premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
values | proof_inputs
sequencelengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
|
|---|---|---|---|---|---|---|---|
If someone is rich then lucy is either not kind or not humble and vice versa.
Everyone who is not quiet is rich or curious and vice versa.
If someone is generous then someone is either wise or rich and vice versa.
If someone is wise then paul is both not strong and kind and vice versa.
Everyone who is happy is either not rich or creative.
If mary is both not generous and brave then paul is either calm or happy.
Everyone who is not generous or rich is either not patient or patient and vice versa.
If someone is not quiet then someone is not old.
If someone is both tall and brave then paul is both quiet and not strong and vice versa.
Everyone who is brave is not funny and vice versa.
Everyone who is both humble and not wise is not creative or not wise.
Everyone who is tall or patient is not strong or strong and vice versa.
Everyone who is not brave or not humble is either brave or not patient and vice versa.
Everyone who is not quiet or kind is both not rich and generous.
Everyone who is not rich or not quiet is funny and vice versa.
If someone is not rich or not calm then susan is not rich or quiet.
Mary is humble or not tall.
Alice is either rich or not wise.
Susan is either not patient or generous.
Someone is happy.
Someone is not calm or not old. | Mary is quiet. | entailment | ((?[X]:(rich(X)))<=>((~kind(lucy)<~>~humble(lucy))))&
(![X]:(~quiet(X)<=>(rich(X)|curious(X))))&
((?[X]:(generous(X)))<=>(?[X]:((wise(X)<~>rich(X)))))&
((?[X]:(wise(X)))<=>((~strong(paul)&kind(paul))))&
(![X]:(happy(X)=>(~rich(X)<~>creative(X))))&
(((~generous(mary)&brave(mary)))=>((calm(paul)<~>happy(paul))))&
(![X]:((~generous(X)|rich(X))<=>(~patient(X)<~>patient(X))))&
((?[X]:(~quiet(X)))=>(?[X]:(~old(X))))&
((?[X]:((tall(X)&brave(X))))<=>((quiet(paul)&~strong(paul))))&
(![X]:(brave(X)<=>~funny(X)))&
(![X]:((humble(X)&~wise(X))=>(~creative(X)|~wise(X))))&
(![X]:((tall(X)|patient(X))<=>(~strong(X)|strong(X))))&
(![X]:((~brave(X)|~humble(X))<=>(brave(X)<~>~patient(X))))&
(![X]:((~quiet(X)|kind(X))=>(~rich(X)&generous(X))))&
(![X]:((~rich(X)|~quiet(X))<=>funny(X)))&
((?[X]:((~rich(X)|~calm(X))))=>((~rich(susan)|quiet(susan))))&
((humble(mary)|~tall(mary)))&
((rich(alice)<~>~wise(alice)))&
((~patient(susan)<~>generous(susan)))&
(?[X]:(happy(X)))&
(?[X]:((~calm(X)|~old(X)))) | quiet(mary) | [
"p1",
"p2",
"p3",
"p6",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 405503752880518719251142
% SZS output start Proof for 405503752880518719251142
2. ! [X0] : (~quiet(X0) <=> (curious(X0) | rich(X0))) [input p1]
3. ? [X0] : generous(X0) <=> ? [X0] : (wise(X0) <~> rich(X0)) [input p2]
4. ? [X0] : wise(X0) <=> (kind(paul) & ~strong(paul)) [input p3]
7. ! [X0] : ((rich(X0) | ~generous(X0)) <=> (~patient(X0) <~> patient(X0))) [input p6]
14. ! [X0] : ((kind(X0) | ~quiet(X0)) => (generous(X0) & ~rich(X0))) [input p13]
22. ~quiet(mary) [input hypothesis]
23. ? [X0] : generous(X0) <=> ? [X1] : (wise(X1) <~> rich(X1)) [rectify 3]
32. ! [X0] : ((generous(X0) & ~rich(X0)) | (~kind(X0) & quiet(X0))) [ennf transformation 14]
39. ! [X0] : ((~quiet(X0) | (~curious(X0) & ~rich(X0))) & ((curious(X0) | rich(X0)) | quiet(X0))) [nnf transformation 2]
40. ! [X0] : ((~quiet(X0) | (~curious(X0) & ~rich(X0))) & (curious(X0) | rich(X0) | quiet(X0))) [flattening 39]
41. (? [X0] : generous(X0) | ! [X1] : ((wise(X1) | ~rich(X1)) & (rich(X1) | ~wise(X1)))) & (? [X1] : ((~rich(X1) | ~wise(X1)) & (rich(X1) | wise(X1))) | ! [X0] : ~generous(X0)) [nnf transformation 23]
42. (? [X0] : generous(X0) | ! [X1] : ((wise(X1) | ~rich(X1)) & (rich(X1) | ~wise(X1)))) & (? [X2] : ((~rich(X2) | ~wise(X2)) & (rich(X2) | wise(X2))) | ! [X3] : ~generous(X3)) [rectify 41]
43. ? [X0] : generous(X0) => generous(sK1) [choice axiom]
44. ? [X2] : ((~rich(X2) | ~wise(X2)) & (rich(X2) | wise(X2))) => ((~rich(sK2) | ~wise(sK2)) & (rich(sK2) | wise(sK2))) [choice axiom]
45. (generous(sK1) | ! [X1] : ((wise(X1) | ~rich(X1)) & (rich(X1) | ~wise(X1)))) & (((~rich(sK2) | ~wise(sK2)) & (rich(sK2) | wise(sK2))) | ! [X3] : ~generous(X3)) [skolemisation 42,44,43]
46. (? [X0] : wise(X0) | (~kind(paul) | strong(paul))) & ((kind(paul) & ~strong(paul)) | ! [X0] : ~wise(X0)) [nnf transformation 4]
47. (? [X0] : wise(X0) | ~kind(paul) | strong(paul)) & ((kind(paul) & ~strong(paul)) | ! [X0] : ~wise(X0)) [flattening 46]
48. (? [X0] : wise(X0) | ~kind(paul) | strong(paul)) & ((kind(paul) & ~strong(paul)) | ! [X1] : ~wise(X1)) [rectify 47]
49. ? [X0] : wise(X0) => wise(sK3) [choice axiom]
50. (wise(sK3) | ~kind(paul) | strong(paul)) & ((kind(paul) & ~strong(paul)) | ! [X1] : ~wise(X1)) [skolemisation 48,49]
53. ! [X0] : (((rich(X0) | ~generous(X0)) | ((~patient(X0) | ~patient(X0)) & (patient(X0) | patient(X0)))) & (((~patient(X0) | patient(X0)) & (patient(X0) | ~patient(X0))) | (~rich(X0) & generous(X0)))) [nnf transformation 7]
54. ! [X0] : ((rich(X0) | ~generous(X0) | ((~patient(X0) | ~patient(X0)) & (patient(X0) | patient(X0)))) & (((~patient(X0) | patient(X0)) & (patient(X0) | ~patient(X0))) | (~rich(X0) & generous(X0)))) [flattening 53]
76. ~quiet(X0) | ~rich(X0) [cnf transformation 40]
78. rich(sK2) | wise(sK2) | ~generous(X3) [cnf transformation 45]
83. kind(paul) | ~wise(X1) [cnf transformation 50]
93. rich(X0) | ~generous(X0) | patient(X0) | patient(X0) [cnf transformation 54]
94. rich(X0) | ~generous(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 54]
112. ~rich(X0) | quiet(X0) [cnf transformation 32]
114. generous(X0) | quiet(X0) [cnf transformation 32]
115. ~kind(X0) | generous(X0) [cnf transformation 32]
127. ~quiet(mary) [cnf transformation 22]
130. rich(X0) | ~generous(X0) | patient(X0) [duplicate literal removal 93]
131. rich(X0) | ~generous(X0) | ~patient(X0) [duplicate literal removal 94]
147. 4 <=> ! [X1] : ~rich(X1) [avatar definition]
148. ~rich(X1) <- (4) [avatar component clause 147]
164. 8 <=> ! [X3] : ~generous(X3) [avatar definition]
165. ~generous(X3) <- (8) [avatar component clause 164]
167. 9 <=> wise(sK2) [avatar definition]
168. wise(sK2) <- (9) [avatar component clause 167]
171. 10 <=> rich(sK2) [avatar definition]
172. rich(sK2) <- (10) [avatar component clause 171]
175. 8 | 9 | 10 [avatar split clause 78,171,167,164]
181. 12 <=> kind(paul) [avatar definition]
182. kind(paul) <- (12) [avatar component clause 181]
190. 14 <=> ! [X1] : ~wise(X1) [avatar definition]
191. ~wise(X1) <- (14) [avatar component clause 190]
192. 14 | 12 [avatar split clause 83,181,190]
212. ~generous(X0) | rich(X0) [subsumption resolution 130,131]
233. ~rich(X0) [subsumption resolution 112,76]
234. 4 [avatar split clause 233,147]
292. $false <- (9, 14) [resolution 191,168]
295. ~9 | ~14 [avatar contradiction clause 292]
297. quiet(X0) <- (8) [resolution 165,114]
300. $false <- (8) [resolution 297,127]
302. ~8 [avatar contradiction clause 300]
303. $false <- (4, 10) [subsumption resolution 172,148]
304. ~4 | ~10 [avatar contradiction clause 303]
305. generous(paul) <- (12) [resolution 182,115]
309. rich(paul) <- (12) [resolution 212,305]
313. $false <- (4, 12) [subsumption resolution 309,148]
314. ~4 | ~12 [avatar contradiction clause 313]
315. $false [avatar sat refutation 175,192,234,295,302,304,314]
% SZS output end Proof for 405503752880518719251142
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is not creative or kind then john is strong or not tall.
If mary is either strong or not humble then someone is either not old or not humble and vice versa.
If fred is either not funny or humble then someone is both not generous and funny.
Everyone who is not old or strong is strong or generous and vice versa.
If someone is either tall or not humble then fred is humble.
Everyone who is either not humble or not funny is both not generous and tall and vice versa.
If fred is not tall then someone is not strong and vice versa.
Everyone who is both not patient and not curious is strong or happy.
Everyone who is either not old or not kind is either patient or not humble and vice versa.
Everyone who is both creative and curious is not creative and vice versa.
If someone is either kind or not rich then someone is either old or brave and vice versa.
Everyone who is not humble is both funny and not patient.
If susan is not tall then someone is either not quiet or strong.
If someone is not generous or not patient then someone is kind.
Everyone who is either curious or not strong is both not creative and kind.
Everyone who is both tall and not funny is happy and vice versa.
Alice is humble.
Someone is both not kind and happy.
Someone is brave or calm.
Lucy is not funny or funny.
Someone is either curious or not humble.
Someone is not patient. | Fred is not funny. | neutral | (((~creative(paul)|kind(paul)))=>((strong(john)|~tall(john))))&
(((strong(mary)<~>~humble(mary)))<=>(?[X]:((~old(X)<~>~humble(X)))))&
(((~funny(fred)<~>humble(fred)))=>(?[X]:((~generous(X)&funny(X)))))&
(![X]:((~old(X)|strong(X))<=>(strong(X)|generous(X))))&
((?[X]:((tall(X)<~>~humble(X))))=>(humble(fred)))&
(![X]:((~humble(X)<~>~funny(X))<=>(~generous(X)&tall(X))))&
((~tall(fred))<=>(?[X]:(~strong(X))))&
(![X]:((~patient(X)&~curious(X))=>(strong(X)|happy(X))))&
(![X]:((~old(X)<~>~kind(X))<=>(patient(X)<~>~humble(X))))&
(![X]:((creative(X)&curious(X))<=>~creative(X)))&
((?[X]:((kind(X)<~>~rich(X))))<=>(?[X]:((old(X)<~>brave(X)))))&
(![X]:(~humble(X)=>(funny(X)&~patient(X))))&
((~tall(susan))=>(?[X]:((~quiet(X)<~>strong(X)))))&
((?[X]:((~generous(X)|~patient(X))))=>(?[X]:(kind(X))))&
(![X]:((curious(X)<~>~strong(X))=>(~creative(X)&kind(X))))&
(![X]:((tall(X)&~funny(X))<=>happy(X)))&
(humble(alice))&
(?[X]:((~kind(X)&happy(X))))&
(?[X]:((brave(X)|calm(X))))&
((~funny(lucy)|funny(lucy)))&
(?[X]:((curious(X)<~>~humble(X))))&
(?[X]:(~patient(X))) | ~funny(fred) | [] | null | 0 |
Everyone who is curious is either not generous or not rich and vice versa.
Everyone who is humble is both not wise and generous.
If susan is tall or creative then someone is both generous and patient.
If someone is both curious and not generous then someone is both not funny and creative.
Everyone who is both not creative and not calm is either not humble or generous.
Everyone who is both not patient and rich is old and vice versa.
Everyone who is either brave or not strong is both wise and not funny.
Everyone who is either funny or not strong is not wise or strong and vice versa.
Everyone who is not strong or not calm is not brave and vice versa.
If someone is both rich and not brave then fred is either calm or funny.
Everyone who is both not brave and tall is both not happy and tall and vice versa.
If paul is either not rich or not funny then someone is either patient or calm and vice versa.
If someone is both not funny and not curious then susan is happy.
If fred is not patient or quiet then john is not calm and vice versa.
Lucy is both humble and not creative.
Susan is generous or patient.
Mary is both not humble and quiet.
John is both kind and not rich.
Fred is not creative.
Paul is strong or patient. | Susan is not strong. | contradiction | (![X]:(curious(X)<=>(~generous(X)<~>~rich(X))))&
(![X]:(humble(X)=>(~wise(X)&generous(X))))&
(((tall(susan)|creative(susan)))=>(?[X]:((generous(X)&patient(X)))))&
((?[X]:((curious(X)&~generous(X))))=>(?[X]:((~funny(X)&creative(X)))))&
(![X]:((~creative(X)&~calm(X))=>(~humble(X)<~>generous(X))))&
(![X]:((~patient(X)&rich(X))<=>old(X)))&
(![X]:((brave(X)<~>~strong(X))=>(wise(X)&~funny(X))))&
(![X]:((funny(X)<~>~strong(X))<=>(~wise(X)|strong(X))))&
(![X]:((~strong(X)|~calm(X))<=>~brave(X)))&
((?[X]:((rich(X)&~brave(X))))=>((calm(fred)<~>funny(fred))))&
(![X]:((~brave(X)&tall(X))<=>(~happy(X)&tall(X))))&
(((~rich(paul)<~>~funny(paul)))<=>(?[X]:((patient(X)<~>calm(X)))))&
((?[X]:((~funny(X)&~curious(X))))=>(happy(susan)))&
(((~patient(fred)|quiet(fred)))<=>(~calm(john)))&
((humble(lucy)&~creative(lucy)))&
((generous(susan)|patient(susan)))&
((~humble(mary)&quiet(mary)))&
((kind(john)&~rich(john)))&
(~creative(fred))&
((strong(paul)|patient(paul))) | ~strong(susan) | [
"p6",
"p7",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 8146899127997970295991751
% SZS output start Proof for 8146899127997970295991751
7. ! [X0] : ((brave(X0) <~> ~strong(X0)) => (~funny(X0) & wise(X0))) [input p6]
8. ! [X0] : ((funny(X0) <~> ~strong(X0)) <=> (strong(X0) | ~wise(X0))) [input p7]
9. ! [X0] : ((~calm(X0) | ~strong(X0)) <=> ~brave(X0)) [input p8]
21. ~strong(susan) [input hypothesis]
29. ! [X0] : ((~funny(X0) & wise(X0)) | (brave(X0) <=> ~strong(X0))) [ennf transformation 7]
39. ! [X0] : ((~funny(X0) & wise(X0)) | ((brave(X0) | strong(X0)) & (~strong(X0) | ~brave(X0)))) [nnf transformation 29]
40. ! [X0] : ((((strong(X0) | ~funny(X0)) & (~strong(X0) | funny(X0))) | (~strong(X0) & wise(X0))) & ((strong(X0) | ~wise(X0)) | ((funny(X0) | strong(X0)) & (~strong(X0) | ~funny(X0))))) [nnf transformation 8]
41. ! [X0] : ((((strong(X0) | ~funny(X0)) & (~strong(X0) | funny(X0))) | (~strong(X0) & wise(X0))) & (strong(X0) | ~wise(X0) | ((funny(X0) | strong(X0)) & (~strong(X0) | ~funny(X0))))) [flattening 40]
42. ! [X0] : (((~calm(X0) | ~strong(X0)) | brave(X0)) & (~brave(X0) | (calm(X0) & strong(X0)))) [nnf transformation 9]
43. ! [X0] : ((~calm(X0) | ~strong(X0) | brave(X0)) & (~brave(X0) | (calm(X0) & strong(X0)))) [flattening 42]
68. strong(X0) | brave(X0) | wise(X0) [cnf transformation 39]
70. ~funny(X0) | brave(X0) | strong(X0) [cnf transformation 39]
72. strong(X0) | ~wise(X0) | funny(X0) | strong(X0) [cnf transformation 41]
74. ~strong(X0) | funny(X0) | ~strong(X0) [cnf transformation 41]
77. ~brave(X0) | strong(X0) [cnf transformation 43]
106. ~strong(susan) [cnf transformation 21]
107. strong(X0) | ~wise(X0) | funny(X0) [duplicate literal removal 72]
108. ~strong(X0) | funny(X0) [duplicate literal removal 74]
142. ~wise(X0) | funny(X0) [subsumption resolution 107,108]
279. brave(X1) | wise(X1) | funny(X1) [resolution 68,108]
282. brave(X1) | funny(X1) [subsumption resolution 279,142]
344. funny(X2) | strong(X2) [resolution 282,77]
346. funny(X2) [subsumption resolution 344,108]
392. brave(X1) | strong(X1) [resolution 346,70]
394. strong(X1) [subsumption resolution 392,77]
459. $false [resolution 394,106]
% SZS output end Proof for 8146899127997970295991751
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not tall and generous is either not calm or not quiet. If someone is either not humble or not tall then someone is either not creative or not old. If paul is either old or wise then someone is wise or humble. Everyone who is not brave or not wise is both not rich and generous and vice versa. If someone is generous or not wise then someone is rich and vice versa. If someone is both not patient and not strong then someone is not patient and vice versa. Everyone who is kind is not wise or brave and vice versa. If someone is not creative then john is either quiet or kind. Everyone who is both curious and happy is either not curious or not humble. Everyone who is both creative and not humble is either rich or happy and vice versa. Everyone who is either kind or creative is strong and vice versa. If someone is both not strong and generous then susan is quiet or wise. If someone is either not brave or calm then someone is both not patient and not curious. If someone is both kind and not old then mary is not patient or calm. Everyone who is not happy or generous is both happy and not curious and vice versa. If someone is not strong or not funny then someone is either quiet or not tall. Lucy is either not quiet or quiet. Alice is funny or not creative. Someone is either not patient or not humble. Someone is not quiet. John is generous or creative. Someone is not generous. | Lucy is curious. | neutral | (![X]:((~tall(X)&generous(X))=>(~calm(X)<~>~quiet(X))))&
((?[X]:((~humble(X)<~>~tall(X))))=>(?[X]:((~creative(X)<~>~old(X)))))&
(((old(paul)<~>wise(paul)))=>(?[X]:((wise(X)|humble(X)))))&
(![X]:((~brave(X)|~wise(X))<=>(~rich(X)&generous(X))))&
((?[X]:((generous(X)|~wise(X))))<=>(?[X]:(rich(X))))&
((?[X]:((~patient(X)&~strong(X))))<=>(?[X]:(~patient(X))))&
(![X]:(kind(X)<=>(~wise(X)|brave(X))))&
((?[X]:(~creative(X)))=>((quiet(john)<~>kind(john))))&
(![X]:((curious(X)&happy(X))=>(~curious(X)<~>~humble(X))))&
(![X]:((creative(X)&~humble(X))<=>(rich(X)<~>happy(X))))&
(![X]:((kind(X)<~>creative(X))<=>strong(X)))&
((?[X]:((~strong(X)&generous(X))))=>((quiet(susan)|wise(susan))))&
((?[X]:((~brave(X)<~>calm(X))))=>(?[X]:((~patient(X)&~curious(X)))))&
((?[X]:((kind(X)&~old(X))))=>((~patient(mary)|calm(mary))))&
(![X]:((~happy(X)|generous(X))<=>(happy(X)&~curious(X))))&
((?[X]:((~strong(X)|~funny(X))))=>(?[X]:((quiet(X)<~>~tall(X)))))&
((~quiet(lucy)<~>quiet(lucy)))&
((funny(alice)|~creative(alice)))&
(?[X]:((~patient(X)<~>~humble(X))))&
(?[X]:(~quiet(X)))&
((generous(john)|creative(john)))&
(?[X]:(~generous(X))) | curious(lucy) | [] | null | 0 |
Everyone who is not old is both curious and not old. If someone is not happy then paul is quiet or humble. If paul is generous then someone is either rich or not humble and vice versa. If john is not humble or not old then someone is old or generous. Everyone who is both not patient and not calm is calm or not creative. If someone is either strong or funny then someone is happy or not old and vice versa. Everyone who is not creative is both calm and not rich. Everyone who is kind or not funny is either creative or not quiet. If someone is creative or kind then alice is either not humble or old. Everyone who is not humble is tall. If someone is either humble or not creative then someone is both not rich and funny and vice versa. If fred is both old and happy then someone is either not funny or not strong and vice versa. Everyone who is not funny is not generous and vice versa. If fred is either not wise or patient then lucy is either not kind or old and vice versa. If fred is humble then someone is not kind or not rich. Everyone who is both calm and not tall is not humble or generous and vice versa. Mary is both rich and quiet. Alice is either humble or rich. Paul is creative or quiet. Someone is calm or generous. Someone is either not patient or tall. Mary is either quiet or not happy. | Paul is not tall. | entailment | (![X]:(~old(X)=>(curious(X)&~old(X))))&
((?[X]:(~happy(X)))=>((quiet(paul)|humble(paul))))&
((generous(paul))<=>(?[X]:((rich(X)<~>~humble(X)))))&
(((~humble(john)|~old(john)))=>(?[X]:((old(X)|generous(X)))))&
(![X]:((~patient(X)&~calm(X))=>(calm(X)|~creative(X))))&
((?[X]:((strong(X)<~>funny(X))))<=>(?[X]:((happy(X)|~old(X)))))&
(![X]:(~creative(X)=>(calm(X)&~rich(X))))&
(![X]:((kind(X)|~funny(X))=>(creative(X)<~>~quiet(X))))&
((?[X]:((creative(X)|kind(X))))=>((~humble(alice)<~>old(alice))))&
(![X]:(~humble(X)=>tall(X)))&
((?[X]:((humble(X)<~>~creative(X))))<=>(?[X]:((~rich(X)&funny(X)))))&
(((old(fred)&happy(fred)))<=>(?[X]:((~funny(X)<~>~strong(X)))))&
(![X]:(~funny(X)<=>~generous(X)))&
(((~wise(fred)<~>patient(fred)))<=>((~kind(lucy)<~>old(lucy))))&
((humble(fred))=>(?[X]:((~kind(X)|~rich(X)))))&
(![X]:((calm(X)&~tall(X))<=>(~humble(X)|generous(X))))&
((rich(mary)&quiet(mary)))&
((humble(alice)<~>rich(alice)))&
((creative(paul)|quiet(paul)))&
(?[X]:((calm(X)|generous(X))))&
(?[X]:((~patient(X)<~>tall(X))))&
((quiet(mary)<~>~happy(mary))) | ~tall(paul) | [
"p2",
"p9",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 2639929344889409899557922
% SZS output start Proof for 2639929344889409899557922
3. generous(paul) <=> ? [X0] : (rich(X0) <~> ~humble(X0)) [input p2]
10. ! [X0] : (~humble(X0) => tall(X0)) [input p9]
16. ! [X0] : ((~tall(X0) & calm(X0)) <=> (generous(X0) | ~humble(X0))) [input p15]
17. quiet(mary) & rich(mary) [input p16]
23. tall(paul) [input hypothesis]
36. ! [X0] : (tall(X0) | humble(X0)) [ennf transformation 10]
38. (generous(paul) | ! [X0] : ((rich(X0) | humble(X0)) & (~humble(X0) | ~rich(X0)))) & (? [X0] : ((humble(X0) | ~rich(X0)) & (~humble(X0) | rich(X0))) | ~generous(paul)) [nnf transformation 3]
39. (generous(paul) | ! [X0] : ((rich(X0) | humble(X0)) & (~humble(X0) | ~rich(X0)))) & (? [X1] : ((humble(X1) | ~rich(X1)) & (~humble(X1) | rich(X1))) | ~generous(paul)) [rectify 38]
40. ? [X1] : ((humble(X1) | ~rich(X1)) & (~humble(X1) | rich(X1))) => ((humble(sK0) | ~rich(sK0)) & (~humble(sK0) | rich(sK0))) [choice axiom]
41. (generous(paul) | ! [X0] : ((rich(X0) | humble(X0)) & (~humble(X0) | ~rich(X0)))) & (((humble(sK0) | ~rich(sK0)) & (~humble(sK0) | rich(sK0))) | ~generous(paul)) [skolemisation 39,40]
65. ! [X0] : (((~tall(X0) & calm(X0)) | (~generous(X0) & humble(X0))) & ((generous(X0) | ~humble(X0)) | (tall(X0) | ~calm(X0)))) [nnf transformation 16]
66. ! [X0] : (((~tall(X0) & calm(X0)) | (~generous(X0) & humble(X0))) & (generous(X0) | ~humble(X0) | tall(X0) | ~calm(X0))) [flattening 65]
78. generous(paul) | ~humble(X0) | ~rich(X0) [cnf transformation 41]
99. tall(X0) | humble(X0) [cnf transformation 36]
126. ~tall(X0) | humble(X0) [cnf transformation 66]
127. ~tall(X0) | ~generous(X0) [cnf transformation 66]
128. rich(mary) [cnf transformation 17]
138. tall(paul) [cnf transformation 23]
156. 5 <=> generous(paul) [avatar definition]
158. generous(paul) <- (5) [avatar component clause 156]
161. 6 <=> ! [X0] : (~humble(X0) | ~rich(X0)) [avatar definition]
162. ~humble(X0) | ~rich(X0) <- (6) [avatar component clause 161]
163. 6 | 5 [avatar split clause 78,156,161]
334. humble(X0) [subsumption resolution 126,99]
362. ~rich(X0) <- (6) [subsumption resolution 162,334]
363. $false <- (6) [resolution 362,128]
364. ~6 [avatar contradiction clause 363]
375. ~generous(paul) [resolution 127,138]
377. $false <- (5) [subsumption resolution 375,158]
378. ~5 [avatar contradiction clause 377]
379. $false [avatar sat refutation 163,364,378]
% SZS output end Proof for 2639929344889409899557922
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If someone is kind or not brave then lucy is either calm or quiet and vice versa. Everyone who is both not old and not strong is either not funny or not generous. Everyone who is both not humble and humble is brave and vice versa. Everyone who is both funny and not humble is humble. If someone is either not curious or wise then alice is both not wise and not quiet. Everyone who is both curious and brave is either not generous or not brave and vice versa. If someone is kind then someone is not rich or rich and vice versa. If fred is either funny or generous then paul is creative. Everyone who is funny or not patient is patient and vice versa. If someone is creative then lucy is either rich or patient. Everyone who is both happy and old is both not funny and funny and vice versa. Everyone who is curious is either old or kind and vice versa. Everyone who is tall or creative is not tall and vice versa. Everyone who is both not funny and not generous is either not kind or rich. Everyone who is both old and not kind is not wise and vice versa. Someone is both rich and not kind. Someone is not brave or not tall. Someone is not generous or wise. John is both happy and not generous. Someone is not curious. | Fred is not humble. | contradiction | ((?[X]:((kind(X)|~brave(X))))<=>((calm(lucy)<~>quiet(lucy))))&
(![X]:((~old(X)&~strong(X))=>(~funny(X)<~>~generous(X))))&
(![X]:((~humble(X)&humble(X))<=>brave(X)))&
(![X]:((funny(X)&~humble(X))=>humble(X)))&
((?[X]:((~curious(X)<~>wise(X))))=>((~wise(alice)&~quiet(alice))))&
(![X]:((curious(X)&brave(X))<=>(~generous(X)<~>~brave(X))))&
((?[X]:(kind(X)))<=>(?[X]:((~rich(X)|rich(X)))))&
(((funny(fred)<~>generous(fred)))=>(creative(paul)))&
(![X]:((funny(X)|~patient(X))<=>patient(X)))&
((?[X]:(creative(X)))=>((rich(lucy)<~>patient(lucy))))&
(![X]:((happy(X)&old(X))<=>(~funny(X)&funny(X))))&
(![X]:(curious(X)<=>(old(X)<~>kind(X))))&
(![X]:((tall(X)|creative(X))<=>~tall(X)))&
(![X]:((~funny(X)&~generous(X))=>(~kind(X)<~>rich(X))))&
(![X]:((old(X)&~kind(X))<=>~wise(X)))&
(?[X]:((rich(X)&~kind(X))))&
(?[X]:((~brave(X)|~tall(X))))&
(?[X]:((~generous(X)|wise(X))))&
((happy(john)&~generous(john)))&
(?[X]:(~curious(X))) | ~humble(fred) | [
"p3",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 2183415597690170193692052
% SZS output start Proof for 2183415597690170193692052
4. ! [X0] : ((~humble(X0) & funny(X0)) => humble(X0)) [input p3]
9. ! [X0] : ((~patient(X0) | funny(X0)) <=> patient(X0)) [input p8]
21. ~humble(fred) [input hypothesis]
24. ! [X0] : (humble(X0) | (humble(X0) | ~funny(X0))) [ennf transformation 4]
25. ! [X0] : (humble(X0) | humble(X0) | ~funny(X0)) [flattening 24]
46. ! [X0] : (((~patient(X0) | funny(X0)) | ~patient(X0)) & (patient(X0) | (patient(X0) & ~funny(X0)))) [nnf transformation 9]
47. ! [X0] : ((~patient(X0) | funny(X0) | ~patient(X0)) & (patient(X0) | (patient(X0) & ~funny(X0)))) [flattening 46]
74. humble(X0) | humble(X0) | ~funny(X0) [cnf transformation 25]
91. patient(X0) | patient(X0) [cnf transformation 47]
92. ~patient(X0) | funny(X0) | ~patient(X0) [cnf transformation 47]
118. ~humble(fred) [cnf transformation 21]
121. patient(X0) [duplicate literal removal 91]
122. ~patient(X0) | funny(X0) [duplicate literal removal 92]
125. ~funny(X0) | humble(X0) [duplicate literal removal 74]
212. funny(X0) [resolution 122,121]
214. humble(X0) [resolution 212,125]
218. $false [resolution 214,118]
% SZS output end Proof for 2183415597690170193692052
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious then paul is either rich or not old.
If lucy is not happy or creative then someone is humble and vice versa.
Everyone who is both happy and not rich is both generous and not generous and vice versa.
Everyone who is not rich or not creative is both generous and patient and vice versa.
Everyone who is either not happy or not brave is both not curious and old.
Everyone who is funny is rich and vice versa.
Everyone who is not happy is not wise.
Everyone who is not happy or not quiet is both brave and not old and vice versa.
If someone is not tall then lucy is either not generous or not rich and vice versa.
Everyone who is both not strong and not curious is both not calm and not funny and vice versa.
If alice is both quiet and strong then someone is both not strong and not funny.
If someone is both not calm and generous then someone is both not wise and brave and vice versa.
Everyone who is funny or patient is both not strong and curious.
If someone is both funny and calm then paul is not humble or calm and vice versa.
If susan is old then susan is either strong or not creative.
Everyone who is wise is both not patient and not generous.
Fred is creative.
Mary is both not strong and not wise.
Someone is either not creative or not patient.
Alice is both not strong and not quiet.
Someone is curious. | Paul is old. | entailment | ((?[X]:(curious(X)))=>((rich(paul)<~>~old(paul))))&
(((~happy(lucy)|creative(lucy)))<=>(?[X]:(humble(X))))&
(![X]:((happy(X)&~rich(X))<=>(generous(X)&~generous(X))))&
(![X]:((~rich(X)|~creative(X))<=>(generous(X)&patient(X))))&
(![X]:((~happy(X)<~>~brave(X))=>(~curious(X)&old(X))))&
(![X]:(funny(X)<=>rich(X)))&
(![X]:(~happy(X)=>~wise(X)))&
(![X]:((~happy(X)|~quiet(X))<=>(brave(X)&~old(X))))&
((?[X]:(~tall(X)))<=>((~generous(lucy)<~>~rich(lucy))))&
(![X]:((~strong(X)&~curious(X))<=>(~calm(X)&~funny(X))))&
(((quiet(alice)&strong(alice)))=>(?[X]:((~strong(X)&~funny(X)))))&
((?[X]:((~calm(X)&generous(X))))<=>(?[X]:((~wise(X)&brave(X)))))&
(![X]:((funny(X)|patient(X))=>(~strong(X)&curious(X))))&
((?[X]:((funny(X)&calm(X))))<=>((~humble(paul)|calm(paul))))&
((old(susan))=>((strong(susan)<~>~creative(susan))))&
(![X]:(wise(X)=>(~patient(X)&~generous(X))))&
(creative(fred))&
((~strong(mary)&~wise(mary)))&
(?[X]:((~creative(X)<~>~patient(X))))&
((~strong(alice)&~quiet(alice)))&
(?[X]:(curious(X))) | old(paul) | [
"p0",
"p2",
"p3",
"p4",
"p5",
"p7",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 856964668153866650171572
% SZS output start Proof for 856964668153866650171572
1. ? [X0] : curious(X0) => (rich(paul) <~> ~old(paul)) [input p0]
3. ! [X0] : ((~rich(X0) & happy(X0)) <=> (~generous(X0) & generous(X0))) [input p2]
4. ! [X0] : ((~creative(X0) | ~rich(X0)) <=> (patient(X0) & generous(X0))) [input p3]
5. ! [X0] : ((~happy(X0) <~> ~brave(X0)) => (old(X0) & ~curious(X0))) [input p4]
6. ! [X0] : (funny(X0) <=> rich(X0)) [input p5]
8. ! [X0] : ((~quiet(X0) | ~happy(X0)) <=> (~old(X0) & brave(X0))) [input p7]
13. ! [X0] : ((patient(X0) | funny(X0)) => (curious(X0) & ~strong(X0))) [input p12]
22. ~old(paul) [input hypothesis]
24. (rich(paul) <~> ~old(paul)) | ! [X0] : ~curious(X0) [ennf transformation 1]
25. ! [X0] : ((old(X0) & ~curious(X0)) | (~happy(X0) <=> ~brave(X0))) [ennf transformation 5]
29. ! [X0] : ((curious(X0) & ~strong(X0)) | (~patient(X0) & ~funny(X0))) [ennf transformation 13]
32. ((old(paul) | ~rich(paul)) & (~old(paul) | rich(paul))) | ! [X0] : ~curious(X0) [nnf transformation 24]
38. ! [X0] : (((~rich(X0) & happy(X0)) | (generous(X0) | ~generous(X0))) & ((~generous(X0) & generous(X0)) | (rich(X0) | ~happy(X0)))) [nnf transformation 3]
39. ! [X0] : (((~rich(X0) & happy(X0)) | generous(X0) | ~generous(X0)) & ((~generous(X0) & generous(X0)) | rich(X0) | ~happy(X0))) [flattening 38]
40. ! [X0] : (((~creative(X0) | ~rich(X0)) | (~patient(X0) | ~generous(X0))) & ((patient(X0) & generous(X0)) | (creative(X0) & rich(X0)))) [nnf transformation 4]
41. ! [X0] : ((~creative(X0) | ~rich(X0) | ~patient(X0) | ~generous(X0)) & ((patient(X0) & generous(X0)) | (creative(X0) & rich(X0)))) [flattening 40]
42. ! [X0] : ((old(X0) & ~curious(X0)) | ((~happy(X0) | brave(X0)) & (~brave(X0) | happy(X0)))) [nnf transformation 25]
43. ! [X0] : ((funny(X0) | ~rich(X0)) & (rich(X0) | ~funny(X0))) [nnf transformation 6]
44. ! [X0] : (((~quiet(X0) | ~happy(X0)) | (old(X0) | ~brave(X0))) & ((~old(X0) & brave(X0)) | (quiet(X0) & happy(X0)))) [nnf transformation 8]
45. ! [X0] : ((~quiet(X0) | ~happy(X0) | old(X0) | ~brave(X0)) & ((~old(X0) & brave(X0)) | (quiet(X0) & happy(X0)))) [flattening 44]
71. old(paul) | ~rich(paul) | ~curious(X0) [cnf transformation 32]
75. generous(X0) | rich(X0) | ~happy(X0) [cnf transformation 39]
76. ~generous(X0) | rich(X0) | ~happy(X0) [cnf transformation 39]
81. patient(X0) | rich(X0) [cnf transformation 41]
86. ~brave(X0) | old(X0) | happy(X0) [cnf transformation 42]
89. ~rich(X0) | funny(X0) [cnf transformation 43]
91. brave(X0) | happy(X0) [cnf transformation 45]
93. ~old(X0) | happy(X0) [cnf transformation 45]
112. ~funny(X0) | curious(X0) [cnf transformation 29]
113. ~patient(X0) | curious(X0) [cnf transformation 29]
131. ~old(paul) [cnf transformation 22]
133. 1 <=> ! [X0] : ~curious(X0) [avatar definition]
134. ~curious(X0) <- (1) [avatar component clause 133]
136. 2 <=> rich(paul) [avatar definition]
138. ~rich(paul) <- (~2) [avatar component clause 136]
140. 3 <=> old(paul) [avatar definition]
143. 1 | ~2 | 3 [avatar split clause 71,140,136,133]
163. ~happy(X0) | rich(X0) [subsumption resolution 75,76]
278. ~3 [avatar split clause 131,140]
287. rich(X1) | curious(X1) [resolution 113,81]
311. curious(X0) | funny(X0) [resolution 287,89]
312. curious(X0) [subsumption resolution 311,112]
313. old(X0) | happy(X0) | happy(X0) [resolution 86,91]
316. old(X0) | happy(X0) [duplicate literal removal 313]
317. happy(X0) [subsumption resolution 316,93]
320. rich(X1) [resolution 317,163]
329. $false <- (~2) [resolution 320,138]
333. 2 [avatar contradiction clause 329]
334. $false <- (1) [subsumption resolution 134,312]
335. ~1 [avatar contradiction clause 334]
336. $false [avatar sat refutation 143,278,333,335]
% SZS output end Proof for 856964668153866650171572
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not creative and happy is not tall. Everyone who is calm is strong or not brave and vice versa. Everyone who is not brave or happy is not kind or not curious and vice versa. Everyone who is not generous or rich is both not strong and not calm. If someone is both wise and not old then fred is curious or not brave and vice versa. Everyone who is both happy and not old is patient or not old. If alice is both wise and funny then someone is creative or rich. Everyone who is not wise is not calm or wise. If fred is not calm or not brave then paul is brave or quiet and vice versa. Everyone who is either curious or generous is humble and vice versa. Everyone who is either tall or not humble is either creative or strong and vice versa. Everyone who is both patient and rich is strong or not strong and vice versa. Everyone who is humble is creative or not patient and vice versa. If paul is either humble or generous then someone is either brave or not quiet and vice versa. If someone is both old and tall then someone is either humble or not quiet. Everyone who is not tall or wise is not creative. John is both quiet and not humble. Paul is either not patient or not funny. Susan is either not quiet or not rich. Someone is rich. Someone is either curious or not wise. Someone is either not kind or not quiet. | Fred is brave. | entailment | (![X]:((~creative(X)&happy(X))=>~tall(X)))&
(![X]:(calm(X)<=>(strong(X)|~brave(X))))&
(![X]:((~brave(X)|happy(X))<=>(~kind(X)|~curious(X))))&
(![X]:((~generous(X)|rich(X))=>(~strong(X)&~calm(X))))&
((?[X]:((wise(X)&~old(X))))<=>((curious(fred)|~brave(fred))))&
(![X]:((happy(X)&~old(X))=>(patient(X)|~old(X))))&
(((wise(alice)&funny(alice)))=>(?[X]:((creative(X)|rich(X)))))&
(![X]:(~wise(X)=>(~calm(X)|wise(X))))&
(((~calm(fred)|~brave(fred)))<=>((brave(paul)|quiet(paul))))&
(![X]:((curious(X)<~>generous(X))<=>humble(X)))&
(![X]:((tall(X)<~>~humble(X))<=>(creative(X)<~>strong(X))))&
(![X]:((patient(X)&rich(X))<=>(strong(X)|~strong(X))))&
(![X]:(humble(X)<=>(creative(X)|~patient(X))))&
(((humble(paul)<~>generous(paul)))<=>(?[X]:((brave(X)<~>~quiet(X)))))&
((?[X]:((old(X)&tall(X))))=>(?[X]:((humble(X)<~>~quiet(X)))))&
(![X]:((~tall(X)|wise(X))=>~creative(X)))&
((quiet(john)&~humble(john)))&
((~patient(paul)<~>~funny(paul)))&
((~quiet(susan)<~>~rich(susan)))&
(?[X]:(rich(X)))&
(?[X]:((curious(X)<~>~wise(X))))&
(?[X]:((~kind(X)<~>~quiet(X)))) | brave(fred) | [
"p1",
"p3",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 7555505413162253983743791
% SZS output start Proof for 7555505413162253983743791
2. ! [X0] : (calm(X0) <=> (~brave(X0) | strong(X0))) [input p1]
4. ! [X0] : ((rich(X0) | ~generous(X0)) => (~calm(X0) & ~strong(X0))) [input p3]
12. ! [X0] : ((rich(X0) & patient(X0)) <=> (~strong(X0) | strong(X0))) [input p11]
23. ~brave(fred) [input hypothesis]
27. ! [X0] : ((~calm(X0) & ~strong(X0)) | (~rich(X0) & generous(X0))) [ennf transformation 4]
36. ! [X0] : ((calm(X0) | (brave(X0) & ~strong(X0))) & ((~brave(X0) | strong(X0)) | ~calm(X0))) [nnf transformation 2]
37. ! [X0] : ((calm(X0) | (brave(X0) & ~strong(X0))) & (~brave(X0) | strong(X0) | ~calm(X0))) [flattening 36]
51. ! [X0] : (((rich(X0) & patient(X0)) | (strong(X0) & ~strong(X0))) & ((~strong(X0) | strong(X0)) | (~rich(X0) | ~patient(X0)))) [nnf transformation 12]
52. ! [X0] : (((rich(X0) & patient(X0)) | (strong(X0) & ~strong(X0))) & (~strong(X0) | strong(X0) | ~rich(X0) | ~patient(X0))) [flattening 51]
76. brave(X0) | calm(X0) [cnf transformation 37]
84. ~rich(X0) | ~calm(X0) [cnf transformation 27]
112. rich(X0) | ~strong(X0) [cnf transformation 52]
113. rich(X0) | strong(X0) [cnf transformation 52]
140. ~brave(fred) [cnf transformation 23]
143. 1 <=> brave(fred) [avatar definition]
144. ~brave(fred) <- (~1) [avatar component clause 143]
188. 11 <=> calm(fred) [avatar definition]
189. calm(fred) <- (11) [avatar component clause 188]
199. rich(X0) [subsumption resolution 112,113]
267. ~1 [avatar split clause 140,143]
268. calm(fred) <- (~1) [resolution 76,144]
270. 11 | 1 [avatar split clause 268,143,188]
274. ~calm(X0) [resolution 84,199]
275. $false <- (11) [resolution 274,189]
278. ~11 [avatar contradiction clause 275]
279. $false [avatar sat refutation 267,270,278]
% SZS output end Proof for 7555505413162253983743791
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both funny and not calm is either happy or not funny and vice versa.
Everyone who is strong or not humble is either not strong or calm and vice versa.
Everyone who is both not strong and not old is quiet.
Everyone who is either not wise or not patient is both not patient and not funny and vice versa.
Everyone who is quiet is both curious and old.
Everyone who is not funny is both happy and not strong.
If someone is either brave or not patient then alice is not kind.
Everyone who is not funny is either humble or kind and vice versa.
If fred is either happy or not humble then mary is both not curious and not humble and vice versa.
If fred is not patient or not wise then someone is both patient and not funny.
Everyone who is both happy and brave is either not old or calm and vice versa.
If someone is either not old or not creative then someone is both not calm and creative and vice versa.
If john is quiet then someone is either brave or patient and vice versa.
Everyone who is brave is curious.
If john is wise then someone is funny or not patient.
Everyone who is wise is either creative or funny.
Someone is either not tall or not humble.
Susan is both not funny and wise.
Someone is either not wise or creative.
Someone is both not rich and not humble.
Alice is not calm.
Fred is either patient or old.
Alice is brave or patient. | Susan is not old. | contradiction | (![X]:((funny(X)&~calm(X))<=>(happy(X)<~>~funny(X))))&
(![X]:((strong(X)|~humble(X))<=>(~strong(X)<~>calm(X))))&
(![X]:((~strong(X)&~old(X))=>quiet(X)))&
(![X]:((~wise(X)<~>~patient(X))<=>(~patient(X)&~funny(X))))&
(![X]:(quiet(X)=>(curious(X)&old(X))))&
(![X]:(~funny(X)=>(happy(X)&~strong(X))))&
((?[X]:((brave(X)<~>~patient(X))))=>(~kind(alice)))&
(![X]:(~funny(X)<=>(humble(X)<~>kind(X))))&
(((happy(fred)<~>~humble(fred)))<=>((~curious(mary)&~humble(mary))))&
(((~patient(fred)|~wise(fred)))=>(?[X]:((patient(X)&~funny(X)))))&
(![X]:((happy(X)&brave(X))<=>(~old(X)<~>calm(X))))&
((?[X]:((~old(X)<~>~creative(X))))<=>(?[X]:((~calm(X)&creative(X)))))&
((quiet(john))<=>(?[X]:((brave(X)<~>patient(X)))))&
(![X]:(brave(X)=>curious(X)))&
((wise(john))=>(?[X]:((funny(X)|~patient(X)))))&
(![X]:(wise(X)=>(creative(X)<~>funny(X))))&
(?[X]:((~tall(X)<~>~humble(X))))&
((~funny(susan)&wise(susan)))&
(?[X]:((~wise(X)<~>creative(X))))&
(?[X]:((~rich(X)&~humble(X))))&
(~calm(alice))&
((patient(fred)<~>old(fred)))&
((brave(alice)|patient(alice))) | ~old(susan) | [
"p2",
"p4",
"p5",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 875804155954199686223150
% SZS output start Proof for 875804155954199686223150
3. ! [X0] : ((~old(X0) & ~strong(X0)) => quiet(X0)) [input p2]
5. ! [X0] : (quiet(X0) => (old(X0) & curious(X0))) [input p4]
6. ! [X0] : (~funny(X0) => (~strong(X0) & happy(X0))) [input p5]
18. wise(susan) & ~funny(susan) [input p17]
24. ~old(susan) [input hypothesis]
27. ! [X0] : (quiet(X0) | (old(X0) | strong(X0))) [ennf transformation 3]
28. ! [X0] : (quiet(X0) | old(X0) | strong(X0)) [flattening 27]
29. ! [X0] : ((old(X0) & curious(X0)) | ~quiet(X0)) [ennf transformation 5]
30. ! [X0] : ((~strong(X0) & happy(X0)) | funny(X0)) [ennf transformation 6]
83. quiet(X0) | old(X0) | strong(X0) [cnf transformation 28]
91. ~quiet(X0) | old(X0) [cnf transformation 29]
93. ~strong(X0) | funny(X0) [cnf transformation 30]
132. ~funny(susan) [cnf transformation 18]
141. ~old(susan) [cnf transformation 24]
337. old(X0) | strong(X0) | old(X0) [resolution 83,91]
339. old(X0) | strong(X0) [duplicate literal removal 337]
379. strong(susan) [resolution 339,141]
391. funny(susan) [resolution 379,93]
402. $false [subsumption resolution 391,132]
% SZS output end Proof for 875804155954199686223150
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 fred is not calm or not old then paul is not generous or tall.
Everyone who is both happy and quiet is strong or not funny and vice versa.
Everyone who is both not wise and strong is not brave and vice versa.
Everyone who is either not creative or creative is either rich or not strong.
If john is tall then someone is either not happy or not humble and vice versa.
If someone is both humble and not patient then mary is both strong and funny.
If alice is both creative and not patient then someone is wise.
Everyone who is not brave is calm and vice versa.
Everyone who is both not calm and not generous is either quiet or calm and vice versa.
Everyone who is tall is funny or not tall and vice versa.
Everyone who is either not humble or kind is generous or patient.
If someone is both brave and humble then paul is tall or not rich and vice versa.
If fred is not brave or not quiet then someone is both not wise and not funny and vice versa.
Everyone who is either not tall or curious is not patient.
Everyone who is not tall is not wise and vice versa.
Someone is either happy or old.
Someone is either rich or not patient.
Someone is patient.
Someone is both strong and happy.
Susan is strong.
Fred is either not creative or not generous. | Paul is brave. | entailment | (((~calm(fred)|~old(fred)))=>((~generous(paul)|tall(paul))))&
(![X]:((happy(X)&quiet(X))<=>(strong(X)|~funny(X))))&
(![X]:((~wise(X)&strong(X))<=>~brave(X)))&
(![X]:((~creative(X)<~>creative(X))=>(rich(X)<~>~strong(X))))&
((tall(john))<=>(?[X]:((~happy(X)<~>~humble(X)))))&
((?[X]:((humble(X)&~patient(X))))=>((strong(mary)&funny(mary))))&
(((creative(alice)&~patient(alice)))=>(?[X]:(wise(X))))&
(![X]:(~brave(X)<=>calm(X)))&
(![X]:((~calm(X)&~generous(X))<=>(quiet(X)<~>calm(X))))&
(![X]:(tall(X)<=>(funny(X)|~tall(X))))&
(![X]:((~humble(X)<~>kind(X))=>(generous(X)|patient(X))))&
((?[X]:((brave(X)&humble(X))))<=>((tall(paul)|~rich(paul))))&
(((~brave(fred)|~quiet(fred)))<=>(?[X]:((~wise(X)&~funny(X)))))&
(![X]:((~tall(X)<~>curious(X))=>~patient(X)))&
(![X]:(~tall(X)<=>~wise(X)))&
(?[X]:((happy(X)<~>old(X))))&
(?[X]:((rich(X)<~>~patient(X))))&
(?[X]:(patient(X)))&
(?[X]:((strong(X)&happy(X))))&
(strong(susan))&
((~creative(fred)<~>~generous(fred))) | brave(paul) | [
"p2",
"p9",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 486516348484747525534814
% SZS output start Proof for 486516348484747525534814
3. ! [X0] : ((strong(X0) & ~wise(X0)) <=> ~brave(X0)) [input p2]
10. ! [X0] : (tall(X0) <=> (~tall(X0) | funny(X0))) [input p9]
15. ! [X0] : (~tall(X0) <=> ~wise(X0)) [input p14]
22. ~brave(paul) [input hypothesis]
34. ! [X0] : (((strong(X0) & ~wise(X0)) | brave(X0)) & (~brave(X0) | (~strong(X0) | wise(X0)))) [nnf transformation 3]
35. ! [X0] : (((strong(X0) & ~wise(X0)) | brave(X0)) & (~brave(X0) | ~strong(X0) | wise(X0))) [flattening 34]
46. ! [X0] : ((tall(X0) | (tall(X0) & ~funny(X0))) & ((~tall(X0) | funny(X0)) | ~tall(X0))) [nnf transformation 10]
47. ! [X0] : ((tall(X0) | (tall(X0) & ~funny(X0))) & (~tall(X0) | funny(X0) | ~tall(X0))) [flattening 46]
60. ! [X0] : ((~tall(X0) | wise(X0)) & (~wise(X0) | tall(X0))) [nnf transformation 15]
80. ~wise(X0) | brave(X0) [cnf transformation 35]
103. tall(X0) | tall(X0) [cnf transformation 47]
119. ~tall(X0) | wise(X0) [cnf transformation 60]
130. ~brave(paul) [cnf transformation 22]
132. tall(X0) [duplicate literal removal 103]
230. wise(X0) [subsumption resolution 119,132]
267. brave(X0) [resolution 80,230]
268. $false [resolution 267,130]
% SZS output end Proof for 486516348484747525534814
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet or not funny then someone is either strong or brave and vice versa.
If lucy is not humble or generous then someone is either not creative or not wise.
If paul is wise or kind then someone is humble or old and vice versa.
Everyone who is not wise or generous is both not strong and quiet and vice versa.
Everyone who is both kind and humble is either humble or not old and vice versa.
If someone is either kind or old then mary is tall or not kind.
Everyone who is not calm or not happy is both strong and not tall.
Everyone who is calm is curious or strong.
If alice is both not humble and brave then someone is both not happy and calm.
Everyone who is patient is either not quiet or strong and vice versa.
Everyone who is funny or wise is happy.
Everyone who is both patient and rich is not funny and vice versa.
If lucy is not humble or happy then susan is either not wise or happy and vice versa.
If someone is not brave or brave then lucy is either not quiet or curious.
Everyone who is either old or wise is both not creative and not funny and vice versa.
Everyone who is either not quiet or curious is kind and vice versa.
Paul is either not humble or not old.
Someone is funny or not rich.
Lucy is not creative or not funny.
Paul is not kind.
Someone is kind.
John is either curious or not brave.
Someone is both curious and not calm.
Someone is calm or not calm. | John is not wise. | contradiction | ((?[X]:((quiet(X)<~>~funny(X))))<=>(?[X]:((strong(X)<~>brave(X)))))&
(((~humble(lucy)|generous(lucy)))=>(?[X]:((~creative(X)<~>~wise(X)))))&
(((wise(paul)|kind(paul)))<=>(?[X]:((humble(X)|old(X)))))&
(![X]:((~wise(X)|generous(X))<=>(~strong(X)&quiet(X))))&
(![X]:((kind(X)&humble(X))<=>(humble(X)<~>~old(X))))&
((?[X]:((kind(X)<~>old(X))))=>((tall(mary)|~kind(mary))))&
(![X]:((~calm(X)|~happy(X))=>(strong(X)&~tall(X))))&
(![X]:(calm(X)=>(curious(X)|strong(X))))&
(((~humble(alice)&brave(alice)))=>(?[X]:((~happy(X)&calm(X)))))&
(![X]:(patient(X)<=>(~quiet(X)<~>strong(X))))&
(![X]:((funny(X)|wise(X))=>happy(X)))&
(![X]:((patient(X)&rich(X))<=>~funny(X)))&
(((~humble(lucy)|happy(lucy)))<=>((~wise(susan)<~>happy(susan))))&
((?[X]:((~brave(X)|brave(X))))=>((~quiet(lucy)<~>curious(lucy))))&
(![X]:((old(X)<~>wise(X))<=>(~creative(X)&~funny(X))))&
(![X]:((~quiet(X)<~>curious(X))<=>kind(X)))&
((~humble(paul)<~>~old(paul)))&
(?[X]:((funny(X)|~rich(X))))&
((~creative(lucy)|~funny(lucy)))&
(~kind(paul))&
(?[X]:(kind(X)))&
((curious(john)<~>~brave(john)))&
(?[X]:((curious(X)&~calm(X))))&
(?[X]:((calm(X)|~calm(X)))) | ~wise(john) | [
"p3",
"p4",
"p6",
"p7",
"p9",
"p11",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8798333870667754669169204
% SZS output start Proof for 8798333870667754669169204
4. ! [X0] : ((generous(X0) | ~wise(X0)) <=> (quiet(X0) & ~strong(X0))) [input p3]
5. ! [X0] : ((humble(X0) & kind(X0)) <=> (humble(X0) <~> ~old(X0))) [input p4]
7. ! [X0] : ((~happy(X0) | ~calm(X0)) => (~tall(X0) & strong(X0))) [input p6]
8. ! [X0] : (calm(X0) => (strong(X0) | curious(X0))) [input p7]
10. ! [X0] : (patient(X0) <=> (~quiet(X0) <~> strong(X0))) [input p9]
12. ! [X0] : ((rich(X0) & patient(X0)) <=> ~funny(X0)) [input p11]
15. ! [X0] : ((old(X0) <~> wise(X0)) <=> (~funny(X0) & ~creative(X0))) [input p14]
16. ! [X0] : ((~quiet(X0) <~> curious(X0)) <=> kind(X0)) [input p15]
25. ~wise(john) [input hypothesis]
30. ! [X0] : ((~tall(X0) & strong(X0)) | (happy(X0) & calm(X0))) [ennf transformation 7]
31. ! [X0] : ((strong(X0) | curious(X0)) | ~calm(X0)) [ennf transformation 8]
32. ! [X0] : (strong(X0) | curious(X0) | ~calm(X0)) [flattening 31]
50. ! [X0] : (((generous(X0) | ~wise(X0)) | (~quiet(X0) | strong(X0))) & ((quiet(X0) & ~strong(X0)) | (~generous(X0) & wise(X0)))) [nnf transformation 4]
51. ! [X0] : ((generous(X0) | ~wise(X0) | ~quiet(X0) | strong(X0)) & ((quiet(X0) & ~strong(X0)) | (~generous(X0) & wise(X0)))) [flattening 50]
52. ! [X0] : (((humble(X0) & kind(X0)) | ((humble(X0) | old(X0)) & (~old(X0) | ~humble(X0)))) & (((old(X0) | ~humble(X0)) & (~old(X0) | humble(X0))) | (~humble(X0) | ~kind(X0)))) [nnf transformation 5]
53. ! [X0] : (((humble(X0) & kind(X0)) | ((humble(X0) | old(X0)) & (~old(X0) | ~humble(X0)))) & (((old(X0) | ~humble(X0)) & (~old(X0) | humble(X0))) | ~humble(X0) | ~kind(X0))) [flattening 52]
57. ! [X0] : ((patient(X0) | ((~quiet(X0) | ~strong(X0)) & (strong(X0) | quiet(X0)))) & (((~strong(X0) | quiet(X0)) & (strong(X0) | ~quiet(X0))) | ~patient(X0))) [nnf transformation 10]
58. ! [X0] : (((rich(X0) & patient(X0)) | funny(X0)) & (~funny(X0) | (~rich(X0) | ~patient(X0)))) [nnf transformation 12]
59. ! [X0] : (((rich(X0) & patient(X0)) | funny(X0)) & (~funny(X0) | ~rich(X0) | ~patient(X0))) [flattening 58]
63. ! [X0] : ((((~wise(X0) | ~old(X0)) & (wise(X0) | old(X0))) | (funny(X0) | creative(X0))) & ((~funny(X0) & ~creative(X0)) | ((old(X0) | ~wise(X0)) & (wise(X0) | ~old(X0))))) [nnf transformation 15]
64. ! [X0] : ((((~wise(X0) | ~old(X0)) & (wise(X0) | old(X0))) | funny(X0) | creative(X0)) & ((~funny(X0) & ~creative(X0)) | ((old(X0) | ~wise(X0)) & (wise(X0) | ~old(X0))))) [flattening 63]
65. ! [X0] : ((((~curious(X0) | quiet(X0)) & (curious(X0) | ~quiet(X0))) | ~kind(X0)) & (kind(X0) | ((~quiet(X0) | ~curious(X0)) & (curious(X0) | quiet(X0))))) [nnf transformation 16]
92. ~strong(X0) | wise(X0) [cnf transformation 51]
94. wise(X0) | quiet(X0) [cnf transformation 51]
98. old(X0) | ~humble(X0) | ~humble(X0) | ~kind(X0) [cnf transformation 53]
102. humble(X0) | humble(X0) | old(X0) [cnf transformation 53]
105. calm(X0) | strong(X0) [cnf transformation 30]
109. strong(X0) | curious(X0) | ~calm(X0) [cnf transformation 32]
112. ~patient(X0) | ~quiet(X0) | strong(X0) [cnf transformation 57]
119. patient(X0) | funny(X0) [cnf transformation 59]
133. ~old(X0) | wise(X0) | ~funny(X0) [cnf transformation 64]
138. ~curious(X0) | ~quiet(X0) | kind(X0) [cnf transformation 65]
152. ~wise(john) [cnf transformation 25]
153. old(X0) | ~humble(X0) | ~kind(X0) [duplicate literal removal 98]
154. old(X0) | humble(X0) [duplicate literal removal 102]
237. ~kind(X0) | old(X0) [subsumption resolution 153,154]
250. curious(X0) | strong(X0) [subsumption resolution 109,105]
326. 37 <=> curious(john) [avatar definition]
327. curious(john) <- (37) [avatar component clause 326]
328. ~curious(john) <- (~37) [avatar component clause 326]
336. quiet(john) [resolution 94,152]
364. strong(john) <- (~37) [resolution 250,328]
368. wise(john) <- (~37) [resolution 364,92]
369. $false <- (~37) [subsumption resolution 368,152]
370. 37 [avatar contradiction clause 369]
371. ~quiet(X0) | strong(X0) | funny(X0) [resolution 112,119]
485. ~quiet(john) | kind(john) <- (37) [resolution 138,327]
487. kind(john) <- (37) [subsumption resolution 485,336]
511. old(john) <- (37) [resolution 487,237]
559. strong(john) | funny(john) [resolution 371,336]
563. 64 <=> funny(john) [avatar definition]
567. 65 <=> strong(john) [avatar definition]
569. strong(john) <- (65) [avatar component clause 567]
570. 64 | 65 [avatar split clause 559,567,563]
632. wise(john) | ~funny(john) <- (37) [resolution 511,133]
635. ~funny(john) <- (37) [subsumption resolution 632,152]
639. ~64 | ~37 [avatar split clause 635,326,563]
653. wise(john) <- (65) [resolution 569,92]
655. $false <- (65) [subsumption resolution 653,152]
656. ~65 [avatar contradiction clause 655]
657. $false [avatar sat refutation 370,570,639,656]
% SZS output end Proof for 8798333870667754669169204
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not rich is creative.
Everyone who is either tall or funny is not generous.
Everyone who is quiet is both patient and not rich and vice versa.
Everyone who is either quiet or not old is strong or not humble.
Everyone who is patient or curious is both curious and strong and vice versa.
Everyone who is not kind or not patient is not humble and vice versa.
Everyone who is not calm is not creative or wise.
If someone is either not calm or creative then susan is both tall and not humble.
Everyone who is either not creative or not funny is not strong.
If someone is both curious and not creative then fred is curious or not funny and vice versa.
Everyone who is patient or not rich is not creative.
Everyone who is rich is quiet or patient and vice versa.
Everyone who is both not old and not patient is both wise and not brave and vice versa.
If someone is not patient then someone is generous or not patient and vice versa.
If someone is either kind or not funny then someone is both patient and rich and vice versa.
If lucy is both not patient and patient then mary is not strong and vice versa.
Mary is either not calm or not curious.
Someone is both not old and not happy.
Mary is humble.
Someone is not happy.
Someone is either not tall or patient.
Alice is creative or tall.
