premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
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sequencelengths 0
15
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stringlengths 684
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If someone is wise or not curious then someone is either creative or not brave. Everyone who is both not humble and not strong is brave and vice versa. If someone is not curious or not creative then fred is kind or wise and vice versa. Everyone who is strong is not tall and vice versa. Everyone who is both patient and rich is both not rich and tall. If john is humble then someone is not strong or not patient. If someone is not humble then lucy is either not humble or not wise. Everyone who is generous is not old. Everyone who is calm or old is not calm or generous. Everyone who is either funny or strong is not patient and vice versa. If someone is either not curious or funny then someone is not curious. If someone is both curious and creative then someone is quiet. If someone is funny then someone is either not generous or not calm. Everyone who is both calm and tall is not generous. Everyone who is not brave is both not funny and not calm. If someone is both not generous and humble then john is both quiet and generous and vice versa. Someone is not brave. Someone is either humble or not funny. Fred is wise. Someone is not strong or kind. Lucy is humble or not patient. Someone is either brave or not humble. Someone is not humble. | Lucy is patient. | neutral | ((?[X]:((wise(X)|~curious(X))))=>(?[X]:((creative(X)<~>~brave(X)))))&
(![X]:((~humble(X)&~strong(X))<=>brave(X)))&
((?[X]:((~curious(X)|~creative(X))))<=>((kind(fred)|wise(fred))))&
(![X]:(strong(X)<=>~tall(X)))&
(![X]:((patient(X)&rich(X))=>(~rich(X)&tall(X))))&
((humble(john))=>(?[X]:((~strong(X)|~patient(X)))))&
((?[X]:(~humble(X)))=>((~humble(lucy)<~>~wise(lucy))))&
(![X]:(generous(X)=>~old(X)))&
(![X]:((calm(X)|old(X))=>(~calm(X)|generous(X))))&
(![X]:((funny(X)<~>strong(X))<=>~patient(X)))&
((?[X]:((~curious(X)<~>funny(X))))=>(?[X]:(~curious(X))))&
((?[X]:((curious(X)&creative(X))))=>(?[X]:(quiet(X))))&
((?[X]:(funny(X)))=>(?[X]:((~generous(X)<~>~calm(X)))))&
(![X]:((calm(X)&tall(X))=>~generous(X)))&
(![X]:(~brave(X)=>(~funny(X)&~calm(X))))&
((?[X]:((~generous(X)&humble(X))))<=>((quiet(john)&generous(john))))&
(?[X]:(~brave(X)))&
(?[X]:((humble(X)<~>~funny(X))))&
(wise(fred))&
(?[X]:((~strong(X)|kind(X))))&
((humble(lucy)|~patient(lucy)))&
(?[X]:((brave(X)<~>~humble(X))))&
(?[X]:(~humble(X))) | patient(lucy) | [] | null | 0 |
If alice is both old and not creative then someone is both not patient and not rich. If someone is not patient or not curious then someone is calm and vice versa. Everyone who is both patient and happy is not tall or happy and vice versa. Everyone who is both not calm and patient is not creative and vice versa. If fred is both not rich and not brave then fred is curious. Everyone who is rich is not old or quiet. If someone is happy or not wise then someone is not generous and vice versa. Everyone who is not wise is not creative or not funny and vice versa. Everyone who is either happy or tall is both wise and not patient and vice versa. Everyone who is both patient and not humble is quiet or funny. Everyone who is not wise is either not calm or strong and vice versa. Everyone who is either kind or humble is either not kind or generous. Everyone who is either creative or not strong is both calm and not calm. Everyone who is either not wise or creative is both brave and not old. Everyone who is not brave is strong or not rich and vice versa. If someone is tall or rich then mary is humble. Someone is either not brave or not strong. Someone is either old or quiet. Someone is not old. Paul is either quiet or not happy. Lucy is either not humble or funny. Susan is rich. | Fred is creative. | entailment | (((old(alice)&~creative(alice)))=>(?[X]:((~patient(X)&~rich(X)))))&
((?[X]:((~patient(X)|~curious(X))))<=>(?[X]:(calm(X))))&
(![X]:((patient(X)&happy(X))<=>(~tall(X)|happy(X))))&
(![X]:((~calm(X)&patient(X))<=>~creative(X)))&
(((~rich(fred)&~brave(fred)))=>(curious(fred)))&
(![X]:(rich(X)=>(~old(X)|quiet(X))))&
((?[X]:((happy(X)|~wise(X))))<=>(?[X]:(~generous(X))))&
(![X]:(~wise(X)<=>(~creative(X)|~funny(X))))&
(![X]:((happy(X)<~>tall(X))<=>(wise(X)&~patient(X))))&
(![X]:((patient(X)&~humble(X))=>(quiet(X)|funny(X))))&
(![X]:(~wise(X)<=>(~calm(X)<~>strong(X))))&
(![X]:((kind(X)<~>humble(X))=>(~kind(X)<~>generous(X))))&
(![X]:((creative(X)<~>~strong(X))=>(calm(X)&~calm(X))))&
(![X]:((~wise(X)<~>creative(X))=>(brave(X)&~old(X))))&
(![X]:(~brave(X)<=>(strong(X)|~rich(X))))&
((?[X]:((tall(X)|rich(X))))=>(humble(mary)))&
(?[X]:((~brave(X)<~>~strong(X))))&
(?[X]:((old(X)<~>quiet(X))))&
(?[X]:(~old(X)))&
((quiet(paul)<~>~happy(paul)))&
((~humble(lucy)<~>funny(lucy)))&
(rich(susan)) | creative(fred) | [
"p3",
"p7",
"p12",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3525971840569716580480792
% SZS output start Proof for 3525971840569716580480792
4. ! [X0] : ((patient(X0) & ~calm(X0)) <=> ~creative(X0)) [input p3]
8. ! [X0] : (~wise(X0) <=> (~funny(X0) | ~creative(X0))) [input p7]
13. ! [X0] : ((creative(X0) <~> ~strong(X0)) => (~calm(X0) & calm(X0))) [input p12]
14. ! [X0] : ((~wise(X0) <~> creative(X0)) => (~old(X0) & brave(X0))) [input p13]
15. ! [X0] : (~brave(X0) <=> (~rich(X0) | strong(X0))) [input p14]
23. ~creative(fred) [input hypothesis]
35. ! [X0] : ((~calm(X0) & calm(X0)) | (creative(X0) <=> ~strong(X0))) [ennf transformation 13]
36. ! [X0] : ((~old(X0) & brave(X0)) | (~wise(X0) <=> creative(X0))) [ennf transformation 14]
47. ! [X0] : (((patient(X0) & ~calm(X0)) | creative(X0)) & (~creative(X0) | (~patient(X0) | calm(X0)))) [nnf transformation 4]
48. ! [X0] : (((patient(X0) & ~calm(X0)) | creative(X0)) & (~creative(X0) | ~patient(X0) | calm(X0))) [flattening 47]
54. ! [X0] : ((~wise(X0) | (funny(X0) & creative(X0))) & ((~funny(X0) | ~creative(X0)) | wise(X0))) [nnf transformation 8]
55. ! [X0] : ((~wise(X0) | (funny(X0) & creative(X0))) & (~funny(X0) | ~creative(X0) | wise(X0))) [flattening 54]
60. ! [X0] : ((~calm(X0) & calm(X0)) | ((creative(X0) | strong(X0)) & (~strong(X0) | ~creative(X0)))) [nnf transformation 35]
61. ! [X0] : ((~old(X0) & brave(X0)) | ((~wise(X0) | ~creative(X0)) & (creative(X0) | wise(X0)))) [nnf transformation 36]
62. ! [X0] : ((~brave(X0) | (rich(X0) & ~strong(X0))) & ((~rich(X0) | strong(X0)) | brave(X0))) [nnf transformation 15]
63. ! [X0] : ((~brave(X0) | (rich(X0) & ~strong(X0))) & (~rich(X0) | strong(X0) | brave(X0))) [flattening 62]
85. ~calm(X0) | creative(X0) [cnf transformation 48]
93. ~wise(X0) | creative(X0) [cnf transformation 55]
111. calm(X0) | creative(X0) | strong(X0) [cnf transformation 60]
114. brave(X0) | creative(X0) | wise(X0) [cnf transformation 61]
115. brave(X0) | ~wise(X0) | ~creative(X0) [cnf transformation 61]
119. ~strong(X0) | ~brave(X0) [cnf transformation 63]
133. ~creative(fred) [cnf transformation 23]
220. strong(X0) | creative(X0) [subsumption resolution 111,85]
224. brave(X0) | ~wise(X0) [subsumption resolution 115,93]
225. brave(X0) | creative(X0) [subsumption resolution 114,224]
286. creative(X1) | ~brave(X1) [resolution 220,119]
287. creative(X1) [subsumption resolution 286,225]
288. $false [resolution 287,133]
% SZS output end Proof for 3525971840569716580480792
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both brave and not creative is either curious or kind and vice versa.
Everyone who is wise or not curious is both not creative and not patient.
If someone is both not rich and not old then someone is either rich or curious.
Everyone who is both humble and creative is not quiet or kind and vice versa.
Everyone who is humble is wise.
Everyone who is both not happy and not funny is both not strong and happy.
Everyone who is not wise is not brave or happy and vice versa.
Everyone who is strong is either funny or curious.
If susan is not wise or not strong then fred is strong and vice versa.
Everyone who is not calm or funny is not funny and vice versa.
Everyone who is either not kind or not tall is either rich or not patient and vice versa.
Everyone who is both happy and not kind is either not strong or not old and vice versa.
If someone is both not patient and old then fred is both not curious and humble and vice versa.
If someone is both not strong and not funny then someone is brave and vice versa.
Everyone who is not funny or curious is not brave or tall and vice versa.
Someone is either kind or patient.
Susan is not patient or not creative.
Someone is either patient or not patient.
Alice is not quiet or not kind.
Susan is either not rich or not quiet. | Alice is not brave. | contradiction | (![X]:((brave(X)&~creative(X))<=>(curious(X)<~>kind(X))))&
(![X]:((wise(X)|~curious(X))=>(~creative(X)&~patient(X))))&
((?[X]:((~rich(X)&~old(X))))=>(?[X]:((rich(X)<~>curious(X)))))&
(![X]:((humble(X)&creative(X))<=>(~quiet(X)|kind(X))))&
(![X]:(humble(X)=>wise(X)))&
(![X]:((~happy(X)&~funny(X))=>(~strong(X)&happy(X))))&
(![X]:(~wise(X)<=>(~brave(X)|happy(X))))&
(![X]:(strong(X)=>(funny(X)<~>curious(X))))&
(((~wise(susan)|~strong(susan)))<=>(strong(fred)))&
(![X]:((~calm(X)|funny(X))<=>~funny(X)))&
(![X]:((~kind(X)<~>~tall(X))<=>(rich(X)<~>~patient(X))))&
(![X]:((happy(X)&~kind(X))<=>(~strong(X)<~>~old(X))))&
((?[X]:((~patient(X)&old(X))))<=>((~curious(fred)&humble(fred))))&
((?[X]:((~strong(X)&~funny(X))))<=>(?[X]:(brave(X))))&
(![X]:((~funny(X)|curious(X))<=>(~brave(X)|tall(X))))&
(?[X]:((kind(X)<~>patient(X))))&
((~patient(susan)|~creative(susan)))&
(?[X]:((patient(X)<~>~patient(X))))&
((~quiet(alice)|~kind(alice)))&
((~rich(susan)<~>~quiet(susan))) | ~brave(alice) | [
"p0",
"p1",
"p3",
"p4",
"p5",
"p6",
"p7",
"p9",
"p11",
"p12",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 6534402979096394843258738
% SZS output start Proof for 6534402979096394843258738
1. ! [X0] : ((~creative(X0) & brave(X0)) <=> (curious(X0) <~> kind(X0))) [input p0]
2. ! [X0] : ((~curious(X0) | wise(X0)) => (~patient(X0) & ~creative(X0))) [input p1]
4. ! [X0] : ((creative(X0) & humble(X0)) <=> (kind(X0) | ~quiet(X0))) [input p3]
5. ! [X0] : (humble(X0) => wise(X0)) [input p4]
6. ! [X0] : ((~funny(X0) & ~happy(X0)) => (happy(X0) & ~strong(X0))) [input p5]
7. ! [X0] : (~wise(X0) <=> (happy(X0) | ~brave(X0))) [input p6]
8. ! [X0] : (strong(X0) => (funny(X0) <~> curious(X0))) [input p7]
10. ! [X0] : ((funny(X0) | ~calm(X0)) <=> ~funny(X0)) [input p9]
12. ! [X0] : ((~kind(X0) & happy(X0)) <=> (~strong(X0) <~> ~old(X0))) [input p11]
13. ? [X0] : (old(X0) & ~patient(X0)) <=> (humble(fred) & ~curious(fred)) [input p12]
19. ~kind(alice) | ~quiet(alice) [input p18]
21. ~brave(alice) [input hypothesis]
24. ! [X0] : ((~patient(X0) & ~creative(X0)) | (curious(X0) & ~wise(X0))) [ennf transformation 2]
26. ! [X0] : (wise(X0) | ~humble(X0)) [ennf transformation 5]
27. ! [X0] : ((happy(X0) & ~strong(X0)) | (funny(X0) | happy(X0))) [ennf transformation 6]
28. ! [X0] : ((happy(X0) & ~strong(X0)) | funny(X0) | happy(X0)) [flattening 27]
29. ! [X0] : ((funny(X0) <~> curious(X0)) | ~strong(X0)) [ennf transformation 8]
30. ! [X0] : (((~creative(X0) & brave(X0)) | ((curious(X0) | ~kind(X0)) & (kind(X0) | ~curious(X0)))) & (((~kind(X0) | ~curious(X0)) & (kind(X0) | curious(X0))) | (creative(X0) | ~brave(X0)))) [nnf transformation 1]
31. ! [X0] : (((~creative(X0) & brave(X0)) | ((curious(X0) | ~kind(X0)) & (kind(X0) | ~curious(X0)))) & (((~kind(X0) | ~curious(X0)) & (kind(X0) | curious(X0))) | creative(X0) | ~brave(X0))) [flattening 30]
36. ! [X0] : (((creative(X0) & humble(X0)) | (~kind(X0) & quiet(X0))) & ((kind(X0) | ~quiet(X0)) | (~creative(X0) | ~humble(X0)))) [nnf transformation 4]
37. ! [X0] : (((creative(X0) & humble(X0)) | (~kind(X0) & quiet(X0))) & (kind(X0) | ~quiet(X0) | ~creative(X0) | ~humble(X0))) [flattening 36]
38. ! [X0] : ((~wise(X0) | (~happy(X0) & brave(X0))) & ((happy(X0) | ~brave(X0)) | wise(X0))) [nnf transformation 7]
39. ! [X0] : ((~wise(X0) | (~happy(X0) & brave(X0))) & (happy(X0) | ~brave(X0) | wise(X0))) [flattening 38]
40. ! [X0] : (((~curious(X0) | ~funny(X0)) & (curious(X0) | funny(X0))) | ~strong(X0)) [nnf transformation 29]
43. ! [X0] : (((funny(X0) | ~calm(X0)) | funny(X0)) & (~funny(X0) | (~funny(X0) & calm(X0)))) [nnf transformation 10]
44. ! [X0] : ((funny(X0) | ~calm(X0) | funny(X0)) & (~funny(X0) | (~funny(X0) & calm(X0)))) [flattening 43]
46. ! [X0] : (((~kind(X0) & happy(X0)) | ((~strong(X0) | old(X0)) & (~old(X0) | strong(X0)))) & (((old(X0) | strong(X0)) & (~old(X0) | ~strong(X0))) | (kind(X0) | ~happy(X0)))) [nnf transformation 12]
47. ! [X0] : (((~kind(X0) & happy(X0)) | ((~strong(X0) | old(X0)) & (~old(X0) | strong(X0)))) & (((old(X0) | strong(X0)) & (~old(X0) | ~strong(X0))) | kind(X0) | ~happy(X0))) [flattening 46]
48. (? [X0] : (old(X0) & ~patient(X0)) | (~humble(fred) | curious(fred))) & ((humble(fred) & ~curious(fred)) | ! [X0] : (~old(X0) | patient(X0))) [nnf transformation 13]
49. (? [X0] : (old(X0) & ~patient(X0)) | ~humble(fred) | curious(fred)) & ((humble(fred) & ~curious(fred)) | ! [X0] : (~old(X0) | patient(X0))) [flattening 48]
50. (? [X0] : (old(X0) & ~patient(X0)) | ~humble(fred) | curious(fred)) & ((humble(fred) & ~curious(fred)) | ! [X1] : (~old(X1) | patient(X1))) [rectify 49]
51. ? [X0] : (old(X0) & ~patient(X0)) => (old(sK1) & ~patient(sK1)) [choice axiom]
52. ((old(sK1) & ~patient(sK1)) | ~humble(fred) | curious(fred)) & ((humble(fred) & ~curious(fred)) | ! [X1] : (~old(X1) | patient(X1))) [skolemisation 50,51]
69. ~curious(X0) | kind(X0) | brave(X0) [cnf transformation 31]
74. ~creative(X0) | curious(X0) [cnf transformation 24]
76. ~patient(X0) | curious(X0) [cnf transformation 24]
80. quiet(X0) | humble(X0) [cnf transformation 37]
83. ~kind(X0) | creative(X0) [cnf transformation 37]
84. ~humble(X0) | wise(X0) [cnf transformation 26]
86. happy(X0) | funny(X0) | happy(X0) [cnf transformation 28]
89. ~happy(X0) | ~wise(X0) [cnf transformation 39]
90. ~strong(X0) | funny(X0) | curious(X0) [cnf transformation 40]
96. ~funny(X0) | ~funny(X0) [cnf transformation 44]
107. ~happy(X0) | strong(X0) | kind(X0) | old(X0) [cnf transformation 47]
113. humble(fred) | ~old(X1) | patient(X1) [cnf transformation 52]
128. ~kind(alice) | ~quiet(alice) [cnf transformation 19]
131. ~brave(alice) [cnf transformation 21]
132. ~funny(X0) [duplicate literal removal 96]
134. funny(X0) | happy(X0) [duplicate literal removal 86]
168. 8 <=> humble(fred) [avatar definition]
169. humble(fred) <- (8) [avatar component clause 168]
182. 11 <=> ! [X1] : (~old(X1) | patient(X1)) [avatar definition]
183. ~old(X1) | patient(X1) <- (11) [avatar component clause 182]
184. 11 | 8 [avatar split clause 113,168,182]
224. 20 <=> quiet(alice) [avatar definition]
226. ~quiet(alice) <- (~20) [avatar component clause 224]
228. 21 <=> kind(alice) [avatar definition]
230. ~kind(alice) <- (~21) [avatar component clause 228]
231. ~20 | ~21 [avatar split clause 128,228,224]
270. happy(X0) [resolution 134,132]
290. ~wise(X0) [resolution 270,89]
332. wise(fred) <- (8) [resolution 169,84]
333. $false <- (8) [subsumption resolution 332,290]
334. ~8 [avatar contradiction clause 333]
458. strong(X0) | kind(X0) | old(X0) [resolution 107,270]
464. kind(X4) | old(X4) | funny(X4) | curious(X4) [resolution 458,90]
477. old(X4) | kind(X4) | curious(X4) [subsumption resolution 464,132]
497. kind(X2) | curious(X2) | patient(X2) <- (11) [resolution 477,183]
501. kind(X2) | curious(X2) <- (11) [subsumption resolution 497,76]
508. curious(X3) | creative(X3) <- (11) [resolution 501,83]
519. curious(X3) <- (11) [subsumption resolution 508,74]
528. kind(X2) | brave(X2) <- (11) [resolution 519,69]
552. brave(alice) <- (11, ~21) [resolution 528,230]
558. $false <- (11, ~21) [subsumption resolution 552,131]
559. ~11 | 21 [avatar contradiction clause 558]
561. humble(alice) <- (~20) [resolution 226,80]
569. wise(alice) <- (~20) [resolution 561,84]
570. $false <- (~20) [subsumption resolution 569,290]
571. 20 [avatar contradiction clause 570]
572. $false [avatar sat refutation 184,231,334,559,571]
% SZS output end Proof for 6534402979096394843258738
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both kind and old then someone is not quiet. Everyone who is either calm or not creative is not calm or brave. If someone is either happy or not funny then someone is both brave and not brave and vice versa. Everyone who is not kind is not patient. If john is either generous or old then someone is not funny. Everyone who is both not curious and curious is both wise and funny. Everyone who is both calm and happy is both not curious and not humble and vice versa. Everyone who is not humble is both not funny and quiet. Everyone who is both brave and not generous is either not tall or quiet and vice versa. Everyone who is old is either not quiet or not patient and vice versa. Everyone who is creative is either not wise or calm. If mary is old then susan is both humble and rich and vice versa. Everyone who is wise or not strong is not wise and vice versa. If mary is either kind or calm then someone is both old and humble and vice versa. If someone is patient or not creative then alice is both not wise and rich. If john is calm then someone is old and vice versa. Someone is kind or not strong. Someone is either not wise or not rich. Susan is patient. Someone is quiet. Someone is not quiet or not strong. | John is generous. | neutral | ((?[X]:((kind(X)&old(X))))=>(?[X]:(~quiet(X))))&
(![X]:((calm(X)<~>~creative(X))=>(~calm(X)|brave(X))))&
((?[X]:((happy(X)<~>~funny(X))))<=>(?[X]:((brave(X)&~brave(X)))))&
(![X]:(~kind(X)=>~patient(X)))&
(((generous(john)<~>old(john)))=>(?[X]:(~funny(X))))&
(![X]:((~curious(X)&curious(X))=>(wise(X)&funny(X))))&
(![X]:((calm(X)&happy(X))<=>(~curious(X)&~humble(X))))&
(![X]:(~humble(X)=>(~funny(X)&quiet(X))))&
(![X]:((brave(X)&~generous(X))<=>(~tall(X)<~>quiet(X))))&
(![X]:(old(X)<=>(~quiet(X)<~>~patient(X))))&
(![X]:(creative(X)=>(~wise(X)<~>calm(X))))&
((old(mary))<=>((humble(susan)&rich(susan))))&
(![X]:((wise(X)|~strong(X))<=>~wise(X)))&
(((kind(mary)<~>calm(mary)))<=>(?[X]:((old(X)&humble(X)))))&
((?[X]:((patient(X)|~creative(X))))=>((~wise(alice)&rich(alice))))&
((calm(john))<=>(?[X]:(old(X))))&
(?[X]:((kind(X)|~strong(X))))&
(?[X]:((~wise(X)<~>~rich(X))))&
(patient(susan))&
(?[X]:(quiet(X)))&
(?[X]:((~quiet(X)|~strong(X)))) | generous(john) | [] | null | 0 |
If alice is either not brave or not patient then alice is not quiet or not generous and vice versa.
Everyone who is either not curious or strong is not old.
If someone is either not funny or not generous then someone is not curious or old and vice versa.
Everyone who is not creative is humble and vice versa.
Everyone who is both not quiet and not rich is strong or rich.
Everyone who is both not wise and brave is not kind and vice versa.
If someone is either patient or creative then someone is both funny and not funny.
Everyone who is not tall or humble is patient and vice versa.
If someone is not kind then someone is both creative and not calm.
If someone is kind or creative then susan is patient and vice versa.
If someone is strong or not happy then alice is both tall and not patient and vice versa.
If mary is rich or not patient then alice is not happy.
Everyone who is both not humble and not curious is both not kind and not tall and vice versa.
Everyone who is not curious is either happy or brave.
Fred is either funny or quiet.
Someone is not happy or curious.
Someone is rich.
Someone is not generous or funny.
Alice is either humble or wise. | Susan is not tall. | entailment | (((~brave(alice)<~>~patient(alice)))<=>((~quiet(alice)|~generous(alice))))&
(![X]:((~curious(X)<~>strong(X))=>~old(X)))&
((?[X]:((~funny(X)<~>~generous(X))))<=>(?[X]:((~curious(X)|old(X)))))&
(![X]:(~creative(X)<=>humble(X)))&
(![X]:((~quiet(X)&~rich(X))=>(strong(X)|rich(X))))&
(![X]:((~wise(X)&brave(X))<=>~kind(X)))&
((?[X]:((patient(X)<~>creative(X))))=>(?[X]:((funny(X)&~funny(X)))))&
(![X]:((~tall(X)|humble(X))<=>patient(X)))&
((?[X]:(~kind(X)))=>(?[X]:((creative(X)&~calm(X)))))&
((?[X]:((kind(X)|creative(X))))<=>(patient(susan)))&
((?[X]:((strong(X)|~happy(X))))<=>((tall(alice)&~patient(alice))))&
(((rich(mary)|~patient(mary)))=>(~happy(alice)))&
(![X]:((~humble(X)&~curious(X))<=>(~kind(X)&~tall(X))))&
(![X]:(~curious(X)=>(happy(X)<~>brave(X))))&
((funny(fred)<~>quiet(fred)))&
(?[X]:((~happy(X)|curious(X))))&
(?[X]:(rich(X)))&
(?[X]:((~generous(X)|funny(X))))&
((humble(alice)<~>wise(alice))) | ~tall(susan) | [
"p3",
"p6",
"p7",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 4715251832566636939258031
% SZS output start Proof for 4715251832566636939258031
4. ! [X0] : (~creative(X0) <=> humble(X0)) [input p3]
7. ? [X0] : (patient(X0) <~> creative(X0)) => ? [X0] : (~funny(X0) & funny(X0)) [input p6]
8. ! [X0] : ((humble(X0) | ~tall(X0)) <=> patient(X0)) [input p7]
10. ? [X0] : (creative(X0) | kind(X0)) <=> patient(susan) [input p9]
20. tall(susan) [input hypothesis]
22. ? [X0] : (patient(X0) <~> creative(X0)) => ? [X1] : (~funny(X1) & funny(X1)) [rectify 7]
28. ? [X1] : (~funny(X1) & funny(X1)) | ! [X0] : (patient(X0) <=> creative(X0)) [ennf transformation 22]
40. ! [X0] : ((~creative(X0) | ~humble(X0)) & (humble(X0) | creative(X0))) [nnf transformation 4]
43. ? [X1] : (~funny(X1) & funny(X1)) | ! [X0] : ((patient(X0) | ~creative(X0)) & (creative(X0) | ~patient(X0))) [nnf transformation 28]
44. ? [X0] : (~funny(X0) & funny(X0)) | ! [X1] : ((patient(X1) | ~creative(X1)) & (creative(X1) | ~patient(X1))) [rectify 43]
45. ? [X0] : (~funny(X0) & funny(X0)) => (~funny(sK2) & funny(sK2)) [choice axiom]
46. (~funny(sK2) & funny(sK2)) | ! [X1] : ((patient(X1) | ~creative(X1)) & (creative(X1) | ~patient(X1))) [skolemisation 44,45]
47. ! [X0] : (((humble(X0) | ~tall(X0)) | ~patient(X0)) & (patient(X0) | (~humble(X0) & tall(X0)))) [nnf transformation 8]
48. ! [X0] : ((humble(X0) | ~tall(X0) | ~patient(X0)) & (patient(X0) | (~humble(X0) & tall(X0)))) [flattening 47]
52. (? [X0] : (creative(X0) | kind(X0)) | ~patient(susan)) & (patient(susan) | ! [X0] : (~creative(X0) & ~kind(X0))) [nnf transformation 10]
53. (? [X0] : (creative(X0) | kind(X0)) | ~patient(susan)) & (patient(susan) | ! [X1] : (~creative(X1) & ~kind(X1))) [rectify 52]
54. ? [X0] : (creative(X0) | kind(X0)) => (creative(sK4) | kind(sK4)) [choice axiom]
55. ((creative(sK4) | kind(sK4)) | ~patient(susan)) & (patient(susan) | ! [X1] : (~creative(X1) & ~kind(X1))) [skolemisation 53,54]
86. humble(X0) | creative(X0) [cnf transformation 40]
87. ~humble(X0) | ~creative(X0) [cnf transformation 40]
92. funny(sK2) | creative(X1) | ~patient(X1) [cnf transformation 46]
94. ~funny(sK2) | creative(X1) | ~patient(X1) [cnf transformation 46]
97. ~humble(X0) | patient(X0) [cnf transformation 48]
98. ~tall(X0) | humble(X0) | ~patient(X0) [cnf transformation 48]
101. patient(susan) | ~creative(X1) [cnf transformation 55]
123. tall(susan) [cnf transformation 20]
185. 14 <=> funny(sK2) [avatar definition]
190. 15 <=> ! [X1] : (creative(X1) | ~patient(X1)) [avatar definition]
191. ~patient(X1) | creative(X1) <- (15) [avatar component clause 190]
192. 15 | ~14 [avatar split clause 94,185,190]
194. 15 | 14 [avatar split clause 92,185,190]
204. 18 <=> patient(susan) [avatar definition]
205. patient(susan) <- (18) [avatar component clause 204]
217. 21 <=> ! [X1] : ~creative(X1) [avatar definition]
218. ~creative(X1) <- (21) [avatar component clause 217]
219. 21 | 18 [avatar split clause 101,204,217]
309. patient(X0) | creative(X0) [resolution 97,86]
312. creative(X0) <- (15) [subsumption resolution 309,191]
328. humble(susan) | ~patient(susan) [resolution 98,123]
331. humble(susan) <- (18) [subsumption resolution 328,205]
346. ~creative(susan) <- (18) [resolution 331,87]
347. $false <- (15, 18) [subsumption resolution 346,312]
348. ~15 | ~18 [avatar contradiction clause 347]
352. $false <- (15, 21) [subsumption resolution 218,312]
353. ~15 | ~21 [avatar contradiction clause 352]
356. $false [avatar sat refutation 192,194,219,348,353]
% SZS output end Proof for 4715251832566636939258031
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both patient and humble is not kind and vice versa. Everyone who is strong is not happy. If john is not strong then someone is calm and vice versa. If someone is either not quiet or quiet then john is both not generous and not creative and vice versa. Everyone who is either patient or not curious is not wise or generous and vice versa. Everyone who is not humble or not curious is not rich. Everyone who is both not brave and curious is either not calm or rich and vice versa. If lucy is either humble or not calm then someone is both quiet and old and vice versa. Everyone who is both brave and not quiet is not calm and vice versa. If mary is either not curious or not brave then someone is not happy or not old and vice versa. If someone is not curious then alice is rich. Everyone who is either not happy or not quiet is not humble and vice versa. Everyone who is calm or creative is quiet or not old. Everyone who is creative or happy is not creative or not quiet and vice versa. If fred is not tall or generous then susan is either not rich or not old and vice versa. If john is patient then someone is happy. Someone is not creative or not rich. Someone is not humble. Someone is either not brave or not creative. Someone is not brave. Someone is both not old and tall. Someone is both patient and not kind. Someone is either not tall or not wise. | Mary is calm. | entailment | (![X]:((patient(X)&humble(X))<=>~kind(X)))&
(![X]:(strong(X)=>~happy(X)))&
((~strong(john))<=>(?[X]:(calm(X))))&
((?[X]:((~quiet(X)<~>quiet(X))))<=>((~generous(john)&~creative(john))))&
(![X]:((patient(X)<~>~curious(X))<=>(~wise(X)|generous(X))))&
(![X]:((~humble(X)|~curious(X))=>~rich(X)))&
(![X]:((~brave(X)&curious(X))<=>(~calm(X)<~>rich(X))))&
(((humble(lucy)<~>~calm(lucy)))<=>(?[X]:((quiet(X)&old(X)))))&
(![X]:((brave(X)&~quiet(X))<=>~calm(X)))&
(((~curious(mary)<~>~brave(mary)))<=>(?[X]:((~happy(X)|~old(X)))))&
((?[X]:(~curious(X)))=>(rich(alice)))&
(![X]:((~happy(X)<~>~quiet(X))<=>~humble(X)))&
(![X]:((calm(X)|creative(X))=>(quiet(X)|~old(X))))&
(![X]:((creative(X)|happy(X))<=>(~creative(X)|~quiet(X))))&
(((~tall(fred)|generous(fred)))<=>((~rich(susan)<~>~old(susan))))&
((patient(john))=>(?[X]:(happy(X))))&
(?[X]:((~creative(X)|~rich(X))))&
(?[X]:(~humble(X)))&
(?[X]:((~brave(X)<~>~creative(X))))&
(?[X]:(~brave(X)))&
(?[X]:((~old(X)&tall(X))))&
(?[X]:((patient(X)&~kind(X))))&
(?[X]:((~tall(X)<~>~wise(X)))) | calm(mary) | [
"p5",
"p6",
"p8",
"p9",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 4777433274776536261421779
% SZS output start Proof for 4777433274776536261421779
6. ! [X0] : ((~curious(X0) | ~humble(X0)) => ~rich(X0)) [input p5]
7. ! [X0] : ((curious(X0) & ~brave(X0)) <=> (~calm(X0) <~> rich(X0))) [input p6]
9. ! [X0] : ((~quiet(X0) & brave(X0)) <=> ~calm(X0)) [input p8]
10. (~curious(mary) <~> ~brave(mary)) <=> ? [X0] : (~old(X0) | ~happy(X0)) [input p9]
21. ? [X0] : (tall(X0) & ~old(X0)) [input p20]
24. ~calm(mary) [input hypothesis]
28. ! [X0] : (~rich(X0) | (curious(X0) & humble(X0))) [ennf transformation 6]
44. ! [X0] : (((curious(X0) & ~brave(X0)) | ((~calm(X0) | ~rich(X0)) & (rich(X0) | calm(X0)))) & (((~rich(X0) | calm(X0)) & (rich(X0) | ~calm(X0))) | (~curious(X0) | brave(X0)))) [nnf transformation 7]
45. ! [X0] : (((curious(X0) & ~brave(X0)) | ((~calm(X0) | ~rich(X0)) & (rich(X0) | calm(X0)))) & (((~rich(X0) | calm(X0)) & (rich(X0) | ~calm(X0))) | ~curious(X0) | brave(X0))) [flattening 44]
50. ! [X0] : (((~quiet(X0) & brave(X0)) | calm(X0)) & (~calm(X0) | (quiet(X0) | ~brave(X0)))) [nnf transformation 9]
51. ! [X0] : (((~quiet(X0) & brave(X0)) | calm(X0)) & (~calm(X0) | quiet(X0) | ~brave(X0))) [flattening 50]
52. (((brave(mary) | curious(mary)) & (~brave(mary) | ~curious(mary))) | ! [X0] : (old(X0) & happy(X0))) & (? [X0] : (~old(X0) | ~happy(X0)) | ((~curious(mary) | brave(mary)) & (~brave(mary) | curious(mary)))) [nnf transformation 10]
53. (((brave(mary) | curious(mary)) & (~brave(mary) | ~curious(mary))) | ! [X0] : (old(X0) & happy(X0))) & (? [X1] : (~old(X1) | ~happy(X1)) | ((~curious(mary) | brave(mary)) & (~brave(mary) | curious(mary)))) [rectify 52]
54. ? [X1] : (~old(X1) | ~happy(X1)) => (~old(sK3) | ~happy(sK3)) [choice axiom]
55. (((brave(mary) | curious(mary)) & (~brave(mary) | ~curious(mary))) | ! [X0] : (old(X0) & happy(X0))) & ((~old(sK3) | ~happy(sK3)) | ((~curious(mary) | brave(mary)) & (~brave(mary) | curious(mary)))) [skolemisation 53,54]
72. ? [X0] : (tall(X0) & ~old(X0)) => (tall(sK9) & ~old(sK9)) [choice axiom]
73. tall(sK9) & ~old(sK9) [skolemisation 21,72]
97. ~rich(X0) | curious(X0) [cnf transformation 28]
102. curious(X0) | rich(X0) | calm(X0) [cnf transformation 45]
111. brave(X0) | calm(X0) [cnf transformation 51]
116. ~brave(mary) | ~curious(mary) | old(X0) [cnf transformation 55]
142. ~old(sK9) [cnf transformation 73]
148. ~calm(mary) [cnf transformation 24]
186. curious(X0) | calm(X0) [subsumption resolution 102,97]
214. 13 <=> ! [X0] : old(X0) [avatar definition]
215. old(X0) <- (13) [avatar component clause 214]
217. 14 <=> curious(mary) [avatar definition]
218. ~curious(mary) <- (~14) [avatar component clause 217]
221. 15 <=> brave(mary) [avatar definition]
222. ~brave(mary) <- (~15) [avatar component clause 221]
229. 13 | ~14 | ~15 [avatar split clause 116,221,217,214]
312. calm(mary) <- (~15) [resolution 111,222]
313. $false <- (~15) [subsumption resolution 312,148]
314. 15 [avatar contradiction clause 313]
317. $false <- (13) [resolution 215,142]
320. ~13 [avatar contradiction clause 317]
328. calm(mary) <- (~14) [resolution 186,218]
329. $false <- (~14) [subsumption resolution 328,148]
330. 14 [avatar contradiction clause 329]
331. $false [avatar sat refutation 229,314,320,330]
% SZS output end Proof for 4777433274776536261421779
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.021 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not wise or generous then someone is both humble and patient and vice versa.
Everyone who is brave or not humble is both not creative and not quiet and vice versa.
If john is either not curious or not wise then someone is not generous and vice versa.
Everyone who is creative or funny is curious and vice versa.
Everyone who is rich is calm and vice versa.
Everyone who is not rich or not creative is both not calm and wise and vice versa.
Everyone who is both not humble and tall is not patient or tall.
If someone is both kind and not creative then lucy is both kind and curious and vice versa.
Everyone who is not creative or tall is either calm or not happy.
If mary is either old or generous then fred is either creative or not brave.
If someone is not brave or strong then john is rich and vice versa.
If someone is kind or creative then someone is rich and vice versa.
Everyone who is not creative or not calm is either calm or tall.
Everyone who is either rich or not kind is both not humble and not calm and vice versa.
If someone is generous or patient then lucy is not wise or funny and vice versa.
Everyone who is both funny and humble is both calm and quiet and vice versa.
Susan is both not curious and not generous.
Someone is both strong and not funny.
Paul is happy or brave.
Someone is both not old and not patient.
Paul is either curious or not kind.
Alice is not patient. | Lucy is not curious. | contradiction | ((?[X]:((~wise(X)|generous(X))))<=>(?[X]:((humble(X)&patient(X)))))&
(![X]:((brave(X)|~humble(X))<=>(~creative(X)&~quiet(X))))&
(((~curious(john)<~>~wise(john)))<=>(?[X]:(~generous(X))))&
(![X]:((creative(X)|funny(X))<=>curious(X)))&
(![X]:(rich(X)<=>calm(X)))&
(![X]:((~rich(X)|~creative(X))<=>(~calm(X)&wise(X))))&
(![X]:((~humble(X)&tall(X))=>(~patient(X)|tall(X))))&
((?[X]:((kind(X)&~creative(X))))<=>((kind(lucy)&curious(lucy))))&
(![X]:((~creative(X)|tall(X))=>(calm(X)<~>~happy(X))))&
(((old(mary)<~>generous(mary)))=>((creative(fred)<~>~brave(fred))))&
((?[X]:((~brave(X)|strong(X))))<=>(rich(john)))&
((?[X]:((kind(X)|creative(X))))<=>(?[X]:(rich(X))))&
(![X]:((~creative(X)|~calm(X))=>(calm(X)<~>tall(X))))&
(![X]:((rich(X)<~>~kind(X))<=>(~humble(X)&~calm(X))))&
((?[X]:((generous(X)|patient(X))))<=>((~wise(lucy)|funny(lucy))))&
(![X]:((funny(X)&humble(X))<=>(calm(X)&quiet(X))))&
((~curious(susan)&~generous(susan)))&
(?[X]:((strong(X)&~funny(X))))&
((happy(paul)|brave(paul)))&
(?[X]:((~old(X)&~patient(X))))&
((curious(paul)<~>~kind(paul)))&
(~patient(alice)) | ~curious(lucy) | [
"p0",
"p2",
"p3",
"p4",
"p5",
"p10",
"p14",
"p16",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 7800142211822893367867006
% SZS output start Proof for 7800142211822893367867006
1. ? [X0] : (generous(X0) | ~wise(X0)) <=> ? [X0] : (patient(X0) & humble(X0)) [input p0]
3. (~curious(john) <~> ~wise(john)) <=> ? [X0] : ~generous(X0) [input p2]
4. ! [X0] : ((funny(X0) | creative(X0)) <=> curious(X0)) [input p3]
5. ! [X0] : (rich(X0) <=> calm(X0)) [input p4]
6. ! [X0] : ((~creative(X0) | ~rich(X0)) <=> (wise(X0) & ~calm(X0))) [input p5]
11. ? [X0] : (strong(X0) | ~brave(X0)) <=> rich(john) [input p10]
15. ? [X0] : (patient(X0) | generous(X0)) <=> (funny(lucy) | ~wise(lucy)) [input p14]
17. ~generous(susan) & ~curious(susan) [input p16]
18. ? [X0] : (~funny(X0) & strong(X0)) [input p17]
23. ~curious(lucy) [input hypothesis]
24. ? [X0] : (generous(X0) | ~wise(X0)) <=> ? [X1] : (patient(X1) & humble(X1)) [rectify 1]
31. (? [X0] : (generous(X0) | ~wise(X0)) | ! [X1] : (~patient(X1) | ~humble(X1))) & (? [X1] : (patient(X1) & humble(X1)) | ! [X0] : (~generous(X0) & wise(X0))) [nnf transformation 24]
32. (? [X0] : (generous(X0) | ~wise(X0)) | ! [X1] : (~patient(X1) | ~humble(X1))) & (? [X2] : (patient(X2) & humble(X2)) | ! [X3] : (~generous(X3) & wise(X3))) [rectify 31]
33. ? [X0] : (generous(X0) | ~wise(X0)) => (generous(sK0) | ~wise(sK0)) [choice axiom]
34. ? [X2] : (patient(X2) & humble(X2)) => (patient(sK1) & humble(sK1)) [choice axiom]
35. ((generous(sK0) | ~wise(sK0)) | ! [X1] : (~patient(X1) | ~humble(X1))) & ((patient(sK1) & humble(sK1)) | ! [X3] : (~generous(X3) & wise(X3))) [skolemisation 32,34,33]
38. (((wise(john) | curious(john)) & (~wise(john) | ~curious(john))) | ! [X0] : generous(X0)) & (? [X0] : ~generous(X0) | ((~curious(john) | wise(john)) & (~wise(john) | curious(john)))) [nnf transformation 3]
39. (((wise(john) | curious(john)) & (~wise(john) | ~curious(john))) | ! [X0] : generous(X0)) & (? [X1] : ~generous(X1) | ((~curious(john) | wise(john)) & (~wise(john) | curious(john)))) [rectify 38]
40. ? [X1] : ~generous(X1) => ~generous(sK2) [choice axiom]
41. (((wise(john) | curious(john)) & (~wise(john) | ~curious(john))) | ! [X0] : generous(X0)) & (~generous(sK2) | ((~curious(john) | wise(john)) & (~wise(john) | curious(john)))) [skolemisation 39,40]
42. ! [X0] : (((funny(X0) | creative(X0)) | ~curious(X0)) & (curious(X0) | (~funny(X0) & ~creative(X0)))) [nnf transformation 4]
43. ! [X0] : ((funny(X0) | creative(X0) | ~curious(X0)) & (curious(X0) | (~funny(X0) & ~creative(X0)))) [flattening 42]
44. ! [X0] : ((rich(X0) | ~calm(X0)) & (calm(X0) | ~rich(X0))) [nnf transformation 5]
45. ! [X0] : (((~creative(X0) | ~rich(X0)) | (~wise(X0) | calm(X0))) & ((wise(X0) & ~calm(X0)) | (creative(X0) & rich(X0)))) [nnf transformation 6]
46. ! [X0] : ((~creative(X0) | ~rich(X0) | ~wise(X0) | calm(X0)) & ((wise(X0) & ~calm(X0)) | (creative(X0) & rich(X0)))) [flattening 45]
54. (? [X0] : (strong(X0) | ~brave(X0)) | ~rich(john)) & (rich(john) | ! [X0] : (~strong(X0) & brave(X0))) [nnf transformation 11]
55. (? [X0] : (strong(X0) | ~brave(X0)) | ~rich(john)) & (rich(john) | ! [X1] : (~strong(X1) & brave(X1))) [rectify 54]
56. ? [X0] : (strong(X0) | ~brave(X0)) => (strong(sK4) | ~brave(sK4)) [choice axiom]
57. ((strong(sK4) | ~brave(sK4)) | ~rich(john)) & (rich(john) | ! [X1] : (~strong(X1) & brave(X1))) [skolemisation 55,56]
66. (? [X0] : (patient(X0) | generous(X0)) | (~funny(lucy) & wise(lucy))) & ((funny(lucy) | ~wise(lucy)) | ! [X0] : (~patient(X0) & ~generous(X0))) [nnf transformation 15]
67. (? [X0] : (patient(X0) | generous(X0)) | (~funny(lucy) & wise(lucy))) & (funny(lucy) | ~wise(lucy) | ! [X0] : (~patient(X0) & ~generous(X0))) [flattening 66]
68. (? [X0] : (patient(X0) | generous(X0)) | (~funny(lucy) & wise(lucy))) & (funny(lucy) | ~wise(lucy) | ! [X1] : (~patient(X1) & ~generous(X1))) [rectify 67]
69. ? [X0] : (patient(X0) | generous(X0)) => (patient(sK7) | generous(sK7)) [choice axiom]
70. ((patient(sK7) | generous(sK7)) | (~funny(lucy) & wise(lucy))) & (funny(lucy) | ~wise(lucy) | ! [X1] : (~patient(X1) & ~generous(X1))) [skolemisation 68,69]
73. ? [X0] : (~funny(X0) & strong(X0)) => (~funny(sK8) & strong(sK8)) [choice axiom]
74. ~funny(sK8) & strong(sK8) [skolemisation 18,73]
80. patient(sK1) | wise(X3) [cnf transformation 35]
90. ~wise(john) | ~curious(john) | generous(X0) [cnf transformation 41]
92. ~creative(X0) | curious(X0) [cnf transformation 43]
93. ~funny(X0) | curious(X0) [cnf transformation 43]
95. ~rich(X0) | calm(X0) [cnf transformation 44]
98. ~calm(X0) | creative(X0) [cnf transformation 46]
100. creative(X0) | wise(X0) [cnf transformation 46]
116. rich(john) | ~strong(X1) [cnf transformation 57]
132. funny(lucy) | ~wise(lucy) | ~patient(X1) [cnf transformation 70]
140. ~generous(susan) [cnf transformation 17]
141. strong(sK8) [cnf transformation 74]
149. ~curious(lucy) [cnf transformation 23]
167. 5 <=> patient(sK1) [avatar definition]
169. patient(sK1) <- (5) [avatar component clause 167]
172. 6 <=> ! [X3] : wise(X3) [avatar definition]
173. wise(X3) <- (6) [avatar component clause 172]
174. 6 | 5 [avatar split clause 80,167,172]
182. 8 <=> ! [X0] : generous(X0) [avatar definition]
183. generous(X0) <- (8) [avatar component clause 182]
185. 9 <=> curious(john) [avatar definition]
189. 10 <=> wise(john) [avatar definition]
190. ~wise(john) <- (~10) [avatar component clause 189]
193. 8 | ~9 | ~10 [avatar split clause 90,189,185,182]
205. 13 <=> curious(lucy) [avatar definition]
207. ~curious(lucy) <- (~13) [avatar component clause 205]
249. 21 <=> rich(john) [avatar definition]
250. rich(john) <- (21) [avatar component clause 249]
262. 24 <=> ! [X1] : ~strong(X1) [avatar definition]
263. ~strong(X1) <- (24) [avatar component clause 262]
264. 24 | 21 [avatar split clause 116,249,262]
296. 32 <=> funny(lucy) [avatar definition]
297. funny(lucy) <- (32) [avatar component clause 296]
309. 35 <=> wise(lucy) [avatar definition]
314. 36 <=> ! [X1] : ~patient(X1) [avatar definition]
315. ~patient(X1) <- (36) [avatar component clause 314]
316. 36 | ~35 | 32 [avatar split clause 132,296,309,314]
337. ~13 [avatar split clause 149,205]
344. $false <- (8) [resolution 183,140]
345. ~8 [avatar contradiction clause 344]
346. $false <- (24) [resolution 263,141]
347. ~24 [avatar contradiction clause 346]
350. calm(john) <- (21) [resolution 95,250]
354. creative(john) <- (21) [resolution 98,350]
356. curious(john) <- (21) [resolution 354,92]
365. curious(X0) | wise(X0) [resolution 100,92]
403. $false <- (6, ~10) [resolution 173,190]
404. ~6 | 10 [avatar contradiction clause 403]
406. 9 | ~21 [avatar split clause 356,249,185]
409. curious(lucy) <- (32) [resolution 297,93]
410. $false <- (~13, 32) [subsumption resolution 409,207]
411. 13 | ~32 [avatar contradiction clause 410]
452. wise(lucy) <- (~13) [resolution 365,207]
457. 35 | 13 [avatar split clause 452,205,309]
458. $false <- (5, 36) [resolution 315,169]
461. ~5 | ~36 [avatar contradiction clause 458]
462. $false [avatar sat refutation 174,193,264,316,337,345,347,404,406,411,457,461]
% SZS output end Proof for 7800142211822893367867006
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is curious or not generous is either not funny or not patient and vice versa.
Everyone who is not tall is funny or not tall and vice versa.
If someone is kind or not rich then fred is not funny or brave.
If alice is curious or not tall then mary is not old and vice versa.
If someone is not old or generous then someone is either not rich or strong.
If alice is not funny then someone is quiet or not funny.
If fred is not strong or not brave then mary is either funny or quiet.
Everyone who is not rich or not creative is creative or strong and vice versa.
Everyone who is both not generous and curious is both not funny and strong and vice versa.
Everyone who is either humble or not humble is either funny or not happy and vice versa.
Everyone who is brave or not curious is rich.
Everyone who is wise is generous or not wise and vice versa.
If someone is both wise and humble then someone is not brave or not strong.
If someone is not curious then someone is either tall or not tall and vice versa.
Everyone who is happy is either not calm or not tall and vice versa.
Everyone who is either kind or creative is not calm.
Paul is patient.
Someone is either not happy or quiet.
Someone is either not tall or not brave.
Someone is not curious.
Fred is either rich or not rich.
Mary is both calm and kind.
Someone is not calm or funny. | Paul is not curious. | neutral | (![X]:((curious(X)|~generous(X))<=>(~funny(X)<~>~patient(X))))&
(![X]:(~tall(X)<=>(funny(X)|~tall(X))))&
((?[X]:((kind(X)|~rich(X))))=>((~funny(fred)|brave(fred))))&
(((curious(alice)|~tall(alice)))<=>(~old(mary)))&
((?[X]:((~old(X)|generous(X))))=>(?[X]:((~rich(X)<~>strong(X)))))&
((~funny(alice))=>(?[X]:((quiet(X)|~funny(X)))))&
(((~strong(fred)|~brave(fred)))=>((funny(mary)<~>quiet(mary))))&
(![X]:((~rich(X)|~creative(X))<=>(creative(X)|strong(X))))&
(![X]:((~generous(X)&curious(X))<=>(~funny(X)&strong(X))))&
(![X]:((humble(X)<~>~humble(X))<=>(funny(X)<~>~happy(X))))&
(![X]:((brave(X)|~curious(X))=>rich(X)))&
(![X]:(wise(X)<=>(generous(X)|~wise(X))))&
((?[X]:((wise(X)&humble(X))))=>(?[X]:((~brave(X)|~strong(X)))))&
((?[X]:(~curious(X)))<=>(?[X]:((tall(X)<~>~tall(X)))))&
(![X]:(happy(X)<=>(~calm(X)<~>~tall(X))))&
(![X]:((kind(X)<~>creative(X))=>~calm(X)))&
(patient(paul))&
(?[X]:((~happy(X)<~>quiet(X))))&
(?[X]:((~tall(X)<~>~brave(X))))&
(?[X]:(~curious(X)))&
((rich(fred)<~>~rich(fred)))&
((calm(mary)&kind(mary)))&
(?[X]:((~calm(X)|funny(X)))) | ~curious(paul) | [] | null | 0 |
If fred is either not generous or not humble then alice is both not quiet and generous.
If john is either not wise or creative then paul is not rich.
If someone is not funny then mary is either not old or curious.
If john is not funny then paul is rich and vice versa.
If alice is both happy and rich then someone is creative or wise and vice versa.
Everyone who is either quiet or kind is rich.
Everyone who is either not creative or generous is both not happy and not humble.
Everyone who is generous or not tall is not calm or wise.
If someone is strong or not funny then someone is happy and vice versa.
Everyone who is either calm or kind is either not humble or not curious and vice versa.
Everyone who is both not strong and not humble is not quiet and vice versa.
Everyone who is generous or not generous is tall and vice versa.
Everyone who is either not creative or calm is not kind.
Everyone who is both not curious and funny is either happy or curious.
Everyone who is creative or generous is both not curious and funny.
If someone is brave or calm then lucy is either strong or not strong and vice versa.
Fred is both not brave and kind.
Someone is either not quiet or not brave.
John is not brave or quiet.
Susan is quiet or wise.
Someone is not brave or happy.
Someone is either curious or not creative.
Someone is either not funny or generous. | Mary is curious. | neutral | (((~generous(fred)<~>~humble(fred)))=>((~quiet(alice)&generous(alice))))&
(((~wise(john)<~>creative(john)))=>(~rich(paul)))&
((?[X]:(~funny(X)))=>((~old(mary)<~>curious(mary))))&
((~funny(john))<=>(rich(paul)))&
(((happy(alice)&rich(alice)))<=>(?[X]:((creative(X)|wise(X)))))&
(![X]:((quiet(X)<~>kind(X))=>rich(X)))&
(![X]:((~creative(X)<~>generous(X))=>(~happy(X)&~humble(X))))&
(![X]:((generous(X)|~tall(X))=>(~calm(X)|wise(X))))&
((?[X]:((strong(X)|~funny(X))))<=>(?[X]:(happy(X))))&
(![X]:((calm(X)<~>kind(X))<=>(~humble(X)<~>~curious(X))))&
(![X]:((~strong(X)&~humble(X))<=>~quiet(X)))&
(![X]:((generous(X)|~generous(X))<=>tall(X)))&
(![X]:((~creative(X)<~>calm(X))=>~kind(X)))&
(![X]:((~curious(X)&funny(X))=>(happy(X)<~>curious(X))))&
(![X]:((creative(X)|generous(X))=>(~curious(X)&funny(X))))&
((?[X]:((brave(X)|calm(X))))<=>((strong(lucy)<~>~strong(lucy))))&
((~brave(fred)&kind(fred)))&
(?[X]:((~quiet(X)<~>~brave(X))))&
((~brave(john)|quiet(john)))&
((quiet(susan)|wise(susan)))&
(?[X]:((~brave(X)|happy(X))))&
(?[X]:((curious(X)<~>~creative(X))))&
(?[X]:((~funny(X)<~>generous(X)))) | curious(mary) | [] | null | 0 |
Everyone who is wise is either curious or not patient and vice versa.
If someone is not brave then someone is both not creative and not old.
Everyone who is both not patient and not happy is either generous or curious and vice versa.
Everyone who is wise is either brave or not generous.
If mary is both not humble and not happy then lucy is curious and vice versa.
Everyone who is both not wise and not happy is kind and vice versa.
Everyone who is both not patient and curious is not tall and vice versa.
If someone is either tall or calm then john is funny or old.
If alice is both not quiet and happy then someone is both rich and strong and vice versa.
If mary is not funny or not humble then lucy is both not kind and not rich.
Everyone who is not brave is rich.
Everyone who is either not rich or tall is not funny or not happy.
If paul is not patient or funny then john is either not creative or not old and vice versa.
If john is both not humble and not patient then someone is not humble and vice versa.
If susan is not strong then someone is either not brave or not happy.
If someone is patient then someone is not old.
Someone is either patient or old.
Susan is old or not old.
Fred is quiet.
Someone is either not quiet or wise.
Someone is both generous and not humble.
Someone is either old or humble.
Fred is either not rich or not happy.
Someone is not brave. | John is not humble. | entailment | (![X]:(wise(X)<=>(curious(X)<~>~patient(X))))&
((?[X]:(~brave(X)))=>(?[X]:((~creative(X)&~old(X)))))&
(![X]:((~patient(X)&~happy(X))<=>(generous(X)<~>curious(X))))&
(![X]:(wise(X)=>(brave(X)<~>~generous(X))))&
(((~humble(mary)&~happy(mary)))<=>(curious(lucy)))&
(![X]:((~wise(X)&~happy(X))<=>kind(X)))&
(![X]:((~patient(X)&curious(X))<=>~tall(X)))&
((?[X]:((tall(X)<~>calm(X))))=>((funny(john)|old(john))))&
(((~quiet(alice)&happy(alice)))<=>(?[X]:((rich(X)&strong(X)))))&
(((~funny(mary)|~humble(mary)))=>((~kind(lucy)&~rich(lucy))))&
(![X]:(~brave(X)=>rich(X)))&
(![X]:((~rich(X)<~>tall(X))=>(~funny(X)|~happy(X))))&
(((~patient(paul)|funny(paul)))<=>((~creative(john)<~>~old(john))))&
(((~humble(john)&~patient(john)))<=>(?[X]:(~humble(X))))&
((~strong(susan))=>(?[X]:((~brave(X)<~>~happy(X)))))&
((?[X]:(patient(X)))=>(?[X]:(~old(X))))&
(?[X]:((patient(X)<~>old(X))))&
((old(susan)|~old(susan)))&
(quiet(fred))&
(?[X]:((~quiet(X)<~>wise(X))))&
(?[X]:((generous(X)&~humble(X))))&
(?[X]:((old(X)<~>humble(X))))&
((~rich(fred)<~>~happy(fred)))&
(?[X]:(~brave(X))) | ~humble(john) | [
"p13",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 3169413244859689628882070
% SZS output start Proof for 3169413244859689628882070
14. (~patient(john) & ~humble(john)) <=> ? [X0] : ~humble(X0) [input p13]
21. ? [X0] : (~humble(X0) & generous(X0)) [input p20]
25. humble(john) [input hypothesis]
61. ((~patient(john) & ~humble(john)) | ! [X0] : humble(X0)) & (? [X0] : ~humble(X0) | (patient(john) | humble(john))) [nnf transformation 14]
62. ((~patient(john) & ~humble(john)) | ! [X0] : humble(X0)) & (? [X0] : ~humble(X0) | patient(john) | humble(john)) [flattening 61]
63. ((~patient(john) & ~humble(john)) | ! [X0] : humble(X0)) & (? [X1] : ~humble(X1) | patient(john) | humble(john)) [rectify 62]
64. ? [X1] : ~humble(X1) => ~humble(sK2) [choice axiom]
65. ((~patient(john) & ~humble(john)) | ! [X0] : humble(X0)) & (~humble(sK2) | patient(john) | humble(john)) [skolemisation 63,64]
78. ? [X0] : (~humble(X0) & generous(X0)) => (~humble(sK7) & generous(sK7)) [choice axiom]
79. ~humble(sK7) & generous(sK7) [skolemisation 21,78]
127. ~humble(john) | humble(X0) [cnf transformation 65]
139. ~humble(sK7) [cnf transformation 79]
145. humble(john) [cnf transformation 25]
248. 22 <=> ! [X0] : humble(X0) [avatar definition]
249. humble(X0) <- (22) [avatar component clause 248]
256. 24 <=> humble(john) [avatar definition]
259. 22 | ~24 [avatar split clause 127,256,248]
327. 24 [avatar split clause 145,256]
330. $false <- (22) [resolution 249,139]
331. ~22 [avatar contradiction clause 330]
332. $false [avatar sat refutation 259,327,331]
% SZS output end Proof for 3169413244859689628882070
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
If someone is rich then someone is kind or not generous.
Everyone who is both strong and curious is either strong or quiet.
Everyone who is not generous is wise and vice versa.
If someone is curious or funny then paul is kind.
If someone is not happy or kind then susan is both kind and curious.
If someone is not brave then someone is brave or old.
Everyone who is not strong or not brave is either wise or happy.
Everyone who is not wise or old is not wise or generous and vice versa.
If mary is not humble then someone is quiet.
If susan is kind then paul is kind and vice versa.
Everyone who is both not curious and rich is both old and not old and vice versa.
Everyone who is not brave or not kind is not wise or not rich.
Everyone who is both wise and old is calm or rich and vice versa.
If someone is not kind or not tall then someone is old or brave and vice versa.
If mary is quiet then someone is both funny and wise and vice versa.
Everyone who is both not calm and kind is humble or not old.
Fred is tall.
Someone is either kind or happy.
John is not strong.
Someone is not humble or generous.
Lucy is happy or strong.
