premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
values | proof_inputs
listlengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
|
|---|---|---|---|---|---|---|---|
Everyone who is not strong is either not generous or curious. Everyone who is both rich and quiet is either not calm or tall and vice versa. Everyone who is not generous or not happy is not happy and vice versa. If lucy is both not creative and not funny then someone is strong or rich. If someone is not rich or tall then someone is both brave and tall and vice versa. Everyone who is both not old and not rich is not tall or creative and vice versa. Everyone who is not strong or old is either funny or happy and vice versa. If mary is not brave or quiet then someone is either calm or tall and vice versa. Everyone who is not wise or not generous is both rich and not funny. If paul is both old and not quiet then john is both kind and not old and vice versa. If someone is either not generous or tall then someone is not curious and vice versa. Everyone who is not wise is not happy or not old and vice versa. Everyone who is either not creative or patient is patient or not funny. If mary is curious or not old then someone is rich. If someone is both humble and quiet then someone is both not curious and not humble and vice versa. Everyone who is patient or generous is both rich and funny and vice versa. Someone is both quiet and kind. Alice is not old or not strong. Someone is not kind or tall. Alice is not generous or not humble. | Alice is not funny. | entailment | (![X]:(~strong(X)=>(~generous(X)<~>curious(X))))&
(![X]:((rich(X)&quiet(X))<=>(~calm(X)<~>tall(X))))&
(![X]:((~generous(X)|~happy(X))<=>~happy(X)))&
(((~creative(lucy)&~funny(lucy)))=>(?[X]:((strong(X)|rich(X)))))&
((?[X]:((~rich(X)|tall(X))))<=>(?[X]:((brave(X)&tall(X)))))&
(![X]:((~old(X)&~rich(X))<=>(~tall(X)|creative(X))))&
(![X]:((~strong(X)|old(X))<=>(funny(X)<~>happy(X))))&
(((~brave(mary)|quiet(mary)))<=>(?[X]:((calm(X)<~>tall(X)))))&
(![X]:((~wise(X)|~generous(X))=>(rich(X)&~funny(X))))&
(((old(paul)&~quiet(paul)))<=>((kind(john)&~old(john))))&
((?[X]:((~generous(X)<~>tall(X))))<=>(?[X]:(~curious(X))))&
(![X]:(~wise(X)<=>(~happy(X)|~old(X))))&
(![X]:((~creative(X)<~>patient(X))=>(patient(X)|~funny(X))))&
(((curious(mary)|~old(mary)))=>(?[X]:(rich(X))))&
((?[X]:((humble(X)&quiet(X))))<=>(?[X]:((~curious(X)&~humble(X)))))&
(![X]:((patient(X)|generous(X))<=>(rich(X)&funny(X))))&
(?[X]:((quiet(X)&kind(X))))&
((~old(alice)|~strong(alice)))&
(?[X]:((~kind(X)|tall(X))))&
((~generous(alice)|~humble(alice))) | ~funny(alice) | [
"p6",
"p8",
"p11",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 1876195578830296752964192
% SZS output start Proof for 1876195578830296752964192
7. ! [X0] : ((old(X0) | ~strong(X0)) <=> (funny(X0) <~> happy(X0))) [input p6]
9. ! [X0] : ((~generous(X0) | ~wise(X0)) => (~funny(X0) & rich(X0))) [input p8]
12. ! [X0] : (~wise(X0) <=> (~old(X0) | ~happy(X0))) [input p11]
18. ~strong(alice) | ~old(alice) [input p17]
21. funny(alice) [input hypothesis]
25. ! [X0] : ((~old(X0) | ~happy(X0)) => ~wise(X0)) [unused predicate definition removal 12]
29. ! [X0] : ((~funny(X0) & rich(X0)) | (generous(X0) & wise(X0))) [ennf transformation 9]
30. ! [X0] : (~wise(X0) | (old(X0) & happy(X0))) [ennf transformation 25]
48. ! [X0] : (((old(X0) | ~strong(X0)) | ((funny(X0) | ~happy(X0)) & (happy(X0) | ~funny(X0)))) & (((~happy(X0) | ~funny(X0)) & (happy(X0) | funny(X0))) | (~old(X0) & strong(X0)))) [nnf transformation 7]
49. ! [X0] : ((old(X0) | ~strong(X0) | ((funny(X0) | ~happy(X0)) & (happy(X0) | ~funny(X0)))) & (((~happy(X0) | ~funny(X0)) & (happy(X0) | funny(X0))) | (~old(X0) & strong(X0)))) [flattening 48]
100. ~funny(X0) | ~happy(X0) | strong(X0) [cnf transformation 49]
112. ~funny(X0) | wise(X0) [cnf transformation 29]
122. ~wise(X0) | happy(X0) [cnf transformation 30]
123. ~wise(X0) | old(X0) [cnf transformation 30]
139. ~strong(alice) | ~old(alice) [cnf transformation 18]
142. funny(alice) [cnf transformation 21]
307. 37 <=> old(alice) [avatar definition]
311. 38 <=> strong(alice) [avatar definition]
313. ~strong(alice) <- (~38) [avatar component clause 311]
314. ~37 | ~38 [avatar split clause 139,311,307]
349. wise(alice) [resolution 112,142]
355. happy(alice) [resolution 122,349]
358. old(alice) [resolution 123,349]
362. 37 [avatar split clause 358,307]
492. ~happy(alice) | strong(alice) [resolution 100,142]
496. strong(alice) [subsumption resolution 492,355]
497. $false <- (~38) [subsumption resolution 496,313]
498. 38 [avatar contradiction clause 497]
499. $false [avatar sat refutation 314,362,498]
% SZS output end Proof for 1876195578830296752964192
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If paul is not funny or not old then susan is both strong and not old and vice versa.
If lucy is not curious or not wise then john is generous or curious.
Everyone who is not old or rich is generous.
Everyone who is both not humble and not funny is not brave.
If someone is patient then someone is patient or not curious and vice versa.
Everyone who is generous is curious or calm.
If paul is either not patient or not calm then alice is strong or not strong.
Everyone who is both wise and quiet is not brave or funny and vice versa.
Everyone who is wise is either not kind or patient and vice versa.
If susan is brave then someone is humble or wise.
Everyone who is not strong is wise or not strong.
If someone is either not brave or old then someone is old and vice versa.
Everyone who is both patient and calm is either not creative or not tall.
Everyone who is wise or strong is not calm or not happy and vice versa.
Everyone who is old is not tall or humble and vice versa.
Everyone who is not generous is both humble and happy.
Lucy is happy.
Someone is both not strong and humble.
John is either brave or not brave.
Someone is either happy or not strong.
Someone is not strong.
Someone is both not brave and quiet.
Fred is both humble and not patient.
Someone is either not funny or old. | Fred is humble. | entailment | (((~funny(paul)|~old(paul)))<=>((strong(susan)&~old(susan))))&
(((~curious(lucy)|~wise(lucy)))=>((generous(john)|curious(john))))&
(![X]:((~old(X)|rich(X))=>generous(X)))&
(![X]:((~humble(X)&~funny(X))=>~brave(X)))&
((?[X]:(patient(X)))<=>(?[X]:((patient(X)|~curious(X)))))&
(![X]:(generous(X)=>(curious(X)|calm(X))))&
(((~patient(paul)<~>~calm(paul)))=>((strong(alice)|~strong(alice))))&
(![X]:((wise(X)&quiet(X))<=>(~brave(X)|funny(X))))&
(![X]:(wise(X)<=>(~kind(X)<~>patient(X))))&
((brave(susan))=>(?[X]:((humble(X)|wise(X)))))&
(![X]:(~strong(X)=>(wise(X)|~strong(X))))&
((?[X]:((~brave(X)<~>old(X))))<=>(?[X]:(old(X))))&
(![X]:((patient(X)&calm(X))=>(~creative(X)<~>~tall(X))))&
(![X]:((wise(X)|strong(X))<=>(~calm(X)|~happy(X))))&
(![X]:(old(X)<=>(~tall(X)|humble(X))))&
(![X]:(~generous(X)=>(humble(X)&happy(X))))&
(happy(lucy))&
(?[X]:((~strong(X)&humble(X))))&
((brave(john)<~>~brave(john)))&
(?[X]:((happy(X)<~>~strong(X))))&
(?[X]:(~strong(X)))&
(?[X]:((~brave(X)&quiet(X))))&
((humble(fred)&~patient(fred)))&
(?[X]:((~funny(X)<~>old(X)))) | humble(fred) | [
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 7359146201862382286595795
% SZS output start Proof for 7359146201862382286595795
23. ~patient(fred) & humble(fred) [input p22]
25. ~humble(fred) [input hypothesis]
131. humble(fred) [cnf transformation 23]
135. ~humble(fred) [cnf transformation 25]
254. $false [subsumption resolution 135,131]
% SZS output end Proof for 7359146201862382286595795
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not wise is not quiet or not patient.
Everyone who is not creative or not tall is not kind or not quiet.
If someone is either not brave or generous then someone is not patient or not kind and vice versa.
If john is both old and not strong then someone is humble or curious and vice versa.
Everyone who is creative or not strong is not wise or not quiet and vice versa.
Everyone who is not tall or happy is either not quiet or patient.
Everyone who is both tall and brave is old or rich and vice versa.
If mary is both not funny and not brave then lucy is creative or not humble and vice versa.
Everyone who is either not strong or strong is not funny or patient and vice versa.
If alice is not kind or not calm then someone is either not wise or generous and vice versa.
If someone is both generous and not old then someone is not brave or wise.
If someone is either funny or not generous then someone is both not generous and not calm and vice versa.
If mary is both not kind and old then someone is either wise or calm and vice versa.
Everyone who is not tall or strong is not patient and vice versa.
If lucy is not strong then someone is both patient and generous and vice versa.
If fred is humble then someone is either strong or curious and vice versa.
Fred is not generous.
Someone is both not patient and not generous.
Someone is not humble or old.
Lucy is not patient or not curious.
Someone is either not wise or not curious.
Someone is both strong and curious.
Lucy is either generous or not strong.
Someone is either calm or not wise. | John is not quiet. | entailment | (![X]:(~wise(X)=>(~quiet(X)|~patient(X))))&
(![X]:((~creative(X)|~tall(X))=>(~kind(X)|~quiet(X))))&
((?[X]:((~brave(X)<~>generous(X))))<=>(?[X]:((~patient(X)|~kind(X)))))&
(((old(john)&~strong(john)))<=>(?[X]:((humble(X)|curious(X)))))&
(![X]:((creative(X)|~strong(X))<=>(~wise(X)|~quiet(X))))&
(![X]:((~tall(X)|happy(X))=>(~quiet(X)<~>patient(X))))&
(![X]:((tall(X)&brave(X))<=>(old(X)|rich(X))))&
(((~funny(mary)&~brave(mary)))<=>((creative(lucy)|~humble(lucy))))&
(![X]:((~strong(X)<~>strong(X))<=>(~funny(X)|patient(X))))&
(((~kind(alice)|~calm(alice)))<=>(?[X]:((~wise(X)<~>generous(X)))))&
((?[X]:((generous(X)&~old(X))))=>(?[X]:((~brave(X)|wise(X)))))&
((?[X]:((funny(X)<~>~generous(X))))<=>(?[X]:((~generous(X)&~calm(X)))))&
(((~kind(mary)&old(mary)))<=>(?[X]:((wise(X)<~>calm(X)))))&
(![X]:((~tall(X)|strong(X))<=>~patient(X)))&
((~strong(lucy))<=>(?[X]:((patient(X)&generous(X)))))&
((humble(fred))<=>(?[X]:((strong(X)<~>curious(X)))))&
(~generous(fred))&
(?[X]:((~patient(X)&~generous(X))))&
(?[X]:((~humble(X)|old(X))))&
((~patient(lucy)|~curious(lucy)))&
(?[X]:((~wise(X)<~>~curious(X))))&
(?[X]:((strong(X)&curious(X))))&
((generous(lucy)<~>~strong(lucy)))&
(?[X]:((calm(X)<~>~wise(X)))) | ~quiet(john) | [
"p0",
"p3",
"p4",
"p6",
"p13",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 3105398698597488309428502
% SZS output start Proof for 3105398698597488309428502
1. ! [X0] : (~wise(X0) => (~patient(X0) | ~quiet(X0))) [input p0]
4. (~strong(john) & old(john)) <=> ? [X0] : (curious(X0) | humble(X0)) [input p3]
5. ! [X0] : ((~strong(X0) | creative(X0)) <=> (~quiet(X0) | ~wise(X0))) [input p4]
7. ! [X0] : ((brave(X0) & tall(X0)) <=> (rich(X0) | old(X0))) [input p6]
14. ! [X0] : ((strong(X0) | ~tall(X0)) <=> ~patient(X0)) [input p13]
22. ? [X0] : (curious(X0) & strong(X0)) [input p21]
25. quiet(john) [input hypothesis]
30. ! [X0] : ((~patient(X0) | ~quiet(X0)) | wise(X0)) [ennf transformation 1]
31. ! [X0] : (~patient(X0) | ~quiet(X0) | wise(X0)) [flattening 30]
41. ((~strong(john) & old(john)) | ! [X0] : (~curious(X0) & ~humble(X0))) & (? [X0] : (curious(X0) | humble(X0)) | (strong(john) | ~old(john))) [nnf transformation 4]
42. ((~strong(john) & old(john)) | ! [X0] : (~curious(X0) & ~humble(X0))) & (? [X0] : (curious(X0) | humble(X0)) | strong(john) | ~old(john)) [flattening 41]
43. ((~strong(john) & old(john)) | ! [X0] : (~curious(X0) & ~humble(X0))) & (? [X1] : (curious(X1) | humble(X1)) | strong(john) | ~old(john)) [rectify 42]
44. ? [X1] : (curious(X1) | humble(X1)) => (curious(sK2) | humble(sK2)) [choice axiom]
45. ((~strong(john) & old(john)) | ! [X0] : (~curious(X0) & ~humble(X0))) & ((curious(sK2) | humble(sK2)) | strong(john) | ~old(john)) [skolemisation 43,44]
46. ! [X0] : (((~strong(X0) | creative(X0)) | (quiet(X0) & wise(X0))) & ((~quiet(X0) | ~wise(X0)) | (strong(X0) & ~creative(X0)))) [nnf transformation 5]
47. ! [X0] : ((~strong(X0) | creative(X0) | (quiet(X0) & wise(X0))) & (~quiet(X0) | ~wise(X0) | (strong(X0) & ~creative(X0)))) [flattening 46]
49. ! [X0] : (((brave(X0) & tall(X0)) | (~rich(X0) & ~old(X0))) & ((rich(X0) | old(X0)) | (~brave(X0) | ~tall(X0)))) [nnf transformation 7]
50. ! [X0] : (((brave(X0) & tall(X0)) | (~rich(X0) & ~old(X0))) & (rich(X0) | old(X0) | ~brave(X0) | ~tall(X0))) [flattening 49]
73. ! [X0] : (((strong(X0) | ~tall(X0)) | patient(X0)) & (~patient(X0) | (~strong(X0) & tall(X0)))) [nnf transformation 14]
74. ! [X0] : ((strong(X0) | ~tall(X0) | patient(X0)) & (~patient(X0) | (~strong(X0) & tall(X0)))) [flattening 73]
90. ? [X0] : (curious(X0) & strong(X0)) => (curious(sK13) & strong(sK13)) [choice axiom]
91. curious(sK13) & strong(sK13) [skolemisation 22,90]
96. ~patient(X0) | ~quiet(X0) | wise(X0) [cnf transformation 31]
107. old(john) | ~curious(X0) [cnf transformation 45]
109. ~strong(john) | ~curious(X0) [cnf transformation 45]
111. ~quiet(X0) | ~wise(X0) | strong(X0) [cnf transformation 47]
117. ~old(X0) | tall(X0) [cnf transformation 50]
153. ~tall(X0) | strong(X0) | patient(X0) [cnf transformation 74]
169. curious(sK13) [cnf transformation 91]
174. quiet(john) [cnf transformation 25]
212. 9 <=> ! [X0] : ~curious(X0) [avatar definition]
213. ~curious(X0) <- (9) [avatar component clause 212]
215. 10 <=> strong(john) [avatar definition]
217. ~strong(john) <- (~10) [avatar component clause 215]
218. 9 | ~10 [avatar split clause 109,215,212]
224. 12 <=> old(john) [avatar definition]
226. old(john) <- (12) [avatar component clause 224]
227. 9 | 12 [avatar split clause 107,224,212]
443. $false <- (9) [resolution 213,169]
444. ~9 [avatar contradiction clause 443]
447. tall(john) <- (12) [resolution 117,226]
465. ~wise(john) | strong(john) [resolution 111,174]
466. ~wise(john) <- (~10) [subsumption resolution 465,217]
490. strong(john) | patient(john) <- (12) [resolution 153,447]
492. patient(john) <- (~10, 12) [subsumption resolution 490,217]
494. ~quiet(john) | wise(john) <- (~10, 12) [resolution 492,96]
496. wise(john) <- (~10, 12) [subsumption resolution 494,174]
497. $false <- (~10, 12) [subsumption resolution 496,466]
498. 10 | ~12 [avatar contradiction clause 497]
499. $false [avatar sat refutation 218,227,444,498]
% SZS output end Proof for 3105398698597488309428502
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is old then someone is rich or not old and vice versa.
If someone is quiet or wise then someone is not brave and vice versa.
If susan is not happy or not wise then lucy is either kind or not old.
If someone is curious then someone is both happy and not happy.
Everyone who is old is humble and vice versa.
If someone is not strong or strong then someone is either not generous or not humble.
Everyone who is either humble or happy is both not tall and brave and vice versa.
Everyone who is not tall is not humble and vice versa.
Everyone who is creative or quiet is both not wise and generous.
If mary is either generous or not rich then someone is patient and vice versa.
Everyone who is both patient and not generous is both not tall and not curious.
Everyone who is not quiet or not old is not patient or tall.
Everyone who is either not rich or not quiet is not brave or humble and vice versa.
Everyone who is either strong or generous is rich or not happy and vice versa.
Someone is not generous.
Someone is not quiet.
Someone is either patient or humble.
Paul is not happy.
Mary is either creative or not rich.
Lucy is either quiet or not curious.
Mary is either not wise or not strong. | Paul is not patient. | entailment | ((old(lucy))<=>(?[X]:((rich(X)|~old(X)))))&
((?[X]:((quiet(X)|wise(X))))<=>(?[X]:(~brave(X))))&
(((~happy(susan)|~wise(susan)))=>((kind(lucy)<~>~old(lucy))))&
((?[X]:(curious(X)))=>(?[X]:((happy(X)&~happy(X)))))&
(![X]:(old(X)<=>humble(X)))&
((?[X]:((~strong(X)|strong(X))))=>(?[X]:((~generous(X)<~>~humble(X)))))&
(![X]:((humble(X)<~>happy(X))<=>(~tall(X)&brave(X))))&
(![X]:(~tall(X)<=>~humble(X)))&
(![X]:((creative(X)|quiet(X))=>(~wise(X)&generous(X))))&
(((generous(mary)<~>~rich(mary)))<=>(?[X]:(patient(X))))&
(![X]:((patient(X)&~generous(X))=>(~tall(X)&~curious(X))))&
(![X]:((~quiet(X)|~old(X))=>(~patient(X)|tall(X))))&
(![X]:((~rich(X)<~>~quiet(X))<=>(~brave(X)|humble(X))))&
(![X]:((strong(X)<~>generous(X))<=>(rich(X)|~happy(X))))&
(?[X]:(~generous(X)))&
(?[X]:(~quiet(X)))&
(?[X]:((patient(X)<~>humble(X))))&
(~happy(paul))&
((creative(mary)<~>~rich(mary)))&
((quiet(lucy)<~>~curious(lucy)))&
((~wise(mary)<~>~strong(mary))) | ~patient(paul) | [
"p4",
"p6",
"p7",
"p11",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 895616137499517542838959
% SZS output start Proof for 895616137499517542838959
5. ! [X0] : (old(X0) <=> humble(X0)) [input p4]
7. ! [X0] : ((humble(X0) <~> happy(X0)) <=> (brave(X0) & ~tall(X0))) [input p6]
8. ! [X0] : (~tall(X0) <=> ~humble(X0)) [input p7]
12. ! [X0] : ((~old(X0) | ~quiet(X0)) => (tall(X0) | ~patient(X0))) [input p11]
18. ~happy(paul) [input p17]
22. patient(paul) [input hypothesis]
32. ! [X0] : ((tall(X0) | ~patient(X0)) | (old(X0) & quiet(X0))) [ennf transformation 12]
33. ! [X0] : (tall(X0) | ~patient(X0) | (old(X0) & quiet(X0))) [flattening 32]
47. ! [X0] : ((old(X0) | ~humble(X0)) & (humble(X0) | ~old(X0))) [nnf transformation 5]
52. ! [X0] : ((((~happy(X0) | ~humble(X0)) & (happy(X0) | humble(X0))) | (~brave(X0) | tall(X0))) & ((brave(X0) & ~tall(X0)) | ((humble(X0) | ~happy(X0)) & (happy(X0) | ~humble(X0))))) [nnf transformation 7]
53. ! [X0] : ((((~happy(X0) | ~humble(X0)) & (happy(X0) | humble(X0))) | ~brave(X0) | tall(X0)) & ((brave(X0) & ~tall(X0)) | ((humble(X0) | ~happy(X0)) & (happy(X0) | ~humble(X0))))) [flattening 52]
54. ! [X0] : ((~tall(X0) | humble(X0)) & (~humble(X0) | tall(X0))) [nnf transformation 8]
85. ~old(X0) | humble(X0) [cnf transformation 47]
91. ~tall(X0) | happy(X0) | ~humble(X0) [cnf transformation 53]
97. ~humble(X0) | tall(X0) [cnf transformation 54]
98. ~tall(X0) | humble(X0) [cnf transformation 54]
110. ~patient(X0) | tall(X0) | old(X0) [cnf transformation 33]
127. ~happy(paul) [cnf transformation 18]
134. patient(paul) [cnf transformation 22]
297. 32 <=> tall(paul) [avatar definition]
298. tall(paul) <- (32) [avatar component clause 297]
299. ~tall(paul) <- (~32) [avatar component clause 297]
332. tall(paul) | old(paul) [resolution 110,134]
335. old(paul) <- (~32) [subsumption resolution 332,299]
431. humble(paul) <- (~32) [resolution 335,85]
559. tall(paul) <- (~32) [resolution 431,97]
563. $false <- (~32) [subsumption resolution 559,299]
564. 32 [avatar contradiction clause 563]
576. happy(paul) | ~humble(paul) <- (32) [resolution 298,91]
577. humble(paul) <- (32) [resolution 298,98]
578. ~humble(paul) <- (32) [subsumption resolution 576,127]
579. $false <- (32) [subsumption resolution 577,578]
580. ~32 [avatar contradiction clause 579]
581. $false [avatar sat refutation 564,580]
% SZS output end Proof for 895616137499517542838959
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not generous or not strong is either curious or calm and vice versa.
Everyone who is either not rich or wise is not humble and vice versa.
Everyone who is both tall and brave is funny.
If someone is calm then lucy is calm or not generous.
Everyone who is not tall or happy is both not tall and not funny and vice versa.
If someone is both tall and creative then john is both not patient and kind.
If susan is both not strong and not humble then someone is both not calm and not creative.
Everyone who is brave is either funny or not tall.
Everyone who is either generous or not strong is either not happy or quiet and vice versa.
Everyone who is not curious or not generous is both patient and strong and vice versa.
Everyone who is both old and funny is humble.
Everyone who is either strong or not creative is both creative and old and vice versa.
Everyone who is both happy and not wise is not funny.
If paul is brave then john is not curious and vice versa.
Everyone who is both rich and not old is both not calm and strong.
If john is both old and happy then alice is calm and vice versa.
Someone is old.
Susan is both patient and not curious.
Someone is not patient.
Someone is funny or not generous.
Mary is humble or brave.
Mary is either not wise or curious.
Paul is calm or strong.
Fred is either funny or curious. | Paul is not happy. | neutral | (![X]:((~generous(X)<~>~strong(X))<=>(curious(X)<~>calm(X))))&
(![X]:((~rich(X)<~>wise(X))<=>~humble(X)))&
(![X]:((tall(X)&brave(X))=>funny(X)))&
((?[X]:(calm(X)))=>((calm(lucy)|~generous(lucy))))&
(![X]:((~tall(X)|happy(X))<=>(~tall(X)&~funny(X))))&
((?[X]:((tall(X)&creative(X))))=>((~patient(john)&kind(john))))&
(((~strong(susan)&~humble(susan)))=>(?[X]:((~calm(X)&~creative(X)))))&
(![X]:(brave(X)=>(funny(X)<~>~tall(X))))&
(![X]:((generous(X)<~>~strong(X))<=>(~happy(X)<~>quiet(X))))&
(![X]:((~curious(X)|~generous(X))<=>(patient(X)&strong(X))))&
(![X]:((old(X)&funny(X))=>humble(X)))&
(![X]:((strong(X)<~>~creative(X))<=>(creative(X)&old(X))))&
(![X]:((happy(X)&~wise(X))=>~funny(X)))&
((brave(paul))<=>(~curious(john)))&
(![X]:((rich(X)&~old(X))=>(~calm(X)&strong(X))))&
(((old(john)&happy(john)))<=>(calm(alice)))&
(?[X]:(old(X)))&
((patient(susan)&~curious(susan)))&
(?[X]:(~patient(X)))&
(?[X]:((funny(X)|~generous(X))))&
((humble(mary)|brave(mary)))&
((~wise(mary)<~>curious(mary)))&
((calm(paul)|strong(paul)))&
((funny(fred)<~>curious(fred))) | ~happy(paul) | [] | null | 0 |
If mary is either not old or not creative then someone is both tall and old.
If someone is both not humble and creative then fred is either not funny or tall and vice versa.
Everyone who is either calm or not kind is calm and vice versa.
If someone is both strong and wise then fred is either wise or tall and vice versa.
Everyone who is either not quiet or not humble is humble or tall.
If john is not patient then mary is both brave and calm and vice versa.
If someone is either patient or wise then someone is both humble and wise.
Everyone who is wise or creative is both rich and strong.
If lucy is either patient or not quiet then mary is either not creative or not humble and vice versa.
Everyone who is both not wise and not humble is curious.
Everyone who is both curious and not strong is either humble or not brave and vice versa.
Everyone who is curious or not old is either not happy or tall and vice versa.
Everyone who is happy or kind is either not patient or generous and vice versa.
If someone is not strong then someone is both not calm and patient and vice versa.
If someone is not creative then fred is not humble or old.
Everyone who is not patient is both strong and old.
Someone is tall or old.
Someone is both kind and wise.
Someone is both not quiet and curious.
Lucy is either not generous or strong.
Fred is either brave or not funny.
Paul is both rich and creative.
Someone is curious or not humble.
Someone is not wise or generous. | John is not kind. | contradiction | (((~old(mary)<~>~creative(mary)))=>(?[X]:((tall(X)&old(X)))))&
((?[X]:((~humble(X)&creative(X))))<=>((~funny(fred)<~>tall(fred))))&
(![X]:((calm(X)<~>~kind(X))<=>calm(X)))&
((?[X]:((strong(X)&wise(X))))<=>((wise(fred)<~>tall(fred))))&
(![X]:((~quiet(X)<~>~humble(X))=>(humble(X)|tall(X))))&
((~patient(john))<=>((brave(mary)&calm(mary))))&
((?[X]:((patient(X)<~>wise(X))))=>(?[X]:((humble(X)&wise(X)))))&
(![X]:((wise(X)|creative(X))=>(rich(X)&strong(X))))&
(((patient(lucy)<~>~quiet(lucy)))<=>((~creative(mary)<~>~humble(mary))))&
(![X]:((~wise(X)&~humble(X))=>curious(X)))&
(![X]:((curious(X)&~strong(X))<=>(humble(X)<~>~brave(X))))&
(![X]:((curious(X)|~old(X))<=>(~happy(X)<~>tall(X))))&
(![X]:((happy(X)|kind(X))<=>(~patient(X)<~>generous(X))))&
((?[X]:(~strong(X)))<=>(?[X]:((~calm(X)&patient(X)))))&
((?[X]:(~creative(X)))=>((~humble(fred)|old(fred))))&
(![X]:(~patient(X)=>(strong(X)&old(X))))&
(?[X]:((tall(X)|old(X))))&
(?[X]:((kind(X)&wise(X))))&
(?[X]:((~quiet(X)&curious(X))))&
((~generous(lucy)<~>strong(lucy)))&
((brave(fred)<~>~funny(fred)))&
((rich(paul)&creative(paul)))&
(?[X]:((curious(X)|~humble(X))))&
(?[X]:((~wise(X)|generous(X)))) | ~kind(john) | [
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 5470611282839308697442271
% SZS output start Proof for 5470611282839308697442271
3. ! [X0] : ((calm(X0) <~> ~kind(X0)) <=> calm(X0)) [input p2]
25. ~kind(john) [input hypothesis]
47. ! [X0] : ((((kind(X0) | ~calm(X0)) & (~kind(X0) | calm(X0))) | ~calm(X0)) & (calm(X0) | ((calm(X0) | kind(X0)) & (~kind(X0) | ~calm(X0))))) [nnf transformation 3]
94. calm(X0) | calm(X0) | kind(X0) [cnf transformation 47]
96. kind(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 47]
159. ~kind(john) [cnf transformation 25]
161. calm(X0) | kind(X0) [duplicate literal removal 94]
162. kind(X0) | ~calm(X0) [duplicate literal removal 96]
208. kind(X0) [subsumption resolution 161,162]
361. $false [subsumption resolution 159,208]
% SZS output end Proof for 5470611282839308697442271
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.018 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is old or funny is both not generous and not quiet and vice versa.
If lucy is rich then paul is either tall or generous and vice versa.
Everyone who is not brave is patient or wise and vice versa.
If someone is generous then someone is both not humble and not patient and vice versa.
Everyone who is generous or not rich is either not creative or funny.
Everyone who is either rich or not humble is strong or brave.
Everyone who is not generous or creative is not strong or not happy and vice versa.
If mary is both not quiet and not funny then lucy is both not curious and not funny.
Everyone who is brave or kind is either patient or wise.
Everyone who is old or curious is rich and vice versa.
Everyone who is both kind and not happy is either not funny or happy.
If alice is both kind and not kind then paul is either happy or tall and vice versa.
Everyone who is both quiet and not happy is both creative and calm.
Everyone who is either curious or brave is not brave or not humble.
Everyone who is either curious or not happy is not quiet and vice versa.
Everyone who is old or tall is either not rich or brave and vice versa.
Someone is either generous or not calm.
Paul is wise.
Paul is rich or not old.
Alice is both not curious and not brave.
Someone is generous or not tall.
Someone is both not tall and not old.
Someone is both curious and kind.
Someone is not wise. | Alice is calm. | neutral | (![X]:((old(X)|funny(X))<=>(~generous(X)&~quiet(X))))&
((rich(lucy))<=>((tall(paul)<~>generous(paul))))&
(![X]:(~brave(X)<=>(patient(X)|wise(X))))&
((?[X]:(generous(X)))<=>(?[X]:((~humble(X)&~patient(X)))))&
(![X]:((generous(X)|~rich(X))=>(~creative(X)<~>funny(X))))&
(![X]:((rich(X)<~>~humble(X))=>(strong(X)|brave(X))))&
(![X]:((~generous(X)|creative(X))<=>(~strong(X)|~happy(X))))&
(((~quiet(mary)&~funny(mary)))=>((~curious(lucy)&~funny(lucy))))&
(![X]:((brave(X)|kind(X))=>(patient(X)<~>wise(X))))&
(![X]:((old(X)|curious(X))<=>rich(X)))&
(![X]:((kind(X)&~happy(X))=>(~funny(X)<~>happy(X))))&
(((kind(alice)&~kind(alice)))<=>((happy(paul)<~>tall(paul))))&
(![X]:((quiet(X)&~happy(X))=>(creative(X)&calm(X))))&
(![X]:((curious(X)<~>brave(X))=>(~brave(X)|~humble(X))))&
(![X]:((curious(X)<~>~happy(X))<=>~quiet(X)))&
(![X]:((old(X)|tall(X))<=>(~rich(X)<~>brave(X))))&
(?[X]:((generous(X)<~>~calm(X))))&
(wise(paul))&
((rich(paul)|~old(paul)))&
((~curious(alice)&~brave(alice)))&
(?[X]:((generous(X)|~tall(X))))&
(?[X]:((~tall(X)&~old(X))))&
(?[X]:((curious(X)&kind(X))))&
(?[X]:(~wise(X))) | calm(alice) | [] | null | 0 |
If susan is either not quiet or not tall then someone is rich or funny and vice versa.
Everyone who is both patient and not humble is either not creative or curious.
If paul is both generous and not tall then someone is either not rich or not kind.
If fred is both not strong and humble then someone is either not happy or strong and vice versa.
If lucy is both not happy and curious then mary is not generous and vice versa.
If someone is not strong or not rich then someone is either not patient or not kind and vice versa.
Everyone who is not wise or patient is either not curious or quiet.
Everyone who is brave or old is not brave or funny and vice versa.
Everyone who is both old and wise is not brave and vice versa.
If someone is either wise or patient then someone is either not creative or happy and vice versa.
If mary is both strong and not strong then someone is strong or creative.
Everyone who is either curious or not quiet is not kind or not happy and vice versa.
Everyone who is either not funny or not happy is both not creative and generous and vice versa.
Everyone who is not curious or not quiet is both not old and not kind.
If lucy is either not patient or brave then susan is tall or not rich and vice versa.
Everyone who is not funny is humble.
Someone is either not brave or not quiet.
Paul is either happy or not humble.
Alice is either creative or not generous.
Alice is not funny or quiet.
Susan is not humble.
Paul is not calm.
Someone is generous. | Alice is not old. | neutral | (((~quiet(susan)<~>~tall(susan)))<=>(?[X]:((rich(X)|funny(X)))))&
(![X]:((patient(X)&~humble(X))=>(~creative(X)<~>curious(X))))&
(((generous(paul)&~tall(paul)))=>(?[X]:((~rich(X)<~>~kind(X)))))&
(((~strong(fred)&humble(fred)))<=>(?[X]:((~happy(X)<~>strong(X)))))&
(((~happy(lucy)&curious(lucy)))<=>(~generous(mary)))&
((?[X]:((~strong(X)|~rich(X))))<=>(?[X]:((~patient(X)<~>~kind(X)))))&
(![X]:((~wise(X)|patient(X))=>(~curious(X)<~>quiet(X))))&
(![X]:((brave(X)|old(X))<=>(~brave(X)|funny(X))))&
(![X]:((old(X)&wise(X))<=>~brave(X)))&
((?[X]:((wise(X)<~>patient(X))))<=>(?[X]:((~creative(X)<~>happy(X)))))&
(((strong(mary)&~strong(mary)))=>(?[X]:((strong(X)|creative(X)))))&
(![X]:((curious(X)<~>~quiet(X))<=>(~kind(X)|~happy(X))))&
(![X]:((~funny(X)<~>~happy(X))<=>(~creative(X)&generous(X))))&
(![X]:((~curious(X)|~quiet(X))=>(~old(X)&~kind(X))))&
(((~patient(lucy)<~>brave(lucy)))<=>((tall(susan)|~rich(susan))))&
(![X]:(~funny(X)=>humble(X)))&
(?[X]:((~brave(X)<~>~quiet(X))))&
((happy(paul)<~>~humble(paul)))&
((creative(alice)<~>~generous(alice)))&
((~funny(alice)|quiet(alice)))&
(~humble(susan))&
(~calm(paul))&
(?[X]:(generous(X))) | ~old(alice) | [] | null | 0 |
If john is not rich then alice is not quiet.
Everyone who is not quiet is not generous.
Everyone who is not calm or not curious is both wise and not wise.
If mary is either not rich or curious then someone is either brave or happy.
Everyone who is either not brave or curious is both strong and kind.
Everyone who is not curious is both quiet and tall and vice versa.
If john is both brave and calm then someone is generous or not brave.
Everyone who is not patient or not creative is both not curious and kind and vice versa.
If paul is patient then someone is both strong and not quiet.
Everyone who is either rich or not tall is either generous or not rich and vice versa.
If mary is not wise then someone is either not rich or wise.
If someone is not humble then someone is both not tall and not rich and vice versa.
Everyone who is not quiet or generous is brave or humble and vice versa.
Everyone who is funny or generous is either strong or old.
Everyone who is either not humble or funny is kind or curious and vice versa.
Everyone who is either not tall or not humble is brave or creative and vice versa.
Mary is not quiet or not curious.
Lucy is either curious or not brave.
Susan is either creative or kind.
Susan is both funny and not quiet.
Someone is not tall or not generous. | Susan is tall. | contradiction | ((~rich(john))=>(~quiet(alice)))&
(![X]:(~quiet(X)=>~generous(X)))&
(![X]:((~calm(X)|~curious(X))=>(wise(X)&~wise(X))))&
(((~rich(mary)<~>curious(mary)))=>(?[X]:((brave(X)<~>happy(X)))))&
(![X]:((~brave(X)<~>curious(X))=>(strong(X)&kind(X))))&
(![X]:(~curious(X)<=>(quiet(X)&tall(X))))&
(((brave(john)&calm(john)))=>(?[X]:((generous(X)|~brave(X)))))&
(![X]:((~patient(X)|~creative(X))<=>(~curious(X)&kind(X))))&
((patient(paul))=>(?[X]:((strong(X)&~quiet(X)))))&
(![X]:((rich(X)<~>~tall(X))<=>(generous(X)<~>~rich(X))))&
((~wise(mary))=>(?[X]:((~rich(X)<~>wise(X)))))&
((?[X]:(~humble(X)))<=>(?[X]:((~tall(X)&~rich(X)))))&
(![X]:((~quiet(X)|generous(X))<=>(brave(X)|humble(X))))&
(![X]:((funny(X)|generous(X))=>(strong(X)<~>old(X))))&
(![X]:((~humble(X)<~>funny(X))<=>(kind(X)|curious(X))))&
(![X]:((~tall(X)<~>~humble(X))<=>(brave(X)|creative(X))))&
((~quiet(mary)|~curious(mary)))&
((curious(lucy)<~>~brave(lucy)))&
((creative(susan)<~>kind(susan)))&
((funny(susan)&~quiet(susan)))&
(?[X]:((~tall(X)|~generous(X)))) | tall(susan) | [
"p1",
"p9",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 4946486699623526300143057
% SZS output start Proof for 4946486699623526300143057
2. ! [X0] : (~quiet(X0) => ~generous(X0)) [input p1]
10. ! [X0] : ((rich(X0) <~> ~tall(X0)) <=> (generous(X0) <~> ~rich(X0))) [input p9]
20. ~quiet(susan) & funny(susan) [input p19]
22. tall(susan) [input hypothesis]
25. ! [X0] : (~generous(X0) | quiet(X0)) [ennf transformation 2]
46. ! [X0] : ((((tall(X0) | ~rich(X0)) & (~tall(X0) | rich(X0))) | ((generous(X0) | rich(X0)) & (~rich(X0) | ~generous(X0)))) & (((rich(X0) | ~generous(X0)) & (~rich(X0) | generous(X0))) | ((rich(X0) | tall(X0)) & (~tall(X0) | ~rich(X0))))) [nnf transformation 10]
67. ~generous(X0) | quiet(X0) [cnf transformation 25]
91. ~rich(X0) | generous(X0) | ~tall(X0) | ~rich(X0) [cnf transformation 46]
96. ~tall(X0) | rich(X0) | generous(X0) | rich(X0) [cnf transformation 46]
130. ~quiet(susan) [cnf transformation 20]
132. tall(susan) [cnf transformation 22]
133. ~rich(X0) | generous(X0) | ~tall(X0) [duplicate literal removal 91]
135. ~tall(X0) | rich(X0) | generous(X0) [duplicate literal removal 96]
186. ~tall(X0) | generous(X0) [subsumption resolution 133,135]
233. generous(susan) [resolution 186,132]
236. quiet(susan) [resolution 233,67]
237. $false [subsumption resolution 236,130]
% SZS output end Proof for 4946486699623526300143057
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave or not wise is either happy or patient and vice versa.
Everyone who is not creative or old is both humble and calm.
If susan is both not humble and not wise then john is rich.
Everyone who is strong or humble is old or not humble and vice versa.
If someone is tall then lucy is both brave and not patient and vice versa.
If lucy is both creative and calm then someone is either not old or humble and vice versa.
Everyone who is not happy or generous is both funny and wise.
If someone is both not happy and not quiet then someone is both wise and not brave and vice versa.
Everyone who is not happy is not tall or not quiet.
If susan is either strong or not calm then someone is not humble and vice versa.
Everyone who is not kind or brave is not happy and vice versa.
If someone is curious then fred is not strong or not patient.
If paul is not wise then someone is either quiet or not creative.
Everyone who is both not wise and curious is either rich or not humble.
If someone is either calm or not funny then alice is either rich or not brave and vice versa.
If fred is brave then john is not funny or brave and vice versa.
Paul is not creative or strong.
Someone is not funny.
Lucy is humble.
Someone is either not happy or patient.
Someone is not quiet. | Fred is not wise. | neutral | (![X]:((brave(X)|~wise(X))<=>(happy(X)<~>patient(X))))&
(![X]:((~creative(X)|old(X))=>(humble(X)&calm(X))))&
(((~humble(susan)&~wise(susan)))=>(rich(john)))&
(![X]:((strong(X)|humble(X))<=>(old(X)|~humble(X))))&
((?[X]:(tall(X)))<=>((brave(lucy)&~patient(lucy))))&
(((creative(lucy)&calm(lucy)))<=>(?[X]:((~old(X)<~>humble(X)))))&
(![X]:((~happy(X)|generous(X))=>(funny(X)&wise(X))))&
((?[X]:((~happy(X)&~quiet(X))))<=>(?[X]:((wise(X)&~brave(X)))))&
(![X]:(~happy(X)=>(~tall(X)|~quiet(X))))&
(((strong(susan)<~>~calm(susan)))<=>(?[X]:(~humble(X))))&
(![X]:((~kind(X)|brave(X))<=>~happy(X)))&
((?[X]:(curious(X)))=>((~strong(fred)|~patient(fred))))&
((~wise(paul))=>(?[X]:((quiet(X)<~>~creative(X)))))&
(![X]:((~wise(X)&curious(X))=>(rich(X)<~>~humble(X))))&
((?[X]:((calm(X)<~>~funny(X))))<=>((rich(alice)<~>~brave(alice))))&
((brave(fred))<=>((~funny(john)|brave(john))))&
((~creative(paul)|strong(paul)))&
(?[X]:(~funny(X)))&
(humble(lucy))&
(?[X]:((~happy(X)<~>patient(X))))&
(?[X]:(~quiet(X))) | ~wise(fred) | [] | null | 0 |
If someone is tall or not wise then susan is old.
Everyone who is patient is creative or brave and vice versa.
Everyone who is not calm is funny.
If alice is both happy and rich then someone is not old.
If someone is either curious or not old then john is not patient and vice versa.
If someone is either not rich or not tall then someone is creative and vice versa.
Everyone who is curious is both curious and not happy and vice versa.
If someone is brave or strong then someone is not generous.
If someone is strong or brave then someone is not tall and vice versa.
If paul is not creative or not happy then paul is not humble or creative and vice versa.
Everyone who is not old is not wise.
If someone is patient or quiet then john is either not generous or curious and vice versa.
If lucy is not calm then alice is not old.
Everyone who is both not happy and not quiet is either creative or rich and vice versa.
Everyone who is old or not old is curious.
Everyone who is not patient or strong is either not old or wise and vice versa.
Someone is both not creative and not strong.
Alice is both not strong and old.
Someone is creative.
Someone is funny or generous.
Someone is not strong.
Lucy is either not tall or not creative. | Lucy is not calm. | contradiction | ((?[X]:((tall(X)|~wise(X))))=>(old(susan)))&
(![X]:(patient(X)<=>(creative(X)|brave(X))))&
(![X]:(~calm(X)=>funny(X)))&
(((happy(alice)&rich(alice)))=>(?[X]:(~old(X))))&
((?[X]:((curious(X)<~>~old(X))))<=>(~patient(john)))&
((?[X]:((~rich(X)<~>~tall(X))))<=>(?[X]:(creative(X))))&
(![X]:(curious(X)<=>(curious(X)&~happy(X))))&
((?[X]:((brave(X)|strong(X))))=>(?[X]:(~generous(X))))&
((?[X]:((strong(X)|brave(X))))<=>(?[X]:(~tall(X))))&
(((~creative(paul)|~happy(paul)))<=>((~humble(paul)|creative(paul))))&
(![X]:(~old(X)=>~wise(X)))&
((?[X]:((patient(X)|quiet(X))))<=>((~generous(john)<~>curious(john))))&
((~calm(lucy))=>(~old(alice)))&
(![X]:((~happy(X)&~quiet(X))<=>(creative(X)<~>rich(X))))&
(![X]:((old(X)|~old(X))=>curious(X)))&
(![X]:((~patient(X)|strong(X))<=>(~old(X)<~>wise(X))))&
(?[X]:((~creative(X)&~strong(X))))&
((~strong(alice)&old(alice)))&
(?[X]:(creative(X)))&
(?[X]:((funny(X)|generous(X))))&
(?[X]:(~strong(X)))&
((~tall(lucy)<~>~creative(lucy))) | ~calm(lucy) | [
"p12",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 1355824850500611241936557
% SZS output start Proof for 1355824850500611241936557
13. ~calm(lucy) => ~old(alice) [input p12]
18. old(alice) & ~strong(alice) [input p17]
23. ~calm(lucy) [input hypothesis]
34. ~old(alice) | calm(lucy) [ennf transformation 13]
109. ~old(alice) | calm(lucy) [cnf transformation 34]
127. old(alice) [cnf transformation 18]
132. ~calm(lucy) [cnf transformation 23]
282. 34 <=> calm(lucy) [avatar definition]
286. 35 <=> old(alice) [avatar definition]
289. 34 | ~35 [avatar split clause 109,286,282]
293. 35 [avatar split clause 127,286]
304. ~34 [avatar split clause 132,282]
305. $false [avatar sat refutation 289,293,304]
% SZS output end Proof for 1355824850500611241936557
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not brave and not quiet is not generous and vice versa.
If fred is either funny or not kind then someone is both wise and not kind and vice versa.
Everyone who is either creative or tall is brave and vice versa.
Everyone who is strong is not humble or old.
Everyone who is either not humble or kind is curious and vice versa.
Everyone who is both not happy and funny is both not brave and not humble and vice versa.
If someone is both not rich and not generous then paul is both calm and brave and vice versa.
Everyone who is both not funny and creative is not generous or tall and vice versa.
If someone is either not quiet or happy then paul is both brave and wise.
If someone is not wise then mary is not curious.
Everyone who is both not rich and not wise is tall and vice versa.
Everyone who is both not calm and old is tall.
Everyone who is not calm is not funny or not wise.
If someone is not creative or happy then someone is not kind or not funny.
If fred is tall then someone is not strong.
Everyone who is either rich or not generous is either brave or quiet and vice versa.
Someone is both not calm and kind.
Someone is either wise or quiet.
Someone is not tall or curious.
Fred is either creative or not generous.
Someone is old.
John is happy.
Lucy is both rich and not quiet. | Lucy is happy. | entailment | (![X]:((~brave(X)&~quiet(X))<=>~generous(X)))&
(((funny(fred)<~>~kind(fred)))<=>(?[X]:((wise(X)&~kind(X)))))&
(![X]:((creative(X)<~>tall(X))<=>brave(X)))&
(![X]:(strong(X)=>(~humble(X)|old(X))))&
(![X]:((~humble(X)<~>kind(X))<=>curious(X)))&
(![X]:((~happy(X)&funny(X))<=>(~brave(X)&~humble(X))))&
((?[X]:((~rich(X)&~generous(X))))<=>((calm(paul)&brave(paul))))&
(![X]:((~funny(X)&creative(X))<=>(~generous(X)|tall(X))))&
((?[X]:((~quiet(X)<~>happy(X))))=>((brave(paul)&wise(paul))))&
((?[X]:(~wise(X)))=>(~curious(mary)))&
(![X]:((~rich(X)&~wise(X))<=>tall(X)))&
(![X]:((~calm(X)&old(X))=>tall(X)))&
(![X]:(~calm(X)=>(~funny(X)|~wise(X))))&
((?[X]:((~creative(X)|happy(X))))=>(?[X]:((~kind(X)|~funny(X)))))&
((tall(fred))=>(?[X]:(~strong(X))))&
(![X]:((rich(X)<~>~generous(X))<=>(brave(X)<~>quiet(X))))&
(?[X]:((~calm(X)&kind(X))))&
(?[X]:((wise(X)<~>quiet(X))))&
(?[X]:((~tall(X)|curious(X))))&
((creative(fred)<~>~generous(fred)))&
(?[X]:(old(X)))&
(happy(john))&
((rich(lucy)&~quiet(lucy))) | happy(lucy) | [
"p0",
"p2",
"p6",
"p7",
"p8",
"p10",
"p12",
"p15",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 3127147446164698335520989
% SZS output start Proof for 3127147446164698335520989
1. ! [X0] : ((~quiet(X0) & ~brave(X0)) <=> ~generous(X0)) [input p0]
3. ! [X0] : ((creative(X0) <~> tall(X0)) <=> brave(X0)) [input p2]
7. ? [X0] : (~generous(X0) & ~rich(X0)) <=> (brave(paul) & calm(paul)) [input p6]
8. ! [X0] : ((creative(X0) & ~funny(X0)) <=> (tall(X0) | ~generous(X0))) [input p7]
9. ? [X0] : (~quiet(X0) <~> happy(X0)) => (wise(paul) & brave(paul)) [input p8]
11. ! [X0] : ((~wise(X0) & ~rich(X0)) <=> tall(X0)) [input p10]
13. ! [X0] : (~calm(X0) => (~wise(X0) | ~funny(X0))) [input p12]
16. ! [X0] : ((rich(X0) <~> ~generous(X0)) <=> (brave(X0) <~> quiet(X0))) [input p15]
23. ~quiet(lucy) & rich(lucy) [input p22]
24. ~happy(lucy) [input hypothesis]
28. (wise(paul) & brave(paul)) | ! [X0] : (~quiet(X0) <=> happy(X0)) [ennf transformation 9]
32. ! [X0] : ((~wise(X0) | ~funny(X0)) | calm(X0)) [ennf transformation 13]
33. ! [X0] : (~wise(X0) | ~funny(X0) | calm(X0)) [flattening 32]
35. ! [X0] : (((~quiet(X0) & ~brave(X0)) | generous(X0)) & (~generous(X0) | (quiet(X0) | brave(X0)))) [nnf transformation 1]
36. ! [X0] : (((~quiet(X0) & ~brave(X0)) | generous(X0)) & (~generous(X0) | quiet(X0) | brave(X0))) [flattening 35]
41. ! [X0] : ((((~tall(X0) | ~creative(X0)) & (tall(X0) | creative(X0))) | ~brave(X0)) & (brave(X0) | ((creative(X0) | ~tall(X0)) & (tall(X0) | ~creative(X0))))) [nnf transformation 3]
45. (? [X0] : (~generous(X0) & ~rich(X0)) | (~brave(paul) | ~calm(paul))) & ((brave(paul) & calm(paul)) | ! [X0] : (generous(X0) | rich(X0))) [nnf transformation 7]
46. (? [X0] : (~generous(X0) & ~rich(X0)) | ~brave(paul) | ~calm(paul)) & ((brave(paul) & calm(paul)) | ! [X0] : (generous(X0) | rich(X0))) [flattening 45]
47. (? [X0] : (~generous(X0) & ~rich(X0)) | ~brave(paul) | ~calm(paul)) & ((brave(paul) & calm(paul)) | ! [X1] : (generous(X1) | rich(X1))) [rectify 46]
48. ? [X0] : (~generous(X0) & ~rich(X0)) => (~generous(sK1) & ~rich(sK1)) [choice axiom]
49. ((~generous(sK1) & ~rich(sK1)) | ~brave(paul) | ~calm(paul)) & ((brave(paul) & calm(paul)) | ! [X1] : (generous(X1) | rich(X1))) [skolemisation 47,48]
50. ! [X0] : (((creative(X0) & ~funny(X0)) | (~tall(X0) & generous(X0))) & ((tall(X0) | ~generous(X0)) | (~creative(X0) | funny(X0)))) [nnf transformation 8]
51. ! [X0] : (((creative(X0) & ~funny(X0)) | (~tall(X0) & generous(X0))) & (tall(X0) | ~generous(X0) | ~creative(X0) | funny(X0))) [flattening 50]
52. (wise(paul) & brave(paul)) | ! [X0] : ((~quiet(X0) | ~happy(X0)) & (happy(X0) | quiet(X0))) [nnf transformation 28]
53. ! [X0] : (((~wise(X0) & ~rich(X0)) | ~tall(X0)) & (tall(X0) | (wise(X0) | rich(X0)))) [nnf transformation 11]
54. ! [X0] : (((~wise(X0) & ~rich(X0)) | ~tall(X0)) & (tall(X0) | wise(X0) | rich(X0))) [flattening 53]
58. ! [X0] : ((((generous(X0) | ~rich(X0)) & (~generous(X0) | rich(X0))) | ((brave(X0) | ~quiet(X0)) & (quiet(X0) | ~brave(X0)))) & (((~quiet(X0) | ~brave(X0)) & (quiet(X0) | brave(X0))) | ((rich(X0) | generous(X0)) & (~generous(X0) | ~rich(X0))))) [nnf transformation 16]
70. ~brave(X0) | generous(X0) [cnf transformation 36]
71. ~quiet(X0) | generous(X0) [cnf transformation 36]
78. ~creative(X0) | tall(X0) | brave(X0) [cnf transformation 41]
80. ~brave(X0) | creative(X0) | tall(X0) [cnf transformation 41]
93. ~generous(sK1) | ~brave(paul) | ~calm(paul) [cnf transformation 49]
94. ~creative(X0) | ~generous(X0) | tall(X0) | funny(X0) [cnf transformation 51]
97. creative(X0) | generous(X0) [cnf transformation 51]
98. ~tall(X0) | creative(X0) [cnf transformation 51]
99. brave(paul) | happy(X0) | quiet(X0) [cnf transformation 52]
101. wise(paul) | happy(X0) | quiet(X0) [cnf transformation 52]
105. ~rich(X0) | ~tall(X0) [cnf transformation 54]
106. ~tall(X0) | ~wise(X0) [cnf transformation 54]
108. ~wise(X0) | ~funny(X0) | calm(X0) [cnf transformation 33]
112. quiet(X0) | brave(X0) | rich(X0) | generous(X0) [cnf transformation 58]
129. ~quiet(lucy) [cnf transformation 23]
130. ~happy(lucy) [cnf transformation 24]
157. 6 <=> calm(paul) [avatar definition]
159. ~calm(paul) <- (~6) [avatar component clause 157]
161. 7 <=> brave(paul) [avatar definition]
162. brave(paul) <- (7) [avatar component clause 161]
165. 8 <=> generous(sK1) [avatar definition]
167. ~generous(sK1) <- (~8) [avatar component clause 165]
168. ~6 | ~7 | ~8 [avatar split clause 93,165,161,157]
175. 10 <=> ! [X1] : (generous(X1) | rich(X1)) [avatar definition]
176. rich(X1) | generous(X1) <- (10) [avatar component clause 175]
183. 12 <=> wise(paul) [avatar definition]
185. wise(paul) <- (12) [avatar component clause 183]
188. 13 <=> ! [X0] : (happy(X0) | quiet(X0)) [avatar definition]
189. happy(X0) | quiet(X0) <- (13) [avatar component clause 188]
190. 13 | 12 [avatar split clause 101,183,188]
192. 13 | 7 [avatar split clause 99,161,188]
220. brave(X0) | rich(X0) | generous(X0) [subsumption resolution 112,71]
221. rich(X0) | generous(X0) [subsumption resolution 220,70]
222. 10 [avatar split clause 221,175]
244. generous(paul) <- (7) [resolution 70,162]
246. ~tall(X0) | generous(X0) <- (10) [resolution 176,105]
260. tall(X0) | brave(X0) | generous(X0) [resolution 78,97]
261. tall(X0) | generous(X0) [subsumption resolution 260,70]
262. generous(X0) <- (10) [subsumption resolution 261,246]
267. creative(paul) | tall(paul) <- (7) [resolution 80,162]
269. creative(paul) <- (7) [subsumption resolution 267,98]
341. ~funny(paul) | calm(paul) <- (12) [resolution 108,185]
352. ~funny(paul) <- (~6, 12) [subsumption resolution 341,159]
404. ~generous(paul) | tall(paul) | funny(paul) <- (7) [resolution 94,269]
409. tall(paul) | funny(paul) <- (7) [subsumption resolution 404,244]
410. tall(paul) <- (~6, 7, 12) [subsumption resolution 409,352]
465. ~wise(paul) <- (~6, 7, 12) [resolution 410,106]
471. $false <- (~6, 7, 12) [subsumption resolution 465,185]
472. 6 | ~7 | ~12 [avatar contradiction clause 471]
483. $false <- (~8, 10) [subsumption resolution 167,262]
484. 8 | ~10 [avatar contradiction clause 483]
515. quiet(lucy) <- (13) [resolution 189,130]
518. $false <- (13) [subsumption resolution 515,129]
519. ~13 [avatar contradiction clause 518]
520. $false [avatar sat refutation 168,190,192,222,472,484,519]
% SZS output end Proof for 3127147446164698335520989
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either kind or quiet is quiet. If lucy is either quiet or humble then susan is old and vice versa. Everyone who is either calm or curious is not curious or old and vice versa. Everyone who is not wise or not tall is not rich. Everyone who is either not patient or quiet is not brave or not happy and vice versa. Everyone who is curious is tall or creative and vice versa. Everyone who is both funny and not wise is not generous or kind and vice versa. Everyone who is not kind is not rich. If lucy is both happy and humble then susan is either humble or not rich and vice versa. If fred is not funny then mary is not curious. If someone is tall then someone is rich or calm and vice versa. If susan is not calm then someone is not curious or not rich. If paul is funny then someone is either curious or not humble. Everyone who is both calm and patient is either quiet or brave and vice versa. If someone is both not patient and patient then alice is generous and vice versa. Everyone who is not funny or strong is not patient or not humble and vice versa. Someone is either patient or not tall. Someone is tall. Someone is not patient or rich. Fred is not humble. Lucy is not quiet. Someone is calm. Someone is either not generous or curious. | Lucy is not happy. | neutral | (![X]:((kind(X)<~>quiet(X))=>quiet(X)))&
(((quiet(lucy)<~>humble(lucy)))<=>(old(susan)))&
(![X]:((calm(X)<~>curious(X))<=>(~curious(X)|old(X))))&
(![X]:((~wise(X)|~tall(X))=>~rich(X)))&
(![X]:((~patient(X)<~>quiet(X))<=>(~brave(X)|~happy(X))))&
(![X]:(curious(X)<=>(tall(X)|creative(X))))&
(![X]:((funny(X)&~wise(X))<=>(~generous(X)|kind(X))))&
(![X]:(~kind(X)=>~rich(X)))&
(((happy(lucy)&humble(lucy)))<=>((humble(susan)<~>~rich(susan))))&
((~funny(fred))=>(~curious(mary)))&
((?[X]:(tall(X)))<=>(?[X]:((rich(X)|calm(X)))))&
((~calm(susan))=>(?[X]:((~curious(X)|~rich(X)))))&
((funny(paul))=>(?[X]:((curious(X)<~>~humble(X)))))&
(![X]:((calm(X)&patient(X))<=>(quiet(X)<~>brave(X))))&
((?[X]:((~patient(X)&patient(X))))<=>(generous(alice)))&
(![X]:((~funny(X)|strong(X))<=>(~patient(X)|~humble(X))))&
(?[X]:((patient(X)<~>~tall(X))))&
(?[X]:(tall(X)))&
(?[X]:((~patient(X)|rich(X))))&
(~humble(fred))&
(~quiet(lucy))&
(?[X]:(calm(X)))&
(?[X]:((~generous(X)<~>curious(X)))) | ~happy(lucy) | [] | null | 0 |
If paul is curious then paul is both not generous and funny. Everyone who is not calm or not patient is generous or strong and vice versa. Everyone who is not humble or strong is both not rich and patient. Everyone who is generous is either kind or not kind and vice versa. If lucy is both not happy and not strong then someone is both not funny and humble. If someone is generous then john is both not curious and strong and vice versa. If fred is kind then lucy is not rich or rich. If mary is both humble and curious then someone is not creative and vice versa. Everyone who is funny is both generous and rich. If someone is not humble or creative then alice is not generous. If someone is patient or not strong then susan is either not patient or not tall and vice versa. If john is generous then someone is old. If alice is either quiet or not tall then alice is not rich. Everyone who is patient or wise is both brave and quiet and vice versa. Everyone who is not wise is rich. If fred is both not funny and patient then lucy is either patient or brave and vice versa. Someone is old or not wise. John is either kind or patient. Susan is either strong or curious. Someone is both not quiet and not happy. Someone is funny. Lucy is both calm and curious. Mary is not generous or wise. Someone is wise or curious. | John is not quiet. | contradiction | ((curious(paul))=>((~generous(paul)&funny(paul))))&
(![X]:((~calm(X)|~patient(X))<=>(generous(X)|strong(X))))&
(![X]:((~humble(X)|strong(X))=>(~rich(X)&patient(X))))&
(![X]:(generous(X)<=>(kind(X)<~>~kind(X))))&
(((~happy(lucy)&~strong(lucy)))=>(?[X]:((~funny(X)&humble(X)))))&
((?[X]:(generous(X)))<=>((~curious(john)&strong(john))))&
((kind(fred))=>((~rich(lucy)|rich(lucy))))&
(((humble(mary)&curious(mary)))<=>(?[X]:(~creative(X))))&
(![X]:(funny(X)=>(generous(X)&rich(X))))&
((?[X]:((~humble(X)|creative(X))))=>(~generous(alice)))&
((?[X]:((patient(X)|~strong(X))))<=>((~patient(susan)<~>~tall(susan))))&
((generous(john))=>(?[X]:(old(X))))&
(((quiet(alice)<~>~tall(alice)))=>(~rich(alice)))&
(![X]:((patient(X)|wise(X))<=>(brave(X)&quiet(X))))&
(![X]:(~wise(X)=>rich(X)))&
(((~funny(fred)&patient(fred)))<=>((patient(lucy)<~>brave(lucy))))&
(?[X]:((old(X)|~wise(X))))&
((kind(john)<~>patient(john)))&
((strong(susan)<~>curious(susan)))&
(?[X]:((~quiet(X)&~happy(X))))&
(?[X]:(funny(X)))&
((calm(lucy)&curious(lucy)))&
((~generous(mary)|wise(mary)))&
(?[X]:((wise(X)|curious(X)))) | ~quiet(john) | [
"p2",
"p3",
"p5",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 64011371340926272956259
% SZS output start Proof for 64011371340926272956259
3. ! [X0] : ((strong(X0) | ~humble(X0)) => (patient(X0) & ~rich(X0))) [input p2]
4. ! [X0] : (generous(X0) <=> (kind(X0) <~> ~kind(X0))) [input p3]
6. ? [X0] : generous(X0) <=> (strong(john) & ~curious(john)) [input p5]
14. ! [X0] : ((wise(X0) | patient(X0)) <=> (quiet(X0) & brave(X0))) [input p13]
25. ~quiet(john) [input hypothesis]
29. ! [X0] : ((patient(X0) & ~rich(X0)) | (~strong(X0) & humble(X0))) [ennf transformation 3]
40. ! [X0] : ((generous(X0) | ((kind(X0) | kind(X0)) & (~kind(X0) | ~kind(X0)))) & (((kind(X0) | ~kind(X0)) & (~kind(X0) | kind(X0))) | ~generous(X0))) [nnf transformation 4]
43. (? [X0] : generous(X0) | (~strong(john) | curious(john))) & ((strong(john) & ~curious(john)) | ! [X0] : ~generous(X0)) [nnf transformation 6]
44. (? [X0] : generous(X0) | ~strong(john) | curious(john)) & ((strong(john) & ~curious(john)) | ! [X0] : ~generous(X0)) [flattening 43]
45. (? [X0] : generous(X0) | ~strong(john) | curious(john)) & ((strong(john) & ~curious(john)) | ! [X1] : ~generous(X1)) [rectify 44]
46. ? [X0] : generous(X0) => generous(sK1) [choice axiom]
47. (generous(sK1) | ~strong(john) | curious(john)) & ((strong(john) & ~curious(john)) | ! [X1] : ~generous(X1)) [skolemisation 45,46]
58. ! [X0] : (((wise(X0) | patient(X0)) | (~quiet(X0) | ~brave(X0))) & ((quiet(X0) & brave(X0)) | (~wise(X0) & ~patient(X0)))) [nnf transformation 14]
59. ! [X0] : ((wise(X0) | patient(X0) | ~quiet(X0) | ~brave(X0)) & ((quiet(X0) & brave(X0)) | (~wise(X0) & ~patient(X0)))) [flattening 58]
79. ~strong(X0) | patient(X0) [cnf transformation 29]
82. generous(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 40]
83. generous(X0) | kind(X0) | kind(X0) [cnf transformation 40]
87. strong(john) | ~generous(X1) [cnf transformation 47]
107. ~patient(X0) | quiet(X0) [cnf transformation 59]
128. ~quiet(john) [cnf transformation 25]
129. generous(X0) | ~kind(X0) [duplicate literal removal 82]
130. generous(X0) | kind(X0) [duplicate literal removal 83]
145. generous(X0) [subsumption resolution 129,130]
164. strong(john) [subsumption resolution 87,145]
245. 24 <=> patient(john) [avatar definition]
246. patient(john) <- (24) [avatar component clause 245]
272. patient(john) [resolution 79,164]
276. 24 [avatar split clause 272,245]
285. quiet(john) <- (24) [resolution 107,246]
286. $false <- (24) [subsumption resolution 285,128]
287. ~24 [avatar contradiction clause 286]
288. $false [avatar sat refutation 276,287]
% SZS output end Proof for 64011371340926272956259
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet and old is creative and vice versa.