Someone is kind or not funny. | Lucy is patient. | entailment | (![X]:(~rich(X)=>creative(X)))&
(![X]:((tall(X)<~>funny(X))=>~generous(X)))&
(![X]:(quiet(X)<=>(patient(X)&~rich(X))))&
(![X]:((quiet(X)<~>~old(X))=>(strong(X)|~humble(X))))&
(![X]:((patient(X)|curious(X))<=>(curious(X)&strong(X))))&
(![X]:((~kind(X)|~patient(X))<=>~humble(X)))&
(![X]:(~calm(X)=>(~creative(X)|wise(X))))&
((?[X]:((~calm(X)<~>creative(X))))=>((tall(susan)&~humble(susan))))&
(![X]:((~creative(X)<~>~funny(X))=>~strong(X)))&
((?[X]:((curious(X)&~creative(X))))<=>((curious(fred)|~funny(fred))))&
(![X]:((patient(X)|~rich(X))=>~creative(X)))&
(![X]:(rich(X)<=>(quiet(X)|patient(X))))&
(![X]:((~old(X)&~patient(X))<=>(wise(X)&~brave(X))))&
((?[X]:(~patient(X)))<=>(?[X]:((generous(X)|~patient(X)))))&
((?[X]:((kind(X)<~>~funny(X))))<=>(?[X]:((patient(X)&rich(X)))))&
(((~patient(lucy)&patient(lucy)))<=>(~strong(mary)))&
((~calm(mary)<~>~curious(mary)))&
(?[X]:((~old(X)&~happy(X))))&
(humble(mary))&
(?[X]:(~happy(X)))&
(?[X]:((~tall(X)<~>patient(X))))&
((creative(alice)|tall(alice)))&
(?[X]:((kind(X)|~funny(X)))) | patient(lucy) | [
"p0",
"p2",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 4216288485945306541745963
% SZS output start Proof for 4216288485945306541745963
1. ! [X0] : (~rich(X0) => creative(X0)) [input p0]
3. ! [X0] : (quiet(X0) <=> (~rich(X0) & patient(X0))) [input p2]
11. ! [X0] : ((~rich(X0) | patient(X0)) => ~creative(X0)) [input p10]
12. ! [X0] : (rich(X0) <=> (patient(X0) | quiet(X0))) [input p11]
24. ~patient(lucy) [input hypothesis]
29. ! [X0] : (creative(X0) | rich(X0)) [ennf transformation 1]
37. ! [X0] : (~creative(X0) | (rich(X0) & ~patient(X0))) [ennf transformation 11]
39. ! [X0] : ((quiet(X0) | (rich(X0) | ~patient(X0))) & ((~rich(X0) & patient(X0)) | ~quiet(X0))) [nnf transformation 3]
40. ! [X0] : ((quiet(X0) | rich(X0) | ~patient(X0)) & ((~rich(X0) & patient(X0)) | ~quiet(X0))) [flattening 39]
53. ! [X0] : ((rich(X0) | (~patient(X0) & ~quiet(X0))) & ((patient(X0) | quiet(X0)) | ~rich(X0))) [nnf transformation 12]
54. ! [X0] : ((rich(X0) | (~patient(X0) & ~quiet(X0))) & (patient(X0) | quiet(X0) | ~rich(X0))) [flattening 53]
77. creative(X0) | rich(X0) [cnf transformation 29]
80. patient(X0) | ~quiet(X0) [cnf transformation 40]
106. ~creative(X0) | rich(X0) [cnf transformation 37]
107. patient(X0) | quiet(X0) | ~rich(X0) [cnf transformation 54]
134. ~patient(lucy) [cnf transformation 24]
177. rich(X0) [subsumption resolution 106,77]
178. patient(X0) | quiet(X0) [subsumption resolution 107,177]
179. patient(X0) [subsumption resolution 178,80]
226. $false [subsumption resolution 134,179]
% SZS output end Proof for 4216288485945306541745963
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not funny or rich is both not brave and patient and vice versa. If someone is not creative then mary is both generous and creative. Everyone who is humble is either quiet or not tall. Everyone who is not curious or not strong is quiet or not rich. Everyone who is not rich or not patient is either not happy or not quiet and vice versa. If susan is both not wise and not quiet then mary is patient. If fred is either curious or quiet then someone is both not creative and not rich. If someone is not patient or not funny then someone is wise or calm and vice versa. If lucy is old then lucy is wise or not curious and vice versa. Everyone who is humble or tall is both happy and not tall and vice versa. If lucy is either not old or tall then fred is not old and vice versa. If alice is happy or kind then alice is both not humble and not rich. If someone is not calm or strong then someone is curious or not brave and vice versa. Everyone who is quiet is both patient and not funny and vice versa. Everyone who is both not calm and kind is not funny or not patient and vice versa. Everyone who is not quiet or strong is either not calm or not old and vice versa. Alice is both funny and not brave. Lucy is both not kind and strong. Fred is not old. Lucy is both not old and humble. Fred is either calm or not kind. Someone is not generous. Someone is both funny and generous. | Susan is not quiet. | neutral | (![X]:((~funny(X)<~>rich(X))<=>(~brave(X)&patient(X))))&
((?[X]:(~creative(X)))=>((generous(mary)&creative(mary))))&
(![X]:(humble(X)=>(quiet(X)<~>~tall(X))))&
(![X]:((~curious(X)|~strong(X))=>(quiet(X)|~rich(X))))&
(![X]:((~rich(X)|~patient(X))<=>(~happy(X)<~>~quiet(X))))&
(((~wise(susan)&~quiet(susan)))=>(patient(mary)))&
(((curious(fred)<~>quiet(fred)))=>(?[X]:((~creative(X)&~rich(X)))))&
((?[X]:((~patient(X)|~funny(X))))<=>(?[X]:((wise(X)|calm(X)))))&
((old(lucy))<=>((wise(lucy)|~curious(lucy))))&
(![X]:((humble(X)|tall(X))<=>(happy(X)&~tall(X))))&
(((~old(lucy)<~>tall(lucy)))<=>(~old(fred)))&
(((happy(alice)|kind(alice)))=>((~humble(alice)&~rich(alice))))&
((?[X]:((~calm(X)|strong(X))))<=>(?[X]:((curious(X)|~brave(X)))))&
(![X]:(quiet(X)<=>(patient(X)&~funny(X))))&
(![X]:((~calm(X)&kind(X))<=>(~funny(X)|~patient(X))))&
(![X]:((~quiet(X)|strong(X))<=>(~calm(X)<~>~old(X))))&
((funny(alice)&~brave(alice)))&
((~kind(lucy)&strong(lucy)))&
(~old(fred))&
((~old(lucy)&humble(lucy)))&
((calm(fred)<~>~kind(fred)))&
(?[X]:(~generous(X)))&
(?[X]:((funny(X)&generous(X)))) | ~quiet(susan) | [] | null | 0 |
Everyone who is both old and kind is not old or wise and vice versa. Everyone who is both wise and not tall is either not generous or not curious and vice versa. Everyone who is curious is both not patient and not calm and vice versa. Everyone who is either curious or tall is not quiet or not curious and vice versa. If someone is funny then alice is both kind and wise. If mary is not wise or not funny then someone is calm and vice versa. If someone is creative or not brave then someone is either not tall or creative. Everyone who is strong is either not quiet or not brave. If someone is both creative and not happy then someone is both not kind and not curious. Everyone who is either not patient or calm is either funny or humble and vice versa. If alice is either not funny or not happy then john is either strong or not tall. If paul is rich then someone is both kind and wise and vice versa. Everyone who is either not curious or quiet is not curious and vice versa. Everyone who is not wise or creative is both patient and kind and vice versa. Everyone who is either brave or patient is either strong or not calm. Everyone who is not patient or not kind is both not happy and brave and vice versa. Someone is either rich or patient. Someone is not brave. Someone is both tall and brave. John is both not strong and not curious. | Mary is humble. | neutral | (![X]:((old(X)&kind(X))<=>(~old(X)|wise(X))))&
(![X]:((wise(X)&~tall(X))<=>(~generous(X)<~>~curious(X))))&
(![X]:(curious(X)<=>(~patient(X)&~calm(X))))&
(![X]:((curious(X)<~>tall(X))<=>(~quiet(X)|~curious(X))))&
((?[X]:(funny(X)))=>((kind(alice)&wise(alice))))&
(((~wise(mary)|~funny(mary)))<=>(?[X]:(calm(X))))&
((?[X]:((creative(X)|~brave(X))))=>(?[X]:((~tall(X)<~>creative(X)))))&
(![X]:(strong(X)=>(~quiet(X)<~>~brave(X))))&
((?[X]:((creative(X)&~happy(X))))=>(?[X]:((~kind(X)&~curious(X)))))&
(![X]:((~patient(X)<~>calm(X))<=>(funny(X)<~>humble(X))))&
(((~funny(alice)<~>~happy(alice)))=>((strong(john)<~>~tall(john))))&
((rich(paul))<=>(?[X]:((kind(X)&wise(X)))))&
(![X]:((~curious(X)<~>quiet(X))<=>~curious(X)))&
(![X]:((~wise(X)|creative(X))<=>(patient(X)&kind(X))))&
(![X]:((brave(X)<~>patient(X))=>(strong(X)<~>~calm(X))))&
(![X]:((~patient(X)|~kind(X))<=>(~happy(X)&brave(X))))&
(?[X]:((rich(X)<~>patient(X))))&
(?[X]:(~brave(X)))&
(?[X]:((tall(X)&brave(X))))&
((~strong(john)&~curious(john))) | humble(mary) | [] | null | 0 |
Everyone who is either happy or funny is wise and vice versa.
Everyone who is either not happy or not funny is generous and vice versa.
If paul is not quiet then fred is either not humble or not strong.
Everyone who is either not calm or quiet is either brave or not happy and vice versa.
Everyone who is not curious or funny is both not tall and calm.
If susan is not strong then someone is generous and vice versa.
Everyone who is either not quiet or not calm is either rich or strong and vice versa.
Everyone who is not strong or not generous is not quiet and vice versa.
Everyone who is not patient or brave is happy or funny.
Everyone who is not rich or brave is either not calm or humble.
If someone is funny or not generous then susan is both brave and not wise.
If lucy is calm or not patient then someone is humble.
If someone is both rich and old then john is either not quiet or curious.
Everyone who is both quiet and not brave is either not rich or not happy and vice versa.
If someone is happy then paul is either not creative or happy.
Someone is creative or happy.
Someone is not quiet or generous.
Someone is not tall.
Fred is not patient.
Someone is either not strong or quiet.
Lucy is not strong or generous. | Susan is not brave. | entailment | (![X]:((happy(X)<~>funny(X))<=>wise(X)))&
(![X]:((~happy(X)<~>~funny(X))<=>generous(X)))&
((~quiet(paul))=>((~humble(fred)<~>~strong(fred))))&
(![X]:((~calm(X)<~>quiet(X))<=>(brave(X)<~>~happy(X))))&
(![X]:((~curious(X)|funny(X))=>(~tall(X)&calm(X))))&
((~strong(susan))<=>(?[X]:(generous(X))))&
(![X]:((~quiet(X)<~>~calm(X))<=>(rich(X)<~>strong(X))))&
(![X]:((~strong(X)|~generous(X))<=>~quiet(X)))&
(![X]:((~patient(X)|brave(X))=>(happy(X)|funny(X))))&
(![X]:((~rich(X)|brave(X))=>(~calm(X)<~>humble(X))))&
((?[X]:((funny(X)|~generous(X))))=>((brave(susan)&~wise(susan))))&
(((calm(lucy)|~patient(lucy)))=>(?[X]:(humble(X))))&
((?[X]:((rich(X)&old(X))))=>((~quiet(john)<~>curious(john))))&
(![X]:((quiet(X)&~brave(X))<=>(~rich(X)<~>~happy(X))))&
((?[X]:(happy(X)))=>((~creative(paul)<~>happy(paul))))&
(?[X]:((creative(X)|happy(X))))&
(?[X]:((~quiet(X)|generous(X))))&
(?[X]:(~tall(X)))&
(~patient(fred))&
(?[X]:((~strong(X)<~>quiet(X))))&
((~strong(lucy)|generous(lucy))) | ~brave(susan) | [
"p0",
"p1",
"p3",
"p4",
"p5",
"p6",
"p7",
"p8",
"p10",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 4440481927654088152542850
% SZS output start Proof for 4440481927654088152542850
1. ! [X0] : ((happy(X0) <~> funny(X0)) <=> wise(X0)) [input p0]
2. ! [X0] : ((~happy(X0) <~> ~funny(X0)) <=> generous(X0)) [input p1]
4. ! [X0] : ((~calm(X0) <~> quiet(X0)) <=> (brave(X0) <~> ~happy(X0))) [input p3]
5. ! [X0] : ((funny(X0) | ~curious(X0)) => (calm(X0) & ~tall(X0))) [input p4]
6. ~strong(susan) <=> ? [X0] : generous(X0) [input p5]
7. ! [X0] : ((~quiet(X0) <~> ~calm(X0)) <=> (rich(X0) <~> strong(X0))) [input p6]
8. ! [X0] : ((~generous(X0) | ~strong(X0)) <=> ~quiet(X0)) [input p7]
9. ! [X0] : ((brave(X0) | ~patient(X0)) => (funny(X0) | happy(X0))) [input p8]
11. ? [X0] : (~generous(X0) | funny(X0)) => (~wise(susan) & brave(susan)) [input p10]
14. ! [X0] : ((~brave(X0) & quiet(X0)) <=> (~rich(X0) <~> ~happy(X0))) [input p13]
22. brave(susan) [input hypothesis]
23. ! [X0] : ((happy(X0) <~> funny(X0)) => wise(X0)) [unused predicate definition removal 1]
25. ! [X0] : (funny(X0) => (calm(X0) & ~tall(X0))) [pure predicate removal 5]
27. ! [X0] : (funny(X0) => calm(X0)) [pure predicate removal 25]
28. ! [X0] : (wise(X0) | (happy(X0) <=> funny(X0))) [ennf transformation 23]
30. ! [X0] : (calm(X0) | ~funny(X0)) [ennf transformation 27]
31. ! [X0] : ((funny(X0) | happy(X0)) | (~brave(X0) & patient(X0))) [ennf transformation 9]
32. ! [X0] : (funny(X0) | happy(X0) | (~brave(X0) & patient(X0))) [flattening 31]
34. (~wise(susan) & brave(susan)) | ! [X0] : (generous(X0) & ~funny(X0)) [ennf transformation 11]
37. ! [X0] : (wise(X0) | ((happy(X0) | ~funny(X0)) & (funny(X0) | ~happy(X0)))) [nnf transformation 28]
38. ! [X0] : ((((funny(X0) | happy(X0)) & (~funny(X0) | ~happy(X0))) | ~generous(X0)) & (generous(X0) | ((~happy(X0) | funny(X0)) & (~funny(X0) | happy(X0))))) [nnf transformation 2]
40. ! [X0] : ((((~quiet(X0) | calm(X0)) & (quiet(X0) | ~calm(X0))) | ((brave(X0) | happy(X0)) & (~happy(X0) | ~brave(X0)))) & (((happy(X0) | ~brave(X0)) & (~happy(X0) | brave(X0))) | ((~calm(X0) | ~quiet(X0)) & (quiet(X0) | calm(X0))))) [nnf transformation 4]
41. (~strong(susan) | ! [X0] : ~generous(X0)) & (? [X0] : generous(X0) | strong(susan)) [nnf transformation 6]
42. (~strong(susan) | ! [X0] : ~generous(X0)) & (? [X1] : generous(X1) | strong(susan)) [rectify 41]
43. ? [X1] : generous(X1) => generous(sK0) [choice axiom]
44. (~strong(susan) | ! [X0] : ~generous(X0)) & (generous(sK0) | strong(susan)) [skolemisation 42,43]
45. ! [X0] : ((((calm(X0) | quiet(X0)) & (~calm(X0) | ~quiet(X0))) | ((rich(X0) | ~strong(X0)) & (strong(X0) | ~rich(X0)))) & (((~strong(X0) | ~rich(X0)) & (strong(X0) | rich(X0))) | ((~quiet(X0) | calm(X0)) & (~calm(X0) | quiet(X0))))) [nnf transformation 7]
46. ! [X0] : (((~generous(X0) | ~strong(X0)) | quiet(X0)) & (~quiet(X0) | (generous(X0) & strong(X0)))) [nnf transformation 8]
47. ! [X0] : ((~generous(X0) | ~strong(X0) | quiet(X0)) & (~quiet(X0) | (generous(X0) & strong(X0)))) [flattening 46]
51. ! [X0] : (((~brave(X0) & quiet(X0)) | ((~rich(X0) | happy(X0)) & (~happy(X0) | rich(X0)))) & (((happy(X0) | rich(X0)) & (~happy(X0) | ~rich(X0))) | (brave(X0) | ~quiet(X0)))) [nnf transformation 14]
52. ! [X0] : (((~brave(X0) & quiet(X0)) | ((~rich(X0) | happy(X0)) & (~happy(X0) | rich(X0)))) & (((happy(X0) | rich(X0)) & (~happy(X0) | ~rich(X0))) | brave(X0) | ~quiet(X0))) [flattening 51]
62. ~funny(X0) | happy(X0) | wise(X0) [cnf transformation 37]
64. ~happy(X0) | generous(X0) | funny(X0) [cnf transformation 38]
73. ~brave(X0) | ~calm(X0) | ~happy(X0) | quiet(X0) [cnf transformation 40]
77. ~funny(X0) | calm(X0) [cnf transformation 30]
79. ~strong(susan) | ~generous(X0) [cnf transformation 44]
86. ~rich(X0) | quiet(X0) | strong(X0) | calm(X0) [cnf transformation 45]
88. ~quiet(X0) | strong(X0) [cnf transformation 47]
89. ~quiet(X0) | generous(X0) [cnf transformation 47]
92. ~brave(X0) | happy(X0) | funny(X0) [cnf transformation 32]
99. ~wise(susan) | ~funny(X0) [cnf transformation 34]
107. ~brave(X0) | ~happy(X0) | rich(X0) [cnf transformation 52]
117. brave(susan) [cnf transformation 22]
133. 4 <=> ! [X0] : ~generous(X0) [avatar definition]
134. ~generous(X0) <- (4) [avatar component clause 133]
136. 5 <=> strong(susan) [avatar definition]
138. ~strong(susan) <- (~5) [avatar component clause 136]
139. 4 | ~5 [avatar split clause 79,136,133]
149. 8 <=> wise(susan) [avatar definition]
154. 9 <=> ! [X0] : ~funny(X0) [avatar definition]
155. ~funny(X0) <- (9) [avatar component clause 154]
156. 9 | ~8 [avatar split clause 99,149,154]
158. 10 <=> brave(susan) [avatar definition]
160. brave(susan) <- (10) [avatar component clause 158]
217. 10 [avatar split clause 117,158]
229. happy(susan) | funny(susan) <- (10) [resolution 92,160]
231. 25 <=> funny(susan) [avatar definition]
233. funny(susan) <- (25) [avatar component clause 231]
235. 26 <=> happy(susan) [avatar definition]
237. happy(susan) <- (26) [avatar component clause 235]
238. 25 | 26 | ~10 [avatar split clause 229,158,235,231]
257. 29 <=> calm(susan) [avatar definition]
259. ~calm(susan) <- (~29) [avatar component clause 257]
263. calm(susan) <- (25) [resolution 233,77]
270. 29 | ~25 [avatar split clause 263,231,257]
272. generous(susan) | funny(susan) <- (26) [resolution 237,64]
288. 32 <=> rich(susan) [avatar definition]
290. rich(susan) <- (32) [avatar component clause 288]
292. 33 <=> quiet(susan) [avatar definition]
293. ~quiet(susan) <- (~33) [avatar component clause 292]
294. quiet(susan) <- (33) [avatar component clause 292]
298. ~happy(susan) | rich(susan) <- (10) [resolution 107,160]
315. ~calm(susan) | ~happy(susan) | quiet(susan) <- (10) [resolution 73,160]
321. generous(susan) <- (33) [resolution 294,89]
323. $false <- (4, 33) [subsumption resolution 321,134]
324. ~4 | ~33 [avatar contradiction clause 323]
327. funny(susan) <- (4, 26) [subsumption resolution 272,134]
328. 25 | ~4 | ~26 [avatar split clause 327,235,133,231]
355. $false <- (9, 25) [resolution 233,155]
357. happy(susan) | wise(susan) <- (25) [resolution 233,62]
359. ~9 | ~25 [avatar contradiction clause 355]
360. 8 | 26 | ~25 [avatar split clause 357,231,235,149]
367. rich(susan) <- (10, 26) [subsumption resolution 298,237]
368. 32 | ~10 | ~26 [avatar split clause 367,235,158,288]
386. strong(susan) <- (33) [resolution 294,88]
387. $false <- (~5, 33) [subsumption resolution 386,138]
388. 5 | ~33 [avatar contradiction clause 387]
391. ~calm(susan) | quiet(susan) <- (10, 26) [subsumption resolution 315,237]
392. 33 | ~29 | ~10 | ~26 [avatar split clause 391,235,158,257,292]
398. quiet(susan) | strong(susan) | calm(susan) <- (32) [resolution 86,290]
399. strong(susan) | calm(susan) <- (32, ~33) [subsumption resolution 398,293]
400. calm(susan) <- (~5, 32, ~33) [subsumption resolution 399,138]
401. $false <- (~5, ~29, 32, ~33) [subsumption resolution 400,259]
402. 5 | 29 | ~32 | 33 [avatar contradiction clause 401]
403. $false [avatar sat refutation 139,156,217,238,270,324,328,359,360,368,388,392,402]
% SZS output end Proof for 4440481927654088152542850
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either curious or strong is both humble and not kind and vice versa.
Everyone who is either not generous or not old is wise.
If someone is either not curious or not creative then lucy is either not funny or patient.
Everyone who is patient is not strong.
If someone is either wise or not rich then someone is not creative or not quiet.
If susan is not strong or brave then someone is both quiet and rich and vice versa.
If fred is both tall and not brave then someone is both not rich and humble and vice versa.
Everyone who is either not tall or not curious is both not happy and quiet.
If mary is old or kind then fred is both calm and old and vice versa.
Everyone who is creative is not curious or not brave.
If someone is not quiet or not brave then alice is strong.
Everyone who is either strong or tall is not calm or old and vice versa.
If someone is both quiet and patient then susan is strong or wise.
Everyone who is either quiet or not kind is not creative or quiet and vice versa.
Everyone who is both strong and not patient is both not old and not curious and vice versa.
If alice is not happy or patient then someone is brave.
Someone is both not rich and calm.
Paul is brave.
Lucy is either not humble or not patient.
Paul is wise or not funny.
Someone is both wise and creative.
Someone is patient or curious.
Someone is both not patient and strong.
Susan is both kind and patient. | Susan is not quiet. | contradiction | (![X]:((curious(X)<~>strong(X))<=>(humble(X)&~kind(X))))&
(![X]:((~generous(X)<~>~old(X))=>wise(X)))&
((?[X]:((~curious(X)<~>~creative(X))))=>((~funny(lucy)<~>patient(lucy))))&
(![X]:(patient(X)=>~strong(X)))&
((?[X]:((wise(X)<~>~rich(X))))=>(?[X]:((~creative(X)|~quiet(X)))))&
(((~strong(susan)|brave(susan)))<=>(?[X]:((quiet(X)&rich(X)))))&
(((tall(fred)&~brave(fred)))<=>(?[X]:((~rich(X)&humble(X)))))&
(![X]:((~tall(X)<~>~curious(X))=>(~happy(X)&quiet(X))))&
(((old(mary)|kind(mary)))<=>((calm(fred)&old(fred))))&
(![X]:(creative(X)=>(~curious(X)|~brave(X))))&
((?[X]:((~quiet(X)|~brave(X))))=>(strong(alice)))&
(![X]:((strong(X)<~>tall(X))<=>(~calm(X)|old(X))))&
((?[X]:((quiet(X)&patient(X))))=>((strong(susan)|wise(susan))))&
(![X]:((quiet(X)<~>~kind(X))<=>(~creative(X)|quiet(X))))&
(![X]:((strong(X)&~patient(X))<=>(~old(X)&~curious(X))))&
(((~happy(alice)|patient(alice)))=>(?[X]:(brave(X))))&
(?[X]:((~rich(X)&calm(X))))&
(brave(paul))&
((~humble(lucy)<~>~patient(lucy)))&
((wise(paul)|~funny(paul)))&
(?[X]:((wise(X)&creative(X))))&
(?[X]:((patient(X)|curious(X))))&
(?[X]:((~patient(X)&strong(X))))&
((kind(susan)&patient(susan))) | ~quiet(susan) | [
"p0",
"p3",
"p7",
"p11",
"p14",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 6620114012242511780664443
% SZS output start Proof for 6620114012242511780664443
1. ! [X0] : ((curious(X0) <~> strong(X0)) <=> (~kind(X0) & humble(X0))) [input p0]
4. ! [X0] : (patient(X0) => ~strong(X0)) [input p3]
8. ! [X0] : ((~tall(X0) <~> ~curious(X0)) => (quiet(X0) & ~happy(X0))) [input p7]
12. ! [X0] : ((strong(X0) <~> tall(X0)) <=> (old(X0) | ~calm(X0))) [input p11]
15. ! [X0] : ((~patient(X0) & strong(X0)) <=> (~curious(X0) & ~old(X0))) [input p14]
24. patient(susan) & kind(susan) [input p23]
25. ~quiet(susan) [input hypothesis]
29. ! [X0] : (~strong(X0) | ~patient(X0)) [ennf transformation 4]
31. ! [X0] : ((quiet(X0) & ~happy(X0)) | (~tall(X0) <=> ~curious(X0))) [ennf transformation 8]
38. ! [X0] : ((((~strong(X0) | ~curious(X0)) & (strong(X0) | curious(X0))) | (kind(X0) | ~humble(X0))) & ((~kind(X0) & humble(X0)) | ((curious(X0) | ~strong(X0)) & (strong(X0) | ~curious(X0))))) [nnf transformation 1]
39. ! [X0] : ((((~strong(X0) | ~curious(X0)) & (strong(X0) | curious(X0))) | kind(X0) | ~humble(X0)) & ((~kind(X0) & humble(X0)) | ((curious(X0) | ~strong(X0)) & (strong(X0) | ~curious(X0))))) [flattening 38]
56. ! [X0] : ((quiet(X0) & ~happy(X0)) | ((~tall(X0) | curious(X0)) & (~curious(X0) | tall(X0)))) [nnf transformation 31]
59. ! [X0] : ((((~tall(X0) | ~strong(X0)) & (tall(X0) | strong(X0))) | (~old(X0) & calm(X0))) & ((old(X0) | ~calm(X0)) | ((strong(X0) | ~tall(X0)) & (tall(X0) | ~strong(X0))))) [nnf transformation 12]
60. ! [X0] : ((((~tall(X0) | ~strong(X0)) & (tall(X0) | strong(X0))) | (~old(X0) & calm(X0))) & (old(X0) | ~calm(X0) | ((strong(X0) | ~tall(X0)) & (tall(X0) | ~strong(X0))))) [flattening 59]
63. ! [X0] : (((~patient(X0) & strong(X0)) | (curious(X0) | old(X0))) & ((~curious(X0) & ~old(X0)) | (patient(X0) | ~strong(X0)))) [nnf transformation 15]
64. ! [X0] : (((~patient(X0) & strong(X0)) | curious(X0) | old(X0)) & ((~curious(X0) & ~old(X0)) | patient(X0) | ~strong(X0))) [flattening 63]
78. ~kind(X0) | strong(X0) | ~curious(X0) [cnf transformation 39]
88. ~patient(X0) | ~strong(X0) [cnf transformation 29]
103. ~tall(X0) | quiet(X0) | curious(X0) [cnf transformation 56]
115. ~old(X0) | strong(X0) | tall(X0) [cnf transformation 60]
128. ~patient(X0) | curious(X0) | old(X0) [cnf transformation 64]
142. kind(susan) [cnf transformation 24]
143. patient(susan) [cnf transformation 24]
144. ~quiet(susan) [cnf transformation 25]
185. 10 <=> strong(susan) [avatar definition]
187. ~strong(susan) <- (~10) [avatar component clause 185]
310. ~strong(susan) [resolution 88,143]
315. ~10 [avatar split clause 310,185]
329. strong(susan) | ~curious(susan) [resolution 78,142]
332. ~curious(susan) <- (~10) [subsumption resolution 329,187]
437. curious(susan) | old(susan) [resolution 128,143]
440. old(susan) <- (~10) [subsumption resolution 437,332]
491. strong(susan) | tall(susan) <- (~10) [resolution 440,115]
494. tall(susan) <- (~10) [subsumption resolution 491,187]
567. quiet(susan) | curious(susan) <- (~10) [resolution 494,103]
568. curious(susan) <- (~10) [subsumption resolution 567,144]
569. $false <- (~10) [subsumption resolution 568,332]
570. 10 [avatar contradiction clause 569]
571. $false [avatar sat refutation 315,570]
% SZS output end Proof for 6620114012242511780664443
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both quiet and tall is tall and vice versa.
Everyone who is wise or not tall is not wise or wise and vice versa.
Everyone who is both not rich and calm is either not strong or not funny.
Everyone who is both not humble and generous is brave and vice versa.
Everyone who is either calm or old is patient and vice versa.
If lucy is either not calm or not curious then someone is either happy or curious.
If john is either not wise or not tall then someone is either not curious or strong and vice versa.
Everyone who is funny or not strong is both not rich and humble and vice versa.
If someone is calm then someone is not quiet or brave.
If mary is both not quiet and creative then john is not calm or creative and vice versa.
If someone is both not funny and old then susan is quiet and vice versa.
Everyone who is both patient and happy is not old and vice versa.
Everyone who is humble or not funny is both rich and calm and vice versa.
Everyone who is either funny or patient is old.
Everyone who is both rich and quiet is either calm or creative.
Everyone who is happy or not rich is both not quiet and wise.
Lucy is either not quiet or curious.
Someone is not creative.
Someone is both not curious and wise.
John is happy.
Mary is either happy or not brave.
Susan is either old or not kind. | John is not calm. | contradiction | (![X]:((quiet(X)&tall(X))<=>tall(X)))&
(![X]:((wise(X)|~tall(X))<=>(~wise(X)|wise(X))))&
(![X]:((~rich(X)&calm(X))=>(~strong(X)<~>~funny(X))))&
(![X]:((~humble(X)&generous(X))<=>brave(X)))&
(![X]:((calm(X)<~>old(X))<=>patient(X)))&
(((~calm(lucy)<~>~curious(lucy)))=>(?[X]:((happy(X)<~>curious(X)))))&
(((~wise(john)<~>~tall(john)))<=>(?[X]:((~curious(X)<~>strong(X)))))&
(![X]:((funny(X)|~strong(X))<=>(~rich(X)&humble(X))))&
((?[X]:(calm(X)))=>(?[X]:((~quiet(X)|brave(X)))))&
(((~quiet(mary)&creative(mary)))<=>((~calm(john)|creative(john))))&
((?[X]:((~funny(X)&old(X))))<=>(quiet(susan)))&
(![X]:((patient(X)&happy(X))<=>~old(X)))&
(![X]:((humble(X)|~funny(X))<=>(rich(X)&calm(X))))&
(![X]:((funny(X)<~>patient(X))=>old(X)))&
(![X]:((rich(X)&quiet(X))=>(calm(X)<~>creative(X))))&
(![X]:((happy(X)|~rich(X))=>(~quiet(X)&wise(X))))&
((~quiet(lucy)<~>curious(lucy)))&
(?[X]:(~creative(X)))&
(?[X]:((~curious(X)&wise(X))))&
(happy(john))&
((happy(mary)<~>~brave(mary)))&
((old(susan)<~>~kind(susan))) | ~calm(john) | [
"p7",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 3684455324743428715472850
% SZS output start Proof for 3684455324743428715472850
8. ! [X0] : ((~strong(X0) | funny(X0)) <=> (humble(X0) & ~rich(X0))) [input p7]
13. ! [X0] : ((~funny(X0) | humble(X0)) <=> (calm(X0) & rich(X0))) [input p12]
23. ~calm(john) [input hypothesis]
48. ! [X0] : (((~strong(X0) | funny(X0)) | (~humble(X0) | rich(X0))) & ((humble(X0) & ~rich(X0)) | (strong(X0) & ~funny(X0)))) [nnf transformation 8]
49. ! [X0] : ((~strong(X0) | funny(X0) | ~humble(X0) | rich(X0)) & ((humble(X0) & ~rich(X0)) | (strong(X0) & ~funny(X0)))) [flattening 48]
61. ! [X0] : (((~funny(X0) | humble(X0)) | (~calm(X0) | ~rich(X0))) & ((calm(X0) & rich(X0)) | (funny(X0) & ~humble(X0)))) [nnf transformation 13]
62. ! [X0] : ((~funny(X0) | humble(X0) | ~calm(X0) | ~rich(X0)) & ((calm(X0) & rich(X0)) | (funny(X0) & ~humble(X0)))) [flattening 61]
102. ~funny(X0) | humble(X0) [cnf transformation 49]
119. ~humble(X0) | calm(X0) [cnf transformation 62]
120. funny(X0) | calm(X0) [cnf transformation 62]
140. ~calm(john) [cnf transformation 23]
217. 16 <=> calm(john) [avatar definition]
218. ~calm(john) <- (~16) [avatar component clause 217]
273. ~16 [avatar split clause 140,217]
287. calm(X0) | humble(X0) [resolution 120,102]
289. calm(X0) [subsumption resolution 287,119]
295. $false <- (~16) [resolution 289,218]
296. 16 [avatar contradiction clause 295]
298. $false [avatar sat refutation 273,296]
% SZS output end Proof for 3684455324743428715472850
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not calm or kind is either not humble or not quiet and vice versa.
Everyone who is rich or strong is both not calm and calm and vice versa.
Everyone who is calm or not brave is either patient or old.
If fred is strong or old then someone is not kind.
Everyone who is both not brave and not humble is both not calm and strong.
Everyone who is either not curious or funny is both curious and creative and vice versa.
Everyone who is both not kind and not curious is both not strong and humble and vice versa.
Everyone who is patient is both brave and not quiet and vice versa.
If mary is brave or quiet then mary is either rich or not patient and vice versa.
Everyone who is both generous and not patient is both not kind and humble.
If someone is either strong or tall then alice is humble.
Everyone who is both not calm and not curious is old or rich and vice versa.
If someone is funny or not brave then someone is not curious or not kind and vice versa.
If someone is not wise or not old then lucy is curious or not calm and vice versa.
If alice is both not humble and funny then someone is not curious and vice versa.
Fred is brave or not humble.
Paul is not curious.
Paul is humble.
Someone is either calm or brave.
Someone is either happy or funny.
Someone is not quiet or strong.
Lucy is not calm or brave. | Mary is not generous. | entailment | (![X]:((~calm(X)<~>kind(X))<=>(~humble(X)<~>~quiet(X))))&
(![X]:((rich(X)|strong(X))<=>(~calm(X)&calm(X))))&
(![X]:((calm(X)|~brave(X))=>(patient(X)<~>old(X))))&
(((strong(fred)|old(fred)))=>(?[X]:(~kind(X))))&
(![X]:((~brave(X)&~humble(X))=>(~calm(X)&strong(X))))&
(![X]:((~curious(X)<~>funny(X))<=>(curious(X)&creative(X))))&
(![X]:((~kind(X)&~curious(X))<=>(~strong(X)&humble(X))))&
(![X]:(patient(X)<=>(brave(X)&~quiet(X))))&
(((brave(mary)|quiet(mary)))<=>((rich(mary)<~>~patient(mary))))&
(![X]:((generous(X)&~patient(X))=>(~kind(X)&humble(X))))&
((?[X]:((strong(X)<~>tall(X))))=>(humble(alice)))&
(![X]:((~calm(X)&~curious(X))<=>(old(X)|rich(X))))&
((?[X]:((funny(X)|~brave(X))))<=>(?[X]:((~curious(X)|~kind(X)))))&
((?[X]:((~wise(X)|~old(X))))<=>((curious(lucy)|~calm(lucy))))&
(((~humble(alice)&funny(alice)))<=>(?[X]:(~curious(X))))&
((brave(fred)|~humble(fred)))&
(~curious(paul))&
(humble(paul))&
(?[X]:((calm(X)<~>brave(X))))&
(?[X]:((happy(X)<~>funny(X))))&
(?[X]:((~quiet(X)|strong(X))))&
((~calm(lucy)|brave(lucy))) | ~generous(mary) | [
"p0",
"p1",
"p2",
"p7",
"p8",
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 50697782364602614351539
% SZS output start Proof for 50697782364602614351539
1. ! [X0] : ((~calm(X0) <~> kind(X0)) <=> (~humble(X0) <~> ~quiet(X0))) [input p0]
2. ! [X0] : ((strong(X0) | rich(X0)) <=> (calm(X0) & ~calm(X0))) [input p1]
3. ! [X0] : ((~brave(X0) | calm(X0)) => (patient(X0) <~> old(X0))) [input p2]
8. ! [X0] : (patient(X0) <=> (~quiet(X0) & brave(X0))) [input p7]
9. (quiet(mary) | brave(mary)) <=> (rich(mary) <~> ~patient(mary)) [input p8]
10. ! [X0] : ((~patient(X0) & generous(X0)) => (humble(X0) & ~kind(X0))) [input p9]
12. ! [X0] : ((~curious(X0) & ~calm(X0)) <=> (rich(X0) | old(X0))) [input p11]
23. generous(mary) [input hypothesis]
25. ! [X0] : ((patient(X0) <~> old(X0)) | (brave(X0) & ~calm(X0))) [ennf transformation 3]
29. ! [X0] : ((humble(X0) & ~kind(X0)) | (patient(X0) | ~generous(X0))) [ennf transformation 10]
30. ! [X0] : ((humble(X0) & ~kind(X0)) | patient(X0) | ~generous(X0)) [flattening 29]
32. ! [X0] : ((((~kind(X0) | calm(X0)) & (kind(X0) | ~calm(X0))) | ((~humble(X0) | quiet(X0)) & (~quiet(X0) | humble(X0)))) & (((quiet(X0) | humble(X0)) & (~quiet(X0) | ~humble(X0))) | ((~calm(X0) | ~kind(X0)) & (kind(X0) | calm(X0))))) [nnf transformation 1]
33. ! [X0] : (((strong(X0) | rich(X0)) | (~calm(X0) | calm(X0))) & ((calm(X0) & ~calm(X0)) | (~strong(X0) & ~rich(X0)))) [nnf transformation 2]
34. ! [X0] : ((strong(X0) | rich(X0) | ~calm(X0) | calm(X0)) & ((calm(X0) & ~calm(X0)) | (~strong(X0) & ~rich(X0)))) [flattening 33]
35. ! [X0] : (((~old(X0) | ~patient(X0)) & (old(X0) | patient(X0))) | (brave(X0) & ~calm(X0))) [nnf transformation 25]
42. ! [X0] : ((patient(X0) | (quiet(X0) | ~brave(X0))) & ((~quiet(X0) & brave(X0)) | ~patient(X0))) [nnf transformation 8]
43. ! [X0] : ((patient(X0) | quiet(X0) | ~brave(X0)) & ((~quiet(X0) & brave(X0)) | ~patient(X0))) [flattening 42]
44. ((quiet(mary) | brave(mary)) | ((rich(mary) | patient(mary)) & (~patient(mary) | ~rich(mary)))) & (((patient(mary) | ~rich(mary)) & (~patient(mary) | rich(mary))) | (~quiet(mary) & ~brave(mary))) [nnf transformation 9]
45. (quiet(mary) | brave(mary) | ((rich(mary) | patient(mary)) & (~patient(mary) | ~rich(mary)))) & (((patient(mary) | ~rich(mary)) & (~patient(mary) | rich(mary))) | (~quiet(mary) & ~brave(mary))) [flattening 44]
47. ! [X0] : (((~curious(X0) & ~calm(X0)) | (~rich(X0) & ~old(X0))) & ((rich(X0) | old(X0)) | (curious(X0) | calm(X0)))) [nnf transformation 12]
48. ! [X0] : (((~curious(X0) & ~calm(X0)) | (~rich(X0) & ~old(X0))) & (rich(X0) | old(X0) | curious(X0) | calm(X0))) [flattening 47]
72. ~quiet(X0) | ~humble(X0) | kind(X0) | calm(X0) [cnf transformation 32]
80. ~calm(X0) | ~rich(X0) [cnf transformation 34]
82. ~rich(X0) | calm(X0) [cnf transformation 34]
85. ~calm(X0) | patient(X0) | old(X0) [cnf transformation 35]
103. ~patient(X0) | brave(X0) [cnf transformation 43]
105. ~brave(X0) | quiet(X0) | patient(X0) [cnf transformation 43]
106. ~patient(mary) | rich(mary) | ~brave(mary) [cnf transformation 45]
111. quiet(mary) | brave(mary) | rich(mary) | patient(mary) [cnf transformation 45]
112. ~generous(X0) | patient(X0) | ~kind(X0) [cnf transformation 30]
113. ~generous(X0) | patient(X0) | humble(X0) [cnf transformation 30]
117. ~old(X0) | ~calm(X0) [cnf transformation 48]
141. generous(mary) [cnf transformation 23]
145. ~rich(X0) [subsumption resolution 80,82]
158. quiet(mary) | brave(mary) | patient(mary) [subsumption resolution 111,145]
159. quiet(mary) | patient(mary) [subsumption resolution 158,105]
161. 3 <=> patient(mary) [avatar definition]
162. ~patient(mary) <- (~3) [avatar component clause 161]
165. 4 <=> quiet(mary) [avatar definition]
167. quiet(mary) <- (4) [avatar component clause 165]
168. 3 | 4 [avatar split clause 159,165,161]
169. ~patient(mary) | ~brave(mary) [subsumption resolution 106,145]
170. ~patient(mary) [subsumption resolution 169,103]
171. ~3 [avatar split clause 170,161]
374. patient(mary) | ~kind(mary) [resolution 112,141]
375. ~kind(mary) <- (~3) [subsumption resolution 374,162]
379. patient(mary) | humble(mary) [resolution 113,141]
380. humble(mary) <- (~3) [subsumption resolution 379,162]
422. ~humble(mary) | kind(mary) | calm(mary) <- (4) [resolution 72,167]
423. kind(mary) | calm(mary) <- (~3, 4) [subsumption resolution 422,380]
424. calm(mary) <- (~3, 4) [subsumption resolution 423,375]
548. patient(mary) | old(mary) <- (~3, 4) [resolution 424,85]
549. old(mary) <- (~3, 4) [subsumption resolution 548,162]
609. ~calm(mary) <- (~3, 4) [resolution 549,117]
610. $false <- (~3, 4) [subsumption resolution 609,424]
611. 3 | ~4 [avatar contradiction clause 610]
612. $false [avatar sat refutation 168,171,611]
% SZS output end Proof for 50697782364602614351539
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either quiet or calm is either happy or not creative and vice versa. If alice is either strong or not happy then someone is not generous. If someone is patient then someone is old. Everyone who is either humble or brave is kind or not generous. Everyone who is wise or not brave is either not tall or wise and vice versa. If someone is either not kind or rich then someone is not patient or calm and vice versa. If someone is strong then mary is not funny or not creative. If someone is calm then someone is not generous and vice versa. Everyone who is both strong and not calm is curious. Everyone who is not wise is kind and vice versa. Everyone who is curious or not strong is either strong or patient. Everyone who is quiet is not funny and vice versa. Everyone who is either creative or wise is not calm. If someone is either not patient or creative then lucy is not wise or not curious and vice versa. If mary is either not creative or not calm then someone is both not generous and not wise. If someone is patient then someone is not generous or patient. Alice is not kind or not rich. Paul is both tall and rich. Someone is not funny or not curious. Someone is tall or rich. Someone is not humble or humble. Someone is old. Someone is not kind. Someone is both not creative and funny. | Lucy is happy. | neutral | (![X]:((quiet(X)<~>calm(X))<=>(happy(X)<~>~creative(X))))&
(((strong(alice)<~>~happy(alice)))=>(?[X]:(~generous(X))))&
((?[X]:(patient(X)))=>(?[X]:(old(X))))&
(![X]:((humble(X)<~>brave(X))=>(kind(X)|~generous(X))))&
(![X]:((wise(X)|~brave(X))<=>(~tall(X)<~>wise(X))))&
((?[X]:((~kind(X)<~>rich(X))))<=>(?[X]:((~patient(X)|calm(X)))))&
((?[X]:(strong(X)))=>((~funny(mary)|~creative(mary))))&
((?[X]:(calm(X)))<=>(?[X]:(~generous(X))))&
(![X]:((strong(X)&~calm(X))=>curious(X)))&
(![X]:(~wise(X)<=>kind(X)))&
(![X]:((curious(X)|~strong(X))=>(strong(X)<~>patient(X))))&
(![X]:(quiet(X)<=>~funny(X)))&
(![X]:((creative(X)<~>wise(X))=>~calm(X)))&
((?[X]:((~patient(X)<~>creative(X))))<=>((~wise(lucy)|~curious(lucy))))&
(((~creative(mary)<~>~calm(mary)))=>(?[X]:((~generous(X)&~wise(X)))))&
((?[X]:(patient(X)))=>(?[X]:((~generous(X)|patient(X)))))&
((~kind(alice)|~rich(alice)))&
((tall(paul)&rich(paul)))&
(?[X]:((~funny(X)|~curious(X))))&
(?[X]:((tall(X)|rich(X))))&
(?[X]:((~humble(X)|humble(X))))&
(?[X]:(old(X)))&
(?[X]:(~kind(X)))&
(?[X]:((~creative(X)&funny(X)))) | happy(lucy) | [] | null | 0 |
If someone is not calm or not generous then susan is not calm or rich. Everyone who is not tall or not brave is either creative or funny and vice versa. If someone is funny then paul is patient. If lucy is not strong then mary is not rich and vice versa. Everyone who is either not curious or not humble is not wise and vice versa. If someone is either not generous or old then someone is calm or brave and vice versa. If fred is not patient then someone is funny or curious. Everyone who is not quiet is brave. If someone is funny or tall then someone is both not funny and not humble. If lucy is curious then someone is either not tall or not old and vice versa. If paul is both not tall and not rich then lucy is either not strong or generous and vice versa. If someone is not wise or generous then someone is not rich and vice versa. Everyone who is either not rich or happy is curious or not patient. Everyone who is not brave or rich is both not funny and not kind and vice versa. Everyone who is funny or brave is both brave and happy. If someone is either humble or happy then fred is generous or not calm. Someone is not wise. Susan is not happy or not rich. Fred is not patient or generous. Someone is not strong or not wise. Susan is either not generous or not happy. Someone is either strong or not strong. Alice is creative. Someone is not brave. | Fred is patient. | neutral | ((?[X]:((~calm(X)|~generous(X))))=>((~calm(susan)|rich(susan))))&
(![X]:((~tall(X)|~brave(X))<=>(creative(X)<~>funny(X))))&
((?[X]:(funny(X)))=>(patient(paul)))&
((~strong(lucy))<=>(~rich(mary)))&
(![X]:((~curious(X)<~>~humble(X))<=>~wise(X)))&
((?[X]:((~generous(X)<~>old(X))))<=>(?[X]:((calm(X)|brave(X)))))&
((~patient(fred))=>(?[X]:((funny(X)|curious(X)))))&
(![X]:(~quiet(X)=>brave(X)))&
((?[X]:((funny(X)|tall(X))))=>(?[X]:((~funny(X)&~humble(X)))))&
((curious(lucy))<=>(?[X]:((~tall(X)<~>~old(X)))))&
(((~tall(paul)&~rich(paul)))<=>((~strong(lucy)<~>generous(lucy))))&
((?[X]:((~wise(X)|generous(X))))<=>(?[X]:(~rich(X))))&
(![X]:((~rich(X)<~>happy(X))=>(curious(X)|~patient(X))))&
(![X]:((~brave(X)|rich(X))<=>(~funny(X)&~kind(X))))&
(![X]:((funny(X)|brave(X))=>(brave(X)&happy(X))))&
((?[X]:((humble(X)<~>happy(X))))=>((generous(fred)|~calm(fred))))&
(?[X]:(~wise(X)))&
((~happy(susan)|~rich(susan)))&
((~patient(fred)|generous(fred)))&
(?[X]:((~strong(X)|~wise(X))))&
((~generous(susan)<~>~happy(susan)))&
(?[X]:((strong(X)<~>~strong(X))))&
(creative(alice))&
(?[X]:(~brave(X))) | patient(fred) | [] | null | 0 |
If paul is either not tall or wise then someone is not kind.
Everyone who is rich is either not curious or funny.
Everyone who is both tall and not humble is either not curious or not funny and vice versa.
Everyone who is not creative or not tall is either not kind or not quiet and vice versa.
If susan is not patient then john is not rich or not kind and vice versa.
Everyone who is either creative or not old is either not brave or old and vice versa.
Everyone who is funny is either wise or not calm and vice versa.
Everyone who is not calm is happy or funny and vice versa.
If susan is not quiet or not calm then someone is not old or not strong and vice versa.
Everyone who is creative or not humble is not tall or not happy.
Everyone who is either not patient or patient is tall and vice versa.
Everyone who is either not rich or not funny is either kind or not humble.
If lucy is curious or not wise then someone is both calm and not happy.
If someone is either not patient or not curious then someone is not tall and vice versa.
Everyone who is not tall or creative is calm and vice versa.
If lucy is creative then paul is both patient and funny and vice versa.
Someone is not strong or not rich.
Someone is quiet or funny.
Alice is both strong and not kind.
Paul is calm.
Someone is kind.
Alice is tall.
John is either happy or not wise.
Someone is rich. | John is not funny. | neutral | (((~tall(paul)<~>wise(paul)))=>(?[X]:(~kind(X))))&
(![X]:(rich(X)=>(~curious(X)<~>funny(X))))&
(![X]:((tall(X)&~humble(X))<=>(~curious(X)<~>~funny(X))))&
(![X]:((~creative(X)|~tall(X))<=>(~kind(X)<~>~quiet(X))))&
((~patient(susan))<=>((~rich(john)|~kind(john))))&
(![X]:((creative(X)<~>~old(X))<=>(~brave(X)<~>old(X))))&
(![X]:(funny(X)<=>(wise(X)<~>~calm(X))))&
(![X]:(~calm(X)<=>(happy(X)|funny(X))))&
(((~quiet(susan)|~calm(susan)))<=>(?[X]:((~old(X)|~strong(X)))))&
(![X]:((creative(X)|~humble(X))=>(~tall(X)|~happy(X))))&
(![X]:((~patient(X)<~>patient(X))<=>tall(X)))&
(![X]:((~rich(X)<~>~funny(X))=>(kind(X)<~>~humble(X))))&
(((curious(lucy)|~wise(lucy)))=>(?[X]:((calm(X)&~happy(X)))))&
((?[X]:((~patient(X)<~>~curious(X))))<=>(?[X]:(~tall(X))))&
(![X]:((~tall(X)|creative(X))<=>calm(X)))&
((creative(lucy))<=>((patient(paul)&funny(paul))))&
(?[X]:((~strong(X)|~rich(X))))&
(?[X]:((quiet(X)|funny(X))))&
((strong(alice)&~kind(alice)))&
(calm(paul))&
(?[X]:(kind(X)))&
(tall(alice))&
((happy(john)<~>~wise(john)))&
(?[X]:(rich(X))) | ~funny(john) | [] | null | 0 |
Everyone who is rich or humble is either tall or not happy. Everyone who is either calm or creative is both funny and not strong. Everyone who is both tall and creative is both generous and calm. If someone is not tall or not calm then someone is humble or old and vice versa. If susan is calm then alice is both patient and calm. If someone is generous or not humble then mary is both kind and not happy. If susan is either not tall or creative then someone is either not old or humble. Everyone who is not generous or happy is not brave and vice versa. If john is both generous and happy then someone is either quiet or not calm and vice versa. Everyone who is either not generous or not funny is funny and vice versa. Everyone who is curious or not old is rich and vice versa. Everyone who is both not tall and not quiet is not humble and vice versa. Everyone who is not tall or brave is either wise or not brave and vice versa. Everyone who is either creative or not humble is both not humble and not wise. Everyone who is both calm and not tall is patient and vice versa. If someone is not happy or rich then someone is brave and vice versa. Someone is funny or rich. Someone is calm or happy. Lucy is not happy or calm. Someone is not brave. Someone is old or not tall. | Lucy is strong. | contradiction | (![X]:((rich(X)|humble(X))=>(tall(X)<~>~happy(X))))&
(![X]:((calm(X)<~>creative(X))=>(funny(X)&~strong(X))))&
(![X]:((tall(X)&creative(X))=>(generous(X)&calm(X))))&
((?[X]:((~tall(X)|~calm(X))))<=>(?[X]:((humble(X)|old(X)))))&
((calm(susan))=>((patient(alice)&calm(alice))))&
((?[X]:((generous(X)|~humble(X))))=>((kind(mary)&~happy(mary))))&
(((~tall(susan)<~>creative(susan)))=>(?[X]:((~old(X)<~>humble(X)))))&
(![X]:((~generous(X)|happy(X))<=>~brave(X)))&
(((generous(john)&happy(john)))<=>(?[X]:((quiet(X)<~>~calm(X)))))&
(![X]:((~generous(X)<~>~funny(X))<=>funny(X)))&
(![X]:((curious(X)|~old(X))<=>rich(X)))&
(![X]:((~tall(X)&~quiet(X))<=>~humble(X)))&
(![X]:((~tall(X)|brave(X))<=>(wise(X)<~>~brave(X))))&
(![X]:((creative(X)<~>~humble(X))=>(~humble(X)&~wise(X))))&
(![X]:((calm(X)&~tall(X))<=>patient(X)))&
((?[X]:((~happy(X)|rich(X))))<=>(?[X]:(brave(X))))&
(?[X]:((funny(X)|rich(X))))&
(?[X]:((calm(X)|happy(X))))&
((~happy(lucy)|calm(lucy)))&
(?[X]:(~brave(X)))&
(?[X]:((old(X)|~tall(X)))) | strong(lucy) | [
"p1",
"p5",
"p7",
"p9",
"p13",
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 6531909393605118267187640
% SZS output start Proof for 6531909393605118267187640
2. ! [X0] : ((calm(X0) <~> creative(X0)) => (~strong(X0) & funny(X0))) [input p1]
6. ? [X0] : (~humble(X0) | generous(X0)) => (~happy(mary) & kind(mary)) [input p5]
8. ! [X0] : ((happy(X0) | ~generous(X0)) <=> ~brave(X0)) [input p7]
10. ! [X0] : ((~generous(X0) <~> ~funny(X0)) <=> funny(X0)) [input p9]
14. ! [X0] : ((creative(X0) <~> ~humble(X0)) => (~wise(X0) & ~humble(X0))) [input p13]
16. ? [X0] : (rich(X0) | ~happy(X0)) <=> ? [X0] : brave(X0) [input p15]
19. calm(lucy) | ~happy(lucy) [input p18]
22. strong(lucy) [input hypothesis]
24. ? [X0] : (rich(X0) | ~happy(X0)) <=> ? [X1] : brave(X1) [rectify 16]
26. ? [X0] : (~humble(X0) | generous(X0)) => ~happy(mary) [pure predicate removal 6]
28. ! [X0] : ((~strong(X0) & funny(X0)) | (calm(X0) <=> creative(X0))) [ennf transformation 2]
32. ~happy(mary) | ! [X0] : (humble(X0) & ~generous(X0)) [ennf transformation 26]
34. ! [X0] : ((~wise(X0) & ~humble(X0)) | (creative(X0) <=> ~humble(X0))) [ennf transformation 14]
37. ! [X0] : ((~strong(X0) & funny(X0)) | ((calm(X0) | ~creative(X0)) & (creative(X0) | ~calm(X0)))) [nnf transformation 28]
46. ! [X0] : (((happy(X0) | ~generous(X0)) | brave(X0)) & (~brave(X0) | (~happy(X0) & generous(X0)))) [nnf transformation 8]
47. ! [X0] : ((happy(X0) | ~generous(X0) | brave(X0)) & (~brave(X0) | (~happy(X0) & generous(X0)))) [flattening 46]
53. ! [X0] : ((((funny(X0) | generous(X0)) & (~funny(X0) | ~generous(X0))) | ~funny(X0)) & (funny(X0) | ((~generous(X0) | funny(X0)) & (~funny(X0) | generous(X0))))) [nnf transformation 10]
60. ! [X0] : ((~wise(X0) & ~humble(X0)) | ((creative(X0) | humble(X0)) & (~humble(X0) | ~creative(X0)))) [nnf transformation 34]
61. (? [X0] : (rich(X0) | ~happy(X0)) | ! [X1] : ~brave(X1)) & (? [X1] : brave(X1) | ! [X0] : (~rich(X0) & happy(X0))) [nnf transformation 24]
62. (? [X0] : (rich(X0) | ~happy(X0)) | ! [X1] : ~brave(X1)) & (? [X2] : brave(X2) | ! [X3] : (~rich(X3) & happy(X3))) [rectify 61]
63. ? [X0] : (rich(X0) | ~happy(X0)) => (rich(sK4) | ~happy(sK4)) [choice axiom]
64. ? [X2] : brave(X2) => brave(sK5) [choice axiom]
65. ((rich(sK4) | ~happy(sK4)) | ! [X1] : ~brave(X1)) & (brave(sK5) | ! [X3] : (~rich(X3) & happy(X3))) [skolemisation 62,64,63]
80. ~strong(X0) | creative(X0) | ~calm(X0) [cnf transformation 37]
91. ~happy(mary) | humble(X0) [cnf transformation 32]
96. ~brave(X0) | generous(X0) [cnf transformation 47]
106. funny(X0) | ~generous(X0) | funny(X0) [cnf transformation 53]
107. ~funny(X0) | ~generous(X0) | ~funny(X0) [cnf transformation 53]
121. ~humble(X0) | ~humble(X0) | ~creative(X0) [cnf transformation 60]
127. brave(sK5) | happy(X3) [cnf transformation 65]
132. calm(lucy) | ~happy(lucy) [cnf transformation 19]
135. strong(lucy) [cnf transformation 22]
136. ~creative(X0) | ~humble(X0) [duplicate literal removal 121]
139. funny(X0) | ~generous(X0) [duplicate literal removal 106]
140. ~generous(X0) | ~funny(X0) [duplicate literal removal 107]
188. 12 <=> ! [X0] : humble(X0) [avatar definition]
189. humble(X0) <- (12) [avatar component clause 188]
191. 13 <=> happy(mary) [avatar definition]
193. ~happy(mary) <- (~13) [avatar component clause 191]
194. 12 | ~13 [avatar split clause 91,191,188]
196. 14 <=> ! [X0] : ~generous(X0) [avatar definition]
197. ~generous(X0) <- (14) [avatar component clause 196]
247. ~generous(X0) [subsumption resolution 139,140]
248. 14 [avatar split clause 247,196]
265. 29 <=> brave(sK5) [avatar definition]
267. brave(sK5) <- (29) [avatar component clause 265]
270. 30 <=> ! [X3] : happy(X3) [avatar definition]
271. happy(X3) <- (30) [avatar component clause 270]
272. 30 | 29 [avatar split clause 127,265,270]
292. 35 <=> happy(lucy) [avatar definition]
294. ~happy(lucy) <- (~35) [avatar component clause 292]
296. 36 <=> calm(lucy) [avatar definition]
298. calm(lucy) <- (36) [avatar component clause 296]
299. ~35 | 36 [avatar split clause 132,296,292]
309. generous(sK5) <- (29) [resolution 96,267]
310. $false <- (14, 29) [subsumption resolution 309,197]
311. ~14 | ~29 [avatar contradiction clause 310]
312. $false <- (~13, 30) [resolution 271,193]
314. $false <- (30, ~35) [resolution 271,294]
317. ~30 | 35 [avatar contradiction clause 314]
319. 13 | ~30 [avatar contradiction clause 312]
359. 42 <=> creative(lucy) [avatar definition]
361. creative(lucy) <- (42) [avatar component clause 359]
363. creative(lucy) | ~calm(lucy) [resolution 80,135]
364. creative(lucy) <- (36) [subsumption resolution 363,298]
365. 42 | ~36 [avatar split clause 364,296,359]
368. ~humble(lucy) <- (42) [resolution 361,136]
369. $false <- (12, 42) [subsumption resolution 368,189]
370. ~12 | ~42 [avatar contradiction clause 369]
371. $false [avatar sat refutation 194,248,272,299,311,317,319,365,370]
% SZS output end Proof for 6531909393605118267187640
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 mary is not strong then someone is wise or quiet.
Everyone who is both not happy and not tall is either tall or happy.
If someone is not patient then fred is either not creative or generous.
Everyone who is either not strong or quiet is both not humble and not happy and vice versa.
If mary is either humble or wise then someone is either rich or happy and vice versa.
If paul is either not quiet or strong then someone is calm or not rich and vice versa.
Everyone who is not old is wise and vice versa.
Everyone who is not old or not rich is creative and vice versa.
If mary is either not calm or strong then someone is not calm or not brave and vice versa.
If someone is either not wise or not humble then someone is wise.
Everyone who is not humble is not creative or old and vice versa.
Everyone who is not rich is humble and vice versa.
Everyone who is not happy or not calm is either not tall or not brave.
If susan is both not humble and generous then someone is both rich and not humble.
Everyone who is not tall or funny is not funny.
Everyone who is strong is not funny or not brave.
John is both not quiet and not wise.
Someone is brave.
Alice is both not wise and not generous.
Susan is not patient or strong.
