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
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|---|---|---|---|---|---|---|---|
Everyone who is both creative and rich is creative or strong and vice versa.
If someone is either rich or happy then someone is both not funny and not curious and vice versa.
If someone is either not humble or not generous then someone is either brave or strong.
Everyone who is not rich or brave is both not tall and strong.
If mary is both brave and not creative then someone is funny or not quiet and vice versa.
Everyone who is either creative or old is both not patient and not kind and vice versa.
Everyone who is either not curious or generous is not rich or humble.
Everyone who is either not strong or not patient is humble.
Everyone who is not brave is not rich.
If mary is both not wise and curious then someone is either calm or not tall and vice versa.
If someone is not old or not quiet then lucy is both not rich and creative and vice versa.
Everyone who is both not humble and wise is not generous.
Everyone who is both not funny and not kind is curious or patient and vice versa.
Everyone who is either not wise or calm is not curious or not brave.
Everyone who is either not old or not quiet is both humble and strong and vice versa.
Paul is both not funny and not kind.
Someone is either kind or not wise.
Someone is not calm. | Lucy is not creative. | contradiction | (![X]:((creative(X)&rich(X))<=>(creative(X)|strong(X))))&
((?[X]:((rich(X)<~>happy(X))))<=>(?[X]:((~funny(X)&~curious(X)))))&
((?[X]:((~humble(X)<~>~generous(X))))=>(?[X]:((brave(X)<~>strong(X)))))&
(![X]:((~rich(X)|brave(X))=>(~tall(X)&strong(X))))&
(((brave(mary)&~creative(mary)))<=>(?[X]:((funny(X)|~quiet(X)))))&
(![X]:((creative(X)<~>old(X))<=>(~patient(X)&~kind(X))))&
(![X]:((~curious(X)<~>generous(X))=>(~rich(X)|humble(X))))&
(![X]:((~strong(X)<~>~patient(X))=>humble(X)))&
(![X]:(~brave(X)=>~rich(X)))&
(((~wise(mary)&curious(mary)))<=>(?[X]:((calm(X)<~>~tall(X)))))&
((?[X]:((~old(X)|~quiet(X))))<=>((~rich(lucy)&creative(lucy))))&
(![X]:((~humble(X)&wise(X))=>~generous(X)))&
(![X]:((~funny(X)&~kind(X))<=>(curious(X)|patient(X))))&
(![X]:((~wise(X)<~>calm(X))=>(~curious(X)|~brave(X))))&
(![X]:((~old(X)<~>~quiet(X))<=>(humble(X)&strong(X))))&
((~funny(paul)&~kind(paul)))&
(?[X]:((kind(X)<~>~wise(X))))&
(?[X]:(~calm(X))) | ~creative(lucy) | [
"p0",
"p3",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 4409077479700749794970260
% SZS output start Proof for 4409077479700749794970260
1. ! [X0] : ((rich(X0) & creative(X0)) <=> (strong(X0) | creative(X0))) [input p0]
4. ! [X0] : ((brave(X0) | ~rich(X0)) => (strong(X0) & ~tall(X0))) [input p3]
9. ! [X0] : (~brave(X0) => ~rich(X0)) [input p8]
19. ~creative(lucy) [input hypothesis]
23. ! [X0] : ((strong(X0) & ~tall(X0)) | (~brave(X0) & rich(X0))) [ennf transformation 4]
27. ! [X0] : (~rich(X0) | brave(X0)) [ennf transformation 9]
32. ! [X0] : (((rich(X0) & creative(X0)) | (~strong(X0) & ~creative(X0))) & ((strong(X0) | creative(X0)) | (~rich(X0) | ~creative(X0)))) [nnf transformation 1]
33. ! [X0] : (((rich(X0) & creative(X0)) | (~strong(X0) & ~creative(X0))) & (strong(X0) | creative(X0) | ~rich(X0) | ~creative(X0))) [flattening 32]
74. ~strong(X0) | creative(X0) [cnf transformation 33]
76. ~strong(X0) | rich(X0) [cnf transformation 33]
89. strong(X0) | rich(X0) [cnf transformation 23]
90. ~brave(X0) | strong(X0) [cnf transformation 23]
106. ~rich(X0) | brave(X0) [cnf transformation 27]
137. ~creative(lucy) [cnf transformation 19]
187. rich(X0) [subsumption resolution 89,76]
217. brave(X0) [subsumption resolution 106,187]
247. 24 <=> creative(lucy) [avatar definition]
248. ~creative(lucy) <- (~24) [avatar component clause 247]
271. ~24 [avatar split clause 137,247]
277. strong(X0) [resolution 90,217]
281. creative(X1) [resolution 277,74]
285. $false <- (~24) [resolution 281,248]
287. 24 [avatar contradiction clause 285]
288. $false [avatar sat refutation 271,287]
% SZS output end Proof for 4409077479700749794970260
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall or creative is old.
Everyone who is either kind or not quiet is either not wise or generous and vice versa.
Everyone who is both kind and not generous is not strong or rich and vice versa.
Everyone who is calm is both not curious and funny.
Everyone who is both not quiet and curious is both not happy and not patient.
Everyone who is both not brave and generous is both not kind and generous.
Everyone who is both creative and not wise is both strong and not quiet and vice versa.
Everyone who is not calm or not quiet is either curious or strong and vice versa.
If someone is either not rich or not humble then alice is either not quiet or funny and vice versa.
Everyone who is patient is both creative and not brave.
If paul is creative then someone is both funny and rich and vice versa.
Everyone who is both quiet and kind is generous or not generous and vice versa.
Everyone who is happy or strong is both not humble and curious.
If susan is both brave and strong then someone is both not kind and not strong.
Everyone who is patient or not funny is both strong and rich and vice versa.
If someone is not humble or not calm then alice is either not humble or old.
Someone is both not rich and not brave.
Someone is either not humble or not calm.
Someone is not curious.
Fred is either not generous or wise.
Someone is old.
Fred is both not brave and not rich.
Alice is not calm. | Fred is not strong. | entailment | (![X]:((tall(X)<~>creative(X))=>old(X)))&
(![X]:((kind(X)<~>~quiet(X))<=>(~wise(X)<~>generous(X))))&
(![X]:((kind(X)&~generous(X))<=>(~strong(X)|rich(X))))&
(![X]:(calm(X)=>(~curious(X)&funny(X))))&
(![X]:((~quiet(X)&curious(X))=>(~happy(X)&~patient(X))))&
(![X]:((~brave(X)&generous(X))=>(~kind(X)&generous(X))))&
(![X]:((creative(X)&~wise(X))<=>(strong(X)&~quiet(X))))&
(![X]:((~calm(X)|~quiet(X))<=>(curious(X)<~>strong(X))))&
((?[X]:((~rich(X)<~>~humble(X))))<=>((~quiet(alice)<~>funny(alice))))&
(![X]:(patient(X)=>(creative(X)&~brave(X))))&
((creative(paul))<=>(?[X]:((funny(X)&rich(X)))))&
(![X]:((quiet(X)&kind(X))<=>(generous(X)|~generous(X))))&
(![X]:((happy(X)|strong(X))=>(~humble(X)&curious(X))))&
(((brave(susan)&strong(susan)))=>(?[X]:((~kind(X)&~strong(X)))))&
(![X]:((patient(X)|~funny(X))<=>(strong(X)&rich(X))))&
((?[X]:((~humble(X)|~calm(X))))=>((~humble(alice)<~>old(alice))))&
(?[X]:((~rich(X)&~brave(X))))&
(?[X]:((~humble(X)<~>~calm(X))))&
(?[X]:(~curious(X)))&
((~generous(fred)<~>wise(fred)))&
(?[X]:(old(X)))&
((~brave(fred)&~rich(fred)))&
(~calm(alice)) | ~strong(fred) | [
"p3",
"p7",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 4203497025485288104695681
% SZS output start Proof for 4203497025485288104695681
4. ! [X0] : (calm(X0) => (funny(X0) & ~curious(X0))) [input p3]
8. ! [X0] : ((~quiet(X0) | ~calm(X0)) <=> (curious(X0) <~> strong(X0))) [input p7]
13. ! [X0] : ((strong(X0) | happy(X0)) => (curious(X0) & ~humble(X0))) [input p12]
24. strong(fred) [input hypothesis]
26. ! [X0] : (strong(X0) => (curious(X0) & ~humble(X0))) [pure predicate removal 13]
28. ! [X0] : ((funny(X0) & ~curious(X0)) | ~calm(X0)) [ennf transformation 4]
34. ! [X0] : ((curious(X0) & ~humble(X0)) | ~strong(X0)) [ennf transformation 26]
44. ! [X0] : (((~quiet(X0) | ~calm(X0)) | ((curious(X0) | ~strong(X0)) & (strong(X0) | ~curious(X0)))) & (((~strong(X0) | ~curious(X0)) & (strong(X0) | curious(X0))) | (quiet(X0) & calm(X0)))) [nnf transformation 8]
45. ! [X0] : ((~quiet(X0) | ~calm(X0) | ((curious(X0) | ~strong(X0)) & (strong(X0) | ~curious(X0)))) & (((~strong(X0) | ~curious(X0)) & (strong(X0) | curious(X0))) | (quiet(X0) & calm(X0)))) [flattening 44]
86. ~curious(X0) | ~calm(X0) [cnf transformation 28]
97. ~strong(X0) | ~curious(X0) | calm(X0) [cnf transformation 45]
120. curious(X0) | ~strong(X0) [cnf transformation 34]
143. strong(fred) [cnf transformation 24]
145. ~strong(X0) | ~curious(X0) [subsumption resolution 97,86]
196. ~strong(X0) [subsumption resolution 120,145]
237. $false [subsumption resolution 143,196]
% SZS output end Proof for 4203497025485288104695681
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 alice is not old or strong then someone is not generous or not funny.
If susan is not old then someone is both not generous and creative.
If lucy is happy then someone is not curious and vice versa.
Everyone who is both generous and old is either rich or not calm and vice versa.
If someone is quiet or not calm then paul is not old.
If someone is not calm or not happy then susan is either not rich or creative and vice versa.
Everyone who is either creative or not curious is both not rich and happy and vice versa.
Everyone who is kind is either generous or not quiet.
Everyone who is patient or wise is tall or not rich and vice versa.
Everyone who is not generous is patient and vice versa.
Everyone who is generous is either calm or kind and vice versa.
Everyone who is calm or not kind is both not generous and generous.
Everyone who is not brave is either not calm or brave and vice versa.
If someone is either not rich or generous then someone is either quiet or brave.
Everyone who is old is both not happy and tall.
Someone is not happy.
Someone is not humble.
Someone is either not creative or not curious.
Someone is either humble or not old.
Someone is either not humble or happy.
Someone is not strong. | Susan is brave. | neutral | (((~old(alice)|strong(alice)))=>(?[X]:((~generous(X)|~funny(X)))))&
((~old(susan))=>(?[X]:((~generous(X)&creative(X)))))&
((happy(lucy))<=>(?[X]:(~curious(X))))&
(![X]:((generous(X)&old(X))<=>(rich(X)<~>~calm(X))))&
((?[X]:((quiet(X)|~calm(X))))=>(~old(paul)))&
((?[X]:((~calm(X)|~happy(X))))<=>((~rich(susan)<~>creative(susan))))&
(![X]:((creative(X)<~>~curious(X))<=>(~rich(X)&happy(X))))&
(![X]:(kind(X)=>(generous(X)<~>~quiet(X))))&
(![X]:((patient(X)|wise(X))<=>(tall(X)|~rich(X))))&
(![X]:(~generous(X)<=>patient(X)))&
(![X]:(generous(X)<=>(calm(X)<~>kind(X))))&
(![X]:((calm(X)|~kind(X))=>(~generous(X)&generous(X))))&
(![X]:(~brave(X)<=>(~calm(X)<~>brave(X))))&
((?[X]:((~rich(X)<~>generous(X))))=>(?[X]:((quiet(X)<~>brave(X)))))&
(![X]:(old(X)=>(~happy(X)&tall(X))))&
(?[X]:(~happy(X)))&
(?[X]:(~humble(X)))&
(?[X]:((~creative(X)<~>~curious(X))))&
(?[X]:((humble(X)<~>~old(X))))&
(?[X]:((~humble(X)<~>happy(X))))&
(?[X]:(~strong(X))) | brave(susan) | [] | null | 0 |
If someone is old then someone is either curious or not patient. Everyone who is not calm or generous is not humble or not wise and vice versa. Everyone who is both rich and not curious is old or creative and vice versa. If someone is not old then fred is both old and patient. Everyone who is both not tall and not happy is not tall or strong. If fred is either wise or generous then someone is either old or calm and vice versa. If someone is not wise or not creative then someone is both happy and not old. If someone is not strong or not funny then fred is brave or not rich. Everyone who is both calm and not tall is funny and vice versa. If someone is either happy or tall then someone is both curious and not calm. If john is both not kind and humble then john is patient or not rich. Everyone who is either not generous or strong is not brave or quiet and vice versa. Everyone who is either generous or strong is not old or not tall. If someone is calm or not rich then someone is quiet or generous and vice versa. Everyone who is either calm or not brave is both old and not curious and vice versa. Everyone who is not patient is either not humble or not patient and vice versa. Susan is happy. Someone is both not happy and not curious. Someone is not happy. John is either patient or not old. Someone is either not tall or creative. Someone is creative or not calm. Someone is kind or not funny. Lucy is either calm or not brave. | Fred is brave. | entailment | ((?[X]:(old(X)))=>(?[X]:((curious(X)<~>~patient(X)))))&
(![X]:((~calm(X)|generous(X))<=>(~humble(X)|~wise(X))))&
(![X]:((rich(X)&~curious(X))<=>(old(X)|creative(X))))&
((?[X]:(~old(X)))=>((old(fred)&patient(fred))))&
(![X]:((~tall(X)&~happy(X))=>(~tall(X)|strong(X))))&
(((wise(fred)<~>generous(fred)))<=>(?[X]:((old(X)<~>calm(X)))))&
((?[X]:((~wise(X)|~creative(X))))=>(?[X]:((happy(X)&~old(X)))))&
((?[X]:((~strong(X)|~funny(X))))=>((brave(fred)|~rich(fred))))&
(![X]:((calm(X)&~tall(X))<=>funny(X)))&
((?[X]:((happy(X)<~>tall(X))))=>(?[X]:((curious(X)&~calm(X)))))&
(((~kind(john)&humble(john)))=>((patient(john)|~rich(john))))&
(![X]:((~generous(X)<~>strong(X))<=>(~brave(X)|quiet(X))))&
(![X]:((generous(X)<~>strong(X))=>(~old(X)|~tall(X))))&
((?[X]:((calm(X)|~rich(X))))<=>(?[X]:((quiet(X)|generous(X)))))&
(![X]:((calm(X)<~>~brave(X))<=>(old(X)&~curious(X))))&
(![X]:(~patient(X)<=>(~humble(X)<~>~patient(X))))&
(happy(susan))&
(?[X]:((~happy(X)&~curious(X))))&
(?[X]:(~happy(X)))&
((patient(john)<~>~old(john)))&
(?[X]:((~tall(X)<~>creative(X))))&
(?[X]:((creative(X)|~calm(X))))&
(?[X]:((kind(X)|~funny(X))))&
((calm(lucy)<~>~brave(lucy))) | brave(fred) | [
"p2",
"p3",
"p7",
"p8",
"p9",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 673296688214745942898568
% SZS output start Proof for 673296688214745942898568
3. ! [X0] : ((~curious(X0) & rich(X0)) <=> (creative(X0) | old(X0))) [input p2]
4. ? [X0] : ~old(X0) => (patient(fred) & old(fred)) [input p3]
8. ? [X0] : (~funny(X0) | ~strong(X0)) => (~rich(fred) | brave(fred)) [input p7]
9. ! [X0] : ((~tall(X0) & calm(X0)) <=> funny(X0)) [input p8]
10. ? [X0] : (happy(X0) <~> tall(X0)) => ? [X0] : (~calm(X0) & curious(X0)) [input p9]
17. happy(susan) [input p16]
25. ~brave(fred) [input hypothesis]
28. ? [X0] : (happy(X0) <~> tall(X0)) => ? [X1] : (~calm(X1) & curious(X1)) [rectify 10]
32. ! [X0] : (funny(X0) => (~tall(X0) & calm(X0))) [unused predicate definition removal 9]
34. (patient(fred) & old(fred)) | ! [X0] : old(X0) [ennf transformation 4]
38. (~rich(fred) | brave(fred)) | ! [X0] : (funny(X0) & strong(X0)) [ennf transformation 8]
39. ~rich(fred) | brave(fred) | ! [X0] : (funny(X0) & strong(X0)) [flattening 38]
40. ! [X0] : ((~tall(X0) & calm(X0)) | ~funny(X0)) [ennf transformation 32]
41. ? [X1] : (~calm(X1) & curious(X1)) | ! [X0] : (happy(X0) <=> tall(X0)) [ennf transformation 28]
50. ! [X0] : (((~curious(X0) & rich(X0)) | (~creative(X0) & ~old(X0))) & ((creative(X0) | old(X0)) | (curious(X0) | ~rich(X0)))) [nnf transformation 3]
51. ! [X0] : (((~curious(X0) & rich(X0)) | (~creative(X0) & ~old(X0))) & (creative(X0) | old(X0) | curious(X0) | ~rich(X0))) [flattening 50]
59. ? [X1] : (~calm(X1) & curious(X1)) | ! [X0] : ((happy(X0) | ~tall(X0)) & (tall(X0) | ~happy(X0))) [nnf transformation 41]
60. ? [X0] : (~calm(X0) & curious(X0)) | ! [X1] : ((happy(X1) | ~tall(X1)) & (tall(X1) | ~happy(X1))) [rectify 59]
61. ? [X0] : (~calm(X0) & curious(X0)) => (~calm(sK3) & curious(sK3)) [choice axiom]
62. (~calm(sK3) & curious(sK3)) | ! [X1] : ((happy(X1) | ~tall(X1)) & (tall(X1) | ~happy(X1))) [skolemisation 60,61]
92. ~old(X0) | rich(X0) [cnf transformation 51]
96. old(fred) | old(X0) [cnf transformation 34]
112. ~rich(fred) | brave(fred) | funny(X0) [cnf transformation 39]
113. ~funny(X0) | calm(X0) [cnf transformation 40]
114. ~funny(X0) | ~tall(X0) [cnf transformation 40]
117. ~calm(sK3) | tall(X1) | ~happy(X1) [cnf transformation 62]
141. happy(susan) [cnf transformation 17]
152. ~brave(fred) [cnf transformation 25]
169. 4 <=> ! [X0] : old(X0) [avatar definition]
170. old(X0) <- (4) [avatar component clause 169]
177. 6 <=> old(fred) [avatar definition]
178. ~old(fred) <- (~6) [avatar component clause 177]
179. old(fred) <- (6) [avatar component clause 177]
180. 4 | 6 [avatar split clause 96,177,169]
230. 17 <=> ! [X0] : funny(X0) [avatar definition]
231. funny(X0) <- (17) [avatar component clause 230]
233. 18 <=> brave(fred) [avatar definition]
237. 19 <=> rich(fred) [avatar definition]
240. 17 | 18 | ~19 [avatar split clause 112,237,233,230]
249. 22 <=> calm(sK3) [avatar definition]
251. ~calm(sK3) <- (~22) [avatar component clause 249]
254. 23 <=> ! [X1] : (tall(X1) | ~happy(X1)) [avatar definition]
255. ~happy(X1) | tall(X1) <- (23) [avatar component clause 254]
256. 23 | ~22 [avatar split clause 117,249,254]
337. ~18 [avatar split clause 152,233]
344. rich(fred) <- (6) [resolution 92,179]
347. 19 | ~6 [avatar split clause 344,177,237]
361. $false <- (4, ~6) [subsumption resolution 178,170]
362. ~4 | 6 [avatar contradiction clause 361]
365. ~tall(X0) <- (17) [resolution 231,114]
366. calm(X1) <- (17) [resolution 231,113]
369. tall(susan) <- (23) [resolution 255,141]
371. $false <- (17, 23) [subsumption resolution 369,365]
372. ~17 | ~23 [avatar contradiction clause 371]
375. $false <- (17, ~22) [subsumption resolution 251,366]
376. ~17 | 22 [avatar contradiction clause 375]
377. $false [avatar sat refutation 180,240,256,337,347,362,372,376]
% SZS output end Proof for 673296688214745942898568
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble and not rich then mary is both not happy and not tall.
Everyone who is both not patient and not wise is both brave and quiet.
Everyone who is tall is both quiet and rich.
Everyone who is both patient and not quiet is both not rich and curious.
Everyone who is either not calm or not humble is either rich or not curious.
If someone is either curious or generous then someone is not curious.
If someone is funny then paul is not kind and vice versa.
Everyone who is both rich and not strong is brave.
Everyone who is either calm or funny is rich.
Everyone who is both wise and 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.
John is kind or creative.
Someone is funny.
Someone is both not wise and not humble.
Someone is wise or not quiet.
Paul is not humble.
Lucy is not kind.
Someone is generous.
Fred is not happy. | Susan is curious. | neutral | ((?[X]:((humble(X)&~rich(X))))=>((~happy(mary)&~tall(mary))))&
(![X]:((~patient(X)&~wise(X))=>(brave(X)&quiet(X))))&
(![X]:(tall(X)=>(quiet(X)&rich(X))))&
(![X]:((patient(X)&~quiet(X))=>(~rich(X)&curious(X))))&
(![X]:((~calm(X)<~>~humble(X))=>(rich(X)<~>~curious(X))))&
((?[X]:((curious(X)<~>generous(X))))=>(?[X]:(~curious(X))))&
((?[X]:(funny(X)))<=>(~kind(paul)))&
(![X]:((rich(X)&~strong(X))=>brave(X)))&
(![X]:((calm(X)<~>funny(X))=>rich(X)))&
(![X]:((wise(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)))))&
((kind(john)|creative(john)))&
(?[X]:(funny(X)))&
(?[X]:((~wise(X)&~humble(X))))&
(?[X]:((wise(X)|~quiet(X))))&
(~humble(paul))&
(~kind(lucy))&
(?[X]:(generous(X)))&
(~happy(fred)) | curious(susan) | [] | null | 0 |
Everyone who is both calm and funny is strong or not curious and vice versa.
If someone is not rich or calm then susan is curious or not curious.
If someone is either brave or quiet then lucy is either strong or tall and vice versa.
If someone is brave then paul is not happy or strong and vice versa.
If alice is generous or not kind then someone is happy or creative and vice versa.
Everyone who is either funny or not calm is humble or curious.
Everyone who is either strong or not quiet is both not quiet and happy.
Everyone who is not funny is either quiet or not wise.
If someone is either not funny or brave then paul is generous or kind and vice versa.
Everyone who is rich or not calm is patient.
Everyone who is both not generous and kind is either not funny or kind.
If someone is both creative and quiet then paul is not happy or creative and vice versa.
If john is rich or patient then mary is either not humble or funny.
Everyone who is both funny and not funny is not humble or happy and vice versa.
If someone is either curious or wise then lucy is not tall and vice versa.
Everyone who is either not tall or not humble is either humble or not strong and vice versa.
Someone is not calm.
Paul is either not kind or tall.
Someone is rich or not quiet.
Fred is either not curious or humble.
Someone is not patient.
Someone is humble.
Lucy is not wise or funny. | Susan is strong. | neutral | (![X]:((calm(X)&funny(X))<=>(strong(X)|~curious(X))))&
((?[X]:((~rich(X)|calm(X))))=>((curious(susan)|~curious(susan))))&
((?[X]:((brave(X)<~>quiet(X))))<=>((strong(lucy)<~>tall(lucy))))&
((?[X]:(brave(X)))<=>((~happy(paul)|strong(paul))))&
(((generous(alice)|~kind(alice)))<=>(?[X]:((happy(X)|creative(X)))))&
(![X]:((funny(X)<~>~calm(X))=>(humble(X)|curious(X))))&
(![X]:((strong(X)<~>~quiet(X))=>(~quiet(X)&happy(X))))&
(![X]:(~funny(X)=>(quiet(X)<~>~wise(X))))&
((?[X]:((~funny(X)<~>brave(X))))<=>((generous(paul)|kind(paul))))&
(![X]:((rich(X)|~calm(X))=>patient(X)))&
(![X]:((~generous(X)&kind(X))=>(~funny(X)<~>kind(X))))&
((?[X]:((creative(X)&quiet(X))))<=>((~happy(paul)|creative(paul))))&
(((rich(john)|patient(john)))=>((~humble(mary)<~>funny(mary))))&
(![X]:((funny(X)&~funny(X))<=>(~humble(X)|happy(X))))&
((?[X]:((curious(X)<~>wise(X))))<=>(~tall(lucy)))&
(![X]:((~tall(X)<~>~humble(X))<=>(humble(X)<~>~strong(X))))&
(?[X]:(~calm(X)))&
((~kind(paul)<~>tall(paul)))&
(?[X]:((rich(X)|~quiet(X))))&
((~curious(fred)<~>humble(fred)))&
(?[X]:(~patient(X)))&
(?[X]:(humble(X)))&
((~wise(lucy)|funny(lucy))) | strong(susan) | [] | null | 0 |
Everyone who is not rich is both rich and not generous and vice versa. If susan is humble then lucy is either not curious or not old. If someone is both tall and not generous then susan is not funny. Everyone who is either strong or brave is happy or creative. Everyone who is both not generous and generous is not happy or not patient and vice versa. If paul is either happy or tall then someone is both not happy and curious. Everyone who is both not brave and creative is rich. Everyone who is both curious and not rich is humble or funny. Everyone who is strong or not creative is humble. Everyone who is not creative or generous is calm and vice versa. Everyone who is calm or creative is quiet and vice versa. Everyone who is either humble or happy is strong. If mary is either kind or not quiet then fred is strong and vice versa. If someone is either not quiet or not tall then fred is strong and vice versa. Everyone who is brave or not calm is not generous and vice versa. Paul is either generous or kind. Paul is curious. John is both funny and curious. Someone is either calm or kind. Alice is both curious and quiet. Someone is not creative or patient. | Fred is generous. | entailment | (![X]:(~rich(X)<=>(rich(X)&~generous(X))))&
((humble(susan))=>((~curious(lucy)<~>~old(lucy))))&
((?[X]:((tall(X)&~generous(X))))=>(~funny(susan)))&
(![X]:((strong(X)<~>brave(X))=>(happy(X)|creative(X))))&
(![X]:((~generous(X)&generous(X))<=>(~happy(X)|~patient(X))))&
(((happy(paul)<~>tall(paul)))=>(?[X]:((~happy(X)&curious(X)))))&
(![X]:((~brave(X)&creative(X))=>rich(X)))&
(![X]:((curious(X)&~rich(X))=>(humble(X)|funny(X))))&
(![X]:((strong(X)|~creative(X))=>humble(X)))&
(![X]:((~creative(X)|generous(X))<=>calm(X)))&
(![X]:((calm(X)|creative(X))<=>quiet(X)))&
(![X]:((humble(X)<~>happy(X))=>strong(X)))&
(((kind(mary)<~>~quiet(mary)))<=>(strong(fred)))&
((?[X]:((~quiet(X)<~>~tall(X))))<=>(strong(fred)))&
(![X]:((brave(X)|~calm(X))<=>~generous(X)))&
((generous(paul)<~>kind(paul)))&
(curious(paul))&
((funny(john)&curious(john)))&
(?[X]:((calm(X)<~>kind(X))))&
((curious(alice)&quiet(alice)))&
(?[X]:((~creative(X)|patient(X)))) | generous(fred) | [
"p0",
"hypothesis"
] | % SZS status Unsatisfiable for 4746903920327740433125844
% SZS output start Proof for 4746903920327740433125844
1. ! [X0] : (~rich(X0) <=> (~generous(X0) & rich(X0))) [input p0]
22. ~generous(fred) [input hypothesis]
34. ! [X0] : ((~rich(X0) | (generous(X0) | ~rich(X0))) & ((~generous(X0) & rich(X0)) | rich(X0))) [nnf transformation 1]
35. ! [X0] : ((~rich(X0) | generous(X0) | ~rich(X0)) & ((~generous(X0) & rich(X0)) | rich(X0))) [flattening 34]
61. rich(X0) | rich(X0) [cnf transformation 35]
63. ~rich(X0) | generous(X0) | ~rich(X0) [cnf transformation 35]
111. ~generous(fred) [cnf transformation 22]
112. rich(X0) [duplicate literal removal 61]
113. ~rich(X0) | generous(X0) [duplicate literal removal 63]
219. generous(X0) [resolution 113,112]
220. $false [resolution 219,111]
% SZS output end Proof for 4746903920327740433125844
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 lucy is either rich or not rich then someone is both not funny and not brave and vice versa.
If alice is either calm or not creative then susan is humble or not happy.
If lucy is either kind or not funny then fred is not wise or not tall.
Everyone who is creative or not patient is either generous or brave.
If someone is not happy or tall then lucy is not kind and vice versa.
Everyone who is both calm and wise is kind or patient and vice versa.
Everyone who is both not brave and not curious is not tall or not strong and vice versa.
Everyone who is not generous or not brave is generous or not funny.
Everyone who is humble or curious is not creative and vice versa.
If someone is not humble then susan is both humble and funny and vice versa.
Everyone who is not brave is not curious and vice versa.
Everyone who is wise is not generous.
If fred is not kind or not rich then alice is either humble or not patient.
Someone is quiet.
Alice is either not quiet or not curious.
Someone is kind or humble.
Alice is either not tall or not calm.
Someone is both strong and creative.
Someone is either happy or not funny.
Alice is both humble and strong. | Alice is happy. | neutral | (((rich(lucy)<~>~rich(lucy)))<=>(?[X]:((~funny(X)&~brave(X)))))&
(((calm(alice)<~>~creative(alice)))=>((humble(susan)|~happy(susan))))&
(((kind(lucy)<~>~funny(lucy)))=>((~wise(fred)|~tall(fred))))&
(![X]:((creative(X)|~patient(X))=>(generous(X)<~>brave(X))))&
((?[X]:((~happy(X)|tall(X))))<=>(~kind(lucy)))&
(![X]:((calm(X)&wise(X))<=>(kind(X)|patient(X))))&
(![X]:((~brave(X)&~curious(X))<=>(~tall(X)|~strong(X))))&
(![X]:((~generous(X)|~brave(X))=>(generous(X)|~funny(X))))&
(![X]:((humble(X)|curious(X))<=>~creative(X)))&
((?[X]:(~humble(X)))<=>((humble(susan)&funny(susan))))&
(![X]:(~brave(X)<=>~curious(X)))&
(![X]:(wise(X)=>~generous(X)))&
(((~kind(fred)|~rich(fred)))=>((humble(alice)<~>~patient(alice))))&
(?[X]:(quiet(X)))&
((~quiet(alice)<~>~curious(alice)))&
(?[X]:((kind(X)|humble(X))))&
((~tall(alice)<~>~calm(alice)))&
(?[X]:((strong(X)&creative(X))))&
(?[X]:((happy(X)<~>~funny(X))))&
((humble(alice)&strong(alice))) | happy(alice) | [] | null | 0 |
If someone is either not creative or wise then someone is curious and vice versa.
Everyone who is both kind and not kind is rich and vice versa.
If fred is both not quiet and not creative then someone is both not kind and not brave and vice versa.
Everyone who is not creative or strong is not quiet.
If alice is not quiet or not tall then lucy is humble and vice versa.
Everyone who is either not wise or patient is both not rich and kind.
Everyone who is not patient is both funny and brave and vice versa.
If susan is either old or not strong then someone is old.
If someone is not kind or calm then someone is both not rich and funny and vice versa.
If someone is not calm then someone is either not strong or not kind.
If someone is not kind or not curious then someone is kind or not old.
Everyone who is humble is not quiet or not funny and vice versa.
If alice is both not generous and generous then susan is either not patient or kind and vice versa.
Everyone who is patient is both not creative and curious.
If someone is both quiet and creative then susan is both patient and not kind.
If lucy is both not old and not patient then someone is either creative or not wise and vice versa.
Someone is not funny or not old.
John is both not happy and patient.
Lucy is both not kind and not curious.
Susan is both not strong and not happy.
Someone is not strong.
Alice is either brave or not funny.
Someone is tall or not tall. | Susan is not tall. | neutral | ((?[X]:((~creative(X)<~>wise(X))))<=>(?[X]:(curious(X))))&
(![X]:((kind(X)&~kind(X))<=>rich(X)))&
(((~quiet(fred)&~creative(fred)))<=>(?[X]:((~kind(X)&~brave(X)))))&
(![X]:((~creative(X)|strong(X))=>~quiet(X)))&
(((~quiet(alice)|~tall(alice)))<=>(humble(lucy)))&
(![X]:((~wise(X)<~>patient(X))=>(~rich(X)&kind(X))))&
(![X]:(~patient(X)<=>(funny(X)&brave(X))))&
(((old(susan)<~>~strong(susan)))=>(?[X]:(old(X))))&
((?[X]:((~kind(X)|calm(X))))<=>(?[X]:((~rich(X)&funny(X)))))&
((?[X]:(~calm(X)))=>(?[X]:((~strong(X)<~>~kind(X)))))&
((?[X]:((~kind(X)|~curious(X))))=>(?[X]:((kind(X)|~old(X)))))&
(![X]:(humble(X)<=>(~quiet(X)|~funny(X))))&
(((~generous(alice)&generous(alice)))<=>((~patient(susan)<~>kind(susan))))&
(![X]:(patient(X)=>(~creative(X)&curious(X))))&
((?[X]:((quiet(X)&creative(X))))=>((patient(susan)&~kind(susan))))&
(((~old(lucy)&~patient(lucy)))<=>(?[X]:((creative(X)<~>~wise(X)))))&
(?[X]:((~funny(X)|~old(X))))&
((~happy(john)&patient(john)))&
((~kind(lucy)&~curious(lucy)))&
((~strong(susan)&~happy(susan)))&
(?[X]:(~strong(X)))&
((brave(alice)<~>~funny(alice)))&
(?[X]:((tall(X)|~tall(X)))) | ~tall(susan) | [] | null | 0 |
If alice is kind then someone is not creative.
Everyone who is either not patient or funny is brave or creative and vice versa.
Everyone who is patient is both wise and patient.
Everyone who is either happy or brave is both not generous and rich and vice versa.
If lucy is not tall then lucy is humble and vice versa.
Everyone who is either not strong or not creative is not creative and vice versa.
If paul is not strong then someone is quiet.
Everyone who is not curious is not strong and vice versa.
Everyone who is strong is both creative and not quiet and vice versa.
Everyone who is both not curious and strong is either strong or rich.
Everyone who is both quiet and not calm is both curious and not strong.
If susan is either not quiet or tall then someone is either brave or not strong.
Everyone who is not patient is quiet.
If someone is either not strong or brave then someone is either not strong or calm and vice versa.
If someone is either wise or quiet then someone is not happy or not creative and vice versa.
Someone is both not old and not kind.
Someone is rich.
Lucy is generous or creative.
Alice is not tall.
Susan is strong or happy.
Someone is not tall or not rich.
John is rich. | Paul is tall. | neutral | ((kind(alice))=>(?[X]:(~creative(X))))&
(![X]:((~patient(X)<~>funny(X))<=>(brave(X)|creative(X))))&
(![X]:(patient(X)=>(wise(X)&patient(X))))&
(![X]:((happy(X)<~>brave(X))<=>(~generous(X)&rich(X))))&
((~tall(lucy))<=>(humble(lucy)))&
(![X]:((~strong(X)<~>~creative(X))<=>~creative(X)))&
((~strong(paul))=>(?[X]:(quiet(X))))&
(![X]:(~curious(X)<=>~strong(X)))&
(![X]:(strong(X)<=>(creative(X)&~quiet(X))))&
(![X]:((~curious(X)&strong(X))=>(strong(X)<~>rich(X))))&
(![X]:((quiet(X)&~calm(X))=>(curious(X)&~strong(X))))&
(((~quiet(susan)<~>tall(susan)))=>(?[X]:((brave(X)<~>~strong(X)))))&
(![X]:(~patient(X)=>quiet(X)))&
((?[X]:((~strong(X)<~>brave(X))))<=>(?[X]:((~strong(X)<~>calm(X)))))&
((?[X]:((wise(X)<~>quiet(X))))<=>(?[X]:((~happy(X)|~creative(X)))))&
(?[X]:((~old(X)&~kind(X))))&
(?[X]:(rich(X)))&
((generous(lucy)|creative(lucy)))&
(~tall(alice))&
((strong(susan)|happy(susan)))&
(?[X]:((~tall(X)|~rich(X))))&
(rich(john)) | tall(paul) | [] | null | 0 |
If someone is both not tall and creative then someone is either not tall or quiet and vice versa.
If someone is either not humble or kind then someone is both calm and creative.
If someone is either not quiet or not calm then someone is either not quiet or old and vice versa.
If fred is not kind or patient then someone is curious and vice versa.
If susan is not rich then someone is not rich and vice versa.
Everyone who is funny is not humble or wise and vice versa.
Everyone who is creative or kind is both quiet and strong and vice versa.
Everyone who is both old and not humble is not wise and vice versa.
If someone is both creative and not kind then paul is old or brave and vice versa.
If fred is both not rich and old then paul is both old and funny.
Everyone who is both not patient and strong is both quiet and not wise.
If fred is curious or not strong then lucy is both rich and not creative and vice versa.
Everyone who is both not wise and curious is either not quiet or not creative and vice versa.
Everyone who is either not funny or not calm is both rich and not creative.
If john is both not creative and patient then john is not strong and vice versa.
Everyone who is not generous is wise and vice versa.
John is not happy or generous.
Mary is either not kind or quiet.
John is patient.
Someone is calm or creative.
Someone is not curious or quiet.
Someone is both not happy and not calm.
Someone is creative or generous.
Someone is both strong and not old. | Lucy is kind. | neutral | ((?[X]:((~tall(X)&creative(X))))<=>(?[X]:((~tall(X)<~>quiet(X)))))&
((?[X]:((~humble(X)<~>kind(X))))=>(?[X]:((calm(X)&creative(X)))))&
((?[X]:((~quiet(X)<~>~calm(X))))<=>(?[X]:((~quiet(X)<~>old(X)))))&
(((~kind(fred)|patient(fred)))<=>(?[X]:(curious(X))))&
((~rich(susan))<=>(?[X]:(~rich(X))))&
(![X]:(funny(X)<=>(~humble(X)|wise(X))))&
(![X]:((creative(X)|kind(X))<=>(quiet(X)&strong(X))))&
(![X]:((old(X)&~humble(X))<=>~wise(X)))&
((?[X]:((creative(X)&~kind(X))))<=>((old(paul)|brave(paul))))&
(((~rich(fred)&old(fred)))=>((old(paul)&funny(paul))))&
(![X]:((~patient(X)&strong(X))=>(quiet(X)&~wise(X))))&
(((curious(fred)|~strong(fred)))<=>((rich(lucy)&~creative(lucy))))&
(![X]:((~wise(X)&curious(X))<=>(~quiet(X)<~>~creative(X))))&
(![X]:((~funny(X)<~>~calm(X))=>(rich(X)&~creative(X))))&
(((~creative(john)&patient(john)))<=>(~strong(john)))&
(![X]:(~generous(X)<=>wise(X)))&
((~happy(john)|generous(john)))&
((~kind(mary)<~>quiet(mary)))&
(patient(john))&
(?[X]:((calm(X)|creative(X))))&
(?[X]:((~curious(X)|quiet(X))))&
(?[X]:((~happy(X)&~calm(X))))&
(?[X]:((creative(X)|generous(X))))&
(?[X]:((strong(X)&~old(X)))) | kind(lucy) | [] | null | 0 |
If john is creative or not kind then john is wise or not patient and vice versa.
Everyone who is not curious is either not brave or tall and vice versa.
If someone is rich then alice is either not creative or not humble and vice versa.
Everyone who is not tall or not curious is either not strong or not calm.
Everyone who is not wise is generous.
Everyone who is both not rich and rich is humble and vice versa.
Everyone who is both not curious and not quiet is not calm and vice versa.
If someone is both happy and creative then susan is not funny or not curious.
If paul is old then someone is both strong and kind.
If alice is both not kind and not creative then someone is not old or not wise.
Everyone who is quiet is either not old or not humble and vice versa.
Everyone who is both not happy and not kind is either not calm or not brave and vice versa.
If mary is either humble or not kind then lucy is not strong or curious and vice versa.
Everyone who is both not funny and not calm is rich and vice versa.
Everyone who is either not funny or generous is not strong.
If someone is calm or not quiet then someone is not brave or curious and vice versa.
John is either not creative or generous.
Someone is quiet or not strong.
Mary is either tall or not patient.
Fred is both patient and not funny.
Someone is either not rich or brave.
Lucy is strong or not curious.
Someone is both wise and not rich.
Susan is not old or kind. | Paul is old. | neutral | (((creative(john)|~kind(john)))<=>((wise(john)|~patient(john))))&
(![X]:(~curious(X)<=>(~brave(X)<~>tall(X))))&
((?[X]:(rich(X)))<=>((~creative(alice)<~>~humble(alice))))&
(![X]:((~tall(X)|~curious(X))=>(~strong(X)<~>~calm(X))))&
(![X]:(~wise(X)=>generous(X)))&
(![X]:((~rich(X)&rich(X))<=>humble(X)))&
(![X]:((~curious(X)&~quiet(X))<=>~calm(X)))&
((?[X]:((happy(X)&creative(X))))=>((~funny(susan)|~curious(susan))))&
((old(paul))=>(?[X]:((strong(X)&kind(X)))))&
(((~kind(alice)&~creative(alice)))=>(?[X]:((~old(X)|~wise(X)))))&
(![X]:(quiet(X)<=>(~old(X)<~>~humble(X))))&
(![X]:((~happy(X)&~kind(X))<=>(~calm(X)<~>~brave(X))))&
(((humble(mary)<~>~kind(mary)))<=>((~strong(lucy)|curious(lucy))))&
(![X]:((~funny(X)&~calm(X))<=>rich(X)))&
(![X]:((~funny(X)<~>generous(X))=>~strong(X)))&
((?[X]:((calm(X)|~quiet(X))))<=>(?[X]:((~brave(X)|curious(X)))))&
((~creative(john)<~>generous(john)))&
(?[X]:((quiet(X)|~strong(X))))&
((tall(mary)<~>~patient(mary)))&
((patient(fred)&~funny(fred)))&
(?[X]:((~rich(X)<~>brave(X))))&
((strong(lucy)|~curious(lucy)))&
(?[X]:((wise(X)&~rich(X))))&
((~old(susan)|kind(susan))) | old(paul) | [] | null | 0 |
Everyone who is either not kind or not happy is not strong and vice versa. If someone is both brave and creative then someone is brave or wise and vice versa. Everyone who is funny is both funny and not creative and vice versa. Everyone who is both funny and creative is either calm or strong and vice versa. If mary is not creative then john is both not calm and humble. If fred is calm then someone is either old or kind. If paul is both funny and not strong then alice is not creative or rich. Everyone who is both calm and kind is either tall or not funny. If john is strong then someone is either not kind or not patient. Everyone who is humble or not humble is funny. Everyone who is either not brave or not wise is both tall and not happy. Everyone who is generous is both not tall and not funny. If someone is either not tall or not rich then someone is curious and vice versa. If someone is either quiet or not funny then fred is wise or not brave. If someone is happy or quiet then someone is not brave. Everyone who is both tall and not rich is both not humble and curious and vice versa. Fred is not happy or not rich. Fred is both patient and not old. Someone is both not kind and not humble. John is either calm or not wise. Someone is wise or not tall. Someone is both not kind and not calm. | Alice is not brave. | entailment | (![X]:((~kind(X)<~>~happy(X))<=>~strong(X)))&
((?[X]:((brave(X)&creative(X))))<=>(?[X]:((brave(X)|wise(X)))))&
(![X]:(funny(X)<=>(funny(X)&~creative(X))))&
(![X]:((funny(X)&creative(X))<=>(calm(X)<~>strong(X))))&
((~creative(mary))=>((~calm(john)&humble(john))))&
((calm(fred))=>(?[X]:((old(X)<~>kind(X)))))&
(((funny(paul)&~strong(paul)))=>((~creative(alice)|rich(alice))))&
(![X]:((calm(X)&kind(X))=>(tall(X)<~>~funny(X))))&
((strong(john))=>(?[X]:((~kind(X)<~>~patient(X)))))&
(![X]:((humble(X)|~humble(X))=>funny(X)))&
(![X]:((~brave(X)<~>~wise(X))=>(tall(X)&~happy(X))))&
(![X]:(generous(X)=>(~tall(X)&~funny(X))))&
((?[X]:((~tall(X)<~>~rich(X))))<=>(?[X]:(curious(X))))&
((?[X]:((quiet(X)<~>~funny(X))))=>((wise(fred)|~brave(fred))))&
((?[X]:((happy(X)|quiet(X))))=>(?[X]:(~brave(X))))&
(![X]:((tall(X)&~rich(X))<=>(~humble(X)&curious(X))))&
((~happy(fred)|~rich(fred)))&
((patient(fred)&~old(fred)))&
(?[X]:((~kind(X)&~humble(X))))&
((calm(john)<~>~wise(john)))&
(?[X]:((wise(X)|~tall(X))))&
(?[X]:((~kind(X)&~calm(X)))) | ~brave(alice) | [
"p1",
"p2",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 897625903930041003590050
% SZS output start Proof for 897625903930041003590050
2. ? [X0] : (creative(X0) & brave(X0)) <=> ? [X0] : (wise(X0) | brave(X0)) [input p1]
3. ! [X0] : (funny(X0) <=> (~creative(X0) & funny(X0))) [input p2]
10. ! [X0] : ((~humble(X0) | humble(X0)) => funny(X0)) [input p9]
23. brave(alice) [input hypothesis]
24. ? [X0] : (creative(X0) & brave(X0)) <=> ? [X1] : (wise(X1) | brave(X1)) [rectify 2]
35. ! [X0] : (funny(X0) | (humble(X0) & ~humble(X0))) [ennf transformation 10]
41. (? [X0] : (creative(X0) & brave(X0)) | ! [X1] : (~wise(X1) & ~brave(X1))) & (? [X1] : (wise(X1) | brave(X1)) | ! [X0] : (~creative(X0) | ~brave(X0))) [nnf transformation 24]
42. (? [X0] : (creative(X0) & brave(X0)) | ! [X1] : (~wise(X1) & ~brave(X1))) & (? [X2] : (wise(X2) | brave(X2)) | ! [X3] : (~creative(X3) | ~brave(X3))) [rectify 41]
43. ? [X0] : (creative(X0) & brave(X0)) => (creative(sK0) & brave(sK0)) [choice axiom]
44. ? [X2] : (wise(X2) | brave(X2)) => (wise(sK1) | brave(sK1)) [choice axiom]
45. ((creative(sK0) & brave(sK0)) | ! [X1] : (~wise(X1) & ~brave(X1))) & ((wise(sK1) | brave(sK1)) | ! [X3] : (~creative(X3) | ~brave(X3))) [skolemisation 42,44,43]
46. ! [X0] : ((funny(X0) | (creative(X0) | ~funny(X0))) & ((~creative(X0) & funny(X0)) | ~funny(X0))) [nnf transformation 3]
47. ! [X0] : ((funny(X0) | creative(X0) | ~funny(X0)) & ((~creative(X0) & funny(X0)) | ~funny(X0))) [flattening 46]
83. creative(sK0) | ~brave(X1) [cnf transformation 45]
86. ~funny(X0) | ~creative(X0) [cnf transformation 47]
103. funny(X0) | ~humble(X0) [cnf transformation 35]
104. humble(X0) | funny(X0) [cnf transformation 35]
131. brave(alice) [cnf transformation 23]
136. 2 <=> creative(sK0) [avatar definition]
138. creative(sK0) <- (2) [avatar component clause 136]
141. 3 <=> ! [X1] : ~brave(X1) [avatar definition]
142. ~brave(X1) <- (3) [avatar component clause 141]
143. 3 | 2 [avatar split clause 83,136,141]
221. funny(X0) [subsumption resolution 103,104]
297. ~creative(X0) [resolution 86,221]
299. $false <- (2) [resolution 297,138]
302. ~2 [avatar contradiction clause 299]
303. $false <- (3) [resolution 142,131]
306. ~3 [avatar contradiction clause 303]
307. $false [avatar sat refutation 143,302,306]
% SZS output end Proof for 897625903930041003590050
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is old or not rich is not quiet or calm and vice versa. If susan is both humble and rich then someone is both quiet and not tall. Everyone who is either quiet or kind is not patient or curious and vice versa. If someone is both curious and not creative then fred is not happy. Everyone who is either happy or not creative is either not curious or calm and vice versa. Everyone who is either curious or wise is creative and vice versa. Everyone who is both funny and calm is either old or brave and vice versa. If someone is both not kind and not brave then fred is both tall and not brave and vice versa. Everyone who is humble or kind is patient or not generous and vice versa. If someone is either not calm or not quiet then fred is both quiet and curious and vice versa. Everyone who is not brave is not wise and vice versa. If lucy is not humble then someone is not rich or generous and vice versa. Everyone who is both patient and funny is either not humble or funny. If someone is either not tall or strong then someone is both generous and funny and vice versa. If someone is creative or rich then alice is either patient or not generous. Lucy is kind. Lucy is either humble or not patient. Someone is either not calm or quiet. Lucy is either patient or not strong. Someone is either not brave or not creative. Someone is calm or not kind. Susan is both wise and rich. Someone is wise or not tall. | Susan is not rich. | contradiction | (![X]:((old(X)|~rich(X))<=>(~quiet(X)|calm(X))))&
(((humble(susan)&rich(susan)))=>(?[X]:((quiet(X)&~tall(X)))))&
(![X]:((quiet(X)<~>kind(X))<=>(~patient(X)|curious(X))))&
((?[X]:((curious(X)&~creative(X))))=>(~happy(fred)))&
(![X]:((happy(X)<~>~creative(X))<=>(~curious(X)<~>calm(X))))&
(![X]:((curious(X)<~>wise(X))<=>creative(X)))&
(![X]:((funny(X)&calm(X))<=>(old(X)<~>brave(X))))&
((?[X]:((~kind(X)&~brave(X))))<=>((tall(fred)&~brave(fred))))&
(![X]:((humble(X)|kind(X))<=>(patient(X)|~generous(X))))&
((?[X]:((~calm(X)<~>~quiet(X))))<=>((quiet(fred)&curious(fred))))&
(![X]:(~brave(X)<=>~wise(X)))&
((~humble(lucy))<=>(?[X]:((~rich(X)|generous(X)))))&
(![X]:((patient(X)&funny(X))=>(~humble(X)<~>funny(X))))&
((?[X]:((~tall(X)<~>strong(X))))<=>(?[X]:((generous(X)&funny(X)))))&
((?[X]:((creative(X)|rich(X))))=>((patient(alice)<~>~generous(alice))))&
(kind(lucy))&
((humble(lucy)<~>~patient(lucy)))&
(?[X]:((~calm(X)<~>quiet(X))))&
((patient(lucy)<~>~strong(lucy)))&
(?[X]:((~brave(X)<~>~creative(X))))&
(?[X]:((calm(X)|~kind(X))))&
((wise(susan)&rich(susan)))&
(?[X]:((wise(X)|~tall(X)))) | ~rich(susan) | [
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 2571112937288485870453721
% SZS output start Proof for 2571112937288485870453721
22. rich(susan) & wise(susan) [input p21]
24. ~rich(susan) [input hypothesis]
151. rich(susan) [cnf transformation 22]
153. ~rich(susan) [cnf transformation 24]
160. 2 <=> rich(susan) [avatar definition]
343. 2 [avatar split clause 151,160]
353. ~2 [avatar split clause 153,160]
354. $false [avatar sat refutation 343,353]
% SZS output end Proof for 2571112937288485870453721
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble and not old then someone is not creative or not curious and vice versa. If someone is old or rich then john is either creative or curious. If susan is both not curious and not calm then someone is tall or not quiet and vice versa. Everyone who is either not patient or not rich is not rich or not strong and vice versa. Everyone who is either not generous or not old is both brave and generous and vice versa. Everyone who is not wise or not brave is both not patient and not humble and vice versa. If someone is both not humble and not kind then fred is not quiet or old and vice versa. If someone is rich or not calm then fred is either not humble or old and vice versa. Everyone who is generous or humble is either not funny or patient and vice versa. If someone is old then someone is both brave and not old. If someone is both happy and wise then someone is both not generous and funny. If alice is either humble or funny then alice is quiet or kind. Everyone who is not curious or not quiet is not strong and vice versa. Everyone who is not creative is both not patient and happy and vice versa. Everyone who is rich or happy is not creative or kind and vice versa. Everyone who is both not curious and creative is patient and vice versa. Someone is curious. Fred is tall. Fred is kind. Alice is not strong. Alice is not rich or not old. Alice is not old or humble. Someone is both generous and not old. | Fred is brave. | neutral | ((?[X]:((humble(X)&~old(X))))<=>(?[X]:((~creative(X)|~curious(X)))))&
((?[X]:((old(X)|rich(X))))=>((creative(john)<~>curious(john))))&
(((~curious(susan)&~calm(susan)))<=>(?[X]:((tall(X)|~quiet(X)))))&
(![X]:((~patient(X)<~>~rich(X))<=>(~rich(X)|~strong(X))))&
(![X]:((~generous(X)<~>~old(X))<=>(brave(X)&generous(X))))&
(![X]:((~wise(X)|~brave(X))<=>(~patient(X)&~humble(X))))&
((?[X]:((~humble(X)&~kind(X))))<=>((~quiet(fred)|old(fred))))&
((?[X]:((rich(X)|~calm(X))))<=>((~humble(fred)<~>old(fred))))&
(![X]:((generous(X)|humble(X))<=>(~funny(X)<~>patient(X))))&
((?[X]:(old(X)))=>(?[X]:((brave(X)&~old(X)))))&
((?[X]:((happy(X)&wise(X))))=>(?[X]:((~generous(X)&funny(X)))))&
(((humble(alice)<~>funny(alice)))=>((quiet(alice)|kind(alice))))&
(![X]:((~curious(X)|~quiet(X))<=>~strong(X)))&
(![X]:(~creative(X)<=>(~patient(X)&happy(X))))&
(![X]:((rich(X)|happy(X))<=>(~creative(X)|kind(X))))&
(![X]:((~curious(X)&creative(X))<=>patient(X)))&
(?[X]:(curious(X)))&
(tall(fred))&
(kind(fred))&
(~strong(alice))&
((~rich(alice)|~old(alice)))&
((~old(alice)|humble(alice)))&
(?[X]:((generous(X)&~old(X)))) | brave(fred) | [] | null | 0 |
Everyone who is either not brave or not happy is not funny.
Everyone who is not quiet or not curious is not kind or not humble.
Everyone who is not humble or brave is both rich and patient and vice versa.
Everyone who is not wise or not calm is either brave or not rich and vice versa.
If someone is either kind or tall then paul is humble or not humble and vice versa.
Everyone who is either not brave or not tall is not brave or not tall.
Everyone who is either not kind or calm is both curious and not humble and vice versa.
If someone is both not humble and not tall then someone is both not brave and not creative and vice versa.
If someone is both tall and patient then alice is humble.
If fred is not happy or not kind then someone is either not rich or funny and vice versa.
Everyone who is either kind or funny is not wise and vice versa.
Everyone who is both not old and quiet is both not quiet and patient and vice versa.
Everyone who is quiet is creative and vice versa.
Everyone who is not quiet is both not wise and not quiet.
Everyone who is not patient is not quiet.
If someone is both strong and not rich then john is both not tall and not happy.
Alice is either not curious or not quiet.
Alice is either wise or not strong.
Someone is not patient or brave.
Someone is either not patient or not old.
Paul is both quiet and old.
John is not rich or not creative.
Paul is either not brave or happy. | Alice is not patient. | neutral | (![X]:((~brave(X)<~>~happy(X))=>~funny(X)))&
(![X]:((~quiet(X)|~curious(X))=>(~kind(X)|~humble(X))))&
(![X]:((~humble(X)|brave(X))<=>(rich(X)&patient(X))))&
(![X]:((~wise(X)|~calm(X))<=>(brave(X)<~>~rich(X))))&
((?[X]:((kind(X)<~>tall(X))))<=>((humble(paul)|~humble(paul))))&
(![X]:((~brave(X)<~>~tall(X))=>(~brave(X)|~tall(X))))&
(![X]:((~kind(X)<~>calm(X))<=>(curious(X)&~humble(X))))&
((?[X]:((~humble(X)&~tall(X))))<=>(?[X]:((~brave(X)&~creative(X)))))&
((?[X]:((tall(X)&patient(X))))=>(humble(alice)))&
(((~happy(fred)|~kind(fred)))<=>(?[X]:((~rich(X)<~>funny(X)))))&
(![X]:((kind(X)<~>funny(X))<=>~wise(X)))&
(![X]:((~old(X)&quiet(X))<=>(~quiet(X)&patient(X))))&
(![X]:(quiet(X)<=>creative(X)))&
(![X]:(~quiet(X)=>(~wise(X)&~quiet(X))))&
(![X]:(~patient(X)=>~quiet(X)))&
((?[X]:((strong(X)&~rich(X))))=>((~tall(john)&~happy(john))))&
((~curious(alice)<~>~quiet(alice)))&
((wise(alice)<~>~strong(alice)))&
(?[X]:((~patient(X)|brave(X))))&
(?[X]:((~patient(X)<~>~old(X))))&
((quiet(paul)&old(paul)))&
((~rich(john)|~creative(john)))&
((~brave(paul)<~>happy(paul))) | ~patient(alice) | [] | null | 0 |
If mary is both creative and not wise then someone is both old and tall and vice versa.
If susan is both not tall and not happy then paul is generous and vice versa.
Everyone who is not tall is either strong or patient.
Everyone who is not happy or strong is both generous and calm and vice versa.
Everyone who is generous or calm is either not quiet or not funny and vice versa.
If someone is either not calm or not wise then someone is both not kind and old.
Everyone who is not wise or not tall is both old and not rich and vice versa.
Everyone who is rich or creative is humble or not happy.
If john is either not kind or not patient then someone is not brave.
If susan is both rich and happy then someone is both not rich and strong and vice versa.
Everyone who is either calm or generous is either kind or not strong.
If someone is either wise or old then someone is either humble or not old.
If mary is not humble then fred is either patient or brave.
Everyone who is both happy and not funny is both humble and generous and vice versa.
If fred is wise then someone is either not kind or not rich and vice versa.
Everyone who is both not tall and not happy is both kind and not calm.
Lucy is quiet or happy.
John is not rich or creative.
Someone is both not patient and kind.
Someone is not kind.
Someone is both patient and brave.
John is wise.
Someone is not humble or kind.
