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
|
|---|---|---|---|---|---|---|---|
Everyone who is generous or tall is both generous and not rich and vice versa.
Everyone who is wise or creative is not old or not curious.
If lucy is both not funny and not calm then someone is either not generous or not old and vice versa.
If someone is wise then someone is either happy or not quiet.
If someone is either generous or not quiet then alice is either creative or not brave and vice versa.
If someone is both not creative and not happy then lucy is tall or calm and vice versa.
Everyone who is both wise and rich is funny.
If lucy is not tall or not generous then someone is strong or old and vice versa.
Everyone who is kind is both calm and not tall.
Everyone who is generous or happy is kind or not tall.
Everyone who is both not funny and happy is either not kind or not tall.
If alice is both creative and curious then someone is both not generous and wise.
Everyone who is both not strong and not tall is not humble or generous and vice versa.
Everyone who is both not calm and not strong is either brave or not patient.
If someone is both not tall and not quiet then mary is brave or not patient and vice versa.
Everyone who is either not kind or generous is both tall and curious and vice versa.
Someone is both strong and brave.
Lucy is curious or not happy.
Lucy is either not humble or generous.
Someone is either not rich or not kind.
Alice is strong or not curious.
Lucy is either patient or kind.
John is not humble. | Lucy is curious. | neutral | (![X]:((generous(X)|tall(X))<=>(generous(X)&~rich(X))))&
(![X]:((wise(X)|creative(X))=>(~old(X)|~curious(X))))&
(((~funny(lucy)&~calm(lucy)))<=>(?[X]:((~generous(X)<~>~old(X)))))&
((?[X]:(wise(X)))=>(?[X]:((happy(X)<~>~quiet(X)))))&
((?[X]:((generous(X)<~>~quiet(X))))<=>((creative(alice)<~>~brave(alice))))&
((?[X]:((~creative(X)&~happy(X))))<=>((tall(lucy)|calm(lucy))))&
(![X]:((wise(X)&rich(X))=>funny(X)))&
(((~tall(lucy)|~generous(lucy)))<=>(?[X]:((strong(X)|old(X)))))&
(![X]:(kind(X)=>(calm(X)&~tall(X))))&
(![X]:((generous(X)|happy(X))=>(kind(X)|~tall(X))))&
(![X]:((~funny(X)&happy(X))=>(~kind(X)<~>~tall(X))))&
(((creative(alice)&curious(alice)))=>(?[X]:((~generous(X)&wise(X)))))&
(![X]:((~strong(X)&~tall(X))<=>(~humble(X)|generous(X))))&
(![X]:((~calm(X)&~strong(X))=>(brave(X)<~>~patient(X))))&
((?[X]:((~tall(X)&~quiet(X))))<=>((brave(mary)|~patient(mary))))&
(![X]:((~kind(X)<~>generous(X))<=>(tall(X)&curious(X))))&
(?[X]:((strong(X)&brave(X))))&
((curious(lucy)|~happy(lucy)))&
((~humble(lucy)<~>generous(lucy)))&
(?[X]:((~rich(X)<~>~kind(X))))&
((strong(alice)|~curious(alice)))&
((patient(lucy)<~>kind(lucy)))&
(~humble(john)) | curious(lucy) | [] | null | 0 |
Everyone who is rich or not strong is not kind.
Everyone who is rich is old and vice versa.
If fred is both funny and not calm then someone is kind or not quiet and vice versa.
Everyone who is not quiet or happy is both patient and generous and vice versa.
If someone is happy then mary is either kind or not patient and vice versa.
If someone is not humble or not patient then someone is not kind or happy.
Everyone who is both not brave and humble is not happy or old and vice versa.
Everyone who is either not calm or kind is both not wise and not funny.
If someone is both kind and creative then someone is either not wise or old and vice versa.
If mary is rich then someone is not humble or not strong.
Everyone who is either creative or not generous is either brave or not rich and vice versa.
Everyone who is both not tall and humble is not patient and vice versa.
Everyone who is either kind or quiet is funny and vice versa.
Everyone who is not generous is both humble and brave and vice versa.
If paul is either not rich or happy then alice is generous or wise and vice versa.
Everyone who is old or not curious is not wise and vice versa.
Someone is tall.
Alice is both calm and patient.
Someone is either strong or wise.
Someone is either not strong or happy.
Someone is not creative.
Someone is either not funny or patient.
Someone is not quiet or brave.
Someone is old. | Paul is not brave. | entailment | (![X]:((rich(X)|~strong(X))=>~kind(X)))&
(![X]:(rich(X)<=>old(X)))&
(((funny(fred)&~calm(fred)))<=>(?[X]:((kind(X)|~quiet(X)))))&
(![X]:((~quiet(X)|happy(X))<=>(patient(X)&generous(X))))&
((?[X]:(happy(X)))<=>((kind(mary)<~>~patient(mary))))&
((?[X]:((~humble(X)|~patient(X))))=>(?[X]:((~kind(X)|happy(X)))))&
(![X]:((~brave(X)&humble(X))<=>(~happy(X)|old(X))))&
(![X]:((~calm(X)<~>kind(X))=>(~wise(X)&~funny(X))))&
((?[X]:((kind(X)&creative(X))))<=>(?[X]:((~wise(X)<~>old(X)))))&
((rich(mary))=>(?[X]:((~humble(X)|~strong(X)))))&
(![X]:((creative(X)<~>~generous(X))<=>(brave(X)<~>~rich(X))))&
(![X]:((~tall(X)&humble(X))<=>~patient(X)))&
(![X]:((kind(X)<~>quiet(X))<=>funny(X)))&
(![X]:(~generous(X)<=>(humble(X)&brave(X))))&
(((~rich(paul)<~>happy(paul)))<=>((generous(alice)|wise(alice))))&
(![X]:((old(X)|~curious(X))<=>~wise(X)))&
(?[X]:(tall(X)))&
((calm(alice)&patient(alice)))&
(?[X]:((strong(X)<~>wise(X))))&
(?[X]:((~strong(X)<~>happy(X))))&
(?[X]:(~creative(X)))&
(?[X]:((~funny(X)<~>patient(X))))&
(?[X]:((~quiet(X)|brave(X))))&
(?[X]:(old(X))) | ~brave(paul) | [
"p1",
"p3",
"p6",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8465221604231899135519834
% SZS output start Proof for 8465221604231899135519834
2. ! [X0] : (rich(X0) <=> old(X0)) [input p1]
4. ! [X0] : ((happy(X0) | ~quiet(X0)) <=> (generous(X0) & patient(X0))) [input p3]
7. ! [X0] : ((humble(X0) & ~brave(X0)) <=> (old(X0) | ~happy(X0))) [input p6]
14. ! [X0] : (~generous(X0) <=> (brave(X0) & humble(X0))) [input p13]
15. (~rich(paul) <~> happy(paul)) <=> (wise(alice) | generous(alice)) [input p14]
25. brave(paul) [input hypothesis]
32. ! [X0] : ((rich(X0) | ~old(X0)) & (old(X0) | ~rich(X0))) [nnf transformation 2]
38. ! [X0] : (((happy(X0) | ~quiet(X0)) | (~generous(X0) | ~patient(X0))) & ((generous(X0) & patient(X0)) | (~happy(X0) & quiet(X0)))) [nnf transformation 4]
39. ! [X0] : ((happy(X0) | ~quiet(X0) | ~generous(X0) | ~patient(X0)) & ((generous(X0) & patient(X0)) | (~happy(X0) & quiet(X0)))) [flattening 38]
47. ! [X0] : (((humble(X0) & ~brave(X0)) | (~old(X0) & happy(X0))) & ((old(X0) | ~happy(X0)) | (~humble(X0) | brave(X0)))) [nnf transformation 7]
48. ! [X0] : (((humble(X0) & ~brave(X0)) | (~old(X0) & happy(X0))) & (old(X0) | ~happy(X0) | ~humble(X0) | brave(X0))) [flattening 47]
61. ! [X0] : ((~generous(X0) | (~brave(X0) | ~humble(X0))) & ((brave(X0) & humble(X0)) | generous(X0))) [nnf transformation 14]
62. ! [X0] : ((~generous(X0) | ~brave(X0) | ~humble(X0)) & ((brave(X0) & humble(X0)) | generous(X0))) [flattening 61]
63. (((~happy(paul) | rich(paul)) & (happy(paul) | ~rich(paul))) | (~wise(alice) & ~generous(alice))) & ((wise(alice) | generous(alice)) | ((~rich(paul) | ~happy(paul)) & (happy(paul) | rich(paul)))) [nnf transformation 15]
64. (((~happy(paul) | rich(paul)) & (happy(paul) | ~rich(paul))) | (~wise(alice) & ~generous(alice))) & (wise(alice) | generous(alice) | ((~rich(paul) | ~happy(paul)) & (happy(paul) | rich(paul)))) [flattening 63]
86. ~rich(X0) | old(X0) [cnf transformation 32]
96. ~happy(X0) | generous(X0) [cnf transformation 39]
105. ~brave(X0) | happy(X0) [cnf transformation 48]
106. ~brave(X0) | ~old(X0) [cnf transformation 48]
136. brave(X0) | generous(X0) [cnf transformation 62]
142. ~happy(paul) | rich(paul) | ~generous(alice) [cnf transformation 64]
159. brave(paul) [cnf transformation 25]
271. 26 <=> rich(paul) [avatar definition]
273. rich(paul) <- (26) [avatar component clause 271]
275. 27 <=> happy(paul) [avatar definition]
280. 28 <=> generous(alice) [avatar definition]
282. ~generous(alice) <- (~28) [avatar component clause 280]
283. ~28 | 26 | ~27 [avatar split clause 142,275,271,280]
334. happy(paul) [resolution 105,159]
337. 27 [avatar split clause 334,275]
341. ~old(paul) [resolution 106,159]
345. generous(X1) | happy(X1) [resolution 136,105]
346. generous(X1) [subsumption resolution 345,96]
347. $false <- (~28) [resolution 346,282]
348. 28 [avatar contradiction clause 347]
349. old(paul) <- (26) [resolution 273,86]
350. $false <- (26) [subsumption resolution 349,341]
351. ~26 [avatar contradiction clause 350]
352. $false [avatar sat refutation 283,337,348,351]
% SZS output end Proof for 8465221604231899135519834
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is either tall or not happy then someone is either happy or kind and vice versa.
Everyone who is kind or not happy is patient or not curious and vice versa.
If someone is happy then someone is either not happy or curious and vice versa.
Everyone who is not old or generous is both not happy and not wise and vice versa.
If mary is funny then someone is not patient or not funny.
Everyone who is either not happy or generous is either not happy or old and vice versa.
Everyone who is not quiet is not tall or happy and vice versa.
If someone is not rich then someone is both patient and kind.
Everyone who is both humble and not wise is both not rich and not funny.
If someone is either not generous or not strong then alice is either calm or old.
If someone is not calm then mary is either funny or tall and vice versa.
Everyone who is either not generous or not creative is not humble or creative and vice versa.
Everyone who is either not quiet or not happy is either not funny or not generous and vice versa.
If alice is not kind or not tall then someone is not patient and vice versa.
If someone is both not kind and calm then someone is not curious or not strong.
If someone is not quiet then susan is not strong.
Someone is kind or not creative.
Paul is calm or wise.
Lucy is not strong or not happy.
Someone is humble or generous.
Someone is both not creative and not rich.
Someone is not quiet or not humble. | Alice is not old. | neutral | (((tall(paul)<~>~happy(paul)))<=>(?[X]:((happy(X)<~>kind(X)))))&
(![X]:((kind(X)|~happy(X))<=>(patient(X)|~curious(X))))&
((?[X]:(happy(X)))<=>(?[X]:((~happy(X)<~>curious(X)))))&
(![X]:((~old(X)|generous(X))<=>(~happy(X)&~wise(X))))&
((funny(mary))=>(?[X]:((~patient(X)|~funny(X)))))&
(![X]:((~happy(X)<~>generous(X))<=>(~happy(X)<~>old(X))))&
(![X]:(~quiet(X)<=>(~tall(X)|happy(X))))&
((?[X]:(~rich(X)))=>(?[X]:((patient(X)&kind(X)))))&
(![X]:((humble(X)&~wise(X))=>(~rich(X)&~funny(X))))&
((?[X]:((~generous(X)<~>~strong(X))))=>((calm(alice)<~>old(alice))))&
((?[X]:(~calm(X)))<=>((funny(mary)<~>tall(mary))))&
(![X]:((~generous(X)<~>~creative(X))<=>(~humble(X)|creative(X))))&
(![X]:((~quiet(X)<~>~happy(X))<=>(~funny(X)<~>~generous(X))))&
(((~kind(alice)|~tall(alice)))<=>(?[X]:(~patient(X))))&
((?[X]:((~kind(X)&calm(X))))=>(?[X]:((~curious(X)|~strong(X)))))&
((?[X]:(~quiet(X)))=>(~strong(susan)))&
(?[X]:((kind(X)|~creative(X))))&
((calm(paul)|wise(paul)))&
((~strong(lucy)|~happy(lucy)))&
(?[X]:((humble(X)|generous(X))))&
(?[X]:((~creative(X)&~rich(X))))&
(?[X]:((~quiet(X)|~humble(X)))) | ~old(alice) | [] | null | 0 |
Everyone who is patient is both not tall and not generous.
If someone is rich then susan is not brave and vice versa.
If john is not wise then someone is both not tall and not calm.
Everyone who is either generous or patient is quiet.
If someone is not happy then someone is both patient and curious.
Everyone who is curious is both calm and not happy.
If someone is either not quiet or not old then someone is either not tall or wise and vice versa.
Everyone who is both quiet and wise is not humble or not calm.
If someone is not curious then someone is humble or kind.
If someone is not tall then someone is both calm and quiet and vice versa.
Everyone who is both not quiet and not funny is not funny or happy.
If someone is either not curious or not happy then someone is either curious or tall and vice versa.
If someone is not old then someone is both calm and creative and vice versa.
Everyone who is rich is both quiet and kind and vice versa.
If someone is curious then susan is tall.
If lucy is both strong and curious then someone is both not tall and not old.
Someone is rich or not happy.
Lucy is kind or strong.
Susan is not calm or not generous.
Someone is not strong or brave.
Someone is not curious.
Someone is not generous.
John is generous or not curious.
Someone is either humble or brave. | Lucy is kind. | neutral | (![X]:(patient(X)=>(~tall(X)&~generous(X))))&
((?[X]:(rich(X)))<=>(~brave(susan)))&
((~wise(john))=>(?[X]:((~tall(X)&~calm(X)))))&
(![X]:((generous(X)<~>patient(X))=>quiet(X)))&
((?[X]:(~happy(X)))=>(?[X]:((patient(X)&curious(X)))))&
(![X]:(curious(X)=>(calm(X)&~happy(X))))&
((?[X]:((~quiet(X)<~>~old(X))))<=>(?[X]:((~tall(X)<~>wise(X)))))&
(![X]:((quiet(X)&wise(X))=>(~humble(X)|~calm(X))))&
((?[X]:(~curious(X)))=>(?[X]:((humble(X)|kind(X)))))&
((?[X]:(~tall(X)))<=>(?[X]:((calm(X)&quiet(X)))))&
(![X]:((~quiet(X)&~funny(X))=>(~funny(X)|happy(X))))&
((?[X]:((~curious(X)<~>~happy(X))))<=>(?[X]:((curious(X)<~>tall(X)))))&
((?[X]:(~old(X)))<=>(?[X]:((calm(X)&creative(X)))))&
(![X]:(rich(X)<=>(quiet(X)&kind(X))))&
((?[X]:(curious(X)))=>(tall(susan)))&
(((strong(lucy)&curious(lucy)))=>(?[X]:((~tall(X)&~old(X)))))&
(?[X]:((rich(X)|~happy(X))))&
((kind(lucy)|strong(lucy)))&
((~calm(susan)|~generous(susan)))&
(?[X]:((~strong(X)|brave(X))))&
(?[X]:(~curious(X)))&
(?[X]:(~generous(X)))&
((generous(john)|~curious(john)))&
(?[X]:((humble(X)<~>brave(X)))) | kind(lucy) | [] | null | 0 |
Everyone who is curious is not kind and vice versa.
If someone is not strong then someone is either not kind or not strong and vice versa.
If someone is either not strong or not rich then someone is both not strong and wise and vice versa.
Everyone who is both not kind and old is not tall or not generous.
If susan is not tall then someone is either creative or old.
If someone is not tall or not kind then someone is both brave and humble and vice versa.
If someone is not funny or brave then fred is either tall or strong and vice versa.
Everyone who is not creative or not funny is patient and vice versa.
Everyone who is patient is either not patient or funny.
Everyone who is either not strong or not creative is not humble.
Everyone who is either happy or creative is not curious or rich.
If fred is not generous or strong then someone is not wise or brave.
If someone is creative or humble then someone is either not curious or old.
If paul is either not brave or not tall then fred is either not kind or not humble and vice versa.
Everyone who is either funny or kind is both happy and creative.
Everyone who is either brave or rich is both creative and not rich and vice versa.
Alice is both not creative and funny.
Fred is not kind or not generous.
Lucy is patient or kind.
Someone is patient or brave.
Fred is not generous or not curious.
Alice is not wise.
Mary is either not funny or tall.
Someone is either not calm or quiet. | Lucy is not kind. | contradiction | (![X]:(curious(X)<=>~kind(X)))&
((?[X]:(~strong(X)))<=>(?[X]:((~kind(X)<~>~strong(X)))))&
((?[X]:((~strong(X)<~>~rich(X))))<=>(?[X]:((~strong(X)&wise(X)))))&
(![X]:((~kind(X)&old(X))=>(~tall(X)|~generous(X))))&
((~tall(susan))=>(?[X]:((creative(X)<~>old(X)))))&
((?[X]:((~tall(X)|~kind(X))))<=>(?[X]:((brave(X)&humble(X)))))&
((?[X]:((~funny(X)|brave(X))))<=>((tall(fred)<~>strong(fred))))&
(![X]:((~creative(X)|~funny(X))<=>patient(X)))&
(![X]:(patient(X)=>(~patient(X)<~>funny(X))))&
(![X]:((~strong(X)<~>~creative(X))=>~humble(X)))&
(![X]:((happy(X)<~>creative(X))=>(~curious(X)|rich(X))))&
(((~generous(fred)|strong(fred)))=>(?[X]:((~wise(X)|brave(X)))))&
((?[X]:((creative(X)|humble(X))))=>(?[X]:((~curious(X)<~>old(X)))))&
(((~brave(paul)<~>~tall(paul)))<=>((~kind(fred)<~>~humble(fred))))&
(![X]:((funny(X)<~>kind(X))=>(happy(X)&creative(X))))&
(![X]:((brave(X)<~>rich(X))<=>(creative(X)&~rich(X))))&
((~creative(alice)&funny(alice)))&
((~kind(fred)|~generous(fred)))&
((patient(lucy)|kind(lucy)))&
(?[X]:((patient(X)|brave(X))))&
((~generous(fred)|~curious(fred)))&
(~wise(alice))&
((~funny(mary)<~>tall(mary)))&
(?[X]:((~calm(X)<~>quiet(X)))) | ~kind(lucy) | [
"p7",
"p8",
"p14",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 7068988629448835452850289
% SZS output start Proof for 7068988629448835452850289
8. ! [X0] : ((~funny(X0) | ~creative(X0)) <=> patient(X0)) [input p7]
9. ! [X0] : (patient(X0) => (~patient(X0) <~> funny(X0))) [input p8]
15. ! [X0] : ((funny(X0) <~> kind(X0)) => (creative(X0) & happy(X0))) [input p14]
19. kind(lucy) | patient(lucy) [input p18]
25. ~kind(lucy) [input hypothesis]
33. ! [X0] : ((~patient(X0) <~> funny(X0)) | ~patient(X0)) [ennf transformation 9]
39. ! [X0] : ((creative(X0) & happy(X0)) | (funny(X0) <=> kind(X0))) [ennf transformation 15]
63. ! [X0] : (((~funny(X0) | ~creative(X0)) | ~patient(X0)) & (patient(X0) | (funny(X0) & creative(X0)))) [nnf transformation 8]
64. ! [X0] : ((~funny(X0) | ~creative(X0) | ~patient(X0)) & (patient(X0) | (funny(X0) & creative(X0)))) [flattening 63]
65. ! [X0] : (((~funny(X0) | patient(X0)) & (funny(X0) | ~patient(X0))) | ~patient(X0)) [nnf transformation 33]
75. ! [X0] : ((creative(X0) & happy(X0)) | ((funny(X0) | ~kind(X0)) & (kind(X0) | ~funny(X0)))) [nnf transformation 39]
111. patient(X0) | funny(X0) [cnf transformation 64]
112. ~patient(X0) | ~creative(X0) | ~funny(X0) [cnf transformation 64]
113. funny(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 65]
135. ~funny(X0) | kind(X0) | creative(X0) [cnf transformation 75]
146. kind(lucy) | patient(lucy) [cnf transformation 19]
154. ~kind(lucy) [cnf transformation 25]
157. funny(X0) | ~patient(X0) [duplicate literal removal 113]
281. 29 <=> ! [X1] : funny(X1) [avatar definition]
282. funny(X1) <- (29) [avatar component clause 281]
286. funny(X0) [subsumption resolution 157,111]
287. 29 [avatar split clause 286,281]
346. 41 <=> patient(lucy) [avatar definition]
348. patient(lucy) <- (41) [avatar component clause 346]
350. 42 <=> kind(lucy) [avatar definition]
351. ~kind(lucy) <- (~42) [avatar component clause 350]
353. 41 | 42 [avatar split clause 146,350,346]
388. ~42 [avatar split clause 154,350]
421. ~creative(lucy) | ~funny(lucy) <- (41) [resolution 112,348]
425. ~creative(lucy) <- (29, 41) [subsumption resolution 421,282]
454. creative(X0) | kind(X0) <- (29) [resolution 135,282]
497. kind(lucy) <- (29, 41) [resolution 454,425]
501. $false <- (29, 41, ~42) [subsumption resolution 497,351]
502. ~29 | ~41 | 42 [avatar contradiction clause 501]
503. $false [avatar sat refutation 287,353,388,502]
% SZS output end Proof for 7068988629448835452850289
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both curious and not rich is not creative or not tall.
Everyone who is not humble or not wise is old.
If alice is both funny and not curious then fred is both quiet and wise and vice versa.
Everyone who is not generous is both creative and not humble.
Everyone who is both generous and not old is both calm and kind.
Everyone who is not quiet or not generous is either happy or generous.
If susan is both kind and creative then fred is both happy and not curious and vice versa.
If someone is happy then someone is either happy or not curious.
If lucy is funny or patient then susan is not tall.
If mary is curious then mary is both generous and patient and vice versa.
Everyone who is both kind and happy is either strong or quiet and vice versa.
Everyone who is both curious and not calm is both wise and not kind and vice versa.
If mary is calm or not happy then lucy is either not funny or happy.
If fred is both humble and not kind then someone is not quiet.
Everyone who is not rich is not patient or generous and vice versa.
Everyone who is either calm or not happy is not creative or rich.
Lucy is not rich or not wise.
John is either tall or calm.
Someone is either not quiet or tall.
Someone is not patient.
Mary is both not humble and old.
Lucy is either not kind or strong.
Susan is not strong or not tall.
Lucy is both quiet and not old. | John is not humble. | neutral | (![X]:((curious(X)&~rich(X))=>(~creative(X)|~tall(X))))&
(![X]:((~humble(X)|~wise(X))=>old(X)))&
(((funny(alice)&~curious(alice)))<=>((quiet(fred)&wise(fred))))&
(![X]:(~generous(X)=>(creative(X)&~humble(X))))&
(![X]:((generous(X)&~old(X))=>(calm(X)&kind(X))))&
(![X]:((~quiet(X)|~generous(X))=>(happy(X)<~>generous(X))))&
(((kind(susan)&creative(susan)))<=>((happy(fred)&~curious(fred))))&
((?[X]:(happy(X)))=>(?[X]:((happy(X)<~>~curious(X)))))&
(((funny(lucy)|patient(lucy)))=>(~tall(susan)))&
((curious(mary))<=>((generous(mary)&patient(mary))))&
(![X]:((kind(X)&happy(X))<=>(strong(X)<~>quiet(X))))&
(![X]:((curious(X)&~calm(X))<=>(wise(X)&~kind(X))))&
(((calm(mary)|~happy(mary)))=>((~funny(lucy)<~>happy(lucy))))&
(((humble(fred)&~kind(fred)))=>(?[X]:(~quiet(X))))&
(![X]:(~rich(X)<=>(~patient(X)|generous(X))))&
(![X]:((calm(X)<~>~happy(X))=>(~creative(X)|rich(X))))&
((~rich(lucy)|~wise(lucy)))&
((tall(john)<~>calm(john)))&
(?[X]:((~quiet(X)<~>tall(X))))&
(?[X]:(~patient(X)))&
((~humble(mary)&old(mary)))&
((~kind(lucy)<~>strong(lucy)))&
((~strong(susan)|~tall(susan)))&
((quiet(lucy)&~old(lucy))) | ~humble(john) | [] | null | 0 |
Everyone who is either creative or patient is old or not humble and vice versa.
If susan is not wise then someone is both kind and not generous and vice versa.
If john is either calm or not funny then mary is kind and vice versa.
Everyone who is kind is both not generous and not creative.
Everyone who is not old or not patient is both not wise and kind.
Everyone who is not rich is not curious.
Everyone who is old is tall and vice versa.
Everyone who is curious or not quiet is not curious and vice versa.
Everyone who is both not strong and happy is not curious.
Everyone who is either not calm or not old is tall or not funny.
If someone is not creative then alice is not funny.
Everyone who is not quiet is either not quiet or curious.
Everyone who is both rich and not rich is both wise and not old.
If mary is quiet or not tall then mary is either not curious or not generous.
If lucy is not kind then susan is not quiet.
If someone is both rich and humble then someone is either patient or rich and vice versa.
Lucy is either humble or happy.
Paul is either humble or not rich.
Someone is either funny or curious.
Paul is tall.
Susan is kind or wise.
Fred is either happy or strong.
Susan is both rich and not old.
Someone is curious or not curious. | Alice is funny. | contradiction | (![X]:((creative(X)<~>patient(X))<=>(old(X)|~humble(X))))&
((~wise(susan))<=>(?[X]:((kind(X)&~generous(X)))))&
(((calm(john)<~>~funny(john)))<=>(kind(mary)))&
(![X]:(kind(X)=>(~generous(X)&~creative(X))))&
(![X]:((~old(X)|~patient(X))=>(~wise(X)&kind(X))))&
(![X]:(~rich(X)=>~curious(X)))&
(![X]:(old(X)<=>tall(X)))&
(![X]:((curious(X)|~quiet(X))<=>~curious(X)))&
(![X]:((~strong(X)&happy(X))=>~curious(X)))&
(![X]:((~calm(X)<~>~old(X))=>(tall(X)|~funny(X))))&
((?[X]:(~creative(X)))=>(~funny(alice)))&
(![X]:(~quiet(X)=>(~quiet(X)<~>curious(X))))&
(![X]:((rich(X)&~rich(X))=>(wise(X)&~old(X))))&
(((quiet(mary)|~tall(mary)))=>((~curious(mary)<~>~generous(mary))))&
((~kind(lucy))=>(~quiet(susan)))&
((?[X]:((rich(X)&humble(X))))<=>(?[X]:((patient(X)<~>rich(X)))))&
((humble(lucy)<~>happy(lucy)))&
((humble(paul)<~>~rich(paul)))&
(?[X]:((funny(X)<~>curious(X))))&
(tall(paul))&
((kind(susan)|wise(susan)))&
((happy(fred)<~>strong(fred)))&
((rich(susan)&~old(susan)))&
(?[X]:((curious(X)|~curious(X)))) | funny(alice) | [
"p3",
"p4",
"p10",
"p20",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 3273941650270814029588967
% SZS output start Proof for 3273941650270814029588967
4. ! [X0] : (kind(X0) => (~creative(X0) & ~generous(X0))) [input p3]
5. ! [X0] : ((~patient(X0) | ~old(X0)) => (kind(X0) & ~wise(X0))) [input p4]
11. ? [X0] : ~creative(X0) => ~funny(alice) [input p10]
21. wise(susan) | kind(susan) [input p20]
23. ~old(susan) & rich(susan) [input p22]
25. funny(alice) [input hypothesis]
27. ! [X0] : ((~creative(X0) & ~generous(X0)) | ~kind(X0)) [ennf transformation 4]
28. ! [X0] : ((kind(X0) & ~wise(X0)) | (patient(X0) & old(X0))) [ennf transformation 5]
34. ~funny(alice) | ! [X0] : creative(X0) [ennf transformation 11]
80. ~kind(X0) | ~creative(X0) [cnf transformation 27]
81. ~wise(X0) | old(X0) [cnf transformation 28]
94. ~funny(alice) | creative(X0) [cnf transformation 34]
117. wise(susan) | kind(susan) [cnf transformation 21]
121. ~old(susan) [cnf transformation 23]
123. funny(alice) [cnf transformation 25]
131. 2 <=> wise(susan) [avatar definition]
132. wise(susan) <- (2) [avatar component clause 131]
163. 8 <=> ! [X0] : creative(X0) [avatar definition]
164. creative(X0) <- (8) [avatar component clause 163]
166. 9 <=> funny(alice) [avatar definition]
169. 8 | ~9 [avatar split clause 94,166,163]
242. 25 <=> kind(susan) [avatar definition]
244. kind(susan) <- (25) [avatar component clause 242]
245. 25 | 2 [avatar split clause 117,131,242]
256. 9 [avatar split clause 123,166]
259. ~creative(susan) <- (25) [resolution 80,244]
264. $false <- (8, 25) [subsumption resolution 259,164]
265. ~8 | ~25 [avatar contradiction clause 264]
267. old(susan) <- (2) [resolution 81,132]
268. $false <- (2) [subsumption resolution 267,121]
269. ~2 [avatar contradiction clause 268]
270. $false [avatar sat refutation 169,245,256,265,269]
% SZS output end Proof for 3273941650270814029588967
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both creative and brave is both not kind and not quiet and vice versa.
Everyone who is either not brave or not creative is both not quiet and not humble and vice versa.
If mary is either strong or funny then alice is both not quiet and brave.
Everyone who is brave or not curious is both not brave and brave and vice versa.
If someone is patient or not curious then fred is either not brave or old and vice versa.
If john is either not strong or not patient then mary is creative and vice versa.
Everyone who is both funny and not kind is not calm or curious.
If someone is either not patient or not generous then susan is both not tall and happy and vice versa.
Everyone who is both not curious and not strong is not patient and vice versa.
If someone is both not quiet and brave then lucy is both not strong and not humble and vice versa.
If mary is not curious then someone is both patient and not humble.
Everyone who is patient is both not generous and calm.
If someone is old or not happy then lucy is patient or strong and vice versa.
Everyone who is both not humble and strong is not funny or old and vice versa.
Everyone who is both patient and funny is either not funny or humble and vice versa.
Someone is rich or not tall.
Someone is funny.
Susan is not brave or not rich.
Lucy is calm or not calm.
John is not creative.
Someone is either rich or not happy. | Lucy is not curious. | contradiction | (![X]:((creative(X)&brave(X))<=>(~kind(X)&~quiet(X))))&
(![X]:((~brave(X)<~>~creative(X))<=>(~quiet(X)&~humble(X))))&
(((strong(mary)<~>funny(mary)))=>((~quiet(alice)&brave(alice))))&
(![X]:((brave(X)|~curious(X))<=>(~brave(X)&brave(X))))&
((?[X]:((patient(X)|~curious(X))))<=>((~brave(fred)<~>old(fred))))&
(((~strong(john)<~>~patient(john)))<=>(creative(mary)))&
(![X]:((funny(X)&~kind(X))=>(~calm(X)|curious(X))))&
((?[X]:((~patient(X)<~>~generous(X))))<=>((~tall(susan)&happy(susan))))&
(![X]:((~curious(X)&~strong(X))<=>~patient(X)))&
((?[X]:((~quiet(X)&brave(X))))<=>((~strong(lucy)&~humble(lucy))))&
((~curious(mary))=>(?[X]:((patient(X)&~humble(X)))))&
(![X]:(patient(X)=>(~generous(X)&calm(X))))&
((?[X]:((old(X)|~happy(X))))<=>((patient(lucy)|strong(lucy))))&
(![X]:((~humble(X)&strong(X))<=>(~funny(X)|old(X))))&
(![X]:((patient(X)&funny(X))<=>(~funny(X)<~>humble(X))))&
(?[X]:((rich(X)|~tall(X))))&
(?[X]:(funny(X)))&
((~brave(susan)|~rich(susan)))&
((calm(lucy)|~calm(lucy)))&
(~creative(john))&
(?[X]:((rich(X)<~>~happy(X)))) | ~curious(lucy) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 317324580285791793295068
% SZS output start Proof for 317324580285791793295068
4. ! [X0] : ((~curious(X0) | brave(X0)) <=> (brave(X0) & ~brave(X0))) [input p3]
22. ~curious(lucy) [input hypothesis]
33. ! [X0] : (((~curious(X0) | brave(X0)) | (~brave(X0) | brave(X0))) & ((brave(X0) & ~brave(X0)) | (curious(X0) & ~brave(X0)))) [nnf transformation 4]
34. ! [X0] : ((~curious(X0) | brave(X0) | ~brave(X0) | brave(X0)) & ((brave(X0) & ~brave(X0)) | (curious(X0) & ~brave(X0)))) [flattening 33]
85. ~brave(X0) | curious(X0) [cnf transformation 34]
87. brave(X0) | curious(X0) [cnf transformation 34]
139. ~curious(lucy) [cnf transformation 22]
167. curious(X0) [subsumption resolution 85,87]
279. $false [subsumption resolution 139,167]
% SZS output end Proof for 317324580285791793295068
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 fred is patient or rich then someone is either creative or not kind and vice versa.
Everyone who is humble or not quiet is not funny or not humble.
If paul is not tall or wise then fred is kind or not old and vice versa.
Everyone who is both not rich and not wise is either creative or curious and vice versa.
If someone is wise or not patient then mary is not tall and vice versa.
If someone is either curious or strong then john is both not kind and not quiet.
If someone is either strong or not brave then someone is humble or calm.
If someone is either not funny or not quiet then susan is calm.
If someone is not tall then someone is either old or quiet.
If someone is both rich and funny then susan is happy.
If john is not strong then someone is tall or not curious.
Everyone who is kind is both humble and not kind.
If mary is patient or happy then mary is either quiet or strong.
Everyone who is either happy or old is either happy or not brave.
Everyone who is not brave is tall or brave and vice versa.
Everyone who is calm is not curious and vice versa.
John is generous or old.
Someone is either not funny or kind.
Fred is both not funny and not brave.
Someone is not strong or kind.
Alice is not funny or tall. | Fred is quiet. | neutral | (((patient(fred)|rich(fred)))<=>(?[X]:((creative(X)<~>~kind(X)))))&
(![X]:((humble(X)|~quiet(X))=>(~funny(X)|~humble(X))))&
(((~tall(paul)|wise(paul)))<=>((kind(fred)|~old(fred))))&
(![X]:((~rich(X)&~wise(X))<=>(creative(X)<~>curious(X))))&
((?[X]:((wise(X)|~patient(X))))<=>(~tall(mary)))&
((?[X]:((curious(X)<~>strong(X))))=>((~kind(john)&~quiet(john))))&
((?[X]:((strong(X)<~>~brave(X))))=>(?[X]:((humble(X)|calm(X)))))&
((?[X]:((~funny(X)<~>~quiet(X))))=>(calm(susan)))&
((?[X]:(~tall(X)))=>(?[X]:((old(X)<~>quiet(X)))))&
((?[X]:((rich(X)&funny(X))))=>(happy(susan)))&
((~strong(john))=>(?[X]:((tall(X)|~curious(X)))))&
(![X]:(kind(X)=>(humble(X)&~kind(X))))&
(((patient(mary)|happy(mary)))=>((quiet(mary)<~>strong(mary))))&
(![X]:((happy(X)<~>old(X))=>(happy(X)<~>~brave(X))))&
(![X]:(~brave(X)<=>(tall(X)|brave(X))))&
(![X]:(calm(X)<=>~curious(X)))&
((generous(john)|old(john)))&
(?[X]:((~funny(X)<~>kind(X))))&
((~funny(fred)&~brave(fred)))&
(?[X]:((~strong(X)|kind(X))))&
((~funny(alice)|tall(alice))) | quiet(fred) | [] | null | 0 |
Everyone who is both calm and rich is not rich or old.
If lucy is wise then alice is both not strong and not happy.
Everyone who is not strong is generous and vice versa.
If lucy is old or creative then someone is both not creative and quiet and vice versa.
If alice is both old and brave then john is either tall or humble.
If fred is not patient or not strong then lucy is not patient and vice versa.
Everyone who is both not rich and not calm is both creative and patient and vice versa.
If someone is kind or old then someone is quiet or strong.
If lucy is not tall then someone is both quiet and old and vice versa.
Everyone who is both wise and humble is generous and vice versa.
Everyone who is either quiet or tall is both rich and kind and vice versa.
If someone is both not kind and rich then john is both tall and strong and vice versa.
Everyone who is not curious is either not curious or not generous and vice versa.
Everyone who is tall or not quiet is brave.
If someone is not calm or not patient then susan is generous or not old and vice versa.
Everyone who is quiet is patient or not kind and vice versa.
Someone is either strong or curious.
Alice is either tall or not calm.
Paul is quiet or not tall.
Someone is both not calm and brave.
Mary is both not old and happy.
Someone is either not patient or not calm.
Paul is either not old or rich.
Lucy is either old or not wise. | Lucy is old. | entailment | (![X]:((calm(X)&rich(X))=>(~rich(X)|old(X))))&
((wise(lucy))=>((~strong(alice)&~happy(alice))))&
(![X]:(~strong(X)<=>generous(X)))&
(((old(lucy)|creative(lucy)))<=>(?[X]:((~creative(X)&quiet(X)))))&
(((old(alice)&brave(alice)))=>((tall(john)<~>humble(john))))&
(((~patient(fred)|~strong(fred)))<=>(~patient(lucy)))&
(![X]:((~rich(X)&~calm(X))<=>(creative(X)&patient(X))))&
((?[X]:((kind(X)|old(X))))=>(?[X]:((quiet(X)|strong(X)))))&
((~tall(lucy))<=>(?[X]:((quiet(X)&old(X)))))&
(![X]:((wise(X)&humble(X))<=>generous(X)))&
(![X]:((quiet(X)<~>tall(X))<=>(rich(X)&kind(X))))&
((?[X]:((~kind(X)&rich(X))))<=>((tall(john)&strong(john))))&
(![X]:(~curious(X)<=>(~curious(X)<~>~generous(X))))&
(![X]:((tall(X)|~quiet(X))=>brave(X)))&
((?[X]:((~calm(X)|~patient(X))))<=>((generous(susan)|~old(susan))))&
(![X]:(quiet(X)<=>(patient(X)|~kind(X))))&
(?[X]:((strong(X)<~>curious(X))))&
((tall(alice)<~>~calm(alice)))&
((quiet(paul)|~tall(paul)))&
(?[X]:((~calm(X)&brave(X))))&
((~old(mary)&happy(mary)))&
(?[X]:((~patient(X)<~>~calm(X))))&
((~old(paul)<~>rich(paul)))&
((old(lucy)<~>~wise(lucy))) | old(lucy) | [
"p2",
"p9",
"p12",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 4022704215677200676735046
% SZS output start Proof for 4022704215677200676735046
3. ! [X0] : (~strong(X0) <=> generous(X0)) [input p2]
10. ! [X0] : ((humble(X0) & wise(X0)) <=> generous(X0)) [input p9]
13. ! [X0] : (~curious(X0) <=> (~curious(X0) <~> ~generous(X0))) [input p12]
24. old(lucy) <~> ~wise(lucy) [input p23]
25. ~old(lucy) [input hypothesis]
34. ! [X0] : ((~strong(X0) | ~generous(X0)) & (generous(X0) | strong(X0))) [nnf transformation 3]
52. ! [X0] : (((humble(X0) & wise(X0)) | ~generous(X0)) & (generous(X0) | (~humble(X0) | ~wise(X0)))) [nnf transformation 10]
53. ! [X0] : (((humble(X0) & wise(X0)) | ~generous(X0)) & (generous(X0) | ~humble(X0) | ~wise(X0))) [flattening 52]
61. ! [X0] : ((~curious(X0) | ((~curious(X0) | generous(X0)) & (~generous(X0) | curious(X0)))) & (((generous(X0) | curious(X0)) & (~generous(X0) | ~curious(X0))) | curious(X0))) [nnf transformation 13]
79. (wise(lucy) | ~old(lucy)) & (~wise(lucy) | old(lucy)) [nnf transformation 24]
83. generous(X0) | strong(X0) [cnf transformation 34]
84. ~generous(X0) | ~strong(X0) [cnf transformation 34]
105. ~generous(X0) | wise(X0) [cnf transformation 53]
118. generous(X0) | curious(X0) | curious(X0) [cnf transformation 61]
120. ~curious(X0) | ~curious(X0) | generous(X0) [cnf transformation 61]
143. ~wise(lucy) | old(lucy) [cnf transformation 79]
145. ~old(lucy) [cnf transformation 25]
146. generous(X0) | curious(X0) [duplicate literal removal 118]
147. ~curious(X0) | generous(X0) [duplicate literal removal 120]
150. 1 <=> wise(lucy) [avatar definition]
152. ~wise(lucy) <- (~1) [avatar component clause 150]
167. 5 <=> old(lucy) [avatar definition]
273. generous(X0) [subsumption resolution 146,147]
339. 5 | ~1 [avatar split clause 143,150,167]
340. ~5 [avatar split clause 145,167]
342. ~strong(X1) [resolution 84,273]
343. wise(X0) | strong(X0) [resolution 105,83]
345. wise(X0) [subsumption resolution 343,342]
350. $false <- (~1) [resolution 345,152]
351. 1 [avatar contradiction clause 350]
352. $false [avatar sat refutation 339,340,351]
% SZS output end Proof for 4022704215677200676735046
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise and not funny is patient and vice versa.
Everyone who is quiet or patient is both not calm and old and vice versa.
If someone is not curious then paul is not curious or rich.
If someone is not tall or not patient then someone is both not calm and not rich and vice versa.
If mary is both not generous and calm then someone is strong or not rich.
Everyone who is wise or rich is either strong or generous.
Everyone who is both kind and old is both generous and not old.
Everyone who is old or humble is calm.
Everyone who is rich or not generous is either not creative or not humble.
If fred is either not brave or not wise then someone is either not kind or humble and vice versa.
Everyone who is both funny and not quiet is not generous or not calm.
Everyone who is both wise and not patient is both patient and brave.
Everyone who is either strong or not patient is either humble or kind.
Everyone who is creative or generous is not calm.
Everyone who is curious or strong is both not wise and not humble and vice versa.
If someone is both not generous and not humble then susan is not generous.
Paul is brave or not brave.
Someone is tall or curious.
Someone is either rich or not brave.
Someone is brave.
Lucy is not wise or not curious.
Someone is either funny or creative.
Mary is not curious.
Someone is both kind and not strong. | Mary is not tall. | neutral | (![X]:((wise(X)&~funny(X))<=>patient(X)))&
(![X]:((quiet(X)|patient(X))<=>(~calm(X)&old(X))))&
((?[X]:(~curious(X)))=>((~curious(paul)|rich(paul))))&
((?[X]:((~tall(X)|~patient(X))))<=>(?[X]:((~calm(X)&~rich(X)))))&
(((~generous(mary)&calm(mary)))=>(?[X]:((strong(X)|~rich(X)))))&
(![X]:((wise(X)|rich(X))=>(strong(X)<~>generous(X))))&
(![X]:((kind(X)&old(X))=>(generous(X)&~old(X))))&
(![X]:((old(X)|humble(X))=>calm(X)))&
(![X]:((rich(X)|~generous(X))=>(~creative(X)<~>~humble(X))))&
(((~brave(fred)<~>~wise(fred)))<=>(?[X]:((~kind(X)<~>humble(X)))))&
(![X]:((funny(X)&~quiet(X))=>(~generous(X)|~calm(X))))&
(![X]:((wise(X)&~patient(X))=>(patient(X)&brave(X))))&
(![X]:((strong(X)<~>~patient(X))=>(humble(X)<~>kind(X))))&
(![X]:((creative(X)|generous(X))=>~calm(X)))&
(![X]:((curious(X)|strong(X))<=>(~wise(X)&~humble(X))))&
((?[X]:((~generous(X)&~humble(X))))=>(~generous(susan)))&
((brave(paul)|~brave(paul)))&
(?[X]:((tall(X)|curious(X))))&
(?[X]:((rich(X)<~>~brave(X))))&
(?[X]:(brave(X)))&
((~wise(lucy)|~curious(lucy)))&
(?[X]:((funny(X)<~>creative(X))))&
(~curious(mary))&
(?[X]:((kind(X)&~strong(X)))) | ~tall(mary) | [] | null | 0 |
Everyone who is both brave and quiet is not generous or not tall.
If paul is rich then someone is not quiet or curious.
Everyone who is either tall or not brave is not brave and vice versa.
Everyone who is creative is both brave and not calm.
If fred is creative then someone is not humble or not kind.
Everyone who is both old and not patient is either not patient or not wise.
Everyone who is not rich or not calm is creative or generous.
Everyone who is not kind is both rich and happy.
If someone is not strong or tall then someone is both not old and quiet.
Everyone who is either patient or brave is either not strong or humble.
If someone is both creative and patient then lucy is both wise and not humble.
Everyone who is not old is both brave and not tall.
If someone is both not old and not quiet then paul is not kind.
Everyone who is not tall or not quiet is either not strong or not old.
Everyone who is both happy and not creative is not brave or brave and vice versa.
Everyone who is not quiet is not funny or creative and vice versa.
Someone is strong.
Someone is funny.
Paul is not wise.
Susan is not brave or calm.
Paul is generous.
Paul is not curious or not generous.
Someone is either strong or curious. | Paul is not wise. | entailment | (![X]:((brave(X)&quiet(X))=>(~generous(X)|~tall(X))))&
((rich(paul))=>(?[X]:((~quiet(X)|curious(X)))))&
(![X]:((tall(X)<~>~brave(X))<=>~brave(X)))&
(![X]:(creative(X)=>(brave(X)&~calm(X))))&
((creative(fred))=>(?[X]:((~humble(X)|~kind(X)))))&
(![X]:((old(X)&~patient(X))=>(~patient(X)<~>~wise(X))))&
(![X]:((~rich(X)|~calm(X))=>(creative(X)|generous(X))))&
(![X]:(~kind(X)=>(rich(X)&happy(X))))&
((?[X]:((~strong(X)|tall(X))))=>(?[X]:((~old(X)&quiet(X)))))&
(![X]:((patient(X)<~>brave(X))=>(~strong(X)<~>humble(X))))&
((?[X]:((creative(X)&patient(X))))=>((wise(lucy)&~humble(lucy))))&
(![X]:(~old(X)=>(brave(X)&~tall(X))))&
((?[X]:((~old(X)&~quiet(X))))=>(~kind(paul)))&
(![X]:((~tall(X)|~quiet(X))=>(~strong(X)<~>~old(X))))&
(![X]:((happy(X)&~creative(X))<=>(~brave(X)|brave(X))))&
(![X]:(~quiet(X)<=>(~funny(X)|creative(X))))&
(?[X]:(strong(X)))&
(?[X]:(funny(X)))&
(~wise(paul))&
((~brave(susan)|calm(susan)))&
(generous(paul))&
((~curious(paul)|~generous(paul)))&
(?[X]:((strong(X)<~>curious(X)))) | ~wise(paul) | [
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 522809730595210425429225
% SZS output start Proof for 522809730595210425429225
19. ~wise(paul) [input p18]
24. wise(paul) [input hypothesis]
106. ~wise(paul) [cnf transformation 19]
112. wise(paul) [cnf transformation 24]
202. $false [subsumption resolution 112,106]
% SZS output end Proof for 522809730595210425429225
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not humble is either humble or not funny.
Everyone who is curious or not curious is not wise.
Everyone who is generous or funny is not strong.
If fred is both not creative and not generous then someone is both not strong and not humble and vice versa.
Everyone who is not wise is tall or not creative and vice versa.
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.
Someone is happy.
Lucy is generous or not brave.
Susan is not creative.
Lucy is both funny and not wise.
Someone is calm or not quiet.
Alice is either not humble or funny. | Lucy is wise. | contradiction | (![X]:(~humble(X)=>(humble(X)<~>~funny(X))))&
(![X]:((curious(X)|~curious(X))=>~wise(X)))&
(![X]:((generous(X)|funny(X))=>~strong(X)))&
(((~creative(fred)&~generous(fred)))<=>(?[X]:((~strong(X)&~humble(X)))))&
(![X]:(~wise(X)<=>(tall(X)|~creative(X))))&
((?[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]:(happy(X)))&
((generous(lucy)|~brave(lucy)))&
(~creative(susan))&
((funny(lucy)&~wise(lucy)))&
(?[X]:((calm(X)|~quiet(X))))&
((~humble(alice)<~>funny(alice))) | wise(lucy) | [
"p1",
"hypothesis"
] | % SZS status Unsatisfiable for 211531019740931423915360
% SZS output start Proof for 211531019740931423915360
2. ! [X0] : ((~curious(X0) | curious(X0)) => ~wise(X0)) [input p1]
22. wise(lucy) [input hypothesis]
27. ! [X0] : (~wise(X0) | (curious(X0) & ~curious(X0))) [ennf transformation 2]
65. ~wise(X0) | ~curious(X0) [cnf transformation 27]
66. ~wise(X0) | curious(X0) [cnf transformation 27]
112. wise(lucy) [cnf transformation 22]
116. ~wise(X0) [subsumption resolution 65,66]
229. $false [subsumption resolution 112,116]
% SZS output end Proof for 211531019740931423915360
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or not generous is either not funny or not patient and vice versa.
Everyone who is not tall is funny or not tall and vice versa.
If someone is kind or not rich then fred is not funny or brave.
If alice is curious or not tall then mary is not old and vice versa.
If someone is not old or generous then someone is either not rich or strong.
If alice is not funny then someone is quiet or not funny.
If fred is not strong or not brave then mary is either funny or quiet.
Everyone who is not rich or not creative is creative or strong and vice versa.
Everyone who is both not generous and curious is both not funny and strong and vice versa.
Everyone who is either humble or not humble is either funny or not happy and vice versa.
Everyone who is brave or not curious is rich.
Everyone who is wise is generous or not wise and vice versa.
If someone is both wise and humble then someone is not brave or not strong.
If someone is not curious then someone is either tall or not tall and vice versa.
Everyone who is happy is either not calm or not tall and vice versa.
Everyone who is either kind or creative is not calm.
Paul is patient.
Someone is either not happy or quiet.
Someone is either not tall or not brave.
Someone is not curious.
Fred is either rich or not rich.
Mary is both calm and kind.
Someone is not calm or funny. | Paul is not funny. | neutral | (![X]:((curious(X)|~generous(X))<=>(~funny(X)<~>~patient(X))))&
(![X]:(~tall(X)<=>(funny(X)|~tall(X))))&
((?[X]:((kind(X)|~rich(X))))=>((~funny(fred)|brave(fred))))&
(((curious(alice)|~tall(alice)))<=>(~old(mary)))&
((?[X]:((~old(X)|generous(X))))=>(?[X]:((~rich(X)<~>strong(X)))))&
((~funny(alice))=>(?[X]:((quiet(X)|~funny(X)))))&
(((~strong(fred)|~brave(fred)))=>((funny(mary)<~>quiet(mary))))&
(![X]:((~rich(X)|~creative(X))<=>(creative(X)|strong(X))))&
(![X]:((~generous(X)&curious(X))<=>(~funny(X)&strong(X))))&
(![X]:((humble(X)<~>~humble(X))<=>(funny(X)<~>~happy(X))))&
(![X]:((brave(X)|~curious(X))=>rich(X)))&
(![X]:(wise(X)<=>(generous(X)|~wise(X))))&
((?[X]:((wise(X)&humble(X))))=>(?[X]:((~brave(X)|~strong(X)))))&
((?[X]:(~curious(X)))<=>(?[X]:((tall(X)<~>~tall(X)))))&
(![X]:(happy(X)<=>(~calm(X)<~>~tall(X))))&
(![X]:((kind(X)<~>creative(X))=>~calm(X)))&
(patient(paul))&
(?[X]:((~happy(X)<~>quiet(X))))&
(?[X]:((~tall(X)<~>~brave(X))))&
(?[X]:(~curious(X)))&
((rich(fred)<~>~rich(fred)))&
((calm(mary)&kind(mary)))&
(?[X]:((~calm(X)|funny(X)))) | ~funny(paul) | [] | null | 0 |
Everyone who is not creative or not kind is both curious and old and vice versa. If lucy is strong then mary is both not rich and brave and vice versa. Everyone who is either not curious or not tall is either patient or tall. Everyone who is not brave or not curious is tall. Everyone who is both not calm and strong is either not generous or not patient. If someone is either not tall or not old then mary is either wise or calm and vice versa. Everyone who is happy is funny or humble. Everyone who is old or not old is either wise or not curious and vice versa. Everyone who is not rich or patient is both not humble and old and vice versa. Everyone who is either quiet or not calm is either funny or not funny. If someone is curious or not kind then susan is generous or not generous and vice versa. Everyone who is old or funny is rich or not kind and vice versa. If someone is not tall then mary is not old or not calm. Everyone who is not rich is either not wise or not creative. Everyone who is patient or happy is both creative and not brave. If someone is old or not kind then fred is not tall. Alice is wise or tall. Lucy is either patient or happy. Someone is creative. Mary is rich or not rich. Paul is either not brave or generous. Alice is both tall and quiet. Someone is not humble or calm. | Mary is not quiet. | neutral | (![X]:((~creative(X)|~kind(X))<=>(curious(X)&old(X))))&
((strong(lucy))<=>((~rich(mary)&brave(mary))))&
(![X]:((~curious(X)<~>~tall(X))=>(patient(X)<~>tall(X))))&
(![X]:((~brave(X)|~curious(X))=>tall(X)))&
(![X]:((~calm(X)&strong(X))=>(~generous(X)<~>~patient(X))))&
((?[X]:((~tall(X)<~>~old(X))))<=>((wise(mary)<~>calm(mary))))&
(![X]:(happy(X)=>(funny(X)|humble(X))))&
(![X]:((old(X)|~old(X))<=>(wise(X)<~>~curious(X))))&
(![X]:((~rich(X)|patient(X))<=>(~humble(X)&old(X))))&
(![X]:((quiet(X)<~>~calm(X))=>(funny(X)<~>~funny(X))))&
((?[X]:((curious(X)|~kind(X))))<=>((generous(susan)|~generous(susan))))&
(![X]:((old(X)|funny(X))<=>(rich(X)|~kind(X))))&
((?[X]:(~tall(X)))=>((~old(mary)|~calm(mary))))&
(![X]:(~rich(X)=>(~wise(X)<~>~creative(X))))&
(![X]:((patient(X)|happy(X))=>(creative(X)&~brave(X))))&
((?[X]:((old(X)|~kind(X))))=>(~tall(fred)))&
((wise(alice)|tall(alice)))&
((patient(lucy)<~>happy(lucy)))&
(?[X]:(creative(X)))&
((rich(mary)|~rich(mary)))&
((~brave(paul)<~>generous(paul)))&
((tall(alice)&quiet(alice)))&
(?[X]:((~humble(X)|calm(X)))) | ~quiet(mary) | [] | null | 0 |
If someone is either not curious or not old then someone is not wise or not humble. Everyone who is either not rich or funny is wise and vice versa. If john is either not patient or not rich then mary is strong. If alice is both patient and not patient then susan is either not humble or not brave and vice versa. If mary is not wise then someone is both old and calm and vice versa. Everyone who is both not wise and not curious is both not old and not rich and vice versa. Everyone who is not quiet is not calm and vice versa. If john is either strong or generous then someone is kind and vice versa. Everyone who is not tall or not brave is both brave and not tall and vice versa. If someone is either kind or not calm then susan is both curious and rich and vice versa. If lucy is either not wise or funny then fred is not calm and vice versa. Everyone who is calm is both not creative and not quiet. Everyone who is both not curious and not humble is both not humble and not strong and vice versa. If someone is either not rich or calm then alice is either not happy or not patient. If lucy is both not calm and not quiet then susan is both not curious and strong and vice versa. If someone is not kind then someone is not curious. Someone is both creative and humble. Alice is funny or not tall. Someone is both not happy and humble. Someone is either not patient or tall. Alice is both strong and rich. Someone is not rich or happy. Fred is not strong or strong. | Susan is patient. | neutral | ((?[X]:((~curious(X)<~>~old(X))))=>(?[X]:((~wise(X)|~humble(X)))))&
(![X]:((~rich(X)<~>funny(X))<=>wise(X)))&
(((~patient(john)<~>~rich(john)))=>(strong(mary)))&
(((patient(alice)&~patient(alice)))<=>((~humble(susan)<~>~brave(susan))))&
((~wise(mary))<=>(?[X]:((old(X)&calm(X)))))&
(![X]:((~wise(X)&~curious(X))<=>(~old(X)&~rich(X))))&
(![X]:(~quiet(X)<=>~calm(X)))&
(((strong(john)<~>generous(john)))<=>(?[X]:(kind(X))))&
(![X]:((~tall(X)|~brave(X))<=>(brave(X)&~tall(X))))&
((?[X]:((kind(X)<~>~calm(X))))<=>((curious(susan)&rich(susan))))&
(((~wise(lucy)<~>funny(lucy)))<=>(~calm(fred)))&
(![X]:(calm(X)=>(~creative(X)&~quiet(X))))&
(![X]:((~curious(X)&~humble(X))<=>(~humble(X)&~strong(X))))&
((?[X]:((~rich(X)<~>calm(X))))=>((~happy(alice)<~>~patient(alice))))&
(((~calm(lucy)&~quiet(lucy)))<=>((~curious(susan)&strong(susan))))&
((?[X]:(~kind(X)))=>(?[X]:(~curious(X))))&
(?[X]:((creative(X)&humble(X))))&
((funny(alice)|~tall(alice)))&
(?[X]:((~happy(X)&humble(X))))&
(?[X]:((~patient(X)<~>tall(X))))&
((strong(alice)&rich(alice)))&
(?[X]:((~rich(X)|happy(X))))&
((~strong(fred)|strong(fred))) | patient(susan) | [] | null | 0 |
Everyone who is not calm or funny is both not funny and rich.
Everyone who is either funny or creative is not rich and vice versa.
If mary is strong then someone is both not calm and creative.
If fred is rich or not funny then someone is either not kind or not tall.
If someone is either tall or not kind then someone is generous.
If susan is not generous then susan is either not strong or not patient and vice versa.
If fred is not curious then lucy is both not funny and kind.
Everyone who is both happy and strong is kind or not wise.
Everyone who is both not strong and creative is funny or calm and vice versa.
Everyone who is rich is either not patient or not wise and vice versa.
If someone is either not calm or not humble then someone is both funny and rich.
Everyone who is both happy and not old is not generous.
If fred is both happy and not kind then susan is either generous or wise.
Everyone who is either funny or not strong is not rich or not happy and vice versa.
Everyone who is not funny or tall is both creative and not curious and vice versa.
If john is tall then fred is wise or not strong and vice versa.
Paul is either not happy or not humble.
Paul is not tall or strong.
Someone is either not tall or strong.
Someone is not calm or not generous.