Someone is not quiet or generous. | Mary is not creative. | entailment | ((~strong(mary))=>(?[X]:((wise(X)|quiet(X)))))&
(![X]:((~happy(X)&~tall(X))=>(tall(X)<~>happy(X))))&
((?[X]:(~patient(X)))=>((~creative(fred)<~>generous(fred))))&
(![X]:((~strong(X)<~>quiet(X))<=>(~humble(X)&~happy(X))))&
(((humble(mary)<~>wise(mary)))<=>(?[X]:((rich(X)<~>happy(X)))))&
(((~quiet(paul)<~>strong(paul)))<=>(?[X]:((calm(X)|~rich(X)))))&
(![X]:(~old(X)<=>wise(X)))&
(![X]:((~old(X)|~rich(X))<=>creative(X)))&
(((~calm(mary)<~>strong(mary)))<=>(?[X]:((~calm(X)|~brave(X)))))&
((?[X]:((~wise(X)<~>~humble(X))))=>(?[X]:(wise(X))))&
(![X]:(~humble(X)<=>(~creative(X)|old(X))))&
(![X]:(~rich(X)<=>humble(X)))&
(![X]:((~happy(X)|~calm(X))=>(~tall(X)<~>~brave(X))))&
(((~humble(susan)&generous(susan)))=>(?[X]:((rich(X)&~humble(X)))))&
(![X]:((~tall(X)|funny(X))=>~funny(X)))&
(![X]:(strong(X)=>(~funny(X)|~brave(X))))&
((~quiet(john)&~wise(john)))&
(?[X]:(brave(X)))&
((~wise(alice)&~generous(alice)))&
((~patient(susan)|strong(susan)))&
(?[X]:((~quiet(X)|generous(X)))) | ~creative(mary) | [
"p3",
"p4",
"p5",
"p6",
"p7",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 4463486017520204117805467
% SZS output start Proof for 4463486017520204117805467
4. ! [X0] : ((~strong(X0) <~> quiet(X0)) <=> (~happy(X0) & ~humble(X0))) [input p3]
5. (humble(mary) <~> wise(mary)) <=> ? [X0] : (rich(X0) <~> happy(X0)) [input p4]
6. (~quiet(paul) <~> strong(paul)) <=> ? [X0] : (~rich(X0) | calm(X0)) [input p5]
7. ! [X0] : (~old(X0) <=> wise(X0)) [input p6]
8. ! [X0] : ((~rich(X0) | ~old(X0)) <=> creative(X0)) [input p7]
11. ! [X0] : (~humble(X0) <=> (old(X0) | ~creative(X0))) [input p10]
12. ! [X0] : (~rich(X0) <=> humble(X0)) [input p11]
22. creative(mary) [input hypothesis]
38. ! [X0] : ((((~quiet(X0) | strong(X0)) & (quiet(X0) | ~strong(X0))) | (happy(X0) | humble(X0))) & ((~happy(X0) & ~humble(X0)) | ((~strong(X0) | ~quiet(X0)) & (quiet(X0) | strong(X0))))) [nnf transformation 4]
39. ! [X0] : ((((~quiet(X0) | strong(X0)) & (quiet(X0) | ~strong(X0))) | happy(X0) | humble(X0)) & ((~happy(X0) & ~humble(X0)) | ((~strong(X0) | ~quiet(X0)) & (quiet(X0) | strong(X0))))) [flattening 38]
40. (((~wise(mary) | ~humble(mary)) & (wise(mary) | humble(mary))) | ! [X0] : ((rich(X0) | ~happy(X0)) & (happy(X0) | ~rich(X0)))) & (? [X0] : ((~happy(X0) | ~rich(X0)) & (happy(X0) | rich(X0))) | ((humble(mary) | ~wise(mary)) & (wise(mary) | ~humble(mary)))) [nnf transformation 5]
41. (((~wise(mary) | ~humble(mary)) & (wise(mary) | humble(mary))) | ! [X0] : ((rich(X0) | ~happy(X0)) & (happy(X0) | ~rich(X0)))) & (? [X1] : ((~happy(X1) | ~rich(X1)) & (happy(X1) | rich(X1))) | ((humble(mary) | ~wise(mary)) & (wise(mary) | ~humble(mary)))) [rectify 40]
42. ? [X1] : ((~happy(X1) | ~rich(X1)) & (happy(X1) | rich(X1))) => ((~happy(sK1) | ~rich(sK1)) & (happy(sK1) | rich(sK1))) [choice axiom]
43. (((~wise(mary) | ~humble(mary)) & (wise(mary) | humble(mary))) | ! [X0] : ((rich(X0) | ~happy(X0)) & (happy(X0) | ~rich(X0)))) & (((~happy(sK1) | ~rich(sK1)) & (happy(sK1) | rich(sK1))) | ((humble(mary) | ~wise(mary)) & (wise(mary) | ~humble(mary)))) [skolemisation 41,42]
44. (((~strong(paul) | quiet(paul)) & (strong(paul) | ~quiet(paul))) | ! [X0] : (rich(X0) & ~calm(X0))) & (? [X0] : (~rich(X0) | calm(X0)) | ((~quiet(paul) | ~strong(paul)) & (strong(paul) | quiet(paul)))) [nnf transformation 6]
45. (((~strong(paul) | quiet(paul)) & (strong(paul) | ~quiet(paul))) | ! [X0] : (rich(X0) & ~calm(X0))) & (? [X1] : (~rich(X1) | calm(X1)) | ((~quiet(paul) | ~strong(paul)) & (strong(paul) | quiet(paul)))) [rectify 44]
46. ? [X1] : (~rich(X1) | calm(X1)) => (~rich(sK2) | calm(sK2)) [choice axiom]
47. (((~strong(paul) | quiet(paul)) & (strong(paul) | ~quiet(paul))) | ! [X0] : (rich(X0) & ~calm(X0))) & ((~rich(sK2) | calm(sK2)) | ((~quiet(paul) | ~strong(paul)) & (strong(paul) | quiet(paul)))) [skolemisation 45,46]
48. ! [X0] : ((~old(X0) | ~wise(X0)) & (wise(X0) | old(X0))) [nnf transformation 7]
49. ! [X0] : (((~rich(X0) | ~old(X0)) | ~creative(X0)) & (creative(X0) | (rich(X0) & old(X0)))) [nnf transformation 8]
50. ! [X0] : ((~rich(X0) | ~old(X0) | ~creative(X0)) & (creative(X0) | (rich(X0) & old(X0)))) [flattening 49]
59. ! [X0] : ((~humble(X0) | (~old(X0) & creative(X0))) & ((old(X0) | ~creative(X0)) | humble(X0))) [nnf transformation 11]
60. ! [X0] : ((~humble(X0) | (~old(X0) & creative(X0))) & (old(X0) | ~creative(X0) | humble(X0))) [flattening 59]
61. ! [X0] : ((~rich(X0) | ~humble(X0)) & (humble(X0) | rich(X0))) [nnf transformation 12]
74. ~humble(X0) | quiet(X0) | strong(X0) [cnf transformation 39]
75. ~humble(X0) | ~strong(X0) | ~quiet(X0) [cnf transformation 39]
76. ~happy(X0) | quiet(X0) | strong(X0) [cnf transformation 39]
77. ~happy(X0) | ~strong(X0) | ~quiet(X0) [cnf transformation 39]
84. wise(mary) | humble(mary) | happy(X0) | ~rich(X0) [cnf transformation 43]
86. ~wise(mary) | ~humble(mary) | happy(X0) | ~rich(X0) [cnf transformation 43]
91. strong(paul) | ~quiet(paul) | rich(X0) [cnf transformation 47]
93. ~strong(paul) | quiet(paul) | rich(X0) [cnf transformation 47]
94. old(X0) | wise(X0) [cnf transformation 48]
95. ~old(X0) | ~wise(X0) [cnf transformation 48]
96. old(X0) | creative(X0) [cnf transformation 50]
98. ~old(X0) | ~rich(X0) | ~creative(X0) [cnf transformation 50]
107. old(X0) | ~creative(X0) | humble(X0) [cnf transformation 60]
109. ~old(X0) | ~humble(X0) [cnf transformation 60]
110. rich(X0) | humble(X0) [cnf transformation 61]
111. ~rich(X0) | ~humble(X0) [cnf transformation 61]
125. creative(mary) [cnf transformation 22]
157. 8 <=> humble(mary) [avatar definition]
158. humble(mary) <- (8) [avatar component clause 157]
159. ~humble(mary) <- (~8) [avatar component clause 157]
161. 9 <=> wise(mary) [avatar definition]
162. wise(mary) <- (9) [avatar component clause 161]
163. ~wise(mary) <- (~9) [avatar component clause 161]
166. 10 <=> ! [X0] : (happy(X0) | ~rich(X0)) [avatar definition]
167. ~rich(X0) | happy(X0) <- (10) [avatar component clause 166]
168. 10 | ~8 | ~9 [avatar split clause 86,161,157,166]
170. 10 | 8 | 9 [avatar split clause 84,161,157,166]
184. 13 <=> ! [X0] : rich(X0) [avatar definition]
185. rich(X0) <- (13) [avatar component clause 184]
187. 14 <=> quiet(paul) [avatar definition]
188. ~quiet(paul) <- (~14) [avatar component clause 187]
189. quiet(paul) <- (14) [avatar component clause 187]
191. 15 <=> strong(paul) [avatar definition]
192. strong(paul) <- (15) [avatar component clause 191]
193. ~strong(paul) <- (~15) [avatar component clause 191]
194. 13 | 14 | ~15 [avatar split clause 93,191,187,184]
199. 13 | ~14 | 15 [avatar split clause 91,191,187,184]
236. 24 <=> ! [X1] : (~wise(X1) | humble(X1)) [avatar definition]
237. ~wise(X1) | humble(X1) <- (24) [avatar component clause 236]
244. 26 <=> ! [X1] : (~humble(X1) | wise(X1)) [avatar definition]
245. ~humble(X1) | wise(X1) <- (26) [avatar component clause 244]
247. old(X0) | humble(X0) [subsumption resolution 107,96]
289. ~humble(X1) | wise(X1) [resolution 109,94]
290. 26 [avatar split clause 289,244]
295. humble(X0) | happy(X0) <- (10) [resolution 167,110]
299. humble(X1) | ~wise(X1) [resolution 247,95]
300. 24 [avatar split clause 299,236]
348. ~rich(X0) | ~creative(X0) | humble(X0) [resolution 98,247]
351. ~rich(X0) | ~creative(X0) [subsumption resolution 348,111]
396. happy(X0) | ~strong(X0) | ~quiet(X0) <- (10) [resolution 295,75]
397. happy(X1) | quiet(X1) | strong(X1) <- (10) [resolution 295,74]
400. ~quiet(X0) | ~strong(X0) <- (10) [subsumption resolution 396,77]
401. quiet(X1) | strong(X1) <- (10) [subsumption resolution 397,76]
428. strong(paul) <- (10, ~14) [resolution 401,188]
434. $false <- (10, ~14, ~15) [subsumption resolution 428,193]
435. ~10 | 14 | 15 [avatar contradiction clause 434]
441. ~strong(paul) <- (10, 14) [resolution 189,400]
443. $false <- (10, 14, 15) [subsumption resolution 441,192]
444. ~10 | ~14 | ~15 [avatar contradiction clause 443]
445. ~creative(X0) <- (13) [resolution 185,351]
460. $false <- (13) [resolution 445,125]
461. ~13 [avatar contradiction clause 460]
500. wise(mary) <- (8, 26) [resolution 158,245]
503. $false <- (8, ~9, 26) [subsumption resolution 500,163]
504. ~8 | 9 | ~26 [avatar contradiction clause 503]
506. humble(mary) <- (9, 24) [resolution 162,237]
507. $false <- (~8, 9, 24) [subsumption resolution 506,159]
508. 8 | ~9 | ~24 [avatar contradiction clause 507]
509. $false [avatar sat refutation 168,170,194,199,290,300,435,444,461,504,508]
% SZS output end Proof for 4463486017520204117805467
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or kind is not funny or brave and vice versa.
If susan is either strong or humble then susan is patient or not rich and vice versa.
If someone is either old or not brave then someone is both not wise and quiet.
Everyone who is both not generous and quiet is either not generous or patient and vice versa.
Everyone who is both funny and not curious is patient or not funny and vice versa.
Everyone who is kind or old is not calm or old.
Everyone who is old is not happy or brave and vice versa.
If someone is either funny or not humble then someone is strong or not kind and vice versa.
Everyone who is kind is not tall.
If susan is either not quiet or not tall then susan is creative and vice versa.
Everyone who is either creative or not quiet is not quiet or curious.
Everyone who is funny is either not humble or creative and vice versa.
Everyone who is both not humble and kind is happy and vice versa.
Everyone who is not old or generous is not rich or patient and vice versa.
Everyone who is either not wise or creative is either not wise or not calm.
If alice is both calm and not brave then mary is strong.
Someone is either not happy or not patient.
Someone is both not brave and not creative.
Someone is old.
Lucy is not rich.
Someone is either not humble or creative.
Mary is funny or patient. | Alice is not quiet. | neutral | (![X]:((~curious(X)|kind(X))<=>(~funny(X)|brave(X))))&
(((strong(susan)<~>humble(susan)))<=>((patient(susan)|~rich(susan))))&
((?[X]:((old(X)<~>~brave(X))))=>(?[X]:((~wise(X)&quiet(X)))))&
(![X]:((~generous(X)&quiet(X))<=>(~generous(X)<~>patient(X))))&
(![X]:((funny(X)&~curious(X))<=>(patient(X)|~funny(X))))&
(![X]:((kind(X)|old(X))=>(~calm(X)|old(X))))&
(![X]:(old(X)<=>(~happy(X)|brave(X))))&
((?[X]:((funny(X)<~>~humble(X))))<=>(?[X]:((strong(X)|~kind(X)))))&
(![X]:(kind(X)=>~tall(X)))&
(((~quiet(susan)<~>~tall(susan)))<=>(creative(susan)))&
(![X]:((creative(X)<~>~quiet(X))=>(~quiet(X)|curious(X))))&
(![X]:(funny(X)<=>(~humble(X)<~>creative(X))))&
(![X]:((~humble(X)&kind(X))<=>happy(X)))&
(![X]:((~old(X)|generous(X))<=>(~rich(X)|patient(X))))&
(![X]:((~wise(X)<~>creative(X))=>(~wise(X)<~>~calm(X))))&
(((calm(alice)&~brave(alice)))=>(strong(mary)))&
(?[X]:((~happy(X)<~>~patient(X))))&
(?[X]:((~brave(X)&~creative(X))))&
(?[X]:(old(X)))&
(~rich(lucy))&
(?[X]:((~humble(X)<~>creative(X))))&
((funny(mary)|patient(mary))) | ~quiet(alice) | [] | null | 0 |
If someone is not funny or quiet then someone is both not rich and not brave and vice versa.
If someone is patient then john is either patient or not curious and vice versa.
Everyone who is both not generous and not funny is strong or not rich.
Everyone who is not kind is not humble.
Everyone who is either tall or not wise is funny and vice versa.
Everyone who is not tall or brave is either not kind or old and vice versa.
Everyone who is not patient is not humble or old and vice versa.
If someone is either not wise or not generous then lucy is both quiet and not humble and vice versa.
If lucy is patient then someone is creative or happy.
If alice is either not wise or generous then someone is both kind and patient.
Everyone who is either not quiet or brave is both generous and not patient and vice versa.
If lucy is either not funny or quiet then someone is not calm and vice versa.
Everyone who is not old is wise or old.
If paul is not creative or strong then someone is either not wise or kind and vice versa.
Everyone who is either not humble or not brave is both not old and not humble and vice versa.
If someone is both not funny and not happy then mary is not strong or not curious.
Someone is both rich and not strong.
Susan is not humble or not generous.
Someone is both not tall and not calm.
Someone is not brave.
Someone is both not kind and happy.
Mary is both not wise and not generous.
Someone is not wise or wise.
Mary is both not funny and not quiet. | Lucy is not quiet. | contradiction | ((?[X]:((~funny(X)|quiet(X))))<=>(?[X]:((~rich(X)&~brave(X)))))&
((?[X]:(patient(X)))<=>((patient(john)<~>~curious(john))))&
(![X]:((~generous(X)&~funny(X))=>(strong(X)|~rich(X))))&
(![X]:(~kind(X)=>~humble(X)))&
(![X]:((tall(X)<~>~wise(X))<=>funny(X)))&
(![X]:((~tall(X)|brave(X))<=>(~kind(X)<~>old(X))))&
(![X]:(~patient(X)<=>(~humble(X)|old(X))))&
((?[X]:((~wise(X)<~>~generous(X))))<=>((quiet(lucy)&~humble(lucy))))&
((patient(lucy))=>(?[X]:((creative(X)|happy(X)))))&
(((~wise(alice)<~>generous(alice)))=>(?[X]:((kind(X)&patient(X)))))&
(![X]:((~quiet(X)<~>brave(X))<=>(generous(X)&~patient(X))))&
(((~funny(lucy)<~>quiet(lucy)))<=>(?[X]:(~calm(X))))&
(![X]:(~old(X)=>(wise(X)|old(X))))&
(((~creative(paul)|strong(paul)))<=>(?[X]:((~wise(X)<~>kind(X)))))&
(![X]:((~humble(X)<~>~brave(X))<=>(~old(X)&~humble(X))))&
((?[X]:((~funny(X)&~happy(X))))=>((~strong(mary)|~curious(mary))))&
(?[X]:((rich(X)&~strong(X))))&
((~humble(susan)|~generous(susan)))&
(?[X]:((~tall(X)&~calm(X))))&
(?[X]:(~brave(X)))&
(?[X]:((~kind(X)&happy(X))))&
((~wise(mary)&~generous(mary)))&
(?[X]:((~wise(X)|wise(X))))&
((~funny(mary)&~quiet(mary))) | ~quiet(lucy) | [
"p5",
"p6",
"p7",
"p9",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3487323723051120327870840
% SZS output start Proof for 3487323723051120327870840
6. ! [X0] : ((brave(X0) | ~tall(X0)) <=> (~kind(X0) <~> old(X0))) [input p5]
7. ! [X0] : (~patient(X0) <=> (old(X0) | ~humble(X0))) [input p6]
8. ? [X0] : (~wise(X0) <~> ~generous(X0)) <=> (~humble(lucy) & quiet(lucy)) [input p7]
10. (~wise(alice) <~> generous(alice)) => ? [X0] : (patient(X0) & kind(X0)) [input p9]
15. ! [X0] : ((~humble(X0) <~> ~brave(X0)) <=> (~humble(X0) & ~old(X0))) [input p14]
25. ~quiet(lucy) [input hypothesis]
33. ? [X0] : (patient(X0) & kind(X0)) | (~wise(alice) <=> generous(alice)) [ennf transformation 10]
46. ! [X0] : (((brave(X0) | ~tall(X0)) | ((~kind(X0) | ~old(X0)) & (old(X0) | kind(X0)))) & (((~old(X0) | kind(X0)) & (old(X0) | ~kind(X0))) | (~brave(X0) & tall(X0)))) [nnf transformation 6]
47. ! [X0] : ((brave(X0) | ~tall(X0) | ((~kind(X0) | ~old(X0)) & (old(X0) | kind(X0)))) & (((~old(X0) | kind(X0)) & (old(X0) | ~kind(X0))) | (~brave(X0) & tall(X0)))) [flattening 46]
48. ! [X0] : ((~patient(X0) | (~old(X0) & humble(X0))) & ((old(X0) | ~humble(X0)) | patient(X0))) [nnf transformation 7]
49. ! [X0] : ((~patient(X0) | (~old(X0) & humble(X0))) & (old(X0) | ~humble(X0) | patient(X0))) [flattening 48]
50. (? [X0] : ((generous(X0) | wise(X0)) & (~generous(X0) | ~wise(X0))) | (humble(lucy) | ~quiet(lucy))) & ((~humble(lucy) & quiet(lucy)) | ! [X0] : ((~wise(X0) | generous(X0)) & (~generous(X0) | wise(X0)))) [nnf transformation 8]
51. (? [X0] : ((generous(X0) | wise(X0)) & (~generous(X0) | ~wise(X0))) | humble(lucy) | ~quiet(lucy)) & ((~humble(lucy) & quiet(lucy)) | ! [X0] : ((~wise(X0) | generous(X0)) & (~generous(X0) | wise(X0)))) [flattening 50]
52. (? [X0] : ((generous(X0) | wise(X0)) & (~generous(X0) | ~wise(X0))) | humble(lucy) | ~quiet(lucy)) & ((~humble(lucy) & quiet(lucy)) | ! [X1] : ((~wise(X1) | generous(X1)) & (~generous(X1) | wise(X1)))) [rectify 51]
53. ? [X0] : ((generous(X0) | wise(X0)) & (~generous(X0) | ~wise(X0))) => ((generous(sK3) | wise(sK3)) & (~generous(sK3) | ~wise(sK3))) [choice axiom]
54. (((generous(sK3) | wise(sK3)) & (~generous(sK3) | ~wise(sK3))) | humble(lucy) | ~quiet(lucy)) & ((~humble(lucy) & quiet(lucy)) | ! [X1] : ((~wise(X1) | generous(X1)) & (~generous(X1) | wise(X1)))) [skolemisation 52,53]
55. ? [X0] : (patient(X0) & kind(X0)) | ((~wise(alice) | ~generous(alice)) & (generous(alice) | wise(alice))) [nnf transformation 33]
56. ? [X0] : (patient(X0) & kind(X0)) => (patient(sK4) & kind(sK4)) [choice axiom]
57. (patient(sK4) & kind(sK4)) | ((~wise(alice) | ~generous(alice)) & (generous(alice) | wise(alice))) [skolemisation 55,56]
69. ! [X0] : ((((brave(X0) | humble(X0)) & (~brave(X0) | ~humble(X0))) | (humble(X0) | old(X0))) & ((~humble(X0) & ~old(X0)) | ((~humble(X0) | brave(X0)) & (~brave(X0) | humble(X0))))) [nnf transformation 15]
70. ! [X0] : ((((brave(X0) | humble(X0)) & (~brave(X0) | ~humble(X0))) | humble(X0) | old(X0)) & ((~humble(X0) & ~old(X0)) | ((~humble(X0) | brave(X0)) & (~brave(X0) | humble(X0))))) [flattening 69]
97. ~kind(X0) | old(X0) | ~brave(X0) [cnf transformation 47]
103. ~patient(X0) | humble(X0) [cnf transformation 49]
104. ~old(X0) | ~patient(X0) [cnf transformation 49]
105. quiet(lucy) | ~generous(X1) | wise(X1) [cnf transformation 54]
106. quiet(lucy) | ~wise(X1) | generous(X1) [cnf transformation 54]
111. kind(sK4) | generous(alice) | wise(alice) [cnf transformation 57]
112. kind(sK4) | ~wise(alice) | ~generous(alice) [cnf transformation 57]
113. patient(sK4) | generous(alice) | wise(alice) [cnf transformation 57]
114. patient(sK4) | ~wise(alice) | ~generous(alice) [cnf transformation 57]
135. ~humble(X0) | ~humble(X0) | brave(X0) [cnf transformation 70]
150. ~quiet(lucy) [cnf transformation 25]
151. ~humble(X0) | brave(X0) [duplicate literal removal 135]
204. 12 <=> quiet(lucy) [avatar definition]
222. 16 <=> ! [X1] : (~wise(X1) | generous(X1)) [avatar definition]
223. ~wise(X1) | generous(X1) <- (16) [avatar component clause 222]
226. 17 <=> ! [X1] : (~generous(X1) | wise(X1)) [avatar definition]
227. ~generous(X1) | wise(X1) <- (17) [avatar component clause 226]
229. 16 | 12 [avatar split clause 106,204,222]
230. 17 | 12 [avatar split clause 105,204,226]
232. 18 <=> generous(alice) [avatar definition]
233. generous(alice) <- (18) [avatar component clause 232]
234. ~generous(alice) <- (~18) [avatar component clause 232]
236. 19 <=> wise(alice) [avatar definition]
237. wise(alice) <- (19) [avatar component clause 236]
238. ~wise(alice) <- (~19) [avatar component clause 236]
240. 20 <=> patient(sK4) [avatar definition]
242. patient(sK4) <- (20) [avatar component clause 240]
243. ~18 | ~19 | 20 [avatar split clause 114,240,236,232]
244. 19 | 18 | 20 [avatar split clause 113,240,232,236]
246. 21 <=> kind(sK4) [avatar definition]
248. kind(sK4) <- (21) [avatar component clause 246]
249. ~18 | ~19 | 21 [avatar split clause 112,246,236,232]
250. 19 | 18 | 21 [avatar split clause 111,246,232,236]
303. ~12 [avatar split clause 150,204]
308. wise(alice) <- (17, 18) [resolution 227,233]
309. $false <- (17, 18, ~19) [subsumption resolution 308,238]
310. ~17 | ~18 | 19 [avatar contradiction clause 309]
311. generous(alice) <- (16, 19) [resolution 237,223]
312. $false <- (16, ~18, 19) [subsumption resolution 311,234]
313. ~16 | 18 | ~19 [avatar contradiction clause 312]
314. humble(sK4) <- (20) [resolution 242,103]
315. brave(sK4) <- (20) [resolution 314,151]
361. 40 <=> old(sK4) [avatar definition]
363. old(sK4) <- (40) [avatar component clause 361]
376. old(sK4) | ~brave(sK4) <- (21) [resolution 97,248]
379. old(sK4) <- (20, 21) [subsumption resolution 376,315]
380. 40 | ~20 | ~21 [avatar split clause 379,246,240,361]
381. ~patient(sK4) <- (40) [resolution 363,104]
382. $false <- (20, 40) [subsumption resolution 381,242]
383. ~20 | ~40 [avatar contradiction clause 382]
384. $false [avatar sat refutation 229,230,243,244,249,250,303,310,313,380,383]
% SZS output end Proof for 3487323723051120327870840
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich or curious is both not old and not generous and vice versa. Everyone who is both generous and patient is both kind and not creative. Everyone who is old or patient is both humble and quiet and vice versa. Everyone who is not patient is not funny or not curious. Everyone who is either not calm or kind is either not patient or curious. If john is not strong or not generous then someone is happy. Everyone who is quiet is not humble. Everyone who is both not old and kind is both generous and not humble and vice versa. Everyone who is both kind and generous is both not funny and quiet and vice versa. Everyone who is happy or not rich is not old. Everyone who is either not tall or old is rich or not old and vice versa. If john is curious or strong then fred is both not old and not curious and vice versa. Everyone who is both funny and not calm is not old or not wise and vice versa. If paul is not happy then someone is both not curious and not humble and vice versa. If mary is either not kind or not brave then lucy is not creative and vice versa. If susan is not creative or not happy then someone is brave or not calm. Someone is patient or wise. Someone is not calm. Paul is wise. Lucy is either not funny or not old. Someone is kind or brave. John is both not tall and not calm. Someone is either not rich or patient. Lucy is quiet or calm. | Lucy is quiet. | entailment | (![X]:((rich(X)|curious(X))<=>(~old(X)&~generous(X))))&
(![X]:((generous(X)&patient(X))=>(kind(X)&~creative(X))))&
(![X]:((old(X)|patient(X))<=>(humble(X)&quiet(X))))&
(![X]:(~patient(X)=>(~funny(X)|~curious(X))))&
(![X]:((~calm(X)<~>kind(X))=>(~patient(X)<~>curious(X))))&
(((~strong(john)|~generous(john)))=>(?[X]:(happy(X))))&
(![X]:(quiet(X)=>~humble(X)))&
(![X]:((~old(X)&kind(X))<=>(generous(X)&~humble(X))))&
(![X]:((kind(X)&generous(X))<=>(~funny(X)&quiet(X))))&
(![X]:((happy(X)|~rich(X))=>~old(X)))&
(![X]:((~tall(X)<~>old(X))<=>(rich(X)|~old(X))))&
(((curious(john)|strong(john)))<=>((~old(fred)&~curious(fred))))&
(![X]:((funny(X)&~calm(X))<=>(~old(X)|~wise(X))))&
((~happy(paul))<=>(?[X]:((~curious(X)&~humble(X)))))&
(((~kind(mary)<~>~brave(mary)))<=>(~creative(lucy)))&
(((~creative(susan)|~happy(susan)))=>(?[X]:((brave(X)|~calm(X)))))&
(?[X]:((patient(X)|wise(X))))&
(?[X]:(~calm(X)))&
(wise(paul))&
((~funny(lucy)<~>~old(lucy)))&
(?[X]:((kind(X)|brave(X))))&
((~tall(john)&~calm(john)))&
(?[X]:((~rich(X)<~>patient(X))))&
((quiet(lucy)|calm(lucy))) | quiet(lucy) | [
"p0",
"p9",
"p12",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 7075082342090616062300324
% SZS output start Proof for 7075082342090616062300324
1. ! [X0] : ((curious(X0) | rich(X0)) <=> (~generous(X0) & ~old(X0))) [input p0]
10. ! [X0] : ((~rich(X0) | happy(X0)) => ~old(X0)) [input p9]
13. ! [X0] : ((~calm(X0) & funny(X0)) <=> (~wise(X0) | ~old(X0))) [input p12]
24. calm(lucy) | quiet(lucy) [input p23]
25. ~quiet(lucy) [input hypothesis]
33. ! [X0] : (~old(X0) | (rich(X0) & ~happy(X0))) [ennf transformation 10]
35. ! [X0] : (((curious(X0) | rich(X0)) | (generous(X0) | old(X0))) & ((~generous(X0) & ~old(X0)) | (~curious(X0) & ~rich(X0)))) [nnf transformation 1]
36. ! [X0] : ((curious(X0) | rich(X0) | generous(X0) | old(X0)) & ((~generous(X0) & ~old(X0)) | (~curious(X0) & ~rich(X0)))) [flattening 35]
50. ! [X0] : (((~calm(X0) & funny(X0)) | (wise(X0) & old(X0))) & ((~wise(X0) | ~old(X0)) | (calm(X0) | ~funny(X0)))) [nnf transformation 13]
51. ! [X0] : (((~calm(X0) & funny(X0)) | (wise(X0) & old(X0))) & (~wise(X0) | ~old(X0) | calm(X0) | ~funny(X0))) [flattening 50]
69. ~old(X0) | ~rich(X0) [cnf transformation 36]
98. ~old(X0) | rich(X0) [cnf transformation 33]
113. ~calm(X0) | old(X0) [cnf transformation 51]
134. calm(lucy) | quiet(lucy) [cnf transformation 24]
135. ~quiet(lucy) [cnf transformation 25]
152. ~old(X0) [subsumption resolution 98,69]
166. ~calm(X0) [subsumption resolution 113,152]
230. quiet(lucy) [subsumption resolution 134,166]
231. $false [subsumption resolution 135,230]
% SZS output end Proof for 7075082342090616062300324
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not curious or quiet then john is creative or tall and vice versa.
Everyone who is either calm or not humble is wise and vice versa.
If someone is not tall then someone is not happy and vice versa.
Everyone who is happy or not tall is rich or not quiet and vice versa.
Everyone who is either not old or not wise is not calm and vice versa.
If someone is happy then john is both not creative and humble and vice versa.
Everyone who is either not old or kind is not wise and vice versa.
If lucy is both old and not tall then someone is not humble.
If john is either not curious or not generous then someone is either not funny or not happy and vice versa.
If paul is both not happy and not brave then someone is either tall or patient and vice versa.
If someone is both not creative and patient then john is kind or not curious.
Everyone who is either funny or not quiet is calm or not funny and vice versa.
If someone is both generous and not rich then mary is either strong or not curious and vice versa.
Everyone who is either not creative or not humble is both humble and generous.
Everyone who is not tall is either not old or brave and vice versa.
Everyone who is not wise or not quiet is both not tall and quiet.
Alice is rich.
Someone is old.
Someone is both not strong and not wise.
Susan is not kind.
Fred is not rich.
John is both not patient and old.
Someone is either rich or not curious. | Lucy is not generous. | neutral | ((?[X]:((~curious(X)<~>quiet(X))))<=>((creative(john)|tall(john))))&
(![X]:((calm(X)<~>~humble(X))<=>wise(X)))&
((?[X]:(~tall(X)))<=>(?[X]:(~happy(X))))&
(![X]:((happy(X)|~tall(X))<=>(rich(X)|~quiet(X))))&
(![X]:((~old(X)<~>~wise(X))<=>~calm(X)))&
((?[X]:(happy(X)))<=>((~creative(john)&humble(john))))&
(![X]:((~old(X)<~>kind(X))<=>~wise(X)))&
(((old(lucy)&~tall(lucy)))=>(?[X]:(~humble(X))))&
(((~curious(john)<~>~generous(john)))<=>(?[X]:((~funny(X)<~>~happy(X)))))&
(((~happy(paul)&~brave(paul)))<=>(?[X]:((tall(X)<~>patient(X)))))&
((?[X]:((~creative(X)&patient(X))))=>((kind(john)|~curious(john))))&
(![X]:((funny(X)<~>~quiet(X))<=>(calm(X)|~funny(X))))&
((?[X]:((generous(X)&~rich(X))))<=>((strong(mary)<~>~curious(mary))))&
(![X]:((~creative(X)<~>~humble(X))=>(humble(X)&generous(X))))&
(![X]:(~tall(X)<=>(~old(X)<~>brave(X))))&
(![X]:((~wise(X)|~quiet(X))=>(~tall(X)&quiet(X))))&
(rich(alice))&
(?[X]:(old(X)))&
(?[X]:((~strong(X)&~wise(X))))&
(~kind(susan))&
(~rich(fred))&
((~patient(john)&old(john)))&
(?[X]:((rich(X)<~>~curious(X)))) | ~generous(lucy) | [] | null | 0 |
Everyone who is patient or not quiet is both not curious and patient and vice versa.
Everyone who is both brave and tall is either not calm or quiet.
If someone is either generous or humble then someone is not humble and vice versa.
Everyone who is either not strong or not kind is not creative and vice versa.
If mary is either old or strong then fred is humble.
If someone is both creative and curious then lucy is tall.
If someone is rich or not quiet then john is rich or kind and vice versa.
If someone is either strong or not generous then fred is strong and vice versa.
If someone is both happy and not creative then fred is either not humble or not funny.
Everyone who is not quiet or not happy is either not wise or not quiet and vice versa.
Everyone who is not patient is both not wise and not strong and vice versa.
If someone is not strong then someone is wise or not creative and vice versa.
If someone is both not happy and not creative then someone is not brave and vice versa.
Everyone who is not funny or not creative is both not humble and happy and vice versa.
Everyone who is both not creative and not tall is either not quiet or tall.
Everyone who is wise or not creative is not curious or not kind and vice versa.
Someone is either not funny or not rich.
Someone is not old or not curious.
Someone is not tall or not rich.
Someone is not curious.
Someone is rich.
Lucy is patient or tall.
Lucy is either happy or brave.
Mary is not curious or not quiet. | Fred is brave. | entailment | (![X]:((patient(X)|~quiet(X))<=>(~curious(X)&patient(X))))&
(![X]:((brave(X)&tall(X))=>(~calm(X)<~>quiet(X))))&
((?[X]:((generous(X)<~>humble(X))))<=>(?[X]:(~humble(X))))&
(![X]:((~strong(X)<~>~kind(X))<=>~creative(X)))&
(((old(mary)<~>strong(mary)))=>(humble(fred)))&
((?[X]:((creative(X)&curious(X))))=>(tall(lucy)))&
((?[X]:((rich(X)|~quiet(X))))<=>((rich(john)|kind(john))))&
((?[X]:((strong(X)<~>~generous(X))))<=>(strong(fred)))&
((?[X]:((happy(X)&~creative(X))))=>((~humble(fred)<~>~funny(fred))))&
(![X]:((~quiet(X)|~happy(X))<=>(~wise(X)<~>~quiet(X))))&
(![X]:(~patient(X)<=>(~wise(X)&~strong(X))))&
((?[X]:(~strong(X)))<=>(?[X]:((wise(X)|~creative(X)))))&
((?[X]:((~happy(X)&~creative(X))))<=>(?[X]:(~brave(X))))&
(![X]:((~funny(X)|~creative(X))<=>(~humble(X)&happy(X))))&
(![X]:((~creative(X)&~tall(X))=>(~quiet(X)<~>tall(X))))&
(![X]:((wise(X)|~creative(X))<=>(~curious(X)|~kind(X))))&
(?[X]:((~funny(X)<~>~rich(X))))&
(?[X]:((~old(X)|~curious(X))))&
(?[X]:((~tall(X)|~rich(X))))&
(?[X]:(~curious(X)))&
(?[X]:(rich(X)))&
((patient(lucy)|tall(lucy)))&
((happy(lucy)<~>brave(lucy)))&
((~curious(mary)|~quiet(mary))) | brave(fred) | [
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 1685012279025022245652686
% SZS output start Proof for 1685012279025022245652686
13. ? [X0] : (~creative(X0) & ~happy(X0)) <=> ? [X0] : ~brave(X0) [input p12]
14. ! [X0] : ((~creative(X0) | ~funny(X0)) <=> (happy(X0) & ~humble(X0))) [input p13]
25. ~brave(fred) [input hypothesis]
28. ? [X0] : (~creative(X0) & ~happy(X0)) <=> ? [X1] : ~brave(X1) [rectify 13]
65. (? [X0] : (~creative(X0) & ~happy(X0)) | ! [X1] : brave(X1)) & (? [X1] : ~brave(X1) | ! [X0] : (creative(X0) | happy(X0))) [nnf transformation 28]
66. (? [X0] : (~creative(X0) & ~happy(X0)) | ! [X1] : brave(X1)) & (? [X2] : ~brave(X2) | ! [X3] : (creative(X3) | happy(X3))) [rectify 65]
67. ? [X0] : (~creative(X0) & ~happy(X0)) => (~creative(sK6) & ~happy(sK6)) [choice axiom]
68. ? [X2] : ~brave(X2) => ~brave(sK7) [choice axiom]
69. ((~creative(sK6) & ~happy(sK6)) | ! [X1] : brave(X1)) & (~brave(sK7) | ! [X3] : (creative(X3) | happy(X3))) [skolemisation 66,68,67]
70. ! [X0] : (((~creative(X0) | ~funny(X0)) | (~happy(X0) | humble(X0))) & ((happy(X0) & ~humble(X0)) | (creative(X0) & funny(X0)))) [nnf transformation 14]
71. ! [X0] : ((~creative(X0) | ~funny(X0) | ~happy(X0) | humble(X0)) & ((happy(X0) & ~humble(X0)) | (creative(X0) & funny(X0)))) [flattening 70]
128. ~happy(sK6) | brave(X1) [cnf transformation 69]
129. ~creative(sK6) | brave(X1) [cnf transformation 69]
133. happy(X0) | creative(X0) [cnf transformation 71]
151. ~brave(fred) [cnf transformation 25]
284. 31 <=> ! [X1] : brave(X1) [avatar definition]
285. brave(X1) <- (31) [avatar component clause 284]
287. 32 <=> creative(sK6) [avatar definition]
290. 31 | ~32 [avatar split clause 129,287,284]
292. 33 <=> happy(sK6) [avatar definition]
294. ~happy(sK6) <- (~33) [avatar component clause 292]
295. 31 | ~33 [avatar split clause 128,292,284]
297. 34 <=> ! [X3] : (creative(X3) | happy(X3)) [avatar definition]
298. happy(X3) | creative(X3) <- (34) [avatar component clause 297]
304. 34 [avatar split clause 133,297]
357. creative(sK6) <- (~33, 34) [resolution 298,294]
360. 32 | 33 | ~34 [avatar split clause 357,297,292,287]
361. $false <- (31) [resolution 285,151]
364. ~31 [avatar contradiction clause 361]
365. $false [avatar sat refutation 290,295,304,360,364]
% SZS output end Proof for 1685012279025022245652686
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise or rich is both strong and not tall. Everyone who is either not curious or strong is not kind and vice versa. If paul is either not kind or not strong then mary is not old or brave and vice versa. Everyone who is either not old or not humble is both rich and not funny and vice versa. If someone is strong then john is generous or quiet and vice versa. Everyone who is either patient or not brave is not tall or old. Everyone who is either not tall or generous is not quiet and vice versa. If someone is brave then someone is kind or patient and vice versa. Everyone who is kind or not kind is humble and vice versa. Everyone who is either rich or not calm is not wise or creative. If someone is either brave or curious then alice is brave or funny. If paul is either quiet or not creative then mary is humble. Everyone who is not curious or kind is not patient or not rich and vice versa. Everyone who is both not humble and happy is both not kind and not curious. If someone is happy or not humble then lucy is either calm or not patient. If lucy is either happy or rich then someone is either calm or curious and vice versa. Mary is either humble or wise. Someone is both not calm and rich. John is either not funny or not old. Susan is patient or quiet. Someone is both creative and not happy. | Paul is not strong. | neutral | (![X]:((wise(X)<~>rich(X))=>(strong(X)&~tall(X))))&
(![X]:((~curious(X)<~>strong(X))<=>~kind(X)))&
(((~kind(paul)<~>~strong(paul)))<=>((~old(mary)|brave(mary))))&
(![X]:((~old(X)<~>~humble(X))<=>(rich(X)&~funny(X))))&
((?[X]:(strong(X)))<=>((generous(john)|quiet(john))))&
(![X]:((patient(X)<~>~brave(X))=>(~tall(X)|old(X))))&
(![X]:((~tall(X)<~>generous(X))<=>~quiet(X)))&
((?[X]:(brave(X)))<=>(?[X]:((kind(X)|patient(X)))))&
(![X]:((kind(X)|~kind(X))<=>humble(X)))&
(![X]:((rich(X)<~>~calm(X))=>(~wise(X)|creative(X))))&
((?[X]:((brave(X)<~>curious(X))))=>((brave(alice)|funny(alice))))&
(((quiet(paul)<~>~creative(paul)))=>(humble(mary)))&
(![X]:((~curious(X)|kind(X))<=>(~patient(X)|~rich(X))))&
(![X]:((~humble(X)&happy(X))=>(~kind(X)&~curious(X))))&
((?[X]:((happy(X)|~humble(X))))=>((calm(lucy)<~>~patient(lucy))))&
(((happy(lucy)<~>rich(lucy)))<=>(?[X]:((calm(X)<~>curious(X)))))&
((humble(mary)<~>wise(mary)))&
(?[X]:((~calm(X)&rich(X))))&
((~funny(john)<~>~old(john)))&
((patient(susan)|quiet(susan)))&
(?[X]:((creative(X)&~happy(X)))) | ~strong(paul) | [] | null | 0 |
If fred is both not creative and funny then john is either not brave or not funny and vice versa. If someone is both kind and funny then someone is both patient and not tall. Everyone who is not kind or not creative is both calm and not patient and vice versa. Everyone who is generous or not kind is either not generous or not brave. If alice is both kind and funny then alice is not calm and vice versa. Everyone who is both not patient and humble is funny and vice versa. If someone is not patient then alice is not old or not wise and vice versa. If susan is either not humble or not funny then someone is both rich and not old. Everyone who is both quiet and not funny is either curious or not generous and vice versa. Everyone who is both tall and not generous is creative or not happy and vice versa. Everyone who is not curious or wise is not creative and vice versa. Everyone who is wise is strong. Everyone who is humble or not rich is old and vice versa. Everyone who is either not generous or strong is either tall or curious and vice versa. Everyone who is either not rich or not wise is creative or not quiet and vice versa. If someone is not curious then someone is both not patient and not tall. John is either not rich or not calm. Someone is not rich or not calm. Alice is either not creative or not kind. Alice is brave or old. Alice is either generous or not funny. Someone is both humble and wise. | John is not calm. | neutral | (((~creative(fred)&funny(fred)))<=>((~brave(john)<~>~funny(john))))&
((?[X]:((kind(X)&funny(X))))=>(?[X]:((patient(X)&~tall(X)))))&
(![X]:((~kind(X)|~creative(X))<=>(calm(X)&~patient(X))))&
(![X]:((generous(X)|~kind(X))=>(~generous(X)<~>~brave(X))))&
(((kind(alice)&funny(alice)))<=>(~calm(alice)))&
(![X]:((~patient(X)&humble(X))<=>funny(X)))&
((?[X]:(~patient(X)))<=>((~old(alice)|~wise(alice))))&
(((~humble(susan)<~>~funny(susan)))=>(?[X]:((rich(X)&~old(X)))))&
(![X]:((quiet(X)&~funny(X))<=>(curious(X)<~>~generous(X))))&
(![X]:((tall(X)&~generous(X))<=>(creative(X)|~happy(X))))&
(![X]:((~curious(X)|wise(X))<=>~creative(X)))&
(![X]:(wise(X)=>strong(X)))&
(![X]:((humble(X)|~rich(X))<=>old(X)))&
(![X]:((~generous(X)<~>strong(X))<=>(tall(X)<~>curious(X))))&
(![X]:((~rich(X)<~>~wise(X))<=>(creative(X)|~quiet(X))))&
((?[X]:(~curious(X)))=>(?[X]:((~patient(X)&~tall(X)))))&
((~rich(john)<~>~calm(john)))&
(?[X]:((~rich(X)|~calm(X))))&
((~creative(alice)<~>~kind(alice)))&
((brave(alice)|old(alice)))&
((generous(alice)<~>~funny(alice)))&
(?[X]:((humble(X)&wise(X)))) | ~calm(john) | [] | null | 0 |
If someone is not humble then someone is both calm and not happy.
If fred is tall then paul is either old or not happy.
Everyone who is either not brave or quiet is curious or not funny and vice versa.
If paul is not humble or old then someone is creative or not humble and vice versa.
If someone is either not creative or not old then someone is both not old and strong and vice versa.
Everyone who is not rich is humble or not generous.
Everyone who is not generous is not strong and vice versa.
Everyone who is both strong and not happy is old and vice versa.
Everyone who is old is not tall or not humble and vice versa.
Everyone who is both funny and not patient is both not funny and not strong.
If someone is happy then someone is both not kind and patient and vice versa.
Everyone who is quiet or calm is not funny and vice versa.
Everyone who is either funny or strong is kind or brave.
If someone is either not old or humble then paul is either happy or not curious.
If someone is both not patient and not rich then paul is funny.
Everyone who is not generous or quiet is either old or rich and vice versa.
Someone is not humble or funny.
Someone is both rich and not creative.
John is rich.
Someone is wise.
Someone is either old or brave. | Paul is not humble. | neutral | ((?[X]:(~humble(X)))=>(?[X]:((calm(X)&~happy(X)))))&
((tall(fred))=>((old(paul)<~>~happy(paul))))&
(![X]:((~brave(X)<~>quiet(X))<=>(curious(X)|~funny(X))))&
(((~humble(paul)|old(paul)))<=>(?[X]:((creative(X)|~humble(X)))))&
((?[X]:((~creative(X)<~>~old(X))))<=>(?[X]:((~old(X)&strong(X)))))&
(![X]:(~rich(X)=>(humble(X)|~generous(X))))&
(![X]:(~generous(X)<=>~strong(X)))&
(![X]:((strong(X)&~happy(X))<=>old(X)))&
(![X]:(old(X)<=>(~tall(X)|~humble(X))))&
(![X]:((funny(X)&~patient(X))=>(~funny(X)&~strong(X))))&
((?[X]:(happy(X)))<=>(?[X]:((~kind(X)&patient(X)))))&
(![X]:((quiet(X)|calm(X))<=>~funny(X)))&
(![X]:((funny(X)<~>strong(X))=>(kind(X)|brave(X))))&
((?[X]:((~old(X)<~>humble(X))))=>((happy(paul)<~>~curious(paul))))&
((?[X]:((~patient(X)&~rich(X))))=>(funny(paul)))&
(![X]:((~generous(X)|quiet(X))<=>(old(X)<~>rich(X))))&
(?[X]:((~humble(X)|funny(X))))&
(?[X]:((rich(X)&~creative(X))))&
(rich(john))&
(?[X]:(wise(X)))&
(?[X]:((old(X)<~>brave(X)))) | ~humble(paul) | [] | null | 0 |
Everyone who is either funny or patient is both not kind and wise.
Everyone who is curious is both brave and not brave and vice versa.
If someone is wise or old then someone is not funny.
Everyone who is not rich is either not old or funny and vice versa.
Everyone who is either not rich or patient is both brave and not tall.
If someone is both not patient and not wise then someone is either not wise or tall.
If alice is either old or curious then paul is not tall or not generous.
If someone is not strong then alice is either humble or wise.
Everyone who is happy is patient.
Everyone who is both patient and funny is either not strong or calm and vice versa.
Everyone who is creative is not curious or not tall.
Everyone who is not humble or old is both not generous and calm.
If john is both not calm and tall then someone is both not funny and brave and vice versa.
If someone is kind then mary is not patient and vice versa.
If lucy is either curious or funny then someone is not creative.
Everyone who is not strong is either curious or generous.
Someone is humble.
Mary is both quiet and happy.
Someone is kind or not quiet.
Fred is generous.
Someone is either strong or generous.
John is not patient or not wise.
Mary is strong.
Someone is either wise or humble. | Lucy is not curious. | entailment | (![X]:((funny(X)<~>patient(X))=>(~kind(X)&wise(X))))&
(![X]:(curious(X)<=>(brave(X)&~brave(X))))&
((?[X]:((wise(X)|old(X))))=>(?[X]:(~funny(X))))&
(![X]:(~rich(X)<=>(~old(X)<~>funny(X))))&
(![X]:((~rich(X)<~>patient(X))=>(brave(X)&~tall(X))))&
((?[X]:((~patient(X)&~wise(X))))=>(?[X]:((~wise(X)<~>tall(X)))))&
(((old(alice)<~>curious(alice)))=>((~tall(paul)|~generous(paul))))&
((?[X]:(~strong(X)))=>((humble(alice)<~>wise(alice))))&
(![X]:(happy(X)=>patient(X)))&
(![X]:((patient(X)&funny(X))<=>(~strong(X)<~>calm(X))))&
(![X]:(creative(X)=>(~curious(X)|~tall(X))))&
(![X]:((~humble(X)|old(X))=>(~generous(X)&calm(X))))&
(((~calm(john)&tall(john)))<=>(?[X]:((~funny(X)&brave(X)))))&
((?[X]:(kind(X)))<=>(~patient(mary)))&
(((curious(lucy)<~>funny(lucy)))=>(?[X]:(~creative(X))))&
(![X]:(~strong(X)=>(curious(X)<~>generous(X))))&
(?[X]:(humble(X)))&
((quiet(mary)&happy(mary)))&
(?[X]:((kind(X)|~quiet(X))))&
(generous(fred))&
(?[X]:((strong(X)<~>generous(X))))&
((~patient(john)|~wise(john)))&
(strong(mary))&
(?[X]:((wise(X)<~>humble(X)))) | ~curious(lucy) | [
"p1",
"hypothesis"
] | % SZS status Unsatisfiable for 978868877679426336503991
% SZS output start Proof for 978868877679426336503991
2. ! [X0] : (curious(X0) <=> (~brave(X0) & brave(X0))) [input p1]
25. curious(lucy) [input hypothesis]
41. ! [X0] : ((curious(X0) | (brave(X0) | ~brave(X0))) & ((~brave(X0) & brave(X0)) | ~curious(X0))) [nnf transformation 2]
42. ! [X0] : ((curious(X0) | brave(X0) | ~brave(X0)) & ((~brave(X0) & brave(X0)) | ~curious(X0))) [flattening 41]
80. brave(X0) | ~curious(X0) [cnf transformation 42]
81. ~brave(X0) | ~curious(X0) [cnf transformation 42]
129. curious(lucy) [cnf transformation 25]
130. ~curious(X0) [subsumption resolution 80,81]
257. $false [subsumption resolution 129,130]
% SZS output end Proof for 978868877679426336503991
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
If alice is either brave or not humble then susan is both humble and not strong. Everyone who is both not generous and quiet is not generous or brave. Everyone who is patient is both not patient and not humble and vice versa. Everyone who is not rich or quiet is creative and vice versa. Everyone who is both not happy and not strong is generous or wise and vice versa. If someone is calm or creative then someone is either happy or not wise and vice versa. If someone is strong then someone is not generous. If fred is not brave or patient then someone is not strong. Everyone who is not wise is creative or patient. Everyone who is either creative or not calm is quiet and vice versa. Everyone who is not strong is humble. Everyone who is not brave or not calm is strong. If fred is both not kind and curious then someone is either not rich or not strong. Everyone who is generous or not curious is humble. If someone is happy then someone is not happy. Everyone who is both calm and happy is kind or not brave. John is either not old or not humble. Someone is strong or not brave. Alice is both rich and not strong. Alice is both curious and not patient. Susan is either not humble or old. Someone is not patient or calm. Someone is either tall or funny. Someone is both strong and brave. | Susan is humble. | entailment | (((brave(alice)<~>~humble(alice)))=>((humble(susan)&~strong(susan))))&
(![X]:((~generous(X)&quiet(X))=>(~generous(X)|brave(X))))&
(![X]:(patient(X)<=>(~patient(X)&~humble(X))))&
(![X]:((~rich(X)|quiet(X))<=>creative(X)))&
(![X]:((~happy(X)&~strong(X))<=>(generous(X)|wise(X))))&
((?[X]:((calm(X)|creative(X))))<=>(?[X]:((happy(X)<~>~wise(X)))))&
((?[X]:(strong(X)))=>(?[X]:(~generous(X))))&
(((~brave(fred)|patient(fred)))=>(?[X]:(~strong(X))))&
(![X]:(~wise(X)=>(creative(X)|patient(X))))&
(![X]:((creative(X)<~>~calm(X))<=>quiet(X)))&
(![X]:(~strong(X)=>humble(X)))&
(![X]:((~brave(X)|~calm(X))=>strong(X)))&
(((~kind(fred)&curious(fred)))=>(?[X]:((~rich(X)<~>~strong(X)))))&
(![X]:((generous(X)|~curious(X))=>humble(X)))&
((?[X]:(happy(X)))=>(?[X]:(~happy(X))))&
(![X]:((calm(X)&happy(X))=>(kind(X)|~brave(X))))&
((~old(john)<~>~humble(john)))&
(?[X]:((strong(X)|~brave(X))))&
((rich(alice)&~strong(alice)))&
((curious(alice)&~patient(alice)))&
((~humble(susan)<~>old(susan)))&
(?[X]:((~patient(X)|calm(X))))&
(?[X]:((tall(X)<~>funny(X))))&
(?[X]:((strong(X)&brave(X)))) | humble(susan) | [
"p0",
"p10",
"p11",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 8534371502271836968131841
% SZS output start Proof for 8534371502271836968131841
1. (brave(alice) <~> ~humble(alice)) => (~strong(susan) & humble(susan)) [input p0]
11. ! [X0] : (~strong(X0) => humble(X0)) [input p10]
12. ! [X0] : ((~calm(X0) | ~brave(X0)) => strong(X0)) [input p11]
19. ~strong(alice) & rich(alice) [input p18]
25. ~humble(susan) [input hypothesis]
33. (~strong(susan) & humble(susan)) | (brave(alice) <=> ~humble(alice)) [ennf transformation 1]
40. ! [X0] : (humble(X0) | strong(X0)) [ennf transformation 11]
41. ! [X0] : (strong(X0) | (calm(X0) & brave(X0))) [ennf transformation 12]
44. (~strong(susan) & humble(susan)) | ((brave(alice) | humble(alice)) & (~humble(alice) | ~brave(alice))) [nnf transformation 33]
76. humble(susan) | ~humble(alice) | ~brave(alice) [cnf transformation 44]
106. strong(X0) | humble(X0) [cnf transformation 40]
107. strong(X0) | brave(X0) [cnf transformation 41]
115. ~strong(alice) [cnf transformation 19]
124. ~humble(susan) [cnf transformation 25]
128. 1 <=> humble(alice) [avatar definition]
132. 2 <=> brave(alice) [avatar definition]
133. ~brave(alice) <- (~2) [avatar component clause 132]
142. 4 <=> humble(susan) [avatar definition]
146. ~2 | ~1 | 4 [avatar split clause 76,142,128,132]
236. ~4 [avatar split clause 124,142]
237. humble(alice) [resolution 106,115]
241. 1 [avatar split clause 237,128]
242. brave(alice) [resolution 107,115]
244. $false <- (~2) [subsumption resolution 242,133]
245. 2 [avatar contradiction clause 244]
246. $false [avatar sat refutation 146,236,241,245]
% SZS output end Proof for 8534371502271836968131841
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not creative and not brave then lucy is either happy or not brave.
Everyone who is either not humble or not tall is either not generous or funny.
Everyone who is either not brave or creative is both not kind and strong.
Everyone who is not happy or not curious is quiet.
If someone is both calm and creative then someone is both quiet and not humble.
Everyone who is both not funny and happy is either not curious or humble and vice versa.
If someone is either humble or generous then someone is either patient or not strong.
Everyone who is not quiet is either brave or kind and vice versa.
Everyone who is either rich or quiet is quiet.
Everyone who is both not brave and not humble is not generous or tall and vice versa.
If susan is both patient and happy then someone is either creative or not generous and vice versa.
If lucy is both generous and patient then susan is not kind or funny and vice versa.
If someone is either not old or not generous then someone is not strong.
If someone is either not wise or tall then fred is either not strong or wise and vice versa.
If alice is either not curious or not creative then susan is either old or not curious.
Everyone who is either brave or wise is both not humble and not funny and vice versa.
Fred is either brave or not curious.
Someone is creative.
Someone is not funny.
Lucy is both humble and not patient.
Someone is humble or calm.
Someone is funny.
Someone is both happy and curious.
Someone is either not generous or not strong. | Lucy is not curious. | entailment | ((?[X]:((~creative(X)&~brave(X))))=>((happy(lucy)<~>~brave(lucy))))&
(![X]:((~humble(X)<~>~tall(X))=>(~generous(X)<~>funny(X))))&
(![X]:((~brave(X)<~>creative(X))=>(~kind(X)&strong(X))))&
(![X]:((~happy(X)|~curious(X))=>quiet(X)))&
((?[X]:((calm(X)&creative(X))))=>(?[X]:((quiet(X)&~humble(X)))))&
(![X]:((~funny(X)&happy(X))<=>(~curious(X)<~>humble(X))))&
((?[X]:((humble(X)<~>generous(X))))=>(?[X]:((patient(X)<~>~strong(X)))))&
(![X]:(~quiet(X)<=>(brave(X)<~>kind(X))))&
(![X]:((rich(X)<~>quiet(X))=>quiet(X)))&
(![X]:((~brave(X)&~humble(X))<=>(~generous(X)|tall(X))))&
(((patient(susan)&happy(susan)))<=>(?[X]:((creative(X)<~>~generous(X)))))&
(((generous(lucy)&patient(lucy)))<=>((~kind(susan)|funny(susan))))&
((?[X]:((~old(X)<~>~generous(X))))=>(?[X]:(~strong(X))))&
((?[X]:((~wise(X)<~>tall(X))))<=>((~strong(fred)<~>wise(fred))))&
(((~curious(alice)<~>~creative(alice)))=>((old(susan)<~>~curious(susan))))&
(![X]:((brave(X)<~>wise(X))<=>(~humble(X)&~funny(X))))&
((brave(fred)<~>~curious(fred)))&
(?[X]:(creative(X)))&
(?[X]:(~funny(X)))&
((humble(lucy)&~patient(lucy)))&
(?[X]:((humble(X)|calm(X))))&
(?[X]:(funny(X)))&
(?[X]:((happy(X)&curious(X))))&
(?[X]:((~generous(X)<~>~strong(X)))) | ~curious(lucy) | [
"p1",
"p5",
"p9",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 492607491806064910196804
% SZS output start Proof for 492607491806064910196804
2. ! [X0] : ((~humble(X0) <~> ~tall(X0)) => (~generous(X0) <~> funny(X0))) [input p1]
6. ! [X0] : ((happy(X0) & ~funny(X0)) <=> (~curious(X0) <~> humble(X0))) [input p5]
10. ! [X0] : ((~humble(X0) & ~brave(X0)) <=> (tall(X0) | ~generous(X0))) [input p9]
20. ~patient(lucy) & humble(lucy) [input p19]
25. curious(lucy) [input hypothesis]
30. ! [X0] : ((~generous(X0) <~> funny(X0)) | (~humble(X0) <=> ~tall(X0))) [ennf transformation 2]
39. ! [X0] : (((~funny(X0) | generous(X0)) & (funny(X0) | ~generous(X0))) | ((~humble(X0) | tall(X0)) & (~tall(X0) | humble(X0)))) [nnf transformation 30]
44. ! [X0] : (((happy(X0) & ~funny(X0)) | ((~curious(X0) | ~humble(X0)) & (humble(X0) | curious(X0)))) & (((~humble(X0) | curious(X0)) & (humble(X0) | ~curious(X0))) | (~happy(X0) | funny(X0)))) [nnf transformation 6]
45. ! [X0] : (((happy(X0) & ~funny(X0)) | ((~curious(X0) | ~humble(X0)) & (humble(X0) | curious(X0)))) & (((~humble(X0) | curious(X0)) & (humble(X0) | ~curious(X0))) | ~happy(X0) | funny(X0))) [flattening 44]
52. ! [X0] : (((~humble(X0) & ~brave(X0)) | (~tall(X0) & generous(X0))) & ((tall(X0) | ~generous(X0)) | (humble(X0) | brave(X0)))) [nnf transformation 10]
53. ! [X0] : (((~humble(X0) & ~brave(X0)) | (~tall(X0) & generous(X0))) & (tall(X0) | ~generous(X0) | humble(X0) | brave(X0))) [flattening 52]
89. ~generous(X0) | funny(X0) | ~humble(X0) | tall(X0) [cnf transformation 39]
103. ~curious(X0) | ~funny(X0) | ~humble(X0) [cnf transformation 45]
119. ~humble(X0) | generous(X0) [cnf transformation 53]
120. ~tall(X0) | ~humble(X0) [cnf transformation 53]
156. humble(lucy) [cnf transformation 20]
164. curious(lucy) [cnf transformation 25]
205. 10 <=> ! [X1] : (generous(X1) | ~humble(X1)) [avatar definition]
206. ~humble(X1) | generous(X1) <- (10) [avatar component clause 205]
210. 10 [avatar split clause 119,205]
254. 20 <=> generous(lucy) [avatar definition]
256. generous(lucy) <- (20) [avatar component clause 254]
352. generous(lucy) <- (10) [resolution 206,156]
354. 20 | ~10 [avatar split clause 352,205,254]
421. ~funny(lucy) | ~humble(lucy) [resolution 103,164]
431. ~funny(lucy) [subsumption resolution 421,156]
551. funny(lucy) | ~humble(lucy) | tall(lucy) <- (20) [resolution 89,256]
555. ~humble(lucy) | tall(lucy) <- (20) [subsumption resolution 551,431]
556. tall(lucy) <- (20) [subsumption resolution 555,156]
654. ~humble(lucy) <- (20) [resolution 556,120]
656. $false <- (20) [subsumption resolution 654,156]
657. ~20 [avatar contradiction clause 656]
660. $false [avatar sat refutation 210,354,657]
% SZS output end Proof for 492607491806064910196804
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not creative is both not generous and not curious. Everyone who is both humble and not strong is both not happy and not funny. If someone is brave or funny then someone is not curious and vice versa. Everyone who is either not happy or calm is both generous and not generous and vice versa. If susan is not patient then fred is either not humble or funny and vice versa. If someone is not wise then someone is funny and vice versa. Everyone who is not kind or humble is both creative and tall and vice versa. If someone is both not humble and not old then lucy is either not funny or not quiet. If someone is not generous or calm then susan is both curious and not old. Everyone who is either generous or calm is either not humble or calm. If someone is generous or tall then someone is both not funny and not tall and vice versa. If someone is either not brave or not strong then someone is not curious or generous. If someone is not strong then fred is either curious or not quiet. Everyone who is generous is generous or not kind. If paul is both creative and not wise then alice is not rich or calm. If john is not humble or not quiet then someone is not quiet or creative. Mary is wise or quiet. Someone is either rich or not patient. Paul is not humble or patient. Someone is either creative or not old. Alice is not brave or not old. Someone is brave or happy. | Paul is not wise. | neutral | (![X]:(~creative(X)=>(~generous(X)&~curious(X))))&
(![X]:((humble(X)&~strong(X))=>(~happy(X)&~funny(X))))&
((?[X]:((brave(X)|funny(X))))<=>(?[X]:(~curious(X))))&
(![X]:((~happy(X)<~>calm(X))<=>(generous(X)&~generous(X))))&
((~patient(susan))<=>((~humble(fred)<~>funny(fred))))&
((?[X]:(~wise(X)))<=>(?[X]:(funny(X))))&
(![X]:((~kind(X)|humble(X))<=>(creative(X)&tall(X))))&
((?[X]:((~humble(X)&~old(X))))=>((~funny(lucy)<~>~quiet(lucy))))&
((?[X]:((~generous(X)|calm(X))))=>((curious(susan)&~old(susan))))&
(![X]:((generous(X)<~>calm(X))=>(~humble(X)<~>calm(X))))&
((?[X]:((generous(X)|tall(X))))<=>(?[X]:((~funny(X)&~tall(X)))))&
((?[X]:((~brave(X)<~>~strong(X))))=>(?[X]:((~curious(X)|generous(X)))))&
((?[X]:(~strong(X)))=>((curious(fred)<~>~quiet(fred))))&
(![X]:(generous(X)=>(generous(X)|~kind(X))))&
(((creative(paul)&~wise(paul)))=>((~rich(alice)|calm(alice))))&
(((~humble(john)|~quiet(john)))=>(?[X]:((~quiet(X)|creative(X)))))&
((wise(mary)|quiet(mary)))&
(?[X]:((rich(X)<~>~patient(X))))&
((~humble(paul)|patient(paul)))&
(?[X]:((creative(X)<~>~old(X))))&
((~brave(alice)|~old(alice)))&
(?[X]:((brave(X)|happy(X)))) | ~wise(paul) | [] | null | 0 |
Everyone who is brave or not quiet is both generous and not old and vice versa. Everyone who is calm or not funny is either not curious or generous and vice versa. Everyone who is either not funny or not rich is not old or not funny. Everyone who is curious or funny is not brave. If someone is either happy or not funny then john is generous or not patient. Everyone who is not rich or not curious is either creative or patient. If someone is either old or kind then someone is not generous and vice versa. Everyone who is either not funny or not rich is rich and vice versa. If paul is both not brave and not quiet then fred is not calm or calm. Everyone who is either not wise or creative is not creative. Everyone who is both tall and old is either not quiet or not happy and vice versa. If fred is either not happy or not old then someone is either not patient or not strong and vice versa. If john is either not kind or wise then susan is both happy and creative. If mary is either tall or creative then lucy is both kind and happy. Everyone who is either not creative or old is both tall and curious. Everyone who is either not generous or not brave is not tall and vice versa. Someone is either happy or generous. Someone is not wise or not strong. Someone is not curious. Paul is quiet or curious. Someone is not generous. Someone is not rich or patient. Someone is creative or not humble. | John is not brave. | entailment | (![X]:((brave(X)|~quiet(X))<=>(generous(X)&~old(X))))&
(![X]:((calm(X)|~funny(X))<=>(~curious(X)<~>generous(X))))&
(![X]:((~funny(X)<~>~rich(X))=>(~old(X)|~funny(X))))&
(![X]:((curious(X)|funny(X))=>~brave(X)))&
((?[X]:((happy(X)<~>~funny(X))))=>((generous(john)|~patient(john))))&
(![X]:((~rich(X)|~curious(X))=>(creative(X)<~>patient(X))))&
((?[X]:((old(X)<~>kind(X))))<=>(?[X]:(~generous(X))))&
(![X]:((~funny(X)<~>~rich(X))<=>rich(X)))&
(((~brave(paul)&~quiet(paul)))=>((~calm(fred)|calm(fred))))&
(![X]:((~wise(X)<~>creative(X))=>~creative(X)))&
(![X]:((tall(X)&old(X))<=>(~quiet(X)<~>~happy(X))))&
(((~happy(fred)<~>~old(fred)))<=>(?[X]:((~patient(X)<~>~strong(X)))))&
(((~kind(john)<~>wise(john)))=>((happy(susan)&creative(susan))))&
(((tall(mary)<~>creative(mary)))=>((kind(lucy)&happy(lucy))))&
(![X]:((~creative(X)<~>old(X))=>(tall(X)&curious(X))))&
(![X]:((~generous(X)<~>~brave(X))<=>~tall(X)))&
(?[X]:((happy(X)<~>generous(X))))&
(?[X]:((~wise(X)|~strong(X))))&
(?[X]:(~curious(X)))&
((quiet(paul)|curious(paul)))&
(?[X]:(~generous(X)))&
(?[X]:((~rich(X)|patient(X))))&
(?[X]:((creative(X)|~humble(X)))) | ~brave(john) | [
"p0",
"p1",
"p3",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 6827015226441933256850964
% SZS output start Proof for 6827015226441933256850964
1. ! [X0] : ((~quiet(X0) | brave(X0)) <=> (~old(X0) & generous(X0))) [input p0]
2. ! [X0] : ((~funny(X0) | calm(X0)) <=> (~curious(X0) <~> generous(X0))) [input p1]
4. ! [X0] : ((funny(X0) | curious(X0)) => ~brave(X0)) [input p3]
8. ! [X0] : ((~funny(X0) <~> ~rich(X0)) <=> rich(X0)) [input p7]
24. brave(john) [input hypothesis]
29. ! [X0] : (~brave(X0) | (~funny(X0) & ~curious(X0))) [ennf transformation 4]
39. ! [X0] : (((~quiet(X0) | brave(X0)) | (old(X0) | ~generous(X0))) & ((~old(X0) & generous(X0)) | (quiet(X0) & ~brave(X0)))) [nnf transformation 1]
40. ! [X0] : ((~quiet(X0) | brave(X0) | old(X0) | ~generous(X0)) & ((~old(X0) & generous(X0)) | (quiet(X0) & ~brave(X0)))) [flattening 39]
41. ! [X0] : (((~funny(X0) | calm(X0)) | ((~curious(X0) | ~generous(X0)) & (generous(X0) | curious(X0)))) & (((~generous(X0) | curious(X0)) & (generous(X0) | ~curious(X0))) | (funny(X0) & ~calm(X0)))) [nnf transformation 2]
42. ! [X0] : ((~funny(X0) | calm(X0) | ((~curious(X0) | ~generous(X0)) & (generous(X0) | curious(X0)))) & (((~generous(X0) | curious(X0)) & (generous(X0) | ~curious(X0))) | (funny(X0) & ~calm(X0)))) [flattening 41]
51. ! [X0] : ((((rich(X0) | funny(X0)) & (~rich(X0) | ~funny(X0))) | ~rich(X0)) & (rich(X0) | ((~funny(X0) | rich(X0)) & (~rich(X0) | funny(X0))))) [nnf transformation 8]
74. ~brave(X0) | generous(X0) [cnf transformation 40]
82. ~generous(X0) | curious(X0) | funny(X0) [cnf transformation 42]
87. ~curious(X0) | ~brave(X0) [cnf transformation 29]
100. rich(X0) | ~funny(X0) | rich(X0) [cnf transformation 51]
101. ~rich(X0) | ~funny(X0) | ~rich(X0) [cnf transformation 51]
143. brave(john) [cnf transformation 24]
145. rich(X0) | ~funny(X0) [duplicate literal removal 100]
146. ~rich(X0) | ~funny(X0) [duplicate literal removal 101]
152. 2 <=> generous(john) [avatar definition]
154. generous(john) <- (2) [avatar component clause 152]
189. ~funny(X0) [subsumption resolution 145,146]
301. generous(john) [resolution 74,143]
302. 2 [avatar split clause 301,152]
312. curious(john) | funny(john) <- (2) [resolution 82,154]
315. curious(john) <- (2) [subsumption resolution 312,189]
332. ~brave(john) <- (2) [resolution 315,87]
333. $false <- (2) [subsumption resolution 332,143]
334. ~2 [avatar contradiction clause 333]
335. $false [avatar sat refutation 302,334]
% SZS output end Proof for 6827015226441933256850964
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not funny is either not calm or not funny.
