premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
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stringclasses 3
values | premise_tptp
stringlengths 721
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stringclasses 224
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sequencelengths 0
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| proof
stringlengths 684
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If alice is either patient or old then someone is humble or not humble. If someone is both funny and not tall then lucy is both generous and curious. Everyone who is either calm or not happy is not kind or happy and vice versa. Everyone who is not patient or patient is both not humble and not funny and vice versa. Everyone who is not old is both not funny and not calm and vice versa. Everyone who is either not kind or happy is either not brave or not generous. Everyone who is either not humble or not rich is either not tall or funny and vice versa. Everyone who is not old or patient is not creative. If someone is both not generous and funny then fred is both funny and not generous and vice versa. If someone is rich then someone is not quiet and vice versa. Everyone who is not old is both wise and strong and vice versa. Everyone who is both not tall and not wise is both not brave and curious and vice versa. Everyone who is not tall is either not generous or not funny and vice versa. Everyone who is calm is funny and vice versa. Everyone who is not humble or not rich is both patient and not old. If someone is not calm then lucy is not tall or not kind and vice versa. Fred is either not tall or calm. Paul is either kind or curious. Paul is strong or not curious. | Alice is calm. | contradiction | (((patient(alice)<~>old(alice)))=>(?[X]:((humble(X)|~humble(X)))))&
((?[X]:((funny(X)&~tall(X))))=>((generous(lucy)&curious(lucy))))&
(![X]:((calm(X)<~>~happy(X))<=>(~kind(X)|happy(X))))&
(![X]:((~patient(X)|patient(X))<=>(~humble(X)&~funny(X))))&
(![X]:(~old(X)<=>(~funny(X)&~calm(X))))&
(![X]:((~kind(X)<~>happy(X))=>(~brave(X)<~>~generous(X))))&
(![X]:((~humble(X)<~>~rich(X))<=>(~tall(X)<~>funny(X))))&
(![X]:((~old(X)|patient(X))=>~creative(X)))&
((?[X]:((~generous(X)&funny(X))))<=>((funny(fred)&~generous(fred))))&
((?[X]:(rich(X)))<=>(?[X]:(~quiet(X))))&
(![X]:(~old(X)<=>(wise(X)&strong(X))))&
(![X]:((~tall(X)&~wise(X))<=>(~brave(X)&curious(X))))&
(![X]:(~tall(X)<=>(~generous(X)<~>~funny(X))))&
(![X]:(calm(X)<=>funny(X)))&
(![X]:((~humble(X)|~rich(X))=>(patient(X)&~old(X))))&
((?[X]:(~calm(X)))<=>((~tall(lucy)|~kind(lucy))))&
((~tall(fred)<~>calm(fred)))&
((kind(paul)<~>curious(paul)))&
((strong(paul)|~curious(paul))) | calm(alice) | [
"p3",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 41406994713995758841589
% SZS output start Proof for 41406994713995758841589
4. ! [X0] : ((patient(X0) | ~patient(X0)) <=> (~funny(X0) & ~humble(X0))) [input p3]
14. ! [X0] : (calm(X0) <=> funny(X0)) [input p13]
20. calm(alice) [input hypothesis]
32. ! [X0] : (((patient(X0) | ~patient(X0)) | (funny(X0) | humble(X0))) & ((~funny(X0) & ~humble(X0)) | (~patient(X0) & patient(X0)))) [nnf transformation 4]
33. ! [X0] : ((patient(X0) | ~patient(X0) | funny(X0) | humble(X0)) & ((~funny(X0) & ~humble(X0)) | (~patient(X0) & patient(X0)))) [flattening 32]
53. ! [X0] : ((calm(X0) | ~funny(X0)) & (funny(X0) | ~calm(X0))) [nnf transformation 14]
73. ~funny(X0) | patient(X0) [cnf transformation 33]
74. ~funny(X0) | ~patient(X0) [cnf transformation 33]
108. funny(X0) | ~calm(X0) [cnf transformation 53]
122. calm(alice) [cnf transformation 20]
139. ~funny(X0) [subsumption resolution 73,74]
164. ~calm(X0) [subsumption resolution 108,139]
193. $false [subsumption resolution 122,164]
% SZS output end Proof for 41406994713995758841589
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is brave is both not rich and not generous.
Everyone who is both tall and not tall is humble or quiet and vice versa.
Everyone who is strong is not generous or humble and vice versa.
Everyone who is happy is both not tall and patient.
If someone is not rich then mary is not tall or not brave.
Everyone who is not curious is tall or not calm and vice versa.
If someone is curious or kind then someone is both brave and not tall and vice versa.
Everyone who is not calm or not kind is quiet or generous and vice versa.
If susan is not old then someone is either strong or not brave.
Everyone who is either curious or not tall is quiet and vice versa.
If mary is either old or not brave then fred is either not happy or calm and vice versa.
Everyone who is either not calm or patient is humble and vice versa.
Everyone who is generous is not rich and vice versa.
If someone is both not creative and curious then mary is not rich.
If someone is either not wise or funny then john is not old and vice versa.
Everyone who is both not strong and not wise is both generous and not brave and vice versa.
Someone is generous.
Someone is not strong.
Lucy is not patient. | Mary is happy. | contradiction | (![X]:(brave(X)=>(~rich(X)&~generous(X))))&
(![X]:((tall(X)&~tall(X))<=>(humble(X)|quiet(X))))&
(![X]:(strong(X)<=>(~generous(X)|humble(X))))&
(![X]:(happy(X)=>(~tall(X)&patient(X))))&
((?[X]:(~rich(X)))=>((~tall(mary)|~brave(mary))))&
(![X]:(~curious(X)<=>(tall(X)|~calm(X))))&
((?[X]:((curious(X)|kind(X))))<=>(?[X]:((brave(X)&~tall(X)))))&
(![X]:((~calm(X)|~kind(X))<=>(quiet(X)|generous(X))))&
((~old(susan))=>(?[X]:((strong(X)<~>~brave(X)))))&
(![X]:((curious(X)<~>~tall(X))<=>quiet(X)))&
(((old(mary)<~>~brave(mary)))<=>((~happy(fred)<~>calm(fred))))&
(![X]:((~calm(X)<~>patient(X))<=>humble(X)))&
(![X]:(generous(X)<=>~rich(X)))&
((?[X]:((~creative(X)&curious(X))))=>(~rich(mary)))&
((?[X]:((~wise(X)<~>funny(X))))<=>(~old(john)))&
(![X]:((~strong(X)&~wise(X))<=>(generous(X)&~brave(X))))&
(?[X]:(generous(X)))&
(?[X]:(~strong(X)))&
(~patient(lucy)) | happy(mary) | [
"p0",
"p1",
"p3",
"p6",
"p9",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 7819010706383835183550334
% SZS output start Proof for 7819010706383835183550334
1. ! [X0] : (brave(X0) => (~generous(X0) & ~rich(X0))) [input p0]
2. ! [X0] : ((~tall(X0) & tall(X0)) <=> (quiet(X0) | humble(X0))) [input p1]
4. ! [X0] : (happy(X0) => (patient(X0) & ~tall(X0))) [input p3]
7. ? [X0] : (kind(X0) | curious(X0)) <=> ? [X0] : (~tall(X0) & brave(X0)) [input p6]
10. ! [X0] : ((curious(X0) <~> ~tall(X0)) <=> quiet(X0)) [input p9]
13. ! [X0] : (generous(X0) <=> ~rich(X0)) [input p12]
20. happy(mary) [input hypothesis]
21. ? [X0] : (kind(X0) | curious(X0)) <=> ? [X1] : (~tall(X1) & brave(X1)) [rectify 7]
23. ! [X0] : ((~generous(X0) & ~rich(X0)) | ~brave(X0)) [ennf transformation 1]
24. ! [X0] : ((patient(X0) & ~tall(X0)) | ~happy(X0)) [ennf transformation 4]
28. ! [X0] : (((~tall(X0) & tall(X0)) | (~quiet(X0) & ~humble(X0))) & ((quiet(X0) | humble(X0)) | (tall(X0) | ~tall(X0)))) [nnf transformation 2]
29. ! [X0] : (((~tall(X0) & tall(X0)) | (~quiet(X0) & ~humble(X0))) & (quiet(X0) | humble(X0) | tall(X0) | ~tall(X0))) [flattening 28]
34. (? [X0] : (kind(X0) | curious(X0)) | ! [X1] : (tall(X1) | ~brave(X1))) & (? [X1] : (~tall(X1) & brave(X1)) | ! [X0] : (~kind(X0) & ~curious(X0))) [nnf transformation 21]
35. (? [X0] : (kind(X0) | curious(X0)) | ! [X1] : (tall(X1) | ~brave(X1))) & (? [X2] : (~tall(X2) & brave(X2)) | ! [X3] : (~kind(X3) & ~curious(X3))) [rectify 34]
36. ? [X0] : (kind(X0) | curious(X0)) => (kind(sK0) | curious(sK0)) [choice axiom]
37. ? [X2] : (~tall(X2) & brave(X2)) => (~tall(sK1) & brave(sK1)) [choice axiom]
38. ((kind(sK0) | curious(sK0)) | ! [X1] : (tall(X1) | ~brave(X1))) & ((~tall(sK1) & brave(sK1)) | ! [X3] : (~kind(X3) & ~curious(X3))) [skolemisation 35,37,36]
44. ! [X0] : ((((tall(X0) | ~curious(X0)) & (~tall(X0) | curious(X0))) | ~quiet(X0)) & (quiet(X0) | ((curious(X0) | tall(X0)) & (~tall(X0) | ~curious(X0))))) [nnf transformation 10]
47. ! [X0] : ((generous(X0) | rich(X0)) & (~rich(X0) | ~generous(X0))) [nnf transformation 13]
58. ~rich(X0) | ~brave(X0) [cnf transformation 23]
59. ~generous(X0) | ~brave(X0) [cnf transformation 23]
62. tall(X0) | ~quiet(X0) [cnf transformation 29]
64. ~quiet(X0) | ~tall(X0) [cnf transformation 29]
68. ~happy(X0) | ~tall(X0) [cnf transformation 24]
74. brave(sK1) | ~curious(X3) [cnf transformation 38]
86. quiet(X0) | curious(X0) | tall(X0) [cnf transformation 44]
102. generous(X0) | rich(X0) [cnf transformation 47]
114. happy(mary) [cnf transformation 20]
115. ~quiet(X0) [subsumption resolution 62,64]
122. 2 <=> tall(mary) [avatar definition]
124. ~tall(mary) <- (~2) [avatar component clause 122]
151. 9 <=> ! [X3] : ~curious(X3) [avatar definition]
152. ~curious(X3) <- (9) [avatar component clause 151]
155. 10 <=> brave(sK1) [avatar definition]
157. brave(sK1) <- (10) [avatar component clause 155]
159. 9 | 10 [avatar split clause 74,155,151]
176. curious(X0) | tall(X0) [subsumption resolution 86,115]
225. ~tall(mary) [resolution 68,114]
226. ~2 [avatar split clause 225,122]
234. rich(X1) | ~brave(X1) [resolution 102,59]
235. ~brave(X1) [subsumption resolution 234,58]
243. tall(X2) <- (9) [resolution 176,152]
244. $false <- (~2, 9) [resolution 243,124]
245. 2 | ~9 [avatar contradiction clause 244]
246. $false <- (10) [subsumption resolution 157,235]
247. ~10 [avatar contradiction clause 246]
248. $false [avatar sat refutation 159,226,245,247]
% SZS output end Proof for 7819010706383835183550334
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both humble and funny then someone is calm or old. If someone is either not humble or not quiet then lucy is either not creative or kind. Everyone who is both old and tall is either not kind or quiet and vice versa. Everyone who is patient is old or not patient and vice versa. Everyone who is both quiet and calm is both not brave and not happy. Everyone who is either creative or old is not old. Everyone who is both not creative and curious is either humble or not curious and vice versa. If lucy is not humble then paul is not kind or not creative. If someone is either humble or not calm then someone is not curious and vice versa. Everyone who is generous is both not generous and funny. If fred is creative or not happy then lucy is not curious or not humble and vice versa. If someone is humble then mary is both not calm and curious and vice versa. Everyone who is not funny is brave. Everyone who is either not brave or not rich is both not patient and not generous. Everyone who is both tall and not brave is not tall and vice versa. Everyone who is not creative or wise is calm or rich and vice versa. Susan is not patient or not humble. Someone is both brave and not kind. Someone is strong. Someone is either creative or not kind. Alice is not kind. Someone is either not happy or not funny. | Mary is not tall. | contradiction | ((?[X]:((humble(X)&funny(X))))=>(?[X]:((calm(X)|old(X)))))&
((?[X]:((~humble(X)<~>~quiet(X))))=>((~creative(lucy)<~>kind(lucy))))&
(![X]:((old(X)&tall(X))<=>(~kind(X)<~>quiet(X))))&
(![X]:(patient(X)<=>(old(X)|~patient(X))))&
(![X]:((quiet(X)&calm(X))=>(~brave(X)&~happy(X))))&
(![X]:((creative(X)<~>old(X))=>~old(X)))&
(![X]:((~creative(X)&curious(X))<=>(humble(X)<~>~curious(X))))&
((~humble(lucy))=>((~kind(paul)|~creative(paul))))&
((?[X]:((humble(X)<~>~calm(X))))<=>(?[X]:(~curious(X))))&
(![X]:(generous(X)=>(~generous(X)&funny(X))))&
(((creative(fred)|~happy(fred)))<=>((~curious(lucy)|~humble(lucy))))&
((?[X]:(humble(X)))<=>((~calm(mary)&curious(mary))))&
(![X]:(~funny(X)=>brave(X)))&
(![X]:((~brave(X)<~>~rich(X))=>(~patient(X)&~generous(X))))&
(![X]:((tall(X)&~brave(X))<=>~tall(X)))&
(![X]:((~creative(X)|wise(X))<=>(calm(X)|rich(X))))&
((~patient(susan)|~humble(susan)))&
(?[X]:((brave(X)&~kind(X))))&
(?[X]:(strong(X)))&
(?[X]:((creative(X)<~>~kind(X))))&
(~kind(alice))&
(?[X]:((~happy(X)<~>~funny(X)))) | ~tall(mary) | [
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4850597360102689418737559
% SZS output start Proof for 4850597360102689418737559
15. ! [X0] : ((~brave(X0) & tall(X0)) <=> ~tall(X0)) [input p14]
23. ~tall(mary) [input hypothesis]
62. ! [X0] : (((~brave(X0) & tall(X0)) | tall(X0)) & (~tall(X0) | (brave(X0) | ~tall(X0)))) [nnf transformation 15]
63. ! [X0] : (((~brave(X0) & tall(X0)) | tall(X0)) & (~tall(X0) | brave(X0) | ~tall(X0))) [flattening 62]
114. tall(X0) | tall(X0) [cnf transformation 63]
128. ~tall(mary) [cnf transformation 23]
130. tall(X0) [duplicate literal removal 114]
239. $false [subsumption resolution 128,130]
% SZS output end Proof for 4850597360102689418737559
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous then someone is patient.
Everyone who is not happy or kind is happy or not tall and vice versa.
Everyone who is strong is both curious and not strong and vice versa.
If john is both not quiet and happy then someone is not tall.
Everyone who is either not happy or quiet is not brave.
Everyone who is either brave or not creative is happy.
If someone is both not old and not quiet then someone is calm or not funny.
If someone is calm or not calm then alice is not happy and vice versa.
Everyone who is not funny is both not happy and not brave and vice versa.
Everyone who is creative is not generous and vice versa.
If someone is both not tall and humble then john is both quiet and not quiet.
Everyone who is not calm is both calm and funny and vice versa.
If john is both not rich and happy then someone is not funny or not happy.
If someone is either not wise or not patient then lucy is generous and vice versa.
If mary is both calm and not brave then someone is kind or not funny and vice versa.
Everyone who is either tall or not old is both not happy and not quiet.
Alice is either not wise or not humble.
Mary is not rich.
Someone is not generous.
Susan is either old or not wise.
Someone is kind or tall. | Lucy is tall. | contradiction | ((?[X]:(generous(X)))=>(?[X]:(patient(X))))&
(![X]:((~happy(X)|kind(X))<=>(happy(X)|~tall(X))))&
(![X]:(strong(X)<=>(curious(X)&~strong(X))))&
(((~quiet(john)&happy(john)))=>(?[X]:(~tall(X))))&
(![X]:((~happy(X)<~>quiet(X))=>~brave(X)))&
(![X]:((brave(X)<~>~creative(X))=>happy(X)))&
((?[X]:((~old(X)&~quiet(X))))=>(?[X]:((calm(X)|~funny(X)))))&
((?[X]:((calm(X)|~calm(X))))<=>(~happy(alice)))&
(![X]:(~funny(X)<=>(~happy(X)&~brave(X))))&
(![X]:(creative(X)<=>~generous(X)))&
((?[X]:((~tall(X)&humble(X))))=>((quiet(john)&~quiet(john))))&
(![X]:(~calm(X)<=>(calm(X)&funny(X))))&
(((~rich(john)&happy(john)))=>(?[X]:((~funny(X)|~happy(X)))))&
((?[X]:((~wise(X)<~>~patient(X))))<=>(generous(lucy)))&
(((calm(mary)&~brave(mary)))<=>(?[X]:((kind(X)|~funny(X)))))&
(![X]:((tall(X)<~>~old(X))=>(~happy(X)&~quiet(X))))&
((~wise(alice)<~>~humble(alice)))&
(~rich(mary))&
(?[X]:(~generous(X)))&
((old(susan)<~>~wise(susan)))&
(?[X]:((kind(X)|tall(X)))) | tall(lucy) | [
"p1",
"p8",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 3361727970566110928134839
% SZS output start Proof for 3361727970566110928134839
2. ! [X0] : ((kind(X0) | ~happy(X0)) <=> (~tall(X0) | happy(X0))) [input p1]
9. ! [X0] : (~funny(X0) <=> (~brave(X0) & ~happy(X0))) [input p8]
12. ! [X0] : (~calm(X0) <=> (funny(X0) & calm(X0))) [input p11]
22. tall(lucy) [input hypothesis]
38. ! [X0] : (((kind(X0) | ~happy(X0)) | (tall(X0) & ~happy(X0))) & ((~tall(X0) | happy(X0)) | (~kind(X0) & happy(X0)))) [nnf transformation 2]
39. ! [X0] : ((kind(X0) | ~happy(X0) | (tall(X0) & ~happy(X0))) & (~tall(X0) | happy(X0) | (~kind(X0) & happy(X0)))) [flattening 38]
53. ! [X0] : ((~funny(X0) | (brave(X0) | happy(X0))) & ((~brave(X0) & ~happy(X0)) | funny(X0))) [nnf transformation 9]
54. ! [X0] : ((~funny(X0) | brave(X0) | happy(X0)) & ((~brave(X0) & ~happy(X0)) | funny(X0))) [flattening 53]
56. ! [X0] : ((~calm(X0) | (~funny(X0) | ~calm(X0))) & ((funny(X0) & calm(X0)) | calm(X0))) [nnf transformation 12]
57. ! [X0] : ((~calm(X0) | ~funny(X0) | ~calm(X0)) & ((funny(X0) & calm(X0)) | calm(X0))) [flattening 56]
77. ~tall(X0) | happy(X0) | happy(X0) [cnf transformation 39]
93. ~happy(X0) | funny(X0) [cnf transformation 54]
100. calm(X0) | calm(X0) [cnf transformation 57]
102. ~calm(X0) | ~funny(X0) | ~calm(X0) [cnf transformation 57]
124. tall(lucy) [cnf transformation 22]
125. calm(X0) [duplicate literal removal 100]
126. ~funny(X0) | ~calm(X0) [duplicate literal removal 102]
129. ~tall(X0) | happy(X0) [duplicate literal removal 77]
165. 9 <=> ! [X1] : calm(X1) [avatar definition]
166. calm(X1) <- (9) [avatar component clause 165]
181. 9 [avatar split clause 125,165]
284. happy(lucy) [resolution 129,124]
285. funny(lucy) [resolution 284,93]
287. ~calm(lucy) [resolution 285,126]
288. $false <- (9) [subsumption resolution 287,166]
289. ~9 [avatar contradiction clause 288]
290. $false [avatar sat refutation 181,289]
% SZS output end Proof for 3361727970566110928134839
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise or happy then someone is both not kind and not brave and vice versa. Everyone who is either quiet or creative is both not quiet and not calm. If john is not funny or not strong then fred is either rich or not creative. Everyone who is both not creative and quiet is not strong or tall and vice versa. If lucy is not brave then someone is both funny and not old and vice versa. If lucy is both funny and not happy then someone is brave or old. If fred is both happy and creative then mary is not strong. Everyone who is brave is not curious or strong. Everyone who is either kind or not happy is not generous or brave. If someone is either kind or not generous then mary is funny. Everyone who is both funny and patient is wise or not kind. If someone is not wise or creative then fred is not wise or humble. If someone is not patient or not calm then someone is either not happy or strong and vice versa. Everyone who is not creative is rich or not tall and vice versa. If someone is not kind then someone is both wise and humble and vice versa. If someone is both strong and not calm then paul is either not rich or not quiet and vice versa. Lucy is not creative or brave. Lucy is both not brave and curious. Someone is either not creative or not funny. Paul is curious. Susan is both brave and not curious. John is not wise or wise. John is not curious. Someone is creative or funny. | Lucy is creative. | contradiction | ((?[X]:((wise(X)|happy(X))))<=>(?[X]:((~kind(X)&~brave(X)))))&
(![X]:((quiet(X)<~>creative(X))=>(~quiet(X)&~calm(X))))&
(((~funny(john)|~strong(john)))=>((rich(fred)<~>~creative(fred))))&
(![X]:((~creative(X)&quiet(X))<=>(~strong(X)|tall(X))))&
((~brave(lucy))<=>(?[X]:((funny(X)&~old(X)))))&
(((funny(lucy)&~happy(lucy)))=>(?[X]:((brave(X)|old(X)))))&
(((happy(fred)&creative(fred)))=>(~strong(mary)))&
(![X]:(brave(X)=>(~curious(X)|strong(X))))&
(![X]:((kind(X)<~>~happy(X))=>(~generous(X)|brave(X))))&
((?[X]:((kind(X)<~>~generous(X))))=>(funny(mary)))&
(![X]:((funny(X)&patient(X))=>(wise(X)|~kind(X))))&
((?[X]:((~wise(X)|creative(X))))=>((~wise(fred)|humble(fred))))&
((?[X]:((~patient(X)|~calm(X))))<=>(?[X]:((~happy(X)<~>strong(X)))))&
(![X]:(~creative(X)<=>(rich(X)|~tall(X))))&
((?[X]:(~kind(X)))<=>(?[X]:((wise(X)&humble(X)))))&
((?[X]:((strong(X)&~calm(X))))<=>((~rich(paul)<~>~quiet(paul))))&
((~creative(lucy)|brave(lucy)))&
((~brave(lucy)&curious(lucy)))&
(?[X]:((~creative(X)<~>~funny(X))))&
(curious(paul))&
((brave(susan)&~curious(susan)))&
((~wise(john)|wise(john)))&
(~curious(john))&
(?[X]:((creative(X)|funny(X)))) | creative(lucy) | [
"p16",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 6782138944459596880469843
% SZS output start Proof for 6782138944459596880469843
17. brave(lucy) | ~creative(lucy) [input p16]
18. curious(lucy) & ~brave(lucy) [input p17]
25. creative(lucy) [input hypothesis]
131. brave(lucy) | ~creative(lucy) [cnf transformation 17]
132. ~brave(lucy) [cnf transformation 18]
142. creative(lucy) [cnf transformation 25]
198. 13 <=> brave(lucy) [avatar definition]
350. 47 <=> creative(lucy) [avatar definition]
353. ~47 | 13 [avatar split clause 131,198,350]
354. ~13 [avatar split clause 132,198]
374. 47 [avatar split clause 142,350]
375. $false [avatar sat refutation 353,354,374]
% SZS output end Proof for 6782138944459596880469843
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.017 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not curious or not funny is funny. If someone is either not calm or not quiet then someone is both not old and creative and vice versa. If lucy is not generous then someone is not brave and vice versa. If someone is not kind then someone is funny and vice versa. Everyone who is not strong or not happy is both humble and not humble and vice versa. If someone is both calm and curious then mary is happy or generous and vice versa. If mary is brave or not generous then susan is either not calm or not creative and vice versa. Everyone who is both not old and not humble is 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. If someone is calm or not strong then someone is either old or quiet and vice versa. If susan is both funny and quiet then mary is both not curious and strong. If john is either not creative or not tall then someone is either not quiet or not brave. Everyone who is both rich and not tall is not brave and vice versa. Everyone who is both calm and not calm is not patient or generous and vice versa. If someone is wise then lucy is not generous. Lucy is either not humble or not quiet. Someone is quiet. Fred is strong. Someone is tall or happy. | Susan is not generous. | entailment | (![X]:((~curious(X)<~>~funny(X))=>funny(X)))&
((?[X]:((~calm(X)<~>~quiet(X))))<=>(?[X]:((~old(X)&creative(X)))))&
((~generous(lucy))<=>(?[X]:(~brave(X))))&
((?[X]:(~kind(X)))<=>(?[X]:(funny(X))))&
(![X]:((~strong(X)|~happy(X))<=>(humble(X)&~humble(X))))&
((?[X]:((calm(X)&curious(X))))<=>((happy(mary)|generous(mary))))&
(((brave(mary)|~generous(mary)))<=>((~calm(susan)<~>~creative(susan))))&
(![X]:((~old(X)&~humble(X))=>~old(X)))&
(![X]:(~brave(X)<=>(strong(X)|~rich(X))))&
((?[X]:((tall(X)|rich(X))))=>(humble(mary)))&
((?[X]:((calm(X)|~strong(X))))<=>(?[X]:((old(X)<~>quiet(X)))))&
(((funny(susan)&quiet(susan)))=>((~curious(mary)&strong(mary))))&
(((~creative(john)<~>~tall(john)))=>(?[X]:((~quiet(X)<~>~brave(X)))))&
(![X]:((rich(X)&~tall(X))<=>~brave(X)))&
(![X]:((calm(X)&~calm(X))<=>(~patient(X)|generous(X))))&
((?[X]:(wise(X)))=>(~generous(lucy)))&
((~humble(lucy)<~>~quiet(lucy)))&
(?[X]:(quiet(X)))&
(strong(fred))&
(?[X]:((tall(X)|happy(X)))) | ~generous(susan) | [
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4985960863177768735768865
% SZS output start Proof for 4985960863177768735768865
15. ! [X0] : ((~calm(X0) & calm(X0)) <=> (generous(X0) | ~patient(X0))) [input p14]
21. generous(susan) [input hypothesis]
69. ! [X0] : (((~calm(X0) & calm(X0)) | (~generous(X0) & patient(X0))) & ((generous(X0) | ~patient(X0)) | (calm(X0) | ~calm(X0)))) [nnf transformation 15]
70. ! [X0] : (((~calm(X0) & calm(X0)) | (~generous(X0) & patient(X0))) & (generous(X0) | ~patient(X0) | calm(X0) | ~calm(X0))) [flattening 69]
127. calm(X0) | ~generous(X0) [cnf transformation 70]
129. ~calm(X0) | ~generous(X0) [cnf transformation 70]
135. generous(susan) [cnf transformation 21]
307. ~generous(X0) [subsumption resolution 127,129]
319. $false [subsumption resolution 135,307]
% SZS output end Proof for 4985960863177768735768865
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich or creative then lucy is tall or not creative and vice versa.
If paul is old or generous then someone is not generous and vice versa.
Everyone who is creative or not wise is happy or not old and vice versa.
Everyone who is both strong and patient is old and vice versa.
Everyone who is both happy and not calm is brave or humble and vice versa.
Everyone who is both rich and calm is not wise or not happy.
Everyone who is both not humble and not rich is both not patient and not curious.
Everyone who is strong is not wise or generous.
Everyone who is tall is both not generous and not calm and vice versa.
If someone is either humble or kind then susan is creative.
Everyone who is both tall and strong is not curious.
Everyone who is both brave and not generous is either not kind or tall and vice versa.
If someone is quiet or not patient then paul is not quiet or not creative.
Everyone who is both not tall and strong is not rich.
Everyone who is not happy is not strong or not wise and vice versa.
Everyone who is both rich and not strong is not humble.
Lucy is not curious.
Susan is either humble or old.
Someone is either not quiet or not calm.
Susan is patient or brave.
Mary is not humble.
Susan is either not old or tall.
Susan is both not tall and funny.
Someone is either kind or not calm. | Susan is generous. | entailment | ((?[X]:((~rich(X)<~>creative(X))))<=>((tall(lucy)|~creative(lucy))))&
(((old(paul)|generous(paul)))<=>(?[X]:(~generous(X))))&
(![X]:((creative(X)|~wise(X))<=>(happy(X)|~old(X))))&
(![X]:((strong(X)&patient(X))<=>old(X)))&
(![X]:((happy(X)&~calm(X))<=>(brave(X)|humble(X))))&
(![X]:((rich(X)&calm(X))=>(~wise(X)|~happy(X))))&
(![X]:((~humble(X)&~rich(X))=>(~patient(X)&~curious(X))))&
(![X]:(strong(X)=>(~wise(X)|generous(X))))&
(![X]:(tall(X)<=>(~generous(X)&~calm(X))))&
((?[X]:((humble(X)<~>kind(X))))=>(creative(susan)))&
(![X]:((tall(X)&strong(X))=>~curious(X)))&
(![X]:((brave(X)&~generous(X))<=>(~kind(X)<~>tall(X))))&
((?[X]:((quiet(X)|~patient(X))))=>((~quiet(paul)|~creative(paul))))&
(![X]:((~tall(X)&strong(X))=>~rich(X)))&
(![X]:(~happy(X)<=>(~strong(X)|~wise(X))))&
(![X]:((rich(X)&~strong(X))=>~humble(X)))&
(~curious(lucy))&
((humble(susan)<~>old(susan)))&
(?[X]:((~quiet(X)<~>~calm(X))))&
((patient(susan)|brave(susan)))&
(~humble(mary))&
((~old(susan)<~>tall(susan)))&
((~tall(susan)&funny(susan)))&
(?[X]:((kind(X)<~>~calm(X)))) | generous(susan) | [
"p4",
"p7",
"p14",
"p17",
"p21",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 6311482773240119760643740
% SZS output start Proof for 6311482773240119760643740
5. ! [X0] : ((~calm(X0) & happy(X0)) <=> (humble(X0) | brave(X0))) [input p4]
8. ! [X0] : (strong(X0) => (generous(X0) | ~wise(X0))) [input p7]
15. ! [X0] : (~happy(X0) <=> (~wise(X0) | ~strong(X0))) [input p14]
18. humble(susan) <~> old(susan) [input p17]
22. ~old(susan) <~> tall(susan) [input p21]
23. funny(susan) & ~tall(susan) [input p22]
25. ~generous(susan) [input hypothesis]
26. ~tall(susan) [pure predicate removal 23]
34. ! [X0] : ((generous(X0) | ~wise(X0)) | ~strong(X0)) [ennf transformation 8]
35. ! [X0] : (generous(X0) | ~wise(X0) | ~strong(X0)) [flattening 34]
57. ! [X0] : (((~calm(X0) & happy(X0)) | (~humble(X0) & ~brave(X0))) & ((humble(X0) | brave(X0)) | (calm(X0) | ~happy(X0)))) [nnf transformation 5]
58. ! [X0] : (((~calm(X0) & happy(X0)) | (~humble(X0) & ~brave(X0))) & (humble(X0) | brave(X0) | calm(X0) | ~happy(X0))) [flattening 57]
64. ! [X0] : ((~happy(X0) | (wise(X0) & strong(X0))) & ((~wise(X0) | ~strong(X0)) | happy(X0))) [nnf transformation 15]
65. ! [X0] : ((~happy(X0) | (wise(X0) & strong(X0))) & (~wise(X0) | ~strong(X0) | happy(X0))) [flattening 64]
66. (~old(susan) | ~humble(susan)) & (old(susan) | humble(susan)) [nnf transformation 18]
70. (~tall(susan) | old(susan)) & (tall(susan) | ~old(susan)) [nnf transformation 22]
92. ~humble(X0) | happy(X0) [cnf transformation 58]
97. ~strong(X0) | ~wise(X0) | generous(X0) [cnf transformation 35]
113. ~happy(X0) | strong(X0) [cnf transformation 65]
114. ~happy(X0) | wise(X0) [cnf transformation 65]
116. old(susan) | humble(susan) [cnf transformation 66]
122. tall(susan) | ~old(susan) [cnf transformation 70]
124. ~tall(susan) [cnf transformation 26]
127. ~generous(susan) [cnf transformation 25]
205. 18 <=> humble(susan) [avatar definition]
206. humble(susan) <- (18) [avatar component clause 205]
209. 19 <=> old(susan) [avatar definition]
213. 18 | 19 [avatar split clause 116,209,205]
234. 24 <=> tall(susan) [avatar definition]
238. ~19 | 24 [avatar split clause 122,234,209]
239. ~24 [avatar split clause 124,234]
254. happy(susan) <- (18) [resolution 92,206]
256. strong(susan) <- (18) [resolution 113,254]
257. wise(susan) <- (18) [resolution 114,254]
288. ~wise(susan) | generous(susan) <- (18) [resolution 97,256]
289. generous(susan) <- (18) [subsumption resolution 288,257]
290. $false <- (18) [subsumption resolution 289,127]
291. ~18 [avatar contradiction clause 290]
292. $false [avatar sat refutation 213,238,239,291]
% SZS output end Proof for 6311482773240119760643740
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not quiet or kind then someone is humble or creative and vice versa.
Everyone who is happy is either not rich or not patient.
Everyone who is both not rich and not tall is not wise.
If someone is both strong and humble then someone is either not humble or rich.
Everyone who is either not curious or strong is not curious or old.
Everyone who is not curious is not patient or brave and vice versa.
Everyone who is not brave is both not wise and not strong.
If someone is curious then someone is rich.
If someone is both not quiet and not strong then someone is both strong and curious and vice versa.
Everyone who is both tall and not generous is funny and vice versa.
Everyone who is either quiet or not kind is not curious and vice versa.
Everyone who is both curious and not happy is both tall and brave.
If paul is both not kind and not strong then someone is patient or strong and vice versa.
Everyone who is curious or not old is either not strong or funny and vice versa.
If someone is either strong or not brave then susan is both generous and calm and vice versa.
If someone is not kind or not patient then someone is patient or funny and vice versa.
Alice is not generous.
Someone is both not strong and not funny.
Alice is both curious and not old.
Someone is either patient or creative.
John is either not wise or rich.
Someone is both generous and rich.
Paul is either tall or not old. | Alice is strong. | contradiction | ((?[X]:((~quiet(X)<~>kind(X))))<=>(?[X]:((humble(X)|creative(X)))))&
(![X]:(happy(X)=>(~rich(X)<~>~patient(X))))&
(![X]:((~rich(X)&~tall(X))=>~wise(X)))&
((?[X]:((strong(X)&humble(X))))=>(?[X]:((~humble(X)<~>rich(X)))))&
(![X]:((~curious(X)<~>strong(X))=>(~curious(X)|old(X))))&
(![X]:(~curious(X)<=>(~patient(X)|brave(X))))&
(![X]:(~brave(X)=>(~wise(X)&~strong(X))))&
((?[X]:(curious(X)))=>(?[X]:(rich(X))))&
((?[X]:((~quiet(X)&~strong(X))))<=>(?[X]:((strong(X)&curious(X)))))&
(![X]:((tall(X)&~generous(X))<=>funny(X)))&
(![X]:((quiet(X)<~>~kind(X))<=>~curious(X)))&
(![X]:((curious(X)&~happy(X))=>(tall(X)&brave(X))))&
(((~kind(paul)&~strong(paul)))<=>(?[X]:((patient(X)|strong(X)))))&
(![X]:((curious(X)|~old(X))<=>(~strong(X)<~>funny(X))))&
((?[X]:((strong(X)<~>~brave(X))))<=>((generous(susan)&calm(susan))))&
((?[X]:((~kind(X)|~patient(X))))<=>(?[X]:((patient(X)|funny(X)))))&
(~generous(alice))&
(?[X]:((~strong(X)&~funny(X))))&
((curious(alice)&~old(alice)))&
(?[X]:((patient(X)<~>creative(X))))&
((~wise(john)<~>rich(john)))&
(?[X]:((generous(X)&rich(X))))&
((tall(paul)<~>~old(paul))) | strong(alice) | [
"p5",
"p6",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 5233384649400276571376721
% SZS output start Proof for 5233384649400276571376721
6. ! [X0] : (~curious(X0) <=> (brave(X0) | ~patient(X0))) [input p5]
7. ! [X0] : (~brave(X0) => (~strong(X0) & ~wise(X0))) [input p6]
19. ~old(alice) & curious(alice) [input p18]
24. strong(alice) [input hypothesis]
36. ! [X0] : ((~strong(X0) & ~wise(X0)) | brave(X0)) [ennf transformation 7]
51. ! [X0] : ((~curious(X0) | (~brave(X0) & patient(X0))) & ((brave(X0) | ~patient(X0)) | curious(X0))) [nnf transformation 6]
52. ! [X0] : ((~curious(X0) | (~brave(X0) & patient(X0))) & (brave(X0) | ~patient(X0) | curious(X0))) [flattening 51]
105. ~brave(X0) | ~curious(X0) [cnf transformation 52]
107. ~strong(X0) | brave(X0) [cnf transformation 36]
146. curious(alice) [cnf transformation 19]
156. strong(alice) [cnf transformation 24]
368. brave(alice) [resolution 107,156]
369. ~curious(alice) [resolution 368,105]
370. $false [subsumption resolution 369,146]
% SZS output end Proof for 5233384649400276571376721
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not funny or creative is not humble and vice versa. If paul is either creative or curious then someone is not generous or rich. If someone is either not rich or not calm then fred is not old. If john is either creative or not strong then someone is not quiet or strong and vice versa. If someone is brave or kind then mary is curious. Everyone who is either not strong or tall is both not funny and not kind. Everyone who is funny or not humble is not wise or not old. If lucy is not humble or not tall then someone is both not brave and not old. If fred is funny then someone is both kind and brave and vice versa. Everyone who is both patient and not patient is not humble and vice versa. Everyone who is tall is either not generous or curious. Everyone who is both calm and not generous is either not curious or tall and vice versa. If mary is both not wise and not kind then someone is rich and vice versa. Everyone who is both strong and not humble is not wise or not quiet. If lucy is not generous or old then someone is not kind and vice versa. Paul is either wise or not generous. Someone is either not generous or calm. Someone is either curious or not calm. Someone is either strong or not strong. Someone is either not curious or quiet. | Lucy is creative. | contradiction | (![X]:((~funny(X)|creative(X))<=>~humble(X)))&
(((creative(paul)<~>curious(paul)))=>(?[X]:((~generous(X)|rich(X)))))&
((?[X]:((~rich(X)<~>~calm(X))))=>(~old(fred)))&
(((creative(john)<~>~strong(john)))<=>(?[X]:((~quiet(X)|strong(X)))))&
((?[X]:((brave(X)|kind(X))))=>(curious(mary)))&
(![X]:((~strong(X)<~>tall(X))=>(~funny(X)&~kind(X))))&
(![X]:((funny(X)|~humble(X))=>(~wise(X)|~old(X))))&
(((~humble(lucy)|~tall(lucy)))=>(?[X]:((~brave(X)&~old(X)))))&
((funny(fred))<=>(?[X]:((kind(X)&brave(X)))))&
(![X]:((patient(X)&~patient(X))<=>~humble(X)))&
(![X]:(tall(X)=>(~generous(X)<~>curious(X))))&
(![X]:((calm(X)&~generous(X))<=>(~curious(X)<~>tall(X))))&
(((~wise(mary)&~kind(mary)))<=>(?[X]:(rich(X))))&
(![X]:((strong(X)&~humble(X))=>(~wise(X)|~quiet(X))))&
(((~generous(lucy)|old(lucy)))<=>(?[X]:(~kind(X))))&
((wise(paul)<~>~generous(paul)))&
(?[X]:((~generous(X)<~>calm(X))))&
(?[X]:((curious(X)<~>~calm(X))))&
(?[X]:((strong(X)<~>~strong(X))))&
(?[X]:((~curious(X)<~>quiet(X)))) | creative(lucy) | [
"p0",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 615166766226233200675631
% SZS output start Proof for 615166766226233200675631
1. ! [X0] : ((creative(X0) | ~funny(X0)) <=> ~humble(X0)) [input p0]
10. ! [X0] : ((~patient(X0) & patient(X0)) <=> ~humble(X0)) [input p9]
21. creative(lucy) [input hypothesis]
32. ! [X0] : (((creative(X0) | ~funny(X0)) | humble(X0)) & (~humble(X0) | (~creative(X0) & funny(X0)))) [nnf transformation 1]
33. ! [X0] : ((creative(X0) | ~funny(X0) | humble(X0)) & (~humble(X0) | (~creative(X0) & funny(X0)))) [flattening 32]
49. ! [X0] : (((~patient(X0) & patient(X0)) | humble(X0)) & (~humble(X0) | (patient(X0) | ~patient(X0)))) [nnf transformation 10]
50. ! [X0] : (((~patient(X0) & patient(X0)) | humble(X0)) & (~humble(X0) | patient(X0) | ~patient(X0))) [flattening 49]
78. ~humble(X0) | ~creative(X0) [cnf transformation 33]
106. patient(X0) | humble(X0) [cnf transformation 50]
107. ~patient(X0) | humble(X0) [cnf transformation 50]
133. creative(lucy) [cnf transformation 21]
242. humble(X0) [subsumption resolution 106,107]
327. ~creative(X0) [resolution 78,242]
328. $false [resolution 327,133]
% SZS output end Proof for 615166766226233200675631
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not kind and not strong is humble or not funny.
Everyone who is not kind or not funny is not humble or not calm.
Everyone who is old or not generous is not tall or old.
If someone is either not humble or not calm then paul is both not creative and rich and vice versa.
If someone is either not humble or happy then john is humble and vice versa.
If susan is both not kind and curious then fred is not rich or not tall and vice versa.
Everyone who is not strong or not humble is patient or strong and vice versa.
If someone is either strong or not curious then mary is curious or humble and vice versa.
Everyone who is either not tall or wise is both old and curious.
Everyone who is not funny or not brave is either not creative or happy and vice versa.
Everyone who is not calm is both patient and happy.
If susan is not strong or not old then someone is not generous and vice versa.
Everyone who is either generous or not happy is creative or patient.
Everyone who is quiet or humble is wise.
Everyone who is either not quiet or rich is not strong and vice versa.
If paul is not creative then someone is both kind and not creative and vice versa.
Paul is kind.
Someone is rich.
Someone is both not brave and creative.
Fred is either patient or old.
Someone is strong or patient.
Susan is not calm.
Alice is calm or curious.
Alice is either creative or generous. | Fred is patient. | neutral | (![X]:((~kind(X)&~strong(X))=>(humble(X)|~funny(X))))&
(![X]:((~kind(X)|~funny(X))=>(~humble(X)|~calm(X))))&
(![X]:((old(X)|~generous(X))=>(~tall(X)|old(X))))&
((?[X]:((~humble(X)<~>~calm(X))))<=>((~creative(paul)&rich(paul))))&
((?[X]:((~humble(X)<~>happy(X))))<=>(humble(john)))&
(((~kind(susan)&curious(susan)))<=>((~rich(fred)|~tall(fred))))&
(![X]:((~strong(X)|~humble(X))<=>(patient(X)|strong(X))))&
((?[X]:((strong(X)<~>~curious(X))))<=>((curious(mary)|humble(mary))))&
(![X]:((~tall(X)<~>wise(X))=>(old(X)&curious(X))))&
(![X]:((~funny(X)|~brave(X))<=>(~creative(X)<~>happy(X))))&
(![X]:(~calm(X)=>(patient(X)&happy(X))))&
(((~strong(susan)|~old(susan)))<=>(?[X]:(~generous(X))))&
(![X]:((generous(X)<~>~happy(X))=>(creative(X)|patient(X))))&
(![X]:((quiet(X)|humble(X))=>wise(X)))&
(![X]:((~quiet(X)<~>rich(X))<=>~strong(X)))&
((~creative(paul))<=>(?[X]:((kind(X)&~creative(X)))))&
(kind(paul))&
(?[X]:(rich(X)))&
(?[X]:((~brave(X)&creative(X))))&
((patient(fred)<~>old(fred)))&
(?[X]:((strong(X)|patient(X))))&
(~calm(susan))&
((calm(alice)|curious(alice)))&
((creative(alice)<~>generous(alice))) | patient(fred) | [] | null | 0 |
Everyone who is both old and not quiet is either not kind or not curious and vice versa.
Everyone who is both curious and not curious is either generous or quiet and vice versa.
Everyone who is not happy is both not calm and not tall.
If john is either not wise or not humble then someone is strong or not calm.
If alice is both not funny and humble then lucy is both old and not tall and vice versa.
Everyone who is either not patient or brave is both humble and not happy and vice versa.
Everyone who is tall or not creative is either not brave or not creative.
Everyone who is not quiet or not curious is happy and vice versa.
If paul is both funny and rich then fred is not rich.
Everyone who is both not strong and happy is both not creative and not kind and vice versa.
Everyone who is funny or creative is not wise and vice versa.
Everyone who is brave or funny is rich or not tall and vice versa.
Everyone who is either not creative or not quiet is either happy or not kind and vice versa.
Everyone who is not funny is either not humble or not strong and vice versa.
If paul is calm then mary is humble or kind.
Everyone who is funny or not humble is either happy or not brave and vice versa.
Mary is either not happy or wise.
Someone is not strong or not quiet.
Someone is either brave or not kind.
John is either generous or not happy.
Someone is both not old and not strong.
Someone is either generous or not kind.
Fred is not happy or not creative. | Mary is wise. | contradiction | (![X]:((old(X)&~quiet(X))<=>(~kind(X)<~>~curious(X))))&
(![X]:((curious(X)&~curious(X))<=>(generous(X)<~>quiet(X))))&
(![X]:(~happy(X)=>(~calm(X)&~tall(X))))&
(((~wise(john)<~>~humble(john)))=>(?[X]:((strong(X)|~calm(X)))))&
(((~funny(alice)&humble(alice)))<=>((old(lucy)&~tall(lucy))))&
(![X]:((~patient(X)<~>brave(X))<=>(humble(X)&~happy(X))))&
(![X]:((tall(X)|~creative(X))=>(~brave(X)<~>~creative(X))))&
(![X]:((~quiet(X)|~curious(X))<=>happy(X)))&
(((funny(paul)&rich(paul)))=>(~rich(fred)))&
(![X]:((~strong(X)&happy(X))<=>(~creative(X)&~kind(X))))&
(![X]:((funny(X)|creative(X))<=>~wise(X)))&
(![X]:((brave(X)|funny(X))<=>(rich(X)|~tall(X))))&
(![X]:((~creative(X)<~>~quiet(X))<=>(happy(X)<~>~kind(X))))&
(![X]:(~funny(X)<=>(~humble(X)<~>~strong(X))))&
((calm(paul))=>((humble(mary)|kind(mary))))&
(![X]:((funny(X)|~humble(X))<=>(happy(X)<~>~brave(X))))&
((~happy(mary)<~>wise(mary)))&
(?[X]:((~strong(X)|~quiet(X))))&
(?[X]:((brave(X)<~>~kind(X))))&
((generous(john)<~>~happy(john)))&
(?[X]:((~old(X)&~strong(X))))&
(?[X]:((generous(X)<~>~kind(X))))&
((~happy(fred)|~creative(fred))) | wise(mary) | [
"p0",
"p6",
"p7",
"p9",
"p10",
"p12",
"p13",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 793702937623106202833611
% SZS output start Proof for 793702937623106202833611
1. ! [X0] : ((~quiet(X0) & old(X0)) <=> (~kind(X0) <~> ~curious(X0))) [input p0]
7. ! [X0] : ((~creative(X0) | tall(X0)) => (~brave(X0) <~> ~creative(X0))) [input p6]
8. ! [X0] : ((~curious(X0) | ~quiet(X0)) <=> happy(X0)) [input p7]
10. ! [X0] : ((happy(X0) & ~strong(X0)) <=> (~kind(X0) & ~creative(X0))) [input p9]
11. ! [X0] : ((creative(X0) | funny(X0)) <=> ~wise(X0)) [input p10]
13. ! [X0] : ((~creative(X0) <~> ~quiet(X0)) <=> (happy(X0) <~> ~kind(X0))) [input p12]
14. ! [X0] : (~funny(X0) <=> (~humble(X0) <~> ~strong(X0))) [input p13]
16. ! [X0] : ((~humble(X0) | funny(X0)) <=> (happy(X0) <~> ~brave(X0))) [input p15]
17. ~happy(mary) <~> wise(mary) [input p16]
24. wise(mary) [input hypothesis]
29. ! [X0] : ((~brave(X0) <~> ~creative(X0)) | (creative(X0) & ~tall(X0))) [ennf transformation 7]
32. ! [X0] : (((~quiet(X0) & old(X0)) | ((~kind(X0) | curious(X0)) & (~curious(X0) | kind(X0)))) & (((curious(X0) | kind(X0)) & (~curious(X0) | ~kind(X0))) | (quiet(X0) | ~old(X0)))) [nnf transformation 1]
33. ! [X0] : (((~quiet(X0) & old(X0)) | ((~kind(X0) | curious(X0)) & (~curious(X0) | kind(X0)))) & (((curious(X0) | kind(X0)) & (~curious(X0) | ~kind(X0))) | quiet(X0) | ~old(X0))) [flattening 32]
40. ! [X0] : (((creative(X0) | brave(X0)) & (~creative(X0) | ~brave(X0))) | (creative(X0) & ~tall(X0))) [nnf transformation 29]
41. ! [X0] : (((~curious(X0) | ~quiet(X0)) | ~happy(X0)) & (happy(X0) | (curious(X0) & quiet(X0)))) [nnf transformation 8]
42. ! [X0] : ((~curious(X0) | ~quiet(X0) | ~happy(X0)) & (happy(X0) | (curious(X0) & quiet(X0)))) [flattening 41]
43. ! [X0] : (((happy(X0) & ~strong(X0)) | (kind(X0) | creative(X0))) & ((~kind(X0) & ~creative(X0)) | (~happy(X0) | strong(X0)))) [nnf transformation 10]
44. ! [X0] : (((happy(X0) & ~strong(X0)) | kind(X0) | creative(X0)) & ((~kind(X0) & ~creative(X0)) | ~happy(X0) | strong(X0))) [flattening 43]
45. ! [X0] : (((creative(X0) | funny(X0)) | wise(X0)) & (~wise(X0) | (~creative(X0) & ~funny(X0)))) [nnf transformation 11]
46. ! [X0] : ((creative(X0) | funny(X0) | wise(X0)) & (~wise(X0) | (~creative(X0) & ~funny(X0)))) [flattening 45]
49. ! [X0] : ((((quiet(X0) | creative(X0)) & (~quiet(X0) | ~creative(X0))) | ((happy(X0) | kind(X0)) & (~kind(X0) | ~happy(X0)))) & (((kind(X0) | ~happy(X0)) & (~kind(X0) | happy(X0))) | ((~creative(X0) | quiet(X0)) & (~quiet(X0) | creative(X0))))) [nnf transformation 13]
50. ! [X0] : ((~funny(X0) | ((~humble(X0) | strong(X0)) & (~strong(X0) | humble(X0)))) & (((strong(X0) | humble(X0)) & (~strong(X0) | ~humble(X0))) | funny(X0))) [nnf transformation 14]
51. ! [X0] : (((~humble(X0) | funny(X0)) | ((happy(X0) | brave(X0)) & (~brave(X0) | ~happy(X0)))) & (((brave(X0) | ~happy(X0)) & (~brave(X0) | happy(X0))) | (humble(X0) & ~funny(X0)))) [nnf transformation 16]
52. ! [X0] : ((~humble(X0) | funny(X0) | ((happy(X0) | brave(X0)) & (~brave(X0) | ~happy(X0)))) & (((brave(X0) | ~happy(X0)) & (~brave(X0) | happy(X0))) | (humble(X0) & ~funny(X0)))) [flattening 51]
53. (~wise(mary) | happy(mary)) & (wise(mary) | ~happy(mary)) [nnf transformation 17]
70. ~kind(X0) | ~quiet(X0) | curious(X0) [cnf transformation 33]
91. creative(X0) | brave(X0) | creative(X0) [cnf transformation 40]
92. happy(X0) | quiet(X0) [cnf transformation 42]
94. ~happy(X0) | ~quiet(X0) | ~curious(X0) [cnf transformation 42]
98. ~strong(X0) | kind(X0) | creative(X0) [cnf transformation 44]
100. ~funny(X0) | ~wise(X0) [cnf transformation 46]
101. ~creative(X0) | ~wise(X0) [cnf transformation 46]
113. quiet(X0) | creative(X0) | ~kind(X0) | ~happy(X0) [cnf transformation 49]
116. funny(X0) | humble(X0) | strong(X0) [cnf transformation 50]
123. ~brave(X0) | funny(X0) | ~humble(X0) | ~happy(X0) [cnf transformation 52]
126. ~wise(mary) | happy(mary) [cnf transformation 53]
137. wise(mary) [cnf transformation 24]
138. creative(X0) | brave(X0) [duplicate literal removal 91]
174. ~kind(X0) | creative(X0) | quiet(X0) [subsumption resolution 113,92]
182. 8 <=> happy(mary) [avatar definition]
184. happy(mary) <- (8) [avatar component clause 182]
186. 9 <=> wise(mary) [avatar definition]
187. wise(mary) <- (9) [avatar component clause 186]
189. 8 | ~9 [avatar split clause 126,186,182]
239. 9 [avatar split clause 137,186]
244. ~wise(X0) | brave(X0) [resolution 138,101]
254. brave(mary) <- (9) [resolution 244,187]
294. 25 <=> humble(mary) [avatar definition]
320. ~quiet(mary) | ~curious(mary) <- (8) [resolution 94,184]
326. 29 <=> curious(mary) [avatar definition]
328. ~curious(mary) <- (~29) [avatar component clause 326]
330. 30 <=> quiet(mary) [avatar definition]
333. ~29 | ~30 | ~8 [avatar split clause 320,182,330,326]
343. 31 <=> strong(mary) [avatar definition]
345. strong(mary) <- (31) [avatar component clause 343]
347. 32 <=> kind(mary) [avatar definition]
348. kind(mary) <- (32) [avatar component clause 347]
414. ~wise(X1) | strong(X1) | humble(X1) [resolution 116,100]
577. funny(mary) | ~humble(mary) | ~happy(mary) <- (9) [resolution 123,254]
586. funny(mary) | ~humble(mary) <- (8, 9) [subsumption resolution 577,184]
588. 52 <=> funny(mary) [avatar definition]
590. funny(mary) <- (52) [avatar component clause 588]
591. ~25 | 52 | ~8 | ~9 [avatar split clause 586,186,182,588,294]
654. strong(mary) | humble(mary) <- (9) [resolution 414,187]
658. kind(mary) | creative(mary) <- (31) [resolution 345,98]
674. 53 <=> creative(mary) [avatar definition]
676. creative(mary) <- (53) [avatar component clause 674]
677. 53 | 32 | ~31 [avatar split clause 658,343,347,674]
680. creative(mary) | quiet(mary) <- (32) [resolution 348,174]
681. ~quiet(mary) | curious(mary) <- (32) [resolution 348,70]
683. 30 | 53 | ~32 [avatar split clause 680,347,674,330]
684. ~quiet(mary) <- (~29, 32) [subsumption resolution 681,328]
685. ~30 | 29 | ~32 [avatar split clause 684,347,326,330]
687. 25 | 31 | ~9 [avatar split clause 654,186,343,294]
700. ~wise(mary) <- (52) [resolution 590,100]
704. $false <- (9, 52) [subsumption resolution 700,187]
705. ~9 | ~52 [avatar contradiction clause 704]
718. ~wise(mary) <- (53) [resolution 676,101]
719. $false <- (9, 53) [subsumption resolution 718,187]
720. ~9 | ~53 [avatar contradiction clause 719]
721. $false [avatar sat refutation 189,239,333,591,677,683,685,687,705,720]
% SZS output end Proof for 793702937623106202833611
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not funny or generous is either quiet or patient.
If lucy is both not rich and generous then lucy is both not quiet and old and vice versa.
If fred is not quiet or not strong then mary is not calm and vice versa.
If mary is either not curious or not quiet then someone is both not kind and curious and vice versa.
Everyone who is either old or brave is not tall and vice versa.
If someone is old then alice is both not happy and brave and vice versa.
Everyone who is humble or not generous is either quiet or tall and vice versa.
If someone is either not calm or not rich then paul is both not humble and rich.
Everyone who is generous or not tall is both not happy and not brave.
Everyone who is not quiet or rich is both quiet and not humble and vice versa.
Everyone who is brave or patient is either not funny or not creative.
If someone is old then lucy is happy or rich.
Everyone who is both happy and curious is strong.
If someone is rich then someone is both not brave and not kind.
Everyone who is not funny or not rich is not tall.
If lucy is not kind or strong then alice is old or not happy and vice versa.
Someone is curious or not brave.
Someone is humble or generous.
Fred is both not happy and rich.
Someone is kind or wise.