Fred is kind. | John is tall. | entailment | (![X]:((~calm(X)|funny(X))=>(~funny(X)&rich(X))))&
(![X]:((funny(X)<~>creative(X))<=>~rich(X)))&
((strong(mary))=>(?[X]:((~calm(X)&creative(X)))))&
(((rich(fred)|~funny(fred)))=>(?[X]:((~kind(X)<~>~tall(X)))))&
((?[X]:((tall(X)<~>~kind(X))))=>(?[X]:(generous(X))))&
((~generous(susan))<=>((~strong(susan)<~>~patient(susan))))&
((~curious(fred))=>((~funny(lucy)&kind(lucy))))&
(![X]:((happy(X)&strong(X))=>(kind(X)|~wise(X))))&
(![X]:((~strong(X)&creative(X))<=>(funny(X)|calm(X))))&
(![X]:(rich(X)<=>(~patient(X)<~>~wise(X))))&
((?[X]:((~calm(X)<~>~humble(X))))=>(?[X]:((funny(X)&rich(X)))))&
(![X]:((happy(X)&~old(X))=>~generous(X)))&
(((happy(fred)&~kind(fred)))=>((generous(susan)<~>wise(susan))))&
(![X]:((funny(X)<~>~strong(X))<=>(~rich(X)|~happy(X))))&
(![X]:((~funny(X)|tall(X))<=>(creative(X)&~curious(X))))&
((tall(john))<=>((wise(fred)|~strong(fred))))&
((~happy(paul)<~>~humble(paul)))&
((~tall(paul)|strong(paul)))&
(?[X]:((~tall(X)<~>strong(X))))&
(?[X]:((~calm(X)|~generous(X))))&
(kind(fred)) | tall(john) | [
"p0",
"p1",
"p8",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8174157020993241518564880
% SZS output start Proof for 8174157020993241518564880
1. ! [X0] : ((funny(X0) | ~calm(X0)) => (rich(X0) & ~funny(X0))) [input p0]
2. ! [X0] : ((funny(X0) <~> creative(X0)) <=> ~rich(X0)) [input p1]
9. ! [X0] : ((creative(X0) & ~strong(X0)) <=> (calm(X0) | funny(X0))) [input p8]
15. ! [X0] : ((tall(X0) | ~funny(X0)) <=> (~curious(X0) & creative(X0))) [input p14]
16. tall(john) <=> (~strong(fred) | wise(fred)) [input p15]
22. ~tall(john) [input hypothesis]
26. ! [X0] : ((rich(X0) & ~funny(X0)) | (~funny(X0) & calm(X0))) [ennf transformation 1]
36. ! [X0] : ((((~creative(X0) | ~funny(X0)) & (creative(X0) | funny(X0))) | rich(X0)) & (~rich(X0) | ((funny(X0) | ~creative(X0)) & (creative(X0) | ~funny(X0))))) [nnf transformation 2]
47. ! [X0] : (((creative(X0) & ~strong(X0)) | (~calm(X0) & ~funny(X0))) & ((calm(X0) | funny(X0)) | (~creative(X0) | strong(X0)))) [nnf transformation 9]
48. ! [X0] : (((creative(X0) & ~strong(X0)) | (~calm(X0) & ~funny(X0))) & (calm(X0) | funny(X0) | ~creative(X0) | strong(X0))) [flattening 47]
57. ! [X0] : (((tall(X0) | ~funny(X0)) | (curious(X0) | ~creative(X0))) & ((~curious(X0) & creative(X0)) | (~tall(X0) & funny(X0)))) [nnf transformation 15]
58. ! [X0] : ((tall(X0) | ~funny(X0) | curious(X0) | ~creative(X0)) & ((~curious(X0) & creative(X0)) | (~tall(X0) & funny(X0)))) [flattening 57]
59. (tall(john) | (strong(fred) & ~wise(fred))) & ((~strong(fred) | wise(fred)) | ~tall(john)) [nnf transformation 16]
60. (tall(john) | (strong(fred) & ~wise(fred))) & (~strong(fred) | wise(fred) | ~tall(john)) [flattening 59]
68. ~funny(X0) | ~funny(X0) [cnf transformation 26]
69. rich(X0) | calm(X0) [cnf transformation 26]
72. ~rich(X0) | funny(X0) | ~creative(X0) [cnf transformation 36]
92. ~strong(X0) | ~calm(X0) [cnf transformation 48]
111. creative(X0) | funny(X0) [cnf transformation 58]
118. tall(john) | strong(fred) [cnf transformation 60]
126. ~tall(john) [cnf transformation 22]
127. ~funny(X0) [duplicate literal removal 68]
129. ~creative(X0) | ~rich(X0) [subsumption resolution 72,127]
234. creative(X0) [subsumption resolution 111,127]
236. 21 <=> strong(fred) [avatar definition]
238. strong(fred) <- (21) [avatar component clause 236]
240. 22 <=> tall(john) [avatar definition]
243. 21 | 22 [avatar split clause 118,240,236]
289. ~22 [avatar split clause 126,240]
292. ~calm(fred) <- (21) [resolution 92,238]
294. ~rich(X1) [resolution 129,234]
295. calm(X0) [resolution 294,69]
297. $false <- (21) [resolution 295,292]
300. ~21 [avatar contradiction clause 297]
302. $false [avatar sat refutation 243,289,300]
% SZS output end Proof for 8174157020993241518564880
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind then someone is quiet.
If someone is not happy or strong then someone is tall and vice versa.
If fred is either not curious or patient then paul is creative and vice versa.
If susan is happy or not creative then someone is tall or generous.
If fred is not happy or not quiet then john is either strong or not old.
Everyone who is both humble and curious is not brave.
Everyone who is not calm or not funny is both creative and not kind and vice versa.
Everyone who is both not quiet and not wise is either old or not quiet and vice versa.
If someone is either not quiet or strong then someone is either brave or calm.
Everyone who is both not strong and not quiet is creative and vice versa.
Everyone who is old or not creative is not strong or patient.
Everyone who is not wise or patient is not strong.
Everyone who is both tall and not old is not quiet or not wise and vice versa.
Everyone who is not brave or not happy is not wise or not generous.
Everyone who is strong is generous and vice versa.
Everyone who is strong is both not kind and not curious and vice versa.
Paul is not quiet.
Paul is either rich or quiet.
Paul is either calm or happy.
Someone is not funny or funny.
John is both not brave and not happy.
Someone is happy or kind.
Mary is either not calm or old.
Someone is not tall. | Paul is not old. | entailment | ((?[X]:(kind(X)))=>(?[X]:(quiet(X))))&
((?[X]:((~happy(X)|strong(X))))<=>(?[X]:(tall(X))))&
(((~curious(fred)<~>patient(fred)))<=>(creative(paul)))&
(((happy(susan)|~creative(susan)))=>(?[X]:((tall(X)|generous(X)))))&
(((~happy(fred)|~quiet(fred)))=>((strong(john)<~>~old(john))))&
(![X]:((humble(X)&curious(X))=>~brave(X)))&
(![X]:((~calm(X)|~funny(X))<=>(creative(X)&~kind(X))))&
(![X]:((~quiet(X)&~wise(X))<=>(old(X)<~>~quiet(X))))&
((?[X]:((~quiet(X)<~>strong(X))))=>(?[X]:((brave(X)<~>calm(X)))))&
(![X]:((~strong(X)&~quiet(X))<=>creative(X)))&
(![X]:((old(X)|~creative(X))=>(~strong(X)|patient(X))))&
(![X]:((~wise(X)|patient(X))=>~strong(X)))&
(![X]:((tall(X)&~old(X))<=>(~quiet(X)|~wise(X))))&
(![X]:((~brave(X)|~happy(X))=>(~wise(X)|~generous(X))))&
(![X]:(strong(X)<=>generous(X)))&
(![X]:(strong(X)<=>(~kind(X)&~curious(X))))&
(~quiet(paul))&
((rich(paul)<~>quiet(paul)))&
((calm(paul)<~>happy(paul)))&
(?[X]:((~funny(X)|funny(X))))&
((~brave(john)&~happy(john)))&
(?[X]:((happy(X)|kind(X))))&
((~calm(mary)<~>old(mary)))&
(?[X]:(~tall(X))) | ~old(paul) | [
"p7",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 640488183555408129913040
% SZS output start Proof for 640488183555408129913040
8. ! [X0] : ((~wise(X0) & ~quiet(X0)) <=> (old(X0) <~> ~quiet(X0))) [input p7]
13. ! [X0] : ((~old(X0) & tall(X0)) <=> (~wise(X0) | ~quiet(X0))) [input p12]
25. old(paul) [input hypothesis]
53. ! [X0] : (((~wise(X0) & ~quiet(X0)) | ((old(X0) | quiet(X0)) & (~quiet(X0) | ~old(X0)))) & (((quiet(X0) | ~old(X0)) & (~quiet(X0) | old(X0))) | (wise(X0) | quiet(X0)))) [nnf transformation 8]
54. ! [X0] : (((~wise(X0) & ~quiet(X0)) | ((old(X0) | quiet(X0)) & (~quiet(X0) | ~old(X0)))) & (((quiet(X0) | ~old(X0)) & (~quiet(X0) | old(X0))) | wise(X0) | quiet(X0))) [flattening 53]
61. ! [X0] : (((~old(X0) & tall(X0)) | (wise(X0) & quiet(X0))) & ((~wise(X0) | ~quiet(X0)) | (old(X0) | ~tall(X0)))) [nnf transformation 13]
62. ! [X0] : (((~old(X0) & tall(X0)) | (wise(X0) & quiet(X0))) & (~wise(X0) | ~quiet(X0) | old(X0) | ~tall(X0))) [flattening 61]
96. ~quiet(X0) | ~quiet(X0) | ~old(X0) [cnf transformation 54]
114. ~old(X0) | quiet(X0) [cnf transformation 62]
135. old(paul) [cnf transformation 25]
137. ~quiet(X0) | ~old(X0) [duplicate literal removal 96]
246. ~old(X0) [subsumption resolution 114,137]
269. $false [subsumption resolution 135,246]
% SZS output end Proof for 640488183555408129913040
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either funny or brave then someone is not kind.
If susan is both not calm and not strong then someone is both not humble and brave.
Everyone who is either rich or not humble is either calm or not funny and vice versa.
Everyone who is both not funny and not quiet is not kind or humble.
Everyone who is not generous is not quiet or creative and vice versa.
If someone is not old or creative then someone is both not funny and patient.
If someone is both not kind and generous then someone is not old and vice versa.
Everyone who is both not happy and tall is either humble or creative.
Everyone who is both tall and quiet is both not humble and quiet and vice versa.
Everyone who is creative is both brave and not creative.
If someone is both not humble and curious then fred is not brave.
Everyone who is both not rich and not patient is happy or old.
Everyone who is not old is both not happy and strong.
If alice is either not funny or not patient then mary is both not strong and quiet and vice versa.
If someone is calm then fred is creative or not strong.
If fred is happy or kind then lucy is both not kind and brave.
Someone is both funny and quiet.
Someone is old.
Someone is calm.
Someone is either not old or tall.
Alice is either not quiet or not rich.
John is not tall or strong.
Someone is either calm or not creative. | Alice is not rich. | neutral | ((?[X]:((funny(X)<~>brave(X))))=>(?[X]:(~kind(X))))&
(((~calm(susan)&~strong(susan)))=>(?[X]:((~humble(X)&brave(X)))))&
(![X]:((rich(X)<~>~humble(X))<=>(calm(X)<~>~funny(X))))&
(![X]:((~funny(X)&~quiet(X))=>(~kind(X)|humble(X))))&
(![X]:(~generous(X)<=>(~quiet(X)|creative(X))))&
((?[X]:((~old(X)|creative(X))))=>(?[X]:((~funny(X)&patient(X)))))&
((?[X]:((~kind(X)&generous(X))))<=>(?[X]:(~old(X))))&
(![X]:((~happy(X)&tall(X))=>(humble(X)<~>creative(X))))&
(![X]:((tall(X)&quiet(X))<=>(~humble(X)&quiet(X))))&
(![X]:(creative(X)=>(brave(X)&~creative(X))))&
((?[X]:((~humble(X)&curious(X))))=>(~brave(fred)))&
(![X]:((~rich(X)&~patient(X))=>(happy(X)|old(X))))&
(![X]:(~old(X)=>(~happy(X)&strong(X))))&
(((~funny(alice)<~>~patient(alice)))<=>((~strong(mary)&quiet(mary))))&
((?[X]:(calm(X)))=>((creative(fred)|~strong(fred))))&
(((happy(fred)|kind(fred)))=>((~kind(lucy)&brave(lucy))))&
(?[X]:((funny(X)&quiet(X))))&
(?[X]:(old(X)))&
(?[X]:(calm(X)))&
(?[X]:((~old(X)<~>tall(X))))&
((~quiet(alice)<~>~rich(alice)))&
((~tall(john)|strong(john)))&
(?[X]:((calm(X)<~>~creative(X)))) | ~rich(alice) | [] | null | 0 |
If someone is both not curious and not calm then someone is tall or not tall.
Everyone who is either quiet or not brave is either not funny or tall and vice versa.
If paul is rich or not strong then mary is either strong or not funny and vice versa.
If someone is both not generous and humble then fred is both rich and curious.
If paul is not curious then someone is not creative and vice versa.
If someone is both strong and not old then alice is not creative or old and vice versa.
If paul is curious or not humble then someone is both not happy and not strong and vice versa.
If mary is generous or creative then someone is either not humble or happy.
Everyone who is not funny is brave or not tall and vice versa.
Everyone who is both strong and not happy is not brave and vice versa.
If someone is both quiet and not humble then someone is both funny and not calm.
Everyone who is humble is either tall or calm.
Everyone who is either calm or funny is not creative and vice versa.
Everyone who is both funny and creative is either rich or not funny and vice versa.
Everyone who is either not kind or wise is rich or calm and vice versa.
Everyone who is both not brave and generous is not patient or rich and vice versa.
Someone is rich.
Mary is not wise.
Paul is humble or funny.
Mary is tall.
Someone is either not old or not kind.
Someone is both not brave and not creative.
Someone is happy or kind.
Someone is rich or creative. | Mary is not funny. | contradiction | ((?[X]:((~curious(X)&~calm(X))))=>(?[X]:((tall(X)|~tall(X)))))&
(![X]:((quiet(X)<~>~brave(X))<=>(~funny(X)<~>tall(X))))&
(((rich(paul)|~strong(paul)))<=>((strong(mary)<~>~funny(mary))))&
((?[X]:((~generous(X)&humble(X))))=>((rich(fred)&curious(fred))))&
((~curious(paul))<=>(?[X]:(~creative(X))))&
((?[X]:((strong(X)&~old(X))))<=>((~creative(alice)|old(alice))))&
(((curious(paul)|~humble(paul)))<=>(?[X]:((~happy(X)&~strong(X)))))&
(((generous(mary)|creative(mary)))=>(?[X]:((~humble(X)<~>happy(X)))))&
(![X]:(~funny(X)<=>(brave(X)|~tall(X))))&
(![X]:((strong(X)&~happy(X))<=>~brave(X)))&
((?[X]:((quiet(X)&~humble(X))))=>(?[X]:((funny(X)&~calm(X)))))&
(![X]:(humble(X)=>(tall(X)<~>calm(X))))&
(![X]:((calm(X)<~>funny(X))<=>~creative(X)))&
(![X]:((funny(X)&creative(X))<=>(rich(X)<~>~funny(X))))&
(![X]:((~kind(X)<~>wise(X))<=>(rich(X)|calm(X))))&
(![X]:((~brave(X)&generous(X))<=>(~patient(X)|rich(X))))&
(?[X]:(rich(X)))&
(~wise(mary))&
((humble(paul)|funny(paul)))&
(tall(mary))&
(?[X]:((~old(X)<~>~kind(X))))&
(?[X]:((~brave(X)&~creative(X))))&
(?[X]:((happy(X)|kind(X))))&
(?[X]:((rich(X)|creative(X)))) | ~funny(mary) | [
"p8",
"p13",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 8167958590582417068831137
% SZS output start Proof for 8167958590582417068831137
9. ! [X0] : (~funny(X0) <=> (~tall(X0) | brave(X0))) [input p8]
14. ! [X0] : ((creative(X0) & funny(X0)) <=> (rich(X0) <~> ~funny(X0))) [input p13]
16. ! [X0] : ((generous(X0) & ~brave(X0)) <=> (rich(X0) | ~patient(X0))) [input p15]
20. tall(mary) [input p19]
25. ~funny(mary) [input hypothesis]
56. ! [X0] : ((~funny(X0) | (tall(X0) & ~brave(X0))) & ((~tall(X0) | brave(X0)) | funny(X0))) [nnf transformation 9]
57. ! [X0] : ((~funny(X0) | (tall(X0) & ~brave(X0))) & (~tall(X0) | brave(X0) | funny(X0))) [flattening 56]
65. ! [X0] : (((creative(X0) & funny(X0)) | ((rich(X0) | funny(X0)) & (~funny(X0) | ~rich(X0)))) & (((funny(X0) | ~rich(X0)) & (~funny(X0) | rich(X0))) | (~creative(X0) | ~funny(X0)))) [nnf transformation 14]
66. ! [X0] : (((creative(X0) & funny(X0)) | ((rich(X0) | funny(X0)) & (~funny(X0) | ~rich(X0)))) & (((funny(X0) | ~rich(X0)) & (~funny(X0) | rich(X0))) | ~creative(X0) | ~funny(X0))) [flattening 65]
69. ! [X0] : (((generous(X0) & ~brave(X0)) | (~rich(X0) & patient(X0))) & ((rich(X0) | ~patient(X0)) | (~generous(X0) | brave(X0)))) [nnf transformation 16]
70. ! [X0] : (((generous(X0) & ~brave(X0)) | (~rich(X0) & patient(X0))) & (rich(X0) | ~patient(X0) | ~generous(X0) | brave(X0))) [flattening 69]
115. ~tall(X0) | brave(X0) | funny(X0) [cnf transformation 57]
116. ~funny(X0) | ~brave(X0) [cnf transformation 57]
132. funny(X0) | rich(X0) | funny(X0) [cnf transformation 66]
143. ~rich(X0) | ~brave(X0) [cnf transformation 70]
149. tall(mary) [cnf transformation 20]
156. ~funny(mary) [cnf transformation 25]
158. rich(X0) | funny(X0) [duplicate literal removal 132]
160. 1 <=> funny(mary) [avatar definition]
161. ~funny(mary) <- (~1) [avatar component clause 160]
310. ~1 [avatar split clause 156,160]
326. funny(X1) | ~brave(X1) [resolution 158,143]
327. ~brave(X1) [subsumption resolution 326,116]
346. brave(mary) | funny(mary) [resolution 115,149]
347. funny(mary) [subsumption resolution 346,327]
348. $false <- (~1) [subsumption resolution 347,161]
349. 1 [avatar contradiction clause 348]
350. $false [avatar sat refutation 310,349]
% SZS output end Proof for 8167958590582417068831137
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative then john is not rich or old and vice versa.
Everyone who is not curious is either not quiet or not patient and vice versa.
Everyone who is funny is not patient or kind and vice versa.
Everyone who is either not quiet or humble is humble and vice versa.
Everyone who is both not curious and not wise is both not quiet and funny.
If someone is generous then mary is not patient and vice versa.
Everyone who is either wise or humble is either not creative or not quiet.
Everyone who is either quiet or curious is quiet and vice versa.
Everyone who is not calm or creative is generous and vice versa.
Everyone who is either not patient or creative is wise or not kind and vice versa.
Everyone who is generous or funny is not old or quiet and vice versa.
Everyone who is old or strong is generous or funny.
If someone is rich or humble then lucy is not humble or happy.
Everyone who is funny or curious is brave or not rich and vice versa.
Everyone who is either creative or curious is calm and vice versa.
If paul is both curious and not happy then paul is humble or not generous and vice versa.
Susan is either not strong or not happy.
Alice is not wise or generous.
Someone is either not old or not happy.
Fred is both not rich and tall.
Alice is either not kind or creative. | Lucy is old. | neutral | ((?[X]:(creative(X)))<=>((~rich(john)|old(john))))&
(![X]:(~curious(X)<=>(~quiet(X)<~>~patient(X))))&
(![X]:(funny(X)<=>(~patient(X)|kind(X))))&
(![X]:((~quiet(X)<~>humble(X))<=>humble(X)))&
(![X]:((~curious(X)&~wise(X))=>(~quiet(X)&funny(X))))&
((?[X]:(generous(X)))<=>(~patient(mary)))&
(![X]:((wise(X)<~>humble(X))=>(~creative(X)<~>~quiet(X))))&
(![X]:((quiet(X)<~>curious(X))<=>quiet(X)))&
(![X]:((~calm(X)|creative(X))<=>generous(X)))&
(![X]:((~patient(X)<~>creative(X))<=>(wise(X)|~kind(X))))&
(![X]:((generous(X)|funny(X))<=>(~old(X)|quiet(X))))&
(![X]:((old(X)|strong(X))=>(generous(X)|funny(X))))&
((?[X]:((rich(X)|humble(X))))=>((~humble(lucy)|happy(lucy))))&
(![X]:((funny(X)|curious(X))<=>(brave(X)|~rich(X))))&
(![X]:((creative(X)<~>curious(X))<=>calm(X)))&
(((curious(paul)&~happy(paul)))<=>((humble(paul)|~generous(paul))))&
((~strong(susan)<~>~happy(susan)))&
((~wise(alice)|generous(alice)))&
(?[X]:((~old(X)<~>~happy(X))))&
((~rich(fred)&tall(fred)))&
((~kind(alice)<~>creative(alice))) | old(lucy) | [] | null | 0 |
Everyone who is either not humble or old is either creative or curious and vice versa. If john is not patient or not wise then alice is not tall. Everyone who is either happy or rich is both not curious and generous. Everyone who is either kind or not kind is not tall and vice versa. Everyone who is not calm is either calm or not rich. Everyone who is either curious or strong is either not brave or not rich. Everyone who is tall is either strong or not generous. Everyone who is either not brave or wise is not old or not brave and vice versa. Everyone who is both not happy and funny is either not humble or patient. If alice is old then someone is not kind. Everyone who is either quiet or not funny is old or not old and vice versa. If mary is both not wise and happy then alice is either humble or not happy. If john is either strong or not humble then john is both brave and not wise. Everyone who is not funny or not wise is both strong and not wise. Everyone who is both not curious and tall is both brave and not wise and vice versa. Everyone who is both not tall and tall is not wise or not calm and vice versa. Fred is creative. Alice is creative. John is both strong and not tall. Paul is either not old or not humble. | Fred is not brave. | contradiction | (![X]:((~humble(X)<~>old(X))<=>(creative(X)<~>curious(X))))&
(((~patient(john)|~wise(john)))=>(~tall(alice)))&
(![X]:((happy(X)<~>rich(X))=>(~curious(X)&generous(X))))&
(![X]:((kind(X)<~>~kind(X))<=>~tall(X)))&
(![X]:(~calm(X)=>(calm(X)<~>~rich(X))))&
(![X]:((curious(X)<~>strong(X))=>(~brave(X)<~>~rich(X))))&
(![X]:(tall(X)=>(strong(X)<~>~generous(X))))&
(![X]:((~brave(X)<~>wise(X))<=>(~old(X)|~brave(X))))&
(![X]:((~happy(X)&funny(X))=>(~humble(X)<~>patient(X))))&
((old(alice))=>(?[X]:(~kind(X))))&
(![X]:((quiet(X)<~>~funny(X))<=>(old(X)|~old(X))))&
(((~wise(mary)&happy(mary)))=>((humble(alice)<~>~happy(alice))))&
(((strong(john)<~>~humble(john)))=>((brave(john)&~wise(john))))&
(![X]:((~funny(X)|~wise(X))=>(strong(X)&~wise(X))))&
(![X]:((~curious(X)&tall(X))<=>(brave(X)&~wise(X))))&
(![X]:((~tall(X)&tall(X))<=>(~wise(X)|~calm(X))))&
(creative(fred))&
(creative(alice))&
((strong(john)&~tall(john)))&
((~old(paul)<~>~humble(paul))) | ~brave(fred) | [
"p3",
"p7",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8073143912118489977196195
% SZS output start Proof for 8073143912118489977196195
4. ! [X0] : ((kind(X0) <~> ~kind(X0)) <=> ~tall(X0)) [input p3]
8. ! [X0] : ((~brave(X0) <~> wise(X0)) <=> (~brave(X0) | ~old(X0))) [input p7]
16. ! [X0] : ((tall(X0) & ~tall(X0)) <=> (~calm(X0) | ~wise(X0))) [input p15]
21. ~brave(fred) [input hypothesis]
36. ! [X0] : ((((kind(X0) | ~kind(X0)) & (~kind(X0) | kind(X0))) | tall(X0)) & (~tall(X0) | ((kind(X0) | kind(X0)) & (~kind(X0) | ~kind(X0))))) [nnf transformation 4]
40. ! [X0] : ((((~wise(X0) | brave(X0)) & (wise(X0) | ~brave(X0))) | (brave(X0) & old(X0))) & ((~brave(X0) | ~old(X0)) | ((~brave(X0) | ~wise(X0)) & (wise(X0) | brave(X0))))) [nnf transformation 8]
41. ! [X0] : ((((~wise(X0) | brave(X0)) & (wise(X0) | ~brave(X0))) | (brave(X0) & old(X0))) & (~brave(X0) | ~old(X0) | ((~brave(X0) | ~wise(X0)) & (wise(X0) | brave(X0))))) [flattening 40]
51. ! [X0] : (((tall(X0) & ~tall(X0)) | (calm(X0) & wise(X0))) & ((~calm(X0) | ~wise(X0)) | (~tall(X0) | tall(X0)))) [nnf transformation 16]
52. ! [X0] : (((tall(X0) & ~tall(X0)) | (calm(X0) & wise(X0))) & (~calm(X0) | ~wise(X0) | ~tall(X0) | tall(X0))) [flattening 51]
68. ~tall(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 36]
69. ~tall(X0) | kind(X0) | kind(X0) [cnf transformation 36]
85. ~wise(X0) | brave(X0) | brave(X0) [cnf transformation 41]
112. tall(X0) | wise(X0) [cnf transformation 52]
120. ~brave(fred) [cnf transformation 21]
122. ~wise(X0) | brave(X0) [duplicate literal removal 85]
124. ~tall(X0) | ~kind(X0) [duplicate literal removal 68]
125. ~tall(X0) | kind(X0) [duplicate literal removal 69]
140. ~tall(X0) [subsumption resolution 124,125]
189. wise(X0) [subsumption resolution 112,140]
202. brave(X0) [resolution 122,189]
203. $false [resolution 202,120]
% SZS output end Proof for 8073143912118489977196195
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is kind is either happy or curious.
Everyone who is not creative is both not brave and generous and vice versa.
If someone is not tall then someone is tall and vice versa.
Everyone who is either rich or happy is not brave.
If someone is not strong or calm then fred is both not creative and patient.
If john is not wise or not happy then someone is both not humble and humble and vice versa.
If fred is both not strong and not humble then susan is rich or curious.
Everyone who is not strong is both happy and not curious and vice versa.
If someone is both strong and not calm then someone is both creative and not wise.
If someone is either not rich or not strong then susan is either not kind or generous.
Everyone who is wise or kind is not calm or happy and vice versa.
Everyone who is either strong or brave is both not old and funny.
Everyone who is both strong and not old is either brave or not wise.
Everyone who is both curious and brave is not curious or not patient and vice versa.
Everyone who is either not happy or not brave is either not generous or calm.
If someone is both generous and not curious then lucy is either not humble or calm.
Someone is not strong or not rich.
Someone is not wise or happy.
Someone is both not funny and kind.
Someone is both quiet and not generous.
Someone is either not humble or not patient.
Fred is either old or funny.
Someone is not strong or not humble.
Alice is both not tall and not rich. | John is not brave. | contradiction | (![X]:(kind(X)=>(happy(X)<~>curious(X))))&
(![X]:(~creative(X)<=>(~brave(X)&generous(X))))&
((?[X]:(~tall(X)))<=>(?[X]:(tall(X))))&
(![X]:((rich(X)<~>happy(X))=>~brave(X)))&
((?[X]:((~strong(X)|calm(X))))=>((~creative(fred)&patient(fred))))&
(((~wise(john)|~happy(john)))<=>(?[X]:((~humble(X)&humble(X)))))&
(((~strong(fred)&~humble(fred)))=>((rich(susan)|curious(susan))))&
(![X]:(~strong(X)<=>(happy(X)&~curious(X))))&
((?[X]:((strong(X)&~calm(X))))=>(?[X]:((creative(X)&~wise(X)))))&
((?[X]:((~rich(X)<~>~strong(X))))=>((~kind(susan)<~>generous(susan))))&
(![X]:((wise(X)|kind(X))<=>(~calm(X)|happy(X))))&
(![X]:((strong(X)<~>brave(X))=>(~old(X)&funny(X))))&
(![X]:((strong(X)&~old(X))=>(brave(X)<~>~wise(X))))&
(![X]:((curious(X)&brave(X))<=>(~curious(X)|~patient(X))))&
(![X]:((~happy(X)<~>~brave(X))=>(~generous(X)<~>calm(X))))&
((?[X]:((generous(X)&~curious(X))))=>((~humble(lucy)<~>calm(lucy))))&
(?[X]:((~strong(X)|~rich(X))))&
(?[X]:((~wise(X)|happy(X))))&
(?[X]:((~funny(X)&kind(X))))&
(?[X]:((quiet(X)&~generous(X))))&
(?[X]:((~humble(X)<~>~patient(X))))&
((old(fred)<~>funny(fred)))&
(?[X]:((~strong(X)|~humble(X))))&
((~tall(alice)&~rich(alice))) | ~brave(john) | [
"p5",
"p7",
"p11",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 1951331129613855624447830
% SZS output start Proof for 1951331129613855624447830
6. (~happy(john) | ~wise(john)) <=> ? [X0] : (humble(X0) & ~humble(X0)) [input p5]
8. ! [X0] : (~strong(X0) <=> (~curious(X0) & happy(X0))) [input p7]
12. ! [X0] : ((strong(X0) <~> brave(X0)) => (funny(X0) & ~old(X0))) [input p11]
13. ! [X0] : ((~old(X0) & strong(X0)) => (brave(X0) <~> ~wise(X0))) [input p12]
14. ! [X0] : ((brave(X0) & curious(X0)) <=> (~patient(X0) | ~curious(X0))) [input p13]
25. ~brave(john) [input hypothesis]
36. ! [X0] : ((funny(X0) & ~old(X0)) | (strong(X0) <=> brave(X0))) [ennf transformation 12]
37. ! [X0] : ((brave(X0) <~> ~wise(X0)) | (old(X0) | ~strong(X0))) [ennf transformation 13]
38. ! [X0] : ((brave(X0) <~> ~wise(X0)) | old(X0) | ~strong(X0)) [flattening 37]
50. ((~happy(john) | ~wise(john)) | ! [X0] : (~humble(X0) | humble(X0))) & (? [X0] : (humble(X0) & ~humble(X0)) | (happy(john) & wise(john))) [nnf transformation 6]
51. (~happy(john) | ~wise(john) | ! [X0] : (~humble(X0) | humble(X0))) & (? [X0] : (humble(X0) & ~humble(X0)) | (happy(john) & wise(john))) [flattening 50]
52. (~happy(john) | ~wise(john) | ! [X0] : (~humble(X0) | humble(X0))) & (? [X1] : (humble(X1) & ~humble(X1)) | (happy(john) & wise(john))) [rectify 51]
53. ? [X1] : (humble(X1) & ~humble(X1)) => (humble(sK2) & ~humble(sK2)) [choice axiom]
54. (~happy(john) | ~wise(john) | ! [X0] : (~humble(X0) | humble(X0))) & ((humble(sK2) & ~humble(sK2)) | (happy(john) & wise(john))) [skolemisation 52,53]
55. ! [X0] : ((~strong(X0) | (curious(X0) | ~happy(X0))) & ((~curious(X0) & happy(X0)) | strong(X0))) [nnf transformation 8]
56. ! [X0] : ((~strong(X0) | curious(X0) | ~happy(X0)) & ((~curious(X0) & happy(X0)) | strong(X0))) [flattening 55]
63. ! [X0] : ((funny(X0) & ~old(X0)) | ((strong(X0) | ~brave(X0)) & (brave(X0) | ~strong(X0)))) [nnf transformation 36]
64. ! [X0] : (((wise(X0) | ~brave(X0)) & (~wise(X0) | brave(X0))) | old(X0) | ~strong(X0)) [nnf transformation 38]
65. ! [X0] : (((brave(X0) & curious(X0)) | (patient(X0) & curious(X0))) & ((~patient(X0) | ~curious(X0)) | (~brave(X0) | ~curious(X0)))) [nnf transformation 14]
66. ! [X0] : (((brave(X0) & curious(X0)) | (patient(X0) & curious(X0))) & (~patient(X0) | ~curious(X0) | ~brave(X0) | ~curious(X0))) [flattening 65]
96. ~humble(sK2) | wise(john) [cnf transformation 54]
98. humble(sK2) | wise(john) [cnf transformation 54]
103. ~curious(X0) | strong(X0) [cnf transformation 56]
115. ~old(X0) | brave(X0) | ~strong(X0) [cnf transformation 63]
119. ~wise(X0) | brave(X0) | old(X0) | ~strong(X0) [cnf transformation 64]
122. curious(X0) | curious(X0) [cnf transformation 66]
144. ~brave(john) [cnf transformation 25]
146. curious(X0) [duplicate literal removal 122]
172. 7 <=> ! [X0] : strong(X0) [avatar definition]
173. strong(X0) <- (7) [avatar component clause 172]
186. 10 <=> humble(sK2) [avatar definition]
191. 11 <=> wise(john) [avatar definition]
193. wise(john) <- (11) [avatar component clause 191]
194. 11 | 10 [avatar split clause 98,186,191]
196. 11 | ~10 [avatar split clause 96,186,191]
245. ~wise(X0) | brave(X0) | ~strong(X0) [subsumption resolution 119,115]
299. strong(X0) [resolution 103,146]
300. 7 [avatar split clause 299,172]
400. brave(john) | ~strong(john) <- (11) [resolution 245,193]
403. ~strong(john) <- (11) [subsumption resolution 400,144]
404. $false <- (7, 11) [subsumption resolution 403,173]
405. ~7 | ~11 [avatar contradiction clause 404]
408. $false [avatar sat refutation 194,196,300,405]
% SZS output end Proof for 1951331129613855624447830
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.022 s
% ------------------------------
% ------------------------------
| 0 |
If alice is strong then paul is generous.
If john is either not happy or old then someone is either not quiet or not rich.
If fred is either happy or not calm then susan is both old and not happy.
Everyone who is either brave or not rich is both tall and not calm and vice versa.
If someone is old then john is not humble and vice versa.
Everyone who is both not old and wise is not kind or patient.
If alice is both not patient and not funny then someone is either humble or not rich.
If someone is wise or not creative then someone is either not happy or kind and vice versa.
Everyone who is humble or not generous is not kind or not old and vice versa.
Everyone who is either not creative or patient is either not funny or calm and vice versa.
Everyone who is brave is rich or happy and vice versa.
If someone is either not quiet or not curious then someone is not funny or generous and vice versa.
Everyone who is curious is either not funny or generous and vice versa.
Everyone who is happy is both not strong and wise.
If lucy is calm or humble then paul is both funny and not brave.
If paul is either not humble or not creative then paul is not wise or calm and vice versa.
Alice is not old.
Someone is both not generous and not brave.
Someone is both not wise and brave.
Paul is either not wise or not brave.
Mary is both not calm and not creative.
Paul is either patient or not generous.
Paul is either strong or not strong.
Someone is tall or not old. | Paul is not tall. | contradiction | ((strong(alice))=>(generous(paul)))&
(((~happy(john)<~>old(john)))=>(?[X]:((~quiet(X)<~>~rich(X)))))&
(((happy(fred)<~>~calm(fred)))=>((old(susan)&~happy(susan))))&
(![X]:((brave(X)<~>~rich(X))<=>(tall(X)&~calm(X))))&
((?[X]:(old(X)))<=>(~humble(john)))&
(![X]:((~old(X)&wise(X))=>(~kind(X)|patient(X))))&
(((~patient(alice)&~funny(alice)))=>(?[X]:((humble(X)<~>~rich(X)))))&
((?[X]:((wise(X)|~creative(X))))<=>(?[X]:((~happy(X)<~>kind(X)))))&
(![X]:((humble(X)|~generous(X))<=>(~kind(X)|~old(X))))&
(![X]:((~creative(X)<~>patient(X))<=>(~funny(X)<~>calm(X))))&
(![X]:(brave(X)<=>(rich(X)|happy(X))))&
((?[X]:((~quiet(X)<~>~curious(X))))<=>(?[X]:((~funny(X)|generous(X)))))&
(![X]:(curious(X)<=>(~funny(X)<~>generous(X))))&
(![X]:(happy(X)=>(~strong(X)&wise(X))))&
(((calm(lucy)|humble(lucy)))=>((funny(paul)&~brave(paul))))&
(((~humble(paul)<~>~creative(paul)))<=>((~wise(paul)|calm(paul))))&
(~old(alice))&
(?[X]:((~generous(X)&~brave(X))))&
(?[X]:((~wise(X)&brave(X))))&
((~wise(paul)<~>~brave(paul)))&
((~calm(mary)&~creative(mary)))&
((patient(paul)<~>~generous(paul)))&
((strong(paul)<~>~strong(paul)))&
(?[X]:((tall(X)|~old(X)))) | ~tall(paul) | [
"p3",
"p10",
"p13",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 7446852489282520165397447
% SZS output start Proof for 7446852489282520165397447
4. ! [X0] : ((brave(X0) <~> ~rich(X0)) <=> (~calm(X0) & tall(X0))) [input p3]
11. ! [X0] : (brave(X0) <=> (happy(X0) | rich(X0))) [input p10]
14. ! [X0] : (happy(X0) => (wise(X0) & ~strong(X0))) [input p13]
20. ~wise(paul) <~> ~brave(paul) [input p19]
25. ~tall(paul) [input hypothesis]
35. ! [X0] : ((wise(X0) & ~strong(X0)) | ~happy(X0)) [ennf transformation 14]
41. ! [X0] : ((((rich(X0) | ~brave(X0)) & (~rich(X0) | brave(X0))) | (calm(X0) | ~tall(X0))) & ((~calm(X0) & tall(X0)) | ((brave(X0) | rich(X0)) & (~rich(X0) | ~brave(X0))))) [nnf transformation 4]
42. ! [X0] : ((((rich(X0) | ~brave(X0)) & (~rich(X0) | brave(X0))) | calm(X0) | ~tall(X0)) & ((~calm(X0) & tall(X0)) | ((brave(X0) | rich(X0)) & (~rich(X0) | ~brave(X0))))) [flattening 41]
58. ! [X0] : ((brave(X0) | (~happy(X0) & ~rich(X0))) & ((happy(X0) | rich(X0)) | ~brave(X0))) [nnf transformation 11]
59. ! [X0] : ((brave(X0) | (~happy(X0) & ~rich(X0))) & (happy(X0) | rich(X0) | ~brave(X0))) [flattening 58]
72. (brave(paul) | wise(paul)) & (~brave(paul) | ~wise(paul)) [nnf transformation 20]
86. ~brave(X0) | ~rich(X0) | tall(X0) [cnf transformation 42]
87. tall(X0) | brave(X0) | rich(X0) [cnf transformation 42]
115. ~brave(X0) | rich(X0) | happy(X0) [cnf transformation 59]
116. ~rich(X0) | brave(X0) [cnf transformation 59]
129. ~happy(X0) | wise(X0) [cnf transformation 35]
145. ~brave(paul) | ~wise(paul) [cnf transformation 72]
154. ~tall(paul) [cnf transformation 25]
308. 35 <=> brave(paul) [avatar definition]
309. brave(paul) <- (35) [avatar component clause 308]
337. 41 <=> wise(paul) [avatar definition]
338. ~wise(paul) <- (~41) [avatar component clause 337]
346. ~41 | ~35 [avatar split clause 145,308,337]
363. ~rich(paul) | tall(paul) <- (35) [resolution 86,309]
373. ~rich(paul) <- (35) [subsumption resolution 363,154]
374. brave(paul) | rich(paul) [resolution 87,154]
383. rich(paul) | happy(paul) <- (35) [resolution 115,309]
386. happy(paul) <- (35) [subsumption resolution 383,373]
423. wise(paul) <- (35) [resolution 386,129]
426. $false <- (35, ~41) [subsumption resolution 423,338]
427. ~35 | 41 [avatar contradiction clause 426]
428. brave(paul) [subsumption resolution 374,116]
429. 35 [avatar split clause 428,308]
430. $false [avatar sat refutation 346,427,429]
% SZS output end Proof for 7446852489282520165397447
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 susan is creative or generous then alice is either not funny or not quiet and vice versa.
Everyone who is both not curious and not brave is either not wise or creative and vice versa.
If mary is curious then someone is not brave and vice versa.
If alice is either old or generous then someone is rich or calm.
Everyone who is either not funny or not rich is either not wise or not rich and vice versa.
Everyone who is both not brave and generous is either funny or not strong and vice versa.
Everyone who is happy is either creative or not tall and vice versa.
Everyone who is either calm or patient is not rich or not strong.
Everyone who is either not wise or not old is both not calm and not old.
Everyone who is wise or rich is not wise.
Everyone who is both rich and kind is patient.
Everyone who is not rich is not generous or creative.
If someone is either not old or kind then someone is not patient or not wise.
If paul is both not tall and tall then someone is both not brave and brave and vice versa.
If susan is kind then someone is not rich and vice versa.
If paul is either not rich or not funny then alice is not curious and vice versa.
Alice is tall or funny.
Fred is either kind or rich.
Susan is either not happy or not strong.
Someone is both patient and quiet.
Susan is not curious or not calm.
Lucy is rich or tall.
Mary is not old or not tall.
Someone is both not strong and not patient. | Mary is not curious. | contradiction | (((creative(susan)|generous(susan)))<=>((~funny(alice)<~>~quiet(alice))))&
(![X]:((~curious(X)&~brave(X))<=>(~wise(X)<~>creative(X))))&
((curious(mary))<=>(?[X]:(~brave(X))))&
(((old(alice)<~>generous(alice)))=>(?[X]:((rich(X)|calm(X)))))&
(![X]:((~funny(X)<~>~rich(X))<=>(~wise(X)<~>~rich(X))))&
(![X]:((~brave(X)&generous(X))<=>(funny(X)<~>~strong(X))))&
(![X]:(happy(X)<=>(creative(X)<~>~tall(X))))&
(![X]:((calm(X)<~>patient(X))=>(~rich(X)|~strong(X))))&
(![X]:((~wise(X)<~>~old(X))=>(~calm(X)&~old(X))))&
(![X]:((wise(X)|rich(X))=>~wise(X)))&
(![X]:((rich(X)&kind(X))=>patient(X)))&
(![X]:(~rich(X)=>(~generous(X)|creative(X))))&
((?[X]:((~old(X)<~>kind(X))))=>(?[X]:((~patient(X)|~wise(X)))))&
(((~tall(paul)&tall(paul)))<=>(?[X]:((~brave(X)&brave(X)))))&
((kind(susan))<=>(?[X]:(~rich(X))))&
(((~rich(paul)<~>~funny(paul)))<=>(~curious(alice)))&
((tall(alice)|funny(alice)))&
((kind(fred)<~>rich(fred)))&
((~happy(susan)<~>~strong(susan)))&
(?[X]:((patient(X)&quiet(X))))&
((~curious(susan)|~calm(susan)))&
((rich(lucy)|tall(lucy)))&
((~old(mary)|~tall(mary)))&
(?[X]:((~strong(X)&~patient(X)))) | ~curious(mary) | [
"p2",
"p4",
"p5",
"p9",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 8670930440658903238672818
% SZS output start Proof for 8670930440658903238672818
3. curious(mary) <=> ? [X0] : ~brave(X0) [input p2]
5. ! [X0] : ((~funny(X0) <~> ~rich(X0)) <=> (~wise(X0) <~> ~rich(X0))) [input p4]
6. ! [X0] : ((generous(X0) & ~brave(X0)) <=> (funny(X0) <~> ~strong(X0))) [input p5]
10. ! [X0] : ((rich(X0) | wise(X0)) => ~wise(X0)) [input p9]
24. ? [X0] : (~patient(X0) & ~strong(X0)) [input p23]
25. ~curious(mary) [input hypothesis]
31. ! [X0] : (~wise(X0) | (~rich(X0) & ~wise(X0))) [ennf transformation 10]
41. (curious(mary) | ! [X0] : brave(X0)) & (? [X0] : ~brave(X0) | ~curious(mary)) [nnf transformation 3]
42. (curious(mary) | ! [X0] : brave(X0)) & (? [X1] : ~brave(X1) | ~curious(mary)) [rectify 41]
43. ? [X1] : ~brave(X1) => ~brave(sK0) [choice axiom]
44. (curious(mary) | ! [X0] : brave(X0)) & (~brave(sK0) | ~curious(mary)) [skolemisation 42,43]
48. ! [X0] : ((((rich(X0) | funny(X0)) & (~rich(X0) | ~funny(X0))) | ((~wise(X0) | rich(X0)) & (~rich(X0) | wise(X0)))) & (((rich(X0) | wise(X0)) & (~rich(X0) | ~wise(X0))) | ((~funny(X0) | rich(X0)) & (~rich(X0) | funny(X0))))) [nnf transformation 5]
49. ! [X0] : (((generous(X0) & ~brave(X0)) | ((funny(X0) | strong(X0)) & (~strong(X0) | ~funny(X0)))) & (((strong(X0) | ~funny(X0)) & (~strong(X0) | funny(X0))) | (~generous(X0) | brave(X0)))) [nnf transformation 6]
50. ! [X0] : (((generous(X0) & ~brave(X0)) | ((funny(X0) | strong(X0)) & (~strong(X0) | ~funny(X0)))) & (((strong(X0) | ~funny(X0)) & (~strong(X0) | funny(X0))) | ~generous(X0) | brave(X0))) [flattening 49]
72. ? [X0] : (~patient(X0) & ~strong(X0)) => (~patient(sK6) & ~strong(sK6)) [choice axiom]
73. ~patient(sK6) & ~strong(sK6) [skolemisation 24,72]
87. curious(mary) | brave(X0) [cnf transformation 44]
93. rich(X0) | wise(X0) | ~funny(X0) | rich(X0) [cnf transformation 48]
94. ~rich(X0) | ~funny(X0) | ~rich(X0) | wise(X0) [cnf transformation 48]
101. ~brave(X0) | funny(X0) | strong(X0) [cnf transformation 50]
114. ~wise(X0) | ~wise(X0) [cnf transformation 31]
140. ~strong(sK6) [cnf transformation 73]
142. ~curious(mary) [cnf transformation 25]
143. ~wise(X0) [duplicate literal removal 114]
146. rich(X0) | wise(X0) | ~funny(X0) [duplicate literal removal 93]
147. ~rich(X0) | ~funny(X0) | wise(X0) [duplicate literal removal 94]
172. 5 <=> ! [X0] : brave(X0) [avatar definition]
173. brave(X0) <- (5) [avatar component clause 172]
175. 6 <=> curious(mary) [avatar definition]
178. 5 | 6 [avatar split clause 87,175,172]
202. ~funny(X0) | wise(X0) [subsumption resolution 146,147]
285. ~6 [avatar split clause 142,175]
296. strong(X0) | funny(X0) <- (5) [resolution 101,173]
297. funny(sK6) <- (5) [resolution 296,140]
306. wise(sK6) <- (5) [resolution 297,202]
307. $false <- (5) [subsumption resolution 306,143]
308. ~5 [avatar contradiction clause 307]
309. $false [avatar sat refutation 178,285,308]
% SZS output end Proof for 8670930440658903238672818
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both patient and creative and vice versa.
Everyone who is both not tall and not kind is not happy or not quiet and vice versa.
Everyone who is not brave is either tall or creative.
Everyone who is not generous is either not old or funny and vice versa.
Everyone who is both old and not tall is both creative and patient.
If someone is humble then susan is either not creative or not happy.
If john is either not patient or calm then someone is old and vice versa.
If someone is not generous then someone is either not rich or creative and vice versa.
Everyone who is kind or not old is both strong and calm and vice versa.
Everyone who is either not happy or strong is not happy and vice versa.
If someone is either humble or patient then someone is either not strong or generous and vice versa.
Everyone who is humble is both humble and not kind.
Everyone who is both curious and quiet is either not rich or kind.
Everyone who is both creative and not quiet is humble or not strong.
Everyone who is either wise or not humble is not strong or not happy and vice versa.
Lucy is humble.
Someone is either generous or not humble.
Susan is tall or curious.
Paul is not happy.
Fred is not funny.
Mary is either tall or not tall.
Someone is not patient or not curious. | John is quiet. | entailment | (![X]:(~calm(X)<=>(patient(X)&creative(X))))&
(![X]:((~tall(X)&~kind(X))<=>(~happy(X)|~quiet(X))))&
(![X]:(~brave(X)=>(tall(X)<~>creative(X))))&
(![X]:(~generous(X)<=>(~old(X)<~>funny(X))))&
(![X]:((old(X)&~tall(X))=>(creative(X)&patient(X))))&
((?[X]:(humble(X)))=>((~creative(susan)<~>~happy(susan))))&
(((~patient(john)<~>calm(john)))<=>(?[X]:(old(X))))&
((?[X]:(~generous(X)))<=>(?[X]:((~rich(X)<~>creative(X)))))&
(![X]:((kind(X)|~old(X))<=>(strong(X)&calm(X))))&
(![X]:((~happy(X)<~>strong(X))<=>~happy(X)))&
((?[X]:((humble(X)<~>patient(X))))<=>(?[X]:((~strong(X)<~>generous(X)))))&
(![X]:(humble(X)=>(humble(X)&~kind(X))))&
(![X]:((curious(X)&quiet(X))=>(~rich(X)<~>kind(X))))&
(![X]:((creative(X)&~quiet(X))=>(humble(X)|~strong(X))))&
(![X]:((wise(X)<~>~humble(X))<=>(~strong(X)|~happy(X))))&
(humble(lucy))&
(?[X]:((generous(X)<~>~humble(X))))&
((tall(susan)|curious(susan)))&
(~happy(paul))&
(~funny(fred))&
((tall(mary)<~>~tall(mary)))&
(?[X]:((~patient(X)|~curious(X)))) | quiet(john) | [
"p0",
"p1",
"p4",
"p6",
"p8",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 4313646129996004416429249
% SZS output start Proof for 4313646129996004416429249
1. ! [X0] : (~calm(X0) <=> (creative(X0) & patient(X0))) [input p0]
2. ! [X0] : ((~kind(X0) & ~tall(X0)) <=> (~quiet(X0) | ~happy(X0))) [input p1]
5. ! [X0] : ((~tall(X0) & old(X0)) => (patient(X0) & creative(X0))) [input p4]
7. (~patient(john) <~> calm(john)) <=> ? [X0] : old(X0) [input p6]
9. ! [X0] : ((~old(X0) | kind(X0)) <=> (calm(X0) & strong(X0))) [input p8]
10. ! [X0] : ((~happy(X0) <~> strong(X0)) <=> ~happy(X0)) [input p9]
23. ~quiet(john) [input hypothesis]
27. ! [X0] : ((patient(X0) & creative(X0)) | (tall(X0) | ~old(X0))) [ennf transformation 5]
28. ! [X0] : ((patient(X0) & creative(X0)) | tall(X0) | ~old(X0)) [flattening 27]
35. ! [X0] : ((~calm(X0) | (~creative(X0) | ~patient(X0))) & ((creative(X0) & patient(X0)) | calm(X0))) [nnf transformation 1]
36. ! [X0] : ((~calm(X0) | ~creative(X0) | ~patient(X0)) & ((creative(X0) & patient(X0)) | calm(X0))) [flattening 35]
37. ! [X0] : (((~kind(X0) & ~tall(X0)) | (quiet(X0) & happy(X0))) & ((~quiet(X0) | ~happy(X0)) | (kind(X0) | tall(X0)))) [nnf transformation 2]
38. ! [X0] : (((~kind(X0) & ~tall(X0)) | (quiet(X0) & happy(X0))) & (~quiet(X0) | ~happy(X0) | kind(X0) | tall(X0))) [flattening 37]
41. (((~calm(john) | patient(john)) & (calm(john) | ~patient(john))) | ! [X0] : ~old(X0)) & (? [X0] : old(X0) | ((~patient(john) | ~calm(john)) & (calm(john) | patient(john)))) [nnf transformation 7]
42. (((~calm(john) | patient(john)) & (calm(john) | ~patient(john))) | ! [X0] : ~old(X0)) & (? [X1] : old(X1) | ((~patient(john) | ~calm(john)) & (calm(john) | patient(john)))) [rectify 41]
43. ? [X1] : old(X1) => old(sK0) [choice axiom]
44. (((~calm(john) | patient(john)) & (calm(john) | ~patient(john))) | ! [X0] : ~old(X0)) & (old(sK0) | ((~patient(john) | ~calm(john)) & (calm(john) | patient(john)))) [skolemisation 42,43]
50. ! [X0] : (((~old(X0) | kind(X0)) | (~calm(X0) | ~strong(X0))) & ((calm(X0) & strong(X0)) | (old(X0) & ~kind(X0)))) [nnf transformation 9]
51. ! [X0] : ((~old(X0) | kind(X0) | ~calm(X0) | ~strong(X0)) & ((calm(X0) & strong(X0)) | (old(X0) & ~kind(X0)))) [flattening 50]
52. ! [X0] : ((((~strong(X0) | happy(X0)) & (strong(X0) | ~happy(X0))) | happy(X0)) & (~happy(X0) | ((~happy(X0) | ~strong(X0)) & (strong(X0) | happy(X0))))) [nnf transformation 10]
67. patient(X0) | calm(X0) [cnf transformation 36]
69. ~creative(X0) | ~calm(X0) | ~patient(X0) [cnf transformation 36]
72. ~tall(X0) | quiet(X0) [cnf transformation 38]
79. ~old(X0) | tall(X0) | creative(X0) [cnf transformation 28]
85. calm(john) | ~patient(john) | ~old(X0) [cnf transformation 44]
86. ~calm(john) | patient(john) | ~old(X0) [cnf transformation 44]
92. strong(X0) | old(X0) [cnf transformation 51]
97. ~happy(X0) | ~happy(X0) | ~strong(X0) [cnf transformation 52]
99. ~strong(X0) | happy(X0) | happy(X0) [cnf transformation 52]
128. ~quiet(john) [cnf transformation 23]
129. ~happy(X0) | ~strong(X0) [duplicate literal removal 97]
130. ~strong(X0) | happy(X0) [duplicate literal removal 99]
144. patient(john) | ~old(X0) [subsumption resolution 86,67]
146. 4 <=> ! [X0] : ~old(X0) [avatar definition]
147. ~old(X0) <- (4) [avatar component clause 146]
149. 5 <=> patient(john) [avatar definition]
151. patient(john) <- (5) [avatar component clause 149]
152. 4 | 5 [avatar split clause 144,149,146]
153. calm(john) | ~old(X0) [subsumption resolution 85,67]
155. 6 <=> calm(john) [avatar definition]
157. calm(john) <- (6) [avatar component clause 155]
158. 4 | 6 [avatar split clause 153,155,146]
189. ~strong(X0) [subsumption resolution 129,130]
259. old(X0) [resolution 92,189]
260. $false <- (4) [subsumption resolution 259,147]
261. ~4 [avatar contradiction clause 260]
293. tall(X1) | creative(X1) [resolution 79,259]
297. quiet(X0) | creative(X0) [resolution 293,72]
307. creative(john) [resolution 297,128]
319. ~calm(john) | ~patient(john) [resolution 307,69]
320. ~patient(john) <- (6) [subsumption resolution 319,157]
321. $false <- (5, 6) [subsumption resolution 320,151]
322. ~5 | ~6 [avatar contradiction clause 321]
323. $false [avatar sat refutation 152,158,261,322]
% SZS output end Proof for 4313646129996004416429249
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble or strong then lucy is either not patient or not strong and vice versa.
Everyone who is either brave or old is either happy or old and vice versa.
If susan is both funny and patient then someone is not brave or not quiet and vice versa.
Everyone who is creative or wise is either not patient or strong.
Everyone who is creative is not creative or calm.
Everyone who is not curious or patient is not creative or not quiet and vice versa.
If someone is funny then someone is not strong.
If someone is not tall then someone is curious or not calm and vice versa.
If john is patient then mary is not creative and vice versa.
If someone is both rich and not brave then someone is both wise and humble.
Everyone who is not curious is generous or creative and vice versa.
If mary is either funny or not creative then someone is both happy and not generous.
Everyone who is both brave and humble is not rich or not generous and vice versa.
If someone is quiet or wise then someone is generous or strong.
Everyone who is either wise or happy is both not humble and not patient and vice versa.
Everyone who is either not kind or not happy is not curious.
Someone is both not rich and funny.
Fred is rich.
Someone is funny.
Someone is both not curious and not humble.
Someone is curious or not patient.
Someone is wise or humble. | Fred is humble. | neutral | ((?[X]:((humble(X)|strong(X))))<=>((~patient(lucy)<~>~strong(lucy))))&
(![X]:((brave(X)<~>old(X))<=>(happy(X)<~>old(X))))&
(((funny(susan)&patient(susan)))<=>(?[X]:((~brave(X)|~quiet(X)))))&
(![X]:((creative(X)|wise(X))=>(~patient(X)<~>strong(X))))&
(![X]:(creative(X)=>(~creative(X)|calm(X))))&
(![X]:((~curious(X)|patient(X))<=>(~creative(X)|~quiet(X))))&
((?[X]:(funny(X)))=>(?[X]:(~strong(X))))&
((?[X]:(~tall(X)))<=>(?[X]:((curious(X)|~calm(X)))))&
((patient(john))<=>(~creative(mary)))&
((?[X]:((rich(X)&~brave(X))))=>(?[X]:((wise(X)&humble(X)))))&
(![X]:(~curious(X)<=>(generous(X)|creative(X))))&
(((funny(mary)<~>~creative(mary)))=>(?[X]:((happy(X)&~generous(X)))))&
(![X]:((brave(X)&humble(X))<=>(~rich(X)|~generous(X))))&
((?[X]:((quiet(X)|wise(X))))=>(?[X]:((generous(X)|strong(X)))))&
(![X]:((wise(X)<~>happy(X))<=>(~humble(X)&~patient(X))))&
(![X]:((~kind(X)<~>~happy(X))=>~curious(X)))&
(?[X]:((~rich(X)&funny(X))))&
(rich(fred))&
(?[X]:(funny(X)))&
(?[X]:((~curious(X)&~humble(X))))&
(?[X]:((curious(X)|~patient(X))))&
(?[X]:((wise(X)|humble(X)))) | humble(fred) | [] | null | 0 |
If fred is generous then alice is both tall and not happy and vice versa. Everyone who is not rich or generous is not old. Everyone who is either not humble or happy is not tall or old. If fred is both not rich and funny then paul is both not happy and strong and vice versa. If someone is not kind or curious then susan is wise. If susan is not calm or not patient then someone is either patient or not brave. Everyone who is either happy or not rich is happy and vice versa. Everyone who is both not rich and not funny is creative and vice versa. If someone is not quiet or rich then alice is kind and vice versa. Everyone who is curious is both not tall and not funny. If someone is both curious and not rich then susan is not brave or patient. If someone is both calm and wise then john is either not tall or creative and vice versa. If paul is both not calm and not rich then someone is not curious and vice versa. If someone is not happy or generous then susan is not tall or happy and vice versa. If someone is wise then susan is not happy or not tall. Everyone who is not wise or not brave is funny or kind and vice versa. Someone is wise. Someone is tall or not creative. Someone is not kind or humble. Someone is either strong or not humble. Susan is old or kind. Someone is funny or not happy. | John is not kind. | neutral | ((generous(fred))<=>((tall(alice)&~happy(alice))))&
(![X]:((~rich(X)|generous(X))=>~old(X)))&
(![X]:((~humble(X)<~>happy(X))=>(~tall(X)|old(X))))&
(((~rich(fred)&funny(fred)))<=>((~happy(paul)&strong(paul))))&
((?[X]:((~kind(X)|curious(X))))=>(wise(susan)))&
(((~calm(susan)|~patient(susan)))=>(?[X]:((patient(X)<~>~brave(X)))))&
(![X]:((happy(X)<~>~rich(X))<=>happy(X)))&
(![X]:((~rich(X)&~funny(X))<=>creative(X)))&
((?[X]:((~quiet(X)|rich(X))))<=>(kind(alice)))&
(![X]:(curious(X)=>(~tall(X)&~funny(X))))&
((?[X]:((curious(X)&~rich(X))))=>((~brave(susan)|patient(susan))))&
((?[X]:((calm(X)&wise(X))))<=>((~tall(john)<~>creative(john))))&
(((~calm(paul)&~rich(paul)))<=>(?[X]:(~curious(X))))&
((?[X]:((~happy(X)|generous(X))))<=>((~tall(susan)|happy(susan))))&
((?[X]:(wise(X)))=>((~happy(susan)|~tall(susan))))&
(![X]:((~wise(X)|~brave(X))<=>(funny(X)|kind(X))))&
(?[X]:(wise(X)))&
(?[X]:((tall(X)|~creative(X))))&
(?[X]:((~kind(X)|humble(X))))&
(?[X]:((strong(X)<~>~humble(X))))&
((old(susan)|kind(susan)))&
(?[X]:((funny(X)|~happy(X)))) | ~kind(john) | [] | null | 0 |
Everyone who is either calm or not creative is not quiet. If lucy is either old or happy then mary is both strong and old and vice versa. If someone is generous or happy then fred is generous or not humble. Everyone who is either not calm or brave is not funny or curious and vice versa. Everyone who is either creative or wise is not rich or strong. If someone is quiet then someone is generous or not curious and vice versa. Everyone who is either brave or not old is either not strong or not funny and vice versa. If john is not old or brave then someone is either quiet or not quiet. Everyone who is not kind is not curious or not quiet and vice versa. If someone is tall then someone is both not old and kind. If fred is both not strong and not funny then someone is both not patient and old. Everyone who is either kind or not strong is either tall or strong and vice versa. Everyone who is either not strong or brave is not tall. Everyone who is not generous is both not brave and generous and vice versa. If someone is not calm then susan is either not curious or not creative and vice versa. Everyone who is both not strong and not quiet is both humble and happy and vice versa. Someone is strong. Fred is kind or not funny. Lucy is funny or wise. Someone is not creative or not brave. Someone is either happy or humble. | John is not tall. | neutral | (![X]:((calm(X)<~>~creative(X))=>~quiet(X)))&
(((old(lucy)<~>happy(lucy)))<=>((strong(mary)&old(mary))))&
((?[X]:((generous(X)|happy(X))))=>((generous(fred)|~humble(fred))))&
(![X]:((~calm(X)<~>brave(X))<=>(~funny(X)|curious(X))))&
(![X]:((creative(X)<~>wise(X))=>(~rich(X)|strong(X))))&
((?[X]:(quiet(X)))<=>(?[X]:((generous(X)|~curious(X)))))&
(![X]:((brave(X)<~>~old(X))<=>(~strong(X)<~>~funny(X))))&
(((~old(john)|brave(john)))=>(?[X]:((quiet(X)<~>~quiet(X)))))&
(![X]:(~kind(X)<=>(~curious(X)|~quiet(X))))&
((?[X]:(tall(X)))=>(?[X]:((~old(X)&kind(X)))))&
(((~strong(fred)&~funny(fred)))=>(?[X]:((~patient(X)&old(X)))))&
(![X]:((kind(X)<~>~strong(X))<=>(tall(X)<~>strong(X))))&
(![X]:((~strong(X)<~>brave(X))=>~tall(X)))&
(![X]:(~generous(X)<=>(~brave(X)&generous(X))))&
((?[X]:(~calm(X)))<=>((~curious(susan)<~>~creative(susan))))&
(![X]:((~strong(X)&~quiet(X))<=>(humble(X)&happy(X))))&
(?[X]:(strong(X)))&
((kind(fred)|~funny(fred)))&
((funny(lucy)|wise(lucy)))&
(?[X]:((~creative(X)|~brave(X))))&
(?[X]:((happy(X)<~>humble(X)))) | ~tall(john) | [] | null | 0 |
If mary is both not patient and old then susan is not tall and vice versa.