Paul is old or not strong. | Lucy is calm. | contradiction | ((?[X]:(rich(X)))=>(?[X]:((kind(X)|~generous(X)))))&
(![X]:((strong(X)&curious(X))=>(strong(X)<~>quiet(X))))&
(![X]:(~generous(X)<=>wise(X)))&
((?[X]:((curious(X)|funny(X))))=>(kind(paul)))&
((?[X]:((~happy(X)|kind(X))))=>((kind(susan)&curious(susan))))&
((?[X]:(~brave(X)))=>(?[X]:((brave(X)|old(X)))))&
(![X]:((~strong(X)|~brave(X))=>(wise(X)<~>happy(X))))&
(![X]:((~wise(X)|old(X))<=>(~wise(X)|generous(X))))&
((~humble(mary))=>(?[X]:(quiet(X))))&
((kind(susan))<=>(kind(paul)))&
(![X]:((~curious(X)&rich(X))<=>(old(X)&~old(X))))&
(![X]:((~brave(X)|~kind(X))=>(~wise(X)|~rich(X))))&
(![X]:((wise(X)&old(X))<=>(calm(X)|rich(X))))&
((?[X]:((~kind(X)|~tall(X))))<=>(?[X]:((old(X)|brave(X)))))&
((quiet(mary))<=>(?[X]:((funny(X)&wise(X)))))&
(![X]:((~calm(X)&kind(X))=>(humble(X)|~old(X))))&
(tall(fred))&
(?[X]:((kind(X)<~>happy(X))))&
(~strong(john))&
(?[X]:((~humble(X)|generous(X))))&
((happy(lucy)|strong(lucy)))&
((old(paul)|~strong(paul))) | calm(lucy) | [
"p2",
"p7",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 311999959188745486555491
% SZS output start Proof for 311999959188745486555491
3. ! [X0] : (~generous(X0) <=> wise(X0)) [input p2]
8. ! [X0] : ((old(X0) | ~wise(X0)) <=> (generous(X0) | ~wise(X0))) [input p7]
13. ! [X0] : ((old(X0) & wise(X0)) <=> (rich(X0) | calm(X0))) [input p12]
23. calm(lucy) [input hypothesis]
43. ! [X0] : ((~generous(X0) | ~wise(X0)) & (wise(X0) | generous(X0))) [nnf transformation 3]
48. ! [X0] : (((old(X0) | ~wise(X0)) | (~generous(X0) & wise(X0))) & ((generous(X0) | ~wise(X0)) | (~old(X0) & wise(X0)))) [nnf transformation 8]
49. ! [X0] : ((old(X0) | ~wise(X0) | (~generous(X0) & wise(X0))) & (generous(X0) | ~wise(X0) | (~old(X0) & wise(X0)))) [flattening 48]
55. ! [X0] : (((old(X0) & wise(X0)) | (~rich(X0) & ~calm(X0))) & ((rich(X0) | calm(X0)) | (~old(X0) | ~wise(X0)))) [nnf transformation 13]
56. ! [X0] : (((old(X0) & wise(X0)) | (~rich(X0) & ~calm(X0))) & (rich(X0) | calm(X0) | ~old(X0) | ~wise(X0))) [flattening 55]
75. ~wise(X0) | ~generous(X0) [cnf transformation 43]
88. generous(X0) | ~wise(X0) | ~old(X0) [cnf transformation 49]
101. ~calm(X0) | wise(X0) [cnf transformation 56]
103. ~calm(X0) | old(X0) [cnf transformation 56]
120. calm(lucy) [cnf transformation 23]
176. ~old(X0) | ~wise(X0) [subsumption resolution 88,75]
283. wise(lucy) [resolution 101,120]
285. old(lucy) [resolution 103,120]
287. ~wise(lucy) [resolution 176,285]
288. $false [subsumption resolution 287,283]
% SZS output end Proof for 311999959188745486555491
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is either not patient or not kind then alice is both tall and strong and vice versa.
Everyone who is either wise or not wise is curious or strong and vice versa.
Everyone who is not generous is either rich or not tall and vice versa.
Everyone who is both not happy and not tall is both creative and brave and vice versa.
Everyone who is both brave and wise is both quiet and not humble and vice versa.
Everyone who is not humble or calm is not calm and vice versa.
If john is both funny and not wise then someone is not patient.
If alice is both not patient and not brave then someone is not tall or happy and vice versa.
If someone is not quiet then someone is both calm and kind.
Everyone who is both not creative and curious is kind and vice versa.
Everyone who is not happy or wise is both old and not patient and vice versa.
Everyone who is either not funny or old is both tall and patient.
Someone is patient or rich.
Someone is either not curious or curious.
Paul is either not strong or creative.
Someone is not tall or brave.
John is either generous or curious. | Lucy is tall. | entailment | (((~patient(lucy)<~>~kind(lucy)))<=>((tall(alice)&strong(alice))))&
(![X]:((wise(X)<~>~wise(X))<=>(curious(X)|strong(X))))&
(![X]:(~generous(X)<=>(rich(X)<~>~tall(X))))&
(![X]:((~happy(X)&~tall(X))<=>(creative(X)&brave(X))))&
(![X]:((brave(X)&wise(X))<=>(quiet(X)&~humble(X))))&
(![X]:((~humble(X)|calm(X))<=>~calm(X)))&
(((funny(john)&~wise(john)))=>(?[X]:(~patient(X))))&
(((~patient(alice)&~brave(alice)))<=>(?[X]:((~tall(X)|happy(X)))))&
((?[X]:(~quiet(X)))=>(?[X]:((calm(X)&kind(X)))))&
(![X]:((~creative(X)&curious(X))<=>kind(X)))&
(![X]:((~happy(X)|wise(X))<=>(old(X)&~patient(X))))&
(![X]:((~funny(X)<~>old(X))=>(tall(X)&patient(X))))&
(?[X]:((patient(X)|rich(X))))&
(?[X]:((~curious(X)<~>curious(X))))&
((~strong(paul)<~>creative(paul)))&
(?[X]:((~tall(X)|brave(X))))&
((generous(john)<~>curious(john))) | tall(lucy) | [
"p4",
"p5",
"p7",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 2167299765229554628262158
% SZS output start Proof for 2167299765229554628262158
5. ! [X0] : ((wise(X0) & brave(X0)) <=> (~humble(X0) & quiet(X0))) [input p4]
6. ! [X0] : ((calm(X0) | ~humble(X0)) <=> ~calm(X0)) [input p5]
8. (~brave(alice) & ~patient(alice)) <=> ? [X0] : (happy(X0) | ~tall(X0)) [input p7]
9. ? [X0] : ~quiet(X0) => ? [X0] : (kind(X0) & calm(X0)) [input p8]
18. ~tall(lucy) [input hypothesis]
19. ? [X0] : ~quiet(X0) => ? [X1] : (kind(X1) & calm(X1)) [rectify 9]
22. ? [X1] : (kind(X1) & calm(X1)) | ! [X0] : quiet(X0) [ennf transformation 19]
31. ! [X0] : (((wise(X0) & brave(X0)) | (humble(X0) | ~quiet(X0))) & ((~humble(X0) & quiet(X0)) | (~wise(X0) | ~brave(X0)))) [nnf transformation 5]
32. ! [X0] : (((wise(X0) & brave(X0)) | humble(X0) | ~quiet(X0)) & ((~humble(X0) & quiet(X0)) | ~wise(X0) | ~brave(X0))) [flattening 31]
33. ! [X0] : (((calm(X0) | ~humble(X0)) | calm(X0)) & (~calm(X0) | (~calm(X0) & humble(X0)))) [nnf transformation 6]
34. ! [X0] : ((calm(X0) | ~humble(X0) | calm(X0)) & (~calm(X0) | (~calm(X0) & humble(X0)))) [flattening 33]
37. ((~brave(alice) & ~patient(alice)) | ! [X0] : (~happy(X0) & tall(X0))) & (? [X0] : (happy(X0) | ~tall(X0)) | (brave(alice) | patient(alice))) [nnf transformation 8]
38. ((~brave(alice) & ~patient(alice)) | ! [X0] : (~happy(X0) & tall(X0))) & (? [X0] : (happy(X0) | ~tall(X0)) | brave(alice) | patient(alice)) [flattening 37]
39. ((~brave(alice) & ~patient(alice)) | ! [X0] : (~happy(X0) & tall(X0))) & (? [X1] : (happy(X1) | ~tall(X1)) | brave(alice) | patient(alice)) [rectify 38]
40. ? [X1] : (happy(X1) | ~tall(X1)) => (happy(sK1) | ~tall(sK1)) [choice axiom]
41. ((~brave(alice) & ~patient(alice)) | ! [X0] : (~happy(X0) & tall(X0))) & ((happy(sK1) | ~tall(sK1)) | brave(alice) | patient(alice)) [skolemisation 39,40]
42. ? [X0] : (kind(X0) & calm(X0)) | ! [X1] : quiet(X1) [rectify 22]
43. ? [X0] : (kind(X0) & calm(X0)) => (kind(sK2) & calm(sK2)) [choice axiom]
44. (kind(sK2) & calm(sK2)) | ! [X1] : quiet(X1) [skolemisation 42,43]
81. ~quiet(X0) | humble(X0) | brave(X0) [cnf transformation 32]
84. ~calm(X0) | ~calm(X0) [cnf transformation 34]
85. calm(X0) | ~humble(X0) | calm(X0) [cnf transformation 34]
90. ~brave(alice) | tall(X0) [cnf transformation 41]
92. calm(sK2) | quiet(X1) [cnf transformation 44]
114. ~tall(lucy) [cnf transformation 18]
115. ~calm(X0) [duplicate literal removal 84]
116. ~humble(X0) | calm(X0) [duplicate literal removal 85]
159. 9 <=> brave(alice) [avatar definition]
161. ~brave(alice) <- (~9) [avatar component clause 159]
164. 10 <=> ! [X0] : tall(X0) [avatar definition]
165. tall(X0) <- (10) [avatar component clause 164]
166. 10 | ~9 [avatar split clause 90,159,164]
183. 14 <=> ! [X1] : quiet(X1) [avatar definition]
184. quiet(X1) <- (14) [avatar component clause 183]
190. quiet(X1) [subsumption resolution 92,115]
191. 14 [avatar split clause 190,183]
263. $false <- (10) [resolution 165,114]
268. ~10 [avatar contradiction clause 263]
288. humble(X0) | brave(X0) <- (14) [resolution 81,184]
290. brave(X1) | calm(X1) <- (14) [resolution 288,116]
291. brave(X1) <- (14) [subsumption resolution 290,115]
293. $false <- (~9, 14) [resolution 291,161]
297. 9 | ~14 [avatar contradiction clause 293]
298. $false [avatar sat refutation 166,191,268,297]
% SZS output end Proof for 2167299765229554628262158
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is funny or brave then someone is rich or brave and vice versa. Everyone who is both kind and wise is both kind and not old. Everyone who is creative is curious and vice versa. If mary is humble or not curious then someone is not calm. Everyone who is strong or not quiet is both not creative and happy. Everyone who is wise is either not strong or not old. Everyone who is happy is both not curious and not calm. Everyone who is not funny is either not strong or not kind and vice versa. Everyone who is funny is either creative or happy and vice versa. Everyone who is both not happy and patient is both old and not brave. If someone is either curious or not creative then someone is both not patient and tall. If someone is either not humble or not patient then someone is both patient and happy and vice versa. Everyone who is not kind is both humble and strong and vice versa. If someone is either not quiet or not happy then fred is both not curious and not creative and vice versa. Everyone who is calm is strong or not rich. If alice is both strong and not curious then paul is either not wise or curious and vice versa. John is humble. Lucy is not wise. Alice is both not happy and not curious. Someone is both quiet and old. Someone is tall or wise. Fred is both not wise and not humble. | Lucy is not kind. | contradiction | (((funny(lucy)|brave(lucy)))<=>(?[X]:((rich(X)|brave(X)))))&
(![X]:((kind(X)&wise(X))=>(kind(X)&~old(X))))&
(![X]:(creative(X)<=>curious(X)))&
(((humble(mary)|~curious(mary)))=>(?[X]:(~calm(X))))&
(![X]:((strong(X)|~quiet(X))=>(~creative(X)&happy(X))))&
(![X]:(wise(X)=>(~strong(X)<~>~old(X))))&
(![X]:(happy(X)=>(~curious(X)&~calm(X))))&
(![X]:(~funny(X)<=>(~strong(X)<~>~kind(X))))&
(![X]:(funny(X)<=>(creative(X)<~>happy(X))))&
(![X]:((~happy(X)&patient(X))=>(old(X)&~brave(X))))&
((?[X]:((curious(X)<~>~creative(X))))=>(?[X]:((~patient(X)&tall(X)))))&
((?[X]:((~humble(X)<~>~patient(X))))<=>(?[X]:((patient(X)&happy(X)))))&
(![X]:(~kind(X)<=>(humble(X)&strong(X))))&
((?[X]:((~quiet(X)<~>~happy(X))))<=>((~curious(fred)&~creative(fred))))&
(![X]:(calm(X)=>(strong(X)|~rich(X))))&
(((strong(alice)&~curious(alice)))<=>((~wise(paul)<~>curious(paul))))&
(humble(john))&
(~wise(lucy))&
((~happy(alice)&~curious(alice)))&
(?[X]:((quiet(X)&old(X))))&
(?[X]:((tall(X)|wise(X))))&
((~wise(fred)&~humble(fred))) | ~kind(lucy) | [
"p4",
"p7",
"p8",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 45896583069910102131697
% SZS output start Proof for 45896583069910102131697
5. ! [X0] : ((~quiet(X0) | strong(X0)) => (happy(X0) & ~creative(X0))) [input p4]
8. ! [X0] : (~funny(X0) <=> (~strong(X0) <~> ~kind(X0))) [input p7]
9. ! [X0] : (funny(X0) <=> (creative(X0) <~> happy(X0))) [input p8]
13. ! [X0] : (~kind(X0) <=> (strong(X0) & humble(X0))) [input p12]
23. ~kind(lucy) [input hypothesis]
33. ! [X0] : ((happy(X0) & ~creative(X0)) | (quiet(X0) & ~strong(X0))) [ennf transformation 5]
46. ! [X0] : ((~funny(X0) | ((~strong(X0) | kind(X0)) & (~kind(X0) | strong(X0)))) & (((kind(X0) | strong(X0)) & (~kind(X0) | ~strong(X0))) | funny(X0))) [nnf transformation 8]
47. ! [X0] : ((funny(X0) | ((creative(X0) | ~happy(X0)) & (happy(X0) | ~creative(X0)))) & (((~happy(X0) | ~creative(X0)) & (happy(X0) | creative(X0))) | ~funny(X0))) [nnf transformation 9]
57. ! [X0] : ((~kind(X0) | (~strong(X0) | ~humble(X0))) & ((strong(X0) & humble(X0)) | kind(X0))) [nnf transformation 13]
58. ! [X0] : ((~kind(X0) | ~strong(X0) | ~humble(X0)) & ((strong(X0) & humble(X0)) | kind(X0))) [flattening 57]
76. ~strong(X0) | ~creative(X0) [cnf transformation 33]
78. ~strong(X0) | happy(X0) [cnf transformation 33]
86. ~strong(X0) | ~funny(X0) | kind(X0) [cnf transformation 46]
90. ~happy(X0) | creative(X0) | funny(X0) [cnf transformation 47]
102. strong(X0) | kind(X0) [cnf transformation 58]
124. ~kind(lucy) [cnf transformation 23]
258. happy(X0) | kind(X0) [resolution 102,78]
259. ~creative(X1) | kind(X1) [resolution 102,76]
311. ~funny(X1) | kind(X1) | kind(X1) [resolution 86,102]
312. ~funny(X1) | kind(X1) [duplicate literal removal 311]
333. creative(X0) | funny(X0) | kind(X0) [resolution 90,258]
335. funny(X0) | kind(X0) [subsumption resolution 333,259]
336. kind(X0) [subsumption resolution 335,312]
376. $false [resolution 336,124]
% SZS output end Proof for 45896583069910102131697
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind is both not tall and not creative. If someone is either old or creative then alice is not wise or quiet and vice versa. Everyone who is brave or tall is both not patient and old and vice versa. If someone is either calm or not strong then mary is either not old or kind. Everyone who is either old or not strong is not kind or not funny. If paul is both not patient and not rich then someone is not generous. Everyone who is not strong or quiet is either not creative or not quiet and vice versa. If alice is funny then someone is funny or wise and vice versa. Everyone who is not kind is quiet and vice versa. If john is either generous or rich then someone is either curious or wise and vice versa. Everyone who is not humble or old is brave or generous and vice versa. Everyone who is both calm and tall is both not tall and not generous. If susan is both quiet and not quiet then someone is not generous and vice versa. If john is either kind or generous then john is either funny or rich and vice versa. If someone is humble or calm then someone is not curious and vice versa. Everyone who is generous is rich or not kind and vice versa. Someone is either rich or generous. Someone is not humble or patient. Alice is wise or happy. John is not happy. Alice is kind or not wise. Fred is not calm. | Paul is generous. | entailment | (![X]:(kind(X)=>(~tall(X)&~creative(X))))&
((?[X]:((old(X)<~>creative(X))))<=>((~wise(alice)|quiet(alice))))&
(![X]:((brave(X)|tall(X))<=>(~patient(X)&old(X))))&
((?[X]:((calm(X)<~>~strong(X))))=>((~old(mary)<~>kind(mary))))&
(![X]:((old(X)<~>~strong(X))=>(~kind(X)|~funny(X))))&
(((~patient(paul)&~rich(paul)))=>(?[X]:(~generous(X))))&
(![X]:((~strong(X)|quiet(X))<=>(~creative(X)<~>~quiet(X))))&
((funny(alice))<=>(?[X]:((funny(X)|wise(X)))))&
(![X]:(~kind(X)<=>quiet(X)))&
(((generous(john)<~>rich(john)))<=>(?[X]:((curious(X)<~>wise(X)))))&
(![X]:((~humble(X)|old(X))<=>(brave(X)|generous(X))))&
(![X]:((calm(X)&tall(X))=>(~tall(X)&~generous(X))))&
(((quiet(susan)&~quiet(susan)))<=>(?[X]:(~generous(X))))&
(((kind(john)<~>generous(john)))<=>((funny(john)<~>rich(john))))&
((?[X]:((humble(X)|calm(X))))<=>(?[X]:(~curious(X))))&
(![X]:(generous(X)<=>(rich(X)|~kind(X))))&
(?[X]:((rich(X)<~>generous(X))))&
(?[X]:((~humble(X)|patient(X))))&
((wise(alice)|happy(alice)))&
(~happy(john))&
((kind(alice)|~wise(alice)))&
(~calm(fred)) | generous(paul) | [
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 198973262386171261764161
% SZS output start Proof for 198973262386171261764161
13. (~quiet(susan) & quiet(susan)) <=> ? [X0] : ~generous(X0) [input p12]
23. ~generous(paul) [input hypothesis]
57. ((~quiet(susan) & quiet(susan)) | ! [X0] : generous(X0)) & (? [X0] : ~generous(X0) | (quiet(susan) | ~quiet(susan))) [nnf transformation 13]
58. ((~quiet(susan) & quiet(susan)) | ! [X0] : generous(X0)) & (? [X0] : ~generous(X0) | quiet(susan) | ~quiet(susan)) [flattening 57]
59. ((~quiet(susan) & quiet(susan)) | ! [X0] : generous(X0)) & (? [X1] : ~generous(X1) | quiet(susan) | ~quiet(susan)) [rectify 58]
60. ? [X1] : ~generous(X1) => ~generous(sK4) [choice axiom]
61. ((~quiet(susan) & quiet(susan)) | ! [X0] : generous(X0)) & (~generous(sK4) | quiet(susan) | ~quiet(susan)) [skolemisation 59,60]
121. quiet(susan) | generous(X0) [cnf transformation 61]
122. ~quiet(susan) | generous(X0) [cnf transformation 61]
144. ~generous(paul) [cnf transformation 23]
259. 25 <=> ! [X0] : generous(X0) [avatar definition]
260. generous(X0) <- (25) [avatar component clause 259]
262. 26 <=> quiet(susan) [avatar definition]
265. 25 | ~26 [avatar split clause 122,262,259]
266. 25 | 26 [avatar split clause 121,262,259]
345. $false <- (25) [resolution 260,144]
346. ~25 [avatar contradiction clause 345]
347. $false [avatar sat refutation 265,266,346]
% SZS output end Proof for 198973262386171261764161
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 john is not strong or rich then someone is humble.
Everyone who is both funny and happy is both curious and not quiet.
Everyone who is both not happy and not tall is not patient or generous.
If lucy is not curious then someone is not funny or humble.
If lucy is not curious or creative then paul is either rich or not patient.
If john is either calm or tall then someone is either not curious or not funny and vice versa.
Everyone who is not quiet or not kind is curious or old and vice versa.
Everyone who is both creative and tall is either rich or calm.
Everyone who is not old is kind and vice versa.
Everyone who is either not quiet or not humble is brave or happy and vice versa.
Everyone who is kind is quiet and vice versa.
If someone is happy then someone is not funny or brave.
If someone is not old or generous then susan is not tall and vice versa.
If someone is either not calm or not humble then someone is either curious or happy and vice versa.
If john is either not calm or curious then fred is both not quiet and not creative and vice versa.
If paul is not brave then lucy is both curious and kind.
Someone is both curious and not humble.
Someone is calm.
Paul is old.
Someone is not brave or not patient.
Susan is tall or not rich.
Mary is not wise or not quiet.
Someone is creative or not strong.
Someone is both wise and patient. | Fred is not quiet. | neutral | (((~strong(john)|rich(john)))=>(?[X]:(humble(X))))&
(![X]:((funny(X)&happy(X))=>(curious(X)&~quiet(X))))&
(![X]:((~happy(X)&~tall(X))=>(~patient(X)|generous(X))))&
((~curious(lucy))=>(?[X]:((~funny(X)|humble(X)))))&
(((~curious(lucy)|creative(lucy)))=>((rich(paul)<~>~patient(paul))))&
(((calm(john)<~>tall(john)))<=>(?[X]:((~curious(X)<~>~funny(X)))))&
(![X]:((~quiet(X)|~kind(X))<=>(curious(X)|old(X))))&
(![X]:((creative(X)&tall(X))=>(rich(X)<~>calm(X))))&
(![X]:(~old(X)<=>kind(X)))&
(![X]:((~quiet(X)<~>~humble(X))<=>(brave(X)|happy(X))))&
(![X]:(kind(X)<=>quiet(X)))&
((?[X]:(happy(X)))=>(?[X]:((~funny(X)|brave(X)))))&
((?[X]:((~old(X)|generous(X))))<=>(~tall(susan)))&
((?[X]:((~calm(X)<~>~humble(X))))<=>(?[X]:((curious(X)<~>happy(X)))))&
(((~calm(john)<~>curious(john)))<=>((~quiet(fred)&~creative(fred))))&
((~brave(paul))=>((curious(lucy)&kind(lucy))))&
(?[X]:((curious(X)&~humble(X))))&
(?[X]:(calm(X)))&
(old(paul))&
(?[X]:((~brave(X)|~patient(X))))&
((tall(susan)|~rich(susan)))&
((~wise(mary)|~quiet(mary)))&
(?[X]:((creative(X)|~strong(X))))&
(?[X]:((wise(X)&patient(X)))) | ~quiet(fred) | [] | null | 0 |
Everyone who is patient or not patient is calm or tall.
Everyone who is both not rich and not humble is both generous and wise and vice versa.
Everyone who is not quiet or not old is calm and vice versa.
If john is not wise or curious then someone is not patient.
If paul is strong or old then paul is not tall and vice versa.
If someone is wise or kind then someone is both quiet and calm and vice versa.
If lucy is both happy and wise then susan is quiet and vice versa.
If alice is curious or brave then someone is tall or not humble.
Everyone who is not old or not humble is funny and vice versa.
If someone is either funny or not humble then someone is either brave or not calm and vice versa.
Everyone who is funny or not old is both wise and not strong and vice versa.
Everyone who is either strong or not funny is either not tall or tall and vice versa.
If fred is not tall or tall then someone is not curious and vice versa.
If someone is both not curious and happy then someone is both not humble and not wise.
If mary is not quiet or not strong then alice is kind or not tall.
If fred is either calm or not curious then lucy is not rich or brave.
Alice is both not tall and creative.
Someone is wise or not wise.
Someone is not funny.
Someone is both creative and happy.
Lucy is not old or not happy.
Lucy is wise or creative. | Alice is happy. | neutral | (![X]:((patient(X)|~patient(X))=>(calm(X)|tall(X))))&
(![X]:((~rich(X)&~humble(X))<=>(generous(X)&wise(X))))&
(![X]:((~quiet(X)|~old(X))<=>calm(X)))&
(((~wise(john)|curious(john)))=>(?[X]:(~patient(X))))&
(((strong(paul)|old(paul)))<=>(~tall(paul)))&
((?[X]:((wise(X)|kind(X))))<=>(?[X]:((quiet(X)&calm(X)))))&
(((happy(lucy)&wise(lucy)))<=>(quiet(susan)))&
(((curious(alice)|brave(alice)))=>(?[X]:((tall(X)|~humble(X)))))&
(![X]:((~old(X)|~humble(X))<=>funny(X)))&
((?[X]:((funny(X)<~>~humble(X))))<=>(?[X]:((brave(X)<~>~calm(X)))))&
(![X]:((funny(X)|~old(X))<=>(wise(X)&~strong(X))))&
(![X]:((strong(X)<~>~funny(X))<=>(~tall(X)<~>tall(X))))&
(((~tall(fred)|tall(fred)))<=>(?[X]:(~curious(X))))&
((?[X]:((~curious(X)&happy(X))))=>(?[X]:((~humble(X)&~wise(X)))))&
(((~quiet(mary)|~strong(mary)))=>((kind(alice)|~tall(alice))))&
(((calm(fred)<~>~curious(fred)))=>((~rich(lucy)|brave(lucy))))&
((~tall(alice)&creative(alice)))&
(?[X]:((wise(X)|~wise(X))))&
(?[X]:(~funny(X)))&
(?[X]:((creative(X)&happy(X))))&
((~old(lucy)|~happy(lucy)))&
((wise(lucy)|creative(lucy))) | happy(alice) | [] | null | 0 |
Everyone who is not strong or creative is not wise and vice versa.
Everyone who is not wise or tall is both not calm and wise and vice versa.
If mary is funny then john is old or patient.
If lucy is both quiet and not rich then mary is not funny or humble.
If someone is both funny and patient then paul is old.
Everyone who is not tall is both not calm and not happy.
If someone is either strong or not patient then someone is either not tall or humble.
Everyone who is not creative or old is curious or not wise and vice versa.
If mary is not kind then john is either not funny or strong.
If john is either not brave or not humble then someone is both not strong and old and vice versa.
Everyone who is not wise or old is either not strong or patient and vice versa.
Everyone who is either curious or not happy is calm and vice versa.
Everyone who is not humble is either patient or not kind and vice versa.
Everyone who is not calm is curious and vice versa.
If someone is both not kind and not strong then someone is both not calm and not generous and vice versa.
Everyone who is either wise or not old is both curious and not quiet.
Lucy is not funny or humble.
Someone is old or not humble.
Alice is generous or humble.
Alice is not old or funny. | Paul is calm. | contradiction | (![X]:((~strong(X)|creative(X))<=>~wise(X)))&
(![X]:((~wise(X)|tall(X))<=>(~calm(X)&wise(X))))&
((funny(mary))=>((old(john)|patient(john))))&
(((quiet(lucy)&~rich(lucy)))=>((~funny(mary)|humble(mary))))&
((?[X]:((funny(X)&patient(X))))=>(old(paul)))&
(![X]:(~tall(X)=>(~calm(X)&~happy(X))))&
((?[X]:((strong(X)<~>~patient(X))))=>(?[X]:((~tall(X)<~>humble(X)))))&
(![X]:((~creative(X)|old(X))<=>(curious(X)|~wise(X))))&
((~kind(mary))=>((~funny(john)<~>strong(john))))&
(((~brave(john)<~>~humble(john)))<=>(?[X]:((~strong(X)&old(X)))))&
(![X]:((~wise(X)|old(X))<=>(~strong(X)<~>patient(X))))&
(![X]:((curious(X)<~>~happy(X))<=>calm(X)))&
(![X]:(~humble(X)<=>(patient(X)<~>~kind(X))))&
(![X]:(~calm(X)<=>curious(X)))&
((?[X]:((~kind(X)&~strong(X))))<=>(?[X]:((~calm(X)&~generous(X)))))&
(![X]:((wise(X)<~>~old(X))=>(curious(X)&~quiet(X))))&
((~funny(lucy)|humble(lucy)))&
(?[X]:((old(X)|~humble(X))))&
((generous(alice)|humble(alice)))&
((~old(alice)|funny(alice))) | calm(paul) | [
"p1",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 7712096588689849713940926
% SZS output start Proof for 7712096588689849713940926
2. ! [X0] : ((tall(X0) | ~wise(X0)) <=> (wise(X0) & ~calm(X0))) [input p1]
6. ! [X0] : (~tall(X0) => (~happy(X0) & ~calm(X0))) [input p5]
21. calm(paul) [input hypothesis]
29. ! [X0] : ((~happy(X0) & ~calm(X0)) | tall(X0)) [ennf transformation 6]
35. ! [X0] : (((tall(X0) | ~wise(X0)) | (~wise(X0) | calm(X0))) & ((wise(X0) & ~calm(X0)) | (~tall(X0) & wise(X0)))) [nnf transformation 2]
36. ! [X0] : ((tall(X0) | ~wise(X0) | ~wise(X0) | calm(X0)) & ((wise(X0) & ~calm(X0)) | (~tall(X0) & wise(X0)))) [flattening 35]
65. ~calm(X0) | ~tall(X0) [cnf transformation 36]
71. ~calm(X0) | tall(X0) [cnf transformation 29]
115. calm(paul) [cnf transformation 21]
139. ~calm(X0) [subsumption resolution 71,65]
262. $false [subsumption resolution 115,139]
% SZS output end Proof for 7712096588689849713940926
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 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 not strong. | 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)) | ~strong(mary) | [] | null | 0 |
If john is happy or curious then someone is either not tall or curious and vice versa.
Everyone who is both not tall and brave is either not strong or generous and vice versa.
Everyone who is both creative and funny is both not curious and generous and vice versa.
If john is either strong or not happy then susan is either calm or strong.
Everyone who is both not curious and wise is both not tall and calm.
Everyone who is wise or patient is both patient and funny.
Everyone who is rich is not happy.
Everyone who is humble is not generous and vice versa.
Everyone who is either calm or old is not creative and vice versa.
Everyone who is either not brave or not rich is either not funny or creative and vice versa.
Everyone who is both patient and old is both kind and not curious and vice versa.
Everyone who is both not old and not humble is both not brave and creative and vice versa.
Everyone who is both not creative and generous is not brave or not humble and vice versa.
Everyone who is brave is either patient or not calm and vice versa.
Everyone who is not rich is patient or curious.
If john is not patient or humble then fred is either not funny or old and vice versa.
Someone is not curious.
Susan is either not generous or not brave.
Someone is both not generous and not kind.
Someone is either strong or not tall.
Paul is both not strong and not kind.
Paul is tall.
Someone is both strong and humble.
Someone is not rich. | Fred is curious. | neutral | (((happy(john)|curious(john)))<=>(?[X]:((~tall(X)<~>curious(X)))))&
(![X]:((~tall(X)&brave(X))<=>(~strong(X)<~>generous(X))))&
(![X]:((creative(X)&funny(X))<=>(~curious(X)&generous(X))))&
(((strong(john)<~>~happy(john)))=>((calm(susan)<~>strong(susan))))&
(![X]:((~curious(X)&wise(X))=>(~tall(X)&calm(X))))&
(![X]:((wise(X)|patient(X))=>(patient(X)&funny(X))))&
(![X]:(rich(X)=>~happy(X)))&
(![X]:(humble(X)<=>~generous(X)))&
(![X]:((calm(X)<~>old(X))<=>~creative(X)))&
(![X]:((~brave(X)<~>~rich(X))<=>(~funny(X)<~>creative(X))))&
(![X]:((patient(X)&old(X))<=>(kind(X)&~curious(X))))&
(![X]:((~old(X)&~humble(X))<=>(~brave(X)&creative(X))))&
(![X]:((~creative(X)&generous(X))<=>(~brave(X)|~humble(X))))&
(![X]:(brave(X)<=>(patient(X)<~>~calm(X))))&
(![X]:(~rich(X)=>(patient(X)|curious(X))))&
(((~patient(john)|humble(john)))<=>((~funny(fred)<~>old(fred))))&
(?[X]:(~curious(X)))&
((~generous(susan)<~>~brave(susan)))&
(?[X]:((~generous(X)&~kind(X))))&
(?[X]:((strong(X)<~>~tall(X))))&
((~strong(paul)&~kind(paul)))&
(tall(paul))&
(?[X]:((strong(X)&humble(X))))&
(?[X]:(~rich(X))) | curious(fred) | [] | null | 0 |
If fred is tall then john is not generous.
Everyone who is creative is not generous or not funny and vice versa.
Everyone who is either generous or quiet is both patient and tall and vice versa.
If someone is not patient or calm then susan is not strong.
Everyone who is either not brave or not creative is not rich.
If someone is tall then susan is wise or curious.
If susan is not patient or humble then someone is either not funny or not humble.
If john is both not patient and not rich then someone is not strong.
Everyone who is humble or not tall is brave.
If mary is not patient or not funny then alice is either happy or not funny.
Everyone who is both patient and not creative is both generous and not funny.
Everyone who is not kind is both quiet and not tall and vice versa.
Everyone who is not wise is kind or not funny.
If someone is patient or curious then mary is both not strong and not funny.
Everyone who is both brave and rich is tall and vice versa.
Everyone who is both strong and creative is either not tall or patient and vice versa.
Lucy is not rich or old.
Someone is either creative or generous.
Someone is either quiet or brave.
Mary is not tall or not rich.
Someone is both not funny and wise.
Someone is both calm and kind.
Susan is generous. | Mary is strong. | neutral | ((tall(fred))=>(~generous(john)))&
(![X]:(creative(X)<=>(~generous(X)|~funny(X))))&
(![X]:((generous(X)<~>quiet(X))<=>(patient(X)&tall(X))))&
((?[X]:((~patient(X)|calm(X))))=>(~strong(susan)))&
(![X]:((~brave(X)<~>~creative(X))=>~rich(X)))&
((?[X]:(tall(X)))=>((wise(susan)|curious(susan))))&
(((~patient(susan)|humble(susan)))=>(?[X]:((~funny(X)<~>~humble(X)))))&
(((~patient(john)&~rich(john)))=>(?[X]:(~strong(X))))&
(![X]:((humble(X)|~tall(X))=>brave(X)))&
(((~patient(mary)|~funny(mary)))=>((happy(alice)<~>~funny(alice))))&
(![X]:((patient(X)&~creative(X))=>(generous(X)&~funny(X))))&
(![X]:(~kind(X)<=>(quiet(X)&~tall(X))))&
(![X]:(~wise(X)=>(kind(X)|~funny(X))))&
((?[X]:((patient(X)|curious(X))))=>((~strong(mary)&~funny(mary))))&
(![X]:((brave(X)&rich(X))<=>tall(X)))&
(![X]:((strong(X)&creative(X))<=>(~tall(X)<~>patient(X))))&
((~rich(lucy)|old(lucy)))&
(?[X]:((creative(X)<~>generous(X))))&
(?[X]:((quiet(X)<~>brave(X))))&
((~tall(mary)|~rich(mary)))&
(?[X]:((~funny(X)&wise(X))))&
(?[X]:((calm(X)&kind(X))))&
(generous(susan)) | strong(mary) | [] | null | 0 |
Everyone who is both not rich and not strong is both rich and not calm and vice versa.
If mary is either not rich or not brave then someone is either curious or humble.
Everyone who is both creative and quiet is both not brave and not funny and vice versa.
If alice is not patient or not humble then john is generous or happy and vice versa.
If john is kind then someone is both not funny and curious and vice versa.
Everyone who is not humble is either kind or old and vice versa.
Everyone who is both not quiet and not curious is not funny or not old.
If someone is old or patient then someone is either kind or old and vice versa.
If someone is both old and not tall then someone is brave.
Everyone who is both generous and old is either not brave or humble and vice versa.
If john is both kind and curious then john is either not tall or strong and vice versa.
If mary is either not rich or not curious then paul is curious and vice versa.
Everyone who is kind is not happy or brave.
Everyone who is old is either brave or calm and vice versa.
If mary is kind or wise then someone is both happy and not tall.
If lucy is both not calm and kind then someone is both strong and not wise and vice versa.
Someone is not kind.
Fred is happy.
Someone is both not strong and wise.
Mary is both not old and not happy.
Lucy is creative or not strong.
Alice is patient.
Someone is wise or not happy.
Paul is either not rich or patient. | Paul is quiet. | neutral | (![X]:((~rich(X)&~strong(X))<=>(rich(X)&~calm(X))))&
(((~rich(mary)<~>~brave(mary)))=>(?[X]:((curious(X)<~>humble(X)))))&
(![X]:((creative(X)&quiet(X))<=>(~brave(X)&~funny(X))))&
(((~patient(alice)|~humble(alice)))<=>((generous(john)|happy(john))))&
((kind(john))<=>(?[X]:((~funny(X)&curious(X)))))&
(![X]:(~humble(X)<=>(kind(X)<~>old(X))))&
(![X]:((~quiet(X)&~curious(X))=>(~funny(X)|~old(X))))&
((?[X]:((old(X)|patient(X))))<=>(?[X]:((kind(X)<~>old(X)))))&
((?[X]:((old(X)&~tall(X))))=>(?[X]:(brave(X))))&
(![X]:((generous(X)&old(X))<=>(~brave(X)<~>humble(X))))&
(((kind(john)&curious(john)))<=>((~tall(john)<~>strong(john))))&
(((~rich(mary)<~>~curious(mary)))<=>(curious(paul)))&
(![X]:(kind(X)=>(~happy(X)|brave(X))))&
(![X]:(old(X)<=>(brave(X)<~>calm(X))))&
(((kind(mary)|wise(mary)))=>(?[X]:((happy(X)&~tall(X)))))&
(((~calm(lucy)&kind(lucy)))<=>(?[X]:((strong(X)&~wise(X)))))&
(?[X]:(~kind(X)))&
(happy(fred))&
(?[X]:((~strong(X)&wise(X))))&
((~old(mary)&~happy(mary)))&
((creative(lucy)|~strong(lucy)))&
(patient(alice))&
(?[X]:((wise(X)|~happy(X))))&
((~rich(paul)<~>patient(paul))) | quiet(paul) | [] | null | 0 |
If someone is not wise or creative then someone is either not patient or old.
Everyone who is brave is not tall or generous and vice versa.
Everyone who is generous or calm is either happy or tall.
If someone is either not curious or rich then paul is creative or not curious and vice versa.
Everyone who is either creative or old is not patient or quiet.
If susan is curious or not generous then fred is both not patient and tall and vice versa.
Everyone who is either not generous or not happy is either not creative or brave and vice versa.
Everyone who is calm or rich is both not creative and not strong and vice versa.
Everyone who is not old or not generous is both happy and wise.
If someone is either kind or not kind then mary is either generous or not wise and vice versa.
Everyone who is either not patient or not funny is either creative or calm and vice versa.
If alice is either not wise or patient then john is not generous or not calm and vice versa.
Everyone who is either not patient or creative is both kind and strong and vice versa.
Everyone who is either not happy or not generous is patient or humble and vice versa.
Everyone who is not quiet or kind is not kind or quiet.
Everyone who is funny or not brave is rich.
Someone is funny.
Fred is not old or not funny.
Someone is either not brave or quiet.
Susan is either not creative or curious.
John is both curious and not quiet.
Someone is not kind.
Fred is curious or quiet.
Lucy is not happy. | Susan is not calm. | entailment | ((?[X]:((~wise(X)|creative(X))))=>(?[X]:((~patient(X)<~>old(X)))))&
(![X]:(brave(X)<=>(~tall(X)|generous(X))))&
(![X]:((generous(X)|calm(X))=>(happy(X)<~>tall(X))))&
((?[X]:((~curious(X)<~>rich(X))))<=>((creative(paul)|~curious(paul))))&
(![X]:((creative(X)<~>old(X))=>(~patient(X)|quiet(X))))&
(((curious(susan)|~generous(susan)))<=>((~patient(fred)&tall(fred))))&
(![X]:((~generous(X)<~>~happy(X))<=>(~creative(X)<~>brave(X))))&
(![X]:((calm(X)|rich(X))<=>(~creative(X)&~strong(X))))&
(![X]:((~old(X)|~generous(X))=>(happy(X)&wise(X))))&
((?[X]:((kind(X)<~>~kind(X))))<=>((generous(mary)<~>~wise(mary))))&
(![X]:((~patient(X)<~>~funny(X))<=>(creative(X)<~>calm(X))))&
(((~wise(alice)<~>patient(alice)))<=>((~generous(john)|~calm(john))))&
(![X]:((~patient(X)<~>creative(X))<=>(kind(X)&strong(X))))&
(![X]:((~happy(X)<~>~generous(X))<=>(patient(X)|humble(X))))&
(![X]:((~quiet(X)|kind(X))=>(~kind(X)|quiet(X))))&
(![X]:((funny(X)|~brave(X))=>rich(X)))&
(?[X]:(funny(X)))&
((~old(fred)|~funny(fred)))&
(?[X]:((~brave(X)<~>quiet(X))))&
((~creative(susan)<~>curious(susan)))&
((curious(john)&~quiet(john)))&
(?[X]:(~kind(X)))&
((curious(fred)|quiet(fred)))&
(~happy(lucy)) | ~calm(susan) | [
"p1",
"p2",
"p5",
"p6",
"p7",
"p8",
"p10",
"p12",
"p13",
"p15",
"p17",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 1349827807326659192149103
% SZS output start Proof for 1349827807326659192149103
2. ! [X0] : (brave(X0) <=> (generous(X0) | ~tall(X0))) [input p1]
3. ! [X0] : ((calm(X0) | generous(X0)) => (happy(X0) <~> tall(X0))) [input p2]
6. (~generous(susan) | curious(susan)) <=> (tall(fred) & ~patient(fred)) [input p5]
7. ! [X0] : ((~generous(X0) <~> ~happy(X0)) <=> (~creative(X0) <~> brave(X0))) [input p6]
8. ! [X0] : ((rich(X0) | calm(X0)) <=> (~strong(X0) & ~creative(X0))) [input p7]
9. ! [X0] : ((~generous(X0) | ~old(X0)) => (wise(X0) & happy(X0))) [input p8]
11. ! [X0] : ((~patient(X0) <~> ~funny(X0)) <=> (creative(X0) <~> calm(X0))) [input p10]
13. ! [X0] : ((~patient(X0) <~> creative(X0)) <=> (strong(X0) & kind(X0))) [input p12]
14. ! [X0] : ((~happy(X0) <~> ~generous(X0)) <=> (humble(X0) | patient(X0))) [input p13]
16. ! [X0] : ((~brave(X0) | funny(X0)) => rich(X0)) [input p15]
18. ~funny(fred) | ~old(fred) [input p17]
20. ~creative(susan) <~> curious(susan) [input p19]
25. calm(susan) [input hypothesis]
28. ! [X0] : ((happy(X0) <~> tall(X0)) | (~calm(X0) & ~generous(X0))) [ennf transformation 3]
31. ! [X0] : ((wise(X0) & happy(X0)) | (generous(X0) & old(X0))) [ennf transformation 9]
34. ! [X0] : (rich(X0) | (brave(X0) & ~funny(X0))) [ennf transformation 16]
39. ! [X0] : ((brave(X0) | (~generous(X0) & tall(X0))) & ((generous(X0) | ~tall(X0)) | ~brave(X0))) [nnf transformation 2]
40. ! [X0] : ((brave(X0) | (~generous(X0) & tall(X0))) & (generous(X0) | ~tall(X0) | ~brave(X0))) [flattening 39]
41. ! [X0] : (((~tall(X0) | ~happy(X0)) & (tall(X0) | happy(X0))) | (~calm(X0) & ~generous(X0))) [nnf transformation 28]
48. ((~generous(susan) | curious(susan)) | (~tall(fred) | patient(fred))) & ((tall(fred) & ~patient(fred)) | (generous(susan) & ~curious(susan))) [nnf transformation 6]
49. (~generous(susan) | curious(susan) | ~tall(fred) | patient(fred)) & ((tall(fred) & ~patient(fred)) | (generous(susan) & ~curious(susan))) [flattening 48]
50. ! [X0] : ((((happy(X0) | generous(X0)) & (~happy(X0) | ~generous(X0))) | ((~creative(X0) | ~brave(X0)) & (brave(X0) | creative(X0)))) & (((~brave(X0) | creative(X0)) & (brave(X0) | ~creative(X0))) | ((~generous(X0) | happy(X0)) & (~happy(X0) | generous(X0))))) [nnf transformation 7]
51. ! [X0] : (((rich(X0) | calm(X0)) | (strong(X0) | creative(X0))) & ((~strong(X0) & ~creative(X0)) | (~rich(X0) & ~calm(X0)))) [nnf transformation 8]
52. ! [X0] : ((rich(X0) | calm(X0) | strong(X0) | creative(X0)) & ((~strong(X0) & ~creative(X0)) | (~rich(X0) & ~calm(X0)))) [flattening 51]
57. ! [X0] : ((((funny(X0) | patient(X0)) & (~funny(X0) | ~patient(X0))) | ((creative(X0) | ~calm(X0)) & (calm(X0) | ~creative(X0)))) & (((~calm(X0) | ~creative(X0)) & (calm(X0) | creative(X0))) | ((~patient(X0) | funny(X0)) & (~funny(X0) | patient(X0))))) [nnf transformation 11]
60. ! [X0] : ((((~creative(X0) | patient(X0)) & (creative(X0) | ~patient(X0))) | (~strong(X0) | ~kind(X0))) & ((strong(X0) & kind(X0)) | ((~patient(X0) | ~creative(X0)) & (creative(X0) | patient(X0))))) [nnf transformation 13]
61. ! [X0] : ((((~creative(X0) | patient(X0)) & (creative(X0) | ~patient(X0))) | ~strong(X0) | ~kind(X0)) & ((strong(X0) & kind(X0)) | ((~patient(X0) | ~creative(X0)) & (creative(X0) | patient(X0))))) [flattening 60]
62. ! [X0] : ((((generous(X0) | happy(X0)) & (~generous(X0) | ~happy(X0))) | (~humble(X0) & ~patient(X0))) & ((humble(X0) | patient(X0)) | ((~happy(X0) | generous(X0)) & (~generous(X0) | happy(X0))))) [nnf transformation 14]
63. ! [X0] : ((((generous(X0) | happy(X0)) & (~generous(X0) | ~happy(X0))) | (~humble(X0) & ~patient(X0))) & (humble(X0) | patient(X0) | ((~happy(X0) | generous(X0)) & (~generous(X0) | happy(X0))))) [flattening 62]
69. (~curious(susan) | creative(susan)) & (curious(susan) | ~creative(susan)) [nnf transformation 20]
76. ~tall(X0) | generous(X0) | ~brave(X0) [cnf transformation 40]
78. ~generous(X0) | brave(X0) [cnf transformation 40]
81. ~happy(X0) | ~tall(X0) | ~generous(X0) [cnf transformation 41]
91. ~patient(fred) | ~curious(susan) [cnf transformation 49]
92. ~patient(fred) | generous(susan) [cnf transformation 49]
93. tall(fred) | ~curious(susan) [cnf transformation 49]
94. tall(fred) | generous(susan) [cnf transformation 49]
99. ~brave(X0) | creative(X0) | ~generous(X0) | happy(X0) [cnf transformation 50]
102. happy(X0) | generous(X0) | brave(X0) | creative(X0) [cnf transformation 50]
104. ~calm(X0) | ~creative(X0) [cnf transformation 52]
105. ~rich(X0) | ~creative(X0) [cnf transformation 52]
106. ~strong(X0) | ~calm(X0) [cnf transformation 52]
107. ~strong(X0) | ~rich(X0) [cnf transformation 52]
109. happy(X0) | old(X0) [cnf transformation 31]
127. funny(X0) | patient(X0) | calm(X0) | ~creative(X0) [cnf transformation 57]
128. funny(X0) | patient(X0) | creative(X0) | ~calm(X0) [cnf transformation 57]
137. strong(X0) | creative(X0) | patient(X0) [cnf transformation 61]
143. ~happy(X0) | ~generous(X0) | ~patient(X0) [cnf transformation 63]
150. rich(X0) | brave(X0) [cnf transformation 34]
152. ~funny(fred) | ~old(fred) [cnf transformation 18]
155. curious(susan) | ~creative(susan) [cnf transformation 69]
162. calm(susan) [cnf transformation 25]
216. 11 <=> patient(fred) [avatar definition]
220. 12 <=> tall(fred) [avatar definition]
221. tall(fred) <- (12) [avatar component clause 220]
224. 13 <=> curious(susan) [avatar definition]
228. 14 <=> generous(susan) [avatar definition]
229. generous(susan) <- (14) [avatar component clause 228]
232. 14 | 12 [avatar split clause 94,220,228]
233. ~13 | 12 [avatar split clause 93,220,224]
234. 14 | ~11 [avatar split clause 92,216,228]
235. ~13 | ~11 [avatar split clause 91,216,224]
236. happy(X0) | brave(X0) | creative(X0) [subsumption resolution 102,78]
238. ~generous(X0) | creative(X0) | happy(X0) [subsumption resolution 99,236]
262. ~calm(X0) | patient(X0) | funny(X0) [subsumption resolution 128,104]
263. ~creative(X0) | patient(X0) | funny(X0) [subsumption resolution 127,262]
291. 23 <=> old(fred) [avatar definition]
295. 24 <=> funny(fred) [avatar definition]
297. ~funny(fred) <- (~24) [avatar component clause 295]
298. ~23 | ~24 [avatar split clause 152,295,291]
310. 27 <=> creative(susan) [avatar definition]
311. ~creative(susan) <- (~27) [avatar component clause 310]
314. ~27 | 13 [avatar split clause 155,224,310]
338. generous(fred) | ~brave(fred) <- (12) [resolution 76,221]
341. 30 <=> brave(fred) [avatar definition]
343. ~brave(fred) <- (~30) [avatar component clause 341]
345. 31 <=> generous(fred) [avatar definition]
347. generous(fred) <- (31) [avatar component clause 345]
348. ~30 | 31 | ~12 [avatar split clause 338,220,345,341]
368. 35 <=> happy(susan) [avatar definition]
369. ~happy(susan) <- (~35) [avatar component clause 368]
370. happy(susan) <- (35) [avatar component clause 368]
373. ~generous(X1) | ~tall(X1) | old(X1) [resolution 81,109]
398. creative(X0) | patient(X0) | ~rich(X0) [resolution 137,107]
399. creative(X1) | patient(X1) | ~calm(X1) [resolution 137,106]
404. ~generous(susan) | ~patient(susan) <- (35) [resolution 143,370]
436. 39 <=> patient(susan) [avatar definition]
531. ~calm(X1) | patient(X1) [subsumption resolution 399,104]
532. ~rich(X0) | patient(X0) [subsumption resolution 398,105]
551. patient(susan) [resolution 531,162]
555. brave(X0) | patient(X0) [resolution 532,150]
573. patient(fred) <- (~30) [resolution 555,343]
577. 11 | 30 [avatar split clause 573,341,216]
582. ~tall(fred) | old(fred) <- (31) [resolution 347,373]
583. creative(fred) | happy(fred) <- (31) [resolution 347,238]
586. old(fred) <- (12, 31) [subsumption resolution 582,221]
587. 23 | ~12 | ~31 [avatar split clause 586,345,220,291]
589. 46 <=> happy(fred) [avatar definition]
591. happy(fred) <- (46) [avatar component clause 589]
593. 47 <=> creative(fred) [avatar definition]
595. creative(fred) <- (47) [avatar component clause 593]
596. 46 | 47 | ~31 [avatar split clause 583,345,593,589]
604. ~tall(fred) | ~generous(fred) <- (46) [resolution 591,81]
608. ~generous(fred) <- (12, 46) [subsumption resolution 604,221]
609. $false <- (12, 31, 46) [subsumption resolution 608,347]
610. ~12 | ~31 | ~46 [avatar contradiction clause 609]
631. patient(fred) | funny(fred) <- (47) [resolution 595,263]
635. patient(fred) <- (~24, 47) [subsumption resolution 631,297]
636. 11 | 24 | ~47 [avatar split clause 635,593,295,216]
637. ~39 | ~14 | ~35 [avatar split clause 404,368,228,436]
638. 39 [avatar split clause 551,436]
652. creative(susan) | happy(susan) <- (14) [resolution 229,238]
655. happy(susan) <- (14, ~27) [subsumption resolution 652,311]
656. $false <- (14, ~27, ~35) [subsumption resolution 655,369]
657. ~14 | 27 | 35 [avatar contradiction clause 656]
658. $false [avatar sat refutation 232,233,234,235,298,314,348,577,587,596,610,636,637,638,657]
% SZS output end Proof for 1349827807326659192149103
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 mary is either generous or not generous then someone is either curious or not brave and vice versa.
Everyone who is not tall is both rich and quiet.
Everyone who is happy is both old and creative and vice versa.
Everyone who is curious is strong or not quiet and vice versa.
Everyone who is strong is wise or funny.
Everyone who is both kind and not kind is either not old or not happy.
Everyone who is both happy and quiet is not curious or quiet.
Everyone who is both wise and patient is either funny or generous.
Everyone who is both not calm and not funny is both not wise and creative.
If alice is old or brave then lucy is both creative and old.
Everyone who is not rich or generous is both not calm and not tall.
If john is quiet or not humble then alice is both kind and not quiet and vice versa.
Everyone who is tall or not kind is either humble or brave and vice versa.
If mary is either not happy or rich then someone is old.
If someone is both rich and not happy then susan is either kind or humble.
Everyone who is either not quiet or not curious is both brave and wise.
Someone is not wise or not rich.
Someone is not strong or funny.
John is calm or brave.
Someone is both not generous and old. | Alice is not wise. | contradiction | (((generous(mary)<~>~generous(mary)))<=>(?[X]:((curious(X)<~>~brave(X)))))&
(![X]:(~tall(X)=>(rich(X)&quiet(X))))&
(![X]:(happy(X)<=>(old(X)&creative(X))))&
(![X]:(curious(X)<=>(strong(X)|~quiet(X))))&
(![X]:(strong(X)=>(wise(X)|funny(X))))&
(![X]:((kind(X)&~kind(X))=>(~old(X)<~>~happy(X))))&
(![X]:((happy(X)&quiet(X))=>(~curious(X)|quiet(X))))&
(![X]:((wise(X)&patient(X))=>(funny(X)<~>generous(X))))&
(![X]:((~calm(X)&~funny(X))=>(~wise(X)&creative(X))))&
(((old(alice)|brave(alice)))=>((creative(lucy)&old(lucy))))&
(![X]:((~rich(X)|generous(X))=>(~calm(X)&~tall(X))))&
(((quiet(john)|~humble(john)))<=>((kind(alice)&~quiet(alice))))&
(![X]:((tall(X)|~kind(X))<=>(humble(X)<~>brave(X))))&
(((~happy(mary)<~>rich(mary)))=>(?[X]:(old(X))))&
((?[X]:((rich(X)&~happy(X))))=>((kind(susan)<~>humble(susan))))&
(![X]:((~quiet(X)<~>~curious(X))=>(brave(X)&wise(X))))&
(?[X]:((~wise(X)|~rich(X))))&
(?[X]:((~strong(X)|funny(X))))&
((calm(john)|brave(john)))&
(?[X]:((~generous(X)&old(X)))) | ~wise(alice) | [
"p1",
"p3",
"p11",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 339341671268329958514967
% SZS output start Proof for 339341671268329958514967
2. ! [X0] : (~tall(X0) => (quiet(X0) & rich(X0))) [input p1]
4. ! [X0] : (curious(X0) <=> (~quiet(X0) | strong(X0))) [input p3]
12. (~humble(john) | quiet(john)) <=> (~quiet(alice) & kind(alice)) [input p11]
13. ! [X0] : ((~kind(X0) | tall(X0)) <=> (humble(X0) <~> brave(X0))) [input p12]
16. ! [X0] : ((~quiet(X0) <~> ~curious(X0)) => (wise(X0) & brave(X0))) [input p15]
21. ~wise(alice) [input hypothesis]
26. ! [X0] : ((quiet(X0) & rich(X0)) | tall(X0)) [ennf transformation 2]
35. ! [X0] : ((wise(X0) & brave(X0)) | (~quiet(X0) <=> ~curious(X0))) [ennf transformation 16]
42. ! [X0] : ((curious(X0) | (quiet(X0) & ~strong(X0))) & ((~quiet(X0) | strong(X0)) | ~curious(X0))) [nnf transformation 4]
43. ! [X0] : ((curious(X0) | (quiet(X0) & ~strong(X0))) & (~quiet(X0) | strong(X0) | ~curious(X0))) [flattening 42]
45. ((~humble(john) | quiet(john)) | (quiet(alice) | ~kind(alice))) & ((~quiet(alice) & kind(alice)) | (humble(john) & ~quiet(john))) [nnf transformation 12]
46. (~humble(john) | quiet(john) | quiet(alice) | ~kind(alice)) & ((~quiet(alice) & kind(alice)) | (humble(john) & ~quiet(john))) [flattening 45]
47. ! [X0] : (((~kind(X0) | tall(X0)) | ((humble(X0) | ~brave(X0)) & (brave(X0) | ~humble(X0)))) & (((~brave(X0) | ~humble(X0)) & (brave(X0) | humble(X0))) | (kind(X0) & ~tall(X0)))) [nnf transformation 13]
48. ! [X0] : ((~kind(X0) | tall(X0) | ((humble(X0) | ~brave(X0)) & (brave(X0) | ~humble(X0)))) & (((~brave(X0) | ~humble(X0)) & (brave(X0) | humble(X0))) | (kind(X0) & ~tall(X0)))) [flattening 47]
53. ! [X0] : ((wise(X0) & brave(X0)) | ((~quiet(X0) | curious(X0)) & (~curious(X0) | quiet(X0)))) [nnf transformation 35]
67. quiet(X0) | tall(X0) [cnf transformation 26]
73. quiet(X0) | curious(X0) [cnf transformation 43]
87. ~quiet(alice) | ~quiet(john) [cnf transformation 46]
88. ~quiet(alice) | humble(john) [cnf transformation 46]
92. ~humble(X0) | ~brave(X0) | ~tall(X0) [cnf transformation 48]
100. brave(X0) | ~curious(X0) | quiet(X0) [cnf transformation 53]
102. wise(X0) | ~curious(X0) | quiet(X0) [cnf transformation 53]
108. ~wise(alice) [cnf transformation 21]
155. 9 <=> quiet(alice) [avatar definition]
159. 10 <=> quiet(john) [avatar definition]
160. ~quiet(john) <- (~10) [avatar component clause 159]
163. 11 <=> humble(john) [avatar definition]
164. humble(john) <- (11) [avatar component clause 163]
167. 11 | ~9 [avatar split clause 88,155,163]
168. ~10 | ~9 [avatar split clause 87,155,159]
197. wise(X0) | quiet(X0) [subsumption resolution 102,73]
199. quiet(X0) | brave(X0) [subsumption resolution 100,73]
206. 18 <=> brave(john) [avatar definition]
208. brave(john) <- (18) [avatar component clause 206]
213. tall(john) <- (~10) [resolution 67,160]
227. quiet(alice) [resolution 197,108]
231. 9 [avatar split clause 227,155]
236. brave(john) <- (~10) [resolution 199,160]
237. 18 | 10 [avatar split clause 236,159,206]
252. ~brave(john) | ~tall(john) <- (11) [resolution 92,164]
254. ~tall(john) <- (11, 18) [subsumption resolution 252,208]
255. $false <- (~10, 11, 18) [subsumption resolution 254,213]
256. 10 | ~11 | ~18 [avatar contradiction clause 255]
257. $false [avatar sat refutation 167,168,231,237,256]
% SZS output end Proof for 339341671268329958514967
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient is either curious or not humble and vice versa.
Everyone who is either generous or quiet is calm.
Everyone who is patient or tall is old or not quiet and vice versa.
Everyone who is calm is not strong or funny.
Everyone who is both calm and not brave is not creative and vice versa.
Everyone who is both wise and not kind is wise.
Everyone who is both not generous and not strong is not patient or calm and vice versa.
Everyone who is either not patient or not calm is either tall or brave and vice versa.
Everyone who is either funny or creative is strong and vice versa.
Everyone who is not tall or not happy is not strong.
Everyone who is not happy or wise is not kind and vice versa.
Everyone who is not calm or tall is not calm and vice versa.
If someone is rich then alice is both not patient and funny.
Everyone who is both curious and strong is both old and not rich.
Everyone who is either curious or creative is both not funny and happy and vice versa.
Everyone who is both not brave and strong is old and vice versa.
Someone is both not happy and not quiet.
Someone is either not rich or brave.
Lucy is either old or not wise.
Lucy is curious or old.
Someone is strong or kind.
Someone is both not old and not funny.