Everyone who is either creative or not creative is either old or not humble.
Everyone who is either patient or not rich is strong and vice versa.
If fred is not happy or kind then someone is both not tall and wise.
Everyone who is either not happy or kind is either not curious or old.
Everyone who is humble or funny is kind or not brave.
Everyone who is creative or strong is both not curious and rich.
If paul is funny or not wise then lucy is not happy or not calm.
If someone is both not tall and calm then someone is both brave and old.
If someone is quiet then paul is either happy or not happy and vice versa.
Everyone who is either old or brave is both not tall and not generous.
Everyone who is either creative or happy is not creative.
If susan is either funny or old then someone is not kind.
Everyone who is either funny or rich is tall or wise and vice versa.
If someone is either not funny or not calm then fred is both strong and patient and vice versa.
If susan is both rich and not curious then lucy is not creative or not quiet and vice versa.
Susan is either kind or humble.
Someone is not brave.
Mary is generous or not brave.
Someone is either generous or not patient.
Someone is curious.
Mary is not rich.
Paul is both not happy and generous. | Mary is patient. | entailment | (![X]:((quiet(X)&old(X))<=>creative(X)))&
(![X]:((creative(X)<~>~creative(X))=>(old(X)<~>~humble(X))))&
(![X]:((patient(X)<~>~rich(X))<=>strong(X)))&
(((~happy(fred)|kind(fred)))=>(?[X]:((~tall(X)&wise(X)))))&
(![X]:((~happy(X)<~>kind(X))=>(~curious(X)<~>old(X))))&
(![X]:((humble(X)|funny(X))=>(kind(X)|~brave(X))))&
(![X]:((creative(X)|strong(X))=>(~curious(X)&rich(X))))&
(((funny(paul)|~wise(paul)))=>((~happy(lucy)|~calm(lucy))))&
((?[X]:((~tall(X)&calm(X))))=>(?[X]:((brave(X)&old(X)))))&
((?[X]:(quiet(X)))<=>((happy(paul)<~>~happy(paul))))&
(![X]:((old(X)<~>brave(X))=>(~tall(X)&~generous(X))))&
(![X]:((creative(X)<~>happy(X))=>~creative(X)))&
(((funny(susan)<~>old(susan)))=>(?[X]:(~kind(X))))&
(![X]:((funny(X)<~>rich(X))<=>(tall(X)|wise(X))))&
((?[X]:((~funny(X)<~>~calm(X))))<=>((strong(fred)&patient(fred))))&
(((rich(susan)&~curious(susan)))<=>((~creative(lucy)|~quiet(lucy))))&
((kind(susan)<~>humble(susan)))&
(?[X]:(~brave(X)))&
((generous(mary)|~brave(mary)))&
(?[X]:((generous(X)<~>~patient(X))))&
(?[X]:(curious(X)))&
(~rich(mary))&
((~happy(paul)&generous(paul))) | patient(mary) | [
"p2",
"p6",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 4034784278541826289710789
% SZS output start Proof for 4034784278541826289710789
3. ! [X0] : ((patient(X0) <~> ~rich(X0)) <=> strong(X0)) [input p2]
7. ! [X0] : ((strong(X0) | creative(X0)) => (rich(X0) & ~curious(X0))) [input p6]
22. ~rich(mary) [input p21]
24. ~patient(mary) [input hypothesis]
31. ! [X0] : ((rich(X0) & ~curious(X0)) | (~strong(X0) & ~creative(X0))) [ennf transformation 7]
41. ! [X0] : ((((rich(X0) | ~patient(X0)) & (~rich(X0) | patient(X0))) | ~strong(X0)) & (strong(X0) | ((patient(X0) | rich(X0)) & (~rich(X0) | ~patient(X0))))) [nnf transformation 3]
82. strong(X0) | patient(X0) | rich(X0) [cnf transformation 41]
98. ~strong(X0) | rich(X0) [cnf transformation 31]
139. ~rich(mary) [cnf transformation 22]
142. ~patient(mary) [cnf transformation 24]
332. patient(X0) | rich(X0) | rich(X0) [resolution 82,98]
333. rich(X0) | patient(X0) [duplicate literal removal 332]
352. patient(mary) [resolution 333,139]
355. $false [subsumption resolution 352,142]
% SZS output end Proof for 4034784278541826289710789
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise or humble is not generous and vice versa. If john is both tall and strong then mary is not quiet or not humble and vice versa. If someone is funny or happy then alice is kind or rich. If someone is either tall or not quiet then mary is either old or not humble and vice versa. Everyone who is either happy or brave is either not creative or kind. Everyone who is not strong or brave is not humble or not happy and vice versa. If paul is either quiet or not old then susan is tall or not generous and vice versa. Everyone who is not curious is not kind or rich and vice versa. Everyone who is calm is both not humble and rich and vice versa. Everyone who is both brave and curious is both brave and not old and vice versa. Everyone who is not brave or brave is both not old and strong. Everyone who is strong is both not creative and not brave and vice versa. If lucy is either rich or calm then paul is not brave. Everyone who is not old is either wise or creative. Everyone who is both patient and humble is both humble and old. Everyone who is either tall or not patient is either not kind or wise and vice versa. Someone is not kind or creative. Lucy is not kind or not patient. John is either generous or wise. | Paul is not curious. | entailment | (![X]:((~wise(X)<~>humble(X))<=>~generous(X)))&
(((tall(john)&strong(john)))<=>((~quiet(mary)|~humble(mary))))&
((?[X]:((funny(X)|happy(X))))=>((kind(alice)|rich(alice))))&
((?[X]:((tall(X)<~>~quiet(X))))<=>((old(mary)<~>~humble(mary))))&
(![X]:((happy(X)<~>brave(X))=>(~creative(X)<~>kind(X))))&
(![X]:((~strong(X)|brave(X))<=>(~humble(X)|~happy(X))))&
(((quiet(paul)<~>~old(paul)))<=>((tall(susan)|~generous(susan))))&
(![X]:(~curious(X)<=>(~kind(X)|rich(X))))&
(![X]:(calm(X)<=>(~humble(X)&rich(X))))&
(![X]:((brave(X)&curious(X))<=>(brave(X)&~old(X))))&
(![X]:((~brave(X)|brave(X))=>(~old(X)&strong(X))))&
(![X]:(strong(X)<=>(~creative(X)&~brave(X))))&
(((rich(lucy)<~>calm(lucy)))=>(~brave(paul)))&
(![X]:(~old(X)=>(wise(X)<~>creative(X))))&
(![X]:((patient(X)&humble(X))=>(humble(X)&old(X))))&
(![X]:((tall(X)<~>~patient(X))<=>(~kind(X)<~>wise(X))))&
(?[X]:((~kind(X)|creative(X))))&
((~kind(lucy)|~patient(lucy)))&
((generous(john)<~>wise(john))) | ~curious(paul) | [
"p0",
"p3",
"p5",
"p6",
"p7",
"p10",
"p11",
"p13",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6340915821810522056194020
% SZS output start Proof for 6340915821810522056194020
1. ! [X0] : ((~wise(X0) <~> humble(X0)) <=> ~generous(X0)) [input p0]
4. ? [X0] : (tall(X0) <~> ~quiet(X0)) <=> (old(mary) <~> ~humble(mary)) [input p3]
6. ! [X0] : ((brave(X0) | ~strong(X0)) <=> (~happy(X0) | ~humble(X0))) [input p5]
7. (quiet(paul) <~> ~old(paul)) <=> (~generous(susan) | tall(susan)) [input p6]
8. ! [X0] : (~curious(X0) <=> (rich(X0) | ~kind(X0))) [input p7]
11. ! [X0] : ((brave(X0) | ~brave(X0)) => (strong(X0) & ~old(X0))) [input p10]
12. ! [X0] : (strong(X0) <=> (~brave(X0) & ~creative(X0))) [input p11]
14. ! [X0] : (~old(X0) => (wise(X0) <~> creative(X0))) [input p13]
15. ! [X0] : ((humble(X0) & patient(X0)) => (old(X0) & humble(X0))) [input p14]
16. ! [X0] : ((tall(X0) <~> ~patient(X0)) <=> (~kind(X0) <~> wise(X0))) [input p15]
20. curious(paul) [input hypothesis]
25. ! [X0] : ((strong(X0) & ~old(X0)) | (~brave(X0) & brave(X0))) [ennf transformation 11]
27. ! [X0] : ((wise(X0) <~> creative(X0)) | old(X0)) [ennf transformation 14]
28. ! [X0] : ((old(X0) & humble(X0)) | (~humble(X0) | ~patient(X0))) [ennf transformation 15]
29. ! [X0] : ((old(X0) & humble(X0)) | ~humble(X0) | ~patient(X0)) [flattening 28]
30. ! [X0] : ((((~humble(X0) | wise(X0)) & (humble(X0) | ~wise(X0))) | generous(X0)) & (~generous(X0) | ((~wise(X0) | ~humble(X0)) & (humble(X0) | wise(X0))))) [nnf transformation 1]
33. (? [X0] : ((quiet(X0) | ~tall(X0)) & (~quiet(X0) | tall(X0))) | ((old(mary) | humble(mary)) & (~humble(mary) | ~old(mary)))) & (((humble(mary) | ~old(mary)) & (~humble(mary) | old(mary))) | ! [X0] : ((tall(X0) | quiet(X0)) & (~quiet(X0) | ~tall(X0)))) [nnf transformation 4]
34. (? [X0] : ((quiet(X0) | ~tall(X0)) & (~quiet(X0) | tall(X0))) | ((old(mary) | humble(mary)) & (~humble(mary) | ~old(mary)))) & (((humble(mary) | ~old(mary)) & (~humble(mary) | old(mary))) | ! [X1] : ((tall(X1) | quiet(X1)) & (~quiet(X1) | ~tall(X1)))) [rectify 33]
35. ? [X0] : ((quiet(X0) | ~tall(X0)) & (~quiet(X0) | tall(X0))) => ((quiet(sK0) | ~tall(sK0)) & (~quiet(sK0) | tall(sK0))) [choice axiom]
36. (((quiet(sK0) | ~tall(sK0)) & (~quiet(sK0) | tall(sK0))) | ((old(mary) | humble(mary)) & (~humble(mary) | ~old(mary)))) & (((humble(mary) | ~old(mary)) & (~humble(mary) | old(mary))) | ! [X1] : ((tall(X1) | quiet(X1)) & (~quiet(X1) | ~tall(X1)))) [skolemisation 34,35]
38. ! [X0] : (((brave(X0) | ~strong(X0)) | (happy(X0) & humble(X0))) & ((~happy(X0) | ~humble(X0)) | (~brave(X0) & strong(X0)))) [nnf transformation 6]
39. ! [X0] : ((brave(X0) | ~strong(X0) | (happy(X0) & humble(X0))) & (~happy(X0) | ~humble(X0) | (~brave(X0) & strong(X0)))) [flattening 38]
40. (((old(paul) | ~quiet(paul)) & (~old(paul) | quiet(paul))) | (generous(susan) & ~tall(susan))) & ((~generous(susan) | tall(susan)) | ((quiet(paul) | old(paul)) & (~old(paul) | ~quiet(paul)))) [nnf transformation 7]
41. (((old(paul) | ~quiet(paul)) & (~old(paul) | quiet(paul))) | (generous(susan) & ~tall(susan))) & (~generous(susan) | tall(susan) | ((quiet(paul) | old(paul)) & (~old(paul) | ~quiet(paul)))) [flattening 40]
42. ! [X0] : ((~curious(X0) | (~rich(X0) & kind(X0))) & ((rich(X0) | ~kind(X0)) | curious(X0))) [nnf transformation 8]
43. ! [X0] : ((~curious(X0) | (~rich(X0) & kind(X0))) & (rich(X0) | ~kind(X0) | curious(X0))) [flattening 42]
48. ! [X0] : ((strong(X0) | (brave(X0) | creative(X0))) & ((~brave(X0) & ~creative(X0)) | ~strong(X0))) [nnf transformation 12]
49. ! [X0] : ((strong(X0) | brave(X0) | creative(X0)) & ((~brave(X0) & ~creative(X0)) | ~strong(X0))) [flattening 48]
51. ! [X0] : (((~creative(X0) | ~wise(X0)) & (creative(X0) | wise(X0))) | old(X0)) [nnf transformation 27]
52. ! [X0] : ((((patient(X0) | ~tall(X0)) & (~patient(X0) | tall(X0))) | ((~kind(X0) | ~wise(X0)) & (wise(X0) | kind(X0)))) & (((~wise(X0) | kind(X0)) & (wise(X0) | ~kind(X0))) | ((tall(X0) | patient(X0)) & (~patient(X0) | ~tall(X0))))) [nnf transformation 16]
57. ~generous(X0) | ~wise(X0) | ~humble(X0) [cnf transformation 30]
67. ~humble(mary) | old(mary) | tall(X1) | quiet(X1) [cnf transformation 36]
80. ~strong(X0) | brave(X0) | humble(X0) [cnf transformation 39]
87. old(paul) | ~quiet(paul) | generous(susan) [cnf transformation 41]
89. ~curious(X0) | kind(X0) [cnf transformation 43]
98. ~old(X0) | brave(X0) [cnf transformation 25]
99. ~brave(X0) | ~old(X0) [cnf transformation 25]
100. strong(X0) | brave(X0) [cnf transformation 25]
101. ~brave(X0) | strong(X0) [cnf transformation 25]
102. ~creative(X0) | ~strong(X0) [cnf transformation 49]
103. ~brave(X0) | ~strong(X0) [cnf transformation 49]
107. creative(X0) | wise(X0) | old(X0) [cnf transformation 51]
110. old(X0) | ~humble(X0) | ~patient(X0) [cnf transformation 29]
118. patient(X0) | ~tall(X0) | ~kind(X0) | ~wise(X0) [cnf transformation 52]
123. curious(paul) [cnf transformation 20]
125. 1 <=> humble(mary) [avatar definition]
126. ~humble(mary) <- (~1) [avatar component clause 125]
158. 8 <=> old(mary) [avatar definition]
160. old(mary) <- (8) [avatar component clause 158]
174. 11 <=> ! [X1] : (tall(X1) | quiet(X1)) [avatar definition]
175. quiet(X1) | tall(X1) <- (11) [avatar component clause 174]
181. 11 | 8 | ~1 [avatar split clause 67,125,158,174]
184. 13 <=> generous(susan) [avatar definition]
186. generous(susan) <- (13) [avatar component clause 184]
188. 14 <=> quiet(paul) [avatar definition]
190. ~quiet(paul) <- (~14) [avatar component clause 188]
192. 15 <=> old(paul) [avatar definition]
194. old(paul) <- (15) [avatar component clause 192]
195. 13 | ~14 | 15 [avatar split clause 87,192,188,184]
205. strong(X0) [subsumption resolution 100,101]
206. ~old(X0) [subsumption resolution 98,99]
207. ~brave(X0) [subsumption resolution 103,205]
208. ~creative(X0) [subsumption resolution 102,205]
209. wise(X0) | old(X0) [subsumption resolution 107,208]
210. wise(X0) [subsumption resolution 209,206]
211. ~patient(X0) | ~humble(X0) [subsumption resolution 110,206]
212. ~kind(X0) | ~tall(X0) | patient(X0) [subsumption resolution 118,210]
227. kind(paul) [resolution 89,123]
237. brave(X0) | humble(X0) [resolution 80,205]
238. humble(X0) [subsumption resolution 237,207]
251. $false <- (~1) [resolution 238,126]
253. 1 [avatar contradiction clause 251]
254. $false <- (8) [subsumption resolution 160,206]
255. ~8 [avatar contradiction clause 254]
258. tall(paul) <- (11, ~14) [resolution 175,190]
265. ~tall(paul) | patient(paul) [resolution 212,227]
267. patient(paul) <- (11, ~14) [subsumption resolution 265,258]
282. ~humble(paul) <- (11, ~14) [resolution 267,211]
283. $false <- (11, ~14) [subsumption resolution 282,238]
284. ~11 | 14 [avatar contradiction clause 283]
294. ~wise(susan) | ~humble(susan) <- (13) [resolution 186,57]
296. ~humble(susan) <- (13) [subsumption resolution 294,210]
297. $false <- (13) [subsumption resolution 296,238]
298. ~13 [avatar contradiction clause 297]
299. $false <- (15) [subsumption resolution 194,206]
300. ~15 [avatar contradiction clause 299]
301. $false [avatar sat refutation 181,195,253,255,284,298,300]
% SZS output end Proof for 6340915821810522056194020
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is strong is either not rich or not brave and vice versa. Everyone who is not creative is old. Everyone who is both not brave and not curious is not calm or rich and vice versa. Everyone who is wise or creative is not strong and vice versa. Everyone who is patient or not tall is either happy or funny and vice versa. If alice is quiet or not kind then someone is either calm or funny. If mary is both rich and not kind then someone is not humble or quiet and vice versa. If john is not funny then someone is not brave or strong. Everyone who is creative is happy and vice versa. If fred is curious or not calm then john is either not generous or not funny and vice versa. If someone is either not kind or old then susan is both not patient and not quiet. If alice is not quiet then someone is not curious or not calm and vice versa. If alice is both not wise and not old then someone is creative. If mary is both happy and not funny then paul is not curious and vice versa. Everyone who is either not kind or kind is tall and vice versa. If fred is not patient then mary is both generous and not tall. Mary is not strong or not generous. Someone is either kind or old. Someone is both not old and creative. Someone is creative or funny. Someone is either not calm or tall. Someone is either rich or generous. Fred is either calm or creative. Someone is both humble and rich. | Mary is not tall. | contradiction | (![X]:(strong(X)<=>(~rich(X)<~>~brave(X))))&
(![X]:(~creative(X)=>old(X)))&
(![X]:((~brave(X)&~curious(X))<=>(~calm(X)|rich(X))))&
(![X]:((wise(X)|creative(X))<=>~strong(X)))&
(![X]:((patient(X)|~tall(X))<=>(happy(X)<~>funny(X))))&
(((quiet(alice)|~kind(alice)))=>(?[X]:((calm(X)<~>funny(X)))))&
(((rich(mary)&~kind(mary)))<=>(?[X]:((~humble(X)|quiet(X)))))&
((~funny(john))=>(?[X]:((~brave(X)|strong(X)))))&
(![X]:(creative(X)<=>happy(X)))&
(((curious(fred)|~calm(fred)))<=>((~generous(john)<~>~funny(john))))&
((?[X]:((~kind(X)<~>old(X))))=>((~patient(susan)&~quiet(susan))))&
((~quiet(alice))<=>(?[X]:((~curious(X)|~calm(X)))))&
(((~wise(alice)&~old(alice)))=>(?[X]:(creative(X))))&
(((happy(mary)&~funny(mary)))<=>(~curious(paul)))&
(![X]:((~kind(X)<~>kind(X))<=>tall(X)))&
((~patient(fred))=>((generous(mary)&~tall(mary))))&
((~strong(mary)|~generous(mary)))&
(?[X]:((kind(X)<~>old(X))))&
(?[X]:((~old(X)&creative(X))))&
(?[X]:((creative(X)|funny(X))))&
(?[X]:((~calm(X)<~>tall(X))))&
(?[X]:((rich(X)<~>generous(X))))&
((calm(fred)<~>creative(fred)))&
(?[X]:((humble(X)&rich(X)))) | ~tall(mary) | [
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8864652119304249552188255
% SZS output start Proof for 8864652119304249552188255
15. ! [X0] : ((~kind(X0) <~> kind(X0)) <=> tall(X0)) [input p14]
25. ~tall(mary) [input hypothesis]
62. ! [X0] : ((((~kind(X0) | kind(X0)) & (kind(X0) | ~kind(X0))) | ~tall(X0)) & (tall(X0) | ((~kind(X0) | ~kind(X0)) & (kind(X0) | kind(X0))))) [nnf transformation 15]
127. tall(X0) | kind(X0) | kind(X0) [cnf transformation 62]
128. tall(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 62]
147. ~tall(mary) [cnf transformation 25]
148. tall(X0) | kind(X0) [duplicate literal removal 127]
149. tall(X0) | ~kind(X0) [duplicate literal removal 128]
288. tall(X0) [subsumption resolution 148,149]
335. $false [subsumption resolution 147,288]
% SZS output end Proof for 8864652119304249552188255
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is both creative and tall then alice is both funny and generous.
If fred is rich or not calm then mary is either kind or not kind and vice versa.
Everyone who is either not curious or not rich is either not wise or wise and vice versa.
If paul is either happy or not wise then someone is both happy and rich.
If someone is patient or old then mary is both not quiet and funny and vice versa.
If someone is either wise or not strong then mary is rich or old.
Everyone who is both not calm and quiet is not old or funny and vice versa.
Everyone who is not kind is both not tall and humble and vice versa.
Everyone who is kind is both funny and calm and vice versa.
Everyone who is not creative is both happy and brave and vice versa.
Everyone who is either patient or not generous is not strong and vice versa.
Everyone who is creative or wise is not old and vice versa.
Everyone who is curious or not funny is not creative.
Everyone who is either not creative or calm is kind and vice versa.
If someone is either not rich or not wise then fred is both patient and not tall.
If lucy is both strong and not rich then lucy is either curious or quiet.
Someone is quiet.
Fred is brave or not curious.
Someone is generous or not happy.
Susan is not wise or not happy.
Susan is not patient or not creative. | Paul is not funny. | contradiction | (((creative(lucy)&tall(lucy)))=>((funny(alice)&generous(alice))))&
(((rich(fred)|~calm(fred)))<=>((kind(mary)<~>~kind(mary))))&
(![X]:((~curious(X)<~>~rich(X))<=>(~wise(X)<~>wise(X))))&
(((happy(paul)<~>~wise(paul)))=>(?[X]:((happy(X)&rich(X)))))&
((?[X]:((patient(X)|old(X))))<=>((~quiet(mary)&funny(mary))))&
((?[X]:((wise(X)<~>~strong(X))))=>((rich(mary)|old(mary))))&
(![X]:((~calm(X)&quiet(X))<=>(~old(X)|funny(X))))&
(![X]:(~kind(X)<=>(~tall(X)&humble(X))))&
(![X]:(kind(X)<=>(funny(X)&calm(X))))&
(![X]:(~creative(X)<=>(happy(X)&brave(X))))&
(![X]:((patient(X)<~>~generous(X))<=>~strong(X)))&
(![X]:((creative(X)|wise(X))<=>~old(X)))&
(![X]:((curious(X)|~funny(X))=>~creative(X)))&
(![X]:((~creative(X)<~>calm(X))<=>kind(X)))&
((?[X]:((~rich(X)<~>~wise(X))))=>((patient(fred)&~tall(fred))))&
(((strong(lucy)&~rich(lucy)))=>((curious(lucy)<~>quiet(lucy))))&
(?[X]:(quiet(X)))&
((brave(fred)|~curious(fred)))&
(?[X]:((generous(X)|~happy(X))))&
((~wise(susan)|~happy(susan)))&
((~patient(susan)|~creative(susan))) | ~funny(paul) | [
"p4",
"p6",
"p8",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 8980092226108794984944316
% SZS output start Proof for 8980092226108794984944316
5. ? [X0] : (old(X0) | patient(X0)) <=> (funny(mary) & ~quiet(mary)) [input p4]
7. ! [X0] : ((quiet(X0) & ~calm(X0)) <=> (funny(X0) | ~old(X0))) [input p6]
9. ! [X0] : (kind(X0) <=> (calm(X0) & funny(X0))) [input p8]
13. ! [X0] : ((~funny(X0) | curious(X0)) => ~creative(X0)) [input p12]
14. ! [X0] : ((~creative(X0) <~> calm(X0)) <=> kind(X0)) [input p13]
22. ~funny(paul) [input hypothesis]
28. ! [X0] : (~creative(X0) | (funny(X0) & ~curious(X0))) [ennf transformation 13]
38. (? [X0] : (old(X0) | patient(X0)) | (~funny(mary) | quiet(mary))) & ((funny(mary) & ~quiet(mary)) | ! [X0] : (~old(X0) & ~patient(X0))) [nnf transformation 5]
39. (? [X0] : (old(X0) | patient(X0)) | ~funny(mary) | quiet(mary)) & ((funny(mary) & ~quiet(mary)) | ! [X0] : (~old(X0) & ~patient(X0))) [flattening 38]
40. (? [X0] : (old(X0) | patient(X0)) | ~funny(mary) | quiet(mary)) & ((funny(mary) & ~quiet(mary)) | ! [X1] : (~old(X1) & ~patient(X1))) [rectify 39]
41. ? [X0] : (old(X0) | patient(X0)) => (old(sK1) | patient(sK1)) [choice axiom]
42. ((old(sK1) | patient(sK1)) | ~funny(mary) | quiet(mary)) & ((funny(mary) & ~quiet(mary)) | ! [X1] : (~old(X1) & ~patient(X1))) [skolemisation 40,41]
44. ! [X0] : (((quiet(X0) & ~calm(X0)) | (~funny(X0) & old(X0))) & ((funny(X0) | ~old(X0)) | (~quiet(X0) | calm(X0)))) [nnf transformation 7]
45. ! [X0] : (((quiet(X0) & ~calm(X0)) | (~funny(X0) & old(X0))) & (funny(X0) | ~old(X0) | ~quiet(X0) | calm(X0))) [flattening 44]
48. ! [X0] : ((kind(X0) | (~calm(X0) | ~funny(X0))) & ((calm(X0) & funny(X0)) | ~kind(X0))) [nnf transformation 9]
49. ! [X0] : ((kind(X0) | ~calm(X0) | ~funny(X0)) & ((calm(X0) & funny(X0)) | ~kind(X0))) [flattening 48]
55. ! [X0] : ((((~calm(X0) | creative(X0)) & (calm(X0) | ~creative(X0))) | ~kind(X0)) & (kind(X0) | ((~creative(X0) | ~calm(X0)) & (calm(X0) | creative(X0))))) [nnf transformation 14]
83. ~quiet(mary) | ~old(X1) [cnf transformation 42]
85. funny(mary) | ~old(X1) [cnf transformation 42]
90. ~calm(X0) | old(X0) [cnf transformation 45]
93. ~funny(X0) | quiet(X0) [cnf transformation 45]
98. ~kind(X0) | calm(X0) [cnf transformation 49]
111. ~creative(X0) | funny(X0) [cnf transformation 28]
112. kind(X0) | calm(X0) | creative(X0) [cnf transformation 55]
115. ~calm(X0) | creative(X0) | ~kind(X0) [cnf transformation 55]
127. ~funny(paul) [cnf transformation 22]
189. 12 <=> quiet(mary) [avatar definition]
193. 13 <=> funny(mary) [avatar definition]
194. funny(mary) <- (13) [avatar component clause 193]
206. 16 <=> ! [X1] : ~old(X1) [avatar definition]
207. ~old(X1) <- (16) [avatar component clause 206]
208. 16 | 13 [avatar split clause 85,193,206]
213. 16 | ~12 [avatar split clause 83,189,206]
231. ~kind(X0) | creative(X0) [subsumption resolution 115,98]
232. calm(X0) | creative(X0) [subsumption resolution 112,231]
305. quiet(mary) <- (13) [resolution 93,194]
322. old(X1) | creative(X1) [resolution 232,90]
332. 12 | ~13 [avatar split clause 305,193,189]
402. creative(X0) <- (16) [resolution 322,207]
406. funny(X1) <- (16) [resolution 402,111]
412. $false <- (16) [resolution 406,127]
417. ~16 [avatar contradiction clause 412]
418. $false [avatar sat refutation 208,213,332,417]
% SZS output end Proof for 8980092226108794984944316
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If john is both old and not strong then someone is not calm. If paul is both not funny and curious then someone is not strong and vice versa. Everyone who is not brave is not happy. Everyone who is patient is both not quiet and not tall. Everyone who is funny is rich and vice versa. Everyone who is both not tall and not wise is strong or brave and vice versa. Everyone who is either strong or calm is both humble and not generous and vice versa. If someone is both creative and not funny then susan is either creative or not creative and vice versa. If alice is either calm or not generous then someone is funny or not tall and vice versa. Everyone who is not kind is either not strong or wise. If someone is wise or funny then someone is creative or kind. If alice is not patient then alice is both not strong and creative. If fred is both not wise and not brave then someone is either happy or not curious and vice versa. Everyone who is either not strong or not brave is not tall. If fred is either generous or not creative then someone is both humble and not kind. Everyone who is not curious or not rich is old or not funny. Someone is both not curious and not funny. Fred is both curious and not wise. Mary is calm. Someone is either strong or humble. Mary is strong. Someone is both not wise and not humble. John is either strong or not wise. Someone is either not curious or tall. | Mary is not kind. | contradiction | (((old(john)&~strong(john)))=>(?[X]:(~calm(X))))&
(((~funny(paul)&curious(paul)))<=>(?[X]:(~strong(X))))&
(![X]:(~brave(X)=>~happy(X)))&
(![X]:(patient(X)=>(~quiet(X)&~tall(X))))&
(![X]:(funny(X)<=>rich(X)))&
(![X]:((~tall(X)&~wise(X))<=>(strong(X)|brave(X))))&
(![X]:((strong(X)<~>calm(X))<=>(humble(X)&~generous(X))))&
((?[X]:((creative(X)&~funny(X))))<=>((creative(susan)<~>~creative(susan))))&
(((calm(alice)<~>~generous(alice)))<=>(?[X]:((funny(X)|~tall(X)))))&
(![X]:(~kind(X)=>(~strong(X)<~>wise(X))))&
((?[X]:((wise(X)|funny(X))))=>(?[X]:((creative(X)|kind(X)))))&
((~patient(alice))=>((~strong(alice)&creative(alice))))&
(((~wise(fred)&~brave(fred)))<=>(?[X]:((happy(X)<~>~curious(X)))))&
(![X]:((~strong(X)<~>~brave(X))=>~tall(X)))&
(((generous(fred)<~>~creative(fred)))=>(?[X]:((humble(X)&~kind(X)))))&
(![X]:((~curious(X)|~rich(X))=>(old(X)|~funny(X))))&
(?[X]:((~curious(X)&~funny(X))))&
((curious(fred)&~wise(fred)))&
(calm(mary))&
(?[X]:((strong(X)<~>humble(X))))&
(strong(mary))&
(?[X]:((~wise(X)&~humble(X))))&
((strong(john)<~>~wise(john)))&
(?[X]:((~curious(X)<~>tall(X)))) | ~kind(mary) | [
"p5",
"p9",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 2196954685002648767229291
% SZS output start Proof for 2196954685002648767229291
6. ! [X0] : ((~wise(X0) & ~tall(X0)) <=> (brave(X0) | strong(X0))) [input p5]
10. ! [X0] : (~kind(X0) => (~strong(X0) <~> wise(X0))) [input p9]
21. strong(mary) [input p20]
25. ~kind(mary) [input hypothesis]
32. ! [X0] : ((~strong(X0) <~> wise(X0)) | kind(X0)) [ennf transformation 10]
47. ! [X0] : (((~wise(X0) & ~tall(X0)) | (~brave(X0) & ~strong(X0))) & ((brave(X0) | strong(X0)) | (wise(X0) | tall(X0)))) [nnf transformation 6]
48. ! [X0] : (((~wise(X0) & ~tall(X0)) | (~brave(X0) & ~strong(X0))) & (brave(X0) | strong(X0) | wise(X0) | tall(X0))) [flattening 47]
59. ! [X0] : (((~wise(X0) | strong(X0)) & (wise(X0) | ~strong(X0))) | kind(X0)) [nnf transformation 32]
94. ~wise(X0) | ~strong(X0) [cnf transformation 48]
114. wise(X0) | ~strong(X0) | kind(X0) [cnf transformation 59]
115. ~wise(X0) | strong(X0) | kind(X0) [cnf transformation 59]
141. strong(mary) [cnf transformation 21]
148. ~kind(mary) [cnf transformation 25]
228. ~wise(X0) | kind(X0) [subsumption resolution 115,94]
229. ~strong(X0) | kind(X0) [subsumption resolution 114,228]
331. kind(mary) [resolution 229,141]
333. $false [subsumption resolution 331,148]
% SZS output end Proof for 2196954685002648767229291
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich or curious is either not old or old. If lucy is not old or not kind then mary is humble and vice versa. If someone is not quiet or tall then someone is either not brave or not humble and vice versa. Everyone who is both not strong and quiet is either not patient or tall and vice versa. Everyone who is not funny or patient is not patient or not humble and vice versa. Everyone who is either strong or not generous is both not creative and not strong and vice versa. If john is either not funny or not brave then someone is both not calm and wise and vice versa. If someone is both strong and generous then susan is calm or not happy and vice versa. Everyone who is either not wise or not creative is not kind or not creative. Everyone who is both not brave and not happy is either quiet or kind. If john is either not creative or not tall then someone is curious. Everyone who is not happy is both funny and kind. If paul is not humble then alice is not funny or not strong. Everyone who is not brave or not patient is not humble and vice versa. Everyone who is both tall and generous is either old or not creative and vice versa. Everyone who is either not generous or not kind is patient or happy. Lucy is not kind or not humble. Someone is generous or curious. Someone is kind. John is curious or not kind. Paul is curious. Someone is quiet or not happy. Someone is both not curious and not calm. | Lucy is not tall. | neutral | (![X]:((~rich(X)|curious(X))=>(~old(X)<~>old(X))))&
(((~old(lucy)|~kind(lucy)))<=>(humble(mary)))&
((?[X]:((~quiet(X)|tall(X))))<=>(?[X]:((~brave(X)<~>~humble(X)))))&
(![X]:((~strong(X)&quiet(X))<=>(~patient(X)<~>tall(X))))&
(![X]:((~funny(X)|patient(X))<=>(~patient(X)|~humble(X))))&
(![X]:((strong(X)<~>~generous(X))<=>(~creative(X)&~strong(X))))&
(((~funny(john)<~>~brave(john)))<=>(?[X]:((~calm(X)&wise(X)))))&
((?[X]:((strong(X)&generous(X))))<=>((calm(susan)|~happy(susan))))&
(![X]:((~wise(X)<~>~creative(X))=>(~kind(X)|~creative(X))))&
(![X]:((~brave(X)&~happy(X))=>(quiet(X)<~>kind(X))))&
(((~creative(john)<~>~tall(john)))=>(?[X]:(curious(X))))&
(![X]:(~happy(X)=>(funny(X)&kind(X))))&
((~humble(paul))=>((~funny(alice)|~strong(alice))))&
(![X]:((~brave(X)|~patient(X))<=>~humble(X)))&
(![X]:((tall(X)&generous(X))<=>(old(X)<~>~creative(X))))&
(![X]:((~generous(X)<~>~kind(X))=>(patient(X)|happy(X))))&
((~kind(lucy)|~humble(lucy)))&
(?[X]:((generous(X)|curious(X))))&
(?[X]:(kind(X)))&
((curious(john)|~kind(john)))&
(curious(paul))&
(?[X]:((quiet(X)|~happy(X))))&
(?[X]:((~curious(X)&~calm(X)))) | ~tall(lucy) | [] | null | 0 |
If mary is both kind and not humble then someone is curious or rich. Everyone who is both generous and not brave is either not rich or humble and vice versa. Everyone who is old is not creative or not old and vice versa. Everyone who is rich is not strong. Everyone who is both not rich and happy is either generous or not happy. If someone is either not humble or wise then fred is either not old or not strong and vice versa. Everyone who is both curious and creative is both tall and funny. Everyone who is both not funny and not rich is either not wise or not tall. If susan is either patient or rich then lucy is wise or quiet and vice versa. If someone is both strong and not old then someone is either not strong or not patient and vice versa. If mary is not rich then someone is either not humble or not patient and vice versa. Everyone who is both curious and old is either quiet or old and vice versa. Everyone who is both not kind and not happy is not wise. Everyone who is either not quiet or not old is not old and vice versa. Everyone who is either not old or not happy is both not creative and old and vice versa. Everyone who is both not quiet and not brave is both not humble and calm and vice versa. Someone is either generous or creative. Lucy is either not happy or not wise. Someone is both rich and old. Someone is either humble or not wise. Mary is brave. Paul is both generous and brave. Alice is not rich or kind. Someone is quiet or rich. | Fred is strong. | contradiction | (((kind(mary)&~humble(mary)))=>(?[X]:((curious(X)|rich(X)))))&
(![X]:((generous(X)&~brave(X))<=>(~rich(X)<~>humble(X))))&
(![X]:(old(X)<=>(~creative(X)|~old(X))))&
(![X]:(rich(X)=>~strong(X)))&
(![X]:((~rich(X)&happy(X))=>(generous(X)<~>~happy(X))))&
((?[X]:((~humble(X)<~>wise(X))))<=>((~old(fred)<~>~strong(fred))))&
(![X]:((curious(X)&creative(X))=>(tall(X)&funny(X))))&
(![X]:((~funny(X)&~rich(X))=>(~wise(X)<~>~tall(X))))&
(((patient(susan)<~>rich(susan)))<=>((wise(lucy)|quiet(lucy))))&
((?[X]:((strong(X)&~old(X))))<=>(?[X]:((~strong(X)<~>~patient(X)))))&
((~rich(mary))<=>(?[X]:((~humble(X)<~>~patient(X)))))&
(![X]:((curious(X)&old(X))<=>(quiet(X)<~>old(X))))&
(![X]:((~kind(X)&~happy(X))=>~wise(X)))&
(![X]:((~quiet(X)<~>~old(X))<=>~old(X)))&
(![X]:((~old(X)<~>~happy(X))<=>(~creative(X)&old(X))))&
(![X]:((~quiet(X)&~brave(X))<=>(~humble(X)&calm(X))))&
(?[X]:((generous(X)<~>creative(X))))&
((~happy(lucy)<~>~wise(lucy)))&
(?[X]:((rich(X)&old(X))))&
(?[X]:((humble(X)<~>~wise(X))))&
(brave(mary))&
((generous(paul)&brave(paul)))&
((~rich(alice)|kind(alice)))&
(?[X]:((quiet(X)|rich(X)))) | strong(fred) | [
"p2",
"p5",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 6547317445945881073532262
% SZS output start Proof for 6547317445945881073532262
3. ! [X0] : (old(X0) <=> (~old(X0) | ~creative(X0))) [input p2]
6. ? [X0] : (~humble(X0) <~> wise(X0)) <=> (~old(fred) <~> ~strong(fred)) [input p5]
20. ? [X0] : (humble(X0) <~> ~wise(X0)) [input p19]
25. strong(fred) [input hypothesis]
41. ! [X0] : ((old(X0) | (old(X0) & creative(X0))) & ((~old(X0) | ~creative(X0)) | ~old(X0))) [nnf transformation 3]
42. ! [X0] : ((old(X0) | (old(X0) & creative(X0))) & (~old(X0) | ~creative(X0) | ~old(X0))) [flattening 41]
44. (? [X0] : ((~wise(X0) | humble(X0)) & (wise(X0) | ~humble(X0))) | ((~old(fred) | strong(fred)) & (~strong(fred) | old(fred)))) & (((strong(fred) | old(fred)) & (~strong(fred) | ~old(fred))) | ! [X0] : ((~humble(X0) | ~wise(X0)) & (wise(X0) | humble(X0)))) [nnf transformation 6]
45. (? [X0] : ((~wise(X0) | humble(X0)) & (wise(X0) | ~humble(X0))) | ((~old(fred) | strong(fred)) & (~strong(fred) | old(fred)))) & (((strong(fred) | old(fred)) & (~strong(fred) | ~old(fred))) | ! [X1] : ((~humble(X1) | ~wise(X1)) & (wise(X1) | humble(X1)))) [rectify 44]
46. ? [X0] : ((~wise(X0) | humble(X0)) & (wise(X0) | ~humble(X0))) => ((~wise(sK1) | humble(sK1)) & (wise(sK1) | ~humble(sK1))) [choice axiom]
47. (((~wise(sK1) | humble(sK1)) & (wise(sK1) | ~humble(sK1))) | ((~old(fred) | strong(fred)) & (~strong(fred) | old(fred)))) & (((strong(fred) | old(fred)) & (~strong(fred) | ~old(fred))) | ! [X1] : ((~humble(X1) | ~wise(X1)) & (wise(X1) | humble(X1)))) [skolemisation 45,46]
72. ? [X0] : ((wise(X0) | ~humble(X0)) & (~wise(X0) | humble(X0))) [nnf transformation 20]
73. ? [X0] : ((wise(X0) | ~humble(X0)) & (~wise(X0) | humble(X0))) => ((wise(sK7) | ~humble(sK7)) & (~wise(sK7) | humble(sK7))) [choice axiom]
74. (wise(sK7) | ~humble(sK7)) & (~wise(sK7) | humble(sK7)) [skolemisation 72,73]
86. old(X0) | old(X0) [cnf transformation 42]
90. ~strong(fred) | ~old(fred) | wise(X1) | humble(X1) [cnf transformation 47]
91. ~strong(fred) | ~old(fred) | ~humble(X1) | ~wise(X1) [cnf transformation 47]
141. ~wise(sK7) | humble(sK7) [cnf transformation 74]
142. wise(sK7) | ~humble(sK7) [cnf transformation 74]
148. strong(fred) [cnf transformation 25]
157. old(X0) [duplicate literal removal 86]
178. 5 <=> strong(fred) [avatar definition]
192. ~strong(fred) | ~humble(X1) | ~wise(X1) [subsumption resolution 91,157]
194. 8 <=> ! [X1] : (~humble(X1) | ~wise(X1)) [avatar definition]
195. ~wise(X1) | ~humble(X1) <- (8) [avatar component clause 194]
196. 8 | ~5 [avatar split clause 192,178,194]
197. ~strong(fred) | wise(X1) | humble(X1) [subsumption resolution 90,157]
199. 9 <=> ! [X1] : (wise(X1) | humble(X1)) [avatar definition]
200. wise(X1) | humble(X1) <- (9) [avatar component clause 199]
201. 9 | ~5 [avatar split clause 197,178,199]
258. 19 <=> humble(sK7) [avatar definition]
259. humble(sK7) <- (19) [avatar component clause 258]
260. ~humble(sK7) <- (~19) [avatar component clause 258]
262. 20 <=> wise(sK7) [avatar definition]
263. ~wise(sK7) <- (~20) [avatar component clause 262]
264. wise(sK7) <- (20) [avatar component clause 262]
265. ~19 | 20 [avatar split clause 142,262,258]
266. 19 | ~20 [avatar split clause 141,262,258]
276. 5 [avatar split clause 148,178]
281. humble(sK7) <- (9, ~20) [resolution 200,263]
283. $false <- (9, ~19, ~20) [subsumption resolution 281,260]
284. ~9 | 19 | 20 [avatar contradiction clause 283]
285. ~humble(sK7) <- (8, 20) [resolution 264,195]
286. $false <- (8, 19, 20) [subsumption resolution 285,259]
287. ~8 | ~19 | ~20 [avatar contradiction clause 286]
288. $false [avatar sat refutation 196,201,265,266,276,284,287]
% SZS output end Proof for 6547317445945881073532262
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich then someone is either not humble or kind. If someone is not quiet or not curious then fred is kind or humble and vice versa. Everyone who is either quiet or not rich is not strong or not quiet and vice versa. If susan is both not funny and humble then john is either wise or happy. Everyone who is both not generous and not humble is curious or kind and vice versa. Everyone who is either funny or curious is not creative or not wise and vice versa. If mary is not funny or not calm then someone is not wise or not brave and vice versa. If someone is calm or not quiet then someone is either not strong or wise. Everyone who is not funny or not strong is either happy or tall and vice versa. Everyone who is funny is strong or tall. Everyone who is generous or wise is either not creative or generous. If someone is not humble or not patient then someone is both not kind and kind. Everyone who is not quiet or creative is not rich. Everyone who is either not happy or old is not kind or not humble. Everyone who is both rich and brave is not creative. Someone is both not brave and patient. Alice is either brave or quiet. Susan is both not old and not wise. Fred is not kind. Someone is old or not curious. Alice is either strong or not strong. | Mary is creative. | contradiction | ((?[X]:(~rich(X)))=>(?[X]:((~humble(X)<~>kind(X)))))&
((?[X]:((~quiet(X)|~curious(X))))<=>((kind(fred)|humble(fred))))&
(![X]:((quiet(X)<~>~rich(X))<=>(~strong(X)|~quiet(X))))&
(((~funny(susan)&humble(susan)))=>((wise(john)<~>happy(john))))&
(![X]:((~generous(X)&~humble(X))<=>(curious(X)|kind(X))))&
(![X]:((funny(X)<~>curious(X))<=>(~creative(X)|~wise(X))))&
(((~funny(mary)|~calm(mary)))<=>(?[X]:((~wise(X)|~brave(X)))))&
((?[X]:((calm(X)|~quiet(X))))=>(?[X]:((~strong(X)<~>wise(X)))))&
(![X]:((~funny(X)|~strong(X))<=>(happy(X)<~>tall(X))))&
(![X]:(funny(X)=>(strong(X)|tall(X))))&
(![X]:((generous(X)|wise(X))=>(~creative(X)<~>generous(X))))&
((?[X]:((~humble(X)|~patient(X))))=>(?[X]:((~kind(X)&kind(X)))))&
(![X]:((~quiet(X)|creative(X))=>~rich(X)))&
(![X]:((~happy(X)<~>old(X))=>(~kind(X)|~humble(X))))&
(![X]:((rich(X)&brave(X))=>~creative(X)))&
(?[X]:((~brave(X)&patient(X))))&
((brave(alice)<~>quiet(alice)))&
((~old(susan)&~wise(susan)))&
(~kind(fred))&
(?[X]:((old(X)|~curious(X))))&
((strong(alice)<~>~strong(alice))) | creative(mary) | [
"p0",
"p4",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 826026808612921926297208
% SZS output start Proof for 826026808612921926297208
1. ? [X0] : ~rich(X0) => ? [X0] : (~humble(X0) <~> kind(X0)) [input p0]
5. ! [X0] : ((~humble(X0) & ~generous(X0)) <=> (kind(X0) | curious(X0))) [input p4]
12. ? [X0] : (~patient(X0) | ~humble(X0)) => ? [X0] : (kind(X0) & ~kind(X0)) [input p11]
13. ! [X0] : ((creative(X0) | ~quiet(X0)) => ~rich(X0)) [input p12]
22. creative(mary) [input hypothesis]
23. ? [X0] : ~rich(X0) => ? [X1] : (~humble(X1) <~> kind(X1)) [rectify 1]
25. ? [X0] : (~patient(X0) | ~humble(X0)) => ? [X1] : (kind(X1) & ~kind(X1)) [rectify 12]
27. ? [X0] : ~humble(X0) => ? [X1] : (kind(X1) & ~kind(X1)) [pure predicate removal 25]
28. ? [X1] : (~humble(X1) <~> kind(X1)) | ! [X0] : rich(X0) [ennf transformation 23]
35. ? [X1] : (kind(X1) & ~kind(X1)) | ! [X0] : humble(X0) [ennf transformation 27]
36. ! [X0] : (~rich(X0) | (~creative(X0) & quiet(X0))) [ennf transformation 13]
41. ? [X1] : ((~kind(X1) | humble(X1)) & (kind(X1) | ~humble(X1))) | ! [X0] : rich(X0) [nnf transformation 28]
42. ? [X0] : ((~kind(X0) | humble(X0)) & (kind(X0) | ~humble(X0))) | ! [X1] : rich(X1) [rectify 41]
43. ? [X0] : ((~kind(X0) | humble(X0)) & (kind(X0) | ~humble(X0))) => ((~kind(sK0) | humble(sK0)) & (kind(sK0) | ~humble(sK0))) [choice axiom]
44. ((~kind(sK0) | humble(sK0)) & (kind(sK0) | ~humble(sK0))) | ! [X1] : rich(X1) [skolemisation 42,43]
53. ! [X0] : (((~humble(X0) & ~generous(X0)) | (~kind(X0) & ~curious(X0))) & ((kind(X0) | curious(X0)) | (humble(X0) | generous(X0)))) [nnf transformation 5]
54. ! [X0] : (((~humble(X0) & ~generous(X0)) | (~kind(X0) & ~curious(X0))) & (kind(X0) | curious(X0) | humble(X0) | generous(X0))) [flattening 53]
69. ? [X0] : (kind(X0) & ~kind(X0)) | ! [X1] : humble(X1) [rectify 35]
70. ? [X0] : (kind(X0) & ~kind(X0)) => (kind(sK4) & ~kind(sK4)) [choice axiom]
71. (kind(sK4) & ~kind(sK4)) | ! [X1] : humble(X1) [skolemisation 69,70]
79. kind(sK0) | ~humble(sK0) | rich(X1) [cnf transformation 44]
97. ~kind(X0) | ~humble(X0) [cnf transformation 54]
123. ~kind(sK4) | humble(X1) [cnf transformation 71]
124. kind(sK4) | humble(X1) [cnf transformation 71]
126. ~creative(X0) | ~rich(X0) [cnf transformation 36]
139. creative(mary) [cnf transformation 22]
144. 1 <=> ! [X1] : rich(X1) [avatar definition]
145. rich(X1) <- (1) [avatar component clause 144]
147. 2 <=> humble(sK0) [avatar definition]
148. ~humble(sK0) <- (~2) [avatar component clause 147]
151. 3 <=> kind(sK0) [avatar definition]
152. kind(sK0) <- (3) [avatar component clause 151]
155. 1 | ~2 | 3 [avatar split clause 79,151,147,144]
243. 23 <=> ! [X1] : humble(X1) [avatar definition]
244. humble(X1) <- (23) [avatar component clause 243]
246. 24 <=> kind(sK4) [avatar definition]
249. 23 | 24 [avatar split clause 124,246,243]
250. 23 | ~24 [avatar split clause 123,246,243]
273. $false <- (~2, 23) [subsumption resolution 148,244]
274. 2 | ~23 [avatar contradiction clause 273]
275. ~rich(mary) [resolution 126,139]
276. $false <- (1) [subsumption resolution 275,145]
277. ~1 [avatar contradiction clause 276]
278. ~humble(sK0) <- (3) [resolution 152,97]
279. $false <- (3, 23) [subsumption resolution 278,244]
280. ~3 | ~23 [avatar contradiction clause 279]
281. $false [avatar sat refutation 155,249,250,274,277,280]
% SZS output end Proof for 826026808612921926297208
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall is either not happy or not generous. If someone is not wise or not creative then john is not calm or kind. Everyone who is either not brave or not curious is not calm. If someone is not curious or not old then alice is both strong and rich and vice versa. Everyone who is wise or kind is not strong. Everyone who is not strong is both not patient and not rich. If someone is not wise then someone is either not kind or funny. Everyone who is not calm is strong. Everyone who is both funny and calm is tall or not funny. Everyone who is not kind or creative is both wise and curious. If lucy is happy then john is tall and vice versa. If susan is not wise or patient then lucy is not tall and vice versa. If mary is both not curious and not strong then someone is both not calm and tall and vice versa. If someone is humble or kind then fred is not humble. Someone is brave or rich. Paul is happy. Fred is either curious or tall. Someone is not rich or tall. Paul is not rich or not happy. Mary is happy. | Paul is not curious. | contradiction | (![X]:(~tall(X)=>(~happy(X)<~>~generous(X))))&
((?[X]:((~wise(X)|~creative(X))))=>((~calm(john)|kind(john))))&
(![X]:((~brave(X)<~>~curious(X))=>~calm(X)))&
((?[X]:((~curious(X)|~old(X))))<=>((strong(alice)&rich(alice))))&
(![X]:((wise(X)|kind(X))=>~strong(X)))&
(![X]:(~strong(X)=>(~patient(X)&~rich(X))))&
((?[X]:(~wise(X)))=>(?[X]:((~kind(X)<~>funny(X)))))&
(![X]:(~calm(X)=>strong(X)))&
(![X]:((funny(X)&calm(X))=>(tall(X)|~funny(X))))&
(![X]:((~kind(X)|creative(X))=>(wise(X)&curious(X))))&
((happy(lucy))<=>(tall(john)))&
(((~wise(susan)|patient(susan)))<=>(~tall(lucy)))&
(((~curious(mary)&~strong(mary)))<=>(?[X]:((~calm(X)&tall(X)))))&
((?[X]:((humble(X)|kind(X))))=>(~humble(fred)))&
(?[X]:((brave(X)|rich(X))))&
(happy(paul))&
((curious(fred)<~>tall(fred)))&
(?[X]:((~rich(X)|tall(X))))&
((~rich(paul)|~happy(paul)))&
(happy(mary)) | ~curious(paul) | [
"p3",
"p4",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 7326320726825779053852906
% SZS output start Proof for 7326320726825779053852906
4. ? [X0] : (~old(X0) | ~curious(X0)) <=> (rich(alice) & strong(alice)) [input p3]
5. ! [X0] : ((kind(X0) | wise(X0)) => ~strong(X0)) [input p4]
10. ! [X0] : ((creative(X0) | ~kind(X0)) => (curious(X0) & wise(X0))) [input p9]
21. ~curious(paul) [input hypothesis]
28. ! [X0] : (~strong(X0) | (~kind(X0) & ~wise(X0))) [ennf transformation 5]
34. ! [X0] : ((curious(X0) & wise(X0)) | (~creative(X0) & kind(X0))) [ennf transformation 10]
37. (? [X0] : (~old(X0) | ~curious(X0)) | (~rich(alice) | ~strong(alice))) & ((rich(alice) & strong(alice)) | ! [X0] : (old(X0) & curious(X0))) [nnf transformation 4]
38. (? [X0] : (~old(X0) | ~curious(X0)) | ~rich(alice) | ~strong(alice)) & ((rich(alice) & strong(alice)) | ! [X0] : (old(X0) & curious(X0))) [flattening 37]
39. (? [X0] : (~old(X0) | ~curious(X0)) | ~rich(alice) | ~strong(alice)) & ((rich(alice) & strong(alice)) | ! [X1] : (old(X1) & curious(X1))) [rectify 38]
40. ? [X0] : (~old(X0) | ~curious(X0)) => (~old(sK0) | ~curious(sK0)) [choice axiom]
41. ((~old(sK0) | ~curious(sK0)) | ~rich(alice) | ~strong(alice)) & ((rich(alice) & strong(alice)) | ! [X1] : (old(X1) & curious(X1))) [skolemisation 39,40]
65. strong(alice) | curious(X1) [cnf transformation 41]
70. ~strong(X0) | ~wise(X0) [cnf transformation 28]
71. ~strong(X0) | ~kind(X0) [cnf transformation 28]
78. kind(X0) | wise(X0) [cnf transformation 34]
98. ~curious(paul) [cnf transformation 21]
117. 5 <=> strong(alice) [avatar definition]
118. strong(alice) <- (5) [avatar component clause 117]
138. 10 <=> ! [X1] : curious(X1) [avatar definition]
139. curious(X1) <- (10) [avatar component clause 138]
142. 10 | 5 [avatar split clause 65,117,138]
230. ~wise(alice) <- (5) [resolution 70,118]
232. ~kind(alice) <- (5) [resolution 71,118]
238. wise(alice) <- (5) [resolution 78,232]
240. $false <- (5) [subsumption resolution 238,230]
241. ~5 [avatar contradiction clause 240]
246. $false <- (10) [resolution 139,98]
249. ~10 [avatar contradiction clause 246]
250. $false [avatar sat refutation 142,241,249]
% SZS output end Proof for 7326320726825779053852906
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is both happy and not generous then someone is humble and vice versa.
If someone is not strong or not creative then john is both not rich and not strong.
If someone is both not quiet and kind then lucy is either calm or not generous.
If someone is not wise or not calm then john is both happy and not creative and vice versa.
If someone is generous then someone is both not tall and not wise.
If susan is not funny or old then someone is either not wise or not calm.
If lucy is either not funny or not humble then paul is happy and vice versa.
Everyone who is not brave or not kind is patient and vice versa.
If john is calm or old then someone is either not brave or not funny and vice versa.
If someone is both not patient and not kind then someone is not rich and vice versa.
Everyone who is both not old and strong is rich or creative.
If lucy is either not curious or not humble then paul is rich.
Everyone who is both not generous and happy is both rich and not kind and vice versa.
Everyone who is either tall or funny is kind or tall and vice versa.
Everyone who is both tall and happy is either not calm or not quiet.
Everyone who is generous or funny is both strong and patient and vice versa.
Lucy is kind.
Fred is not tall.
John is kind or not generous.
Someone is both creative and not funny.