Everyone who is either not patient or creative is either not brave or not kind and vice versa.
If fred is both brave and creative then someone is both not quiet and not old and vice versa.
If someone is either not old or curious then fred is both not patient and humble.
Everyone who is happy or not rich is either not generous or not brave.
If alice is not old or humble then someone is funny and vice versa.
Everyone who is both rich and not quiet is rich or not strong and vice versa.
Everyone who is not funny or not patient is both rich and quiet and vice versa.
Everyone who is either not humble or not funny is either not old or curious.
Everyone who is funny or kind is both funny and quiet and vice versa.
Everyone who is either old or wise is both not old and not happy and vice versa.
Everyone who is both not quiet and not tall is generous and vice versa.
If someone is curious then alice is both not generous and strong.
Everyone who is either patient or not kind is either not brave or not happy.
If lucy is not rich or patient then someone is either quiet or calm.
Someone is not tall.
Someone is not rich.
John is not old.
Susan is wise.
Someone is not kind or calm.
Lucy is either brave or not kind.
John is brave or not tall. | Susan is patient. | entailment | (((~patient(mary)&old(mary)))<=>(~tall(susan)))&
(![X]:((~patient(X)<~>creative(X))<=>(~brave(X)<~>~kind(X))))&
(((brave(fred)&creative(fred)))<=>(?[X]:((~quiet(X)&~old(X)))))&
((?[X]:((~old(X)<~>curious(X))))=>((~patient(fred)&humble(fred))))&
(![X]:((happy(X)|~rich(X))=>(~generous(X)<~>~brave(X))))&
(((~old(alice)|humble(alice)))<=>(?[X]:(funny(X))))&
(![X]:((rich(X)&~quiet(X))<=>(rich(X)|~strong(X))))&
(![X]:((~funny(X)|~patient(X))<=>(rich(X)&quiet(X))))&
(![X]:((~humble(X)<~>~funny(X))=>(~old(X)<~>curious(X))))&
(![X]:((funny(X)|kind(X))<=>(funny(X)&quiet(X))))&
(![X]:((old(X)<~>wise(X))<=>(~old(X)&~happy(X))))&
(![X]:((~quiet(X)&~tall(X))<=>generous(X)))&
((?[X]:(curious(X)))=>((~generous(alice)&strong(alice))))&
(![X]:((patient(X)<~>~kind(X))=>(~brave(X)<~>~happy(X))))&
(((~rich(lucy)|patient(lucy)))=>(?[X]:((quiet(X)<~>calm(X)))))&
(?[X]:(~tall(X)))&
(?[X]:(~rich(X)))&
(~old(john))&
(wise(susan))&
(?[X]:((~kind(X)|calm(X))))&
((brave(lucy)<~>~kind(lucy)))&
((brave(john)|~tall(john))) | patient(susan) | [
"p6",
"p7",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 3251341836755158135784164
% SZS output start Proof for 3251341836755158135784164
7. ! [X0] : ((~quiet(X0) & rich(X0)) <=> (~strong(X0) | rich(X0))) [input p6]
8. ! [X0] : ((~patient(X0) | ~funny(X0)) <=> (quiet(X0) & rich(X0))) [input p7]
10. ! [X0] : ((kind(X0) | funny(X0)) <=> (quiet(X0) & funny(X0))) [input p9]
23. ~patient(susan) [input hypothesis]
45. ! [X0] : (((~quiet(X0) & rich(X0)) | (strong(X0) & ~rich(X0))) & ((~strong(X0) | rich(X0)) | (quiet(X0) | ~rich(X0)))) [nnf transformation 7]
46. ! [X0] : (((~quiet(X0) & rich(X0)) | (strong(X0) & ~rich(X0))) & (~strong(X0) | rich(X0) | quiet(X0) | ~rich(X0))) [flattening 45]
47. ! [X0] : (((~patient(X0) | ~funny(X0)) | (~quiet(X0) | ~rich(X0))) & ((quiet(X0) & rich(X0)) | (patient(X0) & funny(X0)))) [nnf transformation 8]
48. ! [X0] : ((~patient(X0) | ~funny(X0) | ~quiet(X0) | ~rich(X0)) & ((quiet(X0) & rich(X0)) | (patient(X0) & funny(X0)))) [flattening 47]
50. ! [X0] : (((kind(X0) | funny(X0)) | (~quiet(X0) | ~funny(X0))) & ((quiet(X0) & funny(X0)) | (~kind(X0) & ~funny(X0)))) [nnf transformation 10]
51. ! [X0] : ((kind(X0) | funny(X0) | ~quiet(X0) | ~funny(X0)) & ((quiet(X0) & funny(X0)) | (~kind(X0) & ~funny(X0)))) [flattening 50]
96. ~rich(X0) | ~quiet(X0) [cnf transformation 46]
99. rich(X0) | patient(X0) [cnf transformation 48]
100. funny(X0) | quiet(X0) [cnf transformation 48]
109. quiet(X0) | ~funny(X0) [cnf transformation 51]
139. ~patient(susan) [cnf transformation 23]
216. quiet(X0) [subsumption resolution 109,100]
273. patient(X0) | ~quiet(X0) [resolution 99,96]
274. patient(X0) [subsumption resolution 273,216]
281. $false [resolution 274,139]
% SZS output end Proof for 3251341836755158135784164
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not curious or not rich is not strong or patient and vice versa.
Everyone who is either funny or not curious is either generous or happy.
Everyone who is either not happy or not funny is both wise and rich and vice versa.
If fred is either rich or funny then someone is calm.
Everyone who is not generous or not creative is both creative and not humble and vice versa.
Everyone who is tall is old or not funny and vice versa.
If someone is either not curious or brave then john is patient and vice versa.
If someone is humble then someone is funny.
If someone is patient or funny then fred is not strong and vice versa.
Everyone who is both old and not happy is either rich or calm.
If someone is not old then fred is brave and vice versa.
Everyone who is creative or generous is either happy or not old and vice versa.
Everyone who is both not rich and generous is either not calm or funny and vice versa.
Everyone who is generous or curious is patient.
If paul is patient or funny then alice is not happy or not patient and vice versa.
Someone is both curious and humble.
Lucy is either not generous or humble.
Fred is either creative or not wise.
Someone is either not quiet or patient.
John is creative.
Mary is both not curious and quiet.
Someone is both patient and not quiet. | Alice is calm. | neutral | (![X]:((~curious(X)<~>~rich(X))<=>(~strong(X)|patient(X))))&
(![X]:((funny(X)<~>~curious(X))=>(generous(X)<~>happy(X))))&
(![X]:((~happy(X)<~>~funny(X))<=>(wise(X)&rich(X))))&
(((rich(fred)<~>funny(fred)))=>(?[X]:(calm(X))))&
(![X]:((~generous(X)|~creative(X))<=>(creative(X)&~humble(X))))&
(![X]:(tall(X)<=>(old(X)|~funny(X))))&
((?[X]:((~curious(X)<~>brave(X))))<=>(patient(john)))&
((?[X]:(humble(X)))=>(?[X]:(funny(X))))&
((?[X]:((patient(X)|funny(X))))<=>(~strong(fred)))&
(![X]:((old(X)&~happy(X))=>(rich(X)<~>calm(X))))&
((?[X]:(~old(X)))<=>(brave(fred)))&
(![X]:((creative(X)|generous(X))<=>(happy(X)<~>~old(X))))&
(![X]:((~rich(X)&generous(X))<=>(~calm(X)<~>funny(X))))&
(![X]:((generous(X)|curious(X))=>patient(X)))&
(((patient(paul)|funny(paul)))<=>((~happy(alice)|~patient(alice))))&
(?[X]:((curious(X)&humble(X))))&
((~generous(lucy)<~>humble(lucy)))&
((creative(fred)<~>~wise(fred)))&
(?[X]:((~quiet(X)<~>patient(X))))&
(creative(john))&
((~curious(mary)&quiet(mary)))&
(?[X]:((patient(X)&~quiet(X)))) | calm(alice) | [] | null | 0 |
If alice is both not curious and creative then someone is curious or rich and vice versa. If someone is both humble and quiet then mary is not happy or not humble and vice versa. If someone is not humble then john is strong or happy. If john is either funny or not quiet then someone is either not happy or patient and vice versa. Everyone who is rich or calm is either not rich or calm and vice versa. If someone is both old and generous then mary is wise and vice versa. Everyone who is both not creative and not strong is both old and calm and vice versa. If someone is humble then someone is not tall or not funny and vice versa. If someone is not patient or not curious then paul is either quiet or humble and vice versa. Everyone who is not funny is rich and vice versa. If alice is not brave then mary is tall or patient. If someone is either wise or quiet then alice is either not strong or quiet. Everyone who is either not rich or kind is wise or not old and vice versa. If mary is either creative or not old then someone is both wise and brave. Everyone who is humble is either generous or not curious and vice versa. Everyone who is both not brave and tall is either not generous or not patient and vice versa. Someone is either not kind or quiet. Alice is either not strong or not kind. John is curious or quiet. Mary is either not wise or not kind. Someone is both not wise and not creative. Alice is either tall or not strong. Someone is happy or not humble. Someone is not funny. | Alice is not tall. | entailment | (((~curious(alice)&creative(alice)))<=>(?[X]:((curious(X)|rich(X)))))&
((?[X]:((humble(X)&quiet(X))))<=>((~happy(mary)|~humble(mary))))&
((?[X]:(~humble(X)))=>((strong(john)|happy(john))))&
(((funny(john)<~>~quiet(john)))<=>(?[X]:((~happy(X)<~>patient(X)))))&
(![X]:((rich(X)|calm(X))<=>(~rich(X)<~>calm(X))))&
((?[X]:((old(X)&generous(X))))<=>(wise(mary)))&
(![X]:((~creative(X)&~strong(X))<=>(old(X)&calm(X))))&
((?[X]:(humble(X)))<=>(?[X]:((~tall(X)|~funny(X)))))&
((?[X]:((~patient(X)|~curious(X))))<=>((quiet(paul)<~>humble(paul))))&
(![X]:(~funny(X)<=>rich(X)))&
((~brave(alice))=>((tall(mary)|patient(mary))))&
((?[X]:((wise(X)<~>quiet(X))))=>((~strong(alice)<~>quiet(alice))))&
(![X]:((~rich(X)<~>kind(X))<=>(wise(X)|~old(X))))&
(((creative(mary)<~>~old(mary)))=>(?[X]:((wise(X)&brave(X)))))&
(![X]:(humble(X)<=>(generous(X)<~>~curious(X))))&
(![X]:((~brave(X)&tall(X))<=>(~generous(X)<~>~patient(X))))&
(?[X]:((~kind(X)<~>quiet(X))))&
((~strong(alice)<~>~kind(alice)))&
((curious(john)|quiet(john)))&
((~wise(mary)<~>~kind(mary)))&
(?[X]:((~wise(X)&~creative(X))))&
((tall(alice)<~>~strong(alice)))&
(?[X]:((happy(X)|~humble(X))))&
(?[X]:(~funny(X))) | ~tall(alice) | [
"p4",
"p6",
"p12",
"p17",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 7584111243009891909670878
% SZS output start Proof for 7584111243009891909670878
5. ! [X0] : ((calm(X0) | rich(X0)) <=> (~rich(X0) <~> calm(X0))) [input p4]
7. ! [X0] : ((~strong(X0) & ~creative(X0)) <=> (calm(X0) & old(X0))) [input p6]
13. ! [X0] : ((~rich(X0) <~> kind(X0)) <=> (~old(X0) | wise(X0))) [input p12]
18. ~strong(alice) <~> ~kind(alice) [input p17]
22. tall(alice) <~> ~strong(alice) [input p21]
25. tall(alice) [input hypothesis]
47. ! [X0] : (((calm(X0) | rich(X0)) | ((~rich(X0) | ~calm(X0)) & (calm(X0) | rich(X0)))) & (((~calm(X0) | rich(X0)) & (calm(X0) | ~rich(X0))) | (~calm(X0) & ~rich(X0)))) [nnf transformation 5]
48. ! [X0] : ((calm(X0) | rich(X0) | ((~rich(X0) | ~calm(X0)) & (calm(X0) | rich(X0)))) & (((~calm(X0) | rich(X0)) & (calm(X0) | ~rich(X0))) | (~calm(X0) & ~rich(X0)))) [flattening 47]
53. ! [X0] : (((~strong(X0) & ~creative(X0)) | (~calm(X0) | ~old(X0))) & ((calm(X0) & old(X0)) | (strong(X0) | creative(X0)))) [nnf transformation 7]
54. ! [X0] : (((~strong(X0) & ~creative(X0)) | ~calm(X0) | ~old(X0)) & ((calm(X0) & old(X0)) | strong(X0) | creative(X0))) [flattening 53]
66. ! [X0] : ((((~kind(X0) | rich(X0)) & (kind(X0) | ~rich(X0))) | (old(X0) & ~wise(X0))) & ((~old(X0) | wise(X0)) | ((~rich(X0) | ~kind(X0)) & (kind(X0) | rich(X0))))) [nnf transformation 13]
67. ! [X0] : ((((~kind(X0) | rich(X0)) & (kind(X0) | ~rich(X0))) | (old(X0) & ~wise(X0))) & (~old(X0) | wise(X0) | ((~rich(X0) | ~kind(X0)) & (kind(X0) | rich(X0))))) [flattening 66]
77. (kind(alice) | strong(alice)) & (~kind(alice) | ~strong(alice)) [nnf transformation 18]
81. (strong(alice) | ~tall(alice)) & (~strong(alice) | tall(alice)) [nnf transformation 22]
105. calm(X0) | ~rich(X0) | ~rich(X0) [cnf transformation 48]
108. ~calm(X0) | rich(X0) | ~calm(X0) [cnf transformation 48]
109. calm(X0) | rich(X0) | calm(X0) | rich(X0) [cnf transformation 48]
117. ~strong(X0) | ~calm(X0) | ~old(X0) [cnf transformation 54]
137. kind(X0) | ~rich(X0) | old(X0) [cnf transformation 67]
156. ~kind(alice) | ~strong(alice) [cnf transformation 77]
164. strong(alice) | ~tall(alice) [cnf transformation 81]
167. tall(alice) [cnf transformation 25]
168. calm(X0) | ~rich(X0) [duplicate literal removal 105]
169. ~calm(X0) | rich(X0) [duplicate literal removal 108]
170. calm(X0) | rich(X0) [duplicate literal removal 109]
264. rich(X0) [subsumption resolution 169,170]
265. calm(X0) [subsumption resolution 168,264]
284. ~old(X0) | ~strong(X0) [subsumption resolution 117,265]
356. 41 <=> strong(alice) [avatar definition]
358. strong(alice) <- (41) [avatar component clause 356]
370. kind(X0) | old(X0) [subsumption resolution 137,264]
402. 50 <=> kind(alice) [avatar definition]
403. ~kind(alice) <- (~50) [avatar component clause 402]
406. ~41 | ~50 [avatar split clause 156,402,356]
416. 52 <=> tall(alice) [avatar definition]
419. ~52 | 41 [avatar split clause 164,356,416]
430. 52 [avatar split clause 167,416]
445. old(alice) <- (~50) [resolution 370,403]
451. ~strong(alice) <- (~50) [resolution 445,284]
454. $false <- (41, ~50) [subsumption resolution 451,358]
455. ~41 | 50 [avatar contradiction clause 454]
456. $false [avatar sat refutation 406,419,430,455]
% SZS output end Proof for 7584111243009891909670878
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny then someone is either old or not generous and vice versa.
Everyone who is both not kind and old is both strong and not strong.
Everyone who is not creative or old is both not kind and not curious.
If someone is both not funny and not humble then mary is either creative or brave.
If fred is kind or not tall then someone is not funny or kind.
If mary is not calm or rich then someone is not curious and vice versa.
Everyone who is both not rich and tall is kind and vice versa.
Everyone who is not wise or wise is brave or not patient.
If someone is both happy and kind then someone is either not tall or calm and vice versa.
Everyone who is kind is both not generous and kind.
Everyone who is wise or not old is kind.
If fred is generous or tall then someone is wise or generous.
Everyone who is not tall is both not old and not generous.
If mary is both brave and funny then susan is not wise or kind.
Everyone who is generous is either not brave or not funny.
If lucy is both brave and not calm then john is not rich and vice versa.
Alice is both wise and not humble.
Fred is humble.
Susan is strong.
Someone is either not quiet or kind.
Someone is happy.
Someone is both not quiet and kind.
Someone is both brave and not calm. | Lucy is not tall. | contradiction | ((?[X]:(funny(X)))<=>(?[X]:((old(X)<~>~generous(X)))))&
(![X]:((~kind(X)&old(X))=>(strong(X)&~strong(X))))&
(![X]:((~creative(X)|old(X))=>(~kind(X)&~curious(X))))&
((?[X]:((~funny(X)&~humble(X))))=>((creative(mary)<~>brave(mary))))&
(((kind(fred)|~tall(fred)))=>(?[X]:((~funny(X)|kind(X)))))&
(((~calm(mary)|rich(mary)))<=>(?[X]:(~curious(X))))&
(![X]:((~rich(X)&tall(X))<=>kind(X)))&
(![X]:((~wise(X)|wise(X))=>(brave(X)|~patient(X))))&
((?[X]:((happy(X)&kind(X))))<=>(?[X]:((~tall(X)<~>calm(X)))))&
(![X]:(kind(X)=>(~generous(X)&kind(X))))&
(![X]:((wise(X)|~old(X))=>kind(X)))&
(((generous(fred)|tall(fred)))=>(?[X]:((wise(X)|generous(X)))))&
(![X]:(~tall(X)=>(~old(X)&~generous(X))))&
(((brave(mary)&funny(mary)))=>((~wise(susan)|kind(susan))))&
(![X]:(generous(X)=>(~brave(X)<~>~funny(X))))&
(((brave(lucy)&~calm(lucy)))<=>(~rich(john)))&
((wise(alice)&~humble(alice)))&
(humble(fred))&
(strong(susan))&
(?[X]:((~quiet(X)<~>kind(X))))&
(?[X]:(happy(X)))&
(?[X]:((~quiet(X)&kind(X))))&
(?[X]:((brave(X)&~calm(X)))) | ~tall(lucy) | [
"p1",
"p2",
"p6",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 1417530691426340502488766
% SZS output start Proof for 1417530691426340502488766
2. ! [X0] : ((old(X0) & ~kind(X0)) => (~strong(X0) & strong(X0))) [input p1]
3. ! [X0] : ((old(X0) | ~creative(X0)) => (~curious(X0) & ~kind(X0))) [input p2]
7. ! [X0] : ((tall(X0) & ~rich(X0)) <=> kind(X0)) [input p6]
11. ! [X0] : ((~old(X0) | wise(X0)) => kind(X0)) [input p10]
24. ~tall(lucy) [input hypothesis]
28. ! [X0] : ((~strong(X0) & strong(X0)) | (~old(X0) | kind(X0))) [ennf transformation 2]
29. ! [X0] : ((~strong(X0) & strong(X0)) | ~old(X0) | kind(X0)) [flattening 28]
30. ! [X0] : ((~curious(X0) & ~kind(X0)) | (~old(X0) & creative(X0))) [ennf transformation 3]
34. ! [X0] : (kind(X0) | (old(X0) & ~wise(X0))) [ennf transformation 11]
53. ! [X0] : (((tall(X0) & ~rich(X0)) | ~kind(X0)) & (kind(X0) | (~tall(X0) | rich(X0)))) [nnf transformation 7]
54. ! [X0] : (((tall(X0) & ~rich(X0)) | ~kind(X0)) & (kind(X0) | ~tall(X0) | rich(X0))) [flattening 53]
78. strong(X0) | ~old(X0) | kind(X0) [cnf transformation 29]
79. ~strong(X0) | ~old(X0) | kind(X0) [cnf transformation 29]
81. ~kind(X0) | ~old(X0) [cnf transformation 30]
93. ~kind(X0) | tall(X0) [cnf transformation 54]
103. kind(X0) | old(X0) [cnf transformation 34]
125. ~tall(lucy) [cnf transformation 24]
151. ~old(X0) | kind(X0) [subsumption resolution 78,79]
152. ~old(X0) [subsumption resolution 81,151]
233. kind(X0) [subsumption resolution 103,152]
268. tall(X0) [resolution 93,233]
269. $false [resolution 268,125]
% SZS output end Proof for 1417530691426340502488766
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both wise and calm then alice is either creative or not happy and vice versa. Everyone who is both happy and quiet is not rich or not brave and vice versa. If someone is calm or curious then mary is either creative or humble. Everyone who is not humble or not wise is either humble or not quiet. If paul is both generous and tall then susan is both strong and not tall. If lucy is not funny then someone is both kind and not happy and vice versa. Everyone who is both not quiet and not humble is both tall and not calm and vice versa. If susan is both not generous and not rich then fred is not calm or kind. Everyone who is either not creative or creative is both brave and funny and vice versa. Everyone who is not brave or not strong is wise or not creative. Everyone who is either not quiet or not brave is wise and vice versa. Everyone who is not kind is either calm or not calm and vice versa. Everyone who is curious or strong is not funny or not kind and vice versa. Everyone who is both not generous and strong is both curious and wise and vice versa. If someone is both not creative and strong then fred is both old and not happy and vice versa. Everyone who is both not tall and happy is not kind and vice versa. Someone is not curious. Susan is both not calm and not kind. Someone is either not wise or curious. Fred is either not brave or humble. Someone is either creative or not generous. Lucy is either not brave or calm. Someone is not rich. | Mary is rich. | contradiction | ((?[X]:((wise(X)&calm(X))))<=>((creative(alice)<~>~happy(alice))))&
(![X]:((happy(X)&quiet(X))<=>(~rich(X)|~brave(X))))&
((?[X]:((calm(X)|curious(X))))=>((creative(mary)<~>humble(mary))))&
(![X]:((~humble(X)|~wise(X))=>(humble(X)<~>~quiet(X))))&
(((generous(paul)&tall(paul)))=>((strong(susan)&~tall(susan))))&
((~funny(lucy))<=>(?[X]:((kind(X)&~happy(X)))))&
(![X]:((~quiet(X)&~humble(X))<=>(tall(X)&~calm(X))))&
(((~generous(susan)&~rich(susan)))=>((~calm(fred)|kind(fred))))&
(![X]:((~creative(X)<~>creative(X))<=>(brave(X)&funny(X))))&
(![X]:((~brave(X)|~strong(X))=>(wise(X)|~creative(X))))&
(![X]:((~quiet(X)<~>~brave(X))<=>wise(X)))&
(![X]:(~kind(X)<=>(calm(X)<~>~calm(X))))&
(![X]:((curious(X)|strong(X))<=>(~funny(X)|~kind(X))))&
(![X]:((~generous(X)&strong(X))<=>(curious(X)&wise(X))))&
((?[X]:((~creative(X)&strong(X))))<=>((old(fred)&~happy(fred))))&
(![X]:((~tall(X)&happy(X))<=>~kind(X)))&
(?[X]:(~curious(X)))&
((~calm(susan)&~kind(susan)))&
(?[X]:((~wise(X)<~>curious(X))))&
((~brave(fred)<~>humble(fred)))&
(?[X]:((creative(X)<~>~generous(X))))&
((~brave(lucy)<~>calm(lucy)))&
(?[X]:(~rich(X))) | rich(mary) | [
"p1",
"p2",
"p3",
"p6",
"p8",
"p10",
"p11",
"p12",
"p13",
"p14",
"p15",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 7187484679743876262389481
% SZS output start Proof for 7187484679743876262389481
2. ! [X0] : ((quiet(X0) & happy(X0)) <=> (~brave(X0) | ~rich(X0))) [input p1]
3. ? [X0] : (curious(X0) | calm(X0)) => (creative(mary) <~> humble(mary)) [input p2]
4. ! [X0] : ((~wise(X0) | ~humble(X0)) => (humble(X0) <~> ~quiet(X0))) [input p3]
7. ! [X0] : ((~humble(X0) & ~quiet(X0)) <=> (~calm(X0) & tall(X0))) [input p6]
9. ! [X0] : ((~creative(X0) <~> creative(X0)) <=> (funny(X0) & brave(X0))) [input p8]
11. ! [X0] : ((~quiet(X0) <~> ~brave(X0)) <=> wise(X0)) [input p10]
12. ! [X0] : (~kind(X0) <=> (calm(X0) <~> ~calm(X0))) [input p11]
13. ! [X0] : ((strong(X0) | curious(X0)) <=> (~kind(X0) | ~funny(X0))) [input p12]
14. ! [X0] : ((strong(X0) & ~generous(X0)) <=> (wise(X0) & curious(X0))) [input p13]
15. ? [X0] : (strong(X0) & ~creative(X0)) <=> (~happy(fred) & old(fred)) [input p14]
16. ! [X0] : ((happy(X0) & ~tall(X0)) <=> ~kind(X0)) [input p15]
22. ~brave(lucy) <~> calm(lucy) [input p21]
24. rich(mary) [input hypothesis]
25. (creative(mary) <~> humble(mary)) | ! [X0] : (~curious(X0) & ~calm(X0)) [ennf transformation 3]
26. ! [X0] : ((humble(X0) <~> ~quiet(X0)) | (wise(X0) & humble(X0))) [ennf transformation 4]
37. ! [X0] : (((quiet(X0) & happy(X0)) | (brave(X0) & rich(X0))) & ((~brave(X0) | ~rich(X0)) | (~quiet(X0) | ~happy(X0)))) [nnf transformation 2]
38. ! [X0] : (((quiet(X0) & happy(X0)) | (brave(X0) & rich(X0))) & (~brave(X0) | ~rich(X0) | ~quiet(X0) | ~happy(X0))) [flattening 37]
39. ((~humble(mary) | ~creative(mary)) & (humble(mary) | creative(mary))) | ! [X0] : (~curious(X0) & ~calm(X0)) [nnf transformation 25]
40. ! [X0] : (((quiet(X0) | ~humble(X0)) & (~quiet(X0) | humble(X0))) | (wise(X0) & humble(X0))) [nnf transformation 26]
45. ! [X0] : (((~humble(X0) & ~quiet(X0)) | (calm(X0) | ~tall(X0))) & ((~calm(X0) & tall(X0)) | (humble(X0) | quiet(X0)))) [nnf transformation 7]
46. ! [X0] : (((~humble(X0) & ~quiet(X0)) | calm(X0) | ~tall(X0)) & ((~calm(X0) & tall(X0)) | humble(X0) | quiet(X0))) [flattening 45]
47. ! [X0] : ((((~creative(X0) | creative(X0)) & (creative(X0) | ~creative(X0))) | (~funny(X0) | ~brave(X0))) & ((funny(X0) & brave(X0)) | ((~creative(X0) | ~creative(X0)) & (creative(X0) | creative(X0))))) [nnf transformation 9]
48. ! [X0] : ((((~creative(X0) | creative(X0)) & (creative(X0) | ~creative(X0))) | ~funny(X0) | ~brave(X0)) & ((funny(X0) & brave(X0)) | ((~creative(X0) | ~creative(X0)) & (creative(X0) | creative(X0))))) [flattening 47]
49. ! [X0] : ((((brave(X0) | quiet(X0)) & (~brave(X0) | ~quiet(X0))) | ~wise(X0)) & (wise(X0) | ((~quiet(X0) | brave(X0)) & (~brave(X0) | quiet(X0))))) [nnf transformation 11]
50. ! [X0] : ((~kind(X0) | ((calm(X0) | calm(X0)) & (~calm(X0) | ~calm(X0)))) & (((calm(X0) | ~calm(X0)) & (~calm(X0) | calm(X0))) | kind(X0))) [nnf transformation 12]
51. ! [X0] : (((strong(X0) | curious(X0)) | (kind(X0) & funny(X0))) & ((~kind(X0) | ~funny(X0)) | (~strong(X0) & ~curious(X0)))) [nnf transformation 13]
52. ! [X0] : ((strong(X0) | curious(X0) | (kind(X0) & funny(X0))) & (~kind(X0) | ~funny(X0) | (~strong(X0) & ~curious(X0)))) [flattening 51]
53. ! [X0] : (((strong(X0) & ~generous(X0)) | (~wise(X0) | ~curious(X0))) & ((wise(X0) & curious(X0)) | (~strong(X0) | generous(X0)))) [nnf transformation 14]
54. ! [X0] : (((strong(X0) & ~generous(X0)) | ~wise(X0) | ~curious(X0)) & ((wise(X0) & curious(X0)) | ~strong(X0) | generous(X0))) [flattening 53]
55. (? [X0] : (strong(X0) & ~creative(X0)) | (happy(fred) | ~old(fred))) & ((~happy(fred) & old(fred)) | ! [X0] : (~strong(X0) | creative(X0))) [nnf transformation 15]
56. (? [X0] : (strong(X0) & ~creative(X0)) | happy(fred) | ~old(fred)) & ((~happy(fred) & old(fred)) | ! [X0] : (~strong(X0) | creative(X0))) [flattening 55]
57. (? [X0] : (strong(X0) & ~creative(X0)) | happy(fred) | ~old(fred)) & ((~happy(fred) & old(fred)) | ! [X1] : (~strong(X1) | creative(X1))) [rectify 56]
58. ? [X0] : (strong(X0) & ~creative(X0)) => (strong(sK2) & ~creative(sK2)) [choice axiom]
59. ((strong(sK2) & ~creative(sK2)) | happy(fred) | ~old(fred)) & ((~happy(fred) & old(fred)) | ! [X1] : (~strong(X1) | creative(X1))) [skolemisation 57,58]
60. ! [X0] : (((happy(X0) & ~tall(X0)) | kind(X0)) & (~kind(X0) | (~happy(X0) | tall(X0)))) [nnf transformation 16]
61. ! [X0] : (((happy(X0) & ~tall(X0)) | kind(X0)) & (~kind(X0) | ~happy(X0) | tall(X0))) [flattening 60]
71. (~calm(lucy) | brave(lucy)) & (calm(lucy) | ~brave(lucy)) [nnf transformation 22]
80. ~brave(X0) | ~rich(X0) | ~quiet(X0) | ~happy(X0) [cnf transformation 38]
87. ~humble(mary) | ~creative(mary) | ~calm(X0) [cnf transformation 39]
89. ~quiet(X0) | humble(X0) | humble(X0) [cnf transformation 40]
98. tall(X0) | humble(X0) | quiet(X0) [cnf transformation 46]
103. brave(X0) | creative(X0) | creative(X0) [cnf transformation 48]
104. brave(X0) | ~creative(X0) | ~creative(X0) [cnf transformation 48]
111. wise(X0) | ~brave(X0) | quiet(X0) [cnf transformation 49]
117. ~kind(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 50]
118. ~kind(X0) | calm(X0) | calm(X0) [cnf transformation 50]
122. strong(X0) | curious(X0) | kind(X0) [cnf transformation 52]
126. strong(X0) | ~wise(X0) | ~curious(X0) [cnf transformation 54]
128. ~happy(fred) | ~strong(X1) | creative(X1) [cnf transformation 59]
132. ~tall(X0) | kind(X0) [cnf transformation 61]
133. happy(X0) | kind(X0) [cnf transformation 61]
143. calm(lucy) | ~brave(lucy) [cnf transformation 71]
146. rich(mary) [cnf transformation 24]
147. ~kind(X0) | ~calm(X0) [duplicate literal removal 117]
148. ~kind(X0) | calm(X0) [duplicate literal removal 118]
149. brave(X0) | creative(X0) [duplicate literal removal 103]
150. ~creative(X0) | brave(X0) [duplicate literal removal 104]
153. ~quiet(X0) | humble(X0) [duplicate literal removal 89]
183. 7 <=> creative(mary) [avatar definition]
187. 8 <=> humble(mary) [avatar definition]
189. ~humble(mary) <- (~8) [avatar component clause 187]
192. 9 <=> ! [X0] : ~calm(X0) [avatar definition]
193. ~calm(X0) <- (9) [avatar component clause 192]
194. 9 | ~7 | ~8 [avatar split clause 87,187,183,192]
234. tall(X0) | humble(X0) [subsumption resolution 98,153]
253. brave(X0) [subsumption resolution 149,150]
255. quiet(X0) | wise(X0) [subsumption resolution 111,253]
256. ~kind(X0) [subsumption resolution 147,148]
257. strong(X0) | curious(X0) [subsumption resolution 122,256]
258. ~wise(X0) | strong(X0) [subsumption resolution 126,257]
265. 23 <=> happy(fred) [avatar definition]
266. ~happy(fred) <- (~23) [avatar component clause 265]
279. 26 <=> ! [X1] : (~strong(X1) | creative(X1)) [avatar definition]
280. ~strong(X1) | creative(X1) <- (26) [avatar component clause 279]
281. 26 | ~23 [avatar split clause 128,265,279]
283. happy(X0) [subsumption resolution 133,256]
284. ~tall(X0) [subsumption resolution 132,256]
306. calm(lucy) [subsumption resolution 143,253]
307. $false <- (~23) [subsumption resolution 266,283]
308. 23 [avatar contradiction clause 307]
320. humble(X0) [resolution 234,284]
322. $false <- (~8) [resolution 320,189]
323. 8 [avatar contradiction clause 322]
375. ~rich(X2) | ~quiet(X2) | ~happy(X2) [resolution 80,253]
376. ~rich(X2) | ~quiet(X2) [subsumption resolution 375,283]
383. ~quiet(mary) [resolution 376,146]
386. wise(mary) [resolution 383,255]
401. strong(mary) [resolution 386,258]
405. creative(mary) <- (26) [resolution 401,280]
408. 7 | ~26 [avatar split clause 405,279,183]
418. $false <- (9) [resolution 193,306]
419. ~9 [avatar contradiction clause 418]
421. $false [avatar sat refutation 194,281,308,323,408,419]
% SZS output end Proof for 7187484679743876262389481
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not curious is both patient and not patient and vice versa. If paul is both not brave and calm then someone is both not rich and rich. Everyone who is both rich and not rich is not humble or quiet and vice versa. If mary is both humble and funny then mary is rich or not happy and vice versa. If fred is both old and strong then lucy is funny and vice versa. If alice is not generous or humble then mary is not strong or rich and vice versa. Everyone who is strong or quiet is happy or not tall and vice versa. Everyone who is both not rich and old is either not rich or patient and vice versa. Everyone who is both tall and not happy is rich or patient and vice versa. Everyone who is either old or not creative is either curious or calm and vice versa. If someone is either not happy or calm then someone is not calm or kind and vice versa. Everyone who is either not happy or wise is tall or not curious and vice versa. If someone is not kind then fred is either not old or quiet and vice versa. Everyone who is either rich or not happy is either generous or strong and vice versa. If someone is both not quiet and not humble then john is both humble and not strong. Everyone who is both calm and rich is calm or curious and vice versa. Someone is either funny or not rich. Someone is either old or not strong. Someone is both creative and not funny. Someone is brave. Susan is not generous. Fred is either not wise or strong. | Lucy is not quiet. | entailment | (![X]:(~curious(X)<=>(patient(X)&~patient(X))))&
(((~brave(paul)&calm(paul)))=>(?[X]:((~rich(X)&rich(X)))))&
(![X]:((rich(X)&~rich(X))<=>(~humble(X)|quiet(X))))&
(((humble(mary)&funny(mary)))<=>((rich(mary)|~happy(mary))))&
(((old(fred)&strong(fred)))<=>(funny(lucy)))&
(((~generous(alice)|humble(alice)))<=>((~strong(mary)|rich(mary))))&
(![X]:((strong(X)|quiet(X))<=>(happy(X)|~tall(X))))&
(![X]:((~rich(X)&old(X))<=>(~rich(X)<~>patient(X))))&
(![X]:((tall(X)&~happy(X))<=>(rich(X)|patient(X))))&
(![X]:((old(X)<~>~creative(X))<=>(curious(X)<~>calm(X))))&
((?[X]:((~happy(X)<~>calm(X))))<=>(?[X]:((~calm(X)|kind(X)))))&
(![X]:((~happy(X)<~>wise(X))<=>(tall(X)|~curious(X))))&
((?[X]:(~kind(X)))<=>((~old(fred)<~>quiet(fred))))&
(![X]:((rich(X)<~>~happy(X))<=>(generous(X)<~>strong(X))))&
((?[X]:((~quiet(X)&~humble(X))))=>((humble(john)&~strong(john))))&
(![X]:((calm(X)&rich(X))<=>(calm(X)|curious(X))))&
(?[X]:((funny(X)<~>~rich(X))))&
(?[X]:((old(X)<~>~strong(X))))&
(?[X]:((creative(X)&~funny(X))))&
(?[X]:(brave(X)))&
(~generous(susan))&
((~wise(fred)<~>strong(fred))) | ~quiet(lucy) | [
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 404595013238528618247958
% SZS output start Proof for 404595013238528618247958
3. ! [X0] : ((~rich(X0) & rich(X0)) <=> (quiet(X0) | ~humble(X0))) [input p2]
23. quiet(lucy) [input hypothesis]
30. ! [X0] : (((~rich(X0) & rich(X0)) | (~quiet(X0) & humble(X0))) & ((quiet(X0) | ~humble(X0)) | (rich(X0) | ~rich(X0)))) [nnf transformation 3]
31. ! [X0] : (((~rich(X0) & rich(X0)) | (~quiet(X0) & humble(X0))) & (quiet(X0) | ~humble(X0) | rich(X0) | ~rich(X0))) [flattening 30]
73. rich(X0) | ~quiet(X0) [cnf transformation 31]
75. ~rich(X0) | ~quiet(X0) [cnf transformation 31]
151. quiet(lucy) [cnf transformation 23]
155. ~quiet(X0) [subsumption resolution 73,75]
278. $false [subsumption resolution 151,155]
% SZS output end Proof for 404595013238528618247958
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not strong or quiet is rich or strong and vice versa.
If fred is brave or generous then susan is either kind or rich.
Everyone who is old or tall is kind and vice versa.
Everyone who is both wise and not humble is kind and vice versa.
If john is funny or not curious then someone is both not calm and not patient.
Everyone who is not quiet or generous is either creative or tall and vice versa.
Everyone who is both kind and not happy is generous or happy and vice versa.
If lucy is either not creative or not happy then someone is quiet and vice versa.
Everyone who is funny is not humble and vice versa.
If someone is either not tall or funny then someone is not brave and vice versa.
Everyone who is either not kind or happy is not brave.
If someone is both curious and not quiet then someone is not strong and vice versa.
Everyone who is not quiet is both not tall and not kind.
Everyone who is tall is not curious or generous and vice versa.
Everyone who is not quiet or not creative is not tall.
If alice is not patient then someone is either kind or not tall.
Paul is not happy.
Susan is not funny or generous.
Someone is humble or not patient.
Someone is either not humble or quiet.
Someone is not tall or brave. | Lucy is not old. | entailment | (![X]:((~strong(X)|quiet(X))<=>(rich(X)|strong(X))))&
(((brave(fred)|generous(fred)))=>((kind(susan)<~>rich(susan))))&
(![X]:((old(X)|tall(X))<=>kind(X)))&
(![X]:((wise(X)&~humble(X))<=>kind(X)))&
(((funny(john)|~curious(john)))=>(?[X]:((~calm(X)&~patient(X)))))&
(![X]:((~quiet(X)|generous(X))<=>(creative(X)<~>tall(X))))&
(![X]:((kind(X)&~happy(X))<=>(generous(X)|happy(X))))&
(((~creative(lucy)<~>~happy(lucy)))<=>(?[X]:(quiet(X))))&
(![X]:(funny(X)<=>~humble(X)))&
((?[X]:((~tall(X)<~>funny(X))))<=>(?[X]:(~brave(X))))&
(![X]:((~kind(X)<~>happy(X))=>~brave(X)))&
((?[X]:((curious(X)&~quiet(X))))<=>(?[X]:(~strong(X))))&
(![X]:(~quiet(X)=>(~tall(X)&~kind(X))))&
(![X]:(tall(X)<=>(~curious(X)|generous(X))))&
(![X]:((~quiet(X)|~creative(X))=>~tall(X)))&
((~patient(alice))=>(?[X]:((kind(X)<~>~tall(X)))))&
(~happy(paul))&
((~funny(susan)|generous(susan)))&
(?[X]:((humble(X)|~patient(X))))&
(?[X]:((~humble(X)<~>quiet(X))))&
(?[X]:((~tall(X)|brave(X)))) | ~old(lucy) | [
"p2",
"p5",
"p6",
"p7",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 4402855256524055828798662
% SZS output start Proof for 4402855256524055828798662
3. ! [X0] : ((tall(X0) | old(X0)) <=> kind(X0)) [input p2]
6. ! [X0] : ((generous(X0) | ~quiet(X0)) <=> (creative(X0) <~> tall(X0))) [input p5]
7. ! [X0] : ((~happy(X0) & kind(X0)) <=> (happy(X0) | generous(X0))) [input p6]
8. (~creative(lucy) <~> ~happy(lucy)) <=> ? [X0] : quiet(X0) [input p7]
13. ! [X0] : (~quiet(X0) => (~kind(X0) & ~tall(X0))) [input p12]
14. ! [X0] : (tall(X0) <=> (generous(X0) | ~curious(X0))) [input p13]
22. old(lucy) [input hypothesis]
29. ! [X0] : ((~kind(X0) & ~tall(X0)) | quiet(X0)) [ennf transformation 13]
35. ! [X0] : (((tall(X0) | old(X0)) | ~kind(X0)) & (kind(X0) | (~tall(X0) & ~old(X0)))) [nnf transformation 3]
36. ! [X0] : ((tall(X0) | old(X0) | ~kind(X0)) & (kind(X0) | (~tall(X0) & ~old(X0)))) [flattening 35]
41. ! [X0] : (((generous(X0) | ~quiet(X0)) | ((creative(X0) | ~tall(X0)) & (tall(X0) | ~creative(X0)))) & (((~tall(X0) | ~creative(X0)) & (tall(X0) | creative(X0))) | (~generous(X0) & quiet(X0)))) [nnf transformation 6]
42. ! [X0] : ((generous(X0) | ~quiet(X0) | ((creative(X0) | ~tall(X0)) & (tall(X0) | ~creative(X0)))) & (((~tall(X0) | ~creative(X0)) & (tall(X0) | creative(X0))) | (~generous(X0) & quiet(X0)))) [flattening 41]
43. ! [X0] : (((~happy(X0) & kind(X0)) | (~happy(X0) & ~generous(X0))) & ((happy(X0) | generous(X0)) | (happy(X0) | ~kind(X0)))) [nnf transformation 7]
44. ! [X0] : (((~happy(X0) & kind(X0)) | (~happy(X0) & ~generous(X0))) & (happy(X0) | generous(X0) | happy(X0) | ~kind(X0))) [flattening 43]
45. (((happy(lucy) | creative(lucy)) & (~happy(lucy) | ~creative(lucy))) | ! [X0] : ~quiet(X0)) & (? [X0] : quiet(X0) | ((~creative(lucy) | happy(lucy)) & (~happy(lucy) | creative(lucy)))) [nnf transformation 8]
46. (((happy(lucy) | creative(lucy)) & (~happy(lucy) | ~creative(lucy))) | ! [X0] : ~quiet(X0)) & (? [X1] : quiet(X1) | ((~creative(lucy) | happy(lucy)) & (~happy(lucy) | creative(lucy)))) [rectify 45]
47. ? [X1] : quiet(X1) => quiet(sK1) [choice axiom]
48. (((happy(lucy) | creative(lucy)) & (~happy(lucy) | ~creative(lucy))) | ! [X0] : ~quiet(X0)) & (quiet(sK1) | ((~creative(lucy) | happy(lucy)) & (~happy(lucy) | creative(lucy)))) [skolemisation 46,47]
61. ! [X0] : ((tall(X0) | (~generous(X0) & curious(X0))) & ((generous(X0) | ~curious(X0)) | ~tall(X0))) [nnf transformation 14]
62. ! [X0] : ((tall(X0) | (~generous(X0) & curious(X0))) & (generous(X0) | ~curious(X0) | ~tall(X0))) [flattening 61]
81. ~old(X0) | kind(X0) [cnf transformation 36]
92. ~creative(X0) | ~tall(X0) | ~generous(X0) [cnf transformation 42]
95. happy(X0) | generous(X0) | happy(X0) | ~kind(X0) [cnf transformation 44]
99. ~happy(X0) | ~happy(X0) [cnf transformation 44]
103. happy(lucy) | creative(lucy) | ~quiet(X0) [cnf transformation 48]
116. ~kind(X0) | quiet(X0) [cnf transformation 29]
119. ~generous(X0) | tall(X0) [cnf transformation 62]
130. old(lucy) [cnf transformation 22]
131. happy(X0) | generous(X0) | ~kind(X0) [duplicate literal removal 95]
132. ~happy(X0) [duplicate literal removal 99]
169. ~kind(X0) | generous(X0) [subsumption resolution 131,132]
170. creative(lucy) | ~quiet(X0) [subsumption resolution 103,132]
172. 8 <=> ! [X0] : ~quiet(X0) [avatar definition]
173. ~quiet(X0) <- (8) [avatar component clause 172]
175. 9 <=> creative(lucy) [avatar definition]
177. creative(lucy) <- (9) [avatar component clause 175]
178. 8 | 9 [avatar split clause 170,175,172]
284. kind(lucy) [resolution 81,130]
292. quiet(lucy) [resolution 116,284]
293. $false <- (8) [subsumption resolution 292,173]
294. ~8 [avatar contradiction clause 293]
295. generous(lucy) [resolution 169,284]
296. tall(lucy) [resolution 295,119]
309. ~tall(lucy) | ~generous(lucy) <- (9) [resolution 92,177]
311. ~generous(lucy) <- (9) [subsumption resolution 309,296]
312. $false <- (9) [subsumption resolution 311,295]
313. ~9 [avatar contradiction clause 312]
314. $false [avatar sat refutation 178,294,313]
% SZS output end Proof for 4402855256524055828798662
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not wise or brave is not tall or not patient.
Everyone who is both happy and humble is quiet or not humble.
If fred is not kind then someone is either wise or creative.
Everyone who is not old is either not wise or not calm.
Everyone who is not strong is curious or not calm and vice versa.
If john is not tall then someone is not tall.
Everyone who is not rich or happy is not tall.
Everyone who is both not humble and not old is old and vice versa.
Everyone who is not old or brave is either generous or not creative and vice versa.
Everyone who is both generous and not brave is either funny or kind and vice versa.
Everyone who is either curious or rich is strong.
Everyone who is not funny or funny is curious or not humble.
Everyone who is kind is both not humble and funny.
If someone is both quiet and curious then someone is either happy or brave and vice versa.
If someone is brave or curious then paul is either not curious or not generous.
Someone is both not calm and not funny.
Someone is either not wise or not patient.
Someone is either funny or humble.
Paul is both rich and not funny.
John is not funny.
Mary is not generous or calm.
John is both quiet and tall. | Mary is not humble. | contradiction | (![X]:((~wise(X)<~>brave(X))=>(~tall(X)|~patient(X))))&
(![X]:((happy(X)&humble(X))=>(quiet(X)|~humble(X))))&
((~kind(fred))=>(?[X]:((wise(X)<~>creative(X)))))&
(![X]:(~old(X)=>(~wise(X)<~>~calm(X))))&
(![X]:(~strong(X)<=>(curious(X)|~calm(X))))&
((~tall(john))=>(?[X]:(~tall(X))))&
(![X]:((~rich(X)|happy(X))=>~tall(X)))&
(![X]:((~humble(X)&~old(X))<=>old(X)))&
(![X]:((~old(X)|brave(X))<=>(generous(X)<~>~creative(X))))&
(![X]:((generous(X)&~brave(X))<=>(funny(X)<~>kind(X))))&
(![X]:((curious(X)<~>rich(X))=>strong(X)))&
(![X]:((~funny(X)|funny(X))=>(curious(X)|~humble(X))))&
(![X]:(kind(X)=>(~humble(X)&funny(X))))&
((?[X]:((quiet(X)&curious(X))))<=>(?[X]:((happy(X)<~>brave(X)))))&
((?[X]:((brave(X)|curious(X))))=>((~curious(paul)<~>~generous(paul))))&
(?[X]:((~calm(X)&~funny(X))))&
(?[X]:((~wise(X)<~>~patient(X))))&
(?[X]:((funny(X)<~>humble(X))))&
((rich(paul)&~funny(paul)))&
(~funny(john))&
((~generous(mary)|calm(mary)))&
((quiet(john)&tall(john))) | ~humble(mary) | [
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 9091776967092682636145690
% SZS output start Proof for 9091776967092682636145690
8. ! [X0] : ((~old(X0) & ~humble(X0)) <=> old(X0)) [input p7]
23. ~humble(mary) [input hypothesis]
47. ! [X0] : (((~old(X0) & ~humble(X0)) | ~old(X0)) & (old(X0) | (old(X0) | humble(X0)))) [nnf transformation 8]
48. ! [X0] : (((~old(X0) & ~humble(X0)) | ~old(X0)) & (old(X0) | old(X0) | humble(X0))) [flattening 47]
80. old(X0) | old(X0) | humble(X0) [cnf transformation 48]
82. ~old(X0) | ~old(X0) [cnf transformation 48]
123. ~humble(mary) [cnf transformation 23]
124. old(X0) | humble(X0) [duplicate literal removal 80]
125. ~old(X0) [duplicate literal removal 82]
150. humble(X0) [subsumption resolution 124,125]
208. $false [subsumption resolution 123,150]
% SZS output end Proof for 9091776967092682636145690
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative and not patient is not generous or not rich and vice versa.
Everyone who is either not brave or not old is either not funny or not kind and vice versa.
If someone is either not generous or not happy then someone is either not calm or not strong and vice versa.
Everyone who is humble or not quiet is both patient and tall and vice versa.
Everyone who is creative or kind is both wise and strong.
If someone is both creative and not curious then someone is both funny and not humble.
If alice is either happy or quiet then someone is not strong or patient and vice versa.
Everyone who is not old is either not strong or not happy.
Everyone who is not old is either happy or humble.
Everyone who is not generous or not rich is quiet and vice versa.
Everyone who is quiet or not creative is either not creative or happy and vice versa.
If someone is not patient or not creative then someone is not rich or not kind.
Everyone who is quiet or not brave is either brave or patient and vice versa.
If lucy is either kind or not kind then someone is either quiet or funny.
Everyone who is either not happy or not strong is patient and vice versa.
Everyone who is happy or old is either calm or not curious and vice versa.
Someone is quiet or not creative.
Someone is creative or not brave.
Someone is both calm and not rich.
Paul is funny. | Paul is not old. | contradiction | (![X]:((creative(X)&~patient(X))<=>(~generous(X)|~rich(X))))&
(![X]:((~brave(X)<~>~old(X))<=>(~funny(X)<~>~kind(X))))&
((?[X]:((~generous(X)<~>~happy(X))))<=>(?[X]:((~calm(X)<~>~strong(X)))))&
(![X]:((humble(X)|~quiet(X))<=>(patient(X)&tall(X))))&
(![X]:((creative(X)|kind(X))=>(wise(X)&strong(X))))&
((?[X]:((creative(X)&~curious(X))))=>(?[X]:((funny(X)&~humble(X)))))&
(((happy(alice)<~>quiet(alice)))<=>(?[X]:((~strong(X)|patient(X)))))&
(![X]:(~old(X)=>(~strong(X)<~>~happy(X))))&
(![X]:(~old(X)=>(happy(X)<~>humble(X))))&
(![X]:((~generous(X)|~rich(X))<=>quiet(X)))&
(![X]:((quiet(X)|~creative(X))<=>(~creative(X)<~>happy(X))))&
((?[X]:((~patient(X)|~creative(X))))=>(?[X]:((~rich(X)|~kind(X)))))&
(![X]:((quiet(X)|~brave(X))<=>(brave(X)<~>patient(X))))&
(((kind(lucy)<~>~kind(lucy)))=>(?[X]:((quiet(X)<~>funny(X)))))&
(![X]:((~happy(X)<~>~strong(X))<=>patient(X)))&
(![X]:((happy(X)|old(X))<=>(calm(X)<~>~curious(X))))&
(?[X]:((quiet(X)|~creative(X))))&
(?[X]:((creative(X)|~brave(X))))&
(?[X]:((calm(X)&~rich(X))))&
(funny(paul)) | ~old(paul) | [
"p0",
"p3",
"p4",
"p6",
"p7",
"p9",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 617778292831176313751167
% SZS output start Proof for 617778292831176313751167
1. ! [X0] : ((~patient(X0) & creative(X0)) <=> (~rich(X0) | ~generous(X0))) [input p0]
4. ! [X0] : ((~quiet(X0) | humble(X0)) <=> (tall(X0) & patient(X0))) [input p3]
5. ! [X0] : ((kind(X0) | creative(X0)) => (strong(X0) & wise(X0))) [input p4]
7. (happy(alice) <~> quiet(alice)) <=> ? [X0] : (patient(X0) | ~strong(X0)) [input p6]
8. ! [X0] : (~old(X0) => (~strong(X0) <~> ~happy(X0))) [input p7]
10. ! [X0] : ((~rich(X0) | ~generous(X0)) <=> quiet(X0)) [input p9]
11. ! [X0] : ((~creative(X0) | quiet(X0)) <=> (~creative(X0) <~> happy(X0))) [input p10]
15. ! [X0] : ((~happy(X0) <~> ~strong(X0)) <=> patient(X0)) [input p14]
21. ~old(paul) [input hypothesis]
25. ! [X0] : ((kind(X0) | creative(X0)) => strong(X0)) [pure predicate removal 5]
26. ! [X0] : (strong(X0) | (~kind(X0) & ~creative(X0))) [ennf transformation 25]
28. ! [X0] : ((~strong(X0) <~> ~happy(X0)) | old(X0)) [ennf transformation 8]
32. ! [X0] : (((~patient(X0) & creative(X0)) | (rich(X0) & generous(X0))) & ((~rich(X0) | ~generous(X0)) | (patient(X0) | ~creative(X0)))) [nnf transformation 1]
33. ! [X0] : (((~patient(X0) & creative(X0)) | (rich(X0) & generous(X0))) & (~rich(X0) | ~generous(X0) | patient(X0) | ~creative(X0))) [flattening 32]
40. ! [X0] : (((~quiet(X0) | humble(X0)) | (~tall(X0) | ~patient(X0))) & ((tall(X0) & patient(X0)) | (quiet(X0) & ~humble(X0)))) [nnf transformation 4]
41. ! [X0] : ((~quiet(X0) | humble(X0) | ~tall(X0) | ~patient(X0)) & ((tall(X0) & patient(X0)) | (quiet(X0) & ~humble(X0)))) [flattening 40]
45. (((~quiet(alice) | ~happy(alice)) & (quiet(alice) | happy(alice))) | ! [X0] : (~patient(X0) & strong(X0))) & (? [X0] : (patient(X0) | ~strong(X0)) | ((happy(alice) | ~quiet(alice)) & (quiet(alice) | ~happy(alice)))) [nnf transformation 7]
46. (((~quiet(alice) | ~happy(alice)) & (quiet(alice) | happy(alice))) | ! [X0] : (~patient(X0) & strong(X0))) & (? [X1] : (patient(X1) | ~strong(X1)) | ((happy(alice) | ~quiet(alice)) & (quiet(alice) | ~happy(alice)))) [rectify 45]
47. ? [X1] : (patient(X1) | ~strong(X1)) => (patient(sK3) | ~strong(sK3)) [choice axiom]
48. (((~quiet(alice) | ~happy(alice)) & (quiet(alice) | happy(alice))) | ! [X0] : (~patient(X0) & strong(X0))) & ((patient(sK3) | ~strong(sK3)) | ((happy(alice) | ~quiet(alice)) & (quiet(alice) | ~happy(alice)))) [skolemisation 46,47]
49. ! [X0] : (((happy(X0) | strong(X0)) & (~happy(X0) | ~strong(X0))) | old(X0)) [nnf transformation 28]
51. ! [X0] : (((~rich(X0) | ~generous(X0)) | ~quiet(X0)) & (quiet(X0) | (rich(X0) & generous(X0)))) [nnf transformation 10]
52. ! [X0] : ((~rich(X0) | ~generous(X0) | ~quiet(X0)) & (quiet(X0) | (rich(X0) & generous(X0)))) [flattening 51]
53. ! [X0] : (((~creative(X0) | quiet(X0)) | ((~creative(X0) | ~happy(X0)) & (happy(X0) | creative(X0)))) & (((~happy(X0) | creative(X0)) & (happy(X0) | ~creative(X0))) | (creative(X0) & ~quiet(X0)))) [nnf transformation 11]
54. ! [X0] : ((~creative(X0) | quiet(X0) | ((~creative(X0) | ~happy(X0)) & (happy(X0) | creative(X0)))) & (((~happy(X0) | creative(X0)) & (happy(X0) | ~creative(X0))) | (creative(X0) & ~quiet(X0)))) [flattening 53]
63. ! [X0] : ((((strong(X0) | happy(X0)) & (~strong(X0) | ~happy(X0))) | ~patient(X0)) & (patient(X0) | ((~happy(X0) | strong(X0)) & (~strong(X0) | happy(X0))))) [nnf transformation 15]
73. generous(X0) | creative(X0) [cnf transformation 33]
74. rich(X0) | creative(X0) [cnf transformation 33]
94. quiet(X0) | patient(X0) [cnf transformation 41]
98. ~creative(X0) | strong(X0) [cnf transformation 26]
105. quiet(alice) | happy(alice) | ~patient(X0) [cnf transformation 48]
106. ~quiet(alice) | ~happy(alice) | strong(X0) [cnf transformation 48]
107. ~quiet(alice) | ~happy(alice) | ~patient(X0) [cnf transformation 48]
108. ~strong(X0) | ~happy(X0) | old(X0) [cnf transformation 49]
113. quiet(X0) | rich(X0) [cnf transformation 52]
114. ~quiet(X0) | ~generous(X0) | ~rich(X0) [cnf transformation 52]
115. ~quiet(X0) | ~creative(X0) | happy(X0) [cnf transformation 54]
118. ~happy(X0) | creative(X0) | creative(X0) [cnf transformation 54]
133. ~strong(X0) | patient(X0) | happy(X0) [cnf transformation 63]
135. ~strong(X0) | ~happy(X0) | ~patient(X0) [cnf transformation 63]
148. ~old(paul) [cnf transformation 21]
155. ~happy(X0) | creative(X0) [duplicate literal removal 118]
207. 12 <=> ! [X0] : ~patient(X0) [avatar definition]
208. ~patient(X0) <- (12) [avatar component clause 207]
210. 13 <=> happy(alice) [avatar definition]
211. happy(alice) <- (13) [avatar component clause 210]
212. ~happy(alice) <- (~13) [avatar component clause 210]
214. 14 <=> quiet(alice) [avatar definition]
215. quiet(alice) <- (14) [avatar component clause 214]
216. ~quiet(alice) <- (~14) [avatar component clause 214]
217. 12 | ~13 | ~14 [avatar split clause 107,214,210,207]
219. 15 <=> ! [X0] : strong(X0) [avatar definition]
220. strong(X0) <- (15) [avatar component clause 219]
221. 15 | ~13 | ~14 [avatar split clause 106,214,210,219]
222. 12 | 13 | 14 [avatar split clause 105,214,210,207]
287. patient(alice) <- (~14) [resolution 94,216]
299. creative(alice) <- (13) [resolution 155,211]
300. strong(alice) <- (13) [resolution 299,98]
445. ~happy(alice) | ~patient(alice) <- (13) [resolution 300,135]
448. ~patient(alice) <- (13) [subsumption resolution 445,211]
449. $false <- (13, ~14) [subsumption resolution 448,287]
450. ~13 | 14 [avatar contradiction clause 449]
453. ~creative(alice) | happy(alice) <- (14) [resolution 215,115]
454. ~generous(alice) | ~rich(alice) <- (14) [resolution 215,114]
464. ~creative(alice) <- (~13, 14) [subsumption resolution 453,212]
466. 47 <=> rich(alice) [avatar definition]
468. ~rich(alice) <- (~47) [avatar component clause 466]
470. 48 <=> generous(alice) [avatar definition]
472. ~generous(alice) <- (~48) [avatar component clause 470]
473. ~47 | ~48 | ~14 [avatar split clause 454,214,470,466]
475. creative(alice) <- (~48) [resolution 472,73]
476. $false <- (~13, 14, ~48) [subsumption resolution 475,464]
477. 13 | ~14 | 48 [avatar contradiction clause 476]
484. creative(alice) <- (~47) [resolution 468,74]
485. $false <- (~13, 14, ~47) [subsumption resolution 484,464]
486. 13 | ~14 | 47 [avatar contradiction clause 485]
493. rich(alice) <- (~14) [resolution 216,113]
495. patient(alice) <- (~14) [resolution 216,94]
496. 47 | 14 [avatar split clause 493,214,466]
499. $false <- (12, ~14) [subsumption resolution 495,208]
500. ~12 | 14 [avatar contradiction clause 499]
509. patient(X1) | happy(X1) <- (15) [resolution 220,133]
510. ~happy(X2) | old(X2) <- (15) [resolution 220,108]
513. happy(X1) <- (12, 15) [subsumption resolution 509,208]
514. old(X2) <- (12, 15) [subsumption resolution 510,513]
587. $false <- (12, 15) [resolution 514,148]
589. ~12 | ~15 [avatar contradiction clause 587]
590. $false [avatar sat refutation 217,221,222,450,473,477,486,496,500,589]
% SZS output end Proof for 617778292831176313751167
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 alice is both not tall and funny then someone is both not rich and not wise. Everyone who is either tall or not calm is kind. Everyone who is curious is not calm or not patient. Everyone who is either kind or strong is not kind and vice versa. Everyone who is old is both kind and not brave and vice versa. Everyone who is both patient and tall is kind. Everyone who is kind is brave and vice versa. If paul is either not wise or not strong then someone is kind and vice versa. Everyone who is either wise or not calm is rich or wise. Everyone who is not creative is not happy or not quiet and vice versa. If someone is not old or not tall then someone is calm. Everyone who is old or tall is not curious. Everyone who is both not patient and humble is either not strong or not funny. Everyone who is old is both patient and brave and vice versa. If someone is either not tall or humble then someone is humble. Everyone who is not old or wise is both not curious and tall and vice versa. Someone is brave. Susan is either not funny or patient. Alice is not kind. Fred is both happy and not humble. Mary is not calm or happy. Someone is either not generous or not brave. Paul is creative or calm. | Susan is calm. | neutral | (((~tall(alice)&funny(alice)))=>(?[X]:((~rich(X)&~wise(X)))))&
(![X]:((tall(X)<~>~calm(X))=>kind(X)))&
(![X]:(curious(X)=>(~calm(X)|~patient(X))))&
(![X]:((kind(X)<~>strong(X))<=>~kind(X)))&
(![X]:(old(X)<=>(kind(X)&~brave(X))))&
(![X]:((patient(X)&tall(X))=>kind(X)))&
(![X]:(kind(X)<=>brave(X)))&
(((~wise(paul)<~>~strong(paul)))<=>(?[X]:(kind(X))))&
(![X]:((wise(X)<~>~calm(X))=>(rich(X)|wise(X))))&
(![X]:(~creative(X)<=>(~happy(X)|~quiet(X))))&
((?[X]:((~old(X)|~tall(X))))=>(?[X]:(calm(X))))&
(![X]:((old(X)|tall(X))=>~curious(X)))&
(![X]:((~patient(X)&humble(X))=>(~strong(X)<~>~funny(X))))&
(![X]:(old(X)<=>(patient(X)&brave(X))))&
((?[X]:((~tall(X)<~>humble(X))))=>(?[X]:(humble(X))))&
(![X]:((~old(X)|wise(X))<=>(~curious(X)&tall(X))))&
(?[X]:(brave(X)))&
((~funny(susan)<~>patient(susan)))&
(~kind(alice))&
((happy(fred)&~humble(fred)))&
((~calm(mary)|happy(mary)))&
(?[X]:((~generous(X)<~>~brave(X))))&
((creative(paul)|calm(paul))) | calm(susan) | [] | null | 0 |
Everyone who is either rich or not creative is not calm or not patient. If someone is both calm and not creative then someone is not kind and vice versa. Everyone who is kind is both kind and not old. If someone is both not old and tall then someone is either brave or humble and vice versa. If alice is both funny and not brave then fred is not strong or not rich. Everyone who is either calm or quiet is not generous or quiet and vice versa. Everyone who is not wise or not quiet is both not brave and wise and vice versa. Everyone who is kind or quiet is not quiet or tall. Everyone who is quiet is both not creative and not calm and vice versa. If alice is not kind then alice is both not kind and calm and vice versa. Everyone who is both not happy and not patient is either not kind or not humble and vice versa. Everyone who is generous or kind is creative and vice versa. Everyone who is either not funny or not generous is not wise or funny. If paul is either strong or brave then someone is both brave and quiet and vice versa. If someone is both rich and not calm then someone is either curious or funny and vice versa. Everyone who is either humble or patient is either not funny or curious. Lucy is both brave and not happy. Susan is both humble and curious. Someone is not generous. Fred is calm or not humble. Someone is calm or not generous. Fred is both not generous and not funny. Someone is both quiet and rich. | Susan is generous. | neutral | (![X]:((rich(X)<~>~creative(X))=>(~calm(X)|~patient(X))))&
((?[X]:((calm(X)&~creative(X))))<=>(?[X]:(~kind(X))))&
(![X]:(kind(X)=>(kind(X)&~old(X))))&
((?[X]:((~old(X)&tall(X))))<=>(?[X]:((brave(X)<~>humble(X)))))&
(((funny(alice)&~brave(alice)))=>((~strong(fred)|~rich(fred))))&
(![X]:((calm(X)<~>quiet(X))<=>(~generous(X)|quiet(X))))&
(![X]:((~wise(X)|~quiet(X))<=>(~brave(X)&wise(X))))&
(![X]:((kind(X)|quiet(X))=>(~quiet(X)|tall(X))))&
(![X]:(quiet(X)<=>(~creative(X)&~calm(X))))&
((~kind(alice))<=>((~kind(alice)&calm(alice))))&
(![X]:((~happy(X)&~patient(X))<=>(~kind(X)<~>~humble(X))))&
(![X]:((generous(X)|kind(X))<=>creative(X)))&
(![X]:((~funny(X)<~>~generous(X))=>(~wise(X)|funny(X))))&
(((strong(paul)<~>brave(paul)))<=>(?[X]:((brave(X)&quiet(X)))))&
((?[X]:((rich(X)&~calm(X))))<=>(?[X]:((curious(X)<~>funny(X)))))&
(![X]:((humble(X)<~>patient(X))=>(~funny(X)<~>curious(X))))&
((brave(lucy)&~happy(lucy)))&
((humble(susan)&curious(susan)))&
(?[X]:(~generous(X)))&
((calm(fred)|~humble(fred)))&
(?[X]:((calm(X)|~generous(X))))&
((~generous(fred)&~funny(fred)))&
(?[X]:((quiet(X)&rich(X)))) | generous(susan) | [] | null | 0 |
Everyone who is happy or not brave is not happy or generous.