Everyone who is curious is either creative or not quiet.
Everyone who is both not generous and not tall is both not creative and funny.
If someone is old or strong then someone is either not quiet or not brave.
If someone is either not old or wise then someone is either not happy or patient and vice versa.
If someone is quiet then someone is not funny.
If someone is kind then alice is both not funny and not wise.
If paul is both not quiet and not patient then alice is either not quiet or happy and vice versa.
If someone is not strong then someone is both quiet and not tall.
If mary is both not humble and not kind then lucy is tall and vice versa.
Everyone who is quiet or rich is not wise.
Everyone who is not strong or not generous is both not brave and tall and vice versa.
Everyone who is either kind or not generous is brave and vice versa.
Everyone who is either not kind or wise is either not patient or kind and vice versa.
Everyone who is either not patient or happy is not tall.
If lucy is either not humble or wise then someone is both rich and not wise.
Someone is both creative and strong.
Someone is both brave and not rich.
Someone is patient.
Someone is both calm and rich.
Someone is either brave or not generous.
Fred is strong or not humble.
Fred is not wise. | Alice is not funny. | entailment | (![X]:(~funny(X)=>(~calm(X)<~>~funny(X))))&
(![X]:(curious(X)=>(creative(X)<~>~quiet(X))))&
(![X]:((~generous(X)&~tall(X))=>(~creative(X)&funny(X))))&
((?[X]:((old(X)|strong(X))))=>(?[X]:((~quiet(X)<~>~brave(X)))))&
((?[X]:((~old(X)<~>wise(X))))<=>(?[X]:((~happy(X)<~>patient(X)))))&
((?[X]:(quiet(X)))=>(?[X]:(~funny(X))))&
((?[X]:(kind(X)))=>((~funny(alice)&~wise(alice))))&
(((~quiet(paul)&~patient(paul)))<=>((~quiet(alice)<~>happy(alice))))&
((?[X]:(~strong(X)))=>(?[X]:((quiet(X)&~tall(X)))))&
(((~humble(mary)&~kind(mary)))<=>(tall(lucy)))&
(![X]:((quiet(X)|rich(X))=>~wise(X)))&
(![X]:((~strong(X)|~generous(X))<=>(~brave(X)&tall(X))))&
(![X]:((kind(X)<~>~generous(X))<=>brave(X)))&
(![X]:((~kind(X)<~>wise(X))<=>(~patient(X)<~>kind(X))))&
(![X]:((~patient(X)<~>happy(X))=>~tall(X)))&
(((~humble(lucy)<~>wise(lucy)))=>(?[X]:((rich(X)&~wise(X)))))&
(?[X]:((creative(X)&strong(X))))&
(?[X]:((brave(X)&~rich(X))))&
(?[X]:(patient(X)))&
(?[X]:((calm(X)&rich(X))))&
(?[X]:((brave(X)<~>~generous(X))))&
((strong(fred)|~humble(fred)))&
(~wise(fred)) | ~funny(alice) | [
"p6",
"p11",
"p12",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 4799487519229079614137312
% SZS output start Proof for 4799487519229079614137312
7. ? [X0] : kind(X0) => (~wise(alice) & ~funny(alice)) [input p6]
12. ! [X0] : ((~generous(X0) | ~strong(X0)) <=> (tall(X0) & ~brave(X0))) [input p11]
13. ! [X0] : ((kind(X0) <~> ~generous(X0)) <=> brave(X0)) [input p12]
18. ? [X0] : (~rich(X0) & brave(X0)) [input p17]
24. funny(alice) [input hypothesis]
35. (~wise(alice) & ~funny(alice)) | ! [X0] : ~kind(X0) [ennf transformation 7]
60. ! [X0] : (((~generous(X0) | ~strong(X0)) | (~tall(X0) | brave(X0))) & ((tall(X0) & ~brave(X0)) | (generous(X0) & strong(X0)))) [nnf transformation 12]
61. ! [X0] : ((~generous(X0) | ~strong(X0) | ~tall(X0) | brave(X0)) & ((tall(X0) & ~brave(X0)) | (generous(X0) & strong(X0)))) [flattening 60]
62. ! [X0] : ((((generous(X0) | ~kind(X0)) & (~generous(X0) | kind(X0))) | ~brave(X0)) & (brave(X0) | ((kind(X0) | generous(X0)) & (~generous(X0) | ~kind(X0))))) [nnf transformation 13]
70. ? [X0] : (~rich(X0) & brave(X0)) => (~rich(sK7) & brave(sK7)) [choice axiom]
71. ~rich(sK7) & brave(sK7) [skolemisation 18,70]
96. ~funny(alice) | ~kind(X0) [cnf transformation 35]
112. ~brave(X0) | generous(X0) [cnf transformation 61]
118. ~generous(X0) | kind(X0) | ~brave(X0) [cnf transformation 62]
136. brave(sK7) [cnf transformation 71]
145. funny(alice) [cnf transformation 24]
214. 15 <=> ! [X0] : ~kind(X0) [avatar definition]
215. ~kind(X0) <- (15) [avatar component clause 214]
222. 17 <=> funny(alice) [avatar definition]
225. 15 | ~17 [avatar split clause 96,222,214]
276. ~brave(X0) | kind(X0) [subsumption resolution 118,112]
318. 17 [avatar split clause 145,222]
323. kind(sK7) [resolution 276,136]
324. $false <- (15) [subsumption resolution 323,215]
325. ~15 [avatar contradiction clause 324]
326. $false [avatar sat refutation 225,318,325]
% SZS output end Proof for 4799487519229079614137312
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not kind or strong is either happy or brave and vice versa. Everyone who is happy or generous is both not humble and curious and vice versa. If susan is either not calm or not wise then susan is both quiet and not brave. Everyone who is rich is either kind or old. If someone is curious then someone is not kind and vice versa. If susan is both not wise and curious then someone is not patient. Everyone who is either not quiet or not kind is either not calm or tall and vice versa. If paul is both funny and calm then someone is funny and vice versa. Everyone who is either curious or old is both not kind and brave and vice versa. If mary is either funny or strong then someone is both humble and not wise. If someone is not rich then fred is either not creative or tall and vice versa. If someone is either quiet or not quiet then someone is not wise or creative. If mary is both patient and wise then lucy is either not kind or not humble and vice versa. Everyone who is both wise and patient is both calm and brave. Everyone who is both old and not tall is both tall and curious and vice versa. Everyone who is both brave and not wise is both old and patient. Lucy is either not happy or not quiet. Someone is not happy. Paul is either not curious or not funny. Mary is not funny or wise. Paul is tall. Paul is both not humble and not happy. Someone is not humble. Someone is either tall or not curious. | Mary is not creative. | neutral | (![X]:((~kind(X)<~>strong(X))<=>(happy(X)<~>brave(X))))&
(![X]:((happy(X)|generous(X))<=>(~humble(X)&curious(X))))&
(((~calm(susan)<~>~wise(susan)))=>((quiet(susan)&~brave(susan))))&
(![X]:(rich(X)=>(kind(X)<~>old(X))))&
((?[X]:(curious(X)))<=>(?[X]:(~kind(X))))&
(((~wise(susan)&curious(susan)))=>(?[X]:(~patient(X))))&
(![X]:((~quiet(X)<~>~kind(X))<=>(~calm(X)<~>tall(X))))&
(((funny(paul)&calm(paul)))<=>(?[X]:(funny(X))))&
(![X]:((curious(X)<~>old(X))<=>(~kind(X)&brave(X))))&
(((funny(mary)<~>strong(mary)))=>(?[X]:((humble(X)&~wise(X)))))&
((?[X]:(~rich(X)))<=>((~creative(fred)<~>tall(fred))))&
((?[X]:((quiet(X)<~>~quiet(X))))=>(?[X]:((~wise(X)|creative(X)))))&
(((patient(mary)&wise(mary)))<=>((~kind(lucy)<~>~humble(lucy))))&
(![X]:((wise(X)&patient(X))=>(calm(X)&brave(X))))&
(![X]:((old(X)&~tall(X))<=>(tall(X)&curious(X))))&
(![X]:((brave(X)&~wise(X))=>(old(X)&patient(X))))&
((~happy(lucy)<~>~quiet(lucy)))&
(?[X]:(~happy(X)))&
((~curious(paul)<~>~funny(paul)))&
((~funny(mary)|wise(mary)))&
(tall(paul))&
((~humble(paul)&~happy(paul)))&
(?[X]:(~humble(X)))&
(?[X]:((tall(X)<~>~curious(X)))) | ~creative(mary) | [] | null | 0 |
Everyone who is either quiet or not calm is not creative.
If paul is both generous and creative then someone is not funny or happy and vice versa.
Everyone who is patient or not wise is not curious.
If someone is either old or not wise then someone is both not calm and not strong and vice versa.
Everyone who is patient or strong is both kind and happy and vice versa.
Everyone who is both not calm and rich is both quiet and humble and vice versa.
If someone is kind or not old then mary is not rich.
Everyone who is both strong and patient is not rich or wise.
Everyone who is either not kind or not generous is either wise or not funny.
Everyone who is both not brave and curious is strong or brave and vice versa.
If someone is patient or not calm then mary is either happy or humble and vice versa.
If someone is both humble and not old then someone is both wise and not old and vice versa.
If someone is happy then lucy is both not wise and curious and vice versa.
Everyone who is both strong and not patient is not wise or not calm and vice versa.
If john is either tall or not funny then someone is either tall or not humble.
Everyone who is not curious is either not brave or creative and vice versa.
Someone is either not generous or not happy.
Someone is not generous or strong.
Susan is not quiet or not strong.
Someone is patient or not strong.
Susan is both funny and not humble.
Someone is not tall or brave. | Lucy is not creative. | entailment | (![X]:((quiet(X)<~>~calm(X))=>~creative(X)))&
(((generous(paul)&creative(paul)))<=>(?[X]:((~funny(X)|happy(X)))))&
(![X]:((patient(X)|~wise(X))=>~curious(X)))&
((?[X]:((old(X)<~>~wise(X))))<=>(?[X]:((~calm(X)&~strong(X)))))&
(![X]:((patient(X)|strong(X))<=>(kind(X)&happy(X))))&
(![X]:((~calm(X)&rich(X))<=>(quiet(X)&humble(X))))&
((?[X]:((kind(X)|~old(X))))=>(~rich(mary)))&
(![X]:((strong(X)&patient(X))=>(~rich(X)|wise(X))))&
(![X]:((~kind(X)<~>~generous(X))=>(wise(X)<~>~funny(X))))&
(![X]:((~brave(X)&curious(X))<=>(strong(X)|brave(X))))&
((?[X]:((patient(X)|~calm(X))))<=>((happy(mary)<~>humble(mary))))&
((?[X]:((humble(X)&~old(X))))<=>(?[X]:((wise(X)&~old(X)))))&
((?[X]:(happy(X)))<=>((~wise(lucy)&curious(lucy))))&
(![X]:((strong(X)&~patient(X))<=>(~wise(X)|~calm(X))))&
(((tall(john)<~>~funny(john)))=>(?[X]:((tall(X)<~>~humble(X)))))&
(![X]:(~curious(X)<=>(~brave(X)<~>creative(X))))&
(?[X]:((~generous(X)<~>~happy(X))))&
(?[X]:((~generous(X)|strong(X))))&
((~quiet(susan)|~strong(susan)))&
(?[X]:((patient(X)|~strong(X))))&
((funny(susan)&~humble(susan)))&
(?[X]:((~tall(X)|brave(X)))) | ~creative(lucy) | [
"p2",
"p4",
"p9",
"p12",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3964959598134149603208087
% SZS output start Proof for 3964959598134149603208087
3. ! [X0] : ((~wise(X0) | patient(X0)) => ~curious(X0)) [input p2]
5. ! [X0] : ((strong(X0) | patient(X0)) <=> (happy(X0) & kind(X0))) [input p4]
10. ! [X0] : ((curious(X0) & ~brave(X0)) <=> (brave(X0) | strong(X0))) [input p9]
13. ? [X0] : happy(X0) <=> (curious(lucy) & ~wise(lucy)) [input p12]
14. ! [X0] : ((~patient(X0) & strong(X0)) <=> (~calm(X0) | ~wise(X0))) [input p13]
16. ! [X0] : (~curious(X0) <=> (~brave(X0) <~> creative(X0))) [input p15]
23. creative(lucy) [input hypothesis]
27. ! [X0] : (~curious(X0) | (wise(X0) & ~patient(X0))) [ennf transformation 3]
44. ! [X0] : (((strong(X0) | patient(X0)) | (~happy(X0) | ~kind(X0))) & ((happy(X0) & kind(X0)) | (~strong(X0) & ~patient(X0)))) [nnf transformation 5]
45. ! [X0] : ((strong(X0) | patient(X0) | ~happy(X0) | ~kind(X0)) & ((happy(X0) & kind(X0)) | (~strong(X0) & ~patient(X0)))) [flattening 44]
49. ! [X0] : (((curious(X0) & ~brave(X0)) | (~brave(X0) & ~strong(X0))) & ((brave(X0) | strong(X0)) | (~curious(X0) | brave(X0)))) [nnf transformation 10]
50. ! [X0] : (((curious(X0) & ~brave(X0)) | (~brave(X0) & ~strong(X0))) & (brave(X0) | strong(X0) | ~curious(X0) | brave(X0))) [flattening 49]
60. (? [X0] : happy(X0) | (~curious(lucy) | wise(lucy))) & ((curious(lucy) & ~wise(lucy)) | ! [X0] : ~happy(X0)) [nnf transformation 13]
61. (? [X0] : happy(X0) | ~curious(lucy) | wise(lucy)) & ((curious(lucy) & ~wise(lucy)) | ! [X0] : ~happy(X0)) [flattening 60]
62. (? [X0] : happy(X0) | ~curious(lucy) | wise(lucy)) & ((curious(lucy) & ~wise(lucy)) | ! [X1] : ~happy(X1)) [rectify 61]
63. ? [X0] : happy(X0) => happy(sK6) [choice axiom]
64. (happy(sK6) | ~curious(lucy) | wise(lucy)) & ((curious(lucy) & ~wise(lucy)) | ! [X1] : ~happy(X1)) [skolemisation 62,63]
65. ! [X0] : (((~patient(X0) & strong(X0)) | (calm(X0) & wise(X0))) & ((~calm(X0) | ~wise(X0)) | (patient(X0) | ~strong(X0)))) [nnf transformation 14]
66. ! [X0] : (((~patient(X0) & strong(X0)) | (calm(X0) & wise(X0))) & (~calm(X0) | ~wise(X0) | patient(X0) | ~strong(X0))) [flattening 65]
70. ! [X0] : ((~curious(X0) | ((~brave(X0) | ~creative(X0)) & (creative(X0) | brave(X0)))) & (((~creative(X0) | brave(X0)) & (creative(X0) | ~brave(X0))) | curious(X0))) [nnf transformation 16]
88. ~curious(X0) | wise(X0) [cnf transformation 27]
98. ~strong(X0) | happy(X0) [cnf transformation 45]
111. brave(X0) | strong(X0) | ~curious(X0) | brave(X0) [cnf transformation 50]
113. ~brave(X0) | ~brave(X0) [cnf transformation 50]
114. ~strong(X0) | curious(X0) [cnf transformation 50]
126. ~wise(lucy) | ~happy(X1) [cnf transformation 64]
130. strong(X0) | wise(X0) [cnf transformation 66]
139. ~creative(X0) | brave(X0) | curious(X0) [cnf transformation 70]
150. creative(lucy) [cnf transformation 23]
151. brave(X0) | strong(X0) | ~curious(X0) [duplicate literal removal 111]
152. ~brave(X0) [duplicate literal removal 113]
154. 1 <=> ! [X0] : ~happy(X0) [avatar definition]
155. ~happy(X0) <- (1) [avatar component clause 154]
223. ~curious(X0) | strong(X0) [subsumption resolution 151,152]
279. 29 <=> curious(lucy) [avatar definition]
281. curious(lucy) <- (29) [avatar component clause 279]
284. 30 <=> wise(lucy) [avatar definition]
286. ~wise(lucy) <- (~30) [avatar component clause 284]
287. 1 | ~30 [avatar split clause 126,284,154]
310. ~creative(X0) | curious(X0) [subsumption resolution 139,152]
353. wise(X0) | curious(X0) [resolution 130,114]
359. wise(X0) [subsumption resolution 353,88]
360. $false <- (~30) [resolution 359,286]
361. 30 [avatar contradiction clause 360]
396. curious(lucy) [resolution 310,150]
400. 29 [avatar split clause 396,279]
402. strong(lucy) <- (29) [resolution 281,223]
416. happy(lucy) <- (29) [resolution 402,98]
418. $false <- (1, 29) [subsumption resolution 416,155]
419. ~1 | ~29 [avatar contradiction clause 418]
420. $false [avatar sat refutation 287,361,400,419]
% SZS output end Proof for 3964959598134149603208087
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is both curious and not brave then someone is not happy and vice versa. If someone is both tall and not brave then someone is either not wise or not rich. Everyone who is either rich or kind is both not creative and tall. If someone is not creative or not kind then someone is calm. Everyone who is not creative or brave is both not patient and creative and vice versa. If someone is either wise or rich then someone is calm or not quiet. Everyone who is tall is both not old and not creative and vice versa. If someone is both not calm and not strong then someone is brave or not funny and vice versa. Everyone who is tall is creative. Everyone who is not calm or kind is both wise and not brave. Everyone who is not happy is both not kind and curious. Everyone who is not old or wise is either tall or not curious. Everyone who is either not brave or quiet is either not kind or not happy. Everyone who is not calm or generous is both not patient and strong. If susan is not humble or not quiet then mary is tall or brave. Everyone who is either not brave or not tall is both tall and not rich and vice versa. Someone is curious. Someone is not humble. Susan is not curious. Someone is both kind and wise. John is humble. Fred is either strong or not curious. Someone is either quiet or rich. | Susan is humble. | entailment | (((curious(paul)&~brave(paul)))<=>(?[X]:(~happy(X))))&
((?[X]:((tall(X)&~brave(X))))=>(?[X]:((~wise(X)<~>~rich(X)))))&
(![X]:((rich(X)<~>kind(X))=>(~creative(X)&tall(X))))&
((?[X]:((~creative(X)|~kind(X))))=>(?[X]:(calm(X))))&
(![X]:((~creative(X)|brave(X))<=>(~patient(X)&creative(X))))&
((?[X]:((wise(X)<~>rich(X))))=>(?[X]:((calm(X)|~quiet(X)))))&
(![X]:(tall(X)<=>(~old(X)&~creative(X))))&
((?[X]:((~calm(X)&~strong(X))))<=>(?[X]:((brave(X)|~funny(X)))))&
(![X]:(tall(X)=>creative(X)))&
(![X]:((~calm(X)|kind(X))=>(wise(X)&~brave(X))))&
(![X]:(~happy(X)=>(~kind(X)&curious(X))))&
(![X]:((~old(X)|wise(X))=>(tall(X)<~>~curious(X))))&
(![X]:((~brave(X)<~>quiet(X))=>(~kind(X)<~>~happy(X))))&
(![X]:((~calm(X)|generous(X))=>(~patient(X)&strong(X))))&
(((~humble(susan)|~quiet(susan)))=>((tall(mary)|brave(mary))))&
(![X]:((~brave(X)<~>~tall(X))<=>(tall(X)&~rich(X))))&
(?[X]:(curious(X)))&
(?[X]:(~humble(X)))&
(~curious(susan))&
(?[X]:((kind(X)&wise(X))))&
(humble(john))&
((strong(fred)<~>~curious(fred)))&
(?[X]:((quiet(X)<~>rich(X)))) | humble(susan) | [
"p6",
"p8",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2097440974263590889404984
% SZS output start Proof for 2097440974263590889404984
7. ! [X0] : (tall(X0) <=> (~creative(X0) & ~old(X0))) [input p6]
9. ! [X0] : (tall(X0) => creative(X0)) [input p8]
15. (~quiet(susan) | ~humble(susan)) => (brave(mary) | tall(mary)) [input p14]
16. ! [X0] : ((~brave(X0) <~> ~tall(X0)) <=> (~rich(X0) & tall(X0))) [input p15]
24. ~humble(susan) [input hypothesis]
34. ! [X0] : (creative(X0) | ~tall(X0)) [ennf transformation 9]
40. (brave(mary) | tall(mary)) | (quiet(susan) & humble(susan)) [ennf transformation 15]
41. brave(mary) | tall(mary) | (quiet(susan) & humble(susan)) [flattening 40]
61. ! [X0] : ((tall(X0) | (creative(X0) | old(X0))) & ((~creative(X0) & ~old(X0)) | ~tall(X0))) [nnf transformation 7]
62. ! [X0] : ((tall(X0) | creative(X0) | old(X0)) & ((~creative(X0) & ~old(X0)) | ~tall(X0))) [flattening 61]
70. ! [X0] : ((((tall(X0) | brave(X0)) & (~tall(X0) | ~brave(X0))) | (rich(X0) | ~tall(X0))) & ((~rich(X0) & tall(X0)) | ((~brave(X0) | tall(X0)) & (~tall(X0) | brave(X0))))) [nnf transformation 16]
71. ! [X0] : ((((tall(X0) | brave(X0)) & (~tall(X0) | ~brave(X0))) | rich(X0) | ~tall(X0)) & ((~rich(X0) & tall(X0)) | ((~brave(X0) | tall(X0)) & (~tall(X0) | brave(X0))))) [flattening 70]
101. ~creative(X0) | ~tall(X0) [cnf transformation 62]
108. creative(X0) | ~tall(X0) [cnf transformation 34]
125. brave(mary) | tall(mary) | humble(susan) [cnf transformation 41]
128. tall(X0) | ~brave(X0) | tall(X0) [cnf transformation 71]
143. ~humble(susan) [cnf transformation 24]
144. tall(X0) | ~brave(X0) [duplicate literal removal 128]
217. 17 <=> ! [X1] : ~brave(X1) [avatar definition]
218. ~brave(X1) <- (17) [avatar component clause 217]
238. ~tall(X0) [subsumption resolution 108,101]
252. 23 <=> brave(mary) [avatar definition]
254. brave(mary) <- (23) [avatar component clause 252]
256. brave(mary) | humble(susan) [subsumption resolution 125,238]
258. 24 <=> humble(susan) [avatar definition]
261. 24 | 23 [avatar split clause 256,252,258]
263. ~brave(X0) [subsumption resolution 144,238]
264. 17 [avatar split clause 263,217]
285. ~24 [avatar split clause 143,258]
286. $false <- (17, 23) [resolution 254,218]
287. ~17 | ~23 [avatar contradiction clause 286]
288. $false [avatar sat refutation 261,264,285,287]
% SZS output end Proof for 2097440974263590889404984
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is not calm or not funny then someone is curious and vice versa.
If someone is both not funny and funny then someone is happy and vice versa.
Everyone who is not kind or not tall is old or creative and vice versa.
Everyone who is either not happy or happy is not generous and vice versa.
Everyone who is not rich or not generous is brave and vice versa.
Everyone who is either curious or not quiet is either not old or tall.
If someone is both curious and not curious then susan is not calm or strong.
Everyone who is either not strong or happy is both not generous and not old and vice versa.
Everyone who is not quiet is either not kind or tall.
If lucy is not brave then someone is both rich and not calm.
Everyone who is both not strong and not funny is both curious and patient.
If lucy is either tall or creative then susan is brave.
Everyone who is not calm is either not patient or not tall and vice versa.
Everyone who is either not kind or not brave is curious and vice versa.
Everyone who is generous or not strong is not brave.
If lucy is both wise and not rich then paul is either wise or not patient.
John is not rich or generous.
Susan is not patient.
Fred is either calm or not creative.
Mary is curious.
Someone is either old or not wise.
Someone is either not humble or not curious.
Alice is both not humble and tall. | Lucy is tall. | neutral | (((~calm(lucy)|~funny(lucy)))<=>(?[X]:(curious(X))))&
((?[X]:((~funny(X)&funny(X))))<=>(?[X]:(happy(X))))&
(![X]:((~kind(X)|~tall(X))<=>(old(X)|creative(X))))&
(![X]:((~happy(X)<~>happy(X))<=>~generous(X)))&
(![X]:((~rich(X)|~generous(X))<=>brave(X)))&
(![X]:((curious(X)<~>~quiet(X))=>(~old(X)<~>tall(X))))&
((?[X]:((curious(X)&~curious(X))))=>((~calm(susan)|strong(susan))))&
(![X]:((~strong(X)<~>happy(X))<=>(~generous(X)&~old(X))))&
(![X]:(~quiet(X)=>(~kind(X)<~>tall(X))))&
((~brave(lucy))=>(?[X]:((rich(X)&~calm(X)))))&
(![X]:((~strong(X)&~funny(X))=>(curious(X)&patient(X))))&
(((tall(lucy)<~>creative(lucy)))=>(brave(susan)))&
(![X]:(~calm(X)<=>(~patient(X)<~>~tall(X))))&
(![X]:((~kind(X)<~>~brave(X))<=>curious(X)))&
(![X]:((generous(X)|~strong(X))=>~brave(X)))&
(((wise(lucy)&~rich(lucy)))=>((wise(paul)<~>~patient(paul))))&
((~rich(john)|generous(john)))&
(~patient(susan))&
((calm(fred)<~>~creative(fred)))&
(curious(mary))&
(?[X]:((old(X)<~>~wise(X))))&
(?[X]:((~humble(X)<~>~curious(X))))&
((~humble(alice)&tall(alice))) | tall(lucy) | [] | null | 0 |
If susan is not curious then someone is tall or humble and vice versa.
Everyone who is either curious or not humble is not humble or funny and vice versa.
Everyone who is not creative is either not generous or happy and vice versa.
Everyone who is either rich or not generous is either not brave or old.
Everyone who is humble or tall is curious or not tall and vice versa.
Everyone who is funny or not curious is calm or humble and vice versa.
Everyone who is not tall is both not tall and calm.
If someone is either curious or not curious then paul is either generous or not kind and vice versa.
If alice is both not tall and creative then someone is not curious and vice versa.
If someone is wise or quiet then someone is both brave and not calm.
Everyone who is either quiet or generous is humble.
Everyone who is curious or humble is both not rich and not wise.
Everyone who is both creative and not humble is either kind or not tall and vice versa.
Everyone who is both generous and not calm is creative.
Everyone who is creative is either not funny or not rich.
Everyone who is rich or old is not wise and vice versa.
Someone is not humble or not quiet.
Mary is tall or not brave.
Alice is not patient.
Someone is either kind or not creative.
John is not creative.
Someone is strong.
Someone is both not wise and not funny.
Mary is either not brave or not old. | John is rich. | contradiction | ((~curious(susan))<=>(?[X]:((tall(X)|humble(X)))))&
(![X]:((curious(X)<~>~humble(X))<=>(~humble(X)|funny(X))))&
(![X]:(~creative(X)<=>(~generous(X)<~>happy(X))))&
(![X]:((rich(X)<~>~generous(X))=>(~brave(X)<~>old(X))))&
(![X]:((humble(X)|tall(X))<=>(curious(X)|~tall(X))))&
(![X]:((funny(X)|~curious(X))<=>(calm(X)|humble(X))))&
(![X]:(~tall(X)=>(~tall(X)&calm(X))))&
((?[X]:((curious(X)<~>~curious(X))))<=>((generous(paul)<~>~kind(paul))))&
(((~tall(alice)&creative(alice)))<=>(?[X]:(~curious(X))))&
((?[X]:((wise(X)|quiet(X))))=>(?[X]:((brave(X)&~calm(X)))))&
(![X]:((quiet(X)<~>generous(X))=>humble(X)))&
(![X]:((curious(X)|humble(X))=>(~rich(X)&~wise(X))))&
(![X]:((creative(X)&~humble(X))<=>(kind(X)<~>~tall(X))))&
(![X]:((generous(X)&~calm(X))=>creative(X)))&
(![X]:(creative(X)=>(~funny(X)<~>~rich(X))))&
(![X]:((rich(X)|old(X))<=>~wise(X)))&
(?[X]:((~humble(X)|~quiet(X))))&
((tall(mary)|~brave(mary)))&
(~patient(alice))&
(?[X]:((kind(X)<~>~creative(X))))&
(~creative(john))&
(?[X]:(strong(X)))&
(?[X]:((~wise(X)&~funny(X))))&
((~brave(mary)<~>~old(mary))) | rich(john) | [
"p4",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 2177847642361883204865115
% SZS output start Proof for 2177847642361883204865115
5. ! [X0] : ((tall(X0) | humble(X0)) <=> (~tall(X0) | curious(X0))) [input p4]
12. ! [X0] : ((humble(X0) | curious(X0)) => (~wise(X0) & ~rich(X0))) [input p11]
25. rich(john) [input hypothesis]
34. ! [X0] : ((~wise(X0) & ~rich(X0)) | (~humble(X0) & ~curious(X0))) [ennf transformation 12]
48. ! [X0] : (((tall(X0) | humble(X0)) | (tall(X0) & ~curious(X0))) & ((~tall(X0) | curious(X0)) | (~tall(X0) & ~humble(X0)))) [nnf transformation 5]
49. ! [X0] : ((tall(X0) | humble(X0) | (tall(X0) & ~curious(X0))) & (~tall(X0) | curious(X0) | (~tall(X0) & ~humble(X0)))) [flattening 48]
94. ~tall(X0) | curious(X0) | ~tall(X0) [cnf transformation 49]
96. tall(X0) | humble(X0) | tall(X0) [cnf transformation 49]
120. ~rich(X0) | ~curious(X0) [cnf transformation 34]
121. ~rich(X0) | ~humble(X0) [cnf transformation 34]
143. rich(john) [cnf transformation 25]
148. ~tall(X0) | curious(X0) [duplicate literal removal 94]
149. humble(X0) | tall(X0) [duplicate literal removal 96]
264. ~curious(john) [resolution 120,143]
265. ~humble(john) [resolution 121,143]
268. tall(john) [resolution 149,265]
274. curious(john) [resolution 268,148]
275. $false [subsumption resolution 274,264]
% SZS output end Proof for 2177847642361883204865115
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If susan is both calm and curious then alice is wise and vice versa. If lucy is either creative or wise then john is both not happy and not strong. If john is both not happy and not strong then alice is both not generous and wise and vice versa. Everyone who is both not happy and not brave is funny and vice versa. If alice is either tall or funny then lucy is generous. Everyone who is either brave or generous is calm or brave and vice versa. Everyone who is either not wise or not curious is not funny or creative and vice versa. If someone is both humble and not wise then susan is both calm and not curious. If someone is either old or not humble then mary is not wise or funny. If alice is either tall or patient then someone is both not quiet and tall. Everyone who is both not rich and not quiet is not wise or not strong and vice versa. Everyone who is both brave and curious is either not generous or not creative and vice versa. Everyone who is not strong or not brave is not tall and vice versa. Everyone who is old is either not strong or not rich and vice versa. If fred is rich then someone is both brave and patient. Everyone who is strong is generous and vice versa. Paul is patient. Someone is either not old or not humble. Alice is either patient or generous. Fred is not brave. Paul is not quiet. Lucy is not rich or not quiet. | Lucy is rich. | neutral | (((calm(susan)&curious(susan)))<=>(wise(alice)))&
(((creative(lucy)<~>wise(lucy)))=>((~happy(john)&~strong(john))))&
(((~happy(john)&~strong(john)))<=>((~generous(alice)&wise(alice))))&
(![X]:((~happy(X)&~brave(X))<=>funny(X)))&
(((tall(alice)<~>funny(alice)))=>(generous(lucy)))&
(![X]:((brave(X)<~>generous(X))<=>(calm(X)|brave(X))))&
(![X]:((~wise(X)<~>~curious(X))<=>(~funny(X)|creative(X))))&
((?[X]:((humble(X)&~wise(X))))=>((calm(susan)&~curious(susan))))&
((?[X]:((old(X)<~>~humble(X))))=>((~wise(mary)|funny(mary))))&
(((tall(alice)<~>patient(alice)))=>(?[X]:((~quiet(X)&tall(X)))))&
(![X]:((~rich(X)&~quiet(X))<=>(~wise(X)|~strong(X))))&
(![X]:((brave(X)&curious(X))<=>(~generous(X)<~>~creative(X))))&
(![X]:((~strong(X)|~brave(X))<=>~tall(X)))&
(![X]:(old(X)<=>(~strong(X)<~>~rich(X))))&
((rich(fred))=>(?[X]:((brave(X)&patient(X)))))&
(![X]:(strong(X)<=>generous(X)))&
(patient(paul))&
(?[X]:((~old(X)<~>~humble(X))))&
((patient(alice)<~>generous(alice)))&
(~brave(fred))&
(~quiet(paul))&
((~rich(lucy)|~quiet(lucy))) | rich(lucy) | [] | null | 0 |
If someone is kind then fred is curious and vice versa. Everyone who is either humble or calm is calm or wise and vice versa. If fred is both not kind and wise then someone is not humble or calm and vice versa. Everyone who is either tall or curious is quiet. If lucy is both not calm and not curious then someone is both generous and not wise and vice versa. If mary is both kind and not rich then someone is either not creative or not rich. Everyone who is either old or not creative is either tall or calm. Everyone who is both wise and patient is not brave or not old and vice versa. Everyone who is creative or not happy is rich or generous and vice versa. If someone is generous or not rich then alice is not happy. If mary is either not strong or generous then john is both not calm and curious and vice versa. If lucy is both generous and happy then someone is both humble and patient and vice versa. Everyone who is either tall or creative is both not generous and humble and vice versa. Everyone who is both not brave and not happy is both tall and not patient and vice versa. Everyone who is not creative or kind is both wise and not strong and vice versa. If someone is old then mary is not humble or not calm and vice versa. Alice is old or not humble. Fred is either rich or strong. Paul is humble. Mary is both strong and not humble. Someone is old or not generous. Fred is both not patient and not kind. Fred is brave or not kind. Someone is not old or kind. | Lucy is calm. | neutral | ((?[X]:(kind(X)))<=>(curious(fred)))&
(![X]:((humble(X)<~>calm(X))<=>(calm(X)|wise(X))))&
(((~kind(fred)&wise(fred)))<=>(?[X]:((~humble(X)|calm(X)))))&
(![X]:((tall(X)<~>curious(X))=>quiet(X)))&
(((~calm(lucy)&~curious(lucy)))<=>(?[X]:((generous(X)&~wise(X)))))&
(((kind(mary)&~rich(mary)))=>(?[X]:((~creative(X)<~>~rich(X)))))&
(![X]:((old(X)<~>~creative(X))=>(tall(X)<~>calm(X))))&
(![X]:((wise(X)&patient(X))<=>(~brave(X)|~old(X))))&
(![X]:((creative(X)|~happy(X))<=>(rich(X)|generous(X))))&
((?[X]:((generous(X)|~rich(X))))=>(~happy(alice)))&
(((~strong(mary)<~>generous(mary)))<=>((~calm(john)&curious(john))))&
(((generous(lucy)&happy(lucy)))<=>(?[X]:((humble(X)&patient(X)))))&
(![X]:((tall(X)<~>creative(X))<=>(~generous(X)&humble(X))))&
(![X]:((~brave(X)&~happy(X))<=>(tall(X)&~patient(X))))&
(![X]:((~creative(X)|kind(X))<=>(wise(X)&~strong(X))))&
((?[X]:(old(X)))<=>((~humble(mary)|~calm(mary))))&
((old(alice)|~humble(alice)))&
((rich(fred)<~>strong(fred)))&
(humble(paul))&
((strong(mary)&~humble(mary)))&
(?[X]:((old(X)|~generous(X))))&
((~patient(fred)&~kind(fred)))&
((brave(fred)|~kind(fred)))&
(?[X]:((~old(X)|kind(X)))) | calm(lucy) | [] | null | 0 |
Everyone who is not humble or not funny is both strong and brave and vice versa.
If someone is strong or not tall then fred is either rich or not curious.
Everyone who is both funny and not patient is either kind or not creative.
If alice is both funny and not generous then lucy is brave.
Everyone who is either humble or not old is both wise and not strong and vice versa.
Everyone who is not calm or not rich is not old and vice versa.
If someone is either not rich or not patient then someone is wise.
Everyone who is curious or quiet is not creative or wise.
Everyone who is not kind or not old is both not old and kind.
If someone is calm or tall then someone is curious or kind.
If fred is not quiet then paul is humble or strong and vice versa.
If someone is not wise then paul is either generous or not curious.
If susan is brave then fred is not rich or brave.
If susan is generous then john is either rich or patient and vice versa.
Everyone who is either not humble or not old is patient or not creative and vice versa.
If someone is not patient or kind then someone is quiet or creative and vice versa.
Susan is both humble and not patient.
Someone is either not curious or humble.
Someone is either not wise or creative.
Lucy is both not strong and brave.
Someone is either not old or calm.
John is both happy and not calm.
Someone is quiet or kind.
Someone is wise or not quiet. | Lucy is brave. | entailment | (![X]:((~humble(X)|~funny(X))<=>(strong(X)&brave(X))))&
((?[X]:((strong(X)|~tall(X))))=>((rich(fred)<~>~curious(fred))))&
(![X]:((funny(X)&~patient(X))=>(kind(X)<~>~creative(X))))&
(((funny(alice)&~generous(alice)))=>(brave(lucy)))&
(![X]:((humble(X)<~>~old(X))<=>(wise(X)&~strong(X))))&
(![X]:((~calm(X)|~rich(X))<=>~old(X)))&
((?[X]:((~rich(X)<~>~patient(X))))=>(?[X]:(wise(X))))&
(![X]:((curious(X)|quiet(X))=>(~creative(X)|wise(X))))&
(![X]:((~kind(X)|~old(X))=>(~old(X)&kind(X))))&
((?[X]:((calm(X)|tall(X))))=>(?[X]:((curious(X)|kind(X)))))&
((~quiet(fred))<=>((humble(paul)|strong(paul))))&
((?[X]:(~wise(X)))=>((generous(paul)<~>~curious(paul))))&
((brave(susan))=>((~rich(fred)|brave(fred))))&
((generous(susan))<=>((rich(john)<~>patient(john))))&
(![X]:((~humble(X)<~>~old(X))<=>(patient(X)|~creative(X))))&
((?[X]:((~patient(X)|kind(X))))<=>(?[X]:((quiet(X)|creative(X)))))&
((humble(susan)&~patient(susan)))&
(?[X]:((~curious(X)<~>humble(X))))&
(?[X]:((~wise(X)<~>creative(X))))&
((~strong(lucy)&brave(lucy)))&
(?[X]:((~old(X)<~>calm(X))))&
((happy(john)&~calm(john)))&
(?[X]:((quiet(X)|kind(X))))&
(?[X]:((wise(X)|~quiet(X)))) | brave(lucy) | [
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 3580209873157738180742505
% SZS output start Proof for 3580209873157738180742505
20. brave(lucy) & ~strong(lucy) [input p19]
25. ~brave(lucy) [input hypothesis]
140. brave(lucy) [cnf transformation 20]
146. ~brave(lucy) [cnf transformation 25]
175. 7 <=> brave(lucy) [avatar definition]
281. 7 [avatar split clause 140,175]
300. ~7 [avatar split clause 146,175]
301. $false [avatar sat refutation 281,300]
% SZS output end Proof for 3580209873157738180742505
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not patient or not creative is either rich or not calm.
If someone is strong then susan is both not strong and tall and vice versa.
Everyone who is old or calm is either funny or creative.
Everyone who is both happy and not old is strong or not brave and vice versa.
Everyone who is quiet is calm or not patient and vice versa.
Everyone who is either kind or not tall is quiet and vice versa.
Everyone who is not curious or not wise is not curious or old and vice versa.
If someone is either not curious or not wise then fred is either old or not wise and vice versa.
If john is calm or not rich then fred is both curious and not humble and vice versa.
If someone is quiet or brave then fred is humble or wise.
If someone is not tall or not happy then paul is strong.
Everyone who is not brave is not happy or not patient and vice versa.
Everyone who is happy or not funny is either happy or not kind.
If mary is both strong and not old then someone is both not old and humble and vice versa.
If someone is not happy then paul is either patient or not brave.
If someone is either quiet or not tall then alice is either creative or not funny and vice versa.
Someone is either tall or not brave.
John is both not rich and not tall.
Paul is either brave or not kind.
Alice is both not wise and creative.
Mary is either not tall or not funny.
Someone is wise.
Alice is not rich. | Paul is not old. | entailment | (![X]:((~patient(X)<~>~creative(X))=>(rich(X)<~>~calm(X))))&
((?[X]:(strong(X)))<=>((~strong(susan)&tall(susan))))&
(![X]:((old(X)|calm(X))=>(funny(X)<~>creative(X))))&
(![X]:((happy(X)&~old(X))<=>(strong(X)|~brave(X))))&
(![X]:(quiet(X)<=>(calm(X)|~patient(X))))&
(![X]:((kind(X)<~>~tall(X))<=>quiet(X)))&
(![X]:((~curious(X)|~wise(X))<=>(~curious(X)|old(X))))&
((?[X]:((~curious(X)<~>~wise(X))))<=>((old(fred)<~>~wise(fred))))&
(((calm(john)|~rich(john)))<=>((curious(fred)&~humble(fred))))&
((?[X]:((quiet(X)|brave(X))))=>((humble(fred)|wise(fred))))&
((?[X]:((~tall(X)|~happy(X))))=>(strong(paul)))&
(![X]:(~brave(X)<=>(~happy(X)|~patient(X))))&
(![X]:((happy(X)|~funny(X))=>(happy(X)<~>~kind(X))))&
(((strong(mary)&~old(mary)))<=>(?[X]:((~old(X)&humble(X)))))&
((?[X]:(~happy(X)))=>((patient(paul)<~>~brave(paul))))&
((?[X]:((quiet(X)<~>~tall(X))))<=>((creative(alice)<~>~funny(alice))))&
(?[X]:((tall(X)<~>~brave(X))))&
((~rich(john)&~tall(john)))&
((brave(paul)<~>~kind(paul)))&
((~wise(alice)&creative(alice)))&
((~tall(mary)<~>~funny(mary)))&
(?[X]:(wise(X)))&
(~rich(alice)) | ~old(paul) | [
"p3",
"p10",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 3587376183697441522820698
% SZS output start Proof for 3587376183697441522820698
4. ! [X0] : ((~old(X0) & happy(X0)) <=> (~brave(X0) | strong(X0))) [input p3]
11. ? [X0] : (~happy(X0) | ~tall(X0)) => strong(paul) [input p10]
18. ~tall(john) & ~rich(john) [input p17]
24. old(paul) [input hypothesis]
29. strong(paul) | ! [X0] : (happy(X0) & tall(X0)) [ennf transformation 11]
39. ! [X0] : (((~old(X0) & happy(X0)) | (brave(X0) & ~strong(X0))) & ((~brave(X0) | strong(X0)) | (old(X0) | ~happy(X0)))) [nnf transformation 4]
40. ! [X0] : (((~old(X0) & happy(X0)) | (brave(X0) & ~strong(X0))) & (~brave(X0) | strong(X0) | old(X0) | ~happy(X0))) [flattening 39]
86. ~old(X0) | ~strong(X0) [cnf transformation 40]
114. strong(paul) | tall(X0) [cnf transformation 29]
140. ~tall(john) [cnf transformation 18]
149. old(paul) [cnf transformation 24]
232. 18 <=> strong(paul) [avatar definition]
237. 19 <=> ! [X0] : tall(X0) [avatar definition]
238. tall(X0) <- (19) [avatar component clause 237]
239. 19 | 18 [avatar split clause 114,232,237]
334. ~strong(paul) [resolution 86,149]
338. ~18 [avatar split clause 334,232]
339. $false <- (19) [resolution 238,140]
344. ~19 [avatar contradiction clause 339]
345. $false [avatar sat refutation 239,338,344]
% SZS output end Proof for 3587376183697441522820698
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not old is either not tall or not brave and vice versa.
If someone is funny then someone is quiet or curious and vice versa.
Everyone who is old is either happy or patient and vice versa.
If susan is not wise or not creative then susan is either not rich or kind.
If paul is both not rich and tall then john is either not funny or not generous.
If lucy is not humble or not tall then someone is generous or brave and vice versa.
If someone is both not kind and not quiet then someone is both wise and strong and vice versa.
If lucy is both not kind and not old then someone is both not tall and not funny.
Everyone who is humble or quiet is both patient and not quiet.
Everyone who is both not curious and not brave is not curious.
Everyone who is humble or not old is both calm and patient.
Everyone who is happy or patient is calm.
If someone is generous or not curious then someone is humble.
If someone is not humble or not brave then someone is tall.
If lucy is not tall or humble then paul is not kind and vice versa.
Everyone who is not strong is either not funny or not tall.
Someone is curious or not patient.
Someone is patient or strong.
John is either not generous or creative.
Mary is not curious or generous.
Someone is either wise or rich.
Mary is strong or not tall.
Mary is old or not funny.
Someone is not old. | Lucy is not old. | neutral | (![X]:(~old(X)<=>(~tall(X)<~>~brave(X))))&
((?[X]:(funny(X)))<=>(?[X]:((quiet(X)|curious(X)))))&
(![X]:(old(X)<=>(happy(X)<~>patient(X))))&
(((~wise(susan)|~creative(susan)))=>((~rich(susan)<~>kind(susan))))&
(((~rich(paul)&tall(paul)))=>((~funny(john)<~>~generous(john))))&
(((~humble(lucy)|~tall(lucy)))<=>(?[X]:((generous(X)|brave(X)))))&
((?[X]:((~kind(X)&~quiet(X))))<=>(?[X]:((wise(X)&strong(X)))))&
(((~kind(lucy)&~old(lucy)))=>(?[X]:((~tall(X)&~funny(X)))))&
(![X]:((humble(X)|quiet(X))=>(patient(X)&~quiet(X))))&
(![X]:((~curious(X)&~brave(X))=>~curious(X)))&
(![X]:((humble(X)|~old(X))=>(calm(X)&patient(X))))&
(![X]:((happy(X)|patient(X))=>calm(X)))&
((?[X]:((generous(X)|~curious(X))))=>(?[X]:(humble(X))))&
((?[X]:((~humble(X)|~brave(X))))=>(?[X]:(tall(X))))&
(((~tall(lucy)|humble(lucy)))<=>(~kind(paul)))&
(![X]:(~strong(X)=>(~funny(X)<~>~tall(X))))&
(?[X]:((curious(X)|~patient(X))))&
(?[X]:((patient(X)|strong(X))))&
((~generous(john)<~>creative(john)))&
((~curious(mary)|generous(mary)))&
(?[X]:((wise(X)<~>rich(X))))&
((strong(mary)|~tall(mary)))&
((old(mary)|~funny(mary)))&
(?[X]:(~old(X))) | ~old(lucy) | [] | null | 0 |
If someone is not funny then someone is either creative or funny. Everyone who is tall or not wise is not calm or kind and vice versa. Everyone who is both not creative and old is brave or not strong and vice versa. Everyone who is tall is not brave. Everyone who is either brave or not quiet is either not patient or funny and vice versa. Everyone who is tall or not brave is either not curious or not creative and vice versa. If someone is both humble and brave then susan is not generous. If john is happy then fred is both humble and not patient and vice versa. Everyone who is not kind or not humble is either brave or not happy. If someone is both generous and not brave then paul is quiet and vice versa. If someone is not generous or brave then john is either kind or not quiet and vice versa. Everyone who is funny is both rich and calm. Everyone who is both humble and happy is not rich. Everyone who is old is not strong or not happy. Everyone who is not happy is either rich or happy and vice versa. Everyone who is creative or humble is not old or not creative and vice versa. Susan is brave. Mary is either not funny or calm. Mary is either not humble or happy. Fred is patient. Someone is either tall or strong. Someone is not generous. Someone is curious or strong. John is not brave. | Susan is not wise. | entailment | ((?[X]:(~funny(X)))=>(?[X]:((creative(X)<~>funny(X)))))&
(![X]:((tall(X)|~wise(X))<=>(~calm(X)|kind(X))))&
(![X]:((~creative(X)&old(X))<=>(brave(X)|~strong(X))))&
(![X]:(tall(X)=>~brave(X)))&
(![X]:((brave(X)<~>~quiet(X))<=>(~patient(X)<~>funny(X))))&
(![X]:((tall(X)|~brave(X))<=>(~curious(X)<~>~creative(X))))&
((?[X]:((humble(X)&brave(X))))=>(~generous(susan)))&
((happy(john))<=>((humble(fred)&~patient(fred))))&
(![X]:((~kind(X)|~humble(X))=>(brave(X)<~>~happy(X))))&
((?[X]:((generous(X)&~brave(X))))<=>(quiet(paul)))&
((?[X]:((~generous(X)|brave(X))))<=>((kind(john)<~>~quiet(john))))&
(![X]:(funny(X)=>(rich(X)&calm(X))))&
(![X]:((humble(X)&happy(X))=>~rich(X)))&
(![X]:(old(X)=>(~strong(X)|~happy(X))))&
(![X]:(~happy(X)<=>(rich(X)<~>happy(X))))&
(![X]:((creative(X)|humble(X))<=>(~old(X)|~creative(X))))&
(brave(susan))&
((~funny(mary)<~>calm(mary)))&
((~humble(mary)<~>happy(mary)))&
(patient(fred))&
(?[X]:((tall(X)<~>strong(X))))&
(?[X]:(~generous(X)))&
(?[X]:((curious(X)|strong(X))))&
(~brave(john)) | ~wise(susan) | [
"p1",
"p2",
"p3",
"p8",
"p12",
"p14",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 5826524214034724233904970
% SZS output start Proof for 5826524214034724233904970
2. ! [X0] : ((~wise(X0) | tall(X0)) <=> (kind(X0) | ~calm(X0))) [input p1]
3. ! [X0] : ((old(X0) & ~creative(X0)) <=> (~strong(X0) | brave(X0))) [input p2]
4. ! [X0] : (tall(X0) => ~brave(X0)) [input p3]
9. ! [X0] : ((~humble(X0) | ~kind(X0)) => (brave(X0) <~> ~happy(X0))) [input p8]
13. ! [X0] : ((happy(X0) & humble(X0)) => ~rich(X0)) [input p12]
15. ! [X0] : (~happy(X0) <=> (rich(X0) <~> happy(X0))) [input p14]
16. ! [X0] : ((humble(X0) | creative(X0)) <=> (~creative(X0) | ~old(X0))) [input p15]
17. brave(susan) [input p16]
25. wise(susan) [input hypothesis]
28. ! [X0] : (~brave(X0) | ~tall(X0)) [ennf transformation 4]
30. ! [X0] : ((brave(X0) <~> ~happy(X0)) | (humble(X0) & kind(X0))) [ennf transformation 9]
32. ! [X0] : (~rich(X0) | (~happy(X0) | ~humble(X0))) [ennf transformation 13]
33. ! [X0] : (~rich(X0) | ~happy(X0) | ~humble(X0)) [flattening 32]
40. ! [X0] : (((~wise(X0) | tall(X0)) | (~kind(X0) & calm(X0))) & ((kind(X0) | ~calm(X0)) | (wise(X0) & ~tall(X0)))) [nnf transformation 2]
41. ! [X0] : ((~wise(X0) | tall(X0) | (~kind(X0) & calm(X0))) & (kind(X0) | ~calm(X0) | (wise(X0) & ~tall(X0)))) [flattening 40]
42. ! [X0] : (((old(X0) & ~creative(X0)) | (strong(X0) & ~brave(X0))) & ((~strong(X0) | brave(X0)) | (~old(X0) | creative(X0)))) [nnf transformation 3]
43. ! [X0] : (((old(X0) & ~creative(X0)) | (strong(X0) & ~brave(X0))) & (~strong(X0) | brave(X0) | ~old(X0) | creative(X0))) [flattening 42]
49. ! [X0] : (((happy(X0) | ~brave(X0)) & (~happy(X0) | brave(X0))) | (humble(X0) & kind(X0))) [nnf transformation 30]
58. ! [X0] : ((~happy(X0) | ((rich(X0) | ~happy(X0)) & (happy(X0) | ~rich(X0)))) & (((~happy(X0) | ~rich(X0)) & (happy(X0) | rich(X0))) | happy(X0))) [nnf transformation 15]
59. ! [X0] : (((humble(X0) | creative(X0)) | (creative(X0) & old(X0))) & ((~creative(X0) | ~old(X0)) | (~humble(X0) & ~creative(X0)))) [nnf transformation 16]
60. ! [X0] : ((humble(X0) | creative(X0) | (creative(X0) & old(X0))) & (~creative(X0) | ~old(X0) | (~humble(X0) & ~creative(X0)))) [flattening 59]
75. ~kind(X0) | tall(X0) | ~wise(X0) [cnf transformation 41]
77. ~brave(X0) | ~creative(X0) [cnf transformation 43]
81. ~brave(X0) | ~tall(X0) [cnf transformation 28]
102. ~brave(X0) | happy(X0) | kind(X0) [cnf transformation 49]
115. ~rich(X0) | ~happy(X0) | ~humble(X0) [cnf transformation 33]
117. happy(X0) | rich(X0) | happy(X0) [cnf transformation 58]
120. ~happy(X0) | rich(X0) | ~happy(X0) [cnf transformation 58]
124. humble(X0) | creative(X0) | creative(X0) [cnf transformation 60]
125. brave(susan) [cnf transformation 17]
136. wise(susan) [cnf transformation 25]
138. humble(X0) | creative(X0) [duplicate literal removal 124]
139. happy(X0) | rich(X0) [duplicate literal removal 117]
140. ~happy(X0) | rich(X0) [duplicate literal removal 120]
226. rich(X0) [subsumption resolution 139,140]
266. ~creative(susan) [resolution 77,125]
270. ~tall(susan) [resolution 81,125]
287. happy(susan) | kind(susan) [resolution 102,125]
289. 27 <=> kind(susan) [avatar definition]
291. kind(susan) <- (27) [avatar component clause 289]
293. 28 <=> happy(susan) [avatar definition]
295. happy(susan) <- (28) [avatar component clause 293]
296. 27 | 28 [avatar split clause 287,293,289]
297. tall(susan) | ~wise(susan) <- (27) [resolution 291,75]
298. ~wise(susan) <- (27) [subsumption resolution 297,270]
299. $false <- (27) [subsumption resolution 298,136]
300. ~27 [avatar contradiction clause 299]
302. ~happy(X0) | ~humble(X0) [resolution 115,226]
310. ~humble(susan) <- (28) [resolution 302,295]
314. creative(susan) <- (28) [resolution 310,138]
315. $false <- (28) [subsumption resolution 314,266]
316. ~28 [avatar contradiction clause 315]
317. $false [avatar sat refutation 296,300,316]
% SZS output end Proof for 5826524214034724233904970
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not kind then alice is quiet.
Everyone who is both not strong and happy is either calm or not old and vice versa.
Everyone who is both not strong and not calm is both strong and funny.
If someone is either not old or funny then mary is not tall or not rich.
Everyone who is both patient and funny is generous and vice versa.
Everyone who is not brave is not creative or not brave.
If mary is either not tall or happy then someone is not rich or not wise.
Everyone who is not old is either creative or not calm.
If someone is either not creative or creative then someone is wise or not tall.
Everyone who is not strong is old or not rich.
If paul is both not generous and calm then someone is either not quiet or old and vice versa.
If lucy is kind or not old then someone is strong or kind.
If fred is creative or curious then susan is not quiet or not tall.
Everyone who is both not curious and old is not calm and vice versa.
Everyone who is creative is quiet and vice versa.
Everyone who is calm is both rich and not rich and vice versa.
Someone is not kind.
Someone is either not rich or not funny.
Alice is both not humble and not curious.
Someone is rich.
Lucy is curious or brave.