Someone is either not brave or not happy. | Lucy is brave. | neutral | (![X]:(~patient(X)<=>(curious(X)<~>~humble(X))))&
(![X]:((generous(X)<~>quiet(X))=>calm(X)))&
(![X]:((patient(X)|tall(X))<=>(old(X)|~quiet(X))))&
(![X]:(calm(X)=>(~strong(X)|funny(X))))&
(![X]:((calm(X)&~brave(X))<=>~creative(X)))&
(![X]:((wise(X)&~kind(X))=>wise(X)))&
(![X]:((~generous(X)&~strong(X))<=>(~patient(X)|calm(X))))&
(![X]:((~patient(X)<~>~calm(X))<=>(tall(X)<~>brave(X))))&
(![X]:((funny(X)<~>creative(X))<=>strong(X)))&
(![X]:((~tall(X)|~happy(X))=>~strong(X)))&
(![X]:((~happy(X)|wise(X))<=>~kind(X)))&
(![X]:((~calm(X)|tall(X))<=>~calm(X)))&
((?[X]:(rich(X)))=>((~patient(alice)&funny(alice))))&
(![X]:((curious(X)&strong(X))=>(old(X)&~rich(X))))&
(![X]:((curious(X)<~>creative(X))<=>(~funny(X)&happy(X))))&
(![X]:((~brave(X)&strong(X))<=>old(X)))&
(?[X]:((~happy(X)&~quiet(X))))&
(?[X]:((~rich(X)<~>brave(X))))&
((old(lucy)<~>~wise(lucy)))&
((curious(lucy)|old(lucy)))&
(?[X]:((strong(X)|kind(X))))&
(?[X]:((~old(X)&~funny(X))))&
(?[X]:((~brave(X)<~>~happy(X)))) | brave(lucy) | [] | null | 0 |
If someone is not calm or calm then lucy is not quiet. Everyone who is both quiet and not happy is not happy and vice versa. Everyone who is creative is not wise or tall and vice versa. If john is not patient then susan is either not curious or creative and vice versa. If someone is both not funny and not generous then paul is strong or brave and vice versa. If someone is humble then someone is both kind and not funny and vice versa. Everyone who is not happy or strong is either not strong or not patient. Everyone who is not funny is either not patient or strong. Everyone who is not humble is calm or wise. Everyone who is brave is not creative. Everyone who is not happy is not strong or not calm and vice versa. Everyone who is both brave and not patient is wise or brave. If someone is not humble then someone is rich or generous. Everyone who is generous is not quiet. If alice is tall then fred is not quiet and vice versa. Someone is both not happy and tall. Fred is quiet. Someone is rich or not old. Paul is wise. Someone is either not funny or generous. Paul is creative. Fred is not kind. Alice is brave or not funny. | Alice is not creative. | entailment | ((?[X]:((~calm(X)|calm(X))))=>(~quiet(lucy)))&
(![X]:((quiet(X)&~happy(X))<=>~happy(X)))&
(![X]:(creative(X)<=>(~wise(X)|tall(X))))&
((~patient(john))<=>((~curious(susan)<~>creative(susan))))&
((?[X]:((~funny(X)&~generous(X))))<=>((strong(paul)|brave(paul))))&
((?[X]:(humble(X)))<=>(?[X]:((kind(X)&~funny(X)))))&
(![X]:((~happy(X)|strong(X))=>(~strong(X)<~>~patient(X))))&
(![X]:(~funny(X)=>(~patient(X)<~>strong(X))))&
(![X]:(~humble(X)=>(calm(X)|wise(X))))&
(![X]:(brave(X)=>~creative(X)))&
(![X]:(~happy(X)<=>(~strong(X)|~calm(X))))&
(![X]:((brave(X)&~patient(X))=>(wise(X)|brave(X))))&
((?[X]:(~humble(X)))=>(?[X]:((rich(X)|generous(X)))))&
(![X]:(generous(X)=>~quiet(X)))&
((tall(alice))<=>(~quiet(fred)))&
(?[X]:((~happy(X)&tall(X))))&
(quiet(fred))&
(?[X]:((rich(X)|~old(X))))&
(wise(paul))&
(?[X]:((~funny(X)<~>generous(X))))&
(creative(paul))&
(~kind(fred))&
((brave(alice)|~funny(alice))) | ~creative(alice) | [
"p1",
"p4",
"p6",
"p7",
"p9",
"p10",
"p13",
"p20",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 7393495170033566247224547
% SZS output start Proof for 7393495170033566247224547
2. ! [X0] : ((~happy(X0) & quiet(X0)) <=> ~happy(X0)) [input p1]
5. ? [X0] : (~generous(X0) & ~funny(X0)) <=> (brave(paul) | strong(paul)) [input p4]
7. ! [X0] : ((strong(X0) | ~happy(X0)) => (~strong(X0) <~> ~patient(X0))) [input p6]
8. ! [X0] : (~funny(X0) => (~patient(X0) <~> strong(X0))) [input p7]
10. ! [X0] : (brave(X0) => ~creative(X0)) [input p9]
11. ! [X0] : (~happy(X0) <=> (~calm(X0) | ~strong(X0))) [input p10]
14. ! [X0] : (generous(X0) => ~quiet(X0)) [input p13]
21. creative(paul) [input p20]
23. ~funny(alice) | brave(alice) [input p22]
24. creative(alice) [input hypothesis]
30. ! [X0] : ((~strong(X0) <~> ~patient(X0)) | (~strong(X0) & happy(X0))) [ennf transformation 7]
31. ! [X0] : ((~patient(X0) <~> strong(X0)) | funny(X0)) [ennf transformation 8]
34. ! [X0] : (~creative(X0) | ~brave(X0)) [ennf transformation 10]
37. ! [X0] : (~quiet(X0) | ~generous(X0)) [ennf transformation 14]
38. ! [X0] : (((~happy(X0) & quiet(X0)) | happy(X0)) & (~happy(X0) | (happy(X0) | ~quiet(X0)))) [nnf transformation 2]
39. ! [X0] : (((~happy(X0) & quiet(X0)) | happy(X0)) & (~happy(X0) | happy(X0) | ~quiet(X0))) [flattening 38]
43. (? [X0] : (~generous(X0) & ~funny(X0)) | (~brave(paul) & ~strong(paul))) & ((brave(paul) | strong(paul)) | ! [X0] : (generous(X0) | funny(X0))) [nnf transformation 5]
44. (? [X0] : (~generous(X0) & ~funny(X0)) | (~brave(paul) & ~strong(paul))) & (brave(paul) | strong(paul) | ! [X0] : (generous(X0) | funny(X0))) [flattening 43]
45. (? [X0] : (~generous(X0) & ~funny(X0)) | (~brave(paul) & ~strong(paul))) & (brave(paul) | strong(paul) | ! [X1] : (generous(X1) | funny(X1))) [rectify 44]
46. ? [X0] : (~generous(X0) & ~funny(X0)) => (~generous(sK0) & ~funny(sK0)) [choice axiom]
47. ((~generous(sK0) & ~funny(sK0)) | (~brave(paul) & ~strong(paul))) & (brave(paul) | strong(paul) | ! [X1] : (generous(X1) | funny(X1))) [skolemisation 45,46]
53. ! [X0] : (((patient(X0) | strong(X0)) & (~patient(X0) | ~strong(X0))) | (~strong(X0) & happy(X0))) [nnf transformation 30]
54. ! [X0] : (((~strong(X0) | patient(X0)) & (strong(X0) | ~patient(X0))) | funny(X0)) [nnf transformation 31]
55. ! [X0] : ((~happy(X0) | (calm(X0) & strong(X0))) & ((~calm(X0) | ~strong(X0)) | happy(X0))) [nnf transformation 11]
56. ! [X0] : ((~happy(X0) | (calm(X0) & strong(X0))) & (~calm(X0) | ~strong(X0) | happy(X0))) [flattening 55]
66. happy(X0) | quiet(X0) [cnf transformation 39]
75. brave(paul) | strong(paul) | generous(X1) | funny(X1) [cnf transformation 47]
76. ~funny(sK0) | ~strong(paul) [cnf transformation 47]
84. ~patient(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 53]
85. strong(X0) | patient(X0) | happy(X0) [cnf transformation 53]
87. strong(X0) | ~patient(X0) | funny(X0) [cnf transformation 54]
88. ~strong(X0) | patient(X0) | funny(X0) [cnf transformation 54]
90. ~brave(X0) | ~creative(X0) [cnf transformation 34]
92. ~happy(X0) | strong(X0) [cnf transformation 56]
95. ~generous(X0) | ~quiet(X0) [cnf transformation 37]
104. creative(paul) [cnf transformation 21]
106. ~funny(alice) | brave(alice) [cnf transformation 23]
107. creative(alice) [cnf transformation 24]
108. ~strong(X0) | ~patient(X0) [duplicate literal removal 84]
138. 7 <=> brave(paul) [avatar definition]
139. brave(paul) <- (7) [avatar component clause 138]
147. 9 <=> strong(paul) [avatar definition]
152. 10 <=> funny(sK0) [avatar definition]
154. ~funny(sK0) <- (~10) [avatar component clause 152]
156. ~9 | ~10 [avatar split clause 76,152,147]
158. 11 <=> ! [X1] : (generous(X1) | funny(X1)) [avatar definition]
159. generous(X1) | funny(X1) <- (11) [avatar component clause 158]
160. 11 | 9 | 7 [avatar split clause 75,138,147,158]
182. ~strong(X0) | funny(X0) [subsumption resolution 88,108]
183. ~patient(X0) | funny(X0) [subsumption resolution 87,108]
206. 21 <=> brave(alice) [avatar definition]
208. brave(alice) <- (21) [avatar component clause 206]
210. 22 <=> funny(alice) [avatar definition]
212. ~funny(alice) <- (~22) [avatar component clause 210]
213. 21 | ~22 [avatar split clause 106,210,206]
216. ~creative(paul) <- (7) [resolution 90,139]
217. $false <- (7) [subsumption resolution 216,104]
218. ~7 [avatar contradiction clause 217]
219. strong(X0) | quiet(X0) [resolution 92,66]
223. funny(X0) | quiet(X0) [resolution 219,182]
229. patient(X0) | happy(X0) | funny(X0) [resolution 85,182]
231. funny(X0) | happy(X0) [subsumption resolution 229,183]
247. happy(sK0) <- (~10) [resolution 231,154]
251. strong(sK0) <- (~10) [resolution 247,92]
272. funny(sK0) <- (~10) [resolution 251,182]
274. $false <- (~10) [subsumption resolution 272,154]
275. 10 [avatar contradiction clause 274]
285. funny(X0) | ~quiet(X0) <- (11) [resolution 159,95]
288. funny(X0) <- (11) [subsumption resolution 285,223]
299. $false <- (11, ~22) [resolution 288,212]
300. ~11 | 22 [avatar contradiction clause 299]
301. ~creative(alice) <- (21) [resolution 208,90]
302. $false <- (21) [subsumption resolution 301,107]
303. ~21 [avatar contradiction clause 302]
304. $false [avatar sat refutation 156,160,213,218,275,300,303]
% SZS output end Proof for 7393495170033566247224547
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm and curious is wise or happy. If someone is both not calm and quiet then someone is not brave or not tall and vice versa. Everyone who is both not generous and kind is either not kind or not funny and vice versa. Everyone who is wise or quiet is both not curious and brave and vice versa. If someone is either creative or old then someone is both calm and kind. Everyone who is both not curious and not old is brave or rich. Everyone who is either not creative or funny is either not curious or not rich. Everyone who is either not generous or generous is either not wise or happy. Everyone who is both brave and calm is not quiet and vice versa. If someone is either generous or not old then someone is both not curious and happy and vice versa. Everyone who is humble is either not quiet or not calm. Everyone who is not kind or not old is not patient. Everyone who is tall or not calm is both not humble and old and vice versa. If john is humble then someone is either not humble or not calm and vice versa. If someone is not generous then someone is either not old or not calm and vice versa. If someone is funny or not patient then john is either wise or happy and vice versa. Alice is either tall or rich. Fred is either old or not creative. Someone is rich. Mary is not humble. John is funny or tall. | Alice is kind. | entailment | (![X]:((calm(X)&curious(X))=>(wise(X)|happy(X))))&
((?[X]:((~calm(X)&quiet(X))))<=>(?[X]:((~brave(X)|~tall(X)))))&
(![X]:((~generous(X)&kind(X))<=>(~kind(X)<~>~funny(X))))&
(![X]:((wise(X)|quiet(X))<=>(~curious(X)&brave(X))))&
((?[X]:((creative(X)<~>old(X))))=>(?[X]:((calm(X)&kind(X)))))&
(![X]:((~curious(X)&~old(X))=>(brave(X)|rich(X))))&
(![X]:((~creative(X)<~>funny(X))=>(~curious(X)<~>~rich(X))))&
(![X]:((~generous(X)<~>generous(X))=>(~wise(X)<~>happy(X))))&
(![X]:((brave(X)&calm(X))<=>~quiet(X)))&
((?[X]:((generous(X)<~>~old(X))))<=>(?[X]:((~curious(X)&happy(X)))))&
(![X]:(humble(X)=>(~quiet(X)<~>~calm(X))))&
(![X]:((~kind(X)|~old(X))=>~patient(X)))&
(![X]:((tall(X)|~calm(X))<=>(~humble(X)&old(X))))&
((humble(john))<=>(?[X]:((~humble(X)<~>~calm(X)))))&
((?[X]:(~generous(X)))<=>(?[X]:((~old(X)<~>~calm(X)))))&
((?[X]:((funny(X)|~patient(X))))<=>((wise(john)<~>happy(john))))&
((tall(alice)<~>rich(alice)))&
((old(fred)<~>~creative(fred)))&
(?[X]:(rich(X)))&
(~humble(mary))&
((funny(john)|tall(john))) | kind(alice) | [
"p7",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4541065467885543190348223
% SZS output start Proof for 4541065467885543190348223
8. ! [X0] : ((~generous(X0) <~> generous(X0)) => (~wise(X0) <~> happy(X0))) [input p7]
12. ! [X0] : ((~old(X0) | ~kind(X0)) => ~patient(X0)) [input p11]
16. ? [X0] : (~patient(X0) | funny(X0)) <=> (wise(john) <~> happy(john)) [input p15]
22. ~kind(alice) [input hypothesis]
33. ! [X0] : ((~wise(X0) <~> happy(X0)) | (~generous(X0) <=> generous(X0))) [ennf transformation 8]
35. ! [X0] : (~patient(X0) | (old(X0) & kind(X0))) [ennf transformation 12]
50. ! [X0] : (((~happy(X0) | wise(X0)) & (happy(X0) | ~wise(X0))) | ((~generous(X0) | ~generous(X0)) & (generous(X0) | generous(X0)))) [nnf transformation 33]
70. (? [X0] : (~patient(X0) | funny(X0)) | ((wise(john) | ~happy(john)) & (happy(john) | ~wise(john)))) & (((~happy(john) | ~wise(john)) & (happy(john) | wise(john))) | ! [X0] : (patient(X0) & ~funny(X0))) [nnf transformation 16]
71. (? [X0] : (~patient(X0) | funny(X0)) | ((wise(john) | ~happy(john)) & (happy(john) | ~wise(john)))) & (((~happy(john) | ~wise(john)) & (happy(john) | wise(john))) | ! [X1] : (patient(X1) & ~funny(X1))) [rectify 70]
72. ? [X0] : (~patient(X0) | funny(X0)) => (~patient(sK8) | funny(sK8)) [choice axiom]
73. ((~patient(sK8) | funny(sK8)) | ((wise(john) | ~happy(john)) & (happy(john) | ~wise(john)))) & (((~happy(john) | ~wise(john)) & (happy(john) | wise(john))) | ! [X1] : (patient(X1) & ~funny(X1))) [skolemisation 71,72]
104. happy(X0) | ~wise(X0) | generous(X0) | generous(X0) [cnf transformation 50]
105. happy(X0) | ~wise(X0) | ~generous(X0) | ~generous(X0) [cnf transformation 50]
106. ~happy(X0) | wise(X0) | generous(X0) | generous(X0) [cnf transformation 50]
107. ~happy(X0) | wise(X0) | ~generous(X0) | ~generous(X0) [cnf transformation 50]
119. ~patient(X0) | kind(X0) [cnf transformation 35]
135. happy(john) | wise(john) | patient(X1) [cnf transformation 73]
137. ~happy(john) | ~wise(john) | patient(X1) [cnf transformation 73]
147. ~kind(alice) [cnf transformation 22]
148. happy(X0) | ~wise(X0) | generous(X0) [duplicate literal removal 104]
149. happy(X0) | ~wise(X0) | ~generous(X0) [duplicate literal removal 105]
150. ~happy(X0) | wise(X0) | generous(X0) [duplicate literal removal 106]
151. ~happy(X0) | wise(X0) | ~generous(X0) [duplicate literal removal 107]
203. ~happy(X0) | wise(X0) [subsumption resolution 150,151]
204. happy(X0) | ~wise(X0) [subsumption resolution 148,149]
285. ~wise(john) | patient(X1) [subsumption resolution 137,204]
287. 29 <=> ! [X1] : patient(X1) [avatar definition]
288. patient(X1) <- (29) [avatar component clause 287]
290. 30 <=> wise(john) [avatar definition]
293. 29 | ~30 [avatar split clause 285,290,287]
299. wise(john) | patient(X1) [subsumption resolution 135,203]
300. 29 | 30 [avatar split clause 299,290,287]
338. kind(X0) <- (29) [resolution 119,288]
345. $false <- (29) [resolution 338,147]
346. ~29 [avatar contradiction clause 345]
347. $false [avatar sat refutation 293,300,346]
% SZS output end Proof for 4541065467885543190348223
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
If susan is both generous and not kind then someone is happy or not calm. Everyone who is creative is both not creative and quiet and vice versa. If someone is both not patient and not brave then someone is both not quiet and wise. Everyone who is not quiet or not old is either patient or not curious and vice versa. Everyone who is not generous or kind is not wise or patient and vice versa. If john is both funny and not quiet then someone is old or wise. If someone is not patient or kind then mary is both funny and humble and vice versa. If john is both rich and not brave then fred is both patient and wise and vice versa. If someone is old or kind then someone is both wise and curious. If someone is brave or calm then someone is quiet. Everyone who is either not curious or not happy is not brave or funny. Everyone who is generous or patient is both strong and tall and vice versa. Everyone who is both not strong and not curious is both calm and strong and vice versa. Everyone who is either tall or not kind is strong or not quiet. Everyone who is both humble and not kind is funny or quiet. Everyone who is either tall or not happy is both strong and not patient. Someone is both curious and not old. Fred is either generous or brave. Fred is either quiet or not brave. Someone is not happy. Someone is either not kind or happy. Someone is not creative. Someone is creative or not old. Alice is both old and kind. | Fred is not generous. | contradiction | (((generous(susan)&~kind(susan)))=>(?[X]:((happy(X)|~calm(X)))))&
(![X]:(creative(X)<=>(~creative(X)&quiet(X))))&
((?[X]:((~patient(X)&~brave(X))))=>(?[X]:((~quiet(X)&wise(X)))))&
(![X]:((~quiet(X)|~old(X))<=>(patient(X)<~>~curious(X))))&
(![X]:((~generous(X)|kind(X))<=>(~wise(X)|patient(X))))&
(((funny(john)&~quiet(john)))=>(?[X]:((old(X)|wise(X)))))&
((?[X]:((~patient(X)|kind(X))))<=>((funny(mary)&humble(mary))))&
(((rich(john)&~brave(john)))<=>((patient(fred)&wise(fred))))&
((?[X]:((old(X)|kind(X))))=>(?[X]:((wise(X)&curious(X)))))&
((?[X]:((brave(X)|calm(X))))=>(?[X]:(quiet(X))))&
(![X]:((~curious(X)<~>~happy(X))=>(~brave(X)|funny(X))))&
(![X]:((generous(X)|patient(X))<=>(strong(X)&tall(X))))&
(![X]:((~strong(X)&~curious(X))<=>(calm(X)&strong(X))))&
(![X]:((tall(X)<~>~kind(X))=>(strong(X)|~quiet(X))))&
(![X]:((humble(X)&~kind(X))=>(funny(X)|quiet(X))))&
(![X]:((tall(X)<~>~happy(X))=>(strong(X)&~patient(X))))&
(?[X]:((curious(X)&~old(X))))&
((generous(fred)<~>brave(fred)))&
((quiet(fred)<~>~brave(fred)))&
(?[X]:(~happy(X)))&
(?[X]:((~kind(X)<~>happy(X))))&
(?[X]:(~creative(X)))&
(?[X]:((creative(X)|~old(X))))&
((old(alice)&kind(alice))) | ~generous(fred) | [
"p1",
"p17",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 5088118365230670778970010
% SZS output start Proof for 5088118365230670778970010
2. ! [X0] : (creative(X0) <=> (quiet(X0) & ~creative(X0))) [input p1]
18. generous(fred) <~> brave(fred) [input p17]
19. quiet(fred) <~> ~brave(fred) [input p18]
25. ~generous(fred) [input hypothesis]
45. ! [X0] : ((creative(X0) | (~quiet(X0) | creative(X0))) & ((quiet(X0) & ~creative(X0)) | ~creative(X0))) [nnf transformation 2]
46. ! [X0] : ((creative(X0) | ~quiet(X0) | creative(X0)) & ((quiet(X0) & ~creative(X0)) | ~creative(X0))) [flattening 45]
78. (~brave(fred) | ~generous(fred)) & (brave(fred) | generous(fred)) [nnf transformation 18]
79. (brave(fred) | ~quiet(fred)) & (~brave(fred) | quiet(fred)) [nnf transformation 19]
90. ~creative(X0) | ~creative(X0) [cnf transformation 46]
92. creative(X0) | ~quiet(X0) | creative(X0) [cnf transformation 46]
141. brave(fred) | generous(fred) [cnf transformation 78]
143. ~brave(fred) | quiet(fred) [cnf transformation 79]
152. ~generous(fred) [cnf transformation 25]
155. ~creative(X0) [duplicate literal removal 90]
156. ~quiet(X0) | creative(X0) [duplicate literal removal 92]
280. 28 <=> generous(fred) [avatar definition]
284. 29 <=> brave(fred) [avatar definition]
288. 28 | 29 [avatar split clause 141,284,280]
290. 30 <=> quiet(fred) [avatar definition]
291. quiet(fred) <- (30) [avatar component clause 290]
294. 30 | ~29 [avatar split clause 143,284,290]
306. ~28 [avatar split clause 152,280]
313. creative(fred) <- (30) [resolution 156,291]
316. $false <- (30) [subsumption resolution 313,155]
317. ~30 [avatar contradiction clause 316]
318. $false [avatar sat refutation 288,294,306,317]
% SZS output end Proof for 5088118365230670778970010
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not brave then mary is either tall or kind and vice versa.
Everyone who is not old is kind or old and vice versa.
Everyone who is quiet or happy is either patient or old and vice versa.
If fred is either tall or humble then susan is kind or brave and vice versa.
Everyone who is both not rich and quiet is either strong or not curious and vice versa.
If lucy is funny then paul is tall.
If someone is generous then lucy is both not generous and brave.
Everyone who is either old or kind is happy and vice versa.
Everyone who is either curious or not rich is either brave or not wise and vice versa.
If fred is not humble or not patient then someone is not curious or not tall.
Everyone who is both quiet and tall is either calm or quiet and vice versa.
Everyone who is either funny or strong is either not patient or humble.
If someone is not curious then lucy is both quiet and wise and vice versa.
If someone is both not rich and not strong then someone is either happy or not kind.
Everyone who is both happy and not old is not patient or calm.
Everyone who is both not brave and not generous is either not curious or happy.
Susan is not kind or not old.
Someone is both rich and not curious.
Someone is brave.
Someone is creative or generous.
Paul is either funny or not wise. | Fred is tall. | contradiction | ((~brave(mary))<=>((tall(mary)<~>kind(mary))))&
(![X]:(~old(X)<=>(kind(X)|old(X))))&
(![X]:((quiet(X)|happy(X))<=>(patient(X)<~>old(X))))&
(((tall(fred)<~>humble(fred)))<=>((kind(susan)|brave(susan))))&
(![X]:((~rich(X)&quiet(X))<=>(strong(X)<~>~curious(X))))&
((funny(lucy))=>(tall(paul)))&
((?[X]:(generous(X)))=>((~generous(lucy)&brave(lucy))))&
(![X]:((old(X)<~>kind(X))<=>happy(X)))&
(![X]:((curious(X)<~>~rich(X))<=>(brave(X)<~>~wise(X))))&
(((~humble(fred)|~patient(fred)))=>(?[X]:((~curious(X)|~tall(X)))))&
(![X]:((quiet(X)&tall(X))<=>(calm(X)<~>quiet(X))))&
(![X]:((funny(X)<~>strong(X))=>(~patient(X)<~>humble(X))))&
((?[X]:(~curious(X)))<=>((quiet(lucy)&wise(lucy))))&
((?[X]:((~rich(X)&~strong(X))))=>(?[X]:((happy(X)<~>~kind(X)))))&
(![X]:((happy(X)&~old(X))=>(~patient(X)|calm(X))))&
(![X]:((~brave(X)&~generous(X))=>(~curious(X)<~>happy(X))))&
((~kind(susan)|~old(susan)))&
(?[X]:((rich(X)&~curious(X))))&
(?[X]:(brave(X)))&
(?[X]:((creative(X)|generous(X))))&
((funny(paul)<~>~wise(paul))) | tall(fred) | [
"p1",
"p2",
"p7",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 469332787034285567282752
% SZS output start Proof for 469332787034285567282752
2. ! [X0] : (~old(X0) <=> (old(X0) | kind(X0))) [input p1]
3. ! [X0] : ((happy(X0) | quiet(X0)) <=> (patient(X0) <~> old(X0))) [input p2]
8. ! [X0] : ((old(X0) <~> kind(X0)) <=> happy(X0)) [input p7]
11. ! [X0] : ((tall(X0) & quiet(X0)) <=> (calm(X0) <~> quiet(X0))) [input p10]
15. ! [X0] : ((~old(X0) & happy(X0)) => (calm(X0) | ~patient(X0))) [input p14]
22. tall(fred) [input hypothesis]
30. ! [X0] : ((calm(X0) | ~patient(X0)) | (old(X0) | ~happy(X0))) [ennf transformation 15]
31. ! [X0] : (calm(X0) | ~patient(X0) | old(X0) | ~happy(X0)) [flattening 30]
35. ! [X0] : ((~old(X0) | (~old(X0) & ~kind(X0))) & ((old(X0) | kind(X0)) | old(X0))) [nnf transformation 2]
36. ! [X0] : ((~old(X0) | (~old(X0) & ~kind(X0))) & (old(X0) | kind(X0) | old(X0))) [flattening 35]
37. ! [X0] : (((happy(X0) | quiet(X0)) | ((patient(X0) | ~old(X0)) & (old(X0) | ~patient(X0)))) & (((~old(X0) | ~patient(X0)) & (old(X0) | patient(X0))) | (~happy(X0) & ~quiet(X0)))) [nnf transformation 3]
38. ! [X0] : ((happy(X0) | quiet(X0) | ((patient(X0) | ~old(X0)) & (old(X0) | ~patient(X0)))) & (((~old(X0) | ~patient(X0)) & (old(X0) | patient(X0))) | (~happy(X0) & ~quiet(X0)))) [flattening 37]
43. ! [X0] : ((((~kind(X0) | ~old(X0)) & (kind(X0) | old(X0))) | ~happy(X0)) & (happy(X0) | ((old(X0) | ~kind(X0)) & (kind(X0) | ~old(X0))))) [nnf transformation 8]
47. ! [X0] : (((tall(X0) & quiet(X0)) | ((calm(X0) | ~quiet(X0)) & (quiet(X0) | ~calm(X0)))) & (((~quiet(X0) | ~calm(X0)) & (quiet(X0) | calm(X0))) | (~tall(X0) | ~quiet(X0)))) [nnf transformation 11]
48. ! [X0] : (((tall(X0) & quiet(X0)) | ((calm(X0) | ~quiet(X0)) & (quiet(X0) | ~calm(X0)))) & (((~quiet(X0) | ~calm(X0)) & (quiet(X0) | calm(X0))) | ~tall(X0) | ~quiet(X0))) [flattening 47]
69. old(X0) | kind(X0) | old(X0) [cnf transformation 36]
71. ~old(X0) | ~old(X0) [cnf transformation 36]
73. old(X0) | patient(X0) | ~happy(X0) [cnf transformation 38]
94. happy(X0) | old(X0) | ~kind(X0) [cnf transformation 43]
108. ~quiet(X0) | ~calm(X0) | ~tall(X0) | ~quiet(X0) [cnf transformation 48]
109. quiet(X0) | quiet(X0) | ~calm(X0) [cnf transformation 48]
122. calm(X0) | ~patient(X0) | old(X0) | ~happy(X0) [cnf transformation 31]
131. tall(fred) [cnf transformation 22]
132. ~quiet(X0) | ~calm(X0) | ~tall(X0) [duplicate literal removal 108]
133. ~calm(X0) | quiet(X0) [duplicate literal removal 109]
134. old(X0) | kind(X0) [duplicate literal removal 69]
135. ~old(X0) [duplicate literal removal 71]
152. kind(X0) [subsumption resolution 134,135]
154. ~happy(X0) | patient(X0) [subsumption resolution 73,135]
161. 5 <=> tall(fred) [avatar definition]
162. tall(fred) <- (5) [avatar component clause 161]
196. happy(X0) | ~kind(X0) [subsumption resolution 94,135]
197. happy(X0) [subsumption resolution 196,152]
212. ~calm(X0) | ~tall(X0) [subsumption resolution 132,133]
231. calm(X0) | ~patient(X0) | ~happy(X0) [subsumption resolution 122,135]
232. ~patient(X0) | calm(X0) [subsumption resolution 231,197]
244. 5 [avatar split clause 131,161]
247. patient(X0) [resolution 154,197]
249. calm(X0) [resolution 232,247]
250. ~tall(X0) [resolution 249,212]
253. $false <- (5) [resolution 250,162]
254. ~5 [avatar contradiction clause 253]
256. $false [avatar sat refutation 244,254]
% SZS output end Proof for 469332787034285567282752
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is happy is both not happy and not calm and vice versa. If alice is either not happy or patient then john is old. If susan is either tall or creative then someone is curious. Everyone who is rich is calm and vice versa. If someone is not wise then fred is either creative or not brave. Everyone who is either funny or not wise is calm or funny. If someone is not strong then someone is either not wise or creative and vice versa. If lucy is not rich or humble then someone is both not patient and calm. If someone is not humble or not calm then someone is not rich or kind. Everyone who is both creative and not happy is not quiet and vice versa. If someone is not old then paul is not wise. If someone is either not brave or creative then alice is either not humble or rich and vice versa. Everyone who is wise or not humble is happy and vice versa. Everyone who is not curious is either rich or humble and vice versa. If fred is either patient or curious then someone is humble and vice versa. If alice is curious or generous then someone is either not rich or humble and vice versa. Someone is both brave and funny. Someone is either not creative or not rich. Someone is either not quiet or not generous. Someone is not quiet or not patient. Someone is not brave. Fred is both generous and brave. | Fred is happy. | contradiction | (![X]:(happy(X)<=>(~happy(X)&~calm(X))))&
(((~happy(alice)<~>patient(alice)))=>(old(john)))&
(((tall(susan)<~>creative(susan)))=>(?[X]:(curious(X))))&
(![X]:(rich(X)<=>calm(X)))&
((?[X]:(~wise(X)))=>((creative(fred)<~>~brave(fred))))&
(![X]:((funny(X)<~>~wise(X))=>(calm(X)|funny(X))))&
((?[X]:(~strong(X)))<=>(?[X]:((~wise(X)<~>creative(X)))))&
(((~rich(lucy)|humble(lucy)))=>(?[X]:((~patient(X)&calm(X)))))&
((?[X]:((~humble(X)|~calm(X))))=>(?[X]:((~rich(X)|kind(X)))))&
(![X]:((creative(X)&~happy(X))<=>~quiet(X)))&
((?[X]:(~old(X)))=>(~wise(paul)))&
((?[X]:((~brave(X)<~>creative(X))))<=>((~humble(alice)<~>rich(alice))))&
(![X]:((wise(X)|~humble(X))<=>happy(X)))&
(![X]:(~curious(X)<=>(rich(X)<~>humble(X))))&
(((patient(fred)<~>curious(fred)))<=>(?[X]:(humble(X))))&
(((curious(alice)|generous(alice)))<=>(?[X]:((~rich(X)<~>humble(X)))))&
(?[X]:((brave(X)&funny(X))))&
(?[X]:((~creative(X)<~>~rich(X))))&
(?[X]:((~quiet(X)<~>~generous(X))))&
(?[X]:((~quiet(X)|~patient(X))))&
(?[X]:(~brave(X)))&
((generous(fred)&brave(fred))) | happy(fred) | [
"p0",
"hypothesis"
] | % SZS status Unsatisfiable for 475962281096633023921661
% SZS output start Proof for 475962281096633023921661
1. ! [X0] : (happy(X0) <=> (~calm(X0) & ~happy(X0))) [input p0]
23. happy(fred) [input hypothesis]
34. ! [X0] : ((happy(X0) | (calm(X0) | happy(X0))) & ((~calm(X0) & ~happy(X0)) | ~happy(X0))) [nnf transformation 1]
35. ! [X0] : ((happy(X0) | calm(X0) | happy(X0)) & ((~calm(X0) & ~happy(X0)) | ~happy(X0))) [flattening 34]
79. ~happy(X0) | ~happy(X0) [cnf transformation 35]
136. happy(fred) [cnf transformation 23]
138. ~happy(X0) [duplicate literal removal 79]
310. $false [subsumption resolution 136,138]
% SZS output end Proof for 475962281096633023921661
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not old or quiet then someone is either not tall or wise.
Everyone who is both rich and humble is either funny or brave.
Everyone who is not curious or tall is not calm or quiet.
If mary is patient or rich then paul is not strong or rich and vice versa.
Everyone who is both not patient and curious is happy or not creative.
If someone is not calm then someone is tall and vice versa.
Everyone who is not humble or not tall is both humble and not happy and vice versa.
If someone is funny then lucy is both tall and not calm.
If susan is both not quiet and creative then someone is happy or not quiet and vice versa.
If someone is not calm then john is both creative and brave.
Everyone who is quiet or not happy is not humble or not curious.
Everyone who is creative or not old is both not humble and wise.
Everyone who is both not funny and brave is patient or not kind and vice versa.
Mary is either not calm or rich.
Someone is funny or not strong.
Someone is not rich or quiet.
Alice is either brave or not creative.
Someone is either happy or calm. | Alice is not rich. | entailment | ((?[X]:((~old(X)<~>quiet(X))))=>(?[X]:((~tall(X)<~>wise(X)))))&
(![X]:((rich(X)&humble(X))=>(funny(X)<~>brave(X))))&
(![X]:((~curious(X)|tall(X))=>(~calm(X)|quiet(X))))&
(((patient(mary)|rich(mary)))<=>((~strong(paul)|rich(paul))))&
(![X]:((~patient(X)&curious(X))=>(happy(X)|~creative(X))))&
((?[X]:(~calm(X)))<=>(?[X]:(tall(X))))&
(![X]:((~humble(X)|~tall(X))<=>(humble(X)&~happy(X))))&
((?[X]:(funny(X)))=>((tall(lucy)&~calm(lucy))))&
(((~quiet(susan)&creative(susan)))<=>(?[X]:((happy(X)|~quiet(X)))))&
((?[X]:(~calm(X)))=>((creative(john)&brave(john))))&
(![X]:((quiet(X)|~happy(X))=>(~humble(X)|~curious(X))))&
(![X]:((creative(X)|~old(X))=>(~humble(X)&wise(X))))&
(![X]:((~funny(X)&brave(X))<=>(patient(X)|~kind(X))))&
((~calm(mary)<~>rich(mary)))&
(?[X]:((funny(X)|~strong(X))))&
(?[X]:((~rich(X)|quiet(X))))&
((brave(alice)<~>~creative(alice)))&
(?[X]:((happy(X)<~>calm(X)))) | ~rich(alice) | [
"p1",
"p5",
"p6",
"p7",
"p9",
"p11",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 6372369600783344992479046
% SZS output start Proof for 6372369600783344992479046
2. ! [X0] : ((humble(X0) & rich(X0)) => (funny(X0) <~> brave(X0))) [input p1]
6. ? [X0] : ~calm(X0) <=> ? [X0] : tall(X0) [input p5]
7. ! [X0] : ((~tall(X0) | ~humble(X0)) <=> (~happy(X0) & humble(X0))) [input p6]
8. ? [X0] : funny(X0) => (~calm(lucy) & tall(lucy)) [input p7]
10. ? [X0] : ~calm(X0) => (brave(john) & creative(john)) [input p9]
12. ! [X0] : ((~old(X0) | creative(X0)) => (wise(X0) & ~humble(X0))) [input p11]
17. brave(alice) <~> ~creative(alice) [input p16]
19. rich(alice) [input hypothesis]
21. ? [X0] : ~calm(X0) <=> ? [X1] : tall(X1) [rectify 6]
23. ! [X0] : ((funny(X0) <~> brave(X0)) | (~humble(X0) | ~rich(X0))) [ennf transformation 2]
24. ! [X0] : ((funny(X0) <~> brave(X0)) | ~humble(X0) | ~rich(X0)) [flattening 23]
29. (~calm(lucy) & tall(lucy)) | ! [X0] : ~funny(X0) [ennf transformation 8]
30. (brave(john) & creative(john)) | ! [X0] : calm(X0) [ennf transformation 10]
33. ! [X0] : ((wise(X0) & ~humble(X0)) | (old(X0) & ~creative(X0))) [ennf transformation 12]
38. ! [X0] : (((~brave(X0) | ~funny(X0)) & (brave(X0) | funny(X0))) | ~humble(X0) | ~rich(X0)) [nnf transformation 24]
41. (? [X0] : ~calm(X0) | ! [X1] : ~tall(X1)) & (? [X1] : tall(X1) | ! [X0] : calm(X0)) [nnf transformation 21]
42. (? [X0] : ~calm(X0) | ! [X1] : ~tall(X1)) & (? [X2] : tall(X2) | ! [X3] : calm(X3)) [rectify 41]
43. ? [X0] : ~calm(X0) => ~calm(sK1) [choice axiom]
44. ? [X2] : tall(X2) => tall(sK2) [choice axiom]
45. (~calm(sK1) | ! [X1] : ~tall(X1)) & (tall(sK2) | ! [X3] : calm(X3)) [skolemisation 42,44,43]
46. ! [X0] : (((~tall(X0) | ~humble(X0)) | (happy(X0) | ~humble(X0))) & ((~happy(X0) & humble(X0)) | (tall(X0) & humble(X0)))) [nnf transformation 7]
47. ! [X0] : ((~tall(X0) | ~humble(X0) | happy(X0) | ~humble(X0)) & ((~happy(X0) & humble(X0)) | (tall(X0) & humble(X0)))) [flattening 46]
60. (creative(alice) | ~brave(alice)) & (~creative(alice) | brave(alice)) [nnf transformation 17]
68. ~humble(X0) | funny(X0) | brave(X0) | ~rich(X0) [cnf transformation 38]
78. ~calm(sK1) | ~tall(X1) [cnf transformation 45]
79. humble(X0) | humble(X0) [cnf transformation 47]
80. humble(X0) | tall(X0) [cnf transformation 47]
85. ~calm(lucy) | ~funny(X0) [cnf transformation 29]
91. creative(john) | calm(X0) [cnf transformation 30]
95. ~humble(X0) | ~creative(X0) [cnf transformation 33]
109. creative(alice) | ~brave(alice) [cnf transformation 60]
112. rich(alice) [cnf transformation 19]
113. humble(X0) [duplicate literal removal 79]
154. 9 <=> ! [X1] : ~tall(X1) [avatar definition]
155. ~tall(X1) <- (9) [avatar component clause 154]
157. 10 <=> calm(sK1) [avatar definition]
159. ~calm(sK1) <- (~10) [avatar component clause 157]
160. 9 | ~10 [avatar split clause 78,157,154]
162. 11 <=> ! [X3] : calm(X3) [avatar definition]
163. calm(X3) <- (11) [avatar component clause 162]
170. 13 <=> ! [X0] : ~funny(X0) [avatar definition]
171. ~funny(X0) <- (13) [avatar component clause 170]
173. 14 <=> calm(lucy) [avatar definition]
175. ~calm(lucy) <- (~14) [avatar component clause 173]
176. 13 | ~14 [avatar split clause 85,173,170]
215. 23 <=> creative(john) [avatar definition]
217. creative(john) <- (23) [avatar component clause 215]
218. 11 | 23 [avatar split clause 91,215,162]
222. ~creative(X0) [subsumption resolution 95,113]
247. ~brave(alice) [subsumption resolution 109,222]
260. $false <- (~10, 11) [subsumption resolution 159,163]
261. 10 | ~11 [avatar contradiction clause 260]
268. $false <- (23) [subsumption resolution 217,222]
269. ~23 [avatar contradiction clause 268]
285. funny(X0) | brave(X0) | ~rich(X0) | tall(X0) [resolution 68,80]
287. brave(X0) | ~rich(X0) | tall(X0) <- (13) [subsumption resolution 285,171]
288. ~rich(X0) | brave(X0) <- (9, 13) [subsumption resolution 287,155]
289. brave(alice) <- (9, 13) [resolution 288,112]
291. $false <- (9, 13) [subsumption resolution 289,247]
292. ~9 | ~13 [avatar contradiction clause 291]
295. $false <- (11, ~14) [subsumption resolution 175,163]
296. ~11 | 14 [avatar contradiction clause 295]
297. $false [avatar sat refutation 160,176,218,261,269,292,296]
% SZS output end Proof for 6372369600783344992479046
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind or humble.
Everyone who is happy is either curious or not strong and vice versa.
If someone is rich or not happy then someone is either tall or quiet.
Everyone who is humble or not wise is generous and vice versa.
If someone is not generous then someone is both strong and not funny.
Everyone who is either not funny or old is either not funny or not tall.
Everyone who is either not brave or patient is curious and vice versa.
If fred is creative or strong then someone is either happy or kind.
If someone is either not strong or funny then someone is not patient or brave.
Everyone who is not kind is either kind or quiet and vice versa.
If someone is either happy or not happy then someone is calm or quiet and vice versa.
Everyone who is either not humble or not calm is not funny.
Everyone who is either old or calm is not strong.
Everyone who is generous is both funny and calm and vice versa.
Everyone who is both not tall and not humble is both not calm and not creative and vice versa.
Everyone who is happy is either strong or creative and vice versa.
Someone is not quiet or quiet.
Susan is kind or tall.
Someone is either not old or not brave.
Fred is patient or curious.
Someone is either tall or funny.
Paul is either wise or not brave.
Lucy is both not happy and not humble.
Fred is either not brave or not funny. | Lucy is wise. | entailment | (![X]:(funny(X)=>(~kind(X)|humble(X))))&
(![X]:(happy(X)<=>(curious(X)<~>~strong(X))))&
((?[X]:((rich(X)|~happy(X))))=>(?[X]:((tall(X)<~>quiet(X)))))&
(![X]:((humble(X)|~wise(X))<=>generous(X)))&
((?[X]:(~generous(X)))=>(?[X]:((strong(X)&~funny(X)))))&
(![X]:((~funny(X)<~>old(X))=>(~funny(X)<~>~tall(X))))&
(![X]:((~brave(X)<~>patient(X))<=>curious(X)))&
(((creative(fred)|strong(fred)))=>(?[X]:((happy(X)<~>kind(X)))))&
((?[X]:((~strong(X)<~>funny(X))))=>(?[X]:((~patient(X)|brave(X)))))&
(![X]:(~kind(X)<=>(kind(X)<~>quiet(X))))&
((?[X]:((happy(X)<~>~happy(X))))<=>(?[X]:((calm(X)|quiet(X)))))&
(![X]:((~humble(X)<~>~calm(X))=>~funny(X)))&
(![X]:((old(X)<~>calm(X))=>~strong(X)))&
(![X]:(generous(X)<=>(funny(X)&calm(X))))&
(![X]:((~tall(X)&~humble(X))<=>(~calm(X)&~creative(X))))&
(![X]:(happy(X)<=>(strong(X)<~>creative(X))))&
(?[X]:((~quiet(X)|quiet(X))))&
((kind(susan)|tall(susan)))&
(?[X]:((~old(X)<~>~brave(X))))&
((patient(fred)|curious(fred)))&
(?[X]:((tall(X)<~>funny(X))))&
((wise(paul)<~>~brave(paul)))&
((~happy(lucy)&~humble(lucy)))&
((~brave(fred)<~>~funny(fred))) | wise(lucy) | [
"p3",
"p11",
"p13",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 572524469599431251165931
% SZS output start Proof for 572524469599431251165931
4. ! [X0] : ((~wise(X0) | humble(X0)) <=> generous(X0)) [input p3]
12. ! [X0] : ((~humble(X0) <~> ~calm(X0)) => ~funny(X0)) [input p11]
14. ! [X0] : (generous(X0) <=> (calm(X0) & funny(X0))) [input p13]
23. ~humble(lucy) & ~happy(lucy) [input p22]
25. ~wise(lucy) [input hypothesis]
38. ! [X0] : (~funny(X0) | (~humble(X0) <=> ~calm(X0))) [ennf transformation 12]
45. ! [X0] : (((~wise(X0) | humble(X0)) | ~generous(X0)) & (generous(X0) | (wise(X0) & ~humble(X0)))) [nnf transformation 4]
46. ! [X0] : ((~wise(X0) | humble(X0) | ~generous(X0)) & (generous(X0) | (wise(X0) & ~humble(X0)))) [flattening 45]
65. ! [X0] : (~funny(X0) | ((~humble(X0) | calm(X0)) & (~calm(X0) | humble(X0)))) [nnf transformation 38]
67. ! [X0] : ((generous(X0) | (~calm(X0) | ~funny(X0))) & ((calm(X0) & funny(X0)) | ~generous(X0))) [nnf transformation 14]
68. ! [X0] : ((generous(X0) | ~calm(X0) | ~funny(X0)) & ((calm(X0) & funny(X0)) | ~generous(X0))) [flattening 67]
90. generous(X0) | wise(X0) [cnf transformation 46]
118. ~calm(X0) | ~funny(X0) | humble(X0) [cnf transformation 65]
122. ~generous(X0) | funny(X0) [cnf transformation 68]
123. ~generous(X0) | calm(X0) [cnf transformation 68]
143. ~humble(lucy) [cnf transformation 23]
146. ~wise(lucy) [cnf transformation 25]
278. wise(X0) | funny(X0) [resolution 122,90]
280. calm(X0) | wise(X0) [resolution 123,90]
324. ~funny(X0) | humble(X0) | wise(X0) [resolution 118,280]
333. wise(X0) | humble(X0) [subsumption resolution 324,278]
480. humble(lucy) [resolution 333,146]
482. $false [subsumption resolution 480,143]
% SZS output end Proof for 572524469599431251165931
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not calm then someone is both brave and creative and vice versa.
Everyone who is curious or not wise is kind.
Everyone who is either not tall or strong is either not rich or not brave and vice versa.
If someone is not tall or not generous then susan is tall and vice versa.
If alice is not brave then someone is either not funny or not calm.
Everyone who is either not quiet or not humble is not generous or calm and vice versa.
Everyone who is wise or generous is both old and calm.
Everyone who is happy or wise is both brave and not curious and vice versa.
If fred is brave then someone is not brave and vice versa.
Everyone who is either kind or old is not humble or not quiet.
If susan is both generous and creative then someone is not creative.
Everyone who is old is not wise and vice versa.
Everyone who is either kind or not funny is either not quiet or funny.
Everyone who is both not happy and wise is both calm and strong and vice versa.
If someone is not brave then john is not funny and vice versa.
Everyone who is both happy and rich is strong and vice versa.
Someone is funny or tall.
Lucy is either rich or patient.
Lucy is not brave.
Someone is both not curious and quiet.
Someone is brave.
Someone is quiet or not generous.
Someone is not humble. | Susan is not wise. | entailment | ((?[X]:(~calm(X)))<=>(?[X]:((brave(X)&creative(X)))))&
(![X]:((curious(X)|~wise(X))=>kind(X)))&
(![X]:((~tall(X)<~>strong(X))<=>(~rich(X)<~>~brave(X))))&
((?[X]:((~tall(X)|~generous(X))))<=>(tall(susan)))&
((~brave(alice))=>(?[X]:((~funny(X)<~>~calm(X)))))&
(![X]:((~quiet(X)<~>~humble(X))<=>(~generous(X)|calm(X))))&
(![X]:((wise(X)|generous(X))=>(old(X)&calm(X))))&
(![X]:((happy(X)|wise(X))<=>(brave(X)&~curious(X))))&
((brave(fred))<=>(?[X]:(~brave(X))))&
(![X]:((kind(X)<~>old(X))=>(~humble(X)|~quiet(X))))&
(((generous(susan)&creative(susan)))=>(?[X]:(~creative(X))))&
(![X]:(old(X)<=>~wise(X)))&
(![X]:((kind(X)<~>~funny(X))=>(~quiet(X)<~>funny(X))))&
(![X]:((~happy(X)&wise(X))<=>(calm(X)&strong(X))))&
((?[X]:(~brave(X)))<=>(~funny(john)))&
(![X]:((happy(X)&rich(X))<=>strong(X)))&
(?[X]:((funny(X)|tall(X))))&
((rich(lucy)<~>patient(lucy)))&
(~brave(lucy))&
(?[X]:((~curious(X)&quiet(X))))&
(?[X]:(brave(X)))&
(?[X]:((quiet(X)|~generous(X))))&
(?[X]:(~humble(X))) | ~wise(susan) | [
"p6",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 853644731009942170684946
% SZS output start Proof for 853644731009942170684946
7. ! [X0] : ((generous(X0) | wise(X0)) => (calm(X0) & old(X0))) [input p6]
12. ! [X0] : (old(X0) <=> ~wise(X0)) [input p11]
24. wise(susan) [input hypothesis]
28. ! [X0] : ((calm(X0) & old(X0)) | (~generous(X0) & ~wise(X0))) [ennf transformation 7]
58. ! [X0] : ((old(X0) | wise(X0)) & (~wise(X0) | ~old(X0))) [nnf transformation 12]
103. old(X0) | ~wise(X0) [cnf transformation 28]
117. ~wise(X0) | ~old(X0) [cnf transformation 58]
118. old(X0) | wise(X0) [cnf transformation 58]
141. wise(susan) [cnf transformation 24]
226. old(X0) [subsumption resolution 118,103]
227. ~wise(X0) [subsumption resolution 117,226]
267. $false [subsumption resolution 141,227]
% SZS output end Proof for 853644731009942170684946
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not humble is not quiet. If john is funny or not creative then john is both happy and curious and vice versa. If someone is either strong or tall then alice is both not quiet and not old. If lucy is not creative or rich then john is not tall or not kind and vice versa. If susan is either not humble or wise then alice is calm and vice versa. If someone is not strong or tall then alice is either not rich or not creative. Everyone who is both not strong and rich is not quiet or not creative and vice versa. If someone is curious or not calm then someone is not old. If someone is happy then susan is old or tall. If john is quiet then mary is not generous or tall. Everyone who is both humble and tall is brave and vice versa. Everyone who is both not patient and tall is either curious or brave and vice versa. Everyone who is either not curious or not old is either happy or not strong. If john is both not old and patient then fred is generous or not generous and vice versa. Everyone who is either not funny or funny is not kind. If lucy is not curious then someone is not calm and vice versa. Susan is both not funny and not old. Someone is not wise or not funny. Alice is both not patient and not kind. Someone is calm. Someone is not brave. Paul is both not generous and patient. John is not tall. Someone is not funny or brave. | Mary is not kind. | entailment | (![X]:(~humble(X)=>~quiet(X)))&
(((funny(john)|~creative(john)))<=>((happy(john)&curious(john))))&
((?[X]:((strong(X)<~>tall(X))))=>((~quiet(alice)&~old(alice))))&
(((~creative(lucy)|rich(lucy)))<=>((~tall(john)|~kind(john))))&
(((~humble(susan)<~>wise(susan)))<=>(calm(alice)))&
((?[X]:((~strong(X)|tall(X))))=>((~rich(alice)<~>~creative(alice))))&
(![X]:((~strong(X)&rich(X))<=>(~quiet(X)|~creative(X))))&
((?[X]:((curious(X)|~calm(X))))=>(?[X]:(~old(X))))&
((?[X]:(happy(X)))=>((old(susan)|tall(susan))))&
((quiet(john))=>((~generous(mary)|tall(mary))))&
(![X]:((humble(X)&tall(X))<=>brave(X)))&
(![X]:((~patient(X)&tall(X))<=>(curious(X)<~>brave(X))))&
(![X]:((~curious(X)<~>~old(X))=>(happy(X)<~>~strong(X))))&
(((~old(john)&patient(john)))<=>((generous(fred)|~generous(fred))))&
(![X]:((~funny(X)<~>funny(X))=>~kind(X)))&
((~curious(lucy))<=>(?[X]:(~calm(X))))&
((~funny(susan)&~old(susan)))&
(?[X]:((~wise(X)|~funny(X))))&
((~patient(alice)&~kind(alice)))&
(?[X]:(calm(X)))&
(?[X]:(~brave(X)))&
((~generous(paul)&patient(paul)))&
(~tall(john))&
(?[X]:((~funny(X)|brave(X)))) | ~kind(mary) | [
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3871584996133552711213293
% SZS output start Proof for 3871584996133552711213293
15. ! [X0] : ((~funny(X0) <~> funny(X0)) => ~kind(X0)) [input p14]
25. kind(mary) [input hypothesis]
36. ! [X0] : (~kind(X0) | (~funny(X0) <=> funny(X0))) [ennf transformation 15]
56. ! [X0] : (~kind(X0) | ((~funny(X0) | ~funny(X0)) & (funny(X0) | funny(X0)))) [nnf transformation 36]
118. ~kind(X0) | funny(X0) | funny(X0) [cnf transformation 56]
119. ~kind(X0) | ~funny(X0) | ~funny(X0) [cnf transformation 56]
133. kind(mary) [cnf transformation 25]
134. ~kind(X0) | funny(X0) [duplicate literal removal 118]
135. ~kind(X0) | ~funny(X0) [duplicate literal removal 119]
284. ~kind(X0) [subsumption resolution 134,135]
315. $false [subsumption resolution 133,284]
% SZS output end Proof for 3871584996133552711213293
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either wise or generous then someone is both rich and curious and vice versa. Everyone who is not kind is curious or wise. If someone is not rich then susan is not quiet. Everyone who is both not patient and not curious is either not wise or not funny. Everyone who is calm or creative is old and vice versa. If someone is both curious and not brave then someone is happy or tall. Everyone who is both not brave and rich is either generous or kind. Everyone who is either rich or calm is tall or quiet. If someone is both happy and not kind then someone is either not calm or happy. If someone is patient or not curious then susan is not curious. Everyone who is not kind or not old is both kind and not funny and vice versa. Everyone who is not brave is quiet and vice versa. Everyone who is not humble or not old is both not quiet and strong and vice versa. If susan is both calm and creative then john is not quiet or kind and vice versa. If someone is curious then someone is both strong and kind. Everyone who is quiet or wise is either not brave or not rich and vice versa. Someone is either not patient or not strong. Someone is not humble or not quiet. Someone is rich. Someone is not curious or old. Someone is both not funny and patient. Susan is either kind or humble. Fred is generous. Someone is quiet or funny. | Fred is quiet. | contradiction | ((?[X]:((wise(X)<~>generous(X))))<=>(?[X]:((rich(X)&curious(X)))))&
(![X]:(~kind(X)=>(curious(X)|wise(X))))&
((?[X]:(~rich(X)))=>(~quiet(susan)))&
(![X]:((~patient(X)&~curious(X))=>(~wise(X)<~>~funny(X))))&
(![X]:((calm(X)|creative(X))<=>old(X)))&
((?[X]:((curious(X)&~brave(X))))=>(?[X]:((happy(X)|tall(X)))))&
(![X]:((~brave(X)&rich(X))=>(generous(X)<~>kind(X))))&
(![X]:((rich(X)<~>calm(X))=>(tall(X)|quiet(X))))&
((?[X]:((happy(X)&~kind(X))))=>(?[X]:((~calm(X)<~>happy(X)))))&
((?[X]:((patient(X)|~curious(X))))=>(~curious(susan)))&
(![X]:((~kind(X)|~old(X))<=>(kind(X)&~funny(X))))&
(![X]:(~brave(X)<=>quiet(X)))&
(![X]:((~humble(X)|~old(X))<=>(~quiet(X)&strong(X))))&
(((calm(susan)&creative(susan)))<=>((~quiet(john)|kind(john))))&
((?[X]:(curious(X)))=>(?[X]:((strong(X)&kind(X)))))&
(![X]:((quiet(X)|wise(X))<=>(~brave(X)<~>~rich(X))))&
(?[X]:((~patient(X)<~>~strong(X))))&
(?[X]:((~humble(X)|~quiet(X))))&
(?[X]:(rich(X)))&
(?[X]:((~curious(X)|old(X))))&
(?[X]:((~funny(X)&patient(X))))&
((kind(susan)<~>humble(susan)))&
(generous(fred))&
(?[X]:((quiet(X)|funny(X)))) | quiet(fred) | [
"p6",
"p10",
"p11",
"p15",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 8893209022191836436556972
% SZS output start Proof for 8893209022191836436556972
7. ! [X0] : ((rich(X0) & ~brave(X0)) => (generous(X0) <~> kind(X0))) [input p6]
11. ! [X0] : ((~old(X0) | ~kind(X0)) <=> (~funny(X0) & kind(X0))) [input p10]
12. ! [X0] : (~brave(X0) <=> quiet(X0)) [input p11]
16. ! [X0] : ((wise(X0) | quiet(X0)) <=> (~brave(X0) <~> ~rich(X0))) [input p15]
23. generous(fred) [input p22]
25. quiet(fred) [input hypothesis]
37. ! [X0] : ((generous(X0) <~> kind(X0)) | (~rich(X0) | brave(X0))) [ennf transformation 7]
38. ! [X0] : ((generous(X0) <~> kind(X0)) | ~rich(X0) | brave(X0)) [flattening 37]
50. ! [X0] : (((~kind(X0) | ~generous(X0)) & (kind(X0) | generous(X0))) | ~rich(X0) | brave(X0)) [nnf transformation 38]
55. ! [X0] : (((~old(X0) | ~kind(X0)) | (funny(X0) | ~kind(X0))) & ((~funny(X0) & kind(X0)) | (old(X0) & kind(X0)))) [nnf transformation 11]
56. ! [X0] : ((~old(X0) | ~kind(X0) | funny(X0) | ~kind(X0)) & ((~funny(X0) & kind(X0)) | (old(X0) & kind(X0)))) [flattening 55]
57. ! [X0] : ((~brave(X0) | ~quiet(X0)) & (quiet(X0) | brave(X0))) [nnf transformation 12]
65. ! [X0] : (((wise(X0) | quiet(X0)) | ((~brave(X0) | rich(X0)) & (~rich(X0) | brave(X0)))) & (((rich(X0) | brave(X0)) & (~rich(X0) | ~brave(X0))) | (~wise(X0) & ~quiet(X0)))) [nnf transformation 16]
66. ! [X0] : ((wise(X0) | quiet(X0) | ((~brave(X0) | rich(X0)) & (~rich(X0) | brave(X0)))) & (((rich(X0) | brave(X0)) & (~rich(X0) | ~brave(X0))) | (~wise(X0) & ~quiet(X0)))) [flattening 65]
95. ~kind(X0) | ~generous(X0) | ~rich(X0) | brave(X0) [cnf transformation 50]
100. kind(X0) | kind(X0) [cnf transformation 56]
106. ~brave(X0) | ~quiet(X0) [cnf transformation 57]
121. rich(X0) | brave(X0) | ~quiet(X0) [cnf transformation 66]
134. generous(fred) [cnf transformation 23]
136. quiet(fred) [cnf transformation 25]
137. kind(X0) [duplicate literal removal 100]
214. ~quiet(X0) | rich(X0) [subsumption resolution 121,106]
260. rich(fred) [resolution 214,136]
356. ~rich(X1) | ~generous(X1) | brave(X1) [resolution 95,137]
445. ~generous(fred) | brave(fred) [resolution 356,260]
450. brave(fred) [subsumption resolution 445,134]
495. ~quiet(fred) [resolution 450,106]
499. $false [subsumption resolution 495,136]
% SZS output end Proof for 8893209022191836436556972
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Everyone who is not humble is old or not old and vice versa.
Everyone who is both kind and rich is either happy or wise.
If mary is either not curious or not funny then someone is both not tall and strong.
Everyone who is kind or not creative is strong.
Everyone who is brave or not funny is not rich.
If susan is either not generous or not humble then someone is either generous or not happy.
Everyone who is wise is both not old and not calm.
If someone is either not patient or creative then mary is both rich and not generous and vice versa.
Everyone who is either not brave or old is either kind or not generous and vice versa.
Everyone who is wise is rich.
Everyone who is wise is either not wise or patient and vice versa.
If susan is both not curious and not kind then paul is both creative and not calm and vice versa.
If someone is either not curious or creative then someone is both curious and strong and vice versa.
If mary is either rich or not wise then alice is not wise or funny.
If paul is humble or not tall then john is both strong and not funny.
If fred is not funny or brave then lucy is either not creative or brave.
Someone is both not quiet and happy.
Someone is not generous.
Someone is both not happy and tall.
Mary is both not kind and brave.
Lucy is wise or strong.
John is funny.
Fred is either wise or happy.