Everyone who is not brave or not old is kind.
Everyone who is either wise or quiet is either generous or not calm and vice versa.
If someone is both not tall and generous then susan is either not funny or not wise.
If fred is either kind or not old then susan is not generous or funny and vice versa.
Everyone who is both funny and not quiet is both curious and not wise and vice versa.
If someone is both not curious and not generous then someone is not patient and vice versa.
Everyone who is not old or creative is not humble.
Everyone who is not wise is either humble or curious and vice versa.
If lucy is curious then someone is both wise and calm.
Everyone who is both generous and not kind is strong and vice versa.
If someone is either calm or happy then someone is both kind and generous.
If someone is either not rich or calm then someone is curious or not strong and vice versa.
If alice is not wise then someone is both curious and not happy and vice versa.
Everyone who is not curious or happy is quiet or not funny and vice versa.
If paul is funny then susan is either not humble or funny and vice versa.
Someone is rich.
Someone is not tall.
Lucy is either not creative or calm.
Someone is not patient.
Someone is both not brave and curious.
Paul is tall.
Someone is not patient or kind. | Susan is funny. | neutral | (![X]:((happy(X)|~brave(X))=>(~happy(X)|generous(X))))&
(![X]:((~brave(X)|~old(X))=>kind(X)))&
(![X]:((wise(X)<~>quiet(X))<=>(generous(X)<~>~calm(X))))&
((?[X]:((~tall(X)&generous(X))))=>((~funny(susan)<~>~wise(susan))))&
(((kind(fred)<~>~old(fred)))<=>((~generous(susan)|funny(susan))))&
(![X]:((funny(X)&~quiet(X))<=>(curious(X)&~wise(X))))&
((?[X]:((~curious(X)&~generous(X))))<=>(?[X]:(~patient(X))))&
(![X]:((~old(X)|creative(X))=>~humble(X)))&
(![X]:(~wise(X)<=>(humble(X)<~>curious(X))))&
((curious(lucy))=>(?[X]:((wise(X)&calm(X)))))&
(![X]:((generous(X)&~kind(X))<=>strong(X)))&
((?[X]:((calm(X)<~>happy(X))))=>(?[X]:((kind(X)&generous(X)))))&
((?[X]:((~rich(X)<~>calm(X))))<=>(?[X]:((curious(X)|~strong(X)))))&
((~wise(alice))<=>(?[X]:((curious(X)&~happy(X)))))&
(![X]:((~curious(X)|happy(X))<=>(quiet(X)|~funny(X))))&
((funny(paul))<=>((~humble(susan)<~>funny(susan))))&
(?[X]:(rich(X)))&
(?[X]:(~tall(X)))&
((~creative(lucy)<~>calm(lucy)))&
(?[X]:(~patient(X)))&
(?[X]:((~brave(X)&curious(X))))&
(tall(paul))&
(?[X]:((~patient(X)|kind(X)))) | funny(susan) | [] | null | 0 |
Everyone who is both funny and tall is either not funny or not humble. If alice is tall then lucy is both wise and not quiet and vice versa. Everyone who is rich or not brave is both calm and happy and vice versa. If someone is not strong or curious then someone is either not tall or curious and vice versa. If alice is both not kind and not rich then someone is either not wise or tall. If fred is both not curious and not quiet then someone is strong or not rich. Everyone who is both not brave and creative is both kind and not wise. If alice is not happy then someone is not calm and vice versa. Everyone who is both not happy and brave is both happy and kind. Everyone who is both not calm and strong is generous and vice versa. Everyone who is funny is either not curious or happy and vice versa. Everyone who is not patient is both humble and not funny. If lucy is happy then someone is funny or patient. Everyone who is old or not kind is both old and not curious. Everyone who is not calm or tall is both creative and not kind and vice versa. Paul is either strong or quiet. Mary is either not funny or not calm. Lucy is either patient or funny. Someone is tall or old. Paul is either generous or humble. Paul is not quiet. Someone is not patient or not humble. | Alice is generous. | contradiction | (![X]:((funny(X)&tall(X))=>(~funny(X)<~>~humble(X))))&
((tall(alice))<=>((wise(lucy)&~quiet(lucy))))&
(![X]:((rich(X)|~brave(X))<=>(calm(X)&happy(X))))&
((?[X]:((~strong(X)|curious(X))))<=>(?[X]:((~tall(X)<~>curious(X)))))&
(((~kind(alice)&~rich(alice)))=>(?[X]:((~wise(X)<~>tall(X)))))&
(((~curious(fred)&~quiet(fred)))=>(?[X]:((strong(X)|~rich(X)))))&
(![X]:((~brave(X)&creative(X))=>(kind(X)&~wise(X))))&
((~happy(alice))<=>(?[X]:(~calm(X))))&
(![X]:((~happy(X)&brave(X))=>(happy(X)&kind(X))))&
(![X]:((~calm(X)&strong(X))<=>generous(X)))&
(![X]:(funny(X)<=>(~curious(X)<~>happy(X))))&
(![X]:(~patient(X)=>(humble(X)&~funny(X))))&
((happy(lucy))=>(?[X]:((funny(X)|patient(X)))))&
(![X]:((old(X)|~kind(X))=>(old(X)&~curious(X))))&
(![X]:((~calm(X)|tall(X))<=>(creative(X)&~kind(X))))&
((strong(paul)<~>quiet(paul)))&
((~funny(mary)<~>~calm(mary)))&
((patient(lucy)<~>funny(lucy)))&
(?[X]:((tall(X)|old(X))))&
((generous(paul)<~>humble(paul)))&
(~quiet(paul))&
(?[X]:((~patient(X)|~humble(X)))) | generous(alice) | [
"p2",
"p7",
"p8",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 2071251528320457802656848
% SZS output start Proof for 2071251528320457802656848
3. ! [X0] : ((~brave(X0) | rich(X0)) <=> (happy(X0) & calm(X0))) [input p2]
8. ~happy(alice) <=> ? [X0] : ~calm(X0) [input p7]
9. ! [X0] : ((brave(X0) & ~happy(X0)) => (kind(X0) & happy(X0))) [input p8]
10. ! [X0] : ((strong(X0) & ~calm(X0)) <=> generous(X0)) [input p9]
23. generous(alice) [input hypothesis]
33. ! [X0] : ((kind(X0) & happy(X0)) | (~brave(X0) | happy(X0))) [ennf transformation 9]
34. ! [X0] : ((kind(X0) & happy(X0)) | ~brave(X0) | happy(X0)) [flattening 33]
41. ! [X0] : (((~brave(X0) | rich(X0)) | (~happy(X0) | ~calm(X0))) & ((happy(X0) & calm(X0)) | (brave(X0) & ~rich(X0)))) [nnf transformation 3]
42. ! [X0] : ((~brave(X0) | rich(X0) | ~happy(X0) | ~calm(X0)) & ((happy(X0) & calm(X0)) | (brave(X0) & ~rich(X0)))) [flattening 41]
53. (~happy(alice) | ! [X0] : calm(X0)) & (? [X0] : ~calm(X0) | happy(alice)) [nnf transformation 8]
54. (~happy(alice) | ! [X0] : calm(X0)) & (? [X1] : ~calm(X1) | happy(alice)) [rectify 53]
55. ? [X1] : ~calm(X1) => ~calm(sK4) [choice axiom]
56. (~happy(alice) | ! [X0] : calm(X0)) & (~calm(sK4) | happy(alice)) [skolemisation 54,55]
57. ! [X0] : (((strong(X0) & ~calm(X0)) | ~generous(X0)) & (generous(X0) | (~strong(X0) | calm(X0)))) [nnf transformation 10]
58. ! [X0] : (((strong(X0) & ~calm(X0)) | ~generous(X0)) & (generous(X0) | ~strong(X0) | calm(X0))) [flattening 57]
80. happy(X0) | brave(X0) [cnf transformation 42]
94. ~happy(alice) | calm(X0) [cnf transformation 56]
95. happy(X0) | ~brave(X0) | happy(X0) [cnf transformation 34]
98. ~generous(X0) | ~calm(X0) [cnf transformation 58]
127. generous(alice) [cnf transformation 23]
128. happy(X0) | ~brave(X0) [duplicate literal removal 95]
215. 20 <=> ! [X0] : calm(X0) [avatar definition]
216. calm(X0) <- (20) [avatar component clause 215]
218. 21 <=> happy(alice) [avatar definition]
220. ~happy(alice) <- (~21) [avatar component clause 218]
221. 20 | ~21 [avatar split clause 94,218,215]
228. happy(X0) [subsumption resolution 128,80]
284. $false <- (~21) [subsumption resolution 220,228]
285. 21 [avatar contradiction clause 284]
290. ~calm(alice) [resolution 98,127]
292. $false <- (20) [subsumption resolution 290,216]
293. ~20 [avatar contradiction clause 292]
296. $false [avatar sat refutation 221,285,293]
% SZS output end Proof for 2071251528320457802656848
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet or not patient is calm or not generous and vice versa.
Everyone who is not funny is either not old or not kind and vice versa.
If fred is not kind or not happy then someone is not calm and vice versa.
Everyone who is either old or rich is not brave or not kind and vice versa.
If someone is not tall then paul is not strong.
Everyone who is not brave is curious or not strong and vice versa.
Everyone who is both not humble and not strong is either not brave or wise and vice versa.
If someone is wise then someone is not rich and vice versa.
If alice is calm then someone is not happy.
Everyone who is either not calm or strong is creative.
Everyone who is both calm and happy is both strong and not tall and vice versa.
Everyone who is rich is both wise and kind and vice versa.
Everyone who is not creative or not humble is funny and vice versa.
Everyone who is either curious or kind is brave and vice versa.
Everyone who is wise or curious is humble or not calm.
If lucy is quiet or brave then someone is funny.
Someone is both generous and not curious.
Alice is funny.
Paul is not wise.
Fred is tall.
Susan is both tall and rich.
Susan is not happy.
Alice is both happy and not generous. | Lucy is not creative. | contradiction | (![X]:((quiet(X)<~>~patient(X))<=>(calm(X)|~generous(X))))&
(![X]:(~funny(X)<=>(~old(X)<~>~kind(X))))&
(((~kind(fred)|~happy(fred)))<=>(?[X]:(~calm(X))))&
(![X]:((old(X)<~>rich(X))<=>(~brave(X)|~kind(X))))&
((?[X]:(~tall(X)))=>(~strong(paul)))&
(![X]:(~brave(X)<=>(curious(X)|~strong(X))))&
(![X]:((~humble(X)&~strong(X))<=>(~brave(X)<~>wise(X))))&
((?[X]:(wise(X)))<=>(?[X]:(~rich(X))))&
((calm(alice))=>(?[X]:(~happy(X))))&
(![X]:((~calm(X)<~>strong(X))=>creative(X)))&
(![X]:((calm(X)&happy(X))<=>(strong(X)&~tall(X))))&
(![X]:(rich(X)<=>(wise(X)&kind(X))))&
(![X]:((~creative(X)|~humble(X))<=>funny(X)))&
(![X]:((curious(X)<~>kind(X))<=>brave(X)))&
(![X]:((wise(X)|curious(X))=>(humble(X)|~calm(X))))&
(((quiet(lucy)|brave(lucy)))=>(?[X]:(funny(X))))&
(?[X]:((generous(X)&~curious(X))))&
(funny(alice))&
(~wise(paul))&
(tall(fred))&
((tall(susan)&rich(susan)))&
(~happy(susan))&
((happy(alice)&~generous(alice))) | ~creative(lucy) | [
"p1",
"p3",
"p5",
"p6",
"p9",
"p11",
"p12",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2010444126380153934360960
% SZS output start Proof for 2010444126380153934360960
2. ! [X0] : (~funny(X0) <=> (~old(X0) <~> ~kind(X0))) [input p1]
4. ! [X0] : ((old(X0) <~> rich(X0)) <=> (~kind(X0) | ~brave(X0))) [input p3]
6. ! [X0] : (~brave(X0) <=> (~strong(X0) | curious(X0))) [input p5]
7. ! [X0] : ((~strong(X0) & ~humble(X0)) <=> (~brave(X0) <~> wise(X0))) [input p6]
10. ! [X0] : ((~calm(X0) <~> strong(X0)) => creative(X0)) [input p9]
12. ! [X0] : (rich(X0) <=> (kind(X0) & wise(X0))) [input p11]
13. ! [X0] : ((~humble(X0) | ~creative(X0)) <=> funny(X0)) [input p12]
14. ! [X0] : ((curious(X0) <~> kind(X0)) <=> brave(X0)) [input p13]
15. ! [X0] : ((curious(X0) | wise(X0)) => (~calm(X0) | humble(X0))) [input p14]
24. ~creative(lucy) [input hypothesis]
28. ! [X0] : (creative(X0) | (~calm(X0) <=> strong(X0))) [ennf transformation 10]
29. ! [X0] : ((~calm(X0) | humble(X0)) | (~curious(X0) & ~wise(X0))) [ennf transformation 15]
30. ! [X0] : (~calm(X0) | humble(X0) | (~curious(X0) & ~wise(X0))) [flattening 29]
34. ! [X0] : ((~funny(X0) | ((~old(X0) | kind(X0)) & (~kind(X0) | old(X0)))) & (((kind(X0) | old(X0)) & (~kind(X0) | ~old(X0))) | funny(X0))) [nnf transformation 2]
40. ! [X0] : ((((~rich(X0) | ~old(X0)) & (rich(X0) | old(X0))) | (kind(X0) & brave(X0))) & ((~kind(X0) | ~brave(X0)) | ((old(X0) | ~rich(X0)) & (rich(X0) | ~old(X0))))) [nnf transformation 4]
41. ! [X0] : ((((~rich(X0) | ~old(X0)) & (rich(X0) | old(X0))) | (kind(X0) & brave(X0))) & (~kind(X0) | ~brave(X0) | ((old(X0) | ~rich(X0)) & (rich(X0) | ~old(X0))))) [flattening 40]
42. ! [X0] : ((~brave(X0) | (strong(X0) & ~curious(X0))) & ((~strong(X0) | curious(X0)) | brave(X0))) [nnf transformation 6]
43. ! [X0] : ((~brave(X0) | (strong(X0) & ~curious(X0))) & (~strong(X0) | curious(X0) | brave(X0))) [flattening 42]
44. ! [X0] : (((~strong(X0) & ~humble(X0)) | ((~brave(X0) | ~wise(X0)) & (wise(X0) | brave(X0)))) & (((~wise(X0) | brave(X0)) & (wise(X0) | ~brave(X0))) | (strong(X0) | humble(X0)))) [nnf transformation 7]
45. ! [X0] : (((~strong(X0) & ~humble(X0)) | ((~brave(X0) | ~wise(X0)) & (wise(X0) | brave(X0)))) & (((~wise(X0) | brave(X0)) & (wise(X0) | ~brave(X0))) | strong(X0) | humble(X0))) [flattening 44]
53. ! [X0] : (creative(X0) | ((~calm(X0) | ~strong(X0)) & (strong(X0) | calm(X0)))) [nnf transformation 28]
56. ! [X0] : ((rich(X0) | (~kind(X0) | ~wise(X0))) & ((kind(X0) & wise(X0)) | ~rich(X0))) [nnf transformation 12]
57. ! [X0] : ((rich(X0) | ~kind(X0) | ~wise(X0)) & ((kind(X0) & wise(X0)) | ~rich(X0))) [flattening 56]
58. ! [X0] : (((~humble(X0) | ~creative(X0)) | ~funny(X0)) & (funny(X0) | (humble(X0) & creative(X0)))) [nnf transformation 13]
59. ! [X0] : ((~humble(X0) | ~creative(X0) | ~funny(X0)) & (funny(X0) | (humble(X0) & creative(X0)))) [flattening 58]
60. ! [X0] : ((((~kind(X0) | ~curious(X0)) & (kind(X0) | curious(X0))) | ~brave(X0)) & (brave(X0) | ((curious(X0) | ~kind(X0)) & (kind(X0) | ~curious(X0))))) [nnf transformation 14]
73. ~kind(X0) | ~funny(X0) | old(X0) [cnf transformation 34]
74. ~old(X0) | ~funny(X0) | kind(X0) [cnf transformation 34]
78. ~brave(X0) | ~kind(X0) | rich(X0) | ~old(X0) [cnf transformation 41]
80. brave(X0) | old(X0) | rich(X0) [cnf transformation 41]
82. ~rich(X0) | ~old(X0) | brave(X0) [cnf transformation 41]
86. ~curious(X0) | ~brave(X0) [cnf transformation 43]
87. ~brave(X0) | strong(X0) [cnf transformation 43]
90. ~humble(X0) | wise(X0) | brave(X0) [cnf transformation 45]
92. ~strong(X0) | wise(X0) | brave(X0) [cnf transformation 45]
93. ~strong(X0) | ~brave(X0) | ~wise(X0) [cnf transformation 45]
97. creative(X0) | strong(X0) | calm(X0) [cnf transformation 53]
103. ~rich(X0) | wise(X0) [cnf transformation 57]
104. ~rich(X0) | kind(X0) [cnf transformation 57]
105. ~wise(X0) | ~kind(X0) | rich(X0) [cnf transformation 57]
106. creative(X0) | funny(X0) [cnf transformation 59]
110. ~kind(X0) | curious(X0) | brave(X0) [cnf transformation 60]
111. kind(X0) | curious(X0) | ~brave(X0) [cnf transformation 60]
114. ~curious(X0) | humble(X0) | ~calm(X0) [cnf transformation 30]
127. ~creative(lucy) [cnf transformation 24]
154. ~wise(X0) | ~brave(X0) [subsumption resolution 93,87]
181. ~brave(X0) | kind(X0) [subsumption resolution 111,86]
184. 13 <=> brave(lucy) [avatar definition]
185. brave(lucy) <- (13) [avatar component clause 184]
186. ~brave(lucy) <- (~13) [avatar component clause 184]
201. funny(lucy) [resolution 106,127]
227. 18 <=> rich(lucy) [avatar definition]
228. ~rich(lucy) <- (~18) [avatar component clause 227]
229. rich(lucy) <- (18) [avatar component clause 227]
231. 19 <=> old(lucy) [avatar definition]
232. ~old(lucy) <- (~19) [avatar component clause 231]
233. old(lucy) <- (19) [avatar component clause 231]
244. kind(lucy) <- (13) [resolution 185,181]
264. ~funny(lucy) | old(lucy) <- (13) [resolution 244,73]
266. old(lucy) <- (13) [subsumption resolution 264,201]
267. 19 | ~13 [avatar split clause 266,184,231]
268. old(lucy) | rich(lucy) <- (~13) [resolution 186,80]
269. kind(lucy) <- (18) [resolution 229,104]
273. ~old(lucy) | brave(lucy) <- (18) [resolution 82,229]
274. ~old(lucy) <- (~13, 18) [subsumption resolution 273,186]
275. ~19 | 13 | ~18 [avatar split clause 274,227,184,231]
296. strong(lucy) | calm(lucy) [resolution 97,127]
298. 25 <=> calm(lucy) [avatar definition]
300. calm(lucy) <- (25) [avatar component clause 298]
302. 26 <=> strong(lucy) [avatar definition]
304. strong(lucy) <- (26) [avatar component clause 302]
305. 25 | 26 [avatar split clause 296,302,298]
309. ~funny(lucy) | old(lucy) <- (18) [resolution 269,73]
311. old(lucy) <- (18) [subsumption resolution 309,201]
312. $false <- (18, ~19) [subsumption resolution 311,232]
313. ~18 | 19 [avatar contradiction clause 312]
314. 18 | 19 | 13 [avatar split clause 268,184,231,227]
324. ~funny(lucy) | kind(lucy) <- (19) [resolution 233,74]
325. kind(lucy) <- (19) [subsumption resolution 324,201]
333. curious(lucy) | brave(lucy) <- (19) [resolution 110,325]
336. curious(lucy) <- (~13, 19) [subsumption resolution 333,186]
551. humble(lucy) | ~calm(lucy) <- (~13, 19) [resolution 336,114]
554. humble(lucy) <- (~13, 19, 25) [subsumption resolution 551,300]
602. wise(lucy) | brave(lucy) <- (~13, 19, 25) [resolution 554,90]
603. wise(lucy) <- (~13, 19, 25) [subsumption resolution 602,186]
632. ~kind(lucy) | rich(lucy) <- (~13, 19, 25) [resolution 603,105]
634. rich(lucy) <- (~13, 19, 25) [subsumption resolution 632,325]
635. $false <- (~13, ~18, 19, 25) [subsumption resolution 634,228]
636. 13 | 18 | ~19 | ~25 [avatar contradiction clause 635]
645. wise(lucy) | brave(lucy) <- (26) [resolution 304,92]
647. wise(lucy) <- (~13, 26) [subsumption resolution 645,186]
650. ~kind(lucy) | rich(lucy) <- (~13, 26) [resolution 647,105]
652. rich(lucy) <- (~13, 19, 26) [subsumption resolution 650,325]
653. $false <- (~13, ~18, 19, 26) [subsumption resolution 652,228]
654. 13 | 18 | ~19 | ~26 [avatar contradiction clause 653]
661. ~kind(lucy) | rich(lucy) | ~old(lucy) <- (13) [resolution 185,78]
664. rich(lucy) | ~old(lucy) <- (13, 19) [subsumption resolution 661,325]
669. rich(lucy) <- (13, 19) [subsumption resolution 664,233]
670. 18 | ~13 | ~19 [avatar split clause 669,231,184,227]
674. wise(lucy) <- (18) [resolution 229,103]
693. ~brave(lucy) <- (18) [resolution 674,154]
694. $false <- (13, 18) [subsumption resolution 693,185]
695. ~13 | ~18 [avatar contradiction clause 694]
696. $false [avatar sat refutation 267,275,305,313,314,636,654,670,695]
% SZS output end Proof for 2010444126380153934360960
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either wise or not funny is either funny or patient and vice versa. Everyone who is not wise or creative is not tall. If lucy is either not funny or not wise then mary is old. If someone is not strong then alice is both not old and creative. If someone is either wise or humble then alice is kind or not wise. If someone is not kind or not funny then lucy is not strong. Everyone who is both not humble and not brave is both not quiet and old. If susan is funny or not calm then someone is either not funny or kind and vice versa. Everyone who is either calm or generous is either curious or not strong and vice versa. Everyone who is either not strong or quiet is both not quiet and quiet and vice versa. If someone is rich or not patient then john is either not curious or old. Everyone who is generous or not strong is both not patient and not rich. Everyone who is either not calm or not humble is generous or quiet and vice versa. Everyone who is both not wise and not happy is tall or not creative and vice versa. If susan is not patient or not calm then mary is either not rich or curious. If someone is kind then susan is either wise or not happy. Someone is either wise or not funny. Someone is not curious. Someone is both not tall and patient. Someone is either strong or humble. Someone is not patient. Someone is both not brave and funny. John is either not brave or not generous. Someone is not kind. | Lucy is not tall. | entailment | (![X]:((wise(X)<~>~funny(X))<=>(funny(X)<~>patient(X))))&
(![X]:((~wise(X)|creative(X))=>~tall(X)))&
(((~funny(lucy)<~>~wise(lucy)))=>(old(mary)))&
((?[X]:(~strong(X)))=>((~old(alice)&creative(alice))))&
((?[X]:((wise(X)<~>humble(X))))=>((kind(alice)|~wise(alice))))&
((?[X]:((~kind(X)|~funny(X))))=>(~strong(lucy)))&
(![X]:((~humble(X)&~brave(X))=>(~quiet(X)&old(X))))&
(((funny(susan)|~calm(susan)))<=>(?[X]:((~funny(X)<~>kind(X)))))&
(![X]:((calm(X)<~>generous(X))<=>(curious(X)<~>~strong(X))))&
(![X]:((~strong(X)<~>quiet(X))<=>(~quiet(X)&quiet(X))))&
((?[X]:((rich(X)|~patient(X))))=>((~curious(john)<~>old(john))))&
(![X]:((generous(X)|~strong(X))=>(~patient(X)&~rich(X))))&
(![X]:((~calm(X)<~>~humble(X))<=>(generous(X)|quiet(X))))&
(![X]:((~wise(X)&~happy(X))<=>(tall(X)|~creative(X))))&
(((~patient(susan)|~calm(susan)))=>((~rich(mary)<~>curious(mary))))&
((?[X]:(kind(X)))=>((wise(susan)<~>~happy(susan))))&
(?[X]:((wise(X)<~>~funny(X))))&
(?[X]:(~curious(X)))&
(?[X]:((~tall(X)&patient(X))))&
(?[X]:((strong(X)<~>humble(X))))&
(?[X]:(~patient(X)))&
(?[X]:((~brave(X)&funny(X))))&
((~brave(john)<~>~generous(john)))&
(?[X]:(~kind(X))) | ~tall(lucy) | [
"p1",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 6303441234870417990426136
% SZS output start Proof for 6303441234870417990426136
2. ! [X0] : ((creative(X0) | ~wise(X0)) => ~tall(X0)) [input p1]
14. ! [X0] : ((~happy(X0) & ~wise(X0)) <=> (~creative(X0) | tall(X0))) [input p13]
25. tall(lucy) [input hypothesis]
26. ! [X0] : (~tall(X0) | (~creative(X0) & wise(X0))) [ennf transformation 2]
52. ! [X0] : (((~happy(X0) & ~wise(X0)) | (creative(X0) & ~tall(X0))) & ((~creative(X0) | tall(X0)) | (happy(X0) | wise(X0)))) [nnf transformation 14]
53. ! [X0] : (((~happy(X0) & ~wise(X0)) | (creative(X0) & ~tall(X0))) & (~creative(X0) | tall(X0) | happy(X0) | wise(X0))) [flattening 52]
81. ~tall(X0) | wise(X0) [cnf transformation 26]
128. ~wise(X0) | ~tall(X0) [cnf transformation 53]
151. tall(lucy) [cnf transformation 25]
263. ~tall(X0) [subsumption resolution 128,81]
324. $false [subsumption resolution 151,263]
% SZS output end Proof for 6303441234870417990426136
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is curious or not generous is either not patient or not wise.
If lucy is either not strong or not brave then paul is either patient or not humble.
If someone is both not creative and quiet then someone is both wise and not generous and vice versa.
Everyone who is both wise and not humble is not patient or not funny.
Everyone who is kind is kind or not brave and vice versa.
If someone is both strong and not brave then paul is not curious and vice versa.
If lucy is rich or not curious then someone is both not kind and old.
If susan is not brave then someone is both not curious and not tall.
Everyone who is tall is humble or curious and vice versa.
If lucy is either patient or not wise then someone is both strong and not wise.
Everyone who is not tall is either patient or funny and vice versa.
Everyone who is not quiet or quiet is not patient and vice versa.
Everyone who is both calm and not curious is either not calm or old and vice versa.
Everyone who is either tall or not wise is brave.
If paul is both not strong and creative then someone is both wise and not brave.
Everyone who is not happy or strong is not humble or not rich and vice versa.
Lucy is not brave.
Someone is strong.
Someone is both kind and rich.
Mary is either kind or old.
Someone is not old.
Someone is either not humble or not wise. | Lucy is kind. | entailment | (![X]:((curious(X)|~generous(X))=>(~patient(X)<~>~wise(X))))&
(((~strong(lucy)<~>~brave(lucy)))=>((patient(paul)<~>~humble(paul))))&
((?[X]:((~creative(X)&quiet(X))))<=>(?[X]:((wise(X)&~generous(X)))))&
(![X]:((wise(X)&~humble(X))=>(~patient(X)|~funny(X))))&
(![X]:(kind(X)<=>(kind(X)|~brave(X))))&
((?[X]:((strong(X)&~brave(X))))<=>(~curious(paul)))&
(((rich(lucy)|~curious(lucy)))=>(?[X]:((~kind(X)&old(X)))))&
((~brave(susan))=>(?[X]:((~curious(X)&~tall(X)))))&
(![X]:(tall(X)<=>(humble(X)|curious(X))))&
(((patient(lucy)<~>~wise(lucy)))=>(?[X]:((strong(X)&~wise(X)))))&
(![X]:(~tall(X)<=>(patient(X)<~>funny(X))))&
(![X]:((~quiet(X)|quiet(X))<=>~patient(X)))&
(![X]:((calm(X)&~curious(X))<=>(~calm(X)<~>old(X))))&
(![X]:((tall(X)<~>~wise(X))=>brave(X)))&
(((~strong(paul)&creative(paul)))=>(?[X]:((wise(X)&~brave(X)))))&
(![X]:((~happy(X)|strong(X))<=>(~humble(X)|~rich(X))))&
(~brave(lucy))&
(?[X]:(strong(X)))&
(?[X]:((kind(X)&rich(X))))&
((kind(mary)<~>old(mary)))&
(?[X]:(~old(X)))&
(?[X]:((~humble(X)<~>~wise(X)))) | kind(lucy) | [
"p4",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 6985200691816709852129163
% SZS output start Proof for 6985200691816709852129163
5. ! [X0] : (kind(X0) <=> (~brave(X0) | kind(X0))) [input p4]
17. ~brave(lucy) [input p16]
23. ~kind(lucy) [input hypothesis]
42. ! [X0] : ((kind(X0) | (brave(X0) & ~kind(X0))) & ((~brave(X0) | kind(X0)) | ~kind(X0))) [nnf transformation 5]
43. ! [X0] : ((kind(X0) | (brave(X0) & ~kind(X0))) & (~brave(X0) | kind(X0) | ~kind(X0))) [flattening 42]
92. kind(X0) | brave(X0) [cnf transformation 43]
130. ~brave(lucy) [cnf transformation 17]
139. ~kind(lucy) [cnf transformation 23]
143. 1 <=> brave(lucy) [avatar definition]
144. ~brave(lucy) <- (~1) [avatar component clause 143]
280. ~1 [avatar split clause 130,143]
301. brave(lucy) [resolution 92,139]
302. $false <- (~1) [subsumption resolution 301,144]
303. 1 [avatar contradiction clause 302]
304. $false [avatar sat refutation 280,303]
% SZS output end Proof for 6985200691816709852129163
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm then paul is both not creative and not brave.
Everyone who is both not quiet and rich is brave or not brave and vice versa.
Everyone who is not wise or patient is old or not humble and vice versa.
Everyone who is either not happy or not generous is old.
If mary is either not happy or not calm then susan is not tall.
Everyone who is curious or not curious is generous.
If someone is strong or humble then someone is both kind and generous and vice versa.
Everyone who is not curious or not generous is both patient and not funny.
If someone is funny then someone is not creative or not calm and vice versa.
Everyone who is either not tall or not generous is not creative or creative and vice versa.
If fred is both not creative and not funny then someone is both not wise and kind and vice versa.
If someone is humble or wise then fred is not rich and vice versa.
If someone is not happy or funny then mary is creative.
Everyone who is both not happy and patient is either not patient or not calm.
Everyone who is old or not happy is either generous or not tall and vice versa.
Everyone who is not kind or not strong is calm or not quiet and vice versa.
Someone is generous or not kind.
Someone is not funny.
Alice is either old or calm.
Mary is curious.
Susan is either brave or rich.
Paul is patient. | Paul is creative. | contradiction | ((?[X]:((generous(X)<~>~calm(X))))=>((~creative(paul)&~brave(paul))))&
(![X]:((~quiet(X)&rich(X))<=>(brave(X)|~brave(X))))&
(![X]:((~wise(X)|patient(X))<=>(old(X)|~humble(X))))&
(![X]:((~happy(X)<~>~generous(X))=>old(X)))&
(((~happy(mary)<~>~calm(mary)))=>(~tall(susan)))&
(![X]:((curious(X)|~curious(X))=>generous(X)))&
((?[X]:((strong(X)|humble(X))))<=>(?[X]:((kind(X)&generous(X)))))&
(![X]:((~curious(X)|~generous(X))=>(patient(X)&~funny(X))))&
((?[X]:(funny(X)))<=>(?[X]:((~creative(X)|~calm(X)))))&
(![X]:((~tall(X)<~>~generous(X))<=>(~creative(X)|creative(X))))&
(((~creative(fred)&~funny(fred)))<=>(?[X]:((~wise(X)&kind(X)))))&
((?[X]:((humble(X)|wise(X))))<=>(~rich(fred)))&
((?[X]:((~happy(X)|funny(X))))=>(creative(mary)))&
(![X]:((~happy(X)&patient(X))=>(~patient(X)<~>~calm(X))))&
(![X]:((old(X)|~happy(X))<=>(generous(X)<~>~tall(X))))&
(![X]:((~kind(X)|~strong(X))<=>(calm(X)|~quiet(X))))&
(?[X]:((generous(X)|~kind(X))))&
(?[X]:(~funny(X)))&
((old(alice)<~>calm(alice)))&
(curious(mary))&
((brave(susan)<~>rich(susan)))&
(patient(paul)) | creative(paul) | [
"p0",
"p5",
"p9",
"p14",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 80170028598967743001719
% SZS output start Proof for 80170028598967743001719
1. ? [X0] : (generous(X0) <~> ~calm(X0)) => (~brave(paul) & ~creative(paul)) [input p0]
6. ! [X0] : ((~curious(X0) | curious(X0)) => generous(X0)) [input p5]
10. ! [X0] : ((~tall(X0) <~> ~generous(X0)) <=> (creative(X0) | ~creative(X0))) [input p9]
15. ! [X0] : ((~happy(X0) | old(X0)) <=> (generous(X0) <~> ~tall(X0))) [input p14]
19. old(alice) <~> calm(alice) [input p18]
23. creative(paul) [input hypothesis]
26. (~brave(paul) & ~creative(paul)) | ! [X0] : (generous(X0) <=> ~calm(X0)) [ennf transformation 1]
29. ! [X0] : (generous(X0) | (curious(X0) & ~curious(X0))) [ennf transformation 6]
34. (~brave(paul) & ~creative(paul)) | ! [X0] : ((generous(X0) | calm(X0)) & (~calm(X0) | ~generous(X0))) [nnf transformation 26]
51. ! [X0] : ((((generous(X0) | tall(X0)) & (~generous(X0) | ~tall(X0))) | (~creative(X0) & creative(X0))) & ((creative(X0) | ~creative(X0)) | ((~tall(X0) | generous(X0)) & (~generous(X0) | tall(X0))))) [nnf transformation 10]
52. ! [X0] : ((((generous(X0) | tall(X0)) & (~generous(X0) | ~tall(X0))) | (~creative(X0) & creative(X0))) & (creative(X0) | ~creative(X0) | ((~tall(X0) | generous(X0)) & (~generous(X0) | tall(X0))))) [flattening 51]
63. ! [X0] : (((~happy(X0) | old(X0)) | ((generous(X0) | tall(X0)) & (~tall(X0) | ~generous(X0)))) & (((tall(X0) | ~generous(X0)) & (~tall(X0) | generous(X0))) | (happy(X0) & ~old(X0)))) [nnf transformation 15]
64. ! [X0] : ((~happy(X0) | old(X0) | ((generous(X0) | tall(X0)) & (~tall(X0) | ~generous(X0)))) & (((tall(X0) | ~generous(X0)) & (~tall(X0) | generous(X0))) | (happy(X0) & ~old(X0)))) [flattening 63]
71. (~calm(alice) | ~old(alice)) & (calm(alice) | old(alice)) [nnf transformation 19]
73. ~creative(paul) | ~calm(X0) | ~generous(X0) [cnf transformation 34]
90. generous(X0) | ~curious(X0) [cnf transformation 29]
91. generous(X0) | curious(X0) [cnf transformation 29]
106. ~generous(X0) | ~tall(X0) | creative(X0) [cnf transformation 52]
107. ~generous(X0) | ~tall(X0) | ~creative(X0) [cnf transformation 52]
123. tall(X0) | ~generous(X0) | ~old(X0) [cnf transformation 64]
133. calm(alice) | old(alice) [cnf transformation 71]
139. creative(paul) [cnf transformation 23]
150. 3 <=> ! [X0] : (~calm(X0) | ~generous(X0)) [avatar definition]
151. ~calm(X0) | ~generous(X0) <- (3) [avatar component clause 150]
154. 4 <=> creative(paul) [avatar definition]
158. 3 | ~4 [avatar split clause 73,154,150]
175. generous(X0) [subsumption resolution 90,91]
225. ~tall(X0) | ~creative(X0) [subsumption resolution 107,175]
226. ~tall(X0) | creative(X0) [subsumption resolution 106,175]
227. ~tall(X0) [subsumption resolution 226,225]
266. ~generous(X0) | ~old(X0) [subsumption resolution 123,227]
267. ~old(X0) [subsumption resolution 266,175]
269. calm(alice) [subsumption resolution 133,267]
271. 4 [avatar split clause 139,154]
276. ~calm(X0) <- (3) [subsumption resolution 151,175]
283. $false <- (3) [resolution 276,269]
284. ~3 [avatar contradiction clause 283]
285. $false [avatar sat refutation 158,271,284]
% SZS output end Proof for 80170028598967743001719
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not old or curious then someone is either not wise or quiet.
Everyone who is both tall and not kind is humble.
Everyone who is not kind is not calm and vice versa.
Everyone who is either curious or old is quiet.
Everyone who is calm or rich is not old or strong.
Everyone who is either tall or wise is not funny or funny and vice versa.
If lucy is funny or not quiet then alice is both creative and generous and vice versa.
Everyone who is both quiet and old is patient.
Everyone who is both not patient and quiet is both brave and not patient and vice versa.
Everyone who is humble is both wise and not kind.
Everyone who is happy is funny and vice versa.
If john is both not wise and kind then someone is both old and not wise and vice versa.
If susan is both patient and not happy then someone is both not tall and curious.
Everyone who is both not strong and old is not quiet or not wise.
Everyone who is not funny or humble is not strong or not quiet and vice versa.
If someone is both rich and generous then someone is both not kind and not strong and vice versa.
Alice is not strong.
Someone is generous or not tall.
Paul is patient or not brave.
John is strong.
Fred is both creative and not humble.
Lucy is both not tall and not calm.
Someone is both not tall and calm.
John is both creative and not rich. | Lucy is not tall. | entailment | ((?[X]:((~old(X)|curious(X))))=>(?[X]:((~wise(X)<~>quiet(X)))))&
(![X]:((tall(X)&~kind(X))=>humble(X)))&
(![X]:(~kind(X)<=>~calm(X)))&
(![X]:((curious(X)<~>old(X))=>quiet(X)))&
(![X]:((calm(X)|rich(X))=>(~old(X)|strong(X))))&
(![X]:((tall(X)<~>wise(X))<=>(~funny(X)|funny(X))))&
(((funny(lucy)|~quiet(lucy)))<=>((creative(alice)&generous(alice))))&
(![X]:((quiet(X)&old(X))=>patient(X)))&
(![X]:((~patient(X)&quiet(X))<=>(brave(X)&~patient(X))))&
(![X]:(humble(X)=>(wise(X)&~kind(X))))&
(![X]:(happy(X)<=>funny(X)))&
(((~wise(john)&kind(john)))<=>(?[X]:((old(X)&~wise(X)))))&
(((patient(susan)&~happy(susan)))=>(?[X]:((~tall(X)&curious(X)))))&
(![X]:((~strong(X)&old(X))=>(~quiet(X)|~wise(X))))&
(![X]:((~funny(X)|humble(X))<=>(~strong(X)|~quiet(X))))&
((?[X]:((rich(X)&generous(X))))<=>(?[X]:((~kind(X)&~strong(X)))))&
(~strong(alice))&
(?[X]:((generous(X)|~tall(X))))&
((patient(paul)|~brave(paul)))&
(strong(john))&
((creative(fred)&~humble(fred)))&
((~tall(lucy)&~calm(lucy)))&
(?[X]:((~tall(X)&calm(X))))&
((creative(john)&~rich(john))) | ~tall(lucy) | [
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 88294738451781260526877
% SZS output start Proof for 88294738451781260526877
22. ~calm(lucy) & ~tall(lucy) [input p21]
25. tall(lucy) [input hypothesis]
124. ~tall(lucy) [cnf transformation 22]
130. tall(lucy) [cnf transformation 25]
257. $false [subsumption resolution 130,124]
% SZS output end Proof for 88294738451781260526877
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not calm and creative is not creative and vice versa.
Everyone who is not strong or not creative is both strong and kind and vice versa.
If mary is patient or not humble then mary is both not tall and humble.
Everyone who is quiet is not rich or not patient.
If someone is either not old or tall then alice is both funny and not quiet.
Everyone who is both wise and humble is both not strong and not quiet.
Everyone who is either rich or old is happy or not tall and vice versa.
Everyone who is not funny or patient is either quiet or rich and vice versa.
Everyone who is not funny or happy is either not old or not patient.
If fred is either not calm or kind then john is either rich or not brave and vice versa.
Everyone who is both patient and generous is both not brave and not curious and vice versa.
Everyone who is either not brave or not quiet is both not brave and funny and vice versa.
If someone is either curious or tall then john is either not wise or generous and vice versa.
If john is not kind or creative then someone is both curious and quiet.
Everyone who is either not funny or kind is either patient or quiet.
Someone is brave.
Someone is both generous and tall.
Mary is generous or rich.
Alice is brave.
Someone is both creative and not rich.
Someone is creative. | John is not kind. | entailment | (![X]:((~calm(X)&creative(X))<=>~creative(X)))&
(![X]:((~strong(X)|~creative(X))<=>(strong(X)&kind(X))))&
(((patient(mary)|~humble(mary)))=>((~tall(mary)&humble(mary))))&
(![X]:(quiet(X)=>(~rich(X)|~patient(X))))&
((?[X]:((~old(X)<~>tall(X))))=>((funny(alice)&~quiet(alice))))&
(![X]:((wise(X)&humble(X))=>(~strong(X)&~quiet(X))))&
(![X]:((rich(X)<~>old(X))<=>(happy(X)|~tall(X))))&
(![X]:((~funny(X)|patient(X))<=>(quiet(X)<~>rich(X))))&
(![X]:((~funny(X)|happy(X))=>(~old(X)<~>~patient(X))))&
(((~calm(fred)<~>kind(fred)))<=>((rich(john)<~>~brave(john))))&
(![X]:((patient(X)&generous(X))<=>(~brave(X)&~curious(X))))&
(![X]:((~brave(X)<~>~quiet(X))<=>(~brave(X)&funny(X))))&
((?[X]:((curious(X)<~>tall(X))))<=>((~wise(john)<~>generous(john))))&
(((~kind(john)|creative(john)))=>(?[X]:((curious(X)&quiet(X)))))&
(![X]:((~funny(X)<~>kind(X))=>(patient(X)<~>quiet(X))))&
(?[X]:(brave(X)))&
(?[X]:((generous(X)&tall(X))))&
((generous(mary)|rich(mary)))&
(brave(alice))&
(?[X]:((creative(X)&~rich(X))))&
(?[X]:(creative(X))) | ~kind(john) | [
"p0",
"p1",
"hypothesis"
] | % SZS status Unsatisfiable for 3478142983156304766279848
% SZS output start Proof for 3478142983156304766279848
1. ! [X0] : ((creative(X0) & ~calm(X0)) <=> ~creative(X0)) [input p0]
2. ! [X0] : ((~creative(X0) | ~strong(X0)) <=> (kind(X0) & strong(X0))) [input p1]
22. kind(john) [input hypothesis]
32. ! [X0] : (((creative(X0) & ~calm(X0)) | creative(X0)) & (~creative(X0) | (~creative(X0) | calm(X0)))) [nnf transformation 1]
33. ! [X0] : (((creative(X0) & ~calm(X0)) | creative(X0)) & (~creative(X0) | ~creative(X0) | calm(X0))) [flattening 32]
34. ! [X0] : (((~creative(X0) | ~strong(X0)) | (~kind(X0) | ~strong(X0))) & ((kind(X0) & strong(X0)) | (creative(X0) & strong(X0)))) [nnf transformation 2]
35. ! [X0] : ((~creative(X0) | ~strong(X0) | ~kind(X0) | ~strong(X0)) & ((kind(X0) & strong(X0)) | (creative(X0) & strong(X0)))) [flattening 34]
64. creative(X0) | creative(X0) [cnf transformation 33]
65. strong(X0) | strong(X0) [cnf transformation 35]
69. ~creative(X0) | ~strong(X0) | ~kind(X0) | ~strong(X0) [cnf transformation 35]
139. kind(john) [cnf transformation 22]
143. strong(X0) [duplicate literal removal 65]
144. ~creative(X0) | ~strong(X0) | ~kind(X0) [duplicate literal removal 69]
146. creative(X0) [duplicate literal removal 64]
148. ~kind(X0) | ~strong(X0) [subsumption resolution 144,146]
245. ~strong(john) [resolution 148,139]
247. $false [subsumption resolution 245,143]
% SZS output end Proof for 3478142983156304766279848
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny and patient is not patient or calm and vice versa. If alice is not quiet or curious then someone is both patient and humble and vice versa. Everyone who is wise or not strong is not kind or not old and vice versa. Everyone who is either not creative or not calm is not calm. Everyone who is rich is not wise or happy and vice versa. Everyone who is either not strong or not wise is both not tall and not curious and vice versa. Everyone who is patient or old is both happy and wise and vice versa. If someone is not calm or humble then someone is tall. If mary is not strong then someone is not brave and vice versa. Everyone who is not quiet is both not old and not calm and vice versa. If someone is wise or not humble then someone is either not wise or generous. Everyone who is either strong or not funny is creative or funny and vice versa. Everyone who is generous or curious is patient. Everyone who is both not old and not quiet is not generous or not quiet and vice versa. Everyone who is either not patient or not humble is both not generous and not old. Someone is not old. Someone is both brave and happy. Paul is not kind or not patient. Mary is either not generous or not funny. Someone is tall or funny. Someone is both strong and quiet. | Mary is not old. | neutral | (![X]:((funny(X)&patient(X))<=>(~patient(X)|calm(X))))&
(((~quiet(alice)|curious(alice)))<=>(?[X]:((patient(X)&humble(X)))))&
(![X]:((wise(X)|~strong(X))<=>(~kind(X)|~old(X))))&
(![X]:((~creative(X)<~>~calm(X))=>~calm(X)))&
(![X]:(rich(X)<=>(~wise(X)|happy(X))))&
(![X]:((~strong(X)<~>~wise(X))<=>(~tall(X)&~curious(X))))&
(![X]:((patient(X)|old(X))<=>(happy(X)&wise(X))))&
((?[X]:((~calm(X)|humble(X))))=>(?[X]:(tall(X))))&
((~strong(mary))<=>(?[X]:(~brave(X))))&
(![X]:(~quiet(X)<=>(~old(X)&~calm(X))))&
((?[X]:((wise(X)|~humble(X))))=>(?[X]:((~wise(X)<~>generous(X)))))&
(![X]:((strong(X)<~>~funny(X))<=>(creative(X)|funny(X))))&
(![X]:((generous(X)|curious(X))=>patient(X)))&
(![X]:((~old(X)&~quiet(X))<=>(~generous(X)|~quiet(X))))&
(![X]:((~patient(X)<~>~humble(X))=>(~generous(X)&~old(X))))&
(?[X]:(~old(X)))&
(?[X]:((brave(X)&happy(X))))&
((~kind(paul)|~patient(paul)))&
((~generous(mary)<~>~funny(mary)))&
(?[X]:((tall(X)|funny(X))))&
(?[X]:((strong(X)&quiet(X)))) | ~old(mary) | [] | null | 0 |
Everyone who is both generous and not calm is both rich and calm. If lucy is both not kind and brave then someone is not kind or not happy and vice versa. If someone is both not happy and not tall then fred is not strong or not curious. Everyone who is rich or not brave is either strong or quiet and vice versa. Everyone who is both not generous and creative is both not curious and creative and vice versa. If someone is not quiet or patient then someone is not rich and vice versa. Everyone who is both not rich and not creative is both generous and creative and vice versa. Everyone who is curious or not curious is either calm or not strong. If someone is either happy or patient then susan is either funny or not humble. Everyone who is either not brave or wise is either not funny or not curious and vice versa. If someone is either not calm or not wise then someone is either tall or not tall. Everyone who is either not quiet or patient is not old or funny and vice versa. Everyone who is either not tall or not old is both quiet and not generous and vice versa. If paul is either old or not curious then someone is tall or old and vice versa. Everyone who is not generous or calm is happy or not funny. Someone is either strong or patient. Someone is creative or not calm. Lucy is both not wise and calm. Susan is calm. Lucy is either not generous or not old. Mary is strong or not calm. Susan is either rich or patient. | Susan is not creative. | neutral | (![X]:((generous(X)&~calm(X))=>(rich(X)&calm(X))))&
(((~kind(lucy)&brave(lucy)))<=>(?[X]:((~kind(X)|~happy(X)))))&
((?[X]:((~happy(X)&~tall(X))))=>((~strong(fred)|~curious(fred))))&
(![X]:((rich(X)|~brave(X))<=>(strong(X)<~>quiet(X))))&
(![X]:((~generous(X)&creative(X))<=>(~curious(X)&creative(X))))&
((?[X]:((~quiet(X)|patient(X))))<=>(?[X]:(~rich(X))))&
(![X]:((~rich(X)&~creative(X))<=>(generous(X)&creative(X))))&
(![X]:((curious(X)|~curious(X))=>(calm(X)<~>~strong(X))))&
((?[X]:((happy(X)<~>patient(X))))=>((funny(susan)<~>~humble(susan))))&
(![X]:((~brave(X)<~>wise(X))<=>(~funny(X)<~>~curious(X))))&
((?[X]:((~calm(X)<~>~wise(X))))=>(?[X]:((tall(X)<~>~tall(X)))))&
(![X]:((~quiet(X)<~>patient(X))<=>(~old(X)|funny(X))))&
(![X]:((~tall(X)<~>~old(X))<=>(quiet(X)&~generous(X))))&
(((old(paul)<~>~curious(paul)))<=>(?[X]:((tall(X)|old(X)))))&
(![X]:((~generous(X)|calm(X))=>(happy(X)|~funny(X))))&
(?[X]:((strong(X)<~>patient(X))))&
(?[X]:((creative(X)|~calm(X))))&
((~wise(lucy)&calm(lucy)))&
(calm(susan))&
((~generous(lucy)<~>~old(lucy)))&
((strong(mary)|~calm(mary)))&
((rich(susan)<~>patient(susan))) | ~creative(susan) | [] | null | 0 |
Everyone who is strong is either kind or happy and vice versa.
Everyone who is both calm and not brave is not funny or not brave.
Everyone who is not creative is not patient.
Everyone who is both funny and not tall is both kind and not brave.
If someone is both rich and not creative then paul is both not calm and wise and vice versa.
If paul is not funny or old then fred is not rich and vice versa.
If someone is quiet then susan is both funny and not old and vice versa.
If susan is both not funny and humble then alice is both not tall and wise.
Everyone who is humble or not patient is funny.
Everyone who is both funny and calm is either strong or creative and vice versa.
If susan is generous or not kind then someone is either strong or not curious.
If alice is both not kind and quiet then someone is patient or old and vice versa.
Everyone who is not funny is either not rich or quiet and vice versa.
If someone is either not old or quiet then someone is not happy or not creative and vice versa.
If lucy is either quiet or not humble then someone is both tall and strong.
Everyone who is either old or calm is both old and kind.
Someone is both old and not quiet.
John is both humble and kind.
Someone is both brave and not funny.
Someone is either brave or happy.
Fred is tall or wise.
Someone is quiet or not quiet.
Someone is strong.
Someone is both rich and not funny. | Fred is not happy. | neutral | (![X]:(strong(X)<=>(kind(X)<~>happy(X))))&
(![X]:((calm(X)&~brave(X))=>(~funny(X)|~brave(X))))&
(![X]:(~creative(X)=>~patient(X)))&
(![X]:((funny(X)&~tall(X))=>(kind(X)&~brave(X))))&
((?[X]:((rich(X)&~creative(X))))<=>((~calm(paul)&wise(paul))))&
(((~funny(paul)|old(paul)))<=>(~rich(fred)))&
((?[X]:(quiet(X)))<=>((funny(susan)&~old(susan))))&
(((~funny(susan)&humble(susan)))=>((~tall(alice)&wise(alice))))&
(![X]:((humble(X)|~patient(X))=>funny(X)))&
(![X]:((funny(X)&calm(X))<=>(strong(X)<~>creative(X))))&
(((generous(susan)|~kind(susan)))=>(?[X]:((strong(X)<~>~curious(X)))))&
(((~kind(alice)&quiet(alice)))<=>(?[X]:((patient(X)|old(X)))))&
(![X]:(~funny(X)<=>(~rich(X)<~>quiet(X))))&
((?[X]:((~old(X)<~>quiet(X))))<=>(?[X]:((~happy(X)|~creative(X)))))&
(((quiet(lucy)<~>~humble(lucy)))=>(?[X]:((tall(X)&strong(X)))))&
(![X]:((old(X)<~>calm(X))=>(old(X)&kind(X))))&
(?[X]:((old(X)&~quiet(X))))&
((humble(john)&kind(john)))&
(?[X]:((brave(X)&~funny(X))))&
(?[X]:((brave(X)<~>happy(X))))&
((tall(fred)|wise(fred)))&
(?[X]:((quiet(X)|~quiet(X))))&
(?[X]:(strong(X)))&
(?[X]:((rich(X)&~funny(X)))) | ~happy(fred) | [] | null | 0 |
Everyone who is both generous and kind is old.
If john is funny then john is both quiet and not tall and vice versa.
Everyone who is either not patient or not generous is happy or not happy and vice versa.
If susan is both curious and patient then someone is either calm or not rich.
Everyone who is both not happy and curious is both not tall and rich.
Everyone who is brave or not patient is not funny and vice versa.
Everyone who is tall is both not generous and not quiet.
Everyone who is not creative is either kind or creative.
Everyone who is either not calm or not tall is either not strong or not tall and vice versa.
Everyone who is not brave or not patient is humble and vice versa.
Everyone who is not brave or patient is creative or humble.
Everyone who is either tall or not funny is either brave or funny and vice versa.
Everyone who is either kind or quiet is quiet and vice versa.
Everyone who is quiet or funny is not creative and vice versa.
Everyone who is both not wise and tall is both not curious and not patient and vice versa.
Everyone who is tall or not old is not quiet or not old.
Someone is not quiet or not old.
Someone is not wise.
Someone is not rich.
Someone is either curious or not brave.
Susan is happy.