Someone is not calm or not generous. | Mary is old. | contradiction | (![X]:((~funny(X)<~>generous(X))=>(quiet(X)<~>patient(X))))&
(((~rich(lucy)&generous(lucy)))<=>((~quiet(lucy)&old(lucy))))&
(((~quiet(fred)|~strong(fred)))<=>(~calm(mary)))&
(((~curious(mary)<~>~quiet(mary)))<=>(?[X]:((~kind(X)&curious(X)))))&
(![X]:((old(X)<~>brave(X))<=>~tall(X)))&
((?[X]:(old(X)))<=>((~happy(alice)&brave(alice))))&
(![X]:((humble(X)|~generous(X))<=>(quiet(X)<~>tall(X))))&
((?[X]:((~calm(X)<~>~rich(X))))=>((~humble(paul)&rich(paul))))&
(![X]:((generous(X)|~tall(X))=>(~happy(X)&~brave(X))))&
(![X]:((~quiet(X)|rich(X))<=>(quiet(X)&~humble(X))))&
(![X]:((brave(X)|patient(X))=>(~funny(X)<~>~creative(X))))&
((?[X]:(old(X)))=>((happy(lucy)|rich(lucy))))&
(![X]:((happy(X)&curious(X))=>strong(X)))&
((?[X]:(rich(X)))=>(?[X]:((~brave(X)&~kind(X)))))&
(![X]:((~funny(X)|~rich(X))=>~tall(X)))&
(((~kind(lucy)|strong(lucy)))<=>((old(alice)|~happy(alice))))&
(?[X]:((curious(X)|~brave(X))))&
(?[X]:((humble(X)|generous(X))))&
((~happy(fred)&rich(fred)))&
(?[X]:((kind(X)|wise(X))))&
(?[X]:((~calm(X)|~generous(X)))) | old(mary) | [
"p5",
"p6",
"p8",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 667909737377657545710020
% SZS output start Proof for 667909737377657545710020
6. ? [X0] : old(X0) <=> (brave(alice) & ~happy(alice)) [input p5]
7. ! [X0] : ((~generous(X0) | humble(X0)) <=> (quiet(X0) <~> tall(X0))) [input p6]
9. ! [X0] : ((~tall(X0) | generous(X0)) => (~brave(X0) & ~happy(X0))) [input p8]
10. ! [X0] : ((rich(X0) | ~quiet(X0)) <=> (~humble(X0) & quiet(X0))) [input p9]
22. old(mary) [input hypothesis]
27. ! [X0] : ((~brave(X0) & ~happy(X0)) | (tall(X0) & ~generous(X0))) [ennf transformation 9]
45. (? [X0] : old(X0) | (~brave(alice) | happy(alice))) & ((brave(alice) & ~happy(alice)) | ! [X0] : ~old(X0)) [nnf transformation 6]
46. (? [X0] : old(X0) | ~brave(alice) | happy(alice)) & ((brave(alice) & ~happy(alice)) | ! [X0] : ~old(X0)) [flattening 45]
47. (? [X0] : old(X0) | ~brave(alice) | happy(alice)) & ((brave(alice) & ~happy(alice)) | ! [X1] : ~old(X1)) [rectify 46]
48. ? [X0] : old(X0) => old(sK1) [choice axiom]
49. (old(sK1) | ~brave(alice) | happy(alice)) & ((brave(alice) & ~happy(alice)) | ! [X1] : ~old(X1)) [skolemisation 47,48]
50. ! [X0] : (((~generous(X0) | humble(X0)) | ((quiet(X0) | ~tall(X0)) & (tall(X0) | ~quiet(X0)))) & (((~tall(X0) | ~quiet(X0)) & (tall(X0) | quiet(X0))) | (generous(X0) & ~humble(X0)))) [nnf transformation 7]
51. ! [X0] : ((~generous(X0) | humble(X0) | ((quiet(X0) | ~tall(X0)) & (tall(X0) | ~quiet(X0)))) & (((~tall(X0) | ~quiet(X0)) & (tall(X0) | quiet(X0))) | (generous(X0) & ~humble(X0)))) [flattening 50]
53. ! [X0] : (((rich(X0) | ~quiet(X0)) | (humble(X0) | ~quiet(X0))) & ((~humble(X0) & quiet(X0)) | (~rich(X0) & quiet(X0)))) [nnf transformation 10]
54. ! [X0] : ((rich(X0) | ~quiet(X0) | humble(X0) | ~quiet(X0)) & ((~humble(X0) & quiet(X0)) | (~rich(X0) & quiet(X0)))) [flattening 53]
89. brave(alice) | ~old(X1) [cnf transformation 49]
94. ~tall(X0) | ~quiet(X0) | generous(X0) [cnf transformation 51]
103. ~brave(X0) | ~generous(X0) [cnf transformation 27]
104. ~brave(X0) | tall(X0) [cnf transformation 27]
105. quiet(X0) | quiet(X0) [cnf transformation 54]
129. old(mary) [cnf transformation 22]
130. quiet(X0) [duplicate literal removal 105]
197. 14 <=> brave(alice) [avatar definition]
198. brave(alice) <- (14) [avatar component clause 197]
206. 16 <=> ! [X1] : ~old(X1) [avatar definition]
207. ~old(X1) <- (16) [avatar component clause 206]
208. 16 | 14 [avatar split clause 89,197,206]
306. $false <- (16) [resolution 207,129]
309. ~16 [avatar contradiction clause 306]
310. tall(alice) <- (14) [resolution 198,104]
311. ~generous(alice) <- (14) [resolution 198,103]
331. ~quiet(alice) | generous(alice) <- (14) [resolution 94,310]
335. generous(alice) <- (14) [subsumption resolution 331,130]
336. $false <- (14) [subsumption resolution 335,311]
337. ~14 [avatar contradiction clause 336]
339. $false [avatar sat refutation 208,309,337]
% SZS output end Proof for 667909737377657545710020
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy and wise is not quiet or quiet and vice versa. If someone is either humble or patient then paul is old. Everyone who is not strong or kind is both wise and happy and vice versa. Everyone who is not calm or not happy is wise or curious. Everyone who is both kind and not humble is not strong or not patient and vice versa. If someone is both old and humble then someone is either not humble or wise. If someone is both strong and funny then someone is either curious or old and vice versa. If susan is either not humble or generous then someone is not strong and vice versa. If lucy is either not strong or brave then lucy is either funny or rich. Everyone who is both patient and curious is generous and vice versa. Everyone who is calm is creative and vice versa. Everyone who is both not calm and not humble is both wise and not curious and vice versa. Everyone who is both not strong and old is both curious and not happy. Everyone who is not wise or not curious is not old and vice versa. Everyone who is generous or not strong is either curious or wise. If someone is calm or not generous then john is happy or brave. Someone is either not curious or old. Someone is either not patient or not generous. Mary is both happy and funny. Susan is not creative or tall. Someone is either generous or not patient. Susan is both funny and not tall. | Susan is not tall. | entailment | (![X]:((happy(X)&wise(X))<=>(~quiet(X)|quiet(X))))&
((?[X]:((humble(X)<~>patient(X))))=>(old(paul)))&
(![X]:((~strong(X)|kind(X))<=>(wise(X)&happy(X))))&
(![X]:((~calm(X)|~happy(X))=>(wise(X)|curious(X))))&
(![X]:((kind(X)&~humble(X))<=>(~strong(X)|~patient(X))))&
((?[X]:((old(X)&humble(X))))=>(?[X]:((~humble(X)<~>wise(X)))))&
((?[X]:((strong(X)&funny(X))))<=>(?[X]:((curious(X)<~>old(X)))))&
(((~humble(susan)<~>generous(susan)))<=>(?[X]:(~strong(X))))&
(((~strong(lucy)<~>brave(lucy)))=>((funny(lucy)<~>rich(lucy))))&
(![X]:((patient(X)&curious(X))<=>generous(X)))&
(![X]:(calm(X)<=>creative(X)))&
(![X]:((~calm(X)&~humble(X))<=>(wise(X)&~curious(X))))&
(![X]:((~strong(X)&old(X))=>(curious(X)&~happy(X))))&
(![X]:((~wise(X)|~curious(X))<=>~old(X)))&
(![X]:((generous(X)|~strong(X))=>(curious(X)<~>wise(X))))&
((?[X]:((calm(X)|~generous(X))))=>((happy(john)|brave(john))))&
(?[X]:((~curious(X)<~>old(X))))&
(?[X]:((~patient(X)<~>~generous(X))))&
((happy(mary)&funny(mary)))&
((~creative(susan)|tall(susan)))&
(?[X]:((generous(X)<~>~patient(X))))&
((funny(susan)&~tall(susan))) | ~tall(susan) | [
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 1011936783236053578996476
% SZS output start Proof for 1011936783236053578996476
22. ~tall(susan) & funny(susan) [input p21]
23. tall(susan) [input hypothesis]
139. ~tall(susan) [cnf transformation 22]
140. tall(susan) [cnf transformation 23]
264. 24 <=> tall(susan) [avatar definition]
269. ~24 [avatar split clause 139,264]
270. 24 [avatar split clause 140,264]
271. $false [avatar sat refutation 269,270]
% SZS output end Proof for 1011936783236053578996476
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is not happy or not generous then someone is either not rich or quiet and vice versa.
Everyone who is humble is either not rich or happy.
If someone is not rich then someone is rich or not creative.
Everyone who is not creative or rich is not quiet and vice versa.
Everyone who is tall is both not rich and patient and vice versa.
If someone is kind then someone is both not creative and strong and vice versa.
If lucy is not curious or happy then someone is happy or funny and vice versa.
Everyone who is both not tall and humble is both curious and funny.
Everyone who is either brave or wise is both creative and rich.
Everyone who is not patient or curious is old and vice versa.
Everyone who is both strong and not quiet is both creative and calm and vice versa.
If someone is not happy then lucy is either not patient or rich and vice versa.
If someone is funny then someone is either not tall or strong and vice versa.
Everyone who is either not happy or patient is both not calm and brave and vice versa.
If someone is either generous or not creative then someone is patient or not calm.
If someone is not old then someone is not patient.
Mary is not kind.
Someone is either generous or not brave.
Someone is both tall and calm.
Someone is curious or not tall.
Someone is not kind or not creative.
Someone is not wise or not quiet.
Someone is not strong or not happy.
Mary is either not generous or not curious. | Lucy is quiet. | neutral | (((~happy(lucy)|~generous(lucy)))<=>(?[X]:((~rich(X)<~>quiet(X)))))&
(![X]:(humble(X)=>(~rich(X)<~>happy(X))))&
((?[X]:(~rich(X)))=>(?[X]:((rich(X)|~creative(X)))))&
(![X]:((~creative(X)|rich(X))<=>~quiet(X)))&
(![X]:(tall(X)<=>(~rich(X)&patient(X))))&
((?[X]:(kind(X)))<=>(?[X]:((~creative(X)&strong(X)))))&
(((~curious(lucy)|happy(lucy)))<=>(?[X]:((happy(X)|funny(X)))))&
(![X]:((~tall(X)&humble(X))=>(curious(X)&funny(X))))&
(![X]:((brave(X)<~>wise(X))=>(creative(X)&rich(X))))&
(![X]:((~patient(X)|curious(X))<=>old(X)))&
(![X]:((strong(X)&~quiet(X))<=>(creative(X)&calm(X))))&
((?[X]:(~happy(X)))<=>((~patient(lucy)<~>rich(lucy))))&
((?[X]:(funny(X)))<=>(?[X]:((~tall(X)<~>strong(X)))))&
(![X]:((~happy(X)<~>patient(X))<=>(~calm(X)&brave(X))))&
((?[X]:((generous(X)<~>~creative(X))))=>(?[X]:((patient(X)|~calm(X)))))&
((?[X]:(~old(X)))=>(?[X]:(~patient(X))))&
(~kind(mary))&
(?[X]:((generous(X)<~>~brave(X))))&
(?[X]:((tall(X)&calm(X))))&
(?[X]:((curious(X)|~tall(X))))&
(?[X]:((~kind(X)|~creative(X))))&
(?[X]:((~wise(X)|~quiet(X))))&
(?[X]:((~strong(X)|~happy(X))))&
((~generous(mary)<~>~curious(mary))) | quiet(lucy) | [] | null | 0 |
Everyone who is either quiet or not strong is both happy and not quiet and vice versa.
Everyone who is not old is quiet and vice versa.
If mary is either not strong or humble then someone is either humble or strong.
Everyone who is either not patient or not wise is not quiet or wise and vice versa.
Everyone who is either not rich or not wise is not quiet or funny and vice versa.
If someone is humble then someone is old or not patient and vice versa.
If someone is quiet or not calm then mary is creative and vice versa.
Everyone who is quiet is either kind or wise and vice versa.
If alice is curious or not curious then someone is both not kind and creative and vice versa.
Everyone who is not kind is either wise or not creative and vice versa.
If someone is old then someone is old or curious and vice versa.
If mary is not humble then someone is happy or not calm.
If susan is generous or brave then someone is both tall and curious.
Everyone who is curious or brave is not curious or not patient.
If someone is either curious or not humble then mary is both not humble and not strong and vice versa.
Lucy is either kind or brave.
Someone is not rich.
Someone is either not happy or curious.
Someone is either happy or not funny.
Someone is rich.
Someone is generous or humble.
Paul is tall or patient. | Susan is not calm. | neutral | (![X]:((quiet(X)<~>~strong(X))<=>(happy(X)&~quiet(X))))&
(![X]:(~old(X)<=>quiet(X)))&
(((~strong(mary)<~>humble(mary)))=>(?[X]:((humble(X)<~>strong(X)))))&
(![X]:((~patient(X)<~>~wise(X))<=>(~quiet(X)|wise(X))))&
(![X]:((~rich(X)<~>~wise(X))<=>(~quiet(X)|funny(X))))&
((?[X]:(humble(X)))<=>(?[X]:((old(X)|~patient(X)))))&
((?[X]:((quiet(X)|~calm(X))))<=>(creative(mary)))&
(![X]:(quiet(X)<=>(kind(X)<~>wise(X))))&
(((curious(alice)|~curious(alice)))<=>(?[X]:((~kind(X)&creative(X)))))&
(![X]:(~kind(X)<=>(wise(X)<~>~creative(X))))&
((?[X]:(old(X)))<=>(?[X]:((old(X)|curious(X)))))&
((~humble(mary))=>(?[X]:((happy(X)|~calm(X)))))&
(((generous(susan)|brave(susan)))=>(?[X]:((tall(X)&curious(X)))))&
(![X]:((curious(X)|brave(X))=>(~curious(X)|~patient(X))))&
((?[X]:((curious(X)<~>~humble(X))))<=>((~humble(mary)&~strong(mary))))&
((kind(lucy)<~>brave(lucy)))&
(?[X]:(~rich(X)))&
(?[X]:((~happy(X)<~>curious(X))))&
(?[X]:((happy(X)<~>~funny(X))))&
(?[X]:(rich(X)))&
(?[X]:((generous(X)|humble(X))))&
((tall(paul)|patient(paul))) | ~calm(susan) | [] | null | 0 |
Everyone who is both not calm and not strong is either brave or tall and vice versa.
Everyone who is old is both humble and not kind and vice versa.
Everyone who is old is calm or not wise and vice versa.
If lucy is tall or rich then someone is not creative.
If susan is either generous or not humble then someone is either not generous or funny and vice versa.
Everyone who is not curious or tall is either quiet or not humble.
If someone is either curious or quiet then someone is either generous or old.
If someone is generous then someone is both quiet and happy and vice versa.
If someone is both not humble and humble then someone is not old.
Everyone who is both happy and creative is both not kind and curious and vice versa.
Everyone who is either not funny or curious is both quiet and rich.
If someone is both not kind and kind then john is not tall.
Everyone who is not quiet is either happy or not funny and vice versa.
Everyone who is not humble is not funny and vice versa.
Everyone who is not patient or wise is not humble and vice versa.
Everyone who is not patient is quiet.
John is not old.
Someone is creative.
Someone is both not old and not generous.
Susan is both not calm and tall.
Someone is brave or old.
Someone is either not kind or rich.
Lucy is either kind or not humble.
Someone is either not wise or not brave. | Lucy is not quiet. | contradiction | (![X]:((~calm(X)&~strong(X))<=>(brave(X)<~>tall(X))))&
(![X]:(old(X)<=>(humble(X)&~kind(X))))&
(![X]:(old(X)<=>(calm(X)|~wise(X))))&
(((tall(lucy)|rich(lucy)))=>(?[X]:(~creative(X))))&
(((generous(susan)<~>~humble(susan)))<=>(?[X]:((~generous(X)<~>funny(X)))))&
(![X]:((~curious(X)|tall(X))=>(quiet(X)<~>~humble(X))))&
((?[X]:((curious(X)<~>quiet(X))))=>(?[X]:((generous(X)<~>old(X)))))&
((?[X]:(generous(X)))<=>(?[X]:((quiet(X)&happy(X)))))&
((?[X]:((~humble(X)&humble(X))))=>(?[X]:(~old(X))))&
(![X]:((happy(X)&creative(X))<=>(~kind(X)&curious(X))))&
(![X]:((~funny(X)<~>curious(X))=>(quiet(X)&rich(X))))&
((?[X]:((~kind(X)&kind(X))))=>(~tall(john)))&
(![X]:(~quiet(X)<=>(happy(X)<~>~funny(X))))&
(![X]:(~humble(X)<=>~funny(X)))&
(![X]:((~patient(X)|wise(X))<=>~humble(X)))&
(![X]:(~patient(X)=>quiet(X)))&
(~old(john))&
(?[X]:(creative(X)))&
(?[X]:((~old(X)&~generous(X))))&
((~calm(susan)&tall(susan)))&
(?[X]:((brave(X)|old(X))))&
(?[X]:((~kind(X)<~>rich(X))))&
((kind(lucy)<~>~humble(lucy)))&
(?[X]:((~wise(X)<~>~brave(X)))) | ~quiet(lucy) | [
"p1",
"p2",
"p5",
"p9",
"p10",
"p12",
"p13",
"p14",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 3326732265872060288913860
% SZS output start Proof for 3326732265872060288913860
2. ! [X0] : (old(X0) <=> (~kind(X0) & humble(X0))) [input p1]
3. ! [X0] : (old(X0) <=> (~wise(X0) | calm(X0))) [input p2]
6. ! [X0] : ((tall(X0) | ~curious(X0)) => (quiet(X0) <~> ~humble(X0))) [input p5]
10. ! [X0] : ((creative(X0) & happy(X0)) <=> (curious(X0) & ~kind(X0))) [input p9]
11. ! [X0] : ((~funny(X0) <~> curious(X0)) => (rich(X0) & quiet(X0))) [input p10]
13. ! [X0] : (~quiet(X0) <=> (happy(X0) <~> ~funny(X0))) [input p12]
14. ! [X0] : (~humble(X0) <=> ~funny(X0)) [input p13]
15. ! [X0] : ((wise(X0) | ~patient(X0)) <=> ~humble(X0)) [input p14]
23. kind(lucy) <~> ~humble(lucy) [input p22]
25. ~quiet(lucy) [input hypothesis]
30. ! [X0] : ((quiet(X0) <~> ~humble(X0)) | (~tall(X0) & curious(X0))) [ennf transformation 6]
33. ! [X0] : ((rich(X0) & quiet(X0)) | (~funny(X0) <=> curious(X0))) [ennf transformation 11]
38. ! [X0] : ((old(X0) | (kind(X0) | ~humble(X0))) & ((~kind(X0) & humble(X0)) | ~old(X0))) [nnf transformation 2]
39. ! [X0] : ((old(X0) | kind(X0) | ~humble(X0)) & ((~kind(X0) & humble(X0)) | ~old(X0))) [flattening 38]
40. ! [X0] : ((old(X0) | (wise(X0) & ~calm(X0))) & ((~wise(X0) | calm(X0)) | ~old(X0))) [nnf transformation 3]
41. ! [X0] : ((old(X0) | (wise(X0) & ~calm(X0))) & (~wise(X0) | calm(X0) | ~old(X0))) [flattening 40]
48. ! [X0] : (((humble(X0) | ~quiet(X0)) & (~humble(X0) | quiet(X0))) | (~tall(X0) & curious(X0))) [nnf transformation 30]
61. ! [X0] : (((creative(X0) & happy(X0)) | (~curious(X0) | kind(X0))) & ((curious(X0) & ~kind(X0)) | (~creative(X0) | ~happy(X0)))) [nnf transformation 10]
62. ! [X0] : (((creative(X0) & happy(X0)) | ~curious(X0) | kind(X0)) & ((curious(X0) & ~kind(X0)) | ~creative(X0) | ~happy(X0))) [flattening 61]
63. ! [X0] : ((rich(X0) & quiet(X0)) | ((~funny(X0) | ~curious(X0)) & (curious(X0) | funny(X0)))) [nnf transformation 33]
64. ! [X0] : ((~quiet(X0) | ((happy(X0) | funny(X0)) & (~funny(X0) | ~happy(X0)))) & (((funny(X0) | ~happy(X0)) & (~funny(X0) | happy(X0))) | quiet(X0))) [nnf transformation 13]
65. ! [X0] : ((~humble(X0) | funny(X0)) & (~funny(X0) | humble(X0))) [nnf transformation 14]
66. ! [X0] : (((wise(X0) | ~patient(X0)) | humble(X0)) & (~humble(X0) | (~wise(X0) & patient(X0)))) [nnf transformation 15]
67. ! [X0] : ((wise(X0) | ~patient(X0) | humble(X0)) & (~humble(X0) | (~wise(X0) & patient(X0)))) [flattening 66]
77. (humble(lucy) | ~kind(lucy)) & (~humble(lucy) | kind(lucy)) [nnf transformation 23]
88. ~kind(X0) | ~old(X0) [cnf transformation 39]
92. wise(X0) | old(X0) [cnf transformation 41]
103. ~humble(X0) | quiet(X0) | curious(X0) [cnf transformation 48]
117. ~curious(X0) | happy(X0) | kind(X0) [cnf transformation 62]
119. quiet(X0) | curious(X0) | funny(X0) [cnf transformation 63]
125. ~happy(X0) | funny(X0) | quiet(X0) [cnf transformation 64]
128. ~funny(X0) | humble(X0) [cnf transformation 65]
131. ~wise(X0) | ~humble(X0) [cnf transformation 67]
143. ~humble(lucy) | kind(lucy) [cnf transformation 77]
144. humble(lucy) | ~kind(lucy) [cnf transformation 77]
147. ~quiet(lucy) [cnf transformation 25]
251. 23 <=> kind(lucy) [avatar definition]
252. kind(lucy) <- (23) [avatar component clause 251]
253. ~kind(lucy) <- (~23) [avatar component clause 251]
255. 24 <=> humble(lucy) [avatar definition]
257. humble(lucy) <- (24) [avatar component clause 255]
258. ~23 | 24 [avatar split clause 144,255,251]
259. 23 | ~24 [avatar split clause 143,255,251]
277. ~humble(X0) | old(X0) [resolution 131,92]
328. curious(lucy) | funny(lucy) [resolution 119,147]
335. 36 <=> funny(lucy) [avatar definition]
336. ~funny(lucy) <- (~36) [avatar component clause 335]
337. funny(lucy) <- (36) [avatar component clause 335]
339. 37 <=> curious(lucy) [avatar definition]
341. curious(lucy) <- (37) [avatar component clause 339]
342. 36 | 37 [avatar split clause 328,339,335]
345. humble(lucy) <- (36) [resolution 337,128]
348. 24 | ~36 [avatar split clause 345,335,255]
349. ~old(lucy) <- (23) [resolution 252,88]
351. quiet(lucy) | curious(lucy) <- (24) [resolution 257,103]
353. old(lucy) <- (24) [resolution 257,277]
358. curious(lucy) <- (24) [subsumption resolution 351,147]
359. 37 | ~24 [avatar split clause 358,255,339]
360. $false <- (23, 24) [subsumption resolution 353,349]
361. ~23 | ~24 [avatar contradiction clause 360]
368. happy(lucy) | kind(lucy) <- (37) [resolution 341,117]
371. happy(lucy) <- (~23, 37) [subsumption resolution 368,253]
416. funny(lucy) | quiet(lucy) <- (~23, 37) [resolution 371,125]
419. quiet(lucy) <- (~23, ~36, 37) [subsumption resolution 416,336]
420. $false <- (~23, ~36, 37) [subsumption resolution 419,147]
421. 23 | 36 | ~37 [avatar contradiction clause 420]
422. $false [avatar sat refutation 258,259,342,348,359,361,421]
% SZS output end Proof for 3326732265872060288913860
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If alice is rich then fred is creative or happy.
Everyone who is both not kind and not funny is not humble or not funny.
Everyone who is both not generous and patient is both not brave and not patient.
If alice is brave then paul is not quiet.
Everyone who is generous or not funny is either not brave or not rich and vice versa.
Everyone who is not wise is not funny or calm.
If someone is curious or not rich then someone is both funny and not happy and vice versa.
If someone is either not humble or not tall then fred is brave or calm and vice versa.
Everyone who is happy or tall is quiet or not curious.
Everyone who is calm is both calm and strong and vice versa.
Everyone who is both not humble and not kind is either quiet or creative and vice versa.
Everyone who is curious is not calm or old and vice versa.
If alice is not funny then someone is rich.
Everyone who is not generous or kind is not brave and vice versa.
If someone is not funny then lucy is strong.
Everyone who is both not calm and not wise is both not humble and not strong.
Lucy is both funny and not patient.
Fred is not quiet or wise.
Someone is either strong or rich.
Someone is either not calm or not curious.
Fred is both not strong and creative.
Someone is either not strong or not wise.
Susan is generous or not creative.
Paul is kind. | Paul is not brave. | entailment | ((rich(alice))=>((creative(fred)|happy(fred))))&
(![X]:((~kind(X)&~funny(X))=>(~humble(X)|~funny(X))))&
(![X]:((~generous(X)&patient(X))=>(~brave(X)&~patient(X))))&
((brave(alice))=>(~quiet(paul)))&
(![X]:((generous(X)|~funny(X))<=>(~brave(X)<~>~rich(X))))&
(![X]:(~wise(X)=>(~funny(X)|calm(X))))&
((?[X]:((curious(X)|~rich(X))))<=>(?[X]:((funny(X)&~happy(X)))))&
((?[X]:((~humble(X)<~>~tall(X))))<=>((brave(fred)|calm(fred))))&
(![X]:((happy(X)|tall(X))=>(quiet(X)|~curious(X))))&
(![X]:(calm(X)<=>(calm(X)&strong(X))))&
(![X]:((~humble(X)&~kind(X))<=>(quiet(X)<~>creative(X))))&
(![X]:(curious(X)<=>(~calm(X)|old(X))))&
((~funny(alice))=>(?[X]:(rich(X))))&
(![X]:((~generous(X)|kind(X))<=>~brave(X)))&
((?[X]:(~funny(X)))=>(strong(lucy)))&
(![X]:((~calm(X)&~wise(X))=>(~humble(X)&~strong(X))))&
((funny(lucy)&~patient(lucy)))&
((~quiet(fred)|wise(fred)))&
(?[X]:((strong(X)<~>rich(X))))&
(?[X]:((~calm(X)<~>~curious(X))))&
((~strong(fred)&creative(fred)))&
(?[X]:((~strong(X)<~>~wise(X))))&
((generous(susan)|~creative(susan)))&
(kind(paul)) | ~brave(paul) | [
"p13",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 8580116763349326634519807
% SZS output start Proof for 8580116763349326634519807
14. ! [X0] : ((kind(X0) | ~generous(X0)) <=> ~brave(X0)) [input p13]
24. kind(paul) [input p23]
25. brave(paul) [input hypothesis]
62. ! [X0] : (((kind(X0) | ~generous(X0)) | brave(X0)) & (~brave(X0) | (~kind(X0) & generous(X0)))) [nnf transformation 14]
63. ! [X0] : ((kind(X0) | ~generous(X0) | brave(X0)) & (~brave(X0) | (~kind(X0) & generous(X0)))) [flattening 62]
110. ~brave(X0) | ~kind(X0) [cnf transformation 63]
126. kind(paul) [cnf transformation 24]
127. brave(paul) [cnf transformation 25]
287. ~kind(paul) [resolution 110,127]
289. $false [subsumption resolution 287,126]
% SZS output end Proof for 8580116763349326634519807
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 fred is rich then alice is generous or not quiet.
If someone is both curious and not quiet then someone is both not wise and not generous.
If john is strong then someone is not tall or kind.
Everyone who is both not patient and not wise is both not humble and not patient.
Everyone who is strong or not tall is both not calm and rich.
Everyone who is not quiet or not humble is either old or quiet.
Everyone who is not generous is funny.
If susan is not creative then someone is not brave.
Everyone who is calm or not humble is wise.
If someone is kind then alice is either quiet or not kind.
Everyone who is not old is not brave.
Everyone who is humble or not brave is both not happy and happy.
Everyone who is not brave or happy is not patient or strong and vice versa.
Everyone who is both old and calm is either kind or not patient and vice versa.
If someone is either not happy or quiet then someone is curious or funny.
Everyone who is both not curious and funny is both wise and not patient.
Someone is either generous or old.
Alice is brave or not patient.
Someone is either kind or not rich.
Someone is not humble.
Susan is both not happy and not strong.
Someone is both not rich and not patient. | Susan is not generous. | contradiction | ((rich(fred))=>((generous(alice)|~quiet(alice))))&
((?[X]:((curious(X)&~quiet(X))))=>(?[X]:((~wise(X)&~generous(X)))))&
((strong(john))=>(?[X]:((~tall(X)|kind(X)))))&
(![X]:((~patient(X)&~wise(X))=>(~humble(X)&~patient(X))))&
(![X]:((strong(X)|~tall(X))=>(~calm(X)&rich(X))))&
(![X]:((~quiet(X)|~humble(X))=>(old(X)<~>quiet(X))))&
(![X]:(~generous(X)=>funny(X)))&
((~creative(susan))=>(?[X]:(~brave(X))))&
(![X]:((calm(X)|~humble(X))=>wise(X)))&
((?[X]:(kind(X)))=>((quiet(alice)<~>~kind(alice))))&
(![X]:(~old(X)=>~brave(X)))&
(![X]:((humble(X)|~brave(X))=>(~happy(X)&happy(X))))&
(![X]:((~brave(X)|happy(X))<=>(~patient(X)|strong(X))))&
(![X]:((old(X)&calm(X))<=>(kind(X)<~>~patient(X))))&
((?[X]:((~happy(X)<~>quiet(X))))=>(?[X]:((curious(X)|funny(X)))))&
(![X]:((~curious(X)&funny(X))=>(wise(X)&~patient(X))))&
(?[X]:((generous(X)<~>old(X))))&
((brave(alice)|~patient(alice)))&
(?[X]:((kind(X)<~>~rich(X))))&
(?[X]:(~humble(X)))&
((~happy(susan)&~strong(susan)))&
(?[X]:((~rich(X)&~patient(X)))) | ~generous(susan) | [
"p1",
"p5",
"p6",
"p8",
"p10",
"p11",
"p12",
"p15",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 4780310644930722837111758
% SZS output start Proof for 4780310644930722837111758
2. ? [X0] : (~quiet(X0) & curious(X0)) => ? [X0] : (~generous(X0) & ~wise(X0)) [input p1]
6. ! [X0] : ((~humble(X0) | ~quiet(X0)) => (old(X0) <~> quiet(X0))) [input p5]
7. ! [X0] : (~generous(X0) => funny(X0)) [input p6]
9. ! [X0] : ((~humble(X0) | calm(X0)) => wise(X0)) [input p8]
11. ! [X0] : (~old(X0) => ~brave(X0)) [input p10]
12. ! [X0] : ((~brave(X0) | humble(X0)) => (happy(X0) & ~happy(X0))) [input p11]
13. ! [X0] : ((happy(X0) | ~brave(X0)) <=> (strong(X0) | ~patient(X0))) [input p12]
16. ! [X0] : ((funny(X0) & ~curious(X0)) => (~patient(X0) & wise(X0))) [input p15]
21. ~strong(susan) & ~happy(susan) [input p20]
23. ~generous(susan) [input hypothesis]
24. ? [X0] : (~quiet(X0) & curious(X0)) => ? [X1] : (~generous(X1) & ~wise(X1)) [rectify 2]
29. ? [X1] : (~generous(X1) & ~wise(X1)) | ! [X0] : (quiet(X0) | ~curious(X0)) [ennf transformation 24]
34. ! [X0] : ((old(X0) <~> quiet(X0)) | (humble(X0) & quiet(X0))) [ennf transformation 6]
35. ! [X0] : (funny(X0) | generous(X0)) [ennf transformation 7]
36. ! [X0] : (wise(X0) | (humble(X0) & ~calm(X0))) [ennf transformation 9]
38. ! [X0] : (~brave(X0) | old(X0)) [ennf transformation 11]
39. ! [X0] : ((happy(X0) & ~happy(X0)) | (brave(X0) & ~humble(X0))) [ennf transformation 12]
41. ! [X0] : ((~patient(X0) & wise(X0)) | (~funny(X0) | curious(X0))) [ennf transformation 16]
42. ! [X0] : ((~patient(X0) & wise(X0)) | ~funny(X0) | curious(X0)) [flattening 41]
43. ? [X0] : (~generous(X0) & ~wise(X0)) | ! [X1] : (quiet(X1) | ~curious(X1)) [rectify 29]
44. ? [X0] : (~generous(X0) & ~wise(X0)) => (~generous(sK0) & ~wise(sK0)) [choice axiom]
45. (~generous(sK0) & ~wise(sK0)) | ! [X1] : (quiet(X1) | ~curious(X1)) [skolemisation 43,44]
48. ! [X0] : (((~quiet(X0) | ~old(X0)) & (quiet(X0) | old(X0))) | (humble(X0) & quiet(X0))) [nnf transformation 34]
50. ! [X0] : (((happy(X0) | ~brave(X0)) | (~strong(X0) & patient(X0))) & ((strong(X0) | ~patient(X0)) | (~happy(X0) & brave(X0)))) [nnf transformation 13]
51. ! [X0] : ((happy(X0) | ~brave(X0) | (~strong(X0) & patient(X0))) & (strong(X0) | ~patient(X0) | (~happy(X0) & brave(X0)))) [flattening 50]
69. ~wise(sK0) | quiet(X1) | ~curious(X1) [cnf transformation 45]
81. ~old(X0) | ~quiet(X0) | humble(X0) [cnf transformation 48]
82. funny(X0) | generous(X0) [cnf transformation 35]
84. humble(X0) | wise(X0) [cnf transformation 36]
87. ~brave(X0) | old(X0) [cnf transformation 38]
88. ~happy(X0) | ~humble(X0) [cnf transformation 39]
89. ~happy(X0) | brave(X0) [cnf transformation 39]
90. ~humble(X0) | happy(X0) [cnf transformation 39]
91. happy(X0) | brave(X0) [cnf transformation 39]
94. happy(X0) | ~brave(X0) | patient(X0) [cnf transformation 51]
105. ~funny(X0) | ~patient(X0) | curious(X0) [cnf transformation 42]
112. ~happy(susan) [cnf transformation 21]
116. ~generous(susan) [cnf transformation 23]
132. 4 <=> ! [X1] : (quiet(X1) | ~curious(X1)) [avatar definition]
133. ~curious(X1) | quiet(X1) <- (4) [avatar component clause 132]
140. 6 <=> wise(sK0) [avatar definition]
142. ~wise(sK0) <- (~6) [avatar component clause 140]
143. 4 | ~6 [avatar split clause 69,140,132]
166. brave(X0) [subsumption resolution 89,91]
167. ~humble(X0) [subsumption resolution 88,90]
169. happy(X0) | patient(X0) [subsumption resolution 94,166]
207. wise(X0) [resolution 84,167]
208. old(X0) [resolution 87,166]
209. $false <- (~6) [resolution 207,142]
210. 6 [avatar contradiction clause 209]
216. patient(susan) [resolution 169,112]
221. ~quiet(X2) | humble(X2) [resolution 81,208]
223. ~quiet(X2) [subsumption resolution 221,167]
245. ~patient(X0) | curious(X0) | generous(X0) [resolution 105,82]
293. curious(susan) | generous(susan) [resolution 245,216]
295. curious(susan) [subsumption resolution 293,116]
298. quiet(susan) <- (4) [resolution 295,133]
299. $false <- (4) [subsumption resolution 298,223]
300. ~4 [avatar contradiction clause 299]
301. $false [avatar sat refutation 143,210,300]
% SZS output end Proof for 4780310644930722837111758
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either kind or not old then someone is either wise or tall. Everyone who is both funny and not patient is either tall or not happy. If someone is either wise or not happy then someone is either calm or not tall. Everyone who is quiet or not humble is not wise. If susan is either calm or patient then lucy is kind. If someone is not generous or brave then paul is either not humble or happy. Everyone who is either not quiet or not calm is either not quiet or not rich and vice versa. Everyone who is old or not generous is both generous and curious and vice versa. If someone is both not creative and patient then mary is both quiet and patient and vice versa. If someone is not quiet or not funny then someone is wise or kind and vice versa. Everyone who is both strong and rich is either not curious or calm. If someone is not humble or not quiet then someone is both curious and strong. If john is both humble and rich then lucy is not generous or generous. If paul is patient then fred is either not brave or not old and vice versa. Everyone who is tall is quiet or not old and vice versa. Everyone who is both quiet and not rich is not rich and vice versa. Paul is not strong. Fred is both not old and patient. Lucy is humble or not strong. Someone is both curious and not rich. Someone is rich or not calm. Fred is strong. John is both tall and not old. Susan is either curious or happy. | Fred is not calm. | entailment | (((kind(mary)<~>~old(mary)))=>(?[X]:((wise(X)<~>tall(X)))))&
(![X]:((funny(X)&~patient(X))=>(tall(X)<~>~happy(X))))&
((?[X]:((wise(X)<~>~happy(X))))=>(?[X]:((calm(X)<~>~tall(X)))))&
(![X]:((quiet(X)|~humble(X))=>~wise(X)))&
(((calm(susan)<~>patient(susan)))=>(kind(lucy)))&
((?[X]:((~generous(X)|brave(X))))=>((~humble(paul)<~>happy(paul))))&
(![X]:((~quiet(X)<~>~calm(X))<=>(~quiet(X)<~>~rich(X))))&
(![X]:((old(X)|~generous(X))<=>(generous(X)&curious(X))))&
((?[X]:((~creative(X)&patient(X))))<=>((quiet(mary)&patient(mary))))&
((?[X]:((~quiet(X)|~funny(X))))<=>(?[X]:((wise(X)|kind(X)))))&
(![X]:((strong(X)&rich(X))=>(~curious(X)<~>calm(X))))&
((?[X]:((~humble(X)|~quiet(X))))=>(?[X]:((curious(X)&strong(X)))))&
(((humble(john)&rich(john)))=>((~generous(lucy)|generous(lucy))))&
((patient(paul))<=>((~brave(fred)<~>~old(fred))))&
(![X]:(tall(X)<=>(quiet(X)|~old(X))))&
(![X]:((quiet(X)&~rich(X))<=>~rich(X)))&
(~strong(paul))&
((~old(fred)&patient(fred)))&
((humble(lucy)|~strong(lucy)))&
(?[X]:((curious(X)&~rich(X))))&
(?[X]:((rich(X)|~calm(X))))&
(strong(fred))&
((tall(john)&~old(john)))&
((curious(susan)<~>happy(susan))) | ~calm(fred) | [
"p6",
"p7",
"p10",
"p17",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 8987499709772969732997488
% SZS output start Proof for 8987499709772969732997488
7. ! [X0] : ((~quiet(X0) <~> ~calm(X0)) <=> (~quiet(X0) <~> ~rich(X0))) [input p6]
8. ! [X0] : ((~generous(X0) | old(X0)) <=> (curious(X0) & generous(X0))) [input p7]
11. ! [X0] : ((rich(X0) & strong(X0)) => (~curious(X0) <~> calm(X0))) [input p10]
18. patient(fred) & ~old(fred) [input p17]
22. strong(fred) [input p21]
25. calm(fred) [input hypothesis]
36. ! [X0] : ((~curious(X0) <~> calm(X0)) | (~rich(X0) | ~strong(X0))) [ennf transformation 11]
37. ! [X0] : ((~curious(X0) <~> calm(X0)) | ~rich(X0) | ~strong(X0)) [flattening 36]
51. ! [X0] : ((((calm(X0) | quiet(X0)) & (~calm(X0) | ~quiet(X0))) | ((~quiet(X0) | rich(X0)) & (~rich(X0) | quiet(X0)))) & (((rich(X0) | quiet(X0)) & (~rich(X0) | ~quiet(X0))) | ((~quiet(X0) | calm(X0)) & (~calm(X0) | quiet(X0))))) [nnf transformation 7]
52. ! [X0] : (((~generous(X0) | old(X0)) | (~curious(X0) | ~generous(X0))) & ((curious(X0) & generous(X0)) | (generous(X0) & ~old(X0)))) [nnf transformation 8]
53. ! [X0] : ((~generous(X0) | old(X0) | ~curious(X0) | ~generous(X0)) & ((curious(X0) & generous(X0)) | (generous(X0) & ~old(X0)))) [flattening 52]
64. ! [X0] : (((~calm(X0) | curious(X0)) & (calm(X0) | ~curious(X0))) | ~rich(X0) | ~strong(X0)) [nnf transformation 37]
97. ~rich(X0) | ~quiet(X0) | ~quiet(X0) | calm(X0) [cnf transformation 51]
98. rich(X0) | quiet(X0) | ~calm(X0) | quiet(X0) [cnf transformation 51]
101. ~calm(X0) | ~quiet(X0) | ~quiet(X0) | rich(X0) [cnf transformation 51]
102. calm(X0) | quiet(X0) | ~rich(X0) | quiet(X0) [cnf transformation 51]
105. generous(X0) | generous(X0) [cnf transformation 53]
108. ~generous(X0) | old(X0) | ~curious(X0) | ~generous(X0) [cnf transformation 53]
118. ~calm(X0) | curious(X0) | ~rich(X0) | ~strong(X0) [cnf transformation 64]
135. ~old(fred) [cnf transformation 18]
141. strong(fred) [cnf transformation 22]
146. calm(fred) [cnf transformation 25]
147. generous(X0) [duplicate literal removal 105]
148. ~curious(X0) | old(X0) | ~generous(X0) [duplicate literal removal 108]
149. ~rich(X0) | ~quiet(X0) | calm(X0) [duplicate literal removal 97]
150. rich(X0) | quiet(X0) | ~calm(X0) [duplicate literal removal 98]
151. ~quiet(X0) | ~calm(X0) | rich(X0) [duplicate literal removal 101]
152. ~rich(X0) | quiet(X0) | calm(X0) [duplicate literal removal 102]
218. 15 <=> ! [X0] : generous(X0) [avatar definition]
219. generous(X0) <- (15) [avatar component clause 218]
223. ~calm(X0) | rich(X0) [subsumption resolution 150,151]
224. ~rich(X0) | calm(X0) [subsumption resolution 149,152]
225. 15 [avatar split clause 147,218]
281. ~strong(X0) | ~rich(X0) | curious(X0) [subsumption resolution 118,224]
298. 32 <=> old(fred) [avatar definition]
299. ~old(fred) <- (~32) [avatar component clause 298]
313. ~32 [avatar split clause 135,298]
354. rich(fred) [resolution 223,146]
384. ~rich(fred) | curious(fred) [resolution 281,141]
386. curious(fred) [subsumption resolution 384,354]
387. old(fred) | ~generous(fred) [resolution 386,148]
388. ~generous(fred) <- (~32) [subsumption resolution 387,299]
389. $false <- (15, ~32) [subsumption resolution 388,219]
390. ~15 | 32 [avatar contradiction clause 389]
391. $false [avatar sat refutation 225,313,390]
% SZS output end Proof for 8987499709772969732997488
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If alice is both happy and not funny then lucy is either humble or not creative.
If someone is both tall and not kind then someone is not old and vice versa.
If fred is either not rich or not humble then mary is both calm and not kind and vice versa.
Everyone who is both brave and calm is both not rich and not brave and vice versa.
Everyone who is both not happy and not generous is either not wise or humble.
Everyone who is not calm is brave.
If someone is either quiet or not patient then john is rich and vice versa.
Everyone who is not patient or not rich is funny or quiet and vice versa.
If someone is funny then someone is either quiet or not tall.
Everyone who is not quiet or not brave is not kind or funny.
If someone is both not happy and quiet then fred is tall or brave.
Everyone who is not wise or patient is not tall.
Everyone who is not tall or funny is calm and vice versa.
If someone is either not funny or brave then someone is quiet and vice versa.
Everyone who is either patient or not rich is both not tall and not old.
Everyone who is either rich or not rich is funny or patient and vice versa.
Someone is both not tall and generous.
Mary is old or creative.
Someone is either not generous or not kind.
Someone is both not quiet and not old.
Someone is patient or not wise.
Someone is both not funny and not humble.
Someone is wise or happy. | Mary is rich. | entailment | (((happy(alice)&~funny(alice)))=>((humble(lucy)<~>~creative(lucy))))&
((?[X]:((tall(X)&~kind(X))))<=>(?[X]:(~old(X))))&
(((~rich(fred)<~>~humble(fred)))<=>((calm(mary)&~kind(mary))))&
(![X]:((brave(X)&calm(X))<=>(~rich(X)&~brave(X))))&
(![X]:((~happy(X)&~generous(X))=>(~wise(X)<~>humble(X))))&
(![X]:(~calm(X)=>brave(X)))&
((?[X]:((quiet(X)<~>~patient(X))))<=>(rich(john)))&
(![X]:((~patient(X)|~rich(X))<=>(funny(X)|quiet(X))))&
((?[X]:(funny(X)))=>(?[X]:((quiet(X)<~>~tall(X)))))&
(![X]:((~quiet(X)|~brave(X))=>(~kind(X)|funny(X))))&
((?[X]:((~happy(X)&quiet(X))))=>((tall(fred)|brave(fred))))&
(![X]:((~wise(X)|patient(X))=>~tall(X)))&
(![X]:((~tall(X)|funny(X))<=>calm(X)))&
((?[X]:((~funny(X)<~>brave(X))))<=>(?[X]:(quiet(X))))&
(![X]:((patient(X)<~>~rich(X))=>(~tall(X)&~old(X))))&
(![X]:((rich(X)<~>~rich(X))<=>(funny(X)|patient(X))))&
(?[X]:((~tall(X)&generous(X))))&
((old(mary)|creative(mary)))&
(?[X]:((~generous(X)<~>~kind(X))))&
(?[X]:((~quiet(X)&~old(X))))&
(?[X]:((patient(X)|~wise(X))))&
(?[X]:((~funny(X)&~humble(X))))&
(?[X]:((wise(X)|happy(X)))) | rich(mary) | [
"p3",
"p11",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4695855453288239140336835
% SZS output start Proof for 4695855453288239140336835
4. ! [X0] : ((calm(X0) & brave(X0)) <=> (~brave(X0) & ~rich(X0))) [input p3]
12. ! [X0] : ((patient(X0) | ~wise(X0)) => ~tall(X0)) [input p11]
13. ! [X0] : ((funny(X0) | ~tall(X0)) <=> calm(X0)) [input p12]
15. ! [X0] : ((patient(X0) <~> ~rich(X0)) => (~old(X0) & ~tall(X0))) [input p14]
24. ~rich(mary) [input hypothesis]
38. ! [X0] : (~tall(X0) | (~patient(X0) & wise(X0))) [ennf transformation 12]
39. ! [X0] : ((~old(X0) & ~tall(X0)) | (patient(X0) <=> ~rich(X0))) [ennf transformation 15]
48. ! [X0] : (((calm(X0) & brave(X0)) | (brave(X0) | rich(X0))) & ((~brave(X0) & ~rich(X0)) | (~calm(X0) | ~brave(X0)))) [nnf transformation 4]
49. ! [X0] : (((calm(X0) & brave(X0)) | brave(X0) | rich(X0)) & ((~brave(X0) & ~rich(X0)) | ~calm(X0) | ~brave(X0))) [flattening 48]
61. ! [X0] : (((funny(X0) | ~tall(X0)) | ~calm(X0)) & (calm(X0) | (~funny(X0) & tall(X0)))) [nnf transformation 13]
62. ! [X0] : ((funny(X0) | ~tall(X0) | ~calm(X0)) & (calm(X0) | (~funny(X0) & tall(X0)))) [flattening 61]
68. ! [X0] : ((~old(X0) & ~tall(X0)) | ((patient(X0) | rich(X0)) & (~rich(X0) | ~patient(X0)))) [nnf transformation 39]
96. ~brave(X0) | ~calm(X0) | ~brave(X0) [cnf transformation 49]
97. brave(X0) | brave(X0) | rich(X0) [cnf transformation 49]
116. ~patient(X0) | ~tall(X0) [cnf transformation 38]
117. calm(X0) | tall(X0) [cnf transformation 62]
125. ~tall(X0) | patient(X0) | rich(X0) [cnf transformation 68]
145. ~rich(mary) [cnf transformation 24]
148. ~brave(X0) | ~calm(X0) [duplicate literal removal 96]
149. brave(X0) | rich(X0) [duplicate literal removal 97]
283. ~tall(X0) | rich(X0) [subsumption resolution 125,116]
330. ~calm(X0) | rich(X0) [resolution 149,148]
393. rich(X0) | tall(X0) [resolution 330,117]
396. rich(X0) [subsumption resolution 393,283]
398. $false [resolution 396,145]
% SZS output end Proof for 4695855453288239140336835
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not calm and funny is both happy and strong and vice versa.
Everyone who is not kind or not humble is both strong and not rich.
If someone is wise then lucy is not humble.
If someone is wise or not creative then paul is not curious.
If susan is either not tall or not wise then john is both patient and old and vice versa.
Everyone who is calm is either funny or old.
If someone is brave then susan is either tall or wise and vice versa.
If alice is not rich or not tall then someone is either not brave or not curious.
Everyone who is either strong or kind is either not generous or not tall and vice versa.
If someone is strong then someone is both creative and quiet.
Everyone who is not kind is either not funny or not patient and vice versa.
Everyone who is both patient and strong is either not rich or not creative.
Everyone who is both not tall and strong is either not brave or not generous and vice versa.
Everyone who is not quiet or wise is both not kind and not strong and vice versa.
If someone is not generous then someone is both not curious and calm and vice versa.
Everyone who is patient is not generous and vice versa.
Someone is strong or humble.
Someone is creative or not happy.
Someone is either calm or rich.
Someone is not curious or not rich.
Paul is either not wise or creative.
Someone is kind or patient. | John is not wise. | entailment | (![X]:((~calm(X)&funny(X))<=>(happy(X)&strong(X))))&
(![X]:((~kind(X)|~humble(X))=>(strong(X)&~rich(X))))&
((?[X]:(wise(X)))=>(~humble(lucy)))&
((?[X]:((wise(X)|~creative(X))))=>(~curious(paul)))&
(((~tall(susan)<~>~wise(susan)))<=>((patient(john)&old(john))))&
(![X]:(calm(X)=>(funny(X)<~>old(X))))&
((?[X]:(brave(X)))<=>((tall(susan)<~>wise(susan))))&
(((~rich(alice)|~tall(alice)))=>(?[X]:((~brave(X)<~>~curious(X)))))&
(![X]:((strong(X)<~>kind(X))<=>(~generous(X)<~>~tall(X))))&
((?[X]:(strong(X)))=>(?[X]:((creative(X)&quiet(X)))))&
(![X]:(~kind(X)<=>(~funny(X)<~>~patient(X))))&
(![X]:((patient(X)&strong(X))=>(~rich(X)<~>~creative(X))))&
(![X]:((~tall(X)&strong(X))<=>(~brave(X)<~>~generous(X))))&
(![X]:((~quiet(X)|wise(X))<=>(~kind(X)&~strong(X))))&
((?[X]:(~generous(X)))<=>(?[X]:((~curious(X)&calm(X)))))&
(![X]:(patient(X)<=>~generous(X)))&
(?[X]:((strong(X)|humble(X))))&
(?[X]:((creative(X)|~happy(X))))&
(?[X]:((calm(X)<~>rich(X))))&
(?[X]:((~curious(X)|~rich(X))))&
((~wise(paul)<~>creative(paul)))&
(?[X]:((kind(X)|patient(X)))) | ~wise(john) | [
"p1",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 394575702199465363953893
% SZS output start Proof for 394575702199465363953893
2. ! [X0] : ((~humble(X0) | ~kind(X0)) => (~rich(X0) & strong(X0))) [input p1]
14. ! [X0] : ((wise(X0) | ~quiet(X0)) <=> (~strong(X0) & ~kind(X0))) [input p13]
23. wise(john) [input hypothesis]
26. ! [X0] : ((~rich(X0) & strong(X0)) | (humble(X0) & kind(X0))) [ennf transformation 2]
54. ! [X0] : (((wise(X0) | ~quiet(X0)) | (strong(X0) | kind(X0))) & ((~strong(X0) & ~kind(X0)) | (~wise(X0) & quiet(X0)))) [nnf transformation 14]
55. ! [X0] : ((wise(X0) | ~quiet(X0) | strong(X0) | kind(X0)) & ((~strong(X0) & ~kind(X0)) | (~wise(X0) & quiet(X0)))) [flattening 54]
78. kind(X0) | strong(X0) [cnf transformation 26]
124. ~wise(X0) | ~kind(X0) [cnf transformation 55]
126. ~wise(X0) | ~strong(X0) [cnf transformation 55]
141. wise(john) [cnf transformation 23]
306. ~kind(john) [resolution 124,141]
308. ~strong(john) [resolution 126,141]
309. strong(john) [resolution 306,78]
310. $false [subsumption resolution 309,308]
% SZS output end Proof for 394575702199465363953893
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not strong is quiet or not funny and vice versa. If someone is wise or not generous then someone is not funny or rich. If someone is rich then mary is both rich and tall. If someone is not patient or not rich then mary is both not wise and kind and vice versa. If someone is humble or not happy then someone is both happy and quiet. Everyone who is not funny or not generous is not kind and vice versa. If john is not rich then someone is not quiet. Everyone who is either generous or wise is both calm and brave. Everyone who is not curious is not calm or not creative. Everyone who is curious is both generous and not rich. If someone is not strong or strong then someone is either wise or patient and vice versa. Everyone who is funny or wise is both not patient and wise. Everyone who is either generous or wise is either not wise or not happy. Mary is kind or not kind. Paul is not brave or happy. Someone is not wise or calm. Paul is kind or not curious. Someone is not brave. Lucy is not curious. | Mary is generous. | neutral | (![X]:(~strong(X)<=>(quiet(X)|~funny(X))))&
((?[X]:((wise(X)|~generous(X))))=>(?[X]:((~funny(X)|rich(X)))))&
((?[X]:(rich(X)))=>((rich(mary)&tall(mary))))&
((?[X]:((~patient(X)|~rich(X))))<=>((~wise(mary)&kind(mary))))&
((?[X]:((humble(X)|~happy(X))))=>(?[X]:((happy(X)&quiet(X)))))&
(![X]:((~funny(X)|~generous(X))<=>~kind(X)))&
((~rich(john))=>(?[X]:(~quiet(X))))&
(![X]:((generous(X)<~>wise(X))=>(calm(X)&brave(X))))&
(![X]:(~curious(X)=>(~calm(X)|~creative(X))))&
(![X]:(curious(X)=>(generous(X)&~rich(X))))&
((?[X]:((~strong(X)|strong(X))))<=>(?[X]:((wise(X)<~>patient(X)))))&
(![X]:((funny(X)|wise(X))=>(~patient(X)&wise(X))))&
(![X]:((generous(X)<~>wise(X))=>(~wise(X)<~>~happy(X))))&
((kind(mary)|~kind(mary)))&
((~brave(paul)|happy(paul)))&
(?[X]:((~wise(X)|calm(X))))&
((kind(paul)|~curious(paul)))&
(?[X]:(~brave(X)))&
(~curious(lucy)) | generous(mary) | [] | null | 0 |
If someone is not strong or not humble then someone is not rich or not tall.
Everyone who is both humble and tall is not humble or rich.
Everyone who is not creative is not rich and vice versa.
Everyone who is both old and wise is not patient and vice versa.
If someone is either not wise or quiet then someone is either not brave or old and vice versa.
Everyone who is not patient is either rich or not old and vice versa.
Everyone who is not rich or not old is both funny and not patient.
If fred is both patient and not kind then someone is either generous or not creative and vice versa.
Everyone who is either not patient or patient is both not brave and not kind and vice versa.
If mary is both wise and not creative then mary is patient or not calm and vice versa.
If someone is both creative and not wise then fred is patient.
If someone is both quiet and not happy then alice is not old.
If mary is humble then mary is both generous and strong and vice versa.
If someone is curious then john is both not creative and brave and vice versa.
Everyone who is either not funny or not generous is both not creative and brave.
If someone is both rich and not calm then someone is calm or not strong.
Someone is both not calm and creative.
Someone is either not strong or humble.
Someone is not happy or not humble.