Someone is not quiet or not happy. | Paul is not tall. | contradiction | (![X]:(~humble(X)<=>(old(X)|~old(X))))&
(![X]:((kind(X)&rich(X))=>(happy(X)<~>wise(X))))&
(((~curious(mary)<~>~funny(mary)))=>(?[X]:((~tall(X)&strong(X)))))&
(![X]:((kind(X)|~creative(X))=>strong(X)))&
(![X]:((brave(X)|~funny(X))=>~rich(X)))&
(((~generous(susan)<~>~humble(susan)))=>(?[X]:((generous(X)<~>~happy(X)))))&
(![X]:(wise(X)=>(~old(X)&~calm(X))))&
((?[X]:((~patient(X)<~>creative(X))))<=>((rich(mary)&~generous(mary))))&
(![X]:((~brave(X)<~>old(X))<=>(kind(X)<~>~generous(X))))&
(![X]:(wise(X)=>rich(X)))&
(![X]:(wise(X)<=>(~wise(X)<~>patient(X))))&
(((~curious(susan)&~kind(susan)))<=>((creative(paul)&~calm(paul))))&
((?[X]:((~curious(X)<~>creative(X))))<=>(?[X]:((curious(X)&strong(X)))))&
(((rich(mary)<~>~wise(mary)))=>((~wise(alice)|funny(alice))))&
(((humble(paul)|~tall(paul)))=>((strong(john)&~funny(john))))&
(((~funny(fred)|brave(fred)))=>((~creative(lucy)<~>brave(lucy))))&
(?[X]:((~quiet(X)&happy(X))))&
(?[X]:(~generous(X)))&
(?[X]:((~happy(X)&tall(X))))&
((~kind(mary)&brave(mary)))&
((wise(lucy)|strong(lucy)))&
(funny(john))&
((wise(fred)<~>happy(fred)))&
(?[X]:((~quiet(X)|~happy(X)))) | ~tall(paul) | [
"p14",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 6353622399401718834273070
% SZS output start Proof for 6353622399401718834273070
15. (~tall(paul) | humble(paul)) => (~funny(john) & strong(john)) [input p14]
22. funny(john) [input p21]
25. ~tall(paul) [input hypothesis]
39. (~funny(john) & strong(john)) | (tall(paul) & ~humble(paul)) [ennf transformation 15]
126. ~funny(john) | tall(paul) [cnf transformation 39]
138. funny(john) [cnf transformation 22]
141. ~tall(paul) [cnf transformation 25]
278. 28 <=> tall(paul) [avatar definition]
282. 29 <=> funny(john) [avatar definition]
285. 28 | ~29 [avatar split clause 126,282,278]
320. 29 [avatar split clause 138,282]
331. ~28 [avatar split clause 141,278]
332. $false [avatar sat refutation 285,320,331]
% SZS output end Proof for 6353622399401718834273070
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not old and not funny then alice is not humble.
Everyone who is not calm or not wise is both rich and creative and vice versa.
If someone is both not happy and not rich then someone is not creative and vice versa.
If someone is both kind and wise then fred is either generous or not funny.
Everyone who is not tall is not rich and vice versa.
If susan is either not happy or strong then someone is rich.
If someone is old or rich then someone is not wise and vice versa.
Everyone who is not tall or curious is not calm or not generous.
Everyone who is patient is generous or not calm and vice versa.
If someone is not brave then paul is either wise or strong and vice versa.
If alice is both patient and wise then someone is both not rich and strong.
Everyone who is either brave or not creative is not rich.
Everyone who is brave or not rich is not brave.
Everyone who is not old is both not kind and kind.
If someone is not wise or calm then paul is not patient.
If mary is both not strong and not calm then someone is tall or brave.
Paul is not happy.
Fred is wise or strong.
Fred is not generous.
Someone is wise or strong.
Someone is either not kind or not calm.
Paul is either happy or not tall.
Mary is funny.
Someone is both funny and not calm. | Paul is not strong. | entailment | ((?[X]:((~old(X)&~funny(X))))=>(~humble(alice)))&
(![X]:((~calm(X)|~wise(X))<=>(rich(X)&creative(X))))&
((?[X]:((~happy(X)&~rich(X))))<=>(?[X]:(~creative(X))))&
((?[X]:((kind(X)&wise(X))))=>((generous(fred)<~>~funny(fred))))&
(![X]:(~tall(X)<=>~rich(X)))&
(((~happy(susan)<~>strong(susan)))=>(?[X]:(rich(X))))&
((?[X]:((old(X)|rich(X))))<=>(?[X]:(~wise(X))))&
(![X]:((~tall(X)|curious(X))=>(~calm(X)|~generous(X))))&
(![X]:(patient(X)<=>(generous(X)|~calm(X))))&
((?[X]:(~brave(X)))<=>((wise(paul)<~>strong(paul))))&
(((patient(alice)&wise(alice)))=>(?[X]:((~rich(X)&strong(X)))))&
(![X]:((brave(X)<~>~creative(X))=>~rich(X)))&
(![X]:((brave(X)|~rich(X))=>~brave(X)))&
(![X]:(~old(X)=>(~kind(X)&kind(X))))&
((?[X]:((~wise(X)|calm(X))))=>(~patient(paul)))&
(((~strong(mary)&~calm(mary)))=>(?[X]:((tall(X)|brave(X)))))&
(~happy(paul))&
((wise(fred)|strong(fred)))&
(~generous(fred))&
(?[X]:((wise(X)|strong(X))))&
(?[X]:((~kind(X)<~>~calm(X))))&
((happy(paul)<~>~tall(paul)))&
(funny(mary))&
(?[X]:((funny(X)&~calm(X)))) | ~strong(paul) | [
"p1",
"p4",
"p9",
"p12",
"p16",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 5583959340543794280859170
% SZS output start Proof for 5583959340543794280859170
2. ! [X0] : ((~wise(X0) | ~calm(X0)) <=> (creative(X0) & rich(X0))) [input p1]
5. ! [X0] : (~tall(X0) <=> ~rich(X0)) [input p4]
10. ? [X0] : ~brave(X0) <=> (wise(paul) <~> strong(paul)) [input p9]
13. ! [X0] : ((~rich(X0) | brave(X0)) => ~brave(X0)) [input p12]
17. ~happy(paul) [input p16]
22. happy(paul) <~> ~tall(paul) [input p21]
25. strong(paul) [input hypothesis]
39. ! [X0] : (~brave(X0) | (rich(X0) & ~brave(X0))) [ennf transformation 13]
44. ! [X0] : (((~wise(X0) | ~calm(X0)) | (~creative(X0) | ~rich(X0))) & ((creative(X0) & rich(X0)) | (wise(X0) & calm(X0)))) [nnf transformation 2]
45. ! [X0] : ((~wise(X0) | ~calm(X0) | ~creative(X0) | ~rich(X0)) & ((creative(X0) & rich(X0)) | (wise(X0) & calm(X0)))) [flattening 44]
52. ! [X0] : ((~tall(X0) | rich(X0)) & (~rich(X0) | tall(X0))) [nnf transformation 5]
61. (? [X0] : ~brave(X0) | ((wise(paul) | ~strong(paul)) & (strong(paul) | ~wise(paul)))) & (((~strong(paul) | ~wise(paul)) & (strong(paul) | wise(paul))) | ! [X0] : brave(X0)) [nnf transformation 10]
62. (? [X0] : ~brave(X0) | ((wise(paul) | ~strong(paul)) & (strong(paul) | ~wise(paul)))) & (((~strong(paul) | ~wise(paul)) & (strong(paul) | wise(paul))) | ! [X1] : brave(X1)) [rectify 61]
63. ? [X0] : ~brave(X0) => ~brave(sK5) [choice axiom]
64. (~brave(sK5) | ((wise(paul) | ~strong(paul)) & (strong(paul) | ~wise(paul)))) & (((~strong(paul) | ~wise(paul)) & (strong(paul) | wise(paul))) | ! [X1] : brave(X1)) [skolemisation 62,63]
75. (tall(paul) | ~happy(paul)) & (~tall(paul) | happy(paul)) [nnf transformation 22]
79. rich(X0) | wise(X0) [cnf transformation 45]
88. ~rich(X0) | tall(X0) [cnf transformation 52]
99. ~strong(paul) | ~wise(paul) | brave(X1) [cnf transformation 64]
106. ~brave(X0) | ~brave(X0) [cnf transformation 39]
113. ~happy(paul) [cnf transformation 17]
119. ~tall(paul) | happy(paul) [cnf transformation 75]
124. strong(paul) [cnf transformation 25]
125. ~brave(X0) [duplicate literal removal 106]
199. 18 <=> strong(paul) [avatar definition]
203. 19 <=> wise(paul) [avatar definition]
213. 21 <=> ! [X1] : brave(X1) [avatar definition]
214. brave(X1) <- (21) [avatar component clause 213]
215. 21 | ~19 | ~18 [avatar split clause 99,199,203,213]
288. ~tall(paul) [subsumption resolution 119,113]
289. 18 [avatar split clause 124,199]
296. tall(X0) | wise(X0) [resolution 88,79]
300. wise(paul) [resolution 296,288]
304. 19 [avatar split clause 300,203]
305. $false <- (21) [subsumption resolution 214,125]
306. ~21 [avatar contradiction clause 305]
307. $false [avatar sat refutation 215,289,304,306]
% SZS output end Proof for 5583959340543794280859170
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either patient or curious is strong or not quiet.
Everyone who is either brave or not rich is both quiet and not old.
If john is either not old or not wise then alice is either not happy or not quiet and vice versa.
Everyone who is both generous and humble is both happy and old and vice versa.
If someone is not kind or not curious then lucy is generous or not patient and vice versa.
If someone is either not kind or not quiet then someone is both calm and not patient and vice versa.
Everyone who is patient is either calm or not creative.
If susan is both not calm and not strong then someone is not humble and vice versa.
If john is both not happy and not brave then john is both calm and not kind and vice versa.
Everyone who is both quiet and funny is not calm and vice versa.
If paul is both not quiet and creative then paul is both creative and not curious.
Everyone who is strong is both not kind and happy and vice versa.
Everyone who is not curious or tall is both brave and not strong.
Everyone who is happy is both curious and not strong.
Everyone who is both kind and curious is not wise.
If someone is not strong or not funny then lucy is not brave and vice versa.
Lucy is strong or not humble.
Fred is either not kind or strong.
Fred is both generous and not tall.
Alice is either kind or not funny.
Paul is not brave or strong.
John is tall or not kind.
Alice is humble. | Lucy is brave. | contradiction | (![X]:((patient(X)<~>curious(X))=>(strong(X)|~quiet(X))))&
(![X]:((brave(X)<~>~rich(X))=>(quiet(X)&~old(X))))&
(((~old(john)<~>~wise(john)))<=>((~happy(alice)<~>~quiet(alice))))&
(![X]:((generous(X)&humble(X))<=>(happy(X)&old(X))))&
((?[X]:((~kind(X)|~curious(X))))<=>((generous(lucy)|~patient(lucy))))&
((?[X]:((~kind(X)<~>~quiet(X))))<=>(?[X]:((calm(X)&~patient(X)))))&
(![X]:(patient(X)=>(calm(X)<~>~creative(X))))&
(((~calm(susan)&~strong(susan)))<=>(?[X]:(~humble(X))))&
(((~happy(john)&~brave(john)))<=>((calm(john)&~kind(john))))&
(![X]:((quiet(X)&funny(X))<=>~calm(X)))&
(((~quiet(paul)&creative(paul)))=>((creative(paul)&~curious(paul))))&
(![X]:(strong(X)<=>(~kind(X)&happy(X))))&
(![X]:((~curious(X)|tall(X))=>(brave(X)&~strong(X))))&
(![X]:(happy(X)=>(curious(X)&~strong(X))))&
(![X]:((kind(X)&curious(X))=>~wise(X)))&
((?[X]:((~strong(X)|~funny(X))))<=>(~brave(lucy)))&
((strong(lucy)|~humble(lucy)))&
((~kind(fred)<~>strong(fred)))&
((generous(fred)&~tall(fred)))&
((kind(alice)<~>~funny(alice)))&
((~brave(paul)|strong(paul)))&
((tall(john)|~kind(john)))&
(humble(alice)) | brave(lucy) | [
"p11",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3671001986774980687129759
% SZS output start Proof for 3671001986774980687129759
12. ! [X0] : (strong(X0) <=> (happy(X0) & ~kind(X0))) [input p11]
14. ! [X0] : (happy(X0) => (~strong(X0) & curious(X0))) [input p13]
16. ? [X0] : (~funny(X0) | ~strong(X0)) <=> ~brave(lucy) [input p15]
24. brave(lucy) [input hypothesis]
33. ! [X0] : ((~strong(X0) & curious(X0)) | ~happy(X0)) [ennf transformation 14]
61. ! [X0] : ((strong(X0) | (~happy(X0) | kind(X0))) & ((happy(X0) & ~kind(X0)) | ~strong(X0))) [nnf transformation 12]
62. ! [X0] : ((strong(X0) | ~happy(X0) | kind(X0)) & ((happy(X0) & ~kind(X0)) | ~strong(X0))) [flattening 61]
63. (? [X0] : (~funny(X0) | ~strong(X0)) | brave(lucy)) & (~brave(lucy) | ! [X0] : (funny(X0) & strong(X0))) [nnf transformation 16]
64. (? [X0] : (~funny(X0) | ~strong(X0)) | brave(lucy)) & (~brave(lucy) | ! [X1] : (funny(X1) & strong(X1))) [rectify 63]
65. ? [X0] : (~funny(X0) | ~strong(X0)) => (~funny(sK4) | ~strong(sK4)) [choice axiom]
66. ((~funny(sK4) | ~strong(sK4)) | brave(lucy)) & (~brave(lucy) | ! [X1] : (funny(X1) & strong(X1))) [skolemisation 64,65]
112. happy(X0) | ~strong(X0) [cnf transformation 62]
119. ~strong(X0) | ~happy(X0) [cnf transformation 33]
121. ~brave(lucy) | strong(X1) [cnf transformation 66]
134. brave(lucy) [cnf transformation 24]
267. ~strong(X0) [subsumption resolution 119,112]
272. 30 <=> brave(lucy) [avatar definition]
276. ~brave(lucy) [subsumption resolution 121,267]
277. ~30 [avatar split clause 276,272]
296. 30 [avatar split clause 134,272]
297. $false [avatar sat refutation 277,296]
% SZS output end Proof for 3671001986774980687129759
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not wise or old then susan is both strong and kind and vice versa.
If someone is not brave then someone is calm.
If someone is not rich or old then someone is not rich and vice versa.
If mary is both funny and not kind then someone is both brave and wise.
Everyone who is both kind and happy is either not funny or quiet.
If alice is not curious then someone is either not creative or happy and vice versa.
Everyone who is patient is curious.
Everyone who is either not curious or brave is both brave and not brave and vice versa.
If someone is not quiet then lucy is patient or funny.
Everyone who is patient or funny is either brave or not generous.
Everyone who is either strong or humble is both tall and not funny.
Everyone who is not rich is either not generous or humble and vice versa.
Everyone who is both brave and not wise is calm and vice versa.
If mary is either not old or calm then someone is both curious and generous.
If someone is happy then fred is either curious or brave and vice versa.
If lucy is not generous then someone is curious and vice versa.
Someone is both wise and generous.
Someone is either creative or not happy.
John is either rich or humble.
Someone is either not happy or not humble.
Someone is wise.
Susan is calm or not funny.
Someone is not funny. | Susan is wise. | neutral | ((?[X]:((~wise(X)<~>old(X))))<=>((strong(susan)&kind(susan))))&
((?[X]:(~brave(X)))=>(?[X]:(calm(X))))&
((?[X]:((~rich(X)|old(X))))<=>(?[X]:(~rich(X))))&
(((funny(mary)&~kind(mary)))=>(?[X]:((brave(X)&wise(X)))))&
(![X]:((kind(X)&happy(X))=>(~funny(X)<~>quiet(X))))&
((~curious(alice))<=>(?[X]:((~creative(X)<~>happy(X)))))&
(![X]:(patient(X)=>curious(X)))&
(![X]:((~curious(X)<~>brave(X))<=>(brave(X)&~brave(X))))&
((?[X]:(~quiet(X)))=>((patient(lucy)|funny(lucy))))&
(![X]:((patient(X)|funny(X))=>(brave(X)<~>~generous(X))))&
(![X]:((strong(X)<~>humble(X))=>(tall(X)&~funny(X))))&
(![X]:(~rich(X)<=>(~generous(X)<~>humble(X))))&
(![X]:((brave(X)&~wise(X))<=>calm(X)))&
(((~old(mary)<~>calm(mary)))=>(?[X]:((curious(X)&generous(X)))))&
((?[X]:(happy(X)))<=>((curious(fred)<~>brave(fred))))&
((~generous(lucy))<=>(?[X]:(curious(X))))&
(?[X]:((wise(X)&generous(X))))&
(?[X]:((creative(X)<~>~happy(X))))&
((rich(john)<~>humble(john)))&
(?[X]:((~happy(X)<~>~humble(X))))&
(?[X]:(wise(X)))&
((calm(susan)|~funny(susan)))&
(?[X]:(~funny(X))) | wise(susan) | [] | null | 0 |
If someone is not tall then susan is generous or kind and vice versa. Everyone who is not patient is either wise or strong and vice versa. Everyone who is calm is both not wise and not funny. Everyone who is both not curious and not rich is rich and vice versa. If someone is not old or not calm then lucy is funny or happy and vice versa. If mary is either not creative or not funny then alice is both strong and not quiet. If someone is both strong and not curious then someone is not wise or kind. Everyone who is not kind is not curious. If someone is both not old and quiet then someone is not wise or humble. If alice is funny then fred is wise or not kind. If alice is either kind or rich then susan is humble or old and vice versa. If susan is not old or not wise then someone is rich or happy and vice versa. Everyone who is humble or curious is not wise. If alice is either not calm or wise then someone is not generous or not patient and vice versa. Everyone who is not funny is not creative. Everyone who is either old or funny is either strong or rich. Someone is both quiet and creative. Someone is either old or funny. Someone is either brave or not quiet. Someone is strong. Someone is both not old and not calm. Someone is both generous and strong. Someone is quiet or creative. Someone is both not old and creative. | Lucy is rich. | contradiction | ((?[X]:(~tall(X)))<=>((generous(susan)|kind(susan))))&
(![X]:(~patient(X)<=>(wise(X)<~>strong(X))))&
(![X]:(calm(X)=>(~wise(X)&~funny(X))))&
(![X]:((~curious(X)&~rich(X))<=>rich(X)))&
((?[X]:((~old(X)|~calm(X))))<=>((funny(lucy)|happy(lucy))))&
(((~creative(mary)<~>~funny(mary)))=>((strong(alice)&~quiet(alice))))&
((?[X]:((strong(X)&~curious(X))))=>(?[X]:((~wise(X)|kind(X)))))&
(![X]:(~kind(X)=>~curious(X)))&
((?[X]:((~old(X)&quiet(X))))=>(?[X]:((~wise(X)|humble(X)))))&
((funny(alice))=>((wise(fred)|~kind(fred))))&
(((kind(alice)<~>rich(alice)))<=>((humble(susan)|old(susan))))&
(((~old(susan)|~wise(susan)))<=>(?[X]:((rich(X)|happy(X)))))&
(![X]:((humble(X)|curious(X))=>~wise(X)))&
(((~calm(alice)<~>wise(alice)))<=>(?[X]:((~generous(X)|~patient(X)))))&
(![X]:(~funny(X)=>~creative(X)))&
(![X]:((old(X)<~>funny(X))=>(strong(X)<~>rich(X))))&
(?[X]:((quiet(X)&creative(X))))&
(?[X]:((old(X)<~>funny(X))))&
(?[X]:((brave(X)<~>~quiet(X))))&
(?[X]:(strong(X)))&
(?[X]:((~old(X)&~calm(X))))&
(?[X]:((generous(X)&strong(X))))&
(?[X]:((quiet(X)|creative(X))))&
(?[X]:((~old(X)&creative(X)))) | rich(lucy) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 6577363249702166866349481
% SZS output start Proof for 6577363249702166866349481
4. ! [X0] : ((~rich(X0) & ~curious(X0)) <=> rich(X0)) [input p3]
25. rich(lucy) [input hypothesis]
44. ! [X0] : (((~rich(X0) & ~curious(X0)) | ~rich(X0)) & (rich(X0) | (rich(X0) | curious(X0)))) [nnf transformation 4]
45. ! [X0] : (((~rich(X0) & ~curious(X0)) | ~rich(X0)) & (rich(X0) | rich(X0) | curious(X0))) [flattening 44]
99. ~rich(X0) | ~rich(X0) [cnf transformation 45]
149. rich(lucy) [cnf transformation 25]
151. ~rich(X0) [duplicate literal removal 99]
323. $false [subsumption resolution 149,151]
% SZS output end Proof for 6577363249702166866349481
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not funny or strong then someone is both old and not strong. Everyone who is calm or generous is either humble or wise. If mary is not rich then paul is not calm or not happy. Everyone who is curious is creative. If someone is both humble and creative then mary is quiet. Everyone who is not calm is both not brave and old and vice versa. Everyone who is both brave and funny is brave or old and vice versa. If someone is not tall then fred is rich. Everyone who is not rich is generous. Everyone who is either not wise or not tall is patient. Everyone who is curious is either creative or not strong. If lucy is strong then fred is both not strong and patient and vice versa. If someone is both not brave and rich then alice is both not kind and wise and vice versa. If mary is both brave and strong then susan is humble and vice versa. Everyone who is both funny and curious is both not kind and not humble. Everyone who is not humble is either not funny or not patient. Someone is brave or not funny. Someone is tall or not patient. Someone is both not rich and not quiet. Someone is patient or not brave. Susan is not wise or curious. Someone is tall. Someone is both not kind and curious. Alice is both not happy and not quiet. | Lucy is not calm. | contradiction | (((~funny(lucy)<~>strong(lucy)))=>(?[X]:((old(X)&~strong(X)))))&
(![X]:((calm(X)|generous(X))=>(humble(X)<~>wise(X))))&
((~rich(mary))=>((~calm(paul)|~happy(paul))))&
(![X]:(curious(X)=>creative(X)))&
((?[X]:((humble(X)&creative(X))))=>(quiet(mary)))&
(![X]:(~calm(X)<=>(~brave(X)&old(X))))&
(![X]:((brave(X)&funny(X))<=>(brave(X)|old(X))))&
((?[X]:(~tall(X)))=>(rich(fred)))&
(![X]:(~rich(X)=>generous(X)))&
(![X]:((~wise(X)<~>~tall(X))=>patient(X)))&
(![X]:(curious(X)=>(creative(X)<~>~strong(X))))&
((strong(lucy))<=>((~strong(fred)&patient(fred))))&
((?[X]:((~brave(X)&rich(X))))<=>((~kind(alice)&wise(alice))))&
(((brave(mary)&strong(mary)))<=>(humble(susan)))&
(![X]:((funny(X)&curious(X))=>(~kind(X)&~humble(X))))&
(![X]:(~humble(X)=>(~funny(X)<~>~patient(X))))&
(?[X]:((brave(X)|~funny(X))))&
(?[X]:((tall(X)|~patient(X))))&
(?[X]:((~rich(X)&~quiet(X))))&
(?[X]:((patient(X)|~brave(X))))&
((~wise(susan)|curious(susan)))&
(?[X]:(tall(X)))&
(?[X]:((~kind(X)&curious(X))))&
((~happy(alice)&~quiet(alice))) | ~calm(lucy) | [
"p5",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 4549966417368942049390165
% SZS output start Proof for 4549966417368942049390165
6. ! [X0] : (~calm(X0) <=> (old(X0) & ~brave(X0))) [input p5]
7. ! [X0] : ((funny(X0) & brave(X0)) <=> (old(X0) | brave(X0))) [input p6]
25. ~calm(lucy) [input hypothesis]
26. ! [X0] : (~calm(X0) => (old(X0) & ~brave(X0))) [unused predicate definition removal 6]
33. ! [X0] : ((old(X0) & ~brave(X0)) | calm(X0)) [ennf transformation 26]
45. ! [X0] : (((funny(X0) & brave(X0)) | (~old(X0) & ~brave(X0))) & ((old(X0) | brave(X0)) | (~funny(X0) | ~brave(X0)))) [nnf transformation 7]
46. ! [X0] : (((funny(X0) & brave(X0)) | (~old(X0) & ~brave(X0))) & (old(X0) | brave(X0) | ~funny(X0) | ~brave(X0))) [flattening 45]
81. ~brave(X0) | calm(X0) [cnf transformation 33]
82. calm(X0) | old(X0) [cnf transformation 33]
85. ~old(X0) | brave(X0) [cnf transformation 46]
118. ~calm(lucy) [cnf transformation 25]
242. old(lucy) [resolution 82,118]
243. brave(lucy) [resolution 242,85]
245. calm(lucy) [resolution 243,81]
246. $false [subsumption resolution 245,118]
% SZS output end Proof for 4549966417368942049390165
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not wise and calm is both wise and not curious and vice versa. If someone is both not calm and happy then mary is either generous or not generous. Everyone who is not creative is either patient or not strong and vice versa. If someone is not brave then susan is either not tall or not quiet. Everyone who is not brave or not patient is not generous. Everyone who is not brave is funny or not wise. If john is not funny then someone is curious or not brave and vice versa. Everyone who is both kind and not wise is brave or tall and vice versa. Everyone who is both old and not old is either not quiet or not generous and vice versa. Everyone who is both happy and humble is humble. If mary is both not calm and not tall then alice is quiet. If john is both not tall and calm then someone is wise. If someone is either not rich or not patient then someone is both not strong and brave. Everyone who is generous or not calm is not calm and vice versa. Everyone who is either not patient or funny is both not tall and not funny. If someone is rich or not brave then fred is both not quiet and old and vice versa. John is not tall. Someone is not calm. Someone is calm. Alice is creative. Susan is calm or not quiet. Mary is humble. Mary is either funny or not generous. Someone is both not patient and funny. | Susan is wise. | contradiction | (![X]:((~wise(X)&calm(X))<=>(wise(X)&~curious(X))))&
((?[X]:((~calm(X)&happy(X))))=>((generous(mary)<~>~generous(mary))))&
(![X]:(~creative(X)<=>(patient(X)<~>~strong(X))))&
((?[X]:(~brave(X)))=>((~tall(susan)<~>~quiet(susan))))&
(![X]:((~brave(X)|~patient(X))=>~generous(X)))&
(![X]:(~brave(X)=>(funny(X)|~wise(X))))&
((~funny(john))<=>(?[X]:((curious(X)|~brave(X)))))&
(![X]:((kind(X)&~wise(X))<=>(brave(X)|tall(X))))&
(![X]:((old(X)&~old(X))<=>(~quiet(X)<~>~generous(X))))&
(![X]:((happy(X)&humble(X))=>humble(X)))&
(((~calm(mary)&~tall(mary)))=>(quiet(alice)))&
(((~tall(john)&calm(john)))=>(?[X]:(wise(X))))&
((?[X]:((~rich(X)<~>~patient(X))))=>(?[X]:((~strong(X)&brave(X)))))&
(![X]:((generous(X)|~calm(X))<=>~calm(X)))&
(![X]:((~patient(X)<~>funny(X))=>(~tall(X)&~funny(X))))&
((?[X]:((rich(X)|~brave(X))))<=>((~quiet(fred)&old(fred))))&
(~tall(john))&
(?[X]:(~calm(X)))&
(?[X]:(calm(X)))&
(creative(alice))&
((calm(susan)|~quiet(susan)))&
(humble(mary))&
((funny(mary)<~>~generous(mary)))&
(?[X]:((~patient(X)&funny(X)))) | wise(susan) | [
"p3",
"p7",
"p8",
"p13",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 7625163634673131582623402
% SZS output start Proof for 7625163634673131582623402
4. ? [X0] : ~brave(X0) => (~tall(susan) <~> ~quiet(susan)) [input p3]
8. ! [X0] : ((~wise(X0) & kind(X0)) <=> (tall(X0) | brave(X0))) [input p7]
9. ! [X0] : ((~old(X0) & old(X0)) <=> (~quiet(X0) <~> ~generous(X0))) [input p8]
14. ! [X0] : ((~calm(X0) | generous(X0)) <=> ~calm(X0)) [input p13]
21. ~quiet(susan) | calm(susan) [input p20]
25. wise(susan) [input hypothesis]
32. (~tall(susan) <~> ~quiet(susan)) | ! [X0] : brave(X0) [ennf transformation 4]
45. ((quiet(susan) | tall(susan)) & (~quiet(susan) | ~tall(susan))) | ! [X0] : brave(X0) [nnf transformation 32]
50. ! [X0] : (((~wise(X0) & kind(X0)) | (~tall(X0) & ~brave(X0))) & ((tall(X0) | brave(X0)) | (wise(X0) | ~kind(X0)))) [nnf transformation 8]
51. ! [X0] : (((~wise(X0) & kind(X0)) | (~tall(X0) & ~brave(X0))) & (tall(X0) | brave(X0) | wise(X0) | ~kind(X0))) [flattening 50]
52. ! [X0] : (((~old(X0) & old(X0)) | ((~quiet(X0) | generous(X0)) & (~generous(X0) | quiet(X0)))) & (((generous(X0) | quiet(X0)) & (~generous(X0) | ~quiet(X0))) | (old(X0) | ~old(X0)))) [nnf transformation 9]
53. ! [X0] : (((~old(X0) & old(X0)) | ((~quiet(X0) | generous(X0)) & (~generous(X0) | quiet(X0)))) & (((generous(X0) | quiet(X0)) & (~generous(X0) | ~quiet(X0))) | old(X0) | ~old(X0))) [flattening 52]
60. ! [X0] : (((~calm(X0) | generous(X0)) | calm(X0)) & (~calm(X0) | (calm(X0) & ~generous(X0)))) [nnf transformation 14]
61. ! [X0] : ((~calm(X0) | generous(X0) | calm(X0)) & (~calm(X0) | (calm(X0) & ~generous(X0)))) [flattening 60]
82. quiet(susan) | tall(susan) | brave(X0) [cnf transformation 45]
92. ~brave(X0) | ~wise(X0) [cnf transformation 51]
93. ~tall(X0) | ~wise(X0) [cnf transformation 51]
97. old(X0) | ~quiet(X0) | generous(X0) [cnf transformation 53]
99. ~old(X0) | ~quiet(X0) | generous(X0) [cnf transformation 53]
106. ~generous(X0) | ~calm(X0) [cnf transformation 61]
122. ~quiet(susan) | calm(susan) [cnf transformation 21]
127. wise(susan) [cnf transformation 25]
132. 1 <=> ! [X0] : brave(X0) [avatar definition]
133. brave(X0) <- (1) [avatar component clause 132]
135. 2 <=> tall(susan) [avatar definition]
137. tall(susan) <- (2) [avatar component clause 135]
139. 3 <=> quiet(susan) [avatar definition]
141. quiet(susan) <- (3) [avatar component clause 139]
142. 1 | 2 | 3 [avatar split clause 82,139,135,132]
162. ~quiet(X0) | generous(X0) [subsumption resolution 97,99]
234. 23 <=> calm(susan) [avatar definition]
236. calm(susan) <- (23) [avatar component clause 234]
237. 23 | ~3 [avatar split clause 122,139,234]
251. ~wise(susan) <- (2) [resolution 93,137]
252. $false <- (2) [subsumption resolution 251,127]
253. ~2 [avatar contradiction clause 252]
260. generous(susan) <- (3) [resolution 162,141]
264. ~calm(susan) <- (3) [resolution 260,106]
267. $false <- (3, 23) [subsumption resolution 264,236]
268. ~3 | ~23 [avatar contradiction clause 267]
271. ~wise(X0) <- (1) [resolution 133,92]
279. $false <- (1) [resolution 271,127]
284. ~1 [avatar contradiction clause 279]
285. $false [avatar sat refutation 142,237,253,268,284]
% SZS output end Proof for 7625163634673131582623402
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet then fred is either creative or generous.
Everyone who is not kind or not old is creative and vice versa.
Everyone who is either not funny or not rich is curious and vice versa.
If someone is creative then someone is either not tall or patient and vice versa.
Everyone who is both happy and curious is not happy or curious and vice versa.
Everyone who is not curious is both not generous and not humble.
If someone is either patient or funny then someone is either brave or wise and vice versa.
Everyone who is not creative is not patient.
If someone is not old then someone is both not brave and not tall.
Everyone who is both calm and not old is either brave or not tall.
Everyone who is both not generous and not rich is either not creative or rich and vice versa.
Everyone who is both not quiet and kind is creative or not generous.
If someone is old or not tall then alice is both patient and calm and vice versa.
Everyone who is either tall or calm is not tall or not rich and vice versa.
Everyone who is humble or not funny is either not tall or not kind and vice versa.
If someone is both creative and generous then someone is either calm or rich and vice versa.
Fred is either not wise or wise.
Someone is both curious and rich.
Someone is not funny.
Paul is brave.
Paul is either kind or not funny.
Fred is either happy or creative.
John is either funny or tall.
Alice is funny. | Alice is not tall. | entailment | ((?[X]:(quiet(X)))=>((creative(fred)<~>generous(fred))))&
(![X]:((~kind(X)|~old(X))<=>creative(X)))&
(![X]:((~funny(X)<~>~rich(X))<=>curious(X)))&
((?[X]:(creative(X)))<=>(?[X]:((~tall(X)<~>patient(X)))))&
(![X]:((happy(X)&curious(X))<=>(~happy(X)|curious(X))))&
(![X]:(~curious(X)=>(~generous(X)&~humble(X))))&
((?[X]:((patient(X)<~>funny(X))))<=>(?[X]:((brave(X)<~>wise(X)))))&
(![X]:(~creative(X)=>~patient(X)))&
((?[X]:(~old(X)))=>(?[X]:((~brave(X)&~tall(X)))))&
(![X]:((calm(X)&~old(X))=>(brave(X)<~>~tall(X))))&
(![X]:((~generous(X)&~rich(X))<=>(~creative(X)<~>rich(X))))&
(![X]:((~quiet(X)&kind(X))=>(creative(X)|~generous(X))))&
((?[X]:((old(X)|~tall(X))))<=>((patient(alice)&calm(alice))))&
(![X]:((tall(X)<~>calm(X))<=>(~tall(X)|~rich(X))))&
(![X]:((humble(X)|~funny(X))<=>(~tall(X)<~>~kind(X))))&
((?[X]:((creative(X)&generous(X))))<=>(?[X]:((calm(X)<~>rich(X)))))&
((~wise(fred)<~>wise(fred)))&
(?[X]:((curious(X)&rich(X))))&
(?[X]:(~funny(X)))&
(brave(paul))&
((kind(paul)<~>~funny(paul)))&
((happy(fred)<~>creative(fred)))&
((funny(john)<~>tall(john)))&
(funny(alice)) | ~tall(alice) | [
"p7",
"p8",
"p10",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 6714651960548758511624328
% SZS output start Proof for 6714651960548758511624328
8. ! [X0] : (~creative(X0) => ~patient(X0)) [input p7]
9. ? [X0] : ~old(X0) => ? [X0] : (~tall(X0) & ~brave(X0)) [input p8]
11. ! [X0] : ((~rich(X0) & ~generous(X0)) <=> (~creative(X0) <~> rich(X0))) [input p10]
13. ? [X0] : (~tall(X0) | old(X0)) <=> (calm(alice) & patient(alice)) [input p12]
14. ! [X0] : ((tall(X0) <~> calm(X0)) <=> (~rich(X0) | ~tall(X0))) [input p13]
25. tall(alice) [input hypothesis]
28. ? [X0] : ~old(X0) => ? [X1] : (~tall(X1) & ~brave(X1)) [rectify 9]
32. ! [X0] : (~patient(X0) | creative(X0)) [ennf transformation 8]
33. ? [X1] : (~tall(X1) & ~brave(X1)) | ! [X0] : old(X0) [ennf transformation 28]
54. ? [X0] : (~tall(X0) & ~brave(X0)) | ! [X1] : old(X1) [rectify 33]
55. ? [X0] : (~tall(X0) & ~brave(X0)) => (~tall(sK4) & ~brave(sK4)) [choice axiom]
56. (~tall(sK4) & ~brave(sK4)) | ! [X1] : old(X1) [skolemisation 54,55]
58. ! [X0] : (((~rich(X0) & ~generous(X0)) | ((~creative(X0) | ~rich(X0)) & (rich(X0) | creative(X0)))) & (((~rich(X0) | creative(X0)) & (rich(X0) | ~creative(X0))) | (rich(X0) | generous(X0)))) [nnf transformation 11]
59. ! [X0] : (((~rich(X0) & ~generous(X0)) | ((~creative(X0) | ~rich(X0)) & (rich(X0) | creative(X0)))) & (((~rich(X0) | creative(X0)) & (rich(X0) | ~creative(X0))) | rich(X0) | generous(X0))) [flattening 58]
60. (? [X0] : (~tall(X0) | old(X0)) | (~calm(alice) | ~patient(alice))) & ((calm(alice) & patient(alice)) | ! [X0] : (tall(X0) & ~old(X0))) [nnf transformation 13]
61. (? [X0] : (~tall(X0) | old(X0)) | ~calm(alice) | ~patient(alice)) & ((calm(alice) & patient(alice)) | ! [X0] : (tall(X0) & ~old(X0))) [flattening 60]
62. (? [X0] : (~tall(X0) | old(X0)) | ~calm(alice) | ~patient(alice)) & ((calm(alice) & patient(alice)) | ! [X1] : (tall(X1) & ~old(X1))) [rectify 61]
63. ? [X0] : (~tall(X0) | old(X0)) => (~tall(sK5) | old(sK5)) [choice axiom]
64. ((~tall(sK5) | old(sK5)) | ~calm(alice) | ~patient(alice)) & ((calm(alice) & patient(alice)) | ! [X1] : (tall(X1) & ~old(X1))) [skolemisation 62,63]
65. ! [X0] : ((((~calm(X0) | ~tall(X0)) & (calm(X0) | tall(X0))) | (rich(X0) & tall(X0))) & ((~rich(X0) | ~tall(X0)) | ((tall(X0) | ~calm(X0)) & (calm(X0) | ~tall(X0))))) [nnf transformation 14]
66. ! [X0] : ((((~calm(X0) | ~tall(X0)) & (calm(X0) | tall(X0))) | (rich(X0) & tall(X0))) & (~rich(X0) | ~tall(X0) | ((tall(X0) | ~calm(X0)) & (calm(X0) | ~tall(X0))))) [flattening 65]
110. ~patient(X0) | creative(X0) [cnf transformation 32]
112. ~tall(sK4) | old(X1) [cnf transformation 56]
120. ~rich(X0) | ~creative(X0) | ~rich(X0) [cnf transformation 59]
122. patient(alice) | ~old(X1) [cnf transformation 64]
123. patient(alice) | tall(X1) [cnf transformation 64]
124. calm(alice) | ~old(X1) [cnf transformation 64]
125. calm(alice) | tall(X1) [cnf transformation 64]
132. ~calm(X0) | ~tall(X0) | rich(X0) [cnf transformation 66]
158. tall(alice) [cnf transformation 25]
162. ~rich(X0) | ~creative(X0) [duplicate literal removal 120]
241. 18 <=> ! [X1] : old(X1) [avatar definition]
242. old(X1) <- (18) [avatar component clause 241]
244. 19 <=> tall(sK4) [avatar definition]
246. ~tall(sK4) <- (~19) [avatar component clause 244]
247. 18 | ~19 [avatar split clause 112,244,241]
256. 21 <=> patient(alice) [avatar definition]
257. patient(alice) <- (21) [avatar component clause 256]
260. 22 <=> calm(alice) [avatar definition]
261. calm(alice) <- (22) [avatar component clause 260]
273. 25 <=> ! [X1] : tall(X1) [avatar definition]
274. tall(X1) <- (25) [avatar component clause 273]
275. 25 | 22 [avatar split clause 125,260,273]
277. 26 <=> ! [X1] : ~old(X1) [avatar definition]
278. ~old(X1) <- (26) [avatar component clause 277]
279. 26 | 22 [avatar split clause 124,260,277]
280. 25 | 21 [avatar split clause 123,256,273]
281. 26 | 21 [avatar split clause 122,256,277]
404. 42 <=> rich(alice) [avatar definition]
406. rich(alice) <- (42) [avatar component clause 404]
423. $false <- (~19, 25) [resolution 274,246]
426. 19 | ~25 [avatar contradiction clause 423]
428. $false <- (18, 26) [subsumption resolution 242,278]
429. ~18 | ~26 [avatar contradiction clause 428]
432. creative(alice) <- (21) [resolution 257,110]
468. ~tall(alice) | rich(alice) <- (22) [resolution 132,261]
472. rich(alice) <- (22) [subsumption resolution 468,158]
476. 42 | ~22 [avatar split clause 472,260,404]
479. ~creative(alice) <- (42) [resolution 406,162]
480. $false <- (21, 42) [subsumption resolution 479,432]
481. ~21 | ~42 [avatar contradiction clause 480]
482. $false [avatar sat refutation 247,275,279,280,281,426,429,476,481]
% SZS output end Proof for 6714651960548758511624328
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not creative or not humble then someone is both quiet and tall and vice versa.
If paul is either kind or generous then someone is not brave or not kind.
Everyone who is both not happy and tall is both old and not brave and vice versa.
Everyone who is not generous is curious or not happy.
If someone is kind then fred is both not kind and not rich.
Everyone who is both not calm and not patient is either funny or generous.
Everyone who is wise is either strong or not tall.
Everyone who is either strong or calm is not happy.
Everyone who is both quiet and brave is not creative and vice versa.
Everyone who is quiet is both old and quiet and vice versa.
Everyone who is not happy or not strong is generous or patient.
If alice is not funny or not patient then susan is happy or not brave and vice versa.
Everyone who is brave or not old is both not brave and not happy.
Everyone who is not quiet is humble.
Everyone who is not quiet is not brave or happy and vice versa.
If fred is not curious then someone is not generous or not curious.
Someone is both old and not calm.
Someone is either not humble or rich.
Lucy is tall or not wise.
Someone is not calm.
Alice is either funny or not brave.
Someone is either not wise or quiet. | Paul is happy. | contradiction | ((?[X]:((~creative(X)<~>~humble(X))))<=>(?[X]:((quiet(X)&tall(X)))))&
(((kind(paul)<~>generous(paul)))=>(?[X]:((~brave(X)|~kind(X)))))&
(![X]:((~happy(X)&tall(X))<=>(old(X)&~brave(X))))&
(![X]:(~generous(X)=>(curious(X)|~happy(X))))&
((?[X]:(kind(X)))=>((~kind(fred)&~rich(fred))))&
(![X]:((~calm(X)&~patient(X))=>(funny(X)<~>generous(X))))&
(![X]:(wise(X)=>(strong(X)<~>~tall(X))))&
(![X]:((strong(X)<~>calm(X))=>~happy(X)))&
(![X]:((quiet(X)&brave(X))<=>~creative(X)))&
(![X]:(quiet(X)<=>(old(X)&quiet(X))))&
(![X]:((~happy(X)|~strong(X))=>(generous(X)|patient(X))))&
(((~funny(alice)|~patient(alice)))<=>((happy(susan)|~brave(susan))))&
(![X]:((brave(X)|~old(X))=>(~brave(X)&~happy(X))))&
(![X]:(~quiet(X)=>humble(X)))&
(![X]:(~quiet(X)<=>(~brave(X)|happy(X))))&
((~curious(fred))=>(?[X]:((~generous(X)|~curious(X)))))&
(?[X]:((old(X)&~calm(X))))&
(?[X]:((~humble(X)<~>rich(X))))&
((tall(lucy)|~wise(lucy)))&
(?[X]:(~calm(X)))&
((funny(alice)<~>~brave(alice)))&
(?[X]:((~wise(X)<~>quiet(X)))) | happy(paul) | [
"p2",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 5298655328238480685660555
% SZS output start Proof for 5298655328238480685660555
3. ! [X0] : ((tall(X0) & ~happy(X0)) <=> (~brave(X0) & old(X0))) [input p2]
13. ! [X0] : ((~old(X0) | brave(X0)) => (~happy(X0) & ~brave(X0))) [input p12]
23. happy(paul) [input hypothesis]
35. ! [X0] : ((~happy(X0) & ~brave(X0)) | (old(X0) & ~brave(X0))) [ennf transformation 13]
46. ! [X0] : (((tall(X0) & ~happy(X0)) | (brave(X0) | ~old(X0))) & ((~brave(X0) & old(X0)) | (~tall(X0) | happy(X0)))) [nnf transformation 3]
47. ! [X0] : (((tall(X0) & ~happy(X0)) | brave(X0) | ~old(X0)) & ((~brave(X0) & old(X0)) | ~tall(X0) | happy(X0))) [flattening 46]
82. ~old(X0) | brave(X0) | ~happy(X0) [cnf transformation 47]
105. ~brave(X0) | ~brave(X0) [cnf transformation 35]
108. ~happy(X0) | old(X0) [cnf transformation 35]
124. happy(paul) [cnf transformation 23]
125. ~brave(X0) [duplicate literal removal 105]
249. old(paul) [resolution 108,124]
262. brave(paul) | ~happy(paul) [resolution 82,249]
265. ~happy(paul) [subsumption resolution 262,125]
266. $false [subsumption resolution 265,124]
% SZS output end Proof for 5298655328238480685660555
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old is happy or not kind and vice versa.
If someone is not calm or tall then someone is either not humble or not strong and vice versa.
Everyone who is not kind is both wise and not strong.
Everyone who is either old or not curious is either not strong or generous and vice versa.
If someone is either not funny or not creative then someone is either not brave or brave and vice versa.
If someone is either not rich or not wise then paul is either not curious or not brave and vice versa.
If someone is curious or not tall then someone is kind and vice versa.
Everyone who is either not patient or creative is either not patient or not curious and vice versa.
Everyone who is either not patient or quiet is wise or humble and vice versa.
Everyone who is not strong is not old.
Everyone who is either strong or tall is quiet or happy.
Everyone who is either not happy or not strong is both curious and not humble and vice versa.
Everyone who is generous or not brave is either not patient or funny and vice versa.
If fred is both not creative and old then fred is strong or quiet and vice versa.
Everyone who is generous is either not creative or patient.
Everyone who is both not wise and not creative is happy.
Someone is not rich.
Mary is either not strong or not humble.
Someone is not rich or not funny.
Someone is both old and not brave.
Mary is not tall or not kind.
Paul is not quiet.
Someone is not strong.
Someone is either not funny or not old. | Mary is strong. | neutral | (![X]:(old(X)<=>(happy(X)|~kind(X))))&
((?[X]:((~calm(X)|tall(X))))<=>(?[X]:((~humble(X)<~>~strong(X)))))&
(![X]:(~kind(X)=>(wise(X)&~strong(X))))&
(![X]:((old(X)<~>~curious(X))<=>(~strong(X)<~>generous(X))))&
((?[X]:((~funny(X)<~>~creative(X))))<=>(?[X]:((~brave(X)<~>brave(X)))))&
((?[X]:((~rich(X)<~>~wise(X))))<=>((~curious(paul)<~>~brave(paul))))&
((?[X]:((curious(X)|~tall(X))))<=>(?[X]:(kind(X))))&
(![X]:((~patient(X)<~>creative(X))<=>(~patient(X)<~>~curious(X))))&
(![X]:((~patient(X)<~>quiet(X))<=>(wise(X)|humble(X))))&
(![X]:(~strong(X)=>~old(X)))&
(![X]:((strong(X)<~>tall(X))=>(quiet(X)|happy(X))))&
(![X]:((~happy(X)<~>~strong(X))<=>(curious(X)&~humble(X))))&
(![X]:((generous(X)|~brave(X))<=>(~patient(X)<~>funny(X))))&
(((~creative(fred)&old(fred)))<=>((strong(fred)|quiet(fred))))&
(![X]:(generous(X)=>(~creative(X)<~>patient(X))))&
(![X]:((~wise(X)&~creative(X))=>happy(X)))&
(?[X]:(~rich(X)))&
((~strong(mary)<~>~humble(mary)))&
(?[X]:((~rich(X)|~funny(X))))&
(?[X]:((old(X)&~brave(X))))&
((~tall(mary)|~kind(mary)))&
(~quiet(paul))&
(?[X]:(~strong(X)))&
(?[X]:((~funny(X)<~>~old(X)))) | strong(mary) | [] | null | 0 |
If someone is either happy or funny then fred is not quiet or not funny and vice versa. Everyone who is both not happy and not quiet is either wise or not happy and vice versa. Everyone who is either not wise or not brave is both curious and not strong. If fred is old then lucy is either wise or not creative and vice versa. Everyone who is either brave or tall is both wise and not brave. If susan is both generous and not generous then someone is strong or generous and vice versa. If alice is kind then someone is humble or old. Everyone who is not wise or generous is both not strong and quiet and vice versa. Everyone who is both kind and humble is either humble or not old and vice versa. If someone is either kind or old then mary is tall or not kind. Everyone who is not calm or not happy is both strong and not tall. Everyone who is calm is curious or strong. If alice is both not humble and brave then someone is both not happy and calm. Everyone who is patient is either not quiet or strong and vice versa. Everyone who is funny or wise is happy. Everyone who is both patient and rich is not funny and vice versa. Someone is brave. Mary is creative or not patient. Fred is happy. Someone is happy or not happy. Someone is either not tall or humble. | Lucy is not humble. | neutral | ((?[X]:((happy(X)<~>funny(X))))<=>((~quiet(fred)|~funny(fred))))&
(![X]:((~happy(X)&~quiet(X))<=>(wise(X)<~>~happy(X))))&
(![X]:((~wise(X)<~>~brave(X))=>(curious(X)&~strong(X))))&
((old(fred))<=>((wise(lucy)<~>~creative(lucy))))&
(![X]:((brave(X)<~>tall(X))=>(wise(X)&~brave(X))))&
(((generous(susan)&~generous(susan)))<=>(?[X]:((strong(X)|generous(X)))))&
((kind(alice))=>(?[X]:((humble(X)|old(X)))))&
(![X]:((~wise(X)|generous(X))<=>(~strong(X)&quiet(X))))&
(![X]:((kind(X)&humble(X))<=>(humble(X)<~>~old(X))))&
((?[X]:((kind(X)<~>old(X))))=>((tall(mary)|~kind(mary))))&
(![X]:((~calm(X)|~happy(X))=>(strong(X)&~tall(X))))&
(![X]:(calm(X)=>(curious(X)|strong(X))))&
(((~humble(alice)&brave(alice)))=>(?[X]:((~happy(X)&calm(X)))))&
(![X]:(patient(X)<=>(~quiet(X)<~>strong(X))))&
(![X]:((funny(X)|wise(X))=>happy(X)))&
(![X]:((patient(X)&rich(X))<=>~funny(X)))&
(?[X]:(brave(X)))&
((creative(mary)|~patient(mary)))&
(happy(fred))&
(?[X]:((happy(X)|~happy(X))))&
(?[X]:((~tall(X)<~>humble(X)))) | ~humble(lucy) | [] | null | 0 |
If someone is old or wise then alice is calm. Everyone who is either not kind or not happy is either not quiet or old and vice versa. If someone is not old then susan is not funny. If mary is patient then someone is not calm and vice versa. If john is either not happy or rich then someone is old or not strong and vice versa. Everyone who is not quiet or not happy is both not funny and rich and vice versa. Everyone who is either not quiet or calm is both kind and not brave and vice versa. Everyone who is either old or not strong is both patient and not happy and vice versa. Everyone who is both not curious and rich is not strong. Everyone who is both not calm and not quiet is both calm and not creative. Everyone who is both not calm and curious is not funny or not quiet and vice versa. If someone is not creative or strong then fred is quiet or humble. If mary is either humble or happy then someone is not happy or humble and vice versa. Everyone who is either quiet or tall is either not tall or brave and vice versa. Everyone who is quiet or not rich is both quiet and not wise. Someone is kind or funny. Someone is rich or not kind. Someone is either strong or not tall. Someone is either generous or not quiet. Susan is not rich or old. Mary is not kind or not tall. | Alice is wise. | contradiction | ((?[X]:((old(X)|wise(X))))=>(calm(alice)))&
(![X]:((~kind(X)<~>~happy(X))<=>(~quiet(X)<~>old(X))))&
((?[X]:(~old(X)))=>(~funny(susan)))&
((patient(mary))<=>(?[X]:(~calm(X))))&
(((~happy(john)<~>rich(john)))<=>(?[X]:((old(X)|~strong(X)))))&
(![X]:((~quiet(X)|~happy(X))<=>(~funny(X)&rich(X))))&
(![X]:((~quiet(X)<~>calm(X))<=>(kind(X)&~brave(X))))&
(![X]:((old(X)<~>~strong(X))<=>(patient(X)&~happy(X))))&
(![X]:((~curious(X)&rich(X))=>~strong(X)))&
(![X]:((~calm(X)&~quiet(X))=>(calm(X)&~creative(X))))&
(![X]:((~calm(X)&curious(X))<=>(~funny(X)|~quiet(X))))&
((?[X]:((~creative(X)|strong(X))))=>((quiet(fred)|humble(fred))))&
(((humble(mary)<~>happy(mary)))<=>(?[X]:((~happy(X)|humble(X)))))&
(![X]:((quiet(X)<~>tall(X))<=>(~tall(X)<~>brave(X))))&
(![X]:((quiet(X)|~rich(X))=>(quiet(X)&~wise(X))))&
(?[X]:((kind(X)|funny(X))))&
(?[X]:((rich(X)|~kind(X))))&
(?[X]:((strong(X)<~>~tall(X))))&
(?[X]:((generous(X)<~>~quiet(X))))&
((~rich(susan)|old(susan)))&
((~kind(mary)|~tall(mary))) | wise(alice) | [
"p9",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2118836788005547582529051
% SZS output start Proof for 2118836788005547582529051
10. ! [X0] : ((~quiet(X0) & ~calm(X0)) => (~creative(X0) & calm(X0))) [input p9]
11. ! [X0] : ((curious(X0) & ~calm(X0)) <=> (~quiet(X0) | ~funny(X0))) [input p10]
15. ! [X0] : ((~rich(X0) | quiet(X0)) => (~wise(X0) & quiet(X0))) [input p14]
22. wise(alice) [input hypothesis]
27. ! [X0] : ((~creative(X0) & calm(X0)) | (quiet(X0) | calm(X0))) [ennf transformation 10]
28. ! [X0] : ((~creative(X0) & calm(X0)) | quiet(X0) | calm(X0)) [flattening 27]
31. ! [X0] : ((~wise(X0) & quiet(X0)) | (rich(X0) & ~quiet(X0))) [ennf transformation 15]
47. ! [X0] : (((curious(X0) & ~calm(X0)) | (quiet(X0) & funny(X0))) & ((~quiet(X0) | ~funny(X0)) | (~curious(X0) | calm(X0)))) [nnf transformation 11]
48. ! [X0] : (((curious(X0) & ~calm(X0)) | (quiet(X0) & funny(X0))) & (~quiet(X0) | ~funny(X0) | ~curious(X0) | calm(X0))) [flattening 47]
101. calm(X0) | quiet(X0) | calm(X0) [cnf transformation 28]
105. ~calm(X0) | quiet(X0) [cnf transformation 48]
126. ~wise(X0) | ~quiet(X0) [cnf transformation 31]
136. wise(alice) [cnf transformation 22]
141. calm(X0) | quiet(X0) [duplicate literal removal 101]
143. 1 <=> ! [X0] : ~wise(X0) [avatar definition]
144. ~wise(X0) <- (1) [avatar component clause 143]
200. quiet(X0) [subsumption resolution 105,141]
233. ~wise(X0) [subsumption resolution 126,200]
234. 1 [avatar split clause 233,143]
282. $false <- (1) [resolution 144,136]
283. ~1 [avatar contradiction clause 282]
284. $false [avatar sat refutation 234,283]
% SZS output end Proof for 2118836788005547582529051
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 fred is both not creative and not humble then someone is not funny or not kind and vice versa.
Everyone who is not humble is creative.
Everyone who is either wise or not rich is not generous.
If someone is not patient then someone is either old or quiet.
Everyone who is both not curious and not generous is not strong.
Everyone who is both happy and generous is not strong and vice versa.
Everyone who is rich or creative is not generous or humble and vice versa.
If someone is either not strong or not quiet then someone is tall or not wise.
Everyone who is strong or not happy is funny or not curious.
If fred is both not humble and happy then someone is either not creative or strong.
Everyone who is either not quiet or quiet is either kind or brave and vice versa.
Everyone who is either brave or not quiet is kind or brave.
If someone is both not old and not brave then someone is either curious or wise.
Everyone who is curious is either not calm or creative.
Everyone who is either wise or brave is not wise or not strong.
Everyone who is either kind or wise is rich.
Someone is either not calm or quiet.
Lucy is either not wise or patient.
Susan is not strong.
Mary is rich.
Mary is not brave.
Alice is not strong.
Fred is not tall or not humble. | Mary is wise. | contradiction | (((~creative(fred)&~humble(fred)))<=>(?[X]:((~funny(X)|~kind(X)))))&
(![X]:(~humble(X)=>creative(X)))&
(![X]:((wise(X)<~>~rich(X))=>~generous(X)))&
((?[X]:(~patient(X)))=>(?[X]:((old(X)<~>quiet(X)))))&
(![X]:((~curious(X)&~generous(X))=>~strong(X)))&
(![X]:((happy(X)&generous(X))<=>~strong(X)))&
(![X]:((rich(X)|creative(X))<=>(~generous(X)|humble(X))))&
((?[X]:((~strong(X)<~>~quiet(X))))=>(?[X]:((tall(X)|~wise(X)))))&
(![X]:((strong(X)|~happy(X))=>(funny(X)|~curious(X))))&
(((~humble(fred)&happy(fred)))=>(?[X]:((~creative(X)<~>strong(X)))))&
(![X]:((~quiet(X)<~>quiet(X))<=>(kind(X)<~>brave(X))))&
(![X]:((brave(X)<~>~quiet(X))=>(kind(X)|brave(X))))&
((?[X]:((~old(X)&~brave(X))))=>(?[X]:((curious(X)<~>wise(X)))))&
(![X]:(curious(X)=>(~calm(X)<~>creative(X))))&
(![X]:((wise(X)<~>brave(X))=>(~wise(X)|~strong(X))))&
(![X]:((kind(X)<~>wise(X))=>rich(X)))&
(?[X]:((~calm(X)<~>quiet(X))))&
((~wise(lucy)<~>patient(lucy)))&
(~strong(susan))&
(rich(mary))&
(~brave(mary))&
(~strong(alice))&
((~tall(fred)|~humble(fred))) | wise(mary) | [
"p2",
"p5",
"p14",
"p19",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 4520699499345594664377288
% SZS output start Proof for 4520699499345594664377288
3. ! [X0] : ((wise(X0) <~> ~rich(X0)) => ~generous(X0)) [input p2]
6. ! [X0] : ((generous(X0) & happy(X0)) <=> ~strong(X0)) [input p5]
15. ! [X0] : ((wise(X0) <~> brave(X0)) => (~strong(X0) | ~wise(X0))) [input p14]
20. rich(mary) [input p19]
21. ~brave(mary) [input p20]
24. wise(mary) [input hypothesis]
29. ! [X0] : (~generous(X0) | (wise(X0) <=> ~rich(X0))) [ennf transformation 3]
42. ! [X0] : ((~strong(X0) | ~wise(X0)) | (wise(X0) <=> brave(X0))) [ennf transformation 15]
43. ! [X0] : (~strong(X0) | ~wise(X0) | (wise(X0) <=> brave(X0))) [flattening 42]
50. ! [X0] : (~generous(X0) | ((wise(X0) | rich(X0)) & (~rich(X0) | ~wise(X0)))) [nnf transformation 29]
55. ! [X0] : (((generous(X0) & happy(X0)) | strong(X0)) & (~strong(X0) | (~generous(X0) | ~happy(X0)))) [nnf transformation 6]
56. ! [X0] : (((generous(X0) & happy(X0)) | strong(X0)) & (~strong(X0) | ~generous(X0) | ~happy(X0))) [flattening 55]
73. ! [X0] : (~strong(X0) | ~wise(X0) | ((wise(X0) | ~brave(X0)) & (brave(X0) | ~wise(X0)))) [nnf transformation 43]
85. ~generous(X0) | ~rich(X0) | ~wise(X0) [cnf transformation 50]
92. strong(X0) | generous(X0) [cnf transformation 56]
117. ~strong(X0) | ~wise(X0) | brave(X0) | ~wise(X0) [cnf transformation 73]
126. rich(mary) [cnf transformation 20]
127. ~brave(mary) [cnf transformation 21]
130. wise(mary) [cnf transformation 24]
131. ~strong(X0) | ~wise(X0) | brave(X0) [duplicate literal removal 117]
350. ~wise(X0) | brave(X0) | generous(X0) [resolution 131,92]
369. brave(mary) | generous(mary) [resolution 350,130]
371. generous(mary) [subsumption resolution 369,127]
373. ~rich(mary) | ~wise(mary) [resolution 371,85]
375. ~wise(mary) [subsumption resolution 373,126]
376. $false [subsumption resolution 375,130]
% SZS output end Proof for 4520699499345594664377288
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong or creative is not old and vice versa.
Everyone who is both wise and creative is both curious and generous and vice versa.
Everyone who is funny or not creative is both not strong and not wise.
If someone is not rich then john is either brave or funny.
If lucy is both curious and rich then someone is not rich.
Everyone who is both not quiet and strong is not creative and vice versa.
If someone is either not tall or not strong then someone is both strong and not curious.
Everyone who is creative or not rich is quiet.
If paul is either patient or not strong then someone is both brave and not calm and vice versa.
Everyone who is both not creative and strong is not wise and vice versa.
If susan is quiet then mary is quiet or not creative and vice versa.
If alice is not tall or not funny then paul is both rich and kind.
Everyone who is both not humble and not brave is both kind and calm.
If lucy is not rich then someone is both generous and not rich.
Susan is funny or not calm.
Someone is not brave or brave.
John is patient.
Mary is either not generous or not kind.