Someone is either not rich or not kind. | Alice is quiet. | contradiction | ((~kind(john))=>(quiet(alice)))&
(![X]:((~strong(X)&happy(X))<=>(calm(X)<~>~old(X))))&
(![X]:((~strong(X)&~calm(X))=>(strong(X)&funny(X))))&
((?[X]:((~old(X)<~>funny(X))))=>((~tall(mary)|~rich(mary))))&
(![X]:((patient(X)&funny(X))<=>generous(X)))&
(![X]:(~brave(X)=>(~creative(X)|~brave(X))))&
(((~tall(mary)<~>happy(mary)))=>(?[X]:((~rich(X)|~wise(X)))))&
(![X]:(~old(X)=>(creative(X)<~>~calm(X))))&
((?[X]:((~creative(X)<~>creative(X))))=>(?[X]:((wise(X)|~tall(X)))))&
(![X]:(~strong(X)=>(old(X)|~rich(X))))&
(((~generous(paul)&calm(paul)))<=>(?[X]:((~quiet(X)<~>old(X)))))&
(((kind(lucy)|~old(lucy)))=>(?[X]:((strong(X)|kind(X)))))&
(((creative(fred)|curious(fred)))=>((~quiet(susan)|~tall(susan))))&
(![X]:((~curious(X)&old(X))<=>~calm(X)))&
(![X]:(creative(X)<=>quiet(X)))&
(![X]:(calm(X)<=>(rich(X)&~rich(X))))&
(?[X]:(~kind(X)))&
(?[X]:((~rich(X)<~>~funny(X))))&
((~humble(alice)&~curious(alice)))&
(?[X]:(rich(X)))&
((curious(lucy)|brave(lucy)))&
(?[X]:((~rich(X)<~>~kind(X)))) | quiet(alice) | [
"p10",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2674315032411704960208972
% SZS output start Proof for 2674315032411704960208972
11. (calm(paul) & ~generous(paul)) <=> ? [X0] : (~quiet(X0) <~> old(X0)) [input p10]
14. ! [X0] : ((old(X0) & ~curious(X0)) <=> ~calm(X0)) [input p13]
16. ! [X0] : (calm(X0) <=> (~rich(X0) & rich(X0))) [input p15]
23. quiet(alice) [input hypothesis]
54. ((calm(paul) & ~generous(paul)) | ! [X0] : ((~quiet(X0) | ~old(X0)) & (old(X0) | quiet(X0)))) & (? [X0] : ((~old(X0) | quiet(X0)) & (old(X0) | ~quiet(X0))) | (~calm(paul) | generous(paul))) [nnf transformation 11]
55. ((calm(paul) & ~generous(paul)) | ! [X0] : ((~quiet(X0) | ~old(X0)) & (old(X0) | quiet(X0)))) & (? [X0] : ((~old(X0) | quiet(X0)) & (old(X0) | ~quiet(X0))) | ~calm(paul) | generous(paul)) [flattening 54]
56. ((calm(paul) & ~generous(paul)) | ! [X0] : ((~quiet(X0) | ~old(X0)) & (old(X0) | quiet(X0)))) & (? [X1] : ((~old(X1) | quiet(X1)) & (old(X1) | ~quiet(X1))) | ~calm(paul) | generous(paul)) [rectify 55]
57. ? [X1] : ((~old(X1) | quiet(X1)) & (old(X1) | ~quiet(X1))) => ((~old(sK2) | quiet(sK2)) & (old(sK2) | ~quiet(sK2))) [choice axiom]
58. ((calm(paul) & ~generous(paul)) | ! [X0] : ((~quiet(X0) | ~old(X0)) & (old(X0) | quiet(X0)))) & (((~old(sK2) | quiet(sK2)) & (old(sK2) | ~quiet(sK2))) | ~calm(paul) | generous(paul)) [skolemisation 56,57]
61. ! [X0] : (((old(X0) & ~curious(X0)) | calm(X0)) & (~calm(X0) | (~old(X0) | curious(X0)))) [nnf transformation 14]
62. ! [X0] : (((old(X0) & ~curious(X0)) | calm(X0)) & (~calm(X0) | ~old(X0) | curious(X0))) [flattening 61]
64. ! [X0] : ((calm(X0) | (rich(X0) | ~rich(X0))) & ((~rich(X0) & rich(X0)) | ~calm(X0))) [nnf transformation 16]
65. ! [X0] : ((calm(X0) | rich(X0) | ~rich(X0)) & ((~rich(X0) & rich(X0)) | ~calm(X0))) [flattening 64]
103. calm(paul) | ~quiet(X0) | ~old(X0) [cnf transformation 58]
110. old(X0) | calm(X0) [cnf transformation 62]
113. rich(X0) | ~calm(X0) [cnf transformation 65]
114. ~rich(X0) | ~calm(X0) [cnf transformation 65]
124. quiet(alice) [cnf transformation 23]
133. 2 <=> quiet(alice) [avatar definition]
135. quiet(alice) <- (2) [avatar component clause 133]
184. 14 <=> ! [X0] : (~quiet(X0) | ~old(X0)) [avatar definition]
185. ~old(X0) | ~quiet(X0) <- (14) [avatar component clause 184]
187. 15 <=> calm(paul) [avatar definition]
189. calm(paul) <- (15) [avatar component clause 187]
190. 14 | 15 [avatar split clause 103,187,184]
247. ~calm(X0) [subsumption resolution 113,114]
277. 2 [avatar split clause 124,133]
278. $false <- (15) [subsumption resolution 189,247]
279. ~15 [avatar contradiction clause 278]
293. ~quiet(X0) | calm(X0) <- (14) [resolution 185,110]
295. ~quiet(X0) <- (14) [subsumption resolution 293,247]
301. $false <- (2, 14) [resolution 295,135]
302. ~2 | ~14 [avatar contradiction clause 301]
303. $false [avatar sat refutation 190,277,279,302]
% SZS output end Proof for 2674315032411704960208972
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not brave and not calm is either not calm or not strong and vice versa.
Everyone who is both patient and not generous is either quiet or not old and vice versa.
If fred is either tall or not rich then someone is both not calm and not happy.
If mary is either not brave or tall then mary is both kind and generous and vice versa.
Everyone who is either humble or strong is either tall or curious and vice versa.
Everyone who is not wise is either quiet or funny and vice versa.
If someone is brave then someone is curious and vice versa.
If paul is either kind or not tall then alice is not quiet or not kind and vice versa.
If paul is either old or not curious then someone is generous and vice versa.
Everyone who is funny is strong or quiet and vice versa.
If susan is curious or generous then susan is quiet and vice versa.
If someone is either not strong or happy then paul is generous and vice versa.
Everyone who is either rich or not patient is wise or not curious.
Everyone who is not generous is either not curious or not brave and vice versa.
Everyone who is not kind is both generous and not tall.
Everyone who is not tall or not old is both old and not generous and vice versa.
John is both not happy and strong.
Someone is not rich or tall.
John is either strong or creative.
Someone is both wise and not generous.
John is not calm or not old.
Someone is either strong or not wise.
Someone is either not quiet or not brave.
Someone is not tall. | Susan is not generous. | entailment | (![X]:((~brave(X)&~calm(X))<=>(~calm(X)<~>~strong(X))))&
(![X]:((patient(X)&~generous(X))<=>(quiet(X)<~>~old(X))))&
(((tall(fred)<~>~rich(fred)))=>(?[X]:((~calm(X)&~happy(X)))))&
(((~brave(mary)<~>tall(mary)))<=>((kind(mary)&generous(mary))))&
(![X]:((humble(X)<~>strong(X))<=>(tall(X)<~>curious(X))))&
(![X]:(~wise(X)<=>(quiet(X)<~>funny(X))))&
((?[X]:(brave(X)))<=>(?[X]:(curious(X))))&
(((kind(paul)<~>~tall(paul)))<=>((~quiet(alice)|~kind(alice))))&
(((old(paul)<~>~curious(paul)))<=>(?[X]:(generous(X))))&
(![X]:(funny(X)<=>(strong(X)|quiet(X))))&
(((curious(susan)|generous(susan)))<=>(quiet(susan)))&
((?[X]:((~strong(X)<~>happy(X))))<=>(generous(paul)))&
(![X]:((rich(X)<~>~patient(X))=>(wise(X)|~curious(X))))&
(![X]:(~generous(X)<=>(~curious(X)<~>~brave(X))))&
(![X]:(~kind(X)=>(generous(X)&~tall(X))))&
(![X]:((~tall(X)|~old(X))<=>(old(X)&~generous(X))))&
((~happy(john)&strong(john)))&
(?[X]:((~rich(X)|tall(X))))&
((strong(john)<~>creative(john)))&
(?[X]:((wise(X)&~generous(X))))&
((~calm(john)|~old(john)))&
(?[X]:((strong(X)<~>~wise(X))))&
(?[X]:((~quiet(X)<~>~brave(X))))&
(?[X]:(~tall(X))) | ~generous(susan) | [
"p1",
"p10",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 5632634707793695182801908
% SZS output start Proof for 5632634707793695182801908
2. ! [X0] : ((~generous(X0) & patient(X0)) <=> (quiet(X0) <~> ~old(X0))) [input p1]
11. (generous(susan) | curious(susan)) <=> quiet(susan) [input p10]
16. ! [X0] : ((~old(X0) | ~tall(X0)) <=> (~generous(X0) & old(X0))) [input p15]
25. generous(susan) [input hypothesis]
33. ! [X0] : (((~generous(X0) & patient(X0)) | ((quiet(X0) | old(X0)) & (~old(X0) | ~quiet(X0)))) & (((old(X0) | ~quiet(X0)) & (~old(X0) | quiet(X0))) | (generous(X0) | ~patient(X0)))) [nnf transformation 2]
34. ! [X0] : (((~generous(X0) & patient(X0)) | ((quiet(X0) | old(X0)) & (~old(X0) | ~quiet(X0)))) & (((old(X0) | ~quiet(X0)) & (~old(X0) | quiet(X0))) | generous(X0) | ~patient(X0))) [flattening 33]
55. ((generous(susan) | curious(susan)) | ~quiet(susan)) & (quiet(susan) | (~generous(susan) & ~curious(susan))) [nnf transformation 11]
56. (generous(susan) | curious(susan) | ~quiet(susan)) & (quiet(susan) | (~generous(susan) & ~curious(susan))) [flattening 55]
63. ! [X0] : (((~old(X0) | ~tall(X0)) | (generous(X0) | ~old(X0))) & ((~generous(X0) & old(X0)) | (old(X0) & tall(X0)))) [nnf transformation 16]
64. ! [X0] : ((~old(X0) | ~tall(X0) | generous(X0) | ~old(X0)) & ((~generous(X0) & old(X0)) | (old(X0) & tall(X0)))) [flattening 63]
88. ~old(X0) | ~generous(X0) | ~quiet(X0) [cnf transformation 34]
128. quiet(susan) | ~generous(susan) [cnf transformation 56]
143. old(X0) | old(X0) [cnf transformation 64]
160. generous(susan) [cnf transformation 25]
161. old(X0) [duplicate literal removal 143]
266. 21 <=> quiet(susan) [avatar definition]
267. quiet(susan) <- (21) [avatar component clause 266]
274. 23 <=> generous(susan) [avatar definition]
276. generous(susan) <- (23) [avatar component clause 274]
278. ~23 | 21 [avatar split clause 128,266,274]
333. 23 [avatar split clause 160,274]
373. ~quiet(X1) | ~generous(X1) [resolution 88,161]
652. ~generous(susan) <- (21) [resolution 373,267]
654. $false <- (21, 23) [subsumption resolution 652,276]
655. ~21 | ~23 [avatar contradiction clause 654]
656. $false [avatar sat refutation 278,333,655]
% SZS output end Proof for 5632634707793695182801908
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If paul is either not generous or not wise then mary is both funny and not old and vice versa.
If lucy is both calm and curious then someone is either not old or not curious and vice versa.
Everyone who is both tall and not generous is rich or curious.
Everyone who is either not generous or not strong is not generous and vice versa.
Everyone who is rich is not curious or humble and vice versa.
If susan is not kind or not humble then alice is not strong and vice versa.
If alice is both not curious and not tall then alice is either not tall or not funny and vice versa.
Everyone who is either not humble or not wise is funny or curious.
Everyone who is brave or not brave is both happy and funny.
Everyone who is both not curious and not funny is not calm.
Everyone who is both not generous and generous is either not tall or not strong and vice versa.
If mary is either humble or creative then susan is not generous or creative and vice versa.
If lucy is not wise then susan is wise and vice versa.
Everyone who is both old and not wise is rich or not kind and vice versa.
If someone is calm or not creative then someone is both brave and patient and vice versa.
If paul is not kind then someone is both not old and kind and vice versa.
Mary is both not kind and old.
John is wise.
Someone is wise.
Mary is either happy or not happy.
Alice is either creative or not brave.
Someone is both old and not creative.
Someone is tall or not wise.
John is both strong and brave. | Mary is creative. | neutral | (((~generous(paul)<~>~wise(paul)))<=>((funny(mary)&~old(mary))))&
(((calm(lucy)&curious(lucy)))<=>(?[X]:((~old(X)<~>~curious(X)))))&
(![X]:((tall(X)&~generous(X))=>(rich(X)|curious(X))))&
(![X]:((~generous(X)<~>~strong(X))<=>~generous(X)))&
(![X]:(rich(X)<=>(~curious(X)|humble(X))))&
(((~kind(susan)|~humble(susan)))<=>(~strong(alice)))&
(((~curious(alice)&~tall(alice)))<=>((~tall(alice)<~>~funny(alice))))&
(![X]:((~humble(X)<~>~wise(X))=>(funny(X)|curious(X))))&
(![X]:((brave(X)|~brave(X))=>(happy(X)&funny(X))))&
(![X]:((~curious(X)&~funny(X))=>~calm(X)))&
(![X]:((~generous(X)&generous(X))<=>(~tall(X)<~>~strong(X))))&
(((humble(mary)<~>creative(mary)))<=>((~generous(susan)|creative(susan))))&
((~wise(lucy))<=>(wise(susan)))&
(![X]:((old(X)&~wise(X))<=>(rich(X)|~kind(X))))&
((?[X]:((calm(X)|~creative(X))))<=>(?[X]:((brave(X)&patient(X)))))&
((~kind(paul))<=>(?[X]:((~old(X)&kind(X)))))&
((~kind(mary)&old(mary)))&
(wise(john))&
(?[X]:(wise(X)))&
((happy(mary)<~>~happy(mary)))&
((creative(alice)<~>~brave(alice)))&
(?[X]:((old(X)&~creative(X))))&
(?[X]:((tall(X)|~wise(X))))&
((strong(john)&brave(john))) | creative(mary) | [] | null | 0 |
If john is both not creative and patient then someone is brave or curious.
Everyone who is both rich and curious is rich.
If someone is quiet then alice is not generous or generous.
Everyone who is patient is not wise and vice versa.
If someone is wise then fred is both strong and rich.
Everyone who is both not strong and not curious is patient and vice versa.
If susan is not calm then susan is not rich or old and vice versa.
If alice is not wise or not quiet then someone is old.
If fred is quiet or not wise then paul is either creative or not tall and vice versa.
Everyone who is both rich and strong is both not quiet and generous.
If susan is either not happy or old then alice is not old or curious.
If john is both not brave and not strong then someone is brave.
Everyone who is not rich is either not humble or not creative.
Everyone who is both not quiet and not happy is both not tall and quiet and vice versa.
If someone is calm then paul is both not rich and rich.
If mary is not patient then someone is either not old or not creative.
John is both not generous and old.
Alice is both not creative and not strong.
Lucy is either not brave or quiet.
Mary is not strong.
Lucy is happy or strong.
Someone is kind.
Someone is not funny.
Someone is happy or brave. | Paul is calm. | contradiction | (((~creative(john)&patient(john)))=>(?[X]:((brave(X)|curious(X)))))&
(![X]:((rich(X)&curious(X))=>rich(X)))&
((?[X]:(quiet(X)))=>((~generous(alice)|generous(alice))))&
(![X]:(patient(X)<=>~wise(X)))&
((?[X]:(wise(X)))=>((strong(fred)&rich(fred))))&
(![X]:((~strong(X)&~curious(X))<=>patient(X)))&
((~calm(susan))<=>((~rich(susan)|old(susan))))&
(((~wise(alice)|~quiet(alice)))=>(?[X]:(old(X))))&
(((quiet(fred)|~wise(fred)))<=>((creative(paul)<~>~tall(paul))))&
(![X]:((rich(X)&strong(X))=>(~quiet(X)&generous(X))))&
(((~happy(susan)<~>old(susan)))=>((~old(alice)|curious(alice))))&
(((~brave(john)&~strong(john)))=>(?[X]:(brave(X))))&
(![X]:(~rich(X)=>(~humble(X)<~>~creative(X))))&
(![X]:((~quiet(X)&~happy(X))<=>(~tall(X)&quiet(X))))&
((?[X]:(calm(X)))=>((~rich(paul)&rich(paul))))&
((~patient(mary))=>(?[X]:((~old(X)<~>~creative(X)))))&
((~generous(john)&old(john)))&
((~creative(alice)&~strong(alice)))&
((~brave(lucy)<~>quiet(lucy)))&
(~strong(mary))&
((happy(lucy)|strong(lucy)))&
(?[X]:(kind(X)))&
(?[X]:(~funny(X)))&
(?[X]:((happy(X)|brave(X)))) | calm(paul) | [
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4542996790734709863842901
% SZS output start Proof for 4542996790734709863842901
15. ? [X0] : calm(X0) => (rich(paul) & ~rich(paul)) [input p14]
25. calm(paul) [input hypothesis]
43. (rich(paul) & ~rich(paul)) | ! [X0] : ~calm(X0) [ennf transformation 15]
100. ~rich(paul) | ~calm(X0) [cnf transformation 43]
101. rich(paul) | ~calm(X0) [cnf transformation 43]
113. calm(paul) [cnf transformation 25]
225. 24 <=> ! [X0] : ~calm(X0) [avatar definition]
226. ~calm(X0) <- (24) [avatar component clause 225]
228. 25 <=> rich(paul) [avatar definition]
231. 24 | 25 [avatar split clause 101,228,225]
232. 24 | ~25 [avatar split clause 100,228,225]
275. $false <- (24) [resolution 226,113]
276. ~24 [avatar contradiction clause 275]
277. $false [avatar sat refutation 231,232,276]
% SZS output end Proof for 4542996790734709863842901
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble or not creative is not happy or not rich.
Everyone who is not humble or creative is not strong.
Everyone who is not wise is both generous and strong.
If someone is either not quiet or wise then lucy is creative and vice versa.
Everyone who is strong is either curious or calm and vice versa.
If lucy is both quiet and not kind then susan is either tall or not patient.
If someone is not rich then alice is not rich or brave.
Everyone who is either curious or tall is both tall and not happy.
Everyone who is both old and patient is either not brave or not tall and vice versa.
Everyone who is either quiet or happy is not funny or humble and vice versa.
Everyone who is not generous or not kind is not generous and vice versa.
Everyone who is both strong and tall is either not tall or creative and vice versa.
Everyone who is either not rich or not strong is not curious or calm and vice versa.
If paul is either not generous or not wise then mary is rich.
Everyone who is both curious and creative is not creative or not happy and vice versa.
If alice is either not kind or not creative then john is quiet or not happy and vice versa.
Fred is either not rich or not old.
Someone is not curious or not humble.
Someone is both quiet and not tall.
Someone is either generous or happy.
Mary is strong or generous.
Someone is not wise or old. | Susan is calm. | contradiction | (![X]:((humble(X)<~>~creative(X))=>(~happy(X)|~rich(X))))&
(![X]:((~humble(X)|creative(X))=>~strong(X)))&
(![X]:(~wise(X)=>(generous(X)&strong(X))))&
((?[X]:((~quiet(X)<~>wise(X))))<=>(creative(lucy)))&
(![X]:(strong(X)<=>(curious(X)<~>calm(X))))&
(((quiet(lucy)&~kind(lucy)))=>((tall(susan)<~>~patient(susan))))&
((?[X]:(~rich(X)))=>((~rich(alice)|brave(alice))))&
(![X]:((curious(X)<~>tall(X))=>(tall(X)&~happy(X))))&
(![X]:((old(X)&patient(X))<=>(~brave(X)<~>~tall(X))))&
(![X]:((quiet(X)<~>happy(X))<=>(~funny(X)|humble(X))))&
(![X]:((~generous(X)|~kind(X))<=>~generous(X)))&
(![X]:((strong(X)&tall(X))<=>(~tall(X)<~>creative(X))))&
(![X]:((~rich(X)<~>~strong(X))<=>(~curious(X)|calm(X))))&
(((~generous(paul)<~>~wise(paul)))=>(rich(mary)))&
(![X]:((curious(X)&creative(X))<=>(~creative(X)|~happy(X))))&
(((~kind(alice)<~>~creative(alice)))<=>((quiet(john)|~happy(john))))&
((~rich(fred)<~>~old(fred)))&
(?[X]:((~curious(X)|~humble(X))))&
(?[X]:((quiet(X)&~tall(X))))&
(?[X]:((generous(X)<~>happy(X))))&
((strong(mary)|generous(mary)))&
(?[X]:((~wise(X)|old(X)))) | calm(susan) | [
"p1",
"p4",
"p7",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8619628335577897142414765
% SZS output start Proof for 8619628335577897142414765
2. ! [X0] : ((creative(X0) | ~humble(X0)) => ~strong(X0)) [input p1]
5. ! [X0] : (strong(X0) <=> (curious(X0) <~> calm(X0))) [input p4]
8. ! [X0] : ((curious(X0) <~> tall(X0)) => (~happy(X0) & tall(X0))) [input p7]
12. ! [X0] : ((tall(X0) & strong(X0)) <=> (~tall(X0) <~> creative(X0))) [input p11]
15. ! [X0] : ((creative(X0) & curious(X0)) <=> (~happy(X0) | ~creative(X0))) [input p14]
23. calm(susan) [input hypothesis]
26. ! [X0] : (~strong(X0) | (~creative(X0) & humble(X0))) [ennf transformation 2]
32. ! [X0] : ((~happy(X0) & tall(X0)) | (curious(X0) <=> tall(X0))) [ennf transformation 8]
39. ! [X0] : ((strong(X0) | ((curious(X0) | ~calm(X0)) & (calm(X0) | ~curious(X0)))) & (((~calm(X0) | ~curious(X0)) & (calm(X0) | curious(X0))) | ~strong(X0))) [nnf transformation 5]
41. ! [X0] : ((~happy(X0) & tall(X0)) | ((curious(X0) | ~tall(X0)) & (tall(X0) | ~curious(X0)))) [nnf transformation 32]
48. ! [X0] : (((tall(X0) & strong(X0)) | ((~tall(X0) | ~creative(X0)) & (creative(X0) | tall(X0)))) & (((~creative(X0) | tall(X0)) & (creative(X0) | ~tall(X0))) | (~tall(X0) | ~strong(X0)))) [nnf transformation 12]
49. ! [X0] : (((tall(X0) & strong(X0)) | ((~tall(X0) | ~creative(X0)) & (creative(X0) | tall(X0)))) & (((~creative(X0) | tall(X0)) & (creative(X0) | ~tall(X0))) | ~tall(X0) | ~strong(X0))) [flattening 48]
53. ! [X0] : (((creative(X0) & curious(X0)) | (happy(X0) & creative(X0))) & ((~happy(X0) | ~creative(X0)) | (~creative(X0) | ~curious(X0)))) [nnf transformation 15]
54. ! [X0] : (((creative(X0) & curious(X0)) | (happy(X0) & creative(X0))) & (~happy(X0) | ~creative(X0) | ~creative(X0) | ~curious(X0))) [flattening 53]
70. ~strong(X0) | ~creative(X0) [cnf transformation 26]
80. ~calm(X0) | curious(X0) | strong(X0) [cnf transformation 39]
84. tall(X0) | tall(X0) | ~curious(X0) [cnf transformation 41]
106. strong(X0) | ~tall(X0) | ~creative(X0) [cnf transformation 49]
120. creative(X0) | creative(X0) [cnf transformation 54]
137. calm(susan) [cnf transformation 23]
139. creative(X0) [duplicate literal removal 120]
142. ~curious(X0) | tall(X0) [duplicate literal removal 84]
174. 8 <=> tall(susan) [avatar definition]
175. tall(susan) <- (8) [avatar component clause 174]
195. ~tall(X0) | ~creative(X0) [subsumption resolution 106,70]
314. 29 <=> strong(susan) [avatar definition]
315. strong(susan) <- (29) [avatar component clause 314]
318. 30 <=> curious(susan) [avatar definition]
319. curious(susan) <- (30) [avatar component clause 318]
323. curious(susan) | strong(susan) [resolution 80,137]
326. 29 | 30 [avatar split clause 323,318,314]
328. ~creative(susan) <- (29) [resolution 315,70]
330. $false <- (29) [subsumption resolution 328,139]
331. ~29 [avatar contradiction clause 330]
337. tall(susan) <- (30) [resolution 319,142]
340. 8 | ~30 [avatar split clause 337,318,174]
343. ~creative(susan) <- (8) [resolution 175,195]
344. $false <- (8) [subsumption resolution 343,139]
345. ~8 [avatar contradiction clause 344]
346. $false [avatar sat refutation 326,331,340,345]
% SZS output end Proof for 8619628335577897142414765
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either calm or not strong is either brave or quiet.
Everyone who is patient is not rich.
If someone is either not patient or rich then someone is not curious or old and vice versa.
Everyone who is either kind or calm is patient or not kind.
If someone is not generous or old then someone is either brave or funny.
If john is either happy or not curious then mary is either not kind or wise and vice versa.
Everyone who is either not brave or humble is either not rich or not wise.
Everyone who is not kind is brave.
Everyone who is not patient or not old is patient or rich and vice versa.
If someone is either not funny or not patient then paul is creative.
Everyone who is not strong or not kind is kind or curious and vice versa.
If someone is old then fred is not humble and vice versa.
Everyone who is tall is generous and vice versa.
If someone is both curious and funny then someone is either curious or not humble and vice versa.
If paul is both not wise and not kind then someone is not rich or not calm and vice versa.
Everyone who is either not humble or not old is not generous.
Someone is either calm or old.
Lucy is quiet or humble.
Someone is humble or not happy.
Fred is not funny or calm.
Fred is either curious or creative.
John is both patient and not kind.
Someone is either not patient or brave.
Someone is happy. | Paul is not old. | entailment | (![X]:((calm(X)<~>~strong(X))=>(brave(X)<~>quiet(X))))&
(![X]:(patient(X)=>~rich(X)))&
((?[X]:((~patient(X)<~>rich(X))))<=>(?[X]:((~curious(X)|old(X)))))&
(![X]:((kind(X)<~>calm(X))=>(patient(X)|~kind(X))))&
((?[X]:((~generous(X)|old(X))))=>(?[X]:((brave(X)<~>funny(X)))))&
(((happy(john)<~>~curious(john)))<=>((~kind(mary)<~>wise(mary))))&
(![X]:((~brave(X)<~>humble(X))=>(~rich(X)<~>~wise(X))))&
(![X]:(~kind(X)=>brave(X)))&
(![X]:((~patient(X)|~old(X))<=>(patient(X)|rich(X))))&
((?[X]:((~funny(X)<~>~patient(X))))=>(creative(paul)))&
(![X]:((~strong(X)|~kind(X))<=>(kind(X)|curious(X))))&
((?[X]:(old(X)))<=>(~humble(fred)))&
(![X]:(tall(X)<=>generous(X)))&
((?[X]:((curious(X)&funny(X))))<=>(?[X]:((curious(X)<~>~humble(X)))))&
(((~wise(paul)&~kind(paul)))<=>(?[X]:((~rich(X)|~calm(X)))))&
(![X]:((~humble(X)<~>~old(X))=>~generous(X)))&
(?[X]:((calm(X)<~>old(X))))&
((quiet(lucy)|humble(lucy)))&
(?[X]:((humble(X)|~happy(X))))&
((~funny(fred)|calm(fred)))&
((curious(fred)<~>creative(fred)))&
((patient(john)&~kind(john)))&
(?[X]:((~patient(X)<~>brave(X))))&
(?[X]:(happy(X))) | ~old(paul) | [
"p1",
"p2",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 3560122900644876427380887
% SZS output start Proof for 3560122900644876427380887
2. ! [X0] : (patient(X0) => ~rich(X0)) [input p1]
3. ? [X0] : (~patient(X0) <~> rich(X0)) <=> ? [X0] : (old(X0) | ~curious(X0)) [input p2]
9. ! [X0] : ((~old(X0) | ~patient(X0)) <=> (rich(X0) | patient(X0))) [input p8]
25. old(paul) [input hypothesis]
26. ? [X0] : (~patient(X0) <~> rich(X0)) <=> ? [X1] : (old(X1) | ~curious(X1)) [rectify 3]
30. ! [X0] : (~rich(X0) | ~patient(X0)) [ennf transformation 2]
39. (? [X0] : ((~rich(X0) | patient(X0)) & (rich(X0) | ~patient(X0))) | ! [X1] : (~old(X1) & curious(X1))) & (? [X1] : (old(X1) | ~curious(X1)) | ! [X0] : ((~patient(X0) | ~rich(X0)) & (rich(X0) | patient(X0)))) [nnf transformation 26]
40. (? [X0] : ((~rich(X0) | patient(X0)) & (rich(X0) | ~patient(X0))) | ! [X1] : (~old(X1) & curious(X1))) & (? [X2] : (old(X2) | ~curious(X2)) | ! [X3] : ((~patient(X3) | ~rich(X3)) & (rich(X3) | patient(X3)))) [rectify 39]
41. ? [X0] : ((~rich(X0) | patient(X0)) & (rich(X0) | ~patient(X0))) => ((~rich(sK0) | patient(sK0)) & (rich(sK0) | ~patient(sK0))) [choice axiom]
42. ? [X2] : (old(X2) | ~curious(X2)) => (old(sK1) | ~curious(sK1)) [choice axiom]
43. (((~rich(sK0) | patient(sK0)) & (rich(sK0) | ~patient(sK0))) | ! [X1] : (~old(X1) & curious(X1))) & ((old(sK1) | ~curious(sK1)) | ! [X3] : ((~patient(X3) | ~rich(X3)) & (rich(X3) | patient(X3)))) [skolemisation 40,42,41]
51. ! [X0] : (((~old(X0) | ~patient(X0)) | (~rich(X0) & ~patient(X0))) & ((rich(X0) | patient(X0)) | (old(X0) & patient(X0)))) [nnf transformation 9]
52. ! [X0] : ((~old(X0) | ~patient(X0) | (~rich(X0) & ~patient(X0))) & (rich(X0) | patient(X0) | (old(X0) & patient(X0)))) [flattening 51]
86. ~rich(X0) | ~patient(X0) [cnf transformation 30]
90. rich(sK0) | ~patient(sK0) | ~old(X1) [cnf transformation 43]
92. ~rich(sK0) | patient(sK0) | ~old(X1) [cnf transformation 43]
112. rich(X0) | patient(X0) | patient(X0) [cnf transformation 52]
149. old(paul) [cnf transformation 25]
152. rich(X0) | patient(X0) [duplicate literal removal 112]
155. ~rich(sK0) | ~old(X1) [subsumption resolution 92,86]
157. 1 <=> ! [X1] : ~old(X1) [avatar definition]
158. ~old(X1) <- (1) [avatar component clause 157]
160. 2 <=> rich(sK0) [avatar definition]
162. ~rich(sK0) <- (~2) [avatar component clause 160]
163. 1 | ~2 [avatar split clause 155,160,157]
169. ~patient(sK0) | ~old(X1) [subsumption resolution 90,86]
171. 4 <=> patient(sK0) [avatar definition]
173. ~patient(sK0) <- (~4) [avatar component clause 171]
174. 1 | ~4 [avatar split clause 169,171,157]
178. 5 <=> ! [X3] : (rich(X3) | patient(X3)) [avatar definition]
179. rich(X3) | patient(X3) <- (5) [avatar component clause 178]
228. 5 [avatar split clause 152,178]
379. patient(sK0) <- (~2, 5) [resolution 179,162]
382. $false <- (~2, ~4, 5) [subsumption resolution 379,173]
383. 2 | 4 | ~5 [avatar contradiction clause 382]
384. $false <- (1) [resolution 158,149]
387. ~1 [avatar contradiction clause 384]
388. $false [avatar sat refutation 163,174,228,383,387]
% SZS output end Proof for 3560122900644876427380887
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both generous and not happy then someone is generous or not tall. If someone is wise then someone is not humble or old and vice versa. Everyone who is funny or patient is both not kind and humble. If someone is creative or not brave then mary is either rich or patient and vice versa. Everyone who is not rich or not calm is either wise or not humble and vice versa. If someone is either not humble or rich then fred is both brave and wise. If alice is either not kind or curious then someone is not old or happy and vice versa. Everyone who is either happy or strong is not patient and vice versa. If susan is creative then someone is not strong or not happy. If susan is creative then fred is wise and vice versa. If someone is both generous and not brave then someone is not humble or tall. If someone is curious then mary is not generous and vice versa. Everyone who is both not funny and not happy is both creative and not funny. Everyone who is not rich or not quiet is not tall. If lucy is both happy and wise then someone is not kind. Everyone who is both brave and not tall is either rich or not old. Someone is wise or old. Someone is quiet. John is either not strong or not generous. Someone is either generous or not rich. John is both kind and not humble. Susan is not curious. Someone is either patient or wise. Someone is not old or not rich. | John is not patient. | entailment | ((?[X]:((generous(X)&~happy(X))))=>(?[X]:((generous(X)|~tall(X)))))&
((?[X]:(wise(X)))<=>(?[X]:((~humble(X)|old(X)))))&
(![X]:((funny(X)|patient(X))=>(~kind(X)&humble(X))))&
((?[X]:((creative(X)|~brave(X))))<=>((rich(mary)<~>patient(mary))))&
(![X]:((~rich(X)|~calm(X))<=>(wise(X)<~>~humble(X))))&
((?[X]:((~humble(X)<~>rich(X))))=>((brave(fred)&wise(fred))))&
(((~kind(alice)<~>curious(alice)))<=>(?[X]:((~old(X)|happy(X)))))&
(![X]:((happy(X)<~>strong(X))<=>~patient(X)))&
((creative(susan))=>(?[X]:((~strong(X)|~happy(X)))))&
((creative(susan))<=>(wise(fred)))&
((?[X]:((generous(X)&~brave(X))))=>(?[X]:((~humble(X)|tall(X)))))&
((?[X]:(curious(X)))<=>(~generous(mary)))&
(![X]:((~funny(X)&~happy(X))=>(creative(X)&~funny(X))))&
(![X]:((~rich(X)|~quiet(X))=>~tall(X)))&
(((happy(lucy)&wise(lucy)))=>(?[X]:(~kind(X))))&
(![X]:((brave(X)&~tall(X))=>(rich(X)<~>~old(X))))&
(?[X]:((wise(X)|old(X))))&
(?[X]:(quiet(X)))&
((~strong(john)<~>~generous(john)))&
(?[X]:((generous(X)<~>~rich(X))))&
((kind(john)&~humble(john)))&
(~curious(susan))&
(?[X]:((patient(X)<~>wise(X))))&
(?[X]:((~old(X)|~rich(X)))) | ~patient(john) | [
"p2",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 2420573848090869128492007
% SZS output start Proof for 2420573848090869128492007
3. ! [X0] : ((patient(X0) | funny(X0)) => (humble(X0) & ~kind(X0))) [input p2]
21. ~humble(john) & kind(john) [input p20]
25. patient(john) [input hypothesis]
32. ! [X0] : ((humble(X0) & ~kind(X0)) | (~patient(X0) & ~funny(X0))) [ennf transformation 3]
92. ~kind(X0) | ~patient(X0) [cnf transformation 32]
138. kind(john) [cnf transformation 21]
144. patient(john) [cnf transformation 25]
358. ~patient(john) [resolution 92,138]
359. $false [subsumption resolution 358,144]
% SZS output end Proof for 2420573848090869128492007
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy and not creative is not tall or funny. Everyone who is both not generous and not rich is not strong and vice versa. Everyone who is brave is both humble and not curious. If alice is either not quiet or quiet then lucy is either not creative or humble. If someone is brave then someone is either wise or not rich and vice versa. If someone is both calm and not wise then someone is generous or creative. Everyone who is not brave or not strong is both kind and not brave. If alice is curious or creative then someone is not brave or generous. If mary is not curious or not funny then lucy is both brave and not humble and vice versa. Everyone who is either patient or not generous is either not creative or not tall. Everyone who is not happy is either not curious or creative and vice versa. Everyone who is either calm or generous is either quiet or rich. Everyone who is either not brave or not happy is either quiet or not creative and vice versa. Everyone who is either generous or not tall is both not curious and wise. If john is either quiet or not quiet then someone is either not curious or kind and vice versa. Everyone who is either not brave or strong is not kind or not tall and vice versa. Someone is not old or tall. Someone is not wise or humble. Alice is brave. Susan is either curious or not creative. Susan is both not funny and rich. Someone is both generous and not calm. | Susan is wise. | neutral | (![X]:((~happy(X)&~creative(X))=>(~tall(X)|funny(X))))&
(![X]:((~generous(X)&~rich(X))<=>~strong(X)))&
(![X]:(brave(X)=>(humble(X)&~curious(X))))&
(((~quiet(alice)<~>quiet(alice)))=>((~creative(lucy)<~>humble(lucy))))&
((?[X]:(brave(X)))<=>(?[X]:((wise(X)<~>~rich(X)))))&
((?[X]:((calm(X)&~wise(X))))=>(?[X]:((generous(X)|creative(X)))))&
(![X]:((~brave(X)|~strong(X))=>(kind(X)&~brave(X))))&
(((curious(alice)|creative(alice)))=>(?[X]:((~brave(X)|generous(X)))))&
(((~curious(mary)|~funny(mary)))<=>((brave(lucy)&~humble(lucy))))&
(![X]:((patient(X)<~>~generous(X))=>(~creative(X)<~>~tall(X))))&
(![X]:(~happy(X)<=>(~curious(X)<~>creative(X))))&
(![X]:((calm(X)<~>generous(X))=>(quiet(X)<~>rich(X))))&
(![X]:((~brave(X)<~>~happy(X))<=>(quiet(X)<~>~creative(X))))&
(![X]:((generous(X)<~>~tall(X))=>(~curious(X)&wise(X))))&
(((quiet(john)<~>~quiet(john)))<=>(?[X]:((~curious(X)<~>kind(X)))))&
(![X]:((~brave(X)<~>strong(X))<=>(~kind(X)|~tall(X))))&
(?[X]:((~old(X)|tall(X))))&
(?[X]:((~wise(X)|humble(X))))&
(brave(alice))&
((curious(susan)<~>~creative(susan)))&
((~funny(susan)&rich(susan)))&
(?[X]:((generous(X)&~calm(X)))) | wise(susan) | [] | null | 0 |
Everyone who is both quiet and funny is both not rich and quiet and vice versa. Everyone who is both not generous and curious is humble. Everyone who is either quiet or old is either not creative or curious. Everyone who is rich is either kind or not creative. Everyone who is either calm or not calm is generous or tall and vice versa. Everyone who is both not strong and calm is funny. Everyone who is not quiet is both not calm and not happy and vice versa. Everyone who is either rich or funny is humble or not quiet. If susan is not old or brave then someone is either strong or not calm and vice versa. Everyone who is either not funny or not calm is either not rich or not quiet and vice versa. If alice is not strong then mary is both not calm and not patient. If susan is calm or not rich then lucy is both old and not curious. If someone is not patient then paul is both calm and strong and vice versa. Everyone who is not brave or not tall is both not strong and patient. If paul is either not humble or funny then paul is either humble or generous. Everyone who is either not calm or kind is both happy and not calm and vice versa. Paul is not kind or funny. Alice is brave or not strong. Someone is not humble. Someone is both not creative and not humble. Someone is not tall. Someone is not brave or rich. Someone is funny. | Paul is humble. | neutral | (![X]:((quiet(X)&funny(X))<=>(~rich(X)&quiet(X))))&
(![X]:((~generous(X)&curious(X))=>humble(X)))&
(![X]:((quiet(X)<~>old(X))=>(~creative(X)<~>curious(X))))&
(![X]:(rich(X)=>(kind(X)<~>~creative(X))))&
(![X]:((calm(X)<~>~calm(X))<=>(generous(X)|tall(X))))&
(![X]:((~strong(X)&calm(X))=>funny(X)))&
(![X]:(~quiet(X)<=>(~calm(X)&~happy(X))))&
(![X]:((rich(X)<~>funny(X))=>(humble(X)|~quiet(X))))&
(((~old(susan)|brave(susan)))<=>(?[X]:((strong(X)<~>~calm(X)))))&
(![X]:((~funny(X)<~>~calm(X))<=>(~rich(X)<~>~quiet(X))))&
((~strong(alice))=>((~calm(mary)&~patient(mary))))&
(((calm(susan)|~rich(susan)))=>((old(lucy)&~curious(lucy))))&
((?[X]:(~patient(X)))<=>((calm(paul)&strong(paul))))&
(![X]:((~brave(X)|~tall(X))=>(~strong(X)&patient(X))))&
(((~humble(paul)<~>funny(paul)))=>((humble(paul)<~>generous(paul))))&
(![X]:((~calm(X)<~>kind(X))<=>(happy(X)&~calm(X))))&
((~kind(paul)|funny(paul)))&
((brave(alice)|~strong(alice)))&
(?[X]:(~humble(X)))&
(?[X]:((~creative(X)&~humble(X))))&
(?[X]:(~tall(X)))&
(?[X]:((~brave(X)|rich(X))))&
(?[X]:(funny(X))) | humble(paul) | [] | null | 0 |
Everyone who is not creative is tall.
If someone is either wise or not happy then paul is either tall or not funny and vice versa.
Everyone who is either not tall or creative is both funny and not rich and vice versa.
Everyone who is both creative and not old is curious or tall and vice versa.
If someone is either not brave or humble then lucy is not quiet or rich and vice versa.
If someone is not patient or wise then someone is not patient.
If someone is tall then someone is not kind or funny and vice versa.
Everyone who is patient or not old is quiet or not happy and vice versa.
Everyone who is not happy is both old and not old.
If fred is not humble then mary is either not quiet or not humble.
Everyone who is brave or humble is creative.
If mary is wise then fred is kind and vice versa.
Everyone who is humble or wise is either not brave or old and vice versa.
Everyone who is generous or funny is both not funny and not quiet.
If susan is kind or wise then someone is either generous or old and vice versa.
Everyone who is both quiet and calm is both not happy and patient and vice versa.
Paul is both not strong and not brave.
Fred is not generous.
John is curious.
Lucy is both wise and not strong.
Someone is either happy or not strong.
Susan is either tall or kind. | John is not calm. | entailment | (![X]:(~creative(X)=>tall(X)))&
((?[X]:((wise(X)<~>~happy(X))))<=>((tall(paul)<~>~funny(paul))))&
(![X]:((~tall(X)<~>creative(X))<=>(funny(X)&~rich(X))))&
(![X]:((creative(X)&~old(X))<=>(curious(X)|tall(X))))&
((?[X]:((~brave(X)<~>humble(X))))<=>((~quiet(lucy)|rich(lucy))))&
((?[X]:((~patient(X)|wise(X))))=>(?[X]:(~patient(X))))&
((?[X]:(tall(X)))<=>(?[X]:((~kind(X)|funny(X)))))&
(![X]:((patient(X)|~old(X))<=>(quiet(X)|~happy(X))))&
(![X]:(~happy(X)=>(old(X)&~old(X))))&
((~humble(fred))=>((~quiet(mary)<~>~humble(mary))))&
(![X]:((brave(X)|humble(X))=>creative(X)))&
((wise(mary))<=>(kind(fred)))&
(![X]:((humble(X)|wise(X))<=>(~brave(X)<~>old(X))))&
(![X]:((generous(X)|funny(X))=>(~funny(X)&~quiet(X))))&
(((kind(susan)|wise(susan)))<=>(?[X]:((generous(X)<~>old(X)))))&
(![X]:((quiet(X)&calm(X))<=>(~happy(X)&patient(X))))&
((~strong(paul)&~brave(paul)))&
(~generous(fred))&
(curious(john))&
((wise(lucy)&~strong(lucy)))&
(?[X]:((happy(X)<~>~strong(X))))&
((tall(susan)<~>kind(susan))) | ~calm(john) | [
"p3",
"p7",
"p8",
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 4510700471179818200118479
% SZS output start Proof for 4510700471179818200118479
4. ! [X0] : ((~old(X0) & creative(X0)) <=> (tall(X0) | curious(X0))) [input p3]
8. ! [X0] : ((~old(X0) | patient(X0)) <=> (~happy(X0) | quiet(X0))) [input p7]
9. ! [X0] : (~happy(X0) => (~old(X0) & old(X0))) [input p8]
16. ! [X0] : ((calm(X0) & quiet(X0)) <=> (patient(X0) & ~happy(X0))) [input p15]
19. curious(john) [input p18]
23. calm(john) [input hypothesis]
28. ! [X0] : ((~old(X0) & old(X0)) | happy(X0)) [ennf transformation 9]
38. ! [X0] : (((~old(X0) & creative(X0)) | (~tall(X0) & ~curious(X0))) & ((tall(X0) | curious(X0)) | (old(X0) | ~creative(X0)))) [nnf transformation 4]
39. ! [X0] : (((~old(X0) & creative(X0)) | (~tall(X0) & ~curious(X0))) & (tall(X0) | curious(X0) | old(X0) | ~creative(X0))) [flattening 38]
53. ! [X0] : (((~old(X0) | patient(X0)) | (happy(X0) & ~quiet(X0))) & ((~happy(X0) | quiet(X0)) | (old(X0) & ~patient(X0)))) [nnf transformation 8]
54. ! [X0] : ((~old(X0) | patient(X0) | (happy(X0) & ~quiet(X0))) & (~happy(X0) | quiet(X0) | (old(X0) & ~patient(X0)))) [flattening 53]
64. ! [X0] : (((calm(X0) & quiet(X0)) | (~patient(X0) | happy(X0))) & ((patient(X0) & ~happy(X0)) | (~calm(X0) | ~quiet(X0)))) [nnf transformation 16]
65. ! [X0] : (((calm(X0) & quiet(X0)) | ~patient(X0) | happy(X0)) & ((patient(X0) & ~happy(X0)) | ~calm(X0) | ~quiet(X0))) [flattening 64]
88. ~curious(X0) | ~old(X0) [cnf transformation 39]
102. ~happy(X0) | quiet(X0) | old(X0) [cnf transformation 54]
105. old(X0) | happy(X0) [cnf transformation 28]
106. ~old(X0) | happy(X0) [cnf transformation 28]
129. ~happy(X0) | ~calm(X0) | ~quiet(X0) [cnf transformation 65]
136. curious(john) [cnf transformation 19]
143. calm(john) [cnf transformation 23]
243. happy(X0) [subsumption resolution 105,106]
297. ~calm(X0) | ~quiet(X0) [subsumption resolution 129,243]
313. ~old(john) [resolution 88,136]
316. ~quiet(john) [resolution 297,143]
328. quiet(X0) | old(X0) [resolution 102,243]
332. old(john) [resolution 328,316]
334. $false [subsumption resolution 332,313]
% SZS output end Proof for 4510700471179818200118479
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy or generous is brave or not curious. If susan is both not happy and creative then alice is not curious or brave and vice versa. Everyone who is rich is not happy. Everyone who is patient is not funny or not old and vice versa. Everyone who is funny or not calm is either creative or patient. If someone is not funny then fred is not brave. Everyone who is patient or generous is both not curious and not generous and vice versa. If someone is either old or curious then alice is either rich or not happy and vice versa. If someone is not happy then mary is either brave or funny and vice versa. If someone is both old and rich then someone is not wise or not humble and vice versa. If paul is humble or kind then lucy is not happy. Everyone who is calm or brave is either not old or humble and vice versa. If someone is either not strong or creative then john is brave or not quiet. If someone is both generous and happy then someone is humble. Everyone who is funny or not old is either brave or not generous. Everyone who is wise is rich or not old and vice versa. Alice is either quiet or not generous. Someone is not old. Lucy is happy. Someone is not quiet or not creative. Someone is kind. Someone is either brave or wise. John is both strong and not brave. Someone is not wise. | Alice is rich. | neutral | (![X]:((happy(X)|generous(X))=>(brave(X)|~curious(X))))&
(((~happy(susan)&creative(susan)))<=>((~curious(alice)|brave(alice))))&
(![X]:(rich(X)=>~happy(X)))&
(![X]:(patient(X)<=>(~funny(X)|~old(X))))&
(![X]:((funny(X)|~calm(X))=>(creative(X)<~>patient(X))))&
((?[X]:(~funny(X)))=>(~brave(fred)))&
(![X]:((patient(X)|generous(X))<=>(~curious(X)&~generous(X))))&
((?[X]:((old(X)<~>curious(X))))<=>((rich(alice)<~>~happy(alice))))&
((?[X]:(~happy(X)))<=>((brave(mary)<~>funny(mary))))&
((?[X]:((old(X)&rich(X))))<=>(?[X]:((~wise(X)|~humble(X)))))&
(((humble(paul)|kind(paul)))=>(~happy(lucy)))&
(![X]:((calm(X)|brave(X))<=>(~old(X)<~>humble(X))))&
((?[X]:((~strong(X)<~>creative(X))))=>((brave(john)|~quiet(john))))&
((?[X]:((generous(X)&happy(X))))=>(?[X]:(humble(X))))&
(![X]:((funny(X)|~old(X))=>(brave(X)<~>~generous(X))))&
(![X]:(wise(X)<=>(rich(X)|~old(X))))&
((quiet(alice)<~>~generous(alice)))&
(?[X]:(~old(X)))&
(happy(lucy))&
(?[X]:((~quiet(X)|~creative(X))))&
(?[X]:(kind(X)))&
(?[X]:((brave(X)<~>wise(X))))&
((strong(john)&~brave(john)))&
(?[X]:(~wise(X))) | rich(alice) | [] | null | 0 |
If someone is not old then someone is both not creative and not rich.
If someone is either generous or quiet then mary is not generous and vice versa.
Everyone who is funny or not calm is creative or funny and vice versa.
Everyone who is patient or not generous is both not curious and calm.
Everyone who is both not happy and old is both not funny and not curious.
If someone is either wise or not rich then someone is generous or tall.
If mary is strong or funny then susan is not kind and vice versa.
Everyone who is either not funny or not patient is both patient and not rich.
Everyone who is not wise is not funny and vice versa.
Everyone who is both not brave and tall is not brave.
Everyone who is old is not kind or rich and vice versa.
Everyone who is not rich or not funny is not calm or happy and vice versa.
If john is old or tall then someone is not tall or kind and vice versa.
If mary is both not patient and not quiet then susan is not funny and vice versa.
If alice is both not creative and old then someone is both not strong and patient and vice versa.
Everyone who is either curious or not strong is either calm or not generous.
Someone is calm.
Someone is both not wise and happy.
Alice is strong or creative.
Someone is not creative.
Someone is not funny or calm.
Alice is not patient or not brave.
Mary is funny.
Paul is both generous and not happy. | Mary is calm. | entailment | ((?[X]:(~old(X)))=>(?[X]:((~creative(X)&~rich(X)))))&
((?[X]:((generous(X)<~>quiet(X))))<=>(~generous(mary)))&
(![X]:((funny(X)|~calm(X))<=>(creative(X)|funny(X))))&
(![X]:((patient(X)|~generous(X))=>(~curious(X)&calm(X))))&
(![X]:((~happy(X)&old(X))=>(~funny(X)&~curious(X))))&
((?[X]:((wise(X)<~>~rich(X))))=>(?[X]:((generous(X)|tall(X)))))&
(((strong(mary)|funny(mary)))<=>(~kind(susan)))&
(![X]:((~funny(X)<~>~patient(X))=>(patient(X)&~rich(X))))&
(![X]:(~wise(X)<=>~funny(X)))&
(![X]:((~brave(X)&tall(X))=>~brave(X)))&
(![X]:(old(X)<=>(~kind(X)|rich(X))))&
(![X]:((~rich(X)|~funny(X))<=>(~calm(X)|happy(X))))&
(((old(john)|tall(john)))<=>(?[X]:((~tall(X)|kind(X)))))&
(((~patient(mary)&~quiet(mary)))<=>(~funny(susan)))&
(((~creative(alice)&old(alice)))<=>(?[X]:((~strong(X)&patient(X)))))&
(![X]:((curious(X)<~>~strong(X))=>(calm(X)<~>~generous(X))))&
(?[X]:(calm(X)))&
(?[X]:((~wise(X)&happy(X))))&
((strong(alice)|creative(alice)))&
(?[X]:(~creative(X)))&
(?[X]:((~funny(X)|calm(X))))&
((~patient(alice)|~brave(alice)))&
(funny(mary))&
((generous(paul)&~happy(paul))) | calm(mary) | [
"p3",
"p7",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 738614193066481519216427
% SZS output start Proof for 738614193066481519216427
4. ! [X0] : ((~generous(X0) | patient(X0)) => (calm(X0) & ~curious(X0))) [input p3]
8. ! [X0] : ((~funny(X0) <~> ~patient(X0)) => (~rich(X0) & patient(X0))) [input p7]
23. funny(mary) [input p22]
25. ~calm(mary) [input hypothesis]
29. ! [X0] : ((calm(X0) & ~curious(X0)) | (generous(X0) & ~patient(X0))) [ennf transformation 4]
33. ! [X0] : ((~rich(X0) & patient(X0)) | (~funny(X0) <=> ~patient(X0))) [ennf transformation 8]
52. ! [X0] : ((~rich(X0) & patient(X0)) | ((~funny(X0) | patient(X0)) & (~patient(X0) | funny(X0)))) [nnf transformation 33]
91. ~patient(X0) | calm(X0) [cnf transformation 29]
101. patient(X0) | ~funny(X0) | patient(X0) [cnf transformation 52]
136. funny(mary) [cnf transformation 23]
139. ~calm(mary) [cnf transformation 25]
140. ~funny(X0) | patient(X0) [duplicate literal removal 101]
201. 15 <=> funny(mary) [avatar definition]
203. funny(mary) <- (15) [avatar component clause 201]
243. 24 <=> patient(mary) [avatar definition]
244. patient(mary) <- (24) [avatar component clause 243]
298. 15 [avatar split clause 136,201]
306. patient(mary) <- (15) [resolution 140,203]
309. 24 | ~15 [avatar split clause 306,201,243]
312. calm(mary) <- (24) [resolution 244,91]
313. $false <- (24) [subsumption resolution 312,139]
314. ~24 [avatar contradiction clause 313]
315. $false [avatar sat refutation 298,309,314]
% SZS output end Proof for 738614193066481519216427
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If fred is both not curious and wise then susan is not curious or curious and vice versa.
Everyone who is either old or not funny is not patient and vice versa.
If someone is not old then lucy is both not old and generous.
If someone is either not creative or kind then someone is either funny or not calm.
If mary is not humble or happy then someone is both not happy and not generous and vice versa.
If someone is not funny or wise then alice is either not funny or not strong and vice versa.
Everyone who is generous is either not rich or not curious and vice versa.
If someone is either not strong or not wise then fred is both not happy and strong.
Everyone who is not wise is either not kind or not patient.
Everyone who is either not calm or not humble is both old and not happy.
If mary is calm or funny then susan is not strong and vice versa.
If paul is not kind then paul is both not creative and not old.
Everyone who is not calm is strong or rich and vice versa.
Everyone who is either creative or strong is both brave and not happy and vice versa.
Everyone who is both humble and kind is not tall.
Everyone who is either funny or not calm is either happy or not funny and vice versa.
Someone is both quiet and kind.
Lucy is not tall or not quiet.
Someone is not calm or tall.
Mary is both not humble and not wise.
Someone is either funny or strong.
Someone is both creative and not tall.
Susan is either old or not strong.
Someone is either not tall or kind. | Mary is calm. | contradiction | (((~curious(fred)&wise(fred)))<=>((~curious(susan)|curious(susan))))&
(![X]:((old(X)<~>~funny(X))<=>~patient(X)))&
((?[X]:(~old(X)))=>((~old(lucy)&generous(lucy))))&
((?[X]:((~creative(X)<~>kind(X))))=>(?[X]:((funny(X)<~>~calm(X)))))&
(((~humble(mary)|happy(mary)))<=>(?[X]:((~happy(X)&~generous(X)))))&
((?[X]:((~funny(X)|wise(X))))<=>((~funny(alice)<~>~strong(alice))))&
(![X]:(generous(X)<=>(~rich(X)<~>~curious(X))))&
((?[X]:((~strong(X)<~>~wise(X))))=>((~happy(fred)&strong(fred))))&
(![X]:(~wise(X)=>(~kind(X)<~>~patient(X))))&
(![X]:((~calm(X)<~>~humble(X))=>(old(X)&~happy(X))))&
(((calm(mary)|funny(mary)))<=>(~strong(susan)))&
((~kind(paul))=>((~creative(paul)&~old(paul))))&
(![X]:(~calm(X)<=>(strong(X)|rich(X))))&
(![X]:((creative(X)<~>strong(X))<=>(brave(X)&~happy(X))))&
(![X]:((humble(X)&kind(X))=>~tall(X)))&
(![X]:((funny(X)<~>~calm(X))<=>(happy(X)<~>~funny(X))))&
(?[X]:((quiet(X)&kind(X))))&
((~tall(lucy)|~quiet(lucy)))&
(?[X]:((~calm(X)|tall(X))))&
((~humble(mary)&~wise(mary)))&
(?[X]:((funny(X)<~>strong(X))))&
(?[X]:((creative(X)&~tall(X))))&
((old(susan)<~>~strong(susan)))&
(?[X]:((~tall(X)<~>kind(X)))) | calm(mary) | [
"p9",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 6549188823633554090394413
% SZS output start Proof for 6549188823633554090394413
10. ! [X0] : ((~calm(X0) <~> ~humble(X0)) => (~happy(X0) & old(X0))) [input p9]
16. ! [X0] : ((funny(X0) <~> ~calm(X0)) <=> (happy(X0) <~> ~funny(X0))) [input p15]
20. ~wise(mary) & ~humble(mary) [input p19]
25. calm(mary) [input hypothesis]
31. ! [X0] : ((~happy(X0) & old(X0)) | (~calm(X0) <=> ~humble(X0))) [ennf transformation 10]
54. ! [X0] : ((~happy(X0) & old(X0)) | ((~calm(X0) | humble(X0)) & (~humble(X0) | calm(X0)))) [nnf transformation 31]
61. ! [X0] : ((((calm(X0) | ~funny(X0)) & (~calm(X0) | funny(X0))) | ((happy(X0) | funny(X0)) & (~funny(X0) | ~happy(X0)))) & (((funny(X0) | ~happy(X0)) & (~funny(X0) | happy(X0))) | ((funny(X0) | calm(X0)) & (~calm(X0) | ~funny(X0))))) [nnf transformation 16]
114. ~happy(X0) | ~calm(X0) | humble(X0) [cnf transformation 54]
130. ~funny(X0) | happy(X0) | ~calm(X0) | ~funny(X0) [cnf transformation 61]
135. ~calm(X0) | funny(X0) | happy(X0) | funny(X0) [cnf transformation 61]
142. ~humble(mary) [cnf transformation 20]
152. calm(mary) [cnf transformation 25]
153. ~funny(X0) | happy(X0) | ~calm(X0) [duplicate literal removal 130]
155. ~calm(X0) | funny(X0) | happy(X0) [duplicate literal removal 135]
208. 12 <=> humble(mary) [avatar definition]
210. ~humble(mary) <- (~12) [avatar component clause 208]
212. 13 <=> happy(mary) [avatar definition]
214. happy(mary) <- (13) [avatar component clause 212]
279. 27 <=> calm(mary) [avatar definition]
281. calm(mary) <- (27) [avatar component clause 279]
304. ~calm(X0) | happy(X0) [subsumption resolution 153,155]
323. ~12 [avatar split clause 142,208]
350. 27 [avatar split clause 152,279]
357. happy(mary) <- (27) [resolution 304,281]
358. 13 | ~27 [avatar split clause 357,279,212]
432. ~calm(mary) | humble(mary) <- (13) [resolution 114,214]
433. humble(mary) <- (13, 27) [subsumption resolution 432,281]
434. $false <- (~12, 13, 27) [subsumption resolution 433,210]
435. 12 | ~13 | ~27 [avatar contradiction clause 434]
436. $false [avatar sat refutation 323,350,358,435]
% SZS output end Proof for 6549188823633554090394413
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If alice is both generous and not curious then lucy is not tall and vice versa.
If fred is either not creative or curious then paul is either not happy or not tall and vice versa.
Everyone who is wise is generous or not wise and vice versa.
If paul is both not curious and funny then someone is both tall and strong and vice versa.
If someone is both brave and humble then someone is either patient or not curious and vice versa.
Everyone who is both not rich and not quiet is both funny and not calm.
Everyone who is both not generous and not funny is either quiet or not quiet.
Everyone who is happy or funny is not humble and vice versa.
Everyone who is either not happy or not wise is both wise and not brave and vice versa.
Everyone who is either funny or old is brave and vice versa.
Everyone who is calm or not kind is not curious or patient and vice versa.
If mary is not old or tall then someone is both not kind and brave and vice versa.
Everyone who is both not kind and not rich is either old or funny and vice versa.
Everyone who is either calm or not funny is both humble and not old and vice versa.
Everyone who is not wise is not strong and vice versa.
Alice is not brave or not quiet.
John is both rich and not tall.
Lucy is not generous or not old.
Someone is generous or not creative.
Someone is rich.