Someone is either not old or not calm. | Mary is calm. | entailment | ((?[X]:((~strong(X)|~humble(X))))=>(?[X]:((~rich(X)|~tall(X)))))&
(![X]:((humble(X)&tall(X))=>(~humble(X)|rich(X))))&
(![X]:(~creative(X)<=>~rich(X)))&
(![X]:((old(X)&wise(X))<=>~patient(X)))&
((?[X]:((~wise(X)<~>quiet(X))))<=>(?[X]:((~brave(X)<~>old(X)))))&
(![X]:(~patient(X)<=>(rich(X)<~>~old(X))))&
(![X]:((~rich(X)|~old(X))=>(funny(X)&~patient(X))))&
(((patient(fred)&~kind(fred)))<=>(?[X]:((generous(X)<~>~creative(X)))))&
(![X]:((~patient(X)<~>patient(X))<=>(~brave(X)&~kind(X))))&
(((wise(mary)&~creative(mary)))<=>((patient(mary)|~calm(mary))))&
((?[X]:((creative(X)&~wise(X))))=>(patient(fred)))&
((?[X]:((quiet(X)&~happy(X))))=>(~old(alice)))&
((humble(mary))<=>((generous(mary)&strong(mary))))&
((?[X]:(curious(X)))<=>((~creative(john)&brave(john))))&
(![X]:((~funny(X)<~>~generous(X))=>(~creative(X)&brave(X))))&
((?[X]:((rich(X)&~calm(X))))=>(?[X]:((calm(X)|~strong(X)))))&
(?[X]:((~calm(X)&creative(X))))&
(?[X]:((~strong(X)<~>humble(X))))&
(?[X]:((~happy(X)|~humble(X))))&
(?[X]:((~old(X)<~>~calm(X)))) | calm(mary) | [
"p2",
"p3",
"p5",
"p6",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 7399926304309699450141717
% SZS output start Proof for 7399926304309699450141717
3. ! [X0] : (~creative(X0) <=> ~rich(X0)) [input p2]
4. ! [X0] : ((wise(X0) & old(X0)) <=> ~patient(X0)) [input p3]
6. ! [X0] : (~patient(X0) <=> (rich(X0) <~> ~old(X0))) [input p5]
7. ! [X0] : ((~old(X0) | ~rich(X0)) => (~patient(X0) & funny(X0))) [input p6]
10. (~creative(mary) & wise(mary)) <=> (~calm(mary) | patient(mary)) [input p9]
21. ~calm(mary) [input hypothesis]
27. ! [X0] : ((~patient(X0) & funny(X0)) | (old(X0) & rich(X0))) [ennf transformation 7]
32. ! [X0] : ((~creative(X0) | rich(X0)) & (~rich(X0) | creative(X0))) [nnf transformation 3]
33. ! [X0] : (((wise(X0) & old(X0)) | patient(X0)) & (~patient(X0) | (~wise(X0) | ~old(X0)))) [nnf transformation 4]
34. ! [X0] : (((wise(X0) & old(X0)) | patient(X0)) & (~patient(X0) | ~wise(X0) | ~old(X0))) [flattening 33]
40. ! [X0] : ((~patient(X0) | ((rich(X0) | old(X0)) & (~old(X0) | ~rich(X0)))) & (((old(X0) | ~rich(X0)) & (~old(X0) | rich(X0))) | patient(X0))) [nnf transformation 6]
48. ((~creative(mary) & wise(mary)) | (calm(mary) & ~patient(mary))) & ((~calm(mary) | patient(mary)) | (creative(mary) | ~wise(mary))) [nnf transformation 10]
49. ((~creative(mary) & wise(mary)) | (calm(mary) & ~patient(mary))) & (~calm(mary) | patient(mary) | creative(mary) | ~wise(mary)) [flattening 48]
71. ~rich(X0) | creative(X0) [cnf transformation 32]
74. old(X0) | patient(X0) [cnf transformation 34]
84. ~old(X0) | rich(X0) | patient(X0) [cnf transformation 40]
90. ~patient(X0) | rich(X0) [cnf transformation 27]
108. ~creative(mary) | calm(mary) [cnf transformation 49]
129. ~calm(mary) [cnf transformation 21]
171. rich(X0) | patient(X0) [subsumption resolution 84,74]
173. rich(X0) [subsumption resolution 90,171]
205. 15 <=> calm(mary) [avatar definition]
209. 16 <=> creative(mary) [avatar definition]
211. ~creative(mary) <- (~16) [avatar component clause 209]
212. 15 | ~16 [avatar split clause 108,209,205]
283. ~15 [avatar split clause 129,205]
288. creative(X0) [resolution 71,173]
291. $false <- (~16) [resolution 288,211]
293. 16 [avatar contradiction clause 291]
295. $false [avatar sat refutation 212,283,293]
% SZS output end Proof for 7399926304309699450141717
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 susan is kind or calm then someone is not wise and vice versa.
Everyone who is either not generous or humble is either not wise or not kind and vice versa.
Everyone who is not creative is both funny and creative.
Everyone who is not funny is either strong or not rich and vice versa.
If lucy is both rich and not happy then someone is not calm or humble.
If lucy is both not brave and not curious then someone is both generous and wise and vice versa.
Everyone who is not happy is curious and vice versa.
If someone is not kind then fred is both not wise and not patient and vice versa.
If mary is both not curious and not brave then someone is not generous and vice versa.
Everyone who is both not kind and not old is strong and vice versa.
Everyone who is tall or strong is both not calm and humble and vice versa.
Everyone who is either generous or not quiet is tall or calm.
Everyone who is both not humble and not calm is tall or not humble and vice versa.
If john is wise or not generous then someone is humble and vice versa.
Everyone who is both kind and not kind is either not creative or old and vice versa.
Everyone who is both not brave and not patient is funny.
Someone is both not wise and curious.
Lucy is either generous or not tall.
Paul is both curious and not patient.
Someone is both not curious and calm.
John is either not kind or funny.
Susan is either not quiet or quiet.
Someone is either tall or not happy.
Someone is not old or curious. | Mary is not happy. | contradiction | (((kind(susan)|calm(susan)))<=>(?[X]:(~wise(X))))&
(![X]:((~generous(X)<~>humble(X))<=>(~wise(X)<~>~kind(X))))&
(![X]:(~creative(X)=>(funny(X)&creative(X))))&
(![X]:(~funny(X)<=>(strong(X)<~>~rich(X))))&
(((rich(lucy)&~happy(lucy)))=>(?[X]:((~calm(X)|humble(X)))))&
(((~brave(lucy)&~curious(lucy)))<=>(?[X]:((generous(X)&wise(X)))))&
(![X]:(~happy(X)<=>curious(X)))&
((?[X]:(~kind(X)))<=>((~wise(fred)&~patient(fred))))&
(((~curious(mary)&~brave(mary)))<=>(?[X]:(~generous(X))))&
(![X]:((~kind(X)&~old(X))<=>strong(X)))&
(![X]:((tall(X)|strong(X))<=>(~calm(X)&humble(X))))&
(![X]:((generous(X)<~>~quiet(X))=>(tall(X)|calm(X))))&
(![X]:((~humble(X)&~calm(X))<=>(tall(X)|~humble(X))))&
(((wise(john)|~generous(john)))<=>(?[X]:(humble(X))))&
(![X]:((kind(X)&~kind(X))<=>(~creative(X)<~>old(X))))&
(![X]:((~brave(X)&~patient(X))=>funny(X)))&
(?[X]:((~wise(X)&curious(X))))&
((generous(lucy)<~>~tall(lucy)))&
((curious(paul)&~patient(paul)))&
(?[X]:((~curious(X)&calm(X))))&
((~kind(john)<~>funny(john)))&
((~quiet(susan)<~>quiet(susan)))&
(?[X]:((tall(X)<~>~happy(X))))&
(?[X]:((~old(X)|curious(X)))) | ~happy(mary) | [
"p6",
"p8",
"p10",
"p12",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 580053457217580949978713
% SZS output start Proof for 580053457217580949978713
7. ! [X0] : (~happy(X0) <=> curious(X0)) [input p6]
9. (~brave(mary) & ~curious(mary)) <=> ? [X0] : ~generous(X0) [input p8]
11. ! [X0] : ((strong(X0) | tall(X0)) <=> (humble(X0) & ~calm(X0))) [input p10]
13. ! [X0] : ((~calm(X0) & ~humble(X0)) <=> (~humble(X0) | tall(X0))) [input p12]
18. generous(lucy) <~> ~tall(lucy) [input p17]
25. ~happy(mary) [input hypothesis]
47. ! [X0] : ((~happy(X0) | ~curious(X0)) & (curious(X0) | happy(X0))) [nnf transformation 7]
53. ((~brave(mary) & ~curious(mary)) | ! [X0] : generous(X0)) & (? [X0] : ~generous(X0) | (brave(mary) | curious(mary))) [nnf transformation 9]
54. ((~brave(mary) & ~curious(mary)) | ! [X0] : generous(X0)) & (? [X0] : ~generous(X0) | brave(mary) | curious(mary)) [flattening 53]
55. ((~brave(mary) & ~curious(mary)) | ! [X0] : generous(X0)) & (? [X1] : ~generous(X1) | brave(mary) | curious(mary)) [rectify 54]
56. ? [X1] : ~generous(X1) => ~generous(sK4) [choice axiom]
57. ((~brave(mary) & ~curious(mary)) | ! [X0] : generous(X0)) & (~generous(sK4) | brave(mary) | curious(mary)) [skolemisation 55,56]
60. ! [X0] : (((strong(X0) | tall(X0)) | (~humble(X0) | calm(X0))) & ((humble(X0) & ~calm(X0)) | (~strong(X0) & ~tall(X0)))) [nnf transformation 11]
61. ! [X0] : ((strong(X0) | tall(X0) | ~humble(X0) | calm(X0)) & ((humble(X0) & ~calm(X0)) | (~strong(X0) & ~tall(X0)))) [flattening 60]
63. ! [X0] : (((~calm(X0) & ~humble(X0)) | (humble(X0) & ~tall(X0))) & ((~humble(X0) | tall(X0)) | (calm(X0) | humble(X0)))) [nnf transformation 13]
64. ! [X0] : (((~calm(X0) & ~humble(X0)) | (humble(X0) & ~tall(X0))) & (~humble(X0) | tall(X0) | calm(X0) | humble(X0))) [flattening 63]
74. (tall(lucy) | ~generous(lucy)) & (~tall(lucy) | generous(lucy)) [nnf transformation 18]
106. curious(X0) | happy(X0) [cnf transformation 47]
112. ~curious(mary) | generous(X0) [cnf transformation 57]
119. humble(X0) | ~tall(X0) [cnf transformation 61]
125. ~humble(X0) | ~tall(X0) [cnf transformation 64]
142. tall(lucy) | ~generous(lucy) [cnf transformation 74]
154. ~happy(mary) [cnf transformation 25]
233. 18 <=> ! [X0] : generous(X0) [avatar definition]
234. generous(X0) <- (18) [avatar component clause 233]
241. 20 <=> curious(mary) [avatar definition]
243. ~curious(mary) <- (~20) [avatar component clause 241]
244. 18 | ~20 [avatar split clause 112,241,233]
250. ~tall(X0) [subsumption resolution 125,119]
272. ~generous(lucy) [subsumption resolution 142,250]
285. happy(mary) <- (~20) [resolution 106,243]
286. $false <- (~20) [subsumption resolution 285,154]
287. 20 [avatar contradiction clause 286]
289. $false <- (18) [resolution 234,272]
290. ~18 [avatar contradiction clause 289]
292. $false [avatar sat refutation 244,287,290]
% SZS output end Proof for 580053457217580949978713
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not generous is both not happy and not funny and vice versa. If lucy is both not creative and old then someone is strong and vice versa. If someone is either not creative or creative then alice is either rich or kind and vice versa. Everyone who is both not rich and not happy is strong. If fred is kind or patient then susan is both wise and not generous. Everyone who is tall is both not rich and not humble. Everyone who is both not humble and strong is not wise or creative. If lucy is both kind and not tall then john is curious and vice versa. If fred is quiet then someone is either curious or wise. Everyone who is both not brave and not happy is creative or quiet. If someone is both not tall and not wise then someone is not humble or creative and vice versa. Everyone who is both kind and not curious is not old or rich and vice versa. Everyone who is both strong and not tall is not calm. Everyone who is both not humble and not quiet is not kind. If mary is either happy or not calm then someone is either brave or not rich. Everyone who is humble is curious or not strong and vice versa. Someone is not funny. Lucy is both curious and not calm. Someone is either generous or tall. Someone is not tall or patient. Someone is either funny or not wise. Paul is both old and calm. Someone is rich. | Alice is rich. | contradiction | (![X]:(~generous(X)<=>(~happy(X)&~funny(X))))&
(((~creative(lucy)&old(lucy)))<=>(?[X]:(strong(X))))&
((?[X]:((~creative(X)<~>creative(X))))<=>((rich(alice)<~>kind(alice))))&
(![X]:((~rich(X)&~happy(X))=>strong(X)))&
(((kind(fred)|patient(fred)))=>((wise(susan)&~generous(susan))))&
(![X]:(tall(X)=>(~rich(X)&~humble(X))))&
(![X]:((~humble(X)&strong(X))=>(~wise(X)|creative(X))))&
(((kind(lucy)&~tall(lucy)))<=>(curious(john)))&
((quiet(fred))=>(?[X]:((curious(X)<~>wise(X)))))&
(![X]:((~brave(X)&~happy(X))=>(creative(X)|quiet(X))))&
((?[X]:((~tall(X)&~wise(X))))<=>(?[X]:((~humble(X)|creative(X)))))&
(![X]:((kind(X)&~curious(X))<=>(~old(X)|rich(X))))&
(![X]:((strong(X)&~tall(X))=>~calm(X)))&
(![X]:((~humble(X)&~quiet(X))=>~kind(X)))&
(((happy(mary)<~>~calm(mary)))=>(?[X]:((brave(X)<~>~rich(X)))))&
(![X]:(humble(X)<=>(curious(X)|~strong(X))))&
(?[X]:(~funny(X)))&
((curious(lucy)&~calm(lucy)))&
(?[X]:((generous(X)<~>tall(X))))&
(?[X]:((~tall(X)|patient(X))))&
(?[X]:((funny(X)<~>~wise(X))))&
((old(paul)&calm(paul)))&
(?[X]:(rich(X))) | rich(alice) | [
"p2",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 1156766431193213704238792
% SZS output start Proof for 1156766431193213704238792
3. ? [X0] : (~creative(X0) <~> creative(X0)) <=> (rich(alice) <~> kind(alice)) [input p2]
12. ! [X0] : ((~curious(X0) & kind(X0)) <=> (rich(X0) | ~old(X0))) [input p11]
24. rich(alice) [input hypothesis]
47. (? [X0] : ((~creative(X0) | creative(X0)) & (creative(X0) | ~creative(X0))) | ((rich(alice) | ~kind(alice)) & (kind(alice) | ~rich(alice)))) & (((~kind(alice) | ~rich(alice)) & (kind(alice) | rich(alice))) | ! [X0] : ((~creative(X0) | ~creative(X0)) & (creative(X0) | creative(X0)))) [nnf transformation 3]
48. (? [X0] : ((~creative(X0) | creative(X0)) & (creative(X0) | ~creative(X0))) | ((rich(alice) | ~kind(alice)) & (kind(alice) | ~rich(alice)))) & (((~kind(alice) | ~rich(alice)) & (kind(alice) | rich(alice))) | ! [X1] : ((~creative(X1) | ~creative(X1)) & (creative(X1) | creative(X1)))) [rectify 47]
49. ? [X0] : ((~creative(X0) | creative(X0)) & (creative(X0) | ~creative(X0))) => ((~creative(sK1) | creative(sK1)) & (creative(sK1) | ~creative(sK1))) [choice axiom]
50. (((~creative(sK1) | creative(sK1)) & (creative(sK1) | ~creative(sK1))) | ((rich(alice) | ~kind(alice)) & (kind(alice) | ~rich(alice)))) & (((~kind(alice) | ~rich(alice)) & (kind(alice) | rich(alice))) | ! [X1] : ((~creative(X1) | ~creative(X1)) & (creative(X1) | creative(X1)))) [skolemisation 48,49]
61. ! [X0] : (((~curious(X0) & kind(X0)) | (~rich(X0) & old(X0))) & ((rich(X0) | ~old(X0)) | (curious(X0) | ~kind(X0)))) [nnf transformation 12]
62. ! [X0] : (((~curious(X0) & kind(X0)) | (~rich(X0) & old(X0))) & (rich(X0) | ~old(X0) | curious(X0) | ~kind(X0))) [flattening 61]
88. ~kind(alice) | ~rich(alice) | creative(X1) | creative(X1) [cnf transformation 50]
89. ~kind(alice) | ~rich(alice) | ~creative(X1) | ~creative(X1) [cnf transformation 50]
115. ~rich(X0) | kind(X0) [cnf transformation 62]
138. rich(alice) [cnf transformation 24]
141. ~kind(alice) | ~rich(alice) | creative(X1) [duplicate literal removal 88]
142. ~kind(alice) | ~rich(alice) | ~creative(X1) [duplicate literal removal 89]
162. 5 <=> ! [X1] : ~creative(X1) [avatar definition]
163. ~creative(X1) <- (5) [avatar component clause 162]
165. 6 <=> rich(alice) [avatar definition]
166. rich(alice) <- (6) [avatar component clause 165]
169. 7 <=> kind(alice) [avatar definition]
172. 5 | ~6 | ~7 [avatar split clause 142,169,165,162]
174. 8 <=> ! [X1] : creative(X1) [avatar definition]
175. creative(X1) <- (8) [avatar component clause 174]
176. 8 | ~6 | ~7 [avatar split clause 141,169,165,174]
304. 6 [avatar split clause 138,165]
309. kind(alice) <- (6) [resolution 115,166]
312. 7 | ~6 [avatar split clause 309,165,169]
313. $false <- (5, 8) [subsumption resolution 163,175]
314. ~5 | ~8 [avatar contradiction clause 313]
315. $false [avatar sat refutation 172,176,304,312,314]
% SZS output end Proof for 1156766431193213704238792
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not wise or not creative is not strong or not old and vice versa. If alice is old or funny then fred is not humble and vice versa. If fred is either not generous or not tall then paul is either not wise or not quiet. Everyone who is wise is both not generous and not rich. If someone is both not quiet and wise then someone is either tall or not brave and vice versa. If john is either not curious or happy then mary is not humble and vice versa. If mary is both brave and not creative then john is either curious or not quiet. If someone is not curious then someone is rich. If alice is either curious or wise then susan is humble and vice versa. Everyone who is not quiet or not old is kind or funny and vice versa. If someone is not creative or not funny then john is not quiet and vice versa. If someone is brave or not creative then someone is rich or not quiet and vice versa. If john is either not tall or not quiet then someone is either generous or not creative and vice versa. If susan is either not brave or funny then mary is both not kind and not patient and vice versa. If someone is both brave and not rich then someone is not tall or not patient. If someone is not strong then susan is both strong and wise and vice versa. Susan is either not tall or creative. Lucy is not old. Alice is not wise. Lucy is either quiet or not quiet. Fred is either not patient or old. Susan is both generous and kind. Paul is not humble. Lucy is rich. | Alice is old. | contradiction | (![X]:((~wise(X)|~creative(X))<=>(~strong(X)|~old(X))))&
(((old(alice)|funny(alice)))<=>(~humble(fred)))&
(((~generous(fred)<~>~tall(fred)))=>((~wise(paul)<~>~quiet(paul))))&
(![X]:(wise(X)=>(~generous(X)&~rich(X))))&
((?[X]:((~quiet(X)&wise(X))))<=>(?[X]:((tall(X)<~>~brave(X)))))&
(((~curious(john)<~>happy(john)))<=>(~humble(mary)))&
(((brave(mary)&~creative(mary)))=>((curious(john)<~>~quiet(john))))&
((?[X]:(~curious(X)))=>(?[X]:(rich(X))))&
(((curious(alice)<~>wise(alice)))<=>(humble(susan)))&
(![X]:((~quiet(X)|~old(X))<=>(kind(X)|funny(X))))&
((?[X]:((~creative(X)|~funny(X))))<=>(~quiet(john)))&
((?[X]:((brave(X)|~creative(X))))<=>(?[X]:((rich(X)|~quiet(X)))))&
(((~tall(john)<~>~quiet(john)))<=>(?[X]:((generous(X)<~>~creative(X)))))&
(((~brave(susan)<~>funny(susan)))<=>((~kind(mary)&~patient(mary))))&
((?[X]:((brave(X)&~rich(X))))=>(?[X]:((~tall(X)|~patient(X)))))&
((?[X]:(~strong(X)))<=>((strong(susan)&wise(susan))))&
((~tall(susan)<~>creative(susan)))&
(~old(lucy))&
(~wise(alice))&
((quiet(lucy)<~>~quiet(lucy)))&
((~patient(fred)<~>old(fred)))&
((generous(susan)&kind(susan)))&
(~humble(paul))&
(rich(lucy)) | old(alice) | [
"p0",
"p3",
"p15",
"p18",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 3012910928831593390725203
% SZS output start Proof for 3012910928831593390725203
1. ! [X0] : ((~creative(X0) | ~wise(X0)) <=> (~old(X0) | ~strong(X0))) [input p0]
4. ! [X0] : (wise(X0) => (~rich(X0) & ~generous(X0))) [input p3]
16. ? [X0] : ~strong(X0) <=> (wise(susan) & strong(susan)) [input p15]
19. ~wise(alice) [input p18]
22. kind(susan) & generous(susan) [input p21]
25. old(alice) [input hypothesis]
31. ! [X0] : ((~rich(X0) & ~generous(X0)) | ~wise(X0)) [ennf transformation 4]
36. ! [X0] : (((~creative(X0) | ~wise(X0)) | (old(X0) & strong(X0))) & ((~old(X0) | ~strong(X0)) | (creative(X0) & wise(X0)))) [nnf transformation 1]
37. ! [X0] : ((~creative(X0) | ~wise(X0) | (old(X0) & strong(X0))) & (~old(X0) | ~strong(X0) | (creative(X0) & wise(X0)))) [flattening 36]
72. (? [X0] : ~strong(X0) | (~wise(susan) | ~strong(susan))) & ((wise(susan) & strong(susan)) | ! [X0] : strong(X0)) [nnf transformation 16]
73. (? [X0] : ~strong(X0) | ~wise(susan) | ~strong(susan)) & ((wise(susan) & strong(susan)) | ! [X0] : strong(X0)) [flattening 72]
74. (? [X0] : ~strong(X0) | ~wise(susan) | ~strong(susan)) & ((wise(susan) & strong(susan)) | ! [X1] : strong(X1)) [rectify 73]
75. ? [X0] : ~strong(X0) => ~strong(sK8) [choice axiom]
76. (~strong(sK8) | ~wise(susan) | ~strong(susan)) & ((wise(susan) & strong(susan)) | ! [X1] : strong(X1)) [skolemisation 74,75]
80. ~old(X0) | ~strong(X0) | wise(X0) [cnf transformation 37]
91. ~generous(X0) | ~wise(X0) [cnf transformation 31]
137. wise(susan) | strong(X1) [cnf transformation 76]
142. ~wise(alice) [cnf transformation 19]
147. generous(susan) [cnf transformation 22]
151. old(alice) [cnf transformation 25]
157. 2 <=> old(alice) [avatar definition]
159. old(alice) <- (2) [avatar component clause 157]
265. 25 <=> wise(alice) [avatar definition]
267. ~wise(alice) <- (~25) [avatar component clause 265]
383. 50 <=> wise(susan) [avatar definition]
392. 52 <=> ! [X1] : strong(X1) [avatar definition]
393. strong(X1) <- (52) [avatar component clause 392]
394. 52 | 50 [avatar split clause 137,383,392]
406. ~25 [avatar split clause 142,265]
417. 2 [avatar split clause 151,157]
430. ~wise(susan) [resolution 91,147]
433. ~50 [avatar split clause 430,383]
438. ~strong(alice) | wise(alice) <- (2) [resolution 80,159]
439. wise(alice) <- (2, 52) [subsumption resolution 438,393]
440. $false <- (2, ~25, 52) [subsumption resolution 439,267]
441. ~2 | 25 | ~52 [avatar contradiction clause 440]
442. $false [avatar sat refutation 394,406,417,433,441]
% SZS output end Proof for 3012910928831593390725203
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is calm or curious is tall or not generous.
If someone is both old and not calm then fred is calm.
Everyone who is not quiet is patient and vice versa.
If john is kind then someone is brave or curious and vice versa.
Everyone who is not generous or creative is rich or funny and vice versa.
Everyone who is rich is both calm and not kind.
Everyone who is rich is not funny or not creative and vice versa.
If someone is not happy or kind then john is not curious and vice versa.
If someone is either funny or not kind then someone is not old or humble and vice versa.
Everyone who is not tall is not funny.
Everyone who is either not curious or not rich is old.
If someone is both rich and not creative then someone is both rich and not wise.
Everyone who is both not strong and brave is both not happy and calm.
Everyone who is both creative and humble is both not rich and rich.
If someone is either quiet or wise then someone is either old or wise.
If someone is funny or generous then someone is not brave or calm.
John is humble or creative.
John is not wise or not curious.
Someone is either generous or curious.
Someone is both not rich and not happy.
John is both not happy and not tall.
Someone is either not strong or not quiet.
Someone is both patient and not humble.
Paul is rich or not kind. | John is humble. | neutral | (![X]:((calm(X)|curious(X))=>(tall(X)|~generous(X))))&
((?[X]:((old(X)&~calm(X))))=>(calm(fred)))&
(![X]:(~quiet(X)<=>patient(X)))&
((kind(john))<=>(?[X]:((brave(X)|curious(X)))))&
(![X]:((~generous(X)|creative(X))<=>(rich(X)|funny(X))))&
(![X]:(rich(X)=>(calm(X)&~kind(X))))&
(![X]:(rich(X)<=>(~funny(X)|~creative(X))))&
((?[X]:((~happy(X)|kind(X))))<=>(~curious(john)))&
((?[X]:((funny(X)<~>~kind(X))))<=>(?[X]:((~old(X)|humble(X)))))&
(![X]:(~tall(X)=>~funny(X)))&
(![X]:((~curious(X)<~>~rich(X))=>old(X)))&
((?[X]:((rich(X)&~creative(X))))=>(?[X]:((rich(X)&~wise(X)))))&
(![X]:((~strong(X)&brave(X))=>(~happy(X)&calm(X))))&
(![X]:((creative(X)&humble(X))=>(~rich(X)&rich(X))))&
((?[X]:((quiet(X)<~>wise(X))))=>(?[X]:((old(X)<~>wise(X)))))&
((?[X]:((funny(X)|generous(X))))=>(?[X]:((~brave(X)|calm(X)))))&
((humble(john)|creative(john)))&
((~wise(john)|~curious(john)))&
(?[X]:((generous(X)<~>curious(X))))&
(?[X]:((~rich(X)&~happy(X))))&
((~happy(john)&~tall(john)))&
(?[X]:((~strong(X)<~>~quiet(X))))&
(?[X]:((patient(X)&~humble(X))))&
((rich(paul)|~kind(paul))) | humble(john) | [] | null | 0 |
If paul is not wise then someone is either tall or funny.
If susan is not quiet then fred is either not brave or not calm.
Everyone who is calm or rich is humble and vice versa.
Everyone who is not brave or calm is both not happy and funny.
Everyone who is both not generous and funny is happy or brave and vice versa.
If fred is not creative or quiet then someone is patient and vice versa.
Everyone who is generous is either not patient or rich and vice versa.
Everyone who is happy is not funny or not brave.
Everyone who is not humble is both not calm and happy and vice versa.
Everyone who is either not funny or curious is both not patient and strong and vice versa.
Everyone who is not brave is creative.
If someone is not rich then someone is both funny and not rich.
If someone is both not wise and happy then alice is either quiet or not patient and vice versa.
Everyone who is both quiet and generous is not humble or generous.
Everyone who is not kind is either strong or brave and vice versa.
Everyone who is not wise or not happy is both not wise and calm and vice versa.
Susan is either creative or not creative.
Alice is either kind or not humble.
Someone is not generous.
Someone is both creative and generous. | Alice is not humble. | contradiction | ((~wise(paul))=>(?[X]:((tall(X)<~>funny(X)))))&
((~quiet(susan))=>((~brave(fred)<~>~calm(fred))))&
(![X]:((calm(X)|rich(X))<=>humble(X)))&
(![X]:((~brave(X)|calm(X))=>(~happy(X)&funny(X))))&
(![X]:((~generous(X)&funny(X))<=>(happy(X)|brave(X))))&
(((~creative(fred)|quiet(fred)))<=>(?[X]:(patient(X))))&
(![X]:(generous(X)<=>(~patient(X)<~>rich(X))))&
(![X]:(happy(X)=>(~funny(X)|~brave(X))))&
(![X]:(~humble(X)<=>(~calm(X)&happy(X))))&
(![X]:((~funny(X)<~>curious(X))<=>(~patient(X)&strong(X))))&
(![X]:(~brave(X)=>creative(X)))&
((?[X]:(~rich(X)))=>(?[X]:((funny(X)&~rich(X)))))&
((?[X]:((~wise(X)&happy(X))))<=>((quiet(alice)<~>~patient(alice))))&
(![X]:((quiet(X)&generous(X))=>(~humble(X)|generous(X))))&
(![X]:(~kind(X)<=>(strong(X)<~>brave(X))))&
(![X]:((~wise(X)|~happy(X))<=>(~wise(X)&calm(X))))&
((creative(susan)<~>~creative(susan)))&
((kind(alice)<~>~humble(alice)))&
(?[X]:(~generous(X)))&
(?[X]:((creative(X)&generous(X)))) | ~humble(alice) | [
"p3",
"p4",
"p7",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 336979265210880115164556
% SZS output start Proof for 336979265210880115164556
4. ! [X0] : ((calm(X0) | ~brave(X0)) => (funny(X0) & ~happy(X0))) [input p3]
5. ! [X0] : ((funny(X0) & ~generous(X0)) <=> (brave(X0) | happy(X0))) [input p4]
8. ! [X0] : (happy(X0) => (~brave(X0) | ~funny(X0))) [input p7]
9. ! [X0] : (~humble(X0) <=> (happy(X0) & ~calm(X0))) [input p8]
21. ~humble(alice) [input hypothesis]
25. ! [X0] : ((funny(X0) & ~happy(X0)) | (~calm(X0) & brave(X0))) [ennf transformation 4]
26. ! [X0] : ((~brave(X0) | ~funny(X0)) | ~happy(X0)) [ennf transformation 8]
27. ! [X0] : (~brave(X0) | ~funny(X0) | ~happy(X0)) [flattening 26]
38. ! [X0] : (((funny(X0) & ~generous(X0)) | (~brave(X0) & ~happy(X0))) & ((brave(X0) | happy(X0)) | (~funny(X0) | generous(X0)))) [nnf transformation 5]
39. ! [X0] : (((funny(X0) & ~generous(X0)) | (~brave(X0) & ~happy(X0))) & (brave(X0) | happy(X0) | ~funny(X0) | generous(X0))) [flattening 38]
46. ! [X0] : ((~humble(X0) | (~happy(X0) | calm(X0))) & ((happy(X0) & ~calm(X0)) | humble(X0))) [nnf transformation 9]
47. ! [X0] : ((~humble(X0) | ~happy(X0) | calm(X0)) & ((happy(X0) & ~calm(X0)) | humble(X0))) [flattening 46]
73. ~happy(X0) | brave(X0) [cnf transformation 25]
75. funny(X0) | brave(X0) [cnf transformation 25]
81. funny(X0) | ~brave(X0) [cnf transformation 39]
89. ~brave(X0) | ~funny(X0) | ~happy(X0) [cnf transformation 27]
91. happy(X0) | humble(X0) [cnf transformation 47]
125. ~humble(alice) [cnf transformation 21]
154. funny(X0) [subsumption resolution 81,75]
175. ~brave(X0) | ~happy(X0) [subsumption resolution 89,154]
176. ~happy(X0) [subsumption resolution 175,73]
177. humble(X0) [subsumption resolution 91,176]
210. $false [subsumption resolution 125,177]
% SZS output end Proof for 336979265210880115164556
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 4989
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If john is both calm and generous then someone is either calm or not patient and vice versa. Everyone who is not calm is brave or not old and vice versa. If lucy is quiet then john is either funny or strong. Everyone who is not tall or rich is tall or not brave and vice versa. Everyone who is patient is both not curious and not rich and vice versa. Everyone who is either not curious or curious is either old or not rich and vice versa. If someone is calm or not brave then someone is not rich or patient. Everyone who is old is not patient and vice versa. Everyone who is not humble or not curious is either not brave or wise. Everyone who is not patient is either not kind or funny and vice versa. If lucy is not quiet or curious then susan is creative. If john is both tall and old then someone is not curious and vice versa. Everyone who is either not kind or not calm is both not patient and rich. If mary is either not curious or kind then lucy is old. If fred is either not funny or funny then susan is not curious or not rich and vice versa. Someone is both creative and brave. John is either curious or not strong. Susan is not humble or not rich. Someone is either brave or not creative. Alice is both not strong and kind. Alice is either not old or not creative. | John is brave. | contradiction | (((calm(john)&generous(john)))<=>(?[X]:((calm(X)<~>~patient(X)))))&
(![X]:(~calm(X)<=>(brave(X)|~old(X))))&
((quiet(lucy))=>((funny(john)<~>strong(john))))&
(![X]:((~tall(X)|rich(X))<=>(tall(X)|~brave(X))))&
(![X]:(patient(X)<=>(~curious(X)&~rich(X))))&
(![X]:((~curious(X)<~>curious(X))<=>(old(X)<~>~rich(X))))&
((?[X]:((calm(X)|~brave(X))))=>(?[X]:((~rich(X)|patient(X)))))&
(![X]:(old(X)<=>~patient(X)))&
(![X]:((~humble(X)|~curious(X))=>(~brave(X)<~>wise(X))))&
(![X]:(~patient(X)<=>(~kind(X)<~>funny(X))))&
(((~quiet(lucy)|curious(lucy)))=>(creative(susan)))&
(((tall(john)&old(john)))<=>(?[X]:(~curious(X))))&
(![X]:((~kind(X)<~>~calm(X))=>(~patient(X)&rich(X))))&
(((~curious(mary)<~>kind(mary)))=>(old(lucy)))&
(((~funny(fred)<~>funny(fred)))<=>((~curious(susan)|~rich(susan))))&
(?[X]:((creative(X)&brave(X))))&
((curious(john)<~>~strong(john)))&
((~humble(susan)|~rich(susan)))&
(?[X]:((brave(X)<~>~creative(X))))&
((~strong(alice)&kind(alice)))&
((~old(alice)<~>~creative(alice))) | brave(john) | [
"p0",
"p1",
"p4",
"p7",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 3251244539697499469864648
% SZS output start Proof for 3251244539697499469864648
1. (generous(john) & calm(john)) <=> ? [X0] : (calm(X0) <~> ~patient(X0)) [input p0]
2. ! [X0] : (~calm(X0) <=> (~old(X0) | brave(X0))) [input p1]
5. ! [X0] : (patient(X0) <=> (~rich(X0) & ~curious(X0))) [input p4]
8. ! [X0] : (old(X0) <=> ~patient(X0)) [input p7]
12. (old(john) & tall(john)) <=> ? [X0] : ~curious(X0) [input p11]
22. brave(john) [input hypothesis]
30. ((generous(john) & calm(john)) | ! [X0] : ((calm(X0) | patient(X0)) & (~patient(X0) | ~calm(X0)))) & (? [X0] : ((patient(X0) | ~calm(X0)) & (~patient(X0) | calm(X0))) | (~generous(john) | ~calm(john))) [nnf transformation 1]
31. ((generous(john) & calm(john)) | ! [X0] : ((calm(X0) | patient(X0)) & (~patient(X0) | ~calm(X0)))) & (? [X0] : ((patient(X0) | ~calm(X0)) & (~patient(X0) | calm(X0))) | ~generous(john) | ~calm(john)) [flattening 30]
32. ((generous(john) & calm(john)) | ! [X0] : ((calm(X0) | patient(X0)) & (~patient(X0) | ~calm(X0)))) & (? [X1] : ((patient(X1) | ~calm(X1)) & (~patient(X1) | calm(X1))) | ~generous(john) | ~calm(john)) [rectify 31]
33. ? [X1] : ((patient(X1) | ~calm(X1)) & (~patient(X1) | calm(X1))) => ((patient(sK0) | ~calm(sK0)) & (~patient(sK0) | calm(sK0))) [choice axiom]
34. ((generous(john) & calm(john)) | ! [X0] : ((calm(X0) | patient(X0)) & (~patient(X0) | ~calm(X0)))) & (((patient(sK0) | ~calm(sK0)) & (~patient(sK0) | calm(sK0))) | ~generous(john) | ~calm(john)) [skolemisation 32,33]
35. ! [X0] : ((~calm(X0) | (old(X0) & ~brave(X0))) & ((~old(X0) | brave(X0)) | calm(X0))) [nnf transformation 2]
36. ! [X0] : ((~calm(X0) | (old(X0) & ~brave(X0))) & (~old(X0) | brave(X0) | calm(X0))) [flattening 35]
40. ! [X0] : ((patient(X0) | (rich(X0) | curious(X0))) & ((~rich(X0) & ~curious(X0)) | ~patient(X0))) [nnf transformation 5]
41. ! [X0] : ((patient(X0) | rich(X0) | curious(X0)) & ((~rich(X0) & ~curious(X0)) | ~patient(X0))) [flattening 40]
46. ! [X0] : ((old(X0) | patient(X0)) & (~patient(X0) | ~old(X0))) [nnf transformation 8]
49. ((old(john) & tall(john)) | ! [X0] : curious(X0)) & (? [X0] : ~curious(X0) | (~old(john) | ~tall(john))) [nnf transformation 12]
50. ((old(john) & tall(john)) | ! [X0] : curious(X0)) & (? [X0] : ~curious(X0) | ~old(john) | ~tall(john)) [flattening 49]
51. ((old(john) & tall(john)) | ! [X0] : curious(X0)) & (? [X1] : ~curious(X1) | ~old(john) | ~tall(john)) [rectify 50]
52. ? [X1] : ~curious(X1) => ~curious(sK2) [choice axiom]
53. ((old(john) & tall(john)) | ! [X0] : curious(X0)) & (~curious(sK2) | ~old(john) | ~tall(john)) [skolemisation 51,52]
68. calm(john) | calm(X0) | patient(X0) [cnf transformation 34]
72. ~brave(X0) | ~calm(X0) [cnf transformation 36]
80. ~curious(X0) | ~patient(X0) [cnf transformation 41]
93. ~old(X0) | ~patient(X0) [cnf transformation 46]
94. old(X0) | patient(X0) [cnf transformation 46]
107. old(john) | curious(X0) [cnf transformation 53]
131. brave(john) [cnf transformation 22]
141. 1 <=> ! [X0] : (calm(X0) | patient(X0)) [avatar definition]
142. patient(X0) | calm(X0) <- (1) [avatar component clause 141]
153. 4 <=> calm(john) [avatar definition]
154. ~calm(john) <- (~4) [avatar component clause 153]
156. 1 | 4 [avatar split clause 68,153,141]
209. 15 <=> ! [X0] : curious(X0) [avatar definition]
210. curious(X0) <- (15) [avatar component clause 209]
212. 16 <=> old(john) [avatar definition]
213. ~old(john) <- (~16) [avatar component clause 212]
214. old(john) <- (16) [avatar component clause 212]
215. 15 | 16 [avatar split clause 107,212,209]
290. ~calm(john) [resolution 72,131]
293. ~4 [avatar split clause 290,153]
295. ~patient(john) <- (16) [resolution 93,214]
302. calm(john) <- (1, 16) [resolution 142,295]
306. $false <- (1, ~4, 16) [subsumption resolution 302,154]
307. ~1 | 4 | ~16 [avatar contradiction clause 306]
312. ~patient(X0) <- (15) [resolution 210,80]
317. patient(john) <- (~16) [resolution 213,94]
318. $false <- (15, ~16) [subsumption resolution 317,312]
319. ~15 | 16 [avatar contradiction clause 318]
320. $false [avatar sat refutation 156,215,293,307,319]
% SZS output end Proof for 3251244539697499469864648
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient or generous then someone is either not quiet or wise.
If someone is either humble or not happy then john is not wise or not rich and vice versa.
Everyone who is not wise or calm is brave or not humble.
Everyone who is rich or not calm is either quiet or not curious and vice versa.
Everyone who is not calm is tall or rich and vice versa.
If someone is old then someone is both strong and not happy.
Everyone who is either not patient or not humble is patient and vice versa.
Everyone who is strong or kind is either not wise or wise and vice versa.
Everyone who is both not patient and not kind is either humble or not kind and vice versa.
Everyone who is both not humble and calm is both funny and curious.
If alice is both wise and humble then john is either rich or not kind and vice versa.
If mary is either curious or calm then someone is both not curious and not creative and vice versa.
If paul is not patient then john is not old.
Everyone who is not tall or not humble is not kind.
Everyone who is brave is either not funny or wise.
If someone is patient or not humble then lucy is not generous or not creative and vice versa.
Someone is not calm.
Susan is old or humble.
Fred is funny.
John is both curious and not generous.
Someone is not tall or not brave.
Mary is not patient or not curious.
Someone is funny. | Lucy is not patient. | entailment | ((?[X]:((patient(X)|generous(X))))=>(?[X]:((~quiet(X)<~>wise(X)))))&
((?[X]:((humble(X)<~>~happy(X))))<=>((~wise(john)|~rich(john))))&
(![X]:((~wise(X)|calm(X))=>(brave(X)|~humble(X))))&
(![X]:((rich(X)|~calm(X))<=>(quiet(X)<~>~curious(X))))&
(![X]:(~calm(X)<=>(tall(X)|rich(X))))&
((?[X]:(old(X)))=>(?[X]:((strong(X)&~happy(X)))))&
(![X]:((~patient(X)<~>~humble(X))<=>patient(X)))&
(![X]:((strong(X)|kind(X))<=>(~wise(X)<~>wise(X))))&
(![X]:((~patient(X)&~kind(X))<=>(humble(X)<~>~kind(X))))&
(![X]:((~humble(X)&calm(X))=>(funny(X)&curious(X))))&
(((wise(alice)&humble(alice)))<=>((rich(john)<~>~kind(john))))&
(((curious(mary)<~>calm(mary)))<=>(?[X]:((~curious(X)&~creative(X)))))&
((~patient(paul))=>(~old(john)))&
(![X]:((~tall(X)|~humble(X))=>~kind(X)))&
(![X]:(brave(X)=>(~funny(X)<~>wise(X))))&
((?[X]:((patient(X)|~humble(X))))<=>((~generous(lucy)|~creative(lucy))))&
(?[X]:(~calm(X)))&
((old(susan)|humble(susan)))&
(funny(fred))&
((curious(john)&~generous(john)))&
(?[X]:((~tall(X)|~brave(X))))&
((~patient(mary)|~curious(mary)))&
(?[X]:(funny(X))) | ~patient(lucy) | [
"p6",
"p8",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 5549136937385536018869620
% SZS output start Proof for 5549136937385536018869620
7. ! [X0] : ((~patient(X0) <~> ~humble(X0)) <=> patient(X0)) [input p6]
9. ! [X0] : ((~kind(X0) & ~patient(X0)) <=> (humble(X0) <~> ~kind(X0))) [input p8]
14. ! [X0] : ((~humble(X0) | ~tall(X0)) => ~kind(X0)) [input p13]
24. patient(lucy) [input hypothesis]
34. ! [X0] : (~kind(X0) | (humble(X0) & tall(X0))) [ennf transformation 14]
52. ! [X0] : ((((humble(X0) | patient(X0)) & (~humble(X0) | ~patient(X0))) | ~patient(X0)) & (patient(X0) | ((~patient(X0) | humble(X0)) & (~humble(X0) | patient(X0))))) [nnf transformation 7]
55. ! [X0] : (((~kind(X0) & ~patient(X0)) | ((humble(X0) | kind(X0)) & (~kind(X0) | ~humble(X0)))) & (((kind(X0) | ~humble(X0)) & (~kind(X0) | humble(X0))) | (kind(X0) | patient(X0)))) [nnf transformation 9]
56. ! [X0] : (((~kind(X0) & ~patient(X0)) | ((humble(X0) | kind(X0)) & (~kind(X0) | ~humble(X0)))) & (((kind(X0) | ~humble(X0)) & (~kind(X0) | humble(X0))) | kind(X0) | patient(X0))) [flattening 55]
98. patient(X0) | ~humble(X0) | patient(X0) [cnf transformation 52]
100. ~humble(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 52]
111. ~patient(X0) | humble(X0) | kind(X0) [cnf transformation 56]
130. ~kind(X0) | humble(X0) [cnf transformation 34]
145. patient(lucy) [cnf transformation 24]
150. patient(X0) | ~humble(X0) [duplicate literal removal 98]
151. ~humble(X0) | ~patient(X0) [duplicate literal removal 100]
211. ~humble(X0) [subsumption resolution 150,151]
213. ~patient(X0) | kind(X0) [subsumption resolution 111,211]
264. ~kind(X0) [subsumption resolution 130,211]
294. kind(lucy) [resolution 213,145]
295. $false [subsumption resolution 294,264]
% SZS output end Proof for 5549136937385536018869620
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 lucy is not wise then someone is not quiet and vice versa.
Everyone who is not generous or wise is either curious or happy.
Everyone who is not rich or not funny is wise.
Everyone who is both not curious and patient is not calm and vice versa.
If paul is either not humble or old then someone is either tall or not humble and vice versa.
If alice is either not quiet or not creative then lucy is both not funny and not calm and vice versa.
If someone is either not creative or not happy then someone is brave or kind.
If lucy is not calm then someone is not brave and vice versa.
Everyone who is old is either generous or wise and vice versa.
If lucy is strong then someone is either not kind or not rich and vice versa.
Everyone who is either not curious or rich is not creative or not brave and vice versa.
Everyone who is not kind or not patient is both rich and funny.
Everyone who is brave or not patient is both not funny and old.
If someone is both tall and not kind then alice is not creative and vice versa.
Everyone who is either not funny or not happy is either rich or not generous and vice versa.
Everyone who is both not wise and not old is both happy and kind.
Someone is not funny or wise.
Someone is not humble or happy.
Paul is either kind or not rich.
Fred is not brave.
Paul is not happy.
John is both tall and not wise.
Someone is either strong or happy. | Lucy is generous. | neutral | ((~wise(lucy))<=>(?[X]:(~quiet(X))))&
(![X]:((~generous(X)|wise(X))=>(curious(X)<~>happy(X))))&
(![X]:((~rich(X)|~funny(X))=>wise(X)))&
(![X]:((~curious(X)&patient(X))<=>~calm(X)))&
(((~humble(paul)<~>old(paul)))<=>(?[X]:((tall(X)<~>~humble(X)))))&
(((~quiet(alice)<~>~creative(alice)))<=>((~funny(lucy)&~calm(lucy))))&
((?[X]:((~creative(X)<~>~happy(X))))=>(?[X]:((brave(X)|kind(X)))))&
((~calm(lucy))<=>(?[X]:(~brave(X))))&
(![X]:(old(X)<=>(generous(X)<~>wise(X))))&
((strong(lucy))<=>(?[X]:((~kind(X)<~>~rich(X)))))&
(![X]:((~curious(X)<~>rich(X))<=>(~creative(X)|~brave(X))))&
(![X]:((~kind(X)|~patient(X))=>(rich(X)&funny(X))))&
(![X]:((brave(X)|~patient(X))=>(~funny(X)&old(X))))&
((?[X]:((tall(X)&~kind(X))))<=>(~creative(alice)))&
(![X]:((~funny(X)<~>~happy(X))<=>(rich(X)<~>~generous(X))))&
(![X]:((~wise(X)&~old(X))=>(happy(X)&kind(X))))&
(?[X]:((~funny(X)|wise(X))))&
(?[X]:((~humble(X)|happy(X))))&
((kind(paul)<~>~rich(paul)))&
(~brave(fred))&
(~happy(paul))&
((tall(john)&~wise(john)))&
(?[X]:((strong(X)<~>happy(X)))) | generous(lucy) | [] | null | 0 |
Everyone who is either not wise or kind is both creative and calm and vice versa.
If someone is both wise and kind then someone is not old or rich.
If someone is both patient and happy then john is rich.
If mary is funny then someone is not wise or not strong.
Everyone who is curious or not old is brave or not wise.
Everyone who is tall is not generous and vice versa.
Everyone who is brave is patient and vice versa.
Everyone who is either patient or not strong is both not calm and brave and vice versa.
Everyone who is not strong is kind or not calm and vice versa.
If susan is old or not tall then someone is quiet.
If someone is both quiet and happy then fred is happy or generous and vice versa.
Everyone who is not wise or not rich is both not happy and not brave.
Everyone who is either not curious or not brave is curious or funny and vice versa.
Everyone who is not curious or not calm is not calm and vice versa.
Everyone who is either rich or curious is brave or not quiet and vice versa.
Someone is humble or not brave.
Someone is not kind.
Alice is both calm and not tall.
Susan is not funny or funny.
Someone is both not tall and not wise.
Susan is either not generous or rich.
Someone is either not calm or not quiet. | Alice is kind. | contradiction | (![X]:((~wise(X)<~>kind(X))<=>(creative(X)&calm(X))))&
((?[X]:((wise(X)&kind(X))))=>(?[X]:((~old(X)|rich(X)))))&
((?[X]:((patient(X)&happy(X))))=>(rich(john)))&
((funny(mary))=>(?[X]:((~wise(X)|~strong(X)))))&
(![X]:((curious(X)|~old(X))=>(brave(X)|~wise(X))))&
(![X]:(tall(X)<=>~generous(X)))&
(![X]:(brave(X)<=>patient(X)))&
(![X]:((patient(X)<~>~strong(X))<=>(~calm(X)&brave(X))))&
(![X]:(~strong(X)<=>(kind(X)|~calm(X))))&
(((old(susan)|~tall(susan)))=>(?[X]:(quiet(X))))&
((?[X]:((quiet(X)&happy(X))))<=>((happy(fred)|generous(fred))))&
(![X]:((~wise(X)|~rich(X))=>(~happy(X)&~brave(X))))&
(![X]:((~curious(X)<~>~brave(X))<=>(curious(X)|funny(X))))&
(![X]:((~curious(X)|~calm(X))<=>~calm(X)))&
(![X]:((rich(X)<~>curious(X))<=>(brave(X)|~quiet(X))))&
(?[X]:((humble(X)|~brave(X))))&
(?[X]:(~kind(X)))&
((calm(alice)&~tall(alice)))&
((~funny(susan)|funny(susan)))&
(?[X]:((~tall(X)&~wise(X))))&
((~generous(susan)<~>rich(susan)))&
(?[X]:((~calm(X)<~>~quiet(X)))) | kind(alice) | [
"p6",
"p7",
"p8",
"p12",
"p13",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 5499636175950318987396597
% SZS output start Proof for 5499636175950318987396597
7. ! [X0] : (brave(X0) <=> patient(X0)) [input p6]
8. ! [X0] : ((patient(X0) <~> ~strong(X0)) <=> (brave(X0) & ~calm(X0))) [input p7]
9. ! [X0] : (~strong(X0) <=> (~calm(X0) | kind(X0))) [input p8]
13. ! [X0] : ((~curious(X0) <~> ~brave(X0)) <=> (funny(X0) | curious(X0))) [input p12]
14. ! [X0] : ((~calm(X0) | ~curious(X0)) <=> ~calm(X0)) [input p13]
18. ~tall(alice) & calm(alice) [input p17]
23. kind(alice) [input hypothesis]
41. ! [X0] : ((brave(X0) | ~patient(X0)) & (patient(X0) | ~brave(X0))) [nnf transformation 7]
42. ! [X0] : ((((strong(X0) | ~patient(X0)) & (~strong(X0) | patient(X0))) | (~brave(X0) | calm(X0))) & ((brave(X0) & ~calm(X0)) | ((patient(X0) | strong(X0)) & (~strong(X0) | ~patient(X0))))) [nnf transformation 8]
43. ! [X0] : ((((strong(X0) | ~patient(X0)) & (~strong(X0) | patient(X0))) | ~brave(X0) | calm(X0)) & ((brave(X0) & ~calm(X0)) | ((patient(X0) | strong(X0)) & (~strong(X0) | ~patient(X0))))) [flattening 42]
44. ! [X0] : ((~strong(X0) | (calm(X0) & ~kind(X0))) & ((~calm(X0) | kind(X0)) | strong(X0))) [nnf transformation 9]
45. ! [X0] : ((~strong(X0) | (calm(X0) & ~kind(X0))) & (~calm(X0) | kind(X0) | strong(X0))) [flattening 44]
53. ! [X0] : ((((brave(X0) | curious(X0)) & (~brave(X0) | ~curious(X0))) | (~funny(X0) & ~curious(X0))) & ((funny(X0) | curious(X0)) | ((~curious(X0) | brave(X0)) & (~brave(X0) | curious(X0))))) [nnf transformation 13]
54. ! [X0] : ((((brave(X0) | curious(X0)) & (~brave(X0) | ~curious(X0))) | (~funny(X0) & ~curious(X0))) & (funny(X0) | curious(X0) | ((~curious(X0) | brave(X0)) & (~brave(X0) | curious(X0))))) [flattening 53]
55. ! [X0] : (((~calm(X0) | ~curious(X0)) | calm(X0)) & (~calm(X0) | (calm(X0) & curious(X0)))) [nnf transformation 14]
56. ! [X0] : ((~calm(X0) | ~curious(X0) | calm(X0)) & (~calm(X0) | (calm(X0) & curious(X0)))) [flattening 55]
80. ~brave(X0) | patient(X0) [cnf transformation 41]
81. ~patient(X0) | brave(X0) [cnf transformation 41]
85. brave(X0) | patient(X0) | strong(X0) [cnf transformation 43]
89. ~strong(X0) | ~kind(X0) [cnf transformation 45]
104. ~brave(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 54]
108. ~calm(X0) | curious(X0) [cnf transformation 56]
118. calm(alice) [cnf transformation 18]
127. kind(alice) [cnf transformation 23]
129. ~brave(X0) | ~curious(X0) [duplicate literal removal 104]
164. strong(X0) | patient(X0) [subsumption resolution 85,80]
230. curious(alice) [resolution 108,118]
235. ~kind(X1) | patient(X1) [resolution 164,89]
454. patient(alice) [resolution 235,127]
456. brave(alice) [resolution 454,81]
518. ~curious(alice) [resolution 456,129]
526. $false [subsumption resolution 518,230]
% SZS output end Proof for 5499636175950318987396597
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not happy or funny is tall.
If someone is not kind then john is both patient and not strong.
If susan is both wise and quiet then someone is both not calm and not generous.
Everyone who is either not curious or generous is not patient.
If lucy is either not quiet or creative then susan is both not creative and wise.
Everyone who is both not creative and kind is either not generous or generous.
Everyone who is not curious or funny is creative.
Everyone who is not curious is both not patient and not brave and vice versa.
Everyone who is wise is patient and vice versa.
Everyone who is either wise or not kind is not creative or generous.
Everyone who is not wise or funny is generous or kind and vice versa.
Everyone who is both not patient and strong is humble or tall.
Everyone who is not tall or curious is wise and vice versa.
If alice is not generous or curious then lucy is old.
If someone is both not generous and kind then someone is both calm and not kind and vice versa.
Everyone who is both not happy and not wise is both quiet and strong.
Someone is both strong and generous.
Someone is either not generous or not humble.
Someone is either happy or patient.
Someone is curious or humble.
Paul is both kind and not brave.
Someone is either not patient or tall.