Someone is not old or not kind. | Mary is not funny. | entailment | (![X]:((strong(X)|creative(X))<=>~old(X)))&
(![X]:((wise(X)&creative(X))<=>(curious(X)&generous(X))))&
(![X]:((funny(X)|~creative(X))=>(~strong(X)&~wise(X))))&
((?[X]:(~rich(X)))=>((brave(john)<~>funny(john))))&
(((curious(lucy)&rich(lucy)))=>(?[X]:(~rich(X))))&
(![X]:((~quiet(X)&strong(X))<=>~creative(X)))&
((?[X]:((~tall(X)<~>~strong(X))))=>(?[X]:((strong(X)&~curious(X)))))&
(![X]:((creative(X)|~rich(X))=>quiet(X)))&
(((patient(paul)<~>~strong(paul)))<=>(?[X]:((brave(X)&~calm(X)))))&
(![X]:((~creative(X)&strong(X))<=>~wise(X)))&
((quiet(susan))<=>((quiet(mary)|~creative(mary))))&
(((~tall(alice)|~funny(alice)))=>((rich(paul)&kind(paul))))&
(![X]:((~humble(X)&~brave(X))=>(kind(X)&calm(X))))&
((~rich(lucy))=>(?[X]:((generous(X)&~rich(X)))))&
((funny(susan)|~calm(susan)))&
(?[X]:((~brave(X)|brave(X))))&
(patient(john))&
((~generous(mary)<~>~kind(mary)))&
(?[X]:((~old(X)|~kind(X)))) | ~funny(mary) | [
"p2",
"p5",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 5466575086476157943461651
% SZS output start Proof for 5466575086476157943461651
3. ! [X0] : ((~creative(X0) | funny(X0)) => (~wise(X0) & ~strong(X0))) [input p2]
6. ! [X0] : ((strong(X0) & ~quiet(X0)) <=> ~creative(X0)) [input p5]
10. ! [X0] : ((strong(X0) & ~creative(X0)) <=> ~wise(X0)) [input p9]
20. funny(mary) [input hypothesis]
26. ! [X0] : ((~wise(X0) & ~strong(X0)) | (creative(X0) & ~funny(X0))) [ennf transformation 3]
39. ! [X0] : (((strong(X0) & ~quiet(X0)) | creative(X0)) & (~creative(X0) | (~strong(X0) | quiet(X0)))) [nnf transformation 6]
40. ! [X0] : (((strong(X0) & ~quiet(X0)) | creative(X0)) & (~creative(X0) | ~strong(X0) | quiet(X0))) [flattening 39]
49. ! [X0] : (((strong(X0) & ~creative(X0)) | wise(X0)) & (~wise(X0) | (~strong(X0) | creative(X0)))) [nnf transformation 10]
50. ! [X0] : (((strong(X0) & ~creative(X0)) | wise(X0)) & (~wise(X0) | ~strong(X0) | creative(X0))) [flattening 49]
66. ~strong(X0) | creative(X0) [cnf transformation 26]
67. ~funny(X0) | ~wise(X0) [cnf transformation 26]
74. strong(X0) | creative(X0) [cnf transformation 40]
88. ~creative(X0) | wise(X0) [cnf transformation 50]
105. funny(mary) [cnf transformation 20]
132. creative(X0) [subsumption resolution 74,66]
178. wise(X0) [subsumption resolution 88,132]
239. ~wise(mary) [resolution 67,105]
241. $false [subsumption resolution 239,178]
% SZS output end Proof for 5466575086476157943461651
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either patient or not humble is not kind or not creative and vice versa.
Everyone who is either not rich or not generous is both not kind and not brave.
If john is old or calm then someone is not strong or curious and vice versa.
If someone is strong or wise then fred is not tall or not patient and vice versa.
If someone is funny or quiet then mary is not calm and vice versa.
Everyone who is either kind or not wise is either rich or kind and vice versa.
If mary is both generous and not brave then lucy is wise or quiet.
Everyone who is brave or creative is patient or not strong and vice versa.
Everyone who is both not old and creative is both happy and not old and vice versa.
If susan is either humble or not tall then someone is both wise and not brave and vice versa.
Everyone who is wise is generous and vice versa.
If fred is not quiet then john is rich.
Everyone who is both not calm and not curious is both not kind and happy and vice versa.
If fred is not strong or humble then someone is not funny or not quiet.
If someone is not strong or not old then someone is either not humble or quiet.
Everyone who is patient is not patient.
Someone is either wise or brave.
Alice is rich or not wise.
Someone is either not happy or not kind.
Someone is old or patient.
Someone is creative or humble.
Mary is either kind or happy.
Mary is creative. | Mary is wise. | neutral | (![X]:((patient(X)<~>~humble(X))<=>(~kind(X)|~creative(X))))&
(![X]:((~rich(X)<~>~generous(X))=>(~kind(X)&~brave(X))))&
(((old(john)|calm(john)))<=>(?[X]:((~strong(X)|curious(X)))))&
((?[X]:((strong(X)|wise(X))))<=>((~tall(fred)|~patient(fred))))&
((?[X]:((funny(X)|quiet(X))))<=>(~calm(mary)))&
(![X]:((kind(X)<~>~wise(X))<=>(rich(X)<~>kind(X))))&
(((generous(mary)&~brave(mary)))=>((wise(lucy)|quiet(lucy))))&
(![X]:((brave(X)|creative(X))<=>(patient(X)|~strong(X))))&
(![X]:((~old(X)&creative(X))<=>(happy(X)&~old(X))))&
(((humble(susan)<~>~tall(susan)))<=>(?[X]:((wise(X)&~brave(X)))))&
(![X]:(wise(X)<=>generous(X)))&
((~quiet(fred))=>(rich(john)))&
(![X]:((~calm(X)&~curious(X))<=>(~kind(X)&happy(X))))&
(((~strong(fred)|humble(fred)))=>(?[X]:((~funny(X)|~quiet(X)))))&
((?[X]:((~strong(X)|~old(X))))=>(?[X]:((~humble(X)<~>quiet(X)))))&
(![X]:(patient(X)=>~patient(X)))&
(?[X]:((wise(X)<~>brave(X))))&
((rich(alice)|~wise(alice)))&
(?[X]:((~happy(X)<~>~kind(X))))&
(?[X]:((old(X)|patient(X))))&
(?[X]:((creative(X)|humble(X))))&
((kind(mary)<~>happy(mary)))&
(creative(mary)) | wise(mary) | [] | null | 0 |
Everyone who is kind or not quiet is not funny or not kind and vice versa.
Everyone who is strong or patient is either strong or old and vice versa.
If someone is creative then lucy is calm.
If john is funny then mary is not generous or funny.
Everyone who is not patient or not strong is kind.
Everyone who is creative or not funny is not tall or patient.
Everyone who is not strong is quiet.
If paul is not happy or brave then someone is both brave and not wise and vice versa.
Everyone who is either not curious or not quiet is either brave or not generous.
If someone is not kind then someone is calm or brave.
Everyone who is not wise or not generous is brave or generous.
Everyone who is both quiet and brave is not humble or not quiet and vice versa.
If alice is not funny then someone is both not happy and tall.
Everyone who is both creative and not brave is either not generous or not happy.
Everyone who is both not calm and not humble is both generous and not kind and vice versa.
Everyone who is both not rich and old is not humble.
Someone is either not generous or patient.
Susan is either not funny or funny.
Lucy is both not curious and not wise.
Someone is curious or not brave.
Someone is either not patient or calm.
Paul is strong or curious.
Someone is either not curious or not tall.
Lucy is not funny or not curious. | Lucy is quiet. | entailment | (![X]:((kind(X)|~quiet(X))<=>(~funny(X)|~kind(X))))&
(![X]:((strong(X)|patient(X))<=>(strong(X)<~>old(X))))&
((?[X]:(creative(X)))=>(calm(lucy)))&
((funny(john))=>((~generous(mary)|funny(mary))))&
(![X]:((~patient(X)|~strong(X))=>kind(X)))&
(![X]:((creative(X)|~funny(X))=>(~tall(X)|patient(X))))&
(![X]:(~strong(X)=>quiet(X)))&
(((~happy(paul)|brave(paul)))<=>(?[X]:((brave(X)&~wise(X)))))&
(![X]:((~curious(X)<~>~quiet(X))=>(brave(X)<~>~generous(X))))&
((?[X]:(~kind(X)))=>(?[X]:((calm(X)|brave(X)))))&
(![X]:((~wise(X)|~generous(X))=>(brave(X)|generous(X))))&
(![X]:((quiet(X)&brave(X))<=>(~humble(X)|~quiet(X))))&
((~funny(alice))=>(?[X]:((~happy(X)&tall(X)))))&
(![X]:((creative(X)&~brave(X))=>(~generous(X)<~>~happy(X))))&
(![X]:((~calm(X)&~humble(X))<=>(generous(X)&~kind(X))))&
(![X]:((~rich(X)&old(X))=>~humble(X)))&
(?[X]:((~generous(X)<~>patient(X))))&
((~funny(susan)<~>funny(susan)))&
((~curious(lucy)&~wise(lucy)))&
(?[X]:((curious(X)|~brave(X))))&
(?[X]:((~patient(X)<~>calm(X))))&
((strong(paul)|curious(paul)))&
(?[X]:((~curious(X)<~>~tall(X))))&
((~funny(lucy)|~curious(lucy))) | quiet(lucy) | [
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 6799211642039654275384001
% SZS output start Proof for 6799211642039654275384001
12. ! [X0] : ((brave(X0) & quiet(X0)) <=> (~quiet(X0) | ~humble(X0))) [input p11]
25. ~quiet(lucy) [input hypothesis]
55. ! [X0] : (((brave(X0) & quiet(X0)) | (quiet(X0) & humble(X0))) & ((~quiet(X0) | ~humble(X0)) | (~brave(X0) | ~quiet(X0)))) [nnf transformation 12]
56. ! [X0] : (((brave(X0) & quiet(X0)) | (quiet(X0) & humble(X0))) & (~quiet(X0) | ~humble(X0) | ~brave(X0) | ~quiet(X0))) [flattening 55]
102. quiet(X0) | quiet(X0) [cnf transformation 56]
124. ~quiet(lucy) [cnf transformation 25]
126. quiet(X0) [duplicate literal removal 102]
244. $false [subsumption resolution 124,126]
% SZS output end Proof for 6799211642039654275384001
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient then someone is both old and generous. If fred is both not curious and not rich then someone is quiet. Everyone who is both not humble and humble is either not funny or old and vice versa. 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. Someone is not humble or not tall. Someone is not kind. Someone is both old and not generous. Mary is not rich or strong. Paul is both funny and not old. | Susan is creative. | contradiction | ((?[X]:(patient(X)))=>(?[X]:((old(X)&generous(X)))))&
(((~curious(fred)&~rich(fred)))=>(?[X]:(quiet(X))))&
(![X]:((~humble(X)&humble(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]:((~humble(X)|~tall(X))))&
(?[X]:(~kind(X)))&
(?[X]:((old(X)&~generous(X))))&
((~rich(mary)|strong(mary)))&
((funny(paul)&~old(paul))) | creative(susan) | [
"p4",
"p6",
"p10",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1438436800318089627659660
% SZS output start Proof for 1438436800318089627659660
5. ! [X0] : ((creative(X0) & tall(X0)) => ~humble(X0)) [input p4]
7. ? [X0] : (~curious(X0) | creative(X0)) <=> ? [X0] : (wise(X0) & old(X0)) [input p6]
11. ! [X0] : ((tall(X0) & creative(X0)) <=> wise(X0)) [input p10]
16. ! [X0] : ((humble(X0) & calm(X0)) <=> (wise(X0) | ~funny(X0))) [input p15]
22. creative(susan) [input hypothesis]
24. ? [X0] : (~curious(X0) | creative(X0)) <=> ? [X1] : (wise(X1) & old(X1)) [rectify 7]
29. ! [X0] : (~humble(X0) | (~creative(X0) | ~tall(X0))) [ennf transformation 5]
30. ! [X0] : (~humble(X0) | ~creative(X0) | ~tall(X0)) [flattening 29]
48. (? [X0] : (~curious(X0) | creative(X0)) | ! [X1] : (~wise(X1) | ~old(X1))) & (? [X1] : (wise(X1) & old(X1)) | ! [X0] : (curious(X0) & ~creative(X0))) [nnf transformation 24]
49. (? [X0] : (~curious(X0) | creative(X0)) | ! [X1] : (~wise(X1) | ~old(X1))) & (? [X2] : (wise(X2) & old(X2)) | ! [X3] : (curious(X3) & ~creative(X3))) [rectify 48]
50. ? [X0] : (~curious(X0) | creative(X0)) => (~curious(sK2) | creative(sK2)) [choice axiom]
51. ? [X2] : (wise(X2) & old(X2)) => (wise(sK3) & old(sK3)) [choice axiom]
52. ((~curious(sK2) | creative(sK2)) | ! [X1] : (~wise(X1) | ~old(X1))) & ((wise(sK3) & old(sK3)) | ! [X3] : (curious(X3) & ~creative(X3))) [skolemisation 49,51,50]
54. ! [X0] : (((tall(X0) & creative(X0)) | ~wise(X0)) & (wise(X0) | (~tall(X0) | ~creative(X0)))) [nnf transformation 11]
55. ! [X0] : (((tall(X0) & creative(X0)) | ~wise(X0)) & (wise(X0) | ~tall(X0) | ~creative(X0))) [flattening 54]
67. ! [X0] : (((humble(X0) & calm(X0)) | (~wise(X0) & funny(X0))) & ((wise(X0) | ~funny(X0)) | (~humble(X0) | ~calm(X0)))) [nnf transformation 16]
68. ! [X0] : (((humble(X0) & calm(X0)) | (~wise(X0) & funny(X0))) & (wise(X0) | ~funny(X0) | ~humble(X0) | ~calm(X0))) [flattening 67]
88. ~creative(X0) | ~humble(X0) | ~tall(X0) [cnf transformation 30]
95. wise(sK3) | ~creative(X3) [cnf transformation 52]
105. ~wise(X0) | creative(X0) [cnf transformation 55]
106. ~wise(X0) | tall(X0) [cnf transformation 55]
129. ~wise(X0) | humble(X0) [cnf transformation 68]
137. creative(susan) [cnf transformation 22]
184. 11 <=> wise(sK3) [avatar definition]
186. wise(sK3) <- (11) [avatar component clause 184]
189. 12 <=> ! [X3] : ~creative(X3) [avatar definition]
190. ~creative(X3) <- (12) [avatar component clause 189]
191. 12 | 11 [avatar split clause 95,184,189]
318. $false <- (12) [resolution 190,137]
319. ~12 [avatar contradiction clause 318]
322. creative(sK3) <- (11) [resolution 105,186]
323. tall(sK3) <- (11) [resolution 106,186]
327. humble(sK3) <- (11) [resolution 129,186]
393. ~humble(sK3) | ~tall(sK3) <- (11) [resolution 88,322]
395. ~tall(sK3) <- (11) [subsumption resolution 393,327]
396. $false <- (11) [subsumption resolution 395,323]
397. ~11 [avatar contradiction clause 396]
407. $false [avatar sat refutation 191,319,397]
% SZS output end Proof for 1438436800318089627659660
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If fred is generous then alice is both tall and not happy and vice versa. Everyone who is not rich or generous is not old. Everyone who is either not humble or happy is not tall or old. If fred is both not rich and funny then paul is both not happy and strong and vice versa. If someone is not kind or curious then susan is wise. If susan is not calm or not patient then someone is either patient or not brave. Everyone who is either happy or not rich is happy and vice versa. Everyone who is both not rich and not funny is creative and vice versa. If someone is not quiet or rich then alice is kind and vice versa. Everyone who is curious is both not tall and not funny. If someone is both curious and not rich then susan is not brave or patient. If someone is both calm and wise then john is either not tall or creative and vice versa. If paul is both not calm and not rich then someone is not curious and vice versa. If someone is not happy or generous then susan is not tall or happy and vice versa. If someone is wise then susan is not happy or not tall. Everyone who is not wise or not brave is funny or kind and vice versa. Someone is wise. Someone is tall or not creative. Someone is not kind or humble. Someone is either strong or not humble. Susan is old or kind. Someone is funny or not happy. | John is creative. | contradiction | ((generous(fred))<=>((tall(alice)&~happy(alice))))&
(![X]:((~rich(X)|generous(X))=>~old(X)))&
(![X]:((~humble(X)<~>happy(X))=>(~tall(X)|old(X))))&
(((~rich(fred)&funny(fred)))<=>((~happy(paul)&strong(paul))))&
((?[X]:((~kind(X)|curious(X))))=>(wise(susan)))&
(((~calm(susan)|~patient(susan)))=>(?[X]:((patient(X)<~>~brave(X)))))&
(![X]:((happy(X)<~>~rich(X))<=>happy(X)))&
(![X]:((~rich(X)&~funny(X))<=>creative(X)))&
((?[X]:((~quiet(X)|rich(X))))<=>(kind(alice)))&
(![X]:(curious(X)=>(~tall(X)&~funny(X))))&
((?[X]:((curious(X)&~rich(X))))=>((~brave(susan)|patient(susan))))&
((?[X]:((calm(X)&wise(X))))<=>((~tall(john)<~>creative(john))))&
(((~calm(paul)&~rich(paul)))<=>(?[X]:(~curious(X))))&
((?[X]:((~happy(X)|generous(X))))<=>((~tall(susan)|happy(susan))))&
((?[X]:(wise(X)))=>((~happy(susan)|~tall(susan))))&
(![X]:((~wise(X)|~brave(X))<=>(funny(X)|kind(X))))&
(?[X]:(wise(X)))&
(?[X]:((tall(X)|~creative(X))))&
(?[X]:((~kind(X)|humble(X))))&
(?[X]:((strong(X)<~>~humble(X))))&
((old(susan)|kind(susan)))&
(?[X]:((funny(X)|~happy(X)))) | creative(john) | [
"p6",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 3290171602612564084723670
% SZS output start Proof for 3290171602612564084723670
7. ! [X0] : ((happy(X0) <~> ~rich(X0)) <=> happy(X0)) [input p6]
8. ! [X0] : ((~funny(X0) & ~rich(X0)) <=> creative(X0)) [input p7]
23. creative(john) [input hypothesis]
42. ! [X0] : ((((rich(X0) | ~happy(X0)) & (~rich(X0) | happy(X0))) | ~happy(X0)) & (happy(X0) | ((happy(X0) | rich(X0)) & (~rich(X0) | ~happy(X0))))) [nnf transformation 7]
43. ! [X0] : (((~funny(X0) & ~rich(X0)) | ~creative(X0)) & (creative(X0) | (funny(X0) | rich(X0)))) [nnf transformation 8]
44. ! [X0] : (((~funny(X0) & ~rich(X0)) | ~creative(X0)) & (creative(X0) | funny(X0) | rich(X0))) [flattening 43]
94. happy(X0) | happy(X0) | rich(X0) [cnf transformation 42]
96. rich(X0) | ~happy(X0) | ~happy(X0) [cnf transformation 42]
98. ~rich(X0) | ~creative(X0) [cnf transformation 44]
131. creative(john) [cnf transformation 23]
132. happy(X0) | rich(X0) [duplicate literal removal 94]
133. rich(X0) | ~happy(X0) [duplicate literal removal 96]
201. rich(X0) [subsumption resolution 132,133]
202. ~creative(X0) [subsumption resolution 98,201]
293. $false [subsumption resolution 131,202]
% SZS output end Proof for 3290171602612564084723670
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble or brave then someone is creative and vice versa.
If lucy is both not patient and not creative then susan is not calm or not funny and vice versa.
Everyone who is not brave or not wise is not strong or wise.
Everyone who is both not calm and calm is funny or patient and vice versa.
Everyone who is not curious or generous is funny or quiet.
If someone is wise or not rich then someone is either calm or tall and vice versa.
If someone is funny or happy then someone is either strong or calm.
Everyone who is not patient or kind is both not quiet and tall.
If fred is not strong then someone is creative.
If someone is both curious and strong then lucy is not kind.
If someone is patient then someone is humble or brave and vice versa.
If mary is both not strong and not curious then susan is both not curious and wise and vice versa.
Everyone who is funny is both not rich and not patient and vice versa.
Someone is either calm or not patient.
Someone is either not wise or not calm.
Mary is not humble.
Someone is wise or old. | Mary is not funny. | entailment | ((?[X]:((humble(X)|brave(X))))<=>(?[X]:(creative(X))))&
(((~patient(lucy)&~creative(lucy)))<=>((~calm(susan)|~funny(susan))))&
(![X]:((~brave(X)|~wise(X))=>(~strong(X)|wise(X))))&
(![X]:((~calm(X)&calm(X))<=>(funny(X)|patient(X))))&
(![X]:((~curious(X)|generous(X))=>(funny(X)|quiet(X))))&
((?[X]:((wise(X)|~rich(X))))<=>(?[X]:((calm(X)<~>tall(X)))))&
((?[X]:((funny(X)|happy(X))))=>(?[X]:((strong(X)<~>calm(X)))))&
(![X]:((~patient(X)|kind(X))=>(~quiet(X)&tall(X))))&
((~strong(fred))=>(?[X]:(creative(X))))&
((?[X]:((curious(X)&strong(X))))=>(~kind(lucy)))&
((?[X]:(patient(X)))<=>(?[X]:((humble(X)|brave(X)))))&
(((~strong(mary)&~curious(mary)))<=>((~curious(susan)&wise(susan))))&
(![X]:(funny(X)<=>(~rich(X)&~patient(X))))&
(?[X]:((calm(X)<~>~patient(X))))&
(?[X]:((~wise(X)<~>~calm(X))))&
(~humble(mary))&
(?[X]:((wise(X)|old(X)))) | ~funny(mary) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 3866682734131264843710249
% SZS output start Proof for 3866682734131264843710249
4. ! [X0] : ((calm(X0) & ~calm(X0)) <=> (patient(X0) | funny(X0))) [input p3]
18. funny(mary) [input hypothesis]
42. ! [X0] : (((calm(X0) & ~calm(X0)) | (~patient(X0) & ~funny(X0))) & ((patient(X0) | funny(X0)) | (~calm(X0) | calm(X0)))) [nnf transformation 4]
43. ! [X0] : (((calm(X0) & ~calm(X0)) | (~patient(X0) & ~funny(X0))) & (patient(X0) | funny(X0) | ~calm(X0) | calm(X0))) [flattening 42]
81. ~calm(X0) | ~funny(X0) [cnf transformation 43]
83. calm(X0) | ~funny(X0) [cnf transformation 43]
112. funny(mary) [cnf transformation 18]
160. ~funny(X0) [subsumption resolution 81,83]
245. $false [subsumption resolution 112,160]
% SZS output end Proof for 3866682734131264843710249
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall then susan is both not kind and rich and vice versa. If someone is both not creative and wise then someone is not rich or not humble. Everyone who is either not tall or humble is both rich and calm and vice versa. If paul is not brave then john is humble or old and vice versa. Everyone who is either creative or brave is both brave and not creative and vice versa. If alice is curious then susan is not patient. Everyone who is not funny or not wise is both not creative and curious and vice versa. Everyone who is not old is either strong or not funny. Everyone who is not wise or not creative is calm and vice versa. If someone is either rich or funny then someone is either not calm or not strong. Everyone who is not creative is not quiet and vice versa. Everyone who is funny or curious is rich or not rich. Everyone who is either patient or not kind is rich and vice versa. Everyone who is happy is both not funny and creative. If someone is not patient or curious then someone is either kind or not patient and vice versa. If paul is both brave and not quiet then someone is not quiet and vice versa. Someone is either curious or old. Lucy is both not tall and not generous. Someone is creative or happy. Paul is either creative or happy. Paul is happy or creative. Mary is quiet or not kind. | Lucy is not old. | neutral | ((?[X]:(~tall(X)))<=>((~kind(susan)&rich(susan))))&
((?[X]:((~creative(X)&wise(X))))=>(?[X]:((~rich(X)|~humble(X)))))&
(![X]:((~tall(X)<~>humble(X))<=>(rich(X)&calm(X))))&
((~brave(paul))<=>((humble(john)|old(john))))&
(![X]:((creative(X)<~>brave(X))<=>(brave(X)&~creative(X))))&
((curious(alice))=>(~patient(susan)))&
(![X]:((~funny(X)|~wise(X))<=>(~creative(X)&curious(X))))&
(![X]:(~old(X)=>(strong(X)<~>~funny(X))))&
(![X]:((~wise(X)|~creative(X))<=>calm(X)))&
((?[X]:((rich(X)<~>funny(X))))=>(?[X]:((~calm(X)<~>~strong(X)))))&
(![X]:(~creative(X)<=>~quiet(X)))&
(![X]:((funny(X)|curious(X))=>(rich(X)|~rich(X))))&
(![X]:((patient(X)<~>~kind(X))<=>rich(X)))&
(![X]:(happy(X)=>(~funny(X)&creative(X))))&
((?[X]:((~patient(X)|curious(X))))<=>(?[X]:((kind(X)<~>~patient(X)))))&
(((brave(paul)&~quiet(paul)))<=>(?[X]:(~quiet(X))))&
(?[X]:((curious(X)<~>old(X))))&
((~tall(lucy)&~generous(lucy)))&
(?[X]:((creative(X)|happy(X))))&
((creative(paul)<~>happy(paul)))&
((happy(paul)|creative(paul)))&
((quiet(mary)|~kind(mary))) | ~old(lucy) | [] | null | 0 |
Everyone who is not generous or generous is not rich and vice versa.
Everyone who is not funny or quiet is not patient and vice versa.
Everyone who is not old is generous.
If someone is both patient and brave then alice is not creative or generous and vice versa.
Everyone who is both curious and not kind is either rich or not old.
Everyone who is both not happy and not old is both not quiet and not curious and vice versa.
If mary is curious then fred is both not brave and funny.
If lucy is either not rich or kind then someone is not brave and vice versa.
Everyone who is calm is not funny.
Everyone who is humble is both not generous and generous.
Everyone who is not quiet or not old is either not humble or curious and vice versa.
Everyone who is patient or not creative is not patient or not brave.
If someone is both wise and old then susan is both wise and patient.
If john is not brave or not calm then someone is rich and vice versa.
If paul is both creative and not calm then susan is either not kind or humble and vice versa.
If lucy is happy then mary is both not patient and funny and vice versa.
Someone is both funny and brave.
John is not patient.
Paul is both not patient and not curious.
John is either not kind or not calm.
Lucy is either not generous or funny.
Lucy is not rich or wise. | Fred is patient. | neutral | (![X]:((~generous(X)|generous(X))<=>~rich(X)))&
(![X]:((~funny(X)|quiet(X))<=>~patient(X)))&
(![X]:(~old(X)=>generous(X)))&
((?[X]:((patient(X)&brave(X))))<=>((~creative(alice)|generous(alice))))&
(![X]:((curious(X)&~kind(X))=>(rich(X)<~>~old(X))))&
(![X]:((~happy(X)&~old(X))<=>(~quiet(X)&~curious(X))))&
((curious(mary))=>((~brave(fred)&funny(fred))))&
(((~rich(lucy)<~>kind(lucy)))<=>(?[X]:(~brave(X))))&
(![X]:(calm(X)=>~funny(X)))&
(![X]:(humble(X)=>(~generous(X)&generous(X))))&
(![X]:((~quiet(X)|~old(X))<=>(~humble(X)<~>curious(X))))&
(![X]:((patient(X)|~creative(X))=>(~patient(X)|~brave(X))))&
((?[X]:((wise(X)&old(X))))=>((wise(susan)&patient(susan))))&
(((~brave(john)|~calm(john)))<=>(?[X]:(rich(X))))&
(((creative(paul)&~calm(paul)))<=>((~kind(susan)<~>humble(susan))))&
((happy(lucy))<=>((~patient(mary)&funny(mary))))&
(?[X]:((funny(X)&brave(X))))&
(~patient(john))&
((~patient(paul)&~curious(paul)))&
((~kind(john)<~>~calm(john)))&
((~generous(lucy)<~>funny(lucy)))&
((~rich(lucy)|wise(lucy))) | patient(fred) | [] | null | 0 |
Everyone who is tall or not rich is quiet or not brave. Everyone who is not quiet is not happy. If paul is not curious then someone is creative or not generous. If someone is either not wise or not curious then susan is quiet or kind. Everyone who is happy is not curious. If susan is humble then someone is not generous and vice versa. Everyone who is not wise is either not kind or generous. Everyone who is both calm and not kind is both rich and kind and vice versa. If someone is either creative or funny then paul is either not brave or not kind. Everyone who is not calm or kind is either not generous or humble. Everyone who is either not brave or not curious is either happy or humble. Everyone who is not wise is rich and vice versa. Everyone who is either calm or brave is not wise or not old. Everyone who is patient is old. Everyone who is rich or not funny is funny. If someone is both creative and not tall then paul is either patient or not patient and vice versa. Mary is not humble or not tall. Someone is not quiet or not funny. John is kind or not kind. John is strong or not brave. Someone is either calm or rich. Someone is either humble or quiet. Susan is not rich or kind. Paul is calm or not strong. | Paul is not patient. | neutral | (![X]:((tall(X)|~rich(X))=>(quiet(X)|~brave(X))))&
(![X]:(~quiet(X)=>~happy(X)))&
((~curious(paul))=>(?[X]:((creative(X)|~generous(X)))))&
((?[X]:((~wise(X)<~>~curious(X))))=>((quiet(susan)|kind(susan))))&
(![X]:(happy(X)=>~curious(X)))&
((humble(susan))<=>(?[X]:(~generous(X))))&
(![X]:(~wise(X)=>(~kind(X)<~>generous(X))))&
(![X]:((calm(X)&~kind(X))<=>(rich(X)&kind(X))))&
((?[X]:((creative(X)<~>funny(X))))=>((~brave(paul)<~>~kind(paul))))&
(![X]:((~calm(X)|kind(X))=>(~generous(X)<~>humble(X))))&
(![X]:((~brave(X)<~>~curious(X))=>(happy(X)<~>humble(X))))&
(![X]:(~wise(X)<=>rich(X)))&
(![X]:((calm(X)<~>brave(X))=>(~wise(X)|~old(X))))&
(![X]:(patient(X)=>old(X)))&
(![X]:((rich(X)|~funny(X))=>funny(X)))&
((?[X]:((creative(X)&~tall(X))))<=>((patient(paul)<~>~patient(paul))))&
((~humble(mary)|~tall(mary)))&
(?[X]:((~quiet(X)|~funny(X))))&
((kind(john)|~kind(john)))&
((strong(john)|~brave(john)))&
(?[X]:((calm(X)<~>rich(X))))&
(?[X]:((humble(X)<~>quiet(X))))&
((~rich(susan)|kind(susan)))&
((calm(paul)|~strong(paul))) | ~patient(paul) | [] | null | 0 |
If mary is both not happy and rich then someone is either not quiet or kind and vice versa.
Everyone who is calm or humble is not strong or patient.
Everyone who is either patient or not humble is not patient or not quiet.
Everyone who is either not curious or not brave is rich or not tall and vice versa.
If mary is both not creative and not humble then someone is rich.
Everyone who is both kind and quiet is tall or rich and vice versa.
If someone is both rich and calm then someone is either humble or brave and vice versa.
Everyone who is either not tall or not quiet is either not generous or not humble and vice versa.
Everyone who is both old and not strong is both not happy and not wise and vice versa.
If someone is either not brave or creative then lucy is not strong or not tall.
Everyone who is humble is patient.
Everyone who is both not wise and generous is both not generous and quiet and vice versa.
If paul is generous then someone is not strong.
If alice is not happy or not humble then someone is not happy or funny and vice versa.
If mary is strong then susan is both calm and not generous and vice versa.
Everyone who is both funny and not wise is not creative or generous and vice versa.
Someone is not brave or happy.
Alice is funny.
Someone is both not funny and patient.
Paul is both not generous and funny.
Someone is either not patient or not old. | Paul is not curious. | contradiction | (((~happy(mary)&rich(mary)))<=>(?[X]:((~quiet(X)<~>kind(X)))))&
(![X]:((calm(X)|humble(X))=>(~strong(X)|patient(X))))&
(![X]:((patient(X)<~>~humble(X))=>(~patient(X)|~quiet(X))))&
(![X]:((~curious(X)<~>~brave(X))<=>(rich(X)|~tall(X))))&
(((~creative(mary)&~humble(mary)))=>(?[X]:(rich(X))))&
(![X]:((kind(X)&quiet(X))<=>(tall(X)|rich(X))))&
((?[X]:((rich(X)&calm(X))))<=>(?[X]:((humble(X)<~>brave(X)))))&
(![X]:((~tall(X)<~>~quiet(X))<=>(~generous(X)<~>~humble(X))))&
(![X]:((old(X)&~strong(X))<=>(~happy(X)&~wise(X))))&
((?[X]:((~brave(X)<~>creative(X))))=>((~strong(lucy)|~tall(lucy))))&
(![X]:(humble(X)=>patient(X)))&
(![X]:((~wise(X)&generous(X))<=>(~generous(X)&quiet(X))))&
((generous(paul))=>(?[X]:(~strong(X))))&
(((~happy(alice)|~humble(alice)))<=>(?[X]:((~happy(X)|funny(X)))))&
((strong(mary))<=>((calm(susan)&~generous(susan))))&
(![X]:((funny(X)&~wise(X))<=>(~creative(X)|generous(X))))&
(?[X]:((~brave(X)|happy(X))))&
(funny(alice))&
(?[X]:((~funny(X)&patient(X))))&
((~generous(paul)&funny(paul)))&
(?[X]:((~patient(X)<~>~old(X)))) | ~curious(paul) | [
"p3",
"p5",
"p6",
"p7",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2162179738007030803715411
% SZS output start Proof for 2162179738007030803715411
4. ! [X0] : ((~curious(X0) <~> ~brave(X0)) <=> (~tall(X0) | rich(X0))) [input p3]
6. ! [X0] : ((quiet(X0) & kind(X0)) <=> (rich(X0) | tall(X0))) [input p5]
7. ? [X0] : (calm(X0) & rich(X0)) <=> ? [X0] : (humble(X0) <~> brave(X0)) [input p6]
8. ! [X0] : ((~tall(X0) <~> ~quiet(X0)) <=> (~generous(X0) <~> ~humble(X0))) [input p7]
12. ! [X0] : ((generous(X0) & ~wise(X0)) <=> (quiet(X0) & ~generous(X0))) [input p11]
16. ! [X0] : ((~wise(X0) & funny(X0)) <=> (generous(X0) | ~creative(X0))) [input p15]
22. ~curious(paul) [input hypothesis]
23. ? [X0] : (calm(X0) & rich(X0)) <=> ? [X1] : (humble(X1) <~> brave(X1)) [rectify 7]
40. ! [X0] : ((((brave(X0) | curious(X0)) & (~brave(X0) | ~curious(X0))) | (tall(X0) & ~rich(X0))) & ((~tall(X0) | rich(X0)) | ((~curious(X0) | brave(X0)) & (~brave(X0) | curious(X0))))) [nnf transformation 4]
41. ! [X0] : ((((brave(X0) | curious(X0)) & (~brave(X0) | ~curious(X0))) | (tall(X0) & ~rich(X0))) & (~tall(X0) | rich(X0) | ((~curious(X0) | brave(X0)) & (~brave(X0) | curious(X0))))) [flattening 40]
44. ! [X0] : (((quiet(X0) & kind(X0)) | (~rich(X0) & ~tall(X0))) & ((rich(X0) | tall(X0)) | (~quiet(X0) | ~kind(X0)))) [nnf transformation 6]
45. ! [X0] : (((quiet(X0) & kind(X0)) | (~rich(X0) & ~tall(X0))) & (rich(X0) | tall(X0) | ~quiet(X0) | ~kind(X0))) [flattening 44]
46. (? [X0] : (calm(X0) & rich(X0)) | ! [X1] : ((humble(X1) | ~brave(X1)) & (brave(X1) | ~humble(X1)))) & (? [X1] : ((~brave(X1) | ~humble(X1)) & (brave(X1) | humble(X1))) | ! [X0] : (~calm(X0) | ~rich(X0))) [nnf transformation 23]
47. (? [X0] : (calm(X0) & rich(X0)) | ! [X1] : ((humble(X1) | ~brave(X1)) & (brave(X1) | ~humble(X1)))) & (? [X2] : ((~brave(X2) | ~humble(X2)) & (brave(X2) | humble(X2))) | ! [X3] : (~calm(X3) | ~rich(X3))) [rectify 46]
48. ? [X0] : (calm(X0) & rich(X0)) => (calm(sK2) & rich(sK2)) [choice axiom]
49. ? [X2] : ((~brave(X2) | ~humble(X2)) & (brave(X2) | humble(X2))) => ((~brave(sK3) | ~humble(sK3)) & (brave(sK3) | humble(sK3))) [choice axiom]
50. ((calm(sK2) & rich(sK2)) | ! [X1] : ((humble(X1) | ~brave(X1)) & (brave(X1) | ~humble(X1)))) & (((~brave(sK3) | ~humble(sK3)) & (brave(sK3) | humble(sK3))) | ! [X3] : (~calm(X3) | ~rich(X3))) [skolemisation 47,49,48]
51. ! [X0] : ((((quiet(X0) | tall(X0)) & (~quiet(X0) | ~tall(X0))) | ((~generous(X0) | humble(X0)) & (~humble(X0) | generous(X0)))) & (((humble(X0) | generous(X0)) & (~humble(X0) | ~generous(X0))) | ((~tall(X0) | quiet(X0)) & (~quiet(X0) | tall(X0))))) [nnf transformation 8]
55. ! [X0] : (((generous(X0) & ~wise(X0)) | (~quiet(X0) | generous(X0))) & ((quiet(X0) & ~generous(X0)) | (~generous(X0) | wise(X0)))) [nnf transformation 12]
56. ! [X0] : (((generous(X0) & ~wise(X0)) | ~quiet(X0) | generous(X0)) & ((quiet(X0) & ~generous(X0)) | ~generous(X0) | wise(X0))) [flattening 55]
66. ! [X0] : (((~wise(X0) & funny(X0)) | (~generous(X0) & creative(X0))) & ((generous(X0) | ~creative(X0)) | (wise(X0) | ~funny(X0)))) [nnf transformation 16]
67. ! [X0] : (((~wise(X0) & funny(X0)) | (~generous(X0) & creative(X0))) & (generous(X0) | ~creative(X0) | wise(X0) | ~funny(X0))) [flattening 66]
90. tall(X0) | curious(X0) | brave(X0) [cnf transformation 41]
95. ~tall(X0) | quiet(X0) [cnf transformation 45]
96. ~rich(X0) | quiet(X0) [cnf transformation 45]
100. rich(sK2) | humble(X1) | ~brave(X1) [cnf transformation 50]
109. quiet(X0) | tall(X0) | ~humble(X0) | generous(X0) [cnf transformation 51]
118. ~generous(X0) | ~generous(X0) | wise(X0) [cnf transformation 56]
121. generous(X0) | ~quiet(X0) | generous(X0) [cnf transformation 56]
134. ~wise(X0) | ~generous(X0) [cnf transformation 67]
143. ~curious(paul) [cnf transformation 22]
144. ~generous(X0) | wise(X0) [duplicate literal removal 118]
145. ~quiet(X0) | generous(X0) [duplicate literal removal 121]
189. 10 <=> ! [X1] : (humble(X1) | ~brave(X1)) [avatar definition]
190. ~brave(X1) | humble(X1) <- (10) [avatar component clause 189]
201. 13 <=> rich(sK2) [avatar definition]
203. rich(sK2) <- (13) [avatar component clause 201]
204. 10 | 13 [avatar split clause 100,201,189]
220. ~humble(X0) | quiet(X0) | generous(X0) [subsumption resolution 109,95]
289. ~generous(X0) [subsumption resolution 134,144]
325. brave(X0) | curious(X0) | quiet(X0) [resolution 90,95]
416. quiet(sK2) <- (13) [resolution 203,96]
436. generous(sK2) <- (13) [resolution 416,145]
447. $false <- (13) [subsumption resolution 436,289]
448. ~13 [avatar contradiction clause 447]
474. curious(X0) | humble(X0) | quiet(X0) <- (10) [resolution 190,325]
537. humble(paul) | quiet(paul) <- (10) [resolution 474,143]
539. 61 <=> quiet(paul) [avatar definition]
540. ~quiet(paul) <- (~61) [avatar component clause 539]
541. quiet(paul) <- (61) [avatar component clause 539]
543. 62 <=> humble(paul) [avatar definition]
545. humble(paul) <- (62) [avatar component clause 543]
546. 61 | 62 | ~10 [avatar split clause 537,189,543,539]
554. generous(paul) <- (61) [resolution 541,145]
555. $false <- (61) [subsumption resolution 554,289]
556. ~61 [avatar contradiction clause 555]
559. quiet(paul) | generous(paul) <- (62) [resolution 545,220]
562. generous(paul) <- (~61, 62) [subsumption resolution 559,540]
563. $false <- (~61, 62) [subsumption resolution 562,289]
564. 61 | ~62 [avatar contradiction clause 563]
565. $false [avatar sat refutation 204,448,546,556,564]
% SZS output end Proof for 2162179738007030803715411
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave or kind is not strong.
If someone is either not humble or humble then fred is both humble and quiet.
Everyone who is either brave or not calm is not brave and vice versa.
Everyone who is either quiet or creative is not patient and vice versa.
Everyone who is both not quiet and not brave is both not brave and funny and vice versa.
If someone is either humble or not quiet then mary is calm or not quiet.
If mary is quiet then someone is either quiet or not brave.
Everyone who is either generous or not humble is both not rich and calm and vice versa.
Everyone who is not generous is happy.
If lucy is both rich and old then someone is kind.
Everyone who is funny is not happy or not funny.
Everyone who is either tall or funny is not brave and vice versa.
If someone is both not quiet and curious then someone is not kind or kind.
If lucy is both not generous and not kind then someone is curious and vice versa.
If someone is both not funny and quiet then someone is either brave or curious.
Everyone who is creative or rich is both curious and old and vice versa.
Someone is not old.
Someone is either not creative or not old.
Lucy is either kind or creative.
Someone is humble.
Someone is not tall.
Someone is both funny and curious.
Someone is wise.
Someone is not kind or not patient. | Lucy is funny. | contradiction | (![X]:((brave(X)|kind(X))=>~strong(X)))&
((?[X]:((~humble(X)<~>humble(X))))=>((humble(fred)&quiet(fred))))&
(![X]:((brave(X)<~>~calm(X))<=>~brave(X)))&
(![X]:((quiet(X)<~>creative(X))<=>~patient(X)))&
(![X]:((~quiet(X)&~brave(X))<=>(~brave(X)&funny(X))))&
((?[X]:((humble(X)<~>~quiet(X))))=>((calm(mary)|~quiet(mary))))&
((quiet(mary))=>(?[X]:((quiet(X)<~>~brave(X)))))&
(![X]:((generous(X)<~>~humble(X))<=>(~rich(X)&calm(X))))&
(![X]:(~generous(X)=>happy(X)))&
(((rich(lucy)&old(lucy)))=>(?[X]:(kind(X))))&
(![X]:(funny(X)=>(~happy(X)|~funny(X))))&
(![X]:((tall(X)<~>funny(X))<=>~brave(X)))&
((?[X]:((~quiet(X)&curious(X))))=>(?[X]:((~kind(X)|kind(X)))))&
(((~generous(lucy)&~kind(lucy)))<=>(?[X]:(curious(X))))&
((?[X]:((~funny(X)&quiet(X))))=>(?[X]:((brave(X)<~>curious(X)))))&
(![X]:((creative(X)|rich(X))<=>(curious(X)&old(X))))&
(?[X]:(~old(X)))&
(?[X]:((~creative(X)<~>~old(X))))&
((kind(lucy)<~>creative(lucy)))&
(?[X]:(humble(X)))&
(?[X]:(~tall(X)))&
(?[X]:((funny(X)&curious(X))))&
(?[X]:(wise(X)))&
(?[X]:((~kind(X)|~patient(X)))) | funny(lucy) | [
"p8",
"p10",
"p13",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 7127340251570011937136279
% SZS output start Proof for 7127340251570011937136279
9. ! [X0] : (~generous(X0) => happy(X0)) [input p8]
11. ! [X0] : (funny(X0) => (~funny(X0) | ~happy(X0))) [input p10]
14. (~kind(lucy) & ~generous(lucy)) <=> ? [X0] : curious(X0) [input p13]
22. ? [X0] : (curious(X0) & funny(X0)) [input p21]
25. funny(lucy) [input hypothesis]
36. ! [X0] : (happy(X0) | generous(X0)) [ennf transformation 9]
39. ! [X0] : ((~funny(X0) | ~happy(X0)) | ~funny(X0)) [ennf transformation 11]
40. ! [X0] : (~funny(X0) | ~happy(X0) | ~funny(X0)) [flattening 39]
60. ((~kind(lucy) & ~generous(lucy)) | ! [X0] : ~curious(X0)) & (? [X0] : curious(X0) | (kind(lucy) | generous(lucy))) [nnf transformation 14]
61. ((~kind(lucy) & ~generous(lucy)) | ! [X0] : ~curious(X0)) & (? [X0] : curious(X0) | kind(lucy) | generous(lucy)) [flattening 60]
62. ((~kind(lucy) & ~generous(lucy)) | ! [X0] : ~curious(X0)) & (? [X1] : curious(X1) | kind(lucy) | generous(lucy)) [rectify 61]
63. ? [X1] : curious(X1) => curious(sK3) [choice axiom]
64. ((~kind(lucy) & ~generous(lucy)) | ! [X0] : ~curious(X0)) & (curious(sK3) | kind(lucy) | generous(lucy)) [skolemisation 62,63]
81. ? [X0] : (curious(X0) & funny(X0)) => (curious(sK9) & funny(sK9)) [choice axiom]
82. curious(sK9) & funny(sK9) [skolemisation 22,81]
109. happy(X0) | generous(X0) [cnf transformation 36]
111. ~funny(X0) | ~happy(X0) | ~funny(X0) [cnf transformation 40]
118. ~generous(lucy) | ~curious(X0) [cnf transformation 64]
135. curious(sK9) [cnf transformation 82]
137. funny(lucy) [cnf transformation 25]
138. ~happy(X0) | ~funny(X0) [duplicate literal removal 111]
204. 13 <=> ! [X0] : ~curious(X0) [avatar definition]
205. ~curious(X0) <- (13) [avatar component clause 204]
212. 15 <=> generous(lucy) [avatar definition]
214. ~generous(lucy) <- (~15) [avatar component clause 212]
215. 13 | ~15 [avatar split clause 118,212,204]
251. $false <- (13) [resolution 205,135]
252. ~13 [avatar contradiction clause 251]
256. ~funny(X0) | generous(X0) [resolution 138,109]
261. generous(lucy) [resolution 256,137]
263. $false <- (~15) [subsumption resolution 261,214]
264. 15 [avatar contradiction clause 263]
265. $false [avatar sat refutation 215,252,264]
% SZS output end Proof for 7127340251570011937136279
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble or not happy is brave and vice versa. Everyone who is quiet or patient is not strong. Everyone who is either calm or not funny is both not curious and not generous. Everyone who is not generous or creative is either brave or kind and vice versa. Everyone who is humble or not rich is not rich or not brave. Everyone who is both patient and calm is either not funny or not kind and vice versa. Everyone who is brave is not funny or not calm. Everyone who is creative is not funny or not wise and vice versa. Everyone who is not tall or funny is tall or generous and vice versa. Everyone who is brave or not funny is not curious or not calm. Everyone who is strong or quiet is both patient and not strong. Everyone who is both humble and not rich is both generous and quiet and vice versa. If lucy is quiet or not curious then someone is humble. If susan is not kind then someone is creative and vice versa. Everyone who is both quiet and funny is both brave and generous and vice versa. Everyone who is both not wise and quiet is not happy and vice versa. Someone is both not tall and patient. Someone is happy. Susan is tall or not quiet. Susan is either kind or not calm. Someone is either patient or not curious. | Lucy is not wise. | contradiction | (![X]:((humble(X)<~>~happy(X))<=>brave(X)))&
(![X]:((quiet(X)|patient(X))=>~strong(X)))&
(![X]:((calm(X)<~>~funny(X))=>(~curious(X)&~generous(X))))&
(![X]:((~generous(X)|creative(X))<=>(brave(X)<~>kind(X))))&
(![X]:((humble(X)|~rich(X))=>(~rich(X)|~brave(X))))&
(![X]:((patient(X)&calm(X))<=>(~funny(X)<~>~kind(X))))&
(![X]:(brave(X)=>(~funny(X)|~calm(X))))&
(![X]:(creative(X)<=>(~funny(X)|~wise(X))))&
(![X]:((~tall(X)|funny(X))<=>(tall(X)|generous(X))))&
(![X]:((brave(X)|~funny(X))=>(~curious(X)|~calm(X))))&
(![X]:((strong(X)|quiet(X))=>(patient(X)&~strong(X))))&
(![X]:((humble(X)&~rich(X))<=>(generous(X)&quiet(X))))&
(((quiet(lucy)|~curious(lucy)))=>(?[X]:(humble(X))))&
((~kind(susan))<=>(?[X]:(creative(X))))&
(![X]:((quiet(X)&funny(X))<=>(brave(X)&generous(X))))&
(![X]:((~wise(X)&quiet(X))<=>~happy(X)))&
(?[X]:((~tall(X)&patient(X))))&
(?[X]:(happy(X)))&
((tall(susan)|~quiet(susan)))&
((kind(susan)<~>~calm(susan)))&
(?[X]:((patient(X)<~>~curious(X)))) | ~wise(lucy) | [
"p3",
"p5",
"p7",
"p8",
"p13",
"p14",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 7211837808167163055539513
% SZS output start Proof for 7211837808167163055539513
4. ! [X0] : ((creative(X0) | ~generous(X0)) <=> (brave(X0) <~> kind(X0))) [input p3]
6. ! [X0] : ((calm(X0) & patient(X0)) <=> (~funny(X0) <~> ~kind(X0))) [input p5]
8. ! [X0] : (creative(X0) <=> (~wise(X0) | ~funny(X0))) [input p7]
9. ! [X0] : ((funny(X0) | ~tall(X0)) <=> (generous(X0) | tall(X0))) [input p8]
14. ~kind(susan) <=> ? [X0] : creative(X0) [input p13]
15. ! [X0] : ((funny(X0) & quiet(X0)) <=> (generous(X0) & brave(X0))) [input p14]
20. kind(susan) <~> ~calm(susan) [input p19]
22. ~wise(lucy) [input hypothesis]
36. ! [X0] : (((creative(X0) | ~generous(X0)) | ((brave(X0) | ~kind(X0)) & (kind(X0) | ~brave(X0)))) & (((~kind(X0) | ~brave(X0)) & (kind(X0) | brave(X0))) | (~creative(X0) & generous(X0)))) [nnf transformation 4]
37. ! [X0] : ((creative(X0) | ~generous(X0) | ((brave(X0) | ~kind(X0)) & (kind(X0) | ~brave(X0)))) & (((~kind(X0) | ~brave(X0)) & (kind(X0) | brave(X0))) | (~creative(X0) & generous(X0)))) [flattening 36]
38. ! [X0] : (((calm(X0) & patient(X0)) | ((~funny(X0) | kind(X0)) & (~kind(X0) | funny(X0)))) & (((kind(X0) | funny(X0)) & (~kind(X0) | ~funny(X0))) | (~calm(X0) | ~patient(X0)))) [nnf transformation 6]
39. ! [X0] : (((calm(X0) & patient(X0)) | ((~funny(X0) | kind(X0)) & (~kind(X0) | funny(X0)))) & (((kind(X0) | funny(X0)) & (~kind(X0) | ~funny(X0))) | ~calm(X0) | ~patient(X0))) [flattening 38]
40. ! [X0] : ((creative(X0) | (wise(X0) & funny(X0))) & ((~wise(X0) | ~funny(X0)) | ~creative(X0))) [nnf transformation 8]
41. ! [X0] : ((creative(X0) | (wise(X0) & funny(X0))) & (~wise(X0) | ~funny(X0) | ~creative(X0))) [flattening 40]
42. ! [X0] : (((funny(X0) | ~tall(X0)) | (~generous(X0) & ~tall(X0))) & ((generous(X0) | tall(X0)) | (~funny(X0) & tall(X0)))) [nnf transformation 9]
43. ! [X0] : ((funny(X0) | ~tall(X0) | (~generous(X0) & ~tall(X0))) & (generous(X0) | tall(X0) | (~funny(X0) & tall(X0)))) [flattening 42]
48. (~kind(susan) | ! [X0] : ~creative(X0)) & (? [X0] : creative(X0) | kind(susan)) [nnf transformation 14]
49. (~kind(susan) | ! [X0] : ~creative(X0)) & (? [X1] : creative(X1) | kind(susan)) [rectify 48]
50. ? [X1] : creative(X1) => creative(sK1) [choice axiom]
51. (~kind(susan) | ! [X0] : ~creative(X0)) & (creative(sK1) | kind(susan)) [skolemisation 49,50]
52. ! [X0] : (((funny(X0) & quiet(X0)) | (~generous(X0) | ~brave(X0))) & ((generous(X0) & brave(X0)) | (~funny(X0) | ~quiet(X0)))) [nnf transformation 15]
53. ! [X0] : (((funny(X0) & quiet(X0)) | ~generous(X0) | ~brave(X0)) & ((generous(X0) & brave(X0)) | ~funny(X0) | ~quiet(X0))) [flattening 52]
60. (calm(susan) | ~kind(susan)) & (~calm(susan) | kind(susan)) [nnf transformation 20]
73. ~creative(X0) | brave(X0) | kind(X0) [cnf transformation 37]
85. ~funny(X0) | calm(X0) | kind(X0) [cnf transformation 39]
88. creative(X0) | funny(X0) [cnf transformation 41]
89. wise(X0) | creative(X0) [cnf transformation 41]
90. generous(X0) | tall(X0) | tall(X0) [cnf transformation 43]
92. funny(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 43]
104. ~kind(susan) | ~creative(X0) [cnf transformation 51]
108. ~generous(X0) | funny(X0) | ~brave(X0) [cnf transformation 53]
116. ~calm(susan) | kind(susan) [cnf transformation 60]
120. ~wise(lucy) [cnf transformation 22]
121. tall(X0) | generous(X0) [duplicate literal removal 90]
122. ~tall(X0) | funny(X0) [duplicate literal removal 92]
139. 4 <=> ! [X0] : ~creative(X0) [avatar definition]
140. ~creative(X0) <- (4) [avatar component clause 139]
142. 5 <=> kind(susan) [avatar definition]
144. ~kind(susan) <- (~5) [avatar component clause 142]
145. 4 | ~5 [avatar split clause 104,142,139]
161. 9 <=> calm(susan) [avatar definition]
162. ~calm(susan) <- (~9) [avatar component clause 161]
165. 5 | ~9 [avatar split clause 116,161,142]
176. creative(lucy) [resolution 89,120]
181. generous(X0) | funny(X0) [resolution 122,121]
248. kind(X1) | brave(X1) | funny(X1) [resolution 73,88]
268. $false <- (4) [resolution 140,176]
271. ~4 [avatar contradiction clause 268]
385. funny(X0) | ~brave(X0) | funny(X0) [resolution 108,181]
387. funny(X0) | ~brave(X0) [duplicate literal removal 385]
464. brave(susan) | funny(susan) <- (~5) [resolution 248,144]
482. funny(susan) <- (~5) [subsumption resolution 464,387]
527. calm(susan) | kind(susan) <- (~5) [resolution 482,85]
532. kind(susan) <- (~5, ~9) [subsumption resolution 527,162]
533. $false <- (~5, ~9) [subsumption resolution 532,144]
534. 5 | 9 [avatar contradiction clause 533]
535. $false [avatar sat refutation 145,165,271,534]
% SZS output end Proof for 7211837808167163055539513
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich and kind is generous. If someone is both happy and humble then someone is both rich and not patient and vice versa. Everyone who is either wise or kind is generous or not old and vice versa. Everyone who is calm is curious. If john is not funny or not wise then mary is either not brave or not happy and vice versa. Everyone who is either wise or strong is both creative and not wise and vice versa. Everyone who is not brave is not creative or not patient and vice versa. If someone is either not generous or brave then susan is either not humble or strong and vice versa. Everyone who is both not patient and strong is both creative and not generous and vice versa. Everyone who is rich or not humble is either not generous or not quiet and vice versa. If someone is either funny or happy then someone is either wise or old and vice versa. Everyone who is both calm and not kind is both not rich and strong. If someone is creative then mary is both calm and happy. Everyone who is brave or not quiet is both not patient and not rich. Everyone who is either patient or tall is wise or humble. Everyone who is both not quiet and not generous is creative or curious and vice versa. Mary is wise or not strong. John is both calm and not brave. Someone is not generous. Susan is curious or not kind. Someone is brave or not strong. Someone is both not happy and tall. Someone is either tall or not wise. Someone is both wise and tall. | Susan is not patient. | neutral | (![X]:((rich(X)&kind(X))=>generous(X)))&
((?[X]:((happy(X)&humble(X))))<=>(?[X]:((rich(X)&~patient(X)))))&
(![X]:((wise(X)<~>kind(X))<=>(generous(X)|~old(X))))&
(![X]:(calm(X)=>curious(X)))&
(((~funny(john)|~wise(john)))<=>((~brave(mary)<~>~happy(mary))))&
(![X]:((wise(X)<~>strong(X))<=>(creative(X)&~wise(X))))&
(![X]:(~brave(X)<=>(~creative(X)|~patient(X))))&
((?[X]:((~generous(X)<~>brave(X))))<=>((~humble(susan)<~>strong(susan))))&
(![X]:((~patient(X)&strong(X))<=>(creative(X)&~generous(X))))&
(![X]:((rich(X)|~humble(X))<=>(~generous(X)<~>~quiet(X))))&
((?[X]:((funny(X)<~>happy(X))))<=>(?[X]:((wise(X)<~>old(X)))))&
(![X]:((calm(X)&~kind(X))=>(~rich(X)&strong(X))))&
((?[X]:(creative(X)))=>((calm(mary)&happy(mary))))&
(![X]:((brave(X)|~quiet(X))=>(~patient(X)&~rich(X))))&
(![X]:((patient(X)<~>tall(X))=>(wise(X)|humble(X))))&
(![X]:((~quiet(X)&~generous(X))<=>(creative(X)|curious(X))))&
((wise(mary)|~strong(mary)))&
((calm(john)&~brave(john)))&
(?[X]:(~generous(X)))&
((curious(susan)|~kind(susan)))&
(?[X]:((brave(X)|~strong(X))))&
(?[X]:((~happy(X)&tall(X))))&
(?[X]:((tall(X)<~>~wise(X))))&
(?[X]:((wise(X)&tall(X)))) | ~patient(susan) | [] | null | 0 |
If someone is brave or humble then susan is not rich or not generous and vice versa.
If someone is either not generous or not strong then alice is tall and vice versa.
Everyone who is both not wise and not quiet is both not tall and not curious.
If someone is creative then john is both curious and strong.
Everyone who is not generous is either creative or old.
Everyone who is either not wise or rich is creative.
Everyone who is humble is not kind or curious and vice versa.
Everyone who is not rich is not patient.
If someone is kind or tall then fred is not curious or not strong.
If susan is not wise or not calm then paul is calm.
If paul is either calm or patient then someone is either happy or not curious.
If susan is either not kind or generous then someone is generous or kind and vice versa.
Everyone who is not curious is not happy or not humble.
Everyone who is not funny or not generous is both not old and not patient and vice versa.
If someone is both creative and quiet then fred is old or brave.
If someone is not brave then mary is both not humble and creative and vice versa.
Someone is generous.
Someone is either brave or not rich.
Someone is calm or humble.
Fred is not wise.
Someone is both kind and brave.
Someone is either not calm or not creative.
Fred is both rich and happy.
Someone is rich. | Paul is calm. | neutral | ((?[X]:((brave(X)|humble(X))))<=>((~rich(susan)|~generous(susan))))&
((?[X]:((~generous(X)<~>~strong(X))))<=>(tall(alice)))&
(![X]:((~wise(X)&~quiet(X))=>(~tall(X)&~curious(X))))&
((?[X]:(creative(X)))=>((curious(john)&strong(john))))&
(![X]:(~generous(X)=>(creative(X)<~>old(X))))&
(![X]:((~wise(X)<~>rich(X))=>creative(X)))&
(![X]:(humble(X)<=>(~kind(X)|curious(X))))&
(![X]:(~rich(X)=>~patient(X)))&
((?[X]:((kind(X)|tall(X))))=>((~curious(fred)|~strong(fred))))&
(((~wise(susan)|~calm(susan)))=>(calm(paul)))&
(((calm(paul)<~>patient(paul)))=>(?[X]:((happy(X)<~>~curious(X)))))&
(((~kind(susan)<~>generous(susan)))<=>(?[X]:((generous(X)|kind(X)))))&
(![X]:(~curious(X)=>(~happy(X)|~humble(X))))&
(![X]:((~funny(X)|~generous(X))<=>(~old(X)&~patient(X))))&
((?[X]:((creative(X)&quiet(X))))=>((old(fred)|brave(fred))))&
((?[X]:(~brave(X)))<=>((~humble(mary)&creative(mary))))&
(?[X]:(generous(X)))&
(?[X]:((brave(X)<~>~rich(X))))&
(?[X]:((calm(X)|humble(X))))&
(~wise(fred))&
(?[X]:((kind(X)&brave(X))))&
(?[X]:((~calm(X)<~>~creative(X))))&
((rich(fred)&happy(fred)))&
(?[X]:(rich(X))) | calm(paul) | [] | null | 0 |
Everyone who is either not patient or not curious is not funny.
Everyone who is curious is both brave and not quiet and vice versa.
If someone is wise then someone is humble or calm.
Everyone who is both quiet and generous is not old or strong.
If lucy is both not quiet and calm then someone is both not curious and brave.
If someone is funny then someone is either creative or not quiet and vice versa.
