=>(~funny(X)<~>~creative(X))))&
((?[X]:((old(X)&kind(X))))<=>(?[X]:(humble(X))))&
(![X]:(calm(X)<=>(~old(X)&~funny(X))))&
((~curious(mary)&kind(mary)))&
((~quiet(fred)&~kind(fred)))&
(?[X]:((~patient(X)|strong(X))))&
(?[X]:((generous(X)|~happy(X))))&
(?[X]:((humble(X)<~>~patient(X))))&
((~happy(mary)|~wise(mary)))&
((~humble(susan)<~>~kind(susan))) | generous(mary) | [
"p2",
"p3",
"p8",
"p11",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 8345299666477597627546127
% SZS output start Proof for 8345299666477597627546127
3. ? [X0] : (humble(X0) | brave(X0)) => ~generous(mary) [input p2]
4. ! [X0] : (funny(X0) <=> ~quiet(X0)) [input p3]
9. ! [X0] : ((~curious(X0) | ~quiet(X0)) => (tall(X0) & ~strong(X0))) [input p8]
12. ! [X0] : ((brave(X0) <~> tall(X0)) => ~funny(X0)) [input p11]
18. ~kind(fred) & ~quiet(fred) [input p17]
24. generous(mary) [input hypothesis]
31. ~generous(mary) | ! [X0] : (~humble(X0) & ~brave(X0)) [ennf transformation 3]
34. ! [X0] : ((tall(X0) & ~strong(X0)) | (curious(X0) & quiet(X0))) [ennf transformation 9]
35. ! [X0] : (~funny(X0) | (brave(X0) <=> tall(X0))) [ennf transformation 12]
38. ! [X0] : ((funny(X0) | quiet(X0)) & (~quiet(X0) | ~funny(X0))) [nnf transformation 4]
56. ! [X0] : (~funny(X0) | ((brave(X0) | ~tall(X0)) & (tall(X0) | ~brave(X0)))) [nnf transformation 35]
74. ~generous(mary) | ~brave(X0) [cnf transformation 31]
76. ~funny(X0) | ~quiet(X0) [cnf transformation 38]
77. funny(X0) | quiet(X0) [cnf transformation 38]
100. tall(X0) | quiet(X0) [cnf transformation 34]
112. ~tall(X0) | brave(X0) | ~funny(X0) [cnf transformation 56]
125. ~quiet(fred) [cnf transformation 18]
134. generous(mary) [cnf transformation 24]
139. 2 <=> generous(mary) [avatar definition]
144. 3 <=> ! [X0] : ~brave(X0) [avatar definition]
145. ~brave(X0) <- (3) [avatar component clause 144]
146. 3 | ~2 [avatar split clause 74,139,144]
318. 2 [avatar split clause 134,139]
373. brave(X0) | ~funny(X0) | quiet(X0) [resolution 112,100]
375. ~funny(X0) | quiet(X0) <- (3) [subsumption resolution 373,145]
376. ~funny(X0) <- (3) [subsumption resolution 375,76]
378. quiet(X1) <- (3) [resolution 376,77]
405. $false <- (3) [resolution 378,125]
406. ~3 [avatar contradiction clause 405]
407. $false [avatar sat refutation 146,318,406]
% SZS output end Proof for 8345299666477597627546127
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
If susan is not strong then someone is both generous and not happy.
Everyone who is humble is either humble or strong.
If lucy is either creative or old then alice is not curious.
Everyone who is both creative and not brave is not curious or quiet and vice versa.
Everyone who is both not kind and not strong is either not patient or old and vice versa.
Everyone who is creative or patient is not brave and vice versa.
Everyone who is both creative and rich is either rich or not tall and vice versa.
Everyone who is both brave and not generous is either not funny or not rich.
Everyone who is not happy is both old and funny.
If someone is either rich or brave then paul is both not curious and quiet and vice versa.
Everyone who is either humble or rich is funny.
If mary is humble or not creative then alice is creative or not quiet and vice versa.
Everyone who is both not patient and rich is either happy or not patient and vice versa.
Everyone who is either old or not patient is not brave or not generous.
If lucy is generous then mary is funny.
If alice is quiet then someone is not brave or patient.
Susan is wise or not wise.
Someone is either wise or not wise.
Alice is patient or strong.
Someone is both not brave and not creative.
Susan is not old.
Paul is both not kind and generous.
Someone is both strong and happy.
John is brave or patient. | John is patient. | neutral | ((~strong(susan))=>(?[X]:((generous(X)&~happy(X)))))&
(![X]:(humble(X)=>(humble(X)<~>strong(X))))&
(((creative(lucy)<~>old(lucy)))=>(~curious(alice)))&
(![X]:((creative(X)&~brave(X))<=>(~curious(X)|quiet(X))))&
(![X]:((~kind(X)&~strong(X))<=>(~patient(X)<~>old(X))))&
(![X]:((creative(X)|patient(X))<=>~brave(X)))&
(![X]:((creative(X)&rich(X))<=>(rich(X)<~>~tall(X))))&
(![X]:((brave(X)&~generous(X))=>(~funny(X)<~>~rich(X))))&
(![X]:(~happy(X)=>(old(X)&funny(X))))&
((?[X]:((rich(X)<~>brave(X))))<=>((~curious(paul)&quiet(paul))))&
(![X]:((humble(X)<~>rich(X))=>funny(X)))&
(((humble(mary)|~creative(mary)))<=>((creative(alice)|~quiet(alice))))&
(![X]:((~patient(X)&rich(X))<=>(happy(X)<~>~patient(X))))&
(![X]:((old(X)<~>~patient(X))=>(~brave(X)|~generous(X))))&
((generous(lucy))=>(funny(mary)))&
((quiet(alice))=>(?[X]:((~brave(X)|patient(X)))))&
((wise(susan)|~wise(susan)))&
(?[X]:((wise(X)<~>~wise(X))))&
((patient(alice)|strong(alice)))&
(?[X]:((~brave(X)&~creative(X))))&
(~old(susan))&
((~kind(paul)&generous(paul)))&
(?[X]:((strong(X)&happy(X))))&
((brave(john)|patient(john))) | patient(john) | [] | null | 0 |
If someone is not brave or patient then alice is happy or not calm and vice versa.
If mary is not kind then susan is either not rich or generous and vice versa.
If mary is not calm then paul is not quiet or not tall.
Everyone who is kind is both strong and not humble and vice versa.
Everyone who is either not brave or brave is not old or generous.
Everyone who is old or not calm is both patient and curious.
If someone is both kind and quiet then mary is both tall and not happy.
Everyone who is either not quiet or not happy is tall or not old and vice versa.
Everyone who is creative is both not kind and not creative.
If someone is creative then lucy is funny or old and vice versa.
If someone is both patient and not rich then lucy is both creative and not happy.
If someone is not generous or funny then fred is either not generous or generous and vice versa.
Everyone who is both not strong and patient is quiet and vice versa.
Everyone who is not kind or brave is strong.
Everyone who is either not kind or humble is calm or creative and vice versa.
If someone is either not humble or wise then someone is both not curious and not old.
John is not humble.
Fred is either happy or humble.
Someone is not happy.
Alice is strong.
Susan is either rich or funny. | Paul is generous. | neutral | ((?[X]:((~brave(X)|patient(X))))<=>((happy(alice)|~calm(alice))))&
((~kind(mary))<=>((~rich(susan)<~>generous(susan))))&
((~calm(mary))=>((~quiet(paul)|~tall(paul))))&
(![X]:(kind(X)<=>(strong(X)&~humble(X))))&
(![X]:((~brave(X)<~>brave(X))=>(~old(X)|generous(X))))&
(![X]:((old(X)|~calm(X))=>(patient(X)&curious(X))))&
((?[X]:((kind(X)&quiet(X))))=>((tall(mary)&~happy(mary))))&
(![X]:((~quiet(X)<~>~happy(X))<=>(tall(X)|~old(X))))&
(![X]:(creative(X)=>(~kind(X)&~creative(X))))&
((?[X]:(creative(X)))<=>((funny(lucy)|old(lucy))))&
((?[X]:((patient(X)&~rich(X))))=>((creative(lucy)&~happy(lucy))))&
((?[X]:((~generous(X)|funny(X))))<=>((~generous(fred)<~>generous(fred))))&
(![X]:((~strong(X)&patient(X))<=>quiet(X)))&
(![X]:((~kind(X)|brave(X))=>strong(X)))&
(![X]:((~kind(X)<~>humble(X))<=>(calm(X)|creative(X))))&
((?[X]:((~humble(X)<~>wise(X))))=>(?[X]:((~curious(X)&~old(X)))))&
(~humble(john))&
((happy(fred)<~>humble(fred)))&
(?[X]:(~happy(X)))&
(strong(alice))&
((rich(susan)<~>funny(susan))) | generous(paul) | [] | null | 0 |
Everyone who is generous or wise is not patient or not calm and vice versa.
Everyone who is either creative or quiet is quiet or not brave.
If someone is either patient or wise then someone is not rich or not tall.
If alice is either patient or not quiet then someone is either not brave or tall.
If someone is creative then lucy is both not calm and quiet and vice versa.
Everyone who is both quiet and not curious is either old or creative.
Everyone who is either not wise or not strong is either calm or creative.
Everyone who is both generous and curious is curious or not humble.
If mary is either not patient or calm then someone is either brave or not brave.
Everyone who is not tall is both humble and not wise.
If someone is quiet then someone is old.
Everyone who is generous is not creative and vice versa.
If someone is not calm then someone is not patient and vice versa.
Everyone who is both quiet and kind is humble or not generous and vice versa.
If someone is not patient then john is not happy or not strong and vice versa.
Everyone who is not generous is happy or patient and vice versa.
John is both curious and brave.
Someone is old.
Lucy is both not patient and not old.
Alice is patient or not funny.
Lucy is either not brave or not patient.
John is creative or not patient.
Someone is not funny.
Lucy is tall. | John is not quiet. | neutral | (![X]:((generous(X)|wise(X))<=>(~patient(X)|~calm(X))))&
(![X]:((creative(X)<~>quiet(X))=>(quiet(X)|~brave(X))))&
((?[X]:((patient(X)<~>wise(X))))=>(?[X]:((~rich(X)|~tall(X)))))&
(((patient(alice)<~>~quiet(alice)))=>(?[X]:((~brave(X)<~>tall(X)))))&
((?[X]:(creative(X)))<=>((~calm(lucy)&quiet(lucy))))&
(![X]:((quiet(X)&~curious(X))=>(old(X)<~>creative(X))))&
(![X]:((~wise(X)<~>~strong(X))=>(calm(X)<~>creative(X))))&
(![X]:((generous(X)&curious(X))=>(curious(X)|~humble(X))))&
(((~patient(mary)<~>calm(mary)))=>(?[X]:((brave(X)<~>~brave(X)))))&
(![X]:(~tall(X)=>(humble(X)&~wise(X))))&
((?[X]:(quiet(X)))=>(?[X]:(old(X))))&
(![X]:(generous(X)<=>~creative(X)))&
((?[X]:(~calm(X)))<=>(?[X]:(~patient(X))))&
(![X]:((quiet(X)&kind(X))<=>(humble(X)|~generous(X))))&
((?[X]:(~patient(X)))<=>((~happy(john)|~strong(john))))&
(![X]:(~generous(X)<=>(happy(X)|patient(X))))&
((curious(john)&brave(john)))&
(?[X]:(old(X)))&
((~patient(lucy)&~old(lucy)))&
((patient(alice)|~funny(alice)))&
((~brave(lucy)<~>~patient(lucy)))&
((creative(john)|~patient(john)))&
(?[X]:(~funny(X)))&
(tall(lucy)) | ~quiet(john) | [] | null | 0 |
Everyone who is both humble and brave is not patient or old and vice versa.
If someone is both tall and generous then someone is either humble or not funny and vice versa.
If mary is both funny and not patient then mary is both patient and not brave.
If someone is patient then alice is both not brave and kind and vice versa.
If susan is not generous then someone is either not calm or strong.
Everyone who is not kind is either not brave or not kind and vice versa.
Everyone who is either humble or kind is either not quiet or brave.
If someone is quiet or not brave then alice is both not curious and happy.
Everyone who is calm is both strong and not generous.
Everyone who is happy or quiet is either humble or quiet.
If john is not humble or not curious then mary is kind or not generous.
Everyone who is both not strong and old is calm or not kind.
Everyone who is humble or strong is both wise and not curious and vice versa.
If someone is rich or not curious then john is not funny and vice versa.
Everyone who is not tall is not wise and vice versa.
Everyone who is either humble or not generous is rich.
Fred is either brave or quiet.
Someone is not brave or tall.
Someone is not old or kind.
Someone is either curious or not creative.
Alice is both not funny and not quiet. | Alice is generous. | neutral | (![X]:((humble(X)&brave(X))<=>(~patient(X)|old(X))))&
((?[X]:((tall(X)&generous(X))))<=>(?[X]:((humble(X)<~>~funny(X)))))&
(((funny(mary)&~patient(mary)))=>((patient(mary)&~brave(mary))))&
((?[X]:(patient(X)))<=>((~brave(alice)&kind(alice))))&
((~generous(susan))=>(?[X]:((~calm(X)<~>strong(X)))))&
(![X]:(~kind(X)<=>(~brave(X)<~>~kind(X))))&
(![X]:((humble(X)<~>kind(X))=>(~quiet(X)<~>brave(X))))&
((?[X]:((quiet(X)|~brave(X))))=>((~curious(alice)&happy(alice))))&
(![X]:(calm(X)=>(strong(X)&~generous(X))))&
(![X]:((happy(X)|quiet(X))=>(humble(X)<~>quiet(X))))&
(((~humble(john)|~curious(john)))=>((kind(mary)|~generous(mary))))&
(![X]:((~strong(X)&old(X))=>(calm(X)|~kind(X))))&
(![X]:((humble(X)|strong(X))<=>(wise(X)&~curious(X))))&
((?[X]:((rich(X)|~curious(X))))<=>(~funny(john)))&
(![X]:(~tall(X)<=>~wise(X)))&
(![X]:((humble(X)<~>~generous(X))=>rich(X)))&
((brave(fred)<~>quiet(fred)))&
(?[X]:((~brave(X)|tall(X))))&
(?[X]:((~old(X)|kind(X))))&
(?[X]:((curious(X)<~>~creative(X))))&
((~funny(alice)&~quiet(alice))) | generous(alice) | [] | null | 0 |
Everyone who is not patient or wise is both old and not rich. Everyone who is not humble or quiet is not humble. Everyone who is not kind is both old and funny and vice versa. If susan is not tall or tall then someone is funny or kind. If someone is rich or not wise then john is not funny or not humble and vice versa. Everyone who is both calm and not creative is either not funny or not strong and vice versa. If john is either rich or not funny then someone is not old or not humble and vice versa. Everyone who is not patient is both calm and generous and vice versa. Everyone who is both not curious and funny is either not humble or happy and vice versa. Everyone who is both not patient and not strong is either not tall or funny. If john is both not rich and curious then someone is both kind and not strong. Everyone who is brave or humble is not old and vice versa. If someone is wise then someone is both creative and old and vice versa. Everyone who is both rich and tall is either patient or not curious. If alice is either creative or generous then paul is calm or not calm and vice versa. Everyone who is calm is not humble or not brave and vice versa. Someone is funny or not calm. Someone is funny. Someone is kind or not brave. Someone is generous or quiet. Someone is both not funny and old. Susan is calm or wise. Alice is not calm. | Alice is curious. | neutral | (![X]:((~patient(X)|wise(X))=>(old(X)&~rich(X))))&
(![X]:((~humble(X)|quiet(X))=>~humble(X)))&
(![X]:(~kind(X)<=>(old(X)&funny(X))))&
(((~tall(susan)|tall(susan)))=>(?[X]:((funny(X)|kind(X)))))&
((?[X]:((rich(X)|~wise(X))))<=>((~funny(john)|~humble(john))))&
(![X]:((calm(X)&~creative(X))<=>(~funny(X)<~>~strong(X))))&
(((rich(john)<~>~funny(john)))<=>(?[X]:((~old(X)|~humble(X)))))&
(![X]:(~patient(X)<=>(calm(X)&generous(X))))&
(![X]:((~curious(X)&funny(X))<=>(~humble(X)<~>happy(X))))&
(![X]:((~patient(X)&~strong(X))=>(~tall(X)<~>funny(X))))&
(((~rich(john)&curious(john)))=>(?[X]:((kind(X)&~strong(X)))))&
(![X]:((brave(X)|humble(X))<=>~old(X)))&
((?[X]:(wise(X)))<=>(?[X]:((creative(X)&old(X)))))&
(![X]:((rich(X)&tall(X))=>(patient(X)<~>~curious(X))))&
(((creative(alice)<~>generous(alice)))<=>((calm(paul)|~calm(paul))))&
(![X]:(calm(X)<=>(~humble(X)|~brave(X))))&
(?[X]:((funny(X)|~calm(X))))&
(?[X]:(funny(X)))&
(?[X]:((kind(X)|~brave(X))))&
(?[X]:((generous(X)|quiet(X))))&
(?[X]:((~funny(X)&old(X))))&
((calm(susan)|wise(susan)))&
(~calm(alice)) | curious(alice) | [] | null | 0 |
If alice is strong or curious then fred is not creative and vice versa.
Everyone who is either kind or not patient is funny and vice versa.
If someone is either calm or old then paul is rich or brave and vice versa.
Everyone who is either not brave or happy is both brave and kind and vice versa.
Everyone who is both not generous and funny is calm or patient and vice versa.
If lucy is quiet or not rich then susan is happy.
If paul is not humble or not wise then someone is both rich and kind.
Everyone who is brave or not quiet is not happy and vice versa.
If someone is not quiet or not kind then alice is not humble or quiet.
If someone is either calm or happy then alice is not quiet or not rich and vice versa.
Everyone who is both happy and curious is wise or rich and vice versa.
Everyone who is not old is either old or generous and vice versa.
Everyone who is not funny is tall or not strong.
If someone is both not creative and not funny then someone is either strong or not rich.
If paul is not funny then fred is not curious or generous and vice versa.
Everyone who is curious is either not humble or humble.
Someone is tall or not creative.
Someone is either calm or strong.
Someone is both not humble and not wise.
Mary is either not old or generous.
Someone is either not old or strong.
Someone is not patient.
Fred is not strong. | Fred is curious. | neutral | (((strong(alice)|curious(alice)))<=>(~creative(fred)))&
(![X]:((kind(X)<~>~patient(X))<=>funny(X)))&
((?[X]:((calm(X)<~>old(X))))<=>((rich(paul)|brave(paul))))&
(![X]:((~brave(X)<~>happy(X))<=>(brave(X)&kind(X))))&
(![X]:((~generous(X)&funny(X))<=>(calm(X)|patient(X))))&
(((quiet(lucy)|~rich(lucy)))=>(happy(susan)))&
(((~humble(paul)|~wise(paul)))=>(?[X]:((rich(X)&kind(X)))))&
(![X]:((brave(X)|~quiet(X))<=>~happy(X)))&
((?[X]:((~quiet(X)|~kind(X))))=>((~humble(alice)|quiet(alice))))&
((?[X]:((calm(X)<~>happy(X))))<=>((~quiet(alice)|~rich(alice))))&
(![X]:((happy(X)&curious(X))<=>(wise(X)|rich(X))))&
(![X]:(~old(X)<=>(old(X)<~>generous(X))))&
(![X]:(~funny(X)=>(tall(X)|~strong(X))))&
((?[X]:((~creative(X)&~funny(X))))=>(?[X]:((strong(X)<~>~rich(X)))))&
((~funny(paul))<=>((~curious(fred)|generous(fred))))&
(![X]:(curious(X)=>(~humble(X)<~>humble(X))))&
(?[X]:((tall(X)|~creative(X))))&
(?[X]:((calm(X)<~>strong(X))))&
(?[X]:((~humble(X)&~wise(X))))&
((~old(mary)<~>generous(mary)))&
(?[X]:((~old(X)<~>strong(X))))&
(?[X]:(~patient(X)))&
(~strong(fred)) | curious(fred) | [] | null | 0 |
If someone is both generous and patient then susan is both not curious and brave and vice versa.
Everyone who is either calm or not generous is not brave or not creative and vice versa.
Everyone who is humble or old is both not kind and strong.
If john is not old or creative then fred is either old or not old.
Everyone who is either tall or not curious is both not funny and not strong and vice versa.
If someone is either not happy or generous then someone is not funny and vice versa.
If paul is either generous or strong then john is not brave.
If alice is both not tall and happy then someone is either humble or kind and vice versa.
Everyone who is both not brave and not curious is not happy and vice versa.
Everyone who is either not kind or not old is not kind and vice versa.
If someone is both funny and not happy then someone is patient or quiet.
Everyone who is either not brave or not calm is not happy.
If someone is not rich or not curious then someone is rich.
If someone is happy or not calm then alice is curious or not brave and vice versa.
If someone is either funny or not creative then susan is either calm or strong.
If mary is both strong and not old then someone is tall and vice versa.
Lucy is brave.
Someone is both not wise and quiet.
Someone is curious or not humble.
Someone is tall or not humble.
Lucy is either not funny or not old.
Lucy is both not rich and not tall.
Someone is not brave or rich. | Lucy is not old. | contradiction | ((?[X]:((generous(X)&patient(X))))<=>((~curious(susan)&brave(susan))))&
(![X]:((calm(X)<~>~generous(X))<=>(~brave(X)|~creative(X))))&
(![X]:((humble(X)|old(X))=>(~kind(X)&strong(X))))&
(((~old(john)|creative(john)))=>((old(fred)<~>~old(fred))))&
(![X]:((tall(X)<~>~curious(X))<=>(~funny(X)&~strong(X))))&
((?[X]:((~happy(X)<~>generous(X))))<=>(?[X]:(~funny(X))))&
(((generous(paul)<~>strong(paul)))=>(~brave(john)))&
(((~tall(alice)&happy(alice)))<=>(?[X]:((humble(X)<~>kind(X)))))&
(![X]:((~brave(X)&~curious(X))<=>~happy(X)))&
(![X]:((~kind(X)<~>~old(X))<=>~kind(X)))&
((?[X]:((funny(X)&~happy(X))))=>(?[X]:((patient(X)|quiet(X)))))&
(![X]:((~brave(X)<~>~calm(X))=>~happy(X)))&
((?[X]:((~rich(X)|~curious(X))))=>(?[X]:(rich(X))))&
((?[X]:((happy(X)|~calm(X))))<=>((curious(alice)|~brave(alice))))&
((?[X]:((funny(X)<~>~creative(X))))=>((calm(susan)<~>strong(susan))))&
(((strong(mary)&~old(mary)))<=>(?[X]:(tall(X))))&
(brave(lucy))&
(?[X]:((~wise(X)&quiet(X))))&
(?[X]:((curious(X)|~humble(X))))&
(?[X]:((tall(X)|~humble(X))))&
((~funny(lucy)<~>~old(lucy)))&
((~rich(lucy)&~tall(lucy)))&
(?[X]:((~brave(X)|rich(X)))) | ~old(lucy) | [
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 5570647985656883147108730
% SZS output start Proof for 5570647985656883147108730
10. ! [X0] : ((~kind(X0) <~> ~old(X0)) <=> ~kind(X0)) [input p9]
24. ~old(lucy) [input hypothesis]
60. ! [X0] : ((((old(X0) | kind(X0)) & (~old(X0) | ~kind(X0))) | kind(X0)) & (~kind(X0) | ((~kind(X0) | old(X0)) & (~old(X0) | kind(X0))))) [nnf transformation 10]
123. ~kind(X0) | ~kind(X0) | old(X0) [cnf transformation 60]
125. old(X0) | kind(X0) | kind(X0) [cnf transformation 60]
149. ~old(lucy) [cnf transformation 24]
150. ~kind(X0) | old(X0) [duplicate literal removal 123]
151. old(X0) | kind(X0) [duplicate literal removal 125]
245. old(X0) [subsumption resolution 150,151]
324. $false [subsumption resolution 149,245]
% SZS output end Proof for 5570647985656883147108730
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or not old is both patient and creative and vice versa.
Everyone who is not quiet or humble is both not strong and rich.
Everyone who is not happy or creative is both not creative and not brave.
Everyone who is both quiet and not tall is both not funny and not creative and vice versa.
If someone is not quiet then someone is both not patient and strong and vice versa.
Everyone who is calm or not calm is both not wise and not brave and vice versa.
If someone is not rich then fred is not strong.
Everyone who is happy or funny is either old or creative.
Everyone who is either not calm or not quiet is either not funny or patient and vice versa.
If fred is brave or generous then someone is not kind.
If someone is both not humble and strong then paul is wise or kind.
Everyone who is wise is not tall or not happy.
Everyone who is both generous and strong is both not old and funny and vice versa.
If someone is either happy or curious then someone is either not funny or humble.
If someone is curious or not curious then alice is either funny or not rich and vice versa.
Everyone who is quiet is both not brave and not kind and vice versa.
Lucy is either creative or not brave.
Someone is not old.
Someone is both quiet and not kind.
Someone is strong or humble. | Lucy is patient. | neutral | (![X]:((~creative(X)<~>~old(X))<=>(patient(X)&creative(X))))&
(![X]:((~quiet(X)|humble(X))=>(~strong(X)&rich(X))))&
(![X]:((~happy(X)|creative(X))=>(~creative(X)&~brave(X))))&
(![X]:((quiet(X)&~tall(X))<=>(~funny(X)&~creative(X))))&
((?[X]:(~quiet(X)))<=>(?[X]:((~patient(X)&strong(X)))))&
(![X]:((calm(X)|~calm(X))<=>(~wise(X)&~brave(X))))&
((?[X]:(~rich(X)))=>(~strong(fred)))&
(![X]:((happy(X)|funny(X))=>(old(X)<~>creative(X))))&
(![X]:((~calm(X)<~>~quiet(X))<=>(~funny(X)<~>patient(X))))&
(((brave(fred)|generous(fred)))=>(?[X]:(~kind(X))))&
((?[X]:((~humble(X)&strong(X))))=>((wise(paul)|kind(paul))))&
(![X]:(wise(X)=>(~tall(X)|~happy(X))))&
(![X]:((generous(X)&strong(X))<=>(~old(X)&funny(X))))&
((?[X]:((happy(X)<~>curious(X))))=>(?[X]:((~funny(X)<~>humble(X)))))&
((?[X]:((curious(X)|~curious(X))))<=>((funny(alice)<~>~rich(alice))))&
(![X]:(quiet(X)<=>(~brave(X)&~kind(X))))&
((creative(lucy)<~>~brave(lucy)))&
(?[X]:(~old(X)))&
(?[X]:((quiet(X)&~kind(X))))&
(?[X]:((strong(X)|humble(X)))) | patient(lucy) | [] | null | 0 |
If someone is not wise or generous then someone is both humble and patient and vice versa.
Everyone who is brave or not humble is both not creative and not quiet and vice versa.
If john is either not curious or not wise then someone is not generous and vice versa.
Everyone who is creative or funny is curious and vice versa.
Everyone who is rich is calm and vice versa.
Everyone who is not rich or not creative is both not calm and wise and vice versa.
Everyone who is both not humble and tall is not patient or tall.
If someone is both kind and not creative then lucy is both kind and curious and vice versa.
Everyone who is not creative or tall is either calm or not happy.
If mary is either old or generous then fred is either creative or not brave.
If someone is not brave or strong then john is rich and vice versa.
If someone is kind or creative then someone is rich and vice versa.
Everyone who is not creative or not calm is either calm or tall.
Everyone who is either rich or not kind is both not humble and not calm and vice versa.
If someone is generous or patient then lucy is not wise or funny and vice versa.
Everyone who is both funny and humble is both calm and quiet and vice versa.
Susan is both not curious and not generous.
Someone is both strong and not funny.
Paul is happy or brave.
Someone is both not old and not patient.
Paul is either curious or not kind.
Alice is not patient. | Susan is not humble. | entailment | ((?[X]:((~wise(X)|generous(X))))<=>(?[X]:((humble(X)&patient(X)))))&
(![X]:((brave(X)|~humble(X))<=>(~creative(X)&~quiet(X))))&
(((~curious(john)<~>~wise(john)))<=>(?[X]:(~generous(X))))&
(![X]:((creative(X)|funny(X))<=>curious(X)))&
(![X]:(rich(X)<=>calm(X)))&
(![X]:((~rich(X)|~creative(X))<=>(~calm(X)&wise(X))))&
(![X]:((~humble(X)&tall(X))=>(~patient(X)|tall(X))))&
((?[X]:((kind(X)&~creative(X))))<=>((kind(lucy)&curious(lucy))))&
(![X]:((~creative(X)|tall(X))=>(calm(X)<~>~happy(X))))&
(((old(mary)<~>generous(mary)))=>((creative(fred)<~>~brave(fred))))&
((?[X]:((~brave(X)|strong(X))))<=>(rich(john)))&
((?[X]:((kind(X)|creative(X))))<=>(?[X]:(rich(X))))&
(![X]:((~creative(X)|~calm(X))=>(calm(X)<~>tall(X))))&
(![X]:((rich(X)<~>~kind(X))<=>(~humble(X)&~calm(X))))&
((?[X]:((generous(X)|patient(X))))<=>((~wise(lucy)|funny(lucy))))&
(![X]:((funny(X)&humble(X))<=>(calm(X)&quiet(X))))&
((~curious(susan)&~generous(susan)))&
(?[X]:((strong(X)&~funny(X))))&
((happy(paul)|brave(paul)))&
(?[X]:((~old(X)&~patient(X))))&
((curious(paul)<~>~kind(paul)))&
(~patient(alice)) | ~humble(susan) | [
"p0",
"p2",
"p3",
"p4",
"p5",
"p7",
"p10",
"p13",
"p14",
"p15",
"p16",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 4091202029918970414796919
% SZS output start Proof for 4091202029918970414796919
1. ? [X0] : (generous(X0) | ~wise(X0)) <=> ? [X0] : (patient(X0) & humble(X0)) [input p0]
3. (~curious(john) <~> ~wise(john)) <=> ? [X0] : ~generous(X0) [input p2]
4. ! [X0] : ((funny(X0) | creative(X0)) <=> curious(X0)) [input p3]
5. ! [X0] : (rich(X0) <=> calm(X0)) [input p4]
6. ! [X0] : ((~creative(X0) | ~rich(X0)) <=> (wise(X0) & ~calm(X0))) [input p5]
8. ? [X0] : (~creative(X0) & kind(X0)) <=> (curious(lucy) & kind(lucy)) [input p7]
11. ? [X0] : (strong(X0) | ~brave(X0)) <=> rich(john) [input p10]
14. ! [X0] : ((rich(X0) <~> ~kind(X0)) <=> (~calm(X0) & ~humble(X0))) [input p13]
15. ? [X0] : (patient(X0) | generous(X0)) <=> (funny(lucy) | ~wise(lucy)) [input p14]
16. ! [X0] : ((humble(X0) & funny(X0)) <=> (quiet(X0) & calm(X0))) [input p15]
17. ~generous(susan) & ~curious(susan) [input p16]
18. ? [X0] : (~funny(X0) & strong(X0)) [input p17]
23. humble(susan) [input hypothesis]
24. ? [X0] : (generous(X0) | ~wise(X0)) <=> ? [X1] : (patient(X1) & humble(X1)) [rectify 1]
31. (? [X0] : (generous(X0) | ~wise(X0)) | ! [X1] : (~patient(X1) | ~humble(X1))) & (? [X1] : (patient(X1) & humble(X1)) | ! [X0] : (~generous(X0) & wise(X0))) [nnf transformation 24]
32. (? [X0] : (generous(X0) | ~wise(X0)) | ! [X1] : (~patient(X1) | ~humble(X1))) & (? [X2] : (patient(X2) & humble(X2)) | ! [X3] : (~generous(X3) & wise(X3))) [rectify 31]
33. ? [X0] : (generous(X0) | ~wise(X0)) => (generous(sK0) | ~wise(sK0)) [choice axiom]
34. ? [X2] : (patient(X2) & humble(X2)) => (patient(sK1) & humble(sK1)) [choice axiom]
35. ((generous(sK0) | ~wise(sK0)) | ! [X1] : (~patient(X1) | ~humble(X1))) & ((patient(sK1) & humble(sK1)) | ! [X3] : (~generous(X3) & wise(X3))) [skolemisation 32,34,33]
38. (((wise(john) | curious(john)) & (~wise(john) | ~curious(john))) | ! [X0] : generous(X0)) & (? [X0] : ~generous(X0) | ((~curious(john) | wise(john)) & (~wise(john) | curious(john)))) [nnf transformation 3]
39. (((wise(john) | curious(john)) & (~wise(john) | ~curious(john))) | ! [X0] : generous(X0)) & (? [X1] : ~generous(X1) | ((~curious(john) | wise(john)) & (~wise(john) | curious(john)))) [rectify 38]
40. ? [X1] : ~generous(X1) => ~generous(sK2) [choice axiom]
41. (((wise(john) | curious(john)) & (~wise(john) | ~curious(john))) | ! [X0] : generous(X0)) & (~generous(sK2) | ((~curious(john) | wise(john)) & (~wise(john) | curious(john)))) [skolemisation 39,40]
42. ! [X0] : (((funny(X0) | creative(X0)) | ~curious(X0)) & (curious(X0) | (~funny(X0) & ~creative(X0)))) [nnf transformation 4]
43. ! [X0] : ((funny(X0) | creative(X0) | ~curious(X0)) & (curious(X0) | (~funny(X0) & ~creative(X0)))) [flattening 42]
44. ! [X0] : ((rich(X0) | ~calm(X0)) & (calm(X0) | ~rich(X0))) [nnf transformation 5]
45. ! [X0] : (((~creative(X0) | ~rich(X0)) | (~wise(X0) | calm(X0))) & ((wise(X0) & ~calm(X0)) | (creative(X0) & rich(X0)))) [nnf transformation 6]
46. ! [X0] : ((~creative(X0) | ~rich(X0) | ~wise(X0) | calm(X0)) & ((wise(X0) & ~calm(X0)) | (creative(X0) & rich(X0)))) [flattening 45]
47. (? [X0] : (~creative(X0) & kind(X0)) | (~curious(lucy) | ~kind(lucy))) & ((curious(lucy) & kind(lucy)) | ! [X0] : (creative(X0) | ~kind(X0))) [nnf transformation 8]
48. (? [X0] : (~creative(X0) & kind(X0)) | ~curious(lucy) | ~kind(lucy)) & ((curious(lucy) & kind(lucy)) | ! [X0] : (creative(X0) | ~kind(X0))) [flattening 47]
49. (? [X0] : (~creative(X0) & kind(X0)) | ~curious(lucy) | ~kind(lucy)) & ((curious(lucy) & kind(lucy)) | ! [X1] : (creative(X1) | ~kind(X1))) [rectify 48]
50. ? [X0] : (~creative(X0) & kind(X0)) => (~creative(sK3) & kind(sK3)) [choice axiom]
51. ((~creative(sK3) & kind(sK3)) | ~curious(lucy) | ~kind(lucy)) & ((curious(lucy) & kind(lucy)) | ! [X1] : (creative(X1) | ~kind(X1))) [skolemisation 49,50]
54. (? [X0] : (strong(X0) | ~brave(X0)) | ~rich(john)) & (rich(john) | ! [X0] : (~strong(X0) & brave(X0))) [nnf transformation 11]
55. (? [X0] : (strong(X0) | ~brave(X0)) | ~rich(john)) & (rich(john) | ! [X1] : (~strong(X1) & brave(X1))) [rectify 54]
56. ? [X0] : (strong(X0) | ~brave(X0)) => (strong(sK4) | ~brave(sK4)) [choice axiom]
57. ((strong(sK4) | ~brave(sK4)) | ~rich(john)) & (rich(john) | ! [X1] : (~strong(X1) & brave(X1))) [skolemisation 55,56]
64. ! [X0] : ((((kind(X0) | ~rich(X0)) & (~kind(X0) | rich(X0))) | (calm(X0) | humble(X0))) & ((~calm(X0) & ~humble(X0)) | ((rich(X0) | kind(X0)) & (~kind(X0) | ~rich(X0))))) [nnf transformation 14]
65. ! [X0] : ((((kind(X0) | ~rich(X0)) & (~kind(X0) | rich(X0))) | calm(X0) | humble(X0)) & ((~calm(X0) & ~humble(X0)) | ((rich(X0) | kind(X0)) & (~kind(X0) | ~rich(X0))))) [flattening 64]
66. (? [X0] : (patient(X0) | generous(X0)) | (~funny(lucy) & wise(lucy))) & ((funny(lucy) | ~wise(lucy)) | ! [X0] : (~patient(X0) & ~generous(X0))) [nnf transformation 15]
67. (? [X0] : (patient(X0) | generous(X0)) | (~funny(lucy) & wise(lucy))) & (funny(lucy) | ~wise(lucy) | ! [X0] : (~patient(X0) & ~generous(X0))) [flattening 66]
68. (? [X0] : (patient(X0) | generous(X0)) | (~funny(lucy) & wise(lucy))) & (funny(lucy) | ~wise(lucy) | ! [X1] : (~patient(X1) & ~generous(X1))) [rectify 67]
69. ? [X0] : (patient(X0) | generous(X0)) => (patient(sK7) | generous(sK7)) [choice axiom]
70. ((patient(sK7) | generous(sK7)) | (~funny(lucy) & wise(lucy))) & (funny(lucy) | ~wise(lucy) | ! [X1] : (~patient(X1) & ~generous(X1))) [skolemisation 68,69]
71. ! [X0] : (((humble(X0) & funny(X0)) | (~quiet(X0) | ~calm(X0))) & ((quiet(X0) & calm(X0)) | (~humble(X0) | ~funny(X0)))) [nnf transformation 16]
72. ! [X0] : (((humble(X0) & funny(X0)) | ~quiet(X0) | ~calm(X0)) & ((quiet(X0) & calm(X0)) | ~humble(X0) | ~funny(X0))) [flattening 71]
73. ? [X0] : (~funny(X0) & strong(X0)) => (~funny(sK8) & strong(sK8)) [choice axiom]
74. ~funny(sK8) & strong(sK8) [skolemisation 18,73]
80. patient(sK1) | wise(X3) [cnf transformation 35]
90. ~wise(john) | ~curious(john) | generous(X0) [cnf transformation 41]
92. ~creative(X0) | curious(X0) [cnf transformation 43]
95. ~rich(X0) | calm(X0) [cnf transformation 44]
96. ~calm(X0) | rich(X0) [cnf transformation 44]
98. ~calm(X0) | creative(X0) [cnf transformation 46]
99. rich(X0) | wise(X0) [cnf transformation 46]
103. kind(lucy) | creative(X1) | ~kind(X1) [cnf transformation 51]
116. rich(john) | ~strong(X1) [cnf transformation 57]
126. ~humble(X0) | rich(X0) | kind(X0) [cnf transformation 65]
127. ~calm(X0) | ~kind(X0) | ~rich(X0) [cnf transformation 65]
129. ~kind(X0) | rich(X0) | calm(X0) | humble(X0) [cnf transformation 65]
132. funny(lucy) | ~wise(lucy) | ~patient(X1) [cnf transformation 70]
135. ~funny(X0) | ~humble(X0) | calm(X0) [cnf transformation 72]
139. ~curious(susan) [cnf transformation 17]
140. ~generous(susan) [cnf transformation 17]
141. strong(sK8) [cnf transformation 74]
149. humble(susan) [cnf transformation 23]
167. 5 <=> patient(sK1) [avatar definition]
169. patient(sK1) <- (5) [avatar component clause 167]
172. 6 <=> ! [X3] : wise(X3) [avatar definition]
173. wise(X3) <- (6) [avatar component clause 172]
174. 6 | 5 [avatar split clause 80,167,172]
182. 8 <=> ! [X0] : generous(X0) [avatar definition]
183. generous(X0) <- (8) [avatar component clause 182]
185. 9 <=> curious(john) [avatar definition]
189. 10 <=> wise(john) [avatar definition]
190. ~wise(john) <- (~10) [avatar component clause 189]
193. 8 | ~9 | ~10 [avatar split clause 90,189,185,182]
201. 12 <=> kind(lucy) [avatar definition]
202. kind(lucy) <- (12) [avatar component clause 201]
219. 16 <=> ! [X1] : (creative(X1) | ~kind(X1)) [avatar definition]
220. ~kind(X1) | creative(X1) <- (16) [avatar component clause 219]
222. 16 | 12 [avatar split clause 103,201,219]
249. 21 <=> rich(john) [avatar definition]
250. rich(john) <- (21) [avatar component clause 249]
262. 24 <=> ! [X1] : ~strong(X1) [avatar definition]
263. ~strong(X1) <- (24) [avatar component clause 262]
264. 24 | 21 [avatar split clause 116,249,262]
293. ~kind(X0) | calm(X0) | humble(X0) [subsumption resolution 129,95]
294. ~kind(X0) | ~rich(X0) [subsumption resolution 127,95]
296. 32 <=> funny(lucy) [avatar definition]
297. funny(lucy) <- (32) [avatar component clause 296]
309. 35 <=> wise(lucy) [avatar definition]
310. ~wise(lucy) <- (~35) [avatar component clause 309]
314. 36 <=> ! [X1] : ~patient(X1) [avatar definition]
315. ~patient(X1) <- (36) [avatar component clause 314]
316. 36 | ~35 | 32 [avatar split clause 132,296,309,314]
343. $false <- (8) [resolution 183,140]
344. ~8 [avatar contradiction clause 343]
345. $false <- (24) [resolution 263,141]
346. ~24 [avatar contradiction clause 345]
349. calm(john) <- (21) [resolution 95,250]
353. creative(john) <- (21) [resolution 98,349]
355. curious(john) <- (21) [resolution 353,92]
375. ~rich(lucy) <- (12) [resolution 294,202]
378. wise(lucy) <- (12) [resolution 375,99]
379. $false <- (12, ~35) [subsumption resolution 378,310]
380. ~12 | 35 [avatar contradiction clause 379]
401. rich(susan) | kind(susan) [resolution 126,149]
405. 42 <=> kind(susan) [avatar definition]
407. kind(susan) <- (42) [avatar component clause 405]
409. 43 <=> rich(susan) [avatar definition]
411. rich(susan) <- (43) [avatar component clause 409]
412. 42 | 43 [avatar split clause 401,409,405]
425. creative(susan) <- (16, 42) [resolution 407,220]
471. curious(susan) <- (16, 42) [resolution 425,92]
474. $false <- (16, 42) [subsumption resolution 471,139]
475. ~16 | ~42 [avatar contradiction clause 474]
477. 50 <=> creative(susan) [avatar definition]
479. creative(susan) <- (50) [avatar component clause 477]
489. calm(susan) <- (43) [resolution 411,95]
499. creative(susan) <- (43) [resolution 489,98]
502. 50 | ~43 [avatar split clause 499,409,477]
503. curious(susan) <- (50) [resolution 479,92]
506. $false <- (50) [subsumption resolution 503,139]
507. ~50 [avatar contradiction clause 506]
509. 53 <=> rich(lucy) [avatar definition]
510. ~rich(lucy) <- (~53) [avatar component clause 509]
526. calm(lucy) | humble(lucy) <- (12) [resolution 202,293]
527. ~rich(lucy) <- (12) [resolution 202,294]
528. ~53 | ~12 [avatar split clause 527,201,509]
585. $false <- (5, 36) [resolution 315,169]
586. ~5 | ~36 [avatar contradiction clause 585]
589. $false <- (6, ~10) [resolution 173,190]
590. ~6 | 10 [avatar contradiction clause 589]
591. 9 | ~21 [avatar split clause 355,249,185]
593. 62 <=> humble(lucy) [avatar definition]
597. 63 <=> calm(lucy) [avatar definition]
599. calm(lucy) <- (63) [avatar component clause 597]
600. 62 | 63 | ~12 [avatar split clause 526,201,597,593]
603. ~humble(lucy) | calm(lucy) <- (32) [resolution 297,135]
617. rich(lucy) <- (63) [resolution 599,96]
620. $false <- (~53, 63) [subsumption resolution 617,510]
621. 53 | ~63 [avatar contradiction clause 620]
622. 63 | ~62 | ~32 [avatar split clause 603,296,593,597]
623. $false [avatar sat refutation 174,193,222,264,316,344,346,380,412,475,502,507,528,586,590,591,600,621,622]
% SZS output end Proof for 4091202029918970414796919
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.041 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is creative is not strong.
If lucy is not wise then someone is both happy and not wise.
Everyone who is either not brave or old is both wise and strong and vice versa.
Everyone who is either not brave or not humble is both not strong and not calm and vice versa.
Everyone who is not quiet is either strong or old.
Everyone who is either old or not humble is not creative or not tall.
Everyone who is not brave is either creative or not strong and vice versa.
Everyone who is generous is both not funny and funny.
Everyone who is not tall is kind or strong.
If fred is not calm then mary is not patient or happy.
If someone is both not happy and not old then fred is not brave and vice versa.
Everyone who is rich is not brave and vice versa.
Everyone who is patient or not brave is either tall or not wise and vice versa.
If lucy is generous then someone is not happy or calm.
Everyone who is either not brave or not strong is patient or not wise and vice versa.
Everyone who is both not happy and not tall is either not calm or quiet.
Someone is either wise or funny.
John is not calm or creative.
Someone is both not quiet and happy.
Someone is both brave and humble.
Alice is both tall and not generous.
Mary is not kind or not strong.
Someone is both old and tall.
Someone is not generous. | Fred is calm. | neutral | (![X]:(creative(X)=>~strong(X)))&
((~wise(lucy))=>(?[X]:((happy(X)&~wise(X)))))&
(![X]:((~brave(X)<~>old(X))<=>(wise(X)&strong(X))))&
(![X]:((~brave(X)<~>~humble(X))<=>(~strong(X)&~calm(X))))&
(![X]:(~quiet(X)=>(strong(X)<~>old(X))))&
(![X]:((old(X)<~>~humble(X))=>(~creative(X)|~tall(X))))&
(![X]:(~brave(X)<=>(creative(X)<~>~strong(X))))&
(![X]:(generous(X)=>(~funny(X)&funny(X))))&
(![X]:(~tall(X)=>(kind(X)|strong(X))))&
((~calm(fred))=>((~patient(mary)|happy(mary))))&
((?[X]:((~happy(X)&~old(X))))<=>(~brave(fred)))&
(![X]:(rich(X)<=>~brave(X)))&
(![X]:((patient(X)|~brave(X))<=>(tall(X)<~>~wise(X))))&
((generous(lucy))=>(?[X]:((~happy(X)|calm(X)))))&
(![X]:((~brave(X)<~>~strong(X))<=>(patient(X)|~wise(X))))&
(![X]:((~happy(X)&~tall(X))=>(~calm(X)<~>quiet(X))))&
(?[X]:((wise(X)<~>funny(X))))&
((~calm(john)|creative(john)))&
(?[X]:((~quiet(X)&happy(X))))&
(?[X]:((brave(X)&humble(X))))&
((tall(alice)&~generous(alice)))&
((~kind(mary)|~strong(mary)))&
(?[X]:((old(X)&tall(X))))&
(?[X]:(~generous(X))) | calm(fred) | [] | null | 0 |
Everyone who is kind or generous is not funny or not kind.
Everyone who is patient or brave is quiet or curious.
Everyone who is not curious is generous or not generous and vice versa.
If lucy is either not tall or not patient then someone is not humble and vice versa.
Everyone who is both not patient and not happy is not creative and vice versa.
Everyone who is both not creative and tall is both wise and happy.
Everyone who is not calm is either humble or calm.
If someone is brave or not wise then someone is not kind or quiet.
If susan is happy then susan is not brave and vice versa.
If someone is either not creative or not patient then john is generous or brave and vice versa.
Everyone who is kind or not creative is both tall and not tall.
Everyone who is happy is either not generous or patient and vice versa.
Everyone who is both humble and not wise is happy and vice versa.
Everyone who is not happy is both not brave and old.
Everyone who is either not humble or not happy is strong or tall and vice versa.
If someone is not calm or humble then someone is kind or not funny.
Fred is wise.
Someone is happy.
Fred is funny.
Alice is tall or strong.
Paul is either creative or funny.
Someone is calm or generous.