Someone is creative or not tall. | Lucy is strong. | entailment | (((happy(paul)&~generous(paul)))<=>(?[X]:(humble(X))))&
((?[X]:((~strong(X)|~creative(X))))=>((~rich(john)&~strong(john))))&
((?[X]:((~quiet(X)&kind(X))))=>((calm(lucy)<~>~generous(lucy))))&
((?[X]:((~wise(X)|~calm(X))))<=>((happy(john)&~creative(john))))&
((?[X]:(generous(X)))=>(?[X]:((~tall(X)&~wise(X)))))&
(((~funny(susan)|old(susan)))=>(?[X]:((~wise(X)<~>~calm(X)))))&
(((~funny(lucy)<~>~humble(lucy)))<=>(happy(paul)))&
(![X]:((~brave(X)|~kind(X))<=>patient(X)))&
(((calm(john)|old(john)))<=>(?[X]:((~brave(X)<~>~funny(X)))))&
((?[X]:((~patient(X)&~kind(X))))<=>(?[X]:(~rich(X))))&
(![X]:((~old(X)&strong(X))=>(rich(X)|creative(X))))&
(((~curious(lucy)<~>~humble(lucy)))=>(rich(paul)))&
(![X]:((~generous(X)&happy(X))<=>(rich(X)&~kind(X))))&
(![X]:((tall(X)<~>funny(X))<=>(kind(X)|tall(X))))&
(![X]:((tall(X)&happy(X))=>(~calm(X)<~>~quiet(X))))&
(![X]:((generous(X)|funny(X))<=>(strong(X)&patient(X))))&
(kind(lucy))&
(~tall(fred))&
((kind(john)|~generous(john)))&
(?[X]:((creative(X)&~funny(X))))&
(?[X]:((creative(X)|~tall(X)))) | strong(lucy) | [
"p1",
"p7",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 5219921728952258174601071
% SZS output start Proof for 5219921728952258174601071
2. ? [X0] : (~creative(X0) | ~strong(X0)) => (~strong(john) & ~rich(john)) [input p1]
8. ! [X0] : ((~kind(X0) | ~brave(X0)) <=> patient(X0)) [input p7]
10. ? [X0] : (~kind(X0) & ~patient(X0)) <=> ? [X0] : ~rich(X0) [input p9]
22. ~strong(lucy) [input hypothesis]
24. ? [X0] : (~kind(X0) & ~patient(X0)) <=> ? [X1] : ~rich(X1) [rectify 10]
25. (~strong(john) & ~rich(john)) | ! [X0] : (creative(X0) & strong(X0)) [ennf transformation 2]
52. ! [X0] : (((~kind(X0) | ~brave(X0)) | ~patient(X0)) & (patient(X0) | (kind(X0) & brave(X0)))) [nnf transformation 8]
53. ! [X0] : ((~kind(X0) | ~brave(X0) | ~patient(X0)) & (patient(X0) | (kind(X0) & brave(X0)))) [flattening 52]
59. (? [X0] : (~kind(X0) & ~patient(X0)) | ! [X1] : rich(X1)) & (? [X1] : ~rich(X1) | ! [X0] : (kind(X0) | patient(X0))) [nnf transformation 24]
60. (? [X0] : (~kind(X0) & ~patient(X0)) | ! [X1] : rich(X1)) & (? [X2] : ~rich(X2) | ! [X3] : (kind(X3) | patient(X3))) [rectify 59]
61. ? [X0] : (~kind(X0) & ~patient(X0)) => (~kind(sK5) & ~patient(sK5)) [choice axiom]
62. ? [X2] : ~rich(X2) => ~rich(sK6) [choice axiom]
63. ((~kind(sK5) & ~patient(sK5)) | ! [X1] : rich(X1)) & (~rich(sK6) | ! [X3] : (kind(X3) | patient(X3))) [skolemisation 60,62,61]
79. ~rich(john) | strong(X0) [cnf transformation 25]
101. patient(X0) | kind(X0) [cnf transformation 53]
110. ~patient(sK5) | rich(X1) [cnf transformation 63]
111. ~kind(sK5) | rich(X1) [cnf transformation 63]
138. ~strong(lucy) [cnf transformation 22]
168. 7 <=> ! [X0] : strong(X0) [avatar definition]
169. strong(X0) <- (7) [avatar component clause 168]
172. 8 <=> rich(john) [avatar definition]
174. ~rich(john) <- (~8) [avatar component clause 172]
176. 7 | ~8 [avatar split clause 79,172,168]
291. 33 <=> ! [X1] : rich(X1) [avatar definition]
292. rich(X1) <- (33) [avatar component clause 291]
294. 34 <=> kind(sK5) [avatar definition]
297. 33 | ~34 [avatar split clause 111,294,291]
299. 35 <=> patient(sK5) [avatar definition]
301. ~patient(sK5) <- (~35) [avatar component clause 299]
302. 33 | ~35 [avatar split clause 110,299,291]
333. kind(sK5) <- (~35) [resolution 101,301]
336. 34 | 35 [avatar split clause 333,299,294]
337. $false <- (~8, 33) [resolution 292,174]
338. 8 | ~33 [avatar contradiction clause 337]
341. $false <- (7) [resolution 169,138]
344. ~7 [avatar contradiction clause 341]
345. $false [avatar sat refutation 176,297,302,336,338,344]
% SZS output end Proof for 5219921728952258174601071
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous and not patient is not old and vice versa. If someone is not patient then john is either creative or not happy and vice versa. Everyone who is not brave is humble or not calm and vice versa. Everyone who is not rich is calm or happy and vice versa. Everyone who is curious or not funny is both not happy and rich. Everyone who is not generous or not wise is happy. If someone is either wise or not tall then someone is either not calm or not quiet and vice versa. Everyone who is both quiet and not calm is rich or not quiet and vice versa. Everyone who is not tall is both not creative and not humble. Everyone who is both patient and wise is generous or creative and vice versa. If lucy is not kind or not funny then someone is either not calm or humble. Everyone who is either old or happy is not old. If someone is not tall or funny then someone is not generous. If someone is either curious or not rich then someone is either old or humble and vice versa. If someone is not kind or funny then paul is both generous and brave. Someone is not wise or brave. Lucy is funny or not generous. Lucy is either not brave or strong. Someone is either not humble or strong. | Paul is humble. | contradiction | (![X]:((generous(X)&~patient(X))<=>~old(X)))&
((?[X]:(~patient(X)))<=>((creative(john)<~>~happy(john))))&
(![X]:(~brave(X)<=>(humble(X)|~calm(X))))&
(![X]:(~rich(X)<=>(calm(X)|happy(X))))&
(![X]:((curious(X)|~funny(X))=>(~happy(X)&rich(X))))&
(![X]:((~generous(X)|~wise(X))=>happy(X)))&
((?[X]:((wise(X)<~>~tall(X))))<=>(?[X]:((~calm(X)<~>~quiet(X)))))&
(![X]:((quiet(X)&~calm(X))<=>(rich(X)|~quiet(X))))&
(![X]:(~tall(X)=>(~creative(X)&~humble(X))))&
(![X]:((patient(X)&wise(X))<=>(generous(X)|creative(X))))&
(((~kind(lucy)|~funny(lucy)))=>(?[X]:((~calm(X)<~>humble(X)))))&
(![X]:((old(X)<~>happy(X))=>~old(X)))&
((?[X]:((~tall(X)|funny(X))))=>(?[X]:(~generous(X))))&
((?[X]:((curious(X)<~>~rich(X))))<=>(?[X]:((old(X)<~>humble(X)))))&
((?[X]:((~kind(X)|funny(X))))=>((generous(paul)&brave(paul))))&
(?[X]:((~wise(X)|brave(X))))&
((funny(lucy)|~generous(lucy)))&
((~brave(lucy)<~>strong(lucy)))&
(?[X]:((~humble(X)<~>strong(X)))) | humble(paul) | [
"p2",
"p3",
"p4",
"p5",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 67279760600410952858137
% SZS output start Proof for 67279760600410952858137
3. ! [X0] : (~brave(X0) <=> (~calm(X0) | humble(X0))) [input p2]
4. ! [X0] : (~rich(X0) <=> (happy(X0) | calm(X0))) [input p3]
5. ! [X0] : ((~funny(X0) | curious(X0)) => (rich(X0) & ~happy(X0))) [input p4]
6. ! [X0] : ((~wise(X0) | ~generous(X0)) => happy(X0)) [input p5]
15. ? [X0] : (funny(X0) | ~kind(X0)) => (brave(paul) & generous(paul)) [input p14]
16. ? [X0] : (brave(X0) | ~wise(X0)) [input p15]
20. humble(paul) [input hypothesis]
25. ? [X0] : funny(X0) => (brave(paul) & generous(paul)) [pure predicate removal 15]
26. ! [X0] : ((rich(X0) & ~happy(X0)) | (funny(X0) & ~curious(X0))) [ennf transformation 5]
27. ! [X0] : (happy(X0) | (wise(X0) & generous(X0))) [ennf transformation 6]
32. (brave(paul) & generous(paul)) | ! [X0] : ~funny(X0) [ennf transformation 25]
39. ! [X0] : ((~brave(X0) | (calm(X0) & ~humble(X0))) & ((~calm(X0) | humble(X0)) | brave(X0))) [nnf transformation 3]
40. ! [X0] : ((~brave(X0) | (calm(X0) & ~humble(X0))) & (~calm(X0) | humble(X0) | brave(X0))) [flattening 39]
41. ! [X0] : ((~rich(X0) | (~happy(X0) & ~calm(X0))) & ((happy(X0) | calm(X0)) | rich(X0))) [nnf transformation 4]
42. ! [X0] : ((~rich(X0) | (~happy(X0) & ~calm(X0))) & (happy(X0) | calm(X0) | rich(X0))) [flattening 41]
64. ? [X0] : (brave(X0) | ~wise(X0)) => (brave(sK7) | ~wise(sK7)) [choice axiom]
65. brave(sK7) | ~wise(sK7) [skolemisation 16,64]
78. ~humble(X0) | ~brave(X0) [cnf transformation 40]
79. ~brave(X0) | calm(X0) [cnf transformation 40]
81. ~rich(X0) | ~calm(X0) [cnf transformation 42]
82. ~rich(X0) | ~happy(X0) [cnf transformation 42]
86. funny(X0) | rich(X0) [cnf transformation 26]
88. wise(X0) | happy(X0) [cnf transformation 27]
124. brave(paul) | ~funny(X0) [cnf transformation 32]
125. brave(sK7) | ~wise(sK7) [cnf transformation 65]
131. humble(paul) [cnf transformation 20]
207. 16 <=> ! [X1] : ~funny(X1) [avatar definition]
208. ~funny(X1) <- (16) [avatar component clause 207]
236. 23 <=> ! [X3] : rich(X3) [avatar definition]
237. rich(X3) <- (23) [avatar component clause 236]
257. 27 <=> brave(paul) [avatar definition]
260. 16 | 27 [avatar split clause 124,257,207]
267. 29 <=> wise(sK7) [avatar definition]
269. ~wise(sK7) <- (~29) [avatar component clause 267]
271. 30 <=> brave(sK7) [avatar definition]
273. brave(sK7) <- (30) [avatar component clause 271]
274. ~29 | 30 [avatar split clause 125,271,267]
302. ~brave(paul) [resolution 78,131]
303. ~27 [avatar split clause 302,257]
304. rich(X0) <- (16) [resolution 86,208]
305. 23 | ~16 [avatar split clause 304,207,236]
307. ~happy(X0) <- (23) [resolution 237,82]
308. ~calm(X1) <- (23) [resolution 237,81]
316. happy(sK7) <- (~29) [resolution 88,269]
319. $false <- (23, ~29) [subsumption resolution 316,307]
320. ~23 | 29 [avatar contradiction clause 319]
321. calm(sK7) <- (30) [resolution 273,79]
322. $false <- (23, 30) [subsumption resolution 321,308]
323. ~23 | ~30 [avatar contradiction clause 322]
324. $false [avatar sat refutation 260,274,303,305,320,323]
% SZS output end Proof for 67279760600410952858137
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble or not happy then someone is old. Everyone who is either not quiet or not curious is not rich or quiet. If someone is not brave or old then alice is either rich or strong. If someone is not generous or tall then someone is kind and vice versa. Everyone who is both not quiet and not kind is not calm or patient and vice versa. Everyone who is both brave and not kind is not tall or not humble and vice versa. If someone is either funny or old then someone is both generous and not funny and vice versa. If susan is not patient then fred is either not old or humble. If mary is both rich and brave then john is not curious or old. If mary is not generous then someone is quiet or creative. Everyone who is either funny or strong is calm or kind. Everyone who is both not generous and not strong is both not rich and tall. If someone is both wise and not old then susan is not calm and vice versa. Everyone who is kind or old is quiet or not old. If lucy is happy then susan is brave or creative and vice versa. Everyone who is both happy and rich is creative or not generous. Someone is brave. John is not wise or not strong. Lucy is both creative and kind. Someone is happy or wise. Someone is not happy or rich. Mary is not strong or not calm. Fred is either funny or not tall. Someone is either not rich or not wise. | John is wise. | neutral | (((humble(fred)|~happy(fred)))=>(?[X]:(old(X))))&
(![X]:((~quiet(X)<~>~curious(X))=>(~rich(X)|quiet(X))))&
((?[X]:((~brave(X)|old(X))))=>((rich(alice)<~>strong(alice))))&
((?[X]:((~generous(X)|tall(X))))<=>(?[X]:(kind(X))))&
(![X]:((~quiet(X)&~kind(X))<=>(~calm(X)|patient(X))))&
(![X]:((brave(X)&~kind(X))<=>(~tall(X)|~humble(X))))&
((?[X]:((funny(X)<~>old(X))))<=>(?[X]:((generous(X)&~funny(X)))))&
((~patient(susan))=>((~old(fred)<~>humble(fred))))&
(((rich(mary)&brave(mary)))=>((~curious(john)|old(john))))&
((~generous(mary))=>(?[X]:((quiet(X)|creative(X)))))&
(![X]:((funny(X)<~>strong(X))=>(calm(X)|kind(X))))&
(![X]:((~generous(X)&~strong(X))=>(~rich(X)&tall(X))))&
((?[X]:((wise(X)&~old(X))))<=>(~calm(susan)))&
(![X]:((kind(X)|old(X))=>(quiet(X)|~old(X))))&
((happy(lucy))<=>((brave(susan)|creative(susan))))&
(![X]:((happy(X)&rich(X))=>(creative(X)|~generous(X))))&
(?[X]:(brave(X)))&
((~wise(john)|~strong(john)))&
((creative(lucy)&kind(lucy)))&
(?[X]:((happy(X)|wise(X))))&
(?[X]:((~happy(X)|rich(X))))&
((~strong(mary)|~calm(mary)))&
((funny(fred)<~>~tall(fred)))&
(?[X]:((~rich(X)<~>~wise(X)))) | wise(john) | [] | null | 0 |
If someone is old then someone is not rich. Everyone who is not creative is not quiet or happy. Everyone who is both not creative and not kind is both generous and not creative. Everyone who is happy is both calm and not calm. If john is not tall then someone is strong or not patient and vice versa. Everyone who is either not tall or not brave is either patient or wise. Everyone who is not quiet is either not funny or not rich and vice versa. Everyone who is old or not humble is either not rich or humble and vice versa. Everyone who is either brave or tall is funny or happy and vice versa. If someone is either not funny or patient then fred is not curious and vice versa. If john is either happy or tall then someone is both not humble and not strong and vice versa. Everyone who is both not tall and not creative is either rich or strong. Everyone who is both curious and not old is either not old or strong. If someone is not humble then someone is not creative. If someone is either not wise or old then lucy is both not kind and not funny. Everyone who is either not tall or wise is not generous and vice versa. Fred is both not patient and not tall. Someone is either old or quiet. Someone is not tall or not rich. Someone is curious or patient. Paul is rich. Mary is both funny and brave. Mary is either not wise or happy. | Paul is not humble. | contradiction | ((?[X]:(old(X)))=>(?[X]:(~rich(X))))&
(![X]:(~creative(X)=>(~quiet(X)|happy(X))))&
(![X]:((~creative(X)&~kind(X))=>(generous(X)&~creative(X))))&
(![X]:(happy(X)=>(calm(X)&~calm(X))))&
((~tall(john))<=>(?[X]:((strong(X)|~patient(X)))))&
(![X]:((~tall(X)<~>~brave(X))=>(patient(X)<~>wise(X))))&
(![X]:(~quiet(X)<=>(~funny(X)<~>~rich(X))))&
(![X]:((old(X)|~humble(X))<=>(~rich(X)<~>humble(X))))&
(![X]:((brave(X)<~>tall(X))<=>(funny(X)|happy(X))))&
((?[X]:((~funny(X)<~>patient(X))))<=>(~curious(fred)))&
(((happy(john)<~>tall(john)))<=>(?[X]:((~humble(X)&~strong(X)))))&
(![X]:((~tall(X)&~creative(X))=>(rich(X)<~>strong(X))))&
(![X]:((curious(X)&~old(X))=>(~old(X)<~>strong(X))))&
((?[X]:(~humble(X)))=>(?[X]:(~creative(X))))&
((?[X]:((~wise(X)<~>old(X))))=>((~kind(lucy)&~funny(lucy))))&
(![X]:((~tall(X)<~>wise(X))<=>~generous(X)))&
((~patient(fred)&~tall(fred)))&
(?[X]:((old(X)<~>quiet(X))))&
(?[X]:((~tall(X)|~rich(X))))&
(?[X]:((curious(X)|patient(X))))&
(rich(paul))&
((funny(mary)&brave(mary)))&
((~wise(mary)<~>happy(mary))) | ~humble(paul) | [
"p7",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 6256577282354690308895399
% SZS output start Proof for 6256577282354690308895399
8. ! [X0] : ((~humble(X0) | old(X0)) <=> (~rich(X0) <~> humble(X0))) [input p7]
21. rich(paul) [input p20]
24. ~humble(paul) [input hypothesis]
51. ! [X0] : (((~humble(X0) | old(X0)) | ((~rich(X0) | ~humble(X0)) & (humble(X0) | rich(X0)))) & (((~humble(X0) | rich(X0)) & (humble(X0) | ~rich(X0))) | (humble(X0) & ~old(X0)))) [nnf transformation 8]
52. ! [X0] : ((~humble(X0) | old(X0) | ((~rich(X0) | ~humble(X0)) & (humble(X0) | rich(X0)))) & (((~humble(X0) | rich(X0)) & (humble(X0) | ~rich(X0))) | (humble(X0) & ~old(X0)))) [flattening 51]
96. humble(X0) | ~rich(X0) | humble(X0) [cnf transformation 52]
134. rich(paul) [cnf transformation 21]
139. ~humble(paul) [cnf transformation 24]
141. ~rich(X0) | humble(X0) [duplicate literal removal 96]
273. humble(paul) [resolution 141,134]
274. $false [subsumption resolution 273,139]
% SZS output end Proof for 6256577282354690308895399
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall is not humble.
Everyone who is happy or not curious is either generous or not calm.
Everyone who is curious is wise or not curious.
Everyone who is wise is either not rich or not wise.
Everyone who is both creative and not patient is both calm and not generous.
Everyone who is both not old and old is not humble.
Everyone who is both brave and calm is either not old or not patient.
If susan is humble then someone is tall or curious.
Everyone who is not quiet or funny is either kind or brave and vice versa.
Everyone who is either humble or old is curious.
If susan is both not creative and not curious then paul is both tall and generous and vice versa.
Everyone who is both not creative and quiet is either not strong or not patient and vice versa.
Everyone who is both funny and not brave is not brave.
If susan is not rich or strong then someone is quiet.
If someone is both brave and not creative then someone is brave or not old.
If fred is both tall and brave then someone is not old or brave.
Someone is either quiet or not quiet.
Someone is curious or not kind.
Paul is calm or not quiet.
Someone is either funny or kind.
Alice is both not rich and generous.
Someone is not happy.
Someone is both quiet and not calm.
Someone is not kind or quiet. | Fred is not rich. | neutral | (![X]:(tall(X)=>~humble(X)))&
(![X]:((happy(X)|~curious(X))=>(generous(X)<~>~calm(X))))&
(![X]:(curious(X)=>(wise(X)|~curious(X))))&
(![X]:(wise(X)=>(~rich(X)<~>~wise(X))))&
(![X]:((creative(X)&~patient(X))=>(calm(X)&~generous(X))))&
(![X]:((~old(X)&old(X))=>~humble(X)))&
(![X]:((brave(X)&calm(X))=>(~old(X)<~>~patient(X))))&
((humble(susan))=>(?[X]:((tall(X)|curious(X)))))&
(![X]:((~quiet(X)|funny(X))<=>(kind(X)<~>brave(X))))&
(![X]:((humble(X)<~>old(X))=>curious(X)))&
(((~creative(susan)&~curious(susan)))<=>((tall(paul)&generous(paul))))&
(![X]:((~creative(X)&quiet(X))<=>(~strong(X)<~>~patient(X))))&
(![X]:((funny(X)&~brave(X))=>~brave(X)))&
(((~rich(susan)|strong(susan)))=>(?[X]:(quiet(X))))&
((?[X]:((brave(X)&~creative(X))))=>(?[X]:((brave(X)|~old(X)))))&
(((tall(fred)&brave(fred)))=>(?[X]:((~old(X)|brave(X)))))&
(?[X]:((quiet(X)<~>~quiet(X))))&
(?[X]:((curious(X)|~kind(X))))&
((calm(paul)|~quiet(paul)))&
(?[X]:((funny(X)<~>kind(X))))&
((~rich(alice)&generous(alice)))&
(?[X]:(~happy(X)))&
(?[X]:((quiet(X)&~calm(X))))&
(?[X]:((~kind(X)|quiet(X)))) | ~rich(fred) | [] | null | 0 |
If someone is not rich or old then someone is both quiet and not generous.
Everyone who is not rich is not tall.
If someone is either not brave or not happy then fred is calm and vice versa.
If susan is rich then someone is either not funny or not strong.
Everyone who is either rich or quiet is both old and calm.
If susan is happy or generous then someone is not happy or calm and vice versa.
If mary is creative or not strong then someone is not funny.
Everyone who is wise or quiet is either not creative or not tall.
Everyone who is both not tall and patient is tall.
Everyone who is either creative or not tall is not patient and vice versa.
Everyone who is both creative and patient is happy or old.
If fred is either curious or not patient then mary is both not tall and tall.
Everyone who is creative or not calm is strong.
Everyone who is not tall is either not creative or not old and vice versa.
If alice is either wise or not creative then someone is kind or not happy and vice versa.
If fred is both strong and not patient then someone is not curious and vice versa.
Someone is not kind or calm.
Someone is generous or not curious.
Someone is both wise and not curious.
Mary is patient.
Mary is tall or not funny.
Fred is rich.
Someone is both not humble and old.
Someone is strong. | Mary is not tall. | contradiction | ((?[X]:((~rich(X)|old(X))))=>(?[X]:((quiet(X)&~generous(X)))))&
(![X]:(~rich(X)=>~tall(X)))&
((?[X]:((~brave(X)<~>~happy(X))))<=>(calm(fred)))&
((rich(susan))=>(?[X]:((~funny(X)<~>~strong(X)))))&
(![X]:((rich(X)<~>quiet(X))=>(old(X)&calm(X))))&
(((happy(susan)|generous(susan)))<=>(?[X]:((~happy(X)|calm(X)))))&
(((creative(mary)|~strong(mary)))=>(?[X]:(~funny(X))))&
(![X]:((wise(X)|quiet(X))=>(~creative(X)<~>~tall(X))))&
(![X]:((~tall(X)&patient(X))=>tall(X)))&
(![X]:((creative(X)<~>~tall(X))<=>~patient(X)))&
(![X]:((creative(X)&patient(X))=>(happy(X)|old(X))))&
(((curious(fred)<~>~patient(fred)))=>((~tall(mary)&tall(mary))))&
(![X]:((creative(X)|~calm(X))=>strong(X)))&
(![X]:(~tall(X)<=>(~creative(X)<~>~old(X))))&
(((wise(alice)<~>~creative(alice)))<=>(?[X]:((kind(X)|~happy(X)))))&
(((strong(fred)&~patient(fred)))<=>(?[X]:(~curious(X))))&
(?[X]:((~kind(X)|calm(X))))&
(?[X]:((generous(X)|~curious(X))))&
(?[X]:((wise(X)&~curious(X))))&
(patient(mary))&
((tall(mary)|~funny(mary)))&
(rich(fred))&
(?[X]:((~humble(X)&old(X))))&
(?[X]:(strong(X))) | ~tall(mary) | [
"p8",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 1862799196907311760950320
% SZS output start Proof for 1862799196907311760950320
9. ! [X0] : ((patient(X0) & ~tall(X0)) => tall(X0)) [input p8]
20. patient(mary) [input p19]
25. ~tall(mary) [input hypothesis]
34. ! [X0] : (tall(X0) | (~patient(X0) | tall(X0))) [ennf transformation 9]
35. ! [X0] : (tall(X0) | ~patient(X0) | tall(X0)) [flattening 34]
106. tall(X0) | ~patient(X0) | tall(X0) [cnf transformation 35]
135. patient(mary) [cnf transformation 20]
140. ~tall(mary) [cnf transformation 25]
141. ~patient(X0) | tall(X0) [duplicate literal removal 106]
247. 24 <=> tall(mary) [avatar definition]
248. ~tall(mary) <- (~24) [avatar component clause 247]
318. ~24 [avatar split clause 140,247]
323. tall(mary) [resolution 141,135]
324. $false <- (~24) [subsumption resolution 323,248]
325. 24 [avatar contradiction clause 324]
326. $false [avatar sat refutation 318,325]
% SZS output end Proof for 1862799196907311760950320
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If someone is 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 not quiet. | neutral | ((?[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))) | ~quiet(lucy) | [] | null | 0 |
If lucy is both not brave and funny then alice is patient or not old and vice versa. Everyone who is both tall and not calm is strong or old. Everyone who is both brave and happy is tall and vice versa. Everyone who is kind is both not generous and not happy. Everyone who is quiet or not quiet is both not rich and not kind and vice versa. If someone is both not generous and funny then someone is both not kind and humble and vice versa. Everyone who is both not calm and funny is patient and vice versa. If lucy is happy then paul is not creative. Everyone who is both not creative and not kind is both strong and humble and vice versa. Everyone who is either quiet or not wise is both not quiet and not curious. If mary is either not kind or humble then lucy is not calm. If someone is either not happy or not old then lucy is either not calm or calm and vice versa. Everyone who is happy or patient is either quiet or happy. Everyone who is either old or wise is not generous or wise and vice versa. Everyone who is humble or quiet is either rich or generous and vice versa. If paul is quiet or not curious then someone is not rich. Lucy is not brave or quiet. Someone is kind or patient. Someone is both curious and patient. Someone is both not old and happy. Mary is not funny. Someone is brave. Someone is not wise or not funny. | Lucy is tall. | contradiction | (((~brave(lucy)&funny(lucy)))<=>((patient(alice)|~old(alice))))&
(![X]:((tall(X)&~calm(X))=>(strong(X)|old(X))))&
(![X]:((brave(X)&happy(X))<=>tall(X)))&
(![X]:(kind(X)=>(~generous(X)&~happy(X))))&
(![X]:((quiet(X)|~quiet(X))<=>(~rich(X)&~kind(X))))&
((?[X]:((~generous(X)&funny(X))))<=>(?[X]:((~kind(X)&humble(X)))))&
(![X]:((~calm(X)&funny(X))<=>patient(X)))&
((happy(lucy))=>(~creative(paul)))&
(![X]:((~creative(X)&~kind(X))<=>(strong(X)&humble(X))))&
(![X]:((quiet(X)<~>~wise(X))=>(~quiet(X)&~curious(X))))&
(((~kind(mary)<~>humble(mary)))=>(~calm(lucy)))&
((?[X]:((~happy(X)<~>~old(X))))<=>((~calm(lucy)<~>calm(lucy))))&
(![X]:((happy(X)|patient(X))=>(quiet(X)<~>happy(X))))&
(![X]:((old(X)<~>wise(X))<=>(~generous(X)|wise(X))))&
(![X]:((humble(X)|quiet(X))<=>(rich(X)<~>generous(X))))&
(((quiet(paul)|~curious(paul)))=>(?[X]:(~rich(X))))&
((~brave(lucy)|quiet(lucy)))&
(?[X]:((kind(X)|patient(X))))&
(?[X]:((curious(X)&patient(X))))&
(?[X]:((~old(X)&happy(X))))&
(~funny(mary))&
(?[X]:(brave(X)))&
(?[X]:((~wise(X)|~funny(X)))) | tall(lucy) | [
"p2",
"p12",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 8743778004785494840588652
% SZS output start Proof for 8743778004785494840588652
3. ! [X0] : ((happy(X0) & brave(X0)) <=> tall(X0)) [input p2]
13. ! [X0] : ((patient(X0) | happy(X0)) => (quiet(X0) <~> happy(X0))) [input p12]
17. quiet(lucy) | ~brave(lucy) [input p16]
24. tall(lucy) [input hypothesis]
32. ! [X0] : ((quiet(X0) <~> happy(X0)) | (~patient(X0) & ~happy(X0))) [ennf transformation 13]
36. ! [X0] : (((happy(X0) & brave(X0)) | ~tall(X0)) & (tall(X0) | (~happy(X0) | ~brave(X0)))) [nnf transformation 3]
37. ! [X0] : (((happy(X0) & brave(X0)) | ~tall(X0)) & (tall(X0) | ~happy(X0) | ~brave(X0))) [flattening 36]
55. ! [X0] : (((~happy(X0) | ~quiet(X0)) & (happy(X0) | quiet(X0))) | (~patient(X0) & ~happy(X0))) [nnf transformation 32]
79. ~tall(X0) | brave(X0) [cnf transformation 37]
80. ~tall(X0) | happy(X0) [cnf transformation 37]
116. ~happy(X0) | ~quiet(X0) | ~happy(X0) [cnf transformation 55]
132. quiet(lucy) | ~brave(lucy) [cnf transformation 17]
141. tall(lucy) [cnf transformation 24]
144. ~quiet(X0) | ~happy(X0) [duplicate literal removal 116]
165. 4 <=> brave(lucy) [avatar definition]
197. 10 <=> happy(lucy) [avatar definition]
198. happy(lucy) <- (10) [avatar component clause 197]
234. 16 <=> quiet(lucy) [avatar definition]
236. quiet(lucy) <- (16) [avatar component clause 234]
237. ~4 | 16 [avatar split clause 132,234,165]
248. brave(lucy) [resolution 79,141]
251. 4 [avatar split clause 248,165]
252. happy(lucy) [resolution 80,141]
253. 10 [avatar split clause 252,197]
256. ~happy(lucy) <- (16) [resolution 144,236]
257. $false <- (10, 16) [subsumption resolution 256,198]
258. ~10 | ~16 [avatar contradiction clause 257]
259. $false [avatar sat refutation 237,251,253,258]
% SZS output end Proof for 8743778004785494840588652
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not brave or kind is both tall and not curious and vice versa.
If john is calm then someone is not old or not strong and vice versa.
Everyone who is either not strong or curious is both not generous and curious and vice versa.
If john is not creative then someone is either old or happy.
Everyone who is not calm or creative is not brave or generous and vice versa.
Everyone who is either brave or not curious is either old or happy and vice versa.
Everyone who is not generous or patient is not tall and vice versa.
If someone is rich then fred is funny or patient and vice versa.
If john is both brave and not funny then someone is not curious.
Everyone who is tall or not calm is both not tall and kind.
If someone is either not wise or not humble then someone is either not curious or not quiet.
If someone is either not calm or wise then someone is generous.
Everyone who is not quiet is not calm and vice versa.
Everyone who is either calm or not happy is patient and vice versa.
Everyone who is not brave is both not happy and not creative and vice versa.
If someone is both curious and happy then someone is not patient or humble.
John is not tall.
Someone is both patient and not funny.
Someone is both not old and not strong.
Someone is quiet or humble.
Someone is both not curious and not creative.
Someone is curious or not quiet. | Fred is humble. | neutral | (![X]:((~brave(X)|kind(X))<=>(tall(X)&~curious(X))))&
((calm(john))<=>(?[X]:((~old(X)|~strong(X)))))&
(![X]:((~strong(X)<~>curious(X))<=>(~generous(X)&curious(X))))&
((~creative(john))=>(?[X]:((old(X)<~>happy(X)))))&
(![X]:((~calm(X)|creative(X))<=>(~brave(X)|generous(X))))&
(![X]:((brave(X)<~>~curious(X))<=>(old(X)<~>happy(X))))&
(![X]:((~generous(X)|patient(X))<=>~tall(X)))&
((?[X]:(rich(X)))<=>((funny(fred)|patient(fred))))&
(((brave(john)&~funny(john)))=>(?[X]:(~curious(X))))&
(![X]:((tall(X)|~calm(X))=>(~tall(X)&kind(X))))&
((?[X]:((~wise(X)<~>~humble(X))))=>(?[X]:((~curious(X)<~>~quiet(X)))))&
((?[X]:((~calm(X)<~>wise(X))))=>(?[X]:(generous(X))))&
(![X]:(~quiet(X)<=>~calm(X)))&
(![X]:((calm(X)<~>~happy(X))<=>patient(X)))&
(![X]:(~brave(X)<=>(~happy(X)&~creative(X))))&
((?[X]:((curious(X)&happy(X))))=>(?[X]:((~patient(X)|humble(X)))))&
(~tall(john))&
(?[X]:((patient(X)&~funny(X))))&
(?[X]:((~old(X)&~strong(X))))&
(?[X]:((quiet(X)|humble(X))))&
(?[X]:((~curious(X)&~creative(X))))&
(?[X]:((curious(X)|~quiet(X)))) | humble(fred) | [] | null | 0 |
Everyone who is patient is calm or not calm and vice versa.
Everyone who is both rich and not brave is not tall or brave and vice versa.
If someone is not wise then john is either not humble or brave and vice versa.
Everyone who is funny or not curious is either not funny or patient and vice versa.
If someone is both not quiet and happy then someone is not strong or generous.
Everyone who is creative is either not curious or curious and vice versa.
Everyone who is not wise is either happy or kind and vice versa.
If someone is old or not patient then someone is either not wise or rich and vice versa.
If susan is both not quiet and patient then susan is not old and vice versa.
If someone is either tall or not humble then susan is both not wise and humble and vice versa.
Everyone who is happy is not quiet or not generous.
If paul is both calm and not quiet then someone is not creative.
If alice is either patient or not calm then someone is curious.
If someone is both rich and not wise then mary is kind or not wise.
Everyone who is funny or not old is either calm or not humble and vice versa.
Everyone who is both humble and not humble is either not quiet or not strong and vice versa.
Someone is both tall and not quiet.
Fred is not humble.
Someone is kind.
Someone is not strong or wise.
Lucy is not generous or not humble.
John is either creative or funny.
Someone is strong. | John is generous. | neutral | (![X]:(patient(X)<=>(calm(X)|~calm(X))))&
(![X]:((rich(X)&~brave(X))<=>(~tall(X)|brave(X))))&
((?[X]:(~wise(X)))<=>((~humble(john)<~>brave(john))))&
(![X]:((funny(X)|~curious(X))<=>(~funny(X)<~>patient(X))))&
((?[X]:((~quiet(X)&happy(X))))=>(?[X]:((~strong(X)|generous(X)))))&
(![X]:(creative(X)<=>(~curious(X)<~>curious(X))))&
(![X]:(~wise(X)<=>(happy(X)<~>kind(X))))&
((?[X]:((old(X)|~patient(X))))<=>(?[X]:((~wise(X)<~>rich(X)))))&
(((~quiet(susan)&patient(susan)))<=>(~old(susan)))&
((?[X]:((tall(X)<~>~humble(X))))<=>((~wise(susan)&humble(susan))))&
(![X]:(happy(X)=>(~quiet(X)|~generous(X))))&
(((calm(paul)&~quiet(paul)))=>(?[X]:(~creative(X))))&
(((patient(alice)<~>~calm(alice)))=>(?[X]:(curious(X))))&
((?[X]:((rich(X)&~wise(X))))=>((kind(mary)|~wise(mary))))&
(![X]:((funny(X)|~old(X))<=>(calm(X)<~>~humble(X))))&
(![X]:((humble(X)&~humble(X))<=>(~quiet(X)<~>~strong(X))))&
(?[X]:((tall(X)&~quiet(X))))&
(~humble(fred))&
(?[X]:(kind(X)))&
(?[X]:((~strong(X)|wise(X))))&
((~generous(lucy)|~humble(lucy)))&
((creative(john)<~>funny(john)))&
(?[X]:(strong(X))) | generous(john) | [] | null | 0 |
If someone is curious then mary is not curious or funny and vice versa. Everyone who is not happy is either kind or generous. Everyone who is not rich or not patient is either not brave or generous. Everyone who is both not curious and rich is not rich or not funny. Everyone who is both not rich and quiet is both happy and old and vice versa. Everyone who is not creative or creative is not old or quiet and vice versa. Everyone who is quiet is curious or not brave and vice versa. Everyone who is creative or not kind is not wise or not curious. If lucy is wise or not brave then someone is not happy or not funny and vice versa. Everyone who is not creative or strong is both not tall and patient. If someone is old or not funny then mary is old. If alice is both generous and old then susan is humble and vice versa. Everyone who is wise or not old is either rich or not humble. Everyone who is both not strong and brave is strong or old. If someone is either patient or not rich then john is both not quiet and not patient. If alice is either rich or creative then mary is either not generous or humble. Fred is both not old and funny. Paul is not kind or happy. Fred is quiet or generous. John is not creative. Alice is not strong or patient. Someone is both not generous and kind. Alice is patient or rich. | Paul is patient. | neutral | ((?[X]:(curious(X)))<=>((~curious(mary)|funny(mary))))&
(![X]:(~happy(X)=>(kind(X)<~>generous(X))))&
(![X]:((~rich(X)|~patient(X))=>(~brave(X)<~>generous(X))))&
(![X]:((~curious(X)&rich(X))=>(~rich(X)|~funny(X))))&
(![X]:((~rich(X)&quiet(X))<=>(happy(X)&old(X))))&
(![X]:((~creative(X)|creative(X))<=>(~old(X)|quiet(X))))&
(![X]:(quiet(X)<=>(curious(X)|~brave(X))))&
(![X]:((creative(X)|~kind(X))=>(~wise(X)|~curious(X))))&
(((wise(lucy)|~brave(lucy)))<=>(?[X]:((~happy(X)|~funny(X)))))&
(![X]:((~creative(X)|strong(X))=>(~tall(X)&patient(X))))&
((?[X]:((old(X)|~funny(X))))=>(old(mary)))&
(((generous(alice)&old(alice)))<=>(humble(susan)))&
(![X]:((wise(X)|~old(X))=>(rich(X)<~>~humble(X))))&
(![X]:((~strong(X)&brave(X))=>(strong(X)|old(X))))&
((?[X]:((patient(X)<~>~rich(X))))=>((~quiet(john)&~patient(john))))&
(((rich(alice)<~>creative(alice)))=>((~generous(mary)<~>humble(mary))))&
((~old(fred)&funny(fred)))&
((~kind(paul)|happy(paul)))&
((quiet(fred)|generous(fred)))&
(~creative(john))&
((~strong(alice)|patient(alice)))&
(?[X]:((~generous(X)&kind(X))))&
((patient(alice)|rich(alice))) | patient(paul) | [] | null | 0 |
If john is both humble and not creative then paul is either not rich or happy and vice versa. If someone is kind then john is not strong or not quiet. Everyone who is quiet is either old or not funny. If someone is both quiet and not kind then paul is either not wise or patient and vice versa. Everyone who is either generous or patient is strong or old. If mary is either quiet or funny then someone is not strong and vice versa. If someone is both not rich and not happy then paul is either curious or kind and vice versa. If someone is not wise then fred is not quiet and vice versa. If someone is both not tall and rich then alice is not humble or humble and vice versa. Everyone who is creative or not quiet is not rich. If someone is either tall or strong then paul is not strong and vice versa. Everyone who is both kind and rich is not strong. Everyone who is both old and curious is both wise and not strong. If someone is both not generous and humble then someone is funny and vice versa. If someone is not curious or old then someone is not funny or happy and vice versa. Everyone who is either funny or tall is both tall and not creative and vice versa. Someone is not tall or not kind. Mary is both not old and not generous. Someone is both patient and not brave. Someone is not calm or curious. John is both happy and curious. Fred is creative. Susan is generous or not generous. Lucy is both not curious and not humble. | John is not brave. | neutral | (((humble(john)&~creative(john)))<=>((~rich(paul)<~>happy(paul))))&
((?[X]:(kind(X)))=>((~strong(john)|~quiet(john))))&
(![X]:(quiet(X)=>(old(X)<~>~funny(X))))&
((?[X]:((quiet(X)&~kind(X))))<=>((~wise(paul)<~>patient(paul))))&
(![X]:((generous(X)<~>patient(X))=>(strong(X)|old(X))))&
(((quiet(mary)<~>funny(mary)))<=>(?[X]:(~strong(X))))&
((?[X]:((~rich(X)&~happy(X))))<=>((curious(paul)<~>kind(paul))))&
((?[X]:(~wise(X)))<=>(~quiet(fred)))&
((?[X]:((~tall(X)&rich(X))))<=>((~humble(alice)|humble(alice))))&
(![X]:((creative(X)|~quiet(X))=>~rich(X)))&
((?[X]:((tall(X)<~>strong(X))))<=>(~strong(paul)))&
(![X]:((kind(X)&rich(X))=>~strong(X)))&
(![X]:((old(X)&curious(X))=>(wise(X)&~strong(X))))&
((?[X]:((~generous(X)&humble(X))))<=>(?[X]:(funny(X))))&
((?[X]:((~curious(X)|old(X))))<=>(?[X]:((~funny(X)|happy(X)))))&
(![X]:((funny(X)<~>tall(X))<=>(tall(X)&~creative(X))))&
(?[X]:((~tall(X)|~kind(X))))&
((~old(mary)&~generous(mary)))&
(?[X]:((patient(X)&~brave(X))))&
(?[X]:((~calm(X)|curious(X))))&
((happy(john)&curious(john)))&
(creative(fred))&
((generous(susan)|~generous(susan)))&
((~curious(lucy)&~humble(lucy))) | ~brave(john) | [] | null | 0 |
Everyone who is quiet is either not creative or not old.
If someone is either brave or rich then mary is tall or not calm.
If someone is not quiet or not brave then someone is creative or not curious and vice versa.
If someone is both happy and funny then someone is both tall and rich.
If someone is patient then lucy is happy and vice versa.
Everyone who is either not creative or not brave is either happy or patient.
Everyone who is not funny is wise and vice versa.
If someone is strong or generous then lucy is not rich and vice versa.
Everyone who is either happy or not brave is not generous or creative and vice versa.
Everyone who is both not patient and not happy is patient or calm and vice versa.
Everyone who is strong or not creative is old or creative and vice versa.
If someone is both tall and creative then alice is not generous or creative.
If john is either tall or patient then john is not creative and vice versa.
Everyone who is not brave or kind is humble.
Fred is old or creative.
Someone is both not curious and humble.
Someone is both not curious and funny.
Someone is happy.
Someone is both happy and curious.
Mary is curious or old.
Someone is both not brave and not happy.
Someone is either happy or brave. | Lucy is not brave. | entailment | (![X]:(quiet(X)=>(~creative(X)<~>~old(X))))&
((?[X]:((brave(X)<~>rich(X))))=>((tall(mary)|~calm(mary))))&
((?[X]:((~quiet(X)|~brave(X))))<=>(?[X]:((creative(X)|~curious(X)))))&
((?[X]:((happy(X)&funny(X))))=>(?[X]:((tall(X)&rich(X)))))&
((?[X]:(patient(X)))<=>(happy(lucy)))&
(![X]:((~creative(X)<~>~brave(X))=>(happy(X)<~>patient(X))))&
(![X]:(~funny(X)<=>wise(X)))&
((?[X]:((strong(X)|generous(X))))<=>(~rich(lucy)))&
(![X]:((happy(X)<~>~brave(X))<=>(~generous(X)|creative(X))))&
(![X]:((~patient(X)&~happy(X))<=>(patient(X)|calm(X))))&
(![X]:((strong(X)|~creative(X))<=>(old(X)|creative(X))))&
((?[X]:((tall(X)&creative(X))))=>((~generous(alice)|creative(alice))))&
(((tall(john)<~>patient(john)))<=>(~creative(john)))&
(![X]:((~brave(X)|kind(X))=>humble(X)))&
((old(fred)|creative(fred)))&
(?[X]:((~curious(X)&humble(X))))&
(?[X]:((~curious(X)&funny(X))))&
(?[X]:(happy(X)))&
(?[X]:((happy(X)&curious(X))))&
((curious(mary)|old(mary)))&
(?[X]:((~brave(X)&~happy(X))))&
(?[X]:((happy(X)<~>brave(X)))) | ~brave(lucy) | [
"p4",
"p5",
"p8",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 7437324022660038754275233
% SZS output start Proof for 7437324022660038754275233
5. ? [X0] : patient(X0) <=> happy(lucy) [input p4]
6. ! [X0] : ((~creative(X0) <~> ~brave(X0)) => (happy(X0) <~> patient(X0))) [input p5]
9. ! [X0] : ((happy(X0) <~> ~brave(X0)) <=> (creative(X0) | ~generous(X0))) [input p8]
10. ! [X0] : ((~happy(X0) & ~patient(X0)) <=> (calm(X0) | patient(X0))) [input p9]
23. brave(lucy) [input hypothesis]
32. ! [X0] : ((happy(X0) <~> patient(X0)) | (~creative(X0) <=> ~brave(X0))) [ennf transformation 6]
45. (? [X0] : patient(X0) | ~happy(lucy)) & (happy(lucy) | ! [X0] : ~patient(X0)) [nnf transformation 5]
46. (? [X0] : patient(X0) | ~happy(lucy)) & (happy(lucy) | ! [X1] : ~patient(X1)) [rectify 45]
47. ? [X0] : patient(X0) => patient(sK3) [choice axiom]
48. (patient(sK3) | ~happy(lucy)) & (happy(lucy) | ! [X1] : ~patient(X1)) [skolemisation 46,47]
49. ! [X0] : (((~patient(X0) | ~happy(X0)) & (patient(X0) | happy(X0))) | ((~creative(X0) | brave(X0)) & (~brave(X0) | creative(X0)))) [nnf transformation 32]
55. ! [X0] : ((((brave(X0) | ~happy(X0)) & (~brave(X0) | happy(X0))) | (~creative(X0) & generous(X0))) & ((creative(X0) | ~generous(X0)) | ((happy(X0) | brave(X0)) & (~brave(X0) | ~happy(X0))))) [nnf transformation 9]
56. ! [X0] : ((((brave(X0) | ~happy(X0)) & (~brave(X0) | happy(X0))) | (~creative(X0) & generous(X0))) & (creative(X0) | ~generous(X0) | ((happy(X0) | brave(X0)) & (~brave(X0) | ~happy(X0))))) [flattening 55]
57. ! [X0] : (((~happy(X0) & ~patient(X0)) | (~calm(X0) & ~patient(X0))) & ((calm(X0) | patient(X0)) | (happy(X0) | patient(X0)))) [nnf transformation 10]
58. ! [X0] : (((~happy(X0) & ~patient(X0)) | (~calm(X0) & ~patient(X0))) & (calm(X0) | patient(X0) | happy(X0) | patient(X0))) [flattening 57]
86. patient(sK3) | ~happy(lucy) [cnf transformation 48]
87. ~brave(X0) | happy(X0) | patient(X0) | creative(X0) [cnf transformation 49]
99. ~brave(X0) | happy(X0) | ~creative(X0) [cnf transformation 56]
103. ~patient(X0) | ~patient(X0) [cnf transformation 58]
128. brave(lucy) [cnf transformation 23]
132. ~patient(X0) [duplicate literal removal 103]
195. 16 <=> happy(lucy) [avatar definition]
197. ~happy(lucy) <- (~16) [avatar component clause 195]
199. 17 <=> patient(sK3) [avatar definition]
201. patient(sK3) <- (17) [avatar component clause 199]
202. ~16 | 17 [avatar split clause 86,199,195]
204. 18 <=> ! [X1] : ~patient(X1) [avatar definition]
205. ~patient(X1) <- (18) [avatar component clause 204]
228. 18 [avatar split clause 132,204]
285. happy(lucy) | ~creative(lucy) [resolution 99,128]
286. ~creative(lucy) <- (~16) [subsumption resolution 285,197]
327. happy(lucy) | patient(lucy) | creative(lucy) [resolution 87,128]
328. patient(lucy) | creative(lucy) <- (~16) [subsumption resolution 327,197]
329. creative(lucy) <- (~16, 18) [subsumption resolution 328,205]
330. $false <- (~16, 18) [subsumption resolution 329,286]
331. 16 | ~18 [avatar contradiction clause 330]
344. $false <- (17, 18) [subsumption resolution 201,205]
345. ~17 | ~18 [avatar contradiction clause 344]
346. $false [avatar sat refutation 202,228,331,345]
% SZS output end Proof for 7437324022660038754275233
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If mary is both not strong and creative then john is both generous and patient. If someone is wise then susan is patient or not old and vice versa. If someone is either not rich or not old then susan is either humble or curious and vice versa. Everyone who is both not patient and not creative is both not brave and not quiet and vice versa. Everyone who is generous is happy or not generous and vice versa. Everyone who is either not funny or happy is either tall or not generous. If someone is not calm then someone is either not wise or calm. Everyone who is not quiet or calm is either not happy or patient. If someone is wise or curious then someone is both calm and not funny and vice versa. Everyone who is not generous or not strong is both not tall and not rich and vice versa. Everyone who is both generous and tall is both funny and not generous and vice versa. Everyone who is patient is either generous or kind. If susan is either not curious or humble then someone is kind and vice versa. Everyone who is not calm or happy is rich or not creative and vice versa. Everyone who is either generous or not strong is both curious and not patient. If susan is not curious or not kind then someone is not tall and vice versa. Someone is not kind. Someone is generous. Someone is patient. Someone is not humble. Susan is funny or generous. Someone is both patient and not old. | John is calm. | neutral | (((~strong(mary)&creative(mary)))=>((generous(john)&patient(john))))&
((?[X]:(wise(X)))<=>((patient(susan)|~old(susan))))&
((?[X]:((~rich(X)<~>~old(X))))<=>((humble(susan)<~>curious(susan))))&
(![X]:((~patient(X)&~creative(X))<=>(~brave(X)&~quiet(X))))&
(![X]:(generous(X)<=>(happy(X)|~generous(X))))&
(![X]:((~funny(X)<~>happy(X))=>(tall(X)<~>~generous(X))))&
((?[X]:(~calm(X)))=>(?[X]:((~wise(X)<~>calm(X)))))&
(![X]:((~quiet(X)|calm(X))=>(~happy(X)<~>patient(X))))&
((?[X]:((wise(X)|curious(X))))<=>(?[X]:((calm(X)&~funny(X)))))&
(![X]:((~generous(X)|~strong(X))<=>(~tall(X)&~rich(X))))&
(![X]:((generous(X)&tall(X))<=>(funny(X)&~generous(X))))&
(![X]:(patient(X)=>(generous(X)<~>kind(X))))&
(((~curious(susan)<~>humble(susan)))<=>(?[X]:(kind(X))))&
(![X]:((~calm(X)|happy(X))<=>(rich(X)|~creative(X))))&
(![X]:((generous(X)<~>~strong(X))=>(curious(X)&~patient(X))))&
(((~curious(susan)|~kind(susan)))<=>(?[X]:(~tall(X))))&
(?[X]:(~kind(X)))&
(?[X]:(generous(X)))&
(?[X]:(patient(X)))&
(?[X]:(~humble(X)))&
((funny(susan)|generous(susan)))&
(?[X]:((patient(X)&~old(X)))) | calm(john) | [] | null | 0 |
Everyone who is wise or not strong is both tall and not kind.
If someone is both not funny and old then someone is not calm or not rich and vice versa.
Everyone who is both not calm and funny is rich or generous.
If someone is both not wise and not curious then lucy is not wise or not strong and vice versa.
If mary is patient then susan is both humble and not calm and vice versa.
If paul is not strong then someone is either kind or tall and vice versa.
Everyone who is tall is not old and vice versa.
Everyone who is both not creative and humble is tall and vice versa.
If someone is not patient then someone is either creative or tall and vice versa.
If someone is both calm and generous then someone is either generous or strong.
Everyone who is either not patient or wise is calm and vice versa.
Everyone who is not calm is not strong.
Everyone who is not happy or patient is either curious or not generous and vice versa.
Everyone who is not creative is curious or not old.
Everyone who is not generous or not brave is both not happy and not kind.
If someone is either humble or generous then someone is both kind and not wise and vice versa.
Mary is old or not quiet.
Paul is either happy or curious.
Someone is either humble or not kind.
Paul is either not generous or old.
Someone is not brave or not strong.
Mary is both not old and not patient. | Susan is not wise. | entailment | (![X]:((wise(X)|~strong(X))=>(tall(X)&~kind(X))))&
((?[X]:((~funny(X)&old(X))))<=>(?[X]:((~calm(X)|~rich(X)))))&
(![X]:((~calm(X)&funny(X))=>(rich(X)|generous(X))))&
((?[X]:((~wise(X)&~curious(X))))<=>((~wise(lucy)|~strong(lucy))))&
((patient(mary))<=>((humble(susan)&~calm(susan))))&
((~strong(paul))<=>(?[X]:((kind(X)<~>tall(X)))))&
(![X]:(tall(X)<=>~old(X)))&
(![X]:((~creative(X)&humble(X))<=>tall(X)))&
((?[X]:(~patient(X)))<=>(?[X]:((creative(X)<~>tall(X)))))&
((?[X]:((calm(X)&generous(X))))=>(?[X]:((generous(X)<~>strong(X)))))&
(![X]:((~patient(X)<~>wise(X))<=>calm(X)))&
(![X]:(~calm(X)=>~strong(X)))&
(![X]:((~happy(X)|patient(X))<=>(curious(X)<~>~generous(X))))&
(![X]:(~creative(X)=>(curious(X)|~old(X))))&
(![X]:((~generous(X)|~brave(X))=>(~happy(X)&~kind(X))))&
((?[X]:((humble(X)<~>generous(X))))<=>(?[X]:((kind(X)&~wise(X)))))&
((old(mary)|~quiet(mary)))&
((happy(paul)<~>curious(paul)))&
(?[X]:((humble(X)<~>~kind(X))))&
((~generous(paul)<~>old(paul)))&
(?[X]:((~brave(X)|~strong(X))))&
((~old(mary)&~patient(mary))) | ~wise(susan) | [
"p0",
"p5",
"p6",
"p12",
"p14",
"p17",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 5382500216433298949103077
% SZS output start Proof for 5382500216433298949103077
1. ! [X0] : ((~strong(X0) | wise(X0)) => (~kind(X0) & tall(X0))) [input p0]
6. ~strong(paul) <=> ? [X0] : (kind(X0) <~> tall(X0)) [input p5]
7. ! [X0] : (tall(X0) <=> ~old(X0)) [input p6]
13. ! [X0] : ((patient(X0) | ~happy(X0)) <=> (curious(X0) <~> ~generous(X0))) [input p12]
15. ! [X0] : ((~brave(X0) | ~generous(X0)) => (~kind(X0) & ~happy(X0))) [input p14]
18. happy(paul) <~> curious(paul) [input p17]
20. ~generous(paul) <~> old(paul) [input p19]
23. wise(susan) [input hypothesis]
29. ! [X0] : ((~kind(X0) & tall(X0)) | (strong(X0) & ~wise(X0))) [ennf transformation 1]
36. ! [X0] : ((~kind(X0) & ~happy(X0)) | (brave(X0) & generous(X0))) [ennf transformation 15]
49. (~strong(paul) | ! [X0] : ((kind(X0) | ~tall(X0)) & (tall(X0) | ~kind(X0)))) & (? [X0] : ((~tall(X0) | ~kind(X0)) & (tall(X0) | kind(X0))) | strong(paul)) [nnf transformation 6]
50. (~strong(paul) | ! [X0] : ((kind(X0) | ~tall(X0)) & (tall(X0) | ~kind(X0)))) & (? [X1] : ((~tall(X1) | ~kind(X1)) & (tall(X1) | kind(X1))) | strong(paul)) [rectify 49]
51. ? [X1] : ((~tall(X1) | ~kind(X1)) & (tall(X1) | kind(X1))) => ((~tall(sK3) | ~kind(sK3)) & (tall(sK3) | kind(sK3))) [choice axiom]
52. (~strong(paul) | ! [X0] : ((kind(X0) | ~tall(X0)) & (tall(X0) | ~kind(X0)))) & (((~tall(sK3) | ~kind(sK3)) & (tall(sK3) | kind(sK3))) | strong(paul)) [skolemisation 50,51]
53. ! [X0] : ((tall(X0) | old(X0)) & (~old(X0) | ~tall(X0))) [nnf transformation 7]
66. ! [X0] : (((patient(X0) | ~happy(X0)) | ((curious(X0) | generous(X0)) & (~generous(X0) | ~curious(X0)))) & (((generous(X0) | ~curious(X0)) & (~generous(X0) | curious(X0))) | (~patient(X0) & happy(X0)))) [nnf transformation 13]
67. ! [X0] : ((patient(X0) | ~happy(X0) | ((curious(X0) | generous(X0)) & (~generous(X0) | ~curious(X0)))) & (((generous(X0) | ~curious(X0)) & (~generous(X0) | curious(X0))) | (~patient(X0) & happy(X0)))) [flattening 66]
73. (~curious(paul) | ~happy(paul)) & (curious(paul) | happy(paul)) [nnf transformation 18]
77. (~old(paul) | generous(paul)) & (old(paul) | ~generous(paul)) [nnf transformation 20]
80. ~wise(X0) | tall(X0) [cnf transformation 29]
81. tall(X0) | strong(X0) [cnf transformation 29]
82. ~kind(X0) | ~wise(X0) [cnf transformation 29]
101. ~strong(paul) | kind(X0) | ~tall(X0) [cnf transformation 52]
102. ~old(X0) | ~tall(X0) [cnf transformation 53]
120. ~curious(X0) | generous(X0) | happy(X0) [cnf transformation 67]
125. ~happy(X0) | generous(X0) [cnf transformation 36]
135. curious(paul) | happy(paul) [cnf transformation 73]
139. old(paul) | ~generous(paul) [cnf transformation 77]
144. wise(susan) [cnf transformation 23]
215. 16 <=> ! [X0] : (kind(X0) | ~tall(X0)) [avatar definition]
216. ~tall(X0) | kind(X0) <- (16) [avatar component clause 215]
218. 17 <=> strong(paul) [avatar definition]
221. 16 | ~17 [avatar split clause 101,218,215]
309. 37 <=> happy(paul) [avatar definition]
310. happy(paul) <- (37) [avatar component clause 309]
311. ~happy(paul) <- (~37) [avatar component clause 309]
313. 38 <=> curious(paul) [avatar definition]
314. curious(paul) <- (38) [avatar component clause 313]
317. 37 | 38 [avatar split clause 135,313,309]
329. 41 <=> generous(paul) [avatar definition]
330. ~generous(paul) <- (~41) [avatar component clause 329]
333. 42 <=> old(paul) [avatar definition]
334. old(paul) <- (42) [avatar component clause 333]
337. ~41 | 42 [avatar split clause 139,333,329]
356. tall(susan) [resolution 80,144]
374. generous(paul) <- (37) [resolution 125,310]
375. $false <- (37, ~41) [subsumption resolution 374,330]
376. ~37 | 41 [avatar contradiction clause 375]
507. ~tall(paul) <- (42) [resolution 334,102]
516. generous(paul) | happy(paul) <- (38) [resolution 120,314]
545. strong(paul) <- (42) [resolution 507,81]
548. 17 | ~42 [avatar split clause 545,333,218]
573. kind(susan) <- (16) [resolution 216,356]
646. ~wise(susan) <- (16) [resolution 573,82]
649. $false <- (16) [subsumption resolution 646,144]
650. ~16 [avatar contradiction clause 649]
651. generous(paul) <- (~37, 38) [subsumption resolution 516,311]
652. 41 | 37 | ~38 [avatar split clause 651,313,309,329]
653. $false [avatar sat refutation 221,317,337,376,548,650,652]
% SZS output end Proof for 5382500216433298949103077
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Everyone who is not quiet or generous is both not patient and not wise and vice versa.
If fred is patient or not old then lucy is either generous or calm.
If someone is either wise or not humble then alice is either happy or rich and vice versa.
If someone is both rich and not wise then someone is not happy or not generous and vice versa.
Everyone who is not patient is quiet or not patient and vice versa.
If someone is both old and patient then mary is either kind or rich and vice versa.
Everyone who is either strong or quiet is not generous and vice versa.
Everyone who is brave is quiet or not happy.
Everyone who is both not kind and not funny is not creative or not humble and vice versa.
Everyone who is not creative or not brave is strong and vice versa.
Everyone who is either rich or creative is either not curious or not tall and vice versa.
If someone is old or quiet then someone is either not calm or not kind and vice versa.
If mary is both not wise and not generous then someone is both brave and humble.
If paul is either brave or not wise then paul is not funny or curious and vice versa.
If fred is old or calm then paul is curious and vice versa.
Everyone who is both not happy and funny is either old or not creative.
Someone is either generous or not quiet.
John is both curious and not humble.
Paul is both not funny and not kind.
John is tall or not wise.
Someone is either not brave or patient.
Someone is not brave or not old.
Fred is calm or not quiet. | Mary is wise. | neutral | (![X]:((~quiet(X)|generous(X))<=>(~patient(X)&~wise(X))))&
(((patient(fred)|~old(fred)))=>((generous(lucy)<~>calm(lucy))))&
((?[X]:((wise(X)<~>~humble(X))))<=>((happy(alice)<~>rich(alice))))&
((?[X]:((rich(X)&~wise(X))))<=>(?[X]:((~happy(X)|~generous(X)))))&
(![X]:(~patient(X)<=>(quiet(X)|~patient(X))))&
((?[X]:((old(X)&patient(X))))<=>((kind(mary)<~>rich(mary))))&
(![X]:((strong(X)<~>quiet(X))<=>~generous(X)))&
(![X]:(brave(X)=>(quiet(X)|~happy(X))))&
(![X]:((~kind(X)&~funny(X))<=>(~creative(X)|~humble(X))))&
(![X]:((~creative(X)|~brave(X))<=>strong(X)))&
(![X]:((rich(X)<~>creative(X))<=>(~curious(X)<~>~tall(X))))&
((?[X]:((old(X)|quiet(X))))<=>(?[X]:((~calm(X)<~>~kind(X)))))&
(((~wise(mary)&~generous(mary)))=>(?[X]:((brave(X)&humble(X)))))&
(((brave(paul)<~>~wise(paul)))<=>((~funny(paul)|curious(paul))))&
(((old(fred)|calm(fred)))<=>(curious(paul)))&
(![X]:((~happy(X)&funny(X))=>(old(X)<~>~creative(X))))&
(?[X]:((generous(X)<~>~quiet(X))))&
((curious(john)&~humble(john)))&
((~funny(paul)&~kind(paul)))&
((tall(john)|~wise(john)))&
(?[X]:((~brave(X)<~>patient(X))))&
(?[X]:((~brave(X)|~old(X))))&
((calm(fred)|~quiet(fred))) | wise(mary) | [] | null | 0 |
Everyone who is not calm or not tall is tall and vice versa.
Everyone who is kind is either kind or happy and vice versa.
If someone is both kind and calm then someone is calm or quiet and vice versa.
Everyone who is not old is both old and funny and vice versa.
Everyone who is creative is both rich and not quiet and vice versa.
If alice is not rich then someone is not creative.
If someone is either not calm or not kind then someone is either not patient or funny and vice versa.
If someone is not calm then someone is both tall and strong.
If lucy is either not tall or quiet then someone is creative or not generous and vice versa.
If paul is both not creative and patient then susan is both not creative and rich.
Everyone who is either not funny or not old is calm or kind.
If paul is both not kind and not patient then someone is quiet or not strong.
If someone is both wise and not calm then alice is not patient.
Everyone who is either rich or brave is not humble or not rich.
Mary is not strong.
Someone is not humble or not patient.
Someone is strong.
Someone is not humble or not calm.
Someone is not creative or calm.
Alice is not wise or not humble. | Lucy is not patient. | neutral | (![X]:((~calm(X)|~tall(X))<=>tall(X)))&
(![X]:(kind(X)<=>(kind(X)<~>happy(X))))&
((?[X]:((kind(X)&calm(X))))<=>(?[X]:((calm(X)|quiet(X)))))&
(![X]:(~old(X)<=>(old(X)&funny(X))))&
(![X]:(creative(X)<=>(rich(X)&~quiet(X))))&
((~rich(alice))=>(?[X]:(~creative(X))))&
((?[X]:((~calm(X)<~>~kind(X))))<=>(?[X]:((~patient(X)<~>funny(X)))))&
((?[X]:(~calm(X)))=>(?[X]:((tall(X)&strong(X)))))&
(((~tall(lucy)<~>quiet(lucy)))<=>(?[X]:((creative(X)|~generous(X)))))&
(((~creative(paul)&patient(paul)))=>((~creative(susan)&rich(susan))))&
(![X]:((~funny(X)<~>~old(X))=>(calm(X)|kind(X))))&
(((~kind(paul)&~patient(paul)))=>(?[X]:((quiet(X)|~strong(X)))))&
((?[X]:((wise(X)&~calm(X))))=>(~patient(alice)))&
(![X]:((rich(X)<~>brave(X))=>(~humble(X)|~rich(X))))&
(~strong(mary))&
(?[X]:((~humble(X)|~patient(X))))&
(?[X]:(strong(X)))&
(?[X]:((~humble(X)|~calm(X))))&
(?[X]:((~creative(X)|calm(X))))&
((~wise(alice)|~humble(alice))) | ~patient(lucy) | [] | null | 0 |
If someone is not humble then lucy is not funny. Everyone who is calm or not happy is not creative and vice versa. If john is both happy and rich then someone is not old or creative. Everyone who is either not quiet or curious is both calm and not calm. Everyone who is funny or brave is both generous and not funny and vice versa. If fred is either not curious or creative then mary is not strong or brave. If paul is not old then someone is curious or brave and vice versa. If someone is kind or quiet then alice is not tall or not strong. If john is tall then someone is both not rich and not humble. Everyone who is not brave or not kind is either wise or not kind and vice versa. Everyone who is both not funny and humble is not happy. If lucy is curious then someone is both not rich and strong and vice versa. Everyone who is either not happy or not calm is either not funny or not calm and vice versa. If someone is both creative and humble then someone is both not old and creative. Everyone who is both not generous and not wise is either not brave or brave. Everyone who is not brave or curious is either rich or not tall and vice versa. Someone is generous. Susan is funny or not curious. Mary is not quiet or not humble. Paul is not calm or patient. Someone is kind. John is either calm or not wise. Someone is either not quiet or not wise. Someone is not funny or not old. | Alice is not funny. | entailment | ((?[X]:(~humble(X)))=>(~funny(lucy)))&
(![X]:((calm(X)|~happy(X))<=>~creative(X)))&
(((happy(john)&rich(john)))=>(?[X]:((~old(X)|creative(X)))))&
(![X]:((~quiet(X)<~>curious(X))=>(calm(X)&~calm(X))))&
(![X]:((funny(X)|brave(X))<=>(generous(X)&~funny(X))))&
(((~curious(fred)<~>creative(fred)))=>((~strong(mary)|brave(mary))))&
((~old(paul))<=>(?[X]:((curious(X)|brave(X)))))&
((?[X]:((kind(X)|quiet(X))))=>((~tall(alice)|~strong(alice))))&
((tall(john))=>(?[X]:((~rich(X)&~humble(X)))))&
(![X]:((~brave(X)|~kind(X))<=>(wise(X)<~>~kind(X))))&
(![X]:((~funny(X)&humble(X))=>~happy(X)))&
((curious(lucy))<=>(?[X]:((~rich(X)&strong(X)))))&
(![X]:((~happy(X)<~>~calm(X))<=>(~funny(X)<~>~calm(X))))&
((?[X]:((creative(X)&humble(X))))=>(?[X]:((~old(X)&creative(X)))))&
(![X]:((~generous(X)&~wise(X))=>(~brave(X)<~>brave(X))))&
(![X]:((~brave(X)|curious(X))<=>(rich(X)<~>~tall(X))))&
(?[X]:(generous(X)))&
((funny(susan)|~curious(susan)))&
((~quiet(mary)|~humble(mary)))&
((~calm(paul)|patient(paul)))&
(?[X]:(kind(X)))&
((calm(john)<~>~wise(john)))&
(?[X]:((~quiet(X)<~>~wise(X))))&
(?[X]:((~funny(X)|~old(X)))) | ~funny(alice) | [
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 2747529541024704373550422
% SZS output start Proof for 2747529541024704373550422
5. ! [X0] : ((brave(X0) | funny(X0)) <=> (~funny(X0) & generous(X0))) [input p4]
25. funny(alice) [input hypothesis]
47. ! [X0] : (((brave(X0) | funny(X0)) | (funny(X0) | ~generous(X0))) & ((~funny(X0) & generous(X0)) | (~brave(X0) & ~funny(X0)))) [nnf transformation 5]
48. ! [X0] : ((brave(X0) | funny(X0) | funny(X0) | ~generous(X0)) & ((~funny(X0) & generous(X0)) | (~brave(X0) & ~funny(X0)))) [flattening 47]
90. ~funny(X0) | ~funny(X0) [cnf transformation 48]
139. funny(alice) [cnf transformation 25]
146. ~funny(X0) [duplicate literal removal 90]
309. $false [subsumption resolution 139,146]
% SZS output end Proof for 2747529541024704373550422
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble or not happy then someone is not old.