Alice is old or not generous. | John is curious. | entailment | (![X]:((~happy(X)|funny(X))=>tall(X)))&
((?[X]:(~kind(X)))=>((patient(john)&~strong(john))))&
(((wise(susan)&quiet(susan)))=>(?[X]:((~calm(X)&~generous(X)))))&
(![X]:((~curious(X)<~>generous(X))=>~patient(X)))&
(((~quiet(lucy)<~>creative(lucy)))=>((~creative(susan)&wise(susan))))&
(![X]:((~creative(X)&kind(X))=>(~generous(X)<~>generous(X))))&
(![X]:((~curious(X)|funny(X))=>creative(X)))&
(![X]:(~curious(X)<=>(~patient(X)&~brave(X))))&
(![X]:(wise(X)<=>patient(X)))&
(![X]:((wise(X)<~>~kind(X))=>(~creative(X)|generous(X))))&
(![X]:((~wise(X)|funny(X))<=>(generous(X)|kind(X))))&
(![X]:((~patient(X)&strong(X))=>(humble(X)|tall(X))))&
(![X]:((~tall(X)|curious(X))<=>wise(X)))&
(((~generous(alice)|curious(alice)))=>(old(lucy)))&
((?[X]:((~generous(X)&kind(X))))<=>(?[X]:((calm(X)&~kind(X)))))&
(![X]:((~happy(X)&~wise(X))=>(quiet(X)&strong(X))))&
(?[X]:((strong(X)&generous(X))))&
(?[X]:((~generous(X)<~>~humble(X))))&
(?[X]:((happy(X)<~>patient(X))))&
(?[X]:((curious(X)|humble(X))))&
((kind(paul)&~brave(paul)))&
(?[X]:((~patient(X)<~>tall(X))))&
((old(alice)|~generous(alice))) | curious(john) | [
"p1",
"p3",
"p7",
"p8",
"p12",
"p14",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 4615329860955249504974439
% SZS output start Proof for 4615329860955249504974439
2. ? [X0] : ~kind(X0) => (~strong(john) & patient(john)) [input p1]
4. ! [X0] : ((~curious(X0) <~> generous(X0)) => ~patient(X0)) [input p3]
8. ! [X0] : (~curious(X0) <=> (~brave(X0) & ~patient(X0))) [input p7]
9. ! [X0] : (wise(X0) <=> patient(X0)) [input p8]
13. ! [X0] : ((curious(X0) | ~tall(X0)) <=> wise(X0)) [input p12]
15. ? [X0] : (kind(X0) & ~generous(X0)) <=> ? [X0] : (~kind(X0) & calm(X0)) [input p14]
22. ? [X0] : (~patient(X0) <~> tall(X0)) [input p21]
24. ~curious(john) [input hypothesis]
25. ? [X0] : (kind(X0) & ~generous(X0)) <=> ? [X1] : (~kind(X1) & calm(X1)) [rectify 15]
29. (~strong(john) & patient(john)) | ! [X0] : kind(X0) [ennf transformation 2]
32. ! [X0] : (~patient(X0) | (~curious(X0) <=> generous(X0))) [ennf transformation 4]
45. ! [X0] : (~patient(X0) | ((~curious(X0) | ~generous(X0)) & (generous(X0) | curious(X0)))) [nnf transformation 32]
48. ! [X0] : ((~curious(X0) | (brave(X0) | patient(X0))) & ((~brave(X0) & ~patient(X0)) | curious(X0))) [nnf transformation 8]
49. ! [X0] : ((~curious(X0) | brave(X0) | patient(X0)) & ((~brave(X0) & ~patient(X0)) | curious(X0))) [flattening 48]
50. ! [X0] : ((wise(X0) | ~patient(X0)) & (patient(X0) | ~wise(X0))) [nnf transformation 9]
54. ! [X0] : (((curious(X0) | ~tall(X0)) | ~wise(X0)) & (wise(X0) | (~curious(X0) & tall(X0)))) [nnf transformation 13]
55. ! [X0] : ((curious(X0) | ~tall(X0) | ~wise(X0)) & (wise(X0) | (~curious(X0) & tall(X0)))) [flattening 54]
56. (? [X0] : (kind(X0) & ~generous(X0)) | ! [X1] : (kind(X1) | ~calm(X1))) & (? [X1] : (~kind(X1) & calm(X1)) | ! [X0] : (~kind(X0) | generous(X0))) [nnf transformation 25]
57. (? [X0] : (kind(X0) & ~generous(X0)) | ! [X1] : (kind(X1) | ~calm(X1))) & (? [X2] : (~kind(X2) & calm(X2)) | ! [X3] : (~kind(X3) | generous(X3))) [rectify 56]
58. ? [X0] : (kind(X0) & ~generous(X0)) => (kind(sK1) & ~generous(sK1)) [choice axiom]
59. ? [X2] : (~kind(X2) & calm(X2)) => (~kind(sK2) & calm(sK2)) [choice axiom]
60. ((kind(sK1) & ~generous(sK1)) | ! [X1] : (kind(X1) | ~calm(X1))) & ((~kind(sK2) & calm(sK2)) | ! [X3] : (~kind(X3) | generous(X3))) [skolemisation 57,59,58]
71. ? [X0] : ((~tall(X0) | patient(X0)) & (tall(X0) | ~patient(X0))) [nnf transformation 22]
72. ? [X0] : ((~tall(X0) | patient(X0)) & (tall(X0) | ~patient(X0))) => ((~tall(sK7) | patient(sK7)) & (tall(sK7) | ~patient(sK7))) [choice axiom]
73. (~tall(sK7) | patient(sK7)) & (tall(sK7) | ~patient(sK7)) [skolemisation 71,72]
76. patient(john) | kind(X0) [cnf transformation 29]
81. ~curious(X0) | ~patient(X0) | ~generous(X0) [cnf transformation 45]
90. ~patient(X0) | curious(X0) [cnf transformation 49]
93. ~wise(X0) | patient(X0) [cnf transformation 50]
102. wise(X0) | tall(X0) [cnf transformation 55]
106. ~kind(sK2) | ~kind(X3) | generous(X3) [cnf transformation 60]
121. ~tall(sK7) | patient(sK7) [cnf transformation 73]
122. ~curious(john) [cnf transformation 24]
124. 1 <=> ! [X0] : kind(X0) [avatar definition]
125. kind(X0) <- (1) [avatar component clause 124]
132. 3 <=> patient(john) [avatar definition]
134. patient(john) <- (3) [avatar component clause 132]
135. 1 | 3 [avatar split clause 76,132,124]
184. 14 <=> ! [X3] : (~kind(X3) | generous(X3)) [avatar definition]
185. ~kind(X3) | generous(X3) <- (14) [avatar component clause 184]
187. 15 <=> kind(sK2) [avatar definition]
189. ~kind(sK2) <- (~15) [avatar component clause 187]
190. 14 | ~15 [avatar split clause 106,187,184]
226. 23 <=> patient(sK7) [avatar definition]
227. ~patient(sK7) <- (~23) [avatar component clause 226]
228. patient(sK7) <- (23) [avatar component clause 226]
230. 24 <=> tall(sK7) [avatar definition]
232. ~tall(sK7) <- (~24) [avatar component clause 230]
233. 23 | ~24 [avatar split clause 121,230,226]
237. curious(john) <- (3) [resolution 90,134]
238. $false <- (3) [subsumption resolution 237,122]
239. ~3 [avatar contradiction clause 238]
243. patient(X0) | tall(X0) [resolution 102,93]
258. $false <- (1, ~15) [subsumption resolution 189,125]
259. ~1 | 15 [avatar contradiction clause 258]
270. generous(X3) <- (1, 14) [subsumption resolution 185,125]
278. tall(sK7) <- (~23) [resolution 243,227]
279. $false <- (~23, ~24) [subsumption resolution 278,232]
280. 23 | 24 [avatar contradiction clause 279]
283. curious(sK7) <- (23) [resolution 228,90]
290. ~patient(sK7) | ~generous(sK7) <- (23) [resolution 283,81]
292. ~generous(sK7) <- (23) [subsumption resolution 290,228]
293. $false <- (1, 14, 23) [subsumption resolution 292,270]
294. ~1 | ~14 | ~23 [avatar contradiction clause 293]
295. $false [avatar sat refutation 135,190,233,239,259,280,294]
% SZS output end Proof for 4615329860955249504974439
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong then someone is both not generous and tall and vice versa.
Everyone who is both not happy and not funny is not rich.
Everyone who is humble or not generous is both not rich and kind.
If someone is not happy or strong then susan is either not tall or rich.
If lucy is either not rich or rich then lucy is not calm or generous.
If someone is both not humble and quiet then alice is either tall or strong.
If someone is either not brave or funny then someone is not humble.
If lucy is rich or curious then mary is either rich or creative.
Everyone who is not old is old or not kind and vice versa.
Everyone who is both not kind and tall is either not strong or not old.
If someone is both creative and not generous then alice is either not old or not kind.
If john is not rich or creative then susan is not kind.
Everyone who is both creative and wise is not quiet.
If someone is not creative then alice is calm or patient.
Everyone who is either funny or not funny is both patient and not old.
If mary is generous then john is either calm or humble and vice versa.
Alice is patient or humble.
Someone is funny.
Paul is not kind.
Lucy is not wise or tall.
John is either not quiet or brave.
Someone is either not humble or not brave.
Someone is not brave or not tall. | Lucy is not old. | entailment | ((strong(mary))<=>(?[X]:((~generous(X)&tall(X)))))&
(![X]:((~happy(X)&~funny(X))=>~rich(X)))&
(![X]:((humble(X)|~generous(X))=>(~rich(X)&kind(X))))&
((?[X]:((~happy(X)|strong(X))))=>((~tall(susan)<~>rich(susan))))&
(((~rich(lucy)<~>rich(lucy)))=>((~calm(lucy)|generous(lucy))))&
((?[X]:((~humble(X)&quiet(X))))=>((tall(alice)<~>strong(alice))))&
((?[X]:((~brave(X)<~>funny(X))))=>(?[X]:(~humble(X))))&
(((rich(lucy)|curious(lucy)))=>((rich(mary)<~>creative(mary))))&
(![X]:(~old(X)<=>(old(X)|~kind(X))))&
(![X]:((~kind(X)&tall(X))=>(~strong(X)<~>~old(X))))&
((?[X]:((creative(X)&~generous(X))))=>((~old(alice)<~>~kind(alice))))&
(((~rich(john)|creative(john)))=>(~kind(susan)))&
(![X]:((creative(X)&wise(X))=>~quiet(X)))&
((?[X]:(~creative(X)))=>((calm(alice)|patient(alice))))&
(![X]:((funny(X)<~>~funny(X))=>(patient(X)&~old(X))))&
((generous(mary))<=>((calm(john)<~>humble(john))))&
((patient(alice)|humble(alice)))&
(?[X]:(funny(X)))&
(~kind(paul))&
((~wise(lucy)|tall(lucy)))&
((~quiet(john)<~>brave(john)))&
(?[X]:((~humble(X)<~>~brave(X))))&
(?[X]:((~brave(X)|~tall(X)))) | ~old(lucy) | [
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 6801901742039728845761637
% SZS output start Proof for 6801901742039728845761637
9. ! [X0] : (~old(X0) <=> (~kind(X0) | old(X0))) [input p8]
24. old(lucy) [input hypothesis]
58. ! [X0] : ((~old(X0) | (kind(X0) & ~old(X0))) & ((~kind(X0) | old(X0)) | old(X0))) [nnf transformation 9]
59. ! [X0] : ((~old(X0) | (kind(X0) & ~old(X0))) & (~kind(X0) | old(X0) | old(X0))) [flattening 58]
90. ~old(X0) | ~old(X0) [cnf transformation 59]
111. old(lucy) [cnf transformation 24]
115. ~old(X0) [duplicate literal removal 90]
248. $false [subsumption resolution 111,115]
% SZS output end Proof for 6801901742039728845761637
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If john is generous then someone is not old and vice versa.
If someone is either rich or wise then someone is not funny.
Everyone who is funny or curious is both tall and not strong and vice versa.
If someone is either not tall or not curious then someone is quiet and vice versa.
If someone is old or not funny then susan is not happy and vice versa.
If alice is rich then mary is either not curious or creative.
If someone is not creative then someone is creative and vice versa.
Everyone who is either rich or generous is both not funny and wise.
Everyone who is not curious or curious is not generous and vice versa.
Everyone who is either not wise or creative is either not happy or happy and vice versa.
Everyone who is either strong or creative is both not rich and not curious and vice versa.
Everyone who is either not kind or not funny is both not patient and not brave.
Everyone who is both not strong and not rich is either not brave or not patient and vice versa.
Everyone who is happy is not brave or not quiet.
Everyone who is creative is either strong or not old and vice versa.
Someone is both not calm and not kind.
Paul is both calm and not humble.
Fred is strong or happy.
Paul is not creative. | Fred is not kind. | neutral | ((generous(john))<=>(?[X]:(~old(X))))&
((?[X]:((rich(X)<~>wise(X))))=>(?[X]:(~funny(X))))&
(![X]:((funny(X)|curious(X))<=>(tall(X)&~strong(X))))&
((?[X]:((~tall(X)<~>~curious(X))))<=>(?[X]:(quiet(X))))&
((?[X]:((old(X)|~funny(X))))<=>(~happy(susan)))&
((rich(alice))=>((~curious(mary)<~>creative(mary))))&
((?[X]:(~creative(X)))<=>(?[X]:(creative(X))))&
(![X]:((rich(X)<~>generous(X))=>(~funny(X)&wise(X))))&
(![X]:((~curious(X)|curious(X))<=>~generous(X)))&
(![X]:((~wise(X)<~>creative(X))<=>(~happy(X)<~>happy(X))))&
(![X]:((strong(X)<~>creative(X))<=>(~rich(X)&~curious(X))))&
(![X]:((~kind(X)<~>~funny(X))=>(~patient(X)&~brave(X))))&
(![X]:((~strong(X)&~rich(X))<=>(~brave(X)<~>~patient(X))))&
(![X]:(happy(X)=>(~brave(X)|~quiet(X))))&
(![X]:(creative(X)<=>(strong(X)<~>~old(X))))&
(?[X]:((~calm(X)&~kind(X))))&
((calm(paul)&~humble(paul)))&
((strong(fred)|happy(fred)))&
(~creative(paul)) | ~kind(fred) | [] | null | 0 |
If alice is both not funny and curious then lucy is either not creative or not curious and vice versa. If paul is not humble or not calm then alice is not humble and vice versa. Everyone who is quiet is both not quiet and happy and vice versa. If someone is both not funny and old then someone is quiet or calm and vice versa. If someone is both not curious and not quiet then alice is curious or not tall and vice versa. If someone is both not strong and not calm then someone is patient. If someone is not creative then susan is both not calm and not old. If someone is either not old or funny then someone is either curious or funny. If paul is both not wise and strong then susan is funny or not tall and vice versa. If someone is generous or not kind then someone is not quiet and vice versa. If someone is brave then mary is either kind or creative and vice versa. If alice is both not old and quiet then someone is either happy or not happy. Everyone who is kind or not patient is not old. Everyone who is both old and not happy is tall or not happy. Everyone who is not kind is not funny. Alice is either brave or creative. Someone is both not funny and not wise. Someone is not quiet. Someone is quiet or kind. Someone is calm. Someone is not creative. Susan is either not happy or not tall. | Alice is not patient. | neutral | (((~funny(alice)&curious(alice)))<=>((~creative(lucy)<~>~curious(lucy))))&
(((~humble(paul)|~calm(paul)))<=>(~humble(alice)))&
(![X]:(quiet(X)<=>(~quiet(X)&happy(X))))&
((?[X]:((~funny(X)&old(X))))<=>(?[X]:((quiet(X)|calm(X)))))&
((?[X]:((~curious(X)&~quiet(X))))<=>((curious(alice)|~tall(alice))))&
((?[X]:((~strong(X)&~calm(X))))=>(?[X]:(patient(X))))&
((?[X]:(~creative(X)))=>((~calm(susan)&~old(susan))))&
((?[X]:((~old(X)<~>funny(X))))=>(?[X]:((curious(X)<~>funny(X)))))&
(((~wise(paul)&strong(paul)))<=>((funny(susan)|~tall(susan))))&
((?[X]:((generous(X)|~kind(X))))<=>(?[X]:(~quiet(X))))&
((?[X]:(brave(X)))<=>((kind(mary)<~>creative(mary))))&
(((~old(alice)&quiet(alice)))=>(?[X]:((happy(X)<~>~happy(X)))))&
(![X]:((kind(X)|~patient(X))=>~old(X)))&
(![X]:((old(X)&~happy(X))=>(tall(X)|~happy(X))))&
(![X]:(~kind(X)=>~funny(X)))&
((brave(alice)<~>creative(alice)))&
(?[X]:((~funny(X)&~wise(X))))&
(?[X]:(~quiet(X)))&
(?[X]:((quiet(X)|kind(X))))&
(?[X]:(calm(X)))&
(?[X]:(~creative(X)))&
((~happy(susan)<~>~tall(susan))) | ~patient(alice) | [] | null | 0 |
Everyone who is both not humble and not happy is both not curious and patient and vice versa.
Everyone who is not brave or strong is not kind.
Everyone who is not generous is not creative or not rich and vice versa.
If paul is kind then fred is not curious or not humble and vice versa.
If someone is both not calm and not funny then paul is not curious or not funny and vice versa.
Everyone who is both not generous and quiet is not wise or not happy and vice versa.
If someone is brave or not kind then someone is both not humble and patient and vice versa.
If lucy is not generous or not rich then paul is both not creative and humble.
Everyone who is not wise is either quiet or not happy and vice versa.
If paul is either creative or tall then alice is either not patient or not kind and vice versa.
If someone is both brave and not generous then mary is either strong or not funny.
If someone is both wise and strong then someone is either not creative or not humble.
Everyone who is not old or not wise is generous and vice versa.
If someone is both not wise and wise then someone is either not wise or happy and vice versa.
If someone is either not quiet or brave then someone is both not kind and happy and vice versa.
Someone is either not calm or not funny.
Someone is not creative.
Someone is both tall and not happy.
Paul is not quiet or patient.
Someone is not rich.
Someone is both not brave and not strong. | Fred is curious. | entailment | (![X]:((~humble(X)&~happy(X))<=>(~curious(X)&patient(X))))&
(![X]:((~brave(X)|strong(X))=>~kind(X)))&
(![X]:(~generous(X)<=>(~creative(X)|~rich(X))))&
((kind(paul))<=>((~curious(fred)|~humble(fred))))&
((?[X]:((~calm(X)&~funny(X))))<=>((~curious(paul)|~funny(paul))))&
(![X]:((~generous(X)&quiet(X))<=>(~wise(X)|~happy(X))))&
((?[X]:((brave(X)|~kind(X))))<=>(?[X]:((~humble(X)&patient(X)))))&
(((~generous(lucy)|~rich(lucy)))=>((~creative(paul)&humble(paul))))&
(![X]:(~wise(X)<=>(quiet(X)<~>~happy(X))))&
(((creative(paul)<~>tall(paul)))<=>((~patient(alice)<~>~kind(alice))))&
((?[X]:((brave(X)&~generous(X))))=>((strong(mary)<~>~funny(mary))))&
((?[X]:((wise(X)&strong(X))))=>(?[X]:((~creative(X)<~>~humble(X)))))&
(![X]:((~old(X)|~wise(X))<=>generous(X)))&
((?[X]:((~wise(X)&wise(X))))<=>(?[X]:((~wise(X)<~>happy(X)))))&
((?[X]:((~quiet(X)<~>brave(X))))<=>(?[X]:((~kind(X)&happy(X)))))&
(?[X]:((~calm(X)<~>~funny(X))))&
(?[X]:(~creative(X)))&
(?[X]:((tall(X)&~happy(X))))&
((~quiet(paul)|patient(paul)))&
(?[X]:(~rich(X)))&
(?[X]:((~brave(X)&~strong(X)))) | curious(fred) | [
"p1",
"p3",
"p5",
"p12",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8523855985304961829902896
% SZS output start Proof for 8523855985304961829902896
2. ! [X0] : ((strong(X0) | ~brave(X0)) => ~kind(X0)) [input p1]
4. kind(paul) <=> (~humble(fred) | ~curious(fred)) [input p3]
6. ! [X0] : ((quiet(X0) & ~generous(X0)) <=> (~happy(X0) | ~wise(X0))) [input p5]
13. ! [X0] : ((~wise(X0) | ~old(X0)) <=> generous(X0)) [input p12]
14. ? [X0] : (wise(X0) & ~wise(X0)) <=> ? [X0] : (~wise(X0) <~> happy(X0)) [input p13]
15. ? [X0] : (~quiet(X0) <~> brave(X0)) <=> ? [X0] : (happy(X0) & ~kind(X0)) [input p14]
22. ~curious(fred) [input hypothesis]
25. ? [X0] : (wise(X0) & ~wise(X0)) <=> ? [X1] : (~wise(X1) <~> happy(X1)) [rectify 14]
26. ? [X0] : (~quiet(X0) <~> brave(X0)) <=> ? [X1] : (happy(X1) & ~kind(X1)) [rectify 15]
27. ! [X0] : (~kind(X0) | (~strong(X0) & brave(X0))) [ennf transformation 2]
35. (kind(paul) | (humble(fred) & curious(fred))) & ((~humble(fred) | ~curious(fred)) | ~kind(paul)) [nnf transformation 4]
36. (kind(paul) | (humble(fred) & curious(fred))) & (~humble(fred) | ~curious(fred) | ~kind(paul)) [flattening 35]
42. ! [X0] : (((quiet(X0) & ~generous(X0)) | (happy(X0) & wise(X0))) & ((~happy(X0) | ~wise(X0)) | (~quiet(X0) | generous(X0)))) [nnf transformation 6]
43. ! [X0] : (((quiet(X0) & ~generous(X0)) | (happy(X0) & wise(X0))) & (~happy(X0) | ~wise(X0) | ~quiet(X0) | generous(X0))) [flattening 42]
56. ! [X0] : (((~wise(X0) | ~old(X0)) | ~generous(X0)) & (generous(X0) | (wise(X0) & old(X0)))) [nnf transformation 13]
57. ! [X0] : ((~wise(X0) | ~old(X0) | ~generous(X0)) & (generous(X0) | (wise(X0) & old(X0)))) [flattening 56]
58. (? [X0] : (wise(X0) & ~wise(X0)) | ! [X1] : ((~wise(X1) | ~happy(X1)) & (happy(X1) | wise(X1)))) & (? [X1] : ((~happy(X1) | wise(X1)) & (happy(X1) | ~wise(X1))) | ! [X0] : (~wise(X0) | wise(X0))) [nnf transformation 25]
59. (? [X0] : (wise(X0) & ~wise(X0)) | ! [X1] : ((~wise(X1) | ~happy(X1)) & (happy(X1) | wise(X1)))) & (? [X2] : ((~happy(X2) | wise(X2)) & (happy(X2) | ~wise(X2))) | ! [X3] : (~wise(X3) | wise(X3))) [rectify 58]
60. ? [X0] : (wise(X0) & ~wise(X0)) => (wise(sK4) & ~wise(sK4)) [choice axiom]
61. ? [X2] : ((~happy(X2) | wise(X2)) & (happy(X2) | ~wise(X2))) => ((~happy(sK5) | wise(sK5)) & (happy(sK5) | ~wise(sK5))) [choice axiom]
62. ((wise(sK4) & ~wise(sK4)) | ! [X1] : ((~wise(X1) | ~happy(X1)) & (happy(X1) | wise(X1)))) & (((~happy(sK5) | wise(sK5)) & (happy(sK5) | ~wise(sK5))) | ! [X3] : (~wise(X3) | wise(X3))) [skolemisation 59,61,60]
63. (? [X0] : ((~brave(X0) | quiet(X0)) & (brave(X0) | ~quiet(X0))) | ! [X1] : (~happy(X1) | kind(X1))) & (? [X1] : (happy(X1) & ~kind(X1)) | ! [X0] : ((~quiet(X0) | ~brave(X0)) & (brave(X0) | quiet(X0)))) [nnf transformation 26]
64. (? [X0] : ((~brave(X0) | quiet(X0)) & (brave(X0) | ~quiet(X0))) | ! [X1] : (~happy(X1) | kind(X1))) & (? [X2] : (happy(X2) & ~kind(X2)) | ! [X3] : ((~quiet(X3) | ~brave(X3)) & (brave(X3) | quiet(X3)))) [rectify 63]
65. ? [X0] : ((~brave(X0) | quiet(X0)) & (brave(X0) | ~quiet(X0))) => ((~brave(sK6) | quiet(sK6)) & (brave(sK6) | ~quiet(sK6))) [choice axiom]
66. ? [X2] : (happy(X2) & ~kind(X2)) => (happy(sK7) & ~kind(sK7)) [choice axiom]
67. (((~brave(sK6) | quiet(sK6)) & (brave(sK6) | ~quiet(sK6))) | ! [X1] : (~happy(X1) | kind(X1))) & ((happy(sK7) & ~kind(sK7)) | ! [X3] : ((~quiet(X3) | ~brave(X3)) & (brave(X3) | quiet(X3)))) [skolemisation 64,66,65]
83. ~kind(X0) | brave(X0) [cnf transformation 27]
89. kind(paul) | curious(fred) [cnf transformation 36]
97. ~generous(X0) | wise(X0) [cnf transformation 43]
100. quiet(X0) | happy(X0) [cnf transformation 43]
127. generous(X0) | wise(X0) [cnf transformation 57]
132. ~wise(sK4) | ~wise(X1) | ~happy(X1) [cnf transformation 62]
138. happy(sK7) | ~quiet(X3) | ~brave(X3) [cnf transformation 67]
150. ~curious(fred) [cnf transformation 22]
156. 2 <=> kind(paul) [avatar definition]
158. kind(paul) <- (2) [avatar component clause 156]
161. 3 <=> curious(fred) [avatar definition]
164. 3 | 2 [avatar split clause 89,156,161]
276. wise(X0) [subsumption resolution 127,97]
277. ~wise(X1) | ~happy(X1) [subsumption resolution 132,276]
278. ~happy(X1) [subsumption resolution 277,276]
279. ~quiet(X3) | ~brave(X3) [subsumption resolution 138,278]
292. 28 <=> quiet(paul) [avatar definition]
293. quiet(paul) <- (28) [avatar component clause 292]
294. ~quiet(paul) <- (~28) [avatar component clause 292]
300. ~3 [avatar split clause 150,161]
302. brave(paul) <- (2) [resolution 83,158]
304. happy(paul) <- (~28) [resolution 100,294]
305. $false <- (~28) [subsumption resolution 304,278]
306. 28 [avatar contradiction clause 305]
309. ~brave(paul) <- (28) [resolution 279,293]
312. $false <- (2, 28) [subsumption resolution 309,302]
313. ~2 | ~28 [avatar contradiction clause 312]
314. $false [avatar sat refutation 164,300,306,313]
% SZS output end Proof for 8523855985304961829902896
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old or humble then someone is both not funny and funny. Everyone who is either not happy or generous is either not rich or humble and vice versa. Everyone who is either humble or not kind is either humble or not old. Everyone who is both not old and kind is not generous. If lucy is humble or not creative then paul is patient. If someone is strong or not curious then alice is not rich or not creative and vice versa. Everyone who is not rich is not patient. If lucy is not strong then someone is both rich and not brave and vice versa. If alice is either funny or creative then paul is patient or not calm and vice versa. Everyone who is not kind is either not happy or funny. Everyone who is both not humble and not old is either not old or not humble and vice versa. If someone is both kind and not kind then lucy is both not creative and quiet. Everyone who is not brave is either old or quiet. If lucy is humble or not funny then john is both not curious and quiet. If fred is old then john is funny or happy. Someone is either patient or not humble. Fred is both not strong and not tall. Someone is both rich and generous. Susan is tall or strong. Alice is either happy or not old. | John is tall. | neutral | ((?[X]:((old(X)<~>humble(X))))=>(?[X]:((~funny(X)&funny(X)))))&
(![X]:((~happy(X)<~>generous(X))<=>(~rich(X)<~>humble(X))))&
(![X]:((humble(X)<~>~kind(X))=>(humble(X)<~>~old(X))))&
(![X]:((~old(X)&kind(X))=>~generous(X)))&
(((humble(lucy)|~creative(lucy)))=>(patient(paul)))&
((?[X]:((strong(X)|~curious(X))))<=>((~rich(alice)|~creative(alice))))&
(![X]:(~rich(X)=>~patient(X)))&
((~strong(lucy))<=>(?[X]:((rich(X)&~brave(X)))))&
(((funny(alice)<~>creative(alice)))<=>((patient(paul)|~calm(paul))))&
(![X]:(~kind(X)=>(~happy(X)<~>funny(X))))&
(![X]:((~humble(X)&~old(X))<=>(~old(X)<~>~humble(X))))&
((?[X]:((kind(X)&~kind(X))))=>((~creative(lucy)&quiet(lucy))))&
(![X]:(~brave(X)=>(old(X)<~>quiet(X))))&
(((humble(lucy)|~funny(lucy)))=>((~curious(john)&quiet(john))))&
((old(fred))=>((funny(john)|happy(john))))&
(?[X]:((patient(X)<~>~humble(X))))&
((~strong(fred)&~tall(fred)))&
(?[X]:((rich(X)&generous(X))))&
((tall(susan)|strong(susan)))&
((happy(alice)<~>~old(alice))) | tall(john) | [] | null | 0 |
If john is both brave and not tall then paul is not rich.
Everyone who is calm is either not old or creative and vice versa.
If someone is either patient or strong then susan is old.
Everyone who is either not creative or brave is both humble and not kind.
Everyone who is not kind is not brave or wise.
Everyone who is both not strong and quiet is either not creative or not generous and vice versa.
If paul is not creative or happy then fred is not generous.
If john is not kind then john is quiet or not generous.
Everyone who is tall or old is curious or strong.
If mary is either not happy or happy then lucy is old or not quiet and vice versa.
If john is either not brave or not strong then someone is not humble or strong.
If someone is both not creative and not kind then alice is either not patient or not happy.
If susan is either happy or not brave then someone is not humble and vice versa.
Everyone who is both not humble and strong is not tall or generous and vice versa.
If lucy is creative or not curious then someone is either not tall or tall.
Everyone who is happy or strong is not tall.
John is either not patient or not old.
Alice is happy.
Someone is creative or humble.
Someone is both calm and strong.
Mary is both not tall and creative.
John is generous.
Susan is either generous or not wise.
Someone is not kind or generous. | John is creative. | entailment | (((brave(john)&~tall(john)))=>(~rich(paul)))&
(![X]:(calm(X)<=>(~old(X)<~>creative(X))))&
((?[X]:((patient(X)<~>strong(X))))=>(old(susan)))&
(![X]:((~creative(X)<~>brave(X))=>(humble(X)&~kind(X))))&
(![X]:(~kind(X)=>(~brave(X)|wise(X))))&
(![X]:((~strong(X)&quiet(X))<=>(~creative(X)<~>~generous(X))))&
(((~creative(paul)|happy(paul)))=>(~generous(fred)))&
((~kind(john))=>((quiet(john)|~generous(john))))&
(![X]:((tall(X)|old(X))=>(curious(X)|strong(X))))&
(((~happy(mary)<~>happy(mary)))<=>((old(lucy)|~quiet(lucy))))&
(((~brave(john)<~>~strong(john)))=>(?[X]:((~humble(X)|strong(X)))))&
((?[X]:((~creative(X)&~kind(X))))=>((~patient(alice)<~>~happy(alice))))&
(((happy(susan)<~>~brave(susan)))<=>(?[X]:(~humble(X))))&
(![X]:((~humble(X)&strong(X))<=>(~tall(X)|generous(X))))&
(((creative(lucy)|~curious(lucy)))=>(?[X]:((~tall(X)<~>tall(X)))))&
(![X]:((happy(X)|strong(X))=>~tall(X)))&
((~patient(john)<~>~old(john)))&
(happy(alice))&
(?[X]:((creative(X)|humble(X))))&
(?[X]:((calm(X)&strong(X))))&
((~tall(mary)&creative(mary)))&
(generous(john))&
((generous(susan)<~>~wise(susan)))&
(?[X]:((~kind(X)|generous(X)))) | creative(john) | [
"p5",
"p13",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 8406690726800070159183919
% SZS output start Proof for 8406690726800070159183919
6. ! [X0] : ((quiet(X0) & ~strong(X0)) <=> (~creative(X0) <~> ~generous(X0))) [input p5]
14. ! [X0] : ((strong(X0) & ~humble(X0)) <=> (generous(X0) | ~tall(X0))) [input p13]
22. generous(john) [input p21]
25. ~creative(john) [input hypothesis]
45. ! [X0] : (((quiet(X0) & ~strong(X0)) | ((~creative(X0) | generous(X0)) & (~generous(X0) | creative(X0)))) & (((generous(X0) | creative(X0)) & (~generous(X0) | ~creative(X0))) | (~quiet(X0) | strong(X0)))) [nnf transformation 6]
46. ! [X0] : (((quiet(X0) & ~strong(X0)) | ((~creative(X0) | generous(X0)) & (~generous(X0) | creative(X0)))) & (((generous(X0) | creative(X0)) & (~generous(X0) | ~creative(X0))) | ~quiet(X0) | strong(X0))) [flattening 45]
57. ! [X0] : (((strong(X0) & ~humble(X0)) | (~generous(X0) & tall(X0))) & ((generous(X0) | ~tall(X0)) | (~strong(X0) | humble(X0)))) [nnf transformation 14]
58. ! [X0] : (((strong(X0) & ~humble(X0)) | (~generous(X0) & tall(X0))) & (generous(X0) | ~tall(X0) | ~strong(X0) | humble(X0))) [flattening 57]
81. ~generous(X0) | ~strong(X0) | creative(X0) [cnf transformation 46]
106. ~generous(X0) | strong(X0) [cnf transformation 58]
119. generous(john) [cnf transformation 22]
123. ~creative(john) [cnf transformation 25]
161. 9 <=> generous(john) [avatar definition]
162. generous(john) <- (9) [avatar component clause 161]
180. 13 <=> strong(john) [avatar definition]
182. strong(john) <- (13) [avatar component clause 180]
249. 9 [avatar split clause 119,161]
270. strong(john) <- (9) [resolution 106,162]
271. 13 | ~9 [avatar split clause 270,161,180]
364. ~strong(john) | creative(john) <- (9) [resolution 81,162]
365. creative(john) <- (9, 13) [subsumption resolution 364,182]
366. $false <- (9, 13) [subsumption resolution 365,123]
367. ~9 | ~13 [avatar contradiction clause 366]
368. $false [avatar sat refutation 249,271,367]
% SZS output end Proof for 8406690726800070159183919
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not wise or patient is both not rich and not humble and vice versa.
If someone is not happy or not humble then someone is either not brave or not humble.
If someone is not strong or calm then someone is either calm or not humble.
If someone is either not creative or not kind then lucy is strong and vice versa.
If fred is either not patient or not humble then alice is either not quiet or tall and vice versa.
If mary is happy then someone is not brave or patient and vice versa.
Everyone who is wise or not curious is both funny and generous.
Everyone who is both not wise and not tall is either not brave or rich.
If someone is either strong or not strong then lucy is either calm or not wise.
Everyone who is both not happy and not quiet is generous or brave.
Everyone who is either not curious or tall is either quiet or happy.
Everyone who is either happy or not patient is not curious or not creative and vice versa.
If lucy is both creative and not creative then someone is not curious or rich and vice versa.
Everyone who is not tall or not generous is not tall or patient.
If someone is either not creative or not old then someone is funny or old and vice versa.
If mary is either not creative or tall then john is funny or not patient.
Someone is either not happy or kind.
Fred is either rich or wise.
Someone is not generous or happy.
Lucy is either humble or generous.
Someone is either not old or kind.
Someone is either not wise or funny.
Paul is not brave.
Mary is either not patient or not happy. | Mary is creative. | entailment | (![X]:((~wise(X)|patient(X))<=>(~rich(X)&~humble(X))))&
((?[X]:((~happy(X)|~humble(X))))=>(?[X]:((~brave(X)<~>~humble(X)))))&
((?[X]:((~strong(X)|calm(X))))=>(?[X]:((calm(X)<~>~humble(X)))))&
((?[X]:((~creative(X)<~>~kind(X))))<=>(strong(lucy)))&
(((~patient(fred)<~>~humble(fred)))<=>((~quiet(alice)<~>tall(alice))))&
((happy(mary))<=>(?[X]:((~brave(X)|patient(X)))))&
(![X]:((wise(X)|~curious(X))=>(funny(X)&generous(X))))&
(![X]:((~wise(X)&~tall(X))=>(~brave(X)<~>rich(X))))&
((?[X]:((strong(X)<~>~strong(X))))=>((calm(lucy)<~>~wise(lucy))))&
(![X]:((~happy(X)&~quiet(X))=>(generous(X)|brave(X))))&
(![X]:((~curious(X)<~>tall(X))=>(quiet(X)<~>happy(X))))&
(![X]:((happy(X)<~>~patient(X))<=>(~curious(X)|~creative(X))))&
(((creative(lucy)&~creative(lucy)))<=>(?[X]:((~curious(X)|rich(X)))))&
(![X]:((~tall(X)|~generous(X))=>(~tall(X)|patient(X))))&
((?[X]:((~creative(X)<~>~old(X))))<=>(?[X]:((funny(X)|old(X)))))&
(((~creative(mary)<~>tall(mary)))=>((funny(john)|~patient(john))))&
(?[X]:((~happy(X)<~>kind(X))))&
((rich(fred)<~>wise(fred)))&
(?[X]:((~generous(X)|happy(X))))&
((humble(lucy)<~>generous(lucy)))&
(?[X]:((~old(X)<~>kind(X))))&
(?[X]:((~wise(X)<~>funny(X))))&
(~brave(paul))&
((~patient(mary)<~>~happy(mary))) | creative(mary) | [
"p5",
"p11",
"p22",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 5789425693892224370549783
% SZS output start Proof for 5789425693892224370549783
6. happy(mary) <=> ? [X0] : (patient(X0) | ~brave(X0)) [input p5]
12. ! [X0] : ((happy(X0) <~> ~patient(X0)) <=> (~creative(X0) | ~curious(X0))) [input p11]
23. ~brave(paul) [input p22]
24. ~patient(mary) <~> ~happy(mary) [input p23]
25. ~creative(mary) [input hypothesis]
57. (happy(mary) | ! [X0] : (~patient(X0) & brave(X0))) & (? [X0] : (patient(X0) | ~brave(X0)) | ~happy(mary)) [nnf transformation 6]
58. (happy(mary) | ! [X0] : (~patient(X0) & brave(X0))) & (? [X1] : (patient(X1) | ~brave(X1)) | ~happy(mary)) [rectify 57]
59. ? [X1] : (patient(X1) | ~brave(X1)) => (patient(sK3) | ~brave(sK3)) [choice axiom]
60. (happy(mary) | ! [X0] : (~patient(X0) & brave(X0))) & ((patient(sK3) | ~brave(sK3)) | ~happy(mary)) [skolemisation 58,59]
64. ! [X0] : ((((patient(X0) | ~happy(X0)) & (~patient(X0) | happy(X0))) | (creative(X0) & curious(X0))) & ((~creative(X0) | ~curious(X0)) | ((happy(X0) | patient(X0)) & (~patient(X0) | ~happy(X0))))) [nnf transformation 12]
65. ! [X0] : ((((patient(X0) | ~happy(X0)) & (~patient(X0) | happy(X0))) | (creative(X0) & curious(X0))) & (~creative(X0) | ~curious(X0) | ((happy(X0) | patient(X0)) & (~patient(X0) | ~happy(X0))))) [flattening 64]
90. (happy(mary) | patient(mary)) & (~happy(mary) | ~patient(mary)) [nnf transformation 24]
117. happy(mary) | brave(X0) [cnf transformation 60]
139. ~happy(X0) | patient(X0) | creative(X0) [cnf transformation 65]
166. ~brave(paul) [cnf transformation 23]
167. ~happy(mary) | ~patient(mary) [cnf transformation 90]
169. ~creative(mary) [cnf transformation 25]
262. 19 <=> happy(mary) [avatar definition]
264. happy(mary) <- (19) [avatar component clause 262]
267. 20 <=> ! [X0] : brave(X0) [avatar definition]
268. brave(X0) <- (20) [avatar component clause 267]
269. 20 | 19 [avatar split clause 117,262,267]
348. 38 <=> creative(mary) [avatar definition]
350. ~creative(mary) <- (~38) [avatar component clause 348]
412. 51 <=> patient(mary) [avatar definition]
413. ~patient(mary) <- (~51) [avatar component clause 412]
416. ~51 | ~19 [avatar split clause 167,262,412]
417. ~38 [avatar split clause 169,348]
434. patient(mary) | creative(mary) <- (19) [resolution 139,264]
435. creative(mary) <- (19, ~51) [subsumption resolution 434,413]
436. $false <- (19, ~38, ~51) [subsumption resolution 435,350]
437. ~19 | 38 | 51 [avatar contradiction clause 436]
438. $false <- (20) [resolution 268,166]
441. ~20 [avatar contradiction clause 438]
442. $false [avatar sat refutation 269,416,417,437,441]
% SZS output end Proof for 5789425693892224370549783
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either happy or not creative is calm or kind and vice versa.
Everyone who is either not happy or curious is both quiet and not old and vice versa.
Everyone who is not strong is calm or not tall and vice versa.
If someone is not calm or not brave then paul is brave and vice versa.
If someone is both kind and not brave then john is either not generous or calm.
Everyone who is both not calm and not wise is both brave and not generous.
Everyone who is both humble and tall is either wise or not rich and vice versa.
Everyone who is not humble or strong is either not generous or not calm.
If someone is kind then someone is either not rich or patient and vice versa.
If someone is either not wise or not old then john is not strong and vice versa.
Everyone who is patient is not happy and vice versa.
If someone is not humble then mary is not generous.
If someone is not creative or kind then fred is creative or not patient.
If someone is both generous and rich then someone is either old or quiet and vice versa.
Everyone who is kind or not old is both not funny and quiet.
If someone is both not funny and not curious then mary is calm and vice versa.
Alice is old or not kind.
Someone is both brave and not wise.
Lucy is both happy and not curious.
Someone is not old.
Someone is quiet or not brave.
John is not wise or not old.
Someone is both not funny and not curious.
John is not quiet or strong. | Paul is not brave. | contradiction | (![X]:((happy(X)<~>~creative(X))<=>(calm(X)|kind(X))))&
(![X]:((~happy(X)<~>curious(X))<=>(quiet(X)&~old(X))))&
(![X]:(~strong(X)<=>(calm(X)|~tall(X))))&
((?[X]:((~calm(X)|~brave(X))))<=>(brave(paul)))&
((?[X]:((kind(X)&~brave(X))))=>((~generous(john)<~>calm(john))))&
(![X]:((~calm(X)&~wise(X))=>(brave(X)&~generous(X))))&
(![X]:((humble(X)&tall(X))<=>(wise(X)<~>~rich(X))))&
(![X]:((~humble(X)|strong(X))=>(~generous(X)<~>~calm(X))))&
((?[X]:(kind(X)))<=>(?[X]:((~rich(X)<~>patient(X)))))&
((?[X]:((~wise(X)<~>~old(X))))<=>(~strong(john)))&
(![X]:(patient(X)<=>~happy(X)))&
((?[X]:(~humble(X)))=>(~generous(mary)))&
((?[X]:((~creative(X)|kind(X))))=>((creative(fred)|~patient(fred))))&
((?[X]:((generous(X)&rich(X))))<=>(?[X]:((old(X)<~>quiet(X)))))&
(![X]:((kind(X)|~old(X))=>(~funny(X)&quiet(X))))&
((?[X]:((~funny(X)&~curious(X))))<=>(calm(mary)))&
((old(alice)|~kind(alice)))&
(?[X]:((brave(X)&~wise(X))))&
((happy(lucy)&~curious(lucy)))&
(?[X]:(~old(X)))&
(?[X]:((quiet(X)|~brave(X))))&
((~wise(john)|~old(john)))&
(?[X]:((~funny(X)&~curious(X))))&
((~quiet(john)|strong(john))) | ~brave(paul) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 6044764763317400570543759
% SZS output start Proof for 6044764763317400570543759
4. ? [X0] : (~brave(X0) | ~calm(X0)) <=> brave(paul) [input p3]
25. ~brave(paul) [input hypothesis]
42. (? [X0] : (~brave(X0) | ~calm(X0)) | ~brave(paul)) & (brave(paul) | ! [X0] : (brave(X0) & calm(X0))) [nnf transformation 4]
43. (? [X0] : (~brave(X0) | ~calm(X0)) | ~brave(paul)) & (brave(paul) | ! [X1] : (brave(X1) & calm(X1))) [rectify 42]
44. ? [X0] : (~brave(X0) | ~calm(X0)) => (~brave(sK0) | ~calm(sK0)) [choice axiom]
45. ((~brave(sK0) | ~calm(sK0)) | ~brave(paul)) & (brave(paul) | ! [X1] : (brave(X1) & calm(X1))) [skolemisation 43,44]
93. brave(paul) | brave(X1) [cnf transformation 45]
146. ~brave(paul) [cnf transformation 25]
148. 1 <=> brave(paul) [avatar definition]
150. ~brave(paul) <- (~1) [avatar component clause 148]
161. 4 <=> ! [X1] : brave(X1) [avatar definition]
162. brave(X1) <- (4) [avatar component clause 161]
163. 4 | 1 [avatar split clause 93,148,161]
331. ~1 [avatar split clause 146,148]
336. $false <- (~1, 4) [subsumption resolution 150,162]
337. 1 | ~4 [avatar contradiction clause 336]
338. $false [avatar sat refutation 163,331,337]
% SZS output end Proof for 6044764763317400570543759
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind then john is not funny. Everyone who is either tall or not rich is both not happy and patient and vice versa. Everyone who is both happy and old is happy or curious and vice versa. If paul is either rich or not kind then someone is both not happy and not kind. Everyone who is either curious or not curious is both not brave and not old and vice versa. If lucy is not strong then paul is both strong and not quiet. Everyone who is both kind and not funny is curious or quiet and vice versa. Everyone who is funny or not creative is not patient or not funny and vice versa. If someone is not curious then mary is patient. Everyone who is both quiet and kind is either not creative or not wise. Everyone who is either not patient or not wise is kind or rich. If lucy is not curious then mary is either old or strong. Everyone who is both strong and not quiet is either not brave or patient. If lucy is both not happy and rich then mary is calm or not creative and vice versa. If susan is creative or not strong then someone is either calm or strong. Alice is either brave or strong. Lucy is not old. Someone is not rich or kind. Fred is not old or brave. Mary is not brave or not rich. Lucy is either creative or not strong. Someone is humble or wise. | John is not creative. | entailment | ((kind(mary))=>(~funny(john)))&
(![X]:((tall(X)<~>~rich(X))<=>(~happy(X)&patient(X))))&
(![X]:((happy(X)&old(X))<=>(happy(X)|curious(X))))&
(((rich(paul)<~>~kind(paul)))=>(?[X]:((~happy(X)&~kind(X)))))&
(![X]:((curious(X)<~>~curious(X))<=>(~brave(X)&~old(X))))&
((~strong(lucy))=>((strong(paul)&~quiet(paul))))&
(![X]:((kind(X)&~funny(X))<=>(curious(X)|quiet(X))))&
(![X]:((funny(X)|~creative(X))<=>(~patient(X)|~funny(X))))&
((?[X]:(~curious(X)))=>(patient(mary)))&
(![X]:((quiet(X)&kind(X))=>(~creative(X)<~>~wise(X))))&
(![X]:((~patient(X)<~>~wise(X))=>(kind(X)|rich(X))))&
((~curious(lucy))=>((old(mary)<~>strong(mary))))&
(![X]:((strong(X)&~quiet(X))=>(~brave(X)<~>patient(X))))&
(((~happy(lucy)&rich(lucy)))<=>((calm(mary)|~creative(mary))))&
(((creative(susan)|~strong(susan)))=>(?[X]:((calm(X)<~>strong(X)))))&
((brave(alice)<~>strong(alice)))&
(~old(lucy))&
(?[X]:((~rich(X)|kind(X))))&
((~old(fred)|brave(fred)))&
((~brave(mary)|~rich(mary)))&
((creative(lucy)<~>~strong(lucy)))&
(?[X]:((humble(X)|wise(X)))) | ~creative(john) | [
"p0",
"p2",
"p4",
"p6",
"p7",
"p8",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 8944906034977927503557154
% SZS output start Proof for 8944906034977927503557154
1. kind(mary) => ~funny(john) [input p0]
3. ! [X0] : ((old(X0) & happy(X0)) <=> (curious(X0) | happy(X0))) [input p2]
5. ! [X0] : ((curious(X0) <~> ~curious(X0)) <=> (~old(X0) & ~brave(X0))) [input p4]
7. ! [X0] : ((~funny(X0) & kind(X0)) <=> (quiet(X0) | curious(X0))) [input p6]
8. ! [X0] : ((~creative(X0) | funny(X0)) <=> (~funny(X0) | ~patient(X0))) [input p7]
9. ? [X0] : ~curious(X0) => patient(mary) [input p8]
12. ~curious(lucy) => (old(mary) <~> strong(mary)) [input p11]
13. ! [X0] : ((~quiet(X0) & strong(X0)) => (~brave(X0) <~> patient(X0))) [input p12]
23. creative(john) [input hypothesis]
25. ~funny(john) | ~kind(mary) [ennf transformation 1]
28. patient(mary) | ! [X0] : curious(X0) [ennf transformation 9]
33. (old(mary) <~> strong(mary)) | curious(lucy) [ennf transformation 12]
34. ! [X0] : ((~brave(X0) <~> patient(X0)) | (quiet(X0) | ~strong(X0))) [ennf transformation 13]
35. ! [X0] : ((~brave(X0) <~> patient(X0)) | quiet(X0) | ~strong(X0)) [flattening 34]
39. ! [X0] : (((old(X0) & happy(X0)) | (~curious(X0) & ~happy(X0))) & ((curious(X0) | happy(X0)) | (~old(X0) | ~happy(X0)))) [nnf transformation 3]
40. ! [X0] : (((old(X0) & happy(X0)) | (~curious(X0) & ~happy(X0))) & (curious(X0) | happy(X0) | ~old(X0) | ~happy(X0))) [flattening 39]
44. ! [X0] : ((((curious(X0) | ~curious(X0)) & (~curious(X0) | curious(X0))) | (old(X0) | brave(X0))) & ((~old(X0) & ~brave(X0)) | ((curious(X0) | curious(X0)) & (~curious(X0) | ~curious(X0))))) [nnf transformation 5]
45. ! [X0] : ((((curious(X0) | ~curious(X0)) & (~curious(X0) | curious(X0))) | old(X0) | brave(X0)) & ((~old(X0) & ~brave(X0)) | ((curious(X0) | curious(X0)) & (~curious(X0) | ~curious(X0))))) [flattening 44]
46. ! [X0] : (((~funny(X0) & kind(X0)) | (~quiet(X0) & ~curious(X0))) & ((quiet(X0) | curious(X0)) | (funny(X0) | ~kind(X0)))) [nnf transformation 7]
47. ! [X0] : (((~funny(X0) & kind(X0)) | (~quiet(X0) & ~curious(X0))) & (quiet(X0) | curious(X0) | funny(X0) | ~kind(X0))) [flattening 46]
48. ! [X0] : (((~creative(X0) | funny(X0)) | (funny(X0) & patient(X0))) & ((~funny(X0) | ~patient(X0)) | (creative(X0) & ~funny(X0)))) [nnf transformation 8]
49. ! [X0] : ((~creative(X0) | funny(X0) | (funny(X0) & patient(X0))) & (~funny(X0) | ~patient(X0) | (creative(X0) & ~funny(X0)))) [flattening 48]
52. ((~strong(mary) | ~old(mary)) & (strong(mary) | old(mary))) | curious(lucy) [nnf transformation 33]
53. ! [X0] : (((~patient(X0) | brave(X0)) & (patient(X0) | ~brave(X0))) | quiet(X0) | ~strong(X0)) [nnf transformation 35]
63. ~funny(john) | ~kind(mary) [cnf transformation 25]
74. ~curious(X0) | old(X0) [cnf transformation 40]
80. ~brave(X0) | curious(X0) | curious(X0) [cnf transformation 45]
81. ~old(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 45]
82. ~old(X0) | curious(X0) | curious(X0) [cnf transformation 45]
89. ~quiet(X0) | kind(X0) [cnf transformation 47]
95. ~creative(X0) | funny(X0) | funny(X0) [cnf transformation 49]
96. patient(mary) | curious(X0) [cnf transformation 28]
101. strong(mary) | old(mary) | curious(lucy) [cnf transformation 52]
104. ~patient(X0) | brave(X0) | quiet(X0) | ~strong(X0) [cnf transformation 53]
122. creative(john) [cnf transformation 23]
124. ~creative(X0) | funny(X0) [duplicate literal removal 95]
126. ~brave(X0) | curious(X0) [duplicate literal removal 80]
127. ~old(X0) | ~curious(X0) [duplicate literal removal 81]
128. ~old(X0) | curious(X0) [duplicate literal removal 82]
130. 1 <=> kind(mary) [avatar definition]
132. ~kind(mary) <- (~1) [avatar component clause 130]
134. 2 <=> funny(john) [avatar definition]
137. ~1 | ~2 [avatar split clause 63,134,130]
158. ~curious(X0) [subsumption resolution 127,74]
159. ~brave(X0) [subsumption resolution 126,158]
175. patient(mary) [subsumption resolution 96,158]
180. 10 <=> old(mary) [avatar definition]
181. old(mary) <- (10) [avatar component clause 180]
184. 11 <=> strong(mary) [avatar definition]
185. strong(mary) <- (11) [avatar component clause 184]
188. strong(mary) | old(mary) [subsumption resolution 101,158]
189. 10 | 11 [avatar split clause 188,184,180]
190. ~strong(X0) | quiet(X0) | ~patient(X0) [subsumption resolution 104,159]
250. funny(john) [resolution 124,122]
252. 2 [avatar split clause 250,134]
255. curious(mary) <- (10) [resolution 128,181]
256. $false <- (10) [subsumption resolution 255,158]
257. ~10 [avatar contradiction clause 256]
271. quiet(mary) | ~patient(mary) <- (11) [resolution 190,185]
275. quiet(mary) <- (11) [subsumption resolution 271,175]
297. kind(mary) <- (11) [resolution 275,89]
299. $false <- (~1, 11) [subsumption resolution 297,132]
300. 1 | ~11 [avatar contradiction clause 299]
301. $false [avatar sat refutation 137,189,252,257,300]
% SZS output end Proof for 8944906034977927503557154
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not happy is either kind or not brave and vice versa.
Everyone who is not funny is tall and vice versa.
Everyone who is both not patient and not curious is either generous or not generous and vice versa.
If alice is either not strong or not old then alice is not quiet and vice versa.
Everyone who is either calm or tall is wise or kind and vice versa.
If mary is either not kind or patient then someone is both brave and not funny.
Everyone who is both not creative and not curious is both not funny and not curious.
Everyone who is either not generous or kind is both not old and not rich and vice versa.
Everyone who is both brave and old is brave or old and vice versa.
Everyone who is brave or kind is either not kind or quiet.
Everyone who is both not quiet and not happy is creative or not brave.
Everyone who is either not tall or calm is both not happy and not rich and vice versa.
Everyone who is either not quiet or wise is both rich and calm and vice versa.
If someone is old then fred is both humble and not rich and vice versa.
If someone is either not generous or strong then mary is not humble.
If lucy is either tall or not funny then someone is tall and vice versa.
Someone is not calm or not humble.
John is both happy and not generous.
Susan is both not generous and rich.
Someone is not generous.
Someone is either generous or wise. | Mary is patient. | contradiction | (![X]:(~happy(X)<=>(kind(X)<~>~brave(X))))&
(![X]:(~funny(X)<=>tall(X)))&
(![X]:((~patient(X)&~curious(X))<=>(generous(X)<~>~generous(X))))&
(((~strong(alice)<~>~old(alice)))<=>(~quiet(alice)))&
(![X]:((calm(X)<~>tall(X))<=>(wise(X)|kind(X))))&
(((~kind(mary)<~>patient(mary)))=>(?[X]:((brave(X)&~funny(X)))))&
(![X]:((~creative(X)&~curious(X))=>(~funny(X)&~curious(X))))&
(![X]:((~generous(X)<~>kind(X))<=>(~old(X)&~rich(X))))&
(![X]:((brave(X)&old(X))<=>(brave(X)|old(X))))&
(![X]:((brave(X)|kind(X))=>(~kind(X)<~>quiet(X))))&
(![X]:((~quiet(X)&~happy(X))=>(creative(X)|~brave(X))))&
(![X]:((~tall(X)<~>calm(X))<=>(~happy(X)&~rich(X))))&
(![X]:((~quiet(X)<~>wise(X))<=>(rich(X)&calm(X))))&
((?[X]:(old(X)))<=>((humble(fred)&~rich(fred))))&
((?[X]:((~generous(X)<~>strong(X))))=>(~humble(mary)))&
(((tall(lucy)<~>~funny(lucy)))<=>(?[X]:(tall(X))))&
(?[X]:((~calm(X)|~humble(X))))&
((happy(john)&~generous(john)))&
((~generous(susan)&rich(susan)))&
(?[X]:(~generous(X)))&
(?[X]:((generous(X)<~>wise(X)))) | patient(mary) | [
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 7584252531115502370212543
% SZS output start Proof for 7584252531115502370212543
3. ! [X0] : ((~curious(X0) & ~patient(X0)) <=> (generous(X0) <~> ~generous(X0))) [input p2]
22. patient(mary) [input hypothesis]
30. ! [X0] : (((~curious(X0) & ~patient(X0)) | ((generous(X0) | generous(X0)) & (~generous(X0) | ~generous(X0)))) & (((generous(X0) | ~generous(X0)) & (~generous(X0) | generous(X0))) | (curious(X0) | patient(X0)))) [nnf transformation 3]
31. ! [X0] : (((~curious(X0) & ~patient(X0)) | ((generous(X0) | generous(X0)) & (~generous(X0) | ~generous(X0)))) & (((generous(X0) | ~generous(X0)) & (~generous(X0) | generous(X0))) | curious(X0) | patient(X0))) [flattening 30]
72. ~patient(X0) | ~generous(X0) | ~generous(X0) [cnf transformation 31]
73. ~patient(X0) | generous(X0) | generous(X0) [cnf transformation 31]
134. patient(mary) [cnf transformation 22]
136. ~patient(X0) | ~generous(X0) [duplicate literal removal 72]
137. ~patient(X0) | generous(X0) [duplicate literal removal 73]
141. ~patient(X0) [subsumption resolution 136,137]
238. $false [subsumption resolution 134,141]
% SZS output end Proof for 7584252531115502370212543
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is generous is both old and not kind and vice versa. Everyone who is not quiet or not kind is not rich. Everyone who is not rich is both not humble and happy and vice versa. Everyone who is either not humble or not old is either not calm or not old. Everyone who is either not strong or patient is brave and vice versa. If mary is either creative or brave then lucy is tall or not wise and vice versa. Everyone who is humble or not creative is not rich and vice versa. Everyone who is either rich or tall is humble or rich and vice versa. If someone is either quiet or not creative then someone is both not rich and not kind. If someone is either tall or not kind then someone is both strong and creative. Everyone who is tall or not patient is both old and funny. If someone is either not tall or quiet then susan is funny and vice versa. Everyone who is either old or not tall is curious or wise. If susan is not kind or quiet then someone is not patient and vice versa. If paul is either tall or happy then someone is not generous and vice versa. Fred is happy. Someone is not old. John is kind or strong. Lucy is either not wise or kind. Susan is either strong or brave. Fred is not old. | Mary is generous. | neutral | (![X]:(generous(X)<=>(old(X)&~kind(X))))&
(![X]:((~quiet(X)|~kind(X))=>~rich(X)))&
(![X]:(~rich(X)<=>(~humble(X)&happy(X))))&
(![X]:((~humble(X)<~>~old(X))=>(~calm(X)<~>~old(X))))&
(![X]:((~strong(X)<~>patient(X))<=>brave(X)))&
(((creative(mary)<~>brave(mary)))<=>((tall(lucy)|~wise(lucy))))&
(![X]:((humble(X)|~creative(X))<=>~rich(X)))&
(![X]:((rich(X)<~>tall(X))<=>(humble(X)|rich(X))))&
((?[X]:((quiet(X)<~>~creative(X))))=>(?[X]:((~rich(X)&~kind(X)))))&
((?[X]:((tall(X)<~>~kind(X))))=>(?[X]:((strong(X)&creative(X)))))&
(![X]:((tall(X)|~patient(X))=>(old(X)&funny(X))))&
((?[X]:((~tall(X)<~>quiet(X))))<=>(funny(susan)))&
(![X]:((old(X)<~>~tall(X))=>(curious(X)|wise(X))))&
(((~kind(susan)|quiet(susan)))<=>(?[X]:(~patient(X))))&
(((tall(paul)<~>happy(paul)))<=>(?[X]:(~generous(X))))&
(happy(fred))&
(?[X]:(~old(X)))&
((kind(john)|strong(john)))&
((~wise(lucy)<~>kind(lucy)))&
((strong(susan)<~>brave(susan)))&
(~old(fred)) | generous(mary) | [] | null | 0 |
If susan is kind then someone is either happy or not tall and vice versa.