Alice is both not happy and calm. | Alice is strong. | neutral | (![X]:((kind(X)|generous(X))=>(~funny(X)|~kind(X))))&
(![X]:((patient(X)|brave(X))=>(quiet(X)|curious(X))))&
(![X]:(~curious(X)<=>(generous(X)|~generous(X))))&
(((~tall(lucy)<~>~patient(lucy)))<=>(?[X]:(~humble(X))))&
(![X]:((~patient(X)&~happy(X))<=>~creative(X)))&
(![X]:((~creative(X)&tall(X))=>(wise(X)&happy(X))))&
(![X]:(~calm(X)=>(humble(X)<~>calm(X))))&
((?[X]:((brave(X)|~wise(X))))=>(?[X]:((~kind(X)|quiet(X)))))&
((happy(susan))<=>(~brave(susan)))&
((?[X]:((~creative(X)<~>~patient(X))))<=>((generous(john)|brave(john))))&
(![X]:((kind(X)|~creative(X))=>(tall(X)&~tall(X))))&
(![X]:(happy(X)<=>(~generous(X)<~>patient(X))))&
(![X]:((humble(X)&~wise(X))<=>happy(X)))&
(![X]:(~happy(X)=>(~brave(X)&old(X))))&
(![X]:((~humble(X)<~>~happy(X))<=>(strong(X)|tall(X))))&
((?[X]:((~calm(X)|humble(X))))=>(?[X]:((kind(X)|~funny(X)))))&
(wise(fred))&
(?[X]:(happy(X)))&
(funny(fred))&
((tall(alice)|strong(alice)))&
((creative(paul)<~>funny(paul)))&
(?[X]:((calm(X)|generous(X))))&
((~happy(alice)&calm(alice))) | strong(alice) | [] | null | 0 |
Everyone who is rich or not calm is patient or strong. Everyone who is both curious and not old is either not rich or strong and vice versa. Everyone who is brave is both not funny and kind and vice versa. If john is either rich or curious then someone is not humble and vice versa. If someone is funny then susan is old or not humble and vice versa. If lucy is either not quiet or happy then paul is not creative. If alice is either humble or not quiet then someone is both kind and not creative and vice versa. If john is both tall and not happy then someone is both happy and creative. If someone is both funny and not tall then someone is not brave. Everyone who is either strong or not brave is either generous or not rich and vice versa. If fred is either funny or not rich then someone is curious or not kind and vice versa. Everyone who is both brave and not old is both rich and not funny. Everyone who is both curious and not rich is either patient or creative and vice versa. Everyone who is either rich or humble is either not generous or patient and vice versa. Everyone who is both patient and brave is funny or wise. Everyone who is not strong or not funny is not kind. Someone is not old or not generous. Susan is not curious or not funny. Someone is both not humble and not calm. Fred is not humble. Alice is either not calm or curious. Someone is curious. John is both calm and not generous. Someone is both not funny and old. | John is kind. | contradiction | (![X]:((rich(X)|~calm(X))=>(patient(X)|strong(X))))&
(![X]:((curious(X)&~old(X))<=>(~rich(X)<~>strong(X))))&
(![X]:(brave(X)<=>(~funny(X)&kind(X))))&
(((rich(john)<~>curious(john)))<=>(?[X]:(~humble(X))))&
((?[X]:(funny(X)))<=>((old(susan)|~humble(susan))))&
(((~quiet(lucy)<~>happy(lucy)))=>(~creative(paul)))&
(((humble(alice)<~>~quiet(alice)))<=>(?[X]:((kind(X)&~creative(X)))))&
(((tall(john)&~happy(john)))=>(?[X]:((happy(X)&creative(X)))))&
((?[X]:((funny(X)&~tall(X))))=>(?[X]:(~brave(X))))&
(![X]:((strong(X)<~>~brave(X))<=>(generous(X)<~>~rich(X))))&
(((funny(fred)<~>~rich(fred)))<=>(?[X]:((curious(X)|~kind(X)))))&
(![X]:((brave(X)&~old(X))=>(rich(X)&~funny(X))))&
(![X]:((curious(X)&~rich(X))<=>(patient(X)<~>creative(X))))&
(![X]:((rich(X)<~>humble(X))<=>(~generous(X)<~>patient(X))))&
(![X]:((patient(X)&brave(X))=>(funny(X)|wise(X))))&
(![X]:((~strong(X)|~funny(X))=>~kind(X)))&
(?[X]:((~old(X)|~generous(X))))&
((~curious(susan)|~funny(susan)))&
(?[X]:((~humble(X)&~calm(X))))&
(~humble(fred))&
((~calm(alice)<~>curious(alice)))&
(?[X]:(curious(X)))&
((calm(john)&~generous(john)))&
(?[X]:((~funny(X)&old(X)))) | kind(john) | [
"p1",
"p2",
"p3",
"p9",
"p15",
"p19",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 2985459885631937279254632
% SZS output start Proof for 2985459885631937279254632
2. ! [X0] : ((~old(X0) & curious(X0)) <=> (~rich(X0) <~> strong(X0))) [input p1]
3. ! [X0] : (brave(X0) <=> (kind(X0) & ~funny(X0))) [input p2]
4. (rich(john) <~> curious(john)) <=> ? [X0] : ~humble(X0) [input p3]
10. ! [X0] : ((strong(X0) <~> ~brave(X0)) <=> (generous(X0) <~> ~rich(X0))) [input p9]
16. ! [X0] : ((~funny(X0) | ~strong(X0)) => ~kind(X0)) [input p15]
20. ~humble(fred) [input p19]
23. ~generous(john) & calm(john) [input p22]
25. kind(john) [input hypothesis]
36. ! [X0] : (~kind(X0) | (funny(X0) & strong(X0))) [ennf transformation 16]
37. ! [X0] : (((~old(X0) & curious(X0)) | ((~rich(X0) | ~strong(X0)) & (strong(X0) | rich(X0)))) & (((~strong(X0) | rich(X0)) & (strong(X0) | ~rich(X0))) | (old(X0) | ~curious(X0)))) [nnf transformation 2]
38. ! [X0] : (((~old(X0) & curious(X0)) | ((~rich(X0) | ~strong(X0)) & (strong(X0) | rich(X0)))) & (((~strong(X0) | rich(X0)) & (strong(X0) | ~rich(X0))) | old(X0) | ~curious(X0))) [flattening 37]
39. ! [X0] : ((brave(X0) | (~kind(X0) | funny(X0))) & ((kind(X0) & ~funny(X0)) | ~brave(X0))) [nnf transformation 3]
40. ! [X0] : ((brave(X0) | ~kind(X0) | funny(X0)) & ((kind(X0) & ~funny(X0)) | ~brave(X0))) [flattening 39]
41. (((~curious(john) | ~rich(john)) & (curious(john) | rich(john))) | ! [X0] : humble(X0)) & (? [X0] : ~humble(X0) | ((rich(john) | ~curious(john)) & (curious(john) | ~rich(john)))) [nnf transformation 4]
42. (((~curious(john) | ~rich(john)) & (curious(john) | rich(john))) | ! [X0] : humble(X0)) & (? [X1] : ~humble(X1) | ((rich(john) | ~curious(john)) & (curious(john) | ~rich(john)))) [rectify 41]
43. ? [X1] : ~humble(X1) => ~humble(sK0) [choice axiom]
44. (((~curious(john) | ~rich(john)) & (curious(john) | rich(john))) | ! [X0] : humble(X0)) & (~humble(sK0) | ((rich(john) | ~curious(john)) & (curious(john) | ~rich(john)))) [skolemisation 42,43]
60. ! [X0] : ((((brave(X0) | ~strong(X0)) & (~brave(X0) | strong(X0))) | ((generous(X0) | rich(X0)) & (~rich(X0) | ~generous(X0)))) & (((rich(X0) | ~generous(X0)) & (~rich(X0) | generous(X0))) | ((strong(X0) | brave(X0)) & (~brave(X0) | ~strong(X0))))) [nnf transformation 10]
82. ~strong(X0) | ~rich(X0) | curious(X0) [cnf transformation 38]
85. ~funny(X0) | ~brave(X0) [cnf transformation 40]
91. ~curious(john) | ~rich(john) | humble(X0) [cnf transformation 44]
113. ~strong(X0) | brave(X0) | generous(X0) | rich(X0) [cnf transformation 60]
136. ~kind(X0) | strong(X0) [cnf transformation 36]
137. ~kind(X0) | funny(X0) [cnf transformation 36]
142. ~humble(fred) [cnf transformation 20]
147. ~generous(john) [cnf transformation 23]
150. kind(john) [cnf transformation 25]
152. 1 <=> ! [X0] : humble(X0) [avatar definition]
153. humble(X0) <- (1) [avatar component clause 152]
155. 2 <=> rich(john) [avatar definition]
156. rich(john) <- (2) [avatar component clause 155]
157. ~rich(john) <- (~2) [avatar component clause 155]
159. 3 <=> curious(john) [avatar definition]
162. 1 | ~2 | ~3 [avatar split clause 91,159,155,152]
310. strong(john) [resolution 136,150]
311. funny(john) [resolution 137,150]
312. ~brave(john) [resolution 311,85]
326. ~rich(john) | curious(john) [resolution 82,310]
328. curious(john) <- (2) [subsumption resolution 326,156]
331. 3 | ~2 [avatar split clause 328,155,159]
333. $false <- (1) [resolution 153,142]
338. ~1 [avatar contradiction clause 333]
452. brave(john) | generous(john) | rich(john) [resolution 113,310]
454. generous(john) | rich(john) [subsumption resolution 452,312]
455. rich(john) [subsumption resolution 454,147]
456. $false <- (~2) [subsumption resolution 455,157]
457. 2 [avatar contradiction clause 456]
458. $false [avatar sat refutation 162,331,338,457]
% SZS output end Proof for 2985459885631937279254632
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If paul is not tall then lucy is not strong and vice versa. If someone is not generous or humble then someone is both happy and not rich and vice versa. Everyone who is not old is either not funny or generous. Everyone who is happy is both not old and not patient and vice versa. Everyone who is both not creative and old is either not patient or not old and vice versa. Everyone who is either tall or not funny is either calm or old. Everyone who is not curious or wise is both generous and not creative. Everyone who is happy is not wise or happy. If mary is both not old and not generous then fred is not strong and vice versa. If someone is generous or humble then john is not patient or calm and vice versa. Everyone who is not rich or creative is not generous and vice versa. Everyone who is both not patient and not curious is not rich. Everyone who is either not curious or generous is curious or brave and vice versa. Everyone who is not creative or not rich is either not rich or not patient. Everyone who is either rich or happy is not calm or brave and vice versa. If someone is both calm and not generous then paul is calm and vice versa. Mary is either not brave or not tall. Someone is either humble or not funny. John is either tall or not creative. Someone is both not wise and kind. Someone is either tall or not patient. Someone is either not wise or happy. Susan is not tall or patient. | Fred is not strong. | contradiction | ((~tall(paul))<=>(~strong(lucy)))&
((?[X]:((~generous(X)|humble(X))))<=>(?[X]:((happy(X)&~rich(X)))))&
(![X]:(~old(X)=>(~funny(X)<~>generous(X))))&
(![X]:(happy(X)<=>(~old(X)&~patient(X))))&
(![X]:((~creative(X)&old(X))<=>(~patient(X)<~>~old(X))))&
(![X]:((tall(X)<~>~funny(X))=>(calm(X)<~>old(X))))&
(![X]:((~curious(X)|wise(X))=>(generous(X)&~creative(X))))&
(![X]:(happy(X)=>(~wise(X)|happy(X))))&
(((~old(mary)&~generous(mary)))<=>(~strong(fred)))&
((?[X]:((generous(X)|humble(X))))<=>((~patient(john)|calm(john))))&
(![X]:((~rich(X)|creative(X))<=>~generous(X)))&
(![X]:((~patient(X)&~curious(X))=>~rich(X)))&
(![X]:((~curious(X)<~>generous(X))<=>(curious(X)|brave(X))))&
(![X]:((~creative(X)|~rich(X))=>(~rich(X)<~>~patient(X))))&
(![X]:((rich(X)<~>happy(X))<=>(~calm(X)|brave(X))))&
((?[X]:((calm(X)&~generous(X))))<=>(calm(paul)))&
((~brave(mary)<~>~tall(mary)))&
(?[X]:((humble(X)<~>~funny(X))))&
((tall(john)<~>~creative(john)))&
(?[X]:((~wise(X)&kind(X))))&
(?[X]:((tall(X)<~>~patient(X))))&
(?[X]:((~wise(X)<~>happy(X))))&
((~tall(susan)|patient(susan))) | ~strong(fred) | [
"p6",
"p8",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 7472385212251370334348513
% SZS output start Proof for 7472385212251370334348513
7. ! [X0] : ((wise(X0) | ~curious(X0)) => (~creative(X0) & generous(X0))) [input p6]
9. (~generous(mary) & ~old(mary)) <=> ~strong(fred) [input p8]
13. ! [X0] : ((~curious(X0) <~> generous(X0)) <=> (brave(X0) | curious(X0))) [input p12]
24. ~strong(fred) [input hypothesis]
29. ! [X0] : ((~creative(X0) & generous(X0)) | (~wise(X0) & curious(X0))) [ennf transformation 7]
47. ((~generous(mary) & ~old(mary)) | strong(fred)) & (~strong(fred) | (generous(mary) | old(mary))) [nnf transformation 9]
48. ((~generous(mary) & ~old(mary)) | strong(fred)) & (~strong(fred) | generous(mary) | old(mary)) [flattening 47]
56. ! [X0] : ((((~generous(X0) | curious(X0)) & (generous(X0) | ~curious(X0))) | (~brave(X0) & ~curious(X0))) & ((brave(X0) | curious(X0)) | ((~curious(X0) | ~generous(X0)) & (generous(X0) | curious(X0))))) [nnf transformation 13]
57. ! [X0] : ((((~generous(X0) | curious(X0)) & (generous(X0) | ~curious(X0))) | (~brave(X0) & ~curious(X0))) & (brave(X0) | curious(X0) | ((~curious(X0) | ~generous(X0)) & (generous(X0) | curious(X0))))) [flattening 56]
100. generous(X0) | curious(X0) [cnf transformation 29]
107. ~generous(mary) | strong(fred) [cnf transformation 48]
118. generous(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 57]
147. ~strong(fred) [cnf transformation 24]
150. generous(X0) | ~curious(X0) [duplicate literal removal 118]
184. 8 <=> ! [X3] : generous(X3) [avatar definition]
185. generous(X3) <- (8) [avatar component clause 184]
195. 10 <=> strong(fred) [avatar definition]
199. 11 <=> generous(mary) [avatar definition]
201. ~generous(mary) <- (~11) [avatar component clause 199]
202. 10 | ~11 [avatar split clause 107,199,195]
234. generous(X0) [subsumption resolution 150,100]
235. 8 [avatar split clause 234,184]
313. ~10 [avatar split clause 147,195]
318. $false <- (8, ~11) [resolution 201,185]
319. ~8 | 11 [avatar contradiction clause 318]
320. $false [avatar sat refutation 202,235,313,319]
% SZS output end Proof for 7472385212251370334348513
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not creative or not happy then john is both calm and funny and vice versa. Everyone who is not brave is funny. If someone is both humble and creative then someone is both old and not rich. If susan is either patient or not humble then someone is either creative or wise. Everyone who is not rich is not funny and vice versa. Everyone who is either humble or not rich is patient or not humble. If susan is tall or quiet then someone is either not generous or not curious and vice versa. Everyone who is not rich or not kind is not kind or creative. Everyone who is both not old and tall is both humble and not generous and vice versa. Everyone who is both not rich and creative is not happy or patient and vice versa. Everyone who is both not creative and brave is not creative or not happy and vice versa. If fred is humble then someone is either generous or not creative. If someone is both not curious and not tall then someone is either not rich or not old and vice versa. Everyone who is either not calm or not rich is either rich or not humble and vice versa. If someone is either not humble or happy then mary is not generous. Everyone who is tall is brave. Mary is not quiet. Someone is both patient and not kind. Someone is either not generous or funny. Susan is either humble or not funny. Someone is brave or creative. Someone is kind or not patient. Someone is not quiet. Someone is both curious and not kind. | Susan is humble. | contradiction | ((?[X]:((~creative(X)<~>~happy(X))))<=>((calm(john)&funny(john))))&
(![X]:(~brave(X)=>funny(X)))&
((?[X]:((humble(X)&creative(X))))=>(?[X]:((old(X)&~rich(X)))))&
(((patient(susan)<~>~humble(susan)))=>(?[X]:((creative(X)<~>wise(X)))))&
(![X]:(~rich(X)<=>~funny(X)))&
(![X]:((humble(X)<~>~rich(X))=>(patient(X)|~humble(X))))&
(((tall(susan)|quiet(susan)))<=>(?[X]:((~generous(X)<~>~curious(X)))))&
(![X]:((~rich(X)|~kind(X))=>(~kind(X)|creative(X))))&
(![X]:((~old(X)&tall(X))<=>(humble(X)&~generous(X))))&
(![X]:((~rich(X)&creative(X))<=>(~happy(X)|patient(X))))&
(![X]:((~creative(X)&brave(X))<=>(~creative(X)|~happy(X))))&
((humble(fred))=>(?[X]:((generous(X)<~>~creative(X)))))&
((?[X]:((~curious(X)&~tall(X))))<=>(?[X]:((~rich(X)<~>~old(X)))))&
(![X]:((~calm(X)<~>~rich(X))<=>(rich(X)<~>~humble(X))))&
((?[X]:((~humble(X)<~>happy(X))))=>(~generous(mary)))&
(![X]:(tall(X)=>brave(X)))&
(~quiet(mary))&
(?[X]:((patient(X)&~kind(X))))&
(?[X]:((~generous(X)<~>funny(X))))&
((humble(susan)<~>~funny(susan)))&
(?[X]:((brave(X)|creative(X))))&
(?[X]:((kind(X)|~patient(X))))&
(?[X]:(~quiet(X)))&
(?[X]:((curious(X)&~kind(X)))) | humble(susan) | [
"p4",
"p5",
"p9",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 550036527734882119809408
% SZS output start Proof for 550036527734882119809408
5. ! [X0] : (~rich(X0) <=> ~funny(X0)) [input p4]
6. ! [X0] : ((humble(X0) <~> ~rich(X0)) => (~humble(X0) | patient(X0))) [input p5]
10. ! [X0] : ((creative(X0) & ~rich(X0)) <=> (patient(X0) | ~happy(X0))) [input p9]
20. humble(susan) <~> ~funny(susan) [input p19]
25. humble(susan) [input hypothesis]
31. ! [X0] : ((~humble(X0) | patient(X0)) | (humble(X0) <=> ~rich(X0))) [ennf transformation 6]
32. ! [X0] : (~humble(X0) | patient(X0) | (humble(X0) <=> ~rich(X0))) [flattening 31]
49. ! [X0] : ((~rich(X0) | funny(X0)) & (~funny(X0) | rich(X0))) [nnf transformation 5]
50. ! [X0] : (~humble(X0) | patient(X0) | ((humble(X0) | rich(X0)) & (~rich(X0) | ~humble(X0)))) [nnf transformation 32]
58. ! [X0] : (((creative(X0) & ~rich(X0)) | (~patient(X0) & happy(X0))) & ((patient(X0) | ~happy(X0)) | (~creative(X0) | rich(X0)))) [nnf transformation 10]
59. ! [X0] : (((creative(X0) & ~rich(X0)) | (~patient(X0) & happy(X0))) & (patient(X0) | ~happy(X0) | ~creative(X0) | rich(X0))) [flattening 58]
77. (funny(susan) | ~humble(susan)) & (~funny(susan) | humble(susan)) [nnf transformation 20]
99. ~funny(X0) | rich(X0) [cnf transformation 49]
101. ~humble(X0) | patient(X0) | ~rich(X0) | ~humble(X0) [cnf transformation 50]
117. ~patient(X0) | ~rich(X0) [cnf transformation 59]
150. funny(susan) | ~humble(susan) [cnf transformation 77]
156. humble(susan) [cnf transformation 25]
161. ~rich(X0) | patient(X0) | ~humble(X0) [duplicate literal removal 101]
204. 10 <=> humble(susan) [avatar definition]
206. humble(susan) <- (10) [avatar component clause 204]
208. 11 <=> patient(susan) [avatar definition]
210. patient(susan) <- (11) [avatar component clause 208]
319. 34 <=> funny(susan) [avatar definition]
321. funny(susan) <- (34) [avatar component clause 319]
322. ~10 | 34 [avatar split clause 150,319,204]
333. 10 [avatar split clause 156,204]
335. rich(susan) <- (34) [resolution 99,321]
397. patient(susan) | ~humble(susan) <- (34) [resolution 161,335]
412. patient(susan) <- (10, 34) [subsumption resolution 397,206]
413. 11 | ~10 | ~34 [avatar split clause 412,319,204,208]
415. ~rich(susan) <- (11) [resolution 210,117]
416. $false <- (11, 34) [subsumption resolution 415,335]
417. ~11 | ~34 [avatar contradiction clause 416]
418. $false [avatar sat refutation 322,333,413,417]
% SZS output end Proof for 550036527734882119809408
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 fred is curious or kind then lucy is strong and vice versa. If fred is not generous or not funny then john is either calm or not funny and vice versa. Everyone who is humble or tall is not tall or not curious. Everyone who is funny is not tall. Everyone who is not old or generous is both not wise and calm and vice versa. If someone is not rich then someone is strong. If mary is both calm and not wise then fred is either not rich or not strong and vice versa. If fred is humble or not happy then mary is both not calm and not brave and vice versa. If someone is either not rich or not humble then alice is both rich and strong and vice versa. Everyone who is either strong or funny is both curious and quiet and vice versa. Everyone who is funny or not wise is either not strong or not kind and vice versa. Everyone who is patient is both not wise and not quiet. Everyone who is both not happy and generous is both funny and happy. Everyone who is not happy is both not happy and patient and vice versa. Everyone who is both not tall and not strong is not strong or calm and vice versa. Everyone who is quiet or generous is not happy and vice versa. Someone is quiet or not strong. Someone is both curious and funny. Someone is generous or not quiet. Lucy is not quiet or not patient. Someone is either not humble or not generous. Someone is not brave. | Mary is wise. | neutral | (((curious(fred)|kind(fred)))<=>(strong(lucy)))&
(((~generous(fred)|~funny(fred)))<=>((calm(john)<~>~funny(john))))&
(![X]:((humble(X)|tall(X))=>(~tall(X)|~curious(X))))&
(![X]:(funny(X)=>~tall(X)))&
(![X]:((~old(X)|generous(X))<=>(~wise(X)&calm(X))))&
((?[X]:(~rich(X)))=>(?[X]:(strong(X))))&
(((calm(mary)&~wise(mary)))<=>((~rich(fred)<~>~strong(fred))))&
(((humble(fred)|~happy(fred)))<=>((~calm(mary)&~brave(mary))))&
((?[X]:((~rich(X)<~>~humble(X))))<=>((rich(alice)&strong(alice))))&
(![X]:((strong(X)<~>funny(X))<=>(curious(X)&quiet(X))))&
(![X]:((funny(X)|~wise(X))<=>(~strong(X)<~>~kind(X))))&
(![X]:(patient(X)=>(~wise(X)&~quiet(X))))&
(![X]:((~happy(X)&generous(X))=>(funny(X)&happy(X))))&
(![X]:(~happy(X)<=>(~happy(X)&patient(X))))&
(![X]:((~tall(X)&~strong(X))<=>(~strong(X)|calm(X))))&
(![X]:((quiet(X)|generous(X))<=>~happy(X)))&
(?[X]:((quiet(X)|~strong(X))))&
(?[X]:((curious(X)&funny(X))))&
(?[X]:((generous(X)|~quiet(X))))&
((~quiet(lucy)|~patient(lucy)))&
(?[X]:((~humble(X)<~>~generous(X))))&
(?[X]:(~brave(X))) | wise(mary) | [] | null | 0 |
If paul is both not creative and rich then someone is old or happy and vice versa.
If someone is both tall and not strong then someone is either calm or not patient.
If someone is both not creative and not wise then someone is both humble and not wise and vice versa.
Everyone who is tall or not brave is not happy and vice versa.
Everyone who is either generous or creative is either wise or not curious and vice versa.
If someone is strong then susan is not brave and vice versa.
If john is both not kind and not rich then someone is patient and vice versa.
If lucy is funny then fred is either happy or humble.
If alice is both not humble and creative then alice is not funny.
If mary is not strong then fred is both not generous and calm and vice versa.
Everyone who is tall or not brave is not creative or strong.
If someone is either not old or old then someone is not curious and vice versa.
Everyone who is humble or curious is not old or rich and vice versa.
Everyone who is either generous or not generous is either quiet or not brave and vice versa.
Everyone who is not humble or not wise is both not funny and tall.
Everyone who is either not creative or not quiet is both brave and quiet and vice versa.
John is old or not curious.
Alice is either not rich or not generous.
Someone is either generous or not wise.
Someone is not humble.
Someone is either not creative or not patient.
Someone is not tall or humble.
Susan is rich. | John is not curious. | entailment | (((~creative(paul)&rich(paul)))<=>(?[X]:((old(X)|happy(X)))))&
((?[X]:((tall(X)&~strong(X))))=>(?[X]:((calm(X)<~>~patient(X)))))&
((?[X]:((~creative(X)&~wise(X))))<=>(?[X]:((humble(X)&~wise(X)))))&
(![X]:((tall(X)|~brave(X))<=>~happy(X)))&
(![X]:((generous(X)<~>creative(X))<=>(wise(X)<~>~curious(X))))&
((?[X]:(strong(X)))<=>(~brave(susan)))&
(((~kind(john)&~rich(john)))<=>(?[X]:(patient(X))))&
((funny(lucy))=>((happy(fred)<~>humble(fred))))&
(((~humble(alice)&creative(alice)))=>(~funny(alice)))&
((~strong(mary))<=>((~generous(fred)&calm(fred))))&
(![X]:((tall(X)|~brave(X))=>(~creative(X)|strong(X))))&
((?[X]:((~old(X)<~>old(X))))<=>(?[X]:(~curious(X))))&
(![X]:((humble(X)|curious(X))<=>(~old(X)|rich(X))))&
(![X]:((generous(X)<~>~generous(X))<=>(quiet(X)<~>~brave(X))))&
(![X]:((~humble(X)|~wise(X))=>(~funny(X)&tall(X))))&
(![X]:((~creative(X)<~>~quiet(X))<=>(brave(X)&quiet(X))))&
((old(john)|~curious(john)))&
((~rich(alice)<~>~generous(alice)))&
(?[X]:((generous(X)<~>~wise(X))))&
(?[X]:(~humble(X)))&
(?[X]:((~creative(X)<~>~patient(X))))&
(?[X]:((~tall(X)|humble(X))))&
(rich(susan)) | ~curious(john) | [
"p6",
"p12",
"p13",
"p15",
"p16",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 2952028950120515367827585
% SZS output start Proof for 2952028950120515367827585
7. (~rich(john) & ~kind(john)) <=> ? [X0] : patient(X0) [input p6]
13. ! [X0] : ((curious(X0) | humble(X0)) <=> (rich(X0) | ~old(X0))) [input p12]
14. ! [X0] : ((generous(X0) <~> ~generous(X0)) <=> (quiet(X0) <~> ~brave(X0))) [input p13]
16. ! [X0] : ((~creative(X0) <~> ~quiet(X0)) <=> (quiet(X0) & brave(X0))) [input p15]
17. ~curious(john) | old(john) [input p16]
21. ? [X0] : (~creative(X0) <~> ~patient(X0)) [input p20]
24. curious(john) [input hypothesis]
56. ((~rich(john) & ~kind(john)) | ! [X0] : ~patient(X0)) & (? [X0] : patient(X0) | (rich(john) | kind(john))) [nnf transformation 7]
57. ((~rich(john) & ~kind(john)) | ! [X0] : ~patient(X0)) & (? [X0] : patient(X0) | rich(john) | kind(john)) [flattening 56]
58. ((~rich(john) & ~kind(john)) | ! [X0] : ~patient(X0)) & (? [X1] : patient(X1) | rich(john) | kind(john)) [rectify 57]
59. ? [X1] : patient(X1) => patient(sK5) [choice axiom]
60. ((~rich(john) & ~kind(john)) | ! [X0] : ~patient(X0)) & (patient(sK5) | rich(john) | kind(john)) [skolemisation 58,59]
68. ! [X0] : (((curious(X0) | humble(X0)) | (~rich(X0) & old(X0))) & ((rich(X0) | ~old(X0)) | (~curious(X0) & ~humble(X0)))) [nnf transformation 13]
69. ! [X0] : ((curious(X0) | humble(X0) | (~rich(X0) & old(X0))) & (rich(X0) | ~old(X0) | (~curious(X0) & ~humble(X0)))) [flattening 68]
70. ! [X0] : ((((generous(X0) | ~generous(X0)) & (~generous(X0) | generous(X0))) | ((quiet(X0) | brave(X0)) & (~brave(X0) | ~quiet(X0)))) & (((brave(X0) | ~quiet(X0)) & (~brave(X0) | quiet(X0))) | ((generous(X0) | generous(X0)) & (~generous(X0) | ~generous(X0))))) [nnf transformation 14]
71. ! [X0] : ((((quiet(X0) | creative(X0)) & (~quiet(X0) | ~creative(X0))) | (~quiet(X0) | ~brave(X0))) & ((quiet(X0) & brave(X0)) | ((~creative(X0) | quiet(X0)) & (~quiet(X0) | creative(X0))))) [nnf transformation 16]
72. ! [X0] : ((((quiet(X0) | creative(X0)) & (~quiet(X0) | ~creative(X0))) | ~quiet(X0) | ~brave(X0)) & ((quiet(X0) & brave(X0)) | ((~creative(X0) | quiet(X0)) & (~quiet(X0) | creative(X0))))) [flattening 71]
79. ? [X0] : ((patient(X0) | creative(X0)) & (~patient(X0) | ~creative(X0))) [nnf transformation 21]
80. ? [X0] : ((patient(X0) | creative(X0)) & (~patient(X0) | ~creative(X0))) => ((patient(sK10) | creative(sK10)) & (~patient(sK10) | ~creative(sK10))) [choice axiom]
81. (patient(sK10) | creative(sK10)) & (~patient(sK10) | ~creative(sK10)) [skolemisation 79,80]
110. ~rich(john) | ~patient(X0) [cnf transformation 60]
121. ~curious(X0) | ~old(X0) | rich(X0) [cnf transformation 69]
126. brave(X0) | ~quiet(X0) | ~generous(X0) | ~generous(X0) [cnf transformation 70]
127. brave(X0) | ~quiet(X0) | generous(X0) | generous(X0) [cnf transformation 70]
137. quiet(X0) | ~creative(X0) | quiet(X0) [cnf transformation 72]
138. ~quiet(X0) | ~creative(X0) | ~quiet(X0) | ~brave(X0) [cnf transformation 72]
140. ~curious(john) | old(john) [cnf transformation 17]
147. patient(sK10) | creative(sK10) [cnf transformation 81]
150. curious(john) [cnf transformation 24]
151. quiet(X0) | ~creative(X0) [duplicate literal removal 137]
152. ~quiet(X0) | ~creative(X0) | ~brave(X0) [duplicate literal removal 138]
155. brave(X0) | ~quiet(X0) | ~generous(X0) [duplicate literal removal 126]
156. brave(X0) | ~quiet(X0) | generous(X0) [duplicate literal removal 127]
239. 19 <=> ! [X0] : ~patient(X0) [avatar definition]
240. ~patient(X0) <- (19) [avatar component clause 239]
242. 20 <=> rich(john) [avatar definition]
244. ~rich(john) <- (~20) [avatar component clause 242]
245. 19 | ~20 [avatar split clause 110,242,239]
280. ~quiet(X0) | brave(X0) [subsumption resolution 155,156]
282. ~quiet(X0) | ~creative(X0) [subsumption resolution 152,280]
283. ~creative(X0) [subsumption resolution 151,282]
285. 28 <=> old(john) [avatar definition]
287. old(john) <- (28) [avatar component clause 285]
289. 29 <=> curious(john) [avatar definition]
290. curious(john) <- (29) [avatar component clause 289]
292. 28 | ~29 [avatar split clause 140,289,285]
313. patient(sK10) [subsumption resolution 147,283]
315. 29 [avatar split clause 150,289]
319. $false <- (19) [resolution 313,240]
320. ~19 [avatar contradiction clause 319]
361. ~old(john) | rich(john) <- (29) [resolution 121,290]
362. rich(john) <- (28, 29) [subsumption resolution 361,287]
363. $false <- (~20, 28, 29) [subsumption resolution 362,244]
364. 20 | ~28 | ~29 [avatar contradiction clause 363]
365. $false [avatar sat refutation 245,292,315,320,364]
% SZS output end Proof for 2952028950120515367827585
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise and humble is funny or calm and vice versa.
Everyone who is not tall is both not patient and happy and vice versa.
Everyone who is not happy or generous is calm or not brave.
Everyone who is not strong or brave is curious or tall and vice versa.
If susan is rich or kind then lucy is either rich or old.
If someone is curious then susan is patient and vice versa.
If someone is both rich and not humble then someone is kind or not quiet and vice versa.
Everyone who is not kind or strong is either generous or old.
Everyone who is patient or quiet is humble.
If susan is not generous or not old then someone is both not wise and not tall.
Everyone who is both not patient and not old is either not quiet or not brave.
Everyone who is either not wise or not patient is either wise or not kind.
If mary is either not curious or rich then someone is both not rich and not old.
If someone is not calm then someone is curious.
If someone is not tall then someone is either kind or creative.
Fred is not quiet or rich.
Paul is not happy.
Someone is both generous and not tall.
Alice is strong or wise.
Someone is either calm or generous.
Susan is both not happy and not rich.
Someone is not old.
Someone is both calm and not brave. | Mary is not strong. | neutral | (![X]:((~wise(X)&humble(X))<=>(funny(X)|calm(X))))&
(![X]:(~tall(X)<=>(~patient(X)&happy(X))))&
(![X]:((~happy(X)|generous(X))=>(calm(X)|~brave(X))))&
(![X]:((~strong(X)|brave(X))<=>(curious(X)|tall(X))))&
(((rich(susan)|kind(susan)))=>((rich(lucy)<~>old(lucy))))&
((?[X]:(curious(X)))<=>(patient(susan)))&
((?[X]:((rich(X)&~humble(X))))<=>(?[X]:((kind(X)|~quiet(X)))))&
(![X]:((~kind(X)|strong(X))=>(generous(X)<~>old(X))))&
(![X]:((patient(X)|quiet(X))=>humble(X)))&
(((~generous(susan)|~old(susan)))=>(?[X]:((~wise(X)&~tall(X)))))&
(![X]:((~patient(X)&~old(X))=>(~quiet(X)<~>~brave(X))))&
(![X]:((~wise(X)<~>~patient(X))=>(wise(X)<~>~kind(X))))&
(((~curious(mary)<~>rich(mary)))=>(?[X]:((~rich(X)&~old(X)))))&
((?[X]:(~calm(X)))=>(?[X]:(curious(X))))&
((?[X]:(~tall(X)))=>(?[X]:((kind(X)<~>creative(X)))))&
((~quiet(fred)|rich(fred)))&
(~happy(paul))&
(?[X]:((generous(X)&~tall(X))))&
((strong(alice)|wise(alice)))&
(?[X]:((calm(X)<~>generous(X))))&
((~happy(susan)&~rich(susan)))&
(?[X]:(~old(X)))&
(?[X]:((calm(X)&~brave(X)))) | ~strong(mary) | [] | null | 0 |
If mary is quiet then alice is both tall and quiet and vice versa.
Everyone who is not rich is either curious or not rich and vice versa.
If mary is not quiet or patient then lucy is strong or not old and vice versa.
Everyone who is not creative is not generous and vice versa.
Everyone who is either not rich or not kind is not kind and vice versa.
If susan is patient then susan is old or patient and vice versa.
Everyone who is both not brave and not strong is both brave and not creative and vice versa.
Everyone who is generous is funny or not generous.
Everyone who is not generous or not patient is both calm and quiet.
If someone is strong then someone is funny and vice versa.
If someone is wise then alice is creative or not kind and vice versa.
Everyone who is not quiet is not creative or not old and vice versa.
Everyone who is both not happy and not curious is rich and vice versa.
If someone is both funny and not happy then mary is both quiet and calm.
If someone is either not tall or old then mary is not quiet or patient.
Someone is generous.
Someone is either not humble or not funny.
Someone is not strong or patient.
Someone is either calm or not strong.
Susan is not tall.
Susan is either brave or not generous. | Susan is patient. | entailment | ((quiet(mary))<=>((tall(alice)&quiet(alice))))&
(![X]:(~rich(X)<=>(curious(X)<~>~rich(X))))&
(((~quiet(mary)|patient(mary)))<=>((strong(lucy)|~old(lucy))))&
(![X]:(~creative(X)<=>~generous(X)))&
(![X]:((~rich(X)<~>~kind(X))<=>~kind(X)))&
((patient(susan))<=>((old(susan)|patient(susan))))&
(![X]:((~brave(X)&~strong(X))<=>(brave(X)&~creative(X))))&
(![X]:(generous(X)=>(funny(X)|~generous(X))))&
(![X]:((~generous(X)|~patient(X))=>(calm(X)&quiet(X))))&
((?[X]:(strong(X)))<=>(?[X]:(funny(X))))&
((?[X]:(wise(X)))<=>((creative(alice)|~kind(alice))))&
(![X]:(~quiet(X)<=>(~creative(X)|~old(X))))&
(![X]:((~happy(X)&~curious(X))<=>rich(X)))&
((?[X]:((funny(X)&~happy(X))))=>((quiet(mary)&calm(mary))))&
((?[X]:((~tall(X)<~>old(X))))=>((~quiet(mary)|patient(mary))))&
(?[X]:(generous(X)))&
(?[X]:((~humble(X)<~>~funny(X))))&
(?[X]:((~strong(X)|patient(X))))&
(?[X]:((calm(X)<~>~strong(X))))&
(~tall(susan))&
((brave(susan)<~>~generous(susan))) | patient(susan) | [
"p5",
"p8",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 7280372719939253314418689
% SZS output start Proof for 7280372719939253314418689
6. patient(susan) <=> (patient(susan) | old(susan)) [input p5]
9. ! [X0] : ((~patient(X0) | ~generous(X0)) => (quiet(X0) & calm(X0))) [input p8]
12. ! [X0] : (~quiet(X0) <=> (~old(X0) | ~creative(X0))) [input p11]
22. ~patient(susan) [input hypothesis]
26. ! [X0] : ((quiet(X0) & calm(X0)) | (patient(X0) & generous(X0))) [ennf transformation 9]
37. (patient(susan) | (~patient(susan) & ~old(susan))) & ((patient(susan) | old(susan)) | ~patient(susan)) [nnf transformation 6]
38. (patient(susan) | (~patient(susan) & ~old(susan))) & (patient(susan) | old(susan) | ~patient(susan)) [flattening 37]
51. ! [X0] : ((~quiet(X0) | (old(X0) & creative(X0))) & ((~old(X0) | ~creative(X0)) | quiet(X0))) [nnf transformation 12]
52. ! [X0] : ((~quiet(X0) | (old(X0) & creative(X0))) & (~old(X0) | ~creative(X0) | quiet(X0))) [flattening 51]
85. patient(susan) | ~old(susan) [cnf transformation 38]
95. patient(X0) | quiet(X0) [cnf transformation 26]
103. ~quiet(X0) | old(X0) [cnf transformation 52]
120. ~patient(susan) [cnf transformation 22]
162. 7 <=> old(susan) [avatar definition]
164. ~old(susan) <- (~7) [avatar component clause 162]
166. 8 <=> patient(susan) [avatar definition]
167. ~patient(susan) <- (~8) [avatar component clause 166]
169. ~7 | 8 [avatar split clause 85,166,162]
262. ~8 [avatar split clause 120,166]
271. quiet(susan) <- (~8) [resolution 95,167]
292. old(susan) <- (~8) [resolution 271,103]
294. $false <- (~7, ~8) [subsumption resolution 292,164]
295. 7 | 8 [avatar contradiction clause 294]
296. $false [avatar sat refutation 169,262,295]
% SZS output end Proof for 7280372719939253314418689
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not wise then someone is not funny or not happy and vice versa.
Everyone who is humble is patient or strong and vice versa.
If someone is wise or not calm then someone is not curious or not calm and vice versa.
Everyone who is both tall and not wise is either not creative or not tall and vice versa.
Everyone who is both tall and curious is not wise and vice versa.
Everyone who is either not rich or not old is not quiet.
If mary is either not funny or rich then john is rich and vice versa.
Everyone who is either humble or generous is not humble or not generous.
Everyone who is calm or happy is both funny and wise.
Everyone who is either patient or not creative is both not creative and brave and vice versa.
Everyone who is curious is both calm and not kind and vice versa.
Everyone who is not generous is either strong or not strong and vice versa.
If someone is not old or generous then alice is not generous.
Everyone who is either not rich or humble is kind and vice versa.
Everyone who is not generous is not happy or tall and vice versa.
Everyone who is either not humble or not brave is kind or tall.
Someone is not kind.
Mary is humble or not quiet.
Someone is either not old or not tall.
Alice is both kind and not calm.
Someone is not creative or not old.
John is either not humble or creative. | Alice is generous. | contradiction | ((?[X]:(~wise(X)))<=>(?[X]:((~funny(X)|~happy(X)))))&
(![X]:(humble(X)<=>(patient(X)|strong(X))))&
((?[X]:((wise(X)|~calm(X))))<=>(?[X]:((~curious(X)|~calm(X)))))&
(![X]:((tall(X)&~wise(X))<=>(~creative(X)<~>~tall(X))))&
(![X]:((tall(X)&curious(X))<=>~wise(X)))&
(![X]:((~rich(X)<~>~old(X))=>~quiet(X)))&
(((~funny(mary)<~>rich(mary)))<=>(rich(john)))&
(![X]:((humble(X)<~>generous(X))=>(~humble(X)|~generous(X))))&
(![X]:((calm(X)|happy(X))=>(funny(X)&wise(X))))&
(![X]:((patient(X)<~>~creative(X))<=>(~creative(X)&brave(X))))&
(![X]:(curious(X)<=>(calm(X)&~kind(X))))&
(![X]:(~generous(X)<=>(strong(X)<~>~strong(X))))&
((?[X]:((~old(X)|generous(X))))=>(~generous(alice)))&
(![X]:((~rich(X)<~>humble(X))<=>kind(X)))&
(![X]:(~generous(X)<=>(~happy(X)|tall(X))))&
(![X]:((~humble(X)<~>~brave(X))=>(kind(X)|tall(X))))&
(?[X]:(~kind(X)))&
((humble(mary)|~quiet(mary)))&
(?[X]:((~old(X)<~>~tall(X))))&
((kind(alice)&~calm(alice)))&
(?[X]:((~creative(X)|~old(X))))&
((~humble(john)<~>creative(john))) | generous(alice) | [
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 219895417068684184455882
% SZS output start Proof for 219895417068684184455882
12. ! [X0] : (~generous(X0) <=> (strong(X0) <~> ~strong(X0))) [input p11]
23. generous(alice) [input hypothesis]
56. ! [X0] : ((~generous(X0) | ((strong(X0) | strong(X0)) & (~strong(X0) | ~strong(X0)))) & (((strong(X0) | ~strong(X0)) & (~strong(X0) | strong(X0))) | generous(X0))) [nnf transformation 12]
109. ~generous(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 56]
110. ~generous(X0) | strong(X0) | strong(X0) [cnf transformation 56]
130. generous(alice) [cnf transformation 23]
131. ~generous(X0) | ~strong(X0) [duplicate literal removal 109]
132. ~generous(X0) | strong(X0) [duplicate literal removal 110]
209. ~generous(X0) [subsumption resolution 131,132]
240. $false [subsumption resolution 130,209]
% SZS output end Proof for 219895417068684184455882
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy then paul is not old.
If someone is funny then someone is strong.
Everyone who is not calm is both humble and generous.
If john is old or strong then someone is both not old and kind.
If mary is either not quiet or not strong then mary is both not strong and rich.
If lucy is not funny or curious then someone is not creative and vice versa.
Everyone who is both not strong and rich is both tall and patient.
If alice is both not brave and not strong then alice is either kind or not wise.
If paul is quiet then paul is not strong and vice versa.
Everyone who is either humble or wise is not old or quiet.
Everyone who is humble or not humble is not humble.
If fred is both rich and not humble then someone is not strong or not rich and vice versa.
Everyone who is not curious or humble is both not tall and not old and vice versa.
If someone is both patient and not tall then someone is both not rich and not quiet.
If someone is kind or strong then paul is either funny or not curious and vice versa.
Someone is quiet.
John is happy.
Alice is either strong or generous.
Someone is patient.
Someone is not old or not calm.
Mary is wise.
Lucy is either brave or not funny. | John is humble. | contradiction | ((happy(susan))=>(~old(paul)))&
((?[X]:(funny(X)))=>(?[X]:(strong(X))))&
(![X]:(~calm(X)=>(humble(X)&generous(X))))&
(((old(john)|strong(john)))=>(?[X]:((~old(X)&kind(X)))))&
(((~quiet(mary)<~>~strong(mary)))=>((~strong(mary)&rich(mary))))&
(((~funny(lucy)|curious(lucy)))<=>(?[X]:(~creative(X))))&
(![X]:((~strong(X)&rich(X))=>(tall(X)&patient(X))))&
(((~brave(alice)&~strong(alice)))=>((kind(alice)<~>~wise(alice))))&
((quiet(paul))<=>(~strong(paul)))&
(![X]:((humble(X)<~>wise(X))=>(~old(X)|quiet(X))))&
(![X]:((humble(X)|~humble(X))=>~humble(X)))&
(((rich(fred)&~humble(fred)))<=>(?[X]:((~strong(X)|~rich(X)))))&
(![X]:((~curious(X)|humble(X))<=>(~tall(X)&~old(X))))&
((?[X]:((patient(X)&~tall(X))))=>(?[X]:((~rich(X)&~quiet(X)))))&
((?[X]:((kind(X)|strong(X))))<=>((funny(paul)<~>~curious(paul))))&
(?[X]:(quiet(X)))&
(happy(john))&
((strong(alice)<~>generous(alice)))&
(?[X]:(patient(X)))&
(?[X]:((~old(X)|~calm(X))))&
(wise(mary))&
((brave(lucy)<~>~funny(lucy))) | humble(john) | [
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 7954364146172655721415420
% SZS output start Proof for 7954364146172655721415420
11. ! [X0] : ((~humble(X0) | humble(X0)) => ~humble(X0)) [input p10]
23. humble(john) [input hypothesis]
37. ! [X0] : (~humble(X0) | (humble(X0) & ~humble(X0))) [ennf transformation 11]
98. ~humble(X0) | ~humble(X0) [cnf transformation 37]
127. humble(john) [cnf transformation 23]
128. ~humble(X0) [duplicate literal removal 98]
313. $false [subsumption resolution 127,128]
% SZS output end Proof for 7954364146172655721415420
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble is strong or calm and vice versa.
Everyone who is not strong or patient is either funny or not calm.
If someone is not kind or not generous then alice is either not kind or calm.
Everyone who is either funny or not strong is curious or not rich.
If someone is both brave and funny then someone is kind.
Everyone who is both creative and not calm is either strong or not kind and vice versa.
Everyone who is funny is either humble or not quiet and vice versa.
If paul is funny then paul is both old and not funny and vice versa.
Everyone who is not tall is humble and vice versa.
Everyone who is either wise or old is humble or not happy and vice versa.
Everyone who is brave is happy.
If someone is not generous then someone is old and vice versa.
Everyone who is not old or not rich is either not humble or kind.
If someone is either not funny or not calm then alice is both not happy and not calm and vice versa.
Everyone who is curious or not calm is both funny and not brave and vice versa.
If someone is not happy or not tall then someone is not brave or not kind.
Paul is either wise or not brave.
Someone is not rich or old.
Susan is either quiet or old.
Mary is both quiet and not wise.
Someone is either calm or humble.
Someone is humble or not generous.
Someone is strong.
John is not old or not patient. | John is not tall. | contradiction | (![X]:(~humble(X)<=>(strong(X)|calm(X))))&
(![X]:((~strong(X)|patient(X))=>(funny(X)<~>~calm(X))))&
((?[X]:((~kind(X)|~generous(X))))=>((~kind(alice)<~>calm(alice))))&
(![X]:((funny(X)<~>~strong(X))=>(curious(X)|~rich(X))))&
((?[X]:((brave(X)&funny(X))))=>(?[X]:(kind(X))))&
(![X]:((creative(X)&~calm(X))<=>(strong(X)<~>~kind(X))))&
(![X]:(funny(X)<=>(humble(X)<~>~quiet(X))))&
((funny(paul))<=>((old(paul)&~funny(paul))))&
(![X]:(~tall(X)<=>humble(X)))&
(![X]:((wise(X)<~>old(X))<=>(humble(X)|~happy(X))))&
(![X]:(brave(X)=>happy(X)))&
((?[X]:(~generous(X)))<=>(?[X]:(old(X))))&
(![X]:((~old(X)|~rich(X))=>(~humble(X)<~>kind(X))))&
((?[X]:((~funny(X)<~>~calm(X))))<=>((~happy(alice)&~calm(alice))))&
(![X]:((curious(X)|~calm(X))<=>(funny(X)&~brave(X))))&
((?[X]:((~happy(X)|~tall(X))))=>(?[X]:((~brave(X)|~kind(X)))))&
((wise(paul)<~>~brave(paul)))&
(?[X]:((~rich(X)|old(X))))&
((quiet(susan)<~>old(susan)))&
((quiet(mary)&~wise(mary)))&
(?[X]:((calm(X)<~>humble(X))))&
(?[X]:((humble(X)|~generous(X))))&
(?[X]:(strong(X)))&
((~old(john)|~patient(john))) | ~tall(john) | [
"p0",
"p1",
"p8",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2992767951017624338647559
% SZS output start Proof for 2992767951017624338647559
1. ! [X0] : (~humble(X0) <=> (calm(X0) | strong(X0))) [input p0]
2. ! [X0] : ((patient(X0) | ~strong(X0)) => (funny(X0) <~> ~calm(X0))) [input p1]
9. ! [X0] : (~tall(X0) <=> humble(X0)) [input p8]
15. ! [X0] : ((~calm(X0) | curious(X0)) <=> (~brave(X0) & funny(X0))) [input p14]
25. ~tall(john) [input hypothesis]
29. ! [X0] : (~strong(X0) => (funny(X0) <~> ~calm(X0))) [pure predicate removal 2]
31. ! [X0] : ((funny(X0) <~> ~calm(X0)) | strong(X0)) [ennf transformation 29]
39. ! [X0] : ((~humble(X0) | (~calm(X0) & ~strong(X0))) & ((calm(X0) | strong(X0)) | humble(X0))) [nnf transformation 1]
40. ! [X0] : ((~humble(X0) | (~calm(X0) & ~strong(X0))) & (calm(X0) | strong(X0) | humble(X0))) [flattening 39]
41. ! [X0] : (((calm(X0) | ~funny(X0)) & (~calm(X0) | funny(X0))) | strong(X0)) [nnf transformation 31]
52. ! [X0] : ((~tall(X0) | ~humble(X0)) & (humble(X0) | tall(X0))) [nnf transformation 9]
66. ! [X0] : (((~calm(X0) | curious(X0)) | (brave(X0) | ~funny(X0))) & ((~brave(X0) & funny(X0)) | (calm(X0) & ~curious(X0)))) [nnf transformation 15]
67. ! [X0] : ((~calm(X0) | curious(X0) | brave(X0) | ~funny(X0)) & ((~brave(X0) & funny(X0)) | (calm(X0) & ~curious(X0)))) [flattening 66]
83. ~strong(X0) | ~humble(X0) [cnf transformation 40]
84. ~calm(X0) | ~humble(X0) [cnf transformation 40]
86. ~funny(X0) | calm(X0) | strong(X0) [cnf transformation 41]
107. tall(X0) | humble(X0) [cnf transformation 52]
129. funny(X0) | calm(X0) [cnf transformation 67]
146. ~tall(john) [cnf transformation 25]
289. humble(john) [resolution 107,146]
344. calm(X0) | strong(X0) | calm(X0) [resolution 86,129]
346. calm(X0) | strong(X0) [duplicate literal removal 344]
349. strong(X1) | ~humble(X1) [resolution 346,84]
354. ~humble(X1) [subsumption resolution 349,83]
381. $false [resolution 354,289]
% SZS output end Proof for 2992767951017624338647559
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is creative is not generous and vice versa.
If paul is not generous then paul is either strong or not quiet.
Everyone who is not brave or strong is patient.
If someone is both not tall and not wise then someone is both not humble and not creative and vice versa.
If john is tall or not funny then lucy is either tall or not rich.
Everyone who is either funny or tall is not calm or not creative and vice versa.
Everyone who is not humble or not curious is not kind or not brave and vice versa.
Everyone who is either not calm or wise is not calm or happy and vice versa.
Everyone who is not kind or not calm is either creative or kind.
If susan is generous or not curious then alice is kind.
Everyone who is patient is not old.
If someone is strong then john is either tall or curious.
If someone is not humble then someone is rich and vice versa.
If lucy is both not wise and not rich then someone is humble and vice versa.
Everyone who is either tall or generous is wise and vice versa.
Everyone who is either generous or not old is not humble or not quiet and vice versa.
Fred is kind.
Someone is either not quiet or not humble.
Fred is happy or creative.
Someone is either not humble or rich.
Someone is both happy and not strong.
Fred is either rich or kind.
Fred is strong.
Someone is either not patient or not tall. | John is calm. | entailment | (![X]:(creative(X)<=>~generous(X)))&
((~generous(paul))=>((strong(paul)<~>~quiet(paul))))&
(![X]:((~brave(X)|strong(X))=>patient(X)))&
((?[X]:((~tall(X)&~wise(X))))<=>(?[X]:((~humble(X)&~creative(X)))))&
(((tall(john)|~funny(john)))=>((tall(lucy)<~>~rich(lucy))))&
(![X]:((funny(X)<~>tall(X))<=>(~calm(X)|~creative(X))))&
(![X]:((~humble(X)|~curious(X))<=>(~kind(X)|~brave(X))))&
(![X]:((~calm(X)<~>wise(X))<=>(~calm(X)|happy(X))))&
(![X]:((~kind(X)|~calm(X))=>(creative(X)<~>kind(X))))&
(((generous(susan)|~curious(susan)))=>(kind(alice)))&
(![X]:(patient(X)=>~old(X)))&
((?[X]:(strong(X)))=>((tall(john)<~>curious(john))))&
((?[X]:(~humble(X)))<=>(?[X]:(rich(X))))&
(((~wise(lucy)&~rich(lucy)))<=>(?[X]:(humble(X))))&
(![X]:((tall(X)<~>generous(X))<=>wise(X)))&
(![X]:((generous(X)<~>~old(X))<=>(~humble(X)|~quiet(X))))&
(kind(fred))&
(?[X]:((~quiet(X)<~>~humble(X))))&
((happy(fred)|creative(fred)))&
(?[X]:((~humble(X)<~>rich(X))))&
(?[X]:((happy(X)&~strong(X))))&
((rich(fred)<~>kind(fred)))&
(strong(fred))&
(?[X]:((~patient(X)<~>~tall(X)))) | calm(john) | [
"p0",
"p2",
"p3",
"p4",
"p6",
"p7",
"p8",
"p10",
"p13",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 391377121105313574250614
% SZS output start Proof for 391377121105313574250614
1. ! [X0] : (creative(X0) <=> ~generous(X0)) [input p0]
3. ! [X0] : ((strong(X0) | ~brave(X0)) => patient(X0)) [input p2]
4. ? [X0] : (~wise(X0) & ~tall(X0)) <=> ? [X0] : (~creative(X0) & ~humble(X0)) [input p3]
5. (~funny(john) | tall(john)) => (tall(lucy) <~> ~rich(lucy)) [input p4]
7. ! [X0] : ((~curious(X0) | ~humble(X0)) <=> (~brave(X0) | ~kind(X0))) [input p6]
8. ! [X0] : ((~calm(X0) <~> wise(X0)) <=> (happy(X0) | ~calm(X0))) [input p7]
9. ! [X0] : ((~calm(X0) | ~kind(X0)) => (creative(X0) <~> kind(X0))) [input p8]
11. ! [X0] : (patient(X0) => ~old(X0)) [input p10]
14. (~rich(lucy) & ~wise(lucy)) <=> ? [X0] : humble(X0) [input p13]
15. ! [X0] : ((tall(X0) <~> generous(X0)) <=> wise(X0)) [input p14]
16. ! [X0] : ((generous(X0) <~> ~old(X0)) <=> (~quiet(X0) | ~humble(X0))) [input p15]
25. ~calm(john) [input hypothesis]
26. ? [X0] : (~wise(X0) & ~tall(X0)) <=> ? [X1] : (~creative(X1) & ~humble(X1)) [rectify 4]
29. ! [X0] : (patient(X0) | (~strong(X0) & brave(X0))) [ennf transformation 3]
30. (tall(lucy) <~> ~rich(lucy)) | (funny(john) & ~tall(john)) [ennf transformation 5]
31. ! [X0] : ((creative(X0) <~> kind(X0)) | (calm(X0) & kind(X0))) [ennf transformation 9]
33. ! [X0] : (~old(X0) | ~patient(X0)) [ennf transformation 11]
35. ! [X0] : ((creative(X0) | generous(X0)) & (~generous(X0) | ~creative(X0))) [nnf transformation 1]
37. (? [X0] : (~wise(X0) & ~tall(X0)) | ! [X1] : (creative(X1) | humble(X1))) & (? [X1] : (~creative(X1) & ~humble(X1)) | ! [X0] : (wise(X0) | tall(X0))) [nnf transformation 26]
38. (? [X0] : (~wise(X0) & ~tall(X0)) | ! [X1] : (creative(X1) | humble(X1))) & (? [X2] : (~creative(X2) & ~humble(X2)) | ! [X3] : (wise(X3) | tall(X3))) [rectify 37]
39. ? [X0] : (~wise(X0) & ~tall(X0)) => (~wise(sK0) & ~tall(sK0)) [choice axiom]
40. ? [X2] : (~creative(X2) & ~humble(X2)) => (~creative(sK1) & ~humble(sK1)) [choice axiom]
41. ((~wise(sK0) & ~tall(sK0)) | ! [X1] : (creative(X1) | humble(X1))) & ((~creative(sK1) & ~humble(sK1)) | ! [X3] : (wise(X3) | tall(X3))) [skolemisation 38,40,39]
42. ((rich(lucy) | ~tall(lucy)) & (~rich(lucy) | tall(lucy))) | (funny(john) & ~tall(john)) [nnf transformation 30]
45. ! [X0] : (((~curious(X0) | ~humble(X0)) | (brave(X0) & kind(X0))) & ((~brave(X0) | ~kind(X0)) | (curious(X0) & humble(X0)))) [nnf transformation 7]
46. ! [X0] : ((~curious(X0) | ~humble(X0) | (brave(X0) & kind(X0))) & (~brave(X0) | ~kind(X0) | (curious(X0) & humble(X0)))) [flattening 45]
47. ! [X0] : ((((~wise(X0) | calm(X0)) & (wise(X0) | ~calm(X0))) | (~happy(X0) & calm(X0))) & ((happy(X0) | ~calm(X0)) | ((~calm(X0) | ~wise(X0)) & (wise(X0) | calm(X0))))) [nnf transformation 8]
48. ! [X0] : ((((~wise(X0) | calm(X0)) & (wise(X0) | ~calm(X0))) | (~happy(X0) & calm(X0))) & (happy(X0) | ~calm(X0) | ((~calm(X0) | ~wise(X0)) & (wise(X0) | calm(X0))))) [flattening 47]
49. ! [X0] : (((~kind(X0) | ~creative(X0)) & (kind(X0) | creative(X0))) | (calm(X0) & kind(X0))) [nnf transformation 31]
56. ((~rich(lucy) & ~wise(lucy)) | ! [X0] : ~humble(X0)) & (? [X0] : humble(X0) | (rich(lucy) | wise(lucy))) [nnf transformation 14]
57. ((~rich(lucy) & ~wise(lucy)) | ! [X0] : ~humble(X0)) & (? [X0] : humble(X0) | rich(lucy) | wise(lucy)) [flattening 56]
58. ((~rich(lucy) & ~wise(lucy)) | ! [X0] : ~humble(X0)) & (? [X1] : humble(X1) | rich(lucy) | wise(lucy)) [rectify 57]
59. ? [X1] : humble(X1) => humble(sK4) [choice axiom]
60. ((~rich(lucy) & ~wise(lucy)) | ! [X0] : ~humble(X0)) & (humble(sK4) | rich(lucy) | wise(lucy)) [skolemisation 58,59]
61. ! [X0] : ((((~generous(X0) | ~tall(X0)) & (generous(X0) | tall(X0))) | ~wise(X0)) & (wise(X0) | ((tall(X0) | ~generous(X0)) & (generous(X0) | ~tall(X0))))) [nnf transformation 15]
62. ! [X0] : ((((old(X0) | ~generous(X0)) & (~old(X0) | generous(X0))) | (quiet(X0) & humble(X0))) & ((~quiet(X0) | ~humble(X0)) | ((generous(X0) | old(X0)) & (~old(X0) | ~generous(X0))))) [nnf transformation 16]
63. ! [X0] : ((((old(X0) | ~generous(X0)) & (~old(X0) | generous(X0))) | (quiet(X0) & humble(X0))) & (~quiet(X0) | ~humble(X0) | ((generous(X0) | old(X0)) & (~old(X0) | ~generous(X0))))) [flattening 62]
76. ~generous(X0) | ~creative(X0) [cnf transformation 35]
77. generous(X0) | creative(X0) [cnf transformation 35]
80. patient(X0) | brave(X0) [cnf transformation 29]
82. ~humble(sK1) | wise(X3) | tall(X3) [cnf transformation 41]
83. ~creative(sK1) | wise(X3) | tall(X3) [cnf transformation 41]
88. rich(lucy) | ~tall(lucy) | ~tall(john) [cnf transformation 42]
96. ~kind(X0) | ~brave(X0) | humble(X0) [cnf transformation 46]
104. ~wise(X0) | calm(X0) | calm(X0) [cnf transformation 48]
106. kind(X0) | creative(X0) | kind(X0) [cnf transformation 49]
112. ~old(X0) | ~patient(X0) [cnf transformation 33]
118. ~wise(lucy) | ~humble(X0) [cnf transformation 60]
119. ~rich(lucy) | ~humble(X0) [cnf transformation 60]
120. ~tall(X0) | generous(X0) | wise(X0) [cnf transformation 61]
128. ~generous(X0) | old(X0) | humble(X0) [cnf transformation 63]
143. ~calm(john) [cnf transformation 25]
144. kind(X0) | creative(X0) [duplicate literal removal 106]
146. ~wise(X0) | calm(X0) [duplicate literal removal 104]
162. 4 <=> ! [X1] : (creative(X1) | humble(X1)) [avatar definition]
163. humble(X1) | creative(X1) <- (4) [avatar component clause 162]
175. 7 <=> ! [X3] : (wise(X3) | tall(X3)) [avatar definition]
176. wise(X3) | tall(X3) <- (7) [avatar component clause 175]
178. 8 <=> creative(sK1) [avatar definition]
180. ~creative(sK1) <- (~8) [avatar component clause 178]
181. 7 | ~8 [avatar split clause 83,178,175]
183. 9 <=> humble(sK1) [avatar definition]
185. ~humble(sK1) <- (~9) [avatar component clause 183]
186. 7 | ~9 [avatar split clause 82,183,175]
192. 11 <=> tall(lucy) [avatar definition]
194. ~tall(lucy) <- (~11) [avatar component clause 192]
196. 12 <=> rich(lucy) [avatar definition]
201. 13 <=> tall(john) [avatar definition]
202. tall(john) <- (13) [avatar component clause 201]
204. ~13 | ~11 | 12 [avatar split clause 88,196,192,201]
248. 23 <=> ! [X0] : ~humble(X0) [avatar definition]
249. ~humble(X0) <- (23) [avatar component clause 248]
250. 23 | ~12 [avatar split clause 119,196,248]
252. 24 <=> wise(lucy) [avatar definition]
254. ~wise(lucy) <- (~24) [avatar component clause 252]
255. 23 | ~24 [avatar split clause 118,252,248]
311. ~brave(X0) | humble(X0) | creative(X0) [resolution 96,144]
313. ~brave(X0) | creative(X0) <- (23) [subsumption resolution 311,249]
368. 41 <=> wise(john) [avatar definition]
369. ~wise(john) <- (~41) [avatar component clause 368]
370. wise(john) <- (41) [avatar component clause 368]
372. 42 <=> generous(john) [avatar definition]
374. generous(john) <- (42) [avatar component clause 372]
377. generous(john) | wise(john) <- (13) [resolution 202,120]
412. calm(john) <- (41) [resolution 370,146]
415. $false <- (41) [subsumption resolution 412,143]
416. ~41 [avatar contradiction clause 415]
417. 41 | 42 | ~13 [avatar split clause 377,201,372,368]
418. old(X0) | humble(X0) | creative(X0) [resolution 128,77]
419. old(X0) | creative(X0) <- (23) [subsumption resolution 418,249]
422. ~creative(john) <- (42) [resolution 374,76]
473. ~patient(X3) | creative(X3) <- (23) [resolution 419,112]
501. creative(X0) | brave(X0) <- (23) [resolution 473,80]
503. creative(X0) <- (23) [subsumption resolution 501,313]
514. $false <- (23, 42) [resolution 503,422]
515. ~23 | ~42 [avatar contradiction clause 514]
530. tall(john) <- (7, ~41) [resolution 176,369]
542. 13 | ~7 | 41 [avatar split clause 530,368,175,201]
586. tall(lucy) <- (7, ~24) [resolution 254,176]
588. $false <- (7, ~11, ~24) [subsumption resolution 586,194]
589. ~7 | 11 | 24 [avatar contradiction clause 588]
605. creative(sK1) <- (4, ~9) [resolution 163,185]
609. $false <- (4, ~8, ~9) [subsumption resolution 605,180]
610. ~4 | 8 | 9 [avatar contradiction clause 609]
670. ~patient(X3) | creative(X3) | humble(X3) [resolution 418,112]
713. creative(X0) | humble(X0) | brave(X0) [resolution 670,80]
724. creative(X0) | humble(X0) [subsumption resolution 713,311]
725. 4 [avatar split clause 724,162]
726. $false [avatar sat refutation 181,186,204,250,255,416,417,515,542,589,610,725]
% SZS output end Proof for 391377121105313574250614
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not tall or kind then someone is not patient or kind and vice versa.