Everyone who is both creative and not humble is both not brave and wise and vice versa.
Everyone who is both patient and not rich is both not old and old.
Everyone who is both not rich and not funny is both not calm and not wise and vice versa.
If mary is not creative then someone is both not kind and not quiet and vice versa.
Everyone who is both not kind and old is quiet and vice versa.
If fred is either old or generous then someone is happy or calm.
Everyone who is either creative or not curious is not creative or happy.
Everyone who is either humble or not quiet is not patient or not curious and vice versa.
Everyone who is both not happy and wise is both strong and rich and vice versa.
Everyone who is not old is kind or not generous and vice versa.
If someone is old then alice is both not brave and funny and vice versa.
Everyone who is both funny and calm is either tall or not tall and vice versa.
If someone is kind or not generous then someone is both not curious and curious and vice versa.
Someone is either not funny or not wise.
Susan is not wise or not patient.
Susan is rich or tall. | Alice is funny. | entailment | ((?[X]:((humble(X)|~happy(X))))=>(?[X]:(~old(X))))&
(![X]:((creative(X)&~humble(X))<=>(~brave(X)&wise(X))))&
(![X]:((patient(X)&~rich(X))=>(~old(X)&old(X))))&
(![X]:((~rich(X)&~funny(X))<=>(~calm(X)&~wise(X))))&
((~creative(mary))<=>(?[X]:((~kind(X)&~quiet(X)))))&
(![X]:((~kind(X)&old(X))<=>quiet(X)))&
(((old(fred)<~>generous(fred)))=>(?[X]:((happy(X)|calm(X)))))&
(![X]:((creative(X)<~>~curious(X))=>(~creative(X)|happy(X))))&
(![X]:((humble(X)<~>~quiet(X))<=>(~patient(X)|~curious(X))))&
(![X]:((~happy(X)&wise(X))<=>(strong(X)&rich(X))))&
(![X]:(~old(X)<=>(kind(X)|~generous(X))))&
((?[X]:(old(X)))<=>((~brave(alice)&funny(alice))))&
(![X]:((funny(X)&calm(X))<=>(tall(X)<~>~tall(X))))&
((?[X]:((kind(X)|~generous(X))))<=>(?[X]:((~curious(X)&curious(X)))))&
(?[X]:((~funny(X)<~>~wise(X))))&
((~wise(susan)|~patient(susan)))&
((rich(susan)|tall(susan))) | funny(alice) | [
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 5981105751133856748928777
% SZS output start Proof for 5981105751133856748928777
13. ! [X0] : ((calm(X0) & funny(X0)) <=> (tall(X0) <~> ~tall(X0))) [input p12]
18. ~funny(alice) [input hypothesis]
55. ! [X0] : (((calm(X0) & funny(X0)) | ((tall(X0) | tall(X0)) & (~tall(X0) | ~tall(X0)))) & (((tall(X0) | ~tall(X0)) & (~tall(X0) | tall(X0))) | (~calm(X0) | ~funny(X0)))) [nnf transformation 13]
56. ! [X0] : (((calm(X0) & funny(X0)) | ((tall(X0) | tall(X0)) & (~tall(X0) | ~tall(X0)))) & (((tall(X0) | ~tall(X0)) & (~tall(X0) | tall(X0))) | ~calm(X0) | ~funny(X0))) [flattening 55]
105. funny(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 56]
106. funny(X0) | tall(X0) | tall(X0) [cnf transformation 56]
118. ~funny(alice) [cnf transformation 18]
119. funny(X0) | ~tall(X0) [duplicate literal removal 105]
120. funny(X0) | tall(X0) [duplicate literal removal 106]
192. funny(X0) [subsumption resolution 119,120]
226. $false [subsumption resolution 118,192]
% SZS output end Proof for 5981105751133856748928777
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm or not curious is both not humble and wise and vice versa.
Everyone who is generous is quiet or not patient.
Everyone who is both humble and funny is rich.
If alice is both funny and tall then someone is curious and vice versa.
If susan is not happy or creative then someone is humble.
If someone is both not creative and curious then mary is not creative or happy.
If someone is either tall or not generous then someone is either tall or not tall and vice versa.
Everyone who is not rich or not curious is not calm or not brave.
Everyone who is quiet is not happy.
Everyone who is kind is tall or not tall and vice versa.
Everyone who is curious is both humble and not kind and vice versa.
If someone is quiet or tall then someone is not creative and vice versa.
Everyone who is either patient or not patient is not brave and vice versa.
Everyone who is brave or strong is not calm.
If someone is not wise or patient then someone is not rich.
Everyone who is either old or brave is not funny.
Someone is both wise and kind.
Someone is calm or wise.
Someone is either not old or rich.
Someone is both strong and not creative.
Lucy is quiet.
Susan is either not patient or not quiet.
Alice is either brave or calm. | Alice is not calm. | contradiction | (![X]:((calm(X)|~curious(X))<=>(~humble(X)&wise(X))))&
(![X]:(generous(X)=>(quiet(X)|~patient(X))))&
(![X]:((humble(X)&funny(X))=>rich(X)))&
(((funny(alice)&tall(alice)))<=>(?[X]:(curious(X))))&
(((~happy(susan)|creative(susan)))=>(?[X]:(humble(X))))&
((?[X]:((~creative(X)&curious(X))))=>((~creative(mary)|happy(mary))))&
((?[X]:((tall(X)<~>~generous(X))))<=>(?[X]:((tall(X)<~>~tall(X)))))&
(![X]:((~rich(X)|~curious(X))=>(~calm(X)|~brave(X))))&
(![X]:(quiet(X)=>~happy(X)))&
(![X]:(kind(X)<=>(tall(X)|~tall(X))))&
(![X]:(curious(X)<=>(humble(X)&~kind(X))))&
((?[X]:((quiet(X)|tall(X))))<=>(?[X]:(~creative(X))))&
(![X]:((patient(X)<~>~patient(X))<=>~brave(X)))&
(![X]:((brave(X)|strong(X))=>~calm(X)))&
((?[X]:((~wise(X)|patient(X))))=>(?[X]:(~rich(X))))&
(![X]:((old(X)<~>brave(X))=>~funny(X)))&
(?[X]:((wise(X)&kind(X))))&
(?[X]:((calm(X)|wise(X))))&
(?[X]:((~old(X)<~>rich(X))))&
(?[X]:((strong(X)&~creative(X))))&
(quiet(lucy))&
((~patient(susan)<~>~quiet(susan)))&
((brave(alice)<~>calm(alice))) | ~calm(alice) | [
"p12",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 3587234090575924162261315
% SZS output start Proof for 3587234090575924162261315
13. ! [X0] : ((patient(X0) <~> ~patient(X0)) <=> ~brave(X0)) [input p12]
23. brave(alice) <~> calm(alice) [input p22]
24. ~calm(alice) [input hypothesis]
64. ! [X0] : ((((patient(X0) | ~patient(X0)) & (~patient(X0) | patient(X0))) | brave(X0)) & (~brave(X0) | ((patient(X0) | patient(X0)) & (~patient(X0) | ~patient(X0))))) [nnf transformation 13]
79. (~calm(alice) | ~brave(alice)) & (calm(alice) | brave(alice)) [nnf transformation 23]
113. ~brave(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 64]
114. ~brave(X0) | patient(X0) | patient(X0) [cnf transformation 64]
133. calm(alice) | brave(alice) [cnf transformation 79]
135. ~calm(alice) [cnf transformation 24]
136. ~brave(X0) | ~patient(X0) [duplicate literal removal 113]
137. ~brave(X0) | patient(X0) [duplicate literal removal 114]
228. ~brave(X0) [subsumption resolution 136,137]
263. calm(alice) [subsumption resolution 133,228]
264. $false [subsumption resolution 135,263]
% SZS output end Proof for 3587234090575924162261315
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is patient then someone is either not funny or old.
Everyone who is happy or tall is either not curious or creative.
Everyone who is both tall and creative is not humble.
Everyone who is old or not wise is either not funny or patient.
If someone is creative or not curious then someone is both old and wise and vice versa.
If paul is rich then john is both not wise and old.
Everyone who is either strong or not tall is strong.
If paul is both not rich and not humble then mary is both not funny and not curious.
Everyone who is both creative and tall is wise and vice versa.
If someone is either not tall or calm then mary is quiet and vice versa.
If someone is either not strong or brave then fred is either not humble or not brave and vice versa.
Everyone who is not quiet or old is happy or calm.
If susan is not patient or generous then someone is either kind or not curious.
Everyone who is both calm and humble is not funny or wise and vice versa.
Everyone who is either creative or kind is curious and vice versa.
Everyone who is both old and not humble is either brave or not wise.
Someone is both patient and calm.
Paul is both funny and not old.
Someone is curious or not calm.
Someone is either curious or not strong.
Someone is not tall or patient.
Someone is either funny or not wise. | Mary is tall. | contradiction | ((?[X]:(patient(X)))=>(?[X]:((~funny(X)<~>old(X)))))&
(![X]:((happy(X)|tall(X))=>(~curious(X)<~>creative(X))))&
(![X]:((tall(X)&creative(X))=>~humble(X)))&
(![X]:((old(X)|~wise(X))=>(~funny(X)<~>patient(X))))&
((?[X]:((creative(X)|~curious(X))))<=>(?[X]:((old(X)&wise(X)))))&
((rich(paul))=>((~wise(john)&old(john))))&
(![X]:((strong(X)<~>~tall(X))=>strong(X)))&
(((~rich(paul)&~humble(paul)))=>((~funny(mary)&~curious(mary))))&
(![X]:((creative(X)&tall(X))<=>wise(X)))&
((?[X]:((~tall(X)<~>calm(X))))<=>(quiet(mary)))&
((?[X]:((~strong(X)<~>brave(X))))<=>((~humble(fred)<~>~brave(fred))))&
(![X]:((~quiet(X)|old(X))=>(happy(X)|calm(X))))&
(((~patient(susan)|generous(susan)))=>(?[X]:((kind(X)<~>~curious(X)))))&
(![X]:((calm(X)&humble(X))<=>(~funny(X)|wise(X))))&
(![X]:((creative(X)<~>kind(X))<=>curious(X)))&
(![X]:((old(X)&~humble(X))=>(brave(X)<~>~wise(X))))&
(?[X]:((patient(X)&calm(X))))&
((funny(paul)&~old(paul)))&
(?[X]:((curious(X)|~calm(X))))&
(?[X]:((curious(X)<~>~strong(X))))&
(?[X]:((~tall(X)|patient(X))))&
(?[X]:((funny(X)<~>~wise(X)))) | tall(mary) | [
"p1",
"p2",
"p4",
"p8",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 3076051875339088741366734
% SZS output start Proof for 3076051875339088741366734
2. ! [X0] : ((tall(X0) | happy(X0)) => (~curious(X0) <~> creative(X0))) [input p1]
3. ! [X0] : ((creative(X0) & tall(X0)) => ~humble(X0)) [input p2]
5. ? [X0] : (~curious(X0) | creative(X0)) <=> ? [X0] : (wise(X0) & old(X0)) [input p4]
9. ! [X0] : ((tall(X0) & creative(X0)) <=> wise(X0)) [input p8]
14. ! [X0] : ((humble(X0) & calm(X0)) <=> (wise(X0) | ~funny(X0))) [input p13]
23. tall(mary) [input hypothesis]
25. ? [X0] : (~curious(X0) | creative(X0)) <=> ? [X1] : (wise(X1) & old(X1)) [rectify 5]
28. ! [X0] : ((~curious(X0) <~> creative(X0)) | (~tall(X0) & ~happy(X0))) [ennf transformation 2]
29. ! [X0] : (~humble(X0) | (~creative(X0) | ~tall(X0))) [ennf transformation 3]
30. ! [X0] : (~humble(X0) | ~creative(X0) | ~tall(X0)) [flattening 29]
45. ! [X0] : (((~creative(X0) | curious(X0)) & (creative(X0) | ~curious(X0))) | (~tall(X0) & ~happy(X0))) [nnf transformation 28]
47. (? [X0] : (~curious(X0) | creative(X0)) | ! [X1] : (~wise(X1) | ~old(X1))) & (? [X1] : (wise(X1) & old(X1)) | ! [X0] : (curious(X0) & ~creative(X0))) [nnf transformation 25]
48. (? [X0] : (~curious(X0) | creative(X0)) | ! [X1] : (~wise(X1) | ~old(X1))) & (? [X2] : (wise(X2) & old(X2)) | ! [X3] : (curious(X3) & ~creative(X3))) [rectify 47]
49. ? [X0] : (~curious(X0) | creative(X0)) => (~curious(sK1) | creative(sK1)) [choice axiom]
50. ? [X2] : (wise(X2) & old(X2)) => (wise(sK2) & old(sK2)) [choice axiom]
51. ((~curious(sK1) | creative(sK1)) | ! [X1] : (~wise(X1) | ~old(X1))) & ((wise(sK2) & old(sK2)) | ! [X3] : (curious(X3) & ~creative(X3))) [skolemisation 48,50,49]
53. ! [X0] : (((tall(X0) & creative(X0)) | ~wise(X0)) & (wise(X0) | (~tall(X0) | ~creative(X0)))) [nnf transformation 9]
54. ! [X0] : (((tall(X0) & creative(X0)) | ~wise(X0)) & (wise(X0) | ~tall(X0) | ~creative(X0))) [flattening 53]
66. ! [X0] : (((humble(X0) & calm(X0)) | (~wise(X0) & funny(X0))) & ((wise(X0) | ~funny(X0)) | (~humble(X0) | ~calm(X0)))) [nnf transformation 14]
67. ! [X0] : (((humble(X0) & calm(X0)) | (~wise(X0) & funny(X0))) & (wise(X0) | ~funny(X0) | ~humble(X0) | ~calm(X0))) [flattening 66]
85. ~curious(X0) | creative(X0) | ~tall(X0) [cnf transformation 45]
88. ~humble(X0) | ~creative(X0) | ~tall(X0) [cnf transformation 30]
95. wise(sK2) | ~creative(X3) [cnf transformation 51]
96. wise(sK2) | curious(X3) [cnf transformation 51]
105. ~wise(X0) | creative(X0) [cnf transformation 54]
106. ~wise(X0) | tall(X0) [cnf transformation 54]
127. ~wise(X0) | humble(X0) [cnf transformation 67]
144. tall(mary) [cnf transformation 23]
172. 7 <=> ! [X3] : curious(X3) [avatar definition]
173. curious(X3) <- (7) [avatar component clause 172]
175. 8 <=> wise(sK2) [avatar definition]
177. wise(sK2) <- (8) [avatar component clause 175]
178. 7 | 8 [avatar split clause 96,175,172]
180. 9 <=> ! [X3] : ~creative(X3) [avatar definition]
181. ~creative(X3) <- (9) [avatar component clause 180]
182. 9 | 8 [avatar split clause 95,175,180]
350. creative(X0) | ~tall(X0) <- (7) [resolution 85,173]
353. ~tall(X0) <- (7, 9) [subsumption resolution 350,181]
356. $false <- (7, 9) [resolution 353,144]
359. ~7 | ~9 [avatar contradiction clause 356]
372. humble(sK2) <- (8) [resolution 177,127]
374. tall(sK2) <- (8) [resolution 177,106]
375. creative(sK2) <- (8) [resolution 177,105]
433. ~creative(sK2) | ~tall(sK2) <- (8) [resolution 372,88]
434. ~tall(sK2) <- (8) [subsumption resolution 433,375]
435. $false <- (8) [subsumption resolution 434,374]
436. ~8 [avatar contradiction clause 435]
437. $false [avatar sat refutation 178,182,359,436]
% SZS output end Proof for 3076051875339088741366734
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both curious and not happy is either tall or humble and vice versa.
Everyone who is happy is strong.
If mary is humble then someone is either wise or generous.
Everyone who is both creative and rich is both creative and funny.
If john is both strong and funny then someone is not creative.
If someone is happy or curious then someone is either quiet or generous and vice versa.
If alice is wise or old then someone is either old or not tall.
Everyone who is both generous and patient is not happy and vice versa.
Everyone who is both quiet and not wise is not tall or not happy and vice versa.
If someone is either not generous or curious then john is both not brave and not quiet and vice versa.
Everyone who is brave or not rich is both curious and not brave and vice versa.
Everyone who is not wise or strong is both strong and tall.
Everyone who is both not calm and patient is not humble or not calm.
Everyone who is either not generous or calm is both not wise and generous and vice versa.
Susan is humble.
Someone is either rich or not quiet.
Mary is not happy or not old.
Susan is either not happy or not creative.
Susan is rich or curious.
Lucy is either brave or rich. | Mary is not strong. | contradiction | (![X]:((curious(X)&~happy(X))<=>(tall(X)<~>humble(X))))&
(![X]:(happy(X)=>strong(X)))&
((humble(mary))=>(?[X]:((wise(X)<~>generous(X)))))&
(![X]:((creative(X)&rich(X))=>(creative(X)&funny(X))))&
(((strong(john)&funny(john)))=>(?[X]:(~creative(X))))&
((?[X]:((happy(X)|curious(X))))<=>(?[X]:((quiet(X)<~>generous(X)))))&
(((wise(alice)|old(alice)))=>(?[X]:((old(X)<~>~tall(X)))))&
(![X]:((generous(X)&patient(X))<=>~happy(X)))&
(![X]:((quiet(X)&~wise(X))<=>(~tall(X)|~happy(X))))&
((?[X]:((~generous(X)<~>curious(X))))<=>((~brave(john)&~quiet(john))))&
(![X]:((brave(X)|~rich(X))<=>(curious(X)&~brave(X))))&
(![X]:((~wise(X)|strong(X))=>(strong(X)&tall(X))))&
(![X]:((~calm(X)&patient(X))=>(~humble(X)|~calm(X))))&
(![X]:((~generous(X)<~>calm(X))<=>(~wise(X)&generous(X))))&
(humble(susan))&
(?[X]:((rich(X)<~>~quiet(X))))&
((~happy(mary)|~old(mary)))&
((~happy(susan)<~>~creative(susan)))&
((rich(susan)|curious(susan)))&
((brave(lucy)<~>rich(lucy))) | ~strong(mary) | [
"p1",
"p8",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 7377619817319383189936880
% SZS output start Proof for 7377619817319383189936880
2. ! [X0] : (happy(X0) => strong(X0)) [input p1]
9. ! [X0] : ((~wise(X0) & quiet(X0)) <=> (~happy(X0) | ~tall(X0))) [input p8]
12. ! [X0] : ((strong(X0) | ~wise(X0)) => (tall(X0) & strong(X0))) [input p11]
21. ~strong(mary) [input hypothesis]
23. ! [X0] : (strong(X0) | ~happy(X0)) [ennf transformation 2]
30. ! [X0] : ((tall(X0) & strong(X0)) | (~strong(X0) & wise(X0))) [ennf transformation 12]
50. ! [X0] : (((~wise(X0) & quiet(X0)) | (happy(X0) & tall(X0))) & ((~happy(X0) | ~tall(X0)) | (wise(X0) | ~quiet(X0)))) [nnf transformation 9]
51. ! [X0] : (((~wise(X0) & quiet(X0)) | (happy(X0) & tall(X0))) & (~happy(X0) | ~tall(X0) | wise(X0) | ~quiet(X0))) [flattening 50]
72. ~happy(X0) | strong(X0) [cnf transformation 23]
95. ~wise(X0) | happy(X0) [cnf transformation 51]
107. wise(X0) | strong(X0) [cnf transformation 30]
127. ~strong(mary) [cnf transformation 21]
289. strong(X0) | happy(X0) [resolution 107,95]
291. strong(X0) [subsumption resolution 289,72]
297. $false [resolution 291,127]
% SZS output end Proof for 7377619817319383189936880
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 or brave is rich and vice versa. If someone is curious then someone is not generous or patient. Everyone who is not creative or tall is not rich and vice versa. If someone is tall or not wise then someone is both rich and not quiet. If susan is brave then paul is both not funny and brave and vice versa. Everyone who is both not brave and patient is brave or curious. If mary is humble then someone is not creative or rich. If alice is both kind and creative then someone is both not kind and wise. Everyone who is wise is not creative. Everyone who is not happy is both brave and not humble. If someone is not rich or strong then someone is kind. Everyone who is either not quiet or curious is not happy or funny and vice versa. Everyone who is not curious or not calm is humble or quiet. If fred is old then paul is both not generous and not funny and vice versa. If someone is not tall then someone is not curious or not kind. If someone is either not calm or patient then paul is humble and vice versa. Lucy is humble. Someone is either not brave or wise. John is either not funny or not tall. Paul is not patient or humble. Someone is both not wise and kind. Someone is humble or not quiet. Someone is not generous. Alice is not funny or not strong. | John is not funny. | contradiction | (![X]:((~funny(X)|brave(X))<=>rich(X)))&
((?[X]:(curious(X)))=>(?[X]:((~generous(X)|patient(X)))))&
(![X]:((~creative(X)|tall(X))<=>~rich(X)))&
((?[X]:((tall(X)|~wise(X))))=>(?[X]:((rich(X)&~quiet(X)))))&
((brave(susan))<=>((~funny(paul)&brave(paul))))&
(![X]:((~brave(X)&patient(X))=>(brave(X)|curious(X))))&
((humble(mary))=>(?[X]:((~creative(X)|rich(X)))))&
(((kind(alice)&creative(alice)))=>(?[X]:((~kind(X)&wise(X)))))&
(![X]:(wise(X)=>~creative(X)))&
(![X]:(~happy(X)=>(brave(X)&~humble(X))))&
((?[X]:((~rich(X)|strong(X))))=>(?[X]:(kind(X))))&
(![X]:((~quiet(X)<~>curious(X))<=>(~happy(X)|funny(X))))&
(![X]:((~curious(X)|~calm(X))=>(humble(X)|quiet(X))))&
((old(fred))<=>((~generous(paul)&~funny(paul))))&
((?[X]:(~tall(X)))=>(?[X]:((~curious(X)|~kind(X)))))&
((?[X]:((~calm(X)<~>patient(X))))<=>(humble(paul)))&
(humble(lucy))&
(?[X]:((~brave(X)<~>wise(X))))&
((~funny(john)<~>~tall(john)))&
((~patient(paul)|humble(paul)))&
(?[X]:((~wise(X)&kind(X))))&
(?[X]:((humble(X)|~quiet(X))))&
(?[X]:(~generous(X)))&
((~funny(alice)|~strong(alice))) | ~funny(john) | [
"p0",
"p2",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 2121797489500462650572128
% SZS output start Proof for 2121797489500462650572128
1. ! [X0] : ((brave(X0) | ~funny(X0)) <=> rich(X0)) [input p0]
3. ! [X0] : ((tall(X0) | ~creative(X0)) <=> ~rich(X0)) [input p2]
19. ~funny(john) <~> ~tall(john) [input p18]
25. ~funny(john) [input hypothesis]
45. ! [X0] : (((brave(X0) | ~funny(X0)) | ~rich(X0)) & (rich(X0) | (~brave(X0) & funny(X0)))) [nnf transformation 1]
46. ! [X0] : ((brave(X0) | ~funny(X0) | ~rich(X0)) & (rich(X0) | (~brave(X0) & funny(X0)))) [flattening 45]
50. ! [X0] : (((tall(X0) | ~creative(X0)) | rich(X0)) & (~rich(X0) | (~tall(X0) & creative(X0)))) [nnf transformation 3]
51. ! [X0] : ((tall(X0) | ~creative(X0) | rich(X0)) & (~rich(X0) | (~tall(X0) & creative(X0)))) [flattening 50]
78. (tall(john) | funny(john)) & (~tall(john) | ~funny(john)) [nnf transformation 19]
85. rich(X0) | funny(X0) [cnf transformation 46]
90. ~tall(X0) | ~rich(X0) [cnf transformation 51]
127. tall(john) | funny(john) [cnf transformation 78]
133. ~funny(john) [cnf transformation 25]
275. 32 <=> funny(john) [avatar definition]
276. ~funny(john) <- (~32) [avatar component clause 275]
279. 33 <=> tall(john) [avatar definition]
281. tall(john) <- (33) [avatar component clause 279]
282. 32 | 33 [avatar split clause 127,279,275]
298. ~32 [avatar split clause 133,275]
307. ~rich(john) <- (33) [resolution 90,281]
311. funny(john) <- (33) [resolution 307,85]
312. $false <- (~32, 33) [subsumption resolution 311,276]
313. 32 | ~33 [avatar contradiction clause 312]
314. $false [avatar sat refutation 282,298,313]
% SZS output end Proof for 2121797489500462650572128
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is tall or happy is either brave or not kind and vice versa. Everyone who is patient is either patient or brave. Everyone who is either not patient or not generous is either strong or curious and vice versa. Everyone who is creative is not humble. If paul is both wise and calm then someone is both wise and not happy and vice versa. If someone is both calm and wise then someone is happy or not rich and vice versa. If lucy is strong then mary is either not rich or kind. Everyone who is either kind or strong is happy or curious and vice versa. If fred is both old and not rich then john is not humble. Everyone who is not calm is both calm and not generous. If lucy is both old and not tall then alice is creative or happy and vice versa. If paul is quiet or old then alice is not patient or not rich and vice versa. Everyone who is happy or not curious is either generous or wise and vice versa. Everyone who is both wise and not patient is both happy and not calm. If john is both brave and strong then alice is either wise or not rich. If someone is kind then alice is either not calm or generous and vice versa. Someone is curious. Someone is both old and curious. Lucy is happy or rich. Someone is both not happy and strong. Someone is not old. Someone is both patient and not creative. Someone is either wise or kind. Someone is either happy or old. | Paul is not calm. | contradiction | (![X]:((tall(X)|happy(X))<=>(brave(X)<~>~kind(X))))&
(![X]:(patient(X)=>(patient(X)<~>brave(X))))&
(![X]:((~patient(X)<~>~generous(X))<=>(strong(X)<~>curious(X))))&
(![X]:(creative(X)=>~humble(X)))&
(((wise(paul)&calm(paul)))<=>(?[X]:((wise(X)&~happy(X)))))&
((?[X]:((calm(X)&wise(X))))<=>(?[X]:((happy(X)|~rich(X)))))&
((strong(lucy))=>((~rich(mary)<~>kind(mary))))&
(![X]:((kind(X)<~>strong(X))<=>(happy(X)|curious(X))))&
(((old(fred)&~rich(fred)))=>(~humble(john)))&
(![X]:(~calm(X)=>(calm(X)&~generous(X))))&
(((old(lucy)&~tall(lucy)))<=>((creative(alice)|happy(alice))))&
(((quiet(paul)|old(paul)))<=>((~patient(alice)|~rich(alice))))&
(![X]:((happy(X)|~curious(X))<=>(generous(X)<~>wise(X))))&
(![X]:((wise(X)&~patient(X))=>(happy(X)&~calm(X))))&
(((brave(john)&strong(john)))=>((wise(alice)<~>~rich(alice))))&
((?[X]:(kind(X)))<=>((~calm(alice)<~>generous(alice))))&
(?[X]:(curious(X)))&
(?[X]:((old(X)&curious(X))))&
((happy(lucy)|rich(lucy)))&
(?[X]:((~happy(X)&strong(X))))&
(?[X]:(~old(X)))&
(?[X]:((patient(X)&~creative(X))))&
(?[X]:((wise(X)<~>kind(X))))&
(?[X]:((happy(X)<~>old(X)))) | ~calm(paul) | [
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 6044963716186775705470004
% SZS output start Proof for 6044963716186775705470004
10. ! [X0] : (~calm(X0) => (~generous(X0) & calm(X0))) [input p9]
25. ~calm(paul) [input hypothesis]
31. ! [X0] : ((~generous(X0) & calm(X0)) | calm(X0)) [ennf transformation 10]
113. calm(X0) | calm(X0) [cnf transformation 31]
151. ~calm(paul) [cnf transformation 25]
152. calm(X0) [duplicate literal removal 113]
321. $false [subsumption resolution 151,152]
% SZS output end Proof for 6044963716186775705470004
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not patient or not wise is both wise and calm and vice versa. Everyone who is humble is both calm and wise and vice versa. Everyone who is both not tall and not strong is either not wise or not strong and vice versa. Everyone who is both old and creative is either strong or not wise and vice versa. If paul is not brave then alice is brave and vice versa. If mary is creative or not calm then lucy is tall or not strong and vice versa. Everyone who is either creative or not funny is brave and vice versa. If lucy is both not kind and not humble then fred is both not generous and not curious. Everyone who is either patient or tall is strong or not tall and vice versa. Everyone who is not quiet is not wise or not calm. Everyone who is either not wise or tall is both not rich and not quiet. If mary is calm or not curious then mary is not old. If fred is both not quiet and not patient then someone is both tall and not happy. Everyone who is not calm or humble is either not curious or not tall and vice versa. Someone is either brave or calm. Paul is brave. Someone is generous or wise. Someone is either kind or not rich. Someone is kind or not wise. Someone is not patient or funny. | Mary is not curious. | contradiction | (![X]:((~patient(X)<~>~wise(X))<=>(wise(X)&calm(X))))&
(![X]:(humble(X)<=>(calm(X)&wise(X))))&
(![X]:((~tall(X)&~strong(X))<=>(~wise(X)<~>~strong(X))))&
(![X]:((old(X)&creative(X))<=>(strong(X)<~>~wise(X))))&
((~brave(paul))<=>(brave(alice)))&
(((creative(mary)|~calm(mary)))<=>((tall(lucy)|~strong(lucy))))&
(![X]:((creative(X)<~>~funny(X))<=>brave(X)))&
(((~kind(lucy)&~humble(lucy)))=>((~generous(fred)&~curious(fred))))&
(![X]:((patient(X)<~>tall(X))<=>(strong(X)|~tall(X))))&
(![X]:(~quiet(X)=>(~wise(X)|~calm(X))))&
(![X]:((~wise(X)<~>tall(X))=>(~rich(X)&~quiet(X))))&
(((calm(mary)|~curious(mary)))=>(~old(mary)))&
(((~quiet(fred)&~patient(fred)))=>(?[X]:((tall(X)&~happy(X)))))&
(![X]:((~calm(X)|humble(X))<=>(~curious(X)<~>~tall(X))))&
(?[X]:((brave(X)<~>calm(X))))&
(brave(paul))&
(?[X]:((generous(X)|wise(X))))&
(?[X]:((kind(X)<~>~rich(X))))&
(?[X]:((kind(X)|~wise(X))))&
(?[X]:((~patient(X)|funny(X)))) | ~curious(mary) | [
"p0",
"p2",
"p3",
"p8",
"p9",
"p10",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 945479163833719560392076
% SZS output start Proof for 945479163833719560392076
1. ! [X0] : ((~patient(X0) <~> ~wise(X0)) <=> (calm(X0) & wise(X0))) [input p0]
3. ! [X0] : ((~strong(X0) & ~tall(X0)) <=> (~wise(X0) <~> ~strong(X0))) [input p2]
4. ! [X0] : ((creative(X0) & old(X0)) <=> (strong(X0) <~> ~wise(X0))) [input p3]
9. ! [X0] : ((patient(X0) <~> tall(X0)) <=> (~tall(X0) | strong(X0))) [input p8]
10. ! [X0] : (~quiet(X0) => (~calm(X0) | ~wise(X0))) [input p9]
11. ! [X0] : ((~wise(X0) <~> tall(X0)) => (~quiet(X0) & ~rich(X0))) [input p10]
12. (~curious(mary) | calm(mary)) => ~old(mary) [input p11]
14. ! [X0] : ((humble(X0) | ~calm(X0)) <=> (~curious(X0) <~> ~tall(X0))) [input p13]
21. ~curious(mary) [input hypothesis]
25. ! [X0] : ((~calm(X0) | ~wise(X0)) | quiet(X0)) [ennf transformation 10]
26. ! [X0] : (~calm(X0) | ~wise(X0) | quiet(X0)) [flattening 25]
27. ! [X0] : ((~quiet(X0) & ~rich(X0)) | (~wise(X0) <=> tall(X0))) [ennf transformation 11]
28. ~old(mary) | (curious(mary) & ~calm(mary)) [ennf transformation 12]
31. ! [X0] : ((((wise(X0) | patient(X0)) & (~wise(X0) | ~patient(X0))) | (~calm(X0) | ~wise(X0))) & ((calm(X0) & wise(X0)) | ((~patient(X0) | wise(X0)) & (~wise(X0) | patient(X0))))) [nnf transformation 1]
32. ! [X0] : ((((wise(X0) | patient(X0)) & (~wise(X0) | ~patient(X0))) | ~calm(X0) | ~wise(X0)) & ((calm(X0) & wise(X0)) | ((~patient(X0) | wise(X0)) & (~wise(X0) | patient(X0))))) [flattening 31]
35. ! [X0] : (((~strong(X0) & ~tall(X0)) | ((~wise(X0) | strong(X0)) & (~strong(X0) | wise(X0)))) & (((strong(X0) | wise(X0)) & (~strong(X0) | ~wise(X0))) | (strong(X0) | tall(X0)))) [nnf transformation 3]
36. ! [X0] : (((~strong(X0) & ~tall(X0)) | ((~wise(X0) | strong(X0)) & (~strong(X0) | wise(X0)))) & (((strong(X0) | wise(X0)) & (~strong(X0) | ~wise(X0))) | strong(X0) | tall(X0))) [flattening 35]
37. ! [X0] : (((creative(X0) & old(X0)) | ((strong(X0) | wise(X0)) & (~wise(X0) | ~strong(X0)))) & (((wise(X0) | ~strong(X0)) & (~wise(X0) | strong(X0))) | (~creative(X0) | ~old(X0)))) [nnf transformation 4]
38. ! [X0] : (((creative(X0) & old(X0)) | ((strong(X0) | wise(X0)) & (~wise(X0) | ~strong(X0)))) & (((wise(X0) | ~strong(X0)) & (~wise(X0) | strong(X0))) | ~creative(X0) | ~old(X0))) [flattening 37]
43. ! [X0] : ((((~tall(X0) | ~patient(X0)) & (tall(X0) | patient(X0))) | (tall(X0) & ~strong(X0))) & ((~tall(X0) | strong(X0)) | ((patient(X0) | ~tall(X0)) & (tall(X0) | ~patient(X0))))) [nnf transformation 9]
44. ! [X0] : ((((~tall(X0) | ~patient(X0)) & (tall(X0) | patient(X0))) | (tall(X0) & ~strong(X0))) & (~tall(X0) | strong(X0) | ((patient(X0) | ~tall(X0)) & (tall(X0) | ~patient(X0))))) [flattening 43]
45. ! [X0] : ((~quiet(X0) & ~rich(X0)) | ((~wise(X0) | ~tall(X0)) & (tall(X0) | wise(X0)))) [nnf transformation 27]
48. ! [X0] : (((humble(X0) | ~calm(X0)) | ((~curious(X0) | tall(X0)) & (~tall(X0) | curious(X0)))) & (((tall(X0) | curious(X0)) & (~tall(X0) | ~curious(X0))) | (~humble(X0) & calm(X0)))) [nnf transformation 14]
49. ! [X0] : ((humble(X0) | ~calm(X0) | ((~curious(X0) | tall(X0)) & (~tall(X0) | curious(X0)))) & (((tall(X0) | curious(X0)) & (~tall(X0) | ~curious(X0))) | (~humble(X0) & calm(X0)))) [flattening 48]
63. wise(X0) | ~patient(X0) | wise(X0) [cnf transformation 32]
64. ~wise(X0) | calm(X0) | patient(X0) [cnf transformation 32]
66. ~wise(X0) | ~patient(X0) | ~calm(X0) | ~wise(X0) [cnf transformation 32]
74. ~tall(X0) | ~wise(X0) | strong(X0) [cnf transformation 36]
75. ~strong(X0) | ~strong(X0) | wise(X0) [cnf transformation 36]
79. old(X0) | ~wise(X0) | ~strong(X0) [cnf transformation 38]
80. old(X0) | strong(X0) | wise(X0) [cnf transformation 38]
96. ~tall(X0) | strong(X0) | patient(X0) | ~tall(X0) [cnf transformation 44]
98. tall(X0) | patient(X0) | tall(X0) [cnf transformation 44]
101. ~calm(X0) | ~wise(X0) | quiet(X0) [cnf transformation 26]
105. ~quiet(X0) | ~wise(X0) | ~tall(X0) [cnf transformation 45]
107. ~old(mary) | curious(mary) [cnf transformation 28]
111. curious(X0) | tall(X0) | calm(X0) [cnf transformation 49]
123. ~curious(mary) [cnf transformation 21]
124. ~tall(X0) | strong(X0) | patient(X0) [duplicate literal removal 96]
125. tall(X0) | patient(X0) [duplicate literal removal 98]
127. ~strong(X0) | wise(X0) [duplicate literal removal 75]
128. ~patient(X0) | wise(X0) [duplicate literal removal 63]
129. ~calm(X0) | ~patient(X0) | ~wise(X0) [duplicate literal removal 66]
133. old(X0) | wise(X0) [subsumption resolution 80,127]
134. ~strong(X0) | old(X0) [subsumption resolution 79,127]
154. 5 <=> calm(mary) [avatar definition]
155. calm(mary) <- (5) [avatar component clause 154]
156. ~calm(mary) <- (~5) [avatar component clause 154]
183. strong(X0) | patient(X0) [subsumption resolution 124,125]
185. 11 <=> curious(mary) [avatar definition]
186. ~curious(mary) <- (~11) [avatar component clause 185]
189. 12 <=> old(mary) [avatar definition]
191. ~old(mary) <- (~12) [avatar component clause 189]
192. 11 | ~12 [avatar split clause 107,189,185]
255. ~11 [avatar split clause 123,185]
256. wise(mary) <- (~12) [resolution 133,191]
260. patient(X2) | wise(X2) [resolution 183,127]
261. wise(X2) [subsumption resolution 260,128]
266. calm(X0) | patient(X0) [resolution 261,64]
309. ~wise(X0) | quiet(X0) | patient(X0) [resolution 101,266]
310. quiet(X0) | patient(X0) [subsumption resolution 309,261]
322. patient(X0) | ~wise(X0) | ~tall(X0) [resolution 310,105]
323. patient(X0) | ~tall(X0) [subsumption resolution 322,261]
324. patient(X0) [subsumption resolution 323,125]
344. tall(mary) | calm(mary) <- (~11) [resolution 111,186]
349. tall(mary) <- (~5, ~11) [subsumption resolution 344,156]
354. ~wise(mary) | strong(mary) <- (~5, ~11) [resolution 349,74]
355. strong(mary) <- (~5, ~11, ~12) [subsumption resolution 354,256]
364. old(mary) <- (~5, ~11, ~12) [resolution 355,134]
370. $false <- (~5, ~11, ~12) [subsumption resolution 364,191]
371. 5 | 11 | 12 [avatar contradiction clause 370]
384. ~patient(mary) | ~wise(mary) <- (5) [resolution 155,129]
387. ~wise(mary) <- (5) [subsumption resolution 384,324]
388. $false <- (5, ~12) [subsumption resolution 387,256]
389. ~5 | 12 [avatar contradiction clause 388]
392. $false [avatar sat refutation 192,255,371,389]
% SZS output end Proof for 945479163833719560392076
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If susan is wise or not calm then someone is creative.
Everyone who is both not tall and not generous is not calm and vice versa.
If someone is old then someone is either not kind or strong.
If someone is creative then fred is patient.
Everyone who is either tall or creative is either calm or not funny and vice versa.
Everyone who is kind is either not quiet or brave.
Everyone who is funny is generous.
If someone is old then someone is both humble and happy.
Everyone who is either not quiet or not strong is not quiet or not curious.
If alice is both creative and happy then someone is patient and vice versa.
Everyone who is not brave is both quiet and not patient and vice versa.
Everyone who is both not quiet and not happy is brave or generous and vice versa.
Everyone who is old is both strong and not old and vice versa.
If someone is either old or not creative then someone is either wise or not wise and vice versa.
Everyone who is not calm is both not kind and rich and vice versa.
Everyone who is not old is humble.
John is either not patient or old.
Fred is not quiet.
Someone is both creative and happy.
Lucy is either wise or not rich.
Someone is quiet or happy.
Someone is not brave.
Alice is not funny or wise. | Susan is not kind. | entailment | (((wise(susan)|~calm(susan)))=>(?[X]:(creative(X))))&
(![X]:((~tall(X)&~generous(X))<=>~calm(X)))&
((?[X]:(old(X)))=>(?[X]:((~kind(X)<~>strong(X)))))&
((?[X]:(creative(X)))=>(patient(fred)))&
(![X]:((tall(X)<~>creative(X))<=>(calm(X)<~>~funny(X))))&
(![X]:(kind(X)=>(~quiet(X)<~>brave(X))))&
(![X]:(funny(X)=>generous(X)))&
((?[X]:(old(X)))=>(?[X]:((humble(X)&happy(X)))))&
(![X]:((~quiet(X)<~>~strong(X))=>(~quiet(X)|~curious(X))))&
(((creative(alice)&happy(alice)))<=>(?[X]:(patient(X))))&
(![X]:(~brave(X)<=>(quiet(X)&~patient(X))))&
(![X]:((~quiet(X)&~happy(X))<=>(brave(X)|generous(X))))&
(![X]:(old(X)<=>(strong(X)&~old(X))))&
((?[X]:((old(X)<~>~creative(X))))<=>(?[X]:((wise(X)<~>~wise(X)))))&
(![X]:(~calm(X)<=>(~kind(X)&rich(X))))&
(![X]:(~old(X)=>humble(X)))&
((~patient(john)<~>old(john)))&
(~quiet(fred))&
(?[X]:((creative(X)&happy(X))))&
((wise(lucy)<~>~rich(lucy)))&
(?[X]:((quiet(X)|happy(X))))&
(?[X]:(~brave(X)))&
((~funny(alice)|wise(alice))) | ~kind(susan) | [
"p5",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 8042204602328403114592580
% SZS output start Proof for 8042204602328403114592580
6. ! [X0] : (kind(X0) => (~quiet(X0) <~> brave(X0))) [input p5]
11. ! [X0] : (~brave(X0) <=> (~patient(X0) & quiet(X0))) [input p10]
12. ! [X0] : ((~happy(X0) & ~quiet(X0)) <=> (generous(X0) | brave(X0))) [input p11]
24. kind(susan) [input hypothesis]
34. ! [X0] : ((~quiet(X0) <~> brave(X0)) | ~kind(X0)) [ennf transformation 6]
46. ! [X0] : (((~brave(X0) | quiet(X0)) & (brave(X0) | ~quiet(X0))) | ~kind(X0)) [nnf transformation 34]
55. ! [X0] : ((~brave(X0) | (patient(X0) | ~quiet(X0))) & ((~patient(X0) & quiet(X0)) | brave(X0))) [nnf transformation 11]
56. ! [X0] : ((~brave(X0) | patient(X0) | ~quiet(X0)) & ((~patient(X0) & quiet(X0)) | brave(X0))) [flattening 55]
57. ! [X0] : (((~happy(X0) & ~quiet(X0)) | (~generous(X0) & ~brave(X0))) & ((generous(X0) | brave(X0)) | (happy(X0) | quiet(X0)))) [nnf transformation 12]
58. ! [X0] : (((~happy(X0) & ~quiet(X0)) | (~generous(X0) & ~brave(X0))) & (generous(X0) | brave(X0) | happy(X0) | quiet(X0))) [flattening 57]
92. ~quiet(X0) | brave(X0) | ~kind(X0) [cnf transformation 46]
93. ~brave(X0) | quiet(X0) | ~kind(X0) [cnf transformation 46]
99. brave(X0) | quiet(X0) [cnf transformation 56]
103. ~brave(X0) | ~quiet(X0) [cnf transformation 58]
131. kind(susan) [cnf transformation 24]
311. quiet(X0) | ~kind(X0) | quiet(X0) [resolution 93,99]
314. ~kind(X0) | quiet(X0) [duplicate literal removal 311]
393. quiet(susan) [resolution 314,131]
396. brave(susan) | ~kind(susan) [resolution 393,92]
398. brave(susan) [subsumption resolution 396,131]
433. ~quiet(susan) [resolution 398,103]
435. $false [subsumption resolution 433,393]
% SZS output end Proof for 8042204602328403114592580
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either curious or not happy is generous. Everyone who is either patient or tall is not wise or generous. If someone is either patient or not calm then paul is both brave and not quiet and vice versa. If john is creative or not rich then fred is either not quiet or quiet and vice versa. If someone is both not creative and happy then fred is either generous or not curious and vice versa. Everyone who is either patient or not old is either not kind or not brave and vice versa. If someone is generous then mary is funny and vice versa. If someone is not kind then someone is both not brave and calm and vice versa. If someone is both not brave and not happy then mary is either not rich or not curious and vice versa. Everyone who is not tall or happy is both tall and not quiet and vice versa. Everyone who is either wise or not tall is both not patient and strong and vice versa. Everyone who is funny or patient is both not rich and rich. Everyone who is either curious or not strong is not humble or generous. If someone is not happy or not creative then alice is not tall or quiet and vice versa. Everyone who is both patient and brave is either kind or not brave and vice versa. If paul is both not tall and calm then john is both curious and not kind and vice versa. Someone is either happy or curious. Paul is either tall or funny. Someone is not happy or quiet. Someone is either not happy or happy. Alice is not quiet or not rich. Someone is humble. | Mary is patient. | contradiction | (![X]:((curious(X)<~>~happy(X))=>generous(X)))&
(![X]:((patient(X)<~>tall(X))=>(~wise(X)|generous(X))))&
((?[X]:((patient(X)<~>~calm(X))))<=>((brave(paul)&~quiet(paul))))&
(((creative(john)|~rich(john)))<=>((~quiet(fred)<~>quiet(fred))))&
((?[X]:((~creative(X)&happy(X))))<=>((generous(fred)<~>~curious(fred))))&
(![X]:((patient(X)<~>~old(X))<=>(~kind(X)<~>~brave(X))))&
((?[X]:(generous(X)))<=>(funny(mary)))&
((?[X]:(~kind(X)))<=>(?[X]:((~brave(X)&calm(X)))))&
((?[X]:((~brave(X)&~happy(X))))<=>((~rich(mary)<~>~curious(mary))))&
(![X]:((~tall(X)|happy(X))<=>(tall(X)&~quiet(X))))&
(![X]:((wise(X)<~>~tall(X))<=>(~patient(X)&strong(X))))&
(![X]:((funny(X)|patient(X))=>(~rich(X)&rich(X))))&
(![X]:((curious(X)<~>~strong(X))=>(~humble(X)|generous(X))))&
((?[X]:((~happy(X)|~creative(X))))<=>((~tall(alice)|quiet(alice))))&
(![X]:((patient(X)&brave(X))<=>(kind(X)<~>~brave(X))))&
(((~tall(paul)&calm(paul)))<=>((curious(john)&~kind(john))))&
(?[X]:((happy(X)<~>curious(X))))&
((tall(paul)<~>funny(paul)))&
(?[X]:((~happy(X)|quiet(X))))&
(?[X]:((~happy(X)<~>happy(X))))&
((~quiet(alice)|~rich(alice)))&
(?[X]:(humble(X))) | patient(mary) | [
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 8425646034395294018176499
% SZS output start Proof for 8425646034395294018176499
12. ! [X0] : ((patient(X0) | funny(X0)) => (rich(X0) & ~rich(X0))) [input p11]
23. patient(mary) [input hypothesis]
28. ! [X0] : ((rich(X0) & ~rich(X0)) | (~patient(X0) & ~funny(X0))) [ennf transformation 12]
136. ~rich(X0) | ~patient(X0) [cnf transformation 28]
138. rich(X0) | ~patient(X0) [cnf transformation 28]
164. patient(mary) [cnf transformation 23]
300. ~patient(X0) [subsumption resolution 136,138]
357. $false [subsumption resolution 164,300]
% SZS output end Proof for 8425646034395294018176499
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either happy or strong then someone is either not brave or not kind and vice versa.
If john is both not funny and not happy then alice is not rich.
Everyone who is old or creative is not generous and vice versa.
Everyone who is happy is not old or funny.
Everyone who is both not funny and rich is both not old and not strong and vice versa.
Everyone who is curious or humble is generous.
Everyone who is either humble or calm is either not generous or strong and vice versa.
If mary is strong then someone is either rich or tall and vice versa.
If someone is patient or not creative then someone is either not funny or old.
Everyone who is not creative or not kind is either patient or not brave and vice versa.
Everyone who is not creative is both brave and calm and vice versa.
If mary is humble then someone is both not wise and calm.
Everyone who is not quiet is both calm and brave and vice versa.
Everyone who is generous is not patient or not kind and vice versa.
If someone is wise then mary is both strong and generous and vice versa.
Everyone who is either happy or rich is generous or brave and vice versa.
Fred is not old or kind.
Someone is curious.
Someone is not rich.
Lucy is both calm and wise.
Lucy is either not rich or curious.
John is either not wise or not strong.
Lucy is not curious.
Someone is either rich or not happy. | John is funny. | neutral | ((?[X]:((happy(X)<~>strong(X))))<=>(?[X]:((~brave(X)<~>~kind(X)))))&
(((~funny(john)&~happy(john)))=>(~rich(alice)))&
(![X]:((old(X)|creative(X))<=>~generous(X)))&
(![X]:(happy(X)=>(~old(X)|funny(X))))&
(![X]:((~funny(X)&rich(X))<=>(~old(X)&~strong(X))))&
(![X]:((curious(X)|humble(X))=>generous(X)))&
(![X]:((humble(X)<~>calm(X))<=>(~generous(X)<~>strong(X))))&
((strong(mary))<=>(?[X]:((rich(X)<~>tall(X)))))&
((?[X]:((patient(X)|~creative(X))))=>(?[X]:((~funny(X)<~>old(X)))))&
(![X]:((~creative(X)|~kind(X))<=>(patient(X)<~>~brave(X))))&
(![X]:(~creative(X)<=>(brave(X)&calm(X))))&
((humble(mary))=>(?[X]:((~wise(X)&calm(X)))))&
(![X]:(~quiet(X)<=>(calm(X)&brave(X))))&
(![X]:(generous(X)<=>(~patient(X)|~kind(X))))&
((?[X]:(wise(X)))<=>((strong(mary)&generous(mary))))&
(![X]:((happy(X)<~>rich(X))<=>(generous(X)|brave(X))))&
((~old(fred)|kind(fred)))&
(?[X]:(curious(X)))&
(?[X]:(~rich(X)))&
((calm(lucy)&wise(lucy)))&
((~rich(lucy)<~>curious(lucy)))&
((~wise(john)<~>~strong(john)))&
(~curious(lucy))&
(?[X]:((rich(X)<~>~happy(X)))) | funny(john) | [] | null | 0 |
Everyone who is both rich and not old is creative and vice versa.
Everyone who is both not curious and brave is either curious or tall and vice versa.
Everyone who is not kind or not brave is either not rich or curious and vice versa.
Everyone who is happy is tall or rich and vice versa.
If someone is either not kind or not patient then paul is either not funny or brave.
Everyone who is both not humble and not brave is not rich and vice versa.
Everyone who is humble or not funny is both quiet and strong and vice versa.
If alice is not patient or calm then someone is not funny or not strong and vice versa.
If susan is either not creative or humble then susan is not quiet.
If someone is not creative then alice is not wise and vice versa.
Everyone who is creative or patient is either humble or not brave and vice versa.
If susan is creative then someone is both not patient and generous.
If susan is happy or not calm then someone is both rich and not old.
If someone is both not strong and not humble then someone is not kind or not old.
Everyone who is calm or patient is either wise or not rich.
Everyone who is patient is either kind or funny.
Someone is both not rich and not brave.
Someone is not quiet.
Alice is either not funny or not tall.
Someone is not kind or not old.
Someone is either not brave or tall.
Someone is either not generous or rich.
Fred is not strong.
Someone is curious or creative. | Susan is creative. | contradiction | (![X]:((rich(X)&~old(X))<=>creative(X)))&
(![X]:((~curious(X)&brave(X))<=>(curious(X)<~>tall(X))))&
(![X]:((~kind(X)|~brave(X))<=>(~rich(X)<~>curious(X))))&
(![X]:(happy(X)<=>(tall(X)|rich(X))))&
((?[X]:((~kind(X)<~>~patient(X))))=>((~funny(paul)<~>brave(paul))))&
(![X]:((~humble(X)&~brave(X))<=>~rich(X)))&
(![X]:((humble(X)|~funny(X))<=>(quiet(X)&strong(X))))&
(((~patient(alice)|calm(alice)))<=>(?[X]:((~funny(X)|~strong(X)))))&
(((~creative(susan)<~>humble(susan)))=>(~quiet(susan)))&
((?[X]:(~creative(X)))<=>(~wise(alice)))&
(![X]:((creative(X)|patient(X))<=>(humble(X)<~>~brave(X))))&
((creative(susan))=>(?[X]:((~patient(X)&generous(X)))))&
(((happy(susan)|~calm(susan)))=>(?[X]:((rich(X)&~old(X)))))&
((?[X]:((~strong(X)&~humble(X))))=>(?[X]:((~kind(X)|~old(X)))))&
(![X]:((calm(X)|patient(X))=>(wise(X)<~>~rich(X))))&
(![X]:(patient(X)=>(kind(X)<~>funny(X))))&
(?[X]:((~rich(X)&~brave(X))))&
(?[X]:(~quiet(X)))&
((~funny(alice)<~>~tall(alice)))&
(?[X]:((~kind(X)|~old(X))))&
(?[X]:((~brave(X)<~>tall(X))))&
(?[X]:((~generous(X)<~>rich(X))))&
(~strong(fred))&
(?[X]:((curious(X)|creative(X)))) | creative(susan) | [
"p0",
"p5",
"p6",
"p8",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 5243428569972543472517023
% SZS output start Proof for 5243428569972543472517023
1. ! [X0] : ((~old(X0) & rich(X0)) <=> creative(X0)) [input p0]
6. ! [X0] : ((~brave(X0) & ~humble(X0)) <=> ~rich(X0)) [input p5]
7. ! [X0] : ((~funny(X0) | humble(X0)) <=> (strong(X0) & quiet(X0))) [input p6]
9. (~creative(susan) <~> humble(susan)) => ~quiet(susan) [input p8]
11. ! [X0] : ((patient(X0) | creative(X0)) <=> (humble(X0) <~> ~brave(X0))) [input p10]
25. creative(susan) [input hypothesis]
30. ~quiet(susan) | (~creative(susan) <=> humble(susan)) [ennf transformation 9]
36. ! [X0] : (((~old(X0) & rich(X0)) | ~creative(X0)) & (creative(X0) | (old(X0) | ~rich(X0)))) [nnf transformation 1]
37. ! [X0] : (((~old(X0) & rich(X0)) | ~creative(X0)) & (creative(X0) | old(X0) | ~rich(X0))) [flattening 36]
43. ! [X0] : (((~brave(X0) & ~humble(X0)) | rich(X0)) & (~rich(X0) | (brave(X0) | humble(X0)))) [nnf transformation 6]
44. ! [X0] : (((~brave(X0) & ~humble(X0)) | rich(X0)) & (~rich(X0) | brave(X0) | humble(X0))) [flattening 43]
45. ! [X0] : (((~funny(X0) | humble(X0)) | (~strong(X0) | ~quiet(X0))) & ((strong(X0) & quiet(X0)) | (funny(X0) & ~humble(X0)))) [nnf transformation 7]
46. ! [X0] : ((~funny(X0) | humble(X0) | ~strong(X0) | ~quiet(X0)) & ((strong(X0) & quiet(X0)) | (funny(X0) & ~humble(X0)))) [flattening 45]
52. ~quiet(susan) | ((~creative(susan) | ~humble(susan)) & (humble(susan) | creative(susan))) [nnf transformation 30]
57. ! [X0] : (((patient(X0) | creative(X0)) | ((humble(X0) | brave(X0)) & (~brave(X0) | ~humble(X0)))) & (((brave(X0) | ~humble(X0)) & (~brave(X0) | humble(X0))) | (~patient(X0) & ~creative(X0)))) [nnf transformation 11]
58. ! [X0] : ((patient(X0) | creative(X0) | ((humble(X0) | brave(X0)) & (~brave(X0) | ~humble(X0)))) & (((brave(X0) | ~humble(X0)) & (~brave(X0) | humble(X0))) | (~patient(X0) & ~creative(X0)))) [flattening 57]
84. ~creative(X0) | rich(X0) [cnf transformation 37]
104. ~rich(X0) | brave(X0) | humble(X0) [cnf transformation 44]
107. ~humble(X0) | quiet(X0) [cnf transformation 46]
117. ~quiet(susan) | ~creative(susan) | ~humble(susan) [cnf transformation 52]
120. ~brave(X0) | humble(X0) | ~creative(X0) [cnf transformation 58]
151. creative(susan) [cnf transformation 25]
199. ~creative(susan) | ~humble(susan) [subsumption resolution 117,107]
201. 11 <=> humble(susan) [avatar definition]
203. ~humble(susan) <- (~11) [avatar component clause 201]
205. 12 <=> creative(susan) [avatar definition]
206. creative(susan) <- (12) [avatar component clause 205]
208. ~11 | ~12 [avatar split clause 199,205,201]
314. 12 [avatar split clause 151,205]
315. rich(susan) <- (12) [resolution 84,206]
356. 39 <=> brave(susan) [avatar definition]
358. brave(susan) <- (39) [avatar component clause 356]
392. brave(susan) | humble(susan) <- (12) [resolution 104,315]
394. brave(susan) <- (~11, 12) [subsumption resolution 392,203]
395. 39 | 11 | ~12 [avatar split clause 394,205,201,356]
434. humble(susan) | ~creative(susan) <- (39) [resolution 358,120]
437. ~creative(susan) <- (~11, 39) [subsumption resolution 434,203]
438. $false <- (~11, 12, 39) [subsumption resolution 437,206]
439. 11 | ~12 | ~39 [avatar contradiction clause 438]
440. $false [avatar sat refutation 208,314,395,439]
% SZS output end Proof for 5243428569972543472517023
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious and not brave is not happy or humble and vice versa.
Everyone who is not patient or not rich is not humble and vice versa.
If someone is happy or not funny then someone is both not old and not happy.
Everyone who is either strong or funny is both brave and strong.
Everyone who is strong is either wise or not old.
If paul is not humble or not rich then john is either not rich or not funny.
Everyone who is both calm and old is not funny or curious and vice versa.
If someone is rich then someone is not kind.
If someone is both not tall and old then alice is either not curious or not humble.
If mary is rich or not old then alice is either not quiet or creative.
If someone is either humble or not happy then mary is either not wise or not strong and vice versa.
If someone is not wise or happy then someone is either calm or patient and vice versa.
If susan is not curious or brave then someone is either quiet or not rich.
Everyone who is creative is not humble and vice versa.
If alice is either tall or patient then paul is not kind.
If someone is both not old and strong then someone is not brave or not patient.
Someone is both old and generous.
John is rich or not rich.
Alice is old.
Lucy is either patient or generous.