Everyone who is both not kind and humble is not old.
Everyone who is not humble is quiet and vice versa.
If john is creative then john is either not happy or happy.
If someone is either tall or humble then susan is both patient and tall and vice versa.
Everyone who is not humble or humble is tall or wise and vice versa.
Everyone who is either strong or not rich is tall.
Everyone who is either not kind or quiet is curious and vice versa.
Everyone who is both funny and not generous is either not calm or humble and vice versa.
If someone is either curious or not tall then someone is humble and vice versa.
Fred is patient or calm.
Someone is both strong and not rich.
Someone is generous.
Someone is either calm or not calm.
Someone is both not tall and humble.
Paul is both not creative and happy.
John is not wise.
Susan is not happy or not funny. | Susan is not tall. | contradiction | (![X]:((~patient(X)<~>~curious(X))=>~funny(X)))&
(![X]:(curious(X)<=>(brave(X)&~quiet(X))))&
((?[X]:(wise(X)))=>(?[X]:((humble(X)|calm(X)))))&
(![X]:((quiet(X)&generous(X))=>(~old(X)|strong(X))))&
(((~quiet(lucy)&calm(lucy)))=>(?[X]:((~curious(X)&brave(X)))))&
((?[X]:(funny(X)))<=>(?[X]:((creative(X)<~>~quiet(X)))))&
(![X]:((~kind(X)&humble(X))=>~old(X)))&
(![X]:(~humble(X)<=>quiet(X)))&
((creative(john))=>((~happy(john)<~>happy(john))))&
((?[X]:((tall(X)<~>humble(X))))<=>((patient(susan)&tall(susan))))&
(![X]:((~humble(X)|humble(X))<=>(tall(X)|wise(X))))&
(![X]:((strong(X)<~>~rich(X))=>tall(X)))&
(![X]:((~kind(X)<~>quiet(X))<=>curious(X)))&
(![X]:((funny(X)&~generous(X))<=>(~calm(X)<~>humble(X))))&
((?[X]:((curious(X)<~>~tall(X))))<=>(?[X]:(humble(X))))&
((patient(fred)|calm(fred)))&
(?[X]:((strong(X)&~rich(X))))&
(?[X]:(generous(X)))&
(?[X]:((calm(X)<~>~calm(X))))&
(?[X]:((~tall(X)&humble(X))))&
((~creative(paul)&happy(paul)))&
(~wise(john))&
((~happy(susan)|~funny(susan))) | ~tall(susan) | [
"p9",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 1121106566421887118843891
% SZS output start Proof for 1121106566421887118843891
10. ? [X0] : (tall(X0) <~> humble(X0)) <=> (tall(susan) & patient(susan)) [input p9]
20. ? [X0] : (humble(X0) & ~tall(X0)) [input p19]
24. ~tall(susan) [input hypothesis]
51. (? [X0] : ((~humble(X0) | ~tall(X0)) & (humble(X0) | tall(X0))) | (~tall(susan) | ~patient(susan))) & ((tall(susan) & patient(susan)) | ! [X0] : ((tall(X0) | ~humble(X0)) & (humble(X0) | ~tall(X0)))) [nnf transformation 10]
52. (? [X0] : ((~humble(X0) | ~tall(X0)) & (humble(X0) | tall(X0))) | ~tall(susan) | ~patient(susan)) & ((tall(susan) & patient(susan)) | ! [X0] : ((tall(X0) | ~humble(X0)) & (humble(X0) | ~tall(X0)))) [flattening 51]
53. (? [X0] : ((~humble(X0) | ~tall(X0)) & (humble(X0) | tall(X0))) | ~tall(susan) | ~patient(susan)) & ((tall(susan) & patient(susan)) | ! [X1] : ((tall(X1) | ~humble(X1)) & (humble(X1) | ~tall(X1)))) [rectify 52]
54. ? [X0] : ((~humble(X0) | ~tall(X0)) & (humble(X0) | tall(X0))) => ((~humble(sK4) | ~tall(sK4)) & (humble(sK4) | tall(sK4))) [choice axiom]
55. (((~humble(sK4) | ~tall(sK4)) & (humble(sK4) | tall(sK4))) | ~tall(susan) | ~patient(susan)) & ((tall(susan) & patient(susan)) | ! [X1] : ((tall(X1) | ~humble(X1)) & (humble(X1) | ~tall(X1)))) [skolemisation 53,54]
74. ? [X0] : (humble(X0) & ~tall(X0)) => (humble(sK10) & ~tall(sK10)) [choice axiom]
75. humble(sK10) & ~tall(sK10) [skolemisation 20,74]
95. tall(susan) | tall(X1) | ~humble(X1) [cnf transformation 55]
124. ~tall(sK10) [cnf transformation 75]
125. humble(sK10) [cnf transformation 75]
130. ~tall(susan) [cnf transformation 24]
191. 15 <=> tall(susan) [avatar definition]
205. 18 <=> ! [X1] : (tall(X1) | ~humble(X1)) [avatar definition]
206. ~humble(X1) | tall(X1) <- (18) [avatar component clause 205]
207. 18 | 15 [avatar split clause 95,191,205]
260. ~15 [avatar split clause 130,191]
268. tall(sK10) <- (18) [resolution 206,125]
269. $false <- (18) [subsumption resolution 268,124]
270. ~18 [avatar contradiction clause 269]
271. $false [avatar sat refutation 207,260,270]
% SZS output end Proof for 1121106566421887118843891
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 fred is curious or tall then fred is not creative or not tall.
Everyone who is both not strong and old is not tall.
Everyone who is both happy and not old is kind or not calm and vice versa.
If someone is both not quiet and not old then alice is both not calm and not humble and vice versa.
If someone is either not wise or kind then john is both not calm and calm and vice versa.
Everyone who is funny is brave or not quiet.
Everyone who is not creative or not brave is calm or brave.
Everyone who is not happy or not old is both curious and not humble and vice versa.
Everyone who is not creative is both creative and not happy.
If someone is either not funny or old then someone is kind or tall.
Everyone who is both not humble and curious is either funny or wise.
If someone is both not funny and not wise then someone is both generous and not calm.
Everyone who is either not rich or not funny is either not creative or not rich and vice versa.
Everyone who is both patient and not rich is not creative or not strong.
Everyone who is both quiet and tall is not kind and vice versa.
If someone is old then paul is patient or not happy.
Fred is not curious or not calm.
Mary is either kind or rich.
Someone is both rich and calm.
John is both not old and not patient.
Lucy is both not calm and not rich.
Susan is both not patient and not quiet.
Mary is either generous or not kind. | Paul is happy. | entailment | (((curious(fred)|tall(fred)))=>((~creative(fred)|~tall(fred))))&
(![X]:((~strong(X)&old(X))=>~tall(X)))&
(![X]:((happy(X)&~old(X))<=>(kind(X)|~calm(X))))&
((?[X]:((~quiet(X)&~old(X))))<=>((~calm(alice)&~humble(alice))))&
((?[X]:((~wise(X)<~>kind(X))))<=>((~calm(john)&calm(john))))&
(![X]:(funny(X)=>(brave(X)|~quiet(X))))&
(![X]:((~creative(X)|~brave(X))=>(calm(X)|brave(X))))&
(![X]:((~happy(X)|~old(X))<=>(curious(X)&~humble(X))))&
(![X]:(~creative(X)=>(creative(X)&~happy(X))))&
((?[X]:((~funny(X)<~>old(X))))=>(?[X]:((kind(X)|tall(X)))))&
(![X]:((~humble(X)&curious(X))=>(funny(X)<~>wise(X))))&
((?[X]:((~funny(X)&~wise(X))))=>(?[X]:((generous(X)&~calm(X)))))&
(![X]:((~rich(X)<~>~funny(X))<=>(~creative(X)<~>~rich(X))))&
(![X]:((patient(X)&~rich(X))=>(~creative(X)|~strong(X))))&
(![X]:((quiet(X)&tall(X))<=>~kind(X)))&
((?[X]:(old(X)))=>((patient(paul)|~happy(paul))))&
((~curious(fred)|~calm(fred)))&
((kind(mary)<~>rich(mary)))&
(?[X]:((rich(X)&calm(X))))&
((~old(john)&~patient(john)))&
((~calm(lucy)&~rich(lucy)))&
((~patient(susan)&~quiet(susan)))&
((generous(mary)<~>~kind(mary))) | happy(paul) | [
"p2",
"p4",
"p7",
"p8",
"p10",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 235525649109114188616409
% SZS output start Proof for 235525649109114188616409
3. ! [X0] : ((~old(X0) & happy(X0)) <=> (~calm(X0) | kind(X0))) [input p2]
5. ? [X0] : (~wise(X0) <~> kind(X0)) <=> (calm(john) & ~calm(john)) [input p4]
8. ! [X0] : ((~old(X0) | ~happy(X0)) <=> (~humble(X0) & curious(X0))) [input p7]
9. ! [X0] : (~creative(X0) => (~happy(X0) & creative(X0))) [input p8]
11. ! [X0] : ((curious(X0) & ~humble(X0)) => (funny(X0) <~> wise(X0))) [input p10]
13. ! [X0] : ((~rich(X0) <~> ~funny(X0)) <=> (~creative(X0) <~> ~rich(X0))) [input p12]
24. ~happy(paul) [input hypothesis]
33. ! [X0] : ((~happy(X0) & creative(X0)) | creative(X0)) [ennf transformation 9]
35. ! [X0] : ((funny(X0) <~> wise(X0)) | (~curious(X0) | humble(X0))) [ennf transformation 11]
36. ! [X0] : ((funny(X0) <~> wise(X0)) | ~curious(X0) | humble(X0)) [flattening 35]
42. ! [X0] : (((~old(X0) & happy(X0)) | (calm(X0) & ~kind(X0))) & ((~calm(X0) | kind(X0)) | (old(X0) | ~happy(X0)))) [nnf transformation 3]
43. ! [X0] : (((~old(X0) & happy(X0)) | (calm(X0) & ~kind(X0))) & (~calm(X0) | kind(X0) | old(X0) | ~happy(X0))) [flattening 42]
49. (? [X0] : ((~kind(X0) | wise(X0)) & (kind(X0) | ~wise(X0))) | (~calm(john) | calm(john))) & ((calm(john) & ~calm(john)) | ! [X0] : ((~wise(X0) | ~kind(X0)) & (kind(X0) | wise(X0)))) [nnf transformation 5]
50. (? [X0] : ((~kind(X0) | wise(X0)) & (kind(X0) | ~wise(X0))) | ~calm(john) | calm(john)) & ((calm(john) & ~calm(john)) | ! [X0] : ((~wise(X0) | ~kind(X0)) & (kind(X0) | wise(X0)))) [flattening 49]
51. (? [X0] : ((~kind(X0) | wise(X0)) & (kind(X0) | ~wise(X0))) | ~calm(john) | calm(john)) & ((calm(john) & ~calm(john)) | ! [X1] : ((~wise(X1) | ~kind(X1)) & (kind(X1) | wise(X1)))) [rectify 50]
52. ? [X0] : ((~kind(X0) | wise(X0)) & (kind(X0) | ~wise(X0))) => ((~kind(sK1) | wise(sK1)) & (kind(sK1) | ~wise(sK1))) [choice axiom]
53. (((~kind(sK1) | wise(sK1)) & (kind(sK1) | ~wise(sK1))) | ~calm(john) | calm(john)) & ((calm(john) & ~calm(john)) | ! [X1] : ((~wise(X1) | ~kind(X1)) & (kind(X1) | wise(X1)))) [skolemisation 51,52]
54. ! [X0] : (((~old(X0) | ~happy(X0)) | (humble(X0) | ~curious(X0))) & ((~humble(X0) & curious(X0)) | (old(X0) & happy(X0)))) [nnf transformation 8]
55. ! [X0] : ((~old(X0) | ~happy(X0) | humble(X0) | ~curious(X0)) & ((~humble(X0) & curious(X0)) | (old(X0) & happy(X0)))) [flattening 54]
60. ! [X0] : (((~wise(X0) | ~funny(X0)) & (wise(X0) | funny(X0))) | ~curious(X0) | humble(X0)) [nnf transformation 36]
64. ! [X0] : ((((funny(X0) | rich(X0)) & (~funny(X0) | ~rich(X0))) | ((~creative(X0) | rich(X0)) & (~rich(X0) | creative(X0)))) & (((rich(X0) | creative(X0)) & (~rich(X0) | ~creative(X0))) | ((~rich(X0) | funny(X0)) & (~funny(X0) | rich(X0))))) [nnf transformation 13]
75. ~kind(X0) | happy(X0) [cnf transformation 43]
83. ~calm(john) | kind(X1) | wise(X1) [cnf transformation 53]
85. calm(john) | kind(X1) | wise(X1) [cnf transformation 53]
89. happy(X0) | curious(X0) [cnf transformation 55]
91. ~humble(X0) | happy(X0) [cnf transformation 55]
94. creative(X0) | creative(X0) [cnf transformation 33]
99. ~funny(X0) | ~wise(X0) | ~curious(X0) | humble(X0) [cnf transformation 60]
103. ~rich(X0) | ~creative(X0) | ~rich(X0) | funny(X0) [cnf transformation 64]
109. funny(X0) | rich(X0) | ~creative(X0) | rich(X0) [cnf transformation 64]
128. ~happy(paul) [cnf transformation 24]
129. ~rich(X0) | ~creative(X0) | funny(X0) [duplicate literal removal 103]
132. funny(X0) | rich(X0) | ~creative(X0) [duplicate literal removal 109]
133. creative(X0) [duplicate literal removal 94]
176. 10 <=> calm(john) [avatar definition]
181. 11 <=> ! [X1] : (kind(X1) | wise(X1)) [avatar definition]
182. wise(X1) | kind(X1) <- (11) [avatar component clause 181]
183. 11 | 10 [avatar split clause 85,176,181]
185. 11 | ~10 [avatar split clause 83,176,181]
215. rich(X0) | funny(X0) [subsumption resolution 132,133]
216. ~rich(X0) | funny(X0) [subsumption resolution 129,133]
217. funny(X0) [subsumption resolution 216,215]
227. 21 <=> happy(paul) [avatar definition]
229. ~happy(paul) <- (~21) [avatar component clause 227]
252. ~21 [avatar split clause 128,227]
259. curious(paul) <- (~21) [resolution 89,229]
335. ~wise(X0) | ~curious(X0) | humble(X0) [resolution 99,217]
393. ~curious(X0) | humble(X0) | kind(X0) <- (11) [resolution 335,182]
422. humble(paul) | kind(paul) <- (11, ~21) [resolution 393,259]
446. 43 <=> kind(paul) [avatar definition]
448. kind(paul) <- (43) [avatar component clause 446]
450. 44 <=> humble(paul) [avatar definition]
452. humble(paul) <- (44) [avatar component clause 450]
453. 43 | 44 | ~11 | 21 [avatar split clause 422,227,181,450,446]
484. happy(paul) <- (44) [resolution 452,91]
485. $false <- (~21, 44) [subsumption resolution 484,229]
486. 21 | ~44 [avatar contradiction clause 485]
488. happy(paul) <- (43) [resolution 448,75]
489. $false <- (~21, 43) [subsumption resolution 488,229]
490. 21 | ~43 [avatar contradiction clause 489]
491. $false [avatar sat refutation 183,185,252,453,486,490]
% SZS output end Proof for 235525649109114188616409
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet is strong or humble and vice versa.
Everyone who is both not happy and tall is happy or kind and vice versa.
If someone is not old then paul is either creative or not humble and vice versa.
If someone is either funny or not creative then someone is not generous or kind and vice versa.
Everyone who is either wise or not calm is not patient or kind.
Everyone who is both not funny and not kind is generous or not creative.
If fred is not old or not quiet then someone is kind.
Everyone who is both calm and strong is not curious or not tall.
Everyone who is not humble is not strong or generous.
Everyone who is rich is both quiet and not rich and vice versa.
If lucy is either rich or not creative then someone is generous or calm.
If someone is brave or rich then susan is either curious or not calm.
Everyone who is humble or strong is either curious or not rich.
Fred is both not creative and not happy.
Fred is old or brave.
Alice is either not wise or not generous.
Someone is both not creative and not happy.
Someone is not wise.
Paul is either not old or not kind.
Someone is not strong. | Alice is happy. | contradiction | (![X]:(quiet(X)<=>(strong(X)|humble(X))))&
(![X]:((~happy(X)&tall(X))<=>(happy(X)|kind(X))))&
((?[X]:(~old(X)))<=>((creative(paul)<~>~humble(paul))))&
((?[X]:((funny(X)<~>~creative(X))))<=>(?[X]:((~generous(X)|kind(X)))))&
(![X]:((wise(X)<~>~calm(X))=>(~patient(X)|kind(X))))&
(![X]:((~funny(X)&~kind(X))=>(generous(X)|~creative(X))))&
(((~old(fred)|~quiet(fred)))=>(?[X]:(kind(X))))&
(![X]:((calm(X)&strong(X))=>(~curious(X)|~tall(X))))&
(![X]:(~humble(X)=>(~strong(X)|generous(X))))&
(![X]:(rich(X)<=>(quiet(X)&~rich(X))))&
(((rich(lucy)<~>~creative(lucy)))=>(?[X]:((generous(X)|calm(X)))))&
((?[X]:((brave(X)|rich(X))))=>((curious(susan)<~>~calm(susan))))&
(![X]:((humble(X)|strong(X))=>(curious(X)<~>~rich(X))))&
((~creative(fred)&~happy(fred)))&
((old(fred)|brave(fred)))&
((~wise(alice)<~>~generous(alice)))&
(?[X]:((~creative(X)&~happy(X))))&
(?[X]:(~wise(X)))&
((~old(paul)<~>~kind(paul)))&
(?[X]:(~strong(X))) | happy(alice) | [
"p1",
"hypothesis"
] | % SZS status Unsatisfiable for 8672094156284207816779009
% SZS output start Proof for 8672094156284207816779009
2. ! [X0] : ((tall(X0) & ~happy(X0)) <=> (kind(X0) | happy(X0))) [input p1]
21. happy(alice) [input hypothesis]
36. ! [X0] : (((tall(X0) & ~happy(X0)) | (~kind(X0) & ~happy(X0))) & ((kind(X0) | happy(X0)) | (~tall(X0) | happy(X0)))) [nnf transformation 2]
37. ! [X0] : (((tall(X0) & ~happy(X0)) | (~kind(X0) & ~happy(X0))) & (kind(X0) | happy(X0) | ~tall(X0) | happy(X0))) [flattening 36]
68. ~happy(X0) | ~happy(X0) [cnf transformation 37]
111. happy(alice) [cnf transformation 21]
115. ~happy(X0) [duplicate literal removal 68]
238. $false [subsumption resolution 111,115]
% SZS output end Proof for 8672094156284207816779009
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich and patient is strong. Everyone who is calm is not old. If someone is both not curious and old then lucy is not wise. Everyone who is both calm and not brave is either not tall or curious and vice versa. Everyone who is both not rich and not tall is not rich. Everyone who is tall or not wise is strong and vice versa. Everyone who is both tall and calm is not quiet and vice versa. If someone is both generous and not tall then someone is quiet and vice versa. If someone is either not funny or wise then john is not strong or patient. If someone is not kind or not creative then john is both not brave and old. If someone is not generous then fred is strong or not funny. If someone is generous then susan is either funny or humble. If susan is either not funny or not kind then john is both funny and creative and vice versa. Everyone who is not rich is not happy. Everyone who is curious or kind is both not old and patient and vice versa. Everyone who is rich or not quiet is either old or not humble. Someone is both funny and not tall. John is not brave or tall. Someone is either not happy or generous. Someone is either old or not rich. Someone is either strong or not humble. Someone is kind. Someone is not creative. Someone is not humble. | Fred is strong. | neutral | (![X]:((~rich(X)&patient(X))=>strong(X)))&
(![X]:(calm(X)=>~old(X)))&
((?[X]:((~curious(X)&old(X))))=>(~wise(lucy)))&
(![X]:((calm(X)&~brave(X))<=>(~tall(X)<~>curious(X))))&
(![X]:((~rich(X)&~tall(X))=>~rich(X)))&
(![X]:((tall(X)|~wise(X))<=>strong(X)))&
(![X]:((tall(X)&calm(X))<=>~quiet(X)))&
((?[X]:((generous(X)&~tall(X))))<=>(?[X]:(quiet(X))))&
((?[X]:((~funny(X)<~>wise(X))))=>((~strong(john)|patient(john))))&
((?[X]:((~kind(X)|~creative(X))))=>((~brave(john)&old(john))))&
((?[X]:(~generous(X)))=>((strong(fred)|~funny(fred))))&
((?[X]:(generous(X)))=>((funny(susan)<~>humble(susan))))&
(((~funny(susan)<~>~kind(susan)))<=>((funny(john)&creative(john))))&
(![X]:(~rich(X)=>~happy(X)))&
(![X]:((curious(X)|kind(X))<=>(~old(X)&patient(X))))&
(![X]:((rich(X)|~quiet(X))=>(old(X)<~>~humble(X))))&
(?[X]:((funny(X)&~tall(X))))&
((~brave(john)|tall(john)))&
(?[X]:((~happy(X)<~>generous(X))))&
(?[X]:((old(X)<~>~rich(X))))&
(?[X]:((strong(X)<~>~humble(X))))&
(?[X]:(kind(X)))&
(?[X]:(~creative(X)))&
(?[X]:(~humble(X))) | strong(fred) | [] | null | 0 |
Everyone who is both not tall and not old is either strong or patient.
Everyone who is either quiet or not tall is not creative and vice versa.
Everyone who is both not rich and rich is not generous or not curious.
If someone is both not funny and not quiet then someone is both not humble and not patient.
Everyone who is both not quiet and not funny is both not generous and not curious.
Everyone who is both not brave and tall is either generous or funny and vice versa.
Everyone who is both not rich and tall is either quiet or not old and vice versa.
Everyone who is not curious or not kind is not creative or not kind.
If alice is both kind and not calm then someone is kind or not generous and vice versa.
Everyone who is both not tall and not wise is calm or not happy and vice versa.
Everyone who is patient or not funny is not generous or not rich.
Everyone who is brave or funny is both not happy and not tall.
If lucy is either not generous or old then mary is not curious and vice versa.
If someone is both happy and not humble then fred is not tall or generous.
Everyone who is kind or humble is both tall and generous.
Everyone who is either funny or kind is not rich or not quiet and vice versa.
Someone is both not happy and not patient.
Paul is both happy and generous.
Someone is creative or not kind.
Someone is not old or patient.
Someone is creative or not patient.
Mary is either creative or brave.
Someone is tall or not generous. | Mary is humble. | contradiction | (![X]:((~tall(X)&~old(X))=>(strong(X)<~>patient(X))))&
(![X]:((quiet(X)<~>~tall(X))<=>~creative(X)))&
(![X]:((~rich(X)&rich(X))=>(~generous(X)|~curious(X))))&
((?[X]:((~funny(X)&~quiet(X))))=>(?[X]:((~humble(X)&~patient(X)))))&
(![X]:((~quiet(X)&~funny(X))=>(~generous(X)&~curious(X))))&
(![X]:((~brave(X)&tall(X))<=>(generous(X)<~>funny(X))))&
(![X]:((~rich(X)&tall(X))<=>(quiet(X)<~>~old(X))))&
(![X]:((~curious(X)|~kind(X))=>(~creative(X)|~kind(X))))&
(((kind(alice)&~calm(alice)))<=>(?[X]:((kind(X)|~generous(X)))))&
(![X]:((~tall(X)&~wise(X))<=>(calm(X)|~happy(X))))&
(![X]:((patient(X)|~funny(X))=>(~generous(X)|~rich(X))))&
(![X]:((brave(X)|funny(X))=>(~happy(X)&~tall(X))))&
(((~generous(lucy)<~>old(lucy)))<=>(~curious(mary)))&
((?[X]:((happy(X)&~humble(X))))=>((~tall(fred)|generous(fred))))&
(![X]:((kind(X)|humble(X))=>(tall(X)&generous(X))))&
(![X]:((funny(X)<~>kind(X))<=>(~rich(X)|~quiet(X))))&
(?[X]:((~happy(X)&~patient(X))))&
((happy(paul)&generous(paul)))&
(?[X]:((creative(X)|~kind(X))))&
(?[X]:((~old(X)|patient(X))))&
(?[X]:((creative(X)|~patient(X))))&
((creative(mary)<~>brave(mary)))&
(?[X]:((tall(X)|~generous(X)))) | humble(mary) | [
"p1",
"p4",
"p9",
"p11",
"p14",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 7571179680365770865628905
% SZS output start Proof for 7571179680365770865628905
2. ! [X0] : ((quiet(X0) <~> ~tall(X0)) <=> ~creative(X0)) [input p1]
5. ! [X0] : ((~funny(X0) & ~quiet(X0)) => (~curious(X0) & ~generous(X0))) [input p4]
10. ! [X0] : ((~wise(X0) & ~tall(X0)) <=> (~happy(X0) | calm(X0))) [input p9]
12. ! [X0] : ((funny(X0) | brave(X0)) => (~tall(X0) & ~happy(X0))) [input p11]
15. ! [X0] : ((humble(X0) | kind(X0)) => (generous(X0) & tall(X0))) [input p14]
22. creative(mary) <~> brave(mary) [input p21]
24. humble(mary) [input hypothesis]
31. ! [X0] : ((~curious(X0) & ~generous(X0)) | (funny(X0) | quiet(X0))) [ennf transformation 5]
32. ! [X0] : ((~curious(X0) & ~generous(X0)) | funny(X0) | quiet(X0)) [flattening 31]
37. ! [X0] : ((~tall(X0) & ~happy(X0)) | (~funny(X0) & ~brave(X0))) [ennf transformation 12]
40. ! [X0] : ((generous(X0) & tall(X0)) | (~humble(X0) & ~kind(X0))) [ennf transformation 15]
42. ! [X0] : ((((tall(X0) | ~quiet(X0)) & (~tall(X0) | quiet(X0))) | creative(X0)) & (~creative(X0) | ((quiet(X0) | tall(X0)) & (~tall(X0) | ~quiet(X0))))) [nnf transformation 2]
55. ! [X0] : (((~wise(X0) & ~tall(X0)) | (happy(X0) & ~calm(X0))) & ((~happy(X0) | calm(X0)) | (wise(X0) | tall(X0)))) [nnf transformation 10]
56. ! [X0] : (((~wise(X0) & ~tall(X0)) | (happy(X0) & ~calm(X0))) & (~happy(X0) | calm(X0) | wise(X0) | tall(X0))) [flattening 55]
68. (~brave(mary) | ~creative(mary)) & (brave(mary) | creative(mary)) [nnf transformation 22]
73. ~creative(X0) | ~tall(X0) | ~quiet(X0) [cnf transformation 42]
80. ~generous(X0) | funny(X0) | quiet(X0) [cnf transformation 32]
103. ~tall(X0) | happy(X0) [cnf transformation 56]
108. ~happy(X0) | ~brave(X0) [cnf transformation 37]
109. ~happy(X0) | ~funny(X0) [cnf transformation 37]
118. ~humble(X0) | tall(X0) [cnf transformation 40]
120. ~humble(X0) | generous(X0) [cnf transformation 40]
134. brave(mary) | creative(mary) [cnf transformation 68]
137. humble(mary) [cnf transformation 24]
234. 22 <=> creative(mary) [avatar definition]
235. creative(mary) <- (22) [avatar component clause 234]
238. 23 <=> brave(mary) [avatar definition]
242. 22 | 23 [avatar split clause 134,238,234]
265. tall(mary) [resolution 118,137]
266. happy(mary) [resolution 265,103]
267. ~funny(mary) [resolution 266,109]
268. ~brave(mary) [resolution 266,108]
269. generous(mary) [resolution 120,137]
270. ~tall(mary) | ~quiet(mary) <- (22) [resolution 73,235]
271. ~quiet(mary) <- (22) [subsumption resolution 270,265]
288. funny(mary) | quiet(mary) [resolution 80,269]
308. quiet(mary) [subsumption resolution 288,267]
309. $false <- (22) [subsumption resolution 308,271]
310. ~22 [avatar contradiction clause 309]
312. ~23 [avatar split clause 268,238]
313. $false [avatar sat refutation 242,310,312]
% SZS output end Proof for 7571179680365770865628905
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not rich and strong is either patient or not funny and vice versa.
If john is both not curious and happy then someone is either quiet or happy and vice versa.
Everyone who is humble or strong is both not brave and old.
If mary is not kind or not curious then someone is not calm or calm.
Everyone who is either not curious or old is either not tall or creative.
Everyone who is not curious or not kind is both humble and creative and vice versa.
Everyone who is both curious and creative is either creative or funny.
Everyone who is wise is wise or patient.
Everyone who is not funny or creative is not creative or not old.
Everyone who is funny or strong is strong and vice versa.
If alice is tall then mary is patient.
Everyone who is both not humble and not creative is humble.
Everyone who is creative is not funny.
Everyone who is either kind or wise is either generous or not calm.
If john is either not happy or not brave then someone is wise or tall.
If someone is both quiet and kind then someone is both patient and not old.
Someone is not humble.
Someone is not humble or humble.
Someone is creative or not rich.
Mary is either calm or brave.
Someone is either not funny or patient.
Someone is either not strong or strong.
Fred is curious.
Alice is not brave. | Mary is curious. | entailment | (![X]:((~rich(X)&strong(X))<=>(patient(X)<~>~funny(X))))&
(((~curious(john)&happy(john)))<=>(?[X]:((quiet(X)<~>happy(X)))))&
(![X]:((humble(X)|strong(X))=>(~brave(X)&old(X))))&
(((~kind(mary)|~curious(mary)))=>(?[X]:((~calm(X)|calm(X)))))&
(![X]:((~curious(X)<~>old(X))=>(~tall(X)<~>creative(X))))&
(![X]:((~curious(X)|~kind(X))<=>(humble(X)&creative(X))))&
(![X]:((curious(X)&creative(X))=>(creative(X)<~>funny(X))))&
(![X]:(wise(X)=>(wise(X)|patient(X))))&
(![X]:((~funny(X)|creative(X))=>(~creative(X)|~old(X))))&
(![X]:((funny(X)|strong(X))<=>strong(X)))&
((tall(alice))=>(patient(mary)))&
(![X]:((~humble(X)&~creative(X))=>humble(X)))&
(![X]:(creative(X)=>~funny(X)))&
(![X]:((kind(X)<~>wise(X))=>(generous(X)<~>~calm(X))))&
(((~happy(john)<~>~brave(john)))=>(?[X]:((wise(X)|tall(X)))))&
((?[X]:((quiet(X)&kind(X))))=>(?[X]:((patient(X)&~old(X)))))&
(?[X]:(~humble(X)))&
(?[X]:((~humble(X)|humble(X))))&
(?[X]:((creative(X)|~rich(X))))&
((calm(mary)<~>brave(mary)))&
(?[X]:((~funny(X)<~>patient(X))))&
(?[X]:((~strong(X)<~>strong(X))))&
(curious(fred))&
(~brave(alice)) | curious(mary) | [
"p2",
"p5",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 1377522048232068006582168
% SZS output start Proof for 1377522048232068006582168
3. ! [X0] : ((strong(X0) | humble(X0)) => (old(X0) & ~brave(X0))) [input p2]
6. ! [X0] : ((~kind(X0) | ~curious(X0)) <=> (creative(X0) & humble(X0))) [input p5]
9. ! [X0] : ((creative(X0) | ~funny(X0)) => (~old(X0) | ~creative(X0))) [input p8]
25. ~curious(mary) [input hypothesis]
27. ! [X0] : ((old(X0) & ~brave(X0)) | (~strong(X0) & ~humble(X0))) [ennf transformation 3]
34. ! [X0] : ((~old(X0) | ~creative(X0)) | (~creative(X0) & funny(X0))) [ennf transformation 9]
35. ! [X0] : (~old(X0) | ~creative(X0) | (~creative(X0) & funny(X0))) [flattening 34]
53. ! [X0] : (((~kind(X0) | ~curious(X0)) | (~creative(X0) | ~humble(X0))) & ((creative(X0) & humble(X0)) | (kind(X0) & curious(X0)))) [nnf transformation 6]
54. ! [X0] : ((~kind(X0) | ~curious(X0) | ~creative(X0) | ~humble(X0)) & ((creative(X0) & humble(X0)) | (kind(X0) & curious(X0)))) [flattening 53]
92. ~humble(X0) | old(X0) [cnf transformation 27]
100. humble(X0) | curious(X0) [cnf transformation 54]
102. creative(X0) | curious(X0) [cnf transformation 54]
109. ~old(X0) | ~creative(X0) | ~creative(X0) [cnf transformation 35]
135. ~curious(mary) [cnf transformation 25]
137. ~creative(X0) | ~old(X0) [duplicate literal removal 109]
236. curious(X0) | old(X0) [resolution 100,92]
244. ~old(X2) | curious(X2) [resolution 137,102]
245. curious(X2) [subsumption resolution 244,236]
246. $false [resolution 245,135]
% SZS output end Proof for 1377522048232068006582168
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy or not curious is not tall or curious and vice versa.
Everyone who is not wise is either not kind or humble and vice versa.
If lucy is curious or not kind then lucy is both not funny and generous and vice versa.
Everyone who is both not quiet and generous is both not tall and not happy.
Everyone who is both humble and not generous is not funny or rich and vice versa.
If susan is both quiet and strong then fred is both tall and not funny and vice versa.
If someone is both not rich and patient then someone is both patient and curious.
If mary is not curious then someone is either quiet or not funny.
Everyone who is either humble or not funny is either strong or kind.
If someone is happy then someone is both not funny and not strong and vice versa.
If someone is either not happy or wise then someone is either not brave or strong.
Everyone who is not kind is both not creative and not generous and vice versa.
Everyone who is kind is not brave and vice versa.
If susan is happy or not tall then someone is not kind or not humble and vice versa.
Everyone who is both not generous and not creative is calm or patient and vice versa.
If susan is strong then alice is not calm or not quiet and vice versa.
Susan is happy.
John is funny.
Someone is not old.
Fred is both curious and wise.
Someone is not creative.
Lucy is either not wise or not brave.
Mary is happy or not quiet. | Lucy is not humble. | entailment | (![X]:((happy(X)<~>~curious(X))<=>(~tall(X)|curious(X))))&
(![X]:(~wise(X)<=>(~kind(X)<~>humble(X))))&
(((curious(lucy)|~kind(lucy)))<=>((~funny(lucy)&generous(lucy))))&
(![X]:((~quiet(X)&generous(X))=>(~tall(X)&~happy(X))))&
(![X]:((humble(X)&~generous(X))<=>(~funny(X)|rich(X))))&
(((quiet(susan)&strong(susan)))<=>((tall(fred)&~funny(fred))))&
((?[X]:((~rich(X)&patient(X))))=>(?[X]:((patient(X)&curious(X)))))&
((~curious(mary))=>(?[X]:((quiet(X)<~>~funny(X)))))&
(![X]:((humble(X)<~>~funny(X))=>(strong(X)<~>kind(X))))&
((?[X]:(happy(X)))<=>(?[X]:((~funny(X)&~strong(X)))))&
((?[X]:((~happy(X)<~>wise(X))))=>(?[X]:((~brave(X)<~>strong(X)))))&
(![X]:(~kind(X)<=>(~creative(X)&~generous(X))))&
(![X]:(kind(X)<=>~brave(X)))&
(((happy(susan)|~tall(susan)))<=>(?[X]:((~kind(X)|~humble(X)))))&
(![X]:((~generous(X)&~creative(X))<=>(calm(X)|patient(X))))&
((strong(susan))<=>((~calm(alice)|~quiet(alice))))&
(happy(susan))&
(funny(john))&
(?[X]:(~old(X)))&
((curious(fred)&wise(fred)))&
(?[X]:(~creative(X)))&
((~wise(lucy)<~>~brave(lucy)))&
((happy(mary)|~quiet(mary))) | ~humble(lucy) | [
"p1",
"p2",
"p4",
"p12",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 568842647909822985962009
% SZS output start Proof for 568842647909822985962009
2. ! [X0] : (~wise(X0) <=> (~kind(X0) <~> humble(X0))) [input p1]
3. (~kind(lucy) | curious(lucy)) <=> (generous(lucy) & ~funny(lucy)) [input p2]
5. ! [X0] : ((~generous(X0) & humble(X0)) <=> (rich(X0) | ~funny(X0))) [input p4]
13. ! [X0] : (kind(X0) <=> ~brave(X0)) [input p12]
22. ~wise(lucy) <~> ~brave(lucy) [input p21]
24. humble(lucy) [input hypothesis]
37. ! [X0] : ((~wise(X0) | ((~kind(X0) | ~humble(X0)) & (humble(X0) | kind(X0)))) & (((~humble(X0) | kind(X0)) & (humble(X0) | ~kind(X0))) | wise(X0))) [nnf transformation 2]
38. ((~kind(lucy) | curious(lucy)) | (~generous(lucy) | funny(lucy))) & ((generous(lucy) & ~funny(lucy)) | (kind(lucy) & ~curious(lucy))) [nnf transformation 3]
39. (~kind(lucy) | curious(lucy) | ~generous(lucy) | funny(lucy)) & ((generous(lucy) & ~funny(lucy)) | (kind(lucy) & ~curious(lucy))) [flattening 38]
40. ! [X0] : (((~generous(X0) & humble(X0)) | (~rich(X0) & funny(X0))) & ((rich(X0) | ~funny(X0)) | (generous(X0) | ~humble(X0)))) [nnf transformation 5]
41. ! [X0] : (((~generous(X0) & humble(X0)) | (~rich(X0) & funny(X0))) & (rich(X0) | ~funny(X0) | generous(X0) | ~humble(X0))) [flattening 40]
62. ! [X0] : ((kind(X0) | brave(X0)) & (~brave(X0) | ~kind(X0))) [nnf transformation 13]
74. (brave(lucy) | wise(lucy)) & (~brave(lucy) | ~wise(lucy)) [nnf transformation 22]
84. ~humble(X0) | ~kind(X0) | ~wise(X0) [cnf transformation 37]
86. ~funny(lucy) | kind(lucy) [cnf transformation 39]
88. generous(lucy) | kind(lucy) [cnf transformation 39]
95. ~generous(X0) | funny(X0) [cnf transformation 41]
119. ~brave(X0) | ~kind(X0) [cnf transformation 62]
139. brave(lucy) | wise(lucy) [cnf transformation 74]
141. humble(lucy) [cnf transformation 24]
146. 1 <=> funny(lucy) [avatar definition]
147. ~funny(lucy) <- (~1) [avatar component clause 146]
150. 2 <=> generous(lucy) [avatar definition]
151. generous(lucy) <- (2) [avatar component clause 150]
158. 4 <=> kind(lucy) [avatar definition]
159. kind(lucy) <- (4) [avatar component clause 158]
162. 4 | 2 [avatar split clause 88,150,158]
164. 4 | ~1 [avatar split clause 86,146,158]
283. 30 <=> wise(lucy) [avatar definition]
287. 31 <=> brave(lucy) [avatar definition]
289. brave(lucy) <- (31) [avatar component clause 287]
290. 30 | 31 [avatar split clause 139,287,283]
304. funny(lucy) <- (2) [resolution 95,151]
305. $false <- (~1, 2) [subsumption resolution 304,147]
306. 1 | ~2 [avatar contradiction clause 305]
387. ~kind(lucy) | ~wise(lucy) [resolution 84,141]
389. ~wise(lucy) <- (4) [subsumption resolution 387,159]
394. ~30 | ~4 [avatar split clause 389,158,283]
395. ~kind(lucy) <- (31) [resolution 289,119]
396. $false <- (4, 31) [subsumption resolution 395,159]
397. ~4 | ~31 [avatar contradiction clause 396]
398. $false [avatar sat refutation 162,164,290,306,394,397]
% SZS output end Proof for 568842647909822985962009
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble is wise or not wise and vice versa. Everyone who is not old is happy or patient. If someone is old then mary is not tall or strong. Everyone who is both not calm and rich is either not kind or not wise and vice versa. If lucy is either brave or happy then someone is both not kind and not generous and vice versa. If someone is strong then lucy is happy or not wise and vice versa. Everyone who is both patient and not funny is either wise or calm. Everyone who is not wise is patient or quiet and vice versa. If someone is rich or strong then someone is rich. If susan is not kind then alice is funny and vice versa. Everyone who is either generous or not kind is both not patient and not brave and vice versa. Everyone who is brave is kind. Everyone who is not funny is not rich or not strong. If lucy is either not creative or not generous then someone is curious. If alice is either not brave or humble then someone is not strong and vice versa. If someone is not wise then someone is patient or calm. Susan is patient. Someone is not happy or not rich. Someone is not brave or not generous. Fred is not calm. Someone is both not strong and generous. Fred is not rich. Someone is calm. Someone is both not funny and generous. | Alice is not brave. | contradiction | (![X]:(humble(X)<=>(wise(X)|~wise(X))))&
(![X]:(~old(X)=>(happy(X)|patient(X))))&
((?[X]:(old(X)))=>((~tall(mary)|strong(mary))))&
(![X]:((~calm(X)&rich(X))<=>(~kind(X)<~>~wise(X))))&
(((brave(lucy)<~>happy(lucy)))<=>(?[X]:((~kind(X)&~generous(X)))))&
((?[X]:(strong(X)))<=>((happy(lucy)|~wise(lucy))))&
(![X]:((patient(X)&~funny(X))=>(wise(X)<~>calm(X))))&
(![X]:(~wise(X)<=>(patient(X)|quiet(X))))&
((?[X]:((rich(X)|strong(X))))=>(?[X]:(rich(X))))&
((~kind(susan))<=>(funny(alice)))&
(![X]:((generous(X)<~>~kind(X))<=>(~patient(X)&~brave(X))))&
(![X]:(brave(X)=>kind(X)))&
(![X]:(~funny(X)=>(~rich(X)|~strong(X))))&
(((~creative(lucy)<~>~generous(lucy)))=>(?[X]:(curious(X))))&
(((~brave(alice)<~>humble(alice)))<=>(?[X]:(~strong(X))))&
((?[X]:(~wise(X)))=>(?[X]:((patient(X)|calm(X)))))&
(patient(susan))&
(?[X]:((~happy(X)|~rich(X))))&
(?[X]:((~brave(X)|~generous(X))))&
(~calm(fred))&
(?[X]:((~strong(X)&generous(X))))&
(~rich(fred))&
(?[X]:(calm(X)))&
(?[X]:((~funny(X)&generous(X)))) | ~brave(alice) | [
"p0",
"p14",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 6794254783165491967996853
% SZS output start Proof for 6794254783165491967996853
1. ! [X0] : (humble(X0) <=> (~wise(X0) | wise(X0))) [input p0]
15. (~brave(alice) <~> humble(alice)) <=> ? [X0] : ~strong(X0) [input p14]
21. ? [X0] : (generous(X0) & ~strong(X0)) [input p20]
25. ~brave(alice) [input hypothesis]
38. ! [X0] : ((humble(X0) | (wise(X0) & ~wise(X0))) & ((~wise(X0) | wise(X0)) | ~humble(X0))) [nnf transformation 1]
39. ! [X0] : ((humble(X0) | (wise(X0) & ~wise(X0))) & (~wise(X0) | wise(X0) | ~humble(X0))) [flattening 38]
60. (((~humble(alice) | brave(alice)) & (humble(alice) | ~brave(alice))) | ! [X0] : strong(X0)) & (? [X0] : ~strong(X0) | ((~brave(alice) | ~humble(alice)) & (humble(alice) | brave(alice)))) [nnf transformation 15]
61. (((~humble(alice) | brave(alice)) & (humble(alice) | ~brave(alice))) | ! [X0] : strong(X0)) & (? [X1] : ~strong(X1) | ((~brave(alice) | ~humble(alice)) & (humble(alice) | brave(alice)))) [rectify 60]
62. ? [X1] : ~strong(X1) => ~strong(sK3) [choice axiom]
63. (((~humble(alice) | brave(alice)) & (humble(alice) | ~brave(alice))) | ! [X0] : strong(X0)) & (~strong(sK3) | ((~brave(alice) | ~humble(alice)) & (humble(alice) | brave(alice)))) [skolemisation 61,62]
71. ? [X0] : (generous(X0) & ~strong(X0)) => (generous(sK7) & ~strong(sK7)) [choice axiom]
72. generous(sK7) & ~strong(sK7) [skolemisation 21,71]
78. humble(X0) | ~wise(X0) [cnf transformation 39]
79. humble(X0) | wise(X0) [cnf transformation 39]
115. ~humble(alice) | brave(alice) | strong(X0) [cnf transformation 63]
121. ~strong(sK7) [cnf transformation 72]
127. ~brave(alice) [cnf transformation 25]
128. humble(X0) [subsumption resolution 78,79]
187. brave(alice) | strong(X0) [subsumption resolution 115,128]
189. 13 <=> ! [X0] : strong(X0) [avatar definition]
190. strong(X0) <- (13) [avatar component clause 189]
192. 14 <=> brave(alice) [avatar definition]
195. 13 | 14 [avatar split clause 187,192,189]
232. ~14 [avatar split clause 127,192]
235. $false <- (13) [resolution 190,121]
236. ~13 [avatar contradiction clause 235]
237. $false [avatar sat refutation 195,232,236]
% SZS output end Proof for 6794254783165491967996853
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not tall is patient or not patient.
Everyone who is curious or funny is both not humble and not tall.
Everyone who is not rich or not old is not generous and vice versa.
If john is either funny or not rich then someone is creative and vice versa.
If someone is both not brave and not funny then someone is not old and vice versa.
Everyone who is both not rich and not kind is quiet and vice versa.
Everyone who is both curious and generous is both not calm and humble.
If alice is both happy and humble then john is either strong or tall.
If fred is either kind or generous then someone is old or humble and vice versa.
If someone is both not patient and not humble then lucy is not strong or not brave and vice versa.
If someone is not wise or not kind then someone is both quiet and calm.
If fred is not generous or quiet then someone is either not strong or calm and vice versa.
If someone is not generous then someone is both not curious and calm and vice versa.
Everyone who is generous is not curious and vice versa.
Everyone who is not old or not rich is old or not generous.
Everyone who is not calm or curious is calm.
Someone is not wise.
Someone is either calm or not generous.
Someone is tall.
Susan is curious.
Someone is either happy or tall.
Someone is creative or not funny.
Someone is not curious or brave. | Susan is not generous. | entailment | (![X]:(~tall(X)=>(patient(X)|~patient(X))))&
(![X]:((curious(X)|funny(X))=>(~humble(X)&~tall(X))))&
(![X]:((~rich(X)|~old(X))<=>~generous(X)))&
(((funny(john)<~>~rich(john)))<=>(?[X]:(creative(X))))&
((?[X]:((~brave(X)&~funny(X))))<=>(?[X]:(~old(X))))&
(![X]:((~rich(X)&~kind(X))<=>quiet(X)))&
(![X]:((curious(X)&generous(X))=>(~calm(X)&humble(X))))&
(((happy(alice)&humble(alice)))=>((strong(john)<~>tall(john))))&
(((kind(fred)<~>generous(fred)))<=>(?[X]:((old(X)|humble(X)))))&
((?[X]:((~patient(X)&~humble(X))))<=>((~strong(lucy)|~brave(lucy))))&
((?[X]:((~wise(X)|~kind(X))))=>(?[X]:((quiet(X)&calm(X)))))&
(((~generous(fred)|quiet(fred)))<=>(?[X]:((~strong(X)<~>calm(X)))))&
((?[X]:(~generous(X)))<=>(?[X]:((~curious(X)&calm(X)))))&
(![X]:(generous(X)<=>~curious(X)))&
(![X]:((~old(X)|~rich(X))=>(old(X)|~generous(X))))&
(![X]:((~calm(X)|curious(X))=>calm(X)))&
(?[X]:(~wise(X)))&
(?[X]:((calm(X)<~>~generous(X))))&
(?[X]:(tall(X)))&
(curious(susan))&
(?[X]:((happy(X)<~>tall(X))))&
(?[X]:((creative(X)|~funny(X))))&
(?[X]:((~curious(X)|brave(X)))) | ~generous(susan) | [
"p1",
"p6",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 3114206158644384734651902
% SZS output start Proof for 3114206158644384734651902
2. ! [X0] : ((funny(X0) | curious(X0)) => (~tall(X0) & ~humble(X0))) [input p1]
7. ! [X0] : ((generous(X0) & curious(X0)) => (humble(X0) & ~calm(X0))) [input p6]
20. curious(susan) [input p19]
24. generous(susan) [input hypothesis]
30. ! [X0] : ((~tall(X0) & ~humble(X0)) | (~funny(X0) & ~curious(X0))) [ennf transformation 2]
31. ! [X0] : ((humble(X0) & ~calm(X0)) | (~generous(X0) | ~curious(X0))) [ennf transformation 7]
32. ! [X0] : ((humble(X0) & ~calm(X0)) | ~generous(X0) | ~curious(X0)) [flattening 31]
91. ~humble(X0) | ~curious(X0) [cnf transformation 30]
109. humble(X0) | ~generous(X0) | ~curious(X0) [cnf transformation 32]
146. curious(susan) [cnf transformation 20]
151. generous(susan) [cnf transformation 24]
194. ~generous(X0) | ~curious(X0) [subsumption resolution 109,91]
397. ~curious(susan) [resolution 194,151]
399. $false [subsumption resolution 397,146]
% SZS output end Proof for 3114206158644384734651902
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not rich or rich is both not humble and brave.
Everyone who is both strong and brave is not wise.
Everyone who is both not funny and not kind is either strong or happy and vice versa.
If someone is funny then someone is wise or quiet.
Everyone who is not wise or happy is both creative and wise.
If someone is rich or not creative then someone is not curious or old.
If susan is both not curious and happy then someone is both not rich and not tall and vice versa.
If someone is either wise or quiet then paul is both creative and not creative and vice versa.
If susan is both not humble and not old then mary is curious or not old.
If someone is both not humble and not patient then susan is not quiet and vice versa.
Everyone who is not rich is brave and vice versa.
Everyone who is both old and kind is not funny.
If someone is either not quiet or not strong then john is wise.
If someone is either generous or not quiet then mary is both funny and not rich.
Everyone who is either quiet or curious is either creative or rich and vice versa.
If someone is not patient then alice is not funny.
Paul is not tall or strong.
Someone is either not happy or not brave.
Someone is either funny or creative.
Someone is both not old and tall.
Mary is generous or not wise.
Lucy is either not tall or not patient. | Paul is brave. | entailment | (![X]:((~rich(X)|rich(X))=>(~humble(X)&brave(X))))&
(![X]:((strong(X)&brave(X))=>~wise(X)))&
(![X]:((~funny(X)&~kind(X))<=>(strong(X)<~>happy(X))))&
((?[X]:(funny(X)))=>(?[X]:((wise(X)|quiet(X)))))&
(![X]:((~wise(X)|happy(X))=>(creative(X)&wise(X))))&
((?[X]:((rich(X)|~creative(X))))=>(?[X]:((~curious(X)|old(X)))))&
(((~curious(susan)&happy(susan)))<=>(?[X]:((~rich(X)&~tall(X)))))&
((?[X]:((wise(X)<~>quiet(X))))<=>((creative(paul)&~creative(paul))))&
(((~humble(susan)&~old(susan)))=>((curious(mary)|~old(mary))))&
((?[X]:((~humble(X)&~patient(X))))<=>(~quiet(susan)))&
(![X]:(~rich(X)<=>brave(X)))&
(![X]:((old(X)&kind(X))=>~funny(X)))&
((?[X]:((~quiet(X)<~>~strong(X))))=>(wise(john)))&
((?[X]:((generous(X)<~>~quiet(X))))=>((funny(mary)&~rich(mary))))&
(![X]:((quiet(X)<~>curious(X))<=>(creative(X)<~>rich(X))))&
((?[X]:(~patient(X)))=>(~funny(alice)))&
((~tall(paul)|strong(paul)))&
(?[X]:((~happy(X)<~>~brave(X))))&
(?[X]:((funny(X)<~>creative(X))))&
(?[X]:((~old(X)&tall(X))))&
((generous(mary)|~wise(mary)))&
((~tall(lucy)<~>~patient(lucy))) | brave(paul) | [
"p0",
"hypothesis"
] | % SZS status Unsatisfiable for 2318633260401100087295408
% SZS output start Proof for 2318633260401100087295408
1. ! [X0] : ((rich(X0) | ~rich(X0)) => (brave(X0) & ~humble(X0))) [input p0]
23. ~brave(paul) [input hypothesis]
26. ! [X0] : ((brave(X0) & ~humble(X0)) | (~rich(X0) & rich(X0))) [ennf transformation 1]
76. brave(X0) | rich(X0) [cnf transformation 26]
77. brave(X0) | ~rich(X0) [cnf transformation 26]
134. ~brave(paul) [cnf transformation 23]
136. brave(X0) [subsumption resolution 76,77]
285. $false [subsumption resolution 134,136]
% SZS output end Proof for 2318633260401100087295408
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous or not humble then lucy is either not old or humble.
If someone is either creative or not curious then john is either funny or happy and vice versa.
Everyone who is either curious or not generous is calm or curious and vice versa.
If paul is either not old or not funny then someone is both happy and old.
Everyone who is not rich or not generous is not old and vice versa.
Everyone who is not funny is either not brave or not funny.
Everyone who is not old is either not curious or not humble and vice versa.
Everyone who is strong or not tall is not strong or generous and vice versa.
If paul is either not wise or strong then someone is both not funny and funny.
If someone is curious then someone is quiet.
If someone is not kind then someone is either generous or old.
Everyone who is either not creative or not tall is both quiet and not generous.
If someone is not curious then someone is either not calm or not tall and vice versa.
Everyone who is kind is either not generous or not strong.
If john is creative or generous then someone is both generous and not generous.
If mary is not tall then mary is not creative or not old.
Someone is either not patient or funny.
Someone is tall.
Mary is kind.
Someone is either patient or not strong.
Someone is happy.
Lucy is strong or not quiet.
Someone is not creative or not brave.