Everyone who is both not quiet and not wise is happy or not funny.
Everyone who is either generous or not curious is humble or creative and vice versa.
Everyone who is patient or not happy is old or tall and vice versa.
Everyone who is not humble is either not old or not humble and vice versa.
Everyone who is both not old and not funny is both not kind and curious.
If lucy is happy or patient then someone is both not generous and not patient and vice versa.
Everyone who is not happy or tall is both not happy and brave.
If someone is not humble or tall then someone is not wise or creative and vice versa.
Everyone who is both brave and old is not generous or not creative and vice versa.
Everyone who is both wise and not happy is brave and vice versa.
If lucy is wise or funny then alice is wise.
If paul is humble then paul is not tall or not kind.
Everyone who is both not brave and funny is both not curious and not calm and vice versa.
Everyone who is either not curious or not happy is either generous or wise.
Everyone who is tall is humble and vice versa.
Mary is not quiet.
Mary is not happy.
Someone is creative or not brave.
Someone is not funny or not old.
Someone is not funny or not tall.
Someone is both happy and generous.
Susan is strong.
Alice is brave. | Lucy is old. | entailment | ((?[X]:((~tall(X)|kind(X))))<=>(?[X]:((~patient(X)|kind(X)))))&
(![X]:((~quiet(X)&~wise(X))=>(happy(X)|~funny(X))))&
(![X]:((generous(X)<~>~curious(X))<=>(humble(X)|creative(X))))&
(![X]:((patient(X)|~happy(X))<=>(old(X)|tall(X))))&
(![X]:(~humble(X)<=>(~old(X)<~>~humble(X))))&
(![X]:((~old(X)&~funny(X))=>(~kind(X)&curious(X))))&
(((happy(lucy)|patient(lucy)))<=>(?[X]:((~generous(X)&~patient(X)))))&
(![X]:((~happy(X)|tall(X))=>(~happy(X)&brave(X))))&
((?[X]:((~humble(X)|tall(X))))<=>(?[X]:((~wise(X)|creative(X)))))&
(![X]:((brave(X)&old(X))<=>(~generous(X)|~creative(X))))&
(![X]:((wise(X)&~happy(X))<=>brave(X)))&
(((wise(lucy)|funny(lucy)))=>(wise(alice)))&
((humble(paul))=>((~tall(paul)|~kind(paul))))&
(![X]:((~brave(X)&funny(X))<=>(~curious(X)&~calm(X))))&
(![X]:((~curious(X)<~>~happy(X))=>(generous(X)<~>wise(X))))&
(![X]:(tall(X)<=>humble(X)))&
(~quiet(mary))&
(~happy(mary))&
(?[X]:((creative(X)|~brave(X))))&
(?[X]:((~funny(X)|~old(X))))&
(?[X]:((~funny(X)|~tall(X))))&
(?[X]:((happy(X)&generous(X))))&
(strong(susan))&
(brave(alice)) | old(lucy) | [
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 1720086283786611914280170
% SZS output start Proof for 1720086283786611914280170
5. ! [X0] : (~humble(X0) <=> (~old(X0) <~> ~humble(X0))) [input p4]
25. ~old(lucy) [input hypothesis]
47. ! [X0] : ((~humble(X0) | ((~old(X0) | humble(X0)) & (~humble(X0) | old(X0)))) & (((humble(X0) | old(X0)) & (~humble(X0) | ~old(X0))) | humble(X0))) [nnf transformation 5]
90. humble(X0) | old(X0) | humble(X0) [cnf transformation 47]
91. ~humble(X0) | ~humble(X0) | old(X0) [cnf transformation 47]
137. ~old(lucy) [cnf transformation 25]
138. humble(X0) | old(X0) [duplicate literal removal 90]
139. ~humble(X0) | old(X0) [duplicate literal removal 91]
169. old(X0) [subsumption resolution 138,139]
265. $false [subsumption resolution 137,169]
% SZS output end Proof for 1720086283786611914280170
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not generous or humble then someone is either not quiet or old.
If susan is funny or happy then someone is not curious or calm.
Everyone who is both calm and not kind is not creative and vice versa.
If someone is both creative and not funny then someone is funny or not curious.
If someone is both happy and tall then alice is calm.
Everyone who is both not strong and rich is both not strong and not funny and vice versa.
If susan is either tall or not quiet then someone is either brave or not creative.
If someone is both tall and not calm then john is not rich or not strong and vice versa.
Everyone who is generous or brave is both not humble and patient.
If susan is not generous then paul is wise.
Everyone who is not quiet or old is both brave and not patient.
If susan is either kind or calm then fred is either not patient or rich and vice versa.
If john is not creative or brave then alice is creative.
If susan is not curious then someone is not rich.
Everyone who is tall is not quiet and vice versa.
Alice is both rich and wise.
Alice is either patient or curious.
Someone is not funny or humble.
Someone is either not brave or not rich.
John is either not curious or creative.
Mary is either not curious or brave.
Mary is either strong or not creative. | Fred is generous. | entailment | ((?[X]:((~generous(X)|humble(X))))=>(?[X]:((~quiet(X)<~>old(X)))))&
(((funny(susan)|happy(susan)))=>(?[X]:((~curious(X)|calm(X)))))&
(![X]:((calm(X)&~kind(X))<=>~creative(X)))&
((?[X]:((creative(X)&~funny(X))))=>(?[X]:((funny(X)|~curious(X)))))&
((?[X]:((happy(X)&tall(X))))=>(calm(alice)))&
(![X]:((~strong(X)&rich(X))<=>(~strong(X)&~funny(X))))&
(((tall(susan)<~>~quiet(susan)))=>(?[X]:((brave(X)<~>~creative(X)))))&
((?[X]:((tall(X)&~calm(X))))<=>((~rich(john)|~strong(john))))&
(![X]:((generous(X)|brave(X))=>(~humble(X)&patient(X))))&
((~generous(susan))=>(wise(paul)))&
(![X]:((~quiet(X)|old(X))=>(brave(X)&~patient(X))))&
(((kind(susan)<~>calm(susan)))<=>((~patient(fred)<~>rich(fred))))&
(((~creative(john)|brave(john)))=>(creative(alice)))&
((~curious(susan))=>(?[X]:(~rich(X))))&
(![X]:(tall(X)<=>~quiet(X)))&
((rich(alice)&wise(alice)))&
((patient(alice)<~>curious(alice)))&
(?[X]:((~funny(X)|humble(X))))&
(?[X]:((~brave(X)<~>~rich(X))))&
((~curious(john)<~>creative(john)))&
((~curious(mary)<~>brave(mary)))&
((strong(mary)<~>~creative(mary))) | generous(fred) | [
"p0",
"p8",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 8091400908393591152430035
% SZS output start Proof for 8091400908393591152430035
1. ? [X0] : (humble(X0) | ~generous(X0)) => ? [X0] : (~quiet(X0) <~> old(X0)) [input p0]
9. ! [X0] : ((brave(X0) | generous(X0)) => (patient(X0) & ~humble(X0))) [input p8]
11. ! [X0] : ((old(X0) | ~quiet(X0)) => (~patient(X0) & brave(X0))) [input p10]
23. ~generous(fred) [input hypothesis]
24. ? [X0] : (humble(X0) | ~generous(X0)) => ? [X1] : (~quiet(X1) <~> old(X1)) [rectify 1]
30. ? [X1] : (~quiet(X1) <~> old(X1)) | ! [X0] : (~humble(X0) & generous(X0)) [ennf transformation 24]
34. ! [X0] : ((patient(X0) & ~humble(X0)) | (~brave(X0) & ~generous(X0))) [ennf transformation 9]
35. ! [X0] : ((~patient(X0) & brave(X0)) | (~old(X0) & quiet(X0))) [ennf transformation 11]
38. ? [X1] : ((~old(X1) | quiet(X1)) & (old(X1) | ~quiet(X1))) | ! [X0] : (~humble(X0) & generous(X0)) [nnf transformation 30]
39. ? [X0] : ((~old(X0) | quiet(X0)) & (old(X0) | ~quiet(X0))) | ! [X1] : (~humble(X1) & generous(X1)) [rectify 38]
40. ? [X0] : ((~old(X0) | quiet(X0)) & (old(X0) | ~quiet(X0))) => ((~old(sK0) | quiet(sK0)) & (old(sK0) | ~quiet(sK0))) [choice axiom]
41. ((~old(sK0) | quiet(sK0)) & (old(sK0) | ~quiet(sK0))) | ! [X1] : (~humble(X1) & generous(X1)) [skolemisation 39,40]
72. old(sK0) | ~quiet(sK0) | generous(X1) [cnf transformation 41]
97. ~brave(X0) | patient(X0) [cnf transformation 34]
98. brave(X0) | quiet(X0) [cnf transformation 35]
99. ~old(X0) | brave(X0) [cnf transformation 35]
100. ~patient(X0) | quiet(X0) [cnf transformation 35]
101. ~patient(X0) | ~old(X0) [cnf transformation 35]
127. ~generous(fred) [cnf transformation 23]
132. 2 <=> quiet(sK0) [avatar definition]
133. ~quiet(sK0) <- (~2) [avatar component clause 132]
136. 3 <=> old(sK0) [avatar definition]
137. old(sK0) <- (3) [avatar component clause 136]
141. 4 <=> ! [X1] : generous(X1) [avatar definition]
142. generous(X1) <- (4) [avatar component clause 141]
145. 4 | ~2 | 3 [avatar split clause 72,136,132,141]
324. quiet(X0) | patient(X0) [resolution 98,97]
326. quiet(X0) [subsumption resolution 324,100]
329. $false <- (~2) [resolution 326,133]
330. 2 [avatar contradiction clause 329]
331. brave(sK0) <- (3) [resolution 137,99]
332. patient(sK0) <- (3) [resolution 331,97]
341. ~old(sK0) <- (3) [resolution 332,101]
343. $false <- (3) [subsumption resolution 341,137]
344. ~3 [avatar contradiction clause 343]
345. $false <- (4) [resolution 142,127]
347. ~4 [avatar contradiction clause 345]
348. $false [avatar sat refutation 145,330,344,347]
% SZS output end Proof for 8091400908393591152430035
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave and not generous is either rich or not patient and vice versa. Everyone who is both not wise and kind is not humble. Everyone who is happy is patient or not happy. If alice is brave or not tall then someone is quiet. If lucy is both not quiet and creative then fred is tall and vice versa. If someone is not old or not funny then paul is calm and vice versa. Everyone who is not humble is rich or not calm and vice versa. Everyone who is either not rich or not generous is not wise and vice versa. If lucy is either not calm or not patient then john is not wise. Everyone who is not patient is not wise and vice versa. Everyone who is either not creative or not quiet is both not patient and rich. If alice is not quiet then someone is either not happy or generous. Everyone who is either quiet or patient is creative or not old and vice versa. Everyone who is both tall and not rich is not creative and vice versa. If someone is both not rich and strong then paul is creative and vice versa. Everyone who is not brave or strong is not calm and vice versa. John is not happy. Mary is not strong or not quiet. Someone is not generous. Someone is not quiet or not kind. John is either happy or wise. Mary is calm. Mary is either curious or strong. | Fred is not tall. | entailment | (![X]:((~brave(X)&~generous(X))<=>(rich(X)<~>~patient(X))))&
(![X]:((~wise(X)&kind(X))=>~humble(X)))&
(![X]:(happy(X)=>(patient(X)|~happy(X))))&
(((brave(alice)|~tall(alice)))=>(?[X]:(quiet(X))))&
(((~quiet(lucy)&creative(lucy)))<=>(tall(fred)))&
((?[X]:((~old(X)|~funny(X))))<=>(calm(paul)))&
(![X]:(~humble(X)<=>(rich(X)|~calm(X))))&
(![X]:((~rich(X)<~>~generous(X))<=>~wise(X)))&
(((~calm(lucy)<~>~patient(lucy)))=>(~wise(john)))&
(![X]:(~patient(X)<=>~wise(X)))&
(![X]:((~creative(X)<~>~quiet(X))=>(~patient(X)&rich(X))))&
((~quiet(alice))=>(?[X]:((~happy(X)<~>generous(X)))))&
(![X]:((quiet(X)<~>patient(X))<=>(creative(X)|~old(X))))&
(![X]:((tall(X)&~rich(X))<=>~creative(X)))&
((?[X]:((~rich(X)&strong(X))))<=>(creative(paul)))&
(![X]:((~brave(X)|strong(X))<=>~calm(X)))&
(~happy(john))&
((~strong(mary)|~quiet(mary)))&
(?[X]:(~generous(X)))&
(?[X]:((~quiet(X)|~kind(X))))&
((happy(john)<~>wise(john)))&
(calm(mary))&
((curious(mary)<~>strong(mary))) | ~tall(fred) | [
"p4",
"p10",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 807185698333863359654568
% SZS output start Proof for 807185698333863359654568
5. (creative(lucy) & ~quiet(lucy)) <=> tall(fred) [input p4]
11. ! [X0] : ((~creative(X0) <~> ~quiet(X0)) => (rich(X0) & ~patient(X0))) [input p10]
13. ! [X0] : ((quiet(X0) <~> patient(X0)) <=> (~old(X0) | creative(X0))) [input p12]
24. tall(fred) [input hypothesis]
33. ! [X0] : ((rich(X0) & ~patient(X0)) | (~creative(X0) <=> ~quiet(X0))) [ennf transformation 11]
39. ((creative(lucy) & ~quiet(lucy)) | ~tall(fred)) & (tall(fred) | (~creative(lucy) | quiet(lucy))) [nnf transformation 5]
40. ((creative(lucy) & ~quiet(lucy)) | ~tall(fred)) & (tall(fred) | ~creative(lucy) | quiet(lucy)) [flattening 39]
48. ! [X0] : ((rich(X0) & ~patient(X0)) | ((~creative(X0) | quiet(X0)) & (~quiet(X0) | creative(X0)))) [nnf transformation 33]
52. ! [X0] : ((((~patient(X0) | ~quiet(X0)) & (patient(X0) | quiet(X0))) | (old(X0) & ~creative(X0))) & ((~old(X0) | creative(X0)) | ((quiet(X0) | ~patient(X0)) & (patient(X0) | ~quiet(X0))))) [nnf transformation 13]
53. ! [X0] : ((((~patient(X0) | ~quiet(X0)) & (patient(X0) | quiet(X0))) | (old(X0) & ~creative(X0))) & (~old(X0) | creative(X0) | ((quiet(X0) | ~patient(X0)) & (patient(X0) | ~quiet(X0))))) [flattening 52]
76. ~quiet(lucy) | ~tall(fred) [cnf transformation 40]
77. creative(lucy) | ~tall(fred) [cnf transformation 40]
90. ~patient(X0) | ~creative(X0) | quiet(X0) [cnf transformation 48]
97. patient(X0) | quiet(X0) | ~creative(X0) [cnf transformation 53]
118. tall(fred) [cnf transformation 24]
135. 4 <=> tall(fred) [avatar definition]
139. 5 <=> creative(lucy) [avatar definition]
141. creative(lucy) <- (5) [avatar component clause 139]
142. ~4 | 5 [avatar split clause 77,139,135]
144. 6 <=> quiet(lucy) [avatar definition]
146. ~quiet(lucy) <- (~6) [avatar component clause 144]
147. ~4 | ~6 [avatar split clause 76,144,135]
199. ~creative(X0) | quiet(X0) [subsumption resolution 97,90]
237. 4 [avatar split clause 118,135]
249. quiet(lucy) <- (5) [resolution 199,141]
252. $false <- (5, ~6) [subsumption resolution 249,146]
253. ~5 | 6 [avatar contradiction clause 252]
254. $false [avatar sat refutation 142,147,237,253]
% SZS output end Proof for 807185698333863359654568
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave and strong then someone is not brave or patient. If someone is not brave then someone is not tall or calm. Everyone who is either not humble or calm is not happy or not kind and vice versa. If someone is wise then susan is both rich and quiet. Everyone who is not rich or not quiet is not calm or not brave and vice versa. Everyone who is not calm is not old or not happy and vice versa. Everyone who is both strong and humble is old or not brave and vice versa. If someone is both not quiet and not curious then someone is not curious. If mary is tall or calm then fred is either tall or not quiet and vice versa. If someone is kind then someone is both not humble and not brave and vice versa. Everyone who is not generous is either strong or not kind. If fred is either kind or rich then lucy is not happy and vice versa. Everyone who is kind is either not strong or generous and vice versa. Everyone who is not patient is not curious or quiet and vice versa. If fred is both wise and funny then fred is both not curious and not kind and vice versa. If mary is not brave or not quiet then lucy is wise or curious and vice versa. Someone is either not wise or calm. John is both not old and rich. Alice is not funny or not generous. Mary is either funny or calm. Paul is either old or not funny. Someone is either creative or not wise. | John is not funny. | neutral | ((?[X]:((brave(X)&strong(X))))=>(?[X]:((~brave(X)|patient(X)))))&
((?[X]:(~brave(X)))=>(?[X]:((~tall(X)|calm(X)))))&
(![X]:((~humble(X)<~>calm(X))<=>(~happy(X)|~kind(X))))&
((?[X]:(wise(X)))=>((rich(susan)&quiet(susan))))&
(![X]:((~rich(X)|~quiet(X))<=>(~calm(X)|~brave(X))))&
(![X]:(~calm(X)<=>(~old(X)|~happy(X))))&
(![X]:((strong(X)&humble(X))<=>(old(X)|~brave(X))))&
((?[X]:((~quiet(X)&~curious(X))))=>(?[X]:(~curious(X))))&
(((tall(mary)|calm(mary)))<=>((tall(fred)<~>~quiet(fred))))&
((?[X]:(kind(X)))<=>(?[X]:((~humble(X)&~brave(X)))))&
(![X]:(~generous(X)=>(strong(X)<~>~kind(X))))&
(((kind(fred)<~>rich(fred)))<=>(~happy(lucy)))&
(![X]:(kind(X)<=>(~strong(X)<~>generous(X))))&
(![X]:(~patient(X)<=>(~curious(X)|quiet(X))))&
(((wise(fred)&funny(fred)))<=>((~curious(fred)&~kind(fred))))&
(((~brave(mary)|~quiet(mary)))<=>((wise(lucy)|curious(lucy))))&
(?[X]:((~wise(X)<~>calm(X))))&
((~old(john)&rich(john)))&
((~funny(alice)|~generous(alice)))&
((funny(mary)<~>calm(mary)))&
((old(paul)<~>~funny(paul)))&
(?[X]:((creative(X)<~>~wise(X)))) | ~funny(john) | [] | null | 0 |
If someone is calm or not strong then susan is both generous and patient.
If someone is either tall or strong then mary is funny.
If someone is not calm or tall then someone is funny or curious.
Everyone who is strong is both not funny and not tall and vice versa.
Everyone who is not happy or not kind is both rich and brave and vice versa.
If someone is quiet or humble then mary is both not old and not funny and vice versa.
Everyone who is old or not rich is not strong or not creative.
If mary is both patient and quiet then susan is either curious or funny.
If paul is either old or not happy then someone is both not creative and calm and vice versa.
If john is both generous and not generous then someone is not humble or calm.
If someone is humble or not creative then john is both wise and not rich.
Everyone who is not tall or not quiet is either not kind or not wise and vice versa.
Everyone who is rich is both happy and creative and vice versa.
If alice is not kind then someone is strong or not strong.
If someone is both creative and calm then someone is not generous or not strong and vice versa.
If fred is both not calm and not old then someone is not rich.
Someone is either creative or not brave.
Susan is either wise or calm.
Someone is old or wise.
Alice is not curious or funny.
Someone is both brave and creative.
Fred is either strong or brave. | Alice is creative. | entailment | ((?[X]:((calm(X)|~strong(X))))=>((generous(susan)&patient(susan))))&
((?[X]:((tall(X)<~>strong(X))))=>(funny(mary)))&
((?[X]:((~calm(X)|tall(X))))=>(?[X]:((funny(X)|curious(X)))))&
(![X]:(strong(X)<=>(~funny(X)&~tall(X))))&
(![X]:((~happy(X)|~kind(X))<=>(rich(X)&brave(X))))&
((?[X]:((quiet(X)|humble(X))))<=>((~old(mary)&~funny(mary))))&
(![X]:((old(X)|~rich(X))=>(~strong(X)|~creative(X))))&
(((patient(mary)&quiet(mary)))=>((curious(susan)<~>funny(susan))))&
(((old(paul)<~>~happy(paul)))<=>(?[X]:((~creative(X)&calm(X)))))&
(((generous(john)&~generous(john)))=>(?[X]:((~humble(X)|calm(X)))))&
((?[X]:((humble(X)|~creative(X))))=>((wise(john)&~rich(john))))&
(![X]:((~tall(X)|~quiet(X))<=>(~kind(X)<~>~wise(X))))&
(![X]:(rich(X)<=>(happy(X)&creative(X))))&
((~kind(alice))=>(?[X]:((strong(X)|~strong(X)))))&
((?[X]:((creative(X)&calm(X))))<=>(?[X]:((~generous(X)|~strong(X)))))&
(((~calm(fred)&~old(fred)))=>(?[X]:(~rich(X))))&
(?[X]:((creative(X)<~>~brave(X))))&
((wise(susan)<~>calm(susan)))&
(?[X]:((old(X)|wise(X))))&
((~curious(alice)|funny(alice)))&
(?[X]:((brave(X)&creative(X))))&
((strong(fred)<~>brave(fred))) | creative(alice) | [
"p1",
"p3",
"p4",
"p5",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 101090541577670721151279
% SZS output start Proof for 101090541577670721151279
2. ? [X0] : (tall(X0) <~> strong(X0)) => funny(mary) [input p1]
4. ! [X0] : (strong(X0) <=> (~tall(X0) & ~funny(X0))) [input p3]
5. ! [X0] : ((~kind(X0) | ~happy(X0)) <=> (brave(X0) & rich(X0))) [input p4]
6. ? [X0] : (humble(X0) | quiet(X0)) <=> (~funny(mary) & ~old(mary)) [input p5]
11. ? [X0] : (~creative(X0) | humble(X0)) => (~rich(john) & wise(john)) [input p10]
12. ! [X0] : ((~quiet(X0) | ~tall(X0)) <=> (~kind(X0) <~> ~wise(X0))) [input p11]
23. ~creative(alice) [input hypothesis]
27. funny(mary) | ! [X0] : (tall(X0) <=> strong(X0)) [ennf transformation 2]
35. (~rich(john) & wise(john)) | ! [X0] : (creative(X0) & ~humble(X0)) [ennf transformation 11]
39. funny(mary) | ! [X0] : ((tall(X0) | ~strong(X0)) & (strong(X0) | ~tall(X0))) [nnf transformation 27]
43. ! [X0] : ((strong(X0) | (tall(X0) | funny(X0))) & ((~tall(X0) & ~funny(X0)) | ~strong(X0))) [nnf transformation 4]
44. ! [X0] : ((strong(X0) | tall(X0) | funny(X0)) & ((~tall(X0) & ~funny(X0)) | ~strong(X0))) [flattening 43]
45. ! [X0] : (((~kind(X0) | ~happy(X0)) | (~brave(X0) | ~rich(X0))) & ((brave(X0) & rich(X0)) | (kind(X0) & happy(X0)))) [nnf transformation 5]
46. ! [X0] : ((~kind(X0) | ~happy(X0) | ~brave(X0) | ~rich(X0)) & ((brave(X0) & rich(X0)) | (kind(X0) & happy(X0)))) [flattening 45]
47. (? [X0] : (humble(X0) | quiet(X0)) | (funny(mary) | old(mary))) & ((~funny(mary) & ~old(mary)) | ! [X0] : (~humble(X0) & ~quiet(X0))) [nnf transformation 6]
48. (? [X0] : (humble(X0) | quiet(X0)) | funny(mary) | old(mary)) & ((~funny(mary) & ~old(mary)) | ! [X0] : (~humble(X0) & ~quiet(X0))) [flattening 47]
49. (? [X0] : (humble(X0) | quiet(X0)) | funny(mary) | old(mary)) & ((~funny(mary) & ~old(mary)) | ! [X1] : (~humble(X1) & ~quiet(X1))) [rectify 48]
50. ? [X0] : (humble(X0) | quiet(X0)) => (humble(sK1) | quiet(sK1)) [choice axiom]
51. ((humble(sK1) | quiet(sK1)) | funny(mary) | old(mary)) & ((~funny(mary) & ~old(mary)) | ! [X1] : (~humble(X1) & ~quiet(X1))) [skolemisation 49,50]
59. ! [X0] : (((~quiet(X0) | ~tall(X0)) | ((~kind(X0) | wise(X0)) & (~wise(X0) | kind(X0)))) & (((wise(X0) | kind(X0)) & (~wise(X0) | ~kind(X0))) | (quiet(X0) & tall(X0)))) [nnf transformation 12]
60. ! [X0] : ((~quiet(X0) | ~tall(X0) | ((~kind(X0) | wise(X0)) & (~wise(X0) | kind(X0)))) & (((wise(X0) | kind(X0)) & (~wise(X0) | ~kind(X0))) | (quiet(X0) & tall(X0)))) [flattening 59]
85. funny(mary) | strong(X0) | ~tall(X0) [cnf transformation 39]
90. ~tall(X0) | ~strong(X0) [cnf transformation 44]
93. rich(X0) | kind(X0) [cnf transformation 46]
99. ~funny(mary) | ~quiet(X1) [cnf transformation 51]
114. wise(john) | creative(X0) [cnf transformation 35]
116. ~rich(john) | creative(X0) [cnf transformation 35]
117. ~wise(X0) | ~kind(X0) | tall(X0) [cnf transformation 60]
118. ~wise(X0) | ~kind(X0) | quiet(X0) [cnf transformation 60]
143. ~creative(alice) [cnf transformation 23]
166. 6 <=> funny(mary) [avatar definition]
171. 7 <=> ! [X0] : (strong(X0) | ~tall(X0)) [avatar definition]
172. strong(X0) | ~tall(X0) <- (7) [avatar component clause 171]
173. 7 | 6 [avatar split clause 85,166,171]
175. 8 <=> ! [X1] : ~tall(X1) [avatar definition]
176. ~tall(X1) <- (8) [avatar component clause 175]
208. 16 <=> ! [X1] : ~quiet(X1) [avatar definition]
209. ~quiet(X1) <- (16) [avatar component clause 208]
210. 16 | ~6 [avatar split clause 99,166,208]
257. 26 <=> ! [X0] : creative(X0) [avatar definition]
258. creative(X0) <- (26) [avatar component clause 257]
260. 27 <=> rich(john) [avatar definition]
262. ~rich(john) <- (~27) [avatar component clause 260]
263. 26 | ~27 [avatar split clause 116,260,257]
266. 28 <=> wise(john) [avatar definition]
268. wise(john) <- (28) [avatar component clause 266]
269. 26 | 28 [avatar split clause 114,266,257]
363. ~tall(X0) <- (7) [subsumption resolution 172,90]
364. 8 | ~7 [avatar split clause 363,171,175]
366. $false <- (26) [resolution 258,143]
367. ~26 [avatar contradiction clause 366]
376. kind(john) <- (~27) [resolution 93,262]
412. ~kind(john) | tall(john) <- (28) [resolution 117,268]
414. tall(john) <- (~27, 28) [subsumption resolution 412,376]
415. $false <- (8, ~27, 28) [subsumption resolution 414,176]
416. ~8 | 27 | ~28 [avatar contradiction clause 415]
427. ~kind(john) | quiet(john) <- (28) [resolution 118,268]
429. quiet(john) <- (~27, 28) [subsumption resolution 427,376]
430. $false <- (16, ~27, 28) [subsumption resolution 429,209]
431. ~16 | 27 | ~28 [avatar contradiction clause 430]
432. $false [avatar sat refutation 173,210,263,269,364,367,416,431]
% SZS output end Proof for 101090541577670721151279
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not curious or generous is wise and vice versa.
Everyone who is either not wise or not strong is not creative or rich.
Everyone who is generous or not calm is either patient or not humble and vice versa.
If lucy is either not happy or calm then someone is either curious or not curious and vice versa.
If alice is happy then someone is wise or not happy and vice versa.
If susan is not creative then someone is not calm or not humble and vice versa.
Everyone who is either strong or not funny is old and vice versa.
If someone is not quiet or humble then john is both not kind and rich.
If someone is both not generous and curious then mary is curious or quiet and vice versa.
If mary is funny then lucy is both funny and not patient.
If someone is old or rich then fred is both generous and not calm.
If susan is tall then lucy is not brave.
Everyone who is curious or not rich is wise.
Everyone who is brave or not brave is not funny or not wise.
Everyone who is wise is not humble.
Everyone who is both strong and not generous is not humble or wise and vice versa.
Someone is not brave or patient.
Susan is not generous.
John is both not generous and patient.
Susan is not brave. | Susan is not tall. | neutral | (![X]:((~curious(X)<~>generous(X))<=>wise(X)))&
(![X]:((~wise(X)<~>~strong(X))=>(~creative(X)|rich(X))))&
(![X]:((generous(X)|~calm(X))<=>(patient(X)<~>~humble(X))))&
(((~happy(lucy)<~>calm(lucy)))<=>(?[X]:((curious(X)<~>~curious(X)))))&
((happy(alice))<=>(?[X]:((wise(X)|~happy(X)))))&
((~creative(susan))<=>(?[X]:((~calm(X)|~humble(X)))))&
(![X]:((strong(X)<~>~funny(X))<=>old(X)))&
((?[X]:((~quiet(X)|humble(X))))=>((~kind(john)&rich(john))))&
((?[X]:((~generous(X)&curious(X))))<=>((curious(mary)|quiet(mary))))&
((funny(mary))=>((funny(lucy)&~patient(lucy))))&
((?[X]:((old(X)|rich(X))))=>((generous(fred)&~calm(fred))))&
((tall(susan))=>(~brave(lucy)))&
(![X]:((curious(X)|~rich(X))=>wise(X)))&
(![X]:((brave(X)|~brave(X))=>(~funny(X)|~wise(X))))&
(![X]:(wise(X)=>~humble(X)))&
(![X]:((strong(X)&~generous(X))<=>(~humble(X)|wise(X))))&
(?[X]:((~brave(X)|patient(X))))&
(~generous(susan))&
((~generous(john)&patient(john)))&
(~brave(susan)) | ~tall(susan) | [] | null | 0 |
Everyone who is not wise or not kind is not creative.
Everyone who is either not wise or not patient is either wise or not quiet and vice versa.
If someone is both not tall and brave then mary is kind or brave and vice versa.
If lucy is not funny then john is both creative and not quiet and vice versa.
If paul is both not humble and happy then paul is both creative and not patient and vice versa.
If fred is both wise and not rich then paul is both not generous and wise and vice versa.
Everyone who is both quiet and not old is both not old and humble and vice versa.
Everyone who is both not generous and not patient is not quiet.
Everyone who is either curious or old is either humble or not quiet and vice versa.
Everyone who is not happy or not quiet is both rich and old.
If someone is either calm or rich then someone is both wise and not creative and vice versa.
If someone is curious then john is quiet and vice versa.
Everyone who is both not quiet and not kind is generous and vice versa.
If someone is both not patient and not wise then alice is both not creative and wise.
If someone is not humble or not wise then someone is both not curious and patient and vice versa.
If paul is both not wise and not funny then paul is wise or brave.
Someone is kind or patient.
Someone is not brave or generous.
Someone is not generous.
Someone is not rich or kind.
Someone is both not quiet and strong. | Lucy is not humble. | entailment | (![X]:((~wise(X)|~kind(X))=>~creative(X)))&
(![X]:((~wise(X)<~>~patient(X))<=>(wise(X)<~>~quiet(X))))&
((?[X]:((~tall(X)&brave(X))))<=>((kind(mary)|brave(mary))))&
((~funny(lucy))<=>((creative(john)&~quiet(john))))&
(((~humble(paul)&happy(paul)))<=>((creative(paul)&~patient(paul))))&
(((wise(fred)&~rich(fred)))<=>((~generous(paul)&wise(paul))))&
(![X]:((quiet(X)&~old(X))<=>(~old(X)&humble(X))))&
(![X]:((~generous(X)&~patient(X))=>~quiet(X)))&
(![X]:((curious(X)<~>old(X))<=>(humble(X)<~>~quiet(X))))&
(![X]:((~happy(X)|~quiet(X))=>(rich(X)&old(X))))&
((?[X]:((calm(X)<~>rich(X))))<=>(?[X]:((wise(X)&~creative(X)))))&
((?[X]:(curious(X)))<=>(quiet(john)))&
(![X]:((~quiet(X)&~kind(X))<=>generous(X)))&
((?[X]:((~patient(X)&~wise(X))))=>((~creative(alice)&wise(alice))))&
((?[X]:((~humble(X)|~wise(X))))<=>(?[X]:((~curious(X)&patient(X)))))&
(((~wise(paul)&~funny(paul)))=>((wise(paul)|brave(paul))))&
(?[X]:((kind(X)|patient(X))))&
(?[X]:((~brave(X)|generous(X))))&
(?[X]:(~generous(X)))&
(?[X]:((~rich(X)|kind(X))))&
(?[X]:((~quiet(X)&strong(X)))) | ~humble(lucy) | [
"p1",
"p6",
"p7",
"p8",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 7677316287768397682197706
% SZS output start Proof for 7677316287768397682197706
2. ! [X0] : ((~wise(X0) <~> ~patient(X0)) <=> (wise(X0) <~> ~quiet(X0))) [input p1]
7. ! [X0] : ((~old(X0) & quiet(X0)) <=> (humble(X0) & ~old(X0))) [input p6]
8. ! [X0] : ((~patient(X0) & ~generous(X0)) => ~quiet(X0)) [input p7]
9. ! [X0] : ((curious(X0) <~> old(X0)) <=> (humble(X0) <~> ~quiet(X0))) [input p8]
12. ? [X0] : curious(X0) <=> quiet(john) [input p11]
13. ! [X0] : ((~kind(X0) & ~quiet(X0)) <=> generous(X0)) [input p12]
22. humble(lucy) [input hypothesis]
27. ! [X0] : (~quiet(X0) | (patient(X0) | generous(X0))) [ennf transformation 8]
28. ! [X0] : (~quiet(X0) | patient(X0) | generous(X0)) [flattening 27]
33. ! [X0] : ((((patient(X0) | wise(X0)) & (~patient(X0) | ~wise(X0))) | ((wise(X0) | quiet(X0)) & (~quiet(X0) | ~wise(X0)))) & (((quiet(X0) | ~wise(X0)) & (~quiet(X0) | wise(X0))) | ((~wise(X0) | patient(X0)) & (~patient(X0) | wise(X0))))) [nnf transformation 2]
45. ! [X0] : (((~old(X0) & quiet(X0)) | (~humble(X0) | old(X0))) & ((humble(X0) & ~old(X0)) | (old(X0) | ~quiet(X0)))) [nnf transformation 7]
46. ! [X0] : (((~old(X0) & quiet(X0)) | ~humble(X0) | old(X0)) & ((humble(X0) & ~old(X0)) | old(X0) | ~quiet(X0))) [flattening 45]
47. ! [X0] : ((((~old(X0) | ~curious(X0)) & (old(X0) | curious(X0))) | ((humble(X0) | quiet(X0)) & (~quiet(X0) | ~humble(X0)))) & (((quiet(X0) | ~humble(X0)) & (~quiet(X0) | humble(X0))) | ((curious(X0) | ~old(X0)) & (old(X0) | ~curious(X0))))) [nnf transformation 9]
53. (? [X0] : curious(X0) | ~quiet(john)) & (quiet(john) | ! [X0] : ~curious(X0)) [nnf transformation 12]
54. (? [X0] : curious(X0) | ~quiet(john)) & (quiet(john) | ! [X1] : ~curious(X1)) [rectify 53]
55. ? [X0] : curious(X0) => curious(sK3) [choice axiom]
56. (curious(sK3) | ~quiet(john)) & (quiet(john) | ! [X1] : ~curious(X1)) [skolemisation 54,55]
57. ! [X0] : (((~kind(X0) & ~quiet(X0)) | ~generous(X0)) & (generous(X0) | (kind(X0) | quiet(X0)))) [nnf transformation 13]
58. ! [X0] : (((~kind(X0) & ~quiet(X0)) | ~generous(X0)) & (generous(X0) | kind(X0) | quiet(X0))) [flattening 57]
76. ~quiet(X0) | wise(X0) | ~patient(X0) | wise(X0) [cnf transformation 33]
80. ~patient(X0) | ~wise(X0) | ~quiet(X0) | ~wise(X0) [cnf transformation 33]
101. ~quiet(X0) | old(X0) | humble(X0) [cnf transformation 46]
102. ~humble(X0) | quiet(X0) | old(X0) [cnf transformation 46]
104. ~quiet(X0) | patient(X0) | generous(X0) [cnf transformation 28]
108. quiet(X0) | ~humble(X0) | curious(X0) | ~old(X0) [cnf transformation 47]
109. old(X0) | curious(X0) | ~quiet(X0) | ~humble(X0) [cnf transformation 47]
110. old(X0) | curious(X0) | humble(X0) | quiet(X0) [cnf transformation 47]
123. quiet(john) | ~curious(X1) [cnf transformation 56]
126. ~quiet(X0) | ~generous(X0) [cnf transformation 58]
141. humble(lucy) [cnf transformation 22]
143. ~quiet(X0) | wise(X0) | ~patient(X0) [duplicate literal removal 76]
145. ~quiet(X0) | ~wise(X0) | ~patient(X0) [duplicate literal removal 80]
148. ~quiet(X0) | ~patient(X0) [subsumption resolution 143,145]
178. 7 <=> quiet(john) [avatar definition]
180. quiet(john) <- (7) [avatar component clause 178]
228. ~quiet(X0) | generous(X0) [subsumption resolution 104,148]
229. curious(X0) | old(X0) | humble(X0) [subsumption resolution 110,101]
230. old(X0) | curious(X0) | ~humble(X0) [subsumption resolution 109,102]
231. curious(X0) | old(X0) [subsumption resolution 230,229]
232. ~humble(X0) | quiet(X0) | curious(X0) [subsumption resolution 108,231]
271. 25 <=> ! [X1] : ~curious(X1) [avatar definition]
272. ~curious(X1) <- (25) [avatar component clause 271]
273. 25 | 7 [avatar split clause 123,178,271]
274. ~quiet(X0) [subsumption resolution 126,228]
355. $false <- (7) [subsumption resolution 180,274]
356. ~7 [avatar contradiction clause 355]
407. quiet(lucy) | curious(lucy) [resolution 232,141]
408. curious(lucy) [subsumption resolution 407,274]
409. $false <- (25) [subsumption resolution 408,272]
410. ~25 [avatar contradiction clause 409]
411. $false [avatar sat refutation 273,356,410]
% SZS output end Proof for 7677316287768397682197706
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not strong and humble then someone is both happy and rich and vice versa.
Everyone who is rich or not curious is not patient and vice versa.
Everyone who is both old and not old is both not generous and not tall.
If someone is kind then fred is not curious or rich and vice versa.
Everyone who is not tall or not rich is both not old and not calm.
Everyone who is both brave and not quiet is creative and vice versa.
Everyone who is either not creative or funny is not funny or not rich.
Everyone who is not wise is wise.
If someone is not brave then someone is calm.
If someone is brave then someone is rich or not wise and vice versa.
Everyone who is both calm and not quiet is both old and not tall.
If fred is both not funny and not patient then mary is either funny or wise.
Everyone who is not rich is not funny or not strong.
If someone is either not old or not tall then someone is not quiet or not patient and vice versa.
If someone is not curious then paul is either not tall or patient.
Someone is either happy or humble.
Someone is kind.
Susan is both not generous and not kind.
Someone is funny.
Someone is strong.
Someone is either curious or not kind. | Susan is not happy. | neutral | ((?[X]:((~strong(X)&humble(X))))<=>(?[X]:((happy(X)&rich(X)))))&
(![X]:((rich(X)|~curious(X))<=>~patient(X)))&
(![X]:((old(X)&~old(X))=>(~generous(X)&~tall(X))))&
((?[X]:(kind(X)))<=>((~curious(fred)|rich(fred))))&
(![X]:((~tall(X)|~rich(X))=>(~old(X)&~calm(X))))&
(![X]:((brave(X)&~quiet(X))<=>creative(X)))&
(![X]:((~creative(X)<~>funny(X))=>(~funny(X)|~rich(X))))&
(![X]:(~wise(X)=>wise(X)))&
((?[X]:(~brave(X)))=>(?[X]:(calm(X))))&
((?[X]:(brave(X)))<=>(?[X]:((rich(X)|~wise(X)))))&
(![X]:((calm(X)&~quiet(X))=>(old(X)&~tall(X))))&
(((~funny(fred)&~patient(fred)))=>((funny(mary)<~>wise(mary))))&
(![X]:(~rich(X)=>(~funny(X)|~strong(X))))&
((?[X]:((~old(X)<~>~tall(X))))<=>(?[X]:((~quiet(X)|~patient(X)))))&
((?[X]:(~curious(X)))=>((~tall(paul)<~>patient(paul))))&
(?[X]:((happy(X)<~>humble(X))))&
(?[X]:(kind(X)))&
((~generous(susan)&~kind(susan)))&
(?[X]:(funny(X)))&
(?[X]:(strong(X)))&
(?[X]:((curious(X)<~>~kind(X)))) | ~happy(susan) | [] | null | 0 |
Everyone who is either not funny or generous is either quiet or patient.
If lucy is both not rich and generous then lucy is both not quiet and old and vice versa.
If fred is not quiet or not strong then mary is not calm and vice versa.
If mary is either not curious or not quiet then someone is both not kind and curious and vice versa.
Everyone who is either old or brave is not tall and vice versa.
If someone is old then alice is both not happy and brave and vice versa.
Everyone who is humble or not generous is either quiet or tall and vice versa.
If someone is either not calm or not rich then paul is both not humble and rich.
Everyone who is generous or not tall is both not happy and not brave.
Everyone who is not quiet or rich is both quiet and not humble and vice versa.
Everyone who is brave or patient is either not funny or not creative.
If someone is old then lucy is happy or rich.
Everyone who is both happy and curious is strong.
If someone is rich then someone is both not brave and not kind.
Everyone who is not funny or not rich is not tall.
If lucy is not kind or strong then alice is old or not happy and vice versa.
Someone is curious or not brave.
Someone is humble or generous.
Fred is both not happy and rich.
Someone is kind or wise.
Someone is not calm or not generous. | Lucy is not happy. | entailment | (![X]:((~funny(X)<~>generous(X))=>(quiet(X)<~>patient(X))))&
(((~rich(lucy)&generous(lucy)))<=>((~quiet(lucy)&old(lucy))))&
(((~quiet(fred)|~strong(fred)))<=>(~calm(mary)))&
(((~curious(mary)<~>~quiet(mary)))<=>(?[X]:((~kind(X)&curious(X)))))&
(![X]:((old(X)<~>brave(X))<=>~tall(X)))&
((?[X]:(old(X)))<=>((~happy(alice)&brave(alice))))&
(![X]:((humble(X)|~generous(X))<=>(quiet(X)<~>tall(X))))&
((?[X]:((~calm(X)<~>~rich(X))))=>((~humble(paul)&rich(paul))))&
(![X]:((generous(X)|~tall(X))=>(~happy(X)&~brave(X))))&
(![X]:((~quiet(X)|rich(X))<=>(quiet(X)&~humble(X))))&
(![X]:((brave(X)|patient(X))=>(~funny(X)<~>~creative(X))))&
((?[X]:(old(X)))=>((happy(lucy)|rich(lucy))))&
(![X]:((happy(X)&curious(X))=>strong(X)))&
((?[X]:(rich(X)))=>(?[X]:((~brave(X)&~kind(X)))))&
(![X]:((~funny(X)|~rich(X))=>~tall(X)))&
(((~kind(lucy)|strong(lucy)))<=>((old(alice)|~happy(alice))))&
(?[X]:((curious(X)|~brave(X))))&
(?[X]:((humble(X)|generous(X))))&
((~happy(fred)&rich(fred)))&
(?[X]:((kind(X)|wise(X))))&
(?[X]:((~calm(X)|~generous(X)))) | ~happy(lucy) | [
"p6",
"p8",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 4994065227447401051707605
% SZS output start Proof for 4994065227447401051707605
7. ! [X0] : ((~generous(X0) | humble(X0)) <=> (quiet(X0) <~> tall(X0))) [input p6]
9. ! [X0] : ((~tall(X0) | generous(X0)) => (~brave(X0) & ~happy(X0))) [input p8]
10. ! [X0] : ((rich(X0) | ~quiet(X0)) <=> (~humble(X0) & quiet(X0))) [input p9]
22. happy(lucy) [input hypothesis]
27. ! [X0] : ((~brave(X0) & ~happy(X0)) | (tall(X0) & ~generous(X0))) [ennf transformation 9]
50. ! [X0] : (((~generous(X0) | humble(X0)) | ((quiet(X0) | ~tall(X0)) & (tall(X0) | ~quiet(X0)))) & (((~tall(X0) | ~quiet(X0)) & (tall(X0) | quiet(X0))) | (generous(X0) & ~humble(X0)))) [nnf transformation 7]
51. ! [X0] : ((~generous(X0) | humble(X0) | ((quiet(X0) | ~tall(X0)) & (tall(X0) | ~quiet(X0)))) & (((~tall(X0) | ~quiet(X0)) & (tall(X0) | quiet(X0))) | (generous(X0) & ~humble(X0)))) [flattening 50]
53. ! [X0] : (((rich(X0) | ~quiet(X0)) | (humble(X0) | ~quiet(X0))) & ((~humble(X0) & quiet(X0)) | (~rich(X0) & quiet(X0)))) [nnf transformation 10]
54. ! [X0] : ((rich(X0) | ~quiet(X0) | humble(X0) | ~quiet(X0)) & ((~humble(X0) & quiet(X0)) | (~rich(X0) & quiet(X0)))) [flattening 53]
94. ~tall(X0) | ~quiet(X0) | generous(X0) [cnf transformation 51]
101. ~happy(X0) | ~generous(X0) [cnf transformation 27]
102. ~happy(X0) | tall(X0) [cnf transformation 27]
105. quiet(X0) | quiet(X0) [cnf transformation 54]
129. happy(lucy) [cnf transformation 22]
130. quiet(X0) [duplicate literal removal 105]
141. 3 <=> generous(lucy) [avatar definition]
229. 21 <=> happy(lucy) [avatar definition]
231. happy(lucy) <- (21) [avatar component clause 229]
289. 21 [avatar split clause 129,229]
292. ~generous(lucy) <- (21) [resolution 101,231]
293. tall(lucy) <- (21) [resolution 102,231]
362. ~quiet(lucy) | generous(lucy) <- (21) [resolution 94,293]
367. generous(lucy) <- (21) [subsumption resolution 362,130]
374. 3 | ~21 [avatar split clause 367,229,141]
375. ~3 | ~21 [avatar split clause 292,229,141]
376. $false [avatar sat refutation 289,374,375]
% SZS output end Proof for 4994065227447401051707605
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If someone is not strong or funny then someone is both wise and strong and vice versa.
Everyone who is either rich or creative is both tall and not brave and vice versa.
Everyone who is either not happy or not old is both not calm and brave.
Everyone who is both generous and not quiet is not kind or not funny and vice versa.
Everyone who is both happy and funny is creative or not kind.
Everyone who is either not generous or calm is either rich or not creative.
If john is quiet or happy then mary is both wise and not rich.
If someone is old or brave then someone is both not generous and not funny.
Everyone who is either not brave or creative is both funny and rich and vice versa.
Everyone who is not wise or creative is not kind or strong.
If fred is either generous or not kind then alice is curious or tall and vice versa.
If someone is both happy and not brave then someone is both not happy and calm.
Everyone who is not funny or not wise is not funny.
Everyone who is creative or patient is both kind and creative and vice versa.
If alice is both tall and old then mary is both not brave and not rich and vice versa.
If paul is either tall or brave then mary is both humble and not old.
John is kind or humble.
Alice is tall or happy.
Someone is not quiet or tall.
Someone is old or tall.
Mary is not strong.
Someone is both generous and humble. | Fred is generous. | entailment | ((?[X]:((~strong(X)|funny(X))))<=>(?[X]:((wise(X)&strong(X)))))&
(![X]:((rich(X)<~>creative(X))<=>(tall(X)&~brave(X))))&
(![X]:((~happy(X)<~>~old(X))=>(~calm(X)&brave(X))))&
(![X]:((generous(X)&~quiet(X))<=>(~kind(X)|~funny(X))))&
(![X]:((happy(X)&funny(X))=>(creative(X)|~kind(X))))&
(![X]:((~generous(X)<~>calm(X))=>(rich(X)<~>~creative(X))))&
(((quiet(john)|happy(john)))=>((wise(mary)&~rich(mary))))&
((?[X]:((old(X)|brave(X))))=>(?[X]:((~generous(X)&~funny(X)))))&
(![X]:((~brave(X)<~>creative(X))<=>(funny(X)&rich(X))))&
(![X]:((~wise(X)|creative(X))=>(~kind(X)|strong(X))))&
(((generous(fred)<~>~kind(fred)))<=>((curious(alice)|tall(alice))))&
((?[X]:((happy(X)&~brave(X))))=>(?[X]:((~happy(X)&calm(X)))))&
(![X]:((~funny(X)|~wise(X))=>~funny(X)))&
(![X]:((creative(X)|patient(X))<=>(kind(X)&creative(X))))&
(((tall(alice)&old(alice)))<=>((~brave(mary)&~rich(mary))))&
(((tall(paul)<~>brave(paul)))=>((humble(mary)&~old(mary))))&
((kind(john)|humble(john)))&
((tall(alice)|happy(alice)))&
(?[X]:((~quiet(X)|tall(X))))&
(?[X]:((old(X)|tall(X))))&
(~strong(mary))&
(?[X]:((generous(X)&humble(X)))) | generous(fred) | [
"p2",
"p3",
"p7",
"p10",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 2033951011206538006718042
% SZS output start Proof for 2033951011206538006718042
3. ! [X0] : ((~happy(X0) <~> ~old(X0)) => (brave(X0) & ~calm(X0))) [input p2]
4. ! [X0] : ((~quiet(X0) & generous(X0)) <=> (~funny(X0) | ~kind(X0))) [input p3]
8. ? [X0] : (brave(X0) | old(X0)) => ? [X0] : (~funny(X0) & ~generous(X0)) [input p7]
11. (generous(fred) <~> ~kind(fred)) <=> (tall(alice) | curious(alice)) [input p10]
18. happy(alice) | tall(alice) [input p17]
23. ~generous(fred) [input hypothesis]
25. ? [X0] : (brave(X0) | old(X0)) => ? [X1] : (~funny(X1) & ~generous(X1)) [rectify 8]
30. ! [X0] : ((brave(X0) & ~calm(X0)) | (~happy(X0) <=> ~old(X0))) [ennf transformation 3]
35. ? [X1] : (~funny(X1) & ~generous(X1)) | ! [X0] : (~brave(X0) & ~old(X0)) [ennf transformation 25]
48. ! [X0] : ((brave(X0) & ~calm(X0)) | ((~happy(X0) | old(X0)) & (~old(X0) | happy(X0)))) [nnf transformation 30]
49. ! [X0] : (((~quiet(X0) & generous(X0)) | (funny(X0) & kind(X0))) & ((~funny(X0) | ~kind(X0)) | (quiet(X0) | ~generous(X0)))) [nnf transformation 4]
50. ! [X0] : (((~quiet(X0) & generous(X0)) | (funny(X0) & kind(X0))) & (~funny(X0) | ~kind(X0) | quiet(X0) | ~generous(X0))) [flattening 49]
52. ? [X0] : (~funny(X0) & ~generous(X0)) | ! [X1] : (~brave(X1) & ~old(X1)) [rectify 35]
53. ? [X0] : (~funny(X0) & ~generous(X0)) => (~funny(sK2) & ~generous(sK2)) [choice axiom]
54. (~funny(sK2) & ~generous(sK2)) | ! [X1] : (~brave(X1) & ~old(X1)) [skolemisation 52,53]
57. (((kind(fred) | ~generous(fred)) & (~kind(fred) | generous(fred))) | (~tall(alice) & ~curious(alice))) & ((tall(alice) | curious(alice)) | ((generous(fred) | kind(fred)) & (~kind(fred) | ~generous(fred)))) [nnf transformation 11]
58. (((kind(fred) | ~generous(fred)) & (~kind(fred) | generous(fred))) | (~tall(alice) & ~curious(alice))) & (tall(alice) | curious(alice) | ((generous(fred) | kind(fred)) & (~kind(fred) | ~generous(fred)))) [flattening 57]
87. ~happy(X0) | brave(X0) | old(X0) [cnf transformation 48]
89. kind(X0) | generous(X0) [cnf transformation 50]
90. generous(X0) | funny(X0) [cnf transformation 50]
102. ~generous(sK2) | ~old(X1) [cnf transformation 54]
103. ~generous(sK2) | ~brave(X1) [cnf transformation 54]
104. ~funny(sK2) | ~old(X1) [cnf transformation 54]
105. ~funny(sK2) | ~brave(X1) [cnf transformation 54]
117. ~kind(fred) | generous(fred) | ~tall(alice) [cnf transformation 58]
135. happy(alice) | tall(alice) [cnf transformation 18]
140. ~generous(fred) [cnf transformation 23]
192. 12 <=> ! [X1] : ~brave(X1) [avatar definition]
193. ~brave(X1) <- (12) [avatar component clause 192]
195. 13 <=> funny(sK2) [avatar definition]
198. 12 | ~13 [avatar split clause 105,195,192]
200. 14 <=> ! [X1] : ~old(X1) [avatar definition]
201. ~old(X1) <- (14) [avatar component clause 200]
202. 14 | ~13 [avatar split clause 104,195,200]
204. 15 <=> generous(sK2) [avatar definition]
206. ~generous(sK2) <- (~15) [avatar component clause 204]
207. 12 | ~15 [avatar split clause 103,204,192]
208. 14 | ~15 [avatar split clause 102,204,200]
211. 16 <=> tall(alice) [avatar definition]
225. generous(fred) | ~tall(alice) [subsumption resolution 117,89]
227. 19 <=> generous(fred) [avatar definition]
230. ~16 | 19 [avatar split clause 225,227,211]
274. 28 <=> happy(alice) [avatar definition]
276. happy(alice) <- (28) [avatar component clause 274]
277. 16 | 28 [avatar split clause 135,274,211]
296. ~19 [avatar split clause 140,227]
299. funny(sK2) <- (~15) [resolution 90,206]
305. 13 | 15 [avatar split clause 299,204,195]
326. brave(alice) | old(alice) <- (28) [resolution 87,276]
327. old(alice) <- (12, 28) [subsumption resolution 326,193]
328. $false <- (12, 14, 28) [subsumption resolution 327,201]
329. ~12 | ~14 | ~28 [avatar contradiction clause 328]
330. $false [avatar sat refutation 198,202,207,208,230,277,296,305,329]
% SZS output end Proof for 2033951011206538006718042
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old then susan is brave.