Someone is either not rich or not old. | Paul is not curious. | neutral | (((generous(alice)&~curious(alice)))<=>(~tall(lucy)))&
(((~creative(fred)<~>curious(fred)))<=>((~happy(paul)<~>~tall(paul))))&
(![X]:(wise(X)<=>(generous(X)|~wise(X))))&
(((~curious(paul)&funny(paul)))<=>(?[X]:((tall(X)&strong(X)))))&
((?[X]:((brave(X)&humble(X))))<=>(?[X]:((patient(X)<~>~curious(X)))))&
(![X]:((~rich(X)&~quiet(X))=>(funny(X)&~calm(X))))&
(![X]:((~generous(X)&~funny(X))=>(quiet(X)<~>~quiet(X))))&
(![X]:((happy(X)|funny(X))<=>~humble(X)))&
(![X]:((~happy(X)<~>~wise(X))<=>(wise(X)&~brave(X))))&
(![X]:((funny(X)<~>old(X))<=>brave(X)))&
(![X]:((calm(X)|~kind(X))<=>(~curious(X)|patient(X))))&
(((~old(mary)|tall(mary)))<=>(?[X]:((~kind(X)&brave(X)))))&
(![X]:((~kind(X)&~rich(X))<=>(old(X)<~>funny(X))))&
(![X]:((calm(X)<~>~funny(X))<=>(humble(X)&~old(X))))&
(![X]:(~wise(X)<=>~strong(X)))&
((~brave(alice)|~quiet(alice)))&
((rich(john)&~tall(john)))&
((~generous(lucy)|~old(lucy)))&
(?[X]:((generous(X)|~creative(X))))&
(?[X]:(rich(X)))&
(?[X]:((~rich(X)<~>~old(X)))) | ~curious(paul) | [] | null | 0 |
Everyone who is creative or not quiet is either generous or not creative and vice versa. If someone is not wise then alice is not patient and vice versa. If someone is not creative then someone is both brave and not old. Everyone who is quiet is curious. If mary is both strong and not curious then someone is not humble or not brave and vice versa. Everyone who is not happy or not brave is both not patient and not creative and vice versa. Everyone who is brave is not humble or calm and vice versa. Everyone who is either not old or not brave is kind and vice versa. If someone is both not strong and creative then lucy is both not calm and strong and vice versa. If someone is both not creative and not humble then someone is humble or quiet and vice versa. Everyone who is not curious is patient. If john is either creative or humble then lucy is kind and vice versa. Everyone who is both not generous and calm is not creative or generous. If someone is not generous then lucy is calm or old. If someone is both not strong and curious then lucy is both not calm and not patient and vice versa. Everyone who is not generous is humble or kind. John is not humble. Alice is either creative or not generous. Mary is both not tall and not calm. Alice is either old or not patient. Someone is kind. Someone is either not rich or not brave. Someone is either humble or wise. | John is not old. | neutral | (![X]:((creative(X)|~quiet(X))<=>(generous(X)<~>~creative(X))))&
((?[X]:(~wise(X)))<=>(~patient(alice)))&
((?[X]:(~creative(X)))=>(?[X]:((brave(X)&~old(X)))))&
(![X]:(quiet(X)=>curious(X)))&
(((strong(mary)&~curious(mary)))<=>(?[X]:((~humble(X)|~brave(X)))))&
(![X]:((~happy(X)|~brave(X))<=>(~patient(X)&~creative(X))))&
(![X]:(brave(X)<=>(~humble(X)|calm(X))))&
(![X]:((~old(X)<~>~brave(X))<=>kind(X)))&
((?[X]:((~strong(X)&creative(X))))<=>((~calm(lucy)&strong(lucy))))&
((?[X]:((~creative(X)&~humble(X))))<=>(?[X]:((humble(X)|quiet(X)))))&
(![X]:(~curious(X)=>patient(X)))&
(((creative(john)<~>humble(john)))<=>(kind(lucy)))&
(![X]:((~generous(X)&calm(X))=>(~creative(X)|generous(X))))&
((?[X]:(~generous(X)))=>((calm(lucy)|old(lucy))))&
((?[X]:((~strong(X)&curious(X))))<=>((~calm(lucy)&~patient(lucy))))&
(![X]:(~generous(X)=>(humble(X)|kind(X))))&
(~humble(john))&
((creative(alice)<~>~generous(alice)))&
((~tall(mary)&~calm(mary)))&
((old(alice)<~>~patient(alice)))&
(?[X]:(kind(X)))&
(?[X]:((~rich(X)<~>~brave(X))))&
(?[X]:((humble(X)<~>wise(X)))) | ~old(john) | [] | null | 0 |
If someone is not brave then someone is either funny or not rich. Everyone who is either kind or strong is either not funny or calm. If someone is calm or creative then someone is both brave and rich. Everyone who is either brave or patient is not rich and vice versa. Everyone who is not tall is not happy. Everyone who is either calm or tall is both not rich and not tall and vice versa. Everyone who is not kind is both not kind and kind. Everyone who is either not happy or creative is either old or not calm and vice versa. Everyone who is either creative or not kind is patient. Everyone who is humble is wise or happy and vice versa. If alice is either quiet or not creative then someone is not strong. Everyone who is generous or not rich is either not curious or creative. If someone is not humble or curious then paul is either not humble or not generous. Everyone who is either not rich or humble is either generous or not tall and vice versa. Everyone who is wise is either not tall or happy. Paul is not old or old. Someone is kind or rich. Someone is generous. Alice is not wise or quiet. Someone is old or brave. Mary is old or tall. | Mary is not humble. | neutral | ((?[X]:(~brave(X)))=>(?[X]:((funny(X)<~>~rich(X)))))&
(![X]:((kind(X)<~>strong(X))=>(~funny(X)<~>calm(X))))&
((?[X]:((calm(X)|creative(X))))=>(?[X]:((brave(X)&rich(X)))))&
(![X]:((brave(X)<~>patient(X))<=>~rich(X)))&
(![X]:(~tall(X)=>~happy(X)))&
(![X]:((calm(X)<~>tall(X))<=>(~rich(X)&~tall(X))))&
(![X]:(~kind(X)=>(~kind(X)&kind(X))))&
(![X]:((~happy(X)<~>creative(X))<=>(old(X)<~>~calm(X))))&
(![X]:((creative(X)<~>~kind(X))=>patient(X)))&
(![X]:(humble(X)<=>(wise(X)|happy(X))))&
(((quiet(alice)<~>~creative(alice)))=>(?[X]:(~strong(X))))&
(![X]:((generous(X)|~rich(X))=>(~curious(X)<~>creative(X))))&
((?[X]:((~humble(X)|curious(X))))=>((~humble(paul)<~>~generous(paul))))&
(![X]:((~rich(X)<~>humble(X))<=>(generous(X)<~>~tall(X))))&
(![X]:(wise(X)=>(~tall(X)<~>happy(X))))&
((~old(paul)|old(paul)))&
(?[X]:((kind(X)|rich(X))))&
(?[X]:(generous(X)))&
((~wise(alice)|quiet(alice)))&
(?[X]:((old(X)|brave(X))))&
((old(mary)|tall(mary))) | ~humble(mary) | [] | null | 0 |
If alice is rich then someone is either kind or happy and vice versa.
If susan is funny then alice is kind or calm.
If someone is either not happy or generous then someone is either not brave or not humble and vice versa.
Everyone who is happy is not funny or not rich.
If someone is calm or not kind then paul is either kind or not creative.
Everyone who is kind or quiet is funny or not tall and vice versa.
If someone is both kind and not quiet then someone is creative.
If someone is either not strong or brave then someone is both not quiet and not strong.
Everyone who is both not quiet and not funny is either brave or not quiet.
If someone is not wise then alice is strong.
Everyone who is not quiet is both funny and humble and vice versa.
If someone is either rich or not creative then someone is not curious or wise.
Everyone who is not creative or not generous is funny.
If john is not rich or rich then fred is creative.
Everyone who is not funny or generous is either humble or rich and vice versa.
If someone is both not quiet and not generous then paul is both not funny and not generous and vice versa.
Lucy is either not calm or tall.
Someone is both not quiet and tall.
Lucy is either not brave or not patient.
Someone is not brave or happy.
Alice is both tall and creative.
Someone is either strong or not funny.
Alice is not happy.
Someone is both generous and not quiet. | Alice is quiet. | entailment | ((rich(alice))<=>(?[X]:((kind(X)<~>happy(X)))))&
((funny(susan))=>((kind(alice)|calm(alice))))&
((?[X]:((~happy(X)<~>generous(X))))<=>(?[X]:((~brave(X)<~>~humble(X)))))&
(![X]:(happy(X)=>(~funny(X)|~rich(X))))&
((?[X]:((calm(X)|~kind(X))))=>((kind(paul)<~>~creative(paul))))&
(![X]:((kind(X)|quiet(X))<=>(funny(X)|~tall(X))))&
((?[X]:((kind(X)&~quiet(X))))=>(?[X]:(creative(X))))&
((?[X]:((~strong(X)<~>brave(X))))=>(?[X]:((~quiet(X)&~strong(X)))))&
(![X]:((~quiet(X)&~funny(X))=>(brave(X)<~>~quiet(X))))&
((?[X]:(~wise(X)))=>(strong(alice)))&
(![X]:(~quiet(X)<=>(funny(X)&humble(X))))&
((?[X]:((rich(X)<~>~creative(X))))=>(?[X]:((~curious(X)|wise(X)))))&
(![X]:((~creative(X)|~generous(X))=>funny(X)))&
(((~rich(john)|rich(john)))=>(creative(fred)))&
(![X]:((~funny(X)|generous(X))<=>(humble(X)<~>rich(X))))&
((?[X]:((~quiet(X)&~generous(X))))<=>((~funny(paul)&~generous(paul))))&
((~calm(lucy)<~>tall(lucy)))&
(?[X]:((~quiet(X)&tall(X))))&
((~brave(lucy)<~>~patient(lucy)))&
(?[X]:((~brave(X)|happy(X))))&
((tall(alice)&creative(alice)))&
(?[X]:((strong(X)<~>~funny(X))))&
(~happy(alice))&
(?[X]:((generous(X)&~quiet(X)))) | quiet(alice) | [
"p0",
"p5",
"p10",
"p12",
"p14",
"p15",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 8899809580388721244508329
% SZS output start Proof for 8899809580388721244508329
1. rich(alice) <=> ? [X0] : (kind(X0) <~> happy(X0)) [input p0]
6. ! [X0] : ((quiet(X0) | kind(X0)) <=> (~tall(X0) | funny(X0))) [input p5]
11. ! [X0] : (~quiet(X0) <=> (humble(X0) & funny(X0))) [input p10]
13. ! [X0] : ((~generous(X0) | ~creative(X0)) => funny(X0)) [input p12]
15. ! [X0] : ((generous(X0) | ~funny(X0)) <=> (humble(X0) <~> rich(X0))) [input p14]
16. ? [X0] : (~generous(X0) & ~quiet(X0)) <=> (~generous(paul) & ~funny(paul)) [input p15]
23. ~happy(alice) [input p22]
25. ~quiet(alice) [input hypothesis]
41. ! [X0] : (funny(X0) | (generous(X0) & creative(X0))) [ennf transformation 13]
43. (rich(alice) | ! [X0] : ((kind(X0) | ~happy(X0)) & (happy(X0) | ~kind(X0)))) & (? [X0] : ((~happy(X0) | ~kind(X0)) & (happy(X0) | kind(X0))) | ~rich(alice)) [nnf transformation 1]
44. (rich(alice) | ! [X0] : ((kind(X0) | ~happy(X0)) & (happy(X0) | ~kind(X0)))) & (? [X1] : ((~happy(X1) | ~kind(X1)) & (happy(X1) | kind(X1))) | ~rich(alice)) [rectify 43]
45. ? [X1] : ((~happy(X1) | ~kind(X1)) & (happy(X1) | kind(X1))) => ((~happy(sK0) | ~kind(sK0)) & (happy(sK0) | kind(sK0))) [choice axiom]
46. (rich(alice) | ! [X0] : ((kind(X0) | ~happy(X0)) & (happy(X0) | ~kind(X0)))) & (((~happy(sK0) | ~kind(sK0)) & (happy(sK0) | kind(sK0))) | ~rich(alice)) [skolemisation 44,45]
53. ! [X0] : (((quiet(X0) | kind(X0)) | (tall(X0) & ~funny(X0))) & ((~tall(X0) | funny(X0)) | (~quiet(X0) & ~kind(X0)))) [nnf transformation 6]
54. ! [X0] : ((quiet(X0) | kind(X0) | (tall(X0) & ~funny(X0))) & (~tall(X0) | funny(X0) | (~quiet(X0) & ~kind(X0)))) [flattening 53]
63. ! [X0] : ((~quiet(X0) | (~humble(X0) | ~funny(X0))) & ((humble(X0) & funny(X0)) | quiet(X0))) [nnf transformation 11]
64. ! [X0] : ((~quiet(X0) | ~humble(X0) | ~funny(X0)) & ((humble(X0) & funny(X0)) | quiet(X0))) [flattening 63]
65. ! [X0] : (((generous(X0) | ~funny(X0)) | ((humble(X0) | ~rich(X0)) & (rich(X0) | ~humble(X0)))) & (((~rich(X0) | ~humble(X0)) & (rich(X0) | humble(X0))) | (~generous(X0) & funny(X0)))) [nnf transformation 15]
66. ! [X0] : ((generous(X0) | ~funny(X0) | ((humble(X0) | ~rich(X0)) & (rich(X0) | ~humble(X0)))) & (((~rich(X0) | ~humble(X0)) & (rich(X0) | humble(X0))) | (~generous(X0) & funny(X0)))) [flattening 65]
67. (? [X0] : (~generous(X0) & ~quiet(X0)) | (generous(paul) | funny(paul))) & ((~generous(paul) & ~funny(paul)) | ! [X0] : (generous(X0) | quiet(X0))) [nnf transformation 16]
68. (? [X0] : (~generous(X0) & ~quiet(X0)) | generous(paul) | funny(paul)) & ((~generous(paul) & ~funny(paul)) | ! [X0] : (generous(X0) | quiet(X0))) [flattening 67]
69. (? [X0] : (~generous(X0) & ~quiet(X0)) | generous(paul) | funny(paul)) & ((~generous(paul) & ~funny(paul)) | ! [X1] : (generous(X1) | quiet(X1))) [rectify 68]
70. ? [X0] : (~generous(X0) & ~quiet(X0)) => (~generous(sK5) & ~quiet(sK5)) [choice axiom]
71. ((~generous(sK5) & ~quiet(sK5)) | generous(paul) | funny(paul)) & ((~generous(paul) & ~funny(paul)) | ! [X1] : (generous(X1) | quiet(X1))) [skolemisation 69,70]
85. rich(alice) | happy(X0) | ~kind(X0) [cnf transformation 46]
103. ~funny(X0) | kind(X0) | quiet(X0) [cnf transformation 54]
112. quiet(X0) | funny(X0) [cnf transformation 64]
113. quiet(X0) | humble(X0) [cnf transformation 64]
116. generous(X0) | funny(X0) [cnf transformation 41]
122. ~humble(X0) | ~rich(X0) | ~generous(X0) [cnf transformation 66]
125. ~funny(paul) | generous(X1) | quiet(X1) [cnf transformation 71]
126. ~generous(paul) | generous(X1) | quiet(X1) [cnf transformation 71]
140. ~happy(alice) [cnf transformation 23]
143. ~quiet(alice) [cnf transformation 25]
149. 2 <=> rich(alice) [avatar definition]
154. 3 <=> ! [X0] : (happy(X0) | ~kind(X0)) [avatar definition]
155. ~kind(X0) | happy(X0) <- (3) [avatar component clause 154]
156. 3 | 2 [avatar split clause 85,149,154]
172. 7 <=> kind(alice) [avatar definition]
174. kind(alice) <- (7) [avatar component clause 172]
273. 29 <=> ! [X1] : (generous(X1) | quiet(X1)) [avatar definition]
274. quiet(X1) | generous(X1) <- (29) [avatar component clause 273]
276. 30 <=> generous(paul) [avatar definition]
278. ~generous(paul) <- (~30) [avatar component clause 276]
279. 29 | ~30 [avatar split clause 126,276,273]
281. 31 <=> funny(paul) [avatar definition]
283. ~funny(paul) <- (~31) [avatar component clause 281]
284. 29 | ~31 [avatar split clause 125,281,273]
324. funny(alice) [resolution 112,143]
328. humble(alice) [resolution 113,143]
336. funny(paul) <- (~30) [resolution 116,278]
337. $false <- (~30, ~31) [subsumption resolution 336,283]
338. 30 | 31 [avatar contradiction clause 337]
341. generous(alice) <- (29) [resolution 274,143]
380. kind(alice) | quiet(alice) [resolution 103,324]
384. kind(alice) [subsumption resolution 380,143]
385. 7 [avatar split clause 384,172]
487. ~rich(alice) | ~generous(alice) [resolution 122,328]
497. ~rich(alice) <- (29) [subsumption resolution 487,341]
498. ~2 | ~29 [avatar split clause 497,273,149]
503. happy(alice) <- (3, 7) [resolution 155,174]
507. $false <- (3, 7) [subsumption resolution 503,140]
508. ~3 | ~7 [avatar contradiction clause 507]
509. $false [avatar sat refutation 156,279,284,338,385,498,508]
% SZS output end Proof for 8899809580388721244508329
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not old or not kind then someone is either old or quiet and vice versa. Everyone who is both not humble and not patient is both not happy and old. Everyone who is not humble or old is strong or generous and vice versa. If susan is both not strong and not kind then someone is happy and vice versa. Everyone who is either not humble or wise is either kind or patient. Everyone who is not creative or curious is creative or happy. If someone is not strong then mary is both calm and not creative and vice versa. If lucy is either strong or not kind then someone is rich or not strong. Everyone who is not brave or brave is not humble or creative. Everyone who is either creative or quiet is either rich or quiet and vice versa. If mary is both humble and quiet then someone is either not tall or not quiet and vice versa. If someone is not old then someone is wise or humble. If mary is not old or funny then lucy is both generous and not patient and vice versa. If paul is both not strong and calm then someone is either not strong or not creative. Everyone who is not generous is not tall. Everyone who is both curious and not calm is calm and vice versa. Lucy is both not brave and tall. John is both not old and not tall. Susan is either not tall or strong. | Paul is creative. | entailment | (((~old(mary)<~>~kind(mary)))<=>(?[X]:((old(X)<~>quiet(X)))))&
(![X]:((~humble(X)&~patient(X))=>(~happy(X)&old(X))))&
(![X]:((~humble(X)|old(X))<=>(strong(X)|generous(X))))&
(((~strong(susan)&~kind(susan)))<=>(?[X]:(happy(X))))&
(![X]:((~humble(X)<~>wise(X))=>(kind(X)<~>patient(X))))&
(![X]:((~creative(X)|curious(X))=>(creative(X)|happy(X))))&
((?[X]:(~strong(X)))<=>((calm(mary)&~creative(mary))))&
(((strong(lucy)<~>~kind(lucy)))=>(?[X]:((rich(X)|~strong(X)))))&
(![X]:((~brave(X)|brave(X))=>(~humble(X)|creative(X))))&
(![X]:((creative(X)<~>quiet(X))<=>(rich(X)<~>quiet(X))))&
(((humble(mary)&quiet(mary)))<=>(?[X]:((~tall(X)<~>~quiet(X)))))&
((?[X]:(~old(X)))=>(?[X]:((wise(X)|humble(X)))))&
(((~old(mary)|funny(mary)))<=>((generous(lucy)&~patient(lucy))))&
(((~strong(paul)&calm(paul)))=>(?[X]:((~strong(X)<~>~creative(X)))))&
(![X]:(~generous(X)=>~tall(X)))&
(![X]:((curious(X)&~calm(X))<=>calm(X)))&
((~brave(lucy)&tall(lucy)))&
((~old(john)&~tall(john)))&
((~tall(susan)<~>strong(susan))) | creative(paul) | [
"p3",
"p5",
"p6",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 301671303514000312557246
% SZS output start Proof for 301671303514000312557246
4. (~kind(susan) & ~strong(susan)) <=> ? [X0] : happy(X0) [input p3]
6. ! [X0] : ((curious(X0) | ~creative(X0)) => (happy(X0) | creative(X0))) [input p5]
7. ? [X0] : ~strong(X0) <=> (~creative(mary) & calm(mary)) [input p6]
16. ! [X0] : ((~calm(X0) & curious(X0)) <=> calm(X0)) [input p15]
20. ~creative(paul) [input hypothesis]
25. ! [X0] : ((happy(X0) | creative(X0)) | (~curious(X0) & creative(X0))) [ennf transformation 6]
26. ! [X0] : (happy(X0) | creative(X0) | (~curious(X0) & creative(X0))) [flattening 25]
40. ((~kind(susan) & ~strong(susan)) | ! [X0] : ~happy(X0)) & (? [X0] : happy(X0) | (kind(susan) | strong(susan))) [nnf transformation 4]
41. ((~kind(susan) & ~strong(susan)) | ! [X0] : ~happy(X0)) & (? [X0] : happy(X0) | kind(susan) | strong(susan)) [flattening 40]
42. ((~kind(susan) & ~strong(susan)) | ! [X0] : ~happy(X0)) & (? [X1] : happy(X1) | kind(susan) | strong(susan)) [rectify 41]
43. ? [X1] : happy(X1) => happy(sK1) [choice axiom]
44. ((~kind(susan) & ~strong(susan)) | ! [X0] : ~happy(X0)) & (happy(sK1) | kind(susan) | strong(susan)) [skolemisation 42,43]
46. (? [X0] : ~strong(X0) | (creative(mary) | ~calm(mary))) & ((~creative(mary) & calm(mary)) | ! [X0] : strong(X0)) [nnf transformation 7]
47. (? [X0] : ~strong(X0) | creative(mary) | ~calm(mary)) & ((~creative(mary) & calm(mary)) | ! [X0] : strong(X0)) [flattening 46]
48. (? [X0] : ~strong(X0) | creative(mary) | ~calm(mary)) & ((~creative(mary) & calm(mary)) | ! [X1] : strong(X1)) [rectify 47]
49. ? [X0] : ~strong(X0) => ~strong(sK2) [choice axiom]
50. (~strong(sK2) | creative(mary) | ~calm(mary)) & ((~creative(mary) & calm(mary)) | ! [X1] : strong(X1)) [skolemisation 48,49]
68. ! [X0] : (((~calm(X0) & curious(X0)) | ~calm(X0)) & (calm(X0) | (calm(X0) | ~curious(X0)))) [nnf transformation 16]
69. ! [X0] : (((~calm(X0) & curious(X0)) | ~calm(X0)) & (calm(X0) | calm(X0) | ~curious(X0))) [flattening 68]
86. ~strong(susan) | ~happy(X0) [cnf transformation 44]
92. happy(X0) | creative(X0) | creative(X0) [cnf transformation 26]
94. calm(mary) | strong(X1) [cnf transformation 50]
126. ~calm(X0) | ~calm(X0) [cnf transformation 69]
133. ~creative(paul) [cnf transformation 20]
135. ~calm(X0) [duplicate literal removal 126]
140. creative(X0) | happy(X0) [duplicate literal removal 92]
172. 7 <=> ! [X0] : ~happy(X0) [avatar definition]
173. ~happy(X0) <- (7) [avatar component clause 172]
180. 9 <=> strong(susan) [avatar definition]
182. ~strong(susan) <- (~9) [avatar component clause 180]
183. 7 | ~9 [avatar split clause 86,180,172]
190. 11 <=> calm(mary) [avatar definition]
191. calm(mary) <- (11) [avatar component clause 190]
203. 14 <=> ! [X1] : strong(X1) [avatar definition]
204. strong(X1) <- (14) [avatar component clause 203]
206. 14 | 11 [avatar split clause 94,190,203]
310. $false <- (11) [subsumption resolution 191,135]
311. ~11 [avatar contradiction clause 310]
312. $false <- (~9, 14) [resolution 204,182]
315. 9 | ~14 [avatar contradiction clause 312]
327. happy(paul) [resolution 140,133]
329. $false <- (7) [subsumption resolution 327,173]
330. ~7 [avatar contradiction clause 329]
333. $false [avatar sat refutation 183,206,311,315,330]
% SZS output end Proof for 301671303514000312557246
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not rich and not wise is both not generous and not kind and vice versa.
Everyone who is both not wise and patient is either patient or not tall and vice versa.
If someone is tall or generous then someone is not humble.
If someone is strong then someone is both curious and tall.
Everyone who is wise or not strong is not generous or not tall and vice versa.
Everyone who is not calm or not happy is not tall and vice versa.
If someone is not old or quiet then fred is both curious and calm.
Everyone who is old or calm is happy or old and vice versa.
Everyone who is both not brave and not creative is either not kind or rich and vice versa.
Everyone who is either generous or not curious is generous or not tall and vice versa.
If someone is either not rich or not happy then someone is not generous.
Everyone who is not tall is either rich or not wise and vice versa.
If paul is brave then someone is both not humble and not funny and vice versa.
If alice is both brave and rich then someone is happy or not kind.
Everyone who is either not happy or not generous is both not calm and not rich and vice versa.
Everyone who is not quiet is not brave and vice versa.
Susan is not generous or not funny.
Someone is wise or not brave.
Someone is either not rich or patient.
Susan is not wise.
Paul is not calm.
Someone is wise. | Paul is not curious. | neutral | (![X]:((~rich(X)&~wise(X))<=>(~generous(X)&~kind(X))))&
(![X]:((~wise(X)&patient(X))<=>(patient(X)<~>~tall(X))))&
((?[X]:((tall(X)|generous(X))))=>(?[X]:(~humble(X))))&
((?[X]:(strong(X)))=>(?[X]:((curious(X)&tall(X)))))&
(![X]:((wise(X)|~strong(X))<=>(~generous(X)|~tall(X))))&
(![X]:((~calm(X)|~happy(X))<=>~tall(X)))&
((?[X]:((~old(X)|quiet(X))))=>((curious(fred)&calm(fred))))&
(![X]:((old(X)|calm(X))<=>(happy(X)|old(X))))&
(![X]:((~brave(X)&~creative(X))<=>(~kind(X)<~>rich(X))))&
(![X]:((generous(X)<~>~curious(X))<=>(generous(X)|~tall(X))))&
((?[X]:((~rich(X)<~>~happy(X))))=>(?[X]:(~generous(X))))&
(![X]:(~tall(X)<=>(rich(X)<~>~wise(X))))&
((brave(paul))<=>(?[X]:((~humble(X)&~funny(X)))))&
(((brave(alice)&rich(alice)))=>(?[X]:((happy(X)|~kind(X)))))&
(![X]:((~happy(X)<~>~generous(X))<=>(~calm(X)&~rich(X))))&
(![X]:(~quiet(X)<=>~brave(X)))&
((~generous(susan)|~funny(susan)))&
(?[X]:((wise(X)|~brave(X))))&
(?[X]:((~rich(X)<~>patient(X))))&
(~wise(susan))&
(~calm(paul))&
(?[X]:(wise(X))) | ~curious(paul) | [] | null | 0 |
If someone is both not happy and not funny then someone is either not strong or calm. Everyone who is not wise is rich. If someone is rich then john is strong. Everyone who is not quiet or not curious is both generous and not calm and vice versa. Everyone who is either generous or quiet is not kind or not happy and vice versa. If someone is both not humble and creative then someone is not quiet and vice versa. If someone is not calm then susan is generous. Everyone who is either curious or not kind is wise or brave and vice versa. Everyone who is both quiet and not generous is humble and vice versa. Everyone who is both not generous and not brave is both not old and not patient and vice versa. If susan is not wise then someone is not tall. Everyone who is not curious is either not brave or kind and vice versa. If alice is both not wise and wise then fred is both not calm and not creative and vice versa. Everyone who is calm or generous is not generous or happy and vice versa. Everyone who is not old or curious is both strong and not quiet. If someone is both generous and brave then lucy is both not wise and brave. Fred is patient. Paul is calm or not humble. Paul is not rich. Someone is not brave or calm. Lucy is either old or curious. Someone is tall. | Lucy is not kind. | entailment | ((?[X]:((~happy(X)&~funny(X))))=>(?[X]:((~strong(X)<~>calm(X)))))&
(![X]:(~wise(X)=>rich(X)))&
((?[X]:(rich(X)))=>(strong(john)))&
(![X]:((~quiet(X)|~curious(X))<=>(generous(X)&~calm(X))))&
(![X]:((generous(X)<~>quiet(X))<=>(~kind(X)|~happy(X))))&
((?[X]:((~humble(X)&creative(X))))<=>(?[X]:(~quiet(X))))&
((?[X]:(~calm(X)))=>(generous(susan)))&
(![X]:((curious(X)<~>~kind(X))<=>(wise(X)|brave(X))))&
(![X]:((quiet(X)&~generous(X))<=>humble(X)))&
(![X]:((~generous(X)&~brave(X))<=>(~old(X)&~patient(X))))&
((~wise(susan))=>(?[X]:(~tall(X))))&
(![X]:(~curious(X)<=>(~brave(X)<~>kind(X))))&
(((~wise(alice)&wise(alice)))<=>((~calm(fred)&~creative(fred))))&
(![X]:((calm(X)|generous(X))<=>(~generous(X)|happy(X))))&
(![X]:((~old(X)|curious(X))=>(strong(X)&~quiet(X))))&
((?[X]:((generous(X)&brave(X))))=>((~wise(lucy)&brave(lucy))))&
(patient(fred))&
((calm(paul)|~humble(paul)))&
(~rich(paul))&
(?[X]:((~brave(X)|calm(X))))&
((old(lucy)<~>curious(lucy)))&
(?[X]:(tall(X))) | ~kind(lucy) | [
"p3",
"p4",
"p7",
"p11",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 9148073067762641371891960
% SZS output start Proof for 9148073067762641371891960
4. ! [X0] : ((~curious(X0) | ~quiet(X0)) <=> (~calm(X0) & generous(X0))) [input p3]
5. ! [X0] : ((generous(X0) <~> quiet(X0)) <=> (~happy(X0) | ~kind(X0))) [input p4]
8. ! [X0] : ((curious(X0) <~> ~kind(X0)) <=> (brave(X0) | wise(X0))) [input p7]
12. ! [X0] : (~curious(X0) <=> (~brave(X0) <~> kind(X0))) [input p11]
14. ! [X0] : ((generous(X0) | calm(X0)) <=> (happy(X0) | ~generous(X0))) [input p13]
15. ! [X0] : ((curious(X0) | ~old(X0)) => (~quiet(X0) & strong(X0))) [input p14]
23. kind(lucy) [input hypothesis]
28. ! [X0] : ((curious(X0) | ~old(X0)) => ~quiet(X0)) [pure predicate removal 15]
32. ! [X0] : (~quiet(X0) | (~curious(X0) & old(X0))) [ennf transformation 28]
34. ! [X0] : (((~curious(X0) | ~quiet(X0)) | (calm(X0) | ~generous(X0))) & ((~calm(X0) & generous(X0)) | (curious(X0) & quiet(X0)))) [nnf transformation 4]
35. ! [X0] : ((~curious(X0) | ~quiet(X0) | calm(X0) | ~generous(X0)) & ((~calm(X0) & generous(X0)) | (curious(X0) & quiet(X0)))) [flattening 34]
36. ! [X0] : ((((~quiet(X0) | ~generous(X0)) & (quiet(X0) | generous(X0))) | (happy(X0) & kind(X0))) & ((~happy(X0) | ~kind(X0)) | ((generous(X0) | ~quiet(X0)) & (quiet(X0) | ~generous(X0))))) [nnf transformation 5]
37. ! [X0] : ((((~quiet(X0) | ~generous(X0)) & (quiet(X0) | generous(X0))) | (happy(X0) & kind(X0))) & (~happy(X0) | ~kind(X0) | ((generous(X0) | ~quiet(X0)) & (quiet(X0) | ~generous(X0))))) [flattening 36]
43. ! [X0] : ((((kind(X0) | ~curious(X0)) & (~kind(X0) | curious(X0))) | (~brave(X0) & ~wise(X0))) & ((brave(X0) | wise(X0)) | ((curious(X0) | kind(X0)) & (~kind(X0) | ~curious(X0))))) [nnf transformation 8]
44. ! [X0] : ((((kind(X0) | ~curious(X0)) & (~kind(X0) | curious(X0))) | (~brave(X0) & ~wise(X0))) & (brave(X0) | wise(X0) | ((curious(X0) | kind(X0)) & (~kind(X0) | ~curious(X0))))) [flattening 43]
51. ! [X0] : ((~curious(X0) | ((~brave(X0) | ~kind(X0)) & (kind(X0) | brave(X0)))) & (((~kind(X0) | brave(X0)) & (kind(X0) | ~brave(X0))) | curious(X0))) [nnf transformation 12]
54. ! [X0] : (((generous(X0) | calm(X0)) | (~happy(X0) & generous(X0))) & ((happy(X0) | ~generous(X0)) | (~generous(X0) & ~calm(X0)))) [nnf transformation 14]
55. ! [X0] : ((generous(X0) | calm(X0) | (~happy(X0) & generous(X0))) & (happy(X0) | ~generous(X0) | (~generous(X0) & ~calm(X0)))) [flattening 54]
62. generous(X0) | quiet(X0) [cnf transformation 35]
63. generous(X0) | curious(X0) [cnf transformation 35]
67. ~happy(X0) | ~kind(X0) | quiet(X0) | ~generous(X0) [cnf transformation 37]
68. ~happy(X0) | ~kind(X0) | generous(X0) | ~quiet(X0) [cnf transformation 37]
80. ~brave(X0) | curious(X0) | ~kind(X0) [cnf transformation 44]
92. ~kind(X0) | brave(X0) | curious(X0) [cnf transformation 51]
100. happy(X0) | ~generous(X0) | ~generous(X0) [cnf transformation 55]
104. ~curious(X0) | ~quiet(X0) [cnf transformation 32]
114. kind(lucy) [cnf transformation 23]
115. ~generous(X0) | happy(X0) [duplicate literal removal 100]
117. ~kind(X0) | ~happy(X0) | generous(X0) [subsumption resolution 68,62]
118. ~kind(X0) | ~happy(X0) | quiet(X0) [subsumption resolution 67,117]
160. ~kind(X0) | curious(X0) [subsumption resolution 92,80]
212. 21 <=> curious(lucy) [avatar definition]
213. curious(lucy) <- (21) [avatar component clause 212]
226. curious(X0) | happy(X0) [resolution 115,63]
227. quiet(X1) | happy(X1) [resolution 115,62]
236. curious(lucy) [resolution 160,114]
239. 21 [avatar split clause 236,212]
241. ~quiet(lucy) <- (21) [resolution 213,104]
243. happy(X1) | ~quiet(X1) [resolution 226,104]
244. happy(X1) [subsumption resolution 243,227]
315. ~happy(lucy) | quiet(lucy) [resolution 118,114]
317. quiet(lucy) [subsumption resolution 315,244]
318. $false <- (21) [subsumption resolution 317,241]
319. ~21 [avatar contradiction clause 318]
320. $false [avatar sat refutation 239,319]
% SZS output end Proof for 9148073067762641371891960
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not happy and happy then paul is humble or rich.
If lucy is either not calm or curious then lucy is either not brave or old and vice versa.
If mary is both not patient and rich then lucy is both not calm and happy and vice versa.
If someone is wise then mary is both not curious and not wise.
Everyone who is creative or calm is either creative or old.
Everyone who is both creative and kind is not generous or not rich and vice versa.
If someone is either creative or not calm then someone is both not happy and not creative and vice versa.
If someone is quiet then mary is not calm or not happy.
If someone is both not calm and rich then paul is wise.
Everyone who is both funny and patient is both not wise and not curious.
Everyone who is generous is curious or wise and vice versa.
Everyone who is not strong or patient is kind and vice versa.
Everyone who is quiet is both not curious and not old and vice versa.
Everyone who is either happy or rich is humble or patient.
Everyone who is kind is either not tall or funny.
Everyone who is tall is not generous or not quiet.
Someone is either kind or quiet.
Fred is either not kind or not patient.
Mary is not patient.
Someone is not old or not creative.
Paul is either calm or not brave.
Someone is old. | Paul is not happy. | neutral | ((?[X]:((~happy(X)&happy(X))))=>((humble(paul)|rich(paul))))&
(((~calm(lucy)<~>curious(lucy)))<=>((~brave(lucy)<~>old(lucy))))&
(((~patient(mary)&rich(mary)))<=>((~calm(lucy)&happy(lucy))))&
((?[X]:(wise(X)))=>((~curious(mary)&~wise(mary))))&
(![X]:((creative(X)|calm(X))=>(creative(X)<~>old(X))))&
(![X]:((creative(X)&kind(X))<=>(~generous(X)|~rich(X))))&
((?[X]:((creative(X)<~>~calm(X))))<=>(?[X]:((~happy(X)&~creative(X)))))&
((?[X]:(quiet(X)))=>((~calm(mary)|~happy(mary))))&
((?[X]:((~calm(X)&rich(X))))=>(wise(paul)))&
(![X]:((funny(X)&patient(X))=>(~wise(X)&~curious(X))))&
(![X]:(generous(X)<=>(curious(X)|wise(X))))&
(![X]:((~strong(X)|patient(X))<=>kind(X)))&
(![X]:(quiet(X)<=>(~curious(X)&~old(X))))&
(![X]:((happy(X)<~>rich(X))=>(humble(X)|patient(X))))&
(![X]:(kind(X)=>(~tall(X)<~>funny(X))))&
(![X]:(tall(X)=>(~generous(X)|~quiet(X))))&
(?[X]:((kind(X)<~>quiet(X))))&
((~kind(fred)<~>~patient(fred)))&
(~patient(mary))&
(?[X]:((~old(X)|~creative(X))))&
((calm(paul)<~>~brave(paul)))&
(?[X]:(old(X))) | ~happy(paul) | [] | null | 0 |
Everyone who is not brave or humble is both not creative and not tall.
If fred is curious then lucy is not strong or not quiet and vice versa.
If someone is not quiet or curious then someone is wise.
Everyone who is both not old and generous is not brave or brave and vice versa.
Everyone who is both calm and humble is either happy or not rich.
Everyone who is not kind is calm.
Everyone who is calm is either not creative or kind and vice versa.
If lucy is not quiet then someone is either not happy or humble.
If alice is creative or generous then someone is creative or curious and vice versa.
If paul is either not wise or not strong then someone is curious and vice versa.
If john is not curious then someone is both funny and curious.
Everyone who is funny or not happy is not generous and vice versa.
If someone is strong or creative then fred is both not happy and strong.
If john is either not rich or not tall then someone is either humble or not tall.
Everyone who is creative or humble is either happy or not rich and vice versa.
Someone is both calm and brave.
Alice is either wise or not wise.
Someone is not funny.
Someone is both rich and curious.
Someone is curious or tall. | Lucy is old. | contradiction | (![X]:((~brave(X)|humble(X))=>(~creative(X)&~tall(X))))&
((curious(fred))<=>((~strong(lucy)|~quiet(lucy))))&
((?[X]:((~quiet(X)|curious(X))))=>(?[X]:(wise(X))))&
(![X]:((~old(X)&generous(X))<=>(~brave(X)|brave(X))))&
(![X]:((calm(X)&humble(X))=>(happy(X)<~>~rich(X))))&
(![X]:(~kind(X)=>calm(X)))&
(![X]:(calm(X)<=>(~creative(X)<~>kind(X))))&
((~quiet(lucy))=>(?[X]:((~happy(X)<~>humble(X)))))&
(((creative(alice)|generous(alice)))<=>(?[X]:((creative(X)|curious(X)))))&
(((~wise(paul)<~>~strong(paul)))<=>(?[X]:(curious(X))))&
((~curious(john))=>(?[X]:((funny(X)&curious(X)))))&
(![X]:((funny(X)|~happy(X))<=>~generous(X)))&
((?[X]:((strong(X)|creative(X))))=>((~happy(fred)&strong(fred))))&
(((~rich(john)<~>~tall(john)))=>(?[X]:((humble(X)<~>~tall(X)))))&
(![X]:((creative(X)|humble(X))<=>(happy(X)<~>~rich(X))))&
(?[X]:((calm(X)&brave(X))))&
((wise(alice)<~>~wise(alice)))&
(?[X]:(~funny(X)))&
(?[X]:((rich(X)&curious(X))))&
(?[X]:((curious(X)|tall(X)))) | old(lucy) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 6619377449231565469431475
% SZS output start Proof for 6619377449231565469431475
4. ! [X0] : ((generous(X0) & ~old(X0)) <=> (brave(X0) | ~brave(X0))) [input p3]
21. old(lucy) [input hypothesis]
37. ! [X0] : (((generous(X0) & ~old(X0)) | (~brave(X0) & brave(X0))) & ((brave(X0) | ~brave(X0)) | (~generous(X0) | old(X0)))) [nnf transformation 4]
38. ! [X0] : (((generous(X0) & ~old(X0)) | (~brave(X0) & brave(X0))) & (brave(X0) | ~brave(X0) | ~generous(X0) | old(X0))) [flattening 37]
81. ~old(X0) | brave(X0) [cnf transformation 38]
82. ~old(X0) | ~brave(X0) [cnf transformation 38]
129. old(lucy) [cnf transformation 21]
158. ~old(X0) [subsumption resolution 81,82]
270. $false [subsumption resolution 129,158]
% SZS output end Proof for 6619377449231565469431475
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich or happy then susan is both creative and not old.
Everyone who is not curious or patient is either not funny or patient.
Everyone who is not humble or not quiet is either brave or not calm and vice versa.
Everyone who is both not humble and strong is both old and curious and vice versa.
If someone is quiet then someone is not funny.
Everyone who is not rich or kind is calm or humble.
If someone is not tall or humble then alice is curious or not creative and vice versa.
Everyone who is calm is either not quiet or not generous and vice versa.
Everyone who is not brave is quiet.
Everyone who is strong or old is either happy or kind and vice versa.
Everyone who is not humble is both not old and rich.
If someone is either curious or not rich then fred is either kind or not kind.
If someone is kind then someone is brave and vice versa.
Everyone who is not funny is either not happy or calm.
If mary is both not old and not calm then someone is not patient and vice versa.
Everyone who is either old or not funny is both not funny and old.
Alice is both not funny and not brave.
Someone is not happy.
Someone is both quiet and wise.
Someone is either calm or not patient.
Someone is strong or not generous.
Susan is either not creative or not funny.
Someone is creative.
Someone is patient. | Alice is happy. | entailment | ((?[X]:((rich(X)<~>happy(X))))=>((creative(susan)&~old(susan))))&
(![X]:((~curious(X)|patient(X))=>(~funny(X)<~>patient(X))))&
(![X]:((~humble(X)|~quiet(X))<=>(brave(X)<~>~calm(X))))&
(![X]:((~humble(X)&strong(X))<=>(old(X)&curious(X))))&
((?[X]:(quiet(X)))=>(?[X]:(~funny(X))))&
(![X]:((~rich(X)|kind(X))=>(calm(X)|humble(X))))&
((?[X]:((~tall(X)|humble(X))))<=>((curious(alice)|~creative(alice))))&
(![X]:(calm(X)<=>(~quiet(X)<~>~generous(X))))&
(![X]:(~brave(X)=>quiet(X)))&
(![X]:((strong(X)|old(X))<=>(happy(X)<~>kind(X))))&
(![X]:(~humble(X)=>(~old(X)&rich(X))))&
((?[X]:((curious(X)<~>~rich(X))))=>((kind(fred)<~>~kind(fred))))&
((?[X]:(kind(X)))<=>(?[X]:(brave(X))))&
(![X]:(~funny(X)=>(~happy(X)<~>calm(X))))&
(((~old(mary)&~calm(mary)))<=>(?[X]:(~patient(X))))&
(![X]:((old(X)<~>~funny(X))=>(~funny(X)&old(X))))&
((~funny(alice)&~brave(alice)))&
(?[X]:(~happy(X)))&
(?[X]:((quiet(X)&wise(X))))&
(?[X]:((calm(X)<~>~patient(X))))&
(?[X]:((strong(X)|~generous(X))))&
((~creative(susan)<~>~funny(susan)))&
(?[X]:(creative(X)))&
(?[X]:(patient(X))) | happy(alice) | [
"p2",
"p8",
"p10",
"p13",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 3951125393688531472611410
% SZS output start Proof for 3951125393688531472611410
3. ! [X0] : ((~quiet(X0) | ~humble(X0)) <=> (brave(X0) <~> ~calm(X0))) [input p2]
9. ! [X0] : (~brave(X0) => quiet(X0)) [input p8]
11. ! [X0] : (~humble(X0) => (rich(X0) & ~old(X0))) [input p10]
14. ! [X0] : (~funny(X0) => (~happy(X0) <~> calm(X0))) [input p13]
16. ! [X0] : ((old(X0) <~> ~funny(X0)) => (old(X0) & ~funny(X0))) [input p15]
17. ~brave(alice) & ~funny(alice) [input p16]
25. ~happy(alice) [input hypothesis]
34. ! [X0] : (quiet(X0) | brave(X0)) [ennf transformation 9]
35. ! [X0] : ((rich(X0) & ~old(X0)) | humble(X0)) [ennf transformation 11]
37. ! [X0] : ((~happy(X0) <~> calm(X0)) | funny(X0)) [ennf transformation 14]
38. ! [X0] : ((old(X0) & ~funny(X0)) | (old(X0) <=> ~funny(X0))) [ennf transformation 16]
41. ! [X0] : (((~quiet(X0) | ~humble(X0)) | ((brave(X0) | calm(X0)) & (~calm(X0) | ~brave(X0)))) & (((calm(X0) | ~brave(X0)) & (~calm(X0) | brave(X0))) | (quiet(X0) & humble(X0)))) [nnf transformation 3]
42. ! [X0] : ((~quiet(X0) | ~humble(X0) | ((brave(X0) | calm(X0)) & (~calm(X0) | ~brave(X0)))) & (((calm(X0) | ~brave(X0)) & (~calm(X0) | brave(X0))) | (quiet(X0) & humble(X0)))) [flattening 41]
62. ! [X0] : (((~calm(X0) | happy(X0)) & (calm(X0) | ~happy(X0))) | funny(X0)) [nnf transformation 37]
68. ! [X0] : ((old(X0) & ~funny(X0)) | ((old(X0) | funny(X0)) & (~funny(X0) | ~old(X0)))) [nnf transformation 38]
96. ~quiet(X0) | ~humble(X0) | brave(X0) | calm(X0) [cnf transformation 42]
112. brave(X0) | quiet(X0) [cnf transformation 34]
119. ~old(X0) | humble(X0) [cnf transformation 35]
128. ~calm(X0) | happy(X0) | funny(X0) [cnf transformation 62]
135. old(X0) | old(X0) | funny(X0) [cnf transformation 68]
136. ~funny(alice) [cnf transformation 17]
137. ~brave(alice) [cnf transformation 17]
147. ~happy(alice) [cnf transformation 25]
149. funny(X0) | old(X0) [duplicate literal removal 135]
262. quiet(alice) [resolution 112,137]
266. old(alice) [resolution 149,136]
271. humble(alice) [resolution 266,119]
320. 31 <=> calm(alice) [avatar definition]
322. calm(alice) <- (31) [avatar component clause 320]
420. ~humble(alice) | brave(alice) | calm(alice) [resolution 96,262]
433. happy(alice) | funny(alice) <- (31) [resolution 322,128]
437. funny(alice) <- (31) [subsumption resolution 433,147]
438. $false <- (31) [subsumption resolution 437,136]
439. ~31 [avatar contradiction clause 438]
440. brave(alice) | calm(alice) [subsumption resolution 420,271]
441. calm(alice) [subsumption resolution 440,137]
442. 31 [avatar split clause 441,320]
443. $false [avatar sat refutation 439,442]
% SZS output end Proof for 3951125393688531472611410
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not wise and calm is both wise and not curious and vice versa. If someone is both not calm and happy then mary is either generous or not generous. Everyone who is not creative is either patient or not strong and vice versa. If someone is not brave then susan is either not tall or not quiet. Everyone who is not brave or not patient is not generous. Everyone who is not brave is funny or not wise. If john is not funny then someone is curious or not brave and vice versa. Everyone who is both kind and not wise is brave or tall and vice versa. Everyone who is both old and not old is either not quiet or not generous and vice versa. Everyone who is both happy and humble is humble. If mary is both not calm and not tall then alice is quiet. If john is both not tall and calm then someone is wise. If someone is either not rich or not patient then someone is both not strong and brave. Everyone who is generous or not calm is not calm and vice versa. Everyone who is either not patient or funny is both not tall and not funny. If someone is rich or not brave then fred is both not quiet and old and vice versa. John is not tall. Someone is not calm. Someone is calm. Alice is creative. Susan is calm or not quiet. Mary is humble. Mary is either funny or not generous. Someone is both not patient and funny. | Fred is old. | entailment | (![X]:((~wise(X)&calm(X))<=>(wise(X)&~curious(X))))&
((?[X]:((~calm(X)&happy(X))))=>((generous(mary)<~>~generous(mary))))&
(![X]:(~creative(X)<=>(patient(X)<~>~strong(X))))&
((?[X]:(~brave(X)))=>((~tall(susan)<~>~quiet(susan))))&
(![X]:((~brave(X)|~patient(X))=>~generous(X)))&
(![X]:(~brave(X)=>(funny(X)|~wise(X))))&
((~funny(john))<=>(?[X]:((curious(X)|~brave(X)))))&
(![X]:((kind(X)&~wise(X))<=>(brave(X)|tall(X))))&
(![X]:((old(X)&~old(X))<=>(~quiet(X)<~>~generous(X))))&
(![X]:((happy(X)&humble(X))=>humble(X)))&
(((~calm(mary)&~tall(mary)))=>(quiet(alice)))&
(((~tall(john)&calm(john)))=>(?[X]:(wise(X))))&
((?[X]:((~rich(X)<~>~patient(X))))=>(?[X]:((~strong(X)&brave(X)))))&
(![X]:((generous(X)|~calm(X))<=>~calm(X)))&
(![X]:((~patient(X)<~>funny(X))=>(~tall(X)&~funny(X))))&
((?[X]:((rich(X)|~brave(X))))<=>((~quiet(fred)&old(fred))))&
(~tall(john))&
(?[X]:(~calm(X)))&
(?[X]:(calm(X)))&
(creative(alice))&
((calm(susan)|~quiet(susan)))&
(humble(mary))&
((funny(mary)<~>~generous(mary)))&
(?[X]:((~patient(X)&funny(X)))) | old(fred) | [
"p0",
"p7",
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 6880826210815315949656
% SZS output start Proof for 6880826210815315949656
1. ! [X0] : ((calm(X0) & ~wise(X0)) <=> (~curious(X0) & wise(X0))) [input p0]
8. ! [X0] : ((~wise(X0) & kind(X0)) <=> (tall(X0) | brave(X0))) [input p7]
16. ? [X0] : (~brave(X0) | rich(X0)) <=> (old(fred) & ~quiet(fred)) [input p15]
19. ? [X0] : calm(X0) [input p18]
25. ~old(fred) [input hypothesis]
42. ! [X0] : (((calm(X0) & ~wise(X0)) | (curious(X0) | ~wise(X0))) & ((~curious(X0) & wise(X0)) | (~calm(X0) | wise(X0)))) [nnf transformation 1]
43. ! [X0] : (((calm(X0) & ~wise(X0)) | curious(X0) | ~wise(X0)) & ((~curious(X0) & wise(X0)) | ~calm(X0) | wise(X0))) [flattening 42]
50. ! [X0] : (((~wise(X0) & kind(X0)) | (~tall(X0) & ~brave(X0))) & ((tall(X0) | brave(X0)) | (wise(X0) | ~kind(X0)))) [nnf transformation 8]
51. ! [X0] : (((~wise(X0) & kind(X0)) | (~tall(X0) & ~brave(X0))) & (tall(X0) | brave(X0) | wise(X0) | ~kind(X0))) [flattening 50]
63. (? [X0] : (~brave(X0) | rich(X0)) | (~old(fred) | quiet(fred))) & ((old(fred) & ~quiet(fred)) | ! [X0] : (brave(X0) & ~rich(X0))) [nnf transformation 16]
64. (? [X0] : (~brave(X0) | rich(X0)) | ~old(fred) | quiet(fred)) & ((old(fred) & ~quiet(fred)) | ! [X0] : (brave(X0) & ~rich(X0))) [flattening 63]
65. (? [X0] : (~brave(X0) | rich(X0)) | ~old(fred) | quiet(fred)) & ((old(fred) & ~quiet(fred)) | ! [X1] : (brave(X1) & ~rich(X1))) [rectify 64]
66. ? [X0] : (~brave(X0) | rich(X0)) => (~brave(sK3) | rich(sK3)) [choice axiom]
67. ((~brave(sK3) | rich(sK3)) | ~old(fred) | quiet(fred)) & ((old(fred) & ~quiet(fred)) | ! [X1] : (brave(X1) & ~rich(X1))) [skolemisation 65,66]
70. ? [X0] : calm(X0) => calm(sK5) [choice axiom]
71. calm(sK5) [skolemisation 19,70]
75. wise(X0) | ~calm(X0) | wise(X0) [cnf transformation 43]
92. ~brave(X0) | ~wise(X0) [cnf transformation 51]
116. old(fred) | brave(X1) [cnf transformation 67]
120. calm(sK5) [cnf transformation 71]
127. ~old(fred) [cnf transformation 25]
129. ~calm(X0) | wise(X0) [duplicate literal removal 75]
132. 1 <=> ! [X0] : brave(X0) [avatar definition]
133. brave(X0) <- (1) [avatar component clause 132]
213. 19 <=> old(fred) [avatar definition]
225. 1 | 19 [avatar split clause 116,213,132]
248. ~19 [avatar split clause 127,213]
253. ~wise(X0) <- (1) [resolution 92,133]
256. wise(sK5) [resolution 129,120]
258. $false <- (1) [subsumption resolution 256,253]
259. ~1 [avatar contradiction clause 258]
262. $false [avatar sat refutation 225,248,259]
% SZS output end Proof for 6880826210815315949656
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either curious or not strong is not calm and vice versa.
Everyone who is not brave or generous is strong.
Everyone who is both not brave and generous is either calm or not kind.
If fred is both not happy and generous then fred is humble and vice versa.
Everyone who is both wise and not calm is either not creative or calm.
Everyone who is either not humble or not quiet is not brave or not humble and vice versa.
Everyone who is curious or wise is not brave and vice versa.
If paul is either not rich or generous then fred is both kind and not old and vice versa.
If fred is both not tall and not calm then someone is tall or humble and vice versa.
Everyone who is both not happy and patient is not strong.
Everyone who is both brave and curious is either not patient or creative and vice versa.
If someone is both creative and not creative then someone is not calm.
If someone is both kind and not strong then someone is not happy.
Everyone who is both not rich and not funny is both quiet and funny and vice versa.
Everyone who is not calm or not funny is either patient or creative and vice versa.
Everyone who is happy or not brave is brave.
Someone is rich.
Someone is both patient and kind.
Someone is kind.
Lucy is not humble or not brave.
John is not wise or not quiet.
Someone is either quiet or not happy. | Lucy is not curious. | entailment | (![X]:((curious(X)<~>~strong(X))<=>~calm(X)))&
(![X]:((~brave(X)|generous(X))=>strong(X)))&
(![X]:((~brave(X)&generous(X))=>(calm(X)<~>~kind(X))))&
(((~happy(fred)&generous(fred)))<=>(humble(fred)))&
(![X]:((wise(X)&~calm(X))=>(~creative(X)<~>calm(X))))&
(![X]:((~humble(X)<~>~quiet(X))<=>(~brave(X)|~humble(X))))&
(![X]:((curious(X)|wise(X))<=>~brave(X)))&
(((~rich(paul)<~>generous(paul)))<=>((kind(fred)&~old(fred))))&
(((~tall(fred)&~calm(fred)))<=>(?[X]:((tall(X)|humble(X)))))&
(![X]:((~happy(X)&patient(X))=>~strong(X)))&
(![X]:((brave(X)&curious(X))<=>(~patient(X)<~>creative(X))))&
((?[X]:((creative(X)&~creative(X))))=>(?[X]:(~calm(X))))&
((?[X]:((kind(X)&~strong(X))))=>(?[X]:(~happy(X))))&
(![X]:((~rich(X)&~funny(X))<=>(quiet(X)&funny(X))))&
(![X]:((~calm(X)|~funny(X))<=>(patient(X)<~>creative(X))))&
(![X]:((happy(X)|~brave(X))=>brave(X)))&
(?[X]:(rich(X)))&
(?[X]:((patient(X)&kind(X))))&
(?[X]:(kind(X)))&
((~humble(lucy)|~brave(lucy)))&
((~wise(john)|~quiet(john)))&
(?[X]:((quiet(X)<~>~happy(X)))) | ~curious(lucy) | [
"p6",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4269204459804809343102336
% SZS output start Proof for 4269204459804809343102336
7. ! [X0] : ((wise(X0) | curious(X0)) <=> ~brave(X0)) [input p6]
16. ! [X0] : ((~brave(X0) | happy(X0)) => brave(X0)) [input p15]
23. curious(lucy) [input hypothesis]
35. ! [X0] : (brave(X0) | (brave(X0) & ~happy(X0))) [ennf transformation 16]
43. ! [X0] : (((wise(X0) | curious(X0)) | brave(X0)) & (~brave(X0) | (~wise(X0) & ~curious(X0)))) [nnf transformation 7]
44. ! [X0] : ((wise(X0) | curious(X0) | brave(X0)) & (~brave(X0) | (~wise(X0) & ~curious(X0)))) [flattening 43]
92. ~brave(X0) | ~curious(X0) [cnf transformation 44]
126. brave(X0) | brave(X0) [cnf transformation 35]
135. curious(lucy) [cnf transformation 23]
136. brave(X0) [duplicate literal removal 126]
236. ~curious(X1) [resolution 92,136]
237. $false [resolution 236,135]
% SZS output end Proof for 4269204459804809343102336
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise or kind is either not strong or humble and vice versa. Everyone who is wise is both not generous and brave and vice versa. Everyone who is either generous or not curious is not humble or not generous and vice versa. Everyone who is strong or generous is not creative. Everyone who is either brave or not rich is tall. If someone is either strong or old then someone is patient. Everyone who is either not curious or not brave is creative or not curious and vice versa. If someone is generous then alice is not creative and vice versa. Everyone who is not calm or not wise is either not curious or humble. If john is both not happy and not wise then someone is not kind or old. Everyone who is either not humble or not calm is either not old or strong. Everyone who is either old or wise is not kind or brave. Everyone who is either curious or patient is brave or not curious. Everyone who is brave is either happy or kind and vice versa. If fred is not funny then someone is strong or not curious. Everyone who is tall or not humble is either kind or calm. Someone is rich. Lucy is generous or not kind. John is both not generous and tall. Someone is both quiet and brave. Someone is both not strong and not funny. Someone is not tall or not brave. Mary is either not old or not happy. Someone is both brave and happy. | John is wise. | entailment | (![X]:((wise(X)|kind(X))<=>(~strong(X)<~>humble(X))))&
(![X]:(wise(X)<=>(~generous(X)&brave(X))))&
(![X]:((generous(X)<~>~curious(X))<=>(~humble(X)|~generous(X))))&
(![X]:((strong(X)|generous(X))=>~creative(X)))&
(![X]:((brave(X)<~>~rich(X))=>tall(X)))&
((?[X]:((strong(X)<~>old(X))))=>(?[X]:(patient(X))))&
(![X]:((~curious(X)<~>~brave(X))<=>(creative(X)|~curious(X))))&
((?[X]:(generous(X)))<=>(~creative(alice)))&
(![X]:((~calm(X)|~wise(X))=>(~curious(X)<~>humble(X))))&
(((~happy(john)&~wise(john)))=>(?[X]:((~kind(X)|old(X)))))&
(![X]:((~humble(X)<~>~calm(X))=>(~old(X)<~>strong(X))))&
(![X]:((old(X)<~>wise(X))=>(~kind(X)|brave(X))))&
(![X]:((curious(X)<~>patient(X))=>(brave(X)|~curious(X))))&
(![X]:(brave(X)<=>(happy(X)<~>kind(X))))&
((~funny(fred))=>(?[X]:((strong(X)|~curious(X)))))&
(![X]:((tall(X)|~humble(X))=>(kind(X)<~>calm(X))))&
(?[X]:(rich(X)))&
((generous(lucy)|~kind(lucy)))&
((~generous(john)&tall(john)))&
(?[X]:((quiet(X)&brave(X))))&
(?[X]:((~strong(X)&~funny(X))))&
(?[X]:((~tall(X)|~brave(X))))&
((~old(mary)<~>~happy(mary)))&
(?[X]:((brave(X)&happy(X)))) | wise(john) | [
"p1",
"p2",
"p6",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 4291746728796815458865767
% SZS output start Proof for 4291746728796815458865767
2. ! [X0] : (wise(X0) <=> (brave(X0) & ~generous(X0))) [input p1]
3. ! [X0] : ((generous(X0) <~> ~curious(X0)) <=> (~generous(X0) | ~humble(X0))) [input p2]
7. ! [X0] : ((~curious(X0) <~> ~brave(X0)) <=> (~curious(X0) | creative(X0))) [input p6]
19. tall(john) & ~generous(john) [input p18]
25. ~wise(john) [input hypothesis]
43. ! [X0] : ((wise(X0) | (~brave(X0) | generous(X0))) & ((brave(X0) & ~generous(X0)) | ~wise(X0))) [nnf transformation 2]
44. ! [X0] : ((wise(X0) | ~brave(X0) | generous(X0)) & ((brave(X0) & ~generous(X0)) | ~wise(X0))) [flattening 43]
45. ! [X0] : ((((curious(X0) | ~generous(X0)) & (~curious(X0) | generous(X0))) | (generous(X0) & humble(X0))) & ((~generous(X0) | ~humble(X0)) | ((generous(X0) | curious(X0)) & (~curious(X0) | ~generous(X0))))) [nnf transformation 3]
46. ! [X0] : ((((curious(X0) | ~generous(X0)) & (~curious(X0) | generous(X0))) | (generous(X0) & humble(X0))) & (~generous(X0) | ~humble(X0) | ((generous(X0) | curious(X0)) & (~curious(X0) | ~generous(X0))))) [flattening 45]
52. ! [X0] : ((((brave(X0) | curious(X0)) & (~brave(X0) | ~curious(X0))) | (curious(X0) & ~creative(X0))) & ((~curious(X0) | creative(X0)) | ((~curious(X0) | brave(X0)) & (~brave(X0) | curious(X0))))) [nnf transformation 7]
53. ! [X0] : ((((brave(X0) | curious(X0)) & (~brave(X0) | ~curious(X0))) | (curious(X0) & ~creative(X0))) & (~curious(X0) | creative(X0) | ((~curious(X0) | brave(X0)) & (~brave(X0) | curious(X0))))) [flattening 52]
87. ~brave(X0) | wise(X0) | generous(X0) [cnf transformation 44]
91. ~curious(X0) | generous(X0) | generous(X0) [cnf transformation 46]
105. brave(X0) | curious(X0) | curious(X0) [cnf transformation 53]
132. ~generous(john) [cnf transformation 19]
142. ~wise(john) [cnf transformation 25]
145. curious(X0) | brave(X0) [duplicate literal removal 105]
147. ~curious(X0) | generous(X0) [duplicate literal removal 91]
184. 8 <=> wise(john) [avatar definition]
185. ~wise(john) <- (~8) [avatar component clause 184]
240. ~8 [avatar split clause 142,184]
243. brave(X0) | generous(X0) [resolution 147,145]
253. wise(X0) | generous(X0) | generous(X0) [resolution 87,243]
259. generous(X0) | wise(X0) [duplicate literal removal 253]
260. wise(john) [resolution 259,132]
262. $false <- (~8) [subsumption resolution 260,185]
263. 8 [avatar contradiction clause 262]
264. $false [avatar sat refutation 240,263]
% SZS output end Proof for 4291746728796815458865767
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old is strong or not quiet and vice versa.
If lucy is both not strong and tall then someone is patient and vice versa.
If fred is tall then someone is happy or rich and vice versa.
Everyone who is not humble or not strong is both old and happy and vice versa.
If someone is both funny and rich then alice is not creative or not funny.
If someone is both old and brave then susan is either old or not tall.
Everyone who is both not funny and not happy is humble.
If susan is not patient or rich then someone is funny or not brave.
If john is either generous or humble then someone is not creative and vice versa.
Everyone who is either funny or not creative is calm or not rich and vice versa.
If someone is either not strong or creative then someone is not rich or happy and vice versa.
If someone is both not tall and tall then someone is not old or not strong.
Everyone who is humble or not funny is both not generous and patient and vice versa.
Everyone who is either not strong or tall is quiet.
Everyone who is either kind or brave is strong or not rich.
If john is not old then mary is either not wise or rich and vice versa.
Someone is both not happy and curious.
Susan is funny.
Alice is either not calm or not kind.