John is calm. | John is generous. | contradiction | ((?[X]:((~generous(X)|~humble(X))))=>((~old(lucy)<~>humble(lucy))))&
((?[X]:((creative(X)<~>~curious(X))))<=>((funny(john)<~>happy(john))))&
(![X]:((curious(X)<~>~generous(X))<=>(calm(X)|curious(X))))&
(((~old(paul)<~>~funny(paul)))=>(?[X]:((happy(X)&old(X)))))&
(![X]:((~rich(X)|~generous(X))<=>~old(X)))&
(![X]:(~funny(X)=>(~brave(X)<~>~funny(X))))&
(![X]:(~old(X)<=>(~curious(X)<~>~humble(X))))&
(![X]:((strong(X)|~tall(X))<=>(~strong(X)|generous(X))))&
(((~wise(paul)<~>strong(paul)))=>(?[X]:((~funny(X)&funny(X)))))&
((?[X]:(curious(X)))=>(?[X]:(quiet(X))))&
((?[X]:(~kind(X)))=>(?[X]:((generous(X)<~>old(X)))))&
(![X]:((~creative(X)<~>~tall(X))=>(quiet(X)&~generous(X))))&
((?[X]:(~curious(X)))<=>(?[X]:((~calm(X)<~>~tall(X)))))&
(![X]:(kind(X)=>(~generous(X)<~>~strong(X))))&
(((creative(john)|generous(john)))=>(?[X]:((generous(X)&~generous(X)))))&
((~tall(mary))=>((~creative(mary)|~old(mary))))&
(?[X]:((~patient(X)<~>funny(X))))&
(?[X]:(tall(X)))&
(kind(mary))&
(?[X]:((patient(X)<~>~strong(X))))&
(?[X]:(happy(X)))&
((strong(lucy)|~quiet(lucy)))&
(?[X]:((~creative(X)|~brave(X))))&
(calm(john)) | generous(john) | [
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 9125205258044798715738050
% SZS output start Proof for 9125205258044798715738050
15. (generous(john) | creative(john)) => ? [X0] : (~generous(X0) & generous(X0)) [input p14]
25. generous(john) [input hypothesis]
37. ? [X0] : (~generous(X0) & generous(X0)) | (~generous(john) & ~creative(john)) [ennf transformation 15]
73. ? [X0] : (~generous(X0) & generous(X0)) => (~generous(sK7) & generous(sK7)) [choice axiom]
74. (~generous(sK7) & generous(sK7)) | (~generous(john) & ~creative(john)) [skolemisation 37,73]
140. generous(sK7) | ~generous(john) [cnf transformation 74]
142. ~generous(sK7) | ~generous(john) [cnf transformation 74]
154. generous(john) [cnf transformation 25]
296. 29 <=> generous(john) [avatar definition]
300. 30 <=> generous(sK7) [avatar definition]
303. ~29 | ~30 [avatar split clause 142,300,296]
309. ~29 | 30 [avatar split clause 140,300,296]
362. 29 [avatar split clause 154,296]
363. $false [avatar sat refutation 303,309,362]
% SZS output end Proof for 9125205258044798715738050
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not tall or humble is either not creative or not kind and vice versa. If someone is quiet then someone is not calm. If someone is both not humble and creative then lucy is quiet or not tall. Everyone who is either happy or generous is both not creative and quiet. Everyone who is both generous and not quiet is both happy and calm and vice versa. If someone is brave or creative then alice is both not old and not strong and vice versa. If lucy is either strong or not funny then fred is kind or patient and vice versa. If alice is both tall and not calm then someone is both happy and not quiet. Everyone who is not tall is both wise and tall. Everyone who is not generous is not wise or tall and vice versa. Everyone who is either not calm or not wise is happy or calm. Everyone who is old is not generous and vice versa. Everyone who is quiet or old is either rich or not brave and vice versa. Everyone who is not calm or patient is either not funny or not humble and vice versa. Everyone who is either not rich or not quiet is wise or patient and vice versa. Everyone who is curious is not wise and vice versa. John is not kind. Fred is not creative or calm. Someone is either wise or humble. Mary is wise or not tall. Fred is either calm or tall. Mary is either not quiet or old. Alice is either funny or not generous. | Lucy is not creative. | entailment | (![X]:((~tall(X)<~>humble(X))<=>(~creative(X)<~>~kind(X))))&
((?[X]:(quiet(X)))=>(?[X]:(~calm(X))))&
((?[X]:((~humble(X)&creative(X))))=>((quiet(lucy)|~tall(lucy))))&
(![X]:((happy(X)<~>generous(X))=>(~creative(X)&quiet(X))))&
(![X]:((generous(X)&~quiet(X))<=>(happy(X)&calm(X))))&
((?[X]:((brave(X)|creative(X))))<=>((~old(alice)&~strong(alice))))&
(((strong(lucy)<~>~funny(lucy)))<=>((kind(fred)|patient(fred))))&
(((tall(alice)&~calm(alice)))=>(?[X]:((happy(X)&~quiet(X)))))&
(![X]:(~tall(X)=>(wise(X)&tall(X))))&
(![X]:(~generous(X)<=>(~wise(X)|tall(X))))&
(![X]:((~calm(X)<~>~wise(X))=>(happy(X)|calm(X))))&
(![X]:(old(X)<=>~generous(X)))&
(![X]:((quiet(X)|old(X))<=>(rich(X)<~>~brave(X))))&
(![X]:((~calm(X)|patient(X))<=>(~funny(X)<~>~humble(X))))&
(![X]:((~rich(X)<~>~quiet(X))<=>(wise(X)|patient(X))))&
(![X]:(curious(X)<=>~wise(X)))&
(~kind(john))&
((~creative(fred)|calm(fred)))&
(?[X]:((wise(X)<~>humble(X))))&
((wise(mary)|~tall(mary)))&
((calm(fred)<~>tall(fred)))&
((~quiet(mary)<~>old(mary)))&
((funny(alice)<~>~generous(alice))) | ~creative(lucy) | [
"p5",
"p8",
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 8333356010454068181132305
% SZS output start Proof for 8333356010454068181132305
6. ? [X0] : (creative(X0) | brave(X0)) <=> (~strong(alice) & ~old(alice)) [input p5]
9. ! [X0] : (~tall(X0) => (tall(X0) & wise(X0))) [input p8]
10. ! [X0] : (~generous(X0) <=> (tall(X0) | ~wise(X0))) [input p9]
12. ! [X0] : (old(X0) <=> ~generous(X0)) [input p11]
24. creative(lucy) [input hypothesis]
32. ! [X0] : ((tall(X0) & wise(X0)) | tall(X0)) [ennf transformation 9]
42. (? [X0] : (creative(X0) | brave(X0)) | (strong(alice) | old(alice))) & ((~strong(alice) & ~old(alice)) | ! [X0] : (~creative(X0) & ~brave(X0))) [nnf transformation 6]
43. (? [X0] : (creative(X0) | brave(X0)) | strong(alice) | old(alice)) & ((~strong(alice) & ~old(alice)) | ! [X0] : (~creative(X0) & ~brave(X0))) [flattening 42]
44. (? [X0] : (creative(X0) | brave(X0)) | strong(alice) | old(alice)) & ((~strong(alice) & ~old(alice)) | ! [X1] : (~creative(X1) & ~brave(X1))) [rectify 43]
45. ? [X0] : (creative(X0) | brave(X0)) => (creative(sK1) | brave(sK1)) [choice axiom]
46. ((creative(sK1) | brave(sK1)) | strong(alice) | old(alice)) & ((~strong(alice) & ~old(alice)) | ! [X1] : (~creative(X1) & ~brave(X1))) [skolemisation 44,45]
51. ! [X0] : ((~generous(X0) | (~tall(X0) & wise(X0))) & ((tall(X0) | ~wise(X0)) | generous(X0))) [nnf transformation 10]
52. ! [X0] : ((~generous(X0) | (~tall(X0) & wise(X0))) & (tall(X0) | ~wise(X0) | generous(X0))) [flattening 51]
54. ! [X0] : ((old(X0) | generous(X0)) & (~generous(X0) | ~old(X0))) [nnf transformation 12]
86. ~old(alice) | ~creative(X1) [cnf transformation 46]
99. tall(X0) | tall(X0) [cnf transformation 32]
102. ~generous(X0) | ~tall(X0) [cnf transformation 52]
106. old(X0) | generous(X0) [cnf transformation 54]
136. creative(lucy) [cnf transformation 24]
138. tall(X0) [duplicate literal removal 99]
160. 6 <=> old(alice) [avatar definition]
161. ~old(alice) <- (~6) [avatar component clause 160]
177. 10 <=> ! [X1] : ~creative(X1) [avatar definition]
178. ~creative(X1) <- (10) [avatar component clause 177]
184. 10 | ~6 [avatar split clause 86,160,177]
226. ~generous(X0) [subsumption resolution 102,138]
227. old(X0) [subsumption resolution 106,226]
256. $false <- (~6) [subsumption resolution 161,227]
257. 6 [avatar contradiction clause 256]
260. $false <- (10) [resolution 178,136]
261. ~10 [avatar contradiction clause 260]
262. $false [avatar sat refutation 184,257,261]
% SZS output end Proof for 8333356010454068181132305
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not creative or patient then lucy is either strong or not brave and vice versa. Everyone who is old is not humble and vice versa. If someone is either not wise or not funny then susan is both not creative and creative. Everyone who is not patient is curious or not curious. Everyone who is rich is old and vice versa. If alice is not curious or old then someone is both calm and not strong. If john is both not quiet and humble then paul is either quiet or not creative. If someone is both humble and not quiet then someone is not creative or creative. Everyone who is not old is both calm and not funny. Everyone who is both old and not patient is either happy or not curious. Everyone who is old or funny is both not happy and not patient. If john is either humble or not rich then someone is both not kind and tall. If susan is not wise then john is generous or funny and vice versa. If someone is either happy or not generous then john is not funny or wise and vice versa. If alice is either rich or not quiet then someone is not strong. Everyone who is calm or not happy is curious and vice versa. John is not happy. John is not patient. Someone is not curious or not brave. Someone is curious or quiet. Lucy is either not curious or kind. | Alice is not generous. | neutral | (((~creative(fred)<~>patient(fred)))<=>((strong(lucy)<~>~brave(lucy))))&
(![X]:(old(X)<=>~humble(X)))&
((?[X]:((~wise(X)<~>~funny(X))))=>((~creative(susan)&creative(susan))))&
(![X]:(~patient(X)=>(curious(X)|~curious(X))))&
(![X]:(rich(X)<=>old(X)))&
(((~curious(alice)|old(alice)))=>(?[X]:((calm(X)&~strong(X)))))&
(((~quiet(john)&humble(john)))=>((quiet(paul)<~>~creative(paul))))&
((?[X]:((humble(X)&~quiet(X))))=>(?[X]:((~creative(X)|creative(X)))))&
(![X]:(~old(X)=>(calm(X)&~funny(X))))&
(![X]:((old(X)&~patient(X))=>(happy(X)<~>~curious(X))))&
(![X]:((old(X)|funny(X))=>(~happy(X)&~patient(X))))&
(((humble(john)<~>~rich(john)))=>(?[X]:((~kind(X)&tall(X)))))&
((~wise(susan))<=>((generous(john)|funny(john))))&
((?[X]:((happy(X)<~>~generous(X))))<=>((~funny(john)|wise(john))))&
(((rich(alice)<~>~quiet(alice)))=>(?[X]:(~strong(X))))&
(![X]:((calm(X)|~happy(X))<=>curious(X)))&
(~happy(john))&
(~patient(john))&
(?[X]:((~curious(X)|~brave(X))))&
(?[X]:((curious(X)|quiet(X))))&
((~curious(lucy)<~>kind(lucy))) | ~generous(alice) | [] | null | 0 |
If fred is tall or not patient then paul is not kind or happy and vice versa. Everyone who is quiet is kind. Everyone who is either rich or funny is either strong or generous and vice versa. Everyone who is either tall or creative is quiet or not strong. Everyone who is both not tall and wise is not curious and vice versa. Everyone who is generous is brave or old and vice versa. Everyone who is not rich or brave is either brave or not old and vice versa. Everyone who is not humble is kind. If alice is either not quiet or humble then someone is both tall and old and vice versa. Everyone who is creative is either not curious or not funny. Everyone who is both kind and generous is not brave or tall and vice versa. If fred is kind then susan is not curious. If someone is either strong or not quiet then someone is either brave or not rich. If someone is not creative or quiet then john is not generous and vice versa. Everyone who is both creative and not rich is both not wise and not curious and vice versa. If john is either funny or happy then someone is not humble and vice versa. Alice is either not patient or strong. Lucy is either not tall or not curious. Someone is not strong or generous. Alice is either not funny or funny. Someone is old. | Paul is not curious. | contradiction | (((tall(fred)|~patient(fred)))<=>((~kind(paul)|happy(paul))))&
(![X]:(quiet(X)=>kind(X)))&
(![X]:((rich(X)<~>funny(X))<=>(strong(X)<~>generous(X))))&
(![X]:((tall(X)<~>creative(X))=>(quiet(X)|~strong(X))))&
(![X]:((~tall(X)&wise(X))<=>~curious(X)))&
(![X]:(generous(X)<=>(brave(X)|old(X))))&
(![X]:((~rich(X)|brave(X))<=>(brave(X)<~>~old(X))))&
(![X]:(~humble(X)=>kind(X)))&
(((~quiet(alice)<~>humble(alice)))<=>(?[X]:((tall(X)&old(X)))))&
(![X]:(creative(X)=>(~curious(X)<~>~funny(X))))&
(![X]:((kind(X)&generous(X))<=>(~brave(X)|tall(X))))&
((kind(fred))=>(~curious(susan)))&
((?[X]:((strong(X)<~>~quiet(X))))=>(?[X]:((brave(X)<~>~rich(X)))))&
((?[X]:((~creative(X)|quiet(X))))<=>(~generous(john)))&
(![X]:((creative(X)&~rich(X))<=>(~wise(X)&~curious(X))))&
(((funny(john)<~>happy(john)))<=>(?[X]:(~humble(X))))&
((~patient(alice)<~>strong(alice)))&
((~tall(lucy)<~>~curious(lucy)))&
(?[X]:((~strong(X)|generous(X))))&
((~funny(alice)<~>funny(alice)))&
(?[X]:(old(X))) | ~curious(paul) | [
"p2",
"p3",
"p4",
"p5",
"p9",
"p10",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5798737951297405755518675
% SZS output start Proof for 5798737951297405755518675
3. ! [X0] : ((rich(X0) <~> funny(X0)) <=> (strong(X0) <~> generous(X0))) [input p2]
4. ! [X0] : ((tall(X0) <~> creative(X0)) => (~strong(X0) | quiet(X0))) [input p3]
5. ! [X0] : ((wise(X0) & ~tall(X0)) <=> ~curious(X0)) [input p4]
6. ! [X0] : (generous(X0) <=> (old(X0) | brave(X0))) [input p5]
10. ! [X0] : (creative(X0) => (~curious(X0) <~> ~funny(X0))) [input p9]
11. ! [X0] : ((generous(X0) & kind(X0)) <=> (tall(X0) | ~brave(X0))) [input p10]
14. ? [X0] : (quiet(X0) | ~creative(X0)) <=> ~generous(john) [input p13]
15. ! [X0] : ((~rich(X0) & creative(X0)) <=> (~curious(X0) & ~wise(X0))) [input p14]
22. ~curious(paul) [input hypothesis]
25. ! [X0] : ((~strong(X0) | quiet(X0)) | (tall(X0) <=> creative(X0))) [ennf transformation 4]
26. ! [X0] : (~strong(X0) | quiet(X0) | (tall(X0) <=> creative(X0))) [flattening 25]
28. ! [X0] : ((~curious(X0) <~> ~funny(X0)) | ~creative(X0)) [ennf transformation 10]
33. ! [X0] : ((((~funny(X0) | ~rich(X0)) & (funny(X0) | rich(X0))) | ((strong(X0) | ~generous(X0)) & (generous(X0) | ~strong(X0)))) & (((~generous(X0) | ~strong(X0)) & (generous(X0) | strong(X0))) | ((rich(X0) | ~funny(X0)) & (funny(X0) | ~rich(X0))))) [nnf transformation 3]
34. ! [X0] : (~strong(X0) | quiet(X0) | ((tall(X0) | ~creative(X0)) & (creative(X0) | ~tall(X0)))) [nnf transformation 26]
35. ! [X0] : (((wise(X0) & ~tall(X0)) | curious(X0)) & (~curious(X0) | (~wise(X0) | tall(X0)))) [nnf transformation 5]
36. ! [X0] : (((wise(X0) & ~tall(X0)) | curious(X0)) & (~curious(X0) | ~wise(X0) | tall(X0))) [flattening 35]
37. ! [X0] : ((generous(X0) | (~old(X0) & ~brave(X0))) & ((old(X0) | brave(X0)) | ~generous(X0))) [nnf transformation 6]
38. ! [X0] : ((generous(X0) | (~old(X0) & ~brave(X0))) & (old(X0) | brave(X0) | ~generous(X0))) [flattening 37]
45. ! [X0] : (((funny(X0) | curious(X0)) & (~funny(X0) | ~curious(X0))) | ~creative(X0)) [nnf transformation 28]
46. ! [X0] : (((generous(X0) & kind(X0)) | (~tall(X0) & brave(X0))) & ((tall(X0) | ~brave(X0)) | (~generous(X0) | ~kind(X0)))) [nnf transformation 11]
47. ! [X0] : (((generous(X0) & kind(X0)) | (~tall(X0) & brave(X0))) & (tall(X0) | ~brave(X0) | ~generous(X0) | ~kind(X0))) [flattening 46]
52. (? [X0] : (quiet(X0) | ~creative(X0)) | generous(john)) & (~generous(john) | ! [X0] : (~quiet(X0) & creative(X0))) [nnf transformation 14]
53. (? [X0] : (quiet(X0) | ~creative(X0)) | generous(john)) & (~generous(john) | ! [X1] : (~quiet(X1) & creative(X1))) [rectify 52]
54. ? [X0] : (quiet(X0) | ~creative(X0)) => (quiet(sK2) | ~creative(sK2)) [choice axiom]
55. ((quiet(sK2) | ~creative(sK2)) | generous(john)) & (~generous(john) | ! [X1] : (~quiet(X1) & creative(X1))) [skolemisation 53,54]
56. ! [X0] : (((~rich(X0) & creative(X0)) | (curious(X0) | wise(X0))) & ((~curious(X0) & ~wise(X0)) | (rich(X0) | ~creative(X0)))) [nnf transformation 15]
57. ! [X0] : (((~rich(X0) & creative(X0)) | curious(X0) | wise(X0)) & ((~curious(X0) & ~wise(X0)) | rich(X0) | ~creative(X0))) [flattening 56]
81. ~generous(X0) | ~rich(X0) | strong(X0) | ~funny(X0) [cnf transformation 33]
83. ~creative(X0) | quiet(X0) | tall(X0) | ~strong(X0) [cnf transformation 34]
85. ~tall(X0) | curious(X0) [cnf transformation 36]
86. curious(X0) | wise(X0) [cnf transformation 36]
88. ~brave(X0) | generous(X0) [cnf transformation 38]
104. ~creative(X0) | curious(X0) | funny(X0) [cnf transformation 45]
108. generous(X0) | brave(X0) [cnf transformation 47]
115. ~generous(john) | creative(X1) [cnf transformation 55]
116. ~generous(john) | ~quiet(X1) [cnf transformation 55]
118. ~wise(X0) | rich(X0) | ~creative(X0) [cnf transformation 57]
119. ~curious(X0) | rich(X0) | ~creative(X0) [cnf transformation 57]
134. ~curious(paul) [cnf transformation 22]
182. generous(X0) [subsumption resolution 108,88]
211. ~quiet(X1) [subsumption resolution 116,182]
212. creative(X1) [subsumption resolution 115,182]
213. ~curious(X0) | rich(X0) [subsumption resolution 119,212]
214. ~wise(X0) | rich(X0) [subsumption resolution 118,212]
260. rich(X0) | wise(X0) [resolution 213,86]
261. rich(X0) [subsumption resolution 260,214]
283. curious(X0) | funny(X0) [resolution 104,212]
300. funny(paul) [resolution 283,134]
310. ~rich(X0) | strong(X0) | ~funny(X0) [resolution 81,182]
311. ~funny(X0) | strong(X0) [subsumption resolution 310,261]
313. strong(paul) [resolution 311,300]
318. quiet(X0) | tall(X0) | ~strong(X0) [resolution 83,212]
319. ~strong(X0) | tall(X0) [subsumption resolution 318,211]
343. tall(paul) [resolution 313,319]
353. curious(paul) [resolution 343,85]
356. $false [subsumption resolution 353,134]
% SZS output end Proof for 5798737951297405755518675
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not tall then someone is either kind or old.
If mary is either calm or not calm then someone is not funny and vice versa.
If someone is both not creative and calm then lucy is either not humble or not brave and vice versa.
If someone is either rich or not calm then someone is brave or kind.
If susan is either funny or not tall then john is either not quiet or rich and vice versa.
If someone is both tall and funny then lucy is either wise or not wise and vice versa.
Everyone who is both not happy and happy is either not old or not strong and vice versa.
Everyone who is either not brave or not quiet is either happy or generous and vice versa.
If someone is either not strong or funny then someone is either not brave or not old and vice versa.
Everyone who is both strong and not strong is not strong and vice versa.
Everyone who is either strong or not old is either patient or not generous and vice versa.
Everyone who is not quiet or calm is patient.
Everyone who is not quiet is either not wise or not brave.
Everyone who is either tall or patient is not wise and vice versa.
Everyone who is both not quiet and kind is either not wise or not old.
Everyone who is curious or not quiet is quiet or brave and vice versa.
Someone is generous.
Someone is either generous or not wise.
Someone is both humble and funny.
Someone is happy.
Alice is not strong or not kind.
Someone is not curious.
Someone is either not old or not creative. | Alice is not calm. | neutral | ((?[X]:(~tall(X)))=>(?[X]:((kind(X)<~>old(X)))))&
(((calm(mary)<~>~calm(mary)))<=>(?[X]:(~funny(X))))&
((?[X]:((~creative(X)&calm(X))))<=>((~humble(lucy)<~>~brave(lucy))))&
((?[X]:((rich(X)<~>~calm(X))))=>(?[X]:((brave(X)|kind(X)))))&
(((funny(susan)<~>~tall(susan)))<=>((~quiet(john)<~>rich(john))))&
((?[X]:((tall(X)&funny(X))))<=>((wise(lucy)<~>~wise(lucy))))&
(![X]:((~happy(X)&happy(X))<=>(~old(X)<~>~strong(X))))&
(![X]:((~brave(X)<~>~quiet(X))<=>(happy(X)<~>generous(X))))&
((?[X]:((~strong(X)<~>funny(X))))<=>(?[X]:((~brave(X)<~>~old(X)))))&
(![X]:((strong(X)&~strong(X))<=>~strong(X)))&
(![X]:((strong(X)<~>~old(X))<=>(patient(X)<~>~generous(X))))&
(![X]:((~quiet(X)|calm(X))=>patient(X)))&
(![X]:(~quiet(X)=>(~wise(X)<~>~brave(X))))&
(![X]:((tall(X)<~>patient(X))<=>~wise(X)))&
(![X]:((~quiet(X)&kind(X))=>(~wise(X)<~>~old(X))))&
(![X]:((curious(X)|~quiet(X))<=>(quiet(X)|brave(X))))&
(?[X]:(generous(X)))&
(?[X]:((generous(X)<~>~wise(X))))&
(?[X]:((humble(X)&funny(X))))&
(?[X]:(happy(X)))&
((~strong(alice)|~kind(alice)))&
(?[X]:(~curious(X)))&
(?[X]:((~old(X)<~>~creative(X)))) | ~calm(alice) | [] | null | 0 |
Everyone who is creative or not generous is wise.
Everyone who is brave or not rich is not wise or not generous and vice versa.
Everyone who is not quiet or creative is either not quiet or happy and vice versa.
Everyone who is both not quiet and not calm is old or not humble and vice versa.
Everyone who is not calm is wise or strong and vice versa.
Everyone who is calm is not calm or not funny and vice versa.
Everyone who is either calm or not funny is not calm or not rich.
If someone is not quiet then paul is strong or not calm.
If fred is either old or wise then susan is tall or patient.
Everyone who is wise or patient is patient and vice versa.
Everyone who is both quiet and not tall is brave or quiet.
Everyone who is not old or not rich is wise or not brave.
If fred is both not calm and not happy then paul is either not tall or humble and vice versa.
If alice is not patient then lucy is both strong and not quiet and vice versa.
Someone is not old or not creative.
Lucy is either not quiet or generous.
Susan is both curious and not wise.
Someone is not curious.
Someone is humble.
Someone is either generous or not patient. | Alice is rich. | contradiction | (![X]:((creative(X)|~generous(X))=>wise(X)))&
(![X]:((brave(X)|~rich(X))<=>(~wise(X)|~generous(X))))&
(![X]:((~quiet(X)|creative(X))<=>(~quiet(X)<~>happy(X))))&
(![X]:((~quiet(X)&~calm(X))<=>(old(X)|~humble(X))))&
(![X]:(~calm(X)<=>(wise(X)|strong(X))))&
(![X]:(calm(X)<=>(~calm(X)|~funny(X))))&
(![X]:((calm(X)<~>~funny(X))=>(~calm(X)|~rich(X))))&
((?[X]:(~quiet(X)))=>((strong(paul)|~calm(paul))))&
(((old(fred)<~>wise(fred)))=>((tall(susan)|patient(susan))))&
(![X]:((wise(X)|patient(X))<=>patient(X)))&
(![X]:((quiet(X)&~tall(X))=>(brave(X)|quiet(X))))&
(![X]:((~old(X)|~rich(X))=>(wise(X)|~brave(X))))&
(((~calm(fred)&~happy(fred)))<=>((~tall(paul)<~>humble(paul))))&
((~patient(alice))<=>((strong(lucy)&~quiet(lucy))))&
(?[X]:((~old(X)|~creative(X))))&
((~quiet(lucy)<~>generous(lucy)))&
((curious(susan)&~wise(susan)))&
(?[X]:(~curious(X)))&
(?[X]:(humble(X)))&
(?[X]:((generous(X)<~>~patient(X)))) | rich(alice) | [
"p1",
"p3",
"p4",
"p5",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 6627840819426939695962361
% SZS output start Proof for 6627840819426939695962361
2. ! [X0] : ((~rich(X0) | brave(X0)) <=> (~generous(X0) | ~wise(X0))) [input p1]
4. ! [X0] : ((~calm(X0) & ~quiet(X0)) <=> (~humble(X0) | old(X0))) [input p3]
5. ! [X0] : (~calm(X0) <=> (strong(X0) | wise(X0))) [input p4]
6. ! [X0] : (calm(X0) <=> (~funny(X0) | ~calm(X0))) [input p5]
12. ! [X0] : ((~rich(X0) | ~old(X0)) => (~brave(X0) | wise(X0))) [input p11]
21. rich(alice) [input hypothesis]
31. ! [X0] : ((~brave(X0) | wise(X0)) | (rich(X0) & old(X0))) [ennf transformation 12]
32. ! [X0] : (~brave(X0) | wise(X0) | (rich(X0) & old(X0))) [flattening 31]
33. ! [X0] : (((~rich(X0) | brave(X0)) | (generous(X0) & wise(X0))) & ((~generous(X0) | ~wise(X0)) | (rich(X0) & ~brave(X0)))) [nnf transformation 2]
34. ! [X0] : ((~rich(X0) | brave(X0) | (generous(X0) & wise(X0))) & (~generous(X0) | ~wise(X0) | (rich(X0) & ~brave(X0)))) [flattening 33]
37. ! [X0] : (((~calm(X0) & ~quiet(X0)) | (humble(X0) & ~old(X0))) & ((~humble(X0) | old(X0)) | (calm(X0) | quiet(X0)))) [nnf transformation 4]
38. ! [X0] : (((~calm(X0) & ~quiet(X0)) | (humble(X0) & ~old(X0))) & (~humble(X0) | old(X0) | calm(X0) | quiet(X0))) [flattening 37]
39. ! [X0] : ((~calm(X0) | (~strong(X0) & ~wise(X0))) & ((strong(X0) | wise(X0)) | calm(X0))) [nnf transformation 5]
40. ! [X0] : ((~calm(X0) | (~strong(X0) & ~wise(X0))) & (strong(X0) | wise(X0) | calm(X0))) [flattening 39]
41. ! [X0] : ((calm(X0) | (funny(X0) & calm(X0))) & ((~funny(X0) | ~calm(X0)) | ~calm(X0))) [nnf transformation 6]
42. ! [X0] : ((calm(X0) | (funny(X0) & calm(X0))) & (~funny(X0) | ~calm(X0) | ~calm(X0))) [flattening 41]
65. ~rich(X0) | brave(X0) | wise(X0) [cnf transformation 34]
76. ~old(X0) | ~calm(X0) [cnf transformation 38]
79. ~calm(X0) | ~wise(X0) [cnf transformation 40]
82. calm(X0) | calm(X0) [cnf transformation 42]
93. ~brave(X0) | wise(X0) | old(X0) [cnf transformation 32]
113. rich(alice) [cnf transformation 21]
116. calm(X0) [duplicate literal removal 82]
208. ~wise(X0) [resolution 79,116]
224. brave(alice) | wise(alice) [resolution 65,113]
225. brave(alice) [subsumption resolution 224,208]
232. wise(alice) | old(alice) [resolution 93,225]
233. old(alice) [subsumption resolution 232,208]
235. ~calm(alice) [resolution 233,76]
237. $false [subsumption resolution 235,116]
% SZS output end Proof for 6627840819426939695962361
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious is either not generous or not rich and vice versa.
Everyone who is humble is both not wise and generous.
If susan is tall or creative then someone is both generous and patient.
If someone is both curious and not generous then someone is both not funny and creative.
Everyone who is both not creative and not calm is either not humble or generous.
Everyone who is both not patient and rich is old and vice versa.
Everyone who is either brave or not strong is both wise and not funny.
Everyone who is either funny or not strong is not wise or strong and vice versa.
Everyone who is not strong or not calm is not brave and vice versa.
If someone is both rich and not brave then fred is either calm or funny.
Everyone who is both not brave and tall is both not happy and tall and vice versa.
If paul is either not rich or not funny then someone is either patient or calm and vice versa.
If someone is both not funny and not curious then susan is happy.
If fred is not patient or quiet then john is not calm and vice versa.
Lucy is both humble and not creative.
Susan is generous or patient.
Mary is both not humble and quiet.
John is both kind and not rich.
Fred is not creative.
Paul is strong or patient. | Paul is brave. | contradiction | (![X]:(curious(X)<=>(~generous(X)<~>~rich(X))))&
(![X]:(humble(X)=>(~wise(X)&generous(X))))&
(((tall(susan)|creative(susan)))=>(?[X]:((generous(X)&patient(X)))))&
((?[X]:((curious(X)&~generous(X))))=>(?[X]:((~funny(X)&creative(X)))))&
(![X]:((~creative(X)&~calm(X))=>(~humble(X)<~>generous(X))))&
(![X]:((~patient(X)&rich(X))<=>old(X)))&
(![X]:((brave(X)<~>~strong(X))=>(wise(X)&~funny(X))))&
(![X]:((funny(X)<~>~strong(X))<=>(~wise(X)|strong(X))))&
(![X]:((~strong(X)|~calm(X))<=>~brave(X)))&
((?[X]:((rich(X)&~brave(X))))=>((calm(fred)<~>funny(fred))))&
(![X]:((~brave(X)&tall(X))<=>(~happy(X)&tall(X))))&
(((~rich(paul)<~>~funny(paul)))<=>(?[X]:((patient(X)<~>calm(X)))))&
((?[X]:((~funny(X)&~curious(X))))=>(happy(susan)))&
(((~patient(fred)|quiet(fred)))<=>(~calm(john)))&
((humble(lucy)&~creative(lucy)))&
((generous(susan)|patient(susan)))&
((~humble(mary)&quiet(mary)))&
((kind(john)&~rich(john)))&
(~creative(fred))&
((strong(paul)|patient(paul))) | brave(paul) | [
"p6",
"p7",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 821021859484749406940325
% SZS output start Proof for 821021859484749406940325
7. ! [X0] : ((brave(X0) <~> ~strong(X0)) => (~funny(X0) & wise(X0))) [input p6]
8. ! [X0] : ((funny(X0) <~> ~strong(X0)) <=> (strong(X0) | ~wise(X0))) [input p7]
9. ! [X0] : ((~calm(X0) | ~strong(X0)) <=> ~brave(X0)) [input p8]
21. brave(paul) [input hypothesis]
29. ! [X0] : ((~funny(X0) & wise(X0)) | (brave(X0) <=> ~strong(X0))) [ennf transformation 7]
39. ! [X0] : ((~funny(X0) & wise(X0)) | ((brave(X0) | strong(X0)) & (~strong(X0) | ~brave(X0)))) [nnf transformation 29]
40. ! [X0] : ((((strong(X0) | ~funny(X0)) & (~strong(X0) | funny(X0))) | (~strong(X0) & wise(X0))) & ((strong(X0) | ~wise(X0)) | ((funny(X0) | strong(X0)) & (~strong(X0) | ~funny(X0))))) [nnf transformation 8]
41. ! [X0] : ((((strong(X0) | ~funny(X0)) & (~strong(X0) | funny(X0))) | (~strong(X0) & wise(X0))) & (strong(X0) | ~wise(X0) | ((funny(X0) | strong(X0)) & (~strong(X0) | ~funny(X0))))) [flattening 40]
42. ! [X0] : (((~calm(X0) | ~strong(X0)) | brave(X0)) & (~brave(X0) | (calm(X0) & strong(X0)))) [nnf transformation 9]
43. ! [X0] : ((~calm(X0) | ~strong(X0) | brave(X0)) & (~brave(X0) | (calm(X0) & strong(X0)))) [flattening 42]
69. ~strong(X0) | ~funny(X0) | ~brave(X0) [cnf transformation 39]
74. ~strong(X0) | funny(X0) | ~strong(X0) [cnf transformation 41]
77. ~brave(X0) | strong(X0) [cnf transformation 43]
106. brave(paul) [cnf transformation 21]
108. ~strong(X0) | funny(X0) [duplicate literal removal 74]
164. 13 <=> funny(paul) [avatar definition]
165. ~funny(paul) <- (~13) [avatar component clause 164]
166. funny(paul) <- (13) [avatar component clause 164]
219. 24 <=> strong(paul) [avatar definition]
221. strong(paul) <- (24) [avatar component clause 219]
228. strong(paul) [resolution 77,106]
230. funny(paul) <- (24) [resolution 108,221]
231. $false <- (~13, 24) [subsumption resolution 230,165]
232. 13 | ~24 [avatar contradiction clause 231]
233. 24 [avatar split clause 228,219]
293. ~funny(paul) | ~brave(paul) <- (24) [resolution 69,221]
295. ~brave(paul) <- (13, 24) [subsumption resolution 293,166]
296. $false <- (13, 24) [subsumption resolution 295,106]
297. ~13 | ~24 [avatar contradiction clause 296]
298. $false [avatar sat refutation 232,233,297]
% SZS output end Proof for 821021859484749406940325
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.021 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not curious and not strong is either not wise or strong.
If someone is not curious or funny then fred is not patient.
Everyone who is old is either not quiet or quiet and vice versa.
If someone is both not kind and not funny then someone is patient.
If someone is not patient or not humble then someone is tall or happy.
If john is both strong and not happy then john is either not kind or tall and vice versa.
If susan is either calm or not generous then lucy is either patient or wise.
If mary is both not generous and not old then paul is not curious and vice versa.
If fred is not tall or not quiet then paul is both not quiet and tall.
If paul is both not kind and kind then someone is tall or not creative.
If alice is not brave then someone is curious.
Everyone who is not tall is not patient and vice versa.
If susan is both not old and quiet then someone is not brave and vice versa.
If fred is either calm or not kind then someone is tall and vice versa.
Everyone who is funny or kind is either not brave or creative and vice versa.
Everyone who is not calm or kind is both not kind and tall and vice versa.
Someone is tall.
Someone is brave.
Lucy is not kind.
Fred is not curious or happy.
Paul is either old or not brave.
Someone is calm. | Alice is creative. | contradiction | (![X]:((~curious(X)&~strong(X))=>(~wise(X)<~>strong(X))))&
((?[X]:((~curious(X)|funny(X))))=>(~patient(fred)))&
(![X]:(old(X)<=>(~quiet(X)<~>quiet(X))))&
((?[X]:((~kind(X)&~funny(X))))=>(?[X]:(patient(X))))&
((?[X]:((~patient(X)|~humble(X))))=>(?[X]:((tall(X)|happy(X)))))&
(((strong(john)&~happy(john)))<=>((~kind(john)<~>tall(john))))&
(((calm(susan)<~>~generous(susan)))=>((patient(lucy)<~>wise(lucy))))&
(((~generous(mary)&~old(mary)))<=>(~curious(paul)))&
(((~tall(fred)|~quiet(fred)))=>((~quiet(paul)&tall(paul))))&
(((~kind(paul)&kind(paul)))=>(?[X]:((tall(X)|~creative(X)))))&
((~brave(alice))=>(?[X]:(curious(X))))&
(![X]:(~tall(X)<=>~patient(X)))&
(((~old(susan)&quiet(susan)))<=>(?[X]:(~brave(X))))&
(((calm(fred)<~>~kind(fred)))<=>(?[X]:(tall(X))))&
(![X]:((funny(X)|kind(X))<=>(~brave(X)<~>creative(X))))&
(![X]:((~calm(X)|kind(X))<=>(~kind(X)&tall(X))))&
(?[X]:(tall(X)))&
(?[X]:(brave(X)))&
(~kind(lucy))&
((~curious(fred)|happy(fred)))&
((old(paul)<~>~brave(paul)))&
(?[X]:(calm(X))) | creative(alice) | [
"p1",
"p2",
"p8",
"p11",
"p12",
"p13",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1263914497016680152621019
% SZS output start Proof for 1263914497016680152621019
2. ? [X0] : (funny(X0) | ~curious(X0)) => ~patient(fred) [input p1]
3. ! [X0] : (old(X0) <=> (~quiet(X0) <~> quiet(X0))) [input p2]
9. (~quiet(fred) | ~tall(fred)) => (tall(paul) & ~quiet(paul)) [input p8]
12. ! [X0] : (~tall(X0) <=> ~patient(X0)) [input p11]
13. (quiet(susan) & ~old(susan)) <=> ? [X0] : ~brave(X0) [input p12]
14. (calm(fred) <~> ~kind(fred)) <=> ? [X0] : tall(X0) [input p13]
15. ! [X0] : ((kind(X0) | funny(X0)) <=> (~brave(X0) <~> creative(X0))) [input p14]
16. ! [X0] : ((kind(X0) | ~calm(X0)) <=> (tall(X0) & ~kind(X0))) [input p15]
23. creative(alice) [input hypothesis]
29. ~patient(fred) | ! [X0] : (~funny(X0) & curious(X0)) [ennf transformation 2]
33. (tall(paul) & ~quiet(paul)) | (quiet(fred) & tall(fred)) [ennf transformation 9]
38. ! [X0] : ((old(X0) | ((~quiet(X0) | ~quiet(X0)) & (quiet(X0) | quiet(X0)))) & (((~quiet(X0) | quiet(X0)) & (quiet(X0) | ~quiet(X0))) | ~old(X0))) [nnf transformation 3]
54. ! [X0] : ((~tall(X0) | patient(X0)) & (~patient(X0) | tall(X0))) [nnf transformation 12]
55. ((quiet(susan) & ~old(susan)) | ! [X0] : brave(X0)) & (? [X0] : ~brave(X0) | (~quiet(susan) | old(susan))) [nnf transformation 13]
56. ((quiet(susan) & ~old(susan)) | ! [X0] : brave(X0)) & (? [X0] : ~brave(X0) | ~quiet(susan) | old(susan)) [flattening 55]
57. ((quiet(susan) & ~old(susan)) | ! [X0] : brave(X0)) & (? [X1] : ~brave(X1) | ~quiet(susan) | old(susan)) [rectify 56]
58. ? [X1] : ~brave(X1) => ~brave(sK4) [choice axiom]
59. ((quiet(susan) & ~old(susan)) | ! [X0] : brave(X0)) & (~brave(sK4) | ~quiet(susan) | old(susan)) [skolemisation 57,58]
60. (((kind(fred) | ~calm(fred)) & (~kind(fred) | calm(fred))) | ! [X0] : ~tall(X0)) & (? [X0] : tall(X0) | ((calm(fred) | kind(fred)) & (~kind(fred) | ~calm(fred)))) [nnf transformation 14]
61. (((kind(fred) | ~calm(fred)) & (~kind(fred) | calm(fred))) | ! [X0] : ~tall(X0)) & (? [X1] : tall(X1) | ((calm(fred) | kind(fred)) & (~kind(fred) | ~calm(fred)))) [rectify 60]
62. ? [X1] : tall(X1) => tall(sK5) [choice axiom]
63. (((kind(fred) | ~calm(fred)) & (~kind(fred) | calm(fred))) | ! [X0] : ~tall(X0)) & (tall(sK5) | ((calm(fred) | kind(fred)) & (~kind(fred) | ~calm(fred)))) [skolemisation 61,62]
64. ! [X0] : (((kind(X0) | funny(X0)) | ((~brave(X0) | ~creative(X0)) & (creative(X0) | brave(X0)))) & (((~creative(X0) | brave(X0)) & (creative(X0) | ~brave(X0))) | (~kind(X0) & ~funny(X0)))) [nnf transformation 15]
65. ! [X0] : ((kind(X0) | funny(X0) | ((~brave(X0) | ~creative(X0)) & (creative(X0) | brave(X0)))) & (((~creative(X0) | brave(X0)) & (creative(X0) | ~brave(X0))) | (~kind(X0) & ~funny(X0)))) [flattening 64]
66. ! [X0] : (((kind(X0) | ~calm(X0)) | (~tall(X0) | kind(X0))) & ((tall(X0) & ~kind(X0)) | (~kind(X0) & calm(X0)))) [nnf transformation 16]
67. ! [X0] : ((kind(X0) | ~calm(X0) | ~tall(X0) | kind(X0)) & ((tall(X0) & ~kind(X0)) | (~kind(X0) & calm(X0)))) [flattening 66]
78. ~patient(fred) | ~funny(X0) [cnf transformation 29]
81. old(X0) | quiet(X0) | quiet(X0) [cnf transformation 38]
82. old(X0) | ~quiet(X0) | ~quiet(X0) [cnf transformation 38]
100. tall(paul) | tall(fred) [cnf transformation 33]
105. ~tall(X0) | patient(X0) [cnf transformation 54]
107. ~old(susan) | brave(X0) [cnf transformation 59]
112. kind(fred) | ~calm(fred) | ~tall(X0) [cnf transformation 63]
118. ~brave(X0) | funny(X0) | kind(X0) | ~creative(X0) [cnf transformation 65]
120. ~kind(X0) | ~kind(X0) [cnf transformation 67]
121. calm(X0) | tall(X0) [cnf transformation 67]
131. creative(alice) [cnf transformation 23]
132. ~kind(X0) [duplicate literal removal 120]
134. old(X0) | quiet(X0) [duplicate literal removal 81]
135. ~quiet(X0) | old(X0) [duplicate literal removal 82]
138. 1 <=> ! [X0] : ~funny(X0) [avatar definition]
139. ~funny(X0) <- (1) [avatar component clause 138]
141. 2 <=> patient(fred) [avatar definition]
144. 1 | ~2 [avatar split clause 78,141,138]
149. old(X0) [subsumption resolution 134,135]
218. 18 <=> tall(paul) [avatar definition]
220. tall(paul) <- (18) [avatar component clause 218]
223. 19 <=> tall(fred) [avatar definition]
225. tall(fred) <- (19) [avatar component clause 223]
226. 19 | 18 [avatar split clause 100,218,223]
243. 23 <=> ! [X0] : brave(X0) [avatar definition]
244. brave(X0) <- (23) [avatar component clause 243]
250. brave(X0) [subsumption resolution 107,149]
251. 23 [avatar split clause 250,243]
253. 25 <=> ! [X0] : ~tall(X0) [avatar definition]
254. ~tall(X0) <- (25) [avatar component clause 253]
256. 26 <=> calm(fred) [avatar definition]
258. ~calm(fred) <- (~26) [avatar component clause 256]
260. 27 <=> kind(fred) [avatar definition]
262. kind(fred) <- (27) [avatar component clause 260]
263. 25 | ~26 | 27 [avatar split clause 112,260,256,253]
281. $false <- (18, 25) [subsumption resolution 220,254]
282. ~18 | ~25 [avatar contradiction clause 281]
294. patient(fred) <- (19) [resolution 105,225]
301. 2 | ~19 [avatar split clause 294,223,141]
310. tall(fred) <- (~26) [resolution 121,258]
335. funny(X1) | kind(X1) | ~creative(X1) <- (23) [resolution 118,244]
340. kind(X1) | ~creative(X1) <- (1, 23) [subsumption resolution 335,139]
341. ~creative(X1) <- (1, 23) [subsumption resolution 340,132]
342. $false <- (1, 23) [resolution 341,131]
343. ~1 | ~23 [avatar contradiction clause 342]
356. 19 | 26 [avatar split clause 310,256,223]
357. $false <- (27) [subsumption resolution 262,132]
358. ~27 [avatar contradiction clause 357]
359. $false [avatar sat refutation 144,226,251,263,282,301,343,356,358]
% SZS output end Proof for 1263914497016680152621019
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not generous or not wise is either creative or not generous and vice versa.
Everyone who is tall or wise is not curious or not kind and vice versa.
If alice is not funny then someone is not humble or quiet.
If alice is both patient and not tall then someone is both not calm and not strong.
If lucy is not patient then someone is both patient and not patient.
Everyone who is not humble is both not rich and not generous.
Everyone who is quiet is not wise.
If someone is either curious or old then susan is not rich or not strong and vice versa.
Everyone who is both not patient and not creative is funny and vice versa.
Everyone who is either calm or generous is either not generous or not curious.
If someone is funny or not tall then someone is both funny and not happy and vice versa.
Everyone who is both creative and not quiet is patient or not creative and vice versa.
If someone is either not funny or not old then someone is calm.
If paul is creative or old then alice is either not kind or rich and vice versa.
Someone is not curious.
Paul is either not rich or not wise.
Paul is not curious.
John is either generous or not quiet.
Paul is not wise or not creative. | Lucy is patient. | entailment | (![X]:((~generous(X)<~>~wise(X))<=>(creative(X)<~>~generous(X))))&
(![X]:((tall(X)|wise(X))<=>(~curious(X)|~kind(X))))&
((~funny(alice))=>(?[X]:((~humble(X)|quiet(X)))))&
(((patient(alice)&~tall(alice)))=>(?[X]:((~calm(X)&~strong(X)))))&
((~patient(lucy))=>(?[X]:((patient(X)&~patient(X)))))&
(![X]:(~humble(X)=>(~rich(X)&~generous(X))))&
(![X]:(quiet(X)=>~wise(X)))&
((?[X]:((curious(X)<~>old(X))))<=>((~rich(susan)|~strong(susan))))&
(![X]:((~patient(X)&~creative(X))<=>funny(X)))&
(![X]:((calm(X)<~>generous(X))=>(~generous(X)<~>~curious(X))))&
((?[X]:((funny(X)|~tall(X))))<=>(?[X]:((funny(X)&~happy(X)))))&
(![X]:((creative(X)&~quiet(X))<=>(patient(X)|~creative(X))))&
((?[X]:((~funny(X)<~>~old(X))))=>(?[X]:(calm(X))))&
(((creative(paul)|old(paul)))<=>((~kind(alice)<~>rich(alice))))&
(?[X]:(~curious(X)))&
((~rich(paul)<~>~wise(paul)))&
(~curious(paul))&
((generous(john)<~>~quiet(john)))&
((~wise(paul)|~creative(paul))) | patient(lucy) | [
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 1225523355250632732135839
% SZS output start Proof for 1225523355250632732135839
5. ~patient(lucy) => ? [X0] : (~patient(X0) & patient(X0)) [input p4]
20. ~patient(lucy) [input hypothesis]
26. ? [X0] : (~patient(X0) & patient(X0)) | patient(lucy) [ennf transformation 5]
38. ? [X0] : (~patient(X0) & patient(X0)) => (~patient(sK2) & patient(sK2)) [choice axiom]
39. (~patient(sK2) & patient(sK2)) | patient(lucy) [skolemisation 26,38]
80. patient(sK2) | patient(lucy) [cnf transformation 39]
81. ~patient(sK2) | patient(lucy) [cnf transformation 39]
123. ~patient(lucy) [cnf transformation 20]
166. 8 <=> patient(lucy) [avatar definition]
170. 9 <=> patient(sK2) [avatar definition]
173. 8 | ~9 [avatar split clause 81,170,166]
174. 8 | 9 [avatar split clause 80,170,166]
284. ~8 [avatar split clause 123,166]
285. $false [avatar sat refutation 173,174,284]
% SZS output end Proof for 1225523355250632732135839
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If someone is either not funny or curious then lucy is funny and vice versa.
If alice is both not humble and wise then someone is both not brave and generous.
Everyone who is both not creative and old is either generous or calm and vice versa.
Everyone who is either not creative or kind is either not tall or not kind.
Everyone who is either brave or creative is both not brave and generous and vice versa.
Everyone who is both kind and curious is humble or not funny.
Everyone who is not creative is both not humble and happy.
Everyone who is both not quiet and not old is both generous and not patient.
If someone is rich then lucy is both not happy and wise.
Everyone who is either not wise or not humble is not kind and vice versa.
Everyone who is not brave is not humble and vice versa.
Everyone who is either calm or curious is either not patient or patient and vice versa.
Everyone who is either humble or not kind is both not curious and kind.
Everyone who is calm is rich or curious and vice versa.
Everyone who is not humble is either calm or not kind.
Everyone who is not creative is either curious or not wise.
Someone is not patient or strong.
Someone is not humble.
Someone is both not kind and not strong.
Paul is either not brave or generous.
Alice is not happy or old.
Paul is humble.
Susan is either kind or not happy. | Susan is humble. | neutral | ((?[X]:((~funny(X)<~>curious(X))))<=>(funny(lucy)))&
(((~humble(alice)&wise(alice)))=>(?[X]:((~brave(X)&generous(X)))))&
(![X]:((~creative(X)&old(X))<=>(generous(X)<~>calm(X))))&
(![X]:((~creative(X)<~>kind(X))=>(~tall(X)<~>~kind(X))))&
(![X]:((brave(X)<~>creative(X))<=>(~brave(X)&generous(X))))&
(![X]:((kind(X)&curious(X))=>(humble(X)|~funny(X))))&
(![X]:(~creative(X)=>(~humble(X)&happy(X))))&
(![X]:((~quiet(X)&~old(X))=>(generous(X)&~patient(X))))&
((?[X]:(rich(X)))=>((~happy(lucy)&wise(lucy))))&
(![X]:((~wise(X)<~>~humble(X))<=>~kind(X)))&
(![X]:(~brave(X)<=>~humble(X)))&
(![X]:((calm(X)<~>curious(X))<=>(~patient(X)<~>patient(X))))&
(![X]:((humble(X)<~>~kind(X))=>(~curious(X)&kind(X))))&
(![X]:(calm(X)<=>(rich(X)|curious(X))))&
(![X]:(~humble(X)=>(calm(X)<~>~kind(X))))&
(![X]:(~creative(X)=>(curious(X)<~>~wise(X))))&
(?[X]:((~patient(X)|strong(X))))&
(?[X]:(~humble(X)))&
(?[X]:((~kind(X)&~strong(X))))&
((~brave(paul)<~>generous(paul)))&
((~happy(alice)|old(alice)))&
(humble(paul))&
((kind(susan)<~>~happy(susan))) | humble(susan) | [] | null | 0 |
Everyone who is either strong or not calm is strong or not creative and vice versa.
Everyone who is either not brave or brave is both not happy and not tall and vice versa.
If alice is either not generous or not curious then someone is not quiet or not old and vice versa.
Everyone who is not quiet or strong is not calm or calm.
If someone is humble or not creative then lucy is rich and vice versa.
If someone is both not funny and patient then someone is old and vice versa.
If someone is either not curious or tall then someone is either not patient or not rich and vice versa.
Everyone who is not curious is either old or humble.
Everyone who is either not quiet or not strong is not calm and vice versa.
If susan is tall or brave then someone is quiet and vice versa.
Everyone who is either not rich or patient is either happy or not curious.
If someone is either patient or rich then lucy is not generous.
Everyone who is either calm or not tall is not happy or not strong and vice versa.
Everyone who is both generous and strong is either old or not curious.
Someone is either old or not patient.
Fred is either humble or not generous.
Someone is both wise and not creative.
Someone is not patient.
Someone is patient or not old.
Lucy is kind or happy.
Someone is funny or not happy.
Mary is patient. | Alice is not happy. | entailment | (![X]:((strong(X)<~>~calm(X))<=>(strong(X)|~creative(X))))&
(![X]:((~brave(X)<~>brave(X))<=>(~happy(X)&~tall(X))))&
(((~generous(alice)<~>~curious(alice)))<=>(?[X]:((~quiet(X)|~old(X)))))&
(![X]:((~quiet(X)|strong(X))=>(~calm(X)|calm(X))))&
((?[X]:((humble(X)|~creative(X))))<=>(rich(lucy)))&
((?[X]:((~funny(X)&patient(X))))<=>(?[X]:(old(X))))&
((?[X]:((~curious(X)<~>tall(X))))<=>(?[X]:((~patient(X)<~>~rich(X)))))&
(![X]:(~curious(X)=>(old(X)<~>humble(X))))&
(![X]:((~quiet(X)<~>~strong(X))<=>~calm(X)))&
(((tall(susan)|brave(susan)))<=>(?[X]:(quiet(X))))&
(![X]:((~rich(X)<~>patient(X))=>(happy(X)<~>~curious(X))))&
((?[X]:((patient(X)<~>rich(X))))=>(~generous(lucy)))&
(![X]:((calm(X)<~>~tall(X))<=>(~happy(X)|~strong(X))))&
(![X]:((generous(X)&strong(X))=>(old(X)<~>~curious(X))))&
(?[X]:((old(X)<~>~patient(X))))&
((humble(fred)<~>~generous(fred)))&
(?[X]:((wise(X)&~creative(X))))&
(?[X]:(~patient(X)))&
(?[X]:((patient(X)|~old(X))))&
((kind(lucy)|happy(lucy)))&
(?[X]:((funny(X)|~happy(X))))&
(patient(mary)) | ~happy(alice) | [
"p1",
"hypothesis"
] | % SZS status Unsatisfiable for 4240212673050424566710339
% SZS output start Proof for 4240212673050424566710339
2. ! [X0] : ((~brave(X0) <~> brave(X0)) <=> (~tall(X0) & ~happy(X0))) [input p1]
23. happy(alice) [input hypothesis]
37. ! [X0] : ((((~brave(X0) | brave(X0)) & (brave(X0) | ~brave(X0))) | (tall(X0) | happy(X0))) & ((~tall(X0) & ~happy(X0)) | ((~brave(X0) | ~brave(X0)) & (brave(X0) | brave(X0))))) [nnf transformation 2]
38. ! [X0] : ((((~brave(X0) | brave(X0)) & (brave(X0) | ~brave(X0))) | tall(X0) | happy(X0)) & ((~tall(X0) & ~happy(X0)) | ((~brave(X0) | ~brave(X0)) & (brave(X0) | brave(X0))))) [flattening 37]
87. ~happy(X0) | brave(X0) | brave(X0) [cnf transformation 38]
88. ~happy(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 38]
147. happy(alice) [cnf transformation 23]
148. ~happy(X0) | brave(X0) [duplicate literal removal 87]
149. ~happy(X0) | ~brave(X0) [duplicate literal removal 88]
156. ~happy(X0) [subsumption resolution 148,149]
312. $false [subsumption resolution 147,156]
% SZS output end Proof for 4240212673050424566710339
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 lucy is not funny or humble then someone is both generous and not brave and vice versa.
Everyone who is creative or not creative is not rich and vice versa.
If someone is both not funny and not tall then alice is both funny and not kind and vice versa.
Everyone who is not brave or calm is humble or happy and vice versa.
Everyone who is wise is not rich and vice versa.
Everyone who is calm or humble is quiet.
If susan is calm then someone is not strong and vice versa.
If someone is not patient then lucy is not brave or not funny and vice versa.
If lucy is not tall or curious then someone is either creative or not strong and vice versa.
Everyone who is not funny or not strong is both not kind and not curious.
Everyone who is either not quiet or calm is either kind or happy and vice versa.
If mary is not curious then lucy is not happy or kind and vice versa.
Everyone who is not happy is quiet and vice versa.
If john is either patient or not curious then someone is rich or wise and vice versa.
If someone is both not rich and not brave then someone is rich.
Everyone who is both wise and funny is not tall or not patient and vice versa.
Someone is either rich or not rich.
Lucy is quiet.
Someone is either happy or not strong.
Mary is old.
Mary is funny or not rich.
Mary is either not quiet or calm.
Fred is either wise or funny. | Mary is not curious. | entailment | (((~funny(lucy)|humble(lucy)))<=>(?[X]:((generous(X)&~brave(X)))))&
(![X]:((creative(X)|~creative(X))<=>~rich(X)))&
((?[X]:((~funny(X)&~tall(X))))<=>((funny(alice)&~kind(alice))))&
(![X]:((~brave(X)|calm(X))<=>(humble(X)|happy(X))))&
(![X]:(wise(X)<=>~rich(X)))&
(![X]:((calm(X)|humble(X))=>quiet(X)))&
((calm(susan))<=>(?[X]:(~strong(X))))&
((?[X]:(~patient(X)))<=>((~brave(lucy)|~funny(lucy))))&
(((~tall(lucy)|curious(lucy)))<=>(?[X]:((creative(X)<~>~strong(X)))))&
(![X]:((~funny(X)|~strong(X))=>(~kind(X)&~curious(X))))&
(![X]:((~quiet(X)<~>calm(X))<=>(kind(X)<~>happy(X))))&
((~curious(mary))<=>((~happy(lucy)|kind(lucy))))&
(![X]:(~happy(X)<=>quiet(X)))&
(((patient(john)<~>~curious(john)))<=>(?[X]:((rich(X)|wise(X)))))&
((?[X]:((~rich(X)&~brave(X))))=>(?[X]:(rich(X))))&
(![X]:((wise(X)&funny(X))<=>(~tall(X)|~patient(X))))&
(?[X]:((rich(X)<~>~rich(X))))&
(quiet(lucy))&
(?[X]:((happy(X)<~>~strong(X))))&
(old(mary))&
((funny(mary)|~rich(mary)))&
((~quiet(mary)<~>calm(mary)))&
((wise(fred)<~>funny(fred))) | ~curious(mary) | [
"p11",
"p12",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 6160526756611903273235962
% SZS output start Proof for 6160526756611903273235962
12. ~curious(mary) <=> (kind(lucy) | ~happy(lucy)) [input p11]
13. ! [X0] : (~happy(X0) <=> quiet(X0)) [input p12]
18. quiet(lucy) [input p17]
24. curious(mary) [input hypothesis]
60. (~curious(mary) | (~kind(lucy) & happy(lucy))) & ((kind(lucy) | ~happy(lucy)) | curious(mary)) [nnf transformation 12]
61. (~curious(mary) | (~kind(lucy) & happy(lucy))) & (kind(lucy) | ~happy(lucy) | curious(mary)) [flattening 60]
62. ! [X0] : ((~happy(X0) | ~quiet(X0)) & (quiet(X0) | happy(X0))) [nnf transformation 13]
124. ~curious(mary) | happy(lucy) [cnf transformation 61]
127. ~quiet(X0) | ~happy(X0) [cnf transformation 62]
142. quiet(lucy) [cnf transformation 18]
150. curious(mary) [cnf transformation 24]
264. 24 <=> curious(mary) [avatar definition]
269. 25 <=> happy(lucy) [avatar definition]
271. happy(lucy) <- (25) [avatar component clause 269]
272. 25 | ~24 [avatar split clause 124,264,269]
310. 24 [avatar split clause 150,264]
329. ~happy(lucy) [resolution 127,142]
332. $false <- (25) [subsumption resolution 329,271]
333. ~25 [avatar contradiction clause 332]
334. $false [avatar sat refutation 272,310,333]
% SZS output end Proof for 6160526756611903273235962
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is calm is not creative or creative.
Everyone who is either not wise or quiet is either old or not generous.
Everyone who is either brave or strong is both not happy and old and vice versa.
Everyone who is both happy and not patient is both calm and not calm.
If someone is kind or patient then someone is funny or not wise and vice versa.
If someone is both calm and not calm then someone is generous.
If someone is either not quiet or not humble then someone is quiet or not kind and vice versa.
Everyone who is old is humble or brave and vice versa.
Everyone who is wise is both not wise and kind and vice versa.
If susan is curious or not brave then fred is either creative or not generous.
If susan is both tall and not brave then someone is funny.
Everyone who is both not generous and not quiet is not brave or not generous.
Everyone who is not generous or rich is not funny.
If mary is both not funny and not generous then someone is both not curious and not wise.
If someone is either not wise or not curious then someone is rich and vice versa.
If someone is not calm then someone is not calm or funny and vice versa.
Susan is not patient.
Fred is funny or brave.
Susan is not wise.
Someone is both not calm and strong.
Someone is not generous or not quiet.
Someone is not happy.
Someone is strong or not patient.
Lucy is either quiet or not curious. | Susan is strong. | neutral | (![X]:(calm(X)=>(~creative(X)|creative(X))))&
(![X]:((~wise(X)<~>quiet(X))=>(old(X)<~>~generous(X))))&
(![X]:((brave(X)<~>strong(X))<=>(~happy(X)&old(X))))&
(![X]:((happy(X)&~patient(X))=>(calm(X)&~calm(X))))&
((?[X]:((kind(X)|patient(X))))<=>(?[X]:((funny(X)|~wise(X)))))&
((?[X]:((calm(X)&~calm(X))))=>(?[X]:(generous(X))))&
((?[X]:((~quiet(X)<~>~humble(X))))<=>(?[X]:((quiet(X)|~kind(X)))))&
(![X]:(old(X)<=>(humble(X)|brave(X))))&
(![X]:(wise(X)<=>(~wise(X)&kind(X))))&
(((curious(susan)|~brave(susan)))=>((creative(fred)<~>~generous(fred))))&
(((tall(susan)&~brave(susan)))=>(?[X]:(funny(X))))&
(![X]:((~generous(X)&~quiet(X))=>(~brave(X)|~generous(X))))&
(![X]:((~generous(X)|rich(X))=>~funny(X)))&
(((~funny(mary)&~generous(mary)))=>(?[X]:((~curious(X)&~wise(X)))))&
((?[X]:((~wise(X)<~>~curious(X))))<=>(?[X]:(rich(X))))&
((?[X]:(~calm(X)))<=>(?[X]:((~calm(X)|funny(X)))))&
(~patient(susan))&
((funny(fred)|brave(fred)))&
(~wise(susan))&
(?[X]:((~calm(X)&strong(X))))&
(?[X]:((~generous(X)|~quiet(X))))&
(?[X]:(~happy(X)))&
(?[X]:((strong(X)|~patient(X))))&
((quiet(lucy)<~>~curious(lucy))) | strong(susan) | [] | null | 0 |
If someone is quiet or not tall then someone is either tall or brave.
If mary is not tall or humble then alice is not wise or not kind.
If someone is calm then lucy is not kind or not generous and vice versa.
If someone is both not tall and curious then fred is old or humble.
If someone is both tall and not humble then fred is not generous.
If paul is wise or generous then paul is both not old and not funny and vice versa.
Everyone who is either generous or wise is funny or not generous and vice versa.
Everyone who is not strong is either not old or not calm and vice versa.
Everyone who is either not patient or patient is generous.
Everyone who is not calm or not happy is creative or humble.
Everyone who is happy is either calm or not patient and vice versa.
Everyone who is either not generous or not old is funny or quiet.
If someone is not happy then mary is not quiet or not old and vice versa.
Everyone who is not curious is both not tall and not patient and vice versa.
Everyone who is both not happy and funny is not curious.
Everyone who is either not brave or not kind is either wise or funny.
Someone is not happy.
Someone is not funny or not generous.
John is old.
Someone is both not patient and not tall.
Alice is either patient or not humble. | Alice is not happy. | neutral | ((?[X]:((quiet(X)|~tall(X))))=>(?[X]:((tall(X)<~>brave(X)))))&
(((~tall(mary)|humble(mary)))=>((~wise(alice)|~kind(alice))))&
((?[X]:(calm(X)))<=>((~kind(lucy)|~generous(lucy))))&
((?[X]:((~tall(X)&curious(X))))=>((old(fred)|humble(fred))))&
((?[X]:((tall(X)&~humble(X))))=>(~generous(fred)))&
(((wise(paul)|generous(paul)))<=>((~old(paul)&~funny(paul))))&
(![X]:((generous(X)<~>wise(X))<=>(funny(X)|~generous(X))))&
(![X]:(~strong(X)<=>(~old(X)<~>~calm(X))))&
(![X]:((~patient(X)<~>patient(X))=>generous(X)))&
(![X]:((~calm(X)|~happy(X))=>(creative(X)|humble(X))))&
(![X]:(happy(X)<=>(calm(X)<~>~patient(X))))&
(![X]:((~generous(X)<~>~old(X))=>(funny(X)|quiet(X))))&
((?[X]:(~happy(X)))<=>((~quiet(mary)|~old(mary))))&
(![X]:(~curious(X)<=>(~tall(X)&~patient(X))))&
(![X]:((~happy(X)&funny(X))=>~curious(X)))&
(![X]:((~brave(X)<~>~kind(X))=>(wise(X)<~>funny(X))))&
(?[X]:(~happy(X)))&
(?[X]:((~funny(X)|~generous(X))))&
(old(john))&
(?[X]:((~patient(X)&~tall(X))))&
((patient(alice)<~>~humble(alice))) | ~happy(alice) | [] | null | 0 |
Everyone who is both humble and not tall is either not tall or not curious.
If mary is either not old or happy then paul is both happy and creative.
Everyone who is both not creative and not kind is not old and vice versa.
If paul is either not calm or not tall then someone is either not strong or not brave and vice versa.
Everyone who is not old is not happy and vice versa.
Everyone who is either not generous or not humble is either not old or quiet and vice versa.
Everyone who is creative or happy is not humble and vice versa.
Everyone who is either not kind or curious is either creative or humble.
If someone is generous or brave then mary is not curious and vice versa.
Everyone who is brave is either humble or not rich and vice versa.
If someone is both not rich and not humble then someone is generous and vice versa.
If someone is both not wise and not creative then someone is either brave or creative.
If alice is either brave or not generous then someone is brave and vice versa.
Everyone who is either old or humble is generous.
Everyone who is wise is both rich and not calm and vice versa.
Everyone who is strong is brave and vice versa.
Susan is not kind or humble.
Mary is both not creative and not brave.
Someone is happy or not calm.
Someone is either happy or strong.
Alice is either not curious or not kind. | Alice is happy. | neutral | (![X]:((humble(X)&~tall(X))=>(~tall(X)<~>~curious(X))))&
(((~old(mary)<~>happy(mary)))=>((happy(paul)&creative(paul))))&
(![X]:((~creative(X)&~kind(X))<=>~old(X)))&
(((~calm(paul)<~>~tall(paul)))<=>(?[X]:((~strong(X)<~>~brave(X)))))&
(![X]:(~old(X)<=>~happy(X)))&
(![X]:((~generous(X)<~>~humble(X))<=>(~old(X)<~>quiet(X))))&
(![X]:((creative(X)|happy(X))<=>~humble(X)))&
(![X]:((~kind(X)<~>curious(X))=>(creative(X)<~>humble(X))))&
((?[X]:((generous(X)|brave(X))))<=>(~curious(mary)))&
(![X]:(brave(X)<=>(humble(X)<~>~rich(X))))&
((?[X]:((~rich(X)&~humble(X))))<=>(?[X]:(generous(X))))&
((?[X]:((~wise(X)&~creative(X))))=>(?[X]:((brave(X)<~>creative(X)))))&
(((brave(alice)<~>~generous(alice)))<=>(?[X]:(brave(X))))&
(![X]:((old(X)<~>humble(X))=>generous(X)))&
(![X]:(wise(X)<=>(rich(X)&~calm(X))))&
(![X]:(strong(X)<=>brave(X)))&
((~kind(susan)|humble(susan)))&
((~creative(mary)&~brave(mary)))&
(?[X]:((happy(X)|~calm(X))))&
(?[X]:((happy(X)<~>strong(X))))&
((~curious(alice)<~>~kind(alice))) | happy(alice) | [] | null | 0 |
Everyone who is both funny and not humble is not patient.
Everyone who is both old and not rich is not creative or not kind and vice versa.
Everyone who is either creative or not happy is humble.
Everyone who is not tall is not quiet.
Everyone who is not humble is both not rich and kind and vice versa.
Everyone who is not tall or happy is old or not old.