Everyone who is either humble or strong is creative.
If someone is strong or curious then someone is either not curious or not patient and vice versa.
Everyone who is either not strong or tall is funny or old and vice versa.
Everyone who is either humble or not rich is calm.
If alice is both kind and not kind then someone is curious and vice versa.
Everyone who is funny is not rich and vice versa.
Everyone who is not generous is either not patient or not strong and vice versa.
If someone is both tall and not calm then alice is both strong and old.
If alice is both kind and not tall then john is both not rich and not generous and vice versa.
If someone is not strong or not calm then alice is rich and vice versa.
Everyone who is generous is rich or not generous.
If lucy is creative or rich then alice is either funny or wise and vice versa.
If alice is creative or not rich then someone is both rich and not old and vice versa.
Everyone who is either happy or generous is either creative or not rich and vice versa.
Everyone who is both funny and not calm is both not quiet and curious.
Lucy is either not old or rich.
John is either curious or old.
Lucy is generous.
Fred is both not brave and not wise.
John is brave or not old.
Someone is both not quiet and calm. | Alice is not tall. | neutral | ((?[X]:(~old(X)))=>(brave(susan)))&
(![X]:((humble(X)<~>strong(X))=>creative(X)))&
((?[X]:((strong(X)|curious(X))))<=>(?[X]:((~curious(X)<~>~patient(X)))))&
(![X]:((~strong(X)<~>tall(X))<=>(funny(X)|old(X))))&
(![X]:((humble(X)<~>~rich(X))=>calm(X)))&
(((kind(alice)&~kind(alice)))<=>(?[X]:(curious(X))))&
(![X]:(funny(X)<=>~rich(X)))&
(![X]:(~generous(X)<=>(~patient(X)<~>~strong(X))))&
((?[X]:((tall(X)&~calm(X))))=>((strong(alice)&old(alice))))&
(((kind(alice)&~tall(alice)))<=>((~rich(john)&~generous(john))))&
((?[X]:((~strong(X)|~calm(X))))<=>(rich(alice)))&
(![X]:(generous(X)=>(rich(X)|~generous(X))))&
(((creative(lucy)|rich(lucy)))<=>((funny(alice)<~>wise(alice))))&
(((creative(alice)|~rich(alice)))<=>(?[X]:((rich(X)&~old(X)))))&
(![X]:((happy(X)<~>generous(X))<=>(creative(X)<~>~rich(X))))&
(![X]:((funny(X)&~calm(X))=>(~quiet(X)&curious(X))))&
((~old(lucy)<~>rich(lucy)))&
((curious(john)<~>old(john)))&
(generous(lucy))&
((~brave(fred)&~wise(fred)))&
((brave(john)|~old(john)))&
(?[X]:((~quiet(X)&calm(X)))) | ~tall(alice) | [] | null | 0 |
If someone is rich then lucy is both not generous and brave.
If fred is rich or not calm then someone is both curious and not happy.
If lucy is not rich or wise then lucy is not humble and vice versa.
If someone is not kind or not wise then alice is not brave or generous and vice versa.
Everyone who is both not brave and old is both brave and not kind and vice versa.
Everyone who is rich or creative is rich or not creative.
Everyone who is kind is not happy.
If susan is either not happy or not patient then someone is rich or kind and vice versa.
If john is tall or not old then fred is either kind or rich and vice versa.
If alice is both not kind and funny then someone is not old or kind and vice versa.
If susan is not rich then alice is either brave or not old.
Everyone who is either not rich or curious is humble.
If someone is humble then someone is either not creative or tall and vice versa.
If someone is either not generous or kind then someone is generous or not generous and vice versa.
Everyone who is either not rich or funny is funny and vice versa.
Everyone who is creative is either humble or not generous and vice versa.
Someone is curious.
Paul is both not quiet and not happy.
Someone is either quiet or not calm.
Someone is either patient or not curious.
Someone is either not tall or humble.
Someone is not generous.
Lucy is brave or old.
Alice is both calm and not generous. | Alice is old. | contradiction | ((?[X]:(rich(X)))=>((~generous(lucy)&brave(lucy))))&
(((rich(fred)|~calm(fred)))=>(?[X]:((curious(X)&~happy(X)))))&
(((~rich(lucy)|wise(lucy)))<=>(~humble(lucy)))&
((?[X]:((~kind(X)|~wise(X))))<=>((~brave(alice)|generous(alice))))&
(![X]:((~brave(X)&old(X))<=>(brave(X)&~kind(X))))&
(![X]:((rich(X)|creative(X))=>(rich(X)|~creative(X))))&
(![X]:(kind(X)=>~happy(X)))&
(((~happy(susan)<~>~patient(susan)))<=>(?[X]:((rich(X)|kind(X)))))&
(((tall(john)|~old(john)))<=>((kind(fred)<~>rich(fred))))&
(((~kind(alice)&funny(alice)))<=>(?[X]:((~old(X)|kind(X)))))&
((~rich(susan))=>((brave(alice)<~>~old(alice))))&
(![X]:((~rich(X)<~>curious(X))=>humble(X)))&
((?[X]:(humble(X)))<=>(?[X]:((~creative(X)<~>tall(X)))))&
((?[X]:((~generous(X)<~>kind(X))))<=>(?[X]:((generous(X)|~generous(X)))))&
(![X]:((~rich(X)<~>funny(X))<=>funny(X)))&
(![X]:(creative(X)<=>(humble(X)<~>~generous(X))))&
(?[X]:(curious(X)))&
((~quiet(paul)&~happy(paul)))&
(?[X]:((quiet(X)<~>~calm(X))))&
(?[X]:((patient(X)<~>~curious(X))))&
(?[X]:((~tall(X)<~>humble(X))))&
(?[X]:(~generous(X)))&
((brave(lucy)|old(lucy)))&
((calm(alice)&~generous(alice))) | old(alice) | [
"p3",
"p4",
"p9",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 8060547742706801306325337
% SZS output start Proof for 8060547742706801306325337
4. ? [X0] : (~wise(X0) | ~kind(X0)) <=> (generous(alice) | ~brave(alice)) [input p3]
5. ! [X0] : ((old(X0) & ~brave(X0)) <=> (~kind(X0) & brave(X0))) [input p4]
10. (funny(alice) & ~kind(alice)) <=> ? [X0] : (kind(X0) | ~old(X0)) [input p9]
24. ~generous(alice) & calm(alice) [input p23]
25. old(alice) [input hypothesis]
39. (? [X0] : (~wise(X0) | ~kind(X0)) | (~generous(alice) & brave(alice))) & ((generous(alice) | ~brave(alice)) | ! [X0] : (wise(X0) & kind(X0))) [nnf transformation 4]
40. (? [X0] : (~wise(X0) | ~kind(X0)) | (~generous(alice) & brave(alice))) & (generous(alice) | ~brave(alice) | ! [X0] : (wise(X0) & kind(X0))) [flattening 39]
41. (? [X0] : (~wise(X0) | ~kind(X0)) | (~generous(alice) & brave(alice))) & (generous(alice) | ~brave(alice) | ! [X1] : (wise(X1) & kind(X1))) [rectify 40]
42. ? [X0] : (~wise(X0) | ~kind(X0)) => (~wise(sK1) | ~kind(sK1)) [choice axiom]
43. ((~wise(sK1) | ~kind(sK1)) | (~generous(alice) & brave(alice))) & (generous(alice) | ~brave(alice) | ! [X1] : (wise(X1) & kind(X1))) [skolemisation 41,42]
44. ! [X0] : (((old(X0) & ~brave(X0)) | (kind(X0) | ~brave(X0))) & ((~kind(X0) & brave(X0)) | (~old(X0) | brave(X0)))) [nnf transformation 5]
45. ! [X0] : (((old(X0) & ~brave(X0)) | kind(X0) | ~brave(X0)) & ((~kind(X0) & brave(X0)) | ~old(X0) | brave(X0))) [flattening 44]
52. ((funny(alice) & ~kind(alice)) | ! [X0] : (~kind(X0) & old(X0))) & (? [X0] : (kind(X0) | ~old(X0)) | (~funny(alice) | kind(alice))) [nnf transformation 10]
53. ((funny(alice) & ~kind(alice)) | ! [X0] : (~kind(X0) & old(X0))) & (? [X0] : (kind(X0) | ~old(X0)) | ~funny(alice) | kind(alice)) [flattening 52]
54. ((funny(alice) & ~kind(alice)) | ! [X0] : (~kind(X0) & old(X0))) & (? [X1] : (kind(X1) | ~old(X1)) | ~funny(alice) | kind(alice)) [rectify 53]
55. ? [X1] : (kind(X1) | ~old(X1)) => (kind(sK3) | ~old(sK3)) [choice axiom]
56. ((funny(alice) & ~kind(alice)) | ! [X0] : (~kind(X0) & old(X0))) & ((kind(sK3) | ~old(sK3)) | ~funny(alice) | kind(alice)) [skolemisation 54,55]
93. generous(alice) | ~brave(alice) | kind(X1) [cnf transformation 43]
97. brave(X0) | ~old(X0) | brave(X0) [cnf transformation 45]
118. ~kind(alice) | ~kind(X0) [cnf transformation 56]
155. ~generous(alice) [cnf transformation 24]
156. old(alice) [cnf transformation 25]
160. ~old(X0) | brave(X0) [duplicate literal removal 97]
211. 11 <=> generous(alice) [avatar definition]
224. 14 <=> brave(alice) [avatar definition]
233. 16 <=> ! [X1] : kind(X1) [avatar definition]
234. kind(X1) <- (16) [avatar component clause 233]
235. 16 | ~14 | 11 [avatar split clause 93,211,224,233]
237. 17 <=> ! [X0] : ~kind(X0) [avatar definition]
238. ~kind(X0) <- (17) [avatar component clause 237]
289. 27 <=> kind(alice) [avatar definition]
291. ~kind(alice) <- (~27) [avatar component clause 289]
292. 17 | ~27 [avatar split clause 118,289,237]
308. 31 <=> old(alice) [avatar definition]
310. old(alice) <- (31) [avatar component clause 308]
388. ~11 [avatar split clause 155,211]
389. 31 [avatar split clause 156,308]
393. brave(alice) <- (31) [resolution 160,310]
396. 14 | ~31 [avatar split clause 393,308,224]
401. $false <- (16, ~27) [resolution 234,291]
404. ~16 | 27 [avatar contradiction clause 401]
406. $false <- (16, 17) [subsumption resolution 238,234]
407. ~16 | ~17 [avatar contradiction clause 406]
408. $false [avatar sat refutation 235,292,388,389,396,404,407]
% SZS output end Proof for 8060547742706801306325337
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not quiet then alice is either quiet or curious.
Everyone who is patient or not brave is both not calm and rich and vice versa.
If someone is not patient then lucy is humble or not wise and vice versa.
Everyone who is not quiet is both not quiet and generous and vice versa.
Everyone who is not funny is either not generous or not happy and vice versa.
If someone is not kind or not curious then someone is both not wise and funny and vice versa.
Everyone who is both not curious and not generous is brave and vice versa.
Everyone who is both strong and old is either generous or not patient.
Everyone who is either rich or wise is either not funny or not tall and vice versa.
Everyone who is calm is generous or curious.
Everyone who is either calm or not curious is both not wise and not calm.
Everyone who is both not strong and patient is both not strong and not kind and vice versa.
If someone is either funny or tall then someone is both not curious and not brave.
If mary is not wise or happy then someone is both funny and not strong and vice versa.
Everyone who is calm or not quiet is both not humble and wise and vice versa.
If someone is patient then susan is either not patient or not kind and vice versa.
Someone is either not rich or rich.
Someone is both not generous and not patient.
Someone is both rich and not happy.
Susan is either not wise or strong.
Someone is not patient.
Lucy is curious.
Alice is happy or not happy. | Alice is not happy. | neutral | ((?[X]:(~quiet(X)))=>((quiet(alice)<~>curious(alice))))&
(![X]:((patient(X)|~brave(X))<=>(~calm(X)&rich(X))))&
((?[X]:(~patient(X)))<=>((humble(lucy)|~wise(lucy))))&
(![X]:(~quiet(X)<=>(~quiet(X)&generous(X))))&
(![X]:(~funny(X)<=>(~generous(X)<~>~happy(X))))&
((?[X]:((~kind(X)|~curious(X))))<=>(?[X]:((~wise(X)&funny(X)))))&
(![X]:((~curious(X)&~generous(X))<=>brave(X)))&
(![X]:((strong(X)&old(X))=>(generous(X)<~>~patient(X))))&
(![X]:((rich(X)<~>wise(X))<=>(~funny(X)<~>~tall(X))))&
(![X]:(calm(X)=>(generous(X)|curious(X))))&
(![X]:((calm(X)<~>~curious(X))=>(~wise(X)&~calm(X))))&
(![X]:((~strong(X)&patient(X))<=>(~strong(X)&~kind(X))))&
((?[X]:((funny(X)<~>tall(X))))=>(?[X]:((~curious(X)&~brave(X)))))&
(((~wise(mary)|happy(mary)))<=>(?[X]:((funny(X)&~strong(X)))))&
(![X]:((calm(X)|~quiet(X))<=>(~humble(X)&wise(X))))&
((?[X]:(patient(X)))<=>((~patient(susan)<~>~kind(susan))))&
(?[X]:((~rich(X)<~>rich(X))))&
(?[X]:((~generous(X)&~patient(X))))&
(?[X]:((rich(X)&~happy(X))))&
((~wise(susan)<~>strong(susan)))&
(?[X]:(~patient(X)))&
(curious(lucy))&
((happy(alice)|~happy(alice))) | ~happy(alice) | [] | null | 0 |
Everyone who is either kind or not kind is either kind or patient and vice versa.
Everyone who is either not quiet or happy is wise.
Everyone who is not quiet or kind is curious and vice versa.
Everyone who is generous or brave is both happy and brave.
Everyone who is either not quiet or not rich is either creative or generous and vice versa.
If someone is both not humble and not tall then john is either happy or not generous.
Everyone who is rich is either not tall or humble.
Everyone who is not wise or creative is not curious or happy and vice versa.
Everyone who is both not brave and quiet is either calm or brave and vice versa.
Everyone who is both not brave and not patient is either quiet or wise.
Everyone who is either patient or funny is either patient or tall.
Everyone who is not rich is both not kind and not tall and vice versa.
Everyone who is either tall or not happy is either not humble or not calm.
If someone is either funny or strong then someone is curious or not brave and vice versa.
Everyone who is either humble or not humble is either not quiet or not tall.
Everyone who is both kind and creative is either not tall or not humble and vice versa.
Paul is calm.
Mary is either generous or not wise.
Someone is tall.
Someone is not curious.
Susan is creative.
Fred is wise.
Lucy is either generous or calm. | Paul is curious. | contradiction | (![X]:((kind(X)<~>~kind(X))<=>(kind(X)<~>patient(X))))&
(![X]:((~quiet(X)<~>happy(X))=>wise(X)))&
(![X]:((~quiet(X)|kind(X))<=>curious(X)))&
(![X]:((generous(X)|brave(X))=>(happy(X)&brave(X))))&
(![X]:((~quiet(X)<~>~rich(X))<=>(creative(X)<~>generous(X))))&
((?[X]:((~humble(X)&~tall(X))))=>((happy(john)<~>~generous(john))))&
(![X]:(rich(X)=>(~tall(X)<~>humble(X))))&
(![X]:((~wise(X)|creative(X))<=>(~curious(X)|happy(X))))&
(![X]:((~brave(X)&quiet(X))<=>(calm(X)<~>brave(X))))&
(![X]:((~brave(X)&~patient(X))=>(quiet(X)<~>wise(X))))&
(![X]:((patient(X)<~>funny(X))=>(patient(X)<~>tall(X))))&
(![X]:(~rich(X)<=>(~kind(X)&~tall(X))))&
(![X]:((tall(X)<~>~happy(X))=>(~humble(X)<~>~calm(X))))&
((?[X]:((funny(X)<~>strong(X))))<=>(?[X]:((curious(X)|~brave(X)))))&
(![X]:((humble(X)<~>~humble(X))=>(~quiet(X)<~>~tall(X))))&
(![X]:((kind(X)&creative(X))<=>(~tall(X)<~>~humble(X))))&
(calm(paul))&
((generous(mary)<~>~wise(mary)))&
(?[X]:(tall(X)))&
(?[X]:(~curious(X)))&
(creative(susan))&
(wise(fred))&
((generous(lucy)<~>calm(lucy))) | curious(paul) | [
"p0",
"p1",
"p2",
"p3",
"p6",
"p7",
"p8",
"p9",
"p11",
"p12",
"p14",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 6454764886907452874286867
% SZS output start Proof for 6454764886907452874286867
1. ! [X0] : ((kind(X0) <~> ~kind(X0)) <=> (kind(X0) <~> patient(X0))) [input p0]
2. ! [X0] : ((~quiet(X0) <~> happy(X0)) => wise(X0)) [input p1]
3. ! [X0] : ((kind(X0) | ~quiet(X0)) <=> curious(X0)) [input p2]
4. ! [X0] : ((brave(X0) | generous(X0)) => (brave(X0) & happy(X0))) [input p3]
7. ! [X0] : (rich(X0) => (~tall(X0) <~> humble(X0))) [input p6]
8. ! [X0] : ((creative(X0) | ~wise(X0)) <=> (happy(X0) | ~curious(X0))) [input p7]
9. ! [X0] : ((quiet(X0) & ~brave(X0)) <=> (calm(X0) <~> brave(X0))) [input p8]
10. ! [X0] : ((~patient(X0) & ~brave(X0)) => (quiet(X0) <~> wise(X0))) [input p9]
12. ! [X0] : (~rich(X0) <=> (~tall(X0) & ~kind(X0))) [input p11]
13. ! [X0] : ((tall(X0) <~> ~happy(X0)) => (~humble(X0) <~> ~calm(X0))) [input p12]
15. ! [X0] : ((humble(X0) <~> ~humble(X0)) => (~quiet(X0) <~> ~tall(X0))) [input p14]
16. ! [X0] : ((creative(X0) & kind(X0)) <=> (~tall(X0) <~> ~humble(X0))) [input p15]
17. calm(paul) [input p16]
24. curious(paul) [input hypothesis]
26. ! [X0] : (wise(X0) | (~quiet(X0) <=> happy(X0))) [ennf transformation 2]
27. ! [X0] : ((brave(X0) & happy(X0)) | (~brave(X0) & ~generous(X0))) [ennf transformation 4]
29. ! [X0] : ((~tall(X0) <~> humble(X0)) | ~rich(X0)) [ennf transformation 7]
30. ! [X0] : ((quiet(X0) <~> wise(X0)) | (patient(X0) | brave(X0))) [ennf transformation 10]
31. ! [X0] : ((quiet(X0) <~> wise(X0)) | patient(X0) | brave(X0)) [flattening 30]
33. ! [X0] : ((~humble(X0) <~> ~calm(X0)) | (tall(X0) <=> ~happy(X0))) [ennf transformation 13]
34. ! [X0] : ((~quiet(X0) <~> ~tall(X0)) | (humble(X0) <=> ~humble(X0))) [ennf transformation 15]
35. ! [X0] : ((((kind(X0) | ~kind(X0)) & (~kind(X0) | kind(X0))) | ((kind(X0) | ~patient(X0)) & (patient(X0) | ~kind(X0)))) & (((~patient(X0) | ~kind(X0)) & (patient(X0) | kind(X0))) | ((kind(X0) | kind(X0)) & (~kind(X0) | ~kind(X0))))) [nnf transformation 1]
36. ! [X0] : (wise(X0) | ((~quiet(X0) | ~happy(X0)) & (happy(X0) | quiet(X0)))) [nnf transformation 26]
37. ! [X0] : (((kind(X0) | ~quiet(X0)) | ~curious(X0)) & (curious(X0) | (~kind(X0) & quiet(X0)))) [nnf transformation 3]
38. ! [X0] : ((kind(X0) | ~quiet(X0) | ~curious(X0)) & (curious(X0) | (~kind(X0) & quiet(X0)))) [flattening 37]
41. ! [X0] : (((~humble(X0) | tall(X0)) & (humble(X0) | ~tall(X0))) | ~rich(X0)) [nnf transformation 29]
42. ! [X0] : (((creative(X0) | ~wise(X0)) | (~happy(X0) & curious(X0))) & ((happy(X0) | ~curious(X0)) | (~creative(X0) & wise(X0)))) [nnf transformation 8]
43. ! [X0] : ((creative(X0) | ~wise(X0) | (~happy(X0) & curious(X0))) & (happy(X0) | ~curious(X0) | (~creative(X0) & wise(X0)))) [flattening 42]
44. ! [X0] : (((quiet(X0) & ~brave(X0)) | ((calm(X0) | ~brave(X0)) & (brave(X0) | ~calm(X0)))) & (((~brave(X0) | ~calm(X0)) & (brave(X0) | calm(X0))) | (~quiet(X0) | brave(X0)))) [nnf transformation 9]
45. ! [X0] : (((quiet(X0) & ~brave(X0)) | ((calm(X0) | ~brave(X0)) & (brave(X0) | ~calm(X0)))) & (((~brave(X0) | ~calm(X0)) & (brave(X0) | calm(X0))) | ~quiet(X0) | brave(X0))) [flattening 44]
46. ! [X0] : (((~wise(X0) | ~quiet(X0)) & (wise(X0) | quiet(X0))) | patient(X0) | brave(X0)) [nnf transformation 31]
48. ! [X0] : ((~rich(X0) | (tall(X0) | kind(X0))) & ((~tall(X0) & ~kind(X0)) | rich(X0))) [nnf transformation 12]
49. ! [X0] : ((~rich(X0) | tall(X0) | kind(X0)) & ((~tall(X0) & ~kind(X0)) | rich(X0))) [flattening 48]
50. ! [X0] : (((calm(X0) | humble(X0)) & (~calm(X0) | ~humble(X0))) | ((tall(X0) | happy(X0)) & (~happy(X0) | ~tall(X0)))) [nnf transformation 33]
56. ! [X0] : (((tall(X0) | quiet(X0)) & (~tall(X0) | ~quiet(X0))) | ((humble(X0) | humble(X0)) & (~humble(X0) | ~humble(X0)))) [nnf transformation 34]
57. ! [X0] : (((creative(X0) & kind(X0)) | ((~tall(X0) | humble(X0)) & (~humble(X0) | tall(X0)))) & (((humble(X0) | tall(X0)) & (~humble(X0) | ~tall(X0))) | (~creative(X0) | ~kind(X0)))) [nnf transformation 16]
58. ! [X0] : (((creative(X0) & kind(X0)) | ((~tall(X0) | humble(X0)) & (~humble(X0) | tall(X0)))) & (((humble(X0) | tall(X0)) & (~humble(X0) | ~tall(X0))) | ~creative(X0) | ~kind(X0))) [flattening 57]
67. ~patient(X0) | ~kind(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 35]
74. ~happy(X0) | ~quiet(X0) | wise(X0) [cnf transformation 36]
77. ~curious(X0) | ~quiet(X0) | kind(X0) [cnf transformation 38]
79. ~brave(X0) | happy(X0) [cnf transformation 27]
92. ~tall(X0) | humble(X0) | ~rich(X0) [cnf transformation 41]
93. ~humble(X0) | tall(X0) | ~rich(X0) [cnf transformation 41]
94. ~curious(X0) | happy(X0) | wise(X0) [cnf transformation 43]
97. ~wise(X0) | creative(X0) | ~happy(X0) [cnf transformation 43]
102. ~calm(X0) | brave(X0) | quiet(X0) [cnf transformation 45]
105. ~wise(X0) | ~quiet(X0) | patient(X0) | brave(X0) [cnf transformation 46]
110. ~kind(X0) | rich(X0) [cnf transformation 49]
111. ~tall(X0) | rich(X0) [cnf transformation 49]
113. ~calm(X0) | ~humble(X0) | ~happy(X0) | ~tall(X0) [cnf transformation 50]
114. ~calm(X0) | ~humble(X0) | tall(X0) | happy(X0) [cnf transformation 50]
123. ~tall(X0) | ~quiet(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 56]
124. ~tall(X0) | ~quiet(X0) | humble(X0) | humble(X0) [cnf transformation 56]
125. tall(X0) | quiet(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 56]
126. tall(X0) | quiet(X0) | humble(X0) | humble(X0) [cnf transformation 56]
128. ~creative(X0) | tall(X0) | humble(X0) | ~kind(X0) [cnf transformation 58]
133. calm(paul) [cnf transformation 17]
142. curious(paul) [cnf transformation 24]
143. ~tall(X0) | ~quiet(X0) | ~humble(X0) [duplicate literal removal 123]
144. ~tall(X0) | ~quiet(X0) | humble(X0) [duplicate literal removal 124]
145. tall(X0) | quiet(X0) | ~humble(X0) [duplicate literal removal 125]
146. tall(X0) | quiet(X0) | humble(X0) [duplicate literal removal 126]
153. ~patient(X0) | ~kind(X0) [duplicate literal removal 67]
206. tall(X0) | quiet(X0) [subsumption resolution 145,146]
207. ~tall(X0) | ~quiet(X0) [subsumption resolution 143,144]
256. ~quiet(paul) | kind(paul) [resolution 77,142]
259. 18 <=> kind(paul) [avatar definition]
261. kind(paul) <- (18) [avatar component clause 259]
263. 19 <=> quiet(paul) [avatar definition]
264. quiet(paul) <- (19) [avatar component clause 263]
265. ~quiet(paul) <- (~19) [avatar component clause 263]
266. 18 | ~19 [avatar split clause 256,263,259]
272. happy(paul) | wise(paul) [resolution 94,142]
275. 20 <=> wise(paul) [avatar definition]
276. ~wise(paul) <- (~20) [avatar component clause 275]
277. wise(paul) <- (20) [avatar component clause 275]
279. 21 <=> happy(paul) [avatar definition]
280. ~happy(paul) <- (~21) [avatar component clause 279]
281. happy(paul) <- (21) [avatar component clause 279]
282. 20 | 21 [avatar split clause 272,279,275]
319. creative(paul) | ~happy(paul) <- (20) [resolution 97,277]
326. 29 <=> creative(paul) [avatar definition]
328. creative(paul) <- (29) [avatar component clause 326]
329. ~21 | 29 | ~20 [avatar split clause 319,275,326,279]
330. brave(paul) | quiet(paul) [resolution 102,133]
334. brave(paul) <- (~19) [subsumption resolution 330,265]
346. happy(paul) <- (~19) [resolution 334,79]
347. $false <- (~19, ~21) [subsumption resolution 346,280]
348. 19 | 21 [avatar contradiction clause 347]
350. 32 <=> brave(paul) [avatar definition]
352. brave(paul) <- (32) [avatar component clause 350]
355. rich(paul) <- (18) [resolution 261,110]
525. ~quiet(paul) | patient(paul) | brave(paul) <- (20) [resolution 105,277]
528. patient(paul) | brave(paul) <- (19, 20) [subsumption resolution 525,264]
530. 54 <=> patient(paul) [avatar definition]
532. patient(paul) <- (54) [avatar component clause 530]
533. 32 | 54 | ~19 | ~20 [avatar split clause 528,275,263,530,350]
536. ~humble(paul) | ~happy(paul) | ~tall(paul) [resolution 113,133]
572. ~humble(paul) | tall(paul) | happy(paul) [resolution 114,133]
576. ~humble(paul) | tall(paul) <- (~21) [subsumption resolution 572,280]
578. 62 <=> tall(paul) [avatar definition]
579. ~tall(paul) <- (~62) [avatar component clause 578]
580. tall(paul) <- (62) [avatar component clause 578]
582. 63 <=> humble(paul) [avatar definition]
583. humble(paul) <- (63) [avatar component clause 582]
584. ~humble(paul) <- (~63) [avatar component clause 582]
585. 62 | ~63 | 21 [avatar split clause 576,279,582,578]
720. ~kind(paul) <- (54) [resolution 532,153]
721. $false <- (18, 54) [subsumption resolution 720,261]
722. ~18 | ~54 [avatar contradiction clause 721]
725. happy(paul) <- (32) [resolution 352,79]
728. 21 | ~32 [avatar split clause 725,350,279]
729. ~quiet(paul) | wise(paul) <- (21) [resolution 281,74]
735. tall(paul) | humble(paul) | ~kind(paul) <- (29) [resolution 328,128]
754. ~quiet(paul) <- (62) [resolution 580,207]
761. $false <- (19, 62) [subsumption resolution 754,264]
762. ~19 | ~62 [avatar contradiction clause 761]
763. tall(paul) | humble(paul) <- (18, 29) [subsumption resolution 735,261]
764. 63 | 62 | ~18 | ~29 [avatar split clause 763,326,259,578,582]
765. ~humble(paul) | ~tall(paul) <- (21) [subsumption resolution 536,281]
766. ~62 | ~63 | ~21 [avatar split clause 765,279,582,578]
768. quiet(paul) <- (~62) [resolution 579,206]
771. tall(paul) | ~rich(paul) <- (63) [resolution 583,93]
772. ~rich(paul) <- (~62, 63) [subsumption resolution 771,579]
773. $false <- (18, ~62, 63) [subsumption resolution 772,355]
774. ~18 | 62 | ~63 [avatar contradiction clause 773]
777. ~quiet(paul) <- (~20, 21) [subsumption resolution 729,276]
778. ~19 | 20 | ~21 [avatar split clause 777,279,275,263]
779. 19 | 62 [avatar split clause 768,578,263]
781. humble(paul) | ~rich(paul) <- (62) [resolution 580,92]
782. rich(paul) <- (62) [resolution 580,111]
790. ~rich(paul) <- (62, ~63) [subsumption resolution 781,584]
791. $false <- (62, ~63) [subsumption resolution 782,790]
792. ~62 | 63 [avatar contradiction clause 791]
799. $false [avatar sat refutation 266,282,329,348,533,585,722,728,762,764,766,774,778,779,792]
% SZS output end Proof for 6454764886907452874286867
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.041 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not old and not generous then someone is both tall and calm and vice versa.
Everyone who is both not generous and calm is both not curious and not generous and vice versa.
Everyone who is kind or not brave is not wise or not brave.
If someone is both humble and old then mary is both not funny and not creative.
Everyone who is not tall or tall is either not kind or kind and vice versa.
Everyone who is either kind or rich is curious or kind and vice versa.
If lucy is both brave and not curious then someone is not wise and vice versa.
Everyone who is kind or patient is not calm and vice versa.
Everyone who is either kind or creative is not curious and vice versa.
Everyone who is both not quiet and humble is not creative and vice versa.
If someone is either old or happy then someone is either not generous or strong.
Everyone who is kind is creative or not old and vice versa.
Everyone who is both rich and humble is not brave and vice versa.
If alice is curious or strong then someone is not funny and vice versa.
Everyone who is not rich or not funny is not funny or not tall.
Everyone who is wise or not kind is both not quiet and humble.
Mary is both not patient and rich.
Someone is both kind and creative.
Someone is either not funny or old.
Someone is either not wise or not old.
Fred is calm.
Alice is both not kind and patient.
Someone is kind. | Alice is not strong. | neutral | ((?[X]:((~old(X)&~generous(X))))<=>(?[X]:((tall(X)&calm(X)))))&
(![X]:((~generous(X)&calm(X))<=>(~curious(X)&~generous(X))))&
(![X]:((kind(X)|~brave(X))=>(~wise(X)|~brave(X))))&
((?[X]:((humble(X)&old(X))))=>((~funny(mary)&~creative(mary))))&
(![X]:((~tall(X)|tall(X))<=>(~kind(X)<~>kind(X))))&
(![X]:((kind(X)<~>rich(X))<=>(curious(X)|kind(X))))&
(((brave(lucy)&~curious(lucy)))<=>(?[X]:(~wise(X))))&
(![X]:((kind(X)|patient(X))<=>~calm(X)))&
(![X]:((kind(X)<~>creative(X))<=>~curious(X)))&
(![X]:((~quiet(X)&humble(X))<=>~creative(X)))&
((?[X]:((old(X)<~>happy(X))))=>(?[X]:((~generous(X)<~>strong(X)))))&
(![X]:(kind(X)<=>(creative(X)|~old(X))))&
(![X]:((rich(X)&humble(X))<=>~brave(X)))&
(((curious(alice)|strong(alice)))<=>(?[X]:(~funny(X))))&
(![X]:((~rich(X)|~funny(X))=>(~funny(X)|~tall(X))))&
(![X]:((wise(X)|~kind(X))=>(~quiet(X)&humble(X))))&
((~patient(mary)&rich(mary)))&
(?[X]:((kind(X)&creative(X))))&
(?[X]:((~funny(X)<~>old(X))))&
(?[X]:((~wise(X)<~>~old(X))))&
(calm(fred))&
((~kind(alice)&patient(alice)))&
(?[X]:(kind(X))) | ~strong(alice) | [] | null | 0 |
If someone is wise then fred is both patient and not creative and vice versa.
Everyone who is humble or not wise is either kind or not curious and vice versa.
Everyone who is not funny or not calm is funny.
If lucy is both not creative and not kind then someone is either old or humble and vice versa.
If john is both rich and not funny then fred is humble or not tall and vice versa.
If someone is both not strong and humble then fred is old or humble and vice versa.
If paul is either strong or not strong then alice is both tall and curious.
Everyone who is not strong is kind.
If someone is either not strong or humble then john is not funny and vice versa.
Everyone who is not calm is creative or kind and vice versa.
Everyone who is not generous or generous is either rich or generous and vice versa.
Everyone who is wise or quiet is not kind and vice versa.
If susan is not brave or old then mary is not rich or patient.
Everyone who is not strong is not calm or rich.
Everyone who is not wise is both not rich and not calm and vice versa.
Everyone who is not calm is patient or strong.
John is both old and not wise.
John is old.
Mary is either tall or not strong.
Someone is either not patient or wise.
Fred is not patient or strong. | Lucy is calm. | entailment | ((?[X]:(wise(X)))<=>((patient(fred)&~creative(fred))))&
(![X]:((humble(X)|~wise(X))<=>(kind(X)<~>~curious(X))))&
(![X]:((~funny(X)|~calm(X))=>funny(X)))&
(((~creative(lucy)&~kind(lucy)))<=>(?[X]:((old(X)<~>humble(X)))))&
(((rich(john)&~funny(john)))<=>((humble(fred)|~tall(fred))))&
((?[X]:((~strong(X)&humble(X))))<=>((old(fred)|humble(fred))))&
(((strong(paul)<~>~strong(paul)))=>((tall(alice)&curious(alice))))&
(![X]:(~strong(X)=>kind(X)))&
((?[X]:((~strong(X)<~>humble(X))))<=>(~funny(john)))&
(![X]:(~calm(X)<=>(creative(X)|kind(X))))&
(![X]:((~generous(X)|generous(X))<=>(rich(X)<~>generous(X))))&
(![X]:((wise(X)|quiet(X))<=>~kind(X)))&
(((~brave(susan)|old(susan)))=>((~rich(mary)|patient(mary))))&
(![X]:(~strong(X)=>(~calm(X)|rich(X))))&
(![X]:(~wise(X)<=>(~rich(X)&~calm(X))))&
(![X]:(~calm(X)=>(patient(X)|strong(X))))&
((old(john)&~wise(john)))&
(old(john))&
((tall(mary)<~>~strong(mary)))&
(?[X]:((~patient(X)<~>wise(X))))&
((~patient(fred)|strong(fred))) | calm(lucy) | [
"p2",
"p3",
"p4",
"p5",
"p8",
"p9",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 3088178932660100153757791
% SZS output start Proof for 3088178932660100153757791
3. ! [X0] : ((~calm(X0) | ~funny(X0)) => funny(X0)) [input p2]
4. (~kind(lucy) & ~creative(lucy)) <=> ? [X0] : (old(X0) <~> humble(X0)) [input p3]
5. (~funny(john) & rich(john)) <=> (~tall(fred) | humble(fred)) [input p4]
6. ? [X0] : (humble(X0) & ~strong(X0)) <=> (humble(fred) | old(fred)) [input p5]
9. ? [X0] : (~strong(X0) <~> humble(X0)) <=> ~funny(john) [input p8]
10. ! [X0] : (~calm(X0) <=> (kind(X0) | creative(X0))) [input p9]
17. ~wise(john) & old(john) [input p16]
22. ~calm(lucy) [input hypothesis]
24. ! [X0] : (funny(X0) | (calm(X0) & funny(X0))) [ennf transformation 3]
40. ((~kind(lucy) & ~creative(lucy)) | ! [X0] : ((old(X0) | ~humble(X0)) & (humble(X0) | ~old(X0)))) & (? [X0] : ((~humble(X0) | ~old(X0)) & (humble(X0) | old(X0))) | (kind(lucy) | creative(lucy))) [nnf transformation 4]
41. ((~kind(lucy) & ~creative(lucy)) | ! [X0] : ((old(X0) | ~humble(X0)) & (humble(X0) | ~old(X0)))) & (? [X0] : ((~humble(X0) | ~old(X0)) & (humble(X0) | old(X0))) | kind(lucy) | creative(lucy)) [flattening 40]
42. ((~kind(lucy) & ~creative(lucy)) | ! [X0] : ((old(X0) | ~humble(X0)) & (humble(X0) | ~old(X0)))) & (? [X1] : ((~humble(X1) | ~old(X1)) & (humble(X1) | old(X1))) | kind(lucy) | creative(lucy)) [rectify 41]
43. ? [X1] : ((~humble(X1) | ~old(X1)) & (humble(X1) | old(X1))) => ((~humble(sK1) | ~old(sK1)) & (humble(sK1) | old(sK1))) [choice axiom]
44. ((~kind(lucy) & ~creative(lucy)) | ! [X0] : ((old(X0) | ~humble(X0)) & (humble(X0) | ~old(X0)))) & (((~humble(sK1) | ~old(sK1)) & (humble(sK1) | old(sK1))) | kind(lucy) | creative(lucy)) [skolemisation 42,43]
45. ((~funny(john) & rich(john)) | (tall(fred) & ~humble(fred))) & ((~tall(fred) | humble(fred)) | (funny(john) | ~rich(john))) [nnf transformation 5]
46. ((~funny(john) & rich(john)) | (tall(fred) & ~humble(fred))) & (~tall(fred) | humble(fred) | funny(john) | ~rich(john)) [flattening 45]
47. (? [X0] : (humble(X0) & ~strong(X0)) | (~humble(fred) & ~old(fred))) & ((humble(fred) | old(fred)) | ! [X0] : (~humble(X0) | strong(X0))) [nnf transformation 6]
48. (? [X0] : (humble(X0) & ~strong(X0)) | (~humble(fred) & ~old(fred))) & (humble(fred) | old(fred) | ! [X0] : (~humble(X0) | strong(X0))) [flattening 47]
49. (? [X0] : (humble(X0) & ~strong(X0)) | (~humble(fred) & ~old(fred))) & (humble(fred) | old(fred) | ! [X1] : (~humble(X1) | strong(X1))) [rectify 48]
50. ? [X0] : (humble(X0) & ~strong(X0)) => (humble(sK2) & ~strong(sK2)) [choice axiom]
51. ((humble(sK2) & ~strong(sK2)) | (~humble(fred) & ~old(fred))) & (humble(fred) | old(fred) | ! [X1] : (~humble(X1) | strong(X1))) [skolemisation 49,50]
53. (? [X0] : ((~humble(X0) | strong(X0)) & (humble(X0) | ~strong(X0))) | funny(john)) & (~funny(john) | ! [X0] : ((~strong(X0) | ~humble(X0)) & (humble(X0) | strong(X0)))) [nnf transformation 9]
54. (? [X0] : ((~humble(X0) | strong(X0)) & (humble(X0) | ~strong(X0))) | funny(john)) & (~funny(john) | ! [X1] : ((~strong(X1) | ~humble(X1)) & (humble(X1) | strong(X1)))) [rectify 53]
55. ? [X0] : ((~humble(X0) | strong(X0)) & (humble(X0) | ~strong(X0))) => ((~humble(sK3) | strong(sK3)) & (humble(sK3) | ~strong(sK3))) [choice axiom]
56. (((~humble(sK3) | strong(sK3)) & (humble(sK3) | ~strong(sK3))) | funny(john)) & (~funny(john) | ! [X1] : ((~strong(X1) | ~humble(X1)) & (humble(X1) | strong(X1)))) [skolemisation 54,55]
57. ! [X0] : ((~calm(X0) | (~kind(X0) & ~creative(X0))) & ((kind(X0) | creative(X0)) | calm(X0))) [nnf transformation 10]
58. ! [X0] : ((~calm(X0) | (~kind(X0) & ~creative(X0))) & (kind(X0) | creative(X0) | calm(X0))) [flattening 57]
78. funny(X0) | funny(X0) [cnf transformation 24]
82. ~creative(lucy) | humble(X0) | ~old(X0) [cnf transformation 44]
84. ~kind(lucy) | humble(X0) | ~old(X0) [cnf transformation 44]
89. ~funny(john) | ~humble(fred) [cnf transformation 46]
91. humble(fred) | old(fred) | ~humble(X1) | strong(X1) [cnf transformation 51]
101. ~funny(john) | humble(X1) | strong(X1) [cnf transformation 56]
102. ~funny(john) | ~strong(X1) | ~humble(X1) [cnf transformation 56]
105. calm(X0) | creative(X0) | kind(X0) [cnf transformation 58]
123. old(john) [cnf transformation 17]
131. ~calm(lucy) [cnf transformation 22]
140. funny(X0) [duplicate literal removal 78]
163. 6 <=> kind(lucy) [avatar definition]
168. 7 <=> ! [X0] : (humble(X0) | ~old(X0)) [avatar definition]
169. ~old(X0) | humble(X0) <- (7) [avatar component clause 168]
170. 7 | ~6 [avatar split clause 84,163,168]
172. 8 <=> creative(lucy) [avatar definition]
174. ~creative(lucy) <- (~8) [avatar component clause 172]
176. 7 | ~8 [avatar split clause 82,172,168]
188. ~humble(fred) [subsumption resolution 89,140]
190. 11 <=> old(fred) [avatar definition]
191. old(fred) <- (11) [avatar component clause 190]
203. old(fred) | ~humble(X1) | strong(X1) [subsumption resolution 91,188]
205. 14 <=> ! [X1] : (~humble(X1) | strong(X1)) [avatar definition]
206. ~humble(X1) | strong(X1) <- (14) [avatar component clause 205]
207. 14 | 11 [avatar split clause 203,190,205]
224. ~strong(X1) | ~humble(X1) [subsumption resolution 102,140]
225. strong(X1) | humble(X1) [subsumption resolution 101,140]
295. creative(lucy) | kind(lucy) [resolution 105,131]
299. kind(lucy) <- (~8) [subsumption resolution 295,174]
303. 6 | 8 [avatar split clause 299,172,163]
312. humble(john) <- (7) [resolution 169,123]
314. humble(fred) <- (7, 11) [resolution 169,191]
317. $false <- (7, 11) [subsumption resolution 314,188]
318. ~7 | ~11 [avatar contradiction clause 317]
320. strong(X1) <- (14) [subsumption resolution 206,225]
325. ~humble(X0) <- (14) [resolution 320,224]
336. $false <- (7, 14) [resolution 325,312]
337. ~7 | ~14 [avatar contradiction clause 336]
340. $false [avatar sat refutation 170,176,207,303,318,337]
% SZS output end Proof for 3088178932660100153757791
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative and not generous is kind or happy. If someone is either not tall or not quiet then someone is funny or creative and vice versa. Everyone who is either not humble or strong is not happy or not kind. Everyone who is not kind is both creative and not kind. If someone is either not creative or not rich then lucy is wise and vice versa. Everyone who is not patient or funny is either not generous or creative. Everyone who is either humble or not happy is both kind and calm. If someone is both kind and not tall then someone is either not quiet or not rich and vice versa. Everyone who is not strong or not rich is both generous and not patient. Everyone who is both not funny and not tall is wise. If mary is either calm or not wise then someone is not kind. If someone is not strong then john is not happy or tall and vice versa. Everyone who is wise or calm is not creative. Everyone who is both not quiet and not strong is both kind and not wise and vice versa. If someone is either not wise or not quiet then paul is both not patient and brave. Everyone who is either not happy or old is either not humble or strong. Fred is both not humble and not kind. Someone is either happy or not happy. Someone is not curious or curious. Someone is both creative and not quiet. Paul is wise. Mary is either kind or wise. Someone is not funny. | Lucy is not kind. | contradiction | (![X]:((creative(X)&~generous(X))=>(kind(X)|happy(X))))&
((?[X]:((~tall(X)<~>~quiet(X))))<=>(?[X]:((funny(X)|creative(X)))))&
(![X]:((~humble(X)<~>strong(X))=>(~happy(X)|~kind(X))))&
(![X]:(~kind(X)=>(creative(X)&~kind(X))))&
((?[X]:((~creative(X)<~>~rich(X))))<=>(wise(lucy)))&
(![X]:((~patient(X)|funny(X))=>(~generous(X)<~>creative(X))))&
(![X]:((humble(X)<~>~happy(X))=>(kind(X)&calm(X))))&
((?[X]:((kind(X)&~tall(X))))<=>(?[X]:((~quiet(X)<~>~rich(X)))))&
(![X]:((~strong(X)|~rich(X))=>(generous(X)&~patient(X))))&
(![X]:((~funny(X)&~tall(X))=>wise(X)))&
(((calm(mary)<~>~wise(mary)))=>(?[X]:(~kind(X))))&
((?[X]:(~strong(X)))<=>((~happy(john)|tall(john))))&
(![X]:((wise(X)|calm(X))=>~creative(X)))&
(![X]:((~quiet(X)&~strong(X))<=>(kind(X)&~wise(X))))&
((?[X]:((~wise(X)<~>~quiet(X))))=>((~patient(paul)&brave(paul))))&
(![X]:((~happy(X)<~>old(X))=>(~humble(X)<~>strong(X))))&
((~humble(fred)&~kind(fred)))&
(?[X]:((happy(X)<~>~happy(X))))&
(?[X]:((~curious(X)|curious(X))))&
(?[X]:((creative(X)&~quiet(X))))&
(wise(paul))&
((kind(mary)<~>wise(mary)))&
(?[X]:(~funny(X))) | ~kind(lucy) | [
"p3",
"p4",
"p5",
"p8",
"p12",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 825097528445991609862965
% SZS output start Proof for 825097528445991609862965
4. ! [X0] : (~kind(X0) => (~kind(X0) & creative(X0))) [input p3]
5. ? [X0] : (~creative(X0) <~> ~rich(X0)) <=> wise(lucy) [input p4]
6. ! [X0] : ((funny(X0) | ~patient(X0)) => (~generous(X0) <~> creative(X0))) [input p5]
9. ! [X0] : ((~rich(X0) | ~strong(X0)) => (~patient(X0) & generous(X0))) [input p8]
13. ! [X0] : ((calm(X0) | wise(X0)) => ~creative(X0)) [input p12]
21. wise(paul) [input p20]
24. ~kind(lucy) [input hypothesis]
32. ! [X0] : ((~kind(X0) & creative(X0)) | kind(X0)) [ennf transformation 4]
33. ! [X0] : ((~generous(X0) <~> creative(X0)) | (~funny(X0) & patient(X0))) [ennf transformation 6]
35. ! [X0] : ((~patient(X0) & generous(X0)) | (rich(X0) & strong(X0))) [ennf transformation 9]
39. ! [X0] : (~creative(X0) | (~calm(X0) & ~wise(X0))) [ennf transformation 13]
48. (? [X0] : ((rich(X0) | creative(X0)) & (~rich(X0) | ~creative(X0))) | ~wise(lucy)) & (wise(lucy) | ! [X0] : ((~creative(X0) | rich(X0)) & (~rich(X0) | creative(X0)))) [nnf transformation 5]
49. (? [X0] : ((rich(X0) | creative(X0)) & (~rich(X0) | ~creative(X0))) | ~wise(lucy)) & (wise(lucy) | ! [X1] : ((~creative(X1) | rich(X1)) & (~rich(X1) | creative(X1)))) [rectify 48]
50. ? [X0] : ((rich(X0) | creative(X0)) & (~rich(X0) | ~creative(X0))) => ((rich(sK2) | creative(sK2)) & (~rich(sK2) | ~creative(sK2))) [choice axiom]
51. (((rich(sK2) | creative(sK2)) & (~rich(sK2) | ~creative(sK2))) | ~wise(lucy)) & (wise(lucy) | ! [X1] : ((~creative(X1) | rich(X1)) & (~rich(X1) | creative(X1)))) [skolemisation 49,50]
52. ! [X0] : (((~creative(X0) | generous(X0)) & (creative(X0) | ~generous(X0))) | (~funny(X0) & patient(X0))) [nnf transformation 33]
90. kind(X0) | creative(X0) [cnf transformation 32]
92. wise(lucy) | ~rich(X1) | creative(X1) [cnf transformation 51]
93. wise(lucy) | ~creative(X1) | rich(X1) [cnf transformation 51]
96. ~generous(X0) | creative(X0) | patient(X0) [cnf transformation 52]
111. rich(X0) | generous(X0) [cnf transformation 35]
113. ~patient(X0) | rich(X0) [cnf transformation 35]
120. ~wise(X0) | ~creative(X0) [cnf transformation 39]
139. wise(paul) [cnf transformation 21]
143. ~kind(lucy) [cnf transformation 24]
179. 9 <=> wise(lucy) [avatar definition]
180. wise(lucy) <- (9) [avatar component clause 179]
193. 12 <=> ! [X1] : (~creative(X1) | rich(X1)) [avatar definition]
194. ~creative(X1) | rich(X1) <- (12) [avatar component clause 193]
195. 12 | 9 [avatar split clause 93,179,193]
197. 13 <=> ! [X1] : (~rich(X1) | creative(X1)) [avatar definition]
198. ~rich(X1) | creative(X1) <- (13) [avatar component clause 197]
199. 13 | 9 [avatar split clause 92,179,197]
281. creative(lucy) [resolution 90,143]
287. ~creative(paul) [resolution 120,139]
288. ~creative(lucy) <- (9) [resolution 120,180]
290. $false <- (9) [subsumption resolution 288,281]
291. ~9 [avatar contradiction clause 290]
301. generous(X0) | creative(X0) <- (13) [resolution 198,111]
534. creative(X0) | creative(X0) | patient(X0) <- (13) [resolution 301,96]
535. patient(X0) | creative(X0) <- (13) [duplicate literal removal 534]
876. creative(X0) | rich(X0) <- (13) [resolution 535,113]
881. rich(X0) <- (12, 13) [subsumption resolution 876,194]
989. creative(X0) <- (12, 13) [resolution 881,198]
1064. $false <- (12, 13) [resolution 989,287]
1069. ~12 | ~13 [avatar contradiction clause 1064]
1071. $false [avatar sat refutation 195,199,291,1069]
% SZS output end Proof for 825097528445991609862965
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5500
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not rich or old is not tall or funny and vice versa. If alice is both wise and patient then someone is both not creative and not calm. If mary is brave or not tall then susan is calm or not patient. If paul is both wise and funny then alice is not creative or not rich. Everyone who is strong is both not humble and not strong and vice versa. If alice is kind or curious then alice is not old and vice versa. If susan is either not brave or creative then someone is either wise or generous and vice versa. Everyone who is both kind and quiet is happy or not tall and vice versa. Everyone who is quiet is not brave. Everyone who is either not calm or not rich is either not tall or not quiet and vice versa. If mary is not kind then someone is funny or not humble. If someone is either old or not curious then susan is either not patient or not brave. Everyone who is old or not calm is both strong and old and vice versa. If john is kind then someone is both old and quiet and vice versa. If someone is not strong then someone is both not patient and not curious. If someone is not brave then paul is either tall or not brave and vice versa. Paul is either not funny or not old. Someone is either not generous or not calm. John is strong or not funny. Lucy is not quiet or not creative. Mary is both not curious and patient. Alice is patient or tall. | John is brave. | contradiction | (![X]:((~rich(X)<~>old(X))<=>(~tall(X)|funny(X))))&
(((wise(alice)&patient(alice)))=>(?[X]:((~creative(X)&~calm(X)))))&
(((brave(mary)|~tall(mary)))=>((calm(susan)|~patient(susan))))&
(((wise(paul)&funny(paul)))=>((~creative(alice)|~rich(alice))))&
(![X]:(strong(X)<=>(~humble(X)&~strong(X))))&
(((kind(alice)|curious(alice)))<=>(~old(alice)))&
(((~brave(susan)<~>creative(susan)))<=>(?[X]:((wise(X)<~>generous(X)))))&
(![X]:((kind(X)&quiet(X))<=>(happy(X)|~tall(X))))&
(![X]:(quiet(X)=>~brave(X)))&
(![X]:((~calm(X)<~>~rich(X))<=>(~tall(X)<~>~quiet(X))))&
((~kind(mary))=>(?[X]:((funny(X)|~humble(X)))))&
((?[X]:((old(X)<~>~curious(X))))=>((~patient(susan)<~>~brave(susan))))&
(![X]:((old(X)|~calm(X))<=>(strong(X)&old(X))))&
((kind(john))<=>(?[X]:((old(X)&quiet(X)))))&
((?[X]:(~strong(X)))=>(?[X]:((~patient(X)&~curious(X)))))&
((?[X]:(~brave(X)))<=>((tall(paul)<~>~brave(paul))))&
((~funny(paul)<~>~old(paul)))&
(?[X]:((~generous(X)<~>~calm(X))))&
((strong(john)|~funny(john)))&
((~quiet(lucy)|~creative(lucy)))&
((~curious(mary)&patient(mary)))&
((patient(alice)|tall(alice))) | brave(john) | [
"p0",
"p4",
"p7",
"p8",
"p9",
"p12",
"p13",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 5717700010073515666717264
% SZS output start Proof for 5717700010073515666717264
1. ! [X0] : ((~rich(X0) <~> old(X0)) <=> (funny(X0) | ~tall(X0))) [input p0]
5. ! [X0] : (strong(X0) <=> (~strong(X0) & ~humble(X0))) [input p4]
8. ! [X0] : ((quiet(X0) & kind(X0)) <=> (~tall(X0) | happy(X0))) [input p7]
9. ! [X0] : (quiet(X0) => ~brave(X0)) [input p8]
10. ! [X0] : ((~calm(X0) <~> ~rich(X0)) <=> (~tall(X0) <~> ~quiet(X0))) [input p9]
13. ! [X0] : ((~calm(X0) | old(X0)) <=> (old(X0) & strong(X0))) [input p12]
14. kind(john) <=> ? [X0] : (quiet(X0) & old(X0)) [input p13]
19. ~funny(john) | strong(john) [input p18]
23. brave(john) [input hypothesis]
31. ! [X0] : (~brave(X0) | ~quiet(X0)) [ennf transformation 9]
35. ! [X0] : ((((~old(X0) | rich(X0)) & (old(X0) | ~rich(X0))) | (~funny(X0) & tall(X0))) & ((funny(X0) | ~tall(X0)) | ((~rich(X0) | ~old(X0)) & (old(X0) | rich(X0))))) [nnf transformation 1]
36. ! [X0] : ((((~old(X0) | rich(X0)) & (old(X0) | ~rich(X0))) | (~funny(X0) & tall(X0))) & (funny(X0) | ~tall(X0) | ((~rich(X0) | ~old(X0)) & (old(X0) | rich(X0))))) [flattening 35]
39. ! [X0] : ((strong(X0) | (strong(X0) | humble(X0))) & ((~strong(X0) & ~humble(X0)) | ~strong(X0))) [nnf transformation 5]
40. ! [X0] : ((strong(X0) | strong(X0) | humble(X0)) & ((~strong(X0) & ~humble(X0)) | ~strong(X0))) [flattening 39]
47. ! [X0] : (((quiet(X0) & kind(X0)) | (tall(X0) & ~happy(X0))) & ((~tall(X0) | happy(X0)) | (~quiet(X0) | ~kind(X0)))) [nnf transformation 8]
48. ! [X0] : (((quiet(X0) & kind(X0)) | (tall(X0) & ~happy(X0))) & (~tall(X0) | happy(X0) | ~quiet(X0) | ~kind(X0))) [flattening 47]
49. ! [X0] : ((((rich(X0) | calm(X0)) & (~rich(X0) | ~calm(X0))) | ((~tall(X0) | quiet(X0)) & (~quiet(X0) | tall(X0)))) & (((quiet(X0) | tall(X0)) & (~quiet(X0) | ~tall(X0))) | ((~calm(X0) | rich(X0)) & (~rich(X0) | calm(X0))))) [nnf transformation 10]
53. ! [X0] : (((~calm(X0) | old(X0)) | (~old(X0) | ~strong(X0))) & ((old(X0) & strong(X0)) | (calm(X0) & ~old(X0)))) [nnf transformation 13]
54. ! [X0] : ((~calm(X0) | old(X0) | ~old(X0) | ~strong(X0)) & ((old(X0) & strong(X0)) | (calm(X0) & ~old(X0)))) [flattening 53]
55. (kind(john) | ! [X0] : (~quiet(X0) | ~old(X0))) & (? [X0] : (quiet(X0) & old(X0)) | ~kind(john)) [nnf transformation 14]
56. (kind(john) | ! [X0] : (~quiet(X0) | ~old(X0))) & (? [X1] : (quiet(X1) & old(X1)) | ~kind(john)) [rectify 55]
57. ? [X1] : (quiet(X1) & old(X1)) => (quiet(sK3) & old(sK3)) [choice axiom]
58. (kind(john) | ! [X0] : (~quiet(X0) | ~old(X0))) & ((quiet(sK3) & old(sK3)) | ~kind(john)) [skolemisation 56,57]
70. ~tall(X0) | funny(X0) | old(X0) | rich(X0) [cnf transformation 36]
82. ~strong(X0) | ~strong(X0) [cnf transformation 40]
97. kind(X0) | tall(X0) [cnf transformation 48]
99. quiet(X0) | tall(X0) [cnf transformation 48]
100. ~quiet(X0) | ~brave(X0) [cnf transformation 31]
106. ~rich(X0) | ~calm(X0) | ~tall(X0) | quiet(X0) [cnf transformation 49]
114. strong(X0) | ~old(X0) [cnf transformation 54]
117. calm(X0) | old(X0) [cnf transformation 54]
119. old(sK3) | ~kind(john) [cnf transformation 58]
132. ~funny(john) | strong(john) [cnf transformation 19]
137. brave(john) [cnf transformation 23]
138. ~strong(X0) [duplicate literal removal 82]
240. ~calm(X0) | ~rich(X0) | quiet(X0) [subsumption resolution 106,99]
266. ~old(X0) [subsumption resolution 114,138]
268. 27 <=> kind(john) [avatar definition]
270. ~kind(john) <- (~27) [avatar component clause 268]
276. ~kind(john) [subsumption resolution 119,266]
277. ~27 [avatar split clause 276,268]
302. ~funny(john) [subsumption resolution 132,138]
319. tall(john) <- (~27) [resolution 97,270]
334. ~rich(X1) | quiet(X1) | old(X1) [resolution 240,117]
336. ~rich(X1) | quiet(X1) [subsumption resolution 334,266]
341. funny(john) | old(john) | rich(john) <- (~27) [resolution 70,319]
343. old(john) | rich(john) <- (~27) [subsumption resolution 341,302]
344. rich(john) <- (~27) [subsumption resolution 343,266]
356. quiet(john) <- (~27) [resolution 344,336]
366. ~brave(john) <- (~27) [resolution 356,100]
367. $false <- (~27) [subsumption resolution 366,137]
368. 27 [avatar contradiction clause 367]
369. $false [avatar sat refutation 277,368]
% SZS output end Proof for 5717700010073515666717264
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous is both wise and not brave.