Someone is both not rich and not curious. | John is not generous. | neutral | (![X]:((generous(X)&kind(X))=>old(X)))&
((funny(john))<=>((quiet(john)&~tall(john))))&
(![X]:((~patient(X)<~>~generous(X))<=>(happy(X)|~happy(X))))&
(((curious(susan)&patient(susan)))=>(?[X]:((calm(X)<~>~rich(X)))))&
(![X]:((~happy(X)&curious(X))=>(~tall(X)&rich(X))))&
(![X]:((brave(X)|~patient(X))<=>~funny(X)))&
(![X]:(tall(X)=>(~generous(X)&~quiet(X))))&
(![X]:(~creative(X)=>(kind(X)<~>creative(X))))&
(![X]:((~calm(X)<~>~tall(X))<=>(~strong(X)<~>~tall(X))))&
(![X]:((~brave(X)|~patient(X))<=>humble(X)))&
(![X]:((~brave(X)|patient(X))=>(creative(X)|humble(X))))&
(![X]:((tall(X)<~>~funny(X))<=>(brave(X)<~>funny(X))))&
(![X]:((kind(X)<~>quiet(X))<=>quiet(X)))&
(![X]:((quiet(X)|funny(X))<=>~creative(X)))&
(![X]:((~wise(X)&tall(X))<=>(~curious(X)&~patient(X))))&
(![X]:((tall(X)|~old(X))=>(~quiet(X)|~old(X))))&
(?[X]:((~quiet(X)|~old(X))))&
(?[X]:(~wise(X)))&
(?[X]:(~rich(X)))&
(?[X]:((curious(X)<~>~brave(X))))&
(happy(susan))&
(?[X]:((~rich(X)&~curious(X)))) | ~generous(john) | [] | null | 0 |
If mary is both not quiet and not generous then lucy is both not funny and not happy. Everyone who is patient is creative. If alice is either quiet or not old then susan is either not humble or not quiet and vice versa. If someone is strong then mary is kind and vice versa. Everyone who is both kind and not creative is not strong and vice versa. If alice is both brave and curious then john is both not strong and patient and vice versa. Everyone who is both creative and not creative is not old and vice versa. If someone is both humble and wise then susan is both tall and quiet and vice versa. Everyone who is not kind is tall and vice versa. Everyone who is kind is not quiet and vice versa. If paul is both not strong and not quiet then someone is curious or tall. Everyone who is tall is not wise. If alice is not brave then someone is both tall and not old. Everyone who is both not humble and not curious is either old or happy. If alice is not rich or not humble then someone is either not kind or not patient. If susan is both not strong and kind then someone is not happy and vice versa. John is humble or funny. Fred is both patient and brave. Susan is not kind or not generous. Susan is happy or not rich. Someone is not quiet or not happy. Someone is both strong and calm. Someone is not happy. Mary is both not rich and not patient. | Susan is not kind. | contradiction | (((~quiet(mary)&~generous(mary)))=>((~funny(lucy)&~happy(lucy))))&
(![X]:(patient(X)=>creative(X)))&
(((quiet(alice)<~>~old(alice)))<=>((~humble(susan)<~>~quiet(susan))))&
((?[X]:(strong(X)))<=>(kind(mary)))&
(![X]:((kind(X)&~creative(X))<=>~strong(X)))&
(((brave(alice)&curious(alice)))<=>((~strong(john)&patient(john))))&
(![X]:((creative(X)&~creative(X))<=>~old(X)))&
((?[X]:((humble(X)&wise(X))))<=>((tall(susan)&quiet(susan))))&
(![X]:(~kind(X)<=>tall(X)))&
(![X]:(kind(X)<=>~quiet(X)))&
(((~strong(paul)&~quiet(paul)))=>(?[X]:((curious(X)|tall(X)))))&
(![X]:(tall(X)=>~wise(X)))&
((~brave(alice))=>(?[X]:((tall(X)&~old(X)))))&
(![X]:((~humble(X)&~curious(X))=>(old(X)<~>happy(X))))&
(((~rich(alice)|~humble(alice)))=>(?[X]:((~kind(X)<~>~patient(X)))))&
(((~strong(susan)&kind(susan)))<=>(?[X]:(~happy(X))))&
((humble(john)|funny(john)))&
((patient(fred)&brave(fred)))&
((~kind(susan)|~generous(susan)))&
((happy(susan)|~rich(susan)))&
(?[X]:((~quiet(X)|~happy(X))))&
(?[X]:((strong(X)&calm(X))))&
(?[X]:(~happy(X)))&
((~rich(mary)&~patient(mary))) | ~kind(susan) | [
"p15",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 527685680030418585855787
% SZS output start Proof for 527685680030418585855787
16. (kind(susan) & ~strong(susan)) <=> ? [X0] : ~happy(X0) [input p15]
23. ? [X0] : ~happy(X0) [input p22]
25. ~kind(susan) [input hypothesis]
63. ((kind(susan) & ~strong(susan)) | ! [X0] : happy(X0)) & (? [X0] : ~happy(X0) | (~kind(susan) | strong(susan))) [nnf transformation 16]
64. ((kind(susan) & ~strong(susan)) | ! [X0] : happy(X0)) & (? [X0] : ~happy(X0) | ~kind(susan) | strong(susan)) [flattening 63]
65. ((kind(susan) & ~strong(susan)) | ! [X0] : happy(X0)) & (? [X1] : ~happy(X1) | ~kind(susan) | strong(susan)) [rectify 64]
66. ? [X1] : ~happy(X1) => ~happy(sK5) [choice axiom]
67. ((kind(susan) & ~strong(susan)) | ! [X0] : happy(X0)) & (~happy(sK5) | ~kind(susan) | strong(susan)) [skolemisation 65,66]
72. ? [X0] : ~happy(X0) => ~happy(sK8) [choice axiom]
73. ~happy(sK8) [skolemisation 23,72]
117. kind(susan) | happy(X0) [cnf transformation 67]
125. ~happy(sK8) [cnf transformation 73]
128. ~kind(susan) [cnf transformation 25]
270. 29 <=> ! [X0] : happy(X0) [avatar definition]
271. happy(X0) <- (29) [avatar component clause 270]
273. 30 <=> kind(susan) [avatar definition]
276. 29 | 30 [avatar split clause 117,273,270]
320. ~30 [avatar split clause 128,273]
325. $false <- (29) [resolution 271,125]
326. ~29 [avatar contradiction clause 325]
327. $false [avatar sat refutation 276,320,326]
% SZS output end Proof for 527685680030418585855787
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not brave and old is either not quiet or not creative and vice versa.
Everyone who is creative or not generous is both not curious and not creative and vice versa.
If lucy is either kind or tall then lucy is wise.
Everyone who is not old or not happy is either patient or not rich and vice versa.
Everyone who is either strong or generous is not funny.
If someone is both not wise and not funny then mary is both happy and not kind.
Everyone who is curious or brave is either brave or not funny and vice versa.
If someone is both strong and rich then someone is both creative and not strong.
If someone is not happy or wise then paul is either not calm or not funny.
If susan is not tall then mary is tall or strong and vice versa.
If someone is funny or not kind then someone is either wise or rich.
If someone is both not funny and funny then someone is either not old or not creative.
Everyone who is tall is both not wise and not patient.
If lucy is not generous or not funny then someone is either humble or brave and vice versa.
Everyone who is not tall is curious or not old.
Everyone who is not calm is both not rich and not curious.
Lucy is either not old or patient.
Someone is generous.
Susan is either generous or not creative.
Someone is old or not humble.
Lucy is either not rich or humble.
Someone is both not creative and calm.
Someone is both patient and not happy.
Fred is either kind or wise. | Lucy is creative. | contradiction | (![X]:((~brave(X)&old(X))<=>(~quiet(X)<~>~creative(X))))&
(![X]:((creative(X)|~generous(X))<=>(~curious(X)&~creative(X))))&
(((kind(lucy)<~>tall(lucy)))=>(wise(lucy)))&
(![X]:((~old(X)|~happy(X))<=>(patient(X)<~>~rich(X))))&
(![X]:((strong(X)<~>generous(X))=>~funny(X)))&
((?[X]:((~wise(X)&~funny(X))))=>((happy(mary)&~kind(mary))))&
(![X]:((curious(X)|brave(X))<=>(brave(X)<~>~funny(X))))&
((?[X]:((strong(X)&rich(X))))=>(?[X]:((creative(X)&~strong(X)))))&
((?[X]:((~happy(X)|wise(X))))=>((~calm(paul)<~>~funny(paul))))&
((~tall(susan))<=>((tall(mary)|strong(mary))))&
((?[X]:((funny(X)|~kind(X))))=>(?[X]:((wise(X)<~>rich(X)))))&
((?[X]:((~funny(X)&funny(X))))=>(?[X]:((~old(X)<~>~creative(X)))))&
(![X]:(tall(X)=>(~wise(X)&~patient(X))))&
(((~generous(lucy)|~funny(lucy)))<=>(?[X]:((humble(X)<~>brave(X)))))&
(![X]:(~tall(X)=>(curious(X)|~old(X))))&
(![X]:(~calm(X)=>(~rich(X)&~curious(X))))&
((~old(lucy)<~>patient(lucy)))&
(?[X]:(generous(X)))&
((generous(susan)<~>~creative(susan)))&
(?[X]:((old(X)|~humble(X))))&
((~rich(lucy)<~>humble(lucy)))&
(?[X]:((~creative(X)&calm(X))))&
(?[X]:((patient(X)&~happy(X))))&
((kind(fred)<~>wise(fred))) | creative(lucy) | [
"p1",
"hypothesis"
] | % SZS status Unsatisfiable for 66765080495148358978360
% SZS output start Proof for 66765080495148358978360
2. ! [X0] : ((~generous(X0) | creative(X0)) <=> (~creative(X0) & ~curious(X0))) [input p1]
25. creative(lucy) [input hypothesis]
42. ! [X0] : (((~generous(X0) | creative(X0)) | (creative(X0) | curious(X0))) & ((~creative(X0) & ~curious(X0)) | (generous(X0) & ~creative(X0)))) [nnf transformation 2]
43. ! [X0] : ((~generous(X0) | creative(X0) | creative(X0) | curious(X0)) & ((~creative(X0) & ~curious(X0)) | (generous(X0) & ~creative(X0)))) [flattening 42]
89. ~creative(X0) | ~creative(X0) [cnf transformation 43]
150. creative(lucy) [cnf transformation 25]
153. ~creative(X0) [duplicate literal removal 89]
311. $false [subsumption resolution 150,153]
% SZS output end Proof for 66765080495148358978360
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative is not creative or not quiet. If alice is not humble then someone is both rich and happy. Everyone who is not patient is rich or not calm. If john is not humble or calm then mary is funny and vice versa. If mary is not funny then fred is both not funny and not tall. If someone is humble or calm then paul is not strong or not kind. If alice is not quiet or patient then lucy is creative. If someone is either not calm or not creative then someone is quiet or calm and vice versa. Everyone who is strong or not old is creative and vice versa. Everyone who is quiet is rich and vice versa. Everyone who is not funny or not wise is not tall or not funny. If someone is not happy then john is not creative. Everyone who is either curious or not generous is curious or happy. Everyone who is quiet or not kind is either generous or not quiet and vice versa. If susan is either brave or not generous then someone is either happy or not rich and vice versa. If someone is either old or not tall then someone is either not rich or tall and vice versa. Fred is either not kind or not creative. Paul is not creative. John is not humble or old. John is either curious or brave. John is generous or not happy. Paul is not calm. Lucy is not creative or not tall. Fred is tall or not calm. | Fred is not creative. | neutral | (![X]:(~creative(X)=>(~creative(X)|~quiet(X))))&
((~humble(alice))=>(?[X]:((rich(X)&happy(X)))))&
(![X]:(~patient(X)=>(rich(X)|~calm(X))))&
(((~humble(john)|calm(john)))<=>(funny(mary)))&
((~funny(mary))=>((~funny(fred)&~tall(fred))))&
((?[X]:((humble(X)|calm(X))))=>((~strong(paul)|~kind(paul))))&
(((~quiet(alice)|patient(alice)))=>(creative(lucy)))&
((?[X]:((~calm(X)<~>~creative(X))))<=>(?[X]:((quiet(X)|calm(X)))))&
(![X]:((strong(X)|~old(X))<=>creative(X)))&
(![X]:(quiet(X)<=>rich(X)))&
(![X]:((~funny(X)|~wise(X))=>(~tall(X)|~funny(X))))&
((?[X]:(~happy(X)))=>(~creative(john)))&
(![X]:((curious(X)<~>~generous(X))=>(curious(X)|happy(X))))&
(![X]:((quiet(X)|~kind(X))<=>(generous(X)<~>~quiet(X))))&
(((brave(susan)<~>~generous(susan)))<=>(?[X]:((happy(X)<~>~rich(X)))))&
((?[X]:((old(X)<~>~tall(X))))<=>(?[X]:((~rich(X)<~>tall(X)))))&
((~kind(fred)<~>~creative(fred)))&
(~creative(paul))&
((~humble(john)|old(john)))&
((curious(john)<~>brave(john)))&
((generous(john)|~happy(john)))&
(~calm(paul))&
((~creative(lucy)|~tall(lucy)))&
((tall(fred)|~calm(fred))) | ~creative(fred) | [] | null | 0 |
If alice is not funny then fred is rich or not creative and vice versa.
If someone is funny or strong then lucy is not wise and vice versa.
Everyone who is not kind or happy is strong or funny.
Everyone who is either not strong or patient is both not funny and not kind and vice versa.
Everyone who is either tall or not rich is both not wise and not generous and vice versa.
Everyone who is either curious or not rich is both calm and not curious and vice versa.
If mary is patient or not strong then john is both not brave and happy.
If fred is both humble and not creative then lucy is either strong or not happy.
If someone is both not brave and tall then paul is both not strong and not humble and vice versa.
If mary is both not rich and not patient then someone is not tall.
If someone is not rich then lucy is not generous or not humble.
If lucy is quiet then paul is both not tall and not strong.
If john is strong or wise then someone is not rich or quiet and vice versa.
Everyone who is not strong is not calm or not old.
Everyone who is kind is not old.
If someone is not funny or not creative then mary is both not brave and not curious and vice versa.
Someone is not patient.
Someone is curious.
Someone is not old.
Someone is not wise.
Susan is either not tall or rich.
Someone is brave or not strong.
Someone is not curious.
Someone is either not calm or not tall. | Susan is wise. | contradiction | ((~funny(alice))<=>((rich(fred)|~creative(fred))))&
((?[X]:((funny(X)|strong(X))))<=>(~wise(lucy)))&
(![X]:((~kind(X)|happy(X))=>(strong(X)|funny(X))))&
(![X]:((~strong(X)<~>patient(X))<=>(~funny(X)&~kind(X))))&
(![X]:((tall(X)<~>~rich(X))<=>(~wise(X)&~generous(X))))&
(![X]:((curious(X)<~>~rich(X))<=>(calm(X)&~curious(X))))&
(((patient(mary)|~strong(mary)))=>((~brave(john)&happy(john))))&
(((humble(fred)&~creative(fred)))=>((strong(lucy)<~>~happy(lucy))))&
((?[X]:((~brave(X)&tall(X))))<=>((~strong(paul)&~humble(paul))))&
(((~rich(mary)&~patient(mary)))=>(?[X]:(~tall(X))))&
((?[X]:(~rich(X)))=>((~generous(lucy)|~humble(lucy))))&
((quiet(lucy))=>((~tall(paul)&~strong(paul))))&
(((strong(john)|wise(john)))<=>(?[X]:((~rich(X)|quiet(X)))))&
(![X]:(~strong(X)=>(~calm(X)|~old(X))))&
(![X]:(kind(X)=>~old(X)))&
((?[X]:((~funny(X)|~creative(X))))<=>((~brave(mary)&~curious(mary))))&
(?[X]:(~patient(X)))&
(?[X]:(curious(X)))&
(?[X]:(~old(X)))&
(?[X]:(~wise(X)))&
((~tall(susan)<~>rich(susan)))&
(?[X]:((brave(X)|~strong(X))))&
(?[X]:(~curious(X)))&
(?[X]:((~calm(X)<~>~tall(X)))) | wise(susan) | [
"p4",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 812442996076582986083735
% SZS output start Proof for 812442996076582986083735
5. ! [X0] : ((tall(X0) <~> ~rich(X0)) <=> (~generous(X0) & ~wise(X0))) [input p4]
21. ~tall(susan) <~> rich(susan) [input p20]
25. wise(susan) [input hypothesis]
47. ! [X0] : ((((rich(X0) | ~tall(X0)) & (~rich(X0) | tall(X0))) | (generous(X0) | wise(X0))) & ((~generous(X0) & ~wise(X0)) | ((tall(X0) | rich(X0)) & (~rich(X0) | ~tall(X0))))) [nnf transformation 5]
48. ! [X0] : ((((rich(X0) | ~tall(X0)) & (~rich(X0) | tall(X0))) | generous(X0) | wise(X0)) & ((~generous(X0) & ~wise(X0)) | ((tall(X0) | rich(X0)) & (~rich(X0) | ~tall(X0))))) [flattening 47]
75. (~rich(susan) | tall(susan)) & (rich(susan) | ~tall(susan)) [nnf transformation 21]
97. ~tall(X0) | ~rich(X0) | ~wise(X0) [cnf transformation 48]
98. ~wise(X0) | tall(X0) | rich(X0) [cnf transformation 48]
135. rich(susan) | ~tall(susan) [cnf transformation 75]
136. ~rich(susan) | tall(susan) [cnf transformation 75]
141. wise(susan) [cnf transformation 25]
320. 39 <=> tall(susan) [avatar definition]
322. tall(susan) <- (39) [avatar component clause 320]
324. 40 <=> rich(susan) [avatar definition]
325. rich(susan) <- (40) [avatar component clause 324]
327. 39 | ~40 [avatar split clause 136,324,320]
328. ~39 | 40 [avatar split clause 135,324,320]
374. tall(susan) | rich(susan) [resolution 98,141]
378. 40 | 39 [avatar split clause 374,320,324]
379. ~rich(susan) | ~wise(susan) <- (39) [resolution 322,97]
380. ~wise(susan) <- (39, 40) [subsumption resolution 379,325]
381. $false <- (39, 40) [subsumption resolution 380,141]
382. ~39 | ~40 [avatar contradiction clause 381]
383. $false [avatar sat refutation 327,328,378,382]
% SZS output end Proof for 812442996076582986083735
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.018 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is humble is patient and vice versa.
If someone is not rich or quiet then susan is not rich and vice versa.
If alice is both calm and not wise then mary is both not patient and funny.
If someone is both not happy and strong then fred is tall or wise and vice versa.
Everyone who is either not humble or generous is either funny or generous.
If someone is either not quiet or not patient then paul is brave and vice versa.
If mary is calm or not funny then someone is both not curious and funny.
Everyone who is not kind or not old is both not wise and not old and vice versa.
Everyone who is both not creative and rich is patient or not quiet.
If someone is not calm or not humble then paul is strong and vice versa.
If someone is both strong and rich then paul is not rich and vice versa.
Everyone who is calm is both kind and not kind and vice versa.
If fred is curious or rich then john is old and vice versa.
Everyone who is not strong is quiet or not wise.
Everyone who is either patient or old is not rich or not humble.
If someone is either calm or creative then someone is either strong or not rich and vice versa.
Susan is wise.
Someone is not humble.
John is both not happy and not kind.
Fred is not tall or not calm.
Susan is strong.
Susan is either calm or not rich.
Paul is either not creative or funny.
Paul is old. | Paul is not creative. | neutral | (![X]:(humble(X)<=>patient(X)))&
((?[X]:((~rich(X)|quiet(X))))<=>(~rich(susan)))&
(((calm(alice)&~wise(alice)))=>((~patient(mary)&funny(mary))))&
((?[X]:((~happy(X)&strong(X))))<=>((tall(fred)|wise(fred))))&
(![X]:((~humble(X)<~>generous(X))=>(funny(X)<~>generous(X))))&
((?[X]:((~quiet(X)<~>~patient(X))))<=>(brave(paul)))&
(((calm(mary)|~funny(mary)))=>(?[X]:((~curious(X)&funny(X)))))&
(![X]:((~kind(X)|~old(X))<=>(~wise(X)&~old(X))))&
(![X]:((~creative(X)&rich(X))=>(patient(X)|~quiet(X))))&
((?[X]:((~calm(X)|~humble(X))))<=>(strong(paul)))&
((?[X]:((strong(X)&rich(X))))<=>(~rich(paul)))&
(![X]:(calm(X)<=>(kind(X)&~kind(X))))&
(((curious(fred)|rich(fred)))<=>(old(john)))&
(![X]:(~strong(X)=>(quiet(X)|~wise(X))))&
(![X]:((patient(X)<~>old(X))=>(~rich(X)|~humble(X))))&
((?[X]:((calm(X)<~>creative(X))))<=>(?[X]:((strong(X)<~>~rich(X)))))&
(wise(susan))&
(?[X]:(~humble(X)))&
((~happy(john)&~kind(john)))&
((~tall(fred)|~calm(fred)))&
(strong(susan))&
((calm(susan)<~>~rich(susan)))&
((~creative(paul)<~>funny(paul)))&
(old(paul)) | ~creative(paul) | [] | null | 0 |
If someone is both not funny and strong then fred is not old or not strong.
If mary is either not brave or happy then alice is both strong and not wise and vice versa.
Everyone who is either strong or not strong is strong or not kind and vice versa.
Everyone who is both not strong and brave is either rich or not curious and vice versa.
If someone is strong or not generous then someone is either not patient or brave and vice versa.
Everyone who is kind is both not tall and tall.
If lucy is calm then paul is not generous.
Everyone who is either not curious or rich is calm.
Everyone who is rich is either not creative or not funny.
If someone is either not brave or quiet then someone is curious.
Everyone who is not wise or not patient is both funny and not funny and vice versa.
If someone is kind then someone is rich or curious and vice versa.
If fred is either not brave or rich then susan is both not kind and calm.
If john is both strong and not calm then paul is either generous or not humble and vice versa.
Everyone who is both not quiet and not happy is not curious and vice versa.
Everyone who is both rich and not rich is either patient or not rich.
Someone is generous.
Paul is either quiet or not rich.
Someone is both not humble and funny.
Someone is not kind or curious.
Alice is both not quiet and calm. | Mary is curious. | contradiction | ((?[X]:((~funny(X)&strong(X))))=>((~old(fred)|~strong(fred))))&
(((~brave(mary)<~>happy(mary)))<=>((strong(alice)&~wise(alice))))&
(![X]:((strong(X)<~>~strong(X))<=>(strong(X)|~kind(X))))&
(![X]:((~strong(X)&brave(X))<=>(rich(X)<~>~curious(X))))&
((?[X]:((strong(X)|~generous(X))))<=>(?[X]:((~patient(X)<~>brave(X)))))&
(![X]:(kind(X)=>(~tall(X)&tall(X))))&
((calm(lucy))=>(~generous(paul)))&
(![X]:((~curious(X)<~>rich(X))=>calm(X)))&
(![X]:(rich(X)=>(~creative(X)<~>~funny(X))))&
((?[X]:((~brave(X)<~>quiet(X))))=>(?[X]:(curious(X))))&
(![X]:((~wise(X)|~patient(X))<=>(funny(X)&~funny(X))))&
((?[X]:(kind(X)))<=>(?[X]:((rich(X)|curious(X)))))&
(((~brave(fred)<~>rich(fred)))=>((~kind(susan)&calm(susan))))&
(((strong(john)&~calm(john)))<=>((generous(paul)<~>~humble(paul))))&
(![X]:((~quiet(X)&~happy(X))<=>~curious(X)))&
(![X]:((rich(X)&~rich(X))=>(patient(X)<~>~rich(X))))&
(?[X]:(generous(X)))&
((quiet(paul)<~>~rich(paul)))&
(?[X]:((~humble(X)&funny(X))))&
(?[X]:((~kind(X)|curious(X))))&
((~quiet(alice)&calm(alice))) | curious(mary) | [
"p5",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 269919643456224476380932
% SZS output start Proof for 269919643456224476380932
6. ! [X0] : (kind(X0) => (tall(X0) & ~tall(X0))) [input p5]
12. ? [X0] : kind(X0) <=> ? [X0] : (curious(X0) | rich(X0)) [input p11]
22. curious(mary) [input hypothesis]
25. ? [X0] : kind(X0) <=> ? [X1] : (curious(X1) | rich(X1)) [rectify 12]
27. ! [X0] : ((tall(X0) & ~tall(X0)) | ~kind(X0)) [ennf transformation 6]
54. (? [X0] : kind(X0) | ! [X1] : (~curious(X1) & ~rich(X1))) & (? [X1] : (curious(X1) | rich(X1)) | ! [X0] : ~kind(X0)) [nnf transformation 25]
55. (? [X0] : kind(X0) | ! [X1] : (~curious(X1) & ~rich(X1))) & (? [X2] : (curious(X2) | rich(X2)) | ! [X3] : ~kind(X3)) [rectify 54]
56. ? [X0] : kind(X0) => kind(sK3) [choice axiom]
57. ? [X2] : (curious(X2) | rich(X2)) => (curious(sK4) | rich(sK4)) [choice axiom]
58. (kind(sK3) | ! [X1] : (~curious(X1) & ~rich(X1))) & ((curious(sK4) | rich(sK4)) | ! [X3] : ~kind(X3)) [skolemisation 55,57,56]
96. ~tall(X0) | ~kind(X0) [cnf transformation 27]
97. tall(X0) | ~kind(X0) [cnf transformation 27]
112. kind(sK3) | ~curious(X1) [cnf transformation 58]
136. curious(mary) [cnf transformation 22]
199. ~kind(X0) [subsumption resolution 96,97]
223. ~curious(X1) [subsumption resolution 112,199]
255. $false [subsumption resolution 136,223]
% SZS output end Proof for 269919643456224476380932
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet or generous is both tall and creative.
Everyone who is not old or not curious is not quiet.
If someone is not brave then alice is patient and vice versa.
Everyone who is either not tall or quiet is not kind or kind and vice versa.
Everyone who is not curious is not happy or quiet.
If someone is not tall then alice is rich and vice versa.
If someone is both wise and creative then someone is not brave or not curious and vice versa.
If someone is not creative then lucy is either funny or generous.
Everyone who is either not happy or old is both not rich and creative.
Everyone who is not happy or not strong is both calm and not curious.
Everyone who is both funny and patient is not brave.
Everyone who is not rich is not strong or not rich and vice versa.
Everyone who is both funny and calm is not brave and vice versa.
If someone is brave or kind then someone is not calm or not kind and vice versa.
If lucy is either patient or rich then mary is either not rich or not brave.
Everyone who is both wise and not calm is not generous or rich and vice versa.
Alice is humble.
Lucy is either not kind or happy.
Fred is either happy or not patient.
Lucy is not patient.
John is either humble or not kind.
Someone is not patient or tall.
Someone is both not calm and wise. | John is happy. | entailment | (![X]:((quiet(X)|generous(X))=>(tall(X)&creative(X))))&
(![X]:((~old(X)|~curious(X))=>~quiet(X)))&
((?[X]:(~brave(X)))<=>(patient(alice)))&
(![X]:((~tall(X)<~>quiet(X))<=>(~kind(X)|kind(X))))&
(![X]:(~curious(X)=>(~happy(X)|quiet(X))))&
((?[X]:(~tall(X)))<=>(rich(alice)))&
((?[X]:((wise(X)&creative(X))))<=>(?[X]:((~brave(X)|~curious(X)))))&
((?[X]:(~creative(X)))=>((funny(lucy)<~>generous(lucy))))&
(![X]:((~happy(X)<~>old(X))=>(~rich(X)&creative(X))))&
(![X]:((~happy(X)|~strong(X))=>(calm(X)&~curious(X))))&
(![X]:((funny(X)&patient(X))=>~brave(X)))&
(![X]:(~rich(X)<=>(~strong(X)|~rich(X))))&
(![X]:((funny(X)&calm(X))<=>~brave(X)))&
((?[X]:((brave(X)|kind(X))))<=>(?[X]:((~calm(X)|~kind(X)))))&
(((patient(lucy)<~>rich(lucy)))=>((~rich(mary)<~>~brave(mary))))&
(![X]:((wise(X)&~calm(X))<=>(~generous(X)|rich(X))))&
(humble(alice))&
((~kind(lucy)<~>happy(lucy)))&
((happy(fred)<~>~patient(fred)))&
(~patient(lucy))&
((humble(john)<~>~kind(john)))&
(?[X]:((~patient(X)|tall(X))))&
(?[X]:((~calm(X)&wise(X)))) | happy(john) | [
"p0",
"p1",
"p3",
"p9",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1709007609183558145985441
% SZS output start Proof for 1709007609183558145985441
1. ! [X0] : ((generous(X0) | quiet(X0)) => (creative(X0) & tall(X0))) [input p0]
2. ! [X0] : ((~curious(X0) | ~old(X0)) => ~quiet(X0)) [input p1]
4. ! [X0] : ((~tall(X0) <~> quiet(X0)) <=> (kind(X0) | ~kind(X0))) [input p3]
10. ! [X0] : ((~strong(X0) | ~happy(X0)) => (~curious(X0) & calm(X0))) [input p9]
16. ! [X0] : ((~calm(X0) & wise(X0)) <=> (rich(X0) | ~generous(X0))) [input p15]
24. ~happy(john) [input hypothesis]
27. ! [X0] : ((creative(X0) & tall(X0)) | (~generous(X0) & ~quiet(X0))) [ennf transformation 1]
28. ! [X0] : (~quiet(X0) | (curious(X0) & old(X0))) [ennf transformation 2]
33. ! [X0] : ((~curious(X0) & calm(X0)) | (strong(X0) & happy(X0))) [ennf transformation 10]
41. ! [X0] : ((((~quiet(X0) | tall(X0)) & (quiet(X0) | ~tall(X0))) | (~kind(X0) & kind(X0))) & ((kind(X0) | ~kind(X0)) | ((~tall(X0) | ~quiet(X0)) & (quiet(X0) | tall(X0))))) [nnf transformation 4]
42. ! [X0] : ((((~quiet(X0) | tall(X0)) & (quiet(X0) | ~tall(X0))) | (~kind(X0) & kind(X0))) & (kind(X0) | ~kind(X0) | ((~tall(X0) | ~quiet(X0)) & (quiet(X0) | tall(X0))))) [flattening 41]
64. ! [X0] : (((~calm(X0) & wise(X0)) | (~rich(X0) & generous(X0))) & ((rich(X0) | ~generous(X0)) | (calm(X0) | ~wise(X0)))) [nnf transformation 16]
65. ! [X0] : (((~calm(X0) & wise(X0)) | (~rich(X0) & generous(X0))) & (rich(X0) | ~generous(X0) | calm(X0) | ~wise(X0))) [flattening 64]
74. ~generous(X0) | tall(X0) [cnf transformation 27]
78. ~quiet(X0) | curious(X0) [cnf transformation 28]
83. quiet(X0) | ~tall(X0) | kind(X0) [cnf transformation 42]
84. ~kind(X0) | ~tall(X0) | quiet(X0) [cnf transformation 42]
101. calm(X0) | happy(X0) [cnf transformation 33]
103. ~curious(X0) | happy(X0) [cnf transformation 33]
123. ~calm(X0) | generous(X0) [cnf transformation 65]
136. ~happy(john) [cnf transformation 24]
150. ~tall(X0) | quiet(X0) [subsumption resolution 83,84]
311. happy(X2) | generous(X2) [resolution 123,101]
391. generous(john) [resolution 311,136]
400. tall(john) [resolution 391,74]
412. quiet(john) [resolution 400,150]
427. curious(john) [resolution 412,78]
441. happy(john) [resolution 427,103]
442. $false [subsumption resolution 441,136]
% SZS output end Proof for 1709007609183558145985441
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.018 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is either curious or kind then someone is curious and vice versa. If someone is not curious then mary is not patient. Everyone who is either not humble or not brave is both happy and not creative and vice versa. If someone is either not brave or wise then susan is both not wise and kind and vice versa. Everyone who is not creative is not quiet or humble and vice versa. Everyone who is both not old and not calm is old and vice versa. Everyone who is either not quiet or wise is calm. If alice is tall then someone is not old or calm and vice versa. Everyone who is not curious or not generous is not creative or not wise and vice versa. If someone is not humble then someone is both not old and strong. Everyone who is not patient is brave or not calm. If someone is tall then lucy is either not brave or not strong. Everyone who is not brave is old or quiet and vice versa. If someone is both not happy and not humble then someone is not old and vice versa. If someone is humble then someone is both humble and not humble and vice versa. If someone is both not rich and not patient then mary is not happy and vice versa. Fred is both not generous and not brave. Alice is not funny. Alice is kind. Someone is both curious and not kind. Alice is either calm or not brave. Someone is either not happy or not patient. | Susan is not calm. | contradiction | (((curious(lucy)<~>kind(lucy)))<=>(?[X]:(curious(X))))&
((?[X]:(~curious(X)))=>(~patient(mary)))&
(![X]:((~humble(X)<~>~brave(X))<=>(happy(X)&~creative(X))))&
((?[X]:((~brave(X)<~>wise(X))))<=>((~wise(susan)&kind(susan))))&
(![X]:(~creative(X)<=>(~quiet(X)|humble(X))))&
(![X]:((~old(X)&~calm(X))<=>old(X)))&
(![X]:((~quiet(X)<~>wise(X))=>calm(X)))&
((tall(alice))<=>(?[X]:((~old(X)|calm(X)))))&
(![X]:((~curious(X)|~generous(X))<=>(~creative(X)|~wise(X))))&
((?[X]:(~humble(X)))=>(?[X]:((~old(X)&strong(X)))))&
(![X]:(~patient(X)=>(brave(X)|~calm(X))))&
((?[X]:(tall(X)))=>((~brave(lucy)<~>~strong(lucy))))&
(![X]:(~brave(X)<=>(old(X)|quiet(X))))&
((?[X]:((~happy(X)&~humble(X))))<=>(?[X]:(~old(X))))&
((?[X]:(humble(X)))<=>(?[X]:((humble(X)&~humble(X)))))&
((?[X]:((~rich(X)&~patient(X))))<=>(~happy(mary)))&
((~generous(fred)&~brave(fred)))&
(~funny(alice))&
(kind(alice))&
(?[X]:((curious(X)&~kind(X))))&
((calm(alice)<~>~brave(alice)))&
(?[X]:((~happy(X)<~>~patient(X)))) | ~calm(susan) | [
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 21468391275028166665424
% SZS output start Proof for 21468391275028166665424
6. ! [X0] : ((~calm(X0) & ~old(X0)) <=> old(X0)) [input p5]
23. ~calm(susan) [input hypothesis]
47. ! [X0] : (((~calm(X0) & ~old(X0)) | ~old(X0)) & (old(X0) | (calm(X0) | old(X0)))) [nnf transformation 6]
48. ! [X0] : (((~calm(X0) & ~old(X0)) | ~old(X0)) & (old(X0) | calm(X0) | old(X0))) [flattening 47]
102. old(X0) | calm(X0) | old(X0) [cnf transformation 48]
103. ~old(X0) | ~old(X0) [cnf transformation 48]
140. ~calm(susan) [cnf transformation 23]
141. old(X0) | calm(X0) [duplicate literal removal 102]
142. ~old(X0) [duplicate literal removal 103]
198. calm(X0) [subsumption resolution 141,142]
263. $false [subsumption resolution 140,198]
% SZS output end Proof for 21468391275028166665424
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble then fred is both not kind and not tall and vice versa. If susan is generous then someone is both not funny and funny and vice versa. If someone is quiet or not kind then paul is both funny and not funny. If susan is not old then someone is not old or happy and vice versa. If someone is either tall or not kind then fred is either not patient or rich. Everyone who is both not creative and tall is not generous. Everyone who is tall is both brave and rich. Everyone who is both patient and not quiet is humble and vice versa. Everyone who is either kind or not kind is strong or not old and vice versa. If alice is wise or humble then someone is not funny or patient and vice versa. Everyone who is not old or not strong is both not funny and not generous and vice versa. If paul is not creative or wise then someone is quiet. Everyone who is both generous and not strong is both calm and brave. Everyone who is either old or not kind is tall and vice versa. If someone is either old or curious then someone is not happy and vice versa. Everyone who is both not strong and funny is not humble and vice versa. Someone is either brave or not humble. Susan is not tall or curious. Someone is rich or quiet. Fred is either wise or not calm. Someone is not quiet or not generous. | Lucy is old. | contradiction | (((rich(lucy)<~>~humble(lucy)))<=>((~kind(fred)&~tall(fred))))&
((generous(susan))<=>(?[X]:((~funny(X)&funny(X)))))&
((?[X]:((quiet(X)|~kind(X))))=>((funny(paul)&~funny(paul))))&
((~old(susan))<=>(?[X]:((~old(X)|happy(X)))))&
((?[X]:((tall(X)<~>~kind(X))))=>((~patient(fred)<~>rich(fred))))&
(![X]:((~creative(X)&tall(X))=>~generous(X)))&
(![X]:(tall(X)=>(brave(X)&rich(X))))&
(![X]:((patient(X)&~quiet(X))<=>humble(X)))&
(![X]:((kind(X)<~>~kind(X))<=>(strong(X)|~old(X))))&
(((wise(alice)|humble(alice)))<=>(?[X]:((~funny(X)|patient(X)))))&
(![X]:((~old(X)|~strong(X))<=>(~funny(X)&~generous(X))))&
(((~creative(paul)|wise(paul)))=>(?[X]:(quiet(X))))&
(![X]:((generous(X)&~strong(X))=>(calm(X)&brave(X))))&
(![X]:((old(X)<~>~kind(X))<=>tall(X)))&
((?[X]:((old(X)<~>curious(X))))<=>(?[X]:(~happy(X))))&
(![X]:((~strong(X)&funny(X))<=>~humble(X)))&
(?[X]:((brave(X)<~>~humble(X))))&
((~tall(susan)|curious(susan)))&
(?[X]:((rich(X)|quiet(X))))&
((wise(fred)<~>~calm(fred)))&
(?[X]:((~quiet(X)|~generous(X)))) | old(lucy) | [
"p0",
"p2",
"p6",
"p10",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6703635904865175858745192
% SZS output start Proof for 6703635904865175858745192
1. (rich(lucy) <~> ~humble(lucy)) <=> (~tall(fred) & ~kind(fred)) [input p0]
3. ? [X0] : (~kind(X0) | quiet(X0)) => (~funny(paul) & funny(paul)) [input p2]
7. ! [X0] : (tall(X0) => (rich(X0) & brave(X0))) [input p6]
11. ! [X0] : ((~strong(X0) | ~old(X0)) <=> (~generous(X0) & ~funny(X0))) [input p10]
14. ! [X0] : ((old(X0) <~> ~kind(X0)) <=> tall(X0)) [input p13]
16. ! [X0] : ((funny(X0) & ~strong(X0)) <=> ~humble(X0)) [input p15]
22. old(lucy) [input hypothesis]
26. (~funny(paul) & funny(paul)) | ! [X0] : (kind(X0) & ~quiet(X0)) [ennf transformation 3]
28. ! [X0] : ((rich(X0) & brave(X0)) | ~tall(X0)) [ennf transformation 7]
32. (((humble(lucy) | ~rich(lucy)) & (~humble(lucy) | rich(lucy))) | (tall(fred) | kind(fred))) & ((~tall(fred) & ~kind(fred)) | ((rich(lucy) | humble(lucy)) & (~humble(lucy) | ~rich(lucy)))) [nnf transformation 1]
33. (((humble(lucy) | ~rich(lucy)) & (~humble(lucy) | rich(lucy))) | tall(fred) | kind(fred)) & ((~tall(fred) & ~kind(fred)) | ((rich(lucy) | humble(lucy)) & (~humble(lucy) | ~rich(lucy)))) [flattening 32]
52. ! [X0] : (((~strong(X0) | ~old(X0)) | (generous(X0) | funny(X0))) & ((~generous(X0) & ~funny(X0)) | (strong(X0) & old(X0)))) [nnf transformation 11]
53. ! [X0] : ((~strong(X0) | ~old(X0) | generous(X0) | funny(X0)) & ((~generous(X0) & ~funny(X0)) | (strong(X0) & old(X0)))) [flattening 52]
56. ! [X0] : ((((kind(X0) | ~old(X0)) & (~kind(X0) | old(X0))) | ~tall(X0)) & (tall(X0) | ((old(X0) | kind(X0)) & (~kind(X0) | ~old(X0))))) [nnf transformation 14]
62. ! [X0] : (((funny(X0) & ~strong(X0)) | humble(X0)) & (~humble(X0) | (~funny(X0) | strong(X0)))) [nnf transformation 16]
63. ! [X0] : (((funny(X0) & ~strong(X0)) | humble(X0)) & (~humble(X0) | ~funny(X0) | strong(X0))) [flattening 62]
72. ~kind(fred) | ~humble(lucy) | ~rich(lucy) [cnf transformation 33]
82. funny(paul) | kind(X0) [cnf transformation 26]
84. ~funny(paul) | kind(X0) [cnf transformation 26]
93. ~tall(X0) | rich(X0) [cnf transformation 28]
108. ~funny(X0) | strong(X0) [cnf transformation 53]
115. ~old(X0) | ~kind(X0) | tall(X0) [cnf transformation 56]
124. ~strong(X0) | humble(X0) [cnf transformation 63]
125. funny(X0) | humble(X0) [cnf transformation 63]
133. old(lucy) [cnf transformation 22]
137. 1 <=> kind(fred) [avatar definition]
138. ~kind(fred) <- (~1) [avatar component clause 137]
145. 3 <=> rich(lucy) [avatar definition]
147. ~rich(lucy) <- (~3) [avatar component clause 145]
149. 4 <=> humble(lucy) [avatar definition]
150. ~humble(lucy) <- (~4) [avatar component clause 149]
157. ~3 | ~4 | ~1 [avatar split clause 72,137,149,145]
169. 7 <=> ! [X0] : kind(X0) [avatar definition]
170. kind(X0) <- (7) [avatar component clause 169]
172. 8 <=> funny(paul) [avatar definition]
175. 7 | ~8 [avatar split clause 84,172,169]
180. 7 | 8 [avatar split clause 82,172,169]
330. $false <- (~1, 7) [subsumption resolution 138,170]
331. 1 | ~7 [avatar contradiction clause 330]
335. humble(X0) | strong(X0) [resolution 125,108]
337. humble(X0) [subsumption resolution 335,124]
356. $false <- (~4) [resolution 337,150]
360. 4 [avatar contradiction clause 356]
363. ~kind(lucy) | tall(lucy) [resolution 115,133]
365. tall(lucy) <- (7) [subsumption resolution 363,170]
383. rich(lucy) <- (7) [resolution 365,93]
385. $false <- (~3, 7) [subsumption resolution 383,147]
386. 3 | ~7 [avatar contradiction clause 385]
387. $false [avatar sat refutation 157,175,180,331,360,386]
% SZS output end Proof for 6703635904865175858745192
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not funny or generous is either not curious or not wise and vice versa.
Everyone who is both happy and not rich is not generous and vice versa.
Everyone who is both kind and old is both not patient and wise and vice versa.
Everyone who is humble or not happy is tall and vice versa.
If lucy is tall or wise then susan is not calm or not brave.
If lucy is quiet then lucy is both humble and rich and vice versa.
Everyone who is both patient and kind is either humble or not strong.
If lucy is both not funny and humble then someone is not wise.
Everyone who is not generous or not funny is not patient or generous.
Everyone who is both patient and brave is not tall or generous and vice versa.
Everyone who is not curious or patient is not wise or brave and vice versa.
Everyone who is both quiet and funny is both patient and wise and vice versa.
Everyone who is creative or wise is brave.
If alice is either tall or not generous then fred is not old or not kind.
Everyone who is both brave and quiet is either not wise or wise and vice versa.
Everyone who is brave or not rich is not calm.
Someone is not strong.
Someone is either not rich or old.
Mary is happy.
Someone is either not kind or not wise.
Someone is either generous or old. | Susan is funny. | neutral | (![X]:((~funny(X)|generous(X))<=>(~curious(X)<~>~wise(X))))&
(![X]:((happy(X)&~rich(X))<=>~generous(X)))&
(![X]:((kind(X)&old(X))<=>(~patient(X)&wise(X))))&
(![X]:((humble(X)|~happy(X))<=>tall(X)))&
(((tall(lucy)|wise(lucy)))=>((~calm(susan)|~brave(susan))))&
((quiet(lucy))<=>((humble(lucy)&rich(lucy))))&
(![X]:((patient(X)&kind(X))=>(humble(X)<~>~strong(X))))&
(((~funny(lucy)&humble(lucy)))=>(?[X]:(~wise(X))))&
(![X]:((~generous(X)|~funny(X))=>(~patient(X)|generous(X))))&
(![X]:((patient(X)&brave(X))<=>(~tall(X)|generous(X))))&
(![X]:((~curious(X)|patient(X))<=>(~wise(X)|brave(X))))&
(![X]:((quiet(X)&funny(X))<=>(patient(X)&wise(X))))&
(![X]:((creative(X)|wise(X))=>brave(X)))&
(((tall(alice)<~>~generous(alice)))=>((~old(fred)|~kind(fred))))&
(![X]:((brave(X)&quiet(X))<=>(~wise(X)<~>wise(X))))&
(![X]:((brave(X)|~rich(X))=>~calm(X)))&
(?[X]:(~strong(X)))&
(?[X]:((~rich(X)<~>old(X))))&
(happy(mary))&
(?[X]:((~kind(X)<~>~wise(X))))&
(?[X]:((generous(X)<~>old(X)))) | funny(susan) | [] | null | 0 |
Everyone who is both rich and tall is both not old and not patient and vice versa.
Everyone who is not kind or not strong is curious and vice versa.
If paul is both quiet and old then someone is not quiet.
If someone is not strong then someone is both old and not creative.
If someone is either not calm or rich then someone is either not creative or not humble and vice versa.
Everyone who is not brave is generous or not funny and vice versa.
Everyone who is not tall is either old or not creative.
Everyone who is either brave or happy is either not kind or old.
Everyone who is tall is both not curious and curious and vice versa.
If someone is both not humble and strong then paul is both calm and not calm and vice versa.
Everyone who is not kind is both creative and funny and vice versa.
Everyone who is both not happy and calm is not quiet or curious.
If john is strong or not calm then someone is patient or humble.
Everyone who is not old or tall is not patient or not creative.
Everyone who is curious is either quiet or old and vice versa.
If someone is not creative or patient then someone is generous.
Someone is either happy or not funny.
Someone is strong.
Someone is not strong or calm.
Someone is not curious or not quiet.
Mary is calm or quiet.
Paul is old or kind.
Someone is either not old or humble.
Alice is patient. | Paul is not tall. | entailment | (![X]:((rich(X)&tall(X))<=>(~old(X)&~patient(X))))&
(![X]:((~kind(X)|~strong(X))<=>curious(X)))&
(((quiet(paul)&old(paul)))=>(?[X]:(~quiet(X))))&
((?[X]:(~strong(X)))=>(?[X]:((old(X)&~creative(X)))))&
((?[X]:((~calm(X)<~>rich(X))))<=>(?[X]:((~creative(X)<~>~humble(X)))))&
(![X]:(~brave(X)<=>(generous(X)|~funny(X))))&
(![X]:(~tall(X)=>(old(X)<~>~creative(X))))&
(![X]:((brave(X)<~>happy(X))=>(~kind(X)<~>old(X))))&
(![X]:(tall(X)<=>(~curious(X)&curious(X))))&
((?[X]:((~humble(X)&strong(X))))<=>((calm(paul)&~calm(paul))))&
(![X]:(~kind(X)<=>(creative(X)&funny(X))))&
(![X]:((~happy(X)&calm(X))=>(~quiet(X)|curious(X))))&
(((strong(john)|~calm(john)))=>(?[X]:((patient(X)|humble(X)))))&
(![X]:((~old(X)|tall(X))=>(~patient(X)|~creative(X))))&
(![X]:(curious(X)<=>(quiet(X)<~>old(X))))&
((?[X]:((~creative(X)|patient(X))))=>(?[X]:(generous(X))))&
(?[X]:((happy(X)<~>~funny(X))))&
(?[X]:(strong(X)))&
(?[X]:((~strong(X)|calm(X))))&
(?[X]:((~curious(X)|~quiet(X))))&
((calm(mary)|quiet(mary)))&
((old(paul)|kind(paul)))&
(?[X]:((~old(X)<~>humble(X))))&
(patient(alice)) | ~tall(paul) | [
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 6340599309617776070122483
% SZS output start Proof for 6340599309617776070122483
9. ! [X0] : (tall(X0) <=> (curious(X0) & ~curious(X0))) [input p8]
25. tall(paul) [input hypothesis]
58. ! [X0] : ((tall(X0) | (~curious(X0) | curious(X0))) & ((curious(X0) & ~curious(X0)) | ~tall(X0))) [nnf transformation 9]
59. ! [X0] : ((tall(X0) | ~curious(X0) | curious(X0)) & ((curious(X0) & ~curious(X0)) | ~tall(X0))) [flattening 58]
112. ~curious(X0) | ~tall(X0) [cnf transformation 59]
113. curious(X0) | ~tall(X0) [cnf transformation 59]
143. tall(paul) [cnf transformation 25]
206. ~tall(X0) [subsumption resolution 112,113]
298. $false [subsumption resolution 143,206]
% SZS output end Proof for 6340599309617776070122483
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not creative or not brave then someone is kind and vice versa.
Everyone who is either not quiet or old is not quiet and vice versa.
Everyone who is not humble is not brave or not humble and vice versa.
If someone is either not kind or humble then john is not generous or calm.
If someone is old or not happy then someone is both not patient and not wise and vice versa.
Everyone who is not quiet or generous is patient or not creative.
Everyone who is either not curious or not quiet is not rich or not brave and vice versa.
If someone is either not wise or not patient then someone is either humble or happy.
Everyone who is tall is brave or not humble and vice versa.
Everyone who is not wise or brave is happy or kind.
If someone is either brave or calm then susan is wise.
Everyone who is curious or brave is both calm and kind and vice versa.
If alice is both patient and wise then someone is both not creative and kind and vice versa.
Everyone who is both not generous and generous is both happy and rich.
If susan is both not calm and old then someone is not brave and vice versa.
If lucy is old then someone is kind or not brave.
Susan is not old.
Someone is not old or patient.
Someone is either old or brave.
John is both humble and strong.
John is not generous or not old.
Paul is either funny or not brave. | John is not kind. | contradiction | ((?[X]:((~creative(X)<~>~brave(X))))<=>(?[X]:(kind(X))))&
(![X]:((~quiet(X)<~>old(X))<=>~quiet(X)))&
(![X]:(~humble(X)<=>(~brave(X)|~humble(X))))&
((?[X]:((~kind(X)<~>humble(X))))=>((~generous(john)|calm(john))))&
((?[X]:((old(X)|~happy(X))))<=>(?[X]:((~patient(X)&~wise(X)))))&
(![X]:((~quiet(X)|generous(X))=>(patient(X)|~creative(X))))&
(![X]:((~curious(X)<~>~quiet(X))<=>(~rich(X)|~brave(X))))&
((?[X]:((~wise(X)<~>~patient(X))))=>(?[X]:((humble(X)<~>happy(X)))))&
(![X]:(tall(X)<=>(brave(X)|~humble(X))))&
(![X]:((~wise(X)|brave(X))=>(happy(X)|kind(X))))&
((?[X]:((brave(X)<~>calm(X))))=>(wise(susan)))&
(![X]:((curious(X)|brave(X))<=>(calm(X)&kind(X))))&
(((patient(alice)&wise(alice)))<=>(?[X]:((~creative(X)&kind(X)))))&
(![X]:((~generous(X)&generous(X))=>(happy(X)&rich(X))))&
(((~calm(susan)&old(susan)))<=>(?[X]:(~brave(X))))&
((old(lucy))=>(?[X]:((kind(X)|~brave(X)))))&
(~old(susan))&
(?[X]:((~old(X)|patient(X))))&
(?[X]:((old(X)<~>brave(X))))&
((humble(john)&strong(john)))&
((~generous(john)|~old(john)))&
((funny(paul)<~>~brave(paul))) | ~kind(john) | [
"p1",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5030745363425435061912653
% SZS output start Proof for 5030745363425435061912653
2. ! [X0] : ((~quiet(X0) <~> old(X0)) <=> ~quiet(X0)) [input p1]
12. ! [X0] : ((brave(X0) | curious(X0)) <=> (kind(X0) & calm(X0))) [input p11]
15. (old(susan) & ~calm(susan)) <=> ? [X0] : ~brave(X0) [input p14]
23. ~kind(john) [input hypothesis]
44. ! [X0] : ((((~old(X0) | quiet(X0)) & (old(X0) | ~quiet(X0))) | quiet(X0)) & (~quiet(X0) | ((~quiet(X0) | ~old(X0)) & (old(X0) | quiet(X0))))) [nnf transformation 2]
60. ! [X0] : (((brave(X0) | curious(X0)) | (~kind(X0) | ~calm(X0))) & ((kind(X0) & calm(X0)) | (~brave(X0) & ~curious(X0)))) [nnf transformation 12]
61. ! [X0] : ((brave(X0) | curious(X0) | ~kind(X0) | ~calm(X0)) & ((kind(X0) & calm(X0)) | (~brave(X0) & ~curious(X0)))) [flattening 60]
67. ((old(susan) & ~calm(susan)) | ! [X0] : brave(X0)) & (? [X0] : ~brave(X0) | (~old(susan) | calm(susan))) [nnf transformation 15]
68. ((old(susan) & ~calm(susan)) | ! [X0] : brave(X0)) & (? [X0] : ~brave(X0) | ~old(susan) | calm(susan)) [flattening 67]
69. ((old(susan) & ~calm(susan)) | ! [X0] : brave(X0)) & (? [X1] : ~brave(X1) | ~old(susan) | calm(susan)) [rectify 68]
70. ? [X1] : ~brave(X1) => ~brave(sK6) [choice axiom]
71. ((old(susan) & ~calm(susan)) | ! [X0] : brave(X0)) & (~brave(sK6) | ~old(susan) | calm(susan)) [skolemisation 69,70]
85. ~quiet(X0) | ~quiet(X0) | ~old(X0) [cnf transformation 44]
87. ~old(X0) | quiet(X0) | quiet(X0) [cnf transformation 44]
117. ~brave(X0) | kind(X0) [cnf transformation 61]
127. old(susan) | brave(X0) [cnf transformation 71]
137. ~kind(john) [cnf transformation 23]
138. ~quiet(X0) | ~old(X0) [duplicate literal removal 85]
139. ~old(X0) | quiet(X0) [duplicate literal removal 87]
165. ~old(X0) [subsumption resolution 138,139]
258. brave(X0) [subsumption resolution 127,165]
268. kind(X0) [resolution 117,258]
275. $false [resolution 268,137]
% SZS output end Proof for 5030745363425435061912653
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not strong or not generous is not humble or not funny. Everyone who is not kind is both not curious and not patient. If someone is brave then susan is both kind and not kind. Everyone who is curious is not creative and vice versa. Everyone who is not patient or not rich is quiet or not old and vice versa. If someone is either quiet or curious then someone is either not old or calm and vice versa. Everyone who is either not happy or curious is not old. Everyone who is both not brave and curious is either not funny or funny and vice versa. Everyone who is both happy and not quiet is both not brave and not humble and vice versa. If someone is either kind or not old then lucy is happy and vice versa. Everyone who is either kind or not curious is not calm and vice versa. If susan is both generous and not curious then someone is not funny or not old. If someone is not happy then someone is either not happy or not funny. Everyone who is either old or not humble is funny or quiet and vice versa. If lucy is both calm and not old then susan is either creative or quiet. Someone is not kind or curious. Someone is creative or not wise. Mary is quiet. Mary is not calm or quiet. Someone is both not patient and old. Someone is not brave or not tall. | Lucy is not funny. | contradiction | (![X]:((~strong(X)|~generous(X))=>(~humble(X)|~funny(X))))&
(![X]:(~kind(X)=>(~curious(X)&~patient(X))))&
((?[X]:(brave(X)))=>((kind(susan)&~kind(susan))))&
(![X]:(curious(X)<=>~creative(X)))&
(![X]:((~patient(X)|~rich(X))<=>(quiet(X)|~old(X))))&
((?[X]:((quiet(X)<~>curious(X))))<=>(?[X]:((~old(X)<~>calm(X)))))&
(![X]:((~happy(X)<~>curious(X))=>~old(X)))&
(![X]:((~brave(X)&curious(X))<=>(~funny(X)<~>funny(X))))&
(![X]:((happy(X)&~quiet(X))<=>(~brave(X)&~humble(X))))&
((?[X]:((kind(X)<~>~old(X))))<=>(happy(lucy)))&
(![X]:((kind(X)<~>~curious(X))<=>~calm(X)))&
(((generous(susan)&~curious(susan)))=>(?[X]:((~funny(X)|~old(X)))))&
((?[X]:(~happy(X)))=>(?[X]:((~happy(X)<~>~funny(X)))))&
(![X]:((old(X)<~>~humble(X))<=>(funny(X)|quiet(X))))&
(((calm(lucy)&~old(lucy)))=>((creative(susan)<~>quiet(susan))))&
(?[X]:((~kind(X)|curious(X))))&
(?[X]:((creative(X)|~wise(X))))&
(quiet(mary))&
((~calm(mary)|quiet(mary)))&
(?[X]:((~patient(X)&old(X))))&
(?[X]:((~brave(X)|~tall(X)))) | ~funny(lucy) | [
"p1",
"p6",
"p7",
"p8",
"p9",
"p13",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 3612952292068104782460363
% SZS output start Proof for 3612952292068104782460363
2. ! [X0] : (~kind(X0) => (~patient(X0) & ~curious(X0))) [input p1]
7. ! [X0] : ((~happy(X0) <~> curious(X0)) => ~old(X0)) [input p6]
8. ! [X0] : ((curious(X0) & ~brave(X0)) <=> (~funny(X0) <~> funny(X0))) [input p7]
9. ! [X0] : ((~quiet(X0) & happy(X0)) <=> (~humble(X0) & ~brave(X0))) [input p8]
10. ? [X0] : (kind(X0) <~> ~old(X0)) <=> happy(lucy) [input p9]
14. ! [X0] : ((old(X0) <~> ~humble(X0)) <=> (quiet(X0) | funny(X0))) [input p13]
20. ? [X0] : (old(X0) & ~patient(X0)) [input p19]
22. ~funny(lucy) [input hypothesis]
30. ! [X0] : ((~patient(X0) & ~curious(X0)) | kind(X0)) [ennf transformation 2]
32. ! [X0] : (~old(X0) | (~happy(X0) <=> curious(X0))) [ennf transformation 7]
46. ! [X0] : (~old(X0) | ((~happy(X0) | ~curious(X0)) & (curious(X0) | happy(X0)))) [nnf transformation 32]
47. ! [X0] : (((curious(X0) & ~brave(X0)) | ((~funny(X0) | ~funny(X0)) & (funny(X0) | funny(X0)))) & (((~funny(X0) | funny(X0)) & (funny(X0) | ~funny(X0))) | (~curious(X0) | brave(X0)))) [nnf transformation 8]
48. ! [X0] : (((curious(X0) & ~brave(X0)) | ((~funny(X0) | ~funny(X0)) & (funny(X0) | funny(X0)))) & (((~funny(X0) | funny(X0)) & (funny(X0) | ~funny(X0))) | ~curious(X0) | brave(X0))) [flattening 47]
49. ! [X0] : (((~quiet(X0) & happy(X0)) | (humble(X0) | brave(X0))) & ((~humble(X0) & ~brave(X0)) | (quiet(X0) | ~happy(X0)))) [nnf transformation 9]
50. ! [X0] : (((~quiet(X0) & happy(X0)) | humble(X0) | brave(X0)) & ((~humble(X0) & ~brave(X0)) | quiet(X0) | ~happy(X0))) [flattening 49]
51. (? [X0] : ((old(X0) | ~kind(X0)) & (~old(X0) | kind(X0))) | ~happy(lucy)) & (happy(lucy) | ! [X0] : ((kind(X0) | old(X0)) & (~old(X0) | ~kind(X0)))) [nnf transformation 10]
52. (? [X0] : ((old(X0) | ~kind(X0)) & (~old(X0) | kind(X0))) | ~happy(lucy)) & (happy(lucy) | ! [X1] : ((kind(X1) | old(X1)) & (~old(X1) | ~kind(X1)))) [rectify 51]
53. ? [X0] : ((old(X0) | ~kind(X0)) & (~old(X0) | kind(X0))) => ((old(sK2) | ~kind(sK2)) & (~old(sK2) | kind(sK2))) [choice axiom]
54. (((old(sK2) | ~kind(sK2)) & (~old(sK2) | kind(sK2))) | ~happy(lucy)) & (happy(lucy) | ! [X1] : ((kind(X1) | old(X1)) & (~old(X1) | ~kind(X1)))) [skolemisation 52,53]
62. ! [X0] : ((((humble(X0) | ~old(X0)) & (~humble(X0) | old(X0))) | (~quiet(X0) & ~funny(X0))) & ((quiet(X0) | funny(X0)) | ((old(X0) | humble(X0)) & (~humble(X0) | ~old(X0))))) [nnf transformation 14]
63. ! [X0] : ((((humble(X0) | ~old(X0)) & (~humble(X0) | old(X0))) | (~quiet(X0) & ~funny(X0))) & (quiet(X0) | funny(X0) | ((old(X0) | humble(X0)) & (~humble(X0) | ~old(X0))))) [flattening 62]
67. ? [X0] : (old(X0) & ~patient(X0)) => (old(sK6) & ~patient(sK6)) [choice axiom]
68. old(sK6) & ~patient(sK6) [skolemisation 20,67]
70. ~curious(X0) | kind(X0) [cnf transformation 30]
89. ~happy(X0) | ~old(X0) | ~curious(X0) [cnf transformation 46]
92. ~brave(X0) | funny(X0) | funny(X0) [cnf transformation 48]
93. ~brave(X0) | ~funny(X0) | ~funny(X0) [cnf transformation 48]
94. curious(X0) | funny(X0) | funny(X0) [cnf transformation 48]
95. curious(X0) | ~funny(X0) | ~funny(X0) [cnf transformation 48]
97. ~happy(X0) | quiet(X0) | ~humble(X0) [cnf transformation 50]
98. happy(X0) | humble(X0) | brave(X0) [cnf transformation 50]
99. ~quiet(X0) | humble(X0) | brave(X0) [cnf transformation 50]
100. happy(lucy) | ~old(X1) | ~kind(X1) [cnf transformation 54]
112. old(X0) | funny(X0) | quiet(X0) | humble(X0) [cnf transformation 63]
114. ~quiet(X0) | old(X0) | ~humble(X0) [cnf transformation 63]
123. old(sK6) [cnf transformation 68]
124. ~funny(lucy) [cnf transformation 22]
125. ~brave(X0) | funny(X0) [duplicate literal removal 92]
126. ~brave(X0) | ~funny(X0) [duplicate literal removal 93]
127. curious(X0) | funny(X0) [duplicate literal removal 94]
128. ~funny(X0) | curious(X0) [duplicate literal removal 95]
130. 1 <=> ! [X0] : ~brave(X0) [avatar definition]
131. ~brave(X0) <- (1) [avatar component clause 130]
174. curious(X0) [subsumption resolution 127,128]
175. ~brave(X0) [subsumption resolution 125,126]
176. 1 [avatar split clause 175,130]
178. 11 <=> happy(lucy) [avatar definition]
179. happy(lucy) <- (11) [avatar component clause 178]
196. 15 <=> ! [X1] : (~old(X1) | ~kind(X1)) [avatar definition]
197. ~old(X1) | ~kind(X1) <- (15) [avatar component clause 196]
198. 15 | 11 [avatar split clause 100,178,196]
218. 20 <=> old(lucy) [avatar definition]
219. ~old(lucy) <- (~20) [avatar component clause 218]
233. kind(X0) [resolution 70,174]
249. ~old(X1) <- (15) [subsumption resolution 197,233]
252. $false <- (15) [resolution 249,123]
253. ~15 [avatar contradiction clause 252]
280. ~old(lucy) | ~curious(lucy) <- (11) [resolution 89,179]
282. ~old(lucy) <- (11) [subsumption resolution 280,174]
283. ~20 | ~11 [avatar split clause 282,178,218]
287. quiet(lucy) | ~humble(lucy) <- (11) [resolution 97,179]
298. 30 <=> humble(lucy) [avatar definition]
299. humble(lucy) <- (30) [avatar component clause 298]
302. 31 <=> quiet(lucy) [avatar definition]
304. quiet(lucy) <- (31) [avatar component clause 302]
305. ~30 | 31 | ~11 [avatar split clause 287,178,302,298]
308. humble(X2) | brave(X2) | ~old(X2) | ~curious(X2) [resolution 98,89]
309. humble(X2) | ~old(X2) | ~curious(X2) <- (1) [subsumption resolution 308,131]
310. ~old(X2) | humble(X2) <- (1) [subsumption resolution 309,174]
342. funny(X6) | quiet(X6) | humble(X6) | humble(X6) <- (1) [resolution 112,310]
346. quiet(X6) | funny(X6) | humble(X6) <- (1) [duplicate literal removal 342]
391. funny(X1) | humble(X1) | humble(X1) | brave(X1) <- (1) [resolution 346,99]
393. funny(X1) | humble(X1) | brave(X1) <- (1) [duplicate literal removal 391]
394. funny(X1) | humble(X1) <- (1) [subsumption resolution 393,131]
398. humble(lucy) <- (1) [resolution 394,124]
407. 30 | ~1 [avatar split clause 398,130,298]
415. old(lucy) | ~humble(lucy) <- (31) [resolution 304,114]
418. ~humble(lucy) <- (~20, 31) [subsumption resolution 415,219]
419. $false <- (~20, 30, 31) [subsumption resolution 418,299]
420. 20 | ~30 | ~31 [avatar contradiction clause 419]
430. $false [avatar sat refutation 176,198,253,283,305,407,420]
% SZS output end Proof for 3612952292068104782460363
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either curious or kind then fred is tall.