If lucy is calm or not old then fred is not generous and vice versa.
If someone is not happy then paul is not quiet or not wise and vice versa.
If john is both funny and not old then fred is either quiet or funny.
Everyone who is either happy or creative is either not old or not rich and vice versa.
Everyone who is not tall is not creative and vice versa.
Everyone who is either creative or not wise is not tall and vice versa.
Everyone who is either strong or not generous is quiet or not funny and vice versa.
If someone is both humble and not wise then alice is tall.
If someone is both happy and not humble then someone is not curious.
Everyone who is either not kind or happy is rich or quiet.
Susan is humble.
John is not brave.
Someone is calm.
Someone is strong.
Someone is either calm or happy.
Someone is tall.
Someone is either tall or calm.
Someone is either not curious or humble. | Lucy is wise. | contradiction | (![X]:((funny(X)&~humble(X))=>~patient(X)))&
(![X]:((old(X)&~rich(X))<=>(~creative(X)|~kind(X))))&
(![X]:((creative(X)<~>~happy(X))=>humble(X)))&
(![X]:(~tall(X)=>~quiet(X)))&
(![X]:(~humble(X)<=>(~rich(X)&kind(X))))&
(![X]:((~tall(X)|happy(X))=>(old(X)|~old(X))))&
(((calm(lucy)|~old(lucy)))<=>(~generous(fred)))&
((?[X]:(~happy(X)))<=>((~quiet(paul)|~wise(paul))))&
(((funny(john)&~old(john)))=>((quiet(fred)<~>funny(fred))))&
(![X]:((happy(X)<~>creative(X))<=>(~old(X)<~>~rich(X))))&
(![X]:(~tall(X)<=>~creative(X)))&
(![X]:((creative(X)<~>~wise(X))<=>~tall(X)))&
(![X]:((strong(X)<~>~generous(X))<=>(quiet(X)|~funny(X))))&
((?[X]:((humble(X)&~wise(X))))=>(tall(alice)))&
((?[X]:((happy(X)&~humble(X))))=>(?[X]:(~curious(X))))&
(![X]:((~kind(X)<~>happy(X))=>(rich(X)|quiet(X))))&
(humble(susan))&
(~brave(john))&
(?[X]:(calm(X)))&
(?[X]:(strong(X)))&
(?[X]:((calm(X)<~>happy(X))))&
(?[X]:(tall(X)))&
(?[X]:((tall(X)<~>calm(X))))&
(?[X]:((~curious(X)<~>humble(X)))) | wise(lucy) | [
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 2435750933655507068210564
% SZS output start Proof for 2435750933655507068210564
11. ! [X0] : (~tall(X0) <=> ~creative(X0)) [input p10]
12. ! [X0] : ((creative(X0) <~> ~wise(X0)) <=> ~tall(X0)) [input p11]
25. wise(lucy) [input hypothesis]
53. ! [X0] : ((~tall(X0) | creative(X0)) & (~creative(X0) | tall(X0))) [nnf transformation 11]
54. ! [X0] : ((((wise(X0) | ~creative(X0)) & (~wise(X0) | creative(X0))) | tall(X0)) & (~tall(X0) | ((creative(X0) | wise(X0)) & (~wise(X0) | ~creative(X0))))) [nnf transformation 12]
105. ~creative(X0) | tall(X0) [cnf transformation 53]
106. ~tall(X0) | creative(X0) [cnf transformation 53]
107. ~tall(X0) | ~wise(X0) | ~creative(X0) [cnf transformation 54]
109. ~wise(X0) | creative(X0) | tall(X0) [cnf transformation 54]
131. wise(lucy) [cnf transformation 25]
188. ~wise(X0) | tall(X0) [subsumption resolution 109,105]
189. ~wise(X0) | ~creative(X0) [subsumption resolution 107,188]
244. tall(lucy) [resolution 188,131]
246. ~creative(lucy) [resolution 189,131]
249. creative(lucy) [resolution 244,106]
250. $false [subsumption resolution 249,246]
% SZS output end Proof for 2435750933655507068210564
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny and not wise is either not old or not humble. If fred is both calm and not kind then susan is not tall. Everyone who is not generous is brave and vice versa. Everyone who is both patient and creative is not curious. If someone is both not happy and funny then someone is both not wise and rich and vice versa. If someone is funny then mary is wise. If paul is brave or not strong then someone is rich or not wise. Everyone who is either not tall or wise is both happy and quiet and vice versa. If someone is both not tall and quiet then john is not creative and vice versa. Everyone who is either calm or rich is rich or not generous. Everyone who is either creative or strong is both generous and not kind. If someone is quiet then fred is both calm and not old and vice versa. Everyone who is both not generous and not patient is curious and vice versa. If paul is both not kind and not funny then mary is not curious or not funny. Everyone who is both not creative and happy is not kind. Everyone who is not tall is either not generous or not strong and vice versa. Mary is either tall or kind. Lucy is both calm and rich. Someone is either old or not generous. Someone is kind. Someone is brave. Someone is humble. Mary is happy. Susan is either wise or calm. | Mary is not wise. | neutral | (![X]:((funny(X)&~wise(X))=>(~old(X)<~>~humble(X))))&
(((calm(fred)&~kind(fred)))=>(~tall(susan)))&
(![X]:(~generous(X)<=>brave(X)))&
(![X]:((patient(X)&creative(X))=>~curious(X)))&
((?[X]:((~happy(X)&funny(X))))<=>(?[X]:((~wise(X)&rich(X)))))&
((?[X]:(funny(X)))=>(wise(mary)))&
(((brave(paul)|~strong(paul)))=>(?[X]:((rich(X)|~wise(X)))))&
(![X]:((~tall(X)<~>wise(X))<=>(happy(X)&quiet(X))))&
((?[X]:((~tall(X)&quiet(X))))<=>(~creative(john)))&
(![X]:((calm(X)<~>rich(X))=>(rich(X)|~generous(X))))&
(![X]:((creative(X)<~>strong(X))=>(generous(X)&~kind(X))))&
((?[X]:(quiet(X)))<=>((calm(fred)&~old(fred))))&
(![X]:((~generous(X)&~patient(X))<=>curious(X)))&
(((~kind(paul)&~funny(paul)))=>((~curious(mary)|~funny(mary))))&
(![X]:((~creative(X)&happy(X))=>~kind(X)))&
(![X]:(~tall(X)<=>(~generous(X)<~>~strong(X))))&
((tall(mary)<~>kind(mary)))&
((calm(lucy)&rich(lucy)))&
(?[X]:((old(X)<~>~generous(X))))&
(?[X]:(kind(X)))&
(?[X]:(brave(X)))&
(?[X]:(humble(X)))&
(happy(mary))&
((wise(susan)<~>calm(susan))) | ~wise(mary) | [] | null | 0 |
Everyone who is not brave is either not generous or strong and vice versa.
If someone is not calm then lucy is both not wise and not creative.
Everyone who is old or not kind is both not curious and not generous.
Everyone who is both kind and tall is either brave or old.
Everyone who is both not creative and not humble is both not strong and not rich and vice versa.
Everyone who is either humble or tall is quiet and vice versa.
If fred is both patient and not curious then lucy is either old or not happy.
Everyone who is both not funny and not tall is creative or not generous.
Everyone who is either not strong or generous is generous or not kind and vice versa.
Everyone who is brave or not brave is not brave and vice versa.
Everyone who is not quiet or not happy is both wise and strong.
Everyone who is not tall or creative is creative or not patient and vice versa.
Everyone who is both not rich and quiet is either not brave or not humble.
Everyone who is not patient is both quiet and not rich.
Everyone who is quiet is both tall and funny.
Everyone who is not patient is funny or generous.
John is both quiet and not generous.
Alice is either not curious or patient.
John is patient.
Lucy is either not rich or wise.
Someone is not funny or wise.
Paul is either not tall or not kind.
Someone is either not tall or humble. | John is rich. | entailment | (![X]:(~brave(X)<=>(~generous(X)<~>strong(X))))&
((?[X]:(~calm(X)))=>((~wise(lucy)&~creative(lucy))))&
(![X]:((old(X)|~kind(X))=>(~curious(X)&~generous(X))))&
(![X]:((kind(X)&tall(X))=>(brave(X)<~>old(X))))&
(![X]:((~creative(X)&~humble(X))<=>(~strong(X)&~rich(X))))&
(![X]:((humble(X)<~>tall(X))<=>quiet(X)))&
(((patient(fred)&~curious(fred)))=>((old(lucy)<~>~happy(lucy))))&
(![X]:((~funny(X)&~tall(X))=>(creative(X)|~generous(X))))&
(![X]:((~strong(X)<~>generous(X))<=>(generous(X)|~kind(X))))&
(![X]:((brave(X)|~brave(X))<=>~brave(X)))&
(![X]:((~quiet(X)|~happy(X))=>(wise(X)&strong(X))))&
(![X]:((~tall(X)|creative(X))<=>(creative(X)|~patient(X))))&
(![X]:((~rich(X)&quiet(X))=>(~brave(X)<~>~humble(X))))&
(![X]:(~patient(X)=>(quiet(X)&~rich(X))))&
(![X]:(quiet(X)=>(tall(X)&funny(X))))&
(![X]:(~patient(X)=>(funny(X)|generous(X))))&
((quiet(john)&~generous(john)))&
((~curious(alice)<~>patient(alice)))&
(patient(john))&
((~rich(lucy)<~>wise(lucy)))&
(?[X]:((~funny(X)|wise(X))))&
((~tall(paul)<~>~kind(paul)))&
(?[X]:((~tall(X)<~>humble(X)))) | rich(john) | [
"p5",
"p9",
"p12",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 6346494253703526625730864
% SZS output start Proof for 6346494253703526625730864
6. ! [X0] : ((humble(X0) <~> tall(X0)) <=> quiet(X0)) [input p5]
10. ! [X0] : ((~brave(X0) | brave(X0)) <=> ~brave(X0)) [input p9]
13. ! [X0] : ((quiet(X0) & ~rich(X0)) => (~brave(X0) <~> ~humble(X0))) [input p12]
15. ! [X0] : (quiet(X0) => (funny(X0) & tall(X0))) [input p14]
17. ~generous(john) & quiet(john) [input p16]
24. ~rich(john) [input hypothesis]
34. ! [X0] : ((~brave(X0) <~> ~humble(X0)) | (~quiet(X0) | rich(X0))) [ennf transformation 13]
35. ! [X0] : ((~brave(X0) <~> ~humble(X0)) | ~quiet(X0) | rich(X0)) [flattening 34]
37. ! [X0] : ((funny(X0) & tall(X0)) | ~quiet(X0)) [ennf transformation 15]
44. ! [X0] : ((((~tall(X0) | ~humble(X0)) & (tall(X0) | humble(X0))) | ~quiet(X0)) & (quiet(X0) | ((humble(X0) | ~tall(X0)) & (tall(X0) | ~humble(X0))))) [nnf transformation 6]
48. ! [X0] : (((~brave(X0) | brave(X0)) | brave(X0)) & (~brave(X0) | (brave(X0) & ~brave(X0)))) [nnf transformation 10]
49. ! [X0] : ((~brave(X0) | brave(X0) | brave(X0)) & (~brave(X0) | (brave(X0) & ~brave(X0)))) [flattening 48]
52. ! [X0] : (((humble(X0) | brave(X0)) & (~humble(X0) | ~brave(X0))) | ~quiet(X0) | rich(X0)) [nnf transformation 35]
78. ~quiet(X0) | ~humble(X0) | ~tall(X0) [cnf transformation 44]
88. ~brave(X0) | ~brave(X0) [cnf transformation 49]
100. humble(X0) | brave(X0) | ~quiet(X0) | rich(X0) [cnf transformation 52]
103. ~quiet(X0) | tall(X0) [cnf transformation 37]
106. quiet(john) [cnf transformation 17]
118. ~rich(john) [cnf transformation 24]
119. ~brave(X0) [duplicate literal removal 88]
143. ~quiet(X0) | humble(X0) | rich(X0) [subsumption resolution 100,119]
198. tall(john) [resolution 103,106]
259. ~humble(john) | ~tall(john) [resolution 78,106]
264. ~humble(john) [subsumption resolution 259,198]
307. humble(john) | rich(john) [resolution 143,106]
312. rich(john) [subsumption resolution 307,264]
313. $false [subsumption resolution 312,118]
% SZS output end Proof for 6346494253703526625730864
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative then someone is humble and vice versa. If someone is kind then someone is either not happy or happy and vice versa. Everyone who is rich or calm is not calm and vice versa. If paul is either not wise or generous then paul is strong or not strong. If alice is both humble and curious then someone is not funny and vice versa. If someone is old then mary is either not brave or calm and vice versa. If susan is either not calm or patient then someone is both creative and old and vice versa. Everyone who is humble is not quiet or not creative. Everyone who is not calm or old is happy. If paul is not brave then someone is either not calm or strong. Everyone who is not quiet or old is wise or calm. If john is brave then mary is both humble and creative and vice versa. If someone is either tall or not tall then someone is either humble or not tall. Everyone who is not curious is either not old or humble and vice versa. Everyone who is not generous or funny is either funny or not tall. If susan is rich or brave then someone is either not strong or wise and vice versa. Someone is both strong and not tall. Someone is not calm or not quiet. Someone is either not humble or wise. Susan is both not calm and creative. Someone is both not funny and generous. Someone is not generous or not strong. Someone is not patient. | Paul is strong. | neutral | ((?[X]:(~creative(X)))<=>(?[X]:(humble(X))))&
((?[X]:(kind(X)))<=>(?[X]:((~happy(X)<~>happy(X)))))&
(![X]:((rich(X)|calm(X))<=>~calm(X)))&
(((~wise(paul)<~>generous(paul)))=>((strong(paul)|~strong(paul))))&
(((humble(alice)&curious(alice)))<=>(?[X]:(~funny(X))))&
((?[X]:(old(X)))<=>((~brave(mary)<~>calm(mary))))&
(((~calm(susan)<~>patient(susan)))<=>(?[X]:((creative(X)&old(X)))))&
(![X]:(humble(X)=>(~quiet(X)|~creative(X))))&
(![X]:((~calm(X)|old(X))=>happy(X)))&
((~brave(paul))=>(?[X]:((~calm(X)<~>strong(X)))))&
(![X]:((~quiet(X)|old(X))=>(wise(X)|calm(X))))&
((brave(john))<=>((humble(mary)&creative(mary))))&
((?[X]:((tall(X)<~>~tall(X))))=>(?[X]:((humble(X)<~>~tall(X)))))&
(![X]:(~curious(X)<=>(~old(X)<~>humble(X))))&
(![X]:((~generous(X)|funny(X))=>(funny(X)<~>~tall(X))))&
(((rich(susan)|brave(susan)))<=>(?[X]:((~strong(X)<~>wise(X)))))&
(?[X]:((strong(X)&~tall(X))))&
(?[X]:((~calm(X)|~quiet(X))))&
(?[X]:((~humble(X)<~>wise(X))))&
((~calm(susan)&creative(susan)))&
(?[X]:((~funny(X)&generous(X))))&
(?[X]:((~generous(X)|~strong(X))))&
(?[X]:(~patient(X))) | strong(paul) | [] | null | 0 |
Everyone who is both generous and not creative is both happy and humble.
If susan is either not curious or old then john is either not kind or strong and vice versa.
Everyone who is both not funny and patient is not calm and vice versa.
Everyone who is either not quiet or not old is either not quiet or not strong and vice versa.
Everyone who is happy is not tall.
If lucy is either curious or strong then someone is not strong or tall.
If someone is kind or generous then someone is not happy or not wise and vice versa.
Everyone who is strong is both not generous and strong.
Everyone who is strong is both rich and not rich.
If someone is both generous and patient then fred is both kind and happy.
If someone is either funny or not wise then someone is not funny.
Everyone who is either wise or calm is both not old and calm.
If someone is either calm or not patient then paul is either wise or strong.
If lucy is both old and not old then someone is either not rich or strong and vice versa.
Everyone who is not quiet is patient and vice versa.
If susan is both generous and not curious then mary is not calm or generous and vice versa.
John is not quiet or not rich.
Someone is both not old and not funny.
Someone is not happy or old.
Someone is both curious and not humble.
John is either humble or not strong.
Susan is either not quiet or rich.
Someone is not calm.
Lucy is not old or not creative. | Paul is not rich. | contradiction | (![X]:((generous(X)&~creative(X))=>(happy(X)&humble(X))))&
(((~curious(susan)<~>old(susan)))<=>((~kind(john)<~>strong(john))))&
(![X]:((~funny(X)&patient(X))<=>~calm(X)))&
(![X]:((~quiet(X)<~>~old(X))<=>(~quiet(X)<~>~strong(X))))&
(![X]:(happy(X)=>~tall(X)))&
(((curious(lucy)<~>strong(lucy)))=>(?[X]:((~strong(X)|tall(X)))))&
((?[X]:((kind(X)|generous(X))))<=>(?[X]:((~happy(X)|~wise(X)))))&
(![X]:(strong(X)=>(~generous(X)&strong(X))))&
(![X]:(strong(X)=>(rich(X)&~rich(X))))&
((?[X]:((generous(X)&patient(X))))=>((kind(fred)&happy(fred))))&
((?[X]:((funny(X)<~>~wise(X))))=>(?[X]:(~funny(X))))&
(![X]:((wise(X)<~>calm(X))=>(~old(X)&calm(X))))&
((?[X]:((calm(X)<~>~patient(X))))=>((wise(paul)<~>strong(paul))))&
(((old(lucy)&~old(lucy)))<=>(?[X]:((~rich(X)<~>strong(X)))))&
(![X]:(~quiet(X)<=>patient(X)))&
(((generous(susan)&~curious(susan)))<=>((~calm(mary)|generous(mary))))&
((~quiet(john)|~rich(john)))&
(?[X]:((~old(X)&~funny(X))))&
(?[X]:((~happy(X)|old(X))))&
(?[X]:((curious(X)&~humble(X))))&
((humble(john)<~>~strong(john)))&
((~quiet(susan)<~>rich(susan)))&
(?[X]:(~calm(X)))&
((~old(lucy)|~creative(lucy))) | ~rich(paul) | [
"p8",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 1624038899971260045330983
% SZS output start Proof for 1624038899971260045330983
9. ! [X0] : (strong(X0) => (~rich(X0) & rich(X0))) [input p8]
14. (~old(lucy) & old(lucy)) <=> ? [X0] : (~rich(X0) <~> strong(X0)) [input p13]
25. ~rich(paul) [input hypothesis]
33. ! [X0] : ((~rich(X0) & rich(X0)) | ~strong(X0)) [ennf transformation 9]
56. ((~old(lucy) & old(lucy)) | ! [X0] : ((~rich(X0) | ~strong(X0)) & (strong(X0) | rich(X0)))) & (? [X0] : ((~strong(X0) | rich(X0)) & (strong(X0) | ~rich(X0))) | (old(lucy) | ~old(lucy))) [nnf transformation 14]
57. ((~old(lucy) & old(lucy)) | ! [X0] : ((~rich(X0) | ~strong(X0)) & (strong(X0) | rich(X0)))) & (? [X0] : ((~strong(X0) | rich(X0)) & (strong(X0) | ~rich(X0))) | old(lucy) | ~old(lucy)) [flattening 56]
58. ((~old(lucy) & old(lucy)) | ! [X0] : ((~rich(X0) | ~strong(X0)) & (strong(X0) | rich(X0)))) & (? [X1] : ((~strong(X1) | rich(X1)) & (strong(X1) | ~rich(X1))) | old(lucy) | ~old(lucy)) [rectify 57]
59. ? [X1] : ((~strong(X1) | rich(X1)) & (strong(X1) | ~rich(X1))) => ((~strong(sK4) | rich(sK4)) & (strong(sK4) | ~rich(sK4))) [choice axiom]
60. ((~old(lucy) & old(lucy)) | ! [X0] : ((~rich(X0) | ~strong(X0)) & (strong(X0) | rich(X0)))) & (((~strong(sK4) | rich(sK4)) & (strong(sK4) | ~rich(sK4))) | old(lucy) | ~old(lucy)) [skolemisation 58,59]
104. rich(X0) | ~strong(X0) [cnf transformation 33]
105. ~rich(X0) | ~strong(X0) [cnf transformation 33]
120. old(lucy) | strong(X0) | rich(X0) [cnf transformation 60]
122. ~old(lucy) | strong(X0) | rich(X0) [cnf transformation 60]
143. ~rich(paul) [cnf transformation 25]
225. ~strong(X0) [subsumption resolution 104,105]
260. ~old(lucy) | rich(X0) [subsumption resolution 122,225]
262. 25 <=> ! [X0] : rich(X0) [avatar definition]
263. rich(X0) <- (25) [avatar component clause 262]
265. 26 <=> old(lucy) [avatar definition]
268. 25 | ~26 [avatar split clause 260,265,262]
269. old(lucy) | rich(X0) [subsumption resolution 120,225]
270. 25 | 26 [avatar split clause 269,265,262]
322. $false <- (25) [resolution 263,143]
323. ~25 [avatar contradiction clause 322]
324. $false [avatar sat refutation 268,270,323]
% SZS output end Proof for 1624038899971260045330983
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not funny and curious then someone is creative. If lucy is both not old and humble then susan is curious. Everyone who is not funny or funny is funny or not patient and vice versa. Everyone who is happy or not curious is tall and vice versa. Everyone who is both not wise and funny is not brave or strong. Everyone who is brave or not humble is not generous and vice versa. Everyone who is rich or not brave is either not creative or happy. Everyone who is both curious and not old is both not patient and brave and vice versa. If someone is brave then someone is not old and vice versa. If susan is patient then mary is both brave and not tall. If lucy is creative or not generous then susan is both not strong and curious. Everyone who is happy or not curious is either humble or kind. If mary is strong or not quiet then john is both not old and not calm. If someone is not funny then someone is both brave and strong. If someone is both not funny and not patient then someone is funny or not patient. Everyone who is both not wise and not rich is both patient and not generous and vice versa. Susan is generous or not kind. John is strong. Someone is not tall or rich. Someone is either not rich or not brave. Lucy is either not tall or curious. Someone is either not calm or not brave. Lucy is wise. Someone is strong or kind. | Mary is strong. | neutral | ((?[X]:((~funny(X)&curious(X))))=>(?[X]:(creative(X))))&
(((~old(lucy)&humble(lucy)))=>(curious(susan)))&
(![X]:((~funny(X)|funny(X))<=>(funny(X)|~patient(X))))&
(![X]:((happy(X)|~curious(X))<=>tall(X)))&
(![X]:((~wise(X)&funny(X))=>(~brave(X)|strong(X))))&
(![X]:((brave(X)|~humble(X))<=>~generous(X)))&
(![X]:((rich(X)|~brave(X))=>(~creative(X)<~>happy(X))))&
(![X]:((curious(X)&~old(X))<=>(~patient(X)&brave(X))))&
((?[X]:(brave(X)))<=>(?[X]:(~old(X))))&
((patient(susan))=>((brave(mary)&~tall(mary))))&
(((creative(lucy)|~generous(lucy)))=>((~strong(susan)&curious(susan))))&
(![X]:((happy(X)|~curious(X))=>(humble(X)<~>kind(X))))&
(((strong(mary)|~quiet(mary)))=>((~old(john)&~calm(john))))&
((?[X]:(~funny(X)))=>(?[X]:((brave(X)&strong(X)))))&
((?[X]:((~funny(X)&~patient(X))))=>(?[X]:((funny(X)|~patient(X)))))&
(![X]:((~wise(X)&~rich(X))<=>(patient(X)&~generous(X))))&
((generous(susan)|~kind(susan)))&
(strong(john))&
(?[X]:((~tall(X)|rich(X))))&
(?[X]:((~rich(X)<~>~brave(X))))&
((~tall(lucy)<~>curious(lucy)))&
(?[X]:((~calm(X)<~>~brave(X))))&
(wise(lucy))&
(?[X]:((strong(X)|kind(X)))) | strong(mary) | [] | null | 0 |
If someone is both not strong and not quiet then john is both humble and not calm and vice versa.
Everyone who is both not happy and not funny is either old or strong and vice versa.
If someone is generous then someone is either not calm or strong.
Everyone who is generous or not strong is curious or not rich.
Everyone who is both rich and not quiet is brave.
Everyone who is both funny and not tall is either humble or not rich and vice versa.
Everyone who is strong is either patient or old and vice versa.
Everyone who is both not wise and not quiet is not old or creative.
If someone is both not calm and patient then john is both not rich and funny and vice versa.
Everyone who is not strong or not generous is calm or not curious and vice versa.
Everyone who is not generous or not humble is both not happy and humble and vice versa.
Everyone who is brave is calm.
Everyone who is funny or rich is either happy or not strong.
If alice is both not brave and not curious then someone is not patient and vice versa.
If someone is rich then someone is either creative or not kind and vice versa.
If john is both not happy and not tall then alice is either not calm or not brave and vice versa.
Alice is both not tall and generous.
Someone is not creative.
Someone is kind or not kind.
Lucy is not tall or not generous.
Lucy is rich or not brave.
John is not tall or not happy.
Someone is both not brave and creative.
Someone is patient or wise. | Lucy is not wise. | neutral | ((?[X]:((~strong(X)&~quiet(X))))<=>((humble(john)&~calm(john))))&
(![X]:((~happy(X)&~funny(X))<=>(old(X)<~>strong(X))))&
((?[X]:(generous(X)))=>(?[X]:((~calm(X)<~>strong(X)))))&
(![X]:((generous(X)|~strong(X))=>(curious(X)|~rich(X))))&
(![X]:((rich(X)&~quiet(X))=>brave(X)))&
(![X]:((funny(X)&~tall(X))<=>(humble(X)<~>~rich(X))))&
(![X]:(strong(X)<=>(patient(X)<~>old(X))))&
(![X]:((~wise(X)&~quiet(X))=>(~old(X)|creative(X))))&
((?[X]:((~calm(X)&patient(X))))<=>((~rich(john)&funny(john))))&
(![X]:((~strong(X)|~generous(X))<=>(calm(X)|~curious(X))))&
(![X]:((~generous(X)|~humble(X))<=>(~happy(X)&humble(X))))&
(![X]:(brave(X)=>calm(X)))&
(![X]:((funny(X)|rich(X))=>(happy(X)<~>~strong(X))))&
(((~brave(alice)&~curious(alice)))<=>(?[X]:(~patient(X))))&
((?[X]:(rich(X)))<=>(?[X]:((creative(X)<~>~kind(X)))))&
(((~happy(john)&~tall(john)))<=>((~calm(alice)<~>~brave(alice))))&
((~tall(alice)&generous(alice)))&
(?[X]:(~creative(X)))&
(?[X]:((kind(X)|~kind(X))))&
((~tall(lucy)|~generous(lucy)))&
((rich(lucy)|~brave(lucy)))&
((~tall(john)|~happy(john)))&
(?[X]:((~brave(X)&creative(X))))&
(?[X]:((patient(X)|wise(X)))) | ~wise(lucy) | [] | null | 0 |
Everyone who is either not brave or patient is not patient.
If someone is either generous or not old then someone is not old or calm and vice versa.
If someone is generous or calm then fred is generous.
Everyone who is both wise and not happy is both happy and not brave and vice versa.
If someone is tall then someone is not generous.
Everyone who is both not rich and kind is either not happy or not strong and vice versa.
Everyone who is both creative and happy is curious or not funny.
If john is either wise or rich then mary is either kind or calm.
If fred is not brave or not old then mary is kind and vice versa.
Everyone who is humble or creative is either tall or humble and vice versa.
If someone is not happy or tall then alice is not wise or not kind.
Everyone who is not strong or not brave is humble.
Everyone who is both patient and not wise is either wise or not tall and vice versa.
Everyone who is both wise and not creative is either not strong or not funny and vice versa.
If someone is both old and not patient then someone is either funny or kind and vice versa.
If alice is both funny and kind then john is both patient and happy and vice versa.
Someone is generous.
Someone is both humble and not funny.
Fred is both strong and not brave.
Lucy is both old and not creative.
Lucy is either calm or not strong.
Alice is not wise or not curious.
Someone is both not funny and humble. | John is not kind. | neutral | (![X]:((~brave(X)<~>patient(X))=>~patient(X)))&
((?[X]:((generous(X)<~>~old(X))))<=>(?[X]:((~old(X)|calm(X)))))&
((?[X]:((generous(X)|calm(X))))=>(generous(fred)))&
(![X]:((wise(X)&~happy(X))<=>(happy(X)&~brave(X))))&
((?[X]:(tall(X)))=>(?[X]:(~generous(X))))&
(![X]:((~rich(X)&kind(X))<=>(~happy(X)<~>~strong(X))))&
(![X]:((creative(X)&happy(X))=>(curious(X)|~funny(X))))&
(((wise(john)<~>rich(john)))=>((kind(mary)<~>calm(mary))))&
(((~brave(fred)|~old(fred)))<=>(kind(mary)))&
(![X]:((humble(X)|creative(X))<=>(tall(X)<~>humble(X))))&
((?[X]:((~happy(X)|tall(X))))=>((~wise(alice)|~kind(alice))))&
(![X]:((~strong(X)|~brave(X))=>humble(X)))&
(![X]:((patient(X)&~wise(X))<=>(wise(X)<~>~tall(X))))&
(![X]:((wise(X)&~creative(X))<=>(~strong(X)<~>~funny(X))))&
((?[X]:((old(X)&~patient(X))))<=>(?[X]:((funny(X)<~>kind(X)))))&
(((funny(alice)&kind(alice)))<=>((patient(john)&happy(john))))&
(?[X]:(generous(X)))&
(?[X]:((humble(X)&~funny(X))))&
((strong(fred)&~brave(fred)))&
((old(lucy)&~creative(lucy)))&
((calm(lucy)<~>~strong(lucy)))&
((~wise(alice)|~curious(alice)))&
(?[X]:((~funny(X)&humble(X)))) | ~kind(john) | [] | null | 0 |
Everyone who is both not brave and not funny is calm and vice versa.
If someone is both not patient and not humble then someone is not brave or curious and vice versa.
Everyone who is either not strong or brave is curious or funny.
If someone is not calm then fred is not wise or happy and vice versa.
Everyone who is both old and curious is not strong or not funny.
Everyone who is wise or not happy is both not generous and old and vice versa.
Everyone who is both not rich and not kind is generous or not funny and vice versa.
If someone is either not creative or happy then mary is both not tall and not generous and vice versa.
If someone is brave then fred is both kind and not rich and vice versa.
Everyone who is both not funny and not brave is not old and vice versa.
Everyone who is either not creative or old is either humble or generous.
If paul is either not funny or not calm then susan is both not quiet and not creative and vice versa.
Everyone who is not strong is brave.
Everyone who is either happy or patient is either kind or strong.
If lucy is both old and tall then lucy is humble.
Everyone who is both curious and patient is either not humble or not happy and vice versa.
Someone is either not funny or not patient.
Mary is either not brave or strong.
Lucy is both not rich and brave.
Someone is curious.
Someone is both wise and kind.
Alice is not happy or not funny.
Someone is not funny.
Someone is both wise and not quiet. | Fred is wise. | neutral | (![X]:((~brave(X)&~funny(X))<=>calm(X)))&
((?[X]:((~patient(X)&~humble(X))))<=>(?[X]:((~brave(X)|curious(X)))))&
(![X]:((~strong(X)<~>brave(X))=>(curious(X)|funny(X))))&
((?[X]:(~calm(X)))<=>((~wise(fred)|happy(fred))))&
(![X]:((old(X)&curious(X))=>(~strong(X)|~funny(X))))&
(![X]:((wise(X)|~happy(X))<=>(~generous(X)&old(X))))&
(![X]:((~rich(X)&~kind(X))<=>(generous(X)|~funny(X))))&
((?[X]:((~creative(X)<~>happy(X))))<=>((~tall(mary)&~generous(mary))))&
((?[X]:(brave(X)))<=>((kind(fred)&~rich(fred))))&
(![X]:((~funny(X)&~brave(X))<=>~old(X)))&
(![X]:((~creative(X)<~>old(X))=>(humble(X)<~>generous(X))))&
(((~funny(paul)<~>~calm(paul)))<=>((~quiet(susan)&~creative(susan))))&
(![X]:(~strong(X)=>brave(X)))&
(![X]:((happy(X)<~>patient(X))=>(kind(X)<~>strong(X))))&
(((old(lucy)&tall(lucy)))=>(humble(lucy)))&
(![X]:((curious(X)&patient(X))<=>(~humble(X)<~>~happy(X))))&
(?[X]:((~funny(X)<~>~patient(X))))&
((~brave(mary)<~>strong(mary)))&
((~rich(lucy)&brave(lucy)))&
(?[X]:(curious(X)))&
(?[X]:((wise(X)&kind(X))))&
((~happy(alice)|~funny(alice)))&
(?[X]:(~funny(X)))&
(?[X]:((wise(X)&~quiet(X)))) | wise(fred) | [] | null | 0 |
Everyone who is quiet is kind and vice versa.
If susan is both old and kind then someone is both not strong and not creative and vice versa.
Everyone who is not quiet is not creative or not generous.
Everyone who is both curious and not patient is both brave and rich.
Everyone who is generous is either not old or quiet.
Everyone who is both humble and not calm is happy or kind and vice versa.
If someone is both generous and not wise then someone is not tall and vice versa.
Everyone who is funny or not strong is either not strong or not old and vice versa.
Everyone who is either creative or quiet is not tall or not wise and vice versa.
If mary is both brave and not generous then someone is both old and not tall and vice versa.
Everyone who is not humble or not tall is either not generous or not rich and vice versa.
If paul is brave or kind then paul is both not tall and not generous.
If someone is generous then susan is not quiet.
Everyone who is patient is creative and vice versa.
Everyone who is not humble is either kind or brave.
Everyone who is generous is not kind.
Someone is both brave and funny.
Someone is not brave.
Mary is not curious.
John is either strong or creative.
Fred is either not happy or kind.
Mary is both not wise and not rich. | Paul is tall. | entailment | (![X]:(quiet(X)<=>kind(X)))&
(((old(susan)&kind(susan)))<=>(?[X]:((~strong(X)&~creative(X)))))&
(![X]:(~quiet(X)=>(~creative(X)|~generous(X))))&
(![X]:((curious(X)&~patient(X))=>(brave(X)&rich(X))))&
(![X]:(generous(X)=>(~old(X)<~>quiet(X))))&
(![X]:((humble(X)&~calm(X))<=>(happy(X)|kind(X))))&
((?[X]:((generous(X)&~wise(X))))<=>(?[X]:(~tall(X))))&
(![X]:((funny(X)|~strong(X))<=>(~strong(X)<~>~old(X))))&
(![X]:((creative(X)<~>quiet(X))<=>(~tall(X)|~wise(X))))&
(((brave(mary)&~generous(mary)))<=>(?[X]:((old(X)&~tall(X)))))&
(![X]:((~humble(X)|~tall(X))<=>(~generous(X)<~>~rich(X))))&
(((brave(paul)|kind(paul)))=>((~tall(paul)&~generous(paul))))&
((?[X]:(generous(X)))=>(~quiet(susan)))&
(![X]:(patient(X)<=>creative(X)))&
(![X]:(~humble(X)=>(kind(X)<~>brave(X))))&
(![X]:(generous(X)=>~kind(X)))&
(?[X]:((brave(X)&funny(X))))&
(?[X]:(~brave(X)))&
(~curious(mary))&
((strong(john)<~>creative(john)))&
((~happy(fred)<~>kind(fred)))&
((~wise(mary)&~rich(mary))) | tall(paul) | [
"p0",
"p2",
"p6",
"p8",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7791016680143987099302508
% SZS output start Proof for 7791016680143987099302508
1. ! [X0] : (quiet(X0) <=> kind(X0)) [input p0]
3. ! [X0] : (~quiet(X0) => (~generous(X0) | ~creative(X0))) [input p2]
7. ? [X0] : (~wise(X0) & generous(X0)) <=> ? [X0] : ~tall(X0) [input p6]
9. ! [X0] : ((creative(X0) <~> quiet(X0)) <=> (~wise(X0) | ~tall(X0))) [input p8]
16. ! [X0] : (generous(X0) => ~kind(X0)) [input p15]
23. ~tall(paul) [input hypothesis]
24. ? [X0] : (~wise(X0) & generous(X0)) <=> ? [X1] : ~tall(X1) [rectify 7]
29. ! [X0] : ((~generous(X0) | ~creative(X0)) | quiet(X0)) [ennf transformation 3]
30. ! [X0] : (~generous(X0) | ~creative(X0) | quiet(X0)) [flattening 29]
35. ! [X0] : (~kind(X0) | ~generous(X0)) [ennf transformation 16]
36. ! [X0] : ((quiet(X0) | ~kind(X0)) & (kind(X0) | ~quiet(X0))) [nnf transformation 1]
45. (? [X0] : (~wise(X0) & generous(X0)) | ! [X1] : tall(X1)) & (? [X1] : ~tall(X1) | ! [X0] : (wise(X0) | ~generous(X0))) [nnf transformation 24]
46. (? [X0] : (~wise(X0) & generous(X0)) | ! [X1] : tall(X1)) & (? [X2] : ~tall(X2) | ! [X3] : (wise(X3) | ~generous(X3))) [rectify 45]
47. ? [X0] : (~wise(X0) & generous(X0)) => (~wise(sK1) & generous(sK1)) [choice axiom]
48. ? [X2] : ~tall(X2) => ~tall(sK2) [choice axiom]
49. ((~wise(sK1) & generous(sK1)) | ! [X1] : tall(X1)) & (~tall(sK2) | ! [X3] : (wise(X3) | ~generous(X3))) [skolemisation 46,48,47]
52. ! [X0] : ((((~quiet(X0) | ~creative(X0)) & (quiet(X0) | creative(X0))) | (wise(X0) & tall(X0))) & ((~wise(X0) | ~tall(X0)) | ((creative(X0) | ~quiet(X0)) & (quiet(X0) | ~creative(X0))))) [nnf transformation 9]
53. ! [X0] : ((((~quiet(X0) | ~creative(X0)) & (quiet(X0) | creative(X0))) | (wise(X0) & tall(X0))) & (~wise(X0) | ~tall(X0) | ((creative(X0) | ~quiet(X0)) & (quiet(X0) | ~creative(X0))))) [flattening 52]
68. ~quiet(X0) | kind(X0) [cnf transformation 36]
74. ~generous(X0) | ~creative(X0) | quiet(X0) [cnf transformation 30]
83. generous(sK1) | tall(X1) [cnf transformation 49]
84. ~wise(sK1) | tall(X1) [cnf transformation 49]
94. wise(X0) | creative(X0) | quiet(X0) [cnf transformation 53]
114. ~generous(X0) | ~kind(X0) [cnf transformation 35]
124. ~tall(paul) [cnf transformation 23]
151. 6 <=> ! [X1] : tall(X1) [avatar definition]
152. tall(X1) <- (6) [avatar component clause 151]
154. 7 <=> wise(sK1) [avatar definition]
156. ~wise(sK1) <- (~7) [avatar component clause 154]
157. 6 | ~7 [avatar split clause 84,154,151]
159. 8 <=> generous(sK1) [avatar definition]
161. generous(sK1) <- (8) [avatar component clause 159]
162. 6 | 8 [avatar split clause 83,159,151]
209. 19 <=> tall(paul) [avatar definition]
211. ~tall(paul) <- (~19) [avatar component clause 209]
243. ~19 [avatar split clause 124,209]
252. ~kind(sK1) <- (8) [resolution 114,161]
260. ~creative(sK1) | quiet(sK1) <- (8) [resolution 74,161]
262. 26 <=> quiet(sK1) [avatar definition]
264. quiet(sK1) <- (26) [avatar component clause 262]
266. 27 <=> creative(sK1) [avatar definition]
268. ~creative(sK1) <- (~27) [avatar component clause 266]
269. 26 | ~27 | ~8 [avatar split clause 260,159,266,262]
314. $false <- (6, ~19) [resolution 152,211]
315. ~6 | 19 [avatar contradiction clause 314]
318. creative(sK1) | quiet(sK1) <- (~7) [resolution 94,156]
328. quiet(sK1) <- (~7, ~27) [subsumption resolution 318,268]
331. 26 | 7 | 27 [avatar split clause 328,266,154,262]
333. kind(sK1) <- (26) [resolution 264,68]
334. $false <- (8, 26) [subsumption resolution 333,252]
335. ~8 | ~26 [avatar contradiction clause 334]
336. $false [avatar sat refutation 157,162,243,269,315,331,335]
% SZS output end Proof for 7791016680143987099302508
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble or not rich is both not humble and kind.
Everyone who is either funny or rich is not funny.
Everyone who is both curious and not curious is both patient and creative and vice versa.
Everyone who is not curious is not brave and vice versa.
If john is either strong or not funny then paul is brave.
If alice is strong or funny then fred is either tall or not strong.
Everyone who is both not funny and curious is either curious or not brave and vice versa.
If someone is not creative or not generous then someone is calm and vice versa.
Everyone who is either not brave or quiet is happy or not happy.
If fred is either not creative or old then someone is old or not creative.
Everyone who is not tall or calm is strong and vice versa.
If fred is either not generous or brave then someone is both not patient and happy.
If someone is either strong or happy then paul is not wise or not creative and vice versa.
If someone is either curious or not humble then lucy is either not wise or not creative.
If lucy is both happy and not wise then someone is happy or not rich and vice versa.
Everyone who is not funny or not brave is generous or not strong and vice versa.
Someone is not curious or patient.
Mary is creative or old.
Alice is not humble.
Fred is both tall and not wise.
Mary is not patient.
Someone is not funny.
Fred is patient.
Mary is either funny or quiet. | Mary is not quiet. | contradiction | (![X]:((humble(X)<~>~rich(X))=>(~humble(X)&kind(X))))&
(![X]:((funny(X)<~>rich(X))=>~funny(X)))&
(![X]:((curious(X)&~curious(X))<=>(patient(X)&creative(X))))&
(![X]:(~curious(X)<=>~brave(X)))&
(((strong(john)<~>~funny(john)))=>(brave(paul)))&
(((strong(alice)|funny(alice)))=>((tall(fred)<~>~strong(fred))))&
(![X]:((~funny(X)&curious(X))<=>(curious(X)<~>~brave(X))))&
((?[X]:((~creative(X)|~generous(X))))<=>(?[X]:(calm(X))))&
(![X]:((~brave(X)<~>quiet(X))=>(happy(X)|~happy(X))))&
(((~creative(fred)<~>old(fred)))=>(?[X]:((old(X)|~creative(X)))))&
(![X]:((~tall(X)|calm(X))<=>strong(X)))&
(((~generous(fred)<~>brave(fred)))=>(?[X]:((~patient(X)&happy(X)))))&
((?[X]:((strong(X)<~>happy(X))))<=>((~wise(paul)|~creative(paul))))&
((?[X]:((curious(X)<~>~humble(X))))=>((~wise(lucy)<~>~creative(lucy))))&
(((happy(lucy)&~wise(lucy)))<=>(?[X]:((happy(X)|~rich(X)))))&
(![X]:((~funny(X)|~brave(X))<=>(generous(X)|~strong(X))))&
(?[X]:((~curious(X)|patient(X))))&
((creative(mary)|old(mary)))&
(~humble(alice))&
((tall(fred)&~wise(fred)))&
(~patient(mary))&
(?[X]:(~funny(X)))&
(patient(fred))&
((funny(mary)<~>quiet(mary))) | ~quiet(mary) | [
"p3",
"p6",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 4446127447723974680326611
% SZS output start Proof for 4446127447723974680326611
4. ! [X0] : (~curious(X0) <=> ~brave(X0)) [input p3]
7. ! [X0] : ((curious(X0) & ~funny(X0)) <=> (curious(X0) <~> ~brave(X0))) [input p6]
24. funny(mary) <~> quiet(mary) [input p23]
25. ~quiet(mary) [input hypothesis]
41. ! [X0] : ((~curious(X0) | brave(X0)) & (~brave(X0) | curious(X0))) [nnf transformation 4]
44. ! [X0] : (((curious(X0) & ~funny(X0)) | ((curious(X0) | brave(X0)) & (~brave(X0) | ~curious(X0)))) & (((brave(X0) | ~curious(X0)) & (~brave(X0) | curious(X0))) | (~curious(X0) | funny(X0)))) [nnf transformation 7]
45. ! [X0] : (((curious(X0) & ~funny(X0)) | ((curious(X0) | brave(X0)) & (~brave(X0) | ~curious(X0)))) & (((brave(X0) | ~curious(X0)) & (~brave(X0) | curious(X0))) | ~curious(X0) | funny(X0))) [flattening 44]
77. (~quiet(mary) | ~funny(mary)) & (quiet(mary) | funny(mary)) [nnf transformation 24]
86. ~brave(X0) | curious(X0) [cnf transformation 41]
87. ~curious(X0) | brave(X0) [cnf transformation 41]
96. ~funny(X0) | ~brave(X0) | ~curious(X0) [cnf transformation 45]
99. curious(X0) | curious(X0) | brave(X0) [cnf transformation 45]
141. quiet(mary) | funny(mary) [cnf transformation 77]
143. ~quiet(mary) [cnf transformation 25]
145. curious(X0) | brave(X0) [duplicate literal removal 99]
183. brave(X0) [subsumption resolution 145,87]
184. ~curious(X0) | ~funny(X0) [subsumption resolution 96,183]
334. 40 <=> funny(mary) [avatar definition]
335. funny(mary) <- (40) [avatar component clause 334]
338. 41 <=> quiet(mary) [avatar definition]
342. 40 | 41 [avatar split clause 141,338,334]
343. ~41 [avatar split clause 143,338]
344. curious(X0) [resolution 86,183]
352. ~funny(X0) [resolution 184,344]
354. $false <- (40) [resolution 352,335]
355. ~40 [avatar contradiction clause 354]
356. $false [avatar sat refutation 342,343,355]
% SZS output end Proof for 4446127447723974680326611
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both creative and strong then alice is not old or wise and vice versa.
If someone is both kind and calm then lucy is not rich or not wise and vice versa.
If someone is both rich and not curious then someone is not funny or not generous and vice versa.
If alice is both not creative and not kind then someone is happy and vice versa.
If someone is not wise or not curious then someone is both not creative and kind.
If someone is not curious or rich then paul is humble and vice versa.
If john is creative or curious then susan is either not calm or not strong.
Everyone who is strong or tall is not old.
If someone is generous then someone is both not calm and not creative.
Everyone who is generous is not happy.
Everyone who is humble or patient is old.
Everyone who is creative is both brave and not old.
Everyone who is either happy or rich is either quiet or brave.
Everyone who is not happy or funny is either not happy or not generous and vice versa.
Everyone who is both not kind and not old is both humble and not creative and vice versa.
If someone is both not wise and not kind then someone is kind.
John is either not tall or not kind.
Susan is both generous and strong.
Fred is either not brave or tall.
Susan is not funny or not happy.
Someone is both kind and not old.
Someone is not happy or not creative.
Someone is both not brave and generous.
Mary is tall. | Paul is happy. | contradiction | ((?[X]:((creative(X)&strong(X))))<=>((~old(alice)|wise(alice))))&
((?[X]:((kind(X)&calm(X))))<=>((~rich(lucy)|~wise(lucy))))&
((?[X]:((rich(X)&~curious(X))))<=>(?[X]:((~funny(X)|~generous(X)))))&
(((~creative(alice)&~kind(alice)))<=>(?[X]:(happy(X))))&
((?[X]:((~wise(X)|~curious(X))))=>(?[X]:((~creative(X)&kind(X)))))&
((?[X]:((~curious(X)|rich(X))))<=>(humble(paul)))&
(((creative(john)|curious(john)))=>((~calm(susan)<~>~strong(susan))))&
(![X]:((strong(X)|tall(X))=>~old(X)))&
((?[X]:(generous(X)))=>(?[X]:((~calm(X)&~creative(X)))))&
(![X]:(generous(X)=>~happy(X)))&
(![X]:((humble(X)|patient(X))=>old(X)))&
(![X]:(creative(X)=>(brave(X)&~old(X))))&
(![X]:((happy(X)<~>rich(X))=>(quiet(X)<~>brave(X))))&
(![X]:((~happy(X)|funny(X))<=>(~happy(X)<~>~generous(X))))&
(![X]:((~kind(X)&~old(X))<=>(humble(X)&~creative(X))))&
((?[X]:((~wise(X)&~kind(X))))=>(?[X]:(kind(X))))&
((~tall(john)<~>~kind(john)))&
((generous(susan)&strong(susan)))&
((~brave(fred)<~>tall(fred)))&
((~funny(susan)|~happy(susan)))&
(?[X]:((kind(X)&~old(X))))&
(?[X]:((~happy(X)|~creative(X))))&
(?[X]:((~brave(X)&generous(X))))&
(tall(mary)) | happy(paul) | [
"p2",
"p5",
"p9",
"p10",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6017610380066206941229346
% SZS output start Proof for 6017610380066206941229346
3. ? [X0] : (~curious(X0) & rich(X0)) <=> ? [X0] : (~generous(X0) | ~funny(X0)) [input p2]
6. ? [X0] : (rich(X0) | ~curious(X0)) <=> humble(paul) [input p5]
10. ! [X0] : (generous(X0) => ~happy(X0)) [input p9]
11. ! [X0] : ((patient(X0) | humble(X0)) => old(X0)) [input p10]
12. ! [X0] : (creative(X0) => (~old(X0) & brave(X0))) [input p11]
15. ! [X0] : ((~old(X0) & ~kind(X0)) <=> (~creative(X0) & humble(X0))) [input p14]
25. happy(paul) [input hypothesis]
26. ? [X0] : (~curious(X0) & rich(X0)) <=> ? [X1] : (~generous(X1) | ~funny(X1)) [rectify 3]
30. ! [X0] : (humble(X0) => old(X0)) [pure predicate removal 11]
35. ! [X0] : (~happy(X0) | ~generous(X0)) [ennf transformation 10]
36. ! [X0] : (old(X0) | ~humble(X0)) [ennf transformation 30]
37. ! [X0] : ((~old(X0) & brave(X0)) | ~creative(X0)) [ennf transformation 12]
50. (? [X0] : (~curious(X0) & rich(X0)) | ! [X1] : (generous(X1) & funny(X1))) & (? [X1] : (~generous(X1) | ~funny(X1)) | ! [X0] : (curious(X0) | ~rich(X0))) [nnf transformation 26]
51. (? [X0] : (~curious(X0) & rich(X0)) | ! [X1] : (generous(X1) & funny(X1))) & (? [X2] : (~generous(X2) | ~funny(X2)) | ! [X3] : (curious(X3) | ~rich(X3))) [rectify 50]
52. ? [X0] : (~curious(X0) & rich(X0)) => (~curious(sK2) & rich(sK2)) [choice axiom]
53. ? [X2] : (~generous(X2) | ~funny(X2)) => (~generous(sK3) | ~funny(sK3)) [choice axiom]
54. ((~curious(sK2) & rich(sK2)) | ! [X1] : (generous(X1) & funny(X1))) & ((~generous(sK3) | ~funny(sK3)) | ! [X3] : (curious(X3) | ~rich(X3))) [skolemisation 51,53,52]
63. (? [X0] : (rich(X0) | ~curious(X0)) | ~humble(paul)) & (humble(paul) | ! [X0] : (~rich(X0) & curious(X0))) [nnf transformation 6]
64. (? [X0] : (rich(X0) | ~curious(X0)) | ~humble(paul)) & (humble(paul) | ! [X1] : (~rich(X1) & curious(X1))) [rectify 63]
65. ? [X0] : (rich(X0) | ~curious(X0)) => (rich(sK6) | ~curious(sK6)) [choice axiom]
66. ((rich(sK6) | ~curious(sK6)) | ~humble(paul)) & (humble(paul) | ! [X1] : (~rich(X1) & curious(X1))) [skolemisation 64,65]
74. ! [X0] : (((~old(X0) & ~kind(X0)) | (creative(X0) | ~humble(X0))) & ((~creative(X0) & humble(X0)) | (old(X0) | kind(X0)))) [nnf transformation 15]
75. ! [X0] : (((~old(X0) & ~kind(X0)) | creative(X0) | ~humble(X0)) & ((~creative(X0) & humble(X0)) | old(X0) | kind(X0))) [flattening 74]
101. ~curious(sK2) | generous(X1) [cnf transformation 54]
109. humble(paul) | curious(X1) [cnf transformation 66]
120. ~happy(X0) | ~generous(X0) [cnf transformation 35]
121. ~humble(X0) | old(X0) [cnf transformation 36]
123. ~old(X0) | ~creative(X0) [cnf transformation 37]
137. ~old(X0) | creative(X0) | ~humble(X0) [cnf transformation 75]
152. happy(paul) [cnf transformation 25]
204. 11 <=> ! [X1] : generous(X1) [avatar definition]
205. generous(X1) <- (11) [avatar component clause 204]
207. 12 <=> curious(sK2) [avatar definition]
209. ~curious(sK2) <- (~12) [avatar component clause 207]
210. 11 | ~12 [avatar split clause 101,207,204]
252. 22 <=> ! [X1] : curious(X1) [avatar definition]
253. curious(X1) <- (22) [avatar component clause 252]
270. 26 <=> humble(paul) [avatar definition]
271. humble(paul) <- (26) [avatar component clause 270]
286. 22 | 26 [avatar split clause 109,270,252]
321. ~humble(X0) | creative(X0) [subsumption resolution 137,121]
369. ~generous(paul) [resolution 120,152]
371. old(paul) <- (26) [resolution 121,271]
376. ~creative(paul) <- (26) [resolution 371,123]
381. creative(paul) <- (26) [resolution 321,271]
382. $false <- (26) [subsumption resolution 381,376]
383. ~26 [avatar contradiction clause 382]
384. $false <- (~12, 22) [resolution 253,209]
387. 12 | ~22 [avatar contradiction clause 384]
391. $false <- (11) [resolution 205,369]
392. ~11 [avatar contradiction clause 391]
394. $false [avatar sat refutation 210,286,383,387,392]
% SZS output end Proof for 6017610380066206941229346
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble and not tall is humble. If lucy is both not quiet and strong then alice is both not calm and wise and vice versa. If fred is either not patient or brave then mary is both happy and not rich. If john is not creative then paul is creative or old and vice versa. If susan is not patient then john is not creative. Everyone who is both not rich and strong is not strong and vice versa. If someone is not funny then someone is either not curious or tall. If someone is not generous then mary is both not happy and not generous and vice versa. Everyone who is either not generous or happy is not rich. If fred is quiet then alice is both not tall and not generous. Everyone who is not rich or calm is either quiet or funny and vice versa. Everyone who is wise is not strong and vice versa. If alice is either rich or strong then alice is both not tall and not funny and vice versa. Everyone who is curious or kind is wise. Someone is tall or not quiet. Someone is rich. Someone is either not patient or creative. Mary is both not happy and not curious. Paul is not wise. Someone is generous or not tall. | Fred is rich. | entailment | (![X]:((humble(X)&~tall(X))=>humble(X)))&
(((~quiet(lucy)&strong(lucy)))<=>((~calm(alice)&wise(alice))))&
(((~patient(fred)<~>brave(fred)))=>((happy(mary)&~rich(mary))))&
((~creative(john))<=>((creative(paul)|old(paul))))&
((~patient(susan))=>(~creative(john)))&
(![X]:((~rich(X)&strong(X))<=>~strong(X)))&
((?[X]:(~funny(X)))=>(?[X]:((~curious(X)<~>tall(X)))))&
((?[X]:(~generous(X)))<=>((~happy(mary)&~generous(mary))))&
(![X]:((~generous(X)<~>happy(X))=>~rich(X)))&
((quiet(fred))=>((~tall(alice)&~generous(alice))))&
(![X]:((~rich(X)|calm(X))<=>(quiet(X)<~>funny(X))))&
(![X]:(wise(X)<=>~strong(X)))&
(((rich(alice)<~>strong(alice)))<=>((~tall(alice)&~funny(alice))))&
(![X]:((curious(X)|kind(X))=>wise(X)))&
(?[X]:((tall(X)|~quiet(X))))&
(?[X]:(rich(X)))&
(?[X]:((~patient(X)<~>creative(X))))&
((~happy(mary)&~curious(mary)))&
(~wise(paul))&
(?[X]:((generous(X)|~tall(X)))) | rich(fred) | [
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 569976007396368258220636
% SZS output start Proof for 569976007396368258220636
6. ! [X0] : ((strong(X0) & ~rich(X0)) <=> ~strong(X0)) [input p5]
21. ~rich(fred) [input hypothesis]
37. ! [X0] : (((strong(X0) & ~rich(X0)) | strong(X0)) & (~strong(X0) | (~strong(X0) | rich(X0)))) [nnf transformation 6]
38. ! [X0] : (((strong(X0) & ~rich(X0)) | strong(X0)) & (~strong(X0) | ~strong(X0) | rich(X0))) [flattening 37]
76. ~strong(X0) | ~strong(X0) | rich(X0) [cnf transformation 38]
78. strong(X0) | strong(X0) [cnf transformation 38]
111. ~rich(fred) [cnf transformation 21]
112. ~strong(X0) | rich(X0) [duplicate literal removal 76]
113. strong(X0) [duplicate literal removal 78]
174. rich(X0) [subsumption resolution 112,113]
258. $false [subsumption resolution 111,174]
% SZS output end Proof for 569976007396368258220636
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet is not funny or patient and vice versa.
Everyone who is not quiet or not patient is either curious or not brave and vice versa.
If someone is not funny or not wise then someone is brave or not patient.
If alice is not patient or tall then someone is either not rich or calm.
If someone is not brave then someone is both not generous and not humble.
Everyone who is not patient is either not patient or not curious and vice versa.
Everyone who is both quiet and not strong is either not humble or humble.
Everyone who is not brave is patient.
If someone is either not happy or brave then susan is not old and vice versa.
If john is both rich and creative then someone is curious and vice versa.
If alice is both not kind and creative then someone is both tall and not curious.
Everyone who is not patient or patient is not quiet and vice versa.
If susan is not creative then someone is either strong or not creative and vice versa.
Everyone who is either quiet or not humble is either kind or tall and vice versa.
If mary is not generous or not curious then someone is either quiet or not calm and vice versa.
Everyone who is funny is both happy and brave.
Paul is not tall or creative.
Paul is both strong and not generous.
Someone is funny.
Someone is both happy and not old.
Mary is both brave and humble.
Someone is either rich or creative.
Someone is both tall and not creative. | John is patient. | contradiction | (![X]:(quiet(X)<=>(~funny(X)|patient(X))))&
(![X]:((~quiet(X)|~patient(X))<=>(curious(X)<~>~brave(X))))&
((?[X]:((~funny(X)|~wise(X))))=>(?[X]:((brave(X)|~patient(X)))))&
(((~patient(alice)|tall(alice)))=>(?[X]:((~rich(X)<~>calm(X)))))&
((?[X]:(~brave(X)))=>(?[X]:((~generous(X)&~humble(X)))))&
(![X]:(~patient(X)<=>(~patient(X)<~>~curious(X))))&
(![X]:((quiet(X)&~strong(X))=>(~humble(X)<~>humble(X))))&
(![X]:(~brave(X)=>patient(X)))&
((?[X]:((~happy(X)<~>brave(X))))<=>(~old(susan)))&
(((rich(john)&creative(john)))<=>(?[X]:(curious(X))))&
(((~kind(alice)&creative(alice)))=>(?[X]:((tall(X)&~curious(X)))))&
(![X]:((~patient(X)|patient(X))<=>~quiet(X)))&
((~creative(susan))<=>(?[X]:((strong(X)<~>~creative(X)))))&
(![X]:((quiet(X)<~>~humble(X))<=>(kind(X)<~>tall(X))))&
(((~generous(mary)|~curious(mary)))<=>(?[X]:((quiet(X)<~>~calm(X)))))&
(![X]:(funny(X)=>(happy(X)&brave(X))))&
((~tall(paul)|creative(paul)))&
((strong(paul)&~generous(paul)))&
(?[X]:(funny(X)))&
(?[X]:((happy(X)&~old(X))))&
((brave(mary)&humble(mary)))&
(?[X]:((rich(X)<~>creative(X))))&
(?[X]:((tall(X)&~creative(X)))) | patient(john) | [
"p0",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 7794444221794049337370400
% SZS output start Proof for 7794444221794049337370400
1. ! [X0] : (quiet(X0) <=> (patient(X0) | ~funny(X0))) [input p0]
12. ! [X0] : ((patient(X0) | ~patient(X0)) <=> ~quiet(X0)) [input p11]
24. patient(john) [input hypothesis]
37. ! [X0] : ((quiet(X0) | (~patient(X0) & funny(X0))) & ((patient(X0) | ~funny(X0)) | ~quiet(X0))) [nnf transformation 1]
38. ! [X0] : ((quiet(X0) | (~patient(X0) & funny(X0))) & (patient(X0) | ~funny(X0) | ~quiet(X0))) [flattening 37]
63. ! [X0] : (((patient(X0) | ~patient(X0)) | quiet(X0)) & (~quiet(X0) | (~patient(X0) & patient(X0)))) [nnf transformation 12]
64. ! [X0] : ((patient(X0) | ~patient(X0) | quiet(X0)) & (~quiet(X0) | (~patient(X0) & patient(X0)))) [flattening 63]
86. quiet(X0) | ~patient(X0) [cnf transformation 38]
117. ~quiet(X0) | ~patient(X0) [cnf transformation 64]
151. patient(john) [cnf transformation 24]
241. ~patient(X0) [subsumption resolution 117,86]
304. $false [subsumption resolution 151,241]
% SZS output end Proof for 7794444221794049337370400
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
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