Everyone who is both not funny and not brave is both kind and not tall.
If someone is not strong then john is either not creative or not funny and vice versa.
If fred is either quiet or not tall then mary is either not funny or quiet.
Everyone who is not old or not strong is both curious and calm and vice versa.
If someone is either not wise or generous then someone is either kind or not old and vice versa.
If someone is humble then susan is old or not tall and vice versa.
Everyone who is both tall and patient is tall or not rich.
Everyone who is not happy or not curious is curious or not humble.
If someone is not funny then paul is old.
Everyone who is either rich or not quiet is calm or not generous.
If someone is either not tall or not strong then someone is rich and vice versa.
Everyone who is kind is either quiet or not calm and vice versa.
Everyone who is either tall or quiet is not curious.
Everyone who is either happy or strong is tall.
Everyone who is curious is both not calm and not tall.
Someone is not curious or not funny.
Susan is not strong or wise.
Someone is wise or not curious.
Someone is both brave and not wise.
Someone is kind.
Paul is not strong or generous.
Lucy is both happy and not wise.
Paul is creative or not rich. | John is not strong. | contradiction | (![X]:(~generous(X)=>(wise(X)&~brave(X))))&
(![X]:((~funny(X)&~brave(X))=>(kind(X)&~tall(X))))&
((?[X]:(~strong(X)))<=>((~creative(john)<~>~funny(john))))&
(((quiet(fred)<~>~tall(fred)))=>((~funny(mary)<~>quiet(mary))))&
(![X]:((~old(X)|~strong(X))<=>(curious(X)&calm(X))))&
((?[X]:((~wise(X)<~>generous(X))))<=>(?[X]:((kind(X)<~>~old(X)))))&
((?[X]:(humble(X)))<=>((old(susan)|~tall(susan))))&
(![X]:((tall(X)&patient(X))=>(tall(X)|~rich(X))))&
(![X]:((~happy(X)|~curious(X))=>(curious(X)|~humble(X))))&
((?[X]:(~funny(X)))=>(old(paul)))&
(![X]:((rich(X)<~>~quiet(X))=>(calm(X)|~generous(X))))&
((?[X]:((~tall(X)<~>~strong(X))))<=>(?[X]:(rich(X))))&
(![X]:(kind(X)<=>(quiet(X)<~>~calm(X))))&
(![X]:((tall(X)<~>quiet(X))=>~curious(X)))&
(![X]:((happy(X)<~>strong(X))=>tall(X)))&
(![X]:(curious(X)=>(~calm(X)&~tall(X))))&
(?[X]:((~curious(X)|~funny(X))))&
((~strong(susan)|wise(susan)))&
(?[X]:((wise(X)|~curious(X))))&
(?[X]:((brave(X)&~wise(X))))&
(?[X]:(kind(X)))&
((~strong(paul)|generous(paul)))&
((happy(lucy)&~wise(lucy)))&
((creative(paul)|~rich(paul))) | ~strong(john) | [
"p4",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 9165191533876223300939804
% SZS output start Proof for 9165191533876223300939804
5. ! [X0] : ((~strong(X0) | ~old(X0)) <=> (calm(X0) & curious(X0))) [input p4]
16. ! [X0] : (curious(X0) => (~tall(X0) & ~calm(X0))) [input p15]
25. ~strong(john) [input hypothesis]
40. ! [X0] : ((~tall(X0) & ~calm(X0)) | ~curious(X0)) [ennf transformation 16]
46. ! [X0] : (((~strong(X0) | ~old(X0)) | (~calm(X0) | ~curious(X0))) & ((calm(X0) & curious(X0)) | (strong(X0) & old(X0)))) [nnf transformation 5]
47. ! [X0] : ((~strong(X0) | ~old(X0) | ~calm(X0) | ~curious(X0)) & ((calm(X0) & curious(X0)) | (strong(X0) & old(X0)))) [flattening 46]
88. curious(X0) | strong(X0) [cnf transformation 47]
90. calm(X0) | strong(X0) [cnf transformation 47]
120. ~calm(X0) | ~curious(X0) [cnf transformation 40]
132. ~strong(john) [cnf transformation 25]
149. 4 <=> ! [X1] : strong(X1) [avatar definition]
150. strong(X1) <- (4) [avatar component clause 149]
315. ~curious(X0) | strong(X0) [resolution 120,90]
317. strong(X0) [subsumption resolution 315,88]
318. 4 [avatar split clause 317,149]
320. $false <- (4) [resolution 150,132]
329. ~4 [avatar contradiction clause 320]
330. $false [avatar sat refutation 318,329]
% SZS output end Proof for 9165191533876223300939804
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong and happy then fred is both not humble and rich.
If mary is rich or happy then fred is either not tall or happy and vice versa.
Everyone who is not rich or humble is not funny or not humble.
If someone is either quiet or not strong then someone is not generous.
Everyone who is not creative is either old or patient and vice versa.
If someone is either not strong or happy then paul is both funny and not brave.
Everyone who is both not humble and not calm is either rich or humble.
If someone is either not calm or not wise then someone is strong or wise and vice versa.
Everyone who is not calm or happy is not humble and vice versa.
Everyone who is either not funny or calm is both funny and not rich.
Everyone who is both brave and not quiet is both generous and not calm and vice versa.
If susan is not tall then someone is either not happy or not old and vice versa.
Everyone who is not calm or not old is not happy.
If someone is humble or old then someone is both happy and not calm and vice versa.
Everyone who is either old or not funny is either quiet or calm.
Everyone who is both quiet and curious is wise or kind and vice versa.
Someone is happy or strong.
John is either not wise or not happy.
Fred is funny.
John is either tall or not kind.
Someone is both curious and not brave. | Fred is not curious. | neutral | ((?[X]:((strong(X)&happy(X))))=>((~humble(fred)&rich(fred))))&
(((rich(mary)|happy(mary)))<=>((~tall(fred)<~>happy(fred))))&
(![X]:((~rich(X)|humble(X))=>(~funny(X)|~humble(X))))&
((?[X]:((quiet(X)<~>~strong(X))))=>(?[X]:(~generous(X))))&
(![X]:(~creative(X)<=>(old(X)<~>patient(X))))&
((?[X]:((~strong(X)<~>happy(X))))=>((funny(paul)&~brave(paul))))&
(![X]:((~humble(X)&~calm(X))=>(rich(X)<~>humble(X))))&
((?[X]:((~calm(X)<~>~wise(X))))<=>(?[X]:((strong(X)|wise(X)))))&
(![X]:((~calm(X)|happy(X))<=>~humble(X)))&
(![X]:((~funny(X)<~>calm(X))=>(funny(X)&~rich(X))))&
(![X]:((brave(X)&~quiet(X))<=>(generous(X)&~calm(X))))&
((~tall(susan))<=>(?[X]:((~happy(X)<~>~old(X)))))&
(![X]:((~calm(X)|~old(X))=>~happy(X)))&
((?[X]:((humble(X)|old(X))))<=>(?[X]:((happy(X)&~calm(X)))))&
(![X]:((old(X)<~>~funny(X))=>(quiet(X)<~>calm(X))))&
(![X]:((quiet(X)&curious(X))<=>(wise(X)|kind(X))))&
(?[X]:((happy(X)|strong(X))))&
((~wise(john)<~>~happy(john)))&
(funny(fred))&
((tall(john)<~>~kind(john)))&
(?[X]:((curious(X)&~brave(X)))) | ~curious(fred) | [] | null | 0 |
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.
Everyone who is either rich or strong is both tall and not creative.
Everyone who is both not generous and not strong is both not tall and not humble and vice versa.
Everyone who is strong or not funny is either humble or generous and vice versa.
If someone is either not kind or rich then fred is either not funny or not strong and vice versa.
Everyone who is either humble or not funny is patient or not calm and vice versa.
Everyone who is both not creative and not strong is either not curious or old and vice versa.
If someone is not strong or not calm then susan is either not kind or patient and vice versa.
Everyone who is not curious or not patient is both not humble and rich.
Everyone who is either not humble or curious is both old and not tall and vice versa.
If someone is both not curious and funny then fred is either calm or not funny.
If someone is not humble then someone is either humble or rich and vice versa.
Everyone who is either not calm or patient is not patient or kind and vice versa.
Fred is either not rich or curious.
Susan is both brave and wise.
Someone is not rich.
Susan is either rich or not humble.
John is kind.
Someone is quiet or not humble. | Fred is creative. | neutral | (((~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]:((rich(X)<~>strong(X))=>(tall(X)&~creative(X))))&
(![X]:((~generous(X)&~strong(X))<=>(~tall(X)&~humble(X))))&
(![X]:((strong(X)|~funny(X))<=>(humble(X)<~>generous(X))))&
((?[X]:((~kind(X)<~>rich(X))))<=>((~funny(fred)<~>~strong(fred))))&
(![X]:((humble(X)<~>~funny(X))<=>(patient(X)|~calm(X))))&
(![X]:((~creative(X)&~strong(X))<=>(~curious(X)<~>old(X))))&
((?[X]:((~strong(X)|~calm(X))))<=>((~kind(susan)<~>patient(susan))))&
(![X]:((~curious(X)|~patient(X))=>(~humble(X)&rich(X))))&
(![X]:((~humble(X)<~>curious(X))<=>(old(X)&~tall(X))))&
((?[X]:((~curious(X)&funny(X))))=>((calm(fred)<~>~funny(fred))))&
((?[X]:(~humble(X)))<=>(?[X]:((humble(X)<~>rich(X)))))&
(![X]:((~calm(X)<~>patient(X))<=>(~patient(X)|kind(X))))&
((~rich(fred)<~>curious(fred)))&
((brave(susan)&wise(susan)))&
(?[X]:(~rich(X)))&
((rich(susan)<~>~humble(susan)))&
(kind(john))&
(?[X]:((quiet(X)|~humble(X)))) | creative(fred) | [] | null | 0 |
Everyone who is both not calm and not rich is both not kind and not creative.
If someone is not curious then someone is either not strong or wise.
Everyone who is either not strong or not happy is not curious and vice versa.
Everyone who is wise is either generous or not happy.
If someone is not funny or not kind then someone is not tall.
Everyone who is either tall or not humble is both tall and calm and vice versa.
If mary is either not rich or patient then lucy is both funny and not old and vice versa.
Everyone who is not tall or not wise is both calm and not kind.
If someone is strong then fred is both not funny and rich.
Everyone who is calm or not quiet is either tall or not rich and vice versa.
Everyone who is both brave and not generous is both not curious and calm.
If lucy is either strong or not brave then someone is not creative.
If paul is not strong then someone is both creative and brave.
If mary is both old and happy then someone is both not wise and quiet.
Everyone who is both not kind and creative is either wise or kind and vice versa.
Everyone who is both wise and creative is either calm or curious.
Someone is brave or not happy.
Someone is both kind and not patient.
Fred is not curious.
Alice is not old or patient.
Someone is either not funny or rich.
Someone is either old or not creative.
John is not curious or not creative.
Fred is either not rich or not strong. | Fred is not happy. | contradiction | (![X]:((~calm(X)&~rich(X))=>(~kind(X)&~creative(X))))&
((?[X]:(~curious(X)))=>(?[X]:((~strong(X)<~>wise(X)))))&
(![X]:((~strong(X)<~>~happy(X))<=>~curious(X)))&
(![X]:(wise(X)=>(generous(X)<~>~happy(X))))&
((?[X]:((~funny(X)|~kind(X))))=>(?[X]:(~tall(X))))&
(![X]:((tall(X)<~>~humble(X))<=>(tall(X)&calm(X))))&
(((~rich(mary)<~>patient(mary)))<=>((funny(lucy)&~old(lucy))))&
(![X]:((~tall(X)|~wise(X))=>(calm(X)&~kind(X))))&
((?[X]:(strong(X)))=>((~funny(fred)&rich(fred))))&
(![X]:((calm(X)|~quiet(X))<=>(tall(X)<~>~rich(X))))&
(![X]:((brave(X)&~generous(X))=>(~curious(X)&calm(X))))&
(((strong(lucy)<~>~brave(lucy)))=>(?[X]:(~creative(X))))&
((~strong(paul))=>(?[X]:((creative(X)&brave(X)))))&
(((old(mary)&happy(mary)))=>(?[X]:((~wise(X)&quiet(X)))))&
(![X]:((~kind(X)&creative(X))<=>(wise(X)<~>kind(X))))&
(![X]:((wise(X)&creative(X))=>(calm(X)<~>curious(X))))&
(?[X]:((brave(X)|~happy(X))))&
(?[X]:((kind(X)&~patient(X))))&
(~curious(fred))&
((~old(alice)|patient(alice)))&
(?[X]:((~funny(X)<~>rich(X))))&
(?[X]:((old(X)<~>~creative(X))))&
((~curious(john)|~creative(john)))&
((~rich(fred)<~>~strong(fred))) | ~happy(fred) | [
"p2",
"p8",
"p18",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 8594937594506562961312886
% SZS output start Proof for 8594937594506562961312886
3. ! [X0] : ((~strong(X0) <~> ~happy(X0)) <=> ~curious(X0)) [input p2]
9. ? [X0] : strong(X0) => (rich(fred) & ~funny(fred)) [input p8]
19. ~curious(fred) [input p18]
24. ~rich(fred) <~> ~strong(fred) [input p23]
25. ~happy(fred) [input hypothesis]
34. (rich(fred) & ~funny(fred)) | ! [X0] : ~strong(X0) [ennf transformation 9]
47. ! [X0] : ((((happy(X0) | strong(X0)) & (~happy(X0) | ~strong(X0))) | curious(X0)) & (~curious(X0) | ((~strong(X0) | happy(X0)) & (~happy(X0) | strong(X0))))) [nnf transformation 3]
78. (strong(fred) | rich(fred)) & (~strong(fred) | ~rich(fred)) [nnf transformation 24]
86. happy(X0) | strong(X0) | curious(X0) [cnf transformation 47]
108. rich(fred) | ~strong(X0) [cnf transformation 34]
134. ~curious(fred) [cnf transformation 19]
141. ~strong(fred) | ~rich(fred) [cnf transformation 78]
143. ~happy(fred) [cnf transformation 25]
196. 11 <=> ! [X0] : ~strong(X0) [avatar definition]
197. ~strong(X0) <- (11) [avatar component clause 196]
199. 12 <=> rich(fred) [avatar definition]
202. 11 | 12 [avatar split clause 108,199,196]
307. 34 <=> strong(fred) [avatar definition]
309. strong(fred) <- (34) [avatar component clause 307]
311. ~12 | ~34 [avatar split clause 141,307,199]
337. strong(fred) | curious(fred) [resolution 86,143]
355. strong(fred) [subsumption resolution 337,134]
356. 34 [avatar split clause 355,307]
374. $false <- (11, 34) [resolution 309,197]
376. ~11 | ~34 [avatar contradiction clause 374]
377. $false [avatar sat refutation 202,311,356,376]
% SZS output end Proof for 8594937594506562961312886
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If someone is humble then susan is quiet or happy.
If someone is both rich and happy then john is both tall and not patient.
Everyone who is both wise and not wise is either rich or old and vice versa.
Everyone who is creative or not creative is wise or not funny and vice versa.
If someone is not generous then mary is either rich or not strong.
Everyone who is not tall or not strong is either not calm or quiet.
Everyone who is funny or not humble is rich or tall.
If mary is both old and not strong then mary is not rich or brave and vice versa.
Everyone who is either creative or not tall is either creative or brave and vice versa.
Everyone who is not kind or not strong is not funny or not wise.
Everyone who is both not calm and wise is patient or not patient.
If someone is old then someone is both kind and not quiet and vice versa.
Everyone who is either not strong or not humble is creative or not funny.
If fred is either not creative or not curious then mary is both not generous and not curious and vice versa.
Everyone who is funny is not calm and vice versa.
If someone is either not funny or not wise then someone is quiet or not funny and vice versa.
John is both not wise and not strong.
Susan is both not strong and creative.
Someone is not calm or happy.
Someone is either generous or rich.
Lucy is funny.
Alice is both not patient and not kind.
Someone is tall.
Someone is kind or not kind. | Alice is not kind. | entailment | ((?[X]:(humble(X)))=>((quiet(susan)|happy(susan))))&
((?[X]:((rich(X)&happy(X))))=>((tall(john)&~patient(john))))&
(![X]:((wise(X)&~wise(X))<=>(rich(X)<~>old(X))))&
(![X]:((creative(X)|~creative(X))<=>(wise(X)|~funny(X))))&
((?[X]:(~generous(X)))=>((rich(mary)<~>~strong(mary))))&
(![X]:((~tall(X)|~strong(X))=>(~calm(X)<~>quiet(X))))&
(![X]:((funny(X)|~humble(X))=>(rich(X)|tall(X))))&
(((old(mary)&~strong(mary)))<=>((~rich(mary)|brave(mary))))&
(![X]:((creative(X)<~>~tall(X))<=>(creative(X)<~>brave(X))))&
(![X]:((~kind(X)|~strong(X))=>(~funny(X)|~wise(X))))&
(![X]:((~calm(X)&wise(X))=>(patient(X)|~patient(X))))&
((?[X]:(old(X)))<=>(?[X]:((kind(X)&~quiet(X)))))&
(![X]:((~strong(X)<~>~humble(X))=>(creative(X)|~funny(X))))&
(((~creative(fred)<~>~curious(fred)))<=>((~generous(mary)&~curious(mary))))&
(![X]:(funny(X)<=>~calm(X)))&
((?[X]:((~funny(X)<~>~wise(X))))<=>(?[X]:((quiet(X)|~funny(X)))))&
((~wise(john)&~strong(john)))&
((~strong(susan)&creative(susan)))&
(?[X]:((~calm(X)|happy(X))))&
(?[X]:((generous(X)<~>rich(X))))&
(funny(lucy))&
((~patient(alice)&~kind(alice)))&
(?[X]:(tall(X)))&
(?[X]:((kind(X)|~kind(X)))) | ~kind(alice) | [
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 1441273196078941953543701
% SZS output start Proof for 1441273196078941953543701
22. ~kind(alice) & ~patient(alice) [input p21]
25. kind(alice) [input hypothesis]
138. ~kind(alice) [cnf transformation 22]
141. kind(alice) [cnf transformation 25]
303. $false [subsumption resolution 141,138]
% SZS output end Proof for 1441273196078941953543701
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not kind or not brave is either happy or not wise and vice versa. If someone is both not kind and not happy then lucy is kind or not creative and vice versa. Everyone who is either wise or kind is not old or not funny. Everyone who is not creative or not happy is generous. Everyone who is either humble or old is both not curious and not humble and vice versa. Everyone who is patient or not generous is rich. Everyone who is either generous or rich is generous and vice versa. Everyone who is not humble is both happy and strong and vice versa. If someone is not wise then fred is both happy and not happy. If someone is tall then lucy is not generous or not patient and vice versa. If someone is not kind then someone is quiet or generous. If fred is brave or not kind then mary is humble. If someone is either not strong or strong then someone is not tall or strong and vice versa. If someone is both happy and not calm then lucy is not creative or strong. Everyone who is either not curious or not strong is calm or not quiet. If susan is wise or not old then someone is curious or rich. Susan is not old. Someone is strong or funny. Alice is both funny and old. Susan is calm or not happy. Alice is not tall or rich. Someone is not strong or not tall. | Lucy is kind. | neutral | (![X]:((~kind(X)<~>~brave(X))<=>(happy(X)<~>~wise(X))))&
((?[X]:((~kind(X)&~happy(X))))<=>((kind(lucy)|~creative(lucy))))&
(![X]:((wise(X)<~>kind(X))=>(~old(X)|~funny(X))))&
(![X]:((~creative(X)|~happy(X))=>generous(X)))&
(![X]:((humble(X)<~>old(X))<=>(~curious(X)&~humble(X))))&
(![X]:((patient(X)|~generous(X))=>rich(X)))&
(![X]:((generous(X)<~>rich(X))<=>generous(X)))&
(![X]:(~humble(X)<=>(happy(X)&strong(X))))&
((?[X]:(~wise(X)))=>((happy(fred)&~happy(fred))))&
((?[X]:(tall(X)))<=>((~generous(lucy)|~patient(lucy))))&
((?[X]:(~kind(X)))=>(?[X]:((quiet(X)|generous(X)))))&
(((brave(fred)|~kind(fred)))=>(humble(mary)))&
((?[X]:((~strong(X)<~>strong(X))))<=>(?[X]:((~tall(X)|strong(X)))))&
((?[X]:((happy(X)&~calm(X))))=>((~creative(lucy)|strong(lucy))))&
(![X]:((~curious(X)<~>~strong(X))=>(calm(X)|~quiet(X))))&
(((wise(susan)|~old(susan)))=>(?[X]:((curious(X)|rich(X)))))&
(~old(susan))&
(?[X]:((strong(X)|funny(X))))&
((funny(alice)&old(alice)))&
((calm(susan)|~happy(susan)))&
((~tall(alice)|rich(alice)))&
(?[X]:((~strong(X)|~tall(X)))) | kind(lucy) | [] | null | 0 |
If susan is either not brave or generous then someone is not generous.
If john is both not brave and patient then someone is generous or not kind.
If john is both not generous and not humble then alice is not curious and vice versa.
Everyone who is both not generous and strong is not funny or funny.
Everyone who is happy is funny.
Everyone who is not patient is either tall or happy and vice versa.
Everyone who is patient is not kind or curious and vice versa.
If alice is both kind and not wise then susan is not quiet.
Everyone who is either not strong or not rich is rich or funny and vice versa.
If someone is both not creative and happy then someone is either not patient or not quiet and vice versa.
If paul is both humble and not patient then someone is not old or not patient and vice versa.
Everyone who is either not funny or not calm is kind or not humble and vice versa.
Everyone who is humble or tall is either not calm or not curious.
Everyone who is either not tall or curious is both brave and not generous and vice versa.
Everyone who is curious is not generous or not tall.
Everyone who is not funny or not rich is not brave or not funny and vice versa.
Fred is either not strong or not generous.
Alice is tall or not creative.
Someone is old.
Mary is strong.
Alice is strong.
John is generous.
John is either strong or not old.
Someone is not happy or curious. | Paul is not patient. | neutral | (((~brave(susan)<~>generous(susan)))=>(?[X]:(~generous(X))))&
(((~brave(john)&patient(john)))=>(?[X]:((generous(X)|~kind(X)))))&
(((~generous(john)&~humble(john)))<=>(~curious(alice)))&
(![X]:((~generous(X)&strong(X))=>(~funny(X)|funny(X))))&
(![X]:(happy(X)=>funny(X)))&
(![X]:(~patient(X)<=>(tall(X)<~>happy(X))))&
(![X]:(patient(X)<=>(~kind(X)|curious(X))))&
(((kind(alice)&~wise(alice)))=>(~quiet(susan)))&
(![X]:((~strong(X)<~>~rich(X))<=>(rich(X)|funny(X))))&
((?[X]:((~creative(X)&happy(X))))<=>(?[X]:((~patient(X)<~>~quiet(X)))))&
(((humble(paul)&~patient(paul)))<=>(?[X]:((~old(X)|~patient(X)))))&
(![X]:((~funny(X)<~>~calm(X))<=>(kind(X)|~humble(X))))&
(![X]:((humble(X)|tall(X))=>(~calm(X)<~>~curious(X))))&
(![X]:((~tall(X)<~>curious(X))<=>(brave(X)&~generous(X))))&
(![X]:(curious(X)=>(~generous(X)|~tall(X))))&
(![X]:((~funny(X)|~rich(X))<=>(~brave(X)|~funny(X))))&
((~strong(fred)<~>~generous(fred)))&
((tall(alice)|~creative(alice)))&
(?[X]:(old(X)))&
(strong(mary))&
(strong(alice))&
(generous(john))&
((strong(john)<~>~old(john)))&
(?[X]:((~happy(X)|curious(X)))) | ~patient(paul) | [] | null | 0 |
Everyone who is creative or not funny is either calm or not patient. Everyone who is not tall is both not quiet and funny and vice versa. If someone is either rich or quiet then mary is not happy or wise and vice versa. Everyone who is not quiet is both quiet and kind and vice versa. If john is not generous or not calm then alice is either not tall or not strong and vice versa. Everyone who is either calm or not old is both generous and funny and vice versa. If alice is either not kind or not generous then paul is not creative. Everyone who is either not old or brave is not funny or wise. If someone is rich then someone is either strong or funny. Everyone who is both not humble and patient is both wise and calm. If paul is both kind and quiet then paul is either strong or creative and vice versa. Everyone who is either not calm or not brave is both not strong and tall. Everyone who is curious or wise is not funny and vice versa. Everyone who is not funny is not rich. If someone is brave then lucy is both not happy and not kind. Everyone who is both calm and not kind is either curious or not happy and vice versa. Susan is calm. Someone is both happy and funny. Paul is quiet or patient. Someone is wise or old. Susan is calm or not quiet. Lucy is generous. Someone is not rich or curious. Someone is not strong. | John is not kind. | entailment | (![X]:((creative(X)|~funny(X))=>(calm(X)<~>~patient(X))))&
(![X]:(~tall(X)<=>(~quiet(X)&funny(X))))&
((?[X]:((rich(X)<~>quiet(X))))<=>((~happy(mary)|wise(mary))))&
(![X]:(~quiet(X)<=>(quiet(X)&kind(X))))&
(((~generous(john)|~calm(john)))<=>((~tall(alice)<~>~strong(alice))))&
(![X]:((calm(X)<~>~old(X))<=>(generous(X)&funny(X))))&
(((~kind(alice)<~>~generous(alice)))=>(~creative(paul)))&
(![X]:((~old(X)<~>brave(X))=>(~funny(X)|wise(X))))&
((?[X]:(rich(X)))=>(?[X]:((strong(X)<~>funny(X)))))&
(![X]:((~humble(X)&patient(X))=>(wise(X)&calm(X))))&
(((kind(paul)&quiet(paul)))<=>((strong(paul)<~>creative(paul))))&
(![X]:((~calm(X)<~>~brave(X))=>(~strong(X)&tall(X))))&
(![X]:((curious(X)|wise(X))<=>~funny(X)))&
(![X]:(~funny(X)=>~rich(X)))&
((?[X]:(brave(X)))=>((~happy(lucy)&~kind(lucy))))&
(![X]:((calm(X)&~kind(X))<=>(curious(X)<~>~happy(X))))&
(calm(susan))&
(?[X]:((happy(X)&funny(X))))&
((quiet(paul)|patient(paul)))&
(?[X]:((wise(X)|old(X))))&
((calm(susan)|~quiet(susan)))&
(generous(lucy))&
(?[X]:((~rich(X)|curious(X))))&
(?[X]:(~strong(X))) | ~kind(john) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 2898116098966656967849184
% SZS output start Proof for 2898116098966656967849184
4. ! [X0] : (~quiet(X0) <=> (kind(X0) & quiet(X0))) [input p3]
25. kind(john) [input hypothesis]
44. ! [X0] : ((~quiet(X0) | (~kind(X0) | ~quiet(X0))) & ((kind(X0) & quiet(X0)) | quiet(X0))) [nnf transformation 4]
45. ! [X0] : ((~quiet(X0) | ~kind(X0) | ~quiet(X0)) & ((kind(X0) & quiet(X0)) | quiet(X0))) [flattening 44]
84. quiet(X0) | quiet(X0) [cnf transformation 45]
86. ~quiet(X0) | ~kind(X0) | ~quiet(X0) [cnf transformation 45]
136. kind(john) [cnf transformation 25]
137. quiet(X0) [duplicate literal removal 84]
138. ~kind(X0) | ~quiet(X0) [duplicate literal removal 86]
272. ~quiet(john) [resolution 138,136]
274. $false [subsumption resolution 272,137]
% SZS output end Proof for 2898116098966656967849184
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not strong and rich is both not curious and not strong and vice versa.
Everyone who is happy or funny is either not strong or patient.
Everyone who is strong or patient is not wise and vice versa.
Everyone who is not patient or not kind is both funny and not happy and vice versa.
Everyone who is either not old or not rich is both not creative and old and vice versa.
Everyone who is both not happy and quiet is not wise.
If paul is quiet then susan is both rich and humble.
Everyone who is either not curious or not quiet is happy.
Everyone who is generous is creative or not happy and vice versa.
If mary is both creative and not quiet then someone is either not generous or not humble.
If lucy is quiet or brave then someone is both not humble and quiet and vice versa.
If lucy is both not kind and not brave then alice is either happy or old and vice versa.
Everyone who is either generous or not old is either rich or quiet and vice versa.
Everyone who is not generous is both happy and not curious.
Everyone who is happy is either not tall or humble.
Alice is not patient or brave.
Someone is curious or not quiet.
Lucy is wise.
Someone is brave or not rich.
Alice is not strong.
Fred is not patient.
John is either funny or not humble.
Someone is not curious or strong. | Fred is not curious. | entailment | (![X]:((~strong(X)&rich(X))<=>(~curious(X)&~strong(X))))&
(![X]:((happy(X)|funny(X))=>(~strong(X)<~>patient(X))))&
(![X]:((strong(X)|patient(X))<=>~wise(X)))&
(![X]:((~patient(X)|~kind(X))<=>(funny(X)&~happy(X))))&
(![X]:((~old(X)<~>~rich(X))<=>(~creative(X)&old(X))))&
(![X]:((~happy(X)&quiet(X))=>~wise(X)))&
((quiet(paul))=>((rich(susan)&humble(susan))))&
(![X]:((~curious(X)<~>~quiet(X))=>happy(X)))&
(![X]:(generous(X)<=>(creative(X)|~happy(X))))&
(((creative(mary)&~quiet(mary)))=>(?[X]:((~generous(X)<~>~humble(X)))))&
(((quiet(lucy)|brave(lucy)))<=>(?[X]:((~humble(X)&quiet(X)))))&
(((~kind(lucy)&~brave(lucy)))<=>((happy(alice)<~>old(alice))))&
(![X]:((generous(X)<~>~old(X))<=>(rich(X)<~>quiet(X))))&
(![X]:(~generous(X)=>(happy(X)&~curious(X))))&
(![X]:(happy(X)=>(~tall(X)<~>humble(X))))&
((~patient(alice)|brave(alice)))&
(?[X]:((curious(X)|~quiet(X))))&
(wise(lucy))&
(?[X]:((brave(X)|~rich(X))))&
(~strong(alice))&
(~patient(fred))&
((funny(john)<~>~humble(john)))&
(?[X]:((~curious(X)|strong(X)))) | ~curious(fred) | [
"p1",
"p2",
"p3",
"p5",
"p7",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 9041604383236690047409584
% SZS output start Proof for 9041604383236690047409584
2. ! [X0] : ((funny(X0) | happy(X0)) => (~strong(X0) <~> patient(X0))) [input p1]
3. ! [X0] : ((patient(X0) | strong(X0)) <=> ~wise(X0)) [input p2]
4. ! [X0] : ((~kind(X0) | ~patient(X0)) <=> (~happy(X0) & funny(X0))) [input p3]
6. ! [X0] : ((quiet(X0) & ~happy(X0)) => ~wise(X0)) [input p5]
8. ! [X0] : ((~curious(X0) <~> ~quiet(X0)) => happy(X0)) [input p7]
21. ~patient(fred) [input p20]
24. curious(fred) [input hypothesis]
25. ! [X0] : ((~strong(X0) <~> patient(X0)) | (~funny(X0) & ~happy(X0))) [ennf transformation 2]
26. ! [X0] : (~wise(X0) | (~quiet(X0) | happy(X0))) [ennf transformation 6]
27. ! [X0] : (~wise(X0) | ~quiet(X0) | happy(X0)) [flattening 26]
29. ! [X0] : (happy(X0) | (~curious(X0) <=> ~quiet(X0))) [ennf transformation 8]
36. ! [X0] : (((~patient(X0) | strong(X0)) & (patient(X0) | ~strong(X0))) | (~funny(X0) & ~happy(X0))) [nnf transformation 25]
37. ! [X0] : (((patient(X0) | strong(X0)) | wise(X0)) & (~wise(X0) | (~patient(X0) & ~strong(X0)))) [nnf transformation 3]
38. ! [X0] : ((patient(X0) | strong(X0) | wise(X0)) & (~wise(X0) | (~patient(X0) & ~strong(X0)))) [flattening 37]
39. ! [X0] : (((~kind(X0) | ~patient(X0)) | (happy(X0) | ~funny(X0))) & ((~happy(X0) & funny(X0)) | (kind(X0) & patient(X0)))) [nnf transformation 4]
40. ! [X0] : ((~kind(X0) | ~patient(X0) | happy(X0) | ~funny(X0)) & ((~happy(X0) & funny(X0)) | (kind(X0) & patient(X0)))) [flattening 39]
43. ! [X0] : (happy(X0) | ((~curious(X0) | quiet(X0)) & (~quiet(X0) | curious(X0)))) [nnf transformation 29]
70. ~funny(X0) | ~strong(X0) | patient(X0) [cnf transformation 36]
75. wise(X0) | strong(X0) | patient(X0) [cnf transformation 38]
76. patient(X0) | funny(X0) [cnf transformation 40]
78. ~happy(X0) | patient(X0) [cnf transformation 40]
87. ~quiet(X0) | ~wise(X0) | happy(X0) [cnf transformation 27]
91. ~curious(X0) | happy(X0) | quiet(X0) [cnf transformation 43]
125. ~patient(fred) [cnf transformation 21]
129. curious(fred) [cnf transformation 24]
258. funny(fred) [resolution 76,125]
264. 26 <=> strong(fred) [avatar definition]
265. ~strong(fred) <- (~26) [avatar component clause 264]
281. ~strong(fred) | patient(fred) [resolution 70,258]
284. ~strong(fred) [subsumption resolution 281,125]
285. ~26 [avatar split clause 284,264]
319. happy(fred) | quiet(fred) [resolution 91,129]
322. 34 <=> quiet(fred) [avatar definition]
324. quiet(fred) <- (34) [avatar component clause 322]
326. 35 <=> happy(fred) [avatar definition]
327. ~happy(fred) <- (~35) [avatar component clause 326]
328. happy(fred) <- (35) [avatar component clause 326]
329. 34 | 35 [avatar split clause 319,326,322]
339. ~wise(fred) | happy(fred) <- (34) [resolution 324,87]
340. ~wise(fred) <- (34, ~35) [subsumption resolution 339,327]
353. strong(fred) | patient(fred) <- (34, ~35) [resolution 340,75]
354. patient(fred) <- (~26, 34, ~35) [subsumption resolution 353,265]
355. $false <- (~26, 34, ~35) [subsumption resolution 354,125]
356. 26 | ~34 | 35 [avatar contradiction clause 355]
366. patient(fred) <- (35) [resolution 328,78]
367. $false <- (35) [subsumption resolution 366,125]
368. ~35 [avatar contradiction clause 367]
369. $false [avatar sat refutation 285,329,356,368]
% SZS output end Proof for 9041604383236690047409584
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not funny is happy or strong.
If john is both not tall and not funny then someone is either tall or not humble and vice versa.
Everyone who is wise is both wise and strong.
Everyone who is quiet is either creative or funny.
If someone is quiet or not rich then someone is not wise.
Everyone who is not kind is both old and happy.
Everyone who is both rich and strong is both not tall and brave and vice versa.
If fred is humble then john is both funny and not tall.
Everyone who is either humble or happy is both strong and happy.
Everyone who is either humble or not kind is either funny or generous and vice versa.
Everyone who is patient or not funny is either quiet or not tall and vice versa.
Everyone who is both quiet and old is both not funny and not kind.
Everyone who is happy or patient is either humble or old and vice versa.
If someone is curious or tall then paul is both not quiet and quiet.
Everyone who is brave is both not funny and patient and vice versa.
Everyone who is tall or funny is either quiet or calm and vice versa.
Fred is either generous or not tall.
Susan is wise or not old.
Someone is not kind.
John is either not funny or funny.
Someone is both not creative and not rich.
Someone is either wise or not rich.
Lucy is kind or not humble. | Paul is tall. | contradiction | (![X]:(~funny(X)=>(happy(X)|strong(X))))&
(((~tall(john)&~funny(john)))<=>(?[X]:((tall(X)<~>~humble(X)))))&
(![X]:(wise(X)=>(wise(X)&strong(X))))&
(![X]:(quiet(X)=>(creative(X)<~>funny(X))))&
((?[X]:((quiet(X)|~rich(X))))=>(?[X]:(~wise(X))))&
(![X]:(~kind(X)=>(old(X)&happy(X))))&
(![X]:((rich(X)&strong(X))<=>(~tall(X)&brave(X))))&
((humble(fred))=>((funny(john)&~tall(john))))&
(![X]:((humble(X)<~>happy(X))=>(strong(X)&happy(X))))&
(![X]:((humble(X)<~>~kind(X))<=>(funny(X)<~>generous(X))))&
(![X]:((patient(X)|~funny(X))<=>(quiet(X)<~>~tall(X))))&
(![X]:((quiet(X)&old(X))=>(~funny(X)&~kind(X))))&
(![X]:((happy(X)|patient(X))<=>(humble(X)<~>old(X))))&
((?[X]:((curious(X)|tall(X))))=>((~quiet(paul)&quiet(paul))))&
(![X]:(brave(X)<=>(~funny(X)&patient(X))))&
(![X]:((tall(X)|funny(X))<=>(quiet(X)<~>calm(X))))&
((generous(fred)<~>~tall(fred)))&
((wise(susan)|~old(susan)))&
(?[X]:(~kind(X)))&
((~funny(john)<~>funny(john)))&
(?[X]:((~creative(X)&~rich(X))))&
(?[X]:((wise(X)<~>~rich(X))))&
((kind(lucy)|~humble(lucy))) | tall(paul) | [
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 4317311151059943154703847
% SZS output start Proof for 4317311151059943154703847
14. ? [X0] : (tall(X0) | curious(X0)) => (quiet(paul) & ~quiet(paul)) [input p13]
24. tall(paul) [input hypothesis]
26. ? [X0] : tall(X0) => (quiet(paul) & ~quiet(paul)) [pure predicate removal 14]
37. (quiet(paul) & ~quiet(paul)) | ! [X0] : ~tall(X0) [ennf transformation 26]
115. ~quiet(paul) | ~tall(X0) [cnf transformation 37]
116. quiet(paul) | ~tall(X0) [cnf transformation 37]
137. tall(paul) [cnf transformation 24]
188. 11 <=> ! [X0] : ~tall(X0) [avatar definition]
189. ~tall(X0) <- (11) [avatar component clause 188]
191. 12 <=> quiet(paul) [avatar definition]
194. 11 | 12 [avatar split clause 116,191,188]
195. 11 | ~12 [avatar split clause 115,191,188]
235. $false <- (11) [resolution 189,137]
236. ~11 [avatar contradiction clause 235]
237. $false [avatar sat refutation 194,195,236]
% SZS output end Proof for 4317311151059943154703847
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not calm or strong is both curious and not old and vice versa. Everyone who is not kind or kind is not patient or not old and vice versa. Everyone who is both tall and not generous is both not rich and not quiet and vice versa. Everyone who is either not creative or not old is not brave or tall. If someone is patient then someone is kind or not happy and vice versa. If someone is not rich or wise then fred is strong or tall. Everyone who is both creative and old is not creative or creative and vice versa. Everyone who is both not curious and not humble is both patient and not happy. If someone is both generous and brave then john is either not quiet or curious. If mary is both funny and not rich then lucy is creative or not rich and vice versa. If someone is tall then someone is not calm or not rich. If alice is either not brave or not wise then paul is not happy or humble. Everyone who is quiet is either not creative or calm. If paul is either not generous or not creative then someone is either not generous or rich. Everyone who is tall or not funny is both not kind and generous and vice versa. If paul is wise or not strong then john is not generous and vice versa. Someone is not rich. Someone is either wise or not old. John is both calm and not brave. Someone is not brave. Alice is either not quiet or not happy. Lucy is both happy and generous. John is not strong or patient. | Alice is creative. | entailment | (![X]:((~calm(X)|strong(X))<=>(curious(X)&~old(X))))&
(![X]:((~kind(X)|kind(X))<=>(~patient(X)|~old(X))))&
(![X]:((tall(X)&~generous(X))<=>(~rich(X)&~quiet(X))))&
(![X]:((~creative(X)<~>~old(X))=>(~brave(X)|tall(X))))&
((?[X]:(patient(X)))<=>(?[X]:((kind(X)|~happy(X)))))&
((?[X]:((~rich(X)|wise(X))))=>((strong(fred)|tall(fred))))&
(![X]:((creative(X)&old(X))<=>(~creative(X)|creative(X))))&
(![X]:((~curious(X)&~humble(X))=>(patient(X)&~happy(X))))&
((?[X]:((generous(X)&brave(X))))=>((~quiet(john)<~>curious(john))))&
(((funny(mary)&~rich(mary)))<=>((creative(lucy)|~rich(lucy))))&
((?[X]:(tall(X)))=>(?[X]:((~calm(X)|~rich(X)))))&
(((~brave(alice)<~>~wise(alice)))=>((~happy(paul)|humble(paul))))&
(![X]:(quiet(X)=>(~creative(X)<~>calm(X))))&
(((~generous(paul)<~>~creative(paul)))=>(?[X]:((~generous(X)<~>rich(X)))))&
(![X]:((tall(X)|~funny(X))<=>(~kind(X)&generous(X))))&
(((wise(paul)|~strong(paul)))<=>(~generous(john)))&
(?[X]:(~rich(X)))&
(?[X]:((wise(X)<~>~old(X))))&
((calm(john)&~brave(john)))&
(?[X]:(~brave(X)))&
((~quiet(alice)<~>~happy(alice)))&
((happy(lucy)&generous(lucy)))&
((~strong(john)|patient(john))) | creative(alice) | [
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 112161725331950584231511
% SZS output start Proof for 112161725331950584231511
7. ! [X0] : ((old(X0) & creative(X0)) <=> (creative(X0) | ~creative(X0))) [input p6]
24. ~creative(alice) [input hypothesis]
49. ! [X0] : (((old(X0) & creative(X0)) | (~creative(X0) & creative(X0))) & ((creative(X0) | ~creative(X0)) | (~old(X0) | ~creative(X0)))) [nnf transformation 7]
50. ! [X0] : (((old(X0) & creative(X0)) | (~creative(X0) & creative(X0))) & (creative(X0) | ~creative(X0) | ~old(X0) | ~creative(X0))) [flattening 49]
89. creative(X0) | creative(X0) [cnf transformation 50]
122. ~creative(alice) [cnf transformation 24]
124. creative(X0) [duplicate literal removal 89]
249. $false [subsumption resolution 122,124]
% SZS output end Proof for 112161725331950584231511
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet and tall is either curious or funny.
If someone is either strong or happy then someone is not quiet or kind and vice versa.
Everyone who is not generous is both generous and strong.
Everyone who is either not generous or not strong is generous or wise and vice versa.
If someone is not patient then someone is either not wise or strong and vice versa.
Everyone who is not rich is not strong or not wise and vice versa.
Everyone who is both curious and creative is patient and vice versa.
If paul is both not happy and curious then someone is both not generous and not kind and vice versa.
Everyone who is not patient is old or creative.
Everyone who is both generous and tall is both kind and not humble.
If someone is brave then fred is both not quiet and not tall and vice versa.
Everyone who is either not happy or not curious is both quiet and kind and vice versa.
Everyone who is either creative or not old is both quiet and brave and vice versa.
Everyone who is calm or not kind is both tall and curious.
If john is both not kind and curious then someone is not patient and vice versa.
Everyone who is brave or calm is either not calm or quiet and vice versa.
Alice is either generous or old.
John is either humble or not quiet.
Someone is either not patient or old.
Mary is either quiet or happy.
Someone is either wise or not generous.
Susan is either funny or curious.
Susan is both not tall and kind. | Mary is strong. | contradiction | (![X]:((~quiet(X)&tall(X))=>(curious(X)<~>funny(X))))&
((?[X]:((strong(X)<~>happy(X))))<=>(?[X]:((~quiet(X)|kind(X)))))&
(![X]:(~generous(X)=>(generous(X)&strong(X))))&
(![X]:((~generous(X)<~>~strong(X))<=>(generous(X)|wise(X))))&
((?[X]:(~patient(X)))<=>(?[X]:((~wise(X)<~>strong(X)))))&
(![X]:(~rich(X)<=>(~strong(X)|~wise(X))))&
(![X]:((curious(X)&creative(X))<=>patient(X)))&
(((~happy(paul)&curious(paul)))<=>(?[X]:((~generous(X)&~kind(X)))))&
(![X]:(~patient(X)=>(old(X)|creative(X))))&
(![X]:((generous(X)&tall(X))=>(kind(X)&~humble(X))))&
((?[X]:(brave(X)))<=>((~quiet(fred)&~tall(fred))))&
(![X]:((~happy(X)<~>~curious(X))<=>(quiet(X)&kind(X))))&
(![X]:((creative(X)<~>~old(X))<=>(quiet(X)&brave(X))))&
(![X]:((calm(X)|~kind(X))=>(tall(X)&curious(X))))&
(((~kind(john)&curious(john)))<=>(?[X]:(~patient(X))))&
(![X]:((brave(X)|calm(X))<=>(~calm(X)<~>quiet(X))))&
((generous(alice)<~>old(alice)))&
((humble(john)<~>~quiet(john)))&
(?[X]:((~patient(X)<~>old(X))))&
((quiet(mary)<~>happy(mary)))&
(?[X]:((wise(X)<~>~generous(X))))&
((funny(susan)<~>curious(susan)))&
((~tall(susan)&kind(susan))) | strong(mary) | [
"p2",
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 7911402601946970072364766
% SZS output start Proof for 7911402601946970072364766
3. ! [X0] : (~generous(X0) => (strong(X0) & generous(X0))) [input p2]
4. ! [X0] : ((~generous(X0) <~> ~strong(X0)) <=> (wise(X0) | generous(X0))) [input p3]
24. strong(mary) [input hypothesis]
29. ! [X0] : ((strong(X0) & generous(X0)) | generous(X0)) [ennf transformation 3]
41. ! [X0] : ((((strong(X0) | generous(X0)) & (~strong(X0) | ~generous(X0))) | (~wise(X0) & ~generous(X0))) & ((wise(X0) | generous(X0)) | ((~generous(X0) | strong(X0)) & (~strong(X0) | generous(X0))))) [nnf transformation 4]
42. ! [X0] : ((((strong(X0) | generous(X0)) & (~strong(X0) | ~generous(X0))) | (~wise(X0) & ~generous(X0))) & (wise(X0) | generous(X0) | ((~generous(X0) | strong(X0)) & (~strong(X0) | generous(X0))))) [flattening 41]
89. generous(X0) | generous(X0) [cnf transformation 29]
93. ~strong(X0) | ~generous(X0) | ~generous(X0) [cnf transformation 42]
153. strong(mary) [cnf transformation 24]
157. ~strong(X0) | ~generous(X0) [duplicate literal removal 93]
158. generous(X0) [duplicate literal removal 89]
194. ~strong(X0) [subsumption resolution 157,158]
301. $false [subsumption resolution 153,194]
% SZS output end Proof for 7911402601946970072364766
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If fred is both calm and not calm then someone is either kind or generous and vice versa.
Everyone who is either kind or happy is calm or kind and vice versa.
If someone is strong or old then someone is either not funny or strong.
Everyone who is strong or wise is patient and vice versa.
If someone is not rich or not generous then alice is not old.
If someone is strong or patient then alice is curious or brave and vice versa.
Everyone who is both not calm and not tall is either not kind or not wise and vice versa.
If someone is not generous or not old then mary is funny and vice versa.
If someone is tall or curious then alice is both patient and not strong.
Everyone who is not humble is either quiet or not funny and vice versa.
Everyone who is not generous or not curious is both kind and patient and vice versa.
Everyone who is either calm or not tall is strong.
Everyone who is tall is both curious and not creative and vice versa.
Everyone who is either not rich or rich is both not wise and old and vice versa.
Everyone who is not creative is either funny or not wise and vice versa.
Someone is not curious or patient.
Someone is not quiet or strong.
Someone is old or not creative.
Someone is either curious or not curious.