Everyone who is strong is both not old and not wise and vice versa.
If someone is not rich then someone is quiet or not rich.
If someone is not generous or curious then lucy is not brave and vice versa.
Everyone who is brave is both not creative and not quiet and vice versa.
If paul is wise then lucy is happy and vice versa.
Everyone who is both not humble and humble is not calm or not quiet and vice versa.
Everyone who is either funny or not wise is both tall and not quiet and vice versa.
Everyone who is both not curious and not patient is not happy or rich.
If paul is either not tall or not quiet then someone is not curious and vice versa.
If alice is tall then paul is not patient.
If alice is tall then john is not tall or quiet and vice versa.
If someone is not humble or calm then paul is both curious and not brave.
Everyone who is both rich and not old is not patient and vice versa.
Everyone who is either not curious or not kind is not humble.
Everyone who is both brave and not humble is either tall or old.
Someone is both happy and not humble.
Paul is either generous or brave.
Someone is old.
Fred is strong or funny.
Someone is not kind or humble. | Fred is funny. | entailment | ((?[X]:((curious(X)<~>kind(X))))=>(tall(fred)))&
(![X]:(strong(X)<=>(~old(X)&~wise(X))))&
((?[X]:(~rich(X)))=>(?[X]:((quiet(X)|~rich(X)))))&
((?[X]:((~generous(X)|curious(X))))<=>(~brave(lucy)))&
(![X]:(brave(X)<=>(~creative(X)&~quiet(X))))&
((wise(paul))<=>(happy(lucy)))&
(![X]:((~humble(X)&humble(X))<=>(~calm(X)|~quiet(X))))&
(![X]:((funny(X)<~>~wise(X))<=>(tall(X)&~quiet(X))))&
(![X]:((~curious(X)&~patient(X))=>(~happy(X)|rich(X))))&
(((~tall(paul)<~>~quiet(paul)))<=>(?[X]:(~curious(X))))&
((tall(alice))=>(~patient(paul)))&
((tall(alice))<=>((~tall(john)|quiet(john))))&
((?[X]:((~humble(X)|calm(X))))=>((curious(paul)&~brave(paul))))&
(![X]:((rich(X)&~old(X))<=>~patient(X)))&
(![X]:((~curious(X)<~>~kind(X))=>~humble(X)))&
(![X]:((brave(X)&~humble(X))=>(tall(X)<~>old(X))))&
(?[X]:((happy(X)&~humble(X))))&
((generous(paul)<~>brave(paul)))&
(?[X]:(old(X)))&
((strong(fred)|funny(fred)))&
(?[X]:((~kind(X)|humble(X)))) | funny(fred) | [
"p1",
"p6",
"p7",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 6411623741870137867572232
% SZS output start Proof for 6411623741870137867572232
2. ! [X0] : (strong(X0) <=> (~wise(X0) & ~old(X0))) [input p1]
7. ! [X0] : ((humble(X0) & ~humble(X0)) <=> (~quiet(X0) | ~calm(X0))) [input p6]
8. ! [X0] : ((funny(X0) <~> ~wise(X0)) <=> (~quiet(X0) & tall(X0))) [input p7]
20. funny(fred) | strong(fred) [input p19]
22. ~funny(fred) [input hypothesis]
24. ! [X0] : (strong(X0) => (~wise(X0) & ~old(X0))) [unused predicate definition removal 2]
26. ! [X0] : ((~wise(X0) & ~old(X0)) | ~strong(X0)) [ennf transformation 24]
46. ! [X0] : (((humble(X0) & ~humble(X0)) | (quiet(X0) & calm(X0))) & ((~quiet(X0) | ~calm(X0)) | (~humble(X0) | humble(X0)))) [nnf transformation 7]
47. ! [X0] : (((humble(X0) & ~humble(X0)) | (quiet(X0) & calm(X0))) & (~quiet(X0) | ~calm(X0) | ~humble(X0) | humble(X0))) [flattening 46]
48. ! [X0] : ((((wise(X0) | ~funny(X0)) & (~wise(X0) | funny(X0))) | (quiet(X0) | ~tall(X0))) & ((~quiet(X0) & tall(X0)) | ((funny(X0) | wise(X0)) & (~wise(X0) | ~funny(X0))))) [nnf transformation 8]
49. ! [X0] : ((((wise(X0) | ~funny(X0)) & (~wise(X0) | funny(X0))) | quiet(X0) | ~tall(X0)) & ((~quiet(X0) & tall(X0)) | ((funny(X0) | wise(X0)) & (~wise(X0) | ~funny(X0))))) [flattening 48]
70. ~wise(X0) | ~strong(X0) [cnf transformation 26]
82. ~humble(X0) | quiet(X0) [cnf transformation 47]
84. humble(X0) | quiet(X0) [cnf transformation 47]
88. ~quiet(X0) | funny(X0) | wise(X0) [cnf transformation 49]
116. funny(fred) | strong(fred) [cnf transformation 20]
118. ~funny(fred) [cnf transformation 22]
174. quiet(X0) [subsumption resolution 82,84]
176. funny(X0) | wise(X0) [subsumption resolution 88,174]
213. 20 <=> strong(fred) [avatar definition]
215. strong(fred) <- (20) [avatar component clause 213]
217. 21 <=> funny(fred) [avatar definition]
218. ~funny(fred) <- (~21) [avatar component clause 217]
220. 20 | 21 [avatar split clause 116,217,213]
230. ~21 [avatar split clause 118,217]
235. wise(fred) <- (~21) [resolution 176,218]
237. ~strong(fred) <- (~21) [resolution 235,70]
238. $false <- (20, ~21) [subsumption resolution 237,215]
239. ~20 | 21 [avatar contradiction clause 238]
240. $false [avatar sat refutation 220,230,239]
% SZS output end Proof for 6411623741870137867572232
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave and generous is not happy and vice versa.
Everyone who is either not creative or quiet is either not wise or humble and vice versa.
Everyone who is not quiet or not generous is either curious or not old and vice versa.
Everyone who is either not quiet or not patient is both not curious and quiet.
Everyone who is either not old or not rich is both not quiet and calm and vice versa.
If someone is either not wise or not brave then someone is not wise.
If alice is tall or not rich then someone is both calm and not happy and vice versa.
Everyone who is both not brave and not kind is not strong or quiet.
If someone is not humble then john is either brave or rich and vice versa.
If paul is not humble or old then someone is either not creative or not strong.
If alice is both creative and tall then someone is funny and vice versa.
If someone is both not curious and not tall then someone is either curious or not old and vice versa.
Everyone who is not tall or not brave is both kind and curious.
Everyone who is tall or happy is not brave or humble.
If alice is not patient then mary is either not creative or brave and vice versa.
Everyone who is not strong or not wise is both calm and not humble and vice versa.
Someone is both funny and patient.
Fred is quiet.
Someone is either not calm or not kind.
Someone is tall.
Someone is creative.
Mary is either not rich or rich.
Paul is either quiet or old.
Lucy is funny or generous. | Paul is rich. | contradiction | (![X]:((brave(X)&generous(X))<=>~happy(X)))&
(![X]:((~creative(X)<~>quiet(X))<=>(~wise(X)<~>humble(X))))&
(![X]:((~quiet(X)|~generous(X))<=>(curious(X)<~>~old(X))))&
(![X]:((~quiet(X)<~>~patient(X))=>(~curious(X)&quiet(X))))&
(![X]:((~old(X)<~>~rich(X))<=>(~quiet(X)&calm(X))))&
((?[X]:((~wise(X)<~>~brave(X))))=>(?[X]:(~wise(X))))&
(((tall(alice)|~rich(alice)))<=>(?[X]:((calm(X)&~happy(X)))))&
(![X]:((~brave(X)&~kind(X))=>(~strong(X)|quiet(X))))&
((?[X]:(~humble(X)))<=>((brave(john)<~>rich(john))))&
(((~humble(paul)|old(paul)))=>(?[X]:((~creative(X)<~>~strong(X)))))&
(((creative(alice)&tall(alice)))<=>(?[X]:(funny(X))))&
((?[X]:((~curious(X)&~tall(X))))<=>(?[X]:((curious(X)<~>~old(X)))))&
(![X]:((~tall(X)|~brave(X))=>(kind(X)&curious(X))))&
(![X]:((tall(X)|happy(X))=>(~brave(X)|humble(X))))&
((~patient(alice))<=>((~creative(mary)<~>brave(mary))))&
(![X]:((~strong(X)|~wise(X))<=>(calm(X)&~humble(X))))&
(?[X]:((funny(X)&patient(X))))&
(quiet(fred))&
(?[X]:((~calm(X)<~>~kind(X))))&
(?[X]:(tall(X)))&
(?[X]:(creative(X)))&
((~rich(mary)<~>rich(mary)))&
((quiet(paul)<~>old(paul)))&
((funny(lucy)|generous(lucy))) | rich(paul) | [
"p2",
"p4",
"p11",
"p12",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 393227149884910468269071
% SZS output start Proof for 393227149884910468269071
3. ! [X0] : ((~generous(X0) | ~quiet(X0)) <=> (curious(X0) <~> ~old(X0))) [input p2]
5. ! [X0] : ((~old(X0) <~> ~rich(X0)) <=> (calm(X0) & ~quiet(X0))) [input p4]
12. ? [X0] : (~tall(X0) & ~curious(X0)) <=> ? [X0] : (curious(X0) <~> ~old(X0)) [input p11]
13. ! [X0] : ((~brave(X0) | ~tall(X0)) => (curious(X0) & kind(X0))) [input p12]
23. quiet(paul) <~> old(paul) [input p22]
25. rich(paul) [input hypothesis]
27. ? [X0] : (~tall(X0) & ~curious(X0)) <=> ? [X1] : (curious(X1) <~> ~old(X1)) [rectify 12]
33. ! [X0] : ((curious(X0) & kind(X0)) | (brave(X0) & tall(X0))) [ennf transformation 13]
39. ! [X0] : (((~generous(X0) | ~quiet(X0)) | ((curious(X0) | old(X0)) & (~old(X0) | ~curious(X0)))) & (((old(X0) | ~curious(X0)) & (~old(X0) | curious(X0))) | (generous(X0) & quiet(X0)))) [nnf transformation 3]
40. ! [X0] : ((~generous(X0) | ~quiet(X0) | ((curious(X0) | old(X0)) & (~old(X0) | ~curious(X0)))) & (((old(X0) | ~curious(X0)) & (~old(X0) | curious(X0))) | (generous(X0) & quiet(X0)))) [flattening 39]
42. ! [X0] : ((((rich(X0) | old(X0)) & (~rich(X0) | ~old(X0))) | (~calm(X0) | quiet(X0))) & ((calm(X0) & ~quiet(X0)) | ((~old(X0) | rich(X0)) & (~rich(X0) | old(X0))))) [nnf transformation 5]
43. ! [X0] : ((((rich(X0) | old(X0)) & (~rich(X0) | ~old(X0))) | ~calm(X0) | quiet(X0)) & ((calm(X0) & ~quiet(X0)) | ((~old(X0) | rich(X0)) & (~rich(X0) | old(X0))))) [flattening 42]
65. (? [X0] : (~tall(X0) & ~curious(X0)) | ! [X1] : ((curious(X1) | old(X1)) & (~old(X1) | ~curious(X1)))) & (? [X1] : ((old(X1) | ~curious(X1)) & (~old(X1) | curious(X1))) | ! [X0] : (tall(X0) | curious(X0))) [nnf transformation 27]
66. (? [X0] : (~tall(X0) & ~curious(X0)) | ! [X1] : ((curious(X1) | old(X1)) & (~old(X1) | ~curious(X1)))) & (? [X2] : ((old(X2) | ~curious(X2)) & (~old(X2) | curious(X2))) | ! [X3] : (tall(X3) | curious(X3))) [rectify 65]
67. ? [X0] : (~tall(X0) & ~curious(X0)) => (~tall(sK5) & ~curious(sK5)) [choice axiom]
68. ? [X2] : ((old(X2) | ~curious(X2)) & (~old(X2) | curious(X2))) => ((old(sK6) | ~curious(sK6)) & (~old(sK6) | curious(sK6))) [choice axiom]
69. ((~tall(sK5) & ~curious(sK5)) | ! [X1] : ((curious(X1) | old(X1)) & (~old(X1) | ~curious(X1)))) & (((old(sK6) | ~curious(sK6)) & (~old(sK6) | curious(sK6))) | ! [X3] : (tall(X3) | curious(X3))) [skolemisation 66,68,67]
83. (~old(paul) | ~quiet(paul)) & (old(paul) | quiet(paul)) [nnf transformation 23]
95. ~old(X0) | curious(X0) | quiet(X0) [cnf transformation 40]
105. ~rich(X0) | ~quiet(X0) | old(X0) [cnf transformation 43]
132. ~curious(sK5) | ~old(X1) | ~curious(X1) [cnf transformation 69]
134. ~tall(sK5) | ~old(X1) | ~curious(X1) [cnf transformation 69]
138. curious(X0) | tall(X0) [cnf transformation 33]
160. old(paul) | quiet(paul) [cnf transformation 83]
161. ~old(paul) | ~quiet(paul) [cnf transformation 83]
163. rich(paul) [cnf transformation 25]
221. 13 <=> old(paul) [avatar definition]
222. old(paul) <- (13) [avatar component clause 221]
223. ~old(paul) <- (~13) [avatar component clause 221]
258. 21 <=> tall(sK5) [avatar definition]
260. ~tall(sK5) <- (~21) [avatar component clause 258]
263. 22 <=> ! [X1] : (~old(X1) | ~curious(X1)) [avatar definition]
264. ~old(X1) | ~curious(X1) <- (22) [avatar component clause 263]
265. 22 | ~21 [avatar split clause 134,258,263]
267. 23 <=> curious(sK5) [avatar definition]
269. ~curious(sK5) <- (~23) [avatar component clause 267]
271. 22 | ~23 [avatar split clause 132,267,263]
273. 24 <=> ! [X3] : (tall(X3) | curious(X3)) [avatar definition]
274. tall(X3) | curious(X3) <- (24) [avatar component clause 273]
285. 24 [avatar split clause 138,273]
313. 32 <=> quiet(paul) [avatar definition]
314. quiet(paul) <- (32) [avatar component clause 313]
315. ~quiet(paul) <- (~32) [avatar component clause 313]
316. ~32 | ~13 [avatar split clause 161,221,313]
317. 32 | 13 [avatar split clause 160,221,313]
342. curious(sK5) <- (~21, 24) [resolution 274,260]
343. $false <- (~21, ~23, 24) [subsumption resolution 342,269]
344. 21 | 23 | ~24 [avatar contradiction clause 343]
345. ~curious(paul) <- (13, 22) [resolution 264,222]
350. curious(paul) | quiet(paul) <- (13) [resolution 95,222]
353. quiet(paul) <- (13, 22) [subsumption resolution 350,345]
354. $false <- (13, 22, ~32) [subsumption resolution 353,315]
355. ~13 | ~22 | 32 [avatar contradiction clause 354]
373. ~quiet(paul) | old(paul) [resolution 105,163]
376. old(paul) <- (32) [subsumption resolution 373,314]
377. $false <- (~13, 32) [subsumption resolution 376,223]
378. 13 | ~32 [avatar contradiction clause 377]
381. $false [avatar sat refutation 265,271,285,316,317,344,355,378]
% SZS output end Proof for 393227149884910468269071
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either funny or not curious is either old or tall. Everyone who is not patient is happy and vice versa. If lucy is both wise and not wise then someone is not curious or rich. If someone is either not old or not curious then paul is either not happy or kind and vice versa. Everyone who is patient or strong is not curious or not humble. Everyone who is calm or not old is not creative and vice versa. If alice is not strong then someone is not kind. Everyone who is not brave or not humble is brave and vice versa. Everyone who is not rich is both not funny and quiet. If mary is either happy or calm then paul is both calm and not brave and vice versa. Everyone who is either wise or not quiet is either not brave or not quiet and vice versa. If john is funny then paul is not tall. Everyone who is calm is not old or calm. Everyone who is either creative or rich is both not quiet and curious. Everyone who is humble or not happy is creative or not calm. Everyone who is not rich is generous or not humble and vice versa. Mary is curious or strong. Alice is tall or not calm. Someone is not kind or brave. Mary is either not quiet or not rich. Someone is either strong or patient. Someone is both not calm and generous. Someone is not patient. | Alice is creative. | contradiction | (![X]:((funny(X)<~>~curious(X))=>(old(X)<~>tall(X))))&
(![X]:(~patient(X)<=>happy(X)))&
(((wise(lucy)&~wise(lucy)))=>(?[X]:((~curious(X)|rich(X)))))&
((?[X]:((~old(X)<~>~curious(X))))<=>((~happy(paul)<~>kind(paul))))&
(![X]:((patient(X)|strong(X))=>(~curious(X)|~humble(X))))&
(![X]:((calm(X)|~old(X))<=>~creative(X)))&
((~strong(alice))=>(?[X]:(~kind(X))))&
(![X]:((~brave(X)|~humble(X))<=>brave(X)))&
(![X]:(~rich(X)=>(~funny(X)&quiet(X))))&
(((happy(mary)<~>calm(mary)))<=>((calm(paul)&~brave(paul))))&
(![X]:((wise(X)<~>~quiet(X))<=>(~brave(X)<~>~quiet(X))))&
((funny(john))=>(~tall(paul)))&
(![X]:(calm(X)=>(~old(X)|calm(X))))&
(![X]:((creative(X)<~>rich(X))=>(~quiet(X)&curious(X))))&
(![X]:((humble(X)|~happy(X))=>(creative(X)|~calm(X))))&
(![X]:(~rich(X)<=>(generous(X)|~humble(X))))&
((curious(mary)|strong(mary)))&
((tall(alice)|~calm(alice)))&
(?[X]:((~kind(X)|brave(X))))&
((~quiet(mary)<~>~rich(mary)))&
(?[X]:((strong(X)<~>patient(X))))&
(?[X]:((~calm(X)&generous(X))))&
(?[X]:(~patient(X))) | creative(alice) | [
"p7",
"p8",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 876943903285239400278584
% SZS output start Proof for 876943903285239400278584
8. ! [X0] : ((~humble(X0) | ~brave(X0)) <=> brave(X0)) [input p7]
9. ! [X0] : (~rich(X0) => (quiet(X0) & ~funny(X0))) [input p8]
14. ! [X0] : ((creative(X0) <~> rich(X0)) => (curious(X0) & ~quiet(X0))) [input p13]
16. ! [X0] : (~rich(X0) <=> (~humble(X0) | generous(X0))) [input p15]
24. creative(alice) [input hypothesis]
31. ! [X0] : ((quiet(X0) & ~funny(X0)) | rich(X0)) [ennf transformation 9]
35. ! [X0] : ((curious(X0) & ~quiet(X0)) | (creative(X0) <=> rich(X0))) [ennf transformation 14]
50. ! [X0] : (((~humble(X0) | ~brave(X0)) | ~brave(X0)) & (brave(X0) | (humble(X0) & brave(X0)))) [nnf transformation 8]
51. ! [X0] : ((~humble(X0) | ~brave(X0) | ~brave(X0)) & (brave(X0) | (humble(X0) & brave(X0)))) [flattening 50]
55. ! [X0] : ((curious(X0) & ~quiet(X0)) | ((creative(X0) | ~rich(X0)) & (rich(X0) | ~creative(X0)))) [nnf transformation 35]
56. ! [X0] : ((~rich(X0) | (humble(X0) & ~generous(X0))) & ((~humble(X0) | generous(X0)) | rich(X0))) [nnf transformation 16]
57. ! [X0] : ((~rich(X0) | (humble(X0) & ~generous(X0))) & (~humble(X0) | generous(X0) | rich(X0))) [flattening 56]
89. brave(X0) | brave(X0) [cnf transformation 51]
91. ~humble(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 51]
93. quiet(X0) | rich(X0) [cnf transformation 31]
110. ~quiet(X0) | rich(X0) | ~creative(X0) [cnf transformation 55]
118. ~rich(X0) | humble(X0) [cnf transformation 57]
129. creative(alice) [cnf transformation 24]
134. brave(X0) [duplicate literal removal 89]
135. ~brave(X0) | ~humble(X0) [duplicate literal removal 91]
205. ~creative(X0) | rich(X0) [subsumption resolution 110,93]
254. ~humble(X1) [resolution 135,134]
255. rich(alice) [resolution 205,129]
256. humble(alice) [resolution 255,118]
257. $false [subsumption resolution 256,254]
% SZS output end Proof for 876943903285239400278584
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm or not wise is not rich.
If john is humble or happy then someone is both not rich and not brave.
If fred is generous then paul is generous and vice versa.
If someone is either kind or not quiet then john is either not creative or strong.
Everyone who is not quiet is wise or not tall and vice versa.
Everyone who is not old is both not humble and generous.
Everyone who is not old or not tall is not generous.
Everyone who is not brave or not funny is not tall and vice versa.
Everyone who is not brave or curious is both not humble and not old.
Everyone who is not humble or calm is not rich and vice versa.
If someone is calm or not funny then someone is both not old and wise.
If susan is both happy and creative then lucy is tall.
Everyone who is both strong and old is either happy or not patient and vice versa.
Everyone who is both not kind and old is both patient and strong.
If john is both not creative and brave then lucy is both not rich and kind.
Someone is happy.
Someone is wise.
Someone is not wise or happy.
Someone is either not generous or creative.
Someone is either rich or not creative.
Someone is both not humble and not wise. | Paul is not tall. | contradiction | (![X]:((~calm(X)|~wise(X))=>~rich(X)))&
(((humble(john)|happy(john)))=>(?[X]:((~rich(X)&~brave(X)))))&
((generous(fred))<=>(generous(paul)))&
((?[X]:((kind(X)<~>~quiet(X))))=>((~creative(john)<~>strong(john))))&
(![X]:(~quiet(X)<=>(wise(X)|~tall(X))))&
(![X]:(~old(X)=>(~humble(X)&generous(X))))&
(![X]:((~old(X)|~tall(X))=>~generous(X)))&
(![X]:((~brave(X)|~funny(X))<=>~tall(X)))&
(![X]:((~brave(X)|curious(X))=>(~humble(X)&~old(X))))&
(![X]:((~humble(X)|calm(X))<=>~rich(X)))&
((?[X]:((calm(X)|~funny(X))))=>(?[X]:((~old(X)&wise(X)))))&
(((happy(susan)&creative(susan)))=>(tall(lucy)))&
(![X]:((strong(X)&old(X))<=>(happy(X)<~>~patient(X))))&
(![X]:((~kind(X)&old(X))=>(patient(X)&strong(X))))&
(((~creative(john)&brave(john)))=>((~rich(lucy)&kind(lucy))))&
(?[X]:(happy(X)))&
(?[X]:(wise(X)))&
(?[X]:((~wise(X)|happy(X))))&
(?[X]:((~generous(X)<~>creative(X))))&
(?[X]:((rich(X)<~>~creative(X))))&
(?[X]:((~humble(X)&~wise(X)))) | ~tall(paul) | [
"p5",
"p6",
"p7",
"p8",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 6316400508468369613497188
% SZS output start Proof for 6316400508468369613497188
6. ! [X0] : (~old(X0) => (generous(X0) & ~humble(X0))) [input p5]
7. ! [X0] : ((~tall(X0) | ~old(X0)) => ~generous(X0)) [input p6]
8. ! [X0] : ((~funny(X0) | ~brave(X0)) <=> ~tall(X0)) [input p7]
9. ! [X0] : ((curious(X0) | ~brave(X0)) => (~old(X0) & ~humble(X0))) [input p8]
11. ? [X0] : (~funny(X0) | calm(X0)) => ? [X0] : (wise(X0) & ~old(X0)) [input p10]
22. ~tall(paul) [input hypothesis]
23. ? [X0] : (~funny(X0) | calm(X0)) => ? [X1] : (wise(X1) & ~old(X1)) [rectify 11]
24. ! [X0] : (~brave(X0) => (~old(X0) & ~humble(X0))) [pure predicate removal 9]
28. ! [X0] : ((generous(X0) & ~humble(X0)) | old(X0)) [ennf transformation 6]
29. ! [X0] : (~generous(X0) | (tall(X0) & old(X0))) [ennf transformation 7]
30. ! [X0] : ((~old(X0) & ~humble(X0)) | brave(X0)) [ennf transformation 24]
31. ? [X1] : (wise(X1) & ~old(X1)) | ! [X0] : (funny(X0) & ~calm(X0)) [ennf transformation 23]
44. ! [X0] : (((~funny(X0) | ~brave(X0)) | tall(X0)) & (~tall(X0) | (funny(X0) & brave(X0)))) [nnf transformation 8]
45. ! [X0] : ((~funny(X0) | ~brave(X0) | tall(X0)) & (~tall(X0) | (funny(X0) & brave(X0)))) [flattening 44]
48. ? [X0] : (wise(X0) & ~old(X0)) | ! [X1] : (funny(X1) & ~calm(X1)) [rectify 31]
49. ? [X0] : (wise(X0) & ~old(X0)) => (wise(sK1) & ~old(sK1)) [choice axiom]
50. (wise(sK1) & ~old(sK1)) | ! [X1] : (funny(X1) & ~calm(X1)) [skolemisation 48,49]
83. old(X0) | generous(X0) [cnf transformation 28]
84. ~generous(X0) | old(X0) [cnf transformation 29]
88. ~funny(X0) | ~brave(X0) | tall(X0) [cnf transformation 45]
90. ~old(X0) | brave(X0) [cnf transformation 30]
95. ~old(sK1) | funny(X1) [cnf transformation 50]
118. ~tall(paul) [cnf transformation 22]
167. old(X0) [subsumption resolution 84,83]
168. brave(X0) [subsumption resolution 90,167]
172. 11 <=> ! [X1] : funny(X1) [avatar definition]
173. funny(X1) <- (11) [avatar component clause 172]
183. funny(X1) [subsumption resolution 95,167]
184. 11 [avatar split clause 183,172]
232. ~brave(X0) | tall(X0) <- (11) [resolution 88,173]
233. tall(X0) <- (11) [subsumption resolution 232,168]
235. $false <- (11) [resolution 233,118]
239. ~11 [avatar contradiction clause 235]
240. $false [avatar sat refutation 184,239]
% SZS output end Proof for 6316400508468369613497188
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either creative or brave then alice is humble or not patient.
Everyone who is not calm is creative and vice versa.
If susan is either quiet or not wise then john is both brave and humble and vice versa.
Everyone who is kind or wise is old.
If someone is both patient and quiet then someone is both strong and not quiet.
Everyone who is humble is either calm or brave and vice versa.
Everyone who is either not generous or calm is kind.
Everyone who is both not kind and not brave is both not funny and not kind.
Everyone who is not old or quiet is both not old and not happy.
Everyone who is not curious or calm is not happy.
Everyone who is both not creative and not kind is not rich or creative and vice versa.
If susan is not brave then someone is both tall and not tall.
Everyone who is both not rich and not calm is not calm or not happy.
Everyone who is either not generous or not curious is not calm.
Everyone who is either curious or kind is rich or not kind.
Someone is not quiet.
Someone is either not old or creative.
Paul is kind or not happy.
Someone is either patient or not tall.
Paul is not curious.
Fred is funny.
Someone is not tall.
Susan is calm or not rich. | John is creative. | contradiction | ((?[X]:((creative(X)<~>brave(X))))=>((humble(alice)|~patient(alice))))&
(![X]:(~calm(X)<=>creative(X)))&
(((quiet(susan)<~>~wise(susan)))<=>((brave(john)&humble(john))))&
(![X]:((kind(X)|wise(X))=>old(X)))&
((?[X]:((patient(X)&quiet(X))))=>(?[X]:((strong(X)&~quiet(X)))))&
(![X]:(humble(X)<=>(calm(X)<~>brave(X))))&
(![X]:((~generous(X)<~>calm(X))=>kind(X)))&
(![X]:((~kind(X)&~brave(X))=>(~funny(X)&~kind(X))))&
(![X]:((~old(X)|quiet(X))=>(~old(X)&~happy(X))))&
(![X]:((~curious(X)|calm(X))=>~happy(X)))&
(![X]:((~creative(X)&~kind(X))<=>(~rich(X)|creative(X))))&
((~brave(susan))=>(?[X]:((tall(X)&~tall(X)))))&
(![X]:((~rich(X)&~calm(X))=>(~calm(X)|~happy(X))))&
(![X]:((~generous(X)<~>~curious(X))=>~calm(X)))&
(![X]:((curious(X)<~>kind(X))=>(rich(X)|~kind(X))))&
(?[X]:(~quiet(X)))&
(?[X]:((~old(X)<~>creative(X))))&
((kind(paul)|~happy(paul)))&
(?[X]:((patient(X)<~>~tall(X))))&
(~curious(paul))&
(funny(fred))&
(?[X]:(~tall(X)))&
((calm(susan)|~rich(susan))) | creative(john) | [
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 2358849213800705164803062
% SZS output start Proof for 2358849213800705164803062
11. ! [X0] : ((~kind(X0) & ~creative(X0)) <=> (creative(X0) | ~rich(X0))) [input p10]
24. creative(john) [input hypothesis]
52. ! [X0] : (((~kind(X0) & ~creative(X0)) | (~creative(X0) & rich(X0))) & ((creative(X0) | ~rich(X0)) | (kind(X0) | creative(X0)))) [nnf transformation 11]
53. ! [X0] : (((~kind(X0) & ~creative(X0)) | (~creative(X0) & rich(X0))) & (creative(X0) | ~rich(X0) | kind(X0) | creative(X0))) [flattening 52]
93. ~creative(X0) | ~creative(X0) [cnf transformation 53]
111. creative(john) [cnf transformation 24]
114. ~creative(X0) [duplicate literal removal 93]
192. $false [subsumption resolution 111,114]
% SZS output end Proof for 2358849213800705164803062
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not old is either old or not kind and vice versa.
Everyone who is both happy and not generous is either generous or not happy and vice versa.
If someone is either not funny or not creative then lucy is either curious or kind and vice versa.
If someone is both creative and calm then susan is either quiet or not wise.
Everyone who is old is either not quiet or kind.
If alice is either not curious or not brave then someone is either not humble or wise and vice versa.
Everyone who is either funny or not rich is not creative or brave and vice versa.
If someone is not funny then susan is both quiet and old and vice versa.
Everyone who is not patient or not happy is both patient and quiet.
Everyone who is either humble or not calm is not happy or curious and vice versa.
Everyone who is both generous and not calm is happy.
Everyone who is not old is not tall or tall.
If alice is not brave then someone is both old and not rich and vice versa.
If someone is not kind or not creative then someone is quiet or calm and vice versa.
If someone is both not funny and not humble then john is either not tall or tall.
If someone is either not tall or not strong then someone is kind or strong.
Susan is not wise or not humble.
Alice is tall.
Alice is not wise or not calm.
Someone is humble or not funny.
Someone is either generous or happy.
Someone is either funny or kind. | Lucy is not curious. | contradiction | (![X]:(~old(X)<=>(old(X)<~>~kind(X))))&
(![X]:((happy(X)&~generous(X))<=>(generous(X)<~>~happy(X))))&
((?[X]:((~funny(X)<~>~creative(X))))<=>((curious(lucy)<~>kind(lucy))))&
((?[X]:((creative(X)&calm(X))))=>((quiet(susan)<~>~wise(susan))))&
(![X]:(old(X)=>(~quiet(X)<~>kind(X))))&
(((~curious(alice)<~>~brave(alice)))<=>(?[X]:((~humble(X)<~>wise(X)))))&
(![X]:((funny(X)<~>~rich(X))<=>(~creative(X)|brave(X))))&
((?[X]:(~funny(X)))<=>((quiet(susan)&old(susan))))&
(![X]:((~patient(X)|~happy(X))=>(patient(X)&quiet(X))))&
(![X]:((humble(X)<~>~calm(X))<=>(~happy(X)|curious(X))))&
(![X]:((generous(X)&~calm(X))=>happy(X)))&
(![X]:(~old(X)=>(~tall(X)|tall(X))))&
((~brave(alice))<=>(?[X]:((old(X)&~rich(X)))))&
((?[X]:((~kind(X)|~creative(X))))<=>(?[X]:((quiet(X)|calm(X)))))&
((?[X]:((~funny(X)&~humble(X))))=>((~tall(john)<~>tall(john))))&
((?[X]:((~tall(X)<~>~strong(X))))=>(?[X]:((kind(X)|strong(X)))))&
((~wise(susan)|~humble(susan)))&
(tall(alice))&
((~wise(alice)|~calm(alice)))&
(?[X]:((humble(X)|~funny(X))))&
(?[X]:((generous(X)<~>happy(X))))&
(?[X]:((funny(X)<~>kind(X)))) | ~curious(lucy) | [
"p0",
"p1",
"p2",
"p3",
"p4",
"p7",
"p8",
"p9",
"p10",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 130395973353114572822950
% SZS output start Proof for 130395973353114572822950
1. ! [X0] : (~old(X0) <=> (old(X0) <~> ~kind(X0))) [input p0]
2. ! [X0] : ((~generous(X0) & happy(X0)) <=> (generous(X0) <~> ~happy(X0))) [input p1]
3. ? [X0] : (~funny(X0) <~> ~creative(X0)) <=> (curious(lucy) <~> kind(lucy)) [input p2]
4. ? [X0] : (calm(X0) & creative(X0)) => (quiet(susan) <~> ~wise(susan)) [input p3]
5. ! [X0] : (old(X0) => (~quiet(X0) <~> kind(X0))) [input p4]
8. ? [X0] : ~funny(X0) <=> (old(susan) & quiet(susan)) [input p7]
9. ! [X0] : ((~happy(X0) | ~patient(X0)) => (quiet(X0) & patient(X0))) [input p8]
10. ! [X0] : ((humble(X0) <~> ~calm(X0)) <=> (curious(X0) | ~happy(X0))) [input p9]
11. ! [X0] : ((~calm(X0) & generous(X0)) => happy(X0)) [input p10]
17. ~humble(susan) | ~wise(susan) [input p16]
23. ~curious(lucy) [input hypothesis]
26. ! [X0] : (~happy(X0) => quiet(X0)) [pure predicate removal 9]
27. (quiet(susan) <~> ~wise(susan)) | ! [X0] : (~calm(X0) | ~creative(X0)) [ennf transformation 4]
28. ! [X0] : ((~quiet(X0) <~> kind(X0)) | ~old(X0)) [ennf transformation 5]
29. ! [X0] : (quiet(X0) | happy(X0)) [ennf transformation 26]
30. ! [X0] : (happy(X0) | (calm(X0) | ~generous(X0))) [ennf transformation 11]
31. ! [X0] : (happy(X0) | calm(X0) | ~generous(X0)) [flattening 30]
36. ! [X0] : ((~old(X0) | ((old(X0) | kind(X0)) & (~kind(X0) | ~old(X0)))) & (((kind(X0) | ~old(X0)) & (~kind(X0) | old(X0))) | old(X0))) [nnf transformation 1]
37. ! [X0] : (((~generous(X0) & happy(X0)) | ((generous(X0) | happy(X0)) & (~happy(X0) | ~generous(X0)))) & (((happy(X0) | ~generous(X0)) & (~happy(X0) | generous(X0))) | (generous(X0) | ~happy(X0)))) [nnf transformation 2]
38. ! [X0] : (((~generous(X0) & happy(X0)) | ((generous(X0) | happy(X0)) & (~happy(X0) | ~generous(X0)))) & (((happy(X0) | ~generous(X0)) & (~happy(X0) | generous(X0))) | generous(X0) | ~happy(X0))) [flattening 37]
39. (? [X0] : ((creative(X0) | funny(X0)) & (~creative(X0) | ~funny(X0))) | ((curious(lucy) | ~kind(lucy)) & (kind(lucy) | ~curious(lucy)))) & (((~kind(lucy) | ~curious(lucy)) & (kind(lucy) | curious(lucy))) | ! [X0] : ((~funny(X0) | creative(X0)) & (~creative(X0) | funny(X0)))) [nnf transformation 3]
40. (? [X0] : ((creative(X0) | funny(X0)) & (~creative(X0) | ~funny(X0))) | ((curious(lucy) | ~kind(lucy)) & (kind(lucy) | ~curious(lucy)))) & (((~kind(lucy) | ~curious(lucy)) & (kind(lucy) | curious(lucy))) | ! [X1] : ((~funny(X1) | creative(X1)) & (~creative(X1) | funny(X1)))) [rectify 39]
41. ? [X0] : ((creative(X0) | funny(X0)) & (~creative(X0) | ~funny(X0))) => ((creative(sK0) | funny(sK0)) & (~creative(sK0) | ~funny(sK0))) [choice axiom]
42. (((creative(sK0) | funny(sK0)) & (~creative(sK0) | ~funny(sK0))) | ((curious(lucy) | ~kind(lucy)) & (kind(lucy) | ~curious(lucy)))) & (((~kind(lucy) | ~curious(lucy)) & (kind(lucy) | curious(lucy))) | ! [X1] : ((~funny(X1) | creative(X1)) & (~creative(X1) | funny(X1)))) [skolemisation 40,41]
43. ((wise(susan) | ~quiet(susan)) & (~wise(susan) | quiet(susan))) | ! [X0] : (~calm(X0) | ~creative(X0)) [nnf transformation 27]
44. ! [X0] : (((~kind(X0) | quiet(X0)) & (kind(X0) | ~quiet(X0))) | ~old(X0)) [nnf transformation 28]
51. (? [X0] : ~funny(X0) | (~old(susan) | ~quiet(susan))) & ((old(susan) & quiet(susan)) | ! [X0] : funny(X0)) [nnf transformation 8]
52. (? [X0] : ~funny(X0) | ~old(susan) | ~quiet(susan)) & ((old(susan) & quiet(susan)) | ! [X0] : funny(X0)) [flattening 51]
53. (? [X0] : ~funny(X0) | ~old(susan) | ~quiet(susan)) & ((old(susan) & quiet(susan)) | ! [X1] : funny(X1)) [rectify 52]
54. ? [X0] : ~funny(X0) => ~funny(sK2) [choice axiom]
55. (~funny(sK2) | ~old(susan) | ~quiet(susan)) & ((old(susan) & quiet(susan)) | ! [X1] : funny(X1)) [skolemisation 53,54]
56. ! [X0] : ((((calm(X0) | ~humble(X0)) & (~calm(X0) | humble(X0))) | (~curious(X0) & happy(X0))) & ((curious(X0) | ~happy(X0)) | ((humble(X0) | calm(X0)) & (~calm(X0) | ~humble(X0))))) [nnf transformation 10]
57. ! [X0] : ((((calm(X0) | ~humble(X0)) & (~calm(X0) | humble(X0))) | (~curious(X0) & happy(X0))) & (curious(X0) | ~happy(X0) | ((humble(X0) | calm(X0)) & (~calm(X0) | ~humble(X0))))) [flattening 56]
80. ~kind(X0) | old(X0) | old(X0) [cnf transformation 36]
82. ~old(X0) | ~kind(X0) | ~old(X0) [cnf transformation 36]
84. ~happy(X0) | generous(X0) | generous(X0) | ~happy(X0) [cnf transformation 38]
87. happy(X0) | generous(X0) | happy(X0) [cnf transformation 38]
88. ~generous(X0) | ~happy(X0) | ~generous(X0) [cnf transformation 38]
91. kind(lucy) | curious(lucy) | ~funny(X1) | creative(X1) [cnf transformation 42]
99. wise(susan) | ~quiet(susan) | ~calm(X0) | ~creative(X0) [cnf transformation 43]
100. kind(X0) | ~quiet(X0) | ~old(X0) [cnf transformation 44]
117. old(susan) | funny(X1) [cnf transformation 55]
119. quiet(X0) | happy(X0) [cnf transformation 29]
122. ~calm(X0) | humble(X0) | happy(X0) [cnf transformation 57]
126. happy(X0) | calm(X0) | ~generous(X0) [cnf transformation 31]
139. ~humble(susan) | ~wise(susan) [cnf transformation 17]
147. ~curious(lucy) [cnf transformation 23]
148. ~happy(X0) | generous(X0) [duplicate literal removal 84]
149. generous(X0) | happy(X0) [duplicate literal removal 87]
150. ~generous(X0) | ~happy(X0) [duplicate literal removal 88]
151. ~kind(X0) | old(X0) [duplicate literal removal 80]
152. ~kind(X0) | ~old(X0) [duplicate literal removal 82]
153. ~kind(X0) [subsumption resolution 151,152]
154. generous(X0) [subsumption resolution 148,149]
157. 1 <=> curious(lucy) [avatar definition]
171. curious(lucy) | ~funny(X1) | creative(X1) [subsumption resolution 91,153]
173. 4 <=> ! [X1] : (~funny(X1) | creative(X1)) [avatar definition]
174. ~funny(X1) | creative(X1) <- (4) [avatar component clause 173]
175. 4 | 1 [avatar split clause 171,157,173]
182. 6 <=> ! [X0] : (~calm(X0) | ~creative(X0)) [avatar definition]
183. ~calm(X0) | ~creative(X0) <- (6) [avatar component clause 182]
185. 7 <=> quiet(susan) [avatar definition]
186. quiet(susan) <- (7) [avatar component clause 185]
187. ~quiet(susan) <- (~7) [avatar component clause 185]
189. 8 <=> wise(susan) [avatar definition]
192. 6 | ~7 | 8 [avatar split clause 99,189,185,182]
194. ~quiet(X0) | ~old(X0) [subsumption resolution 100,153]
226. 15 <=> ! [X1] : funny(X1) [avatar definition]
227. funny(X1) <- (15) [avatar component clause 226]
229. 16 <=> old(susan) [avatar definition]
231. old(susan) <- (16) [avatar component clause 229]
232. 15 | 16 [avatar split clause 117,229,226]
234. calm(X0) | happy(X0) [subsumption resolution 126,154]
250. 20 <=> ! [X3] : creative(X3) [avatar definition]
251. creative(X3) <- (20) [avatar component clause 250]
278. 26 <=> humble(susan) [avatar definition]
280. ~humble(susan) <- (~26) [avatar component clause 278]
281. ~8 | ~26 [avatar split clause 139,278,189]
301. ~1 [avatar split clause 147,157]
302. creative(X1) <- (4, 15) [subsumption resolution 174,227]
303. 20 | ~4 | ~15 [avatar split clause 302,226,173,250]
305. ~happy(X1) [resolution 150,154]
308. ~old(susan) <- (7) [resolution 194,186]
311. $false <- (7, 16) [subsumption resolution 308,231]
312. ~7 | ~16 [avatar contradiction clause 311]
318. happy(X0) | ~creative(X0) <- (6) [resolution 234,183]
319. ~creative(X0) <- (6) [subsumption resolution 318,305]
320. $false <- (6, 20) [subsumption resolution 319,251]
321. ~6 | ~20 [avatar contradiction clause 320]
326. humble(X0) | happy(X0) | happy(X0) [resolution 122,234]
327. humble(X0) | happy(X0) [duplicate literal removal 326]
328. humble(X0) [subsumption resolution 327,305]
333. $false <- (~26) [resolution 328,280]
334. 26 [avatar contradiction clause 333]
336. happy(susan) <- (~7) [resolution 187,119]
337. $false <- (~7) [subsumption resolution 336,305]
338. 7 [avatar contradiction clause 337]
339. $false [avatar sat refutation 175,192,232,281,301,303,312,321,334,338]
% SZS output end Proof for 130395973353114572822950
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
If someone is humble then someone is old or calm and vice versa. If susan is rich or humble then lucy is both funny and not strong and vice versa. Everyone who is not tall is either not humble or kind. Everyone who is both creative and not rich is either creative or funny and vice versa. Everyone who is quiet or happy is both patient and rich. Everyone who is not generous is either not tall or not funny and vice versa. If someone is not calm then someone is not funny and vice versa. Everyone who is both creative and not old is both not kind and not generous and vice versa. Everyone who is not generous or patient is wise and vice versa. Everyone who is both not quiet and calm is both not generous and not humble and vice versa. If fred is not strong or generous then fred is both not old and not funny and vice versa. Everyone who is both creative and not curious is not quiet or funny and vice versa. If john is not patient then someone is either quiet or humble and vice versa. Everyone who is not curious is curious or not old. Everyone who is either kind or curious is both not calm and kind. If someone is old or patient then alice is wise or calm and vice versa. Someone is both not kind and quiet. Someone is both patient and not kind. Someone is either funny or not quiet. Fred is both not quiet and not funny. Someone is either happy or curious. | Lucy is not strong. | neutral | ((?[X]:(humble(X)))<=>(?[X]:((old(X)|calm(X)))))&
(((rich(susan)|humble(susan)))<=>((funny(lucy)&~strong(lucy))))&
(![X]:(~tall(X)=>(~humble(X)<~>kind(X))))&
(![X]:((creative(X)&~rich(X))<=>(creative(X)<~>funny(X))))&
(![X]:((quiet(X)|happy(X))=>(patient(X)&rich(X))))&
(![X]:(~generous(X)<=>(~tall(X)<~>~funny(X))))&
((?[X]:(~calm(X)))<=>(?[X]:(~funny(X))))&
(![X]:((creative(X)&~old(X))<=>(~kind(X)&~generous(X))))&
(![X]:((~generous(X)|patient(X))<=>wise(X)))&
(![X]:((~quiet(X)&calm(X))<=>(~generous(X)&~humble(X))))&
(((~strong(fred)|generous(fred)))<=>((~old(fred)&~funny(fred))))&
(![X]:((creative(X)&~curious(X))<=>(~quiet(X)|funny(X))))&
((~patient(john))<=>(?[X]:((quiet(X)<~>humble(X)))))&
(![X]:(~curious(X)=>(curious(X)|~old(X))))&
(![X]:((kind(X)<~>curious(X))=>(~calm(X)&kind(X))))&
((?[X]:((old(X)|patient(X))))<=>((wise(alice)|calm(alice))))&
(?[X]:((~kind(X)&quiet(X))))&
(?[X]:((patient(X)&~kind(X))))&
(?[X]:((funny(X)<~>~quiet(X))))&
((~quiet(fred)&~funny(fred)))&
(?[X]:((happy(X)<~>curious(X)))) | ~strong(lucy) | [] | null | 0 |
If someone is not wise then fred is not kind or strong and vice versa.
If lucy is either not wise or patient then mary is not generous.
Everyone who is not calm is both not brave and kind and vice versa.
If someone is either funny or creative then alice is either not curious or wise and vice versa.
If someone is not kind then john is both humble and not humble.
Everyone who is either not funny or quiet is not wise.
If someone is not creative or kind then fred is either not rich or strong and vice versa.
If alice is old or not old then paul is kind or not brave and vice versa.
Everyone who is either rich or not happy is not generous and vice versa.
Everyone who is both not humble and not kind is either wise or quiet and vice versa.
If someone is both not quiet and not strong then someone is not strong or humble.
If someone is both not humble and not quiet then john is not old or not happy and vice versa.
If alice is either not generous or not humble then someone is either not rich or brave and vice versa.
Everyone who is quiet or calm is either not calm or not quiet and vice versa.
If someone is either creative or not creative then lucy is rich or wise.
Everyone who is not wise is old or curious and vice versa.
Someone is either not calm or not old.
Someone is both brave and not patient.
Paul is either not calm or not strong.
Someone is not generous or not tall.
Lucy is both tall and not brave.
Alice is either generous or patient.
Someone is not patient or not funny. | Lucy is not rich. | neutral | ((?[X]:(~wise(X)))<=>((~kind(fred)|strong(fred))))&
(((~wise(lucy)<~>patient(lucy)))=>(~generous(mary)))&
(![X]:(~calm(X)<=>(~brave(X)&kind(X))))&
((?[X]:((funny(X)<~>creative(X))))<=>((~curious(alice)<~>wise(alice))))&
((?[X]:(~kind(X)))=>((humble(john)&~humble(john))))&
(![X]:((~funny(X)<~>quiet(X))=>~wise(X)))&
((?[X]:((~creative(X)|kind(X))))<=>((~rich(fred)<~>strong(fred))))&
(((old(alice)|~old(alice)))<=>((kind(paul)|~brave(paul))))&
(![X]:((rich(X)<~>~happy(X))<=>~generous(X)))&
(![X]:((~humble(X)&~kind(X))<=>(wise(X)<~>quiet(X))))&
((?[X]:((~quiet(X)&~strong(X))))=>(?[X]:((~strong(X)|humble(X)))))&
((?[X]:((~humble(X)&~quiet(X))))<=>((~old(john)|~happy(john))))&
(((~generous(alice)<~>~humble(alice)))<=>(?[X]:((~rich(X)<~>brave(X)))))&
(![X]:((quiet(X)|calm(X))<=>(~calm(X)<~>~quiet(X))))&
((?[X]:((creative(X)<~>~creative(X))))=>((rich(lucy)|wise(lucy))))&
(![X]:(~wise(X)<=>(old(X)|curious(X))))&
(?[X]:((~calm(X)<~>~old(X))))&
(?[X]:((brave(X)&~patient(X))))&
((~calm(paul)<~>~strong(paul)))&
(?[X]:((~generous(X)|~tall(X))))&
((tall(lucy)&~brave(lucy)))&
((generous(alice)<~>patient(alice)))&
(?[X]:((~patient(X)|~funny(X)))) | ~rich(lucy) | [] | null | 0 |
If someone is quiet or not rich then someone is not old or happy and vice versa. Everyone who is wise or curious is not quiet. Everyone who is quiet is either strong or not humble. If alice is not curious then someone is both kind and not calm. Everyone who is both wise and not kind is old or kind and vice versa. Everyone who is both creative and humble is not old. If someone is not tall or quiet then alice is both creative and not funny. If lucy is both creative and brave then someone is both not quiet and tall. Everyone who is old is not happy or not generous. If someone is rich then susan is both not happy and not generous. Everyone who is calm or generous is not generous or wise and vice versa. If susan is either patient or creative then someone is not strong and vice versa. If someone is both brave and not tall then mary is patient and vice versa. Everyone who is both happy and strong is generous or tall and vice versa. Everyone who is either generous or calm is curious or humble. If someone is either not humble or funny then alice is generous or not brave. Paul is not patient or wise. Fred is not kind or not calm. Lucy is both not wise and creative. John is either not brave or not patient. Someone is both brave and tall. Someone is not quiet or not wise. | John is kind. | contradiction | ((?[X]:((quiet(X)|~rich(X))))<=>(?[X]:((~old(X)|happy(X)))))&
(![X]:((wise(X)|curious(X))=>~quiet(X)))&
(![X]:(quiet(X)=>(strong(X)<~>~humble(X))))&
((~curious(alice))=>(?[X]:((kind(X)&~calm(X)))))&
(![X]:((wise(X)&~kind(X))<=>(old(X)|kind(X))))&
(![X]:((creative(X)&humble(X))=>~old(X)))&
((?[X]:((~tall(X)|quiet(X))))=>((creative(alice)&~funny(alice))))&
(((creative(lucy)&brave(lucy)))=>(?[X]:((~quiet(X)&tall(X)))))&
(![X]:(old(X)=>(~happy(X)|~generous(X))))&
((?[X]:(rich(X)))=>((~happy(susan)&~generous(susan))))&
(![X]:((calm(X)|generous(X))<=>(~generous(X)|wise(X))))&
(((patient(susan)<~>creative(susan)))<=>(?[X]:(~strong(X))))&
((?[X]:((brave(X)&~tall(X))))<=>(patient(mary)))&
(![X]:((happy(X)&strong(X))<=>(generous(X)|tall(X))))&
(![X]:((generous(X)<~>calm(X))=>(curious(X)|humble(X))))&
((?[X]:((~humble(X)<~>funny(X))))=>((generous(alice)|~brave(alice))))&
((~patient(paul)|wise(paul)))&
((~kind(fred)|~calm(fred)))&
((~wise(lucy)&creative(lucy)))&
((~brave(john)<~>~patient(john)))&
(?[X]:((brave(X)&tall(X))))&
(?[X]:((~quiet(X)|~wise(X)))) | kind(john) | [
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 189294788448616454086129
% SZS output start Proof for 189294788448616454086129
5. ! [X0] : ((~kind(X0) & wise(X0)) <=> (kind(X0) | old(X0))) [input p4]
23. kind(john) [input hypothesis]
48. ! [X0] : (((~kind(X0) & wise(X0)) | (~kind(X0) & ~old(X0))) & ((kind(X0) | old(X0)) | (kind(X0) | ~wise(X0)))) [nnf transformation 5]
49. ! [X0] : (((~kind(X0) & wise(X0)) | (~kind(X0) & ~old(X0))) & (kind(X0) | old(X0) | kind(X0) | ~wise(X0))) [flattening 48]
85. ~kind(X0) | ~kind(X0) [cnf transformation 49]
125. kind(john) [cnf transformation 23]
129. ~kind(X0) [duplicate literal removal 85]
298. $false [subsumption resolution 125,129]
% SZS output end Proof for 189294788448616454086129
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not old or not quiet then alice is both not quiet and not wise and vice versa. If mary is not kind or not wise then alice is either old or not calm. Everyone who is not rich is old. Everyone who is happy or not quiet is not curious or curious and vice versa. If lucy is not old then alice is not old and vice versa. If lucy is either calm or not generous then someone is calm or not rich. Everyone who is either not quiet or tall is both generous and happy and vice versa. If someone is calm or not funny then someone is either not rich or not kind and vice versa. Everyone who is not strong is either patient or old. Everyone who is not patient or not curious is old or not curious and vice versa. Everyone who is quiet or old is both not funny and rich and vice versa. If fred is both rich and not strong then someone is both not old and not rich. Everyone who is both not creative and not brave is humble. If mary is both wise and tall then alice is either not kind or generous. If paul is either not creative or kind then alice is generous or creative. If fred is not generous or not humble then fred is strong. Someone is quiet or not strong. Fred is both not generous and patient. Alice is not generous or generous. Someone is not funny or old. Paul is brave or generous. Someone is both not funny and not tall. Someone is both patient and curious. Someone is curious. | Paul is creative. | neutral | ((?[X]:((~old(X)|~quiet(X))))<=>((~quiet(alice)&~wise(alice))))&
(((~kind(mary)|~wise(mary)))=>((old(alice)<~>~calm(alice))))&
(![X]:(~rich(X)=>old(X)))&
(![X]:((happy(X)|~quiet(X))<=>(~curious(X)|curious(X))))&
((~old(lucy))<=>(~old(alice)))&
(((calm(lucy)<~>~generous(lucy)))=>(?[X]:((calm(X)|~rich(X)))))&
(![X]:((~quiet(X)<~>tall(X))<=>(generous(X)&happy(X))))&
((?[X]:((calm(X)|~funny(X))))<=>(?[X]:((~rich(X)<~>~kind(X)))))&
(![X]:(~strong(X)=>(patient(X)<~>old(X))))&
(![X]:((~patient(X)|~curious(X))<=>(old(X)|~curious(X))))&
(![X]:((quiet(X)|old(X))<=>(~funny(X)&rich(X))))&
(((rich(fred)&~strong(fred)))=>(?[X]:((~old(X)&~rich(X)))))&
(![X]:((~creative(X)&~brave(X))=>humble(X)))&
(((wise(mary)&tall(mary)))=>((~kind(alice)<~>generous(alice))))&
(((~creative(paul)<~>kind(paul)))=>((generous(alice)|creative(alice))))&
(((~generous(fred)|~humble(fred)))=>(strong(fred)))&
(?[X]:((quiet(X)|~strong(X))))&
((~generous(fred)&patient(fred)))&
((~generous(alice)|generous(alice)))&
(?[X]:((~funny(X)|old(X))))&
((brave(paul)|generous(paul)))&
(?[X]:((~funny(X)&~tall(X))))&
(?[X]:((patient(X)&curious(X))))&
(?[X]:(curious(X))) | creative(paul) | [] | null | 0 |
If susan is not generous or not wise then someone is either not patient or not brave and vice versa.
If someone is not generous or strong then someone is both strong and quiet and vice versa.
Everyone who is both creative and not calm is humble or generous and vice versa.
Everyone who is strong is either not patient or creative.
Everyone who is either creative or strong is patient or brave and vice versa.
If someone is either creative or not strong then fred is both wise and brave.
If someone is not kind or not creative then lucy is either not kind or not funny.
If someone is either not generous or not creative then someone is not patient and vice versa.
Everyone who is both not kind and not tall is not creative.
If lucy is both not patient and wise then someone is tall or not kind.
Everyone who is patient is both happy and rich and vice versa.
If someone is creative then someone is both not strong and rich and vice versa.
If someone is either not patient or strong then lucy is both strong and not rich.
If mary is either not curious or curious then someone is either not funny or funny.
If alice is quiet then paul is not patient or not rich.
Everyone who is quiet or not quiet is either funny or quiet.
Susan is old.
Paul is brave.
Someone is either funny or wise.
Fred is patient.
Someone is not kind or funny.
Someone is either tall or not curious.
Susan is not generous.