Fred is both not patient and brave. | Lucy is not old. | contradiction | (![X]:(~old(X)<=>(strong(X)|~quiet(X))))&
(((~strong(lucy)&tall(lucy)))<=>(?[X]:(patient(X))))&
((tall(fred))<=>(?[X]:((happy(X)|rich(X)))))&
(![X]:((~humble(X)|~strong(X))<=>(old(X)&happy(X))))&
((?[X]:((funny(X)&rich(X))))=>((~creative(alice)|~funny(alice))))&
((?[X]:((old(X)&brave(X))))=>((old(susan)<~>~tall(susan))))&
(![X]:((~funny(X)&~happy(X))=>humble(X)))&
(((~patient(susan)|rich(susan)))=>(?[X]:((funny(X)|~brave(X)))))&
(((generous(john)<~>humble(john)))<=>(?[X]:(~creative(X))))&
(![X]:((funny(X)<~>~creative(X))<=>(calm(X)|~rich(X))))&
((?[X]:((~strong(X)<~>creative(X))))<=>(?[X]:((~rich(X)|happy(X)))))&
((?[X]:((~tall(X)&tall(X))))=>(?[X]:((~old(X)|~strong(X)))))&
(![X]:((humble(X)|~funny(X))<=>(~generous(X)&patient(X))))&
(![X]:((~strong(X)<~>tall(X))=>quiet(X)))&
(![X]:((kind(X)<~>brave(X))=>(strong(X)|~rich(X))))&
((~old(john))<=>((~wise(mary)<~>rich(mary))))&
(?[X]:((~happy(X)&curious(X))))&
(funny(susan))&
((~calm(alice)<~>~kind(alice)))&
((~patient(fred)&brave(fred))) | ~old(lucy) | [
"p1",
"p3",
"p12",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 1703382423373083729155553
% SZS output start Proof for 1703382423373083729155553
2. (tall(lucy) & ~strong(lucy)) <=> ? [X0] : patient(X0) [input p1]
4. ! [X0] : ((~strong(X0) | ~humble(X0)) <=> (happy(X0) & old(X0))) [input p3]
13. ! [X0] : ((~funny(X0) | humble(X0)) <=> (patient(X0) & ~generous(X0))) [input p12]
17. ? [X0] : (curious(X0) & ~happy(X0)) [input p16]
21. ~old(lucy) [input hypothesis]
24. ? [X0] : ~happy(X0) [pure predicate removal 17]
37. ((tall(lucy) & ~strong(lucy)) | ! [X0] : ~patient(X0)) & (? [X0] : patient(X0) | (~tall(lucy) | strong(lucy))) [nnf transformation 2]
38. ((tall(lucy) & ~strong(lucy)) | ! [X0] : ~patient(X0)) & (? [X0] : patient(X0) | ~tall(lucy) | strong(lucy)) [flattening 37]
39. ((tall(lucy) & ~strong(lucy)) | ! [X0] : ~patient(X0)) & (? [X1] : patient(X1) | ~tall(lucy) | strong(lucy)) [rectify 38]
40. ? [X1] : patient(X1) => patient(sK0) [choice axiom]
41. ((tall(lucy) & ~strong(lucy)) | ! [X0] : ~patient(X0)) & (patient(sK0) | ~tall(lucy) | strong(lucy)) [skolemisation 39,40]
46. ! [X0] : (((~strong(X0) | ~humble(X0)) | (~happy(X0) | ~old(X0))) & ((happy(X0) & old(X0)) | (strong(X0) & humble(X0)))) [nnf transformation 4]
47. ! [X0] : ((~strong(X0) | ~humble(X0) | ~happy(X0) | ~old(X0)) & ((happy(X0) & old(X0)) | (strong(X0) & humble(X0)))) [flattening 46]
65. ! [X0] : (((~funny(X0) | humble(X0)) | (~patient(X0) | generous(X0))) & ((patient(X0) & ~generous(X0)) | (funny(X0) & ~humble(X0)))) [nnf transformation 13]
66. ! [X0] : ((~funny(X0) | humble(X0) | ~patient(X0) | generous(X0)) & ((patient(X0) & ~generous(X0)) | (funny(X0) & ~humble(X0)))) [flattening 65]
70. ? [X0] : ~happy(X0) => ~happy(sK7) [choice axiom]
71. ~happy(sK7) [skolemisation 24,70]
77. ~strong(lucy) | ~patient(X0) [cnf transformation 41]
83. strong(X0) | old(X0) [cnf transformation 47]
84. humble(X0) | happy(X0) [cnf transformation 47]
112. ~humble(X0) | patient(X0) [cnf transformation 66]
123. ~happy(sK7) [cnf transformation 71]
129. ~old(lucy) [cnf transformation 21]
131. 1 <=> ! [X0] : ~patient(X0) [avatar definition]
132. ~patient(X0) <- (1) [avatar component clause 131]
139. 3 <=> strong(lucy) [avatar definition]
141. ~strong(lucy) <- (~3) [avatar component clause 139]
142. 1 | ~3 [avatar split clause 77,139,131]
293. old(lucy) <- (~3) [resolution 83,141]
296. $false <- (~3) [subsumption resolution 293,129]
297. 3 [avatar contradiction clause 296]
308. patient(X0) | happy(X0) [resolution 112,84]
311. happy(X0) <- (1) [subsumption resolution 308,132]
332. $false <- (1) [resolution 311,123]
333. ~1 [avatar contradiction clause 332]
334. $false [avatar sat refutation 142,297,333]
% SZS output end Proof for 1703382423373083729155553
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave or wise is not wise or not old.
Everyone who is not calm is not humble.
If fred is both not brave and strong then alice is both tall and not generous.
If paul is both not calm and funny then someone is not creative and vice versa.
Everyone who is not wise or not funny is either tall or not happy.
If susan is not kind or calm then someone is strong or tall.
Everyone who is both not funny and curious is calm.
If mary is both not patient and not rich then someone is not brave and vice versa.
Everyone who is quiet or generous is not strong.
If paul is strong or calm then someone is either not happy or not creative.
If mary is strong then someone is both not generous and generous.
Everyone who is both not strong and patient is not happy.
Everyone who is either kind or curious is not rich or not curious and vice versa.
If susan is not old or generous then susan is both not quiet and happy.
If lucy is not patient then paul is not humble or generous and vice versa.
Everyone who is either not quiet or creative is old and vice versa.
Someone is tall or patient.
Mary is both creative and rich.
Lucy is both not funny and humble.
Paul is both not funny and humble.
Someone is curious or not quiet.
John is either happy or humble.
Alice is generous or tall. | Susan is not creative. | contradiction | (![X]:((brave(X)|wise(X))=>(~wise(X)|~old(X))))&
(![X]:(~calm(X)=>~humble(X)))&
(((~brave(fred)&strong(fred)))=>((tall(alice)&~generous(alice))))&
(((~calm(paul)&funny(paul)))<=>(?[X]:(~creative(X))))&
(![X]:((~wise(X)|~funny(X))=>(tall(X)<~>~happy(X))))&
(((~kind(susan)|calm(susan)))=>(?[X]:((strong(X)|tall(X)))))&
(![X]:((~funny(X)&curious(X))=>calm(X)))&
(((~patient(mary)&~rich(mary)))<=>(?[X]:(~brave(X))))&
(![X]:((quiet(X)|generous(X))=>~strong(X)))&
(((strong(paul)|calm(paul)))=>(?[X]:((~happy(X)<~>~creative(X)))))&
((strong(mary))=>(?[X]:((~generous(X)&generous(X)))))&
(![X]:((~strong(X)&patient(X))=>~happy(X)))&
(![X]:((kind(X)<~>curious(X))<=>(~rich(X)|~curious(X))))&
(((~old(susan)|generous(susan)))=>((~quiet(susan)&happy(susan))))&
((~patient(lucy))<=>((~humble(paul)|generous(paul))))&
(![X]:((~quiet(X)<~>creative(X))<=>old(X)))&
(?[X]:((tall(X)|patient(X))))&
((creative(mary)&rich(mary)))&
((~funny(lucy)&humble(lucy)))&
((~funny(paul)&humble(paul)))&
(?[X]:((curious(X)|~quiet(X))))&
((happy(john)<~>humble(john)))&
((generous(alice)|tall(alice))) | ~creative(susan) | [
"p3",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 3650899767771724009257271
% SZS output start Proof for 3650899767771724009257271
4. (funny(paul) & ~calm(paul)) <=> ? [X0] : ~creative(X0) [input p3]
20. humble(paul) & ~funny(paul) [input p19]
24. ~creative(susan) [input hypothesis]
40. ((funny(paul) & ~calm(paul)) | ! [X0] : creative(X0)) & (? [X0] : ~creative(X0) | (~funny(paul) | calm(paul))) [nnf transformation 4]
41. ((funny(paul) & ~calm(paul)) | ! [X0] : creative(X0)) & (? [X0] : ~creative(X0) | ~funny(paul) | calm(paul)) [flattening 40]
42. ((funny(paul) & ~calm(paul)) | ! [X0] : creative(X0)) & (? [X1] : ~creative(X1) | ~funny(paul) | calm(paul)) [rectify 41]
43. ? [X1] : ~creative(X1) => ~creative(sK0) [choice axiom]
44. ((funny(paul) & ~calm(paul)) | ! [X0] : creative(X0)) & (~creative(sK0) | ~funny(paul) | calm(paul)) [skolemisation 42,43]
75. funny(paul) | creative(X0) [cnf transformation 44]
117. ~funny(paul) [cnf transformation 20]
123. ~creative(susan) [cnf transformation 24]
146. 5 <=> ! [X0] : creative(X0) [avatar definition]
147. creative(X0) <- (5) [avatar component clause 146]
149. 6 <=> funny(paul) [avatar definition]
152. 5 | 6 [avatar split clause 75,149,146]
272. ~6 [avatar split clause 117,149]
293. $false <- (5) [resolution 147,123]
294. ~5 [avatar contradiction clause 293]
295. $false [avatar sat refutation 152,272,294]
% SZS output end Proof for 3650899767771724009257271
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave or old is both not funny and kind.
If alice is quiet then someone is both old and not brave.
Everyone who is both humble and not wise is not quiet and vice versa.
If mary is not quiet then someone is not generous and vice versa.
Everyone who is not humble is either not happy or brave and vice versa.
If someone is not funny then someone is rich or patient and vice versa.
If someone is not old or not wise then someone is either not patient or not happy.
If john is both not patient and not strong then lucy is both not brave and generous.
If someone is creative or calm then john is tall or not creative and vice versa.
If mary is creative then john is old.
Everyone who is not happy or quiet is both not humble and funny.
If someone is patient then someone is not funny.
Everyone who is quiet is either not creative or happy.
Everyone who is both happy and generous is both not curious and curious and vice versa.
Everyone who is both not wise and wise is patient.
Lucy is either not rich or not strong.
Alice is not patient or not kind.
Someone is not wise or wise.
Someone is not wise or not patient.
Lucy is humble or generous.
Fred is not calm.
Someone is either quiet or brave. | Fred is calm. | contradiction | (![X]:((brave(X)|old(X))=>(~funny(X)&kind(X))))&
((quiet(alice))=>(?[X]:((old(X)&~brave(X)))))&
(![X]:((humble(X)&~wise(X))<=>~quiet(X)))&
((~quiet(mary))<=>(?[X]:(~generous(X))))&
(![X]:(~humble(X)<=>(~happy(X)<~>brave(X))))&
((?[X]:(~funny(X)))<=>(?[X]:((rich(X)|patient(X)))))&
((?[X]:((~old(X)|~wise(X))))=>(?[X]:((~patient(X)<~>~happy(X)))))&
(((~patient(john)&~strong(john)))=>((~brave(lucy)&generous(lucy))))&
((?[X]:((creative(X)|calm(X))))<=>((tall(john)|~creative(john))))&
((creative(mary))=>(old(john)))&
(![X]:((~happy(X)|quiet(X))=>(~humble(X)&funny(X))))&
((?[X]:(patient(X)))=>(?[X]:(~funny(X))))&
(![X]:(quiet(X)=>(~creative(X)<~>happy(X))))&
(![X]:((happy(X)&generous(X))<=>(~curious(X)&curious(X))))&
(![X]:((~wise(X)&wise(X))=>patient(X)))&
((~rich(lucy)<~>~strong(lucy)))&
((~patient(alice)|~kind(alice)))&
(?[X]:((~wise(X)|wise(X))))&
(?[X]:((~wise(X)|~patient(X))))&
((humble(lucy)|generous(lucy)))&
(~calm(fred))&
(?[X]:((quiet(X)<~>brave(X)))) | calm(fred) | [
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 6680245908806049481947872
% SZS output start Proof for 6680245908806049481947872
21. ~calm(fred) [input p20]
23. calm(fred) [input hypothesis]
122. ~calm(fred) [cnf transformation 21]
125. calm(fred) [cnf transformation 23]
297. $false [subsumption resolution 125,122]
% SZS output end Proof for 6680245908806049481947872
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not kind is generous and vice versa.
If someone is rich then someone is not funny.
Everyone who is both not calm and not generous is not brave or quiet.
If alice is either not wise or strong then paul is both brave and creative.
Everyone who is both calm and patient is both not generous and not patient.
Everyone who is kind or not strong is both quiet and not happy.
If mary is not old or strong then someone is not brave or tall and vice versa.
If alice is either calm or not curious then john is strong.
If alice is happy then someone is either not kind or patient and vice versa.
Everyone who is both happy and generous is both happy and curious and vice versa.
Everyone who is either wise or not humble is both humble and not patient.
Everyone who is either funny or strong is either not tall or funny.
Everyone who is not happy is brave.
Everyone who is not strong or not quiet is both rich and happy.
Everyone who is both calm and not curious is either strong or kind and vice versa.
If mary is not funny then mary is either not humble or creative.
Someone is rich.
Someone is either not wise or not strong.
Someone is wise.
Someone is not quiet or creative.
Alice is either not wise or not creative.
Mary is not creative or not old.
Susan is both not generous and not humble. | Mary is not patient. | entailment | (![X]:(~kind(X)<=>generous(X)))&
((?[X]:(rich(X)))=>(?[X]:(~funny(X))))&
(![X]:((~calm(X)&~generous(X))=>(~brave(X)|quiet(X))))&
(((~wise(alice)<~>strong(alice)))=>((brave(paul)&creative(paul))))&
(![X]:((calm(X)&patient(X))=>(~generous(X)&~patient(X))))&
(![X]:((kind(X)|~strong(X))=>(quiet(X)&~happy(X))))&
(((~old(mary)|strong(mary)))<=>(?[X]:((~brave(X)|tall(X)))))&
(((calm(alice)<~>~curious(alice)))=>(strong(john)))&
((happy(alice))<=>(?[X]:((~kind(X)<~>patient(X)))))&
(![X]:((happy(X)&generous(X))<=>(happy(X)&curious(X))))&
(![X]:((wise(X)<~>~humble(X))=>(humble(X)&~patient(X))))&
(![X]:((funny(X)<~>strong(X))=>(~tall(X)<~>funny(X))))&
(![X]:(~happy(X)=>brave(X)))&
(![X]:((~strong(X)|~quiet(X))=>(rich(X)&happy(X))))&
(![X]:((calm(X)&~curious(X))<=>(strong(X)<~>kind(X))))&
((~funny(mary))=>((~humble(mary)<~>creative(mary))))&
(?[X]:(rich(X)))&
(?[X]:((~wise(X)<~>~strong(X))))&
(?[X]:(wise(X)))&
(?[X]:((~quiet(X)|creative(X))))&
((~wise(alice)<~>~creative(alice)))&
((~creative(mary)|~old(mary)))&
((~generous(susan)&~humble(susan))) | ~patient(mary) | [
"p0",
"p4",
"p5",
"p8",
"p9",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 1567930272204362067935268
% SZS output start Proof for 1567930272204362067935268
1. ! [X0] : (~kind(X0) <=> generous(X0)) [input p0]
5. ! [X0] : ((patient(X0) & calm(X0)) => (~patient(X0) & ~generous(X0))) [input p4]
6. ! [X0] : ((~strong(X0) | kind(X0)) => (~happy(X0) & quiet(X0))) [input p5]
9. happy(alice) <=> ? [X0] : (~kind(X0) <~> patient(X0)) [input p8]
10. ! [X0] : ((generous(X0) & happy(X0)) <=> (curious(X0) & happy(X0))) [input p9]
14. ! [X0] : ((~quiet(X0) | ~strong(X0)) => (happy(X0) & rich(X0))) [input p13]
15. ! [X0] : ((~curious(X0) & calm(X0)) <=> (strong(X0) <~> kind(X0))) [input p14]
24. patient(mary) [input hypothesis]
30. ! [X0] : ((~patient(X0) & ~generous(X0)) | (~patient(X0) | ~calm(X0))) [ennf transformation 5]
31. ! [X0] : ((~patient(X0) & ~generous(X0)) | ~patient(X0) | ~calm(X0)) [flattening 30]
32. ! [X0] : ((~happy(X0) & quiet(X0)) | (strong(X0) & ~kind(X0))) [ennf transformation 6]
37. ! [X0] : ((happy(X0) & rich(X0)) | (quiet(X0) & strong(X0))) [ennf transformation 14]
39. ! [X0] : ((~kind(X0) | ~generous(X0)) & (generous(X0) | kind(X0))) [nnf transformation 1]
50. (happy(alice) | ! [X0] : ((~kind(X0) | ~patient(X0)) & (patient(X0) | kind(X0)))) & (? [X0] : ((~patient(X0) | kind(X0)) & (patient(X0) | ~kind(X0))) | ~happy(alice)) [nnf transformation 9]
51. (happy(alice) | ! [X0] : ((~kind(X0) | ~patient(X0)) & (patient(X0) | kind(X0)))) & (? [X1] : ((~patient(X1) | kind(X1)) & (patient(X1) | ~kind(X1))) | ~happy(alice)) [rectify 50]
52. ? [X1] : ((~patient(X1) | kind(X1)) & (patient(X1) | ~kind(X1))) => ((~patient(sK2) | kind(sK2)) & (patient(sK2) | ~kind(sK2))) [choice axiom]
53. (happy(alice) | ! [X0] : ((~kind(X0) | ~patient(X0)) & (patient(X0) | kind(X0)))) & (((~patient(sK2) | kind(sK2)) & (patient(sK2) | ~kind(sK2))) | ~happy(alice)) [skolemisation 51,52]
54. ! [X0] : (((generous(X0) & happy(X0)) | (~curious(X0) | ~happy(X0))) & ((curious(X0) & happy(X0)) | (~generous(X0) | ~happy(X0)))) [nnf transformation 10]
55. ! [X0] : (((generous(X0) & happy(X0)) | ~curious(X0) | ~happy(X0)) & ((curious(X0) & happy(X0)) | ~generous(X0) | ~happy(X0))) [flattening 54]
58. ! [X0] : (((~curious(X0) & calm(X0)) | ((strong(X0) | ~kind(X0)) & (kind(X0) | ~strong(X0)))) & (((~kind(X0) | ~strong(X0)) & (kind(X0) | strong(X0))) | (curious(X0) | ~calm(X0)))) [nnf transformation 15]
59. ! [X0] : (((~curious(X0) & calm(X0)) | ((strong(X0) | ~kind(X0)) & (kind(X0) | ~strong(X0)))) & (((~kind(X0) | ~strong(X0)) & (kind(X0) | strong(X0))) | curious(X0) | ~calm(X0))) [flattening 58]
71. generous(X0) | kind(X0) [cnf transformation 39]
80. ~patient(X0) | ~patient(X0) | ~calm(X0) [cnf transformation 31]
83. ~happy(X0) | ~kind(X0) [cnf transformation 32]
84. ~happy(X0) | strong(X0) [cnf transformation 32]
94. happy(alice) | ~kind(X0) | ~patient(X0) [cnf transformation 53]
96. ~happy(X0) | ~generous(X0) | curious(X0) [cnf transformation 55]
110. happy(X0) | strong(X0) [cnf transformation 37]
114. calm(X0) | kind(X0) | ~strong(X0) [cnf transformation 59]
116. ~curious(X0) | kind(X0) | ~strong(X0) [cnf transformation 59]
130. patient(mary) [cnf transformation 24]
134. ~patient(X0) | ~calm(X0) [duplicate literal removal 80]
190. 13 <=> curious(alice) [avatar definition]
191. ~curious(alice) <- (~13) [avatar component clause 190]
192. curious(alice) <- (13) [avatar component clause 190]
204. 16 <=> ! [X0] : (~kind(X0) | ~patient(X0)) [avatar definition]
205. ~patient(X0) | ~kind(X0) <- (16) [avatar component clause 204]
207. 17 <=> happy(alice) [avatar definition]
209. happy(alice) <- (17) [avatar component clause 207]
210. 16 | 17 [avatar split clause 94,207,204]
225. strong(X0) [subsumption resolution 110,84]
226. ~curious(X0) | kind(X0) [subsumption resolution 116,225]
227. calm(X0) | kind(X0) [subsumption resolution 114,225]
265. ~kind(alice) <- (17) [resolution 83,209]
274. ~calm(mary) [resolution 134,130]
275. kind(alice) <- (13) [resolution 226,192]
276. $false <- (13, 17) [subsumption resolution 275,265]
277. ~13 | ~17 [avatar contradiction clause 276]
278. kind(mary) [resolution 227,274]
280. ~generous(alice) | curious(alice) <- (17) [resolution 96,209]
283. ~generous(alice) <- (~13, 17) [subsumption resolution 280,191]
284. kind(alice) <- (~13, 17) [resolution 283,71]
285. $false <- (~13, 17) [subsumption resolution 284,265]
286. 13 | ~17 [avatar contradiction clause 285]
289. ~kind(mary) <- (16) [resolution 205,130]
290. $false <- (16) [subsumption resolution 289,278]
291. ~16 [avatar contradiction clause 290]
292. $false [avatar sat refutation 210,277,286,291]
% SZS output end Proof for 1567930272204362067935268
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not curious and generous is both rich and not tall and vice versa.
Everyone who is strong or curious is tall or brave and vice versa.
If john is tall then someone is either not patient or creative and vice versa.
If susan is either not kind or quiet then alice is not generous and vice versa.
If alice is tall or quiet then someone is not kind or creative and vice versa.
Everyone who is either not funny or not strong is either not old or not quiet.
If mary is not wise then fred is not patient or not happy.
Everyone who is not quiet or strong is either tall or not rich and vice versa.
If someone is either creative or old then lucy is generous and vice versa.
If someone is both calm and funny then alice is quiet or calm and vice versa.
Everyone who is either not quiet or not brave is not patient.
If someone is either strong or funny then alice is not wise or not rich and vice versa.
If someone is both not curious and funny then fred is calm or not happy.
Everyone who is not wise or curious is not generous.
If someone is not quiet or generous then lucy is not tall and vice versa.
Everyone who is not humble or kind is not wise or not strong.
Someone is not generous.
Someone is either not humble or wise.
Someone is both not generous and not wise.
Someone is quiet.
Lucy is not generous or humble.
Lucy is both tall and not rich.
Someone is either old or strong.
Lucy is rich or wise. | Susan is not kind. | contradiction | (![X]:((~curious(X)&generous(X))<=>(rich(X)&~tall(X))))&
(![X]:((strong(X)|curious(X))<=>(tall(X)|brave(X))))&
((tall(john))<=>(?[X]:((~patient(X)<~>creative(X)))))&
(((~kind(susan)<~>quiet(susan)))<=>(~generous(alice)))&
(((tall(alice)|quiet(alice)))<=>(?[X]:((~kind(X)|creative(X)))))&
(![X]:((~funny(X)<~>~strong(X))=>(~old(X)<~>~quiet(X))))&
((~wise(mary))=>((~patient(fred)|~happy(fred))))&
(![X]:((~quiet(X)|strong(X))<=>(tall(X)<~>~rich(X))))&
((?[X]:((creative(X)<~>old(X))))<=>(generous(lucy)))&
((?[X]:((calm(X)&funny(X))))<=>((quiet(alice)|calm(alice))))&
(![X]:((~quiet(X)<~>~brave(X))=>~patient(X)))&
((?[X]:((strong(X)<~>funny(X))))<=>((~wise(alice)|~rich(alice))))&
((?[X]:((~curious(X)&funny(X))))=>((calm(fred)|~happy(fred))))&
(![X]:((~wise(X)|curious(X))=>~generous(X)))&
((?[X]:((~quiet(X)|generous(X))))<=>(~tall(lucy)))&
(![X]:((~humble(X)|kind(X))=>(~wise(X)|~strong(X))))&
(?[X]:(~generous(X)))&
(?[X]:((~humble(X)<~>wise(X))))&
(?[X]:((~generous(X)&~wise(X))))&
(?[X]:(quiet(X)))&
((~generous(lucy)|humble(lucy)))&
((tall(lucy)&~rich(lucy)))&
(?[X]:((old(X)<~>strong(X))))&
((rich(lucy)|wise(lucy))) | ~kind(susan) | [
"p3",
"p14",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 5893012742492599230594657
% SZS output start Proof for 5893012742492599230594657
4. (~kind(susan) <~> quiet(susan)) <=> ~generous(alice) [input p3]
15. ? [X0] : (generous(X0) | ~quiet(X0)) <=> ~tall(lucy) [input p14]
22. ~rich(lucy) & tall(lucy) [input p21]
25. ~kind(susan) [input hypothesis]
41. (((~quiet(susan) | kind(susan)) & (quiet(susan) | ~kind(susan))) | generous(alice)) & (~generous(alice) | ((~kind(susan) | ~quiet(susan)) & (quiet(susan) | kind(susan)))) [nnf transformation 4]
65. (? [X0] : (generous(X0) | ~quiet(X0)) | tall(lucy)) & (~tall(lucy) | ! [X0] : (~generous(X0) & quiet(X0))) [nnf transformation 15]
66. (? [X0] : (generous(X0) | ~quiet(X0)) | tall(lucy)) & (~tall(lucy) | ! [X1] : (~generous(X1) & quiet(X1))) [rectify 65]
67. ? [X0] : (generous(X0) | ~quiet(X0)) => (generous(sK5) | ~quiet(sK5)) [choice axiom]
68. ((generous(sK5) | ~quiet(sK5)) | tall(lucy)) & (~tall(lucy) | ! [X1] : (~generous(X1) & quiet(X1))) [skolemisation 66,67]
96. ~quiet(susan) | kind(susan) | generous(alice) [cnf transformation 41]
130. ~tall(lucy) | quiet(X1) [cnf transformation 68]
131. ~tall(lucy) | ~generous(X1) [cnf transformation 68]
142. tall(lucy) [cnf transformation 22]
147. ~kind(susan) [cnf transformation 25]
171. 6 <=> generous(alice) [avatar definition]
173. generous(alice) <- (6) [avatar component clause 171]
175. 7 <=> kind(susan) [avatar definition]
179. 8 <=> quiet(susan) [avatar definition]
181. ~quiet(susan) <- (~8) [avatar component clause 179]
182. 6 | 7 | ~8 [avatar split clause 96,179,175,171]
283. 30 <=> tall(lucy) [avatar definition]
296. 33 <=> ! [X1] : ~generous(X1) [avatar definition]
297. ~generous(X1) <- (33) [avatar component clause 296]
298. 33 | ~30 [avatar split clause 131,283,296]
300. 34 <=> ! [X1] : quiet(X1) [avatar definition]
301. quiet(X1) <- (34) [avatar component clause 300]
302. 34 | ~30 [avatar split clause 130,283,300]
318. 30 [avatar split clause 142,283]
330. ~7 [avatar split clause 147,175]
333. $false <- (~8, 34) [subsumption resolution 181,301]
334. 8 | ~34 [avatar contradiction clause 333]
335. $false <- (6, 33) [subsumption resolution 173,297]
336. ~6 | ~33 [avatar contradiction clause 335]
337. $false [avatar sat refutation 182,298,302,318,330,334,336]
% SZS output end Proof for 5893012742492599230594657
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.021 s
% ------------------------------
% ------------------------------
| 0 |
If alice is not funny then fred is both not curious and creative.
If john is either tall or quiet then someone is either not calm or not curious.
If fred is either not brave or tall then paul is calm.
Everyone who is not kind or not rich is either calm or wise.
Everyone who is either not generous or rich is both quiet and old.
If susan is both not kind and not calm then susan is either old or not happy.
Everyone who is both not funny and rich is both not happy and patient and vice versa.
If someone is both brave and tall then someone is quiet or not calm.
Everyone who is not rich or patient is both old and not happy and vice versa.
If someone is both quiet and strong then someone is not brave or old and vice versa.
If someone is not strong then alice is both happy and not brave.
Everyone who is both humble and funny is old.
Everyone who is either quiet or rich is happy and vice versa.
Everyone who is not happy or not wise is not strong or not quiet and vice versa.
Someone is not patient or creative.
Lucy is not brave or not old.
Lucy is not humble or happy.
Someone is either not wise or curious. | Lucy is patient. | contradiction | ((~funny(alice))=>((~curious(fred)&creative(fred))))&
(((tall(john)<~>quiet(john)))=>(?[X]:((~calm(X)<~>~curious(X)))))&
(((~brave(fred)<~>tall(fred)))=>(calm(paul)))&
(![X]:((~kind(X)|~rich(X))=>(calm(X)<~>wise(X))))&
(![X]:((~generous(X)<~>rich(X))=>(quiet(X)&old(X))))&
(((~kind(susan)&~calm(susan)))=>((old(susan)<~>~happy(susan))))&
(![X]:((~funny(X)&rich(X))<=>(~happy(X)&patient(X))))&
((?[X]:((brave(X)&tall(X))))=>(?[X]:((quiet(X)|~calm(X)))))&
(![X]:((~rich(X)|patient(X))<=>(old(X)&~happy(X))))&
((?[X]:((quiet(X)&strong(X))))<=>(?[X]:((~brave(X)|old(X)))))&
((?[X]:(~strong(X)))=>((happy(alice)&~brave(alice))))&
(![X]:((humble(X)&funny(X))=>old(X)))&
(![X]:((quiet(X)<~>rich(X))<=>happy(X)))&
(![X]:((~happy(X)|~wise(X))<=>(~strong(X)|~quiet(X))))&
(?[X]:((~patient(X)|creative(X))))&
((~brave(lucy)|~old(lucy)))&
((~humble(lucy)|happy(lucy)))&
(?[X]:((~wise(X)<~>curious(X)))) | patient(lucy) | [
"p8",
"p9",
"p12",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3877911741709214655266909
% SZS output start Proof for 3877911741709214655266909
9. ! [X0] : ((patient(X0) | ~rich(X0)) <=> (~happy(X0) & old(X0))) [input p8]
10. ? [X0] : (strong(X0) & quiet(X0)) <=> ? [X0] : (old(X0) | ~brave(X0)) [input p9]
13. ! [X0] : ((quiet(X0) <~> rich(X0)) <=> happy(X0)) [input p12]
14. ! [X0] : ((~wise(X0) | ~happy(X0)) <=> (~quiet(X0) | ~strong(X0))) [input p13]
16. ~old(lucy) | ~brave(lucy) [input p15]
19. patient(lucy) [input hypothesis]
21. ? [X0] : (strong(X0) & quiet(X0)) <=> ? [X1] : (old(X1) | ~brave(X1)) [rectify 10]
46. ! [X0] : (((patient(X0) | ~rich(X0)) | (happy(X0) | ~old(X0))) & ((~happy(X0) & old(X0)) | (~patient(X0) & rich(X0)))) [nnf transformation 9]
47. ! [X0] : ((patient(X0) | ~rich(X0) | happy(X0) | ~old(X0)) & ((~happy(X0) & old(X0)) | (~patient(X0) & rich(X0)))) [flattening 46]
48. (? [X0] : (strong(X0) & quiet(X0)) | ! [X1] : (~old(X1) & brave(X1))) & (? [X1] : (old(X1) | ~brave(X1)) | ! [X0] : (~strong(X0) | ~quiet(X0))) [nnf transformation 21]
49. (? [X0] : (strong(X0) & quiet(X0)) | ! [X1] : (~old(X1) & brave(X1))) & (? [X2] : (old(X2) | ~brave(X2)) | ! [X3] : (~strong(X3) | ~quiet(X3))) [rectify 48]
50. ? [X0] : (strong(X0) & quiet(X0)) => (strong(sK2) & quiet(sK2)) [choice axiom]
51. ? [X2] : (old(X2) | ~brave(X2)) => (old(sK3) | ~brave(sK3)) [choice axiom]
52. ((strong(sK2) & quiet(sK2)) | ! [X1] : (~old(X1) & brave(X1))) & ((old(sK3) | ~brave(sK3)) | ! [X3] : (~strong(X3) | ~quiet(X3))) [skolemisation 49,51,50]
53. ! [X0] : ((((~rich(X0) | ~quiet(X0)) & (rich(X0) | quiet(X0))) | ~happy(X0)) & (happy(X0) | ((quiet(X0) | ~rich(X0)) & (rich(X0) | ~quiet(X0))))) [nnf transformation 13]
54. ! [X0] : (((~wise(X0) | ~happy(X0)) | (quiet(X0) & strong(X0))) & ((~quiet(X0) | ~strong(X0)) | (wise(X0) & happy(X0)))) [nnf transformation 14]
55. ! [X0] : ((~wise(X0) | ~happy(X0) | (quiet(X0) & strong(X0))) & (~quiet(X0) | ~strong(X0) | (wise(X0) & happy(X0)))) [flattening 54]
78. ~patient(X0) | old(X0) [cnf transformation 47]
79. ~happy(X0) | rich(X0) [cnf transformation 47]
83. quiet(sK2) | brave(X1) [cnf transformation 52]
85. strong(sK2) | brave(X1) [cnf transformation 52]
92. ~rich(X0) | ~quiet(X0) | ~happy(X0) [cnf transformation 53]
93. ~quiet(X0) | ~strong(X0) | happy(X0) [cnf transformation 55]
97. ~old(lucy) | ~brave(lucy) [cnf transformation 16]
100. patient(lucy) [cnf transformation 19]
160. 14 <=> strong(sK2) [avatar definition]
162. strong(sK2) <- (14) [avatar component clause 160]
165. 15 <=> ! [X1] : brave(X1) [avatar definition]
166. brave(X1) <- (15) [avatar component clause 165]
167. 15 | 14 [avatar split clause 85,160,165]
169. 16 <=> quiet(sK2) [avatar definition]
171. quiet(sK2) <- (16) [avatar component clause 169]
173. 15 | 16 [avatar split clause 83,169,165]
175. 17 <=> ! [X3] : (~strong(X3) | ~quiet(X3)) [avatar definition]
176. ~strong(X3) | ~quiet(X3) <- (17) [avatar component clause 175]
199. ~quiet(X0) | ~happy(X0) [subsumption resolution 92,79]
202. ~quiet(X0) | ~strong(X0) [subsumption resolution 93,199]
203. 17 [avatar split clause 202,175]
205. 23 <=> brave(lucy) [avatar definition]
207. ~brave(lucy) <- (~23) [avatar component clause 205]
209. 24 <=> old(lucy) [avatar definition]
211. ~old(lucy) <- (~24) [avatar component clause 209]
212. ~23 | ~24 [avatar split clause 97,209,205]
228. old(lucy) [resolution 78,100]
229. $false <- (~24) [subsumption resolution 228,211]
230. 24 [avatar contradiction clause 229]
235. $false <- (15, ~23) [subsumption resolution 207,166]
236. ~15 | 23 [avatar contradiction clause 235]
241. ~quiet(sK2) <- (14, 17) [resolution 176,162]
242. $false <- (14, 16, 17) [subsumption resolution 241,171]
243. ~14 | ~16 | ~17 [avatar contradiction clause 242]
244. $false [avatar sat refutation 167,173,203,212,230,236,243]
% SZS output end Proof for 3877911741709214655266909
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If susan is either not wise or not strong then someone is both not patient and rich and vice versa. If someone is curious then susan is not brave or rich and vice versa. If alice is kind then someone is not strong or not curious and vice versa. Everyone who is both brave and not strong is patient or not quiet and vice versa. If mary is both funny and not tall then mary is patient and vice versa. If paul is both not quiet and not rich then someone is rich or not funny and vice versa. Everyone who is generous is either not kind or not humble. Everyone who is rich or not rich is not kind. If susan is either not creative or old then someone is generous or calm and vice versa. Everyone who is both not funny and not happy is curious or kind. Everyone who is not generous is not quiet or old and vice versa. If someone is not old then paul is not curious or old and vice versa. Everyone who is either wise or not tall is both not wise and not happy and vice versa. Everyone who is rich or wise is creative and vice versa. Someone is not funny or not patient. John is both not happy and old. Mary is not humble. Someone is tall or not patient. Someone is either not quiet or calm. Alice is strong or not patient. Someone is both strong and calm. John is not humble. | John is not funny. | contradiction | (((~wise(susan)<~>~strong(susan)))<=>(?[X]:((~patient(X)&rich(X)))))&
((?[X]:(curious(X)))<=>((~brave(susan)|rich(susan))))&
((kind(alice))<=>(?[X]:((~strong(X)|~curious(X)))))&
(![X]:((brave(X)&~strong(X))<=>(patient(X)|~quiet(X))))&
(((funny(mary)&~tall(mary)))<=>(patient(mary)))&
(((~quiet(paul)&~rich(paul)))<=>(?[X]:((rich(X)|~funny(X)))))&
(![X]:(generous(X)=>(~kind(X)<~>~humble(X))))&
(![X]:((rich(X)|~rich(X))=>~kind(X)))&
(((~creative(susan)<~>old(susan)))<=>(?[X]:((generous(X)|calm(X)))))&
(![X]:((~funny(X)&~happy(X))=>(curious(X)|kind(X))))&
(![X]:(~generous(X)<=>(~quiet(X)|old(X))))&
((?[X]:(~old(X)))<=>((~curious(paul)|old(paul))))&
(![X]:((wise(X)<~>~tall(X))<=>(~wise(X)&~happy(X))))&
(![X]:((rich(X)|wise(X))<=>creative(X)))&
(?[X]:((~funny(X)|~patient(X))))&
((~happy(john)&old(john)))&
(~humble(mary))&
(?[X]:((tall(X)|~patient(X))))&
(?[X]:((~quiet(X)<~>calm(X))))&
((strong(alice)|~patient(alice)))&
(?[X]:((strong(X)&calm(X))))&
(~humble(john)) | ~funny(john) | [
"p2",
"p3",
"p5",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 6455561987910462681106875
% SZS output start Proof for 6455561987910462681106875
3. kind(alice) <=> ? [X0] : (~curious(X0) | ~strong(X0)) [input p2]
4. ! [X0] : ((~strong(X0) & brave(X0)) <=> (~quiet(X0) | patient(X0))) [input p3]
6. (~rich(paul) & ~quiet(paul)) <=> ? [X0] : (~funny(X0) | rich(X0)) [input p5]
8. ! [X0] : ((~rich(X0) | rich(X0)) => ~kind(X0)) [input p7]
23. ~funny(john) [input hypothesis]
25. ! [X0] : (~kind(X0) | (rich(X0) & ~rich(X0))) [ennf transformation 8]
37. (kind(alice) | ! [X0] : (curious(X0) & strong(X0))) & (? [X0] : (~curious(X0) | ~strong(X0)) | ~kind(alice)) [nnf transformation 3]
38. (kind(alice) | ! [X0] : (curious(X0) & strong(X0))) & (? [X1] : (~curious(X1) | ~strong(X1)) | ~kind(alice)) [rectify 37]
39. ? [X1] : (~curious(X1) | ~strong(X1)) => (~curious(sK2) | ~strong(sK2)) [choice axiom]
40. (kind(alice) | ! [X0] : (curious(X0) & strong(X0))) & ((~curious(sK2) | ~strong(sK2)) | ~kind(alice)) [skolemisation 38,39]
41. ! [X0] : (((~strong(X0) & brave(X0)) | (quiet(X0) & ~patient(X0))) & ((~quiet(X0) | patient(X0)) | (strong(X0) | ~brave(X0)))) [nnf transformation 4]
42. ! [X0] : (((~strong(X0) & brave(X0)) | (quiet(X0) & ~patient(X0))) & (~quiet(X0) | patient(X0) | strong(X0) | ~brave(X0))) [flattening 41]
45. ((~rich(paul) & ~quiet(paul)) | ! [X0] : (funny(X0) & ~rich(X0))) & (? [X0] : (~funny(X0) | rich(X0)) | (rich(paul) | quiet(paul))) [nnf transformation 6]
46. ((~rich(paul) & ~quiet(paul)) | ! [X0] : (funny(X0) & ~rich(X0))) & (? [X0] : (~funny(X0) | rich(X0)) | rich(paul) | quiet(paul)) [flattening 45]
47. ((~rich(paul) & ~quiet(paul)) | ! [X0] : (funny(X0) & ~rich(X0))) & (? [X1] : (~funny(X1) | rich(X1)) | rich(paul) | quiet(paul)) [rectify 46]
48. ? [X1] : (~funny(X1) | rich(X1)) => (~funny(sK3) | rich(sK3)) [choice axiom]
49. ((~rich(paul) & ~quiet(paul)) | ! [X0] : (funny(X0) & ~rich(X0))) & ((~funny(sK3) | rich(sK3)) | rich(paul) | quiet(paul)) [skolemisation 47,48]
85. kind(alice) | strong(X0) [cnf transformation 40]
91. ~strong(X0) | quiet(X0) [cnf transformation 42]
97. ~quiet(paul) | funny(X0) [cnf transformation 49]
102. ~kind(X0) | ~rich(X0) [cnf transformation 25]
103. ~kind(X0) | rich(X0) [cnf transformation 25]
137. ~funny(john) [cnf transformation 23]
187. 11 <=> kind(alice) [avatar definition]
189. kind(alice) <- (11) [avatar component clause 187]
192. 12 <=> ! [X0] : strong(X0) [avatar definition]
193. strong(X0) <- (12) [avatar component clause 192]
194. 12 | 11 [avatar split clause 85,187,192]
220. 18 <=> ! [X0] : funny(X0) [avatar definition]
221. funny(X0) <- (18) [avatar component clause 220]
232. 21 <=> quiet(paul) [avatar definition]
234. ~quiet(paul) <- (~21) [avatar component clause 232]
235. 18 | ~21 [avatar split clause 97,232,220]
246. ~kind(X0) [subsumption resolution 102,103]
325. $false <- (11) [subsumption resolution 189,246]
326. ~11 [avatar contradiction clause 325]
338. quiet(X0) <- (12) [resolution 91,193]
339. $false <- (12, ~21) [resolution 338,234]
342. ~12 | 21 [avatar contradiction clause 339]
343. $false <- (18) [resolution 221,137]
348. ~18 [avatar contradiction clause 343]
349. $false [avatar sat refutation 194,235,326,342,348]
% SZS output end Proof for 6455561987910462681106875
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both tall and not humble is not funny or kind and vice versa. If john is both not generous and creative then someone is either not humble or quiet. Everyone who is either funny or not brave is both not strong and old and vice versa. Everyone who is not quiet or humble is either curious or not creative. If someone is either rich or generous then someone is both not humble and not generous. Everyone who is calm is not brave and vice versa. If lucy is either not rich or not humble then someone is both kind and wise. If fred is either not humble or not wise then someone is tall. Everyone who is not strong is both strong and not quiet. If susan is not rich then john is either not tall or calm. Everyone who is generous is not brave. Everyone who is not happy is either not patient or brave. Everyone who is both strong and not kind is not patient and vice versa. If john is curious then someone is either strong or not generous. Everyone who is not strong is not tall and vice versa. Everyone who is both humble and quiet is rich and vice versa. Paul is calm or humble. Someone is either patient or brave. Someone is not happy. Lucy is not tall or not curious. Susan is not wise or not calm. Someone is not old. Fred is either not wise or tall. | Paul is brave. | contradiction | (![X]:((tall(X)&~humble(X))<=>(~funny(X)|kind(X))))&
(((~generous(john)&creative(john)))=>(?[X]:((~humble(X)<~>quiet(X)))))&
(![X]:((funny(X)<~>~brave(X))<=>(~strong(X)&old(X))))&
(![X]:((~quiet(X)|humble(X))=>(curious(X)<~>~creative(X))))&
((?[X]:((rich(X)<~>generous(X))))=>(?[X]:((~humble(X)&~generous(X)))))&
(![X]:(calm(X)<=>~brave(X)))&
(((~rich(lucy)<~>~humble(lucy)))=>(?[X]:((kind(X)&wise(X)))))&
(((~humble(fred)<~>~wise(fred)))=>(?[X]:(tall(X))))&
(![X]:(~strong(X)=>(strong(X)&~quiet(X))))&
((~rich(susan))=>((~tall(john)<~>calm(john))))&
(![X]:(generous(X)=>~brave(X)))&
(![X]:(~happy(X)=>(~patient(X)<~>brave(X))))&
(![X]:((strong(X)&~kind(X))<=>~patient(X)))&
((curious(john))=>(?[X]:((strong(X)<~>~generous(X)))))&
(![X]:(~strong(X)<=>~tall(X)))&
(![X]:((humble(X)&quiet(X))<=>rich(X)))&
((calm(paul)|humble(paul)))&
(?[X]:((patient(X)<~>brave(X))))&
(?[X]:(~happy(X)))&
((~tall(lucy)|~curious(lucy)))&
((~wise(susan)|~calm(susan)))&
(?[X]:(~old(X)))&
((~wise(fred)<~>tall(fred))) | brave(paul) | [
"p0",
"p2",
"p5",
"p8",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 3950959888782003433724164
% SZS output start Proof for 3950959888782003433724164
1. ! [X0] : ((~humble(X0) & tall(X0)) <=> (kind(X0) | ~funny(X0))) [input p0]
3. ! [X0] : ((funny(X0) <~> ~brave(X0)) <=> (old(X0) & ~strong(X0))) [input p2]
6. ! [X0] : (calm(X0) <=> ~brave(X0)) [input p5]
9. ! [X0] : (~strong(X0) => (~quiet(X0) & strong(X0))) [input p8]
17. humble(paul) | calm(paul) [input p16]
24. brave(paul) [input hypothesis]
32. ! [X0] : ((~quiet(X0) & strong(X0)) | strong(X0)) [ennf transformation 9]
37. ! [X0] : (((~humble(X0) & tall(X0)) | (~kind(X0) & funny(X0))) & ((kind(X0) | ~funny(X0)) | (humble(X0) | ~tall(X0)))) [nnf transformation 1]
38. ! [X0] : (((~humble(X0) & tall(X0)) | (~kind(X0) & funny(X0))) & (kind(X0) | ~funny(X0) | humble(X0) | ~tall(X0))) [flattening 37]
42. ! [X0] : ((((brave(X0) | ~funny(X0)) & (~brave(X0) | funny(X0))) | (~old(X0) | strong(X0))) & ((old(X0) & ~strong(X0)) | ((funny(X0) | brave(X0)) & (~brave(X0) | ~funny(X0))))) [nnf transformation 3]
43. ! [X0] : ((((brave(X0) | ~funny(X0)) & (~brave(X0) | funny(X0))) | ~old(X0) | strong(X0)) & ((old(X0) & ~strong(X0)) | ((funny(X0) | brave(X0)) & (~brave(X0) | ~funny(X0))))) [flattening 42]
49. ! [X0] : ((calm(X0) | brave(X0)) & (~brave(X0) | ~calm(X0))) [nnf transformation 6]
77. ~humble(X0) | funny(X0) [cnf transformation 38]
81. ~strong(X0) | ~brave(X0) | ~funny(X0) [cnf transformation 43]
95. ~calm(X0) | ~brave(X0) [cnf transformation 49]
103. strong(X0) | strong(X0) [cnf transformation 32]
120. humble(paul) | calm(paul) [cnf transformation 17]
129. brave(paul) [cnf transformation 24]
130. strong(X0) [duplicate literal removal 103]
228. 21 <=> calm(paul) [avatar definition]
230. calm(paul) <- (21) [avatar component clause 228]
232. 22 <=> humble(paul) [avatar definition]
234. humble(paul) <- (22) [avatar component clause 232]
235. 21 | 22 [avatar split clause 120,232,228]
261. ~brave(paul) <- (21) [resolution 95,230]
262. $false <- (21) [subsumption resolution 261,129]
263. ~21 [avatar contradiction clause 262]
264. funny(paul) <- (22) [resolution 234,77]
276. ~brave(X0) | ~funny(X0) [resolution 81,130]
295. ~funny(paul) [resolution 276,129]
297. $false <- (22) [subsumption resolution 295,264]
298. ~22 [avatar contradiction clause 297]
299. $false [avatar sat refutation 235,263,298]
% SZS output end Proof for 3950959888782003433724164
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 mary is not funny or not generous then someone is quiet and vice versa.
If mary is curious then someone is wise or funny.
Everyone who is not humble is brave or not quiet and vice versa.
Everyone who is both wise and not generous is not strong or wise and vice versa.
Everyone who is wise is funny or wise and vice versa.
If alice is both kind and happy then someone is both not kind and quiet.
If susan is both not old and kind then fred is either old or calm and vice versa.
If john is kind then someone is both old and brave.
If lucy is curious or not old then lucy is either not humble or brave.
Everyone who is humble is both calm and not calm and vice versa.
Everyone who is not curious or creative is both not patient and not old and vice versa.
If john is brave or calm then john is patient or strong and vice versa.
Everyone who is either not humble or patient is either happy or not patient and vice versa.
Everyone who is either strong or creative is tall or patient.
Everyone who is not kind or not calm is both curious and creative and vice versa.
Everyone who is both old and not strong is not humble or strong and vice versa.
Someone is not quiet.
Someone is either not quiet or not creative.
Someone is either rich or humble.
Lucy is not tall or not wise.
Lucy is either wise or generous.
Alice is either humble or patient. | Alice is calm. | entailment | (((~funny(mary)|~generous(mary)))<=>(?[X]:(quiet(X))))&
((curious(mary))=>(?[X]:((wise(X)|funny(X)))))&
(![X]:(~humble(X)<=>(brave(X)|~quiet(X))))&
(![X]:((wise(X)&~generous(X))<=>(~strong(X)|wise(X))))&
(![X]:(wise(X)<=>(funny(X)|wise(X))))&
(((kind(alice)&happy(alice)))=>(?[X]:((~kind(X)&quiet(X)))))&
(((~old(susan)&kind(susan)))<=>((old(fred)<~>calm(fred))))&
((kind(john))=>(?[X]:((old(X)&brave(X)))))&
(((curious(lucy)|~old(lucy)))=>((~humble(lucy)<~>brave(lucy))))&
(![X]:(humble(X)<=>(calm(X)&~calm(X))))&
(![X]:((~curious(X)|creative(X))<=>(~patient(X)&~old(X))))&
(((brave(john)|calm(john)))<=>((patient(john)|strong(john))))&
(![X]:((~humble(X)<~>patient(X))<=>(happy(X)<~>~patient(X))))&
(![X]:((strong(X)<~>creative(X))=>(tall(X)|patient(X))))&
(![X]:((~kind(X)|~calm(X))<=>(curious(X)&creative(X))))&
(![X]:((old(X)&~strong(X))<=>(~humble(X)|strong(X))))&
(?[X]:(~quiet(X)))&
(?[X]:((~quiet(X)<~>~creative(X))))&
(?[X]:((rich(X)<~>humble(X))))&
((~tall(lucy)|~wise(lucy)))&
((wise(lucy)<~>generous(lucy)))&
((humble(alice)<~>patient(alice))) | calm(alice) | [
"p9",
"p10",
"p14",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 3530547449573273898933459
% SZS output start Proof for 3530547449573273898933459
10. ! [X0] : (humble(X0) <=> (~calm(X0) & calm(X0))) [input p9]
11. ! [X0] : ((creative(X0) | ~curious(X0)) <=> (~old(X0) & ~patient(X0))) [input p10]
15. ! [X0] : ((~calm(X0) | ~kind(X0)) <=> (creative(X0) & curious(X0))) [input p14]
22. humble(alice) <~> patient(alice) [input p21]
23. ~calm(alice) [input hypothesis]
51. ! [X0] : ((humble(X0) | (calm(X0) | ~calm(X0))) & ((~calm(X0) & calm(X0)) | ~humble(X0))) [nnf transformation 10]
52. ! [X0] : ((humble(X0) | calm(X0) | ~calm(X0)) & ((~calm(X0) & calm(X0)) | ~humble(X0))) [flattening 51]
53. ! [X0] : (((creative(X0) | ~curious(X0)) | (old(X0) | patient(X0))) & ((~old(X0) & ~patient(X0)) | (~creative(X0) & curious(X0)))) [nnf transformation 11]
54. ! [X0] : ((creative(X0) | ~curious(X0) | old(X0) | patient(X0)) & ((~old(X0) & ~patient(X0)) | (~creative(X0) & curious(X0)))) [flattening 53]
59. ! [X0] : (((~calm(X0) | ~kind(X0)) | (~creative(X0) | ~curious(X0))) & ((creative(X0) & curious(X0)) | (calm(X0) & kind(X0)))) [nnf transformation 15]
60. ! [X0] : ((~calm(X0) | ~kind(X0) | ~creative(X0) | ~curious(X0)) & ((creative(X0) & curious(X0)) | (calm(X0) & kind(X0)))) [flattening 59]
72. (~patient(alice) | ~humble(alice)) & (patient(alice) | humble(alice)) [nnf transformation 22]
102. calm(X0) | ~humble(X0) [cnf transformation 52]
103. ~calm(X0) | ~humble(X0) [cnf transformation 52]
106. ~patient(X0) | ~creative(X0) [cnf transformation 54]
127. creative(X0) | calm(X0) [cnf transformation 60]
142. patient(alice) | humble(alice) [cnf transformation 72]
144. ~calm(alice) [cnf transformation 23]
260. ~humble(X0) [subsumption resolution 102,103]
311. patient(alice) [subsumption resolution 142,260]
320. ~creative(alice) [resolution 106,311]
337. calm(alice) [resolution 127,320]
339. $false [subsumption resolution 337,144]
% SZS output end Proof for 3530547449573273898933459
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not quiet then someone is both not curious and tall and vice versa.
Everyone who is both brave and not kind is not creative and vice versa.
If alice is curious or not creative then someone is kind.
Everyone who is both curious and not humble is quiet and vice versa.
Everyone who is both wise and creative is not quiet.
If paul is both not quiet and not humble then someone is either strong or brave and vice versa.
Everyone who is both happy and curious is wise.
Everyone who is both rich and not wise is not curious and vice versa.
If someone is either happy or strong then someone is old.
If someone is not rich or not tall then mary is not old.
If someone is both generous and not old then lucy is either not curious or not generous.
Everyone who is either tall or kind is either kind or not kind and vice versa.
Everyone who is either patient or not strong is not patient or old and vice versa.
Everyone who is either calm or not strong is either kind or not brave and vice versa.
Everyone who is both not patient and not funny is both old and not quiet.
Everyone who is not quiet or wise is not strong or funny and vice versa.
Someone is either curious or creative.
Someone is either not old or rich.
Fred is both curious and brave.
Someone is either not curious or creative.
Someone is creative.
Someone is either creative or humble.
John is not patient or calm. | Lucy is not generous. | neutral | ((?[X]:(~quiet(X)))<=>(?[X]:((~curious(X)&tall(X)))))&
(![X]:((brave(X)&~kind(X))<=>~creative(X)))&
(((curious(alice)|~creative(alice)))=>(?[X]:(kind(X))))&
(![X]:((curious(X)&~humble(X))<=>quiet(X)))&
(![X]:((wise(X)&creative(X))=>~quiet(X)))&
(((~quiet(paul)&~humble(paul)))<=>(?[X]:((strong(X)<~>brave(X)))))&
(![X]:((happy(X)&curious(X))=>wise(X)))&
(![X]:((rich(X)&~wise(X))<=>~curious(X)))&
((?[X]:((happy(X)<~>strong(X))))=>(?[X]:(old(X))))&
((?[X]:((~rich(X)|~tall(X))))=>(~old(mary)))&
((?[X]:((generous(X)&~old(X))))=>((~curious(lucy)<~>~generous(lucy))))&
(![X]:((tall(X)<~>kind(X))<=>(kind(X)<~>~kind(X))))&
(![X]:((patient(X)<~>~strong(X))<=>(~patient(X)|old(X))))&
(![X]:((calm(X)<~>~strong(X))<=>(kind(X)<~>~brave(X))))&
(![X]:((~patient(X)&~funny(X))=>(old(X)&~quiet(X))))&
(![X]:((~quiet(X)|wise(X))<=>(~strong(X)|funny(X))))&
(?[X]:((curious(X)<~>creative(X))))&
(?[X]:((~old(X)<~>rich(X))))&
((curious(fred)&brave(fred)))&
(?[X]:((~curious(X)<~>creative(X))))&
(?[X]:(creative(X)))&
(?[X]:((creative(X)<~>humble(X))))&
((~patient(john)|calm(john))) | ~generous(lucy) | [] | null | 0 |
If paul is either not rich or not kind then susan is either not brave or brave and vice versa. If someone is either not old or not humble then someone is either patient or strong and vice versa. If someone is either kind or generous then john is both happy and brave and vice versa. If someone is either not creative or not happy then fred is not tall or not strong. Everyone who is either not curious or patient is not patient and vice versa. Everyone who is both curious and not quiet is either not kind or not brave and vice versa. If someone is creative or curious then john is not quiet or generous. If someone is patient or not strong then someone is both not happy and kind and vice versa. Everyone who is both calm and strong is either not wise or old. If someone is tall or not humble then someone is either creative or generous. Everyone who is not tall or not rich is both old and not curious. If john is either not funny or creative then paul is humble or curious and vice versa. Everyone who is wise is old or strong. Everyone who is not funny or brave is curious and vice versa. Everyone who is humble is both not curious and not kind and vice versa. Everyone who is either not tall or old is both not creative and patient. Someone is either generous or not curious. Someone is either not tall or happy. Fred is not quiet or not tall. Someone is not quiet or strong. Paul is both old and not creative. | Paul is not humble. | contradiction | (((~rich(paul)<~>~kind(paul)))<=>((~brave(susan)<~>brave(susan))))&
((?[X]:((~old(X)<~>~humble(X))))<=>(?[X]:((patient(X)<~>strong(X)))))&
((?[X]:((kind(X)<~>generous(X))))<=>((happy(john)&brave(john))))&
((?[X]:((~creative(X)<~>~happy(X))))=>((~tall(fred)|~strong(fred))))&
(![X]:((~curious(X)<~>patient(X))<=>~patient(X)))&
(![X]:((curious(X)&~quiet(X))<=>(~kind(X)<~>~brave(X))))&
((?[X]:((creative(X)|curious(X))))=>((~quiet(john)|generous(john))))&
((?[X]:((patient(X)|~strong(X))))<=>(?[X]:((~happy(X)&kind(X)))))&
(![X]:((calm(X)&strong(X))=>(~wise(X)<~>old(X))))&
((?[X]:((tall(X)|~humble(X))))=>(?[X]:((creative(X)<~>generous(X)))))&
(![X]:((~tall(X)|~rich(X))=>(old(X)&~curious(X))))&
(((~funny(john)<~>creative(john)))<=>((humble(paul)|curious(paul))))&
(![X]:(wise(X)=>(old(X)|strong(X))))&
(![X]:((~funny(X)|brave(X))<=>curious(X)))&
(![X]:(humble(X)<=>(~curious(X)&~kind(X))))&
(![X]:((~tall(X)<~>old(X))=>(~creative(X)&patient(X))))&
(?[X]:((generous(X)<~>~curious(X))))&
(?[X]:((~tall(X)<~>happy(X))))&
((~quiet(fred)|~tall(fred)))&
(?[X]:((~quiet(X)|strong(X))))&
((old(paul)&~creative(paul))) | ~humble(paul) | [
"p4",
"p5",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4533957403398883742771750
% SZS output start Proof for 4533957403398883742771750
5. ! [X0] : ((~curious(X0) <~> patient(X0)) <=> ~patient(X0)) [input p4]
6. ! [X0] : ((~quiet(X0) & curious(X0)) <=> (~kind(X0) <~> ~brave(X0))) [input p5]
14. ! [X0] : ((brave(X0) | ~funny(X0)) <=> curious(X0)) [input p13]
15. ! [X0] : (humble(X0) <=> (~kind(X0) & ~curious(X0))) [input p14]
22. ~humble(paul) [input hypothesis]
47. ! [X0] : ((((~patient(X0) | curious(X0)) & (patient(X0) | ~curious(X0))) | patient(X0)) & (~patient(X0) | ((~curious(X0) | ~patient(X0)) & (patient(X0) | curious(X0))))) [nnf transformation 5]
48. ! [X0] : (((~quiet(X0) & curious(X0)) | ((~kind(X0) | brave(X0)) & (~brave(X0) | kind(X0)))) & (((brave(X0) | kind(X0)) & (~brave(X0) | ~kind(X0))) | (quiet(X0) | ~curious(X0)))) [nnf transformation 6]
49. ! [X0] : (((~quiet(X0) & curious(X0)) | ((~kind(X0) | brave(X0)) & (~brave(X0) | kind(X0)))) & (((brave(X0) | kind(X0)) & (~brave(X0) | ~kind(X0))) | quiet(X0) | ~curious(X0))) [flattening 48]
61. ! [X0] : (((brave(X0) | ~funny(X0)) | ~curious(X0)) & (curious(X0) | (~brave(X0) & funny(X0)))) [nnf transformation 14]
62. ! [X0] : ((brave(X0) | ~funny(X0) | ~curious(X0)) & (curious(X0) | (~brave(X0) & funny(X0)))) [flattening 61]
63. ! [X0] : ((humble(X0) | (kind(X0) | curious(X0))) & ((~kind(X0) & ~curious(X0)) | ~humble(X0))) [nnf transformation 15]
64. ! [X0] : ((humble(X0) | kind(X0) | curious(X0)) & ((~kind(X0) & ~curious(X0)) | ~humble(X0))) [flattening 63]
99. ~patient(X0) | ~curious(X0) | ~patient(X0) [cnf transformation 47]
100. patient(X0) | ~curious(X0) | patient(X0) [cnf transformation 47]
105. curious(X0) | ~kind(X0) | brave(X0) [cnf transformation 49]
130. curious(X0) | ~brave(X0) [cnf transformation 62]
134. humble(X0) | kind(X0) | curious(X0) [cnf transformation 64]
147. ~humble(paul) [cnf transformation 22]
148. ~patient(X0) | ~curious(X0) [duplicate literal removal 99]
149. ~curious(X0) | patient(X0) [duplicate literal removal 100]
163. 3 <=> kind(paul) [avatar definition]
165. kind(paul) <- (3) [avatar component clause 163]
250. ~curious(X0) [subsumption resolution 148,149]
251. ~kind(X0) | brave(X0) [subsumption resolution 105,250]
314. 36 <=> humble(paul) [avatar definition]
316. ~humble(paul) <- (~36) [avatar component clause 314]
331. ~brave(X0) [subsumption resolution 130,250]
333. humble(X0) | kind(X0) [subsumption resolution 134,250]
359. ~36 [avatar split clause 147,314]
377. kind(paul) <- (~36) [resolution 333,316]
381. 3 | 36 [avatar split clause 377,314,163]
383. brave(paul) <- (3) [resolution 165,251]
385. $false <- (3) [subsumption resolution 383,331]
386. ~3 [avatar contradiction clause 385]
387. $false [avatar sat refutation 359,381,386]
% SZS output end Proof for 4533957403398883742771750
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet or not kind is old or tall. Everyone who is creative is either patient or wise and vice versa. Everyone who is both not quiet and not old is creative or not happy and vice versa. Everyone who is not happy is not brave and vice versa. If someone is both not old and kind then someone is not brave or not wise. If someone is both not kind and brave then someone is both calm and not rich. If someone is both humble and not calm then fred is both not quiet and not calm. If someone is not humble or brave then someone is both wise and strong and vice versa. Everyone who is not curious is both humble and calm and vice versa. Everyone who is either old or creative is both not kind and not curious and vice versa. Everyone who is strong is humble and vice versa. Everyone who is both curious and tall is curious and vice versa. Everyone who is either strong or quiet is either patient or not brave. If someone is both not quiet and not kind then susan is funny or not patient. If lucy is either patient or not happy then paul is either brave or not brave and vice versa. Everyone who is both brave and not old is kind and vice versa. Someone is either not generous or strong. Fred is not calm or old. Someone is both quiet and not humble. Someone is old or not creative. Lucy is not tall. Alice is either rich or not patient. Someone is both not wise and not kind. Someone is not wise or not generous. | Paul is not humble. | neutral | (![X]:((quiet(X)|~kind(X))=>(old(X)|tall(X))))&
(![X]:(creative(X)<=>(patient(X)<~>wise(X))))&
(![X]:((~quiet(X)&~old(X))<=>(creative(X)|~happy(X))))&
(![X]:(~happy(X)<=>~brave(X)))&
((?[X]:((~old(X)&kind(X))))=>(?[X]:((~brave(X)|~wise(X)))))&
((?[X]:((~kind(X)&brave(X))))=>(?[X]:((calm(X)&~rich(X)))))&
((?[X]:((humble(X)&~calm(X))))=>((~quiet(fred)&~calm(fred))))&
((?[X]:((~humble(X)|brave(X))))<=>(?[X]:((wise(X)&strong(X)))))&
(![X]:(~curious(X)<=>(humble(X)&calm(X))))&
(![X]:((old(X)<~>creative(X))<=>(~kind(X)&~curious(X))))&
(![X]:(strong(X)<=>humble(X)))&
(![X]:((curious(X)&tall(X))<=>curious(X)))&
(![X]:((strong(X)<~>quiet(X))=>(patient(X)<~>~brave(X))))&
((?[X]:((~quiet(X)&~kind(X))))=>((funny(susan)|~patient(susan))))&
(((patient(lucy)<~>~happy(lucy)))<=>((brave(paul)<~>~brave(paul))))&
(![X]:((brave(X)&~old(X))<=>kind(X)))&
(?[X]:((~generous(X)<~>strong(X))))&
((~calm(fred)|old(fred)))&
(?[X]:((quiet(X)&~humble(X))))&
(?[X]:((old(X)|~creative(X))))&
(~tall(lucy))&
((rich(alice)<~>~patient(alice)))&
(?[X]:((~wise(X)&~kind(X))))&
(?[X]:((~wise(X)|~generous(X)))) | ~humble(paul) | [] | null | 0 |
Everyone who is either not rich or not curious is either old or not creative.