Susan is either not generous or old. | Mary is not wise. | contradiction | (![X]:((curious(X)&~brave(X))<=>(~happy(X)|humble(X))))&
(![X]:((~patient(X)|~rich(X))<=>~humble(X)))&
((?[X]:((happy(X)|~funny(X))))=>(?[X]:((~old(X)&~happy(X)))))&
(![X]:((strong(X)<~>funny(X))=>(brave(X)&strong(X))))&
(![X]:(strong(X)=>(wise(X)<~>~old(X))))&
(((~humble(paul)|~rich(paul)))=>((~rich(john)<~>~funny(john))))&
(![X]:((calm(X)&old(X))<=>(~funny(X)|curious(X))))&
((?[X]:(rich(X)))=>(?[X]:(~kind(X))))&
((?[X]:((~tall(X)&old(X))))=>((~curious(alice)<~>~humble(alice))))&
(((rich(mary)|~old(mary)))=>((~quiet(alice)<~>creative(alice))))&
((?[X]:((humble(X)<~>~happy(X))))<=>((~wise(mary)<~>~strong(mary))))&
((?[X]:((~wise(X)|happy(X))))<=>(?[X]:((calm(X)<~>patient(X)))))&
(((~curious(susan)|brave(susan)))=>(?[X]:((quiet(X)<~>~rich(X)))))&
(![X]:(creative(X)<=>~humble(X)))&
(((tall(alice)<~>patient(alice)))=>(~kind(paul)))&
((?[X]:((~old(X)&strong(X))))=>(?[X]:((~brave(X)|~patient(X)))))&
(?[X]:((old(X)&generous(X))))&
((rich(john)|~rich(john)))&
(old(alice))&
((patient(lucy)<~>generous(lucy)))&
((~generous(susan)<~>old(susan))) | ~wise(mary) | [
"p0",
"p2",
"p3",
"p4",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 2242894079257887743612866
% SZS output start Proof for 2242894079257887743612866
1. ! [X0] : ((~brave(X0) & curious(X0)) <=> (humble(X0) | ~happy(X0))) [input p0]
3. ? [X0] : (~funny(X0) | happy(X0)) => ? [X0] : (~happy(X0) & ~old(X0)) [input p2]
4. ! [X0] : ((strong(X0) <~> funny(X0)) => (strong(X0) & brave(X0))) [input p3]
5. ! [X0] : (strong(X0) => (wise(X0) <~> ~old(X0))) [input p4]
7. ! [X0] : ((old(X0) & calm(X0)) <=> (curious(X0) | ~funny(X0))) [input p6]
22. ~wise(mary) [input hypothesis]
23. ? [X0] : (~funny(X0) | happy(X0)) => ? [X1] : (~happy(X1) & ~old(X1)) [rectify 3]
30. ? [X1] : (~happy(X1) & ~old(X1)) | ! [X0] : (funny(X0) & ~happy(X0)) [ennf transformation 23]
31. ! [X0] : ((strong(X0) & brave(X0)) | (strong(X0) <=> funny(X0))) [ennf transformation 4]
32. ! [X0] : ((wise(X0) <~> ~old(X0)) | ~strong(X0)) [ennf transformation 5]
37. ! [X0] : (((~brave(X0) & curious(X0)) | (~humble(X0) & happy(X0))) & ((humble(X0) | ~happy(X0)) | (brave(X0) | ~curious(X0)))) [nnf transformation 1]
38. ! [X0] : (((~brave(X0) & curious(X0)) | (~humble(X0) & happy(X0))) & (humble(X0) | ~happy(X0) | brave(X0) | ~curious(X0))) [flattening 37]
41. ? [X0] : (~happy(X0) & ~old(X0)) | ! [X1] : (funny(X1) & ~happy(X1)) [rectify 30]
42. ? [X0] : (~happy(X0) & ~old(X0)) => (~happy(sK0) & ~old(sK0)) [choice axiom]
43. (~happy(sK0) & ~old(sK0)) | ! [X1] : (funny(X1) & ~happy(X1)) [skolemisation 41,42]
44. ! [X0] : ((strong(X0) & brave(X0)) | ((strong(X0) | ~funny(X0)) & (funny(X0) | ~strong(X0)))) [nnf transformation 31]
45. ! [X0] : (((old(X0) | ~wise(X0)) & (~old(X0) | wise(X0))) | ~strong(X0)) [nnf transformation 32]
47. ! [X0] : (((old(X0) & calm(X0)) | (~curious(X0) & funny(X0))) & ((curious(X0) | ~funny(X0)) | (~old(X0) | ~calm(X0)))) [nnf transformation 7]
48. ! [X0] : (((old(X0) & calm(X0)) | (~curious(X0) & funny(X0))) & (curious(X0) | ~funny(X0) | ~old(X0) | ~calm(X0))) [flattening 47]
71. happy(X0) | curious(X0) [cnf transformation 38]
78. ~old(sK0) | ~happy(X1) [cnf transformation 43]
79. ~old(sK0) | funny(X1) [cnf transformation 43]
80. ~happy(sK0) | ~happy(X1) [cnf transformation 43]
85. strong(X0) | strong(X0) | ~funny(X0) [cnf transformation 44]
86. ~strong(X0) | wise(X0) | ~old(X0) [cnf transformation 45]
96. ~curious(X0) | old(X0) [cnf transformation 48]
130. ~wise(mary) [cnf transformation 22]
131. ~funny(X0) | strong(X0) [duplicate literal removal 85]
133. 1 <=> ! [X1] : funny(X1) [avatar definition]
134. funny(X1) <- (1) [avatar component clause 133]
136. 2 <=> happy(sK0) [avatar definition]
137. happy(sK0) <- (2) [avatar component clause 136]
138. ~happy(sK0) <- (~2) [avatar component clause 136]
141. 3 <=> ! [X1] : ~happy(X1) [avatar definition]
142. ~happy(X1) <- (3) [avatar component clause 141]
143. 3 | ~2 [avatar split clause 80,136,141]
145. 4 <=> old(sK0) [avatar definition]
147. ~old(sK0) <- (~4) [avatar component clause 145]
148. 1 | ~4 [avatar split clause 79,145,133]
149. 3 | ~4 [avatar split clause 78,145,141]
191. 13 <=> strong(mary) [avatar definition]
192. ~strong(mary) <- (~13) [avatar component clause 191]
193. strong(mary) <- (13) [avatar component clause 191]
195. 14 <=> wise(mary) [avatar definition]
197. ~wise(mary) <- (~14) [avatar component clause 195]
303. ~14 [avatar split clause 130,195]
304. curious(sK0) <- (~2) [resolution 71,138]
310. old(sK0) <- (~2) [resolution 96,304]
312. $false <- (~2, ~4) [subsumption resolution 310,147]
313. 2 | 4 [avatar contradiction clause 312]
314. $false <- (2, 3) [subsumption resolution 137,142]
315. ~2 | ~3 [avatar contradiction clause 314]
318. curious(X0) <- (3) [resolution 142,71]
319. old(X0) <- (3) [resolution 318,96]
327. strong(X0) <- (1) [resolution 131,134]
331. wise(mary) | ~old(mary) <- (13) [resolution 86,193]
333. ~old(mary) <- (13, ~14) [subsumption resolution 331,197]
334. $false <- (3, 13, ~14) [subsumption resolution 333,319]
335. ~3 | ~13 | 14 [avatar contradiction clause 334]
339. $false <- (1, ~13) [subsumption resolution 192,327]
340. ~1 | 13 [avatar contradiction clause 339]
341. $false [avatar sat refutation 143,148,149,303,313,315,335,340]
% SZS output end Proof for 2242894079257887743612866
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not funny or not creative is curious.
Everyone who is both kind and rich is old or brave and vice versa.
If lucy is either not humble or patient then alice is both not curious and not tall and vice versa.
Everyone who is both old and not strong is tall or not wise and vice versa.
Everyone who is both not creative and not funny is kind and vice versa.
Everyone who is both patient and curious is not tall.
Everyone who is brave or humble is not strong and vice versa.
If susan is both not humble and brave then someone is both happy and not generous and vice versa.
Everyone who is both quiet and not quiet is not old or not calm and vice versa.
If susan is calm then fred is kind and vice versa.
Everyone who is wise or not curious is either strong or quiet.
Everyone who is not brave or kind is generous.
If mary is either not generous or creative then paul is patient.
Everyone who is kind is not strong and vice versa.
If someone is not brave then lucy is quiet or not creative and vice versa.
Everyone who is happy is not old.
Someone is quiet or not kind.
Mary is either funny or not humble.
Someone is not humble or humble.
John is either not quiet or funny.
Someone is rich.
John is not happy. | Paul is not curious. | contradiction | (![X]:((~funny(X)|~creative(X))=>curious(X)))&
(![X]:((kind(X)&rich(X))<=>(old(X)|brave(X))))&
(((~humble(lucy)<~>patient(lucy)))<=>((~curious(alice)&~tall(alice))))&
(![X]:((old(X)&~strong(X))<=>(tall(X)|~wise(X))))&
(![X]:((~creative(X)&~funny(X))<=>kind(X)))&
(![X]:((patient(X)&curious(X))=>~tall(X)))&
(![X]:((brave(X)|humble(X))<=>~strong(X)))&
(((~humble(susan)&brave(susan)))<=>(?[X]:((happy(X)&~generous(X)))))&
(![X]:((quiet(X)&~quiet(X))<=>(~old(X)|~calm(X))))&
((calm(susan))<=>(kind(fred)))&
(![X]:((wise(X)|~curious(X))=>(strong(X)<~>quiet(X))))&
(![X]:((~brave(X)|kind(X))=>generous(X)))&
(((~generous(mary)<~>creative(mary)))=>(patient(paul)))&
(![X]:(kind(X)<=>~strong(X)))&
((?[X]:(~brave(X)))<=>((quiet(lucy)|~creative(lucy))))&
(![X]:(happy(X)=>~old(X)))&
(?[X]:((quiet(X)|~kind(X))))&
((funny(mary)<~>~humble(mary)))&
(?[X]:((~humble(X)|humble(X))))&
((~quiet(john)<~>funny(john)))&
(?[X]:(rich(X)))&
(~happy(john)) | ~curious(paul) | [
"p0",
"p1",
"p4",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 22597771118278112573974
% SZS output start Proof for 22597771118278112573974
1. ! [X0] : ((~creative(X0) | ~funny(X0)) => curious(X0)) [input p0]
2. ! [X0] : ((rich(X0) & kind(X0)) <=> (brave(X0) | old(X0))) [input p1]
5. ! [X0] : ((~funny(X0) & ~creative(X0)) <=> kind(X0)) [input p4]
9. ! [X0] : ((~quiet(X0) & quiet(X0)) <=> (~calm(X0) | ~old(X0))) [input p8]
23. ~curious(paul) [input hypothesis]
24. ! [X0] : (curious(X0) | (creative(X0) & funny(X0))) [ennf transformation 1]
31. ! [X0] : (((rich(X0) & kind(X0)) | (~brave(X0) & ~old(X0))) & ((brave(X0) | old(X0)) | (~rich(X0) | ~kind(X0)))) [nnf transformation 2]
32. ! [X0] : (((rich(X0) & kind(X0)) | (~brave(X0) & ~old(X0))) & (brave(X0) | old(X0) | ~rich(X0) | ~kind(X0))) [flattening 31]
37. ! [X0] : (((~funny(X0) & ~creative(X0)) | ~kind(X0)) & (kind(X0) | (funny(X0) | creative(X0)))) [nnf transformation 5]
38. ! [X0] : (((~funny(X0) & ~creative(X0)) | ~kind(X0)) & (kind(X0) | funny(X0) | creative(X0))) [flattening 37]
46. ! [X0] : (((~quiet(X0) & quiet(X0)) | (calm(X0) & old(X0))) & ((~calm(X0) | ~old(X0)) | (quiet(X0) | ~quiet(X0)))) [nnf transformation 9]
47. ! [X0] : (((~quiet(X0) & quiet(X0)) | (calm(X0) & old(X0))) & (~calm(X0) | ~old(X0) | quiet(X0) | ~quiet(X0))) [flattening 46]
66. curious(X0) | creative(X0) [cnf transformation 24]
68. ~old(X0) | kind(X0) [cnf transformation 32]
84. ~kind(X0) | ~creative(X0) [cnf transformation 38]
95. quiet(X0) | old(X0) [cnf transformation 47]
97. ~quiet(X0) | old(X0) [cnf transformation 47]
123. ~curious(paul) [cnf transformation 23]
170. old(X0) [subsumption resolution 95,97]
237. creative(paul) [resolution 66,123]
239. kind(X0) [resolution 68,170]
244. ~creative(X0) [resolution 84,239]
248. $false [resolution 244,237]
% SZS output end Proof for 22597771118278112573974
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If alice is not humble or calm then someone is either creative or not strong. If someone is both not tall and not strong then someone is either generous or wise. Everyone who is old is both humble and happy and vice versa. If someone is both generous and not funny then someone is either calm or generous. If someone is either wise or not old then someone is tall or not generous and vice versa. Everyone who is both not wise and old is both brave and not quiet and vice versa. Everyone who is not old or not brave is not curious or not creative and vice versa. Everyone who is not quiet is both not tall and not generous. Everyone who is not creative or not rich is both wise and not wise. If mary is curious then susan is either not tall or quiet. If someone is either kind or wise then susan is either not calm or generous. Everyone who is either curious or not wise is not rich and vice versa. Everyone who is both rich and curious is both generous and not funny. If someone is both not quiet and kind then someone is not funny or rich and vice versa. If paul is not tall then someone is both not creative and patient. Everyone who is both not tall and patient is not kind or not creative and vice versa. Someone is curious or funny. Someone is either patient or generous. Someone is either curious or quiet. Someone is not rich or not strong. | Susan is wise. | entailment | (((~humble(alice)|calm(alice)))=>(?[X]:((creative(X)<~>~strong(X)))))&
((?[X]:((~tall(X)&~strong(X))))=>(?[X]:((generous(X)<~>wise(X)))))&
(![X]:(old(X)<=>(humble(X)&happy(X))))&
((?[X]:((generous(X)&~funny(X))))=>(?[X]:((calm(X)<~>generous(X)))))&
((?[X]:((wise(X)<~>~old(X))))<=>(?[X]:((tall(X)|~generous(X)))))&
(![X]:((~wise(X)&old(X))<=>(brave(X)&~quiet(X))))&
(![X]:((~old(X)|~brave(X))<=>(~curious(X)|~creative(X))))&
(![X]:(~quiet(X)=>(~tall(X)&~generous(X))))&
(![X]:((~creative(X)|~rich(X))=>(wise(X)&~wise(X))))&
((curious(mary))=>((~tall(susan)<~>quiet(susan))))&
((?[X]:((kind(X)<~>wise(X))))=>((~calm(susan)<~>generous(susan))))&
(![X]:((curious(X)<~>~wise(X))<=>~rich(X)))&
(![X]:((rich(X)&curious(X))=>(generous(X)&~funny(X))))&
((?[X]:((~quiet(X)&kind(X))))<=>(?[X]:((~funny(X)|rich(X)))))&
((~tall(paul))=>(?[X]:((~creative(X)&patient(X)))))&
(![X]:((~tall(X)&patient(X))<=>(~kind(X)|~creative(X))))&
(?[X]:((curious(X)|funny(X))))&
(?[X]:((patient(X)<~>generous(X))))&
(?[X]:((curious(X)<~>quiet(X))))&
(?[X]:((~rich(X)|~strong(X)))) | wise(susan) | [
"p5",
"p6",
"p7",
"p8",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 5724789069667985073890304
% SZS output start Proof for 5724789069667985073890304
6. ! [X0] : ((old(X0) & ~wise(X0)) <=> (~quiet(X0) & brave(X0))) [input p5]
7. ! [X0] : ((~brave(X0) | ~old(X0)) <=> (~creative(X0) | ~curious(X0))) [input p6]
8. ! [X0] : (~quiet(X0) => (~generous(X0) & ~tall(X0))) [input p7]
9. ! [X0] : ((~rich(X0) | ~creative(X0)) => (~wise(X0) & wise(X0))) [input p8]
12. ! [X0] : ((curious(X0) <~> ~wise(X0)) <=> ~rich(X0)) [input p11]
13. ! [X0] : ((curious(X0) & rich(X0)) => (~funny(X0) & generous(X0))) [input p12]
21. ~wise(susan) [input hypothesis]
29. ! [X0] : ((~generous(X0) & ~tall(X0)) | quiet(X0)) [ennf transformation 8]
30. ! [X0] : ((~wise(X0) & wise(X0)) | (rich(X0) & creative(X0))) [ennf transformation 9]
33. ! [X0] : ((~funny(X0) & generous(X0)) | (~curious(X0) | ~rich(X0))) [ennf transformation 13]
34. ! [X0] : ((~funny(X0) & generous(X0)) | ~curious(X0) | ~rich(X0)) [flattening 33]
54. ! [X0] : (((old(X0) & ~wise(X0)) | (quiet(X0) | ~brave(X0))) & ((~quiet(X0) & brave(X0)) | (~old(X0) | wise(X0)))) [nnf transformation 6]
55. ! [X0] : (((old(X0) & ~wise(X0)) | quiet(X0) | ~brave(X0)) & ((~quiet(X0) & brave(X0)) | ~old(X0) | wise(X0))) [flattening 54]
56. ! [X0] : (((~brave(X0) | ~old(X0)) | (creative(X0) & curious(X0))) & ((~creative(X0) | ~curious(X0)) | (brave(X0) & old(X0)))) [nnf transformation 7]
57. ! [X0] : ((~brave(X0) | ~old(X0) | (creative(X0) & curious(X0))) & (~creative(X0) | ~curious(X0) | (brave(X0) & old(X0)))) [flattening 56]
60. ! [X0] : ((((wise(X0) | ~curious(X0)) & (~wise(X0) | curious(X0))) | rich(X0)) & (~rich(X0) | ((curious(X0) | wise(X0)) & (~wise(X0) | ~curious(X0))))) [nnf transformation 12]
98. ~quiet(X0) | ~old(X0) | wise(X0) [cnf transformation 55]
101. ~curious(X0) | ~creative(X0) | old(X0) [cnf transformation 57]
106. ~generous(X0) | quiet(X0) [cnf transformation 29]
107. wise(X0) | creative(X0) [cnf transformation 30]
108. wise(X0) | rich(X0) [cnf transformation 30]
109. ~wise(X0) | creative(X0) [cnf transformation 30]
110. ~wise(X0) | rich(X0) [cnf transformation 30]
118. ~rich(X0) | curious(X0) | wise(X0) [cnf transformation 60]
121. generous(X0) | ~curious(X0) | ~rich(X0) [cnf transformation 34]
141. ~wise(susan) [cnf transformation 21]
207. 15 <=> ! [X3] : (wise(X3) | old(X3)) [avatar definition]
208. old(X3) | wise(X3) <- (15) [avatar component clause 207]
222. rich(X0) [subsumption resolution 108,110]
223. creative(X0) [subsumption resolution 107,109]
233. 21 <=> quiet(susan) [avatar definition]
234. quiet(susan) <- (21) [avatar component clause 233]
245. 24 <=> generous(susan) [avatar definition]
246. generous(susan) <- (24) [avatar component clause 245]
255. curious(X0) | wise(X0) [subsumption resolution 118,222]
258. ~curious(X0) | generous(X0) [subsumption resolution 121,222]
321. wise(X0) | generous(X0) [resolution 258,255]
344. ~creative(X0) | old(X0) | wise(X0) [resolution 101,255]
346. old(X0) | wise(X0) [subsumption resolution 344,223]
347. 15 [avatar split clause 346,207]
396. generous(susan) [resolution 321,141]
399. 24 [avatar split clause 396,245]
400. quiet(susan) <- (24) [resolution 246,106]
401. 21 | ~24 [avatar split clause 400,245,233]
402. ~old(susan) | wise(susan) <- (21) [resolution 234,98]
403. ~old(susan) <- (21) [subsumption resolution 402,141]
404. wise(susan) <- (15, 21) [resolution 403,208]
405. $false <- (15, 21) [subsumption resolution 404,141]
406. ~15 | ~21 [avatar contradiction clause 405]
407. $false [avatar sat refutation 347,399,401,406]
% SZS output end Proof for 5724789069667985073890304
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not calm or generous is not humble or not wise and vice versa. Everyone who is both rich and not curious is old or creative and vice versa. If someone is not old then fred is both old and patient. Everyone who is both not tall and not happy is not tall or strong. If fred is either wise or generous then someone is either old or calm and vice versa. If someone is not wise or not creative then someone is both happy and not old. If someone is not strong or not funny then fred is brave or not rich. Everyone who is both calm and not tall is funny and vice versa. If someone is either happy or tall then someone is both curious and not calm. If john is both not kind and humble then john is patient or not rich. Everyone who is either not generous or strong is not brave or quiet and vice versa. Everyone who is either generous or strong is not old or not tall. If someone is calm or not rich then someone is quiet or generous and vice versa. Everyone who is either calm or not brave is both old and not curious and vice versa. Everyone who is not patient is either not humble or not patient and vice versa. Everyone who is either not wise or not strong is both not humble and not happy. John is either patient or not old. Someone is either not tall or creative. Someone is creative or not calm. Someone is kind or not funny. Lucy is either calm or not brave. Alice is tall or not quiet. Someone is either not brave or curious. Fred is wise or not patient. | John is rich. | neutral | (![X]:((~calm(X)|generous(X))<=>(~humble(X)|~wise(X))))&
(![X]:((rich(X)&~curious(X))<=>(old(X)|creative(X))))&
((?[X]:(~old(X)))=>((old(fred)&patient(fred))))&
(![X]:((~tall(X)&~happy(X))=>(~tall(X)|strong(X))))&
(((wise(fred)<~>generous(fred)))<=>(?[X]:((old(X)<~>calm(X)))))&
((?[X]:((~wise(X)|~creative(X))))=>(?[X]:((happy(X)&~old(X)))))&
((?[X]:((~strong(X)|~funny(X))))=>((brave(fred)|~rich(fred))))&
(![X]:((calm(X)&~tall(X))<=>funny(X)))&
((?[X]:((happy(X)<~>tall(X))))=>(?[X]:((curious(X)&~calm(X)))))&
(((~kind(john)&humble(john)))=>((patient(john)|~rich(john))))&
(![X]:((~generous(X)<~>strong(X))<=>(~brave(X)|quiet(X))))&
(![X]:((generous(X)<~>strong(X))=>(~old(X)|~tall(X))))&
((?[X]:((calm(X)|~rich(X))))<=>(?[X]:((quiet(X)|generous(X)))))&
(![X]:((calm(X)<~>~brave(X))<=>(old(X)&~curious(X))))&
(![X]:(~patient(X)<=>(~humble(X)<~>~patient(X))))&
(![X]:((~wise(X)<~>~strong(X))=>(~humble(X)&~happy(X))))&
((patient(john)<~>~old(john)))&
(?[X]:((~tall(X)<~>creative(X))))&
(?[X]:((creative(X)|~calm(X))))&
(?[X]:((kind(X)|~funny(X))))&
((calm(lucy)<~>~brave(lucy)))&
((tall(alice)|~quiet(alice)))&
(?[X]:((~brave(X)<~>curious(X))))&
((wise(fred)|~patient(fred))) | rich(john) | [] | null | 0 |
Everyone who is either not strong or wise is patient and vice versa. Everyone who is creative or not old is funny. If alice is either tall or not generous then someone is not strong or generous and vice versa. Everyone who is not quiet is both not curious and brave and vice versa. If alice is strong then fred is not calm or not kind and vice versa. If fred is both not wise and curious then susan is both not brave and not happy and vice versa. If john is not calm then someone is either curious or rich. Everyone who is wise or not quiet is both not rich and creative. If someone is both calm and patient then alice is not happy or quiet. If susan is not brave or humble then alice is not happy or not generous and vice versa. Everyone who is either humble or quiet is either not patient or curious and vice versa. Everyone who is both not patient and not brave is not curious or not tall and vice versa. Everyone who is either not happy or humble is not rich and vice versa. Everyone who is strong is not curious and vice versa. Everyone who is either old or strong is either not funny or patient and vice versa. Everyone who is both rich and kind is both not quiet and brave. Someone is not old or creative. Someone is both strong and not happy. Someone is either not strong or humble. Someone is either not kind or brave. John is creative. Susan is humble or not wise. Mary is either not curious or brave. John is both creative and patient. | John is wise. | contradiction | (![X]:((~strong(X)<~>wise(X))<=>patient(X)))&
(![X]:((creative(X)|~old(X))=>funny(X)))&
(((tall(alice)<~>~generous(alice)))<=>(?[X]:((~strong(X)|generous(X)))))&
(![X]:(~quiet(X)<=>(~curious(X)&brave(X))))&
((strong(alice))<=>((~calm(fred)|~kind(fred))))&
(((~wise(fred)&curious(fred)))<=>((~brave(susan)&~happy(susan))))&
((~calm(john))=>(?[X]:((curious(X)<~>rich(X)))))&
(![X]:((wise(X)|~quiet(X))=>(~rich(X)&creative(X))))&
((?[X]:((calm(X)&patient(X))))=>((~happy(alice)|quiet(alice))))&
(((~brave(susan)|humble(susan)))<=>((~happy(alice)|~generous(alice))))&
(![X]:((humble(X)<~>quiet(X))<=>(~patient(X)<~>curious(X))))&
(![X]:((~patient(X)&~brave(X))<=>(~curious(X)|~tall(X))))&
(![X]:((~happy(X)<~>humble(X))<=>~rich(X)))&
(![X]:(strong(X)<=>~curious(X)))&
(![X]:((old(X)<~>strong(X))<=>(~funny(X)<~>patient(X))))&
(![X]:((rich(X)&kind(X))=>(~quiet(X)&brave(X))))&
(?[X]:((~old(X)|creative(X))))&
(?[X]:((strong(X)&~happy(X))))&
(?[X]:((~strong(X)<~>humble(X))))&
(?[X]:((~kind(X)<~>brave(X))))&
(creative(john))&
((humble(susan)|~wise(susan)))&
((~curious(mary)<~>brave(mary)))&
((creative(john)&patient(john))) | wise(john) | [
"p0",
"p11",
"p13",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 4749938704478637679126912
% SZS output start Proof for 4749938704478637679126912
1. ! [X0] : ((~strong(X0) <~> wise(X0)) <=> patient(X0)) [input p0]
12. ! [X0] : ((~brave(X0) & ~patient(X0)) <=> (~tall(X0) | ~curious(X0))) [input p11]
14. ! [X0] : (strong(X0) <=> ~curious(X0)) [input p13]
24. patient(john) & creative(john) [input p23]
25. wise(john) [input hypothesis]
33. ! [X0] : ((((~wise(X0) | strong(X0)) & (wise(X0) | ~strong(X0))) | ~patient(X0)) & (patient(X0) | ((~strong(X0) | ~wise(X0)) & (wise(X0) | strong(X0))))) [nnf transformation 1]
50. ! [X0] : (((~brave(X0) & ~patient(X0)) | (tall(X0) & curious(X0))) & ((~tall(X0) | ~curious(X0)) | (brave(X0) | patient(X0)))) [nnf transformation 12]
51. ! [X0] : (((~brave(X0) & ~patient(X0)) | (tall(X0) & curious(X0))) & (~tall(X0) | ~curious(X0) | brave(X0) | patient(X0))) [flattening 50]
53. ! [X0] : ((strong(X0) | curious(X0)) & (~curious(X0) | ~strong(X0))) [nnf transformation 14]
69. ~patient(X0) | strong(X0) | ~wise(X0) [cnf transformation 33]
108. ~patient(X0) | curious(X0) [cnf transformation 51]
116. ~curious(X0) | ~strong(X0) [cnf transformation 53]
140. patient(john) [cnf transformation 24]
141. wise(john) [cnf transformation 25]
295. curious(john) [resolution 108,140]
301. ~strong(john) [resolution 116,295]
312. strong(john) | ~wise(john) [resolution 69,140]
315. ~wise(john) [subsumption resolution 312,301]
316. $false [subsumption resolution 315,141]
% SZS output end Proof for 4749938704478637679126912
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not funny then lucy is both creative and not curious and vice versa.
Everyone who is either kind or not humble is either not humble or calm.
If someone is either not old or not calm then lucy is not kind and vice versa.
If someone is not brave then someone is not brave or wise.
Everyone who is wise or not humble is not rich.
Everyone who is either not rich or rich is either creative or brave.
Everyone who is not creative is either not creative or wise.
Everyone who is both not creative and creative is creative and vice versa.
If paul is patient then someone is either happy or not curious.
If someone is not creative or not kind then someone is not tall.
If someone is both old and not calm then someone is not strong and vice versa.
If susan is old then lucy is either rich or happy.
Everyone who is not tall or patient is not calm.
Everyone who is not rich or not calm is either wise or not rich.
If alice is not humble or not quiet then lucy is tall or not humble and vice versa.
Everyone who is not calm or generous is not funny or not calm and vice versa.
Lucy is quiet or curious.
Lucy is not humble.
Someone is not happy or generous.
Someone is quiet.
Lucy is either not tall or curious.
John is either not funny or not humble.
Someone is not strong.
Susan is old or brave. | Paul is not creative. | entailment | ((?[X]:(~funny(X)))<=>((creative(lucy)&~curious(lucy))))&
(![X]:((kind(X)<~>~humble(X))=>(~humble(X)<~>calm(X))))&
((?[X]:((~old(X)<~>~calm(X))))<=>(~kind(lucy)))&
((?[X]:(~brave(X)))=>(?[X]:((~brave(X)|wise(X)))))&
(![X]:((wise(X)|~humble(X))=>~rich(X)))&
(![X]:((~rich(X)<~>rich(X))=>(creative(X)<~>brave(X))))&
(![X]:(~creative(X)=>(~creative(X)<~>wise(X))))&
(![X]:((~creative(X)&creative(X))<=>creative(X)))&
((patient(paul))=>(?[X]:((happy(X)<~>~curious(X)))))&
((?[X]:((~creative(X)|~kind(X))))=>(?[X]:(~tall(X))))&
((?[X]:((old(X)&~calm(X))))<=>(?[X]:(~strong(X))))&
((old(susan))=>((rich(lucy)<~>happy(lucy))))&
(![X]:((~tall(X)|patient(X))=>~calm(X)))&
(![X]:((~rich(X)|~calm(X))=>(wise(X)<~>~rich(X))))&
(((~humble(alice)|~quiet(alice)))<=>((tall(lucy)|~humble(lucy))))&
(![X]:((~calm(X)|generous(X))<=>(~funny(X)|~calm(X))))&
((quiet(lucy)|curious(lucy)))&
(~humble(lucy))&
(?[X]:((~happy(X)|generous(X))))&
(?[X]:(quiet(X)))&
((~tall(lucy)<~>curious(lucy)))&
((~funny(john)<~>~humble(john)))&
(?[X]:(~strong(X)))&
((old(susan)|brave(susan))) | ~creative(paul) | [
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 7667743462365143270811366
% SZS output start Proof for 7667743462365143270811366
8. ! [X0] : ((creative(X0) & ~creative(X0)) <=> creative(X0)) [input p7]
25. creative(paul) [input hypothesis]
55. ! [X0] : (((creative(X0) & ~creative(X0)) | ~creative(X0)) & (creative(X0) | (~creative(X0) | creative(X0)))) [nnf transformation 8]
56. ! [X0] : (((creative(X0) & ~creative(X0)) | ~creative(X0)) & (creative(X0) | ~creative(X0) | creative(X0))) [flattening 55]
100. ~creative(X0) | ~creative(X0) [cnf transformation 56]
132. creative(paul) [cnf transformation 25]
135. ~creative(X0) [duplicate literal removal 100]
294. $false [subsumption resolution 132,135]
% SZS output end Proof for 7667743462365143270811366
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If john is quiet then someone is either humble or not patient and vice versa.
Everyone who is either wise or happy is both creative and not generous and vice versa.
Everyone who is generous is both not strong and not curious.
If someone is not calm or generous then alice is both wise and not humble.
Everyone who is not strong or not creative is not patient.
If someone is not old or generous then someone is not generous and vice versa.
Everyone who is not quiet or strong is both not rich and not tall.
Everyone who is rich is both rich and not generous and vice versa.
If someone is either not humble or creative then someone is calm and vice versa.
If lucy is not tall then someone is not brave.
If mary is either brave or curious then paul is both not kind and not quiet and vice versa.
Everyone who is both curious and generous is both strong and not old and vice versa.
Everyone who is either wise or creative is both not humble and tall and vice versa.
If someone is quiet then someone is either not rich or not strong.
Everyone who is not funny or brave is not curious.
Everyone who is tall or not happy is both calm and happy and vice versa.
Someone is both happy and not patient.
Someone is both not generous and curious.
Someone is either not rich or not wise.
Someone is not old.
Fred is either not creative or quiet.
Someone is not strong.
Someone is both tall and humble. | Lucy is strong. | contradiction | ((quiet(john))<=>(?[X]:((humble(X)<~>~patient(X)))))&
(![X]:((wise(X)<~>happy(X))<=>(creative(X)&~generous(X))))&
(![X]:(generous(X)=>(~strong(X)&~curious(X))))&
((?[X]:((~calm(X)|generous(X))))=>((wise(alice)&~humble(alice))))&
(![X]:((~strong(X)|~creative(X))=>~patient(X)))&
((?[X]:((~old(X)|generous(X))))<=>(?[X]:(~generous(X))))&
(![X]:((~quiet(X)|strong(X))=>(~rich(X)&~tall(X))))&
(![X]:(rich(X)<=>(rich(X)&~generous(X))))&
((?[X]:((~humble(X)<~>creative(X))))<=>(?[X]:(calm(X))))&
((~tall(lucy))=>(?[X]:(~brave(X))))&
(((brave(mary)<~>curious(mary)))<=>((~kind(paul)&~quiet(paul))))&
(![X]:((curious(X)&generous(X))<=>(strong(X)&~old(X))))&
(![X]:((wise(X)<~>creative(X))<=>(~humble(X)&tall(X))))&
((?[X]:(quiet(X)))=>(?[X]:((~rich(X)<~>~strong(X)))))&
(![X]:((~funny(X)|brave(X))=>~curious(X)))&
(![X]:((tall(X)|~happy(X))<=>(calm(X)&happy(X))))&
(?[X]:((happy(X)&~patient(X))))&
(?[X]:((~generous(X)&curious(X))))&
(?[X]:((~rich(X)<~>~wise(X))))&
(?[X]:(~old(X)))&
((~creative(fred)<~>quiet(fred)))&
(?[X]:(~strong(X)))&
(?[X]:((tall(X)&humble(X)))) | strong(lucy) | [
"p1",
"p2",
"p6",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8784772030571263570152043
% SZS output start Proof for 8784772030571263570152043
2. ! [X0] : ((wise(X0) <~> happy(X0)) <=> (~generous(X0) & creative(X0))) [input p1]
3. ! [X0] : (generous(X0) => (~curious(X0) & ~strong(X0))) [input p2]
7. ! [X0] : ((strong(X0) | ~quiet(X0)) => (~tall(X0) & ~rich(X0))) [input p6]
13. ! [X0] : ((wise(X0) <~> creative(X0)) <=> (tall(X0) & ~humble(X0))) [input p12]
16. ! [X0] : ((~happy(X0) | tall(X0)) <=> (happy(X0) & calm(X0))) [input p15]
24. strong(lucy) [input hypothesis]
29. ! [X0] : ((~curious(X0) & ~strong(X0)) | ~generous(X0)) [ennf transformation 3]
32. ! [X0] : ((~tall(X0) & ~rich(X0)) | (~strong(X0) & quiet(X0))) [ennf transformation 7]
40. ! [X0] : ((((~happy(X0) | ~wise(X0)) & (happy(X0) | wise(X0))) | (generous(X0) | ~creative(X0))) & ((~generous(X0) & creative(X0)) | ((wise(X0) | ~happy(X0)) & (happy(X0) | ~wise(X0))))) [nnf transformation 2]
41. ! [X0] : ((((~happy(X0) | ~wise(X0)) & (happy(X0) | wise(X0))) | generous(X0) | ~creative(X0)) & ((~generous(X0) & creative(X0)) | ((wise(X0) | ~happy(X0)) & (happy(X0) | ~wise(X0))))) [flattening 40]
60. ! [X0] : ((((~creative(X0) | ~wise(X0)) & (creative(X0) | wise(X0))) | (~tall(X0) | humble(X0))) & ((tall(X0) & ~humble(X0)) | ((wise(X0) | ~creative(X0)) & (creative(X0) | ~wise(X0))))) [nnf transformation 13]
61. ! [X0] : ((((~creative(X0) | ~wise(X0)) & (creative(X0) | wise(X0))) | ~tall(X0) | humble(X0)) & ((tall(X0) & ~humble(X0)) | ((wise(X0) | ~creative(X0)) & (creative(X0) | ~wise(X0))))) [flattening 60]
66. ! [X0] : (((~happy(X0) | tall(X0)) | (~happy(X0) | ~calm(X0))) & ((happy(X0) & calm(X0)) | (happy(X0) & ~tall(X0)))) [nnf transformation 16]
67. ! [X0] : ((~happy(X0) | tall(X0) | ~happy(X0) | ~calm(X0)) & ((happy(X0) & calm(X0)) | (happy(X0) & ~tall(X0)))) [flattening 66]
87. ~happy(X0) | wise(X0) | creative(X0) [cnf transformation 41]
91. ~creative(X0) | ~wise(X0) | generous(X0) | ~happy(X0) [cnf transformation 41]
92. ~strong(X0) | ~generous(X0) [cnf transformation 29]
106. ~tall(X0) | ~strong(X0) [cnf transformation 32]
127. ~wise(X0) | creative(X0) | tall(X0) [cnf transformation 61]
128. ~creative(X0) | wise(X0) | tall(X0) [cnf transformation 61]
137. happy(X0) | happy(X0) [cnf transformation 67]
151. strong(lucy) [cnf transformation 24]
152. happy(X0) [duplicate literal removal 137]
241. 21 <=> tall(lucy) [avatar definition]
243. tall(lucy) <- (21) [avatar component clause 241]
306. ~generous(lucy) [resolution 92,151]
319. creative(X0) | wise(X0) [resolution 87,152]
336. wise(X0) | tall(X0) | wise(X0) [resolution 128,319]
337. tall(X0) | wise(X0) [duplicate literal removal 336]
420. ~strong(X3) | wise(X3) [resolution 337,106]
425. wise(lucy) [resolution 420,151]
453. creative(lucy) | tall(lucy) [resolution 425,127]
457. 41 <=> creative(lucy) [avatar definition]
459. creative(lucy) <- (41) [avatar component clause 457]
460. 21 | 41 [avatar split clause 453,457,241]
469. ~strong(lucy) <- (21) [resolution 243,106]
474. $false <- (21) [subsumption resolution 469,151]
475. ~21 [avatar contradiction clause 474]
487. ~wise(lucy) | generous(lucy) | ~happy(lucy) <- (41) [resolution 459,91]
491. generous(lucy) | ~happy(lucy) <- (41) [subsumption resolution 487,425]
492. ~happy(lucy) <- (41) [subsumption resolution 491,306]
493. $false <- (41) [subsumption resolution 492,152]
494. ~41 [avatar contradiction clause 493]
495. $false [avatar sat refutation 460,475,494]
% SZS output end Proof for 8784772030571263570152043
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich or calm then susan is generous or happy. Everyone who is both not humble and patient is both not happy and strong and vice versa. Everyone who is not patient is both not funny and strong. If someone is either patient or not curious then someone is kind and vice versa. If someone is either not old or not funny then fred is either not creative or not rich. Everyone who is either rich or not rich is not creative and vice versa. If susan is patient then someone is funny or not creative. If someone is either curious or funny then someone is both not kind and happy. Everyone who is both curious and rich is not funny or not creative and vice versa. If john is brave or old then john is both not strong and kind and vice versa. If mary is either creative or not quiet then lucy is both generous and not calm and vice versa. Everyone who is either creative or not quiet is both brave and not funny and vice versa. If someone is both tall and not patient then someone is both not rich and not quiet and vice versa. Everyone who is funny is not brave and vice versa. Everyone who is not wise or curious is kind. Everyone who is not humble or curious is generous. Someone is not humble or calm. Alice is not tall. Someone is not brave. Someone is both humble and calm. Alice is either not humble or not calm. Fred is both curious and generous. Someone is not old. Someone is both not brave and not old. | Mary is not brave. | entailment | ((?[X]:((rich(X)|calm(X))))=>((generous(susan)|happy(susan))))&
(![X]:((~humble(X)&patient(X))<=>(~happy(X)&strong(X))))&
(![X]:(~patient(X)=>(~funny(X)&strong(X))))&
((?[X]:((patient(X)<~>~curious(X))))<=>(?[X]:(kind(X))))&
((?[X]:((~old(X)<~>~funny(X))))=>((~creative(fred)<~>~rich(fred))))&
(![X]:((rich(X)<~>~rich(X))<=>~creative(X)))&
((patient(susan))=>(?[X]:((funny(X)|~creative(X)))))&
((?[X]:((curious(X)<~>funny(X))))=>(?[X]:((~kind(X)&happy(X)))))&
(![X]:((curious(X)&rich(X))<=>(~funny(X)|~creative(X))))&
(((brave(john)|old(john)))<=>((~strong(john)&kind(john))))&
(((creative(mary)<~>~quiet(mary)))<=>((generous(lucy)&~calm(lucy))))&
(![X]:((creative(X)<~>~quiet(X))<=>(brave(X)&~funny(X))))&
((?[X]:((tall(X)&~patient(X))))<=>(?[X]:((~rich(X)&~quiet(X)))))&
(![X]:(funny(X)<=>~brave(X)))&
(![X]:((~wise(X)|curious(X))=>kind(X)))&
(![X]:((~humble(X)|curious(X))=>generous(X)))&
(?[X]:((~humble(X)|calm(X))))&
(~tall(alice))&
(?[X]:(~brave(X)))&
(?[X]:((humble(X)&calm(X))))&
((~humble(alice)<~>~calm(alice)))&
((curious(fred)&generous(fred)))&
(?[X]:(~old(X)))&
(?[X]:((~brave(X)&~old(X)))) | ~brave(mary) | [
"p5",
"p7",
"p8",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3351551244573003400209377
% SZS output start Proof for 3351551244573003400209377
6. ! [X0] : ((rich(X0) <~> ~rich(X0)) <=> ~creative(X0)) [input p5]
8. ? [X0] : (curious(X0) <~> funny(X0)) => ? [X0] : (happy(X0) & ~kind(X0)) [input p7]
9. ! [X0] : ((rich(X0) & curious(X0)) <=> (~creative(X0) | ~funny(X0))) [input p8]
14. ! [X0] : (funny(X0) <=> ~brave(X0)) [input p13]
15. ! [X0] : ((curious(X0) | ~wise(X0)) => kind(X0)) [input p14]
25. brave(mary) [input hypothesis]
27. ? [X0] : (curious(X0) <~> funny(X0)) => ? [X1] : (happy(X1) & ~kind(X1)) [rectify 8]
29. ! [X0] : (curious(X0) => kind(X0)) [pure predicate removal 15]
35. ? [X1] : (happy(X1) & ~kind(X1)) | ! [X0] : (curious(X0) <=> funny(X0)) [ennf transformation 27]
36. ! [X0] : (kind(X0) | ~curious(X0)) [ennf transformation 29]
46. ! [X0] : ((((rich(X0) | ~rich(X0)) & (~rich(X0) | rich(X0))) | creative(X0)) & (~creative(X0) | ((rich(X0) | rich(X0)) & (~rich(X0) | ~rich(X0))))) [nnf transformation 6]
49. ? [X1] : (happy(X1) & ~kind(X1)) | ! [X0] : ((curious(X0) | ~funny(X0)) & (funny(X0) | ~curious(X0))) [nnf transformation 35]
50. ? [X0] : (happy(X0) & ~kind(X0)) | ! [X1] : ((curious(X1) | ~funny(X1)) & (funny(X1) | ~curious(X1))) [rectify 49]
51. ? [X0] : (happy(X0) & ~kind(X0)) => (happy(sK3) & ~kind(sK3)) [choice axiom]
52. (happy(sK3) & ~kind(sK3)) | ! [X1] : ((curious(X1) | ~funny(X1)) & (funny(X1) | ~curious(X1))) [skolemisation 50,51]
53. ! [X0] : (((rich(X0) & curious(X0)) | (creative(X0) & funny(X0))) & ((~creative(X0) | ~funny(X0)) | (~rich(X0) | ~curious(X0)))) [nnf transformation 9]
54. ! [X0] : (((rich(X0) & curious(X0)) | (creative(X0) & funny(X0))) & (~creative(X0) | ~funny(X0) | ~rich(X0) | ~curious(X0))) [flattening 53]
66. ! [X0] : ((funny(X0) | brave(X0)) & (~brave(X0) | ~funny(X0))) [nnf transformation 14]
94. ~creative(X0) | ~rich(X0) | ~rich(X0) [cnf transformation 46]
95. ~creative(X0) | rich(X0) | rich(X0) [cnf transformation 46]
99. ~kind(sK3) | funny(X1) | ~curious(X1) [cnf transformation 52]
105. curious(X0) | creative(X0) [cnf transformation 54]
129. ~brave(X0) | ~funny(X0) [cnf transformation 66]
131. kind(X0) | ~curious(X0) [cnf transformation 36]
146. brave(mary) [cnf transformation 25]
147. ~creative(X0) | ~rich(X0) [duplicate literal removal 94]
148. ~creative(X0) | rich(X0) [duplicate literal removal 95]
208. ~creative(X0) [subsumption resolution 147,148]
218. 17 <=> ! [X1] : (funny(X1) | ~curious(X1)) [avatar definition]
219. funny(X1) | ~curious(X1) <- (17) [avatar component clause 218]
222. 18 <=> kind(sK3) [avatar definition]
224. ~kind(sK3) <- (~18) [avatar component clause 222]
226. 17 | ~18 [avatar split clause 99,222,218]
228. curious(X0) [subsumption resolution 105,208]
281. kind(X0) [subsumption resolution 131,228]
304. $false <- (~18) [subsumption resolution 224,281]
305. 18 [avatar contradiction clause 304]
312. funny(X1) <- (17) [subsumption resolution 219,228]
316. ~funny(mary) [resolution 129,146]
317. $false <- (17) [subsumption resolution 316,312]
318. ~17 [avatar contradiction clause 317]
319. $false [avatar sat refutation 226,305,318]
% SZS output end Proof for 3351551244573003400209377
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not creative then fred is either not strong or not curious.
Everyone who is not calm or not curious is either generous or creative.
Everyone who is either not generous or humble is not tall or quiet.
If someone is humble then lucy is humble.
If mary is not humble then susan is both not patient and not quiet and vice versa.
If susan is funny or wise then someone is both not funny and not generous.
Everyone who is wise is not generous and vice versa.
If someone is either calm or humble then fred is not brave or not kind and vice versa.
If alice is both rich and happy then someone is either not patient or not tall.
Everyone who is either wise or generous is both not humble and wise.
Everyone who is not tall or funny is kind or not happy.
If someone is not creative then someone is not quiet.
Everyone who is not quiet or funny is both kind and not tall and vice versa.
Everyone who is both not rich and not curious is not quiet or not calm.
Everyone who is not patient or not wise is creative.
Lucy is either not generous or tall.
Someone is not old.
Someone is either not tall or humble.
Fred is quiet.
Paul is either not funny or not curious.
Alice is not calm.
Someone is either not rich or not strong. | Lucy is not tall. | entailment | ((?[X]:(~creative(X)))=>((~strong(fred)<~>~curious(fred))))&
(![X]:((~calm(X)|~curious(X))=>(generous(X)<~>creative(X))))&
(![X]:((~generous(X)<~>humble(X))=>(~tall(X)|quiet(X))))&
((?[X]:(humble(X)))=>(humble(lucy)))&
((~humble(mary))<=>((~patient(susan)&~quiet(susan))))&
(((funny(susan)|wise(susan)))=>(?[X]:((~funny(X)&~generous(X)))))&
(![X]:(wise(X)<=>~generous(X)))&
((?[X]:((calm(X)<~>humble(X))))<=>((~brave(fred)|~kind(fred))))&
(((rich(alice)&happy(alice)))=>(?[X]:((~patient(X)<~>~tall(X)))))&
(![X]:((wise(X)<~>generous(X))=>(~humble(X)&wise(X))))&
(![X]:((~tall(X)|funny(X))=>(kind(X)|~happy(X))))&
((?[X]:(~creative(X)))=>(?[X]:(~quiet(X))))&
(![X]:((~quiet(X)|funny(X))<=>(kind(X)&~tall(X))))&
(![X]:((~rich(X)&~curious(X))=>(~quiet(X)|~calm(X))))&
(![X]:((~patient(X)|~wise(X))=>creative(X)))&
((~generous(lucy)<~>tall(lucy)))&
(?[X]:(~old(X)))&
(?[X]:((~tall(X)<~>humble(X))))&
(quiet(fred))&
((~funny(paul)<~>~curious(paul)))&
(~calm(alice))&
(?[X]:((~rich(X)<~>~strong(X)))) | ~tall(lucy) | [
"p6",
"p9",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3500230458020833193519481
% SZS output start Proof for 3500230458020833193519481
7. ! [X0] : (wise(X0) <=> ~generous(X0)) [input p6]
10. ! [X0] : ((wise(X0) <~> generous(X0)) => (wise(X0) & ~humble(X0))) [input p9]
16. ~generous(lucy) <~> tall(lucy) [input p15]
23. tall(lucy) [input hypothesis]
34. ! [X0] : ((wise(X0) & ~humble(X0)) | (wise(X0) <=> generous(X0))) [ennf transformation 10]
46. ! [X0] : ((wise(X0) | generous(X0)) & (~generous(X0) | ~wise(X0))) [nnf transformation 7]
52. ! [X0] : ((wise(X0) & ~humble(X0)) | ((wise(X0) | ~generous(X0)) & (generous(X0) | ~wise(X0)))) [nnf transformation 34]
58. (~tall(lucy) | generous(lucy)) & (tall(lucy) | ~generous(lucy)) [nnf transformation 16]
82. ~wise(X0) | ~generous(X0) [cnf transformation 46]
83. wise(X0) | generous(X0) [cnf transformation 46]
93. wise(X0) | wise(X0) | ~generous(X0) [cnf transformation 52]
104. ~tall(lucy) | generous(lucy) [cnf transformation 58]
113. tall(lucy) [cnf transformation 23]
114. wise(X0) | ~generous(X0) [duplicate literal removal 93]
199. wise(X0) [subsumption resolution 114,83]
207. 20 <=> generous(lucy) [avatar definition]
209. generous(lucy) <- (20) [avatar component clause 207]
211. 21 <=> tall(lucy) [avatar definition]
214. 20 | ~21 [avatar split clause 104,211,207]
246. 21 [avatar split clause 113,211]
247. ~generous(X0) [resolution 82,199]
248. $false <- (20) [resolution 247,209]
249. ~20 [avatar contradiction clause 248]
250. $false [avatar sat refutation 214,246,249]
% SZS output end Proof for 3500230458020833193519481
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny is not happy or strong.
Everyone who is creative or not rich is both not rich and happy and vice versa.
If susan is not brave or not calm then someone is either not humble or not strong and vice versa.
Everyone who is not strong is both not calm and rich.
If fred is both not patient and not old then susan is either creative or not rich.
Everyone who is brave is both not strong and not tall and vice versa.
Everyone who is not humble or not rich is both wise and not brave and vice versa.
Everyone who is both generous and not generous is not patient or not happy and vice versa.
Everyone who is not wise or not happy is not old and vice versa.
Everyone who is both curious and not generous is either patient or not old.
If paul is both strong and creative then someone is both kind and not old.
Everyone who is both not humble and old is not old or not curious.
Everyone who is rich is both not tall and creative.
If someone is either not patient or happy then someone is not kind or rich and vice versa.
If paul is both not tall and not kind then someone is either rich or not strong.
If susan is both not funny and creative then susan is wise.
Alice is kind.
Someone is not creative.
Someone is either not strong or not humble.
John is either funny or not humble.
Someone is both not funny and not humble.
Someone is both calm and happy. | Fred is rich. | contradiction | (![X]:(funny(X)=>(~happy(X)|strong(X))))&
(![X]:((creative(X)|~rich(X))<=>(~rich(X)&happy(X))))&
(((~brave(susan)|~calm(susan)))<=>(?[X]:((~humble(X)<~>~strong(X)))))&
(![X]:(~strong(X)=>(~calm(X)&rich(X))))&
(((~patient(fred)&~old(fred)))=>((creative(susan)<~>~rich(susan))))&
(![X]:(brave(X)<=>(~strong(X)&~tall(X))))&
(![X]:((~humble(X)|~rich(X))<=>(wise(X)&~brave(X))))&
(![X]:((generous(X)&~generous(X))<=>(~patient(X)|~happy(X))))&
(![X]:((~wise(X)|~happy(X))<=>~old(X)))&
(![X]:((curious(X)&~generous(X))=>(patient(X)<~>~old(X))))&
(((strong(paul)&creative(paul)))=>(?[X]:((kind(X)&~old(X)))))&
(![X]:((~humble(X)&old(X))=>(~old(X)|~curious(X))))&
(![X]:(rich(X)=>(~tall(X)&creative(X))))&
((?[X]:((~patient(X)<~>happy(X))))<=>(?[X]:((~kind(X)|rich(X)))))&
(((~tall(paul)&~kind(paul)))=>(?[X]:((rich(X)<~>~strong(X)))))&
(((~funny(susan)&creative(susan)))=>(wise(susan)))&
(kind(alice))&
(?[X]:(~creative(X)))&
(?[X]:((~strong(X)<~>~humble(X))))&
((funny(john)<~>~humble(john)))&
(?[X]:((~funny(X)&~humble(X))))&
(?[X]:((calm(X)&happy(X)))) | rich(fred) | [
"p1",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 7332772512124682032518076
% SZS output start Proof for 7332772512124682032518076
2. ! [X0] : ((~rich(X0) | creative(X0)) <=> (happy(X0) & ~rich(X0))) [input p1]
13. ! [X0] : (rich(X0) => (creative(X0) & ~tall(X0))) [input p12]
23. rich(fred) [input hypothesis]
34. ! [X0] : ((creative(X0) & ~tall(X0)) | ~rich(X0)) [ennf transformation 13]
39. ! [X0] : (((~rich(X0) | creative(X0)) | (~happy(X0) | rich(X0))) & ((happy(X0) & ~rich(X0)) | (rich(X0) & ~creative(X0)))) [nnf transformation 2]
40. ! [X0] : ((~rich(X0) | creative(X0) | ~happy(X0) | rich(X0)) & ((happy(X0) & ~rich(X0)) | (rich(X0) & ~creative(X0)))) [flattening 39]
76. ~rich(X0) | ~creative(X0) [cnf transformation 40]
110. creative(X0) | ~rich(X0) [cnf transformation 34]
130. rich(fred) [cnf transformation 23]
200. ~rich(X0) [subsumption resolution 110,76]
247. $false [subsumption resolution 130,200]
% SZS output end Proof for 7332772512124682032518076
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not strong is not humble and vice versa.
Everyone who is both not patient and not happy is both funny and not calm.
Everyone who is either not calm or wise is rich or not curious.
Everyone who is both not patient and humble is either creative or curious and vice versa.
Everyone who is not rich or not curious is not wise.
If someone is not tall then someone is not kind.
If alice is old then someone is not wise or not funny and vice versa.
If someone is not funny then john is both not old and creative.
Everyone who is not calm is kind or curious.
Everyone who is brave is either not calm or strong.
Everyone who is both not happy and curious is strong and vice versa.
If someone is humble or not old then john is both not tall and calm and vice versa.
If someone is both tall and humble then fred is both not old and humble and vice versa.
Everyone who is not old is either strong or not old and vice versa.
If someone is both not happy and not humble then someone is not brave.
Everyone who is not rich or brave is both creative and not generous and vice versa.
Lucy is both not patient and rich.
John is either patient or tall.
Susan is not kind.
Someone is either not old or tall.
Someone is calm or happy.
Someone is either not happy or kind.
Someone is both not kind and not creative. | Alice is not old. | contradiction | (![X]:(~strong(X)<=>~humble(X)))&
(![X]:((~patient(X)&~happy(X))=>(funny(X)&~calm(X))))&
(![X]:((~calm(X)<~>wise(X))=>(rich(X)|~curious(X))))&
(![X]:((~patient(X)&humble(X))<=>(creative(X)<~>curious(X))))&
(![X]:((~rich(X)|~curious(X))=>~wise(X)))&
((?[X]:(~tall(X)))=>(?[X]:(~kind(X))))&
((old(alice))<=>(?[X]:((~wise(X)|~funny(X)))))&
((?[X]:(~funny(X)))=>((~old(john)&creative(john))))&
(![X]:(~calm(X)=>(kind(X)|curious(X))))&
(![X]:(brave(X)=>(~calm(X)<~>strong(X))))&
(![X]:((~happy(X)&curious(X))<=>strong(X)))&
((?[X]:((humble(X)|~old(X))))<=>((~tall(john)&calm(john))))&
((?[X]:((tall(X)&humble(X))))<=>((~old(fred)&humble(fred))))&
(![X]:(~old(X)<=>(strong(X)<~>~old(X))))&
((?[X]:((~happy(X)&~humble(X))))=>(?[X]:(~brave(X))))&
(![X]:((~rich(X)|brave(X))<=>(creative(X)&~generous(X))))&
((~patient(lucy)&rich(lucy)))&
((patient(john)<~>tall(john)))&
(~kind(susan))&
(?[X]:((~old(X)<~>tall(X))))&
(?[X]:((calm(X)|happy(X))))&
(?[X]:((~happy(X)<~>kind(X))))&
(?[X]:((~kind(X)&~creative(X)))) | ~old(alice) | [
"p0",
"p3",
"p4",
"p6",
"p13",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 3035501699894040488782098
% SZS output start Proof for 3035501699894040488782098
1. ! [X0] : (~strong(X0) <=> ~humble(X0)) [input p0]
4. ! [X0] : ((humble(X0) & ~patient(X0)) <=> (creative(X0) <~> curious(X0))) [input p3]
5. ! [X0] : ((~curious(X0) | ~rich(X0)) => ~wise(X0)) [input p4]
7. old(alice) <=> ? [X0] : (~funny(X0) | ~wise(X0)) [input p6]
14. ! [X0] : (~old(X0) <=> (strong(X0) <~> ~old(X0))) [input p13]
23. ? [X0] : (~creative(X0) & ~kind(X0)) [input p22]
24. ~old(alice) [input hypothesis]
31. ! [X0] : (~wise(X0) | (curious(X0) & rich(X0))) [ennf transformation 5]
38. ! [X0] : ((~strong(X0) | humble(X0)) & (~humble(X0) | strong(X0))) [nnf transformation 1]
40. ! [X0] : (((humble(X0) & ~patient(X0)) | ((creative(X0) | ~curious(X0)) & (curious(X0) | ~creative(X0)))) & (((~curious(X0) | ~creative(X0)) & (curious(X0) | creative(X0))) | (~humble(X0) | patient(X0)))) [nnf transformation 4]
41. ! [X0] : (((humble(X0) & ~patient(X0)) | ((creative(X0) | ~curious(X0)) & (curious(X0) | ~creative(X0)))) & (((~curious(X0) | ~creative(X0)) & (curious(X0) | creative(X0))) | ~humble(X0) | patient(X0))) [flattening 40]
45. (old(alice) | ! [X0] : (funny(X0) & wise(X0))) & (? [X0] : (~funny(X0) | ~wise(X0)) | ~old(alice)) [nnf transformation 7]
46. (old(alice) | ! [X0] : (funny(X0) & wise(X0))) & (? [X1] : (~funny(X1) | ~wise(X1)) | ~old(alice)) [rectify 45]
47. ? [X1] : (~funny(X1) | ~wise(X1)) => (~funny(sK1) | ~wise(sK1)) [choice axiom]
48. (old(alice) | ! [X0] : (funny(X0) & wise(X0))) & ((~funny(sK1) | ~wise(sK1)) | ~old(alice)) [skolemisation 46,47]
62. ! [X0] : ((~old(X0) | ((strong(X0) | old(X0)) & (~old(X0) | ~strong(X0)))) & (((old(X0) | ~strong(X0)) & (~old(X0) | strong(X0))) | old(X0))) [nnf transformation 14]
77. ? [X0] : (~creative(X0) & ~kind(X0)) => (~creative(sK8) & ~kind(sK8)) [choice axiom]
78. ~creative(sK8) & ~kind(sK8) [skolemisation 23,77]
79. ~humble(X0) | strong(X0) [cnf transformation 38]
90. ~curious(X0) | creative(X0) | humble(X0) [cnf transformation 41]
92. ~wise(X0) | curious(X0) [cnf transformation 31]
95. old(alice) | wise(X0) [cnf transformation 48]
115. old(X0) | ~strong(X0) | old(X0) [cnf transformation 62]
116. ~old(X0) | ~old(X0) | ~strong(X0) [cnf transformation 62]
135. ~creative(sK8) [cnf transformation 78]
136. ~old(alice) [cnf transformation 24]
137. old(X0) | ~strong(X0) [duplicate literal removal 115]
138. ~old(X0) | ~strong(X0) [duplicate literal removal 116]
151. 4 <=> old(alice) [avatar definition]
156. 5 <=> ! [X0] : wise(X0) [avatar definition]
157. wise(X0) <- (5) [avatar component clause 156]
158. 5 | 4 [avatar split clause 95,151,156]
228. ~strong(X0) [subsumption resolution 137,138]
272. ~4 [avatar split clause 136,151]
284. curious(X0) <- (5) [resolution 92,157]
302. creative(X0) | humble(X0) <- (5) [resolution 90,284]
303. humble(sK8) <- (5) [resolution 302,135]
311. strong(sK8) <- (5) [resolution 303,79]
312. $false <- (5) [subsumption resolution 311,228]
313. ~5 [avatar contradiction clause 312]
314. $false [avatar sat refutation 158,272,313]
% SZS output end Proof for 3035501699894040488782098
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
If alice is either not curious or not generous then alice is either brave or not generous and vice versa.
If mary is either not curious or not old then john is not quiet or humble and vice versa.
If fred is not old or not curious then someone is both not humble and patient and vice versa.
If someone is both not kind and calm then paul is either calm or strong.
Everyone who is either tall or not old is both not generous and creative and vice versa.
Everyone who is not happy or not funny is both kind and creative.
Everyone who is either humble or not funny is either not humble or humble and vice versa.
If someone is not rich or not old then fred is both not brave and strong and vice versa.
Everyone who is kind or quiet is both quiet and not rich.
Everyone who is not brave is generous.
If john is both not brave and not tall then susan is both not happy and creative.
If susan is both not calm and not old then susan is both strong and rich.
If lucy is both not generous and not funny then someone is either not happy or not wise and vice versa.
Everyone who is either happy or not tall is humble or not humble and vice versa.
Everyone who is both quiet and not funny is either not humble or not rich.
If someone is either quiet or not rich then someone is both humble and not patient.
Paul is either not tall or not funny.
Someone is not funny or quiet.
Paul is either not funny or patient.
Mary is both not patient and not rich.
John is not brave or not calm.
John is either brave or not old.
Someone is humble or rich.
Mary is either not generous or brave. | Alice is humble. | entailment | (((~curious(alice)<~>~generous(alice)))<=>((brave(alice)<~>~generous(alice))))&
(((~curious(mary)<~>~old(mary)))<=>((~quiet(john)|humble(john))))&
(((~old(fred)|~curious(fred)))<=>(?[X]:((~humble(X)&patient(X)))))&
((?[X]:((~kind(X)&calm(X))))=>((calm(paul)<~>strong(paul))))&
(![X]:((tall(X)<~>~old(X))<=>(~generous(X)&creative(X))))&
(![X]:((~happy(X)|~funny(X))=>(kind(X)&creative(X))))&
(![X]:((humble(X)<~>~funny(X))<=>(~humble(X)<~>humble(X))))&
((?[X]:((~rich(X)|~old(X))))<=>((~brave(fred)&strong(fred))))&
(![X]:((kind(X)|quiet(X))=>(quiet(X)&~rich(X))))&
(![X]:(~brave(X)=>generous(X)))&
(((~brave(john)&~tall(john)))=>((~happy(susan)&creative(susan))))&
(((~calm(susan)&~old(susan)))=>((strong(susan)&rich(susan))))&
(((~generous(lucy)&~funny(lucy)))<=>(?[X]:((~happy(X)<~>~wise(X)))))&
(![X]:((happy(X)<~>~tall(X))<=>(humble(X)|~humble(X))))&
(![X]:((quiet(X)&~funny(X))=>(~humble(X)<~>~rich(X))))&
((?[X]:((quiet(X)<~>~rich(X))))=>(?[X]:((humble(X)&~patient(X)))))&
((~tall(paul)<~>~funny(paul)))&
(?[X]:((~funny(X)|quiet(X))))&
((~funny(paul)<~>patient(paul)))&
((~patient(mary)&~rich(mary)))&
((~brave(john)|~calm(john)))&
((brave(john)<~>~old(john)))&
(?[X]:((humble(X)|rich(X))))&
((~generous(mary)<~>brave(mary))) | humble(alice) | [
"p5",
"p6",
"p8",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8312767892481935104240567
% SZS output start Proof for 8312767892481935104240567
6. ! [X0] : ((~funny(X0) | ~happy(X0)) => (creative(X0) & kind(X0))) [input p5]
7. ! [X0] : ((humble(X0) <~> ~funny(X0)) <=> (~humble(X0) <~> humble(X0))) [input p6]
9. ! [X0] : ((quiet(X0) | kind(X0)) => (~rich(X0) & quiet(X0))) [input p8]
15. ! [X0] : ((~funny(X0) & quiet(X0)) => (~humble(X0) <~> ~rich(X0))) [input p14]
25. ~humble(alice) [input hypothesis]
28. ! [X0] : ((creative(X0) & kind(X0)) | (funny(X0) & happy(X0))) [ennf transformation 6]
29. ! [X0] : ((~rich(X0) & quiet(X0)) | (~quiet(X0) & ~kind(X0))) [ennf transformation 9]
35. ! [X0] : ((~humble(X0) <~> ~rich(X0)) | (funny(X0) | ~quiet(X0))) [ennf transformation 15]
36. ! [X0] : ((~humble(X0) <~> ~rich(X0)) | funny(X0) | ~quiet(X0)) [flattening 35]
49. ! [X0] : ((((funny(X0) | ~humble(X0)) & (~funny(X0) | humble(X0))) | ((~humble(X0) | ~humble(X0)) & (humble(X0) | humble(X0)))) & (((~humble(X0) | humble(X0)) & (humble(X0) | ~humble(X0))) | ((humble(X0) | funny(X0)) & (~funny(X0) | ~humble(X0))))) [nnf transformation 7]
62. ! [X0] : (((rich(X0) | humble(X0)) & (~rich(X0) | ~humble(X0))) | funny(X0) | ~quiet(X0)) [nnf transformation 36]
103. funny(X0) | kind(X0) [cnf transformation 28]
110. ~funny(X0) | humble(X0) | humble(X0) | humble(X0) [cnf transformation 49]
113. funny(X0) | ~humble(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 49]
119. ~kind(X0) | quiet(X0) [cnf transformation 29]
122. ~rich(X0) | ~quiet(X0) [cnf transformation 29]
141. rich(X0) | humble(X0) | funny(X0) | ~quiet(X0) [cnf transformation 62]
159. ~humble(alice) [cnf transformation 25]
164. ~funny(X0) | humble(X0) [duplicate literal removal 110]
167. ~humble(X0) | funny(X0) [duplicate literal removal 113]
340. humble(X0) | funny(X0) | ~quiet(X0) [subsumption resolution 141,122]
341. ~quiet(X0) | funny(X0) [subsumption resolution 340,167]
415. kind(X1) | humble(X1) [resolution 164,103]
485. humble(X0) | quiet(X0) [resolution 415,119]
502. quiet(X0) | funny(X0) [resolution 485,167]
503. funny(X0) [subsumption resolution 502,341]
547. humble(X0) [resolution 503,164]
557. $false [resolution 547,159]
% SZS output end Proof for 8312767892481935104240567
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is generous is both not calm and kind.