Susan is generous or not patient. | Mary is rich. | entailment | (((calm(fred)&~calm(fred)))<=>(?[X]:((kind(X)<~>generous(X)))))&
(![X]:((kind(X)<~>happy(X))<=>(calm(X)|kind(X))))&
((?[X]:((strong(X)|old(X))))=>(?[X]:((~funny(X)<~>strong(X)))))&
(![X]:((strong(X)|wise(X))<=>patient(X)))&
((?[X]:((~rich(X)|~generous(X))))=>(~old(alice)))&
((?[X]:((strong(X)|patient(X))))<=>((curious(alice)|brave(alice))))&
(![X]:((~calm(X)&~tall(X))<=>(~kind(X)<~>~wise(X))))&
((?[X]:((~generous(X)|~old(X))))<=>(funny(mary)))&
((?[X]:((tall(X)|curious(X))))=>((patient(alice)&~strong(alice))))&
(![X]:(~humble(X)<=>(quiet(X)<~>~funny(X))))&
(![X]:((~generous(X)|~curious(X))<=>(kind(X)&patient(X))))&
(![X]:((calm(X)<~>~tall(X))=>strong(X)))&
(![X]:(tall(X)<=>(curious(X)&~creative(X))))&
(![X]:((~rich(X)<~>rich(X))<=>(~wise(X)&old(X))))&
(![X]:(~creative(X)<=>(funny(X)<~>~wise(X))))&
(?[X]:((~curious(X)|patient(X))))&
(?[X]:((~quiet(X)|strong(X))))&
(?[X]:((old(X)|~creative(X))))&
(?[X]:((curious(X)<~>~curious(X))))&
((generous(susan)|~patient(susan))) | rich(mary) | [
"p4",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 7866460184995849937250341
% SZS output start Proof for 7866460184995849937250341
5. ? [X0] : (~generous(X0) | ~rich(X0)) => ~old(alice) [input p4]
14. ! [X0] : ((~rich(X0) <~> rich(X0)) <=> (old(X0) & ~wise(X0))) [input p13]
21. ~rich(mary) [input hypothesis]
25. ~old(alice) | ! [X0] : (generous(X0) & rich(X0)) [ennf transformation 5]
57. ! [X0] : ((((~rich(X0) | rich(X0)) & (rich(X0) | ~rich(X0))) | (~old(X0) | wise(X0))) & ((old(X0) & ~wise(X0)) | ((~rich(X0) | ~rich(X0)) & (rich(X0) | rich(X0))))) [nnf transformation 14]
58. ! [X0] : ((((~rich(X0) | rich(X0)) & (rich(X0) | ~rich(X0))) | ~old(X0) | wise(X0)) & ((old(X0) & ~wise(X0)) | ((~rich(X0) | ~rich(X0)) & (rich(X0) | rich(X0))))) [flattening 57]
86. ~old(alice) | rich(X0) [cnf transformation 25]
117. old(X0) | rich(X0) | rich(X0) [cnf transformation 58]
118. old(X0) | ~rich(X0) | ~rich(X0) [cnf transformation 58]
130. ~rich(mary) [cnf transformation 21]
133. old(X0) | rich(X0) [duplicate literal removal 117]
134. old(X0) | ~rich(X0) [duplicate literal removal 118]
174. 9 <=> old(alice) [avatar definition]
176. ~old(alice) <- (~9) [avatar component clause 174]
179. 10 <=> ! [X0] : rich(X0) [avatar definition]
180. rich(X0) <- (10) [avatar component clause 179]
181. 10 | ~9 [avatar split clause 86,174,179]
217. 18 <=> ! [X1] : old(X1) [avatar definition]
218. old(X1) <- (18) [avatar component clause 217]
239. old(X0) [subsumption resolution 133,134]
240. 18 [avatar split clause 239,217]
257. $false <- (~9, 18) [subsumption resolution 176,218]
258. 9 | ~18 [avatar contradiction clause 257]
260. $false <- (10) [resolution 180,130]
261. ~10 [avatar contradiction clause 260]
262. $false [avatar sat refutation 181,240,258,261]
% SZS output end Proof for 7866460184995849937250341
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet then susan is either kind or quiet and vice versa.
Everyone who is not creative or humble is not happy or not humble and vice versa.
If lucy is humble then someone is not wise and vice versa.
Everyone who is funny or not funny is not calm or not patient and vice versa.
If someone is not happy then someone is both not funny and not happy.
Everyone who is calm or not humble is either not quiet or rich.
If someone is both not happy and humble then someone is either happy or not happy and vice versa.
If someone is both not brave and wise then someone is happy or not happy.
If fred is either patient or not creative then someone is either happy or curious and vice versa.
If someone is not strong or not calm then someone is both brave and not curious.
If someone is either funny or not wise then susan is not wise.
Everyone who is either not happy or brave is either kind or wise.
If someone is either not brave or humble then susan is either not happy or quiet.
Everyone who is either wise or not brave is both curious and generous.
If someone is not quiet then someone is either not kind or not quiet.
Everyone who is either rich or not calm is strong or rich.
Alice is both not funny and brave.
Someone is both not calm and not strong.
Someone is not brave.
Someone is not funny or not humble.
Someone is not old or not kind.
Someone is either not quiet or not happy.
Someone is both not generous and happy.
Someone is not happy. | Lucy is not humble. | contradiction | ((?[X]:(quiet(X)))<=>((kind(susan)<~>quiet(susan))))&
(![X]:((~creative(X)|humble(X))<=>(~happy(X)|~humble(X))))&
((humble(lucy))<=>(?[X]:(~wise(X))))&
(![X]:((funny(X)|~funny(X))<=>(~calm(X)|~patient(X))))&
((?[X]:(~happy(X)))=>(?[X]:((~funny(X)&~happy(X)))))&
(![X]:((calm(X)|~humble(X))=>(~quiet(X)<~>rich(X))))&
((?[X]:((~happy(X)&humble(X))))<=>(?[X]:((happy(X)<~>~happy(X)))))&
((?[X]:((~brave(X)&wise(X))))=>(?[X]:((happy(X)|~happy(X)))))&
(((patient(fred)<~>~creative(fred)))<=>(?[X]:((happy(X)<~>curious(X)))))&
((?[X]:((~strong(X)|~calm(X))))=>(?[X]:((brave(X)&~curious(X)))))&
((?[X]:((funny(X)<~>~wise(X))))=>(~wise(susan)))&
(![X]:((~happy(X)<~>brave(X))=>(kind(X)<~>wise(X))))&
((?[X]:((~brave(X)<~>humble(X))))=>((~happy(susan)<~>quiet(susan))))&
(![X]:((wise(X)<~>~brave(X))=>(curious(X)&generous(X))))&
((?[X]:(~quiet(X)))=>(?[X]:((~kind(X)<~>~quiet(X)))))&
(![X]:((rich(X)<~>~calm(X))=>(strong(X)|rich(X))))&
((~funny(alice)&brave(alice)))&
(?[X]:((~calm(X)&~strong(X))))&
(?[X]:(~brave(X)))&
(?[X]:((~funny(X)|~humble(X))))&
(?[X]:((~old(X)|~kind(X))))&
(?[X]:((~quiet(X)<~>~happy(X))))&
(?[X]:((~generous(X)&happy(X))))&
(?[X]:(~happy(X))) | ~humble(lucy) | [
"p2",
"p9",
"p13",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 4203047060136572152849205
% SZS output start Proof for 4203047060136572152849205
3. humble(lucy) <=> ? [X0] : ~wise(X0) [input p2]
10. ? [X0] : (~calm(X0) | ~strong(X0)) => ? [X0] : (~curious(X0) & brave(X0)) [input p9]
14. ! [X0] : ((wise(X0) <~> ~brave(X0)) => (generous(X0) & curious(X0))) [input p13]
18. ? [X0] : (~strong(X0) & ~calm(X0)) [input p17]
25. ~humble(lucy) [input hypothesis]
29. ? [X0] : (~calm(X0) | ~strong(X0)) => ? [X1] : (~curious(X1) & brave(X1)) [rectify 10]
35. ? [X1] : (~curious(X1) & brave(X1)) | ! [X0] : (calm(X0) & strong(X0)) [ennf transformation 29]
39. ! [X0] : ((generous(X0) & curious(X0)) | (wise(X0) <=> ~brave(X0))) [ennf transformation 14]
49. (humble(lucy) | ! [X0] : wise(X0)) & (? [X0] : ~wise(X0) | ~humble(lucy)) [nnf transformation 3]
50. (humble(lucy) | ! [X0] : wise(X0)) & (? [X1] : ~wise(X1) | ~humble(lucy)) [rectify 49]
51. ? [X1] : ~wise(X1) => ~wise(sK1) [choice axiom]
52. (humble(lucy) | ! [X0] : wise(X0)) & (~wise(sK1) | ~humble(lucy)) [skolemisation 50,51]
71. ? [X0] : (~curious(X0) & brave(X0)) | ! [X1] : (calm(X1) & strong(X1)) [rectify 35]
72. ? [X0] : (~curious(X0) & brave(X0)) => (~curious(sK7) & brave(sK7)) [choice axiom]
73. (~curious(sK7) & brave(sK7)) | ! [X1] : (calm(X1) & strong(X1)) [skolemisation 71,72]
77. ! [X0] : ((generous(X0) & curious(X0)) | ((wise(X0) | brave(X0)) & (~brave(X0) | ~wise(X0)))) [nnf transformation 39]
83. ? [X0] : (~strong(X0) & ~calm(X0)) => (~strong(sK9) & ~calm(sK9)) [choice axiom]
84. ~strong(sK9) & ~calm(sK9) [skolemisation 18,83]
105. humble(lucy) | wise(X0) [cnf transformation 52]
131. brave(sK7) | strong(X1) [cnf transformation 73]
133. ~curious(sK7) | strong(X1) [cnf transformation 73]
145. ~brave(X0) | curious(X0) | ~wise(X0) [cnf transformation 77]
156. ~strong(sK9) [cnf transformation 84]
164. ~humble(lucy) [cnf transformation 25]
192. 5 <=> ! [X0] : wise(X0) [avatar definition]
193. wise(X0) <- (5) [avatar component clause 192]
195. 6 <=> humble(lucy) [avatar definition]
198. 5 | 6 [avatar split clause 105,195,192]
267. 21 <=> curious(sK7) [avatar definition]
269. ~curious(sK7) <- (~21) [avatar component clause 267]
272. 22 <=> ! [X1] : strong(X1) [avatar definition]
273. strong(X1) <- (22) [avatar component clause 272]
274. 22 | ~21 [avatar split clause 133,267,272]
276. 23 <=> brave(sK7) [avatar definition]
278. brave(sK7) <- (23) [avatar component clause 276]
280. 22 | 23 [avatar split clause 131,276,272]
339. ~6 [avatar split clause 164,195]
346. $false <- (22) [resolution 273,156]
347. ~22 [avatar contradiction clause 346]
365. curious(sK7) | ~wise(sK7) <- (23) [resolution 145,278]
367. ~wise(sK7) <- (~21, 23) [subsumption resolution 365,269]
368. $false <- (5, ~21, 23) [subsumption resolution 367,193]
369. ~5 | 21 | ~23 [avatar contradiction clause 368]
370. $false [avatar sat refutation 198,274,280,339,347,369]
% SZS output end Proof for 4203047060136572152849205
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both curious and not kind is both not kind and funny and vice versa.
If john is either not kind or not old then paul is rich or not happy and vice versa.
Everyone who is either patient or not wise is rich or quiet.
Everyone who is calm or not happy is quiet.
Everyone who is not happy is both not generous and not tall and vice versa.
Everyone who is not creative is calm and vice versa.
If susan is not creative or not wise then fred is happy or curious and vice versa.
Everyone who is both not wise and not kind is not tall.
Everyone who is funny or not kind is either strong or not generous and vice versa.
If lucy is either not tall or curious then lucy is not curious or not kind.
Everyone who is funny or creative is calm or not funny and vice versa.
If john is not tall or kind then john is both funny and kind and vice versa.
If john is patient or generous then susan is both not rich and strong.
If susan is both brave and not patient then lucy is patient and vice versa.
If someone is either old or not kind then mary is either not brave or calm and vice versa.
Everyone who is not patient or not old is brave or creative and vice versa.
John is rich or not happy.
Someone is not funny.
Alice is not humble or not kind.
Alice is either not brave or old.
Alice is both creative and not happy.
Lucy is not tall.
Susan is either curious or tall.
Fred is both generous and patient. | Fred is creative. | neutral | (![X]:((curious(X)&~kind(X))<=>(~kind(X)&funny(X))))&
(((~kind(john)<~>~old(john)))<=>((rich(paul)|~happy(paul))))&
(![X]:((patient(X)<~>~wise(X))=>(rich(X)|quiet(X))))&
(![X]:((calm(X)|~happy(X))=>quiet(X)))&
(![X]:(~happy(X)<=>(~generous(X)&~tall(X))))&
(![X]:(~creative(X)<=>calm(X)))&
(((~creative(susan)|~wise(susan)))<=>((happy(fred)|curious(fred))))&
(![X]:((~wise(X)&~kind(X))=>~tall(X)))&
(![X]:((funny(X)|~kind(X))<=>(strong(X)<~>~generous(X))))&
(((~tall(lucy)<~>curious(lucy)))=>((~curious(lucy)|~kind(lucy))))&
(![X]:((funny(X)|creative(X))<=>(calm(X)|~funny(X))))&
(((~tall(john)|kind(john)))<=>((funny(john)&kind(john))))&
(((patient(john)|generous(john)))=>((~rich(susan)&strong(susan))))&
(((brave(susan)&~patient(susan)))<=>(patient(lucy)))&
((?[X]:((old(X)<~>~kind(X))))<=>((~brave(mary)<~>calm(mary))))&
(![X]:((~patient(X)|~old(X))<=>(brave(X)|creative(X))))&
((rich(john)|~happy(john)))&
(?[X]:(~funny(X)))&
((~humble(alice)|~kind(alice)))&
((~brave(alice)<~>old(alice)))&
((creative(alice)&~happy(alice)))&
(~tall(lucy))&
((curious(susan)<~>tall(susan)))&
((generous(fred)&patient(fred))) | creative(fred) | [] | null | 0 |
If someone is both not strong and happy then someone is both happy and strong.
If someone is both not generous and generous then susan is kind or not generous and vice versa.
Everyone who is not patient is both creative and not funny.
If someone is patient then lucy is both funny and humble and vice versa.
Everyone who is generous is not happy or not tall.
Everyone who is both not kind and not calm is humble or not creative and vice versa.
Everyone who is brave or not patient is both not generous and not wise and vice versa.
If john is either patient or brave then mary is not brave.
Everyone who is either not wise or not old is either not tall or brave and vice versa.
If someone is either not calm or brave then someone is either humble or not strong and vice versa.
Everyone who is strong or calm is both old and rich.
If john is both kind and not patient then someone is not quiet.
Everyone who is not calm is either brave or old.
Everyone who is brave or not happy is either humble or not curious.
Everyone who is not calm is patient and vice versa.
Everyone who is both humble and curious is both tall and humble and vice versa.
Paul is either not wise or not generous.
Someone is calm.
Lucy is not creative.
Lucy is either creative or generous.
Paul is wise or patient.
Someone is not strong.
Alice is either not old or brave.
Lucy is tall. | Alice is generous. | contradiction | ((?[X]:((~strong(X)&happy(X))))=>(?[X]:((happy(X)&strong(X)))))&
((?[X]:((~generous(X)&generous(X))))<=>((kind(susan)|~generous(susan))))&
(![X]:(~patient(X)=>(creative(X)&~funny(X))))&
((?[X]:(patient(X)))<=>((funny(lucy)&humble(lucy))))&
(![X]:(generous(X)=>(~happy(X)|~tall(X))))&
(![X]:((~kind(X)&~calm(X))<=>(humble(X)|~creative(X))))&
(![X]:((brave(X)|~patient(X))<=>(~generous(X)&~wise(X))))&
(((patient(john)<~>brave(john)))=>(~brave(mary)))&
(![X]:((~wise(X)<~>~old(X))<=>(~tall(X)<~>brave(X))))&
((?[X]:((~calm(X)<~>brave(X))))<=>(?[X]:((humble(X)<~>~strong(X)))))&
(![X]:((strong(X)|calm(X))=>(old(X)&rich(X))))&
(((kind(john)&~patient(john)))=>(?[X]:(~quiet(X))))&
(![X]:(~calm(X)=>(brave(X)<~>old(X))))&
(![X]:((brave(X)|~happy(X))=>(humble(X)<~>~curious(X))))&
(![X]:(~calm(X)<=>patient(X)))&
(![X]:((humble(X)&curious(X))<=>(tall(X)&humble(X))))&
((~wise(paul)<~>~generous(paul)))&
(?[X]:(calm(X)))&
(~creative(lucy))&
((creative(lucy)<~>generous(lucy)))&
((wise(paul)|patient(paul)))&
(?[X]:(~strong(X)))&
((~old(alice)<~>brave(alice)))&
(tall(lucy)) | generous(alice) | [
"p6",
"p10",
"p12",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 484735184471165279766989
% SZS output start Proof for 484735184471165279766989
7. ! [X0] : ((~patient(X0) | brave(X0)) <=> (~wise(X0) & ~generous(X0))) [input p6]
11. ! [X0] : ((calm(X0) | strong(X0)) => (rich(X0) & old(X0))) [input p10]
13. ! [X0] : (~calm(X0) => (brave(X0) <~> old(X0))) [input p12]
23. ~old(alice) <~> brave(alice) [input p22]
25. generous(alice) [input hypothesis]
29. ! [X0] : ((calm(X0) | strong(X0)) => old(X0)) [pure predicate removal 11]
35. ! [X0] : (old(X0) | (~calm(X0) & ~strong(X0))) [ennf transformation 29]
36. ! [X0] : ((brave(X0) <~> old(X0)) | calm(X0)) [ennf transformation 13]
53. ! [X0] : (((~patient(X0) | brave(X0)) | (wise(X0) | generous(X0))) & ((~wise(X0) & ~generous(X0)) | (patient(X0) & ~brave(X0)))) [nnf transformation 7]
54. ! [X0] : ((~patient(X0) | brave(X0) | wise(X0) | generous(X0)) & ((~wise(X0) & ~generous(X0)) | (patient(X0) & ~brave(X0)))) [flattening 53]
62. ! [X0] : (((~old(X0) | ~brave(X0)) & (old(X0) | brave(X0))) | calm(X0)) [nnf transformation 36]
73. (~brave(alice) | old(alice)) & (brave(alice) | ~old(alice)) [nnf transformation 23]
92. ~brave(X0) | ~generous(X0) [cnf transformation 54]
116. old(X0) | ~calm(X0) [cnf transformation 35]
117. old(X0) | brave(X0) | calm(X0) [cnf transformation 62]
137. brave(alice) | ~old(alice) [cnf transformation 73]
138. ~brave(alice) | old(alice) [cnf transformation 73]
140. generous(alice) [cnf transformation 25]
242. old(X0) | brave(X0) [subsumption resolution 117,116]
255. old(alice) [subsumption resolution 138,242]
256. brave(alice) [subsumption resolution 137,255]
262. ~generous(alice) [resolution 92,256]
263. $false [subsumption resolution 262,140]
% SZS output end Proof for 484735184471165279766989
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If paul is quiet then mary is creative and vice versa.
If someone is not happy or tall then susan is both not generous and wise and vice versa.
If paul is not creative or not patient then someone is not creative or strong and vice versa.
Everyone who is not humble or not generous is humble and vice versa.
Everyone who is humble is kind or not strong.
If lucy is humble then someone is both not creative and not curious and vice versa.
If someone is both strong and not creative then someone is brave or generous and vice versa.
If susan is either creative or not strong then lucy is not curious or not kind and vice versa.
If susan is happy then someone is not kind or happy.
Everyone who is calm is not kind and vice versa.
If susan is not generous or not curious then mary is both strong and happy and vice versa.
Everyone who is not calm is both not brave and wise and vice versa.
If someone is calm or curious then someone is both not happy and not kind.
If john is strong or not strong then fred is brave.
Everyone who is not curious is not rich or calm and vice versa.
If someone is both happy and not quiet then alice is brave.
Someone is not wise.
Someone is brave.
Someone is both not kind and not happy.
Alice is happy.
Someone is not wise or calm.
Someone is not quiet.
Someone is either not humble or not tall. | Mary is not wise. | contradiction | ((quiet(paul))<=>(creative(mary)))&
((?[X]:((~happy(X)|tall(X))))<=>((~generous(susan)&wise(susan))))&
(((~creative(paul)|~patient(paul)))<=>(?[X]:((~creative(X)|strong(X)))))&
(![X]:((~humble(X)|~generous(X))<=>humble(X)))&
(![X]:(humble(X)=>(kind(X)|~strong(X))))&
((humble(lucy))<=>(?[X]:((~creative(X)&~curious(X)))))&
((?[X]:((strong(X)&~creative(X))))<=>(?[X]:((brave(X)|generous(X)))))&
(((creative(susan)<~>~strong(susan)))<=>((~curious(lucy)|~kind(lucy))))&
((happy(susan))=>(?[X]:((~kind(X)|happy(X)))))&
(![X]:(calm(X)<=>~kind(X)))&
(((~generous(susan)|~curious(susan)))<=>((strong(mary)&happy(mary))))&
(![X]:(~calm(X)<=>(~brave(X)&wise(X))))&
((?[X]:((calm(X)|curious(X))))=>(?[X]:((~happy(X)&~kind(X)))))&
(((strong(john)|~strong(john)))=>(brave(fred)))&
(![X]:(~curious(X)<=>(~rich(X)|calm(X))))&
((?[X]:((happy(X)&~quiet(X))))=>(brave(alice)))&
(?[X]:(~wise(X)))&
(?[X]:(brave(X)))&
(?[X]:((~kind(X)&~happy(X))))&
(happy(alice))&
(?[X]:((~wise(X)|calm(X))))&
(?[X]:(~quiet(X)))&
(?[X]:((~humble(X)<~>~tall(X)))) | ~wise(mary) | [
"p3",
"p4",
"p9",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 3506561987898923916960073
% SZS output start Proof for 3506561987898923916960073
4. ! [X0] : ((~generous(X0) | ~humble(X0)) <=> humble(X0)) [input p3]
5. ! [X0] : (humble(X0) => (~strong(X0) | kind(X0))) [input p4]
10. ! [X0] : (calm(X0) <=> ~kind(X0)) [input p9]
11. (~curious(susan) | ~generous(susan)) <=> (happy(mary) & strong(mary)) [input p10]
12. ! [X0] : (~calm(X0) <=> (wise(X0) & ~brave(X0))) [input p11]
24. ~wise(mary) [input hypothesis]
27. ! [X0] : ((~strong(X0) | kind(X0)) | ~humble(X0)) [ennf transformation 5]
28. ! [X0] : (~strong(X0) | kind(X0) | ~humble(X0)) [flattening 27]
44. ! [X0] : (((~generous(X0) | ~humble(X0)) | ~humble(X0)) & (humble(X0) | (generous(X0) & humble(X0)))) [nnf transformation 4]
45. ! [X0] : ((~generous(X0) | ~humble(X0) | ~humble(X0)) & (humble(X0) | (generous(X0) & humble(X0)))) [flattening 44]
59. ! [X0] : ((calm(X0) | kind(X0)) & (~kind(X0) | ~calm(X0))) [nnf transformation 10]
60. ((~curious(susan) | ~generous(susan)) | (~happy(mary) | ~strong(mary))) & ((happy(mary) & strong(mary)) | (curious(susan) & generous(susan))) [nnf transformation 11]
61. (~curious(susan) | ~generous(susan) | ~happy(mary) | ~strong(mary)) & ((happy(mary) & strong(mary)) | (curious(susan) & generous(susan))) [flattening 60]
62. ! [X0] : ((~calm(X0) | (~wise(X0) | brave(X0))) & ((wise(X0) & ~brave(X0)) | calm(X0))) [nnf transformation 12]
63. ! [X0] : ((~calm(X0) | ~wise(X0) | brave(X0)) & ((wise(X0) & ~brave(X0)) | calm(X0))) [flattening 62]
93. humble(X0) | humble(X0) [cnf transformation 45]
95. ~generous(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 45]
96. ~strong(X0) | kind(X0) | ~humble(X0) [cnf transformation 28]
112. ~calm(X0) | ~kind(X0) [cnf transformation 59]
114. strong(mary) | generous(susan) [cnf transformation 61]
120. calm(X0) | wise(X0) [cnf transformation 63]
141. ~wise(mary) [cnf transformation 24]
142. humble(X0) [duplicate literal removal 93]
143. ~humble(X0) | ~generous(X0) [duplicate literal removal 95]
155. 3 <=> generous(susan) [avatar definition]
157. generous(susan) <- (3) [avatar component clause 155]
207. ~strong(X0) | kind(X0) [subsumption resolution 96,142]
211. 15 <=> ! [X1] : ~generous(X1) [avatar definition]
212. ~generous(X1) <- (15) [avatar component clause 211]
276. 29 <=> strong(mary) [avatar definition]
277. strong(mary) <- (29) [avatar component clause 276]
291. 3 | 29 [avatar split clause 114,276,155]
338. ~kind(X0) | wise(X0) [resolution 120,112]
347. ~generous(X1) [resolution 143,142]
349. kind(mary) <- (29) [resolution 207,277]
358. 15 [avatar split clause 347,211]
380. wise(mary) <- (29) [resolution 338,349]
381. $false <- (29) [subsumption resolution 380,141]
382. ~29 [avatar contradiction clause 381]
383. $false <- (3, 15) [subsumption resolution 157,212]
384. ~3 | ~15 [avatar contradiction clause 383]
385. $false [avatar sat refutation 291,358,382,384]
% SZS output end Proof for 3506561987898923916960073
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not happy or not tall is brave and vice versa.
Everyone who is both calm and generous is strong or not brave.
If someone is both not funny and not happy then paul is both not patient and not creative and vice versa.
If someone is either brave or not brave then john is both not tall and not old and vice versa.
Everyone who is either not wise or not curious is either creative or not funny.
Everyone who is not curious or not rich is old and vice versa.
Everyone who is either not creative or creative is not curious or humble.
Everyone who is calm is either kind or not quiet and vice versa.
Everyone who is both strong and not happy is either not calm or not brave.
Everyone who is both funny and not rich is either generous or patient and vice versa.
If john is rich then someone is both not curious and not funny.
Everyone who is not quiet is not patient or wise and vice versa.
Everyone who is quiet or not rich is both quiet and not quiet and vice versa.
If someone is not brave then john is both creative and brave.
If paul is both curious and tall then lucy is either curious or calm.
If fred is either not patient or not curious then someone is not old and vice versa.
Susan is tall.
John is rich or quiet.
Susan is both not curious and not quiet.
Someone is either curious or not quiet.
John is either creative or humble.
Someone is not patient or kind.
Someone is either calm or quiet. | Paul is tall. | neutral | (![X]:((~happy(X)<~>~tall(X))<=>brave(X)))&
(![X]:((calm(X)&generous(X))=>(strong(X)|~brave(X))))&
((?[X]:((~funny(X)&~happy(X))))<=>((~patient(paul)&~creative(paul))))&
((?[X]:((brave(X)<~>~brave(X))))<=>((~tall(john)&~old(john))))&
(![X]:((~wise(X)<~>~curious(X))=>(creative(X)<~>~funny(X))))&
(![X]:((~curious(X)|~rich(X))<=>old(X)))&
(![X]:((~creative(X)<~>creative(X))=>(~curious(X)|humble(X))))&
(![X]:(calm(X)<=>(kind(X)<~>~quiet(X))))&
(![X]:((strong(X)&~happy(X))=>(~calm(X)<~>~brave(X))))&
(![X]:((funny(X)&~rich(X))<=>(generous(X)<~>patient(X))))&
((rich(john))=>(?[X]:((~curious(X)&~funny(X)))))&
(![X]:(~quiet(X)<=>(~patient(X)|wise(X))))&
(![X]:((quiet(X)|~rich(X))<=>(quiet(X)&~quiet(X))))&
((?[X]:(~brave(X)))=>((creative(john)&brave(john))))&
(((curious(paul)&tall(paul)))=>((curious(lucy)<~>calm(lucy))))&
(((~patient(fred)<~>~curious(fred)))<=>(?[X]:(~old(X))))&
(tall(susan))&
((rich(john)|quiet(john)))&
((~curious(susan)&~quiet(susan)))&
(?[X]:((curious(X)<~>~quiet(X))))&
((creative(john)<~>humble(john)))&
(?[X]:((~patient(X)|kind(X))))&
(?[X]:((calm(X)<~>quiet(X)))) | tall(paul) | [] | null | 0 |
Everyone who is wise is either kind or not kind and vice versa.
If paul is either patient or generous then someone is either tall or brave.
Everyone who is both not curious and not funny is curious or not curious.
Everyone who is either not kind or strong is either generous or not wise.
Everyone who is either not quiet or old is both quiet and not rich and vice versa.
If someone is happy or humble then someone is both not humble and strong.
Everyone who is not old or funny is both rich and calm and vice versa.
If paul is not rich then someone is strong or not brave.
Everyone who is either not patient or funny is patient and vice versa.
Everyone who is not happy is not kind or strong and vice versa.
Everyone who is both not generous and brave is not humble or not brave.
Everyone who is calm or not calm is both rich and strong and vice versa.
Everyone who is both patient and not kind is both not curious and not old and vice versa.
Everyone who is not curious or not calm is not wise or not humble.
If john is not calm or not old then someone is patient or generous and vice versa.
Everyone who is either not wise or not tall is tall or strong and vice versa.
Susan is happy or quiet.
John is not wise or patient.
Someone is either not old or strong.
Alice is not kind.
Susan is not brave or generous.
Paul is either kind or not brave. | Susan is tall. | contradiction | (![X]:(wise(X)<=>(kind(X)<~>~kind(X))))&
(((patient(paul)<~>generous(paul)))=>(?[X]:((tall(X)<~>brave(X)))))&
(![X]:((~curious(X)&~funny(X))=>(curious(X)|~curious(X))))&
(![X]:((~kind(X)<~>strong(X))=>(generous(X)<~>~wise(X))))&
(![X]:((~quiet(X)<~>old(X))<=>(quiet(X)&~rich(X))))&
((?[X]:((happy(X)|humble(X))))=>(?[X]:((~humble(X)&strong(X)))))&
(![X]:((~old(X)|funny(X))<=>(rich(X)&calm(X))))&
((~rich(paul))=>(?[X]:((strong(X)|~brave(X)))))&
(![X]:((~patient(X)<~>funny(X))<=>patient(X)))&
(![X]:(~happy(X)<=>(~kind(X)|strong(X))))&
(![X]:((~generous(X)&brave(X))=>(~humble(X)|~brave(X))))&
(![X]:((calm(X)|~calm(X))<=>(rich(X)&strong(X))))&
(![X]:((patient(X)&~kind(X))<=>(~curious(X)&~old(X))))&
(![X]:((~curious(X)|~calm(X))=>(~wise(X)|~humble(X))))&
(((~calm(john)|~old(john)))<=>(?[X]:((patient(X)|generous(X)))))&
(![X]:((~wise(X)<~>~tall(X))<=>(tall(X)|strong(X))))&
((happy(susan)|quiet(susan)))&
((~wise(john)|patient(john)))&
(?[X]:((~old(X)<~>strong(X))))&
(~kind(alice))&
((~brave(susan)|generous(susan)))&
((kind(paul)<~>~brave(paul))) | tall(susan) | [
"p0",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3683570294426894618685438
% SZS output start Proof for 3683570294426894618685438
1. ! [X0] : (wise(X0) <=> (kind(X0) <~> ~kind(X0))) [input p0]
12. ! [X0] : ((~calm(X0) | calm(X0)) <=> (strong(X0) & rich(X0))) [input p11]
16. ! [X0] : ((~wise(X0) <~> ~tall(X0)) <=> (strong(X0) | tall(X0))) [input p15]
23. tall(susan) [input hypothesis]
34. ! [X0] : ((wise(X0) | ((kind(X0) | kind(X0)) & (~kind(X0) | ~kind(X0)))) & (((kind(X0) | ~kind(X0)) & (~kind(X0) | kind(X0))) | ~wise(X0))) [nnf transformation 1]
51. ! [X0] : (((~calm(X0) | calm(X0)) | (~strong(X0) | ~rich(X0))) & ((strong(X0) & rich(X0)) | (calm(X0) & ~calm(X0)))) [nnf transformation 12]
52. ! [X0] : ((~calm(X0) | calm(X0) | ~strong(X0) | ~rich(X0)) & ((strong(X0) & rich(X0)) | (calm(X0) & ~calm(X0)))) [flattening 51]
60. ! [X0] : ((((tall(X0) | wise(X0)) & (~tall(X0) | ~wise(X0))) | (~strong(X0) & ~tall(X0))) & ((strong(X0) | tall(X0)) | ((~wise(X0) | tall(X0)) & (~tall(X0) | wise(X0))))) [nnf transformation 16]
61. ! [X0] : ((((tall(X0) | wise(X0)) & (~tall(X0) | ~wise(X0))) | (~strong(X0) & ~tall(X0))) & (strong(X0) | tall(X0) | ((~wise(X0) | tall(X0)) & (~tall(X0) | wise(X0))))) [flattening 60]
68. wise(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 34]
69. wise(X0) | kind(X0) | kind(X0) [cnf transformation 34]
101. strong(X0) | ~calm(X0) [cnf transformation 52]
102. strong(X0) | calm(X0) [cnf transformation 52]
115. ~tall(X0) | ~wise(X0) | ~strong(X0) [cnf transformation 61]
126. tall(susan) [cnf transformation 23]
134. wise(X0) | ~kind(X0) [duplicate literal removal 68]
135. wise(X0) | kind(X0) [duplicate literal removal 69]
136. wise(X0) [subsumption resolution 134,135]
181. strong(X0) [subsumption resolution 101,102]
209. ~tall(X0) | ~strong(X0) [subsumption resolution 115,136]
210. ~tall(X0) [subsumption resolution 209,181]
241. $false [subsumption resolution 126,210]
% SZS output end Proof for 3683570294426894618685438
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not wise or generous is not generous or not brave and vice versa. If mary is both not calm and happy then lucy is either not strong or funny. Everyone who is not generous or strong is either creative or not strong and vice versa. If someone is brave or old then lucy is not old. If alice is both tall and not funny then someone is not humble and vice versa. If susan is both tall and happy then someone is not brave or humble and vice versa. Everyone who is not rich or generous is humble or brave and vice versa. If john is either not quiet or tall then lucy is both not kind and kind and vice versa. Everyone who is both not creative and not wise is not wise. If lucy is either not wise or old then someone is either not patient or not curious and vice versa. If fred is quiet then someone is funny or generous and vice versa. If fred is either creative or not funny then someone is not wise or tall and vice versa. If lucy is both not wise and not funny then someone is not curious or not strong. Everyone who is either not calm or creative is either wise or not creative. Everyone who is both not humble and happy is creative and vice versa. Everyone who is either creative or not strong is both generous and wise. Someone is not quiet or happy. Mary is both kind and not humble. John is both funny and not tall. Someone is both tall and patient. Fred is not tall. Someone is curious or strong. Mary is generous or not happy. | Fred is wise. | contradiction | (![X]:((~wise(X)<~>generous(X))<=>(~generous(X)|~brave(X))))&
(((~calm(mary)&happy(mary)))=>((~strong(lucy)<~>funny(lucy))))&
(![X]:((~generous(X)|strong(X))<=>(creative(X)<~>~strong(X))))&
((?[X]:((brave(X)|old(X))))=>(~old(lucy)))&
(((tall(alice)&~funny(alice)))<=>(?[X]:(~humble(X))))&
(((tall(susan)&happy(susan)))<=>(?[X]:((~brave(X)|humble(X)))))&
(![X]:((~rich(X)|generous(X))<=>(humble(X)|brave(X))))&
(((~quiet(john)<~>tall(john)))<=>((~kind(lucy)&kind(lucy))))&
(![X]:((~creative(X)&~wise(X))=>~wise(X)))&
(((~wise(lucy)<~>old(lucy)))<=>(?[X]:((~patient(X)<~>~curious(X)))))&
((quiet(fred))<=>(?[X]:((funny(X)|generous(X)))))&
(((creative(fred)<~>~funny(fred)))<=>(?[X]:((~wise(X)|tall(X)))))&
(((~wise(lucy)&~funny(lucy)))=>(?[X]:((~curious(X)|~strong(X)))))&
(![X]:((~calm(X)<~>creative(X))=>(wise(X)<~>~creative(X))))&
(![X]:((~humble(X)&happy(X))<=>creative(X)))&
(![X]:((creative(X)<~>~strong(X))=>(generous(X)&wise(X))))&
(?[X]:((~quiet(X)|happy(X))))&
((kind(mary)&~humble(mary)))&
((funny(john)&~tall(john)))&
(?[X]:((tall(X)&patient(X))))&
(~tall(fred))&
(?[X]:((curious(X)|strong(X))))&
((generous(mary)|~happy(mary))) | wise(fred) | [
"p0",
"p2",
"p6",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8231937346524253343800952
% SZS output start Proof for 8231937346524253343800952
1. ! [X0] : ((~wise(X0) <~> generous(X0)) <=> (~brave(X0) | ~generous(X0))) [input p0]
3. ! [X0] : ((strong(X0) | ~generous(X0)) <=> (creative(X0) <~> ~strong(X0))) [input p2]
7. ! [X0] : ((generous(X0) | ~rich(X0)) <=> (brave(X0) | humble(X0))) [input p6]
15. ! [X0] : ((happy(X0) & ~humble(X0)) <=> creative(X0)) [input p14]
16. ! [X0] : ((creative(X0) <~> ~strong(X0)) => (wise(X0) & generous(X0))) [input p15]
24. wise(fred) [input hypothesis]
33. ! [X0] : ((wise(X0) & generous(X0)) | (creative(X0) <=> ~strong(X0))) [ennf transformation 16]
34. ! [X0] : ((((~generous(X0) | wise(X0)) & (generous(X0) | ~wise(X0))) | (brave(X0) & generous(X0))) & ((~brave(X0) | ~generous(X0)) | ((~wise(X0) | ~generous(X0)) & (generous(X0) | wise(X0))))) [nnf transformation 1]
35. ! [X0] : ((((~generous(X0) | wise(X0)) & (generous(X0) | ~wise(X0))) | (brave(X0) & generous(X0))) & (~brave(X0) | ~generous(X0) | ((~wise(X0) | ~generous(X0)) & (generous(X0) | wise(X0))))) [flattening 34]
37. ! [X0] : (((strong(X0) | ~generous(X0)) | ((creative(X0) | strong(X0)) & (~strong(X0) | ~creative(X0)))) & (((strong(X0) | ~creative(X0)) & (~strong(X0) | creative(X0))) | (~strong(X0) & generous(X0)))) [nnf transformation 3]
38. ! [X0] : ((strong(X0) | ~generous(X0) | ((creative(X0) | strong(X0)) & (~strong(X0) | ~creative(X0)))) & (((strong(X0) | ~creative(X0)) & (~strong(X0) | creative(X0))) | (~strong(X0) & generous(X0)))) [flattening 37]
49. ! [X0] : (((generous(X0) | ~rich(X0)) | (~brave(X0) & ~humble(X0))) & ((brave(X0) | humble(X0)) | (~generous(X0) & rich(X0)))) [nnf transformation 7]
50. ! [X0] : ((generous(X0) | ~rich(X0) | (~brave(X0) & ~humble(X0))) & (brave(X0) | humble(X0) | (~generous(X0) & rich(X0)))) [flattening 49]
68. ! [X0] : (((happy(X0) & ~humble(X0)) | ~creative(X0)) & (creative(X0) | (~happy(X0) | humble(X0)))) [nnf transformation 15]
69. ! [X0] : (((happy(X0) & ~humble(X0)) | ~creative(X0)) & (creative(X0) | ~happy(X0) | humble(X0))) [flattening 68]
70. ! [X0] : ((wise(X0) & generous(X0)) | ((creative(X0) | strong(X0)) & (~strong(X0) | ~creative(X0)))) [nnf transformation 33]
78. ~brave(X0) | ~generous(X0) | ~wise(X0) | ~generous(X0) [cnf transformation 35]
79. generous(X0) | ~wise(X0) | generous(X0) [cnf transformation 35]
86. ~strong(X0) | creative(X0) | ~strong(X0) [cnf transformation 38]
90. strong(X0) | ~generous(X0) | creative(X0) | strong(X0) [cnf transformation 38]
102. ~generous(X0) | humble(X0) | brave(X0) [cnf transformation 50]
135. ~humble(X0) | ~creative(X0) [cnf transformation 69]
138. generous(X0) | creative(X0) | strong(X0) [cnf transformation 70]
151. wise(fred) [cnf transformation 24]
154. ~strong(X0) | creative(X0) [duplicate literal removal 86]
155. strong(X0) | ~generous(X0) | creative(X0) [duplicate literal removal 90]
156. ~brave(X0) | ~generous(X0) | ~wise(X0) [duplicate literal removal 78]
157. ~wise(X0) | generous(X0) [duplicate literal removal 79]
158. ~brave(X0) | ~wise(X0) [subsumption resolution 156,157]
336. creative(X0) | strong(X0) [subsumption resolution 138,155]
337. creative(X0) [subsumption resolution 336,154]
386. generous(fred) [resolution 157,151]
411. humble(fred) | brave(fred) [resolution 102,386]
421. 44 <=> brave(fred) [avatar definition]
423. brave(fred) <- (44) [avatar component clause 421]
425. 45 <=> humble(fred) [avatar definition]
427. humble(fred) <- (45) [avatar component clause 425]
428. 44 | 45 [avatar split clause 411,425,421]
440. ~wise(fred) <- (44) [resolution 423,158]
441. $false <- (44) [subsumption resolution 440,151]
442. ~44 [avatar contradiction clause 441]
446. ~creative(fred) <- (45) [resolution 427,135]
447. $false <- (45) [subsumption resolution 446,337]
448. ~45 [avatar contradiction clause 447]
449. $false [avatar sat refutation 428,442,448]
% SZS output end Proof for 8231937346524253343800952
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not quiet and not generous is either patient or rich and vice versa. Everyone who is generous or not funny is either calm or not brave. Everyone who is either brave or rich is not calm. Everyone who is not wise or brave is both happy and rich. If mary is funny then susan is both brave and not rich. Everyone who is either not curious or old is both rich and not old. If alice is both not happy and not generous then lucy is either not calm or not kind and vice versa. Everyone who is not quiet is brave and vice versa. Everyone who is not brave is not happy or old and vice versa. Everyone who is both quiet and strong is funny and vice versa. Everyone who is patient is both strong and calm and vice versa. Everyone who is funny or not funny is both patient and not humble and vice versa. If someone is both not strong and curious then alice is humble. If someone is not generous or not old then someone is not quiet and vice versa. Everyone who is not patient is funny and vice versa. Everyone who is either old or humble is both creative and wise and vice versa. John is either not brave or creative. Someone is patient or not wise. Susan is either not creative or not patient. Someone is creative or not strong. Lucy is either rich or tall. Someone is not kind. | Susan is happy. | entailment | (![X]:((~quiet(X)&~generous(X))<=>(patient(X)<~>rich(X))))&
(![X]:((generous(X)|~funny(X))=>(calm(X)<~>~brave(X))))&
(![X]:((brave(X)<~>rich(X))=>~calm(X)))&
(![X]:((~wise(X)|brave(X))=>(happy(X)&rich(X))))&
((funny(mary))=>((brave(susan)&~rich(susan))))&
(![X]:((~curious(X)<~>old(X))=>(rich(X)&~old(X))))&
(((~happy(alice)&~generous(alice)))<=>((~calm(lucy)<~>~kind(lucy))))&
(![X]:(~quiet(X)<=>brave(X)))&
(![X]:(~brave(X)<=>(~happy(X)|old(X))))&
(![X]:((quiet(X)&strong(X))<=>funny(X)))&
(![X]:(patient(X)<=>(strong(X)&calm(X))))&
(![X]:((funny(X)|~funny(X))<=>(patient(X)&~humble(X))))&
((?[X]:((~strong(X)&curious(X))))=>(humble(alice)))&
((?[X]:((~generous(X)|~old(X))))<=>(?[X]:(~quiet(X))))&
(![X]:(~patient(X)<=>funny(X)))&
(![X]:((old(X)<~>humble(X))<=>(creative(X)&wise(X))))&
((~brave(john)<~>creative(john)))&
(?[X]:((patient(X)|~wise(X))))&
((~creative(susan)<~>~patient(susan)))&
(?[X]:((creative(X)|~strong(X))))&
((rich(lucy)<~>tall(lucy)))&
(?[X]:(~kind(X))) | happy(susan) | [
"p1",
"p3",
"p7",
"p10",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6533175685614109437427931
% SZS output start Proof for 6533175685614109437427931
2. ! [X0] : ((~funny(X0) | generous(X0)) => (calm(X0) <~> ~brave(X0))) [input p1]
4. ! [X0] : ((brave(X0) | ~wise(X0)) => (rich(X0) & happy(X0))) [input p3]
8. ! [X0] : (~quiet(X0) <=> brave(X0)) [input p7]
11. ! [X0] : (patient(X0) <=> (calm(X0) & strong(X0))) [input p10]
12. ! [X0] : ((~funny(X0) | funny(X0)) <=> (~humble(X0) & patient(X0))) [input p11]
15. ! [X0] : (~patient(X0) <=> funny(X0)) [input p14]
23. ~happy(susan) [input hypothesis]
25. ! [X0] : ((calm(X0) <~> ~brave(X0)) | (funny(X0) & ~generous(X0))) [ennf transformation 2]
27. ! [X0] : ((rich(X0) & happy(X0)) | (~brave(X0) & wise(X0))) [ennf transformation 4]
33. ! [X0] : (((brave(X0) | ~calm(X0)) & (~brave(X0) | calm(X0))) | (funny(X0) & ~generous(X0))) [nnf transformation 25]
38. ! [X0] : ((~quiet(X0) | ~brave(X0)) & (brave(X0) | quiet(X0))) [nnf transformation 8]
43. ! [X0] : ((patient(X0) | (~calm(X0) | ~strong(X0))) & ((calm(X0) & strong(X0)) | ~patient(X0))) [nnf transformation 11]
44. ! [X0] : ((patient(X0) | ~calm(X0) | ~strong(X0)) & ((calm(X0) & strong(X0)) | ~patient(X0))) [flattening 43]
45. ! [X0] : (((~funny(X0) | funny(X0)) | (humble(X0) | ~patient(X0))) & ((~humble(X0) & patient(X0)) | (funny(X0) & ~funny(X0)))) [nnf transformation 12]
46. ! [X0] : ((~funny(X0) | funny(X0) | humble(X0) | ~patient(X0)) & ((~humble(X0) & patient(X0)) | (funny(X0) & ~funny(X0)))) [flattening 45]
52. ! [X0] : ((~patient(X0) | ~funny(X0)) & (funny(X0) | patient(X0))) [nnf transformation 15]
73. ~calm(X0) | brave(X0) | funny(X0) [cnf transformation 33]
77. ~brave(X0) | happy(X0) [cnf transformation 27]
92. brave(X0) | quiet(X0) [cnf transformation 38]
93. ~brave(X0) | ~quiet(X0) [cnf transformation 38]
101. ~patient(X0) | calm(X0) [cnf transformation 44]
103. patient(X0) | ~funny(X0) [cnf transformation 46]
104. funny(X0) | patient(X0) [cnf transformation 46]
113. ~patient(X0) | ~funny(X0) [cnf transformation 52]
129. ~happy(susan) [cnf transformation 23]
168. patient(X0) [subsumption resolution 103,104]
194. ~funny(X0) [subsumption resolution 113,168]
232. happy(X1) | quiet(X1) [resolution 92,77]
237. calm(X0) [resolution 101,168]
249. quiet(susan) [resolution 232,129]
257. brave(X0) | funny(X0) [resolution 73,237]
258. brave(X0) [subsumption resolution 257,194]
262. ~quiet(X2) [resolution 258,93]
267. $false [resolution 262,249]
% SZS output end Proof for 6533175685614109437427931
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is calm is either wise or tall and vice versa.
Everyone who is rich is both wise and not strong and vice versa.
Everyone who is either not old or not happy is not tall or wise.
Everyone who is either curious or not rich is both humble and not patient and vice versa.
Everyone who is humble is both not happy and not old.
Everyone who is not creative is curious or kind.
If someone is either not old or not humble then paul is either not generous or quiet.
Everyone who is either brave or happy is tall or generous and vice versa.
If someone is not happy then mary is curious.
If alice is not wise then fred is not old or brave and vice versa.
If alice is both calm and generous then susan is both not calm and patient and vice versa.
Everyone who is both not curious and kind is not curious or not brave and vice versa.
If paul is not creative then fred is not brave or kind and vice versa.
Everyone who is not wise is old.
If someone is either wise or funny then john is either creative or generous.
Everyone who is not patient or not creative is humble and vice versa.
Someone is either humble or not generous.
Someone is either not humble or calm.
Lucy is both kind and not tall.
Fred is brave.
Someone is either not funny or not calm.
Alice is not calm.
Someone is either quiet or not humble. | Alice is not tall. | entailment | (![X]:(calm(X)<=>(wise(X)<~>tall(X))))&
(![X]:(rich(X)<=>(wise(X)&~strong(X))))&
(![X]:((~old(X)<~>~happy(X))=>(~tall(X)|wise(X))))&
(![X]:((curious(X)<~>~rich(X))<=>(humble(X)&~patient(X))))&
(![X]:(humble(X)=>(~happy(X)&~old(X))))&
(![X]:(~creative(X)=>(curious(X)|kind(X))))&
((?[X]:((~old(X)<~>~humble(X))))=>((~generous(paul)<~>quiet(paul))))&
(![X]:((brave(X)<~>happy(X))<=>(tall(X)|generous(X))))&
((?[X]:(~happy(X)))=>(curious(mary)))&
((~wise(alice))<=>((~old(fred)|brave(fred))))&
(((calm(alice)&generous(alice)))<=>((~calm(susan)&patient(susan))))&
(![X]:((~curious(X)&kind(X))<=>(~curious(X)|~brave(X))))&
((~creative(paul))<=>((~brave(fred)|kind(fred))))&
(![X]:(~wise(X)=>old(X)))&
((?[X]:((wise(X)<~>funny(X))))=>((creative(john)<~>generous(john))))&
(![X]:((~patient(X)|~creative(X))<=>humble(X)))&
(?[X]:((humble(X)<~>~generous(X))))&
(?[X]:((~humble(X)<~>calm(X))))&
((kind(lucy)&~tall(lucy)))&
(brave(fred))&
(?[X]:((~funny(X)<~>~calm(X))))&
(~calm(alice))&
(?[X]:((quiet(X)<~>~humble(X)))) | ~tall(alice) | [
"p0",
"p9",
"p19",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 7422116484155016544241075
% SZS output start Proof for 7422116484155016544241075
1. ! [X0] : (calm(X0) <=> (wise(X0) <~> tall(X0))) [input p0]
10. ~wise(alice) <=> (brave(fred) | ~old(fred)) [input p9]
20. brave(fred) [input p19]
22. ~calm(alice) [input p21]
24. tall(alice) [input hypothesis]
34. ! [X0] : ((calm(X0) | ((wise(X0) | ~tall(X0)) & (tall(X0) | ~wise(X0)))) & (((~tall(X0) | ~wise(X0)) & (tall(X0) | wise(X0))) | ~calm(X0))) [nnf transformation 1]
43. (~wise(alice) | (~brave(fred) & old(fred))) & ((brave(fred) | ~old(fred)) | wise(alice)) [nnf transformation 10]
44. (~wise(alice) | (~brave(fred) & old(fred))) & (brave(fred) | ~old(fred) | wise(alice)) [flattening 43]
69. ~tall(X0) | wise(X0) | calm(X0) [cnf transformation 34]
97. ~wise(alice) | ~brave(fred) [cnf transformation 44]
124. brave(fred) [cnf transformation 20]
127. ~calm(alice) [cnf transformation 22]
130. tall(alice) [cnf transformation 24]
162. 7 <=> brave(fred) [avatar definition]
166. 8 <=> wise(alice) [avatar definition]
168. ~wise(alice) <- (~8) [avatar component clause 166]
169. ~7 | ~8 [avatar split clause 97,166,162]
190. 13 <=> calm(alice) [avatar definition]
191. ~calm(alice) <- (~13) [avatar component clause 190]
246. 7 [avatar split clause 124,162]
257. ~13 [avatar split clause 127,190]
279. wise(alice) | calm(alice) [resolution 69,130]
280. calm(alice) <- (~8) [subsumption resolution 279,168]
281. $false <- (~8, ~13) [subsumption resolution 280,191]
282. 8 | 13 [avatar contradiction clause 281]
283. $false [avatar sat refutation 169,246,257,282]
% SZS output end Proof for 7422116484155016544241075
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not tall or happy is kind and vice versa.
If fred is not funny or strong then fred is both not brave and not quiet.
Everyone who is either patient or funny is both curious and humble.
If susan is both quiet and tall then lucy is not rich.
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.
John is either not tall or brave.
Someone is not calm or calm.
Someone is either not patient or not rich.
Someone is wise.
Alice is both tall and not old.
Someone is not old or not generous. | Lucy is not wise. | contradiction | (![X]:((~tall(X)|happy(X))<=>kind(X)))&
(((~funny(fred)|strong(fred)))=>((~brave(fred)&~quiet(fred))))&
(![X]:((patient(X)<~>funny(X))=>(curious(X)&humble(X))))&
(((quiet(susan)&tall(susan)))=>(~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))))&
((~tall(john)<~>brave(john)))&
(?[X]:((~calm(X)|calm(X))))&
(?[X]:((~patient(X)<~>~rich(X))))&
(?[X]:(wise(X)))&
((tall(alice)&~old(alice)))&
(?[X]:((~old(X)|~generous(X)))) | ~wise(lucy) | [
"p0",
"p6",
"p8",
"p12",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1566488630222648655758332
% SZS output start Proof for 1566488630222648655758332
1. ! [X0] : ((happy(X0) | ~tall(X0)) <=> kind(X0)) [input p0]
7. ? [X0] : (~wise(X0) | ~creative(X0)) => (patient(lucy) & ~curious(lucy)) [input p6]
9. ! [X0] : ((~happy(X0) | tall(X0)) <=> (curious(X0) <~> wise(X0))) [input p8]
13. ! [X0] : (happy(X0) => (~old(X0) & funny(X0))) [input p12]
15. ! [X0] : ((~happy(X0) <~> brave(X0)) <=> (funny(X0) | ~old(X0))) [input p14]
16. ! [X0] : ((brave(X0) <~> ~old(X0)) <=> (kind(X0) | wise(X0))) [input p15]
23. ~wise(lucy) [input hypothesis]
30. (patient(lucy) & ~curious(lucy)) | ! [X0] : (wise(X0) & creative(X0)) [ennf transformation 7]
33. ! [X0] : ((~old(X0) & funny(X0)) | ~happy(X0)) [ennf transformation 13]
35. ! [X0] : (((happy(X0) | ~tall(X0)) | ~kind(X0)) & (kind(X0) | (~happy(X0) & tall(X0)))) [nnf transformation 1]
36. ! [X0] : ((happy(X0) | ~tall(X0) | ~kind(X0)) & (kind(X0) | (~happy(X0) & tall(X0)))) [flattening 35]
41. ! [X0] : (((~happy(X0) | tall(X0)) | ((curious(X0) | ~wise(X0)) & (wise(X0) | ~curious(X0)))) & (((~wise(X0) | ~curious(X0)) & (wise(X0) | curious(X0))) | (happy(X0) & ~tall(X0)))) [nnf transformation 9]
42. ! [X0] : ((~happy(X0) | tall(X0) | ((curious(X0) | ~wise(X0)) & (wise(X0) | ~curious(X0)))) & (((~wise(X0) | ~curious(X0)) & (wise(X0) | curious(X0))) | (happy(X0) & ~tall(X0)))) [flattening 41]
50. ! [X0] : ((((~brave(X0) | happy(X0)) & (brave(X0) | ~happy(X0))) | (~funny(X0) & old(X0))) & ((funny(X0) | ~old(X0)) | ((~happy(X0) | ~brave(X0)) & (brave(X0) | happy(X0))))) [nnf transformation 15]
51. ! [X0] : ((((~brave(X0) | happy(X0)) & (brave(X0) | ~happy(X0))) | (~funny(X0) & old(X0))) & (funny(X0) | ~old(X0) | ((~happy(X0) | ~brave(X0)) & (brave(X0) | happy(X0))))) [flattening 50]
52. ! [X0] : ((((old(X0) | ~brave(X0)) & (~old(X0) | brave(X0))) | (~kind(X0) & ~wise(X0))) & ((kind(X0) | wise(X0)) | ((brave(X0) | old(X0)) & (~old(X0) | ~brave(X0))))) [nnf transformation 16]
53. ! [X0] : ((((old(X0) | ~brave(X0)) & (~old(X0) | brave(X0))) | (~kind(X0) & ~wise(X0))) & (kind(X0) | wise(X0) | ((brave(X0) | old(X0)) & (~old(X0) | ~brave(X0))))) [flattening 52]
63. ~happy(X0) | kind(X0) [cnf transformation 36]
78. ~curious(lucy) | wise(X0) [cnf transformation 30]
84. wise(X0) | curious(X0) | happy(X0) [cnf transformation 42]
101. ~happy(X0) | funny(X0) [cnf transformation 33]
102. ~old(X0) | ~happy(X0) [cnf transformation 33]
108. brave(X0) | ~happy(X0) | ~funny(X0) [cnf transformation 51]
116. ~brave(X0) | old(X0) | ~kind(X0) [cnf transformation 53]
125. ~wise(lucy) [cnf transformation 23]
171. 10 <=> ! [X0] : wise(X0) [avatar definition]
172. wise(X0) <- (10) [avatar component clause 171]
183. 13 <=> curious(lucy) [avatar definition]
185. ~curious(lucy) <- (~13) [avatar component clause 183]
186. 10 | ~13 [avatar split clause 78,183,171]
206. ~happy(X0) | brave(X0) [subsumption resolution 108,101]
273. curious(lucy) | happy(lucy) [resolution 84,125]
274. happy(lucy) <- (~13) [subsumption resolution 273,185]
293. brave(lucy) <- (~13) [resolution 274,206]
295. kind(lucy) <- (~13) [resolution 274,63]
363. old(lucy) | ~kind(lucy) <- (~13) [resolution 116,293]
365. old(lucy) <- (~13) [subsumption resolution 363,295]
569. ~happy(lucy) <- (~13) [resolution 365,102]
571. $false <- (~13) [subsumption resolution 569,274]
572. 13 [avatar contradiction clause 571]
587. $false <- (10) [resolution 172,125]
593. ~10 [avatar contradiction clause 587]
594. $false [avatar sat refutation 186,572,593]
% SZS output end Proof for 1566488630222648655758332
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If susan is not wise or not happy then paul is not calm and vice versa.