Someone is both strong and funny. | Lucy is calm. | neutral | (((creative(mary)&~wise(mary)))<=>(?[X]:((old(X)&tall(X)))))&
(((~tall(susan)&~happy(susan)))<=>(generous(paul)))&
(![X]:(~tall(X)=>(strong(X)<~>patient(X))))&
(![X]:((~happy(X)|strong(X))<=>(generous(X)&calm(X))))&
(![X]:((generous(X)|calm(X))<=>(~quiet(X)<~>~funny(X))))&
((?[X]:((~calm(X)<~>~wise(X))))=>(?[X]:((~kind(X)&old(X)))))&
(![X]:((~wise(X)|~tall(X))<=>(old(X)&~rich(X))))&
(![X]:((rich(X)|creative(X))=>(humble(X)|~happy(X))))&
(((~kind(john)<~>~patient(john)))=>(?[X]:(~brave(X))))&
(((rich(susan)&happy(susan)))<=>(?[X]:((~rich(X)&strong(X)))))&
(![X]:((calm(X)<~>generous(X))=>(kind(X)<~>~strong(X))))&
((?[X]:((wise(X)<~>old(X))))=>(?[X]:((humble(X)<~>~old(X)))))&
((~humble(mary))=>((patient(fred)<~>brave(fred))))&
(![X]:((happy(X)&~funny(X))<=>(humble(X)&generous(X))))&
((wise(fred))<=>(?[X]:((~kind(X)<~>~rich(X)))))&
(![X]:((~tall(X)&~happy(X))=>(kind(X)&~calm(X))))&
((quiet(lucy)|happy(lucy)))&
((~rich(john)|creative(john)))&
(?[X]:((~patient(X)&kind(X))))&
(?[X]:(~kind(X)))&
(?[X]:((patient(X)&brave(X))))&
(wise(john))&
(?[X]:((~humble(X)|kind(X))))&
(?[X]:((strong(X)&funny(X)))) | calm(lucy) | [] | null | 0 |
Everyone who is not tall is not calm and vice versa.
If paul is both not humble and not patient then someone is strong or not quiet and vice versa.
Everyone who is either rich or not funny is both not calm and calm and vice versa.
If someone is both not strong and tall then someone is old.
Everyone who is quiet or wise is patient or not curious.
Everyone who is not happy or not calm is generous or creative and vice versa.
Everyone who is both not happy and rich is humble or not funny.
Everyone who is patient is not wise or curious and vice versa.
Everyone who is funny is tall or generous.
If lucy is both creative and not strong then mary is kind and vice versa.
Everyone who is both curious and strong is either strong or not curious.
Everyone who is not funny or not rich is both not wise and brave and vice versa.
If john is either generous or not creative then lucy is kind or funny.
Everyone who is either not patient or not creative is either calm or strong and vice versa.
Everyone who is not brave or not patient is brave or patient.
Everyone who is calm is both generous and not brave and vice versa.
Mary is generous.
Paul is either not patient or patient.
Someone is not happy.
Someone is not happy or brave.
John is both rich and not happy. | Lucy is not humble. | neutral | (![X]:(~tall(X)<=>~calm(X)))&
(((~humble(paul)&~patient(paul)))<=>(?[X]:((strong(X)|~quiet(X)))))&
(![X]:((rich(X)<~>~funny(X))<=>(~calm(X)&calm(X))))&
((?[X]:((~strong(X)&tall(X))))=>(?[X]:(old(X))))&
(![X]:((quiet(X)|wise(X))=>(patient(X)|~curious(X))))&
(![X]:((~happy(X)|~calm(X))<=>(generous(X)|creative(X))))&
(![X]:((~happy(X)&rich(X))=>(humble(X)|~funny(X))))&
(![X]:(patient(X)<=>(~wise(X)|curious(X))))&
(![X]:(funny(X)=>(tall(X)|generous(X))))&
(((creative(lucy)&~strong(lucy)))<=>(kind(mary)))&
(![X]:((curious(X)&strong(X))=>(strong(X)<~>~curious(X))))&
(![X]:((~funny(X)|~rich(X))<=>(~wise(X)&brave(X))))&
(((generous(john)<~>~creative(john)))=>((kind(lucy)|funny(lucy))))&
(![X]:((~patient(X)<~>~creative(X))<=>(calm(X)<~>strong(X))))&
(![X]:((~brave(X)|~patient(X))=>(brave(X)|patient(X))))&
(![X]:(calm(X)<=>(generous(X)&~brave(X))))&
(generous(mary))&
((~patient(paul)<~>patient(paul)))&
(?[X]:(~happy(X)))&
(?[X]:((~happy(X)|brave(X))))&
((rich(john)&~happy(john))) | ~humble(lucy) | [] | null | 0 |
If fred is either strong or not kind then someone is both funny and not happy.
If paul is not old then susan is not patient or rich and vice versa.
Everyone who is not happy is not happy or humble and vice versa.
If mary is both kind and funny then someone is funny or not creative and vice versa.
Everyone who is humble or not rich is not creative and vice versa.
Everyone who is either not rich or strong is either not brave or not tall.
If someone is either creative or not old then mary is either calm or funny and vice versa.
Everyone who is either not calm or calm is not calm and vice versa.
If alice is strong then someone is both not calm and not generous and vice versa.
If lucy is brave or kind then mary is both not kind and calm.
If someone is not strong then someone is not quiet.
If paul is strong or not wise then someone is calm or not strong and vice versa.
Everyone who is both rich and not humble is old or not calm.
Everyone who is either not kind or humble is not kind or not brave and vice versa.
If susan is strong or not tall then someone is both curious and patient and vice versa.
If someone is not happy then someone is not calm and vice versa.
Lucy is not wise.
Alice is either patient or not humble.
Lucy is not humble.
Fred is not happy or happy.
Fred is generous or wise.
Someone is strong. | Fred is humble. | neutral | (((strong(fred)<~>~kind(fred)))=>(?[X]:((funny(X)&~happy(X)))))&
((~old(paul))<=>((~patient(susan)|rich(susan))))&
(![X]:(~happy(X)<=>(~happy(X)|humble(X))))&
(((kind(mary)&funny(mary)))<=>(?[X]:((funny(X)|~creative(X)))))&
(![X]:((humble(X)|~rich(X))<=>~creative(X)))&
(![X]:((~rich(X)<~>strong(X))=>(~brave(X)<~>~tall(X))))&
((?[X]:((creative(X)<~>~old(X))))<=>((calm(mary)<~>funny(mary))))&
(![X]:((~calm(X)<~>calm(X))<=>~calm(X)))&
((strong(alice))<=>(?[X]:((~calm(X)&~generous(X)))))&
(((brave(lucy)|kind(lucy)))=>((~kind(mary)&calm(mary))))&
((?[X]:(~strong(X)))=>(?[X]:(~quiet(X))))&
(((strong(paul)|~wise(paul)))<=>(?[X]:((calm(X)|~strong(X)))))&
(![X]:((rich(X)&~humble(X))=>(old(X)|~calm(X))))&
(![X]:((~kind(X)<~>humble(X))<=>(~kind(X)|~brave(X))))&
(((strong(susan)|~tall(susan)))<=>(?[X]:((curious(X)&patient(X)))))&
((?[X]:(~happy(X)))<=>(?[X]:(~calm(X))))&
(~wise(lucy))&
((patient(alice)<~>~humble(alice)))&
(~humble(lucy))&
((~happy(fred)|happy(fred)))&
((generous(fred)|wise(fred)))&
(?[X]:(strong(X))) | humble(fred) | [] | null | 0 |
If john is either not kind or not rich then susan is strong and vice versa. Everyone who is either not brave or not curious is both quiet and generous. Everyone who is generous or happy is either not funny or strong and vice versa. If susan is both funny and not curious then fred is either not quiet or not patient and vice versa. Everyone who is both not brave and not humble is not creative or humble. If someone is not patient or not rich then someone is not creative or not kind and vice versa. If alice is not funny then someone is both not old and not calm and vice versa. If someone is either happy or funny then susan is both generous and not humble. If john is humble or not creative then fred is both not calm and funny. If someone is generous then john is not calm and vice versa. Everyone who is calm is either not calm or not wise and vice versa. Everyone who is either wise or not wise is both not curious and not funny and vice versa. If someone is either not rich or patient then mary is both not tall and not calm and vice versa. If paul is both not humble and humble then mary is either old or not creative. Everyone who is rich or humble is not generous. If lucy is not quiet then susan is either calm or not old. Susan is either not old or curious. Mary is both not humble and quiet. Someone is not funny. Fred is patient. Mary is either not brave or not tall. Someone is wise or happy. John is not kind or not rich. | Susan is not generous. | contradiction | (((~kind(john)<~>~rich(john)))<=>(strong(susan)))&
(![X]:((~brave(X)<~>~curious(X))=>(quiet(X)&generous(X))))&
(![X]:((generous(X)|happy(X))<=>(~funny(X)<~>strong(X))))&
(((funny(susan)&~curious(susan)))<=>((~quiet(fred)<~>~patient(fred))))&
(![X]:((~brave(X)&~humble(X))=>(~creative(X)|humble(X))))&
((?[X]:((~patient(X)|~rich(X))))<=>(?[X]:((~creative(X)|~kind(X)))))&
((~funny(alice))<=>(?[X]:((~old(X)&~calm(X)))))&
((?[X]:((happy(X)<~>funny(X))))=>((generous(susan)&~humble(susan))))&
(((humble(john)|~creative(john)))=>((~calm(fred)&funny(fred))))&
((?[X]:(generous(X)))<=>(~calm(john)))&
(![X]:(calm(X)<=>(~calm(X)<~>~wise(X))))&
(![X]:((wise(X)<~>~wise(X))<=>(~curious(X)&~funny(X))))&
((?[X]:((~rich(X)<~>patient(X))))<=>((~tall(mary)&~calm(mary))))&
(((~humble(paul)&humble(paul)))=>((old(mary)<~>~creative(mary))))&
(![X]:((rich(X)|humble(X))=>~generous(X)))&
((~quiet(lucy))=>((calm(susan)<~>~old(susan))))&
((~old(susan)<~>curious(susan)))&
((~humble(mary)&quiet(mary)))&
(?[X]:(~funny(X)))&
(patient(fred))&
((~brave(mary)<~>~tall(mary)))&
(?[X]:((wise(X)|happy(X))))&
((~kind(john)|~rich(john))) | ~generous(susan) | [
"p7",
"p10",
"p11",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 1113281906017978968683895
% SZS output start Proof for 1113281906017978968683895
8. ? [X0] : (happy(X0) <~> funny(X0)) => (~humble(susan) & generous(susan)) [input p7]
11. ! [X0] : (calm(X0) <=> (~calm(X0) <~> ~wise(X0))) [input p10]
12. ! [X0] : ((wise(X0) <~> ~wise(X0)) <=> (~funny(X0) & ~curious(X0))) [input p11]
22. ? [X0] : (happy(X0) | wise(X0)) [input p21]
24. ~generous(susan) [input hypothesis]
29. (~humble(susan) & generous(susan)) | ! [X0] : (happy(X0) <=> funny(X0)) [ennf transformation 8]
50. (~humble(susan) & generous(susan)) | ! [X0] : ((happy(X0) | ~funny(X0)) & (funny(X0) | ~happy(X0))) [nnf transformation 29]
55. ! [X0] : ((calm(X0) | ((~calm(X0) | wise(X0)) & (~wise(X0) | calm(X0)))) & (((wise(X0) | calm(X0)) & (~wise(X0) | ~calm(X0))) | ~calm(X0))) [nnf transformation 11]
56. ! [X0] : ((((wise(X0) | ~wise(X0)) & (~wise(X0) | wise(X0))) | (funny(X0) | curious(X0))) & ((~funny(X0) & ~curious(X0)) | ((wise(X0) | wise(X0)) & (~wise(X0) | ~wise(X0))))) [nnf transformation 12]
57. ! [X0] : ((((wise(X0) | ~wise(X0)) & (~wise(X0) | wise(X0))) | funny(X0) | curious(X0)) & ((~funny(X0) & ~curious(X0)) | ((wise(X0) | wise(X0)) & (~wise(X0) | ~wise(X0))))) [flattening 56]
69. ? [X0] : (happy(X0) | wise(X0)) => (happy(sK6) | wise(sK6)) [choice axiom]
70. happy(sK6) | wise(sK6) [skolemisation 22,69]
99. generous(susan) | funny(X0) | ~happy(X0) [cnf transformation 50]
109. ~wise(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 55]
111. calm(X0) | ~wise(X0) | calm(X0) [cnf transformation 55]
116. ~funny(X0) | wise(X0) | wise(X0) [cnf transformation 57]
139. happy(sK6) | wise(sK6) [cnf transformation 70]
141. ~generous(susan) [cnf transformation 24]
145. ~funny(X0) | wise(X0) [duplicate literal removal 116]
146. ~wise(X0) | ~calm(X0) [duplicate literal removal 109]
147. calm(X0) | ~wise(X0) [duplicate literal removal 111]
246. 22 <=> ! [X0] : (funny(X0) | ~happy(X0)) [avatar definition]
247. funny(X0) | ~happy(X0) <- (22) [avatar component clause 246]
250. 23 <=> generous(susan) [avatar definition]
254. 22 | 23 [avatar split clause 99,250,246]
288. ~wise(X0) [subsumption resolution 146,147]
289. ~funny(X0) [subsumption resolution 145,288]
342. happy(sK6) [subsumption resolution 139,288]
344. ~23 [avatar split clause 141,250]
345. ~happy(X0) <- (22) [subsumption resolution 247,289]
346. $false <- (22) [resolution 345,342]
347. ~22 [avatar contradiction clause 346]
348. $false [avatar sat refutation 254,344,347]
% SZS output end Proof for 1113281906017978968683895
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or tall is humble or not quiet.
Everyone who is not old is both calm and not strong.
Everyone who is calm or funny is either brave or not old.
If susan is both not rich and wise then alice is not curious.
Everyone who is not wise or curious is not quiet or quiet.
Everyone who is either brave or not quiet is not patient or patient.
Everyone who is either old or not generous is either not quiet or not strong and vice versa.
If someone is both creative and not generous then mary is either not tall or not wise and vice versa.
Everyone who is not happy is either wise or old and vice versa.
Everyone who is both humble and not generous is not tall.
If susan is both strong and not kind then john is both not generous and not old.
Everyone who is either wise or rich is both old and not old.
Everyone who is both wise and not calm is either generous or creative.
If someone is tall then lucy is either rich or quiet.
Everyone who is kind is not patient and vice versa.
If someone is either not rich or not happy then fred is not wise or happy and vice versa.
Someone is patient or generous.
Someone is both rich and not kind.
Someone is both not patient and not calm.
Someone is not brave or creative.
Someone is creative or not rich. | Lucy is kind. | neutral | (![X]:((creative(X)|tall(X))=>(humble(X)|~quiet(X))))&
(![X]:(~old(X)=>(calm(X)&~strong(X))))&
(![X]:((calm(X)|funny(X))=>(brave(X)<~>~old(X))))&
(((~rich(susan)&wise(susan)))=>(~curious(alice)))&
(![X]:((~wise(X)|curious(X))=>(~quiet(X)|quiet(X))))&
(![X]:((brave(X)<~>~quiet(X))=>(~patient(X)|patient(X))))&
(![X]:((old(X)<~>~generous(X))<=>(~quiet(X)<~>~strong(X))))&
((?[X]:((creative(X)&~generous(X))))<=>((~tall(mary)<~>~wise(mary))))&
(![X]:(~happy(X)<=>(wise(X)<~>old(X))))&
(![X]:((humble(X)&~generous(X))=>~tall(X)))&
(((strong(susan)&~kind(susan)))=>((~generous(john)&~old(john))))&
(![X]:((wise(X)<~>rich(X))=>(old(X)&~old(X))))&
(![X]:((wise(X)&~calm(X))=>(generous(X)<~>creative(X))))&
((?[X]:(tall(X)))=>((rich(lucy)<~>quiet(lucy))))&
(![X]:(kind(X)<=>~patient(X)))&
((?[X]:((~rich(X)<~>~happy(X))))<=>((~wise(fred)|happy(fred))))&
(?[X]:((patient(X)|generous(X))))&
(?[X]:((rich(X)&~kind(X))))&
(?[X]:((~patient(X)&~calm(X))))&
(?[X]:((~brave(X)|creative(X))))&
(?[X]:((creative(X)|~rich(X)))) | kind(lucy) | [] | null | 0 |
Everyone who is either not calm or not quiet is old.
If paul is brave or generous then lucy is either not funny or wise.
If paul is both funny and tall then paul is either brave or happy and vice versa.
Everyone who is not funny or creative is not rich or not brave.
Everyone who is either not kind or calm is both not creative and old and vice versa.
If lucy is calm then paul is not kind or not wise and vice versa.
Everyone who is generous is calm.
If someone is patient or curious then susan is both generous and not patient.
If susan is not calm or creative then fred is not patient or not humble and vice versa.
If someone is strong then someone is patient.
Everyone who is not wise is both not creative and tall and vice versa.
Everyone who is either not rich or kind is either creative or not brave.
If susan is either not rich or not old then alice is wise and vice versa.
Everyone who is not wise is not curious or not rich.
Everyone who is not curious is not patient or generous.
Everyone who is not rich or brave is both curious and patient and vice versa.
Someone is not rich or tall.
Alice is either not funny or not strong.
Lucy is either funny or old.
Mary is not curious.
Someone is either tall or not wise.
Alice is not old or quiet.
Alice is curious. | Mary is happy. | neutral | (![X]:((~calm(X)<~>~quiet(X))=>old(X)))&
(((brave(paul)|generous(paul)))=>((~funny(lucy)<~>wise(lucy))))&
(((funny(paul)&tall(paul)))<=>((brave(paul)<~>happy(paul))))&
(![X]:((~funny(X)|creative(X))=>(~rich(X)|~brave(X))))&
(![X]:((~kind(X)<~>calm(X))<=>(~creative(X)&old(X))))&
((calm(lucy))<=>((~kind(paul)|~wise(paul))))&
(![X]:(generous(X)=>calm(X)))&
((?[X]:((patient(X)|curious(X))))=>((generous(susan)&~patient(susan))))&
(((~calm(susan)|creative(susan)))<=>((~patient(fred)|~humble(fred))))&
((?[X]:(strong(X)))=>(?[X]:(patient(X))))&
(![X]:(~wise(X)<=>(~creative(X)&tall(X))))&
(![X]:((~rich(X)<~>kind(X))=>(creative(X)<~>~brave(X))))&
(((~rich(susan)<~>~old(susan)))<=>(wise(alice)))&
(![X]:(~wise(X)=>(~curious(X)|~rich(X))))&
(![X]:(~curious(X)=>(~patient(X)|generous(X))))&
(![X]:((~rich(X)|brave(X))<=>(curious(X)&patient(X))))&
(?[X]:((~rich(X)|tall(X))))&
((~funny(alice)<~>~strong(alice)))&
((funny(lucy)<~>old(lucy)))&
(~curious(mary))&
(?[X]:((tall(X)<~>~wise(X))))&
((~old(alice)|quiet(alice)))&
(curious(alice)) | happy(mary) | [] | null | 0 |
Everyone who is either calm or funny is calm or wise. Everyone who is both not wise and not tall is not generous. Everyone who is not generous or tall is both not tall and not humble. If someone is either not wise or not kind then someone is not old. If someone is not kind then someone is both not strong and kind and vice versa. Everyone who is both not strong and rich is either not tall or not curious and vice versa. If someone is old or not creative then mary is not wise or not rich and vice versa. If susan is either not curious or not rich then someone is both tall and old. Everyone who is not quiet is either creative or not rich and vice versa. Everyone who is both curious and not happy is either wise or kind and vice versa. If lucy is both not generous and kind then someone is either not curious or curious and vice versa. Everyone who is both funny and not humble is not kind and vice versa. Everyone who is both rich and not brave is either happy or not strong and vice versa. If someone is calm then someone is not brave or not rich and vice versa. Everyone who is not kind or rich is either strong or not funny and vice versa. If someone is not rich then mary is tall. Someone is old or not brave. Someone is either tall or old. John is calm or not happy. Susan is either old or not generous. Someone is both calm and not quiet. John is either not tall or not funny. | Lucy is not rich. | contradiction | (![X]:((calm(X)<~>funny(X))=>(calm(X)|wise(X))))&
(![X]:((~wise(X)&~tall(X))=>~generous(X)))&
(![X]:((~generous(X)|tall(X))=>(~tall(X)&~humble(X))))&
((?[X]:((~wise(X)<~>~kind(X))))=>(?[X]:(~old(X))))&
((?[X]:(~kind(X)))<=>(?[X]:((~strong(X)&kind(X)))))&
(![X]:((~strong(X)&rich(X))<=>(~tall(X)<~>~curious(X))))&
((?[X]:((old(X)|~creative(X))))<=>((~wise(mary)|~rich(mary))))&
(((~curious(susan)<~>~rich(susan)))=>(?[X]:((tall(X)&old(X)))))&
(![X]:(~quiet(X)<=>(creative(X)<~>~rich(X))))&
(![X]:((curious(X)&~happy(X))<=>(wise(X)<~>kind(X))))&
(((~generous(lucy)&kind(lucy)))<=>(?[X]:((~curious(X)<~>curious(X)))))&
(![X]:((funny(X)&~humble(X))<=>~kind(X)))&
(![X]:((rich(X)&~brave(X))<=>(happy(X)<~>~strong(X))))&
((?[X]:(calm(X)))<=>(?[X]:((~brave(X)|~rich(X)))))&
(![X]:((~kind(X)|rich(X))<=>(strong(X)<~>~funny(X))))&
((?[X]:(~rich(X)))=>(tall(mary)))&
(?[X]:((old(X)|~brave(X))))&
(?[X]:((tall(X)<~>old(X))))&
((calm(john)|~happy(john)))&
((old(susan)<~>~generous(susan)))&
(?[X]:((calm(X)&~quiet(X))))&
((~tall(john)<~>~funny(john))) | ~rich(lucy) | [
"p2",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7901237280781730197837037
% SZS output start Proof for 7901237280781730197837037
3. ! [X0] : ((tall(X0) | ~generous(X0)) => (~humble(X0) & ~tall(X0))) [input p2]
16. ? [X0] : ~rich(X0) => tall(mary) [input p15]
23. ~rich(lucy) [input hypothesis]
32. ! [X0] : ((~humble(X0) & ~tall(X0)) | (~tall(X0) & generous(X0))) [ennf transformation 3]
36. tall(mary) | ! [X0] : rich(X0) [ennf transformation 16]
89. ~tall(X0) | ~tall(X0) [cnf transformation 32]
143. tall(mary) | rich(X0) [cnf transformation 36]
154. ~rich(lucy) [cnf transformation 23]
159. ~tall(X0) [duplicate literal removal 89]
257. 22 <=> ! [X1] : rich(X1) [avatar definition]
258. rich(X1) <- (22) [avatar component clause 257]
282. rich(X0) [subsumption resolution 143,159]
283. 22 [avatar split clause 282,257]
321. $false <- (22) [resolution 258,154]
322. ~22 [avatar contradiction clause 321]
323. $false [avatar sat refutation 283,322]
% SZS output end Proof for 7901237280781730197837037
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If mary is both strong and patient then someone is either not rich or not brave.
Everyone who is not brave is old.
If fred is not happy or happy then lucy is both not creative and not patient and vice versa.
Everyone who is both happy and patient is creative or brave and vice versa.
If someone is patient then lucy is either funny or not curious.
Everyone who is humble is kind or funny and vice versa.
Everyone who is both not happy and brave is either curious or funny.
If lucy is not strong then susan is either curious or not old.
Everyone who is both creative and strong is not funny or not quiet and vice versa.
If someone is either not rich or wise then someone is not generous or not wise.
If fred is either creative or not calm then susan is either not wise or tall and vice versa.
If someone is either curious or not kind then someone is either not rich or creative and vice versa.
If someone is patient or not wise then john is not old and vice versa.
Everyone who is both calm and strong is brave and vice versa.
If someone is either rich or tall then alice is humble and vice versa.
Everyone who is not happy is wise and vice versa.
Someone is creative or strong.
Alice is not tall.
Someone is both not wise and not curious.
Fred is not funny.
Someone is both not creative and generous.
Someone is tall.
Someone is both not quiet and not old.
Someone is old. | Lucy is patient. | contradiction | (((strong(mary)&patient(mary)))=>(?[X]:((~rich(X)<~>~brave(X)))))&
(![X]:(~brave(X)=>old(X)))&
(((~happy(fred)|happy(fred)))<=>((~creative(lucy)&~patient(lucy))))&
(![X]:((happy(X)&patient(X))<=>(creative(X)|brave(X))))&
((?[X]:(patient(X)))=>((funny(lucy)<~>~curious(lucy))))&
(![X]:(humble(X)<=>(kind(X)|funny(X))))&
(![X]:((~happy(X)&brave(X))=>(curious(X)<~>funny(X))))&
((~strong(lucy))=>((curious(susan)<~>~old(susan))))&
(![X]:((creative(X)&strong(X))<=>(~funny(X)|~quiet(X))))&
((?[X]:((~rich(X)<~>wise(X))))=>(?[X]:((~generous(X)|~wise(X)))))&
(((creative(fred)<~>~calm(fred)))<=>((~wise(susan)<~>tall(susan))))&
((?[X]:((curious(X)<~>~kind(X))))<=>(?[X]:((~rich(X)<~>creative(X)))))&
((?[X]:((patient(X)|~wise(X))))<=>(~old(john)))&
(![X]:((calm(X)&strong(X))<=>brave(X)))&
((?[X]:((rich(X)<~>tall(X))))<=>(humble(alice)))&
(![X]:(~happy(X)<=>wise(X)))&
(?[X]:((creative(X)|strong(X))))&
(~tall(alice))&
(?[X]:((~wise(X)&~curious(X))))&
(~funny(fred))&
(?[X]:((~creative(X)&generous(X))))&
(?[X]:(tall(X)))&
(?[X]:((~quiet(X)&~old(X))))&
(?[X]:(old(X))) | patient(lucy) | [
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 698015855545368734703667
% SZS output start Proof for 698015855545368734703667
3. (happy(fred) | ~happy(fred)) <=> (~patient(lucy) & ~creative(lucy)) [input p2]
25. patient(lucy) [input hypothesis]
39. ((happy(fred) | ~happy(fred)) | (patient(lucy) | creative(lucy))) & ((~patient(lucy) & ~creative(lucy)) | (~happy(fred) & happy(fred))) [nnf transformation 3]
40. (happy(fred) | ~happy(fred) | patient(lucy) | creative(lucy)) & ((~patient(lucy) & ~creative(lucy)) | (~happy(fred) & happy(fred))) [flattening 39]
88. ~patient(lucy) | happy(fred) [cnf transformation 40]
89. ~patient(lucy) | ~happy(fred) [cnf transformation 40]
151. patient(lucy) [cnf transformation 25]
171. 5 <=> happy(fred) [avatar definition]
175. 6 <=> patient(lucy) [avatar definition]
178. ~5 | ~6 [avatar split clause 89,175,171]
179. 5 | ~6 [avatar split clause 88,175,171]
338. 6 [avatar split clause 151,175]
339. $false [avatar sat refutation 178,179,338]
% SZS output end Proof for 698015855545368734703667
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not happy and tall is either not kind or not curious and vice versa. If susan is quiet or rich then paul is either humble or not strong. If someone is patient or generous then alice is both generous and tall. If someone is either not curious or funny then someone is either not humble or not rich and vice versa. Everyone who is patient is both creative and not humble and vice versa. If someone is quiet then alice is brave or creative and vice versa. Everyone who is funny or not wise is wise and vice versa. Everyone who is either not kind or not tall is happy and vice versa. Everyone who is curious is either quiet or not funny. If someone is either not brave or humble then someone is patient or not creative. Everyone who is not generous or not humble is not old or not brave and vice versa. If someone is quiet or not calm then susan is not strong or not generous. Everyone who is both old and patient is either not patient or rich and vice versa. If lucy is not humble then mary is either not creative or calm. Everyone who is both rich and not humble is strong. Everyone who is either wise or funny is rich and vice versa. Someone is funny or tall. Mary is not quiet or funny. Someone is kind. Someone is both calm and not old. Someone is not generous. Someone is not curious. Alice is either not rich or not strong. Mary is patient. | Lucy is not curious. | entailment | (![X]:((~happy(X)&tall(X))<=>(~kind(X)<~>~curious(X))))&
(((quiet(susan)|rich(susan)))=>((humble(paul)<~>~strong(paul))))&
((?[X]:((patient(X)|generous(X))))=>((generous(alice)&tall(alice))))&
((?[X]:((~curious(X)<~>funny(X))))<=>(?[X]:((~humble(X)<~>~rich(X)))))&
(![X]:(patient(X)<=>(creative(X)&~humble(X))))&
((?[X]:(quiet(X)))<=>((brave(alice)|creative(alice))))&
(![X]:((funny(X)|~wise(X))<=>wise(X)))&
(![X]:((~kind(X)<~>~tall(X))<=>happy(X)))&
(![X]:(curious(X)=>(quiet(X)<~>~funny(X))))&
((?[X]:((~brave(X)<~>humble(X))))=>(?[X]:((patient(X)|~creative(X)))))&
(![X]:((~generous(X)|~humble(X))<=>(~old(X)|~brave(X))))&
((?[X]:((quiet(X)|~calm(X))))=>((~strong(susan)|~generous(susan))))&
(![X]:((old(X)&patient(X))<=>(~patient(X)<~>rich(X))))&
((~humble(lucy))=>((~creative(mary)<~>calm(mary))))&
(![X]:((rich(X)&~humble(X))=>strong(X)))&
(![X]:((wise(X)<~>funny(X))<=>rich(X)))&
(?[X]:((funny(X)|tall(X))))&
((~quiet(mary)|funny(mary)))&
(?[X]:(kind(X)))&
(?[X]:((calm(X)&~old(X))))&
(?[X]:(~generous(X)))&
(?[X]:(~curious(X)))&
((~rich(alice)<~>~strong(alice)))&
(patient(mary)) | ~curious(lucy) | [
"p3",
"p4",
"p6",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2637806846631120659343285
% SZS output start Proof for 2637806846631120659343285
4. ? [X0] : (~curious(X0) <~> funny(X0)) <=> ? [X0] : (~humble(X0) <~> ~rich(X0)) [input p3]
5. ! [X0] : (patient(X0) <=> (~humble(X0) & creative(X0))) [input p4]
7. ! [X0] : ((~wise(X0) | funny(X0)) <=> wise(X0)) [input p6]
13. ! [X0] : ((patient(X0) & old(X0)) <=> (~patient(X0) <~> rich(X0))) [input p12]
16. ! [X0] : ((wise(X0) <~> funny(X0)) <=> rich(X0)) [input p15]
25. curious(lucy) [input hypothesis]
26. ? [X0] : (~curious(X0) <~> funny(X0)) <=> ? [X1] : (~humble(X1) <~> ~rich(X1)) [rectify 4]
40. (? [X0] : ((~funny(X0) | curious(X0)) & (funny(X0) | ~curious(X0))) | ! [X1] : ((~humble(X1) | rich(X1)) & (~rich(X1) | humble(X1)))) & (? [X1] : ((rich(X1) | humble(X1)) & (~rich(X1) | ~humble(X1))) | ! [X0] : ((~curious(X0) | ~funny(X0)) & (funny(X0) | curious(X0)))) [nnf transformation 26]
41. (? [X0] : ((~funny(X0) | curious(X0)) & (funny(X0) | ~curious(X0))) | ! [X1] : ((~humble(X1) | rich(X1)) & (~rich(X1) | humble(X1)))) & (? [X2] : ((rich(X2) | humble(X2)) & (~rich(X2) | ~humble(X2))) | ! [X3] : ((~curious(X3) | ~funny(X3)) & (funny(X3) | curious(X3)))) [rectify 40]
42. ? [X0] : ((~funny(X0) | curious(X0)) & (funny(X0) | ~curious(X0))) => ((~funny(sK0) | curious(sK0)) & (funny(sK0) | ~curious(sK0))) [choice axiom]
43. ? [X2] : ((rich(X2) | humble(X2)) & (~rich(X2) | ~humble(X2))) => ((rich(sK1) | humble(sK1)) & (~rich(sK1) | ~humble(sK1))) [choice axiom]
44. (((~funny(sK0) | curious(sK0)) & (funny(sK0) | ~curious(sK0))) | ! [X1] : ((~humble(X1) | rich(X1)) & (~rich(X1) | humble(X1)))) & (((rich(sK1) | humble(sK1)) & (~rich(sK1) | ~humble(sK1))) | ! [X3] : ((~curious(X3) | ~funny(X3)) & (funny(X3) | curious(X3)))) [skolemisation 41,43,42]
45. ! [X0] : ((patient(X0) | (humble(X0) | ~creative(X0))) & ((~humble(X0) & creative(X0)) | ~patient(X0))) [nnf transformation 5]
46. ! [X0] : ((patient(X0) | humble(X0) | ~creative(X0)) & ((~humble(X0) & creative(X0)) | ~patient(X0))) [flattening 45]
52. ! [X0] : (((~wise(X0) | funny(X0)) | ~wise(X0)) & (wise(X0) | (wise(X0) & ~funny(X0)))) [nnf transformation 7]
53. ! [X0] : ((~wise(X0) | funny(X0) | ~wise(X0)) & (wise(X0) | (wise(X0) & ~funny(X0)))) [flattening 52]
62. ! [X0] : (((patient(X0) & old(X0)) | ((~patient(X0) | ~rich(X0)) & (rich(X0) | patient(X0)))) & (((~rich(X0) | patient(X0)) & (rich(X0) | ~patient(X0))) | (~patient(X0) | ~old(X0)))) [nnf transformation 13]
63. ! [X0] : (((patient(X0) & old(X0)) | ((~patient(X0) | ~rich(X0)) & (rich(X0) | patient(X0)))) & (((~rich(X0) | patient(X0)) & (rich(X0) | ~patient(X0))) | ~patient(X0) | ~old(X0))) [flattening 62]
65. ! [X0] : ((((~funny(X0) | ~wise(X0)) & (funny(X0) | wise(X0))) | ~rich(X0)) & (rich(X0) | ((wise(X0) | ~funny(X0)) & (funny(X0) | ~wise(X0))))) [nnf transformation 16]
94. rich(sK1) | humble(sK1) | ~curious(X3) | ~funny(X3) [cnf transformation 44]
100. ~patient(X0) | ~humble(X0) [cnf transformation 46]
106. wise(X0) | wise(X0) [cnf transformation 53]
107. ~wise(X0) | funny(X0) | ~wise(X0) [cnf transformation 53]
126. patient(X0) | rich(X0) | patient(X0) [cnf transformation 63]
134. ~funny(X0) | ~wise(X0) | ~rich(X0) [cnf transformation 65]
145. curious(lucy) [cnf transformation 25]
147. patient(X0) | rich(X0) [duplicate literal removal 126]
148. wise(X0) [duplicate literal removal 106]
149. ~wise(X0) | funny(X0) [duplicate literal removal 107]
189. 9 <=> ! [X1] : (~humble(X1) | rich(X1)) [avatar definition]
190. ~humble(X1) | rich(X1) <- (9) [avatar component clause 189]
207. 13 <=> ! [X3] : (~curious(X3) | ~funny(X3)) [avatar definition]
208. ~curious(X3) | ~funny(X3) <- (13) [avatar component clause 207]
210. 14 <=> humble(sK1) [avatar definition]
212. humble(sK1) <- (14) [avatar component clause 210]
214. 15 <=> rich(sK1) [avatar definition]
215. ~rich(sK1) <- (~15) [avatar component clause 214]
216. rich(sK1) <- (15) [avatar component clause 214]
217. 13 | 14 | 15 [avatar split clause 94,214,210,207]
286. ~funny(X0) | ~rich(X0) [subsumption resolution 134,148]
324. rich(X0) | ~humble(X0) [resolution 147,100]
326. 9 [avatar split clause 324,189]
327. funny(X0) [resolution 149,148]
328. rich(sK1) <- (9, 14) [resolution 190,212]
330. $false <- (9, 14, ~15) [subsumption resolution 328,215]
331. ~9 | ~14 | 15 [avatar contradiction clause 330]
339. ~rich(X0) [resolution 286,327]
454. $false <- (15) [resolution 339,216]
457. ~15 [avatar contradiction clause 454]
459. ~curious(X3) <- (13) [subsumption resolution 208,327]
460. $false <- (13) [resolution 459,145]
463. ~13 [avatar contradiction clause 460]
464. $false [avatar sat refutation 217,326,331,457,463]
% SZS output end Proof for 2637806846631120659343285
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not tall is either funny or not patient and vice versa.
If mary is not patient or wise then fred is not humble.
If someone is both not funny and not tall then someone is both not strong and brave and vice versa.
If someone is tall or not curious then someone is both not kind and not humble and vice versa.
Everyone who is either not brave or not quiet is both funny and not curious and vice versa.
Everyone who is both not curious and wise is strong or curious and vice versa.
Everyone who is both creative and not curious is curious and vice versa.
If mary is both kind and rich then john is both kind and not curious.
If someone is either creative or not kind then lucy is either not humble or tall.
Everyone who is funny or not tall is both quiet and patient and vice versa.
Everyone who is either not humble or not creative is not strong or kind.
Everyone who is both not generous and wise is curious and vice versa.
If someone is tall or creative then someone is either not brave or not quiet.
Everyone who is not funny or not wise is tall or strong.
Everyone who is not strong or not brave is not creative and vice versa.
Someone is either calm or strong.
Someone is rich or strong.
Someone is not wise or not patient.
Lucy is patient.
Someone is either not calm or funny.
Paul is both not humble and not generous.
Alice is both funny and not humble. | Lucy is not brave. | entailment | (![X]:(~tall(X)<=>(funny(X)<~>~patient(X))))&
(((~patient(mary)|wise(mary)))=>(~humble(fred)))&
((?[X]:((~funny(X)&~tall(X))))<=>(?[X]:((~strong(X)&brave(X)))))&
((?[X]:((tall(X)|~curious(X))))<=>(?[X]:((~kind(X)&~humble(X)))))&
(![X]:((~brave(X)<~>~quiet(X))<=>(funny(X)&~curious(X))))&
(![X]:((~curious(X)&wise(X))<=>(strong(X)|curious(X))))&
(![X]:((creative(X)&~curious(X))<=>curious(X)))&
(((kind(mary)&rich(mary)))=>((kind(john)&~curious(john))))&
((?[X]:((creative(X)<~>~kind(X))))=>((~humble(lucy)<~>tall(lucy))))&
(![X]:((funny(X)|~tall(X))<=>(quiet(X)&patient(X))))&
(![X]:((~humble(X)<~>~creative(X))=>(~strong(X)|kind(X))))&
(![X]:((~generous(X)&wise(X))<=>curious(X)))&
((?[X]:((tall(X)|creative(X))))=>(?[X]:((~brave(X)<~>~quiet(X)))))&
(![X]:((~funny(X)|~wise(X))=>(tall(X)|strong(X))))&
(![X]:((~strong(X)|~brave(X))<=>~creative(X)))&
(?[X]:((calm(X)<~>strong(X))))&
(?[X]:((rich(X)|strong(X))))&
(?[X]:((~wise(X)|~patient(X))))&
(patient(lucy))&
(?[X]:((~calm(X)<~>funny(X))))&
((~humble(paul)&~generous(paul)))&
((funny(alice)&~humble(alice))) | ~brave(lucy) | [
"p0",
"p2",
"p5",
"p6",
"p9",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6484016993941289589625359
% SZS output start Proof for 6484016993941289589625359
1. ! [X0] : (~tall(X0) <=> (funny(X0) <~> ~patient(X0))) [input p0]
3. ? [X0] : (~tall(X0) & ~funny(X0)) <=> ? [X0] : (brave(X0) & ~strong(X0)) [input p2]
6. ! [X0] : ((wise(X0) & ~curious(X0)) <=> (curious(X0) | strong(X0))) [input p5]
7. ! [X0] : ((~curious(X0) & creative(X0)) <=> curious(X0)) [input p6]
10. ! [X0] : ((~tall(X0) | funny(X0)) <=> (patient(X0) & quiet(X0))) [input p9]
15. ! [X0] : ((~brave(X0) | ~strong(X0)) <=> ~creative(X0)) [input p14]
23. brave(lucy) [input hypothesis]
24. ? [X0] : (~tall(X0) & ~funny(X0)) <=> ? [X1] : (brave(X1) & ~strong(X1)) [rectify 3]
36. ! [X0] : ((~tall(X0) | ((funny(X0) | patient(X0)) & (~patient(X0) | ~funny(X0)))) & (((patient(X0) | ~funny(X0)) & (~patient(X0) | funny(X0))) | tall(X0))) [nnf transformation 1]
37. (? [X0] : (~tall(X0) & ~funny(X0)) | ! [X1] : (~brave(X1) | strong(X1))) & (? [X1] : (brave(X1) & ~strong(X1)) | ! [X0] : (tall(X0) | funny(X0))) [nnf transformation 24]
38. (? [X0] : (~tall(X0) & ~funny(X0)) | ! [X1] : (~brave(X1) | strong(X1))) & (? [X2] : (brave(X2) & ~strong(X2)) | ! [X3] : (tall(X3) | funny(X3))) [rectify 37]
39. ? [X0] : (~tall(X0) & ~funny(X0)) => (~tall(sK0) & ~funny(sK0)) [choice axiom]
40. ? [X2] : (brave(X2) & ~strong(X2)) => (brave(sK1) & ~strong(sK1)) [choice axiom]
41. ((~tall(sK0) & ~funny(sK0)) | ! [X1] : (~brave(X1) | strong(X1))) & ((brave(sK1) & ~strong(sK1)) | ! [X3] : (tall(X3) | funny(X3))) [skolemisation 38,40,39]
49. ! [X0] : (((wise(X0) & ~curious(X0)) | (~curious(X0) & ~strong(X0))) & ((curious(X0) | strong(X0)) | (~wise(X0) | curious(X0)))) [nnf transformation 6]
50. ! [X0] : (((wise(X0) & ~curious(X0)) | (~curious(X0) & ~strong(X0))) & (curious(X0) | strong(X0) | ~wise(X0) | curious(X0))) [flattening 49]
51. ! [X0] : (((~curious(X0) & creative(X0)) | ~curious(X0)) & (curious(X0) | (curious(X0) | ~creative(X0)))) [nnf transformation 7]
52. ! [X0] : (((~curious(X0) & creative(X0)) | ~curious(X0)) & (curious(X0) | curious(X0) | ~creative(X0))) [flattening 51]
54. ! [X0] : (((~tall(X0) | funny(X0)) | (~patient(X0) | ~quiet(X0))) & ((patient(X0) & quiet(X0)) | (tall(X0) & ~funny(X0)))) [nnf transformation 10]
55. ! [X0] : ((~tall(X0) | funny(X0) | ~patient(X0) | ~quiet(X0)) & ((patient(X0) & quiet(X0)) | (tall(X0) & ~funny(X0)))) [flattening 54]
63. ! [X0] : (((~brave(X0) | ~strong(X0)) | creative(X0)) & (~creative(X0) | (brave(X0) & strong(X0)))) [nnf transformation 15]
64. ! [X0] : ((~brave(X0) | ~strong(X0) | creative(X0)) & (~creative(X0) | (brave(X0) & strong(X0)))) [flattening 63]
75. ~patient(X0) | funny(X0) | tall(X0) [cnf transformation 36]
83. ~funny(sK0) | ~brave(X1) | strong(X1) [cnf transformation 41]
84. ~tall(sK0) | ~brave(X1) | strong(X1) [cnf transformation 41]
98. ~curious(X0) | ~curious(X0) [cnf transformation 50]
101. curious(X0) | curious(X0) | ~creative(X0) [cnf transformation 52]
113. patient(X0) | tall(X0) [cnf transformation 55]
128. ~brave(X0) | ~strong(X0) | creative(X0) [cnf transformation 64]
140. brave(lucy) [cnf transformation 23]
141. curious(X0) | ~creative(X0) [duplicate literal removal 101]
144. ~curious(X0) [duplicate literal removal 98]
160. 4 <=> ! [X1] : (~brave(X1) | strong(X1)) [avatar definition]
161. ~brave(X1) | strong(X1) <- (4) [avatar component clause 160]
163. 5 <=> tall(sK0) [avatar definition]
165. ~tall(sK0) <- (~5) [avatar component clause 163]
166. 4 | ~5 [avatar split clause 84,163,160]
168. 6 <=> funny(sK0) [avatar definition]
170. ~funny(sK0) <- (~6) [avatar component clause 168]
171. 4 | ~6 [avatar split clause 83,168,160]
173. 7 <=> ! [X3] : (tall(X3) | funny(X3)) [avatar definition]
174. funny(X3) | tall(X3) <- (7) [avatar component clause 173]
216. ~creative(X0) [subsumption resolution 141,144]
259. ~brave(X0) | ~strong(X0) [subsumption resolution 128,216]
318. funny(X0) | tall(X0) | tall(X0) [resolution 75,113]
320. funny(X0) | tall(X0) [duplicate literal removal 318]
322. 7 [avatar split clause 320,173]
324. tall(sK0) <- (~6, 7) [resolution 174,170]
327. $false <- (~5, ~6, 7) [subsumption resolution 324,165]
328. 5 | 6 | ~7 [avatar contradiction clause 327]
329. ~brave(X1) <- (4) [subsumption resolution 161,259]
332. $false <- (4) [resolution 329,140]
335. ~4 [avatar contradiction clause 332]
336. $false [avatar sat refutation 166,171,322,328,335]
% SZS output end Proof for 6484016993941289589625359
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble or not creative is not calm.
Everyone who is happy or not rich is either not generous or creative.
Everyone who is both not generous and wise is curious or not happy and vice versa.
Everyone who is not tall is either strong or not tall.
Everyone who is both not curious and brave is not kind or not curious and vice versa.
Everyone who is kind is old.
If john is quiet then someone is either not wise or brave and vice versa.
If someone is either calm or not creative then someone is either wise or tall.
If someone is humble or not rich then someone is either generous or quiet and vice versa.
Everyone who is either happy or calm is either not old or not happy and vice versa.
If someone is both funny and creative then fred is either not patient or not happy.
Everyone who is not curious or not brave is either wise or not rich.
If someone is curious then someone is happy or calm.
Everyone who is not calm or happy is both wise and not rich.
Alice is not generous.
Alice is both funny and not patient.
Someone is funny or creative.
Alice is tall or happy.
Susan is funny.
Someone is not happy or tall. | Fred is curious. | entailment | (![X]:((humble(X)|~creative(X))=>~calm(X)))&
(![X]:((happy(X)|~rich(X))=>(~generous(X)<~>creative(X))))&
(![X]:((~generous(X)&wise(X))<=>(curious(X)|~happy(X))))&
(![X]:(~tall(X)=>(strong(X)<~>~tall(X))))&
(![X]:((~curious(X)&brave(X))<=>(~kind(X)|~curious(X))))&
(![X]:(kind(X)=>old(X)))&
((quiet(john))<=>(?[X]:((~wise(X)<~>brave(X)))))&
((?[X]:((calm(X)<~>~creative(X))))=>(?[X]:((wise(X)<~>tall(X)))))&
((?[X]:((humble(X)|~rich(X))))<=>(?[X]:((generous(X)<~>quiet(X)))))&
(![X]:((happy(X)<~>calm(X))<=>(~old(X)<~>~happy(X))))&
((?[X]:((funny(X)&creative(X))))=>((~patient(fred)<~>~happy(fred))))&
(![X]:((~curious(X)|~brave(X))=>(wise(X)<~>~rich(X))))&
((?[X]:(curious(X)))=>(?[X]:((happy(X)|calm(X)))))&
(![X]:((~calm(X)|happy(X))=>(wise(X)&~rich(X))))&
(~generous(alice))&
((funny(alice)&~patient(alice)))&
(?[X]:((funny(X)|creative(X))))&
((tall(alice)|happy(alice)))&
(funny(susan))&
(?[X]:((~happy(X)|tall(X)))) | curious(fred) | [
"p0",
"p1",
"p2",
"p4",
"p5",
"p6",
"p8",
"p9",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 4615779818146232370491707
% SZS output start Proof for 4615779818146232370491707
1. ! [X0] : ((~creative(X0) | humble(X0)) => ~calm(X0)) [input p0]
2. ! [X0] : ((~rich(X0) | happy(X0)) => (~generous(X0) <~> creative(X0))) [input p1]
3. ! [X0] : ((wise(X0) & ~generous(X0)) <=> (~happy(X0) | curious(X0))) [input p2]
5. ! [X0] : ((brave(X0) & ~curious(X0)) <=> (~curious(X0) | ~kind(X0))) [input p4]
6. ! [X0] : (kind(X0) => old(X0)) [input p5]
7. quiet(john) <=> ? [X0] : (~wise(X0) <~> brave(X0)) [input p6]
9. ? [X0] : (~rich(X0) | humble(X0)) <=> ? [X0] : (generous(X0) <~> quiet(X0)) [input p8]
10. ! [X0] : ((happy(X0) <~> calm(X0)) <=> (~old(X0) <~> ~happy(X0))) [input p9]
12. ! [X0] : ((~brave(X0) | ~curious(X0)) => (wise(X0) <~> ~rich(X0))) [input p11]
14. ! [X0] : ((happy(X0) | ~calm(X0)) => (~rich(X0) & wise(X0))) [input p13]
21. ~curious(fred) [input hypothesis]
23. ? [X0] : (~rich(X0) | humble(X0)) <=> ? [X1] : (generous(X1) <~> quiet(X1)) [rectify 9]
25. ! [X0] : (~calm(X0) | (creative(X0) & ~humble(X0))) [ennf transformation 1]
26. ! [X0] : ((~generous(X0) <~> creative(X0)) | (rich(X0) & ~happy(X0))) [ennf transformation 2]
28. ! [X0] : (old(X0) | ~kind(X0)) [ennf transformation 6]
31. ! [X0] : ((wise(X0) <~> ~rich(X0)) | (brave(X0) & curious(X0))) [ennf transformation 12]
33. ! [X0] : ((~rich(X0) & wise(X0)) | (~happy(X0) & calm(X0))) [ennf transformation 14]
34. ! [X0] : (((~creative(X0) | generous(X0)) & (creative(X0) | ~generous(X0))) | (rich(X0) & ~happy(X0))) [nnf transformation 26]
35. ! [X0] : (((wise(X0) & ~generous(X0)) | (happy(X0) & ~curious(X0))) & ((~happy(X0) | curious(X0)) | (~wise(X0) | generous(X0)))) [nnf transformation 3]
36. ! [X0] : (((wise(X0) & ~generous(X0)) | (happy(X0) & ~curious(X0))) & (~happy(X0) | curious(X0) | ~wise(X0) | generous(X0))) [flattening 35]
38. ! [X0] : (((brave(X0) & ~curious(X0)) | (curious(X0) & kind(X0))) & ((~curious(X0) | ~kind(X0)) | (~brave(X0) | curious(X0)))) [nnf transformation 5]
39. ! [X0] : (((brave(X0) & ~curious(X0)) | (curious(X0) & kind(X0))) & (~curious(X0) | ~kind(X0) | ~brave(X0) | curious(X0))) [flattening 38]
40. (quiet(john) | ! [X0] : ((~wise(X0) | ~brave(X0)) & (brave(X0) | wise(X0)))) & (? [X0] : ((~brave(X0) | wise(X0)) & (brave(X0) | ~wise(X0))) | ~quiet(john)) [nnf transformation 7]
41. (quiet(john) | ! [X0] : ((~wise(X0) | ~brave(X0)) & (brave(X0) | wise(X0)))) & (? [X1] : ((~brave(X1) | wise(X1)) & (brave(X1) | ~wise(X1))) | ~quiet(john)) [rectify 40]
42. ? [X1] : ((~brave(X1) | wise(X1)) & (brave(X1) | ~wise(X1))) => ((~brave(sK0) | wise(sK0)) & (brave(sK0) | ~wise(sK0))) [choice axiom]
43. (quiet(john) | ! [X0] : ((~wise(X0) | ~brave(X0)) & (brave(X0) | wise(X0)))) & (((~brave(sK0) | wise(sK0)) & (brave(sK0) | ~wise(sK0))) | ~quiet(john)) [skolemisation 41,42]
48. (? [X0] : (~rich(X0) | humble(X0)) | ! [X1] : ((generous(X1) | ~quiet(X1)) & (quiet(X1) | ~generous(X1)))) & (? [X1] : ((~quiet(X1) | ~generous(X1)) & (quiet(X1) | generous(X1))) | ! [X0] : (rich(X0) & ~humble(X0))) [nnf transformation 23]
49. (? [X0] : (~rich(X0) | humble(X0)) | ! [X1] : ((generous(X1) | ~quiet(X1)) & (quiet(X1) | ~generous(X1)))) & (? [X2] : ((~quiet(X2) | ~generous(X2)) & (quiet(X2) | generous(X2))) | ! [X3] : (rich(X3) & ~humble(X3))) [rectify 48]
50. ? [X0] : (~rich(X0) | humble(X0)) => (~rich(sK2) | humble(sK2)) [choice axiom]
51. ? [X2] : ((~quiet(X2) | ~generous(X2)) & (quiet(X2) | generous(X2))) => ((~quiet(sK3) | ~generous(sK3)) & (quiet(sK3) | generous(sK3))) [choice axiom]
52. ((~rich(sK2) | humble(sK2)) | ! [X1] : ((generous(X1) | ~quiet(X1)) & (quiet(X1) | ~generous(X1)))) & (((~quiet(sK3) | ~generous(sK3)) & (quiet(sK3) | generous(sK3))) | ! [X3] : (rich(X3) & ~humble(X3))) [skolemisation 49,51,50]
53. ! [X0] : ((((~calm(X0) | ~happy(X0)) & (calm(X0) | happy(X0))) | ((~old(X0) | happy(X0)) & (~happy(X0) | old(X0)))) & (((happy(X0) | old(X0)) & (~happy(X0) | ~old(X0))) | ((happy(X0) | ~calm(X0)) & (calm(X0) | ~happy(X0))))) [nnf transformation 10]
55. ! [X0] : (((rich(X0) | ~wise(X0)) & (~rich(X0) | wise(X0))) | (brave(X0) & curious(X0))) [nnf transformation 31]
63. ~calm(X0) | ~humble(X0) [cnf transformation 25]
64. ~calm(X0) | creative(X0) [cnf transformation 25]
68. ~creative(X0) | generous(X0) | rich(X0) [cnf transformation 34]
70. ~curious(X0) | ~generous(X0) [cnf transformation 36]
71. ~generous(X0) | happy(X0) [cnf transformation 36]
73. wise(X0) | happy(X0) [cnf transformation 36]
77. ~curious(X0) | kind(X0) [cnf transformation 39]
80. brave(X0) | curious(X0) [cnf transformation 39]
81. ~kind(X0) | old(X0) [cnf transformation 28]
85. quiet(john) | ~wise(X0) | ~brave(X0) [cnf transformation 43]
95. ~rich(sK2) | humble(sK2) | generous(X1) | ~quiet(X1) [cnf transformation 52]
96. ~happy(X0) | ~old(X0) | calm(X0) | ~happy(X0) [cnf transformation 53]
101. calm(X0) | happy(X0) | ~old(X0) | happy(X0) [cnf transformation 53]
108. ~wise(X0) | rich(X0) | curious(X0) [cnf transformation 55]
112. wise(X0) | ~happy(X0) [cnf transformation 33]
113. ~rich(X0) | calm(X0) [cnf transformation 33]
114. ~rich(X0) | ~happy(X0) [cnf transformation 33]
122. ~curious(fred) [cnf transformation 21]
123. ~happy(X0) | ~old(X0) | calm(X0) [duplicate literal removal 96]
125. ~old(X0) | happy(X0) | calm(X0) [duplicate literal removal 101]
129. 1 <=> ! [X0] : (~wise(X0) | ~brave(X0)) [avatar definition]
130. ~wise(X0) | ~brave(X0) <- (1) [avatar component clause 129]
132. 2 <=> quiet(john) [avatar definition]
134. quiet(john) <- (2) [avatar component clause 132]
135. 1 | 2 [avatar split clause 85,132,129]
152. 6 <=> ! [X1] : creative(X1) [avatar definition]
153. creative(X1) <- (6) [avatar component clause 152]
173. 10 <=> ! [X1] : (generous(X1) | ~quiet(X1)) [avatar definition]
174. ~quiet(X1) | generous(X1) <- (10) [avatar component clause 173]
176. 11 <=> humble(sK2) [avatar definition]
178. humble(sK2) <- (11) [avatar component clause 176]
180. 12 <=> rich(sK2) [avatar definition]
181. rich(sK2) <- (12) [avatar component clause 180]
182. ~rich(sK2) <- (~12) [avatar component clause 180]
183. 10 | 11 | ~12 [avatar split clause 95,180,176,173]
189. 14 <=> ! [X3] : rich(X3) [avatar definition]
190. rich(X3) <- (14) [avatar component clause 189]
207. ~old(X0) | calm(X0) [subsumption resolution 123,125]
234. wise(X0) [subsumption resolution 112,73]
277. curious(X1) | rich(X1) [resolution 108,234]
281. $false <- (~12, 14) [resolution 190,182]
286. 12 | ~14 [avatar contradiction clause 281]
299. calm(sK2) <- (12) [resolution 181,113]
314. ~humble(sK2) <- (12) [resolution 299,63]
315. $false <- (11, 12) [subsumption resolution 314,178]
316. ~11 | ~12 [avatar contradiction clause 315]
320. kind(X0) | rich(X0) [resolution 277,77]
322. ~generous(X2) | rich(X2) [resolution 277,70]
347. old(X0) | rich(X0) [resolution 320,81]
352. rich(X1) | calm(X1) [resolution 347,207]
354. calm(X1) [subsumption resolution 352,113]
359. creative(X1) [resolution 354,64]
361. 6 [avatar split clause 359,152]
363. generous(X0) | rich(X0) <- (6) [resolution 153,68]
372. rich(X0) <- (6) [subsumption resolution 363,322]
373. 14 | ~6 [avatar split clause 372,152,189]
377. ~happy(X2) <- (14) [resolution 190,114]
383. generous(john) <- (2, 10) [resolution 174,134]
397. happy(john) <- (2, 10) [resolution 383,71]
398. $false <- (2, 10, 14) [subsumption resolution 397,377]
399. ~2 | ~10 | ~14 [avatar contradiction clause 398]
400. ~brave(X0) <- (1) [subsumption resolution 130,234]
404. curious(X2) <- (1) [resolution 400,80]
408. $false <- (1) [resolution 404,122]
412. ~1 [avatar contradiction clause 408]
413. $false [avatar sat refutation 135,183,286,316,361,373,399,412]
% SZS output end Proof for 4615779818146232370491707
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If fred is old then john is not rich. If someone is humble then someone is both tall and not humble and vice versa. Everyone who is either kind or not calm is not brave and vice versa. If someone is tall then someone is wise and vice versa. Everyone who is not curious or curious is either not funny or brave. Everyone who is both brave and kind is not strong or happy and vice versa. If john is not happy or patient then someone is kind. Everyone who is strong is both not tall and funny and vice versa. If paul is either not wise or old then someone is not funny or not rich. If someone is tall or not tall then someone is not happy and vice versa. If alice is not generous or not quiet then someone is both not brave and not strong and vice versa. Everyone who is either not strong or not generous is patient. Everyone who is rich is not calm or not brave. Mary is not kind or creative. Someone is not curious. Mary is both not patient and rich. Someone is both not creative and calm. Fred is either creative or generous. Someone is both not calm and old. | Alice is not funny. | contradiction | ((old(fred))=>(~rich(john)))&
((?[X]:(humble(X)))<=>(?[X]:((tall(X)&~humble(X)))))&
(![X]:((kind(X)<~>~calm(X))<=>~brave(X)))&
((?[X]:(tall(X)))<=>(?[X]:(wise(X))))&
(![X]:((~curious(X)|curious(X))=>(~funny(X)<~>brave(X))))&
(![X]:((brave(X)&kind(X))<=>(~strong(X)|happy(X))))&
(((~happy(john)|patient(john)))=>(?[X]:(kind(X))))&
(![X]:(strong(X)<=>(~tall(X)&funny(X))))&
(((~wise(paul)<~>old(paul)))=>(?[X]:((~funny(X)|~rich(X)))))&
((?[X]:((tall(X)|~tall(X))))<=>(?[X]:(~happy(X))))&
(((~generous(alice)|~quiet(alice)))<=>(?[X]:((~brave(X)&~strong(X)))))&
(![X]:((~strong(X)<~>~generous(X))=>patient(X)))&
(![X]:(rich(X)=>(~calm(X)|~brave(X))))&
((~kind(mary)|creative(mary)))&
(?[X]:(~curious(X)))&
((~patient(mary)&rich(mary)))&
(?[X]:((~creative(X)&calm(X))))&
((creative(fred)<~>generous(fred)))&
(?[X]:((~calm(X)&old(X)))) | ~funny(alice) | [
"p4",
"p5",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 5408373811902567921642480
% SZS output start Proof for 5408373811902567921642480
5. ! [X0] : ((curious(X0) | ~curious(X0)) => (~funny(X0) <~> brave(X0))) [input p4]
6. ! [X0] : ((kind(X0) & brave(X0)) <=> (happy(X0) | ~strong(X0))) [input p5]
8. ! [X0] : (strong(X0) <=> (funny(X0) & ~tall(X0))) [input p7]
20. ~funny(alice) [input hypothesis]
25. ! [X0] : ((~funny(X0) <~> brave(X0)) | (~curious(X0) & curious(X0))) [ennf transformation 5]
42. ! [X0] : (((~brave(X0) | funny(X0)) & (brave(X0) | ~funny(X0))) | (~curious(X0) & curious(X0))) [nnf transformation 25]
43. ! [X0] : (((kind(X0) & brave(X0)) | (~happy(X0) & strong(X0))) & ((happy(X0) | ~strong(X0)) | (~kind(X0) | ~brave(X0)))) [nnf transformation 6]
44. ! [X0] : (((kind(X0) & brave(X0)) | (~happy(X0) & strong(X0))) & (happy(X0) | ~strong(X0) | ~kind(X0) | ~brave(X0))) [flattening 43]
47. ! [X0] : ((strong(X0) | (~funny(X0) | tall(X0))) & ((funny(X0) & ~tall(X0)) | ~strong(X0))) [nnf transformation 8]
48. ! [X0] : ((strong(X0) | ~funny(X0) | tall(X0)) & ((funny(X0) & ~tall(X0)) | ~strong(X0))) [flattening 47]
82. ~brave(X0) | funny(X0) | curious(X0) [cnf transformation 42]
83. ~brave(X0) | funny(X0) | ~curious(X0) [cnf transformation 42]
85. strong(X0) | brave(X0) [cnf transformation 44]
92. ~strong(X0) | funny(X0) [cnf transformation 48]
117. ~funny(alice) [cnf transformation 20]
164. ~brave(X0) | funny(X0) [subsumption resolution 82,83]
253. funny(X1) | brave(X1) [resolution 92,85]
255. funny(X1) [subsumption resolution 253,164]
256. $false [resolution 255,117]
% SZS output end Proof for 5408373811902567921642480
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is calm is curious or not humble. Everyone who is either not strong or not quiet is both calm and not generous and vice versa. If someone is either not funny or patient then someone is not patient or generous. If lucy is either quiet or kind then someone is generous or not old and vice versa. If mary is both not generous and humble then someone is both not funny and not rich and vice versa. Everyone who is not brave is quiet and vice versa. If someone is either old or not patient then john is not patient. If susan is wise then someone is wise or not creative and vice versa. Everyone who is either not kind or not curious is either rich or not curious and vice versa. If someone is either quiet or curious then lucy is either not strong or quiet. Everyone who is either not wise or old is either not brave or not calm and vice versa. Everyone who is both strong and not calm is not brave and vice versa. If someone is patient or not strong then fred is not calm and vice versa. Everyone who is either creative or happy is both kind and not happy. If someone is not kind or not old then someone is either not tall or not rich and vice versa. Everyone who is not creative or not patient is both not generous and not patient and vice versa. Someone is not happy. Someone is wise or not rich. Someone is either humble or calm. John is both humble and brave. Alice is quiet or curious. Paul is patient. Lucy is either funny or not kind. Someone is either not funny or calm. | Mary is strong. | neutral | (![X]:(calm(X)=>(curious(X)|~humble(X))))&
(![X]:((~strong(X)<~>~quiet(X))<=>(calm(X)&~generous(X))))&
((?[X]:((~funny(X)<~>patient(X))))=>(?[X]:((~patient(X)|generous(X)))))&
(((quiet(lucy)<~>kind(lucy)))<=>(?[X]:((generous(X)|~old(X)))))&
(((~generous(mary)&humble(mary)))<=>(?[X]:((~funny(X)&~rich(X)))))&
(![X]:(~brave(X)<=>quiet(X)))&
((?[X]:((old(X)<~>~patient(X))))=>(~patient(john)))&
((wise(susan))<=>(?[X]:((wise(X)|~creative(X)))))&
(![X]:((~kind(X)<~>~curious(X))<=>(rich(X)<~>~curious(X))))&
((?[X]:((quiet(X)<~>curious(X))))=>((~strong(lucy)<~>quiet(lucy))))&
(![X]:((~wise(X)<~>old(X))<=>(~brave(X)<~>~calm(X))))&
(![X]:((strong(X)&~calm(X))<=>~brave(X)))&
((?[X]:((patient(X)|~strong(X))))<=>(~calm(fred)))&
(![X]:((creative(X)<~>happy(X))=>(kind(X)&~happy(X))))&
((?[X]:((~kind(X)|~old(X))))<=>(?[X]:((~tall(X)<~>~rich(X)))))&
(![X]:((~creative(X)|~patient(X))<=>(~generous(X)&~patient(X))))&
(?[X]:(~happy(X)))&
(?[X]:((wise(X)|~rich(X))))&
(?[X]:((humble(X)<~>calm(X))))&
((humble(john)&brave(john)))&
((quiet(alice)|curious(alice)))&
(patient(paul))&
((funny(lucy)<~>~kind(lucy)))&
(?[X]:((~funny(X)<~>calm(X)))) | strong(mary) | [] | null | 0 |
Everyone who is patient is both tall and not calm.