Everyone who is not curious is both not brave and not wise and vice versa.
If someone is both not rich and not strong then lucy is both not generous and quiet and vice versa.
Everyone who is either curious or generous is wise or tall and vice versa.
If someone is both old and not happy then alice is not curious or curious and vice versa.
If lucy is both patient and kind then someone is wise and vice versa.
If someone is not creative or calm then someone is creative or not brave.
If someone is tall or kind then someone is not tall or not funny.
If someone is both not tall and kind then someone is either not old or not generous and vice versa.
Everyone who is both not happy and not tall is not wise or brave.
Everyone who is happy or creative is not happy.
Everyone who is strong is either not calm or not old and vice versa.
If lucy is either not rich or quiet then someone is humble or patient and vice versa.
Everyone who is not patient or not humble is both brave and not quiet.
Everyone who is either kind or not tall is either strong or funny.
If someone is either not tall or generous then someone is tall and vice versa.
Someone is either humble or brave.
Lucy is either humble or wise.
Someone is kind or strong.
Susan is not rich or strong.
Lucy is not patient or not calm.
Susan is both not creative and tall. | Lucy is generous. | neutral | (![X]:(generous(X)=>(~calm(X)&kind(X))))&
(![X]:(~curious(X)<=>(~brave(X)&~wise(X))))&
((?[X]:((~rich(X)&~strong(X))))<=>((~generous(lucy)&quiet(lucy))))&
(![X]:((curious(X)<~>generous(X))<=>(wise(X)|tall(X))))&
((?[X]:((old(X)&~happy(X))))<=>((~curious(alice)|curious(alice))))&
(((patient(lucy)&kind(lucy)))<=>(?[X]:(wise(X))))&
((?[X]:((~creative(X)|calm(X))))=>(?[X]:((creative(X)|~brave(X)))))&
((?[X]:((tall(X)|kind(X))))=>(?[X]:((~tall(X)|~funny(X)))))&
((?[X]:((~tall(X)&kind(X))))<=>(?[X]:((~old(X)<~>~generous(X)))))&
(![X]:((~happy(X)&~tall(X))=>(~wise(X)|brave(X))))&
(![X]:((happy(X)|creative(X))=>~happy(X)))&
(![X]:(strong(X)<=>(~calm(X)<~>~old(X))))&
(((~rich(lucy)<~>quiet(lucy)))<=>(?[X]:((humble(X)|patient(X)))))&
(![X]:((~patient(X)|~humble(X))=>(brave(X)&~quiet(X))))&
(![X]:((kind(X)<~>~tall(X))=>(strong(X)<~>funny(X))))&
((?[X]:((~tall(X)<~>generous(X))))<=>(?[X]:(tall(X))))&
(?[X]:((humble(X)<~>brave(X))))&
((humble(lucy)<~>wise(lucy)))&
(?[X]:((kind(X)|strong(X))))&
((~rich(susan)|strong(susan)))&
((~patient(lucy)|~calm(lucy)))&
((~creative(susan)&tall(susan))) | generous(lucy) | [] | null | 0 |
If someone is funny or generous then lucy is not calm. Everyone who is not tall is not calm or not kind and vice versa. Everyone who is either not strong or not happy is not quiet or kind and vice versa. Everyone who is not wise is old. If someone is both wise and brave then someone is not happy or quiet and vice versa. If someone is either strong or old then fred is strong or not curious and vice versa. Everyone who is humble or not tall is either not quiet or not tall and vice versa. Everyone who is funny or not funny is either strong or not strong. Everyone who is either rich or old is kind. Everyone who is funny or generous is not creative or humble and vice versa. Everyone who is funny is tall or funny and vice versa. Everyone who is either not happy or creative is not kind or curious and vice versa. Everyone who is both not rich and old is kind or not kind. If mary is not curious or kind then mary is both not creative and not rich and vice versa. Everyone who is not curious or tall is either not generous or rich and vice versa. Alice is both happy and rich. Someone is not strong. Someone is not patient. Someone is kind. Someone is both not creative and strong. Someone is either not happy or kind. Paul is both patient and tall. | Paul is wise. | neutral | ((?[X]:((funny(X)|generous(X))))=>(~calm(lucy)))&
(![X]:(~tall(X)<=>(~calm(X)|~kind(X))))&
(![X]:((~strong(X)<~>~happy(X))<=>(~quiet(X)|kind(X))))&
(![X]:(~wise(X)=>old(X)))&
((?[X]:((wise(X)&brave(X))))<=>(?[X]:((~happy(X)|quiet(X)))))&
((?[X]:((strong(X)<~>old(X))))<=>((strong(fred)|~curious(fred))))&
(![X]:((humble(X)|~tall(X))<=>(~quiet(X)<~>~tall(X))))&
(![X]:((funny(X)|~funny(X))=>(strong(X)<~>~strong(X))))&
(![X]:((rich(X)<~>old(X))=>kind(X)))&
(![X]:((funny(X)|generous(X))<=>(~creative(X)|humble(X))))&
(![X]:(funny(X)<=>(tall(X)|funny(X))))&
(![X]:((~happy(X)<~>creative(X))<=>(~kind(X)|curious(X))))&
(![X]:((~rich(X)&old(X))=>(kind(X)|~kind(X))))&
(((~curious(mary)|kind(mary)))<=>((~creative(mary)&~rich(mary))))&
(![X]:((~curious(X)|tall(X))<=>(~generous(X)<~>rich(X))))&
((happy(alice)&rich(alice)))&
(?[X]:(~strong(X)))&
(?[X]:(~patient(X)))&
(?[X]:(kind(X)))&
(?[X]:((~creative(X)&strong(X))))&
(?[X]:((~happy(X)<~>kind(X))))&
((patient(paul)&tall(paul))) | wise(paul) | [] | null | 0 |
Everyone who is either not happy or happy is both not kind and not creative. Everyone who is either brave or generous is both not funny and brave. Everyone who is either not creative or not wise is not wise or not tall and vice versa. Everyone who is both not curious and not old is humble or tall. If lucy is both not quiet and rich then lucy is not rich and vice versa. Everyone who is both rich and not generous is either strong or brave and vice versa. If lucy is not wise or old then someone is brave or not strong and vice versa. If someone is not patient then fred is both not quiet and calm. If lucy is not brave or brave then fred is both old and brave and vice versa. Everyone who is both not rich and not brave is both old and generous. If someone is funny or calm then susan is funny. If someone is not patient or not strong then someone is not generous or not quiet. If someone is not kind then alice is both not calm and quiet. Everyone who is not patient is not strong. If someone is either curious or brave then john is curious or not rich and vice versa. Fred is both not kind and not humble. John is both quiet and not kind. John is generous. Someone is either funny or not strong. Paul is curious. Alice is not humble. Susan is either rich or funny. | Fred is not old. | contradiction | (![X]:((~happy(X)<~>happy(X))=>(~kind(X)&~creative(X))))&
(![X]:((brave(X)<~>generous(X))=>(~funny(X)&brave(X))))&
(![X]:((~creative(X)<~>~wise(X))<=>(~wise(X)|~tall(X))))&
(![X]:((~curious(X)&~old(X))=>(humble(X)|tall(X))))&
(((~quiet(lucy)&rich(lucy)))<=>(~rich(lucy)))&
(![X]:((rich(X)&~generous(X))<=>(strong(X)<~>brave(X))))&
(((~wise(lucy)|old(lucy)))<=>(?[X]:((brave(X)|~strong(X)))))&
((?[X]:(~patient(X)))=>((~quiet(fred)&calm(fred))))&
(((~brave(lucy)|brave(lucy)))<=>((old(fred)&brave(fred))))&
(![X]:((~rich(X)&~brave(X))=>(old(X)&generous(X))))&
((?[X]:((funny(X)|calm(X))))=>(funny(susan)))&
((?[X]:((~patient(X)|~strong(X))))=>(?[X]:((~generous(X)|~quiet(X)))))&
((?[X]:(~kind(X)))=>((~calm(alice)&quiet(alice))))&
(![X]:(~patient(X)=>~strong(X)))&
((?[X]:((curious(X)<~>brave(X))))<=>((curious(john)|~rich(john))))&
((~kind(fred)&~humble(fred)))&
((quiet(john)&~kind(john)))&
(generous(john))&
(?[X]:((funny(X)<~>~strong(X))))&
(curious(paul))&
(~humble(alice))&
((rich(susan)<~>funny(susan))) | ~old(fred) | [
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 1194840595072437792540240
% SZS output start Proof for 1194840595072437792540240
9. (brave(lucy) | ~brave(lucy)) <=> (brave(fred) & old(fred)) [input p8]
23. ~old(fred) [input hypothesis]
52. ((brave(lucy) | ~brave(lucy)) | (~brave(fred) | ~old(fred))) & ((brave(fred) & old(fred)) | (~brave(lucy) & brave(lucy))) [nnf transformation 9]
53. (brave(lucy) | ~brave(lucy) | ~brave(fred) | ~old(fred)) & ((brave(fred) & old(fred)) | (~brave(lucy) & brave(lucy))) [flattening 52]
94. old(fred) | brave(lucy) [cnf transformation 53]
95. old(fred) | ~brave(lucy) [cnf transformation 53]
121. ~old(fred) [cnf transformation 23]
165. 6 <=> brave(lucy) [avatar definition]
175. 8 <=> old(fred) [avatar definition]
178. ~6 | 8 [avatar split clause 95,175,165]
179. 6 | 8 [avatar split clause 94,175,165]
243. ~8 [avatar split clause 121,175]
244. $false [avatar sat refutation 178,179,243]
% SZS output end Proof for 1194840595072437792540240
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not humble or curious is kind or generous.
If someone is both not brave and creative then alice is either strong or not humble and vice versa.
Everyone who is quiet or happy is not rich or not happy and vice versa.
Everyone who is either not kind or not creative is kind or not old and vice versa.
If paul is tall then someone is not humble or patient.
Everyone who is either humble or old is both not quiet and generous.
If lucy is either not rich or creative then someone is calm and vice versa.
Everyone who is old or not patient is generous.
If someone is either not rich or wise then someone is not happy and vice versa.
If alice is both not old and rich then someone is not humble.
Everyone who is either not tall or not generous is either creative or not rich and vice versa.
Everyone who is not strong or not quiet is both brave and not humble and vice versa.
Everyone who is strong or not creative is creative or not calm.
Everyone who is either not curious or not old is either happy or not generous and vice versa.
If someone is not patient or not brave then someone is not curious and vice versa.
Someone is either not wise or not generous.
Someone is not happy.
Someone is not strong.
Someone is either not kind or old.
John is not patient.
Someone is both quiet and not generous.
Someone is both not happy and tall. | Alice is not rich. | neutral | (![X]:((~humble(X)|curious(X))=>(kind(X)|generous(X))))&
((?[X]:((~brave(X)&creative(X))))<=>((strong(alice)<~>~humble(alice))))&
(![X]:((quiet(X)|happy(X))<=>(~rich(X)|~happy(X))))&
(![X]:((~kind(X)<~>~creative(X))<=>(kind(X)|~old(X))))&
((tall(paul))=>(?[X]:((~humble(X)|patient(X)))))&
(![X]:((humble(X)<~>old(X))=>(~quiet(X)&generous(X))))&
(((~rich(lucy)<~>creative(lucy)))<=>(?[X]:(calm(X))))&
(![X]:((old(X)|~patient(X))=>generous(X)))&
((?[X]:((~rich(X)<~>wise(X))))<=>(?[X]:(~happy(X))))&
(((~old(alice)&rich(alice)))=>(?[X]:(~humble(X))))&
(![X]:((~tall(X)<~>~generous(X))<=>(creative(X)<~>~rich(X))))&
(![X]:((~strong(X)|~quiet(X))<=>(brave(X)&~humble(X))))&
(![X]:((strong(X)|~creative(X))=>(creative(X)|~calm(X))))&
(![X]:((~curious(X)<~>~old(X))<=>(happy(X)<~>~generous(X))))&
((?[X]:((~patient(X)|~brave(X))))<=>(?[X]:(~curious(X))))&
(?[X]:((~wise(X)<~>~generous(X))))&
(?[X]:(~happy(X)))&
(?[X]:(~strong(X)))&
(?[X]:((~kind(X)<~>old(X))))&
(~patient(john))&
(?[X]:((quiet(X)&~generous(X))))&
(?[X]:((~happy(X)&tall(X)))) | ~rich(alice) | [] | null | 0 |
If someone is not tall or not brave then lucy is rich or kind and vice versa. If mary is both not humble and not tall then mary is not calm or not wise and vice versa. Everyone who is either kind or not wise is curious or not old and vice versa. If someone is not strong then someone is quiet. Everyone who is both not curious and quiet is not old and vice versa. Everyone who is both curious and calm is either not calm or not old and vice versa. Everyone who is either funny or not brave is either not quiet or not kind and vice versa. Everyone who is rich or humble is patient or not tall. Everyone who is both patient and humble is not happy. If someone is not tall or not brave then someone is either not tall or not funny. If someone is strong then someone is kind and vice versa. If fred is either tall or humble then alice is wise or not wise and vice versa. Everyone who is brave is both quiet and wise. If paul is not old or humble then john is happy or tall. Everyone who is old is either kind or brave. Everyone who is either not wise or not patient is not patient and vice versa. Fred is not curious. Someone is not patient. Someone is not quiet or funny. Susan is generous. Alice is both tall and humble. Mary is creative or humble. Someone is both tall and not funny. | Mary is kind. | entailment | ((?[X]:((~tall(X)|~brave(X))))<=>((rich(lucy)|kind(lucy))))&
(((~humble(mary)&~tall(mary)))<=>((~calm(mary)|~wise(mary))))&
(![X]:((kind(X)<~>~wise(X))<=>(curious(X)|~old(X))))&
((?[X]:(~strong(X)))=>(?[X]:(quiet(X))))&
(![X]:((~curious(X)&quiet(X))<=>~old(X)))&
(![X]:((curious(X)&calm(X))<=>(~calm(X)<~>~old(X))))&
(![X]:((funny(X)<~>~brave(X))<=>(~quiet(X)<~>~kind(X))))&
(![X]:((rich(X)|humble(X))=>(patient(X)|~tall(X))))&
(![X]:((patient(X)&humble(X))=>~happy(X)))&
((?[X]:((~tall(X)|~brave(X))))=>(?[X]:((~tall(X)<~>~funny(X)))))&
((?[X]:(strong(X)))<=>(?[X]:(kind(X))))&
(((tall(fred)<~>humble(fred)))<=>((wise(alice)|~wise(alice))))&
(![X]:(brave(X)=>(quiet(X)&wise(X))))&
(((~old(paul)|humble(paul)))=>((happy(john)|tall(john))))&
(![X]:(old(X)=>(kind(X)<~>brave(X))))&
(![X]:((~wise(X)<~>~patient(X))<=>~patient(X)))&
(~curious(fred))&
(?[X]:(~patient(X)))&
(?[X]:((~quiet(X)|funny(X))))&
(generous(susan))&
((tall(alice)&humble(alice)))&
((creative(mary)|humble(mary)))&
(?[X]:((tall(X)&~funny(X)))) | kind(mary) | [
"p2",
"p4",
"p5",
"p12",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6984677198013512021588326
% SZS output start Proof for 6984677198013512021588326
3. ! [X0] : ((kind(X0) <~> ~wise(X0)) <=> (~old(X0) | curious(X0))) [input p2]
5. ! [X0] : ((quiet(X0) & ~curious(X0)) <=> ~old(X0)) [input p4]
6. ! [X0] : ((calm(X0) & curious(X0)) <=> (~calm(X0) <~> ~old(X0))) [input p5]
13. ! [X0] : (brave(X0) => (wise(X0) & quiet(X0))) [input p12]
15. ! [X0] : (old(X0) => (kind(X0) <~> brave(X0))) [input p14]
16. ! [X0] : ((~wise(X0) <~> ~patient(X0)) <=> ~patient(X0)) [input p15]
24. ~kind(mary) [input hypothesis]
36. ! [X0] : ((wise(X0) & quiet(X0)) | ~brave(X0)) [ennf transformation 13]
39. ! [X0] : ((kind(X0) <~> brave(X0)) | ~old(X0)) [ennf transformation 15]
47. ! [X0] : ((((wise(X0) | ~kind(X0)) & (~wise(X0) | kind(X0))) | (old(X0) & ~curious(X0))) & ((~old(X0) | curious(X0)) | ((kind(X0) | wise(X0)) & (~wise(X0) | ~kind(X0))))) [nnf transformation 3]
48. ! [X0] : ((((wise(X0) | ~kind(X0)) & (~wise(X0) | kind(X0))) | (old(X0) & ~curious(X0))) & (~old(X0) | curious(X0) | ((kind(X0) | wise(X0)) & (~wise(X0) | ~kind(X0))))) [flattening 47]
52. ! [X0] : (((quiet(X0) & ~curious(X0)) | old(X0)) & (~old(X0) | (~quiet(X0) | curious(X0)))) [nnf transformation 5]
53. ! [X0] : (((quiet(X0) & ~curious(X0)) | old(X0)) & (~old(X0) | ~quiet(X0) | curious(X0))) [flattening 52]
54. ! [X0] : (((calm(X0) & curious(X0)) | ((~calm(X0) | old(X0)) & (~old(X0) | calm(X0)))) & (((old(X0) | calm(X0)) & (~old(X0) | ~calm(X0))) | (~calm(X0) | ~curious(X0)))) [nnf transformation 6]
55. ! [X0] : (((calm(X0) & curious(X0)) | ((~calm(X0) | old(X0)) & (~old(X0) | calm(X0)))) & (((old(X0) | calm(X0)) & (~old(X0) | ~calm(X0))) | ~calm(X0) | ~curious(X0))) [flattening 54]
68. ! [X0] : (((~brave(X0) | ~kind(X0)) & (brave(X0) | kind(X0))) | ~old(X0)) [nnf transformation 39]
69. ! [X0] : ((((patient(X0) | wise(X0)) & (~patient(X0) | ~wise(X0))) | patient(X0)) & (~patient(X0) | ((~wise(X0) | patient(X0)) & (~patient(X0) | wise(X0))))) [nnf transformation 16]
88. ~wise(X0) | kind(X0) | old(X0) [cnf transformation 48]
92. ~quiet(X0) | ~old(X0) | curious(X0) [cnf transformation 53]
93. ~curious(X0) | old(X0) [cnf transformation 53]
95. ~old(X0) | ~calm(X0) | ~calm(X0) | ~curious(X0) [cnf transformation 55]
98. curious(X0) | ~calm(X0) | old(X0) [cnf transformation 55]
99. calm(X0) | ~old(X0) | calm(X0) [cnf transformation 55]
124. ~brave(X0) | quiet(X0) [cnf transformation 36]
128. ~old(X0) | kind(X0) | brave(X0) [cnf transformation 68]
130. ~patient(X0) | ~patient(X0) | wise(X0) [cnf transformation 69]
133. patient(X0) | wise(X0) | patient(X0) [cnf transformation 69]
141. ~kind(mary) [cnf transformation 24]
142. ~patient(X0) | wise(X0) [duplicate literal removal 130]
143. patient(X0) | wise(X0) [duplicate literal removal 133]
144. ~old(X0) | ~calm(X0) | ~curious(X0) [duplicate literal removal 95]
145. ~old(X0) | calm(X0) [duplicate literal removal 99]
182. 9 <=> calm(mary) [avatar definition]
183. ~calm(mary) <- (~9) [avatar component clause 182]
184. calm(mary) <- (9) [avatar component clause 182]
201. ~calm(X0) | old(X0) [subsumption resolution 98,93]
202. ~curious(X0) | ~calm(X0) [subsumption resolution 144,93]
265. wise(X0) [subsumption resolution 142,143]
289. old(X0) | kind(X0) [resolution 88,265]
290. calm(X0) | kind(X0) [resolution 289,145]
291. kind(mary) <- (~9) [resolution 290,183]
293. $false <- (~9) [subsumption resolution 291,141]
294. 9 [avatar contradiction clause 293]
297. old(mary) <- (9) [resolution 184,201]
324. kind(X0) | brave(X0) | kind(X0) [resolution 128,289]
326. kind(X0) | brave(X0) [duplicate literal removal 324]
357. brave(mary) [resolution 326,141]
368. quiet(mary) [resolution 357,124]
378. ~old(mary) | curious(mary) [resolution 368,92]
379. curious(mary) <- (9) [subsumption resolution 378,297]
404. ~calm(mary) <- (9) [resolution 379,202]
409. $false <- (9) [subsumption resolution 404,184]
410. ~9 [avatar contradiction clause 409]
411. $false [avatar sat refutation 294,410]
% SZS output end Proof for 6984677198013512021588326
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise or not humble then someone is both not creative and tall and vice versa.
If someone is old or not kind then someone is patient or not humble.
Everyone who is not happy or rich is kind and vice versa.
Everyone who is not wise is not wise or curious and vice versa.
Everyone who is brave is both not calm and strong.
Everyone who is both not tall and happy is both not rich and not happy.
Everyone who is both not strong and funny is generous or not happy.
If paul is either not curious or rich then someone is both curious and not funny.
Everyone who is not humble is either not calm or happy and vice versa.
Everyone who is not quiet is either not kind or not quiet.
Everyone who is generous is both creative and not rich.
Everyone who is not old is not generous or patient and vice versa.
If alice is not generous then someone is not happy and vice versa.
If someone is both not generous and not old then someone is creative.
If john is happy or old then someone is not curious or not tall.
If mary is not generous or funny then someone is both patient and not old.
John is both not humble and curious.
Someone is both rich and not humble.
John is not rich or wise.
Mary is either not strong or kind.
Someone is wise.
Mary is not patient or old.
Someone is not brave.
Someone is not funny or not strong. | Alice is not generous. | neutral | ((?[X]:((~wise(X)|~humble(X))))<=>(?[X]:((~creative(X)&tall(X)))))&
((?[X]:((old(X)|~kind(X))))=>(?[X]:((patient(X)|~humble(X)))))&
(![X]:((~happy(X)|rich(X))<=>kind(X)))&
(![X]:(~wise(X)<=>(~wise(X)|curious(X))))&
(![X]:(brave(X)=>(~calm(X)&strong(X))))&
(![X]:((~tall(X)&happy(X))=>(~rich(X)&~happy(X))))&
(![X]:((~strong(X)&funny(X))=>(generous(X)|~happy(X))))&
(((~curious(paul)<~>rich(paul)))=>(?[X]:((curious(X)&~funny(X)))))&
(![X]:(~humble(X)<=>(~calm(X)<~>happy(X))))&
(![X]:(~quiet(X)=>(~kind(X)<~>~quiet(X))))&
(![X]:(generous(X)=>(creative(X)&~rich(X))))&
(![X]:(~old(X)<=>(~generous(X)|patient(X))))&
((~generous(alice))<=>(?[X]:(~happy(X))))&
((?[X]:((~generous(X)&~old(X))))=>(?[X]:(creative(X))))&
(((happy(john)|old(john)))=>(?[X]:((~curious(X)|~tall(X)))))&
(((~generous(mary)|funny(mary)))=>(?[X]:((patient(X)&~old(X)))))&
((~humble(john)&curious(john)))&
(?[X]:((rich(X)&~humble(X))))&
((~rich(john)|wise(john)))&
((~strong(mary)<~>kind(mary)))&
(?[X]:(wise(X)))&
((~patient(mary)|old(mary)))&
(?[X]:(~brave(X)))&
(?[X]:((~funny(X)|~strong(X)))) | ~generous(alice) | [] | null | 0 |
Everyone who is brave or not generous is not calm and vice versa.
Everyone who is not wise or not calm is both not brave and brave and vice versa.
If fred is either not calm or creative then someone is either happy or curious and vice versa.
Everyone who is rich or strong is kind or not quiet.
Everyone who is not quiet is patient or not calm.
If john is either not quiet or not funny then alice is either happy or wise.
If someone is either happy or not humble then someone is both wise and strong and vice versa.
If alice is either not kind or strong then mary is either generous or not patient and vice versa.
If fred is not kind then john is not quiet and vice versa.
If someone is both patient and generous then someone is creative or generous and vice versa.
Everyone who is either not calm or not strong is both not generous and wise.
If fred is either not wise or humble then paul is both tall and curious and vice versa.
Everyone who is funny or wise is either not old or not patient.
If john is not wise or wise then susan is both strong and wise.
If someone is either not humble or not curious then paul is either happy or patient and vice versa.
John is either not wise or not kind.
Fred is either not kind or not curious.
Someone is rich or wise.
Lucy is either not creative or rich.
Someone is creative.
John is creative or not patient.
Lucy is creative.
Paul is kind. | Fred is not quiet. | entailment | (![X]:((brave(X)|~generous(X))<=>~calm(X)))&
(![X]:((~wise(X)|~calm(X))<=>(~brave(X)&brave(X))))&
(((~calm(fred)<~>creative(fred)))<=>(?[X]:((happy(X)<~>curious(X)))))&
(![X]:((rich(X)|strong(X))=>(kind(X)|~quiet(X))))&
(![X]:(~quiet(X)=>(patient(X)|~calm(X))))&
(((~quiet(john)<~>~funny(john)))=>((happy(alice)<~>wise(alice))))&
((?[X]:((happy(X)<~>~humble(X))))<=>(?[X]:((wise(X)&strong(X)))))&
(((~kind(alice)<~>strong(alice)))<=>((generous(mary)<~>~patient(mary))))&
((~kind(fred))<=>(~quiet(john)))&
((?[X]:((patient(X)&generous(X))))<=>(?[X]:((creative(X)|generous(X)))))&
(![X]:((~calm(X)<~>~strong(X))=>(~generous(X)&wise(X))))&
(((~wise(fred)<~>humble(fred)))<=>((tall(paul)&curious(paul))))&
(![X]:((funny(X)|wise(X))=>(~old(X)<~>~patient(X))))&
(((~wise(john)|wise(john)))=>((strong(susan)&wise(susan))))&
((?[X]:((~humble(X)<~>~curious(X))))<=>((happy(paul)<~>patient(paul))))&
((~wise(john)<~>~kind(john)))&
((~kind(fred)<~>~curious(fred)))&
(?[X]:((rich(X)|wise(X))))&
((~creative(lucy)<~>rich(lucy)))&
(?[X]:(creative(X)))&
((creative(john)|~patient(john)))&
(creative(lucy))&
(kind(paul)) | ~quiet(fred) | [
"p0",
"p1",
"p3",
"p8",
"p10",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 185826388987063878617494
% SZS output start Proof for 185826388987063878617494
1. ! [X0] : ((~generous(X0) | brave(X0)) <=> ~calm(X0)) [input p0]
2. ! [X0] : ((~calm(X0) | ~wise(X0)) <=> (brave(X0) & ~brave(X0))) [input p1]
4. ! [X0] : ((strong(X0) | rich(X0)) => (~quiet(X0) | kind(X0))) [input p3]
9. ~kind(fred) <=> ~quiet(john) [input p8]
11. ! [X0] : ((~calm(X0) <~> ~strong(X0)) => (wise(X0) & ~generous(X0))) [input p10]
16. ~wise(john) <~> ~kind(john) [input p15]
24. quiet(fred) [input hypothesis]
27. ! [X0] : ((~quiet(X0) | kind(X0)) | (~strong(X0) & ~rich(X0))) [ennf transformation 4]
28. ! [X0] : (~quiet(X0) | kind(X0) | (~strong(X0) & ~rich(X0))) [flattening 27]
32. ! [X0] : ((wise(X0) & ~generous(X0)) | (~calm(X0) <=> ~strong(X0))) [ennf transformation 11]
35. ! [X0] : (((~generous(X0) | brave(X0)) | calm(X0)) & (~calm(X0) | (generous(X0) & ~brave(X0)))) [nnf transformation 1]
36. ! [X0] : ((~generous(X0) | brave(X0) | calm(X0)) & (~calm(X0) | (generous(X0) & ~brave(X0)))) [flattening 35]
37. ! [X0] : (((~calm(X0) | ~wise(X0)) | (~brave(X0) | brave(X0))) & ((brave(X0) & ~brave(X0)) | (calm(X0) & wise(X0)))) [nnf transformation 2]
38. ! [X0] : ((~calm(X0) | ~wise(X0) | ~brave(X0) | brave(X0)) & ((brave(X0) & ~brave(X0)) | (calm(X0) & wise(X0)))) [flattening 37]
50. (~kind(fred) | quiet(john)) & (~quiet(john) | kind(fred)) [nnf transformation 9]
56. ! [X0] : ((wise(X0) & ~generous(X0)) | ((~calm(X0) | strong(X0)) & (~strong(X0) | calm(X0)))) [nnf transformation 32]
64. (kind(john) | wise(john)) & (~kind(john) | ~wise(john)) [nnf transformation 16]
72. ~calm(X0) | generous(X0) [cnf transformation 36]
74. ~brave(X0) | wise(X0) [cnf transformation 38]
75. ~brave(X0) | calm(X0) [cnf transformation 38]
76. wise(X0) | brave(X0) [cnf transformation 38]
77. calm(X0) | brave(X0) [cnf transformation 38]
88. ~quiet(X0) | kind(X0) | ~strong(X0) [cnf transformation 28]
109. ~kind(fred) | quiet(john) [cnf transformation 50]
116. ~generous(X0) | ~calm(X0) | strong(X0) [cnf transformation 56]
141. ~kind(john) | ~wise(john) [cnf transformation 64]
152. quiet(fred) [cnf transformation 24]
153. calm(X0) [subsumption resolution 75,77]
154. wise(X0) [subsumption resolution 74,76]
188. 7 <=> quiet(john) [avatar definition]
189. quiet(john) <- (7) [avatar component clause 188]
250. 19 <=> kind(fred) [avatar definition]
253. 7 | ~19 [avatar split clause 109,250,188]
285. ~generous(X0) | strong(X0) [subsumption resolution 116,153]
337. ~kind(john) [subsumption resolution 141,154]
371. generous(X0) [resolution 72,153]
390. strong(X0) [resolution 285,371]
399. kind(fred) | ~strong(fred) [resolution 88,152]
400. kind(john) | ~strong(john) <- (7) [resolution 88,189]
401. ~strong(john) <- (7) [subsumption resolution 400,337]
402. $false <- (7) [subsumption resolution 401,390]
403. ~7 [avatar contradiction clause 402]
405. kind(fred) [subsumption resolution 399,390]
406. 19 [avatar split clause 405,250]
412. $false [avatar sat refutation 253,403,406]
% SZS output end Proof for 185826388987063878617494
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is curious or strong then fred is brave. Everyone who is brave is not humble and vice versa. If lucy is not funny or strong then fred is not rich. Everyone who is either not brave or old is either not funny or not tall and vice versa. If alice is both not kind and not funny then someone is either not quiet or not humble. If lucy is not generous then paul is either not funny or not rich and vice versa. Everyone who is both not old and not curious is not rich or generous and vice versa. Everyone who is both not old and not curious is not kind or not quiet. If fred is not brave or humble then alice is not wise or humble. Everyone who is not rich or not quiet is not patient. Everyone who is tall or quiet is curious and vice versa. Everyone who is either not strong or not calm is not happy and vice versa. Everyone who is not happy or calm is not calm or curious. Everyone who is not funny or patient is both brave and creative. Everyone who is both not tall and wise is kind or not creative and vice versa. If john is both not old and not strong then paul is happy. Someone is either not tall or humble. Fred is not funny. Alice is either not quiet or brave. Someone is kind or wise. Someone is either not old or not quiet. Fred is either not quiet or kind. Someone is tall or creative. Alice is happy or not kind. | Alice is funny. | neutral | ((?[X]:((curious(X)|strong(X))))=>(brave(fred)))&
(![X]:(brave(X)<=>~humble(X)))&
(((~funny(lucy)|strong(lucy)))=>(~rich(fred)))&
(![X]:((~brave(X)<~>old(X))<=>(~funny(X)<~>~tall(X))))&
(((~kind(alice)&~funny(alice)))=>(?[X]:((~quiet(X)<~>~humble(X)))))&
((~generous(lucy))<=>((~funny(paul)<~>~rich(paul))))&
(![X]:((~old(X)&~curious(X))<=>(~rich(X)|generous(X))))&
(![X]:((~old(X)&~curious(X))=>(~kind(X)|~quiet(X))))&
(((~brave(fred)|humble(fred)))=>((~wise(alice)|humble(alice))))&
(![X]:((~rich(X)|~quiet(X))=>~patient(X)))&
(![X]:((tall(X)|quiet(X))<=>curious(X)))&
(![X]:((~strong(X)<~>~calm(X))<=>~happy(X)))&
(![X]:((~happy(X)|calm(X))=>(~calm(X)|curious(X))))&
(![X]:((~funny(X)|patient(X))=>(brave(X)&creative(X))))&
(![X]:((~tall(X)&wise(X))<=>(kind(X)|~creative(X))))&
(((~old(john)&~strong(john)))=>(happy(paul)))&
(?[X]:((~tall(X)<~>humble(X))))&
(~funny(fred))&
((~quiet(alice)<~>brave(alice)))&
(?[X]:((kind(X)|wise(X))))&
(?[X]:((~old(X)<~>~quiet(X))))&
((~quiet(fred)<~>kind(fred)))&
(?[X]:((tall(X)|creative(X))))&
((happy(alice)|~kind(alice))) | funny(alice) | [] | null | 0 |
If lucy is not patient or curious then lucy is calm. Everyone who is brave or wise is not tall or patient and vice versa. Everyone who is not wise or not generous is both not wise and not funny. If someone is not kind then someone is both quiet and not quiet and vice versa. Everyone who is both not wise and not calm is both not tall and not happy and vice versa. If someone is quiet then fred is either strong or brave. If someone is both not humble and not tall then someone is patient or kind. If someone is not wise or humble then susan is not curious or old. Everyone who is either not calm or kind is either not humble or not quiet and vice versa. Everyone who is rich or strong is both not calm and calm and vice versa. Everyone who is either patient or happy is either quiet or kind. If someone is not kind or not happy then susan is either not humble or not rich. If fred is both happy and rich then someone is both wise and calm. Everyone who is both not kind and happy is rich. If alice is either patient or not quiet then someone is tall and vice versa. Everyone who is either not funny or rich is quiet. Someone is not strong or not funny. Lucy is both calm and not quiet. Someone is not calm or generous. Mary is not old. Someone is both not tall and not happy. Someone is both kind and not humble. Someone is either humble or not generous. Someone is not quiet. | Fred is not brave. | contradiction | (((~patient(lucy)|curious(lucy)))=>(calm(lucy)))&
(![X]:((brave(X)|wise(X))<=>(~tall(X)|patient(X))))&
(![X]:((~wise(X)|~generous(X))=>(~wise(X)&~funny(X))))&
((?[X]:(~kind(X)))<=>(?[X]:((quiet(X)&~quiet(X)))))&
(![X]:((~wise(X)&~calm(X))<=>(~tall(X)&~happy(X))))&
((?[X]:(quiet(X)))=>((strong(fred)<~>brave(fred))))&
((?[X]:((~humble(X)&~tall(X))))=>(?[X]:((patient(X)|kind(X)))))&
((?[X]:((~wise(X)|humble(X))))=>((~curious(susan)|old(susan))))&
(![X]:((~calm(X)<~>kind(X))<=>(~humble(X)<~>~quiet(X))))&
(![X]:((rich(X)|strong(X))<=>(~calm(X)&calm(X))))&
(![X]:((patient(X)<~>happy(X))=>(quiet(X)<~>kind(X))))&
((?[X]:((~kind(X)|~happy(X))))=>((~humble(susan)<~>~rich(susan))))&
(((happy(fred)&rich(fred)))=>(?[X]:((wise(X)&calm(X)))))&
(![X]:((~kind(X)&happy(X))=>rich(X)))&
(((patient(alice)<~>~quiet(alice)))<=>(?[X]:(tall(X))))&
(![X]:((~funny(X)<~>rich(X))=>quiet(X)))&
(?[X]:((~strong(X)|~funny(X))))&
((calm(lucy)&~quiet(lucy)))&
(?[X]:((~calm(X)|generous(X))))&
(~old(mary))&
(?[X]:((~tall(X)&~happy(X))))&
(?[X]:((kind(X)&~humble(X))))&
(?[X]:((humble(X)<~>~generous(X))))&
(?[X]:(~quiet(X))) | ~brave(fred) | [
"p2",
"p4",
"p5",
"p9",
"p15",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 3756703155341831905899550
% SZS output start Proof for 3756703155341831905899550
3. ! [X0] : ((~generous(X0) | ~wise(X0)) => (~funny(X0) & ~wise(X0))) [input p2]
5. ! [X0] : ((~calm(X0) & ~wise(X0)) <=> (~happy(X0) & ~tall(X0))) [input p4]
6. ? [X0] : quiet(X0) => (strong(fred) <~> brave(fred)) [input p5]
10. ! [X0] : ((strong(X0) | rich(X0)) <=> (calm(X0) & ~calm(X0))) [input p9]
16. ! [X0] : ((~funny(X0) <~> rich(X0)) => quiet(X0)) [input p15]
21. ? [X0] : (~happy(X0) & ~tall(X0)) [input p20]
25. ~brave(fred) [input hypothesis]
32. ! [X0] : ((~funny(X0) & ~wise(X0)) | (generous(X0) & wise(X0))) [ennf transformation 3]
33. (strong(fred) <~> brave(fred)) | ! [X0] : ~quiet(X0) [ennf transformation 6]
41. ! [X0] : (quiet(X0) | (~funny(X0) <=> rich(X0))) [ennf transformation 16]
49. ! [X0] : (((~calm(X0) & ~wise(X0)) | (happy(X0) | tall(X0))) & ((~happy(X0) & ~tall(X0)) | (calm(X0) | wise(X0)))) [nnf transformation 5]
50. ! [X0] : (((~calm(X0) & ~wise(X0)) | happy(X0) | tall(X0)) & ((~happy(X0) & ~tall(X0)) | calm(X0) | wise(X0))) [flattening 49]
51. ((~brave(fred) | ~strong(fred)) & (brave(fred) | strong(fred))) | ! [X0] : ~quiet(X0) [nnf transformation 33]
56. ! [X0] : (((strong(X0) | rich(X0)) | (~calm(X0) | calm(X0))) & ((calm(X0) & ~calm(X0)) | (~strong(X0) & ~rich(X0)))) [nnf transformation 10]
57. ! [X0] : ((strong(X0) | rich(X0) | ~calm(X0) | calm(X0)) & ((calm(X0) & ~calm(X0)) | (~strong(X0) & ~rich(X0)))) [flattening 56]
66. ! [X0] : (quiet(X0) | ((~funny(X0) | ~rich(X0)) & (rich(X0) | funny(X0)))) [nnf transformation 41]
71. ? [X0] : (~happy(X0) & ~tall(X0)) => (~happy(sK7) & ~tall(sK7)) [choice axiom]
72. ~happy(sK7) & ~tall(sK7) [skolemisation 21,71]
87. ~funny(X0) | wise(X0) [cnf transformation 32]
94. ~wise(X0) | happy(X0) | tall(X0) [cnf transformation 50]
96. brave(fred) | strong(fred) | ~quiet(X0) [cnf transformation 51]
107. ~calm(X0) | ~rich(X0) [cnf transformation 57]
108. ~calm(X0) | ~strong(X0) [cnf transformation 57]
109. ~rich(X0) | calm(X0) [cnf transformation 57]
110. ~strong(X0) | calm(X0) [cnf transformation 57]
127. quiet(X0) | rich(X0) | funny(X0) [cnf transformation 66]
133. ~tall(sK7) [cnf transformation 72]
134. ~happy(sK7) [cnf transformation 72]
140. ~brave(fred) [cnf transformation 25]
160. 5 <=> ! [X0] : ~quiet(X0) [avatar definition]
161. ~quiet(X0) <- (5) [avatar component clause 160]
163. 6 <=> strong(fred) [avatar definition]
164. strong(fred) <- (6) [avatar component clause 163]
167. 7 <=> brave(fred) [avatar definition]
171. 5 | 6 | 7 [avatar split clause 96,167,163,160]
184. ~strong(X0) [subsumption resolution 108,110]
185. ~rich(X0) [subsumption resolution 107,109]
217. quiet(X0) | funny(X0) [subsumption resolution 127,185]
238. ~7 [avatar split clause 140,167]
254. $false <- (6) [subsumption resolution 164,184]
255. ~6 [avatar contradiction clause 254]
256. funny(X0) <- (5) [resolution 161,217]
264. 21 <=> wise(sK7) [avatar definition]
265. ~wise(sK7) <- (~21) [avatar component clause 264]
266. wise(sK7) <- (21) [avatar component clause 264]
281. wise(X1) <- (5) [resolution 256,87]
283. happy(sK7) | tall(sK7) <- (21) [resolution 94,266]
284. tall(sK7) <- (21) [subsumption resolution 283,134]
285. $false <- (21) [subsumption resolution 284,133]
286. ~21 [avatar contradiction clause 285]
287. $false <- (5, ~21) [subsumption resolution 265,281]
288. ~5 | 21 [avatar contradiction clause 287]
289. $false [avatar sat refutation 171,238,255,286,288]
% SZS output end Proof for 3756703155341831905899550
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall or not strong is either humble or rich and vice versa. Everyone who is not rich is not calm or humble. Everyone who is either not brave or quiet is not happy. If mary is humble or funny then someone is not happy or old. If someone is not old or not generous then fred is both calm and kind and vice versa. Everyone who is both happy and curious is either not happy or old and vice versa. If someone is both not rich and calm then someone is calm and vice versa. Everyone who is rich is not old or not brave. If fred is creative or not kind then someone is either not calm or not brave. If someone is both curious and quiet then someone is creative or funny and vice versa. If susan is brave or rich then someone is quiet or not happy. Everyone who is both creative and calm is either creative or not generous and vice versa. Everyone who is tall is brave or generous. Everyone who is not curious or not patient is happy. Everyone who is either calm or curious is not wise or funny. Everyone who is not rich or happy is both brave and not generous and vice versa. Someone is either not old or not wise. Alice is patient. John is either not funny or quiet. Someone is not quiet. Mary is patient. Someone is brave or not calm. Someone is strong. | Fred is funny. | neutral | (![X]:((tall(X)|~strong(X))<=>(humble(X)<~>rich(X))))&
(![X]:(~rich(X)=>(~calm(X)|humble(X))))&
(![X]:((~brave(X)<~>quiet(X))=>~happy(X)))&
(((humble(mary)|funny(mary)))=>(?[X]:((~happy(X)|old(X)))))&
((?[X]:((~old(X)|~generous(X))))<=>((calm(fred)&kind(fred))))&
(![X]:((happy(X)&curious(X))<=>(~happy(X)<~>old(X))))&
((?[X]:((~rich(X)&calm(X))))<=>(?[X]:(calm(X))))&
(![X]:(rich(X)=>(~old(X)|~brave(X))))&
(((creative(fred)|~kind(fred)))=>(?[X]:((~calm(X)<~>~brave(X)))))&
((?[X]:((curious(X)&quiet(X))))<=>(?[X]:((creative(X)|funny(X)))))&
(((brave(susan)|rich(susan)))=>(?[X]:((quiet(X)|~happy(X)))))&
(![X]:((creative(X)&calm(X))<=>(creative(X)<~>~generous(X))))&
(![X]:(tall(X)=>(brave(X)|generous(X))))&
(![X]:((~curious(X)|~patient(X))=>happy(X)))&
(![X]:((calm(X)<~>curious(X))=>(~wise(X)|funny(X))))&
(![X]:((~rich(X)|happy(X))<=>(brave(X)&~generous(X))))&
(?[X]:((~old(X)<~>~wise(X))))&
(patient(alice))&
((~funny(john)<~>quiet(john)))&
(?[X]:(~quiet(X)))&
(patient(mary))&
(?[X]:((brave(X)|~calm(X))))&
(?[X]:(strong(X))) | funny(fred) | [] | null | 0 |
Everyone who is not humble or curious is happy.
Everyone who is both patient and not patient is not old or wise and vice versa.
Everyone who is either not happy or patient is old.
Everyone who is kind is both funny and not funny.
If fred is not patient then someone is either generous or creative and vice versa.
If alice is not brave then paul is either not creative or wise and vice versa.
Everyone who is not creative or not rich is both funny and not curious and vice versa.
If john is both rich and creative then paul is old or strong and vice versa.
If someone is not patient then susan is calm and vice versa.
Everyone who is not curious or tall is tall or calm and vice versa.
Everyone who is both not humble and patient is both calm and patient.
If someone is not kind then someone is both not creative and not brave.
Everyone who is both rich and not happy is not funny.
If someone is either tall or not tall then susan is either patient or not old.
If someone is either old or not strong then fred is both brave and rich.
Everyone who is not old is both quiet and not generous and vice versa.
Someone is not tall or rich.
Paul is not humble or kind.
Someone is both not calm and not tall.
Someone is either wise or not brave.
Someone is both not wise and not happy.
Susan is both not quiet and not wise.
John is both not generous and not quiet. | Susan is not calm. | contradiction | (![X]:((~humble(X)|curious(X))=>happy(X)))&
(![X]:((patient(X)&~patient(X))<=>(~old(X)|wise(X))))&
(![X]:((~happy(X)<~>patient(X))=>old(X)))&
(![X]:(kind(X)=>(funny(X)&~funny(X))))&
((~patient(fred))<=>(?[X]:((generous(X)<~>creative(X)))))&
((~brave(alice))<=>((~creative(paul)<~>wise(paul))))&
(![X]:((~creative(X)|~rich(X))<=>(funny(X)&~curious(X))))&
(((rich(john)&creative(john)))<=>((old(paul)|strong(paul))))&
((?[X]:(~patient(X)))<=>(calm(susan)))&
(![X]:((~curious(X)|tall(X))<=>(tall(X)|calm(X))))&
(![X]:((~humble(X)&patient(X))=>(calm(X)&patient(X))))&
((?[X]:(~kind(X)))=>(?[X]:((~creative(X)&~brave(X)))))&
(![X]:((rich(X)&~happy(X))=>~funny(X)))&
((?[X]:((tall(X)<~>~tall(X))))=>((patient(susan)<~>~old(susan))))&
((?[X]:((old(X)<~>~strong(X))))=>((brave(fred)&rich(fred))))&
(![X]:(~old(X)<=>(quiet(X)&~generous(X))))&
(?[X]:((~tall(X)|rich(X))))&
((~humble(paul)|kind(paul)))&
(?[X]:((~calm(X)&~tall(X))))&
(?[X]:((wise(X)<~>~brave(X))))&
(?[X]:((~wise(X)&~happy(X))))&
((~quiet(susan)&~wise(susan)))&
((~generous(john)&~quiet(john))) | ~calm(susan) | [
"p1",
"p4",
"p7",
"p8",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 7270485698991763041209400
% SZS output start Proof for 7270485698991763041209400
2. ! [X0] : ((~patient(X0) & patient(X0)) <=> (wise(X0) | ~old(X0))) [input p1]
5. ~patient(fred) <=> ? [X0] : (generous(X0) <~> creative(X0)) [input p4]
8. (creative(john) & rich(john)) <=> (strong(paul) | old(paul)) [input p7]
9. ? [X0] : ~patient(X0) <=> calm(susan) [input p8]
23. ~quiet(john) & ~generous(john) [input p22]
24. ~calm(susan) [input hypothesis]
36. ! [X0] : (((~patient(X0) & patient(X0)) | (~wise(X0) & old(X0))) & ((wise(X0) | ~old(X0)) | (patient(X0) | ~patient(X0)))) [nnf transformation 2]
37. ! [X0] : (((~patient(X0) & patient(X0)) | (~wise(X0) & old(X0))) & (wise(X0) | ~old(X0) | patient(X0) | ~patient(X0))) [flattening 36]
39. (~patient(fred) | ! [X0] : ((generous(X0) | ~creative(X0)) & (creative(X0) | ~generous(X0)))) & (? [X0] : ((~creative(X0) | ~generous(X0)) & (creative(X0) | generous(X0))) | patient(fred)) [nnf transformation 5]
40. (~patient(fred) | ! [X0] : ((generous(X0) | ~creative(X0)) & (creative(X0) | ~generous(X0)))) & (? [X1] : ((~creative(X1) | ~generous(X1)) & (creative(X1) | generous(X1))) | patient(fred)) [rectify 39]
41. ? [X1] : ((~creative(X1) | ~generous(X1)) & (creative(X1) | generous(X1))) => ((~creative(sK0) | ~generous(sK0)) & (creative(sK0) | generous(sK0))) [choice axiom]
42. (~patient(fred) | ! [X0] : ((generous(X0) | ~creative(X0)) & (creative(X0) | ~generous(X0)))) & (((~creative(sK0) | ~generous(sK0)) & (creative(sK0) | generous(sK0))) | patient(fred)) [skolemisation 40,41]
46. ((creative(john) & rich(john)) | (~strong(paul) & ~old(paul))) & ((strong(paul) | old(paul)) | (~creative(john) | ~rich(john))) [nnf transformation 8]
47. ((creative(john) & rich(john)) | (~strong(paul) & ~old(paul))) & (strong(paul) | old(paul) | ~creative(john) | ~rich(john)) [flattening 46]
48. (? [X0] : ~patient(X0) | ~calm(susan)) & (calm(susan) | ! [X0] : patient(X0)) [nnf transformation 9]
49. (? [X0] : ~patient(X0) | ~calm(susan)) & (calm(susan) | ! [X1] : patient(X1)) [rectify 48]
50. ? [X0] : ~patient(X0) => ~patient(sK1) [choice axiom]
51. (~patient(sK1) | ~calm(susan)) & (calm(susan) | ! [X1] : patient(X1)) [skolemisation 49,50]
73. patient(X0) | old(X0) [cnf transformation 37]
75. ~patient(X0) | old(X0) [cnf transformation 37]
84. ~patient(fred) | generous(X0) | ~creative(X0) [cnf transformation 42]
97. creative(john) | ~old(paul) [cnf transformation 47]
99. calm(susan) | patient(X1) [cnf transformation 51]
131. ~generous(john) [cnf transformation 23]
133. ~calm(susan) [cnf transformation 24]
139. old(X0) [subsumption resolution 73,75]
142. 1 <=> ! [X0] : (generous(X0) | ~creative(X0)) [avatar definition]
143. ~creative(X0) | generous(X0) <- (1) [avatar component clause 142]
145. 2 <=> patient(fred) [avatar definition]
147. ~patient(fred) <- (~2) [avatar component clause 145]
148. 1 | ~2 [avatar split clause 84,145,142]
180. 9 <=> creative(john) [avatar definition]
182. creative(john) <- (9) [avatar component clause 180]
184. creative(john) [subsumption resolution 97,139]
185. 9 [avatar split clause 184,180]
194. 11 <=> calm(susan) [avatar definition]
203. 13 <=> ! [X1] : patient(X1) [avatar definition]
204. patient(X1) <- (13) [avatar component clause 203]
205. 13 | 11 [avatar split clause 99,194,203]
249. ~11 [avatar split clause 133,194]
250. $false <- (~2, 13) [subsumption resolution 147,204]
251. 2 | ~13 [avatar contradiction clause 250]
261. generous(john) <- (1, 9) [resolution 143,182]
263. $false <- (1, 9) [subsumption resolution 261,131]
264. ~1 | ~9 [avatar contradiction clause 263]
265. $false [avatar sat refutation 148,185,205,249,251,264]
% SZS output end Proof for 7270485698991763041209400
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or brave is either not tall or old and vice versa.
If someone is not strong or old then someone is either curious or not creative.
If someone is calm then john is not humble and vice versa.
If someone is quiet or old then someone is both not tall and calm.
Everyone who is not wise is either strong or not quiet and vice versa.
Everyone who is both curious and generous is funny or not strong and vice versa.
Everyone who is either not tall or strong is both not curious and funny.
If john is not rich or not old then mary is both quiet and not calm and vice versa.
Everyone who is both not creative and old is quiet or not humble and vice versa.
Everyone who is kind or not wise is both wise and not strong and vice versa.
If someone is kind or not creative then someone is both not happy and strong and vice versa.
Everyone who is not tall is not strong or calm.
If someone is both patient and curious then john is patient.
Everyone who is both not strong and not funny is either not funny or brave.
Everyone who is not brave is either not old or humble.
Everyone who is either old or funny is either creative or wise.
Someone is both curious and not generous.
Someone is happy.
Paul is funny.
Someone is not old or not strong.
Someone is either not strong or not wise.
Paul is not rich or not generous.
Someone is not patient or not quiet.
Someone is either not generous or not patient. | John is not old. | contradiction | (![X]:((creative(X)|brave(X))<=>(~tall(X)<~>old(X))))&
((?[X]:((~strong(X)|old(X))))=>(?[X]:((curious(X)<~>~creative(X)))))&
((?[X]:(calm(X)))<=>(~humble(john)))&
((?[X]:((quiet(X)|old(X))))=>(?[X]:((~tall(X)&calm(X)))))&
(![X]:(~wise(X)<=>(strong(X)<~>~quiet(X))))&
(![X]:((curious(X)&generous(X))<=>(funny(X)|~strong(X))))&
(![X]:((~tall(X)<~>strong(X))=>(~curious(X)&funny(X))))&
(((~rich(john)|~old(john)))<=>((quiet(mary)&~calm(mary))))&
(![X]:((~creative(X)&old(X))<=>(quiet(X)|~humble(X))))&
(![X]:((kind(X)|~wise(X))<=>(wise(X)&~strong(X))))&
((?[X]:((kind(X)|~creative(X))))<=>(?[X]:((~happy(X)&strong(X)))))&
(![X]:(~tall(X)=>(~strong(X)|calm(X))))&
((?[X]:((patient(X)&curious(X))))=>(patient(john)))&
(![X]:((~strong(X)&~funny(X))=>(~funny(X)<~>brave(X))))&
(![X]:(~brave(X)=>(~old(X)<~>humble(X))))&
(![X]:((old(X)<~>funny(X))=>(creative(X)<~>wise(X))))&
(?[X]:((curious(X)&~generous(X))))&
(?[X]:(happy(X)))&
(funny(paul))&
(?[X]:((~old(X)|~strong(X))))&
(?[X]:((~strong(X)<~>~wise(X))))&
((~rich(paul)|~generous(paul)))&
(?[X]:((~patient(X)|~quiet(X))))&
(?[X]:((~generous(X)<~>~patient(X)))) | ~old(john) | [
"p2",
"p3",
"p7",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 6217425522684187500499204
% SZS output start Proof for 6217425522684187500499204
3. ? [X0] : calm(X0) <=> ~humble(john) [input p2]
4. ? [X0] : (old(X0) | quiet(X0)) => ? [X0] : (calm(X0) & ~tall(X0)) [input p3]
8. (~old(john) | ~rich(john)) <=> (~calm(mary) & quiet(mary)) [input p7]
9. ! [X0] : ((old(X0) & ~creative(X0)) <=> (~humble(X0) | quiet(X0))) [input p8]
25. ~old(john) [input hypothesis]
27. ? [X0] : (old(X0) | quiet(X0)) => ? [X1] : (calm(X1) & ~tall(X1)) [rectify 4]
30. ? [X1] : (calm(X1) & ~tall(X1)) | ! [X0] : (~old(X0) & ~quiet(X0)) [ennf transformation 27]
45. (? [X0] : calm(X0) | humble(john)) & (~humble(john) | ! [X0] : ~calm(X0)) [nnf transformation 3]
46. (? [X0] : calm(X0) | humble(john)) & (~humble(john) | ! [X1] : ~calm(X1)) [rectify 45]
47. ? [X0] : calm(X0) => calm(sK1) [choice axiom]
48. (calm(sK1) | humble(john)) & (~humble(john) | ! [X1] : ~calm(X1)) [skolemisation 46,47]
49. ? [X0] : (calm(X0) & ~tall(X0)) | ! [X1] : (~old(X1) & ~quiet(X1)) [rectify 30]
50. ? [X0] : (calm(X0) & ~tall(X0)) => (calm(sK2) & ~tall(sK2)) [choice axiom]
51. (calm(sK2) & ~tall(sK2)) | ! [X1] : (~old(X1) & ~quiet(X1)) [skolemisation 49,50]
56. ((~old(john) | ~rich(john)) | (calm(mary) | ~quiet(mary))) & ((~calm(mary) & quiet(mary)) | (old(john) & rich(john))) [nnf transformation 8]
57. (~old(john) | ~rich(john) | calm(mary) | ~quiet(mary)) & ((~calm(mary) & quiet(mary)) | (old(john) & rich(john))) [flattening 56]
58. ! [X0] : (((old(X0) & ~creative(X0)) | (humble(X0) & ~quiet(X0))) & ((~humble(X0) | quiet(X0)) | (~old(X0) | creative(X0)))) [nnf transformation 9]
59. ! [X0] : (((old(X0) & ~creative(X0)) | (humble(X0) & ~quiet(X0))) & (~humble(X0) | quiet(X0) | ~old(X0) | creative(X0))) [flattening 58]
94. ~humble(john) | ~calm(X1) [cnf transformation 48]
98. calm(sK2) | ~quiet(X1) [cnf transformation 51]
114. quiet(mary) | old(john) [cnf transformation 57]
122. humble(X0) | old(X0) [cnf transformation 59]
154. ~old(john) [cnf transformation 25]
177. 5 <=> humble(john) [avatar definition]
178. ~humble(john) <- (~5) [avatar component clause 177]
186. 7 <=> ! [X1] : ~calm(X1) [avatar definition]
187. ~calm(X1) <- (7) [avatar component clause 186]
188. 7 | ~5 [avatar split clause 94,177,186]
190. 8 <=> calm(sK2) [avatar definition]
192. calm(sK2) <- (8) [avatar component clause 190]
195. 9 <=> ! [X1] : ~quiet(X1) [avatar definition]
196. ~quiet(X1) <- (9) [avatar component clause 195]
197. 9 | 8 [avatar split clause 98,190,195]
206. 11 <=> quiet(mary) [avatar definition]
207. quiet(mary) <- (11) [avatar component clause 206]
218. 14 <=> old(john) [avatar definition]
220. ~old(john) <- (~14) [avatar component clause 218]
224. 14 | 11 [avatar split clause 114,206,218]
307. ~14 [avatar split clause 154,218]
315. old(john) <- (~5) [resolution 122,178]
316. $false <- (~5, ~14) [subsumption resolution 315,220]
317. 5 | 14 [avatar contradiction clause 316]
319. $false <- (7, 8) [resolution 187,192]
320. ~7 | ~8 [avatar contradiction clause 319]
322. $false <- (9, 11) [resolution 196,207]
323. ~9 | ~11 [avatar contradiction clause 322]
324. $false [avatar sat refutation 188,197,224,307,317,320,323]
% SZS output end Proof for 6217425522684187500499204
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise and kind is both not kind and funny. Everyone who is both not quiet and not kind is both rich and kind. Everyone who is not strong is both humble and not patient and vice versa. If susan is either not rich or not humble then someone is quiet and vice versa. If paul is not generous or patient then someone is either kind or old. Everyone who is wise is brave or not kind. Everyone who is either old or humble is tall. Everyone who is old or not curious is tall and vice versa. Everyone who is not funny or not brave is patient. If mary is not generous then susan is both generous and not curious and vice versa. Everyone who is both not funny and not generous is not curious. Everyone who is both not curious and old is not funny or kind and vice versa. Everyone who is humble or quiet is either tall or not strong. If someone is not brave then fred is not calm or not wise. Everyone who is patient or tall is rich. If susan is old then alice is tall or not humble and vice versa. Fred is either not curious or not happy. Alice is not happy. Someone is not curious. Fred is either generous or not tall. Someone is both kind and strong. Someone is not brave or generous. Someone is both not funny and not quiet. | Paul is happy. | neutral | (![X]:((~wise(X)&kind(X))=>(~kind(X)&funny(X))))&
(![X]:((~quiet(X)&~kind(X))=>(rich(X)&kind(X))))&
(![X]:(~strong(X)<=>(humble(X)&~patient(X))))&
(((~rich(susan)<~>~humble(susan)))<=>(?[X]:(quiet(X))))&
(((~generous(paul)|patient(paul)))=>(?[X]:((kind(X)<~>old(X)))))&
(![X]:(wise(X)=>(brave(X)|~kind(X))))&
(![X]:((old(X)<~>humble(X))=>tall(X)))&
(![X]:((old(X)|~curious(X))<=>tall(X)))&
(![X]:((~funny(X)|~brave(X))=>patient(X)))&
((~generous(mary))<=>((generous(susan)&~curious(susan))))&
(![X]:((~funny(X)&~generous(X))=>~curious(X)))&
(![X]:((~curious(X)&old(X))<=>(~funny(X)|kind(X))))&
(![X]:((humble(X)|quiet(X))=>(tall(X)<~>~strong(X))))&
((?[X]:(~brave(X)))=>((~calm(fred)|~wise(fred))))&
(![X]:((patient(X)|tall(X))=>rich(X)))&
((old(susan))<=>((tall(alice)|~humble(alice))))&
((~curious(fred)<~>~happy(fred)))&
(~happy(alice))&
(?[X]:(~curious(X)))&
((generous(fred)<~>~tall(fred)))&
(?[X]:((kind(X)&strong(X))))&
(?[X]:((~brave(X)|generous(X))))&
(?[X]:((~funny(X)&~quiet(X)))) | happy(paul) | [] | null | 0 |
Everyone who is not quiet is either patient or not happy. Everyone who is either calm or brave is kind or curious. Everyone who is strong or not quiet is either curious or funny and vice versa. If paul is either generous or not generous then alice is either humble or wise and vice versa. If someone is both not tall and not generous then alice is both brave and not creative and vice versa. Everyone who is not quiet is not humble or creative and vice versa. Everyone who is not happy or creative is not calm. Everyone who is quiet or old is not happy. Everyone who is either old or not generous is patient or not creative. Everyone who is either not brave or not happy is humble. Everyone who is either not patient or not funny is not patient or wise. Everyone who is either not happy or strong is not generous and vice versa. If susan is generous or not creative then someone is both not patient and calm and vice versa. If someone is not strong or happy then someone is either wise or funny. If someone is either generous or curious then paul is not generous or not patient. Everyone who is either not patient or not brave is not funny or not brave and vice versa. Susan is both kind and funny. Someone is brave or not creative. Someone is tall. Someone is either not brave or rich. Alice is both not kind and not humble. Mary is either not strong or happy. Someone is strong. Fred is both not wise and not happy. | Susan is not happy. | contradiction | (![X]:(~quiet(X)=>(patient(X)<~>~happy(X))))&
(![X]:((calm(X)<~>brave(X))=>(kind(X)|curious(X))))&
(![X]:((strong(X)|~quiet(X))<=>(curious(X)<~>funny(X))))&
(((generous(paul)<~>~generous(paul)))<=>((humble(alice)<~>wise(alice))))&
((?[X]:((~tall(X)&~generous(X))))<=>((brave(alice)&~creative(alice))))&
(![X]:(~quiet(X)<=>(~humble(X)|creative(X))))&
(![X]:((~happy(X)|creative(X))=>~calm(X)))&
(![X]:((quiet(X)|old(X))=>~happy(X)))&
(![X]:((old(X)<~>~generous(X))=>(patient(X)|~creative(X))))&
(![X]:((~brave(X)<~>~happy(X))=>humble(X)))&
(![X]:((~patient(X)<~>~funny(X))=>(~patient(X)|wise(X))))&
(![X]:((~happy(X)<~>strong(X))<=>~generous(X)))&
(((generous(susan)|~creative(susan)))<=>(?[X]:((~patient(X)&calm(X)))))&
((?[X]:((~strong(X)|happy(X))))=>(?[X]:((wise(X)<~>funny(X)))))&
((?[X]:((generous(X)<~>curious(X))))=>((~generous(paul)|~patient(paul))))&
(![X]:((~patient(X)<~>~brave(X))<=>(~funny(X)|~brave(X))))&
((kind(susan)&funny(susan)))&
(?[X]:((brave(X)|~creative(X))))&
(?[X]:(tall(X)))&
(?[X]:((~brave(X)<~>rich(X))))&
((~kind(alice)&~humble(alice)))&
((~strong(mary)<~>happy(mary)))&
(?[X]:(strong(X)))&
((~wise(fred)&~happy(fred))) | ~happy(susan) | [
"p0",
"p5",
"p6",
"p7",
"p12",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 470360407483082453859412
% SZS output start Proof for 470360407483082453859412
1. ! [X0] : (~quiet(X0) => (patient(X0) <~> ~happy(X0))) [input p0]
6. ! [X0] : (~quiet(X0) <=> (creative(X0) | ~humble(X0))) [input p5]
7. ! [X0] : ((creative(X0) | ~happy(X0)) => ~calm(X0)) [input p6]
8. ! [X0] : ((old(X0) | quiet(X0)) => ~happy(X0)) [input p7]
13. (~creative(susan) | generous(susan)) <=> ? [X0] : (calm(X0) & ~patient(X0)) [input p12]
16. ! [X0] : ((~patient(X0) <~> ~brave(X0)) <=> (~brave(X0) | ~funny(X0))) [input p15]
17. funny(susan) & kind(susan) [input p16]
25. ~happy(susan) [input hypothesis]
27. ! [X0] : ((patient(X0) <~> ~happy(X0)) | quiet(X0)) [ennf transformation 1]
30. ! [X0] : (~calm(X0) | (~creative(X0) & happy(X0))) [ennf transformation 7]
31. ! [X0] : (~happy(X0) | (~old(X0) & ~quiet(X0))) [ennf transformation 8]
40. ! [X0] : (((happy(X0) | ~patient(X0)) & (~happy(X0) | patient(X0))) | quiet(X0)) [nnf transformation 27]
50. ! [X0] : ((~quiet(X0) | (~creative(X0) & humble(X0))) & ((creative(X0) | ~humble(X0)) | quiet(X0))) [nnf transformation 6]
51. ! [X0] : ((~quiet(X0) | (~creative(X0) & humble(X0))) & (creative(X0) | ~humble(X0) | quiet(X0))) [flattening 50]
56. ((~creative(susan) | generous(susan)) | ! [X0] : (~calm(X0) | patient(X0))) & (? [X0] : (calm(X0) & ~patient(X0)) | (creative(susan) & ~generous(susan))) [nnf transformation 13]
57. (~creative(susan) | generous(susan) | ! [X0] : (~calm(X0) | patient(X0))) & (? [X0] : (calm(X0) & ~patient(X0)) | (creative(susan) & ~generous(susan))) [flattening 56]
58. (~creative(susan) | generous(susan) | ! [X0] : (~calm(X0) | patient(X0))) & (? [X1] : (calm(X1) & ~patient(X1)) | (creative(susan) & ~generous(susan))) [rectify 57]
59. ? [X1] : (calm(X1) & ~patient(X1)) => (calm(sK1) & ~patient(sK1)) [choice axiom]
60. (~creative(susan) | generous(susan) | ! [X0] : (~calm(X0) | patient(X0))) & ((calm(sK1) & ~patient(sK1)) | (creative(susan) & ~generous(susan))) [skolemisation 58,59]
66. ! [X0] : ((((brave(X0) | patient(X0)) & (~brave(X0) | ~patient(X0))) | (brave(X0) & funny(X0))) & ((~brave(X0) | ~funny(X0)) | ((~patient(X0) | brave(X0)) & (~brave(X0) | patient(X0))))) [nnf transformation 16]
67. ! [X0] : ((((brave(X0) | patient(X0)) & (~brave(X0) | ~patient(X0))) | (brave(X0) & funny(X0))) & (~brave(X0) | ~funny(X0) | ((~patient(X0) | brave(X0)) & (~brave(X0) | patient(X0))))) [flattening 66]
78. ~happy(X0) | patient(X0) | quiet(X0) [cnf transformation 40]
79. ~patient(X0) | happy(X0) | quiet(X0) [cnf transformation 40]
102. ~creative(X0) | ~quiet(X0) [cnf transformation 51]
103. ~calm(X0) | happy(X0) [cnf transformation 30]
105. ~happy(X0) | ~quiet(X0) [cnf transformation 31]
118. ~patient(sK1) | creative(susan) [cnf transformation 60]
120. calm(sK1) | creative(susan) [cnf transformation 60]
128. ~brave(X0) | ~funny(X0) | ~brave(X0) | patient(X0) [cnf transformation 67]
133. brave(X0) | patient(X0) | brave(X0) [cnf transformation 67]
135. funny(susan) [cnf transformation 17]
147. ~happy(susan) [cnf transformation 25]
148. ~brave(X0) | ~funny(X0) | patient(X0) [duplicate literal removal 128]
149. brave(X0) | patient(X0) [duplicate literal removal 133]
202. 11 <=> creative(susan) [avatar definition]
203. creative(susan) <- (11) [avatar component clause 202]
207. 12 <=> calm(sK1) [avatar definition]
209. calm(sK1) <- (12) [avatar component clause 207]
210. 11 | 12 [avatar split clause 120,207,202]
213. 13 <=> patient(sK1) [avatar definition]
215. ~patient(sK1) <- (~13) [avatar component clause 213]
216. 11 | ~13 [avatar split clause 118,213,202]
248. ~funny(X0) | patient(X0) [subsumption resolution 148,149]
279. ~quiet(susan) <- (11) [resolution 102,203]
282. patient(susan) [resolution 248,135]
284. happy(susan) | quiet(susan) [resolution 79,282]
294. quiet(susan) [subsumption resolution 284,147]
295. $false <- (11) [subsumption resolution 294,279]
296. ~11 [avatar contradiction clause 295]
298. happy(sK1) <- (12) [resolution 209,103]
301. patient(sK1) | quiet(sK1) <- (12) [resolution 298,78]
302. ~quiet(sK1) <- (12) [resolution 298,105]
303. quiet(sK1) <- (12, ~13) [subsumption resolution 301,215]
304. $false <- (12, ~13) [subsumption resolution 302,303]
305. ~12 | 13 [avatar contradiction clause 304]
306. $false [avatar sat refutation 210,216,296,305]
% SZS output end Proof for 470360407483082453859412
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not creative or brave is not old.