Someone is funny or strong. | Fred is not rich. | contradiction | (((~generous(susan)|~wise(susan)))<=>(?[X]:((~patient(X)<~>~brave(X)))))&
((?[X]:((~generous(X)|strong(X))))<=>(?[X]:((strong(X)&quiet(X)))))&
(![X]:((creative(X)&~calm(X))<=>(humble(X)|generous(X))))&
(![X]:(strong(X)=>(~patient(X)<~>creative(X))))&
(![X]:((creative(X)<~>strong(X))<=>(patient(X)|brave(X))))&
((?[X]:((creative(X)<~>~strong(X))))=>((wise(fred)&brave(fred))))&
((?[X]:((~kind(X)|~creative(X))))=>((~kind(lucy)<~>~funny(lucy))))&
((?[X]:((~generous(X)<~>~creative(X))))<=>(?[X]:(~patient(X))))&
(![X]:((~kind(X)&~tall(X))=>~creative(X)))&
(((~patient(lucy)&wise(lucy)))=>(?[X]:((tall(X)|~kind(X)))))&
(![X]:(patient(X)<=>(happy(X)&rich(X))))&
((?[X]:(creative(X)))<=>(?[X]:((~strong(X)&rich(X)))))&
((?[X]:((~patient(X)<~>strong(X))))=>((strong(lucy)&~rich(lucy))))&
(((~curious(mary)<~>curious(mary)))=>(?[X]:((~funny(X)<~>funny(X)))))&
((quiet(alice))=>((~patient(paul)|~rich(paul))))&
(![X]:((quiet(X)|~quiet(X))=>(funny(X)<~>quiet(X))))&
(old(susan))&
(brave(paul))&
(?[X]:((funny(X)<~>wise(X))))&
(patient(fred))&
(?[X]:((~kind(X)|funny(X))))&
(?[X]:((tall(X)<~>~curious(X))))&
(~generous(susan))&
(?[X]:((funny(X)|strong(X)))) | ~rich(fred) | [
"p10",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 2967097561237728498988117
% SZS output start Proof for 2967097561237728498988117
11. ! [X0] : (patient(X0) <=> (rich(X0) & happy(X0))) [input p10]
20. patient(fred) [input p19]
25. ~rich(fred) [input hypothesis]
66. ! [X0] : ((patient(X0) | (~rich(X0) | ~happy(X0))) & ((rich(X0) & happy(X0)) | ~patient(X0))) [nnf transformation 11]
67. ! [X0] : ((patient(X0) | ~rich(X0) | ~happy(X0)) & ((rich(X0) & happy(X0)) | ~patient(X0))) [flattening 66]
127. ~patient(X0) | rich(X0) [cnf transformation 67]
148. patient(fred) [cnf transformation 20]
154. ~rich(fred) [cnf transformation 25]
399. rich(fred) [resolution 127,148]
402. $false [subsumption resolution 399,154]
% SZS output end Proof for 2967097561237728498988117
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not patient or quiet is patient and vice versa. Everyone who is strong or not old is not funny and vice versa. Everyone who is not calm or happy is curious or generous and vice versa. If alice is generous or not quiet then someone is not happy and vice versa. Everyone who is both humble and not strong is both not quiet and not funny and vice versa. If someone is either not wise or not creative then someone is either not strong or calm and vice versa. Everyone who is either generous or kind is patient. Everyone who is not kind or calm is curious or rich and vice versa. Everyone who is not curious is either not brave or old and vice versa. If someone is either old or not happy then someone is either not brave or humble. Everyone who is old is not patient or not tall. If alice is rich or strong then someone is either generous or not humble and vice versa. Everyone who is both not funny and strong is both not calm and calm. Everyone who is old or not wise is not quiet or wise and vice versa. Everyone who is happy is both not generous and brave. If mary is both quiet and not calm then lucy is not brave or happy and vice versa. Fred is strong or not kind. Alice is both old and not creative. Paul is either not old or not creative. Someone is not creative. Someone is kind. Someone is not happy or not humble. | Paul is humble. | contradiction | (![X]:((~patient(X)|quiet(X))<=>patient(X)))&
(![X]:((strong(X)|~old(X))<=>~funny(X)))&
(![X]:((~calm(X)|happy(X))<=>(curious(X)|generous(X))))&
(((generous(alice)|~quiet(alice)))<=>(?[X]:(~happy(X))))&
(![X]:((humble(X)&~strong(X))<=>(~quiet(X)&~funny(X))))&
((?[X]:((~wise(X)<~>~creative(X))))<=>(?[X]:((~strong(X)<~>calm(X)))))&
(![X]:((generous(X)<~>kind(X))=>patient(X)))&
(![X]:((~kind(X)|calm(X))<=>(curious(X)|rich(X))))&
(![X]:(~curious(X)<=>(~brave(X)<~>old(X))))&
((?[X]:((old(X)<~>~happy(X))))=>(?[X]:((~brave(X)<~>humble(X)))))&
(![X]:(old(X)=>(~patient(X)|~tall(X))))&
(((rich(alice)|strong(alice)))<=>(?[X]:((generous(X)<~>~humble(X)))))&
(![X]:((~funny(X)&strong(X))=>(~calm(X)&calm(X))))&
(![X]:((old(X)|~wise(X))<=>(~quiet(X)|wise(X))))&
(![X]:(happy(X)=>(~generous(X)&brave(X))))&
(((quiet(mary)&~calm(mary)))<=>((~brave(lucy)|happy(lucy))))&
((strong(fred)|~kind(fred)))&
((old(alice)&~creative(alice)))&
((~old(paul)<~>~creative(paul)))&
(?[X]:(~creative(X)))&
(?[X]:(kind(X)))&
(?[X]:((~happy(X)|~humble(X)))) | humble(paul) | [
"p0",
"p1",
"p4",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 3823637136985769565401333
% SZS output start Proof for 3823637136985769565401333
1. ! [X0] : ((quiet(X0) | ~patient(X0)) <=> patient(X0)) [input p0]
2. ! [X0] : ((~old(X0) | strong(X0)) <=> ~funny(X0)) [input p1]
5. ! [X0] : ((~strong(X0) & humble(X0)) <=> (~funny(X0) & ~quiet(X0))) [input p4]
13. ! [X0] : ((strong(X0) & ~funny(X0)) => (calm(X0) & ~calm(X0))) [input p12]
14. ! [X0] : ((~wise(X0) | old(X0)) <=> (wise(X0) | ~quiet(X0))) [input p13]
23. humble(paul) [input hypothesis]
29. ! [X0] : ((calm(X0) & ~calm(X0)) | (~strong(X0) | funny(X0))) [ennf transformation 13]
30. ! [X0] : ((calm(X0) & ~calm(X0)) | ~strong(X0) | funny(X0)) [flattening 29]
32. ! [X0] : (((quiet(X0) | ~patient(X0)) | ~patient(X0)) & (patient(X0) | (~quiet(X0) & patient(X0)))) [nnf transformation 1]
33. ! [X0] : ((quiet(X0) | ~patient(X0) | ~patient(X0)) & (patient(X0) | (~quiet(X0) & patient(X0)))) [flattening 32]
34. ! [X0] : (((~old(X0) | strong(X0)) | funny(X0)) & (~funny(X0) | (old(X0) & ~strong(X0)))) [nnf transformation 2]
35. ! [X0] : ((~old(X0) | strong(X0) | funny(X0)) & (~funny(X0) | (old(X0) & ~strong(X0)))) [flattening 34]
43. ! [X0] : (((~strong(X0) & humble(X0)) | (funny(X0) | quiet(X0))) & ((~funny(X0) & ~quiet(X0)) | (strong(X0) | ~humble(X0)))) [nnf transformation 5]
44. ! [X0] : (((~strong(X0) & humble(X0)) | funny(X0) | quiet(X0)) & ((~funny(X0) & ~quiet(X0)) | strong(X0) | ~humble(X0))) [flattening 43]
63. ! [X0] : (((~wise(X0) | old(X0)) | (~wise(X0) & quiet(X0))) & ((wise(X0) | ~quiet(X0)) | (wise(X0) & ~old(X0)))) [nnf transformation 14]
64. ! [X0] : ((~wise(X0) | old(X0) | (~wise(X0) & quiet(X0))) & (wise(X0) | ~quiet(X0) | (wise(X0) & ~old(X0)))) [flattening 63]
74. patient(X0) | patient(X0) [cnf transformation 33]
76. quiet(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 33]
77. ~funny(X0) | ~strong(X0) [cnf transformation 35]
79. ~old(X0) | strong(X0) | funny(X0) [cnf transformation 35]
88. ~funny(X0) | strong(X0) | ~humble(X0) [cnf transformation 44]
119. ~calm(X0) | ~strong(X0) | funny(X0) [cnf transformation 30]
120. calm(X0) | ~strong(X0) | funny(X0) [cnf transformation 30]
122. wise(X0) | ~quiet(X0) | wise(X0) [cnf transformation 64]
124. ~wise(X0) | old(X0) | ~wise(X0) [cnf transformation 64]
140. humble(paul) [cnf transformation 23]
141. ~quiet(X0) | wise(X0) [duplicate literal removal 122]
142. ~wise(X0) | old(X0) [duplicate literal removal 124]
143. patient(X0) [duplicate literal removal 74]
144. ~patient(X0) | quiet(X0) [duplicate literal removal 76]
164. ~humble(X0) | ~funny(X0) [subsumption resolution 88,77]
247. ~strong(X0) | calm(X0) [subsumption resolution 120,77]
248. ~calm(X0) | ~strong(X0) [subsumption resolution 119,77]
249. ~strong(X0) [subsumption resolution 248,247]
273. 27 <=> old(paul) [avatar definition]
274. ~old(paul) <- (~27) [avatar component clause 273]
275. old(paul) <- (27) [avatar component clause 273]
292. quiet(X0) [resolution 144,143]
295. wise(X0) [resolution 292,141]
305. ~funny(paul) [resolution 164,140]
306. old(X0) [resolution 295,142]
308. strong(paul) | funny(paul) <- (27) [resolution 79,275]
311. funny(paul) <- (27) [subsumption resolution 308,249]
312. $false <- (27) [subsumption resolution 311,305]
313. ~27 [avatar contradiction clause 312]
315. $false <- (~27) [subsumption resolution 274,306]
316. 27 [avatar contradiction clause 315]
317. $false [avatar sat refutation 313,316]
% SZS output end Proof for 3823637136985769565401333
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not strong or not creative then john is both not creative and wise and vice versa. Everyone who is both humble and tall is wise or not humble. Everyone who is not quiet or calm is old. Everyone who is either not creative or not generous is funny. Everyone who is not old or not humble is not tall or happy and vice versa. Everyone who is both curious and quiet is not brave. Everyone who is not old is both not tall and not happy. If someone is brave or not creative then susan is both brave and not kind and vice versa. Everyone who is not calm or not humble is not tall and vice versa. Everyone who is not funny or kind is either not patient or humble and vice versa. If someone is either not patient or not creative then someone is humble and vice versa. Everyone who is either not curious or curious is rich and vice versa. Everyone who is either happy or not creative is both not brave and funny and vice versa. If alice is not wise or calm then john is both not kind and old. Everyone who is not patient is both not creative and not old. Everyone who is both brave and not humble is not tall. Someone is both not strong and not curious. Fred is not old or old. Fred is not happy. Someone is both not happy and patient. Alice is either strong or humble. Someone is calm or not generous. Paul is both old and humble. | John is funny. | entailment | ((?[X]:((~strong(X)|~creative(X))))<=>((~creative(john)&wise(john))))&
(![X]:((humble(X)&tall(X))=>(wise(X)|~humble(X))))&
(![X]:((~quiet(X)|calm(X))=>old(X)))&
(![X]:((~creative(X)<~>~generous(X))=>funny(X)))&
(![X]:((~old(X)|~humble(X))<=>(~tall(X)|happy(X))))&
(![X]:((curious(X)&quiet(X))=>~brave(X)))&
(![X]:(~old(X)=>(~tall(X)&~happy(X))))&
((?[X]:((brave(X)|~creative(X))))<=>((brave(susan)&~kind(susan))))&
(![X]:((~calm(X)|~humble(X))<=>~tall(X)))&
(![X]:((~funny(X)|kind(X))<=>(~patient(X)<~>humble(X))))&
((?[X]:((~patient(X)<~>~creative(X))))<=>(?[X]:(humble(X))))&
(![X]:((~curious(X)<~>curious(X))<=>rich(X)))&
(![X]:((happy(X)<~>~creative(X))<=>(~brave(X)&funny(X))))&
(((~wise(alice)|calm(alice)))=>((~kind(john)&old(john))))&
(![X]:(~patient(X)=>(~creative(X)&~old(X))))&
(![X]:((brave(X)&~humble(X))=>~tall(X)))&
(?[X]:((~strong(X)&~curious(X))))&
((~old(fred)|old(fred)))&
(~happy(fred))&
(?[X]:((~happy(X)&patient(X))))&
((strong(alice)<~>humble(alice)))&
(?[X]:((calm(X)|~generous(X))))&
((old(paul)&humble(paul))) | funny(john) | [
"p0",
"p4",
"p6",
"p9",
"p12",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 4634910054771702230214715
% SZS output start Proof for 4634910054771702230214715
1. ? [X0] : (~creative(X0) | ~strong(X0)) <=> (wise(john) & ~creative(john)) [input p0]
5. ! [X0] : ((~humble(X0) | ~old(X0)) <=> (happy(X0) | ~tall(X0))) [input p4]
7. ! [X0] : (~old(X0) => (~happy(X0) & ~tall(X0))) [input p6]
10. ! [X0] : ((kind(X0) | ~funny(X0)) <=> (~patient(X0) <~> humble(X0))) [input p9]
13. ! [X0] : ((happy(X0) <~> ~creative(X0)) <=> (funny(X0) & ~brave(X0))) [input p12]
15. ! [X0] : (~patient(X0) => (~old(X0) & ~creative(X0))) [input p14]
17. ? [X0] : (~curious(X0) & ~strong(X0)) [input p16]
24. ~funny(john) [input hypothesis]
27. ? [X0] : ~strong(X0) [pure predicate removal 17]
33. ! [X0] : ((~happy(X0) & ~tall(X0)) | old(X0)) [ennf transformation 7]
35. ! [X0] : ((~old(X0) & ~creative(X0)) | patient(X0)) [ennf transformation 15]
38. (? [X0] : (~creative(X0) | ~strong(X0)) | (~wise(john) | creative(john))) & ((wise(john) & ~creative(john)) | ! [X0] : (creative(X0) & strong(X0))) [nnf transformation 1]
39. (? [X0] : (~creative(X0) | ~strong(X0)) | ~wise(john) | creative(john)) & ((wise(john) & ~creative(john)) | ! [X0] : (creative(X0) & strong(X0))) [flattening 38]
40. (? [X0] : (~creative(X0) | ~strong(X0)) | ~wise(john) | creative(john)) & ((wise(john) & ~creative(john)) | ! [X1] : (creative(X1) & strong(X1))) [rectify 39]
41. ? [X0] : (~creative(X0) | ~strong(X0)) => (~creative(sK0) | ~strong(sK0)) [choice axiom]
42. ((~creative(sK0) | ~strong(sK0)) | ~wise(john) | creative(john)) & ((wise(john) & ~creative(john)) | ! [X1] : (creative(X1) & strong(X1))) [skolemisation 40,41]
44. ! [X0] : (((~humble(X0) | ~old(X0)) | (~happy(X0) & tall(X0))) & ((happy(X0) | ~tall(X0)) | (humble(X0) & old(X0)))) [nnf transformation 5]
45. ! [X0] : ((~humble(X0) | ~old(X0) | (~happy(X0) & tall(X0))) & (happy(X0) | ~tall(X0) | (humble(X0) & old(X0)))) [flattening 44]
53. ! [X0] : (((kind(X0) | ~funny(X0)) | ((~patient(X0) | ~humble(X0)) & (humble(X0) | patient(X0)))) & (((~humble(X0) | patient(X0)) & (humble(X0) | ~patient(X0))) | (~kind(X0) & funny(X0)))) [nnf transformation 10]
54. ! [X0] : ((kind(X0) | ~funny(X0) | ((~patient(X0) | ~humble(X0)) & (humble(X0) | patient(X0)))) & (((~humble(X0) | patient(X0)) & (humble(X0) | ~patient(X0))) | (~kind(X0) & funny(X0)))) [flattening 53]
60. ! [X0] : ((((creative(X0) | ~happy(X0)) & (~creative(X0) | happy(X0))) | (~funny(X0) | brave(X0))) & ((funny(X0) & ~brave(X0)) | ((happy(X0) | creative(X0)) & (~creative(X0) | ~happy(X0))))) [nnf transformation 13]
61. ! [X0] : ((((creative(X0) | ~happy(X0)) & (~creative(X0) | happy(X0))) | ~funny(X0) | brave(X0)) & ((funny(X0) & ~brave(X0)) | ((happy(X0) | creative(X0)) & (~creative(X0) | ~happy(X0))))) [flattening 60]
62. ? [X0] : ~strong(X0) => ~strong(sK4) [choice axiom]
63. ~strong(sK4) [skolemisation 27,62]
69. ~creative(john) | strong(X1) [cnf transformation 42]
81. ~happy(X0) | ~old(X0) | ~humble(X0) [cnf transformation 45]
83. ~happy(X0) | old(X0) [cnf transformation 33]
92. ~patient(X0) | humble(X0) | funny(X0) [cnf transformation 54]
105. happy(X0) | funny(X0) | creative(X0) [cnf transformation 61]
113. ~old(X0) | patient(X0) [cnf transformation 35]
115. ~strong(sK4) [cnf transformation 63]
125. ~funny(john) [cnf transformation 24]
128. 1 <=> creative(john) [avatar definition]
129. ~creative(john) <- (~1) [avatar component clause 128]
149. 6 <=> ! [X1] : strong(X1) [avatar definition]
150. strong(X1) <- (6) [avatar component clause 149]
153. 6 | ~1 [avatar split clause 69,128,149]
208. 19 <=> old(john) [avatar definition]
210. old(john) <- (19) [avatar component clause 208]
260. $false <- (6) [resolution 150,115]
261. ~6 [avatar contradiction clause 260]
374. ~old(X1) | creative(X1) | funny(X1) | ~humble(X1) [resolution 105,81]
375. funny(X2) | creative(X2) | old(X2) [resolution 105,83]
481. creative(john) | old(john) [resolution 375,125]
484. old(john) <- (~1) [subsumption resolution 481,129]
489. 19 | 1 [avatar split clause 484,128,208]
491. patient(john) <- (19) [resolution 210,113]
497. 57 <=> humble(john) [avatar definition]
498. humble(john) <- (57) [avatar component clause 497]
503. humble(john) | funny(john) <- (19) [resolution 491,92]
507. humble(john) <- (19) [subsumption resolution 503,125]
508. 57 | ~19 [avatar split clause 507,208,497]
519. creative(john) | funny(john) | ~humble(john) <- (19) [resolution 374,210]
523. funny(john) | ~humble(john) <- (~1, 19) [subsumption resolution 519,129]
524. ~humble(john) <- (~1, 19) [subsumption resolution 523,125]
525. $false <- (~1, 19, 57) [subsumption resolution 524,498]
526. 1 | ~19 | ~57 [avatar contradiction clause 525]
527. $false [avatar sat refutation 153,261,489,508,526]
% SZS output end Proof for 4634910054771702230214715
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not happy or curious then mary is both not creative and creative. Everyone who is not humble or not tall is both generous and strong and vice versa. Everyone who is either not calm or not generous is either not kind or brave. Everyone who is either happy or not rich is both not brave and not strong. Everyone who is both not rich and not quiet is curious and vice versa. Everyone who is either happy or humble is brave. If fred is both not rich and tall then someone is quiet or not patient and vice versa. If someone is both not curious and not strong then someone is happy or not quiet. Everyone who is not funny or generous is not kind and vice versa. Everyone who is both not brave and wise is happy and vice versa. If lucy is curious then john is patient or not old. Everyone who is creative is either strong or not happy. If lucy is creative or not funny then fred is either creative or not generous and vice versa. Everyone who is not creative is rich and vice versa. Everyone who is not rich is both not strong and not patient and vice versa. If paul is quiet then someone is both not generous and quiet. Paul is rich. John is kind. Someone is not funny or funny. | Paul is strong. | contradiction | ((?[X]:((~happy(X)<~>curious(X))))=>((~creative(mary)&creative(mary))))&
(![X]:((~humble(X)|~tall(X))<=>(generous(X)&strong(X))))&
(![X]:((~calm(X)<~>~generous(X))=>(~kind(X)<~>brave(X))))&
(![X]:((happy(X)<~>~rich(X))=>(~brave(X)&~strong(X))))&
(![X]:((~rich(X)&~quiet(X))<=>curious(X)))&
(![X]:((happy(X)<~>humble(X))=>brave(X)))&
(((~rich(fred)&tall(fred)))<=>(?[X]:((quiet(X)|~patient(X)))))&
((?[X]:((~curious(X)&~strong(X))))=>(?[X]:((happy(X)|~quiet(X)))))&
(![X]:((~funny(X)|generous(X))<=>~kind(X)))&
(![X]:((~brave(X)&wise(X))<=>happy(X)))&
((curious(lucy))=>((patient(john)|~old(john))))&
(![X]:(creative(X)=>(strong(X)<~>~happy(X))))&
(((creative(lucy)|~funny(lucy)))<=>((creative(fred)<~>~generous(fred))))&
(![X]:(~creative(X)<=>rich(X)))&
(![X]:(~rich(X)<=>(~strong(X)&~patient(X))))&
((quiet(paul))=>(?[X]:((~generous(X)&quiet(X)))))&
(rich(paul))&
(kind(john))&
(?[X]:((~funny(X)|funny(X)))) | strong(paul) | [
"p0",
"p3",
"p4",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 374235923889361792251435
% SZS output start Proof for 374235923889361792251435
1. ? [X0] : (~happy(X0) <~> curious(X0)) => (creative(mary) & ~creative(mary)) [input p0]
4. ! [X0] : ((happy(X0) <~> ~rich(X0)) => (~strong(X0) & ~brave(X0))) [input p3]
5. ! [X0] : ((~quiet(X0) & ~rich(X0)) <=> curious(X0)) [input p4]
17. rich(paul) [input p16]
20. strong(paul) [input hypothesis]
23. (creative(mary) & ~creative(mary)) | ! [X0] : (~happy(X0) <=> curious(X0)) [ennf transformation 1]
25. ! [X0] : ((~strong(X0) & ~brave(X0)) | (happy(X0) <=> ~rich(X0))) [ennf transformation 4]
30. (creative(mary) & ~creative(mary)) | ! [X0] : ((~happy(X0) | ~curious(X0)) & (curious(X0) | happy(X0))) [nnf transformation 23]
34. ! [X0] : ((~strong(X0) & ~brave(X0)) | ((happy(X0) | rich(X0)) & (~rich(X0) | ~happy(X0)))) [nnf transformation 25]
35. ! [X0] : (((~quiet(X0) & ~rich(X0)) | ~curious(X0)) & (curious(X0) | (quiet(X0) | rich(X0)))) [nnf transformation 5]
36. ! [X0] : (((~quiet(X0) & ~rich(X0)) | ~curious(X0)) & (curious(X0) | quiet(X0) | rich(X0))) [flattening 35]
60. ~creative(mary) | curious(X0) | happy(X0) [cnf transformation 30]
62. creative(mary) | curious(X0) | happy(X0) [cnf transformation 30]
75. ~rich(X0) | ~strong(X0) | ~happy(X0) [cnf transformation 34]
78. ~rich(X0) | ~curious(X0) [cnf transformation 36]
109. rich(paul) [cnf transformation 17]
112. strong(paul) [cnf transformation 20]
117. 2 <=> creative(mary) [avatar definition]
122. 3 <=> ! [X0] : (curious(X0) | happy(X0)) [avatar definition]
123. curious(X0) | happy(X0) <- (3) [avatar component clause 122]
124. 3 | 2 [avatar split clause 62,117,122]
126. 3 | ~2 [avatar split clause 60,117,122]
204. ~curious(paul) [resolution 78,109]
225. happy(paul) <- (3) [resolution 123,204]
235. ~strong(paul) | ~happy(paul) [resolution 75,109]
239. ~happy(paul) [subsumption resolution 235,112]
240. $false <- (3) [subsumption resolution 239,225]
241. ~3 [avatar contradiction clause 240]
243. $false [avatar sat refutation 124,126,241]
% SZS output end Proof for 374235923889361792251435
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not happy is both not old and not calm.
Everyone who is both strong and brave is not strong and vice versa.
If alice is both not creative and rich then someone is both tall and humble and vice versa.
Everyone who is not strong is not generous and vice versa.
If fred is creative or not kind then someone is not creative or creative and vice versa.
Everyone who is patient is not calm or not strong and vice versa.
If someone is strong then john is either generous or happy.
If someone is either generous or not brave then mary is either calm or not quiet.
Everyone who is either kind or wise is both not curious and calm and vice versa.
Everyone who is either not strong or quiet is both wise and not patient.
Everyone who is not happy or patient is not wise and vice versa.
Everyone who is either not creative or not patient is either not happy or not old and vice versa.
Everyone who is patient or not creative is both rich and not humble.
Everyone who is funny is either not rich or not wise and vice versa.
Someone is both not tall and happy.
Someone is not strong or strong.
Someone is humble.
Someone is patient or not quiet.
Mary is either brave or creative.
Someone is either not quiet or calm. | John is funny. | entailment | (![X]:(~happy(X)=>(~old(X)&~calm(X))))&
(![X]:((strong(X)&brave(X))<=>~strong(X)))&
(((~creative(alice)&rich(alice)))<=>(?[X]:((tall(X)&humble(X)))))&
(![X]:(~strong(X)<=>~generous(X)))&
(((creative(fred)|~kind(fred)))<=>(?[X]:((~creative(X)|creative(X)))))&
(![X]:(patient(X)<=>(~calm(X)|~strong(X))))&
((?[X]:(strong(X)))=>((generous(john)<~>happy(john))))&
((?[X]:((generous(X)<~>~brave(X))))=>((calm(mary)<~>~quiet(mary))))&
(![X]:((kind(X)<~>wise(X))<=>(~curious(X)&calm(X))))&
(![X]:((~strong(X)<~>quiet(X))=>(wise(X)&~patient(X))))&
(![X]:((~happy(X)|patient(X))<=>~wise(X)))&
(![X]:((~creative(X)<~>~patient(X))<=>(~happy(X)<~>~old(X))))&
(![X]:((patient(X)|~creative(X))=>(rich(X)&~humble(X))))&
(![X]:(funny(X)<=>(~rich(X)<~>~wise(X))))&
(?[X]:((~tall(X)&happy(X))))&
(?[X]:((~strong(X)|strong(X))))&
(?[X]:(humble(X)))&
(?[X]:((patient(X)|~quiet(X))))&
((brave(mary)<~>creative(mary)))&
(?[X]:((~quiet(X)<~>calm(X)))) | funny(john) | [
"p0",
"p1",
"p3",
"p5",
"p6",
"p10",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 428629386604518090727520
% SZS output start Proof for 428629386604518090727520
1. ! [X0] : (~happy(X0) => (~calm(X0) & ~old(X0))) [input p0]
2. ! [X0] : ((brave(X0) & strong(X0)) <=> ~strong(X0)) [input p1]
4. ! [X0] : (~strong(X0) <=> ~generous(X0)) [input p3]
6. ! [X0] : (patient(X0) <=> (~strong(X0) | ~calm(X0))) [input p5]
7. ? [X0] : strong(X0) => (generous(john) <~> happy(john)) [input p6]
11. ! [X0] : ((patient(X0) | ~happy(X0)) <=> ~wise(X0)) [input p10]
13. ! [X0] : ((~creative(X0) | patient(X0)) => (~humble(X0) & rich(X0))) [input p12]
14. ! [X0] : (funny(X0) <=> (~rich(X0) <~> ~wise(X0))) [input p13]
21. ~funny(john) [input hypothesis]
22. ! [X0] : ((~rich(X0) <~> ~wise(X0)) => funny(X0)) [unused predicate definition removal 14]
23. ! [X0] : ((~calm(X0) & ~old(X0)) | happy(X0)) [ennf transformation 1]
24. (generous(john) <~> happy(john)) | ! [X0] : ~strong(X0) [ennf transformation 7]
27. ! [X0] : ((~humble(X0) & rich(X0)) | (creative(X0) & ~patient(X0))) [ennf transformation 13]
28. ! [X0] : (funny(X0) | (~rich(X0) <=> ~wise(X0))) [ennf transformation 22]
29. ! [X0] : (((brave(X0) & strong(X0)) | strong(X0)) & (~strong(X0) | (~brave(X0) | ~strong(X0)))) [nnf transformation 2]
30. ! [X0] : (((brave(X0) & strong(X0)) | strong(X0)) & (~strong(X0) | ~brave(X0) | ~strong(X0))) [flattening 29]
36. ! [X0] : ((~strong(X0) | generous(X0)) & (~generous(X0) | strong(X0))) [nnf transformation 4]
42. ! [X0] : ((patient(X0) | (strong(X0) & calm(X0))) & ((~strong(X0) | ~calm(X0)) | ~patient(X0))) [nnf transformation 6]
43. ! [X0] : ((patient(X0) | (strong(X0) & calm(X0))) & (~strong(X0) | ~calm(X0) | ~patient(X0))) [flattening 42]
44. ((~happy(john) | ~generous(john)) & (happy(john) | generous(john))) | ! [X0] : ~strong(X0) [nnf transformation 24]
49. ! [X0] : (((patient(X0) | ~happy(X0)) | wise(X0)) & (~wise(X0) | (~patient(X0) & happy(X0)))) [nnf transformation 11]
50. ! [X0] : ((patient(X0) | ~happy(X0) | wise(X0)) & (~wise(X0) | (~patient(X0) & happy(X0)))) [flattening 49]
52. ! [X0] : (funny(X0) | ((~rich(X0) | wise(X0)) & (~wise(X0) | rich(X0)))) [nnf transformation 28]
66. ~calm(X0) | happy(X0) [cnf transformation 23]
68. strong(X0) | strong(X0) [cnf transformation 30]
75. ~strong(X0) | generous(X0) [cnf transformation 36]
81. patient(X0) | calm(X0) [cnf transformation 43]
84. ~happy(john) | ~generous(john) | ~strong(X0) [cnf transformation 44]
99. ~wise(X0) | happy(X0) [cnf transformation 50]
110. ~patient(X0) | rich(X0) [cnf transformation 27]
115. ~rich(X0) | funny(X0) | wise(X0) [cnf transformation 52]
125. ~funny(john) [cnf transformation 21]
127. strong(X0) [duplicate literal removal 68]
152. generous(X0) [subsumption resolution 75,127]
170. ~happy(john) | ~strong(X0) [subsumption resolution 84,152]
171. ~happy(john) [subsumption resolution 170,127]
191. rich(X0) | calm(X0) [resolution 110,81]
234. funny(X0) | wise(X0) | calm(X0) [resolution 115,191]
387. 37 <=> wise(john) [avatar definition]
389. wise(john) <- (37) [avatar component clause 387]
466. wise(john) | calm(john) [resolution 234,125]
468. 46 <=> calm(john) [avatar definition]
470. calm(john) <- (46) [avatar component clause 468]
471. 46 | 37 [avatar split clause 466,387,468]
476. happy(john) <- (37) [resolution 389,99]
489. $false <- (37) [subsumption resolution 476,171]
490. ~37 [avatar contradiction clause 489]
492. happy(john) <- (46) [resolution 470,66]
495. $false <- (46) [subsumption resolution 492,171]
496. ~46 [avatar contradiction clause 495]
497. $false [avatar sat refutation 471,490,496]
% SZS output end Proof for 428629386604518090727520
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not tall and not quiet is not funny or curious.
Everyone who is either not brave or not generous is both not calm and kind and vice versa.
Everyone who is wise or curious is either not creative or not patient and vice versa.
If someone is not tall or not patient then someone is both kind and quiet and vice versa.
Everyone who is both strong and not old is not kind and vice versa.
Everyone who is creative is not strong or rich and vice versa.
If susan is both not tall and curious then paul is old.
Everyone who is either not tall or happy is not calm.
Everyone who is either patient or funny is not tall.
If someone is creative or not strong then someone is both humble and happy.
If someone is either not happy or strong then mary is not creative or not generous and vice versa.
If someone is either quiet or not rich then someone is either not strong or not quiet.
Everyone who is both old and not calm is both not patient and tall.
If john is both not rich and happy then someone is both funny and not funny.
If susan is either happy or not generous then mary is not tall.
If someone is both not quiet and not rich then someone is tall and vice versa.
Susan is not generous.
John is either wise or not old.
Someone is either not tall or calm.
Someone is humble.
Paul is either strong or humble.
Someone is either not happy or old.
Someone is both strong and not quiet.
Susan is either strong or kind. | Susan is generous. | contradiction | (![X]:((~tall(X)&~quiet(X))=>(~funny(X)|curious(X))))&
(![X]:((~brave(X)<~>~generous(X))<=>(~calm(X)&kind(X))))&
(![X]:((wise(X)|curious(X))<=>(~creative(X)<~>~patient(X))))&
((?[X]:((~tall(X)|~patient(X))))<=>(?[X]:((kind(X)&quiet(X)))))&
(![X]:((strong(X)&~old(X))<=>~kind(X)))&
(![X]:(creative(X)<=>(~strong(X)|rich(X))))&
(((~tall(susan)&curious(susan)))=>(old(paul)))&
(![X]:((~tall(X)<~>happy(X))=>~calm(X)))&
(![X]:((patient(X)<~>funny(X))=>~tall(X)))&
((?[X]:((creative(X)|~strong(X))))=>(?[X]:((humble(X)&happy(X)))))&
((?[X]:((~happy(X)<~>strong(X))))<=>((~creative(mary)|~generous(mary))))&
((?[X]:((quiet(X)<~>~rich(X))))=>(?[X]:((~strong(X)<~>~quiet(X)))))&
(![X]:((old(X)&~calm(X))=>(~patient(X)&tall(X))))&
(((~rich(john)&happy(john)))=>(?[X]:((funny(X)&~funny(X)))))&
(((happy(susan)<~>~generous(susan)))=>(~tall(mary)))&
((?[X]:((~quiet(X)&~rich(X))))<=>(?[X]:(tall(X))))&
(~generous(susan))&
((wise(john)<~>~old(john)))&
(?[X]:((~tall(X)<~>calm(X))))&
(?[X]:(humble(X)))&
((strong(paul)<~>humble(paul)))&
(?[X]:((~happy(X)<~>old(X))))&
(?[X]:((strong(X)&~quiet(X))))&
((strong(susan)<~>kind(susan))) | generous(susan) | [
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 522611166004463066484273
% SZS output start Proof for 522611166004463066484273
17. ~generous(susan) [input p16]
25. generous(susan) [input hypothesis]
143. ~generous(susan) [cnf transformation 17]
157. generous(susan) [cnf transformation 25]
280. 28 <=> generous(susan) [avatar definition]
311. ~28 [avatar split clause 143,280]
361. 28 [avatar split clause 157,280]
362. $false [avatar sat refutation 311,361]
% SZS output end Proof for 522611166004463066484273
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both happy and kind then someone is both quiet and strong and vice versa.
If someone is rich then someone is both quiet and not quiet.
Everyone who is either generous or not funny is either old or brave and vice versa.
Everyone who is not generous or quiet is not humble and vice versa.
Everyone who is rich is either not generous or not humble.
Everyone who is not calm or not strong is either not generous or not brave and vice versa.
Everyone who is both not generous and wise is both not creative and tall.
If fred is not strong or not calm then paul is either not quiet or tall.
If someone is generous or not tall then john is tall or not curious.
If lucy is both generous and not generous then someone is either not calm or funny and vice versa.
Everyone who is tall or not brave is either humble or rich and vice versa.
If someone is either not patient or not strong then mary is not rich or funny.
If paul is either not humble or not brave then paul is not happy and vice versa.
Everyone who is either patient or not brave is not calm or not quiet and vice versa.
If paul is either not humble or not quiet then paul is funny or happy.
Everyone who is calm is either not quiet or not creative and vice versa.
Someone is calm or not calm.
Paul is not creative.
Fred is either rich or not calm.
Someone is either not humble or kind.
Someone is not quiet.
Paul is both not curious and patient.
Someone is brave or old. | Mary is rich. | contradiction | ((?[X]:((happy(X)&kind(X))))<=>(?[X]:((quiet(X)&strong(X)))))&
((?[X]:(rich(X)))=>(?[X]:((quiet(X)&~quiet(X)))))&
(![X]:((generous(X)<~>~funny(X))<=>(old(X)<~>brave(X))))&
(![X]:((~generous(X)|quiet(X))<=>~humble(X)))&
(![X]:(rich(X)=>(~generous(X)<~>~humble(X))))&
(![X]:((~calm(X)|~strong(X))<=>(~generous(X)<~>~brave(X))))&
(![X]:((~generous(X)&wise(X))=>(~creative(X)&tall(X))))&
(((~strong(fred)|~calm(fred)))=>((~quiet(paul)<~>tall(paul))))&
((?[X]:((generous(X)|~tall(X))))=>((tall(john)|~curious(john))))&
(((generous(lucy)&~generous(lucy)))<=>(?[X]:((~calm(X)<~>funny(X)))))&
(![X]:((tall(X)|~brave(X))<=>(humble(X)<~>rich(X))))&
((?[X]:((~patient(X)<~>~strong(X))))=>((~rich(mary)|funny(mary))))&
(((~humble(paul)<~>~brave(paul)))<=>(~happy(paul)))&
(![X]:((patient(X)<~>~brave(X))<=>(~calm(X)|~quiet(X))))&
(((~humble(paul)<~>~quiet(paul)))=>((funny(paul)|happy(paul))))&
(![X]:(calm(X)<=>(~quiet(X)<~>~creative(X))))&
(?[X]:((calm(X)|~calm(X))))&
(~creative(paul))&
((rich(fred)<~>~calm(fred)))&
(?[X]:((~humble(X)<~>kind(X))))&
(?[X]:(~quiet(X)))&
((~curious(paul)&patient(paul)))&
(?[X]:((brave(X)|old(X)))) | rich(mary) | [
"p1",
"hypothesis"
] | % SZS status Unsatisfiable for 90097959516782178854384
% SZS output start Proof for 90097959516782178854384
2. ? [X0] : rich(X0) => ? [X0] : (~quiet(X0) & quiet(X0)) [input p1]
24. rich(mary) [input hypothesis]
26. ? [X0] : rich(X0) => ? [X1] : (~quiet(X1) & quiet(X1)) [rectify 2]
30. ? [X1] : (~quiet(X1) & quiet(X1)) | ! [X0] : ~rich(X0) [ennf transformation 26]
42. ? [X0] : (~quiet(X0) & quiet(X0)) | ! [X1] : ~rich(X1) [rectify 30]
43. ? [X0] : (~quiet(X0) & quiet(X0)) => (~quiet(sK2) & quiet(sK2)) [choice axiom]
44. (~quiet(sK2) & quiet(sK2)) | ! [X1] : ~rich(X1) [skolemisation 42,43]
79. quiet(sK2) | ~rich(X1) [cnf transformation 44]
80. ~quiet(sK2) | ~rich(X1) [cnf transformation 44]
143. rich(mary) [cnf transformation 24]
171. 7 <=> ! [X1] : ~rich(X1) [avatar definition]
172. ~rich(X1) <- (7) [avatar component clause 171]
174. 8 <=> quiet(sK2) [avatar definition]
177. 7 | ~8 [avatar split clause 80,174,171]
178. 7 | 8 [avatar split clause 79,174,171]
221. 17 <=> rich(mary) [avatar definition]
222. rich(mary) <- (17) [avatar component clause 221]
282. 17 [avatar split clause 143,221]
283. $false <- (7, 17) [resolution 222,172]
284. ~7 | ~17 [avatar contradiction clause 283]
285. $false [avatar sat refutation 177,178,282,284]
% SZS output end Proof for 90097959516782178854384
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or not humble is not curious and vice versa.
If someone is both not old and not funny then someone is either not funny or wise and vice versa.
Everyone who is either not patient or not strong is happy or funny.
Everyone who is both not kind and tall is both happy and tall and vice versa.
If someone is both not happy and happy then someone is quiet and vice versa.
Everyone who is generous or old is not happy or not brave and vice versa.
If someone is not rich then someone is either patient or funny and vice versa.
If lucy is both not humble and not generous then someone is not wise or patient and vice versa.
If lucy is both not funny and kind then alice is patient or rich.
Everyone who is either not generous or not patient is both strong and happy and vice versa.
Everyone who is brave is either not kind or not tall and vice versa.
If someone is either not humble or not rich then someone is not funny and vice versa.
If susan is not quiet or happy then someone is both strong and not calm.
Everyone who is humble or strong is either curious or not rich.
Everyone who is not happy is not curious or old.
Everyone who is both rich and wise is either not tall or not humble and vice versa.
Someone is either wise or creative.
Someone is not wise or rich.
John is wise.
Someone is curious.
Someone is either brave or patient.
Susan is both funny and not creative.
Lucy is strong or not rich. | Alice is not wise. | neutral | (![X]:((~creative(X)|~humble(X))<=>~curious(X)))&
((?[X]:((~old(X)&~funny(X))))<=>(?[X]:((~funny(X)<~>wise(X)))))&
(![X]:((~patient(X)<~>~strong(X))=>(happy(X)|funny(X))))&
(![X]:((~kind(X)&tall(X))<=>(happy(X)&tall(X))))&
((?[X]:((~happy(X)&happy(X))))<=>(?[X]:(quiet(X))))&
(![X]:((generous(X)|old(X))<=>(~happy(X)|~brave(X))))&
((?[X]:(~rich(X)))<=>(?[X]:((patient(X)<~>funny(X)))))&
(((~humble(lucy)&~generous(lucy)))<=>(?[X]:((~wise(X)|patient(X)))))&
(((~funny(lucy)&kind(lucy)))=>((patient(alice)|rich(alice))))&
(![X]:((~generous(X)<~>~patient(X))<=>(strong(X)&happy(X))))&
(![X]:(brave(X)<=>(~kind(X)<~>~tall(X))))&
((?[X]:((~humble(X)<~>~rich(X))))<=>(?[X]:(~funny(X))))&
(((~quiet(susan)|happy(susan)))=>(?[X]:((strong(X)&~calm(X)))))&
(![X]:((humble(X)|strong(X))=>(curious(X)<~>~rich(X))))&
(![X]:(~happy(X)=>(~curious(X)|old(X))))&
(![X]:((rich(X)&wise(X))<=>(~tall(X)<~>~humble(X))))&
(?[X]:((wise(X)<~>creative(X))))&
(?[X]:((~wise(X)|rich(X))))&
(wise(john))&
(?[X]:(curious(X)))&
(?[X]:((brave(X)<~>patient(X))))&
((funny(susan)&~creative(susan)))&
((strong(lucy)|~rich(lucy))) | ~wise(alice) | [] | null | 0 |
Everyone who is not funny is both old and quiet.
Everyone who is either kind or curious is calm.
If alice is not curious or happy then someone is wise and vice versa.
If fred is both not wise and humble then paul is both tall and curious.
Everyone who is funny or wise is either not old or not patient.
If john is not wise or wise then susan is both strong and wise.
If someone is either not humble or not curious then paul is either happy or patient and vice versa.
If someone is either not wise or not calm then susan is either not brave or not strong and vice versa.
Everyone who is calm is humble.
If someone is not calm or creative then alice is rich and vice versa.
Everyone who is not strong or strong is not happy.
Everyone who is patient or kind is old.
If john is quiet or not happy then someone is not creative or funny and vice versa.
Everyone who is not rich is either not humble or not funny and vice versa.
Everyone who is both humble and not wise is either brave or curious and vice versa.
If someone is old or not brave then paul is wise and vice versa.
Someone is not happy or not funny.
Someone is kind.
Fred is brave or not patient.
Someone is not humble.
Someone is both calm and not wise.
John is either not wise or not rich.
Someone is either not happy or curious.
Susan is both old and not brave. | Alice is funny. | contradiction | (![X]:(~funny(X)=>(old(X)&quiet(X))))&
(![X]:((kind(X)<~>curious(X))=>calm(X)))&
(((~curious(alice)|happy(alice)))<=>(?[X]:(wise(X))))&
(((~wise(fred)&humble(fred)))=>((tall(paul)&curious(paul))))&
(![X]:((funny(X)|wise(X))=>(~old(X)<~>~patient(X))))&
(((~wise(john)|wise(john)))=>((strong(susan)&wise(susan))))&
((?[X]:((~humble(X)<~>~curious(X))))<=>((happy(paul)<~>patient(paul))))&
((?[X]:((~wise(X)<~>~calm(X))))<=>((~brave(susan)<~>~strong(susan))))&
(![X]:(calm(X)=>humble(X)))&
((?[X]:((~calm(X)|creative(X))))<=>(rich(alice)))&
(![X]:((~strong(X)|strong(X))=>~happy(X)))&
(![X]:((patient(X)|kind(X))=>old(X)))&
(((quiet(john)|~happy(john)))<=>(?[X]:((~creative(X)|funny(X)))))&
(![X]:(~rich(X)<=>(~humble(X)<~>~funny(X))))&
(![X]:((humble(X)&~wise(X))<=>(brave(X)<~>curious(X))))&
((?[X]:((old(X)|~brave(X))))<=>(wise(paul)))&
(?[X]:((~happy(X)|~funny(X))))&
(?[X]:(kind(X)))&
((brave(fred)|~patient(fred)))&
(?[X]:(~humble(X)))&
(?[X]:((calm(X)&~wise(X))))&
((~wise(john)<~>~rich(john)))&
(?[X]:((~happy(X)<~>curious(X))))&
((old(susan)&~brave(susan))) | funny(alice) | [
"p0",
"p2",
"p4",
"p6",
"p8",
"p9",
"p10",
"p11",
"p13",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 6115300327376740656593306
% SZS output start Proof for 6115300327376740656593306
1. ! [X0] : (~funny(X0) => (quiet(X0) & old(X0))) [input p0]
3. (happy(alice) | ~curious(alice)) <=> ? [X0] : wise(X0) [input p2]
5. ! [X0] : ((wise(X0) | funny(X0)) => (~old(X0) <~> ~patient(X0))) [input p4]
7. ? [X0] : (~humble(X0) <~> ~curious(X0)) <=> (happy(paul) <~> patient(paul)) [input p6]
9. ! [X0] : (calm(X0) => humble(X0)) [input p8]
10. ? [X0] : (creative(X0) | ~calm(X0)) <=> rich(alice) [input p9]
11. ! [X0] : ((strong(X0) | ~strong(X0)) => ~happy(X0)) [input p10]
12. ! [X0] : ((kind(X0) | patient(X0)) => old(X0)) [input p11]
14. ! [X0] : (~rich(X0) <=> (~humble(X0) <~> ~funny(X0))) [input p13]
16. ? [X0] : (~brave(X0) | old(X0)) <=> wise(paul) [input p15]
20. ? [X0] : ~humble(X0) [input p19]
25. funny(alice) [input hypothesis]
27. ! [X0] : ((quiet(X0) & old(X0)) | funny(X0)) [ennf transformation 1]
31. ! [X0] : ((~old(X0) <~> ~patient(X0)) | (~wise(X0) & ~funny(X0))) [ennf transformation 5]
33. ! [X0] : (humble(X0) | ~calm(X0)) [ennf transformation 9]
34. ! [X0] : (~happy(X0) | (~strong(X0) & strong(X0))) [ennf transformation 11]
35. ! [X0] : (old(X0) | (~kind(X0) & ~patient(X0))) [ennf transformation 12]
37. ((happy(alice) | ~curious(alice)) | ! [X0] : ~wise(X0)) & (? [X0] : wise(X0) | (~happy(alice) & curious(alice))) [nnf transformation 3]
38. (happy(alice) | ~curious(alice) | ! [X0] : ~wise(X0)) & (? [X0] : wise(X0) | (~happy(alice) & curious(alice))) [flattening 37]
39. (happy(alice) | ~curious(alice) | ! [X0] : ~wise(X0)) & (? [X1] : wise(X1) | (~happy(alice) & curious(alice))) [rectify 38]
40. ? [X1] : wise(X1) => wise(sK0) [choice axiom]
41. (happy(alice) | ~curious(alice) | ! [X0] : ~wise(X0)) & (wise(sK0) | (~happy(alice) & curious(alice))) [skolemisation 39,40]
42. ! [X0] : (((patient(X0) | old(X0)) & (~patient(X0) | ~old(X0))) | (~wise(X0) & ~funny(X0))) [nnf transformation 31]
43. (? [X0] : ((curious(X0) | humble(X0)) & (~curious(X0) | ~humble(X0))) | ((happy(paul) | ~patient(paul)) & (patient(paul) | ~happy(paul)))) & (((~patient(paul) | ~happy(paul)) & (patient(paul) | happy(paul))) | ! [X0] : ((~humble(X0) | curious(X0)) & (~curious(X0) | humble(X0)))) [nnf transformation 7]
44. (? [X0] : ((curious(X0) | humble(X0)) & (~curious(X0) | ~humble(X0))) | ((happy(paul) | ~patient(paul)) & (patient(paul) | ~happy(paul)))) & (((~patient(paul) | ~happy(paul)) & (patient(paul) | happy(paul))) | ! [X1] : ((~humble(X1) | curious(X1)) & (~curious(X1) | humble(X1)))) [rectify 43]
45. ? [X0] : ((curious(X0) | humble(X0)) & (~curious(X0) | ~humble(X0))) => ((curious(sK1) | humble(sK1)) & (~curious(sK1) | ~humble(sK1))) [choice axiom]
46. (((curious(sK1) | humble(sK1)) & (~curious(sK1) | ~humble(sK1))) | ((happy(paul) | ~patient(paul)) & (patient(paul) | ~happy(paul)))) & (((~patient(paul) | ~happy(paul)) & (patient(paul) | happy(paul))) | ! [X1] : ((~humble(X1) | curious(X1)) & (~curious(X1) | humble(X1)))) [skolemisation 44,45]
51. (? [X0] : (creative(X0) | ~calm(X0)) | ~rich(alice)) & (rich(alice) | ! [X0] : (~creative(X0) & calm(X0))) [nnf transformation 10]
52. (? [X0] : (creative(X0) | ~calm(X0)) | ~rich(alice)) & (rich(alice) | ! [X1] : (~creative(X1) & calm(X1))) [rectify 51]
53. ? [X0] : (creative(X0) | ~calm(X0)) => (creative(sK3) | ~calm(sK3)) [choice axiom]
54. ((creative(sK3) | ~calm(sK3)) | ~rich(alice)) & (rich(alice) | ! [X1] : (~creative(X1) & calm(X1))) [skolemisation 52,53]
60. ! [X0] : ((~rich(X0) | ((~humble(X0) | funny(X0)) & (~funny(X0) | humble(X0)))) & (((funny(X0) | humble(X0)) & (~funny(X0) | ~humble(X0))) | rich(X0))) [nnf transformation 14]
63. (? [X0] : (~brave(X0) | old(X0)) | ~wise(paul)) & (wise(paul) | ! [X0] : (brave(X0) & ~old(X0))) [nnf transformation 16]
64. (? [X0] : (~brave(X0) | old(X0)) | ~wise(paul)) & (wise(paul) | ! [X1] : (brave(X1) & ~old(X1))) [rectify 63]
65. ? [X0] : (~brave(X0) | old(X0)) => (~brave(sK5) | old(sK5)) [choice axiom]
66. ((~brave(sK5) | old(sK5)) | ~wise(paul)) & (wise(paul) | ! [X1] : (brave(X1) & ~old(X1))) [skolemisation 64,65]
71. ? [X0] : ~humble(X0) => ~humble(sK8) [choice axiom]
72. ~humble(sK8) [skolemisation 20,71]
79. old(X0) | funny(X0) [cnf transformation 27]
85. happy(alice) | ~curious(alice) | ~wise(X0) [cnf transformation 41]
88. ~patient(X0) | ~old(X0) | ~wise(X0) [cnf transformation 42]
89. patient(X0) | old(X0) | ~funny(X0) [cnf transformation 42]
96. patient(paul) | happy(paul) | ~humble(X1) | curious(X1) [cnf transformation 46]
111. ~calm(X0) | humble(X0) [cnf transformation 33]
112. rich(alice) | calm(X1) [cnf transformation 54]
115. ~happy(X0) | strong(X0) [cnf transformation 34]
116. ~strong(X0) | ~happy(X0) [cnf transformation 34]
117. old(X0) | ~patient(X0) [cnf transformation 35]
125. ~rich(X0) | ~funny(X0) | humble(X0) [cnf transformation 60]
133. wise(paul) | ~old(X1) [cnf transformation 66]
139. ~humble(sK8) [cnf transformation 72]
148. funny(alice) [cnf transformation 25]
150. 1 <=> ! [X0] : ~wise(X0) [avatar definition]
151. ~wise(X0) <- (1) [avatar component clause 150]
153. 2 <=> curious(alice) [avatar definition]
157. 3 <=> happy(alice) [avatar definition]
159. happy(alice) <- (3) [avatar component clause 157]
160. 1 | ~2 | 3 [avatar split clause 85,157,153,150]
180. patient(X0) | old(X0) [subsumption resolution 89,79]
198. 11 <=> patient(paul) [avatar definition]
199. patient(paul) <- (11) [avatar component clause 198]
202. 12 <=> happy(paul) [avatar definition]
204. happy(paul) <- (12) [avatar component clause 202]
218. 15 <=> ! [X1] : (~humble(X1) | curious(X1)) [avatar definition]
219. ~humble(X1) | curious(X1) <- (15) [avatar component clause 218]
225. 15 | 12 | 11 [avatar split clause 96,198,202,218]
254. 22 <=> rich(alice) [avatar definition]
255. rich(alice) <- (22) [avatar component clause 254]
271. 26 <=> ! [X1] : calm(X1) [avatar definition]
272. calm(X1) <- (26) [avatar component clause 271]
273. 26 | 22 [avatar split clause 112,254,271]
274. ~happy(X0) [subsumption resolution 115,116]
275. old(X0) [subsumption resolution 117,180]
295. 31 <=> wise(paul) [avatar definition]
297. wise(paul) <- (31) [avatar component clause 295]
299. wise(paul) [subsumption resolution 133,275]
300. 31 [avatar split clause 299,295]
336. ~old(paul) | ~wise(paul) <- (11) [resolution 88,199]
338. ~wise(paul) <- (11) [subsumption resolution 336,275]
339. $false <- (11, 31) [subsumption resolution 338,297]
340. ~11 | ~31 [avatar contradiction clause 339]
341. $false <- (12) [subsumption resolution 204,274]
342. ~12 [avatar contradiction clause 341]
391. ~funny(alice) | humble(alice) <- (22) [resolution 125,255]
394. humble(alice) <- (22) [subsumption resolution 391,148]
399. curious(alice) <- (15, 22) [resolution 394,219]
402. 2 | ~15 | ~22 [avatar split clause 399,254,218,153]
403. $false <- (1, 31) [resolution 151,297]
412. ~1 | ~31 [avatar contradiction clause 403]
413. $false <- (3) [subsumption resolution 159,274]
414. ~3 [avatar contradiction clause 413]
418. humble(X0) <- (26) [resolution 272,111]
425. $false <- (26) [resolution 418,139]
426. ~26 [avatar contradiction clause 425]
429. $false [avatar sat refutation 160,225,273,300,340,342,402,412,414,426]
% SZS output end Proof for 6115300327376740656593306
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either funny or not calm is generous or calm and vice versa.
If paul is either kind or quiet then lucy is strong or brave and vice versa.
Everyone who is not generous is not strong.
If john is funny or not funny then susan is either not calm or not generous.
Everyone who is both rich and not wise is either strong or not patient.
Everyone who is rich or not kind is either not happy or wise.
Everyone who is happy is strong.
Everyone who is both not wise and creative is creative or not calm and vice versa.
Everyone who is both humble and not creative is either generous or not calm and vice versa.
If paul is wise then mary is not patient and vice versa.
Everyone who is both calm and patient is both quiet and not old.
If someone is both tall and creative then alice is both happy and not creative.
If someone is either curious or happy then someone is both not happy and tall.
Everyone who is either strong or humble is not strong and vice versa.
If susan is either rich or strong then someone is tall and vice versa.
Everyone who is both rich and not generous is both not strong and generous and vice versa.
Someone is either not strong or kind.
Someone is either not quiet or generous.
Someone is not rich.
Someone is either calm or old.
Someone is either old or calm.
Lucy is not strong or not brave.
Paul is calm. | Mary is not patient. | neutral | (![X]:((funny(X)<~>~calm(X))<=>(generous(X)|calm(X))))&
(((kind(paul)<~>quiet(paul)))<=>((strong(lucy)|brave(lucy))))&
(![X]:(~generous(X)=>~strong(X)))&
(((funny(john)|~funny(john)))=>((~calm(susan)<~>~generous(susan))))&
(![X]:((rich(X)&~wise(X))=>(strong(X)<~>~patient(X))))&
(![X]:((rich(X)|~kind(X))=>(~happy(X)<~>wise(X))))&
(![X]:(happy(X)=>strong(X)))&
(![X]:((~wise(X)&creative(X))<=>(creative(X)|~calm(X))))&
(![X]:((humble(X)&~creative(X))<=>(generous(X)<~>~calm(X))))&
((wise(paul))<=>(~patient(mary)))&
(![X]:((calm(X)&patient(X))=>(quiet(X)&~old(X))))&
((?[X]:((tall(X)&creative(X))))=>((happy(alice)&~creative(alice))))&
((?[X]:((curious(X)<~>happy(X))))=>(?[X]:((~happy(X)&tall(X)))))&
(![X]:((strong(X)<~>humble(X))<=>~strong(X)))&
(((rich(susan)<~>strong(susan)))<=>(?[X]:(tall(X))))&
(![X]:((rich(X)&~generous(X))<=>(~strong(X)&generous(X))))&
(?[X]:((~strong(X)<~>kind(X))))&
(?[X]:((~quiet(X)<~>generous(X))))&
(?[X]:(~rich(X)))&
(?[X]:((calm(X)<~>old(X))))&
(?[X]:((old(X)<~>calm(X))))&
((~strong(lucy)|~brave(lucy)))&
(calm(paul)) | ~patient(mary) | [] | null | 0 |
If fred is not old then john is not funny.
Everyone who is both kind and not humble is curious or rich.
Everyone who is both generous and not brave is either not rich or humble and vice versa.
Everyone who is old is not creative or not old and vice versa.
Everyone who is rich is not strong.
Everyone who is both not rich and happy is either generous or not happy.
If someone is either not humble or wise then fred is either not old or not strong and vice versa.
Everyone who is both curious and creative is both tall and funny.
Everyone who is both not funny and not rich is either not wise or not tall.
If susan is either patient or rich then lucy is wise or quiet and vice versa.
If someone is both strong and not old then someone is either not strong or not patient and vice versa.
If mary is not rich then someone is either not humble or not patient and vice versa.
Everyone who is both curious and old is either quiet or old and vice versa.
Everyone who is both not kind and not happy is not wise.
Everyone who is either not quiet or not old is not old and vice versa.
Everyone who is either not old or not happy is both not creative and old and vice versa.
Someone is not calm or calm.
John is both not brave and not funny.
Someone is either generous or creative.
Lucy is either not happy or not wise.
Someone is both rich and old.
Someone is either humble or not wise.
Mary is brave.
Paul is both generous and brave. | Lucy is rich. | neutral | ((~old(fred))=>(~funny(john)))&
(![X]:((kind(X)&~humble(X))=>(curious(X)|rich(X))))&
(![X]:((generous(X)&~brave(X))<=>(~rich(X)<~>humble(X))))&
(![X]:(old(X)<=>(~creative(X)|~old(X))))&
(![X]:(rich(X)=>~strong(X)))&
(![X]:((~rich(X)&happy(X))=>(generous(X)<~>~happy(X))))&
((?[X]:((~humble(X)<~>wise(X))))<=>((~old(fred)<~>~strong(fred))))&
(![X]:((curious(X)&creative(X))=>(tall(X)&funny(X))))&
(![X]:((~funny(X)&~rich(X))=>(~wise(X)<~>~tall(X))))&
(((patient(susan)<~>rich(susan)))<=>((wise(lucy)|quiet(lucy))))&
((?[X]:((strong(X)&~old(X))))<=>(?[X]:((~strong(X)<~>~patient(X)))))&
((~rich(mary))<=>(?[X]:((~humble(X)<~>~patient(X)))))&
(![X]:((curious(X)&old(X))<=>(quiet(X)<~>old(X))))&
(![X]:((~kind(X)&~happy(X))=>~wise(X)))&
(![X]:((~quiet(X)<~>~old(X))<=>~old(X)))&
(![X]:((~old(X)<~>~happy(X))<=>(~creative(X)&old(X))))&
(?[X]:((~calm(X)|calm(X))))&
((~brave(john)&~funny(john)))&
(?[X]:((generous(X)<~>creative(X))))&
((~happy(lucy)<~>~wise(lucy)))&
(?[X]:((rich(X)&old(X))))&
(?[X]:((humble(X)<~>~wise(X))))&
(brave(mary))&
((generous(paul)&brave(paul))) | rich(lucy) | [] | null | 0 |
Everyone who is either kind or not old is kind or not generous and vice versa.
If alice is both not creative and creative then paul is funny.
Everyone who is both not wise and not old is both not calm and not rich.
If someone is both curious and strong then someone is both not creative and not rich and vice versa.
If mary is both not wise and not calm then paul is both old and patient and vice versa.
If someone is both tall and not generous then someone is either not calm or humble and vice versa.
If john is quiet or wise then someone is either tall or not strong.
Everyone who is funny is both rich and not funny and vice versa.
If alice is either calm or not happy then alice is not strong or not happy.
Everyone who is calm or curious is not tall and vice versa.
Everyone who is humble or not quiet is curious.
If someone is either creative or happy then john is both not humble and wise and vice versa.
Everyone who is either not brave or not rich is either wise or not curious.
Everyone who is not tall or calm is not old or not brave and vice versa.
Everyone who is funny or humble is both not curious and not old.
If someone is not kind or creative then someone is both not wise and not funny.
Someone is not funny.
Someone is both wise and not curious.
Mary is both not rich and old.
Susan is either rich or not happy.
Someone is patient.
Paul is both brave and not rich.