If someone is both funny and not calm then susan is both not patient and generous.
Everyone who is quiet or not strong is not strong or not kind and vice versa.
If someone is both curious and kind then someone is both not rich and generous and vice versa.
If susan is both not quiet and not generous then someone is funny.
Everyone who is brave is not funny and vice versa.
Everyone who is calm is both not old and calm and vice versa.
If paul is not curious then john is patient and vice versa.
Everyone who is brave or not old is either not quiet or strong.
If john is not funny or not calm then someone is both not humble and not curious.
Everyone who is strong is both not strong and strong and vice versa.
Everyone who is both strong and funny is not quiet and vice versa.
If someone is both old and kind then lucy is either creative or not kind.
Everyone who is generous or tall is funny or old.
Everyone who is both not funny and kind is curious.
If someone is either not funny or curious then someone is either not brave or not quiet.
Lucy is either generous or tall.
John is not brave.
Someone is either not curious or strong.
Someone is wise.
Susan is not wise.
Someone is calm or not tall.
Paul is not humble or not calm.
Paul is both happy and not kind. | Paul is strong. | contradiction | ((kind(susan))<=>(?[X]:((happy(X)<~>~tall(X)))))&
((?[X]:((funny(X)&~calm(X))))=>((~patient(susan)&generous(susan))))&
(![X]:((quiet(X)|~strong(X))<=>(~strong(X)|~kind(X))))&
((?[X]:((curious(X)&kind(X))))<=>(?[X]:((~rich(X)&generous(X)))))&
(((~quiet(susan)&~generous(susan)))=>(?[X]:(funny(X))))&
(![X]:(brave(X)<=>~funny(X)))&
(![X]:(calm(X)<=>(~old(X)&calm(X))))&
((~curious(paul))<=>(patient(john)))&
(![X]:((brave(X)|~old(X))=>(~quiet(X)<~>strong(X))))&
(((~funny(john)|~calm(john)))=>(?[X]:((~humble(X)&~curious(X)))))&
(![X]:(strong(X)<=>(~strong(X)&strong(X))))&
(![X]:((strong(X)&funny(X))<=>~quiet(X)))&
((?[X]:((old(X)&kind(X))))=>((creative(lucy)<~>~kind(lucy))))&
(![X]:((generous(X)|tall(X))=>(funny(X)|old(X))))&
(![X]:((~funny(X)&kind(X))=>curious(X)))&
((?[X]:((~funny(X)<~>curious(X))))=>(?[X]:((~brave(X)<~>~quiet(X)))))&
((generous(lucy)<~>tall(lucy)))&
(~brave(john))&
(?[X]:((~curious(X)<~>strong(X))))&
(?[X]:(wise(X)))&
(~wise(susan))&
(?[X]:((calm(X)|~tall(X))))&
((~humble(paul)|~calm(paul)))&
((happy(paul)&~kind(paul))) | strong(paul) | [
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 6574182230140172581700197
% SZS output start Proof for 6574182230140172581700197
11. ! [X0] : (strong(X0) <=> (strong(X0) & ~strong(X0))) [input p10]
25. strong(paul) [input hypothesis]
61. ! [X0] : ((strong(X0) | (~strong(X0) | strong(X0))) & ((strong(X0) & ~strong(X0)) | ~strong(X0))) [nnf transformation 11]
62. ! [X0] : ((strong(X0) | ~strong(X0) | strong(X0)) & ((strong(X0) & ~strong(X0)) | ~strong(X0))) [flattening 61]
106. ~strong(X0) | ~strong(X0) [cnf transformation 62]
131. strong(paul) [cnf transformation 25]
132. ~strong(X0) [duplicate literal removal 106]
276. $false [subsumption resolution 131,132]
% SZS output end Proof for 6574182230140172581700197
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not calm or not tall is tall and vice versa.
Everyone who is kind is either kind or happy and vice versa.
If someone is both kind and calm then someone is calm or quiet and vice versa.
Everyone who is not old is both old and funny and vice versa.
Everyone who is creative is both rich and not quiet and vice versa.
If alice is not rich then someone is not creative.
If someone is either not calm or not kind then someone is either not patient or funny and vice versa.
If someone is not calm then someone is both tall and strong.
If lucy is either not tall or quiet then someone is creative or not generous and vice versa.
If paul is both not creative and patient then susan is both not creative and rich.
Everyone who is either not funny or not old is calm or kind.
If paul is both not kind and not patient then someone is quiet or not strong.
If someone is both wise and not calm then alice is not patient.
Everyone who is either rich or brave is not humble or not rich.
Mary is not strong.
Someone is not humble or not patient.
Someone is strong.
Someone is not humble or not calm.
Someone is not creative or calm.
Alice is not wise or not humble. | Susan is humble. | neutral | (![X]:((~calm(X)|~tall(X))<=>tall(X)))&
(![X]:(kind(X)<=>(kind(X)<~>happy(X))))&
((?[X]:((kind(X)&calm(X))))<=>(?[X]:((calm(X)|quiet(X)))))&
(![X]:(~old(X)<=>(old(X)&funny(X))))&
(![X]:(creative(X)<=>(rich(X)&~quiet(X))))&
((~rich(alice))=>(?[X]:(~creative(X))))&
((?[X]:((~calm(X)<~>~kind(X))))<=>(?[X]:((~patient(X)<~>funny(X)))))&
((?[X]:(~calm(X)))=>(?[X]:((tall(X)&strong(X)))))&
(((~tall(lucy)<~>quiet(lucy)))<=>(?[X]:((creative(X)|~generous(X)))))&
(((~creative(paul)&patient(paul)))=>((~creative(susan)&rich(susan))))&
(![X]:((~funny(X)<~>~old(X))=>(calm(X)|kind(X))))&
(((~kind(paul)&~patient(paul)))=>(?[X]:((quiet(X)|~strong(X)))))&
((?[X]:((wise(X)&~calm(X))))=>(~patient(alice)))&
(![X]:((rich(X)<~>brave(X))=>(~humble(X)|~rich(X))))&
(~strong(mary))&
(?[X]:((~humble(X)|~patient(X))))&
(?[X]:(strong(X)))&
(?[X]:((~humble(X)|~calm(X))))&
(?[X]:((~creative(X)|calm(X))))&
((~wise(alice)|~humble(alice))) | humble(susan) | [] | null | 0 |
Everyone who is creative is not humble and vice versa.
If someone is not tall or not humble then mary is both brave and curious and vice versa.
If fred is calm then someone is not quiet and vice versa.
Everyone who is both strong and not wise is not rich.
Everyone who is not creative is kind or quiet and vice versa.
Everyone who is both not happy and funny is either tall or brave and vice versa.
Everyone who is either old or not kind is creative.
Everyone who is both not quiet and not brave is both not quiet and curious and vice versa.
If paul is tall then fred is either old or creative.
Everyone who is not brave or curious is both strong and not kind.
Everyone who is humble or not generous is both not curious and happy.
If someone is not rich or patient then mary is brave.
Everyone who is either quiet or wise is not quiet and vice versa.
If fred is both not curious and not calm then someone is either not humble or not tall.
Everyone who is happy is either not generous or not rich.
If lucy is humble then someone is either creative or not generous and vice versa.
Mary is not brave or tall.
Someone is rich or not happy.
John is either not kind or patient. | Mary is not funny. | neutral | (![X]:(creative(X)<=>~humble(X)))&
((?[X]:((~tall(X)|~humble(X))))<=>((brave(mary)&curious(mary))))&
((calm(fred))<=>(?[X]:(~quiet(X))))&
(![X]:((strong(X)&~wise(X))=>~rich(X)))&
(![X]:(~creative(X)<=>(kind(X)|quiet(X))))&
(![X]:((~happy(X)&funny(X))<=>(tall(X)<~>brave(X))))&
(![X]:((old(X)<~>~kind(X))=>creative(X)))&
(![X]:((~quiet(X)&~brave(X))<=>(~quiet(X)&curious(X))))&
((tall(paul))=>((old(fred)<~>creative(fred))))&
(![X]:((~brave(X)|curious(X))=>(strong(X)&~kind(X))))&
(![X]:((humble(X)|~generous(X))=>(~curious(X)&happy(X))))&
((?[X]:((~rich(X)|patient(X))))=>(brave(mary)))&
(![X]:((quiet(X)<~>wise(X))<=>~quiet(X)))&
(((~curious(fred)&~calm(fred)))=>(?[X]:((~humble(X)<~>~tall(X)))))&
(![X]:(happy(X)=>(~generous(X)<~>~rich(X))))&
((humble(lucy))<=>(?[X]:((creative(X)<~>~generous(X)))))&
((~brave(mary)|tall(mary)))&
(?[X]:((rich(X)|~happy(X))))&
((~kind(john)<~>patient(john))) | ~funny(mary) | [] | null | 0 |
If someone is both rich and creative then someone is both not funny and not strong.
Everyone who is either not calm or not wise is either happy or not happy and vice versa.
Everyone who is either generous or not old is not patient or not kind and vice versa.
If lucy is either curious or brave then paul is both rich and happy and vice versa.
If someone is both not strong and generous then john is either brave or not generous.
Everyone who is not curious is both not tall and not funny.
Everyone who is not wise is either not old or creative.
If someone is either old or not wise then alice is not tall and vice versa.
If john is not kind then someone is both not wise and not humble.
If someone is either rich or strong then mary is not brave.
Everyone who is rich is both not kind and not quiet and vice versa.
Everyone who is not funny is not calm or humble and vice versa.
Everyone who is either patient or kind is not calm or not humble.
Everyone who is either not strong or funny is both strong and not brave.
If someone is both not patient and wise then someone is strong.
If john is either not wise or tall then someone is both patient and old.
Alice is funny.
Someone is both not tall and funny.
Alice is either not brave or humble.
Alice is either not funny or tall.
Lucy is both rich and patient.
Fred is not kind.
Someone is not curious.
Someone is either not quiet or not calm. | Lucy is wise. | entailment | ((?[X]:((rich(X)&creative(X))))=>(?[X]:((~funny(X)&~strong(X)))))&
(![X]:((~calm(X)<~>~wise(X))<=>(happy(X)<~>~happy(X))))&
(![X]:((generous(X)<~>~old(X))<=>(~patient(X)|~kind(X))))&
(((curious(lucy)<~>brave(lucy)))<=>((rich(paul)&happy(paul))))&
((?[X]:((~strong(X)&generous(X))))=>((brave(john)<~>~generous(john))))&
(![X]:(~curious(X)=>(~tall(X)&~funny(X))))&
(![X]:(~wise(X)=>(~old(X)<~>creative(X))))&
((?[X]:((old(X)<~>~wise(X))))<=>(~tall(alice)))&
((~kind(john))=>(?[X]:((~wise(X)&~humble(X)))))&
((?[X]:((rich(X)<~>strong(X))))=>(~brave(mary)))&
(![X]:(rich(X)<=>(~kind(X)&~quiet(X))))&
(![X]:(~funny(X)<=>(~calm(X)|humble(X))))&
(![X]:((patient(X)<~>kind(X))=>(~calm(X)|~humble(X))))&
(![X]:((~strong(X)<~>funny(X))=>(strong(X)&~brave(X))))&
((?[X]:((~patient(X)&wise(X))))=>(?[X]:(strong(X))))&
(((~wise(john)<~>tall(john)))=>(?[X]:((patient(X)&old(X)))))&
(funny(alice))&
(?[X]:((~tall(X)&funny(X))))&
((~brave(alice)<~>humble(alice)))&
((~funny(alice)<~>tall(alice)))&
((rich(lucy)&patient(lucy)))&
(~kind(fred))&
(?[X]:(~curious(X)))&
(?[X]:((~quiet(X)<~>~calm(X)))) | wise(lucy) | [
"p0",
"p6",
"p7",
"p13",
"p16",
"p19",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 4650296406237671362974939
% SZS output start Proof for 4650296406237671362974939
1. ? [X0] : (creative(X0) & rich(X0)) => ? [X0] : (~strong(X0) & ~funny(X0)) [input p0]
7. ! [X0] : (~wise(X0) => (~old(X0) <~> creative(X0))) [input p6]
8. ? [X0] : (old(X0) <~> ~wise(X0)) <=> ~tall(alice) [input p7]
14. ! [X0] : ((~strong(X0) <~> funny(X0)) => (~brave(X0) & strong(X0))) [input p13]
17. funny(alice) [input p16]
20. ~funny(alice) <~> tall(alice) [input p19]
21. patient(lucy) & rich(lucy) [input p20]
25. ~wise(lucy) [input hypothesis]
26. ? [X0] : (creative(X0) & rich(X0)) => ? [X1] : (~strong(X1) & ~funny(X1)) [rectify 1]
28. ? [X1] : (~strong(X1) & ~funny(X1)) | ! [X0] : (~creative(X0) | ~rich(X0)) [ennf transformation 26]
31. ! [X0] : ((~old(X0) <~> creative(X0)) | wise(X0)) [ennf transformation 7]
36. ! [X0] : ((~brave(X0) & strong(X0)) | (~strong(X0) <=> funny(X0))) [ennf transformation 14]
39. ? [X0] : (~strong(X0) & ~funny(X0)) | ! [X1] : (~creative(X1) | ~rich(X1)) [rectify 28]
40. ? [X0] : (~strong(X0) & ~funny(X0)) => (~strong(sK0) & ~funny(sK0)) [choice axiom]
41. (~strong(sK0) & ~funny(sK0)) | ! [X1] : (~creative(X1) | ~rich(X1)) [skolemisation 39,40]
48. ! [X0] : (((~creative(X0) | old(X0)) & (creative(X0) | ~old(X0))) | wise(X0)) [nnf transformation 31]
49. (? [X0] : ((wise(X0) | ~old(X0)) & (~wise(X0) | old(X0))) | tall(alice)) & (~tall(alice) | ! [X0] : ((old(X0) | wise(X0)) & (~wise(X0) | ~old(X0)))) [nnf transformation 8]
50. (? [X0] : ((wise(X0) | ~old(X0)) & (~wise(X0) | old(X0))) | tall(alice)) & (~tall(alice) | ! [X1] : ((old(X1) | wise(X1)) & (~wise(X1) | ~old(X1)))) [rectify 49]
51. ? [X0] : ((wise(X0) | ~old(X0)) & (~wise(X0) | old(X0))) => ((wise(sK1) | ~old(sK1)) & (~wise(sK1) | old(sK1))) [choice axiom]
52. (((wise(sK1) | ~old(sK1)) & (~wise(sK1) | old(sK1))) | tall(alice)) & (~tall(alice) | ! [X1] : ((old(X1) | wise(X1)) & (~wise(X1) | ~old(X1)))) [skolemisation 50,51]
61. ! [X0] : ((~brave(X0) & strong(X0)) | ((~strong(X0) | ~funny(X0)) & (funny(X0) | strong(X0)))) [nnf transformation 36]
71. (~tall(alice) | funny(alice)) & (tall(alice) | ~funny(alice)) [nnf transformation 20]
77. ~funny(sK0) | ~creative(X1) | ~rich(X1) [cnf transformation 41]
78. ~strong(sK0) | ~creative(X1) | ~rich(X1) [cnf transformation 41]
103. ~old(X0) | creative(X0) | wise(X0) [cnf transformation 48]
106. ~tall(alice) | old(X1) | wise(X1) [cnf transformation 52]
121. strong(X0) | funny(X0) | strong(X0) [cnf transformation 61]
130. funny(alice) [cnf transformation 17]
135. tall(alice) | ~funny(alice) [cnf transformation 71]
137. rich(lucy) [cnf transformation 21]
143. ~wise(lucy) [cnf transformation 25]
144. strong(X0) | funny(X0) [duplicate literal removal 121]
150. 1 <=> ! [X1] : (~creative(X1) | ~rich(X1)) [avatar definition]
151. ~creative(X1) | ~rich(X1) <- (1) [avatar component clause 150]
153. 2 <=> strong(sK0) [avatar definition]
155. ~strong(sK0) <- (~2) [avatar component clause 153]
156. 1 | ~2 [avatar split clause 78,153,150]
158. 3 <=> funny(sK0) [avatar definition]
160. ~funny(sK0) <- (~3) [avatar component clause 158]
161. 1 | ~3 [avatar split clause 77,158,150]
200. 11 <=> tall(alice) [avatar definition]
214. 14 <=> ! [X1] : (old(X1) | wise(X1)) [avatar definition]
215. old(X1) | wise(X1) <- (14) [avatar component clause 214]
216. 14 | ~11 [avatar split clause 106,200,214]
285. tall(alice) [subsumption resolution 135,130]
286. 11 [avatar split clause 285,200]
304. funny(sK0) <- (~2) [resolution 144,155]
305. $false <- (~2, ~3) [subsumption resolution 304,160]
306. 2 | 3 [avatar contradiction clause 305]
316. creative(X0) | wise(X0) | wise(X0) <- (14) [resolution 103,215]
317. wise(X0) | creative(X0) <- (14) [duplicate literal removal 316]
320. creative(lucy) <- (14) [resolution 317,143]
325. ~rich(lucy) <- (1, 14) [resolution 320,151]
326. $false <- (1, 14) [subsumption resolution 325,137]
327. ~1 | ~14 [avatar contradiction clause 326]
328. $false [avatar sat refutation 156,161,216,286,306,327]
% SZS output end Proof for 4650296406237671362974939
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich or rich is humble.
Everyone who is not rich or humble is both not curious and rich and vice versa.
If alice is both not curious and creative then someone is both not curious and rich.
Everyone who is both not old and not kind is either not happy or not kind and vice versa.
Everyone who is both creative and not calm is either not strong or quiet and vice versa.
Everyone who is both generous and kind is not curious and vice versa.
Everyone who is not humble is both not wise and funny and vice versa.
Everyone who is not generous is both calm and not humble.
If someone is both curious and not old then alice is both funny and calm and vice versa.
Everyone who is both patient and not creative is not patient or rich and vice versa.
Everyone who is happy is not humble or patient.
Everyone who is curious or not happy is not funny and vice versa.
If someone is either quiet or brave then paul is both humble and tall.
Everyone who is either creative or not brave is both strong and curious and vice versa.
If someone is either tall or quiet then paul is kind or humble and vice versa.
If someone is not curious or not patient then someone is both patient and not strong and vice versa.
Someone is both funny and not quiet.
John is either calm or not strong.
Someone is both brave and kind.
Someone is humble or brave. | Paul is not patient. | contradiction | (![X]:((~rich(X)<~>rich(X))=>humble(X)))&
(![X]:((~rich(X)|humble(X))<=>(~curious(X)&rich(X))))&
(((~curious(alice)&creative(alice)))=>(?[X]:((~curious(X)&rich(X)))))&
(![X]:((~old(X)&~kind(X))<=>(~happy(X)<~>~kind(X))))&
(![X]:((creative(X)&~calm(X))<=>(~strong(X)<~>quiet(X))))&
(![X]:((generous(X)&kind(X))<=>~curious(X)))&
(![X]:(~humble(X)<=>(~wise(X)&funny(X))))&
(![X]:(~generous(X)=>(calm(X)&~humble(X))))&
((?[X]:((curious(X)&~old(X))))<=>((funny(alice)&calm(alice))))&
(![X]:((patient(X)&~creative(X))<=>(~patient(X)|rich(X))))&
(![X]:(happy(X)=>(~humble(X)|patient(X))))&
(![X]:((curious(X)|~happy(X))<=>~funny(X)))&
((?[X]:((quiet(X)<~>brave(X))))=>((humble(paul)&tall(paul))))&
(![X]:((creative(X)<~>~brave(X))<=>(strong(X)&curious(X))))&
((?[X]:((tall(X)<~>quiet(X))))<=>((kind(paul)|humble(paul))))&
((?[X]:((~curious(X)|~patient(X))))<=>(?[X]:((patient(X)&~strong(X)))))&
(?[X]:((funny(X)&~quiet(X))))&
((calm(john)<~>~strong(john)))&
(?[X]:((brave(X)&kind(X))))&
(?[X]:((humble(X)|brave(X)))) | ~patient(paul) | [
"p0",
"p1",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 6027827634714802573150901
% SZS output start Proof for 6027827634714802573150901
1. ! [X0] : ((~rich(X0) <~> rich(X0)) => humble(X0)) [input p0]
2. ! [X0] : ((humble(X0) | ~rich(X0)) <=> (rich(X0) & ~curious(X0))) [input p1]
10. ! [X0] : ((~creative(X0) & patient(X0)) <=> (rich(X0) | ~patient(X0))) [input p9]
21. ~patient(paul) [input hypothesis]
23. ! [X0] : (humble(X0) | (~rich(X0) <=> rich(X0))) [ennf transformation 1]
30. ! [X0] : (humble(X0) | ((~rich(X0) | ~rich(X0)) & (rich(X0) | rich(X0)))) [nnf transformation 23]
31. ! [X0] : (((humble(X0) | ~rich(X0)) | (~rich(X0) | curious(X0))) & ((rich(X0) & ~curious(X0)) | (~humble(X0) & rich(X0)))) [nnf transformation 2]
32. ! [X0] : ((humble(X0) | ~rich(X0) | ~rich(X0) | curious(X0)) & ((rich(X0) & ~curious(X0)) | (~humble(X0) & rich(X0)))) [flattening 31]
48. ! [X0] : (((~creative(X0) & patient(X0)) | (~rich(X0) & patient(X0))) & ((rich(X0) | ~patient(X0)) | (creative(X0) | ~patient(X0)))) [nnf transformation 10]
49. ! [X0] : (((~creative(X0) & patient(X0)) | (~rich(X0) & patient(X0))) & (rich(X0) | ~patient(X0) | creative(X0) | ~patient(X0))) [flattening 48]
72. humble(X0) | rich(X0) | rich(X0) [cnf transformation 30]
73. humble(X0) | ~rich(X0) | ~rich(X0) [cnf transformation 30]
77. rich(X0) | ~humble(X0) [cnf transformation 32]
107. patient(X0) | ~rich(X0) [cnf transformation 49]
142. ~patient(paul) [cnf transformation 21]
149. humble(X0) | rich(X0) [duplicate literal removal 72]
150. humble(X0) | ~rich(X0) [duplicate literal removal 73]
151. humble(X0) [subsumption resolution 149,150]
152. rich(X0) [subsumption resolution 77,151]
174. patient(X0) [subsumption resolution 107,152]
217. $false [subsumption resolution 142,174]
% SZS output end Proof for 6027827634714802573150901
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 4989
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If mary is not wise or not creative then someone is not rich. Everyone who is both not wise and not rich is funny and vice versa. Everyone who is either generous or not old is both not humble and old. If mary is either not strong or not generous then paul is either generous or wise. If john is not generous or wise then someone is both not quiet and not strong and vice versa. Everyone who is both kind and not quiet is both not kind and funny. Everyone who is either old or not curious is strong. If paul is both not strong and generous then john is not strong or not wise and vice versa. Everyone who is either calm or not calm is both not tall and curious and vice versa. If paul is both kind and not quiet then someone is not rich and vice versa. If fred is either tall or not calm then someone is both old and not tall and vice versa. Everyone who is both not quiet and strong is both not curious and not brave. Everyone who is creative is both not calm and not patient and vice versa. Everyone who is generous is kind or not humble and vice versa. Everyone who is both brave and funny is patient or not wise. Everyone who is rich is either generous or calm and vice versa. Someone is both humble and strong. Someone is old or kind. Alice is strong. Mary is curious or quiet. John is either not calm or wise. Someone is happy. Someone is either not funny or not quiet. Mary is wise or not tall. | Fred is not rich. | contradiction | (((~wise(mary)|~creative(mary)))=>(?[X]:(~rich(X))))&
(![X]:((~wise(X)&~rich(X))<=>funny(X)))&
(![X]:((generous(X)<~>~old(X))=>(~humble(X)&old(X))))&
(((~strong(mary)<~>~generous(mary)))=>((generous(paul)<~>wise(paul))))&
(((~generous(john)|wise(john)))<=>(?[X]:((~quiet(X)&~strong(X)))))&
(![X]:((kind(X)&~quiet(X))=>(~kind(X)&funny(X))))&
(![X]:((old(X)<~>~curious(X))=>strong(X)))&
(((~strong(paul)&generous(paul)))<=>((~strong(john)|~wise(john))))&
(![X]:((calm(X)<~>~calm(X))<=>(~tall(X)&curious(X))))&
(((kind(paul)&~quiet(paul)))<=>(?[X]:(~rich(X))))&
(((tall(fred)<~>~calm(fred)))<=>(?[X]:((old(X)&~tall(X)))))&
(![X]:((~quiet(X)&strong(X))=>(~curious(X)&~brave(X))))&
(![X]:(creative(X)<=>(~calm(X)&~patient(X))))&
(![X]:(generous(X)<=>(kind(X)|~humble(X))))&
(![X]:((brave(X)&funny(X))=>(patient(X)|~wise(X))))&
(![X]:(rich(X)<=>(generous(X)<~>calm(X))))&
(?[X]:((humble(X)&strong(X))))&
(?[X]:((old(X)|kind(X))))&
(strong(alice))&
((curious(mary)|quiet(mary)))&
((~calm(john)<~>wise(john)))&
(?[X]:(happy(X)))&
(?[X]:((~funny(X)<~>~quiet(X))))&
((wise(mary)|~tall(mary))) | ~rich(fred) | [
"p5",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 2810252250706096263278417
% SZS output start Proof for 2810252250706096263278417
6. ! [X0] : ((~quiet(X0) & kind(X0)) => (funny(X0) & ~kind(X0))) [input p5]
10. (~quiet(paul) & kind(paul)) <=> ? [X0] : ~rich(X0) [input p9]
25. ~rich(fred) [input hypothesis]
34. ! [X0] : ((funny(X0) & ~kind(X0)) | (quiet(X0) | ~kind(X0))) [ennf transformation 6]
35. ! [X0] : ((funny(X0) & ~kind(X0)) | quiet(X0) | ~kind(X0)) [flattening 34]
56. ((~quiet(paul) & kind(paul)) | ! [X0] : rich(X0)) & (? [X0] : ~rich(X0) | (quiet(paul) | ~kind(paul))) [nnf transformation 10]
57. ((~quiet(paul) & kind(paul)) | ! [X0] : rich(X0)) & (? [X0] : ~rich(X0) | quiet(paul) | ~kind(paul)) [flattening 56]
58. ((~quiet(paul) & kind(paul)) | ! [X0] : rich(X0)) & (? [X1] : ~rich(X1) | quiet(paul) | ~kind(paul)) [rectify 57]
59. ? [X1] : ~rich(X1) => ~rich(sK2) [choice axiom]
60. ((~quiet(paul) & kind(paul)) | ! [X0] : rich(X0)) & (~rich(sK2) | quiet(paul) | ~kind(paul)) [skolemisation 58,59]
94. ~kind(X0) | quiet(X0) | ~kind(X0) [cnf transformation 35]
110. kind(paul) | rich(X0) [cnf transformation 60]
111. ~quiet(paul) | rich(X0) [cnf transformation 60]
137. ~rich(fred) [cnf transformation 25]
142. ~kind(X0) | quiet(X0) [duplicate literal removal 94]
218. 15 <=> ! [X0] : rich(X0) [avatar definition]
219. rich(X0) <- (15) [avatar component clause 218]
221. 16 <=> quiet(paul) [avatar definition]
223. ~quiet(paul) <- (~16) [avatar component clause 221]
224. 15 | ~16 [avatar split clause 111,221,218]
226. 17 <=> kind(paul) [avatar definition]
228. kind(paul) <- (17) [avatar component clause 226]
229. 15 | 17 [avatar split clause 110,226,218]
282. quiet(paul) <- (17) [resolution 142,228]
283. $false <- (~16, 17) [subsumption resolution 282,223]
284. 16 | ~17 [avatar contradiction clause 283]
285. $false <- (15) [resolution 219,137]
288. ~15 [avatar contradiction clause 285]
289. $false [avatar sat refutation 224,229,284,288]
% SZS output end Proof for 2810252250706096263278417
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both strong and tall then someone is not creative or curious and vice versa.
Everyone who is wise or not rich is both wise and kind.
If fred is not humble or tall then someone is patient and vice versa.
Everyone who is not tall or happy is both wise and not old and vice versa.
If alice is kind then susan is both old and strong.
If john is both not curious and kind then someone is either not patient or not quiet.
If susan is either rich or not happy then someone is not generous or not rich.
Everyone who is both not tall and not generous is happy or brave.
If fred is humble then someone is calm or not happy.
Everyone who is rich is not tall or creative.
Everyone who is either not patient or creative is not creative or quiet and vice versa.
Everyone who is not patient or generous is either quiet or tall.
Everyone who is either not tall or not humble is both not creative and curious.
Everyone who is either not quiet or not curious is not brave or not curious and vice versa.
Everyone who is kind is both creative and not strong and vice versa.
If someone is not patient or not generous then someone is not rich or strong and vice versa.
Lucy is not brave or not generous.
Paul is both not curious and not rich.
Someone is both humble and not patient.
Fred is either generous or funny.
Someone is brave or not kind.
Someone is both brave and patient.
Alice is not rich or not kind. | Alice is creative. | entailment | ((?[X]:((strong(X)&tall(X))))<=>(?[X]:((~creative(X)|curious(X)))))&
(![X]:((wise(X)|~rich(X))=>(wise(X)&kind(X))))&
(((~humble(fred)|tall(fred)))<=>(?[X]:(patient(X))))&
(![X]:((~tall(X)|happy(X))<=>(wise(X)&~old(X))))&
((kind(alice))=>((old(susan)&strong(susan))))&
(((~curious(john)&kind(john)))=>(?[X]:((~patient(X)<~>~quiet(X)))))&
(((rich(susan)<~>~happy(susan)))=>(?[X]:((~generous(X)|~rich(X)))))&
(![X]:((~tall(X)&~generous(X))=>(happy(X)|brave(X))))&
((humble(fred))=>(?[X]:((calm(X)|~happy(X)))))&
(![X]:(rich(X)=>(~tall(X)|creative(X))))&
(![X]:((~patient(X)<~>creative(X))<=>(~creative(X)|quiet(X))))&
(![X]:((~patient(X)|generous(X))=>(quiet(X)<~>tall(X))))&
(![X]:((~tall(X)<~>~humble(X))=>(~creative(X)&curious(X))))&
(![X]:((~quiet(X)<~>~curious(X))<=>(~brave(X)|~curious(X))))&
(![X]:(kind(X)<=>(creative(X)&~strong(X))))&
((?[X]:((~patient(X)|~generous(X))))<=>(?[X]:((~rich(X)|strong(X)))))&
((~brave(lucy)|~generous(lucy)))&
((~curious(paul)&~rich(paul)))&
(?[X]:((humble(X)&~patient(X))))&
((generous(fred)<~>funny(fred)))&
(?[X]:((brave(X)|~kind(X))))&
(?[X]:((brave(X)&patient(X))))&
((~rich(alice)|~kind(alice))) | creative(alice) | [
"p1",
"p3",
"p9",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2352008142483284729857092
% SZS output start Proof for 2352008142483284729857092
2. ! [X0] : ((~rich(X0) | wise(X0)) => (kind(X0) & wise(X0))) [input p1]
4. ! [X0] : ((happy(X0) | ~tall(X0)) <=> (~old(X0) & wise(X0))) [input p3]
10. ! [X0] : (rich(X0) => (creative(X0) | ~tall(X0))) [input p9]
15. ! [X0] : (kind(X0) <=> (~strong(X0) & creative(X0))) [input p14]
24. ~creative(alice) [input hypothesis]
28. ! [X0] : ((kind(X0) & wise(X0)) | (rich(X0) & ~wise(X0))) [ennf transformation 2]
35. ! [X0] : ((creative(X0) | ~tall(X0)) | ~rich(X0)) [ennf transformation 10]
36. ! [X0] : (creative(X0) | ~tall(X0) | ~rich(X0)) [flattening 35]
49. ! [X0] : (((happy(X0) | ~tall(X0)) | (old(X0) | ~wise(X0))) & ((~old(X0) & wise(X0)) | (~happy(X0) & tall(X0)))) [nnf transformation 4]
50. ! [X0] : ((happy(X0) | ~tall(X0) | old(X0) | ~wise(X0)) & ((~old(X0) & wise(X0)) | (~happy(X0) & tall(X0)))) [flattening 49]
63. ! [X0] : ((kind(X0) | (strong(X0) | ~creative(X0))) & ((~strong(X0) & creative(X0)) | ~kind(X0))) [nnf transformation 15]
64. ! [X0] : ((kind(X0) | strong(X0) | ~creative(X0)) & ((~strong(X0) & creative(X0)) | ~kind(X0))) [flattening 63]
84. ~wise(X0) | kind(X0) [cnf transformation 28]
85. kind(X0) | rich(X0) [cnf transformation 28]
89. wise(X0) | tall(X0) [cnf transformation 50]
101. ~rich(X0) | ~tall(X0) | creative(X0) [cnf transformation 36]
122. ~kind(X0) | creative(X0) [cnf transformation 64]
140. ~creative(alice) [cnf transformation 24]
194. 12 <=> kind(alice) [avatar definition]
195. kind(alice) <- (12) [avatar component clause 194]
196. ~kind(alice) <- (~12) [avatar component clause 194]
307. 37 <=> rich(alice) [avatar definition]
308. rich(alice) <- (37) [avatar component clause 307]
317. rich(alice) <- (~12) [resolution 85,196]
320. 37 | 12 [avatar split clause 317,194,307]
321. kind(X0) | tall(X0) [resolution 89,84]
335. ~tall(alice) | creative(alice) <- (37) [resolution 101,308]
339. ~tall(alice) <- (37) [subsumption resolution 335,140]
373. tall(alice) <- (~12) [resolution 321,196]
376. $false <- (~12, 37) [subsumption resolution 373,339]
377. 12 | ~37 [avatar contradiction clause 376]
383. creative(alice) <- (12) [resolution 195,122]
384. $false <- (12) [subsumption resolution 383,140]
385. ~12 [avatar contradiction clause 384]
386. $false [avatar sat refutation 320,377,385]
% SZS output end Proof for 2352008142483284729857092
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not strong or rich then someone is either not rich or not generous and vice versa.
If someone is funny then paul is not calm or not humble.
If someone is both not strong and rich then mary is kind.
If someone is creative then someone is humble or rich.
Everyone who is both not tall and patient is either not brave or not happy.
If someone is not calm or not old then fred is both strong and funny and vice versa.
If someone is not old then someone is not quiet or not curious.
If someone is old then someone is wise or curious and vice versa.
Everyone who is either rich or patient is quiet or not patient and vice versa.
If someone is not calm then paul is quiet or not curious.
If someone is either brave or quiet then paul is not tall or patient.
Everyone who is both tall and not humble is both patient and not strong and vice versa.
Everyone who is funny is either quiet or not brave.
If someone is not patient or happy then susan is not kind or not brave.
If someone is either not happy or not wise then someone is quiet.
Everyone who is wise or not strong is not generous.
John is not tall.
Susan is not creative or not calm.
Someone is not curious or not kind.
Fred is patient or wise.
Alice is not brave or not curious.
Paul is both brave and not patient.
Lucy is calm or old.
Lucy is both patient and rich. | Lucy is rich. | entailment | ((?[X]:((~strong(X)<~>rich(X))))<=>(?[X]:((~rich(X)<~>~generous(X)))))&
((?[X]:(funny(X)))=>((~calm(paul)|~humble(paul))))&
((?[X]:((~strong(X)&rich(X))))=>(kind(mary)))&
((?[X]:(creative(X)))=>(?[X]:((humble(X)|rich(X)))))&
(![X]:((~tall(X)&patient(X))=>(~brave(X)<~>~happy(X))))&
((?[X]:((~calm(X)|~old(X))))<=>((strong(fred)&funny(fred))))&
((?[X]:(~old(X)))=>(?[X]:((~quiet(X)|~curious(X)))))&
((?[X]:(old(X)))<=>(?[X]:((wise(X)|curious(X)))))&
(![X]:((rich(X)<~>patient(X))<=>(quiet(X)|~patient(X))))&
((?[X]:(~calm(X)))=>((quiet(paul)|~curious(paul))))&
((?[X]:((brave(X)<~>quiet(X))))=>((~tall(paul)|patient(paul))))&
(![X]:((tall(X)&~humble(X))<=>(patient(X)&~strong(X))))&
(![X]:(funny(X)=>(quiet(X)<~>~brave(X))))&
((?[X]:((~patient(X)|happy(X))))=>((~kind(susan)|~brave(susan))))&
((?[X]:((~happy(X)<~>~wise(X))))=>(?[X]:(quiet(X))))&
(![X]:((wise(X)|~strong(X))=>~generous(X)))&
(~tall(john))&
((~creative(susan)|~calm(susan)))&
(?[X]:((~curious(X)|~kind(X))))&
((patient(fred)|wise(fred)))&
((~brave(alice)|~curious(alice)))&
((brave(paul)&~patient(paul)))&
((calm(lucy)|old(lucy)))&
((patient(lucy)&rich(lucy))) | rich(lucy) | [
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 1579635375086328374165785
% SZS output start Proof for 1579635375086328374165785
24. rich(lucy) & patient(lucy) [input p23]
25. ~rich(lucy) [input hypothesis]
129. rich(lucy) [cnf transformation 24]
130. ~rich(lucy) [cnf transformation 25]
340. $false [subsumption resolution 130,129]
% SZS output end Proof for 1579635375086328374165785
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
If alice is not tall then mary is not creative or creative.
Everyone who is humble is either not kind or funny and vice versa.
If fred is strong or not tall then someone is generous and vice versa.
If susan is strong then alice is tall or not old and vice versa.
If alice is both generous and not wise then lucy is not quiet and vice versa.
Everyone who is not tall is not calm and vice versa.
If paul is both not humble and not patient then someone is strong or not quiet and vice versa.
Everyone who is either rich or not funny is both not calm and calm and vice versa.
If someone is both not strong and tall then someone is old.
Everyone who is quiet or wise is patient or not curious.
Everyone who is not happy or not calm is generous or creative and vice versa.
Everyone who is both not happy and rich is humble or not funny.
Everyone who is patient is not wise or curious and vice versa.
Everyone who is funny is tall or generous.
If lucy is both creative and not strong then mary is kind and vice versa.
Everyone who is both curious and strong is either strong or not curious.
Paul is either generous or not rich.
John is not patient or not funny.
Alice is either funny or not curious.
Lucy is kind or funny.
Someone is strong or not creative.
Fred is funny.
John is not old. | Fred is strong. | neutral | ((~tall(alice))=>((~creative(mary)|creative(mary))))&
(![X]:(humble(X)<=>(~kind(X)<~>funny(X))))&
(((strong(fred)|~tall(fred)))<=>(?[X]:(generous(X))))&
((strong(susan))<=>((tall(alice)|~old(alice))))&
(((generous(alice)&~wise(alice)))<=>(~quiet(lucy)))&
(![X]:(~tall(X)<=>~calm(X)))&
(((~humble(paul)&~patient(paul)))<=>(?[X]:((strong(X)|~quiet(X)))))&
(![X]:((rich(X)<~>~funny(X))<=>(~calm(X)&calm(X))))&
((?[X]:((~strong(X)&tall(X))))=>(?[X]:(old(X))))&
(![X]:((quiet(X)|wise(X))=>(patient(X)|~curious(X))))&
(![X]:((~happy(X)|~calm(X))<=>(generous(X)|creative(X))))&
(![X]:((~happy(X)&rich(X))=>(humble(X)|~funny(X))))&
(![X]:(patient(X)<=>(~wise(X)|curious(X))))&
(![X]:(funny(X)=>(tall(X)|generous(X))))&
(((creative(lucy)&~strong(lucy)))<=>(kind(mary)))&
(![X]:((curious(X)&strong(X))=>(strong(X)<~>~curious(X))))&
((generous(paul)<~>~rich(paul)))&
((~patient(john)|~funny(john)))&
((funny(alice)<~>~curious(alice)))&
((kind(lucy)|funny(lucy)))&
(?[X]:((strong(X)|~creative(X))))&
(funny(fred))&
(~old(john)) | strong(fred) | [] | null | 0 |
If susan is generous or not wise then someone is not wise and vice versa.
Everyone who is curious or not rich is happy.
If susan is wise then paul is not happy or tall.
Everyone who is not kind or not strong is humble or tall.
If someone is either not brave or not quiet then alice is either not tall or old.
If someone is not kind or rich then someone is both not tall and not calm.
Everyone who is either old or wise is generous or not patient and vice versa.
If alice is wise or not patient then john is either not brave or not tall.
Everyone who is funny is not curious or strong and vice versa.
Everyone who is either not humble or not calm is curious.
If alice is not funny then someone is both curious and strong and vice versa.
Everyone who is not tall or calm is either not tall or not humble.
If paul is either kind or not old then fred is either not wise or old and vice versa.
Everyone who is either patient or not old is both humble and old and vice versa.
If john is old then someone is both not curious and curious.
Someone is not patient.
Paul is either not tall or rich.
Paul is both not rich and creative.
Someone is not wise or rich.
Someone is not strong.
John is not humble.
Someone is both not curious and humble. | John is patient. | entailment | (((generous(susan)|~wise(susan)))<=>(?[X]:(~wise(X))))&
(![X]:((curious(X)|~rich(X))=>happy(X)))&
((wise(susan))=>((~happy(paul)|tall(paul))))&
(![X]:((~kind(X)|~strong(X))=>(humble(X)|tall(X))))&
((?[X]:((~brave(X)<~>~quiet(X))))=>((~tall(alice)<~>old(alice))))&
((?[X]:((~kind(X)|rich(X))))=>(?[X]:((~tall(X)&~calm(X)))))&
(![X]:((old(X)<~>wise(X))<=>(generous(X)|~patient(X))))&
(((wise(alice)|~patient(alice)))=>((~brave(john)<~>~tall(john))))&
(![X]:(funny(X)<=>(~curious(X)|strong(X))))&
(![X]:((~humble(X)<~>~calm(X))=>curious(X)))&
((~funny(alice))<=>(?[X]:((curious(X)&strong(X)))))&
(![X]:((~tall(X)|calm(X))=>(~tall(X)<~>~humble(X))))&
(((kind(paul)<~>~old(paul)))<=>((~wise(fred)<~>old(fred))))&
(![X]:((patient(X)<~>~old(X))<=>(humble(X)&old(X))))&
((old(john))=>(?[X]:((~curious(X)&curious(X)))))&
(?[X]:(~patient(X)))&
((~tall(paul)<~>rich(paul)))&
((~rich(paul)&creative(paul)))&
(?[X]:((~wise(X)|rich(X))))&
(?[X]:(~strong(X)))&
(~humble(john))&
(?[X]:((~curious(X)&humble(X)))) | patient(john) | [
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6054215613826415134441460
% SZS output start Proof for 6054215613826415134441460
14. ! [X0] : ((patient(X0) <~> ~old(X0)) <=> (old(X0) & humble(X0))) [input p13]
15. old(john) => ? [X0] : (curious(X0) & ~curious(X0)) [input p14]
23. ~patient(john) [input hypothesis]
36. ? [X0] : (curious(X0) & ~curious(X0)) | ~old(john) [ennf transformation 15]
58. ! [X0] : ((((old(X0) | ~patient(X0)) & (~old(X0) | patient(X0))) | (~old(X0) | ~humble(X0))) & ((old(X0) & humble(X0)) | ((patient(X0) | old(X0)) & (~old(X0) | ~patient(X0))))) [nnf transformation 14]
59. ! [X0] : ((((old(X0) | ~patient(X0)) & (~old(X0) | patient(X0))) | ~old(X0) | ~humble(X0)) & ((old(X0) & humble(X0)) | ((patient(X0) | old(X0)) & (~old(X0) | ~patient(X0))))) [flattening 58]
60. ? [X0] : (curious(X0) & ~curious(X0)) => (curious(sK3) & ~curious(sK3)) [choice axiom]
61. (curious(sK3) & ~curious(sK3)) | ~old(john) [skolemisation 36,60]
120. old(X0) | patient(X0) | old(X0) [cnf transformation 59]
123. ~curious(sK3) | ~old(john) [cnf transformation 61]
124. curious(sK3) | ~old(john) [cnf transformation 61]
134. ~patient(john) [cnf transformation 23]
135. patient(X0) | old(X0) [duplicate literal removal 120]
264. 27 <=> old(john) [avatar definition]
266. ~old(john) <- (~27) [avatar component clause 264]
268. 28 <=> curious(sK3) [avatar definition]
271. ~27 | 28 [avatar split clause 124,268,264]
272. ~27 | ~28 [avatar split clause 123,268,264]
290. old(john) [resolution 135,134]
291. $false <- (~27) [subsumption resolution 290,266]
292. 27 [avatar contradiction clause 291]
293. $false [avatar sat refutation 271,272,292]
% SZS output end Proof for 6054215613826415134441460
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not calm then mary is happy or not kind and vice versa.
If mary is either quiet or not kind then someone is both not kind and not calm and vice versa.
If paul is generous then someone is not curious.
If someone is not kind or funny then someone is both patient and happy and vice versa.
If lucy is both not curious and curious then mary is not wise and vice versa.
Everyone who is both not generous and old is not rich or creative and vice versa.
Everyone who is not happy is not old.
Everyone who is patient or calm is either not strong or wise.
If lucy is both kind and tall then mary is both calm and not happy.
Everyone who is both creative and not quiet is both not wise and not strong and vice versa.
Everyone who is either calm or not happy is tall or wise.
If mary is both not curious and strong then someone is either not strong or humble.
If lucy is rich then someone is old or not wise.
If lucy is both old and generous then paul is not funny and vice versa.
If paul is both not calm and strong then susan is creative and vice versa.
If someone is both quiet and calm then someone is not curious or strong and vice versa.
Fred is either calm or funny.
Someone is quiet.
Someone is not calm or wise.
Mary is both not quiet and calm.
Someone is both happy and not old.
Someone is not quiet.
Mary is either not old or not happy.
Someone is either not happy or not old. | Mary is not rich. | contradiction | ((~calm(fred))<=>((happy(mary)|~kind(mary))))&
(((quiet(mary)<~>~kind(mary)))<=>(?[X]:((~kind(X)&~calm(X)))))&
((generous(paul))=>(?[X]:(~curious(X))))&
((?[X]:((~kind(X)|funny(X))))<=>(?[X]:((patient(X)&happy(X)))))&
(((~curious(lucy)&curious(lucy)))<=>(~wise(mary)))&
(![X]:((~generous(X)&old(X))<=>(~rich(X)|creative(X))))&
(![X]:(~happy(X)=>~old(X)))&
(![X]:((patient(X)|calm(X))=>(~strong(X)<~>wise(X))))&
(((kind(lucy)&tall(lucy)))=>((calm(mary)&~happy(mary))))&
(![X]:((creative(X)&~quiet(X))<=>(~wise(X)&~strong(X))))&
(![X]:((calm(X)<~>~happy(X))=>(tall(X)|wise(X))))&
(((~curious(mary)&strong(mary)))=>(?[X]:((~strong(X)<~>humble(X)))))&
((rich(lucy))=>(?[X]:((old(X)|~wise(X)))))&
(((old(lucy)&generous(lucy)))<=>(~funny(paul)))&
(((~calm(paul)&strong(paul)))<=>(creative(susan)))&
((?[X]:((quiet(X)&calm(X))))<=>(?[X]:((~curious(X)|strong(X)))))&
((calm(fred)<~>funny(fred)))&
(?[X]:(quiet(X)))&
(?[X]:((~calm(X)|wise(X))))&
((~quiet(mary)&calm(mary)))&
(?[X]:((happy(X)&~old(X))))&
(?[X]:(~quiet(X)))&
((~old(mary)<~>~happy(mary)))&
(?[X]:((~happy(X)<~>~old(X)))) | ~rich(mary) | [
"p5",
"p6",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 740707909154266422753650
% SZS output start Proof for 740707909154266422753650
6. ! [X0] : ((old(X0) & ~generous(X0)) <=> (creative(X0) | ~rich(X0))) [input p5]
7. ! [X0] : (~happy(X0) => ~old(X0)) [input p6]
23. ~old(mary) <~> ~happy(mary) [input p22]
25. ~rich(mary) [input hypothesis]
29. ! [X0] : (~old(X0) | happy(X0)) [ennf transformation 7]
53. ! [X0] : (((old(X0) & ~generous(X0)) | (~creative(X0) & rich(X0))) & ((creative(X0) | ~rich(X0)) | (~old(X0) | generous(X0)))) [nnf transformation 6]
54. ! [X0] : (((old(X0) & ~generous(X0)) | (~creative(X0) & rich(X0))) & (creative(X0) | ~rich(X0) | ~old(X0) | generous(X0))) [flattening 53]
82. (happy(mary) | old(mary)) & (~happy(mary) | ~old(mary)) [nnf transformation 23]
107. rich(X0) | old(X0) [cnf transformation 54]
109. ~old(X0) | happy(X0) [cnf transformation 29]
145. ~happy(mary) | ~old(mary) [cnf transformation 82]
149. ~rich(mary) [cnf transformation 25]
359. ~old(mary) [subsumption resolution 145,109]
372. old(mary) [resolution 107,149]
373. $false [subsumption resolution 372,359]
% SZS output end Proof for 740707909154266422753650
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not kind or calm is generous.
Everyone who is brave or wise is not old and vice versa.
Everyone who is not calm or not generous is not strong.
If someone is both strong and rich then someone is either kind or not generous and vice versa.
If someone is both not tall and not quiet then susan is both curious and brave.
Everyone who is either not curious or old is tall and vice versa.
Everyone who is either generous or tall is old and vice versa.
If john is not tall or not wise then fred is not tall.
Everyone who is tall is not rich or not strong and vice versa.
Everyone who is tall or not tall is both not kind and not creative and vice versa.
If susan is both not humble and old then someone is both not rich and not strong.
Everyone who is both not rich and not humble is either not generous or wise and vice versa.
Everyone who is not calm is both not brave and not funny and vice versa.
If someone is not old then lucy is not creative or not strong.
If fred is both not old and curious then john is either funny or brave and vice versa.
Lucy is either not calm or not generous.
Someone is old or happy.
John is quiet or kind.
Someone is strong or not curious. | John is rich. | contradiction | (![X]:((~kind(X)|calm(X))=>generous(X)))&
(![X]:((brave(X)|wise(X))<=>~old(X)))&
(![X]:((~calm(X)|~generous(X))=>~strong(X)))&
((?[X]:((strong(X)&rich(X))))<=>(?[X]:((kind(X)<~>~generous(X)))))&
((?[X]:((~tall(X)&~quiet(X))))=>((curious(susan)&brave(susan))))&
(![X]:((~curious(X)<~>old(X))<=>tall(X)))&
(![X]:((generous(X)<~>tall(X))<=>old(X)))&
(((~tall(john)|~wise(john)))=>(~tall(fred)))&
(![X]:(tall(X)<=>(~rich(X)|~strong(X))))&
(![X]:((tall(X)|~tall(X))<=>(~kind(X)&~creative(X))))&
(((~humble(susan)&old(susan)))=>(?[X]:((~rich(X)&~strong(X)))))&
(![X]:((~rich(X)&~humble(X))<=>(~generous(X)<~>wise(X))))&
(![X]:(~calm(X)<=>(~brave(X)&~funny(X))))&
((?[X]:(~old(X)))=>((~creative(lucy)|~strong(lucy))))&
(((~old(fred)&curious(fred)))<=>((funny(john)<~>brave(john))))&
((~calm(lucy)<~>~generous(lucy)))&
(?[X]:((old(X)|happy(X))))&
((quiet(john)|kind(john)))&
(?[X]:((strong(X)|~curious(X)))) | rich(john) | [
"p0",
"p3",
"p7",
"p8",
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 5731515613505120360477957
% SZS output start Proof for 5731515613505120360477957
1. ! [X0] : ((calm(X0) | ~kind(X0)) => generous(X0)) [input p0]
4. ? [X0] : (rich(X0) & strong(X0)) <=> ? [X0] : (kind(X0) <~> ~generous(X0)) [input p3]
8. (~wise(john) | ~tall(john)) => ~tall(fred) [input p7]
9. ! [X0] : (tall(X0) <=> (~strong(X0) | ~rich(X0))) [input p8]
10. ! [X0] : ((~tall(X0) | tall(X0)) <=> (~creative(X0) & ~kind(X0))) [input p9]
12. ! [X0] : ((~humble(X0) & ~rich(X0)) <=> (~generous(X0) <~> wise(X0))) [input p11]
20. rich(john) [input hypothesis]
21. ? [X0] : (rich(X0) & strong(X0)) <=> ? [X1] : (kind(X1) <~> ~generous(X1)) [rectify 4]
25. ! [X0] : (generous(X0) | (~calm(X0) & kind(X0))) [ennf transformation 1]
27. ~tall(fred) | (wise(john) & tall(john)) [ennf transformation 8]
34. (? [X0] : (rich(X0) & strong(X0)) | ! [X1] : ((kind(X1) | generous(X1)) & (~generous(X1) | ~kind(X1)))) & (? [X1] : ((generous(X1) | ~kind(X1)) & (~generous(X1) | kind(X1))) | ! [X0] : (~rich(X0) | ~strong(X0))) [nnf transformation 21]
35. (? [X0] : (rich(X0) & strong(X0)) | ! [X1] : ((kind(X1) | generous(X1)) & (~generous(X1) | ~kind(X1)))) & (? [X2] : ((generous(X2) | ~kind(X2)) & (~generous(X2) | kind(X2))) | ! [X3] : (~rich(X3) | ~strong(X3))) [rectify 34]
36. ? [X0] : (rich(X0) & strong(X0)) => (rich(sK0) & strong(sK0)) [choice axiom]
37. ? [X2] : ((generous(X2) | ~kind(X2)) & (~generous(X2) | kind(X2))) => ((generous(sK1) | ~kind(sK1)) & (~generous(sK1) | kind(sK1))) [choice axiom]
38. ((rich(sK0) & strong(sK0)) | ! [X1] : ((kind(X1) | generous(X1)) & (~generous(X1) | ~kind(X1)))) & (((generous(sK1) | ~kind(sK1)) & (~generous(sK1) | kind(sK1))) | ! [X3] : (~rich(X3) | ~strong(X3))) [skolemisation 35,37,36]
41. ! [X0] : ((tall(X0) | (strong(X0) & rich(X0))) & ((~strong(X0) | ~rich(X0)) | ~tall(X0))) [nnf transformation 9]
42. ! [X0] : ((tall(X0) | (strong(X0) & rich(X0))) & (~strong(X0) | ~rich(X0) | ~tall(X0))) [flattening 41]
43. ! [X0] : (((~tall(X0) | tall(X0)) | (creative(X0) | kind(X0))) & ((~creative(X0) & ~kind(X0)) | (tall(X0) & ~tall(X0)))) [nnf transformation 10]
44. ! [X0] : ((~tall(X0) | tall(X0) | creative(X0) | kind(X0)) & ((~creative(X0) & ~kind(X0)) | (tall(X0) & ~tall(X0)))) [flattening 43]
47. ! [X0] : (((~humble(X0) & ~rich(X0)) | ((~generous(X0) | ~wise(X0)) & (wise(X0) | generous(X0)))) & (((~wise(X0) | generous(X0)) & (wise(X0) | ~generous(X0))) | (humble(X0) | rich(X0)))) [nnf transformation 12]
48. ! [X0] : (((~humble(X0) & ~rich(X0)) | ((~generous(X0) | ~wise(X0)) & (wise(X0) | generous(X0)))) & (((~wise(X0) | generous(X0)) & (wise(X0) | ~generous(X0))) | humble(X0) | rich(X0))) [flattening 47]
56. generous(X0) | kind(X0) [cnf transformation 25]
63. ~generous(sK1) | kind(sK1) | ~rich(X3) | ~strong(X3) [cnf transformation 38]
78. ~tall(fred) | wise(john) [cnf transformation 27]
80. tall(X0) | rich(X0) [cnf transformation 42]
81. tall(X0) | strong(X0) [cnf transformation 42]
82. ~kind(X0) | ~tall(X0) [cnf transformation 44]
83. ~kind(X0) | tall(X0) [cnf transformation 44]
92. ~rich(X0) | ~generous(X0) | ~wise(X0) [cnf transformation 48]
108. rich(john) [cnf transformation 20]
124. 4 <=> ! [X3] : (~rich(X3) | ~strong(X3)) [avatar definition]
125. ~rich(X3) | ~strong(X3) <- (4) [avatar component clause 124]
131. kind(sK1) | ~rich(X3) | ~strong(X3) [subsumption resolution 63,56]
133. 6 <=> kind(sK1) [avatar definition]
135. kind(sK1) <- (6) [avatar component clause 133]
136. 4 | 6 [avatar split clause 131,133,124]
138. 7 <=> wise(john) [avatar definition]
140. wise(john) <- (7) [avatar component clause 138]
142. 8 <=> tall(fred) [avatar definition]
144. ~tall(fred) <- (~8) [avatar component clause 142]
145. 7 | ~8 [avatar split clause 78,142,138]
152. ~kind(X0) [subsumption resolution 82,83]
207. rich(fred) <- (~8) [resolution 80,144]
208. strong(fred) <- (~8) [resolution 81,144]
214. ~strong(fred) <- (4, ~8) [resolution 125,207]
217. $false <- (4, ~8) [subsumption resolution 214,208]
218. ~4 | 8 [avatar contradiction clause 217]
313. ~generous(john) | ~wise(john) [resolution 92,108]
314. ~generous(john) <- (7) [subsumption resolution 313,140]
315. kind(john) <- (7) [resolution 314,56]
316. $false <- (7) [subsumption resolution 315,152]
317. ~7 [avatar contradiction clause 316]
332. $false <- (6) [subsumption resolution 135,152]
333. ~6 [avatar contradiction clause 332]
334. $false [avatar sat refutation 136,145,218,317,333]
% SZS output end Proof for 5731515613505120360477957
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not brave or not happy is not funny.