If susan is not old then someone is either funny or not creative and vice versa.
Everyone who is not rich or not generous is either not humble or not patient.
If mary is funny then someone is patient.
Everyone who is quiet or not strong is both not kind and tall.
Everyone who is either creative or not wise is not generous and vice versa.
Everyone who is quiet is both not generous and not tall and vice versa.
If someone is curious then someone is not curious and vice versa.
Everyone who is both not strong and not old is generous.
If mary is not calm or rich then someone is either not kind or not calm and vice versa.
If alice is either curious or not old then someone is either not rich or not strong.
Everyone who is curious or wise is either calm or humble.
If someone is both not quiet and not rich then alice is both patient and old and vice versa.
Everyone who is not old or creative is both not calm and not tall and vice versa.
Everyone who is either not rich or brave is both not brave and not happy and vice versa.
If john is not creative or humble then mary is not calm.
Someone is patient or wise.
Someone is either not kind or funny.
Fred is both not patient and tall.
John is tall or kind.
Someone is either not patient or calm.
Paul is either not humble or not quiet.
Someone is not strong.
Someone is either not calm or patient. | Alice is quiet. | contradiction | (![X]:((~creative(X)<~>brave(X))=>~old(X)))&
((~old(susan))<=>(?[X]:((funny(X)<~>~creative(X)))))&
(![X]:((~rich(X)|~generous(X))=>(~humble(X)<~>~patient(X))))&
((funny(mary))=>(?[X]:(patient(X))))&
(![X]:((quiet(X)|~strong(X))=>(~kind(X)&tall(X))))&
(![X]:((creative(X)<~>~wise(X))<=>~generous(X)))&
(![X]:(quiet(X)<=>(~generous(X)&~tall(X))))&
((?[X]:(curious(X)))<=>(?[X]:(~curious(X))))&
(![X]:((~strong(X)&~old(X))=>generous(X)))&
(((~calm(mary)|rich(mary)))<=>(?[X]:((~kind(X)<~>~calm(X)))))&
(((curious(alice)<~>~old(alice)))=>(?[X]:((~rich(X)<~>~strong(X)))))&
(![X]:((curious(X)|wise(X))=>(calm(X)<~>humble(X))))&
((?[X]:((~quiet(X)&~rich(X))))<=>((patient(alice)&old(alice))))&
(![X]:((~old(X)|creative(X))<=>(~calm(X)&~tall(X))))&
(![X]:((~rich(X)<~>brave(X))<=>(~brave(X)&~happy(X))))&
(((~creative(john)|humble(john)))=>(~calm(mary)))&
(?[X]:((patient(X)|wise(X))))&
(?[X]:((~kind(X)<~>funny(X))))&
((~patient(fred)&tall(fred)))&
((tall(john)|kind(john)))&
(?[X]:((~patient(X)<~>calm(X))))&
((~humble(paul)<~>~quiet(paul)))&
(?[X]:(~strong(X)))&
(?[X]:((~calm(X)<~>patient(X)))) | quiet(alice) | [
"p4",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 1128543938837366536966023
% SZS output start Proof for 1128543938837366536966023
5. ! [X0] : ((~strong(X0) | quiet(X0)) => (tall(X0) & ~kind(X0))) [input p4]
7. ! [X0] : (quiet(X0) <=> (~tall(X0) & ~generous(X0))) [input p6]
25. quiet(alice) [input hypothesis]
30. ! [X0] : ((tall(X0) & ~kind(X0)) | (strong(X0) & ~quiet(X0))) [ennf transformation 5]
45. ! [X0] : ((quiet(X0) | (tall(X0) | generous(X0))) & ((~tall(X0) & ~generous(X0)) | ~quiet(X0))) [nnf transformation 7]
46. ! [X0] : ((quiet(X0) | tall(X0) | generous(X0)) & ((~tall(X0) & ~generous(X0)) | ~quiet(X0))) [flattening 45]
97. tall(X0) | ~quiet(X0) [cnf transformation 30]
104. ~tall(X0) | ~quiet(X0) [cnf transformation 46]
153. quiet(alice) [cnf transformation 25]
188. ~quiet(X0) [subsumption resolution 104,97]
328. $false [subsumption resolution 153,188]
% SZS output end Proof for 1128543938837366536966023
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
If someone is funny then alice is either not kind or rich and vice versa.
If someone is either funny or not brave then someone is not rich or humble and vice versa.
Everyone who is either old or calm is strong or not quiet and vice versa.
Everyone who is patient or old is either quiet or not funny.
Everyone who is brave or kind is either creative or calm and vice versa.
If paul is not happy then someone is not strong or tall and vice versa.
Everyone who is both not calm and happy is both tall and generous and vice versa.
If alice is both not strong and quiet then lucy is not brave and vice versa.
If john is rich or happy then someone is humble or strong and vice versa.
Everyone who is either not curious or funny is either not generous or old and vice versa.
If someone is not humble or not funny then someone is either not calm or not kind.
Everyone who is both not rich and humble is strong or not calm.
If someone is not funny then someone is curious or old and vice versa.
Everyone who is not calm or not patient is both not happy and not rich and vice versa.
Everyone who is not tall or generous is both humble and not generous and vice versa.
If susan is not generous or not happy then susan is either kind or not quiet.
Someone is not funny.
John is either not rich or not generous.
Someone is either brave or rich.
John is strong or calm.
Someone is not rich.
Alice is calm.
Mary is kind or not wise. | Susan is creative. | neutral | ((?[X]:(funny(X)))<=>((~kind(alice)<~>rich(alice))))&
((?[X]:((funny(X)<~>~brave(X))))<=>(?[X]:((~rich(X)|humble(X)))))&
(![X]:((old(X)<~>calm(X))<=>(strong(X)|~quiet(X))))&
(![X]:((patient(X)|old(X))=>(quiet(X)<~>~funny(X))))&
(![X]:((brave(X)|kind(X))<=>(creative(X)<~>calm(X))))&
((~happy(paul))<=>(?[X]:((~strong(X)|tall(X)))))&
(![X]:((~calm(X)&happy(X))<=>(tall(X)&generous(X))))&
(((~strong(alice)&quiet(alice)))<=>(~brave(lucy)))&
(((rich(john)|happy(john)))<=>(?[X]:((humble(X)|strong(X)))))&
(![X]:((~curious(X)<~>funny(X))<=>(~generous(X)<~>old(X))))&
((?[X]:((~humble(X)|~funny(X))))=>(?[X]:((~calm(X)<~>~kind(X)))))&
(![X]:((~rich(X)&humble(X))=>(strong(X)|~calm(X))))&
((?[X]:(~funny(X)))<=>(?[X]:((curious(X)|old(X)))))&
(![X]:((~calm(X)|~patient(X))<=>(~happy(X)&~rich(X))))&
(![X]:((~tall(X)|generous(X))<=>(humble(X)&~generous(X))))&
(((~generous(susan)|~happy(susan)))=>((kind(susan)<~>~quiet(susan))))&
(?[X]:(~funny(X)))&
((~rich(john)<~>~generous(john)))&
(?[X]:((brave(X)<~>rich(X))))&
((strong(john)|calm(john)))&
(?[X]:(~rich(X)))&
(calm(alice))&
((kind(mary)|~wise(mary))) | creative(susan) | [] | null | 0 |
If fred is either wise or creative then someone is brave. If lucy is both funny and calm then someone is both not tall and wise. Everyone who is rich or not brave is brave or not patient. If someone is not old then paul is both patient and not rich and vice versa. If fred is not old then paul is either happy or creative. If susan is happy then someone is both not calm and not generous and vice versa. Everyone who is funny or not happy is both quiet and not brave. Everyone who is both calm and curious is either creative or calm and vice versa. Everyone who is both old and creative is not funny or not tall. Everyone who is not funny is old. Everyone who is either rich or curious is either calm or not funny and vice versa. Everyone who is both patient and brave is either not curious or not patient. Everyone who is funny is not wise or rich. Everyone who is not generous or kind is generous and vice versa. If someone is patient or old then someone is either patient or tall and vice versa. If someone is humble or curious then someone is both rich and humble and vice versa. Alice is both not old and not strong. Fred is tall. Fred is not creative. Mary is not kind or not happy. Someone is either brave or not kind. Someone is quiet or not brave. Lucy is tall. | Paul is not calm. | contradiction | (((wise(fred)<~>creative(fred)))=>(?[X]:(brave(X))))&
(((funny(lucy)&calm(lucy)))=>(?[X]:((~tall(X)&wise(X)))))&
(![X]:((rich(X)|~brave(X))=>(brave(X)|~patient(X))))&
((?[X]:(~old(X)))<=>((patient(paul)&~rich(paul))))&
((~old(fred))=>((happy(paul)<~>creative(paul))))&
((happy(susan))<=>(?[X]:((~calm(X)&~generous(X)))))&
(![X]:((funny(X)|~happy(X))=>(quiet(X)&~brave(X))))&
(![X]:((calm(X)&curious(X))<=>(creative(X)<~>calm(X))))&
(![X]:((old(X)&creative(X))=>(~funny(X)|~tall(X))))&
(![X]:(~funny(X)=>old(X)))&
(![X]:((rich(X)<~>curious(X))<=>(calm(X)<~>~funny(X))))&
(![X]:((patient(X)&brave(X))=>(~curious(X)<~>~patient(X))))&
(![X]:(funny(X)=>(~wise(X)|rich(X))))&
(![X]:((~generous(X)|kind(X))<=>generous(X)))&
((?[X]:((patient(X)|old(X))))<=>(?[X]:((patient(X)<~>tall(X)))))&
((?[X]:((humble(X)|curious(X))))<=>(?[X]:((rich(X)&humble(X)))))&
((~old(alice)&~strong(alice)))&
(tall(fred))&
(~creative(fred))&
((~kind(mary)|~happy(mary)))&
(?[X]:((brave(X)<~>~kind(X))))&
(?[X]:((quiet(X)|~brave(X))))&
(tall(lucy)) | ~calm(paul) | [
"p2",
"p3",
"p6",
"p10",
"p11",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 289837921765827103372385
% SZS output start Proof for 289837921765827103372385
3. ! [X0] : ((~brave(X0) | rich(X0)) => (~patient(X0) | brave(X0))) [input p2]
4. ? [X0] : ~old(X0) <=> (~rich(paul) & patient(paul)) [input p3]
7. ! [X0] : ((~happy(X0) | funny(X0)) => (~brave(X0) & quiet(X0))) [input p6]
11. ! [X0] : ((rich(X0) <~> curious(X0)) <=> (calm(X0) <~> ~funny(X0))) [input p10]
12. ! [X0] : ((brave(X0) & patient(X0)) => (~curious(X0) <~> ~patient(X0))) [input p11]
17. ~strong(alice) & ~old(alice) [input p16]
24. ~calm(paul) [input hypothesis]
27. ~old(alice) [pure predicate removal 17]
28. ! [X0] : ((~happy(X0) | funny(X0)) => ~brave(X0)) [pure predicate removal 7]
33. ! [X0] : ((~patient(X0) | brave(X0)) | (brave(X0) & ~rich(X0))) [ennf transformation 3]
34. ! [X0] : (~patient(X0) | brave(X0) | (brave(X0) & ~rich(X0))) [flattening 33]
36. ! [X0] : (~brave(X0) | (happy(X0) & ~funny(X0))) [ennf transformation 28]
40. ! [X0] : ((~curious(X0) <~> ~patient(X0)) | (~brave(X0) | ~patient(X0))) [ennf transformation 12]
41. ! [X0] : ((~curious(X0) <~> ~patient(X0)) | ~brave(X0) | ~patient(X0)) [flattening 40]
49. (? [X0] : ~old(X0) | (rich(paul) | ~patient(paul))) & ((~rich(paul) & patient(paul)) | ! [X0] : old(X0)) [nnf transformation 4]
50. (? [X0] : ~old(X0) | rich(paul) | ~patient(paul)) & ((~rich(paul) & patient(paul)) | ! [X0] : old(X0)) [flattening 49]
51. (? [X0] : ~old(X0) | rich(paul) | ~patient(paul)) & ((~rich(paul) & patient(paul)) | ! [X1] : old(X1)) [rectify 50]
52. ? [X0] : ~old(X0) => ~old(sK2) [choice axiom]
53. (~old(sK2) | rich(paul) | ~patient(paul)) & ((~rich(paul) & patient(paul)) | ! [X1] : old(X1)) [skolemisation 51,52]
61. ! [X0] : ((((~curious(X0) | ~rich(X0)) & (curious(X0) | rich(X0))) | ((calm(X0) | funny(X0)) & (~funny(X0) | ~calm(X0)))) & (((funny(X0) | ~calm(X0)) & (~funny(X0) | calm(X0))) | ((rich(X0) | ~curious(X0)) & (curious(X0) | ~rich(X0))))) [nnf transformation 11]
62. ! [X0] : (((patient(X0) | curious(X0)) & (~patient(X0) | ~curious(X0))) | ~brave(X0) | ~patient(X0)) [nnf transformation 41]
83. ~patient(X0) | brave(X0) | brave(X0) [cnf transformation 34]
84. patient(paul) | old(X1) [cnf transformation 53]
85. ~rich(paul) | old(X1) [cnf transformation 53]
92. ~funny(X0) | ~brave(X0) [cnf transformation 36]
107. curious(X0) | rich(X0) | calm(X0) | funny(X0) [cnf transformation 61]
110. ~patient(X0) | ~curious(X0) | ~brave(X0) | ~patient(X0) [cnf transformation 62]
127. ~old(alice) [cnf transformation 27]
134. ~calm(paul) [cnf transformation 24]
137. ~patient(X0) | ~curious(X0) | ~brave(X0) [duplicate literal removal 110]
140. ~patient(X0) | brave(X0) [duplicate literal removal 83]
174. 8 <=> patient(paul) [avatar definition]
175. patient(paul) <- (8) [avatar component clause 174]
178. 9 <=> rich(paul) [avatar definition]
179. ~rich(paul) <- (~9) [avatar component clause 178]
187. 11 <=> ! [X1] : old(X1) [avatar definition]
188. old(X1) <- (11) [avatar component clause 187]
189. 11 | ~9 [avatar split clause 85,178,187]
190. 11 | 8 [avatar split clause 84,174,187]
224. ~curious(X0) | ~patient(X0) [subsumption resolution 137,140]
323. $false <- (11) [resolution 188,127]
326. ~11 [avatar contradiction clause 323]
327. brave(paul) <- (8) [resolution 175,140]
355. ~patient(X2) | calm(X2) | funny(X2) | rich(X2) [resolution 107,224]
397. calm(paul) | funny(paul) | rich(paul) <- (8) [resolution 355,175]
424. funny(paul) | rich(paul) <- (8) [subsumption resolution 397,134]
425. funny(paul) <- (8, ~9) [subsumption resolution 424,179]
437. ~brave(paul) <- (8, ~9) [resolution 425,92]
439. $false <- (8, ~9) [subsumption resolution 437,327]
440. ~8 | 9 [avatar contradiction clause 439]
441. $false [avatar sat refutation 189,190,326,440]
% SZS output end Proof for 289837921765827103372385
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not tall is old or rich and vice versa. If fred is both curious and funny then alice is not wise. If someone is either not patient or strong then john is both not calm and strong. Everyone who is either not humble or funny is both not old and curious. If alice is either strong or quiet then someone is happy or not happy and vice versa. Everyone who is kind or not kind is both not quiet and patient and vice versa. Everyone who is strong is not kind. If john is either brave or not rich then someone is not wise or curious and vice versa. If alice is either not happy or not funny then paul is both not quiet and happy and vice versa. If lucy is funny or humble then lucy is both quiet and not creative and vice versa. Everyone who is either kind or strong is not rich. Everyone who is not wise or kind is either not tall or not creative and vice versa. If someone is either patient or curious then someone is not generous or not wise and vice versa. If mary is both not brave and humble then someone is funny. Everyone who is both not old and curious is not patient or not wise and vice versa. If susan is not old then lucy is strong. Someone is tall. Paul is not generous. Fred is either old or kind. Someone is not strong or generous. Alice is either not funny or not wise. Alice is not tall. Mary is funny or not tall. Someone is both happy and patient. | John is rich. | contradiction | (![X]:((~wise(X)&~tall(X))<=>(old(X)|rich(X))))&
(((curious(fred)&funny(fred)))=>(~wise(alice)))&
((?[X]:((~patient(X)<~>strong(X))))=>((~calm(john)&strong(john))))&
(![X]:((~humble(X)<~>funny(X))=>(~old(X)&curious(X))))&
(((strong(alice)<~>quiet(alice)))<=>(?[X]:((happy(X)|~happy(X)))))&
(![X]:((kind(X)|~kind(X))<=>(~quiet(X)&patient(X))))&
(![X]:(strong(X)=>~kind(X)))&
(((brave(john)<~>~rich(john)))<=>(?[X]:((~wise(X)|curious(X)))))&
(((~happy(alice)<~>~funny(alice)))<=>((~quiet(paul)&happy(paul))))&
(((funny(lucy)|humble(lucy)))<=>((quiet(lucy)&~creative(lucy))))&
(![X]:((kind(X)<~>strong(X))=>~rich(X)))&
(![X]:((~wise(X)|kind(X))<=>(~tall(X)<~>~creative(X))))&
((?[X]:((patient(X)<~>curious(X))))<=>(?[X]:((~generous(X)|~wise(X)))))&
(((~brave(mary)&humble(mary)))=>(?[X]:(funny(X))))&
(![X]:((~old(X)&curious(X))<=>(~patient(X)|~wise(X))))&
((~old(susan))=>(strong(lucy)))&
(?[X]:(tall(X)))&
(~generous(paul))&
((old(fred)<~>kind(fred)))&
(?[X]:((~strong(X)|generous(X))))&
((~funny(alice)<~>~wise(alice)))&
(~tall(alice))&
((funny(mary)|~tall(mary)))&
(?[X]:((happy(X)&patient(X)))) | rich(john) | [
"p0",
"p2",
"p5",
"p6",
"p10",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1337230832564962398971224
% SZS output start Proof for 1337230832564962398971224
1. ! [X0] : ((~tall(X0) & ~wise(X0)) <=> (rich(X0) | old(X0))) [input p0]
3. ? [X0] : (~patient(X0) <~> strong(X0)) => (strong(john) & ~calm(john)) [input p2]
6. ! [X0] : ((~kind(X0) | kind(X0)) <=> (patient(X0) & ~quiet(X0))) [input p5]
7. ! [X0] : (strong(X0) => ~kind(X0)) [input p6]
11. ! [X0] : ((kind(X0) <~> strong(X0)) => ~rich(X0)) [input p10]
15. ! [X0] : ((curious(X0) & ~old(X0)) <=> (~wise(X0) | ~patient(X0))) [input p14]
16. ~old(susan) => strong(lucy) [input p15]
25. rich(john) [input hypothesis]
27. ? [X0] : (~patient(X0) <~> strong(X0)) => strong(john) [pure predicate removal 3]
30. strong(john) | ! [X0] : (~patient(X0) <=> strong(X0)) [ennf transformation 27]
32. ! [X0] : (~kind(X0) | ~strong(X0)) [ennf transformation 7]
33. ! [X0] : (~rich(X0) | (kind(X0) <=> strong(X0))) [ennf transformation 11]
36. strong(lucy) | old(susan) [ennf transformation 16]
37. ! [X0] : (((~tall(X0) & ~wise(X0)) | (~rich(X0) & ~old(X0))) & ((rich(X0) | old(X0)) | (tall(X0) | wise(X0)))) [nnf transformation 1]
38. ! [X0] : (((~tall(X0) & ~wise(X0)) | (~rich(X0) & ~old(X0))) & (rich(X0) | old(X0) | tall(X0) | wise(X0))) [flattening 37]
39. strong(john) | ! [X0] : ((~patient(X0) | ~strong(X0)) & (strong(X0) | patient(X0))) [nnf transformation 30]
45. ! [X0] : (((~kind(X0) | kind(X0)) | (~patient(X0) | quiet(X0))) & ((patient(X0) & ~quiet(X0)) | (kind(X0) & ~kind(X0)))) [nnf transformation 6]
46. ! [X0] : ((~kind(X0) | kind(X0) | ~patient(X0) | quiet(X0)) & ((patient(X0) & ~quiet(X0)) | (kind(X0) & ~kind(X0)))) [flattening 45]
55. ! [X0] : (~rich(X0) | ((kind(X0) | ~strong(X0)) & (strong(X0) | ~kind(X0)))) [nnf transformation 33]
65. ! [X0] : (((curious(X0) & ~old(X0)) | (wise(X0) & patient(X0))) & ((~wise(X0) | ~patient(X0)) | (~curious(X0) | old(X0)))) [nnf transformation 15]
66. ! [X0] : (((curious(X0) & ~old(X0)) | (wise(X0) & patient(X0))) & (~wise(X0) | ~patient(X0) | ~curious(X0) | old(X0))) [flattening 65]
76. ~old(X0) | ~wise(X0) [cnf transformation 38]
82. strong(john) | ~patient(X0) | ~strong(X0) [cnf transformation 39]
95. patient(X0) | ~kind(X0) [cnf transformation 46]
96. kind(X0) | patient(X0) [cnf transformation 46]
98. ~kind(X0) | ~strong(X0) [cnf transformation 32]
117. ~rich(X0) | kind(X0) | ~strong(X0) [cnf transformation 55]
133. ~old(X0) | wise(X0) [cnf transformation 66]
136. strong(lucy) | old(susan) [cnf transformation 36]
148. rich(john) [cnf transformation 25]
163. 4 <=> ! [X0] : (~patient(X0) | ~strong(X0)) [avatar definition]
164. ~patient(X0) | ~strong(X0) <- (4) [avatar component clause 163]
166. 5 <=> strong(john) [avatar definition]
168. strong(john) <- (5) [avatar component clause 166]
169. 4 | 5 [avatar split clause 82,166,163]
192. patient(X0) [subsumption resolution 95,96]
202. 13 <=> rich(john) [avatar definition]
204. rich(john) <- (13) [avatar component clause 202]
258. ~strong(X0) | ~rich(X0) [subsumption resolution 117,98]
297. ~old(X0) [subsumption resolution 133,76]
300. strong(lucy) [subsumption resolution 136,297]
322. 13 [avatar split clause 148,202]
328. ~rich(john) <- (5) [resolution 258,168]
331. $false <- (5, 13) [subsumption resolution 328,204]
332. ~5 | ~13 [avatar contradiction clause 331]
333. ~strong(X0) <- (4) [subsumption resolution 164,192]
334. $false <- (4) [resolution 333,300]
337. ~4 [avatar contradiction clause 334]
338. $false [avatar sat refutation 169,322,332,337]
% SZS output end Proof for 1337230832564962398971224
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not wise or curious is both patient and quiet and vice versa.
If mary is either old or not brave then fred is either not happy or calm and vice versa.
Everyone who is either not calm or patient is humble and vice versa.
Everyone who is generous is not rich and vice versa.
If someone is both not creative and curious then mary is not rich.
If someone is either not wise or funny then john is not old and vice versa.
Everyone who is both not strong and not wise is both generous and not brave and vice versa.
Everyone who is either patient or calm is either wise or not strong.
Everyone who is wise or generous is both not old and strong and vice versa.
Everyone who is both kind and tall is both kind and not tall.
Everyone who is curious is not patient.
Everyone who is both creative and not kind is not patient.
If someone is both rich and tall then mary is both not tall and tall and vice versa.
Everyone who is either not quiet or strong is either not curious or not tall.
Everyone who is not old or not wise is both humble and not rich.
If lucy is not tall then fred is either brave or strong and vice versa.
Someone is not old or not brave.
John is either brave or calm.
Someone is rich or tall.
Mary is either kind or not happy.
Alice is old or not wise.
Someone is not kind or not funny. | Alice is curious. | contradiction | (![X]:((~wise(X)|curious(X))<=>(patient(X)&quiet(X))))&
(((old(mary)<~>~brave(mary)))<=>((~happy(fred)<~>calm(fred))))&
(![X]:((~calm(X)<~>patient(X))<=>humble(X)))&
(![X]:(generous(X)<=>~rich(X)))&
((?[X]:((~creative(X)&curious(X))))=>(~rich(mary)))&
((?[X]:((~wise(X)<~>funny(X))))<=>(~old(john)))&
(![X]:((~strong(X)&~wise(X))<=>(generous(X)&~brave(X))))&
(![X]:((patient(X)<~>calm(X))=>(wise(X)<~>~strong(X))))&
(![X]:((wise(X)|generous(X))<=>(~old(X)&strong(X))))&
(![X]:((kind(X)&tall(X))=>(kind(X)&~tall(X))))&
(![X]:(curious(X)=>~patient(X)))&
(![X]:((creative(X)&~kind(X))=>~patient(X)))&
((?[X]:((rich(X)&tall(X))))<=>((~tall(mary)&tall(mary))))&
(![X]:((~quiet(X)<~>strong(X))=>(~curious(X)<~>~tall(X))))&
(![X]:((~old(X)|~wise(X))=>(humble(X)&~rich(X))))&
((~tall(lucy))<=>((brave(fred)<~>strong(fred))))&
(?[X]:((~old(X)|~brave(X))))&
((brave(john)<~>calm(john)))&
(?[X]:((rich(X)|tall(X))))&
((kind(mary)<~>~happy(mary)))&
((old(alice)|~wise(alice)))&
(?[X]:((~kind(X)|~funny(X)))) | curious(alice) | [
"p0",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 5031380332793930889987449
% SZS output start Proof for 5031380332793930889987449
1. ! [X0] : ((curious(X0) | ~wise(X0)) <=> (quiet(X0) & patient(X0))) [input p0]
11. ! [X0] : (curious(X0) => ~patient(X0)) [input p10]
23. curious(alice) [input hypothesis]
30. ! [X0] : (~patient(X0) | ~curious(X0)) [ennf transformation 11]
35. ! [X0] : (((curious(X0) | ~wise(X0)) | (~quiet(X0) | ~patient(X0))) & ((quiet(X0) & patient(X0)) | (~curious(X0) & wise(X0)))) [nnf transformation 1]
36. ! [X0] : ((curious(X0) | ~wise(X0) | ~quiet(X0) | ~patient(X0)) & ((quiet(X0) & patient(X0)) | (~curious(X0) & wise(X0)))) [flattening 35]
65. patient(X0) | ~curious(X0) [cnf transformation 36]
101. ~patient(X0) | ~curious(X0) [cnf transformation 30]
127. curious(alice) [cnf transformation 23]
186. ~curious(X0) [subsumption resolution 101,65]
262. $false [subsumption resolution 127,186]
% SZS output end Proof for 5031380332793930889987449
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If susan is either not rich or wise then someone is either quiet or not calm. If mary is calm then someone is happy or rich and vice versa. If john is either brave or old then someone is either old or not curious and vice versa. Everyone who is old or not brave is both not patient and curious. If someone is not creative or calm then someone is both strong and not creative. Everyone who is not tall or funny is either calm or not happy. Everyone who is both creative and brave is both creative and not kind and vice versa. If someone is both happy and not calm then john is both not humble and not rich. Everyone who is calm is both old and patient and vice versa. Everyone who is both generous and quiet is either not brave or tall. Everyone who is both kind and brave is both not patient and not tall. Everyone who is either not funny or rich is either not curious or not kind. Everyone who is not brave or not quiet is funny or not calm and vice versa. Everyone who is not rich or humble is strong or humble. Everyone who is both funny and not curious is curious and vice versa. If someone is both not strong and wise then alice is happy and vice versa. John is both not curious and not funny. Someone is not creative or not happy. Someone is either not kind or not wise. Lucy is not curious. Someone is not calm. | Alice is not tall. | entailment | (((~rich(susan)<~>wise(susan)))=>(?[X]:((quiet(X)<~>~calm(X)))))&
((calm(mary))<=>(?[X]:((happy(X)|rich(X)))))&
(((brave(john)<~>old(john)))<=>(?[X]:((old(X)<~>~curious(X)))))&
(![X]:((old(X)|~brave(X))=>(~patient(X)&curious(X))))&
((?[X]:((~creative(X)|calm(X))))=>(?[X]:((strong(X)&~creative(X)))))&
(![X]:((~tall(X)|funny(X))=>(calm(X)<~>~happy(X))))&
(![X]:((creative(X)&brave(X))<=>(creative(X)&~kind(X))))&
((?[X]:((happy(X)&~calm(X))))=>((~humble(john)&~rich(john))))&
(![X]:(calm(X)<=>(old(X)&patient(X))))&
(![X]:((generous(X)&quiet(X))=>(~brave(X)<~>tall(X))))&
(![X]:((kind(X)&brave(X))=>(~patient(X)&~tall(X))))&
(![X]:((~funny(X)<~>rich(X))=>(~curious(X)<~>~kind(X))))&
(![X]:((~brave(X)|~quiet(X))<=>(funny(X)|~calm(X))))&
(![X]:((~rich(X)|humble(X))=>(strong(X)|humble(X))))&
(![X]:((funny(X)&~curious(X))<=>curious(X)))&
((?[X]:((~strong(X)&wise(X))))<=>(happy(alice)))&
((~curious(john)&~funny(john)))&
(?[X]:((~creative(X)|~happy(X))))&
(?[X]:((~kind(X)<~>~wise(X))))&
(~curious(lucy))&
(?[X]:(~calm(X))) | ~tall(alice) | [
"p1",
"p3",
"p8",
"p10",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5752580329892423807815172
% SZS output start Proof for 5752580329892423807815172
2. calm(mary) <=> ? [X0] : (rich(X0) | happy(X0)) [input p1]
4. ! [X0] : ((~brave(X0) | old(X0)) => (curious(X0) & ~patient(X0))) [input p3]
9. ! [X0] : (calm(X0) <=> (patient(X0) & old(X0))) [input p8]
11. ! [X0] : ((brave(X0) & kind(X0)) => (~tall(X0) & ~patient(X0))) [input p10]
12. ! [X0] : ((~funny(X0) <~> rich(X0)) => (~curious(X0) <~> ~kind(X0))) [input p11]
15. ! [X0] : ((~curious(X0) & funny(X0)) <=> curious(X0)) [input p14]
22. tall(alice) [input hypothesis]
26. ! [X0] : ((curious(X0) & ~patient(X0)) | (brave(X0) & ~old(X0))) [ennf transformation 4]
30. ! [X0] : ((~tall(X0) & ~patient(X0)) | (~brave(X0) | ~kind(X0))) [ennf transformation 11]
31. ! [X0] : ((~tall(X0) & ~patient(X0)) | ~brave(X0) | ~kind(X0)) [flattening 30]
32. ! [X0] : ((~curious(X0) <~> ~kind(X0)) | (~funny(X0) <=> rich(X0))) [ennf transformation 12]
38. (calm(mary) | ! [X0] : (~rich(X0) & ~happy(X0))) & (? [X0] : (rich(X0) | happy(X0)) | ~calm(mary)) [nnf transformation 2]
39. (calm(mary) | ! [X0] : (~rich(X0) & ~happy(X0))) & (? [X1] : (rich(X1) | happy(X1)) | ~calm(mary)) [rectify 38]
40. ? [X1] : (rich(X1) | happy(X1)) => (rich(sK1) | happy(sK1)) [choice axiom]
41. (calm(mary) | ! [X0] : (~rich(X0) & ~happy(X0))) & ((rich(sK1) | happy(sK1)) | ~calm(mary)) [skolemisation 39,40]
52. ! [X0] : ((calm(X0) | (~patient(X0) | ~old(X0))) & ((patient(X0) & old(X0)) | ~calm(X0))) [nnf transformation 9]
53. ! [X0] : ((calm(X0) | ~patient(X0) | ~old(X0)) & ((patient(X0) & old(X0)) | ~calm(X0))) [flattening 52]
54. ! [X0] : (((kind(X0) | curious(X0)) & (~kind(X0) | ~curious(X0))) | ((~funny(X0) | ~rich(X0)) & (rich(X0) | funny(X0)))) [nnf transformation 32]
57. ! [X0] : (((~curious(X0) & funny(X0)) | ~curious(X0)) & (curious(X0) | (curious(X0) | ~funny(X0)))) [nnf transformation 15]
58. ! [X0] : (((~curious(X0) & funny(X0)) | ~curious(X0)) & (curious(X0) | curious(X0) | ~funny(X0))) [flattening 57]
76. calm(mary) | ~rich(X0) [cnf transformation 41]
87. ~old(X0) | curious(X0) [cnf transformation 26]
88. curious(X0) | brave(X0) [cnf transformation 26]
103. ~calm(X0) | old(X0) [cnf transformation 53]
107. ~kind(X0) | ~brave(X0) | ~tall(X0) [cnf transformation 31]
110. kind(X0) | curious(X0) | rich(X0) | funny(X0) [cnf transformation 54]
118. curious(X0) | curious(X0) | ~funny(X0) [cnf transformation 58]
120. ~curious(X0) | ~curious(X0) [cnf transformation 58]
131. tall(alice) [cnf transformation 22]
132. curious(X0) | ~funny(X0) [duplicate literal removal 118]
133. ~curious(X0) [duplicate literal removal 120]
155. 5 <=> ! [X0] : ~rich(X0) [avatar definition]
156. ~rich(X0) <- (5) [avatar component clause 155]
158. 6 <=> calm(mary) [avatar definition]
160. calm(mary) <- (6) [avatar component clause 158]
161. 5 | 6 [avatar split clause 76,158,155]
237. ~funny(X0) [subsumption resolution 132,133]
281. brave(X0) [resolution 88,133]
282. old(mary) <- (6) [resolution 103,160]
283. curious(mary) <- (6) [resolution 282,87]
284. $false <- (6) [subsumption resolution 283,133]
285. ~6 [avatar contradiction clause 284]
313. curious(X2) | rich(X2) | funny(X2) | ~brave(X2) | ~tall(X2) [resolution 110,107]
317. rich(X2) | funny(X2) | ~brave(X2) | ~tall(X2) [subsumption resolution 313,133]
318. funny(X2) | ~brave(X2) | ~tall(X2) <- (5) [subsumption resolution 317,156]
319. ~brave(X2) | ~tall(X2) <- (5) [subsumption resolution 318,237]
320. ~tall(X2) <- (5) [subsumption resolution 319,281]
328. $false <- (5) [resolution 320,131]
329. ~5 [avatar contradiction clause 328]
330. $false [avatar sat refutation 161,285,329]
% SZS output end Proof for 5752580329892423807815172
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.018 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is not calm or not happy then john is both funny and wise.
If susan is both funny and curious then john is not brave or funny and vice versa.
Everyone who is not generous is both funny and happy and vice versa.
Everyone who is rich is not curious or not wise and vice versa.
Everyone who is wise is both wise and not strong and vice versa.
Everyone who is not calm is not calm or creative.
If someone is not kind or rich then paul is funny.
Everyone who is kind or not funny is humble.
If someone is not calm then alice is both not happy and not generous and vice versa.
If susan is rich or not generous then someone is either not wise or generous.
Everyone who is happy or not curious is both not quiet and tall and vice versa.
Everyone who is not happy is both not funny and old.
If alice is not quiet then mary is either curious or patient and vice versa.
Everyone who is either curious or generous is not happy or not strong and vice versa.
If someone is not tall then lucy is both not kind and not generous and vice versa.
Everyone who is strong is not quiet.
Someone is either old or patient.
Someone is both not patient and not brave.
Lucy is not tall or tall.
Someone is both generous and happy. | Mary is humble. | neutral | (((~calm(lucy)|~happy(lucy)))=>((funny(john)&wise(john))))&
(((funny(susan)&curious(susan)))<=>((~brave(john)|funny(john))))&
(![X]:(~generous(X)<=>(funny(X)&happy(X))))&
(![X]:(rich(X)<=>(~curious(X)|~wise(X))))&
(![X]:(wise(X)<=>(wise(X)&~strong(X))))&
(![X]:(~calm(X)=>(~calm(X)|creative(X))))&
((?[X]:((~kind(X)|rich(X))))=>(funny(paul)))&
(![X]:((kind(X)|~funny(X))=>humble(X)))&
((?[X]:(~calm(X)))<=>((~happy(alice)&~generous(alice))))&
(((rich(susan)|~generous(susan)))=>(?[X]:((~wise(X)<~>generous(X)))))&
(![X]:((happy(X)|~curious(X))<=>(~quiet(X)&tall(X))))&
(![X]:(~happy(X)=>(~funny(X)&old(X))))&
((~quiet(alice))<=>((curious(mary)<~>patient(mary))))&
(![X]:((curious(X)<~>generous(X))<=>(~happy(X)|~strong(X))))&
((?[X]:(~tall(X)))<=>((~kind(lucy)&~generous(lucy))))&
(![X]:(strong(X)=>~quiet(X)))&
(?[X]:((old(X)<~>patient(X))))&
(?[X]:((~patient(X)&~brave(X))))&
((~tall(lucy)|tall(lucy)))&
(?[X]:((generous(X)&happy(X)))) | humble(mary) | [] | null | 0 |
If mary is not brave or not patient then lucy is both creative and calm.
Everyone who is both funny and not kind is both not curious and not tall.
If susan is not quiet then someone is both not quiet and not creative.
Everyone who is both tall and funny is not brave or not kind and vice versa.
If someone is both old and happy then john is both not curious and not funny and vice versa.
If someone is not tall or not calm then someone is kind or not curious and vice versa.
If someone is not patient then someone is not patient or not rich.
Everyone who is not wise is either not brave or not patient and vice versa.
Everyone who is both not rich and humble is both humble and not funny and vice versa.
If someone is both not creative and not generous then someone is both not funny and wise and vice versa.
If someone is either not generous or tall then someone is both not creative and not rich.
If someone is either not curious or generous then paul is tall and vice versa.
Everyone who is both quiet and not happy is generous or strong.
If someone is both kind and curious then alice is generous or funny.
Everyone who is both not quiet and rich is not old.
Everyone who is both wise and not brave is either not curious or strong.
Lucy is not quiet.
Lucy is either humble or wise.
Someone is both not generous and not quiet.
Susan is funny or not brave.
Lucy is both kind and creative.
Someone is generous.
Someone is either patient or tall.
Mary is either not patient or not curious. | Susan is not kind. | contradiction | (((~brave(mary)|~patient(mary)))=>((creative(lucy)&calm(lucy))))&
(![X]:((funny(X)&~kind(X))=>(~curious(X)&~tall(X))))&
((~quiet(susan))=>(?[X]:((~quiet(X)&~creative(X)))))&
(![X]:((tall(X)&funny(X))<=>(~brave(X)|~kind(X))))&
((?[X]:((old(X)&happy(X))))<=>((~curious(john)&~funny(john))))&
((?[X]:((~tall(X)|~calm(X))))<=>(?[X]:((kind(X)|~curious(X)))))&
((?[X]:(~patient(X)))=>(?[X]:((~patient(X)|~rich(X)))))&
(![X]:(~wise(X)<=>(~brave(X)<~>~patient(X))))&
(![X]:((~rich(X)&humble(X))<=>(humble(X)&~funny(X))))&
((?[X]:((~creative(X)&~generous(X))))<=>(?[X]:((~funny(X)&wise(X)))))&
((?[X]:((~generous(X)<~>tall(X))))=>(?[X]:((~creative(X)&~rich(X)))))&
((?[X]:((~curious(X)<~>generous(X))))<=>(tall(paul)))&
(![X]:((quiet(X)&~happy(X))=>(generous(X)|strong(X))))&
((?[X]:((kind(X)&curious(X))))=>((generous(alice)|funny(alice))))&
(![X]:((~quiet(X)&rich(X))=>~old(X)))&
(![X]:((wise(X)&~brave(X))=>(~curious(X)<~>strong(X))))&
(~quiet(lucy))&
((humble(lucy)<~>wise(lucy)))&
(?[X]:((~generous(X)&~quiet(X))))&
((funny(susan)|~brave(susan)))&
((kind(lucy)&creative(lucy)))&
(?[X]:(generous(X)))&
(?[X]:((patient(X)<~>tall(X))))&
((~patient(mary)<~>~curious(mary))) | ~kind(susan) | [
"p1",
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 7174976034057098358843561
% SZS output start Proof for 7174976034057098358843561
2. ! [X0] : ((~kind(X0) & funny(X0)) => (~tall(X0) & ~curious(X0))) [input p1]
4. ! [X0] : ((funny(X0) & tall(X0)) <=> (~kind(X0) | ~brave(X0))) [input p3]
25. ~kind(susan) [input hypothesis]
31. ! [X0] : ((~tall(X0) & ~curious(X0)) | (kind(X0) | ~funny(X0))) [ennf transformation 2]
32. ! [X0] : ((~tall(X0) & ~curious(X0)) | kind(X0) | ~funny(X0)) [flattening 31]
46. ! [X0] : (((funny(X0) & tall(X0)) | (kind(X0) & brave(X0))) & ((~kind(X0) | ~brave(X0)) | (~funny(X0) | ~tall(X0)))) [nnf transformation 4]
47. ! [X0] : (((funny(X0) & tall(X0)) | (kind(X0) & brave(X0))) & (~kind(X0) | ~brave(X0) | ~funny(X0) | ~tall(X0))) [flattening 46]
92. ~tall(X0) | kind(X0) | ~funny(X0) [cnf transformation 32]
97. tall(X0) | kind(X0) [cnf transformation 47]
99. kind(X0) | funny(X0) [cnf transformation 47]
147. ~kind(susan) [cnf transformation 25]
371. kind(X0) | ~funny(X0) | kind(X0) [resolution 92,97]
373. kind(X0) | ~funny(X0) [duplicate literal removal 371]
375. kind(X0) [subsumption resolution 373,99]
381. $false [resolution 375,147]
% SZS output end Proof for 7174976034057098358843561
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is happy or brave then someone is quiet and vice versa.
Everyone who is not calm is humble or not happy and vice versa.
Everyone who is both not creative and rich is not brave and vice versa.
If lucy is both not quiet and patient then susan is both not funny and not patient.
Everyone who is generous is either brave or not humble.
Everyone who is either patient or generous is not funny or not kind and vice versa.
Everyone who is brave is creative or not strong.
If alice is kind or not curious then someone is not strong or tall and vice versa.
Everyone who is not rich is either not calm or not patient and vice versa.
Everyone who is funny or brave is curious and vice versa.
If fred is either curious or not rich then someone is either patient or happy.
If lucy is rich or brave then lucy is either kind or not quiet and vice versa.
Everyone who is not creative is not wise or not tall.
Everyone who is both not humble and generous is old or funny.
If lucy is both creative and old then someone is wise.
If someone is both not patient and strong then lucy is not curious and vice versa.
Someone is either not wise or old.
Someone is either old or not rich.
John is funny or not patient.
Mary is both not generous and rich.
Susan is either generous or not calm.
Someone is funny.
Someone is wise.
Someone is both not curious and not creative. | Mary is rich. | entailment | ((?[X]:((happy(X)|brave(X))))<=>(?[X]:(quiet(X))))&
(![X]:(~calm(X)<=>(humble(X)|~happy(X))))&
(![X]:((~creative(X)&rich(X))<=>~brave(X)))&
(((~quiet(lucy)&patient(lucy)))=>((~funny(susan)&~patient(susan))))&
(![X]:(generous(X)=>(brave(X)<~>~humble(X))))&
(![X]:((patient(X)<~>generous(X))<=>(~funny(X)|~kind(X))))&
(![X]:(brave(X)=>(creative(X)|~strong(X))))&
(((kind(alice)|~curious(alice)))<=>(?[X]:((~strong(X)|tall(X)))))&
(![X]:(~rich(X)<=>(~calm(X)<~>~patient(X))))&
(![X]:((funny(X)|brave(X))<=>curious(X)))&
(((curious(fred)<~>~rich(fred)))=>(?[X]:((patient(X)<~>happy(X)))))&
(((rich(lucy)|brave(lucy)))<=>((kind(lucy)<~>~quiet(lucy))))&
(![X]:(~creative(X)=>(~wise(X)|~tall(X))))&
(![X]:((~humble(X)&generous(X))=>(old(X)|funny(X))))&
(((creative(lucy)&old(lucy)))=>(?[X]:(wise(X))))&
((?[X]:((~patient(X)&strong(X))))<=>(~curious(lucy)))&
(?[X]:((~wise(X)<~>old(X))))&
(?[X]:((old(X)<~>~rich(X))))&
((funny(john)|~patient(john)))&
((~generous(mary)&rich(mary)))&
((generous(susan)<~>~calm(susan)))&
(?[X]:(funny(X)))&
(?[X]:(wise(X)))&
(?[X]:((~curious(X)&~creative(X)))) | rich(mary) | [
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 2252061091378753684534668
% SZS output start Proof for 2252061091378753684534668
20. rich(mary) & ~generous(mary) [input p19]
25. ~rich(mary) [input hypothesis]
136. rich(mary) [cnf transformation 20]
143. ~rich(mary) [cnf transformation 25]
318. $false [subsumption resolution 143,136]
% SZS output end Proof for 2252061091378753684534668
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not tall is not old or wise.
Everyone who is either funny or not happy is either not happy or not rich and vice versa.
Everyone who is strong is either not old or funny.
Everyone who is both not happy and not tall is either not generous or not calm and vice versa.
If someone is not old then paul is not tall.
Everyone who is both not quiet and not curious is both humble and curious and vice versa.
Everyone who is not patient is both humble and brave and vice versa.
Everyone who is old or not strong is generous and vice versa.
Everyone who is either calm or curious is generous.
Everyone who is not kind or strong is patient or not kind.
Everyone who is either not humble or humble is both not curious and not creative.
Everyone who is generous is not wise and vice versa.
Everyone who is both rich and brave is both happy and not wise and vice versa.
If someone is both not creative and happy then mary is both not brave and generous.
If lucy is either not happy or rich then paul is either generous or calm.
If someone is both wise and kind then mary is not creative or not happy.
Paul is both happy and not brave.
Someone is both not rich and brave.
Lucy is not happy.
Someone is strong.
Someone is rich.
Fred is either not brave or not old.
Someone is both strong and not kind. | Lucy is not happy. | entailment | (![X]:(~tall(X)=>(~old(X)|wise(X))))&
(![X]:((funny(X)<~>~happy(X))<=>(~happy(X)<~>~rich(X))))&
(![X]:(strong(X)=>(~old(X)<~>funny(X))))&
(![X]:((~happy(X)&~tall(X))<=>(~generous(X)<~>~calm(X))))&
((?[X]:(~old(X)))=>(~tall(paul)))&
(![X]:((~quiet(X)&~curious(X))<=>(humble(X)&curious(X))))&
(![X]:(~patient(X)<=>(humble(X)&brave(X))))&
(![X]:((old(X)|~strong(X))<=>generous(X)))&
(![X]:((calm(X)<~>curious(X))=>generous(X)))&
(![X]:((~kind(X)|strong(X))=>(patient(X)|~kind(X))))&
(![X]:((~humble(X)<~>humble(X))=>(~curious(X)&~creative(X))))&
(![X]:(generous(X)<=>~wise(X)))&
(![X]:((rich(X)&brave(X))<=>(happy(X)&~wise(X))))&
((?[X]:((~creative(X)&happy(X))))=>((~brave(mary)&generous(mary))))&
(((~happy(lucy)<~>rich(lucy)))=>((generous(paul)<~>calm(paul))))&
((?[X]:((wise(X)&kind(X))))=>((~creative(mary)|~happy(mary))))&
((happy(paul)&~brave(paul)))&
(?[X]:((~rich(X)&brave(X))))&
(~happy(lucy))&
(?[X]:(strong(X)))&
(?[X]:(rich(X)))&
((~brave(fred)<~>~old(fred)))&
(?[X]:((strong(X)&~kind(X)))) | ~happy(lucy) | [
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 6592191277018931638853531
% SZS output start Proof for 6592191277018931638853531
19. ~happy(lucy) [input p18]
24. happy(lucy) [input hypothesis]
114. ~happy(lucy) [cnf transformation 19]
121. happy(lucy) [cnf transformation 24]
164. 7 <=> happy(lucy) [avatar definition]
179. ~7 [avatar split clause 114,164]
190. 7 [avatar split clause 121,164]
191. $false [avatar sat refutation 179,190]
% SZS output end Proof for 6592191277018931638853531
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 4989
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If alice is both quiet and not generous then paul is both strong and humble. Everyone who is rich or curious is calm or creative and vice versa. Everyone who is not strong is both rich and not rich and vice versa. Everyone who is both not funny and humble is wise. Everyone who is both not rich and tall is both happy and generous. If john is tall then someone is not curious. Everyone who is rich is either generous or calm and vice versa. If someone is generous then someone is either not wise or not patient and vice versa. Everyone who is quiet is both not strong and tall and vice versa. If someone is both not kind and not strong then someone is not brave or not kind and vice versa. If paul is not funny or not creative then someone is not happy or not tall. If someone is either generous or patient then fred is humble and vice versa. Everyone who is either not humble or not patient is either happy or funny. Everyone who is either not patient or not humble is both happy and not calm. If fred is not calm then alice is not quiet or not tall. Everyone who is strong is not wise and vice versa. Someone is both not happy and not calm. Someone is both not curious and old. Paul is both not patient and not old. Alice is either kind or not humble. Alice is strong or creative. Someone is both not patient and generous. | Alice is generous. | neutral | (((quiet(alice)&~generous(alice)))=>((strong(paul)&humble(paul))))&
(![X]:((rich(X)|curious(X))<=>(calm(X)|creative(X))))&
(![X]:(~strong(X)<=>(rich(X)&~rich(X))))&
(![X]:((~funny(X)&humble(X))=>wise(X)))&
(![X]:((~rich(X)&tall(X))=>(happy(X)&generous(X))))&
((tall(john))=>(?[X]:(~curious(X))))&
(![X]:(rich(X)<=>(generous(X)<~>calm(X))))&
((?[X]:(generous(X)))<=>(?[X]:((~wise(X)<~>~patient(X)))))&
(![X]:(quiet(X)<=>(~strong(X)&tall(X))))&
((?[X]:((~kind(X)&~strong(X))))<=>(?[X]:((~brave(X)|~kind(X)))))&
(((~funny(paul)|~creative(paul)))=>(?[X]:((~happy(X)|~tall(X)))))&
((?[X]:((generous(X)<~>patient(X))))<=>(humble(fred)))&
(![X]:((~humble(X)<~>~patient(X))=>(happy(X)<~>funny(X))))&
(![X]:((~patient(X)<~>~humble(X))=>(happy(X)&~calm(X))))&
((~calm(fred))=>((~quiet(alice)|~tall(alice))))&
(![X]:(strong(X)<=>~wise(X)))&
(?[X]:((~happy(X)&~calm(X))))&
(?[X]:((~curious(X)&old(X))))&
((~patient(paul)&~old(paul)))&
((kind(alice)<~>~humble(alice)))&
((strong(alice)|creative(alice)))&
(?[X]:((~patient(X)&generous(X)))) | generous(alice) | [] | null | 0 |
Everyone who is quiet is not quiet or not creative and vice versa. If someone is either happy or quiet then alice is either rich or happy. If someone is happy or not humble then someone is funny. If fred is tall then someone is curious or not funny. If fred is both not rich and calm then someone is either not brave or not rich. Everyone who is not rich or not happy is either not brave or strong and vice versa. Everyone who is tall is wise. If susan is tall then paul is not old or happy. If susan is either not funny or rich then someone is rich or humble and vice versa. If someone is not old then paul is not old and vice versa. If someone is either rich or kind then someone is either tall or not strong. Everyone who is either not tall or generous is both rich and humble and vice versa. If someone is creative then susan is both not wise and not rich and vice versa. Everyone who is either brave or quiet is not rich or brave and vice versa. Everyone who is either kind or not tall is both strong and kind and vice versa. If alice is not wise or not humble then someone is rich or not rich. Someone is not happy. Paul is either not rich or not humble. Someone is not tall. Someone is either wise or not wise. Someone is quiet. Someone is either not old or not wise. | Fred is not rich. | entailment | (![X]:(quiet(X)<=>(~quiet(X)|~creative(X))))&
((?[X]:((happy(X)<~>quiet(X))))=>((rich(alice)<~>happy(alice))))&
((?[X]:((happy(X)|~humble(X))))=>(?[X]:(funny(X))))&
((tall(fred))=>(?[X]:((curious(X)|~funny(X)))))&
(((~rich(fred)&calm(fred)))=>(?[X]:((~brave(X)<~>~rich(X)))))&
(![X]:((~rich(X)|~happy(X))<=>(~brave(X)<~>strong(X))))&
(![X]:(tall(X)=>wise(X)))&
((tall(susan))=>((~old(paul)|happy(paul))))&
(((~funny(susan)<~>rich(susan)))<=>(?[X]:((rich(X)|humble(X)))))&
((?[X]:(~old(X)))<=>(~old(paul)))&
((?[X]:((rich(X)<~>kind(X))))=>(?[X]:((tall(X)<~>~strong(X)))))&
(![X]:((~tall(X)<~>generous(X))<=>(rich(X)&humble(X))))&
((?[X]:(creative(X)))<=>((~wise(susan)&~rich(susan))))&
(![X]:((brave(X)<~>quiet(X))<=>(~rich(X)|brave(X))))&
(![X]:((kind(X)<~>~tall(X))<=>(strong(X)&kind(X))))&
(((~wise(alice)|~humble(alice)))=>(?[X]:((rich(X)|~rich(X)))))&
(?[X]:(~happy(X)))&
((~rich(paul)<~>~humble(paul)))&
(?[X]:(~tall(X)))&
(?[X]:((wise(X)<~>~wise(X))))&
(?[X]:(quiet(X)))&
(?[X]:((~old(X)<~>~wise(X)))) | ~rich(fred) | [
"p0",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 65272208391407453764297
% SZS output start Proof for 65272208391407453764297
1. ! [X0] : (quiet(X0) <=> (~creative(X0) | ~quiet(X0))) [input p0]
14. ! [X0] : ((brave(X0) <~> quiet(X0)) <=> (brave(X0) | ~rich(X0))) [input p13]
23. rich(fred) [input hypothesis]
35. ! [X0] : ((quiet(X0) | (creative(X0) & quiet(X0))) & ((~creative(X0) | ~quiet(X0)) | ~quiet(X0))) [nnf transformation 1]
36. ! [X0] : ((quiet(X0) | (creative(X0) & quiet(X0))) & (~creative(X0) | ~quiet(X0) | ~quiet(X0))) [flattening 35]
62. ! [X0] : ((((~quiet(X0) | ~brave(X0)) & (quiet(X0) | brave(X0))) | (~brave(X0) & rich(X0))) & ((brave(X0) | ~rich(X0)) | ((brave(X0) | ~quiet(X0)) & (quiet(X0) | ~brave(X0))))) [nnf transformation 14]
63. ! [X0] : ((((~quiet(X0) | ~brave(X0)) & (quiet(X0) | brave(X0))) | (~brave(X0) & rich(X0))) & (brave(X0) | ~rich(X0) | ((brave(X0) | ~quiet(X0)) & (quiet(X0) | ~brave(X0))))) [flattening 62]
82. quiet(X0) | quiet(X0) [cnf transformation 36]
120. brave(X0) | ~rich(X0) | brave(X0) | ~quiet(X0) [cnf transformation 63]
124. ~quiet(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 63]
142. rich(fred) [cnf transformation 23]
145. brave(X0) | ~rich(X0) | ~quiet(X0) [duplicate literal removal 120]
146. ~quiet(X0) | ~brave(X0) [duplicate literal removal 124]
148. quiet(X0) [duplicate literal removal 82]
203. 13 <=> ! [X0] : ~rich(X0) [avatar definition]
204. ~rich(X0) <- (13) [avatar component clause 203]
251. ~brave(X0) [subsumption resolution 146,148]
252. ~rich(X0) | ~quiet(X0) [subsumption resolution 145,251]
253. ~rich(X0) [subsumption resolution 252,148]
254. 13 [avatar split clause 253,203]
279. $false <- (13) [resolution 204,142]
280. ~13 [avatar contradiction clause 279]
281. $false [avatar sat refutation 254,280]
% SZS output end Proof for 65272208391407453764297
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative and not happy is old or kind and vice versa. Everyone who is rich or tall is either not curious or kind and vice versa. Everyone who is either calm or patient is either not calm or humble. Everyone who is funny or not happy is not creative and vice versa. Everyone who is happy or not creative is either patient or not funny. Everyone who is patient is curious or not quiet and vice versa. If lucy is both not humble and not funny then lucy is both quiet and not rich and vice versa. Everyone who is either brave or not rich is curious and vice versa. Everyone who is not old or creative is either not quiet or curious. Everyone who is both not happy and not creative is curious and vice versa. If john is either not happy or not generous then someone is not quiet. Everyone who is either not happy or quiet is calm or humble and vice versa. If someone is old or wise then alice is old. If someone is funny or not kind then someone is not humble or not strong. Everyone who is either not generous or rich is both not quiet and not rich. Everyone who is old or not brave is not patient. Susan is either rich or not creative. Someone is either not kind or not creative. Mary is both funny and not strong. Someone is not rich or not funny. Alice is tall or not brave. Mary is not wise. | Lucy is funny. | entailment | (![X]:((~creative(X)&~happy(X))<=>(old(X)|kind(X))))&
(![X]:((rich(X)|tall(X))<=>(~curious(X)<~>kind(X))))&
(![X]:((calm(X)<~>patient(X))=>(~calm(X)<~>humble(X))))&
(![X]:((funny(X)|~happy(X))<=>~creative(X)))&
(![X]:((happy(X)|~creative(X))=>(patient(X)<~>~funny(X))))&
(![X]:(patient(X)<=>(curious(X)|~quiet(X))))&
(((~humble(lucy)&~funny(lucy)))<=>((quiet(lucy)&~rich(lucy))))&
(![X]:((brave(X)<~>~rich(X))<=>curious(X)))&
(![X]:((~old(X)|creative(X))=>(~quiet(X)<~>curious(X))))&
(![X]:((~happy(X)&~creative(X))<=>curious(X)))&
(((~happy(john)<~>~generous(john)))=>(?[X]:(~quiet(X))))&
(![X]:((~happy(X)<~>quiet(X))<=>(calm(X)|humble(X))))&
((?[X]:((old(X)|wise(X))))=>(old(alice)))&
((?[X]:((funny(X)|~kind(X))))=>(?[X]:((~humble(X)|~strong(X)))))&
(![X]:((~generous(X)<~>rich(X))=>(~quiet(X)&~rich(X))))&
(![X]:((old(X)|~brave(X))=>~patient(X)))&
((rich(susan)<~>~creative(susan)))&
(?[X]:((~kind(X)<~>~creative(X))))&
((funny(mary)&~strong(mary)))&
(?[X]:((~rich(X)|~funny(X))))&
((tall(alice)|~brave(alice)))&
(~wise(mary)) | funny(lucy) | [
"p0",
"p3",
"p4",
"p5",
"p8",
"p9",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3396410332810090335794932
% SZS output start Proof for 3396410332810090335794932
1. ! [X0] : ((~happy(X0) & ~creative(X0)) <=> (kind(X0) | old(X0))) [input p0]
4. ! [X0] : ((~happy(X0) | funny(X0)) <=> ~creative(X0)) [input p3]
5. ! [X0] : ((~creative(X0) | happy(X0)) => (patient(X0) <~> ~funny(X0))) [input p4]
6. ! [X0] : (patient(X0) <=> (~quiet(X0) | curious(X0))) [input p5]
9. ! [X0] : ((creative(X0) | ~old(X0)) => (~quiet(X0) <~> curious(X0))) [input p8]
10. ! [X0] : ((~creative(X0) & ~happy(X0)) <=> curious(X0)) [input p9]
16. ! [X0] : ((~brave(X0) | old(X0)) => ~patient(X0)) [input p15]
23. ~funny(lucy) [input hypothesis]
30. ! [X0] : ((patient(X0) <~> ~funny(X0)) | (creative(X0) & ~happy(X0))) [ennf transformation 5]
31. ! [X0] : ((~quiet(X0) <~> curious(X0)) | (~creative(X0) & old(X0))) [ennf transformation 9]
35. ! [X0] : (~patient(X0) | (brave(X0) & ~old(X0))) [ennf transformation 16]
36. ! [X0] : (((~happy(X0) & ~creative(X0)) | (~kind(X0) & ~old(X0))) & ((kind(X0) | old(X0)) | (happy(X0) | creative(X0)))) [nnf transformation 1]
37. ! [X0] : (((~happy(X0) & ~creative(X0)) | (~kind(X0) & ~old(X0))) & (kind(X0) | old(X0) | happy(X0) | creative(X0))) [flattening 36]
41. ! [X0] : (((~happy(X0) | funny(X0)) | creative(X0)) & (~creative(X0) | (happy(X0) & ~funny(X0)))) [nnf transformation 4]
42. ! [X0] : ((~happy(X0) | funny(X0) | creative(X0)) & (~creative(X0) | (happy(X0) & ~funny(X0)))) [flattening 41]
43. ! [X0] : (((funny(X0) | ~patient(X0)) & (~funny(X0) | patient(X0))) | (creative(X0) & ~happy(X0))) [nnf transformation 30]
44. ! [X0] : ((patient(X0) | (quiet(X0) & ~curious(X0))) & ((~quiet(X0) | curious(X0)) | ~patient(X0))) [nnf transformation 6]
45. ! [X0] : ((patient(X0) | (quiet(X0) & ~curious(X0))) & (~quiet(X0) | curious(X0) | ~patient(X0))) [flattening 44]
49. ! [X0] : (((~curious(X0) | quiet(X0)) & (curious(X0) | ~quiet(X0))) | (~creative(X0) & old(X0))) [nnf transformation 31]
50. ! [X0] : (((~creative(X0) & ~happy(X0)) | ~curious(X0)) & (curious(X0) | (creative(X0) | happy(X0)))) [nnf transformation 10]
51. ! [X0] : (((~creative(X0) & ~happy(X0)) | ~curious(X0)) & (curious(X0) | creative(X0) | happy(X0))) [flattening 50]
67. ~old(X0) | ~happy(X0) [cnf transformation 37]
80. ~creative(X0) | happy(X0) [cnf transformation 42]
84. ~patient(X0) | funny(X0) | ~happy(X0) [cnf transformation 43]
85. ~patient(X0) | funny(X0) | creative(X0) [cnf transformation 43]
87. ~curious(X0) | patient(X0) [cnf transformation 45]
88. quiet(X0) | patient(X0) [cnf transformation 45]
97. ~quiet(X0) | curious(X0) | old(X0) [cnf transformation 49]
101. curious(X0) | creative(X0) | happy(X0) [cnf transformation 51]
103. ~curious(X0) | ~creative(X0) [cnf transformation 51]
117. ~patient(X0) | ~old(X0) [cnf transformation 35]
126. ~funny(lucy) [cnf transformation 23]
132. 1 <=> quiet(lucy) [avatar definition]
133. quiet(lucy) <- (1) [avatar component clause 132]
134. ~quiet(lucy) <- (~1) [avatar component clause 132]
140. 3 <=> funny(lucy) [avatar definition]
142. ~funny(lucy) <- (~3) [avatar component clause 140]
151. curious(X0) | happy(X0) [subsumption resolution 101,80]
167. 8 <=> ! [X0] : ~old(X0) [avatar definition]
168. ~old(X0) <- (8) [avatar component clause 167]
211. ~3 [avatar split clause 126,140]
216. patient(lucy) <- (~1) [resolution 88,134]
227. patient(X2) | happy(X2) [resolution 151,87]
230. happy(X1) | ~old(X1) [resolution 227,117]
254. funny(lucy) | ~happy(lucy) <- (~1) [resolution 84,216]
257. ~happy(lucy) <- (~1, ~3) [subsumption resolution 254,142]
268. funny(lucy) | creative(lucy) <- (~1) [resolution 85,216]
272. creative(lucy) <- (~1, ~3) [subsumption resolution 268,142]
285. 25 <=> curious(lucy) [avatar definition]
287. curious(lucy) <- (25) [avatar component clause 285]
326. happy(lucy) <- (~1, ~3) [resolution 272,80]
327. $false <- (~1, ~3) [subsumption resolution 326,257]
328. 1 | 3 [avatar contradiction clause 327]
331. 31 <=> patient(lucy) [avatar definition]
332. patient(lucy) <- (31) [avatar component clause 331]
336. curious(lucy) | old(lucy) <- (1) [resolution 97,133]
339. curious(lucy) <- (1, 8) [subsumption resolution 336,168]
340. 25 | ~1 | ~8 [avatar split clause 339,167,132,285]
347. ~old(X1) [subsumption resolution 230,67]
348. 8 [avatar split clause 347,167]
365. patient(lucy) <- (25) [resolution 287,87]
370. ~creative(lucy) <- (25) [resolution 287,103]
386. 31 | ~25 [avatar split clause 365,285,331]
390. funny(lucy) | creative(lucy) <- (31) [resolution 332,85]
394. creative(lucy) <- (~3, 31) [subsumption resolution 390,142]
395. $false <- (~3, 25, 31) [subsumption resolution 394,370]
396. 3 | ~25 | ~31 [avatar contradiction clause 395]
397. $false [avatar sat refutation 211,328,340,348,386,396]
% SZS output end Proof for 3396410332810090335794932
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 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.