If lucy is both not calm and not curious then alice is not old or humble and vice versa.
If fred is either not humble or calm then someone is either not funny or not generous.
Everyone who is quiet or not strong is both not rich and calm.
If fred is both not creative and generous then someone is either not rich or not generous and vice versa.
If lucy is both old and creative then someone is humble or rich.
Everyone who is not brave is not creative and vice versa.
If paul is not tall or not curious then fred is not creative and vice versa.
Everyone who is strong or calm is either not patient or wise and vice versa.
If someone is wise then someone is both happy and quiet and vice versa.
Everyone who is not creative is both brave and humble and vice versa.
Everyone who is either strong or not patient is not rich and vice versa.
If someone is funny or not quiet then someone is wise or not happy.
Everyone who is both not tall and not strong is both happy and not funny.
Everyone who is not creative is either quiet or not humble and vice versa.
If someone is not patient or kind then someone is either calm or curious.
Paul is quiet or not old.
John is tall or strong.
Someone is either not creative or calm.
Someone is both not wise and not generous.
John is both brave and not wise. | Alice is patient. | contradiction | (![X]:(patient(X)=>(tall(X)&~calm(X))))&
(((~calm(lucy)&~curious(lucy)))<=>((~old(alice)|humble(alice))))&
(((~humble(fred)<~>calm(fred)))=>(?[X]:((~funny(X)<~>~generous(X)))))&
(![X]:((quiet(X)|~strong(X))=>(~rich(X)&calm(X))))&
(((~creative(fred)&generous(fred)))<=>(?[X]:((~rich(X)<~>~generous(X)))))&
(((old(lucy)&creative(lucy)))=>(?[X]:((humble(X)|rich(X)))))&
(![X]:(~brave(X)<=>~creative(X)))&
(((~tall(paul)|~curious(paul)))<=>(~creative(fred)))&
(![X]:((strong(X)|calm(X))<=>(~patient(X)<~>wise(X))))&
((?[X]:(wise(X)))<=>(?[X]:((happy(X)&quiet(X)))))&
(![X]:(~creative(X)<=>(brave(X)&humble(X))))&
(![X]:((strong(X)<~>~patient(X))<=>~rich(X)))&
((?[X]:((funny(X)|~quiet(X))))=>(?[X]:((wise(X)|~happy(X)))))&
(![X]:((~tall(X)&~strong(X))=>(happy(X)&~funny(X))))&
(![X]:(~creative(X)<=>(quiet(X)<~>~humble(X))))&
((?[X]:((~patient(X)|kind(X))))=>(?[X]:((calm(X)<~>curious(X)))))&
((quiet(paul)|~old(paul)))&
((tall(john)|strong(john)))&
(?[X]:((~creative(X)<~>calm(X))))&
(?[X]:((~wise(X)&~generous(X))))&
((brave(john)&~wise(john))) | patient(alice) | [
"p0",
"p3",
"p6",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 97872702627685737486728
% SZS output start Proof for 97872702627685737486728
1. ! [X0] : (patient(X0) => (~calm(X0) & tall(X0))) [input p0]
4. ! [X0] : ((~strong(X0) | quiet(X0)) => (calm(X0) & ~rich(X0))) [input p3]
7. ! [X0] : (~brave(X0) <=> ~creative(X0)) [input p6]
11. ! [X0] : (~creative(X0) <=> (humble(X0) & brave(X0))) [input p10]
15. ! [X0] : (~creative(X0) <=> (quiet(X0) <~> ~humble(X0))) [input p14]
22. patient(alice) [input hypothesis]
27. ! [X0] : ((~calm(X0) & tall(X0)) | ~patient(X0)) [ennf transformation 1]
29. ! [X0] : ((calm(X0) & ~rich(X0)) | (strong(X0) & ~quiet(X0))) [ennf transformation 4]
48. ! [X0] : ((~brave(X0) | creative(X0)) & (~creative(X0) | brave(X0))) [nnf transformation 7]
58. ! [X0] : ((~creative(X0) | (~humble(X0) | ~brave(X0))) & ((humble(X0) & brave(X0)) | creative(X0))) [nnf transformation 11]
59. ! [X0] : ((~creative(X0) | ~humble(X0) | ~brave(X0)) & ((humble(X0) & brave(X0)) | creative(X0))) [flattening 58]
64. ! [X0] : ((~creative(X0) | ((quiet(X0) | humble(X0)) & (~humble(X0) | ~quiet(X0)))) & (((humble(X0) | ~quiet(X0)) & (~humble(X0) | quiet(X0))) | creative(X0))) [nnf transformation 15]
75. ~calm(X0) | ~patient(X0) [cnf transformation 27]
87. ~quiet(X0) | calm(X0) [cnf transformation 29]
96. ~creative(X0) | brave(X0) [cnf transformation 48]
97. ~brave(X0) | creative(X0) [cnf transformation 48]
110. brave(X0) | creative(X0) [cnf transformation 59]
112. ~creative(X0) | ~humble(X0) | ~brave(X0) [cnf transformation 59]
124. ~creative(X0) | quiet(X0) | humble(X0) [cnf transformation 64]
135. patient(alice) [cnf transformation 22]
255. ~creative(X0) | ~humble(X0) [subsumption resolution 112,96]
256. creative(X0) [subsumption resolution 110,97]
275. quiet(X0) | humble(X0) [subsumption resolution 124,256]
326. ~humble(X1) [resolution 255,256]
328. humble(X0) | calm(X0) [resolution 275,87]
329. calm(X0) [subsumption resolution 328,326]
331. ~patient(X0) [resolution 329,75]
333. $false [resolution 331,135]
% SZS output end Proof for 97872702627685737486728
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not calm is strong or not humble. Everyone who is not quiet or not happy is either not brave or not curious. Everyone who is not humble or kind is both tall and brave and vice versa. Everyone who is not old or not generous is either strong or brave. Everyone who is brave or not curious is both wise and not humble. Everyone who is both not humble and not quiet is generous or not wise. Everyone who is either not creative or happy is humble or not tall and vice versa. Everyone who is creative is both brave and curious and vice versa. Everyone who is not quiet is both not wise and quiet and vice versa. Everyone who is not kind or not rich is either not kind or humble. If lucy is either not tall or tall then paul is happy and vice versa. If someone is both wise and not kind then mary is creative and vice versa. If someone is either strong or not wise then someone is both not calm and old. If paul is not old then someone is both strong and tall. Someone is either not rich or not old. Someone is either kind or generous. Someone is quiet or wise. Mary is wise. Someone is not curious or generous. | Mary is not calm. | neutral | (![X]:(~calm(X)=>(strong(X)|~humble(X))))&
(![X]:((~quiet(X)|~happy(X))=>(~brave(X)<~>~curious(X))))&
(![X]:((~humble(X)|kind(X))<=>(tall(X)&brave(X))))&
(![X]:((~old(X)|~generous(X))=>(strong(X)<~>brave(X))))&
(![X]:((brave(X)|~curious(X))=>(wise(X)&~humble(X))))&
(![X]:((~humble(X)&~quiet(X))=>(generous(X)|~wise(X))))&
(![X]:((~creative(X)<~>happy(X))<=>(humble(X)|~tall(X))))&
(![X]:(creative(X)<=>(brave(X)&curious(X))))&
(![X]:(~quiet(X)<=>(~wise(X)&quiet(X))))&
(![X]:((~kind(X)|~rich(X))=>(~kind(X)<~>humble(X))))&
(((~tall(lucy)<~>tall(lucy)))<=>(happy(paul)))&
((?[X]:((wise(X)&~kind(X))))<=>(creative(mary)))&
((?[X]:((strong(X)<~>~wise(X))))=>(?[X]:((~calm(X)&old(X)))))&
((~old(paul))=>(?[X]:((strong(X)&tall(X)))))&
(?[X]:((~rich(X)<~>~old(X))))&
(?[X]:((kind(X)<~>generous(X))))&
(?[X]:((quiet(X)|wise(X))))&
(wise(mary))&
(?[X]:((~curious(X)|generous(X)))) | ~calm(mary) | [] | null | 0 |
If someone is both not generous and not old then mary is both not funny and wise. Everyone who is not humble is either kind or not funny. Everyone who is both not funny and generous is not funny and vice versa. Everyone who is not quiet or funny is happy. If someone is either humble or not funny then someone is not funny. If someone is either generous or happy then someone is either not funny or happy and vice versa. Everyone who is either not happy or not humble is not patient or not strong and vice versa. If someone is creative then someone is funny. If alice is both not generous and not tall then someone is both not patient and strong. Everyone who is wise or not wise is both not generous and not humble and vice versa. If john is both not calm and strong then someone is both tall and humble. If alice is either not curious or not humble then someone is either strong or not wise. If mary is both not brave and strong then someone is old or not happy and vice versa. Everyone who is either curious or tall is either funny or not generous and vice versa. Everyone who is both quiet and not creative is wise or tall and vice versa. If paul is both not creative and wise then john is either humble or not kind and vice versa. Lucy is both not creative and calm. Paul is tall or not brave. Someone is both strong and not curious. John is wise or not patient. Someone is either not kind or not curious. Mary is creative or generous. Someone is not patient or humble. | Alice is kind. | entailment | ((?[X]:((~generous(X)&~old(X))))=>((~funny(mary)&wise(mary))))&
(![X]:(~humble(X)=>(kind(X)<~>~funny(X))))&
(![X]:((~funny(X)&generous(X))<=>~funny(X)))&
(![X]:((~quiet(X)|funny(X))=>happy(X)))&
((?[X]:((humble(X)<~>~funny(X))))=>(?[X]:(~funny(X))))&
((?[X]:((generous(X)<~>happy(X))))<=>(?[X]:((~funny(X)<~>happy(X)))))&
(![X]:((~happy(X)<~>~humble(X))<=>(~patient(X)|~strong(X))))&
((?[X]:(creative(X)))=>(?[X]:(funny(X))))&
(((~generous(alice)&~tall(alice)))=>(?[X]:((~patient(X)&strong(X)))))&
(![X]:((wise(X)|~wise(X))<=>(~generous(X)&~humble(X))))&
(((~calm(john)&strong(john)))=>(?[X]:((tall(X)&humble(X)))))&
(((~curious(alice)<~>~humble(alice)))=>(?[X]:((strong(X)<~>~wise(X)))))&
(((~brave(mary)&strong(mary)))<=>(?[X]:((old(X)|~happy(X)))))&
(![X]:((curious(X)<~>tall(X))<=>(funny(X)<~>~generous(X))))&
(![X]:((quiet(X)&~creative(X))<=>(wise(X)|tall(X))))&
(((~creative(paul)&wise(paul)))<=>((humble(john)<~>~kind(john))))&
((~creative(lucy)&calm(lucy)))&
((tall(paul)|~brave(paul)))&
(?[X]:((strong(X)&~curious(X))))&
((wise(john)|~patient(john)))&
(?[X]:((~kind(X)<~>~curious(X))))&
((creative(mary)|generous(mary)))&
(?[X]:((~patient(X)|humble(X)))) | kind(alice) | [
"p1",
"p2",
"p4",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 5107761771217647235532287
% SZS output start Proof for 5107761771217647235532287
2. ! [X0] : (~humble(X0) => (kind(X0) <~> ~funny(X0))) [input p1]
3. ! [X0] : ((generous(X0) & ~funny(X0)) <=> ~funny(X0)) [input p2]
5. ? [X0] : (humble(X0) <~> ~funny(X0)) => ? [X0] : ~funny(X0) [input p4]
10. ! [X0] : ((~wise(X0) | wise(X0)) <=> (~humble(X0) & ~generous(X0))) [input p9]
24. ~kind(alice) [input hypothesis]
25. ? [X0] : (humble(X0) <~> ~funny(X0)) => ? [X1] : ~funny(X1) [rectify 5]
31. ! [X0] : ((kind(X0) <~> ~funny(X0)) | humble(X0)) [ennf transformation 2]
33. ? [X1] : ~funny(X1) | ! [X0] : (humble(X0) <=> ~funny(X0)) [ennf transformation 25]
38. ! [X0] : (((funny(X0) | ~kind(X0)) & (~funny(X0) | kind(X0))) | humble(X0)) [nnf transformation 31]
39. ! [X0] : (((generous(X0) & ~funny(X0)) | funny(X0)) & (~funny(X0) | (~generous(X0) | funny(X0)))) [nnf transformation 3]
40. ! [X0] : (((generous(X0) & ~funny(X0)) | funny(X0)) & (~funny(X0) | ~generous(X0) | funny(X0))) [flattening 39]
41. ? [X1] : ~funny(X1) | ! [X0] : ((humble(X0) | funny(X0)) & (~funny(X0) | ~humble(X0))) [nnf transformation 33]
42. ? [X0] : ~funny(X0) | ! [X1] : ((humble(X1) | funny(X1)) & (~funny(X1) | ~humble(X1))) [rectify 41]
43. ? [X0] : ~funny(X0) => ~funny(sK0) [choice axiom]
44. ~funny(sK0) | ! [X1] : ((humble(X1) | funny(X1)) & (~funny(X1) | ~humble(X1))) [skolemisation 42,43]
57. ! [X0] : (((~wise(X0) | wise(X0)) | (humble(X0) | generous(X0))) & ((~humble(X0) & ~generous(X0)) | (wise(X0) & ~wise(X0)))) [nnf transformation 10]
58. ! [X0] : ((~wise(X0) | wise(X0) | humble(X0) | generous(X0)) & ((~humble(X0) & ~generous(X0)) | (wise(X0) & ~wise(X0)))) [flattening 57]
81. ~funny(X0) | kind(X0) | humble(X0) [cnf transformation 38]
85. funny(X0) | generous(X0) [cnf transformation 40]
89. ~funny(sK0) | humble(X1) | funny(X1) [cnf transformation 44]
107. ~generous(X0) | ~wise(X0) [cnf transformation 58]
108. ~generous(X0) | wise(X0) [cnf transformation 58]
109. ~humble(X0) | ~wise(X0) [cnf transformation 58]
110. ~humble(X0) | wise(X0) [cnf transformation 58]
149. ~kind(alice) [cnf transformation 24]
164. 4 <=> ! [X1] : (humble(X1) | funny(X1)) [avatar definition]
165. humble(X1) | funny(X1) <- (4) [avatar component clause 164]
167. 5 <=> funny(sK0) [avatar definition]
169. ~funny(sK0) <- (~5) [avatar component clause 167]
170. 4 | ~5 [avatar split clause 89,167,164]
239. ~humble(X0) [subsumption resolution 109,110]
240. ~generous(X0) [subsumption resolution 107,108]
339. generous(sK0) <- (~5) [resolution 85,169]
342. $false <- (~5) [subsumption resolution 339,240]
343. 5 [avatar contradiction clause 342]
344. funny(X1) <- (4) [subsumption resolution 165,239]
369. kind(X0) | humble(X0) <- (4) [resolution 81,344]
373. kind(X0) <- (4) [subsumption resolution 369,239]
382. $false <- (4) [resolution 373,149]
384. ~4 [avatar contradiction clause 382]
385. $false [avatar sat refutation 170,343,384]
% SZS output end Proof for 5107761771217647235532287
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not old or wise is not tall or happy and vice versa.
Everyone who is both not happy and patient is both generous and not happy.
Everyone who is either not wise or humble is both not kind and not brave.
Everyone who is either brave or old is both not kind and strong and vice versa.
Everyone who is funny is not patient or not old.
Everyone who is quiet is curious and vice versa.
Everyone who is both brave and funny is both not creative and strong and vice versa.
If john is both tall and not kind then someone is both not rich and wise and vice versa.
Everyone who is old is both brave and humble and vice versa.
If mary is not curious or wise then someone is not curious and vice versa.
Everyone who is either not humble or patient is strong.
Everyone who is both funny and not old is both not humble and not brave and vice versa.
Everyone who is calm is not strong.
If lucy is quiet then paul is both not curious and quiet.
Everyone who is either not quiet or not curious is not happy and vice versa.
If paul is both creative and not kind then someone is either patient or not calm.
Someone is not quiet.
Fred is either old or not curious.
Alice is not old.
Paul is not tall.
Alice is either not quiet or old.
Mary is tall.
Someone is wise or generous.
Lucy is both not patient and not generous. | Fred is rich. | neutral | (![X]:((~old(X)|wise(X))<=>(~tall(X)|happy(X))))&
(![X]:((~happy(X)&patient(X))=>(generous(X)&~happy(X))))&
(![X]:((~wise(X)<~>humble(X))=>(~kind(X)&~brave(X))))&
(![X]:((brave(X)<~>old(X))<=>(~kind(X)&strong(X))))&
(![X]:(funny(X)=>(~patient(X)|~old(X))))&
(![X]:(quiet(X)<=>curious(X)))&
(![X]:((brave(X)&funny(X))<=>(~creative(X)&strong(X))))&
(((tall(john)&~kind(john)))<=>(?[X]:((~rich(X)&wise(X)))))&
(![X]:(old(X)<=>(brave(X)&humble(X))))&
(((~curious(mary)|wise(mary)))<=>(?[X]:(~curious(X))))&
(![X]:((~humble(X)<~>patient(X))=>strong(X)))&
(![X]:((funny(X)&~old(X))<=>(~humble(X)&~brave(X))))&
(![X]:(calm(X)=>~strong(X)))&
((quiet(lucy))=>((~curious(paul)&quiet(paul))))&
(![X]:((~quiet(X)<~>~curious(X))<=>~happy(X)))&
(((creative(paul)&~kind(paul)))=>(?[X]:((patient(X)<~>~calm(X)))))&
(?[X]:(~quiet(X)))&
((old(fred)<~>~curious(fred)))&
(~old(alice))&
(~tall(paul))&
((~quiet(alice)<~>old(alice)))&
(tall(mary))&
(?[X]:((wise(X)|generous(X))))&
((~patient(lucy)&~generous(lucy))) | rich(fred) | [] | null | 0 |
Everyone who is patient is both not rich and not patient.
If fred is either not humble or rich then someone is not quiet or not humble.
Everyone who is generous is curious or not brave and vice versa.
Everyone who is not humble is either quiet or not funny and vice versa.
Everyone who is both not happy and wise is either brave or not old.
Everyone who is patient is not strong or not calm and vice versa.
Everyone who is tall or creative is creative or old.
Everyone who is not patient or not funny is not creative or not quiet.
Everyone who is quiet or curious is both wise and not kind.
If someone is rich or creative then mary is creative.
Everyone who is brave is patient.
If someone is either not calm or not rich then someone is strong or curious and vice versa.
If someone is not generous or old then someone is either kind or not brave.
If someone is both not happy and not generous then someone is brave or not creative and vice versa.
Everyone who is both funny and happy is both not humble and calm and vice versa.
Paul is both not tall and rich.
Someone is curious.
Mary is not brave or creative.
John is not curious or not calm.
Fred is rich or happy.
Someone is kind.
Alice is either curious or not wise. | John is funny. | entailment | (![X]:(patient(X)=>(~rich(X)&~patient(X))))&
(((~humble(fred)<~>rich(fred)))=>(?[X]:((~quiet(X)|~humble(X)))))&
(![X]:(generous(X)<=>(curious(X)|~brave(X))))&
(![X]:(~humble(X)<=>(quiet(X)<~>~funny(X))))&
(![X]:((~happy(X)&wise(X))=>(brave(X)<~>~old(X))))&
(![X]:(patient(X)<=>(~strong(X)|~calm(X))))&
(![X]:((tall(X)|creative(X))=>(creative(X)|old(X))))&
(![X]:((~patient(X)|~funny(X))=>(~creative(X)|~quiet(X))))&
(![X]:((quiet(X)|curious(X))=>(wise(X)&~kind(X))))&
((?[X]:((rich(X)|creative(X))))=>(creative(mary)))&
(![X]:(brave(X)=>patient(X)))&
((?[X]:((~calm(X)<~>~rich(X))))<=>(?[X]:((strong(X)|curious(X)))))&
((?[X]:((~generous(X)|old(X))))=>(?[X]:((kind(X)<~>~brave(X)))))&
((?[X]:((~happy(X)&~generous(X))))<=>(?[X]:((brave(X)|~creative(X)))))&
(![X]:((funny(X)&happy(X))<=>(~humble(X)&calm(X))))&
((~tall(paul)&rich(paul)))&
(?[X]:(curious(X)))&
((~brave(mary)|creative(mary)))&
((~curious(john)|~calm(john)))&
((rich(fred)|happy(fred)))&
(?[X]:(kind(X)))&
((curious(alice)<~>~wise(alice))) | funny(john) | [
"p0",
"p2",
"p3",
"p5",
"p7",
"p10",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2780790415386858147905705
% SZS output start Proof for 2780790415386858147905705
1. ! [X0] : (patient(X0) => (~patient(X0) & ~rich(X0))) [input p0]
3. ! [X0] : (generous(X0) <=> (~brave(X0) | curious(X0))) [input p2]
4. ! [X0] : (~humble(X0) <=> (quiet(X0) <~> ~funny(X0))) [input p3]
6. ! [X0] : (patient(X0) <=> (~calm(X0) | ~strong(X0))) [input p5]
8. ! [X0] : ((~funny(X0) | ~patient(X0)) => (~quiet(X0) | ~creative(X0))) [input p7]
11. ! [X0] : (brave(X0) => patient(X0)) [input p10]
14. ? [X0] : (~generous(X0) & ~happy(X0)) <=> ? [X0] : (~creative(X0) | brave(X0)) [input p13]
15. ! [X0] : ((happy(X0) & funny(X0)) <=> (calm(X0) & ~humble(X0))) [input p14]
23. ~funny(john) [input hypothesis]
26. ? [X0] : (~generous(X0) & ~happy(X0)) <=> ? [X1] : (~creative(X1) | brave(X1)) [rectify 14]
29. ! [X0] : ((~patient(X0) & ~rich(X0)) | ~patient(X0)) [ennf transformation 1]
35. ! [X0] : ((~quiet(X0) | ~creative(X0)) | (funny(X0) & patient(X0))) [ennf transformation 8]
36. ! [X0] : (~quiet(X0) | ~creative(X0) | (funny(X0) & patient(X0))) [flattening 35]
39. ! [X0] : (patient(X0) | ~brave(X0)) [ennf transformation 11]
44. ! [X0] : ((generous(X0) | (brave(X0) & ~curious(X0))) & ((~brave(X0) | curious(X0)) | ~generous(X0))) [nnf transformation 3]
45. ! [X0] : ((generous(X0) | (brave(X0) & ~curious(X0))) & (~brave(X0) | curious(X0) | ~generous(X0))) [flattening 44]
46. ! [X0] : ((~humble(X0) | ((quiet(X0) | funny(X0)) & (~funny(X0) | ~quiet(X0)))) & (((funny(X0) | ~quiet(X0)) & (~funny(X0) | quiet(X0))) | humble(X0))) [nnf transformation 4]
48. ! [X0] : ((patient(X0) | (calm(X0) & strong(X0))) & ((~calm(X0) | ~strong(X0)) | ~patient(X0))) [nnf transformation 6]
49. ! [X0] : ((patient(X0) | (calm(X0) & strong(X0))) & (~calm(X0) | ~strong(X0) | ~patient(X0))) [flattening 48]
59. (? [X0] : (~generous(X0) & ~happy(X0)) | ! [X1] : (creative(X1) & ~brave(X1))) & (? [X1] : (~creative(X1) | brave(X1)) | ! [X0] : (generous(X0) | happy(X0))) [nnf transformation 26]
60. (? [X0] : (~generous(X0) & ~happy(X0)) | ! [X1] : (creative(X1) & ~brave(X1))) & (? [X2] : (~creative(X2) | brave(X2)) | ! [X3] : (generous(X3) | happy(X3))) [rectify 59]
61. ? [X0] : (~generous(X0) & ~happy(X0)) => (~generous(sK4) & ~happy(sK4)) [choice axiom]
62. ? [X2] : (~creative(X2) | brave(X2)) => (~creative(sK5) | brave(sK5)) [choice axiom]
63. ((~generous(sK4) & ~happy(sK4)) | ! [X1] : (creative(X1) & ~brave(X1))) & ((~creative(sK5) | brave(sK5)) | ! [X3] : (generous(X3) | happy(X3))) [skolemisation 60,62,61]
64. ! [X0] : (((happy(X0) & funny(X0)) | (~calm(X0) | humble(X0))) & ((calm(X0) & ~humble(X0)) | (~happy(X0) | ~funny(X0)))) [nnf transformation 15]
65. ! [X0] : (((happy(X0) & funny(X0)) | ~calm(X0) | humble(X0)) & ((calm(X0) & ~humble(X0)) | ~happy(X0) | ~funny(X0))) [flattening 64]
72. ~patient(X0) | ~patient(X0) [cnf transformation 29]
77. brave(X0) | generous(X0) [cnf transformation 45]
81. ~humble(X0) | quiet(X0) | funny(X0) [cnf transformation 46]
86. patient(X0) | calm(X0) [cnf transformation 49]
88. ~quiet(X0) | ~creative(X0) | patient(X0) [cnf transformation 36]
96. patient(X0) | ~brave(X0) [cnf transformation 39]
111. ~generous(sK4) | creative(X1) [cnf transformation 63]
114. funny(X0) | ~calm(X0) | humble(X0) [cnf transformation 65]
124. ~funny(john) [cnf transformation 23]
125. ~patient(X0) [duplicate literal removal 72]
144. calm(X0) [subsumption resolution 86,125]
146. ~creative(X0) | ~quiet(X0) [subsumption resolution 88,125]
159. ~brave(X0) [subsumption resolution 96,125]
183. 12 <=> ! [X1] : generous(X1) [avatar definition]
184. generous(X1) <- (12) [avatar component clause 183]
187. 13 <=> ! [X1] : creative(X1) [avatar definition]
188. creative(X1) <- (13) [avatar component clause 187]
190. 14 <=> generous(sK4) [avatar definition]
192. ~generous(sK4) <- (~14) [avatar component clause 190]
193. 13 | ~14 [avatar split clause 111,190,187]
209. funny(X0) | humble(X0) [subsumption resolution 114,144]
226. generous(X0) [resolution 77,159]
227. 12 [avatar split clause 226,183]
228. $false <- (12, ~14) [resolution 184,192]
229. ~12 | 14 [avatar contradiction clause 228]
236. ~quiet(X0) <- (13) [resolution 146,188]
238. humble(john) [resolution 209,124]
247. quiet(john) | funny(john) [resolution 81,238]
250. funny(john) <- (13) [subsumption resolution 247,236]
251. $false <- (13) [subsumption resolution 250,124]
252. ~13 [avatar contradiction clause 251]
254. $false [avatar sat refutation 193,227,229,252]
% SZS output end Proof for 2780790415386858147905705
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not old then mary is not strong. If alice is both not funny and kind then alice is rich. Everyone who is either old or not generous is both quiet and not curious and vice versa. Everyone who is either not kind or not rich is either not tall or happy. Everyone who is not creative or not patient is either not happy or brave and vice versa. If alice is not quiet or not calm then someone is both not rich and strong. Everyone who is humble is either not humble or not old. Everyone who is not wise or funny is both not strong and quiet and vice versa. If someone is not brave then someone is happy or strong and vice versa. Everyone who is both old and generous is tall and vice versa. Everyone who is not creative is both not strong and not rich and vice versa. Everyone who is either not brave or wise is either not old or calm and vice versa. If mary is either funny or wise then someone is both funny and not tall and vice versa. If someone is not strong then someone is generous. If lucy is both old and not quiet then fred is not wise or not funny and vice versa. If someone is both old and happy then someone is either not patient or not generous and vice versa. Someone is both kind and patient. Fred is both not creative and not wise. Alice is either kind or not happy. Mary is not wise or happy. Someone is either funny or old. Someone is not rich or not tall. John is funny. | Lucy is humble. | contradiction | ((?[X]:(~old(X)))=>(~strong(mary)))&
(((~funny(alice)&kind(alice)))=>(rich(alice)))&
(![X]:((old(X)<~>~generous(X))<=>(quiet(X)&~curious(X))))&
(![X]:((~kind(X)<~>~rich(X))=>(~tall(X)<~>happy(X))))&
(![X]:((~creative(X)|~patient(X))<=>(~happy(X)<~>brave(X))))&
(((~quiet(alice)|~calm(alice)))=>(?[X]:((~rich(X)&strong(X)))))&
(![X]:(humble(X)=>(~humble(X)<~>~old(X))))&
(![X]:((~wise(X)|funny(X))<=>(~strong(X)&quiet(X))))&
((?[X]:(~brave(X)))<=>(?[X]:((happy(X)|strong(X)))))&
(![X]:((old(X)&generous(X))<=>tall(X)))&
(![X]:(~creative(X)<=>(~strong(X)&~rich(X))))&
(![X]:((~brave(X)<~>wise(X))<=>(~old(X)<~>calm(X))))&
(((funny(mary)<~>wise(mary)))<=>(?[X]:((funny(X)&~tall(X)))))&
((?[X]:(~strong(X)))=>(?[X]:(generous(X))))&
(((old(lucy)&~quiet(lucy)))<=>((~wise(fred)|~funny(fred))))&
((?[X]:((old(X)&happy(X))))<=>(?[X]:((~patient(X)<~>~generous(X)))))&
(?[X]:((kind(X)&patient(X))))&
((~creative(fred)&~wise(fred)))&
((kind(alice)<~>~happy(alice)))&
((~wise(mary)|happy(mary)))&
(?[X]:((funny(X)<~>old(X))))&
(?[X]:((~rich(X)|~tall(X))))&
(funny(john)) | humble(lucy) | [
"p6",
"p14",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 262937615755846809284644
% SZS output start Proof for 262937615755846809284644
7. ! [X0] : (humble(X0) => (~humble(X0) <~> ~old(X0))) [input p6]
15. (~quiet(lucy) & old(lucy)) <=> (~funny(fred) | ~wise(fred)) [input p14]
18. ~wise(fred) & ~creative(fred) [input p17]
24. humble(lucy) [input hypothesis]
33. ! [X0] : ((~humble(X0) <~> ~old(X0)) | ~humble(X0)) [ennf transformation 7]
42. ! [X0] : (((old(X0) | humble(X0)) & (~old(X0) | ~humble(X0))) | ~humble(X0)) [nnf transformation 33]
62. ((~quiet(lucy) & old(lucy)) | (funny(fred) & wise(fred))) & ((~funny(fred) | ~wise(fred)) | (quiet(lucy) | ~old(lucy))) [nnf transformation 15]
63. ((~quiet(lucy) & old(lucy)) | (funny(fred) & wise(fred))) & (~funny(fred) | ~wise(fred) | quiet(lucy) | ~old(lucy)) [flattening 62]
99. ~old(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 42]
131. old(lucy) | wise(fred) [cnf transformation 63]
144. ~wise(fred) [cnf transformation 18]
152. humble(lucy) [cnf transformation 24]
153. ~humble(X0) | ~old(X0) [duplicate literal removal 99]
262. 25 <=> wise(fred) [avatar definition]
267. 26 <=> old(lucy) [avatar definition]
269. old(lucy) <- (26) [avatar component clause 267]
271. 25 | 26 [avatar split clause 131,267,262]
304. ~25 [avatar split clause 144,262]
347. ~old(lucy) [resolution 153,152]
348. $false <- (26) [subsumption resolution 347,269]
349. ~26 [avatar contradiction clause 348]
350. $false [avatar sat refutation 271,304,349]
% SZS output end Proof for 262937615755846809284644
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If susan is both funny and not funny then john is not funny or not patient. Everyone who is not brave is curious and vice versa. Everyone who is not patient is both curious and rich and vice versa. If paul is not calm or not old then john is not rich and vice versa. If someone is both kind and not funny then someone is either not wise or not creative and vice versa. If lucy is curious or not patient then lucy is not generous and vice versa. Everyone who is strong or kind is not generous. Everyone who is not creative is either tall or humble. Everyone who is calm is both patient and not humble. If paul is strong or humble then someone is either not curious or calm. If someone is rich or wise then mary is both not calm and happy. If someone is not funny then someone is not creative. If alice is either not happy or old then someone is both funny and not kind and vice versa. If susan is both funny and not strong then alice is both not wise and not funny. If someone is both not tall and not strong then mary is either calm or not brave and vice versa. Everyone who is not curious or brave is not patient or kind and vice versa. Mary is curious or old. Mary is strong. Someone is rich. Someone is not creative. Mary is both not creative and not kind. Fred is either rich or brave. Someone is not calm. | Fred is curious. | contradiction | (((funny(susan)&~funny(susan)))=>((~funny(john)|~patient(john))))&
(![X]:(~brave(X)<=>curious(X)))&
(![X]:(~patient(X)<=>(curious(X)&rich(X))))&
(((~calm(paul)|~old(paul)))<=>(~rich(john)))&
((?[X]:((kind(X)&~funny(X))))<=>(?[X]:((~wise(X)<~>~creative(X)))))&
(((curious(lucy)|~patient(lucy)))<=>(~generous(lucy)))&
(![X]:((strong(X)|kind(X))=>~generous(X)))&
(![X]:(~creative(X)=>(tall(X)<~>humble(X))))&
(![X]:(calm(X)=>(patient(X)&~humble(X))))&
(((strong(paul)|humble(paul)))=>(?[X]:((~curious(X)<~>calm(X)))))&
((?[X]:((rich(X)|wise(X))))=>((~calm(mary)&happy(mary))))&
((?[X]:(~funny(X)))=>(?[X]:(~creative(X))))&
(((~happy(alice)<~>old(alice)))<=>(?[X]:((funny(X)&~kind(X)))))&
(((funny(susan)&~strong(susan)))=>((~wise(alice)&~funny(alice))))&
((?[X]:((~tall(X)&~strong(X))))<=>((calm(mary)<~>~brave(mary))))&
(![X]:((~curious(X)|brave(X))<=>(~patient(X)|kind(X))))&
((curious(mary)|old(mary)))&
(strong(mary))&
(?[X]:(rich(X)))&
(?[X]:(~creative(X)))&
((~creative(mary)&~kind(mary)))&
((rich(fred)<~>brave(fred)))&
(?[X]:(~calm(X))) | curious(fred) | [
"p1",
"p2",
"p15",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 4815597813314242469808613
% SZS output start Proof for 4815597813314242469808613
2. ! [X0] : (~brave(X0) <=> curious(X0)) [input p1]
3. ! [X0] : (~patient(X0) <=> (rich(X0) & curious(X0))) [input p2]
16. ! [X0] : ((brave(X0) | ~curious(X0)) <=> (kind(X0) | ~patient(X0))) [input p15]
22. rich(fred) <~> brave(fred) [input p21]
24. curious(fred) [input hypothesis]
37. ! [X0] : ((~brave(X0) | ~curious(X0)) & (curious(X0) | brave(X0))) [nnf transformation 2]
38. ! [X0] : ((~patient(X0) | (~rich(X0) | ~curious(X0))) & ((rich(X0) & curious(X0)) | patient(X0))) [nnf transformation 3]
39. ! [X0] : ((~patient(X0) | ~rich(X0) | ~curious(X0)) & ((rich(X0) & curious(X0)) | patient(X0))) [flattening 38]
64. ! [X0] : (((brave(X0) | ~curious(X0)) | (~kind(X0) & patient(X0))) & ((kind(X0) | ~patient(X0)) | (~brave(X0) & curious(X0)))) [nnf transformation 16]
65. ! [X0] : ((brave(X0) | ~curious(X0) | (~kind(X0) & patient(X0))) & (kind(X0) | ~patient(X0) | (~brave(X0) & curious(X0)))) [flattening 64]
70. (~brave(fred) | ~rich(fred)) & (brave(fred) | rich(fred)) [nnf transformation 22]
75. ~curious(X0) | ~brave(X0) [cnf transformation 37]
76. curious(X0) | patient(X0) [cnf transformation 39]
78. ~rich(X0) | ~patient(X0) | ~curious(X0) [cnf transformation 39]
122. brave(X0) | ~curious(X0) | patient(X0) [cnf transformation 65]
130. brave(fred) | rich(fred) [cnf transformation 70]
133. curious(fred) [cnf transformation 24]
307. brave(X0) | patient(X0) [subsumption resolution 122,76]
319. 39 <=> rich(fred) [avatar definition]
320. rich(fred) <- (39) [avatar component clause 319]
323. 40 <=> brave(fred) [avatar definition]
327. 39 | 40 [avatar split clause 130,323,319]
331. ~brave(fred) [resolution 75,133]
332. patient(X0) | ~brave(X0) [resolution 76,75]
333. patient(X0) [subsumption resolution 332,307]
343. ~patient(fred) | ~curious(fred) <- (39) [resolution 78,320]
346. ~curious(fred) <- (39) [subsumption resolution 343,333]
347. $false <- (39) [subsumption resolution 346,133]
348. ~39 [avatar contradiction clause 347]
349. ~40 [avatar split clause 331,323]
350. $false [avatar sat refutation 327,348,349]
% SZS output end Proof for 4815597813314242469808613
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not happy then fred is strong. If susan is both calm and happy then mary is both old and patient. Everyone who is not generous or calm is not kind. Everyone who is not creative is patient or not curious and vice versa. If lucy is not curious or happy then someone is generous. Everyone who is either not strong or curious is not strong. If someone is either not generous or not tall then someone is not happy and vice versa. Everyone who is creative is happy or not happy. If someone is calm or wise then someone is either strong or kind and vice versa. If lucy is both not tall and not generous then someone is both rich and tall and vice versa. Everyone who is wise or not kind is both not funny and not wise and vice versa. If someone is quiet or humble then susan is creative or not generous and vice versa. Everyone who is either not kind or not wise is not curious or creative and vice versa. Everyone who is either not patient or strong is either not strong or strong and vice versa. Everyone who is either not humble or not generous is not quiet or humble and vice versa. Everyone who is not patient is creative. Someone is either not strong or old. Paul is patient. Someone is not happy. Paul is both brave and rich. John is either creative or tall. Someone is brave or tall. Paul is not humble. | Susan is not humble. | entailment | ((?[X]:(~happy(X)))=>(strong(fred)))&
(((calm(susan)&happy(susan)))=>((old(mary)&patient(mary))))&
(![X]:((~generous(X)|calm(X))=>~kind(X)))&
(![X]:(~creative(X)<=>(patient(X)|~curious(X))))&
(((~curious(lucy)|happy(lucy)))=>(?[X]:(generous(X))))&
(![X]:((~strong(X)<~>curious(X))=>~strong(X)))&
((?[X]:((~generous(X)<~>~tall(X))))<=>(?[X]:(~happy(X))))&
(![X]:(creative(X)=>(happy(X)|~happy(X))))&
((?[X]:((calm(X)|wise(X))))<=>(?[X]:((strong(X)<~>kind(X)))))&
(((~tall(lucy)&~generous(lucy)))<=>(?[X]:((rich(X)&tall(X)))))&
(![X]:((wise(X)|~kind(X))<=>(~funny(X)&~wise(X))))&
((?[X]:((quiet(X)|humble(X))))<=>((creative(susan)|~generous(susan))))&
(![X]:((~kind(X)<~>~wise(X))<=>(~curious(X)|creative(X))))&
(![X]:((~patient(X)<~>strong(X))<=>(~strong(X)<~>strong(X))))&
(![X]:((~humble(X)<~>~generous(X))<=>(~quiet(X)|humble(X))))&
(![X]:(~patient(X)=>creative(X)))&
(?[X]:((~strong(X)<~>old(X))))&
(patient(paul))&
(?[X]:(~happy(X)))&
((brave(paul)&rich(paul)))&
((creative(john)<~>tall(john)))&
(?[X]:((brave(X)|tall(X))))&
(~humble(paul)) | ~humble(susan) | [
"p2",
"p5",
"p10",
"p12",
"p13",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3930531815660882419931376
% SZS output start Proof for 3930531815660882419931376
3. ! [X0] : ((calm(X0) | ~generous(X0)) => ~kind(X0)) [input p2]
6. ! [X0] : ((~strong(X0) <~> curious(X0)) => ~strong(X0)) [input p5]
11. ! [X0] : ((~kind(X0) | wise(X0)) <=> (~wise(X0) & ~funny(X0))) [input p10]
13. ! [X0] : ((~kind(X0) <~> ~wise(X0)) <=> (creative(X0) | ~curious(X0))) [input p12]
14. ! [X0] : ((~patient(X0) <~> strong(X0)) <=> (~strong(X0) <~> strong(X0))) [input p13]
15. ! [X0] : ((~humble(X0) <~> ~generous(X0)) <=> (humble(X0) | ~quiet(X0))) [input p14]
16. ! [X0] : (~patient(X0) => creative(X0)) [input p15]
24. humble(susan) [input hypothesis]
32. ! [X0] : (~kind(X0) | (~calm(X0) & generous(X0))) [ennf transformation 3]
34. ! [X0] : (~strong(X0) | (~strong(X0) <=> curious(X0))) [ennf transformation 6]
37. ! [X0] : (creative(X0) | patient(X0)) [ennf transformation 16]
42. ! [X0] : (~strong(X0) | ((~strong(X0) | ~curious(X0)) & (curious(X0) | strong(X0)))) [nnf transformation 34]
58. ! [X0] : (((~kind(X0) | wise(X0)) | (wise(X0) | funny(X0))) & ((~wise(X0) & ~funny(X0)) | (kind(X0) & ~wise(X0)))) [nnf transformation 11]
59. ! [X0] : ((~kind(X0) | wise(X0) | wise(X0) | funny(X0)) & ((~wise(X0) & ~funny(X0)) | (kind(X0) & ~wise(X0)))) [flattening 58]
65. ! [X0] : ((((wise(X0) | kind(X0)) & (~wise(X0) | ~kind(X0))) | (~creative(X0) & curious(X0))) & ((creative(X0) | ~curious(X0)) | ((~kind(X0) | wise(X0)) & (~wise(X0) | kind(X0))))) [nnf transformation 13]
66. ! [X0] : ((((wise(X0) | kind(X0)) & (~wise(X0) | ~kind(X0))) | (~creative(X0) & curious(X0))) & (creative(X0) | ~curious(X0) | ((~kind(X0) | wise(X0)) & (~wise(X0) | kind(X0))))) [flattening 65]
67. ! [X0] : ((((~strong(X0) | patient(X0)) & (strong(X0) | ~patient(X0))) | ((~strong(X0) | ~strong(X0)) & (strong(X0) | strong(X0)))) & (((~strong(X0) | strong(X0)) & (strong(X0) | ~strong(X0))) | ((~patient(X0) | ~strong(X0)) & (strong(X0) | patient(X0))))) [nnf transformation 14]
68. ! [X0] : ((((generous(X0) | humble(X0)) & (~generous(X0) | ~humble(X0))) | (~humble(X0) & quiet(X0))) & ((humble(X0) | ~quiet(X0)) | ((~humble(X0) | generous(X0)) & (~generous(X0) | humble(X0))))) [nnf transformation 15]
69. ! [X0] : ((((generous(X0) | humble(X0)) & (~generous(X0) | ~humble(X0))) | (~humble(X0) & quiet(X0))) & (humble(X0) | ~quiet(X0) | ((~humble(X0) | generous(X0)) & (~generous(X0) | humble(X0))))) [flattening 68]
79. ~kind(X0) | generous(X0) [cnf transformation 32]
87. ~strong(X0) | ~strong(X0) | ~curious(X0) [cnf transformation 42]
106. ~wise(X0) | kind(X0) [cnf transformation 59]
116. wise(X0) | kind(X0) | curious(X0) [cnf transformation 66]
117. wise(X0) | kind(X0) | ~creative(X0) [cnf transformation 66]
122. strong(X0) | ~patient(X0) | strong(X0) | strong(X0) [cnf transformation 67]
129. ~generous(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 69]
132. creative(X0) | patient(X0) [cnf transformation 37]
141. humble(susan) [cnf transformation 24]
143. ~humble(X0) | ~generous(X0) [duplicate literal removal 129]
148. ~patient(X0) | strong(X0) [duplicate literal removal 122]
154. ~curious(X0) | ~strong(X0) [duplicate literal removal 87]
230. 18 <=> ! [X1] : (kind(X1) | ~strong(X1)) [avatar definition]
231. ~strong(X1) | kind(X1) <- (18) [avatar component clause 230]
276. 28 <=> generous(susan) [avatar definition]
277. ~generous(susan) <- (~28) [avatar component clause 276]
301. ~creative(X0) | kind(X0) [subsumption resolution 117,106]
302. curious(X0) | kind(X0) [subsumption resolution 116,106]
330. ~generous(susan) [resolution 143,141]
340. kind(X0) | patient(X0) [resolution 301,132]
343. kind(X0) | ~strong(X0) [resolution 302,154]
344. 18 [avatar split clause 343,230]
386. generous(X2) | patient(X2) [resolution 340,79]
400. patient(susan) <- (~28) [resolution 386,277]
407. strong(susan) <- (~28) [resolution 400,148]
411. kind(susan) <- (18, ~28) [resolution 407,231]
423. generous(susan) <- (18, ~28) [resolution 411,79]
425. $false <- (18, ~28) [subsumption resolution 423,277]
426. ~18 | 28 [avatar contradiction clause 425]
427. ~28 [avatar split clause 330,276]
428. $false [avatar sat refutation 344,426,427]
% SZS output end Proof for 3930531815660882419931376
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not kind and not happy then someone is not old and vice versa.
If someone is brave or humble then someone is either not humble or curious.
Everyone who is either tall or humble is either funny or generous.
Everyone who is both generous and not creative is rich and vice versa.
Everyone who is not happy is either rich or wise.
Everyone who is both not rich and not old is both generous and not patient.
Everyone who is not old or generous is strong or creative.
If susan is humble or not old then susan is either not generous or not kind and vice versa.
Everyone who is not patient is not curious and vice versa.
Everyone who is either not humble or not brave is not calm and vice versa.
Everyone who is happy is patient.
If someone is not wise then someone is both curious and wise.
Everyone who is either not creative or not strong is not patient or not curious.
If someone is both not tall and not kind then alice is either not patient or not strong and vice versa.
Everyone who is either not happy or rich is either not quiet or not wise and vice versa.
Everyone who is not happy or not tall is both creative and tall.
Paul is kind.
Mary is old or strong.
Someone is both old and patient.
Alice is either not humble or brave.
Someone is not happy.
Susan is kind.
Alice is either wise or not generous.
Susan is generous. | Alice is not creative. | contradiction | ((?[X]:((~kind(X)&~happy(X))))<=>(?[X]:(~old(X))))&
((?[X]:((brave(X)|humble(X))))=>(?[X]:((~humble(X)<~>curious(X)))))&
(![X]:((tall(X)<~>humble(X))=>(funny(X)<~>generous(X))))&
(![X]:((generous(X)&~creative(X))<=>rich(X)))&
(![X]:(~happy(X)=>(rich(X)<~>wise(X))))&
(![X]:((~rich(X)&~old(X))=>(generous(X)&~patient(X))))&
(![X]:((~old(X)|generous(X))=>(strong(X)|creative(X))))&
(((humble(susan)|~old(susan)))<=>((~generous(susan)<~>~kind(susan))))&
(![X]:(~patient(X)<=>~curious(X)))&
(![X]:((~humble(X)<~>~brave(X))<=>~calm(X)))&
(![X]:(happy(X)=>patient(X)))&
((?[X]:(~wise(X)))=>(?[X]:((curious(X)&wise(X)))))&
(![X]:((~creative(X)<~>~strong(X))=>(~patient(X)|~curious(X))))&
((?[X]:((~tall(X)&~kind(X))))<=>((~patient(alice)<~>~strong(alice))))&
(![X]:((~happy(X)<~>rich(X))<=>(~quiet(X)<~>~wise(X))))&
(![X]:((~happy(X)|~tall(X))=>(creative(X)&tall(X))))&
(kind(paul))&
((old(mary)|strong(mary)))&
(?[X]:((old(X)&patient(X))))&
((~humble(alice)<~>brave(alice)))&
(?[X]:(~happy(X)))&
(kind(susan))&
((wise(alice)<~>~generous(alice)))&
(generous(susan)) | ~creative(alice) | [
"p8",
"p10",
"p12",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 177756394948518311637147
% SZS output start Proof for 177756394948518311637147
9. ! [X0] : (~patient(X0) <=> ~curious(X0)) [input p8]
11. ! [X0] : (happy(X0) => patient(X0)) [input p10]
13. ! [X0] : ((~creative(X0) <~> ~strong(X0)) => (~curious(X0) | ~patient(X0))) [input p12]
14. ? [X0] : (~kind(X0) & ~tall(X0)) <=> (~patient(alice) <~> ~strong(alice)) [input p13]
16. ! [X0] : ((~tall(X0) | ~happy(X0)) => (tall(X0) & creative(X0))) [input p15]
25. ~creative(alice) [input hypothesis]
36. ! [X0] : (patient(X0) | ~happy(X0)) [ennf transformation 11]
38. ! [X0] : ((~curious(X0) | ~patient(X0)) | (~creative(X0) <=> ~strong(X0))) [ennf transformation 13]
39. ! [X0] : (~curious(X0) | ~patient(X0) | (~creative(X0) <=> ~strong(X0))) [flattening 38]
40. ! [X0] : ((tall(X0) & creative(X0)) | (tall(X0) & happy(X0))) [ennf transformation 16]
56. ! [X0] : ((~patient(X0) | curious(X0)) & (~curious(X0) | patient(X0))) [nnf transformation 9]
60. ! [X0] : (~curious(X0) | ~patient(X0) | ((~creative(X0) | strong(X0)) & (~strong(X0) | creative(X0)))) [nnf transformation 39]
61. (? [X0] : (~kind(X0) & ~tall(X0)) | ((~patient(alice) | strong(alice)) & (~strong(alice) | patient(alice)))) & (((strong(alice) | patient(alice)) & (~strong(alice) | ~patient(alice))) | ! [X0] : (kind(X0) | tall(X0))) [nnf transformation 14]
62. (? [X0] : (~kind(X0) & ~tall(X0)) | ((~patient(alice) | strong(alice)) & (~strong(alice) | patient(alice)))) & (((strong(alice) | patient(alice)) & (~strong(alice) | ~patient(alice))) | ! [X1] : (kind(X1) | tall(X1))) [rectify 61]
63. ? [X0] : (~kind(X0) & ~tall(X0)) => (~kind(sK4) & ~tall(sK4)) [choice axiom]
64. ((~kind(sK4) & ~tall(sK4)) | ((~patient(alice) | strong(alice)) & (~strong(alice) | patient(alice)))) & (((strong(alice) | patient(alice)) & (~strong(alice) | ~patient(alice))) | ! [X1] : (kind(X1) | tall(X1))) [skolemisation 62,63]
99. ~patient(X0) | curious(X0) [cnf transformation 56]
100. ~happy(X0) | patient(X0) [cnf transformation 36]
103. ~curious(X0) | ~patient(X0) | ~strong(X0) | creative(X0) [cnf transformation 60]
108. ~tall(sK4) | ~patient(alice) | strong(alice) [cnf transformation 64]
119. creative(X0) | happy(X0) [cnf transformation 40]
122. tall(X0) | tall(X0) [cnf transformation 40]
134. ~creative(alice) [cnf transformation 25]
135. tall(X0) [duplicate literal removal 122]
213. ~strong(X0) | ~patient(X0) | creative(X0) [subsumption resolution 103,99]
215. 17 <=> strong(alice) [avatar definition]
217. strong(alice) <- (17) [avatar component clause 215]
219. 18 <=> patient(alice) [avatar definition]
220. patient(alice) <- (18) [avatar component clause 219]
229. 20 <=> tall(sK4) [avatar definition]
231. ~tall(sK4) <- (~20) [avatar component clause 229]
232. 17 | ~18 | ~20 [avatar split clause 108,229,219,215]
274. $false <- (~20) [subsumption resolution 231,135]
275. 20 [avatar contradiction clause 274]
283. happy(alice) [resolution 119,134]
286. patient(alice) [resolution 283,100]
339. ~patient(alice) | creative(alice) <- (17) [resolution 213,217]
342. creative(alice) <- (17, 18) [subsumption resolution 339,220]
343. $false <- (17, 18) [subsumption resolution 342,134]
344. ~17 | ~18 [avatar contradiction clause 343]
345. 18 [avatar split clause 286,219]
346. $false [avatar sat refutation 232,275,344,345]
% SZS output end Proof for 177756394948518311637147
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy is strong or not funny and vice versa.
Everyone who is both not old and not patient is rich.
Everyone who is both not strong and calm is not calm and vice versa.
If susan is strong then someone is old.
If someone is both not rich and strong then someone is either brave or not generous.
Everyone who is both not happy and not creative is not humble.
If someone is kind or humble then paul is both not quiet and humble.
If someone is both kind and brave then someone is not patient and vice versa.
Everyone who is either not wise or tall is either not tall or kind and vice versa.
Everyone who is either patient or not creative is not curious or brave and vice versa.
If john is either not quiet or old then susan is old.
If someone is not creative then alice is both not curious and not happy.
Everyone who is either brave or tall is generous.
Everyone who is happy or not rich is not wise.
If lucy is funny or not wise then paul is both not quiet and brave and vice versa.
Everyone who is either not funny or tall is strong or not patient.
Someone is not happy.
Someone is not patient.
Someone is both not brave and tall.
Lucy is not wise.
Lucy is both not generous and old.
Someone is tall.