Everyone who is either brave or not rich is not calm.
Everyone who is brave or not tall is brave or strong and vice versa.
If someone is creative then someone is both calm and not calm and vice versa.
Everyone who is quiet is funny or patient.
Everyone who is not happy is either not rich or brave and vice versa.
If someone is either quiet or brave then susan is not patient or not brave.
If someone is both curious and not tall then paul is either not curious or not brave and vice versa.
Everyone who is both not rich and kind is either not funny or creative.
If paul is both not old and quiet then someone is both not quiet and patient.
Everyone who is quiet is creative and vice versa.
Everyone who is not quiet is both not wise and not quiet.
Everyone who is not patient is not quiet.
If someone is both strong and not rich then john is both not tall and not happy.
Everyone who is not brave or not quiet is either strong or happy and vice versa.
If someone is patient or brave then someone is either not patient or not old and vice versa.
Someone is both patient and not quiet.
John is not rich or not creative.
Paul is either not brave or happy.
Susan is either happy or not generous.
Someone is both tall and kind.
Susan is not creative. | Paul is not strong. | neutral | (![X]:((~brave(X)<~>~happy(X))=>~funny(X)))&
(![X]:((brave(X)<~>~rich(X))=>~calm(X)))&
(![X]:((brave(X)|~tall(X))<=>(brave(X)|strong(X))))&
((?[X]:(creative(X)))<=>(?[X]:((calm(X)&~calm(X)))))&
(![X]:(quiet(X)=>(funny(X)|patient(X))))&
(![X]:(~happy(X)<=>(~rich(X)<~>brave(X))))&
((?[X]:((quiet(X)<~>brave(X))))=>((~patient(susan)|~brave(susan))))&
((?[X]:((curious(X)&~tall(X))))<=>((~curious(paul)<~>~brave(paul))))&
(![X]:((~rich(X)&kind(X))=>(~funny(X)<~>creative(X))))&
(((~old(paul)&quiet(paul)))=>(?[X]:((~quiet(X)&patient(X)))))&
(![X]:(quiet(X)<=>creative(X)))&
(![X]:(~quiet(X)=>(~wise(X)&~quiet(X))))&
(![X]:(~patient(X)=>~quiet(X)))&
((?[X]:((strong(X)&~rich(X))))=>((~tall(john)&~happy(john))))&
(![X]:((~brave(X)|~quiet(X))<=>(strong(X)<~>happy(X))))&
((?[X]:((patient(X)|brave(X))))<=>(?[X]:((~patient(X)<~>~old(X)))))&
(?[X]:((patient(X)&~quiet(X))))&
((~rich(john)|~creative(john)))&
((~brave(paul)<~>happy(paul)))&
((happy(susan)<~>~generous(susan)))&
(?[X]:((tall(X)&kind(X))))&
(~creative(susan)) | ~strong(paul) | [] | null | 0 |
If someone is not happy then someone is both not tall and patient and vice versa. Everyone who is not tall or not calm is tall or strong. If someone is either happy or not calm then someone is kind or tall. Everyone who is kind is not happy and vice versa. If john is both quiet and funny then someone is either not creative or humble and vice versa. If someone is old then john is both brave and not rich and vice versa. Everyone who is either calm or not tall is both not creative and calm. If someone is tall or quiet then someone is not funny and vice versa. If someone is happy then someone is either quiet or not old. Everyone who is not kind or not funny is either not kind or humble and vice versa. Everyone who is both quiet and not generous is both not patient and not old. If paul is both happy and not calm then lucy is calm or strong and vice versa. If fred is not quiet then someone is both old and generous and vice versa. If someone is not curious or funny then mary is both not wise and old. Everyone who is either not strong or not funny is both happy and not brave and vice versa. Everyone who is not humble is either wise or old and vice versa. Someone is either not old or calm. John is both not strong and kind. Fred is both not humble and not calm. Susan is both not happy and generous. Someone is funny. Someone is not calm. | Mary is quiet. | neutral | ((?[X]:(~happy(X)))<=>(?[X]:((~tall(X)&patient(X)))))&
(![X]:((~tall(X)|~calm(X))=>(tall(X)|strong(X))))&
((?[X]:((happy(X)<~>~calm(X))))=>(?[X]:((kind(X)|tall(X)))))&
(![X]:(kind(X)<=>~happy(X)))&
(((quiet(john)&funny(john)))<=>(?[X]:((~creative(X)<~>humble(X)))))&
((?[X]:(old(X)))<=>((brave(john)&~rich(john))))&
(![X]:((calm(X)<~>~tall(X))=>(~creative(X)&calm(X))))&
((?[X]:((tall(X)|quiet(X))))<=>(?[X]:(~funny(X))))&
((?[X]:(happy(X)))=>(?[X]:((quiet(X)<~>~old(X)))))&
(![X]:((~kind(X)|~funny(X))<=>(~kind(X)<~>humble(X))))&
(![X]:((quiet(X)&~generous(X))=>(~patient(X)&~old(X))))&
(((happy(paul)&~calm(paul)))<=>((calm(lucy)|strong(lucy))))&
((~quiet(fred))<=>(?[X]:((old(X)&generous(X)))))&
((?[X]:((~curious(X)|funny(X))))=>((~wise(mary)&old(mary))))&
(![X]:((~strong(X)<~>~funny(X))<=>(happy(X)&~brave(X))))&
(![X]:(~humble(X)<=>(wise(X)<~>old(X))))&
(?[X]:((~old(X)<~>calm(X))))&
((~strong(john)&kind(john)))&
((~humble(fred)&~calm(fred)))&
((~happy(susan)&generous(susan)))&
(?[X]:(funny(X)))&
(?[X]:(~calm(X))) | quiet(mary) | [] | null | 0 |
Everyone who is not calm is both not curious and curious.
Everyone who is strong or not patient is either not creative or humble and vice versa.
Everyone who is not generous is either not calm or not brave and vice versa.
Everyone who is either not rich or not old is not funny.
Everyone who is not happy or not curious is both quiet and not kind and vice versa.
If someone is both not kind and humble then someone is both not strong and not patient and vice versa.
Everyone who is not strong or tall is either tall or not kind and vice versa.
Everyone who is either kind or quiet is not humble and vice versa.
If someone is either funny or brave then someone is both strong and brave.
If john is either patient or not happy then john is both strong and creative.
If someone is either not old or not patient then someone is not brave or not patient and vice versa.
If someone is not quiet or tall then paul is not kind or not brave.
If someone is either brave or not generous then someone is either creative or not brave and vice versa.
If john is not rich then someone is not old or not creative and vice versa.
Everyone who is both kind and calm is both curious and not wise.
Everyone who is both not humble and not generous is not calm.
Paul is both calm and kind.
Someone is brave.
Someone is not calm or tall.
Someone is brave or not patient.
Paul is tall or not generous.
Lucy is both rich and not curious.
Someone is not patient.
Someone is not old. | Paul is not patient. | neutral | (![X]:(~calm(X)=>(~curious(X)&curious(X))))&
(![X]:((strong(X)|~patient(X))<=>(~creative(X)<~>humble(X))))&
(![X]:(~generous(X)<=>(~calm(X)<~>~brave(X))))&
(![X]:((~rich(X)<~>~old(X))=>~funny(X)))&
(![X]:((~happy(X)|~curious(X))<=>(quiet(X)&~kind(X))))&
((?[X]:((~kind(X)&humble(X))))<=>(?[X]:((~strong(X)&~patient(X)))))&
(![X]:((~strong(X)|tall(X))<=>(tall(X)<~>~kind(X))))&
(![X]:((kind(X)<~>quiet(X))<=>~humble(X)))&
((?[X]:((funny(X)<~>brave(X))))=>(?[X]:((strong(X)&brave(X)))))&
(((patient(john)<~>~happy(john)))=>((strong(john)&creative(john))))&
((?[X]:((~old(X)<~>~patient(X))))<=>(?[X]:((~brave(X)|~patient(X)))))&
((?[X]:((~quiet(X)|tall(X))))=>((~kind(paul)|~brave(paul))))&
((?[X]:((brave(X)<~>~generous(X))))<=>(?[X]:((creative(X)<~>~brave(X)))))&
((~rich(john))<=>(?[X]:((~old(X)|~creative(X)))))&
(![X]:((kind(X)&calm(X))=>(curious(X)&~wise(X))))&
(![X]:((~humble(X)&~generous(X))=>~calm(X)))&
((calm(paul)&kind(paul)))&
(?[X]:(brave(X)))&
(?[X]:((~calm(X)|tall(X))))&
(?[X]:((brave(X)|~patient(X))))&
((tall(paul)|~generous(paul)))&
((rich(lucy)&~curious(lucy)))&
(?[X]:(~patient(X)))&
(?[X]:(~old(X))) | ~patient(paul) | [] | null | 0 |
If alice is not calm or rich then someone is both not tall and curious.
Everyone who is both calm and not wise is wise or not strong and vice versa.
If someone is not curious or not rich then mary is either calm or not curious.
If mary is funny or tall then mary is both generous and happy.
If susan is either not brave or not humble then paul is both strong and not humble and vice versa.
If mary is both creative and not happy then john is either happy or kind.
If alice is either not calm or creative then paul is either not creative or not humble and vice versa.
Everyone who is not wise or brave is both not curious and happy and vice versa.
If john is both creative and kind then someone is wise and vice versa.
If susan is both not quiet and not creative then someone is not quiet and vice versa.
Everyone who is both funny and strong is rich.
If someone is not rich then someone is not humble and vice versa.
Everyone who is not rich or not humble is both happy and not curious and vice versa.
If someone is tall then john is funny or not happy and vice versa.
Everyone who is not calm is both not rich and kind.
Someone is both not curious and humble.
Paul is kind or generous.
Mary is either tall or not old.
Paul is both calm and generous.
Paul is quiet.
Paul is not kind.
John is both not tall and happy.
Alice is not creative or strong. | Alice is calm. | entailment | (((~calm(alice)|rich(alice)))=>(?[X]:((~tall(X)&curious(X)))))&
(![X]:((calm(X)&~wise(X))<=>(wise(X)|~strong(X))))&
((?[X]:((~curious(X)|~rich(X))))=>((calm(mary)<~>~curious(mary))))&
(((funny(mary)|tall(mary)))=>((generous(mary)&happy(mary))))&
(((~brave(susan)<~>~humble(susan)))<=>((strong(paul)&~humble(paul))))&
(((creative(mary)&~happy(mary)))=>((happy(john)<~>kind(john))))&
(((~calm(alice)<~>creative(alice)))<=>((~creative(paul)<~>~humble(paul))))&
(![X]:((~wise(X)|brave(X))<=>(~curious(X)&happy(X))))&
(((creative(john)&kind(john)))<=>(?[X]:(wise(X))))&
(((~quiet(susan)&~creative(susan)))<=>(?[X]:(~quiet(X))))&
(![X]:((funny(X)&strong(X))=>rich(X)))&
((?[X]:(~rich(X)))<=>(?[X]:(~humble(X))))&
(![X]:((~rich(X)|~humble(X))<=>(happy(X)&~curious(X))))&
((?[X]:(tall(X)))<=>((funny(john)|~happy(john))))&
(![X]:(~calm(X)=>(~rich(X)&kind(X))))&
(?[X]:((~curious(X)&humble(X))))&
((kind(paul)|generous(paul)))&
((tall(mary)<~>~old(mary)))&
((calm(paul)&generous(paul)))&
(quiet(paul))&
(~kind(paul))&
((~tall(john)&happy(john)))&
((~creative(alice)|strong(alice))) | calm(alice) | [
"p0",
"p1",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 1389031789569618517393621
% SZS output start Proof for 1389031789569618517393621
1. (rich(alice) | ~calm(alice)) => ? [X0] : (curious(X0) & ~tall(X0)) [input p0]
2. ! [X0] : ((~wise(X0) & calm(X0)) <=> (~strong(X0) | wise(X0))) [input p1]
8. ! [X0] : ((brave(X0) | ~wise(X0)) <=> (happy(X0) & ~curious(X0))) [input p7]
24. ~calm(alice) [input hypothesis]
29. ? [X0] : (curious(X0) & ~tall(X0)) | (~rich(alice) & calm(alice)) [ennf transformation 1]
37. ? [X0] : (curious(X0) & ~tall(X0)) => (curious(sK0) & ~tall(sK0)) [choice axiom]
38. (curious(sK0) & ~tall(sK0)) | (~rich(alice) & calm(alice)) [skolemisation 29,37]
39. ! [X0] : (((~wise(X0) & calm(X0)) | (strong(X0) & ~wise(X0))) & ((~strong(X0) | wise(X0)) | (wise(X0) | ~calm(X0)))) [nnf transformation 2]
40. ! [X0] : (((~wise(X0) & calm(X0)) | (strong(X0) & ~wise(X0))) & (~strong(X0) | wise(X0) | wise(X0) | ~calm(X0))) [flattening 39]
46. ! [X0] : (((brave(X0) | ~wise(X0)) | (~happy(X0) | curious(X0))) & ((happy(X0) & ~curious(X0)) | (~brave(X0) & wise(X0)))) [nnf transformation 8]
47. ! [X0] : ((brave(X0) | ~wise(X0) | ~happy(X0) | curious(X0)) & ((happy(X0) & ~curious(X0)) | (~brave(X0) & wise(X0)))) [flattening 46]
75. curious(sK0) | calm(alice) [cnf transformation 38]
80. ~wise(X0) | ~wise(X0) [cnf transformation 40]
104. ~curious(X0) | wise(X0) [cnf transformation 47]
138. ~calm(alice) [cnf transformation 24]
140. ~wise(X0) [duplicate literal removal 80]
146. 2 <=> curious(sK0) [avatar definition]
148. curious(sK0) <- (2) [avatar component clause 146]
151. 3 <=> calm(alice) [avatar definition]
154. 3 | 2 [avatar split clause 75,146,151]
247. ~curious(X0) [subsumption resolution 104,140]
312. ~3 [avatar split clause 138,151]
313. $false <- (2) [subsumption resolution 148,247]
314. ~2 [avatar contradiction clause 313]
315. $false [avatar sat refutation 154,312,314]
% SZS output end Proof for 1389031789569618517393621
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If susan is either not quiet or funny then paul is wise and vice versa.
Everyone who is either not quiet or not creative is both rich and happy.
Everyone who is both not old and generous is brave.
Everyone who is either not generous or not happy is either not quiet or kind.
Everyone who is not generous is curious and vice versa.
If susan is both not calm and old then alice is tall or generous.
If someone is kind or not quiet then someone is not calm or not humble and vice versa.
If someone is not strong then alice is not generous.
Everyone who is not old is not curious or not calm and vice versa.
If lucy is either not tall or generous then mary is patient.
Everyone who is either wise or generous is happy and vice versa.
Everyone who is not tall is not happy or not patient and vice versa.
If susan is quiet or not quiet then alice is both not creative and generous.
Everyone who is not humble or not patient is both not funny and generous.
Everyone who is both not creative and brave is both strong and not calm.
If someone is both quiet and humble then someone is both not brave and rich and vice versa.
Alice is patient or quiet.
Susan is calm.
Someone is either not rich or happy.
Someone is both not tall and quiet.
Someone is either not creative or not quiet.
Fred is either not humble or funny.
Lucy is either not strong or tall. | Lucy is patient. | entailment | (((~quiet(susan)<~>funny(susan)))<=>(wise(paul)))&
(![X]:((~quiet(X)<~>~creative(X))=>(rich(X)&happy(X))))&
(![X]:((~old(X)&generous(X))=>brave(X)))&
(![X]:((~generous(X)<~>~happy(X))=>(~quiet(X)<~>kind(X))))&
(![X]:(~generous(X)<=>curious(X)))&
(((~calm(susan)&old(susan)))=>((tall(alice)|generous(alice))))&
((?[X]:((kind(X)|~quiet(X))))<=>(?[X]:((~calm(X)|~humble(X)))))&
((?[X]:(~strong(X)))=>(~generous(alice)))&
(![X]:(~old(X)<=>(~curious(X)|~calm(X))))&
(((~tall(lucy)<~>generous(lucy)))=>(patient(mary)))&
(![X]:((wise(X)<~>generous(X))<=>happy(X)))&
(![X]:(~tall(X)<=>(~happy(X)|~patient(X))))&
(((quiet(susan)|~quiet(susan)))=>((~creative(alice)&generous(alice))))&
(![X]:((~humble(X)|~patient(X))=>(~funny(X)&generous(X))))&
(![X]:((~creative(X)&brave(X))=>(strong(X)&~calm(X))))&
((?[X]:((quiet(X)&humble(X))))<=>(?[X]:((~brave(X)&rich(X)))))&
((patient(alice)|quiet(alice)))&
(calm(susan))&
(?[X]:((~rich(X)<~>happy(X))))&
(?[X]:((~tall(X)&quiet(X))))&
(?[X]:((~creative(X)<~>~quiet(X))))&
((~humble(fred)<~>funny(fred)))&
((~strong(lucy)<~>tall(lucy))) | patient(lucy) | [
"p7",
"p11",
"p12",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 1377508245135297814415937
% SZS output start Proof for 1377508245135297814415937
8. ? [X0] : ~strong(X0) => ~generous(alice) [input p7]
12. ! [X0] : (~tall(X0) <=> (~patient(X0) | ~happy(X0))) [input p11]
13. (~quiet(susan) | quiet(susan)) => (generous(alice) & ~creative(alice)) [input p12]
23. ~strong(lucy) <~> tall(lucy) [input p22]
24. ~patient(lucy) [input hypothesis]
33. ~generous(alice) | ! [X0] : strong(X0) [ennf transformation 8]
35. (generous(alice) & ~creative(alice)) | (quiet(susan) & ~quiet(susan)) [ennf transformation 13]
52. ! [X0] : ((~tall(X0) | (patient(X0) & happy(X0))) & ((~patient(X0) | ~happy(X0)) | tall(X0))) [nnf transformation 12]
53. ! [X0] : ((~tall(X0) | (patient(X0) & happy(X0))) & (~patient(X0) | ~happy(X0) | tall(X0))) [flattening 52]
68. (~tall(lucy) | strong(lucy)) & (tall(lucy) | ~strong(lucy)) [nnf transformation 23]
89. ~generous(alice) | strong(X0) [cnf transformation 33]
101. ~tall(X0) | patient(X0) [cnf transformation 53]
104. generous(alice) | ~quiet(susan) [cnf transformation 35]
105. generous(alice) | quiet(susan) [cnf transformation 35]
126. tall(lucy) | ~strong(lucy) [cnf transformation 68]
128. ~patient(lucy) [cnf transformation 24]
134. 2 <=> quiet(susan) [avatar definition]
158. 7 <=> generous(alice) [avatar definition]
195. 16 <=> ! [X0] : strong(X0) [avatar definition]
196. strong(X0) <- (16) [avatar component clause 195]
197. 16 | ~7 [avatar split clause 89,158,195]
203. 18 <=> tall(lucy) [avatar definition]
204. tall(lucy) <- (18) [avatar component clause 203]
212. 2 | 7 [avatar split clause 105,158,134]
213. ~2 | 7 [avatar split clause 104,158,134]
286. 35 <=> strong(lucy) [avatar definition]
287. ~strong(lucy) <- (~35) [avatar component clause 286]
290. ~35 | 18 [avatar split clause 126,203,286]
291. $false <- (16, ~35) [resolution 287,196]
292. ~16 | 35 [avatar contradiction clause 291]
295. patient(lucy) <- (18) [resolution 101,204]
296. $false <- (18) [subsumption resolution 295,128]
297. ~18 [avatar contradiction clause 296]
298. $false [avatar sat refutation 197,212,213,290,292,297]
% SZS output end Proof for 1377508245135297814415937
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not kind and old is humble or not generous and vice versa.
If someone is not funny or not brave then someone is calm or not tall.
If john is both not brave and kind then someone is not patient or not generous and vice versa.
If lucy is either brave or not humble then someone is either tall or not curious.
Everyone who is quiet is either rich or not old.
If someone is kind or not patient then fred is both rich and generous and vice versa.
If someone is either kind or not funny then john is both creative and generous.
Everyone who is not tall is either patient or not old.
If mary is not happy or not generous then mary is brave and vice versa.
If susan is brave or funny then someone is either tall or not calm.
Everyone who is not quiet or tall is creative and vice versa.
If lucy is both humble and creative then john is both not brave and generous.
Everyone who is both creative and wise is generous.
Everyone who is not kind is not curious or creative and vice versa.
If john is not calm then someone is not wise.
Someone is either not generous or funny.
Fred is not happy.
Someone is either rich or funny.
Someone is generous or wise.
Someone is not rich.
Someone is not curious or quiet.
John is either not kind or creative.
Paul is both creative and generous. | Fred is patient. | entailment | (![X]:((~kind(X)&old(X))<=>(humble(X)|~generous(X))))&
((?[X]:((~funny(X)|~brave(X))))=>(?[X]:((calm(X)|~tall(X)))))&
(((~brave(john)&kind(john)))<=>(?[X]:((~patient(X)|~generous(X)))))&
(((brave(lucy)<~>~humble(lucy)))=>(?[X]:((tall(X)<~>~curious(X)))))&
(![X]:(quiet(X)=>(rich(X)<~>~old(X))))&
((?[X]:((kind(X)|~patient(X))))<=>((rich(fred)&generous(fred))))&
((?[X]:((kind(X)<~>~funny(X))))=>((creative(john)&generous(john))))&
(![X]:(~tall(X)=>(patient(X)<~>~old(X))))&
(((~happy(mary)|~generous(mary)))<=>(brave(mary)))&
(((brave(susan)|funny(susan)))=>(?[X]:((tall(X)<~>~calm(X)))))&
(![X]:((~quiet(X)|tall(X))<=>creative(X)))&
(((humble(lucy)&creative(lucy)))=>((~brave(john)&generous(john))))&
(![X]:((creative(X)&wise(X))=>generous(X)))&
(![X]:(~kind(X)<=>(~curious(X)|creative(X))))&
((~calm(john))=>(?[X]:(~wise(X))))&
(?[X]:((~generous(X)<~>funny(X))))&
(~happy(fred))&
(?[X]:((rich(X)<~>funny(X))))&
(?[X]:((generous(X)|wise(X))))&
(?[X]:(~rich(X)))&
(?[X]:((~curious(X)|quiet(X))))&
((~kind(john)<~>creative(john)))&
((creative(paul)&generous(paul))) | patient(fred) | [
"p2",
"p13",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 5911687363873708685181419
% SZS output start Proof for 5911687363873708685181419
3. (kind(john) & ~brave(john)) <=> ? [X0] : (~generous(X0) | ~patient(X0)) [input p2]
14. ! [X0] : (~kind(X0) <=> (creative(X0) | ~curious(X0))) [input p13]
22. ~kind(john) <~> creative(john) [input p21]
24. ~patient(fred) [input hypothesis]
42. ((kind(john) & ~brave(john)) | ! [X0] : (generous(X0) & patient(X0))) & (? [X0] : (~generous(X0) | ~patient(X0)) | (~kind(john) | brave(john))) [nnf transformation 3]
43. ((kind(john) & ~brave(john)) | ! [X0] : (generous(X0) & patient(X0))) & (? [X0] : (~generous(X0) | ~patient(X0)) | ~kind(john) | brave(john)) [flattening 42]
44. ((kind(john) & ~brave(john)) | ! [X0] : (generous(X0) & patient(X0))) & (? [X1] : (~generous(X1) | ~patient(X1)) | ~kind(john) | brave(john)) [rectify 43]
45. ? [X1] : (~generous(X1) | ~patient(X1)) => (~generous(sK1) | ~patient(sK1)) [choice axiom]
46. ((kind(john) & ~brave(john)) | ! [X0] : (generous(X0) & patient(X0))) & ((~generous(sK1) | ~patient(sK1)) | ~kind(john) | brave(john)) [skolemisation 44,45]
65. ! [X0] : ((~kind(X0) | (~creative(X0) & curious(X0))) & ((creative(X0) | ~curious(X0)) | kind(X0))) [nnf transformation 14]
66. ! [X0] : ((~kind(X0) | (~creative(X0) & curious(X0))) & (creative(X0) | ~curious(X0) | kind(X0))) [flattening 65]
81. (~creative(john) | kind(john)) & (creative(john) | ~kind(john)) [nnf transformation 22]
92. kind(john) | patient(X0) [cnf transformation 46]
126. ~kind(X0) | ~creative(X0) [cnf transformation 66]
136. creative(john) | ~kind(john) [cnf transformation 81]
140. ~patient(fred) [cnf transformation 24]
161. 6 <=> kind(john) [avatar definition]
166. 7 <=> ! [X0] : patient(X0) [avatar definition]
167. patient(X0) <- (7) [avatar component clause 166]
168. 7 | 6 [avatar split clause 92,161,166]
336. ~kind(john) [subsumption resolution 136,126]
337. ~6 [avatar split clause 336,161]
338. $false <- (7) [resolution 167,140]
339. ~7 [avatar contradiction clause 338]
340. $false [avatar sat refutation 168,337,339]
% SZS output end Proof for 5911687363873708685181419
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy or not strong is funny and vice versa. Everyone who is happy is quiet and vice versa. If someone is both calm and curious then paul is both not creative and humble and vice versa. If lucy is curious or happy then susan is either not wise or rich and vice versa. Everyone who is either patient or not old is either not generous or calm. If fred is not patient then lucy is either strong or not wise and vice versa. Everyone who is not happy or humble is strong and vice versa. Everyone who is happy is either tall or not tall. If susan is quiet or old then susan is not funny or not tall and vice versa. Everyone who is not old or strong is old or calm and vice versa. Everyone who is not tall or not happy is both wise and calm and vice versa. Everyone who is either humble or not brave is not humble or not kind. Everyone who is either tall or wise is both wise and not strong and vice versa. Everyone who is both curious and not quiet is not creative or humble and vice versa. If someone is not brave then susan is either quiet or humble and vice versa. Everyone who is not tall is both wise and not wise. Mary is quiet or not rich. Someone is either not quiet or not calm. Fred is humble or strong. Mary is not generous. Paul is not quiet or not strong. Susan is generous or curious. Alice is brave. | Lucy is not brave. | neutral | (![X]:((happy(X)|~strong(X))<=>funny(X)))&
(![X]:(happy(X)<=>quiet(X)))&
((?[X]:((calm(X)&curious(X))))<=>((~creative(paul)&humble(paul))))&
(((curious(lucy)|happy(lucy)))<=>((~wise(susan)<~>rich(susan))))&
(![X]:((patient(X)<~>~old(X))=>(~generous(X)<~>calm(X))))&
((~patient(fred))<=>((strong(lucy)<~>~wise(lucy))))&
(![X]:((~happy(X)|humble(X))<=>strong(X)))&
(![X]:(happy(X)=>(tall(X)<~>~tall(X))))&
(((quiet(susan)|old(susan)))<=>((~funny(susan)|~tall(susan))))&
(![X]:((~old(X)|strong(X))<=>(old(X)|calm(X))))&
(![X]:((~tall(X)|~happy(X))<=>(wise(X)&calm(X))))&
(![X]:((humble(X)<~>~brave(X))=>(~humble(X)|~kind(X))))&
(![X]:((tall(X)<~>wise(X))<=>(wise(X)&~strong(X))))&
(![X]:((curious(X)&~quiet(X))<=>(~creative(X)|humble(X))))&
((?[X]:(~brave(X)))<=>((quiet(susan)<~>humble(susan))))&
(![X]:(~tall(X)=>(wise(X)&~wise(X))))&
((quiet(mary)|~rich(mary)))&
(?[X]:((~quiet(X)<~>~calm(X))))&
((humble(fred)|strong(fred)))&
(~generous(mary))&
((~quiet(paul)|~strong(paul)))&
((generous(susan)|curious(susan)))&
(brave(alice)) | ~brave(lucy) | [] | null | 0 |
If john is either tall or quiet then alice is happy or not kind.
Everyone who is either not strong or patient is either not strong or not generous.
Everyone who is not old or old is either old or not old and vice versa.
Everyone who is both not calm and quiet is not quiet and vice versa.
If alice is brave or humble then someone is not funny.
If someone is both not patient and patient then fred is not calm or not strong and vice versa.
If someone is quiet or not curious then john is not creative or patient.
Everyone who is quiet is both curious and wise.
Everyone who is either not calm or not strong is both old and not brave and vice versa.
Everyone who is either not generous or calm is both not tall and not funny.
Everyone who is quiet or generous is humble or not wise.
Everyone who is either not humble or humble is humble and vice versa.
Everyone who is not generous is not creative.
Everyone who is not humble is both quiet and not kind and vice versa.
If mary is both happy and not generous then mary is both humble and calm.
If lucy is patient or not brave then alice is old and vice versa.
Lucy is not tall.
Someone is both patient and not strong.
Someone is not creative.
Someone is generous.
Someone is wise or tall.
Someone is patient.
Alice is funny or not brave. | Fred is not brave. | neutral | (((tall(john)<~>quiet(john)))=>((happy(alice)|~kind(alice))))&
(![X]:((~strong(X)<~>patient(X))=>(~strong(X)<~>~generous(X))))&
(![X]:((~old(X)|old(X))<=>(old(X)<~>~old(X))))&
(![X]:((~calm(X)&quiet(X))<=>~quiet(X)))&
(((brave(alice)|humble(alice)))=>(?[X]:(~funny(X))))&
((?[X]:((~patient(X)&patient(X))))<=>((~calm(fred)|~strong(fred))))&
((?[X]:((quiet(X)|~curious(X))))=>((~creative(john)|patient(john))))&
(![X]:(quiet(X)=>(curious(X)&wise(X))))&
(![X]:((~calm(X)<~>~strong(X))<=>(old(X)&~brave(X))))&
(![X]:((~generous(X)<~>calm(X))=>(~tall(X)&~funny(X))))&
(![X]:((quiet(X)|generous(X))=>(humble(X)|~wise(X))))&
(![X]:((~humble(X)<~>humble(X))<=>humble(X)))&
(![X]:(~generous(X)=>~creative(X)))&
(![X]:(~humble(X)<=>(quiet(X)&~kind(X))))&
(((happy(mary)&~generous(mary)))=>((humble(mary)&calm(mary))))&
(((patient(lucy)|~brave(lucy)))<=>(old(alice)))&
(~tall(lucy))&
(?[X]:((patient(X)&~strong(X))))&
(?[X]:(~creative(X)))&
(?[X]:(generous(X)))&
(?[X]:((wise(X)|tall(X))))&
(?[X]:(patient(X)))&
((funny(alice)|~brave(alice))) | ~brave(fred) | [] | null | 0 |
Everyone who is either happy or not happy is not happy or not brave. Everyone who is tall or not humble is both not rich and happy. Everyone who is both not happy and tall is either not humble or not wise and vice versa. If someone is not curious then john is not wise. Everyone who is not generous is tall and vice versa. Everyone who is either not tall or generous is patient or not curious. If susan is not strong then fred is both not humble and not quiet and vice versa. If alice is either not rich or not humble then paul is either not kind or not humble. If john is both curious and not strong then someone is either not rich or old and vice versa. Everyone who is both kind and not old is either generous or patient. If someone is generous or brave then someone is old or not generous. Everyone who is both humble and brave is not kind and vice versa. Everyone who is wise is not patient and vice versa. If susan is old or not funny then john is either old or not brave and vice versa. Everyone who is both wise and patient is either not strong or not tall and vice versa. If someone is old or not brave then john is both funny and not kind and vice versa. Someone is not tall or not patient. Alice is not generous or not old. John is strong or rich. Alice is humble or funny. Someone is patient. Lucy is either humble or not tall. Someone is both funny and not happy. Someone is both not brave and rich. | Alice is not humble. | neutral | (![X]:((happy(X)<~>~happy(X))=>(~happy(X)|~brave(X))))&
(![X]:((tall(X)|~humble(X))=>(~rich(X)&happy(X))))&
(![X]:((~happy(X)&tall(X))<=>(~humble(X)<~>~wise(X))))&
((?[X]:(~curious(X)))=>(~wise(john)))&
(![X]:(~generous(X)<=>tall(X)))&
(![X]:((~tall(X)<~>generous(X))=>(patient(X)|~curious(X))))&
((~strong(susan))<=>((~humble(fred)&~quiet(fred))))&
(((~rich(alice)<~>~humble(alice)))=>((~kind(paul)<~>~humble(paul))))&
(((curious(john)&~strong(john)))<=>(?[X]:((~rich(X)<~>old(X)))))&
(![X]:((kind(X)&~old(X))=>(generous(X)<~>patient(X))))&
((?[X]:((generous(X)|brave(X))))=>(?[X]:((old(X)|~generous(X)))))&
(![X]:((humble(X)&brave(X))<=>~kind(X)))&
(![X]:(wise(X)<=>~patient(X)))&
(((old(susan)|~funny(susan)))<=>((old(john)<~>~brave(john))))&
(![X]:((wise(X)&patient(X))<=>(~strong(X)<~>~tall(X))))&
((?[X]:((old(X)|~brave(X))))<=>((funny(john)&~kind(john))))&
(?[X]:((~tall(X)|~patient(X))))&
((~generous(alice)|~old(alice)))&
((strong(john)|rich(john)))&
((humble(alice)|funny(alice)))&
(?[X]:(patient(X)))&
((humble(lucy)<~>~tall(lucy)))&
(?[X]:((funny(X)&~happy(X))))&
(?[X]:((~brave(X)&rich(X)))) | ~humble(alice) | [] | null | 0 |
If someone is humble then someone is not patient or happy.
Everyone who is not humble is not happy and vice versa.
Everyone who is both kind and not patient is not patient or not wise.
Everyone who is both not tall and not patient is both not generous and calm and vice versa.
Everyone who is either not brave or not curious is both strong and calm and vice versa.
Everyone who is both not patient and tall is both humble and not happy and vice versa.
If john is not creative then someone is either rich or kind.
Everyone who is not rich is not generous or not rich.
Everyone who is both kind and not creative is not funny and vice versa.
Everyone who is either tall or kind is not curious.
If someone is either calm or rich then someone is both not brave and not old.
Everyone who is not wise is either happy or old.
If fred is both patient and not quiet then someone is both calm and not curious.
Everyone who is not wise or quiet is not humble and vice versa.
Everyone who is not strong or curious is not brave and vice versa.
If someone is both rich and not quiet then someone is either not creative or not wise.
Someone is humble or rich.
Lucy is either not brave or not strong.
Susan is either not quiet or rich.
Someone is not old.
Someone is both not curious and not strong.
Someone is either old or not curious.
Someone is funny or not tall. | Lucy is strong. | entailment | ((?[X]:(humble(X)))=>(?[X]:((~patient(X)|happy(X)))))&
(![X]:(~humble(X)<=>~happy(X)))&
(![X]:((kind(X)&~patient(X))=>(~patient(X)|~wise(X))))&
(![X]:((~tall(X)&~patient(X))<=>(~generous(X)&calm(X))))&
(![X]:((~brave(X)<~>~curious(X))<=>(strong(X)&calm(X))))&
(![X]:((~patient(X)&tall(X))<=>(humble(X)&~happy(X))))&
((~creative(john))=>(?[X]:((rich(X)<~>kind(X)))))&
(![X]:(~rich(X)=>(~generous(X)|~rich(X))))&
(![X]:((kind(X)&~creative(X))<=>~funny(X)))&
(![X]:((tall(X)<~>kind(X))=>~curious(X)))&
((?[X]:((calm(X)<~>rich(X))))=>(?[X]:((~brave(X)&~old(X)))))&
(![X]:(~wise(X)=>(happy(X)<~>old(X))))&
(((patient(fred)&~quiet(fred)))=>(?[X]:((calm(X)&~curious(X)))))&
(![X]:((~wise(X)|quiet(X))<=>~humble(X)))&
(![X]:((~strong(X)|curious(X))<=>~brave(X)))&
((?[X]:((rich(X)&~quiet(X))))=>(?[X]:((~creative(X)<~>~wise(X)))))&
(?[X]:((humble(X)|rich(X))))&
((~brave(lucy)<~>~strong(lucy)))&
((~quiet(susan)<~>rich(susan)))&
(?[X]:(~old(X)))&
(?[X]:((~curious(X)&~strong(X))))&
(?[X]:((old(X)<~>~curious(X))))&
(?[X]:((funny(X)|~tall(X)))) | strong(lucy) | [
"p14",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 1239442223759570169998474
% SZS output start Proof for 1239442223759570169998474
15. ! [X0] : ((curious(X0) | ~strong(X0)) <=> ~brave(X0)) [input p14]
18. ~brave(lucy) <~> ~strong(lucy) [input p17]
24. ~strong(lucy) [input hypothesis]
66. ! [X0] : (((curious(X0) | ~strong(X0)) | brave(X0)) & (~brave(X0) | (~curious(X0) & strong(X0)))) [nnf transformation 15]
67. ! [X0] : ((curious(X0) | ~strong(X0) | brave(X0)) & (~brave(X0) | (~curious(X0) & strong(X0)))) [flattening 66]
74. (strong(lucy) | brave(lucy)) & (~strong(lucy) | ~brave(lucy)) [nnf transformation 18]
120. ~brave(X0) | strong(X0) [cnf transformation 67]
127. strong(lucy) | brave(lucy) [cnf transformation 74]
136. ~strong(lucy) [cnf transformation 24]
221. strong(lucy) [subsumption resolution 127,120]
252. $false [subsumption resolution 136,221]
% SZS output end Proof for 1239442223759570169998474
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong or not wise is both creative and generous.
Everyone who is either not patient or funny is funny and vice versa.
If someone is both old and not creative then someone is both not wise and not humble.
Everyone who is not humble is not old or happy and vice versa.
Everyone who is curious or not patient is either tall or not strong.
Everyone who is generous or curious is both calm and curious and vice versa.
Everyone who is old is either not brave 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. | Alice is kind. | neutral | (![X]:((strong(X)<~>~wise(X))=>(creative(X)&generous(X))))&
(![X]:((~patient(X)<~>funny(X))<=>funny(X)))&
((?[X]:((old(X)&~creative(X))))=>(?[X]:((~wise(X)&~humble(X)))))&
(![X]:(~humble(X)<=>(~old(X)|happy(X))))&
(![X]:((curious(X)|~patient(X))=>(tall(X)<~>~strong(X))))&
(![X]:((generous(X)|curious(X))<=>(calm(X)&curious(X))))&
(![X]:(old(X)=>(~brave(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)) | kind(alice) | [] | null | 0 |
Everyone who is both not creative and strong is not rich or not quiet and vice versa.
If fred is both wise and funny then john is either brave or not wise and vice versa.
If lucy is not happy or patient then fred is humble and vice versa.
Everyone who is both tall and old is both generous and not funny.
If john is either strong or not generous then alice is either not curious or calm and vice versa.
Everyone who is wise is not humble and vice versa.
If lucy is either rich or not curious then someone is brave or not quiet and vice versa.
Everyone who is strong is both not curious and brave.
If paul is both quiet and not wise then someone is both not patient and brave and vice versa.
If paul is both wise and not old then someone is creative or curious and vice versa.
If someone is not funny then mary is either funny or wise and vice versa.
If lucy is both humble and not curious then someone is curious or not humble and vice versa.
Everyone who is not humble or not brave is either quiet or not rich.
Everyone who is wise or kind is both not patient and not brave.
If someone is either not old or calm then someone is quiet or not brave.
If susan is either not brave or not tall then someone is either funny or rich and vice versa.
Lucy is creative.
Paul is not generous or not funny.
Someone is rich or not generous.
Someone is wise.
Someone is brave or wise.
Someone is calm.
Someone is generous or calm. | Alice is not strong. | entailment | (![X]:((~creative(X)&strong(X))<=>(~rich(X)|~quiet(X))))&
(((wise(fred)&funny(fred)))<=>((brave(john)<~>~wise(john))))&
(((~happy(lucy)|patient(lucy)))<=>(humble(fred)))&
(![X]:((tall(X)&old(X))=>(generous(X)&~funny(X))))&
(((strong(john)<~>~generous(john)))<=>((~curious(alice)<~>calm(alice))))&
(![X]:(wise(X)<=>~humble(X)))&
(((rich(lucy)<~>~curious(lucy)))<=>(?[X]:((brave(X)|~quiet(X)))))&
(![X]:(strong(X)=>(~curious(X)&brave(X))))&
(((quiet(paul)&~wise(paul)))<=>(?[X]:((~patient(X)&brave(X)))))&
(((wise(paul)&~old(paul)))<=>(?[X]:((creative(X)|curious(X)))))&
((?[X]:(~funny(X)))<=>((funny(mary)<~>wise(mary))))&
(((humble(lucy)&~curious(lucy)))<=>(?[X]:((curious(X)|~humble(X)))))&
(![X]:((~humble(X)|~brave(X))=>(quiet(X)<~>~rich(X))))&
(![X]:((wise(X)|kind(X))=>(~patient(X)&~brave(X))))&
((?[X]:((~old(X)<~>calm(X))))=>(?[X]:((quiet(X)|~brave(X)))))&
(((~brave(susan)<~>~tall(susan)))<=>(?[X]:((funny(X)<~>rich(X)))))&
(creative(lucy))&
((~generous(paul)|~funny(paul)))&
(?[X]:((rich(X)|~generous(X))))&
(?[X]:(wise(X)))&
(?[X]:((brave(X)|wise(X))))&
(?[X]:(calm(X)))&
(?[X]:((generous(X)|calm(X)))) | ~strong(alice) | [
"p0",
"p6",
"p7",
"p11",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 718626960760028590992032
% SZS output start Proof for 718626960760028590992032
1. ! [X0] : ((strong(X0) & ~creative(X0)) <=> (~quiet(X0) | ~rich(X0))) [input p0]
7. (rich(lucy) <~> ~curious(lucy)) <=> ? [X0] : (~quiet(X0) | brave(X0)) [input p6]
8. ! [X0] : (strong(X0) => (brave(X0) & ~curious(X0))) [input p7]
12. (~curious(lucy) & humble(lucy)) <=> ? [X0] : (~humble(X0) | curious(X0)) [input p11]
17. creative(lucy) [input p16]
24. strong(alice) [input hypothesis]
29. ! [X0] : ((brave(X0) & ~curious(X0)) | ~strong(X0)) [ennf transformation 8]
33. ! [X0] : (((strong(X0) & ~creative(X0)) | (quiet(X0) & rich(X0))) & ((~quiet(X0) | ~rich(X0)) | (~strong(X0) | creative(X0)))) [nnf transformation 1]
34. ! [X0] : (((strong(X0) & ~creative(X0)) | (quiet(X0) & rich(X0))) & (~quiet(X0) | ~rich(X0) | ~strong(X0) | creative(X0))) [flattening 33]
41. (((curious(lucy) | ~rich(lucy)) & (~curious(lucy) | rich(lucy))) | ! [X0] : (quiet(X0) & ~brave(X0))) & (? [X0] : (~quiet(X0) | brave(X0)) | ((rich(lucy) | curious(lucy)) & (~curious(lucy) | ~rich(lucy)))) [nnf transformation 7]
42. (((curious(lucy) | ~rich(lucy)) & (~curious(lucy) | rich(lucy))) | ! [X0] : (quiet(X0) & ~brave(X0))) & (? [X1] : (~quiet(X1) | brave(X1)) | ((rich(lucy) | curious(lucy)) & (~curious(lucy) | ~rich(lucy)))) [rectify 41]
43. ? [X1] : (~quiet(X1) | brave(X1)) => (~quiet(sK0) | brave(sK0)) [choice axiom]
44. (((curious(lucy) | ~rich(lucy)) & (~curious(lucy) | rich(lucy))) | ! [X0] : (quiet(X0) & ~brave(X0))) & ((~quiet(sK0) | brave(sK0)) | ((rich(lucy) | curious(lucy)) & (~curious(lucy) | ~rich(lucy)))) [skolemisation 42,43]
59. ((~curious(lucy) & humble(lucy)) | ! [X0] : (humble(X0) & ~curious(X0))) & (? [X0] : (~humble(X0) | curious(X0)) | (curious(lucy) | ~humble(lucy))) [nnf transformation 12]
60. ((~curious(lucy) & humble(lucy)) | ! [X0] : (humble(X0) & ~curious(X0))) & (? [X0] : (~humble(X0) | curious(X0)) | curious(lucy) | ~humble(lucy)) [flattening 59]
61. ((~curious(lucy) & humble(lucy)) | ! [X0] : (humble(X0) & ~curious(X0))) & (? [X1] : (~humble(X1) | curious(X1)) | curious(lucy) | ~humble(lucy)) [rectify 60]
62. ? [X1] : (~humble(X1) | curious(X1)) => (~humble(sK4) | curious(sK4)) [choice axiom]
63. ((~curious(lucy) & humble(lucy)) | ! [X0] : (humble(X0) & ~curious(X0))) & ((~humble(sK4) | curious(sK4)) | curious(lucy) | ~humble(lucy)) [skolemisation 61,62]
84. ~creative(X0) | rich(X0) [cnf transformation 34]
113. curious(lucy) | ~rich(lucy) | ~brave(X0) [cnf transformation 44]
116. ~strong(X0) | brave(X0) [cnf transformation 29]
133. ~curious(lucy) | ~curious(X0) [cnf transformation 63]
151. creative(lucy) [cnf transformation 17]
158. strong(alice) [cnf transformation 24]
224. 13 <=> rich(lucy) [avatar definition]
228. 14 <=> curious(lucy) [avatar definition]
230. curious(lucy) <- (14) [avatar component clause 228]
233. 15 <=> ! [X0] : ~brave(X0) [avatar definition]
234. ~brave(X0) <- (15) [avatar component clause 233]
235. 15 | ~13 | 14 [avatar split clause 113,228,224,233]
272. 23 <=> ! [X0] : ~curious(X0) [avatar definition]
273. ~curious(X0) <- (23) [avatar component clause 272]
317. 23 | ~14 [avatar split clause 133,228,272]
423. rich(lucy) [resolution 84,151]
426. 13 [avatar split clause 423,224]
440. brave(alice) [resolution 116,158]
441. $false <- (15) [subsumption resolution 440,234]
442. ~15 [avatar contradiction clause 441]
443. $false <- (14, 23) [subsumption resolution 230,273]
444. ~14 | ~23 [avatar contradiction clause 443]
445. $false [avatar sat refutation 235,317,426,442,444]
% SZS output end Proof for 718626960760028590992032
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 mary is not generous then someone is both calm and not funny.
Everyone who is not tall is either wise or not happy and vice versa.
Everyone who is not funny is patient.
If alice is not happy then someone is not generous.
Everyone who is either not quiet or kind is both not happy and strong and vice versa.
If mary is kind then someone is either not patient or old and vice versa.
Everyone who is not happy is both quiet and creative.
If lucy is both generous and not wise then susan is both not tall and old.
Everyone who is not patient is either not kind or happy.
Everyone who is kind is either happy or not kind.
Everyone who is brave or not generous is not brave and vice versa.
If fred is either wise or tall then someone is calm and vice versa.
If john is not wise then susan is not curious or not creative.
If fred is either generous or not creative then susan is rich or not generous and vice versa.
Everyone who is either not old or wise is not calm.
If someone is both not patient and not kind then lucy is not creative and vice versa.
Someone is both old and not calm.
John is rich or not strong.
Someone is both humble and tall.
Alice is not calm.
Someone is not tall or not brave.
Susan is either not curious or not wise.
Someone is patient.
John is both curious and not happy. | Susan is curious. | neutral | ((~generous(mary))=>(?[X]:((calm(X)&~funny(X)))))&
(![X]:(~tall(X)<=>(wise(X)<~>~happy(X))))&
(![X]:(~funny(X)=>patient(X)))&
((~happy(alice))=>(?[X]:(~generous(X))))&
(![X]:((~quiet(X)<~>kind(X))<=>(~happy(X)&strong(X))))&
((kind(mary))<=>(?[X]:((~patient(X)<~>old(X)))))&
(![X]:(~happy(X)=>(quiet(X)&creative(X))))&
(((generous(lucy)&~wise(lucy)))=>((~tall(susan)&old(susan))))&
(![X]:(~patient(X)=>(~kind(X)<~>happy(X))))&
(![X]:(kind(X)=>(happy(X)<~>~kind(X))))&
(![X]:((brave(X)|~generous(X))<=>~brave(X)))&
(((wise(fred)<~>tall(fred)))<=>(?[X]:(calm(X))))&
((~wise(john))=>((~curious(susan)|~creative(susan))))&
(((generous(fred)<~>~creative(fred)))<=>((rich(susan)|~generous(susan))))&
(![X]:((~old(X)<~>wise(X))=>~calm(X)))&
((?[X]:((~patient(X)&~kind(X))))<=>(~creative(lucy)))&
(?[X]:((old(X)&~calm(X))))&
((rich(john)|~strong(john)))&
(?[X]:((humble(X)&tall(X))))&
(~calm(alice))&
(?[X]:((~tall(X)|~brave(X))))&
((~curious(susan)<~>~wise(susan)))&
(?[X]:(patient(X)))&
((curious(john)&~happy(john))) | curious(susan) | [] | null | 0 |
Everyone who is calm is brave and vice versa. Everyone who is not strong is not funny. Everyone who is either quiet or not quiet is either not happy or not generous and vice versa. Everyone who is not strong is either not creative or not humble. Everyone who is both strong and not humble is both not rich and calm. If someone is either happy or not tall then paul is kind or not generous. Everyone who is both not wise and not happy is both not old and humble. Everyone who is both wise and not brave is not curious or humble. If someone is not brave then paul is either not kind or old and vice versa. If someone is quiet or not curious then someone is both not tall and brave. Everyone who is both curious and rich is either not funny or not old and vice versa. Everyone who is humble is both not tall and not generous. Everyone who is either patient or not old is curious or not happy. Everyone who is brave is either not strong or not happy and vice versa. If someone is both not humble and not generous then someone is either not happy or not generous. If lucy is both not creative and curious then someone is tall or rich. Someone is both not curious and not generous. Lucy is both not patient and old. Mary is both not kind and not wise. Someone is both not wise and not creative. Someone is either not patient or tall. Someone is not strong or not tall. Someone is both not funny and generous. | Mary is wise. | contradiction | (![X]:(calm(X)<=>brave(X)))&
(![X]:(~strong(X)=>~funny(X)))&
(![X]:((quiet(X)<~>~quiet(X))<=>(~happy(X)<~>~generous(X))))&
(![X]:(~strong(X)=>(~creative(X)<~>~humble(X))))&
(![X]:((strong(X)&~humble(X))=>(~rich(X)&calm(X))))&
((?[X]:((happy(X)<~>~tall(X))))=>((kind(paul)|~generous(paul))))&
(![X]:((~wise(X)&~happy(X))=>(~old(X)&humble(X))))&
(![X]:((wise(X)&~brave(X))=>(~curious(X)|humble(X))))&
((?[X]:(~brave(X)))<=>((~kind(paul)<~>old(paul))))&
((?[X]:((quiet(X)|~curious(X))))=>(?[X]:((~tall(X)&brave(X)))))&
(![X]:((curious(X)&rich(X))<=>(~funny(X)<~>~old(X))))&
(![X]:(humble(X)=>(~tall(X)&~generous(X))))&
(![X]:((patient(X)<~>~old(X))=>(curious(X)|~happy(X))))&
(![X]:(brave(X)<=>(~strong(X)<~>~happy(X))))&
((?[X]:((~humble(X)&~generous(X))))=>(?[X]:((~happy(X)<~>~generous(X)))))&
(((~creative(lucy)&curious(lucy)))=>(?[X]:((tall(X)|rich(X)))))&
(?[X]:((~curious(X)&~generous(X))))&
((~patient(lucy)&old(lucy)))&
((~kind(mary)&~wise(mary)))&
(?[X]:((~wise(X)&~creative(X))))&
(?[X]:((~patient(X)<~>tall(X))))&
(?[X]:((~strong(X)|~tall(X))))&
(?[X]:((~funny(X)&generous(X)))) | wise(mary) | [
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 4085940248857226203612885
% SZS output start Proof for 4085940248857226203612885
19. ~wise(mary) & ~kind(mary) [input p18]
24. wise(mary) [input hypothesis]
126. ~wise(mary) [cnf transformation 19]
134. wise(mary) [cnf transformation 24]
226. $false [subsumption resolution 134,126]
% SZS output end Proof for 4085940248857226203612885
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both patient and not strong is either not wise or not strong and vice versa.
Everyone who is either wise or not patient is curious or not calm.
If someone is both wise and not curious then someone is either curious or humble.
Everyone who is either patient or not kind is both not brave and not creative.
If susan is both humble and happy then someone is calm or not curious and vice versa.
Everyone who is not rich or humble is wise.
If someone is not patient then lucy is not calm.
If someone is brave or not funny then john is both not strong and old.
Everyone who is both quiet and rich is both generous and not wise.
Everyone who is either not strong or brave is both wise and not tall.
Everyone who is tall is wise and vice versa.
If fred is generous then lucy is both not generous and funny and vice versa.
If someone is curious or not patient then someone is either tall or not tall and vice versa.
Everyone who is not happy or happy is not old.
If mary is generous then susan is creative and vice versa.
Everyone who is either old or not funny is patient or quiet and vice versa.
John is not happy or generous.
Mary is both not quiet and not brave.
Susan is not calm.
Someone is not happy or wise.
Someone is either happy or not humble.
Someone is either not creative or not curious.
Someone is both creative and strong.
Someone is not brave or not generous. | Lucy is not patient. | entailment | (![X]:((patient(X)&~strong(X))<=>(~wise(X)<~>~strong(X))))&
(![X]:((wise(X)<~>~patient(X))=>(curious(X)|~calm(X))))&
((?[X]:((wise(X)&~curious(X))))=>(?[X]:((curious(X)<~>humble(X)))))&
(![X]:((patient(X)<~>~kind(X))=>(~brave(X)&~creative(X))))&
(((humble(susan)&happy(susan)))<=>(?[X]:((calm(X)|~curious(X)))))&
(![X]:((~rich(X)|humble(X))=>wise(X)))&
((?[X]:(~patient(X)))=>(~calm(lucy)))&
((?[X]:((brave(X)|~funny(X))))=>((~strong(john)&old(john))))&
(![X]:((quiet(X)&rich(X))=>(generous(X)&~wise(X))))&
(![X]:((~strong(X)<~>brave(X))=>(wise(X)&~tall(X))))&
(![X]:(tall(X)<=>wise(X)))&
((generous(fred))<=>((~generous(lucy)&funny(lucy))))&
((?[X]:((curious(X)|~patient(X))))<=>(?[X]:((tall(X)<~>~tall(X)))))&
(![X]:((~happy(X)|happy(X))=>~old(X)))&
((generous(mary))<=>(creative(susan)))&
(![X]:((old(X)<~>~funny(X))<=>(patient(X)|quiet(X))))&
((~happy(john)|generous(john)))&
((~quiet(mary)&~brave(mary)))&
(~calm(susan))&
(?[X]:((~happy(X)|wise(X))))&
(?[X]:((happy(X)<~>~humble(X))))&
(?[X]:((~creative(X)<~>~curious(X))))&
(?[X]:((creative(X)&strong(X))))&
(?[X]:((~brave(X)|~generous(X)))) | ~patient(lucy) | [
"p7",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 494770492112328963599089
% SZS output start Proof for 494770492112328963599089
8. ? [X0] : (~funny(X0) | brave(X0)) => (old(john) & ~strong(john)) [input p7]
14. ! [X0] : ((happy(X0) | ~happy(X0)) => ~old(X0)) [input p13]
16. ! [X0] : ((old(X0) <~> ~funny(X0)) <=> (quiet(X0) | patient(X0))) [input p15]
25. patient(lucy) [input hypothesis]
34. (old(john) & ~strong(john)) | ! [X0] : (funny(X0) & ~brave(X0)) [ennf transformation 8]
38. ! [X0] : (~old(X0) | (~happy(X0) & happy(X0))) [ennf transformation 14]
62. ! [X0] : ((((funny(X0) | ~old(X0)) & (~funny(X0) | old(X0))) | (~quiet(X0) & ~patient(X0))) & ((quiet(X0) | patient(X0)) | ((old(X0) | funny(X0)) & (~funny(X0) | ~old(X0))))) [nnf transformation 16]
63. ! [X0] : ((((funny(X0) | ~old(X0)) & (~funny(X0) | old(X0))) | (~quiet(X0) & ~patient(X0))) & (quiet(X0) | patient(X0) | ((old(X0) | funny(X0)) & (~funny(X0) | ~old(X0))))) [flattening 62]
101. old(john) | funny(X0) [cnf transformation 34]
119. ~old(X0) | happy(X0) [cnf transformation 38]
120. ~old(X0) | ~happy(X0) [cnf transformation 38]
125. ~funny(X0) | old(X0) | ~patient(X0) [cnf transformation 63]
141. patient(lucy) [cnf transformation 25]
198. 12 <=> ! [X0] : funny(X0) [avatar definition]
199. funny(X0) <- (12) [avatar component clause 198]
201. 13 <=> old(john) [avatar definition]
203. old(john) <- (13) [avatar component clause 201]
204. 12 | 13 [avatar split clause 101,201,198]
247. ~old(X0) [subsumption resolution 119,120]
259. ~funny(X0) | ~patient(X0) [subsumption resolution 125,247]
308. $false <- (13) [subsumption resolution 203,247]
309. ~13 [avatar contradiction clause 308]
325. ~patient(X0) <- (12) [resolution 259,199]
329. $false <- (12) [resolution 325,141]
330. ~12 [avatar contradiction clause 329]
331. $false [avatar sat refutation 204,309,330]
% SZS output end Proof for 494770492112328963599089
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not patient is both wise and not generous and vice versa. Everyone who is calm or not quiet is either not curious or not calm and vice versa. 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. Everyone who is either tall or generous is rich or not strong and vice versa. If susan is patient or not funny then paul is either not creative or not wise and vice versa. If susan is both not generous and not quiet then lucy is not happy or kind and vice versa. Everyone who is both not happy and not creative is not kind or tall. If fred is not happy or creative then someone is not funny. Everyone who is happy or not patient is rich or happy. Everyone who is not brave is both not tall and not funny. If someone is not brave or not creative then mary is either humble or brave and vice versa. If someone is both strong and not rich then someone is either strong or rich. If susan is both kind and not old then fred is either not kind or not humble and vice versa. Fred is tall or rich. Someone is not happy or not tall. Lucy is not curious or not kind. Lucy is not wise or calm. Someone is not curious. Susan is either not humble or funny. | Lucy is not rich. | neutral | (![X]:(~patient(X)<=>(wise(X)&~generous(X))))&
(![X]:((calm(X)|~quiet(X))<=>(~curious(X)<~>~calm(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]:((tall(X)<~>generous(X))<=>(rich(X)|~strong(X))))&
(((patient(susan)|~funny(susan)))<=>((~creative(paul)<~>~wise(paul))))&
(((~generous(susan)&~quiet(susan)))<=>((~happy(lucy)|kind(lucy))))&
(![X]:((~happy(X)&~creative(X))=>(~kind(X)|tall(X))))&
(((~happy(fred)|creative(fred)))=>(?[X]:(~funny(X))))&
(![X]:((happy(X)|~patient(X))=>(rich(X)|happy(X))))&
(![X]:(~brave(X)=>(~tall(X)&~funny(X))))&
((?[X]:((~brave(X)|~creative(X))))<=>((humble(mary)<~>brave(mary))))&
((?[X]:((strong(X)&~rich(X))))=>(?[X]:((strong(X)<~>rich(X)))))&
(((kind(susan)&~old(susan)))<=>((~kind(fred)<~>~humble(fred))))&
((tall(fred)|rich(fred)))&
(?[X]:((~happy(X)|~tall(X))))&
((~curious(lucy)|~kind(lucy)))&
((~wise(lucy)|calm(lucy)))&
(?[X]:(~curious(X)))&
((~humble(susan)<~>funny(susan))) | ~rich(lucy) | [] | null | 0 |
Everyone who is either quiet or not kind is both not creative and generous.