Lucy is not funny. | Paul is not kind. | neutral | (![X]:((kind(X)<~>~old(X))<=>(kind(X)|~generous(X))))&
(((~creative(alice)&creative(alice)))=>(funny(paul)))&
(![X]:((~wise(X)&~old(X))=>(~calm(X)&~rich(X))))&
((?[X]:((curious(X)&strong(X))))<=>(?[X]:((~creative(X)&~rich(X)))))&
(((~wise(mary)&~calm(mary)))<=>((old(paul)&patient(paul))))&
((?[X]:((tall(X)&~generous(X))))<=>(?[X]:((~calm(X)<~>humble(X)))))&
(((quiet(john)|wise(john)))=>(?[X]:((tall(X)<~>~strong(X)))))&
(![X]:(funny(X)<=>(rich(X)&~funny(X))))&
(((calm(alice)<~>~happy(alice)))=>((~strong(alice)|~happy(alice))))&
(![X]:((calm(X)|curious(X))<=>~tall(X)))&
(![X]:((humble(X)|~quiet(X))=>curious(X)))&
((?[X]:((creative(X)<~>happy(X))))<=>((~humble(john)&wise(john))))&
(![X]:((~brave(X)<~>~rich(X))=>(wise(X)<~>~curious(X))))&
(![X]:((~tall(X)|calm(X))<=>(~old(X)|~brave(X))))&
(![X]:((funny(X)|humble(X))=>(~curious(X)&~old(X))))&
((?[X]:((~kind(X)|creative(X))))=>(?[X]:((~wise(X)&~funny(X)))))&
(?[X]:(~funny(X)))&
(?[X]:((wise(X)&~curious(X))))&
((~rich(mary)&old(mary)))&
((rich(susan)<~>~happy(susan)))&
(?[X]:(patient(X)))&
((brave(paul)&~rich(paul)))&
(~funny(lucy)) | ~kind(paul) | [] | null | 0 |
Everyone who is either strong or happy is both not curious and not wise and vice versa.
If john is not brave then someone is both curious and tall and vice versa.
Everyone who is either humble or tall is either not wise or humble.
Everyone who is either curious or patient is rich.
If alice is both not kind and tall then someone is either tall or curious and vice versa.
Everyone who is both tall and not patient is either strong or not funny and vice versa.
Everyone who is both curious and not patient is either strong or old and vice versa.
If mary is not strong then lucy is not old and vice versa.
If someone is curious then john is kind and vice versa.
If lucy is creative then someone is both happy and funny.
Everyone who is both quiet and humble is both not old and not funny and vice versa.
Everyone who is old is both humble and not tall and vice versa.
If mary is not curious or funny then john is either wise or kind and vice versa.
If alice is both wise and not calm then alice is funny.
Everyone who is calm is both not generous and curious and vice versa.
If someone is quiet then paul is generous or humble and vice versa.
Someone is either not generous or not creative.
Someone is both old and curious.
Paul is either not old or strong.
Someone is not brave.
Someone is humble or not humble.
Someone is either not funny or calm.
Susan is both happy and generous. | Mary is creative. | neutral | (![X]:((strong(X)<~>happy(X))<=>(~curious(X)&~wise(X))))&
((~brave(john))<=>(?[X]:((curious(X)&tall(X)))))&
(![X]:((humble(X)<~>tall(X))=>(~wise(X)<~>humble(X))))&
(![X]:((curious(X)<~>patient(X))=>rich(X)))&
(((~kind(alice)&tall(alice)))<=>(?[X]:((tall(X)<~>curious(X)))))&
(![X]:((tall(X)&~patient(X))<=>(strong(X)<~>~funny(X))))&
(![X]:((curious(X)&~patient(X))<=>(strong(X)<~>old(X))))&
((~strong(mary))<=>(~old(lucy)))&
((?[X]:(curious(X)))<=>(kind(john)))&
((creative(lucy))=>(?[X]:((happy(X)&funny(X)))))&
(![X]:((quiet(X)&humble(X))<=>(~old(X)&~funny(X))))&
(![X]:(old(X)<=>(humble(X)&~tall(X))))&
(((~curious(mary)|funny(mary)))<=>((wise(john)<~>kind(john))))&
(((wise(alice)&~calm(alice)))=>(funny(alice)))&
(![X]:(calm(X)<=>(~generous(X)&curious(X))))&
((?[X]:(quiet(X)))<=>((generous(paul)|humble(paul))))&
(?[X]:((~generous(X)<~>~creative(X))))&
(?[X]:((old(X)&curious(X))))&
((~old(paul)<~>strong(paul)))&
(?[X]:(~brave(X)))&
(?[X]:((humble(X)|~humble(X))))&
(?[X]:((~funny(X)<~>calm(X))))&
((happy(susan)&generous(susan))) | creative(mary) | [] | null | 0 |
Everyone who is tall is both kind and strong.
Everyone who is both not happy and kind is either not humble or brave and vice versa.
Everyone who is both happy and patient is not brave.
Everyone who is brave or rich is not creative and vice versa.
If alice is either not generous or not brave then someone is both wise and not brave and vice versa.
If paul is brave or curious then lucy is not curious or quiet and vice versa.
Everyone who is either not strong or rich is not rich or not calm.
If someone is quiet then someone is both quiet and not happy.
Everyone who is not happy is both old and not old.
If fred is not humble then mary is either not quiet or not humble.
Everyone who is brave or humble is creative.
If mary is wise then fred is kind and vice versa.
Everyone who is humble or wise is either not brave or old and vice versa.
Everyone who is generous or funny is both not funny and not quiet.
If susan is kind or wise then someone is either generous or old and vice versa.
Everyone who is both quiet and calm is both not happy and patient and vice versa.
Paul is both not strong and not brave.
Fred is not generous.
John is curious.
Lucy is both wise and not strong.
Fred is both calm and patient.
Someone is either happy or not strong.
Susan is either tall or kind. | Fred is kind. | neutral | (![X]:(tall(X)=>(kind(X)&strong(X))))&
(![X]:((~happy(X)&kind(X))<=>(~humble(X)<~>brave(X))))&
(![X]:((happy(X)&patient(X))=>~brave(X)))&
(![X]:((brave(X)|rich(X))<=>~creative(X)))&
(((~generous(alice)<~>~brave(alice)))<=>(?[X]:((wise(X)&~brave(X)))))&
(((brave(paul)|curious(paul)))<=>((~curious(lucy)|quiet(lucy))))&
(![X]:((~strong(X)<~>rich(X))=>(~rich(X)|~calm(X))))&
((?[X]:(quiet(X)))=>(?[X]:((quiet(X)&~happy(X)))))&
(![X]:(~happy(X)=>(old(X)&~old(X))))&
((~humble(fred))=>((~quiet(mary)<~>~humble(mary))))&
(![X]:((brave(X)|humble(X))=>creative(X)))&
((wise(mary))<=>(kind(fred)))&
(![X]:((humble(X)|wise(X))<=>(~brave(X)<~>old(X))))&
(![X]:((generous(X)|funny(X))=>(~funny(X)&~quiet(X))))&
(((kind(susan)|wise(susan)))<=>(?[X]:((generous(X)<~>old(X)))))&
(![X]:((quiet(X)&calm(X))<=>(~happy(X)&patient(X))))&
((~strong(paul)&~brave(paul)))&
(~generous(fred))&
(curious(john))&
((wise(lucy)&~strong(lucy)))&
((calm(fred)&patient(fred)))&
(?[X]:((happy(X)<~>~strong(X))))&
((tall(susan)<~>kind(susan))) | kind(fred) | [] | null | 0 |
Everyone who is either curious or not tall is not brave.
If fred is kind or not tall then alice is both not curious and rich.
Everyone who is calm is both kind and strong and vice versa.
Everyone who is quiet or not happy is both creative and not tall.
Everyone who is either not strong or humble is both not generous and not quiet and vice versa.
Everyone who is either not humble or tall is both generous and quiet.
If someone is kind or tall then paul is not curious.
Everyone who is not happy is patient.
Everyone who is not happy or not brave is not funny or calm.
If someone is either rich or funny then someone is either not brave or calm.
If susan is both not tall and not wise then someone is both not curious and not calm and vice versa.
If someone is either not strong or tall then susan is both wise and not tall and vice versa.
If paul is both not strong and not tall then someone is not kind and vice versa.
If someone is rich then someone is not funny.
Everyone who is wise or humble is not patient or not curious.
If someone is either creative or calm then someone is wise or not creative and vice versa.
Someone is both humble and not old.
Paul is not old or not curious.
John is either not brave or not curious.
Someone is generous.
Someone is either patient or not calm.
Someone is both curious and generous.
Someone is curious. | John is brave. | neutral | (![X]:((curious(X)<~>~tall(X))=>~brave(X)))&
(((kind(fred)|~tall(fred)))=>((~curious(alice)&rich(alice))))&
(![X]:(calm(X)<=>(kind(X)&strong(X))))&
(![X]:((quiet(X)|~happy(X))=>(creative(X)&~tall(X))))&
(![X]:((~strong(X)<~>humble(X))<=>(~generous(X)&~quiet(X))))&
(![X]:((~humble(X)<~>tall(X))=>(generous(X)&quiet(X))))&
((?[X]:((kind(X)|tall(X))))=>(~curious(paul)))&
(![X]:(~happy(X)=>patient(X)))&
(![X]:((~happy(X)|~brave(X))=>(~funny(X)|calm(X))))&
((?[X]:((rich(X)<~>funny(X))))=>(?[X]:((~brave(X)<~>calm(X)))))&
(((~tall(susan)&~wise(susan)))<=>(?[X]:((~curious(X)&~calm(X)))))&
((?[X]:((~strong(X)<~>tall(X))))<=>((wise(susan)&~tall(susan))))&
(((~strong(paul)&~tall(paul)))<=>(?[X]:(~kind(X))))&
((?[X]:(rich(X)))=>(?[X]:(~funny(X))))&
(![X]:((wise(X)|humble(X))=>(~patient(X)|~curious(X))))&
((?[X]:((creative(X)<~>calm(X))))<=>(?[X]:((wise(X)|~creative(X)))))&
(?[X]:((humble(X)&~old(X))))&
((~old(paul)|~curious(paul)))&
((~brave(john)<~>~curious(john)))&
(?[X]:(generous(X)))&
(?[X]:((patient(X)<~>~calm(X))))&
(?[X]:((curious(X)&generous(X))))&
(?[X]:(curious(X))) | brave(john) | [] | null | 0 |
Everyone who is not generous is not happy and vice versa.
If someone is both not brave and not strong then lucy is either not tall or rich and vice versa.
Everyone who is old or not calm is tall or quiet.
Everyone who is both not wise and old is either not rich or funny and vice versa.
Everyone who is either calm or not generous is not old or calm and vice versa.
Everyone who is brave is both kind and wise.
Everyone who is tall or patient is both old and not quiet.
If someone is either not tall or not generous then someone is happy or funny and vice versa.
If alice is tall then someone is both old and creative.
If someone is not kind then john is both not creative and not curious and vice versa.
Everyone who is either not creative or generous is both not calm and not tall.
If mary is generous then someone is either not quiet or quiet and vice versa.
Everyone who is both generous and humble is not brave or not kind and vice versa.
Everyone who is not old or not happy is generous and vice versa.
If someone is either brave or not rich then susan is either not creative or not generous and vice versa.
Everyone who is not tall is either not generous or strong.
Someone is humble.
John is not creative.
Susan is both not creative and generous.
Susan is either generous or not happy.
Mary is either not wise or not curious.
Someone is generous or not calm. | Susan is strong. | entailment | (![X]:(~generous(X)<=>~happy(X)))&
((?[X]:((~brave(X)&~strong(X))))<=>((~tall(lucy)<~>rich(lucy))))&
(![X]:((old(X)|~calm(X))=>(tall(X)|quiet(X))))&
(![X]:((~wise(X)&old(X))<=>(~rich(X)<~>funny(X))))&
(![X]:((calm(X)<~>~generous(X))<=>(~old(X)|calm(X))))&
(![X]:(brave(X)=>(kind(X)&wise(X))))&
(![X]:((tall(X)|patient(X))=>(old(X)&~quiet(X))))&
((?[X]:((~tall(X)<~>~generous(X))))<=>(?[X]:((happy(X)|funny(X)))))&
((tall(alice))=>(?[X]:((old(X)&creative(X)))))&
((?[X]:(~kind(X)))<=>((~creative(john)&~curious(john))))&
(![X]:((~creative(X)<~>generous(X))=>(~calm(X)&~tall(X))))&
((generous(mary))<=>(?[X]:((~quiet(X)<~>quiet(X)))))&
(![X]:((generous(X)&humble(X))<=>(~brave(X)|~kind(X))))&
(![X]:((~old(X)|~happy(X))<=>generous(X)))&
((?[X]:((brave(X)<~>~rich(X))))<=>((~creative(susan)<~>~generous(susan))))&
(![X]:(~tall(X)=>(~generous(X)<~>strong(X))))&
(?[X]:(humble(X)))&
(~creative(john))&
((~creative(susan)&generous(susan)))&
((generous(susan)<~>~happy(susan)))&
((~wise(mary)<~>~curious(mary)))&
(?[X]:((generous(X)|~calm(X)))) | strong(susan) | [
"p0",
"p4",
"p6",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2750693988342449464202794
% SZS output start Proof for 2750693988342449464202794
1. ! [X0] : (~generous(X0) <=> ~happy(X0)) [input p0]
5. ! [X0] : ((calm(X0) <~> ~generous(X0)) <=> (calm(X0) | ~old(X0))) [input p4]
7. ! [X0] : ((patient(X0) | tall(X0)) => (~quiet(X0) & old(X0))) [input p6]
14. ! [X0] : ((~happy(X0) | ~old(X0)) <=> generous(X0)) [input p13]
16. ! [X0] : (~tall(X0) => (~generous(X0) <~> strong(X0))) [input p15]
23. ~strong(susan) [input hypothesis]
25. ! [X0] : (tall(X0) => (~quiet(X0) & old(X0))) [pure predicate removal 7]
29. ! [X0] : ((~quiet(X0) & old(X0)) | ~tall(X0)) [ennf transformation 25]
32. ! [X0] : ((~generous(X0) <~> strong(X0)) | tall(X0)) [ennf transformation 16]
33. ! [X0] : ((~generous(X0) | happy(X0)) & (~happy(X0) | generous(X0))) [nnf transformation 1]
40. ! [X0] : ((((generous(X0) | ~calm(X0)) & (~generous(X0) | calm(X0))) | (~calm(X0) & old(X0))) & ((calm(X0) | ~old(X0)) | ((calm(X0) | generous(X0)) & (~generous(X0) | ~calm(X0))))) [nnf transformation 5]
41. ! [X0] : ((((generous(X0) | ~calm(X0)) & (~generous(X0) | calm(X0))) | (~calm(X0) & old(X0))) & (calm(X0) | ~old(X0) | ((calm(X0) | generous(X0)) & (~generous(X0) | ~calm(X0))))) [flattening 40]
61. ! [X0] : (((~happy(X0) | ~old(X0)) | ~generous(X0)) & (generous(X0) | (happy(X0) & old(X0)))) [nnf transformation 14]
62. ! [X0] : ((~happy(X0) | ~old(X0) | ~generous(X0)) & (generous(X0) | (happy(X0) & old(X0)))) [flattening 61]
67. ! [X0] : (((~strong(X0) | generous(X0)) & (strong(X0) | ~generous(X0))) | tall(X0)) [nnf transformation 32]
75. ~generous(X0) | happy(X0) [cnf transformation 33]
91. calm(X0) | ~old(X0) | calm(X0) | generous(X0) [cnf transformation 41]
95. generous(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 41]
98. ~tall(X0) | old(X0) [cnf transformation 29]
124. generous(X0) | old(X0) [cnf transformation 62]
125. generous(X0) | happy(X0) [cnf transformation 62]
126. ~happy(X0) | ~old(X0) | ~generous(X0) [cnf transformation 62]
135. strong(X0) | ~generous(X0) | tall(X0) [cnf transformation 67]
146. ~strong(susan) [cnf transformation 23]
149. calm(X0) | ~old(X0) | generous(X0) [duplicate literal removal 91]
150. ~calm(X0) | generous(X0) [duplicate literal removal 95]
176. ~old(X0) | generous(X0) [subsumption resolution 149,150]
257. ~old(X0) | ~happy(X0) [subsumption resolution 126,176]
258. happy(X0) [subsumption resolution 125,75]
259. generous(X0) [subsumption resolution 124,176]
286. tall(X0) | strong(X0) [subsumption resolution 135,259]
308. old(X0) | strong(X0) [resolution 286,98]
324. strong(X1) | ~happy(X1) [resolution 308,257]
326. strong(X1) [subsumption resolution 324,258]
328. $false [resolution 326,146]
% SZS output end Proof for 2750693988342449464202794
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not old or old is either happy or rich.
If paul is calm or tall then mary is either not rich or old.
Everyone who is both patient and not creative is not creative or funny and vice versa.
Everyone who is both strong and not calm is both not rich and kind.
Everyone who is strong is both generous and funny and vice versa.
If someone is either old or not generous then someone is quiet or not creative and vice versa.
If someone is both not wise and not funny then mary is not old or rich and vice versa.
Everyone who is rich or not happy is both not rich and generous and vice versa.
If someone is both not kind and happy then susan is calm or not brave.
Everyone who is not brave is either not calm or not old and vice versa.
Everyone who is either calm or not curious is both rich and humble and vice versa.
If someone is creative or kind then fred is both not tall and not quiet.
If someone is either not curious or not creative then someone is either not generous or not brave and vice versa.
If john is patient or humble then someone is both creative and not happy.
Everyone who is both not brave and not generous is strong or not patient and vice versa.
Paul is brave or not rich.
Mary is either not funny or not generous.
Alice is funny.
Someone is not creative.
Someone is tall or old.
Someone is not calm.
Someone is generous or not kind.
John is either curious or kind. | Paul is generous. | contradiction | (![X]:((~old(X)<~>old(X))=>(happy(X)<~>rich(X))))&
(((calm(paul)|tall(paul)))=>((~rich(mary)<~>old(mary))))&
(![X]:((patient(X)&~creative(X))<=>(~creative(X)|funny(X))))&
(![X]:((strong(X)&~calm(X))=>(~rich(X)&kind(X))))&
(![X]:(strong(X)<=>(generous(X)&funny(X))))&
((?[X]:((old(X)<~>~generous(X))))<=>(?[X]:((quiet(X)|~creative(X)))))&
((?[X]:((~wise(X)&~funny(X))))<=>((~old(mary)|rich(mary))))&
(![X]:((rich(X)|~happy(X))<=>(~rich(X)&generous(X))))&
((?[X]:((~kind(X)&happy(X))))=>((calm(susan)|~brave(susan))))&
(![X]:(~brave(X)<=>(~calm(X)<~>~old(X))))&
(![X]:((calm(X)<~>~curious(X))<=>(rich(X)&humble(X))))&
((?[X]:((creative(X)|kind(X))))=>((~tall(fred)&~quiet(fred))))&
((?[X]:((~curious(X)<~>~creative(X))))<=>(?[X]:((~generous(X)<~>~brave(X)))))&
(((patient(john)|humble(john)))=>(?[X]:((creative(X)&~happy(X)))))&
(![X]:((~brave(X)&~generous(X))<=>(strong(X)|~patient(X))))&
((brave(paul)|~rich(paul)))&
((~funny(mary)<~>~generous(mary)))&
(funny(alice))&
(?[X]:(~creative(X)))&
(?[X]:((tall(X)|old(X))))&
(?[X]:(~calm(X)))&
(?[X]:((generous(X)|~kind(X))))&
((curious(john)<~>kind(john))) | generous(paul) | [
"p0",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 2264679603250372018488953
% SZS output start Proof for 2264679603250372018488953
1. ! [X0] : ((~old(X0) <~> old(X0)) => (happy(X0) <~> rich(X0))) [input p0]
8. ! [X0] : ((~happy(X0) | rich(X0)) <=> (generous(X0) & ~rich(X0))) [input p7]
24. generous(paul) [input hypothesis]
27. ! [X0] : ((happy(X0) <~> rich(X0)) | (~old(X0) <=> old(X0))) [ennf transformation 1]
35. ! [X0] : (((~rich(X0) | ~happy(X0)) & (rich(X0) | happy(X0))) | ((~old(X0) | ~old(X0)) & (old(X0) | old(X0)))) [nnf transformation 27]
51. ! [X0] : (((~happy(X0) | rich(X0)) | (~generous(X0) | rich(X0))) & ((generous(X0) & ~rich(X0)) | (happy(X0) & ~rich(X0)))) [nnf transformation 8]
52. ! [X0] : ((~happy(X0) | rich(X0) | ~generous(X0) | rich(X0)) & ((generous(X0) & ~rich(X0)) | (happy(X0) & ~rich(X0)))) [flattening 51]
75. rich(X0) | happy(X0) | old(X0) | old(X0) [cnf transformation 35]
76. rich(X0) | happy(X0) | ~old(X0) | ~old(X0) [cnf transformation 35]
104. ~rich(X0) | ~rich(X0) [cnf transformation 52]
108. ~happy(X0) | rich(X0) | ~generous(X0) | rich(X0) [cnf transformation 52]
151. generous(paul) [cnf transformation 24]
152. ~rich(X0) [duplicate literal removal 104]
153. ~happy(X0) | rich(X0) | ~generous(X0) [duplicate literal removal 108]
154. rich(X0) | happy(X0) | old(X0) [duplicate literal removal 75]
155. rich(X0) | happy(X0) | ~old(X0) [duplicate literal removal 76]
159. rich(X0) | happy(X0) [subsumption resolution 154,155]
230. ~generous(X0) | rich(X0) [subsumption resolution 153,159]
360. rich(paul) [resolution 230,151]
363. $false [subsumption resolution 360,152]
% SZS output end Proof for 2264679603250372018488953
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.042 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not humble or creative then john is curious or not creative.
Everyone who is either quiet or not calm is both tall and not patient.
Everyone who is either not wise or not humble is either strong or not wise and vice versa.
If someone is happy or creative then paul is either not strong or not generous and vice versa.
If someone is not kind or rich then someone is strong and vice versa.
If someone is either not calm or not creative then lucy is both not wise and not old and vice versa.
If susan is quiet or not kind then susan is both not happy and not kind and vice versa.
Everyone who is both brave and happy is not happy and vice versa.
Everyone who is not humble is both not rich and old and vice versa.
Everyone who is either not humble or not curious is wise.
If john is not creative or not calm then someone is not tall or not humble and vice versa.
If paul is quiet or happy then fred is not brave or old and vice versa.
Everyone who is not creative is funny.
If alice is either not brave or not creative then alice is not funny or not strong.
Everyone who is either not humble or not patient is both not quiet and not curious and vice versa.
Everyone who is both patient and not humble is either not quiet or wise.
Someone is either not patient or not kind.
Someone is not funny.
Fred is both quiet and not old.
Paul is not calm.
Someone is both tall and patient.
Lucy is both not creative and wise.
Fred is patient. | Paul is not curious. | neutral | ((?[X]:((~humble(X)<~>creative(X))))=>((curious(john)|~creative(john))))&
(![X]:((quiet(X)<~>~calm(X))=>(tall(X)&~patient(X))))&
(![X]:((~wise(X)<~>~humble(X))<=>(strong(X)<~>~wise(X))))&
((?[X]:((happy(X)|creative(X))))<=>((~strong(paul)<~>~generous(paul))))&
((?[X]:((~kind(X)|rich(X))))<=>(?[X]:(strong(X))))&
((?[X]:((~calm(X)<~>~creative(X))))<=>((~wise(lucy)&~old(lucy))))&
(((quiet(susan)|~kind(susan)))<=>((~happy(susan)&~kind(susan))))&
(![X]:((brave(X)&happy(X))<=>~happy(X)))&
(![X]:(~humble(X)<=>(~rich(X)&old(X))))&
(![X]:((~humble(X)<~>~curious(X))=>wise(X)))&
(((~creative(john)|~calm(john)))<=>(?[X]:((~tall(X)|~humble(X)))))&
(((quiet(paul)|happy(paul)))<=>((~brave(fred)|old(fred))))&
(![X]:(~creative(X)=>funny(X)))&
(((~brave(alice)<~>~creative(alice)))=>((~funny(alice)|~strong(alice))))&
(![X]:((~humble(X)<~>~patient(X))<=>(~quiet(X)&~curious(X))))&
(![X]:((patient(X)&~humble(X))=>(~quiet(X)<~>wise(X))))&
(?[X]:((~patient(X)<~>~kind(X))))&
(?[X]:(~funny(X)))&
((quiet(fred)&~old(fred)))&
(~calm(paul))&
(?[X]:((tall(X)&patient(X))))&
((~creative(lucy)&wise(lucy)))&
(patient(fred)) | ~curious(paul) | [] | null | 0 |
Everyone who is both old and not brave is either humble or funny. Everyone who is not rich or not wise is both kind and not generous. Everyone who is either not funny or funny is wise and vice versa. If someone is both not tall and happy then someone is both not kind and not funny and vice versa. If someone is not humble then someone is both creative and not rich. Everyone who is both generous and kind is not rich and vice versa. If mary is either not funny or patient then someone is old or not calm. Everyone who is both not kind and tall is either funny or not brave. Everyone who is wise or patient is kind. Everyone who is tall is either not brave or generous. If mary is creative then someone is either not tall or creative. If susan is not humble or happy then mary is both not rich and not old and vice versa. If someone is both not curious and wise then mary is not curious or old and vice versa. If someone is generous or not funny then someone is both not quiet and not curious and vice versa. Everyone who is either creative or brave is kind. Lucy is brave or tall. Someone is both calm and not creative. Someone is either not rich or not tall. Fred is tall. Someone is rich or patient. Susan is not humble or humble. | Fred is not calm. | neutral | (![X]:((old(X)&~brave(X))=>(humble(X)<~>funny(X))))&
(![X]:((~rich(X)|~wise(X))=>(kind(X)&~generous(X))))&
(![X]:((~funny(X)<~>funny(X))<=>wise(X)))&
((?[X]:((~tall(X)&happy(X))))<=>(?[X]:((~kind(X)&~funny(X)))))&
((?[X]:(~humble(X)))=>(?[X]:((creative(X)&~rich(X)))))&
(![X]:((generous(X)&kind(X))<=>~rich(X)))&
(((~funny(mary)<~>patient(mary)))=>(?[X]:((old(X)|~calm(X)))))&
(![X]:((~kind(X)&tall(X))=>(funny(X)<~>~brave(X))))&
(![X]:((wise(X)|patient(X))=>kind(X)))&
(![X]:(tall(X)=>(~brave(X)<~>generous(X))))&
((creative(mary))=>(?[X]:((~tall(X)<~>creative(X)))))&
(((~humble(susan)|happy(susan)))<=>((~rich(mary)&~old(mary))))&
((?[X]:((~curious(X)&wise(X))))<=>((~curious(mary)|old(mary))))&
((?[X]:((generous(X)|~funny(X))))<=>(?[X]:((~quiet(X)&~curious(X)))))&
(![X]:((creative(X)<~>brave(X))=>kind(X)))&
((brave(lucy)|tall(lucy)))&
(?[X]:((calm(X)&~creative(X))))&
(?[X]:((~rich(X)<~>~tall(X))))&
(tall(fred))&
(?[X]:((rich(X)|patient(X))))&
((~humble(susan)|humble(susan))) | ~calm(fred) | [] | null | 0 |
Everyone who is not wise is both calm and creative.
Everyone who is brave is not creative or not quiet and vice versa.
Everyone who is not old or not quiet is not patient or not wise.
If fred is either not kind or funny then john is happy or tall.
Everyone who is tall is both humble and old and vice versa.
Everyone who is patient is calm or rich and vice versa.
Everyone who is quiet is either tall or not generous and vice versa.
If lucy is both not humble and not tall then someone is humble or not funny.
Everyone who is quiet is either not calm or not happy.
Everyone who is funny is creative or not creative.
Everyone who is either not creative or tall is either not calm or not wise.
Everyone who is calm is either not strong or humble and vice versa.
Everyone who is not rich or patient is both not happy and not quiet and vice versa.
Everyone who is both not generous and brave is funny or not quiet and vice versa.
If someone is both not humble and not curious then mary is both old and not strong and vice versa.
Everyone who is not calm is not calm or not strong.
Mary is not brave or calm.
Someone is curious.
Fred is tall or brave.
Someone is rich. | Mary is strong. | entailment | (![X]:(~wise(X)=>(calm(X)&creative(X))))&
(![X]:(brave(X)<=>(~creative(X)|~quiet(X))))&
(![X]:((~old(X)|~quiet(X))=>(~patient(X)|~wise(X))))&
(((~kind(fred)<~>funny(fred)))=>((happy(john)|tall(john))))&
(![X]:(tall(X)<=>(humble(X)&old(X))))&
(![X]:(patient(X)<=>(calm(X)|rich(X))))&
(![X]:(quiet(X)<=>(tall(X)<~>~generous(X))))&
(((~humble(lucy)&~tall(lucy)))=>(?[X]:((humble(X)|~funny(X)))))&
(![X]:(quiet(X)=>(~calm(X)<~>~happy(X))))&
(![X]:(funny(X)=>(creative(X)|~creative(X))))&
(![X]:((~creative(X)<~>tall(X))=>(~calm(X)<~>~wise(X))))&
(![X]:(calm(X)<=>(~strong(X)<~>humble(X))))&
(![X]:((~rich(X)|patient(X))<=>(~happy(X)&~quiet(X))))&
(![X]:((~generous(X)&brave(X))<=>(funny(X)|~quiet(X))))&
((?[X]:((~humble(X)&~curious(X))))<=>((old(mary)&~strong(mary))))&
(![X]:(~calm(X)=>(~calm(X)|~strong(X))))&
((~brave(mary)|calm(mary)))&
(?[X]:(curious(X)))&
((tall(fred)|brave(fred)))&
(?[X]:(rich(X))) | strong(mary) | [
"p1",
"p4",
"p5",
"p6",
"p11",
"p12",
"p13",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 3376255318438852005215102
% SZS output start Proof for 3376255318438852005215102
2. ! [X0] : (brave(X0) <=> (~quiet(X0) | ~creative(X0))) [input p1]
5. ! [X0] : (tall(X0) <=> (old(X0) & humble(X0))) [input p4]
6. ! [X0] : (patient(X0) <=> (rich(X0) | calm(X0))) [input p5]
7. ! [X0] : (quiet(X0) <=> (tall(X0) <~> ~generous(X0))) [input p6]
12. ! [X0] : (calm(X0) <=> (~strong(X0) <~> humble(X0))) [input p11]
13. ! [X0] : ((patient(X0) | ~rich(X0)) <=> (~quiet(X0) & ~happy(X0))) [input p12]
14. ! [X0] : ((brave(X0) & ~generous(X0)) <=> (~quiet(X0) | funny(X0))) [input p13]
17. calm(mary) | ~brave(mary) [input p16]
21. ~strong(mary) [input hypothesis]
35. ! [X0] : ((brave(X0) | (quiet(X0) & creative(X0))) & ((~quiet(X0) | ~creative(X0)) | ~brave(X0))) [nnf transformation 2]
36. ! [X0] : ((brave(X0) | (quiet(X0) & creative(X0))) & (~quiet(X0) | ~creative(X0) | ~brave(X0))) [flattening 35]
38. ! [X0] : ((tall(X0) | (~old(X0) | ~humble(X0))) & ((old(X0) & humble(X0)) | ~tall(X0))) [nnf transformation 5]
39. ! [X0] : ((tall(X0) | ~old(X0) | ~humble(X0)) & ((old(X0) & humble(X0)) | ~tall(X0))) [flattening 38]
40. ! [X0] : ((patient(X0) | (~rich(X0) & ~calm(X0))) & ((rich(X0) | calm(X0)) | ~patient(X0))) [nnf transformation 6]
41. ! [X0] : ((patient(X0) | (~rich(X0) & ~calm(X0))) & (rich(X0) | calm(X0) | ~patient(X0))) [flattening 40]
42. ! [X0] : ((quiet(X0) | ((tall(X0) | generous(X0)) & (~generous(X0) | ~tall(X0)))) & (((generous(X0) | ~tall(X0)) & (~generous(X0) | tall(X0))) | ~quiet(X0))) [nnf transformation 7]
47. ! [X0] : ((calm(X0) | ((~strong(X0) | ~humble(X0)) & (humble(X0) | strong(X0)))) & (((~humble(X0) | strong(X0)) & (humble(X0) | ~strong(X0))) | ~calm(X0))) [nnf transformation 12]
48. ! [X0] : (((patient(X0) | ~rich(X0)) | (quiet(X0) | happy(X0))) & ((~quiet(X0) & ~happy(X0)) | (~patient(X0) & rich(X0)))) [nnf transformation 13]
49. ! [X0] : ((patient(X0) | ~rich(X0) | quiet(X0) | happy(X0)) & ((~quiet(X0) & ~happy(X0)) | (~patient(X0) & rich(X0)))) [flattening 48]
50. ! [X0] : (((brave(X0) & ~generous(X0)) | (quiet(X0) & ~funny(X0))) & ((~quiet(X0) | funny(X0)) | (~brave(X0) | generous(X0)))) [nnf transformation 14]
51. ! [X0] : (((brave(X0) & ~generous(X0)) | (quiet(X0) & ~funny(X0))) & (~quiet(X0) | funny(X0) | ~brave(X0) | generous(X0))) [flattening 50]
65. quiet(X0) | brave(X0) [cnf transformation 36]
70. ~tall(X0) | humble(X0) [cnf transformation 39]
74. ~calm(X0) | patient(X0) [cnf transformation 41]
75. ~rich(X0) | patient(X0) [cnf transformation 41]
79. generous(X0) | tall(X0) | quiet(X0) [cnf transformation 42]
89. ~humble(X0) | strong(X0) | ~calm(X0) [cnf transformation 47]
94. ~quiet(X0) | rich(X0) [cnf transformation 49]
95. ~patient(X0) | ~quiet(X0) [cnf transformation 49]
99. ~generous(X0) | quiet(X0) [cnf transformation 51]
107. calm(mary) | ~brave(mary) [cnf transformation 17]
111. ~strong(mary) [cnf transformation 21]
150. 9 <=> strong(mary) [avatar definition]
151. ~strong(mary) <- (~9) [avatar component clause 150]
169. 13 <=> brave(mary) [avatar definition]
171. ~brave(mary) <- (~13) [avatar component clause 169]
173. 14 <=> calm(mary) [avatar definition]
175. calm(mary) <- (14) [avatar component clause 173]
176. ~13 | 14 [avatar split clause 107,173,169]
186. ~9 [avatar split clause 111,150]
192. rich(X0) | brave(X0) [resolution 94,65]
197. patient(X0) | brave(X0) [resolution 192,75]
215. brave(X2) | ~quiet(X2) [resolution 197,95]
217. brave(X2) [subsumption resolution 215,65]
221. $false <- (~13) [resolution 217,171]
222. 13 [avatar contradiction clause 221]
223. patient(mary) <- (14) [resolution 175,74]
227. ~quiet(mary) <- (14) [resolution 223,95]
229. 19 <=> quiet(mary) [avatar definition]
230. ~quiet(mary) <- (~19) [avatar component clause 229]
237. ~19 | ~14 [avatar split clause 227,173,229]
252. tall(X2) | quiet(X2) | quiet(X2) [resolution 79,99]
254. tall(X2) | quiet(X2) [duplicate literal removal 252]
259. humble(X2) | quiet(X2) [resolution 254,70]
295. ~calm(X0) | strong(X0) | quiet(X0) [resolution 89,259]
348. strong(mary) | quiet(mary) <- (14) [resolution 295,175]
351. quiet(mary) <- (~9, 14) [subsumption resolution 348,151]
352. $false <- (~9, 14, ~19) [subsumption resolution 351,230]
353. 9 | ~14 | 19 [avatar contradiction clause 352]
354. $false [avatar sat refutation 176,186,222,237,353]
% SZS output end Proof for 3376255318438852005215102
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 john is brave then lucy is either not brave or not strong and vice versa.
Everyone who is either not humble or generous is either not humble or not strong and vice versa.
If paul is generous then lucy is kind or creative and vice versa.
Everyone who is not funny or not strong is not funny and vice versa.
If john is both quiet and old then fred is not old.
Everyone who is both not humble and tall is funny or not creative.
Everyone who is both not wise and happy is either wise or not tall.
Everyone who is funny or strong is not tall or happy and vice versa.
If mary is either wise or tall then susan is not happy.
Everyone who is both quiet and not strong is both old and not kind.
Everyone who is both old and not funny is wise or not generous.
Everyone who is both not rich and quiet is both brave and not funny.
If susan is both funny and patient then someone is tall or rich and vice versa.
Everyone who is not wise or humble is not funny and vice versa.
Everyone who is kind is not creative or not strong and vice versa.
If lucy is tall or not humble then mary is both not calm and old.
Someone is both quiet and not generous.
Someone is old or not calm.
Alice is not wise.
Someone is either not humble or curious.
John is not wise.
Someone is calm.
Someone is not creative. | John is old. | neutral | ((brave(john))<=>((~brave(lucy)<~>~strong(lucy))))&
(![X]:((~humble(X)<~>generous(X))<=>(~humble(X)<~>~strong(X))))&
((generous(paul))<=>((kind(lucy)|creative(lucy))))&
(![X]:((~funny(X)|~strong(X))<=>~funny(X)))&
(((quiet(john)&old(john)))=>(~old(fred)))&
(![X]:((~humble(X)&tall(X))=>(funny(X)|~creative(X))))&
(![X]:((~wise(X)&happy(X))=>(wise(X)<~>~tall(X))))&
(![X]:((funny(X)|strong(X))<=>(~tall(X)|happy(X))))&
(((wise(mary)<~>tall(mary)))=>(~happy(susan)))&
(![X]:((quiet(X)&~strong(X))=>(old(X)&~kind(X))))&
(![X]:((old(X)&~funny(X))=>(wise(X)|~generous(X))))&
(![X]:((~rich(X)&quiet(X))=>(brave(X)&~funny(X))))&
(((funny(susan)&patient(susan)))<=>(?[X]:((tall(X)|rich(X)))))&
(![X]:((~wise(X)|humble(X))<=>~funny(X)))&
(![X]:(kind(X)<=>(~creative(X)|~strong(X))))&
(((tall(lucy)|~humble(lucy)))=>((~calm(mary)&old(mary))))&
(?[X]:((quiet(X)&~generous(X))))&
(?[X]:((old(X)|~calm(X))))&
(~wise(alice))&
(?[X]:((~humble(X)<~>curious(X))))&
(~wise(john))&
(?[X]:(calm(X)))&
(?[X]:(~creative(X))) | old(john) | [] | null | 0 |
Everyone who is not quiet or brave is curious or generous.
Everyone who is both not brave and generous is not rich and vice versa.
If someone is either not quiet or creative then someone is patient and vice versa.
Everyone who is not funny or strong is strong or not generous and vice versa.
If someone is not quiet or curious then lucy is humble or happy.
Everyone who is either humble or curious is not humble.
Everyone who is calm or strong is both strong and not strong.
Everyone who is both brave and not funny is not strong or creative and vice versa.
Everyone who is wise is rich.
Everyone who is either creative or old is patient or not creative and vice versa.
Everyone who is both not strong and not old is either rich or creative and vice versa.
If paul is both not kind and brave then paul is either strong or not patient.
If mary is not happy or not calm then someone is kind.
Everyone who is not rich is both not calm and kind.
If paul is curious then susan is calm or old.
If someone is wise then mary is happy.
Someone is both not wise and humble.
Someone is either old or not kind.
Someone is both not humble and curious.
Someone is not wise or not humble.
Someone is both not happy and not kind. | Mary is not old. | contradiction | (![X]:((~quiet(X)|brave(X))=>(curious(X)|generous(X))))&
(![X]:((~brave(X)&generous(X))<=>~rich(X)))&
((?[X]:((~quiet(X)<~>creative(X))))<=>(?[X]:(patient(X))))&
(![X]:((~funny(X)|strong(X))<=>(strong(X)|~generous(X))))&
((?[X]:((~quiet(X)|curious(X))))=>((humble(lucy)|happy(lucy))))&
(![X]:((humble(X)<~>curious(X))=>~humble(X)))&
(![X]:((calm(X)|strong(X))=>(strong(X)&~strong(X))))&
(![X]:((brave(X)&~funny(X))<=>(~strong(X)|creative(X))))&
(![X]:(wise(X)=>rich(X)))&
(![X]:((creative(X)<~>old(X))<=>(patient(X)|~creative(X))))&
(![X]:((~strong(X)&~old(X))<=>(rich(X)<~>creative(X))))&
(((~kind(paul)&brave(paul)))=>((strong(paul)<~>~patient(paul))))&
(((~happy(mary)|~calm(mary)))=>(?[X]:(kind(X))))&
(![X]:(~rich(X)=>(~calm(X)&kind(X))))&
((curious(paul))=>((calm(susan)|old(susan))))&
((?[X]:(wise(X)))=>(happy(mary)))&
(?[X]:((~wise(X)&humble(X))))&
(?[X]:((old(X)<~>~kind(X))))&
(?[X]:((~humble(X)&curious(X))))&
(?[X]:((~wise(X)|~humble(X))))&
(?[X]:((~happy(X)&~kind(X)))) | ~old(mary) | [
"p1",
"p6",
"p7",
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 3277605138472761713120665
% SZS output start Proof for 3277605138472761713120665
2. ! [X0] : ((generous(X0) & ~brave(X0)) <=> ~rich(X0)) [input p1]
7. ! [X0] : ((strong(X0) | calm(X0)) => (~strong(X0) & strong(X0))) [input p6]
8. ! [X0] : ((~funny(X0) & brave(X0)) <=> (creative(X0) | ~strong(X0))) [input p7]
10. ! [X0] : ((creative(X0) <~> old(X0)) <=> (~creative(X0) | patient(X0))) [input p9]
11. ! [X0] : ((~old(X0) & ~strong(X0)) <=> (rich(X0) <~> creative(X0))) [input p10]
22. ~old(mary) [input hypothesis]
33. ! [X0] : ((~strong(X0) & strong(X0)) | (~strong(X0) & ~calm(X0))) [ennf transformation 7]
40. ! [X0] : (((generous(X0) & ~brave(X0)) | rich(X0)) & (~rich(X0) | (~generous(X0) | brave(X0)))) [nnf transformation 2]
41. ! [X0] : (((generous(X0) & ~brave(X0)) | rich(X0)) & (~rich(X0) | ~generous(X0) | brave(X0))) [flattening 40]
50. ! [X0] : (((~funny(X0) & brave(X0)) | (~creative(X0) & strong(X0))) & ((creative(X0) | ~strong(X0)) | (funny(X0) | ~brave(X0)))) [nnf transformation 8]
51. ! [X0] : (((~funny(X0) & brave(X0)) | (~creative(X0) & strong(X0))) & (creative(X0) | ~strong(X0) | funny(X0) | ~brave(X0))) [flattening 50]
52. ! [X0] : ((((~old(X0) | ~creative(X0)) & (old(X0) | creative(X0))) | (creative(X0) & ~patient(X0))) & ((~creative(X0) | patient(X0)) | ((creative(X0) | ~old(X0)) & (old(X0) | ~creative(X0))))) [nnf transformation 10]
53. ! [X0] : ((((~old(X0) | ~creative(X0)) & (old(X0) | creative(X0))) | (creative(X0) & ~patient(X0))) & (~creative(X0) | patient(X0) | ((creative(X0) | ~old(X0)) & (old(X0) | ~creative(X0))))) [flattening 52]
54. ! [X0] : (((~old(X0) & ~strong(X0)) | ((rich(X0) | ~creative(X0)) & (creative(X0) | ~rich(X0)))) & (((~creative(X0) | ~rich(X0)) & (creative(X0) | rich(X0))) | (old(X0) | strong(X0)))) [nnf transformation 11]
55. ! [X0] : (((~old(X0) & ~strong(X0)) | ((rich(X0) | ~creative(X0)) & (creative(X0) | ~rich(X0)))) & (((~creative(X0) | ~rich(X0)) & (creative(X0) | rich(X0))) | old(X0) | strong(X0))) [flattening 54]
71. ~brave(X0) | rich(X0) [cnf transformation 41]
88. ~strong(X0) | ~strong(X0) [cnf transformation 33]
90. brave(X0) | strong(X0) [cnf transformation 51]
97. old(X0) | creative(X0) | creative(X0) [cnf transformation 53]
101. ~creative(X0) | ~rich(X0) | old(X0) | strong(X0) [cnf transformation 55]
120. ~old(mary) [cnf transformation 22]
122. old(X0) | creative(X0) [duplicate literal removal 97]
123. ~strong(X0) [duplicate literal removal 88]
168. brave(X0) [subsumption resolution 90,123]
171. ~creative(X0) | ~rich(X0) | old(X0) [subsumption resolution 101,123]
172. ~rich(X0) | old(X0) [subsumption resolution 171,122]
205. rich(X0) [resolution 71,168]
219. old(X1) [resolution 172,205]
232. $false [resolution 219,120]
% SZS output end Proof for 3277605138472761713120665
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not kind and not funny then fred is not strong or not happy and vice versa.
Everyone who is either not rich or not happy is both not generous and not patient.
Everyone who is curious is either not wise or not brave and vice versa.
Everyone who is generous is either not calm or old and vice versa.
Everyone who is either curious or not generous is tall and vice versa.
If mary is not creative then lucy is either not kind or curious and vice versa.
Everyone who is both not patient and patient is either not funny or not curious.
Everyone who is both brave and creative is patient.
Everyone who is brave or not wise is calm.
Everyone who is not humble or not old is either patient or tall and vice versa.
Everyone who is not calm or tall is wise.
If john is both rich and brave then someone is either not creative or rich.
Everyone who is both not tall and rich is creative or not funny.
Everyone who is either not wise or rich is both rich and humble.
Everyone who is both not curious and happy is rich.
If lucy is not generous or wise then mary is both old and not humble.
Mary is either generous or not kind.
Someone is both not brave and not creative.
Someone is not tall or not happy.
John is wise.
Fred is curious.
Someone is either not kind or not wise.
Someone is not kind or not quiet.
Lucy is not patient. | Mary is creative. | neutral | ((?[X]:((~kind(X)&~funny(X))))<=>((~strong(fred)|~happy(fred))))&
(![X]:((~rich(X)<~>~happy(X))=>(~generous(X)&~patient(X))))&
(![X]:(curious(X)<=>(~wise(X)<~>~brave(X))))&
(![X]:(generous(X)<=>(~calm(X)<~>old(X))))&
(![X]:((curious(X)<~>~generous(X))<=>tall(X)))&
((~creative(mary))<=>((~kind(lucy)<~>curious(lucy))))&
(![X]:((~patient(X)&patient(X))=>(~funny(X)<~>~curious(X))))&
(![X]:((brave(X)&creative(X))=>patient(X)))&
(![X]:((brave(X)|~wise(X))=>calm(X)))&
(![X]:((~humble(X)|~old(X))<=>(patient(X)<~>tall(X))))&
(![X]:((~calm(X)|tall(X))=>wise(X)))&
(((rich(john)&brave(john)))=>(?[X]:((~creative(X)<~>rich(X)))))&
(![X]:((~tall(X)&rich(X))=>(creative(X)|~funny(X))))&
(![X]:((~wise(X)<~>rich(X))=>(rich(X)&humble(X))))&
(![X]:((~curious(X)&happy(X))=>rich(X)))&
(((~generous(lucy)|wise(lucy)))=>((old(mary)&~humble(mary))))&
((generous(mary)<~>~kind(mary)))&
(?[X]:((~brave(X)&~creative(X))))&
(?[X]:((~tall(X)|~happy(X))))&
(wise(john))&
(curious(fred))&
(?[X]:((~kind(X)<~>~wise(X))))&
(?[X]:((~kind(X)|~quiet(X))))&
(~patient(lucy)) | creative(mary) | [] | null | 0 |
Everyone who is not curious or patient is not creative or not quiet and vice versa. If fred is both generous and not quiet then john is wise or brave and vice versa. Everyone who is both humble and not patient is tall. If someone is not rich or not old then someone is either not strong or not tall and vice versa. If someone is not kind or not brave then paul is strong. Everyone who is calm is either not generous or calm. If someone is not humble then john is either creative or not old. Everyone who is both strong and not kind is not old and vice versa. If mary is funny or not strong then susan is both not tall and generous. Everyone who is both strong and not generous is both not kind and not quiet. If someone is not quiet or funny then someone is calm or not quiet. Everyone who is not kind is rich and vice versa. If someone is calm or not humble then someone is either not calm or not patient and vice versa. Everyone who is either not patient or not rich is happy. If someone is either not quiet or not generous then someone is both not curious and not calm. Everyone who is both humble and not calm is both tall and generous and vice versa. Someone is both curious and not humble. Fred is both brave and not rich. John is either not calm or creative. Susan is wise. Someone is both not creative and not quiet. Someone is either not humble or not curious. Someone is calm or not strong. Someone is curious or not creative. | John is creative. | neutral | (![X]:((~curious(X)|patient(X))<=>(~creative(X)|~quiet(X))))&
(((generous(fred)&~quiet(fred)))<=>((wise(john)|brave(john))))&
(![X]:((humble(X)&~patient(X))=>tall(X)))&
((?[X]:((~rich(X)|~old(X))))<=>(?[X]:((~strong(X)<~>~tall(X)))))&
((?[X]:((~kind(X)|~brave(X))))=>(strong(paul)))&
(![X]:(calm(X)=>(~generous(X)<~>calm(X))))&
((?[X]:(~humble(X)))=>((creative(john)<~>~old(john))))&
(![X]:((strong(X)&~kind(X))<=>~old(X)))&
(((funny(mary)|~strong(mary)))=>((~tall(susan)&generous(susan))))&
(![X]:((strong(X)&~generous(X))=>(~kind(X)&~quiet(X))))&
((?[X]:((~quiet(X)|funny(X))))=>(?[X]:((calm(X)|~quiet(X)))))&
(![X]:(~kind(X)<=>rich(X)))&
((?[X]:((calm(X)|~humble(X))))<=>(?[X]:((~calm(X)<~>~patient(X)))))&
(![X]:((~patient(X)<~>~rich(X))=>happy(X)))&
((?[X]:((~quiet(X)<~>~generous(X))))=>(?[X]:((~curious(X)&~calm(X)))))&
(![X]:((humble(X)&~calm(X))<=>(tall(X)&generous(X))))&
(?[X]:((curious(X)&~humble(X))))&
((brave(fred)&~rich(fred)))&
((~calm(john)<~>creative(john)))&
(wise(susan))&
(?[X]:((~creative(X)&~quiet(X))))&
(?[X]:((~humble(X)<~>~curious(X))))&
(?[X]:((calm(X)|~strong(X))))&
(?[X]:((curious(X)|~creative(X)))) | creative(john) | [] | null | 0 |
Everyone who is either rich or patient is generous and vice versa.
Everyone who is creative or old is both strong and not creative and vice versa.
Everyone who is either tall or generous is humble and vice versa.
Everyone who is either funny or not funny is both not patient and not brave and vice versa.
Everyone who is both not quiet and not strong is both not wise and strong.
If someone is both not kind and creative then someone is not rich or humble and vice versa.
If someone is funny then fred is either generous or not calm and vice versa.
Everyone who is wise is old.
Everyone who is both not kind and wise is rich and vice versa.
Everyone who is not funny or not tall is either not calm or strong and vice versa.
If paul is either not wise or not funny then someone is not brave or wise and vice versa.
If someone is not tall or curious then lucy is not tall or not strong.
If someone is both calm and not humble then someone is brave or old.
If someone is either not curious or not brave then someone is both kind and not strong.
Everyone who is either creative or happy is both patient and creative and vice versa.
If susan is not calm or not kind then someone is either not happy or not old and vice versa.
Someone is not humble or not kind.
Mary is not funny or not patient.
Someone is not calm or not rich. | Fred is funny. | contradiction | (![X]:((rich(X)<~>patient(X))<=>generous(X)))&
(![X]:((creative(X)|old(X))<=>(strong(X)&~creative(X))))&
(![X]:((tall(X)<~>generous(X))<=>humble(X)))&
(![X]:((funny(X)<~>~funny(X))<=>(~patient(X)&~brave(X))))&
(![X]:((~quiet(X)&~strong(X))=>(~wise(X)&strong(X))))&
((?[X]:((~kind(X)&creative(X))))<=>(?[X]:((~rich(X)|humble(X)))))&
((?[X]:(funny(X)))<=>((generous(fred)<~>~calm(fred))))&
(![X]:(wise(X)=>old(X)))&
(![X]:((~kind(X)&wise(X))<=>rich(X)))&
(![X]:((~funny(X)|~tall(X))<=>(~calm(X)<~>strong(X))))&
(((~wise(paul)<~>~funny(paul)))<=>(?[X]:((~brave(X)|wise(X)))))&
((?[X]:((~tall(X)|curious(X))))=>((~tall(lucy)|~strong(lucy))))&
((?[X]:((calm(X)&~humble(X))))=>(?[X]:((brave(X)|old(X)))))&
((?[X]:((~curious(X)<~>~brave(X))))=>(?[X]:((kind(X)&~strong(X)))))&
(![X]:((creative(X)<~>happy(X))<=>(patient(X)&creative(X))))&
(((~calm(susan)|~kind(susan)))<=>(?[X]:((~happy(X)<~>~old(X)))))&
(?[X]:((~humble(X)|~kind(X))))&
((~funny(mary)|~patient(mary)))&
(?[X]:((~calm(X)|~rich(X)))) | funny(fred) | [
"p0",
"p1",
"p2",
"p3",
"p5",
"p6",
"p7",
"p8",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 6205079310360886746243427
% SZS output start Proof for 6205079310360886746243427
1. ! [X0] : ((rich(X0) <~> patient(X0)) <=> generous(X0)) [input p0]
2. ! [X0] : ((old(X0) | creative(X0)) <=> (~creative(X0) & strong(X0))) [input p1]
3. ! [X0] : ((tall(X0) <~> generous(X0)) <=> humble(X0)) [input p2]
4. ! [X0] : ((funny(X0) <~> ~funny(X0)) <=> (~brave(X0) & ~patient(X0))) [input p3]
6. ? [X0] : (creative(X0) & ~kind(X0)) <=> ? [X0] : (humble(X0) | ~rich(X0)) [input p5]
7. ? [X0] : funny(X0) <=> (generous(fred) <~> ~calm(fred)) [input p6]
8. ! [X0] : (wise(X0) => old(X0)) [input p7]
9. ! [X0] : ((wise(X0) & ~kind(X0)) <=> rich(X0)) [input p8]
10. ! [X0] : ((~tall(X0) | ~funny(X0)) <=> (~calm(X0) <~> strong(X0))) [input p9]
20. funny(fred) [input hypothesis]
21. ? [X0] : (creative(X0) & ~kind(X0)) <=> ? [X1] : (humble(X1) | ~rich(X1)) [rectify 6]
25. ! [X0] : (old(X0) | ~wise(X0)) [ennf transformation 8]
30. ! [X0] : ((((~patient(X0) | ~rich(X0)) & (patient(X0) | rich(X0))) | ~generous(X0)) & (generous(X0) | ((rich(X0) | ~patient(X0)) & (patient(X0) | ~rich(X0))))) [nnf transformation 1]
31. ! [X0] : (((old(X0) | creative(X0)) | (creative(X0) | ~strong(X0))) & ((~creative(X0) & strong(X0)) | (~old(X0) & ~creative(X0)))) [nnf transformation 2]
32. ! [X0] : ((old(X0) | creative(X0) | creative(X0) | ~strong(X0)) & ((~creative(X0) & strong(X0)) | (~old(X0) & ~creative(X0)))) [flattening 31]
33. ! [X0] : ((((~generous(X0) | ~tall(X0)) & (generous(X0) | tall(X0))) | ~humble(X0)) & (humble(X0) | ((tall(X0) | ~generous(X0)) & (generous(X0) | ~tall(X0))))) [nnf transformation 3]
34. ! [X0] : ((((funny(X0) | ~funny(X0)) & (~funny(X0) | funny(X0))) | (brave(X0) | patient(X0))) & ((~brave(X0) & ~patient(X0)) | ((funny(X0) | funny(X0)) & (~funny(X0) | ~funny(X0))))) [nnf transformation 4]
35. ! [X0] : ((((funny(X0) | ~funny(X0)) & (~funny(X0) | funny(X0))) | brave(X0) | patient(X0)) & ((~brave(X0) & ~patient(X0)) | ((funny(X0) | funny(X0)) & (~funny(X0) | ~funny(X0))))) [flattening 34]
36. (? [X0] : (creative(X0) & ~kind(X0)) | ! [X1] : (~humble(X1) & rich(X1))) & (? [X1] : (humble(X1) | ~rich(X1)) | ! [X0] : (~creative(X0) | kind(X0))) [nnf transformation 21]
37. (? [X0] : (creative(X0) & ~kind(X0)) | ! [X1] : (~humble(X1) & rich(X1))) & (? [X2] : (humble(X2) | ~rich(X2)) | ! [X3] : (~creative(X3) | kind(X3))) [rectify 36]
38. ? [X0] : (creative(X0) & ~kind(X0)) => (creative(sK0) & ~kind(sK0)) [choice axiom]
39. ? [X2] : (humble(X2) | ~rich(X2)) => (humble(sK1) | ~rich(sK1)) [choice axiom]
40. ((creative(sK0) & ~kind(sK0)) | ! [X1] : (~humble(X1) & rich(X1))) & ((humble(sK1) | ~rich(sK1)) | ! [X3] : (~creative(X3) | kind(X3))) [skolemisation 37,39,38]
41. (? [X0] : funny(X0) | ((generous(fred) | calm(fred)) & (~calm(fred) | ~generous(fred)))) & (((calm(fred) | ~generous(fred)) & (~calm(fred) | generous(fred))) | ! [X0] : ~funny(X0)) [nnf transformation 7]
42. (? [X0] : funny(X0) | ((generous(fred) | calm(fred)) & (~calm(fred) | ~generous(fred)))) & (((calm(fred) | ~generous(fred)) & (~calm(fred) | generous(fred))) | ! [X1] : ~funny(X1)) [rectify 41]
43. ? [X0] : funny(X0) => funny(sK2) [choice axiom]
44. (funny(sK2) | ((generous(fred) | calm(fred)) & (~calm(fred) | ~generous(fred)))) & (((calm(fred) | ~generous(fred)) & (~calm(fred) | generous(fred))) | ! [X1] : ~funny(X1)) [skolemisation 42,43]
45. ! [X0] : (((wise(X0) & ~kind(X0)) | ~rich(X0)) & (rich(X0) | (~wise(X0) | kind(X0)))) [nnf transformation 9]
46. ! [X0] : (((wise(X0) & ~kind(X0)) | ~rich(X0)) & (rich(X0) | ~wise(X0) | kind(X0))) [flattening 45]
47. ! [X0] : (((~tall(X0) | ~funny(X0)) | ((~calm(X0) | ~strong(X0)) & (strong(X0) | calm(X0)))) & (((~strong(X0) | calm(X0)) & (strong(X0) | ~calm(X0))) | (tall(X0) & funny(X0)))) [nnf transformation 10]
48. ! [X0] : ((~tall(X0) | ~funny(X0) | ((~calm(X0) | ~strong(X0)) & (strong(X0) | calm(X0)))) & (((~strong(X0) | calm(X0)) & (strong(X0) | ~calm(X0))) | (tall(X0) & funny(X0)))) [flattening 47]
71. ~rich(X0) | patient(X0) | generous(X0) [cnf transformation 30]
76. ~old(X0) | strong(X0) [cnf transformation 32]
77. ~creative(X0) | ~creative(X0) [cnf transformation 32]
81. ~generous(X0) | tall(X0) | humble(X0) [cnf transformation 33]
84. ~patient(X0) | ~funny(X0) | ~funny(X0) [cnf transformation 35]
85. ~patient(X0) | funny(X0) | funny(X0) [cnf transformation 35]
93. creative(sK0) | rich(X1) [cnf transformation 40]
94. creative(sK0) | ~humble(X1) [cnf transformation 40]
96. calm(fred) | ~generous(fred) | ~funny(X1) [cnf transformation 44]
99. ~wise(X0) | old(X0) [cnf transformation 25]
102. wise(X0) | ~rich(X0) [cnf transformation 46]
108. ~calm(X0) | ~funny(X0) | ~tall(X0) | ~strong(X0) [cnf transformation 48]
137. funny(fred) [cnf transformation 20]
140. ~patient(X0) | ~funny(X0) [duplicate literal removal 84]
141. ~patient(X0) | funny(X0) [duplicate literal removal 85]
144. ~creative(X0) [duplicate literal removal 77]
147. ~patient(X0) [subsumption resolution 140,141]
148. ~humble(X1) [subsumption resolution 94,144]
149. rich(X1) [subsumption resolution 93,144]
151. 1 <=> calm(fred) [avatar definition]
153. calm(fred) <- (1) [avatar component clause 151]
155. 2 <=> generous(fred) [avatar definition]
156. ~generous(fred) <- (~2) [avatar component clause 155]
165. 4 <=> ! [X1] : ~funny(X1) [avatar definition]
166. ~funny(X1) <- (4) [avatar component clause 165]
167. 4 | ~2 | 1 [avatar split clause 96,151,155,165]
169. wise(X0) [subsumption resolution 102,149]
186. 8 <=> ! [X0] : tall(X0) [avatar definition]
187. tall(X0) <- (8) [avatar component clause 186]
214. old(X0) [resolution 99,169]
216. strong(X1) [resolution 214,76]
219. patient(X0) | generous(X0) [resolution 71,149]
220. generous(X0) [subsumption resolution 219,147]
221. $false <- (~2) [resolution 220,156]
222. 2 [avatar contradiction clause 221]
223. $false <- (4) [resolution 166,137]
226. ~4 [avatar contradiction clause 223]
231. tall(X0) | humble(X0) [resolution 81,220]
232. tall(X0) [subsumption resolution 231,148]
233. 8 [avatar split clause 232,186]
262. ~funny(fred) | ~tall(fred) | ~strong(fred) <- (1) [resolution 108,153]
264. ~tall(fred) | ~strong(fred) <- (1) [subsumption resolution 262,137]
265. ~strong(fred) <- (1, 8) [subsumption resolution 264,187]
266. $false <- (1, 8) [subsumption resolution 265,216]
267. ~1 | ~8 [avatar contradiction clause 266]
268. $false [avatar sat refutation 167,222,226,233,267]
% SZS output end Proof for 6205079310360886746243427
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
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