Someone is either not humble or quiet. | Susan is old. | neutral | (![X]:(~happy(X)<=>(strong(X)|~funny(X))))&
(![X]:((~old(X)&~patient(X))=>rich(X)))&
(![X]:((~strong(X)&calm(X))<=>~calm(X)))&
((strong(susan))=>(?[X]:(old(X))))&
((?[X]:((~rich(X)&strong(X))))=>(?[X]:((brave(X)<~>~generous(X)))))&
(![X]:((~happy(X)&~creative(X))=>~humble(X)))&
((?[X]:((kind(X)|humble(X))))=>((~quiet(paul)&humble(paul))))&
((?[X]:((kind(X)&brave(X))))<=>(?[X]:(~patient(X))))&
(![X]:((~wise(X)<~>tall(X))<=>(~tall(X)<~>kind(X))))&
(![X]:((patient(X)<~>~creative(X))<=>(~curious(X)|brave(X))))&
(((~quiet(john)<~>old(john)))=>(old(susan)))&
((?[X]:(~creative(X)))=>((~curious(alice)&~happy(alice))))&
(![X]:((brave(X)<~>tall(X))=>generous(X)))&
(![X]:((happy(X)|~rich(X))=>~wise(X)))&
(((funny(lucy)|~wise(lucy)))<=>((~quiet(paul)&brave(paul))))&
(![X]:((~funny(X)<~>tall(X))=>(strong(X)|~patient(X))))&
(?[X]:(~happy(X)))&
(?[X]:(~patient(X)))&
(?[X]:((~brave(X)&tall(X))))&
(~wise(lucy))&
((~generous(lucy)&old(lucy)))&
(?[X]:(tall(X)))&
(?[X]:((~humble(X)<~>quiet(X)))) | old(susan) | [] | null | 0 |
Everyone who is creative is not funny or not quiet and vice versa.
If paul is not patient then someone is both humble and patient.
Everyone who is either not wise or not creative is either not funny or not tall.
If someone is either not tall or not humble then someone is either not kind or funny.
If someone is happy or brave then someone is old or funny and vice versa.
Everyone who is curious is not brave or strong.
If someone is not wise or funny then mary is both old and tall and vice versa.
If someone is not old then paul is both not generous and tall.
If someone is rich or creative then paul is old and vice versa.
Everyone who is wise or strong is not old or not wise.
Everyone who is either funny or not patient is not kind or not old.
Everyone who is both strong and kind is not strong and vice versa.
Everyone who is generous or not kind is curious.
If someone is either not patient or kind then someone is wise or not happy.
If someone is both not happy and strong then someone is generous or not patient.
Someone is curious.
Susan is not generous.
Someone is patient.
Someone is both not creative and not old.
John is both wise and not quiet.
Someone is either quiet or happy. | Mary is tall. | entailment | (![X]:(creative(X)<=>(~funny(X)|~quiet(X))))&
((~patient(paul))=>(?[X]:((humble(X)&patient(X)))))&
(![X]:((~wise(X)<~>~creative(X))=>(~funny(X)<~>~tall(X))))&
((?[X]:((~tall(X)<~>~humble(X))))=>(?[X]:((~kind(X)<~>funny(X)))))&
((?[X]:((happy(X)|brave(X))))<=>(?[X]:((old(X)|funny(X)))))&
(![X]:(curious(X)=>(~brave(X)|strong(X))))&
((?[X]:((~wise(X)|funny(X))))<=>((old(mary)&tall(mary))))&
((?[X]:(~old(X)))=>((~generous(paul)&tall(paul))))&
((?[X]:((rich(X)|creative(X))))<=>(old(paul)))&
(![X]:((wise(X)|strong(X))=>(~old(X)|~wise(X))))&
(![X]:((funny(X)<~>~patient(X))=>(~kind(X)|~old(X))))&
(![X]:((strong(X)&kind(X))<=>~strong(X)))&
(![X]:((generous(X)|~kind(X))=>curious(X)))&
((?[X]:((~patient(X)<~>kind(X))))=>(?[X]:((wise(X)|~happy(X)))))&
((?[X]:((~happy(X)&strong(X))))=>(?[X]:((generous(X)|~patient(X)))))&
(?[X]:(curious(X)))&
(~generous(susan))&
(?[X]:(patient(X)))&
(?[X]:((~creative(X)&~old(X))))&
((wise(john)&~quiet(john)))&
(?[X]:((quiet(X)<~>happy(X)))) | tall(mary) | [
"p0",
"p6",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 3210328555205495649368702
% SZS output start Proof for 3210328555205495649368702
1. ! [X0] : (creative(X0) <=> (~quiet(X0) | ~funny(X0))) [input p0]
7. ? [X0] : (funny(X0) | ~wise(X0)) <=> (tall(mary) & old(mary)) [input p6]
19. ? [X0] : (~old(X0) & ~creative(X0)) [input p18]
22. ~tall(mary) [input hypothesis]
40. ! [X0] : ((creative(X0) | (quiet(X0) & funny(X0))) & ((~quiet(X0) | ~funny(X0)) | ~creative(X0))) [nnf transformation 1]
41. ! [X0] : ((creative(X0) | (quiet(X0) & funny(X0))) & (~quiet(X0) | ~funny(X0) | ~creative(X0))) [flattening 40]
54. (? [X0] : (funny(X0) | ~wise(X0)) | (~tall(mary) | ~old(mary))) & ((tall(mary) & old(mary)) | ! [X0] : (~funny(X0) & wise(X0))) [nnf transformation 7]
55. (? [X0] : (funny(X0) | ~wise(X0)) | ~tall(mary) | ~old(mary)) & ((tall(mary) & old(mary)) | ! [X0] : (~funny(X0) & wise(X0))) [flattening 54]
56. (? [X0] : (funny(X0) | ~wise(X0)) | ~tall(mary) | ~old(mary)) & ((tall(mary) & old(mary)) | ! [X1] : (~funny(X1) & wise(X1))) [rectify 55]
57. ? [X0] : (funny(X0) | ~wise(X0)) => (funny(sK4) | ~wise(sK4)) [choice axiom]
58. ((funny(sK4) | ~wise(sK4)) | ~tall(mary) | ~old(mary)) & ((tall(mary) & old(mary)) | ! [X1] : (~funny(X1) & wise(X1))) [skolemisation 56,57]
77. ? [X0] : (~old(X0) & ~creative(X0)) => (~old(sK10) & ~creative(sK10)) [choice axiom]
78. ~old(sK10) & ~creative(sK10) [skolemisation 19,77]
83. funny(X0) | creative(X0) [cnf transformation 41]
103. tall(mary) | ~funny(X1) [cnf transformation 58]
125. ~creative(sK10) [cnf transformation 78]
131. ~tall(mary) [cnf transformation 22]
170. 8 <=> ! [X1] : ~funny(X1) [avatar definition]
171. ~funny(X1) <- (8) [avatar component clause 170]
206. 17 <=> tall(mary) [avatar definition]
218. 8 | 17 [avatar split clause 103,206,170]
297. ~17 [avatar split clause 131,206]
300. creative(X0) <- (8) [resolution 83,171]
301. $false <- (8) [resolution 300,125]
302. ~8 [avatar contradiction clause 301]
303. $false [avatar sat refutation 218,297,302]
% SZS output end Proof for 3210328555205495649368702
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny then paul is strong or not strong.
If someone is not curious then susan is strong or not quiet and vice versa.
If someone is not funny or not strong then someone is both old and patient.
Everyone who is either not humble or generous is not quiet.
Everyone who is generous is either not kind or creative and vice versa.
If john is both not wise and not calm then someone is humble or tall.
Everyone who is not generous is brave.
If someone is not strong then someone is calm and vice versa.
If alice is not strong or not happy then someone is rich or not patient.
Everyone who is either not kind or curious is generous and vice versa.
Everyone who is not quiet is not strong and vice versa.
Everyone who is not happy is both not kind and not calm and vice versa.
If john is not curious or not humble then someone is both calm and not quiet.
Everyone who is not calm or funny is not funny and vice versa.
If paul is not creative or funny then someone is not calm or not happy.
Everyone who is not calm or old is either not patient or tall.
John is not old or not tall.
Someone is patient.
Alice is funny or curious.
Someone is either calm or rich.
John is not wise or not generous.
Someone is either not old or wise.
Someone is calm or brave.
Susan is curious. | Susan is creative. | entailment | ((?[X]:(funny(X)))=>((strong(paul)|~strong(paul))))&
((?[X]:(~curious(X)))<=>((strong(susan)|~quiet(susan))))&
((?[X]:((~funny(X)|~strong(X))))=>(?[X]:((old(X)&patient(X)))))&
(![X]:((~humble(X)<~>generous(X))=>~quiet(X)))&
(![X]:(generous(X)<=>(~kind(X)<~>creative(X))))&
(((~wise(john)&~calm(john)))=>(?[X]:((humble(X)|tall(X)))))&
(![X]:(~generous(X)=>brave(X)))&
((?[X]:(~strong(X)))<=>(?[X]:(calm(X))))&
(((~strong(alice)|~happy(alice)))=>(?[X]:((rich(X)|~patient(X)))))&
(![X]:((~kind(X)<~>curious(X))<=>generous(X)))&
(![X]:(~quiet(X)<=>~strong(X)))&
(![X]:(~happy(X)<=>(~kind(X)&~calm(X))))&
(((~curious(john)|~humble(john)))=>(?[X]:((calm(X)&~quiet(X)))))&
(![X]:((~calm(X)|funny(X))<=>~funny(X)))&
(((~creative(paul)|funny(paul)))=>(?[X]:((~calm(X)|~happy(X)))))&
(![X]:((~calm(X)|old(X))=>(~patient(X)<~>tall(X))))&
((~old(john)|~tall(john)))&
(?[X]:(patient(X)))&
((funny(alice)|curious(alice)))&
(?[X]:((calm(X)<~>rich(X))))&
((~wise(john)|~generous(john)))&
(?[X]:((~old(X)<~>wise(X))))&
(?[X]:((calm(X)|brave(X))))&
(curious(susan)) | creative(susan) | [
"p4",
"p9",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 5562604732446243426773103
% SZS output start Proof for 5562604732446243426773103
5. ! [X0] : (generous(X0) <=> (~kind(X0) <~> creative(X0))) [input p4]
10. ! [X0] : ((~kind(X0) <~> curious(X0)) <=> generous(X0)) [input p9]
24. curious(susan) [input p23]
25. ~creative(susan) [input hypothesis]
49. ! [X0] : ((generous(X0) | ((~kind(X0) | ~creative(X0)) & (creative(X0) | kind(X0)))) & (((~creative(X0) | kind(X0)) & (creative(X0) | ~kind(X0))) | ~generous(X0))) [nnf transformation 5]
59. ! [X0] : ((((~curious(X0) | kind(X0)) & (curious(X0) | ~kind(X0))) | ~generous(X0)) & (generous(X0) | ((~kind(X0) | ~curious(X0)) & (curious(X0) | kind(X0))))) [nnf transformation 10]
88. ~kind(X0) | creative(X0) | ~generous(X0) [cnf transformation 49]
90. creative(X0) | generous(X0) | kind(X0) [cnf transformation 49]
98. ~kind(X0) | generous(X0) | ~curious(X0) [cnf transformation 59]
100. ~generous(X0) | kind(X0) | ~curious(X0) [cnf transformation 59]
127. curious(susan) [cnf transformation 24]
128. ~creative(susan) [cnf transformation 25]
304. generous(susan) | kind(susan) [resolution 90,128]
308. 33 <=> kind(susan) [avatar definition]
309. ~kind(susan) <- (~33) [avatar component clause 308]
310. kind(susan) <- (33) [avatar component clause 308]
312. 34 <=> generous(susan) [avatar definition]
313. ~generous(susan) <- (~34) [avatar component clause 312]
314. generous(susan) <- (34) [avatar component clause 312]
315. 33 | 34 [avatar split clause 304,312,308]
316. creative(susan) | ~generous(susan) <- (33) [resolution 310,88]
318. ~generous(susan) <- (33) [subsumption resolution 316,128]
319. ~34 | ~33 [avatar split clause 318,308,312]
325. generous(susan) | ~curious(susan) <- (33) [resolution 98,310]
328. ~curious(susan) <- (33, ~34) [subsumption resolution 325,313]
329. $false <- (33, ~34) [subsumption resolution 328,127]
330. ~33 | 34 [avatar contradiction clause 329]
337. kind(susan) | ~curious(susan) <- (34) [resolution 100,314]
338. ~curious(susan) <- (~33, 34) [subsumption resolution 337,309]
339. $false <- (~33, 34) [subsumption resolution 338,127]
340. 33 | ~34 [avatar contradiction clause 339]
341. $false [avatar sat refutation 315,319,330,340]
% SZS output end Proof for 5562604732446243426773103
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not old or humble is either rich or curious.
Everyone who is old or wise is either brave or not curious and vice versa.
Everyone who is either not quiet or not humble is either funny or not creative and vice versa.
If someone is either humble or not old then lucy is both brave and generous and vice versa.
Everyone who is both not strong and quiet is not patient.
Everyone who is either not old or not humble is not generous or not wise and vice versa.
Everyone who is creative or not curious is creative.
Everyone who is either not tall or calm is brave or happy and vice versa.
If paul is not rich or not calm then someone is either kind or not rich and vice versa.
Everyone who is both creative and not calm is either old or not old and vice versa.
If someone is either calm or not curious then someone is not funny or not generous and vice versa.
If someone is not tall or calm then susan is both not quiet and strong.
Everyone who is either creative or not humble is both not kind and not strong and vice versa.
Everyone who is not rich or patient is both humble and rich and vice versa.
If someone is not creative or not humble then someone is not kind and vice versa.
Someone is either not brave or kind.
Alice is not tall or not rich.
Paul is not kind or calm.
John is either generous or not calm.
John is either funny or curious.
Fred is brave or not curious.
Paul is both old and patient.
Lucy is either not kind or tall. | Susan is not humble. | entailment | (![X]:((~old(X)|humble(X))=>(rich(X)<~>curious(X))))&
(![X]:((old(X)|wise(X))<=>(brave(X)<~>~curious(X))))&
(![X]:((~quiet(X)<~>~humble(X))<=>(funny(X)<~>~creative(X))))&
((?[X]:((humble(X)<~>~old(X))))<=>((brave(lucy)&generous(lucy))))&
(![X]:((~strong(X)&quiet(X))=>~patient(X)))&
(![X]:((~old(X)<~>~humble(X))<=>(~generous(X)|~wise(X))))&
(![X]:((creative(X)|~curious(X))=>creative(X)))&
(![X]:((~tall(X)<~>calm(X))<=>(brave(X)|happy(X))))&
(((~rich(paul)|~calm(paul)))<=>(?[X]:((kind(X)<~>~rich(X)))))&
(![X]:((creative(X)&~calm(X))<=>(old(X)<~>~old(X))))&
((?[X]:((calm(X)<~>~curious(X))))<=>(?[X]:((~funny(X)|~generous(X)))))&
((?[X]:((~tall(X)|calm(X))))=>((~quiet(susan)&strong(susan))))&
(![X]:((creative(X)<~>~humble(X))<=>(~kind(X)&~strong(X))))&
(![X]:((~rich(X)|patient(X))<=>(humble(X)&rich(X))))&
((?[X]:((~creative(X)|~humble(X))))<=>(?[X]:(~kind(X))))&
(?[X]:((~brave(X)<~>kind(X))))&
((~tall(alice)|~rich(alice)))&
((~kind(paul)|calm(paul)))&
((generous(john)<~>~calm(john)))&
((funny(john)<~>curious(john)))&
((brave(fred)|~curious(fred)))&
((old(paul)&patient(paul)))&
((~kind(lucy)<~>tall(lucy))) | ~humble(susan) | [
"p9",
"p11",
"p12",
"p13",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 7630884222134515141957374
% SZS output start Proof for 7630884222134515141957374
10. ! [X0] : ((~calm(X0) & creative(X0)) <=> (old(X0) <~> ~old(X0))) [input p9]
12. ? [X0] : (calm(X0) | ~tall(X0)) => (strong(susan) & ~quiet(susan)) [input p11]
13. ! [X0] : ((creative(X0) <~> ~humble(X0)) <=> (~strong(X0) & ~kind(X0))) [input p12]
14. ! [X0] : ((patient(X0) | ~rich(X0)) <=> (rich(X0) & humble(X0))) [input p13]
17. ~rich(alice) | ~tall(alice) [input p16]
24. humble(susan) [input hypothesis]
31. (strong(susan) & ~quiet(susan)) | ! [X0] : (~calm(X0) & tall(X0)) [ennf transformation 12]
50. ! [X0] : (((~calm(X0) & creative(X0)) | ((old(X0) | old(X0)) & (~old(X0) | ~old(X0)))) & (((old(X0) | ~old(X0)) & (~old(X0) | old(X0))) | (calm(X0) | ~creative(X0)))) [nnf transformation 10]
51. ! [X0] : (((~calm(X0) & creative(X0)) | ((old(X0) | old(X0)) & (~old(X0) | ~old(X0)))) & (((old(X0) | ~old(X0)) & (~old(X0) | old(X0))) | calm(X0) | ~creative(X0))) [flattening 50]
57. ! [X0] : ((((humble(X0) | ~creative(X0)) & (~humble(X0) | creative(X0))) | (strong(X0) | kind(X0))) & ((~strong(X0) & ~kind(X0)) | ((creative(X0) | humble(X0)) & (~humble(X0) | ~creative(X0))))) [nnf transformation 13]
58. ! [X0] : ((((humble(X0) | ~creative(X0)) & (~humble(X0) | creative(X0))) | strong(X0) | kind(X0)) & ((~strong(X0) & ~kind(X0)) | ((creative(X0) | humble(X0)) & (~humble(X0) | ~creative(X0))))) [flattening 57]
59. ! [X0] : (((patient(X0) | ~rich(X0)) | (~rich(X0) | ~humble(X0))) & ((rich(X0) & humble(X0)) | (~patient(X0) & rich(X0)))) [nnf transformation 14]
60. ! [X0] : ((patient(X0) | ~rich(X0) | ~rich(X0) | ~humble(X0)) & ((rich(X0) & humble(X0)) | (~patient(X0) & rich(X0)))) [flattening 59]
119. creative(X0) | ~old(X0) | ~old(X0) [cnf transformation 51]
120. creative(X0) | old(X0) | old(X0) [cnf transformation 51]
131. strong(susan) | tall(X0) [cnf transformation 31]
135. ~strong(X0) | ~humble(X0) | ~creative(X0) [cnf transformation 58]
141. rich(X0) | rich(X0) [cnf transformation 60]
149. ~rich(alice) | ~tall(alice) [cnf transformation 17]
160. humble(susan) [cnf transformation 24]
161. rich(X0) [duplicate literal removal 141]
163. creative(X0) | ~old(X0) [duplicate literal removal 119]
164. creative(X0) | old(X0) [duplicate literal removal 120]
224. creative(X0) [subsumption resolution 163,164]
253. 19 <=> ! [X0] : tall(X0) [avatar definition]
254. tall(X0) <- (19) [avatar component clause 253]
256. 20 <=> strong(susan) [avatar definition]
258. strong(susan) <- (20) [avatar component clause 256]
259. 19 | 20 [avatar split clause 131,256,253]
266. ~strong(X0) | ~humble(X0) [subsumption resolution 135,224]
295. ~tall(alice) [subsumption resolution 149,161]
334. $false <- (19) [resolution 295,254]
335. ~19 [avatar contradiction clause 334]
347. ~humble(susan) <- (20) [resolution 266,258]
348. $false <- (20) [subsumption resolution 347,160]
349. ~20 [avatar contradiction clause 348]
350. $false [avatar sat refutation 259,335,349]
% SZS output end Proof for 7630884222134515141957374
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not humble is both strong and not strong and vice versa. If someone is humble then fred is either not old or not patient and vice versa. If lucy is curious then someone is brave or happy and vice versa. If someone is generous or not kind then fred is either happy or not curious. Everyone who is tall or not tall is either wise or not old. Everyone who is happy is not patient. Everyone who is both not tall and not creative is not old or not generous and vice versa. Everyone who is not happy is not curious. If someone is both rich and kind then someone is either brave or not quiet. If paul is not calm or strong then someone is not wise or not patient and vice versa. Everyone who is funny is both quiet and funny. Everyone who is not wise is not curious or not calm. Everyone who is not patient or curious is not calm or patient and vice versa. If someone is either creative or old then someone is wise. Everyone who is brave is patient and vice versa. If alice is tall or patient then lucy is kind. Paul is either not old or curious. Someone is not generous or brave. Lucy is both not quiet and curious. Alice is not generous. Someone is not tall or old. Someone is not happy or not kind. | Lucy is not calm. | entailment | (![X]:(~humble(X)<=>(strong(X)&~strong(X))))&
((?[X]:(humble(X)))<=>((~old(fred)<~>~patient(fred))))&
((curious(lucy))<=>(?[X]:((brave(X)|happy(X)))))&
((?[X]:((generous(X)|~kind(X))))=>((happy(fred)<~>~curious(fred))))&
(![X]:((tall(X)|~tall(X))=>(wise(X)<~>~old(X))))&
(![X]:(happy(X)=>~patient(X)))&
(![X]:((~tall(X)&~creative(X))<=>(~old(X)|~generous(X))))&
(![X]:(~happy(X)=>~curious(X)))&
((?[X]:((rich(X)&kind(X))))=>(?[X]:((brave(X)<~>~quiet(X)))))&
(((~calm(paul)|strong(paul)))<=>(?[X]:((~wise(X)|~patient(X)))))&
(![X]:(funny(X)=>(quiet(X)&funny(X))))&
(![X]:(~wise(X)=>(~curious(X)|~calm(X))))&
(![X]:((~patient(X)|curious(X))<=>(~calm(X)|patient(X))))&
((?[X]:((creative(X)<~>old(X))))=>(?[X]:(wise(X))))&
(![X]:(brave(X)<=>patient(X)))&
(((tall(alice)|patient(alice)))=>(kind(lucy)))&
((~old(paul)<~>curious(paul)))&
(?[X]:((~generous(X)|brave(X))))&
((~quiet(lucy)&curious(lucy)))&
(~generous(alice))&
(?[X]:((~tall(X)|old(X))))&
(?[X]:((~happy(X)|~kind(X)))) | ~calm(lucy) | [
"p5",
"p7",
"p12",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 7953466286552895228435296
% SZS output start Proof for 7953466286552895228435296
6. ! [X0] : (happy(X0) => ~patient(X0)) [input p5]
8. ! [X0] : (~happy(X0) => ~curious(X0)) [input p7]
13. ! [X0] : ((curious(X0) | ~patient(X0)) <=> (patient(X0) | ~calm(X0))) [input p12]
19. curious(lucy) & ~quiet(lucy) [input p18]
23. calm(lucy) [input hypothesis]
29. ! [X0] : (~patient(X0) | ~happy(X0)) [ennf transformation 6]
30. ! [X0] : (~curious(X0) | happy(X0)) [ennf transformation 8]
55. ! [X0] : (((curious(X0) | ~patient(X0)) | (~patient(X0) & calm(X0))) & ((patient(X0) | ~calm(X0)) | (~curious(X0) & patient(X0)))) [nnf transformation 13]
56. ! [X0] : ((curious(X0) | ~patient(X0) | (~patient(X0) & calm(X0))) & (patient(X0) | ~calm(X0) | (~curious(X0) & patient(X0)))) [flattening 55]
87. ~happy(X0) | ~patient(X0) [cnf transformation 29]
93. ~curious(X0) | happy(X0) [cnf transformation 30]
101. patient(X0) | ~calm(X0) | patient(X0) [cnf transformation 56]
115. curious(lucy) [cnf transformation 19]
119. calm(lucy) [cnf transformation 23]
120. ~calm(X0) | patient(X0) [duplicate literal removal 101]
139. 4 <=> curious(lucy) [avatar definition]
141. curious(lucy) <- (4) [avatar component clause 139]
243. 4 [avatar split clause 115,139]
253. happy(lucy) <- (4) [resolution 93,141]
254. ~patient(lucy) <- (4) [resolution 253,87]
259. patient(lucy) [resolution 120,119]
260. $false <- (4) [subsumption resolution 259,254]
261. ~4 [avatar contradiction clause 260]
262. $false [avatar sat refutation 243,261]
% SZS output end Proof for 7953466286552895228435296
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both funny and not kind then someone is either old or strong and vice versa. Everyone who is both curious and not wise is not happy or calm and vice versa. If john is either happy or not strong then paul is both not curious and creative. Everyone who is not rich or tall is either tall or not old and vice versa. Everyone who is both not kind and not rich is funny and vice versa. Everyone who is happy is not strong or tall and vice versa. If lucy is not humble then john is either rich or not funny. If paul is both not wise and not rich then someone is not happy or not curious. Everyone who is old is not humble. If mary is quiet then someone is both not creative and not funny and vice versa. Everyone who is not old or brave is both happy and not rich and vice versa. Everyone who is both strong and kind is both not humble and humble. Everyone who is either not rich or not funny is either not tall or not humble. Everyone who is both not patient and rich is brave or not brave. If mary is not calm or happy then someone is either quiet or happy and vice versa. Someone is curious or not funny. Susan is kind or not happy. Someone is not brave or not strong. Someone is not humble or not tall. | Susan is brave. | neutral | ((?[X]:((funny(X)&~kind(X))))<=>(?[X]:((old(X)<~>strong(X)))))&
(![X]:((curious(X)&~wise(X))<=>(~happy(X)|calm(X))))&
(((happy(john)<~>~strong(john)))=>((~curious(paul)&creative(paul))))&
(![X]:((~rich(X)|tall(X))<=>(tall(X)<~>~old(X))))&
(![X]:((~kind(X)&~rich(X))<=>funny(X)))&
(![X]:(happy(X)<=>(~strong(X)|tall(X))))&
((~humble(lucy))=>((rich(john)<~>~funny(john))))&
(((~wise(paul)&~rich(paul)))=>(?[X]:((~happy(X)|~curious(X)))))&
(![X]:(old(X)=>~humble(X)))&
((quiet(mary))<=>(?[X]:((~creative(X)&~funny(X)))))&
(![X]:((~old(X)|brave(X))<=>(happy(X)&~rich(X))))&
(![X]:((strong(X)&kind(X))=>(~humble(X)&humble(X))))&
(![X]:((~rich(X)<~>~funny(X))=>(~tall(X)<~>~humble(X))))&
(![X]:((~patient(X)&rich(X))=>(brave(X)|~brave(X))))&
(((~calm(mary)|happy(mary)))<=>(?[X]:((quiet(X)<~>happy(X)))))&
(?[X]:((curious(X)|~funny(X))))&
((kind(susan)|~happy(susan)))&
(?[X]:((~brave(X)|~strong(X))))&
(?[X]:((~humble(X)|~tall(X)))) | brave(susan) | [] | null | 0 |
Everyone who is not calm or calm is both calm and not old and vice versa. If someone is both brave and not quiet then alice is not generous or patient and vice versa. Everyone who is both strong and rich is both happy and not kind. If someone is both kind and quiet then john is happy or not funny. Everyone who is either humble or not strong is either not happy or happy. Everyone who is brave or curious is wise. If someone is both kind and not funny then someone is either not quiet or patient and vice versa. If paul is not funny then someone is quiet. Everyone who is rich or wise is quiet and vice versa. If someone is either old or not strong then fred is not wise. Everyone who is not generous or calm is either not curious or not brave and vice versa. If someone is either patient or generous then someone is not funny or not strong. Everyone who is not patient or brave is not curious. Everyone who is either generous or calm is both not wise and not rich. Everyone who is patient or quiet is not kind and vice versa. If fred is both not happy and kind then someone is not creative and vice versa. Someone is either creative or not tall. Mary is not old. Someone is not generous or not humble. Someone is both happy and wise. Someone is either funny or curious. | Mary is not kind. | entailment | (![X]:((~calm(X)|calm(X))<=>(calm(X)&~old(X))))&
((?[X]:((brave(X)&~quiet(X))))<=>((~generous(alice)|patient(alice))))&
(![X]:((strong(X)&rich(X))=>(happy(X)&~kind(X))))&
((?[X]:((kind(X)&quiet(X))))=>((happy(john)|~funny(john))))&
(![X]:((humble(X)<~>~strong(X))=>(~happy(X)<~>happy(X))))&
(![X]:((brave(X)|curious(X))=>wise(X)))&
((?[X]:((kind(X)&~funny(X))))<=>(?[X]:((~quiet(X)<~>patient(X)))))&
((~funny(paul))=>(?[X]:(quiet(X))))&
(![X]:((rich(X)|wise(X))<=>quiet(X)))&
((?[X]:((old(X)<~>~strong(X))))=>(~wise(fred)))&
(![X]:((~generous(X)|calm(X))<=>(~curious(X)<~>~brave(X))))&
((?[X]:((patient(X)<~>generous(X))))=>(?[X]:((~funny(X)|~strong(X)))))&
(![X]:((~patient(X)|brave(X))=>~curious(X)))&
(![X]:((generous(X)<~>calm(X))=>(~wise(X)&~rich(X))))&
(![X]:((patient(X)|quiet(X))<=>~kind(X)))&
(((~happy(fred)&kind(fred)))<=>(?[X]:(~creative(X))))&
(?[X]:((creative(X)<~>~tall(X))))&
(~old(mary))&
(?[X]:((~generous(X)|~humble(X))))&
(?[X]:((happy(X)&wise(X))))&
(?[X]:((funny(X)<~>curious(X)))) | ~kind(mary) | [
"p0",
"p5",
"p8",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3537614265400373665535784
% SZS output start Proof for 3537614265400373665535784
1. ! [X0] : ((calm(X0) | ~calm(X0)) <=> (~old(X0) & calm(X0))) [input p0]
6. ! [X0] : ((curious(X0) | brave(X0)) => wise(X0)) [input p5]
9. ! [X0] : ((wise(X0) | rich(X0)) <=> quiet(X0)) [input p8]
11. ! [X0] : ((calm(X0) | ~generous(X0)) <=> (~curious(X0) <~> ~brave(X0))) [input p10]
15. ! [X0] : ((quiet(X0) | patient(X0)) <=> ~kind(X0)) [input p14]
22. kind(mary) [input hypothesis]
30. ! [X0] : (wise(X0) | (~curious(X0) & ~brave(X0))) [ennf transformation 6]
36. ! [X0] : (((calm(X0) | ~calm(X0)) | (old(X0) | ~calm(X0))) & ((~old(X0) & calm(X0)) | (~calm(X0) & calm(X0)))) [nnf transformation 1]
37. ! [X0] : ((calm(X0) | ~calm(X0) | old(X0) | ~calm(X0)) & ((~old(X0) & calm(X0)) | (~calm(X0) & calm(X0)))) [flattening 36]
51. ! [X0] : (((wise(X0) | rich(X0)) | ~quiet(X0)) & (quiet(X0) | (~wise(X0) & ~rich(X0)))) [nnf transformation 9]
52. ! [X0] : ((wise(X0) | rich(X0) | ~quiet(X0)) & (quiet(X0) | (~wise(X0) & ~rich(X0)))) [flattening 51]
54. ! [X0] : (((calm(X0) | ~generous(X0)) | ((~curious(X0) | brave(X0)) & (~brave(X0) | curious(X0)))) & (((brave(X0) | curious(X0)) & (~brave(X0) | ~curious(X0))) | (~calm(X0) & generous(X0)))) [nnf transformation 11]
55. ! [X0] : ((calm(X0) | ~generous(X0) | ((~curious(X0) | brave(X0)) & (~brave(X0) | curious(X0)))) & (((brave(X0) | curious(X0)) & (~brave(X0) | ~curious(X0))) | (~calm(X0) & generous(X0)))) [flattening 54]
61. ! [X0] : (((quiet(X0) | patient(X0)) | kind(X0)) & (~kind(X0) | (~quiet(X0) & ~patient(X0)))) [nnf transformation 15]
62. ! [X0] : ((quiet(X0) | patient(X0) | kind(X0)) & (~kind(X0) | (~quiet(X0) & ~patient(X0)))) [flattening 61]
78. calm(X0) | calm(X0) [cnf transformation 37]
95. ~brave(X0) | wise(X0) [cnf transformation 30]
96. ~curious(X0) | wise(X0) [cnf transformation 30]
105. ~wise(X0) | quiet(X0) [cnf transformation 52]
112. brave(X0) | curious(X0) | ~calm(X0) [cnf transformation 55]
124. ~kind(X0) | ~quiet(X0) [cnf transformation 62]
137. kind(mary) [cnf transformation 22]
138. calm(X0) [duplicate literal removal 78]
166. 6 <=> ! [X0] : (~quiet(X0) | ~kind(X0)) [avatar definition]
167. ~kind(X0) | ~quiet(X0) <- (6) [avatar component clause 166]
226. curious(X0) | brave(X0) [subsumption resolution 112,138]
246. 6 [avatar split clause 124,166]
303. ~quiet(mary) <- (6) [resolution 167,137]
320. brave(X1) | wise(X1) [resolution 226,96]
321. wise(X1) [subsumption resolution 320,95]
326. quiet(X0) [resolution 321,105]
331. $false <- (6) [resolution 326,303]
338. ~6 [avatar contradiction clause 331]
340. $false [avatar sat refutation 246,338]
% SZS output end Proof for 3537614265400373665535784
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not strong and kind is either not rich or patient.
Everyone who is brave or not happy is tall or generous and vice versa.
Everyone who is not tall or humble is either wise or curious.
If john is rich then lucy is not generous.
Everyone who is not generous or kind is either not humble or creative and vice versa.
If paul is either not tall or creative then someone is either generous or not brave and vice versa.
Everyone who is either old or generous is either not generous or not patient.
Everyone who is not brave is quiet or not old.
If someone is both not calm and not wise then someone is either happy or brave.
Everyone who is both not creative and not kind is both not curious and not kind.
Everyone who is both not wise and not old is strong and vice versa.
Everyone who is either not creative or not brave is either not strong or strong and vice versa.
Everyone who is patient or calm is both creative and not tall and vice versa.
Everyone who is both not wise and not kind is rich or not creative.
Everyone who is not calm or not tall is happy and vice versa.
If alice is both not kind and not tall then alice is not brave.
Fred is quiet or not quiet.
Someone is not old or strong.
Someone is both not old and not brave.
Someone is generous or not wise.
Someone is either not rich or strong.
John is not creative or old.
Alice is strong or wise.
Someone is wise. | Paul is not creative. | entailment | (![X]:((~strong(X)&kind(X))=>(~rich(X)<~>patient(X))))&
(![X]:((brave(X)|~happy(X))<=>(tall(X)|generous(X))))&
(![X]:((~tall(X)|humble(X))=>(wise(X)<~>curious(X))))&
((rich(john))=>(~generous(lucy)))&
(![X]:((~generous(X)|kind(X))<=>(~humble(X)<~>creative(X))))&
(((~tall(paul)<~>creative(paul)))<=>(?[X]:((generous(X)<~>~brave(X)))))&
(![X]:((old(X)<~>generous(X))=>(~generous(X)<~>~patient(X))))&
(![X]:(~brave(X)=>(quiet(X)|~old(X))))&
((?[X]:((~calm(X)&~wise(X))))=>(?[X]:((happy(X)<~>brave(X)))))&
(![X]:((~creative(X)&~kind(X))=>(~curious(X)&~kind(X))))&
(![X]:((~wise(X)&~old(X))<=>strong(X)))&
(![X]:((~creative(X)<~>~brave(X))<=>(~strong(X)<~>strong(X))))&
(![X]:((patient(X)|calm(X))<=>(creative(X)&~tall(X))))&
(![X]:((~wise(X)&~kind(X))=>(rich(X)|~creative(X))))&
(![X]:((~calm(X)|~tall(X))<=>happy(X)))&
(((~kind(alice)&~tall(alice)))=>(~brave(alice)))&
((quiet(fred)|~quiet(fred)))&
(?[X]:((~old(X)|strong(X))))&
(?[X]:((~old(X)&~brave(X))))&
(?[X]:((generous(X)|~wise(X))))&
(?[X]:((~rich(X)<~>strong(X))))&
((~creative(john)|old(john)))&
((strong(alice)|wise(alice)))&
(?[X]:(wise(X))) | ~creative(paul) | [
"p1",
"p5",
"p11",
"p12",
"p14",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 3655196890534598847903912
% SZS output start Proof for 3655196890534598847903912
2. ! [X0] : ((~happy(X0) | brave(X0)) <=> (generous(X0) | tall(X0))) [input p1]
6. (~tall(paul) <~> creative(paul)) <=> ? [X0] : (generous(X0) <~> ~brave(X0)) [input p5]
12. ! [X0] : ((~creative(X0) <~> ~brave(X0)) <=> (~strong(X0) <~> strong(X0))) [input p11]
13. ! [X0] : ((calm(X0) | patient(X0)) <=> (~tall(X0) & creative(X0))) [input p12]
15. ! [X0] : ((~tall(X0) | ~calm(X0)) <=> happy(X0)) [input p14]
19. ? [X0] : (~brave(X0) & ~old(X0)) [input p18]
25. creative(paul) [input hypothesis]
42. ! [X0] : (((~happy(X0) | brave(X0)) | (~generous(X0) & ~tall(X0))) & ((generous(X0) | tall(X0)) | (happy(X0) & ~brave(X0)))) [nnf transformation 2]
43. ! [X0] : ((~happy(X0) | brave(X0) | (~generous(X0) & ~tall(X0))) & (generous(X0) | tall(X0) | (happy(X0) & ~brave(X0)))) [flattening 42]
47. (((~creative(paul) | tall(paul)) & (creative(paul) | ~tall(paul))) | ! [X0] : ((generous(X0) | brave(X0)) & (~brave(X0) | ~generous(X0)))) & (? [X0] : ((brave(X0) | ~generous(X0)) & (~brave(X0) | generous(X0))) | ((~tall(paul) | ~creative(paul)) & (creative(paul) | tall(paul)))) [nnf transformation 6]
48. (((~creative(paul) | tall(paul)) & (creative(paul) | ~tall(paul))) | ! [X0] : ((generous(X0) | brave(X0)) & (~brave(X0) | ~generous(X0)))) & (? [X1] : ((brave(X1) | ~generous(X1)) & (~brave(X1) | generous(X1))) | ((~tall(paul) | ~creative(paul)) & (creative(paul) | tall(paul)))) [rectify 47]
49. ? [X1] : ((brave(X1) | ~generous(X1)) & (~brave(X1) | generous(X1))) => ((brave(sK0) | ~generous(sK0)) & (~brave(sK0) | generous(sK0))) [choice axiom]
50. (((~creative(paul) | tall(paul)) & (creative(paul) | ~tall(paul))) | ! [X0] : ((generous(X0) | brave(X0)) & (~brave(X0) | ~generous(X0)))) & (((brave(sK0) | ~generous(sK0)) & (~brave(sK0) | generous(sK0))) | ((~tall(paul) | ~creative(paul)) & (creative(paul) | tall(paul)))) [skolemisation 48,49]
58. ! [X0] : ((((brave(X0) | creative(X0)) & (~brave(X0) | ~creative(X0))) | ((~strong(X0) | ~strong(X0)) & (strong(X0) | strong(X0)))) & (((~strong(X0) | strong(X0)) & (strong(X0) | ~strong(X0))) | ((~creative(X0) | brave(X0)) & (~brave(X0) | creative(X0))))) [nnf transformation 12]
59. ! [X0] : (((calm(X0) | patient(X0)) | (tall(X0) | ~creative(X0))) & ((~tall(X0) & creative(X0)) | (~calm(X0) & ~patient(X0)))) [nnf transformation 13]
60. ! [X0] : ((calm(X0) | patient(X0) | tall(X0) | ~creative(X0)) & ((~tall(X0) & creative(X0)) | (~calm(X0) & ~patient(X0)))) [flattening 59]
61. ! [X0] : (((~tall(X0) | ~calm(X0)) | ~happy(X0)) & (happy(X0) | (tall(X0) & calm(X0)))) [nnf transformation 15]
62. ! [X0] : ((~tall(X0) | ~calm(X0) | ~happy(X0)) & (happy(X0) | (tall(X0) & calm(X0)))) [flattening 61]
65. ? [X0] : (~brave(X0) & ~old(X0)) => (~brave(sK3) & ~old(sK3)) [choice axiom]
66. ~brave(sK3) & ~old(sK3) [skolemisation 19,65]
78. ~tall(X0) | brave(X0) | ~happy(X0) [cnf transformation 43]
79. ~generous(X0) | brave(X0) | ~happy(X0) [cnf transformation 43]
98. ~creative(paul) | tall(paul) | generous(X0) | brave(X0) [cnf transformation 50]
115. ~brave(X0) | ~creative(X0) | strong(X0) | strong(X0) [cnf transformation 58]
116. ~brave(X0) | ~creative(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 58]
122. ~calm(X0) | ~tall(X0) [cnf transformation 60]
125. calm(X0) | happy(X0) [cnf transformation 62]
126. tall(X0) | happy(X0) [cnf transformation 62]
132. ~brave(sK3) [cnf transformation 66]
139. creative(paul) [cnf transformation 25]
140. ~brave(X0) | ~creative(X0) | strong(X0) [duplicate literal removal 115]
141. ~brave(X0) | ~creative(X0) | ~strong(X0) [duplicate literal removal 116]
156. 3 <=> ! [X0] : (generous(X0) | brave(X0)) [avatar definition]
157. generous(X0) | brave(X0) <- (3) [avatar component clause 156]
159. 4 <=> tall(paul) [avatar definition]
161. tall(paul) <- (4) [avatar component clause 159]
163. 5 <=> creative(paul) [avatar definition]
164. creative(paul) <- (5) [avatar component clause 163]
166. 3 | 4 | ~5 [avatar split clause 98,163,159,156]
199. ~creative(X0) | ~brave(X0) [subsumption resolution 140,141]
251. 5 [avatar split clause 139,163]
254. happy(X0) | ~tall(X0) [resolution 125,122]
256. happy(X0) [subsumption resolution 254,126]
261. ~brave(paul) <- (5) [resolution 199,164]
277. brave(paul) | ~happy(paul) <- (4) [resolution 78,161]
279. ~happy(paul) <- (4, 5) [subsumption resolution 277,261]
280. $false <- (4, 5) [subsumption resolution 279,256]
281. ~4 | ~5 [avatar contradiction clause 280]
292. brave(X0) | ~happy(X0) | brave(X0) <- (3) [resolution 79,157]
295. brave(X0) | ~happy(X0) <- (3) [duplicate literal removal 292]
296. brave(X0) <- (3) [subsumption resolution 295,256]
302. $false <- (3) [resolution 296,132]
303. ~3 [avatar contradiction clause 302]
308. $false [avatar sat refutation 166,251,281,303]
% SZS output end Proof for 3655196890534598847903912
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not strong or old then someone is both calm and not quiet. If someone is either not patient or not rich then mary is either strong or not calm. Everyone who is both not old and not quiet is not creative or not calm and vice versa. Everyone who is both not generous and not curious is both not humble and creative and vice versa. If mary is brave or not quiet then mary is not wise and vice versa. Everyone who is both curious and quiet is both brave and tall. Everyone who is creative is either not quiet or not calm. Everyone who is not happy is either old or not kind and vice versa. If someone is not humble then someone is kind. Everyone who is both not kind and not humble is brave or not wise and vice versa. If paul is both humble and patient then someone is both not happy and old. If someone is both rich and not funny then paul is wise or not curious and vice versa. If fred is both quiet and rich then paul is quiet and vice versa. If someone is tall then someone is both not strong and tall. If someone is quiet then someone is old or not strong and vice versa. Everyone who is not creative or quiet is either not curious or not old and vice versa. Someone is either not old or kind. Paul is both not tall and happy. Someone is either not curious or not generous. Someone is both patient and not old. Alice is either not creative or generous. Someone is not patient. | Alice is strong. | entailment | ((?[X]:((~strong(X)|old(X))))=>(?[X]:((calm(X)&~quiet(X)))))&
((?[X]:((~patient(X)<~>~rich(X))))=>((strong(mary)<~>~calm(mary))))&
(![X]:((~old(X)&~quiet(X))<=>(~creative(X)|~calm(X))))&
(![X]:((~generous(X)&~curious(X))<=>(~humble(X)&creative(X))))&
(((brave(mary)|~quiet(mary)))<=>(~wise(mary)))&
(![X]:((curious(X)&quiet(X))=>(brave(X)&tall(X))))&
(![X]:(creative(X)=>(~quiet(X)<~>~calm(X))))&
(![X]:(~happy(X)<=>(old(X)<~>~kind(X))))&
((?[X]:(~humble(X)))=>(?[X]:(kind(X))))&
(![X]:((~kind(X)&~humble(X))<=>(brave(X)|~wise(X))))&
(((humble(paul)&patient(paul)))=>(?[X]:((~happy(X)&old(X)))))&
((?[X]:((rich(X)&~funny(X))))<=>((wise(paul)|~curious(paul))))&
(((quiet(fred)&rich(fred)))<=>(quiet(paul)))&
((?[X]:(tall(X)))=>(?[X]:((~strong(X)&tall(X)))))&
((?[X]:(quiet(X)))<=>(?[X]:((old(X)|~strong(X)))))&
(![X]:((~creative(X)|quiet(X))<=>(~curious(X)<~>~old(X))))&
(?[X]:((~old(X)<~>kind(X))))&
((~tall(paul)&happy(paul)))&
(?[X]:((~curious(X)<~>~generous(X))))&
(?[X]:((patient(X)&~old(X))))&
((~creative(alice)<~>generous(alice)))&
(?[X]:(~patient(X))) | strong(alice) | [
"p2",
"p6",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3741361410944678100747472
% SZS output start Proof for 3741361410944678100747472
3. ! [X0] : ((~quiet(X0) & ~old(X0)) <=> (~calm(X0) | ~creative(X0))) [input p2]
7. ! [X0] : (creative(X0) => (~quiet(X0) <~> ~calm(X0))) [input p6]
15. ? [X0] : quiet(X0) <=> ? [X0] : (~strong(X0) | old(X0)) [input p14]
23. ~strong(alice) [input hypothesis]
27. ? [X0] : quiet(X0) <=> ? [X1] : (~strong(X1) | old(X1)) [rectify 15]
32. ! [X0] : ((~quiet(X0) <~> ~calm(X0)) | ~creative(X0)) [ennf transformation 7]
41. ! [X0] : (((~quiet(X0) & ~old(X0)) | (calm(X0) & creative(X0))) & ((~calm(X0) | ~creative(X0)) | (quiet(X0) | old(X0)))) [nnf transformation 3]
42. ! [X0] : (((~quiet(X0) & ~old(X0)) | (calm(X0) & creative(X0))) & (~calm(X0) | ~creative(X0) | quiet(X0) | old(X0))) [flattening 41]
47. ! [X0] : (((calm(X0) | quiet(X0)) & (~calm(X0) | ~quiet(X0))) | ~creative(X0)) [nnf transformation 32]
66. (? [X0] : quiet(X0) | ! [X1] : (strong(X1) & ~old(X1))) & (? [X1] : (~strong(X1) | old(X1)) | ! [X0] : ~quiet(X0)) [nnf transformation 27]
67. (? [X0] : quiet(X0) | ! [X1] : (strong(X1) & ~old(X1))) & (? [X2] : (~strong(X2) | old(X2)) | ! [X3] : ~quiet(X3)) [rectify 66]
68. ? [X0] : quiet(X0) => quiet(sK5) [choice axiom]
69. ? [X2] : (~strong(X2) | old(X2)) => (~strong(sK6) | old(sK6)) [choice axiom]
70. (quiet(sK5) | ! [X1] : (strong(X1) & ~old(X1))) & ((~strong(sK6) | old(sK6)) | ! [X3] : ~quiet(X3)) [skolemisation 67,69,68]
95. ~quiet(X0) | creative(X0) [cnf transformation 42]
96. ~quiet(X0) | calm(X0) [cnf transformation 42]
106. ~calm(X0) | ~quiet(X0) | ~creative(X0) [cnf transformation 47]
107. calm(X0) | quiet(X0) | ~creative(X0) [cnf transformation 47]
132. quiet(sK5) | strong(X1) [cnf transformation 70]
150. ~strong(alice) [cnf transformation 23]
160. 3 <=> ! [X1] : strong(X1) [avatar definition]
161. strong(X1) <- (3) [avatar component clause 160]
202. calm(X0) | ~creative(X0) [subsumption resolution 107,96]
203. ~quiet(X0) | ~creative(X0) [subsumption resolution 106,202]
204. ~quiet(X0) [subsumption resolution 203,95]
268. strong(X1) [subsumption resolution 132,204]
269. 3 [avatar split clause 268,160]
306. $false <- (3) [resolution 161,150]
307. ~3 [avatar contradiction clause 306]
308. $false [avatar sat refutation 269,307]
% SZS output end Proof for 3741361410944678100747472
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not brave or not happy is not funny.
Everyone who is not quiet or not curious is not kind or not humble.
Everyone who is not wise or creative is either not patient or not humble and vice versa.
If lucy is both not calm and not happy then fred is not creative and vice versa.
If someone is creative then someone is both calm and not calm and vice versa.
Everyone who is quiet is funny or patient.
Everyone who is not happy is either not rich or brave and vice versa.
If someone is either quiet or brave then susan is not patient or not brave.
If someone is both curious and not tall then paul is either not curious or not brave and vice versa.
Everyone who is both not rich and kind is either not funny or creative.
If paul is both not old and quiet then someone is both not quiet and patient.
Everyone who is quiet is creative and vice versa.
Everyone who is not quiet is both not wise and not quiet.
Everyone who is not patient is not quiet.
If someone is both strong and not rich then john is both not tall and not happy.
Everyone who is not brave or not quiet is either strong or happy and vice versa.
Someone is generous.
Fred is either not old or kind.
John is happy or curious.
Someone is both not wise and not calm.
Lucy is not generous or curious. | John is not wise. | entailment | (![X]:((~brave(X)<~>~happy(X))=>~funny(X)))&
(![X]:((~quiet(X)|~curious(X))=>(~kind(X)|~humble(X))))&
(![X]:((~wise(X)|creative(X))<=>(~patient(X)<~>~humble(X))))&
(((~calm(lucy)&~happy(lucy)))<=>(~creative(fred)))&
((?[X]:(creative(X)))<=>(?[X]:((calm(X)&~calm(X)))))&
(![X]:(quiet(X)=>(funny(X)|patient(X))))&
(![X]:(~happy(X)<=>(~rich(X)<~>brave(X))))&
((?[X]:((quiet(X)<~>brave(X))))=>((~patient(susan)|~brave(susan))))&
((?[X]:((curious(X)&~tall(X))))<=>((~curious(paul)<~>~brave(paul))))&
(![X]:((~rich(X)&kind(X))=>(~funny(X)<~>creative(X))))&
(((~old(paul)&quiet(paul)))=>(?[X]:((~quiet(X)&patient(X)))))&
(![X]:(quiet(X)<=>creative(X)))&
(![X]:(~quiet(X)=>(~wise(X)&~quiet(X))))&
(![X]:(~patient(X)=>~quiet(X)))&
((?[X]:((strong(X)&~rich(X))))=>((~tall(john)&~happy(john))))&
(![X]:((~brave(X)|~quiet(X))<=>(strong(X)<~>happy(X))))&
(?[X]:(generous(X)))&
((~old(fred)<~>kind(fred)))&
((happy(john)|curious(john)))&
(?[X]:((~wise(X)&~calm(X))))&
((~generous(lucy)|curious(lucy))) | ~wise(john) | [
"p4",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 3604558736000706495903556
% SZS output start Proof for 3604558736000706495903556
5. ? [X0] : creative(X0) <=> ? [X0] : (~calm(X0) & calm(X0)) [input p4]
12. ! [X0] : (quiet(X0) <=> creative(X0)) [input p11]
13. ! [X0] : (~quiet(X0) => (~quiet(X0) & ~wise(X0))) [input p12]
22. wise(john) [input hypothesis]
23. ? [X0] : creative(X0) <=> ? [X1] : (~calm(X1) & calm(X1)) [rectify 5]
35. ! [X0] : ((~quiet(X0) & ~wise(X0)) | quiet(X0)) [ennf transformation 13]
43. (? [X0] : creative(X0) | ! [X1] : (calm(X1) | ~calm(X1))) & (? [X1] : (~calm(X1) & calm(X1)) | ! [X0] : ~creative(X0)) [nnf transformation 23]
44. (? [X0] : creative(X0) | ! [X1] : (calm(X1) | ~calm(X1))) & (? [X2] : (~calm(X2) & calm(X2)) | ! [X3] : ~creative(X3)) [rectify 43]
45. ? [X0] : creative(X0) => creative(sK0) [choice axiom]
46. ? [X2] : (~calm(X2) & calm(X2)) => (~calm(sK1) & calm(sK1)) [choice axiom]
47. (creative(sK0) | ! [X1] : (calm(X1) | ~calm(X1))) & ((~calm(sK1) & calm(sK1)) | ! [X3] : ~creative(X3)) [skolemisation 44,46,45]
57. ! [X0] : ((quiet(X0) | ~creative(X0)) & (creative(X0) | ~quiet(X0))) [nnf transformation 12]
78. calm(sK1) | ~creative(X3) [cnf transformation 47]
79. ~calm(sK1) | ~creative(X3) [cnf transformation 47]
98. ~quiet(X0) | creative(X0) [cnf transformation 57]
100. ~wise(X0) | quiet(X0) [cnf transformation 35]
118. wise(john) [cnf transformation 22]
135. 4 <=> ! [X3] : ~creative(X3) [avatar definition]
136. ~creative(X3) <- (4) [avatar component clause 135]
138. 5 <=> calm(sK1) [avatar definition]
141. 4 | ~5 [avatar split clause 79,138,135]
142. 4 | 5 [avatar split clause 78,138,135]
239. quiet(john) [resolution 100,118]
240. creative(john) [resolution 239,98]
241. $false <- (4) [subsumption resolution 240,136]
242. ~4 [avatar contradiction clause 241]
243. $false [avatar sat refutation 141,142,242]
% SZS output end Proof for 3604558736000706495903556
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is not patient then lucy is both not funny and calm. If fred is tall or not generous then lucy is not brave and vice versa. Everyone who is funny or not tall is either not creative or generous and vice versa. If fred is wise then susan is either curious or not strong. Everyone who is both patient and strong is patient or tall. If someone is not rich then susan is either not humble or not happy. If someone is either not humble or not old then someone is calm. Everyone who is both curious and patient is humble and vice versa. If lucy is not calm or not tall then mary is either generous or not generous and vice versa. Everyone who is both not calm and old is not brave or wise and vice versa. If john is either kind or not creative then someone is both rich and old and vice versa. If someone is either tall or not calm then john is both not brave and funny and vice versa. If john is brave then someone is not patient or old and vice versa. If someone is either kind or not tall then someone is brave or not tall. If fred is both not wise and calm then paul is either kind or wise. Everyone who is either happy or not wise is both not funny and old and vice versa. Someone is not curious or brave. Someone is creative. John is both strong and not creative. Mary is generous or not humble. Alice is both old and curious. Susan is either rich or not curious. Fred is both not creative and not funny. Someone is either not wise or not funny. | Lucy is not tall. | contradiction | ((~patient(lucy))=>((~funny(lucy)&calm(lucy))))&
(((tall(fred)|~generous(fred)))<=>(~brave(lucy)))&
(![X]:((funny(X)|~tall(X))<=>(~creative(X)<~>generous(X))))&
((wise(fred))=>((curious(susan)<~>~strong(susan))))&
(![X]:((patient(X)&strong(X))=>(patient(X)|tall(X))))&
((?[X]:(~rich(X)))=>((~humble(susan)<~>~happy(susan))))&
((?[X]:((~humble(X)<~>~old(X))))=>(?[X]:(calm(X))))&
(![X]:((curious(X)&patient(X))<=>humble(X)))&
(((~calm(lucy)|~tall(lucy)))<=>((generous(mary)<~>~generous(mary))))&
(![X]:((~calm(X)&old(X))<=>(~brave(X)|wise(X))))&
(((kind(john)<~>~creative(john)))<=>(?[X]:((rich(X)&old(X)))))&
((?[X]:((tall(X)<~>~calm(X))))<=>((~brave(john)&funny(john))))&
((brave(john))<=>(?[X]:((~patient(X)|old(X)))))&
((?[X]:((kind(X)<~>~tall(X))))=>(?[X]:((brave(X)|~tall(X)))))&
(((~wise(fred)&calm(fred)))=>((kind(paul)<~>wise(paul))))&
(![X]:((happy(X)<~>~wise(X))<=>(~funny(X)&old(X))))&
(?[X]:((~curious(X)|brave(X))))&
(?[X]:(creative(X)))&
((strong(john)&~creative(john)))&
((generous(mary)|~humble(mary)))&
((old(alice)&curious(alice)))&
((rich(susan)<~>~curious(susan)))&
((~creative(fred)&~funny(fred)))&
(?[X]:((~wise(X)<~>~funny(X)))) | ~tall(lucy) | [
"p1",
"p2",
"p9",
"p11",
"p12",
"p20",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 4413189128032147638530854
% SZS output start Proof for 4413189128032147638530854
2. (~generous(fred) | tall(fred)) <=> ~brave(lucy) [input p1]
3. ! [X0] : ((~tall(X0) | funny(X0)) <=> (~creative(X0) <~> generous(X0))) [input p2]
10. ! [X0] : ((old(X0) & ~calm(X0)) <=> (wise(X0) | ~brave(X0))) [input p9]
12. ? [X0] : (tall(X0) <~> ~calm(X0)) <=> (funny(john) & ~brave(john)) [input p11]
13. brave(john) <=> ? [X0] : (old(X0) | ~patient(X0)) [input p12]
21. curious(alice) & old(alice) [input p20]
23. ~funny(fred) & ~creative(fred) [input p22]
25. ~tall(lucy) [input hypothesis]
37. ((~generous(fred) | tall(fred)) | brave(lucy)) & (~brave(lucy) | (generous(fred) & ~tall(fred))) [nnf transformation 2]
38. (~generous(fred) | tall(fred) | brave(lucy)) & (~brave(lucy) | (generous(fred) & ~tall(fred))) [flattening 37]
39. ! [X0] : (((~tall(X0) | funny(X0)) | ((~creative(X0) | ~generous(X0)) & (generous(X0) | creative(X0)))) & (((~generous(X0) | creative(X0)) & (generous(X0) | ~creative(X0))) | (tall(X0) & ~funny(X0)))) [nnf transformation 3]
40. ! [X0] : ((~tall(X0) | funny(X0) | ((~creative(X0) | ~generous(X0)) & (generous(X0) | creative(X0)))) & (((~generous(X0) | creative(X0)) & (generous(X0) | ~creative(X0))) | (tall(X0) & ~funny(X0)))) [flattening 39]
51. ! [X0] : (((old(X0) & ~calm(X0)) | (~wise(X0) & brave(X0))) & ((wise(X0) | ~brave(X0)) | (~old(X0) | calm(X0)))) [nnf transformation 10]
52. ! [X0] : (((old(X0) & ~calm(X0)) | (~wise(X0) & brave(X0))) & (wise(X0) | ~brave(X0) | ~old(X0) | calm(X0))) [flattening 51]
57. (? [X0] : ((calm(X0) | ~tall(X0)) & (~calm(X0) | tall(X0))) | (~funny(john) | brave(john))) & ((funny(john) & ~brave(john)) | ! [X0] : ((tall(X0) | calm(X0)) & (~calm(X0) | ~tall(X0)))) [nnf transformation 12]
58. (? [X0] : ((calm(X0) | ~tall(X0)) & (~calm(X0) | tall(X0))) | ~funny(john) | brave(john)) & ((funny(john) & ~brave(john)) | ! [X0] : ((tall(X0) | calm(X0)) & (~calm(X0) | ~tall(X0)))) [flattening 57]
59. (? [X0] : ((calm(X0) | ~tall(X0)) & (~calm(X0) | tall(X0))) | ~funny(john) | brave(john)) & ((funny(john) & ~brave(john)) | ! [X1] : ((tall(X1) | calm(X1)) & (~calm(X1) | ~tall(X1)))) [rectify 58]
60. ? [X0] : ((calm(X0) | ~tall(X0)) & (~calm(X0) | tall(X0))) => ((calm(sK2) | ~tall(sK2)) & (~calm(sK2) | tall(sK2))) [choice axiom]
61. (((calm(sK2) | ~tall(sK2)) & (~calm(sK2) | tall(sK2))) | ~funny(john) | brave(john)) & ((funny(john) & ~brave(john)) | ! [X1] : ((tall(X1) | calm(X1)) & (~calm(X1) | ~tall(X1)))) [skolemisation 59,60]
62. (brave(john) | ! [X0] : (~old(X0) & patient(X0))) & (? [X0] : (old(X0) | ~patient(X0)) | ~brave(john)) [nnf transformation 13]
63. (brave(john) | ! [X0] : (~old(X0) & patient(X0))) & (? [X1] : (old(X1) | ~patient(X1)) | ~brave(john)) [rectify 62]
64. ? [X1] : (old(X1) | ~patient(X1)) => (old(sK3) | ~patient(sK3)) [choice axiom]
65. (brave(john) | ! [X0] : (~old(X0) & patient(X0))) & ((old(sK3) | ~patient(sK3)) | ~brave(john)) [skolemisation 63,64]
83. ~brave(lucy) | ~tall(fred) [cnf transformation 38]
84. ~brave(lucy) | generous(fred) [cnf transformation 38]
89. ~generous(X0) | creative(X0) | tall(X0) [cnf transformation 40]
109. ~calm(X0) | brave(X0) [cnf transformation 52]
120. ~brave(john) | tall(X1) | calm(X1) [cnf transformation 61]
127. brave(john) | ~old(X0) [cnf transformation 65]
143. old(alice) [cnf transformation 21]
147. ~creative(fred) [cnf transformation 23]
151. ~tall(lucy) [cnf transformation 25]
159. 2 <=> calm(lucy) [avatar definition]
160. ~calm(lucy) <- (~2) [avatar component clause 159]
161. calm(lucy) <- (2) [avatar component clause 159]
169. 4 <=> brave(lucy) [avatar definition]
170. ~brave(lucy) <- (~4) [avatar component clause 169]
173. 5 <=> tall(fred) [avatar definition]
174. ~tall(fred) <- (~5) [avatar component clause 173]
177. 6 <=> generous(fred) [avatar definition]
178. generous(fred) <- (6) [avatar component clause 177]
181. 6 | ~4 [avatar split clause 84,169,177]
182. ~5 | ~4 [avatar split clause 83,169,173]
227. 17 <=> tall(lucy) [avatar definition]
229. ~tall(lucy) <- (~17) [avatar component clause 227]
258. 23 <=> brave(john) [avatar definition]
276. 27 <=> ! [X1] : (tall(X1) | calm(X1)) [avatar definition]
277. tall(X1) | calm(X1) <- (27) [avatar component clause 276]
283. 27 | ~23 [avatar split clause 120,258,276]
286. 29 <=> ! [X0] : ~old(X0) [avatar definition]
287. ~old(X0) <- (29) [avatar component clause 286]
288. 29 | 23 [avatar split clause 127,258,286]
367. ~17 [avatar split clause 151,227]
373. brave(lucy) <- (2) [resolution 109,161]
375. $false <- (2, ~4) [subsumption resolution 373,170]
376. ~2 | 4 [avatar contradiction clause 375]
382. calm(lucy) <- (~17, 27) [resolution 277,229]
384. $false <- (~2, ~17, 27) [subsumption resolution 382,160]
385. 2 | 17 | ~27 [avatar contradiction clause 384]
386. $false <- (29) [resolution 287,143]
390. ~29 [avatar contradiction clause 386]
427. creative(fred) | tall(fred) <- (6) [resolution 89,178]
429. tall(fred) <- (6) [subsumption resolution 427,147]
430. $false <- (~5, 6) [subsumption resolution 429,174]
431. 5 | ~6 [avatar contradiction clause 430]
432. $false [avatar sat refutation 181,182,283,288,367,376,385,390,431]
% SZS output end Proof for 4413189128032147638530854
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not quiet or not strong is either old or not curious.