If someone is not patient or not creative then someone is both not rich and generous and vice versa.
Everyone who is not tall is kind and vice versa.
Everyone who is both wise and brave is both not generous and not brave.
If susan is both not rich and brave then someone is curious and vice versa.
Everyone who is both patient and happy is both not humble and rich and vice versa.
Everyone who is either not happy or not curious is both generous and tall.
Everyone who is not kind or not old is both not calm and funny.
Everyone who is not quiet or tall is not humble or tall and vice versa.
Everyone who is not calm or not tall is tall or generous.
If someone is either quiet or not rich then john is both not curious and strong and vice versa.
If someone is not strong then someone is both not curious and not strong and vice versa.
If someone is rich then someone is either not creative or happy and vice versa.
Everyone who is not humble is not rich.
Everyone who is not quiet or old is both not creative and creative and vice versa.
If alice is both not calm and not old then fred is not kind or creative.
Susan is either not quiet or tall.
Someone is strong.
Mary is rich or curious.
Someone is either rich or not wise.
Someone is both rich and not brave.
Someone is either calm or not curious.
Fred is both not rich and not brave.
Someone is either patient or not calm. | Susan is not quiet. | contradiction | (![X]:((quiet(X)<~>~kind(X))=>(~creative(X)&generous(X))))&
((?[X]:((~patient(X)|~creative(X))))<=>(?[X]:((~rich(X)&generous(X)))))&
(![X]:(~tall(X)<=>kind(X)))&
(![X]:((wise(X)&brave(X))=>(~generous(X)&~brave(X))))&
(((~rich(susan)&brave(susan)))<=>(?[X]:(curious(X))))&
(![X]:((patient(X)&happy(X))<=>(~humble(X)&rich(X))))&
(![X]:((~happy(X)<~>~curious(X))=>(generous(X)&tall(X))))&
(![X]:((~kind(X)|~old(X))=>(~calm(X)&funny(X))))&
(![X]:((~quiet(X)|tall(X))<=>(~humble(X)|tall(X))))&
(![X]:((~calm(X)|~tall(X))=>(tall(X)|generous(X))))&
((?[X]:((quiet(X)<~>~rich(X))))<=>((~curious(john)&strong(john))))&
((?[X]:(~strong(X)))<=>(?[X]:((~curious(X)&~strong(X)))))&
((?[X]:(rich(X)))<=>(?[X]:((~creative(X)<~>happy(X)))))&
(![X]:(~humble(X)=>~rich(X)))&
(![X]:((~quiet(X)|old(X))<=>(~creative(X)&creative(X))))&
(((~calm(alice)&~old(alice)))=>((~kind(fred)|creative(fred))))&
((~quiet(susan)<~>tall(susan)))&
(?[X]:(strong(X)))&
((rich(mary)|curious(mary)))&
(?[X]:((rich(X)<~>~wise(X))))&
(?[X]:((rich(X)&~brave(X))))&
(?[X]:((calm(X)<~>~curious(X))))&
((~rich(fred)&~brave(fred)))&
(?[X]:((patient(X)<~>~calm(X)))) | ~quiet(susan) | [
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 1179676785541918500941697
% SZS output start Proof for 1179676785541918500941697
15. ! [X0] : ((old(X0) | ~quiet(X0)) <=> (creative(X0) & ~creative(X0))) [input p14]
25. ~quiet(susan) [input hypothesis]
72. ! [X0] : (((old(X0) | ~quiet(X0)) | (~creative(X0) | creative(X0))) & ((creative(X0) & ~creative(X0)) | (~old(X0) & quiet(X0)))) [nnf transformation 15]
73. ! [X0] : ((old(X0) | ~quiet(X0) | ~creative(X0) | creative(X0)) & ((creative(X0) & ~creative(X0)) | (~old(X0) & quiet(X0)))) [flattening 72]
134. ~creative(X0) | quiet(X0) [cnf transformation 73]
136. creative(X0) | quiet(X0) [cnf transformation 73]
154. ~quiet(susan) [cnf transformation 25]
280. quiet(X0) [subsumption resolution 134,136]
335. $false [subsumption resolution 154,280]
% SZS output end Proof for 1179676785541918500941697
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative and not creative then someone is not creative.
If john is both not curious and curious then someone is both not curious and not quiet and vice versa.
Everyone who is not strong or creative is either not brave or happy and vice versa.
Everyone who is not brave is either not brave or not generous and vice versa.
If someone is wise then john is kind or not curious and vice versa.
Everyone who is not wise is not creative and vice versa.
Everyone who is both not humble and not strong is both tall and not patient.
Everyone who is both not kind and not wise is not humble.
Everyone who is not quiet is happy.
If mary is strong or not generous then someone is rich and vice versa.
Everyone who is both quiet and not wise is kind.
Everyone who is funny is rich and vice versa.
If paul is both not rich and not happy then someone is not tall and vice versa.
If someone is either not funny or brave then someone is either curious or not wise and vice versa.
If paul is not quiet or strong then someone is both not brave and not curious.
Everyone who is not patient is not funny or humble.
Fred is both not calm and wise.
Someone is funny.
Fred is both quiet and not kind.
Susan is both calm and patient.
Someone is brave or curious.
Paul is not funny.
Susan is curious or not patient.
Mary is both not calm and creative. | John is not funny. | neutral | (((creative(fred)&~creative(fred)))=>(?[X]:(~creative(X))))&
(((~curious(john)&curious(john)))<=>(?[X]:((~curious(X)&~quiet(X)))))&
(![X]:((~strong(X)|creative(X))<=>(~brave(X)<~>happy(X))))&
(![X]:(~brave(X)<=>(~brave(X)<~>~generous(X))))&
((?[X]:(wise(X)))<=>((kind(john)|~curious(john))))&
(![X]:(~wise(X)<=>~creative(X)))&
(![X]:((~humble(X)&~strong(X))=>(tall(X)&~patient(X))))&
(![X]:((~kind(X)&~wise(X))=>~humble(X)))&
(![X]:(~quiet(X)=>happy(X)))&
(((strong(mary)|~generous(mary)))<=>(?[X]:(rich(X))))&
(![X]:((quiet(X)&~wise(X))=>kind(X)))&
(![X]:(funny(X)<=>rich(X)))&
(((~rich(paul)&~happy(paul)))<=>(?[X]:(~tall(X))))&
((?[X]:((~funny(X)<~>brave(X))))<=>(?[X]:((curious(X)<~>~wise(X)))))&
(((~quiet(paul)|strong(paul)))=>(?[X]:((~brave(X)&~curious(X)))))&
(![X]:(~patient(X)=>(~funny(X)|humble(X))))&
((~calm(fred)&wise(fred)))&
(?[X]:(funny(X)))&
((quiet(fred)&~kind(fred)))&
((calm(susan)&patient(susan)))&
(?[X]:((brave(X)|curious(X))))&
(~funny(paul))&
((curious(susan)|~patient(susan)))&
((~calm(mary)&creative(mary))) | ~funny(john) | [] | null | 0 |
Everyone who is both not funny and old is either wise or not strong and vice versa.
Everyone who is not old or patient is generous.
If someone is not curious then paul is patient or calm.
Everyone who is patient is both not quiet and old.
If someone is both not happy and not kind then someone is both not calm and patient and vice versa.
If someone is strong then lucy is either humble or creative and vice versa.
Everyone who is creative is either curious or creative.
If alice is not tall then someone is not kind and vice versa.
If someone is either curious or old then someone is curious and vice versa.
Everyone who is not humble is either not rich or tall and vice versa.
If someone is either creative or not humble then alice is both not generous and creative and vice versa.
If someone is not tall then someone is either not curious or not wise.
If alice is funny then fred is not tall.
If lucy is both not kind and not patient then susan is not humble or generous and vice versa.
If lucy is both brave and not tall then someone is both calm and kind.
Everyone who is quiet or not old is quiet and vice versa.
Fred is not kind or rich.
Someone is not funny or not happy.
Fred is either not brave or not funny.
Someone is not creative.
Someone is rich or strong.
Someone is both not brave and quiet.
Someone is not kind or not strong.
Mary is both tall and not patient. | Alice is funny. | neutral | (![X]:((~funny(X)&old(X))<=>(wise(X)<~>~strong(X))))&
(![X]:((~old(X)|patient(X))=>generous(X)))&
((?[X]:(~curious(X)))=>((patient(paul)|calm(paul))))&
(![X]:(patient(X)=>(~quiet(X)&old(X))))&
((?[X]:((~happy(X)&~kind(X))))<=>(?[X]:((~calm(X)&patient(X)))))&
((?[X]:(strong(X)))<=>((humble(lucy)<~>creative(lucy))))&
(![X]:(creative(X)=>(curious(X)<~>creative(X))))&
((~tall(alice))<=>(?[X]:(~kind(X))))&
((?[X]:((curious(X)<~>old(X))))<=>(?[X]:(curious(X))))&
(![X]:(~humble(X)<=>(~rich(X)<~>tall(X))))&
((?[X]:((creative(X)<~>~humble(X))))<=>((~generous(alice)&creative(alice))))&
((?[X]:(~tall(X)))=>(?[X]:((~curious(X)<~>~wise(X)))))&
((funny(alice))=>(~tall(fred)))&
(((~kind(lucy)&~patient(lucy)))<=>((~humble(susan)|generous(susan))))&
(((brave(lucy)&~tall(lucy)))=>(?[X]:((calm(X)&kind(X)))))&
(![X]:((quiet(X)|~old(X))<=>quiet(X)))&
((~kind(fred)|rich(fred)))&
(?[X]:((~funny(X)|~happy(X))))&
((~brave(fred)<~>~funny(fred)))&
(?[X]:(~creative(X)))&
(?[X]:((rich(X)|strong(X))))&
(?[X]:((~brave(X)&quiet(X))))&
(?[X]:((~kind(X)|~strong(X))))&
((tall(mary)&~patient(mary))) | funny(alice) | [] | null | 0 |
If mary is either not happy or curious then mary is brave and vice versa. If mary is both happy and not tall then someone is not funny. If lucy is creative or humble then alice is not calm or not creative and vice versa. Everyone who is not creative or funny is not rich or not generous and vice versa. Everyone who is both not curious and not funny is both curious and kind and vice versa. Everyone who is both wise and not funny is curious or happy and vice versa. Everyone who is either kind or not generous is patient or not generous. Everyone who is not curious or kind is not creative and vice versa. Everyone who is not funny is either strong or not old. If fred is either not creative or tall then alice is both funny and happy and vice versa. If fred is either not patient or curious then paul is either quiet or happy and vice versa. Everyone who is both not quiet and rich is either not kind or brave. If paul is both tall and not creative then lucy is not wise and vice versa. Everyone who is both not tall and not creative is not brave. Everyone who is wise or kind is both wise and happy. Everyone who is both creative and quiet is either not kind or not brave and vice versa. Someone is not generous. Someone is happy or not humble. Lucy is not creative. Alice is both not quiet and not curious. Paul is funny or not generous. Alice is not happy or tall. Someone is either curious or old. Someone is funny. | Alice is quiet. | contradiction | (((~happy(mary)<~>curious(mary)))<=>(brave(mary)))&
(((happy(mary)&~tall(mary)))=>(?[X]:(~funny(X))))&
(((creative(lucy)|humble(lucy)))<=>((~calm(alice)|~creative(alice))))&
(![X]:((~creative(X)|funny(X))<=>(~rich(X)|~generous(X))))&
(![X]:((~curious(X)&~funny(X))<=>(curious(X)&kind(X))))&
(![X]:((wise(X)&~funny(X))<=>(curious(X)|happy(X))))&
(![X]:((kind(X)<~>~generous(X))=>(patient(X)|~generous(X))))&
(![X]:((~curious(X)|kind(X))<=>~creative(X)))&
(![X]:(~funny(X)=>(strong(X)<~>~old(X))))&
(((~creative(fred)<~>tall(fred)))<=>((funny(alice)&happy(alice))))&
(((~patient(fred)<~>curious(fred)))<=>((quiet(paul)<~>happy(paul))))&
(![X]:((~quiet(X)&rich(X))=>(~kind(X)<~>brave(X))))&
(((tall(paul)&~creative(paul)))<=>(~wise(lucy)))&
(![X]:((~tall(X)&~creative(X))=>~brave(X)))&
(![X]:((wise(X)|kind(X))=>(wise(X)&happy(X))))&
(![X]:((creative(X)&quiet(X))<=>(~kind(X)<~>~brave(X))))&
(?[X]:(~generous(X)))&
(?[X]:((happy(X)|~humble(X))))&
(~creative(lucy))&
((~quiet(alice)&~curious(alice)))&
((funny(paul)|~generous(paul)))&
((~happy(alice)|tall(alice)))&
(?[X]:((curious(X)<~>old(X))))&
(?[X]:(funny(X))) | quiet(alice) | [
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 10503084868221256750296
% SZS output start Proof for 10503084868221256750296
20. ~curious(alice) & ~quiet(alice) [input p19]
25. quiet(alice) [input hypothesis]
130. ~quiet(alice) [cnf transformation 20]
137. quiet(alice) [cnf transformation 25]
282. $false [subsumption resolution 137,130]
% SZS output end Proof for 10503084868221256750296
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If susan is not generous or patient then someone is both calm and funny and vice versa. Everyone who is both creative and funny is creative or not curious. If someone is not patient then john is not happy. Everyone who is not generous or not tall is strong and vice versa. If mary is either happy or not wise then mary is patient or not quiet and vice versa. Everyone who is happy or patient is either patient or not patient. If mary is brave or not happy then someone is either not funny or creative. Everyone who is either humble or not brave is either happy or not old and vice versa. Everyone who is either calm or not old is kind or tall. If someone is either not funny or not creative then alice is both brave and old. Everyone who is funny or not quiet is not brave and vice versa. Everyone who is not generous or not calm is both not happy and curious and vice versa. Everyone who is either tall or generous is either wise or not kind and vice versa. If someone is either not tall or creative then paul is not creative or humble. Everyone who is either not humble or kind is both not generous and humble and vice versa. If someone is not happy then someone is both quiet and old. Someone is both not generous and wise. Someone is not strong. Someone is both creative and not funny. Someone is not generous or not quiet. John is both kind and not generous. Someone is not generous or old. Someone is kind. | Mary is happy. | neutral | (((~generous(susan)|patient(susan)))<=>(?[X]:((calm(X)&funny(X)))))&
(![X]:((creative(X)&funny(X))=>(creative(X)|~curious(X))))&
((?[X]:(~patient(X)))=>(~happy(john)))&
(![X]:((~generous(X)|~tall(X))<=>strong(X)))&
(((happy(mary)<~>~wise(mary)))<=>((patient(mary)|~quiet(mary))))&
(![X]:((happy(X)|patient(X))=>(patient(X)<~>~patient(X))))&
(((brave(mary)|~happy(mary)))=>(?[X]:((~funny(X)<~>creative(X)))))&
(![X]:((humble(X)<~>~brave(X))<=>(happy(X)<~>~old(X))))&
(![X]:((calm(X)<~>~old(X))=>(kind(X)|tall(X))))&
((?[X]:((~funny(X)<~>~creative(X))))=>((brave(alice)&old(alice))))&
(![X]:((funny(X)|~quiet(X))<=>~brave(X)))&
(![X]:((~generous(X)|~calm(X))<=>(~happy(X)&curious(X))))&
(![X]:((tall(X)<~>generous(X))<=>(wise(X)<~>~kind(X))))&
((?[X]:((~tall(X)<~>creative(X))))=>((~creative(paul)|humble(paul))))&
(![X]:((~humble(X)<~>kind(X))<=>(~generous(X)&humble(X))))&
((?[X]:(~happy(X)))=>(?[X]:((quiet(X)&old(X)))))&
(?[X]:((~generous(X)&wise(X))))&
(?[X]:(~strong(X)))&
(?[X]:((creative(X)&~funny(X))))&
(?[X]:((~generous(X)|~quiet(X))))&
((kind(john)&~generous(john)))&
(?[X]:((~generous(X)|old(X))))&
(?[X]:(kind(X))) | happy(mary) | [] | null | 0 |
Everyone who is not creative or creative is not calm and vice versa. Everyone who is both patient and humble is creative and vice versa. If someone is not quiet then someone is either strong or not generous. Everyone who is quiet or not strong is both quiet and calm and vice versa. Everyone who is both not kind and happy is not creative and vice versa. Everyone who is both funny and not curious is wise and vice versa. Everyone who is not old is quiet. Everyone who is either not happy or not wise is not rich or old and vice versa. If fred is not brave then someone is not creative or not funny and vice versa. If fred is either not wise or old then someone is both not funny and not tall. Everyone who is old is not wise or not patient. If lucy is either not patient or not creative then someone is brave or wise and vice versa. Everyone who is not rich is not humble or strong and vice versa. If paul is not strong then mary is not funny or not happy. Everyone who is not creative or not curious is both not strong and not patient and vice versa. If paul is either not curious or humble then someone is generous. Lucy is either patient or not patient. Someone is either strong or not tall. Alice is tall. Alice is either not patient or not calm. Alice is creative. Lucy is happy or not kind. | Paul is strong. | entailment | (![X]:((~creative(X)|creative(X))<=>~calm(X)))&
(![X]:((patient(X)&humble(X))<=>creative(X)))&
((?[X]:(~quiet(X)))=>(?[X]:((strong(X)<~>~generous(X)))))&
(![X]:((quiet(X)|~strong(X))<=>(quiet(X)&calm(X))))&
(![X]:((~kind(X)&happy(X))<=>~creative(X)))&
(![X]:((funny(X)&~curious(X))<=>wise(X)))&
(![X]:(~old(X)=>quiet(X)))&
(![X]:((~happy(X)<~>~wise(X))<=>(~rich(X)|old(X))))&
((~brave(fred))<=>(?[X]:((~creative(X)|~funny(X)))))&
(((~wise(fred)<~>old(fred)))=>(?[X]:((~funny(X)&~tall(X)))))&
(![X]:(old(X)=>(~wise(X)|~patient(X))))&
(((~patient(lucy)<~>~creative(lucy)))<=>(?[X]:((brave(X)|wise(X)))))&
(![X]:(~rich(X)<=>(~humble(X)|strong(X))))&
((~strong(paul))=>((~funny(mary)|~happy(mary))))&
(![X]:((~creative(X)|~curious(X))<=>(~strong(X)&~patient(X))))&
(((~curious(paul)<~>humble(paul)))=>(?[X]:(generous(X))))&
((patient(lucy)<~>~patient(lucy)))&
(?[X]:((strong(X)<~>~tall(X))))&
(tall(alice))&
((~patient(alice)<~>~calm(alice)))&
(creative(alice))&
((happy(lucy)|~kind(lucy))) | strong(paul) | [
"p0",
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 5625386112841306503500952
% SZS output start Proof for 5625386112841306503500952
1. ! [X0] : ((creative(X0) | ~creative(X0)) <=> ~calm(X0)) [input p0]
4. ! [X0] : ((~strong(X0) | quiet(X0)) <=> (calm(X0) & quiet(X0))) [input p3]
23. ~strong(paul) [input hypothesis]
33. ! [X0] : (((creative(X0) | ~creative(X0)) | calm(X0)) & (~calm(X0) | (~creative(X0) & creative(X0)))) [nnf transformation 1]
34. ! [X0] : ((creative(X0) | ~creative(X0) | calm(X0)) & (~calm(X0) | (~creative(X0) & creative(X0)))) [flattening 33]
41. ! [X0] : (((~strong(X0) | quiet(X0)) | (~calm(X0) | ~quiet(X0))) & ((calm(X0) & quiet(X0)) | (strong(X0) & ~quiet(X0)))) [nnf transformation 4]
42. ! [X0] : ((~strong(X0) | quiet(X0) | ~calm(X0) | ~quiet(X0)) & ((calm(X0) & quiet(X0)) | (strong(X0) & ~quiet(X0)))) [flattening 41]
72. ~calm(X0) | creative(X0) [cnf transformation 34]
73. ~calm(X0) | ~creative(X0) [cnf transformation 34]
83. calm(X0) | strong(X0) [cnf transformation 42]
132. ~strong(paul) [cnf transformation 23]
133. ~calm(X0) [subsumption resolution 72,73]
147. strong(X0) [subsumption resolution 83,133]
246. $false [subsumption resolution 132,147]
% SZS output end Proof for 5625386112841306503500952
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If mary is not quiet then someone is both not kind and not brave and vice versa.
Everyone who is either creative or patient is either tall or not tall.
If john is both kind and funny then fred is both not curious and tall.
Everyone who is both not old and not humble is happy and vice versa.
If someone is old then someone is either not creative or not tall.
If someone is either happy or not strong then someone is quiet.
If someone is tall or not curious then paul is either not tall or generous and vice versa.
Everyone who is either not kind or not funny is either brave or curious and vice versa.
Everyone who is old is both brave and strong and vice versa.
Everyone who is either funny or curious is either not creative or not patient.
Everyone who is not curious is not humble or patient and vice versa.
Everyone who is both patient and brave is either not old or strong and vice versa.
If susan is either strong or not rich then susan is patient and vice versa.
Everyone who is generous is either old or quiet and vice versa.
Everyone who is not old is either brave or not curious and vice versa.
If someone is creative or not tall then mary is funny or not brave.
Someone is curious or creative.
Fred is not quiet or not kind.
Fred is old.
Someone is both brave and not generous.
Paul is either not wise or rich.
Someone is both happy and not funny.
Someone is both not patient and not old. | Paul is wise. | neutral | ((~quiet(mary))<=>(?[X]:((~kind(X)&~brave(X)))))&
(![X]:((creative(X)<~>patient(X))=>(tall(X)<~>~tall(X))))&
(((kind(john)&funny(john)))=>((~curious(fred)&tall(fred))))&
(![X]:((~old(X)&~humble(X))<=>happy(X)))&
((?[X]:(old(X)))=>(?[X]:((~creative(X)<~>~tall(X)))))&
((?[X]:((happy(X)<~>~strong(X))))=>(?[X]:(quiet(X))))&
((?[X]:((tall(X)|~curious(X))))<=>((~tall(paul)<~>generous(paul))))&
(![X]:((~kind(X)<~>~funny(X))<=>(brave(X)<~>curious(X))))&
(![X]:(old(X)<=>(brave(X)&strong(X))))&
(![X]:((funny(X)<~>curious(X))=>(~creative(X)<~>~patient(X))))&
(![X]:(~curious(X)<=>(~humble(X)|patient(X))))&
(![X]:((patient(X)&brave(X))<=>(~old(X)<~>strong(X))))&
(((strong(susan)<~>~rich(susan)))<=>(patient(susan)))&
(![X]:(generous(X)<=>(old(X)<~>quiet(X))))&
(![X]:(~old(X)<=>(brave(X)<~>~curious(X))))&
((?[X]:((creative(X)|~tall(X))))=>((funny(mary)|~brave(mary))))&
(?[X]:((curious(X)|creative(X))))&
((~quiet(fred)|~kind(fred)))&
(old(fred))&
(?[X]:((brave(X)&~generous(X))))&
((~wise(paul)<~>rich(paul)))&
(?[X]:((happy(X)&~funny(X))))&
(?[X]:((~patient(X)&~old(X)))) | wise(paul) | [] | null | 0 |
Everyone who is either not strong or not rich is both rich and not old.
If someone is not kind then mary is both happy and not happy.
If susan is kind then someone is not old and vice versa.
If john is rich then someone is not brave and vice versa.
If john is not quiet then john is both curious and not humble.
Everyone who is humble or not rich is both happy and brave.
Everyone who is either not strong or not curious is either kind or patient.
If fred is either funny or humble then someone is happy or generous.
If someone is not strong or strong then someone is creative.
If susan is either not happy or not curious then mary is both not old and calm and vice versa.
If paul is not quiet then mary is either generous or old.
If susan is both generous and tall then someone is either not quiet or strong.
If alice is both curious and not creative then john is either old or curious.
Everyone who is not rich is both not quiet and not calm and vice versa.
Everyone who is tall or curious is either calm or not kind.
Everyone who is strong or not calm is either curious or strong.
Someone is either humble or not quiet.
Someone is both not strong and tall.
Someone is either strong or curious.
Lucy is either not humble or funny.
Someone is both not wise and not brave.
Lucy is either happy or calm.
Someone is curious.
Fred is happy or funny. | Lucy is not rich. | contradiction | (![X]:((~strong(X)<~>~rich(X))=>(rich(X)&~old(X))))&
((?[X]:(~kind(X)))=>((happy(mary)&~happy(mary))))&
((kind(susan))<=>(?[X]:(~old(X))))&
((rich(john))<=>(?[X]:(~brave(X))))&
((~quiet(john))=>((curious(john)&~humble(john))))&
(![X]:((humble(X)|~rich(X))=>(happy(X)&brave(X))))&
(![X]:((~strong(X)<~>~curious(X))=>(kind(X)<~>patient(X))))&
(((funny(fred)<~>humble(fred)))=>(?[X]:((happy(X)|generous(X)))))&
((?[X]:((~strong(X)|strong(X))))=>(?[X]:(creative(X))))&
(((~happy(susan)<~>~curious(susan)))<=>((~old(mary)&calm(mary))))&
((~quiet(paul))=>((generous(mary)<~>old(mary))))&
(((generous(susan)&tall(susan)))=>(?[X]:((~quiet(X)<~>strong(X)))))&
(((curious(alice)&~creative(alice)))=>((old(john)<~>curious(john))))&
(![X]:(~rich(X)<=>(~quiet(X)&~calm(X))))&
(![X]:((tall(X)|curious(X))=>(calm(X)<~>~kind(X))))&
(![X]:((strong(X)|~calm(X))=>(curious(X)<~>strong(X))))&
(?[X]:((humble(X)<~>~quiet(X))))&
(?[X]:((~strong(X)&tall(X))))&
(?[X]:((strong(X)<~>curious(X))))&
((~humble(lucy)<~>funny(lucy)))&
(?[X]:((~wise(X)&~brave(X))))&
((happy(lucy)<~>calm(lucy)))&
(?[X]:(curious(X)))&
((happy(fred)|funny(fred))) | ~rich(lucy) | [
"p0",
"p1",
"p5",
"p14",
"p15",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 7179962031490975430780018
% SZS output start Proof for 7179962031490975430780018
1. ! [X0] : ((~strong(X0) <~> ~rich(X0)) => (~old(X0) & rich(X0))) [input p0]
2. ? [X0] : ~kind(X0) => (~happy(mary) & happy(mary)) [input p1]
6. ! [X0] : ((~rich(X0) | humble(X0)) => (brave(X0) & happy(X0))) [input p5]
15. ! [X0] : ((curious(X0) | tall(X0)) => (calm(X0) <~> ~kind(X0))) [input p14]
16. ! [X0] : ((~calm(X0) | strong(X0)) => (curious(X0) <~> strong(X0))) [input p15]
22. happy(lucy) <~> calm(lucy) [input p21]
25. ~rich(lucy) [input hypothesis]
30. ! [X0] : ((~old(X0) & rich(X0)) | (~strong(X0) <=> ~rich(X0))) [ennf transformation 1]
31. (~happy(mary) & happy(mary)) | ! [X0] : kind(X0) [ennf transformation 2]
33. ! [X0] : ((brave(X0) & happy(X0)) | (rich(X0) & ~humble(X0))) [ennf transformation 6]
39. ! [X0] : ((calm(X0) <~> ~kind(X0)) | (~curious(X0) & ~tall(X0))) [ennf transformation 15]
40. ! [X0] : ((curious(X0) <~> strong(X0)) | (calm(X0) & ~strong(X0))) [ennf transformation 16]
41. ! [X0] : ((~old(X0) & rich(X0)) | ((~strong(X0) | rich(X0)) & (~rich(X0) | strong(X0)))) [nnf transformation 30]
62. ! [X0] : (((kind(X0) | ~calm(X0)) & (~kind(X0) | calm(X0))) | (~curious(X0) & ~tall(X0))) [nnf transformation 39]
63. ! [X0] : (((~strong(X0) | ~curious(X0)) & (strong(X0) | curious(X0))) | (calm(X0) & ~strong(X0))) [nnf transformation 40]
75. (~calm(lucy) | ~happy(lucy)) & (calm(lucy) | happy(lucy)) [nnf transformation 22]
79. rich(X0) | ~strong(X0) | rich(X0) [cnf transformation 41]
82. happy(mary) | kind(X0) [cnf transformation 31]
83. ~happy(mary) | kind(X0) [cnf transformation 31]
91. happy(X0) | rich(X0) [cnf transformation 33]
114. ~curious(X0) | calm(X0) | ~kind(X0) [cnf transformation 62]
118. calm(X0) | curious(X0) | strong(X0) [cnf transformation 63]
131. ~calm(lucy) | ~happy(lucy) [cnf transformation 75]
134. ~rich(lucy) [cnf transformation 25]
136. ~strong(X0) | rich(X0) [duplicate literal removal 79]
138. 1 <=> ! [X0] : kind(X0) [avatar definition]
139. kind(X0) <- (1) [avatar component clause 138]
141. 2 <=> happy(mary) [avatar definition]
144. 1 | ~2 [avatar split clause 83,141,138]
145. 1 | 2 [avatar split clause 82,141,138]
284. 32 <=> happy(lucy) [avatar definition]
286. ~happy(lucy) <- (~32) [avatar component clause 284]
288. 33 <=> calm(lucy) [avatar definition]
290. ~calm(lucy) <- (~33) [avatar component clause 288]
291. ~32 | ~33 [avatar split clause 131,288,284]
391. 45 <=> strong(lucy) [avatar definition]
393. strong(lucy) <- (45) [avatar component clause 391]
395. 46 <=> curious(lucy) [avatar definition]
397. curious(lucy) <- (46) [avatar component clause 395]
400. rich(lucy) <- (~32) [resolution 286,91]
401. $false <- (~32) [subsumption resolution 400,134]
402. 32 [avatar contradiction clause 401]
403. curious(lucy) | strong(lucy) <- (~33) [resolution 290,118]
410. rich(lucy) <- (45) [resolution 393,136]
411. $false <- (45) [subsumption resolution 410,134]
412. ~45 [avatar contradiction clause 411]
413. 45 | 46 | 33 [avatar split clause 403,288,395,391]
416. calm(lucy) | ~kind(lucy) <- (46) [resolution 397,114]
418. ~kind(lucy) <- (~33, 46) [subsumption resolution 416,290]
419. $false <- (1, ~33, 46) [subsumption resolution 418,139]
420. ~1 | 33 | ~46 [avatar contradiction clause 419]
421. $false [avatar sat refutation 144,145,291,402,412,413,420]
% SZS output end Proof for 7179962031490975430780018
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
If susan is not brave then fred is either not tall or not funny.
Everyone who is either rich or not happy is not tall or kind.
Everyone who is generous or not brave is both old and not creative and vice versa.
Everyone who is not quiet or generous is either wise or humble.
Everyone who is not rich or not humble is both not quiet and not creative.
Everyone who is either kind or calm is not happy or not quiet.
If susan is not happy then susan is old or not kind.
If lucy is either not kind or curious then someone is both rich and happy and vice versa.
Everyone who is not brave is old or not quiet and vice versa.
Everyone who is curious is not wise or quiet.
If fred is old or wise then someone is both strong and not rich.
If someone is both not wise and funny then mary is either strong or creative.
If fred is strong then someone is either brave or humble.
If alice is rich then someone is both not calm and happy.
Everyone who is both rich and old is not quiet or not calm and vice versa.
If someone is curious then john is tall and vice versa.
Someone is curious.
Someone is both patient and not tall.
Someone is rich.
Mary is both not strong and not curious.
Someone is both kind and not old.
Susan is patient.
Someone is not generous.
Someone is wise or quiet. | Fred is not generous. | entailment | ((~brave(susan))=>((~tall(fred)<~>~funny(fred))))&
(![X]:((rich(X)<~>~happy(X))=>(~tall(X)|kind(X))))&
(![X]:((generous(X)|~brave(X))<=>(old(X)&~creative(X))))&
(![X]:((~quiet(X)|generous(X))=>(wise(X)<~>humble(X))))&
(![X]:((~rich(X)|~humble(X))=>(~quiet(X)&~creative(X))))&
(![X]:((kind(X)<~>calm(X))=>(~happy(X)|~quiet(X))))&
((~happy(susan))=>((old(susan)|~kind(susan))))&
(((~kind(lucy)<~>curious(lucy)))<=>(?[X]:((rich(X)&happy(X)))))&
(![X]:(~brave(X)<=>(old(X)|~quiet(X))))&
(![X]:(curious(X)=>(~wise(X)|quiet(X))))&
(((old(fred)|wise(fred)))=>(?[X]:((strong(X)&~rich(X)))))&
((?[X]:((~wise(X)&funny(X))))=>((strong(mary)<~>creative(mary))))&
((strong(fred))=>(?[X]:((brave(X)<~>humble(X)))))&
((rich(alice))=>(?[X]:((~calm(X)&happy(X)))))&
(![X]:((rich(X)&old(X))<=>(~quiet(X)|~calm(X))))&
((?[X]:(curious(X)))<=>(tall(john)))&
(?[X]:(curious(X)))&
(?[X]:((patient(X)&~tall(X))))&
(?[X]:(rich(X)))&
((~strong(mary)&~curious(mary)))&
(?[X]:((kind(X)&~old(X))))&
(patient(susan))&
(?[X]:(~generous(X)))&
(?[X]:((wise(X)|quiet(X)))) | ~generous(fred) | [
"p2",
"p4",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2886411169259153679202914
% SZS output start Proof for 2886411169259153679202914
3. ! [X0] : ((~brave(X0) | generous(X0)) <=> (~creative(X0) & old(X0))) [input p2]
5. ! [X0] : ((~humble(X0) | ~rich(X0)) => (~creative(X0) & ~quiet(X0))) [input p4]
11. (wise(fred) | old(fred)) => ? [X0] : (~rich(X0) & strong(X0)) [input p10]
15. ! [X0] : ((old(X0) & rich(X0)) <=> (~calm(X0) | ~quiet(X0))) [input p14]
25. generous(fred) [input hypothesis]
32. ! [X0] : ((~creative(X0) & ~quiet(X0)) | (humble(X0) & rich(X0))) [ennf transformation 5]
39. ? [X0] : (~rich(X0) & strong(X0)) | (~wise(fred) & ~old(fred)) [ennf transformation 11]
45. ! [X0] : (((~brave(X0) | generous(X0)) | (creative(X0) | ~old(X0))) & ((~creative(X0) & old(X0)) | (brave(X0) & ~generous(X0)))) [nnf transformation 3]
46. ! [X0] : ((~brave(X0) | generous(X0) | creative(X0) | ~old(X0)) & ((~creative(X0) & old(X0)) | (brave(X0) & ~generous(X0)))) [flattening 45]
55. ? [X0] : (~rich(X0) & strong(X0)) => (~rich(sK1) & strong(sK1)) [choice axiom]
56. (~rich(sK1) & strong(sK1)) | (~wise(fred) & ~old(fred)) [skolemisation 39,55]
63. ! [X0] : (((old(X0) & rich(X0)) | (calm(X0) & quiet(X0))) & ((~calm(X0) | ~quiet(X0)) | (~old(X0) | ~rich(X0)))) [nnf transformation 15]
64. ! [X0] : (((old(X0) & rich(X0)) | (calm(X0) & quiet(X0))) & (~calm(X0) | ~quiet(X0) | ~old(X0) | ~rich(X0))) [flattening 63]
85. ~generous(X0) | old(X0) [cnf transformation 46]
94. ~quiet(X0) | rich(X0) [cnf transformation 32]
113. ~rich(sK1) | ~old(fred) [cnf transformation 56]
122. rich(X0) | quiet(X0) [cnf transformation 64]
137. generous(fred) [cnf transformation 25]
195. 13 <=> rich(sK1) [avatar definition]
197. ~rich(sK1) <- (~13) [avatar component clause 195]
200. 14 <=> old(fred) [avatar definition]
202. ~old(fred) <- (~14) [avatar component clause 200]
203. ~14 | ~13 [avatar split clause 113,195,200]
251. rich(X0) [subsumption resolution 122,94]
278. $false <- (~13) [subsumption resolution 197,251]
279. 13 [avatar contradiction clause 278]
283. old(fred) [resolution 85,137]
284. $false <- (~14) [subsumption resolution 283,202]
285. 14 [avatar contradiction clause 284]
286. $false [avatar sat refutation 203,279,285]
% SZS output end Proof for 2886411169259153679202914
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is tall or not strong is not brave. Everyone who is both old and tall is both not calm and not strong. Everyone who is both not patient and creative is either not happy or kind and vice versa. Everyone who is both not tall and not strong is both creative and quiet and vice versa. Everyone who is rich or not brave is both not generous and tall and vice versa. If alice is not creative or not brave then someone is creative or generous and vice versa. Everyone who is both not rich and not humble is not brave or kind and vice versa. Everyone who is both not patient and happy is not patient and vice versa. Everyone who is humble or not patient is both creative and not wise. Everyone who is either creative or old is old. If mary is curious or not old then someone is either brave or not kind. Everyone who is not happy or brave is not calm. Everyone who is either not happy or generous is either old or curious and vice versa. If someone is not calm or wise then alice is either generous or strong and vice versa. Everyone who is either funny or not quiet is both wise and not kind and vice versa. Everyone who is either not patient or not quiet is both not brave and kind and vice versa. Fred is either brave or not patient. Paul is quiet. Fred is generous or not old. Paul is generous. Someone is both not tall and happy. Paul is both not creative and generous. Someone is tall. | Fred is humble. | contradiction | (![X]:((tall(X)|~strong(X))=>~brave(X)))&
(![X]:((old(X)&tall(X))=>(~calm(X)&~strong(X))))&
(![X]:((~patient(X)&creative(X))<=>(~happy(X)<~>kind(X))))&
(![X]:((~tall(X)&~strong(X))<=>(creative(X)&quiet(X))))&
(![X]:((rich(X)|~brave(X))<=>(~generous(X)&tall(X))))&
(((~creative(alice)|~brave(alice)))<=>(?[X]:((creative(X)|generous(X)))))&
(![X]:((~rich(X)&~humble(X))<=>(~brave(X)|kind(X))))&
(![X]:((~patient(X)&happy(X))<=>~patient(X)))&
(![X]:((humble(X)|~patient(X))=>(creative(X)&~wise(X))))&
(![X]:((creative(X)<~>old(X))=>old(X)))&
(((curious(mary)|~old(mary)))=>(?[X]:((brave(X)<~>~kind(X)))))&
(![X]:((~happy(X)|brave(X))=>~calm(X)))&
(![X]:((~happy(X)<~>generous(X))<=>(old(X)<~>curious(X))))&
((?[X]:((~calm(X)|wise(X))))<=>((generous(alice)<~>strong(alice))))&
(![X]:((funny(X)<~>~quiet(X))<=>(wise(X)&~kind(X))))&
(![X]:((~patient(X)<~>~quiet(X))<=>(~brave(X)&kind(X))))&
((brave(fred)<~>~patient(fred)))&
(quiet(paul))&
((generous(fred)|~old(fred)))&
(generous(paul))&
(?[X]:((~tall(X)&happy(X))))&
((~creative(paul)&generous(paul)))&
(?[X]:(tall(X))) | humble(fred) | [
"p0",
"p3",
"p6",
"p8",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 8701947990534537644705532
% SZS output start Proof for 8701947990534537644705532
1. ! [X0] : ((~strong(X0) | tall(X0)) => ~brave(X0)) [input p0]
4. ! [X0] : ((~strong(X0) & ~tall(X0)) <=> (quiet(X0) & creative(X0))) [input p3]
7. ! [X0] : ((~humble(X0) & ~rich(X0)) <=> (kind(X0) | ~brave(X0))) [input p6]
9. ! [X0] : ((~patient(X0) | humble(X0)) => (~wise(X0) & creative(X0))) [input p8]
16. ! [X0] : ((~patient(X0) <~> ~quiet(X0)) <=> (kind(X0) & ~brave(X0))) [input p15]
17. brave(fred) <~> ~patient(fred) [input p16]
24. humble(fred) [input hypothesis]
25. ! [X0] : (~brave(X0) | (strong(X0) & ~tall(X0))) [ennf transformation 1]
28. ! [X0] : ((~wise(X0) & creative(X0)) | (patient(X0) & ~humble(X0))) [ennf transformation 9]
34. ! [X0] : (((~strong(X0) & ~tall(X0)) | (~quiet(X0) | ~creative(X0))) & ((quiet(X0) & creative(X0)) | (strong(X0) | tall(X0)))) [nnf transformation 4]
35. ! [X0] : (((~strong(X0) & ~tall(X0)) | ~quiet(X0) | ~creative(X0)) & ((quiet(X0) & creative(X0)) | strong(X0) | tall(X0))) [flattening 34]
43. ! [X0] : (((~humble(X0) & ~rich(X0)) | (~kind(X0) & brave(X0))) & ((kind(X0) | ~brave(X0)) | (humble(X0) | rich(X0)))) [nnf transformation 7]
44. ! [X0] : (((~humble(X0) & ~rich(X0)) | (~kind(X0) & brave(X0))) & (kind(X0) | ~brave(X0) | humble(X0) | rich(X0))) [flattening 43]
58. ! [X0] : ((((quiet(X0) | patient(X0)) & (~quiet(X0) | ~patient(X0))) | (~kind(X0) | brave(X0))) & ((kind(X0) & ~brave(X0)) | ((~patient(X0) | quiet(X0)) & (~quiet(X0) | patient(X0))))) [nnf transformation 16]
59. ! [X0] : ((((quiet(X0) | patient(X0)) & (~quiet(X0) | ~patient(X0))) | ~kind(X0) | brave(X0)) & ((kind(X0) & ~brave(X0)) | ((~patient(X0) | quiet(X0)) & (~quiet(X0) | patient(X0))))) [flattening 58]
60. (patient(fred) | ~brave(fred)) & (~patient(fred) | brave(fred)) [nnf transformation 17]
66. ~brave(X0) | strong(X0) [cnf transformation 25]
78. ~quiet(X0) | ~strong(X0) | ~creative(X0) [cnf transformation 35]
91. ~humble(X0) | brave(X0) [cnf transformation 44]
96. ~humble(X0) | creative(X0) [cnf transformation 28]
129. ~patient(X0) | ~brave(X0) | quiet(X0) [cnf transformation 59]
135. patient(fred) | ~brave(fred) [cnf transformation 60]
144. humble(fred) [cnf transformation 24]
221. 17 <=> brave(fred) [avatar definition]
222. brave(fred) <- (17) [avatar component clause 221]
225. 18 <=> patient(fred) [avatar definition]
227. patient(fred) <- (18) [avatar component clause 225]
228. ~17 | 18 [avatar split clause 135,225,221]
248. brave(fred) [resolution 91,144]
251. 17 [avatar split clause 248,221]
252. strong(fred) <- (17) [resolution 222,66]
255. creative(fred) [resolution 96,144]
317. ~brave(fred) | quiet(fred) <- (18) [resolution 129,227]
320. quiet(fred) <- (17, 18) [subsumption resolution 317,222]
325. ~strong(fred) | ~creative(fred) <- (17, 18) [resolution 320,78]
327. ~creative(fred) <- (17, 18) [subsumption resolution 325,252]
328. $false <- (17, 18) [subsumption resolution 327,255]
329. ~17 | ~18 [avatar contradiction clause 328]
330. $false [avatar sat refutation 228,251,329]
% SZS output end Proof for 8701947990534537644705532
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not generous or wise is not tall or rich.
Everyone who is either not wise or not funny is old and vice versa.
If mary is either not strong or not tall then someone is either not calm or not strong and vice versa.
Everyone who is strong is either not old or humble.
Everyone who is not creative or not humble is both not old and not tall.
If someone is not brave or not strong then fred is patient or tall.
Everyone who is either wise or strong is not calm and vice versa.
Everyone who is either strong or not strong is both not creative and curious and vice versa.
If paul is not generous or tall then paul is not happy or not quiet and vice versa.
Everyone who is funny is not funny or not calm and vice versa.
Everyone who is not brave is creative or tall and vice versa.
Everyone who is funny is both happy and not quiet and vice versa.
Everyone who is both not rich and creative is either humble or not funny and vice versa.
If paul is not wise then someone is both not humble and not tall.
Everyone who is both generous and brave is both not calm and rich and vice versa.
If someone is rich then someone is both happy and funny and vice versa.
Someone is both not calm and not strong.
Susan is not tall.
Lucy is either rich or not humble. | Mary is not wise. | contradiction | (![X]:((~generous(X)<~>wise(X))=>(~tall(X)|rich(X))))&
(![X]:((~wise(X)<~>~funny(X))<=>old(X)))&
(((~strong(mary)<~>~tall(mary)))<=>(?[X]:((~calm(X)<~>~strong(X)))))&
(![X]:(strong(X)=>(~old(X)<~>humble(X))))&
(![X]:((~creative(X)|~humble(X))=>(~old(X)&~tall(X))))&
((?[X]:((~brave(X)|~strong(X))))=>((patient(fred)|tall(fred))))&
(![X]:((wise(X)<~>strong(X))<=>~calm(X)))&
(![X]:((strong(X)<~>~strong(X))<=>(~creative(X)&curious(X))))&
(((~generous(paul)|tall(paul)))<=>((~happy(paul)|~quiet(paul))))&
(![X]:(funny(X)<=>(~funny(X)|~calm(X))))&
(![X]:(~brave(X)<=>(creative(X)|tall(X))))&
(![X]:(funny(X)<=>(happy(X)&~quiet(X))))&
(![X]:((~rich(X)&creative(X))<=>(humble(X)<~>~funny(X))))&
((~wise(paul))=>(?[X]:((~humble(X)&~tall(X)))))&
(![X]:((generous(X)&brave(X))<=>(~calm(X)&rich(X))))&
((?[X]:(rich(X)))<=>(?[X]:((happy(X)&funny(X)))))&
(?[X]:((~calm(X)&~strong(X))))&
(~tall(susan))&
((rich(lucy)<~>~humble(lucy))) | ~wise(mary) | [
"p1",
"p4",
"p7",
"p9",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 2509814588673223082418640
% SZS output start Proof for 2509814588673223082418640
2. ! [X0] : ((~wise(X0) <~> ~funny(X0)) <=> old(X0)) [input p1]
5. ! [X0] : ((~humble(X0) | ~creative(X0)) => (~tall(X0) & ~old(X0))) [input p4]
8. ! [X0] : ((strong(X0) <~> ~strong(X0)) <=> (curious(X0) & ~creative(X0))) [input p7]
10. ! [X0] : (funny(X0) <=> (~calm(X0) | ~funny(X0))) [input p9]
13. ! [X0] : ((creative(X0) & ~rich(X0)) <=> (humble(X0) <~> ~funny(X0))) [input p12]
20. ~wise(mary) [input hypothesis]
26. ! [X0] : ((~tall(X0) & ~old(X0)) | (humble(X0) & creative(X0))) [ennf transformation 5]
29. ! [X0] : ((((funny(X0) | wise(X0)) & (~funny(X0) | ~wise(X0))) | ~old(X0)) & (old(X0) | ((~wise(X0) | funny(X0)) & (~funny(X0) | wise(X0))))) [nnf transformation 2]
36. ! [X0] : ((((strong(X0) | ~strong(X0)) & (~strong(X0) | strong(X0))) | (~curious(X0) | creative(X0))) & ((curious(X0) & ~creative(X0)) | ((strong(X0) | strong(X0)) & (~strong(X0) | ~strong(X0))))) [nnf transformation 8]
37. ! [X0] : ((((strong(X0) | ~strong(X0)) & (~strong(X0) | strong(X0))) | ~curious(X0) | creative(X0)) & ((curious(X0) & ~creative(X0)) | ((strong(X0) | strong(X0)) & (~strong(X0) | ~strong(X0))))) [flattening 36]
40. ! [X0] : ((funny(X0) | (calm(X0) & funny(X0))) & ((~calm(X0) | ~funny(X0)) | ~funny(X0))) [nnf transformation 10]
41. ! [X0] : ((funny(X0) | (calm(X0) & funny(X0))) & (~calm(X0) | ~funny(X0) | ~funny(X0))) [flattening 40]
46. ! [X0] : (((creative(X0) & ~rich(X0)) | ((humble(X0) | funny(X0)) & (~funny(X0) | ~humble(X0)))) & (((funny(X0) | ~humble(X0)) & (~funny(X0) | humble(X0))) | (~creative(X0) | rich(X0)))) [nnf transformation 13]
47. ! [X0] : (((creative(X0) & ~rich(X0)) | ((humble(X0) | funny(X0)) & (~funny(X0) | ~humble(X0)))) & (((funny(X0) | ~humble(X0)) & (~funny(X0) | humble(X0))) | ~creative(X0) | rich(X0))) [flattening 46]
62. ~funny(X0) | old(X0) | wise(X0) [cnf transformation 29]
77. ~old(X0) | humble(X0) [cnf transformation 26]
84. ~creative(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 37]
85. ~creative(X0) | strong(X0) | strong(X0) [cnf transformation 37]
95. funny(X0) | funny(X0) [cnf transformation 41]
107. creative(X0) | ~funny(X0) | ~humble(X0) [cnf transformation 47]
123. ~wise(mary) [cnf transformation 20]
125. funny(X0) [duplicate literal removal 95]
126. ~creative(X0) | ~strong(X0) [duplicate literal removal 84]
127. ~creative(X0) | strong(X0) [duplicate literal removal 85]
161. ~creative(X0) [subsumption resolution 126,127]
186. ~funny(X0) | ~humble(X0) [subsumption resolution 107,161]
187. ~humble(X0) [subsumption resolution 186,125]
220. old(X0) | wise(X0) [resolution 62,125]
221. wise(X0) | humble(X0) [resolution 220,77]
223. wise(X0) [subsumption resolution 221,187]
225. $false [resolution 223,123]
% SZS output end Proof for 2509814588673223082418640
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If alice is either not happy or tall then someone is both not funny and not wise and vice versa.
Everyone who is not strong is kind.
Everyone who is not strong or brave is not humble.
If susan is not wise then susan is not tall or not calm and vice versa.
Everyone who is not strong or creative is creative and vice versa.
If susan is both old and not strong then someone is not brave or strong.
Everyone who is quiet is either not generous or not humble.
If someone is either generous or not rich then alice is both not kind and quiet and vice versa.
If someone is not funny then someone is both patient and brave and vice versa.
Everyone who is either not brave or old is either happy or creative.
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.
If someone is rich then someone is either not brave or not old and vice versa.
If paul is not patient or strong then alice is not brave or curious and vice versa.
Everyone who is both not curious and curious is generous or not strong and vice versa.
Someone is either kind or funny.
Someone is either curious or brave.
Mary is curious.
Lucy is generous or brave.
Mary is either strong or quiet. | Paul is not tall. | neutral | (((~happy(alice)<~>tall(alice)))<=>(?[X]:((~funny(X)&~wise(X)))))&
(![X]:(~strong(X)=>kind(X)))&
(![X]:((~strong(X)|brave(X))=>~humble(X)))&
((~wise(susan))<=>((~tall(susan)|~calm(susan))))&
(![X]:((~strong(X)|creative(X))<=>creative(X)))&
(((old(susan)&~strong(susan)))=>(?[X]:((~brave(X)|strong(X)))))&
(![X]:(quiet(X)=>(~generous(X)<~>~humble(X))))&
((?[X]:((generous(X)<~>~rich(X))))<=>((~kind(alice)&quiet(alice))))&
((?[X]:(~funny(X)))<=>(?[X]:((patient(X)&brave(X)))))&
(![X]:((~brave(X)<~>old(X))=>(happy(X)<~>creative(X))))&
(![X]:((old(X)<~>humble(X))=>generous(X)))&
(![X]:(wise(X)<=>(rich(X)&~calm(X))))&
(![X]:(strong(X)<=>brave(X)))&
((?[X]:(rich(X)))<=>(?[X]:((~brave(X)<~>~old(X)))))&
(((~patient(paul)|strong(paul)))<=>((~brave(alice)|curious(alice))))&
(![X]:((~curious(X)&curious(X))<=>(generous(X)|~strong(X))))&
(?[X]:((kind(X)<~>funny(X))))&
(?[X]:((curious(X)<~>brave(X))))&
(curious(mary))&
((generous(lucy)|brave(lucy)))&
((strong(mary)<~>quiet(mary))) | ~tall(paul) | [] | null | 0 |
Everyone who is funny is not old or not creative and vice versa.
If someone is creative then someone is quiet or humble and vice versa.
Everyone who is humble is not strong or not calm.
Everyone who is not happy is not old.
If someone is not patient then john is either wise or not old and vice versa.
Everyone who is either humble or calm is not old.
Everyone who is either not happy or brave is quiet.
Everyone who is not rich or brave is both curious and not calm and vice versa.
Everyone who is not funny is either not happy or not wise and vice versa.
Everyone who is either wise or brave is either rich or not old.
Everyone who is not wise is either not happy or wise.
If someone is not creative or not rich then someone is wise and vice versa.
If paul is not rich then alice is not old and vice versa.
Everyone who is both not funny and not tall is either not calm or not kind and vice versa.
If someone is either not humble or rich then lucy is both not strong and patient.
If someone is tall then someone is not kind or curious and vice versa.
Someone is quiet.
Lucy is not patient or curious.
Someone is both strong and not quiet.
Someone is both brave and not generous.
Alice is both tall and old.
Susan is not funny or kind.