Everyone who is both wise and not generous is both quiet and kind and vice versa.
Everyone who is generous is strong.
Everyone who is either rich or not generous is either not happy or not generous and vice versa.
Everyone who is not patient or not funny is not old or not creative.
If someone is both not kind and not humble then someone is rich.
Everyone who is not rich or not quiet is both not tall and rich.
If someone is curious or not happy then someone is generous or not generous and vice versa.
Everyone who is not tall is not funny or not old and vice versa.
Everyone who is creative or rich is not quiet and vice versa.
If alice is not calm then mary is not kind or not curious.
Everyone who is not calm is either strong or not strong and vice versa.
If someone is not humble then someone is old.
Everyone who is not generous or strong is old or not funny and vice versa.
If paul is patient or not quiet then alice is either curious or not brave.
If someone is not calm or humble then someone is either kind or not happy and vice versa.
Alice is humble.
Someone is curious.
Mary is both kind and creative.
Someone is strong or not brave.
Mary is either not funny or not brave.
Someone is funny or humble.
Someone is creative.
Alice is creative. | Mary is kind. | entailment | (((~wise(susan)|~happy(susan)))<=>(~calm(paul)))&
(![X]:((wise(X)&~generous(X))<=>(quiet(X)&kind(X))))&
(![X]:(generous(X)=>strong(X)))&
(![X]:((rich(X)<~>~generous(X))<=>(~happy(X)<~>~generous(X))))&
(![X]:((~patient(X)|~funny(X))=>(~old(X)|~creative(X))))&
((?[X]:((~kind(X)&~humble(X))))=>(?[X]:(rich(X))))&
(![X]:((~rich(X)|~quiet(X))=>(~tall(X)&rich(X))))&
((?[X]:((curious(X)|~happy(X))))<=>(?[X]:((generous(X)|~generous(X)))))&
(![X]:(~tall(X)<=>(~funny(X)|~old(X))))&
(![X]:((creative(X)|rich(X))<=>~quiet(X)))&
((~calm(alice))=>((~kind(mary)|~curious(mary))))&
(![X]:(~calm(X)<=>(strong(X)<~>~strong(X))))&
((?[X]:(~humble(X)))=>(?[X]:(old(X))))&
(![X]:((~generous(X)|strong(X))<=>(old(X)|~funny(X))))&
(((patient(paul)|~quiet(paul)))=>((curious(alice)<~>~brave(alice))))&
((?[X]:((~calm(X)|humble(X))))<=>(?[X]:((kind(X)<~>~happy(X)))))&
(humble(alice))&
(?[X]:(curious(X)))&
((kind(mary)&creative(mary)))&
(?[X]:((strong(X)|~brave(X))))&
((~funny(mary)<~>~brave(mary)))&
(?[X]:((funny(X)|humble(X))))&
(?[X]:(creative(X)))&
(creative(alice)) | kind(mary) | [
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 4491652540550286033155945
% SZS output start Proof for 4491652540550286033155945
19. creative(mary) & kind(mary) [input p18]
25. ~kind(mary) [input hypothesis]
131. kind(mary) [cnf transformation 19]
139. ~kind(mary) [cnf transformation 25]
194. 11 <=> kind(mary) [avatar definition]
246. 11 [avatar split clause 131,194]
275. ~11 [avatar split clause 139,194]
276. $false [avatar sat refutation 246,275]
% SZS output end Proof for 4491652540550286033155945
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not creative or tall is not funny. If someone is both rich and not old then fred is both not creative and not patient and vice versa. Everyone who is either curious or tall is not happy and vice versa. If john is not strong or not kind then fred is both not happy and humble. Everyone who is not humble is either wise or rich. If alice is both generous and humble then someone is wise or not humble. If fred is kind or wise then someone is either patient or not humble. If john is calm or not strong then alice is both patient and quiet and vice versa. Everyone who is not creative or not rich is not generous or not brave and vice versa. Everyone who is either humble or not tall is curious and vice versa. Everyone who is either funny or not wise is both not old and humble and vice versa. If fred is creative or not rich then fred is generous and vice versa. If someone is rich or not brave then paul is not old or wise. Everyone who is both not curious and rich is either strong or quiet and vice versa. Everyone who is both brave and not patient is either not rich or funny and vice versa. If someone is both not wise and not strong then alice is either not patient or kind. Paul is both funny and not wise. Alice is both wise and not quiet. Mary is strong. Lucy is both old and not generous. Someone is not creative or funny. Someone is brave or quiet. | Paul is not quiet. | neutral | (![X]:((~creative(X)|tall(X))=>~funny(X)))&
((?[X]:((rich(X)&~old(X))))<=>((~creative(fred)&~patient(fred))))&
(![X]:((curious(X)<~>tall(X))<=>~happy(X)))&
(((~strong(john)|~kind(john)))=>((~happy(fred)&humble(fred))))&
(![X]:(~humble(X)=>(wise(X)<~>rich(X))))&
(((generous(alice)&humble(alice)))=>(?[X]:((wise(X)|~humble(X)))))&
(((kind(fred)|wise(fred)))=>(?[X]:((patient(X)<~>~humble(X)))))&
(((calm(john)|~strong(john)))<=>((patient(alice)&quiet(alice))))&
(![X]:((~creative(X)|~rich(X))<=>(~generous(X)|~brave(X))))&
(![X]:((humble(X)<~>~tall(X))<=>curious(X)))&
(![X]:((funny(X)<~>~wise(X))<=>(~old(X)&humble(X))))&
(((creative(fred)|~rich(fred)))<=>(generous(fred)))&
((?[X]:((rich(X)|~brave(X))))=>((~old(paul)|wise(paul))))&
(![X]:((~curious(X)&rich(X))<=>(strong(X)<~>quiet(X))))&
(![X]:((brave(X)&~patient(X))<=>(~rich(X)<~>funny(X))))&
((?[X]:((~wise(X)&~strong(X))))=>((~patient(alice)<~>kind(alice))))&
((funny(paul)&~wise(paul)))&
((wise(alice)&~quiet(alice)))&
(strong(mary))&
((old(lucy)&~generous(lucy)))&
(?[X]:((~creative(X)|funny(X))))&
(?[X]:((brave(X)|quiet(X)))) | ~quiet(paul) | [] | null | 0 |
Everyone who is either tall or calm is both curious and not kind and vice versa. If someone is creative then someone is not humble and vice versa. If someone is either not quiet or wise then someone is both rich and not quiet and vice versa. Everyone who is not old or tall is both happy and not calm and vice versa. Everyone who is either old or not kind is both kind and patient. Everyone who is strong is either not funny or not curious. Everyone who is not calm or not rich is not tall and vice versa. If someone is both not old and tall then someone is not humble and vice versa. If alice is not quiet then someone is patient or wise and vice versa. If lucy is either not brave or not old then someone is not tall. If someone is both funny and quiet then fred is not kind or not calm. Everyone who is both not quiet and not rich is not wise. If someone is quiet or brave then mary is happy or rich. If mary is not wise or not curious then someone is not creative. Everyone who is not funny or old is both quiet and creative. If someone is not curious then someone is both not creative and wise. Someone is not patient or not quiet. Someone is rich. Someone is both kind and funny. Someone is both brave and not old. Someone is not curious. | Lucy is funny. | entailment | (![X]:((tall(X)<~>calm(X))<=>(curious(X)&~kind(X))))&
((?[X]:(creative(X)))<=>(?[X]:(~humble(X))))&
((?[X]:((~quiet(X)<~>wise(X))))<=>(?[X]:((rich(X)&~quiet(X)))))&
(![X]:((~old(X)|tall(X))<=>(happy(X)&~calm(X))))&
(![X]:((old(X)<~>~kind(X))=>(kind(X)&patient(X))))&
(![X]:(strong(X)=>(~funny(X)<~>~curious(X))))&
(![X]:((~calm(X)|~rich(X))<=>~tall(X)))&
((?[X]:((~old(X)&tall(X))))<=>(?[X]:(~humble(X))))&
((~quiet(alice))<=>(?[X]:((patient(X)|wise(X)))))&
(((~brave(lucy)<~>~old(lucy)))=>(?[X]:(~tall(X))))&
((?[X]:((funny(X)&quiet(X))))=>((~kind(fred)|~calm(fred))))&
(![X]:((~quiet(X)&~rich(X))=>~wise(X)))&
((?[X]:((quiet(X)|brave(X))))=>((happy(mary)|rich(mary))))&
(((~wise(mary)|~curious(mary)))=>(?[X]:(~creative(X))))&
(![X]:((~funny(X)|old(X))=>(quiet(X)&creative(X))))&
((?[X]:(~curious(X)))=>(?[X]:((~creative(X)&wise(X)))))&
(?[X]:((~patient(X)|~quiet(X))))&
(?[X]:(rich(X)))&
(?[X]:((kind(X)&funny(X))))&
(?[X]:((brave(X)&~old(X))))&
(?[X]:(~curious(X))) | funny(lucy) | [
"p1",
"p3",
"p6",
"p7",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 464765940658376736735704
% SZS output start Proof for 464765940658376736735704
2. ? [X0] : creative(X0) <=> ? [X0] : ~humble(X0) [input p1]
4. ! [X0] : ((tall(X0) | ~old(X0)) <=> (~calm(X0) & happy(X0))) [input p3]
7. ! [X0] : ((~rich(X0) | ~calm(X0)) <=> ~tall(X0)) [input p6]
8. ? [X0] : (tall(X0) & ~old(X0)) <=> ? [X0] : ~humble(X0) [input p7]
15. ! [X0] : ((old(X0) | ~funny(X0)) => (creative(X0) & quiet(X0))) [input p14]
22. ~funny(lucy) [input hypothesis]
23. ? [X0] : creative(X0) <=> ? [X1] : ~humble(X1) [rectify 2]
25. ? [X0] : (tall(X0) & ~old(X0)) <=> ? [X1] : ~humble(X1) [rectify 8]
37. ! [X0] : ((creative(X0) & quiet(X0)) | (~old(X0) & funny(X0))) [ennf transformation 15]
41. (? [X0] : creative(X0) | ! [X1] : humble(X1)) & (? [X1] : ~humble(X1) | ! [X0] : ~creative(X0)) [nnf transformation 23]
42. (? [X0] : creative(X0) | ! [X1] : humble(X1)) & (? [X2] : ~humble(X2) | ! [X3] : ~creative(X3)) [rectify 41]
43. ? [X0] : creative(X0) => creative(sK0) [choice axiom]
44. ? [X2] : ~humble(X2) => ~humble(sK1) [choice axiom]
45. (creative(sK0) | ! [X1] : humble(X1)) & (~humble(sK1) | ! [X3] : ~creative(X3)) [skolemisation 42,44,43]
51. ! [X0] : (((tall(X0) | ~old(X0)) | (calm(X0) | ~happy(X0))) & ((~calm(X0) & happy(X0)) | (~tall(X0) & old(X0)))) [nnf transformation 4]
52. ! [X0] : ((tall(X0) | ~old(X0) | calm(X0) | ~happy(X0)) & ((~calm(X0) & happy(X0)) | (~tall(X0) & old(X0)))) [flattening 51]
54. ! [X0] : (((~rich(X0) | ~calm(X0)) | tall(X0)) & (~tall(X0) | (rich(X0) & calm(X0)))) [nnf transformation 7]
55. ! [X0] : ((~rich(X0) | ~calm(X0) | tall(X0)) & (~tall(X0) | (rich(X0) & calm(X0)))) [flattening 54]
56. (? [X0] : (tall(X0) & ~old(X0)) | ! [X1] : humble(X1)) & (? [X1] : ~humble(X1) | ! [X0] : (~tall(X0) | old(X0))) [nnf transformation 25]
57. (? [X0] : (tall(X0) & ~old(X0)) | ! [X1] : humble(X1)) & (? [X2] : ~humble(X2) | ! [X3] : (~tall(X3) | old(X3))) [rectify 56]
58. ? [X0] : (tall(X0) & ~old(X0)) => (tall(sK4) & ~old(sK4)) [choice axiom]
59. ? [X2] : ~humble(X2) => ~humble(sK5) [choice axiom]
60. ((tall(sK4) & ~old(sK4)) | ! [X1] : humble(X1)) & (~humble(sK5) | ! [X3] : (~tall(X3) | old(X3))) [skolemisation 57,59,58]
89. ~humble(sK1) | ~creative(X3) [cnf transformation 45]
100. ~calm(X0) | ~tall(X0) [cnf transformation 52]
106. ~tall(X0) | calm(X0) [cnf transformation 55]
111. tall(sK4) | humble(X1) [cnf transformation 60]
125. funny(X0) | creative(X0) [cnf transformation 37]
136. ~funny(lucy) [cnf transformation 22]
139. 1 <=> ! [X1] : humble(X1) [avatar definition]
140. humble(X1) <- (1) [avatar component clause 139]
147. 3 <=> ! [X3] : ~creative(X3) [avatar definition]
148. ~creative(X3) <- (3) [avatar component clause 147]
150. 4 <=> humble(sK1) [avatar definition]
152. ~humble(sK1) <- (~4) [avatar component clause 150]
153. 3 | ~4 [avatar split clause 89,150,147]
186. ~tall(X0) [subsumption resolution 106,100]
187. humble(X1) [subsumption resolution 111,186]
188. 1 [avatar split clause 187,139]
282. $false <- (1, ~4) [resolution 152,140]
283. ~1 | 4 [avatar contradiction clause 282]
291. creative(lucy) [resolution 125,136]
292. $false <- (3) [subsumption resolution 291,148]
293. ~3 [avatar contradiction clause 292]
294. $false [avatar sat refutation 153,188,283,293]
% SZS output end Proof for 464765940658376736735704
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or not happy is rich.
Everyone who is not quiet is wise.
If john is generous or not rich then mary is either quiet or patient.
If someone is not quiet or strong then john is old or not wise.
If someone is quiet or patient then paul is not humble and vice versa.
If someone is both humble and happy then someone is both curious and not patient and vice versa.
Everyone who is both not strong and humble is both not creative and curious and vice versa.
If someone is old or kind then someone is both not brave and not creative and vice versa.
Everyone who is both funny and calm is not humble and vice versa.
If someone is either not brave or not tall then alice is not quiet or brave.
Everyone who is not curious is both calm and not strong and vice versa.
Everyone who is calm or creative is quiet or strong.
Everyone who is both not brave and tall is either creative or brave and vice versa.
Everyone who is quiet or humble is both not calm and not tall and vice versa.
Everyone who is both kind and humble is either not curious or not tall.
Susan is both not old and not kind.
Someone is not humble or patient. | Alice is not curious. | contradiction | (![X]:((creative(X)|~happy(X))=>rich(X)))&
(![X]:(~quiet(X)=>wise(X)))&
(((generous(john)|~rich(john)))=>((quiet(mary)<~>patient(mary))))&
((?[X]:((~quiet(X)|strong(X))))=>((old(john)|~wise(john))))&
((?[X]:((quiet(X)|patient(X))))<=>(~humble(paul)))&
((?[X]:((humble(X)&happy(X))))<=>(?[X]:((curious(X)&~patient(X)))))&
(![X]:((~strong(X)&humble(X))<=>(~creative(X)&curious(X))))&
((?[X]:((old(X)|kind(X))))<=>(?[X]:((~brave(X)&~creative(X)))))&
(![X]:((funny(X)&calm(X))<=>~humble(X)))&
((?[X]:((~brave(X)<~>~tall(X))))=>((~quiet(alice)|brave(alice))))&
(![X]:(~curious(X)<=>(calm(X)&~strong(X))))&
(![X]:((calm(X)|creative(X))=>(quiet(X)|strong(X))))&
(![X]:((~brave(X)&tall(X))<=>(creative(X)<~>brave(X))))&
(![X]:((quiet(X)|humble(X))<=>(~calm(X)&~tall(X))))&
(![X]:((kind(X)&humble(X))=>(~curious(X)<~>~tall(X))))&
((~old(susan)&~kind(susan)))&
(?[X]:((~humble(X)|patient(X)))) | ~curious(alice) | [
"p10",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 1144274759372198696333066
% SZS output start Proof for 1144274759372198696333066
11. ! [X0] : (~curious(X0) <=> (~strong(X0) & calm(X0))) [input p10]
12. ! [X0] : ((creative(X0) | calm(X0)) => (strong(X0) | quiet(X0))) [input p11]
14. ! [X0] : ((humble(X0) | quiet(X0)) <=> (~tall(X0) & ~calm(X0))) [input p13]
18. ~curious(alice) [input hypothesis]
29. ! [X0] : ((strong(X0) | quiet(X0)) | (~creative(X0) & ~calm(X0))) [ennf transformation 12]
30. ! [X0] : (strong(X0) | quiet(X0) | (~creative(X0) & ~calm(X0))) [flattening 29]
52. ! [X0] : ((~curious(X0) | (strong(X0) | ~calm(X0))) & ((~strong(X0) & calm(X0)) | curious(X0))) [nnf transformation 11]
53. ! [X0] : ((~curious(X0) | strong(X0) | ~calm(X0)) & ((~strong(X0) & calm(X0)) | curious(X0))) [flattening 52]
56. ! [X0] : (((humble(X0) | quiet(X0)) | (tall(X0) | calm(X0))) & ((~tall(X0) & ~calm(X0)) | (~humble(X0) & ~quiet(X0)))) [nnf transformation 14]
57. ! [X0] : ((humble(X0) | quiet(X0) | tall(X0) | calm(X0)) & ((~tall(X0) & ~calm(X0)) | (~humble(X0) & ~quiet(X0)))) [flattening 56]
85. calm(X0) | curious(X0) [cnf transformation 53]
86. ~strong(X0) | curious(X0) [cnf transformation 53]
88. ~calm(X0) | quiet(X0) | strong(X0) [cnf transformation 30]
96. ~calm(X0) | ~quiet(X0) [cnf transformation 57]
106. ~curious(alice) [cnf transformation 18]
233. ~quiet(X0) | curious(X0) [resolution 96,85]
283. quiet(X0) | strong(X0) | curious(X0) [resolution 88,85]
285. strong(X0) | curious(X0) [subsumption resolution 283,233]
286. curious(X0) [subsumption resolution 285,86]
288. $false [resolution 286,106]
% SZS output end Proof for 1144274759372198696333066
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient and not old is either calm or not brave and vice versa.
Everyone who is not tall is both wise and calm and vice versa.
Everyone who is both calm and patient is both not strong and funny.
Everyone who is either not patient or generous is both not quiet and calm and vice versa.
Everyone who is quiet or not generous is either not kind or not humble and vice versa.
Everyone who is either brave or curious is kind.
Everyone who is not brave or not quiet is both not patient and not old and vice versa.
Everyone who is curious is either creative or not humble.
If fred is brave or not kind then someone is both creative and old.
Everyone who is wise is either strong or humble.
Everyone who is rich is both not happy and patient.
Everyone who is both not quiet and patient is either patient or tall and vice versa.
Everyone who is not quiet is either strong or not brave and vice versa.
Everyone who is both creative and brave is not humble or happy and vice versa.
Everyone who is funny or happy is either creative or not creative and vice versa.
Everyone who is not brave or kind is not humble or not strong.
Fred is both not generous and funny.
Alice is either strong or not humble.
Someone is not kind.
Someone is either happy or creative.
Susan is both not funny and not generous.
Someone is strong or calm.
Alice is funny. | Alice is humble. | contradiction | (![X]:((patient(X)&~old(X))<=>(calm(X)<~>~brave(X))))&
(![X]:(~tall(X)<=>(wise(X)&calm(X))))&
(![X]:((calm(X)&patient(X))=>(~strong(X)&funny(X))))&
(![X]:((~patient(X)<~>generous(X))<=>(~quiet(X)&calm(X))))&
(![X]:((quiet(X)|~generous(X))<=>(~kind(X)<~>~humble(X))))&
(![X]:((brave(X)<~>curious(X))=>kind(X)))&
(![X]:((~brave(X)|~quiet(X))<=>(~patient(X)&~old(X))))&
(![X]:(curious(X)=>(creative(X)<~>~humble(X))))&
(((brave(fred)|~kind(fred)))=>(?[X]:((creative(X)&old(X)))))&
(![X]:(wise(X)=>(strong(X)<~>humble(X))))&
(![X]:(rich(X)=>(~happy(X)&patient(X))))&
(![X]:((~quiet(X)&patient(X))<=>(patient(X)<~>tall(X))))&
(![X]:(~quiet(X)<=>(strong(X)<~>~brave(X))))&
(![X]:((creative(X)&brave(X))<=>(~humble(X)|happy(X))))&
(![X]:((funny(X)|happy(X))<=>(creative(X)<~>~creative(X))))&
(![X]:((~brave(X)|kind(X))=>(~humble(X)|~strong(X))))&
((~generous(fred)&funny(fred)))&
((strong(alice)<~>~humble(alice)))&
(?[X]:(~kind(X)))&
(?[X]:((happy(X)<~>creative(X))))&
((~funny(susan)&~generous(susan)))&
(?[X]:((strong(X)|calm(X))))&
(funny(alice)) | humble(alice) | [
"p0",
"p1",
"p6",
"p11",
"p12",
"p13",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 3164906799858014383280882
% SZS output start Proof for 3164906799858014383280882
1. ! [X0] : ((~old(X0) & patient(X0)) <=> (calm(X0) <~> ~brave(X0))) [input p0]
2. ! [X0] : (~tall(X0) <=> (calm(X0) & wise(X0))) [input p1]
7. ! [X0] : ((~quiet(X0) | ~brave(X0)) <=> (~old(X0) & ~patient(X0))) [input p6]
12. ! [X0] : ((patient(X0) & ~quiet(X0)) <=> (patient(X0) <~> tall(X0))) [input p11]
13. ! [X0] : (~quiet(X0) <=> (strong(X0) <~> ~brave(X0))) [input p12]
14. ! [X0] : ((brave(X0) & creative(X0)) <=> (happy(X0) | ~humble(X0))) [input p13]
16. ! [X0] : ((kind(X0) | ~brave(X0)) => (~strong(X0) | ~humble(X0))) [input p15]
18. strong(alice) <~> ~humble(alice) [input p17]
24. humble(alice) [input hypothesis]
32. ! [X0] : ((~strong(X0) | ~humble(X0)) | (~kind(X0) & brave(X0))) [ennf transformation 16]
33. ! [X0] : (~strong(X0) | ~humble(X0) | (~kind(X0) & brave(X0))) [flattening 32]
34. ! [X0] : (((~old(X0) & patient(X0)) | ((calm(X0) | brave(X0)) & (~brave(X0) | ~calm(X0)))) & (((brave(X0) | ~calm(X0)) & (~brave(X0) | calm(X0))) | (old(X0) | ~patient(X0)))) [nnf transformation 1]
35. ! [X0] : (((~old(X0) & patient(X0)) | ((calm(X0) | brave(X0)) & (~brave(X0) | ~calm(X0)))) & (((brave(X0) | ~calm(X0)) & (~brave(X0) | calm(X0))) | old(X0) | ~patient(X0))) [flattening 34]
36. ! [X0] : ((~tall(X0) | (~calm(X0) | ~wise(X0))) & ((calm(X0) & wise(X0)) | tall(X0))) [nnf transformation 2]
37. ! [X0] : ((~tall(X0) | ~calm(X0) | ~wise(X0)) & ((calm(X0) & wise(X0)) | tall(X0))) [flattening 36]
43. ! [X0] : (((~quiet(X0) | ~brave(X0)) | (old(X0) | patient(X0))) & ((~old(X0) & ~patient(X0)) | (quiet(X0) & brave(X0)))) [nnf transformation 7]
44. ! [X0] : ((~quiet(X0) | ~brave(X0) | old(X0) | patient(X0)) & ((~old(X0) & ~patient(X0)) | (quiet(X0) & brave(X0)))) [flattening 43]
49. ! [X0] : (((patient(X0) & ~quiet(X0)) | ((patient(X0) | ~tall(X0)) & (tall(X0) | ~patient(X0)))) & (((~tall(X0) | ~patient(X0)) & (tall(X0) | patient(X0))) | (~patient(X0) | quiet(X0)))) [nnf transformation 12]
50. ! [X0] : (((patient(X0) & ~quiet(X0)) | ((patient(X0) | ~tall(X0)) & (tall(X0) | ~patient(X0)))) & (((~tall(X0) | ~patient(X0)) & (tall(X0) | patient(X0))) | ~patient(X0) | quiet(X0))) [flattening 49]
51. ! [X0] : ((~quiet(X0) | ((strong(X0) | brave(X0)) & (~brave(X0) | ~strong(X0)))) & (((brave(X0) | ~strong(X0)) & (~brave(X0) | strong(X0))) | quiet(X0))) [nnf transformation 13]
52. ! [X0] : (((brave(X0) & creative(X0)) | (~happy(X0) & humble(X0))) & ((happy(X0) | ~humble(X0)) | (~brave(X0) | ~creative(X0)))) [nnf transformation 14]
53. ! [X0] : (((brave(X0) & creative(X0)) | (~happy(X0) & humble(X0))) & (happy(X0) | ~humble(X0) | ~brave(X0) | ~creative(X0))) [flattening 52]
56. (humble(alice) | ~strong(alice)) & (~humble(alice) | strong(alice)) [nnf transformation 18]
66. ~brave(X0) | patient(X0) | ~calm(X0) [cnf transformation 35]
71. tall(X0) | calm(X0) [cnf transformation 37]
90. ~patient(X0) | quiet(X0) [cnf transformation 44]
107. patient(X0) | patient(X0) | ~tall(X0) [cnf transformation 50]
110. ~quiet(X0) | ~brave(X0) | ~strong(X0) [cnf transformation 51]
115. humble(X0) | brave(X0) [cnf transformation 53]
123. ~strong(X0) | ~humble(X0) | brave(X0) [cnf transformation 33]
127. ~humble(alice) | strong(alice) [cnf transformation 56]
136. humble(alice) [cnf transformation 24]
140. ~tall(X0) | patient(X0) [duplicate literal removal 107]
164. ~strong(X0) | brave(X0) [subsumption resolution 123,115]
166. 5 <=> strong(alice) [avatar definition]
167. strong(alice) <- (5) [avatar component clause 166]
170. 6 <=> humble(alice) [avatar definition]
174. 5 | ~6 [avatar split clause 127,170,166]
186. 6 [avatar split clause 136,170]
189. patient(X0) | calm(X0) [resolution 140,71]
193. brave(alice) <- (5) [resolution 164,167]
197. patient(alice) | ~calm(alice) <- (5) [resolution 193,66]
198. patient(alice) <- (5) [subsumption resolution 197,189]
228. quiet(alice) <- (5) [resolution 198,90]
321. ~brave(alice) | ~strong(alice) <- (5) [resolution 110,228]
323. ~strong(alice) <- (5) [subsumption resolution 321,193]
324. $false <- (5) [subsumption resolution 323,167]
325. ~5 [avatar contradiction clause 324]
329. $false [avatar sat refutation 174,186,325]
% SZS output end Proof for 3164906799858014383280882
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong or not tall is either not curious or kind and vice versa. If someone is either humble or tall then someone is kind. If someone is brave then someone is either brave or not funny and vice versa. Everyone who is brave or old is not wise or not brave and vice versa. If mary is not creative or not kind then john is humble or funny and vice versa. If someone is both humble and not humble then susan is both not patient and not curious and vice versa. Everyone who is not quiet is both not curious and not generous. Everyone who is not wise is either generous or wise. Everyone who is either not old or old is not generous. If john is not brave or not tall then john is not kind or not rich. If someone is not humble then someone is either creative or generous and vice versa. If paul is not generous then someone is both calm and not brave and vice versa. If someone is both strong and not strong then paul is kind. Everyone who is patient is either quiet or creative and vice versa. If john is both calm and not quiet then someone is either quiet or strong. Someone is either not curious or not old. Someone is either humble or funny. Lucy is not creative. John is tall. Mary is both not humble and creative. Paul is brave or not generous. John is either creative or not tall. | Lucy is generous. | contradiction | (![X]:((~strong(X)|~tall(X))<=>(~curious(X)<~>kind(X))))&
((?[X]:((humble(X)<~>tall(X))))=>(?[X]:(kind(X))))&
((?[X]:(brave(X)))<=>(?[X]:((brave(X)<~>~funny(X)))))&
(![X]:((brave(X)|old(X))<=>(~wise(X)|~brave(X))))&
(((~creative(mary)|~kind(mary)))<=>((humble(john)|funny(john))))&
((?[X]:((humble(X)&~humble(X))))<=>((~patient(susan)&~curious(susan))))&
(![X]:(~quiet(X)=>(~curious(X)&~generous(X))))&
(![X]:(~wise(X)=>(generous(X)<~>wise(X))))&
(![X]:((~old(X)<~>old(X))=>~generous(X)))&
(((~brave(john)|~tall(john)))=>((~kind(john)|~rich(john))))&
((?[X]:(~humble(X)))<=>(?[X]:((creative(X)<~>generous(X)))))&
((~generous(paul))<=>(?[X]:((calm(X)&~brave(X)))))&
((?[X]:((strong(X)&~strong(X))))=>(kind(paul)))&
(![X]:(patient(X)<=>(quiet(X)<~>creative(X))))&
(((calm(john)&~quiet(john)))=>(?[X]:((quiet(X)<~>strong(X)))))&
(?[X]:((~curious(X)<~>~old(X))))&
(?[X]:((humble(X)<~>funny(X))))&
(~creative(lucy))&
(tall(john))&
((~humble(mary)&creative(mary)))&
((brave(paul)|~generous(paul)))&
((creative(john)<~>~tall(john))) | generous(lucy) | [
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 6478760969352136196107556
% SZS output start Proof for 6478760969352136196107556
9. ! [X0] : ((~old(X0) <~> old(X0)) => ~generous(X0)) [input p8]
23. generous(lucy) [input hypothesis]
31. ! [X0] : (~generous(X0) | (~old(X0) <=> old(X0))) [ennf transformation 9]
56. ! [X0] : (~generous(X0) | ((~old(X0) | ~old(X0)) & (old(X0) | old(X0)))) [nnf transformation 31]
105. ~generous(X0) | old(X0) | old(X0) [cnf transformation 56]
106. ~generous(X0) | ~old(X0) | ~old(X0) [cnf transformation 56]
132. generous(lucy) [cnf transformation 23]
133. ~generous(X0) | old(X0) [duplicate literal removal 105]
134. ~generous(X0) | ~old(X0) [duplicate literal removal 106]
209. ~generous(X0) [subsumption resolution 133,134]
270. $false [subsumption resolution 132,209]
% SZS output end Proof for 6478760969352136196107556
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall and not generous is not creative. Everyone who is either curious or rich is generous or not funny and vice versa. Everyone who is either not funny or curious is either tall or not funny. If fred is both wise and kind then john is both not brave and not patient and vice versa. If john is both rich and not creative then lucy is not tall and vice versa. If someone is not funny or wise then someone is brave and vice versa. Everyone who is both creative and old is not brave or generous. If someone is both old and not brave then someone is not kind or creative. Everyone who is both humble and tall is both not quiet and not patient. Everyone who is both not creative and patient is wise or happy and vice versa. If susan is either not funny or calm then someone is either funny or tall. Everyone who is either generous or quiet is brave and vice versa. If alice is both not humble and happy then someone is not tall or happy and vice versa. Everyone who is either not tall or old is not kind or not calm and vice versa. If someone is not calm then someone is old. If someone is not kind or not brave then fred is rich. Someone is creative. Alice is both quiet and not brave. Someone is rich or wise. Someone is calm or not rich. Lucy is not old. Mary is not tall or not strong. Someone is both not happy and not old. John is both not creative and not quiet. | Alice is not patient. | neutral | (![X]:((tall(X)&~generous(X))=>~creative(X)))&
(![X]:((curious(X)<~>rich(X))<=>(generous(X)|~funny(X))))&
(![X]:((~funny(X)<~>curious(X))=>(tall(X)<~>~funny(X))))&
(((wise(fred)&kind(fred)))<=>((~brave(john)&~patient(john))))&
(((rich(john)&~creative(john)))<=>(~tall(lucy)))&
((?[X]:((~funny(X)|wise(X))))<=>(?[X]:(brave(X))))&
(![X]:((creative(X)&old(X))=>(~brave(X)|generous(X))))&
((?[X]:((old(X)&~brave(X))))=>(?[X]:((~kind(X)|creative(X)))))&
(![X]:((humble(X)&tall(X))=>(~quiet(X)&~patient(X))))&
(![X]:((~creative(X)&patient(X))<=>(wise(X)|happy(X))))&
(((~funny(susan)<~>calm(susan)))=>(?[X]:((funny(X)<~>tall(X)))))&
(![X]:((generous(X)<~>quiet(X))<=>brave(X)))&
(((~humble(alice)&happy(alice)))<=>(?[X]:((~tall(X)|happy(X)))))&
(![X]:((~tall(X)<~>old(X))<=>(~kind(X)|~calm(X))))&
((?[X]:(~calm(X)))=>(?[X]:(old(X))))&
((?[X]:((~kind(X)|~brave(X))))=>(rich(fred)))&
(?[X]:(creative(X)))&
((quiet(alice)&~brave(alice)))&
(?[X]:((rich(X)|wise(X))))&
(?[X]:((calm(X)|~rich(X))))&
(~old(lucy))&
((~tall(mary)|~strong(mary)))&
(?[X]:((~happy(X)&~old(X))))&
((~creative(john)&~quiet(john))) | ~patient(alice) | [] | null | 0 |
Everyone who is both not brave and creative is humble or not patient.
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.
If someone is not creative then someone is not calm and vice versa.
If fred is either not wise or not humble then susan is brave and vice versa.
If someone is both not creative and not rich then paul is either not wise or not calm.
If someone is either not patient or not generous then susan is both creative and wise and vice versa.
If fred is both funny and not creative then lucy is old and vice versa.
Everyone who is both brave and not old is not funny or happy and vice versa.
Everyone who is either happy or not wise is both rich and tall.
Everyone who is humble is both strong and generous and vice versa.
Someone is both humble and not tall.
Someone is both not old and not brave.
Alice is either wise or not old.
Someone is generous or not curious.
Mary is not humble or not funny.
Someone is both humble and not rich.
Mary is either humble or calm.
Paul is either wise or not old. | Fred is quiet. | neutral | (![X]:((~brave(X)&creative(X))=>(humble(X)|~patient(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]:(~creative(X)))<=>(?[X]:(~calm(X))))&
(((~wise(fred)<~>~humble(fred)))<=>(brave(susan)))&
((?[X]:((~creative(X)&~rich(X))))=>((~wise(paul)<~>~calm(paul))))&
((?[X]:((~patient(X)<~>~generous(X))))<=>((creative(susan)&wise(susan))))&
(((funny(fred)&~creative(fred)))<=>(old(lucy)))&
(![X]:((brave(X)&~old(X))<=>(~funny(X)|happy(X))))&
(![X]:((happy(X)<~>~wise(X))=>(rich(X)&tall(X))))&
(![X]:(humble(X)<=>(strong(X)&generous(X))))&
(?[X]:((humble(X)&~tall(X))))&
(?[X]:((~old(X)&~brave(X))))&
((wise(alice)<~>~old(alice)))&
(?[X]:((generous(X)|~curious(X))))&
((~humble(mary)|~funny(mary)))&
(?[X]:((humble(X)&~rich(X))))&
((humble(mary)<~>calm(mary)))&
((wise(paul)<~>~old(paul))) | quiet(fred) | [] | null | 0 |
If fred is both not calm and creative then alice is not patient and vice versa. If someone is both not strong and quiet then lucy is old and vice versa. Everyone who is both not wise and quiet is curious or not kind. If someone is both not strong and not happy then someone is not kind or not quiet. Everyone who is not tall is either funny or happy. Everyone who is humble or not strong is both not funny and patient. If someone is not curious then someone is funny and vice versa. Everyone who is both happy and not brave is not patient or brave. If someone is both generous and brave then someone is happy. If john is either not happy or brave then lucy is both not curious and not generous. Everyone who is both not happy and generous is calm or not old. If someone is both not rich and curious then susan is funny or not quiet. Everyone who is not creative or not happy is generous or not generous and vice versa. Everyone who is rich or strong is not wise. If fred is both not brave and not quiet then someone is both generous and happy and vice versa. If john is old or brave then alice is patient and vice versa. Someone is not quiet. Someone is not creative or kind. Someone is old or curious. Someone is not rich or generous. Someone is rich. Fred is not calm or not patient. Alice is not creative. Fred is both not funny and creative. | John is creative. | neutral | (((~calm(fred)&creative(fred)))<=>(~patient(alice)))&
((?[X]:((~strong(X)&quiet(X))))<=>(old(lucy)))&
(![X]:((~wise(X)&quiet(X))=>(curious(X)|~kind(X))))&
((?[X]:((~strong(X)&~happy(X))))=>(?[X]:((~kind(X)|~quiet(X)))))&
(![X]:(~tall(X)=>(funny(X)<~>happy(X))))&
(![X]:((humble(X)|~strong(X))=>(~funny(X)&patient(X))))&
((?[X]:(~curious(X)))<=>(?[X]:(funny(X))))&
(![X]:((happy(X)&~brave(X))=>(~patient(X)|brave(X))))&
((?[X]:((generous(X)&brave(X))))=>(?[X]:(happy(X))))&
(((~happy(john)<~>brave(john)))=>((~curious(lucy)&~generous(lucy))))&
(![X]:((~happy(X)&generous(X))=>(calm(X)|~old(X))))&
((?[X]:((~rich(X)&curious(X))))=>((funny(susan)|~quiet(susan))))&
(![X]:((~creative(X)|~happy(X))<=>(generous(X)|~generous(X))))&
(![X]:((rich(X)|strong(X))=>~wise(X)))&
(((~brave(fred)&~quiet(fred)))<=>(?[X]:((generous(X)&happy(X)))))&
(((old(john)|brave(john)))<=>(patient(alice)))&
(?[X]:(~quiet(X)))&
(?[X]:((~creative(X)|kind(X))))&
(?[X]:((old(X)|curious(X))))&
(?[X]:((~rich(X)|generous(X))))&
(?[X]:(rich(X)))&
((~calm(fred)|~patient(fred)))&
(~creative(alice))&
((~funny(fred)&creative(fred))) | creative(john) | [] | null | 0 |
Everyone who is either not strong or not calm is brave or not kind and vice versa.
Everyone who is either creative or not old is both generous and not tall and vice versa.
Everyone who is not funny is either quiet or not brave and vice versa.
If someone is not funny or tall then someone is both not brave and not kind and vice versa.
Everyone who is not generous is either patient or curious and vice versa.
If someone is both creative and curious then lucy is both not funny and not old and vice versa.
Everyone who is generous is not old or curious and vice versa.
If paul is old or not generous then someone is both not old and not tall.
Everyone who is tall is both not old and calm and vice versa.
Everyone who is not brave or not generous is not generous or old.
Everyone who is both patient and not tall is either not creative or old and vice versa.
Everyone who is not old or rich is generous and vice versa.
Everyone who is either old or not humble is both wise and strong.
If susan is both curious and happy then someone is patient or creative.
If paul is brave or tall then someone is calm and vice versa.
Everyone who is not tall is either strong or old.
Someone is patient.
Someone is not calm or not quiet.
Someone is both not happy and not calm.
Someone is not brave or strong.
Someone is not wise.
Someone is both generous and not old.
Someone is both wise and not happy.
Someone is not tall or quiet. | Lucy is not humble. | neutral | (![X]:((~strong(X)<~>~calm(X))<=>(brave(X)|~kind(X))))&
(![X]:((creative(X)<~>~old(X))<=>(generous(X)&~tall(X))))&
(![X]:(~funny(X)<=>(quiet(X)<~>~brave(X))))&
((?[X]:((~funny(X)|tall(X))))<=>(?[X]:((~brave(X)&~kind(X)))))&
(![X]:(~generous(X)<=>(patient(X)<~>curious(X))))&
((?[X]:((creative(X)&curious(X))))<=>((~funny(lucy)&~old(lucy))))&
(![X]:(generous(X)<=>(~old(X)|curious(X))))&
(((old(paul)|~generous(paul)))=>(?[X]:((~old(X)&~tall(X)))))&
(![X]:(tall(X)<=>(~old(X)&calm(X))))&
(![X]:((~brave(X)|~generous(X))=>(~generous(X)|old(X))))&
(![X]:((patient(X)&~tall(X))<=>(~creative(X)<~>old(X))))&
(![X]:((~old(X)|rich(X))<=>generous(X)))&
(![X]:((old(X)<~>~humble(X))=>(wise(X)&strong(X))))&
(((curious(susan)&happy(susan)))=>(?[X]:((patient(X)|creative(X)))))&
(((brave(paul)|tall(paul)))<=>(?[X]:(calm(X))))&
(![X]:(~tall(X)=>(strong(X)<~>old(X))))&
(?[X]:(patient(X)))&
(?[X]:((~calm(X)|~quiet(X))))&
(?[X]:((~happy(X)&~calm(X))))&
(?[X]:((~brave(X)|strong(X))))&
(?[X]:(~wise(X)))&
(?[X]:((generous(X)&~old(X))))&
(?[X]:((wise(X)&~happy(X))))&
(?[X]:((~tall(X)|quiet(X)))) | ~humble(lucy) | [] | null | 0 |
If alice is rich or tall then alice is not kind. Everyone who is both curious and kind is either creative or quiet and vice versa. If someone is both not kind and rich then someone is quiet and vice versa. If someone is patient then someone is kind. Everyone who is rich is patient and vice versa. Everyone who is both humble and not rich is not quiet and vice versa. Everyone who is not patient or funny is not curious or not generous. Everyone who is both funny and not old is not happy or not strong. If someone is old then mary is not creative and vice versa. Everyone who is not old is calm or old and vice versa. Everyone who is both not funny and brave is strong or not strong. Everyone who is not funny or patient is not curious or patient and vice versa. If lucy is not kind or happy then susan is both not calm and creative. If paul is both creative and rich then mary is either not brave or not rich and vice versa. Everyone who is both curious and not humble is wise and vice versa. If john is not quiet then susan is either not humble or funny. Someone is not kind or kind. Lucy is either not calm or not tall. John is patient. Someone is both not brave and not generous. Fred is curious or not tall. Someone is not quiet. Someone is rich. | John is creative. | neutral | (((rich(alice)|tall(alice)))=>(~kind(alice)))&
(![X]:((curious(X)&kind(X))<=>(creative(X)<~>quiet(X))))&
((?[X]:((~kind(X)&rich(X))))<=>(?[X]:(quiet(X))))&
((?[X]:(patient(X)))=>(?[X]:(kind(X))))&
(![X]:(rich(X)<=>patient(X)))&
(![X]:((humble(X)&~rich(X))<=>~quiet(X)))&
(![X]:((~patient(X)|funny(X))=>(~curious(X)|~generous(X))))&
(![X]:((funny(X)&~old(X))=>(~happy(X)|~strong(X))))&
((?[X]:(old(X)))<=>(~creative(mary)))&
(![X]:(~old(X)<=>(calm(X)|old(X))))&
(![X]:((~funny(X)&brave(X))=>(strong(X)|~strong(X))))&
(![X]:((~funny(X)|patient(X))<=>(~curious(X)|patient(X))))&
(((~kind(lucy)|happy(lucy)))=>((~calm(susan)&creative(susan))))&
(((creative(paul)&rich(paul)))<=>((~brave(mary)<~>~rich(mary))))&
(![X]:((curious(X)&~humble(X))<=>wise(X)))&
((~quiet(john))=>((~humble(susan)<~>funny(susan))))&
(?[X]:((~kind(X)|kind(X))))&
((~calm(lucy)<~>~tall(lucy)))&
(patient(john))&
(?[X]:((~brave(X)&~generous(X))))&
((curious(fred)|~tall(fred)))&
(?[X]:(~quiet(X)))&
(?[X]:(rich(X))) | creative(john) | [] | null | 0 |
Everyone who is curious is not wise or not tall and vice versa.
Everyone who is either quiet or calm is either happy or not happy and vice versa.
If mary is either brave or old then susan is funny and vice versa.
Everyone who is strong is both creative and not calm.
Everyone who is both old and kind is not old and vice versa.
If alice is either old or not funny then someone is both creative and generous and vice versa.
Everyone who is either not humble or calm is both not brave and not generous.
Everyone who is either brave or not tall is both not patient and tall and vice versa.
If fred is both kind and not old then someone is not wise and vice versa.
Everyone who is either quiet or funny is not brave.
If someone is both patient and not rich then lucy is not patient.
If someone is either not strong or rich then lucy is both quiet and curious.
If alice is happy then lucy is either not humble or patient.
Everyone who is not brave or strong is happy and vice versa.
If alice is not creative or not rich then susan is either not brave or humble.
If someone is brave or humble then someone is either strong or funny.
Someone is both not creative and wise.
Fred is not rich.
Someone is both happy and patient.
Someone is both brave and not patient.
John is not quiet or funny.
Someone is not calm or not quiet. | Alice is rich. | neutral | (![X]:(curious(X)<=>(~wise(X)|~tall(X))))&
(![X]:((quiet(X)<~>calm(X))<=>(happy(X)<~>~happy(X))))&
(((brave(mary)<~>old(mary)))<=>(funny(susan)))&
(![X]:(strong(X)=>(creative(X)&~calm(X))))&
(![X]:((old(X)&kind(X))<=>~old(X)))&
(((old(alice)<~>~funny(alice)))<=>(?[X]:((creative(X)&generous(X)))))&
(![X]:((~humble(X)<~>calm(X))=>(~brave(X)&~generous(X))))&
(![X]:((brave(X)<~>~tall(X))<=>(~patient(X)&tall(X))))&
(((kind(fred)&~old(fred)))<=>(?[X]:(~wise(X))))&
(![X]:((quiet(X)<~>funny(X))=>~brave(X)))&
((?[X]:((patient(X)&~rich(X))))=>(~patient(lucy)))&
((?[X]:((~strong(X)<~>rich(X))))=>((quiet(lucy)&curious(lucy))))&
((happy(alice))=>((~humble(lucy)<~>patient(lucy))))&
(![X]:((~brave(X)|strong(X))<=>happy(X)))&
(((~creative(alice)|~rich(alice)))=>((~brave(susan)<~>humble(susan))))&
((?[X]:((brave(X)|humble(X))))=>(?[X]:((strong(X)<~>funny(X)))))&
(?[X]:((~creative(X)&wise(X))))&
(~rich(fred))&
(?[X]:((happy(X)&patient(X))))&
(?[X]:((brave(X)&~patient(X))))&
((~quiet(john)|funny(john)))&
(?[X]:((~calm(X)|~quiet(X)))) | rich(alice) | [] | null | 0 |
Everyone who is humble or kind is either generous or not quiet and vice versa.
If paul is not funny then lucy is both happy and rich.
If mary is not kind or calm then someone is both not brave and quiet.
Everyone who is strong or not creative is humble and vice versa.
Everyone who is generous is not brave or not funny.
Everyone who is both funny and not kind is kind.
If someone is not rich then someone is not kind or not patient.
If someone is generous or not quiet then someone is kind or not humble and vice versa.
Everyone who is either happy or rich is both not curious and kind and vice versa.
Everyone who is either not humble or calm is not patient.
Everyone who is both not quiet and generous is both not generous and not old.
If mary is not generous or not old then someone is both humble and not patient and vice versa.
If someone is rich then mary is old.
If paul is brave then john is both old and calm and vice versa.
If mary is old or quiet then someone is not tall or creative.
If someone is curious or rich then paul is both not kind and calm.
Mary is both not happy and creative.
Someone is either not generous or not curious.
Alice is either not patient or not tall.
Fred is not strong or creative.
Alice is either calm or not creative.
Someone is tall.
Mary is not brave or old.
John is rich. | Lucy is rich. | entailment | (![X]:((humble(X)|kind(X))<=>(generous(X)<~>~quiet(X))))&
((~funny(paul))=>((happy(lucy)&rich(lucy))))&
(((~kind(mary)|calm(mary)))=>(?[X]:((~brave(X)&quiet(X)))))&
(![X]:((strong(X)|~creative(X))<=>humble(X)))&
(![X]:(generous(X)=>(~brave(X)|~funny(X))))&
(![X]:((funny(X)&~kind(X))=>kind(X)))&
((?[X]:(~rich(X)))=>(?[X]:((~kind(X)|~patient(X)))))&
((?[X]:((generous(X)|~quiet(X))))<=>(?[X]:((kind(X)|~humble(X)))))&
(![X]:((happy(X)<~>rich(X))<=>(~curious(X)&kind(X))))&
(![X]:((~humble(X)<~>calm(X))=>~patient(X)))&
(![X]:((~quiet(X)&generous(X))=>(~generous(X)&~old(X))))&
(((~generous(mary)|~old(mary)))<=>(?[X]:((humble(X)&~patient(X)))))&
((?[X]:(rich(X)))=>(old(mary)))&
((brave(paul))<=>((old(john)&calm(john))))&
(((old(mary)|quiet(mary)))=>(?[X]:((~tall(X)|creative(X)))))&
((?[X]:((curious(X)|rich(X))))=>((~kind(paul)&calm(paul))))&
((~happy(mary)&creative(mary)))&
(?[X]:((~generous(X)<~>~curious(X))))&
((~patient(alice)<~>~tall(alice)))&
((~strong(fred)|creative(fred)))&
((calm(alice)<~>~creative(alice)))&
(?[X]:(tall(X)))&
((~brave(mary)|old(mary)))&
(rich(john)) | rich(lucy) | [
"p1",
"p5",
"p15",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 902745346268986829522582
% SZS output start Proof for 902745346268986829522582
2. ~funny(paul) => (rich(lucy) & happy(lucy)) [input p1]
6. ! [X0] : ((~kind(X0) & funny(X0)) => kind(X0)) [input p5]
16. ? [X0] : (rich(X0) | curious(X0)) => (calm(paul) & ~kind(paul)) [input p15]
24. rich(john) [input p23]
25. ~rich(lucy) [input hypothesis]
28. (rich(lucy) & happy(lucy)) | funny(paul) [ennf transformation 2]
32. ! [X0] : (kind(X0) | (kind(X0) | ~funny(X0))) [ennf transformation 6]
33. ! [X0] : (kind(X0) | kind(X0) | ~funny(X0)) [flattening 32]
40. (calm(paul) & ~kind(paul)) | ! [X0] : (~rich(X0) & ~curious(X0)) [ennf transformation 16]
81. rich(lucy) | funny(paul) [cnf transformation 28]
90. kind(X0) | kind(X0) | ~funny(X0) [cnf transformation 33]
118. ~kind(paul) | ~rich(X0) [cnf transformation 40]
132. rich(john) [cnf transformation 24]
133. ~rich(lucy) [cnf transformation 25]
135. ~funny(X0) | kind(X0) [duplicate literal removal 90]
137. 1 <=> funny(paul) [avatar definition]
139. funny(paul) <- (1) [avatar component clause 137]
141. 2 <=> rich(lucy) [avatar definition]
144. 1 | 2 [avatar split clause 81,141,137]
239. 24 <=> ! [X0] : ~rich(X0) [avatar definition]
240. ~rich(X0) <- (24) [avatar component clause 239]
281. 33 <=> kind(paul) [avatar definition]
284. 24 | ~33 [avatar split clause 118,281,239]
330. ~2 [avatar split clause 133,141]
335. kind(paul) <- (1) [resolution 135,139]
338. 33 | ~1 [avatar split clause 335,137,281]
339. $false <- (24) [resolution 240,132]
340. ~24 [avatar contradiction clause 339]
341. $false [avatar sat refutation 144,284,330,338,340]
% SZS output end Proof for 902745346268986829522582
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious is both brave and not happy and vice versa.
Everyone who is both wise and calm is both calm and not rich.
Everyone who is not creative is both not happy and rich.
If someone is generous or not quiet then someone is both curious and happy.
Everyone who is not rich or not wise is not patient or patient and vice versa.
Everyone who is not tall is either funny or rich.
If susan is not brave then someone is either calm or not humble.
If someone is old then someone is not tall.
Everyone who is calm is both happy and quiet.
If someone is curious then lucy is either strong or curious.
If someone is tall then someone is quiet or wise and vice versa.
If someone is either not curious or not creative then mary is not happy or quiet.
If someone is either not generous or curious then lucy is both not wise and calm and vice versa.
If john is both not kind and brave then someone is not generous or not old and vice versa.
If someone is calm then someone is either not generous or not tall and vice versa.
Everyone who is either not quiet or curious is tall or not calm and vice versa.
Fred is either happy or generous.
Fred is funny or not quiet.
John is either kind or not brave.
Someone is quiet.
Someone is either happy or not patient.
Someone is either creative or not strong.