Everyone who is old is not strong or wise.
If susan is either tall or not strong then fred is patient or not quiet and vice versa.
If susan is not strong or not patient then john is not strong.
Everyone who is either funny or quiet is both strong and old and vice versa.
If someone is both not calm and kind then someone is either not rich or not brave and vice versa.
Everyone who is curious or brave is both not kind and creative.
If john is both curious and not brave then john is not rich.
Everyone who is either not patient or not generous is both kind and calm.
Everyone who is not curious is humble and vice versa.
If mary is calm then someone is both humble and not humble and vice versa.
If fred is either funny or not patient then someone is both kind and not funny and vice versa.
Everyone who is both strong and funny is both not tall and not humble.
Everyone who is strong is not funny.
Everyone who is either curious or humble is curious.
Everyone who is either not funny or patient is funny and vice versa.
Susan is not funny or wise.
Susan is old.
Fred is not quiet.
Someone is both funny and quiet.
Someone is generous.
Lucy is both not strong and calm.
Mary is patient or not generous. | John is not generous. | contradiction | (![X]:((~quiet(X)<~>~strong(X))=>(old(X)<~>~curious(X))))&
(![X]:(old(X)=>(~strong(X)|wise(X))))&
(((tall(susan)<~>~strong(susan)))<=>((patient(fred)|~quiet(fred))))&
(((~strong(susan)|~patient(susan)))=>(~strong(john)))&
(![X]:((funny(X)<~>quiet(X))<=>(strong(X)&old(X))))&
((?[X]:((~calm(X)&kind(X))))<=>(?[X]:((~rich(X)<~>~brave(X)))))&
(![X]:((curious(X)|brave(X))=>(~kind(X)&creative(X))))&
(((curious(john)&~brave(john)))=>(~rich(john)))&
(![X]:((~patient(X)<~>~generous(X))=>(kind(X)&calm(X))))&
(![X]:(~curious(X)<=>humble(X)))&
((calm(mary))<=>(?[X]:((humble(X)&~humble(X)))))&
(((funny(fred)<~>~patient(fred)))<=>(?[X]:((kind(X)&~funny(X)))))&
(![X]:((strong(X)&funny(X))=>(~tall(X)&~humble(X))))&
(![X]:(strong(X)=>~funny(X)))&
(![X]:((curious(X)<~>humble(X))=>curious(X)))&
(![X]:((~funny(X)<~>patient(X))<=>funny(X)))&
((~funny(susan)|wise(susan)))&
(old(susan))&
(~quiet(fred))&
(?[X]:((funny(X)&quiet(X))))&
(?[X]:(generous(X)))&
((~strong(lucy)&calm(lucy)))&
((patient(mary)|~generous(mary))) | ~generous(john) | [
"p6",
"p8",
"p9",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3483580237560036297919005
% SZS output start Proof for 3483580237560036297919005
7. ! [X0] : ((brave(X0) | curious(X0)) => (creative(X0) & ~kind(X0))) [input p6]
9. ! [X0] : ((~patient(X0) <~> ~generous(X0)) => (calm(X0) & kind(X0))) [input p8]
10. ! [X0] : (~curious(X0) <=> humble(X0)) [input p9]
15. ! [X0] : ((curious(X0) <~> humble(X0)) => curious(X0)) [input p14]
16. ! [X0] : ((~funny(X0) <~> patient(X0)) <=> funny(X0)) [input p15]
24. ~generous(john) [input hypothesis]
26. ! [X0] : ((brave(X0) | curious(X0)) => ~kind(X0)) [pure predicate removal 7]
31. ! [X0] : (~kind(X0) | (~brave(X0) & ~curious(X0))) [ennf transformation 26]
34. ! [X0] : ((calm(X0) & kind(X0)) | (~patient(X0) <=> ~generous(X0))) [ennf transformation 9]
38. ! [X0] : (curious(X0) | (curious(X0) <=> humble(X0))) [ennf transformation 15]
49. ! [X0] : ((calm(X0) & kind(X0)) | ((~patient(X0) | generous(X0)) & (~generous(X0) | patient(X0)))) [nnf transformation 34]
50. ! [X0] : ((~curious(X0) | ~humble(X0)) & (humble(X0) | curious(X0))) [nnf transformation 10]
59. ! [X0] : (curious(X0) | ((curious(X0) | ~humble(X0)) & (humble(X0) | ~curious(X0)))) [nnf transformation 38]
60. ! [X0] : ((((~patient(X0) | funny(X0)) & (patient(X0) | ~funny(X0))) | ~funny(X0)) & (funny(X0) | ((~funny(X0) | ~patient(X0)) & (patient(X0) | funny(X0))))) [nnf transformation 16]
89. ~kind(X0) | ~curious(X0) [cnf transformation 31]
93. ~patient(X0) | kind(X0) | generous(X0) [cnf transformation 49]
96. humble(X0) | curious(X0) [cnf transformation 50]
97. ~humble(X0) | ~curious(X0) [cnf transformation 50]
111. curious(X0) | curious(X0) | ~humble(X0) [cnf transformation 59]
112. funny(X0) | patient(X0) | funny(X0) [cnf transformation 60]
114. patient(X0) | ~funny(X0) | ~funny(X0) [cnf transformation 60]
124. ~generous(john) [cnf transformation 24]
125. funny(X0) | patient(X0) [duplicate literal removal 112]
126. ~funny(X0) | patient(X0) [duplicate literal removal 114]
127. curious(X0) | ~humble(X0) [duplicate literal removal 111]
235. ~humble(X0) [subsumption resolution 127,97]
236. patient(X0) [subsumption resolution 125,126]
239. curious(X0) [resolution 96,235]
252. generous(X0) | kind(X0) [resolution 93,236]
254. kind(john) [resolution 252,124]
261. ~curious(john) [resolution 254,89]
262. $false [subsumption resolution 261,239]
% SZS output end Proof for 3483580237560036297919005
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny is either patient or wise.
Everyone who is not funny is tall.
Everyone who is not tall or rich is kind or not quiet and vice versa.
Everyone who is either generous or not old is both creative and not calm.
If someone is both calm and tall then someone is either not calm or not strong and vice versa.
Everyone who is both tall and not old is either rich or calm and vice versa.
If alice is both not funny and curious then lucy is not curious and vice versa.
Everyone who is either strong or creative is not kind and vice versa.
Everyone who is not creative is either generous or not humble and vice versa.
Everyone who is both brave and not kind is happy or patient.
Everyone who is either creative or not quiet is calm.
Everyone who is not quiet is not creative and vice versa.
If paul is either brave or creative then susan is kind.
Everyone who is generous is calm or tall and vice versa.
Everyone who is not patient or tall is not old and vice versa.
If john is not calm or not happy then lucy is either not quiet or not creative and vice versa.
Someone is curious.
Someone is both creative and kind.
Someone is not curious or strong.
Susan is both quiet and calm.
Alice is rich or wise.
Mary is both wise and funny.
Mary is not quiet. | Paul is not rich. | neutral | (![X]:(funny(X)=>(patient(X)<~>wise(X))))&
(![X]:(~funny(X)=>tall(X)))&
(![X]:((~tall(X)|rich(X))<=>(kind(X)|~quiet(X))))&
(![X]:((generous(X)<~>~old(X))=>(creative(X)&~calm(X))))&
((?[X]:((calm(X)&tall(X))))<=>(?[X]:((~calm(X)<~>~strong(X)))))&
(![X]:((tall(X)&~old(X))<=>(rich(X)<~>calm(X))))&
(((~funny(alice)&curious(alice)))<=>(~curious(lucy)))&
(![X]:((strong(X)<~>creative(X))<=>~kind(X)))&
(![X]:(~creative(X)<=>(generous(X)<~>~humble(X))))&
(![X]:((brave(X)&~kind(X))=>(happy(X)|patient(X))))&
(![X]:((creative(X)<~>~quiet(X))=>calm(X)))&
(![X]:(~quiet(X)<=>~creative(X)))&
(((brave(paul)<~>creative(paul)))=>(kind(susan)))&
(![X]:(generous(X)<=>(calm(X)|tall(X))))&
(![X]:((~patient(X)|tall(X))<=>~old(X)))&
(((~calm(john)|~happy(john)))<=>((~quiet(lucy)<~>~creative(lucy))))&
(?[X]:(curious(X)))&
(?[X]:((creative(X)&kind(X))))&
(?[X]:((~curious(X)|strong(X))))&
((quiet(susan)&calm(susan)))&
((rich(alice)|wise(alice)))&
((wise(mary)&funny(mary)))&
(~quiet(mary)) | ~rich(paul) | [] | null | 0 |
Everyone who is not quiet is humble and vice versa.
Everyone who is not rich or rich is not tall.
Everyone who is kind is either humble or not rich and vice versa.
If someone is tall then paul is both not curious and not strong.
Everyone who is brave is either not brave or patient.
Everyone who is both not brave and kind is patient and vice versa.
Everyone who is both funny and humble is both not patient and not humble.
Everyone who is not curious is both brave and old and vice versa.
Everyone who is both old and not generous is both not creative and curious.
Everyone who is humble or strong is both not creative and not funny.
Everyone who is wise or not generous is both not rich and not patient.
If john is brave or not funny then someone is either rich or not quiet and vice versa.
Everyone who is either wise or not wise is either not rich or funny and vice versa.
Everyone who is either not calm or quiet is both not calm and not old.
If mary is not kind or happy then lucy is either not creative or quiet.
John is funny or not tall.
Someone is patient.
Lucy is curious or not happy.
John is kind or not rich.
Susan is patient or brave. | John is not curious. | contradiction | (![X]:(~quiet(X)<=>humble(X)))&
(![X]:((~rich(X)|rich(X))=>~tall(X)))&
(![X]:(kind(X)<=>(humble(X)<~>~rich(X))))&
((?[X]:(tall(X)))=>((~curious(paul)&~strong(paul))))&
(![X]:(brave(X)=>(~brave(X)<~>patient(X))))&
(![X]:((~brave(X)&kind(X))<=>patient(X)))&
(![X]:((funny(X)&humble(X))=>(~patient(X)&~humble(X))))&
(![X]:(~curious(X)<=>(brave(X)&old(X))))&
(![X]:((old(X)&~generous(X))=>(~creative(X)&curious(X))))&
(![X]:((humble(X)|strong(X))=>(~creative(X)&~funny(X))))&
(![X]:((wise(X)|~generous(X))=>(~rich(X)&~patient(X))))&
(((brave(john)|~funny(john)))<=>(?[X]:((rich(X)<~>~quiet(X)))))&
(![X]:((wise(X)<~>~wise(X))<=>(~rich(X)<~>funny(X))))&
(![X]:((~calm(X)<~>quiet(X))=>(~calm(X)&~old(X))))&
(((~kind(mary)|happy(mary)))=>((~creative(lucy)<~>quiet(lucy))))&
((funny(john)|~tall(john)))&
(?[X]:(patient(X)))&
((curious(lucy)|~happy(lucy)))&
((kind(john)|~rich(john)))&
((patient(susan)|brave(susan))) | ~curious(john) | [
"p4",
"p5",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 2599581402819983487595229
% SZS output start Proof for 2599581402819983487595229
5. ! [X0] : (brave(X0) => (~brave(X0) <~> patient(X0))) [input p4]
6. ! [X0] : ((kind(X0) & ~brave(X0)) <=> patient(X0)) [input p5]
8. ! [X0] : (~curious(X0) <=> (old(X0) & brave(X0))) [input p7]
21. ~curious(john) [input hypothesis]
31. ! [X0] : (~curious(X0) => (old(X0) & brave(X0))) [unused predicate definition removal 8]
32. ! [X0] : ((~brave(X0) <~> patient(X0)) | ~brave(X0)) [ennf transformation 5]
35. ! [X0] : ((old(X0) & brave(X0)) | curious(X0)) [ennf transformation 31]
42. ! [X0] : (((~patient(X0) | brave(X0)) & (patient(X0) | ~brave(X0))) | ~brave(X0)) [nnf transformation 32]
43. ! [X0] : (((kind(X0) & ~brave(X0)) | ~patient(X0)) & (patient(X0) | (~kind(X0) | brave(X0)))) [nnf transformation 6]
44. ! [X0] : (((kind(X0) & ~brave(X0)) | ~patient(X0)) & (patient(X0) | ~kind(X0) | brave(X0))) [flattening 43]
61. patient(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 42]
64. ~brave(X0) | ~patient(X0) [cnf transformation 44]
68. brave(X0) | curious(X0) [cnf transformation 35]
97. ~curious(john) [cnf transformation 21]
104. patient(X0) | ~brave(X0) [duplicate literal removal 61]
105. ~brave(X0) [subsumption resolution 64,104]
107. curious(X0) [subsumption resolution 68,105]
158. $false [subsumption resolution 97,107]
% SZS output end Proof for 2599581402819983487595229
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 4989
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is creative or not happy then someone is calm.
Everyone who is not tall or wise is quiet.
If someone is not brave or wise then susan is strong or old.
Everyone who is not tall is happy or not funny.
Everyone who is either wise or quiet is not brave.
Everyone who is both not humble and generous is brave or not tall and vice versa.
Everyone who is not quiet or not generous is both not generous and rich and vice versa.
If mary is brave then someone is not old and vice versa.
Everyone who is either happy or not happy is either not generous or not brave.
Everyone who is either creative or brave is not generous.
Everyone who is both happy and not humble is either humble or not humble and vice versa.
If paul is both old and brave then paul is either not quiet or not happy and vice versa.
Everyone who is either not calm or tall is both wise and rich.
Everyone who is both old and rich is either humble or not kind and vice versa.
Everyone who is both not kind and old is not old.
If someone is not rich then susan is not wise and vice versa.
Someone is not kind or not humble.
Someone is not brave.
Paul is both strong and funny.
Someone is not old or not curious.
Paul is either not creative or brave.
Paul is quiet or old. | Paul is old. | entailment | ((?[X]:((creative(X)|~happy(X))))=>(?[X]:(calm(X))))&
(![X]:((~tall(X)|wise(X))=>quiet(X)))&
((?[X]:((~brave(X)|wise(X))))=>((strong(susan)|old(susan))))&
(![X]:(~tall(X)=>(happy(X)|~funny(X))))&
(![X]:((wise(X)<~>quiet(X))=>~brave(X)))&
(![X]:((~humble(X)&generous(X))<=>(brave(X)|~tall(X))))&
(![X]:((~quiet(X)|~generous(X))<=>(~generous(X)&rich(X))))&
((brave(mary))<=>(?[X]:(~old(X))))&
(![X]:((happy(X)<~>~happy(X))=>(~generous(X)<~>~brave(X))))&
(![X]:((creative(X)<~>brave(X))=>~generous(X)))&
(![X]:((happy(X)&~humble(X))<=>(humble(X)<~>~humble(X))))&
(((old(paul)&brave(paul)))<=>((~quiet(paul)<~>~happy(paul))))&
(![X]:((~calm(X)<~>tall(X))=>(wise(X)&rich(X))))&
(![X]:((old(X)&rich(X))<=>(humble(X)<~>~kind(X))))&
(![X]:((~kind(X)&old(X))=>~old(X)))&
((?[X]:(~rich(X)))<=>(~wise(susan)))&
(?[X]:((~kind(X)|~humble(X))))&
(?[X]:(~brave(X)))&
((strong(paul)&funny(paul)))&
(?[X]:((~old(X)|~curious(X))))&
((~creative(paul)<~>brave(paul)))&
((quiet(paul)|old(paul))) | old(paul) | [
"p5",
"p7",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 4722525765645337231899876
% SZS output start Proof for 4722525765645337231899876
6. ! [X0] : ((generous(X0) & ~humble(X0)) <=> (~tall(X0) | brave(X0))) [input p5]
8. brave(mary) <=> ? [X0] : ~old(X0) [input p7]
9. ! [X0] : ((happy(X0) <~> ~happy(X0)) => (~generous(X0) <~> ~brave(X0))) [input p8]
23. ~old(paul) [input hypothesis]
33. ! [X0] : ((~generous(X0) <~> ~brave(X0)) | (happy(X0) <=> ~happy(X0))) [ennf transformation 9]
42. ! [X0] : (((generous(X0) & ~humble(X0)) | (tall(X0) & ~brave(X0))) & ((~tall(X0) | brave(X0)) | (~generous(X0) | humble(X0)))) [nnf transformation 6]
43. ! [X0] : (((generous(X0) & ~humble(X0)) | (tall(X0) & ~brave(X0))) & (~tall(X0) | brave(X0) | ~generous(X0) | humble(X0))) [flattening 42]
46. (brave(mary) | ! [X0] : old(X0)) & (? [X0] : ~old(X0) | ~brave(mary)) [nnf transformation 8]
47. (brave(mary) | ! [X0] : old(X0)) & (? [X1] : ~old(X1) | ~brave(mary)) [rectify 46]
48. ? [X1] : ~old(X1) => ~old(sK1) [choice axiom]
49. (brave(mary) | ! [X0] : old(X0)) & (~old(sK1) | ~brave(mary)) [skolemisation 47,48]
50. ! [X0] : (((brave(X0) | generous(X0)) & (~brave(X0) | ~generous(X0))) | ((happy(X0) | happy(X0)) & (~happy(X0) | ~happy(X0)))) [nnf transformation 33]
78. generous(X0) | ~brave(X0) [cnf transformation 43]
86. brave(mary) | old(X0) [cnf transformation 49]
87. ~brave(X0) | ~generous(X0) | ~happy(X0) | ~happy(X0) [cnf transformation 50]
88. ~brave(X0) | ~generous(X0) | happy(X0) | happy(X0) [cnf transformation 50]
89. brave(X0) | generous(X0) | ~happy(X0) | ~happy(X0) [cnf transformation 50]
90. brave(X0) | generous(X0) | happy(X0) | happy(X0) [cnf transformation 50]
124. ~old(paul) [cnf transformation 23]
132. ~brave(X0) | ~generous(X0) | ~happy(X0) [duplicate literal removal 87]
133. ~brave(X0) | ~generous(X0) | happy(X0) [duplicate literal removal 88]
134. brave(X0) | generous(X0) | ~happy(X0) [duplicate literal removal 89]
135. brave(X0) | generous(X0) | happy(X0) [duplicate literal removal 90]
149. 4 <=> ! [X0] : old(X0) [avatar definition]
150. old(X0) <- (4) [avatar component clause 149]
152. 5 <=> brave(mary) [avatar definition]
154. brave(mary) <- (5) [avatar component clause 152]
155. 4 | 5 [avatar split clause 86,152,149]
161. generous(X0) | happy(X0) [subsumption resolution 135,78]
162. generous(X0) | ~happy(X0) [subsumption resolution 134,78]
163. generous(X0) [subsumption resolution 162,161]
164. ~brave(X0) | happy(X0) [subsumption resolution 133,163]
165. ~brave(X0) | ~happy(X0) [subsumption resolution 132,163]
166. ~brave(X0) [subsumption resolution 165,164]
185. 9 <=> old(paul) [avatar definition]
186. ~old(paul) <- (~9) [avatar component clause 185]
209. ~9 [avatar split clause 124,185]
212. $false <- (4, ~9) [resolution 186,150]
213. ~4 | 9 [avatar contradiction clause 212]
214. $false <- (5) [subsumption resolution 154,166]
215. ~5 [avatar contradiction clause 214]
216. $false [avatar sat refutation 155,209,213,215]
% SZS output end Proof for 4722525765645337231899876
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not humble is not kind or not tall. If someone is humble or not happy then john is both not strong and tall. If someone is not strong or brave then someone is happy or rich. If john is quiet or not brave then someone is either tall or not generous. Everyone who is happy or not generous is both calm and not old. Everyone who is either not curious or old is not kind. If someone is either funny or not humble then alice is both not old and rich and vice versa. If someone is both rich and old then someone is not funny and vice versa. Everyone who is either quiet or tall is both not rich and not strong and vice versa. If alice is not tall then paul is calm or not creative and vice versa. If alice is both not curious and not old then someone is not rich or calm and vice versa. If susan is curious or funny then someone is not brave or patient. If paul is strong then john is both happy and kind. Everyone who is kind or not rich is not curious or not wise. Everyone who is either old or not tall is either not kind or generous and vice versa. Everyone who is not funny or wise is humble or not happy and vice versa. Lucy is not creative or not generous. John is either rich or old. Someone is both old and generous. John is kind or calm. Someone is not rich. Someone is both funny and not happy. Paul is kind or not humble. Someone is either patient or kind. | Paul is calm. | neutral | (![X]:(~humble(X)=>(~kind(X)|~tall(X))))&
((?[X]:((humble(X)|~happy(X))))=>((~strong(john)&tall(john))))&
((?[X]:((~strong(X)|brave(X))))=>(?[X]:((happy(X)|rich(X)))))&
(((quiet(john)|~brave(john)))=>(?[X]:((tall(X)<~>~generous(X)))))&
(![X]:((happy(X)|~generous(X))=>(calm(X)&~old(X))))&
(![X]:((~curious(X)<~>old(X))=>~kind(X)))&
((?[X]:((funny(X)<~>~humble(X))))<=>((~old(alice)&rich(alice))))&
((?[X]:((rich(X)&old(X))))<=>(?[X]:(~funny(X))))&
(![X]:((quiet(X)<~>tall(X))<=>(~rich(X)&~strong(X))))&
((~tall(alice))<=>((calm(paul)|~creative(paul))))&
(((~curious(alice)&~old(alice)))<=>(?[X]:((~rich(X)|calm(X)))))&
(((curious(susan)|funny(susan)))=>(?[X]:((~brave(X)|patient(X)))))&
((strong(paul))=>((happy(john)&kind(john))))&
(![X]:((kind(X)|~rich(X))=>(~curious(X)|~wise(X))))&
(![X]:((old(X)<~>~tall(X))<=>(~kind(X)<~>generous(X))))&
(![X]:((~funny(X)|wise(X))<=>(humble(X)|~happy(X))))&
((~creative(lucy)|~generous(lucy)))&
((rich(john)<~>old(john)))&
(?[X]:((old(X)&generous(X))))&
((kind(john)|calm(john)))&
(?[X]:(~rich(X)))&
(?[X]:((funny(X)&~happy(X))))&
((kind(paul)|~humble(paul)))&
(?[X]:((patient(X)<~>kind(X)))) | calm(paul) | [] | null | 0 |
Everyone who is either not kind or not brave is either old or not kind and vice versa.
Everyone who is not rich or curious is generous or patient.
Everyone who is either tall or wise is not patient and vice versa.
Everyone who is tall or not strong is either not wise or calm and vice versa.
If someone is not rich then someone is either not strong or quiet.
Everyone who is patient is both not quiet and rich and vice versa.
If someone is happy or wise then someone is humble or not happy.
If someone is generous or not curious then someone is not humble or strong and vice versa.
If paul is quiet then someone is not tall.
Everyone who is old is not rich or kind.
If someone is both not patient and not creative then someone is patient or not strong.
Everyone who is either not tall or not patient is either wise or tall and vice versa.
If someone is both not humble and not kind then someone is both not patient and rich and vice versa.
If paul is not generous then mary is either not calm or not happy and vice versa.
Everyone who is creative or wise is not brave or kind and vice versa.
Everyone who is humble or not wise is not old.
Lucy is either not tall or not happy.
Someone is not tall or humble.
Mary is both tall and brave.
Someone is not kind or happy.
Someone is not generous.
Someone is both funny and not happy.
Mary is not creative.
Someone is both not wise and humble. | Lucy is not wise. | neutral | (![X]:((~kind(X)<~>~brave(X))<=>(old(X)<~>~kind(X))))&
(![X]:((~rich(X)|curious(X))=>(generous(X)|patient(X))))&
(![X]:((tall(X)<~>wise(X))<=>~patient(X)))&
(![X]:((tall(X)|~strong(X))<=>(~wise(X)<~>calm(X))))&
((?[X]:(~rich(X)))=>(?[X]:((~strong(X)<~>quiet(X)))))&
(![X]:(patient(X)<=>(~quiet(X)&rich(X))))&
((?[X]:((happy(X)|wise(X))))=>(?[X]:((humble(X)|~happy(X)))))&
((?[X]:((generous(X)|~curious(X))))<=>(?[X]:((~humble(X)|strong(X)))))&
((quiet(paul))=>(?[X]:(~tall(X))))&
(![X]:(old(X)=>(~rich(X)|kind(X))))&
((?[X]:((~patient(X)&~creative(X))))=>(?[X]:((patient(X)|~strong(X)))))&
(![X]:((~tall(X)<~>~patient(X))<=>(wise(X)<~>tall(X))))&
((?[X]:((~humble(X)&~kind(X))))<=>(?[X]:((~patient(X)&rich(X)))))&
((~generous(paul))<=>((~calm(mary)<~>~happy(mary))))&
(![X]:((creative(X)|wise(X))<=>(~brave(X)|kind(X))))&
(![X]:((humble(X)|~wise(X))=>~old(X)))&
((~tall(lucy)<~>~happy(lucy)))&
(?[X]:((~tall(X)|humble(X))))&
((tall(mary)&brave(mary)))&
(?[X]:((~kind(X)|happy(X))))&
(?[X]:(~generous(X)))&
(?[X]:((funny(X)&~happy(X))))&
(~creative(mary))&
(?[X]:((~wise(X)&humble(X)))) | ~wise(lucy) | [] | null | 0 |
If susan is not quiet or curious then susan is not strong and vice versa.
If someone is curious or brave then paul is patient or curious.
If someone is not kind or humble then john is either not calm or quiet and vice versa.
If susan is curious or not curious then mary is either not strong or not tall.
If someone is both not old and not calm then john is either funny or curious and vice versa.
If fred is both not kind and curious then paul is either not funny or not strong and vice versa.
Everyone who is brave or not old is either not strong or not quiet and vice versa.
Everyone who is either not old or not curious is both strong and wise and vice versa.
If fred is not creative then lucy is either calm or not calm.
Everyone who is not curious or funny is both kind and not calm and vice versa.
If fred is either rich or generous then paul is either funny or not creative.
Everyone who is old is not quiet.
If alice is not calm or not curious then mary is generous.
If someone is both not tall and old then paul is either strong or not patient and vice versa.
Everyone who is tall or not curious is not rich or not old.
Everyone who is not old or kind is not patient or not tall.
Susan is kind or not old.
Mary is either brave or not humble.
Someone is curious.
Fred is either strong or humble.
Someone is both not generous and not kind.
Paul is not funny.
Someone is not humble. | John is not tall. | neutral | (((~quiet(susan)|curious(susan)))<=>(~strong(susan)))&
((?[X]:((curious(X)|brave(X))))=>((patient(paul)|curious(paul))))&
((?[X]:((~kind(X)|humble(X))))<=>((~calm(john)<~>quiet(john))))&
(((curious(susan)|~curious(susan)))=>((~strong(mary)<~>~tall(mary))))&
((?[X]:((~old(X)&~calm(X))))<=>((funny(john)<~>curious(john))))&
(((~kind(fred)&curious(fred)))<=>((~funny(paul)<~>~strong(paul))))&
(![X]:((brave(X)|~old(X))<=>(~strong(X)<~>~quiet(X))))&
(![X]:((~old(X)<~>~curious(X))<=>(strong(X)&wise(X))))&
((~creative(fred))=>((calm(lucy)<~>~calm(lucy))))&
(![X]:((~curious(X)|funny(X))<=>(kind(X)&~calm(X))))&
(((rich(fred)<~>generous(fred)))=>((funny(paul)<~>~creative(paul))))&
(![X]:(old(X)=>~quiet(X)))&
(((~calm(alice)|~curious(alice)))=>(generous(mary)))&
((?[X]:((~tall(X)&old(X))))<=>((strong(paul)<~>~patient(paul))))&
(![X]:((tall(X)|~curious(X))=>(~rich(X)|~old(X))))&
(![X]:((~old(X)|kind(X))=>(~patient(X)|~tall(X))))&
((kind(susan)|~old(susan)))&
((brave(mary)<~>~humble(mary)))&
(?[X]:(curious(X)))&
((strong(fred)<~>humble(fred)))&
(?[X]:((~generous(X)&~kind(X))))&
(~funny(paul))&
(?[X]:(~humble(X))) | ~tall(john) | [] | null | 0 |
If lucy is either not tall or tall then someone is either generous or not kind and vice versa.
If someone is not quiet or tall then alice is humble or not wise and vice versa.
Everyone who is not generous is not patient and vice versa.
Everyone who is either not generous or not funny is both not creative and not patient and vice versa.
Everyone who is humble or not strong is both patient and not brave and vice versa.
Everyone who is not quiet or not generous is humble or kind and vice versa.
If someone is curious then someone is both generous and not rich.
If alice is both old and not happy then john is not strong and vice versa.
Everyone who is not happy is both brave and not kind and vice versa.
If someone is not creative then mary is both not patient and quiet and vice versa.
Everyone who is not curious is both not humble and tall.
If someone is generous then someone is wise.
Everyone who is either patient or creative is both not old and not quiet.
If paul is happy then someone is not patient or generous.
If someone is not quiet then someone is curious or strong.
Everyone who is either patient or generous is either humble or not funny and vice versa.
Lucy is either creative or funny.
Someone is both not curious and brave.
Someone is both not wise and kind.
Someone is both not wise and creative.
Paul is either not generous or not happy.
Someone is creative.
John is rich or not wise.
Lucy is not calm or not old. | John is strong. | neutral | (((~tall(lucy)<~>tall(lucy)))<=>(?[X]:((generous(X)<~>~kind(X)))))&
((?[X]:((~quiet(X)|tall(X))))<=>((humble(alice)|~wise(alice))))&
(![X]:(~generous(X)<=>~patient(X)))&
(![X]:((~generous(X)<~>~funny(X))<=>(~creative(X)&~patient(X))))&
(![X]:((humble(X)|~strong(X))<=>(patient(X)&~brave(X))))&
(![X]:((~quiet(X)|~generous(X))<=>(humble(X)|kind(X))))&
((?[X]:(curious(X)))=>(?[X]:((generous(X)&~rich(X)))))&
(((old(alice)&~happy(alice)))<=>(~strong(john)))&
(![X]:(~happy(X)<=>(brave(X)&~kind(X))))&
((?[X]:(~creative(X)))<=>((~patient(mary)&quiet(mary))))&
(![X]:(~curious(X)=>(~humble(X)&tall(X))))&
((?[X]:(generous(X)))=>(?[X]:(wise(X))))&
(![X]:((patient(X)<~>creative(X))=>(~old(X)&~quiet(X))))&
((happy(paul))=>(?[X]:((~patient(X)|generous(X)))))&
((?[X]:(~quiet(X)))=>(?[X]:((curious(X)|strong(X)))))&
(![X]:((patient(X)<~>generous(X))<=>(humble(X)<~>~funny(X))))&
((creative(lucy)<~>funny(lucy)))&
(?[X]:((~curious(X)&brave(X))))&
(?[X]:((~wise(X)&kind(X))))&
(?[X]:((~wise(X)&creative(X))))&
((~generous(paul)<~>~happy(paul)))&
(?[X]:(creative(X)))&
((rich(john)|~wise(john)))&
((~calm(lucy)|~old(lucy))) | strong(john) | [] | null | 0 |
If lucy is curious or funny then lucy is not quiet.
Everyone who is not tall or old is not tall or brave.
Everyone who is both not happy and not quiet is both patient and not strong and vice versa.
If john is creative then lucy is calm or not generous.
Everyone who is both not tall and not kind is not strong and vice versa.
Everyone who is both kind and creative is wise and vice versa.
Everyone who is not creative is either kind or not patient and vice versa.
Everyone who is either tall or not creative is either tall or not funny.
If john is humble or not creative then someone is not kind.
Everyone who is not generous or not wise is both strong and not rich.
If fred is wise then someone is both not funny and not calm.
Everyone who is creative or rich is not quiet or wise and vice versa.
Everyone who is both tall and patient is not old or not funny.
If someone is not creative then someone is not tall or funny.
If someone is either funny or kind then someone is either not rich or creative and vice versa.
Everyone who is either quiet or not tall is either not happy or creative and vice versa.
John is quiet or not creative.
Fred is either happy or quiet.
Someone is curious or not creative.
Someone is either not rich or tall.
Someone is either strong or not wise.
Alice is tall or not generous.
Lucy is not curious.
John is not happy or curious. | John is strong. | entailment | (((curious(lucy)|funny(lucy)))=>(~quiet(lucy)))&
(![X]:((~tall(X)|old(X))=>(~tall(X)|brave(X))))&
(![X]:((~happy(X)&~quiet(X))<=>(patient(X)&~strong(X))))&
((creative(john))=>((calm(lucy)|~generous(lucy))))&
(![X]:((~tall(X)&~kind(X))<=>~strong(X)))&
(![X]:((kind(X)&creative(X))<=>wise(X)))&
(![X]:(~creative(X)<=>(kind(X)<~>~patient(X))))&
(![X]:((tall(X)<~>~creative(X))=>(tall(X)<~>~funny(X))))&
(((humble(john)|~creative(john)))=>(?[X]:(~kind(X))))&
(![X]:((~generous(X)|~wise(X))=>(strong(X)&~rich(X))))&
((wise(fred))=>(?[X]:((~funny(X)&~calm(X)))))&
(![X]:((creative(X)|rich(X))<=>(~quiet(X)|wise(X))))&
(![X]:((tall(X)&patient(X))=>(~old(X)|~funny(X))))&
((?[X]:(~creative(X)))=>(?[X]:((~tall(X)|funny(X)))))&
((?[X]:((funny(X)<~>kind(X))))<=>(?[X]:((~rich(X)<~>creative(X)))))&
(![X]:((quiet(X)<~>~tall(X))<=>(~happy(X)<~>creative(X))))&
((quiet(john)|~creative(john)))&
((happy(fred)<~>quiet(fred)))&
(?[X]:((curious(X)|~creative(X))))&
(?[X]:((~rich(X)<~>tall(X))))&
(?[X]:((strong(X)<~>~wise(X))))&
((tall(alice)|~generous(alice)))&
(~curious(lucy))&
((~happy(john)|curious(john))) | strong(john) | [
"p4",
"p5",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 403283689099576094588567
% SZS output start Proof for 403283689099576094588567
5. ! [X0] : ((~kind(X0) & ~tall(X0)) <=> ~strong(X0)) [input p4]
6. ! [X0] : ((creative(X0) & kind(X0)) <=> wise(X0)) [input p5]
10. ! [X0] : ((~wise(X0) | ~generous(X0)) => (~rich(X0) & strong(X0))) [input p9]
25. ~strong(john) [input hypothesis]
36. ! [X0] : ((~rich(X0) & strong(X0)) | (wise(X0) & generous(X0))) [ennf transformation 10]
41. ! [X0] : (((~kind(X0) & ~tall(X0)) | strong(X0)) & (~strong(X0) | (kind(X0) | tall(X0)))) [nnf transformation 5]
42. ! [X0] : (((~kind(X0) & ~tall(X0)) | strong(X0)) & (~strong(X0) | kind(X0) | tall(X0))) [flattening 41]
43. ! [X0] : (((creative(X0) & kind(X0)) | ~wise(X0)) & (wise(X0) | (~creative(X0) | ~kind(X0)))) [nnf transformation 6]
44. ! [X0] : (((creative(X0) & kind(X0)) | ~wise(X0)) & (wise(X0) | ~creative(X0) | ~kind(X0))) [flattening 43]
80. ~kind(X0) | strong(X0) [cnf transformation 42]
82. ~wise(X0) | kind(X0) [cnf transformation 44]
94. wise(X0) | strong(X0) [cnf transformation 36]
131. ~strong(john) [cnf transformation 25]
289. strong(X1) | kind(X1) [resolution 94,82]
290. strong(X1) [subsumption resolution 289,80]
291. $false [resolution 290,131]
% SZS output end Proof for 403283689099576094588567
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If fred is not creative or not wise then alice is both not old and quiet.
If someone is either not creative or not curious then mary is either calm or not funny and vice versa.
Everyone who is not wise or old is both old and strong.
Everyone who is either kind or generous is both funny and not calm.
Everyone who is not happy is either not funny or not kind.
Everyone who is both calm and old is both curious and quiet.
If fred is not old then lucy is either strong or not calm and vice versa.
If fred is not kind then someone is not tall or not happy.
If someone is either not rich or tall then someone is either patient or not calm.
If someone is either happy or not tall then fred is calm and vice versa.
If alice is either not curious or not old then someone is curious or quiet.
Everyone who is both calm and not strong is happy and vice versa.
If susan is not wise then someone is both not generous and quiet.
If mary is not curious then someone is both tall and not humble.
If someone is not funny or brave then someone is kind or not happy.
If someone is both calm and not funny then someone is either happy or funny.
Lucy is not wise.
Mary is not curious.
Someone is not calm or not brave.
Mary is not rich or rich.
Someone is either not rich or old.
Someone is not curious.
Mary is patient or wise.
John is humble or happy. | Mary is curious. | contradiction | (((~creative(fred)|~wise(fred)))=>((~old(alice)&quiet(alice))))&
((?[X]:((~creative(X)<~>~curious(X))))<=>((calm(mary)<~>~funny(mary))))&
(![X]:((~wise(X)|old(X))=>(old(X)&strong(X))))&
(![X]:((kind(X)<~>generous(X))=>(funny(X)&~calm(X))))&
(![X]:(~happy(X)=>(~funny(X)<~>~kind(X))))&
(![X]:((calm(X)&old(X))=>(curious(X)&quiet(X))))&
((~old(fred))<=>((strong(lucy)<~>~calm(lucy))))&
((~kind(fred))=>(?[X]:((~tall(X)|~happy(X)))))&
((?[X]:((~rich(X)<~>tall(X))))=>(?[X]:((patient(X)<~>~calm(X)))))&
((?[X]:((happy(X)<~>~tall(X))))<=>(calm(fred)))&
(((~curious(alice)<~>~old(alice)))=>(?[X]:((curious(X)|quiet(X)))))&
(![X]:((calm(X)&~strong(X))<=>happy(X)))&
((~wise(susan))=>(?[X]:((~generous(X)&quiet(X)))))&
((~curious(mary))=>(?[X]:((tall(X)&~humble(X)))))&
((?[X]:((~funny(X)|brave(X))))=>(?[X]:((kind(X)|~happy(X)))))&
((?[X]:((calm(X)&~funny(X))))=>(?[X]:((happy(X)<~>funny(X)))))&
(~wise(lucy))&
(~curious(mary))&
(?[X]:((~calm(X)|~brave(X))))&
((~rich(mary)|rich(mary)))&
(?[X]:((~rich(X)<~>old(X))))&
(?[X]:(~curious(X)))&
((patient(mary)|wise(mary)))&
((humble(john)|happy(john))) | curious(mary) | [
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 1795264960604807025847204
% SZS output start Proof for 1795264960604807025847204
18. ~curious(mary) [input p17]
25. curious(mary) [input hypothesis]
126. ~curious(mary) [cnf transformation 18]
133. curious(mary) [cnf transformation 25]
257. 27 <=> curious(mary) [avatar definition]
295. ~27 [avatar split clause 126,257]
324. 27 [avatar split clause 133,257]
325. $false [avatar sat refutation 295,324]
% SZS output end Proof for 1795264960604807025847204
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 john is happy or old then someone is creative.
Everyone who is rich is not kind or quiet.
Everyone who is either not humble or not rich is brave.
If someone is tall then someone is both kind and brave.
If mary is not wise or creative then alice is not happy or not funny and vice versa.
Everyone who is quiet is not strong and vice versa.
Everyone who is not rich is either not quiet or generous.
If someone is either not happy or not funny then someone is not happy or not tall.
Everyone who is either generous or happy is old.
If mary is tall then someone is not tall or not brave and vice versa.
If someone is both calm and not old then paul is strong and vice versa.
Everyone who is both calm and not old is not curious.
If someone is wise then someone is both not calm and not brave and vice versa.
Everyone who is generous or rich is calm and vice versa.
Everyone who is both not calm and happy is not quiet or happy and vice versa.
If lucy is either not quiet or old then john is either not creative or not old and vice versa.
Someone is both not strong and kind.
Someone is either not patient or not quiet.
Someone is not humble or not brave.
Someone is calm.
Fred is both brave and not curious.
John is not strong or not happy.
Someone is happy.
Someone is rich. | John is not calm. | contradiction | (((happy(john)|old(john)))=>(?[X]:(creative(X))))&
(![X]:(rich(X)=>(~kind(X)|quiet(X))))&
(![X]:((~humble(X)<~>~rich(X))=>brave(X)))&
((?[X]:(tall(X)))=>(?[X]:((kind(X)&brave(X)))))&
(((~wise(mary)|creative(mary)))<=>((~happy(alice)|~funny(alice))))&
(![X]:(quiet(X)<=>~strong(X)))&
(![X]:(~rich(X)=>(~quiet(X)<~>generous(X))))&
((?[X]:((~happy(X)<~>~funny(X))))=>(?[X]:((~happy(X)|~tall(X)))))&
(![X]:((generous(X)<~>happy(X))=>old(X)))&
((tall(mary))<=>(?[X]:((~tall(X)|~brave(X)))))&
((?[X]:((calm(X)&~old(X))))<=>(strong(paul)))&
(![X]:((calm(X)&~old(X))=>~curious(X)))&
((?[X]:(wise(X)))<=>(?[X]:((~calm(X)&~brave(X)))))&
(![X]:((generous(X)|rich(X))<=>calm(X)))&
(![X]:((~calm(X)&happy(X))<=>(~quiet(X)|happy(X))))&
(((~quiet(lucy)<~>old(lucy)))<=>((~creative(john)<~>~old(john))))&
(?[X]:((~strong(X)&kind(X))))&
(?[X]:((~patient(X)<~>~quiet(X))))&
(?[X]:((~humble(X)|~brave(X))))&
(?[X]:(calm(X)))&
((brave(fred)&~curious(fred)))&
((~strong(john)|~happy(john)))&
(?[X]:(happy(X)))&
(?[X]:(rich(X))) | ~calm(john) | [
"p5",
"p6",
"p13",
"p14",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 273489151898543438704829
% SZS output start Proof for 273489151898543438704829
6. ! [X0] : (quiet(X0) <=> ~strong(X0)) [input p5]
7. ! [X0] : (~rich(X0) => (~quiet(X0) <~> generous(X0))) [input p6]
14. ! [X0] : ((rich(X0) | generous(X0)) <=> calm(X0)) [input p13]
15. ! [X0] : ((happy(X0) & ~calm(X0)) <=> (happy(X0) | ~quiet(X0))) [input p14]
22. ~happy(john) | ~strong(john) [input p21]
25. ~calm(john) [input hypothesis]
36. ! [X0] : ((~quiet(X0) <~> generous(X0)) | rich(X0)) [ennf transformation 7]
47. ! [X0] : ((quiet(X0) | strong(X0)) & (~strong(X0) | ~quiet(X0))) [nnf transformation 6]
48. ! [X0] : (((~generous(X0) | quiet(X0)) & (generous(X0) | ~quiet(X0))) | rich(X0)) [nnf transformation 36]
67. ! [X0] : (((rich(X0) | generous(X0)) | ~calm(X0)) & (calm(X0) | (~rich(X0) & ~generous(X0)))) [nnf transformation 14]
68. ! [X0] : ((rich(X0) | generous(X0) | ~calm(X0)) & (calm(X0) | (~rich(X0) & ~generous(X0)))) [flattening 67]
69. ! [X0] : (((happy(X0) & ~calm(X0)) | (~happy(X0) & quiet(X0))) & ((happy(X0) | ~quiet(X0)) | (~happy(X0) | calm(X0)))) [nnf transformation 15]
70. ! [X0] : (((happy(X0) & ~calm(X0)) | (~happy(X0) & quiet(X0))) & (happy(X0) | ~quiet(X0) | ~happy(X0) | calm(X0))) [flattening 69]
97. strong(X0) | quiet(X0) [cnf transformation 47]
98. ~quiet(X0) | generous(X0) | rich(X0) [cnf transformation 48]
113. ~generous(X0) | calm(X0) [cnf transformation 68]
114. ~rich(X0) | calm(X0) [cnf transformation 68]
119. quiet(X0) | happy(X0) [cnf transformation 70]
136. ~happy(john) | ~strong(john) [cnf transformation 22]
139. ~calm(john) [cnf transformation 25]
150. 3 <=> happy(john) [avatar definition]
303. 36 <=> strong(john) [avatar definition]
305. ~strong(john) <- (~36) [avatar component clause 303]
306. ~36 | ~3 [avatar split clause 136,150,303]
349. generous(X0) | rich(X0) | happy(X0) [resolution 98,119]
437. rich(X2) | happy(X2) | calm(X2) [resolution 349,113]
440. calm(X2) | happy(X2) [subsumption resolution 437,114]
511. happy(john) [resolution 440,139]
516. 3 [avatar split clause 511,150]
519. quiet(john) <- (~36) [resolution 305,97]
526. 62 <=> generous(john) [avatar definition]
528. generous(john) <- (62) [avatar component clause 526]
530. generous(john) | rich(john) <- (~36) [resolution 519,98]
532. 63 <=> rich(john) [avatar definition]
534. rich(john) <- (63) [avatar component clause 532]
535. 63 | 62 | 36 [avatar split clause 530,303,526,532]
537. calm(john) <- (63) [resolution 534,114]
547. $false <- (63) [subsumption resolution 537,139]
548. ~63 [avatar contradiction clause 547]
551. calm(john) <- (62) [resolution 528,113]
552. $false <- (62) [subsumption resolution 551,139]
553. ~62 [avatar contradiction clause 552]
554. $false [avatar sat refutation 306,516,535,548,553]
% SZS output end Proof for 273489151898543438704829
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is both not happy and not humble then someone is not humble. If fred is funny then paul is humble or not generous. Everyone who is not curious is curious or kind and vice versa. Everyone who is quiet is not old or not kind and vice versa. If mary is either brave or not humble then susan is creative. Everyone who is happy is both kind and calm and vice versa. Everyone who is kind is not wise or not old and vice versa. Everyone who is both quiet and funny is either tall or funny and vice versa. Everyone who is both humble and old is either tall or quiet. Everyone who is both not brave and not funny is kind and vice versa. If mary is happy or kind then someone is either patient or creative. Everyone who is patient or generous is old. If lucy is either humble or not curious then someone is generous or wise. Everyone who is either not curious or not generous is either not curious or not old and vice versa. Everyone who is both humble and creative is either creative or not humble and vice versa. Everyone who is both generous and not rich is either generous or creative. Alice is funny or not quiet. Someone is either not brave or not strong. Someone is not strong. Paul is calm or not creative. John is either curious or generous. Someone is rich. | John is not creative. | contradiction | (((~happy(paul)&~humble(paul)))=>(?[X]:(~humble(X))))&
((funny(fred))=>((humble(paul)|~generous(paul))))&
(![X]:(~curious(X)<=>(curious(X)|kind(X))))&
(![X]:(quiet(X)<=>(~old(X)|~kind(X))))&
(((brave(mary)<~>~humble(mary)))=>(creative(susan)))&
(![X]:(happy(X)<=>(kind(X)&calm(X))))&
(![X]:(kind(X)<=>(~wise(X)|~old(X))))&
(![X]:((quiet(X)&funny(X))<=>(tall(X)<~>funny(X))))&
(![X]:((humble(X)&old(X))=>(tall(X)<~>quiet(X))))&
(![X]:((~brave(X)&~funny(X))<=>kind(X)))&
(((happy(mary)|kind(mary)))=>(?[X]:((patient(X)<~>creative(X)))))&
(![X]:((patient(X)|generous(X))=>old(X)))&
(((humble(lucy)<~>~curious(lucy)))=>(?[X]:((generous(X)|wise(X)))))&
(![X]:((~curious(X)<~>~generous(X))<=>(~curious(X)<~>~old(X))))&
(![X]:((humble(X)&creative(X))<=>(creative(X)<~>~humble(X))))&
(![X]:((generous(X)&~rich(X))=>(generous(X)<~>creative(X))))&
((funny(alice)|~quiet(alice)))&
(?[X]:((~brave(X)<~>~strong(X))))&
(?[X]:(~strong(X)))&
((calm(paul)|~creative(paul)))&
((curious(john)<~>generous(john)))&
(?[X]:(rich(X))) | ~creative(john) | [
"p2",
"p3",
"p7",
"p8",
"p9",
"p11",
"p14",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 5026250827624056145673429
% SZS output start Proof for 5026250827624056145673429
3. ! [X0] : (~curious(X0) <=> (kind(X0) | curious(X0))) [input p2]
4. ! [X0] : (quiet(X0) <=> (~kind(X0) | ~old(X0))) [input p3]
8. ! [X0] : ((funny(X0) & quiet(X0)) <=> (tall(X0) <~> funny(X0))) [input p7]
9. ! [X0] : ((old(X0) & humble(X0)) => (tall(X0) <~> quiet(X0))) [input p8]
10. ! [X0] : ((~funny(X0) & ~brave(X0)) <=> kind(X0)) [input p9]
12. ! [X0] : ((generous(X0) | patient(X0)) => old(X0)) [input p11]
15. ! [X0] : ((creative(X0) & humble(X0)) <=> (creative(X0) <~> ~humble(X0))) [input p14]
21. curious(john) <~> generous(john) [input p20]
23. ~creative(john) [input hypothesis]
31. ! [X0] : ((tall(X0) <~> quiet(X0)) | (~old(X0) | ~humble(X0))) [ennf transformation 9]
32. ! [X0] : ((tall(X0) <~> quiet(X0)) | ~old(X0) | ~humble(X0)) [flattening 31]
34. ! [X0] : (old(X0) | (~generous(X0) & ~patient(X0))) [ennf transformation 12]
38. ! [X0] : ((~curious(X0) | (~kind(X0) & ~curious(X0))) & ((kind(X0) | curious(X0)) | curious(X0))) [nnf transformation 3]
39. ! [X0] : ((~curious(X0) | (~kind(X0) & ~curious(X0))) & (kind(X0) | curious(X0) | curious(X0))) [flattening 38]
40. ! [X0] : ((quiet(X0) | (kind(X0) & old(X0))) & ((~kind(X0) | ~old(X0)) | ~quiet(X0))) [nnf transformation 4]
41. ! [X0] : ((quiet(X0) | (kind(X0) & old(X0))) & (~kind(X0) | ~old(X0) | ~quiet(X0))) [flattening 40]
47. ! [X0] : (((funny(X0) & quiet(X0)) | ((tall(X0) | ~funny(X0)) & (funny(X0) | ~tall(X0)))) & (((~funny(X0) | ~tall(X0)) & (funny(X0) | tall(X0))) | (~funny(X0) | ~quiet(X0)))) [nnf transformation 8]
48. ! [X0] : (((funny(X0) & quiet(X0)) | ((tall(X0) | ~funny(X0)) & (funny(X0) | ~tall(X0)))) & (((~funny(X0) | ~tall(X0)) & (funny(X0) | tall(X0))) | ~funny(X0) | ~quiet(X0))) [flattening 47]
49. ! [X0] : (((~quiet(X0) | ~tall(X0)) & (quiet(X0) | tall(X0))) | ~old(X0) | ~humble(X0)) [nnf transformation 32]
50. ! [X0] : (((~funny(X0) & ~brave(X0)) | ~kind(X0)) & (kind(X0) | (funny(X0) | brave(X0)))) [nnf transformation 10]
51. ! [X0] : (((~funny(X0) & ~brave(X0)) | ~kind(X0)) & (kind(X0) | funny(X0) | brave(X0))) [flattening 50]
59. ! [X0] : (((creative(X0) & humble(X0)) | ((creative(X0) | humble(X0)) & (~humble(X0) | ~creative(X0)))) & (((humble(X0) | ~creative(X0)) & (~humble(X0) | creative(X0))) | (~creative(X0) | ~humble(X0)))) [nnf transformation 15]
60. ! [X0] : (((creative(X0) & humble(X0)) | ((creative(X0) | humble(X0)) & (~humble(X0) | ~creative(X0)))) & (((humble(X0) | ~creative(X0)) & (~humble(X0) | creative(X0))) | ~creative(X0) | ~humble(X0))) [flattening 59]
66. (~generous(john) | ~curious(john)) & (generous(john) | curious(john)) [nnf transformation 21]
69. kind(X0) | curious(X0) | curious(X0) [cnf transformation 39]
70. ~curious(X0) | ~curious(X0) [cnf transformation 39]
72. ~kind(X0) | ~old(X0) | ~quiet(X0) [cnf transformation 41]
87. funny(X0) | funny(X0) | ~tall(X0) [cnf transformation 48]
89. quiet(X0) | tall(X0) | ~old(X0) | ~humble(X0) [cnf transformation 49]
93. ~funny(X0) | ~kind(X0) [cnf transformation 51]
99. ~generous(X0) | old(X0) [cnf transformation 34]
115. creative(X0) | creative(X0) | humble(X0) [cnf transformation 60]
121. generous(john) | curious(john) [cnf transformation 66]
123. ~creative(john) [cnf transformation 23]
127. creative(X0) | humble(X0) [duplicate literal removal 115]
133. ~tall(X0) | funny(X0) [duplicate literal removal 87]
134. kind(X0) | curious(X0) [duplicate literal removal 69]
135. ~curious(X0) [duplicate literal removal 70]
158. kind(X0) [subsumption resolution 134,135]
159. ~old(X0) | ~quiet(X0) [subsumption resolution 72,158]
177. ~old(X0) | tall(X0) | ~humble(X0) [subsumption resolution 89,159]
178. ~funny(X0) [subsumption resolution 93,158]
224. generous(john) [subsumption resolution 121,135]
227. old(john) [resolution 99,224]
228. humble(john) [resolution 127,123]
247. tall(john) | ~humble(john) [resolution 177,227]
249. tall(john) [subsumption resolution 247,228]
293. funny(john) [resolution 249,133]
294. $false [subsumption resolution 293,178]
% SZS output end Proof for 5026250827624056145673429
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old or curious then lucy is either rich or not quiet and vice versa.
Everyone who is either not generous or not calm is not tall or patient.
Everyone who is not brave is both strong and quiet and vice versa.
Everyone who is not creative is brave and vice versa.
If someone is either generous or quiet then someone is either not calm or not brave.
Everyone who is both not tall and strong is not tall.
If lucy is not brave then someone is not wise or not happy.
If someone is either humble or creative then john is not kind or not curious.
Everyone who is not creative or not curious is both not humble and not funny.
Everyone who is old or tall is not curious or generous and vice versa.
If someone is not happy then mary is not creative or not kind and vice versa.
Everyone who is not calm or strong is either not rich or patient.
Everyone who is either creative or calm is either not tall or not funny.
Everyone who is either not quiet or quiet is rich or not calm and vice versa.
Everyone who is kind or not generous is either not happy or tall.
Everyone who is either brave or funny is both calm and not wise and vice versa.
John is not rich or not tall.
Someone is quiet.
Alice is both not calm and not humble.
Someone is not humble or not patient.
Someone is patient or not kind.
Someone is not humble.
Someone is rich.