Lucy is either not humble or generous. | John is generous. | neutral | (![X]:(funny(X)<=>(~old(X)|~creative(X))))&
((?[X]:(creative(X)))<=>(?[X]:((quiet(X)|humble(X)))))&
(![X]:(humble(X)=>(~strong(X)|~calm(X))))&
(![X]:(~happy(X)=>~old(X)))&
((?[X]:(~patient(X)))<=>((wise(john)<~>~old(john))))&
(![X]:((humble(X)<~>calm(X))=>~old(X)))&
(![X]:((~happy(X)<~>brave(X))=>quiet(X)))&
(![X]:((~rich(X)|brave(X))<=>(curious(X)&~calm(X))))&
(![X]:(~funny(X)<=>(~happy(X)<~>~wise(X))))&
(![X]:((wise(X)<~>brave(X))=>(rich(X)<~>~old(X))))&
(![X]:(~wise(X)=>(~happy(X)<~>wise(X))))&
((?[X]:((~creative(X)|~rich(X))))<=>(?[X]:(wise(X))))&
((~rich(paul))<=>(~old(alice)))&
(![X]:((~funny(X)&~tall(X))<=>(~calm(X)<~>~kind(X))))&
((?[X]:((~humble(X)<~>rich(X))))=>((~strong(lucy)&patient(lucy))))&
((?[X]:(tall(X)))<=>(?[X]:((~kind(X)|curious(X)))))&
(?[X]:(quiet(X)))&
((~patient(lucy)|curious(lucy)))&
(?[X]:((strong(X)&~quiet(X))))&
(?[X]:((brave(X)&~generous(X))))&
((tall(alice)&old(alice)))&
((~funny(susan)|kind(susan)))&
((~humble(lucy)<~>generous(lucy))) | generous(john) | [] | null | 0 |
If someone is not kind or rich then someone is either old or not kind. Everyone who is both kind and brave is not humble and vice versa. If someone is not patient or not rich then someone is either curious or not generous and vice versa. If someone is both rich and patient then someone is either not creative or old and vice versa. If fred is both kind and curious then someone is happy or not generous. If lucy is both not patient and happy then someone is both not brave and not generous. Everyone who is not generous or old is not curious and vice versa. Everyone who is tall or not happy is both quiet and brave and vice versa. If john is not rich or not kind then fred is either tall or old. Everyone who is not strong or calm is both tall and not creative. Everyone who is kind or not generous is generous or curious and vice versa. If john is either calm or not happy then susan is not tall. Everyone who is not rich or not curious is not calm and vice versa. Everyone who is both rich and humble is both not kind and patient. Everyone who is either not old or not humble is either humble or tall and vice versa. If someone is both not quiet and tall then lucy is not funny and vice versa. Paul is not creative or funny. Alice is not creative. Susan is either not patient or not strong. John is either not happy or old. Someone is happy. | John is not old. | contradiction | ((?[X]:((~kind(X)|rich(X))))=>(?[X]:((old(X)<~>~kind(X)))))&
(![X]:((kind(X)&brave(X))<=>~humble(X)))&
((?[X]:((~patient(X)|~rich(X))))<=>(?[X]:((curious(X)<~>~generous(X)))))&
((?[X]:((rich(X)&patient(X))))<=>(?[X]:((~creative(X)<~>old(X)))))&
(((kind(fred)&curious(fred)))=>(?[X]:((happy(X)|~generous(X)))))&
(((~patient(lucy)&happy(lucy)))=>(?[X]:((~brave(X)&~generous(X)))))&
(![X]:((~generous(X)|old(X))<=>~curious(X)))&
(![X]:((tall(X)|~happy(X))<=>(quiet(X)&brave(X))))&
(((~rich(john)|~kind(john)))=>((tall(fred)<~>old(fred))))&
(![X]:((~strong(X)|calm(X))=>(tall(X)&~creative(X))))&
(![X]:((kind(X)|~generous(X))<=>(generous(X)|curious(X))))&
(((calm(john)<~>~happy(john)))=>(~tall(susan)))&
(![X]:((~rich(X)|~curious(X))<=>~calm(X)))&
(![X]:((rich(X)&humble(X))=>(~kind(X)&patient(X))))&
(![X]:((~old(X)<~>~humble(X))<=>(humble(X)<~>tall(X))))&
((?[X]:((~quiet(X)&tall(X))))<=>(~funny(lucy)))&
((~creative(paul)|funny(paul)))&
(~creative(alice))&
((~patient(susan)<~>~strong(susan)))&
((~happy(john)<~>old(john)))&
(?[X]:(happy(X))) | ~old(john) | [
"p6",
"p8",
"p9",
"p10",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2104793264363515318929776
% SZS output start Proof for 2104793264363515318929776
7. ! [X0] : ((old(X0) | ~generous(X0)) <=> ~curious(X0)) [input p6]
9. (~kind(john) | ~rich(john)) => (tall(fred) <~> old(fred)) [input p8]
10. ! [X0] : ((calm(X0) | ~strong(X0)) => (~creative(X0) & tall(X0))) [input p9]
11. ! [X0] : ((~generous(X0) | kind(X0)) <=> (curious(X0) | generous(X0))) [input p10]
13. ! [X0] : ((~curious(X0) | ~rich(X0)) <=> ~calm(X0)) [input p12]
15. ! [X0] : ((~old(X0) <~> ~humble(X0)) <=> (humble(X0) <~> tall(X0))) [input p14]
22. ~old(john) [input hypothesis]
31. (tall(fred) <~> old(fred)) | (kind(john) & rich(john)) [ennf transformation 9]
32. ! [X0] : ((~creative(X0) & tall(X0)) | (~calm(X0) & strong(X0))) [ennf transformation 10]
56. ! [X0] : (((old(X0) | ~generous(X0)) | curious(X0)) & (~curious(X0) | (~old(X0) & generous(X0)))) [nnf transformation 7]
57. ! [X0] : ((old(X0) | ~generous(X0) | curious(X0)) & (~curious(X0) | (~old(X0) & generous(X0)))) [flattening 56]
60. ((~old(fred) | ~tall(fred)) & (old(fred) | tall(fred))) | (kind(john) & rich(john)) [nnf transformation 31]
61. ! [X0] : (((~generous(X0) | kind(X0)) | (~curious(X0) & ~generous(X0))) & ((curious(X0) | generous(X0)) | (generous(X0) & ~kind(X0)))) [nnf transformation 11]
62. ! [X0] : ((~generous(X0) | kind(X0) | (~curious(X0) & ~generous(X0))) & (curious(X0) | generous(X0) | (generous(X0) & ~kind(X0)))) [flattening 61]
64. ! [X0] : (((~curious(X0) | ~rich(X0)) | calm(X0)) & (~calm(X0) | (curious(X0) & rich(X0)))) [nnf transformation 13]
65. ! [X0] : ((~curious(X0) | ~rich(X0) | calm(X0)) & (~calm(X0) | (curious(X0) & rich(X0)))) [flattening 64]
66. ! [X0] : ((((humble(X0) | old(X0)) & (~humble(X0) | ~old(X0))) | ((humble(X0) | ~tall(X0)) & (tall(X0) | ~humble(X0)))) & (((~tall(X0) | ~humble(X0)) & (tall(X0) | humble(X0))) | ((~old(X0) | humble(X0)) & (~humble(X0) | old(X0))))) [nnf transformation 15]
97. ~curious(X0) | generous(X0) [cnf transformation 57]
99. ~generous(X0) | old(X0) | curious(X0) [cnf transformation 57]
105. old(fred) | tall(fred) | rich(john) [cnf transformation 60]
107. ~old(fred) | ~tall(fred) | rich(john) [cnf transformation 60]
110. ~calm(X0) | tall(X0) [cnf transformation 32]
114. curious(X0) | generous(X0) | generous(X0) [cnf transformation 62]
121. ~curious(X0) | ~rich(X0) | calm(X0) [cnf transformation 65]
125. tall(X0) | humble(X0) | ~old(X0) | humble(X0) [cnf transformation 66]
126. ~tall(X0) | ~humble(X0) | ~humble(X0) | old(X0) [cnf transformation 66]
128. ~humble(X0) | ~old(X0) | tall(X0) | ~humble(X0) [cnf transformation 66]
131. humble(X0) | old(X0) | humble(X0) | ~tall(X0) [cnf transformation 66]
142. ~old(john) [cnf transformation 22]
143. tall(X0) | humble(X0) | ~old(X0) [duplicate literal removal 125]
144. ~tall(X0) | ~humble(X0) | old(X0) [duplicate literal removal 126]
145. ~humble(X0) | ~old(X0) | tall(X0) [duplicate literal removal 128]
146. ~tall(X0) | old(X0) | humble(X0) [duplicate literal removal 131]
147. curious(X0) | generous(X0) [duplicate literal removal 114]
272. 29 <=> tall(fred) [avatar definition]
273. tall(fred) <- (29) [avatar component clause 272]
274. ~tall(fred) <- (~29) [avatar component clause 272]
276. 30 <=> old(fred) [avatar definition]
277. old(fred) <- (30) [avatar component clause 276]
278. ~old(fred) <- (~30) [avatar component clause 276]
281. 31 <=> rich(john) [avatar definition]
283. rich(john) <- (31) [avatar component clause 281]
284. 31 | ~29 | ~30 [avatar split clause 107,276,272,281]
286. 31 | 29 | 30 [avatar split clause 105,276,272,281]
288. generous(X0) [subsumption resolution 147,97]
294. 33 <=> calm(john) [avatar definition]
296. calm(john) <- (33) [avatar component clause 294]
303. ~tall(X0) | old(X0) [subsumption resolution 144,146]
304. ~old(X0) | tall(X0) [subsumption resolution 143,145]
339. 42 <=> old(john) [avatar definition]
341. ~old(john) <- (~42) [avatar component clause 339]
344. ~42 [avatar split clause 142,339]
392. old(fred) <- (29) [resolution 303,273]
393. $false <- (29, ~30) [subsumption resolution 392,278]
394. ~29 | 30 [avatar contradiction clause 393]
396. tall(fred) <- (30) [resolution 304,277]
398. $false <- (~29, 30) [subsumption resolution 396,274]
399. 29 | ~30 [avatar contradiction clause 398]
413. curious(X0) | old(X0) [resolution 99,288]
438. ~rich(X0) | old(X0) | calm(X0) [resolution 413,121]
459. old(john) | calm(john) <- (31) [resolution 438,283]
460. calm(john) <- (31, ~42) [subsumption resolution 459,341]
463. 33 | ~31 | 42 [avatar split clause 460,339,281,294]
467. tall(john) <- (33) [resolution 296,110]
488. old(john) <- (33) [resolution 467,303]
492. $false <- (33, ~42) [subsumption resolution 488,341]
493. ~33 | 42 [avatar contradiction clause 492]
494. $false [avatar sat refutation 284,286,344,394,399,463,493]
% SZS output end Proof for 2104793264363515318929776
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both 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. | Alice is not kind. | 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)))) | ~kind(alice) | [
"p8",
"p10",
"p11",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 768813210862941382656812
% SZS output start Proof for 768813210862941382656812
9. (~calm(alice) & kind(alice)) <=> ? [X0] : (~generous(X0) | kind(X0)) [input p8]
11. ! [X0] : ((~funny(X0) | patient(X0)) => (~rich(X0) | ~generous(X0))) [input p10]
12. ! [X0] : ((funny(X0) | brave(X0)) => (~tall(X0) & ~happy(X0))) [input p11]
16. ! [X0] : ((funny(X0) <~> kind(X0)) <=> (~quiet(X0) | ~rich(X0))) [input p15]
18. generous(paul) & happy(paul) [input p17]
24. ~kind(alice) [input hypothesis]
35. ! [X0] : ((~rich(X0) | ~generous(X0)) | (funny(X0) & ~patient(X0))) [ennf transformation 11]
36. ! [X0] : (~rich(X0) | ~generous(X0) | (funny(X0) & ~patient(X0))) [flattening 35]
37. ! [X0] : ((~tall(X0) & ~happy(X0)) | (~funny(X0) & ~brave(X0))) [ennf transformation 12]
50. ((~calm(alice) & kind(alice)) | ! [X0] : (generous(X0) & ~kind(X0))) & (? [X0] : (~generous(X0) | kind(X0)) | (calm(alice) | ~kind(alice))) [nnf transformation 9]
51. ((~calm(alice) & kind(alice)) | ! [X0] : (generous(X0) & ~kind(X0))) & (? [X0] : (~generous(X0) | kind(X0)) | calm(alice) | ~kind(alice)) [flattening 50]
52. ((~calm(alice) & kind(alice)) | ! [X0] : (generous(X0) & ~kind(X0))) & (? [X1] : (~generous(X1) | kind(X1)) | calm(alice) | ~kind(alice)) [rectify 51]
53. ? [X1] : (~generous(X1) | kind(X1)) => (~generous(sK1) | kind(sK1)) [choice axiom]
54. ((~calm(alice) & kind(alice)) | ! [X0] : (generous(X0) & ~kind(X0))) & ((~generous(sK1) | kind(sK1)) | calm(alice) | ~kind(alice)) [skolemisation 52,53]
58. ! [X0] : ((((~kind(X0) | ~funny(X0)) & (kind(X0) | funny(X0))) | (quiet(X0) & rich(X0))) & ((~quiet(X0) | ~rich(X0)) | ((funny(X0) | ~kind(X0)) & (kind(X0) | ~funny(X0))))) [nnf transformation 16]
59. ! [X0] : ((((~kind(X0) | ~funny(X0)) & (kind(X0) | funny(X0))) | (quiet(X0) & rich(X0))) & (~quiet(X0) | ~rich(X0) | ((funny(X0) | ~kind(X0)) & (kind(X0) | ~funny(X0))))) [flattening 58]
97. kind(alice) | ~kind(X0) [cnf transformation 54]
98. kind(alice) | generous(X0) [cnf transformation 54]
107. ~generous(X0) | ~rich(X0) | funny(X0) [cnf transformation 36]
109. ~happy(X0) | ~funny(X0) [cnf transformation 37]
123. kind(X0) | funny(X0) | rich(X0) [cnf transformation 59]
129. happy(paul) [cnf transformation 18]
137. ~kind(alice) [cnf transformation 24]
152. 4 <=> ! [X0] : generous(X0) [avatar definition]
153. generous(X0) <- (4) [avatar component clause 152]
160. 6 <=> ! [X0] : ~kind(X0) [avatar definition]
161. ~kind(X0) <- (6) [avatar component clause 160]
164. 7 <=> kind(alice) [avatar definition]
167. 4 | 7 [avatar split clause 98,164,152]
168. 6 | 7 [avatar split clause 97,164,160]
252. ~7 [avatar split clause 137,164]
260. ~funny(paul) [resolution 109,129]
357. ~rich(X0) | funny(X0) <- (4) [resolution 107,153]
363. funny(X3) | rich(X3) <- (6) [resolution 123,161]
367. funny(X3) <- (4, 6) [subsumption resolution 363,357]
374. $false <- (4, 6) [resolution 367,260]
379. ~4 | ~6 [avatar contradiction clause 374]
380. $false [avatar sat refutation 167,168,252,379]
% SZS output end Proof for 768813210862941382656812
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is strong is not generous or not rich.
Everyone who is not kind or humble is kind and vice versa.
If susan is happy or old then someone is not tall and vice versa.
Everyone who is not happy is both not creative and wise and vice versa.
If fred is either not funny or not calm then mary is not brave and vice versa.
Everyone who is tall or not funny is not curious and vice versa.
If someone is not humble then someone is not calm.
Everyone who is both not creative and not strong is happy or not creative.
Everyone who is kind or strong is either not quiet or not curious.
Everyone who is strong or curious is either tall or creative.
If alice is not strong then alice is not tall and vice versa.
If alice is not wise then fred is happy and vice versa.
If someone is funny then someone is not kind.
If alice is either not rich or not calm then someone is calm or not wise.
Everyone who is either tall or not old is both not creative and wise and vice versa.
Everyone who is either not rich or not creative is not brave.
Someone is not curious.
Someone is both not patient and wise.
Someone is either not rich or funny.
Someone is rich.
Someone is either happy or not strong.
Someone is either not generous or strong. | Alice is calm. | neutral | (![X]:(strong(X)=>(~generous(X)|~rich(X))))&
(![X]:((~kind(X)|humble(X))<=>kind(X)))&
(((happy(susan)|old(susan)))<=>(?[X]:(~tall(X))))&
(![X]:(~happy(X)<=>(~creative(X)&wise(X))))&
(((~funny(fred)<~>~calm(fred)))<=>(~brave(mary)))&
(![X]:((tall(X)|~funny(X))<=>~curious(X)))&
((?[X]:(~humble(X)))=>(?[X]:(~calm(X))))&
(![X]:((~creative(X)&~strong(X))=>(happy(X)|~creative(X))))&
(![X]:((kind(X)|strong(X))=>(~quiet(X)<~>~curious(X))))&
(![X]:((strong(X)|curious(X))=>(tall(X)<~>creative(X))))&
((~strong(alice))<=>(~tall(alice)))&
((~wise(alice))<=>(happy(fred)))&
((?[X]:(funny(X)))=>(?[X]:(~kind(X))))&
(((~rich(alice)<~>~calm(alice)))=>(?[X]:((calm(X)|~wise(X)))))&
(![X]:((tall(X)<~>~old(X))<=>(~creative(X)&wise(X))))&
(![X]:((~rich(X)<~>~creative(X))=>~brave(X)))&
(?[X]:(~curious(X)))&
(?[X]:((~patient(X)&wise(X))))&
(?[X]:((~rich(X)<~>funny(X))))&
(?[X]:(rich(X)))&
(?[X]:((happy(X)<~>~strong(X))))&
(?[X]:((~generous(X)<~>strong(X)))) | calm(alice) | [] | null | 0 |
If someone is either not happy or not patient then mary is not creative. If someone is not curious or not kind then paul is both creative and not generous. Everyone who is not funny or not quiet is not funny or creative and vice versa. If someone is not brave or not generous then susan is not patient. Everyone who is either not happy or not brave is both funny and not generous. Everyone who is either rich or not wise is not patient. If lucy is either not brave or not generous then alice is either not tall or funny and vice versa. Everyone who is both generous and not wise is both brave and strong. Everyone who is either not happy or happy is funny or humble and vice versa. If someone is either not kind or not brave then susan is happy or not kind and vice versa. Everyone who is not calm is not strong and vice versa. Everyone who is either not generous or not quiet is kind or rich and vice versa. Everyone who is not creative is either quiet or not quiet. If paul is either not strong or strong then someone is not wise or creative. Everyone who is not kind is old or not brave and vice versa. If lucy is either tall or not curious then someone is either not generous or not funny and vice versa. John is both not patient and not creative. Someone is either kind or creative. Someone is either wise or funny. John is both not rich and not funny. Paul is both brave and generous. Paul is either not old or not humble. | Paul is not old. | entailment | ((?[X]:((~happy(X)<~>~patient(X))))=>(~creative(mary)))&
((?[X]:((~curious(X)|~kind(X))))=>((creative(paul)&~generous(paul))))&
(![X]:((~funny(X)|~quiet(X))<=>(~funny(X)|creative(X))))&
((?[X]:((~brave(X)|~generous(X))))=>(~patient(susan)))&
(![X]:((~happy(X)<~>~brave(X))=>(funny(X)&~generous(X))))&
(![X]:((rich(X)<~>~wise(X))=>~patient(X)))&
(((~brave(lucy)<~>~generous(lucy)))<=>((~tall(alice)<~>funny(alice))))&
(![X]:((generous(X)&~wise(X))=>(brave(X)&strong(X))))&
(![X]:((~happy(X)<~>happy(X))<=>(funny(X)|humble(X))))&
((?[X]:((~kind(X)<~>~brave(X))))<=>((happy(susan)|~kind(susan))))&
(![X]:(~calm(X)<=>~strong(X)))&
(![X]:((~generous(X)<~>~quiet(X))<=>(kind(X)|rich(X))))&
(![X]:(~creative(X)=>(quiet(X)<~>~quiet(X))))&
(((~strong(paul)<~>strong(paul)))=>(?[X]:((~wise(X)|creative(X)))))&
(![X]:(~kind(X)<=>(old(X)|~brave(X))))&
(((tall(lucy)<~>~curious(lucy)))<=>(?[X]:((~generous(X)<~>~funny(X)))))&
((~patient(john)&~creative(john)))&
(?[X]:((kind(X)<~>creative(X))))&
(?[X]:((wise(X)<~>funny(X))))&
((~rich(john)&~funny(john)))&
((brave(paul)&generous(paul)))&
((~old(paul)<~>~humble(paul))) | ~old(paul) | [
"p1",
"p14",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 362845607320834119430626
% SZS output start Proof for 362845607320834119430626
2. ? [X0] : (~kind(X0) | ~curious(X0)) => (~generous(paul) & creative(paul)) [input p1]
15. ! [X0] : (~kind(X0) <=> (~brave(X0) | old(X0))) [input p14]
21. generous(paul) & brave(paul) [input p20]
23. old(paul) [input hypothesis]
25. (~generous(paul) & creative(paul)) | ! [X0] : (kind(X0) & curious(X0)) [ennf transformation 2]
52. ! [X0] : ((~kind(X0) | (brave(X0) & ~old(X0))) & ((~brave(X0) | old(X0)) | kind(X0))) [nnf transformation 15]
53. ! [X0] : ((~kind(X0) | (brave(X0) & ~old(X0))) & (~brave(X0) | old(X0) | kind(X0))) [flattening 52]
70. ~generous(paul) | kind(X0) [cnf transformation 25]
116. ~old(X0) | ~kind(X0) [cnf transformation 53]
135. generous(paul) [cnf transformation 21]
138. old(paul) [cnf transformation 23]
156. 4 <=> ! [X0] : kind(X0) [avatar definition]
157. kind(X0) <- (4) [avatar component clause 156]
159. 5 <=> generous(paul) [avatar definition]
162. 4 | ~5 [avatar split clause 70,159,156]
303. 5 [avatar split clause 135,159]
305. 34 <=> old(paul) [avatar definition]
307. old(paul) <- (34) [avatar component clause 305]
314. 34 [avatar split clause 138,305]
319. ~kind(paul) <- (34) [resolution 116,307]
320. $false <- (4, 34) [subsumption resolution 319,157]
321. ~4 | ~34 [avatar contradiction clause 320]
322. $false [avatar sat refutation 162,303,314,321]
% SZS output end Proof for 362845607320834119430626
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If alice is either wise or not patient then fred is both old and not funny and vice versa.
Everyone who is not generous or not quiet is both rich and kind and vice versa.
If paul is not quiet or kind then someone is both not creative and not calm and vice versa.
If paul is both not quiet and quiet then paul is both not creative and brave and vice versa.
Everyone who is generous or not patient is not happy and vice versa.
If alice is not wise then mary is both not tall and not kind.
Everyone who is happy is wise.
If someone is not old or humble then lucy is humble and vice versa.
If someone is not strong or old then john is both not kind and not creative and vice versa.
Everyone who is both wise and generous is not funny.
If john is both creative and wise then alice is either not curious or not calm.
Everyone who is not calm or old is curious and vice versa.
Everyone who is happy is curious and vice versa.
Everyone who is rich or happy is either brave or not humble.
Everyone who is either not strong or not old is not humble and vice versa.
Everyone who is either brave or quiet is curious and vice versa.
Fred is patient.
Susan is either curious or not quiet.
Someone is not generous.
Someone is both not patient and wise.
Someone is either not rich or calm.
Fred is not patient or not calm.
Someone is strong or curious. | Paul is not patient. | neutral | (((wise(alice)<~>~patient(alice)))<=>((old(fred)&~funny(fred))))&
(![X]:((~generous(X)|~quiet(X))<=>(rich(X)&kind(X))))&
(((~quiet(paul)|kind(paul)))<=>(?[X]:((~creative(X)&~calm(X)))))&
(((~quiet(paul)&quiet(paul)))<=>((~creative(paul)&brave(paul))))&
(![X]:((generous(X)|~patient(X))<=>~happy(X)))&
((~wise(alice))=>((~tall(mary)&~kind(mary))))&
(![X]:(happy(X)=>wise(X)))&
((?[X]:((~old(X)|humble(X))))<=>(humble(lucy)))&
((?[X]:((~strong(X)|old(X))))<=>((~kind(john)&~creative(john))))&
(![X]:((wise(X)&generous(X))=>~funny(X)))&
(((creative(john)&wise(john)))=>((~curious(alice)<~>~calm(alice))))&
(![X]:((~calm(X)|old(X))<=>curious(X)))&
(![X]:(happy(X)<=>curious(X)))&
(![X]:((rich(X)|happy(X))=>(brave(X)<~>~humble(X))))&
(![X]:((~strong(X)<~>~old(X))<=>~humble(X)))&
(![X]:((brave(X)<~>quiet(X))<=>curious(X)))&
(patient(fred))&
((curious(susan)<~>~quiet(susan)))&
(?[X]:(~generous(X)))&
(?[X]:((~patient(X)&wise(X))))&
(?[X]:((~rich(X)<~>calm(X))))&
((~patient(fred)|~calm(fred)))&
(?[X]:((strong(X)|curious(X)))) | ~patient(paul) | [] | null | 0 |
Everyone who is either not patient or kind is either not generous or quiet.
If alice is not happy then someone is either curious or not brave and vice versa.
If someone is both old and not kind then someone is not curious or generous and vice versa.
If someone is either creative or quiet then someone is not old and vice versa.
Everyone who is not wise is quiet or not creative and vice versa.
Everyone who is not patient is either not calm or not quiet.
Everyone who is either not rich or brave is both kind and rich and vice versa.
Everyone who is wise is either wise or not wise and vice versa.
Everyone who is curious is not curious or not happy and vice versa.
Everyone who is both not generous and calm is both strong and not happy and vice versa.
Everyone who is either not kind or generous is either happy or not funny and vice versa.
Everyone who is tall or not old is not funny or not creative and vice versa.
If fred is not patient or quiet then someone is not brave.
Everyone who is either tall or not happy is quiet or not humble and vice versa.
If susan is either funny or not wise then someone is either not funny or not calm.
Everyone who is not happy is humble and vice versa.
Fred is not old or happy.
Susan is not kind.
Alice is patient or old.
Someone is not brave.
Someone is not calm.
Someone is either not creative or not kind.
Fred is either strong or old.
Someone is brave or not wise. | Alice is not strong. | neutral | (![X]:((~patient(X)<~>kind(X))=>(~generous(X)<~>quiet(X))))&
((~happy(alice))<=>(?[X]:((curious(X)<~>~brave(X)))))&
((?[X]:((old(X)&~kind(X))))<=>(?[X]:((~curious(X)|generous(X)))))&
((?[X]:((creative(X)<~>quiet(X))))<=>(?[X]:(~old(X))))&
(![X]:(~wise(X)<=>(quiet(X)|~creative(X))))&
(![X]:(~patient(X)=>(~calm(X)<~>~quiet(X))))&
(![X]:((~rich(X)<~>brave(X))<=>(kind(X)&rich(X))))&
(![X]:(wise(X)<=>(wise(X)<~>~wise(X))))&
(![X]:(curious(X)<=>(~curious(X)|~happy(X))))&
(![X]:((~generous(X)&calm(X))<=>(strong(X)&~happy(X))))&
(![X]:((~kind(X)<~>generous(X))<=>(happy(X)<~>~funny(X))))&
(![X]:((tall(X)|~old(X))<=>(~funny(X)|~creative(X))))&
(((~patient(fred)|quiet(fred)))=>(?[X]:(~brave(X))))&
(![X]:((tall(X)<~>~happy(X))<=>(quiet(X)|~humble(X))))&
(((funny(susan)<~>~wise(susan)))=>(?[X]:((~funny(X)<~>~calm(X)))))&
(![X]:(~happy(X)<=>humble(X)))&
((~old(fred)|happy(fred)))&
(~kind(susan))&
((patient(alice)|old(alice)))&
(?[X]:(~brave(X)))&
(?[X]:(~calm(X)))&
(?[X]:((~creative(X)<~>~kind(X))))&
((strong(fred)<~>old(fred)))&
(?[X]:((brave(X)|~wise(X)))) | ~strong(alice) | [] | null | 0 |
If someone is either not kind or not humble then someone is both not funny and funny and vice versa.
If someone is either happy or wise then lucy is tall or not happy.
Everyone who is both curious and calm is both not tall and strong.
Everyone who is not wise or wise is both humble and brave and vice versa.
If someone is not wise then lucy is either not generous or not happy and vice versa.
Everyone who is old or not old is either curious or not quiet.
Everyone who is either strong or patient is both not wise and not old and vice versa.
If alice is both not kind and not funny then lucy is either not calm or funny.
If susan is kind then fred is both not old and tall.
Everyone who is not wise is not brave and vice versa.
If someone is either not old or curious then mary is both curious and not generous.
Everyone who is either curious or not rich is brave and vice versa.
Everyone who is tall is both patient and creative and vice versa.
If lucy is both not kind and not creative then john is both strong and rich and vice versa.
Everyone who is not strong is not rich or creative.
If alice is not rich then someone is not calm or kind and vice versa.
Someone is not humble or funny.
John is tall or not patient.
Someone is both not rich and tall.
Paul is not curious or humble.
John is not old or curious.
Susan is not curious or generous.
Someone is both patient and not generous. | Mary is not patient. | neutral | ((?[X]:((~kind(X)<~>~humble(X))))<=>(?[X]:((~funny(X)&funny(X)))))&
((?[X]:((happy(X)<~>wise(X))))=>((tall(lucy)|~happy(lucy))))&
(![X]:((curious(X)&calm(X))=>(~tall(X)&strong(X))))&
(![X]:((~wise(X)|wise(X))<=>(humble(X)&brave(X))))&
((?[X]:(~wise(X)))<=>((~generous(lucy)<~>~happy(lucy))))&
(![X]:((old(X)|~old(X))=>(curious(X)<~>~quiet(X))))&
(![X]:((strong(X)<~>patient(X))<=>(~wise(X)&~old(X))))&
(((~kind(alice)&~funny(alice)))=>((~calm(lucy)<~>funny(lucy))))&
((kind(susan))=>((~old(fred)&tall(fred))))&
(![X]:(~wise(X)<=>~brave(X)))&
((?[X]:((~old(X)<~>curious(X))))=>((curious(mary)&~generous(mary))))&
(![X]:((curious(X)<~>~rich(X))<=>brave(X)))&
(![X]:(tall(X)<=>(patient(X)&creative(X))))&
(((~kind(lucy)&~creative(lucy)))<=>((strong(john)&rich(john))))&
(![X]:(~strong(X)=>(~rich(X)|creative(X))))&
((~rich(alice))<=>(?[X]:((~calm(X)|kind(X)))))&
(?[X]:((~humble(X)|funny(X))))&
((tall(john)|~patient(john)))&
(?[X]:((~rich(X)&tall(X))))&
((~curious(paul)|humble(paul)))&
((~old(john)|curious(john)))&
((~curious(susan)|generous(susan)))&
(?[X]:((patient(X)&~generous(X)))) | ~patient(mary) | [] | null | 0 |
Everyone who is both humble and not patient is either not funny or not curious and vice versa.
Everyone who is kind is not old or strong.
Everyone who is either not calm or rich is both quiet and not patient.
Everyone who is both not curious and funny is not humble and vice versa.
If someone is either not funny or not brave then paul is funny.
If someone is curious or not tall then someone is happy or not creative.
If paul is either not creative or quiet then paul is both not rich and quiet.
If someone is either creative or calm then fred is either not patient or not creative.
If someone is not wise then someone is both rich and generous.
Everyone who is humble or not wise is generous or not tall.
Everyone who is both not patient and brave is not curious or kind.
Everyone who is not creative or happy is not wise and vice versa.
Everyone who is humble or brave is not funny.
Everyone who is not curious or funny is old.
Everyone who is strong is either curious or not wise.
Everyone who is not brave is either tall or not funny and vice versa.
Someone is either not humble or not tall.
Someone is not creative or humble.
Alice is generous.
Someone is wise or creative.
Paul is not calm or not quiet.
Paul is not calm or humble.
Paul is rich or generous.
Susan is either not brave or patient. | Susan is curious. | entailment | (![X]:((humble(X)&~patient(X))<=>(~funny(X)<~>~curious(X))))&
(![X]:(kind(X)=>(~old(X)|strong(X))))&
(![X]:((~calm(X)<~>rich(X))=>(quiet(X)&~patient(X))))&
(![X]:((~curious(X)&funny(X))<=>~humble(X)))&
((?[X]:((~funny(X)<~>~brave(X))))=>(funny(paul)))&
((?[X]:((curious(X)|~tall(X))))=>(?[X]:((happy(X)|~creative(X)))))&
(((~creative(paul)<~>quiet(paul)))=>((~rich(paul)&quiet(paul))))&
((?[X]:((creative(X)<~>calm(X))))=>((~patient(fred)<~>~creative(fred))))&
((?[X]:(~wise(X)))=>(?[X]:((rich(X)&generous(X)))))&
(![X]:((humble(X)|~wise(X))=>(generous(X)|~tall(X))))&
(![X]:((~patient(X)&brave(X))=>(~curious(X)|kind(X))))&
(![X]:((~creative(X)|happy(X))<=>~wise(X)))&
(![X]:((humble(X)|brave(X))=>~funny(X)))&
(![X]:((~curious(X)|funny(X))=>old(X)))&
(![X]:(strong(X)=>(curious(X)<~>~wise(X))))&
(![X]:(~brave(X)<=>(tall(X)<~>~funny(X))))&
(?[X]:((~humble(X)<~>~tall(X))))&
(?[X]:((~creative(X)|humble(X))))&
(generous(alice))&
(?[X]:((wise(X)|creative(X))))&
((~calm(paul)|~quiet(paul)))&
((~calm(paul)|humble(paul)))&
((rich(paul)|generous(paul)))&
((~brave(susan)<~>patient(susan))) | curious(susan) | [
"p0",
"p3",
"p4",
"p12",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 5880920099591293369436586
% SZS output start Proof for 5880920099591293369436586
1. ! [X0] : ((~patient(X0) & humble(X0)) <=> (~funny(X0) <~> ~curious(X0))) [input p0]
4. ! [X0] : ((funny(X0) & ~curious(X0)) <=> ~humble(X0)) [input p3]
5. ? [X0] : (~funny(X0) <~> ~brave(X0)) => funny(paul) [input p4]
13. ! [X0] : ((brave(X0) | humble(X0)) => ~funny(X0)) [input p12]
24. ~brave(susan) <~> patient(susan) [input p23]
25. ~curious(susan) [input hypothesis]
35. funny(paul) | ! [X0] : (~funny(X0) <=> ~brave(X0)) [ennf transformation 5]
42. ! [X0] : (~funny(X0) | (~brave(X0) & ~humble(X0))) [ennf transformation 13]
45. ! [X0] : (((~patient(X0) & humble(X0)) | ((~funny(X0) | curious(X0)) & (~curious(X0) | funny(X0)))) & (((curious(X0) | funny(X0)) & (~curious(X0) | ~funny(X0))) | (patient(X0) | ~humble(X0)))) [nnf transformation 1]
46. ! [X0] : (((~patient(X0) & humble(X0)) | ((~funny(X0) | curious(X0)) & (~curious(X0) | funny(X0)))) & (((curious(X0) | funny(X0)) & (~curious(X0) | ~funny(X0))) | patient(X0) | ~humble(X0))) [flattening 45]
48. ! [X0] : (((funny(X0) & ~curious(X0)) | humble(X0)) & (~humble(X0) | (~funny(X0) | curious(X0)))) [nnf transformation 4]
49. ! [X0] : (((funny(X0) & ~curious(X0)) | humble(X0)) & (~humble(X0) | ~funny(X0) | curious(X0))) [flattening 48]
50. funny(paul) | ! [X0] : ((~funny(X0) | brave(X0)) & (~brave(X0) | funny(X0))) [nnf transformation 35]
70. (~patient(susan) | brave(susan)) & (patient(susan) | ~brave(susan)) [nnf transformation 24]
72. ~humble(X0) | funny(X0) | patient(X0) | curious(X0) [cnf transformation 46]
74. ~funny(X0) | humble(X0) | curious(X0) [cnf transformation 46]
82. ~humble(X0) | ~funny(X0) | curious(X0) [cnf transformation 49]
83. ~curious(X0) | humble(X0) [cnf transformation 49]
84. funny(X0) | humble(X0) [cnf transformation 49]
85. funny(paul) | ~brave(X0) | funny(X0) [cnf transformation 50]
86. funny(paul) | ~funny(X0) | brave(X0) [cnf transformation 50]
102. ~funny(X0) | ~humble(X0) [cnf transformation 42]
103. ~brave(X0) | ~funny(X0) [cnf transformation 42]
119. ~patient(susan) | brave(susan) [cnf transformation 70]
120. ~curious(susan) [cnf transformation 25]
122. ~funny(X0) | curious(X0) [subsumption resolution 82,74]
124. 1 <=> ! [X0] : (~funny(X0) | brave(X0)) [avatar definition]
125. ~funny(X0) | brave(X0) <- (1) [avatar component clause 124]
127. 2 <=> funny(paul) [avatar definition]
129. funny(paul) <- (2) [avatar component clause 127]
130. 1 | 2 [avatar split clause 86,127,124]
132. 3 <=> ! [X0] : (~brave(X0) | funny(X0)) [avatar definition]
133. ~brave(X0) | funny(X0) <- (3) [avatar component clause 132]
134. 3 | 2 [avatar split clause 85,127,132]
220. 22 <=> humble(paul) [avatar definition]
221. ~humble(paul) <- (~22) [avatar component clause 220]
225. 23 <=> brave(susan) [avatar definition]
227. brave(susan) <- (23) [avatar component clause 225]
229. 24 <=> patient(susan) [avatar definition]
232. 23 | ~24 [avatar split clause 119,229,225]
241. ~humble(paul) <- (2) [resolution 102,129]
243. ~22 | ~2 [avatar split clause 241,127,220]
247. curious(X0) | humble(X0) [resolution 122,84]
248. humble(X0) [subsumption resolution 247,83]
250. $false <- (~22) [resolution 248,221]
251. 22 [avatar contradiction clause 250]
252. ~brave(X0) <- (3) [subsumption resolution 133,103]
253. ~funny(X0) <- (1, 3) [subsumption resolution 125,252]
332. funny(X0) | patient(X0) | curious(X0) [resolution 72,248]
343. curious(X0) | patient(X0) <- (1, 3) [subsumption resolution 332,253]
352. patient(susan) <- (1, 3) [resolution 343,120]
360. 24 | ~1 | ~3 [avatar split clause 352,132,124,229]
361. $false <- (3, 23) [subsumption resolution 227,252]
362. ~3 | ~23 [avatar contradiction clause 361]
363. $false [avatar sat refutation 130,134,232,243,251,360,362]
% SZS output end Proof for 5880920099591293369436586
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is either not generous or old then lucy is either not brave or not tall and vice versa.
Everyone who is not tall is tall.
Everyone who is not curious or humble is brave.
If alice is both not strong and not old then john is funny or not happy.
If susan is either happy or not calm then someone is not brave.
Everyone who is either strong or not strong is either not humble or kind.
Everyone who is both rich and curious is not strong or not brave.
If susan is either not old or calm then john is calm or not tall and vice versa.
Everyone who is not creative or curious is either wise or tall and vice versa.
If someone is both creative and brave then someone is both rich and not funny and vice versa.
Everyone who is not quiet is not kind or calm and vice versa.
If someone is not creative or not old then fred is not kind or humble.
Everyone who is not humble is both not curious and not funny and vice versa.
If mary is both not curious and not generous then alice is either not curious or creative.
Everyone who is both not tall and old is either not kind or creative.
Everyone who is not strong or not tall is not curious and vice versa.
Someone is both curious and tall.
Someone is both not curious and not rich.
Lucy is not generous or brave.
Fred is wise or curious.
Mary is both brave and wise.
Alice is tall or not creative. | Alice is calm. | neutral | (((~generous(lucy)<~>old(lucy)))<=>((~brave(lucy)<~>~tall(lucy))))&
(![X]:(~tall(X)=>tall(X)))&
(![X]:((~curious(X)|humble(X))=>brave(X)))&
(((~strong(alice)&~old(alice)))=>((funny(john)|~happy(john))))&
(((happy(susan)<~>~calm(susan)))=>(?[X]:(~brave(X))))&
(![X]:((strong(X)<~>~strong(X))=>(~humble(X)<~>kind(X))))&
(![X]:((rich(X)&curious(X))=>(~strong(X)|~brave(X))))&
(((~old(susan)<~>calm(susan)))<=>((calm(john)|~tall(john))))&
(![X]:((~creative(X)|curious(X))<=>(wise(X)<~>tall(X))))&
((?[X]:((creative(X)&brave(X))))<=>(?[X]:((rich(X)&~funny(X)))))&
(![X]:(~quiet(X)<=>(~kind(X)|calm(X))))&
((?[X]:((~creative(X)|~old(X))))=>((~kind(fred)|humble(fred))))&
(![X]:(~humble(X)<=>(~curious(X)&~funny(X))))&
(((~curious(mary)&~generous(mary)))=>((~curious(alice)<~>creative(alice))))&
(![X]:((~tall(X)&old(X))=>(~kind(X)<~>creative(X))))&
(![X]:((~strong(X)|~tall(X))<=>~curious(X)))&
(?[X]:((curious(X)&tall(X))))&
(?[X]:((~curious(X)&~rich(X))))&
((~generous(lucy)|brave(lucy)))&
((wise(fred)|curious(fred)))&
((brave(mary)&wise(mary)))&
((tall(alice)|~creative(alice))) | calm(alice) | [] | null | 0 |
If someone is either creative or not brave then someone is not strong or not brave. Everyone who is old or strong is humble and vice versa. Everyone who is not rich or brave is either generous or quiet. Everyone who is calm or not patient is both happy and old. If someone is not humble or generous then someone is not generous and vice versa. If paul is creative or not patient then someone is either not strong or not patient and vice versa. Everyone who is not wise or creative is not patient or not old. Everyone who is either wise or strong is not humble or not wise and vice versa. Everyone who is not brave or not creative is curious or not brave and vice versa. Everyone who is tall or humble is tall. Everyone who is not tall is brave or not generous and vice versa. If someone is both kind and calm then lucy is not funny or strong. Everyone who is either tall or generous is either not humble or rich. Everyone who is quiet is old or not rich and vice versa. Everyone who is not humble is not kind or happy. If john is wise or curious then someone is either humble or not humble. Someone is not generous. Mary is happy. John is not funny or not creative. Someone is either generous or old. Lucy is both kind and not patient. Fred is either brave or old. Lucy is curious or happy. Lucy is rich or not tall. | Fred is not rich. | neutral | ((?[X]:((creative(X)<~>~brave(X))))=>(?[X]:((~strong(X)|~brave(X)))))&
(![X]:((old(X)|strong(X))<=>humble(X)))&
(![X]:((~rich(X)|brave(X))=>(generous(X)<~>quiet(X))))&
(![X]:((calm(X)|~patient(X))=>(happy(X)&old(X))))&
((?[X]:((~humble(X)|generous(X))))<=>(?[X]:(~generous(X))))&
(((creative(paul)|~patient(paul)))<=>(?[X]:((~strong(X)<~>~patient(X)))))&
(![X]:((~wise(X)|creative(X))=>(~patient(X)|~old(X))))&
(![X]:((wise(X)<~>strong(X))<=>(~humble(X)|~wise(X))))&
(![X]:((~brave(X)|~creative(X))<=>(curious(X)|~brave(X))))&
(![X]:((tall(X)|humble(X))=>tall(X)))&
(![X]:(~tall(X)<=>(brave(X)|~generous(X))))&
((?[X]:((kind(X)&calm(X))))=>((~funny(lucy)|strong(lucy))))&
(![X]:((tall(X)<~>generous(X))=>(~humble(X)<~>rich(X))))&
(![X]:(quiet(X)<=>(old(X)|~rich(X))))&
(![X]:(~humble(X)=>(~kind(X)|happy(X))))&
(((wise(john)|curious(john)))=>(?[X]:((humble(X)<~>~humble(X)))))&
(?[X]:(~generous(X)))&
(happy(mary))&
((~funny(john)|~creative(john)))&
(?[X]:((generous(X)<~>old(X))))&
((kind(lucy)&~patient(lucy)))&
((brave(fred)<~>old(fred)))&
((curious(lucy)|happy(lucy)))&
((rich(lucy)|~tall(lucy))) | ~rich(fred) | [] | null | 0 |
Everyone who is calm is old or not creative and vice versa. If alice is either not wise or old then lucy is not humble or old and vice versa. Everyone who is both generous and not funny is not curious and vice versa. Everyone who is either not brave or not generous is wise or tall and vice versa. If someone is either not strong or not creative then someone is either old or not quiet and vice versa. Everyone who is both not rich and kind is not tall or rich and vice versa. Everyone who is not strong is generous or old and vice versa. Everyone who is curious is both not curious and not patient and vice versa. Everyone who is old is not kind or tall and vice versa. If someone is both rich and patient then fred is both not quiet and not brave. Everyone who is calm or brave is both not wise and brave and vice versa. If someone is either funny or not creative then someone is not curious and vice versa. If someone is both not generous and not tall then someone is not humble or not calm. Everyone who is curious or generous is either not happy or calm and vice versa. If someone is both tall and not wise then fred is both not wise and brave and vice versa. Someone is either not generous or not happy. Mary is old or kind. Someone is kind or not humble. Someone is not brave. Fred is not brave. Mary is patient or funny. | Alice is wise. | neutral | (![X]:(calm(X)<=>(old(X)|~creative(X))))&
(((~wise(alice)<~>old(alice)))<=>((~humble(lucy)|old(lucy))))&
(![X]:((generous(X)&~funny(X))<=>~curious(X)))&
(![X]:((~brave(X)<~>~generous(X))<=>(wise(X)|tall(X))))&
((?[X]:((~strong(X)<~>~creative(X))))<=>(?[X]:((old(X)<~>~quiet(X)))))&
(![X]:((~rich(X)&kind(X))<=>(~tall(X)|rich(X))))&
(![X]:(~strong(X)<=>(generous(X)|old(X))))&
(![X]:(curious(X)<=>(~curious(X)&~patient(X))))&
(![X]:(old(X)<=>(~kind(X)|tall(X))))&
((?[X]:((rich(X)&patient(X))))=>((~quiet(fred)&~brave(fred))))&
(![X]:((calm(X)|brave(X))<=>(~wise(X)&brave(X))))&
((?[X]:((funny(X)<~>~creative(X))))<=>(?[X]:(~curious(X))))&
((?[X]:((~generous(X)&~tall(X))))=>(?[X]:((~humble(X)|~calm(X)))))&
(![X]:((curious(X)|generous(X))<=>(~happy(X)<~>calm(X))))&
((?[X]:((tall(X)&~wise(X))))<=>((~wise(fred)&brave(fred))))&
(?[X]:((~generous(X)<~>~happy(X))))&
((old(mary)|kind(mary)))&
(?[X]:((kind(X)|~humble(X))))&
(?[X]:(~brave(X)))&
(~brave(fred))&
((patient(mary)|funny(mary))) | wise(alice) | [] | null | 0 |
If someone is not wise or wise then john is either not calm or kind and vice versa. If susan is either not brave or not happy then someone is either not curious or generous and vice versa. Everyone who is kind is either wise or funny and vice versa. Everyone who is both quiet and creative is creative or wise. If someone is both humble and old then someone is either brave or kind and vice versa. Everyone who is not strong or not funny is not strong or rich. Everyone who is not wise or generous is either brave or not happy. If paul is both not curious and patient then someone is not patient or not calm and vice versa. Everyone who is both not quiet and tall is old or rich and vice versa. Everyone who is not tall is not happy and vice versa. If susan is both not strong and curious then someone is not funny or creative and vice versa. Everyone who is not generous is curious or not humble and vice versa. Everyone who is brave is both not curious and not calm and vice versa. Everyone who is either curious or kind is both strong and old. If fred is not creative or generous then paul is either curious or humble. Susan is both not creative and quiet. Someone is rich or quiet. Alice is not curious or not humble. Paul is not wise. Someone is happy or calm. Mary is both curious and not happy. Susan is funny or calm. | Fred is not funny. | neutral | ((?[X]:((~wise(X)|wise(X))))<=>((~calm(john)<~>kind(john))))&
(((~brave(susan)<~>~happy(susan)))<=>(?[X]:((~curious(X)<~>generous(X)))))&
(![X]:(kind(X)<=>(wise(X)<~>funny(X))))&
(![X]:((quiet(X)&creative(X))=>(creative(X)|wise(X))))&
((?[X]:((humble(X)&old(X))))<=>(?[X]:((brave(X)<~>kind(X)))))&
(![X]:((~strong(X)|~funny(X))=>(~strong(X)|rich(X))))&
(![X]:((~wise(X)|generous(X))=>(brave(X)<~>~happy(X))))&
(((~curious(paul)&patient(paul)))<=>(?[X]:((~patient(X)|~calm(X)))))&
(![X]:((~quiet(X)&tall(X))<=>(old(X)|rich(X))))&
(![X]:(~tall(X)<=>~happy(X)))&
(((~strong(susan)&curious(susan)))<=>(?[X]:((~funny(X)|creative(X)))))&
(![X]:(~generous(X)<=>(curious(X)|~humble(X))))&
(![X]:(brave(X)<=>(~curious(X)&~calm(X))))&
(![X]:((curious(X)<~>kind(X))=>(strong(X)&old(X))))&
(((~creative(fred)|generous(fred)))=>((curious(paul)<~>humble(paul))))&
((~creative(susan)&quiet(susan)))&
(?[X]:((rich(X)|quiet(X))))&
((~curious(alice)|~humble(alice)))&
(~wise(paul))&
(?[X]:((happy(X)|calm(X))))&
((curious(mary)&~happy(mary)))&
((funny(susan)|calm(susan))) | ~funny(fred) | [] | null | 0 |
If susan is either generous or calm then susan is not old or not humble and vice versa.
Everyone who is not creative is not generous or kind and vice versa.
If someone is both not tall and quiet then someone is both not kind and not wise and vice versa.
If someone is not kind then lucy is either creative or old.
Everyone who is either not curious or wise is both wise and not curious and vice versa.
Everyone who is not happy is generous or tall and vice versa.
Everyone who is either not old or generous is generous and vice versa.
If someone is not brave or generous then mary is not patient.
If someone is either not generous or curious then someone is not generous or not brave.
Everyone who is not brave or not old is both old and strong.
If paul is both happy and kind then mary is kind and vice versa.
Everyone who is brave or curious is either not tall or not rich and vice versa.
Everyone who is either strong or tall is both not creative and not generous.
If someone is not creative then fred is not tall and vice versa.
Everyone who is either not tall or quiet is not quiet or wise and vice versa.
If someone is brave then susan is generous or not curious.
Someone is not old or not tall.
Paul is both rich and not calm.
Mary is either not wise or not strong.
John is not quiet.
Paul is both curious and not calm.
Susan is not brave.
Susan is humble. | Paul is not calm. | entailment | (((generous(susan)<~>calm(susan)))<=>((~old(susan)|~humble(susan))))&
(![X]:(~creative(X)<=>(~generous(X)|kind(X))))&
((?[X]:((~tall(X)&quiet(X))))<=>(?[X]:((~kind(X)&~wise(X)))))&
((?[X]:(~kind(X)))=>((creative(lucy)<~>old(lucy))))&
(![X]:((~curious(X)<~>wise(X))<=>(wise(X)&~curious(X))))&
(![X]:(~happy(X)<=>(generous(X)|tall(X))))&
(![X]:((~old(X)<~>generous(X))<=>generous(X)))&
((?[X]:((~brave(X)|generous(X))))=>(~patient(mary)))&
((?[X]:((~generous(X)<~>curious(X))))=>(?[X]:((~generous(X)|~brave(X)))))&
(![X]:((~brave(X)|~old(X))=>(old(X)&strong(X))))&
(((happy(paul)&kind(paul)))<=>(kind(mary)))&
(![X]:((brave(X)|curious(X))<=>(~tall(X)<~>~rich(X))))&
(![X]:((strong(X)<~>tall(X))=>(~creative(X)&~generous(X))))&
((?[X]:(~creative(X)))<=>(~tall(fred)))&
(![X]:((~tall(X)<~>quiet(X))<=>(~quiet(X)|wise(X))))&
((?[X]:(brave(X)))=>((generous(susan)|~curious(susan))))&
(?[X]:((~old(X)|~tall(X))))&
((rich(paul)&~calm(paul)))&
((~wise(mary)<~>~strong(mary)))&
(~quiet(john))&
((curious(paul)&~calm(paul)))&
(~brave(susan))&
(humble(susan)) | ~calm(paul) | [
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 8380601296345009137643419
% SZS output start Proof for 8380601296345009137643419
18. ~calm(paul) & rich(paul) [input p17]
24. calm(paul) [input hypothesis]
125. ~calm(paul) [cnf transformation 18]
133. calm(paul) [cnf transformation 24]
258. $false [subsumption resolution 133,125]
% SZS output end Proof for 8380601296345009137643419
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is calm then mary is quiet and vice versa.
Everyone who is either not strong or strong is both not strong and happy and vice versa.
If someone is curious or quiet then someone is both not rich and not happy.
Everyone who is not rich is both brave and not creative.
If mary is either creative or calm then alice is either not old or not tall.
Everyone who is not strong or not creative is both not quiet and not curious.
Everyone who is both kind and generous is wise or patient.
Everyone who is not humble or happy is either curious or funny.
Everyone who is both humble and calm is both happy and kind.
If someone is not calm or old then alice is either not wise or generous.
Everyone who is not funny is either rich or not calm.
If someone is either kind or not wise then fred is both not rich and not patient and vice versa.
If someone is either not funny or kind then someone is both generous and not kind and vice versa.
Everyone who is either not kind or not calm is both rich and old.
Someone is not old.
Fred is not calm.
Paul is wise or humble.
Paul is either kind or not calm.
Paul is creative or not generous.
Susan is quiet or not brave.
Someone is tall or old.
Someone is not strong. | Paul is happy. | entailment | ((calm(paul))<=>(quiet(mary)))&
(![X]:((~strong(X)<~>strong(X))<=>(~strong(X)&happy(X))))&
((?[X]:((curious(X)|quiet(X))))=>(?[X]:((~rich(X)&~happy(X)))))&
(![X]:(~rich(X)=>(brave(X)&~creative(X))))&
(((creative(mary)<~>calm(mary)))=>((~old(alice)<~>~tall(alice))))&
(![X]:((~strong(X)|~creative(X))=>(~quiet(X)&~curious(X))))&
(![X]:((kind(X)&generous(X))=>(wise(X)|patient(X))))&
(![X]:((~humble(X)|happy(X))=>(curious(X)<~>funny(X))))&
(![X]:((humble(X)&calm(X))=>(happy(X)&kind(X))))&
((?[X]:((~calm(X)|old(X))))=>((~wise(alice)<~>generous(alice))))&
(![X]:(~funny(X)=>(rich(X)<~>~calm(X))))&
((?[X]:((kind(X)<~>~wise(X))))<=>((~rich(fred)&~patient(fred))))&
((?[X]:((~funny(X)<~>kind(X))))<=>(?[X]:((generous(X)&~kind(X)))))&
(![X]:((~kind(X)<~>~calm(X))=>(rich(X)&old(X))))&
(?[X]:(~old(X)))&
(~calm(fred))&
((wise(paul)|humble(paul)))&
((kind(paul)<~>~calm(paul)))&
((creative(paul)|~generous(paul)))&
((quiet(susan)|~brave(susan)))&
(?[X]:((tall(X)|old(X))))&
(?[X]:(~strong(X))) | happy(paul) | [
"p1",
"hypothesis"
] | % SZS status Unsatisfiable for 1324742347454243929234301
% SZS output start Proof for 1324742347454243929234301
2. ! [X0] : ((~strong(X0) <~> strong(X0)) <=> (happy(X0) & ~strong(X0))) [input p1]
23. ~happy(paul) [input hypothesis]
39. ! [X0] : ((((~strong(X0) | strong(X0)) & (strong(X0) | ~strong(X0))) | (~happy(X0) | strong(X0))) & ((happy(X0) & ~strong(X0)) | ((~strong(X0) | ~strong(X0)) & (strong(X0) | strong(X0))))) [nnf transformation 2]
40. ! [X0] : ((((~strong(X0) | strong(X0)) & (strong(X0) | ~strong(X0))) | ~happy(X0) | strong(X0)) & ((happy(X0) & ~strong(X0)) | ((~strong(X0) | ~strong(X0)) & (strong(X0) | strong(X0))))) [flattening 39]
70. happy(X0) | strong(X0) | strong(X0) [cnf transformation 40]
71. happy(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 40]
126. ~happy(paul) [cnf transformation 23]
129. happy(X0) | strong(X0) [duplicate literal removal 70]
130. happy(X0) | ~strong(X0) [duplicate literal removal 71]
143. happy(X0) [subsumption resolution 129,130]
272. $false [subsumption resolution 126,143]
% SZS output end Proof for 1324742347454243929234301
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is not patient then john is rich or humble. If someone is not creative then paul is funny and vice versa. Everyone who is both not curious and curious is brave or humble and vice versa. Everyone who is either creative or funny is not kind. Everyone who is either generous or brave is not patient or quiet. If someone is quiet then someone is not quiet and vice versa. Everyone who is not happy or not patient is both strong and funny and vice versa. If lucy is either wise or not creative then john is both old and not old and vice versa. If someone is either calm or not tall then someone is either not funny or wise and vice versa. If alice is not wise then someone is both not strong and not old and vice versa. If paul is both not funny and calm then john is curious. If mary is either not patient or funny then lucy is either not quiet or funny and vice versa. If someone is not wise or wise then someone is not happy and vice versa. Everyone who is either kind or tall is rich or calm and vice versa. If someone is either not quiet or kind then someone is not humble or creative and vice versa. Paul is both generous and not happy. Someone is either generous or not kind. Someone is not wise or brave. Fred is either not funny or kind. Fred is both not patient and not generous. Mary is both calm and creative. Paul is both not humble and not patient. | John is calm. | neutral | ((~patient(paul))=>((rich(john)|humble(john))))&
((?[X]:(~creative(X)))<=>(funny(paul)))&
(![X]:((~curious(X)&curious(X))<=>(brave(X)|humble(X))))&
(![X]:((creative(X)<~>funny(X))=>~kind(X)))&
(![X]:((generous(X)<~>brave(X))=>(~patient(X)|quiet(X))))&
((?[X]:(quiet(X)))<=>(?[X]:(~quiet(X))))&
(![X]:((~happy(X)|~patient(X))<=>(strong(X)&funny(X))))&
(((wise(lucy)<~>~creative(lucy)))<=>((old(john)&~old(john))))&
((?[X]:((calm(X)<~>~tall(X))))<=>(?[X]:((~funny(X)<~>wise(X)))))&
((~wise(alice))<=>(?[X]:((~strong(X)&~old(X)))))&
(((~funny(paul)&calm(paul)))=>(curious(john)))&
(((~patient(mary)<~>funny(mary)))<=>((~quiet(lucy)<~>funny(lucy))))&
((?[X]:((~wise(X)|wise(X))))<=>(?[X]:(~happy(X))))&
(![X]:((kind(X)<~>tall(X))<=>(rich(X)|calm(X))))&
((?[X]:((~quiet(X)<~>kind(X))))<=>(?[X]:((~humble(X)|creative(X)))))&
((generous(paul)&~happy(paul)))&
(?[X]:((generous(X)<~>~kind(X))))&
(?[X]:((~wise(X)|brave(X))))&
((~funny(fred)<~>kind(fred)))&
((~patient(fred)&~generous(fred)))&
((calm(mary)&creative(mary)))&
((~humble(paul)&~patient(paul))) | calm(john) | [] | null | 0 |
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