Everyone who is funny is either not brave or wise and vice versa.
Everyone who is both patient and strong is strong and vice versa.
If someone is either not patient or not humble then someone is both creative and not creative.
Someone is either not patient or not wise.
Susan is either not happy or wise.
Paul is strong or brave. | Paul is rich. | contradiction | (![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))))&
(![X]:(funny(X)<=>(~brave(X)<~>wise(X))))&
(![X]:((patient(X)&strong(X))<=>strong(X)))&
((?[X]:((~patient(X)<~>~humble(X))))=>(?[X]:((creative(X)&~creative(X)))))&
(?[X]:((~patient(X)<~>~wise(X))))&
((~happy(susan)<~>wise(susan)))&
((strong(paul)|brave(paul))) | rich(paul) | [
"p0",
"p2",
"p4",
"p5",
"p6",
"p8",
"p12",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4259303326885856551244970
% SZS output start Proof for 4259303326885856551244970
1. ! [X0] : ((strong(X0) & ~funny(X0)) <=> (quiet(X0) | wise(X0))) [input p0]
3. ! [X0] : (~curious(X0) <=> patient(X0)) [input p2]
5. ! [X0] : ((old(X0) | ~strong(X0)) => (~tall(X0) & funny(X0))) [input p4]
6. ! [X0] : ((~brave(X0) | ~creative(X0)) <=> (curious(X0) & tall(X0))) [input p5]
7. ! [X0] : ((~patient(X0) & funny(X0)) <=> (rich(X0) <~> ~calm(X0))) [input p6]
9. ! [X0] : ((~old(X0) <~> ~calm(X0)) <=> (strong(X0) | ~strong(X0))) [input p8]
13. ! [X0] : ((~brave(X0) <~> ~wise(X0)) => (~funny(X0) <~> curious(X0))) [input p12]
14. ! [X0] : (funny(X0) <=> (~brave(X0) <~> wise(X0))) [input p13]
15. ! [X0] : ((strong(X0) & patient(X0)) <=> strong(X0)) [input p14]
20. rich(paul) [input hypothesis]
24. ! [X0] : ((~tall(X0) & funny(X0)) | (~old(X0) & strong(X0))) [ennf transformation 5]
28. ! [X0] : ((~funny(X0) <~> curious(X0)) | (~brave(X0) <=> ~wise(X0))) [ennf transformation 13]
30. ! [X0] : (((strong(X0) & ~funny(X0)) | (~quiet(X0) & ~wise(X0))) & ((quiet(X0) | wise(X0)) | (~strong(X0) | funny(X0)))) [nnf transformation 1]
31. ! [X0] : (((strong(X0) & ~funny(X0)) | (~quiet(X0) & ~wise(X0))) & (quiet(X0) | wise(X0) | ~strong(X0) | funny(X0))) [flattening 30]
34. ! [X0] : ((~curious(X0) | ~patient(X0)) & (patient(X0) | curious(X0))) [nnf transformation 3]
36. ! [X0] : (((~brave(X0) | ~creative(X0)) | (~curious(X0) | ~tall(X0))) & ((curious(X0) & tall(X0)) | (brave(X0) & creative(X0)))) [nnf transformation 6]
37. ! [X0] : ((~brave(X0) | ~creative(X0) | ~curious(X0) | ~tall(X0)) & ((curious(X0) & tall(X0)) | (brave(X0) & creative(X0)))) [flattening 36]
38. ! [X0] : (((~patient(X0) & funny(X0)) | ((rich(X0) | calm(X0)) & (~calm(X0) | ~rich(X0)))) & (((calm(X0) | ~rich(X0)) & (~calm(X0) | rich(X0))) | (patient(X0) | ~funny(X0)))) [nnf transformation 7]
39. ! [X0] : (((~patient(X0) & funny(X0)) | ((rich(X0) | calm(X0)) & (~calm(X0) | ~rich(X0)))) & (((calm(X0) | ~rich(X0)) & (~calm(X0) | rich(X0))) | patient(X0) | ~funny(X0))) [flattening 38]
45. ! [X0] : ((((calm(X0) | old(X0)) & (~calm(X0) | ~old(X0))) | (~strong(X0) & strong(X0))) & ((strong(X0) | ~strong(X0)) | ((~old(X0) | calm(X0)) & (~calm(X0) | old(X0))))) [nnf transformation 9]
46. ! [X0] : ((((calm(X0) | old(X0)) & (~calm(X0) | ~old(X0))) | (~strong(X0) & strong(X0))) & (strong(X0) | ~strong(X0) | ((~old(X0) | calm(X0)) & (~calm(X0) | old(X0))))) [flattening 45]
50. ! [X0] : (((~curious(X0) | funny(X0)) & (curious(X0) | ~funny(X0))) | ((~brave(X0) | wise(X0)) & (~wise(X0) | brave(X0)))) [nnf transformation 28]
51. ! [X0] : ((funny(X0) | ((~brave(X0) | ~wise(X0)) & (wise(X0) | brave(X0)))) & (((~wise(X0) | brave(X0)) & (wise(X0) | ~brave(X0))) | ~funny(X0))) [nnf transformation 14]
52. ! [X0] : (((strong(X0) & patient(X0)) | ~strong(X0)) & (strong(X0) | (~strong(X0) | ~patient(X0)))) [nnf transformation 15]
53. ! [X0] : (((strong(X0) & patient(X0)) | ~strong(X0)) & (strong(X0) | ~strong(X0) | ~patient(X0))) [flattening 52]
63. ~wise(X0) | ~funny(X0) [cnf transformation 31]
70. ~patient(X0) | ~curious(X0) [cnf transformation 34]
73. strong(X0) | funny(X0) [cnf transformation 24]
74. ~old(X0) | funny(X0) [cnf transformation 24]
75. ~tall(X0) | strong(X0) [cnf transformation 24]
78. tall(X0) | brave(X0) [cnf transformation 37]
80. curious(X0) | brave(X0) [cnf transformation 37]
84. ~calm(X0) | funny(X0) | ~rich(X0) [cnf transformation 39]
95. calm(X0) | old(X0) | strong(X0) [cnf transformation 46]
96. ~strong(X0) | old(X0) | calm(X0) [cnf transformation 46]
111. ~curious(X0) | funny(X0) | ~wise(X0) | brave(X0) [cnf transformation 50]
113. wise(X0) | ~brave(X0) | ~funny(X0) [cnf transformation 51]
116. funny(X0) | ~brave(X0) | ~wise(X0) [cnf transformation 51]
118. ~strong(X0) | patient(X0) [cnf transformation 53]
129. rich(paul) [cnf transformation 20]
144. 4 <=> brave(paul) [avatar definition]
145. brave(paul) <- (4) [avatar component clause 144]
146. ~brave(paul) <- (~4) [avatar component clause 144]
169. calm(X0) | old(X0) [subsumption resolution 95,96]
175. ~curious(X0) | ~wise(X0) | brave(X0) [subsumption resolution 111,63]
176. ~wise(X0) | brave(X0) [subsumption resolution 175,80]
179. ~brave(X0) | ~wise(X0) [subsumption resolution 116,63]
180. ~wise(X0) [subsumption resolution 179,176]
182. ~brave(X0) | ~funny(X0) [subsumption resolution 113,180]
196. brave(X0) | strong(X0) [resolution 78,75]
203. ~funny(paul) <- (4) [resolution 182,145]
209. funny(X0) | ~rich(X0) | old(X0) [resolution 84,169]
210. ~rich(X0) | funny(X0) [subsumption resolution 209,74]
214. strong(X0) | ~funny(X0) [resolution 196,182]
215. strong(X0) [subsumption resolution 214,73]
218. patient(X0) [resolution 215,118]
243. ~curious(X2) [resolution 218,70]
263. brave(X0) [resolution 243,80]
287. funny(paul) [resolution 210,129]
288. $false <- (4) [subsumption resolution 287,203]
289. ~4 [avatar contradiction clause 288]
292. $false <- (~4) [subsumption resolution 146,263]
293. 4 [avatar contradiction clause 292]
294. $false [avatar sat refutation 289,293]
% SZS output end Proof for 4259303326885856551244970
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative is not happy and vice versa.
Everyone who is either not kind or not old is either humble or strong and vice versa.
If john is both not wise and not rich then someone is old or not old and vice versa.
If paul is both calm and creative then someone is happy and vice versa.
Everyone who is not curious is either strong or not strong and vice versa.
If fred is both old and quiet then paul is either not brave or not kind and vice versa.
If alice is both not old and happy then someone is either not generous or creative.
Everyone who is both rich and not tall is either rich or not calm.
Everyone who is both not kind and creative is either not humble or creative and vice versa.
Everyone who is not kind is both not rich and not creative and vice versa.
If mary is funny then someone is tall or not happy.
If someone is both rich and funny then someone is not funny or not quiet.
If someone is not tall then fred is either not wise or happy.
Everyone who is either rich or generous is not happy or strong.
Everyone who is both not rich and old is rich.
If fred is generous then lucy is brave or happy.
Fred is either funny or tall.
Fred is either not quiet or quiet.
Someone is strong or creative.
Susan is curious or not happy.
Alice is either not curious or calm.
John is old or not generous.
Alice is both funny and not quiet.
Someone is either brave or kind. | John is generous. | contradiction | (![X]:(creative(X)<=>~happy(X)))&
(![X]:((~kind(X)<~>~old(X))<=>(humble(X)<~>strong(X))))&
(((~wise(john)&~rich(john)))<=>(?[X]:((old(X)|~old(X)))))&
(((calm(paul)&creative(paul)))<=>(?[X]:(happy(X))))&
(![X]:(~curious(X)<=>(strong(X)<~>~strong(X))))&
(((old(fred)&quiet(fred)))<=>((~brave(paul)<~>~kind(paul))))&
(((~old(alice)&happy(alice)))=>(?[X]:((~generous(X)<~>creative(X)))))&
(![X]:((rich(X)&~tall(X))=>(rich(X)<~>~calm(X))))&
(![X]:((~kind(X)&creative(X))<=>(~humble(X)<~>creative(X))))&
(![X]:(~kind(X)<=>(~rich(X)&~creative(X))))&
((funny(mary))=>(?[X]:((tall(X)|~happy(X)))))&
((?[X]:((rich(X)&funny(X))))=>(?[X]:((~funny(X)|~quiet(X)))))&
((?[X]:(~tall(X)))=>((~wise(fred)<~>happy(fred))))&
(![X]:((rich(X)<~>generous(X))=>(~happy(X)|strong(X))))&
(![X]:((~rich(X)&old(X))=>rich(X)))&
((generous(fred))=>((brave(lucy)|happy(lucy))))&
((funny(fred)<~>tall(fred)))&
((~quiet(fred)<~>quiet(fred)))&
(?[X]:((strong(X)|creative(X))))&
((curious(susan)|~happy(susan)))&
((~curious(alice)<~>calm(alice)))&
((old(john)|~generous(john)))&
((funny(alice)&~quiet(alice)))&
(?[X]:((brave(X)<~>kind(X)))) | generous(john) | [
"p2",
"p14",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 6061089076236061022255942
% SZS output start Proof for 6061089076236061022255942
3. (~rich(john) & ~wise(john)) <=> ? [X0] : (~old(X0) | old(X0)) [input p2]
15. ! [X0] : ((old(X0) & ~rich(X0)) => rich(X0)) [input p14]
22. ~generous(john) | old(john) [input p21]
25. generous(john) [input hypothesis]
36. ! [X0] : (rich(X0) | (~old(X0) | rich(X0))) [ennf transformation 15]
37. ! [X0] : (rich(X0) | ~old(X0) | rich(X0)) [flattening 36]
42. ((~rich(john) & ~wise(john)) | ! [X0] : (old(X0) & ~old(X0))) & (? [X0] : (~old(X0) | old(X0)) | (rich(john) | wise(john))) [nnf transformation 3]
43. ((~rich(john) & ~wise(john)) | ! [X0] : (old(X0) & ~old(X0))) & (? [X0] : (~old(X0) | old(X0)) | rich(john) | wise(john)) [flattening 42]
44. ((~rich(john) & ~wise(john)) | ! [X0] : (old(X0) & ~old(X0))) & (? [X1] : (~old(X1) | old(X1)) | rich(john) | wise(john)) [rectify 43]
45. ? [X1] : (~old(X1) | old(X1)) => (~old(sK0) | old(sK0)) [choice axiom]
46. ((~rich(john) & ~wise(john)) | ! [X0] : (old(X0) & ~old(X0))) & ((~old(sK0) | old(sK0)) | rich(john) | wise(john)) [skolemisation 44,45]
91. ~rich(john) | ~old(X0) [cnf transformation 46]
92. ~rich(john) | old(X0) [cnf transformation 46]
125. rich(X0) | ~old(X0) | rich(X0) [cnf transformation 37]
135. ~generous(john) | old(john) [cnf transformation 22]
140. generous(john) [cnf transformation 25]
141. ~old(X0) | rich(X0) [duplicate literal removal 125]
148. 1 <=> ! [X0] : old(X0) [avatar definition]
149. old(X0) <- (1) [avatar component clause 148]
151. 2 <=> rich(john) [avatar definition]
154. 1 | ~2 [avatar split clause 92,151,148]
156. 3 <=> ! [X0] : ~old(X0) [avatar definition]
157. ~old(X0) <- (3) [avatar component clause 156]
158. 3 | ~2 [avatar split clause 91,151,156]
298. 33 <=> old(john) [avatar definition]
300. old(john) <- (33) [avatar component clause 298]
302. 34 <=> generous(john) [avatar definition]
305. 33 | ~34 [avatar split clause 135,302,298]
316. 34 [avatar split clause 140,302]
326. rich(john) <- (33) [resolution 141,300]
329. 2 | ~33 [avatar split clause 326,298,151]
330. $false <- (1, 3) [subsumption resolution 149,157]
331. ~1 | ~3 [avatar contradiction clause 330]
332. $false [avatar sat refutation 154,158,305,316,329,331]
% SZS output end Proof for 6061089076236061022255942
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind or not patient is either brave or calm and vice versa. If someone is patient or not kind then someone is both not funny and tall and vice versa. If someone is either calm or not curious then someone is both not tall and not brave. Everyone who is either curious or not tall is creative or not quiet and vice versa. Everyone who is either old or not strong is not strong and vice versa. If someone is either old or wise then someone is not humble or funny and vice versa. Everyone who is happy or funny is funny or not brave and vice versa. Everyone who is not tall or rich is creative or 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. John is not strong. Lucy is wise. Someone is quiet. Paul is not curious or not funny. | Lucy is funny. | entailment | (![X]:((~kind(X)|~patient(X))<=>(brave(X)<~>calm(X))))&
((?[X]:((patient(X)|~kind(X))))<=>(?[X]:((~funny(X)&tall(X)))))&
((?[X]:((calm(X)<~>~curious(X))))=>(?[X]:((~tall(X)&~brave(X)))))&
(![X]:((curious(X)<~>~tall(X))<=>(creative(X)|~quiet(X))))&
(![X]:((old(X)<~>~strong(X))<=>~strong(X)))&
((?[X]:((old(X)<~>wise(X))))<=>(?[X]:((~humble(X)|funny(X)))))&
(![X]:((happy(X)|funny(X))<=>(funny(X)|~brave(X))))&
(![X]:((~tall(X)|rich(X))<=>(creative(X)|brave(X))))&
(![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)))&
(~strong(john))&
(wise(lucy))&
(?[X]:(quiet(X)))&
((~curious(paul)|~funny(paul))) | funny(lucy) | [
"p1",
"p6",
"p8",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 6534048947863722386878030
% SZS output start Proof for 6534048947863722386878030
2. ? [X0] : (~kind(X0) | patient(X0)) <=> ? [X0] : (tall(X0) & ~funny(X0)) [input p1]
7. ! [X0] : ((funny(X0) | happy(X0)) <=> (~brave(X0) | funny(X0))) [input p6]
9. ! [X0] : ((~generous(X0) | humble(X0)) <=> (quiet(X0) <~> tall(X0))) [input p8]
11. ! [X0] : ((~tall(X0) | generous(X0)) => (~brave(X0) & ~happy(X0))) [input p10]
12. ! [X0] : ((rich(X0) | ~quiet(X0)) <=> (~humble(X0) & quiet(X0))) [input p11]
20. ~funny(lucy) [input hypothesis]
21. ? [X0] : (~kind(X0) | patient(X0)) <=> ? [X1] : (tall(X1) & ~funny(X1)) [rectify 2]
26. ! [X0] : ((~brave(X0) & ~happy(X0)) | (tall(X0) & ~generous(X0))) [ennf transformation 11]
34. (? [X0] : (~kind(X0) | patient(X0)) | ! [X1] : (~tall(X1) | funny(X1))) & (? [X1] : (tall(X1) & ~funny(X1)) | ! [X0] : (kind(X0) & ~patient(X0))) [nnf transformation 21]
35. (? [X0] : (~kind(X0) | patient(X0)) | ! [X1] : (~tall(X1) | funny(X1))) & (? [X2] : (tall(X2) & ~funny(X2)) | ! [X3] : (kind(X3) & ~patient(X3))) [rectify 34]
36. ? [X0] : (~kind(X0) | patient(X0)) => (~kind(sK0) | patient(sK0)) [choice axiom]
37. ? [X2] : (tall(X2) & ~funny(X2)) => (tall(sK1) & ~funny(sK1)) [choice axiom]
38. ((~kind(sK0) | patient(sK0)) | ! [X1] : (~tall(X1) | funny(X1))) & ((tall(sK1) & ~funny(sK1)) | ! [X3] : (kind(X3) & ~patient(X3))) [skolemisation 35,37,36]
51. ! [X0] : (((funny(X0) | happy(X0)) | (brave(X0) & ~funny(X0))) & ((~brave(X0) | funny(X0)) | (~funny(X0) & ~happy(X0)))) [nnf transformation 7]
52. ! [X0] : ((funny(X0) | happy(X0) | (brave(X0) & ~funny(X0))) & (~brave(X0) | funny(X0) | (~funny(X0) & ~happy(X0)))) [flattening 51]
55. ! [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 9]
56. ! [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 55]
58. ! [X0] : (((rich(X0) | ~quiet(X0)) | (humble(X0) | ~quiet(X0))) & ((~humble(X0) & quiet(X0)) | (~rich(X0) & quiet(X0)))) [nnf transformation 12]
59. ! [X0] : ((rich(X0) | ~quiet(X0) | humble(X0) | ~quiet(X0)) & ((~humble(X0) & quiet(X0)) | (~rich(X0) & quiet(X0)))) [flattening 58]
69. ~funny(sK1) | ~patient(X3) [cnf transformation 38]
70. ~funny(sK1) | kind(X3) [cnf transformation 38]
71. tall(sK1) | ~patient(X3) [cnf transformation 38]
72. tall(sK1) | kind(X3) [cnf transformation 38]
73. ~kind(sK0) | patient(sK0) | ~tall(X1) | funny(X1) [cnf transformation 38]
97. happy(X0) | funny(X0) | brave(X0) [cnf transformation 52]
105. ~quiet(X0) | ~tall(X0) | generous(X0) [cnf transformation 56]
112. ~generous(X0) | ~happy(X0) [cnf transformation 26]
113. ~happy(X0) | tall(X0) [cnf transformation 26]
114. ~generous(X0) | ~brave(X0) [cnf transformation 26]
115. ~brave(X0) | tall(X0) [cnf transformation 26]
116. quiet(X0) | quiet(X0) [cnf transformation 59]
131. ~funny(lucy) [cnf transformation 20]
132. quiet(X0) [duplicate literal removal 116]
137. 1 <=> ! [X1] : (~tall(X1) | funny(X1)) [avatar definition]
138. ~tall(X1) | funny(X1) <- (1) [avatar component clause 137]
140. 2 <=> patient(sK0) [avatar definition]
142. patient(sK0) <- (2) [avatar component clause 140]
144. 3 <=> kind(sK0) [avatar definition]
146. ~kind(sK0) <- (~3) [avatar component clause 144]
147. 1 | 2 | ~3 [avatar split clause 73,144,140,137]
149. 4 <=> ! [X3] : kind(X3) [avatar definition]
150. kind(X3) <- (4) [avatar component clause 149]
152. 5 <=> tall(sK1) [avatar definition]
154. tall(sK1) <- (5) [avatar component clause 152]
155. 4 | 5 [avatar split clause 72,152,149]
157. 6 <=> ! [X3] : ~patient(X3) [avatar definition]
158. ~patient(X3) <- (6) [avatar component clause 157]
159. 6 | 5 [avatar split clause 71,152,157]
161. 7 <=> funny(sK1) [avatar definition]
163. ~funny(sK1) <- (~7) [avatar component clause 161]
164. 4 | ~7 [avatar split clause 70,161,149]
165. 6 | ~7 [avatar split clause 69,161,157]
249. funny(X1) | brave(X1) | tall(X1) [resolution 97,113]
251. tall(X1) | funny(X1) [subsumption resolution 249,115]
274. 26 <=> brave(sK1) [avatar definition]
284. ~tall(X0) | generous(X0) [resolution 105,132]
285. generous(sK1) <- (5) [resolution 284,154]
288. ~brave(sK1) <- (5) [resolution 285,114]
289. ~happy(sK1) <- (5) [resolution 285,112]
293. funny(sK1) | brave(sK1) <- (5) [resolution 289,97]
294. brave(sK1) <- (5, ~7) [subsumption resolution 293,163]
297. 26 | ~5 | 7 [avatar split clause 294,161,152,274]
298. ~26 | ~5 [avatar split clause 288,152,274]
300. $false <- (~3, 4) [resolution 150,146]
301. 3 | ~4 [avatar contradiction clause 300]
302. $false <- (2, 6) [subsumption resolution 142,158]
303. ~2 | ~6 [avatar contradiction clause 302]
304. funny(X1) <- (1) [subsumption resolution 138,251]
305. $false <- (1) [resolution 304,131]
308. ~1 [avatar contradiction clause 305]
309. $false [avatar sat refutation 147,155,159,164,165,297,298,301,303,308]
% SZS output end Proof for 6534048947863722386878030
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not humble then lucy is both not creative and not calm and vice versa.
If paul is creative or not generous then someone is both old and strong.
If paul is not funny then paul is humble or not quiet.
If john is generous then mary is strong and vice versa.
Everyone who is both not wise and generous is not kind or not brave and vice versa.
If lucy is either tall or not humble then someone is either curious or tall and vice versa.
Everyone who is either not funny or creative is not tall and vice versa.
If fred is both not happy and old then john is both brave and not brave.
If mary is not calm then fred is not creative.
If mary is curious then someone is not generous and vice versa.
If someone is either not happy or not old then john is not creative and vice versa.
Everyone who is tall is either old or quiet.
Everyone who is not creative is both not wise and curious.
Everyone who is both quiet and generous is creative and vice versa.
Everyone who is either not funny or generous is both wise and kind and vice versa.
Everyone who is not kind is wise and vice versa.
Fred is either not creative or not old.
Mary is kind or not generous.
Someone is curious.
Paul is either not generous or creative.
Someone is either funny or generous.
Someone is not generous or wise.
John is happy. | Mary is funny. | neutral | ((~humble(paul))<=>((~creative(lucy)&~calm(lucy))))&
(((creative(paul)|~generous(paul)))=>(?[X]:((old(X)&strong(X)))))&
((~funny(paul))=>((humble(paul)|~quiet(paul))))&
((generous(john))<=>(strong(mary)))&
(![X]:((~wise(X)&generous(X))<=>(~kind(X)|~brave(X))))&
(((tall(lucy)<~>~humble(lucy)))<=>(?[X]:((curious(X)<~>tall(X)))))&
(![X]:((~funny(X)<~>creative(X))<=>~tall(X)))&
(((~happy(fred)&old(fred)))=>((brave(john)&~brave(john))))&
((~calm(mary))=>(~creative(fred)))&
((curious(mary))<=>(?[X]:(~generous(X))))&
((?[X]:((~happy(X)<~>~old(X))))<=>(~creative(john)))&
(![X]:(tall(X)=>(old(X)<~>quiet(X))))&
(![X]:(~creative(X)=>(~wise(X)&curious(X))))&
(![X]:((quiet(X)&generous(X))<=>creative(X)))&
(![X]:((~funny(X)<~>generous(X))<=>(wise(X)&kind(X))))&
(![X]:(~kind(X)<=>wise(X)))&
((~creative(fred)<~>~old(fred)))&
((kind(mary)|~generous(mary)))&
(?[X]:(curious(X)))&
((~generous(paul)<~>creative(paul)))&
(?[X]:((funny(X)<~>generous(X))))&
(?[X]:((~generous(X)|wise(X))))&
(happy(john)) | funny(mary) | [] | null | 0 |
If paul is not old or rich then someone is either not creative or creative and vice versa. Everyone who is patient or not creative is not kind. Everyone who is both not wise and generous is both not happy and not patient and vice versa. If someone is both not curious and quiet then someone is both funny and calm. Everyone who is quiet is either not tall or quiet and vice versa. If someone is quiet or not kind then fred is either not creative or curious and vice versa. Everyone who is either creative or not happy is either not tall or not brave and vice versa. Everyone who is generous is not humble or not quiet and vice versa. If mary is humble then someone is not tall. Everyone who is both not happy and calm is not kind. Everyone who is both not strong and not patient is not creative and vice versa. Everyone who is happy or not tall is both curious and not generous. Everyone who is strong is not tall and vice versa. If paul is strong or not strong then fred is either not quiet or strong. Everyone who is patient or happy is both not creative and not brave. If someone is both not funny and generous then someone is either tall or not curious and vice versa. Someone is humble. Someone is old. Paul is funny or generous. Lucy is both not kind and humble. Lucy is not funny or quiet. Someone is either strong or generous. | Fred is generous. | entailment | (((~old(paul)|rich(paul)))<=>(?[X]:((~creative(X)<~>creative(X)))))&
(![X]:((patient(X)|~creative(X))=>~kind(X)))&
(![X]:((~wise(X)&generous(X))<=>(~happy(X)&~patient(X))))&
((?[X]:((~curious(X)&quiet(X))))=>(?[X]:((funny(X)&calm(X)))))&
(![X]:(quiet(X)<=>(~tall(X)<~>quiet(X))))&
((?[X]:((quiet(X)|~kind(X))))<=>((~creative(fred)<~>curious(fred))))&
(![X]:((creative(X)<~>~happy(X))<=>(~tall(X)<~>~brave(X))))&
(![X]:(generous(X)<=>(~humble(X)|~quiet(X))))&
((humble(mary))=>(?[X]:(~tall(X))))&
(![X]:((~happy(X)&calm(X))=>~kind(X)))&
(![X]:((~strong(X)&~patient(X))<=>~creative(X)))&
(![X]:((happy(X)|~tall(X))=>(curious(X)&~generous(X))))&
(![X]:(strong(X)<=>~tall(X)))&
(((strong(paul)|~strong(paul)))=>((~quiet(fred)<~>strong(fred))))&
(![X]:((patient(X)|happy(X))=>(~creative(X)&~brave(X))))&
((?[X]:((~funny(X)&generous(X))))<=>(?[X]:((tall(X)<~>~curious(X)))))&
(?[X]:(humble(X)))&
(?[X]:(old(X)))&
((funny(paul)|generous(paul)))&
((~kind(lucy)&humble(lucy)))&
((~funny(lucy)|quiet(lucy)))&
(?[X]:((strong(X)<~>generous(X)))) | generous(fred) | [
"p4",
"p7",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 3773097178436622010267377
% SZS output start Proof for 3773097178436622010267377
5. ! [X0] : (quiet(X0) <=> (~tall(X0) <~> quiet(X0))) [input p4]
8. ! [X0] : (generous(X0) <=> (~quiet(X0) | ~humble(X0))) [input p7]
13. ! [X0] : (strong(X0) <=> ~tall(X0)) [input p12]
14. (~strong(paul) | strong(paul)) => (~quiet(fred) <~> strong(fred)) [input p13]
23. ~generous(fred) [input hypothesis]
32. (~quiet(fred) <~> strong(fred)) | (strong(paul) & ~strong(paul)) [ennf transformation 14]
44. ! [X0] : ((quiet(X0) | ((~tall(X0) | ~quiet(X0)) & (quiet(X0) | tall(X0)))) & (((~quiet(X0) | tall(X0)) & (quiet(X0) | ~tall(X0))) | ~quiet(X0))) [nnf transformation 5]
50. ! [X0] : ((generous(X0) | (quiet(X0) & humble(X0))) & ((~quiet(X0) | ~humble(X0)) | ~generous(X0))) [nnf transformation 8]
51. ! [X0] : ((generous(X0) | (quiet(X0) & humble(X0))) & (~quiet(X0) | ~humble(X0) | ~generous(X0))) [flattening 50]
56. ! [X0] : ((strong(X0) | tall(X0)) & (~tall(X0) | ~strong(X0))) [nnf transformation 13]
57. ((~strong(fred) | quiet(fred)) & (strong(fred) | ~quiet(fred))) | (strong(paul) & ~strong(paul)) [nnf transformation 32]
85. ~quiet(X0) | tall(X0) | ~quiet(X0) [cnf transformation 44]
86. quiet(X0) | quiet(X0) | tall(X0) [cnf transformation 44]
104. quiet(X0) | generous(X0) [cnf transformation 51]
114. ~tall(X0) | ~strong(X0) [cnf transformation 56]
117. strong(fred) | ~quiet(fred) | strong(paul) [cnf transformation 57]
138. ~generous(fred) [cnf transformation 23]
139. ~quiet(X0) | tall(X0) [duplicate literal removal 85]
140. quiet(X0) | tall(X0) [duplicate literal removal 86]
172. tall(X0) [subsumption resolution 139,140]
206. ~strong(X0) [subsumption resolution 114,172]
207. ~quiet(fred) | strong(paul) [subsumption resolution 117,206]
208. ~quiet(fred) [subsumption resolution 207,206]
256. generous(fred) [resolution 104,208]
257. $false [subsumption resolution 256,138]
% SZS output end Proof for 3773097178436622010267377
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny and rich is calm or not tall and vice versa.
Everyone who is both old and not generous is either not funny or not quiet.
Everyone who is not old or not happy is not patient or rich and vice versa.
Everyone who is quiet is not generous.
Everyone who is humble or wise is either not happy or not kind and vice versa.
Everyone who is not calm or quiet is humble and vice versa.
Everyone who is patient is humble or happy.
Everyone who is both not creative and happy is both funny and rich.
If someone is humble then lucy is either not creative or brave and vice versa.
Everyone who is either not rich or creative is both not quiet and funny and vice versa.
Everyone who is kind or not quiet is either old or rich.
Everyone who is not patient or humble is either old or not patient.
If someone is either funny or not wise then alice is both not happy and quiet.
Everyone who is not happy or not kind is patient.
If alice is not creative then someone is both not quiet and not humble.
If fred is either calm or not wise then alice is strong.
Someone is not strong or wise.
Someone is not kind.
Someone is not calm or not brave.
John is both not funny and quiet.
Alice is either not funny or rich.
Paul is funny or quiet.
Someone is either not generous or kind. | Paul is not rich. | entailment | (![X]:((~funny(X)&rich(X))<=>(calm(X)|~tall(X))))&
(![X]:((old(X)&~generous(X))=>(~funny(X)<~>~quiet(X))))&
(![X]:((~old(X)|~happy(X))<=>(~patient(X)|rich(X))))&
(![X]:(quiet(X)=>~generous(X)))&
(![X]:((humble(X)|wise(X))<=>(~happy(X)<~>~kind(X))))&
(![X]:((~calm(X)|quiet(X))<=>humble(X)))&
(![X]:(patient(X)=>(humble(X)|happy(X))))&
(![X]:((~creative(X)&happy(X))=>(funny(X)&rich(X))))&
((?[X]:(humble(X)))<=>((~creative(lucy)<~>brave(lucy))))&
(![X]:((~rich(X)<~>creative(X))<=>(~quiet(X)&funny(X))))&
(![X]:((kind(X)|~quiet(X))=>(old(X)<~>rich(X))))&
(![X]:((~patient(X)|humble(X))=>(old(X)<~>~patient(X))))&
((?[X]:((funny(X)<~>~wise(X))))=>((~happy(alice)&quiet(alice))))&
(![X]:((~happy(X)|~kind(X))=>patient(X)))&
((~creative(alice))=>(?[X]:((~quiet(X)&~humble(X)))))&
(((calm(fred)<~>~wise(fred)))=>(strong(alice)))&
(?[X]:((~strong(X)|wise(X))))&
(?[X]:(~kind(X)))&
(?[X]:((~calm(X)|~brave(X))))&
((~funny(john)&quiet(john)))&
((~funny(alice)<~>rich(alice)))&
((funny(paul)|quiet(paul)))&
(?[X]:((~generous(X)<~>kind(X)))) | ~rich(paul) | [
"p0",
"p2",
"p4",
"p5",
"p6",
"p10",
"p11",
"p13",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 693088598901803419855819
% SZS output start Proof for 693088598901803419855819
1. ! [X0] : ((rich(X0) & ~funny(X0)) <=> (~tall(X0) | calm(X0))) [input p0]
3. ! [X0] : ((~happy(X0) | ~old(X0)) <=> (rich(X0) | ~patient(X0))) [input p2]
5. ! [X0] : ((wise(X0) | humble(X0)) <=> (~happy(X0) <~> ~kind(X0))) [input p4]
6. ! [X0] : ((quiet(X0) | ~calm(X0)) <=> humble(X0)) [input p5]
7. ! [X0] : (patient(X0) => (happy(X0) | humble(X0))) [input p6]
11. ! [X0] : ((~quiet(X0) | kind(X0)) => (old(X0) <~> rich(X0))) [input p10]
12. ! [X0] : ((humble(X0) | ~patient(X0)) => (old(X0) <~> ~patient(X0))) [input p11]
14. ! [X0] : ((~kind(X0) | ~happy(X0)) => patient(X0)) [input p13]
22. quiet(paul) | funny(paul) [input p21]
24. rich(paul) [input hypothesis]
28. ! [X0] : ((happy(X0) | humble(X0)) | ~patient(X0)) [ennf transformation 7]
29. ! [X0] : (happy(X0) | humble(X0) | ~patient(X0)) [flattening 28]
32. ! [X0] : ((old(X0) <~> rich(X0)) | (quiet(X0) & ~kind(X0))) [ennf transformation 11]
33. ! [X0] : ((old(X0) <~> ~patient(X0)) | (~humble(X0) & patient(X0))) [ennf transformation 12]
35. ! [X0] : (patient(X0) | (kind(X0) & happy(X0))) [ennf transformation 14]
38. ! [X0] : (((rich(X0) & ~funny(X0)) | (tall(X0) & ~calm(X0))) & ((~tall(X0) | calm(X0)) | (~rich(X0) | funny(X0)))) [nnf transformation 1]
39. ! [X0] : (((rich(X0) & ~funny(X0)) | (tall(X0) & ~calm(X0))) & (~tall(X0) | calm(X0) | ~rich(X0) | funny(X0))) [flattening 38]
41. ! [X0] : (((~happy(X0) | ~old(X0)) | (~rich(X0) & patient(X0))) & ((rich(X0) | ~patient(X0)) | (happy(X0) & old(X0)))) [nnf transformation 3]
42. ! [X0] : ((~happy(X0) | ~old(X0) | (~rich(X0) & patient(X0))) & (rich(X0) | ~patient(X0) | (happy(X0) & old(X0)))) [flattening 41]
43. ! [X0] : (((wise(X0) | humble(X0)) | ((~happy(X0) | kind(X0)) & (~kind(X0) | happy(X0)))) & (((kind(X0) | happy(X0)) & (~kind(X0) | ~happy(X0))) | (~wise(X0) & ~humble(X0)))) [nnf transformation 5]
44. ! [X0] : ((wise(X0) | humble(X0) | ((~happy(X0) | kind(X0)) & (~kind(X0) | happy(X0)))) & (((kind(X0) | happy(X0)) & (~kind(X0) | ~happy(X0))) | (~wise(X0) & ~humble(X0)))) [flattening 43]
45. ! [X0] : (((quiet(X0) | ~calm(X0)) | ~humble(X0)) & (humble(X0) | (~quiet(X0) & calm(X0)))) [nnf transformation 6]
46. ! [X0] : ((quiet(X0) | ~calm(X0) | ~humble(X0)) & (humble(X0) | (~quiet(X0) & calm(X0)))) [flattening 45]
53. ! [X0] : (((~rich(X0) | ~old(X0)) & (rich(X0) | old(X0))) | (quiet(X0) & ~kind(X0))) [nnf transformation 32]
54. ! [X0] : (((patient(X0) | ~old(X0)) & (~patient(X0) | old(X0))) | (~humble(X0) & patient(X0))) [nnf transformation 33]
70. ~calm(X0) | ~funny(X0) [cnf transformation 39]
79. ~happy(X0) | ~old(X0) | ~rich(X0) [cnf transformation 42]
81. ~kind(X0) | ~happy(X0) | ~humble(X0) [cnf transformation 44]
83. ~humble(X0) | happy(X0) | kind(X0) [cnf transformation 44]
87. humble(X0) | calm(X0) [cnf transformation 46]
88. ~quiet(X0) | humble(X0) [cnf transformation 46]
89. ~humble(X0) | ~calm(X0) | quiet(X0) [cnf transformation 46]
90. ~patient(X0) | humble(X0) | happy(X0) [cnf transformation 29]
105. ~kind(X0) | ~old(X0) | ~rich(X0) [cnf transformation 53]
108. ~humble(X0) | old(X0) | ~patient(X0) [cnf transformation 54]
115. patient(X0) | happy(X0) [cnf transformation 35]
116. kind(X0) | patient(X0) [cnf transformation 35]
128. quiet(paul) | funny(paul) [cnf transformation 22]
131. rich(paul) [cnf transformation 24]
227. 21 <=> funny(paul) [avatar definition]
229. funny(paul) <- (21) [avatar component clause 227]
231. 22 <=> quiet(paul) [avatar definition]
232. ~quiet(paul) <- (~22) [avatar component clause 231]
233. quiet(paul) <- (22) [avatar component clause 231]
234. 21 | 22 [avatar split clause 128,231,227]
280. ~happy(X0) | ~humble(X0) | patient(X0) [resolution 81,116]
282. ~humble(X0) | patient(X0) [subsumption resolution 280,115]
375. humble(X0) | happy(X0) | happy(X0) [resolution 90,115]
377. humble(X0) | happy(X0) [duplicate literal removal 375]
465. ~patient(X0) | old(X0) | calm(X0) [resolution 108,87]
569. humble(paul) <- (22) [resolution 233,88]
573. 63 <=> old(paul) [avatar definition]
574. old(paul) <- (63) [avatar component clause 573]
575. ~old(paul) <- (~63) [avatar component clause 573]
587. old(paul) | ~patient(paul) <- (22) [resolution 569,108]
590. ~patient(paul) <- (22, ~63) [subsumption resolution 587,575]
670. patient(X0) | calm(X0) [resolution 282,87]
672. patient(paul) <- (22) [resolution 282,569]
676. $false <- (22, ~63) [subsumption resolution 672,590]
677. ~22 | 63 [avatar contradiction clause 676]
699. happy(X4) | happy(X4) | kind(X4) [resolution 377,83]
700. kind(X4) | happy(X4) [duplicate literal removal 699]
865. 77 <=> humble(paul) [avatar definition]
866. ~humble(paul) <- (~77) [avatar component clause 865]
867. humble(paul) <- (77) [avatar component clause 865]
934. calm(X0) | old(X0) | calm(X0) [resolution 670,465]
938. old(X0) | calm(X0) [duplicate literal removal 934]
946. happy(X1) | ~old(X1) | ~rich(X1) [resolution 700,105]
955. ~old(X1) | ~rich(X1) [subsumption resolution 946,79]
1095. calm(paul) <- (~77) [resolution 866,87]
1156. calm(paul) <- (~63) [resolution 938,575]
1295. ~funny(paul) <- (~77) [resolution 1095,70]
1296. $false <- (21, ~77) [subsumption resolution 1295,229]
1297. ~21 | 77 [avatar contradiction clause 1296]
1309. ~calm(paul) | quiet(paul) <- (77) [resolution 867,89]
1314. quiet(paul) <- (~63, 77) [subsumption resolution 1309,1156]
1315. $false <- (~22, ~63, 77) [subsumption resolution 1314,232]
1316. 22 | 63 | ~77 [avatar contradiction clause 1315]
1339. ~rich(paul) <- (63) [resolution 574,955]
1345. $false <- (63) [subsumption resolution 1339,131]
1346. ~63 [avatar contradiction clause 1345]
1347. $false [avatar sat refutation 234,677,1297,1316,1346]
% SZS output end Proof for 693088598901803419855819
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5500
% Time elapsed: 0.043 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not patient or not rich is both not brave and not calm and vice versa.
If alice is brave or not brave then someone is both happy and kind.
If john is both calm and not curious then someone is not calm or not creative and vice versa.
Everyone who is both wise and patient is either not wise or not tall and vice versa.
Everyone who is not humble or generous is both not funny and funny.
Everyone who is not humble is both kind and not old.
If lucy is not strong or brave then mary is quiet or not kind and vice versa.
Everyone who is not happy or not patient is either old or tall and vice versa.
Everyone who is not rich is either not calm or not happy and vice versa.
If paul is both not creative and not calm then susan is both funny and not happy and vice versa.
If lucy is old then someone is both not creative and not wise and vice versa.
Everyone who is calm or old is wise or old.
If fred is not creative then someone is either strong or not humble and vice versa.
Everyone who is either not curious or not quiet is not rich and vice versa.
Someone is either not quiet or creative.
Mary is not kind.
Fred is not patient.
Someone is either humble or not curious. | Mary is funny. | neutral | (![X]:((~patient(X)|~rich(X))<=>(~brave(X)&~calm(X))))&
(((brave(alice)|~brave(alice)))=>(?[X]:((happy(X)&kind(X)))))&
(((calm(john)&~curious(john)))<=>(?[X]:((~calm(X)|~creative(X)))))&
(![X]:((wise(X)&patient(X))<=>(~wise(X)<~>~tall(X))))&
(![X]:((~humble(X)|generous(X))=>(~funny(X)&funny(X))))&
(![X]:(~humble(X)=>(kind(X)&~old(X))))&
(((~strong(lucy)|brave(lucy)))<=>((quiet(mary)|~kind(mary))))&
(![X]:((~happy(X)|~patient(X))<=>(old(X)<~>tall(X))))&
(![X]:(~rich(X)<=>(~calm(X)<~>~happy(X))))&
(((~creative(paul)&~calm(paul)))<=>((funny(susan)&~happy(susan))))&
((old(lucy))<=>(?[X]:((~creative(X)&~wise(X)))))&
(![X]:((calm(X)|old(X))=>(wise(X)|old(X))))&
((~creative(fred))<=>(?[X]:((strong(X)<~>~humble(X)))))&
(![X]:((~curious(X)<~>~quiet(X))<=>~rich(X)))&
(?[X]:((~quiet(X)<~>creative(X))))&
(~kind(mary))&
(~patient(fred))&
(?[X]:((humble(X)<~>~curious(X)))) | funny(mary) | [] | null | 0 |
If alice is either not patient or not calm then someone is both not creative and humble.
Everyone who is both humble and not kind is either not funny or wise and vice versa.
Everyone who is both creative and curious is either not generous or not funny.
Everyone who is happy or not wise is both brave and not happy.
If someone is not kind then alice is both not patient and not brave.
Everyone who is both funny and not happy is either not curious or not strong.
Everyone who is both strong and not old is not funny and vice versa.
If someone is rich or not patient then fred is either not patient or tall.
If john is both not kind and creative then someone is both kind and generous.
Everyone who is not patient is either not wise or not tall and vice versa.
Everyone who is curious is either kind or tall.
If someone is either kind or brave then someone is not generous and vice versa.
If someone is not funny or not creative then lucy is both curious and not funny and vice versa.
If someone is calm then someone is either not brave or creative and vice versa.
If someone is both brave and humble then someone is both calm and wise and vice versa.
Everyone who is both not creative and not quiet is generous or kind.
Someone is creative or kind.
Mary is not patient or creative.
Susan is patient or not strong.
Someone is either not wise or not tall.
Someone is patient.
Someone is either curious or not strong.
Paul is both not kind and not calm.
Someone is both creative and calm. | Lucy is not funny. | entailment | (((~patient(alice)<~>~calm(alice)))=>(?[X]:((~creative(X)&humble(X)))))&
(![X]:((humble(X)&~kind(X))<=>(~funny(X)<~>wise(X))))&
(![X]:((creative(X)&curious(X))=>(~generous(X)<~>~funny(X))))&
(![X]:((happy(X)|~wise(X))=>(brave(X)&~happy(X))))&
((?[X]:(~kind(X)))=>((~patient(alice)&~brave(alice))))&
(![X]:((funny(X)&~happy(X))=>(~curious(X)<~>~strong(X))))&
(![X]:((strong(X)&~old(X))<=>~funny(X)))&
((?[X]:((rich(X)|~patient(X))))=>((~patient(fred)<~>tall(fred))))&
(((~kind(john)&creative(john)))=>(?[X]:((kind(X)&generous(X)))))&
(![X]:(~patient(X)<=>(~wise(X)<~>~tall(X))))&
(![X]:(curious(X)=>(kind(X)<~>tall(X))))&
((?[X]:((kind(X)<~>brave(X))))<=>(?[X]:(~generous(X))))&
((?[X]:((~funny(X)|~creative(X))))<=>((curious(lucy)&~funny(lucy))))&
((?[X]:(calm(X)))<=>(?[X]:((~brave(X)<~>creative(X)))))&
((?[X]:((brave(X)&humble(X))))<=>(?[X]:((calm(X)&wise(X)))))&
(![X]:((~creative(X)&~quiet(X))=>(generous(X)|kind(X))))&
(?[X]:((creative(X)|kind(X))))&
((~patient(mary)|creative(mary)))&
((patient(susan)|~strong(susan)))&
(?[X]:((~wise(X)<~>~tall(X))))&
(?[X]:(patient(X)))&
(?[X]:((curious(X)<~>~strong(X))))&
((~kind(paul)&~calm(paul)))&
(?[X]:((creative(X)&calm(X)))) | ~funny(lucy) | [
"p3",
"p5",
"p12",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 8756561479902176228407956
% SZS output start Proof for 8756561479902176228407956
4. ! [X0] : ((~wise(X0) | happy(X0)) => (~happy(X0) & brave(X0))) [input p3]
6. ! [X0] : ((~happy(X0) & funny(X0)) => (~curious(X0) <~> ~strong(X0))) [input p5]
13. ? [X0] : (~creative(X0) | ~funny(X0)) <=> (~funny(lucy) & curious(lucy)) [input p12]
22. ? [X0] : (curious(X0) <~> ~strong(X0)) [input p21]
25. funny(lucy) [input hypothesis]
34. ! [X0] : ((~happy(X0) & brave(X0)) | (wise(X0) & ~happy(X0))) [ennf transformation 4]
36. ! [X0] : ((~curious(X0) <~> ~strong(X0)) | (happy(X0) | ~funny(X0))) [ennf transformation 6]
37. ! [X0] : ((~curious(X0) <~> ~strong(X0)) | happy(X0) | ~funny(X0)) [flattening 36]
48. ! [X0] : (((strong(X0) | curious(X0)) & (~strong(X0) | ~curious(X0))) | happy(X0) | ~funny(X0)) [nnf transformation 37]
61. (? [X0] : (~creative(X0) | ~funny(X0)) | (funny(lucy) | ~curious(lucy))) & ((~funny(lucy) & curious(lucy)) | ! [X0] : (creative(X0) & funny(X0))) [nnf transformation 13]
62. (? [X0] : (~creative(X0) | ~funny(X0)) | funny(lucy) | ~curious(lucy)) & ((~funny(lucy) & curious(lucy)) | ! [X0] : (creative(X0) & funny(X0))) [flattening 61]
63. (? [X0] : (~creative(X0) | ~funny(X0)) | funny(lucy) | ~curious(lucy)) & ((~funny(lucy) & curious(lucy)) | ! [X1] : (creative(X1) & funny(X1))) [rectify 62]
64. ? [X0] : (~creative(X0) | ~funny(X0)) => (~creative(sK4) | ~funny(sK4)) [choice axiom]
65. ((~creative(sK4) | ~funny(sK4)) | funny(lucy) | ~curious(lucy)) & ((~funny(lucy) & curious(lucy)) | ! [X1] : (creative(X1) & funny(X1))) [skolemisation 63,64]
83. ? [X0] : ((strong(X0) | ~curious(X0)) & (~strong(X0) | curious(X0))) [nnf transformation 22]
84. ? [X0] : ((strong(X0) | ~curious(X0)) & (~strong(X0) | curious(X0))) => ((strong(sK12) | ~curious(sK12)) & (~strong(sK12) | curious(sK12))) [choice axiom]
85. (strong(sK12) | ~curious(sK12)) & (~strong(sK12) | curious(sK12)) [skolemisation 83,84]
102. ~happy(X0) | ~happy(X0) [cnf transformation 34]
106. ~strong(X0) | ~curious(X0) | happy(X0) | ~funny(X0) [cnf transformation 48]
107. strong(X0) | curious(X0) | happy(X0) | ~funny(X0) [cnf transformation 48]
127. ~funny(lucy) | funny(X1) [cnf transformation 65]
144. ~strong(sK12) | curious(sK12) [cnf transformation 85]
145. strong(sK12) | ~curious(sK12) [cnf transformation 85]
150. funny(lucy) [cnf transformation 25]
151. ~happy(X0) [duplicate literal removal 102]
181. ~funny(X0) | curious(X0) | strong(X0) [subsumption resolution 107,151]
182. ~strong(X0) | ~curious(X0) | ~funny(X0) [subsumption resolution 106,151]
244. 21 <=> funny(lucy) [avatar definition]
261. 25 <=> ! [X1] : funny(X1) [avatar definition]
262. funny(X1) <- (25) [avatar component clause 261]
263. 25 | ~21 [avatar split clause 127,244,261]
355. 46 <=> curious(sK12) [avatar definition]
356. curious(sK12) <- (46) [avatar component clause 355]
357. ~curious(sK12) <- (~46) [avatar component clause 355]
359. 47 <=> strong(sK12) [avatar definition]
360. ~strong(sK12) <- (~47) [avatar component clause 359]
361. strong(sK12) <- (47) [avatar component clause 359]
362. ~46 | 47 [avatar split clause 145,359,355]
363. 46 | ~47 [avatar split clause 144,359,355]
364. 21 [avatar split clause 150,244]
424. strong(X0) | curious(X0) <- (25) [resolution 181,262]
431. curious(sK12) <- (25, ~47) [resolution 424,360]
434. $false <- (25, ~46, ~47) [subsumption resolution 431,357]
435. ~25 | 46 | 47 [avatar contradiction clause 434]
447. ~curious(sK12) | ~funny(sK12) <- (47) [resolution 361,182]
449. ~funny(sK12) <- (46, 47) [subsumption resolution 447,356]
450. $false <- (25, 46, 47) [subsumption resolution 449,262]
451. ~25 | ~46 | ~47 [avatar contradiction clause 450]
453. $false [avatar sat refutation 263,362,363,364,435,451]
% SZS output end Proof for 8756561479902176228407956
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall and happy is not patient.
If someone is funny or rich then paul is funny or not generous and vice versa.
If someone is not tall then someone is wise or not curious and vice versa.
If someone is wise or not creative then mary is not creative or not rich.
If fred is either not calm or humble then paul is both not curious and quiet.
If someone is not old or patient then paul is both creative and rich and vice versa.
Everyone who is both brave and not kind is not rich or brave.
If paul is creative then alice is not rich and vice versa.
If paul is not patient then someone is either tall or curious and vice versa.
Everyone who is either funny or patient is rich or not creative.
Everyone who is both humble and brave is not kind or wise.
Everyone who is not calm or calm is not creative.
If fred is brave then someone is either humble or not wise and vice versa.
Everyone who is either funny or not curious is either not strong or not curious.
Everyone who is not creative is not happy or brave and vice versa.
If someone is not happy then someone is quiet or not funny.
Someone is not wise.
Someone is kind.
Someone is both not patient and brave.
Fred is not curious or not humble.
Someone is not patient.
Paul is both wise and not generous.
Mary is not wise or rich. | Mary is wise. | neutral | (![X]:((tall(X)&happy(X))=>~patient(X)))&
((?[X]:((funny(X)|rich(X))))<=>((funny(paul)|~generous(paul))))&
((?[X]:(~tall(X)))<=>(?[X]:((wise(X)|~curious(X)))))&
((?[X]:((wise(X)|~creative(X))))=>((~creative(mary)|~rich(mary))))&
(((~calm(fred)<~>humble(fred)))=>((~curious(paul)&quiet(paul))))&
((?[X]:((~old(X)|patient(X))))<=>((creative(paul)&rich(paul))))&
(![X]:((brave(X)&~kind(X))=>(~rich(X)|brave(X))))&
((creative(paul))<=>(~rich(alice)))&
((~patient(paul))<=>(?[X]:((tall(X)<~>curious(X)))))&
(![X]:((funny(X)<~>patient(X))=>(rich(X)|~creative(X))))&
(![X]:((humble(X)&brave(X))=>(~kind(X)|wise(X))))&
(![X]:((~calm(X)|calm(X))=>~creative(X)))&
((brave(fred))<=>(?[X]:((humble(X)<~>~wise(X)))))&
(![X]:((funny(X)<~>~curious(X))=>(~strong(X)<~>~curious(X))))&
(![X]:(~creative(X)<=>(~happy(X)|brave(X))))&
((?[X]:(~happy(X)))=>(?[X]:((quiet(X)|~funny(X)))))&
(?[X]:(~wise(X)))&
(?[X]:(kind(X)))&
(?[X]:((~patient(X)&brave(X))))&
((~curious(fred)|~humble(fred)))&
(?[X]:(~patient(X)))&
((wise(paul)&~generous(paul)))&
((~wise(mary)|rich(mary))) | wise(mary) | [] | null | 0 |
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