Someone is brave or curious. | John is quiet. | entailment | ((?[X]:((old(X)<~>curious(X))))<=>((rich(lucy)<~>~quiet(lucy))))&
(![X]:((~generous(X)<~>~calm(X))=>(~tall(X)|patient(X))))&
(![X]:(~brave(X)<=>(strong(X)&quiet(X))))&
(![X]:(~creative(X)<=>brave(X)))&
((?[X]:((generous(X)<~>quiet(X))))=>(?[X]:((~calm(X)<~>~brave(X)))))&
(![X]:((~tall(X)&strong(X))=>~tall(X)))&
((~brave(lucy))=>(?[X]:((~wise(X)|~happy(X)))))&
((?[X]:((humble(X)<~>creative(X))))=>((~kind(john)|~curious(john))))&
(![X]:((~creative(X)|~curious(X))=>(~humble(X)&~funny(X))))&
(![X]:((old(X)|tall(X))<=>(~curious(X)|generous(X))))&
((?[X]:(~happy(X)))<=>((~creative(mary)|~kind(mary))))&
(![X]:((~calm(X)|strong(X))=>(~rich(X)<~>patient(X))))&
(![X]:((creative(X)<~>calm(X))=>(~tall(X)<~>~funny(X))))&
(![X]:((~quiet(X)<~>quiet(X))<=>(rich(X)|~calm(X))))&
(![X]:((kind(X)|~generous(X))=>(~happy(X)<~>tall(X))))&
(![X]:((brave(X)<~>funny(X))<=>(calm(X)&~wise(X))))&
((~rich(john)|~tall(john)))&
(?[X]:(quiet(X)))&
((~calm(alice)&~humble(alice)))&
(?[X]:((~humble(X)|~patient(X))))&
(?[X]:((patient(X)|~kind(X))))&
(?[X]:(~humble(X)))&
(?[X]:(rich(X)))&
(?[X]:((brave(X)|curious(X)))) | quiet(john) | [
"p1",
"p2",
"p3",
"p8",
"p9",
"p11",
"p12",
"p13",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 1211432945283286076268993
% SZS output start Proof for 1211432945283286076268993
2. ! [X0] : ((~generous(X0) <~> ~calm(X0)) => (patient(X0) | ~tall(X0))) [input p1]
3. ! [X0] : (~brave(X0) <=> (quiet(X0) & strong(X0))) [input p2]
4. ! [X0] : (~creative(X0) <=> brave(X0)) [input p3]
9. ! [X0] : ((~curious(X0) | ~creative(X0)) => (~funny(X0) & ~humble(X0))) [input p8]
10. ! [X0] : ((tall(X0) | old(X0)) <=> (generous(X0) | ~curious(X0))) [input p9]
12. ! [X0] : ((strong(X0) | ~calm(X0)) => (~rich(X0) <~> patient(X0))) [input p11]
13. ! [X0] : ((creative(X0) <~> calm(X0)) => (~tall(X0) <~> ~funny(X0))) [input p12]
14. ! [X0] : ((~quiet(X0) <~> quiet(X0)) <=> (~calm(X0) | rich(X0))) [input p13]
16. ! [X0] : ((brave(X0) <~> funny(X0)) <=> (~wise(X0) & calm(X0))) [input p15]
17. ~tall(john) | ~rich(john) [input p16]
25. ~quiet(john) [input hypothesis]
27. ! [X0] : ((patient(X0) | ~tall(X0)) | (~generous(X0) <=> ~calm(X0))) [ennf transformation 2]
28. ! [X0] : (patient(X0) | ~tall(X0) | (~generous(X0) <=> ~calm(X0))) [flattening 27]
35. ! [X0] : ((~funny(X0) & ~humble(X0)) | (curious(X0) & creative(X0))) [ennf transformation 9]
36. ! [X0] : ((~rich(X0) <~> patient(X0)) | (~strong(X0) & calm(X0))) [ennf transformation 12]
37. ! [X0] : ((~tall(X0) <~> ~funny(X0)) | (creative(X0) <=> calm(X0))) [ennf transformation 13]
43. ! [X0] : (patient(X0) | ~tall(X0) | ((~generous(X0) | calm(X0)) & (~calm(X0) | generous(X0)))) [nnf transformation 28]
44. ! [X0] : ((~brave(X0) | (~quiet(X0) | ~strong(X0))) & ((quiet(X0) & strong(X0)) | brave(X0))) [nnf transformation 3]
45. ! [X0] : ((~brave(X0) | ~quiet(X0) | ~strong(X0)) & ((quiet(X0) & strong(X0)) | brave(X0))) [flattening 44]
46. ! [X0] : ((~creative(X0) | ~brave(X0)) & (brave(X0) | creative(X0))) [nnf transformation 4]
54. ! [X0] : (((tall(X0) | old(X0)) | (~generous(X0) & curious(X0))) & ((generous(X0) | ~curious(X0)) | (~tall(X0) & ~old(X0)))) [nnf transformation 10]
55. ! [X0] : ((tall(X0) | old(X0) | (~generous(X0) & curious(X0))) & (generous(X0) | ~curious(X0) | (~tall(X0) & ~old(X0)))) [flattening 54]
61. ! [X0] : (((~patient(X0) | rich(X0)) & (patient(X0) | ~rich(X0))) | (~strong(X0) & calm(X0))) [nnf transformation 36]
62. ! [X0] : (((funny(X0) | tall(X0)) & (~funny(X0) | ~tall(X0))) | ((creative(X0) | ~calm(X0)) & (calm(X0) | ~creative(X0)))) [nnf transformation 37]
63. ! [X0] : ((((~quiet(X0) | quiet(X0)) & (quiet(X0) | ~quiet(X0))) | (calm(X0) & ~rich(X0))) & ((~calm(X0) | rich(X0)) | ((~quiet(X0) | ~quiet(X0)) & (quiet(X0) | quiet(X0))))) [nnf transformation 14]
64. ! [X0] : ((((~quiet(X0) | quiet(X0)) & (quiet(X0) | ~quiet(X0))) | (calm(X0) & ~rich(X0))) & (~calm(X0) | rich(X0) | ((~quiet(X0) | ~quiet(X0)) & (quiet(X0) | quiet(X0))))) [flattening 63]
66. ! [X0] : ((((~funny(X0) | ~brave(X0)) & (funny(X0) | brave(X0))) | (wise(X0) | ~calm(X0))) & ((~wise(X0) & calm(X0)) | ((brave(X0) | ~funny(X0)) & (funny(X0) | ~brave(X0))))) [nnf transformation 16]
67. ! [X0] : ((((~funny(X0) | ~brave(X0)) & (funny(X0) | brave(X0))) | wise(X0) | ~calm(X0)) & ((~wise(X0) & calm(X0)) | ((brave(X0) | ~funny(X0)) & (funny(X0) | ~brave(X0))))) [flattening 66]
89. ~tall(X0) | patient(X0) | ~generous(X0) | calm(X0) [cnf transformation 43]
91. brave(X0) | quiet(X0) [cnf transformation 45]
93. creative(X0) | brave(X0) [cnf transformation 46]
94. ~creative(X0) | ~brave(X0) [cnf transformation 46]
105. ~funny(X0) | creative(X0) [cnf transformation 35]
106. ~funny(X0) | curious(X0) [cnf transformation 35]
108. ~tall(X0) | ~curious(X0) | generous(X0) [cnf transformation 55]
116. ~patient(X0) | rich(X0) | calm(X0) [cnf transformation 61]
120. ~creative(X0) | tall(X0) | calm(X0) | funny(X0) [cnf transformation 62]
121. funny(X0) | tall(X0) | creative(X0) | ~calm(X0) [cnf transformation 62]
122. ~calm(X0) | rich(X0) | quiet(X0) | quiet(X0) [cnf transformation 64]
123. ~calm(X0) | rich(X0) | ~quiet(X0) | ~quiet(X0) [cnf transformation 64]
132. ~brave(X0) | funny(X0) | calm(X0) [cnf transformation 67]
138. ~tall(john) | ~rich(john) [cnf transformation 17]
147. ~quiet(john) [cnf transformation 25]
148. ~calm(X0) | rich(X0) | quiet(X0) [duplicate literal removal 122]
149. ~calm(X0) | rich(X0) | ~quiet(X0) [duplicate literal removal 123]
219. 16 <=> curious(john) [avatar definition]
246. ~calm(X0) | creative(X0) | tall(X0) [subsumption resolution 121,105]
248. ~calm(X0) | rich(X0) [subsumption resolution 148,149]
250. 22 <=> rich(john) [avatar definition]
252. ~rich(john) <- (~22) [avatar component clause 250]
254. 23 <=> tall(john) [avatar definition]
255. tall(john) <- (23) [avatar component clause 254]
256. ~tall(john) <- (~23) [avatar component clause 254]
257. ~22 | ~23 [avatar split clause 138,254,250]
309. funny(X0) | calm(X0) | quiet(X0) [resolution 132,91]
392. tall(X0) | calm(X0) | funny(X0) | brave(X0) [resolution 120,93]
394. funny(X0) | calm(X0) | tall(X0) [subsumption resolution 392,132]
453. calm(X4) | quiet(X4) | curious(X4) [resolution 309,106]
463. calm(X5) | tall(X5) | creative(X5) [resolution 394,105]
467. creative(X5) | tall(X5) [subsumption resolution 463,246]
521. ~brave(X1) | tall(X1) [resolution 467,94]
523. tall(X0) | quiet(X0) [resolution 521,91]
528. quiet(X4) | curious(X4) | rich(X4) [resolution 453,248]
598. 68 <=> calm(john) [avatar definition]
600. calm(john) <- (68) [avatar component clause 598]
609. 70 <=> generous(john) [avatar definition]
630. curious(john) | rich(john) [resolution 528,147]
682. quiet(john) <- (~23) [resolution 523,256]
689. $false <- (~23) [subsumption resolution 682,147]
690. 23 [avatar contradiction clause 689]
693. patient(john) | ~generous(john) | calm(john) <- (23) [resolution 255,89]
696. ~curious(john) | generous(john) <- (23) [resolution 255,108]
698. 77 <=> patient(john) [avatar definition]
700. patient(john) <- (77) [avatar component clause 698]
701. 68 | ~70 | 77 | ~23 [avatar split clause 693,254,698,609,598]
710. 70 | ~16 | ~23 [avatar split clause 696,254,219,609]
711. curious(john) <- (~22) [subsumption resolution 630,252]
712. 16 | 22 [avatar split clause 711,250,219]
718. rich(john) | calm(john) <- (77) [resolution 700,116]
721. calm(john) <- (~22, 77) [subsumption resolution 718,252]
724. 68 | 22 | ~77 [avatar split clause 721,698,250,598]
730. rich(john) <- (68) [resolution 600,248]
731. $false <- (~22, 68) [subsumption resolution 730,252]
732. 22 | ~68 [avatar contradiction clause 731]
733. $false [avatar sat refutation 257,690,701,710,712,724,732]
% SZS output end Proof for 1211432945283286076268993
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.041 s
% ------------------------------
% ------------------------------
| 0 |
If someone is strong then mary is either funny or not tall and vice versa.
Everyone who is both calm and tall is not happy and vice versa.
Everyone who is kind or humble is both tall and not calm.
Everyone who is not old is not patient.
If susan is tall then someone is either not humble or not kind and vice versa.
If mary is either not tall or not brave then someone is either generous or not patient.
Everyone who is either generous or not quiet is either tall or generous.
Everyone who is not wise or strong is both not calm and not kind.
Everyone who is generous is both not tall and rich.
If mary is humble then alice is not wise or not generous and vice versa.
If paul is not funny or not kind then someone is both not funny and not happy.
Everyone who is either not funny or funny is either not generous or not rich and vice versa.
If someone is old then someone is creative.
Everyone who is either tall or not funny is not tall.
If someone is not funny or brave then someone is creative or not creative and vice versa.
If fred is both not wise and brave then john is patient.
Fred is quiet or brave.
Someone is happy or not brave.
Susan is either not tall or not happy.
Someone is either funny or strong.
Someone is not generous.
Someone is not kind or patient.
Someone is both brave and not tall. | Susan is not strong. | entailment | ((?[X]:(strong(X)))<=>((funny(mary)<~>~tall(mary))))&
(![X]:((calm(X)&tall(X))<=>~happy(X)))&
(![X]:((kind(X)|humble(X))=>(tall(X)&~calm(X))))&
(![X]:(~old(X)=>~patient(X)))&
((tall(susan))<=>(?[X]:((~humble(X)<~>~kind(X)))))&
(((~tall(mary)<~>~brave(mary)))=>(?[X]:((generous(X)<~>~patient(X)))))&
(![X]:((generous(X)<~>~quiet(X))=>(tall(X)<~>generous(X))))&
(![X]:((~wise(X)|strong(X))=>(~calm(X)&~kind(X))))&
(![X]:(generous(X)=>(~tall(X)&rich(X))))&
((humble(mary))<=>((~wise(alice)|~generous(alice))))&
(((~funny(paul)|~kind(paul)))=>(?[X]:((~funny(X)&~happy(X)))))&
(![X]:((~funny(X)<~>funny(X))<=>(~generous(X)<~>~rich(X))))&
((?[X]:(old(X)))=>(?[X]:(creative(X))))&
(![X]:((tall(X)<~>~funny(X))=>~tall(X)))&
((?[X]:((~funny(X)|brave(X))))<=>(?[X]:((creative(X)|~creative(X)))))&
(((~wise(fred)&brave(fred)))=>(patient(john)))&
((quiet(fred)|brave(fred)))&
(?[X]:((happy(X)|~brave(X))))&
((~tall(susan)<~>~happy(susan)))&
(?[X]:((funny(X)<~>strong(X))))&
(?[X]:(~generous(X)))&
(?[X]:((~kind(X)|patient(X))))&
(?[X]:((brave(X)&~tall(X)))) | ~strong(susan) | [
"p0",
"p2",
"p8",
"p9",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 5410530047935355546891532
% SZS output start Proof for 5410530047935355546891532
1. ? [X0] : strong(X0) <=> (funny(mary) <~> ~tall(mary)) [input p0]
3. ! [X0] : ((humble(X0) | kind(X0)) => (~calm(X0) & tall(X0))) [input p2]
9. ! [X0] : (generous(X0) => (rich(X0) & ~tall(X0))) [input p8]
10. humble(mary) <=> (~generous(alice) | ~wise(alice)) [input p9]
12. ! [X0] : ((~funny(X0) <~> funny(X0)) <=> (~generous(X0) <~> ~rich(X0))) [input p11]
14. ! [X0] : ((tall(X0) <~> ~funny(X0)) => ~tall(X0)) [input p13]
24. strong(susan) [input hypothesis]
27. ! [X0] : ((~calm(X0) & tall(X0)) | (~humble(X0) & ~kind(X0))) [ennf transformation 3]
32. ! [X0] : ((rich(X0) & ~tall(X0)) | ~generous(X0)) [ennf transformation 9]
35. ! [X0] : (~tall(X0) | (tall(X0) <=> ~funny(X0))) [ennf transformation 14]
38. (? [X0] : strong(X0) | ((funny(mary) | tall(mary)) & (~tall(mary) | ~funny(mary)))) & (((tall(mary) | ~funny(mary)) & (~tall(mary) | funny(mary))) | ! [X0] : ~strong(X0)) [nnf transformation 1]
39. (? [X0] : strong(X0) | ((funny(mary) | tall(mary)) & (~tall(mary) | ~funny(mary)))) & (((tall(mary) | ~funny(mary)) & (~tall(mary) | funny(mary))) | ! [X1] : ~strong(X1)) [rectify 38]
40. ? [X0] : strong(X0) => strong(sK0) [choice axiom]
41. (strong(sK0) | ((funny(mary) | tall(mary)) & (~tall(mary) | ~funny(mary)))) & (((tall(mary) | ~funny(mary)) & (~tall(mary) | funny(mary))) | ! [X1] : ~strong(X1)) [skolemisation 39,40]
52. (humble(mary) | (generous(alice) & wise(alice))) & ((~generous(alice) | ~wise(alice)) | ~humble(mary)) [nnf transformation 10]
53. (humble(mary) | (generous(alice) & wise(alice))) & (~generous(alice) | ~wise(alice) | ~humble(mary)) [flattening 52]
56. ! [X0] : ((((~funny(X0) | funny(X0)) & (funny(X0) | ~funny(X0))) | ((~generous(X0) | rich(X0)) & (~rich(X0) | generous(X0)))) & (((rich(X0) | generous(X0)) & (~rich(X0) | ~generous(X0))) | ((~funny(X0) | ~funny(X0)) & (funny(X0) | funny(X0))))) [nnf transformation 12]
60. ! [X0] : (~tall(X0) | ((tall(X0) | funny(X0)) & (~funny(X0) | ~tall(X0)))) [nnf transformation 35]
78. ~tall(mary) | funny(mary) | ~strong(X1) [cnf transformation 41]
86. ~humble(X0) | tall(X0) [cnf transformation 27]
107. ~generous(X0) | rich(X0) [cnf transformation 32]
110. humble(mary) | generous(alice) [cnf transformation 53]
115. ~rich(X0) | ~generous(X0) | funny(X0) | funny(X0) [cnf transformation 56]
116. ~rich(X0) | ~generous(X0) | ~funny(X0) | ~funny(X0) [cnf transformation 56]
117. rich(X0) | generous(X0) | funny(X0) | funny(X0) [cnf transformation 56]
118. rich(X0) | generous(X0) | ~funny(X0) | ~funny(X0) [cnf transformation 56]
124. ~tall(X0) | ~funny(X0) | ~tall(X0) [cnf transformation 60]
141. strong(susan) [cnf transformation 24]
142. ~tall(X0) | ~funny(X0) [duplicate literal removal 124]
143. ~rich(X0) | ~generous(X0) | funny(X0) [duplicate literal removal 115]
144. ~rich(X0) | ~generous(X0) | ~funny(X0) [duplicate literal removal 116]
145. rich(X0) | generous(X0) | funny(X0) [duplicate literal removal 117]
146. rich(X0) | generous(X0) | ~funny(X0) [duplicate literal removal 118]
150. 1 <=> tall(mary) [avatar definition]
151. ~tall(mary) <- (~1) [avatar component clause 150]
152. tall(mary) <- (1) [avatar component clause 150]
154. 2 <=> funny(mary) [avatar definition]
156. funny(mary) <- (2) [avatar component clause 154]
164. 4 <=> ! [X1] : ~strong(X1) [avatar definition]
165. ~strong(X1) <- (4) [avatar component clause 164]
167. 4 | 2 | ~1 [avatar split clause 78,150,154,164]
207. 13 <=> generous(alice) [avatar definition]
209. generous(alice) <- (13) [avatar component clause 207]
211. 14 <=> humble(mary) [avatar definition]
213. humble(mary) <- (14) [avatar component clause 211]
214. 13 | 14 [avatar split clause 110,211,207]
241. rich(X0) | ~funny(X0) [subsumption resolution 146,107]
242. rich(X0) | funny(X0) [subsumption resolution 145,107]
243. rich(X0) [subsumption resolution 242,241]
244. ~generous(X0) | ~funny(X0) [subsumption resolution 144,243]
245. ~generous(X0) | funny(X0) [subsumption resolution 143,243]
246. ~generous(X0) [subsumption resolution 245,244]
324. tall(mary) <- (14) [resolution 86,213]
325. $false <- (~1, 14) [subsumption resolution 324,151]
326. 1 | ~14 [avatar contradiction clause 325]
327. $false <- (13) [subsumption resolution 209,246]
328. ~13 [avatar contradiction clause 327]
329. $false <- (4) [resolution 165,141]
332. ~4 [avatar contradiction clause 329]
338. ~funny(mary) <- (1) [resolution 142,152]
339. $false <- (1, 2) [subsumption resolution 338,156]
340. ~1 | ~2 [avatar contradiction clause 339]
341. $false [avatar sat refutation 167,214,326,328,332,340]
% SZS output end Proof for 5410530047935355546891532
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not generous and not patient is not generous.
If someone is either not creative or not old then someone is both strong and not old and vice versa.
Everyone who is either wise or not happy is either not quiet or not kind.
If susan is creative or not kind then alice is both calm and old.
If someone is not rich then someone is both not old and brave.
Everyone who is rich is either not generous or calm and vice versa.
Everyone who is rich is either not strong or not happy.
Everyone who is not kind is kind or old.
Everyone who is either generous or humble is not humble and vice versa.
Everyone who is old is either not patient or quiet.
If someone is both not happy and happy then alice is not old and vice versa.
Everyone who is either not creative or rich is both happy and not happy.
Everyone who is tall is either happy or humble and vice versa.
If someone is wise then lucy is not creative and vice versa.
Everyone who is both humble and not patient is either quiet or not happy and vice versa.
If fred is both creative and generous then someone is not quiet.
Someone is not happy or not curious.
Lucy is rich.
Someone is not kind or rich.
Lucy is not quiet.
Someone is both not patient and not funny.
Someone is not happy. | Lucy is tall. | neutral | (![X]:((~generous(X)&~patient(X))=>~generous(X)))&
((?[X]:((~creative(X)<~>~old(X))))<=>(?[X]:((strong(X)&~old(X)))))&
(![X]:((wise(X)<~>~happy(X))=>(~quiet(X)<~>~kind(X))))&
(((creative(susan)|~kind(susan)))=>((calm(alice)&old(alice))))&
((?[X]:(~rich(X)))=>(?[X]:((~old(X)&brave(X)))))&
(![X]:(rich(X)<=>(~generous(X)<~>calm(X))))&
(![X]:(rich(X)=>(~strong(X)<~>~happy(X))))&
(![X]:(~kind(X)=>(kind(X)|old(X))))&
(![X]:((generous(X)<~>humble(X))<=>~humble(X)))&
(![X]:(old(X)=>(~patient(X)<~>quiet(X))))&
((?[X]:((~happy(X)&happy(X))))<=>(~old(alice)))&
(![X]:((~creative(X)<~>rich(X))=>(happy(X)&~happy(X))))&
(![X]:(tall(X)<=>(happy(X)<~>humble(X))))&
((?[X]:(wise(X)))<=>(~creative(lucy)))&
(![X]:((humble(X)&~patient(X))<=>(quiet(X)<~>~happy(X))))&
(((creative(fred)&generous(fred)))=>(?[X]:(~quiet(X))))&
(?[X]:((~happy(X)|~curious(X))))&
(rich(lucy))&
(?[X]:((~kind(X)|rich(X))))&
(~quiet(lucy))&
(?[X]:((~patient(X)&~funny(X))))&
(?[X]:(~happy(X))) | tall(lucy) | [] | null | 0 |
If someone is not brave then paul is both not rich and not strong.
Everyone who is either not calm or not curious is both funny and not old and vice versa.
Everyone who is both not humble and not strong is either not rich or not strong and vice versa.
If someone is both happy and not curious then alice is both generous and not old and vice versa.
Everyone who is not wise is either not happy or wise.
Everyone who is not rich or not humble is both not kind and rich.
Everyone who is happy or not brave is either quiet or old and vice versa.
Everyone who is wise or not curious is not strong and vice versa.
Everyone who is not patient is patient.
If susan is brave then someone is tall.
Everyone who is not old or happy is both old and not wise and vice versa.
If someone is either funny or kind then someone is strong.
Everyone who is both not strong and not wise is either not generous or old.
If someone is not brave then john is not calm or funny.
If someone is either not kind or generous then lucy is both not brave and not creative.
Lucy is not humble.
Someone is either not rich or quiet.
Someone is both not creative and not calm. | Susan is humble. | contradiction | ((?[X]:(~brave(X)))=>((~rich(paul)&~strong(paul))))&
(![X]:((~calm(X)<~>~curious(X))<=>(funny(X)&~old(X))))&
(![X]:((~humble(X)&~strong(X))<=>(~rich(X)<~>~strong(X))))&
((?[X]:((happy(X)&~curious(X))))<=>((generous(alice)&~old(alice))))&
(![X]:(~wise(X)=>(~happy(X)<~>wise(X))))&
(![X]:((~rich(X)|~humble(X))=>(~kind(X)&rich(X))))&
(![X]:((happy(X)|~brave(X))<=>(quiet(X)<~>old(X))))&
(![X]:((wise(X)|~curious(X))<=>~strong(X)))&
(![X]:(~patient(X)=>patient(X)))&
((brave(susan))=>(?[X]:(tall(X))))&
(![X]:((~old(X)|happy(X))<=>(old(X)&~wise(X))))&
((?[X]:((funny(X)<~>kind(X))))=>(?[X]:(strong(X))))&
(![X]:((~strong(X)&~wise(X))=>(~generous(X)<~>old(X))))&
((?[X]:(~brave(X)))=>((~calm(john)|funny(john))))&
((?[X]:((~kind(X)<~>generous(X))))=>((~brave(lucy)&~creative(lucy))))&
(~humble(lucy))&
(?[X]:((~rich(X)<~>quiet(X))))&
(?[X]:((~creative(X)&~calm(X)))) | humble(susan) | [
"p2",
"p4",
"p5",
"p7",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 166372735238059170912529
% SZS output start Proof for 166372735238059170912529
3. ! [X0] : ((~strong(X0) & ~humble(X0)) <=> (~rich(X0) <~> ~strong(X0))) [input p2]
5. ! [X0] : (~wise(X0) => (~happy(X0) <~> wise(X0))) [input p4]
6. ! [X0] : ((~humble(X0) | ~rich(X0)) => (rich(X0) & ~kind(X0))) [input p5]
8. ! [X0] : ((~curious(X0) | wise(X0)) <=> ~strong(X0)) [input p7]
11. ! [X0] : ((happy(X0) | ~old(X0)) <=> (~wise(X0) & old(X0))) [input p10]
19. humble(susan) [input hypothesis]
26. ! [X0] : ((~happy(X0) <~> wise(X0)) | wise(X0)) [ennf transformation 5]
27. ! [X0] : ((rich(X0) & ~kind(X0)) | (humble(X0) & rich(X0))) [ennf transformation 6]
36. ! [X0] : (((~strong(X0) & ~humble(X0)) | ((~rich(X0) | strong(X0)) & (~strong(X0) | rich(X0)))) & (((strong(X0) | rich(X0)) & (~strong(X0) | ~rich(X0))) | (strong(X0) | humble(X0)))) [nnf transformation 3]
37. ! [X0] : (((~strong(X0) & ~humble(X0)) | ((~rich(X0) | strong(X0)) & (~strong(X0) | rich(X0)))) & (((strong(X0) | rich(X0)) & (~strong(X0) | ~rich(X0))) | strong(X0) | humble(X0))) [flattening 36]
43. ! [X0] : (((~wise(X0) | happy(X0)) & (wise(X0) | ~happy(X0))) | wise(X0)) [nnf transformation 26]
46. ! [X0] : (((~curious(X0) | wise(X0)) | strong(X0)) & (~strong(X0) | (curious(X0) & ~wise(X0)))) [nnf transformation 8]
47. ! [X0] : ((~curious(X0) | wise(X0) | strong(X0)) & (~strong(X0) | (curious(X0) & ~wise(X0)))) [flattening 46]
48. ! [X0] : (((happy(X0) | ~old(X0)) | (wise(X0) | ~old(X0))) & ((~wise(X0) & old(X0)) | (~happy(X0) & old(X0)))) [nnf transformation 11]
49. ! [X0] : ((happy(X0) | ~old(X0) | wise(X0) | ~old(X0)) & ((~wise(X0) & old(X0)) | (~happy(X0) & old(X0)))) [flattening 48]
72. ~humble(X0) | ~rich(X0) | strong(X0) [cnf transformation 37]
79. wise(X0) | ~happy(X0) | wise(X0) [cnf transformation 43]
83. rich(X0) | rich(X0) [cnf transformation 27]
91. ~wise(X0) | ~strong(X0) [cnf transformation 47]
94. old(X0) | old(X0) [cnf transformation 49]
98. happy(X0) | ~old(X0) | wise(X0) | ~old(X0) [cnf transformation 49]
110. humble(susan) [cnf transformation 19]
111. old(X0) [duplicate literal removal 94]
112. happy(X0) | ~old(X0) | wise(X0) [duplicate literal removal 98]
113. rich(X0) [duplicate literal removal 83]
114. ~happy(X0) | wise(X0) [duplicate literal removal 79]
154. ~old(X0) | wise(X0) [subsumption resolution 112,114]
201. wise(X0) [resolution 154,111]
203. ~strong(X1) [resolution 201,91]
211. ~rich(susan) | strong(susan) [resolution 72,110]
213. strong(susan) [subsumption resolution 211,113]
214. $false [subsumption resolution 213,203]
% SZS output end Proof for 166372735238059170912529
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious is not generous or creative.
If someone is calm then alice is brave and vice versa.
If someone is generous or calm then fred is not generous and vice versa.
If someone is not kind then someone is tall or not kind and vice versa.
Everyone who is both humble and not tall is not funny or calm and vice versa.
If someone is strong or funny then someone is tall.
If someone is either not calm or kind then someone is both not happy and not curious and vice versa.
Everyone who is not wise is both not happy and not humble and vice versa.
Everyone who is not tall is either old or rich and vice versa.
If john is not old then someone is either not brave or calm.
Everyone who is either old or kind is both not creative and not brave and vice versa.
Everyone who is brave or not tall is both patient and not strong and vice versa.
Everyone who is creative or strong is generous and vice versa.
Everyone who is both tall and old is not strong and vice versa.
If someone is rich then john is not quiet or not tall.
If someone is both wise and creative then alice is both tall and not generous and vice versa.
John is not patient or generous.
Someone is either kind or generous.
Someone is either not quiet or not happy.
Susan is old.
Mary is both not curious and not humble.
Lucy is both not kind and not calm. | Fred is generous. | contradiction | (![X]:(curious(X)=>(~generous(X)|creative(X))))&
((?[X]:(calm(X)))<=>(brave(alice)))&
((?[X]:((generous(X)|calm(X))))<=>(~generous(fred)))&
((?[X]:(~kind(X)))<=>(?[X]:((tall(X)|~kind(X)))))&
(![X]:((humble(X)&~tall(X))<=>(~funny(X)|calm(X))))&
((?[X]:((strong(X)|funny(X))))=>(?[X]:(tall(X))))&
((?[X]:((~calm(X)<~>kind(X))))<=>(?[X]:((~happy(X)&~curious(X)))))&
(![X]:(~wise(X)<=>(~happy(X)&~humble(X))))&
(![X]:(~tall(X)<=>(old(X)<~>rich(X))))&
((~old(john))=>(?[X]:((~brave(X)<~>calm(X)))))&
(![X]:((old(X)<~>kind(X))<=>(~creative(X)&~brave(X))))&
(![X]:((brave(X)|~tall(X))<=>(patient(X)&~strong(X))))&
(![X]:((creative(X)|strong(X))<=>generous(X)))&
(![X]:((tall(X)&old(X))<=>~strong(X)))&
((?[X]:(rich(X)))=>((~quiet(john)|~tall(john))))&
((?[X]:((wise(X)&creative(X))))<=>((tall(alice)&~generous(alice))))&
((~patient(john)|generous(john)))&
(?[X]:((kind(X)<~>generous(X))))&
(?[X]:((~quiet(X)<~>~happy(X))))&
(old(susan))&
((~curious(mary)&~humble(mary)))&
((~kind(lucy)&~calm(lucy))) | generous(fred) | [
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 4309459886972445790882502
% SZS output start Proof for 4309459886972445790882502
3. ? [X0] : (calm(X0) | generous(X0)) <=> ~generous(fred) [input p2]
23. generous(fred) [input hypothesis]
37. (? [X0] : (calm(X0) | generous(X0)) | generous(fred)) & (~generous(fred) | ! [X0] : (~calm(X0) & ~generous(X0))) [nnf transformation 3]
38. (? [X0] : (calm(X0) | generous(X0)) | generous(fred)) & (~generous(fred) | ! [X1] : (~calm(X1) & ~generous(X1))) [rectify 37]
39. ? [X0] : (calm(X0) | generous(X0)) => (calm(sK1) | generous(sK1)) [choice axiom]
40. ((calm(sK1) | generous(sK1)) | generous(fred)) & (~generous(fred) | ! [X1] : (~calm(X1) & ~generous(X1))) [skolemisation 38,39]
84. ~generous(fred) | ~generous(X1) [cnf transformation 40]
144. generous(fred) [cnf transformation 23]
159. 4 <=> generous(fred) [avatar definition]
161. generous(fred) <- (4) [avatar component clause 159]
173. 7 <=> ! [X1] : ~generous(X1) [avatar definition]
174. ~generous(X1) <- (7) [avatar component clause 173]
175. 7 | ~4 [avatar split clause 84,159,173]
314. 4 [avatar split clause 144,159]
315. $false <- (4, 7) [subsumption resolution 161,174]
316. ~4 | ~7 [avatar contradiction clause 315]
317. $false [avatar sat refutation 175,314,316]
% SZS output end Proof for 4309459886972445790882502
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not brave or not kind then someone is either not creative or quiet.
Everyone who is not humble or happy is not old or strong and vice versa.
Everyone who is both not generous and calm is either wise or not kind and vice versa.
If mary is either not kind or not curious then fred is not rich or not creative.
Everyone who is old or not strong is both wise and generous.
If someone is both not quiet and not funny then someone is creative or not rich and vice versa.
If john is not creative or not rich then alice is either not quiet or not curious.
If someone is either not brave or not happy then lucy is both not humble and humble.
Everyone who is happy is humble or happy and vice versa.
Everyone who is rich is both not happy and generous.
If fred is not strong or happy then someone is not patient.
Everyone who is not creative is both humble and rich and vice versa.
If lucy is not happy or not creative then someone is either not brave or not old.
Everyone who is not generous or not brave is not happy or quiet.
If someone is not quiet then someone is both quiet and not wise and vice versa.
Everyone who is both quiet and not tall is either not patient or creative.
Alice is happy.
Someone is both not humble and not quiet.
John is both not patient and not humble.
Alice is either tall or not humble.
Someone is not strong.
Mary is both generous and not brave.
Lucy is not rich or not brave. | John is brave. | neutral | ((?[X]:((~brave(X)<~>~kind(X))))=>(?[X]:((~creative(X)<~>quiet(X)))))&
(![X]:((~humble(X)|happy(X))<=>(~old(X)|strong(X))))&
(![X]:((~generous(X)&calm(X))<=>(wise(X)<~>~kind(X))))&
(((~kind(mary)<~>~curious(mary)))=>((~rich(fred)|~creative(fred))))&
(![X]:((old(X)|~strong(X))=>(wise(X)&generous(X))))&
((?[X]:((~quiet(X)&~funny(X))))<=>(?[X]:((creative(X)|~rich(X)))))&
(((~creative(john)|~rich(john)))=>((~quiet(alice)<~>~curious(alice))))&
((?[X]:((~brave(X)<~>~happy(X))))=>((~humble(lucy)&humble(lucy))))&
(![X]:(happy(X)<=>(humble(X)|happy(X))))&
(![X]:(rich(X)=>(~happy(X)&generous(X))))&
(((~strong(fred)|happy(fred)))=>(?[X]:(~patient(X))))&
(![X]:(~creative(X)<=>(humble(X)&rich(X))))&
(((~happy(lucy)|~creative(lucy)))=>(?[X]:((~brave(X)<~>~old(X)))))&
(![X]:((~generous(X)|~brave(X))=>(~happy(X)|quiet(X))))&
((?[X]:(~quiet(X)))<=>(?[X]:((quiet(X)&~wise(X)))))&
(![X]:((quiet(X)&~tall(X))=>(~patient(X)<~>creative(X))))&
(happy(alice))&
(?[X]:((~humble(X)&~quiet(X))))&
((~patient(john)&~humble(john)))&
((tall(alice)<~>~humble(alice)))&
(?[X]:(~strong(X)))&
((generous(mary)&~brave(mary)))&
((~rich(lucy)|~brave(lucy))) | brave(john) | [] | null | 0 |
If susan is not rich then lucy is both wise and generous. Everyone who is not humble is not quiet and vice versa. Everyone who is either not strong or wise is either not humble or not calm. Everyone who is quiet is not kind or humble and vice versa. Everyone who is quiet or not rich is old or not humble. Everyone who is not funny or kind is both quiet and not creative. Everyone who is not kind is wise and vice versa. Everyone who is either funny or calm is not brave or quiet. If someone is not happy then alice is either not rich or not quiet. Everyone who is both not humble and not generous is either not rich or not old and vice versa. If someone is both not quiet and not brave then someone is both not wise and not quiet and vice versa. If someone is generous or tall then alice is strong and vice versa. Everyone who is not happy is brave or humble. Everyone who is not happy or not funny is both creative and quiet. Everyone who is not patient is both not kind and happy and vice versa. Someone is brave or wise. Susan is both brave and not strong. Someone is kind or happy. Someone is both not kind and not creative. Alice is not tall or not old. Someone is not calm or funny. Mary is not rich or curious. | Alice is not rich. | contradiction | ((~rich(susan))=>((wise(lucy)&generous(lucy))))&
(![X]:(~humble(X)<=>~quiet(X)))&
(![X]:((~strong(X)<~>wise(X))=>(~humble(X)<~>~calm(X))))&
(![X]:(quiet(X)<=>(~kind(X)|humble(X))))&
(![X]:((quiet(X)|~rich(X))=>(old(X)|~humble(X))))&
(![X]:((~funny(X)|kind(X))=>(quiet(X)&~creative(X))))&
(![X]:(~kind(X)<=>wise(X)))&
(![X]:((funny(X)<~>calm(X))=>(~brave(X)|quiet(X))))&
((?[X]:(~happy(X)))=>((~rich(alice)<~>~quiet(alice))))&
(![X]:((~humble(X)&~generous(X))<=>(~rich(X)<~>~old(X))))&
((?[X]:((~quiet(X)&~brave(X))))<=>(?[X]:((~wise(X)&~quiet(X)))))&
((?[X]:((generous(X)|tall(X))))<=>(strong(alice)))&
(![X]:(~happy(X)=>(brave(X)|humble(X))))&
(![X]:((~happy(X)|~funny(X))=>(creative(X)&quiet(X))))&
(![X]:(~patient(X)<=>(~kind(X)&happy(X))))&
(?[X]:((brave(X)|wise(X))))&
((brave(susan)&~strong(susan)))&
(?[X]:((kind(X)|happy(X))))&
(?[X]:((~kind(X)&~creative(X))))&
((~tall(alice)|~old(alice)))&
(?[X]:((~calm(X)|funny(X))))&
((~rich(mary)|curious(mary))) | ~rich(alice) | [
"p1",
"p3",
"p4",
"p5",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 1088981115056892016243700
% SZS output start Proof for 1088981115056892016243700
2. ! [X0] : (~humble(X0) <=> ~quiet(X0)) [input p1]
4. ! [X0] : (quiet(X0) <=> (humble(X0) | ~kind(X0))) [input p3]
5. ! [X0] : ((~rich(X0) | quiet(X0)) => (~humble(X0) | old(X0))) [input p4]
6. ! [X0] : ((kind(X0) | ~funny(X0)) => (~creative(X0) & quiet(X0))) [input p5]
10. ! [X0] : ((~generous(X0) & ~humble(X0)) <=> (~rich(X0) <~> ~old(X0))) [input p9]
23. ~rich(alice) [input hypothesis]
32. ! [X0] : ((~humble(X0) | old(X0)) | (rich(X0) & ~quiet(X0))) [ennf transformation 5]
33. ! [X0] : (~humble(X0) | old(X0) | (rich(X0) & ~quiet(X0))) [flattening 32]
34. ! [X0] : ((~creative(X0) & quiet(X0)) | (~kind(X0) & funny(X0))) [ennf transformation 6]
38. ! [X0] : ((~humble(X0) | quiet(X0)) & (~quiet(X0) | humble(X0))) [nnf transformation 2]
40. ! [X0] : ((quiet(X0) | (~humble(X0) & kind(X0))) & ((humble(X0) | ~kind(X0)) | ~quiet(X0))) [nnf transformation 4]
41. ! [X0] : ((quiet(X0) | (~humble(X0) & kind(X0))) & (humble(X0) | ~kind(X0) | ~quiet(X0))) [flattening 40]
44. ! [X0] : (((~generous(X0) & ~humble(X0)) | ((~rich(X0) | old(X0)) & (~old(X0) | rich(X0)))) & (((old(X0) | rich(X0)) & (~old(X0) | ~rich(X0))) | (generous(X0) | humble(X0)))) [nnf transformation 10]
45. ! [X0] : (((~generous(X0) & ~humble(X0)) | ((~rich(X0) | old(X0)) & (~old(X0) | rich(X0)))) & (((old(X0) | rich(X0)) & (~old(X0) | ~rich(X0))) | generous(X0) | humble(X0))) [flattening 44]
63. ~quiet(X0) | humble(X0) [cnf transformation 38]
70. kind(X0) | quiet(X0) [cnf transformation 41]
73. ~humble(X0) | old(X0) | rich(X0) [cnf transformation 33]
75. quiet(X0) | ~kind(X0) [cnf transformation 34]
84. ~humble(X0) | ~old(X0) | rich(X0) [cnf transformation 45]
85. ~humble(X0) | ~rich(X0) | old(X0) [cnf transformation 45]
104. ~rich(alice) [cnf transformation 23]
120. quiet(X0) [subsumption resolution 75,70]
121. ~humble(X0) | old(X0) [subsumption resolution 85,73]
122. ~humble(X0) | rich(X0) [subsumption resolution 84,121]
164. humble(X0) [resolution 63,120]
174. rich(X0) [resolution 122,164]
176. $false [resolution 174,104]
% SZS output end Proof for 1088981115056892016243700
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous or not tall then someone is not patient and vice versa.
If someone is not generous then someone is both not strong and curious and vice versa.
If alice is either not generous or not tall then someone is either not happy or old.
Everyone who is both rich and tall is not kind and vice versa.
Everyone who is both not humble and not old is not rich and vice versa.
If susan is both funny and not creative then susan is both not old and not happy and vice versa.
If lucy is either rich or not kind then someone is either not wise or not quiet and vice versa.
If someone is either happy or not tall then someone is humble and vice versa.
If someone is not strong or humble then fred is calm or not strong.
Everyone who is old is both not calm and quiet and vice versa.
If fred is happy or brave then someone is either not kind or tall and vice versa.
If john is calm or brave then mary is both not quiet and not humble and vice versa.
Everyone who is both kind and not old is humble or strong.
If mary is humble or not curious then someone is not calm.
Everyone who is strong or not quiet is both not creative and happy.
Everyone who is wise is either not strong or not old.
Mary is generous.
John is either brave or not humble.
Paul is wise or not creative.
Someone is both not curious and not patient.
Someone is humble or not wise.
Fred is either curious or patient.
John is either not creative or strong.
Someone is humble or not quiet. | John is strong. | contradiction | ((?[X]:((generous(X)|~tall(X))))<=>(?[X]:(~patient(X))))&
((?[X]:(~generous(X)))<=>(?[X]:((~strong(X)&curious(X)))))&
(((~generous(alice)<~>~tall(alice)))=>(?[X]:((~happy(X)<~>old(X)))))&
(![X]:((rich(X)&tall(X))<=>~kind(X)))&
(![X]:((~humble(X)&~old(X))<=>~rich(X)))&
(((funny(susan)&~creative(susan)))<=>((~old(susan)&~happy(susan))))&
(((rich(lucy)<~>~kind(lucy)))<=>(?[X]:((~wise(X)<~>~quiet(X)))))&
((?[X]:((happy(X)<~>~tall(X))))<=>(?[X]:(humble(X))))&
((?[X]:((~strong(X)|humble(X))))=>((calm(fred)|~strong(fred))))&
(![X]:(old(X)<=>(~calm(X)&quiet(X))))&
(((happy(fred)|brave(fred)))<=>(?[X]:((~kind(X)<~>tall(X)))))&
(((calm(john)|brave(john)))<=>((~quiet(mary)&~humble(mary))))&
(![X]:((kind(X)&~old(X))=>(humble(X)|strong(X))))&
(((humble(mary)|~curious(mary)))=>(?[X]:(~calm(X))))&
(![X]:((strong(X)|~quiet(X))=>(~creative(X)&happy(X))))&
(![X]:(wise(X)=>(~strong(X)<~>~old(X))))&
(generous(mary))&
((brave(john)<~>~humble(john)))&
((wise(paul)|~creative(paul)))&
(?[X]:((~curious(X)&~patient(X))))&
(?[X]:((humble(X)|~wise(X))))&
((curious(fred)<~>patient(fred)))&
((~creative(john)<~>strong(john)))&
(?[X]:((humble(X)|~quiet(X)))) | strong(john) | [
"p14",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 7655355481669714608725791
% SZS output start Proof for 7655355481669714608725791
15. ! [X0] : ((~quiet(X0) | strong(X0)) => (happy(X0) & ~creative(X0))) [input p14]
23. ~creative(john) <~> strong(john) [input p22]
25. strong(john) [input hypothesis]
35. ! [X0] : ((happy(X0) & ~creative(X0)) | (quiet(X0) & ~strong(X0))) [ennf transformation 15]
83. (~strong(john) | creative(john)) & (strong(john) | ~creative(john)) [nnf transformation 23]
137. ~creative(X0) | ~strong(X0) [cnf transformation 35]
153. ~strong(john) | creative(john) [cnf transformation 83]
155. strong(john) [cnf transformation 25]
404. ~strong(john) [subsumption resolution 153,137]
415. $false [subsumption resolution 155,404]
% SZS output end Proof for 7655355481669714608725791
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not wise then susan is not strong or calm.
Everyone who is both old and not strong is both tall and old.
Everyone who is either not strong or patient is either happy or creative and vice versa.
If susan is either patient or not rich then someone is both curious and not calm.
If fred is not funny or quiet then someone is patient and vice versa.
If someone is not funny or kind then paul is curious.
Everyone who is not curious or not kind is rich and vice versa.
If john is quiet or funny then someone is both creative and not patient and vice versa.
If paul is either patient or kind then paul is humble.
Everyone who is rich or not calm is tall or not old and vice versa.
Everyone who is both not curious and brave is tall and vice versa.
Everyone who is not rich is both not kind and funny and vice versa.
If someone is either not creative or not kind then someone is strong or not quiet.
Everyone who is either humble or not calm is not curious.
Everyone who is both kind and creative is either wise or not kind.
Everyone who is either curious or not rich is either not patient or creative.
Lucy is not generous.
Someone is funny.
Susan is either not kind or not funny.
Alice is both rich and not wise.
Paul is either quiet or not calm.
Someone is either brave or calm.
Someone is not kind.
Someone is generous or rich. | Susan is not funny. | entailment | ((?[X]:(~wise(X)))=>((~strong(susan)|calm(susan))))&
(![X]:((old(X)&~strong(X))=>(tall(X)&old(X))))&
(![X]:((~strong(X)<~>patient(X))<=>(happy(X)<~>creative(X))))&
(((patient(susan)<~>~rich(susan)))=>(?[X]:((curious(X)&~calm(X)))))&
(((~funny(fred)|quiet(fred)))<=>(?[X]:(patient(X))))&
((?[X]:((~funny(X)|kind(X))))=>(curious(paul)))&
(![X]:((~curious(X)|~kind(X))<=>rich(X)))&
(((quiet(john)|funny(john)))<=>(?[X]:((creative(X)&~patient(X)))))&
(((patient(paul)<~>kind(paul)))=>(humble(paul)))&
(![X]:((rich(X)|~calm(X))<=>(tall(X)|~old(X))))&
(![X]:((~curious(X)&brave(X))<=>tall(X)))&
(![X]:(~rich(X)<=>(~kind(X)&funny(X))))&
((?[X]:((~creative(X)<~>~kind(X))))=>(?[X]:((strong(X)|~quiet(X)))))&
(![X]:((humble(X)<~>~calm(X))=>~curious(X)))&
(![X]:((kind(X)&creative(X))=>(wise(X)<~>~kind(X))))&
(![X]:((curious(X)<~>~rich(X))=>(~patient(X)<~>creative(X))))&
(~generous(lucy))&
(?[X]:(funny(X)))&
((~kind(susan)<~>~funny(susan)))&
((rich(alice)&~wise(alice)))&
((quiet(paul)<~>~calm(paul)))&
(?[X]:((brave(X)<~>calm(X))))&
(?[X]:(~kind(X)))&
(?[X]:((generous(X)|rich(X)))) | ~funny(susan) | [
"p6",
"p11",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 1475357682997918704917219
% SZS output start Proof for 1475357682997918704917219
7. ! [X0] : ((~kind(X0) | ~curious(X0)) <=> rich(X0)) [input p6]
12. ! [X0] : (~rich(X0) <=> (funny(X0) & ~kind(X0))) [input p11]
19. ~kind(susan) <~> ~funny(susan) [input p18]
25. funny(susan) [input hypothesis]
48. ! [X0] : (((~kind(X0) | ~curious(X0)) | ~rich(X0)) & (rich(X0) | (kind(X0) & curious(X0)))) [nnf transformation 7]
49. ! [X0] : ((~kind(X0) | ~curious(X0) | ~rich(X0)) & (rich(X0) | (kind(X0) & curious(X0)))) [flattening 48]
60. ! [X0] : ((~rich(X0) | (~funny(X0) | kind(X0))) & ((funny(X0) & ~kind(X0)) | rich(X0))) [nnf transformation 12]
61. ! [X0] : ((~rich(X0) | ~funny(X0) | kind(X0)) & ((funny(X0) & ~kind(X0)) | rich(X0))) [flattening 60]
71. (funny(susan) | kind(susan)) & (~funny(susan) | ~kind(susan)) [nnf transformation 19]
101. rich(X0) | kind(X0) [cnf transformation 49]
119. ~rich(X0) | ~funny(X0) | kind(X0) [cnf transformation 61]
132. ~funny(susan) | ~kind(susan) [cnf transformation 71]
133. funny(susan) | kind(susan) [cnf transformation 71]
142. funny(susan) [cnf transformation 25]
244. ~funny(X0) | kind(X0) [subsumption resolution 119,101]
264. kind(susan) [subsumption resolution 133,244]
265. ~funny(susan) [subsumption resolution 132,264]
286. $false [subsumption resolution 142,265]
% SZS output end Proof for 1475357682997918704917219
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old or quiet then someone is either not kind or wise.
Everyone who is patient is both not patient and quiet and vice versa.
If paul is strong then someone is strong.
Everyone who is old or not quiet is both curious and not brave.
If paul is either wise or not old then fred is tall.
Everyone who is both not quiet and not patient is both not tall and old.
Everyone who is both not quiet and quiet is either not generous or not curious and vice versa.
If someone is not creative then alice is either not brave or not curious.
If alice is curious then someone is either not humble or not creative and vice versa.
Everyone who is both creative and not creative is both not strong and strong.
Everyone who is both not strong and generous is quiet and vice versa.
Everyone who is both kind and not old is either not strong or not funny and vice versa.
If john is either kind or quiet then paul is either kind or tall.
Everyone who is both not brave and happy is both tall and wise.
Everyone who is either old or tall is old and vice versa.
Everyone who is not humble or tall is not wise.
Someone is kind or not happy.
Someone is not kind.
Lucy is either calm or happy.
Paul is not funny or generous.
Someone is generous. | John is old. | entailment | ((?[X]:((~old(X)<~>quiet(X))))=>(?[X]:((~kind(X)<~>wise(X)))))&
(![X]:(patient(X)<=>(~patient(X)&quiet(X))))&
((strong(paul))=>(?[X]:(strong(X))))&
(![X]:((old(X)|~quiet(X))=>(curious(X)&~brave(X))))&
(((wise(paul)<~>~old(paul)))=>(tall(fred)))&
(![X]:((~quiet(X)&~patient(X))=>(~tall(X)&old(X))))&
(![X]:((~quiet(X)&quiet(X))<=>(~generous(X)<~>~curious(X))))&
((?[X]:(~creative(X)))=>((~brave(alice)<~>~curious(alice))))&
((curious(alice))<=>(?[X]:((~humble(X)<~>~creative(X)))))&
(![X]:((creative(X)&~creative(X))=>(~strong(X)&strong(X))))&
(![X]:((~strong(X)&generous(X))<=>quiet(X)))&
(![X]:((kind(X)&~old(X))<=>(~strong(X)<~>~funny(X))))&
(((kind(john)<~>quiet(john)))=>((kind(paul)<~>tall(paul))))&
(![X]:((~brave(X)&happy(X))=>(tall(X)&wise(X))))&
(![X]:((old(X)<~>tall(X))<=>old(X)))&
(![X]:((~humble(X)|tall(X))=>~wise(X)))&
(?[X]:((kind(X)|~happy(X))))&
(?[X]:(~kind(X)))&
((calm(lucy)<~>happy(lucy)))&
((~funny(paul)|generous(paul)))&
(?[X]:(generous(X))) | old(john) | [
"p1",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 7074494074016103189960817
% SZS output start Proof for 7074494074016103189960817
2. ! [X0] : (patient(X0) <=> (quiet(X0) & ~patient(X0))) [input p1]
6. ! [X0] : ((~patient(X0) & ~quiet(X0)) => (old(X0) & ~tall(X0))) [input p5]
22. ~old(john) [input hypothesis]
28. ! [X0] : ((old(X0) & ~tall(X0)) | (patient(X0) | quiet(X0))) [ennf transformation 6]
29. ! [X0] : ((old(X0) & ~tall(X0)) | patient(X0) | quiet(X0)) [flattening 28]
41. ! [X0] : ((patient(X0) | (~quiet(X0) | patient(X0))) & ((quiet(X0) & ~patient(X0)) | ~patient(X0))) [nnf transformation 2]
42. ! [X0] : ((patient(X0) | ~quiet(X0) | patient(X0)) & ((quiet(X0) & ~patient(X0)) | ~patient(X0))) [flattening 41]
70. ~patient(X0) | ~patient(X0) [cnf transformation 42]
72. patient(X0) | ~quiet(X0) | patient(X0) [cnf transformation 42]
81. old(X0) | patient(X0) | quiet(X0) [cnf transformation 29]
123. ~old(john) [cnf transformation 22]
126. ~patient(X0) [duplicate literal removal 70]
127. ~quiet(X0) | patient(X0) [duplicate literal removal 72]
141. 4 <=> ! [X1] : (quiet(X1) | old(X1)) [avatar definition]
142. quiet(X1) | old(X1) <- (4) [avatar component clause 141]
169. old(X0) | quiet(X0) [subsumption resolution 81,126]
170. 4 [avatar split clause 169,141]
209. 17 <=> quiet(john) [avatar definition]
210. quiet(john) <- (17) [avatar component clause 209]
211. ~quiet(john) <- (~17) [avatar component clause 209]
255. old(john) <- (4, ~17) [resolution 142,211]
257. $false <- (4, ~17) [subsumption resolution 255,123]
258. ~4 | 17 [avatar contradiction clause 257]
260. patient(john) <- (17) [resolution 210,127]
261. $false <- (17) [subsumption resolution 260,126]
262. ~17 [avatar contradiction clause 261]
263. $false [avatar sat refutation 170,258,262]
% SZS output end Proof for 7074494074016103189960817
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm and not patient is patient or brave and vice versa.
If someone is both wise and curious then someone is not humble and vice versa.
Everyone who is either not brave or not tall is both not calm and calm.
Everyone who is not rich or generous is not funny and vice versa.
Everyone who is either humble or old is either wise or kind.
Everyone who is not creative or funny is both calm and not kind.
Everyone who is either not creative or tall is kind and vice versa.
If someone is both not rich and not generous then someone is not strong and vice versa.
Everyone who is funny or not brave is either brave or strong.
Everyone who is either curious or not curious is not funny or not generous.
Everyone who is either not generous or funny is either kind or not happy.
Everyone who is funny or not brave is not quiet or curious.
If someone is kind then john is either not kind or patient and vice versa.
Everyone who is generous is tall or brave.
Everyone who is patient is strong or not brave.
If someone is both patient and not patient then someone is curious or not creative.
Someone is both generous and not humble.
Alice is curious or not strong.
Susan is both calm and not generous.
Someone is quiet.
Someone is not generous.
Susan is both kind and humble.
Mary is humble. | Alice is not tall. | neutral | (![X]:((calm(X)&~patient(X))<=>(patient(X)|brave(X))))&
((?[X]:((wise(X)&curious(X))))<=>(?[X]:(~humble(X))))&
(![X]:((~brave(X)<~>~tall(X))=>(~calm(X)&calm(X))))&
(![X]:((~rich(X)|generous(X))<=>~funny(X)))&
(![X]:((humble(X)<~>old(X))=>(wise(X)<~>kind(X))))&
(![X]:((~creative(X)|funny(X))=>(calm(X)&~kind(X))))&
(![X]:((~creative(X)<~>tall(X))<=>kind(X)))&
((?[X]:((~rich(X)&~generous(X))))<=>(?[X]:(~strong(X))))&
(![X]:((funny(X)|~brave(X))=>(brave(X)<~>strong(X))))&
(![X]:((curious(X)<~>~curious(X))=>(~funny(X)|~generous(X))))&
(![X]:((~generous(X)<~>funny(X))=>(kind(X)<~>~happy(X))))&
(![X]:((funny(X)|~brave(X))=>(~quiet(X)|curious(X))))&
((?[X]:(kind(X)))<=>((~kind(john)<~>patient(john))))&
(![X]:(generous(X)=>(tall(X)|brave(X))))&
(![X]:(patient(X)=>(strong(X)|~brave(X))))&
((?[X]:((patient(X)&~patient(X))))=>(?[X]:((curious(X)|~creative(X)))))&
(?[X]:((generous(X)&~humble(X))))&
((curious(alice)|~strong(alice)))&
((calm(susan)&~generous(susan)))&
(?[X]:(quiet(X)))&
(?[X]:(~generous(X)))&
((kind(susan)&humble(susan)))&
(humble(mary)) | ~tall(alice) | [] | null | 0 |
Everyone who is kind or not creative is humble and vice versa.
Everyone who is old or funny is both funny and not calm and vice versa.
Everyone who is not old or not generous is either not old or humble and vice versa.
Everyone who is brave is both not rich and not old and vice versa.
Everyone who is both calm and creative is generous or wise and vice versa.
If someone is creative or not rich then john is either calm or not kind and vice versa.
If paul is either not kind or humble then lucy is either not funny or rich and vice versa.
If paul is both not rich and not happy then someone is either quiet or brave.
Everyone who is happy is curious or brave.
If someone is strong then john is not old or happy.
Everyone who is wise is strong and vice versa.
Everyone who is funny or strong is either not wise or strong.
Everyone who is not humble is either tall or wise and vice versa.
Everyone who is not tall is not happy and vice versa.
Everyone who is not humble or not funny is both not kind and not brave and vice versa.
Everyone who is either patient or not wise is old.
Alice is brave or not funny.
John is either not quiet or creative.
Susan is both rich and not quiet.
Someone is not curious or not tall.
Someone is not tall or old.
Paul is either not patient or creative.