Alice is not wise. | Lucy is happy. | entailment | (![X]:(~curious(X)<=>(brave(X)&~happy(X))))&
(![X]:((wise(X)&calm(X))=>(calm(X)&~rich(X))))&
(![X]:(~creative(X)=>(~happy(X)&rich(X))))&
((?[X]:((generous(X)|~quiet(X))))=>(?[X]:((curious(X)&happy(X)))))&
(![X]:((~rich(X)|~wise(X))<=>(~patient(X)|patient(X))))&
(![X]:(~tall(X)=>(funny(X)<~>rich(X))))&
((~brave(susan))=>(?[X]:((calm(X)<~>~humble(X)))))&
((?[X]:(old(X)))=>(?[X]:(~tall(X))))&
(![X]:(calm(X)=>(happy(X)&quiet(X))))&
((?[X]:(curious(X)))=>((strong(lucy)<~>curious(lucy))))&
((?[X]:(tall(X)))<=>(?[X]:((quiet(X)|wise(X)))))&
((?[X]:((~curious(X)<~>~creative(X))))=>((~happy(mary)|quiet(mary))))&
((?[X]:((~generous(X)<~>curious(X))))<=>((~wise(lucy)&calm(lucy))))&
(((~kind(john)&brave(john)))<=>(?[X]:((~generous(X)|~old(X)))))&
((?[X]:(calm(X)))<=>(?[X]:((~generous(X)<~>~tall(X)))))&
(![X]:((~quiet(X)<~>curious(X))<=>(tall(X)|~calm(X))))&
((happy(fred)<~>generous(fred)))&
((funny(fred)|~quiet(fred)))&
((kind(john)<~>~brave(john)))&
(?[X]:(quiet(X)))&
(?[X]:((happy(X)<~>~patient(X))))&
(?[X]:((creative(X)<~>~strong(X))))&
(~wise(alice)) | happy(lucy) | [
"p3",
"p8",
"p12",
"p13",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 2492732633996370158173559
% SZS output start Proof for 2492732633996370158173559
4. ? [X0] : (~quiet(X0) | generous(X0)) => ? [X0] : (happy(X0) & curious(X0)) [input p3]
9. ! [X0] : (calm(X0) => (quiet(X0) & happy(X0))) [input p8]
13. ? [X0] : (~generous(X0) <~> curious(X0)) <=> (calm(lucy) & ~wise(lucy)) [input p12]
14. (brave(john) & ~kind(john)) <=> ? [X0] : (~old(X0) | ~generous(X0)) [input p13]
19. kind(john) <~> ~brave(john) [input p18]
24. ~happy(lucy) [input hypothesis]
25. ? [X0] : (~quiet(X0) | generous(X0)) => ? [X1] : (happy(X1) & curious(X1)) [rectify 4]
32. ? [X1] : (happy(X1) & curious(X1)) | ! [X0] : (quiet(X0) & ~generous(X0)) [ennf transformation 25]
36. ! [X0] : ((quiet(X0) & happy(X0)) | ~calm(X0)) [ennf transformation 9]
42. ? [X0] : (happy(X0) & curious(X0)) | ! [X1] : (quiet(X1) & ~generous(X1)) [rectify 32]
43. ? [X0] : (happy(X0) & curious(X0)) => (happy(sK0) & curious(sK0)) [choice axiom]
44. (happy(sK0) & curious(sK0)) | ! [X1] : (quiet(X1) & ~generous(X1)) [skolemisation 42,43]
61. (? [X0] : ((~curious(X0) | generous(X0)) & (curious(X0) | ~generous(X0))) | (~calm(lucy) | wise(lucy))) & ((calm(lucy) & ~wise(lucy)) | ! [X0] : ((~generous(X0) | ~curious(X0)) & (curious(X0) | generous(X0)))) [nnf transformation 13]
62. (? [X0] : ((~curious(X0) | generous(X0)) & (curious(X0) | ~generous(X0))) | ~calm(lucy) | wise(lucy)) & ((calm(lucy) & ~wise(lucy)) | ! [X0] : ((~generous(X0) | ~curious(X0)) & (curious(X0) | generous(X0)))) [flattening 61]
63. (? [X0] : ((~curious(X0) | generous(X0)) & (curious(X0) | ~generous(X0))) | ~calm(lucy) | wise(lucy)) & ((calm(lucy) & ~wise(lucy)) | ! [X1] : ((~generous(X1) | ~curious(X1)) & (curious(X1) | generous(X1)))) [rectify 62]
64. ? [X0] : ((~curious(X0) | generous(X0)) & (curious(X0) | ~generous(X0))) => ((~curious(sK5) | generous(sK5)) & (curious(sK5) | ~generous(sK5))) [choice axiom]
65. (((~curious(sK5) | generous(sK5)) & (curious(sK5) | ~generous(sK5))) | ~calm(lucy) | wise(lucy)) & ((calm(lucy) & ~wise(lucy)) | ! [X1] : ((~generous(X1) | ~curious(X1)) & (curious(X1) | generous(X1)))) [skolemisation 63,64]
66. ((brave(john) & ~kind(john)) | ! [X0] : (old(X0) & generous(X0))) & (? [X0] : (~old(X0) | ~generous(X0)) | (~brave(john) | kind(john))) [nnf transformation 14]
67. ((brave(john) & ~kind(john)) | ! [X0] : (old(X0) & generous(X0))) & (? [X0] : (~old(X0) | ~generous(X0)) | ~brave(john) | kind(john)) [flattening 66]
68. ((brave(john) & ~kind(john)) | ! [X0] : (old(X0) & generous(X0))) & (? [X1] : (~old(X1) | ~generous(X1)) | ~brave(john) | kind(john)) [rectify 67]
69. ? [X1] : (~old(X1) | ~generous(X1)) => (~old(sK6) | ~generous(sK6)) [choice axiom]
70. ((brave(john) & ~kind(john)) | ! [X0] : (old(X0) & generous(X0))) & ((~old(sK6) | ~generous(sK6)) | ~brave(john) | kind(john)) [skolemisation 68,69]
79. (brave(john) | ~kind(john)) & (~brave(john) | kind(john)) [nnf transformation 19]
95. curious(sK0) | ~generous(X1) [cnf transformation 44]
108. ~calm(X0) | happy(X0) [cnf transformation 36]
120. calm(lucy) | ~generous(X1) | ~curious(X1) [cnf transformation 65]
124. ~kind(john) | generous(X0) [cnf transformation 70]
126. brave(john) | generous(X0) [cnf transformation 70]
141. ~brave(john) | kind(john) [cnf transformation 79]
149. ~happy(lucy) [cnf transformation 24]
159. 3 <=> ! [X1] : ~generous(X1) [avatar definition]
160. ~generous(X1) <- (3) [avatar component clause 159]
163. 4 <=> curious(sK0) [avatar definition]
165. curious(sK0) <- (4) [avatar component clause 163]
167. 3 | 4 [avatar split clause 95,163,159]
192. 10 <=> ! [X0] : ~curious(X0) [avatar definition]
193. ~curious(X0) <- (10) [avatar component clause 192]
249. 24 <=> calm(lucy) [avatar definition]
250. calm(lucy) <- (24) [avatar component clause 249]
263. 27 <=> ! [X1] : (~generous(X1) | ~curious(X1)) [avatar definition]
264. ~generous(X1) | ~curious(X1) <- (27) [avatar component clause 263]
265. 27 | 24 [avatar split clause 120,249,263]
276. 30 <=> brave(john) [avatar definition]
281. 31 <=> ! [X0] : generous(X0) [avatar definition]
282. generous(X0) <- (31) [avatar component clause 281]
283. 31 | 30 [avatar split clause 126,276,281]
285. 32 <=> kind(john) [avatar definition]
289. 31 | ~32 [avatar split clause 124,285,281]
346. 32 | ~30 [avatar split clause 141,276,285]
375. $false <- (4, 10) [subsumption resolution 165,193]
376. ~4 | ~10 [avatar contradiction clause 375]
380. ~curious(X1) <- (27, 31) [subsumption resolution 264,282]
381. 10 | ~27 | ~31 [avatar split clause 380,281,263,192]
386. $false <- (3, 31) [subsumption resolution 160,282]
387. ~3 | ~31 [avatar contradiction clause 386]
401. happy(lucy) <- (24) [resolution 108,250]
403. $false <- (24) [subsumption resolution 401,149]
404. ~24 [avatar contradiction clause 403]
405. $false [avatar sat refutation 167,265,283,289,346,376,381,387,404]
% SZS output end Proof for 2492732633996370158173559
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich is not wise or not calm.
Everyone who is both not quiet and quiet is not wise and vice versa.
If fred is both not curious and not funny then paul is either humble or not generous.
Everyone who is not calm or not brave is not humble or humble.
Everyone who is both patient and humble is not strong or not kind and vice versa.
If someone is both not creative and not calm then someone is either humble or quiet.
If john is not tall or kind then someone is not quiet or not creative and vice versa.
If someone is not brave then mary is strong.
If fred is rich then fred is either not brave or not calm.
If mary is both not calm and strong then someone is brave.
Everyone who is both not old and strong is not curious and vice versa.
If someone is quiet or not wise then someone is either quiet or not quiet.
If paul is both not calm and wise then someone is both not strong and not kind.
If lucy is rich or not strong then someone is either happy or not old and vice versa.
If someone is not creative then susan is both not creative and happy.
Everyone who is both curious and not wise is both not creative and happy and vice versa.
Alice is both not quiet and old.
Someone is patient.
Someone is both not generous and not funny.
Someone is generous or humble.
Someone is not old or generous.
Fred is both creative and not happy.
Lucy is not kind. | John is not wise. | contradiction | (![X]:(rich(X)=>(~wise(X)|~calm(X))))&
(![X]:((~quiet(X)&quiet(X))<=>~wise(X)))&
(((~curious(fred)&~funny(fred)))=>((humble(paul)<~>~generous(paul))))&
(![X]:((~calm(X)|~brave(X))=>(~humble(X)|humble(X))))&
(![X]:((patient(X)&humble(X))<=>(~strong(X)|~kind(X))))&
((?[X]:((~creative(X)&~calm(X))))=>(?[X]:((humble(X)<~>quiet(X)))))&
(((~tall(john)|kind(john)))<=>(?[X]:((~quiet(X)|~creative(X)))))&
((?[X]:(~brave(X)))=>(strong(mary)))&
((rich(fred))=>((~brave(fred)<~>~calm(fred))))&
(((~calm(mary)&strong(mary)))=>(?[X]:(brave(X))))&
(![X]:((~old(X)&strong(X))<=>~curious(X)))&
((?[X]:((quiet(X)|~wise(X))))=>(?[X]:((quiet(X)<~>~quiet(X)))))&
(((~calm(paul)&wise(paul)))=>(?[X]:((~strong(X)&~kind(X)))))&
(((rich(lucy)|~strong(lucy)))<=>(?[X]:((happy(X)<~>~old(X)))))&
((?[X]:(~creative(X)))=>((~creative(susan)&happy(susan))))&
(![X]:((curious(X)&~wise(X))<=>(~creative(X)&happy(X))))&
((~quiet(alice)&old(alice)))&
(?[X]:(patient(X)))&
(?[X]:((~generous(X)&~funny(X))))&
(?[X]:((generous(X)|humble(X))))&
(?[X]:((~old(X)|generous(X))))&
((creative(fred)&~happy(fred)))&
(~kind(lucy)) | ~wise(john) | [
"p1",
"hypothesis"
] | % SZS status Unsatisfiable for 7031054030648518452439968
% SZS output start Proof for 7031054030648518452439968
2. ! [X0] : ((quiet(X0) & ~quiet(X0)) <=> ~wise(X0)) [input p1]
24. ~wise(john) [input hypothesis]
42. ! [X0] : (((quiet(X0) & ~quiet(X0)) | wise(X0)) & (~wise(X0) | (~quiet(X0) | quiet(X0)))) [nnf transformation 2]
43. ! [X0] : (((quiet(X0) & ~quiet(X0)) | wise(X0)) & (~wise(X0) | ~quiet(X0) | quiet(X0))) [flattening 42]
84. ~quiet(X0) | wise(X0) [cnf transformation 43]
85. quiet(X0) | wise(X0) [cnf transformation 43]
136. ~wise(john) [cnf transformation 24]
137. wise(X0) [subsumption resolution 84,85]
299. $false [subsumption resolution 136,137]
% SZS output end Proof for 7031054030648518452439968
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both tall and strong is not creative or rich and vice versa. If fred is both tall and rich then someone is either humble or wise and vice versa. Everyone who is old is humble and vice versa. If someone is both not brave and not patient then someone is both not happy and not old. Everyone who is calm or brave is either not humble or rich and vice versa. Everyone who is both not curious and not rich is curious or not generous and vice versa. If susan is not calm then john is both not curious and wise and vice versa. Everyone who is not tall or not happy is either patient or not generous and vice versa. Everyone who is both not tall and not calm is not quiet or funny. Everyone who is not curious or calm is either old or not tall and vice versa. Everyone who is calm is both rich and not generous and vice versa. Everyone who is both not humble and not strong is either generous or kind and vice versa. Everyone who is not humble or strong is either not quiet or quiet and vice versa. Everyone who is both brave and curious is both not strong and wise. Everyone who is either brave or calm is generous. If someone is quiet then john is both funny and not calm and vice versa. John is patient. Lucy is patient or brave. Someone is not funny or not rich. John is either not humble or generous. Someone is either not kind or curious. Someone is either not old or creative. Someone is not creative or old. | Fred is tall. | entailment | (![X]:((tall(X)&strong(X))<=>(~creative(X)|rich(X))))&
(((tall(fred)&rich(fred)))<=>(?[X]:((humble(X)<~>wise(X)))))&
(![X]:(old(X)<=>humble(X)))&
((?[X]:((~brave(X)&~patient(X))))=>(?[X]:((~happy(X)&~old(X)))))&
(![X]:((calm(X)|brave(X))<=>(~humble(X)<~>rich(X))))&
(![X]:((~curious(X)&~rich(X))<=>(curious(X)|~generous(X))))&
((~calm(susan))<=>((~curious(john)&wise(john))))&
(![X]:((~tall(X)|~happy(X))<=>(patient(X)<~>~generous(X))))&
(![X]:((~tall(X)&~calm(X))=>(~quiet(X)|funny(X))))&
(![X]:((~curious(X)|calm(X))<=>(old(X)<~>~tall(X))))&
(![X]:(calm(X)<=>(rich(X)&~generous(X))))&
(![X]:((~humble(X)&~strong(X))<=>(generous(X)<~>kind(X))))&
(![X]:((~humble(X)|strong(X))<=>(~quiet(X)<~>quiet(X))))&
(![X]:((brave(X)&curious(X))=>(~strong(X)&wise(X))))&
(![X]:((brave(X)<~>calm(X))=>generous(X)))&
((?[X]:(quiet(X)))<=>((funny(john)&~calm(john))))&
(patient(john))&
((patient(lucy)|brave(lucy)))&
(?[X]:((~funny(X)|~rich(X))))&
((~humble(john)<~>generous(john)))&
(?[X]:((~kind(X)<~>curious(X))))&
(?[X]:((~old(X)<~>creative(X))))&
(?[X]:((~creative(X)|old(X)))) | tall(fred) | [
"p0",
"p2",
"p4",
"p5",
"p9",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6652266811750335852388008
% SZS output start Proof for 6652266811750335852388008
1. ! [X0] : ((strong(X0) & tall(X0)) <=> (rich(X0) | ~creative(X0))) [input p0]
3. ! [X0] : (old(X0) <=> humble(X0)) [input p2]
5. ! [X0] : ((brave(X0) | calm(X0)) <=> (~humble(X0) <~> rich(X0))) [input p4]
6. ! [X0] : ((~rich(X0) & ~curious(X0)) <=> (~generous(X0) | curious(X0))) [input p5]
10. ! [X0] : ((calm(X0) | ~curious(X0)) <=> (old(X0) <~> ~tall(X0))) [input p9]
11. ! [X0] : (calm(X0) <=> (~generous(X0) & rich(X0))) [input p10]
15. ! [X0] : ((brave(X0) <~> calm(X0)) => generous(X0)) [input p14]
24. ~tall(fred) [input hypothesis]
31. ! [X0] : (generous(X0) | (brave(X0) <=> calm(X0))) [ennf transformation 15]
32. ! [X0] : (((strong(X0) & tall(X0)) | (~rich(X0) & creative(X0))) & ((rich(X0) | ~creative(X0)) | (~strong(X0) | ~tall(X0)))) [nnf transformation 1]
33. ! [X0] : (((strong(X0) & tall(X0)) | (~rich(X0) & creative(X0))) & (rich(X0) | ~creative(X0) | ~strong(X0) | ~tall(X0))) [flattening 32]
39. ! [X0] : ((old(X0) | ~humble(X0)) & (humble(X0) | ~old(X0))) [nnf transformation 3]
43. ! [X0] : (((brave(X0) | calm(X0)) | ((~humble(X0) | ~rich(X0)) & (rich(X0) | humble(X0)))) & (((~rich(X0) | humble(X0)) & (rich(X0) | ~humble(X0))) | (~brave(X0) & ~calm(X0)))) [nnf transformation 5]
44. ! [X0] : ((brave(X0) | calm(X0) | ((~humble(X0) | ~rich(X0)) & (rich(X0) | humble(X0)))) & (((~rich(X0) | humble(X0)) & (rich(X0) | ~humble(X0))) | (~brave(X0) & ~calm(X0)))) [flattening 43]
45. ! [X0] : (((~rich(X0) & ~curious(X0)) | (generous(X0) & ~curious(X0))) & ((~generous(X0) | curious(X0)) | (rich(X0) | curious(X0)))) [nnf transformation 6]
46. ! [X0] : (((~rich(X0) & ~curious(X0)) | (generous(X0) & ~curious(X0))) & (~generous(X0) | curious(X0) | rich(X0) | curious(X0))) [flattening 45]
51. ! [X0] : (((calm(X0) | ~curious(X0)) | ((old(X0) | tall(X0)) & (~tall(X0) | ~old(X0)))) & (((tall(X0) | ~old(X0)) & (~tall(X0) | old(X0))) | (~calm(X0) & curious(X0)))) [nnf transformation 10]
52. ! [X0] : ((calm(X0) | ~curious(X0) | ((old(X0) | tall(X0)) & (~tall(X0) | ~old(X0)))) & (((tall(X0) | ~old(X0)) & (~tall(X0) | old(X0))) | (~calm(X0) & curious(X0)))) [flattening 51]
53. ! [X0] : ((calm(X0) | (generous(X0) | ~rich(X0))) & ((~generous(X0) & rich(X0)) | ~calm(X0))) [nnf transformation 11]
54. ! [X0] : ((calm(X0) | generous(X0) | ~rich(X0)) & ((~generous(X0) & rich(X0)) | ~calm(X0))) [flattening 53]
59. ! [X0] : (generous(X0) | ((brave(X0) | ~calm(X0)) & (calm(X0) | ~brave(X0)))) [nnf transformation 31]
78. ~rich(X0) | tall(X0) [cnf transformation 33]
88. ~humble(X0) | old(X0) [cnf transformation 39]
95. calm(X0) | brave(X0) | rich(X0) | humble(X0) [cnf transformation 44]
97. ~generous(X0) | curious(X0) | rich(X0) | curious(X0) [cnf transformation 46]
98. ~curious(X0) | ~curious(X0) [cnf transformation 46]
101. ~rich(X0) | generous(X0) [cnf transformation 46]
114. tall(X0) | ~old(X0) | curious(X0) [cnf transformation 52]
118. ~calm(X0) | rich(X0) [cnf transformation 54]
119. ~generous(X0) | ~calm(X0) [cnf transformation 54]
135. ~brave(X0) | calm(X0) | generous(X0) [cnf transformation 59]
136. generous(X0) | brave(X0) | ~calm(X0) [cnf transformation 59]
150. ~tall(fred) [cnf transformation 24]
153. ~generous(X0) | curious(X0) | rich(X0) [duplicate literal removal 97]
154. ~curious(X0) [duplicate literal removal 98]
168. 4 <=> tall(fred) [avatar definition]
169. ~tall(fred) <- (~4) [avatar component clause 168]
198. ~generous(X0) | rich(X0) [subsumption resolution 153,154]
210. ~old(X0) | tall(X0) [subsumption resolution 114,154]
213. ~calm(X0) | brave(X0) [subsumption resolution 136,119]
280. ~4 [avatar split clause 150,168]
415. brave(X4) | rich(X4) | humble(X4) | brave(X4) [resolution 95,213]
420. brave(X4) | rich(X4) | humble(X4) [duplicate literal removal 415]
507. rich(X0) | humble(X0) | calm(X0) | generous(X0) [resolution 420,135]
513. generous(X0) | calm(X0) | humble(X0) [subsumption resolution 507,101]
569. calm(X6) | humble(X6) | rich(X6) [resolution 513,198]
572. humble(X6) | rich(X6) [subsumption resolution 569,118]
604. old(X3) | rich(X3) [resolution 572,88]
676. rich(X0) | tall(X0) [resolution 604,210]
678. tall(X0) [subsumption resolution 676,78]
704. $false <- (~4) [resolution 678,169]
706. 4 [avatar contradiction clause 704]
707. $false [avatar sat refutation 280,706]
% SZS output end Proof for 6652266811750335852388008
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not happy and not old then lucy is either not old or not kind and vice versa.
If someone is not calm or not funny then mary is old or not humble and vice versa.
Everyone who is either patient or not happy is both not calm and not patient and vice versa.
Everyone who is both humble and not creative is strong and vice versa.
If susan is not kind or not brave then someone is both tall and not brave.
Everyone who is either patient or not tall is patient or creative and vice versa.
If someone is both not funny and not strong then paul is not rich or calm.
Everyone who is either calm or wise is not humble.
Everyone who is patient is not creative or not tall and vice versa.
If someone is both not curious and not brave then john is both not humble and not brave and vice versa.
Everyone who is both funny and wise is either not brave or strong.
If susan is both happy and not calm then paul is either old or quiet and vice versa.
If mary is brave then fred is strong or not humble and vice versa.
If someone is either old or not calm then john is not brave and vice versa.
Everyone who is either not kind or happy is creative.
If susan is either not brave or not tall then someone is both patient and not rich and vice versa.
Lucy is both not funny and not old.
Someone is either not rich or generous.
Alice is either strong or patient.
Someone is either not wise or funny.
Someone is funny.
John is calm or not happy.
John is either not calm or curious. | Mary is tall. | entailment | ((?[X]:((~happy(X)&~old(X))))<=>((~old(lucy)<~>~kind(lucy))))&
((?[X]:((~calm(X)|~funny(X))))<=>((old(mary)|~humble(mary))))&
(![X]:((patient(X)<~>~happy(X))<=>(~calm(X)&~patient(X))))&
(![X]:((humble(X)&~creative(X))<=>strong(X)))&
(((~kind(susan)|~brave(susan)))=>(?[X]:((tall(X)&~brave(X)))))&
(![X]:((patient(X)<~>~tall(X))<=>(patient(X)|creative(X))))&
((?[X]:((~funny(X)&~strong(X))))=>((~rich(paul)|calm(paul))))&
(![X]:((calm(X)<~>wise(X))=>~humble(X)))&
(![X]:(patient(X)<=>(~creative(X)|~tall(X))))&
((?[X]:((~curious(X)&~brave(X))))<=>((~humble(john)&~brave(john))))&
(![X]:((funny(X)&wise(X))=>(~brave(X)<~>strong(X))))&
(((happy(susan)&~calm(susan)))<=>((old(paul)<~>quiet(paul))))&
((brave(mary))<=>((strong(fred)|~humble(fred))))&
((?[X]:((old(X)<~>~calm(X))))<=>(~brave(john)))&
(![X]:((~kind(X)<~>happy(X))=>creative(X)))&
(((~brave(susan)<~>~tall(susan)))<=>(?[X]:((patient(X)&~rich(X)))))&
((~funny(lucy)&~old(lucy)))&
(?[X]:((~rich(X)<~>generous(X))))&
((strong(alice)<~>patient(alice)))&
(?[X]:((~wise(X)<~>funny(X))))&
(?[X]:(funny(X)))&
((calm(john)|~happy(john)))&
((~calm(john)<~>curious(john))) | tall(mary) | [
"p5",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 4819487292783269308458048
% SZS output start Proof for 4819487292783269308458048
6. ! [X0] : ((patient(X0) <~> ~tall(X0)) <=> (creative(X0) | patient(X0))) [input p5]
9. ! [X0] : (patient(X0) <=> (~tall(X0) | ~creative(X0))) [input p8]
24. ~tall(mary) [input hypothesis]
47. ! [X0] : ((((tall(X0) | ~patient(X0)) & (~tall(X0) | patient(X0))) | (~creative(X0) & ~patient(X0))) & ((creative(X0) | patient(X0)) | ((patient(X0) | tall(X0)) & (~tall(X0) | ~patient(X0))))) [nnf transformation 6]
48. ! [X0] : ((((tall(X0) | ~patient(X0)) & (~tall(X0) | patient(X0))) | (~creative(X0) & ~patient(X0))) & (creative(X0) | patient(X0) | ((patient(X0) | tall(X0)) & (~tall(X0) | ~patient(X0))))) [flattening 47]
50. ! [X0] : ((patient(X0) | (tall(X0) & creative(X0))) & ((~tall(X0) | ~creative(X0)) | ~patient(X0))) [nnf transformation 9]
51. ! [X0] : ((patient(X0) | (tall(X0) & creative(X0))) & (~tall(X0) | ~creative(X0) | ~patient(X0))) [flattening 50]
108. tall(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 48]
115. patient(X0) | tall(X0) [cnf transformation 51]
155. ~tall(mary) [cnf transformation 24]
157. tall(X0) | ~patient(X0) [duplicate literal removal 108]
244. tall(X0) [subsumption resolution 115,157]
387. $false [subsumption resolution 155,244]
% SZS output end Proof for 4819487292783269308458048
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is humble or quiet is both not calm and funny and vice versa.
Everyone who is strong is either not creative or happy.
If fred is both patient and funny then someone is either tall or strong and vice versa.
If someone is both calm and happy then mary is both wise and generous and vice versa.
If paul is not calm or not brave then someone is both quiet and not wise and vice versa.
Everyone who is not rich is tall and vice versa.
Everyone who is not tall is creative or patient and vice versa.
If someone is either creative or not humble then someone is not happy or old and vice versa.
Everyone who is both not generous and humble is both happy and brave.
Everyone who is either not generous or not old is both not kind and not curious and vice versa.
If someone is both not happy and not calm then someone is either calm or rich and vice versa.
Everyone who is not brave is strong.
Everyone who is tall is both not wise and not funny.
Everyone who is either not humble or old is both not rich and not old.
Everyone who is wise or patient is not tall or not rich and vice versa.
Everyone who is strong or not generous is not rich.
Susan is either not curious or not brave.
Someone is not humble or rich.
Someone is both not old and not creative.
Someone is quiet. | Fred is strong. | contradiction | (![X]:((humble(X)|quiet(X))<=>(~calm(X)&funny(X))))&
(![X]:(strong(X)=>(~creative(X)<~>happy(X))))&
(((patient(fred)&funny(fred)))<=>(?[X]:((tall(X)<~>strong(X)))))&
((?[X]:((calm(X)&happy(X))))<=>((wise(mary)&generous(mary))))&
(((~calm(paul)|~brave(paul)))<=>(?[X]:((quiet(X)&~wise(X)))))&
(![X]:(~rich(X)<=>tall(X)))&
(![X]:(~tall(X)<=>(creative(X)|patient(X))))&
((?[X]:((creative(X)<~>~humble(X))))<=>(?[X]:((~happy(X)|old(X)))))&
(![X]:((~generous(X)&humble(X))=>(happy(X)&brave(X))))&
(![X]:((~generous(X)<~>~old(X))<=>(~kind(X)&~curious(X))))&
((?[X]:((~happy(X)&~calm(X))))<=>(?[X]:((calm(X)<~>rich(X)))))&
(![X]:(~brave(X)=>strong(X)))&
(![X]:(tall(X)=>(~wise(X)&~funny(X))))&
(![X]:((~humble(X)<~>old(X))=>(~rich(X)&~old(X))))&
(![X]:((wise(X)|patient(X))<=>(~tall(X)|~rich(X))))&
(![X]:((strong(X)|~generous(X))=>~rich(X)))&
((~curious(susan)<~>~brave(susan)))&
(?[X]:((~humble(X)|rich(X))))&
(?[X]:((~old(X)&~creative(X))))&
(?[X]:(quiet(X))) | strong(fred) | [
"p5",
"p6",
"p12",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7596646686667362205138068
% SZS output start Proof for 7596646686667362205138068
6. ! [X0] : (~rich(X0) <=> tall(X0)) [input p5]
7. ! [X0] : (~tall(X0) <=> (patient(X0) | creative(X0))) [input p6]
13. ! [X0] : (tall(X0) => (~funny(X0) & ~wise(X0))) [input p12]
15. ! [X0] : ((patient(X0) | wise(X0)) <=> (~rich(X0) | ~tall(X0))) [input p14]
16. ! [X0] : ((~generous(X0) | strong(X0)) => ~rich(X0)) [input p15]
21. strong(fred) [input hypothesis]
28. ! [X0] : ((~funny(X0) & ~wise(X0)) | ~tall(X0)) [ennf transformation 13]
30. ! [X0] : (~rich(X0) | (generous(X0) & ~strong(X0))) [ennf transformation 16]
49. ! [X0] : ((~rich(X0) | ~tall(X0)) & (tall(X0) | rich(X0))) [nnf transformation 6]
50. ! [X0] : ((~tall(X0) | (~patient(X0) & ~creative(X0))) & ((patient(X0) | creative(X0)) | tall(X0))) [nnf transformation 7]
51. ! [X0] : ((~tall(X0) | (~patient(X0) & ~creative(X0))) & (patient(X0) | creative(X0) | tall(X0))) [flattening 50]
65. ! [X0] : (((patient(X0) | wise(X0)) | (rich(X0) & tall(X0))) & ((~rich(X0) | ~tall(X0)) | (~patient(X0) & ~wise(X0)))) [nnf transformation 15]
66. ! [X0] : ((patient(X0) | wise(X0) | (rich(X0) & tall(X0))) & (~rich(X0) | ~tall(X0) | (~patient(X0) & ~wise(X0)))) [flattening 65]
96. rich(X0) | tall(X0) [cnf transformation 49]
97. ~rich(X0) | ~tall(X0) [cnf transformation 49]
100. ~tall(X0) | ~patient(X0) [cnf transformation 51]
122. ~wise(X0) | ~tall(X0) [cnf transformation 28]
131. rich(X0) | wise(X0) | patient(X0) [cnf transformation 66]
132. ~rich(X0) | ~strong(X0) [cnf transformation 30]
140. strong(fred) [cnf transformation 21]
143. 1 <=> ! [X0] : (tall(X0) | ~strong(X0)) [avatar definition]
144. ~strong(X0) | tall(X0) <- (1) [avatar component clause 143]
312. ~strong(X0) | tall(X0) [resolution 132,96]
313. 1 [avatar split clause 312,143]
315. tall(fred) <- (1) [resolution 144,140]
430. wise(X4) | patient(X4) | ~tall(X4) [resolution 131,97]
431. patient(X4) | ~tall(X4) [subsumption resolution 430,122]
432. ~tall(X4) [subsumption resolution 431,100]
433. $false <- (1) [resolution 432,315]
437. ~1 [avatar contradiction clause 433]
438. $false [avatar sat refutation 313,437]
% SZS output end Proof for 7596646686667362205138068
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not quiet is not tall or wise.
Everyone who is either happy or quiet is either quiet or humble.
Everyone who is not curious or strong is not patient and vice versa.
If someone is not happy or rich then someone is calm or old.
Everyone who is quiet is strong or creative and vice versa.
Everyone who is generous is either quiet or not funny and vice versa.
Everyone who is not old is either patient or not patient and vice versa.
If someone is not kind then lucy is either not rich or not creative.
If someone is both happy and not humble then lucy is either humble or calm.
Everyone who is not humble is either old or calm.
If john is creative or not quiet then someone is not happy or not quiet.
Everyone who is either creative or not kind is not tall.
Everyone who is humble or kind is funny or not wise and vice versa.
Everyone who is happy is either not calm or not curious and vice versa.
If john is funny or not curious then john is strong or not funny and vice versa.
If alice is calm or brave then fred is rich.
Someone is either not patient or not tall.
Someone is either brave or not kind.
John is not rich or not creative.
Someone is creative.
Someone is both strong and not happy.
Someone is both not wise and funny.
Someone is creative or kind.
Someone is both not kind and strong. | John is not creative. | neutral | (![X]:(~quiet(X)=>(~tall(X)|wise(X))))&
(![X]:((happy(X)<~>quiet(X))=>(quiet(X)<~>humble(X))))&
(![X]:((~curious(X)|strong(X))<=>~patient(X)))&
((?[X]:((~happy(X)|rich(X))))=>(?[X]:((calm(X)|old(X)))))&
(![X]:(quiet(X)<=>(strong(X)|creative(X))))&
(![X]:(generous(X)<=>(quiet(X)<~>~funny(X))))&
(![X]:(~old(X)<=>(patient(X)<~>~patient(X))))&
((?[X]:(~kind(X)))=>((~rich(lucy)<~>~creative(lucy))))&
((?[X]:((happy(X)&~humble(X))))=>((humble(lucy)<~>calm(lucy))))&
(![X]:(~humble(X)=>(old(X)<~>calm(X))))&
(((creative(john)|~quiet(john)))=>(?[X]:((~happy(X)|~quiet(X)))))&
(![X]:((creative(X)<~>~kind(X))=>~tall(X)))&
(![X]:((humble(X)|kind(X))<=>(funny(X)|~wise(X))))&
(![X]:(happy(X)<=>(~calm(X)<~>~curious(X))))&
(((funny(john)|~curious(john)))<=>((strong(john)|~funny(john))))&
(((calm(alice)|brave(alice)))=>(rich(fred)))&
(?[X]:((~patient(X)<~>~tall(X))))&
(?[X]:((brave(X)<~>~kind(X))))&
((~rich(john)|~creative(john)))&
(?[X]:(creative(X)))&
(?[X]:((strong(X)&~happy(X))))&
(?[X]:((~wise(X)&funny(X))))&
(?[X]:((creative(X)|kind(X))))&
(?[X]:((~kind(X)&strong(X)))) | ~creative(john) | [] | null | 0 |
Everyone who is either curious or brave is tall or humble.
If john is both not generous and not patient then alice is not rich.
Everyone who is both not happy and not tall is both humble and old.
Everyone who is both not generous and calm is either not kind or old and vice versa.
Everyone who is not generous is both kind and not quiet and vice versa.
Everyone who is humble or generous is not wise or not happy and vice versa.
If alice is not creative or not kind then someone is not funny or old and vice versa.
If paul is not calm or not generous then lucy is not old or not tall and vice versa.
If someone is not calm then fred is not curious or strong and vice versa.
If john is both old and rich then someone is both not wise and not kind.
Everyone who is not brave is both funny and not wise and vice versa.
Everyone who is happy or not quiet is quiet and vice versa.
Everyone who is kind or not rich is brave or not wise.
Everyone who is quiet or not happy is both kind and not tall.
Everyone who is brave or not wise is rich or brave.
Everyone who is both not quiet and curious is either curious or funny.
Someone is both generous and not creative.
Alice is rich or creative.
Fred is either old or funny.
Susan is not funny.
Alice is not wise. | Lucy is old. | contradiction | (![X]:((curious(X)<~>brave(X))=>(tall(X)|humble(X))))&
(((~generous(john)&~patient(john)))=>(~rich(alice)))&
(![X]:((~happy(X)&~tall(X))=>(humble(X)&old(X))))&
(![X]:((~generous(X)&calm(X))<=>(~kind(X)<~>old(X))))&
(![X]:(~generous(X)<=>(kind(X)&~quiet(X))))&
(![X]:((humble(X)|generous(X))<=>(~wise(X)|~happy(X))))&
(((~creative(alice)|~kind(alice)))<=>(?[X]:((~funny(X)|old(X)))))&
(((~calm(paul)|~generous(paul)))<=>((~old(lucy)|~tall(lucy))))&
((?[X]:(~calm(X)))<=>((~curious(fred)|strong(fred))))&
(((old(john)&rich(john)))=>(?[X]:((~wise(X)&~kind(X)))))&
(![X]:(~brave(X)<=>(funny(X)&~wise(X))))&
(![X]:((happy(X)|~quiet(X))<=>quiet(X)))&
(![X]:((kind(X)|~rich(X))=>(brave(X)|~wise(X))))&
(![X]:((quiet(X)|~happy(X))=>(kind(X)&~tall(X))))&
(![X]:((brave(X)|~wise(X))=>(rich(X)|brave(X))))&
(![X]:((~quiet(X)&curious(X))=>(curious(X)<~>funny(X))))&
(?[X]:((generous(X)&~creative(X))))&
((rich(alice)|creative(alice)))&
((old(fred)<~>funny(fred)))&
(~funny(susan))&
(~wise(alice)) | old(lucy) | [
"p3",
"p4",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 220248703364184827754770
% SZS output start Proof for 220248703364184827754770
4. ! [X0] : ((calm(X0) & ~generous(X0)) <=> (~kind(X0) <~> old(X0))) [input p3]
5. ! [X0] : (~generous(X0) <=> (~quiet(X0) & kind(X0))) [input p4]
12. ! [X0] : ((~quiet(X0) | happy(X0)) <=> quiet(X0)) [input p11]
14. ! [X0] : ((~happy(X0) | quiet(X0)) => (~tall(X0) & kind(X0))) [input p13]
22. old(lucy) [input hypothesis]
32. ! [X0] : ((~tall(X0) & kind(X0)) | (happy(X0) & ~quiet(X0))) [ennf transformation 14]
38. ! [X0] : (((calm(X0) & ~generous(X0)) | ((~kind(X0) | ~old(X0)) & (old(X0) | kind(X0)))) & (((~old(X0) | kind(X0)) & (old(X0) | ~kind(X0))) | (~calm(X0) | generous(X0)))) [nnf transformation 4]
39. ! [X0] : (((calm(X0) & ~generous(X0)) | ((~kind(X0) | ~old(X0)) & (old(X0) | kind(X0)))) & (((~old(X0) | kind(X0)) & (old(X0) | ~kind(X0))) | ~calm(X0) | generous(X0))) [flattening 38]
40. ! [X0] : ((~generous(X0) | (quiet(X0) | ~kind(X0))) & ((~quiet(X0) & kind(X0)) | generous(X0))) [nnf transformation 5]
41. ! [X0] : ((~generous(X0) | quiet(X0) | ~kind(X0)) & ((~quiet(X0) & kind(X0)) | generous(X0))) [flattening 40]
60. ! [X0] : (((~quiet(X0) | happy(X0)) | ~quiet(X0)) & (quiet(X0) | (quiet(X0) & ~happy(X0)))) [nnf transformation 12]
61. ! [X0] : ((~quiet(X0) | happy(X0) | ~quiet(X0)) & (quiet(X0) | (quiet(X0) & ~happy(X0)))) [flattening 60]
73. ~kind(X0) | ~generous(X0) | ~old(X0) [cnf transformation 39]
77. ~quiet(X0) | generous(X0) [cnf transformation 41]
100. quiet(X0) | quiet(X0) [cnf transformation 61]
104. kind(X0) | ~quiet(X0) [cnf transformation 32]
119. old(lucy) [cnf transformation 22]
121. quiet(X0) [duplicate literal removal 100]
124. 1 <=> ! [X0] : ~old(X0) [avatar definition]
125. ~old(X0) <- (1) [avatar component clause 124]
163. 10 <=> old(lucy) [avatar definition]
165. old(lucy) <- (10) [avatar component clause 163]
206. kind(X0) [subsumption resolution 104,121]
223. 10 [avatar split clause 119,163]
226. generous(X0) [resolution 77,121]
236. ~generous(X2) | ~old(X2) [resolution 73,206]
237. ~old(X2) [subsumption resolution 236,226]
238. 1 [avatar split clause 237,124]
239. $false <- (1, 10) [resolution 125,165]
243. ~1 | ~10 [avatar contradiction clause 239]
244. $false [avatar sat refutation 223,238,243]
% SZS output end Proof for 220248703364184827754770
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
If mary is not wise then someone is old or not tall and vice versa.
Everyone who is brave or not generous is curious.
Everyone who is either quiet or not humble is both generous and wise and vice versa.
Everyone who is not wise or not generous is wise or curious.
Everyone who is tall or quiet is not kind.
Everyone who is both funny and not humble is not curious or curious and vice versa.
If someone is tall then someone is both calm and curious and vice versa.
Everyone who is either generous or not calm is not brave.
If susan is either not curious or creative then mary is either funny or kind.
Everyone who is not funny is either brave or curious and vice versa.
If mary is not generous then someone is either patient or not patient and vice versa.
If fred is either tall or rich then someone is old.
Everyone who is either not brave or curious is both brave and not patient.
If someone is either not funny or calm then john is funny or humble and vice versa.
Everyone who is kind or not brave is old or wise and vice versa.
Mary is either humble or happy.
Someone is funny or not brave.
John is curious or humble.
Mary is not patient or not tall.
John is strong or not quiet.
Fred is either calm or kind.
Fred is tall. | John is not patient. | entailment | ((~wise(mary))<=>(?[X]:((old(X)|~tall(X)))))&
(![X]:((brave(X)|~generous(X))=>curious(X)))&
(![X]:((quiet(X)<~>~humble(X))<=>(generous(X)&wise(X))))&
(![X]:((~wise(X)|~generous(X))=>(wise(X)|curious(X))))&
(![X]:((tall(X)|quiet(X))=>~kind(X)))&
(![X]:((funny(X)&~humble(X))<=>(~curious(X)|curious(X))))&
((?[X]:(tall(X)))<=>(?[X]:((calm(X)&curious(X)))))&
(![X]:((generous(X)<~>~calm(X))=>~brave(X)))&
(((~curious(susan)<~>creative(susan)))=>((funny(mary)<~>kind(mary))))&
(![X]:(~funny(X)<=>(brave(X)<~>curious(X))))&
((~generous(mary))<=>(?[X]:((patient(X)<~>~patient(X)))))&
(((tall(fred)<~>rich(fred)))=>(?[X]:(old(X))))&
(![X]:((~brave(X)<~>curious(X))=>(brave(X)&~patient(X))))&
((?[X]:((~funny(X)<~>calm(X))))<=>((funny(john)|humble(john))))&
(![X]:((kind(X)|~brave(X))<=>(old(X)|wise(X))))&
((humble(mary)<~>happy(mary)))&
(?[X]:((funny(X)|~brave(X))))&
((curious(john)|humble(john)))&
((~patient(mary)|~tall(mary)))&
((strong(john)|~quiet(john)))&
((calm(fred)<~>kind(fred)))&
(tall(fred)) | ~patient(john) | [
"p1",
"p5",
"p9",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 2082803577739085566240971
% SZS output start Proof for 2082803577739085566240971
2. ! [X0] : ((~generous(X0) | brave(X0)) => curious(X0)) [input p1]
6. ! [X0] : ((~humble(X0) & funny(X0)) <=> (curious(X0) | ~curious(X0))) [input p5]
10. ! [X0] : (~funny(X0) <=> (brave(X0) <~> curious(X0))) [input p9]
13. ! [X0] : ((~brave(X0) <~> curious(X0)) => (~patient(X0) & brave(X0))) [input p12]
23. patient(john) [input hypothesis]
26. ! [X0] : (curious(X0) | (generous(X0) & ~brave(X0))) [ennf transformation 2]
33. ! [X0] : ((~patient(X0) & brave(X0)) | (~brave(X0) <=> curious(X0))) [ennf transformation 13]
40. ! [X0] : (((~humble(X0) & funny(X0)) | (~curious(X0) & curious(X0))) & ((curious(X0) | ~curious(X0)) | (humble(X0) | ~funny(X0)))) [nnf transformation 6]
41. ! [X0] : (((~humble(X0) & funny(X0)) | (~curious(X0) & curious(X0))) & (curious(X0) | ~curious(X0) | humble(X0) | ~funny(X0))) [flattening 40]
49. ! [X0] : ((~funny(X0) | ((brave(X0) | ~curious(X0)) & (curious(X0) | ~brave(X0)))) & (((~curious(X0) | ~brave(X0)) & (curious(X0) | brave(X0))) | funny(X0))) [nnf transformation 10]
57. ! [X0] : ((~patient(X0) & brave(X0)) | ((~brave(X0) | ~curious(X0)) & (curious(X0) | brave(X0)))) [nnf transformation 33]
72. ~brave(X0) | curious(X0) [cnf transformation 26]
85. funny(X0) | curious(X0) [cnf transformation 41]
86. ~curious(X0) | funny(X0) [cnf transformation 41]
101. ~funny(X0) | brave(X0) | ~curious(X0) [cnf transformation 49]
108. brave(X0) | curious(X0) | brave(X0) [cnf transformation 57]
111. ~patient(X0) | ~brave(X0) | ~curious(X0) [cnf transformation 57]
130. patient(john) [cnf transformation 23]
131. brave(X0) | curious(X0) [duplicate literal removal 108]
157. funny(X0) [subsumption resolution 85,86]
195. ~curious(X0) | brave(X0) [subsumption resolution 101,157]
222. ~patient(X0) | ~curious(X0) [subsumption resolution 111,195]
224. curious(X0) [subsumption resolution 131,72]
260. ~curious(john) [resolution 222,130]
261. $false [subsumption resolution 260,224]
% SZS output end Proof for 2082803577739085566240971
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If someone is both strong and not funny then paul is wise or not kind.
Everyone who is both humble and calm is either humble or not old.
Everyone who is calm or not strong is both calm and quiet and vice versa.
Everyone who is either not strong or funny is strong or calm and vice versa.
If susan is tall then someone is not calm and vice versa.
If mary is not generous then lucy is either not rich or wise and vice versa.
Everyone who is both not curious and not quiet is either not funny or not wise and vice versa.
If lucy is not generous then someone is both not generous and not quiet and vice versa.
If someone is not happy then fred is calm.
If alice is not curious or not creative then alice is funny or not funny.
If lucy is both not funny and curious then someone is tall or not strong and vice versa.
Everyone who is not happy is strong and vice versa.
Everyone who is either old or not tall is rich or patient.
Everyone who is generous or tall is not kind or not rich and vice versa.
Everyone who is not tall or kind is both kind and not quiet.
Everyone who is either not funny or not creative is both not creative and not rich.
Someone is not kind.
John is not kind or not old.
Someone is both rich and brave.
Someone is either kind or tall.
Fred is old.
Mary is not curious. | Mary is patient. | neutral | ((?[X]:((strong(X)&~funny(X))))=>((wise(paul)|~kind(paul))))&
(![X]:((humble(X)&calm(X))=>(humble(X)<~>~old(X))))&
(![X]:((calm(X)|~strong(X))<=>(calm(X)&quiet(X))))&
(![X]:((~strong(X)<~>funny(X))<=>(strong(X)|calm(X))))&
((tall(susan))<=>(?[X]:(~calm(X))))&
((~generous(mary))<=>((~rich(lucy)<~>wise(lucy))))&
(![X]:((~curious(X)&~quiet(X))<=>(~funny(X)<~>~wise(X))))&
((~generous(lucy))<=>(?[X]:((~generous(X)&~quiet(X)))))&
((?[X]:(~happy(X)))=>(calm(fred)))&
(((~curious(alice)|~creative(alice)))=>((funny(alice)|~funny(alice))))&
(((~funny(lucy)&curious(lucy)))<=>(?[X]:((tall(X)|~strong(X)))))&
(![X]:(~happy(X)<=>strong(X)))&
(![X]:((old(X)<~>~tall(X))=>(rich(X)|patient(X))))&
(![X]:((generous(X)|tall(X))<=>(~kind(X)|~rich(X))))&
(![X]:((~tall(X)|kind(X))=>(kind(X)&~quiet(X))))&
(![X]:((~funny(X)<~>~creative(X))=>(~creative(X)&~rich(X))))&
(?[X]:(~kind(X)))&
((~kind(john)|~old(john)))&
(?[X]:((rich(X)&brave(X))))&
(?[X]:((kind(X)<~>tall(X))))&
(old(fred))&
(~curious(mary)) | patient(mary) | [] | null | 0 |
If lucy is either not funny or strong then fred is both creative and calm and vice versa.
Everyone who is both not curious and not quiet is either not tall or not rich.
If mary is either generous or not creative then susan is either brave or not strong and vice versa.
Everyone who is both not funny and patient is both rich and tall.
Everyone who is brave is not creative or strong.
Everyone who is patient is either not happy or creative.
If someone is both not old and funny then alice is both not creative and not curious.
Everyone who is both generous and not generous is not curious or not generous and vice versa.
If fred is brave then someone is not generous and vice versa.
Everyone who is not quiet or not patient is not curious.
If lucy is both funny and not rich then mary is either kind or curious and vice versa.
If someone is both wise and not calm then someone is wise or curious and vice versa.
If lucy is either not happy or not rich then someone is both not wise and not generous.
If someone is both not kind and not patient then john is not strong or not brave and vice versa.
Everyone who is rich is not quiet or old and vice versa.
If someone is both not patient and funny then lucy is not rich or not brave.
Someone is generous or not brave.
Fred is not humble or quiet.
Susan is both brave and strong.
Paul is not calm.
Someone is old or wise. | Lucy is not happy. | contradiction | (((~funny(lucy)<~>strong(lucy)))<=>((creative(fred)&calm(fred))))&
(![X]:((~curious(X)&~quiet(X))=>(~tall(X)<~>~rich(X))))&
(((generous(mary)<~>~creative(mary)))<=>((brave(susan)<~>~strong(susan))))&
(![X]:((~funny(X)&patient(X))=>(rich(X)&tall(X))))&
(![X]:(brave(X)=>(~creative(X)|strong(X))))&
(![X]:(patient(X)=>(~happy(X)<~>creative(X))))&
((?[X]:((~old(X)&funny(X))))=>((~creative(alice)&~curious(alice))))&
(![X]:((generous(X)&~generous(X))<=>(~curious(X)|~generous(X))))&
((brave(fred))<=>(?[X]:(~generous(X))))&
(![X]:((~quiet(X)|~patient(X))=>~curious(X)))&
(((funny(lucy)&~rich(lucy)))<=>((kind(mary)<~>curious(mary))))&
((?[X]:((wise(X)&~calm(X))))<=>(?[X]:((wise(X)|curious(X)))))&
(((~happy(lucy)<~>~rich(lucy)))=>(?[X]:((~wise(X)&~generous(X)))))&
((?[X]:((~kind(X)&~patient(X))))<=>((~strong(john)|~brave(john))))&
(![X]:(rich(X)<=>(~quiet(X)|old(X))))&
((?[X]:((~patient(X)&funny(X))))=>((~rich(lucy)|~brave(lucy))))&
(?[X]:((generous(X)|~brave(X))))&
((~humble(fred)|quiet(fred)))&
((brave(susan)&strong(susan)))&
(~calm(paul))&
(?[X]:((old(X)|wise(X)))) | ~happy(lucy) | [
"p3",
"p6",
"p7",
"p9",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5146170192698574848185564
% SZS output start Proof for 5146170192698574848185564
4. ! [X0] : ((patient(X0) & ~funny(X0)) => (tall(X0) & rich(X0))) [input p3]
7. ? [X0] : (funny(X0) & ~old(X0)) => (~curious(alice) & ~creative(alice)) [input p6]
8. ! [X0] : ((~generous(X0) & generous(X0)) <=> (~generous(X0) | ~curious(X0))) [input p7]
10. ! [X0] : ((~patient(X0) | ~quiet(X0)) => ~curious(X0)) [input p9]
13. (~happy(lucy) <~> ~rich(lucy)) => ? [X0] : (~generous(X0) & ~wise(X0)) [input p12]
15. ! [X0] : (rich(X0) <=> (old(X0) | ~quiet(X0))) [input p14]
22. ~happy(lucy) [input hypothesis]
27. ! [X0] : ((tall(X0) & rich(X0)) | (~patient(X0) | funny(X0))) [ennf transformation 4]
28. ! [X0] : ((tall(X0) & rich(X0)) | ~patient(X0) | funny(X0)) [flattening 27]
32. (~curious(alice) & ~creative(alice)) | ! [X0] : (~funny(X0) | old(X0)) [ennf transformation 7]
33. ! [X0] : (~curious(X0) | (patient(X0) & quiet(X0))) [ennf transformation 10]
34. ? [X0] : (~generous(X0) & ~wise(X0)) | (~happy(lucy) <=> ~rich(lucy)) [ennf transformation 13]
42. ! [X0] : (((~generous(X0) & generous(X0)) | (generous(X0) & curious(X0))) & ((~generous(X0) | ~curious(X0)) | (generous(X0) | ~generous(X0)))) [nnf transformation 8]
43. ! [X0] : (((~generous(X0) & generous(X0)) | (generous(X0) & curious(X0))) & (~generous(X0) | ~curious(X0) | generous(X0) | ~generous(X0))) [flattening 42]
55. ? [X0] : (~generous(X0) & ~wise(X0)) | ((~happy(lucy) | rich(lucy)) & (~rich(lucy) | happy(lucy))) [nnf transformation 34]
56. ? [X0] : (~generous(X0) & ~wise(X0)) => (~generous(sK3) & ~wise(sK3)) [choice axiom]
57. (~generous(sK3) & ~wise(sK3)) | ((~happy(lucy) | rich(lucy)) & (~rich(lucy) | happy(lucy))) [skolemisation 55,56]
63. ! [X0] : ((rich(X0) | (~old(X0) & quiet(X0))) & ((old(X0) | ~quiet(X0)) | ~rich(X0))) [nnf transformation 15]
64. ! [X0] : ((rich(X0) | (~old(X0) & quiet(X0))) & (old(X0) | ~quiet(X0) | ~rich(X0))) [flattening 63]
85. ~patient(X0) | rich(X0) | funny(X0) [cnf transformation 28]
91. ~curious(alice) | ~funny(X0) | old(X0) [cnf transformation 32]
94. generous(X0) | generous(X0) [cnf transformation 43]
95. ~generous(X0) | curious(X0) [cnf transformation 43]
100. ~curious(X0) | patient(X0) [cnf transformation 33]
114. ~generous(sK3) | ~rich(lucy) | happy(lucy) [cnf transformation 57]
123. ~old(X0) | rich(X0) [cnf transformation 64]
130. ~happy(lucy) [cnf transformation 22]
132. generous(X0) [duplicate literal removal 94]
142. 3 <=> funny(lucy) [avatar definition]
143. ~funny(lucy) <- (~3) [avatar component clause 142]
144. funny(lucy) <- (3) [avatar component clause 142]
180. 9 <=> ! [X0] : (~funny(X0) | old(X0)) [avatar definition]
181. ~funny(X0) | old(X0) <- (9) [avatar component clause 180]
183. 10 <=> curious(alice) [avatar definition]
185. ~curious(alice) <- (~10) [avatar component clause 183]
186. 9 | ~10 [avatar split clause 91,183,180]
202. 14 <=> rich(lucy) [avatar definition]
204. ~rich(lucy) <- (~14) [avatar component clause 202]
243. 22 <=> happy(lucy) [avatar definition]
247. ~rich(lucy) | happy(lucy) [subsumption resolution 114,132]
248. 22 | ~14 [avatar split clause 247,202,243]
298. ~22 [avatar split clause 130,243]
301. curious(X0) [resolution 95,132]
304. $false <- (~10) [subsumption resolution 185,301]
305. 10 [avatar contradiction clause 304]
311. patient(X0) [resolution 100,301]
316. old(lucy) <- (3, 9) [resolution 181,144]
320. rich(X0) | funny(X0) [resolution 85,311]
321. rich(lucy) <- (3, 9) [resolution 316,123]
322. $false <- (3, 9, ~14) [subsumption resolution 321,204]
323. ~3 | ~9 | 14 [avatar contradiction clause 322]
324. funny(lucy) <- (~14) [resolution 320,204]
325. $false <- (~3, ~14) [subsumption resolution 324,143]
326. 3 | 14 [avatar contradiction clause 325]
327. $false [avatar sat refutation 186,248,298,305,323,326]
% SZS output end Proof for 5146170192698574848185564
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
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