Everyone who is both kind and not humble is either not tall or not wise.
Everyone who is not brave is calm and vice versa.
Everyone who is creative is not wise.
Everyone who is both creative and not brave is both not calm and not humble and vice versa.
Everyone who is not strong is both kind and not calm and vice versa.
If someone is both patient and not happy then john is happy and vice versa.
If someone is not strong or wise then someone is generous or tall and vice versa.
If someone is either not strong or not rich then someone is either tall or funny and vice versa.
If john is both kind and patient then lucy is not calm.
If someone is both funny and generous then someone is both not kind and not old.
Everyone who is either not wise or old is both creative and kind and vice versa.
If someone is either brave or not funny then lucy is not generous.
If someone is not strong or rich then alice is patient and vice versa.
If someone is not happy or not calm then alice is both not quiet and old and vice versa.
If someone is both not brave and strong then someone is happy or tall.
Someone is either not curious or not calm.
Someone is both not curious and funny.
Susan is both kind and not old.
Someone is not old.
Susan is either tall or patient.
Mary is both strong and old.
Someone is either quiet or happy.
Someone is either brave or happy. | Lucy is generous. | neutral | (![X]:((~rich(X)<~>~curious(X))=>(old(X)<~>~creative(X))))&
(![X]:((kind(X)&~humble(X))=>(~tall(X)<~>~wise(X))))&
(![X]:(~brave(X)<=>calm(X)))&
(![X]:(creative(X)=>~wise(X)))&
(![X]:((creative(X)&~brave(X))<=>(~calm(X)&~humble(X))))&
(![X]:(~strong(X)<=>(kind(X)&~calm(X))))&
((?[X]:((patient(X)&~happy(X))))<=>(happy(john)))&
((?[X]:((~strong(X)|wise(X))))<=>(?[X]:((generous(X)|tall(X)))))&
((?[X]:((~strong(X)<~>~rich(X))))<=>(?[X]:((tall(X)<~>funny(X)))))&
(((kind(john)&patient(john)))=>(~calm(lucy)))&
((?[X]:((funny(X)&generous(X))))=>(?[X]:((~kind(X)&~old(X)))))&
(![X]:((~wise(X)<~>old(X))<=>(creative(X)&kind(X))))&
((?[X]:((brave(X)<~>~funny(X))))=>(~generous(lucy)))&
((?[X]:((~strong(X)|rich(X))))<=>(patient(alice)))&
((?[X]:((~happy(X)|~calm(X))))<=>((~quiet(alice)&old(alice))))&
((?[X]:((~brave(X)&strong(X))))=>(?[X]:((happy(X)|tall(X)))))&
(?[X]:((~curious(X)<~>~calm(X))))&
(?[X]:((~curious(X)&funny(X))))&
((kind(susan)&~old(susan)))&
(?[X]:(~old(X)))&
((tall(susan)<~>patient(susan)))&
((strong(mary)&old(mary)))&
(?[X]:((quiet(X)<~>happy(X))))&
(?[X]:((brave(X)<~>happy(X)))) | generous(lucy) | [] | null | 0 |
If someone is either funny or not curious then someone is either not humble or not happy. If someone is funny then alice is creative. If paul is not kind then alice is both not brave and not calm. If someone is creative or funny then someone is both not brave and rich and vice versa. Everyone who is either not tall or creative is both tall and patient. If someone is brave or not wise then someone is patient or happy. If alice is either not generous or not brave then susan is curious or not generous and vice versa. Everyone who is curious or not funny is both generous and curious. If someone is either quiet or humble then someone is either tall or strong. Everyone who is both not happy and not patient is wise. If someone is strong then someone is generous or not calm and vice versa. Everyone who is not calm is creative and vice versa. Everyone who is kind or generous is calm or not rich. Everyone who is both not quiet and rich is both not brave and quiet. Everyone who is happy or not strong is happy and vice versa. Everyone who is either patient or not tall is not curious and vice versa. Someone is curious. Someone is not generous or not creative. Mary is either rich or not quiet. Someone is not patient. Susan is quiet. Susan is not funny. Someone is both patient and happy. Alice is happy or curious. | Paul is kind. | neutral | ((?[X]:((funny(X)<~>~curious(X))))=>(?[X]:((~humble(X)<~>~happy(X)))))&
((?[X]:(funny(X)))=>(creative(alice)))&
((~kind(paul))=>((~brave(alice)&~calm(alice))))&
((?[X]:((creative(X)|funny(X))))<=>(?[X]:((~brave(X)&rich(X)))))&
(![X]:((~tall(X)<~>creative(X))=>(tall(X)&patient(X))))&
((?[X]:((brave(X)|~wise(X))))=>(?[X]:((patient(X)|happy(X)))))&
(((~generous(alice)<~>~brave(alice)))<=>((curious(susan)|~generous(susan))))&
(![X]:((curious(X)|~funny(X))=>(generous(X)&curious(X))))&
((?[X]:((quiet(X)<~>humble(X))))=>(?[X]:((tall(X)<~>strong(X)))))&
(![X]:((~happy(X)&~patient(X))=>wise(X)))&
((?[X]:(strong(X)))<=>(?[X]:((generous(X)|~calm(X)))))&
(![X]:(~calm(X)<=>creative(X)))&
(![X]:((kind(X)|generous(X))=>(calm(X)|~rich(X))))&
(![X]:((~quiet(X)&rich(X))=>(~brave(X)&quiet(X))))&
(![X]:((happy(X)|~strong(X))<=>happy(X)))&
(![X]:((patient(X)<~>~tall(X))<=>~curious(X)))&
(?[X]:(curious(X)))&
(?[X]:((~generous(X)|~creative(X))))&
((rich(mary)<~>~quiet(mary)))&
(?[X]:(~patient(X)))&
(quiet(susan))&
(~funny(susan))&
(?[X]:((patient(X)&happy(X))))&
((happy(alice)|curious(alice))) | kind(paul) | [] | null | 0 |
Everyone who is either funny or happy is both not calm and strong and vice versa.
Everyone who is both not calm and calm is humble or creative and vice versa.
Everyone who is both not funny and not patient is not kind or not patient.
If lucy is both not happy and not patient then someone is quiet or not old and vice versa.
Everyone who is both not old and brave is not funny or happy and vice versa.
If lucy is both creative and not curious then someone is either not funny or humble.
Everyone who is not patient or funny is not funny.
If someone is both not quiet and not strong then fred is not funny or calm and vice versa.
If lucy is both brave and not tall then lucy is not patient or not creative.
Everyone who is either curious or tall is happy.
If fred is rich then someone is both not creative and not brave and vice versa.
Everyone who is not quiet or tall is not funny or happy.
Everyone who is both not brave and tall is wise or not humble.
If lucy is not humble then alice is both not curious and strong and vice versa.
Someone is both patient and curious.
Alice is not curious or wise.
Someone is not wise.
Alice is not rich.
Someone is either wise or not funny.
Someone is either not rich or strong.
Susan is quiet. | Alice is strong. | entailment | (![X]:((funny(X)<~>happy(X))<=>(~calm(X)&strong(X))))&
(![X]:((~calm(X)&calm(X))<=>(humble(X)|creative(X))))&
(![X]:((~funny(X)&~patient(X))=>(~kind(X)|~patient(X))))&
(((~happy(lucy)&~patient(lucy)))<=>(?[X]:((quiet(X)|~old(X)))))&
(![X]:((~old(X)&brave(X))<=>(~funny(X)|happy(X))))&
(((creative(lucy)&~curious(lucy)))=>(?[X]:((~funny(X)<~>humble(X)))))&
(![X]:((~patient(X)|funny(X))=>~funny(X)))&
((?[X]:((~quiet(X)&~strong(X))))<=>((~funny(fred)|calm(fred))))&
(((brave(lucy)&~tall(lucy)))=>((~patient(lucy)|~creative(lucy))))&
(![X]:((curious(X)<~>tall(X))=>happy(X)))&
((rich(fred))<=>(?[X]:((~creative(X)&~brave(X)))))&
(![X]:((~quiet(X)|tall(X))=>(~funny(X)|happy(X))))&
(![X]:((~brave(X)&tall(X))=>(wise(X)|~humble(X))))&
((~humble(lucy))<=>((~curious(alice)&strong(alice))))&
(?[X]:((patient(X)&curious(X))))&
((~curious(alice)|wise(alice)))&
(?[X]:(~wise(X)))&
(~rich(alice))&
(?[X]:((wise(X)<~>~funny(X))))&
(?[X]:((~rich(X)<~>strong(X))))&
(quiet(susan)) | strong(alice) | [
"p1",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 988685979233528172994944
% SZS output start Proof for 988685979233528172994944
2. ! [X0] : ((calm(X0) & ~calm(X0)) <=> (creative(X0) | humble(X0))) [input p1]
14. ~humble(lucy) <=> (strong(alice) & ~curious(alice)) [input p13]
22. ~strong(alice) [input hypothesis]
36. ! [X0] : (((calm(X0) & ~calm(X0)) | (~creative(X0) & ~humble(X0))) & ((creative(X0) | humble(X0)) | (~calm(X0) | calm(X0)))) [nnf transformation 2]
37. ! [X0] : (((calm(X0) & ~calm(X0)) | (~creative(X0) & ~humble(X0))) & (creative(X0) | humble(X0) | ~calm(X0) | calm(X0))) [flattening 36]
58. (~humble(lucy) | (~strong(alice) | curious(alice))) & ((strong(alice) & ~curious(alice)) | humble(lucy)) [nnf transformation 14]
59. (~humble(lucy) | ~strong(alice) | curious(alice)) & ((strong(alice) & ~curious(alice)) | humble(lucy)) [flattening 58]
77. ~calm(X0) | ~humble(X0) [cnf transformation 37]
79. calm(X0) | ~humble(X0) [cnf transformation 37]
110. strong(alice) | humble(lucy) [cnf transformation 59]
122. ~strong(alice) [cnf transformation 22]
125. ~humble(X0) [subsumption resolution 77,79]
185. strong(alice) [subsumption resolution 110,125]
198. $false [subsumption resolution 122,185]
% SZS output end Proof for 988685979233528172994944
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is old or not calm is either calm or funny and vice versa.
If someone is both funny and not creative then fred is strong or creative.
Everyone who is both strong and creative is either not kind or not happy.
Everyone who is brave or not generous is both not calm and kind.
Everyone who is not brave or not rich is both funny and patient and vice versa.
Everyone who is either old or not brave is curious or calm and vice versa.
If someone is patient then john is either not happy or rich.
If fred is either not curious or not creative then someone is either not kind or not rich and vice versa.
Everyone who is not tall or not generous is either not old or rich.
If someone is kind then someone is not kind or not funny and vice versa.
If fred is not brave then someone is both not patient and not funny.
If someone is either kind or not generous then someone is quiet.
Everyone who is either funny or not wise is both not happy and creative and vice versa.
If lucy is brave or strong then john is humble or strong and vice versa.
Everyone who is both not patient and not brave is either calm or curious.
Everyone who is either happy or not quiet is old.
Susan is either old or not kind.
Someone is tall.
Someone is both kind and wise.
Someone is not brave.
Someone is both happy and not kind.
John is both brave and not generous.
Someone is creative or not brave.
Susan is either funny or rich. | Fred is not kind. | contradiction | (![X]:((old(X)|~calm(X))<=>(calm(X)<~>funny(X))))&
((?[X]:((funny(X)&~creative(X))))=>((strong(fred)|creative(fred))))&
(![X]:((strong(X)&creative(X))=>(~kind(X)<~>~happy(X))))&
(![X]:((brave(X)|~generous(X))=>(~calm(X)&kind(X))))&
(![X]:((~brave(X)|~rich(X))<=>(funny(X)&patient(X))))&
(![X]:((old(X)<~>~brave(X))<=>(curious(X)|calm(X))))&
((?[X]:(patient(X)))=>((~happy(john)<~>rich(john))))&
(((~curious(fred)<~>~creative(fred)))<=>(?[X]:((~kind(X)<~>~rich(X)))))&
(![X]:((~tall(X)|~generous(X))=>(~old(X)<~>rich(X))))&
((?[X]:(kind(X)))<=>(?[X]:((~kind(X)|~funny(X)))))&
((~brave(fred))=>(?[X]:((~patient(X)&~funny(X)))))&
((?[X]:((kind(X)<~>~generous(X))))=>(?[X]:(quiet(X))))&
(![X]:((funny(X)<~>~wise(X))<=>(~happy(X)&creative(X))))&
(((brave(lucy)|strong(lucy)))<=>((humble(john)|strong(john))))&
(![X]:((~patient(X)&~brave(X))=>(calm(X)<~>curious(X))))&
(![X]:((happy(X)<~>~quiet(X))=>old(X)))&
((old(susan)<~>~kind(susan)))&
(?[X]:(tall(X)))&
(?[X]:((kind(X)&wise(X))))&
(?[X]:(~brave(X)))&
(?[X]:((happy(X)&~kind(X))))&
((brave(john)&~generous(john)))&
(?[X]:((creative(X)|~brave(X))))&
((funny(susan)<~>rich(susan))) | ~kind(fred) | [
"p0",
"p3",
"p4",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 4573257645214578537269916
% SZS output start Proof for 4573257645214578537269916
1. ! [X0] : ((~calm(X0) | old(X0)) <=> (calm(X0) <~> funny(X0))) [input p0]
4. ! [X0] : ((~generous(X0) | brave(X0)) => (kind(X0) & ~calm(X0))) [input p3]
5. ! [X0] : ((~rich(X0) | ~brave(X0)) <=> (patient(X0) & funny(X0))) [input p4]
11. ~brave(fred) => ? [X0] : (~funny(X0) & ~patient(X0)) [input p10]
25. ~kind(fred) [input hypothesis]
34. ! [X0] : ((kind(X0) & ~calm(X0)) | (generous(X0) & ~brave(X0))) [ennf transformation 4]
37. ? [X0] : (~funny(X0) & ~patient(X0)) | brave(fred) [ennf transformation 11]
42. ! [X0] : (((~calm(X0) | old(X0)) | ((calm(X0) | ~funny(X0)) & (funny(X0) | ~calm(X0)))) & (((~funny(X0) | ~calm(X0)) & (funny(X0) | calm(X0))) | (calm(X0) & ~old(X0)))) [nnf transformation 1]
43. ! [X0] : ((~calm(X0) | old(X0) | ((calm(X0) | ~funny(X0)) & (funny(X0) | ~calm(X0)))) & (((~funny(X0) | ~calm(X0)) & (funny(X0) | calm(X0))) | (calm(X0) & ~old(X0)))) [flattening 42]
45. ! [X0] : (((~rich(X0) | ~brave(X0)) | (~patient(X0) | ~funny(X0))) & ((patient(X0) & funny(X0)) | (rich(X0) & brave(X0)))) [nnf transformation 5]
46. ! [X0] : ((~rich(X0) | ~brave(X0) | ~patient(X0) | ~funny(X0)) & ((patient(X0) & funny(X0)) | (rich(X0) & brave(X0)))) [flattening 45]
60. ? [X0] : (~funny(X0) & ~patient(X0)) => (~funny(sK3) & ~patient(sK3)) [choice axiom]
61. (~funny(sK3) & ~patient(sK3)) | brave(fred) [skolemisation 37,60]
83. funny(X0) | calm(X0) | calm(X0) [cnf transformation 43]
91. ~brave(X0) | ~calm(X0) [cnf transformation 34]
93. ~brave(X0) | kind(X0) [cnf transformation 34]
95. brave(X0) | funny(X0) [cnf transformation 46]
122. ~funny(sK3) | brave(fred) [cnf transformation 61]
151. ~kind(fred) [cnf transformation 25]
152. funny(X0) | calm(X0) [duplicate literal removal 83]
208. 12 <=> ! [X1] : funny(X1) [avatar definition]
209. funny(X1) <- (12) [avatar component clause 208]
232. 18 <=> brave(fred) [avatar definition]
234. brave(fred) <- (18) [avatar component clause 232]
236. 19 <=> funny(sK3) [avatar definition]
238. ~funny(sK3) <- (~19) [avatar component clause 236]
239. 18 | ~19 [avatar split clause 122,236,232]
305. funny(X1) | ~calm(X1) [resolution 95,91]
309. funny(X1) [subsumption resolution 305,152]
310. 12 [avatar split clause 309,208]
312. $false <- (12, ~19) [resolution 209,238]
315. ~12 | 19 [avatar contradiction clause 312]
317. kind(fred) <- (18) [resolution 234,93]
319. $false <- (18) [subsumption resolution 317,151]
320. ~18 [avatar contradiction clause 319]
321. $false [avatar sat refutation 239,310,315,320]
% SZS output end Proof for 4573257645214578537269916
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 susan is patient or not kind then someone is either curious or not wise and vice versa.
If paul is both not curious and not funny then susan is both quiet and not generous and vice versa.
Everyone who is both not kind and not creative is both not curious and brave.
Everyone who is both humble and generous is either rich or kind.
Everyone who is both not funny and not patient is either quiet or not brave.
If lucy is both not wise and brave then mary is both not happy and not creative and vice versa.
If susan is not kind or not rich then fred is not calm or happy.
If someone is calm then john is both quiet and not creative.
Everyone who is either not generous or kind is generous or strong.
If paul is quiet then someone is either not rich or wise.
Everyone who is both brave and not humble is either not generous or tall and vice versa.
Everyone who is both not patient and curious is strong or not quiet and vice versa.
If someone is both funny and patient then someone is generous.
Everyone who is either patient or not patient is either not humble or funny and vice versa.
Everyone who is not humble is either not humble or not rich and vice versa.
If john is not old then fred is not strong or not quiet.
Lucy is either curious or patient.
Susan is funny.
Someone is either strong or not patient.
Someone is funny or not strong.
Someone is not patient.
Someone is either patient or not creative.
John is not funny. | Paul is not curious. | neutral | (((patient(susan)|~kind(susan)))<=>(?[X]:((curious(X)<~>~wise(X)))))&
(((~curious(paul)&~funny(paul)))<=>((quiet(susan)&~generous(susan))))&
(![X]:((~kind(X)&~creative(X))=>(~curious(X)&brave(X))))&
(![X]:((humble(X)&generous(X))=>(rich(X)<~>kind(X))))&
(![X]:((~funny(X)&~patient(X))=>(quiet(X)<~>~brave(X))))&
(((~wise(lucy)&brave(lucy)))<=>((~happy(mary)&~creative(mary))))&
(((~kind(susan)|~rich(susan)))=>((~calm(fred)|happy(fred))))&
((?[X]:(calm(X)))=>((quiet(john)&~creative(john))))&
(![X]:((~generous(X)<~>kind(X))=>(generous(X)|strong(X))))&
((quiet(paul))=>(?[X]:((~rich(X)<~>wise(X)))))&
(![X]:((brave(X)&~humble(X))<=>(~generous(X)<~>tall(X))))&
(![X]:((~patient(X)&curious(X))<=>(strong(X)|~quiet(X))))&
((?[X]:((funny(X)&patient(X))))=>(?[X]:(generous(X))))&
(![X]:((patient(X)<~>~patient(X))<=>(~humble(X)<~>funny(X))))&
(![X]:(~humble(X)<=>(~humble(X)<~>~rich(X))))&
((~old(john))=>((~strong(fred)|~quiet(fred))))&
((curious(lucy)<~>patient(lucy)))&
(funny(susan))&
(?[X]:((strong(X)<~>~patient(X))))&
(?[X]:((funny(X)|~strong(X))))&
(?[X]:(~patient(X)))&
(?[X]:((patient(X)<~>~creative(X))))&
(~funny(john)) | ~curious(paul) | [] | null | 0 |
If someone is either not curious or not quiet then lucy is not calm or not humble.
Everyone who is tall or creative is creative or not wise.
Everyone who is quiet or not strong is either brave or not generous and vice versa.
If fred is not patient then lucy is wise.
If john is wise or patient then someone is both creative and generous and vice versa.
If susan is both curious and not wise then someone is either patient or calm and vice versa.
Everyone who is either patient or quiet is either not creative or not brave and vice versa.
If someone is either not kind or not quiet then mary is not calm.
Everyone who is tall is rich or wise and vice versa.
If someone is humble or quiet then fred is not wise.
Everyone who is both calm and not happy is brave or strong and vice versa.
Everyone who is both not creative and funny is not calm or happy.
If someone is both tall and not funny then someone is humble or rich and vice versa.
Everyone who is rich is calm or brave.
If someone is both creative and strong then mary is both not kind and happy and vice versa.
If susan is not brave or kind then fred is either not old or not funny.
John is either not brave or quiet.
Someone is either not brave or not strong.
Someone is strong.
Mary is not rich or calm.
Someone is both old and patient.
Someone is both old and generous.
Lucy is both not brave and wise.
Mary is either tall or generous. | John is quiet. | neutral | ((?[X]:((~curious(X)<~>~quiet(X))))=>((~calm(lucy)|~humble(lucy))))&
(![X]:((tall(X)|creative(X))=>(creative(X)|~wise(X))))&
(![X]:((quiet(X)|~strong(X))<=>(brave(X)<~>~generous(X))))&
((~patient(fred))=>(wise(lucy)))&
(((wise(john)|patient(john)))<=>(?[X]:((creative(X)&generous(X)))))&
(((curious(susan)&~wise(susan)))<=>(?[X]:((patient(X)<~>calm(X)))))&
(![X]:((patient(X)<~>quiet(X))<=>(~creative(X)<~>~brave(X))))&
((?[X]:((~kind(X)<~>~quiet(X))))=>(~calm(mary)))&
(![X]:(tall(X)<=>(rich(X)|wise(X))))&
((?[X]:((humble(X)|quiet(X))))=>(~wise(fred)))&
(![X]:((calm(X)&~happy(X))<=>(brave(X)|strong(X))))&
(![X]:((~creative(X)&funny(X))=>(~calm(X)|happy(X))))&
((?[X]:((tall(X)&~funny(X))))<=>(?[X]:((humble(X)|rich(X)))))&
(![X]:(rich(X)=>(calm(X)|brave(X))))&
((?[X]:((creative(X)&strong(X))))<=>((~kind(mary)&happy(mary))))&
(((~brave(susan)|kind(susan)))=>((~old(fred)<~>~funny(fred))))&
((~brave(john)<~>quiet(john)))&
(?[X]:((~brave(X)<~>~strong(X))))&
(?[X]:(strong(X)))&
((~rich(mary)|calm(mary)))&
(?[X]:((old(X)&patient(X))))&
(?[X]:((old(X)&generous(X))))&
((~brave(lucy)&wise(lucy)))&
((tall(mary)<~>generous(mary))) | quiet(john) | [] | null | 0 |
If mary is both not old and not generous then fred is either not tall or not brave and vice versa.
If someone is both not old and not creative then someone is not brave or brave and vice versa.
Everyone who is not calm is either not funny or funny and vice versa.
If someone is both not kind and not tall then mary is humble.
If someone is either tall or not calm then mary is kind or strong and vice versa.
Everyone who is both not calm and not funny is both not old and strong and vice versa.
Everyone who is both not wise and not kind is either happy or brave and vice versa.
If lucy is not kind or patient then lucy is both not curious and happy.
If fred is either not creative or not patient then someone is not tall.
Everyone who is either strong or creative is not strong.
Everyone who is creative or tall is either not calm or curious and vice versa.
If someone is not rich or not generous then someone is not calm.
If paul is either not calm or not happy then susan is either not quiet or not strong.
If paul is funny or humble then susan is both not brave and brave and vice versa.
If someone is both not strong and tall then someone is not curious and vice versa.
If someone is patient or calm then someone is either patient or not kind.
Someone is quiet.
Someone is either creative or patient.
Paul is brave.
Mary is both not wise and not quiet.
Someone is curious or quiet.
Someone is humble or not wise.
John is generous.
Someone is old. | Susan is calm. | contradiction | (((~old(mary)&~generous(mary)))<=>((~tall(fred)<~>~brave(fred))))&
((?[X]:((~old(X)&~creative(X))))<=>(?[X]:((~brave(X)|brave(X)))))&
(![X]:(~calm(X)<=>(~funny(X)<~>funny(X))))&
((?[X]:((~kind(X)&~tall(X))))=>(humble(mary)))&
((?[X]:((tall(X)<~>~calm(X))))<=>((kind(mary)|strong(mary))))&
(![X]:((~calm(X)&~funny(X))<=>(~old(X)&strong(X))))&
(![X]:((~wise(X)&~kind(X))<=>(happy(X)<~>brave(X))))&
(((~kind(lucy)|patient(lucy)))=>((~curious(lucy)&happy(lucy))))&
(((~creative(fred)<~>~patient(fred)))=>(?[X]:(~tall(X))))&
(![X]:((strong(X)<~>creative(X))=>~strong(X)))&
(![X]:((creative(X)|tall(X))<=>(~calm(X)<~>curious(X))))&
((?[X]:((~rich(X)|~generous(X))))=>(?[X]:(~calm(X))))&
(((~calm(paul)<~>~happy(paul)))=>((~quiet(susan)<~>~strong(susan))))&
(((funny(paul)|humble(paul)))<=>((~brave(susan)&brave(susan))))&
((?[X]:((~strong(X)&tall(X))))<=>(?[X]:(~curious(X))))&
((?[X]:((patient(X)|calm(X))))=>(?[X]:((patient(X)<~>~kind(X)))))&
(?[X]:(quiet(X)))&
(?[X]:((creative(X)<~>patient(X))))&
(brave(paul))&
((~wise(mary)&~quiet(mary)))&
(?[X]:((curious(X)|quiet(X))))&
(?[X]:((humble(X)|~wise(X))))&
(generous(john))&
(?[X]:(old(X))) | calm(susan) | [
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 7638761871810352372953728
% SZS output start Proof for 7638761871810352372953728
3. ! [X0] : (~calm(X0) <=> (~funny(X0) <~> funny(X0))) [input p2]
25. calm(susan) [input hypothesis]
45. ! [X0] : ((~calm(X0) | ((~funny(X0) | ~funny(X0)) & (funny(X0) | funny(X0)))) & (((~funny(X0) | funny(X0)) & (funny(X0) | ~funny(X0))) | calm(X0))) [nnf transformation 3]
100. ~calm(X0) | funny(X0) | funny(X0) [cnf transformation 45]
101. ~calm(X0) | ~funny(X0) | ~funny(X0) [cnf transformation 45]
160. calm(susan) [cnf transformation 25]
162. ~calm(X0) | funny(X0) [duplicate literal removal 100]
163. ~calm(X0) | ~funny(X0) [duplicate literal removal 101]
204. ~calm(X0) [subsumption resolution 162,163]
367. $false [subsumption resolution 160,204]
% SZS output end Proof for 7638761871810352372953728
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not 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. | Fred is patient. | 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))) | patient(fred) | [
"p0",
"p1",
"p3",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3066855138691277160173433
% SZS output start Proof for 3066855138691277160173433
1. ! [X0] : ((creative(X0) | ~creative(X0)) <=> ~calm(X0)) [input p0]
2. ! [X0] : ((humble(X0) & patient(X0)) <=> creative(X0)) [input p1]
4. ! [X0] : ((~strong(X0) | quiet(X0)) <=> (calm(X0) & quiet(X0))) [input p3]
15. ! [X0] : ((~curious(X0) | ~creative(X0)) <=> (~patient(X0) & ~strong(X0))) [input p14]
23. ~patient(fred) [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]
35. ! [X0] : (((humble(X0) & patient(X0)) | ~creative(X0)) & (creative(X0) | (~humble(X0) | ~patient(X0)))) [nnf transformation 2]
36. ! [X0] : (((humble(X0) & patient(X0)) | ~creative(X0)) & (creative(X0) | ~humble(X0) | ~patient(X0))) [flattening 35]
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]
62. ! [X0] : (((~curious(X0) | ~creative(X0)) | (patient(X0) | strong(X0))) & ((~patient(X0) & ~strong(X0)) | (curious(X0) & creative(X0)))) [nnf transformation 15]
63. ! [X0] : ((~curious(X0) | ~creative(X0) | patient(X0) | strong(X0)) & ((~patient(X0) & ~strong(X0)) | (curious(X0) & creative(X0)))) [flattening 62]
72. ~calm(X0) | creative(X0) [cnf transformation 34]
73. ~calm(X0) | ~creative(X0) [cnf transformation 34]
76. ~creative(X0) | patient(X0) [cnf transformation 36]
83. calm(X0) | strong(X0) [cnf transformation 42]
116. ~strong(X0) | creative(X0) [cnf transformation 63]
132. ~patient(fred) [cnf transformation 23]
133. ~calm(X0) [subsumption resolution 72,73]
147. strong(X0) [subsumption resolution 83,133]
161. 6 <=> ! [X0] : creative(X0) [avatar definition]
162. creative(X0) <- (6) [avatar component clause 161]
223. creative(X0) [subsumption resolution 116,147]
224. 6 [avatar split clause 223,161]
249. patient(X0) <- (6) [resolution 76,162]
252. $false <- (6) [resolution 249,132]
255. ~6 [avatar contradiction clause 252]
256. $false [avatar sat refutation 224,255]
% SZS output end Proof for 3066855138691277160173433
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either brave or not brave is not quiet or generous and vice versa.
If someone is calm or not brave then someone is both wise and brave.
Everyone who is not happy is either funny or not happy.
If someone is both not happy and wise then alice is both not patient and calm.
If susan is both rich and not tall then someone is both humble and wise and vice versa.
If someone is either brave or kind then someone is both brave and tall and vice versa.
Everyone who is both calm and curious is not wise or wise.
Everyone who is not creative is both tall and wise and vice versa.
Everyone who is not curious or wise is calm or tall and vice versa.
Everyone who is not strong or not patient is both quiet and kind and vice versa.
If lucy is strong then susan is not generous.
If mary is rich or not brave then lucy is both not funny and patient.
Everyone who is not happy or not tall is tall or curious and vice versa.
Everyone who is both not curious and not generous is either wise or old and vice versa.
If susan is generous or tall then someone is not rich or not kind.
If susan is both kind and tall then paul is both funny and not happy.
Someone is calm.
Someone is either not humble or strong.
Someone is not curious.
Someone is both not wise and not calm.
Paul is curious or rich.
Someone is not patient.
Mary is both rich and humble.
Paul is old or not old. | Alice is quiet. | neutral | (![X]:((brave(X)<~>~brave(X))<=>(~quiet(X)|generous(X))))&
((?[X]:((calm(X)|~brave(X))))=>(?[X]:((wise(X)&brave(X)))))&
(![X]:(~happy(X)=>(funny(X)<~>~happy(X))))&
((?[X]:((~happy(X)&wise(X))))=>((~patient(alice)&calm(alice))))&
(((rich(susan)&~tall(susan)))<=>(?[X]:((humble(X)&wise(X)))))&
((?[X]:((brave(X)<~>kind(X))))<=>(?[X]:((brave(X)&tall(X)))))&
(![X]:((calm(X)&curious(X))=>(~wise(X)|wise(X))))&
(![X]:(~creative(X)<=>(tall(X)&wise(X))))&
(![X]:((~curious(X)|wise(X))<=>(calm(X)|tall(X))))&
(![X]:((~strong(X)|~patient(X))<=>(quiet(X)&kind(X))))&
((strong(lucy))=>(~generous(susan)))&
(((rich(mary)|~brave(mary)))=>((~funny(lucy)&patient(lucy))))&
(![X]:((~happy(X)|~tall(X))<=>(tall(X)|curious(X))))&
(![X]:((~curious(X)&~generous(X))<=>(wise(X)<~>old(X))))&
(((generous(susan)|tall(susan)))=>(?[X]:((~rich(X)|~kind(X)))))&
(((kind(susan)&tall(susan)))=>((funny(paul)&~happy(paul))))&
(?[X]:(calm(X)))&
(?[X]:((~humble(X)<~>strong(X))))&
(?[X]:(~curious(X)))&
(?[X]:((~wise(X)&~calm(X))))&
((curious(paul)|rich(paul)))&
(?[X]:(~patient(X)))&
((rich(mary)&humble(mary)))&
((old(paul)|~old(paul))) | quiet(alice) | [] | null | 0 |
If someone is either rich or funny then paul is not generous.
Everyone who is both funny and not brave is both not calm and humble and vice versa.
If fred is rich or not generous then john is not wise or not strong.
If fred is either brave or not happy then paul is quiet.
Everyone who is either not humble or not brave is tall and vice versa.
Everyone who is creative or tall is funny or not tall.
If someone is funny or happy then someone is not funny or not generous and vice versa.
If susan is not kind or generous then someone is either curious or generous and vice versa.
Everyone who is both calm and not curious is funny and vice versa.
Everyone who is not old is both not humble and not tall and vice versa.
If someone is not creative or wise then someone is both not humble and quiet and vice versa.
If someone is both patient and not funny then paul is either not old or happy and vice versa.
If someone is not funny then john is happy or funny and vice versa.
If someone is either funny or not brave then someone is both strong and not strong.
Everyone who is either not strong or quiet is not tall.
If someone is not humble then someone is either humble or not humble.
Mary is either not brave or not quiet.
Someone is generous.
Someone is either not tall or not creative.
Someone is old or wise.
Alice is either not generous or humble.
Someone is either not patient or not tall. | Alice is not curious. | contradiction | ((?[X]:((rich(X)<~>funny(X))))=>(~generous(paul)))&
(![X]:((funny(X)&~brave(X))<=>(~calm(X)&humble(X))))&
(((rich(fred)|~generous(fred)))=>((~wise(john)|~strong(john))))&
(((brave(fred)<~>~happy(fred)))=>(quiet(paul)))&
(![X]:((~humble(X)<~>~brave(X))<=>tall(X)))&
(![X]:((creative(X)|tall(X))=>(funny(X)|~tall(X))))&
((?[X]:((funny(X)|happy(X))))<=>(?[X]:((~funny(X)|~generous(X)))))&
(((~kind(susan)|generous(susan)))<=>(?[X]:((curious(X)<~>generous(X)))))&
(![X]:((calm(X)&~curious(X))<=>funny(X)))&
(![X]:(~old(X)<=>(~humble(X)&~tall(X))))&
((?[X]:((~creative(X)|wise(X))))<=>(?[X]:((~humble(X)&quiet(X)))))&
((?[X]:((patient(X)&~funny(X))))<=>((~old(paul)<~>happy(paul))))&
((?[X]:(~funny(X)))<=>((happy(john)|funny(john))))&
((?[X]:((funny(X)<~>~brave(X))))=>(?[X]:((strong(X)&~strong(X)))))&
(![X]:((~strong(X)<~>quiet(X))=>~tall(X)))&
((?[X]:(~humble(X)))=>(?[X]:((humble(X)<~>~humble(X)))))&
((~brave(mary)<~>~quiet(mary)))&
(?[X]:(generous(X)))&
(?[X]:((~tall(X)<~>~creative(X))))&
(?[X]:((old(X)|wise(X))))&
((~generous(alice)<~>humble(alice)))&
(?[X]:((~patient(X)<~>~tall(X)))) | ~curious(alice) | [
"p1",
"p4",
"p5",
"p8",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 644535452778489097526229
% SZS output start Proof for 644535452778489097526229
2. ! [X0] : ((~brave(X0) & funny(X0)) <=> (humble(X0) & ~calm(X0))) [input p1]
5. ! [X0] : ((~humble(X0) <~> ~brave(X0)) <=> tall(X0)) [input p4]
6. ! [X0] : ((tall(X0) | creative(X0)) => (~tall(X0) | funny(X0))) [input p5]
9. ! [X0] : ((~curious(X0) & calm(X0)) <=> funny(X0)) [input p8]
14. ? [X0] : (funny(X0) <~> ~brave(X0)) => ? [X0] : (~strong(X0) & strong(X0)) [input p13]
23. ~curious(alice) [input hypothesis]
26. ? [X0] : (funny(X0) <~> ~brave(X0)) => ? [X1] : (~strong(X1) & strong(X1)) [rectify 14]
32. ! [X0] : ((~tall(X0) | funny(X0)) | (~tall(X0) & ~creative(X0))) [ennf transformation 6]
33. ! [X0] : (~tall(X0) | funny(X0) | (~tall(X0) & ~creative(X0))) [flattening 32]
34. ? [X1] : (~strong(X1) & strong(X1)) | ! [X0] : (funny(X0) <=> ~brave(X0)) [ennf transformation 26]
38. ! [X0] : (((~brave(X0) & funny(X0)) | (~humble(X0) | calm(X0))) & ((humble(X0) & ~calm(X0)) | (brave(X0) | ~funny(X0)))) [nnf transformation 2]
39. ! [X0] : (((~brave(X0) & funny(X0)) | ~humble(X0) | calm(X0)) & ((humble(X0) & ~calm(X0)) | brave(X0) | ~funny(X0))) [flattening 38]
41. ! [X0] : ((((brave(X0) | humble(X0)) & (~brave(X0) | ~humble(X0))) | ~tall(X0)) & (tall(X0) | ((~humble(X0) | brave(X0)) & (~brave(X0) | humble(X0))))) [nnf transformation 5]
52. ! [X0] : (((~curious(X0) & calm(X0)) | ~funny(X0)) & (funny(X0) | (curious(X0) | ~calm(X0)))) [nnf transformation 9]
53. ! [X0] : (((~curious(X0) & calm(X0)) | ~funny(X0)) & (funny(X0) | curious(X0) | ~calm(X0))) [flattening 52]
70. ? [X1] : (~strong(X1) & strong(X1)) | ! [X0] : ((funny(X0) | brave(X0)) & (~brave(X0) | ~funny(X0))) [nnf transformation 34]
71. ? [X0] : (~strong(X0) & strong(X0)) | ! [X1] : ((funny(X1) | brave(X1)) & (~brave(X1) | ~funny(X1))) [rectify 70]
72. ? [X0] : (~strong(X0) & strong(X0)) => (~strong(sK7) & strong(sK7)) [choice axiom]
73. (~strong(sK7) & strong(sK7)) | ! [X1] : ((funny(X1) | brave(X1)) & (~brave(X1) | ~funny(X1))) [skolemisation 71,72]
93. ~calm(X0) | brave(X0) | ~funny(X0) [cnf transformation 39]
95. ~humble(X0) | funny(X0) | calm(X0) [cnf transformation 39]
101. ~brave(X0) | tall(X0) | humble(X0) [cnf transformation 41]
106. ~tall(X0) | funny(X0) | ~tall(X0) [cnf transformation 33]
117. ~calm(X0) | curious(X0) | funny(X0) [cnf transformation 53]
118. ~funny(X0) | calm(X0) [cnf transformation 53]
137. strong(sK7) | ~brave(X1) | ~funny(X1) [cnf transformation 73]
138. strong(sK7) | funny(X1) | brave(X1) [cnf transformation 73]
139. ~strong(sK7) | ~brave(X1) | ~funny(X1) [cnf transformation 73]
140. ~strong(sK7) | funny(X1) | brave(X1) [cnf transformation 73]
155. ~curious(alice) [cnf transformation 23]
156. ~tall(X0) | funny(X0) [duplicate literal removal 106]
230. 18 <=> ! [X3] : ~funny(X3) [avatar definition]
231. ~funny(X3) <- (18) [avatar component clause 230]
332. 40 <=> ! [X1] : (funny(X1) | brave(X1)) [avatar definition]
333. brave(X1) | funny(X1) <- (40) [avatar component clause 332]
335. 41 <=> strong(sK7) [avatar definition]
338. 40 | ~41 [avatar split clause 140,335,332]
340. 42 <=> ! [X1] : (~brave(X1) | ~funny(X1)) [avatar definition]
341. ~brave(X1) | ~funny(X1) <- (42) [avatar component clause 340]
342. 42 | ~41 [avatar split clause 139,335,340]
343. 40 | 41 [avatar split clause 138,335,332]
344. 42 | 41 [avatar split clause 137,335,340]
442. tall(X0) | humble(X0) | funny(X0) <- (40) [resolution 101,333]
461. humble(X0) | funny(X0) <- (40) [subsumption resolution 442,156]
566. funny(X2) | funny(X2) | calm(X2) <- (40) [resolution 461,95]
571. funny(X2) | calm(X2) <- (40) [duplicate literal removal 566]
573. calm(X2) <- (40) [subsumption resolution 571,118]
607. curious(X0) | funny(X0) <- (40) [resolution 573,117]
608. brave(X1) | ~funny(X1) <- (40) [resolution 573,93]
609. brave(X1) <- (40) [subsumption resolution 608,333]
649. ~funny(X2) <- (40, 42) [resolution 609,341]
650. 18 | ~40 | ~42 [avatar split clause 649,340,332,230]
662. funny(alice) <- (40) [resolution 607,155]
664. $false <- (18, 40) [subsumption resolution 662,231]
665. ~18 | ~40 [avatar contradiction clause 664]
666. $false [avatar sat refutation 338,342,343,344,650,665]
% SZS output end Proof for 644535452778489097526229
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is kind or not humble is both old and not tall.
Everyone who is strong or old is both not wise and rich and vice versa.
Everyone who is calm or old is both not patient and old and vice versa.
If someone is either not creative or quiet then fred is kind or not happy and vice versa.
If lucy is either not tall or generous then john is either generous or happy.
Everyone who is brave is not kind.
Everyone who is either not patient or patient is either not old or old and vice versa.
Everyone who is both old and funny is both not calm and old.
Everyone who is not wise is not tall.
Everyone who is not brave or strong is generous or not curious and vice versa.
Everyone who is either wise or not funny is both not humble and not patient and vice versa.
Everyone who is both not creative and creative is both not funny and wise and vice versa.
If someone is tall or not curious then fred is wise and vice versa.
If john is not patient then someone is both wise and happy.
If someone is either not humble or not old then someone is both not tall and not creative.
Someone is strong.
Someone is both not happy and calm.
Someone is creative or kind.
Paul is either not humble or not quiet.
Someone is either not creative or not happy.
Alice is either patient or rich.
Someone is creative. | Paul is curious. | entailment | (![X]:((kind(X)|~humble(X))=>(old(X)&~tall(X))))&
(![X]:((strong(X)|old(X))<=>(~wise(X)&rich(X))))&
(![X]:((calm(X)|old(X))<=>(~patient(X)&old(X))))&
((?[X]:((~creative(X)<~>quiet(X))))<=>((kind(fred)|~happy(fred))))&
(((~tall(lucy)<~>generous(lucy)))=>((generous(john)<~>happy(john))))&
(![X]:(brave(X)=>~kind(X)))&
(![X]:((~patient(X)<~>patient(X))<=>(~old(X)<~>old(X))))&
(![X]:((old(X)&funny(X))=>(~calm(X)&old(X))))&
(![X]:(~wise(X)=>~tall(X)))&
(![X]:((~brave(X)|strong(X))<=>(generous(X)|~curious(X))))&
(![X]:((wise(X)<~>~funny(X))<=>(~humble(X)&~patient(X))))&
(![X]:((~creative(X)&creative(X))<=>(~funny(X)&wise(X))))&
((?[X]:((tall(X)|~curious(X))))<=>(wise(fred)))&
((~patient(john))=>(?[X]:((wise(X)&happy(X)))))&
((?[X]:((~humble(X)<~>~old(X))))=>(?[X]:((~tall(X)&~creative(X)))))&
(?[X]:(strong(X)))&
(?[X]:((~happy(X)&calm(X))))&
(?[X]:((creative(X)|kind(X))))&
((~humble(paul)<~>~quiet(paul)))&
(?[X]:((~creative(X)<~>~happy(X))))&
((patient(alice)<~>rich(alice)))&
(?[X]:(creative(X))) | curious(paul) | [
"p0",
"p1",
"p10",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 5053717834264987348507658
% SZS output start Proof for 5053717834264987348507658
1. ! [X0] : ((~humble(X0) | kind(X0)) => (~tall(X0) & old(X0))) [input p0]
2. ! [X0] : ((old(X0) | strong(X0)) <=> (rich(X0) & ~wise(X0))) [input p1]
11. ! [X0] : ((wise(X0) <~> ~funny(X0)) <=> (~patient(X0) & ~humble(X0))) [input p10]
12. ! [X0] : ((creative(X0) & ~creative(X0)) <=> (wise(X0) & ~funny(X0))) [input p11]
13. ? [X0] : (~curious(X0) | tall(X0)) <=> wise(fred) [input p12]
23. ~curious(paul) [input hypothesis]
25. ! [X0] : ((~tall(X0) & old(X0)) | (humble(X0) & ~kind(X0))) [ennf transformation 1]
33. ! [X0] : (((old(X0) | strong(X0)) | (~rich(X0) | wise(X0))) & ((rich(X0) & ~wise(X0)) | (~old(X0) & ~strong(X0)))) [nnf transformation 2]
34. ! [X0] : ((old(X0) | strong(X0) | ~rich(X0) | wise(X0)) & ((rich(X0) & ~wise(X0)) | (~old(X0) & ~strong(X0)))) [flattening 33]
46. ! [X0] : ((((funny(X0) | ~wise(X0)) & (~funny(X0) | wise(X0))) | (patient(X0) | humble(X0))) & ((~patient(X0) & ~humble(X0)) | ((wise(X0) | funny(X0)) & (~funny(X0) | ~wise(X0))))) [nnf transformation 11]
47. ! [X0] : ((((funny(X0) | ~wise(X0)) & (~funny(X0) | wise(X0))) | patient(X0) | humble(X0)) & ((~patient(X0) & ~humble(X0)) | ((wise(X0) | funny(X0)) & (~funny(X0) | ~wise(X0))))) [flattening 46]
48. ! [X0] : (((creative(X0) & ~creative(X0)) | (~wise(X0) | funny(X0))) & ((wise(X0) & ~funny(X0)) | (~creative(X0) | creative(X0)))) [nnf transformation 12]
49. ! [X0] : (((creative(X0) & ~creative(X0)) | ~wise(X0) | funny(X0)) & ((wise(X0) & ~funny(X0)) | ~creative(X0) | creative(X0))) [flattening 48]
50. (? [X0] : (~curious(X0) | tall(X0)) | ~wise(fred)) & (wise(fred) | ! [X0] : (curious(X0) & ~tall(X0))) [nnf transformation 13]
51. (? [X0] : (~curious(X0) | tall(X0)) | ~wise(fred)) & (wise(fred) | ! [X1] : (curious(X1) & ~tall(X1))) [rectify 50]
52. ? [X0] : (~curious(X0) | tall(X0)) => (~curious(sK1) | tall(sK1)) [choice axiom]
53. ((~curious(sK1) | tall(sK1)) | ~wise(fred)) & (wise(fred) | ! [X1] : (curious(X1) & ~tall(X1))) [skolemisation 51,52]
74. old(X0) | humble(X0) [cnf transformation 25]
78. ~wise(X0) | ~old(X0) [cnf transformation 34]
113. ~funny(X0) | ~humble(X0) | ~wise(X0) [cnf transformation 47]
121. ~creative(X0) | ~wise(X0) | funny(X0) [cnf transformation 49]
122. creative(X0) | ~wise(X0) | funny(X0) [cnf transformation 49]
124. wise(fred) | curious(X1) [cnf transformation 53]
143. ~curious(paul) [cnf transformation 23]
201. ~wise(X0) | funny(X0) [subsumption resolution 121,122]
203. 11 <=> wise(fred) [avatar definition]
204. wise(fred) <- (11) [avatar component clause 203]
216. 14 <=> ! [X1] : curious(X1) [avatar definition]
217. curious(X1) <- (14) [avatar component clause 216]
218. 14 | 11 [avatar split clause 124,203,216]
299. ~old(fred) <- (11) [resolution 78,204]
300. humble(fred) <- (11) [resolution 299,74]
311. funny(fred) <- (11) [resolution 201,204]
314. ~humble(fred) | ~wise(fred) <- (11) [resolution 113,311]
315. ~wise(fred) <- (11) [subsumption resolution 314,300]
316. $false <- (11) [subsumption resolution 315,204]
317. ~11 [avatar contradiction clause 316]
318. $false <- (14) [resolution 217,143]
323. ~14 [avatar contradiction clause 318]
324. $false [avatar sat refutation 218,317,323]
% SZS output end Proof for 5053717834264987348507658
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.045 s
% ------------------------------
% ------------------------------
| 0 |
If someone is strong then paul is not humble and vice versa. Everyone who is not kind is both not tall and not patient and vice versa. Everyone who is both quiet and not kind is generous or not kind and vice versa. Everyone who is either not strong or not generous is not brave. If someone is either not happy or not rich then john is not funny and vice versa. Everyone who is strong or quiet is generous. Everyone who is not humble is both rich and not patient and vice versa. If someone is both happy and rich then someone is old and vice versa. Everyone who is either old or calm is either not strong or tall. Everyone who is either patient or not funny is calm. Everyone who is both not quiet and happy is not brave and vice versa. Everyone who is not happy is not quiet or humble. Everyone who is not creative is both not tall and not old. If susan is not happy or humble then someone is happy. Everyone who is patient or rich is not kind or not strong and vice versa. Everyone who is funny is either not creative or not funny. Someone is either tall or not wise. John is either rich or not happy. Susan is not brave. Fred is humble or happy. Mary is old or generous. Paul is either not rich or old. Someone is either not wise or not tall. | Mary is humble. | neutral | ((?[X]:(strong(X)))<=>(~humble(paul)))&
(![X]:(~kind(X)<=>(~tall(X)&~patient(X))))&
(![X]:((quiet(X)&~kind(X))<=>(generous(X)|~kind(X))))&
(![X]:((~strong(X)<~>~generous(X))=>~brave(X)))&
((?[X]:((~happy(X)<~>~rich(X))))<=>(~funny(john)))&
(![X]:((strong(X)|quiet(X))=>generous(X)))&
(![X]:(~humble(X)<=>(rich(X)&~patient(X))))&
((?[X]:((happy(X)&rich(X))))<=>(?[X]:(old(X))))&
(![X]:((old(X)<~>calm(X))=>(~strong(X)<~>tall(X))))&
(![X]:((patient(X)<~>~funny(X))=>calm(X)))&
(![X]:((~quiet(X)&happy(X))<=>~brave(X)))&
(![X]:(~happy(X)=>(~quiet(X)|humble(X))))&
(![X]:(~creative(X)=>(~tall(X)&~old(X))))&
(((~happy(susan)|humble(susan)))=>(?[X]:(happy(X))))&
(![X]:((patient(X)|rich(X))<=>(~kind(X)|~strong(X))))&
(![X]:(funny(X)=>(~creative(X)<~>~funny(X))))&
(?[X]:((tall(X)<~>~wise(X))))&
((rich(john)<~>~happy(john)))&
(~brave(susan))&
((humble(fred)|happy(fred)))&
((old(mary)|generous(mary)))&
((~rich(paul)<~>old(paul)))&
(?[X]:((~wise(X)<~>~tall(X)))) | humble(mary) | [] | null | 0 |
If someone is either not funny or not creative then fred is both calm and humble and vice versa. If someone is either calm or not kind then someone is either not happy or quiet and vice versa. If mary is either patient or rich then someone is funny and vice versa. If john is not funny then fred is not humble or not strong and vice versa. If someone is both not strong and quiet then someone is not brave or quiet. Everyone who is not curious or not strong is wise. Everyone who is not humble is not wise and vice versa. Everyone who is not quiet is not kind or tall and vice versa. Everyone who is both not strong and old is either not quiet or patient and vice versa. Everyone who is both brave and not generous is either not creative or kind and vice versa. Everyone who is both not wise and not kind is both funny and not happy. Everyone who is either not tall or happy is both brave and funny and vice versa. Everyone who is old or not calm is calm or not quiet and vice versa. Everyone who is not generous or not humble is either kind or not tall and vice versa. Everyone who is not curious is either not happy or happy and vice versa. Everyone who is both not curious and not happy is humble. Someone is patient or not strong. Susan is strong. Someone is quiet. Susan is not creative. John is both not patient and not rich. Paul is both not rich and not patient. Alice is rich or generous. | Susan is not humble. | contradiction | ((?[X]:((~funny(X)<~>~creative(X))))<=>((calm(fred)&humble(fred))))&
((?[X]:((calm(X)<~>~kind(X))))<=>(?[X]:((~happy(X)<~>quiet(X)))))&
(((patient(mary)<~>rich(mary)))<=>(?[X]:(funny(X))))&
((~funny(john))<=>((~humble(fred)|~strong(fred))))&
((?[X]:((~strong(X)&quiet(X))))=>(?[X]:((~brave(X)|quiet(X)))))&
(![X]:((~curious(X)|~strong(X))=>wise(X)))&
(![X]:(~humble(X)<=>~wise(X)))&
(![X]:(~quiet(X)<=>(~kind(X)|tall(X))))&
(![X]:((~strong(X)&old(X))<=>(~quiet(X)<~>patient(X))))&
(![X]:((brave(X)&~generous(X))<=>(~creative(X)<~>kind(X))))&
(![X]:((~wise(X)&~kind(X))=>(funny(X)&~happy(X))))&
(![X]:((~tall(X)<~>happy(X))<=>(brave(X)&funny(X))))&
(![X]:((old(X)|~calm(X))<=>(calm(X)|~quiet(X))))&
(![X]:((~generous(X)|~humble(X))<=>(kind(X)<~>~tall(X))))&
(![X]:(~curious(X)<=>(~happy(X)<~>happy(X))))&
(![X]:((~curious(X)&~happy(X))=>humble(X)))&
(?[X]:((patient(X)|~strong(X))))&
(strong(susan))&
(?[X]:(quiet(X)))&
(~creative(susan))&
((~patient(john)&~rich(john)))&
((~rich(paul)&~patient(paul)))&
((rich(alice)|generous(alice))) | ~humble(susan) | [
"p5",
"p6",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5153054028239947903651671
% SZS output start Proof for 5153054028239947903651671
6. ! [X0] : ((~strong(X0) | ~curious(X0)) => wise(X0)) [input p5]
7. ! [X0] : (~humble(X0) <=> ~wise(X0)) [input p6]
15. ! [X0] : (~curious(X0) <=> (~happy(X0) <~> happy(X0))) [input p14]
24. ~humble(susan) [input hypothesis]
27. ! [X0] : ((~happy(X0) <~> happy(X0)) => ~curious(X0)) [unused predicate definition removal 15]
29. ! [X0] : (wise(X0) | (strong(X0) & curious(X0))) [ennf transformation 6]
32. ! [X0] : (~curious(X0) | (~happy(X0) <=> happy(X0))) [ennf transformation 27]
54. ! [X0] : ((~humble(X0) | wise(X0)) & (~wise(X0) | humble(X0))) [nnf transformation 7]
67. ! [X0] : (~curious(X0) | ((~happy(X0) | ~happy(X0)) & (happy(X0) | happy(X0)))) [nnf transformation 32]
94. wise(X0) | curious(X0) [cnf transformation 29]
96. ~wise(X0) | humble(X0) [cnf transformation 54]
131. ~curious(X0) | happy(X0) | happy(X0) [cnf transformation 67]
132. ~curious(X0) | ~happy(X0) | ~happy(X0) [cnf transformation 67]
143. ~humble(susan) [cnf transformation 24]
144. ~curious(X0) | happy(X0) [duplicate literal removal 131]
145. ~curious(X0) | ~happy(X0) [duplicate literal removal 132]
254. ~curious(X0) [subsumption resolution 144,145]
276. humble(X1) | curious(X1) [resolution 96,94]
277. humble(X1) [subsumption resolution 276,254]
278. $false [resolution 277,143]
% SZS output end Proof for 5153054028239947903651671
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not strong and not rich is not calm or calm and vice versa. Everyone who is either brave or funny is wise or not quiet and vice versa. Everyone who is both curious and quiet is both quiet and not funny and vice versa. If someone is either tall or calm then alice is not quiet or not patient. If someone is both tall and not happy then susan is calm. If someone is either not creative or strong then john is either wise or not curious. If someone is not wise then john is both not funny and brave and vice versa. If someone is not calm or happy then susan is not tall and vice versa. Everyone who is wise is either not funny or quiet and vice versa. If lucy is calm or creative then paul is not wise and vice versa. If paul is both not rich and old then someone is happy and vice versa. Everyone who is both funny and not rich is happy or rich and vice versa. Everyone who is both not strong and funny is not wise or generous and vice versa. If someone is not kind or not quiet then susan is either creative or not brave. If fred is both not funny and calm then someone is not quiet or not strong and vice versa. If john is calm or brave then someone is both not wise and kind. Alice is either quiet or funny. Paul is generous. Fred is not strong. Someone is both happy and not strong. Someone is either not funny or not strong. John is either happy or not humble. Someone is both not kind and humble. Someone is either not quiet or quiet. | John is not funny. | entailment | (![X]:((~strong(X)&~rich(X))<=>(~calm(X)|calm(X))))&
(![X]:((brave(X)<~>funny(X))<=>(wise(X)|~quiet(X))))&
(![X]:((curious(X)&quiet(X))<=>(quiet(X)&~funny(X))))&
((?[X]:((tall(X)<~>calm(X))))=>((~quiet(alice)|~patient(alice))))&
((?[X]:((tall(X)&~happy(X))))=>(calm(susan)))&
((?[X]:((~creative(X)<~>strong(X))))=>((wise(john)<~>~curious(john))))&
((?[X]:(~wise(X)))<=>((~funny(john)&brave(john))))&
((?[X]:((~calm(X)|happy(X))))<=>(~tall(susan)))&
(![X]:(wise(X)<=>(~funny(X)<~>quiet(X))))&
(((calm(lucy)|creative(lucy)))<=>(~wise(paul)))&
(((~rich(paul)&old(paul)))<=>(?[X]:(happy(X))))&
(![X]:((funny(X)&~rich(X))<=>(happy(X)|rich(X))))&
(![X]:((~strong(X)&funny(X))<=>(~wise(X)|generous(X))))&
((?[X]:((~kind(X)|~quiet(X))))=>((creative(susan)<~>~brave(susan))))&
(((~funny(fred)&calm(fred)))<=>(?[X]:((~quiet(X)|~strong(X)))))&
(((calm(john)|brave(john)))=>(?[X]:((~wise(X)&kind(X)))))&
((quiet(alice)<~>funny(alice)))&
(generous(paul))&
(~strong(fred))&
(?[X]:((happy(X)&~strong(X))))&
(?[X]:((~funny(X)<~>~strong(X))))&
((happy(john)<~>~humble(john)))&
(?[X]:((~kind(X)&humble(X))))&
(?[X]:((~quiet(X)<~>quiet(X)))) | ~funny(john) | [
"p6",
"p8",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 1787722848586678711295321
% SZS output start Proof for 1787722848586678711295321
7. ? [X0] : ~wise(X0) <=> (brave(john) & ~funny(john)) [input p6]
9. ! [X0] : (wise(X0) <=> (~funny(X0) <~> quiet(X0))) [input p8]
17. quiet(alice) <~> funny(alice) [input p16]
25. funny(john) [input hypothesis]
38. (? [X0] : ~wise(X0) | (~brave(john) | funny(john))) & ((brave(john) & ~funny(john)) | ! [X0] : wise(X0)) [nnf transformation 7]
39. (? [X0] : ~wise(X0) | ~brave(john) | funny(john)) & ((brave(john) & ~funny(john)) | ! [X0] : wise(X0)) [flattening 38]
40. (? [X0] : ~wise(X0) | ~brave(john) | funny(john)) & ((brave(john) & ~funny(john)) | ! [X1] : wise(X1)) [rectify 39]
41. ? [X0] : ~wise(X0) => ~wise(sK0) [choice axiom]
42. (~wise(sK0) | ~brave(john) | funny(john)) & ((brave(john) & ~funny(john)) | ! [X1] : wise(X1)) [skolemisation 40,41]
47. ! [X0] : ((wise(X0) | ((~funny(X0) | ~quiet(X0)) & (quiet(X0) | funny(X0)))) & (((~quiet(X0) | funny(X0)) & (quiet(X0) | ~funny(X0))) | ~wise(X0))) [nnf transformation 9]
67. (~funny(alice) | ~quiet(alice)) & (funny(alice) | quiet(alice)) [nnf transformation 17]
99. ~funny(john) | wise(X1) [cnf transformation 42]
105. ~wise(X0) | ~funny(X0) | quiet(X0) [cnf transformation 47]
106. ~quiet(X0) | funny(X0) | ~wise(X0) [cnf transformation 47]
138. funny(alice) | quiet(alice) [cnf transformation 67]
139. ~funny(alice) | ~quiet(alice) [cnf transformation 67]
152. funny(john) [cnf transformation 25]
181. 6 <=> funny(john) [avatar definition]
194. 9 <=> ! [X1] : wise(X1) [avatar definition]
195. wise(X1) <- (9) [avatar component clause 194]
197. 9 | ~6 [avatar split clause 99,181,194]
284. 27 <=> quiet(alice) [avatar definition]
285. quiet(alice) <- (27) [avatar component clause 284]
286. ~quiet(alice) <- (~27) [avatar component clause 284]
288. 28 <=> funny(alice) [avatar definition]
289. funny(alice) <- (28) [avatar component clause 288]
290. ~funny(alice) <- (~28) [avatar component clause 288]
291. ~27 | ~28 [avatar split clause 139,288,284]
292. 27 | 28 [avatar split clause 138,288,284]
304. 6 [avatar split clause 152,181]
388. ~funny(X1) | quiet(X1) <- (9) [resolution 105,195]
390. funny(alice) | ~wise(alice) <- (27) [resolution 106,285]
393. ~wise(alice) <- (27, ~28) [subsumption resolution 390,290]
394. $false <- (9, 27, ~28) [subsumption resolution 393,195]
395. ~9 | ~27 | 28 [avatar contradiction clause 394]
429. quiet(alice) <- (9, 28) [resolution 388,289]
435. $false <- (9, ~27, 28) [subsumption resolution 429,286]
436. ~9 | 27 | ~28 [avatar contradiction clause 435]
443. $false [avatar sat refutation 197,291,292,304,395,436]
% SZS output end Proof for 1787722848586678711295321
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
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