Someone is either quiet or not old. | Alice is not funny. | entailment | (![X]:((kind(X)|~creative(X))<=>humble(X)))&
(![X]:((old(X)|funny(X))<=>(funny(X)&~calm(X))))&
(![X]:((~old(X)|~generous(X))<=>(~old(X)<~>humble(X))))&
(![X]:(brave(X)<=>(~rich(X)&~old(X))))&
(![X]:((calm(X)&creative(X))<=>(generous(X)|wise(X))))&
((?[X]:((creative(X)|~rich(X))))<=>((calm(john)<~>~kind(john))))&
(((~kind(paul)<~>humble(paul)))<=>((~funny(lucy)<~>rich(lucy))))&
(((~rich(paul)&~happy(paul)))=>(?[X]:((quiet(X)<~>brave(X)))))&
(![X]:(happy(X)=>(curious(X)|brave(X))))&
((?[X]:(strong(X)))=>((~old(john)|happy(john))))&
(![X]:(wise(X)<=>strong(X)))&
(![X]:((funny(X)|strong(X))=>(~wise(X)<~>strong(X))))&
(![X]:(~humble(X)<=>(tall(X)<~>wise(X))))&
(![X]:(~tall(X)<=>~happy(X)))&
(![X]:((~humble(X)|~funny(X))<=>(~kind(X)&~brave(X))))&
(![X]:((patient(X)<~>~wise(X))=>old(X)))&
((brave(alice)|~funny(alice)))&
((~quiet(john)<~>creative(john)))&
((rich(susan)&~quiet(susan)))&
(?[X]:((~curious(X)|~tall(X))))&
(?[X]:((~tall(X)|old(X))))&
((~patient(paul)<~>creative(paul)))&
(?[X]:((quiet(X)<~>~old(X)))) | ~funny(alice) | [
"p2",
"p3",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 4322728871810409985478009
% SZS output start Proof for 4322728871810409985478009
3. ! [X0] : ((~generous(X0) | ~old(X0)) <=> (~old(X0) <~> humble(X0))) [input p2]
4. ! [X0] : (brave(X0) <=> (~old(X0) & ~rich(X0))) [input p3]
15. ! [X0] : ((~funny(X0) | ~humble(X0)) <=> (~brave(X0) & ~kind(X0))) [input p14]
17. ~funny(alice) | brave(alice) [input p16]
24. funny(alice) [input hypothesis]
37. ! [X0] : (((~generous(X0) | ~old(X0)) | ((~old(X0) | ~humble(X0)) & (humble(X0) | old(X0)))) & (((~humble(X0) | old(X0)) & (humble(X0) | ~old(X0))) | (generous(X0) & old(X0)))) [nnf transformation 3]
38. ! [X0] : ((~generous(X0) | ~old(X0) | ((~old(X0) | ~humble(X0)) & (humble(X0) | old(X0)))) & (((~humble(X0) | old(X0)) & (humble(X0) | ~old(X0))) | (generous(X0) & old(X0)))) [flattening 37]
39. ! [X0] : ((brave(X0) | (old(X0) | rich(X0))) & ((~old(X0) & ~rich(X0)) | ~brave(X0))) [nnf transformation 4]
40. ! [X0] : ((brave(X0) | old(X0) | rich(X0)) & ((~old(X0) & ~rich(X0)) | ~brave(X0))) [flattening 39]
55. ! [X0] : (((~funny(X0) | ~humble(X0)) | (brave(X0) | kind(X0))) & ((~brave(X0) & ~kind(X0)) | (funny(X0) & humble(X0)))) [nnf transformation 15]
56. ! [X0] : ((~funny(X0) | ~humble(X0) | brave(X0) | kind(X0)) & ((~brave(X0) & ~kind(X0)) | (funny(X0) & humble(X0)))) [flattening 55]
77. ~humble(X0) | old(X0) | old(X0) [cnf transformation 38]
82. ~brave(X0) | ~old(X0) [cnf transformation 40]
121. ~brave(X0) | humble(X0) [cnf transformation 56]
126. ~funny(alice) | brave(alice) [cnf transformation 17]
137. funny(alice) [cnf transformation 24]
139. ~humble(X0) | old(X0) [duplicate literal removal 77]
226. 18 <=> brave(alice) [avatar definition]
228. brave(alice) <- (18) [avatar component clause 226]
230. 19 <=> funny(alice) [avatar definition]
233. 18 | ~19 [avatar split clause 126,230,226]
282. 19 [avatar split clause 137,230]
289. ~old(alice) <- (18) [resolution 82,228]
290. humble(alice) <- (18) [resolution 121,228]
294. old(alice) <- (18) [resolution 139,290]
295. $false <- (18) [subsumption resolution 294,289]
296. ~18 [avatar contradiction clause 295]
297. $false [avatar sat refutation 233,282,296]
% SZS output end Proof for 4322728871810409985478009
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient then john is both happy and kind.
Everyone who is either wise or curious is not happy and vice versa.
If mary is both not wise and not creative then john is both funny and humble and vice versa.
If fred is not old then susan is not humble.
If someone is brave then someone is either generous or curious.
If mary is not humble or not old then someone is both happy and not quiet and vice versa.
If alice is rich or not quiet then someone is generous and vice versa.
If mary is not humble or strong then paul is both not patient and wise.
If susan is brave or humble then paul is both strong and not humble and vice versa.
Everyone who is not humble is quiet.
If someone is brave then alice is either not wise or not calm.
If someone is both patient and rich then someone is not curious.
Everyone who is kind or not generous is either not calm or old.
Everyone who is not old or creative is both not brave and generous and vice versa.
Everyone who is happy is both tall and old.
Everyone who is creative is either not creative or brave.
Someone is both not quiet and humble.
Someone is tall or not rich.
Lucy is not old or creative.
Lucy is either not tall or not happy.
Someone is either old or not old.
Someone is either not wise or tall.
John is both not old and rich.
Someone is strong or not happy. | John is patient. | entailment | ((~patient(john))=>((happy(john)&kind(john))))&
(![X]:((wise(X)<~>curious(X))<=>~happy(X)))&
(((~wise(mary)&~creative(mary)))<=>((funny(john)&humble(john))))&
((~old(fred))=>(~humble(susan)))&
((?[X]:(brave(X)))=>(?[X]:((generous(X)<~>curious(X)))))&
(((~humble(mary)|~old(mary)))<=>(?[X]:((happy(X)&~quiet(X)))))&
(((rich(alice)|~quiet(alice)))<=>(?[X]:(generous(X))))&
(((~humble(mary)|strong(mary)))=>((~patient(paul)&wise(paul))))&
(((brave(susan)|humble(susan)))<=>((strong(paul)&~humble(paul))))&
(![X]:(~humble(X)=>quiet(X)))&
((?[X]:(brave(X)))=>((~wise(alice)<~>~calm(alice))))&
((?[X]:((patient(X)&rich(X))))=>(?[X]:(~curious(X))))&
(![X]:((kind(X)|~generous(X))=>(~calm(X)<~>old(X))))&
(![X]:((~old(X)|creative(X))<=>(~brave(X)&generous(X))))&
(![X]:(happy(X)=>(tall(X)&old(X))))&
(![X]:(creative(X)=>(~creative(X)<~>brave(X))))&
(?[X]:((~quiet(X)&humble(X))))&
(?[X]:((tall(X)|~rich(X))))&
((~old(lucy)|creative(lucy)))&
((~tall(lucy)<~>~happy(lucy)))&
(?[X]:((old(X)<~>~old(X))))&
(?[X]:((~wise(X)<~>tall(X))))&
((~old(john)&rich(john)))&
(?[X]:((strong(X)|~happy(X)))) | patient(john) | [
"p0",
"p14",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 624095960270999142302380
% SZS output start Proof for 624095960270999142302380
1. ~patient(john) => (kind(john) & happy(john)) [input p0]
15. ! [X0] : (happy(X0) => (old(X0) & tall(X0))) [input p14]
23. rich(john) & ~old(john) [input p22]
25. ~patient(john) [input hypothesis]
28. (kind(john) & happy(john)) | patient(john) [ennf transformation 1]
36. ! [X0] : ((old(X0) & tall(X0)) | ~happy(X0)) [ennf transformation 15]
78. happy(john) | patient(john) [cnf transformation 28]
122. ~happy(X0) | old(X0) [cnf transformation 36]
135. ~old(john) [cnf transformation 23]
138. ~patient(john) [cnf transformation 25]
141. 1 <=> patient(john) [avatar definition]
150. 3 <=> happy(john) [avatar definition]
152. happy(john) <- (3) [avatar component clause 150]
153. 1 | 3 [avatar split clause 78,150,141]
321. ~1 [avatar split clause 138,141]
332. old(john) <- (3) [resolution 122,152]
333. $false <- (3) [subsumption resolution 332,135]
334. ~3 [avatar contradiction clause 333]
335. $false [avatar sat refutation 153,321,334]
% SZS output end Proof for 624095960270999142302380
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both humble and funny is not quiet or not wise and vice versa. Everyone who is not patient is not curious or old. If someone is both rich and generous then alice is brave and vice versa. Everyone who is curious is strong. If john is not kind or curious then paul is funny. Everyone who is either not strong or humble is either brave or humble. If paul is both not curious and curious then someone is not tall or wise and vice versa. If mary is either not funny or wise then someone is calm or tall. If someone is not patient or kind then someone is tall. Everyone who is happy is either happy or not quiet. If someone is both not rich and not calm then paul is either strong or not strong. Everyone who is either tall or not wise is wise. Everyone who is patient or not happy is curious or not quiet and vice versa. Everyone who is both humble and not happy is either not funny or not generous. If someone is calm then alice is wise. Everyone who is calm or curious is curious and vice versa. Someone is either curious or not calm. Lucy is both quiet and not kind. Someone is either happy or wise. Paul is either kind or not kind. Someone is patient or not creative. Someone is not wise. Someone is either not creative or not kind. | Paul is humble. | entailment | (![X]:((humble(X)&funny(X))<=>(~quiet(X)|~wise(X))))&
(![X]:(~patient(X)=>(~curious(X)|old(X))))&
((?[X]:((rich(X)&generous(X))))<=>(brave(alice)))&
(![X]:(curious(X)=>strong(X)))&
(((~kind(john)|curious(john)))=>(funny(paul)))&
(![X]:((~strong(X)<~>humble(X))=>(brave(X)<~>humble(X))))&
(((~curious(paul)&curious(paul)))<=>(?[X]:((~tall(X)|wise(X)))))&
(((~funny(mary)<~>wise(mary)))=>(?[X]:((calm(X)|tall(X)))))&
((?[X]:((~patient(X)|kind(X))))=>(?[X]:(tall(X))))&
(![X]:(happy(X)=>(happy(X)<~>~quiet(X))))&
((?[X]:((~rich(X)&~calm(X))))=>((strong(paul)<~>~strong(paul))))&
(![X]:((tall(X)<~>~wise(X))=>wise(X)))&
(![X]:((patient(X)|~happy(X))<=>(curious(X)|~quiet(X))))&
(![X]:((humble(X)&~happy(X))=>(~funny(X)<~>~generous(X))))&
((?[X]:(calm(X)))=>(wise(alice)))&
(![X]:((calm(X)|curious(X))<=>curious(X)))&
(?[X]:((curious(X)<~>~calm(X))))&
((quiet(lucy)&~kind(lucy)))&
(?[X]:((happy(X)<~>wise(X))))&
((kind(paul)<~>~kind(paul)))&
(?[X]:((patient(X)|~creative(X))))&
(?[X]:(~wise(X)))&
(?[X]:((~creative(X)<~>~kind(X)))) | humble(paul) | [
"p0",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 29112894722426545686278
% SZS output start Proof for 29112894722426545686278
1. ! [X0] : ((funny(X0) & humble(X0)) <=> (~wise(X0) | ~quiet(X0))) [input p0]
7. (curious(paul) & ~curious(paul)) <=> ? [X0] : (wise(X0) | ~tall(X0)) [input p6]
24. ~humble(paul) [input hypothesis]
38. ! [X0] : (((funny(X0) & humble(X0)) | (wise(X0) & quiet(X0))) & ((~wise(X0) | ~quiet(X0)) | (~funny(X0) | ~humble(X0)))) [nnf transformation 1]
39. ! [X0] : (((funny(X0) & humble(X0)) | (wise(X0) & quiet(X0))) & (~wise(X0) | ~quiet(X0) | ~funny(X0) | ~humble(X0))) [flattening 38]
45. ((curious(paul) & ~curious(paul)) | ! [X0] : (~wise(X0) & tall(X0))) & (? [X0] : (wise(X0) | ~tall(X0)) | (~curious(paul) | curious(paul))) [nnf transformation 7]
46. ((curious(paul) & ~curious(paul)) | ! [X0] : (~wise(X0) & tall(X0))) & (? [X0] : (wise(X0) | ~tall(X0)) | ~curious(paul) | curious(paul)) [flattening 45]
47. ((curious(paul) & ~curious(paul)) | ! [X0] : (~wise(X0) & tall(X0))) & (? [X1] : (wise(X1) | ~tall(X1)) | ~curious(paul) | curious(paul)) [rectify 46]
48. ? [X1] : (wise(X1) | ~tall(X1)) => (wise(sK1) | ~tall(sK1)) [choice axiom]
49. ((curious(paul) & ~curious(paul)) | ! [X0] : (~wise(X0) & tall(X0))) & ((wise(sK1) | ~tall(sK1)) | ~curious(paul) | curious(paul)) [skolemisation 47,48]
80. wise(X0) | humble(X0) [cnf transformation 39]
95. ~curious(paul) | ~wise(X0) [cnf transformation 49]
97. curious(paul) | ~wise(X0) [cnf transformation 49]
130. ~humble(paul) [cnf transformation 24]
168. 8 <=> ! [X0] : ~wise(X0) [avatar definition]
169. ~wise(X0) <- (8) [avatar component clause 168]
171. 9 <=> curious(paul) [avatar definition]
174. 8 | 9 [avatar split clause 97,171,168]
179. 8 | ~9 [avatar split clause 95,171,168]
256. humble(X0) <- (8) [resolution 80,169]
260. $false <- (8) [resolution 256,130]
261. ~8 [avatar contradiction clause 260]
262. $false [avatar sat refutation 174,179,261]
% SZS output end Proof for 29112894722426545686278
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy or creative is either brave or not kind and vice versa. Everyone who is old or not creative is either curious or quiet. Everyone who is either not humble or not tall is both not curious and not brave and vice versa. Everyone who is either not curious or not strong is not rich or old. Everyone who is either not wise or wise is either not humble or brave. If mary is either generous or calm then paul is not calm. Everyone who is not creative is either generous or happy. Everyone who is either funny or humble is both not happy and not rich and vice versa. If someone is either tall or old then someone is either happy or not happy and vice versa. Everyone who is curious or generous is not kind. If john is either wise or generous then someone is funny. Everyone who is not kind or not humble is either not happy or not brave. Everyone who is either not funny or not patient is both not quiet and happy and vice versa. Everyone who is either calm or not creative is either not generous or not wise and vice versa. Everyone who is either funny or not tall is either strong or kind and vice versa. Everyone who is either brave or not quiet is rich. Lucy is both humble and patient. Susan is calm. Someone is both generous and not rich. Lucy is either not patient or funny. Fred is either funny or not brave. Susan is either rich or not strong. | Paul is not creative. | neutral | (![X]:((~happy(X)|creative(X))<=>(brave(X)<~>~kind(X))))&
(![X]:((old(X)|~creative(X))=>(curious(X)<~>quiet(X))))&
(![X]:((~humble(X)<~>~tall(X))<=>(~curious(X)&~brave(X))))&
(![X]:((~curious(X)<~>~strong(X))=>(~rich(X)|old(X))))&
(![X]:((~wise(X)<~>wise(X))=>(~humble(X)<~>brave(X))))&
(((generous(mary)<~>calm(mary)))=>(~calm(paul)))&
(![X]:(~creative(X)=>(generous(X)<~>happy(X))))&
(![X]:((funny(X)<~>humble(X))<=>(~happy(X)&~rich(X))))&
((?[X]:((tall(X)<~>old(X))))<=>(?[X]:((happy(X)<~>~happy(X)))))&
(![X]:((curious(X)|generous(X))=>~kind(X)))&
(((wise(john)<~>generous(john)))=>(?[X]:(funny(X))))&
(![X]:((~kind(X)|~humble(X))=>(~happy(X)<~>~brave(X))))&
(![X]:((~funny(X)<~>~patient(X))<=>(~quiet(X)&happy(X))))&
(![X]:((calm(X)<~>~creative(X))<=>(~generous(X)<~>~wise(X))))&
(![X]:((funny(X)<~>~tall(X))<=>(strong(X)<~>kind(X))))&
(![X]:((brave(X)<~>~quiet(X))=>rich(X)))&
((humble(lucy)&patient(lucy)))&
(calm(susan))&
(?[X]:((generous(X)&~rich(X))))&
((~patient(lucy)<~>funny(lucy)))&
((funny(fred)<~>~brave(fred)))&
((rich(susan)<~>~strong(susan))) | ~creative(paul) | [] | null | 0 |
If fred is humble or creative then someone is not curious or quiet and vice versa.
Everyone who is both happy and patient is not humble or not old.
Everyone who is not brave or wise is old.
Everyone who is either not brave or not patient is both humble and creative and vice versa.
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.
Everyone who is either not creative or not old is both not kind and not strong and vice versa.
If someone is either not rich or curious then alice is brave and vice versa.
Mary is not tall.
Susan is either curious or not creative.
Susan is both not funny and rich.
Someone is both generous and not calm.
Someone is either not tall or curious.
Alice is curious or quiet.
Mary is not generous.
Alice is either humble or wise. | Lucy is brave. | entailment | (((humble(fred)|creative(fred)))<=>(?[X]:((~curious(X)|quiet(X)))))&
(![X]:((happy(X)&patient(X))=>(~humble(X)|~old(X))))&
(![X]:((~brave(X)|wise(X))=>old(X)))&
(![X]:((~brave(X)<~>~patient(X))<=>(humble(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]:((~creative(X)<~>~old(X))<=>(~kind(X)&~strong(X))))&
((?[X]:((~rich(X)<~>curious(X))))<=>(brave(alice)))&
(~tall(mary))&
((curious(susan)<~>~creative(susan)))&
((~funny(susan)&rich(susan)))&
(?[X]:((generous(X)&~calm(X))))&
(?[X]:((~tall(X)<~>curious(X))))&
((curious(alice)|quiet(alice)))&
(~generous(mary))&
((humble(alice)<~>wise(alice))) | brave(lucy) | [
"p6",
"p11",
"p16",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 155458933395177952594939
% SZS output start Proof for 155458933395177952594939
7. (~funny(mary) | ~curious(mary)) <=> (~humble(lucy) & brave(lucy)) [input p6]
12. ! [X0] : ((generous(X0) <~> ~tall(X0)) => (wise(X0) & ~curious(X0))) [input p11]
17. ~tall(mary) [input p16]
23. ~generous(mary) [input p22]
25. ~brave(lucy) [input hypothesis]
33. ! [X0] : ((wise(X0) & ~curious(X0)) | (generous(X0) <=> ~tall(X0))) [ennf transformation 12]
43. ((~funny(mary) | ~curious(mary)) | (humble(lucy) | ~brave(lucy))) & ((~humble(lucy) & brave(lucy)) | (funny(mary) & curious(mary))) [nnf transformation 7]
44. (~funny(mary) | ~curious(mary) | humble(lucy) | ~brave(lucy)) & ((~humble(lucy) & brave(lucy)) | (funny(mary) & curious(mary))) [flattening 43]
49. ! [X0] : ((wise(X0) & ~curious(X0)) | ((generous(X0) | tall(X0)) & (~tall(X0) | ~generous(X0)))) [nnf transformation 33]
88. brave(lucy) | curious(mary) [cnf transformation 44]
114. ~curious(X0) | generous(X0) | tall(X0) [cnf transformation 49]
141. ~tall(mary) [cnf transformation 17]
151. ~generous(mary) [cnf transformation 23]
154. ~brave(lucy) [cnf transformation 25]
204. 11 <=> brave(lucy) [avatar definition]
212. 13 <=> curious(mary) [avatar definition]
213. curious(mary) <- (13) [avatar component clause 212]
223. 13 | 11 [avatar split clause 88,204,212]
300. ~11 [avatar split clause 154,204]
358. generous(mary) | tall(mary) <- (13) [resolution 114,213]
369. tall(mary) <- (13) [subsumption resolution 358,151]
370. $false <- (13) [subsumption resolution 369,141]
371. ~13 [avatar contradiction clause 370]
381. $false [avatar sat refutation 223,300,371]
% SZS output end Proof for 155458933395177952594939
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 alice is not curious then mary is funny.
If someone is not kind or wise then someone is both not strong and generous.
If someone is either not rich or strong then paul is either not tall or funny.
Everyone who is tall or not old is both not wise and not old.
If paul is either not rich or not quiet then someone is both not brave and not curious.
If someone is both old and not happy then lucy is not old or generous.
Everyone who is not old or not brave is not calm.
Everyone who is brave is either brave or not wise.
Everyone who is not tall or quiet is both rich and not curious and vice versa.
If lucy is either not patient or not generous then someone is not rich and vice versa.
Everyone who is not wise is both not wise and brave and vice versa.
If someone is not calm then paul is both not humble and creative.
Everyone who is either tall or funny is either patient or not calm and vice versa.
Everyone who is both not humble and patient is not calm or generous.
If paul is either not old or quiet then someone is kind or not creative.
Someone is rich or not brave.
Someone is either funny or not strong.
Someone is happy or not creative.
Someone is quiet or not old.
Someone is not funny.
Someone is not funny or not happy. | Alice is old. | entailment | ((~curious(alice))=>(funny(mary)))&
((?[X]:((~kind(X)|wise(X))))=>(?[X]:((~strong(X)&generous(X)))))&
((?[X]:((~rich(X)<~>strong(X))))=>((~tall(paul)<~>funny(paul))))&
(![X]:((tall(X)|~old(X))=>(~wise(X)&~old(X))))&
(((~rich(paul)<~>~quiet(paul)))=>(?[X]:((~brave(X)&~curious(X)))))&
((?[X]:((old(X)&~happy(X))))=>((~old(lucy)|generous(lucy))))&
(![X]:((~old(X)|~brave(X))=>~calm(X)))&
(![X]:(brave(X)=>(brave(X)<~>~wise(X))))&
(![X]:((~tall(X)|quiet(X))<=>(rich(X)&~curious(X))))&
(((~patient(lucy)<~>~generous(lucy)))<=>(?[X]:(~rich(X))))&
(![X]:(~wise(X)<=>(~wise(X)&brave(X))))&
((?[X]:(~calm(X)))=>((~humble(paul)&creative(paul))))&
(![X]:((tall(X)<~>funny(X))<=>(patient(X)<~>~calm(X))))&
(![X]:((~humble(X)&patient(X))=>(~calm(X)|generous(X))))&
(((~old(paul)<~>quiet(paul)))=>(?[X]:((kind(X)|~creative(X)))))&
(?[X]:((rich(X)|~brave(X))))&
(?[X]:((funny(X)<~>~strong(X))))&
(?[X]:((happy(X)|~creative(X))))&
(?[X]:((quiet(X)|~old(X))))&
(?[X]:(~funny(X)))&
(?[X]:((~funny(X)|~happy(X)))) | old(alice) | [
"p3",
"p7",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 6541711226758015040705632
% SZS output start Proof for 6541711226758015040705632
4. ! [X0] : ((~old(X0) | tall(X0)) => (~old(X0) & ~wise(X0))) [input p3]
8. ! [X0] : (brave(X0) => (brave(X0) <~> ~wise(X0))) [input p7]
11. ! [X0] : (~wise(X0) <=> (brave(X0) & ~wise(X0))) [input p10]
22. ~old(alice) [input hypothesis]
29. ! [X0] : ((~old(X0) & ~wise(X0)) | (old(X0) & ~tall(X0))) [ennf transformation 4]
34. ! [X0] : ((brave(X0) <~> ~wise(X0)) | ~brave(X0)) [ennf transformation 8]
45. ! [X0] : (((wise(X0) | ~brave(X0)) & (~wise(X0) | brave(X0))) | ~brave(X0)) [nnf transformation 34]
52. ! [X0] : ((~wise(X0) | (~brave(X0) | wise(X0))) & ((brave(X0) & ~wise(X0)) | wise(X0))) [nnf transformation 11]
53. ! [X0] : ((~wise(X0) | ~brave(X0) | wise(X0)) & ((brave(X0) & ~wise(X0)) | wise(X0))) [flattening 52]
76. ~wise(X0) | old(X0) [cnf transformation 29]
87. wise(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 45]
98. brave(X0) | wise(X0) [cnf transformation 53]
118. ~old(alice) [cnf transformation 22]
119. wise(X0) | ~brave(X0) [duplicate literal removal 87]
207. wise(X0) [subsumption resolution 98,119]
269. old(X0) [resolution 76,207]
270. $false [resolution 269,118]
% SZS output end Proof for 6541711226758015040705632
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not generous is either quiet or not patient and vice versa.
Everyone who is tall is both not tall and generous and vice versa.
If mary is not strong then susan is both creative and not tall and vice versa.
If mary is both not tall and not quiet then susan is either wise or strong and vice versa.
If lucy is either funny or calm then lucy is both curious and tall and vice versa.
If mary is either not calm or kind then someone is either tall or calm.
Everyone who is either brave or not curious is tall.
If someone is strong or rich then paul is either not patient or not happy and vice versa.
Everyone who is not funny is either humble or patient and vice versa.
Everyone who is both not strong and humble is not quiet or not old.
If someone is both not curious and curious then lucy is happy or tall and vice versa.
If someone is both not generous and calm then paul is humble.
If lucy is not humble then someone is either calm or not generous.
Everyone who is not quiet is both generous and rich and vice versa.
If someone is not tall or calm then paul is either not rich or humble and vice versa.
Alice is both not strong and not brave.
John is curious.
Someone is not old.
Someone is not tall or quiet.
Someone is not brave or funny.
Alice is either wise or strong.
Fred is rich.
Someone is either rich or not kind. | Paul is not patient. | contradiction | (![X]:(~generous(X)<=>(quiet(X)<~>~patient(X))))&
(![X]:(tall(X)<=>(~tall(X)&generous(X))))&
((~strong(mary))<=>((creative(susan)&~tall(susan))))&
(((~tall(mary)&~quiet(mary)))<=>((wise(susan)<~>strong(susan))))&
(((funny(lucy)<~>calm(lucy)))<=>((curious(lucy)&tall(lucy))))&
(((~calm(mary)<~>kind(mary)))=>(?[X]:((tall(X)<~>calm(X)))))&
(![X]:((brave(X)<~>~curious(X))=>tall(X)))&
((?[X]:((strong(X)|rich(X))))<=>((~patient(paul)<~>~happy(paul))))&
(![X]:(~funny(X)<=>(humble(X)<~>patient(X))))&
(![X]:((~strong(X)&humble(X))=>(~quiet(X)|~old(X))))&
((?[X]:((~curious(X)&curious(X))))<=>((happy(lucy)|tall(lucy))))&
((?[X]:((~generous(X)&calm(X))))=>(humble(paul)))&
((~humble(lucy))=>(?[X]:((calm(X)<~>~generous(X)))))&
(![X]:(~quiet(X)<=>(generous(X)&rich(X))))&
((?[X]:((~tall(X)|calm(X))))<=>((~rich(paul)<~>humble(paul))))&
((~strong(alice)&~brave(alice)))&
(curious(john))&
(?[X]:(~old(X)))&
(?[X]:((~tall(X)|quiet(X))))&
(?[X]:((~brave(X)|funny(X))))&
((wise(alice)<~>strong(alice)))&
(rich(fred))&
(?[X]:((rich(X)<~>~kind(X)))) | ~patient(paul) | [
"p0",
"p1",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 2650420872357855702151839
% SZS output start Proof for 2650420872357855702151839
1. ! [X0] : (~generous(X0) <=> (quiet(X0) <~> ~patient(X0))) [input p0]
2. ! [X0] : (tall(X0) <=> (generous(X0) & ~tall(X0))) [input p1]
14. ! [X0] : (~quiet(X0) <=> (rich(X0) & generous(X0))) [input p13]
24. ~patient(paul) [input hypothesis]
31. ! [X0] : ((~generous(X0) | ((quiet(X0) | patient(X0)) & (~patient(X0) | ~quiet(X0)))) & (((patient(X0) | ~quiet(X0)) & (~patient(X0) | quiet(X0))) | generous(X0))) [nnf transformation 1]
32. ! [X0] : ((tall(X0) | (~generous(X0) | tall(X0))) & ((generous(X0) & ~tall(X0)) | ~tall(X0))) [nnf transformation 2]
33. ! [X0] : ((tall(X0) | ~generous(X0) | tall(X0)) & ((generous(X0) & ~tall(X0)) | ~tall(X0))) [flattening 32]
57. ! [X0] : ((~quiet(X0) | (~rich(X0) | ~generous(X0))) & ((rich(X0) & generous(X0)) | quiet(X0))) [nnf transformation 14]
58. ! [X0] : ((~quiet(X0) | ~rich(X0) | ~generous(X0)) & ((rich(X0) & generous(X0)) | quiet(X0))) [flattening 57]
72. ~quiet(X0) | patient(X0) | generous(X0) [cnf transformation 31]
75. ~tall(X0) | ~tall(X0) [cnf transformation 33]
77. tall(X0) | ~generous(X0) | tall(X0) [cnf transformation 33]
117. quiet(X0) | generous(X0) [cnf transformation 58]
136. ~patient(paul) [cnf transformation 24]
137. ~tall(X0) [duplicate literal removal 75]
138. ~generous(X0) | tall(X0) [duplicate literal removal 77]
209. 13 <=> patient(paul) [avatar definition]
211. ~patient(paul) <- (~13) [avatar component clause 209]
297. ~13 [avatar split clause 136,209]
307. patient(X0) | generous(X0) | generous(X0) [resolution 72,117]
311. patient(X0) | generous(X0) [duplicate literal removal 307]
312. generous(paul) <- (~13) [resolution 311,211]
316. tall(paul) <- (~13) [resolution 312,138]
317. $false <- (~13) [subsumption resolution 316,137]
318. 13 [avatar contradiction clause 317]
319. $false [avatar sat refutation 297,318]
% SZS output end Proof for 2650420872357855702151839
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either generous or not humble then susan is not strong and vice versa. Everyone who is not generous is old or not quiet and vice versa. Everyone who is not strong or not generous is either not brave or calm and vice versa. Everyone who is calm is rich or humble and vice versa. Everyone who is kind is not kind or not quiet and vice versa. If lucy is not tall then someone is both not brave and rich. Everyone who is both curious and humble is humble. If fred is calm or generous then someone is either not funny or wise and vice versa. If someone is not humble or happy then someone is not strong and vice versa. If lucy is either not brave or creative then alice is either not wise or creative and vice versa. Everyone who is both quiet and not brave is not brave and vice versa. If susan is either not curious or not calm then alice is both happy and funny and vice versa. If mary is either not patient or rich then someone is funny or curious and vice versa. Everyone who is funny is both strong and generous. If someone is old or rich then fred is both generous and creative and vice versa. Everyone who is both strong and wise is either funny or not brave. John is wise or humble. Alice is both brave and happy. Lucy is both not funny and not rich. Someone is humble. Someone is creative. Someone is either strong or kind. | Susan is not humble. | contradiction | ((?[X]:((generous(X)<~>~humble(X))))<=>(~strong(susan)))&
(![X]:(~generous(X)<=>(old(X)|~quiet(X))))&
(![X]:((~strong(X)|~generous(X))<=>(~brave(X)<~>calm(X))))&
(![X]:(calm(X)<=>(rich(X)|humble(X))))&
(![X]:(kind(X)<=>(~kind(X)|~quiet(X))))&
((~tall(lucy))=>(?[X]:((~brave(X)&rich(X)))))&
(![X]:((curious(X)&humble(X))=>humble(X)))&
(((calm(fred)|generous(fred)))<=>(?[X]:((~funny(X)<~>wise(X)))))&
((?[X]:((~humble(X)|happy(X))))<=>(?[X]:(~strong(X))))&
(((~brave(lucy)<~>creative(lucy)))<=>((~wise(alice)<~>creative(alice))))&
(![X]:((quiet(X)&~brave(X))<=>~brave(X)))&
(((~curious(susan)<~>~calm(susan)))<=>((happy(alice)&funny(alice))))&
(((~patient(mary)<~>rich(mary)))<=>(?[X]:((funny(X)|curious(X)))))&
(![X]:(funny(X)=>(strong(X)&generous(X))))&
((?[X]:((old(X)|rich(X))))<=>((generous(fred)&creative(fred))))&
(![X]:((strong(X)&wise(X))=>(funny(X)<~>~brave(X))))&
((wise(john)|humble(john)))&
((brave(alice)&happy(alice)))&
((~funny(lucy)&~rich(lucy)))&
(?[X]:(humble(X)))&
(?[X]:(creative(X)))&
(?[X]:((strong(X)<~>kind(X)))) | ~humble(susan) | [
"p1",
"p2",
"p3",
"p4",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 1309514548459834100895003
% SZS output start Proof for 1309514548459834100895003
2. ! [X0] : (~generous(X0) <=> (~quiet(X0) | old(X0))) [input p1]
3. ! [X0] : ((~generous(X0) | ~strong(X0)) <=> (~brave(X0) <~> calm(X0))) [input p2]
4. ! [X0] : (calm(X0) <=> (humble(X0) | rich(X0))) [input p3]
5. ! [X0] : (kind(X0) <=> (~quiet(X0) | ~kind(X0))) [input p4]
11. ! [X0] : ((~brave(X0) & quiet(X0)) <=> ~brave(X0)) [input p10]
15. ? [X0] : (rich(X0) | old(X0)) <=> (creative(fred) & generous(fred)) [input p14]
23. ~humble(susan) [input hypothesis]
35. ! [X0] : ((~generous(X0) | (quiet(X0) & ~old(X0))) & ((~quiet(X0) | old(X0)) | generous(X0))) [nnf transformation 2]
36. ! [X0] : ((~generous(X0) | (quiet(X0) & ~old(X0))) & (~quiet(X0) | old(X0) | generous(X0))) [flattening 35]
37. ! [X0] : (((~generous(X0) | ~strong(X0)) | ((~brave(X0) | ~calm(X0)) & (calm(X0) | brave(X0)))) & (((~calm(X0) | brave(X0)) & (calm(X0) | ~brave(X0))) | (generous(X0) & strong(X0)))) [nnf transformation 3]
38. ! [X0] : ((~generous(X0) | ~strong(X0) | ((~brave(X0) | ~calm(X0)) & (calm(X0) | brave(X0)))) & (((~calm(X0) | brave(X0)) & (calm(X0) | ~brave(X0))) | (generous(X0) & strong(X0)))) [flattening 37]
39. ! [X0] : ((calm(X0) | (~humble(X0) & ~rich(X0))) & ((humble(X0) | rich(X0)) | ~calm(X0))) [nnf transformation 4]
40. ! [X0] : ((calm(X0) | (~humble(X0) & ~rich(X0))) & (humble(X0) | rich(X0) | ~calm(X0))) [flattening 39]
41. ! [X0] : ((kind(X0) | (quiet(X0) & kind(X0))) & ((~quiet(X0) | ~kind(X0)) | ~kind(X0))) [nnf transformation 5]
42. ! [X0] : ((kind(X0) | (quiet(X0) & kind(X0))) & (~quiet(X0) | ~kind(X0) | ~kind(X0))) [flattening 41]
54. ! [X0] : (((~brave(X0) & quiet(X0)) | brave(X0)) & (~brave(X0) | (brave(X0) | ~quiet(X0)))) [nnf transformation 11]
55. ! [X0] : (((~brave(X0) & quiet(X0)) | brave(X0)) & (~brave(X0) | brave(X0) | ~quiet(X0))) [flattening 54]
62. (? [X0] : (rich(X0) | old(X0)) | (~creative(fred) | ~generous(fred))) & ((creative(fred) & generous(fred)) | ! [X0] : (~rich(X0) & ~old(X0))) [nnf transformation 15]
63. (? [X0] : (rich(X0) | old(X0)) | ~creative(fred) | ~generous(fred)) & ((creative(fred) & generous(fred)) | ! [X0] : (~rich(X0) & ~old(X0))) [flattening 62]
64. (? [X0] : (rich(X0) | old(X0)) | ~creative(fred) | ~generous(fred)) & ((creative(fred) & generous(fred)) | ! [X1] : (~rich(X1) & ~old(X1))) [rectify 63]
65. ? [X0] : (rich(X0) | old(X0)) => (rich(sK5) | old(sK5)) [choice axiom]
66. ((rich(sK5) | old(sK5)) | ~creative(fred) | ~generous(fred)) & ((creative(fred) & generous(fred)) | ! [X1] : (~rich(X1) & ~old(X1))) [skolemisation 64,65]
81. ~generous(X0) | quiet(X0) [cnf transformation 36]
83. ~brave(X0) | calm(X0) | generous(X0) [cnf transformation 38]
88. ~calm(X0) | rich(X0) | humble(X0) [cnf transformation 40]
91. ~quiet(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 42]
92. kind(X0) | kind(X0) [cnf transformation 42]
113. quiet(X0) | brave(X0) [cnf transformation 55]
130. generous(fred) | ~rich(X1) [cnf transformation 66]
145. ~humble(susan) [cnf transformation 23]
146. ~quiet(X0) | ~kind(X0) [duplicate literal removal 91]
147. kind(X0) [duplicate literal removal 92]
163. 4 <=> ! [X1] : (generous(X1) | humble(X1)) [avatar definition]
164. humble(X1) | generous(X1) <- (4) [avatar component clause 163]
170. ~quiet(X0) [subsumption resolution 146,147]
179. 8 <=> generous(fred) [avatar definition]
181. generous(fred) <- (8) [avatar component clause 179]
247. brave(X0) [subsumption resolution 113,170]
312. 35 <=> ! [X1] : ~rich(X1) [avatar definition]
313. ~rich(X1) <- (35) [avatar component clause 312]
319. 35 | 8 [avatar split clause 130,179,312]
336. quiet(fred) <- (8) [resolution 81,181]
337. $false <- (8) [subsumption resolution 336,170]
338. ~8 [avatar contradiction clause 337]
352. generous(susan) <- (4) [resolution 164,145]
361. quiet(susan) <- (4) [resolution 352,81]
362. $false <- (4) [subsumption resolution 361,170]
363. ~4 [avatar contradiction clause 362]
368. calm(X0) | generous(X0) [resolution 83,247]
381. rich(X0) | humble(X0) | generous(X0) [resolution 88,368]
386. humble(X0) | generous(X0) <- (35) [subsumption resolution 381,313]
387. 4 | ~35 [avatar split clause 386,312,163]
393. $false [avatar sat refutation 319,338,363,387]
% SZS output end Proof for 1309514548459834100895003
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not rich or patient is either not generous or not kind and vice versa.
Everyone who is not wise is rich.
Everyone who is either not kind or not humble is kind.
If someone is both happy and 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.
If mary is either quiet or not humble then someone is both not humble and strong and vice versa.
If susan is not tall then someone is strong or not patient and vice versa.
If someone is curious or old then lucy is both not old and rich and vice versa.
Everyone who is not rich or not brave is funny and vice versa.
If someone is not generous then mary is both curious and not happy and vice versa.
John is both not calm and old.
Mary is either not funny or not tall.
Someone is both not curious and not happy.
Someone is brave.
Someone is both generous and funny.
Someone is either wise or not kind.
Someone is both creative and not old.
John is both not creative and not generous. | Mary is patient. | entailment | (![X]:((~rich(X)|patient(X))<=>(~generous(X)<~>~kind(X))))&
(![X]:(~wise(X)=>rich(X)))&
(![X]:((~kind(X)<~>~humble(X))=>kind(X)))&
((?[X]:((happy(X)&~brave(X))))<=>((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(mary)<~>~humble(mary)))<=>(?[X]:((~humble(X)&strong(X)))))&
((~tall(susan))<=>(?[X]:((strong(X)|~patient(X)))))&
((?[X]:((curious(X)|old(X))))<=>((~old(lucy)&rich(lucy))))&
(![X]:((~rich(X)|~brave(X))<=>funny(X)))&
((?[X]:(~generous(X)))<=>((curious(mary)&~happy(mary))))&
((~calm(john)&old(john)))&
((~funny(mary)<~>~tall(mary)))&
(?[X]:((~curious(X)&~happy(X))))&
(?[X]:(brave(X)))&
(?[X]:((generous(X)&funny(X))))&
(?[X]:((wise(X)<~>~kind(X))))&
(?[X]:((creative(X)&~old(X))))&
((~creative(john)&~generous(john))) | patient(mary) | [
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 251958224097436923577633
% SZS output start Proof for 251958224097436923577633
7. ! [X0] : ((rich(X0) & patient(X0)) <=> (~strong(X0) | strong(X0))) [input p6]
25. ~patient(mary) [input hypothesis]
42. ! [X0] : (((rich(X0) & patient(X0)) | (strong(X0) & ~strong(X0))) & ((~strong(X0) | strong(X0)) | (~rich(X0) | ~patient(X0)))) [nnf transformation 7]
43. ! [X0] : (((rich(X0) & patient(X0)) | (strong(X0) & ~strong(X0))) & (~strong(X0) | strong(X0) | ~rich(X0) | ~patient(X0))) [flattening 42]
113. patient(X0) | ~strong(X0) [cnf transformation 43]
114. patient(X0) | strong(X0) [cnf transformation 43]
166. ~patient(mary) [cnf transformation 25]
193. patient(X0) [subsumption resolution 113,114]
338. $false [subsumption resolution 166,193]
% SZS output end Proof for 251958224097436923577633
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If susan is both not humble and not strong then fred is both not funny and not tall and vice versa. Everyone who is both patient and not tall is both curious and not calm and vice versa. If someone is not creative then fred is either not old or strong. Everyone who is both happy and not brave is both not funny and not rich. Everyone who is wise is not curious. If someone is quiet or strong then someone is creative or kind and vice versa. Everyone who is not tall is either curious or kind. If someone is old then someone is both not strong and patient. Everyone who is either strong or not calm is curious. Everyone who is both not kind and not old is both not kind and brave. Everyone who is old or brave is either not rich or rich and vice versa. Everyone who is either calm or humble is either patient or not strong. If susan is both not patient and not rich then someone is either humble or not funny. Everyone who is tall or not creative is generous or calm. Everyone who is either not wise or not funny is creative or not rich and vice versa. Everyone who is not kind or not happy is tall. Susan is tall or strong. Lucy is either old or quiet. Someone is strong. Someone is kind. Someone is wise or not rich. Alice is curious. Someone is quiet or old. | Susan is not calm. | neutral | (((~humble(susan)&~strong(susan)))<=>((~funny(fred)&~tall(fred))))&
(![X]:((patient(X)&~tall(X))<=>(curious(X)&~calm(X))))&
((?[X]:(~creative(X)))=>((~old(fred)<~>strong(fred))))&
(![X]:((happy(X)&~brave(X))=>(~funny(X)&~rich(X))))&
(![X]:(wise(X)=>~curious(X)))&
((?[X]:((quiet(X)|strong(X))))<=>(?[X]:((creative(X)|kind(X)))))&
(![X]:(~tall(X)=>(curious(X)<~>kind(X))))&
((?[X]:(old(X)))=>(?[X]:((~strong(X)&patient(X)))))&
(![X]:((strong(X)<~>~calm(X))=>curious(X)))&
(![X]:((~kind(X)&~old(X))=>(~kind(X)&brave(X))))&
(![X]:((old(X)|brave(X))<=>(~rich(X)<~>rich(X))))&
(![X]:((calm(X)<~>humble(X))=>(patient(X)<~>~strong(X))))&
(((~patient(susan)&~rich(susan)))=>(?[X]:((humble(X)<~>~funny(X)))))&
(![X]:((tall(X)|~creative(X))=>(generous(X)|calm(X))))&
(![X]:((~wise(X)<~>~funny(X))<=>(creative(X)|~rich(X))))&
(![X]:((~kind(X)|~happy(X))=>tall(X)))&
((tall(susan)|strong(susan)))&
((old(lucy)<~>quiet(lucy)))&
(?[X]:(strong(X)))&
(?[X]:(kind(X)))&
(?[X]:((wise(X)|~rich(X))))&
(curious(alice))&
(?[X]:((quiet(X)|old(X)))) | ~calm(susan) | [] | null | 0 |
Everyone who is creative or tall is either wise or old and vice versa.
If someone is either rich or wise then someone is both wise and not happy.
If someone is kind or humble then lucy is not old or not 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.
Everyone who is either generous or not tall is happy or not tall and vice versa.
Everyone who is not funny or not wise is not calm or happy.
If someone is both old and calm then susan is not creative and vice versa.
Everyone who is not humble is either not strong or not humble.
If someone is curious then someone is either not strong or curious.
If susan is not generous then someone is either creative or tall and vice versa.
Someone is not creative or generous.
Someone is not happy.
Someone is not kind.
Fred is either not curious or not wise.
Someone is not funny or not wise.
Lucy is both not funny and strong.
Someone is both not quiet and creative.
Someone is tall or not curious. | Lucy is curious. | neutral | (![X]:((creative(X)|tall(X))<=>(wise(X)<~>old(X))))&
((?[X]:((rich(X)<~>wise(X))))=>(?[X]:((wise(X)&~happy(X)))))&
((?[X]:((kind(X)|humble(X))))=>((~old(lucy)|~patient(lucy))))&
(![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]:((generous(X)<~>~tall(X))<=>(happy(X)|~tall(X))))&
(![X]:((~funny(X)|~wise(X))=>(~calm(X)|happy(X))))&
((?[X]:((old(X)&calm(X))))<=>(~creative(susan)))&
(![X]:(~humble(X)=>(~strong(X)<~>~humble(X))))&
((?[X]:(curious(X)))=>(?[X]:((~strong(X)<~>curious(X)))))&
((~generous(susan))<=>(?[X]:((creative(X)<~>tall(X)))))&
(?[X]:((~creative(X)|generous(X))))&
(?[X]:(~happy(X)))&
(?[X]:(~kind(X)))&
((~curious(fred)<~>~wise(fred)))&
(?[X]:((~funny(X)|~wise(X))))&
((~funny(lucy)&strong(lucy)))&
(?[X]:((~quiet(X)&creative(X))))&
(?[X]:((tall(X)|~curious(X)))) | curious(lucy) | [] | null | 0 |
If mary is not funny or not strong then someone is either not creative or rich.
Everyone who is generous is either not kind or brave.
If paul is both creative and not rich then fred is both creative and curious and vice versa.
If someone is not patient or old then someone is either tall or not patient and vice versa.
Everyone who is not old or not happy is not tall and vice versa.
If susan is not old or generous then someone is not funny.
Everyone who is both not happy and not funny is not happy and vice versa.
Everyone who is either not curious or happy is either not calm or rich and vice versa.
Everyone who is humble or old is either patient or old.
If lucy is both wise and not quiet then lucy is either quiet or not brave and vice versa.
Everyone who is not kind or not quiet is both patient and not creative and vice versa.
Everyone who is rich is both humble and not happy and vice versa.
Everyone who is not funny or not tall is rich and vice versa.
If susan is not brave or not patient then susan is not happy or not quiet.
Everyone who is happy is funny.
If susan is not quiet or creative then paul is both not tall and curious.
Someone is not kind or creative.
Someone is both happy and brave.
Someone is both not tall and kind.
Someone is tall or not kind.
Mary is wise.
Someone is curious.
Alice is either not rich or calm.
Paul is patient. | Susan is rich. | entailment | (((~funny(mary)|~strong(mary)))=>(?[X]:((~creative(X)<~>rich(X)))))&
(![X]:(generous(X)=>(~kind(X)<~>brave(X))))&
(((creative(paul)&~rich(paul)))<=>((creative(fred)&curious(fred))))&
((?[X]:((~patient(X)|old(X))))<=>(?[X]:((tall(X)<~>~patient(X)))))&
(![X]:((~old(X)|~happy(X))<=>~tall(X)))&
(((~old(susan)|generous(susan)))=>(?[X]:(~funny(X))))&
(![X]:((~happy(X)&~funny(X))<=>~happy(X)))&
(![X]:((~curious(X)<~>happy(X))<=>(~calm(X)<~>rich(X))))&
(![X]:((humble(X)|old(X))=>(patient(X)<~>old(X))))&
(((wise(lucy)&~quiet(lucy)))<=>((quiet(lucy)<~>~brave(lucy))))&
(![X]:((~kind(X)|~quiet(X))<=>(patient(X)&~creative(X))))&
(![X]:(rich(X)<=>(humble(X)&~happy(X))))&
(![X]:((~funny(X)|~tall(X))<=>rich(X)))&
(((~brave(susan)|~patient(susan)))=>((~happy(susan)|~quiet(susan))))&
(![X]:(happy(X)=>funny(X)))&
(((~quiet(susan)|creative(susan)))=>((~tall(paul)&curious(paul))))&
(?[X]:((~kind(X)|creative(X))))&
(?[X]:((happy(X)&brave(X))))&
(?[X]:((~tall(X)&kind(X))))&
(?[X]:((tall(X)|~kind(X))))&
(wise(mary))&
(?[X]:(curious(X)))&
((~rich(alice)<~>calm(alice)))&
(patient(paul)) | rich(susan) | [
"p4",
"p6",
"p8",
"p10",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 3091268813147733632172180
% SZS output start Proof for 3091268813147733632172180
5. ! [X0] : ((~happy(X0) | ~old(X0)) <=> ~tall(X0)) [input p4]
7. ! [X0] : ((~funny(X0) & ~happy(X0)) <=> ~happy(X0)) [input p6]
9. ! [X0] : ((old(X0) | humble(X0)) => (patient(X0) <~> old(X0))) [input p8]
11. ! [X0] : ((~quiet(X0) | ~kind(X0)) <=> (~creative(X0) & patient(X0))) [input p10]
13. ! [X0] : ((~tall(X0) | ~funny(X0)) <=> rich(X0)) [input p12]
14. (~patient(susan) | ~brave(susan)) => (~quiet(susan) | ~happy(susan)) [input p13]
25. ~rich(susan) [input hypothesis]
32. ! [X0] : ((patient(X0) <~> old(X0)) | (~old(X0) & ~humble(X0))) [ennf transformation 9]
33. (~quiet(susan) | ~happy(susan)) | (patient(susan) & brave(susan)) [ennf transformation 14]
34. ~quiet(susan) | ~happy(susan) | (patient(susan) & brave(susan)) [flattening 33]
47. ! [X0] : (((~happy(X0) | ~old(X0)) | tall(X0)) & (~tall(X0) | (happy(X0) & old(X0)))) [nnf transformation 5]
48. ! [X0] : ((~happy(X0) | ~old(X0) | tall(X0)) & (~tall(X0) | (happy(X0) & old(X0)))) [flattening 47]
51. ! [X0] : (((~funny(X0) & ~happy(X0)) | happy(X0)) & (~happy(X0) | (funny(X0) | happy(X0)))) [nnf transformation 7]
52. ! [X0] : (((~funny(X0) & ~happy(X0)) | happy(X0)) & (~happy(X0) | funny(X0) | happy(X0))) [flattening 51]
54. ! [X0] : (((~old(X0) | ~patient(X0)) & (old(X0) | patient(X0))) | (~old(X0) & ~humble(X0))) [nnf transformation 32]
57. ! [X0] : (((~quiet(X0) | ~kind(X0)) | (creative(X0) | ~patient(X0))) & ((~creative(X0) & patient(X0)) | (quiet(X0) & kind(X0)))) [nnf transformation 11]
58. ! [X0] : ((~quiet(X0) | ~kind(X0) | creative(X0) | ~patient(X0)) & ((~creative(X0) & patient(X0)) | (quiet(X0) & kind(X0)))) [flattening 57]
61. ! [X0] : (((~tall(X0) | ~funny(X0)) | ~rich(X0)) & (rich(X0) | (tall(X0) & funny(X0)))) [nnf transformation 13]
62. ! [X0] : ((~tall(X0) | ~funny(X0) | ~rich(X0)) & (rich(X0) | (tall(X0) & funny(X0)))) [flattening 61]
86. ~tall(X0) | old(X0) [cnf transformation 48]
92. ~funny(X0) | happy(X0) [cnf transformation 52]
104. ~old(X0) | ~patient(X0) | ~old(X0) [cnf transformation 54]
112. quiet(X0) | patient(X0) [cnf transformation 58]
119. rich(X0) | funny(X0) [cnf transformation 62]
120. tall(X0) | rich(X0) [cnf transformation 62]
123. ~quiet(susan) | ~happy(susan) | patient(susan) [cnf transformation 34]
140. ~rich(susan) [cnf transformation 25]
143. ~old(X0) | ~patient(X0) [duplicate literal removal 104]
213. 16 <=> old(susan) [avatar definition]
214. ~old(susan) <- (~16) [avatar component clause 213]
215. old(susan) <- (16) [avatar component clause 213]
237. ~happy(susan) | patient(susan) [subsumption resolution 123,112]
239. 21 <=> patient(susan) [avatar definition]
241. patient(susan) <- (21) [avatar component clause 239]
243. 22 <=> happy(susan) [avatar definition]
246. 21 | ~22 [avatar split clause 237,243,239]
305. funny(susan) [resolution 119,140]
309. happy(susan) [resolution 305,92]
312. 22 [avatar split clause 309,243]
318. old(X1) | rich(X1) [resolution 120,86]
525. rich(susan) <- (~16) [resolution 318,214]
527. $false <- (~16) [subsumption resolution 525,140]
528. 16 [avatar contradiction clause 527]
531. ~patient(susan) <- (16) [resolution 215,143]
532. $false <- (16, 21) [subsumption resolution 531,241]
533. ~16 | ~21 [avatar contradiction clause 532]
534. $false [avatar sat refutation 246,312,528,533]
% SZS output end Proof for 3091268813147733632172180
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong or calm is not patient and vice versa.
Everyone who is either rich or not creative is curious and vice versa.
Everyone who is either old or curious is either happy or not strong.
Everyone who is both brave and strong is either happy or not strong and vice versa.
Everyone who is not strong or tall is both old and generous and vice versa.
Everyone who is generous is not kind.
Everyone who is either old or quiet is not patient.
If someone is either curious or not happy then someone is generous.
Everyone who is either not calm or rich is not brave or not creative and vice versa.
Everyone who is funny or not creative is creative or generous and vice versa.
Everyone who is happy or brave is both brave and not funny.
If someone is calm or not generous then someone is either patient or creative and vice versa.
Everyone who is either happy or kind is both not wise and patient.
If john is not strong or quiet then john is both quiet and happy.
Everyone who is both calm and happy is either old or humble and vice versa.
Someone is not funny or not wise.
Someone is not strong or humble. | John is humble. | neutral | (![X]:((~strong(X)|calm(X))<=>~patient(X)))&
(![X]:((rich(X)<~>~creative(X))<=>curious(X)))&
(![X]:((old(X)<~>curious(X))=>(happy(X)<~>~strong(X))))&
(![X]:((brave(X)&strong(X))<=>(happy(X)<~>~strong(X))))&
(![X]:((~strong(X)|tall(X))<=>(old(X)&generous(X))))&
(![X]:(generous(X)=>~kind(X)))&
(![X]:((old(X)<~>quiet(X))=>~patient(X)))&
((?[X]:((curious(X)<~>~happy(X))))=>(?[X]:(generous(X))))&
(![X]:((~calm(X)<~>rich(X))<=>(~brave(X)|~creative(X))))&
(![X]:((funny(X)|~creative(X))<=>(creative(X)|generous(X))))&
(![X]:((happy(X)|brave(X))=>(brave(X)&~funny(X))))&
((?[X]:((calm(X)|~generous(X))))<=>(?[X]:((patient(X)<~>creative(X)))))&
(![X]:((happy(X)<~>kind(X))=>(~wise(X)&patient(X))))&
(((~strong(john)|quiet(john)))=>((quiet(john)&happy(john))))&
(![X]:((calm(X)&happy(X))<=>(old(X)<~>humble(X))))&
(?[X]:((~funny(X)|~wise(X))))&
(?[X]:((~strong(X)|humble(X)))) | humble(john) | [] | null | 0 |
Everyone who is not wise is strong or not quiet and vice versa.
Everyone who is both happy and not calm is not funny or strong.
If alice is not creative or old then paul is patient and vice versa.
Everyone who is either not generous or creative is not strong and vice versa.
If alice is not brave then someone is either calm or not patient.
Everyone who is not creative or rich is not humble or quiet.
Everyone who is funny is either creative or patient and vice versa.
Everyone who is both not curious and not happy is not calm.
Everyone who is not generous or funny is not wise or not humble and vice versa.
Everyone who is either strong or not funny is both calm and not generous.
Everyone who is either not tall or not wise is either humble or not patient and vice versa.
Everyone who is not kind or happy is generous or not kind.
Everyone who is either not calm or not old is both not old and not tall and vice versa.
Everyone who is both not calm and not old is wise or brave and vice versa.
Everyone who is both not quiet and not generous is either not rich or not calm and vice versa.
Everyone who is not funny is both curious and calm.
Someone is not quiet or strong.
John is either kind or not creative.
Someone is old or patient.
Susan is happy.
Someone is both not rich and not calm.
Someone is both not brave and generous.
Lucy is not brave.
Someone is either not happy or brave. | Alice is not strong. | neutral | (![X]:(~wise(X)<=>(strong(X)|~quiet(X))))&
(![X]:((happy(X)&~calm(X))=>(~funny(X)|strong(X))))&
(((~creative(alice)|old(alice)))<=>(patient(paul)))&
(![X]:((~generous(X)<~>creative(X))<=>~strong(X)))&
((~brave(alice))=>(?[X]:((calm(X)<~>~patient(X)))))&
(![X]:((~creative(X)|rich(X))=>(~humble(X)|quiet(X))))&
(![X]:(funny(X)<=>(creative(X)<~>patient(X))))&
(![X]:((~curious(X)&~happy(X))=>~calm(X)))&
(![X]:((~generous(X)|funny(X))<=>(~wise(X)|~humble(X))))&
(![X]:((strong(X)<~>~funny(X))=>(calm(X)&~generous(X))))&
(![X]:((~tall(X)<~>~wise(X))<=>(humble(X)<~>~patient(X))))&
(![X]:((~kind(X)|happy(X))=>(generous(X)|~kind(X))))&
(![X]:((~calm(X)<~>~old(X))<=>(~old(X)&~tall(X))))&
(![X]:((~calm(X)&~old(X))<=>(wise(X)|brave(X))))&
(![X]:((~quiet(X)&~generous(X))<=>(~rich(X)<~>~calm(X))))&
(![X]:(~funny(X)=>(curious(X)&calm(X))))&
(?[X]:((~quiet(X)|strong(X))))&
((kind(john)<~>~creative(john)))&
(?[X]:((old(X)|patient(X))))&
(happy(susan))&
(?[X]:((~rich(X)&~calm(X))))&
(?[X]:((~brave(X)&generous(X))))&
(~brave(lucy))&
(?[X]:((~happy(X)<~>brave(X)))) | ~strong(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 738614193066481519555856
% SZS output start Proof for 738614193066481519555856
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 738614193066481519555856
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy is either not quiet or generous and vice versa.
Everyone who is either old or not brave is not humble or patient.
Everyone who is either not strong or not humble is either wise or not happy.
Everyone who is both kind and patient is quiet and vice versa.
Everyone who is either not funny or not rich is not wise or not creative.
Everyone who is curious or brave is both generous and not happy and vice versa.
Everyone who is either not brave or generous is rich or calm.
Everyone who is wise is not creative or not rich and vice versa.
If alice is not quiet or not wise then fred is either not tall or not humble.
Everyone who is brave is not wise.
Everyone who is both not creative and not rich is either happy or not old.
Everyone who is either not humble or brave is creative.
If lucy is either happy or curious then someone is not funny or funny.
Everyone who is both rich and generous is either generous or quiet and vice versa.
If paul is either brave or not quiet then alice is either rich or strong and vice versa.
If alice is either tall or not wise then paul is not generous or not humble.
Someone is patient or creative.
Alice is funny.
Someone is both not brave and creative.
Someone is not old or not strong.
Someone is both not brave and rich.
Paul is humble or patient.
Someone is happy.
Someone is either not humble or not curious. | Lucy is not curious. | neutral | (![X]:(happy(X)<=>(~quiet(X)<~>generous(X))))&
(![X]:((old(X)<~>~brave(X))=>(~humble(X)|patient(X))))&
(![X]:((~strong(X)<~>~humble(X))=>(wise(X)<~>~happy(X))))&
(![X]:((kind(X)&patient(X))<=>quiet(X)))&
(![X]:((~funny(X)<~>~rich(X))=>(~wise(X)|~creative(X))))&
(![X]:((curious(X)|brave(X))<=>(generous(X)&~happy(X))))&
(![X]:((~brave(X)<~>generous(X))=>(rich(X)|calm(X))))&
(![X]:(wise(X)<=>(~creative(X)|~rich(X))))&
(((~quiet(alice)|~wise(alice)))=>((~tall(fred)<~>~humble(fred))))&
(![X]:(brave(X)=>~wise(X)))&
(![X]:((~creative(X)&~rich(X))=>(happy(X)<~>~old(X))))&
(![X]:((~humble(X)<~>brave(X))=>creative(X)))&
(((happy(lucy)<~>curious(lucy)))=>(?[X]:((~funny(X)|funny(X)))))&
(![X]:((rich(X)&generous(X))<=>(generous(X)<~>quiet(X))))&
(((brave(paul)<~>~quiet(paul)))<=>((rich(alice)<~>strong(alice))))&
(((tall(alice)<~>~wise(alice)))=>((~generous(paul)|~humble(paul))))&
(?[X]:((patient(X)|creative(X))))&
(funny(alice))&
(?[X]:((~brave(X)&creative(X))))&
(?[X]:((~old(X)|~strong(X))))&
(?[X]:((~brave(X)&rich(X))))&
((humble(paul)|patient(paul)))&
(?[X]:(happy(X)))&
(?[X]:((~humble(X)<~>~curious(X)))) | ~curious(lucy) | [] | null | 0 |
Everyone who is curious or not brave is brave.
If fred is generous or not happy then paul is both wise and not brave.
Everyone who is both strong and not curious is not brave.
If someone is quiet or not patient then someone is either not kind or not funny.
If alice is not rich then someone is both not happy and funny.
Everyone who is not strong is both curious and not patient.
Everyone who is not funny or not tall is either not generous or funny.
If someone is not brave or not funny then someone is either not humble or brave.
If susan is not old then someone is kind or wise.
If mary is either not rich or wise then someone is either patient or funny.
If fred is humble or creative then someone is wise and vice versa.
If fred is both patient and generous then someone is not happy and vice versa.
If susan is either quiet or tall then someone is brave or not humble and vice versa.
Everyone who is either funny or generous is creative or not creative.
If someone is either not funny or not curious then someone is both calm and not curious and vice versa.
Everyone who is quiet is both strong and not creative.
Paul is both not quiet and patient.
Someone is either not curious or not quiet.
Lucy is both not patient and not rich.
Someone is not funny or funny.
Someone is brave.
Paul is happy.
Fred is either not old or not brave.
Someone is both not calm and happy. | Fred is not happy. | contradiction | (![X]:((curious(X)|~brave(X))=>brave(X)))&
(((generous(fred)|~happy(fred)))=>((wise(paul)&~brave(paul))))&
(![X]:((strong(X)&~curious(X))=>~brave(X)))&
((?[X]:((quiet(X)|~patient(X))))=>(?[X]:((~kind(X)<~>~funny(X)))))&
((~rich(alice))=>(?[X]:((~happy(X)&funny(X)))))&
(![X]:(~strong(X)=>(curious(X)&~patient(X))))&
(![X]:((~funny(X)|~tall(X))=>(~generous(X)<~>funny(X))))&
((?[X]:((~brave(X)|~funny(X))))=>(?[X]:((~humble(X)<~>brave(X)))))&
((~old(susan))=>(?[X]:((kind(X)|wise(X)))))&
(((~rich(mary)<~>wise(mary)))=>(?[X]:((patient(X)<~>funny(X)))))&
(((humble(fred)|creative(fred)))<=>(?[X]:(wise(X))))&
(((patient(fred)&generous(fred)))<=>(?[X]:(~happy(X))))&
(((quiet(susan)<~>tall(susan)))<=>(?[X]:((brave(X)|~humble(X)))))&
(![X]:((funny(X)<~>generous(X))=>(creative(X)|~creative(X))))&
((?[X]:((~funny(X)<~>~curious(X))))<=>(?[X]:((calm(X)&~curious(X)))))&
(![X]:(quiet(X)=>(strong(X)&~creative(X))))&
((~quiet(paul)&patient(paul)))&
(?[X]:((~curious(X)<~>~quiet(X))))&
((~patient(lucy)&~rich(lucy)))&
(?[X]:((~funny(X)|funny(X))))&
(?[X]:(brave(X)))&
(happy(paul))&
((~old(fred)<~>~brave(fred)))&
(?[X]:((~calm(X)&happy(X)))) | ~happy(fred) | [
"p0",
"p1",
"hypothesis"
] | % SZS status Unsatisfiable for 202922219539103527568660
% SZS output start Proof for 202922219539103527568660
1. ! [X0] : ((~brave(X0) | curious(X0)) => brave(X0)) [input p0]
2. (~happy(fred) | generous(fred)) => (~brave(paul) & wise(paul)) [input p1]
25. ~happy(fred) [input hypothesis]
29. ! [X0] : (brave(X0) | (brave(X0) & ~curious(X0))) [ennf transformation 1]
30. (~brave(paul) & wise(paul)) | (happy(fred) & ~generous(fred)) [ennf transformation 2]
90. brave(X0) | brave(X0) [cnf transformation 29]
94. ~brave(paul) | happy(fred) [cnf transformation 30]
152. ~happy(fred) [cnf transformation 25]
154. brave(X0) [duplicate literal removal 90]
155. happy(fred) [subsumption resolution 94,154]
280. $false [subsumption resolution 152,155]
% SZS output end Proof for 202922219539103527568660
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny or not brave then susan is both not generous and not wise. If mary is both tall and curious then someone is funny. If mary is not kind or not funny then someone is either not wise or creative and vice versa. Everyone who is wise is creative or kind and vice versa. If someone is not kind or curious then someone is both humble and not patient and vice versa. Everyone who is either not curious or rich is not rich. Everyone who is humble is not creative. Everyone who is not happy or not humble is either not rich or tall. If someone is not humble then someone is either not brave or not curious and vice versa. Everyone who is both not rich and rich is not curious. Everyone who is both humble and not calm is both calm and brave. If lucy is both not brave and creative then someone is curious or old. If someone is not wise then fred is both not kind and curious and vice versa. Everyone who is not humble is curious and vice versa. If lucy is either generous or not tall then alice is either funny or quiet. If someone is either old or not wise then alice is not rich or not funny. Someone is either not quiet or wise. Someone is either not old or brave. Someone is not quiet or rich. Someone is not curious or tall. Someone is both humble and not creative. Fred is either creative or not generous. Someone is not rich or humble. Lucy is brave. | Susan is wise. | neutral | ((?[X]:((funny(X)|~brave(X))))=>((~generous(susan)&~wise(susan))))&
(((tall(mary)&curious(mary)))=>(?[X]:(funny(X))))&
(((~kind(mary)|~funny(mary)))<=>(?[X]:((~wise(X)<~>creative(X)))))&
(![X]:(wise(X)<=>(creative(X)|kind(X))))&
((?[X]:((~kind(X)|curious(X))))<=>(?[X]:((humble(X)&~patient(X)))))&
(![X]:((~curious(X)<~>rich(X))=>~rich(X)))&
(![X]:(humble(X)=>~creative(X)))&
(![X]:((~happy(X)|~humble(X))=>(~rich(X)<~>tall(X))))&
((?[X]:(~humble(X)))<=>(?[X]:((~brave(X)<~>~curious(X)))))&
(![X]:((~rich(X)&rich(X))=>~curious(X)))&
(![X]:((humble(X)&~calm(X))=>(calm(X)&brave(X))))&
(((~brave(lucy)&creative(lucy)))=>(?[X]:((curious(X)|old(X)))))&
((?[X]:(~wise(X)))<=>((~kind(fred)&curious(fred))))&
(![X]:(~humble(X)<=>curious(X)))&
(((generous(lucy)<~>~tall(lucy)))=>((funny(alice)<~>quiet(alice))))&
((?[X]:((old(X)<~>~wise(X))))=>((~rich(alice)|~funny(alice))))&
(?[X]:((~quiet(X)<~>wise(X))))&
(?[X]:((~old(X)<~>brave(X))))&
(?[X]:((~quiet(X)|rich(X))))&
(?[X]:((~curious(X)|tall(X))))&
(?[X]:((humble(X)&~creative(X))))&
((creative(fred)<~>~generous(fred)))&
(?[X]:((~rich(X)|humble(X))))&
(brave(lucy)) | wise(susan) | [] | null | 0 |
If mary is old or not quiet then susan is patient or kind and vice versa.
Everyone who is not humble is both not creative and not old and vice versa.
Everyone who is both quiet and happy is both not creative and old.
Everyone who is both not old and brave is both calm and not wise and vice versa.
Everyone who is humble or not rich is either not tall or calm and vice versa.
Everyone who is not kind is either strong or not happy.
If someone is tall or not funny then lucy is not humble and vice versa.
Everyone who is happy is both not patient and not brave and vice versa.
Everyone who is generous is not curious and vice versa.
If fred is patient then someone is either not old or not strong and vice versa.
If lucy is not funny or calm then susan is kind or not happy.
If someone is brave or quiet then someone is both patient and kind and vice versa.
If fred is funny then someone is not strong.
Everyone who is either not old or kind is both not patient and old.
If someone is creative or not wise then paul is both calm and not creative and vice versa.
If susan is humble or generous then mary is both not rich and not humble and vice versa.
Susan is both happy and not generous.
Mary is both old and generous.
Someone is not brave.
Someone is humble or not tall.
Someone is both not creative and not kind.
Someone is calm or happy.
Lucy is tall. | Susan is generous. | contradiction | (((old(mary)|~quiet(mary)))<=>((patient(susan)|kind(susan))))&
(![X]:(~humble(X)<=>(~creative(X)&~old(X))))&
(![X]:((quiet(X)&happy(X))=>(~creative(X)&old(X))))&
(![X]:((~old(X)&brave(X))<=>(calm(X)&~wise(X))))&
(![X]:((humble(X)|~rich(X))<=>(~tall(X)<~>calm(X))))&
(![X]:(~kind(X)=>(strong(X)<~>~happy(X))))&
((?[X]:((tall(X)|~funny(X))))<=>(~humble(lucy)))&
(![X]:(happy(X)<=>(~patient(X)&~brave(X))))&
(![X]:(generous(X)<=>~curious(X)))&
((patient(fred))<=>(?[X]:((~old(X)<~>~strong(X)))))&
(((~funny(lucy)|calm(lucy)))=>((kind(susan)|~happy(susan))))&
((?[X]:((brave(X)|quiet(X))))<=>(?[X]:((patient(X)&kind(X)))))&
((funny(fred))=>(?[X]:(~strong(X))))&
(![X]:((~old(X)<~>kind(X))=>(~patient(X)&old(X))))&
((?[X]:((creative(X)|~wise(X))))<=>((calm(paul)&~creative(paul))))&
(((humble(susan)|generous(susan)))<=>((~rich(mary)&~humble(mary))))&
((happy(susan)&~generous(susan)))&
((old(mary)&generous(mary)))&
(?[X]:(~brave(X)))&
(?[X]:((humble(X)|~tall(X))))&
(?[X]:((~creative(X)&~kind(X))))&
(?[X]:((calm(X)|happy(X))))&
(tall(lucy)) | generous(susan) | [
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 330719723313200688428528
% SZS output start Proof for 330719723313200688428528
17. ~generous(susan) & happy(susan) [input p16]
24. generous(susan) [input hypothesis]
132. ~generous(susan) [cnf transformation 17]
141. generous(susan) [cnf transformation 24]
299. 36 <=> generous(susan) [avatar definition]
307. ~36 [avatar split clause 132,299]
328. 36 [avatar split clause 141,299]
329. $false [avatar sat refutation 307,328]
% SZS output end Proof for 330719723313200688428528
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is generous or curious is either not brave or old and vice versa.
Everyone who is both strong and not creative is not happy or happy and vice versa.
Everyone who is both not patient and not calm is strong or tall.
Everyone who is curious is strong.
Everyone who is patient or not strong is curious and vice versa.
If lucy is not quiet then john is either old or quiet.
Everyone who is not creative is either not strong or not humble.
If someone is not funny or not brave then someone is either tall or strong and vice versa.
If someone is both not funny and not tall then someone is not wise.
Everyone who is both not generous and strong is patient and vice versa.
If someone is curious then someone is happy.
If someone is both not wise and strong then someone is either not funny or not creative and vice versa.
If someone is generous then someone is both tall and kind.
If someone is generous or not strong then someone is not creative or not humble.
If mary is both curious and not creative then someone is not generous or not happy and vice versa.
Everyone who is funny is strong and vice versa.
John is not tall or not humble.
Paul is old or kind.
Someone is either brave or generous.
Mary is both not curious and kind.
Someone is happy.
Someone is wise or curious.
Lucy is either not happy or not calm. | John is not happy. | contradiction | (![X]:((generous(X)|curious(X))<=>(~brave(X)<~>old(X))))&
(![X]:((strong(X)&~creative(X))<=>(~happy(X)|happy(X))))&
(![X]:((~patient(X)&~calm(X))=>(strong(X)|tall(X))))&
(![X]:(curious(X)=>strong(X)))&
(![X]:((patient(X)|~strong(X))<=>curious(X)))&
((~quiet(lucy))=>((old(john)<~>quiet(john))))&
(![X]:(~creative(X)=>(~strong(X)<~>~humble(X))))&
((?[X]:((~funny(X)|~brave(X))))<=>(?[X]:((tall(X)<~>strong(X)))))&
((?[X]:((~funny(X)&~tall(X))))=>(?[X]:(~wise(X))))&
(![X]:((~generous(X)&strong(X))<=>patient(X)))&
((?[X]:(curious(X)))=>(?[X]:(happy(X))))&
((?[X]:((~wise(X)&strong(X))))<=>(?[X]:((~funny(X)<~>~creative(X)))))&
((?[X]:(generous(X)))=>(?[X]:((tall(X)&kind(X)))))&
((?[X]:((generous(X)|~strong(X))))=>(?[X]:((~creative(X)|~humble(X)))))&
(((curious(mary)&~creative(mary)))<=>(?[X]:((~generous(X)|~happy(X)))))&
(![X]:(funny(X)<=>strong(X)))&
((~tall(john)|~humble(john)))&
((old(paul)|kind(paul)))&
(?[X]:((brave(X)<~>generous(X))))&
((~curious(mary)&kind(mary)))&
(?[X]:(happy(X)))&
(?[X]:((wise(X)|curious(X))))&
((~happy(lucy)<~>~calm(lucy))) | ~happy(john) | [
"p14",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 1063006174438147243449803
% SZS output start Proof for 1063006174438147243449803
15. (~creative(mary) & curious(mary)) <=> ? [X0] : (~happy(X0) | ~generous(X0)) [input p14]
20. kind(mary) & ~curious(mary) [input p19]
24. ~happy(john) [input hypothesis]
33. ~curious(mary) [pure predicate removal 20]
75. ((~creative(mary) & curious(mary)) | ! [X0] : (happy(X0) & generous(X0))) & (? [X0] : (~happy(X0) | ~generous(X0)) | (creative(mary) | ~curious(mary))) [nnf transformation 15]
76. ((~creative(mary) & curious(mary)) | ! [X0] : (happy(X0) & generous(X0))) & (? [X0] : (~happy(X0) | ~generous(X0)) | creative(mary) | ~curious(mary)) [flattening 75]
77. ((~creative(mary) & curious(mary)) | ! [X0] : (happy(X0) & generous(X0))) & (? [X1] : (~happy(X1) | ~generous(X1)) | creative(mary) | ~curious(mary)) [rectify 76]
78. ? [X1] : (~happy(X1) | ~generous(X1)) => (~happy(sK8) | ~generous(sK8)) [choice axiom]
79. ((~creative(mary) & curious(mary)) | ! [X0] : (happy(X0) & generous(X0))) & ((~happy(sK8) | ~generous(sK8)) | creative(mary) | ~curious(mary)) [skolemisation 77,78]
131. curious(mary) | happy(X0) [cnf transformation 79]
139. ~curious(mary) [cnf transformation 33]
144. ~happy(john) [cnf transformation 24]
236. 20 <=> ! [X0] : happy(X0) [avatar definition]
237. happy(X0) <- (20) [avatar component clause 236]
239. 21 <=> curious(mary) [avatar definition]
242. 20 | 21 [avatar split clause 131,239,236]
269. ~21 [avatar split clause 139,239]
297. $false <- (20) [resolution 237,144]
298. ~20 [avatar contradiction clause 297]
299. $false [avatar sat refutation 242,269,298]
% SZS output end Proof for 1063006174438147243449803
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not quiet or not tall then someone is both not creative and not tall.
Everyone who is either not strong or creative is strong and vice versa.
If john is both not humble and tall then lucy is not quiet.
If someone is not rich then paul is either not brave or not humble.
Everyone who is happy is not curious.
If susan is either wise or tall then alice is both not humble and not funny and vice versa.
Everyone who is either not funny or not quiet is curious or not tall and vice versa.
Everyone who is both not calm and strong is both not strong and quiet and vice versa.
If paul is funny then someone is not happy or not creative.
If fred is either kind or brave then someone is not strong or not tall.
Everyone who is either not old or not wise is both not curious and old and vice versa.
If someone is both brave and kind then susan is either tall or not funny.
Everyone who is creative or generous is brave.
If paul is either old or wise then someone is either creative or calm and vice versa.
If someone is both generous and not strong then john is both strong and quiet and vice versa.
Everyone who is strong is not humble and vice versa.
John is not generous or quiet.
Someone is either brave or patient.
Alice is generous or patient.
Someone is quiet or not strong.
Someone is not rich.
John is both not calm and kind.
Mary is calm. | Alice is not humble. | entailment | ((?[X]:((~quiet(X)<~>~tall(X))))=>(?[X]:((~creative(X)&~tall(X)))))&
(![X]:((~strong(X)<~>creative(X))<=>strong(X)))&
(((~humble(john)&tall(john)))=>(~quiet(lucy)))&
((?[X]:(~rich(X)))=>((~brave(paul)<~>~humble(paul))))&
(![X]:(happy(X)=>~curious(X)))&
(((wise(susan)<~>tall(susan)))<=>((~humble(alice)&~funny(alice))))&
(![X]:((~funny(X)<~>~quiet(X))<=>(curious(X)|~tall(X))))&
(![X]:((~calm(X)&strong(X))<=>(~strong(X)&quiet(X))))&
((funny(paul))=>(?[X]:((~happy(X)|~creative(X)))))&
(((kind(fred)<~>brave(fred)))=>(?[X]:((~strong(X)|~tall(X)))))&
(![X]:((~old(X)<~>~wise(X))<=>(~curious(X)&old(X))))&
((?[X]:((brave(X)&kind(X))))=>((tall(susan)<~>~funny(susan))))&
(![X]:((creative(X)|generous(X))=>brave(X)))&
(((old(paul)<~>wise(paul)))<=>(?[X]:((creative(X)<~>calm(X)))))&
((?[X]:((generous(X)&~strong(X))))<=>((strong(john)&quiet(john))))&
(![X]:(strong(X)<=>~humble(X)))&
((~generous(john)|quiet(john)))&
(?[X]:((brave(X)<~>patient(X))))&
((generous(alice)|patient(alice)))&
(?[X]:((quiet(X)|~strong(X))))&
(?[X]:(~rich(X)))&
((~calm(john)&kind(john)))&
(calm(mary)) | ~humble(alice) | [
"p0",
"p1",
"p5",
"p6",
"p10",
"p11",
"p12",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 1740817977037929104772414
% SZS output start Proof for 1740817977037929104772414
1. ? [X0] : (~quiet(X0) <~> ~tall(X0)) => ? [X0] : (~tall(X0) & ~creative(X0)) [input p0]
2. ! [X0] : ((~strong(X0) <~> creative(X0)) <=> strong(X0)) [input p1]
6. (wise(susan) <~> tall(susan)) <=> (~funny(alice) & ~humble(alice)) [input p5]
7. ! [X0] : ((~funny(X0) <~> ~quiet(X0)) <=> (~tall(X0) | curious(X0))) [input p6]
11. ! [X0] : ((~old(X0) <~> ~wise(X0)) <=> (old(X0) & ~curious(X0))) [input p10]
12. ? [X0] : (kind(X0) & brave(X0)) => (tall(susan) <~> ~funny(susan)) [input p11]
13. ! [X0] : ((generous(X0) | creative(X0)) => brave(X0)) [input p12]
22. kind(john) & ~calm(john) [input p21]
24. humble(alice) [input hypothesis]
25. ? [X0] : (~quiet(X0) <~> ~tall(X0)) => ? [X1] : (~tall(X1) & ~creative(X1)) [rectify 1]
28. ? [X1] : (~tall(X1) & ~creative(X1)) | ! [X0] : (~quiet(X0) <=> ~tall(X0)) [ennf transformation 25]
33. (tall(susan) <~> ~funny(susan)) | ! [X0] : (~kind(X0) | ~brave(X0)) [ennf transformation 12]
34. ! [X0] : (brave(X0) | (~generous(X0) & ~creative(X0))) [ennf transformation 13]
35. ? [X1] : (~tall(X1) & ~creative(X1)) | ! [X0] : ((~quiet(X0) | tall(X0)) & (~tall(X0) | quiet(X0))) [nnf transformation 28]
36. ? [X0] : (~tall(X0) & ~creative(X0)) | ! [X1] : ((~quiet(X1) | tall(X1)) & (~tall(X1) | quiet(X1))) [rectify 35]
37. ? [X0] : (~tall(X0) & ~creative(X0)) => (~tall(sK0) & ~creative(sK0)) [choice axiom]
38. (~tall(sK0) & ~creative(sK0)) | ! [X1] : ((~quiet(X1) | tall(X1)) & (~tall(X1) | quiet(X1))) [skolemisation 36,37]
39. ! [X0] : ((((~creative(X0) | strong(X0)) & (creative(X0) | ~strong(X0))) | ~strong(X0)) & (strong(X0) | ((~strong(X0) | ~creative(X0)) & (creative(X0) | strong(X0))))) [nnf transformation 2]
41. (((~tall(susan) | ~wise(susan)) & (tall(susan) | wise(susan))) | (funny(alice) | humble(alice))) & ((~funny(alice) & ~humble(alice)) | ((wise(susan) | ~tall(susan)) & (tall(susan) | ~wise(susan)))) [nnf transformation 6]
42. (((~tall(susan) | ~wise(susan)) & (tall(susan) | wise(susan))) | funny(alice) | humble(alice)) & ((~funny(alice) & ~humble(alice)) | ((wise(susan) | ~tall(susan)) & (tall(susan) | ~wise(susan)))) [flattening 41]
43. ! [X0] : ((((quiet(X0) | funny(X0)) & (~quiet(X0) | ~funny(X0))) | (tall(X0) & ~curious(X0))) & ((~tall(X0) | curious(X0)) | ((~funny(X0) | quiet(X0)) & (~quiet(X0) | funny(X0))))) [nnf transformation 7]
44. ! [X0] : ((((quiet(X0) | funny(X0)) & (~quiet(X0) | ~funny(X0))) | (tall(X0) & ~curious(X0))) & (~tall(X0) | curious(X0) | ((~funny(X0) | quiet(X0)) & (~quiet(X0) | funny(X0))))) [flattening 43]
50. ! [X0] : ((((wise(X0) | old(X0)) & (~wise(X0) | ~old(X0))) | (~old(X0) | curious(X0))) & ((old(X0) & ~curious(X0)) | ((~old(X0) | wise(X0)) & (~wise(X0) | old(X0))))) [nnf transformation 11]
51. ! [X0] : ((((wise(X0) | old(X0)) & (~wise(X0) | ~old(X0))) | ~old(X0) | curious(X0)) & ((old(X0) & ~curious(X0)) | ((~old(X0) | wise(X0)) & (~wise(X0) | old(X0))))) [flattening 50]
52. ((funny(susan) | ~tall(susan)) & (~funny(susan) | tall(susan))) | ! [X0] : (~kind(X0) | ~brave(X0)) [nnf transformation 33]
70. ~creative(sK0) | ~tall(X1) | quiet(X1) [cnf transformation 38]
71. ~creative(sK0) | ~quiet(X1) | tall(X1) [cnf transformation 38]
74. strong(X0) | creative(X0) | strong(X0) [cnf transformation 39]
76. creative(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 39]
82. ~humble(alice) | wise(susan) | ~tall(susan) [cnf transformation 42]
89. ~funny(X0) | ~quiet(X0) | ~curious(X0) [cnf transformation 44]
92. funny(X0) | quiet(X0) | tall(X0) [cnf transformation 44]
101. old(X0) | ~wise(X0) | old(X0) [cnf transformation 51]
103. ~wise(X0) | ~old(X0) | ~old(X0) | curious(X0) [cnf transformation 51]
105. ~funny(susan) | tall(susan) | ~kind(X0) | ~brave(X0) [cnf transformation 52]
106. funny(susan) | ~tall(susan) | ~kind(X0) | ~brave(X0) [cnf transformation 52]
107. brave(X0) | ~creative(X0) [cnf transformation 34]
130. kind(john) [cnf transformation 22]
132. humble(alice) [cnf transformation 24]
133. ~wise(X0) | old(X0) [duplicate literal removal 101]
134. ~old(X0) | ~wise(X0) | curious(X0) [duplicate literal removal 103]
137. strong(X0) | creative(X0) [duplicate literal removal 74]
138. ~strong(X0) | creative(X0) [duplicate literal removal 76]
140. 1 <=> ! [X1] : (~quiet(X1) | tall(X1)) [avatar definition]
141. ~quiet(X1) | tall(X1) <- (1) [avatar component clause 140]
148. 3 <=> ! [X1] : (~tall(X1) | quiet(X1)) [avatar definition]
149. ~tall(X1) | quiet(X1) <- (3) [avatar component clause 148]
152. 4 <=> creative(sK0) [avatar definition]
154. ~creative(sK0) <- (~4) [avatar component clause 152]
155. 1 | ~4 [avatar split clause 71,152,140]
156. 3 | ~4 [avatar split clause 70,152,148]
157. creative(X0) [subsumption resolution 137,138]
185. 11 <=> humble(alice) [avatar definition]
193. 13 <=> wise(susan) [avatar definition]
194. wise(susan) <- (13) [avatar component clause 193]
197. 14 <=> tall(susan) [avatar definition]
198. tall(susan) <- (14) [avatar component clause 197]
204. ~14 | 13 | ~11 [avatar split clause 82,185,193,197]
225. 19 <=> ! [X0] : (~kind(X0) | ~brave(X0)) [avatar definition]
226. ~kind(X0) | ~brave(X0) <- (19) [avatar component clause 225]
228. 20 <=> funny(susan) [avatar definition]
229. ~funny(susan) <- (~20) [avatar component clause 228]
230. funny(susan) <- (20) [avatar component clause 228]
231. 19 | ~14 | 20 [avatar split clause 106,228,197,225]
232. 19 | 14 | ~20 [avatar split clause 105,228,197,225]
233. brave(X0) [subsumption resolution 107,157]
306. 11 [avatar split clause 132,185]
307. $false <- (~4) [subsumption resolution 154,157]
308. 4 [avatar contradiction clause 307]
339. quiet(susan) | tall(susan) <- (~20) [resolution 92,229]
348. tall(susan) <- (1, ~20) [subsumption resolution 339,141]
349. 14 | ~1 | 20 [avatar split clause 348,228,140,197]
350. ~kind(X0) <- (19) [subsumption resolution 226,233]
351. old(susan) <- (13) [resolution 194,133]
352. quiet(susan) <- (3, 14) [resolution 198,149]
353. $false <- (19) [resolution 350,130]
354. ~19 [avatar contradiction clause 353]
356. ~quiet(susan) | ~curious(susan) <- (20) [resolution 230,89]
357. ~curious(susan) <- (3, 14, 20) [subsumption resolution 356,352]
366. ~wise(susan) | curious(susan) <- (13) [resolution 134,351]
367. curious(susan) <- (13) [subsumption resolution 366,194]
368. $false <- (3, 13, 14, 20) [subsumption resolution 367,357]
369. ~3 | ~13 | ~14 | ~20 [avatar contradiction clause 368]
370. $false [avatar sat refutation 155,156,204,231,232,306,308,349,354,369]
% SZS output end Proof for 1740817977037929104772414
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is calm or happy then alice is happy or not strong.
If someone is not old then mary is both not rich and not calm.
If someone is happy or wise then someone is not curious or quiet and vice versa.
If paul is not wise or not patient then someone is strong.
If paul is either quiet or humble then someone is not happy and vice versa.
Everyone who is strong or not humble is both old and not humble and vice versa.
Everyone who is both not funny and humble is rich.
Everyone who is either creative or not funny is not brave or generous and vice versa.
Everyone who is calm is either not happy or not old.
If someone is either not creative or calm then fred is old or creative and vice versa.
If someone is creative or not quiet then susan is kind or calm.
Everyone who is not kind is both not quiet and calm and vice versa.
Everyone who is not quiet is not humble.
Everyone who is not happy or not curious is not rich or not old and vice versa.
If alice is humble then someone is both not kind and brave and vice versa.
If someone is either not calm or tall then someone is not rich.
Someone is happy.
Someone is not curious or brave.
Someone is both not quiet and not generous.
Someone is not kind.
Someone is both not tall and not kind.
Susan is either not creative or funny.
Mary is either not humble or not calm.
Someone is not calm. | Fred is old. | neutral | ((?[X]:((calm(X)|happy(X))))=>((happy(alice)|~strong(alice))))&
((?[X]:(~old(X)))=>((~rich(mary)&~calm(mary))))&
((?[X]:((happy(X)|wise(X))))<=>(?[X]:((~curious(X)|quiet(X)))))&
(((~wise(paul)|~patient(paul)))=>(?[X]:(strong(X))))&
(((quiet(paul)<~>humble(paul)))<=>(?[X]:(~happy(X))))&
(![X]:((strong(X)|~humble(X))<=>(old(X)&~humble(X))))&
(![X]:((~funny(X)&humble(X))=>rich(X)))&
(![X]:((creative(X)<~>~funny(X))<=>(~brave(X)|generous(X))))&
(![X]:(calm(X)=>(~happy(X)<~>~old(X))))&
((?[X]:((~creative(X)<~>calm(X))))<=>((old(fred)|creative(fred))))&
((?[X]:((creative(X)|~quiet(X))))=>((kind(susan)|calm(susan))))&
(![X]:(~kind(X)<=>(~quiet(X)&calm(X))))&
(![X]:(~quiet(X)=>~humble(X)))&
(![X]:((~happy(X)|~curious(X))<=>(~rich(X)|~old(X))))&
((humble(alice))<=>(?[X]:((~kind(X)&brave(X)))))&
((?[X]:((~calm(X)<~>tall(X))))=>(?[X]:(~rich(X))))&
(?[X]:(happy(X)))&
(?[X]:((~curious(X)|brave(X))))&
(?[X]:((~quiet(X)&~generous(X))))&
(?[X]:(~kind(X)))&
(?[X]:((~tall(X)&~kind(X))))&
((~creative(susan)<~>funny(susan)))&
((~humble(mary)<~>~calm(mary)))&
(?[X]:(~calm(X))) | old(fred) | [] | null | 0 |
Everyone who is calm or not curious is not brave and vice versa. If someone is both strong and brave then someone is not brave or not kind. Everyone who is quiet or calm is both not humble and wise and vice versa. Everyone who is either not quiet or not happy is not patient. If someone is both happy and funny then someone is strong. Everyone who is both patient and not rich is humble and vice versa. Everyone who is both not rich and not quiet is not calm or not brave and vice versa. If someone is rich then someone is strong. Everyone who is not rich or not kind is not quiet and vice versa. Everyone who is both happy and not happy is kind and vice versa. If alice is funny then mary is either not humble or generous. If john is old then someone is not creative or patient. If lucy is not creative or not funny then alice is either not strong or curious and vice versa. If john is rich then lucy is either curious or humble. Everyone who is both generous and not happy is not quiet. If someone is both curious and funny then susan is old and vice versa. Someone is rich or not rich. Mary is either not patient or not wise. Fred is not old or not wise. Susan is both strong and not brave. Fred is both brave and not generous. Someone is both not quiet and not rich. | Mary is not kind. | entailment | (![X]:((calm(X)|~curious(X))<=>~brave(X)))&
((?[X]:((strong(X)&brave(X))))=>(?[X]:((~brave(X)|~kind(X)))))&
(![X]:((quiet(X)|calm(X))<=>(~humble(X)&wise(X))))&
(![X]:((~quiet(X)<~>~happy(X))=>~patient(X)))&
((?[X]:((happy(X)&funny(X))))=>(?[X]:(strong(X))))&
(![X]:((patient(X)&~rich(X))<=>humble(X)))&
(![X]:((~rich(X)&~quiet(X))<=>(~calm(X)|~brave(X))))&
((?[X]:(rich(X)))=>(?[X]:(strong(X))))&
(![X]:((~rich(X)|~kind(X))<=>~quiet(X)))&
(![X]:((happy(X)&~happy(X))<=>kind(X)))&
((funny(alice))=>((~humble(mary)<~>generous(mary))))&
((old(john))=>(?[X]:((~creative(X)|patient(X)))))&
(((~creative(lucy)|~funny(lucy)))<=>((~strong(alice)<~>curious(alice))))&
((rich(john))=>((curious(lucy)<~>humble(lucy))))&
(![X]:((generous(X)&~happy(X))=>~quiet(X)))&
((?[X]:((curious(X)&funny(X))))<=>(old(susan)))&
(?[X]:((rich(X)|~rich(X))))&
((~patient(mary)<~>~wise(mary)))&
((~old(fred)|~wise(fred)))&
((strong(susan)&~brave(susan)))&
((brave(fred)&~generous(fred)))&
(?[X]:((~quiet(X)&~rich(X)))) | ~kind(mary) | [
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 8338539827389042542306508
% SZS output start Proof for 8338539827389042542306508
10. ! [X0] : ((~happy(X0) & happy(X0)) <=> kind(X0)) [input p9]
23. kind(mary) [input hypothesis]
56. ! [X0] : (((~happy(X0) & happy(X0)) | ~kind(X0)) & (kind(X0) | (happy(X0) | ~happy(X0)))) [nnf transformation 10]
57. ! [X0] : (((~happy(X0) & happy(X0)) | ~kind(X0)) & (kind(X0) | happy(X0) | ~happy(X0))) [flattening 56]
98. happy(X0) | ~kind(X0) [cnf transformation 57]
99. ~happy(X0) | ~kind(X0) [cnf transformation 57]
125. kind(mary) [cnf transformation 23]
154. ~kind(X0) [subsumption resolution 98,99]
255. $false [subsumption resolution 125,154]
% SZS output end Proof for 8338539827389042542306508
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either rich or funny then paul is either humble or happy.
If someone is not kind then someone is not rich or not curious and vice versa.
If john is both not strong and not patient then lucy is either not patient or not tall and vice versa.
If someone is wise then paul is rich or not calm.
Everyone who is both kind and not patient is not strong or patient and vice versa.
If someone is not calm then fred is not funny and vice versa.
Everyone who is either humble or calm is not quiet or rich.
If someone is kind or not patient then someone is not patient and vice versa.
If susan is either not wise or not brave then susan is both humble and not tall.
If paul is strong then alice is either tall or not strong and vice versa.
Everyone who is both not happy and kind is both not strong and not funny.
Everyone who is both brave and rich is not curious or not kind and vice versa.
If someone is either patient or not strong then someone is either not curious or not wise.
Everyone who is not creative or not old is not quiet or not brave.
Everyone who is kind is funny or not strong and vice versa.
Everyone who is both patient and not creative is patient or not old and vice versa.
Someone is rich or patient.
Fred is old or rich.
Lucy is not brave or creative.
Someone is both not humble and not calm.
Lucy is not kind.
Fred is not wise or not creative.
Alice is not wise or not kind. | Paul is rich. | neutral | (((rich(john)<~>funny(john)))=>((humble(paul)<~>happy(paul))))&
((?[X]:(~kind(X)))<=>(?[X]:((~rich(X)|~curious(X)))))&
(((~strong(john)&~patient(john)))<=>((~patient(lucy)<~>~tall(lucy))))&
((?[X]:(wise(X)))=>((rich(paul)|~calm(paul))))&
(![X]:((kind(X)&~patient(X))<=>(~strong(X)|patient(X))))&
((?[X]:(~calm(X)))<=>(~funny(fred)))&
(![X]:((humble(X)<~>calm(X))=>(~quiet(X)|rich(X))))&
((?[X]:((kind(X)|~patient(X))))<=>(?[X]:(~patient(X))))&
(((~wise(susan)<~>~brave(susan)))=>((humble(susan)&~tall(susan))))&
((strong(paul))<=>((tall(alice)<~>~strong(alice))))&
(![X]:((~happy(X)&kind(X))=>(~strong(X)&~funny(X))))&
(![X]:((brave(X)&rich(X))<=>(~curious(X)|~kind(X))))&
((?[X]:((patient(X)<~>~strong(X))))=>(?[X]:((~curious(X)<~>~wise(X)))))&
(![X]:((~creative(X)|~old(X))=>(~quiet(X)|~brave(X))))&
(![X]:(kind(X)<=>(funny(X)|~strong(X))))&
(![X]:((patient(X)&~creative(X))<=>(patient(X)|~old(X))))&
(?[X]:((rich(X)|patient(X))))&
((old(fred)|rich(fred)))&
((~brave(lucy)|creative(lucy)))&
(?[X]:((~humble(X)&~calm(X))))&
(~kind(lucy))&
((~wise(fred)|~creative(fred)))&
((~wise(alice)|~kind(alice))) | rich(paul) | [] | null | 0 |
Everyone who is calm or not rich is either creative or happy.
If fred is either not happy or not patient then mary is funny and vice versa.
If john is strong then john is both not generous and rich.
If someone is both not rich and strong then someone is both not calm and strong and vice versa.
If someone is happy or not curious then someone is either not quiet or old.
Everyone who is either happy or patient is both tall and old.
If someone is not happy or funny then john is brave or not quiet and vice versa.
Everyone who is not quiet is either not strong or brave and vice versa.
Everyone who is patient or not curious is not calm.
If someone is either not generous or patient then someone is either not curious or tall.
Everyone who is funny or happy is not tall.
Everyone who is rich or not tall is curious or not brave and vice versa.
Everyone who is patient is either not creative or calm and vice versa.
Everyone who is not brave is not old.
If someone is both patient and strong then mary is both not patient and humble.
Everyone who is both not rich and happy is both quiet and not humble and vice versa.
John is either funny or not humble.
Someone is either quiet or creative.
Someone is creative.
Someone is quiet or calm.
Lucy is both rich and patient.
Someone is generous.
Paul is not quiet.
Someone is not quiet or calm. | Mary is curious. | neutral | (![X]:((calm(X)|~rich(X))=>(creative(X)<~>happy(X))))&
(((~happy(fred)<~>~patient(fred)))<=>(funny(mary)))&
((strong(john))=>((~generous(john)&rich(john))))&
((?[X]:((~rich(X)&strong(X))))<=>(?[X]:((~calm(X)&strong(X)))))&
((?[X]:((happy(X)|~curious(X))))=>(?[X]:((~quiet(X)<~>old(X)))))&
(![X]:((happy(X)<~>patient(X))=>(tall(X)&old(X))))&
((?[X]:((~happy(X)|funny(X))))<=>((brave(john)|~quiet(john))))&
(![X]:(~quiet(X)<=>(~strong(X)<~>brave(X))))&
(![X]:((patient(X)|~curious(X))=>~calm(X)))&
((?[X]:((~generous(X)<~>patient(X))))=>(?[X]:((~curious(X)<~>tall(X)))))&
(![X]:((funny(X)|happy(X))=>~tall(X)))&
(![X]:((rich(X)|~tall(X))<=>(curious(X)|~brave(X))))&
(![X]:(patient(X)<=>(~creative(X)<~>calm(X))))&
(![X]:(~brave(X)=>~old(X)))&
((?[X]:((patient(X)&strong(X))))=>((~patient(mary)&humble(mary))))&
(![X]:((~rich(X)&happy(X))<=>(quiet(X)&~humble(X))))&
((funny(john)<~>~humble(john)))&
(?[X]:((quiet(X)<~>creative(X))))&
(?[X]:(creative(X)))&
(?[X]:((quiet(X)|calm(X))))&
((rich(lucy)&patient(lucy)))&
(?[X]:(generous(X)))&
(~quiet(paul))&
(?[X]:((~quiet(X)|calm(X)))) | curious(mary) | [] | null | 0 |
If susan is either not brave or generous then someone is generous or not brave and vice versa.
If someone is not strong or not calm then someone is tall or calm.
If someone is either brave or not generous then fred is both not happy and happy.
If fred is tall or funny then someone is calm or generous.
If someone is both creative and tall then someone is both quiet and not old and vice versa.
If someone is not funny then someone is both humble and generous and vice versa.
Everyone who is either not wise or not calm is not humble or not kind and vice versa.
If fred is either humble or not quiet then someone is not humble and vice versa.
If someone is either not humble or happy then someone is either not kind or old and vice versa.
If someone is not wise or wise then someone is either humble or funny and vice versa.
Everyone who is either brave or quiet is either not old or happy.
Everyone who is happy is not generous or rich.
Everyone who is creative is humble and vice versa.
If mary is both rich and not generous then someone is not quiet and vice versa.
Everyone who is happy is tall or not creative.
If someone is either humble or funny then someone is either patient or rich.
Someone is wise.
Someone is both creative and not patient.
Lucy is humble or not tall.
John is not brave or kind.
Someone is both brave and old.
Someone is both not generous and kind.
Fred is both rich and not quiet. | Lucy is not brave. | contradiction | (((~brave(susan)<~>generous(susan)))<=>(?[X]:((generous(X)|~brave(X)))))&
((?[X]:((~strong(X)|~calm(X))))=>(?[X]:((tall(X)|calm(X)))))&
((?[X]:((brave(X)<~>~generous(X))))=>((~happy(fred)&happy(fred))))&
(((tall(fred)|funny(fred)))=>(?[X]:((calm(X)|generous(X)))))&
((?[X]:((creative(X)&tall(X))))<=>(?[X]:((quiet(X)&~old(X)))))&
((?[X]:(~funny(X)))<=>(?[X]:((humble(X)&generous(X)))))&
(![X]:((~wise(X)<~>~calm(X))<=>(~humble(X)|~kind(X))))&
(((humble(fred)<~>~quiet(fred)))<=>(?[X]:(~humble(X))))&
((?[X]:((~humble(X)<~>happy(X))))<=>(?[X]:((~kind(X)<~>old(X)))))&
((?[X]:((~wise(X)|wise(X))))<=>(?[X]:((humble(X)<~>funny(X)))))&
(![X]:((brave(X)<~>quiet(X))=>(~old(X)<~>happy(X))))&
(![X]:(happy(X)=>(~generous(X)|rich(X))))&
(![X]:(creative(X)<=>humble(X)))&
(((rich(mary)&~generous(mary)))<=>(?[X]:(~quiet(X))))&
(![X]:(happy(X)=>(tall(X)|~creative(X))))&
((?[X]:((humble(X)<~>funny(X))))=>(?[X]:((patient(X)<~>rich(X)))))&
(?[X]:(wise(X)))&
(?[X]:((creative(X)&~patient(X))))&
((humble(lucy)|~tall(lucy)))&
((~brave(john)|kind(john)))&
(?[X]:((brave(X)&old(X))))&
(?[X]:((~generous(X)&kind(X))))&
((rich(fred)&~quiet(fred))) | ~brave(lucy) | [
"p0",
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 5216889076658937140500418
% SZS output start Proof for 5216889076658937140500418
1. (~brave(susan) <~> generous(susan)) <=> ? [X0] : (~brave(X0) | generous(X0)) [input p0]
3. ? [X0] : (brave(X0) <~> ~generous(X0)) => (happy(fred) & ~happy(fred)) [input p2]
24. ~brave(lucy) [input hypothesis]
33. (happy(fred) & ~happy(fred)) | ! [X0] : (brave(X0) <=> ~generous(X0)) [ennf transformation 3]
41. (((~generous(susan) | brave(susan)) & (generous(susan) | ~brave(susan))) | ! [X0] : (brave(X0) & ~generous(X0))) & (? [X0] : (~brave(X0) | generous(X0)) | ((~brave(susan) | ~generous(susan)) & (generous(susan) | brave(susan)))) [nnf transformation 1]
42. (((~generous(susan) | brave(susan)) & (generous(susan) | ~brave(susan))) | ! [X0] : (brave(X0) & ~generous(X0))) & (? [X1] : (~brave(X1) | generous(X1)) | ((~brave(susan) | ~generous(susan)) & (generous(susan) | brave(susan)))) [rectify 41]
43. ? [X1] : (~brave(X1) | generous(X1)) => (~brave(sK0) | generous(sK0)) [choice axiom]
44. (((~generous(susan) | brave(susan)) & (generous(susan) | ~brave(susan))) | ! [X0] : (brave(X0) & ~generous(X0))) & ((~brave(sK0) | generous(sK0)) | ((~brave(susan) | ~generous(susan)) & (generous(susan) | brave(susan)))) [skolemisation 42,43]
48. (happy(fred) & ~happy(fred)) | ! [X0] : ((brave(X0) | generous(X0)) & (~generous(X0) | ~brave(X0))) [nnf transformation 33]
99. generous(susan) | ~brave(susan) | brave(X0) [cnf transformation 44]
101. ~generous(susan) | brave(susan) | brave(X0) [cnf transformation 44]
103. ~happy(fred) | ~generous(X0) | ~brave(X0) [cnf transformation 48]
104. ~happy(fred) | brave(X0) | generous(X0) [cnf transformation 48]
105. happy(fred) | ~generous(X0) | ~brave(X0) [cnf transformation 48]
106. happy(fred) | brave(X0) | generous(X0) [cnf transformation 48]
166. ~brave(lucy) [cnf transformation 24]
168. 1 <=> ! [X0] : brave(X0) [avatar definition]
169. brave(X0) <- (1) [avatar component clause 168]
171. 2 <=> brave(susan) [avatar definition]
172. ~brave(susan) <- (~2) [avatar component clause 171]
175. 3 <=> generous(susan) [avatar definition]
176. generous(susan) <- (3) [avatar component clause 175]
177. ~generous(susan) <- (~3) [avatar component clause 175]
178. 1 | 2 | ~3 [avatar split clause 101,175,171,168]
183. 1 | ~2 | 3 [avatar split clause 99,175,171,168]
208. 10 <=> ! [X0] : (brave(X0) | generous(X0)) [avatar definition]
209. generous(X0) | brave(X0) <- (10) [avatar component clause 208]
211. 11 <=> happy(fred) [avatar definition]
214. 10 | 11 [avatar split clause 106,211,208]
216. 12 <=> ! [X0] : (~generous(X0) | ~brave(X0)) [avatar definition]
217. ~generous(X0) | ~brave(X0) <- (12) [avatar component clause 216]
218. 12 | 11 [avatar split clause 105,211,216]
219. 10 | ~11 [avatar split clause 104,211,208]
220. 12 | ~11 [avatar split clause 103,211,216]
429. brave(susan) <- (~3, 10) [resolution 209,177]
431. $false <- (~2, ~3, 10) [subsumption resolution 429,172]
432. 2 | 3 | ~10 [avatar contradiction clause 431]
436. ~brave(susan) <- (3, 12) [resolution 217,176]
439. ~2 | ~3 | ~12 [avatar split clause 436,216,175,171]
440. $false <- (1) [resolution 169,166]
445. ~1 [avatar contradiction clause 440]
446. $false [avatar sat refutation 178,183,214,218,219,220,432,439,445]
% SZS output end Proof for 5216889076658937140500418
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 lucy is either not funny or not curious then fred is either not brave or generous and vice versa.
Everyone who is both not generous and curious is both not patient and humble and vice versa.
If fred is either not tall or brave then someone is both funny and brave and vice versa.
Everyone who is not happy or creative is not patient and vice versa.
Everyone who is either brave or not curious is quiet.
Everyone who is both not wise and strong is not happy or curious.
Everyone who is both not happy and not quiet is either humble or funny and vice versa.
Everyone who is both brave and not kind is not funny or quiet and vice versa.
Everyone who is patient is both not wise and wise and vice versa.
If fred is curious then john is humble and vice versa.
If someone is patient or funny then someone is not funny.
If someone is tall then lucy is both curious and not rich.
If susan is quiet or old then fred is either not kind or not happy and vice versa.
If john is brave then john is either not rich or tall.
If someone is calm or funny then john is both not brave and not generous.
Everyone who is both quiet and kind is both not brave and humble and vice versa.
Someone is not tall.
Alice is not wise or brave.
Someone is not quiet or not generous.
Someone is rich.
Someone is rich or not happy.
John is not curious or not strong. | Fred is not tall. | entailment | (((~funny(lucy)<~>~curious(lucy)))<=>((~brave(fred)<~>generous(fred))))&
(![X]:((~generous(X)&curious(X))<=>(~patient(X)&humble(X))))&
(((~tall(fred)<~>brave(fred)))<=>(?[X]:((funny(X)&brave(X)))))&
(![X]:((~happy(X)|creative(X))<=>~patient(X)))&
(![X]:((brave(X)<~>~curious(X))=>quiet(X)))&
(![X]:((~wise(X)&strong(X))=>(~happy(X)|curious(X))))&
(![X]:((~happy(X)&~quiet(X))<=>(humble(X)<~>funny(X))))&
(![X]:((brave(X)&~kind(X))<=>(~funny(X)|quiet(X))))&
(![X]:(patient(X)<=>(~wise(X)&wise(X))))&
((curious(fred))<=>(humble(john)))&
((?[X]:((patient(X)|funny(X))))=>(?[X]:(~funny(X))))&
((?[X]:(tall(X)))=>((curious(lucy)&~rich(lucy))))&
(((quiet(susan)|old(susan)))<=>((~kind(fred)<~>~happy(fred))))&
((brave(john))=>((~rich(john)<~>tall(john))))&
((?[X]:((calm(X)|funny(X))))=>((~brave(john)&~generous(john))))&
(![X]:((quiet(X)&kind(X))<=>(~brave(X)&humble(X))))&
(?[X]:(~tall(X)))&
((~wise(alice)|brave(alice)))&
(?[X]:((~quiet(X)|~generous(X))))&
(?[X]:(rich(X)))&
(?[X]:((rich(X)|~happy(X))))&
((~curious(john)|~strong(john))) | ~tall(fred) | [
"p1",
"p2",
"p4",
"p7",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4106061296421250261439787
% SZS output start Proof for 4106061296421250261439787
2. ! [X0] : ((curious(X0) & ~generous(X0)) <=> (humble(X0) & ~patient(X0))) [input p1]
3. (~tall(fred) <~> brave(fred)) <=> ? [X0] : (brave(X0) & funny(X0)) [input p2]
5. ! [X0] : ((brave(X0) <~> ~curious(X0)) => quiet(X0)) [input p4]
8. ! [X0] : ((~kind(X0) & brave(X0)) <=> (quiet(X0) | ~funny(X0))) [input p7]
15. ? [X0] : (funny(X0) | calm(X0)) => (~generous(john) & ~brave(john)) [input p14]
16. ! [X0] : ((kind(X0) & quiet(X0)) <=> (humble(X0) & ~brave(X0))) [input p15]
23. tall(fred) [input hypothesis]
25. ? [X0] : funny(X0) => (~generous(john) & ~brave(john)) [pure predicate removal 15]
28. ! [X0] : (quiet(X0) | (brave(X0) <=> ~curious(X0))) [ennf transformation 5]
32. (~generous(john) & ~brave(john)) | ! [X0] : ~funny(X0) [ennf transformation 25]
34. ! [X0] : (((curious(X0) & ~generous(X0)) | (~humble(X0) | patient(X0))) & ((humble(X0) & ~patient(X0)) | (~curious(X0) | generous(X0)))) [nnf transformation 2]
35. ! [X0] : (((curious(X0) & ~generous(X0)) | ~humble(X0) | patient(X0)) & ((humble(X0) & ~patient(X0)) | ~curious(X0) | generous(X0))) [flattening 34]
36. (((~brave(fred) | tall(fred)) & (brave(fred) | ~tall(fred))) | ! [X0] : (~brave(X0) | ~funny(X0))) & (? [X0] : (brave(X0) & funny(X0)) | ((~tall(fred) | ~brave(fred)) & (brave(fred) | tall(fred)))) [nnf transformation 3]
37. (((~brave(fred) | tall(fred)) & (brave(fred) | ~tall(fred))) | ! [X0] : (~brave(X0) | ~funny(X0))) & (? [X1] : (brave(X1) & funny(X1)) | ((~tall(fred) | ~brave(fred)) & (brave(fred) | tall(fred)))) [rectify 36]
38. ? [X1] : (brave(X1) & funny(X1)) => (brave(sK0) & funny(sK0)) [choice axiom]
39. (((~brave(fred) | tall(fred)) & (brave(fred) | ~tall(fred))) | ! [X0] : (~brave(X0) | ~funny(X0))) & ((brave(sK0) & funny(sK0)) | ((~tall(fred) | ~brave(fred)) & (brave(fred) | tall(fred)))) [skolemisation 37,38]
42. ! [X0] : (quiet(X0) | ((brave(X0) | curious(X0)) & (~curious(X0) | ~brave(X0)))) [nnf transformation 28]
45. ! [X0] : (((~kind(X0) & brave(X0)) | (~quiet(X0) & funny(X0))) & ((quiet(X0) | ~funny(X0)) | (kind(X0) | ~brave(X0)))) [nnf transformation 8]
46. ! [X0] : (((~kind(X0) & brave(X0)) | (~quiet(X0) & funny(X0))) & (quiet(X0) | ~funny(X0) | kind(X0) | ~brave(X0))) [flattening 45]
56. ! [X0] : (((kind(X0) & quiet(X0)) | (~humble(X0) | brave(X0))) & ((humble(X0) & ~brave(X0)) | (~kind(X0) | ~quiet(X0)))) [nnf transformation 16]
57. ! [X0] : (((kind(X0) & quiet(X0)) | ~humble(X0) | brave(X0)) & ((humble(X0) & ~brave(X0)) | ~kind(X0) | ~quiet(X0))) [flattening 56]
75. ~curious(X0) | humble(X0) | generous(X0) [cnf transformation 35]
79. funny(sK0) | ~tall(fred) | ~brave(fred) [cnf transformation 39]
88. quiet(X0) | brave(X0) | curious(X0) [cnf transformation 42]
96. brave(X0) | funny(X0) [cnf transformation 46]
97. ~quiet(X0) | brave(X0) [cnf transformation 46]
117. ~brave(john) | ~funny(X0) [cnf transformation 32]
118. ~generous(john) | ~funny(X0) [cnf transformation 32]
121. quiet(X0) | ~humble(X0) | brave(X0) [cnf transformation 57]
128. tall(fred) [cnf transformation 23]
134. 2 <=> brave(fred) [avatar definition]
136. ~brave(fred) <- (~2) [avatar component clause 134]
157. 6 <=> tall(fred) [avatar definition]
169. 8 <=> funny(sK0) [avatar definition]
171. funny(sK0) <- (8) [avatar component clause 169]
172. ~2 | ~6 | 8 [avatar split clause 79,169,157,134]
176. 9 <=> humble(john) [avatar definition]
177. humble(john) <- (9) [avatar component clause 176]
178. ~humble(john) <- (~9) [avatar component clause 176]
186. 11 <=> ! [X1] : ~funny(X1) [avatar definition]
187. ~funny(X1) <- (11) [avatar component clause 186]
225. 19 <=> brave(john) [avatar definition]
227. ~brave(john) <- (~19) [avatar component clause 225]
239. 22 <=> generous(john) [avatar definition]
241. ~generous(john) <- (~22) [avatar component clause 239]
242. 11 | ~22 [avatar split clause 118,239,186]
243. 11 | ~19 [avatar split clause 117,225,186]
244. ~humble(X0) | brave(X0) [subsumption resolution 121,97]
272. 6 [avatar split clause 128,157]
273. funny(fred) <- (~2) [resolution 96,136]
292. brave(X0) | curious(X0) | brave(X0) [resolution 88,97]
293. brave(X0) | curious(X0) [duplicate literal removal 292]
361. brave(john) <- (9) [resolution 177,244]
365. 19 | ~9 [avatar split clause 361,176,225]
374. $false <- (~2, 11) [resolution 187,273]
375. 2 | ~11 [avatar contradiction clause 374]
381. $false <- (8, 11) [subsumption resolution 171,187]
382. ~8 | ~11 [avatar contradiction clause 381]
398. curious(john) <- (~19) [resolution 227,293]
486. humble(john) | generous(john) <- (~19) [resolution 398,75]
487. generous(john) <- (~9, ~19) [subsumption resolution 486,178]
488. $false <- (~9, ~19, ~22) [subsumption resolution 487,241]
489. 9 | 19 | 22 [avatar contradiction clause 488]
490. $false [avatar sat refutation 172,242,243,272,365,375,382,489]
% SZS output end Proof for 4106061296421250261439787
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If mary is both not kind and quiet then someone is quiet or not tall.
Everyone who is not kind or happy is not tall or rich.
Everyone who is both not humble and not curious is not rich and vice versa.
If someone is both not funny and not rich then someone is either not generous or not old.
If someone is not generous or happy then someone is not creative and vice versa.
Everyone who is rich is both old and happy.
Everyone who is both not kind and kind is either old or tall and vice versa.
Everyone who is both not old and not generous is either generous or old.
Everyone who is either patient or old is either happy or not curious and vice versa.
Everyone who is not kind is both not strong and calm.
Everyone who is not old or generous is not wise or not old and vice versa.
Everyone who is either not happy or brave is either not calm or rich and vice versa.
Everyone who is generous or rich is either old or rich.
If someone is either funny or humble then someone is creative.
If someone is either not quiet or not kind then someone is either humble or not humble.
If someone is not curious or funny then someone is calm.
Someone is either tall or calm.
John is either kind or generous.
Lucy is not strong or not happy.
Someone is not creative or not brave.
Someone is either not creative or not curious.
Mary is not funny or strong.
Someone is either not patient or brave. | Lucy is not brave. | neutral | (((~kind(mary)&quiet(mary)))=>(?[X]:((quiet(X)|~tall(X)))))&
(![X]:((~kind(X)|happy(X))=>(~tall(X)|rich(X))))&
(![X]:((~humble(X)&~curious(X))<=>~rich(X)))&
((?[X]:((~funny(X)&~rich(X))))=>(?[X]:((~generous(X)<~>~old(X)))))&
((?[X]:((~generous(X)|happy(X))))<=>(?[X]:(~creative(X))))&
(![X]:(rich(X)=>(old(X)&happy(X))))&
(![X]:((~kind(X)&kind(X))<=>(old(X)<~>tall(X))))&
(![X]:((~old(X)&~generous(X))=>(generous(X)<~>old(X))))&
(![X]:((patient(X)<~>old(X))<=>(happy(X)<~>~curious(X))))&
(![X]:(~kind(X)=>(~strong(X)&calm(X))))&
(![X]:((~old(X)|generous(X))<=>(~wise(X)|~old(X))))&
(![X]:((~happy(X)<~>brave(X))<=>(~calm(X)<~>rich(X))))&
(![X]:((generous(X)|rich(X))=>(old(X)<~>rich(X))))&
((?[X]:((funny(X)<~>humble(X))))=>(?[X]:(creative(X))))&
((?[X]:((~quiet(X)<~>~kind(X))))=>(?[X]:((humble(X)<~>~humble(X)))))&
((?[X]:((~curious(X)|funny(X))))=>(?[X]:(calm(X))))&
(?[X]:((tall(X)<~>calm(X))))&
((kind(john)<~>generous(john)))&
((~strong(lucy)|~happy(lucy)))&
(?[X]:((~creative(X)|~brave(X))))&
(?[X]:((~creative(X)<~>~curious(X))))&
((~funny(mary)|strong(mary)))&
(?[X]:((~patient(X)<~>brave(X)))) | ~brave(lucy) | [] | null | 0 |
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